LMFDB - Embedded newform 74.6.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(1,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, 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("74.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.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:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 849x^{3} - 2565x^{2} + 113184x + 425655 $ x^5 - 2x^4 - 849x^3 - 2565x^2 + 113184x + 425655
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$12.6543$ of defining polynomial
Character	$\chi$	$=$	74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} -20.5447 q^{3} +16.0000 q^{4} -32.9694 q^{5} +82.1788 q^{6} -257.230 q^{7} -64.0000 q^{8} +179.084 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -20.5447 q^{3} +16.0000 q^{4} -32.9694 q^{5} +82.1788 q^{6} -257.230 q^{7} -64.0000 q^{8} +179.084 q^{9} +131.878 q^{10} -56.7286 q^{11} -328.715 q^{12} -978.805 q^{13} +1028.92 q^{14} +677.346 q^{15} +256.000 q^{16} -136.635 q^{17} -716.337 q^{18} +2509.39 q^{19} -527.511 q^{20} +5284.72 q^{21} +226.914 q^{22} +2963.83 q^{23} +1314.86 q^{24} -2038.02 q^{25} +3915.22 q^{26} +1313.13 q^{27} -4115.68 q^{28} -7285.78 q^{29} -2709.39 q^{30} +4215.03 q^{31} -1024.00 q^{32} +1165.47 q^{33} +546.541 q^{34} +8480.73 q^{35} +2865.35 q^{36} +1369.00 q^{37} -10037.6 q^{38} +20109.2 q^{39} +2110.04 q^{40} -7690.88 q^{41} -21138.9 q^{42} -7215.39 q^{43} -907.658 q^{44} -5904.31 q^{45} -11855.3 q^{46} -29686.3 q^{47} -5259.44 q^{48} +49360.4 q^{49} +8152.07 q^{50} +2807.13 q^{51} -15660.9 q^{52} -5256.61 q^{53} -5252.51 q^{54} +1870.31 q^{55} +16462.7 q^{56} -51554.7 q^{57} +29143.1 q^{58} +5731.07 q^{59} +10837.5 q^{60} +67.8155 q^{61} -16860.1 q^{62} -46065.9 q^{63} +4096.00 q^{64} +32270.6 q^{65} -4661.89 q^{66} +26266.3 q^{67} -2186.16 q^{68} -60891.0 q^{69} -33922.9 q^{70} -38790.7 q^{71} -11461.4 q^{72} -9683.80 q^{73} -5476.00 q^{74} +41870.4 q^{75} +40150.3 q^{76} +14592.3 q^{77} -80437.0 q^{78} +8779.86 q^{79} -8440.17 q^{80} -70495.3 q^{81} +30763.5 q^{82} +81769.5 q^{83} +84555.5 q^{84} +4504.78 q^{85} +28861.5 q^{86} +149684. q^{87} +3630.63 q^{88} -4912.90 q^{89} +23617.2 q^{90} +251778. q^{91} +47421.3 q^{92} -86596.5 q^{93} +118745. q^{94} -82733.2 q^{95} +21037.8 q^{96} +128380. q^{97} -197442. q^{98} -10159.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 20 q^{2} + 19 q^{3} + 80 q^{4} - 67 q^{5} - 76 q^{6} + 182 q^{7} - 320 q^{8} + 598 q^{9}+O(q^{10}) $ 5 * q - 20 * q^2 + 19 * q^3 + 80 * q^4 - 67 * q^5 - 76 * q^6 + 182 * q^7 - 320 * q^8 + 598 * q^9	\( 5 q - 20 q^{2} + 19 q^{3} + 80 q^{4} - 67 q^{5} - 76 q^{6} + 182 q^{7} - 320 q^{8} + 598 q^{9} + 268 q^{10} - 409 q^{11} + 304 q^{12} - 679 q^{13} - 728 q^{14} + 1272 q^{15} + 1280 q^{16} - 114 q^{17} - 2392 q^{18} + 4180 q^{19} - 1072 q^{20} + 13712 q^{21} + 1636 q^{22} + 6837 q^{23} - 1216 q^{24} + 16866 q^{25} + 2716 q^{26} + 15010 q^{27} + 2912 q^{28} + 4137 q^{29} - 5088 q^{30} + 19875 q^{31} - 5120 q^{32} + 8646 q^{33} + 456 q^{34} + 1980 q^{35} + 9568 q^{36} + 6845 q^{37} - 16720 q^{38} - 13843 q^{39} + 4288 q^{40} - 29367 q^{41} - 54848 q^{42} - 18282 q^{43} - 6544 q^{44} + 1440 q^{45} - 27348 q^{46} - 50386 q^{47} + 4864 q^{48} + 48659 q^{49} - 67464 q^{50} - 12006 q^{51} - 10864 q^{52} + 21048 q^{53} - 60040 q^{54} - 31181 q^{55} - 11648 q^{56} - 74590 q^{57} - 16548 q^{58} - 20350 q^{59} + 20352 q^{60} + 20031 q^{61} - 79500 q^{62} + 81446 q^{63} + 20480 q^{64} - 48402 q^{65} - 34584 q^{66} + 8003 q^{67} - 1824 q^{68} - 75165 q^{69} - 7920 q^{70} - 65400 q^{71} - 38272 q^{72} + 24867 q^{73} - 27380 q^{74} + 277846 q^{75} + 66880 q^{76} + 19842 q^{77} + 55372 q^{78} + 154397 q^{79} - 17152 q^{80} + 20425 q^{81} + 117468 q^{82} + 191072 q^{83} + 219392 q^{84} - 119046 q^{85} + 73128 q^{86} + 61953 q^{87} + 26176 q^{88} - 226894 q^{89} - 5760 q^{90} + 151222 q^{91} + 109392 q^{92} + 158246 q^{93} + 201544 q^{94} - 502130 q^{95} - 19456 q^{96} - 40678 q^{97} - 194636 q^{98} + 71094 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + 19 * q^3 + 80 * q^4 - 67 * q^5 - 76 * q^6 + 182 * q^7 - 320 * q^8 + 598 * q^9 + 268 * q^10 - 409 * q^11 + 304 * q^12 - 679 * q^13 - 728 * q^14 + 1272 * q^15 + 1280 * q^16 - 114 * q^17 - 2392 * q^18 + 4180 * q^19 - 1072 * q^20 + 13712 * q^21 + 1636 * q^22 + 6837 * q^23 - 1216 * q^24 + 16866 * q^25 + 2716 * q^26 + 15010 * q^27 + 2912 * q^28 + 4137 * q^29 - 5088 * q^30 + 19875 * q^31 - 5120 * q^32 + 8646 * q^33 + 456 * q^34 + 1980 * q^35 + 9568 * q^36 + 6845 * q^37 - 16720 * q^38 - 13843 * q^39 + 4288 * q^40 - 29367 * q^41 - 54848 * q^42 - 18282 * q^43 - 6544 * q^44 + 1440 * q^45 - 27348 * q^46 - 50386 * q^47 + 4864 * q^48 + 48659 * q^49 - 67464 * q^50 - 12006 * q^51 - 10864 * q^52 + 21048 * q^53 - 60040 * q^54 - 31181 * q^55 - 11648 * q^56 - 74590 * q^57 - 16548 * q^58 - 20350 * q^59 + 20352 * q^60 + 20031 * q^61 - 79500 * q^62 + 81446 * q^63 + 20480 * q^64 - 48402 * q^65 - 34584 * q^66 + 8003 * q^67 - 1824 * q^68 - 75165 * q^69 - 7920 * q^70 - 65400 * q^71 - 38272 * q^72 + 24867 * q^73 - 27380 * q^74 + 277846 * q^75 + 66880 * q^76 + 19842 * q^77 + 55372 * q^78 + 154397 * q^79 - 17152 * q^80 + 20425 * q^81 + 117468 * q^82 + 191072 * q^83 + 219392 * q^84 - 119046 * q^85 + 73128 * q^86 + 61953 * q^87 + 26176 * q^88 - 226894 * q^89 - 5760 * q^90 + 151222 * q^91 + 109392 * q^92 + 158246 * q^93 + 201544 * q^94 - 502130 * q^95 - 19456 * q^96 - 40678 * q^97 - 194636 * q^98 + 71094 * 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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−20.5447	−1.31794	−0.658971	−	0.752168i	$-0.729008\pi$
$3$	−20.5447	−1.31794	−0.658971	+	0.752168i	$0.729008\pi$
$4$	16.0000	0.500000
$5$	−32.9694	−0.589775	−0.294887	−	0.955532i	$-0.595282\pi$
$5$	−32.9694	−0.589775	−0.294887	+	0.955532i	$0.595282\pi$
$6$	82.1788	0.931926
$7$	−257.230	−1.98416	−0.992081	−	0.125603i	$-0.959913\pi$
$7$	−257.230	−1.98416	−0.992081	+	0.125603i	$0.959913\pi$
$8$	−64.0000	−0.353553
$9$	179.084	0.736973
$10$	131.878	0.417034
$11$	−56.7286	−0.141358	−0.0706790	−	0.997499i	$-0.522517\pi$
$11$	−56.7286	−0.141358	−0.0706790	+	0.997499i	$0.522517\pi$
$12$	−328.715	−0.658971
$13$	−978.805	−1.60634	−0.803171	−	0.595749i	$-0.796855\pi$
$13$	−978.805	−1.60634	−0.803171	+	0.595749i	$0.796855\pi$
$14$	1028.92	1.40301
$15$	677.346	0.777289
$16$	256.000	0.250000
$17$	−136.635	−0.114668	−0.0573338	−	0.998355i	$-0.518260\pi$
$17$	−136.635	−0.114668	−0.0573338	+	0.998355i	$0.518260\pi$
$18$	−716.337	−0.521118
$19$	2509.39	1.59472	0.797360	−	0.603504i	$-0.206229\pi$
$19$	2509.39	1.59472	0.797360	+	0.603504i	$0.206229\pi$
$20$	−527.511	−0.294887
$21$	5284.72	2.61501
$22$	226.914	0.0999552
$23$	2963.83	1.16824	0.584122	−	0.811666i	$-0.301439\pi$
$23$	2963.83	1.16824	0.584122	+	0.811666i	$0.301439\pi$
$24$	1314.86	0.465963
$25$	−2038.02	−0.652166
$26$	3915.22	1.13585
$27$	1313.13	0.346655
$28$	−4115.68	−0.992081
$29$	−7285.78	−1.60872	−0.804361	−	0.594141i	$-0.797492\pi$
$29$	−7285.78	−1.60872	−0.804361	+	0.594141i	$0.797492\pi$
$30$	−2709.39	−0.549627
$31$	4215.03	0.787765	0.393883	−	0.919161i	$-0.371132\pi$
$31$	4215.03	0.787765	0.393883	+	0.919161i	$0.371132\pi$
$32$	−1024.00	−0.176777
$33$	1165.47	0.186302
$34$	546.541	0.0810822
$35$	8480.73	1.17021
$36$	2865.35	0.368486
$37$	1369.00	0.164399
$37$	1369.00	0.164399
$38$	−10037.6	−1.12764
$39$	20109.2	2.11707
$40$	2110.04	0.208517
$41$	−7690.88	−0.714523	−0.357262	−	0.934004i	$-0.616290\pi$
$41$	−7690.88	−0.714523	−0.357262	+	0.934004i	$0.616290\pi$
$42$	−21138.9	−1.84909
$43$	−7215.39	−0.595098	−0.297549	−	0.954707i	$-0.596169\pi$
$43$	−7215.39	−0.595098	−0.297549	+	0.954707i	$0.596169\pi$
$44$	−907.658	−0.0706790
$45$	−5904.31	−0.434648
$46$	−11855.3	−0.826074
$47$	−29686.3	−1.96025	−0.980126	−	0.198377i	$-0.936433\pi$
$47$	−29686.3	−1.96025	−0.980126	+	0.198377i	$0.936433\pi$
$48$	−5259.44	−0.329486
$49$	49360.4	2.93690
$50$	8152.07	0.461151
$51$	2807.13	0.151125
$52$	−15660.9	−0.803171
$53$	−5256.61	−0.257049	−0.128524	−	0.991706i	$-0.541024\pi$
$53$	−5256.61	−0.257049	−0.128524	+	0.991706i	$0.541024\pi$
$54$	−5252.51	−0.245122
$55$	1870.31	0.0833694
$56$	16462.7	0.701507
$57$	−51554.7	−2.10175
$58$	29143.1	1.13754
$59$	5731.07	0.214341	0.107171	−	0.994241i	$-0.465821\pi$
$59$	5731.07	0.214341	0.107171	+	0.994241i	$0.465821\pi$
$60$	10837.5	0.388645
$61$	67.8155	0.00233348	0.00116674	−	0.999999i	$-0.499629\pi$
$61$	67.8155	0.00233348	0.00116674	+	0.999999i	$0.499629\pi$
$62$	−16860.1	−0.557034
$63$	−46065.9	−1.46227
$64$	4096.00	0.125000
$65$	32270.6	0.947380
$66$	−4661.89	−0.131735
$67$	26266.3	0.714844	0.357422	−	0.933943i	$-0.383656\pi$
$67$	26266.3	0.714844	0.357422	+	0.933943i	$0.383656\pi$
$68$	−2186.16	−0.0573338
$69$	−60891.0	−1.53968
$70$	−33922.9	−0.827462
$71$	−38790.7	−0.913233	−0.456617	−	0.889664i	$-0.650939\pi$
$71$	−38790.7	−0.913233	−0.456617	+	0.889664i	$0.650939\pi$
$72$	−11461.4	−0.260559
$73$	−9683.80	−0.212686	−0.106343	−	0.994330i	$-0.533914\pi$
$73$	−9683.80	−0.212686	−0.106343	+	0.994330i	$0.533914\pi$
$74$	−5476.00	−0.116248
$75$	41870.4	0.859517
$76$	40150.3	0.797360
$77$	14592.3	0.280477
$78$	−80437.0	−1.49699
$79$	8779.86	0.158278	0.0791389	−	0.996864i	$-0.474783\pi$
$79$	8779.86	0.158278	0.0791389	+	0.996864i	$0.474783\pi$
$80$	−8440.17	−0.147444
$81$	−70495.3	−1.19384
$82$	30763.5	0.505244
$83$	81769.5	1.30286	0.651428	−	0.758711i	$-0.274170\pi$
$83$	81769.5	1.30286	0.651428	+	0.758711i	$0.274170\pi$
$84$	84555.5	1.30751
$85$	4504.78	0.0676280
$86$	28861.5	0.420798
$87$	149684.	2.12020
$88$	3630.63	0.0499776
$89$	−4912.90	−0.0657450	−0.0328725	−	0.999460i	$-0.510466\pi$
$89$	−4912.90	−0.0657450	−0.0328725	+	0.999460i	$0.510466\pi$
$90$	23617.2	0.307342
$91$	251778.	3.18724
$92$	47421.3	0.584122
$93$	−86596.5	−1.03823
$94$	118745.	1.38611
$95$	−82733.2	−0.940526
$96$	21037.8	0.232982
$97$	128380.	1.38538	0.692691	−	0.721235i	$-0.256425\pi$
$97$	128380.	1.38538	0.692691	+	0.721235i	$0.256425\pi$
$98$	−197442.	−2.07670
$99$	−10159.2	−0.104177
$100$	−32608.3	−0.326083
$101$	−45729.2	−0.446057	−0.223029	−	0.974812i	$-0.571594\pi$
$101$	−45729.2	−0.446057	−0.223029	+	0.974812i	$0.571594\pi$
$102$	−11228.5	−0.106862
$103$	−69844.6	−0.648694	−0.324347	−	0.945938i	$-0.605145\pi$
$103$	−69844.6	−0.648694	−0.324347	+	0.945938i	$0.605145\pi$
$104$	62643.5	0.567927
$105$	−174234.	−1.54227
$106$	21026.4	0.181761
$107$	−146333.	−1.23562	−0.617808	−	0.786329i	$-0.711979\pi$
$107$	−146333.	−1.23562	−0.617808	+	0.786329i	$0.711979\pi$
$108$	21010.0	0.173328
$109$	−1138.95	−0.00918200	−0.00459100	−	0.999989i	$-0.501461\pi$
$109$	−1138.95	−0.00918200	−0.00459100	+	0.999989i	$0.501461\pi$
$110$	−7481.24	−0.0589511
$111$	−28125.7	−0.216668
$112$	−65850.9	−0.496040
$113$	134807.	0.993151	0.496576	−	0.867994i	$-0.334591\pi$
$113$	134807.	0.993151	0.496576	+	0.867994i	$0.334591\pi$
$114$	206219.	1.48616
$115$	−97715.8	−0.689001
$116$	−116572.	−0.804361
$117$	−175289.	−1.18383
$118$	−22924.3	−0.151562
$119$	35146.7	0.227519
$120$	−43350.2	−0.274813
$121$	−157833.	−0.980018
$122$	−271.262	−0.00165002
$123$	158007.	0.941700
$124$	67440.5	0.393883
$125$	170222.	0.974406
$126$	184264.	1.03398
$127$	117886.	0.648561	0.324281	−	0.945961i	$-0.394878\pi$
$127$	117886.	0.648561	0.324281	+	0.945961i	$0.394878\pi$
$128$	−16384.0	−0.0883883
$129$	148238.	0.784305
$130$	−129083.	−0.669899
$131$	242924.	1.23678	0.618390	−	0.785872i	$-0.287785\pi$
$131$	242924.	1.23678	0.618390	+	0.785872i	$0.287785\pi$
$132$	18647.6	0.0931509
$133$	−645491.	−3.16418
$134$	−105065.	−0.505471
$135$	−43293.0	−0.204448
$136$	8744.66	0.0405411
$137$	−92798.4	−0.422415	−0.211207	−	0.977441i	$-0.567740\pi$
$137$	−92798.4	−0.422415	−0.211207	+	0.977441i	$0.567740\pi$
$138$	243564.	1.08872
$139$	−237204.	−1.04132	−0.520662	−	0.853763i	$-0.674315\pi$
$139$	−237204.	−1.04132	−0.520662	+	0.853763i	$0.674315\pi$
$140$	135692.	0.585104
$141$	609896.	2.58350
$142$	155163.	0.645753
$143$	55526.3	0.227069
$144$	45845.6	0.184243
$145$	240208.	0.948784
$146$	38735.2	0.150392
$147$	−1.01409e6	−3.87066
$148$	21904.0	0.0821995
$149$	−379035.	−1.39867	−0.699333	−	0.714796i	$-0.746519\pi$
$149$	−379035.	−1.39867	−0.699333	+	0.714796i	$0.746519\pi$
$150$	−167482.	−0.607770
$151$	−102937.	−0.367391	−0.183695	−	0.982983i	$-0.558806\pi$
$151$	−102937.	−0.367391	−0.183695	+	0.982983i	$0.558806\pi$
$152$	−160601.	−0.563819
$153$	−24469.2	−0.0845068
$154$	−58369.3	−0.198327
$155$	−138967.	−0.464604
$156$	321748.	1.05853
$157$	390011.	1.26278	0.631390	−	0.775465i	$-0.282485\pi$
$157$	390011.	1.26278	0.631390	+	0.775465i	$0.282485\pi$
$158$	−35119.4	−0.111919
$159$	107995.	0.338776
$160$	33760.7	0.104258
$161$	−762387.	−2.31799
$162$	281981.	0.844175
$163$	327835.	0.966464	0.483232	−	0.875492i	$-0.339463\pi$
$163$	327835.	0.966464	0.483232	+	0.875492i	$0.339463\pi$
$164$	−123054.	−0.357262
$165$	−38424.9	−0.109876
$166$	−327078.	−0.921258
$167$	−98245.8	−0.272598	−0.136299	−	0.990668i	$-0.543521\pi$
$167$	−98245.8	−0.272598	−0.136299	+	0.990668i	$0.543521\pi$
$168$	−338222.	−0.924546
$169$	586767.	1.58033
$170$	−18019.1	−0.0478202
$171$	449393.	1.17526
$172$	−115446.	−0.297549
$173$	72912.6	0.185220	0.0926098	−	0.995702i	$-0.470479\pi$
$173$	72912.6	0.185220	0.0926098	+	0.995702i	$0.470479\pi$
$174$	−598736.	−1.49921
$175$	524240.	1.29400
$176$	−14522.5	−0.0353395
$177$	−117743.	−0.282489
$178$	19651.6	0.0464887
$179$	−143764.	−0.335366	−0.167683	−	0.985841i	$-0.553628\pi$
$179$	−143764.	−0.335366	−0.167683	+	0.985841i	$0.553628\pi$
$180$	−94468.9	−0.217324
$181$	506958.	1.15020	0.575102	−	0.818081i	$-0.304962\pi$
$181$	506958.	1.15020	0.575102	+	0.818081i	$0.304962\pi$
$182$	−1.00711e6	−2.25372
$183$	−1393.25	−0.00307539
$184$	−189685.	−0.413037
$185$	−45135.1	−0.0969584
$186$	346386.	0.734139
$187$	7751.13	0.0162092
$188$	−474981.	−0.980126
$189$	−337776.	−0.687819
$190$	330933.	0.665052
$191$	96855.5	0.192106	0.0960530	−	0.995376i	$-0.469378\pi$
$191$	96855.5	0.192106	0.0960530	+	0.995376i	$0.469378\pi$
$192$	−84151.1	−0.164743
$193$	109989.	0.212548	0.106274	−	0.994337i	$-0.466108\pi$
$193$	109989.	0.212548	0.106274	+	0.994337i	$0.466108\pi$
$194$	−513521.	−0.979612
$195$	−662990.	−1.24859
$196$	789766.	1.46845
$197$	241552.	0.443450	0.221725	−	0.975109i	$-0.428831\pi$
$197$	241552.	0.443450	0.221725	+	0.975109i	$0.428831\pi$
$198$	40636.8	0.0736643
$199$	141495.	0.253284	0.126642	−	0.991948i	$-0.459580\pi$
$199$	141495.	0.253284	0.126642	+	0.991948i	$0.459580\pi$
$200$	130433.	0.230575
$201$	−539632.	−0.942123
$202$	182917.	0.315410
$203$	1.87412e6	3.19196
$204$	44914.1	0.0755626
$205$	253564.	0.421408
$206$	279379.	0.458696
$207$	530776.	0.860964
$208$	−250574.	−0.401585
$209$	−142354.	−0.225426
$210$	696936.	1.09055
$211$	1.10812e6	1.71348	0.856742	−	0.515745i	$-0.172485\pi$
$211$	1.10812e6	1.71348	0.856742	+	0.515745i	$0.172485\pi$
$212$	−84105.7	−0.128524
$213$	796943.	1.20359
$214$	585333.	0.873712
$215$	237887.	0.350974
$216$	−84040.2	−0.122561
$217$	−1.08423e6	−1.56305
$218$	4555.79	0.00649266
$219$	198951.	0.280308
$220$	29924.9	0.0416847
$221$	133739.	0.184195
$222$	112503.	0.153208
$223$	−331546.	−0.446458	−0.223229	−	0.974766i	$-0.571660\pi$
$223$	−331546.	−0.446458	−0.223229	+	0.974766i	$0.571660\pi$
$224$	263404.	0.350753
$225$	−364977.	−0.480628
$226$	−539227.	−0.702264
$227$	621907.	0.801052	0.400526	−	0.916285i	$-0.368827\pi$
$227$	621907.	0.801052	0.400526	+	0.916285i	$0.368827\pi$
$228$	−824875.	−1.05087
$229$	1.37642e6	1.73445	0.867224	−	0.497919i	$-0.165902\pi$
$229$	1.37642e6	1.73445	0.867224	+	0.497919i	$0.165902\pi$
$230$	390863.	0.487197
$231$	−299795.	−0.369653
$232$	466290.	0.568769
$233$	−1.56659e6	−1.89045	−0.945227	−	0.326414i	$-0.894160\pi$
$233$	−1.56659e6	−1.89045	−0.945227	+	0.326414i	$0.894160\pi$
$234$	701155.	0.837094
$235$	978741.	1.15611
$236$	91697.1	0.107171
$237$	−180379.	−0.208601
$238$	−140587.	−0.160880
$239$	−758997.	−0.859499	−0.429749	−	0.902948i	$-0.641398\pi$
$239$	−758997.	−0.859499	−0.429749	+	0.902948i	$0.641398\pi$
$240$	173401.	0.194322
$241$	−175112.	−0.194211	−0.0971053	−	0.995274i	$-0.530958\pi$
$241$	−175112.	−0.194211	−0.0971053	+	0.995274i	$0.530958\pi$
$242$	631331.	0.692977
$243$	1.12921e6	1.22676
$244$	1085.05	0.00116674
$245$	−1.62738e6	−1.73211
$246$	−632027.	−0.665883
$247$	−2.45621e6	−2.56166
$248$	−269762.	−0.278517
$249$	−1.67993e6	−1.71709
$250$	−680887.	−0.689009
$251$	1.01023e6	1.01213	0.506063	−	0.862497i	$-0.331100\pi$
$251$	1.01023e6	1.01213	0.506063	+	0.862497i	$0.331100\pi$
$252$	−737055.	−0.731136
$253$	−168134.	−0.165141
$254$	−471542.	−0.458602
$255$	−92549.4	−0.0891298
$256$	65536.0	0.0625000
$257$	539957.	0.509948	0.254974	−	0.966948i	$-0.417933\pi$
$257$	539957.	0.509948	0.254974	+	0.966948i	$0.417933\pi$
$258$	−592951.	−0.554587
$259$	−352148.	−0.326194
$260$	516330.	0.473690
$261$	−1.30477e6	−1.18558
$262$	−971696.	−0.874535
$263$	1.25531e6	1.11908	0.559541	−	0.828802i	$-0.310977\pi$
$263$	1.25531e6	1.11908	0.559541	+	0.828802i	$0.310977\pi$
$264$	−74590.2	−0.0658676
$265$	173307.	0.151601
$266$	2.58197e6	2.23741
$267$	100934.	0.0866481
$268$	420260.	0.357422
$269$	769826.	0.648652	0.324326	−	0.945945i	$-0.394863\pi$
$269$	769826.	0.648652	0.324326	+	0.945945i	$0.394863\pi$
$270$	173172.	0.144567
$271$	527116.	0.435997	0.217998	−	0.975949i	$-0.430047\pi$
$271$	527116.	0.435997	0.217998	+	0.975949i	$0.430047\pi$
$272$	−34978.6	−0.0286669
$273$	−5.17271e6	−4.20060
$274$	371194.	0.298692
$275$	115614.	0.0921889
$276$	−974256.	−0.769840
$277$	2.32028e6	1.81694	0.908471	−	0.417948i	$-0.137250\pi$
$277$	2.32028e6	1.81694	0.908471	+	0.417948i	$0.137250\pi$
$278$	948817.	0.736327
$279$	754846.	0.580561
$280$	−542767.	−0.413731
$281$	−1.51023e6	−1.14098	−0.570490	−	0.821304i	$-0.693247\pi$
$281$	−1.51023e6	−1.14098	−0.570490	+	0.821304i	$0.693247\pi$
$282$	−2.43959e6	−1.82681
$283$	−1.51357e6	−1.12340	−0.561702	−	0.827340i	$-0.689853\pi$
$283$	−1.51357e6	−1.12340	−0.561702	+	0.827340i	$0.689853\pi$
$284$	−620651.	−0.456617
$285$	1.69973e6	1.23956
$286$	−222105.	−0.160562
$287$	1.97833e6	1.41773
$288$	−183382.	−0.130280
$289$	−1.40119e6	−0.986851
$290$	−960831.	−0.670891
$291$	−2.63754e6	−1.82585
$292$	−154941.	−0.106343
$293$	−952226.	−0.647994	−0.323997	−	0.946058i	$-0.605027\pi$
$293$	−952226.	−0.647994	−0.323997	+	0.946058i	$0.605027\pi$
$294$	4.05638e6	2.73697
$295$	−188950.	−0.126413
$296$	−87616.0	−0.0581238
$297$	−74491.9	−0.0490025
$298$	1.51614e6	0.989006
$299$	−2.90101e6	−1.87660
$300$	669927.	0.429758
$301$	1.85602e6	1.18077
$302$	411747.	0.259784
$303$	939493.	0.587878
$304$	642404.	0.398680
$305$	−2235.84	−0.00137623
$306$	97876.9	0.0597554
$307$	83904.7	0.0508089	0.0254045	−	0.999677i	$-0.491913\pi$
$307$	83904.7	0.0508089	0.0254045	+	0.999677i	$0.491913\pi$
$308$	233477.	0.140239
$309$	1.43494e6	0.854942
$310$	555869.	0.328525
$311$	1.08603e6	0.636708	0.318354	−	0.947972i	$-0.396870\pi$
$311$	1.08603e6	0.636708	0.318354	+	0.947972i	$0.396870\pi$
$312$	−1.28699e6	−0.748496
$313$	−1.24408e6	−0.717771	−0.358886	−	0.933382i	$-0.616843\pi$
$313$	−1.24408e6	−0.717771	−0.358886	+	0.933382i	$0.616843\pi$
$314$	−1.56004e6	−0.892920
$315$	1.51877e6	0.862411
$316$	140478.	0.0791389
$317$	−1.75822e6	−0.982707	−0.491354	−	0.870960i	$-0.663498\pi$
$317$	−1.75822e6	−0.982707	−0.491354	+	0.870960i	$0.663498\pi$
$318$	−431981.	−0.239551
$319$	413312.	0.227406
$320$	−135043.	−0.0737218
$321$	3.00637e6	1.62847
$322$	3.04955e6	1.63906
$323$	−342871.	−0.182863
$324$	−1.12792e6	−0.596922
$325$	1.99482e6	1.04760
$326$	−1.31134e6	−0.683393
$327$	23399.3	0.0121013
$328$	492216.	0.252622
$329$	7.63622e6	3.88946
$330$	153700.	0.0776941
$331$	−2.81022e6	−1.40984	−0.704920	−	0.709287i	$-0.749017\pi$
$331$	−2.81022e6	−1.40984	−0.704920	+	0.709287i	$0.749017\pi$
$332$	1.30831e6	0.651428
$333$	245166.	0.121158
$334$	392983.	0.192756
$335$	−865983.	−0.421597
$336$	1.35289e6	0.653753
$337$	−688669.	−0.330321	−0.165160	−	0.986267i	$-0.552814\pi$
$337$	−688669.	−0.330321	−0.165160	+	0.986267i	$0.552814\pi$
$338$	−2.34707e6	−1.11746
$339$	−2.76956e6	−1.30892
$340$	72076.5	0.0338140
$341$	−239113.	−0.111357
$342$	−1.79757e6	−0.831038
$343$	−8.37372e6	−3.84311
$344$	461785.	0.210399
$345$	2.00754e6	0.908064
$346$	−291650.	−0.130970
$347$	3.49248e6	1.55708	0.778538	−	0.627597i	$-0.215962\pi$
$347$	3.49248e6	1.55708	0.778538	+	0.627597i	$0.215962\pi$
$348$	2.39495e6	1.06010
$349$	−112109.	−0.0492693	−0.0246346	−	0.999697i	$-0.507842\pi$
$349$	−112109.	−0.0492693	−0.0246346	+	0.999697i	$0.507842\pi$
$350$	−2.09696e6	−0.914997
$351$	−1.28530e6	−0.556846
$352$	58090.1	0.0249888
$353$	−3.09157e6	−1.32051	−0.660256	−	0.751041i	$-0.729552\pi$
$353$	−3.09157e6	−1.32051	−0.660256	+	0.751041i	$0.729552\pi$
$354$	470972.	0.199750
$355$	1.27891e6	0.538602
$356$	−78606.3	−0.0328725
$357$	−722079.	−0.299857
$358$	575058.	0.237140
$359$	429465.	0.175870	0.0879350	−	0.996126i	$-0.471973\pi$
$359$	429465.	0.175870	0.0879350	+	0.996126i	$0.471973\pi$
$360$	377876.	0.153671
$361$	3.82095e6	1.54313
$362$	−2.02783e6	−0.813318
$363$	3.24263e6	1.29161
$364$	4.02845e6	1.59362
$365$	319269.	0.125437
$366$	5572.99	0.00217463
$367$	2.48619e6	0.963537	0.481769	−	0.876298i	$-0.339995\pi$
$367$	2.48619e6	0.963537	0.481769	+	0.876298i	$0.339995\pi$
$368$	758741.	0.292061
$369$	−1.37732e6	−0.526584
$370$	180541.	0.0685599
$371$	1.35216e6	0.510027
$372$	−1.38554e6	−0.519115
$373$	−1.89779e6	−0.706278	−0.353139	−	0.935571i	$-0.614886\pi$
$373$	−1.89779e6	−0.706278	−0.353139	+	0.935571i	$0.614886\pi$
$374$	−31004.5	−0.0114616
$375$	−3.49715e6	−1.28421
$376$	1.89993e6	0.693054
$377$	7.13136e6	2.58416
$378$	1.35110e6	0.486362
$379$	2.47797e6	0.886131	0.443066	−	0.896489i	$-0.353891\pi$
$379$	2.47797e6	0.886131	0.443066	+	0.896489i	$0.353891\pi$
$380$	−1.32373e6	−0.470263
$381$	−2.42192e6	−0.854767
$382$	−387422.	−0.135839
$383$	−3.67122e6	−1.27883	−0.639415	−	0.768861i	$-0.720824\pi$
$383$	−3.67122e6	−1.27883	−0.639415	+	0.768861i	$0.720824\pi$
$384$	336604.	0.116491
$385$	−481100.	−0.165418
$386$	−439956.	−0.150294
$387$	−1.29216e6	−0.438571
$388$	2.05409e6	0.692691
$389$	−2.73587e6	−0.916687	−0.458344	−	0.888775i	$-0.651557\pi$
$389$	−2.73587e6	−0.916687	−0.458344	+	0.888775i	$0.651557\pi$
$390$	2.65196e6	0.882888
$391$	−404964.	−0.133960
$392$	−3.15907e6	−1.03835
$393$	−4.99080e6	−1.63000
$394$	−966208.	−0.313567
$395$	−289467.	−0.0933482
$396$	−162547.	−0.0520885
$397$	3.48782e6	1.11065	0.555326	−	0.831633i	$-0.312593\pi$
$397$	3.48782e6	1.11065	0.555326	+	0.831633i	$0.312593\pi$
$398$	−565980.	−0.179099
$399$	1.32614e7	4.17021
$400$	−521733.	−0.163041
$401$	4.02103e6	1.24875	0.624377	−	0.781123i	$-0.285353\pi$
$401$	4.02103e6	1.24875	0.624377	+	0.781123i	$0.285353\pi$
$402$	2.15853e6	0.666182
$403$	−4.12570e6	−1.26542
$404$	−731668.	−0.223029
$405$	2.32419e6	0.704099
$406$	−7.49649e6	−2.25706
$407$	−77661.5	−0.0232391
$408$	−179656.	−0.0534308
$409$	−4.52746e6	−1.33828	−0.669139	−	0.743137i	$-0.733337\pi$
$409$	−4.52746e6	−1.33828	−0.669139	+	0.743137i	$0.733337\pi$
$410$	−1.01425e6	−0.297980
$411$	1.90651e6	0.556719
$412$	−1.11751e6	−0.324347
$413$	−1.47420e6	−0.425287
$414$	−2.12310e6	−0.608794
$415$	−2.69589e6	−0.768391
$416$	1.00230e6	0.283964
$417$	4.87329e6	1.37240
$418$	569417.	0.159401
$419$	1.00223e6	0.278890	0.139445	−	0.990230i	$-0.455468\pi$
$419$	1.00223e6	0.278890	0.139445	+	0.990230i	$0.455468\pi$
$420$	−2.78774e6	−0.771134
$421$	2.39459e6	0.658454	0.329227	−	0.944251i	$-0.393212\pi$
$421$	2.39459e6	0.658454	0.329227	+	0.944251i	$0.393212\pi$
$422$	−4.43248e6	−1.21162
$423$	−5.31636e6	−1.44465
$424$	336423.	0.0908805
$425$	278465.	0.0747822
$426$	−3.18777e6	−0.851066
$427$	−17444.2	−0.00463000
$428$	−2.34133e6	−0.617808
$429$	−1.14077e6	−0.299264
$430$	−951548.	−0.248176
$431$	−6.11624e6	−1.58596	−0.792978	−	0.609251i	$-0.791470\pi$
$431$	−6.11624e6	−1.58596	−0.792978	+	0.609251i	$0.791470\pi$
$432$	336161.	0.0866638
$433$	−2.99653e6	−0.768067	−0.384034	−	0.923319i	$-0.625465\pi$
$433$	−2.99653e6	−0.768067	−0.384034	+	0.923319i	$0.625465\pi$
$434$	4.33694e6	1.10525
$435$	−4.93500e6	−1.25044
$436$	−18223.2	−0.00459100
$437$	7.43741e6	1.86302
$438$	−795803.	−0.198208
$439$	1.17128e6	0.290068	0.145034	−	0.989427i	$-0.453671\pi$
$439$	1.17128e6	0.290068	0.145034	+	0.989427i	$0.453671\pi$
$440$	−119700.	−0.0294755
$441$	8.83968e6	2.16441
$442$	−534957.	−0.130246
$443$	−2.03011e6	−0.491484	−0.245742	−	0.969335i	$-0.579032\pi$
$443$	−2.03011e6	−0.491484	−0.245742	+	0.969335i	$0.579032\pi$
$444$	−450011.	−0.108334
$445$	161975.	0.0387747
$446$	1.32618e6	0.315694
$447$	7.78716e6	1.84336
$448$	−1.05362e6	−0.248020
$449$	−1.76655e6	−0.413533	−0.206767	−	0.978390i	$-0.566294\pi$
$449$	−1.76655e6	−0.413533	−0.206767	+	0.978390i	$0.566294\pi$
$450$	1.45991e6	0.339855
$451$	436293.	0.101004
$452$	2.15691e6	0.496576
$453$	2.11480e6	0.484200
$454$	−2.48763e6	−0.566429
$455$	−8.30098e6	−1.87975
$456$	3.29950e6	0.743081
$457$	613214.	0.137348	0.0686739	−	0.997639i	$-0.478123\pi$
$457$	613214.	0.137348	0.0686739	+	0.997639i	$0.478123\pi$
$458$	−5.50567e6	−1.22644
$459$	−179420.	−0.0397501
$460$	−1.56345e6	−0.344501
$461$	−1.81264e6	−0.397245	−0.198623	−	0.980076i	$-0.563647\pi$
$461$	−1.81264e6	−0.397245	−0.198623	+	0.980076i	$0.563647\pi$
$462$	1.19918e6	0.261384
$463$	−7.35116e6	−1.59369	−0.796844	−	0.604185i	$-0.793499\pi$
$463$	−7.35116e6	−1.59369	−0.796844	+	0.604185i	$0.793499\pi$
$464$	−1.86516e6	−0.402180
$465$	2.85504e6	0.612321
$466$	6.26637e6	1.33675
$467$	4.24895e6	0.901550	0.450775	−	0.892638i	$-0.351148\pi$
$467$	4.24895e6	0.901550	0.450775	+	0.892638i	$0.351148\pi$
$468$	−2.80462e6	−0.591915
$469$	−6.75648e6	−1.41837
$470$	−3.91496e6	−0.817491
$471$	−8.01266e6	−1.66427
$472$	−366788.	−0.0757810
$473$	409319.	0.0841219
$474$	721518.	0.147503
$475$	−5.11418e6	−1.04002
$476$	562348.	0.113759
$477$	−941376.	−0.189438
$478$	3.03599e6	0.607757
$479$	5.25047e6	1.04558	0.522792	−	0.852460i	$-0.324890\pi$
$479$	5.25047e6	1.04558	0.522792	+	0.852460i	$0.324890\pi$
$480$	−693603.	−0.137407
$481$	−1.33998e6	−0.264081
$482$	700448.	0.137328
$483$	1.56630e7	3.05497
$484$	−2.52533e6	−0.490009
$485$	−4.23263e6	−0.817063
$486$	−4.51686e6	−0.867452
$487$	−4.08908e6	−0.781273	−0.390637	−	0.920545i	$-0.627745\pi$
$487$	−4.08908e6	−0.781273	−0.390637	+	0.920545i	$0.627745\pi$
$488$	−4340.19	−0.000825010 0
$489$	−6.73526e6	−1.27374
$490$	6.50953e6	1.22478
$491$	5.79392e6	1.08460	0.542299	−	0.840186i	$-0.317554\pi$
$491$	5.79392e6	1.08460	0.542299	+	0.840186i	$0.317554\pi$
$492$	2.52811e6	0.470850
$493$	995494.	0.184468
$494$	9.82482e6	1.81137
$495$	334943.	0.0614410
$496$	1.07905e6	0.196941
$497$	9.97814e6	1.81200
$498$	6.71972e6	1.21416
$499$	−3.70130e6	−0.665430	−0.332715	−	0.943027i	$-0.607965\pi$
$499$	−3.70130e6	−0.665430	−0.332715	+	0.943027i	$0.607965\pi$
$500$	2.72355e6	0.487203
$501$	2.01843e6	0.359269
$502$	−4.04090e6	−0.715681
$503$	162962.	0.0287188	0.0143594	−	0.999897i	$-0.495429\pi$
$503$	162962.	0.0287188	0.0143594	+	0.999897i	$0.495429\pi$
$504$	2.94822e6	0.516991
$505$	1.50767e6	0.263073
$506$	672536.	0.116772
$507$	−1.20549e7	−2.08279
$508$	1.88617e6	0.324281
$509$	−7.76653e6	−1.32872	−0.664358	−	0.747414i	$-0.731295\pi$
$509$	−7.76653e6	−1.32872	−0.664358	+	0.747414i	$0.731295\pi$
$510$	370198.	0.0630243
$511$	2.49097e6	0.422003
$512$	−262144.	−0.0441942
$513$	3.29515e6	0.552818
$514$	−2.15983e6	−0.360588
$515$	2.30274e6	0.382584
$516$	2.37181e6	0.392152
$517$	1.68406e6	0.277097
$518$	1.40859e6	0.230654
$519$	−1.49797e6	−0.244109
$520$	−2.06532e6	−0.334949
$521$	3.99715e6	0.645143	0.322572	−	0.946545i	$-0.395453\pi$
$521$	3.99715e6	0.645143	0.322572	+	0.946545i	$0.395453\pi$
$522$	5.21908e6	0.838334
$523$	7.36035e6	1.17664	0.588321	−	0.808628i	$-0.299789\pi$
$523$	7.36035e6	1.17664	0.588321	+	0.808628i	$0.299789\pi$
$524$	3.88678e6	0.618390
$525$	−1.07703e7	−1.70542
$526$	−5.02125e6	−0.791311
$527$	−575922.	−0.0903311
$528$	298361.	0.0465754
$529$	2.34795e6	0.364796
$530$	−693229.	−0.107198
$531$	1.02634e6	0.157964
$532$	−1.03279e7	−1.58209
$533$	7.52787e6	1.14777
$534$	−403736.	−0.0612695
$535$	4.82452e6	0.728735
$536$	−1.68104e6	−0.252735
$537$	2.95360e6	0.441993
$538$	−3.07930e6	−0.458666
$539$	−2.80015e6	−0.415154
$540$	−692689.	−0.102224
$541$	−7.51070e6	−1.10328	−0.551642	−	0.834081i	$-0.685998\pi$
$541$	−7.51070e6	−1.10328	−0.551642	+	0.834081i	$0.685998\pi$
$542$	−2.10846e6	−0.308296
$543$	−1.04153e7	−1.51590
$544$	139915.	0.0202705
$545$	37550.4	0.00541531
$546$	2.06908e7	2.97027
$547$	−4.16872e6	−0.595710	−0.297855	−	0.954611i	$-0.596271\pi$
$547$	−4.16872e6	−0.595710	−0.297855	+	0.954611i	$0.596271\pi$
$548$	−1.48477e6	−0.211207
$549$	12144.7	0.00171971
$550$	−462456.	−0.0651874
$551$	−1.82829e7	−2.56546
$552$	3.89702e6	0.544359
$553$	−2.25845e6	−0.314049
$554$	−9.28112e6	−1.28477
$555$	927287.	0.127786
$556$	−3.79527e6	−0.520662
$557$	1.19455e7	1.63143	0.815713	−	0.578457i	$-0.196345\pi$
$557$	1.19455e7	1.63143	0.815713	+	0.578457i	$0.196345\pi$
$558$	−3.01939e6	−0.410519
$559$	7.06246e6	0.955930
$560$	2.17107e6	0.292552
$561$	−159245.	−0.0213628
$562$	6.04093e6	0.806795
$563$	1.13262e6	0.150596	0.0752980	−	0.997161i	$-0.476009\pi$
$563$	1.13262e6	0.150596	0.0752980	+	0.997161i	$0.476009\pi$
$564$	9.75834e6	1.29175
$565$	−4.44450e6	−0.585735
$566$	6.05427e6	0.794367
$567$	1.81335e7	2.36878
$568$	2.48260e6	0.322877
$569$	7.00412e6	0.906929	0.453464	−	0.891274i	$-0.350188\pi$
$569$	7.00412e6	0.906929	0.453464	+	0.891274i	$0.350188\pi$
$570$	−6.79891e6	−0.876500
$571$	1.38934e6	0.178328	0.0891638	−	0.996017i	$-0.471581\pi$
$571$	1.38934e6	0.178328	0.0891638	+	0.996017i	$0.471581\pi$
$572$	888420.	0.113535
$573$	−1.98987e6	−0.253185
$574$	−7.91331e6	−1.00249
$575$	−6.04034e6	−0.761889
$576$	733529.	0.0921216
$577$	467149.	0.0584138	0.0292069	−	0.999573i	$-0.490702\pi$
$577$	467149.	0.0584138	0.0292069	+	0.999573i	$0.490702\pi$
$578$	5.60475e6	0.697809
$579$	−2.25969e6	−0.280126
$580$	3.84333e6	0.474392
$581$	−2.10336e7	−2.58507
$582$	1.05501e7	1.29107
$583$	298200.	0.0363359
$584$	619763.	0.0751958
$585$	5.77916e6	0.698193
$586$	3.80890e6	0.458201
$587$	2.83355e6	0.339418	0.169709	−	0.985494i	$-0.445717\pi$
$587$	2.83355e6	0.339418	0.169709	+	0.985494i	$0.445717\pi$
$588$	−1.62255e7	−1.93533
$589$	1.05772e7	1.25626
$590$	755800.	0.0893875
$591$	−4.96261e6	−0.584442
$592$	350464.	0.0410997
$593$	1.17412e7	1.37112	0.685559	−	0.728017i	$-0.259558\pi$
$593$	1.17412e7	1.37112	0.685559	+	0.728017i	$0.259558\pi$
$594$	297968.	0.0346500
$595$	−1.15877e6	−0.134185
$596$	−6.06456e6	−0.699333
$597$	−2.90697e6	−0.333814
$598$	1.16041e7	1.32696
$599$	475738.	0.0541753	0.0270876	−	0.999633i	$-0.491377\pi$
$599$	475738.	0.0541753	0.0270876	+	0.999633i	$0.491377\pi$
$600$	−2.67971e6	−0.303885
$601$	−2.04605e6	−0.231063	−0.115532	−	0.993304i	$-0.536857\pi$
$601$	−2.04605e6	−0.231063	−0.115532	+	0.993304i	$0.536857\pi$
$602$	−7.42406e6	−0.834931
$603$	4.70387e6	0.526820
$604$	−1.64699e6	−0.183695
$605$	5.20366e6	0.577990
$606$	−3.75797e6	−0.415692
$607$	6.02736e6	0.663980	0.331990	−	0.943283i	$-0.392280\pi$
$607$	6.02736e6	0.663980	0.331990	+	0.943283i	$0.392280\pi$
$608$	−2.56962e6	−0.281909
$609$	−3.85033e7	−4.20682
$610$	8943.34	0.000973140 0
$611$	2.90571e7	3.14883
$612$	−391508.	−0.0422534
$613$	1.54063e7	1.65595	0.827973	−	0.560769i	$-0.189494\pi$
$613$	1.54063e7	1.65595	0.827973	+	0.560769i	$0.189494\pi$
$614$	−335619.	−0.0359274
$615$	−5.20939e6	−0.555391
$616$	−933908.	−0.0991636
$617$	6.22046e6	0.657824	0.328912	−	0.944361i	$-0.393318\pi$
$617$	6.22046e6	0.657824	0.328912	+	0.944361i	$0.393318\pi$
$618$	−5.73975e6	−0.604535
$619$	1.42963e7	1.49967	0.749836	−	0.661623i	$-0.230132\pi$
$619$	1.42963e7	1.49967	0.749836	+	0.661623i	$0.230132\pi$
$620$	−2.22347e6	−0.232302
$621$	3.89189e6	0.404978
$622$	−4.34411e6	−0.450220
$623$	1.26375e6	0.130449
$624$	5.14797e6	0.529266
$625$	756697.	0.0774858
$626$	4.97630e6	0.507541
$627$	2.92463e6	0.297099
$628$	6.24018e6	0.631390
$629$	−187054.	−0.0188512
$630$	−6.07506e6	−0.609817
$631$	1.09962e7	1.09943	0.549717	−	0.835351i	$-0.314736\pi$
$631$	1.09962e7	1.09943	0.549717	+	0.835351i	$0.314736\pi$
$632$	−561911.	−0.0559596
$633$	−2.27660e7	−2.25827
$634$	7.03287e6	0.694879
$635$	−3.88662e6	−0.382505
$636$	1.72793e6	0.169388
$637$	−4.83142e7	−4.71766
$638$	−1.65325e6	−0.160800
$639$	−6.94680e6	−0.673028
$640$	540171.	0.0521292
$641$	5.58109e6	0.536505	0.268253	−	0.963349i	$-0.413554\pi$
$641$	5.58109e6	0.536505	0.268253	+	0.963349i	$0.413554\pi$
$642$	−1.20255e7	−1.15150
$643$	−1.62315e7	−1.54822	−0.774109	−	0.633052i	$-0.781802\pi$
$643$	−1.62315e7	−1.54822	−0.774109	+	0.633052i	$0.781802\pi$
$644$	−1.21982e7	−1.15899
$645$	−4.88732e6	−0.462563
$646$	1.37149e6	0.129303
$647$	−1.90169e7	−1.78599	−0.892993	−	0.450070i	$-0.851399\pi$
$647$	−1.90169e7	−1.78599	−0.892993	+	0.450070i	$0.851399\pi$
$648$	4.51170e6	0.422088
$649$	−325116.	−0.0302988
$650$	−7.97929e6	−0.740766
$651$	2.22753e7	2.06001
$652$	5.24535e6	0.483232
$653$	−9.90641e6	−0.909145	−0.454573	−	0.890710i	$-0.650208\pi$
$653$	−9.90641e6	−0.909145	−0.454573	+	0.890710i	$0.650208\pi$
$654$	−93597.3	−0.00855695
$655$	−8.00906e6	−0.729421
$656$	−1.96886e6	−0.178631
$657$	−1.73422e6	−0.156744
$658$	−3.05449e7	−2.75026
$659$	1.67262e7	1.50032	0.750159	−	0.661257i	$-0.229977\pi$
$659$	1.67262e7	1.50032	0.750159	+	0.661257i	$0.229977\pi$
$660$	−614799.	−0.0549380
$661$	7.16932e6	0.638226	0.319113	−	0.947717i	$-0.396615\pi$
$661$	7.16932e6	0.638226	0.319113	+	0.947717i	$0.396615\pi$
$662$	1.12409e7	0.996907
$663$	−2.74763e6	−0.242759
$664$	−5.23325e6	−0.460629
$665$	2.12815e7	1.86615
$666$	−980666.	−0.0856713
$667$	−2.15938e7	−1.87938
$668$	−1.57193e6	−0.136299
$669$	6.81150e6	0.588407
$670$	3.46393e6	0.298114
$671$	−3847.08	−0.000329856 0
$672$	−5.41155e6	−0.462273
$673$	1.31559e7	1.11965	0.559826	−	0.828611i	$-0.310868\pi$
$673$	1.31559e7	1.11965	0.559826	+	0.828611i	$0.310868\pi$
$674$	2.75468e6	0.233572
$675$	−2.67618e6	−0.226077
$676$	9.38826e6	0.790166
$677$	3.87633e6	0.325049	0.162525	−	0.986704i	$-0.448036\pi$
$677$	3.87633e6	0.325049	0.162525	+	0.986704i	$0.448036\pi$
$678$	1.10782e7	0.925543
$679$	−3.30233e7	−2.74882
$680$	−288306.	−0.0239101
$681$	−1.27769e7	−1.05574
$682$	956452.	0.0787412
$683$	−1.92317e7	−1.57749	−0.788743	−	0.614723i	$-0.789268\pi$
$683$	−1.92317e7	−1.57749	−0.788743	+	0.614723i	$0.789268\pi$
$684$	7.19028e6	0.587632
$685$	3.05951e6	0.249130
$686$	3.34949e7	2.71749
$687$	−2.82780e7	−2.28590
$688$	−1.84714e6	−0.148774
$689$	5.14519e6	0.412908
$690$	−8.03016e6	−0.642098
$691$	385456.	0.0307100	0.0153550	−	0.999882i	$-0.495112\pi$
$691$	385456.	0.0307100	0.0153550	+	0.999882i	$0.495112\pi$
$692$	1.16660e6	0.0926098
$693$	2.61326e6	0.206704
$694$	−1.39699e7	−1.10102
$695$	7.82048e6	0.614146
$696$	−9.57978e6	−0.749605
$697$	1.05085e6	0.0819326
$698$	448435.	0.0348386
$699$	3.21851e7	2.49151
$700$	8.38784e6	0.647001
$701$	−1.61600e7	−1.24207	−0.621037	−	0.783781i	$-0.713288\pi$
$701$	−1.61600e7	−1.24207	−0.621037	+	0.783781i	$0.713288\pi$
$702$	5.14118e6	0.393750
$703$	3.43536e6	0.262170
$704$	−232360.	−0.0176698
$705$	−2.01079e7	−1.52368
$706$	1.23663e7	0.933743
$707$	1.17629e7	0.885050
$708$	−1.88389e6	−0.141245
$709$	−1.19773e7	−0.894837	−0.447419	−	0.894325i	$-0.647657\pi$
$709$	−1.19773e7	−0.894837	−0.447419	+	0.894325i	$0.647657\pi$
$710$	−5.11562e6	−0.380849
$711$	1.57234e6	0.116646
$712$	314425.	0.0232444
$713$	1.24926e7	0.920302
$714$	2.88831e6	0.212031
$715$	−1.83067e6	−0.133920
$716$	−2.30023e6	−0.167683
$717$	1.55934e7	1.13277
$718$	−1.71786e6	−0.124359
$719$	1.01315e7	0.730886	0.365443	−	0.930834i	$-0.380917\pi$
$719$	1.01315e7	0.730886	0.365443	+	0.930834i	$0.380917\pi$
$720$	−1.51150e6	−0.108662
$721$	1.79662e7	1.28711
$722$	−1.52838e7	−1.09116
$723$	3.59762e6	0.255958
$724$	8.11132e6	0.575102
$725$	1.48485e7	1.04915
$726$	−1.29705e7	−0.913304
$727$	2.61614e7	1.83580	0.917899	−	0.396813i	$-0.129884\pi$
$727$	2.61614e7	1.83580	0.917899	+	0.396813i	$0.129884\pi$
$728$	−1.61138e7	−1.12686
$729$	−6.06900e6	−0.422959
$730$	−1.27708e6	−0.0886972
$731$	985876.	0.0682384
$732$	−22292.0	−0.00153770
$733$	6.71541e6	0.461650	0.230825	−	0.972995i	$-0.425858\pi$
$733$	6.71541e6	0.461650	0.230825	+	0.972995i	$0.425858\pi$
$734$	−9.94475e6	−0.681324
$735$	3.34341e7	2.28282
$736$	−3.03496e6	−0.206518
$737$	−1.49005e6	−0.101049
$738$	5.50926e6	0.372351
$739$	8.37999e6	0.564459	0.282229	−	0.959347i	$-0.408926\pi$
$739$	8.37999e6	0.564459	0.282229	+	0.959347i	$0.408926\pi$
$740$	−722162.	−0.0484792
$741$	5.04620e7	3.37613
$742$	−5.40863e6	−0.360643
$743$	1.69555e7	1.12678	0.563390	−	0.826191i	$-0.309497\pi$
$743$	1.69555e7	1.12678	0.563390	+	0.826191i	$0.309497\pi$
$744$	5.54218e6	0.367069
$745$	1.24966e7	0.824898
$746$	7.59115e6	0.499414
$747$	1.46436e7	0.960169
$748$	124018.	0.00810459
$749$	3.76413e7	2.45166
$750$	1.39886e7	0.908074
$751$	2.80473e6	0.181464	0.0907321	−	0.995875i	$-0.471079\pi$
$751$	2.80473e6	0.181464	0.0907321	+	0.995875i	$0.471079\pi$
$752$	−7.59970e6	−0.490063
$753$	−2.07548e7	−1.33392
$754$	−2.85254e7	−1.82727
$755$	3.39376e6	0.216678
$756$	−5.40442e6	−0.343910
$757$	3.23909e6	0.205439	0.102720	−	0.994710i	$-0.467246\pi$
$757$	3.23909e6	0.205439	0.102720	+	0.994710i	$0.467246\pi$
$758$	−9.91188e6	−0.626590
$759$	3.45426e6	0.217646
$760$	5.29492e6	0.332526
$761$	−2.76822e7	−1.73276	−0.866381	−	0.499384i	$-0.833560\pi$
$761$	−2.76822e7	−1.73276	−0.866381	+	0.499384i	$0.833560\pi$
$762$	9.68769e6	0.604411
$763$	292972.	0.0182186
$764$	1.54969e6	0.0960530
$765$	806736.	0.0498400
$766$	1.46849e7	0.904270
$767$	−5.60960e6	−0.344305
$768$	−1.34642e6	−0.0823714
$769$	3.12687e6	0.190675	0.0953377	−	0.995445i	$-0.469607\pi$
$769$	3.12687e6	0.190675	0.0953377	+	0.995445i	$0.469607\pi$
$770$	1.92440e6	0.116968
$771$	−1.10932e7	−0.672083
$772$	1.75983e6	0.106274
$773$	−1.81928e7	−1.09509	−0.547547	−	0.836775i	$-0.684438\pi$
$773$	−1.81928e7	−1.09509	−0.547547	+	0.836775i	$0.684438\pi$
$774$	5.16865e6	0.310116
$775$	−8.59031e6	−0.513753
$776$	−8.21634e6	−0.489806
$777$	7.23478e6	0.429905
$778$	1.09435e7	0.648196
$779$	−1.92994e7	−1.13946
$780$	−1.06078e7	−0.624296
$781$	2.20054e6	0.129093
$782$	1.61986e6	0.0947238
$783$	−9.56716e6	−0.557672
$784$	1.26363e7	0.734224
$785$	−1.28584e7	−0.744756
$786$	1.99632e7	1.15259
$787$	1.00439e7	0.578048	0.289024	−	0.957322i	$-0.406669\pi$
$787$	1.00439e7	0.578048	0.289024	+	0.957322i	$0.406669\pi$
$788$	3.86483e6	0.221725
$789$	−2.57900e7	−1.47489
$790$	1.15787e6	0.0660072
$791$	−3.46764e7	−1.97057
$792$	650189.	0.0368321
$793$	−66378.1	−0.00374837
$794$	−1.39513e7	−0.785350
$795$	−3.56054e6	−0.199801
$796$	2.26392e6	0.126642
$797$	1.87840e7	1.04747	0.523737	−	0.851880i	$-0.324538\pi$
$797$	1.87840e7	1.04747	0.523737	+	0.851880i	$0.324538\pi$
$798$	−5.30457e7	−2.94878
$799$	4.05620e6	0.224777
$800$	2.08693e6	0.115288
$801$	−879823.	−0.0484522
$802$	−1.60841e7	−0.883002
$803$	549349.	0.0300649
$804$	−8.63411e6	−0.471062
$805$	2.51355e7	1.36709
$806$	1.65028e7	0.894787
$807$	−1.58158e7	−0.854886
$808$	2.92667e6	0.157705
$809$	−2.53632e7	−1.36249	−0.681245	−	0.732055i	$-0.738561\pi$
$809$	−2.53632e7	−1.36249	−0.681245	+	0.732055i	$0.738561\pi$
$810$	−9.29675e6	−0.497873
$811$	2.41930e7	1.29163	0.645813	−	0.763495i	$-0.276518\pi$
$811$	2.41930e7	1.29163	0.645813	+	0.763495i	$0.276518\pi$
$812$	2.99860e7	1.59598
$813$	−1.08294e7	−0.574618
$814$	310646.	0.0164325
$815$	−1.08085e7	−0.569996
$816$	718625.	0.0377813
$817$	−1.81062e7	−0.949014
$818$	1.81099e7	0.946306
$819$	4.50896e7	2.34891
$820$	4.05702e6	0.210704
$821$	−2.05378e7	−1.06340	−0.531699	−	0.846933i	$-0.678446\pi$
$821$	−2.05378e7	−1.06340	−0.531699	+	0.846933i	$0.678446\pi$
$822$	−7.62606e6	−0.393659
$823$	−1.97453e7	−1.01616	−0.508082	−	0.861309i	$-0.669645\pi$
$823$	−1.97453e7	−1.01616	−0.508082	+	0.861309i	$0.669645\pi$
$824$	4.47006e6	0.229348
$825$	−2.37525e6	−0.121500
$826$	5.89682e6	0.300724
$827$	−2.18474e7	−1.11080	−0.555400	−	0.831584i	$-0.687435\pi$
$827$	−2.18474e7	−1.11080	−0.555400	+	0.831584i	$0.687435\pi$
$828$	8.49241e6	0.430482
$829$	−7.33304e6	−0.370593	−0.185297	−	0.982683i	$-0.559325\pi$
$829$	−7.33304e6	−0.370593	−0.185297	+	0.982683i	$0.559325\pi$
$830$	1.07836e7	0.543335
$831$	−4.76695e7	−2.39463
$832$	−4.00919e6	−0.200793
$833$	−6.74437e6	−0.336767
$834$	−1.94932e7	−0.970436
$835$	3.23911e6	0.160772
$836$	−2.27767e6	−0.112713
$837$	5.53488e6	0.273083
$838$	−4.00893e6	−0.197205
$839$	−1.86783e7	−0.916080	−0.458040	−	0.888932i	$-0.651448\pi$
$839$	−1.86783e7	−0.916080	−0.458040	+	0.888932i	$0.651448\pi$
$840$	1.11510e7	0.545274
$841$	3.25714e7	1.58799
$842$	−9.57836e6	−0.465598
$843$	3.10273e7	1.50375
$844$	1.77299e7	0.856742
$845$	−1.93453e7	−0.932041
$846$	2.12654e7	1.02152
$847$	4.05994e7	1.94451
$848$	−1.34569e6	−0.0642622
$849$	3.10958e7	1.48058
$850$	−1.11386e6	−0.0528790
$851$	4.05748e6	0.192058
$852$	1.27511e7	0.601794
$853$	−1.26207e7	−0.593897	−0.296948	−	0.954894i	$-0.595969\pi$
$853$	−1.26207e7	−0.593897	−0.296948	+	0.954894i	$0.595969\pi$
$854$	69776.8	0.00327391
$855$	−1.48162e7	−0.693142
$856$	9.36533e6	0.436856
$857$	−3.24918e7	−1.51120	−0.755599	−	0.655035i	$-0.772654\pi$
$857$	−3.24918e7	−1.51120	−0.755599	+	0.655035i	$0.772654\pi$
$858$	4.56308e6	0.211612
$859$	−1.25398e7	−0.579840	−0.289920	−	0.957051i	$-0.593629\pi$
$859$	−1.25398e7	−0.579840	−0.289920	+	0.957051i	$0.593629\pi$
$860$	3.80619e6	0.175487
$861$	−4.06441e7	−1.86849
$862$	2.44649e7	1.12144
$863$	3.53124e7	1.61399	0.806993	−	0.590561i	$-0.201094\pi$
$863$	3.53124e7	1.61399	0.806993	+	0.590561i	$0.201094\pi$
$864$	−1.34464e6	−0.0612805
$865$	−2.40388e6	−0.109238
$866$	1.19861e7	0.543106
$867$	2.87870e7	1.30061
$868$	−1.73477e7	−0.781526
$869$	−498069.	−0.0223738
$870$	1.97400e7	0.884196
$871$	−2.57095e7	−1.14828
$872$	72892.6	0.00324633
$873$	2.29909e7	1.02099
$874$	−2.97496e7	−1.31736
$875$	−4.37862e7	−1.93338
$876$	3.18321e6	0.140154
$877$	−3.85693e6	−0.169334	−0.0846668	−	0.996409i	$-0.526983\pi$
$877$	−3.85693e6	−0.169334	−0.0846668	+	0.996409i	$0.526983\pi$
$878$	−4.68512e6	−0.205109
$879$	1.95632e7	0.854019
$880$	478799.	0.0208424
$881$	−7.10078e6	−0.308224	−0.154112	−	0.988053i	$-0.549252\pi$
$881$	−7.10078e6	−0.308224	−0.154112	+	0.988053i	$0.549252\pi$
$882$	−3.53587e7	−1.53047
$883$	−3.20647e7	−1.38397	−0.691983	−	0.721913i	$-0.743263\pi$
$883$	−3.20647e7	−1.38397	−0.691983	+	0.721913i	$0.743263\pi$
$884$	2.13983e6	0.0920976
$885$	3.88192e6	0.166605
$886$	8.12043e6	0.347532
$887$	4.46115e7	1.90387	0.951936	−	0.306298i	$-0.0990903\pi$
$887$	4.46115e7	1.90387	0.951936	+	0.306298i	$0.0990903\pi$
$888$	1.80004e6	0.0766039
$889$	−3.03237e7	−1.28685
$890$	−647901.	−0.0274179
$891$	3.99910e6	0.168759
$892$	−5.30473e6	−0.223229
$893$	−7.44946e7	−3.12605
$894$	−3.11487e7	−1.30345
$895$	4.73983e6	0.197790
$896$	4.21446e6	0.175377
$897$	5.96004e7	2.47325
$898$	7.06621e6	0.292412
$899$	−3.07098e7	−1.26729
$900$	−5.83963e6	−0.240314
$901$	718238.	0.0294752
$902$	−1.74517e6	−0.0714203
$903$	−3.81313e7	−1.55619
$904$	−8.62763e6	−0.351132
$905$	−1.67141e7	−0.678362
$906$	−8.45921e6	−0.342381
$907$	3.40803e7	1.37558	0.687789	−	0.725911i	$-0.258581\pi$
$907$	3.40803e7	1.37558	0.687789	+	0.725911i	$0.258581\pi$
$908$	9.95051e6	0.400526
$909$	−8.18939e6	−0.328732
$910$	3.32039e7	1.32919
$911$	3.34979e7	1.33728	0.668639	−	0.743587i	$-0.266877\pi$
$911$	3.34979e7	1.33728	0.668639	+	0.743587i	$0.266877\pi$
$912$	−1.31980e7	−0.525437
$913$	−4.63867e6	−0.184169
$914$	−2.45286e6	−0.0971195
$915$	45934.6	0.00181379
$916$	2.20227e7	0.867224
$917$	−6.24874e7	−2.45397
$918$	717678.	0.0281075
$919$	−2.08868e7	−0.815797	−0.407899	−	0.913027i	$-0.633738\pi$
$919$	−2.08868e7	−0.815797	−0.407899	+	0.913027i	$0.633738\pi$
$920$	6.25381e6	0.243599
$921$	−1.72380e6	−0.0669633
$922$	7.25055e6	0.280895
$923$	3.79685e7	1.46696
$924$	−4.79671e6	−0.184826
$925$	−2.79005e6	−0.107215
$926$	2.94046e7	1.12691
$927$	−1.25081e7	−0.478070
$928$	7.46064e6	0.284385
$929$	−3.48907e7	−1.32639	−0.663193	−	0.748448i	$-0.730799\pi$
$929$	−3.48907e7	−1.32639	−0.663193	+	0.748448i	$0.730799\pi$
$930$	−1.14201e7	−0.432977
$931$	1.23865e8	4.68353
$932$	−2.50655e7	−0.945227
$933$	−2.23121e7	−0.839144
$934$	−1.69958e7	−0.637492
$935$	−255550.	−0.00955976
$936$	1.12185e7	0.418547
$937$	−4.91364e6	−0.182833	−0.0914164	−	0.995813i	$-0.529139\pi$
$937$	−4.91364e6	−0.182833	−0.0914164	+	0.995813i	$0.529139\pi$
$938$	2.70259e7	1.00294
$939$	2.55592e7	0.945981
$940$	1.56599e7	0.578054
$941$	−2.19110e7	−0.806656	−0.403328	−	0.915055i	$-0.632147\pi$
$941$	−2.19110e7	−0.806656	−0.403328	+	0.915055i	$0.632147\pi$
$942$	3.20506e7	1.17682
$943$	−2.27945e7	−0.834738
$944$	1.46715e6	0.0535853
$945$	1.11363e7	0.405659
$946$	−1.63728e6	−0.0594831
$947$	−5.22836e6	−0.189448	−0.0947241	−	0.995504i	$-0.530197\pi$
$947$	−5.22836e6	−0.189448	−0.0947241	+	0.995504i	$0.530197\pi$
$948$	−2.88607e6	−0.104300
$949$	9.47855e6	0.341646
$950$	2.04567e7	0.735406
$951$	3.61220e7	1.29515
$952$	−2.24939e6	−0.0804401
$953$	2.00312e7	0.714454	0.357227	−	0.934018i	$-0.383722\pi$
$953$	2.00312e7	0.714454	0.357227	+	0.934018i	$0.383722\pi$
$954$	3.76550e6	0.133953
$955$	−3.19327e6	−0.113299
$956$	−1.21439e7	−0.429749
$957$	−8.49137e6	−0.299708
$958$	−2.10019e7	−0.739340
$959$	2.38706e7	0.838139
$960$	2.77441e6	0.0971612
$961$	−1.08627e7	−0.379426
$962$	5.35994e6	0.186733
$963$	−2.62060e7	−0.910615
$964$	−2.80179e6	−0.0971053
$965$	−3.62628e6	−0.125355
$966$	−6.26520e7	−2.16019
$967$	−3.84501e7	−1.32230	−0.661152	−	0.750252i	$-0.729932\pi$
$967$	−3.84501e7	−1.32230	−0.661152	+	0.750252i	$0.729932\pi$
$968$	1.01013e7	0.346489
$969$	7.04419e6	0.241002
$970$	1.69305e7	0.577751
$971$	−1.04270e7	−0.354904	−0.177452	−	0.984129i	$-0.556785\pi$
$971$	−1.04270e7	−0.354904	−0.177452	+	0.984129i	$0.556785\pi$
$972$	1.80674e7	0.613381
$973$	6.10161e7	2.06615
$974$	1.63563e7	0.552444
$975$	−4.09830e7	−1.38068
$976$	17360.8	0.000583370 0
$977$	2.47868e7	0.830775	0.415388	−	0.909644i	$-0.363646\pi$
$977$	2.47868e7	0.830775	0.415388	+	0.909644i	$0.363646\pi$
$978$	2.69410e7	0.900673
$979$	278702.	0.00929358
$980$	−2.60381e7	−0.866054
$981$	−203968.	−0.00676688
$982$	−2.31757e7	−0.766926
$983$	5.88739e7	1.94330	0.971649	−	0.236429i	$-0.0759770\pi$
$983$	5.88739e7	1.94330	0.971649	+	0.236429i	$0.0759770\pi$
$984$	−1.01124e7	−0.332941
$985$	−7.96383e6	−0.261536
$986$	−3.98198e6	−0.130439
$987$	−1.56884e8	−5.12608
$988$	−3.92993e7	−1.28083
$989$	−2.13852e7	−0.695220
$990$	−1.33977e6	−0.0434453
$991$	4.06850e7	1.31598	0.657991	−	0.753025i	$-0.271406\pi$
$991$	4.06850e7	1.31598	0.657991	+	0.753025i	$0.271406\pi$
$992$	−4.31619e6	−0.139258
$993$	5.77350e7	1.85809
$994$	−3.99126e7	−1.28128
$995$	−4.66501e6	−0.149381
$996$	−2.68789e7	−0.858544
$997$	4.64039e7	1.47848	0.739242	−	0.673439i	$-0.235184\pi$
$997$	4.64039e7	1.47848	0.739242	+	0.673439i	$0.235184\pi$
$998$	1.48052e7	0.470530
$999$	1.79767e6	0.0569897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.a.d.1.1	✓	5
3.2	odd	2		666.6.a.o.1.3		5
4.3	odd	2		592.6.a.d.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.a.d.1.1	✓	5	1.1	even	1	trivial
592.6.a.d.1.5		5	4.3	odd	2
666.6.a.o.1.3		5	3.2	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -20.5447 q^{3} +16.0000 q^{4} -32.9694 q^{5} +82.1788 q^{6} -257.230 q^{7} -64.0000 q^{8} +179.084 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -20.5447 q^{3} +16.0000 q^{4} -32.9694 q^{5} +82.1788 q^{6} -257.230 q^{7} -64.0000 q^{8} +179.084 q^{9} +131.878 q^{10} -56.7286 q^{11} -328.715 q^{12} -978.805 q^{13} +1028.92 q^{14} +677.346 q^{15} +256.000 q^{16} -136.635 q^{17} -716.337 q^{18} +2509.39 q^{19} -527.511 q^{20} +5284.72 q^{21} +226.914 q^{22} +2963.83 q^{23} +1314.86 q^{24} -2038.02 q^{25} +3915.22 q^{26} +1313.13 q^{27} -4115.68 q^{28} -7285.78 q^{29} -2709.39 q^{30} +4215.03 q^{31} -1024.00 q^{32} +1165.47 q^{33} +546.541 q^{34} +8480.73 q^{35} +2865.35 q^{36} +1369.00 q^{37} -10037.6 q^{38} +20109.2 q^{39} +2110.04 q^{40} -7690.88 q^{41} -21138.9 q^{42} -7215.39 q^{43} -907.658 q^{44} -5904.31 q^{45} -11855.3 q^{46} -29686.3 q^{47} -5259.44 q^{48} +49360.4 q^{49} +8152.07 q^{50} +2807.13 q^{51} -15660.9 q^{52} -5256.61 q^{53} -5252.51 q^{54} +1870.31 q^{55} +16462.7 q^{56} -51554.7 q^{57} +29143.1 q^{58} +5731.07 q^{59} +10837.5 q^{60} +67.8155 q^{61} -16860.1 q^{62} -46065.9 q^{63} +4096.00 q^{64} +32270.6 q^{65} -4661.89 q^{66} +26266.3 q^{67} -2186.16 q^{68} -60891.0 q^{69} -33922.9 q^{70} -38790.7 q^{71} -11461.4 q^{72} -9683.80 q^{73} -5476.00 q^{74} +41870.4 q^{75} +40150.3 q^{76} +14592.3 q^{77} -80437.0 q^{78} +8779.86 q^{79} -8440.17 q^{80} -70495.3 q^{81} +30763.5 q^{82} +81769.5 q^{83} +84555.5 q^{84} +4504.78 q^{85} +28861.5 q^{86} +149684. q^{87} +3630.63 q^{88} -4912.90 q^{89} +23617.2 q^{90} +251778. q^{91} +47421.3 q^{92} -86596.5 q^{93} +118745. q^{94} -82733.2 q^{95} +21037.8 q^{96} +128380. q^{97} -197442. q^{98} -10159.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20 q^{2} + 19 q^{3} + 80 q^{4} - 67 q^{5} - 76 q^{6} + 182 q^{7} - 320 q^{8} + 598 q^{9}+O(q^{10}) \) 5 * q - 20 * q^2 + 19 * q^3 + 80 * q^4 - 67 * q^5 - 76 * q^6 + 182 * q^7 - 320 * q^8 + 598 * q^9	\( 5 q - 20 q^{2} + 19 q^{3} + 80 q^{4} - 67 q^{5} - 76 q^{6} + 182 q^{7} - 320 q^{8} + 598 q^{9} + 268 q^{10} - 409 q^{11} + 304 q^{12} - 679 q^{13} - 728 q^{14} + 1272 q^{15} + 1280 q^{16} - 114 q^{17} - 2392 q^{18} + 4180 q^{19} - 1072 q^{20} + 13712 q^{21} + 1636 q^{22} + 6837 q^{23} - 1216 q^{24} + 16866 q^{25} + 2716 q^{26} + 15010 q^{27} + 2912 q^{28} + 4137 q^{29} - 5088 q^{30} + 19875 q^{31} - 5120 q^{32} + 8646 q^{33} + 456 q^{34} + 1980 q^{35} + 9568 q^{36} + 6845 q^{37} - 16720 q^{38} - 13843 q^{39} + 4288 q^{40} - 29367 q^{41} - 54848 q^{42} - 18282 q^{43} - 6544 q^{44} + 1440 q^{45} - 27348 q^{46} - 50386 q^{47} + 4864 q^{48} + 48659 q^{49} - 67464 q^{50} - 12006 q^{51} - 10864 q^{52} + 21048 q^{53} - 60040 q^{54} - 31181 q^{55} - 11648 q^{56} - 74590 q^{57} - 16548 q^{58} - 20350 q^{59} + 20352 q^{60} + 20031 q^{61} - 79500 q^{62} + 81446 q^{63} + 20480 q^{64} - 48402 q^{65} - 34584 q^{66} + 8003 q^{67} - 1824 q^{68} - 75165 q^{69} - 7920 q^{70} - 65400 q^{71} - 38272 q^{72} + 24867 q^{73} - 27380 q^{74} + 277846 q^{75} + 66880 q^{76} + 19842 q^{77} + 55372 q^{78} + 154397 q^{79} - 17152 q^{80} + 20425 q^{81} + 117468 q^{82} + 191072 q^{83} + 219392 q^{84} - 119046 q^{85} + 73128 q^{86} + 61953 q^{87} + 26176 q^{88} - 226894 q^{89} - 5760 q^{90} + 151222 q^{91} + 109392 q^{92} + 158246 q^{93} + 201544 q^{94} - 502130 q^{95} - 19456 q^{96} - 40678 q^{97} - 194636 q^{98} + 71094 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + 19 * q^3 + 80 * q^4 - 67 * q^5 - 76 * q^6 + 182 * q^7 - 320 * q^8 + 598 * q^9 + 268 * q^10 - 409 * q^11 + 304 * q^12 - 679 * q^13 - 728 * q^14 + 1272 * q^15 + 1280 * q^16 - 114 * q^17 - 2392 * q^18 + 4180 * q^19 - 1072 * q^20 + 13712 * q^21 + 1636 * q^22 + 6837 * q^23 - 1216 * q^24 + 16866 * q^25 + 2716 * q^26 + 15010 * q^27 + 2912 * q^28 + 4137 * q^29 - 5088 * q^30 + 19875 * q^31 - 5120 * q^32 + 8646 * q^33 + 456 * q^34 + 1980 * q^35 + 9568 * q^36 + 6845 * q^37 - 16720 * q^38 - 13843 * q^39 + 4288 * q^40 - 29367 * q^41 - 54848 * q^42 - 18282 * q^43 - 6544 * q^44 + 1440 * q^45 - 27348 * q^46 - 50386 * q^47 + 4864 * q^48 + 48659 * q^49 - 67464 * q^50 - 12006 * q^51 - 10864 * q^52 + 21048 * q^53 - 60040 * q^54 - 31181 * q^55 - 11648 * q^56 - 74590 * q^57 - 16548 * q^58 - 20350 * q^59 + 20352 * q^60 + 20031 * q^61 - 79500 * q^62 + 81446 * q^63 + 20480 * q^64 - 48402 * q^65 - 34584 * q^66 + 8003 * q^67 - 1824 * q^68 - 75165 * q^69 - 7920 * q^70 - 65400 * q^71 - 38272 * q^72 + 24867 * q^73 - 27380 * q^74 + 277846 * q^75 + 66880 * q^76 + 19842 * q^77 + 55372 * q^78 + 154397 * q^79 - 17152 * q^80 + 20425 * q^81 + 117468 * q^82 + 191072 * q^83 + 219392 * q^84 - 119046 * q^85 + 73128 * q^86 + 61953 * q^87 + 26176 * q^88 - 226894 * q^89 - 5760 * q^90 + 151222 * q^91 + 109392 * q^92 + 158246 * q^93 + 201544 * q^94 - 502130 * q^95 - 19456 * q^96 - 40678 * q^97 - 194636 * q^98 + 71094 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more