LMFDB - Embedded newform 29.6.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,6,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, 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("29.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	29.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:	$4.65113077458$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.3257317.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 34x^{2} - 27x + 10 $ x^4 - 34x^2 - 27x + 10
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.10057$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.16235 q^{2} -17.5258 q^{3} -14.6748 q^{4} +32.5670 q^{5} -72.9487 q^{6} -220.793 q^{7} -194.277 q^{8} +64.1549 q^{9} +O(q^{10})$	\(q+4.16235 q^{2} -17.5258 q^{3} -14.6748 q^{4} +32.5670 q^{5} -72.9487 q^{6} -220.793 q^{7} -194.277 q^{8} +64.1549 q^{9} +135.555 q^{10} -85.7296 q^{11} +257.189 q^{12} +1034.02 q^{13} -919.018 q^{14} -570.765 q^{15} -339.054 q^{16} -313.020 q^{17} +267.035 q^{18} +458.534 q^{19} -477.916 q^{20} +3869.58 q^{21} -356.836 q^{22} -3448.84 q^{23} +3404.87 q^{24} -2064.39 q^{25} +4303.94 q^{26} +3134.41 q^{27} +3240.10 q^{28} -841.000 q^{29} -2375.72 q^{30} -7983.23 q^{31} +4805.60 q^{32} +1502.48 q^{33} -1302.90 q^{34} -7190.58 q^{35} -941.463 q^{36} +152.624 q^{37} +1908.58 q^{38} -18122.0 q^{39} -6327.03 q^{40} -18492.2 q^{41} +16106.6 q^{42} +2072.84 q^{43} +1258.07 q^{44} +2089.33 q^{45} -14355.3 q^{46} +15845.6 q^{47} +5942.21 q^{48} +31942.6 q^{49} -8592.70 q^{50} +5485.94 q^{51} -15174.0 q^{52} +9240.52 q^{53} +13046.5 q^{54} -2791.96 q^{55} +42895.0 q^{56} -8036.19 q^{57} -3500.54 q^{58} -14323.2 q^{59} +8375.88 q^{60} -19580.2 q^{61} -33229.0 q^{62} -14165.0 q^{63} +30852.3 q^{64} +33674.9 q^{65} +6253.86 q^{66} -9193.70 q^{67} +4593.53 q^{68} +60443.8 q^{69} -29929.7 q^{70} -19374.7 q^{71} -12463.8 q^{72} -56912.4 q^{73} +635.276 q^{74} +36180.1 q^{75} -6728.91 q^{76} +18928.5 q^{77} -75430.1 q^{78} +51573.6 q^{79} -11042.0 q^{80} -70522.8 q^{81} -76971.0 q^{82} +19978.1 q^{83} -56785.5 q^{84} -10194.2 q^{85} +8627.87 q^{86} +14739.2 q^{87} +16655.3 q^{88} +130663. q^{89} +8696.54 q^{90} -228304. q^{91} +50611.1 q^{92} +139913. q^{93} +65954.9 q^{94} +14933.1 q^{95} -84222.2 q^{96} +43603.5 q^{97} +132956. q^{98} -5499.97 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 28 q^{3} + 10 q^{4} - 68 q^{5} - 194 q^{6} - 208 q^{7} - 504 q^{8} - 280 q^{9}+O(q^{10}) $ 4 * q - 28 * q^3 + 10 * q^4 - 68 * q^5 - 194 * q^6 - 208 * q^7 - 504 * q^8 - 280 * q^9	\( 4 q - 28 q^{3} + 10 q^{4} - 68 q^{5} - 194 q^{6} - 208 q^{7} - 504 q^{8} - 280 q^{9} - 788 q^{10} - 124 q^{11} + 20 q^{12} - 460 q^{13} + 768 q^{14} + 932 q^{15} - 414 q^{16} + 184 q^{17} + 3208 q^{18} - 2392 q^{19} + 2822 q^{20} + 992 q^{21} + 5538 q^{22} - 1192 q^{23} + 6786 q^{24} + 1824 q^{25} + 4724 q^{26} + 2468 q^{27} + 44 q^{28} - 3364 q^{29} + 8186 q^{30} - 19212 q^{31} + 6552 q^{32} - 10580 q^{33} - 7612 q^{34} - 22944 q^{35} - 7468 q^{36} - 10928 q^{37} - 456 q^{38} - 8732 q^{39} - 20 q^{40} - 1120 q^{41} + 1844 q^{42} - 21420 q^{43} - 1932 q^{44} - 8344 q^{45} - 7588 q^{46} + 23772 q^{47} + 33060 q^{48} + 10452 q^{49} + 43240 q^{50} + 12744 q^{51} - 29062 q^{52} + 8860 q^{53} + 35410 q^{54} - 52652 q^{55} + 34304 q^{56} + 48944 q^{57} - 10840 q^{59} + 25200 q^{60} + 49448 q^{61} + 18518 q^{62} + 27488 q^{63} - 20734 q^{64} + 97836 q^{65} - 47744 q^{66} - 7840 q^{67} + 20724 q^{68} + 58792 q^{69} - 77496 q^{70} - 48744 q^{71} + 8088 q^{72} - 74992 q^{73} - 35920 q^{74} - 90448 q^{75} - 140792 q^{76} + 128656 q^{77} + 2982 q^{78} - 106076 q^{79} + 58638 q^{80} - 59692 q^{81} - 234132 q^{82} + 62888 q^{83} - 59832 q^{84} + 23848 q^{85} - 216014 q^{86} + 23548 q^{87} - 39426 q^{88} + 107568 q^{89} + 41552 q^{90} - 268896 q^{91} - 26268 q^{92} + 221460 q^{93} + 30542 q^{94} + 147352 q^{95} - 78606 q^{96} - 49520 q^{97} + 242304 q^{98} + 166720 q^{99}+O(q^{100}) \) 4 * q - 28 * q^3 + 10 * q^4 - 68 * q^5 - 194 * q^6 - 208 * q^7 - 504 * q^8 - 280 * q^9 - 788 * q^10 - 124 * q^11 + 20 * q^12 - 460 * q^13 + 768 * q^14 + 932 * q^15 - 414 * q^16 + 184 * q^17 + 3208 * q^18 - 2392 * q^19 + 2822 * q^20 + 992 * q^21 + 5538 * q^22 - 1192 * q^23 + 6786 * q^24 + 1824 * q^25 + 4724 * q^26 + 2468 * q^27 + 44 * q^28 - 3364 * q^29 + 8186 * q^30 - 19212 * q^31 + 6552 * q^32 - 10580 * q^33 - 7612 * q^34 - 22944 * q^35 - 7468 * q^36 - 10928 * q^37 - 456 * q^38 - 8732 * q^39 - 20 * q^40 - 1120 * q^41 + 1844 * q^42 - 21420 * q^43 - 1932 * q^44 - 8344 * q^45 - 7588 * q^46 + 23772 * q^47 + 33060 * q^48 + 10452 * q^49 + 43240 * q^50 + 12744 * q^51 - 29062 * q^52 + 8860 * q^53 + 35410 * q^54 - 52652 * q^55 + 34304 * q^56 + 48944 * q^57 - 10840 * q^59 + 25200 * q^60 + 49448 * q^61 + 18518 * q^62 + 27488 * q^63 - 20734 * q^64 + 97836 * q^65 - 47744 * q^66 - 7840 * q^67 + 20724 * q^68 + 58792 * q^69 - 77496 * q^70 - 48744 * q^71 + 8088 * q^72 - 74992 * q^73 - 35920 * q^74 - 90448 * q^75 - 140792 * q^76 + 128656 * q^77 + 2982 * q^78 - 106076 * q^79 + 58638 * q^80 - 59692 * q^81 - 234132 * q^82 + 62888 * q^83 - 59832 * q^84 + 23848 * q^85 - 216014 * q^86 + 23548 * q^87 - 39426 * q^88 + 107568 * q^89 + 41552 * q^90 - 268896 * q^91 - 26268 * q^92 + 221460 * q^93 + 30542 * q^94 + 147352 * q^95 - 78606 * q^96 - 49520 * q^97 + 242304 * q^98 + 166720 * 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 $

$2$	4.16235	0.735806	0.367903	−	0.929864i	$-0.380076\pi$
$2$	4.16235	0.735806	0.367903	+	0.929864i	$0.380076\pi$
$3$	−17.5258	−1.12428	−0.562141	−	0.827041i	$-0.690022\pi$
$3$	−17.5258	−1.12428	−0.562141	+	0.827041i	$0.690022\pi$
$4$	−14.6748	−0.458589
$5$	32.5670	0.582577	0.291289	−	0.956635i	$-0.405916\pi$
$5$	32.5670	0.582577	0.291289	+	0.956635i	$0.405916\pi$
$6$	−72.9487	−0.827255
$7$	−220.793	−1.70310	−0.851551	−	0.524272i	$-0.824337\pi$
$7$	−220.793	−1.70310	−0.851551	+	0.524272i	$0.824337\pi$
$8$	−194.277	−1.07324
$9$	64.1549	0.264012
$10$	135.555	0.428664
$11$	−85.7296	−0.213623	−0.106812	−	0.994279i	$-0.534064\pi$
$11$	−85.7296	−0.213623	−0.106812	+	0.994279i	$0.534064\pi$
$12$	257.189	0.515584
$13$	1034.02	1.69695	0.848475	−	0.529235i	$-0.177521\pi$
$13$	1034.02	1.69695	0.848475	+	0.529235i	$0.177521\pi$
$14$	−919.018	−1.25315
$15$	−570.765	−0.654981
$16$	−339.054	−0.331108
$17$	−313.020	−0.262694	−0.131347	−	0.991336i	$-0.541930\pi$
$17$	−313.020	−0.262694	−0.131347	+	0.991336i	$0.541930\pi$
$18$	267.035	0.194262
$19$	458.534	0.291398	0.145699	−	0.989329i	$-0.453457\pi$
$19$	458.534	0.291398	0.145699	+	0.989329i	$0.453457\pi$
$20$	−477.916	−0.267163
$21$	3869.58	1.91477
$22$	−356.836	−0.157186
$23$	−3448.84	−1.35942	−0.679709	−	0.733482i	$-0.737894\pi$
$23$	−3448.84	−1.35942	−0.679709	+	0.733482i	$0.737894\pi$
$24$	3404.87	1.20662
$25$	−2064.39	−0.660604
$26$	4303.94	1.24863
$27$	3134.41	0.827459
$28$	3240.10	0.781023
$29$	−841.000	−0.185695
$29$	−841.000	−0.185695
$30$	−2375.72	−0.481940
$31$	−7983.23	−1.49202	−0.746009	−	0.665936i	$-0.768033\pi$
$31$	−7983.23	−1.49202	−0.746009	+	0.665936i	$0.768033\pi$
$32$	4805.60	0.829608
$33$	1502.48	0.240173
$34$	−1302.90	−0.193292
$35$	−7190.58	−0.992188
$36$	−941.463	−0.121073
$37$	152.624	0.0183282	0.00916409	−	0.999958i	$-0.497083\pi$
$37$	152.624	0.0183282	0.00916409	+	0.999958i	$0.497083\pi$
$38$	1908.58	0.214413
$39$	−18122.0	−1.90785
$40$	−6327.03	−0.625244
$41$	−18492.2	−1.71802	−0.859011	−	0.511957i	$-0.828921\pi$
$41$	−18492.2	−1.71802	−0.859011	+	0.511957i	$0.828921\pi$
$42$	16106.6	1.40890
$43$	2072.84	0.170960	0.0854799	−	0.996340i	$-0.472758\pi$
$43$	2072.84	0.170960	0.0854799	+	0.996340i	$0.472758\pi$
$44$	1258.07	0.0979653
$45$	2089.33	0.153807
$46$	−14355.3	−1.00027
$47$	15845.6	1.04632	0.523159	−	0.852235i	$-0.324753\pi$
$47$	15845.6	1.04632	0.523159	+	0.852235i	$0.324753\pi$
$48$	5942.21	0.372258
$49$	31942.6	1.90055
$50$	−8592.70	−0.486077
$51$	5485.94	0.295343
$52$	−15174.0	−0.778203
$53$	9240.52	0.451863	0.225931	−	0.974143i	$-0.427457\pi$
$53$	9240.52	0.451863	0.225931	+	0.974143i	$0.427457\pi$
$54$	13046.5	0.608850
$55$	−2791.96	−0.124452
$56$	42895.0	1.82783
$57$	−8036.19	−0.327614
$58$	−3500.54	−0.136636
$59$	−14323.2	−0.535686	−0.267843	−	0.963463i	$-0.586311\pi$
$59$	−14323.2	−0.535686	−0.267843	+	0.963463i	$0.586311\pi$
$60$	8375.88	0.300367
$61$	−19580.2	−0.673739	−0.336870	−	0.941551i	$-0.609368\pi$
$61$	−19580.2	−0.673739	−0.336870	+	0.941551i	$0.609368\pi$
$62$	−33229.0	−1.09784
$63$	−14165.0	−0.449639
$64$	30852.3	0.941539
$65$	33674.9	0.988604
$66$	6253.86	0.176721
$67$	−9193.70	−0.250209	−0.125105	−	0.992144i	$-0.539927\pi$
$67$	−9193.70	−0.250209	−0.125105	+	0.992144i	$0.539927\pi$
$68$	4593.53	0.120469
$69$	60443.8	1.52837
$70$	−29929.7	−0.730058
$71$	−19374.7	−0.456131	−0.228066	−	0.973646i	$-0.573240\pi$
$71$	−19374.7	−0.456131	−0.228066	+	0.973646i	$0.573240\pi$
$72$	−12463.8	−0.283348
$73$	−56912.4	−1.24997	−0.624985	−	0.780637i	$-0.714895\pi$
$73$	−56912.4	−1.24997	−0.624985	+	0.780637i	$0.714895\pi$
$74$	635.276	0.0134860
$75$	36180.1	0.742706
$76$	−6728.91	−0.133632
$77$	18928.5	0.363822
$78$	−75430.1	−1.40381
$79$	51573.6	0.929736	0.464868	−	0.885380i	$-0.346102\pi$
$79$	51573.6	0.929736	0.464868	+	0.885380i	$0.346102\pi$
$80$	−11042.0	−0.192896
$81$	−70522.8	−1.19431
$82$	−76971.0	−1.26413
$83$	19978.1	0.318317	0.159158	−	0.987253i	$-0.449122\pi$
$83$	19978.1	0.318317	0.159158	+	0.987253i	$0.449122\pi$
$84$	−56785.5	−0.878091
$85$	−10194.2	−0.153040
$86$	8627.87	0.125793
$87$	14739.2	0.208774
$88$	16655.3	0.229269
$89$	130663.	1.74855	0.874274	−	0.485432i	$-0.161338\pi$
$89$	130663.	1.74855	0.874274	+	0.485432i	$0.161338\pi$
$90$	8696.54	0.113172
$91$	−228304.	−2.89008
$92$	50611.1	0.623414
$93$	139913.	1.67745
$94$	65954.9	0.769888
$95$	14933.1	0.169762
$96$	−84222.2	−0.932714
$97$	43603.5	0.470535	0.235268	−	0.971931i	$-0.424403\pi$
$97$	43603.5	0.470535	0.235268	+	0.971931i	$0.424403\pi$
$98$	132956.	1.39844
$99$	−5499.97	−0.0563991
$100$	30294.6	0.302946
$101$	−56686.0	−0.552933	−0.276467	−	0.961024i	$-0.589164\pi$
$101$	−56686.0	−0.552933	−0.276467	+	0.961024i	$0.589164\pi$
$102$	22834.4	0.217315
$103$	−111450.	−1.03511	−0.517556	−	0.855649i	$-0.673158\pi$
$103$	−111450.	−1.03511	−0.517556	+	0.855649i	$0.673158\pi$
$104$	−200886.	−1.82123
$105$	126021.	1.11550
$106$	38462.3	0.332484
$107$	189434.	1.59955	0.799775	−	0.600300i	$-0.204952\pi$
$107$	189434.	1.59955	0.799775	+	0.600300i	$0.204952\pi$
$108$	−45997.0	−0.379463
$109$	100232.	0.808054	0.404027	−	0.914747i	$-0.367610\pi$
$109$	100232.	0.808054	0.404027	+	0.914747i	$0.367610\pi$
$110$	−11621.1	−0.0915727
$111$	−2674.87	−0.0206061
$112$	74860.8	0.563910
$113$	−103444.	−0.762092	−0.381046	−	0.924556i	$-0.624436\pi$
$113$	−103444.	−0.762092	−0.381046	+	0.924556i	$0.624436\pi$
$114$	−33449.4	−0.241061
$115$	−112318.	−0.791966
$116$	12341.5	0.0851578
$117$	66337.2	0.448015
$118$	−59618.2	−0.394161
$119$	69112.8	0.447395
$120$	110886.	0.702952
$121$	−153701.	−0.954365
$122$	−81499.5	−0.495742
$123$	324091.	1.93154
$124$	117153.	0.684223
$125$	−169003.	−0.967430
$126$	−58959.5	−0.330847
$127$	−247538.	−1.36186	−0.680930	−	0.732349i	$-0.738424\pi$
$127$	−247538.	−1.36186	−0.680930	+	0.732349i	$0.738424\pi$
$128$	−25361.1	−0.136818
$129$	−36328.2	−0.192207
$130$	140167.	0.727422
$131$	198458.	1.01040	0.505198	−	0.863004i	$-0.331420\pi$
$131$	198458.	1.01040	0.505198	+	0.863004i	$0.331420\pi$
$132$	−22048.7	−0.110141
$133$	−101241.	−0.496281
$134$	−38267.4	−0.184106
$135$	102078.	0.482059
$136$	60812.7	0.281934
$137$	141442.	0.643839	0.321920	−	0.946767i	$-0.395672\pi$
$137$	141442.	0.643839	0.321920	+	0.946767i	$0.395672\pi$
$138$	251588.	1.12459
$139$	−325330.	−1.42819	−0.714097	−	0.700047i	$-0.753162\pi$
$139$	−325330.	−1.42819	−0.714097	+	0.700047i	$0.753162\pi$
$140$	105521.	0.455006
$141$	−277707.	−1.17636
$142$	−80644.4	−0.335624
$143$	−88645.8	−0.362508
$144$	−21752.0	−0.0874163
$145$	−27388.9	−0.108182
$146$	−236889.	−0.919736
$147$	−559821.	−2.13676
$148$	−2239.74	−0.00840510
$149$	−391462.	−1.44452	−0.722261	−	0.691621i	$-0.756897\pi$
$149$	−391462.	−1.44452	−0.722261	+	0.691621i	$0.756897\pi$
$150$	150594.	0.546488
$151$	−216585.	−0.773013	−0.386507	−	0.922287i	$-0.626318\pi$
$151$	−216585.	−0.773013	−0.386507	+	0.922287i	$0.626318\pi$
$152$	−89082.6	−0.312740
$153$	−20081.8	−0.0693544
$154$	78787.0	0.267703
$155$	−259990.	−0.869216
$156$	265938.	0.874920
$157$	564396.	1.82740	0.913702	−	0.406385i	$-0.133211\pi$
$157$	564396.	1.82740	0.913702	+	0.406385i	$0.133211\pi$
$158$	214667.	0.684106
$159$	−161948.	−0.508022
$160$	156504.	0.483311
$161$	761480.	2.31523
$162$	−293541.	−0.878781
$163$	476986.	1.40617	0.703083	−	0.711108i	$-0.251806\pi$
$163$	476986.	1.40617	0.703083	+	0.711108i	$0.251806\pi$
$164$	271370.	0.787866
$165$	48931.4	0.139919
$166$	83155.9	0.234219
$167$	−203397.	−0.564357	−0.282178	−	0.959362i	$-0.591057\pi$
$167$	−203397.	−0.564357	−0.282178	+	0.959362i	$0.591057\pi$
$168$	−751771.	−2.05500
$169$	697898.	1.87964
$170$	−42431.6	−0.112608
$171$	29417.2	0.0769327
$172$	−30418.6	−0.0784003
$173$	−95409.0	−0.242367	−0.121184	−	0.992630i	$-0.538669\pi$
$173$	−95409.0	−0.242367	−0.121184	+	0.992630i	$0.538669\pi$
$174$	61349.8	0.153617
$175$	455803.	1.12508
$176$	29067.0	0.0707323
$177$	251026.	0.602263
$178$	543865.	1.28659
$179$	−327011.	−0.762833	−0.381416	−	0.924403i	$-0.624564\pi$
$179$	−327011.	−0.762833	−0.381416	+	0.924403i	$0.624564\pi$
$180$	−30660.7	−0.0705343
$181$	108581.	0.246353	0.123177	−	0.992385i	$-0.460692\pi$
$181$	108581.	0.246353	0.123177	+	0.992385i	$0.460692\pi$
$182$	−950280.	−2.12654
$183$	343159.	0.757473
$184$	670030.	1.45898
$185$	4970.52	0.0106776
$186$	582366.	1.23428
$187$	26835.1	0.0561176
$188$	−232532.	−0.479830
$189$	−692056.	−1.40925
$190$	62156.7	0.124912
$191$	−315738.	−0.626244	−0.313122	−	0.949713i	$-0.601375\pi$
$191$	−315738.	−0.626244	−0.313122	+	0.949713i	$0.601375\pi$
$192$	−540713.	−1.05856
$193$	41432.1	0.0800651	0.0400326	−	0.999198i	$-0.487254\pi$
$193$	41432.1	0.0800651	0.0400326	+	0.999198i	$0.487254\pi$
$194$	181493.	0.346223
$195$	−590180.	−1.11147
$196$	−468753.	−0.871573
$197$	354739.	0.651243	0.325622	−	0.945500i	$-0.394426\pi$
$197$	354739.	0.651243	0.325622	+	0.945500i	$0.394426\pi$
$198$	−22892.8	−0.0414988
$199$	−949129.	−1.69900	−0.849498	−	0.527591i	$-0.823095\pi$
$199$	−949129.	−1.69900	−0.849498	+	0.527591i	$0.823095\pi$
$200$	401063.	0.708986
$201$	161127.	0.281306
$202$	−235947.	−0.406852
$203$	185687.	0.316258
$204$	−80505.4	−0.135441
$205$	−602236.	−1.00088
$206$	−463894.	−0.761642
$207$	−221260.	−0.358903
$208$	−350588.	−0.561873
$209$	−39309.9	−0.0622495
$210$	524543.	0.820792
$211$	−380574.	−0.588481	−0.294241	−	0.955731i	$-0.595067\pi$
$211$	−380574.	−0.588481	−0.294241	+	0.955731i	$0.595067\pi$
$212$	−135603.	−0.207219
$213$	339558.	0.512820
$214$	788489.	1.17696
$215$	67506.2	0.0995973
$216$	−608944.	−0.888061
$217$	1.76264e6	2.54106
$218$	417201.	0.594571
$219$	997437.	1.40532
$220$	40971.5	0.0570723
$221$	−323668.	−0.445779
$222$	−11133.7	−0.0151621
$223$	−68362.6	−0.0920569	−0.0460284	−	0.998940i	$-0.514656\pi$
$223$	−68362.6	−0.0920569	−0.0460284	+	0.998940i	$0.514656\pi$
$224$	−1.06104e6	−1.41291
$225$	−132441.	−0.174407
$226$	−430569.	−0.560753
$227$	−1.07914e6	−1.39000	−0.694998	−	0.719012i	$-0.744595\pi$
$227$	−1.07914e6	−1.39000	−0.694998	+	0.719012i	$0.744595\pi$
$228$	117930.	0.150240
$229$	−724221.	−0.912604	−0.456302	−	0.889825i	$-0.650826\pi$
$229$	−724221.	−0.912604	−0.456302	+	0.889825i	$0.650826\pi$
$230$	−467509.	−0.582734
$231$	−331738.	−0.409039
$232$	163387.	0.199296
$233$	1.37311e6	1.65697	0.828486	−	0.560009i	$-0.189203\pi$
$233$	1.37311e6	1.65697	0.828486	+	0.560009i	$0.189203\pi$
$234$	276119.	0.329652
$235$	516044.	0.609561
$236$	210191.	0.245660
$237$	−903870.	−1.04529
$238$	287672.	0.329196
$239$	1.11446e6	1.26204	0.631018	−	0.775769i	$-0.282638\pi$
$239$	1.11446e6	1.26204	0.631018	+	0.775769i	$0.282638\pi$
$240$	193520.	0.216869
$241$	−1.47058e6	−1.63097	−0.815486	−	0.578776i	$-0.803530\pi$
$241$	−1.47058e6	−1.63097	−0.815486	+	0.578776i	$0.803530\pi$
$242$	−639759.	−0.702228
$243$	474309.	0.515283
$244$	287336.	0.308969
$245$	1.04028e6	1.10722
$246$	1.34898e6	1.42124
$247$	474132.	0.494489
$248$	1.55096e6	1.60129
$249$	−350133.	−0.357878
$250$	−703450.	−0.711841
$251$	375105.	0.375810	0.187905	−	0.982187i	$-0.439830\pi$
$251$	375105.	0.375810	0.187905	+	0.982187i	$0.439830\pi$
$252$	207868.	0.206199
$253$	295667.	0.290404
$254$	−1.03034e6	−1.00207
$255$	178661.	0.172060
$256$	−1.09284e6	−1.04221
$257$	−471074.	−0.444894	−0.222447	−	0.974945i	$-0.571404\pi$
$257$	−471074.	−0.444894	−0.222447	+	0.974945i	$0.571404\pi$
$258$	−151211.	−0.141427
$259$	−33698.4	−0.0312147
$260$	−494173.	−0.453363
$261$	−53954.3	−0.0490258
$262$	826053.	0.743455
$263$	1.11373e6	0.992865	0.496433	−	0.868075i	$-0.334643\pi$
$263$	1.11373e6	0.992865	0.496433	+	0.868075i	$0.334643\pi$
$264$	−291898.	−0.257763
$265$	300936.	0.263245
$266$	−421401.	−0.365167
$267$	−2.28998e6	−1.96586
$268$	134916.	0.114743
$269$	−381568.	−0.321508	−0.160754	−	0.986995i	$-0.551393\pi$
$269$	−381568.	−0.321508	−0.160754	+	0.986995i	$0.551393\pi$
$270$	424886.	0.354702
$271$	1.08834e6	0.900208	0.450104	−	0.892976i	$-0.351387\pi$
$271$	1.08834e6	0.900208	0.450104	+	0.892976i	$0.351387\pi$
$272$	106131.	0.0869800
$273$	4.00121e6	3.24927
$274$	588732.	0.473741
$275$	176979.	0.141120
$276$	−887003.	−0.700894
$277$	−2.18958e6	−1.71459	−0.857295	−	0.514825i	$-0.827857\pi$
$277$	−2.18958e6	−1.71459	−0.857295	+	0.514825i	$0.827857\pi$
$278$	−1.35414e6	−1.05087
$279$	−512163.	−0.393911
$280$	1.39696e6	1.06485
$281$	−1.02712e6	−0.775992	−0.387996	−	0.921661i	$-0.626833\pi$
$281$	−1.02712e6	−0.775992	−0.387996	+	0.921661i	$0.626833\pi$
$282$	−1.15592e6	−0.865572
$283$	889156.	0.659952	0.329976	−	0.943989i	$-0.392959\pi$
$283$	889156.	0.659952	0.329976	+	0.943989i	$0.392959\pi$
$284$	284321.	0.209177
$285$	−261715.	−0.190861
$286$	−368975.	−0.266736
$287$	4.08295e6	2.92597
$288$	308303.	0.219026
$289$	−1.32188e6	−0.930992
$290$	−114002.	−0.0796009
$291$	−764188.	−0.529015
$292$	835180.	0.573222
$293$	−482000.	−0.328003	−0.164001	−	0.986460i	$-0.552440\pi$
$293$	−482000.	−0.328003	−0.164001	+	0.986460i	$0.552440\pi$
$294$	−2.33017e6	−1.57224
$295$	−466465.	−0.312079
$296$	−29651.4	−0.0196705
$297$	−268712.	−0.176765
$298$	−1.62940e6	−1.06289
$299$	−3.56616e6	−2.30687
$300$	−530937.	−0.340597
$301$	−457668.	−0.291162
$302$	−901505.	−0.568788
$303$	993470.	0.621653
$304$	−155468.	−0.0964842
$305$	−637668.	−0.392505
$306$	−83587.4	−0.0510314
$307$	229158.	0.138768	0.0693839	−	0.997590i	$-0.477897\pi$
$307$	229158.	0.138768	0.0693839	+	0.997590i	$0.477897\pi$
$308$	−277773.	−0.166845
$309$	1.95326e6	1.16376
$310$	−1.08217e6	−0.639575
$311$	2.49699e6	1.46392	0.731958	−	0.681350i	$-0.238607\pi$
$311$	2.49699e6	1.46392	0.731958	+	0.681350i	$0.238607\pi$
$312$	3.52069e6	2.04758
$313$	−2.78111e6	−1.60457	−0.802283	−	0.596944i	$-0.796381\pi$
$313$	−2.78111e6	−1.60457	−0.802283	+	0.596944i	$0.796381\pi$
$314$	2.34921e6	1.34462
$315$	−461311.	−0.261949
$316$	−756834.	−0.426366
$317$	1.94375e6	1.08641	0.543203	−	0.839602i	$-0.317212\pi$
$317$	1.94375e6	1.08641	0.543203	+	0.839602i	$0.317212\pi$
$318$	−674083.	−0.373806
$319$	72098.6	0.0396689
$320$	1.00477e6	0.548519
$321$	−3.31998e6	−1.79835
$322$	3.16955e6	1.70356
$323$	−143530.	−0.0765487
$324$	1.03491e6	0.547697
$325$	−2.13461e6	−1.12101
$326$	1.98538e6	1.03467
$327$	−1.75665e6	−0.908481
$328$	3.59261e6	1.84385
$329$	−3.49860e6	−1.78199
$330$	203670.	0.102954
$331$	−60445.1	−0.0303243	−0.0151622	−	0.999885i	$-0.504826\pi$
$331$	−60445.1	−0.0303243	−0.0151622	+	0.999885i	$0.504826\pi$
$332$	−293176.	−0.145976
$333$	9791.59	0.00483886
$334$	−846611.	−0.415258
$335$	−299412.	−0.145766
$336$	−1.31200e6	−0.633994
$337$	−1.72999e6	−0.829791	−0.414895	−	0.909869i	$-0.636182\pi$
$337$	−1.72999e6	−0.829791	−0.414895	+	0.909869i	$0.636182\pi$
$338$	2.90489e6	1.38305
$339$	1.81294e6	0.856807
$340$	149598.	0.0701822
$341$	684398.	0.318730
$342$	122445.	0.0566075
$343$	−3.34184e6	−1.53373
$344$	−402705.	−0.183481
$345$	1.96847e6	0.890394
$346$	−397126.	−0.178335
$347$	1.17667e6	0.524605	0.262303	−	0.964986i	$-0.415518\pi$
$347$	1.17667e6	0.524605	0.262303	+	0.964986i	$0.415518\pi$
$348$	−216296.	−0.0957415
$349$	1.20893e6	0.531297	0.265648	−	0.964070i	$-0.414414\pi$
$349$	1.20893e6	0.531297	0.265648	+	0.964070i	$0.414414\pi$
$350$	1.89721e6	0.827838
$351$	3.24103e6	1.40416
$352$	−411982.	−0.177224
$353$	1.00723e6	0.430223	0.215111	−	0.976589i	$-0.430989\pi$
$353$	1.00723e6	0.430223	0.215111	+	0.976589i	$0.430989\pi$
$354$	1.04486e6	0.443149
$355$	−630978.	−0.265732
$356$	−1.91746e6	−0.801865
$357$	−1.21126e6	−0.502998
$358$	−1.36113e6	−0.561297
$359$	1.10145e6	0.451055	0.225527	−	0.974237i	$-0.427589\pi$
$359$	1.10145e6	0.451055	0.225527	+	0.974237i	$0.427589\pi$
$360$	−405910.	−0.165072
$361$	−2.26585e6	−0.915087
$362$	451953.	0.181268
$363$	2.69375e6	1.07298
$364$	3.35032e6	1.32536
$365$	−1.85347e6	−0.728204
$366$	1.42835e6	0.557354
$367$	2.99288e6	1.15991	0.579955	−	0.814648i	$-0.303070\pi$
$367$	2.99288e6	1.15991	0.579955	+	0.814648i	$0.303070\pi$
$368$	1.16934e6	0.450114
$369$	−1.18636e6	−0.453578
$370$	20689.0	0.00785663
$371$	−2.04024e6	−0.769568
$372$	−2.05320e6	−0.769260
$373$	4.23178e6	1.57489	0.787446	−	0.616384i	$-0.211403\pi$
$373$	4.23178e6	1.57489	0.787446	+	0.616384i	$0.211403\pi$
$374$	111697.	0.0412917
$375$	2.96192e6	1.08766
$376$	−3.07844e6	−1.12295
$377$	−869608.	−0.315116
$378$	−2.88058e6	−1.03693
$379$	1.06268e6	0.380018	0.190009	−	0.981782i	$-0.439148\pi$
$379$	1.06268e6	0.380018	0.190009	+	0.981782i	$0.439148\pi$
$380$	−219141.	−0.0778510
$381$	4.33831e6	1.53112
$382$	−1.31421e6	−0.460794
$383$	−3.75736e6	−1.30884	−0.654418	−	0.756133i	$-0.727087\pi$
$383$	−3.75736e6	−1.30884	−0.654418	+	0.756133i	$0.727087\pi$
$384$	444474.	0.153822
$385$	616445.	0.211955
$386$	172455.	0.0589125
$387$	132983.	0.0451354
$388$	−639875.	−0.215782
$389$	−3.88561e6	−1.30192	−0.650961	−	0.759112i	$-0.725634\pi$
$389$	−3.88561e6	−1.30192	−0.650961	+	0.759112i	$0.725634\pi$
$390$	−2.45654e6	−0.817828
$391$	1.07956e6	0.357111
$392$	−6.20571e6	−2.03975
$393$	−3.47815e6	−1.13597
$394$	1.47655e6	0.479189
$395$	1.67960e6	0.541643
$396$	80711.2	0.0258640
$397$	719537.	0.229127	0.114564	−	0.993416i	$-0.463453\pi$
$397$	719537.	0.229127	0.114564	+	0.993416i	$0.463453\pi$
$398$	−3.95061e6	−1.25013
$399$	1.77433e6	0.557960
$400$	699939.	0.218731
$401$	−1.57519e6	−0.489185	−0.244592	−	0.969626i	$-0.578654\pi$
$401$	−1.57519e6	−0.489185	−0.244592	+	0.969626i	$0.578654\pi$
$402$	670668.	0.206987
$403$	−8.25479e6	−2.53188
$404$	831859.	0.253569
$405$	−2.29672e6	−0.695777
$406$	772894.	0.232705
$407$	−13084.4	−0.00391533
$408$	−1.06579e6	−0.316973
$409$	−3.35355e6	−0.991279	−0.495639	−	0.868528i	$-0.665066\pi$
$409$	−3.35355e6	−0.991279	−0.495639	+	0.868528i	$0.665066\pi$
$410$	−2.50672e6	−0.736454
$411$	−2.47889e6	−0.723857
$412$	1.63551e6	0.474691
$413$	3.16247e6	0.912328
$414$	−920961.	−0.264083
$415$	650628.	0.185444
$416$	4.96907e6	1.40780
$417$	5.70168e6	1.60569
$418$	−163622.	−0.0458036
$419$	6.79853e6	1.89182	0.945911	−	0.324427i	$-0.105171\pi$
$419$	6.79853e6	1.89182	0.945911	+	0.324427i	$0.105171\pi$
$420$	−1.84934e6	−0.511556
$421$	−1.77259e6	−0.487420	−0.243710	−	0.969848i	$-0.578365\pi$
$421$	−1.77259e6	−0.487420	−0.243710	+	0.969848i	$0.578365\pi$
$422$	−1.58408e6	−0.433008
$423$	1.01657e6	0.276241
$424$	−1.79522e6	−0.484957
$425$	646196.	0.173537
$426$	1.41336e6	0.377337
$427$	4.32317e6	1.14745
$428$	−2.77991e6	−0.733536
$429$	1.55359e6	0.407562
$430$	280984.	0.0732843
$431$	1.30221e6	0.337666	0.168833	−	0.985645i	$-0.446000\pi$
$431$	1.30221e6	0.337666	0.168833	+	0.985645i	$0.446000\pi$
$432$	−1.06273e6	−0.273978
$433$	2.15386e6	0.552074	0.276037	−	0.961147i	$-0.410979\pi$
$433$	2.15386e6	0.552074	0.276037	+	0.961147i	$0.410979\pi$
$434$	7.33673e6	1.86973
$435$	480013.	0.121627
$436$	−1.47089e6	−0.370564
$437$	−1.58141e6	−0.396133
$438$	4.15168e6	1.03404
$439$	−5.81916e6	−1.44112	−0.720558	−	0.693394i	$-0.756114\pi$
$439$	−5.81916e6	−1.44112	−0.720558	+	0.693394i	$0.756114\pi$
$440$	542413.	0.133567
$441$	2.04927e6	0.501769
$442$	−1.34722e6	−0.328007
$443$	4.34332e6	1.05151	0.525754	−	0.850637i	$-0.323783\pi$
$443$	4.34332e6	1.05151	0.525754	+	0.850637i	$0.323783\pi$
$444$	39253.3	0.00944970
$445$	4.25531e6	1.01866
$446$	−284549.	−0.0677361
$447$	6.86070e6	1.62405
$448$	−6.81198e6	−1.60354
$449$	2.68108e6	0.627615	0.313807	−	0.949487i	$-0.398395\pi$
$449$	2.68108e6	0.627615	0.313807	+	0.949487i	$0.398395\pi$
$450$	−551264.	−0.128330
$451$	1.58533e6	0.367010
$452$	1.51802e6	0.349487
$453$	3.79584e6	0.869086
$454$	−4.49176e6	−1.02277
$455$	−7.43518e6	−1.68369
$456$	1.56125e6	0.351609
$457$	−4.29834e6	−0.962743	−0.481371	−	0.876517i	$-0.659861\pi$
$457$	−4.29834e6	−0.962743	−0.481371	+	0.876517i	$0.659861\pi$
$458$	−3.01446e6	−0.671500
$459$	−981134.	−0.217369
$460$	1.64826e6	0.363187
$461$	2.28441e6	0.500636	0.250318	−	0.968164i	$-0.419465\pi$
$461$	2.28441e6	0.500636	0.250318	+	0.968164i	$0.419465\pi$
$462$	−1.38081e6	−0.300974
$463$	1.51960e6	0.329440	0.164720	−	0.986340i	$-0.447328\pi$
$463$	1.51960e6	0.329440	0.164720	+	0.986340i	$0.447328\pi$
$464$	285144.	0.0614851
$465$	4.55654e6	0.977244
$466$	5.71536e6	1.21921
$467$	−4.71846e6	−1.00117	−0.500585	−	0.865687i	$-0.666882\pi$
$467$	−4.71846e6	−1.00117	−0.500585	+	0.865687i	$0.666882\pi$
$468$	−973488.	−0.205455
$469$	2.02991e6	0.426132
$470$	2.14796e6	0.448519
$471$	−9.89151e6	−2.05452
$472$	2.78267e6	0.574919
$473$	−177703.	−0.0365210
$474$	−3.76222e6	−0.769128
$475$	−946591.	−0.192499
$476$	−1.01422e6	−0.205170
$477$	592824.	0.119297
$478$	4.63879e6	0.928614
$479$	5.85157e6	1.16529	0.582644	−	0.812727i	$-0.302018\pi$
$479$	5.85157e6	1.16529	0.582644	+	0.812727i	$0.302018\pi$
$480$	−2.74287e6	−0.543378
$481$	157816.	0.0311020
$482$	−6.12108e6	−1.20008
$483$	−1.33456e7	−2.60297
$484$	2.25554e6	0.437661
$485$	1.42004e6	0.274123
$486$	1.97424e6	0.379149
$487$	1.83575e6	0.350745	0.175372	−	0.984502i	$-0.443887\pi$
$487$	1.83575e6	0.350745	0.175372	+	0.984502i	$0.443887\pi$
$488$	3.80398e6	0.723083
$489$	−8.35958e6	−1.58093
$490$	4.32999e6	0.814699
$491$	−5.75635e6	−1.07757	−0.538783	−	0.842445i	$-0.681116\pi$
$491$	−5.75635e6	−1.07757	−0.538783	+	0.842445i	$0.681116\pi$
$492$	−4.75599e6	−0.885784
$493$	263250.	0.0487811
$494$	1.97350e6	0.363848
$495$	−179118.	−0.0328568
$496$	2.70675e6	0.494019
$497$	4.27781e6	0.776838
$498$	−1.45738e6	−0.263329
$499$	4.10166e6	0.737409	0.368705	−	0.929547i	$-0.379801\pi$
$499$	4.10166e6	0.737409	0.368705	+	0.929547i	$0.379801\pi$
$500$	2.48009e6	0.443652
$501$	3.56471e6	0.634497
$502$	1.56132e6	0.276523
$503$	−1.12157e6	−0.197654	−0.0988270	−	0.995105i	$-0.531509\pi$
$503$	−1.12157e6	−0.197654	−0.0988270	+	0.995105i	$0.531509\pi$
$504$	2.75193e6	0.482570
$505$	−1.84610e6	−0.322126
$506$	1.23067e6	0.213681
$507$	−1.22312e7	−2.11325
$508$	3.63258e6	0.624534
$509$	−2.68902e6	−0.460045	−0.230023	−	0.973185i	$-0.573880\pi$
$509$	−2.68902e6	−0.460045	−0.230023	+	0.973185i	$0.573880\pi$
$510$	743650.	0.126603
$511$	1.25659e7	2.12883
$512$	−3.73721e6	−0.630047
$513$	1.43723e6	0.241120
$514$	−1.96078e6	−0.327356
$515$	−3.62960e6	−0.603033
$516$	533111.	0.0881441
$517$	−1.35844e6	−0.223518
$518$	−140264.	−0.0229680
$519$	1.67212e6	0.272489
$520$	−6.54225e6	−1.06101
$521$	2.88911e6	0.466305	0.233152	−	0.972440i	$-0.425096\pi$
$521$	2.88911e6	0.466305	0.233152	+	0.972440i	$0.425096\pi$
$522$	−224576.	−0.0360735
$523$	−1.40417e6	−0.224474	−0.112237	−	0.993681i	$-0.535802\pi$
$523$	−1.40417e6	−0.224474	−0.112237	+	0.993681i	$0.535802\pi$
$524$	−2.91235e6	−0.463356
$525$	−7.98832e6	−1.26490
$526$	4.63573e6	0.730557
$527$	2.49891e6	0.391945
$528$	−509423.	−0.0795231
$529$	5.45814e6	0.848019
$530$	1.25260e6	0.193697
$531$	−918904.	−0.141428
$532$	1.48570e6	0.227589
$533$	−1.91212e7	−2.91540
$534$	−9.53169e6	−1.44650
$535$	6.16930e6	0.931861
$536$	1.78612e6	0.268534
$537$	5.73113e6	0.857640
$538$	−1.58822e6	−0.236568
$539$	−2.73843e6	−0.406003
$540$	−1.49799e6	−0.221067
$541$	−211154.	−0.0310174	−0.0155087	−	0.999880i	$-0.504937\pi$
$541$	−211154.	−0.0310174	−0.0155087	+	0.999880i	$0.504937\pi$
$542$	4.53007e6	0.662379
$543$	−1.90298e6	−0.276971
$544$	−1.50425e6	−0.217933
$545$	3.26426e6	0.470754
$546$	1.66545e7	2.39083
$547$	−4.61571e6	−0.659584	−0.329792	−	0.944054i	$-0.606979\pi$
$547$	−4.61571e6	−0.659584	−0.329792	+	0.944054i	$0.606979\pi$
$548$	−2.07564e6	−0.295257
$549$	−1.25616e6	−0.177875
$550$	736649.	0.103837
$551$	−385627.	−0.0541113
$552$	−1.17428e7	−1.64031
$553$	−1.13871e7	−1.58343
$554$	−9.11378e6	−1.26161
$555$	−87112.5	−0.0120046
$556$	4.77416e6	0.654953
$557$	1.01209e7	1.38223	0.691114	−	0.722746i	$-0.257120\pi$
$557$	1.01209e7	1.38223	0.691114	+	0.722746i	$0.257120\pi$
$558$	−2.13180e6	−0.289842
$559$	2.14335e6	0.290110
$560$	2.43800e6	0.328521
$561$	−470308.	−0.0630921
$562$	−4.27525e6	−0.570980
$563$	3.84774e6	0.511604	0.255802	−	0.966729i	$-0.417660\pi$
$563$	3.84774e6	0.511604	0.255802	+	0.966729i	$0.417660\pi$
$564$	4.07531e6	0.539465
$565$	−3.36885e6	−0.443978
$566$	3.70098e6	0.485597
$567$	1.55709e7	2.03403
$568$	3.76406e6	0.489538
$569$	4.38443e6	0.567718	0.283859	−	0.958866i	$-0.408385\pi$
$569$	4.38443e6	0.567718	0.283859	+	0.958866i	$0.408385\pi$
$570$	−1.08935e6	−0.140436
$571$	2.61241e6	0.335313	0.167656	−	0.985845i	$-0.446380\pi$
$571$	2.61241e6	0.335313	0.167656	+	0.985845i	$0.446380\pi$
$572$	1.30086e6	0.166242
$573$	5.53357e6	0.704075
$574$	1.69947e7	2.15295
$575$	7.11974e6	0.898037
$576$	1.97933e6	0.248577
$577$	−7.06124e6	−0.882961	−0.441480	−	0.897271i	$-0.645547\pi$
$577$	−7.06124e6	−0.882961	−0.441480	+	0.897271i	$0.645547\pi$
$578$	−5.50211e6	−0.685030
$579$	−726132.	−0.0900159
$580$	401928.	0.0496110
$581$	−4.41103e6	−0.542125
$582$	−3.18082e6	−0.389252
$583$	−792186.	−0.0965285
$584$	1.10568e7	1.34152
$585$	2.16041e6	0.261003
$586$	−2.00625e6	−0.241347
$587$	−8.18957e6	−0.980993	−0.490496	−	0.871443i	$-0.663185\pi$
$587$	−8.18957e6	−0.980993	−0.490496	+	0.871443i	$0.663185\pi$
$588$	8.21528e6	0.979894
$589$	−3.66058e6	−0.434772
$590$	−1.94159e6	−0.229629
$591$	−6.21710e6	−0.732182
$592$	−51747.9	−0.00606860
$593$	−9.78828e6	−1.14306	−0.571531	−	0.820580i	$-0.693650\pi$
$593$	−9.78828e6	−1.14306	−0.571531	+	0.820580i	$0.693650\pi$
$594$	−1.11847e6	−0.130065
$595$	2.25080e6	0.260642
$596$	5.74465e6	0.662442
$597$	1.66343e7	1.91015
$598$	−1.48436e7	−1.69741
$599$	4.44247e6	0.505892	0.252946	−	0.967480i	$-0.418600\pi$
$599$	4.44247e6	0.505892	0.252946	+	0.967480i	$0.418600\pi$
$600$	−7.02897e6	−0.797101
$601$	248973.	0.0281168	0.0140584	−	0.999901i	$-0.495525\pi$
$601$	248973.	0.0281168	0.0140584	+	0.999901i	$0.495525\pi$
$602$	−1.90498e6	−0.214239
$603$	−589821.	−0.0660582
$604$	3.17836e6	0.354495
$605$	−5.00560e6	−0.555991
$606$	4.13517e6	0.457417
$607$	−5.61487e6	−0.618540	−0.309270	−	0.950974i	$-0.600085\pi$
$607$	−5.61487e6	−0.618540	−0.309270	+	0.950974i	$0.600085\pi$
$608$	2.20353e6	0.241747
$609$	−3.25432e6	−0.355563
$610$	−2.65420e6	−0.288808
$611$	1.63846e7	1.77555
$612$	294697.	0.0318051
$613$	7.11213e6	0.764449	0.382225	−	0.924069i	$-0.375158\pi$
$613$	7.11213e6	0.764449	0.382225	+	0.924069i	$0.375158\pi$
$614$	953834.	0.102106
$615$	1.05547e7	1.12527
$616$	−3.67737e6	−0.390468
$617$	872669.	0.0922862	0.0461431	−	0.998935i	$-0.485307\pi$
$617$	872669.	0.0922862	0.0461431	+	0.998935i	$0.485307\pi$
$618$	8.13014e6	0.856301
$619$	−9.40244e6	−0.986312	−0.493156	−	0.869941i	$-0.664157\pi$
$619$	−9.40244e6	−0.986312	−0.493156	+	0.869941i	$0.664157\pi$
$620$	3.81531e6	0.398613
$621$	−1.08101e7	−1.12486
$622$	1.03934e7	1.07716
$623$	−2.88495e7	−2.97796
$624$	6.14434e6	0.631704
$625$	947282.	0.0970017
$626$	−1.15760e7	−1.18065
$627$	688939.	0.0699861
$628$	−8.28242e6	−0.838027
$629$	−47774.5	−0.00481470
$630$	−1.92014e6	−0.192744
$631$	−1.90990e7	−1.90957	−0.954786	−	0.297293i	$-0.903916\pi$
$631$	−1.90990e7	−1.90957	−0.954786	+	0.297293i	$0.903916\pi$
$632$	−1.00196e7	−0.997829
$633$	6.66987e6	0.661619
$634$	8.09056e6	0.799384
$635$	−8.06158e6	−0.793388
$636$	2.37656e6	0.232973
$637$	3.30292e7	3.22515
$638$	300099.	0.0291886
$639$	−1.24298e6	−0.120424
$640$	−825936.	−0.0797070
$641$	−4.06757e6	−0.391012	−0.195506	−	0.980703i	$-0.562635\pi$
$641$	−4.06757e6	−0.391012	−0.195506	+	0.980703i	$0.562635\pi$
$642$	−1.38189e7	−1.32324
$643$	−1.00899e6	−0.0962410	−0.0481205	−	0.998842i	$-0.515323\pi$
$643$	−1.00899e6	−0.0962410	−0.0481205	+	0.998842i	$0.515323\pi$
$644$	−1.11746e7	−1.06174
$645$	−1.18310e6	−0.111975
$646$	−597424.	−0.0563250
$647$	1.99986e7	1.87819	0.939095	−	0.343657i	$-0.111666\pi$
$647$	1.99986e7	1.87819	0.939095	+	0.343657i	$0.111666\pi$
$648$	1.37010e7	1.28178
$649$	1.22792e6	0.114435
$650$	−8.88500e6	−0.824848
$651$	−3.08918e7	−2.85687
$652$	−6.99970e6	−0.644852
$653$	−1.16599e7	−1.07007	−0.535035	−	0.844830i	$-0.679702\pi$
$653$	−1.16599e7	−1.07007	−0.535035	+	0.844830i	$0.679702\pi$
$654$	−7.31179e6	−0.668466
$655$	6.46320e6	0.588633
$656$	6.26986e6	0.568850
$657$	−3.65121e6	−0.330007
$658$	−1.45624e7	−1.31120
$659$	1.40204e7	1.25761	0.628806	−	0.777562i	$-0.283544\pi$
$659$	1.40204e7	1.25761	0.628806	+	0.777562i	$0.283544\pi$
$660$	−718061.	−0.0641654
$661$	5.39932e6	0.480657	0.240328	−	0.970692i	$-0.422745\pi$
$661$	5.39932e6	0.480657	0.240328	+	0.970692i	$0.422745\pi$
$662$	−251594.	−0.0223128
$663$	5.67256e6	0.501182
$664$	−3.88129e6	−0.341630
$665$	−3.29712e6	−0.289122
$666$	40756.0	0.00356046
$667$	2.90047e6	0.252438
$668$	2.98482e6	0.258808
$669$	1.19811e6	0.103498
$670$	−1.24626e6	−0.107256
$671$	1.67860e6	0.143926
$672$	1.85957e7	1.58851
$673$	2.37236e6	0.201903	0.100951	−	0.994891i	$-0.467811\pi$
$673$	2.37236e6	0.201903	0.100951	+	0.994891i	$0.467811\pi$
$674$	−7.20082e6	−0.610565
$675$	−6.47064e6	−0.546623
$676$	−1.02415e7	−0.861983
$677$	1.48279e7	1.24339	0.621695	−	0.783260i	$-0.286444\pi$
$677$	1.48279e7	1.24339	0.621695	+	0.783260i	$0.286444\pi$
$678$	7.54607e6	0.630444
$679$	−9.62736e6	−0.801369
$680$	1.98049e6	0.164248
$681$	1.89128e7	1.56275
$682$	2.84871e6	0.234524
$683$	−1.45710e7	−1.19519	−0.597594	−	0.801799i	$-0.703877\pi$
$683$	−1.45710e7	−1.19519	−0.597594	+	0.801799i	$0.703877\pi$
$684$	−431692.	−0.0352805
$685$	4.60635e6	0.375086
$686$	−1.39099e7	−1.12853
$687$	1.26926e7	1.02603
$688$	−702804.	−0.0566061
$689$	9.55485e6	0.766789
$690$	8.19348e6	0.655158
$691$	−2.39101e6	−0.190496	−0.0952480	−	0.995454i	$-0.530364\pi$
$691$	−2.39101e6	−0.190496	−0.0952480	+	0.995454i	$0.530364\pi$
$692$	1.40011e6	0.111147
$693$	1.21436e6	0.0960534
$694$	4.89773e6	0.386008
$695$	−1.05950e7	−0.832033
$696$	−2.86349e6	−0.224065
$697$	5.78844e6	0.451315
$698$	5.03198e6	0.390932
$699$	−2.40649e7	−1.86291
$700$	−6.68883e6	−0.515947
$701$	−2.67685e6	−0.205745	−0.102872	−	0.994695i	$-0.532803\pi$
$701$	−2.67685e6	−0.205745	−0.102872	+	0.994695i	$0.532803\pi$
$702$	1.34903e7	1.03319
$703$	69983.4	0.00534080
$704$	−2.64496e6	−0.201135
$705$	−9.04411e6	−0.685319
$706$	4.19246e6	0.316561
$707$	1.25159e7	0.941701
$708$	−3.68377e6	−0.276191
$709$	1.61177e7	1.20417	0.602085	−	0.798432i	$-0.294337\pi$
$709$	1.61177e7	1.20417	0.602085	+	0.798432i	$0.294337\pi$
$710$	−2.62635e6	−0.195527
$711$	3.30870e6	0.245461
$712$	−2.53848e7	−1.87661
$713$	2.75329e7	2.02828
$714$	−5.04168e6	−0.370109
$715$	−2.88693e6	−0.211189
$716$	4.79883e6	0.349826
$717$	−1.95319e7	−1.41888
$718$	4.58463e6	0.331889
$719$	2.74012e7	1.97673	0.988363	−	0.152111i	$-0.0486070\pi$
$719$	2.74012e7	1.97673	0.988363	+	0.152111i	$0.0486070\pi$
$720$	−708398.	−0.0509267
$721$	2.46074e7	1.76290
$722$	−9.43124e6	−0.673327
$723$	2.57732e7	1.83367
$724$	−1.59341e6	−0.112975
$725$	1.73615e6	0.122671
$726$	1.12123e7	0.789503
$727$	−1.44905e7	−1.01683	−0.508413	−	0.861113i	$-0.669768\pi$
$727$	−1.44905e7	−1.01683	−0.508413	+	0.861113i	$0.669768\pi$
$728$	4.43542e7	3.10175
$729$	8.82438e6	0.614986
$730$	−7.71478e6	−0.535817
$731$	−648840.	−0.0449101
$732$	−5.03580e6	−0.347369
$733$	9.24243e6	0.635370	0.317685	−	0.948196i	$-0.397095\pi$
$733$	9.24243e6	0.635370	0.317685	+	0.948196i	$0.397095\pi$
$734$	1.24574e7	0.853470
$735$	−1.82317e7	−1.24483
$736$	−1.65737e7	−1.12778
$737$	788172.	0.0534505
$738$	−4.93807e6	−0.333746
$739$	−270924.	−0.0182489	−0.00912445	−	0.999958i	$-0.502904\pi$
$739$	−270924.	−0.0182489	−0.00912445	+	0.999958i	$0.502904\pi$
$740$	−72941.6	−0.00489662
$741$	−8.30955e6	−0.555945
$742$	−8.49221e6	−0.566253
$743$	1.56128e7	1.03755	0.518776	−	0.854910i	$-0.326388\pi$
$743$	1.56128e7	1.03755	0.518776	+	0.854910i	$0.326388\pi$
$744$	−2.71818e7	−1.80031
$745$	−1.27488e7	−0.841545
$746$	1.76141e7	1.15882
$747$	1.28169e6	0.0840394
$748$	−393801.	−0.0257349
$749$	−4.18257e7	−2.72420
$750$	1.23285e7	0.800311
$751$	2.81796e6	0.182320	0.0911600	−	0.995836i	$-0.470943\pi$
$751$	2.81796e6	0.182320	0.0911600	+	0.995836i	$0.470943\pi$
$752$	−5.37251e6	−0.346444
$753$	−6.57403e6	−0.422517
$754$	−3.61961e6	−0.231864
$755$	−7.05355e6	−0.450340
$756$	1.01558e7	0.646264
$757$	1.47622e6	0.0936293	0.0468146	−	0.998904i	$-0.485093\pi$
$757$	1.47622e6	0.0936293	0.0468146	+	0.998904i	$0.485093\pi$
$758$	4.42325e6	0.279620
$759$	−5.18182e6	−0.326496
$760$	−2.90116e6	−0.182195
$761$	−1.59710e7	−0.999700	−0.499850	−	0.866112i	$-0.666612\pi$
$761$	−1.59710e7	−0.999700	−0.499850	+	0.866112i	$0.666612\pi$
$762$	1.80576e7	1.12660
$763$	−2.21305e7	−1.37620
$764$	4.63340e6	0.287188
$765$	−654005.	−0.0404043
$766$	−1.56394e7	−0.963051
$767$	−1.48104e7	−0.909033
$768$	1.91529e7	1.17174
$769$	−2.69038e7	−1.64058	−0.820291	−	0.571947i	$-0.806188\pi$
$769$	−2.69038e7	−1.64058	−0.820291	+	0.571947i	$0.806188\pi$
$770$	2.56586e6	0.155958
$771$	8.25597e6	0.500187
$772$	−608009.	−0.0367170
$773$	2.10506e7	1.26711	0.633556	−	0.773697i	$-0.281595\pi$
$773$	2.10506e7	1.26711	0.633556	+	0.773697i	$0.281595\pi$
$774$	553520.	0.0332109
$775$	1.64805e7	0.985633
$776$	−8.47116e6	−0.504997
$777$	590592.	0.0350942
$778$	−1.61732e7	−0.957962
$779$	−8.47930e6	−0.500629
$780$	8.66080e6	0.509708
$781$	1.66099e6	0.0974403
$782$	4.49349e6	0.262765
$783$	−2.63604e6	−0.153655
$784$	−1.08303e7	−0.629288
$785$	1.83807e7	1.06460
$786$	−1.44773e7	−0.835854
$787$	−1.46428e7	−0.842728	−0.421364	−	0.906892i	$-0.638448\pi$
$787$	−1.46428e7	−0.842728	−0.421364	+	0.906892i	$0.638448\pi$
$788$	−5.20574e6	−0.298653
$789$	−1.95190e7	−1.11626
$790$	6.99108e6	0.398544
$791$	2.28396e7	1.29792
$792$	1.06852e6	0.0605297
$793$	−2.02462e7	−1.14330
$794$	2.99496e6	0.168593
$795$	−5.27416e6	−0.295962
$796$	1.39283e7	0.779141
$797$	−1.53622e7	−0.856660	−0.428330	−	0.903622i	$-0.640898\pi$
$797$	−1.53622e7	−0.856660	−0.428330	+	0.903622i	$0.640898\pi$
$798$	7.38540e6	0.410551
$799$	−4.96000e6	−0.274862
$800$	−9.92063e6	−0.548042
$801$	8.38267e6	0.461638
$802$	−6.55651e6	−0.359945
$803$	4.87907e6	0.267023
$804$	−2.36452e6	−0.129004
$805$	2.47991e7	1.34880
$806$	−3.43593e7	−1.86298
$807$	6.68730e6	0.361466
$808$	1.10128e7	0.593430
$809$	−7.26215e6	−0.390116	−0.195058	−	0.980792i	$-0.562490\pi$
$809$	−7.26215e6	−0.390116	−0.195058	+	0.980792i	$0.562490\pi$
$810$	−9.55975e6	−0.511957
$811$	4.17728e6	0.223019	0.111510	−	0.993763i	$-0.464431\pi$
$811$	4.17728e6	0.223019	0.111510	+	0.993763i	$0.464431\pi$
$812$	−2.72493e6	−0.145032
$813$	−1.90741e7	−1.01209
$814$	−54461.9	−0.00288092
$815$	1.55340e7	0.819200
$816$	−1.86003e6	−0.0977901
$817$	950466.	0.0498174
$818$	−1.39586e7	−0.729390
$819$	−1.46468e7	−0.763015
$820$	8.83772e6	0.458993
$821$	2.70285e7	1.39947	0.699736	−	0.714402i	$-0.253301\pi$
$821$	2.70285e7	1.39947	0.699736	+	0.714402i	$0.253301\pi$
$822$	−1.03180e7	−0.532619
$823$	−6.95032e6	−0.357689	−0.178844	−	0.983877i	$-0.557236\pi$
$823$	−6.95032e6	−0.357689	−0.178844	+	0.983877i	$0.557236\pi$
$824$	2.16522e7	1.11092
$825$	−3.10171e6	−0.158659
$826$	1.31633e7	0.671297
$827$	−370060.	−0.0188152	−0.00940759	−	0.999956i	$-0.502995\pi$
$827$	−370060.	−0.0188152	−0.00940759	+	0.999956i	$0.502995\pi$
$828$	3.24695e6	0.164589
$829$	1.38451e7	0.699698	0.349849	−	0.936806i	$-0.386233\pi$
$829$	1.38451e7	0.699698	0.349849	+	0.936806i	$0.386233\pi$
$830$	2.70814e6	0.136451
$831$	3.83741e7	1.92768
$832$	3.19018e7	1.59774
$833$	−9.99869e6	−0.499264
$834$	2.37324e7	1.18148
$835$	−6.62405e6	−0.328781
$836$	576867.	0.0285469
$837$	−2.50227e7	−1.23458
$838$	2.82979e7	1.39201
$839$	1.86174e7	0.913089	0.456544	−	0.889701i	$-0.349087\pi$
$839$	1.86174e7	0.913089	0.456544	+	0.889701i	$0.349087\pi$
$840$	−2.44830e7	−1.19720
$841$	707281.	0.0344828
$842$	−7.37815e6	−0.358647
$843$	1.80012e7	0.872435
$844$	5.58486e6	0.269871
$845$	2.27285e7	1.09504
$846$	4.23133e6	0.203260
$847$	3.39362e7	1.62538
$848$	−3.13304e6	−0.149615
$849$	−1.55832e7	−0.741972
$850$	2.68969e6	0.127690
$851$	−526376.	−0.0249157
$852$	−4.98296e6	−0.235174
$853$	2.15389e6	0.101356	0.0506782	−	0.998715i	$-0.483862\pi$
$853$	2.15389e6	0.101356	0.0506782	+	0.998715i	$0.483862\pi$
$854$	1.79945e7	0.844298
$855$	958031.	0.0448192
$856$	−3.68026e7	−1.71670
$857$	−3.33513e7	−1.55118	−0.775588	−	0.631239i	$-0.782547\pi$
$857$	−3.33513e7	−1.55118	−0.775588	+	0.631239i	$0.782547\pi$
$858$	6.46659e6	0.299887
$859$	−3.11061e7	−1.43834	−0.719171	−	0.694833i	$-0.755478\pi$
$859$	−3.11061e7	−1.43834	−0.719171	+	0.694833i	$0.755478\pi$
$860$	−990643.	−0.0456742
$861$	−7.15571e7	−3.28961
$862$	5.42025e6	0.248457
$863$	−1.59387e7	−0.728494	−0.364247	−	0.931302i	$-0.618674\pi$
$863$	−1.59387e7	−0.728494	−0.364247	+	0.931302i	$0.618674\pi$
$864$	1.50627e7	0.686467
$865$	−3.10719e6	−0.141198
$866$	8.96511e6	0.406220
$867$	2.31670e7	1.04670
$868$	−2.58665e7	−1.16530
$869$	−4.42138e6	−0.198613
$870$	1.99798e6	0.0894939
$871$	−9.50644e6	−0.424593
$872$	−1.94728e7	−0.867235
$873$	2.79738e6	0.124227
$874$	−6.58238e6	−0.291477
$875$	3.73147e7	1.64763
$876$	−1.46372e7	−0.644464
$877$	666578.	0.0292652	0.0146326	−	0.999893i	$-0.495342\pi$
$877$	666578.	0.0292652	0.0146326	+	0.999893i	$0.495342\pi$
$878$	−2.42214e7	−1.06038
$879$	8.44745e6	0.368768
$880$	946625.	0.0412070
$881$	−2.30910e7	−1.00231	−0.501155	−	0.865358i	$-0.667091\pi$
$881$	−2.30910e7	−1.00231	−0.501155	+	0.865358i	$0.667091\pi$
$882$	8.52980e6	0.369205
$883$	3.85060e6	0.166198	0.0830992	−	0.996541i	$-0.473518\pi$
$883$	3.85060e6	0.166198	0.0830992	+	0.996541i	$0.473518\pi$
$884$	4.74978e6	0.204429
$885$	8.17519e6	0.350864
$886$	1.80784e7	0.773706
$887$	−4.14426e7	−1.76863	−0.884316	−	0.466889i	$-0.845375\pi$
$887$	−4.14426e7	−1.76863	−0.884316	+	0.466889i	$0.845375\pi$
$888$	519665.	0.0221152
$889$	5.46547e7	2.31939
$890$	1.77121e7	0.749540
$891$	6.04589e6	0.255133
$892$	1.00321e6	0.0422163
$893$	7.26574e6	0.304896
$894$	2.85566e7	1.19499
$895$	−1.06498e7	−0.444409
$896$	5.59955e6	0.233015
$897$	6.24999e7	2.59357
$898$	1.11596e7	0.461803
$899$	6.71389e6	0.277061
$900$	1.94354e6	0.0799812
$901$	−2.89247e6	−0.118702
$902$	6.59869e6	0.270048
$903$	8.02102e6	0.327348
$904$	2.00967e7	0.817907
$905$	3.53617e6	0.143520
$906$	1.57996e7	0.639479
$907$	−4.63163e7	−1.86946	−0.934729	−	0.355363i	$-0.884357\pi$
$907$	−4.63163e7	−1.86946	−0.934729	+	0.355363i	$0.884357\pi$
$908$	1.58362e7	0.637436
$909$	−3.63669e6	−0.145981
$910$	−3.09478e7	−1.23887
$911$	2.69515e6	0.107594	0.0537969	−	0.998552i	$-0.482868\pi$
$911$	2.69515e6	0.107594	0.0537969	+	0.998552i	$0.482868\pi$
$912$	2.72470e6	0.108476
$913$	−1.71272e6	−0.0679999
$914$	−1.78912e7	−0.708392
$915$	1.11757e7	0.441286
$916$	1.06278e7	0.418510
$917$	−4.38183e7	−1.72081
$918$	−4.08383e6	−0.159941
$919$	1.39792e7	0.546000	0.273000	−	0.962014i	$-0.411984\pi$
$919$	1.39792e7	0.546000	0.273000	+	0.962014i	$0.411984\pi$
$920$	2.18209e7	0.849969
$921$	−4.01618e6	−0.156014
$922$	9.50852e6	0.368371
$923$	−2.00338e7	−0.774032
$924$	4.86820e6	0.187581
$925$	−315076.	−0.0121077
$926$	6.32510e6	0.242404
$927$	−7.15007e6	−0.273282
$928$	−4.04151e6	−0.154054
$929$	−7.25580e6	−0.275833	−0.137916	−	0.990444i	$-0.544041\pi$
$929$	−7.25580e6	−0.275833	−0.137916	+	0.990444i	$0.544041\pi$
$930$	1.89659e7	0.719063
$931$	1.46468e7	0.553819
$932$	−2.01502e7	−0.759869
$933$	−4.37619e7	−1.64586
$934$	−1.96399e7	−0.736667
$935$	873940.	0.0326928
$936$	−1.28878e7	−0.480827
$937$	3.95850e6	0.147293	0.0736464	−	0.997284i	$-0.476536\pi$
$937$	3.95850e6	0.147293	0.0736464	+	0.997284i	$0.476536\pi$
$938$	8.44918e6	0.313550
$939$	4.87413e7	1.80399
$940$	−7.57287e6	−0.279538
$941$	−4.07672e7	−1.50085	−0.750425	−	0.660956i	$-0.770151\pi$
$941$	−4.07672e7	−1.50085	−0.750425	+	0.660956i	$0.770151\pi$
$942$	−4.11719e7	−1.51173
$943$	6.37766e7	2.33551
$944$	4.85635e6	0.177370
$945$	−2.25382e7	−0.820994
$946$	−739664.	−0.0268724
$947$	−2.67878e7	−0.970650	−0.485325	−	0.874334i	$-0.661299\pi$
$947$	−2.67878e7	−0.970650	−0.485325	+	0.874334i	$0.661299\pi$
$948$	1.32641e7	0.479356
$949$	−5.88484e7	−2.12114
$950$	−3.94004e6	−0.141642
$951$	−3.40658e7	−1.22143
$952$	−1.34270e7	−0.480162
$953$	−1.81430e7	−0.647107	−0.323553	−	0.946210i	$-0.604877\pi$
$953$	−1.81430e7	−0.647107	−0.323553	+	0.946210i	$0.604877\pi$
$954$	2.46754e6	0.0877796
$955$	−1.02827e7	−0.364835
$956$	−1.63546e7	−0.578755
$957$	−1.26359e6	−0.0445990
$958$	2.43563e7	0.857427
$959$	−3.12294e7	−1.09652
$960$	−1.76094e7	−0.616690
$961$	3.51028e7	1.22612
$962$	656886.	0.0228851
$963$	1.21531e7	0.422300
$964$	2.15806e7	0.747946
$965$	1.34932e6	0.0466441
$966$	−5.55489e7	−1.91528
$967$	−1.40529e7	−0.483282	−0.241641	−	0.970366i	$-0.577686\pi$
$967$	−1.40529e7	−0.483282	−0.241641	+	0.970366i	$0.577686\pi$
$968$	2.98607e7	1.02426
$969$	2.51549e6	0.0860624
$970$	5.91069e6	0.201702
$971$	1.77622e7	0.604573	0.302287	−	0.953217i	$-0.402250\pi$
$971$	1.77622e7	0.604573	0.302287	+	0.953217i	$0.402250\pi$
$972$	−6.96041e6	−0.236303
$973$	7.18306e7	2.43236
$974$	7.64103e6	0.258080
$975$	3.74108e7	1.26034
$976$	6.63873e6	0.223080
$977$	−1.66625e7	−0.558474	−0.279237	−	0.960222i	$-0.590082\pi$
$977$	−1.66625e7	−0.558474	−0.279237	+	0.960222i	$0.590082\pi$
$978$	−3.47955e7	−1.16326
$979$	−1.12017e7	−0.373531
$980$	−1.52659e7	−0.507758
$981$	6.43037e6	0.213336
$982$	−2.39600e7	−0.792880
$983$	−2.28571e7	−0.754461	−0.377231	−	0.926119i	$-0.623124\pi$
$983$	−2.28571e7	−0.754461	−0.377231	+	0.926119i	$0.623124\pi$
$984$	−6.29635e7	−2.07301
$985$	1.15528e7	0.379399
$986$	1.09574e6	0.0358934
$987$	6.13159e7	2.00346
$988$	−6.95781e6	−0.226767
$989$	−7.14888e6	−0.232406
$990$	−745551.	−0.0241763
$991$	−2.52864e7	−0.817904	−0.408952	−	0.912556i	$-0.634106\pi$
$991$	−2.52864e7	−0.817904	−0.408952	+	0.912556i	$0.634106\pi$
$992$	−3.83642e7	−1.23779
$993$	1.05935e6	0.0340931
$994$	1.78057e7	0.571602
$995$	−3.09103e7	−0.989796
$996$	5.13815e6	0.164119
$997$	4.44014e7	1.41468	0.707340	−	0.706873i	$-0.249895\pi$
$997$	4.44014e7	1.41468	0.707340	+	0.706873i	$0.249895\pi$
$998$	1.70726e7	0.542590
$999$	478387.	0.0151658

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.6.a.a.1.3	✓	4
3.2	odd	2		261.6.a.a.1.2		4
4.3	odd	2		464.6.a.i.1.3		4
5.4	even	2		725.6.a.a.1.2		4
29.28	even	2		841.6.a.a.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.a.a.1.3	✓	4	1.1	even	1	trivial
261.6.a.a.1.2		4	3.2	odd	2
464.6.a.i.1.3		4	4.3	odd	2
725.6.a.a.1.2		4	5.4	even	2
841.6.a.a.1.2		4	29.28	even	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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+4.16235 q^{2} -17.5258 q^{3} -14.6748 q^{4} +32.5670 q^{5} -72.9487 q^{6} -220.793 q^{7} -194.277 q^{8} +64.1549 q^{9} +O(q^{10})\)	\(q+4.16235 q^{2} -17.5258 q^{3} -14.6748 q^{4} +32.5670 q^{5} -72.9487 q^{6} -220.793 q^{7} -194.277 q^{8} +64.1549 q^{9} +135.555 q^{10} -85.7296 q^{11} +257.189 q^{12} +1034.02 q^{13} -919.018 q^{14} -570.765 q^{15} -339.054 q^{16} -313.020 q^{17} +267.035 q^{18} +458.534 q^{19} -477.916 q^{20} +3869.58 q^{21} -356.836 q^{22} -3448.84 q^{23} +3404.87 q^{24} -2064.39 q^{25} +4303.94 q^{26} +3134.41 q^{27} +3240.10 q^{28} -841.000 q^{29} -2375.72 q^{30} -7983.23 q^{31} +4805.60 q^{32} +1502.48 q^{33} -1302.90 q^{34} -7190.58 q^{35} -941.463 q^{36} +152.624 q^{37} +1908.58 q^{38} -18122.0 q^{39} -6327.03 q^{40} -18492.2 q^{41} +16106.6 q^{42} +2072.84 q^{43} +1258.07 q^{44} +2089.33 q^{45} -14355.3 q^{46} +15845.6 q^{47} +5942.21 q^{48} +31942.6 q^{49} -8592.70 q^{50} +5485.94 q^{51} -15174.0 q^{52} +9240.52 q^{53} +13046.5 q^{54} -2791.96 q^{55} +42895.0 q^{56} -8036.19 q^{57} -3500.54 q^{58} -14323.2 q^{59} +8375.88 q^{60} -19580.2 q^{61} -33229.0 q^{62} -14165.0 q^{63} +30852.3 q^{64} +33674.9 q^{65} +6253.86 q^{66} -9193.70 q^{67} +4593.53 q^{68} +60443.8 q^{69} -29929.7 q^{70} -19374.7 q^{71} -12463.8 q^{72} -56912.4 q^{73} +635.276 q^{74} +36180.1 q^{75} -6728.91 q^{76} +18928.5 q^{77} -75430.1 q^{78} +51573.6 q^{79} -11042.0 q^{80} -70522.8 q^{81} -76971.0 q^{82} +19978.1 q^{83} -56785.5 q^{84} -10194.2 q^{85} +8627.87 q^{86} +14739.2 q^{87} +16655.3 q^{88} +130663. q^{89} +8696.54 q^{90} -228304. q^{91} +50611.1 q^{92} +139913. q^{93} +65954.9 q^{94} +14933.1 q^{95} -84222.2 q^{96} +43603.5 q^{97} +132956. q^{98} -5499.97 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 28 q^{3} + 10 q^{4} - 68 q^{5} - 194 q^{6} - 208 q^{7} - 504 q^{8} - 280 q^{9}+O(q^{10}) \) 4 * q - 28 * q^3 + 10 * q^4 - 68 * q^5 - 194 * q^6 - 208 * q^7 - 504 * q^8 - 280 * q^9	\( 4 q - 28 q^{3} + 10 q^{4} - 68 q^{5} - 194 q^{6} - 208 q^{7} - 504 q^{8} - 280 q^{9} - 788 q^{10} - 124 q^{11} + 20 q^{12} - 460 q^{13} + 768 q^{14} + 932 q^{15} - 414 q^{16} + 184 q^{17} + 3208 q^{18} - 2392 q^{19} + 2822 q^{20} + 992 q^{21} + 5538 q^{22} - 1192 q^{23} + 6786 q^{24} + 1824 q^{25} + 4724 q^{26} + 2468 q^{27} + 44 q^{28} - 3364 q^{29} + 8186 q^{30} - 19212 q^{31} + 6552 q^{32} - 10580 q^{33} - 7612 q^{34} - 22944 q^{35} - 7468 q^{36} - 10928 q^{37} - 456 q^{38} - 8732 q^{39} - 20 q^{40} - 1120 q^{41} + 1844 q^{42} - 21420 q^{43} - 1932 q^{44} - 8344 q^{45} - 7588 q^{46} + 23772 q^{47} + 33060 q^{48} + 10452 q^{49} + 43240 q^{50} + 12744 q^{51} - 29062 q^{52} + 8860 q^{53} + 35410 q^{54} - 52652 q^{55} + 34304 q^{56} + 48944 q^{57} - 10840 q^{59} + 25200 q^{60} + 49448 q^{61} + 18518 q^{62} + 27488 q^{63} - 20734 q^{64} + 97836 q^{65} - 47744 q^{66} - 7840 q^{67} + 20724 q^{68} + 58792 q^{69} - 77496 q^{70} - 48744 q^{71} + 8088 q^{72} - 74992 q^{73} - 35920 q^{74} - 90448 q^{75} - 140792 q^{76} + 128656 q^{77} + 2982 q^{78} - 106076 q^{79} + 58638 q^{80} - 59692 q^{81} - 234132 q^{82} + 62888 q^{83} - 59832 q^{84} + 23848 q^{85} - 216014 q^{86} + 23548 q^{87} - 39426 q^{88} + 107568 q^{89} + 41552 q^{90} - 268896 q^{91} - 26268 q^{92} + 221460 q^{93} + 30542 q^{94} + 147352 q^{95} - 78606 q^{96} - 49520 q^{97} + 242304 q^{98} + 166720 q^{99}+O(q^{100}) \) 4 * q - 28 * q^3 + 10 * q^4 - 68 * q^5 - 194 * q^6 - 208 * q^7 - 504 * q^8 - 280 * q^9 - 788 * q^10 - 124 * q^11 + 20 * q^12 - 460 * q^13 + 768 * q^14 + 932 * q^15 - 414 * q^16 + 184 * q^17 + 3208 * q^18 - 2392 * q^19 + 2822 * q^20 + 992 * q^21 + 5538 * q^22 - 1192 * q^23 + 6786 * q^24 + 1824 * q^25 + 4724 * q^26 + 2468 * q^27 + 44 * q^28 - 3364 * q^29 + 8186 * q^30 - 19212 * q^31 + 6552 * q^32 - 10580 * q^33 - 7612 * q^34 - 22944 * q^35 - 7468 * q^36 - 10928 * q^37 - 456 * q^38 - 8732 * q^39 - 20 * q^40 - 1120 * q^41 + 1844 * q^42 - 21420 * q^43 - 1932 * q^44 - 8344 * q^45 - 7588 * q^46 + 23772 * q^47 + 33060 * q^48 + 10452 * q^49 + 43240 * q^50 + 12744 * q^51 - 29062 * q^52 + 8860 * q^53 + 35410 * q^54 - 52652 * q^55 + 34304 * q^56 + 48944 * q^57 - 10840 * q^59 + 25200 * q^60 + 49448 * q^61 + 18518 * q^62 + 27488 * q^63 - 20734 * q^64 + 97836 * q^65 - 47744 * q^66 - 7840 * q^67 + 20724 * q^68 + 58792 * q^69 - 77496 * q^70 - 48744 * q^71 + 8088 * q^72 - 74992 * q^73 - 35920 * q^74 - 90448 * q^75 - 140792 * q^76 + 128656 * q^77 + 2982 * q^78 - 106076 * q^79 + 58638 * q^80 - 59692 * q^81 - 234132 * q^82 + 62888 * q^83 - 59832 * q^84 + 23848 * q^85 - 216014 * q^86 + 23548 * q^87 - 39426 * q^88 + 107568 * q^89 + 41552 * q^90 - 268896 * q^91 - 26268 * q^92 + 221460 * q^93 + 30542 * q^94 + 147352 * q^95 - 78606 * q^96 - 49520 * q^97 + 242304 * q^98 + 166720 * q^99

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