LMFDB - Embedded newform 82.6.f.b.45.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,6,Mod(23,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.23"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([9])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	82.f (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.1514732247$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			45.5
Character	$\chi$	$=$	82.45
Dual form			82.6.f.b.31.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.23607 - 2.35114i) q^{2} -2.80079i q^{3} +(4.94427 - 15.2169i) q^{4} +(-7.78267 + 23.9526i) q^{5} +(-6.58504 - 9.06354i) q^{6} +(-138.019 + 189.966i) q^{7} +(-19.7771 - 60.8676i) q^{8} +235.156 q^{9} +(31.1307 + 95.8103i) q^{10} +(-705.977 + 229.386i) q^{11} +(-42.6193 - 13.8478i) q^{12} +(317.562 + 437.087i) q^{13} +939.246i q^{14} +(67.0861 + 21.7976i) q^{15} +(-207.108 - 150.473i) q^{16} +(1207.87 - 392.460i) q^{17} +(760.979 - 552.884i) q^{18} +(-234.336 + 322.536i) q^{19} +(326.005 + 236.856i) q^{20} +(532.055 + 386.561i) q^{21} +(-1745.27 + 2402.16i) q^{22} +(-2981.00 + 2165.82i) q^{23} +(-170.477 + 55.3914i) q^{24} +(2015.02 + 1464.00i) q^{25} +(2055.30 + 667.809i) q^{26} -1339.21i q^{27} +(2208.30 + 3039.46i) q^{28} +(-1881.45 - 611.319i) q^{29} +(268.344 - 87.1903i) q^{30} +(535.171 + 1647.09i) q^{31} -1024.00 q^{32} +(642.461 + 1977.29i) q^{33} +(2986.01 - 4109.89i) q^{34} +(-3476.03 - 4784.35i) q^{35} +(1162.67 - 3578.34i) q^{36} +(1242.16 - 3822.98i) q^{37} +1594.70i q^{38} +(1224.19 - 889.423i) q^{39} +1611.86 q^{40} +(-714.154 + 10739.9i) q^{41} +2630.63 q^{42} +(-911.132 + 661.977i) q^{43} +11876.9i q^{44} +(-1830.14 + 5632.58i) q^{45} +(-4554.56 + 14017.5i) q^{46} +(359.145 + 494.321i) q^{47} +(-421.443 + 580.066i) q^{48} +(-11844.4 - 36453.4i) q^{49} +9962.82 q^{50} +(-1099.20 - 3382.98i) q^{51} +(8221.22 - 2671.24i) q^{52} +(-25690.2 - 8347.26i) q^{53} +(-3148.68 - 4333.78i) q^{54} -18695.2i q^{55} +(14292.4 + 4643.89i) q^{56} +(903.354 + 656.325i) q^{57} +(-7525.78 + 2445.28i) q^{58} +(37756.3 - 27431.6i) q^{59} +(663.384 - 913.069i) q^{60} +(-16969.1 - 12328.8i) q^{61} +(5604.39 + 4071.83i) q^{62} +(-32455.9 + 44671.7i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(-12940.8 + 4204.73i) q^{65} +(6727.94 + 4888.13i) q^{66} +(9457.07 + 3072.79i) q^{67} -20320.4i q^{68} +(6066.00 + 8349.13i) q^{69} +(-22497.4 - 7309.84i) q^{70} +(-25657.7 + 8336.70i) q^{71} +(-4650.69 - 14313.4i) q^{72} -16509.9 q^{73} +(-4968.64 - 15291.9i) q^{74} +(4100.35 - 5643.65i) q^{75} +(3749.37 + 5160.57i) q^{76} +(53862.4 - 165771. i) q^{77} +(1870.39 - 5756.47i) q^{78} -24849.6i q^{79} +(5216.07 - 3789.70i) q^{80} +53392.0 q^{81} +(22940.0 + 36434.2i) q^{82} +51644.9 q^{83} +(8512.89 - 6184.97i) q^{84} +31985.9i q^{85} +(-1392.09 + 4284.40i) q^{86} +(-1712.17 + 5269.53i) q^{87} +(27924.3 + 38434.5i) q^{88} +(-23792.8 + 32748.0i) q^{89} +(7320.55 + 22530.3i) q^{90} -126861. q^{91} +(18218.2 + 56069.9i) q^{92} +(4613.14 - 1498.90i) q^{93} +(2324.44 + 755.255i) q^{94} +(-5901.80 - 8123.14i) q^{95} +2868.01i q^{96} +(169673. + 55130.0i) q^{97} +(-124037. - 90117.8i) q^{98} +(-166014. + 53941.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 160 q^{4} + 24 q^{5} - 100 q^{6} + 640 q^{8} - 4576 q^{9} - 96 q^{10} + 20 q^{11} + 400 q^{12} - 275 q^{13} + 1385 q^{15} - 2560 q^{16} - 105 q^{17} - 2476 q^{18} + 4720 q^{19} + 1424 q^{20}+ \cdots - 537690 q^{99}+O(q^{100}) $ 40 * q + 40 * q^2 - 160 * q^4 + 24 * q^5 - 100 * q^6 + 640 * q^8 - 4576 * q^9 - 96 * q^10 + 20 * q^11 + 400 * q^12 - 275 * q^13 + 1385 * q^15 - 2560 * q^16 - 105 * q^17 - 2476 * q^18 + 4720 * q^19 + 1424 * q^20 + 6961 * q^21 - 4140 * q^22 - 1019 * q^23 + 1600 * q^24 - 2006 * q^25 - 8620 * q^26 - 12525 * q^29 + 5540 * q^30 + 8900 * q^31 - 40960 * q^32 + 17684 * q^33 - 13100 * q^34 - 29955 * q^35 + 26704 * q^36 - 31651 * q^37 - 10104 * q^39 + 14464 * q^40 + 35044 * q^41 + 32776 * q^42 - 15615 * q^43 - 39955 * q^45 - 3224 * q^46 + 8330 * q^47 - 6400 * q^48 + 48406 * q^49 - 135016 * q^50 + 120325 * q^51 - 34480 * q^52 + 145425 * q^53 + 72200 * q^54 + 17600 * q^56 + 31992 * q^57 - 50100 * q^58 + 18978 * q^59 + 1680 * q^60 + 52673 * q^61 + 66140 * q^62 - 88455 * q^63 - 40960 * q^64 + 204480 * q^65 - 17556 * q^66 - 149205 * q^67 - 249735 * q^69 - 49100 * q^70 + 151175 * q^71 - 106816 * q^72 - 107670 * q^73 + 126604 * q^74 + 120180 * q^75 - 75520 * q^76 - 207367 * q^77 - 99284 * q^78 + 22784 * q^80 + 1167568 * q^81 + 84204 * q^82 - 281376 * q^83 + 111376 * q^84 - 131400 * q^86 - 141269 * q^87 + 66240 * q^88 - 277775 * q^89 + 159820 * q^90 - 518682 * q^91 + 12896 * q^92 - 172375 * q^93 + 16320 * q^94 + 149585 * q^95 + 330875 * q^97 - 171004 * q^98 - 537690 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	3.23607	−	2.35114i	0.572061	−	0.415627i
$2$	3.23607	−	2.35114i	0.572061	−	0.415627i
$3$		−	2.80079i		−	0.179671i	−0.995957	−	0.0898353i	$-0.971366\pi$
$3$		−	2.80079i		−	0.179671i	0.995957	−	0.0898353i	$-0.0286341\pi$
$4$	4.94427	−	15.2169i	0.154508	−	0.475528i
$5$	−7.78267	+	23.9526i	−0.139221	+	0.428477i	−0.996223	−	0.0868362i	$-0.972324\pi$
$5$	−7.78267	+	23.9526i	−0.139221	+	0.428477i	0.857002	+	0.515313i	$0.172324\pi$
$6$	−6.58504	−	9.06354i	−0.0746759	−	0.102783i
$7$	−138.019	+	189.966i	−1.06462	+	1.46532i	−0.189205	+	0.981938i	$0.560591\pi$
$7$	−138.019	+	189.966i	−1.06462	+	1.46532i	−0.875411	+	0.483380i	$0.839409\pi$
$8$	−19.7771	−	60.8676i	−0.109254	−	0.336249i
$9$	235.156			0.967718
$10$	31.1307	+	95.8103i	0.0984438	+	0.302979i
$11$	−705.977	+	229.386i	−1.75917	+	0.571590i	−0.997114	−	0.0759164i	$-0.975812\pi$
$11$	−705.977	+	229.386i	−1.75917	+	0.571590i	−0.762060	+	0.647507i	$0.775812\pi$
$12$	−42.6193	−	13.8478i	−0.0854384	−	0.0277606i
$13$	317.562	+	437.087i	0.521159	+	0.717314i	0.985751	−	0.168211i	$-0.0537990\pi$
$13$	317.562	+	437.087i	0.521159	+	0.717314i	−0.464592	+	0.885525i	$0.653799\pi$
$14$			939.246i			1.28073i
$15$	67.0861	+	21.7976i	0.0769847	+	0.0250138i
$16$	−207.108	−	150.473i	−0.202254	−	0.146946i
$17$	1207.87	−	392.460i	1.01367	−	0.329361i	0.245355	−	0.969433i	$-0.421095\pi$
$17$	1207.87	−	392.460i	1.01367	−	0.329361i	0.768315	+	0.640072i	$0.221095\pi$
$18$	760.979	−	552.884i	0.553594	−	0.402210i
$19$	−234.336	+	322.536i	−0.148921	+	0.204972i	−0.876960	−	0.480564i	$-0.840432\pi$
$19$	−234.336	+	322.536i	−0.148921	+	0.204972i	0.728039	+	0.685536i	$0.240432\pi$
$20$	326.005	+	236.856i	0.182242	+	0.132407i
$21$	532.055	+	386.561i	0.263274	+	0.191280i
$22$	−1745.27	+	2402.16i	−0.768787	+	1.05814i
$23$	−2981.00	+	2165.82i	−1.17501	+	0.853695i	−0.991600	−	0.129341i	$-0.958714\pi$
$23$	−2981.00	+	2165.82i	−1.17501	+	0.853695i	−0.183410	+	0.983036i	$0.558714\pi$
$24$	−170.477	+	55.3914i	−0.0604141	+	0.0196297i
$25$	2015.02	+	1464.00i	0.644807	+	0.468480i
$26$	2055.30	+	667.809i	0.596270	+	0.193740i
$27$		−	1339.21i		−	0.353541i
$28$	2208.30	+	3039.46i	0.532308	+	0.732659i
$29$	−1881.45	−	611.319i	−0.415429	−	0.134981i	0.0938424	−	0.995587i	$-0.470085\pi$
$29$	−1881.45	−	611.319i	−0.415429	−	0.134981i	−0.509271	+	0.860606i	$0.670085\pi$
$30$	268.344	−	87.1903i	0.0544364	−	0.0176875i
$31$	535.171	+	1647.09i	0.100020	+	0.307831i	0.988530	−	0.151028i	$-0.0482583\pi$
$31$	535.171	+	1647.09i	0.100020	+	0.307831i	−0.888509	+	0.458859i	$0.848258\pi$
$32$	−1024.00			−0.176777
$33$	642.461	+	1977.29i	0.102698	+	0.316072i
$34$	2986.01	−	4109.89i	0.442990	−	0.609724i
$35$	−3476.03	−	4784.35i	−0.479638	−	0.660165i
$36$	1162.67	−	3578.34i	0.149521	−	0.460177i
$37$	1242.16	−	3822.98i	0.149167	−	0.459090i	−0.848356	−	0.529426i	$-0.822407\pi$
$37$	1242.16	−	3822.98i	0.149167	−	0.459090i	0.997523	+	0.0703365i	$0.0224073\pi$
$38$			1594.70i			0.179152i
$39$	1224.19	−	889.423i	0.128880	−	0.0936369i
$40$	1611.86			0.159285
$41$	−714.154	+	10739.9i	−0.0663487	+	0.997796i
$41$	−714.154	+	10739.9i	−0.0663487	+	0.997796i
$42$	2630.63			0.230110
$43$	−911.132	+	661.977i	−0.0751468	+	0.0545973i	−0.624724	−	0.780845i	$-0.714789\pi$
$43$	−911.132	+	661.977i	−0.0751468	+	0.0545973i	0.549578	+	0.835443i	$0.314789\pi$
$44$			11876.9i			0.924852i
$45$	−1830.14	+	5632.58i	−0.134726	+	0.414645i
$46$	−4554.56	+	14017.5i	−0.317359	+	0.976732i
$47$	359.145	+	494.321i	0.0237151	+	0.0326411i	0.820710	−	0.571345i	$-0.193578\pi$
$47$	359.145	+	494.321i	0.0237151	+	0.0326411i	−0.796995	+	0.603986i	$0.793578\pi$
$48$	−421.443	+	580.066i	−0.0264019	+	0.0363391i
$49$	−11844.4	−	36453.4i	−0.704732	−	2.16894i
$50$	9962.82			0.563582
$51$	−1099.20	−	3382.98i	−0.0591765	−	0.182127i
$52$	8221.22	−	2671.24i	0.421626	−	0.136995i
$53$	−25690.2	−	8347.26i	−1.25626	−	0.408182i	−0.396097	−	0.918209i	$-0.629636\pi$
$53$	−25690.2	−	8347.26i	−1.25626	−	0.408182i	−0.860159	+	0.510027i	$0.829636\pi$
$54$	−3148.68	−	4333.78i	−0.146941	−	0.202247i
$55$		−	18695.2i		−	0.833342i
$56$	14292.4	+	4643.89i	0.609025	+	0.197884i
$57$	903.354	+	656.325i	0.0368274	+	0.0267566i
$58$	−7525.78	+	2445.28i	−0.293753	+	0.0954460i
$59$	37756.3	−	27431.6i	1.41208	−	1.02594i	0.419065	−	0.907956i	$-0.362358\pi$
$59$	37756.3	−	27431.6i	1.41208	−	1.02594i	0.993016	−	0.117981i	$-0.0376422\pi$
$60$	663.384	−	913.069i	0.0237896	−	0.0327435i
$61$	−16969.1	−	12328.8i	−0.583895	−	0.424224i	0.256231	−	0.966615i	$-0.417519\pi$
$61$	−16969.1	−	12328.8i	−0.583895	−	0.424224i	−0.840126	+	0.542391i	$0.817519\pi$
$62$	5604.39	+	4071.83i	0.185161	+	0.134527i
$63$	−32455.9	+	44671.7i	−1.03025	+	1.41801i
$64$	−3313.73	+	2407.57i	−0.101127	+	0.0734732i
$65$	−12940.8	+	4204.73i	−0.379908	+	0.123440i
$66$	6727.94	+	4888.13i	0.190117	+	0.138128i
$67$	9457.07	+	3072.79i	0.257377	+	0.0836268i	0.434863	−	0.900496i	$-0.356797\pi$
$67$	9457.07	+	3072.79i	0.257377	+	0.0836268i	−0.177487	+	0.984123i	$0.556797\pi$
$68$		−	20320.4i		−	0.532918i
$69$	6066.00	+	8349.13i	0.153384	+	0.211115i
$70$	−22497.4	−	7309.84i	−0.548765	−	0.178305i
$71$	−25657.7	+	8336.70i	−0.604049	+	0.196267i	−0.595046	−	0.803692i	$-0.702866\pi$
$71$	−25657.7	+	8336.70i	−0.604049	+	0.196267i	−0.00900362	+	0.999959i	$0.502866\pi$
$72$	−4650.69	−	14313.4i	−0.105727	−	0.325395i
$73$	−16509.9			−0.362608			−0.181304	−	0.983427i	$-0.558032\pi$
$73$	−16509.9			−0.362608			−0.181304	+	0.983427i	$0.558032\pi$
$74$	−4968.64	−	15291.9i	−0.105477	−	0.324625i
$75$	4100.35	−	5643.65i	0.0841720	−	0.115853i
$76$	3749.37	+	5160.57i	0.0744603	+	0.102486i
$77$	53862.4	−	165771.i	1.03528	−	3.18627i
$78$	1870.39	−	5756.47i	0.0348093	−	0.107132i
$79$		−	24849.6i		−	0.447972i	−0.974592	−	0.223986i	$-0.928093\pi$
$79$		−	24849.6i		−	0.447972i	0.974592	−	0.223986i	$-0.0719071\pi$
$80$	5216.07	−	3789.70i	0.0911210	−	0.0662033i
$81$	53392.0			0.904198
$82$	22940.0	+	36434.2i	0.376756	+	0.598377i
$83$	51644.9			0.822871			0.411436	−	0.911439i	$-0.365028\pi$
$83$	51644.9			0.822871			0.411436	+	0.911439i	$0.365028\pi$
$84$	8512.89	−	6184.97i	0.131637	−	0.0956400i
$85$			31985.9i			0.480188i
$86$	−1392.09	+	4284.40i	−0.0202965	+	0.0624661i
$87$	−1712.17	+	5269.53i	−0.0242521	+	0.0746403i
$88$	27924.3	+	38434.5i	0.384394	+	0.529072i
$89$	−23792.8	+	32748.0i	−0.318398	+	0.438238i	−0.937977	−	0.346697i	$-0.887303\pi$
$89$	−23792.8	+	32748.0i	−0.318398	+	0.438238i	0.619579	+	0.784934i	$0.287303\pi$
$90$	7320.55	+	22530.3i	0.0952659	+	0.293198i
$91$	−126861.			−1.60593
$92$	18218.2	+	56069.9i	0.224407	+	0.690654i
$93$	4613.14	−	1498.90i	0.0553082	−	0.0179707i
$94$	2324.44	+	755.255i	0.0271330	+	0.00881605i
$95$	−5901.80	−	8123.14i	−0.0670928	−	0.0923453i
$96$			2868.01i			0.0317616i
$97$	169673.	+	55130.0i	1.83098	+	0.594920i	0.999208	+	0.0397985i	$0.0126716\pi$
$97$	169673.	+	55130.0i	1.83098	+	0.594920i	0.831769	+	0.555122i	$0.187328\pi$
$98$	−124037.	−	90117.8i	−1.30462	−	0.947863i
$99$	−166014.	+	53941.4i	−1.70239	+	0.553138i
$100$	32240.3	−	23424.0i	0.322403	−	0.234240i
$101$	−81511.7	+	112191.i	−0.795090	+	1.09435i	0.198365	+	0.980128i	$0.436437\pi$
$101$	−81511.7	+	112191.i	−0.795090	+	1.09435i	−0.993455	+	0.114220i	$0.963563\pi$
$102$	−11510.9	−	8363.18i	−0.109549	−	0.0795923i
$103$	73991.4	+	53757.9i	0.687208	+	0.499286i	0.875741	−	0.482781i	$-0.160373\pi$
$103$	73991.4	+	53757.9i	0.687208	+	0.499286i	−0.188533	+	0.982067i	$0.560373\pi$
$104$	20324.0	−	27973.5i	0.184257	−	0.253609i
$105$	−13399.9	+	9735.63i	−0.118612	+	0.0861769i
$106$	−102761.	+	33389.0i	−0.888307	+	0.288628i
$107$	167159.	+	121448.i	1.41147	+	1.02549i	0.993107	+	0.117211i	$0.0373953\pi$
$107$	167159.	+	121448.i	1.41147	+	1.02549i	0.418361	+	0.908281i	$0.362605\pi$
$108$	−20378.7	−	6621.43i	−0.168119	−	0.0546251i
$109$			164076.i			1.32276i	0.750053	+	0.661378i	$0.230028\pi$
$109$			164076.i			1.32276i	−0.750053	+	0.661378i	$0.769972\pi$
$110$	−43955.1	−	60498.9i	−0.346360	−	0.476723i
$111$	−10707.3	−	3479.03i	−0.0824849	−	0.0268010i
$112$	57169.6	−	18575.5i	0.430646	−	0.139925i
$113$	24524.2	+	75477.7i	0.180675	+	0.556061i	0.999847	−	0.0174868i	$-0.00556651\pi$
$113$	24524.2	+	75477.7i	0.180675	+	0.556061i	−0.819172	+	0.573548i	$0.805567\pi$
$114$	4466.43			0.0321883
$115$	−28676.9	−	88258.4i	−0.202203	−	0.622317i
$116$	−18604.8	+	25607.3i	−0.128375	+	0.176692i
$117$	74676.5	+	102783.i	0.504335	+	0.694158i
$118$	57686.5	−	177541.i	0.381390	−	1.17380i
$119$	−92154.0	+	283621.i	−0.596550	+	1.83599i
$120$		−	4514.46i		−	0.0286189i
$121$	315493.	−	229219.i	1.95896	−	1.42327i
$122$	−83899.9			−0.510343
$123$	30080.3	+	2000.19i	0.179275	+	0.0119209i
$124$	27709.6			0.161836
$125$	−114422.	+	83132.1i	−0.654987	+	0.475876i
$126$			220869.i			1.23939i
$127$	6957.32	−	21412.4i	0.0382765	−	0.117803i	−0.930093	−	0.367325i	$-0.880274\pi$
$127$	6957.32	−	21412.4i	0.0382765	−	0.117803i	0.968369	+	0.249522i	$0.0802736\pi$
$128$	−5062.93	+	15582.1i	−0.0273135	+	0.0840623i
$129$	1854.05	+	2551.89i	0.00980953	+	0.0135017i
$130$	−31991.5	+	44032.5i	−0.166026	+	0.228515i
$131$	−55311.3	−	170231.i	−0.281602	−	0.866681i	−0.987397	−	0.158265i	$-0.949410\pi$
$131$	−55311.3	−	170231.i	−0.281602	−	0.866681i	0.705795	−	0.708416i	$-0.250590\pi$
$132$	33264.7			0.166169
$133$	−28928.2	−	89031.9i	−0.141805	−	0.436432i
$134$	37828.3	−	12291.2i	0.181993	−	0.0591331i
$135$	32077.6	+	10422.6i	0.151484	+	0.0492202i
$136$	−47776.2	−	65758.3i	−0.221495	−	0.304862i
$137$		−	53948.7i		−	0.245573i	−0.992433	−	0.122786i	$-0.960817\pi$
$137$		−	53948.7i		−	0.245573i	0.992433	−	0.122786i	$-0.0391830\pi$
$138$	39260.0	+	12756.3i	0.175490	+	0.0570201i
$139$	−93695.1	−	68073.4i	−0.411320	−	0.298841i	0.362816	−	0.931861i	$-0.381815\pi$
$139$	−93695.1	−	68073.4i	−0.411320	−	0.298841i	−0.774136	+	0.633019i	$0.781815\pi$
$140$	−89989.4	+	29239.3i	−0.388035	+	0.126080i
$141$	1384.49	−	1005.89i	0.00586464	−	0.00426091i
$142$	−63429.4	+	87303.1i	−0.263979	+	0.363336i
$143$	−324453.	−	235729.i	−1.32682	−	0.963990i
$144$	−48702.7	−	35384.6i	−0.195725	−	0.142203i
$145$	29285.3	−	40307.8i	0.115672	−	0.159210i
$146$	−53427.1	+	38817.1i	−0.207434	+	0.150709i
$147$	−102098.	+	33173.7i	−0.389695	+	0.126620i
$148$	−52032.3	−	37803.7i	−0.195262	−	0.141866i
$149$	260996.	+	84802.9i	0.963095	+	0.312928i	0.748025	−	0.663670i	$-0.231002\pi$
$149$	260996.	+	84802.9i	0.963095	+	0.312928i	0.215069	+	0.976599i	$0.431002\pi$
$150$		−	27903.7i		−	0.101259i
$151$	247709.	+	340943.i	0.884097	+	1.21686i	0.975269	+	0.221020i	$0.0709387\pi$
$151$	247709.	+	340943.i	0.884097	+	1.21686i	−0.0911720	+	0.995835i	$0.529061\pi$
$152$	24266.5	+	7884.65i	0.0851917	+	0.0276805i
$153$	284037.	−	92289.1i	0.980948	−	0.318729i
$154$	−215450.	−	663086.i	−0.732055	−	2.25303i
$155$	−43617.1			−0.145823
$156$	−7481.56	−	23025.9i	−0.0246139	−	0.0757538i
$157$	−124138.	+	170861.i	−0.401933	+	0.553214i	−0.961228	−	0.275755i	$-0.911072\pi$
$157$	−124138.	+	170861.i	−0.401933	+	0.553214i	0.559295	+	0.828969i	$0.311072\pi$
$158$	−58424.9	−	80414.9i	−0.186189	−	0.256268i
$159$	−23378.9	+	71952.8i	−0.0733383	+	0.225712i
$160$	7969.45	−	24527.4i	0.0246110	−	0.0757447i
$161$		−	865213.i		−	2.63062i
$162$	172780.	−	125532.i	0.517257	−	0.375809i
$163$	622460.			1.83503			0.917514	−	0.397704i	$-0.130193\pi$
$163$	622460.			1.83503			0.917514	+	0.397704i	$0.130193\pi$
$164$	159898.	+	63968.4i	0.464229	+	0.185719i
$165$	−52361.3			−0.149727
$166$	167126.	−	121424.i	0.470733	−	0.342007i
$167$		−	497206.i		−	1.37957i	−0.724012	−	0.689787i	$-0.757704\pi$
$167$		−	497206.i		−	1.37957i	0.724012	−	0.689787i	$-0.242296\pi$
$168$	13006.5	−	40030.0i	0.0355540	−	0.109424i
$169$	24536.8	−	75516.4i	0.0660847	−	0.203388i
$170$	75203.4	+	103509.i	0.199579	+	0.274697i
$171$	−55105.4	+	75846.1i	−0.144113	+	0.198355i
$172$	5568.35	+	17137.6i	0.0143518	+	0.0441702i
$173$	−83712.9			−0.212656			−0.106328	−	0.994331i	$-0.533909\pi$
$173$	−83712.9			−0.212656			−0.106328	+	0.994331i	$0.533909\pi$
$174$	6848.69	+	21078.1i	0.0171488	+	0.0527787i
$175$	−556221.	+	180727.i	−1.37294	+	0.446096i
$176$	180730.	+	58722.8i	0.439793	+	0.142898i
$177$	−76830.0	−	105747.i	−0.184331	−	0.253709i
$178$			161915.i			0.383034i
$179$	−465937.	−	151392.i	−1.08691	−	0.353159i	−0.289860	−	0.957069i	$-0.593609\pi$
$179$	−465937.	−	151392.i	−1.08691	−	0.353159i	−0.797053	+	0.603910i	$0.793609\pi$
$180$	76661.8	+	55698.1i	0.176359	+	0.128132i
$181$	96136.7	−	31236.7i	0.218119	−	0.0708710i	−0.197919	−	0.980218i	$-0.563418\pi$
$181$	96136.7	−	31236.7i	0.218119	−	0.0708710i	0.416038	+	0.909347i	$0.363418\pi$
$182$	−410532.	+	298269.i	−0.918688	+	0.667466i
$183$	−34530.3	+	47526.9i	−0.0762206	+	0.104909i
$184$	190784.	+	138612.i	0.415429	+	0.301827i
$185$	81902.9	+	59505.9i	0.175942	+	0.127829i
$186$	11404.3	−	15696.7i	0.0241706	−	0.0332679i
$187$	−762701.	+	554135.i	−1.59496	+	1.15881i
$188$	9297.74	−	3021.02i	0.0191859	−	0.00623389i
$189$	254405.	+	184836.i	0.518050	+	0.376385i
$190$	−38197.3	−	12411.0i	−0.0767624	−	0.0249416i
$191$		−	553289.i		−	1.09741i	−0.836016	−	0.548705i	$-0.815121\pi$
$191$		−	553289.i		−	1.09741i	0.836016	−	0.548705i	$-0.184879\pi$
$192$	6743.08	+	9281.06i	0.0132010	+	0.0181696i
$193$	158001.	+	51337.5i	0.305327	+	0.0992068i	0.457673	−	0.889120i	$-0.348683\pi$
$193$	158001.	+	51337.5i	0.305327	+	0.0992068i	−0.152346	+	0.988327i	$0.548683\pi$
$194$	678691.	−	220520.i	1.29470	−	0.420672i
$195$	11776.6	+	36244.5i	0.0221785	+	0.0682583i
$196$	−613270.			−1.14028
$197$	−221530.	−	681798.i	−0.406693	−	1.25167i	−0.919474	−	0.393152i	$-0.871385\pi$
$197$	−221530.	−	681798.i	−0.406693	−	1.25167i	0.512781	−	0.858519i	$-0.328615\pi$
$198$	−410410.	+	564881.i	−0.743970	+	1.02399i
$199$	551757.	+	759428.i	0.987677	+	1.35942i	0.932589	+	0.360940i	$0.117544\pi$
$199$	551757.	+	759428.i	0.987677	+	1.35942i	0.0550883	+	0.998481i	$0.482456\pi$
$200$	49258.9	−	151603.i	0.0870782	−	0.267999i
$201$	8606.22	−	26487.2i	0.0150253	−	0.0462430i
$202$			554704.i			0.956495i
$203$	375805.	−	273038.i	0.640062	−	0.465032i
$204$	−56913.2			−0.0957497
$205$	−251691.	−	100691.i	−0.418296	−	0.167343i
$206$	365834.			0.600642
$207$	−700998.	+	509305.i	−1.13708	+	0.826137i
$208$		−	138309.i		−	0.221662i
$209$	91450.6	−	281456.i	0.144817	−	0.445702i
$210$	−20473.3	+	63010.3i	−0.0320361	+	0.0985969i
$211$	81766.4	+	112542.i	0.126435	+	0.174023i	0.867542	−	0.497364i	$-0.165699\pi$
$211$	81766.4	+	112542.i	0.126435	+	0.174023i	−0.741107	+	0.671387i	$0.765699\pi$
$212$	−254039.	+	349654.i	−0.388204	+	0.534317i
$213$	23349.3	+	71861.8i	0.0352635	+	0.108530i
$214$	826481.			1.23367
$215$	−8765.01	−	26975.9i	−0.0129317	−	0.0397997i
$216$	−81514.6	+	26485.7i	−0.118878	+	0.0386258i
$217$	−386755.	−	125664.i	−0.557554	−	0.181160i
$218$	385767.	+	530962.i	0.549773	+	0.756698i
$219$			46240.7i			0.0651499i
$220$	−284483.	−	92434.2i	−0.396278	−	0.128758i
$221$	555111.	+	403312.i	0.764539	+	0.555470i
$222$	−42829.4	+	13916.1i	−0.0583256	+	0.0189511i
$223$	−285038.	+	207092.i	−0.383832	+	0.278870i	−0.762923	−	0.646489i	$-0.776237\pi$
$223$	−285038.	+	207092.i	−0.383832	+	0.278870i	0.379091	+	0.925359i	$0.376237\pi$
$224$	141331.	−	194526.i	0.188199	−	0.259034i
$225$	473844.	+	344268.i	0.623992	+	0.453356i
$226$	256821.	+	186591.i	0.334471	+	0.243008i
$227$	−41413.0	+	57000.2i	−0.0533424	+	0.0734195i	−0.834855	−	0.550470i	$-0.814449\pi$
$227$	−41413.0	+	57000.2i	−0.0533424	+	0.0734195i	0.781513	+	0.623890i	$0.214449\pi$
$228$	14453.7	−	10501.2i	0.0184137	−	0.0133783i
$229$	−572652.	+	186066.i	−0.721610	+	0.234465i	−0.646721	−	0.762727i	$-0.723860\pi$
$229$	−572652.	+	186066.i	−0.721610	+	0.234465i	−0.0748887	+	0.997192i	$0.523860\pi$
$230$	−300308.	−	218187.i	−0.374324	−	0.271962i
$231$	−464290.	−	150857.i	−0.572479	−	0.186010i
$232$			126609.i			0.154435i
$233$	−26606.2	−	36620.3i	−0.0321065	−	0.0441909i	0.792662	−	0.609661i	$-0.208695\pi$
$233$	−26606.2	−	36620.3i	−0.0321065	−	0.0441909i	−0.824768	+	0.565471i	$0.808695\pi$
$234$	483316.	+	157039.i	0.577021	+	0.187486i
$235$	−14635.4	+	4755.32i	−0.0172876	+	0.00561707i
$236$	−230746.	−	710164.i	−0.269684	−	0.830001i
$237$	−69598.4			−0.0804874
$238$	368616.	+	1.13448e6i	0.421825	+	1.29824i
$239$	242481.	−	333746.i	0.274588	−	0.377938i	−0.649344	−	0.760495i	$-0.724956\pi$
$239$	242481.	−	333746.i	0.274588	−	0.377938i	0.923932	+	0.382557i	$0.124956\pi$
$240$	−10614.1	−	14609.1i	−0.0118948	−	0.0163718i
$241$	−502200.	+	1.54561e6i	−0.556973	+	1.71419i	0.133702	+	0.991022i	$0.457313\pi$
$241$	−502200.	+	1.54561e6i	−0.556973	+	1.71419i	−0.690675	+	0.723165i	$0.742687\pi$
$242$	482030.	−	1.48353e6i	0.529097	−	1.62839i
$243$		−	474968.i		−	0.515999i
$244$	−271506.	+	197260.i	−0.291947	+	0.212112i
$245$	965335.			1.02746
$246$	102045.	−	64250.2i	0.107511	−	0.0676919i
$247$	−215392.			−0.224640
$248$	89670.2	−	65149.2i	0.0925804	−	0.0672636i
$249$		−	144646.i		−	0.147846i
$250$	−174821.	+	538042.i	−0.176906	+	0.544461i
$251$	−221092.	+	680453.i	−0.221508	+	0.681732i	0.777119	+	0.629353i	$0.216680\pi$
$251$	−221092.	+	680453.i	−0.221508	+	0.681732i	−0.998627	+	0.0523784i	$0.983320\pi$
$252$	519294.	+	714747.i	0.515124	+	0.709007i
$253$	1.60771e6	−	2.21282e6i	1.57908	−	2.17342i
$254$	−27829.3	−	85649.7i	−0.0270656	−	0.0832993i
$255$	89585.7			0.0862757
$256$	20251.7	+	62328.4i	0.0193136	+	0.0594410i
$257$	−320001.	+	103975.i	−0.302217	+	0.0981961i	−0.456200	−	0.889877i	$-0.650790\pi$
$257$	−320001.	+	103975.i	−0.302217	+	0.0981961i	0.153983	+	0.988073i	$0.450790\pi$
$258$	11999.7	+	3898.94i	0.0112233	+	0.00364667i
$259$	554796.	+	763611.i	0.513906	+	0.707331i
$260$			217709.i			0.199730i
$261$	−442433.	−	143755.i	−0.402018	−	0.130624i
$262$	−579227.	−	420833.i	−0.521309	−	0.378753i
$263$	−1.09308e6	+	355164.i	−0.974460	+	0.316621i	−0.752615	−	0.658461i	$-0.771208\pi$
$263$	−1.09308e6	+	355164.i	−0.974460	+	0.316621i	−0.221845	+	0.975082i	$0.571208\pi$
$264$	107647.	−	78210.1i	0.0950587	−	0.0690642i
$265$	399877.	−	550383.i	0.349793	−	0.481449i
$266$	−302940.	−	220099.i	−0.262514	−	0.190728i
$267$	91720.2	+	66638.6i	0.0787384	+	0.0572068i
$268$	93516.6	−	128715.i	0.0795338	−	0.109469i
$269$	1.50854e6	−	1.09602e6i	1.27109	−	0.923499i	0.271841	−	0.962342i	$-0.412367\pi$
$269$	1.50854e6	−	1.09602e6i	1.27109	−	0.923499i	0.999245	+	0.0388435i	$0.0123674\pi$
$270$	128310.	−	41690.5i	0.107115	−	0.0348039i
$271$	−847756.	−	615931.i	−0.701210	−	0.509459i	0.179116	−	0.983828i	$-0.442676\pi$
$271$	−847756.	−	615931.i	−0.701210	−	0.509459i	−0.880326	+	0.474369i	$0.842676\pi$
$272$	−309214.	−	100470.i	−0.253418	−	0.0823404i
$273$			355311.i			0.288538i
$274$	−126841.	−	174582.i	−0.102067	−	0.140483i
$275$	−1.75838e6	−	571332.i	−1.40211	−	0.455572i
$276$	157040.	−	51025.4i	0.124090	−	0.0403193i
$277$	451613.	+	1.38992e6i	0.353644	+	1.08841i	0.956791	+	0.290775i	$0.0939132\pi$
$277$	451613.	+	1.38992e6i	0.353644	+	1.08841i	−0.603147	+	0.797630i	$0.706087\pi$
$278$	−463254.			−0.359507
$279$	125849.	+	387322.i	0.0967916	+	0.297894i
$280$	−222466.	+	306198.i	−0.169578	+	0.233404i
$281$	1.13857e6	+	1.56710e6i	0.860186	+	1.18394i	0.981525	+	0.191333i	$0.0612810\pi$
$281$	1.13857e6	+	1.56710e6i	0.860186	+	1.18394i	−0.121340	+	0.992611i	$0.538719\pi$
$282$	2115.31	−	6510.25i	0.00158398	−	0.00487500i
$283$	312412.	−	961505.i	0.231879	−	0.713650i	−0.765641	−	0.643268i	$-0.777578\pi$
$283$	312412.	−	961505.i	0.231879	−	0.713650i	0.997520	−	0.0703822i	$-0.0224219\pi$
$284$			431650.i			0.317567i
$285$	−22751.2	+	16529.7i	−0.0165917	+	0.0120546i
$286$	−1.60418e6			−1.15968
$287$	−1.94166e6	−	1.61798e6i	−1.39145	−	1.15949i
$288$	−240799.			−0.171070
$289$	156229.	−	113507.i	0.110032	−	0.0799426i
$290$		−	199293.i		−	0.139154i
$291$	154407.	−	475217.i	0.106890	−	0.328973i
$292$	−81629.4	+	251229.i	−0.0560260	+	0.172430i
$293$	−871378.	−	1.19935e6i	−0.592977	−	0.816162i	0.402066	−	0.915611i	$-0.368292\pi$
$293$	−871378.	−	1.19935e6i	−0.592977	−	0.816162i	−0.995043	+	0.0994483i	$0.968292\pi$
$294$	−252401.	+	347400.i	−0.170303	+	0.234402i
$295$	363212.	+	1.11785e6i	0.243000	+	0.747876i
$296$	−257262.			−0.170666
$297$	307196.	+	945453.i	0.202081	+	0.621940i
$298$	1.04399e6	−	339212.i	0.681011	−	0.221274i
$299$	−1.89330e6	−	615171.i	−1.22473	−	0.397940i
$300$	−65605.6	−	90298.3i	−0.0420860	−	0.0579264i
$301$		−	264450.i		−	0.168239i
$302$	1.60321e6	+	520914.i	1.01152	+	0.328661i
$303$	314224.	+	228297.i	0.196622	+	0.142854i
$304$	97065.8	−	31538.6i	0.0602397	−	0.0195730i
$305$	427371.	−	310503.i	0.263060	−	0.191125i
$306$	702177.	−	966464.i	0.428690	−	0.590041i
$307$	2.19858e6	+	1.59736e6i	1.33136	+	0.967292i	0.999715	+	0.0238897i	$0.00760506\pi$
$307$	2.19858e6	+	1.59736e6i	1.33136	+	0.967292i	0.331649	+	0.943403i	$0.392395\pi$
$308$	−2.25622e6	−	1.63924e6i	−1.35520	−	0.984612i
$309$	150564.	−	207234.i	0.0897070	−	0.123471i
$310$	−141148.	+	102550.i	−0.0834199	+	0.0606081i
$311$	1.57740e6	−	512528.i	0.924784	−	0.300481i	0.192356	−	0.981325i	$-0.438387\pi$
$311$	1.57740e6	−	512528.i	0.924784	−	0.300481i	0.732428	+	0.680845i	$0.238387\pi$
$312$	−78347.9	−	56923.1i	−0.0455660	−	0.0331056i
$313$	−1.29425e6	−	420527.i	−0.746718	−	0.242624i	−0.0891498	−	0.996018i	$-0.528415\pi$
$313$	−1.29425e6	−	420527.i	−0.746718	−	0.242624i	−0.657569	+	0.753395i	$0.728415\pi$
$314$			844782.i			0.483527i
$315$	−817409.	−	1.12507e6i	−0.464155	−	0.638854i
$316$	−378134.	−	122863.i	−0.213024	−	0.0692155i
$317$	639441.	−	207767.i	0.357398	−	0.116126i	−0.124814	−	0.992180i	$-0.539833\pi$
$317$	639441.	−	207767.i	0.357398	−	0.116126i	0.482212	+	0.876054i	$0.339833\pi$
$318$	93515.5	+	287811.i	0.0518580	+	0.159603i
$319$	1.46849e6			0.807966
$320$	−31877.8	−	98109.8i	−0.0174026	−	0.0535596i
$321$	340151.	−	468177.i	0.184251	−	0.253599i
$322$	−2.03424e6	−	2.79989e6i	−1.09336	−	1.50488i
$323$	−156464.	+	481548.i	−0.0834466	+	0.256822i
$324$	263984.	−	812460.i	0.139706	−	0.429972i
$325$			1.34565e6i			0.706681i
$326$	2.01432e6	−	1.46349e6i	1.04975	−	0.762687i
$327$	459543.			0.237660
$328$	667838.	−	168936.i	0.342757	−	0.0867036i
$329$	−143473.			−0.0730770
$330$	−169445.	+	123109.i	−0.0856531	+	0.0622306i
$331$			1.90485e6i			0.955634i	0.878459	+	0.477817i	$0.158572\pi$
$331$			1.90485e6i			0.955634i	−0.878459	+	0.477817i	$0.841428\pi$
$332$	255346.	−	785875.i	0.127141	−	0.391298i
$333$	292101.	−	898994.i	0.144352	−	0.444269i
$334$	−1.16900e6	−	1.60899e6i	−0.573388	−	0.789201i
$335$	−147202.	+	202607.i	−0.0716643	+	0.0986375i
$336$	−52026.1	−	160120.i	−0.0251405	−	0.0773744i
$337$	−2.85211e6			−1.36802			−0.684010	−	0.729473i	$-0.739765\pi$
$337$	−2.85211e6			−1.36802			−0.684010	+	0.729473i	$0.739765\pi$
$338$	−98147.1	−	302066.i	−0.0467289	−	0.143817i
$339$	211397.	−	68687.1i	0.0999079	−	0.0324620i
$340$	486727.	+	158147.i	0.228343	+	0.0741931i
$341$	−755637.	−	1.04005e6i	−0.351907	−	0.484358i
$342$			375004.i			0.173368i
$343$	4.80636e6	+	1.56168e6i	2.20587	+	0.716732i
$344$	58312.5	+	42366.5i	0.0265684	+	0.0193031i
$345$	−247193.	+	80317.9i	−0.111812	+	0.0363299i
$346$	−270901.	+	196821.i	−0.121652	+	0.0883855i
$347$	−794551.	+	1.09361e6i	−0.354240	+	0.487570i	−0.948533	−	0.316679i	$-0.897432\pi$
$347$	−794551.	+	1.09361e6i	−0.354240	+	0.487570i	0.594292	+	0.804249i	$0.297432\pi$
$348$	71720.5	+	52108.0i	0.0317464	+	0.0230651i
$349$	−1.48854e6	−	1.08149e6i	−0.654179	−	0.475289i	0.210513	−	0.977591i	$-0.432486\pi$
$349$	−1.48854e6	−	1.08149e6i	−0.654179	−	0.475289i	−0.864692	+	0.502302i	$0.832486\pi$
$350$	−1.37505e6	+	1.89260e6i	−0.599998	+	0.825827i
$351$	585351.	−	425283.i	0.253600	−	0.184251i
$352$	722920.	−	234891.i	0.310981	−	0.101044i
$353$	−2.11833e6	−	1.53906e6i	−0.904808	−	0.657382i	0.0348884	−	0.999391i	$-0.488892\pi$
$353$	−2.11833e6	−	1.53906e6i	−0.904808	−	0.657382i	−0.939696	+	0.342010i	$0.888892\pi$
$354$	−497254.	−	161568.i	−0.210897	−	0.0685246i
$355$		−	679451.i		−	0.286146i
$356$	380685.	+	523968.i	0.159199	+	0.219119i
$357$	794362.	+	258104.i	0.329874	+	0.107182i
$358$	−1.86375e6	+	605569.i	−0.768563	+	0.249721i
$359$	1.41988e6	+	4.36995e6i	0.581455	+	1.78954i	0.613062	+	0.790035i	$0.289938\pi$
$359$	1.41988e6	+	4.36995e6i	0.581455	+	1.78954i	−0.0316062	+	0.999500i	$0.510062\pi$
$360$	379037.			0.154143
$361$	716041.	+	2.20375e6i	0.289181	+	0.890008i
$362$	237663.	−	327115.i	0.0953213	−	0.131199i
$363$	−641993.	−	883627.i	−0.255719	−	0.351967i
$364$	−627237.	+	1.93044e6i	−0.248129	+	0.763663i
$365$	128491.	−	395454.i	0.0504824	−	0.155369i
$366$			234986.i			0.0916935i
$367$	−1.85038e6	+	1.34438e6i	−0.717128	+	0.521024i	−0.885465	−	0.464706i	$-0.846160\pi$
$367$	−1.85038e6	+	1.34438e6i	−0.717128	+	0.521024i	0.168338	+	0.985729i	$0.446160\pi$
$368$	943287.			0.363098
$369$	−167937.	+	2.52556e6i	−0.0642068	+	0.965586i
$370$	404950.			0.153779
$371$	5.13143e6	−	3.72820e6i	1.93555	−	1.40626i
$372$		−	77608.7i		−	0.0290772i
$373$	914411.	−	2.81427e6i	0.340306	−	1.04735i	−0.623743	−	0.781629i	$-0.714389\pi$
$373$	914411.	−	2.81427e6i	0.340306	−	1.04735i	0.964049	−	0.265725i	$-0.0856112\pi$
$374$	−1.16530e6	+	3.58644e6i	−0.430785	+	1.32582i
$375$	232835.	+	320470.i	0.0855009	+	0.117682i
$376$	22985.3	−	31636.5i	0.00838456	−	0.0115404i
$377$	−330276.	−	1.01649e6i	−0.119681	−	0.368339i
$378$	1.25785e6			0.452792
$379$	−131577.	−	404952.i	−0.0470523	−	0.144812i	0.924770	−	0.380526i	$-0.124257\pi$
$379$	−131577.	−	404952.i	−0.0470523	−	0.144812i	−0.971822	+	0.235714i	$0.924257\pi$
$380$	−152789.	+	49644.2i	−0.0542792	+	0.0176364i
$381$	−59971.6	−	19486.0i	−0.0211657	−	0.00687717i
$382$	−1.30086e6	−	1.79048e6i	−0.456113	−	0.627786i
$383$		−	4.52931e6i		−	1.57774i	−0.614561	−	0.788869i	$-0.710667\pi$
$383$		−	4.52931e6i		−	1.57774i	0.614561	−	0.788869i	$-0.289333\pi$
$384$	43642.2	+	14180.2i	0.0151035	+	0.00490743i
$385$	3.55146e6	+	2.58029e6i	1.22111	+	0.887189i
$386$	632002.	−	205350.i	0.215899	−	0.0701498i
$387$	−214258.	+	155667.i	−0.0727209	+	0.0528349i
$388$	1.67782e6	−	2.30932e6i	0.565803	−	0.778761i
$389$	−3.02245e6	−	2.19594e6i	−1.01271	−	0.735777i	−0.0479341	−	0.998851i	$-0.515264\pi$
$389$	−3.02245e6	−	2.19594e6i	−1.01271	−	0.735777i	−0.964776	+	0.263074i	$0.915264\pi$
$390$	123326.	+	89601.3i	0.0410575	+	0.0298300i
$391$	−2.75065e6	+	3.78594e6i	−0.909899	+	1.25237i
$392$	−1.98458e6	+	1.44189e6i	−0.652311	+	0.473931i
$393$	−476779.	+	154915.i	−0.155717	+	0.0505955i
$394$	−2.31989e6	−	1.68550e6i	−0.752881	−	0.547000i
$395$	595212.	+	193396.i	0.191946	+	0.0623670i
$396$			2.79293e6i			0.894997i
$397$	1.48561e6	+	2.04476e6i	0.473072	+	0.651128i	0.977155	−	0.212527i	$-0.0681694\pi$
$397$	1.48561e6	+	2.04476e6i	0.473072	+	0.651128i	−0.504083	+	0.863655i	$0.668169\pi$
$398$	3.57105e6	+	1.16030e6i	1.13002	+	0.367167i
$399$	−249359.	+	81021.8i	−0.0784140	+	0.0254782i
$400$	−197035.	−	606413.i	−0.0615736	−	0.189504i
$401$	3.56029e6			1.10567			0.552833	−	0.833292i	$-0.313547\pi$
$401$	3.56029e6			1.10567			0.552833	+	0.833292i	$0.313547\pi$
$402$	−34424.9	−	105949.i	−0.0106245	−	0.0326988i
$403$	−549970.	+	756969.i	−0.168685	+	0.232175i
$404$	1.30419e6	+	1.79506e6i	0.397545	+	0.547174i
$405$	−415532.	+	1.27888e6i	−0.125883	+	0.387428i
$406$	574179.	−	1.76714e6i	0.172875	−	0.532054i
$407$			2.98387e6i			0.892881i
$408$	−184175.	+	133811.i	−0.0547747	+	0.0397961i
$409$	−6.03039e6			−1.78253			−0.891266	−	0.453481i	$-0.850182\pi$
$409$	−6.03039e6			−1.78253			−0.891266	+	0.453481i	$0.850182\pi$
$410$	−1.05123e6	+	265918.i	−0.308843	+	0.0781246i
$411$	−151099.			−0.0441221
$412$	1.18386e6	−	860127.i	0.343604	−	0.249643i
$413$			1.09585e7i			3.16138i
$414$	−1.07103e6	+	3.29629e6i	−0.307115	+	0.945202i
$415$	−401935.	+	1.23703e6i	−0.114561	+	0.352581i
$416$	−325183.	−	447577.i	−0.0921287	−	0.126804i
$417$	−190659.	+	262420.i	−0.0536930	+	0.0739021i
$418$	−365802.	−	1.12582e6i	−0.102401	−	0.315159i
$419$	−5.07087e6			−1.41107			−0.705533	−	0.708677i	$-0.749292\pi$
$419$	−5.07087e6			−1.41107			−0.705533	+	0.708677i	$0.749292\pi$
$420$	81893.1	+	252041.i	0.0226529	+	0.0697185i
$421$	−3.37026e6	+	1.09506e6i	−0.926741	+	0.301116i	−0.733229	−	0.679981i	$-0.761988\pi$
$421$	−3.37026e6	+	1.09506e6i	−0.926741	+	0.301116i	−0.193512	+	0.981098i	$0.561988\pi$
$422$	529203.	+	171948.i	0.144658	+	0.0470021i
$423$	84455.0	+	116242.i	0.0229496	+	0.0315874i
$424$			1.72879e6i			0.467011i
$425$	3.00844e6	+	977501.i	0.807921	+	0.262509i
$426$	244517.	+	177652.i	0.0652808	+	0.0474293i
$427$	4.68411e6	−	1.52196e6i	1.24325	−	0.403955i
$428$	2.67455e6	−	1.94317e6i	0.705734	−	0.512746i
$429$	−660226.	+	908723.i	−0.173201	+	0.238390i
$430$	−91788.3	−	66688.1i	−0.0239396	−	0.0173931i
$431$	−1.57719e6	−	1.14590e6i	−0.408970	−	0.297134i	0.364215	−	0.931315i	$-0.381337\pi$
$431$	−1.57719e6	−	1.14590e6i	−0.408970	−	0.297134i	−0.773185	+	0.634181i	$0.781337\pi$
$432$	−201515.	+	277362.i	−0.0519516	+	0.0715052i
$433$	2.64484e6	−	1.92159e6i	0.677922	−	0.492539i	−0.194746	−	0.980854i	$-0.562388\pi$
$433$	2.64484e6	−	1.92159e6i	0.677922	−	0.492539i	0.872668	+	0.488315i	$0.162388\pi$
$434$	−1.54702e6	+	502657.i	−0.394250	+	0.128100i
$435$	−112894.	−	82022.0i	−0.0286053	−	0.0207829i
$436$	2.49673e6	+	811238.i	0.629008	+	0.204377i
$437$		−	1.46901e6i		−	0.367977i
$438$	108718.	+	149638.i	0.0270781	+	0.0372697i
$439$	4.35517e6	+	1.41508e6i	1.07856	+	0.350445i	0.793815	−	0.608159i	$-0.208092\pi$
$439$	4.35517e6	+	1.41508e6i	1.07856	+	0.350445i	0.284743	+	0.958604i	$0.408092\pi$
$440$	−1.13793e6	+	369737.i	−0.280211	+	0.0910460i
$441$	−2.78529e6	−	8.57223e6i	−0.681982	−	2.09893i
$442$	2.74462e6			0.668231
$443$	−2.31648e6	−	7.12939e6i	−0.560814	−	1.72601i	−0.680072	−	0.733145i	$-0.738052\pi$
$443$	−2.31648e6	−	7.12939e6i	−0.560814	−	1.72601i	0.119258	−	0.992863i	$-0.461948\pi$
$444$	−105880.	+	145731.i	−0.0254892	+	0.0350829i
$445$	−599228.	−	824766.i	−0.143447	−	0.197438i
$446$	−435500.	+	1.34033e6i	−0.103669	+	0.319062i
$447$	237515.	−	730995.i	0.0562240	−	0.173040i
$448$		−	961788.i		−	0.226404i
$449$	−1.71563e6	+	1.24648e6i	−0.401614	+	0.291790i	−0.770198	−	0.637805i	$-0.779843\pi$
$449$	−1.71563e6	+	1.24648e6i	−0.401614	+	0.291790i	0.368584	+	0.929594i	$0.379843\pi$
$450$	2.34281e6			0.545389
$451$	−1.95941e6	−	7.74596e6i	−0.453612	−	1.79322i
$452$	1.26979e6			0.292339
$453$	954908.	−	693781.i	0.218633	−	0.158846i
$454$			281824.i			0.0641710i
$455$	987319.	−	3.03865e6i	0.223578	−	0.688102i
$456$	22083.2	−	67965.2i	0.00497337	−	0.0153064i
$457$	544220.	+	749055.i	0.121894	+	0.167773i	0.865603	−	0.500730i	$-0.166935\pi$
$457$	544220.	+	749055.i	0.121894	+	0.167773i	−0.743709	+	0.668504i	$0.766935\pi$
$458$	−1.41567e6	+	1.94851e6i	−0.315355	+	0.434049i
$459$	−525587.	−	1.61759e6i	−0.116443	−	0.358374i
$460$	−1.48481e6			−0.327171
$461$	1.34322e6	+	4.13401e6i	0.294372	+	0.905982i	0.983432	+	0.181278i	$0.0580235\pi$
$461$	1.34322e6	+	4.13401e6i	0.294372	+	0.905982i	−0.689060	+	0.724704i	$0.741977\pi$
$462$	−1.85716e6	+	603428.i	−0.404804	+	0.131529i
$463$	2.76518e6	+	898463.i	0.599476	+	0.194781i	0.593007	−	0.805198i	$-0.297941\pi$
$463$	2.76518e6	+	898463.i	0.599476	+	0.194781i	0.00646906	+	0.999979i	$0.497941\pi$
$464$	297676.	+	409716.i	0.0641873	+	0.0883462i
$465$			122162.i			0.0262002i
$466$	−172199.	−	55950.9i	−0.0367338	−	0.0119355i
$467$	−5.69566e6	−	4.13814e6i	−1.20851	−	0.878037i	−0.213419	−	0.976961i	$-0.568460\pi$
$467$	−5.69566e6	−	4.13814e6i	−1.20851	−	0.878037i	−0.995095	+	0.0989241i	$0.968460\pi$
$468$	1.93327e6	−	628156.i	0.408016	−	0.132572i
$469$	−1.88898e6	+	1.37242e6i	−0.396547	+	0.288108i
$470$	−36180.6	+	49798.3i	−0.00755494	+	0.0103985i
$471$	478544.	+	347683.i	0.0993962	+	0.0722156i
$472$	−2.41640e6	−	1.75562e6i	−0.499246	−	0.362724i
$473$	491390.	−	676341.i	0.100989	−	0.138999i
$474$	−225225.	+	163636.i	−0.0460438	+	0.0334527i
$475$	−944384.	+	306849.i	−0.192050	+	0.0624009i
$476$	3.86020e6	+	2.80460e6i	0.780894	+	0.567353i
$477$	−6.04120e6	−	1.96290e6i	−1.21570	−	0.395005i
$478$		−	1.65013e6i		−	0.330330i
$479$	3.63334e6	+	5.00087e6i	0.723548	+	0.995879i	0.999399	+	0.0346782i	$0.0110406\pi$
$479$	3.63334e6	+	5.00087e6i	0.723548	+	0.995879i	−0.275850	+	0.961201i	$0.588959\pi$
$480$	−68696.1	−	22320.7i	−0.0136091	−	0.00442186i
$481$	2.06544e6	−	671101.i	0.407051	−	0.132259i
$482$	2.00880e6	+	6.18245e6i	0.393839	+	1.21211i
$483$	−2.42328e6			−0.472645
$484$	−1.92812e6	−	5.93414e6i	−0.374128	−	1.15145i
$485$	−2.64101e6	+	3.63504e6i	−0.509819	+	0.701706i
$486$	−1.11672e6	−	1.53703e6i	−0.214463	−	0.295183i
$487$	1.67432e6	−	5.15304e6i	0.319902	−	0.984557i	−0.653788	−	0.756678i	$-0.726821\pi$
$487$	1.67432e6	−	5.15304e6i	0.319902	−	0.984557i	0.973690	−	0.227879i	$-0.0731790\pi$
$488$	−414824.	+	1.27670e6i	−0.0788523	+	0.242682i
$489$		−	1.74338e6i		−	0.329700i
$490$	3.12389e6	−	2.26964e6i	0.587767	−	0.427038i
$491$	200321.			0.0374993			0.0187496	−	0.999824i	$-0.494031\pi$
$491$	200321.			0.0374993			0.0187496	+	0.999824i	$0.494031\pi$
$492$	179162.	−	447839.i	0.0333682	−	0.0834083i
$493$	−2.51245e6			−0.465566
$494$	−697024.	+	506417.i	−0.128508	+	0.0933665i
$495$		−	4.39628e6i		−	0.806441i
$496$	137004.	−	421655.i	0.0250051	−	0.0769578i
$497$	1.95755e6	−	6.02473e6i	0.355486	−	1.09407i
$498$	−340084.	−	468085.i	−0.0614487	−	0.0845768i
$499$	4.47018e6	−	6.15267e6i	0.803662	−	1.10615i	−0.188609	−	0.982052i	$-0.560398\pi$
$499$	4.47018e6	−	6.15267e6i	0.803662	−	1.10615i	0.992271	−	0.124094i	$-0.0396023\pi$
$500$	699282.	+	2.15217e6i	0.125091	+	0.384992i
$501$	−1.39257e6			−0.247869
$502$	884370.	+	2.72181e6i	0.156630	+	0.482057i
$503$	−2.71181e6	+	881121.i	−0.477903	+	0.155280i	−0.538056	−	0.842909i	$-0.680841\pi$
$503$	−2.71181e6	+	881121.i	−0.477903	+	0.155280i	0.0601533	+	0.998189i	$0.480841\pi$
$504$	3.36094e6	+	1.09204e6i	0.589365	+	0.191496i
$505$	−2.05289e6	−	2.82556e6i	−0.358210	−	0.493034i
$506$		−	1.09408e7i		−	1.89964i
$507$	−211505.	−	68722.3i	−0.0365428	−	0.0118735i
$508$	−291432.	−	211738.i	−0.0501046	−	0.0364031i
$509$	2.75600e6	−	895479.i	0.471504	−	0.153201i	−0.0636206	−	0.997974i	$-0.520265\pi$
$509$	2.75600e6	−	895479.i	0.471504	−	0.153201i	0.535124	+	0.844773i	$0.320265\pi$
$510$	289905.	−	210629.i	0.0493550	−	0.0358585i
$511$	2.27867e6	−	3.13632e6i	0.386038	−	0.531335i
$512$	212079.	+	154084.i	0.0357538	+	0.0259767i
$513$	431944.	+	313825.i	0.0724659	+	0.0526495i
$514$	−791086.	+	1.08884e6i	−0.132074	+	0.181784i
$515$	−1.86349e6	+	1.35391e6i	−0.309606	+	0.224942i
$516$	47998.8	−	15595.7i	0.00793608	−	0.00257859i
$517$	−366938.	−	266596.i	−0.0603763	−	0.0438660i
$518$	3.59071e6	+	1.16669e6i	0.587972	+	0.191044i
$519$			234462.i			0.0382080i
$520$	511864.	+	704520.i	0.0830130	+	0.114258i
$521$	−3.83419e6	−	1.24580e6i	−0.618841	−	0.201074i	−0.0172156	−	0.999852i	$-0.505480\pi$
$521$	−3.83419e6	−	1.24580e6i	−0.618841	−	0.201074i	−0.601626	+	0.798778i	$0.705480\pi$
$522$	−1.76973e6	+	575020.i	−0.284270	+	0.0923649i
$523$	−707524.	−	2.17753e6i	−0.113106	−	0.348105i	0.878441	−	0.477851i	$-0.158584\pi$
$523$	−707524.	−	2.17753e6i	−0.113106	−	0.348105i	−0.991547	+	0.129745i	$0.958584\pi$
$524$	−2.86386e6			−0.455641
$525$	506178.	+	1.55786e6i	0.0801503	+	0.246677i
$526$	−2.70225e6	+	3.71933e6i	−0.425855	+	0.586139i
$527$	1.29283e6	+	1.77943e6i	0.202775	+	0.279096i
$528$	164470.	−	506186.i	0.0256745	−	0.0790179i
$529$	2.20662e6	−	6.79127e6i	0.342837	−	1.05514i
$530$		−	2.72124e6i		−	0.420802i
$531$	8.87861e6	−	6.45069e6i	1.36650	−	0.992818i
$532$	−1.49782e6			−0.229446
$533$	−4.92107e6	+	3.09845e6i	−0.750311	+	0.472418i
$534$	453489.			0.0688199
$535$	−4.20995e6	+	3.05870e6i	−0.635905	+	0.462012i
$536$		−	636400.i		−	0.0956793i
$537$	−424017.	+	1.30499e6i	−0.0634523	+	0.195286i
$538$	2.30484e6	−	7.09357e6i	0.343309	−	1.05660i
$539$	1.67238e7	+	2.30183e7i	2.47949	+	3.41273i
$540$	317201.	−	436589.i	0.0468112	−	0.0644301i
$541$	1.81444e6	+	5.58426e6i	0.266532	+	0.820300i	0.991337	+	0.131346i	$0.0419299\pi$
$541$	1.81444e6	+	5.58426e6i	0.266532	+	0.820300i	−0.724805	+	0.688954i	$0.758070\pi$
$542$	−4.19154e6			−0.612880
$543$	−87487.3	−	269258.i	−0.0127334	−	0.0391895i
$544$	−1.23686e6	+	401879.i	−0.179193	+	0.0582234i
$545$	−3.93005e6	−	1.27695e6i	−0.566770	−	0.184155i
$546$	835387.	+	1.14981e6i	0.119924	+	0.165061i
$547$			3.81037e6i			0.544501i	0.962226	+	0.272250i	$0.0877679\pi$
$547$			3.81037e6i			0.544501i	−0.962226	+	0.272250i	$0.912232\pi$
$548$	−820933.	−	266737.i	−0.116777	−	0.0379430i
$549$	−3.99038e6	−	2.89918e6i	−0.565046	−	0.410530i
$550$	−7.03352e6	+	2.28533e6i	−0.991439	+	0.322138i
$551$	638062.	−	463579.i	0.0895332	−	0.0650497i
$552$	388224.	−	534344.i	0.0542294	−	0.0746403i
$553$	4.72059e6	+	3.42971e6i	0.656422	+	0.476918i
$554$	4.72935e6	+	3.43607e6i	0.654677	+	0.475650i
$555$	166663.	−	229392.i	0.0229672	−	0.0316116i
$556$	−1.49912e6	+	1.08918e6i	−0.205660	+	0.149421i
$557$	−7.18311e6	+	2.33393e6i	−0.981012	+	0.318750i	−0.755253	−	0.655433i	$-0.772486\pi$
$557$	−7.18311e6	+	2.33393e6i	−0.981012	+	0.318750i	−0.225759	+	0.974183i	$0.572486\pi$
$558$	1.31790e6	+	957513.i	0.179183	+	0.130184i
$559$	−578682.	−	188025.i	−0.0783268	−	0.0254499i
$560$			1.51393e6i			0.204002i
$561$	1.55201e6	+	2.13616e6i	0.208204	+	0.286568i
$562$	7.36895e6	+	2.39432e6i	0.984158	+	0.319772i
$563$	2.57288e6	−	835980.i	0.342097	−	0.111154i	−0.132930	−	0.991125i	$-0.542438\pi$
$563$	2.57288e6	−	835980.i	0.342097	−	0.111154i	0.475026	+	0.879972i	$0.342438\pi$
$564$	−8461.23	−	26041.0i	−0.00112005	−	0.00344715i
$565$	−1.99875e6			−0.263413
$566$	−1.24965e6	−	3.84602e6i	−0.163963	−	0.504627i
$567$	−7.36909e6	+	1.01427e7i	−0.962623	+	1.32494i
$568$	1.01487e6	+	1.39685e6i	0.131990	+	0.181668i
$569$	−462005.	+	1.42191e6i	−0.0598227	+	0.184115i	−0.976502	−	0.215508i	$-0.930859\pi$
$569$	−462005.	+	1.42191e6i	−0.0598227	+	0.184115i	0.916679	+	0.399624i	$0.130859\pi$
$570$	−34760.7	+	106982.i	−0.00448127	+	0.0137919i
$571$		−	7.52669e6i		−	0.966082i	−0.875598	−	0.483041i	$-0.839532\pi$
$571$		−	7.52669e6i		−	0.966082i	0.875598	−	0.483041i	$-0.160468\pi$
$572$	−5.19125e6	+	3.77166e6i	−0.663409	+	0.481995i
$573$	−1.54965e6			−0.197172
$574$	−1.00874e7	−	670766.i	−1.27791	−	0.0849750i
$575$	−9.17753e6			−1.15759
$576$	−779243.	+	566153.i	−0.0978626	+	0.0711013i
$577$		−	1.32739e6i		−	0.165982i	−0.996550	−	0.0829909i	$-0.973553\pi$
$577$		−	1.32739e6i		−	0.165982i	0.996550	−	0.0829909i	$-0.0264472\pi$
$578$	238697.	−	734633.i	0.0297185	−	0.0914642i
$579$	143785.	−	442526.i	0.0178245	−	0.0548583i
$580$	−468565.	−	644925.i	−0.0578362	−	0.0796048i
$581$	−7.12795e6	+	9.81079e6i	−0.876041	+	1.20577i
$582$	−617630.	−	1.90087e6i	−0.0755824	−	0.232619i
$583$	2.00514e7			2.44328
$584$	326517.	+	1.00492e6i	0.0396163	+	0.121927i
$585$	−3.04311e6	+	988766.i	−0.367644	+	0.119455i
$586$	−5.63968e6	−	1.83244e6i	−0.678438	−	0.220438i
$587$	6.15163e6	+	8.46700e6i	0.736877	+	1.01422i	0.998792	+	0.0491337i	$0.0156460\pi$
$587$	6.15163e6	+	8.46700e6i	0.736877	+	1.01422i	−0.261915	+	0.965091i	$0.584354\pi$
$588$			1.71764e6i			0.204875i
$589$	−656655.	−	213360.i	−0.0779918	−	0.0253411i
$590$	3.80361e6	+	2.76348e6i	0.449848	+	0.326834i
$591$	−1.90957e6	+	620457.i	−0.224888	+	0.0730707i
$592$	−832517.	+	604859.i	−0.0976312	+	0.0709332i
$593$	463797.	−	638361.i	0.0541615	−	0.0745469i	−0.781077	−	0.624435i	$-0.785329\pi$
$593$	463797.	−	638361.i	0.0541615	−	0.0745469i	0.835239	+	0.549888i	$0.185329\pi$
$594$	3.21700e6	+	2.33729e6i	0.374098	+	0.271798i
$595$	−6.07625e6	−	4.41465e6i	−0.703628	−	0.511216i
$596$	2.58087e6	−	3.55227e6i	0.297613	−	0.409629i
$597$	2.12700e6	−	1.54535e6i	0.244248	−	0.177457i
$598$	−7.57321e6	+	2.46068e6i	−0.866018	+	0.281386i
$599$	1.04561e7	+	7.59681e6i	1.19070	+	0.865095i	0.993338	−	0.115235i	$-0.0367621\pi$
$599$	1.04561e7	+	7.59681e6i	1.19070	+	0.865095i	0.197363	+	0.980330i	$0.436762\pi$
$600$	−424608.	−	137964.i	−0.0481515	−	0.0156454i
$601$			1.25310e7i			1.41514i	0.706645	+	0.707568i	$0.250208\pi$
$601$			1.25310e7i			1.41514i	−0.706645	+	0.707568i	$0.749792\pi$
$602$	−621759.	−	855777.i	−0.0699247	−	0.0962431i
$603$	2.22388e6	+	722583.i	0.249068	+	0.0809272i
$604$	6.41283e6	−	2.08366e6i	0.715250	−	0.232399i
$605$	3.03501e6	+	9.34079e6i	0.337110	+	1.03752i
$606$	1.55361e6			0.171854
$607$	−800962.	−	2.46511e6i	−0.0882348	−	0.271559i	0.897197	−	0.441631i	$-0.145600\pi$
$607$	−800962.	−	2.46511e6i	−0.0882348	−	0.271559i	−0.985432	+	0.170072i	$0.945600\pi$
$608$	239960.	−	330277.i	0.0263257	−	0.0362342i
$609$	−764721.	−	1.05255e6i	−0.0835526	−	0.115000i
$610$	652965.	−	2.00962e6i	0.0710502	−	0.218670i
$611$	−102010.	+	313955.i	−0.0110545	+	0.0340224i
$612$		−	4.77846e6i		−	0.515715i
$613$	1.33836e7	−	9.72377e6i	1.43854	−	1.04516i	0.450197	−	0.892930i	$-0.351354\pi$
$613$	1.33836e7	−	9.72377e6i	1.43854	−	1.04516i	0.988345	−	0.152232i	$-0.0486461\pi$
$614$	1.08704e7			1.16365
$615$	−282014.	+	704933.i	−0.0300665	+	0.0751554i
$616$	−1.11554e7			−1.18449
$617$	881355.	−	640342.i	0.0932048	−	0.0677172i	−0.540207	−	0.841532i	$-0.681654\pi$
$617$	881355.	−	640342.i	0.0932048	−	0.0677172i	0.633412	+	0.773815i	$0.281654\pi$
$618$		−	1.02462e6i		−	0.107918i
$619$	−1.24522e6	+	3.83239e6i	−0.130623	+	0.402016i	−0.994884	−	0.101028i	$-0.967787\pi$
$619$	−1.24522e6	+	3.83239e6i	−0.130623	+	0.402016i	0.864261	+	0.503044i	$0.167787\pi$
$620$	−215655.	+	663717.i	−0.0225310	+	0.0693432i
$621$	2.90049e6	+	3.99218e6i	0.301816	+	0.415414i
$622$	3.89954e6	−	5.36726e6i	0.404145	−	0.556259i
$623$	−2.93717e6	−	9.03967e6i	−0.303186	−	0.933109i
$624$	−387373.			−0.0398262
$625$	1.30449e6	+	4.01482e6i	0.133580	+	0.411117i
$626$	−5.17699e6	+	1.68211e6i	−0.528010	+	0.171561i
$627$	−788298.	−	256134.i	−0.0800796	−	0.0260194i
$628$	1.98620e6	+	2.73377e6i	0.200967	+	0.276607i
$629$		−	5.10515e6i		−	0.514495i
$630$	−5.29038e6	−	1.71895e6i	−0.531050	−	0.172549i
$631$	4.77325e6	+	3.46797e6i	0.477244	+	0.346738i	0.800258	−	0.599656i	$-0.204696\pi$
$631$	4.77325e6	+	3.46797e6i	0.477244	+	0.346738i	−0.323014	+	0.946394i	$0.604696\pi$
$632$	−1.51253e6	+	491452.i	−0.150630	+	0.0489428i
$633$	315205.	−	229010.i	0.0312669	−	0.0227167i
$634$	1.58079e6	−	2.17576e6i	0.156189	−	0.214975i
$635$	458736.	+	333292.i	0.0451470	+	0.0328012i
$636$	979307.	+	711508.i	0.0960011	+	0.0697489i
$637$	1.21720e7	−	1.67533e7i	1.18853	−	1.63588i
$638$	4.75212e6	−	3.45262e6i	0.462206	−	0.335812i
$639$	−6.03356e6	+	1.96042e6i	−0.584550	+	0.189932i
$640$	−333829.	−	242541.i	−0.0322162	−	0.0234064i
$641$	3.79744e6	+	1.23386e6i	0.365044	+	0.118610i	0.485795	−	0.874073i	$-0.338530\pi$
$641$	3.79744e6	+	1.23386e6i	0.365044	+	0.118610i	−0.120751	+	0.992683i	$0.538530\pi$
$642$		−	2.31480e6i		−	0.221654i
$643$	−5.18205e6	−	7.13248e6i	−0.494281	−	0.680319i	0.486889	−	0.873464i	$-0.338131\pi$
$643$	−5.18205e6	−	7.13248e6i	−0.494281	−	0.680319i	−0.981170	+	0.193144i	$0.938131\pi$
$644$	−1.31659e7	−	4.27785e6i	−1.25093	−	0.406453i
$645$	−75553.8	+	24548.9i	−0.00715084	+	0.00232345i
$646$	625857.	+	1.92619e6i	0.0590057	+	0.181601i
$647$	115953.			0.0108899			0.00544494	−	0.999985i	$-0.498267\pi$
$647$	115953.			0.0108899			0.00544494	+	0.999985i	$0.498267\pi$
$648$	−1.05594e6	−	3.24984e6i	−0.0987872	−	0.304036i
$649$	−2.03627e7	+	2.80268e7i	−1.89768	+	2.61193i
$650$	3.16381e6	+	4.35461e6i	0.293716	+	0.404265i
$651$	−351959.	+	1.08322e6i	−0.0325491	+	0.100176i
$652$	3.07761e6	−	9.47192e6i	0.283527	−	0.872607i
$653$		−	9.83517e6i		−	0.902608i	−0.892370	−	0.451304i	$-0.850959\pi$
$653$		−	9.83517e6i		−	0.902608i	0.892370	−	0.451304i	$-0.149041\pi$
$654$	1.48711e6	−	1.08045e6i	0.135956	−	0.0987780i
$655$	4.50793e6			0.410557
$656$	1.76398e6	−	2.11687e6i	0.160042	−	0.192059i
$657$	−3.88239e6			−0.350902
$658$	−464289.	+	337325.i	−0.0418045	+	0.0303728i
$659$			86792.9i			0.00778522i	0.999992	+	0.00389261i	$0.00123906\pi$
$659$			86792.9i			0.00778522i	−0.999992	+	0.00389261i	$0.998761\pi$
$660$	−258888.	+	796776.i	−0.0231341	+	0.0711995i
$661$	−1.61244e6	+	4.96259e6i	−0.143543	+	0.441779i	−0.996821	−	0.0796774i	$-0.974611\pi$
$661$	−1.61244e6	+	4.96259e6i	−0.143543	+	0.441779i	0.853278	+	0.521456i	$0.174611\pi$
$662$	4.47858e6	+	6.16424e6i	0.397187	+	0.546682i
$663$	1.12959e6	−	1.55475e6i	0.0998016	−	0.137365i
$664$	−1.02138e6	−	3.14350e6i	−0.0899020	−	0.276690i
$665$	2.35768e6			0.206743
$666$	−1.16840e6	−	3.59598e6i	−0.102072	−	0.314146i
$667$	6.93259e6	−	2.25253e6i	0.603366	−	0.196046i
$668$	−7.56593e6	−	2.45832e6i	−0.656026	−	0.213156i
$669$	580022.	+	798331.i	0.0501048	+	0.0689633i
$670$			1.00174e6i			0.0862123i
$671$	1.48078e7	+	4.81136e6i	1.26965	+	0.412536i
$672$	−544825.	−	395838.i	−0.0465408	−	0.0338139i
$673$	1.80385e6	−	586107.i	0.153519	−	0.0498815i	−0.231249	−	0.972895i	$-0.574281\pi$
$673$	1.80385e6	−	586107.i	0.153519	−	0.0498815i	0.384769	+	0.923013i	$0.374281\pi$
$674$	−9.22964e6	+	6.70572e6i	−0.782591	+	0.568586i
$675$	1.96060e6	−	2.69854e6i	0.165627	−	0.227966i
$676$	−1.02781e6	−	746748.i	−0.0865060	−	0.0628503i
$677$	8.83273e6	+	6.41736e6i	0.740668	+	0.538127i	0.892920	−	0.450215i	$-0.148653\pi$
$677$	8.83273e6	+	6.41736e6i	0.740668	+	0.538127i	−0.152252	+	0.988342i	$0.548653\pi$
$678$	522602.	−	719300.i	0.0436613	−	0.0600947i
$679$	−3.38909e7	+	2.46232e7i	−2.82103	+	2.04960i
$680$	1.94691e6	−	632588.i	0.161463	−	0.0524625i
$681$	159645.	+	115989.i	0.0131913	+	0.00958406i
$682$	−4.89059e6	−	1.58905e6i	−0.402624	−	0.130821i
$683$		−	9.48062e6i		−	0.777652i	−0.921311	−	0.388826i	$-0.872881\pi$
$683$		−	9.48062e6i		−	0.777652i	0.921311	−	0.388826i	$-0.127119\pi$
$684$	881686.	+	1.21354e6i	0.0720566	+	0.0991774i
$685$	1.29221e6	+	419865.i	0.105222	+	0.0341887i
$686$	1.92254e7	−	6.24672e6i	1.55979	−	0.506806i
$687$	521131.	+	1.60388e6i	0.0421265	+	0.129652i
$688$	288313.			0.0232216
$689$	−4.50976e6	−	1.38796e7i	−0.361914	−	1.11386i
$690$	−611095.	+	841099.i	−0.0488636	+	0.0672550i
$691$	−1.29486e7	−	1.78222e7i	−1.03164	−	1.41992i	−0.903713	−	0.428140i	$-0.859169\pi$
$691$	−1.29486e7	−	1.78222e7i	−1.03164	−	1.41992i	−0.127922	−	0.991784i	$-0.540831\pi$
$692$	−413900.	+	1.27385e6i	−0.0328571	+	0.101124i
$693$	1.26660e7	−	3.89821e7i	1.00186	−	3.08341i
$694$			5.40708e6i			0.426152i
$695$	2.35973e6	−	1.71445e6i	0.185311	−	0.134636i
$696$	354605.			0.0277474
$697$	3.35239e6	+	1.32527e7i	0.261380	+	1.03329i
$698$	−7.35974e6			−0.571773
$699$	−102566.	+	74518.3i	−0.00793979	+	0.00576860i
$700$			9.35753e6i			0.721799i
$701$	3.69409e6	−	1.13692e7i	0.283931	−	0.873849i	−0.702786	−	0.711401i	$-0.748061\pi$
$701$	3.69409e6	−	1.13692e7i	0.283931	−	0.873849i	0.986717	−	0.162448i	$-0.0519390\pi$
$702$	894337.	−	2.75249e6i	0.0684950	−	0.210806i
$703$	941964.	+	1.29650e6i	0.0718863	+	0.0989429i
$704$	1.78716e6	−	2.45981e6i	0.135904	−	0.187055i
$705$	13318.6	+	40990.5i	0.00100922	+	0.00310607i
$706$	−1.04736e7			−0.790831
$707$	−1.00624e7	−	3.09690e7i	−0.757102	−	2.33012i
$708$	−1.98902e6	+	646271.i	−0.149127	+	0.0484542i
$709$	1.21281e7	+	3.94064e6i	0.906098	+	0.294409i	0.724752	−	0.689010i	$-0.241954\pi$
$709$	1.21281e7	+	3.94064e6i	0.906098	+	0.294409i	0.181347	+	0.983419i	$0.441954\pi$
$710$	−1.59748e6	−	2.19875e6i	−0.118930	−	0.163693i
$711$		−	5.84352e6i		−	0.433511i
$712$	2.46385e6	+	800552.i	0.182143	+	0.0591820i
$713$	−5.16264e6	−	3.75088e6i	−0.380319	−	0.276318i
$714$	3.17745e6	−	1.03241e6i	0.233256	−	0.0757894i
$715$	8.17142e6	−	5.93689e6i	0.597768	−	0.434304i
$716$	−4.60744e6	+	6.34160e6i	−0.335875	+	0.462292i
$717$	−934751.	−	679136.i	−0.0679044	−	0.0493354i
$718$	1.48692e7	+	1.08031e7i	1.07641	+	0.782056i
$719$	−9.19085e6	+	1.26501e7i	−0.663030	+	0.912583i	−0.999577	−	0.0290839i	$-0.990741\pi$
$719$	−9.19085e6	+	1.26501e7i	−0.663030	+	0.912583i	0.336547	+	0.941667i	$0.390741\pi$
$720$	1.22659e6	−	891169.i	0.0881795	−	0.0640662i
$721$	−2.04244e7	+	6.63629e6i	−1.46323	+	0.475431i
$722$	7.49848e6	+	5.44796e6i	0.535340	+	0.388948i
$723$	4.32893e6	+	1.40655e6i	0.307989	+	0.100072i
$724$		−	1.61735e6i		−	0.114672i
$725$	−2.89618e6	−	3.98626e6i	−0.204636	−	0.281657i
$726$	−4.15506e6	−	1.35006e6i	−0.292574	−	0.0950632i
$727$	1.08374e6	−	352128.i	0.0760482	−	0.0247096i	−0.270746	−	0.962651i	$-0.587270\pi$
$727$	1.08374e6	−	352128.i	0.0760482	−	0.0247096i	0.346794	+	0.937941i	$0.387270\pi$
$728$	2.50895e6	+	7.72174e6i	0.175454	+	0.539991i
$729$	1.16440e7			0.811488
$730$	−513964.	−	1.58182e6i	−0.0356965	−	0.109862i
$731$	−840728.	+	1.15716e6i	−0.0581918	+	0.0800942i
$732$	552484.	+	760430.i	0.0381103	+	0.0524543i
$733$	4.71746e6	−	1.45189e7i	0.324301	−	0.998097i	−0.647454	−	0.762105i	$-0.724166\pi$
$733$	4.71746e6	−	1.45189e7i	0.324301	−	0.998097i	0.971755	−	0.235992i	$-0.0758339\pi$
$734$	−2.82713e6	+	8.70102e6i	−0.193690	+	0.596115i
$735$		−	2.70370e6i		−	0.184603i
$736$	3.05254e6	−	2.21780e6i	0.207714	−	0.150913i
$737$	−7.38133e6			−0.500571
$738$	5.39448e6	+	8.56771e6i	0.364593	+	0.579061i
$739$	−9.06822e6			−0.610817			−0.305408	−	0.952221i	$-0.598793\pi$
$739$	−9.06822e6			−0.610817			−0.305408	+	0.952221i	$0.598793\pi$
$740$	1.31045e6	−	952095.i	0.0879710	−	0.0639147i
$741$			603268.i			0.0403612i
$742$	7.84012e6	−	2.41294e7i	0.522773	−	1.60893i
$743$	−8.16269e6	+	2.51222e7i	−0.542452	+	1.66949i	0.184521	+	0.982829i	$0.440927\pi$
$743$	−8.16269e6	+	2.51222e7i	−0.542452	+	1.66949i	−0.726973	+	0.686666i	$0.759073\pi$
$744$	−182469.	−	251147.i	−0.0120853	−	0.0166340i
$745$	−4.06250e6	+	5.59155e6i	−0.268165	+	0.369098i
$746$	−3.65765e6	−	1.12571e7i	−0.240633	−	0.740591i
$747$	1.21446e7			0.796308
$748$	4.66122e6	+	1.43457e7i	0.304611	+	0.937496i
$749$	−4.61422e7	+	1.49925e7i	−3.00534	+	0.976495i
$750$	1.50694e6	+	489635.i	0.0978235	+	0.0317848i
$751$	8.87996e6	+	1.22222e7i	0.574528	+	0.790770i	0.993082	−	0.117422i	$-0.0374631\pi$
$751$	8.87996e6	+	1.22222e7i	0.574528	+	0.790770i	−0.418554	+	0.908192i	$0.637463\pi$
$752$		−	156420.i		−	0.0100866i
$753$	1.90580e6	+	619233.i	0.122487	+	0.0397985i
$754$	−3.45870e6	−	2.51289e6i	−0.221557	−	0.160970i
$755$	−1.00943e7	+	3.27984e6i	−0.644479	+	0.209404i
$756$	4.07048e6	−	2.95738e6i	0.259025	−	0.188193i
$757$	1.02374e7	−	1.40906e7i	0.649307	−	0.893694i	−0.349762	−	0.936839i	$-0.613738\pi$
$757$	1.02374e7	−	1.40906e7i	0.649307	−	0.893694i	0.999069	+	0.0431444i	$0.0137376\pi$
$758$	−1.37789e6	−	1.00110e6i	−0.0871047	−	0.0632852i
$759$	−6.19763e6	−	4.50284e6i	−0.390500	−	0.283715i
$760$	−377715.	+	519881.i	−0.0237209	+	0.0326490i
$761$	2.19727e7	−	1.59641e7i	1.37538	−	0.999270i	0.378082	−	0.925772i	$-0.376584\pi$
$761$	2.19727e7	−	1.59641e7i	1.37538	−	0.999270i	0.997295	−	0.0734978i	$-0.0234162\pi$
$762$	−239887.	+	77943.9i	−0.0149664	+	0.00486289i
$763$	−3.11690e7	−	2.26456e7i	−1.93826	−	1.40823i
$764$	−8.41935e6	−	2.73561e6i	−0.521850	−	0.169559i
$765$			7.52167e6i			0.464687i
$766$	−1.06490e7	−	1.46571e7i	−0.655750	−	0.902563i
$767$	2.39799e7	+	7.79156e6i	1.47184	+	0.478229i
$768$	174569.	−	56720.8i	0.0106798	−	0.00347008i
$769$	6.56016e6	+	2.01901e7i	0.400035	+	1.23118i	0.924970	+	0.380040i	$0.124090\pi$
$769$	6.56016e6	+	2.01901e7i	0.400035	+	1.23118i	−0.524935	+	0.851142i	$0.675910\pi$
$770$	1.75594e7			1.06729
$771$	291211.	+	896254.i	0.0176430	+	0.0542994i
$772$	1.56240e6	−	2.15045e6i	0.0943513	−	0.129863i
$773$	9.98204e6	+	1.37391e7i	0.600856	+	0.827008i	0.995786	−	0.0917033i	$-0.0292311\pi$
$773$	9.98204e6	+	1.37391e7i	0.600856	+	0.827008i	−0.394930	+	0.918711i	$0.629231\pi$
$774$	−327357.	+	1.00750e6i	−0.0196413	+	0.0604496i
$775$	−1.33295e6	+	4.10241e6i	−0.0797188	+	0.245349i
$776$		−	1.14179e7i		−	0.680662i
$777$	2.13871e6	−	1.55386e6i	0.127087	−	0.0923338i
$778$	−1.49438e7			−0.885141
$779$	−3.29666e6	−	2.74709e6i	−0.194639	−	0.162192i
$780$	609756.			0.0358855
$781$	1.62014e7	−	1.17710e7i	0.950443	−	0.690537i
$782$			1.87187e7i			1.09461i
$783$	−818685.	+	2.51965e6i	−0.0477213	+	0.146871i
$784$	−3.03218e6	+	9.33208e6i	−0.176183	+	0.542236i
$785$	−3.12643e6	−	4.30317e6i	−0.181082	−	0.249238i
$786$	−1.17866e6	+	1.62229e6i	−0.0680508	+	0.0936639i
$787$	−2.55228e6	−	7.85511e6i	−0.146890	−	0.452080i	0.850359	−	0.526202i	$-0.176385\pi$
$787$	−2.55228e6	−	7.85511e6i	−0.146890	−	0.452080i	−0.997249	+	0.0741222i	$0.976385\pi$
$788$	−1.14702e7			−0.658042
$789$	994740.	+	3.06149e6i	0.0568875	+	0.175082i
$790$	2.38085e6	−	773584.i	0.135726	−	0.0441001i
$791$	−1.77230e7	−	5.75856e6i	−1.00716	−	0.327245i
$792$	6.56656e6	+	9.03810e6i	0.371985	+	0.511993i
$793$		−	1.13321e7i		−	0.639924i
$794$	9.61505e6	+	3.12412e6i	0.541253	+	0.175864i
$795$	−1.54151e6	−	1.11997e6i	−0.0865022	−	0.0628475i
$796$	1.42842e7	−	4.64121e6i	0.799048	−	0.259626i
$797$	−729027.	+	529669.i	−0.0406535	+	0.0295365i	−0.607926	−	0.793993i	$-0.707998\pi$
$797$	−729027.	+	529669.i	−0.0406535	+	0.0295365i	0.567273	+	0.823530i	$0.307998\pi$
$798$	−616450.	+	848471.i	−0.0342682	+	0.0471661i
$799$	627800.	+	456124.i	0.0347900	+	0.0252764i
$800$	−2.06338e6	−	1.49913e6i	−0.113987	−	0.0828163i
$801$	−5.59501e6	+	7.70088e6i	−0.308120	+	0.424091i
$802$	1.15213e7	−	8.37073e6i	0.632509	−	0.459545i
$803$	1.16556e7	−	3.78713e6i	0.637890	−	0.207263i
$804$	−360502.	−	261920.i	−0.0196683	−	0.0142899i
$805$	2.07241e7	+	6.73366e6i	1.12716	+	0.366236i
$806$			3.74266e6i			0.202928i
$807$	−3.06971e6	−	4.22509e6i	−0.165925	−	0.228377i
$808$	8.44088e6	+	2.74261e6i	0.454841	+	0.147787i
$809$	1.50525e7	−	4.89084e6i	0.808604	−	0.262731i	0.124598	−	0.992207i	$-0.460236\pi$
$809$	1.50525e7	−	4.89084e6i	0.808604	−	0.262731i	0.684007	+	0.729476i	$0.260236\pi$
$810$	1.66213e6	+	5.11550e6i	0.0890126	+	0.273953i
$811$	−7.20654e6			−0.384747			−0.192373	−	0.981322i	$-0.561618\pi$
$811$	−7.20654e6			−0.384747			−0.192373	+	0.981322i	$0.561618\pi$
$812$	−2.29671e6	−	7.06856e6i	−0.122241	−	0.376219i
$813$	−1.72509e6	+	2.37438e6i	−0.0915347	+	0.125987i
$814$	7.01549e6	+	9.65600e6i	0.371105	+	0.510783i
$815$	−4.84440e6	+	1.49095e7i	−0.255474	+	0.786267i
$816$	−281394.	+	866042.i	−0.0147941	+	0.0455317i
$817$		−	448998.i		−	0.0235336i
$818$	−1.95148e7	+	1.41783e7i	−1.01972	+	0.740868i
$819$	−2.98321e7			−1.55408
$820$	−2.77664e6	+	3.33212e6i	−0.144206	+	0.173056i
$821$	1.23518e7			0.639544			0.319772	−	0.947494i	$-0.396394\pi$
$821$	1.23518e7			0.639544			0.319772	+	0.947494i	$0.396394\pi$
$822$	−488966.	+	355255.i	−0.0252406	+	0.0183384i
$823$		−	2.31382e7i		−	1.19078i	−0.803438	−	0.595388i	$-0.796998\pi$
$823$		−	2.31382e7i		−	1.19078i	0.803438	−	0.595388i	$-0.203002\pi$
$824$	1.80878e6	−	5.56686e6i	0.0928043	−	0.285622i
$825$	−1.60018e6	+	4.92485e6i	−0.0818528	+	0.251917i
$826$	2.57650e7	+	3.54625e7i	1.31395	+	1.80850i
$827$	1.91234e7	−	2.63211e7i	0.972303	−	1.33826i	0.0314288	−	0.999506i	$-0.489994\pi$
$827$	1.91234e7	−	2.63211e7i	0.972303	−	1.33826i	0.940875	−	0.338755i	$-0.110006\pi$
$828$	4.28412e6	+	1.31852e7i	0.217163	+	0.668359i
$829$	−1.31939e7			−0.666786			−0.333393	−	0.942788i	$-0.608194\pi$
$829$	−1.31939e7			−0.666786			−0.333393	+	0.942788i	$0.608194\pi$
$830$	1.60774e6	+	4.94811e6i	0.0810066	+	0.249313i
$831$	3.89287e6	−	1.26487e6i	0.195554	−	0.0635395i
$832$	−2.10463e6	−	683836.i	−0.105407	−	0.0342487i
$833$	−2.86130e7	−	3.93824e7i	−1.42873	−	1.96648i
$834$			1.29748e6i			0.0645928i
$835$	1.19094e7	+	3.86959e6i	0.591115	+	0.192065i
$836$	−3.83073e6	−	2.78319e6i	−0.189569	−	0.137730i
$837$	2.20580e6	−	716708.i	0.108831	−	0.0353613i
$838$	−1.64097e7	+	1.19223e7i	−0.807217	+	0.586477i
$839$	−1.82037e7	+	2.50553e7i	−0.892803	+	1.22884i	0.0799037	+	0.996803i	$0.474539\pi$
$839$	−1.82037e7	+	2.50553e7i	−0.892803	+	1.22884i	−0.972707	+	0.232036i	$0.925461\pi$
$840$	857596.	+	623080.i	0.0419358	+	0.0304681i
$841$	−1.34277e7	−	9.75582e6i	−0.654656	−	0.475635i
$842$	−8.33175e6	+	1.14677e7i	−0.405001	+	0.557436i
$843$	4.38911e6	−	3.18888e6i	0.212720	−	0.154550i
$844$	2.11681e6	−	687794.i	0.102288	−	0.0332355i
$845$	1.61785e6	+	1.17544e6i	0.0779466	+	0.0566315i
$846$	546604.	+	177602.i	0.0262571	+	0.00853145i
$847$			9.15695e7i			4.38573i
$848$	4.06462e6	+	5.59447e6i	0.194102	+	0.267159i
$849$	−2.69297e6	−	874999.i	−0.128222	−	0.0416618i
$850$	1.20338e7	−	3.91000e6i	0.571286	−	0.185622i
$851$	4.57701e6	+	1.40866e7i	0.216649	+	0.666778i
$852$	1.20896e6			0.0570575
$853$	−2.52875e6	−	7.78268e6i	−0.118996	−	0.366232i	0.873763	−	0.486351i	$-0.161672\pi$
$853$	−2.52875e6	−	7.78268e6i	−0.118996	−	0.366232i	−0.992760	+	0.120119i	$0.961672\pi$
$854$	1.15798e7	−	1.59382e7i	0.543319	−	0.747814i
$855$	−1.38784e6	−	1.91020e6i	−0.0649269	−	0.0893642i
$856$	4.08635e6	−	1.25765e7i	0.190612	−	0.586644i
$857$	6.50103e6	−	2.00081e7i	0.302364	−	0.930580i	−0.678284	−	0.734800i	$-0.737276\pi$
$857$	6.50103e6	−	2.00081e7i	0.302364	−	0.930580i	0.980648	−	0.195780i	$-0.0627240\pi$
$858$			4.49297e6i			0.208361i
$859$	1.03417e7	−	7.51366e6i	0.478198	−	0.347431i	−0.322430	−	0.946593i	$-0.604500\pi$
$859$	1.03417e7	−	7.51366e6i	0.478198	−	0.347431i	0.800628	+	0.599162i	$0.204500\pi$
$860$	−453827.			−0.0209240
$861$	−4.53161e6	+	5.43818e6i	−0.208326	+	0.250003i
$862$	−7.79806e6			−0.357453
$863$	1.47342e7	−	1.07051e7i	0.673443	−	0.489285i	−0.197733	−	0.980256i	$-0.563358\pi$
$863$	1.47342e7	−	1.07051e7i	0.673443	−	0.489285i	0.871176	+	0.490971i	$0.163358\pi$
$864$			1.37135e6i			0.0624978i
$865$	651510.	−	2.00514e6i	0.0296061	−	0.0911181i
$866$	4.04096e6	−	1.24368e7i	0.183100	−	0.563525i
$867$	−317909.	−	437564.i	−0.0143633	−	0.0197694i
$868$	−3.82444e6	+	5.26390e6i	−0.172294	+	0.237142i
$869$	5.70014e6	+	1.75432e7i	0.256057	+	0.788061i
$870$	−558176.			−0.0250019
$871$	1.66013e6	+	5.10936e6i	0.0741476	+	0.228203i
$872$	9.98694e6	−	3.24495e6i	0.444776	−	0.144516i
$873$	3.98995e7	+	1.29641e7i	1.77187	+	0.575715i
$874$	−3.45384e6	−	4.75381e6i	−0.152941	−	0.210505i
$875$		−	3.32100e7i		−	1.46639i
$876$	703640.	+	228626.i	0.0309806	+	0.0100662i
$877$	1.08198e7	+	7.86101e6i	0.475027	+	0.345127i	0.799397	−	0.600803i	$-0.205152\pi$
$877$	1.08198e7	+	7.86101e6i	0.475027	+	0.345127i	−0.324370	+	0.945930i	$0.605152\pi$
$878$	1.74207e7	−	5.66032e6i	0.762656	−	0.247802i
$879$	−3.35912e6	+	2.44054e6i	−0.146640	+	0.106540i
$880$	−2.81312e6	+	3.87193e6i	−0.122457	+	0.168547i
$881$	3.08122e7	+	2.23864e7i	1.33747	+	0.971726i	0.999533	+	0.0305564i	$0.00972792\pi$
$881$	3.08122e7	+	2.23864e7i	1.33747	+	0.971726i	0.337934	+	0.941170i	$0.390272\pi$
$882$	−2.91679e7	−	2.11917e7i	−1.26251	−	0.917264i
$883$	−2.26800e7	+	3.12164e7i	−0.978908	+	1.34735i	−0.0414924	+	0.999139i	$0.513211\pi$
$883$	−2.26800e7	+	3.12164e7i	−0.978908	+	1.34735i	−0.937416	+	0.348213i	$0.886789\pi$
$884$	8.88178e6	−	6.45299e6i	0.382269	−	0.277735i
$885$	3.13087e6	−	1.01728e6i	0.134371	−	0.0436599i
$886$	−2.42585e7	−	1.76248e7i	−1.03820	−	0.754293i
$887$	1.75757e7	+	5.71069e6i	0.750073	+	0.243713i	0.659012	−	0.752132i	$-0.270974\pi$
$887$	1.75757e7	+	5.71069e6i	0.750073	+	0.243713i	0.0910602	+	0.995845i	$0.470974\pi$
$888$			720535.i			0.0306636i
$889$	3.10740e6	+	4.27697e6i	0.131869	+	0.181502i
$890$	−3.87828e6	−	1.26013e6i	−0.164121	−	0.0533262i
$891$	−3.76935e7	+	1.22474e7i	−1.59064	+	0.516831i
$892$	1.74200e6	+	5.36132e6i	0.0733054	+	0.225611i
$893$	−243597.			−0.0102222
$894$	−950059.	−	2.92398e6i	−0.0397564	−	0.122358i
$895$	7.25247e6	−	9.98216e6i	0.302641	−	0.416550i
$896$	−2.26130e6	−	3.11241e6i	−0.0940996	−	0.129517i
$897$	−1.72296e6	+	5.30273e6i	−0.0714981	+	0.220049i
$898$	−2.62126e6	+	8.06740e6i	−0.108472	+	0.333843i
$899$		−	3.42607e6i		−	0.141383i
$900$	7.58150e6	−	5.50828e6i	0.311996	−	0.226678i
$901$	−3.43063e7			−1.40787
$902$	−2.45526e7	−	2.04596e7i	−1.00481	−	0.837300i
$903$	−740667.			−0.0302276
$904$	4.10913e6	−	2.98546e6i	0.167236	−	0.121504i
$905$			2.54583e6i			0.103325i
$906$	1.45897e6	−	4.49024e6i	0.0590508	−	0.181740i
$907$	−8.95008e6	+	2.75455e7i	−0.361251	+	1.11182i	0.591045	+	0.806639i	$0.298716\pi$
$907$	−8.95008e6	+	2.75455e7i	−0.361251	+	1.11182i	−0.952296	+	0.305177i	$0.901284\pi$
$908$	662609.	+	912003.i	0.0266712	+	0.0367097i
$909$	−1.91679e7	+	2.63824e7i	−0.769424	+	1.05902i
$910$	−3.94928e6	−	1.21546e7i	−0.158093	−	0.486562i
$911$	−3.57310e7			−1.42643			−0.713213	−	0.700948i	$-0.752761\pi$
$911$	−3.57310e7			−1.42643			−0.713213	+	0.700948i	$0.752761\pi$
$912$	−88332.9	−	271861.i	−0.00351670	−	0.0108233i
$913$	−3.64601e7	+	1.18466e7i	−1.44757	+	0.470345i
$914$	3.52227e6	+	1.14445e6i	0.139462	+	0.0453140i
$915$	−869653.	−	1.19698e6i	−0.0343395	−	0.0472642i
$916$			9.63396e6i			0.379373i
$917$	3.99721e7	+	1.29877e7i	1.56976	+	0.510046i
$918$	−5.50401e6	−	3.99890e6i	−0.215562	−	0.156615i
$919$	2.77310e7	−	9.01034e6i	1.08312	−	0.351927i	0.287536	−	0.957770i	$-0.407164\pi$
$919$	2.77310e7	−	9.01034e6i	1.08312	−	0.351927i	0.795584	+	0.605843i	$0.207164\pi$
$920$	−4.80493e6	+	3.49099e6i	−0.187162	+	0.135981i
$921$	4.47387e6	−	6.15776e6i	0.173794	−	0.239207i
$922$	1.40664e7	+	1.02198e7i	0.544949	+	0.395929i
$923$	−1.17918e7	−	8.56723e6i	−0.455591	−	0.331006i
$924$	−4.59116e6	+	6.31918e6i	−0.176906	+	0.243490i
$925$	8.09982e6	−	5.88486e6i	0.311258	−	0.226142i
$926$	1.10607e7	−	3.59385e6i	0.423893	−	0.137731i
$927$	1.73995e7	+	1.26415e7i	0.665024	+	0.483168i
$928$	1.92660e6	+	625990.i	0.0734382	+	0.0238615i
$929$		−	3.49910e7i		−	1.33020i	−0.746754	−	0.665100i	$-0.768389\pi$
$929$		−	3.49910e7i		−	1.33020i	0.746754	−	0.665100i	$-0.231611\pi$
$930$	287220.	+	395325.i	0.0108895	+	0.0149881i
$931$	1.45331e7	+	4.72209e6i	0.549521	+	0.178550i
$932$	−688796.	+	223803.i	−0.0259747	+	0.00843970i
$933$	−1.43548e6	−	4.41796e6i	−0.0539875	−	0.166156i
$934$	−2.81609e7			−1.05628
$935$	−7.33711e6	−	2.25813e7i	−0.274471	−	0.844734i
$936$	4.77929e6	−	6.57813e6i	0.178309	−	0.245422i
$937$	377033.	+	518941.i	0.0140291	+	0.0193094i	0.815974	−	0.578089i	$-0.196201\pi$
$937$	377033.	+	518941.i	0.0140291	+	0.0193094i	−0.801945	+	0.597398i	$0.796201\pi$
$938$	−2.88610e6	+	8.88251e6i	−0.107104	+	0.329631i
$939$	−1.17781e6	+	3.62491e6i	−0.0435923	+	0.134163i
$940$			246217.i			0.00908861i
$941$	−1.15161e7	+	8.36690e6i	−0.423965	+	0.308028i	−0.779231	−	0.626737i	$-0.784390\pi$
$941$	−1.15161e7	+	8.36690e6i	−0.423965	+	0.308028i	0.355266	+	0.934765i	$0.384390\pi$
$942$	2.36605e6			0.0868755
$943$	−2.11319e7	−	3.35624e7i	−0.773854	−	1.22906i
$944$	−1.19474e7			−0.436357
$945$	−6.40726e6	+	4.65514e6i	−0.233396	+	0.169572i
$946$		−	3.34401e6i		−	0.121490i
$947$	5.79248e6	−	1.78274e7i	0.209889	−	0.645972i	−0.789588	−	0.613637i	$-0.789706\pi$
$947$	5.79248e6	−	1.78274e7i	0.209889	−	0.645972i	0.999477	−	0.0323345i	$-0.0102942\pi$
$948$	−344113.	+	1.05907e6i	−0.0124360	+	0.0382741i
$949$	−5.24291e6	−	7.21625e6i	−0.188976	−	0.260103i
$950$	−2.33465e6	+	3.21336e6i	−0.0839290	+	0.115518i
$951$	−581911.	−	1.79094e6i	−0.0208644	−	0.0642139i
$952$	1.90859e7			0.682526
$953$	−5.58503e6	−	1.71889e7i	−0.199202	−	0.613080i	−0.999902	−	0.0140143i	$-0.995539\pi$
$953$	−5.58503e6	−	1.71889e7i	−0.199202	−	0.613080i	0.800700	−	0.599065i	$-0.204461\pi$
$954$	−2.41648e7	+	7.85162e6i	−0.859631	+	0.279311i
$955$	1.32527e7	+	4.30607e6i	0.470215	+	0.152782i
$956$	−3.87969e6	−	5.33993e6i	−0.137294	−	0.188969i
$957$		−	4.11291e6i		−	0.145168i
$958$	2.35155e7	+	7.64064e6i	0.827828	+	0.268978i
$959$	1.02484e7	+	7.44593e6i	0.359842	+	0.261440i
$960$	−274785.	+	89282.9i	−0.00962308	+	0.00312673i
$961$	2.07350e7	−	1.50648e7i	0.724261	−	0.526206i
$962$	5.10604e6	−	7.02786e6i	0.177888	−	0.244842i
$963$	3.93084e7	+	2.85593e7i	1.36590	+	0.992387i
$964$	2.10364e7	+	1.52839e7i	0.729087	+	0.529713i
$965$	−2.45933e6	+	3.38498e6i	−0.0850156	+	0.117014i
$966$	−7.84189e6	+	5.69746e6i	−0.270382	+	0.196444i
$967$	−5.18915e7	+	1.68606e7i	−1.78456	+	0.579838i	−0.999230	−	0.0392433i	$-0.987505\pi$
$967$	−5.18915e7	+	1.68606e7i	−1.78456	+	0.579838i	−0.785327	+	0.619081i	$0.787505\pi$
$968$	−2.01915e7	−	1.46700e7i	−0.692597	−	0.503201i
$969$	1.34871e6	+	438223.i	0.0461434	+	0.0149929i
$970$			1.79726e7i			0.613313i
$971$	−1.19391e7	−	1.64328e7i	−0.406373	−	0.559324i	0.555956	−	0.831211i	$-0.312352\pi$
$971$	−1.19391e7	−	1.64328e7i	−0.406373	−	0.559324i	−0.962329	+	0.271888i	$0.912352\pi$
$972$	−7.22754e6	−	2.34837e6i	−0.245372	−	0.0797262i
$973$	2.58633e7	−	8.40351e6i	0.875795	−	0.284563i
$974$	−6.69729e6	−	2.06121e7i	−0.226205	−	0.696187i
$975$	3.76888e6			0.126970
$976$	1.65930e6	+	5.10679e6i	0.0557570	+	0.171602i
$977$	2.96498e7	−	4.08094e7i	0.993767	−	1.36780i	0.0646952	−	0.997905i	$-0.479392\pi$
$977$	2.96498e7	−	4.08094e7i	0.993767	−	1.36780i	0.929072	−	0.369898i	$-0.120608\pi$
$978$	−4.09893e6	−	5.64169e6i	−0.137032	−	0.188609i
$979$	9.28525e6	−	2.85771e7i	0.309626	−	0.952930i
$980$	4.77288e6	−	1.46894e7i	0.158751	−	0.488584i
$981$			3.85835e7i			1.28006i
$982$	648253.	−	470983.i	0.0214519	−	0.0155857i
$983$	−3.13402e7			−1.03447			−0.517235	−	0.855844i	$-0.673039\pi$
$983$	−3.13402e7			−1.03447			−0.517235	+	0.855844i	$0.673039\pi$
$984$	−473153.	−	1.87047e6i	−0.0155781	−	0.0615834i
$985$	1.80549e7			0.592932
$986$	−8.13047e6	+	5.90713e6i	−0.266332	+	0.193502i
$987$			401837.i			0.0131298i
$988$	−1.06496e6	+	3.27760e6i	−0.0347088	+	0.106823i
$989$	1.28236e6	−	3.94670e6i	0.0416888	−	0.128305i
$990$	−1.03363e7	−	1.42267e7i	−0.335179	−	0.461334i
$991$	2.17848e7	−	2.99842e7i	0.704643	−	0.969859i	−0.295252	−	0.955419i	$-0.595404\pi$
$991$	2.17848e7	−	2.99842e7i	0.704643	−	0.969859i	0.999896	−	0.0144392i	$-0.00459631\pi$
$992$	−548015.	−	1.68662e6i	−0.0176813	−	0.0544174i
$993$	5.33509e6			0.171699
$994$	−7.83021e6	−	2.40989e7i	−0.251366	−	0.773627i
$995$	−2.24844e7	+	7.30563e6i	−0.719986	+	0.233937i
$996$	−2.20107e6	−	715170.i	−0.0703048	−	0.0228434i
$997$	−3.28883e7	−	4.52669e7i	−1.04786	−	1.44226i	−0.890648	−	0.454693i	$-0.849749\pi$
$997$	−3.28883e7	−	4.52669e7i	−1.04786	−	1.44226i	−0.157213	−	0.987565i	$-0.550251\pi$
$998$		−	3.04205e7i		−	0.966807i
$999$	−5.11978e6	−	1.66352e6i	−0.162307	−	0.0527367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.f.b.45.5	yes	40
41.31	even	10	inner	82.6.f.b.31.6	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.f.b.31.6	✓	40	41.31	even	10	inner
82.6.f.b.45.5	yes	40	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	82.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.23607 - 2.35114i) q^{2} -2.80079i q^{3} +(4.94427 - 15.2169i) q^{4} +(-7.78267 + 23.9526i) q^{5} +(-6.58504 - 9.06354i) q^{6} +(-138.019 + 189.966i) q^{7} +(-19.7771 - 60.8676i) q^{8} +235.156 q^{9} +(31.1307 + 95.8103i) q^{10} +(-705.977 + 229.386i) q^{11} +(-42.6193 - 13.8478i) q^{12} +(317.562 + 437.087i) q^{13} +939.246i q^{14} +(67.0861 + 21.7976i) q^{15} +(-207.108 - 150.473i) q^{16} +(1207.87 - 392.460i) q^{17} +(760.979 - 552.884i) q^{18} +(-234.336 + 322.536i) q^{19} +(326.005 + 236.856i) q^{20} +(532.055 + 386.561i) q^{21} +(-1745.27 + 2402.16i) q^{22} +(-2981.00 + 2165.82i) q^{23} +(-170.477 + 55.3914i) q^{24} +(2015.02 + 1464.00i) q^{25} +(2055.30 + 667.809i) q^{26} -1339.21i q^{27} +(2208.30 + 3039.46i) q^{28} +(-1881.45 - 611.319i) q^{29} +(268.344 - 87.1903i) q^{30} +(535.171 + 1647.09i) q^{31} -1024.00 q^{32} +(642.461 + 1977.29i) q^{33} +(2986.01 - 4109.89i) q^{34} +(-3476.03 - 4784.35i) q^{35} +(1162.67 - 3578.34i) q^{36} +(1242.16 - 3822.98i) q^{37} +1594.70i q^{38} +(1224.19 - 889.423i) q^{39} +1611.86 q^{40} +(-714.154 + 10739.9i) q^{41} +2630.63 q^{42} +(-911.132 + 661.977i) q^{43} +11876.9i q^{44} +(-1830.14 + 5632.58i) q^{45} +(-4554.56 + 14017.5i) q^{46} +(359.145 + 494.321i) q^{47} +(-421.443 + 580.066i) q^{48} +(-11844.4 - 36453.4i) q^{49} +9962.82 q^{50} +(-1099.20 - 3382.98i) q^{51} +(8221.22 - 2671.24i) q^{52} +(-25690.2 - 8347.26i) q^{53} +(-3148.68 - 4333.78i) q^{54} -18695.2i q^{55} +(14292.4 + 4643.89i) q^{56} +(903.354 + 656.325i) q^{57} +(-7525.78 + 2445.28i) q^{58} +(37756.3 - 27431.6i) q^{59} +(663.384 - 913.069i) q^{60} +(-16969.1 - 12328.8i) q^{61} +(5604.39 + 4071.83i) q^{62} +(-32455.9 + 44671.7i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(-12940.8 + 4204.73i) q^{65} +(6727.94 + 4888.13i) q^{66} +(9457.07 + 3072.79i) q^{67} -20320.4i q^{68} +(6066.00 + 8349.13i) q^{69} +(-22497.4 - 7309.84i) q^{70} +(-25657.7 + 8336.70i) q^{71} +(-4650.69 - 14313.4i) q^{72} -16509.9 q^{73} +(-4968.64 - 15291.9i) q^{74} +(4100.35 - 5643.65i) q^{75} +(3749.37 + 5160.57i) q^{76} +(53862.4 - 165771. i) q^{77} +(1870.39 - 5756.47i) q^{78} -24849.6i q^{79} +(5216.07 - 3789.70i) q^{80} +53392.0 q^{81} +(22940.0 + 36434.2i) q^{82} +51644.9 q^{83} +(8512.89 - 6184.97i) q^{84} +31985.9i q^{85} +(-1392.09 + 4284.40i) q^{86} +(-1712.17 + 5269.53i) q^{87} +(27924.3 + 38434.5i) q^{88} +(-23792.8 + 32748.0i) q^{89} +(7320.55 + 22530.3i) q^{90} -126861. q^{91} +(18218.2 + 56069.9i) q^{92} +(4613.14 - 1498.90i) q^{93} +(2324.44 + 755.255i) q^{94} +(-5901.80 - 8123.14i) q^{95} +2868.01i q^{96} +(169673. + 55130.0i) q^{97} +(-124037. - 90117.8i) q^{98} +(-166014. + 53941.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 160 q^{4} + 24 q^{5} - 100 q^{6} + 640 q^{8} - 4576 q^{9} - 96 q^{10} + 20 q^{11} + 400 q^{12} - 275 q^{13} + 1385 q^{15} - 2560 q^{16} - 105 q^{17} - 2476 q^{18} + 4720 q^{19} + 1424 q^{20}+ \cdots - 537690 q^{99}+O(q^{100}) \) 40 * q + 40 * q^2 - 160 * q^4 + 24 * q^5 - 100 * q^6 + 640 * q^8 - 4576 * q^9 - 96 * q^10 + 20 * q^11 + 400 * q^12 - 275 * q^13 + 1385 * q^15 - 2560 * q^16 - 105 * q^17 - 2476 * q^18 + 4720 * q^19 + 1424 * q^20 + 6961 * q^21 - 4140 * q^22 - 1019 * q^23 + 1600 * q^24 - 2006 * q^25 - 8620 * q^26 - 12525 * q^29 + 5540 * q^30 + 8900 * q^31 - 40960 * q^32 + 17684 * q^33 - 13100 * q^34 - 29955 * q^35 + 26704 * q^36 - 31651 * q^37 - 10104 * q^39 + 14464 * q^40 + 35044 * q^41 + 32776 * q^42 - 15615 * q^43 - 39955 * q^45 - 3224 * q^46 + 8330 * q^47 - 6400 * q^48 + 48406 * q^49 - 135016 * q^50 + 120325 * q^51 - 34480 * q^52 + 145425 * q^53 + 72200 * q^54 + 17600 * q^56 + 31992 * q^57 - 50100 * q^58 + 18978 * q^59 + 1680 * q^60 + 52673 * q^61 + 66140 * q^62 - 88455 * q^63 - 40960 * q^64 + 204480 * q^65 - 17556 * q^66 - 149205 * q^67 - 249735 * q^69 - 49100 * q^70 + 151175 * q^71 - 106816 * q^72 - 107670 * q^73 + 126604 * q^74 + 120180 * q^75 - 75520 * q^76 - 207367 * q^77 - 99284 * q^78 + 22784 * q^80 + 1167568 * q^81 + 84204 * q^82 - 281376 * q^83 + 111376 * q^84 - 131400 * q^86 - 141269 * q^87 + 66240 * q^88 - 277775 * q^89 + 159820 * q^90 - 518682 * q^91 + 12896 * q^92 - 172375 * q^93 + 16320 * q^94 + 149585 * q^95 + 330875 * q^97 - 171004 * q^98 - 537690 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more