LMFDB - Embedded newform 1003.6.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,6,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1003.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1003.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:	$160.864971272$
Analytic rank:	$0$
Dimension:	$100$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.0372 q^{2} +11.4506 q^{3} +89.8190 q^{4} +107.836 q^{5} -126.382 q^{6} -170.958 q^{7} -638.158 q^{8} -111.883 q^{9} +O(q^{10})$	\(q-11.0372 q^{2} +11.4506 q^{3} +89.8190 q^{4} +107.836 q^{5} -126.382 q^{6} -170.958 q^{7} -638.158 q^{8} -111.883 q^{9} -1190.20 q^{10} -590.309 q^{11} +1028.48 q^{12} -910.603 q^{13} +1886.89 q^{14} +1234.79 q^{15} +4169.25 q^{16} -289.000 q^{17} +1234.87 q^{18} -26.3629 q^{19} +9685.71 q^{20} -1957.57 q^{21} +6515.34 q^{22} -1007.10 q^{23} -7307.31 q^{24} +8503.57 q^{25} +10050.5 q^{26} -4063.63 q^{27} -15355.2 q^{28} -1798.23 q^{29} -13628.6 q^{30} -7040.59 q^{31} -25595.6 q^{32} -6759.41 q^{33} +3189.74 q^{34} -18435.4 q^{35} -10049.2 q^{36} -2016.62 q^{37} +290.972 q^{38} -10427.0 q^{39} -68816.3 q^{40} +14311.2 q^{41} +21606.0 q^{42} +19090.3 q^{43} -53021.0 q^{44} -12065.0 q^{45} +11115.5 q^{46} +11145.6 q^{47} +47740.5 q^{48} +12419.5 q^{49} -93855.3 q^{50} -3309.23 q^{51} -81789.5 q^{52} -6413.02 q^{53} +44851.0 q^{54} -63656.5 q^{55} +109098. q^{56} -301.872 q^{57} +19847.3 q^{58} +3481.00 q^{59} +110907. q^{60} -24672.6 q^{61} +77708.1 q^{62} +19127.3 q^{63} +149087. q^{64} -98195.7 q^{65} +74604.7 q^{66} +4.05357 q^{67} -25957.7 q^{68} -11531.9 q^{69} +203474. q^{70} -61.4530 q^{71} +71399.1 q^{72} +45600.9 q^{73} +22257.8 q^{74} +97371.2 q^{75} -2367.89 q^{76} +100918. q^{77} +115084. q^{78} -81629.5 q^{79} +449594. q^{80} -19343.6 q^{81} -157956. q^{82} -109902. q^{83} -175827. q^{84} -31164.6 q^{85} -210703. q^{86} -20590.8 q^{87} +376711. q^{88} +31346.3 q^{89} +133164. q^{90} +155675. q^{91} -90456.9 q^{92} -80619.1 q^{93} -123015. q^{94} -2842.87 q^{95} -293086. q^{96} +72889.7 q^{97} -137076. q^{98} +66045.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 25 q^{2} + 63 q^{3} + 1707 q^{4} + 509 q^{5} + 207 q^{6} + 247 q^{7} + 765 q^{8} + 9003 q^{9}+O(q^{10}) $ 100 * q + 25 * q^2 + 63 * q^3 + 1707 * q^4 + 509 * q^5 + 207 * q^6 + 247 * q^7 + 765 * q^8 + 9003 * q^9	\( 100 q + 25 q^{2} + 63 q^{3} + 1707 q^{4} + 509 q^{5} + 207 q^{6} + 247 q^{7} + 765 q^{8} + 9003 q^{9} + 424 q^{11} + 2880 q^{12} + 2426 q^{13} + 1069 q^{14} + 3699 q^{15} + 25895 q^{16} - 28900 q^{17} + 6644 q^{18} + 2224 q^{19} + 11919 q^{20} + 12248 q^{21} + 1160 q^{22} + 4675 q^{23} + 6477 q^{24} + 76925 q^{25} + 26507 q^{26} + 18465 q^{27} + 7371 q^{28} + 13905 q^{29} + 42029 q^{30} + 11503 q^{31} + 31765 q^{32} + 34053 q^{33} - 7225 q^{34} + 26861 q^{35} + 210764 q^{36} - 4418 q^{37} + 55637 q^{38} - 5718 q^{39} + 24116 q^{40} + 50715 q^{41} + 145355 q^{42} + 36979 q^{43} - 6793 q^{44} + 88939 q^{45} + 23917 q^{46} + 162533 q^{47} + 219761 q^{48} + 276061 q^{49} + 204874 q^{50} - 18207 q^{51} + 73665 q^{52} + 144329 q^{53} + 112241 q^{54} + 63002 q^{55} + 234871 q^{56} + 94768 q^{57} + 22318 q^{58} + 348100 q^{59} + 390780 q^{60} - 45447 q^{61} + 146617 q^{62} + 88467 q^{63} + 580433 q^{64} - 49981 q^{65} - 14744 q^{66} + 113930 q^{67} - 493323 q^{68} + 49070 q^{69} + 86899 q^{70} + 138703 q^{71} + 319055 q^{72} + 174214 q^{73} - 139931 q^{74} + 295788 q^{75} + 272539 q^{76} + 642017 q^{77} + 93149 q^{78} - 240788 q^{79} + 582895 q^{80} + 690560 q^{81} + 164633 q^{82} + 324136 q^{83} + 775436 q^{84} - 147101 q^{85} + 113296 q^{86} + 612596 q^{87} - 227510 q^{88} + 348396 q^{89} + 750464 q^{90} - 100399 q^{91} + 453265 q^{92} + 660393 q^{93} + 183864 q^{94} + 341370 q^{95} + 209486 q^{96} + 288603 q^{97} + 1100905 q^{98} + 301794 q^{99}+O(q^{100}) \) 100 * q + 25 * q^2 + 63 * q^3 + 1707 * q^4 + 509 * q^5 + 207 * q^6 + 247 * q^7 + 765 * q^8 + 9003 * q^9 + 424 * q^11 + 2880 * q^12 + 2426 * q^13 + 1069 * q^14 + 3699 * q^15 + 25895 * q^16 - 28900 * q^17 + 6644 * q^18 + 2224 * q^19 + 11919 * q^20 + 12248 * q^21 + 1160 * q^22 + 4675 * q^23 + 6477 * q^24 + 76925 * q^25 + 26507 * q^26 + 18465 * q^27 + 7371 * q^28 + 13905 * q^29 + 42029 * q^30 + 11503 * q^31 + 31765 * q^32 + 34053 * q^33 - 7225 * q^34 + 26861 * q^35 + 210764 * q^36 - 4418 * q^37 + 55637 * q^38 - 5718 * q^39 + 24116 * q^40 + 50715 * q^41 + 145355 * q^42 + 36979 * q^43 - 6793 * q^44 + 88939 * q^45 + 23917 * q^46 + 162533 * q^47 + 219761 * q^48 + 276061 * q^49 + 204874 * q^50 - 18207 * q^51 + 73665 * q^52 + 144329 * q^53 + 112241 * q^54 + 63002 * q^55 + 234871 * q^56 + 94768 * q^57 + 22318 * q^58 + 348100 * q^59 + 390780 * q^60 - 45447 * q^61 + 146617 * q^62 + 88467 * q^63 + 580433 * q^64 - 49981 * q^65 - 14744 * q^66 + 113930 * q^67 - 493323 * q^68 + 49070 * q^69 + 86899 * q^70 + 138703 * q^71 + 319055 * q^72 + 174214 * q^73 - 139931 * q^74 + 295788 * q^75 + 272539 * q^76 + 642017 * q^77 + 93149 * q^78 - 240788 * q^79 + 582895 * q^80 + 690560 * q^81 + 164633 * q^82 + 324136 * q^83 + 775436 * q^84 - 147101 * q^85 + 113296 * q^86 + 612596 * q^87 - 227510 * q^88 + 348396 * q^89 + 750464 * q^90 - 100399 * q^91 + 453265 * q^92 + 660393 * q^93 + 183864 * q^94 + 341370 * q^95 + 209486 * q^96 + 288603 * q^97 + 1100905 * q^98 + 301794 * 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 $

$2$	−11.0372	−1.95111	−0.975557	−	0.219748i	$-0.929477\pi$
$2$	−11.0372	−1.95111	−0.975557	+	0.219748i	$0.929477\pi$
$3$	11.4506	0.734558	0.367279	−	0.930111i	$-0.380289\pi$
$3$	11.4506	0.734558	0.367279	+	0.930111i	$0.380289\pi$
$4$	89.8190	2.80684
$5$	107.836	1.92903	0.964513	−	0.264035i	$-0.0850535\pi$
$5$	107.836	1.92903	0.964513	+	0.264035i	$0.0850535\pi$
$6$	−126.382	−1.43321
$7$	−170.958	−1.31869	−0.659346	−	0.751840i	$-0.729167\pi$
$7$	−170.958	−1.31869	−0.659346	+	0.751840i	$0.729167\pi$
$8$	−638.158	−3.52536
$9$	−111.883	−0.460424
$10$	−1190.20	−3.76375
$11$	−590.309	−1.47095	−0.735475	−	0.677552i	$-0.763041\pi$
$11$	−590.309	−1.47095	−0.735475	+	0.677552i	$0.763041\pi$
$12$	1028.48	2.06179
$13$	−910.603	−1.49441	−0.747207	−	0.664592i	$-0.768606\pi$
$13$	−910.603	−1.49441	−0.747207	+	0.664592i	$0.768606\pi$
$14$	1886.89	2.57292
$15$	1234.79	1.41698
$16$	4169.25	4.07153
$17$	−289.000	−0.242536
$17$	−289.000	−0.242536
$18$	1234.87	0.898340
$19$	−26.3629	−0.0167537	−0.00837683	−	0.999965i	$-0.502666\pi$
$19$	−26.3629	−0.0167537	−0.00837683	+	0.999965i	$0.502666\pi$
$20$	9685.71	5.41448
$21$	−1957.57	−0.968656
$22$	6515.34	2.86999
$23$	−1007.10	−0.396966	−0.198483	−	0.980104i	$-0.563602\pi$
$23$	−1007.10	−0.396966	−0.198483	+	0.980104i	$0.563602\pi$
$24$	−7307.31	−2.58958
$25$	8503.57	2.72114
$26$	10050.5	2.91577
$27$	−4063.63	−1.07277
$28$	−15355.2	−3.70136
$29$	−1798.23	−0.397054	−0.198527	−	0.980095i	$-0.563616\pi$
$29$	−1798.23	−0.397054	−0.198527	+	0.980095i	$0.563616\pi$
$30$	−13628.6	−2.76469
$31$	−7040.59	−1.31584	−0.657922	−	0.753086i	$-0.728564\pi$
$31$	−7040.59	−1.31584	−0.657922	+	0.753086i	$0.728564\pi$
$32$	−25595.6	−4.41866
$33$	−6759.41	−1.08050
$34$	3189.74	0.473215
$35$	−18435.4	−2.54379
$36$	−10049.2	−1.29234
$37$	−2016.62	−0.242169	−0.121085	−	0.992642i	$-0.538637\pi$
$37$	−2016.62	−0.242169	−0.121085	+	0.992642i	$0.538637\pi$
$38$	290.972	0.0326883
$39$	−10427.0	−1.09773
$40$	−68816.3	−6.80051
$41$	14311.2	1.32959	0.664795	−	0.747026i	$-0.268519\pi$
$41$	14311.2	1.32959	0.664795	+	0.747026i	$0.268519\pi$
$42$	21606.0	1.88996
$43$	19090.3	1.57450	0.787248	−	0.616637i	$-0.211505\pi$
$43$	19090.3	1.57450	0.787248	+	0.616637i	$0.211505\pi$
$44$	−53021.0	−4.12873
$45$	−12065.0	−0.888171
$46$	11115.5	0.774527
$47$	11145.6	0.735966	0.367983	−	0.929833i	$-0.380048\pi$
$47$	11145.6	0.735966	0.367983	+	0.929833i	$0.380048\pi$
$48$	47740.5	2.99077
$49$	12419.5	0.738949
$50$	−93855.3	−5.30926
$51$	−3309.23	−0.178157
$52$	−81789.5	−4.19459
$53$	−6413.02	−0.313598	−0.156799	−	0.987631i	$-0.550117\pi$
$53$	−6413.02	−0.313598	−0.156799	+	0.987631i	$0.550117\pi$
$54$	44851.0	2.09309
$55$	−63656.5	−2.83750
$56$	109098.	4.64886
$57$	−301.872	−0.0123065
$58$	19847.3	0.774698
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	110907.	3.97725
$61$	−24672.6	−0.848965	−0.424483	−	0.905436i	$-0.639544\pi$
$61$	−24672.6	−0.848965	−0.424483	+	0.905436i	$0.639544\pi$
$62$	77708.1	2.56736
$63$	19127.3	0.607158
$64$	149087.	4.54977
$65$	−98195.7	−2.88276
$66$	74604.7	2.10817
$67$	4.05357	0.000110319 0	5.51595e−5	−	1.00000i	$-0.499982\pi$
$67$	4.05357	0.000110319 0	5.51595e−5		1.00000i	$0.499982\pi$
$68$	−25957.7	−0.680760
$69$	−11531.9	−0.291595
$70$	203474.	4.96323
$71$	−61.4530	−0.00144676	−0.000723381	−	1.00000i	$-0.500230\pi$
$71$	−61.4530	−0.00144676	−0.000723381		1.00000i	$0.500230\pi$
$72$	71399.1	1.62316
$73$	45600.9	1.00154	0.500768	−	0.865582i	$-0.333051\pi$
$73$	45600.9	1.00154	0.500768	+	0.865582i	$0.333051\pi$
$74$	22257.8	0.472500
$75$	97371.2	1.99884
$76$	−2367.89	−0.0470249
$77$	100918.	1.93973
$78$	115084.	2.14180
$79$	−81629.5	−1.47156	−0.735782	−	0.677218i	$-0.763185\pi$
$79$	−81629.5	−1.47156	−0.735782	+	0.677218i	$0.763185\pi$
$80$	449594.	7.85409
$81$	−19343.6	−0.327585
$82$	−157956.	−2.59418
$83$	−109902.	−1.75109	−0.875545	−	0.483136i	$-0.839498\pi$
$83$	−109902.	−1.75109	−0.875545	+	0.483136i	$0.839498\pi$
$84$	−175827.	−2.71887
$85$	−31164.6	−0.467858
$86$	−210703.	−3.07202
$87$	−20590.8	−0.291659
$88$	376711.	5.18562
$89$	31346.3	0.419480	0.209740	−	0.977757i	$-0.432738\pi$
$89$	31346.3	0.419480	0.209740	+	0.977757i	$0.432738\pi$
$90$	133164.	1.73292
$91$	155675.	1.97067
$92$	−90456.9	−1.11422
$93$	−80619.1	−0.966564
$94$	−123015.	−1.43595
$95$	−2842.87	−0.0323182
$96$	−293086.	−3.24576
$97$	72889.7	0.786569	0.393284	−	0.919417i	$-0.371339\pi$
$97$	72889.7	0.786569	0.393284	+	0.919417i	$0.371339\pi$
$98$	−137076.	−1.44177
$99$	66045.7	0.677261
$100$	763782.	7.63782
$101$	−144533.	−1.40982	−0.704909	−	0.709298i	$-0.749012\pi$
$101$	−144533.	−1.40982	−0.704909	+	0.709298i	$0.749012\pi$
$102$	36524.5	0.347604
$103$	26222.0	0.243541	0.121771	−	0.992558i	$-0.461143\pi$
$103$	26222.0	0.243541	0.121771	+	0.992558i	$0.461143\pi$
$104$	581109.	5.26834
$105$	−211096.	−1.86856
$106$	70781.5	0.611865
$107$	−57212.5	−0.483094	−0.241547	−	0.970389i	$-0.577655\pi$
$107$	−57212.5	−0.483094	−0.241547	+	0.970389i	$0.577655\pi$
$108$	−364992.	−3.01109
$109$	119755.	0.965447	0.482723	−	0.875773i	$-0.339648\pi$
$109$	119755.	0.965447	0.482723	+	0.875773i	$0.339648\pi$
$110$	702587.	5.53629
$111$	−23091.5	−0.177888
$112$	−712764.	−5.36909
$113$	154661.	1.13942	0.569712	−	0.821844i	$-0.307055\pi$
$113$	154661.	1.13942	0.569712	+	0.821844i	$0.307055\pi$
$114$	3331.81	0.0240114
$115$	−108602.	−0.765759
$116$	−161515.	−1.11447
$117$	101881.	0.688065
$118$	−38420.4	−0.254013
$119$	49406.8	0.319830
$120$	−787990.	−4.99537
$121$	187414.	1.16369
$122$	272315.	1.65643
$123$	163873.	0.976661
$124$	−632378.	−3.69337
$125$	580002.	3.32013
$126$	−211111.	−1.18463
$127$	325427.	1.79038	0.895189	−	0.445687i	$-0.147041\pi$
$127$	325427.	1.79038	0.895189	+	0.445687i	$0.147041\pi$
$128$	−826438.	−4.45847
$129$	218596.	1.15656
$130$	1.08380e6	5.62460
$131$	−332581.	−1.69324	−0.846622	−	0.532195i	$-0.821367\pi$
$131$	−332581.	−1.69324	−0.846622	+	0.532195i	$0.821367\pi$
$132$	−607124.	−3.03279
$133$	4506.94	0.0220929
$134$	−44.7399	−0.000215245 0
$135$	−438205.	−2.06939
$136$	184428.	0.855025
$137$	41183.3	0.187465	0.0937325	−	0.995597i	$-0.470120\pi$
$137$	41183.3	0.187465	0.0937325	+	0.995597i	$0.470120\pi$
$138$	127280.	0.568935
$139$	67399.3	0.295882	0.147941	−	0.988996i	$-0.452735\pi$
$139$	67399.3	0.295882	0.147941	+	0.988996i	$0.452735\pi$
$140$	−1.65585e6	−7.14003
$141$	127624.	0.540610
$142$	678.267	0.00282280
$143$	537538.	2.19821
$144$	−466468.	−1.87463
$145$	−193914.	−0.765928
$146$	−503305.	−1.95411
$147$	142211.	0.542801
$148$	−181131.	−0.679732
$149$	223917.	0.826268	0.413134	−	0.910670i	$-0.364434\pi$
$149$	223917.	0.826268	0.413134	+	0.910670i	$0.364434\pi$
$150$	−1.07470e6	−3.89996
$151$	−369666.	−1.31937	−0.659687	−	0.751541i	$-0.729311\pi$
$151$	−369666.	−1.31937	−0.659687	+	0.751541i	$0.729311\pi$
$152$	16823.7	0.0590626
$153$	32334.2	0.111669
$154$	−1.11385e6	−3.78463
$155$	−759228.	−2.53830
$156$	−936541.	−3.08117
$157$	384399.	1.24461	0.622305	−	0.782775i	$-0.286197\pi$
$157$	384399.	1.24461	0.622305	+	0.782775i	$0.286197\pi$
$158$	900958.	2.87119
$159$	−73433.1	−0.230356
$160$	−2.76012e6	−8.52371
$161$	172172.	0.523477
$162$	213498.	0.639155
$163$	−282661.	−0.833291	−0.416645	−	0.909069i	$-0.636794\pi$
$163$	−282661.	−0.833291	−0.416645	+	0.909069i	$0.636794\pi$
$164$	1.28542e6	3.73195
$165$	−728907.	−2.08431
$166$	1.21300e6	3.41658
$167$	596355.	1.65468	0.827340	−	0.561702i	$-0.189853\pi$
$167$	596355.	1.65468	0.827340	+	0.561702i	$0.189853\pi$
$168$	1.24924e6	3.41486
$169$	457905.	1.23327
$170$	343968.	0.912843
$171$	2949.57	0.00771379
$172$	1.71467e6	4.41936
$173$	−308149.	−0.782790	−0.391395	−	0.920223i	$-0.628007\pi$
$173$	−308149.	−0.782790	−0.391395	+	0.920223i	$0.628007\pi$
$174$	227265.	0.569061
$175$	−1.45375e6	−3.58835
$176$	−2.46114e6	−5.98901
$177$	39859.6	0.0956313
$178$	−345974.	−0.818453
$179$	484811.	1.13094	0.565471	−	0.824768i	$-0.308695\pi$
$179$	484811.	1.13094	0.565471	+	0.824768i	$0.308695\pi$
$180$	−1.08367e6	−2.49296
$181$	−465931.	−1.05712	−0.528562	−	0.848895i	$-0.677268\pi$
$181$	−465931.	−1.05712	−0.528562	+	0.848895i	$0.677268\pi$
$182$	−1.71821e6	−3.84500
$183$	−282516.	−0.623614
$184$	642690.	1.39945
$185$	−217464.	−0.467151
$186$	889807.	1.88588
$187$	170599.	0.356758
$188$	1.00108e6	2.06574
$189$	694709.	1.41465
$190$	31377.2	0.0630565
$191$	21464.5	0.0425732	0.0212866	−	0.999773i	$-0.493224\pi$
$191$	21464.5	0.0425732	0.0212866	+	0.999773i	$0.493224\pi$
$192$	1.70714e6	3.34207
$193$	659870.	1.27516	0.637581	−	0.770383i	$-0.279935\pi$
$193$	659870.	1.27516	0.637581	+	0.770383i	$0.279935\pi$
$194$	−804495.	−1.53468
$195$	−1.12440e6	−2.11756
$196$	1.11551e6	2.07411
$197$	−442148.	−0.811712	−0.405856	−	0.913937i	$-0.633027\pi$
$197$	−442148.	−0.811712	−0.405856	+	0.913937i	$0.633027\pi$
$198$	−728957.	−1.32141
$199$	447625.	0.801276	0.400638	−	0.916236i	$-0.368789\pi$
$199$	447625.	0.801276	0.400638	+	0.916236i	$0.368789\pi$
$200$	−5.42662e6	−9.59300
$201$	46.4159	8.10358e−5 0
$202$	1.59523e6	2.75071
$203$	307421.	0.523592
$204$	−297232.	−0.500057
$205$	1.54326e6	2.56481
$206$	−289417.	−0.475177
$207$	112678.	0.182773
$208$	−3.79653e6	−6.08455
$209$	15562.3	0.0246438
$210$	2.32991e6	3.64578
$211$	181592.	0.280795	0.140398	−	0.990095i	$-0.455162\pi$
$211$	181592.	0.280795	0.140398	+	0.990095i	$0.455162\pi$
$212$	−576011.	−0.880220
$213$	−703.675	−0.00106273
$214$	631464.	0.942571
$215$	2.05862e6	3.03724
$216$	2.59324e6	3.78189
$217$	1.20364e6	1.73519
$218$	−1.32176e6	−1.88370
$219$	522159.	0.735686
$220$	−5.71756e6	−7.96442
$221$	263164.	0.362449
$222$	254865.	0.347079
$223$	732974.	0.987021	0.493511	−	0.869740i	$-0.335713\pi$
$223$	732974.	0.987021	0.493511	+	0.869740i	$0.335713\pi$
$224$	4.37576e6	5.82685
$225$	−951406.	−1.25288
$226$	−1.70702e6	−2.22315
$227$	−706661.	−0.910220	−0.455110	−	0.890435i	$-0.650400\pi$
$227$	−706661.	−0.910220	−0.455110	+	0.890435i	$0.650400\pi$
$228$	−27113.8	−0.0345425
$229$	−264858.	−0.333753	−0.166876	−	0.985978i	$-0.553368\pi$
$229$	−264858.	−0.333753	−0.166876	+	0.985978i	$0.553368\pi$
$230$	1.19865e6	1.49408
$231$	1.15557e6	1.42484
$232$	1.14755e6	1.39976
$233$	580362.	0.700341	0.350170	−	0.936686i	$-0.386124\pi$
$233$	580362.	0.700341	0.350170	+	0.936686i	$0.386124\pi$
$234$	−1.12448e6	−1.34249
$235$	1.20189e6	1.41970
$236$	312660.	0.365420
$237$	−934709.	−1.08095
$238$	−545311.	−0.624024
$239$	1.46662e6	1.66082	0.830408	−	0.557155i	$-0.188107\pi$
$239$	1.46662e6	1.66082	0.830408	+	0.557155i	$0.188107\pi$
$240$	5.14813e6	5.76928
$241$	−1.40172e6	−1.55460	−0.777300	−	0.629130i	$-0.783411\pi$
$241$	−1.40172e6	−1.55460	−0.777300	+	0.629130i	$0.783411\pi$
$242$	−2.06852e6	−2.27050
$243$	765967.	0.832136
$244$	−2.21607e6	−2.38291
$245$	1.33927e6	1.42545
$246$	−1.80869e6	−1.90558
$247$	24006.2	0.0250369
$248$	4.49301e6	4.63882
$249$	−1.25844e6	−1.28628
$250$	−6.40158e6	−6.47795
$251$	−1.42425e6	−1.42693	−0.713464	−	0.700692i	$-0.752875\pi$
$251$	−1.42425e6	−1.42693	−0.713464	+	0.700692i	$0.752875\pi$
$252$	1.71799e6	1.70420
$253$	594502.	0.583918
$254$	−3.59179e6	−3.49323
$255$	−356854.	−0.343669
$256$	4.35075e6	4.14920
$257$	−285678.	−0.269801	−0.134901	−	0.990859i	$-0.543071\pi$
$257$	−285678.	−0.269801	−0.134901	+	0.990859i	$0.543071\pi$
$258$	−2.41268e6	−2.25658
$259$	344756.	0.319347
$260$	−8.81984e6	−8.09147
$261$	201191.	0.182814
$262$	3.67075e6	3.30371
$263$	253791.	0.226249	0.113124	−	0.993581i	$-0.463914\pi$
$263$	253791.	0.226249	0.113124	+	0.993581i	$0.463914\pi$
$264$	4.31357e6	3.80914
$265$	−691553.	−0.604938
$266$	−49743.9	−0.0431058
$267$	358935.	0.308132
$268$	364.088	0.000309648 0
$269$	1.16340e6	0.980273	0.490137	−	0.871646i	$-0.336947\pi$
$269$	1.16340e6	0.980273	0.490137	+	0.871646i	$0.336947\pi$
$270$	4.83655e6	4.03762
$271$	212686.	0.175920	0.0879600	−	0.996124i	$-0.471965\pi$
$271$	212686.	0.175920	0.0879600	+	0.996124i	$0.471965\pi$
$272$	−1.20491e6	−0.987491
$273$	1.78257e6	1.44757
$274$	−454547.	−0.365765
$275$	−5.01973e6	−4.00266
$276$	−1.03579e6	−0.818461
$277$	1.77052e6	1.38644	0.693222	−	0.720724i	$-0.256190\pi$
$277$	1.77052e6	1.38644	0.693222	+	0.720724i	$0.256190\pi$
$278$	−743898.	−0.577299
$279$	787723.	0.605847
$280$	1.17647e7	8.96778
$281$	1.27815e6	0.965645	0.482822	−	0.875718i	$-0.339612\pi$
$281$	1.27815e6	0.965645	0.482822	+	0.875718i	$0.339612\pi$
$282$	−1.40860e6	−1.05479
$283$	−1.41902e6	−1.05322	−0.526612	−	0.850106i	$-0.676538\pi$
$283$	−1.41902e6	−1.05322	−0.526612	+	0.850106i	$0.676538\pi$
$284$	−5519.65	−0.00406083
$285$	−32552.6	−0.0237396
$286$	−5.93289e6	−4.28895
$287$	−2.44662e6	−1.75332
$288$	2.86372e6	2.03446
$289$	83521.0	0.0588235
$290$	2.14026e6	1.49441
$291$	834632.	0.577780
$292$	4.09583e6	2.81115
$293$	98644.3	0.0671278	0.0335639	−	0.999437i	$-0.489314\pi$
$293$	98644.3	0.0671278	0.0335639	+	0.999437i	$0.489314\pi$
$294$	−1.56961e6	−1.05907
$295$	375377.	0.251138
$296$	1.28692e6	0.853734
$297$	2.39880e6	1.57799
$298$	−2.47141e6	−1.61214
$299$	917070.	0.593232
$300$	8.74578e6	5.61042
$301$	−3.26363e6	−2.07628
$302$	4.08007e6	2.57425
$303$	−1.65499e6	−1.03559
$304$	−109913.	−0.0682130
$305$	−2.66059e6	−1.63768
$306$	−356878.	−0.217880
$307$	−36970.5	−0.0223877	−0.0111938	−	0.999937i	$-0.503563\pi$
$307$	−36970.5	−0.0223877	−0.0111938	+	0.999937i	$0.503563\pi$
$308$	9.06434e6	5.44452
$309$	300258.	0.178895
$310$	8.37972e6	4.95251
$311$	554272.	0.324954	0.162477	−	0.986712i	$-0.448052\pi$
$311$	554272.	0.324954	0.162477	+	0.986712i	$0.448052\pi$
$312$	6.65406e6	3.86990
$313$	−14282.1	−0.00824007	−0.00412004	−	0.999992i	$-0.501311\pi$
$313$	−14282.1	−0.00824007	−0.00412004	+	0.999992i	$0.501311\pi$
$314$	−4.24267e6	−2.42837
$315$	2.06261e6	1.17122
$316$	−7.33188e6	−4.13045
$317$	700685.	0.391629	0.195815	−	0.980641i	$-0.437265\pi$
$317$	700685.	0.391629	0.195815	+	0.980641i	$0.437265\pi$
$318$	810493.	0.449450
$319$	1.06151e6	0.584047
$320$	1.60769e7	8.77663
$321$	−655119.	−0.354861
$322$	−1.90029e6	−1.02136
$323$	7618.88	0.00406336
$324$	−1.73742e6	−0.919480
$325$	−7.74338e6	−4.06651
$326$	3.11977e6	1.62584
$327$	1.37127e6	0.709177
$328$	−9.13283e6	−4.68728
$329$	−1.90542e6	−0.970512
$330$	8.04506e6	4.06672
$331$	1.25674e6	0.630486	0.315243	−	0.949011i	$-0.397914\pi$
$331$	1.25674e6	0.630486	0.315243	+	0.949011i	$0.397914\pi$
$332$	−9.87125e6	−4.91504
$333$	225626.	0.111501
$334$	−6.58207e6	−3.22847
$335$	437.120	0.000212808 0
$336$	−8.16160e6	−3.94391
$337$	−2.60475e6	−1.24937	−0.624685	−	0.780876i	$-0.714773\pi$
$337$	−2.60475e6	−1.24937	−0.624685	+	0.780876i	$0.714773\pi$
$338$	−5.05398e6	−2.40625
$339$	1.77097e6	0.836974
$340$	−2.79917e6	−1.31320
$341$	4.15612e6	1.93554
$342$	−32554.8	−0.0150505
$343$	750074.	0.344246
$344$	−1.21826e7	−5.55066
$345$	−1.24356e6	−0.562494
$346$	3.40109e6	1.52731
$347$	2.66754e6	1.18929	0.594645	−	0.803988i	$-0.297293\pi$
$347$	2.66754e6	1.18929	0.594645	+	0.803988i	$0.297293\pi$
$348$	−1.84945e6	−0.818643
$349$	−1.09602e6	−0.481678	−0.240839	−	0.970565i	$-0.577423\pi$
$349$	−1.09602e6	−0.481678	−0.240839	+	0.970565i	$0.577423\pi$
$350$	1.60453e7	7.00127
$351$	3.70036e6	1.60316
$352$	1.51093e7	6.49962
$353$	1.53507e6	0.655679	0.327839	−	0.944733i	$-0.393680\pi$
$353$	1.53507e6	0.655679	0.327839	+	0.944733i	$0.393680\pi$
$354$	−439937.	−0.186588
$355$	−6626.83	−0.00279084
$356$	2.81549e6	1.17741
$357$	565738.	0.234934
$358$	−5.35094e6	−2.20660
$359$	241056.	0.0987147	0.0493573	−	0.998781i	$-0.484283\pi$
$359$	241056.	0.0987147	0.0493573	+	0.998781i	$0.484283\pi$
$360$	7.69938e6	3.13112
$361$	−2.47540e6	−0.999719
$362$	5.14256e6	2.06257
$363$	2.14601e6	0.854801
$364$	1.39825e7	5.53137
$365$	4.91741e6	1.93199
$366$	3.11818e6	1.21674
$367$	44546.1	0.0172641	0.00863207	−	0.999963i	$-0.497252\pi$
$367$	44546.1	0.0172641	0.00863207	+	0.999963i	$0.497252\pi$
$368$	−4.19885e6	−1.61626
$369$	−1.60119e6	−0.612176
$370$	2.40018e6	0.911465
$371$	1.09635e6	0.413539
$372$	−7.24113e6	−2.71300
$373$	−1.93246e6	−0.719180	−0.359590	−	0.933110i	$-0.617083\pi$
$373$	−1.93246e6	−0.719180	−0.359590	+	0.933110i	$0.617083\pi$
$374$	−1.88293e6	−0.696075
$375$	6.64139e6	2.43883
$376$	−7.11263e6	−2.59454
$377$	1.63747e6	0.593363
$378$	−7.66762e6	−2.76014
$379$	−3.25462e6	−1.16386	−0.581932	−	0.813237i	$-0.697703\pi$
$379$	−3.25462e6	−1.16386	−0.581932	+	0.813237i	$0.697703\pi$
$380$	−255344.	−0.0907122
$381$	3.72635e6	1.31514
$382$	−236907.	−0.0830652
$383$	3.39642e6	1.18311	0.591554	−	0.806265i	$-0.298514\pi$
$383$	3.39642e6	1.18311	0.591554	+	0.806265i	$0.298514\pi$
$384$	−9.46324e6	−3.27500
$385$	1.08826e7	3.74179
$386$	−7.28310e6	−2.48799
$387$	−2.13588e6	−0.724936
$388$	6.54688e6	2.20778
$389$	5.21340e6	1.74681	0.873407	−	0.486991i	$-0.161905\pi$
$389$	5.21340e6	1.74681	0.873407	+	0.486991i	$0.161905\pi$
$390$	1.24102e7	4.13159
$391$	291052.	0.0962785
$392$	−7.92561e6	−2.60506
$393$	−3.80826e6	−1.24379
$394$	4.88006e6	1.58374
$395$	−8.80258e6	−2.83869
$396$	5.93215e6	1.90097
$397$	−1.80275e6	−0.574064	−0.287032	−	0.957921i	$-0.592669\pi$
$397$	−1.80275e6	−0.574064	−0.287032	+	0.957921i	$0.592669\pi$
$398$	−4.94052e6	−1.56338
$399$	51607.3	0.0162285
$400$	3.54535e7	11.0792
$401$	1.38359e6	0.429680	0.214840	−	0.976649i	$-0.431077\pi$
$401$	1.38359e6	0.429680	0.214840	+	0.976649i	$0.431077\pi$
$402$	−512.300	−0.000158110 0
$403$	6.41118e6	1.96642
$404$	−1.29818e7	−3.95714
$405$	−2.08593e6	−0.631920
$406$	−3.39306e6	−1.02159
$407$	1.19043e6	0.356219
$408$	2.11181e6	0.628065
$409$	−3.89983e6	−1.15276	−0.576378	−	0.817183i	$-0.695534\pi$
$409$	−3.89983e6	−1.15276	−0.576378	+	0.817183i	$0.695534\pi$
$410$	−1.70333e7	−5.00424
$411$	471575.	0.137704
$412$	2.35523e6	0.683583
$413$	−595104.	−0.171679
$414$	−1.24364e6	−0.356611
$415$	−1.18513e7	−3.37790
$416$	2.33074e7	6.60330
$417$	771765.	0.217343
$418$	−171763.	−0.0480828
$419$	6.43896e6	1.79176	0.895882	−	0.444292i	$-0.146545\pi$
$419$	6.43896e6	1.79176	0.895882	+	0.444292i	$0.146545\pi$
$420$	−1.89605e7	−5.24476
$421$	−1.48152e6	−0.407381	−0.203691	−	0.979035i	$-0.565294\pi$
$421$	−1.48152e6	−0.407381	−0.203691	+	0.979035i	$0.565294\pi$
$422$	−2.00426e6	−0.547864
$423$	−1.24700e6	−0.338857
$424$	4.09252e6	1.10554
$425$	−2.45753e6	−0.659974
$426$	7766.58	0.00207351
$427$	4.21797e6	1.11952
$428$	−5.13877e6	−1.35597
$429$	6.15514e6	1.61471
$430$	−2.27213e7	−5.92601
$431$	−2.40475e6	−0.623559	−0.311779	−	0.950155i	$-0.600925\pi$
$431$	−2.40475e6	−0.623559	−0.311779	+	0.950155i	$0.600925\pi$
$432$	−1.69423e7	−4.36780
$433$	2.29670e6	0.588688	0.294344	−	0.955699i	$-0.404899\pi$
$433$	2.29670e6	0.588688	0.294344	+	0.955699i	$0.404899\pi$
$434$	−1.32848e7	−3.38556
$435$	−2.22043e6	−0.562619
$436$	1.07563e7	2.70986
$437$	26550.1	0.00665064
$438$	−5.76315e6	−1.43541
$439$	−3.83179e6	−0.948944	−0.474472	−	0.880271i	$-0.657361\pi$
$439$	−3.83179e6	−0.948944	−0.474472	+	0.880271i	$0.657361\pi$
$440$	4.06229e7	10.0032
$441$	−1.38953e6	−0.340230
$442$	−2.90459e6	−0.707178
$443$	4.44886e6	1.07706	0.538529	−	0.842607i	$-0.318980\pi$
$443$	4.44886e6	1.07706	0.538529	+	0.842607i	$0.318980\pi$
$444$	−2.07406e6	−0.499303
$445$	3.38025e6	0.809188
$446$	−8.08996e6	−1.92579
$447$	2.56399e6	0.606942
$448$	−2.54876e7	−5.99975
$449$	2.31639e6	0.542245	0.271123	−	0.962545i	$-0.412605\pi$
$449$	2.31639e6	0.542245	0.271123	+	0.962545i	$0.412605\pi$
$450$	1.05008e7	2.44451
$451$	−8.44806e6	−1.95576
$452$	1.38915e7	3.19819
$453$	−4.23291e6	−0.969156
$454$	7.79953e6	1.77594
$455$	1.67873e7	3.80148
$456$	192642.	0.0433849
$457$	1.91964e6	0.429962	0.214981	−	0.976618i	$-0.431031\pi$
$457$	1.91964e6	0.429962	0.214981	+	0.976618i	$0.431031\pi$
$458$	2.92328e6	0.651189
$459$	1.17439e6	0.260184
$460$	−9.75449e6	−2.14936
$461$	2.99680e6	0.656757	0.328379	−	0.944546i	$-0.393498\pi$
$461$	2.99680e6	0.656757	0.328379	+	0.944546i	$0.393498\pi$
$462$	−1.27542e7	−2.78003
$463$	−120798.	−0.0261883	−0.0130941	−	0.999914i	$-0.504168\pi$
$463$	−120798.	−0.0261883	−0.0130941	+	0.999914i	$0.504168\pi$
$464$	−7.49726e6	−1.61662
$465$	−8.69363e6	−1.86453
$466$	−6.40556e6	−1.36644
$467$	−1.22233e6	−0.259355	−0.129677	−	0.991556i	$-0.541394\pi$
$467$	−1.22233e6	−0.259355	−0.129677	+	0.991556i	$0.541394\pi$
$468$	9.15086e6	1.93129
$469$	−692.989	−0.000145477 0
$470$	−1.32655e7	−2.76999
$471$	4.40161e6	0.914238
$472$	−2.22143e6	−0.458962
$473$	−1.12692e7	−2.31600
$474$	1.03165e7	2.10906
$475$	−224179.	−0.0455891
$476$	4.43767e6	0.897712
$477$	717509.	0.144388
$478$	−1.61873e7	−3.24044
$479$	−2.91933e6	−0.581359	−0.290680	−	0.956820i	$-0.593881\pi$
$479$	−2.91933e6	−0.581359	−0.290680	+	0.956820i	$0.593881\pi$
$480$	−3.16051e7	−6.26116
$481$	1.83634e6	0.361901
$482$	1.54710e7	3.03320
$483$	1.97147e6	0.384524
$484$	1.68333e7	3.26631
$485$	7.86012e6	1.51731
$486$	−8.45411e6	−1.62359
$487$	5.39149e6	1.03012	0.515058	−	0.857155i	$-0.327770\pi$
$487$	5.39149e6	1.03012	0.515058	+	0.857155i	$0.327770\pi$
$488$	1.57450e7	2.99291
$489$	−3.23664e6	−0.612100
$490$	−1.47817e7	−2.78122
$491$	7.52162e6	1.40802	0.704008	−	0.710192i	$-0.251392\pi$
$491$	7.52162e6	1.40802	0.704008	+	0.710192i	$0.251392\pi$
$492$	1.47189e7	2.74133
$493$	519688.	0.0962998
$494$	−264960.	−0.0488498
$495$	7.12209e6	1.30645
$496$	−2.93539e7	−5.35750
$497$	10505.9	0.00190783
$498$	1.38896e7	2.50967
$499$	−6.35028e6	−1.14167	−0.570836	−	0.821064i	$-0.693381\pi$
$499$	−6.35028e6	−1.14167	−0.570836	+	0.821064i	$0.693381\pi$
$500$	5.20952e7	9.31908
$501$	6.82864e6	1.21546
$502$	1.57197e7	2.78410
$503$	−1.65226e6	−0.291177	−0.145589	−	0.989345i	$-0.546508\pi$
$503$	−1.65226e6	−0.291177	−0.145589	+	0.989345i	$0.546508\pi$
$504$	−1.22062e7	−2.14045
$505$	−1.55858e7	−2.71958
$506$	−6.56161e6	−1.13929
$507$	5.24330e6	0.905910
$508$	2.92296e7	5.02531
$509$	7.65764e6	1.31009	0.655044	−	0.755590i	$-0.272650\pi$
$509$	7.65764e6	1.31009	0.655044	+	0.755590i	$0.272650\pi$
$510$	3.93865e6	0.670536
$511$	−7.79582e6	−1.32072
$512$	−2.15739e7	−3.63710
$513$	107129.	0.0179728
$514$	3.15307e6	0.526413
$515$	2.82767e6	0.469798
$516$	1.96341e7	3.24628
$517$	−6.57933e6	−1.08257
$518$	−3.80513e6	−0.623082
$519$	−3.52850e6	−0.575005
$520$	6.26643e7	10.1628
$521$	−8.82026e6	−1.42360	−0.711799	−	0.702384i	$-0.752119\pi$
$521$	−8.82026e6	−1.42360	−0.711799	+	0.702384i	$0.752119\pi$
$522$	−2.22058e6	−0.356690
$523$	−6.32146e6	−1.01056	−0.505281	−	0.862955i	$-0.668611\pi$
$523$	−6.32146e6	−1.01056	−0.505281	+	0.862955i	$0.668611\pi$
$524$	−2.98721e7	−4.75267
$525$	−1.66463e7	−2.63585
$526$	−2.80113e6	−0.441437
$527$	2.03473e6	0.319139
$528$	−2.81816e7	−4.39928
$529$	−5.42209e6	−0.842418
$530$	7.63279e6	1.18030
$531$	−389465.	−0.0599422
$532$	404809.	0.0620113
$533$	−1.30319e7	−1.98696
$534$	−3.96162e6	−0.601201
$535$	−6.16956e6	−0.931901
$536$	−2586.82	−0.000388914 0
$537$	5.55139e6	0.830742
$538$	−1.28406e7	−1.91262
$539$	−7.33136e6	−1.08696
$540$	−3.93592e7	−5.80847
$541$	1.05261e7	1.54623	0.773115	−	0.634266i	$-0.218698\pi$
$541$	1.05261e7	1.54623	0.773115	+	0.634266i	$0.218698\pi$
$542$	−2.34745e6	−0.343240
$543$	−5.33521e6	−0.776518
$544$	7.39713e6	1.07168
$545$	1.29139e7	1.86237
$546$	−1.96745e7	−2.82438
$547$	4.61354e6	0.659273	0.329637	−	0.944108i	$-0.393074\pi$
$547$	4.61354e6	0.659273	0.329637	+	0.944108i	$0.393074\pi$
$548$	3.69905e6	0.526185
$549$	2.76045e6	0.390884
$550$	5.54036e7	7.80965
$551$	47406.6	0.00665211
$552$	7.35920e6	1.02798
$553$	1.39552e7	1.94054
$554$	−1.95416e7	−2.70511
$555$	−2.49010e6	−0.343150
$556$	6.05374e6	0.830495
$557$	1.24592e7	1.70158	0.850791	−	0.525504i	$-0.176123\pi$
$557$	1.24592e7	1.70158	0.850791	+	0.525504i	$0.176123\pi$
$558$	−8.69423e6	−1.18208
$559$	−1.73837e7	−2.35295
$560$	−7.68615e7	−10.3571
$561$	1.95347e6	0.262059
$562$	−1.41072e7	−1.88408
$563$	−4.81579e6	−0.640319	−0.320160	−	0.947364i	$-0.603737\pi$
$563$	−4.81579e6	−0.640319	−0.320160	+	0.947364i	$0.603737\pi$
$564$	1.14630e7	1.51741
$565$	1.66780e7	2.19798
$566$	1.56619e7	2.05496
$567$	3.30693e6	0.431984
$568$	39216.7	0.00510035
$569$	−7.86304e6	−1.01815	−0.509073	−	0.860723i	$-0.670012\pi$
$569$	−7.86304e6	−1.01815	−0.509073	+	0.860723i	$0.670012\pi$
$570$	359289.	0.0463187
$571$	−7.49642e6	−0.962196	−0.481098	−	0.876667i	$-0.659762\pi$
$571$	−7.49642e6	−0.962196	−0.481098	+	0.876667i	$0.659762\pi$
$572$	4.82811e7	6.17003
$573$	245782.	0.0312725
$574$	2.70037e7	3.42093
$575$	−8.56396e6	−1.08020
$576$	−1.66803e7	−2.09483
$577$	2.38318e6	0.298001	0.149001	−	0.988837i	$-0.452394\pi$
$577$	2.38318e6	0.298001	0.149001	+	0.988837i	$0.452394\pi$
$578$	−921835.	−0.114771
$579$	7.55593e6	0.936681
$580$	−1.74171e7	−2.14984
$581$	1.87885e7	2.30915
$582$	−9.21198e6	−1.12732
$583$	3.78566e6	0.461286
$584$	−2.91006e7	−3.53077
$585$	1.09864e7	1.32729
$586$	−1.08875e6	−0.130974
$587$	−7.67345e6	−0.919170	−0.459585	−	0.888134i	$-0.652002\pi$
$587$	−7.67345e6	−0.919170	−0.459585	+	0.888134i	$0.652002\pi$
$588$	1.27733e7	1.52356
$589$	185610.	0.0220452
$590$	−4.14309e6	−0.489998
$591$	−5.06287e6	−0.596250
$592$	−8.40778e6	−0.986000
$593$	1.26514e7	1.47741	0.738706	−	0.674028i	$-0.235437\pi$
$593$	1.26514e7	1.47741	0.738706	+	0.674028i	$0.235437\pi$
$594$	−2.64760e7	−3.07883
$595$	5.32782e6	0.616960
$596$	2.01120e7	2.31920
$597$	5.12559e6	0.588584
$598$	−1.01219e7	−1.15746
$599$	2.80656e6	0.319600	0.159800	−	0.987149i	$-0.448915\pi$
$599$	2.80656e6	0.319600	0.159800	+	0.987149i	$0.448915\pi$
$600$	−6.21382e7	−7.04661
$601$	−9.55936e6	−1.07955	−0.539775	−	0.841809i	$-0.681491\pi$
$601$	−9.55936e6	−1.07955	−0.539775	+	0.841809i	$0.681491\pi$
$602$	3.60212e7	4.05105
$603$	−453.526	−5.07936e−5 0
$604$	−3.32031e7	−3.70327
$605$	2.02099e7	2.24480
$606$	1.82664e7	2.02056
$607$	5.00732e6	0.551611	0.275806	−	0.961213i	$-0.411055\pi$
$607$	5.00732e6	0.551611	0.275806	+	0.961213i	$0.411055\pi$
$608$	674775.	0.0740286
$609$	3.52016e6	0.384609
$610$	2.93653e7	3.19529
$611$	−1.01492e7	−1.09984
$612$	2.90423e6	0.313438
$613$	4.74142e6	0.509633	0.254817	−	0.966989i	$-0.417985\pi$
$613$	4.74142e6	0.509633	0.254817	+	0.966989i	$0.417985\pi$
$614$	408049.	0.0436809
$615$	1.76713e7	1.88400
$616$	−6.44015e7	−6.83824
$617$	854386.	0.0903527	0.0451763	−	0.998979i	$-0.485615\pi$
$617$	854386.	0.0903527	0.0451763	+	0.998979i	$0.485615\pi$
$618$	−3.31400e6	−0.349045
$619$	−6.16916e6	−0.647142	−0.323571	−	0.946204i	$-0.604883\pi$
$619$	−6.16916e6	−0.647142	−0.323571	+	0.946204i	$0.604883\pi$
$620$	−6.81931e7	−7.12461
$621$	4.09249e6	0.425852
$622$	−6.11759e6	−0.634022
$623$	−5.35889e6	−0.553165
$624$	−4.34726e7	−4.46945
$625$	3.59714e7	3.68347
$626$	157634.	0.0160773
$627$	178198.	0.0181023
$628$	3.45263e7	3.49342
$629$	582803.	0.0587347
$630$	−2.27653e7	−2.28519
$631$	−1.14313e7	−1.14294	−0.571469	−	0.820624i	$-0.693626\pi$
$631$	−1.14313e7	−1.14294	−0.571469	+	0.820624i	$0.693626\pi$
$632$	5.20925e7	5.18779
$633$	2.07934e6	0.206261
$634$	−7.73358e6	−0.764113
$635$	3.50927e7	3.45368
$636$	−6.59569e6	−0.646572
$637$	−1.13093e7	−1.10430
$638$	−1.17161e7	−1.13954
$639$	6875.55	0.000666125 0
$640$	−8.91197e7	−8.60050
$641$	−2.05453e7	−1.97500	−0.987502	−	0.157606i	$-0.949623\pi$
$641$	−2.05453e7	−1.97500	−0.987502	+	0.157606i	$0.949623\pi$
$642$	7.23066e6	0.692373
$643$	−9.74778e6	−0.929776	−0.464888	−	0.885369i	$-0.653905\pi$
$643$	−9.74778e6	−0.929776	−0.464888	+	0.885369i	$0.653905\pi$
$644$	1.54643e7	1.46932
$645$	2.35725e7	2.23103
$646$	−84090.9	−0.00792807
$647$	−1.83506e7	−1.72341	−0.861706	−	0.507409i	$-0.830604\pi$
$647$	−1.83506e7	−1.72341	−0.861706	+	0.507409i	$0.830604\pi$
$648$	1.23442e7	1.15485
$649$	−2.05487e6	−0.191501
$650$	8.54649e7	7.93423
$651$	1.37825e7	1.27460
$652$	−2.53883e7	−2.33892
$653$	−3.61684e6	−0.331930	−0.165965	−	0.986132i	$-0.553074\pi$
$653$	−3.61684e6	−0.331930	−0.165965	+	0.986132i	$0.553074\pi$
$654$	−1.51350e7	−1.38368
$655$	−3.58642e7	−3.26631
$656$	5.96671e7	5.41346
$657$	−5.10197e6	−0.461131
$658$	2.10304e7	1.89358
$659$	2.79325e6	0.250551	0.125276	−	0.992122i	$-0.460018\pi$
$659$	2.79325e6	0.250551	0.125276	+	0.992122i	$0.460018\pi$
$660$	−6.54697e7	−5.85033
$661$	1.52583e7	1.35832	0.679159	−	0.733991i	$-0.262345\pi$
$661$	1.52583e7	1.35832	0.679159	+	0.733991i	$0.262345\pi$
$662$	−1.38708e7	−1.23015
$663$	3.01340e6	0.266240
$664$	7.01346e7	6.17322
$665$	486010.	0.0426178
$666$	−2.49027e6	−0.217551
$667$	1.81100e6	0.157617
$668$	5.35640e7	4.64443
$669$	8.39301e6	0.725024
$670$	−4824.57	−0.000415213 0
$671$	1.45645e7	1.24879
$672$	5.01052e7	4.28016
$673$	−1.43988e7	−1.22543	−0.612714	−	0.790305i	$-0.709922\pi$
$673$	−1.43988e7	−1.22543	−0.612714	+	0.790305i	$0.709922\pi$
$674$	2.87491e7	2.43766
$675$	−3.45554e7	−2.91915
$676$	4.11286e7	3.46160
$677$	−4.74865e6	−0.398197	−0.199099	−	0.979979i	$-0.563801\pi$
$677$	−4.74865e6	−0.398197	−0.199099	+	0.979979i	$0.563801\pi$
$678$	−1.95465e7	−1.63303
$679$	−1.24610e7	−1.03724
$680$	1.98879e7	1.64937
$681$	−8.09171e6	−0.668609
$682$	−4.58718e7	−3.77646
$683$	1.13681e7	0.932469	0.466234	−	0.884661i	$-0.345610\pi$
$683$	1.13681e7	0.932469	0.466234	+	0.884661i	$0.345610\pi$
$684$	264927.	0.0216514
$685$	4.44104e6	0.361625
$686$	−8.27869e6	−0.671663
$687$	−3.03279e6	−0.245161
$688$	7.95921e7	6.41060
$689$	5.83972e6	0.468645
$690$	1.37253e7	1.09749
$691$	7.89743e6	0.629203	0.314602	−	0.949224i	$-0.398129\pi$
$691$	7.89743e6	0.629203	0.314602	+	0.949224i	$0.398129\pi$
$692$	−2.76776e7	−2.19717
$693$	−1.12910e7	−0.893099
$694$	−2.94421e7	−2.32044
$695$	7.26806e6	0.570764
$696$	1.31402e7	1.02820
$697$	−4.13595e6	−0.322473
$698$	1.20970e7	0.939808
$699$	6.64551e6	0.514441
$700$	−1.30574e8	−10.0719
$701$	1.27877e7	0.982871	0.491436	−	0.870914i	$-0.336472\pi$
$701$	1.27877e7	0.982871	0.491436	+	0.870914i	$0.336472\pi$
$702$	−4.08415e7	−3.12794
$703$	53163.9	0.00405722
$704$	−8.80074e7	−6.69249
$705$	1.37624e7	1.04285
$706$	−1.69428e7	−1.27930
$707$	2.47090e7	1.85912
$708$	3.58015e6	0.268422
$709$	1.12172e6	0.0838050	0.0419025	−	0.999122i	$-0.486658\pi$
$709$	1.12172e6	0.0838050	0.0419025	+	0.999122i	$0.486658\pi$
$710$	73141.5	0.00544525
$711$	9.13296e6	0.677544
$712$	−2.00039e7	−1.47882
$713$	7.09059e6	0.522346
$714$	−6.24415e6	−0.458382
$715$	5.79658e7	4.24040
$716$	4.35453e7	3.17438
$717$	1.67937e7	1.21997
$718$	−2.66057e6	−0.192604
$719$	1.85760e7	1.34007	0.670037	−	0.742327i	$-0.266278\pi$
$719$	1.85760e7	1.34007	0.670037	+	0.742327i	$0.266278\pi$
$720$	−5.03020e7	−3.61621
$721$	−4.48285e6	−0.321156
$722$	2.73214e7	1.95057
$723$	−1.60506e7	−1.14194
$724$	−4.18495e7	−2.96718
$725$	−1.52914e7	−1.08044
$726$	−2.36858e7	−1.66781
$727$	−1.89859e7	−1.33228	−0.666141	−	0.745826i	$-0.732055\pi$
$727$	−1.89859e7	−1.33228	−0.666141	+	0.745826i	$0.732055\pi$
$728$	−9.93450e7	−6.94732
$729$	1.34713e7	0.938837
$730$	−5.42743e7	−3.76953
$731$	−5.51710e6	−0.381871
$732$	−2.53753e7	−1.75039
$733$	−2.70292e6	−0.185812	−0.0929058	−	0.995675i	$-0.529616\pi$
$733$	−2.70292e6	−0.185812	−0.0929058	+	0.995675i	$0.529616\pi$
$734$	−491663.	−0.0336843
$735$	1.53355e7	1.04708
$736$	2.57774e7	1.75406
$737$	−2392.86	−0.000162274 0
$738$	1.76726e7	1.19442
$739$	1.96388e7	1.32283	0.661416	−	0.750019i	$-0.269956\pi$
$739$	1.96388e7	1.32283	0.661416	+	0.750019i	$0.269956\pi$
$740$	−1.95324e7	−1.31122
$741$	274886.	0.0183910
$742$	−1.21006e7	−0.806861
$743$	5.02285e6	0.333794	0.166897	−	0.985974i	$-0.446625\pi$
$743$	5.02285e6	0.333794	0.166897	+	0.985974i	$0.446625\pi$
$744$	5.14477e7	3.40748
$745$	2.41462e7	1.59389
$746$	2.13288e7	1.40320
$747$	1.22961e7	0.806245
$748$	1.53231e7	1.00136
$749$	9.78092e6	0.637052
$750$	−7.33021e7	−4.75843
$751$	−2.64419e7	−1.71077	−0.855387	−	0.517989i	$-0.826681\pi$
$751$	−2.64419e7	−1.71077	−0.855387	+	0.517989i	$0.826681\pi$
$752$	4.64686e7	2.99651
$753$	−1.63086e7	−1.04816
$754$	−1.80731e7	−1.15772
$755$	−3.98633e7	−2.54511
$756$	6.23981e7	3.97070
$757$	−7.07076e6	−0.448463	−0.224231	−	0.974536i	$-0.571987\pi$
$757$	−7.07076e6	−0.448463	−0.224231	+	0.974536i	$0.571987\pi$
$758$	3.59218e7	2.27083
$759$	6.80742e6	0.428921
$760$	1.81420e6	0.113933
$761$	2.09660e7	1.31236	0.656181	−	0.754603i	$-0.272171\pi$
$761$	2.09660e7	1.31236	0.656181	+	0.754603i	$0.272171\pi$
$762$	−4.11283e7	−2.56598
$763$	−2.04731e7	−1.27313
$764$	1.92792e6	0.119496
$765$	3.48679e6	0.215413
$766$	−3.74869e7	−2.30838
$767$	−3.16981e6	−0.194556
$768$	4.98188e7	3.04783
$769$	1.16870e7	0.712666	0.356333	−	0.934359i	$-0.384027\pi$
$769$	1.16870e7	0.712666	0.356333	+	0.934359i	$0.384027\pi$
$770$	−1.20113e8	−7.30066
$771$	−3.27119e6	−0.198185
$772$	5.92689e7	3.57918
$773$	−1.15685e7	−0.696349	−0.348175	−	0.937430i	$-0.613198\pi$
$773$	−1.15685e7	−0.696349	−0.348175	+	0.937430i	$0.613198\pi$
$774$	2.35741e7	1.41443
$775$	−5.98701e7	−3.58060
$776$	−4.65151e7	−2.77294
$777$	3.94768e6	0.234579
$778$	−5.75411e7	−3.40823
$779$	−377286.	−0.0222755
$780$	−1.00993e8	−5.94365
$781$	36276.3	0.00212811
$782$	−3.21239e6	−0.187850
$783$	7.30734e6	0.425947
$784$	5.17800e7	3.00865
$785$	4.14520e7	2.40088
$786$	4.20324e7	2.42677
$787$	−2.55491e7	−1.47041	−0.735204	−	0.677845i	$-0.762914\pi$
$787$	−2.55491e7	−1.47041	−0.735204	+	0.677845i	$0.762914\pi$
$788$	−3.97133e7	−2.27835
$789$	2.90606e6	0.166193
$790$	9.71556e7	5.53860
$791$	−2.64405e7	−1.50255
$792$	−4.21476e7	−2.38759
$793$	2.24669e7	1.26871
$794$	1.98973e7	1.12006
$795$	−7.91872e6	−0.444362
$796$	4.02053e7	2.24906
$797$	−1.63519e7	−0.911848	−0.455924	−	0.890019i	$-0.650691\pi$
$797$	−1.63519e7	−0.911848	−0.455924	+	0.890019i	$0.650691\pi$
$798$	−569598.	−0.0316637
$799$	−3.22107e6	−0.178498
$800$	−2.17654e8	−12.0238
$801$	−3.50712e6	−0.193139
$802$	−1.52709e7	−0.838354
$803$	−2.69186e7	−1.47321
$804$	4169.03	0.000227455 0
$805$	1.85663e7	1.00980
$806$	−7.07613e7	−3.83670
$807$	1.33216e7	0.720068
$808$	9.22348e7	4.97011
$809$	−1.85669e7	−0.997399	−0.498699	−	0.866775i	$-0.666189\pi$
$809$	−1.85669e7	−0.997399	−0.498699	+	0.866775i	$0.666189\pi$
$810$	2.30227e7	1.23295
$811$	3.02246e7	1.61365	0.806823	−	0.590794i	$-0.201185\pi$
$811$	3.02246e7	1.61365	0.806823	+	0.590794i	$0.201185\pi$
$812$	2.76122e7	1.46964
$813$	2.43539e6	0.129224
$814$	−1.31390e7	−0.695024
$815$	−3.04810e7	−1.60744
$816$	−1.37970e7	−0.725369
$817$	−503276.	−0.0263786
$818$	4.30431e7	2.24916
$819$	−1.74174e7	−0.907345
$820$	1.38614e8	7.19903
$821$	1.28010e7	0.662806	0.331403	−	0.943489i	$-0.392478\pi$
$821$	1.28010e7	0.662806	0.331403	+	0.943489i	$0.392478\pi$
$822$	−5.20485e6	−0.268676
$823$	−2.48797e7	−1.28040	−0.640199	−	0.768209i	$-0.721148\pi$
$823$	−2.48797e7	−1.28040	−0.640199	+	0.768209i	$0.721148\pi$
$824$	−1.67338e7	−0.858570
$825$	−5.74791e7	−2.94019
$826$	6.56826e6	0.334965
$827$	8.59877e6	0.437192	0.218596	−	0.975815i	$-0.429852\pi$
$827$	8.59877e6	0.437192	0.218596	+	0.975815i	$0.429852\pi$
$828$	1.01206e7	0.513015
$829$	1.93004e7	0.975392	0.487696	−	0.873013i	$-0.337837\pi$
$829$	1.93004e7	0.975392	0.487696	+	0.873013i	$0.337837\pi$
$830$	1.30805e8	6.59067
$831$	2.02736e7	1.01842
$832$	−1.35759e8	−6.79924
$833$	−3.58924e6	−0.179221
$834$	−8.51809e6	−0.424060
$835$	6.43085e7	3.19192
$836$	1.39779e6	0.0691712
$837$	2.86104e7	1.41159
$838$	−7.10679e7	−3.49594
$839$	−6.84359e6	−0.335644	−0.167822	−	0.985817i	$-0.553673\pi$
$839$	−6.84359e6	−0.335644	−0.167822	+	0.985817i	$0.553673\pi$
$840$	1.34713e8	6.58735
$841$	−1.72775e7	−0.842348
$842$	1.63517e7	0.794847
$843$	1.46357e7	0.709322
$844$	1.63104e7	0.788149
$845$	4.93786e7	2.37901
$846$	1.37634e7	0.661148
$847$	−3.20399e7	−1.53455
$848$	−2.67374e7	−1.27682
$849$	−1.62486e7	−0.773655
$850$	2.71242e7	1.28768
$851$	2.03094e6	0.0961332
$852$	−63203.4	−0.00298292
$853$	1.53375e7	0.721743	0.360871	−	0.932616i	$-0.382479\pi$
$853$	1.53375e7	0.721743	0.360871	+	0.932616i	$0.382479\pi$
$854$	−4.65544e7	−2.18432
$855$	318069.	0.0148801
$856$	3.65106e7	1.70308
$857$	3.50423e7	1.62982	0.814912	−	0.579585i	$-0.196785\pi$
$857$	3.50423e7	1.62982	0.814912	+	0.579585i	$0.196785\pi$
$858$	−6.79353e7	−3.15048
$859$	9.37391e6	0.433449	0.216724	−	0.976233i	$-0.430463\pi$
$859$	9.37391e6	0.433449	0.216724	+	0.976233i	$0.430463\pi$
$860$	1.84903e8	8.52507
$861$	−2.80153e7	−1.28792
$862$	2.65417e7	1.21663
$863$	−3.74619e7	−1.71223	−0.856116	−	0.516784i	$-0.827129\pi$
$863$	−3.74619e7	−1.71223	−0.856116	+	0.516784i	$0.827129\pi$
$864$	1.04011e8	4.74019
$865$	−3.32295e7	−1.51002
$866$	−2.53491e7	−1.14860
$867$	956368.	0.0432093
$868$	1.08110e8	4.87042
$869$	4.81866e7	2.16460
$870$	2.45073e7	1.09773
$871$	−3691.19	−0.000164862 0
$872$	−7.64227e7	−3.40354
$873$	−8.15513e6	−0.362155
$874$	−293038.	−0.0129761
$875$	−9.91558e7	−4.37823
$876$	4.68998e7	2.06496
$877$	−1.29603e7	−0.569006	−0.284503	−	0.958675i	$-0.591829\pi$
$877$	−1.29603e7	−0.569006	−0.284503	+	0.958675i	$0.591829\pi$
$878$	4.22921e7	1.85150
$879$	1.12954e6	0.0493093
$880$	−2.65400e8	−11.5530
$881$	2.97810e7	1.29271	0.646353	−	0.763039i	$-0.276293\pi$
$881$	2.97810e7	1.29271	0.646353	+	0.763039i	$0.276293\pi$
$882$	1.53365e7	0.663828
$883$	2.39887e7	1.03539	0.517696	−	0.855565i	$-0.326790\pi$
$883$	2.39887e7	1.03539	0.517696	+	0.855565i	$0.326790\pi$
$884$	2.36372e7	1.01734
$885$	4.29830e6	0.184475
$886$	−4.91028e7	−2.10146
$887$	4.11502e7	1.75616	0.878078	−	0.478518i	$-0.158826\pi$
$887$	4.11502e7	1.75616	0.878078	+	0.478518i	$0.158826\pi$
$888$	1.47361e7	0.627117
$889$	−5.56343e7	−2.36096
$890$	−3.73084e7	−1.57882
$891$	1.14187e7	0.481861
$892$	6.58350e7	2.77041
$893$	−293830.	−0.0123301
$894$	−2.82991e7	−1.18421
$895$	5.22800e7	2.18162
$896$	1.41286e8	5.87934
$897$	1.05010e7	0.435763
$898$	−2.55664e7	−1.05798
$899$	1.26606e7	0.522462
$900$	−8.54543e7	−3.51664
$901$	1.85336e6	0.0760586
$902$	9.32426e7	3.81591
$903$	−3.73706e7	−1.52514
$904$	−9.86984e7	−4.01688
$905$	−5.02441e7	−2.03922
$906$	4.67194e7	1.89093
$907$	−1.16971e7	−0.472128	−0.236064	−	0.971738i	$-0.575857\pi$
$907$	−1.16971e7	−0.472128	−0.236064	+	0.971738i	$0.575857\pi$
$908$	−6.34716e7	−2.55485
$909$	1.61708e7	0.649115
$910$	−1.85284e8	−7.41711
$911$	−2.51547e7	−1.00421	−0.502104	−	0.864807i	$-0.667440\pi$
$911$	−2.51547e7	−1.00421	−0.502104	+	0.864807i	$0.667440\pi$
$912$	−1.25858e6	−0.0501064
$913$	6.48759e7	2.57577
$914$	−2.11874e7	−0.838904
$915$	−3.04654e7	−1.20297
$916$	−2.37893e7	−0.936792
$917$	5.68573e7	2.23287
$918$	−1.29619e7	−0.507649
$919$	−8.14806e6	−0.318248	−0.159124	−	0.987259i	$-0.550867\pi$
$919$	−8.14806e6	−0.318248	−0.159124	+	0.987259i	$0.550867\pi$
$920$	6.93050e7	2.69957
$921$	−423335.	−0.0164451
$922$	−3.30761e7	−1.28141
$923$	55959.3	0.00216206
$924$	1.03792e8	3.99932
$925$	−1.71485e7	−0.658978
$926$	1.33327e6	0.0510963
$927$	−2.93380e6	−0.112132
$928$	4.60267e7	1.75445
$929$	−1.27055e7	−0.483007	−0.241503	−	0.970400i	$-0.577640\pi$
$929$	−1.27055e7	−0.483007	−0.241503	+	0.970400i	$0.577640\pi$
$930$	9.59530e7	3.63791
$931$	−327415.	−0.0123801
$932$	5.21276e7	1.96575
$933$	6.34676e6	0.238698
$934$	1.34910e7	0.506031
$935$	1.83967e7	0.688195
$936$	−6.50163e7	−2.42567
$937$	−4.07528e6	−0.151638	−0.0758190	−	0.997122i	$-0.524157\pi$
$937$	−4.07528e6	−0.151638	−0.0758190	+	0.997122i	$0.524157\pi$
$938$	7648.63	0.000283842 0
$939$	−163539.	−0.00605281
$940$	1.07953e8	3.98487
$941$	3.49080e7	1.28514	0.642571	−	0.766226i	$-0.277868\pi$
$941$	3.49080e7	1.28514	0.642571	+	0.766226i	$0.277868\pi$
$942$	−4.85813e7	−1.78378
$943$	−1.44129e7	−0.527802
$944$	1.45131e7	0.530068
$945$	7.49146e7	2.72889
$946$	1.24380e8	4.51879
$947$	−4.91223e7	−1.77993	−0.889967	−	0.456025i	$-0.849273\pi$
$947$	−4.91223e7	−1.77993	−0.889967	+	0.456025i	$0.849273\pi$
$948$	−8.39546e7	−3.03406
$949$	−4.15243e7	−1.49671
$950$	2.47430e6	0.0889494
$951$	8.02329e6	0.287674
$952$	−3.15293e7	−1.12751
$953$	−8.61599e6	−0.307307	−0.153654	−	0.988125i	$-0.549104\pi$
$953$	−8.61599e6	−0.307307	−0.153654	+	0.988125i	$0.549104\pi$
$954$	−7.91926e6	−0.281717
$955$	2.31464e6	0.0821249
$956$	1.31730e8	4.66165
$957$	1.21550e7	0.429016
$958$	3.22211e7	1.13430
$959$	−7.04061e6	−0.247209
$960$	1.84091e8	6.44695
$961$	2.09407e7	0.731447
$962$	−2.02680e7	−0.706111
$963$	6.40112e6	0.222428
$964$	−1.25901e8	−4.36352
$965$	7.11577e7	2.45982
$966$	−2.17595e7	−0.750250
$967$	3.40344e7	1.17045	0.585223	−	0.810872i	$-0.301007\pi$
$967$	3.40344e7	1.17045	0.585223	+	0.810872i	$0.301007\pi$
$968$	−1.19600e8	−4.10244
$969$	87241.0	0.00298477
$970$	−8.67534e7	−2.96045
$971$	−2.32694e7	−0.792021	−0.396010	−	0.918246i	$-0.629606\pi$
$971$	−2.32694e7	−0.792021	−0.396010	+	0.918246i	$0.629606\pi$
$972$	6.87984e7	2.33568
$973$	−1.15224e7	−0.390177
$974$	−5.95068e7	−2.00988
$975$	−8.86665e7	−2.98709
$976$	−1.02866e8	−3.45659
$977$	3.35905e7	1.12585	0.562925	−	0.826508i	$-0.309676\pi$
$977$	3.35905e7	1.12585	0.562925	+	0.826508i	$0.309676\pi$
$978$	3.57234e7	1.19428
$979$	−1.85040e7	−0.617034
$980$	1.20292e8	4.00102
$981$	−1.33986e7	−0.444515
$982$	−8.30174e7	−2.74720
$983$	−1.84099e6	−0.0607670	−0.0303835	−	0.999538i	$-0.509673\pi$
$983$	−1.84099e6	−0.0607670	−0.0303835	+	0.999538i	$0.509673\pi$
$984$	−1.04577e8	−3.44308
$985$	−4.76794e7	−1.56581
$986$	−5.73588e6	−0.187892
$987$	−2.18183e7	−0.712898
$988$	2.15621e6	0.0702746
$989$	−1.92259e7	−0.625022
$990$	−7.86077e7	−2.54904
$991$	−2.43765e7	−0.788473	−0.394237	−	0.919009i	$-0.628991\pi$
$991$	−2.43765e7	−0.788473	−0.394237	+	0.919009i	$0.628991\pi$
$992$	1.80208e8	5.81427
$993$	1.43905e7	0.463129
$994$	−115955.	−0.00372240
$995$	4.82701e7	1.54568
$996$	−1.13032e8	−3.61038
$997$	−1.33681e7	−0.425924	−0.212962	−	0.977061i	$-0.568311\pi$
$997$	−1.33681e7	−0.425924	−0.212962	+	0.977061i	$0.568311\pi$
$998$	7.00891e7	2.22753
$999$	8.19480e6	0.259791

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.6.a.d.1.2	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.6.a.d.1.2	✓	100	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q-11.0372 q^{2} +11.4506 q^{3} +89.8190 q^{4} +107.836 q^{5} -126.382 q^{6} -170.958 q^{7} -638.158 q^{8} -111.883 q^{9} +O(q^{10})\)	\(q-11.0372 q^{2} +11.4506 q^{3} +89.8190 q^{4} +107.836 q^{5} -126.382 q^{6} -170.958 q^{7} -638.158 q^{8} -111.883 q^{9} -1190.20 q^{10} -590.309 q^{11} +1028.48 q^{12} -910.603 q^{13} +1886.89 q^{14} +1234.79 q^{15} +4169.25 q^{16} -289.000 q^{17} +1234.87 q^{18} -26.3629 q^{19} +9685.71 q^{20} -1957.57 q^{21} +6515.34 q^{22} -1007.10 q^{23} -7307.31 q^{24} +8503.57 q^{25} +10050.5 q^{26} -4063.63 q^{27} -15355.2 q^{28} -1798.23 q^{29} -13628.6 q^{30} -7040.59 q^{31} -25595.6 q^{32} -6759.41 q^{33} +3189.74 q^{34} -18435.4 q^{35} -10049.2 q^{36} -2016.62 q^{37} +290.972 q^{38} -10427.0 q^{39} -68816.3 q^{40} +14311.2 q^{41} +21606.0 q^{42} +19090.3 q^{43} -53021.0 q^{44} -12065.0 q^{45} +11115.5 q^{46} +11145.6 q^{47} +47740.5 q^{48} +12419.5 q^{49} -93855.3 q^{50} -3309.23 q^{51} -81789.5 q^{52} -6413.02 q^{53} +44851.0 q^{54} -63656.5 q^{55} +109098. q^{56} -301.872 q^{57} +19847.3 q^{58} +3481.00 q^{59} +110907. q^{60} -24672.6 q^{61} +77708.1 q^{62} +19127.3 q^{63} +149087. q^{64} -98195.7 q^{65} +74604.7 q^{66} +4.05357 q^{67} -25957.7 q^{68} -11531.9 q^{69} +203474. q^{70} -61.4530 q^{71} +71399.1 q^{72} +45600.9 q^{73} +22257.8 q^{74} +97371.2 q^{75} -2367.89 q^{76} +100918. q^{77} +115084. q^{78} -81629.5 q^{79} +449594. q^{80} -19343.6 q^{81} -157956. q^{82} -109902. q^{83} -175827. q^{84} -31164.6 q^{85} -210703. q^{86} -20590.8 q^{87} +376711. q^{88} +31346.3 q^{89} +133164. q^{90} +155675. q^{91} -90456.9 q^{92} -80619.1 q^{93} -123015. q^{94} -2842.87 q^{95} -293086. q^{96} +72889.7 q^{97} -137076. q^{98} +66045.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 25 q^{2} + 63 q^{3} + 1707 q^{4} + 509 q^{5} + 207 q^{6} + 247 q^{7} + 765 q^{8} + 9003 q^{9}+O(q^{10}) \) 100 * q + 25 * q^2 + 63 * q^3 + 1707 * q^4 + 509 * q^5 + 207 * q^6 + 247 * q^7 + 765 * q^8 + 9003 * q^9	\( 100 q + 25 q^{2} + 63 q^{3} + 1707 q^{4} + 509 q^{5} + 207 q^{6} + 247 q^{7} + 765 q^{8} + 9003 q^{9} + 424 q^{11} + 2880 q^{12} + 2426 q^{13} + 1069 q^{14} + 3699 q^{15} + 25895 q^{16} - 28900 q^{17} + 6644 q^{18} + 2224 q^{19} + 11919 q^{20} + 12248 q^{21} + 1160 q^{22} + 4675 q^{23} + 6477 q^{24} + 76925 q^{25} + 26507 q^{26} + 18465 q^{27} + 7371 q^{28} + 13905 q^{29} + 42029 q^{30} + 11503 q^{31} + 31765 q^{32} + 34053 q^{33} - 7225 q^{34} + 26861 q^{35} + 210764 q^{36} - 4418 q^{37} + 55637 q^{38} - 5718 q^{39} + 24116 q^{40} + 50715 q^{41} + 145355 q^{42} + 36979 q^{43} - 6793 q^{44} + 88939 q^{45} + 23917 q^{46} + 162533 q^{47} + 219761 q^{48} + 276061 q^{49} + 204874 q^{50} - 18207 q^{51} + 73665 q^{52} + 144329 q^{53} + 112241 q^{54} + 63002 q^{55} + 234871 q^{56} + 94768 q^{57} + 22318 q^{58} + 348100 q^{59} + 390780 q^{60} - 45447 q^{61} + 146617 q^{62} + 88467 q^{63} + 580433 q^{64} - 49981 q^{65} - 14744 q^{66} + 113930 q^{67} - 493323 q^{68} + 49070 q^{69} + 86899 q^{70} + 138703 q^{71} + 319055 q^{72} + 174214 q^{73} - 139931 q^{74} + 295788 q^{75} + 272539 q^{76} + 642017 q^{77} + 93149 q^{78} - 240788 q^{79} + 582895 q^{80} + 690560 q^{81} + 164633 q^{82} + 324136 q^{83} + 775436 q^{84} - 147101 q^{85} + 113296 q^{86} + 612596 q^{87} - 227510 q^{88} + 348396 q^{89} + 750464 q^{90} - 100399 q^{91} + 453265 q^{92} + 660393 q^{93} + 183864 q^{94} + 341370 q^{95} + 209486 q^{96} + 288603 q^{97} + 1100905 q^{98} + 301794 q^{99}+O(q^{100}) \) 100 * q + 25 * q^2 + 63 * q^3 + 1707 * q^4 + 509 * q^5 + 207 * q^6 + 247 * q^7 + 765 * q^8 + 9003 * q^9 + 424 * q^11 + 2880 * q^12 + 2426 * q^13 + 1069 * q^14 + 3699 * q^15 + 25895 * q^16 - 28900 * q^17 + 6644 * q^18 + 2224 * q^19 + 11919 * q^20 + 12248 * q^21 + 1160 * q^22 + 4675 * q^23 + 6477 * q^24 + 76925 * q^25 + 26507 * q^26 + 18465 * q^27 + 7371 * q^28 + 13905 * q^29 + 42029 * q^30 + 11503 * q^31 + 31765 * q^32 + 34053 * q^33 - 7225 * q^34 + 26861 * q^35 + 210764 * q^36 - 4418 * q^37 + 55637 * q^38 - 5718 * q^39 + 24116 * q^40 + 50715 * q^41 + 145355 * q^42 + 36979 * q^43 - 6793 * q^44 + 88939 * q^45 + 23917 * q^46 + 162533 * q^47 + 219761 * q^48 + 276061 * q^49 + 204874 * q^50 - 18207 * q^51 + 73665 * q^52 + 144329 * q^53 + 112241 * q^54 + 63002 * q^55 + 234871 * q^56 + 94768 * q^57 + 22318 * q^58 + 348100 * q^59 + 390780 * q^60 - 45447 * q^61 + 146617 * q^62 + 88467 * q^63 + 580433 * q^64 - 49981 * q^65 - 14744 * q^66 + 113930 * q^67 - 493323 * q^68 + 49070 * q^69 + 86899 * q^70 + 138703 * q^71 + 319055 * q^72 + 174214 * q^73 - 139931 * q^74 + 295788 * q^75 + 272539 * q^76 + 642017 * q^77 + 93149 * q^78 - 240788 * q^79 + 582895 * q^80 + 690560 * q^81 + 164633 * q^82 + 324136 * q^83 + 775436 * q^84 - 147101 * q^85 + 113296 * q^86 + 612596 * q^87 - 227510 * q^88 + 348396 * q^89 + 750464 * q^90 - 100399 * q^91 + 453265 * q^92 + 660393 * q^93 + 183864 * q^94 + 341370 * q^95 + 209486 * q^96 + 288603 * q^97 + 1100905 * q^98 + 301794 * q^99

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