LMFDB - Embedded newform 59.6.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [59,6,Mod(1,59)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(59, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("59.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	59.a (trivial)

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:	yes
Analytic conductor:	$9.46264536897$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 3 x^{14} - 387 x^{13} + 1023 x^{12} + 57328 x^{11} - 124838 x^{10} - 4067604 x^{9} + \cdots - 6425465344 $ x^15 - 3x^14 - 387x^13 + 1023x^12 + 57328x^11 - 124838x^10 - 4067604x^9 + 6474028x^8 + 141305760x^7 - 129401208x^6 - 2211672000x^5 + 786583520x^4 + 12769149184x^3 - 857496704x^2 - 15832169472x - 6425465344
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$11.0327$ of defining polynomial
Character	$\chi$	$=$	59.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.0327 q^{2} +3.29128 q^{3} +89.7201 q^{4} +56.1267 q^{5} +36.3117 q^{6} -171.191 q^{7} +636.807 q^{8} -232.167 q^{9} +O(q^{10})$	\(q+11.0327 q^{2} +3.29128 q^{3} +89.7201 q^{4} +56.1267 q^{5} +36.3117 q^{6} -171.191 q^{7} +636.807 q^{8} -232.167 q^{9} +619.228 q^{10} -663.594 q^{11} +295.294 q^{12} +301.482 q^{13} -1888.69 q^{14} +184.729 q^{15} +4154.65 q^{16} +1410.14 q^{17} -2561.43 q^{18} +831.656 q^{19} +5035.69 q^{20} -563.437 q^{21} -7321.22 q^{22} -1146.69 q^{23} +2095.91 q^{24} +25.2049 q^{25} +3326.15 q^{26} -1563.91 q^{27} -15359.2 q^{28} -1757.82 q^{29} +2038.05 q^{30} -9499.49 q^{31} +25459.1 q^{32} -2184.08 q^{33} +15557.6 q^{34} -9608.37 q^{35} -20830.1 q^{36} +14967.6 q^{37} +9175.39 q^{38} +992.261 q^{39} +35741.9 q^{40} +111.687 q^{41} -6216.22 q^{42} -2588.81 q^{43} -59537.7 q^{44} -13030.8 q^{45} -12651.1 q^{46} +19760.1 q^{47} +13674.1 q^{48} +12499.3 q^{49} +278.078 q^{50} +4641.17 q^{51} +27049.0 q^{52} +12788.9 q^{53} -17254.1 q^{54} -37245.3 q^{55} -109015. q^{56} +2737.21 q^{57} -19393.5 q^{58} +3481.00 q^{59} +16573.9 q^{60} -30191.9 q^{61} -104805. q^{62} +39744.9 q^{63} +147933. q^{64} +16921.2 q^{65} -24096.2 q^{66} +10697.5 q^{67} +126518. q^{68} -3774.08 q^{69} -106006. q^{70} +8850.58 q^{71} -147846. q^{72} +2294.68 q^{73} +165133. q^{74} +82.9565 q^{75} +74616.2 q^{76} +113601. q^{77} +10947.3 q^{78} -17196.8 q^{79} +233187. q^{80} +51269.4 q^{81} +1232.20 q^{82} +20617.1 q^{83} -50551.6 q^{84} +79146.5 q^{85} -28561.5 q^{86} -5785.49 q^{87} -422581. q^{88} -13628.1 q^{89} -143765. q^{90} -51610.9 q^{91} -102881. q^{92} -31265.5 q^{93} +218007. q^{94} +46678.1 q^{95} +83793.0 q^{96} -54346.9 q^{97} +137900. q^{98} +154065. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 3 q^{2} + 18 q^{3} + 303 q^{4} + 128 q^{5} + 14 q^{6} + 282 q^{7} + 249 q^{8} + 1621 q^{9}+O(q^{10}) $ 15 * q + 3 * q^2 + 18 * q^3 + 303 * q^4 + 128 * q^5 + 14 * q^6 + 282 * q^7 + 249 * q^8 + 1621 * q^9	\( 15 q + 3 q^{2} + 18 q^{3} + 303 q^{4} + 128 q^{5} + 14 q^{6} + 282 q^{7} + 249 q^{8} + 1621 q^{9} + 598 q^{10} + 34 q^{11} + 864 q^{12} + 1790 q^{13} + 1087 q^{14} + 2900 q^{15} + 12155 q^{16} + 6130 q^{17} + 10417 q^{18} + 5342 q^{19} + 11772 q^{20} + 7976 q^{21} + 7657 q^{22} + 1552 q^{23} + 612 q^{24} + 10587 q^{25} - 7885 q^{26} + 3072 q^{27} - 3541 q^{28} + 7476 q^{29} - 25854 q^{30} - 3468 q^{31} - 9479 q^{32} - 11228 q^{33} + 2177 q^{34} - 15556 q^{35} - 39367 q^{36} + 22158 q^{37} - 60264 q^{38} + 8000 q^{39} - 11660 q^{40} + 4670 q^{41} - 130868 q^{42} + 20134 q^{43} - 74355 q^{44} - 22660 q^{45} - 15144 q^{46} - 23192 q^{47} - 77896 q^{48} + 75323 q^{49} - 110939 q^{50} - 22092 q^{51} - 104973 q^{52} + 22148 q^{53} - 122246 q^{54} - 27480 q^{55} - 103031 q^{56} - 65580 q^{57} + 60642 q^{58} + 52215 q^{59} - 1822 q^{60} + 156158 q^{61} - 262068 q^{62} + 283004 q^{63} + 209263 q^{64} + 148264 q^{65} - 32770 q^{66} + 166884 q^{67} + 290919 q^{68} + 221972 q^{69} - 50302 q^{70} - 3954 q^{71} + 62839 q^{72} + 32606 q^{73} + 105727 q^{74} + 305348 q^{75} + 96994 q^{76} + 143452 q^{77} - 71054 q^{78} + 352558 q^{79} + 696 q^{80} + 405359 q^{81} - 76879 q^{82} + 153906 q^{83} - 157160 q^{84} + 327528 q^{85} - 81369 q^{86} - 82912 q^{87} + 252111 q^{88} + 20806 q^{89} - 162642 q^{90} + 88714 q^{91} - 163940 q^{92} + 16120 q^{93} + 109102 q^{94} - 87254 q^{95} - 118508 q^{96} + 45926 q^{97} - 601532 q^{98} - 13706 q^{99}+O(q^{100}) \) 15 * q + 3 * q^2 + 18 * q^3 + 303 * q^4 + 128 * q^5 + 14 * q^6 + 282 * q^7 + 249 * q^8 + 1621 * q^9 + 598 * q^10 + 34 * q^11 + 864 * q^12 + 1790 * q^13 + 1087 * q^14 + 2900 * q^15 + 12155 * q^16 + 6130 * q^17 + 10417 * q^18 + 5342 * q^19 + 11772 * q^20 + 7976 * q^21 + 7657 * q^22 + 1552 * q^23 + 612 * q^24 + 10587 * q^25 - 7885 * q^26 + 3072 * q^27 - 3541 * q^28 + 7476 * q^29 - 25854 * q^30 - 3468 * q^31 - 9479 * q^32 - 11228 * q^33 + 2177 * q^34 - 15556 * q^35 - 39367 * q^36 + 22158 * q^37 - 60264 * q^38 + 8000 * q^39 - 11660 * q^40 + 4670 * q^41 - 130868 * q^42 + 20134 * q^43 - 74355 * q^44 - 22660 * q^45 - 15144 * q^46 - 23192 * q^47 - 77896 * q^48 + 75323 * q^49 - 110939 * q^50 - 22092 * q^51 - 104973 * q^52 + 22148 * q^53 - 122246 * q^54 - 27480 * q^55 - 103031 * q^56 - 65580 * q^57 + 60642 * q^58 + 52215 * q^59 - 1822 * q^60 + 156158 * q^61 - 262068 * q^62 + 283004 * q^63 + 209263 * q^64 + 148264 * q^65 - 32770 * q^66 + 166884 * q^67 + 290919 * q^68 + 221972 * q^69 - 50302 * q^70 - 3954 * q^71 + 62839 * q^72 + 32606 * q^73 + 105727 * q^74 + 305348 * q^75 + 96994 * q^76 + 143452 * q^77 - 71054 * q^78 + 352558 * q^79 + 696 * q^80 + 405359 * q^81 - 76879 * q^82 + 153906 * q^83 - 157160 * q^84 + 327528 * q^85 - 81369 * q^86 - 82912 * q^87 + 252111 * q^88 + 20806 * q^89 - 162642 * q^90 + 88714 * q^91 - 163940 * q^92 + 16120 * q^93 + 109102 * q^94 - 87254 * q^95 - 118508 * q^96 + 45926 * q^97 - 601532 * q^98 - 13706 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	11.0327	1.95032	0.975160	−	0.221500i	$-0.0710951\pi$
$2$	11.0327	1.95032	0.975160	+	0.221500i	$0.0710951\pi$
$3$	3.29128	0.211136	0.105568	−	0.994412i	$-0.466334\pi$
$3$	3.29128	0.211136	0.105568	+	0.994412i	$0.466334\pi$
$4$	89.7201	2.80375
$5$	56.1267	1.00402	0.502012	−	0.864860i	$-0.332593\pi$
$5$	56.1267	1.00402	0.502012	+	0.864860i	$0.332593\pi$
$6$	36.3117	0.411783
$7$	−171.191	−1.32049	−0.660245	−	0.751050i	$-0.729548\pi$
$7$	−171.191	−1.32049	−0.660245	+	0.751050i	$0.729548\pi$
$8$	636.807	3.51789
$9$	−232.167	−0.955422
$10$	619.228	1.95817
$11$	−663.594	−1.65356	−0.826782	−	0.562523i	$-0.809831\pi$
$11$	−663.594	−1.65356	−0.826782	+	0.562523i	$0.809831\pi$
$12$	295.294	0.591973
$13$	301.482	0.494769	0.247385	−	0.968917i	$-0.420429\pi$
$13$	301.482	0.494769	0.247385	+	0.968917i	$0.420429\pi$
$14$	−1888.69	−2.57538
$15$	184.729	0.211986
$16$	4154.65	4.05727
$17$	1410.14	1.18342	0.591711	−	0.806150i	$-0.298453\pi$
$17$	1410.14	1.18342	0.591711	+	0.806150i	$0.298453\pi$
$18$	−2561.43	−1.86338
$19$	831.656	0.528518	0.264259	−	0.964452i	$-0.414873\pi$
$19$	831.656	0.528518	0.264259	+	0.964452i	$0.414873\pi$
$20$	5035.69	2.81504
$21$	−563.437	−0.278803
$22$	−7321.22	−3.22498
$23$	−1146.69	−0.451987	−0.225993	−	0.974129i	$-0.572563\pi$
$23$	−1146.69	−0.451987	−0.225993	+	0.974129i	$0.572563\pi$
$24$	2095.91	0.742754
$25$	25.2049	0.00806558
$26$	3326.15	0.964958
$27$	−1563.91	−0.412860
$28$	−15359.2	−3.70233
$29$	−1757.82	−0.388132	−0.194066	−	0.980988i	$-0.562168\pi$
$29$	−1757.82	−0.388132	−0.194066	+	0.980988i	$0.562168\pi$
$30$	2038.05	0.413440
$31$	−9499.49	−1.77540	−0.887699	−	0.460423i	$-0.847698\pi$
$31$	−9499.49	−1.77540	−0.887699	+	0.460423i	$0.847698\pi$
$32$	25459.1	4.39509
$33$	−2184.08	−0.349127
$34$	15557.6	2.30805
$35$	−9608.37	−1.32580
$36$	−20830.1	−2.67877
$37$	14967.6	1.79741	0.898706	−	0.438551i	$-0.144508\pi$
$37$	14967.6	1.79741	0.898706	+	0.438551i	$0.144508\pi$
$38$	9175.39	1.03078
$39$	992.261	0.104464
$40$	35741.9	3.53205
$41$	111.687	0.0103763	0.00518814	−	0.999987i	$-0.498349\pi$
$41$	111.687	0.0103763	0.00518814	+	0.999987i	$0.498349\pi$
$42$	−6216.22	−0.543755
$43$	−2588.81	−0.213516	−0.106758	−	0.994285i	$-0.534047\pi$
$43$	−2588.81	−0.213516	−0.106758	+	0.994285i	$0.534047\pi$
$44$	−59537.7	−4.63618
$45$	−13030.8	−0.959267
$46$	−12651.1	−0.881520
$47$	19760.1	1.30480	0.652402	−	0.757873i	$-0.273762\pi$
$47$	19760.1	1.30480	0.652402	+	0.757873i	$0.273762\pi$
$48$	13674.1	0.856636
$49$	12499.3	0.743694
$50$	278.078	0.0157305
$51$	4641.17	0.249863
$52$	27049.0	1.38721
$53$	12788.9	0.625381	0.312691	−	0.949855i	$-0.398770\pi$
$53$	12788.9	0.625381	0.312691	+	0.949855i	$0.398770\pi$
$54$	−17254.1	−0.805209
$55$	−37245.3	−1.66022
$56$	−109015.	−4.64534
$57$	2737.21	0.111589
$58$	−19393.5	−0.756983
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	16573.9	0.594355
$61$	−30191.9	−1.03888	−0.519440	−	0.854507i	$-0.673860\pi$
$61$	−30191.9	−1.03888	−0.519440	+	0.854507i	$0.673860\pi$
$62$	−104805.	−3.46260
$63$	39744.9	1.26162
$64$	147933.	4.51456
$65$	16921.2	0.496760
$66$	−24096.2	−0.680909
$67$	10697.5	0.291136	0.145568	−	0.989348i	$-0.453499\pi$
$67$	10697.5	0.291136	0.145568	+	0.989348i	$0.453499\pi$
$68$	126518.	3.31802
$69$	−3774.08	−0.0954307
$70$	−106006.	−2.58574
$71$	8850.58	0.208366	0.104183	−	0.994558i	$-0.466777\pi$
$71$	8850.58	0.208366	0.104183	+	0.994558i	$0.466777\pi$
$72$	−147846.	−3.36107
$73$	2294.68	0.0503981	0.0251991	−	0.999682i	$-0.491978\pi$
$73$	2294.68	0.0503981	0.0251991	+	0.999682i	$0.491978\pi$
$74$	165133.	3.50553
$75$	82.9565	0.00170293
$76$	74616.2	1.48183
$77$	113601.	2.18351
$78$	10947.3	0.203737
$79$	−17196.8	−0.310013	−0.155006	−	0.987913i	$-0.549540\pi$
$79$	−17196.8	−0.310013	−0.155006	+	0.987913i	$0.549540\pi$
$80$	233187.	4.07360
$81$	51269.4	0.868252
$82$	1232.20	0.0202371
$83$	20617.1	0.328497	0.164249	−	0.986419i	$-0.447480\pi$
$83$	20617.1	0.328497	0.164249	+	0.986419i	$0.447480\pi$
$84$	−50551.6	−0.781694
$85$	79146.5	1.18819
$86$	−28561.5	−0.416424
$87$	−5785.49	−0.0819487
$88$	−422581.	−5.81706
$89$	−13628.1	−0.182373	−0.0911867	−	0.995834i	$-0.529066\pi$
$89$	−13628.1	−0.182373	−0.0911867	+	0.995834i	$0.529066\pi$
$90$	−143765.	−1.87088
$91$	−51610.9	−0.653337
$92$	−102881.	−1.26726
$93$	−31265.5	−0.374850
$94$	218007.	2.54479
$95$	46678.1	0.530645
$96$	83793.0	0.927961
$97$	−54346.9	−0.586470	−0.293235	−	0.956040i	$-0.594732\pi$
$97$	−54346.9	−0.586470	−0.293235	+	0.956040i	$0.594732\pi$
$98$	137900.	1.45044
$99$	154065.	1.57985
$100$	2261.39	0.0226139
$101$	−50768.4	−0.495210	−0.247605	−	0.968861i	$-0.579644\pi$
$101$	−50768.4	−0.495210	−0.247605	+	0.968861i	$0.579644\pi$
$102$	51204.5	0.487313
$103$	−15432.5	−0.143332	−0.0716661	−	0.997429i	$-0.522832\pi$
$103$	−15432.5	−0.143332	−0.0716661	+	0.997429i	$0.522832\pi$
$104$	191986.	1.74055
$105$	−31623.9	−0.279925
$106$	141096.	1.21969
$107$	84607.0	0.714409	0.357204	−	0.934026i	$-0.383730\pi$
$107$	84607.0	0.714409	0.357204	+	0.934026i	$0.383730\pi$
$108$	−140314.	−1.15756
$109$	−88928.8	−0.716929	−0.358465	−	0.933543i	$-0.616700\pi$
$109$	−88928.8	−0.716929	−0.358465	+	0.933543i	$0.616700\pi$
$110$	−410916.	−3.23796
$111$	49262.6	0.379498
$112$	−711237.	−5.35759
$113$	195803.	1.44253	0.721263	−	0.692661i	$-0.243562\pi$
$113$	195803.	1.44253	0.721263	+	0.692661i	$0.243562\pi$
$114$	30198.8	0.217635
$115$	−64359.8	−0.453806
$116$	−157712.	−1.08823
$117$	−69994.2	−0.472713
$118$	38404.8	0.253910
$119$	−241403.	−1.56270
$120$	117637.	0.745743
$121$	279306.	1.73427
$122$	−333097.	−2.02615
$123$	367.592	0.00219080
$124$	−852295.	−4.97778
$125$	−173981.	−0.995927
$126$	438493.	2.46057
$127$	200941.	1.10550	0.552751	−	0.833347i	$-0.313578\pi$
$127$	200941.	1.10550	0.552751	+	0.833347i	$0.313578\pi$
$128$	817409.	4.40975
$129$	−8520.51	−0.0450808
$130$	186686.	0.968842
$131$	96136.4	0.489451	0.244726	−	0.969592i	$-0.421302\pi$
$131$	96136.4	0.489451	0.244726	+	0.969592i	$0.421302\pi$
$132$	−195955.	−0.978864
$133$	−142372.	−0.697902
$134$	118022.	0.567810
$135$	−87777.1	−0.414521
$136$	897987.	4.16316
$137$	224535.	1.02208	0.511038	−	0.859558i	$-0.329261\pi$
$137$	224535.	1.02208	0.511038	+	0.859558i	$0.329261\pi$
$138$	−41638.2	−0.186120
$139$	143742.	0.631024	0.315512	−	0.948922i	$-0.397824\pi$
$139$	143742.	0.631024	0.315512	+	0.948922i	$0.397824\pi$
$140$	−862063.	−3.71723
$141$	65036.2	0.275491
$142$	97645.6	0.406380
$143$	−200061.	−0.818132
$144$	−964574.	−3.87641
$145$	−98660.7	−0.389694
$146$	25316.4	0.0982925
$147$	41138.6	0.157020
$148$	1.34289e6	5.03950
$149$	−371225.	−1.36984	−0.684922	−	0.728616i	$-0.740164\pi$
$149$	−371225.	−1.36984	−0.684922	+	0.728616i	$0.740164\pi$
$150$	915.233	0.00332127
$151$	314243.	1.12156	0.560782	−	0.827964i	$-0.310501\pi$
$151$	314243.	1.12156	0.560782	+	0.827964i	$0.310501\pi$
$152$	529604.	1.85927
$153$	−327388.	−1.13067
$154$	1.25333e6	4.25855
$155$	−533175.	−1.78254
$156$	89025.8	0.292890
$157$	−605650.	−1.96098	−0.980488	−	0.196577i	$-0.937018\pi$
$157$	−605650.	−1.96098	−0.980488	+	0.196577i	$0.937018\pi$
$158$	−189727.	−0.604624
$159$	42092.0	0.132040
$160$	1.42893e6	4.41278
$161$	196302.	0.596844
$162$	565639.	1.69337
$163$	−332113.	−0.979077	−0.489538	−	0.871982i	$-0.662835\pi$
$163$	−332113.	−0.979077	−0.489538	+	0.871982i	$0.662835\pi$
$164$	10020.5	0.0290925
$165$	−122585.	−0.350532
$166$	227461.	0.640675
$167$	−455412.	−1.26361	−0.631806	−	0.775127i	$-0.717686\pi$
$167$	−455412.	−1.26361	−0.631806	+	0.775127i	$0.717686\pi$
$168$	−358801.	−0.980799
$169$	−280402.	−0.755204
$170$	873198.	2.31734
$171$	−193083.	−0.504957
$172$	−232268.	−0.598644
$173$	311295.	0.790782	0.395391	−	0.918513i	$-0.370609\pi$
$173$	311295.	0.790782	0.395391	+	0.918513i	$0.370609\pi$
$174$	−63829.5	−0.159826
$175$	−4314.85	−0.0106505
$176$	−2.75700e6	−6.70896
$177$	11457.0	0.0274876
$178$	−150355.	−0.355687
$179$	−305027.	−0.711551	−0.355775	−	0.934571i	$-0.615783\pi$
$179$	−305027.	−0.711551	−0.355775	+	0.934571i	$0.615783\pi$
$180$	−1.16912e6	−2.68955
$181$	−710.209	−0.00161135	−0.000805674	−	1.00000i	$-0.500256\pi$
$181$	−710.209	−0.00161135	−0.000805674		1.00000i	$0.500256\pi$
$182$	−569406.	−1.27422
$183$	−99370.0	−0.219345
$184$	−730219.	−1.59004
$185$	840082.	1.80465
$186$	−344942.	−0.731079
$187$	−935760.	−1.95686
$188$	1.77288e6	3.65835
$189$	267727.	0.545177
$190$	514984.	1.03493
$191$	18902.1	0.0374910	0.0187455	−	0.999824i	$-0.494033\pi$
$191$	18902.1	0.0374910	0.0187455	+	0.999824i	$0.494033\pi$
$192$	486890.	0.953186
$193$	128481.	0.248283	0.124141	−	0.992265i	$-0.460382\pi$
$193$	128481.	0.248283	0.124141	+	0.992265i	$0.460382\pi$
$194$	−599592.	−1.14380
$195$	55692.3	0.104884
$196$	1.12143e6	2.08513
$197$	120999.	0.222134	0.111067	−	0.993813i	$-0.464573\pi$
$197$	120999.	0.222134	0.111067	+	0.993813i	$0.464573\pi$
$198$	1.69975e6	3.08121
$199$	595869.	1.06664	0.533320	−	0.845913i	$-0.320944\pi$
$199$	595869.	1.06664	0.533320	+	0.845913i	$0.320944\pi$
$200$	16050.7	0.0283738
$201$	35208.6	0.0614694
$202$	−560111.	−0.965819
$203$	300923.	0.512525
$204$	416406.	0.700554
$205$	6268.60	0.0104180
$206$	−170262.	−0.279544
$207$	266224.	0.431838
$208$	1.25255e6	2.00741
$209$	−551882.	−0.873937
$210$	−348896.	−0.545943
$211$	−1.24212e6	−1.92069	−0.960347	−	0.278807i	$-0.910061\pi$
$211$	−1.24212e6	−1.92069	−0.960347	+	0.278807i	$0.910061\pi$
$212$	1.14742e6	1.75341
$213$	29129.8	0.0439934
$214$	933442.	1.39333
$215$	−145301.	−0.214375
$216$	−995909.	−1.45240
$217$	1.62622e6	2.34440
$218$	−981123.	−1.39824
$219$	7552.43	0.0106409
$220$	−3.34165e6	−4.65484
$221$	425131.	0.585521
$222$	543499.	0.740144
$223$	677141.	0.911837	0.455918	−	0.890022i	$-0.349311\pi$
$223$	677141.	0.911837	0.455918	+	0.890022i	$0.349311\pi$
$224$	−4.35836e6	−5.80367
$225$	−5851.76	−0.00770603
$226$	2.16023e6	2.81339
$227$	−1.07934e6	−1.39026	−0.695129	−	0.718885i	$-0.744653\pi$
$227$	−1.07934e6	−1.39026	−0.695129	+	0.718885i	$0.744653\pi$
$228$	245583.	0.312868
$229$	1.47763e6	1.86199	0.930996	−	0.365031i	$-0.118941\pi$
$229$	1.47763e6	1.86199	0.930996	+	0.365031i	$0.118941\pi$
$230$	−710062.	−0.885068
$231$	373893.	0.461018
$232$	−1.11939e6	−1.36541
$233$	492548.	0.594373	0.297186	−	0.954820i	$-0.403952\pi$
$233$	492548.	0.594373	0.297186	+	0.954820i	$0.403952\pi$
$234$	−772224.	−0.921942
$235$	1.10907e6	1.31005
$236$	312316.	0.365017
$237$	−56599.5	−0.0654548
$238$	−2.66332e6	−3.04776
$239$	−1.40516e6	−1.59122	−0.795609	−	0.605811i	$-0.792849\pi$
$239$	−1.40516e6	−1.59122	−0.795609	+	0.605811i	$0.792849\pi$
$240$	767483.	0.860084
$241$	142448.	0.157984	0.0789920	−	0.996875i	$-0.474830\pi$
$241$	142448.	0.157984	0.0789920	+	0.996875i	$0.474830\pi$
$242$	3.08149e6	3.38238
$243$	548772.	0.596179
$244$	−2.70882e6	−2.91276
$245$	701542.	0.746687
$246$	4055.53	0.00427277
$247$	250729.	0.261494
$248$	−6.04934e6	−6.24567
$249$	67856.6	0.0693575
$250$	−1.91948e6	−1.94238
$251$	−156982.	−0.157277	−0.0786387	−	0.996903i	$-0.525057\pi$
$251$	−156982.	−0.157277	−0.0786387	+	0.996903i	$0.525057\pi$
$252$	3.56592e6	3.53728
$253$	760936.	0.747389
$254$	2.21692e6	2.15608
$255$	260493.	0.250869
$256$	4.28435e6	4.08587
$257$	−193786.	−0.183017	−0.0915083	−	0.995804i	$-0.529169\pi$
$257$	−193786.	−0.183017	−0.0915083	+	0.995804i	$0.529169\pi$
$258$	−94004.1	−0.0879220
$259$	−2.56231e6	−2.37347
$260$	1.51817e6	1.39279
$261$	408109.	0.370830
$262$	1.06064e6	0.954587
$263$	−1.84977e6	−1.64903	−0.824513	−	0.565844i	$-0.808551\pi$
$263$	−1.84977e6	−1.64903	−0.824513	+	0.565844i	$0.808551\pi$
$264$	−1.39083e6	−1.22819
$265$	717801.	0.627898
$266$	−1.57074e6	−1.36113
$267$	−44854.1	−0.0385056
$268$	959783.	0.816274
$269$	−1.99094e6	−1.67756	−0.838778	−	0.544474i	$-0.816729\pi$
$269$	−1.99094e6	−1.67756	−0.838778	+	0.544474i	$0.816729\pi$
$270$	−968417.	−0.808450
$271$	464669.	0.384345	0.192172	−	0.981361i	$-0.438447\pi$
$271$	464669.	0.384345	0.192172	+	0.981361i	$0.438447\pi$
$272$	5.85863e6	4.80147
$273$	−169866.	−0.137943
$274$	2.47723e6	1.99338
$275$	−16725.8	−0.0133369
$276$	−338610.	−0.267564
$277$	589369.	0.461517	0.230758	−	0.973011i	$-0.425879\pi$
$277$	589369.	0.461517	0.230758	+	0.973011i	$0.425879\pi$
$278$	1.58586e6	1.23070
$279$	2.20547e6	1.69625
$280$	−6.11868e6	−4.66404
$281$	−437756.	−0.330724	−0.165362	−	0.986233i	$-0.552879\pi$
$281$	−437756.	−0.330724	−0.165362	+	0.986233i	$0.552879\pi$
$282$	717523.	0.537296
$283$	1.36994e6	1.01680	0.508399	−	0.861122i	$-0.330238\pi$
$283$	1.36994e6	1.01680	0.508399	+	0.861122i	$0.330238\pi$
$284$	794075.	0.584205
$285$	153631.	0.112038
$286$	−2.20721e6	−1.59562
$287$	−19119.7	−0.0137018
$288$	−5.91077e6	−4.19916
$289$	568636.	0.400488
$290$	−1.08849e6	−0.760029
$291$	−178871.	−0.123825
$292$	205878.	0.141304
$293$	144494.	0.0983288	0.0491644	−	0.998791i	$-0.484344\pi$
$293$	144494.	0.0983288	0.0491644	+	0.998791i	$0.484344\pi$
$294$	453869.	0.306240
$295$	195377.	0.130713
$296$	9.53147e6	6.32311
$297$	1.03780e6	0.682690
$298$	−4.09560e6	−2.67164
$299$	−345706.	−0.223629
$300$	7442.87	0.00477460
$301$	443181.	0.281945
$302$	3.46695e6	2.18741
$303$	−167093.	−0.104557
$304$	3.45524e6	2.14434
$305$	−1.69457e6	−1.04306
$306$	−3.61197e6	−2.20516
$307$	−2.77546e6	−1.68069	−0.840347	−	0.542049i	$-0.817649\pi$
$307$	−2.77546e6	−1.68069	−0.840347	+	0.542049i	$0.817649\pi$
$308$	1.01923e7	6.12203
$309$	−50792.8	−0.0302626
$310$	−5.88235e6	−3.47653
$311$	−1.80091e6	−1.05582	−0.527912	−	0.849299i	$-0.677025\pi$
$311$	−1.80091e6	−1.05582	−0.527912	+	0.849299i	$0.677025\pi$
$312$	631879.	0.367492
$313$	370381.	0.213692	0.106846	−	0.994276i	$-0.465925\pi$
$313$	370381.	0.213692	0.106846	+	0.994276i	$0.465925\pi$
$314$	−6.68194e6	−3.82453
$315$	2.23075e6	1.26670
$316$	−1.54290e6	−0.869198
$317$	−36599.0	−0.0204560	−0.0102280	−	0.999948i	$-0.503256\pi$
$317$	−36599.0	−0.0204560	−0.0102280	+	0.999948i	$0.503256\pi$
$318$	464388.	0.257521
$319$	1.16648e6	0.641801
$320$	8.30300e6	4.53273
$321$	278466.	0.150837
$322$	2.16574e6	1.16404
$323$	1.17275e6	0.625460
$324$	4.59990e6	2.43436
$325$	7598.82	0.00399060
$326$	−3.66410e6	−1.90951
$327$	−292690.	−0.151369
$328$	71122.8	0.0365026
$329$	−3.38275e6	−1.72298
$330$	−1.35244e6	−0.683649
$331$	−1.10864e6	−0.556185	−0.278092	−	0.960554i	$-0.589702\pi$
$331$	−1.10864e6	−0.556185	−0.278092	+	0.960554i	$0.589702\pi$
$332$	1.84976e6	0.921024
$333$	−3.47499e6	−1.71729
$334$	−5.02442e6	−2.46445
$335$	600417.	0.292308
$336$	−2.34088e6	−1.13118
$337$	2.48755e6	1.19315	0.596577	−	0.802556i	$-0.296527\pi$
$337$	2.48755e6	1.19315	0.596577	+	0.802556i	$0.296527\pi$
$338$	−3.09358e6	−1.47289
$339$	644444.	0.304569
$340$	7.10102e6	3.33138
$341$	6.30380e6	2.93573
$342$	−2.13023e6	−0.984829
$343$	737445.	0.338450
$344$	−1.64857e6	−0.751125
$345$	−211826.	−0.0958148
$346$	3.43442e6	1.54228
$347$	−2.65969e6	−1.18579	−0.592895	−	0.805280i	$-0.702015\pi$
$347$	−2.65969e6	−1.18579	−0.592895	+	0.805280i	$0.702015\pi$
$348$	−519074.	−0.229764
$349$	−3.30170e6	−1.45102	−0.725511	−	0.688210i	$-0.758397\pi$
$349$	−3.30170e6	−1.45102	−0.725511	+	0.688210i	$0.758397\pi$
$350$	−47604.3	−0.0207719
$351$	−471490.	−0.204270
$352$	−1.68945e7	−7.26756
$353$	1.95282e6	0.834113	0.417057	−	0.908881i	$-0.363062\pi$
$353$	1.95282e6	0.834113	0.417057	+	0.908881i	$0.363062\pi$
$354$	126401.	0.0536096
$355$	496754.	0.209204
$356$	−1.22272e6	−0.511330
$357$	−794525.	−0.329941
$358$	−3.36527e6	−1.38775
$359$	662233.	0.271191	0.135595	−	0.990764i	$-0.456705\pi$
$359$	662233.	0.271191	0.135595	+	0.990764i	$0.456705\pi$
$360$	−8.29810e6	−3.37460
$361$	−1.78445e6	−0.720669
$362$	−7835.51	−0.00314265
$363$	919275.	0.366167
$364$	−4.63053e6	−1.83180
$365$	128793.	0.0506009
$366$	−1.09632e6	−0.427793
$367$	−2.69952e6	−1.04622	−0.523109	−	0.852266i	$-0.675228\pi$
$367$	−2.69952e6	−1.04622	−0.523109	+	0.852266i	$0.675228\pi$
$368$	−4.76409e6	−1.83383
$369$	−25930.0	−0.00991372
$370$	9.26835e6	3.51964
$371$	−2.18935e6	−0.825810
$372$	−2.80514e6	−1.05099
$373$	4.89224e6	1.82069	0.910345	−	0.413850i	$-0.135816\pi$
$373$	4.89224e6	1.82069	0.910345	+	0.413850i	$0.135816\pi$
$374$	−1.03239e7	−3.81651
$375$	−572621.	−0.210276
$376$	1.25834e7	4.59016
$377$	−529951.	−0.192036
$378$	2.95375e6	1.06327
$379$	2.76854e6	0.990040	0.495020	−	0.868882i	$-0.335161\pi$
$379$	2.76854e6	0.990040	0.495020	+	0.868882i	$0.335161\pi$
$380$	4.18796e6	1.48780
$381$	661354.	0.233411
$382$	208541.	0.0731195
$383$	−1.18573e6	−0.413037	−0.206519	−	0.978443i	$-0.566213\pi$
$383$	−1.18573e6	−0.413037	−0.206519	+	0.978443i	$0.566213\pi$
$384$	2.69032e6	0.931057
$385$	6.37606e6	2.19230
$386$	1.41749e6	0.484231
$387$	601038.	0.203997
$388$	−4.87601e6	−1.64432
$389$	1.89012e6	0.633307	0.316654	−	0.948541i	$-0.397441\pi$
$389$	1.89012e6	0.633307	0.316654	+	0.948541i	$0.397441\pi$
$390$	614436.	0.204557
$391$	−1.61699e6	−0.534891
$392$	7.95961e6	2.61624
$393$	316412.	0.103341
$394$	1.33494e6	0.433233
$395$	−965198.	−0.311260
$396$	1.38227e7	4.42951
$397$	−1.04871e6	−0.333948	−0.166974	−	0.985961i	$-0.553400\pi$
$397$	−1.04871e6	−0.333948	−0.166974	+	0.985961i	$0.553400\pi$
$398$	6.57403e6	2.08029
$399$	−468586.	−0.147352
$400$	104718.	0.0327242
$401$	−5.70224e6	−1.77086	−0.885431	−	0.464770i	$-0.846137\pi$
$401$	−5.70224e6	−1.77086	−0.885431	+	0.464770i	$0.846137\pi$
$402$	388445.	0.119885
$403$	−2.86392e6	−0.878412
$404$	−4.55494e6	−1.38845
$405$	2.87758e6	0.871747
$406$	3.31999e6	0.999588
$407$	−9.93241e6	−2.97214
$408$	2.95553e6	0.878992
$409$	2.56148e6	0.757153	0.378576	−	0.925570i	$-0.376414\pi$
$409$	2.56148e6	0.757153	0.378576	+	0.925570i	$0.376414\pi$
$410$	69159.4	0.0203185
$411$	739009.	0.215797
$412$	−1.38461e6	−0.401868
$413$	−595915.	−0.171913
$414$	2.93716e6	0.842223
$415$	1.15717e6	0.329819
$416$	7.67544e6	2.17455
$417$	473095.	0.133232
$418$	−6.08874e6	−1.70446
$419$	6.24405e6	1.73753	0.868763	−	0.495228i	$-0.164916\pi$
$419$	6.24405e6	1.73753	0.868763	+	0.495228i	$0.164916\pi$
$420$	−2.83729e6	−0.784840
$421$	5.51810e6	1.51735	0.758673	−	0.651472i	$-0.225848\pi$
$421$	5.51810e6	1.51735	0.758673	+	0.651472i	$0.225848\pi$
$422$	−1.37039e7	−3.74597
$423$	−4.58766e6	−1.24664
$424$	8.14409e6	2.20003
$425$	35542.5	0.00954498
$426$	321379.	0.0858013
$427$	5.16857e6	1.37183
$428$	7.59094e6	2.00302
$429$	−658459.	−0.172737
$430$	−1.60306e6	−0.418100
$431$	3.61988e6	0.938645	0.469322	−	0.883027i	$-0.344498\pi$
$431$	3.61988e6	0.938645	0.469322	+	0.883027i	$0.344498\pi$
$432$	−6.49750e6	−1.67508
$433$	−2.23554e6	−0.573010	−0.286505	−	0.958079i	$-0.592494\pi$
$433$	−2.23554e6	−0.573010	−0.286505	+	0.958079i	$0.592494\pi$
$434$	1.79416e7	4.57233
$435$	−324720.	−0.0822785
$436$	−7.97870e6	−2.01009
$437$	−953650.	−0.238883
$438$	83323.5	0.0207531
$439$	−2.85597e6	−0.707282	−0.353641	−	0.935381i	$-0.615057\pi$
$439$	−2.85597e6	−0.707282	−0.353641	+	0.935381i	$0.615057\pi$
$440$	−2.37181e7	−5.84047
$441$	−2.90192e6	−0.710541
$442$	4.69034e6	1.14195
$443$	2.51972e6	0.610020	0.305010	−	0.952349i	$-0.401340\pi$
$443$	2.51972e6	0.610020	0.305010	+	0.952349i	$0.401340\pi$
$444$	4.41984e6	1.06402
$445$	−764902.	−0.183107
$446$	7.47068e6	1.77837
$447$	−1.22181e6	−0.289223
$448$	−2.53248e7	−5.96143
$449$	−2.41301e6	−0.564863	−0.282431	−	0.959287i	$-0.591141\pi$
$449$	−2.41301e6	−0.564863	−0.282431	+	0.959287i	$0.591141\pi$
$450$	−64560.6	−0.0150292
$451$	−74114.6	−0.0171578
$452$	1.75675e7	4.04449
$453$	1.03426e6	0.236802
$454$	−1.19081e7	−2.71145
$455$	−2.89675e6	−0.655967
$456$	1.74308e6	0.392559
$457$	3.64998e6	0.817522	0.408761	−	0.912641i	$-0.365961\pi$
$457$	3.64998e6	0.817522	0.408761	+	0.912641i	$0.365961\pi$
$458$	1.63022e7	3.63148
$459$	−2.20533e6	−0.488587
$460$	−5.77437e6	−1.27236
$461$	−3.01979e6	−0.661796	−0.330898	−	0.943667i	$-0.607352\pi$
$461$	−3.01979e6	−0.661796	−0.330898	+	0.943667i	$0.607352\pi$
$462$	4.12505e6	0.899133
$463$	1.10271e6	0.239060	0.119530	−	0.992831i	$-0.461861\pi$
$463$	1.10271e6	0.239060	0.119530	+	0.992831i	$0.461861\pi$
$464$	−7.30313e6	−1.57476
$465$	−1.75483e6	−0.376359
$466$	5.43413e6	1.15922
$467$	3.05799e6	0.648850	0.324425	−	0.945911i	$-0.394829\pi$
$467$	3.05799e6	0.648850	0.324425	+	0.945911i	$0.394829\pi$
$468$	−6.27989e6	−1.32537
$469$	−1.83132e6	−0.384443
$470$	1.22360e7	2.55503
$471$	−1.99337e6	−0.414033
$472$	2.21673e6	0.457991
$473$	1.71792e6	0.353061
$474$	−624444.	−0.127658
$475$	20961.8	0.00426280
$476$	−2.16587e7	−4.38142
$477$	−2.96918e6	−0.597503
$478$	−1.55026e7	−3.10339
$479$	2.27178e6	0.452405	0.226202	−	0.974080i	$-0.427369\pi$
$479$	2.27178e6	0.452405	0.226202	+	0.974080i	$0.427369\pi$
$480$	4.70302e6	0.931696
$481$	4.51246e6	0.889304
$482$	1.57158e6	0.308120
$483$	646087.	0.126015
$484$	2.50594e7	4.86247
$485$	−3.05031e6	−0.588830
$486$	6.05443e6	1.16274
$487$	4.44628e6	0.849521	0.424761	−	0.905306i	$-0.360358\pi$
$487$	4.44628e6	0.849521	0.424761	+	0.905306i	$0.360358\pi$
$488$	−1.92264e7	−3.65467
$489$	−1.09308e6	−0.206718
$490$	7.73989e6	1.45628
$491$	2.04686e6	0.383164	0.191582	−	0.981477i	$-0.438638\pi$
$491$	2.04686e6	0.383164	0.191582	+	0.981477i	$0.438638\pi$
$492$	32980.4	0.00614247
$493$	−2.47877e6	−0.459325
$494$	2.76621e6	0.509998
$495$	8.64715e6	1.58621
$496$	−3.94670e7	−7.20328
$497$	−1.51514e6	−0.275145
$498$	748640.	0.135269
$499$	2.10930e6	0.379217	0.189608	−	0.981860i	$-0.439278\pi$
$499$	2.10930e6	0.379217	0.189608	+	0.981860i	$0.439278\pi$
$500$	−1.56096e7	−2.79233
$501$	−1.49889e6	−0.266794
$502$	−1.73193e6	−0.306741
$503$	7.48966e6	1.31990	0.659951	−	0.751308i	$-0.270577\pi$
$503$	7.48966e6	1.31990	0.659951	+	0.751308i	$0.270577\pi$
$504$	2.53098e7	4.43826
$505$	−2.84946e6	−0.497204
$506$	8.39516e6	1.45765
$507$	−922882.	−0.159451
$508$	1.80284e7	3.09955
$509$	−1.22019e6	−0.208752	−0.104376	−	0.994538i	$-0.533285\pi$
$509$	−1.22019e6	−0.208752	−0.104376	+	0.994538i	$0.533285\pi$
$510$	2.87394e6	0.489274
$511$	−392827.	−0.0665502
$512$	2.11108e7	3.55901
$513$	−1.30064e6	−0.218204
$514$	−2.13798e6	−0.356941
$515$	−866177.	−0.143909
$516$	−764461.	−0.126395
$517$	−1.31127e7	−2.15757
$518$	−2.82692e7	−4.62902
$519$	1.02456e6	0.166963
$520$	1.07755e7	1.74755
$521$	1.20183e6	0.193976	0.0969882	−	0.995286i	$-0.469079\pi$
$521$	1.20183e6	0.193976	0.0969882	+	0.995286i	$0.469079\pi$
$522$	4.50254e6	0.723238
$523$	−2.50054e6	−0.399742	−0.199871	−	0.979822i	$-0.564052\pi$
$523$	−2.50054e6	−0.399742	−0.199871	+	0.979822i	$0.564052\pi$
$524$	8.62536e6	1.37230
$525$	−14201.4	−0.00224871
$526$	−2.04079e7	−3.21613
$527$	−1.33956e7	−2.10105
$528$	−9.07406e6	−1.41650
$529$	−5.12145e6	−0.795708
$530$	7.91927e6	1.22460
$531$	−808175.	−0.124385
$532$	−1.27736e7	−1.95675
$533$	33671.5	0.00513386
$534$	−494861.	−0.0750982
$535$	4.74871e6	0.717284
$536$	6.81226e6	1.02419
$537$	−1.00393e6	−0.150234
$538$	−2.19654e7	−3.27177
$539$	−8.29443e6	−1.22974
$540$	−7.87537e6	−1.16221
$541$	1.15705e7	1.69964	0.849821	−	0.527072i	$-0.176710\pi$
$541$	1.15705e7	1.69964	0.849821	+	0.527072i	$0.176710\pi$
$542$	5.12655e6	0.749595
$543$	−2337.50	−0.000340214 0
$544$	3.59008e7	5.20125
$545$	−4.99128e6	−0.719815
$546$	−1.87408e6	−0.269033
$547$	4.19769e6	0.599850	0.299925	−	0.953963i	$-0.403038\pi$
$547$	4.19769e6	0.599850	0.299925	+	0.953963i	$0.403038\pi$
$548$	2.01453e7	2.86565
$549$	7.00957e6	0.992569
$550$	−184531.	−0.0260113
$551$	−1.46190e6	−0.205135
$552$	−2.40336e6	−0.335715
$553$	2.94393e6	0.409368
$554$	6.50232e6	0.900106
$555$	2.76495e6	0.381026
$556$	1.28965e7	1.76923
$557$	6.95806e6	0.950276	0.475138	−	0.879911i	$-0.342398\pi$
$557$	6.95806e6	0.950276	0.475138	+	0.879911i	$0.342398\pi$
$558$	2.43323e7	3.30824
$559$	−780479.	−0.105641
$560$	−3.99194e7	−5.37915
$561$	−3.07985e6	−0.413164
$562$	−4.82962e6	−0.645019
$563$	−4.07131e6	−0.541331	−0.270665	−	0.962673i	$-0.587244\pi$
$563$	−4.07131e6	−0.541331	−0.270665	+	0.962673i	$0.587244\pi$
$564$	5.83505e6	0.772408
$565$	1.09898e7	1.44833
$566$	1.51141e7	1.98308
$567$	−8.77685e6	−1.14652
$568$	5.63611e6	0.733008
$569$	−9.42608e6	−1.22054	−0.610268	−	0.792195i	$-0.708938\pi$
$569$	−9.42608e6	−1.22054	−0.610268	+	0.792195i	$0.708938\pi$
$570$	1.69496e6	0.218510
$571$	7.80683e6	1.00204	0.501019	−	0.865436i	$-0.332959\pi$
$571$	7.80683e6	1.00204	0.501019	+	0.865436i	$0.332959\pi$
$572$	−1.79495e7	−2.29384
$573$	62212.2	0.00791570
$574$	−210942.	−0.0267228
$575$	−28902.2	−0.00364554
$576$	−3.43453e7	−4.31331
$577$	1.01715e6	0.127188	0.0635941	−	0.997976i	$-0.479744\pi$
$577$	1.01715e6	0.127188	0.0635941	+	0.997976i	$0.479744\pi$
$578$	6.27358e6	0.781081
$579$	422868.	0.0524214
$580$	−8.85185e6	−1.09261
$581$	−3.52945e6	−0.433777
$582$	−1.97343e6	−0.241498
$583$	−8.48667e6	−1.03411
$584$	1.46127e6	0.177295
$585$	−3.92854e6	−0.474616
$586$	1.59416e6	0.191773
$587$	−1.54914e7	−1.85565	−0.927825	−	0.373016i	$-0.878324\pi$
$587$	−1.54914e7	−1.85565	−0.927825	+	0.373016i	$0.878324\pi$
$588$	3.69096e6	0.440246
$589$	−7.90030e6	−0.938330
$590$	2.15553e6	0.254932
$591$	398241.	0.0469005
$592$	6.21851e7	7.29259
$593$	−7.82187e6	−0.913427	−0.456714	−	0.889614i	$-0.650974\pi$
$593$	−7.82187e6	−0.913427	−0.456714	+	0.889614i	$0.650974\pi$
$594$	1.14497e7	1.33146
$595$	−1.35491e7	−1.56899
$596$	−3.33063e7	−3.84070
$597$	1.96117e6	0.225206
$598$	−3.81406e6	−0.436149
$599$	3.35169e6	0.381677	0.190839	−	0.981621i	$-0.438879\pi$
$599$	3.35169e6	0.381677	0.190839	+	0.981621i	$0.438879\pi$
$600$	52827.3	0.00599074
$601$	−9.72180e6	−1.09789	−0.548947	−	0.835857i	$-0.684971\pi$
$601$	−9.72180e6	−1.09789	−0.548947	+	0.835857i	$0.684971\pi$
$602$	4.88947e6	0.549883
$603$	−2.48362e6	−0.278158
$604$	2.81939e7	3.14458
$605$	1.56765e7	1.74125
$606$	−1.84348e6	−0.203919
$607$	1.57259e7	1.73238	0.866192	−	0.499712i	$-0.166561\pi$
$607$	1.57259e7	1.73238	0.866192	+	0.499712i	$0.166561\pi$
$608$	2.11732e7	2.32288
$609$	990422.	0.108212
$610$	−1.86957e7	−2.03431
$611$	5.95732e6	0.645576
$612$	−2.93733e7	−3.17011
$613$	45307.5	0.00486988	0.00243494	−	0.999997i	$-0.499225\pi$
$613$	45307.5	0.00486988	0.00243494	+	0.999997i	$0.499225\pi$
$614$	−3.06207e7	−3.27789
$615$	20631.7	0.00219962
$616$	7.23420e7	7.68137
$617$	989224.	0.104612	0.0523060	−	0.998631i	$-0.483343\pi$
$617$	989224.	0.104612	0.0523060	+	0.998631i	$0.483343\pi$
$618$	−560381.	−0.0590218
$619$	−1.67965e7	−1.76194	−0.880972	−	0.473168i	$-0.843110\pi$
$619$	−1.67965e7	−1.76194	−0.880972	+	0.473168i	$0.843110\pi$
$620$	−4.78365e7	−4.99781
$621$	1.79332e6	0.186607
$622$	−1.98689e7	−2.05920
$623$	2.33301e6	0.240822
$624$	4.12250e6	0.423837
$625$	−9.84376e6	−1.00800
$626$	4.08629e6	0.416767
$627$	−1.81640e6	−0.184520
$628$	−5.43389e7	−5.49809
$629$	2.11064e7	2.12710
$630$	2.46112e7	2.47048
$631$	1.74332e7	1.74303	0.871515	−	0.490370i	$-0.163138\pi$
$631$	1.74332e7	1.74303	0.871515	+	0.490370i	$0.163138\pi$
$632$	−1.09510e7	−1.09059
$633$	−4.08818e6	−0.405528
$634$	−403785.	−0.0398958
$635$	1.12782e7	1.10995
$636$	3.77650e6	0.370209
$637$	3.76830e6	0.367957
$638$	1.28694e7	1.25172
$639$	−2.05482e6	−0.199077
$640$	4.58784e7	4.42750
$641$	1.26907e7	1.21994	0.609972	−	0.792423i	$-0.291181\pi$
$641$	1.26907e7	1.21994	0.609972	+	0.792423i	$0.291181\pi$
$642$	3.07222e6	0.294181
$643$	9.05736e6	0.863921	0.431960	−	0.901893i	$-0.357822\pi$
$643$	9.05736e6	0.863921	0.431960	+	0.901893i	$0.357822\pi$
$644$	1.76123e7	1.67340
$645$	−478228.	−0.0452622
$646$	1.29386e7	1.21985
$647$	−7.11502e6	−0.668214	−0.334107	−	0.942535i	$-0.608435\pi$
$647$	−7.11502e6	−0.668214	−0.334107	+	0.942535i	$0.608435\pi$
$648$	3.26487e7	3.05442
$649$	−2.30997e6	−0.215276
$650$	83835.4	0.00778294
$651$	5.35236e6	0.494986
$652$	−2.97972e7	−2.74509
$653$	−2.14039e6	−0.196431	−0.0982156	−	0.995165i	$-0.531313\pi$
$653$	−2.14039e6	−0.196431	−0.0982156	+	0.995165i	$0.531313\pi$
$654$	−3.22915e6	−0.295219
$655$	5.39582e6	0.491421
$656$	464018.	0.0420994
$657$	−532749.	−0.0481514
$658$	−3.73208e7	−3.36036
$659$	1.09159e7	0.979144	0.489572	−	0.871963i	$-0.337153\pi$
$659$	1.09159e7	0.979144	0.489572	+	0.871963i	$0.337153\pi$
$660$	−1.09983e7	−0.982804
$661$	7.91113e6	0.704263	0.352132	−	0.935951i	$-0.385457\pi$
$661$	7.91113e6	0.704263	0.352132	+	0.935951i	$0.385457\pi$
$662$	−1.22312e7	−1.08474
$663$	1.39923e6	0.123624
$664$	1.31291e7	1.15562
$665$	−7.99085e6	−0.700711
$666$	−3.83385e7	−3.34926
$667$	2.01567e6	0.175431
$668$	−4.08596e7	−3.54285
$669$	2.22866e6	0.192521
$670$	6.62421e6	0.570095
$671$	2.00352e7	1.71785
$672$	−1.43446e7	−1.22536
$673$	−1.91665e6	−0.163119	−0.0815595	−	0.996668i	$-0.525990\pi$
$673$	−1.91665e6	−0.163119	−0.0815595	+	0.996668i	$0.525990\pi$
$674$	2.74443e7	2.32703
$675$	−39418.2	−0.00332995
$676$	−2.51577e7	−2.11740
$677$	1.15807e7	0.971098	0.485549	−	0.874210i	$-0.338620\pi$
$677$	1.15807e7	0.971098	0.485549	+	0.874210i	$0.338620\pi$
$678$	7.10994e6	0.594007
$679$	9.30369e6	0.774427
$680$	5.04010e7	4.17991
$681$	−3.55243e6	−0.293533
$682$	6.95479e7	5.72562
$683$	−2.62961e6	−0.215695	−0.107847	−	0.994167i	$-0.534396\pi$
$683$	−2.62961e6	−0.215695	−0.107847	+	0.994167i	$0.534396\pi$
$684$	−1.73235e7	−1.41577
$685$	1.26024e7	1.02619
$686$	8.13600e6	0.660086
$687$	4.86331e6	0.393133
$688$	−1.07556e7	−0.866291
$689$	3.85563e6	0.309419
$690$	−2.33701e6	−0.186870
$691$	−1.50999e7	−1.20304	−0.601520	−	0.798858i	$-0.705438\pi$
$691$	−1.50999e7	−1.20304	−0.601520	+	0.798858i	$0.705438\pi$
$692$	2.79294e7	2.21716
$693$	−2.63745e7	−2.08618
$694$	−2.93435e7	−2.31267
$695$	8.06774e6	0.633563
$696$	−3.68424e6	−0.288287
$697$	157494.	0.0122795
$698$	−3.64266e7	−2.82996
$699$	1.62112e6	0.125493
$700$	−387128.	−0.0298614
$701$	−1.33562e7	−1.02657	−0.513286	−	0.858218i	$-0.671572\pi$
$701$	−1.33562e7	−1.02657	−0.513286	+	0.858218i	$0.671572\pi$
$702$	−5.20180e6	−0.398392
$703$	1.24479e7	0.949965
$704$	−9.81675e7	−7.46511
$705$	3.65026e6	0.276600
$706$	2.15448e7	1.62679
$707$	8.69107e6	0.653920
$708$	1.02792e6	0.0770683
$709$	−7.29003e6	−0.544645	−0.272323	−	0.962206i	$-0.587792\pi$
$709$	−7.29003e6	−0.544645	−0.272323	+	0.962206i	$0.587792\pi$
$710$	5.48053e6	0.408015
$711$	3.99253e6	0.296193
$712$	−8.67850e6	−0.641571
$713$	1.08930e7	0.802457
$714$	−8.76574e6	−0.643492
$715$	−1.12288e7	−0.821425
$716$	−2.73671e7	−1.99501
$717$	−4.62476e6	−0.335963
$718$	7.30620e6	0.528909
$719$	1.39934e7	1.00949	0.504743	−	0.863270i	$-0.331587\pi$
$719$	1.39934e7	1.00949	0.504743	+	0.863270i	$0.331587\pi$
$720$	−5.41383e7	−3.89201
$721$	2.64190e6	0.189269
$722$	−1.96872e7	−1.40554
$723$	468836.	0.0333561
$724$	−63720.0	−0.00451782
$725$	−44305.8	−0.00313051
$726$	1.01421e7	0.714143
$727$	−7.25058e6	−0.508788	−0.254394	−	0.967101i	$-0.581876\pi$
$727$	−7.25058e6	−0.508788	−0.254394	+	0.967101i	$0.581876\pi$
$728$	−3.28662e7	−2.29837
$729$	−1.06523e7	−0.742377
$730$	1.42093e6	0.0986881
$731$	−3.65059e6	−0.252679
$732$	−8.91549e6	−0.614989
$733$	8.25970e6	0.567812	0.283906	−	0.958852i	$-0.408370\pi$
$733$	8.25970e6	0.567812	0.283906	+	0.958852i	$0.408370\pi$
$734$	−2.97830e7	−2.04046
$735$	2.30897e6	0.157652
$736$	−2.91936e7	−1.98652
$737$	−7.09882e6	−0.481413
$738$	−286077.	−0.0193349
$739$	1.23836e7	0.834131	0.417065	−	0.908876i	$-0.363059\pi$
$739$	1.23836e7	0.834131	0.417065	+	0.908876i	$0.363059\pi$
$740$	7.53722e7	5.05978
$741$	825220.	0.0552108
$742$	−2.41544e7	−1.61059
$743$	1.62778e7	1.08174	0.540872	−	0.841105i	$-0.318094\pi$
$743$	1.62778e7	1.08174	0.540872	+	0.841105i	$0.318094\pi$
$744$	−1.99101e7	−1.31868
$745$	−2.08356e7	−1.37536
$746$	5.39746e7	3.55093
$747$	−4.78661e6	−0.313853
$748$	−8.39565e7	−5.48656
$749$	−1.44839e7	−0.943370
$750$	−6.31755e6	−0.410105
$751$	−8.19272e6	−0.530064	−0.265032	−	0.964240i	$-0.585382\pi$
$751$	−8.19272e6	−0.530064	−0.265032	+	0.964240i	$0.585382\pi$
$752$	8.20964e7	5.29394
$753$	−516673.	−0.0332069
$754$	−5.84678e6	−0.374532
$755$	1.76374e7	1.12608
$756$	2.40205e7	1.52854
$757$	1.38120e7	0.876027	0.438014	−	0.898968i	$-0.355682\pi$
$757$	1.38120e7	0.876027	0.438014	+	0.898968i	$0.355682\pi$
$758$	3.05444e7	1.93090
$759$	2.50446e6	0.157801
$760$	2.97249e7	1.86675
$761$	2.45133e7	1.53441	0.767203	−	0.641404i	$-0.221648\pi$
$761$	2.45133e7	1.53441	0.767203	+	0.641404i	$0.221648\pi$
$762$	7.29650e6	0.455226
$763$	1.52238e7	0.946698
$764$	1.69590e6	0.105116
$765$	−1.83752e7	−1.13522
$766$	−1.30818e7	−0.805555
$767$	1.04946e6	0.0644134
$768$	1.41010e7	0.862675
$769$	−1.49124e7	−0.909354	−0.454677	−	0.890656i	$-0.650245\pi$
$769$	−1.49124e7	−0.909354	−0.454677	+	0.890656i	$0.650245\pi$
$770$	7.03450e7	4.27569
$771$	−637806.	−0.0386414
$772$	1.15273e7	0.696123
$773$	96137.6	0.00578688	0.00289344	−	0.999996i	$-0.499079\pi$
$773$	96137.6	0.00578688	0.00289344	+	0.999996i	$0.499079\pi$
$774$	6.63106e6	0.397860
$775$	−239434.	−0.0143196
$776$	−3.46085e7	−2.06314
$777$	−8.43330e6	−0.501124
$778$	2.08530e7	1.23515
$779$	92884.8	0.00548404
$780$	4.99672e6	0.294069
$781$	−5.87319e6	−0.344546
$782$	−1.78397e7	−1.04321
$783$	2.74908e6	0.160244
$784$	5.19300e7	3.01737
$785$	−3.39931e7	−1.96887
$786$	3.49087e6	0.201548
$787$	2.73801e7	1.57579	0.787894	−	0.615811i	$-0.211172\pi$
$787$	2.73801e7	1.57579	0.787894	+	0.615811i	$0.211172\pi$
$788$	1.08560e7	0.622809
$789$	−6.08810e6	−0.348168
$790$	−1.06487e7	−0.607057
$791$	−3.35197e7	−1.90484
$792$	9.81096e7	5.55775
$793$	−9.10230e6	−0.514006
$794$	−1.15701e7	−0.651305
$795$	2.36249e6	0.132572
$796$	5.34614e7	2.99059
$797$	−1.20856e7	−0.673944	−0.336972	−	0.941515i	$-0.609403\pi$
$797$	−1.20856e7	−0.673944	−0.336972	+	0.941515i	$0.609403\pi$
$798$	−5.16976e6	−0.287384
$799$	2.78645e7	1.54413
$800$	641694.	0.0354489
$801$	3.16401e6	0.174244
$802$	−6.29110e7	−3.45375
$803$	−1.52273e6	−0.0833365
$804$	3.15892e6	0.172345
$805$	1.10178e7	0.599246
$806$	−3.15967e7	−1.71319
$807$	−6.55274e6	−0.354192
$808$	−3.23297e7	−1.74210
$809$	−1.94149e7	−1.04295	−0.521475	−	0.853267i	$-0.674618\pi$
$809$	−1.94149e7	−1.04295	−0.521475	+	0.853267i	$0.674618\pi$
$810$	3.17475e7	1.70019
$811$	−924926.	−0.0493804	−0.0246902	−	0.999695i	$-0.507860\pi$
$811$	−924926.	−0.0493804	−0.0246902	+	0.999695i	$0.507860\pi$
$812$	2.69988e7	1.43699
$813$	1.52936e6	0.0811489
$814$	−1.09581e8	−5.79662
$815$	−1.86404e7	−0.983017
$816$	1.92824e7	1.01376
$817$	−2.15300e6	−0.112847
$818$	2.82600e7	1.47669
$819$	1.19824e7	0.624213
$820$	562419.	0.0292096
$821$	2.35080e7	1.21719	0.608594	−	0.793482i	$-0.291734\pi$
$821$	2.35080e7	1.21719	0.608594	+	0.793482i	$0.291734\pi$
$822$	8.15325e6	0.420873
$823$	1.86174e7	0.958118	0.479059	−	0.877783i	$-0.340978\pi$
$823$	1.86174e7	0.958118	0.479059	+	0.877783i	$0.340978\pi$
$824$	−9.82754e6	−0.504228
$825$	−55049.5	−0.00281591
$826$	−6.57454e6	−0.335286
$827$	−8.63285e6	−0.438925	−0.219463	−	0.975621i	$-0.570430\pi$
$827$	−8.63285e6	−0.438925	−0.219463	+	0.975621i	$0.570430\pi$
$828$	2.38856e7	1.21077
$829$	−1.62505e7	−0.821260	−0.410630	−	0.911802i	$-0.634691\pi$
$829$	−1.62505e7	−0.821260	−0.410630	+	0.911802i	$0.634691\pi$
$830$	1.27667e7	0.643253
$831$	1.93978e6	0.0974428
$832$	4.45991e7	2.23366
$833$	1.76257e7	0.880104
$834$	5.21950e6	0.259845
$835$	−2.55608e7	−1.26870
$836$	−4.95149e7	−2.45030
$837$	1.48563e7	0.732991
$838$	6.88886e7	3.38873
$839$	1.76389e7	0.865099	0.432549	−	0.901610i	$-0.357614\pi$
$839$	1.76389e7	0.865099	0.432549	+	0.901610i	$0.357614\pi$
$840$	−2.01383e7	−0.984746
$841$	−1.74212e7	−0.849353
$842$	6.08795e7	2.95931
$843$	−1.44078e6	−0.0698278
$844$	−1.11443e8	−5.38515
$845$	−1.57380e7	−0.758243
$846$	−5.06142e7	−2.43134
$847$	−4.78146e7	−2.29009
$848$	5.31335e7	2.53734
$849$	4.50885e6	0.214682
$850$	392129.	0.0186158
$851$	−1.71632e7	−0.812407
$852$	2.61352e6	0.123347
$853$	−8.43099e6	−0.396740	−0.198370	−	0.980127i	$-0.563565\pi$
$853$	−8.43099e6	−0.396740	−0.198370	+	0.980127i	$0.563565\pi$
$854$	5.70232e7	2.67551
$855$	−1.08371e7	−0.506990
$856$	5.38783e7	2.51322
$857$	−3.53082e7	−1.64219	−0.821096	−	0.570791i	$-0.806637\pi$
$857$	−3.53082e7	−1.64219	−0.821096	+	0.570791i	$0.806637\pi$
$858$	−7.26457e6	−0.336893
$859$	−2.74643e7	−1.26995	−0.634973	−	0.772535i	$-0.718989\pi$
$859$	−2.74643e7	−1.26995	−0.634973	+	0.772535i	$0.718989\pi$
$860$	−1.30365e7	−0.601054
$861$	−62928.4	−0.00289293
$862$	3.99370e7	1.83066
$863$	2.90550e7	1.32799	0.663994	−	0.747738i	$-0.268860\pi$
$863$	2.90550e7	1.32799	0.663994	+	0.747738i	$0.268860\pi$
$864$	−3.98157e7	−1.81456
$865$	1.74720e7	0.793965
$866$	−2.46640e7	−1.11755
$867$	1.87154e6	0.0845575
$868$	1.45905e8	6.57311
$869$	1.14117e7	0.512625
$870$	−3.58254e6	−0.160469
$871$	3.22511e6	0.144045
$872$	−5.66305e7	−2.52208
$873$	1.26176e7	0.560326
$874$	−1.05213e7	−0.465899
$875$	2.97840e7	1.31511
$876$	677604.	0.0298343
$877$	−3.98178e6	−0.174815	−0.0874075	−	0.996173i	$-0.527858\pi$
$877$	−3.98178e6	−0.174815	−0.0874075	+	0.996173i	$0.527858\pi$
$878$	−3.15090e7	−1.37943
$879$	475571.	0.0207607
$880$	−1.54741e8	−6.73596
$881$	2.15116e6	0.0933754	0.0466877	−	0.998910i	$-0.485133\pi$
$881$	2.15116e6	0.0933754	0.0466877	+	0.998910i	$0.485133\pi$
$882$	−3.20160e7	−1.38578
$883$	−1.43667e7	−0.620091	−0.310046	−	0.950722i	$-0.600344\pi$
$883$	−1.43667e7	−0.620091	−0.310046	+	0.950722i	$0.600344\pi$
$884$	3.81428e7	1.64165
$885$	643041.	0.0275982
$886$	2.77993e7	1.18973
$887$	−3.07249e7	−1.31124	−0.655619	−	0.755092i	$-0.727592\pi$
$887$	−3.07249e7	−1.31124	−0.655619	+	0.755092i	$0.727592\pi$
$888$	3.13708e7	1.33504
$889$	−3.43992e7	−1.45980
$890$	−8.43892e6	−0.357118
$891$	−3.40221e7	−1.43571
$892$	6.07531e7	2.55656
$893$	1.64336e7	0.689612
$894$	−1.34798e7	−0.564078
$895$	−1.71202e7	−0.714415
$896$	−1.39933e8	−5.82304
$897$	−1.13781e6	−0.0472161
$898$	−2.66220e7	−1.10166
$899$	1.66984e7	0.689090
$900$	−525021.	−0.0216058
$901$	1.80342e7	0.740090
$902$	−817682.	−0.0334633
$903$	1.45863e6	0.0595287
$904$	1.24689e8	5.07466
$905$	−39861.7	−0.00161783
$906$	1.14107e7	0.461840
$907$	4.56411e6	0.184221	0.0921103	−	0.995749i	$-0.470639\pi$
$907$	4.56411e6	0.184221	0.0921103	+	0.995749i	$0.470639\pi$
$908$	−9.68389e7	−3.89794
$909$	1.17868e7	0.473135
$910$	−3.19589e7	−1.27935
$911$	1.59238e7	0.635698	0.317849	−	0.948141i	$-0.397040\pi$
$911$	1.59238e7	0.635698	0.317849	+	0.948141i	$0.397040\pi$
$912$	1.13722e7	0.452747
$913$	−1.36814e7	−0.543191
$914$	4.02690e7	1.59443
$915$	−5.57731e6	−0.220228
$916$	1.32573e8	5.22056
$917$	−1.64577e7	−0.646316
$918$	−2.43307e7	−0.952902
$919$	8.47450e6	0.330998	0.165499	−	0.986210i	$-0.447077\pi$
$919$	8.47450e6	0.330998	0.165499	+	0.986210i	$0.447077\pi$
$920$	−4.09848e7	−1.59644
$921$	−9.13482e6	−0.354855
$922$	−3.33164e7	−1.29071
$923$	2.66829e6	0.103093
$924$	3.35457e7	1.29258
$925$	377257.	0.0144972
$926$	1.21658e7	0.466245
$927$	3.58293e6	0.136943
$928$	−4.47525e7	−1.70588
$929$	−3.77271e7	−1.43421	−0.717107	−	0.696964i	$-0.754534\pi$
$929$	−3.77271e7	−1.43421	−0.717107	+	0.696964i	$0.754534\pi$
$930$	−1.93605e7	−0.734021
$931$	1.03951e7	0.393055
$932$	4.41914e7	1.66647
$933$	−5.92732e6	−0.222923
$934$	3.37379e7	1.26547
$935$	−5.25211e7	−1.96474
$936$	−4.45728e7	−1.66295
$937$	−9.70466e6	−0.361103	−0.180552	−	0.983566i	$-0.557788\pi$
$937$	−9.70466e6	−0.361103	−0.180552	+	0.983566i	$0.557788\pi$
$938$	−2.02043e7	−0.749787
$939$	1.21903e6	0.0451180
$940$	9.95059e7	3.67307
$941$	3.77870e7	1.39113	0.695566	−	0.718462i	$-0.255154\pi$
$941$	3.77870e7	1.39113	0.695566	+	0.718462i	$0.255154\pi$
$942$	−2.19922e7	−0.807497
$943$	−128070.	−0.00468994
$944$	1.44623e7	0.528212
$945$	1.50266e7	0.547371
$946$	1.89533e7	0.688583
$947$	−3.33772e7	−1.20941	−0.604706	−	0.796449i	$-0.706709\pi$
$947$	−3.33772e7	−1.20941	−0.604706	+	0.796449i	$0.706709\pi$
$948$	−5.07811e6	−0.183519
$949$	691803.	0.0249354
$950$	231265.	0.00831383
$951$	−120458.	−0.00431900
$952$	−1.53727e8	−5.49740
$953$	4.31712e6	0.153979	0.0769895	−	0.997032i	$-0.475469\pi$
$953$	4.31712e6	0.153979	0.0769895	+	0.997032i	$0.475469\pi$
$954$	−3.27580e7	−1.16532
$955$	1.06091e6	0.0376419
$956$	−1.26071e8	−4.46138
$957$	3.83922e6	0.135507
$958$	2.50638e7	0.882334
$959$	−3.84383e7	−1.34964
$960$	2.73275e7	0.957022
$961$	6.16111e7	2.15204
$962$	4.97845e7	1.73443
$963$	−1.96430e7	−0.682562
$964$	1.27804e7	0.442948
$965$	7.21123e6	0.249282
$966$	7.12807e6	0.245770
$967$	1.16014e6	0.0398975	0.0199487	−	0.999801i	$-0.493650\pi$
$967$	1.16014e6	0.0398975	0.0199487	+	0.999801i	$0.493650\pi$
$968$	1.77864e8	6.10098
$969$	3.85985e6	0.132057
$970$	−3.36531e7	−1.14841
$971$	2.33652e7	0.795282	0.397641	−	0.917541i	$-0.369829\pi$
$971$	2.33652e7	0.795282	0.397641	+	0.917541i	$0.369829\pi$
$972$	4.92359e7	1.67154
$973$	−2.46072e7	−0.833261
$974$	4.90544e7	1.65684
$975$	25009.9	0.000842558 0
$976$	−1.25437e8	−4.21502
$977$	3.02812e7	1.01493	0.507466	−	0.861672i	$-0.330582\pi$
$977$	3.02812e7	1.01493	0.507466	+	0.861672i	$0.330582\pi$
$978$	−1.20596e7	−0.403167
$979$	9.04355e6	0.301566
$980$	6.29424e7	2.09352
$981$	2.06464e7	0.684970
$982$	2.25824e7	0.747293
$983$	−3.39515e7	−1.12066	−0.560331	−	0.828269i	$-0.689326\pi$
$983$	−3.39515e7	−1.12066	−0.560331	+	0.828269i	$0.689326\pi$
$984$	234085.	0.00770702
$985$	6.79126e6	0.223028
$986$	−2.73475e7	−0.895830
$987$	−1.11336e7	−0.363783
$988$	2.24954e7	0.733165
$989$	2.96856e6	0.0965062
$990$	9.54013e7	3.09362
$991$	4.70332e7	1.52132	0.760659	−	0.649152i	$-0.224876\pi$
$991$	4.70332e7	1.52132	0.760659	+	0.649152i	$0.224876\pi$
$992$	−2.41848e8	−7.80304
$993$	−3.64884e6	−0.117431
$994$	−1.67160e7	−0.536620
$995$	3.34441e7	1.07093
$996$	6.08810e6	0.194461
$997$	2.66198e7	0.848139	0.424069	−	0.905630i	$-0.360601\pi$
$997$	2.66198e7	0.848139	0.424069	+	0.905630i	$0.360601\pi$
$998$	2.32713e7	0.739595
$999$	−2.34080e7	−0.742079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	59.6.a.b.1.15	✓	15
3.2	odd	2		531.6.a.f.1.1		15
4.3	odd	2		944.6.a.h.1.7		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.6.a.b.1.15	✓	15	1.1	even	1	trivial
531.6.a.f.1.1		15	3.2	odd	2
944.6.a.h.1.7		15	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	59.a (trivial)

\(f(q)\)	\(=\)	\(q+11.0327 q^{2} +3.29128 q^{3} +89.7201 q^{4} +56.1267 q^{5} +36.3117 q^{6} -171.191 q^{7} +636.807 q^{8} -232.167 q^{9} +O(q^{10})\)	\(q+11.0327 q^{2} +3.29128 q^{3} +89.7201 q^{4} +56.1267 q^{5} +36.3117 q^{6} -171.191 q^{7} +636.807 q^{8} -232.167 q^{9} +619.228 q^{10} -663.594 q^{11} +295.294 q^{12} +301.482 q^{13} -1888.69 q^{14} +184.729 q^{15} +4154.65 q^{16} +1410.14 q^{17} -2561.43 q^{18} +831.656 q^{19} +5035.69 q^{20} -563.437 q^{21} -7321.22 q^{22} -1146.69 q^{23} +2095.91 q^{24} +25.2049 q^{25} +3326.15 q^{26} -1563.91 q^{27} -15359.2 q^{28} -1757.82 q^{29} +2038.05 q^{30} -9499.49 q^{31} +25459.1 q^{32} -2184.08 q^{33} +15557.6 q^{34} -9608.37 q^{35} -20830.1 q^{36} +14967.6 q^{37} +9175.39 q^{38} +992.261 q^{39} +35741.9 q^{40} +111.687 q^{41} -6216.22 q^{42} -2588.81 q^{43} -59537.7 q^{44} -13030.8 q^{45} -12651.1 q^{46} +19760.1 q^{47} +13674.1 q^{48} +12499.3 q^{49} +278.078 q^{50} +4641.17 q^{51} +27049.0 q^{52} +12788.9 q^{53} -17254.1 q^{54} -37245.3 q^{55} -109015. q^{56} +2737.21 q^{57} -19393.5 q^{58} +3481.00 q^{59} +16573.9 q^{60} -30191.9 q^{61} -104805. q^{62} +39744.9 q^{63} +147933. q^{64} +16921.2 q^{65} -24096.2 q^{66} +10697.5 q^{67} +126518. q^{68} -3774.08 q^{69} -106006. q^{70} +8850.58 q^{71} -147846. q^{72} +2294.68 q^{73} +165133. q^{74} +82.9565 q^{75} +74616.2 q^{76} +113601. q^{77} +10947.3 q^{78} -17196.8 q^{79} +233187. q^{80} +51269.4 q^{81} +1232.20 q^{82} +20617.1 q^{83} -50551.6 q^{84} +79146.5 q^{85} -28561.5 q^{86} -5785.49 q^{87} -422581. q^{88} -13628.1 q^{89} -143765. q^{90} -51610.9 q^{91} -102881. q^{92} -31265.5 q^{93} +218007. q^{94} +46678.1 q^{95} +83793.0 q^{96} -54346.9 q^{97} +137900. q^{98} +154065. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 3 q^{2} + 18 q^{3} + 303 q^{4} + 128 q^{5} + 14 q^{6} + 282 q^{7} + 249 q^{8} + 1621 q^{9}+O(q^{10}) \) 15 * q + 3 * q^2 + 18 * q^3 + 303 * q^4 + 128 * q^5 + 14 * q^6 + 282 * q^7 + 249 * q^8 + 1621 * q^9	\( 15 q + 3 q^{2} + 18 q^{3} + 303 q^{4} + 128 q^{5} + 14 q^{6} + 282 q^{7} + 249 q^{8} + 1621 q^{9} + 598 q^{10} + 34 q^{11} + 864 q^{12} + 1790 q^{13} + 1087 q^{14} + 2900 q^{15} + 12155 q^{16} + 6130 q^{17} + 10417 q^{18} + 5342 q^{19} + 11772 q^{20} + 7976 q^{21} + 7657 q^{22} + 1552 q^{23} + 612 q^{24} + 10587 q^{25} - 7885 q^{26} + 3072 q^{27} - 3541 q^{28} + 7476 q^{29} - 25854 q^{30} - 3468 q^{31} - 9479 q^{32} - 11228 q^{33} + 2177 q^{34} - 15556 q^{35} - 39367 q^{36} + 22158 q^{37} - 60264 q^{38} + 8000 q^{39} - 11660 q^{40} + 4670 q^{41} - 130868 q^{42} + 20134 q^{43} - 74355 q^{44} - 22660 q^{45} - 15144 q^{46} - 23192 q^{47} - 77896 q^{48} + 75323 q^{49} - 110939 q^{50} - 22092 q^{51} - 104973 q^{52} + 22148 q^{53} - 122246 q^{54} - 27480 q^{55} - 103031 q^{56} - 65580 q^{57} + 60642 q^{58} + 52215 q^{59} - 1822 q^{60} + 156158 q^{61} - 262068 q^{62} + 283004 q^{63} + 209263 q^{64} + 148264 q^{65} - 32770 q^{66} + 166884 q^{67} + 290919 q^{68} + 221972 q^{69} - 50302 q^{70} - 3954 q^{71} + 62839 q^{72} + 32606 q^{73} + 105727 q^{74} + 305348 q^{75} + 96994 q^{76} + 143452 q^{77} - 71054 q^{78} + 352558 q^{79} + 696 q^{80} + 405359 q^{81} - 76879 q^{82} + 153906 q^{83} - 157160 q^{84} + 327528 q^{85} - 81369 q^{86} - 82912 q^{87} + 252111 q^{88} + 20806 q^{89} - 162642 q^{90} + 88714 q^{91} - 163940 q^{92} + 16120 q^{93} + 109102 q^{94} - 87254 q^{95} - 118508 q^{96} + 45926 q^{97} - 601532 q^{98} - 13706 q^{99}+O(q^{100}) \) 15 * q + 3 * q^2 + 18 * q^3 + 303 * q^4 + 128 * q^5 + 14 * q^6 + 282 * q^7 + 249 * q^8 + 1621 * q^9 + 598 * q^10 + 34 * q^11 + 864 * q^12 + 1790 * q^13 + 1087 * q^14 + 2900 * q^15 + 12155 * q^16 + 6130 * q^17 + 10417 * q^18 + 5342 * q^19 + 11772 * q^20 + 7976 * q^21 + 7657 * q^22 + 1552 * q^23 + 612 * q^24 + 10587 * q^25 - 7885 * q^26 + 3072 * q^27 - 3541 * q^28 + 7476 * q^29 - 25854 * q^30 - 3468 * q^31 - 9479 * q^32 - 11228 * q^33 + 2177 * q^34 - 15556 * q^35 - 39367 * q^36 + 22158 * q^37 - 60264 * q^38 + 8000 * q^39 - 11660 * q^40 + 4670 * q^41 - 130868 * q^42 + 20134 * q^43 - 74355 * q^44 - 22660 * q^45 - 15144 * q^46 - 23192 * q^47 - 77896 * q^48 + 75323 * q^49 - 110939 * q^50 - 22092 * q^51 - 104973 * q^52 + 22148 * q^53 - 122246 * q^54 - 27480 * q^55 - 103031 * q^56 - 65580 * q^57 + 60642 * q^58 + 52215 * q^59 - 1822 * q^60 + 156158 * q^61 - 262068 * q^62 + 283004 * q^63 + 209263 * q^64 + 148264 * q^65 - 32770 * q^66 + 166884 * q^67 + 290919 * q^68 + 221972 * q^69 - 50302 * q^70 - 3954 * q^71 + 62839 * q^72 + 32606 * q^73 + 105727 * q^74 + 305348 * q^75 + 96994 * q^76 + 143452 * q^77 - 71054 * q^78 + 352558 * q^79 + 696 * q^80 + 405359 * q^81 - 76879 * q^82 + 153906 * q^83 - 157160 * q^84 + 327528 * q^85 - 81369 * q^86 - 82912 * q^87 + 252111 * q^88 + 20806 * q^89 - 162642 * q^90 + 88714 * q^91 - 163940 * q^92 + 16120 * q^93 + 109102 * q^94 - 87254 * q^95 - 118508 * q^96 + 45926 * q^97 - 601532 * q^98 - 13706 * q^99

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