LMFDB - Embedded newform 38.6.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(1,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, 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("38.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.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:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1441}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 360 $ x^2 - x - 360
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-18.4803$ of defining polynomial
Character	$\chi$	$=$	38.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +20.4803 q^{3} +16.0000 q^{4} +34.4408 q^{5} -81.9210 q^{6} -18.9210 q^{7} -64.0000 q^{8} +176.441 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +20.4803 q^{3} +16.0000 q^{4} +34.4408 q^{5} -81.9210 q^{6} -18.9210 q^{7} -64.0000 q^{8} +176.441 q^{9} -137.763 q^{10} +349.480 q^{11} +327.684 q^{12} +711.599 q^{13} +75.6840 q^{14} +705.355 q^{15} +256.000 q^{16} +221.803 q^{17} -705.763 q^{18} +361.000 q^{19} +551.052 q^{20} -387.507 q^{21} -1397.92 q^{22} -662.468 q^{23} -1310.74 q^{24} -1938.83 q^{25} -2846.39 q^{26} -1363.15 q^{27} -302.736 q^{28} -7219.28 q^{29} -2821.42 q^{30} +5407.76 q^{31} -1024.00 q^{32} +7157.44 q^{33} -887.210 q^{34} -651.654 q^{35} +2823.05 q^{36} +1979.40 q^{37} -1444.00 q^{38} +14573.7 q^{39} -2204.21 q^{40} -3111.11 q^{41} +1550.03 q^{42} +318.049 q^{43} +5591.68 q^{44} +6076.75 q^{45} +2649.87 q^{46} -27240.5 q^{47} +5242.94 q^{48} -16449.0 q^{49} +7755.34 q^{50} +4542.57 q^{51} +11385.6 q^{52} -1114.63 q^{53} +5452.60 q^{54} +12036.4 q^{55} +1210.94 q^{56} +7393.37 q^{57} +28877.1 q^{58} -37904.9 q^{59} +11285.7 q^{60} +37469.2 q^{61} -21631.0 q^{62} -3338.44 q^{63} +4096.00 q^{64} +24508.0 q^{65} -28629.8 q^{66} -54955.3 q^{67} +3548.84 q^{68} -13567.5 q^{69} +2606.62 q^{70} -7177.04 q^{71} -11292.2 q^{72} +64746.1 q^{73} -7917.59 q^{74} -39707.8 q^{75} +5776.00 q^{76} -6612.52 q^{77} -58294.9 q^{78} +36104.4 q^{79} +8816.83 q^{80} -70792.8 q^{81} +12444.4 q^{82} -51782.7 q^{83} -6200.11 q^{84} +7639.05 q^{85} -1272.20 q^{86} -147853. q^{87} -22366.7 q^{88} +145254. q^{89} -24307.0 q^{90} -13464.2 q^{91} -10599.5 q^{92} +110752. q^{93} +108962. q^{94} +12433.1 q^{95} -20971.8 q^{96} +39512.8 q^{97} +65796.0 q^{98} +61662.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} + 3 q^{3} + 32 q^{4} - 45 q^{5} - 12 q^{6} + 114 q^{7} - 128 q^{8} + 239 q^{9}+O(q^{10}) $ 2 * q - 8 * q^2 + 3 * q^3 + 32 * q^4 - 45 * q^5 - 12 * q^6 + 114 * q^7 - 128 * q^8 + 239 * q^9	\( 2 q - 8 q^{2} + 3 q^{3} + 32 q^{4} - 45 q^{5} - 12 q^{6} + 114 q^{7} - 128 q^{8} + 239 q^{9} + 180 q^{10} + 661 q^{11} + 48 q^{12} + 1613 q^{13} - 456 q^{14} + 2094 q^{15} + 512 q^{16} + 64 q^{17} - 956 q^{18} + 722 q^{19} - 720 q^{20} - 2711 q^{21} - 2644 q^{22} - 3185 q^{23} - 192 q^{24} + 1247 q^{25} - 6452 q^{26} + 1791 q^{27} + 1824 q^{28} - 2481 q^{29} - 8376 q^{30} - 1180 q^{31} - 2048 q^{32} + 1712 q^{33} - 256 q^{34} - 11211 q^{35} + 3824 q^{36} + 10488 q^{37} - 2888 q^{38} - 1183 q^{39} + 2880 q^{40} + 16630 q^{41} + 10844 q^{42} + 11303 q^{43} + 10576 q^{44} + 1107 q^{45} + 12740 q^{46} - 12155 q^{47} + 768 q^{48} - 15588 q^{49} - 4988 q^{50} + 7301 q^{51} + 25808 q^{52} + 20585 q^{53} - 7164 q^{54} - 12711 q^{55} - 7296 q^{56} + 1083 q^{57} + 9924 q^{58} - 78581 q^{59} + 33504 q^{60} + 43621 q^{61} + 4720 q^{62} + 4977 q^{63} + 8192 q^{64} - 47100 q^{65} - 6848 q^{66} + 7805 q^{67} + 1024 q^{68} + 30527 q^{69} + 44844 q^{70} - 62488 q^{71} - 15296 q^{72} + 16218 q^{73} - 41952 q^{74} - 95397 q^{75} + 11552 q^{76} + 34795 q^{77} + 4732 q^{78} + 67122 q^{79} - 11520 q^{80} - 141130 q^{81} - 66520 q^{82} - 10714 q^{83} - 43376 q^{84} + 20175 q^{85} - 45212 q^{86} - 230679 q^{87} - 42304 q^{88} + 128188 q^{89} - 4428 q^{90} + 106351 q^{91} - 50960 q^{92} + 225908 q^{93} + 48620 q^{94} - 16245 q^{95} - 3072 q^{96} + 178558 q^{97} + 62352 q^{98} + 81151 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 + 3 * q^3 + 32 * q^4 - 45 * q^5 - 12 * q^6 + 114 * q^7 - 128 * q^8 + 239 * q^9 + 180 * q^10 + 661 * q^11 + 48 * q^12 + 1613 * q^13 - 456 * q^14 + 2094 * q^15 + 512 * q^16 + 64 * q^17 - 956 * q^18 + 722 * q^19 - 720 * q^20 - 2711 * q^21 - 2644 * q^22 - 3185 * q^23 - 192 * q^24 + 1247 * q^25 - 6452 * q^26 + 1791 * q^27 + 1824 * q^28 - 2481 * q^29 - 8376 * q^30 - 1180 * q^31 - 2048 * q^32 + 1712 * q^33 - 256 * q^34 - 11211 * q^35 + 3824 * q^36 + 10488 * q^37 - 2888 * q^38 - 1183 * q^39 + 2880 * q^40 + 16630 * q^41 + 10844 * q^42 + 11303 * q^43 + 10576 * q^44 + 1107 * q^45 + 12740 * q^46 - 12155 * q^47 + 768 * q^48 - 15588 * q^49 - 4988 * q^50 + 7301 * q^51 + 25808 * q^52 + 20585 * q^53 - 7164 * q^54 - 12711 * q^55 - 7296 * q^56 + 1083 * q^57 + 9924 * q^58 - 78581 * q^59 + 33504 * q^60 + 43621 * q^61 + 4720 * q^62 + 4977 * q^63 + 8192 * q^64 - 47100 * q^65 - 6848 * q^66 + 7805 * q^67 + 1024 * q^68 + 30527 * q^69 + 44844 * q^70 - 62488 * q^71 - 15296 * q^72 + 16218 * q^73 - 41952 * q^74 - 95397 * q^75 + 11552 * q^76 + 34795 * q^77 + 4732 * q^78 + 67122 * q^79 - 11520 * q^80 - 141130 * q^81 - 66520 * q^82 - 10714 * q^83 - 43376 * q^84 + 20175 * q^85 - 45212 * q^86 - 230679 * q^87 - 42304 * q^88 + 128188 * q^89 - 4428 * q^90 + 106351 * q^91 - 50960 * q^92 + 225908 * q^93 + 48620 * q^94 - 16245 * q^95 - 3072 * q^96 + 178558 * q^97 + 62352 * q^98 + 81151 * 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
$3$	20.4803	1.31381	0.656904	−	0.753974i	$-0.271865\pi$
$3$	20.4803	1.31381	0.656904	+	0.753974i	$0.271865\pi$
$4$	16.0000	0.500000
$5$	34.4408	0.616095	0.308048	−	0.951371i	$-0.400324\pi$
$5$	34.4408	0.616095	0.308048	+	0.951371i	$0.400324\pi$
$6$	−81.9210	−0.929003
$7$	−18.9210	−0.145948	−0.0729742	−	0.997334i	$-0.523249\pi$
$7$	−18.9210	−0.145948	−0.0729742	+	0.997334i	$0.523249\pi$
$8$	−64.0000	−0.353553
$9$	176.441	0.726094
$10$	−137.763	−0.435645
$11$	349.480	0.870845	0.435423	−	0.900226i	$-0.356599\pi$
$11$	349.480	0.870845	0.435423	+	0.900226i	$0.356599\pi$
$12$	327.684	0.656904
$13$	711.599	1.16782	0.583911	−	0.811818i	$-0.301522\pi$
$13$	711.599	1.16782	0.583911	+	0.811818i	$0.301522\pi$
$14$	75.6840	0.103201
$15$	705.355	0.809431
$16$	256.000	0.250000
$17$	221.803	0.186142	0.0930710	−	0.995659i	$-0.470332\pi$
$17$	221.803	0.186142	0.0930710	+	0.995659i	$0.470332\pi$
$18$	−705.763	−0.513426
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	551.052	0.308048
$21$	−387.507	−0.191748
$22$	−1397.92	−0.615780
$23$	−662.468	−0.261123	−0.130561	−	0.991440i	$-0.541678\pi$
$23$	−662.468	−0.261123	−0.130561	+	0.991440i	$0.541678\pi$
$24$	−1310.74	−0.464502
$25$	−1938.83	−0.620427
$26$	−2846.39	−0.825775
$27$	−1363.15	−0.359861
$28$	−302.736	−0.0729742
$29$	−7219.28	−1.59404	−0.797019	−	0.603954i	$-0.793591\pi$
$29$	−7219.28	−1.59404	−0.797019	+	0.603954i	$0.793591\pi$
$30$	−2821.42	−0.572354
$31$	5407.76	1.01068	0.505339	−	0.862921i	$-0.331367\pi$
$31$	5407.76	1.01068	0.505339	+	0.862921i	$0.331367\pi$
$32$	−1024.00	−0.176777
$33$	7157.44	1.14412
$34$	−887.210	−0.131622
$35$	−651.654	−0.0899181
$36$	2823.05	0.363047
$37$	1979.40	0.237700	0.118850	−	0.992912i	$-0.462079\pi$
$37$	1979.40	0.237700	0.118850	+	0.992912i	$0.462079\pi$
$38$	−1444.00	−0.162221
$39$	14573.7	1.53430
$40$	−2204.21	−0.217822
$41$	−3111.11	−0.289039	−0.144519	−	0.989502i	$-0.546164\pi$
$41$	−3111.11	−0.289039	−0.144519	+	0.989502i	$0.546164\pi$
$42$	1550.03	0.135586
$43$	318.049	0.0262315	0.0131157	−	0.999914i	$-0.495825\pi$
$43$	318.049	0.0262315	0.0131157	+	0.999914i	$0.495825\pi$
$44$	5591.68	0.435423
$45$	6076.75	0.447343
$46$	2649.87	0.184642
$47$	−27240.5	−1.79875	−0.899374	−	0.437181i	$-0.855977\pi$
$47$	−27240.5	−1.79875	−0.899374	+	0.437181i	$0.855977\pi$
$48$	5242.94	0.328452
$49$	−16449.0	−0.978699
$50$	7755.34	0.438708
$51$	4542.57	0.244555
$52$	11385.6	0.583911
$53$	−1114.63	−0.0545057	−0.0272528	−	0.999629i	$-0.508676\pi$
$53$	−1114.63	−0.0545057	−0.0272528	+	0.999629i	$0.508676\pi$
$54$	5452.60	0.254460
$55$	12036.4	0.536523
$56$	1210.94	0.0516005
$57$	7393.37	0.301408
$58$	28877.1	1.12716
$59$	−37904.9	−1.41764	−0.708820	−	0.705390i	$-0.750772\pi$
$59$	−37904.9	−1.41764	−0.708820	+	0.705390i	$0.750772\pi$
$60$	11285.7	0.404716
$61$	37469.2	1.28929	0.644644	−	0.764483i	$-0.277006\pi$
$61$	37469.2	1.28929	0.644644	+	0.764483i	$0.277006\pi$
$62$	−21631.0	−0.714658
$63$	−3338.44	−0.105972
$64$	4096.00	0.125000
$65$	24508.0	0.719490
$66$	−28629.8	−0.809018
$67$	−54955.3	−1.49562	−0.747812	−	0.663911i	$-0.768895\pi$
$67$	−54955.3	−1.49562	−0.747812	+	0.663911i	$0.768895\pi$
$68$	3548.84	0.0930710
$69$	−13567.5	−0.343066
$70$	2606.62	0.0635817
$71$	−7177.04	−0.168966	−0.0844830	−	0.996425i	$-0.526924\pi$
$71$	−7177.04	−0.168966	−0.0844830	+	0.996425i	$0.526924\pi$
$72$	−11292.2	−0.256713
$73$	64746.1	1.42202	0.711011	−	0.703181i	$-0.248238\pi$
$73$	64746.1	1.42202	0.711011	+	0.703181i	$0.248238\pi$
$74$	−7917.59	−0.168079
$75$	−39707.8	−0.815122
$76$	5776.00	0.114708
$77$	−6612.52	−0.127098
$78$	−58294.9	−1.08491
$79$	36104.4	0.650866	0.325433	−	0.945565i	$-0.394490\pi$
$79$	36104.4	0.650866	0.325433	+	0.945565i	$0.394490\pi$
$80$	8816.83	0.154024
$81$	−70792.8	−1.19888
$82$	12444.4	0.204381
$83$	−51782.7	−0.825067	−0.412534	−	0.910942i	$-0.635356\pi$
$83$	−51782.7	−0.825067	−0.412534	+	0.910942i	$0.635356\pi$
$84$	−6200.11	−0.0958741
$85$	7639.05	0.114681
$86$	−1272.20	−0.0185485
$87$	−147853.	−2.09426
$88$	−22366.7	−0.307890
$89$	145254.	1.94380	0.971900	−	0.235392i	$-0.0756375\pi$
$89$	145254.	1.94380	0.971900	+	0.235392i	$0.0756375\pi$
$90$	−24307.0	−0.316319
$91$	−13464.2	−0.170442
$92$	−10599.5	−0.130561
$93$	110752.	1.32784
$94$	108962.	1.27191
$95$	12433.1	0.141342
$96$	−20971.8	−0.232251
$97$	39512.8	0.426391	0.213196	−	0.977010i	$-0.431613\pi$
$97$	39512.8	0.426391	0.213196	+	0.977010i	$0.431613\pi$
$98$	65796.0	0.692045
$99$	61662.6	0.632315
$100$	−31021.3	−0.310213
$101$	−16722.9	−0.163120	−0.0815602	−	0.996668i	$-0.525990\pi$
$101$	−16722.9	−0.163120	−0.0815602	+	0.996668i	$0.525990\pi$
$102$	−18170.3	−0.172926
$103$	92664.4	0.860636	0.430318	−	0.902677i	$-0.358401\pi$
$103$	92664.4	0.860636	0.430318	+	0.902677i	$0.358401\pi$
$104$	−45542.3	−0.412888
$105$	−13346.0	−0.118135
$106$	4458.53	0.0385413
$107$	−47156.3	−0.398180	−0.199090	−	0.979981i	$-0.563799\pi$
$107$	−47156.3	−0.398180	−0.199090	+	0.979981i	$0.563799\pi$
$108$	−21810.4	−0.179930
$109$	52450.1	0.422844	0.211422	−	0.977395i	$-0.432191\pi$
$109$	52450.1	0.422844	0.211422	+	0.977395i	$0.432191\pi$
$110$	−48145.5	−0.379379
$111$	40538.5	0.312292
$112$	−4843.78	−0.0364871
$113$	150596.	1.10947	0.554737	−	0.832026i	$-0.312819\pi$
$113$	150596.	1.10947	0.554737	+	0.832026i	$0.312819\pi$
$114$	−29573.5	−0.213128
$115$	−22815.9	−0.160877
$116$	−115508.	−0.797019
$117$	125555.	0.847948
$118$	151620.	1.00242
$119$	−4196.73	−0.0271671
$120$	−45142.7	−0.286177
$121$	−38914.6	−0.241629
$122$	−149877.	−0.911664
$123$	−63716.4	−0.379742
$124$	86524.2	0.505339
$125$	−174402.	−0.998337
$126$	13353.8	0.0749337
$127$	352240.	1.93789	0.968945	−	0.247276i	$-0.0795353\pi$
$127$	352240.	1.93789	0.968945	+	0.247276i	$0.0795353\pi$
$128$	−16384.0	−0.0883883
$129$	6513.72	0.0344632
$130$	−98032.0	−0.508756
$131$	19070.2	0.0970907	0.0485453	−	0.998821i	$-0.484541\pi$
$131$	19070.2	0.0970907	0.0485453	+	0.998821i	$0.484541\pi$
$132$	114519.	0.572062
$133$	−6830.49	−0.0334829
$134$	219821.	1.05757
$135$	−46947.9	−0.221708
$136$	−14195.4	−0.0658111
$137$	−266677.	−1.21390	−0.606952	−	0.794738i	$-0.707608\pi$
$137$	−266677.	−1.21390	−0.606952	+	0.794738i	$0.707608\pi$
$138$	54270.0	0.242584
$139$	−294888.	−1.29456	−0.647278	−	0.762254i	$-0.724093\pi$
$139$	−294888.	−1.29456	−0.647278	+	0.762254i	$0.724093\pi$
$140$	−10426.5	−0.0449590
$141$	−557892.	−2.36321
$142$	28708.2	0.119477
$143$	248690.	1.01699
$144$	45168.8	0.181523
$145$	−248637.	−0.982079
$146$	−258984.	−1.00552
$147$	−336880.	−1.28582
$148$	31670.3	0.118850
$149$	−103990.	−0.383729	−0.191864	−	0.981421i	$-0.561453\pi$
$149$	−103990.	−0.383729	−0.191864	+	0.981421i	$0.561453\pi$
$150$	158831.	0.576379
$151$	−477343.	−1.70368	−0.851840	−	0.523802i	$-0.824513\pi$
$151$	−477343.	−1.70368	−0.851840	+	0.523802i	$0.824513\pi$
$152$	−23104.0	−0.0811107
$153$	39135.0	0.135156
$154$	26450.1	0.0898722
$155$	186247.	0.622674
$156$	233180.	0.767148
$157$	434955.	1.40830	0.704151	−	0.710051i	$-0.251328\pi$
$157$	434955.	1.40830	0.704151	+	0.710051i	$0.251328\pi$
$158$	−144417.	−0.460232
$159$	−22827.9	−0.0716101
$160$	−35267.3	−0.108911
$161$	12534.6	0.0381105
$162$	283171.	0.847737
$163$	−255083.	−0.751990	−0.375995	−	0.926622i	$-0.622699\pi$
$163$	−255083.	−0.751990	−0.375995	+	0.926622i	$0.622699\pi$
$164$	−49777.8	−0.144519
$165$	246508.	0.704889
$166$	207131.	0.583411
$167$	510501.	1.41646	0.708232	−	0.705980i	$-0.249493\pi$
$167$	510501.	1.41646	0.708232	+	0.705980i	$0.249493\pi$
$168$	24800.5	0.0677932
$169$	135080.	0.363809
$170$	−30556.2	−0.0810918
$171$	63695.1	0.166577
$172$	5088.78	0.0131157
$173$	773453.	1.96480	0.982401	−	0.186783i	$-0.0598062\pi$
$173$	773453.	1.96480	0.982401	+	0.186783i	$0.0598062\pi$
$174$	591411.	1.48087
$175$	36684.7	0.0905503
$176$	89466.9	0.217711
$177$	−776303.	−1.86251
$178$	−581014.	−1.37447
$179$	−477664.	−1.11427	−0.557135	−	0.830422i	$-0.688099\pi$
$179$	−477664.	−1.11427	−0.557135	+	0.830422i	$0.688099\pi$
$180$	97228.1	0.223671
$181$	729114.	1.65424	0.827121	−	0.562024i	$-0.189977\pi$
$181$	729114.	1.65424	0.827121	+	0.562024i	$0.189977\pi$
$182$	53856.7	0.120521
$183$	767379.	1.69388
$184$	42397.9	0.0923209
$185$	68171.9	0.146446
$186$	−443009.	−0.938924
$187$	77515.6	0.162101
$188$	−435848.	−0.899374
$189$	25792.2	0.0525211
$190$	−49732.5	−0.0999438
$191$	−285584.	−0.566435	−0.283218	−	0.959056i	$-0.591402\pi$
$191$	−285584.	−0.566435	−0.283218	+	0.959056i	$0.591402\pi$
$192$	83887.1	0.164226
$193$	−53690.2	−0.103753	−0.0518766	−	0.998654i	$-0.516520\pi$
$193$	−53690.2	−0.103753	−0.0518766	+	0.998654i	$0.516520\pi$
$194$	−158051.	−0.301504
$195$	501930.	0.945272
$196$	−263184.	−0.489350
$197$	14538.9	0.0266910	0.0133455	−	0.999911i	$-0.495752\pi$
$197$	14538.9	0.0266910	0.0133455	+	0.999911i	$0.495752\pi$
$198$	−246650.	−0.447114
$199$	−143700.	−0.257232	−0.128616	−	0.991695i	$-0.541053\pi$
$199$	−143700.	−0.257232	−0.128616	+	0.991695i	$0.541053\pi$
$200$	124085.	0.219354
$201$	−1.12550e6	−1.96496
$202$	66891.6	0.115343
$203$	136596.	0.232647
$204$	72681.2	0.122277
$205$	−107149.	−0.178075
$206$	−370658.	−0.608562
$207$	−116886.	−0.189600
$208$	182169.	0.291956
$209$	126162.	0.199786
$210$	53384.2	0.0835342
$211$	83653.6	0.129354	0.0646768	−	0.997906i	$-0.479398\pi$
$211$	83653.6	0.129354	0.0646768	+	0.997906i	$0.479398\pi$
$212$	−17834.1	−0.0272528
$213$	−146988.	−0.221989
$214$	188625.	0.281556
$215$	10953.8	0.0161611
$216$	87241.6	0.127230
$217$	−102320.	−0.147507
$218$	−209800.	−0.298996
$219$	1.32602e6	1.86826
$220$	192582.	0.268262
$221$	157834.	0.217381
$222$	−162154.	−0.220824
$223$	−665414.	−0.896045	−0.448022	−	0.894022i	$-0.647872\pi$
$223$	−665414.	−0.896045	−0.448022	+	0.894022i	$0.647872\pi$
$224$	19375.1	0.0258003
$225$	−342089.	−0.450488
$226$	−602384.	−0.784517
$227$	1.15382e6	1.48619	0.743096	−	0.669185i	$-0.233357\pi$
$227$	1.15382e6	1.48619	0.743096	+	0.669185i	$0.233357\pi$
$228$	118294.	0.150704
$229$	−433691.	−0.546502	−0.273251	−	0.961943i	$-0.588099\pi$
$229$	−433691.	−0.546502	−0.273251	+	0.961943i	$0.588099\pi$
$230$	91263.5	0.113757
$231$	−135426.	−0.166983
$232$	462034.	0.563578
$233$	387173.	0.467214	0.233607	−	0.972331i	$-0.424947\pi$
$233$	387173.	0.467214	0.233607	+	0.972331i	$0.424947\pi$
$234$	−502220.	−0.599590
$235$	−938183.	−1.10820
$236$	−606479.	−0.708820
$237$	739426.	0.855114
$238$	16786.9	0.0192100
$239$	−622463.	−0.704886	−0.352443	−	0.935833i	$-0.614649\pi$
$239$	−622463.	−0.704886	−0.352443	+	0.935833i	$0.614649\pi$
$240$	180571.	0.202358
$241$	−371454.	−0.411967	−0.205984	−	0.978555i	$-0.566039\pi$
$241$	−371454.	−0.411967	−0.205984	+	0.978555i	$0.566039\pi$
$242$	155658.	0.170857
$243$	−1.11861e6	−1.21524
$244$	599507.	0.644644
$245$	−566516.	−0.602972
$246$	254865.	0.268518
$247$	256887.	0.267917
$248$	−346097.	−0.357329
$249$	−1.06052e6	−1.08398
$250$	697609.	0.705931
$251$	376098.	0.376805	0.188403	−	0.982092i	$-0.439669\pi$
$251$	376098.	0.376805	0.188403	+	0.982092i	$0.439669\pi$
$252$	−53415.0	−0.0529861
$253$	−231519.	−0.227398
$254$	−1.40896e6	−1.37030
$255$	156450.	0.150669
$256$	65536.0	0.0625000
$257$	1.64382e6	1.55247	0.776233	−	0.630446i	$-0.217128\pi$
$257$	1.64382e6	1.55247	0.776233	+	0.630446i	$0.217128\pi$
$258$	−26054.9	−0.0243691
$259$	−37452.2	−0.0346919
$260$	392128.	0.359745
$261$	−1.27378e6	−1.15742
$262$	−76280.9	−0.0686535
$263$	775299.	0.691162	0.345581	−	0.938389i	$-0.387682\pi$
$263$	775299.	0.691162	0.345581	+	0.938389i	$0.387682\pi$
$264$	−458076.	−0.404509
$265$	−38388.8	−0.0335807
$266$	27321.9	0.0236760
$267$	2.97483e6	2.55378
$268$	−879284.	−0.747812
$269$	334851.	0.282144	0.141072	−	0.989999i	$-0.454945\pi$
$269$	334851.	0.282144	0.141072	+	0.989999i	$0.454945\pi$
$270$	187792.	0.156771
$271$	893377.	0.738944	0.369472	−	0.929242i	$-0.379539\pi$
$271$	893377.	0.738944	0.369472	+	0.929242i	$0.379539\pi$
$272$	56781.4	0.0465355
$273$	−275750.	−0.223928
$274$	1.06671e6	0.858360
$275$	−677584.	−0.540296
$276$	−217080.	−0.171533
$277$	−1.13462e6	−0.888483	−0.444242	−	0.895907i	$-0.646527\pi$
$277$	−1.13462e6	−0.888483	−0.444242	+	0.895907i	$0.646527\pi$
$278$	1.17955e6	0.915389
$279$	954149.	0.733847
$280$	41705.9	0.0317908
$281$	−1.98111e6	−1.49672	−0.748362	−	0.663290i	$-0.769159\pi$
$281$	−1.98111e6	−1.49672	−0.748362	+	0.663290i	$0.769159\pi$
$282$	2.23157e6	1.67104
$283$	1.32192e6	0.981161	0.490580	−	0.871396i	$-0.336785\pi$
$283$	1.32192e6	0.981161	0.490580	+	0.871396i	$0.336785\pi$
$284$	−114833.	−0.0844830
$285$	254633.	0.185696
$286$	−994759.	−0.719122
$287$	58865.4	0.0421847
$288$	−180675.	−0.128356
$289$	−1.37066e6	−0.965351
$290$	994550.	0.694435
$291$	809232.	0.560197
$292$	1.03594e6	0.711011
$293$	1.35808e6	0.924179	0.462089	−	0.886833i	$-0.347100\pi$
$293$	1.35808e6	0.924179	0.462089	+	0.886833i	$0.347100\pi$
$294$	1.34752e6	0.909215
$295$	−1.30547e6	−0.873401
$296$	−126681.	−0.0840395
$297$	−476394.	−0.313383
$298$	415959.	0.271337
$299$	−471411.	−0.304945
$300$	−635325.	−0.407561
$301$	−6017.81	−0.00382844
$302$	1.90937e6	1.20468
$303$	−342489.	−0.214309
$304$	92416.0	0.0573539
$305$	1.29047e6	0.794324
$306$	−156540.	−0.0955701
$307$	−1.23842e6	−0.749930	−0.374965	−	0.927039i	$-0.622345\pi$
$307$	−1.23842e6	−0.749930	−0.374965	+	0.927039i	$0.622345\pi$
$308$	−105800.	−0.0635492
$309$	1.89779e6	1.13071
$310$	−744989.	−0.440297
$311$	−1.78565e6	−1.04688	−0.523439	−	0.852063i	$-0.675351\pi$
$311$	−1.78565e6	−1.04688	−0.523439	+	0.852063i	$0.675351\pi$
$312$	−932718.	−0.542455
$313$	−3.01608e6	−1.74013	−0.870066	−	0.492935i	$-0.835924\pi$
$313$	−3.01608e6	−1.74013	−0.870066	+	0.492935i	$0.835924\pi$
$314$	−1.73982e6	−0.995819
$315$	−114978.	−0.0652889
$316$	577670.	0.325433
$317$	515839.	0.288314	0.144157	−	0.989555i	$-0.453953\pi$
$317$	515839.	0.288314	0.144157	+	0.989555i	$0.453953\pi$
$318$	91311.8	0.0506360
$319$	−2.52300e6	−1.38816
$320$	141069.	0.0770119
$321$	−965772.	−0.523133
$322$	−50138.2	−0.0269482
$323$	80070.7	0.0427039
$324$	−1.13268e6	−0.599441
$325$	−1.37967e6	−0.724548
$326$	1.02033e6	0.531737
$327$	1.07419e6	0.555536
$328$	199111.	0.102191
$329$	515417.	0.262524
$330$	−986031.	−0.498432
$331$	−2.25449e6	−1.13104	−0.565521	−	0.824734i	$-0.691325\pi$
$331$	−2.25449e6	−1.13104	−0.565521	+	0.824734i	$0.691325\pi$
$332$	−828523.	−0.412534
$333$	349246.	0.172592
$334$	−2.04200e6	−1.00159
$335$	−1.89270e6	−0.921446
$336$	−99201.8	−0.0479371
$337$	2.40261e6	1.15242	0.576208	−	0.817303i	$-0.304532\pi$
$337$	2.40261e6	1.15242	0.576208	+	0.817303i	$0.304532\pi$
$338$	−540319.	−0.257252
$339$	3.08424e6	1.45764
$340$	122225.	0.0573406
$341$	1.88991e6	0.880145
$342$	−254780.	−0.117788
$343$	629237.	0.288788
$344$	−20355.1	−0.00927423
$345$	−467275.	−0.211361
$346$	−3.09381e6	−1.38933
$347$	−684693.	−0.305262	−0.152631	−	0.988283i	$-0.548775\pi$
$347$	−684693.	−0.305262	−0.152631	+	0.988283i	$0.548775\pi$
$348$	−2.36564e6	−1.04713
$349$	2.19857e6	0.966220	0.483110	−	0.875560i	$-0.339507\pi$
$349$	2.19857e6	0.966220	0.483110	+	0.875560i	$0.339507\pi$
$350$	−146739.	−0.0640287
$351$	−970016.	−0.420253
$352$	−357868.	−0.153945
$353$	2.03446e6	0.868987	0.434493	−	0.900675i	$-0.356927\pi$
$353$	2.03446e6	0.868987	0.434493	+	0.900675i	$0.356927\pi$
$354$	3.10521e6	1.31699
$355$	−247183.	−0.104099
$356$	2.32406e6	0.971900
$357$	−85950.1	−0.0356924
$358$	1.91066e6	0.787907
$359$	2.30592e6	0.944298	0.472149	−	0.881519i	$-0.343478\pi$
$359$	2.30592e6	0.944298	0.472149	+	0.881519i	$0.343478\pi$
$360$	−388912.	−0.158160
$361$	130321.	0.0526316
$362$	−2.91646e6	−1.16973
$363$	−796980.	−0.317454
$364$	−215427.	−0.0852209
$365$	2.22990e6	0.876101
$366$	−3.06952e6	−1.19775
$367$	2.64475e6	1.02499	0.512495	−	0.858690i	$-0.328721\pi$
$367$	2.64475e6	1.02499	0.512495	+	0.858690i	$0.328721\pi$
$368$	−169592.	−0.0652807
$369$	−548927.	−0.209869
$370$	−272688.	−0.103553
$371$	21090.0	0.00795502
$372$	1.77204e6	0.663919
$373$	173405.	0.0645342	0.0322671	−	0.999479i	$-0.489727\pi$
$373$	173405.	0.0645342	0.0322671	+	0.999479i	$0.489727\pi$
$374$	−310062.	−0.114623
$375$	−3.57180e6	−1.31162
$376$	1.74339e6	0.635953
$377$	−5.13723e6	−1.86155
$378$	−103169.	−0.0371380
$379$	2.23408e6	0.798915	0.399458	−	0.916752i	$-0.369198\pi$
$379$	2.23408e6	0.798915	0.399458	+	0.916752i	$0.369198\pi$
$380$	198930.	0.0706709
$381$	7.21396e6	2.54602
$382$	1.14234e6	0.400530
$383$	−4.44976e6	−1.55003	−0.775014	−	0.631944i	$-0.782257\pi$
$383$	−4.44976e6	−1.55003	−0.775014	+	0.631944i	$0.782257\pi$
$384$	−335548.	−0.116125
$385$	−227740.	−0.0783047
$386$	214761.	0.0733646
$387$	56116.8	0.0190465
$388$	632204.	0.213196
$389$	2.43083e6	0.814480	0.407240	−	0.913321i	$-0.366491\pi$
$389$	2.43083e6	0.814480	0.407240	+	0.913321i	$0.366491\pi$
$390$	−2.00772e6	−0.668408
$391$	−146937.	−0.0486059
$392$	1.05274e6	0.346022
$393$	390563.	0.127559
$394$	−58155.5	−0.0188734
$395$	1.24346e6	0.400996
$396$	986601.	0.316158
$397$	2.61205e6	0.831775	0.415887	−	0.909416i	$-0.363471\pi$
$397$	2.61205e6	0.831775	0.415887	+	0.909416i	$0.363471\pi$
$398$	574800.	0.181890
$399$	−139890.	−0.0439901
$400$	−496342.	−0.155107
$401$	1.42660e6	0.443038	0.221519	−	0.975156i	$-0.428899\pi$
$401$	1.42660e6	0.443038	0.221519	+	0.975156i	$0.428899\pi$
$402$	4.50199e6	1.38944
$403$	3.84816e6	1.18029
$404$	−267566.	−0.0815602
$405$	−2.43816e6	−0.738625
$406$	−546384.	−0.164507
$407$	691760.	0.207000
$408$	−290725.	−0.0864632
$409$	4.73321e6	1.39910	0.699548	−	0.714586i	$-0.253385\pi$
$409$	4.73321e6	1.39910	0.699548	+	0.714586i	$0.253385\pi$
$410$	428596.	0.125918
$411$	−5.46162e6	−1.59484
$412$	1.48263e6	0.430318
$413$	717200.	0.206902
$414$	467545.	0.134067
$415$	−1.78344e6	−0.508320
$416$	−728677.	−0.206444
$417$	−6.03939e6	−1.70080
$418$	−504649.	−0.141270
$419$	−357759.	−0.0995531	−0.0497766	−	0.998760i	$-0.515851\pi$
$419$	−357759.	−0.0995531	−0.0497766	+	0.998760i	$0.515851\pi$
$420$	−213537.	−0.0590676
$421$	652504.	0.179423	0.0897115	−	0.995968i	$-0.471405\pi$
$421$	652504.	0.179423	0.0897115	+	0.995968i	$0.471405\pi$
$422$	−334614.	−0.0914668
$423$	−4.80633e6	−1.30606
$424$	71336.4	0.0192707
$425$	−430038.	−0.115487
$426$	587950.	0.156970
$427$	−708955.	−0.188169
$428$	−754500.	−0.199090
$429$	5.09323e6	1.33613
$430$	−43815.4	−0.0114276
$431$	−6.25148e6	−1.62103	−0.810513	−	0.585721i	$-0.800812\pi$
$431$	−6.25148e6	−1.62103	−0.810513	+	0.585721i	$0.800812\pi$
$432$	−348966.	−0.0899651
$433$	4.45832e6	1.14275	0.571375	−	0.820689i	$-0.306410\pi$
$433$	4.45832e6	1.14275	0.571375	+	0.820689i	$0.306410\pi$
$434$	409281.	0.104303
$435$	−5.09216e6	−1.29026
$436$	839201.	0.211422
$437$	−239151.	−0.0599057
$438$	−5.30406e6	−1.32106
$439$	5.00652e6	1.23986	0.619932	−	0.784655i	$-0.287160\pi$
$439$	5.00652e6	1.23986	0.619932	+	0.784655i	$0.287160\pi$
$440$	−770327.	−0.189690
$441$	−2.90227e6	−0.710627
$442$	−631338.	−0.153711
$443$	715908.	0.173320	0.0866599	−	0.996238i	$-0.472381\pi$
$443$	715908.	0.173320	0.0866599	+	0.996238i	$0.472381\pi$
$444$	648617.	0.156146
$445$	5.00264e6	1.19757
$446$	2.66166e6	0.633599
$447$	−2.12974e6	−0.504147
$448$	−77500.5	−0.0182435
$449$	−4.83183e6	−1.13109	−0.565544	−	0.824718i	$-0.691334\pi$
$449$	−4.83183e6	−1.13109	−0.565544	+	0.824718i	$0.691334\pi$
$450$	1.36836e6	0.318543
$451$	−1.08727e6	−0.251708
$452$	2.40954e6	0.554737
$453$	−9.77610e6	−2.23831
$454$	−4.61530e6	−1.05090
$455$	−463716.	−0.105008
$456$	−473176.	−0.106564
$457$	−6.44410e6	−1.44335	−0.721675	−	0.692232i	$-0.756628\pi$
$457$	−6.44410e6	−1.44335	−0.721675	+	0.692232i	$0.756628\pi$
$458$	1.73477e6	0.386436
$459$	−302350.	−0.0669851
$460$	−365054.	−0.0804383
$461$	−4.10108e6	−0.898764	−0.449382	−	0.893340i	$-0.648356\pi$
$461$	−4.10108e6	−0.898764	−0.449382	+	0.893340i	$0.648356\pi$
$462$	541704.	0.118075
$463$	8.98683e6	1.94829	0.974146	−	0.225919i	$-0.0725386\pi$
$463$	8.98683e6	1.94829	0.974146	+	0.225919i	$0.0725386\pi$
$464$	−1.84814e6	−0.398510
$465$	3.81439e6	0.818075
$466$	−1.54869e6	−0.330370
$467$	−8.84409e6	−1.87655	−0.938276	−	0.345886i	$-0.887578\pi$
$467$	−8.84409e6	−1.87655	−0.938276	+	0.345886i	$0.887578\pi$
$468$	2.00888e6	0.423974
$469$	1.03981e6	0.218284
$470$	3.75273e6	0.783615
$471$	8.90800e6	1.85024
$472$	2.42592e6	0.501211
$473$	111152.	0.0228436
$474$	−2.95771e6	−0.604657
$475$	−699919.	−0.142336
$476$	−67147.7	−0.0135836
$477$	−196667.	−0.0395762
$478$	2.48985e6	0.498430
$479$	2.89320e6	0.576155	0.288077	−	0.957607i	$-0.406984\pi$
$479$	2.89320e6	0.576155	0.288077	+	0.957607i	$0.406984\pi$
$480$	−722284.	−0.143089
$481$	1.40854e6	0.277591
$482$	1.48582e6	0.291305
$483$	256711.	0.0500699
$484$	−622633.	−0.120814
$485$	1.36085e6	0.262697
$486$	4.47443e6	0.859305
$487$	−3.18166e6	−0.607900	−0.303950	−	0.952688i	$-0.598306\pi$
$487$	−3.18166e6	−0.607900	−0.303950	+	0.952688i	$0.598306\pi$
$488$	−2.39803e6	−0.455832
$489$	−5.22416e6	−0.987971
$490$	2.26606e6	0.426365
$491$	−4.45509e6	−0.833975	−0.416987	−	0.908912i	$-0.636914\pi$
$491$	−4.45509e6	−0.833975	−0.416987	+	0.908912i	$0.636914\pi$
$492$	−1.01946e6	−0.189871
$493$	−1.60125e6	−0.296717
$494$	−1.02755e6	−0.189446
$495$	2.12371e6	0.389566
$496$	1.38439e6	0.252670
$497$	135797.	0.0246603
$498$	4.24209e6	0.766490
$499$	9.31472e6	1.67463	0.837315	−	0.546721i	$-0.184124\pi$
$499$	9.31472e6	1.67463	0.837315	+	0.546721i	$0.184124\pi$
$500$	−2.79044e6	−0.499168
$501$	1.04552e7	1.86096
$502$	−1.50439e6	−0.266442
$503$	−2.04835e6	−0.360980	−0.180490	−	0.983577i	$-0.557768\pi$
$503$	−2.04835e6	−0.360980	−0.180490	+	0.983577i	$0.557768\pi$
$504$	213660.	0.0374668
$505$	−575949.	−0.100498
$506$	926077.	0.160794
$507$	2.76647e6	0.477976
$508$	5.63584e6	0.968945
$509$	−166211.	−0.0284358	−0.0142179	−	0.999899i	$-0.504526\pi$
$509$	−166211.	−0.0284358	−0.0142179	+	0.999899i	$0.504526\pi$
$510$	−625798.	−0.106539
$511$	−1.22506e6	−0.207542
$512$	−262144.	−0.0441942
$513$	−492097.	−0.0825577
$514$	−6.57529e6	−1.09776
$515$	3.19143e6	0.530234
$516$	104220.	0.0172316
$517$	−9.52001e6	−1.56643
$518$	149809.	0.0245309
$519$	1.58405e7	2.58137
$520$	−1.56851e6	−0.254378
$521$	2.64602e6	0.427069	0.213535	−	0.976935i	$-0.431502\pi$
$521$	2.64602e6	0.427069	0.213535	+	0.976935i	$0.431502\pi$
$522$	5.09510e6	0.818421
$523$	−7.02287e6	−1.12269	−0.561346	−	0.827581i	$-0.689716\pi$
$523$	−7.02287e6	−1.12269	−0.561346	+	0.827581i	$0.689716\pi$
$524$	305124.	0.0485453
$525$	751312.	0.118966
$526$	−3.10120e6	−0.488726
$527$	1.19945e6	0.188130
$528$	1.83231e6	0.286031
$529$	−5.99748e6	−0.931815
$530$	153555.	0.0237451
$531$	−6.68798e6	−1.02934
$532$	−109288.	−0.0167414
$533$	−2.21386e6	−0.337546
$534$	−1.18993e7	−1.80580
$535$	−1.62410e6	−0.245317
$536$	3.51714e6	0.528783
$537$	−9.78268e6	−1.46394
$538$	−1.33940e6	−0.199506
$539$	−5.74860e6	−0.852295
$540$	−751167.	−0.110854
$541$	4.35066e6	0.639090	0.319545	−	0.947571i	$-0.396470\pi$
$541$	4.35066e6	0.639090	0.319545	+	0.947571i	$0.396470\pi$
$542$	−3.57351e6	−0.522512
$543$	1.49324e7	2.17336
$544$	−227126.	−0.0329056
$545$	1.80642e6	0.260512
$546$	1.10300e6	0.158341
$547$	9.77794e6	1.39727	0.698633	−	0.715480i	$-0.253792\pi$
$547$	9.77794e6	1.39727	0.698633	+	0.715480i	$0.253792\pi$
$548$	−4.26684e6	−0.606952
$549$	6.61110e6	0.936144
$550$	2.71034e6	0.382047
$551$	−2.60616e6	−0.365698
$552$	868320.	0.121292
$553$	−683131.	−0.0949929
$554$	4.53846e6	0.628252
$555$	1.39618e6	0.192401
$556$	−4.71822e6	−0.647278
$557$	6.69323e6	0.914108	0.457054	−	0.889439i	$-0.348905\pi$
$557$	6.69323e6	0.914108	0.457054	+	0.889439i	$0.348905\pi$
$558$	−3.81660e6	−0.518909
$559$	226323.	0.0306337
$560$	−166823.	−0.0224795
$561$	1.58754e6	0.212969
$562$	7.92442e6	1.05834
$563$	7.54034e6	1.00258	0.501291	−	0.865279i	$-0.332859\pi$
$563$	7.54034e6	1.00258	0.501291	+	0.865279i	$0.332859\pi$
$564$	−8.92627e6	−1.18161
$565$	5.18664e6	0.683542
$566$	−5.28769e6	−0.693785
$567$	1.33947e6	0.174975
$568$	459331.	0.0597385
$569$	1.34726e6	0.174450	0.0872252	−	0.996189i	$-0.472200\pi$
$569$	1.34726e6	0.174450	0.0872252	+	0.996189i	$0.472200\pi$
$570$	−1.01853e6	−0.131307
$571$	2.05762e6	0.264104	0.132052	−	0.991243i	$-0.457843\pi$
$571$	2.05762e6	0.264104	0.132052	+	0.991243i	$0.457843\pi$
$572$	3.97904e6	0.508496
$573$	−5.84883e6	−0.744188
$574$	−235462.	−0.0298291
$575$	1.28441e6	0.162008
$576$	722701.	0.0907617
$577$	7.88561e6	0.986043	0.493021	−	0.870017i	$-0.335892\pi$
$577$	7.88561e6	0.986043	0.493021	+	0.870017i	$0.335892\pi$
$578$	5.48264e6	0.682606
$579$	−1.09959e6	−0.136312
$580$	−3.97820e6	−0.491040
$581$	979781.	0.120417
$582$	−3.23693e6	−0.396119
$583$	−389542.	−0.0474660
$584$	−4.14375e6	−0.502761
$585$	4.32421e6	0.522417
$586$	−5.43232e6	−0.653493
$587$	1.90439e6	0.228119	0.114059	−	0.993474i	$-0.463615\pi$
$587$	1.90439e6	0.228119	0.114059	+	0.993474i	$0.463615\pi$
$588$	−5.39007e6	−0.642912
$589$	1.95220e6	0.231866
$590$	5.22190e6	0.617588
$591$	297760.	0.0350669
$592$	506726.	0.0594249
$593$	−1.35835e7	−1.58626	−0.793132	−	0.609050i	$-0.791551\pi$
$593$	−1.35835e7	−1.58626	−0.793132	+	0.609050i	$0.791551\pi$
$594$	1.90558e6	0.221595
$595$	−144539.	−0.0167375
$596$	−1.66384e6	−0.191864
$597$	−2.94301e6	−0.337953
$598$	1.88564e6	0.215629
$599$	−1.04361e7	−1.18842	−0.594212	−	0.804309i	$-0.702536\pi$
$599$	−1.04361e7	−1.18842	−0.594212	+	0.804309i	$0.702536\pi$
$600$	2.54130e6	0.288189
$601$	−1.17196e7	−1.32351	−0.661753	−	0.749722i	$-0.730187\pi$
$601$	−1.17196e7	−1.32351	−0.661753	+	0.749722i	$0.730187\pi$
$602$	24071.2	0.00270712
$603$	−9.69635e6	−1.08596
$604$	−7.63749e6	−0.851840
$605$	−1.34025e6	−0.148866
$606$	1.36996e6	0.151539
$607$	−7.53524e6	−0.830091	−0.415045	−	0.909801i	$-0.636234\pi$
$607$	−7.53524e6	−0.830091	−0.415045	+	0.909801i	$0.636234\pi$
$608$	−369664.	−0.0405554
$609$	2.79752e6	0.305654
$610$	−5.16187e6	−0.561672
$611$	−1.93843e7	−2.10062
$612$	626160.	0.0675782
$613$	−4.37292e6	−0.470025	−0.235012	−	0.971992i	$-0.575513\pi$
$613$	−4.37292e6	−0.470025	−0.235012	+	0.971992i	$0.575513\pi$
$614$	4.95366e6	0.530280
$615$	−2.19444e6	−0.233957
$616$	423201.	0.0449361
$617$	−7.50595e6	−0.793767	−0.396883	−	0.917869i	$-0.629908\pi$
$617$	−7.50595e6	−0.793767	−0.396883	+	0.917869i	$0.629908\pi$
$618$	−7.59116e6	−0.799534
$619$	−1.30877e7	−1.37289	−0.686447	−	0.727180i	$-0.740831\pi$
$619$	−1.30877e7	−1.37289	−0.686447	+	0.727180i	$0.740831\pi$
$620$	2.97996e6	0.311337
$621$	903043.	0.0939679
$622$	7.14261e6	0.740254
$623$	−2.74834e6	−0.283695
$624$	3.73087e6	0.383574
$625$	52309.5	0.00535649
$626$	1.20643e7	1.23046
$627$	2.58384e6	0.262480
$628$	6.95929e6	0.704151
$629$	439035.	0.0442459
$630$	459913.	0.0461662
$631$	8.92096e6	0.891945	0.445972	−	0.895047i	$-0.352858\pi$
$631$	8.92096e6	0.891945	0.445972	+	0.895047i	$0.352858\pi$
$632$	−2.31068e6	−0.230116
$633$	1.71325e6	0.169946
$634$	−2.06336e6	−0.203869
$635$	1.21314e7	1.19392
$636$	−365247.	−0.0358050
$637$	−1.17051e7	−1.14295
$638$	1.00920e7	0.981578
$639$	−1.26632e6	−0.122685
$640$	−564277.	−0.0544556
$641$	1.45438e7	1.39808	0.699041	−	0.715082i	$-0.253611\pi$
$641$	1.45438e7	1.39808	0.699041	+	0.715082i	$0.253611\pi$
$642$	3.86309e6	0.369911
$643$	1.45757e7	1.39028	0.695140	−	0.718874i	$-0.255342\pi$
$643$	1.45757e7	1.39028	0.695140	+	0.718874i	$0.255342\pi$
$644$	200553.	0.0190552
$645$	224338.	0.0212326
$646$	−320283.	−0.0301962
$647$	−2.24522e6	−0.210862	−0.105431	−	0.994427i	$-0.533622\pi$
$647$	−2.24522e6	−0.210862	−0.105431	+	0.994427i	$0.533622\pi$
$648$	4.53074e6	0.423869
$649$	−1.32470e7	−1.23454
$650$	5.51869e6	0.512333
$651$	−2.09555e6	−0.193796
$652$	−4.08132e6	−0.375995
$653$	1.54461e7	1.41754	0.708770	−	0.705440i	$-0.249251\pi$
$653$	1.54461e7	1.41754	0.708770	+	0.705440i	$0.249251\pi$
$654$	−4.29676e6	−0.392823
$655$	656793.	0.0598171
$656$	−796445.	−0.0722597
$657$	1.14238e7	1.03252
$658$	−2.06167e6	−0.185633
$659$	8.68940e6	0.779429	0.389714	−	0.920936i	$-0.372574\pi$
$659$	8.68940e6	0.779429	0.389714	+	0.920936i	$0.372574\pi$
$660$	3.94412e6	0.352445
$661$	−2.03442e7	−1.81108	−0.905538	−	0.424266i	$-0.860532\pi$
$661$	−2.03442e7	−1.81108	−0.905538	+	0.424266i	$0.860532\pi$
$662$	9.01797e6	0.799767
$663$	3.23249e6	0.285597
$664$	3.31409e6	0.291705
$665$	−235247.	−0.0206286
$666$	−1.39698e6	−0.122041
$667$	4.78254e6	0.416240
$668$	8.16802e6	0.708232
$669$	−1.36278e7	−1.17723
$670$	7.57080e6	0.651561
$671$	1.30947e7	1.12277
$672$	396807.	0.0338966
$673$	1.71139e7	1.45650	0.728251	−	0.685310i	$-0.240333\pi$
$673$	1.71139e7	1.45650	0.728251	+	0.685310i	$0.240333\pi$
$674$	−9.61045e6	−0.814881
$675$	2.64292e6	0.223267
$676$	2.16128e6	0.181905
$677$	2.25299e6	0.188924	0.0944621	−	0.995528i	$-0.469887\pi$
$677$	2.25299e6	0.188924	0.0944621	+	0.995528i	$0.469887\pi$
$678$	−1.23370e7	−1.03071
$679$	−747622.	−0.0622311
$680$	−488899.	−0.0405459
$681$	2.36306e7	1.95257
$682$	−7.55962e6	−0.622356
$683$	5.33481e6	0.437590	0.218795	−	0.975771i	$-0.429787\pi$
$683$	5.33481e6	0.437590	0.218795	+	0.975771i	$0.429787\pi$
$684$	1.01912e6	0.0832887
$685$	−9.18457e6	−0.747881
$686$	−2.51695e6	−0.204204
$687$	−8.88211e6	−0.718000
$688$	81420.5	0.00655787
$689$	−793171.	−0.0636530
$690$	1.86910e6	0.149455
$691$	8.08495e6	0.644143	0.322071	−	0.946715i	$-0.395621\pi$
$691$	8.08495e6	0.644143	0.322071	+	0.946715i	$0.395621\pi$
$692$	1.23753e7	0.982401
$693$	−1.16672e6	−0.0922854
$694$	2.73877e6	0.215853
$695$	−1.01562e7	−0.797569
$696$	9.46257e6	0.740433
$697$	−690053.	−0.0538022
$698$	−8.79427e6	−0.683221
$699$	7.92941e6	0.613829
$700$	586955.	0.0452751
$701$	7.88116e6	0.605752	0.302876	−	0.953030i	$-0.402053\pi$
$701$	7.88116e6	0.605752	0.302876	+	0.953030i	$0.402053\pi$
$702$	3.88006e6	0.297164
$703$	714562.	0.0545320
$704$	1.43147e6	0.108856
$705$	−1.92142e7	−1.45596
$706$	−8.13786e6	−0.614467
$707$	316414.	0.0238071
$708$	−1.24208e7	−0.931254
$709$	−2.07701e7	−1.55175	−0.775876	−	0.630885i	$-0.782692\pi$
$709$	−2.07701e7	−1.55175	−0.775876	+	0.630885i	$0.782692\pi$
$710$	988731.	0.0736092
$711$	6.37028e6	0.472590
$712$	−9.29623e6	−0.687237
$713$	−3.58247e6	−0.263911
$714$	343800.	0.0252383
$715$	8.56506e6	0.626564
$716$	−7.64263e6	−0.557135
$717$	−1.27482e7	−0.926086
$718$	−9.22370e6	−0.667719
$719$	1.03826e7	0.749004	0.374502	−	0.927226i	$-0.377814\pi$
$719$	1.03826e7	0.749004	0.374502	+	0.927226i	$0.377814\pi$
$720$	1.55565e6	0.111836
$721$	−1.75330e6	−0.125608
$722$	−521284.	−0.0372161
$723$	−7.60748e6	−0.541246
$724$	1.16658e7	0.827121
$725$	1.39970e7	0.988985
$726$	3.18792e6	0.224474
$727$	−6.52486e6	−0.457863	−0.228931	−	0.973443i	$-0.573523\pi$
$727$	−6.52486e6	−0.457863	−0.228931	+	0.973443i	$0.573523\pi$
$728$	861707.	0.0602603
$729$	−5.70674e6	−0.397712
$730$	−8.91962e6	−0.619497
$731$	70544.1	0.00488278
$732$	1.22781e7	0.846939
$733$	−2.46101e6	−0.169182	−0.0845908	−	0.996416i	$-0.526958\pi$
$733$	−2.46101e6	−0.169182	−0.0845908	+	0.996416i	$0.526958\pi$
$734$	−1.05790e7	−0.724778
$735$	−1.16024e7	−0.792189
$736$	678367.	0.0461605
$737$	−1.92058e7	−1.30246
$738$	2.19571e6	0.148400
$739$	−7.33586e6	−0.494128	−0.247064	−	0.968999i	$-0.579466\pi$
$739$	−7.33586e6	−0.494128	−0.247064	+	0.968999i	$0.579466\pi$
$740$	1.09075e6	0.0732228
$741$	5.26111e6	0.351991
$742$	−84359.9	−0.00562505
$743$	2.44394e7	1.62412	0.812060	−	0.583574i	$-0.198346\pi$
$743$	2.44394e7	1.62412	0.812060	+	0.583574i	$0.198346\pi$
$744$	−7.08815e6	−0.469462
$745$	−3.58148e6	−0.236414
$746$	−693621.	−0.0456326
$747$	−9.13658e6	−0.599076
$748$	1.24025e6	0.0810504
$749$	892244.	0.0581138
$750$	1.42872e7	0.927458
$751$	−2.11169e6	−0.136625	−0.0683126	−	0.997664i	$-0.521762\pi$
$751$	−2.11169e6	−0.136625	−0.0683126	+	0.997664i	$0.521762\pi$
$752$	−6.97356e6	−0.449687
$753$	7.70259e6	0.495050
$754$	2.05489e7	1.31632
$755$	−1.64401e7	−1.04963
$756$	412675.	0.0262605
$757$	−1.47627e7	−0.936325	−0.468162	−	0.883642i	$-0.655084\pi$
$757$	−1.47627e7	−0.936325	−0.468162	+	0.883642i	$0.655084\pi$
$758$	−8.93632e6	−0.564919
$759$	−4.74157e6	−0.298757
$760$	−795719.	−0.0499719
$761$	2.67074e7	1.67174	0.835871	−	0.548926i	$-0.184963\pi$
$761$	2.67074e7	1.67174	0.835871	+	0.548926i	$0.184963\pi$
$762$	−2.88558e7	−1.80031
$763$	−992408.	−0.0617133
$764$	−4.56934e6	−0.283218
$765$	1.34784e6	0.0832692
$766$	1.77990e7	1.09604
$767$	−2.69731e7	−1.65555
$768$	1.34219e6	0.0821131
$769$	3.05104e6	0.186051	0.0930256	−	0.995664i	$-0.470346\pi$
$769$	3.05104e6	0.186051	0.0930256	+	0.995664i	$0.470346\pi$
$770$	910961.	0.0553698
$771$	3.36659e7	2.03964
$772$	−859043.	−0.0518766
$773$	−2.18723e7	−1.31657	−0.658287	−	0.752767i	$-0.728719\pi$
$773$	−2.18723e7	−1.31657	−0.658287	+	0.752767i	$0.728719\pi$
$774$	−224467.	−0.0134679
$775$	−1.04847e7	−0.627052
$776$	−2.52882e6	−0.150752
$777$	−767030.	−0.0455785
$778$	−9.72331e6	−0.575924
$779$	−1.12311e6	−0.0663100
$780$	8.03088e6	0.472636
$781$	−2.50823e6	−0.147143
$782$	587748.	0.0343696
$783$	9.84096e6	0.573632
$784$	−4.21094e6	−0.244675
$785$	1.49802e7	0.867647
$786$	−1.56225e6	−0.0901975
$787$	−1.26837e7	−0.729975	−0.364987	−	0.931013i	$-0.618927\pi$
$787$	−1.26837e7	−0.729975	−0.364987	+	0.931013i	$0.618927\pi$
$788$	232622.	0.0133455
$789$	1.58783e7	0.908055
$790$	−4.97385e6	−0.283547
$791$	−2.84943e6	−0.161926
$792$	−3.94640e6	−0.223557
$793$	2.66630e7	1.50566
$794$	−1.04482e7	−0.588154
$795$	−786212.	−0.0441186
$796$	−2.29920e6	−0.128616
$797$	7.28989e6	0.406514	0.203257	−	0.979125i	$-0.434847\pi$
$797$	7.28989e6	0.406514	0.203257	+	0.979125i	$0.434847\pi$
$798$	559560.	0.0311057
$799$	−6.04201e6	−0.334822
$800$	1.98537e6	0.109677
$801$	2.56286e7	1.41138
$802$	−5.70640e6	−0.313275
$803$	2.26275e7	1.23836
$804$	−1.80080e7	−0.982482
$805$	431700.	0.0234797
$806$	−1.53926e7	−0.834593
$807$	6.85783e6	0.370683
$808$	1.07027e6	0.0576717
$809$	−2.72506e7	−1.46388	−0.731939	−	0.681370i	$-0.761385\pi$
$809$	−2.72506e7	−1.46388	−0.731939	+	0.681370i	$0.761385\pi$
$810$	9.75263e6	0.522287
$811$	1.45954e7	0.779229	0.389615	−	0.920978i	$-0.372608\pi$
$811$	1.45954e7	0.779229	0.389615	+	0.920978i	$0.372608\pi$
$812$	2.18554e6	0.116324
$813$	1.82966e7	0.970831
$814$	−2.76704e6	−0.146371
$815$	−8.78524e6	−0.463297
$816$	1.16290e6	0.0611387
$817$	114816.	0.00601791
$818$	−1.89328e7	−0.989310
$819$	−2.37563e6	−0.123757
$820$	−1.71439e6	−0.0890377
$821$	4.16570e6	0.215690	0.107845	−	0.994168i	$-0.465605\pi$
$821$	4.16570e6	0.215690	0.107845	+	0.994168i	$0.465605\pi$
$822$	2.18465e7	1.12772
$823$	−9.74487e6	−0.501506	−0.250753	−	0.968051i	$-0.580678\pi$
$823$	−9.74487e6	−0.501506	−0.250753	+	0.968051i	$0.580678\pi$
$824$	−5.93052e6	−0.304281
$825$	−1.38771e7	−0.709845
$826$	−2.86880e6	−0.146302
$827$	1.04970e6	0.0533707	0.0266854	−	0.999644i	$-0.491505\pi$
$827$	1.04970e6	0.0533707	0.0266854	+	0.999644i	$0.491505\pi$
$828$	−1.87018e6	−0.0947999
$829$	1.87001e7	0.945056	0.472528	−	0.881316i	$-0.343342\pi$
$829$	1.87001e7	0.945056	0.472528	+	0.881316i	$0.343342\pi$
$830$	7.13374e6	0.359436
$831$	−2.32372e7	−1.16730
$832$	2.91471e6	0.145978
$833$	−3.64843e6	−0.182177
$834$	2.41576e7	1.20265
$835$	1.75820e7	0.872676
$836$	2.01860e6	0.0998928
$837$	−7.37159e6	−0.363703
$838$	1.43103e6	0.0703947
$839$	1.96094e7	0.961742	0.480871	−	0.876791i	$-0.340320\pi$
$839$	1.96094e7	0.961742	0.480871	+	0.876791i	$0.340320\pi$
$840$	854146.	0.0417671
$841$	3.16068e7	1.54096
$842$	−2.61002e6	−0.126871
$843$	−4.05735e7	−1.96641
$844$	1.33846e6	0.0646768
$845$	4.65225e6	0.224141
$846$	1.92253e7	0.923523
$847$	736303.	0.0352653
$848$	−285346.	−0.0136264
$849$	2.70733e7	1.28906
$850$	1.72015e6	0.0816620
$851$	−1.31129e6	−0.0620688
$852$	−2.35180e6	−0.110995
$853$	−5.00288e6	−0.235422	−0.117711	−	0.993048i	$-0.537556\pi$
$853$	−5.00288e6	−0.235422	−0.117711	+	0.993048i	$0.537556\pi$
$854$	2.83582e6	0.133056
$855$	2.19371e6	0.102627
$856$	3.01800e6	0.140778
$857$	1.36218e7	0.633553	0.316776	−	0.948500i	$-0.397400\pi$
$857$	1.36218e7	0.633553	0.316776	+	0.948500i	$0.397400\pi$
$858$	−2.03729e7	−0.944789
$859$	1.88600e7	0.872084	0.436042	−	0.899926i	$-0.356380\pi$
$859$	1.88600e7	0.872084	0.436042	+	0.899926i	$0.356380\pi$
$860$	175262.	0.00808054
$861$	1.20558e6	0.0554227
$862$	2.50059e7	1.14624
$863$	−3.62744e7	−1.65796	−0.828979	−	0.559280i	$-0.811078\pi$
$863$	−3.62744e7	−1.65796	−0.828979	+	0.559280i	$0.811078\pi$
$864$	1.39587e6	0.0636150
$865$	2.66383e7	1.21050
$866$	−1.78333e7	−0.808047
$867$	−2.80715e7	−1.26829
$868$	−1.63712e6	−0.0737535
$869$	1.26178e7	0.566804
$870$	2.03686e7	0.912355
$871$	−3.91061e7	−1.74662
$872$	−3.35680e6	−0.149498
$873$	6.97166e6	0.309600
$874$	956603.	0.0423597
$875$	3.29987e6	0.145706
$876$	2.12163e7	0.934132
$877$	−1.47531e7	−0.647715	−0.323857	−	0.946106i	$-0.604980\pi$
$877$	−1.47531e7	−0.647715	−0.323857	+	0.946106i	$0.604980\pi$
$878$	−2.00261e7	−0.876717
$879$	2.78138e7	1.21419
$880$	3.08131e6	0.134131
$881$	1.41746e7	0.615277	0.307638	−	0.951503i	$-0.400461\pi$
$881$	1.41746e7	0.615277	0.307638	+	0.951503i	$0.400461\pi$
$882$	1.16091e7	0.502489
$883$	2.05570e7	0.887276	0.443638	−	0.896206i	$-0.353688\pi$
$883$	2.05570e7	0.887276	0.443638	+	0.896206i	$0.353688\pi$
$884$	2.52535e6	0.108690
$885$	−2.67365e7	−1.14748
$886$	−2.86363e6	−0.122556
$887$	−9.48962e6	−0.404986	−0.202493	−	0.979284i	$-0.564904\pi$
$887$	−9.48962e6	−0.404986	−0.202493	+	0.979284i	$0.564904\pi$
$888$	−2.59447e6	−0.110412
$889$	−6.66473e6	−0.282832
$890$	−2.00106e7	−0.846807
$891$	−2.47407e7	−1.04404
$892$	−1.06466e7	−0.448022
$893$	−9.83381e6	−0.412661
$894$	8.51894e6	0.356485
$895$	−1.64511e7	−0.686496
$896$	310002.	0.0129001
$897$	−9.65462e6	−0.400640
$898$	1.93273e7	0.799800
$899$	−3.90401e7	−1.61106
$900$	−5.47343e6	−0.225244
$901$	−247228.	−0.0101458
$902$	4.34909e6	0.177984
$903$	−123246.	−0.00502984
$904$	−9.63814e6	−0.392258
$905$	2.51112e7	1.01917
$906$	3.91044e7	1.58272
$907$	1.30672e7	0.527428	0.263714	−	0.964601i	$-0.415053\pi$
$907$	1.30672e7	0.527428	0.263714	+	0.964601i	$0.415053\pi$
$908$	1.84612e7	0.743096
$909$	−2.95060e6	−0.118441
$910$	1.85486e6	0.0742521
$911$	−4.60549e7	−1.83857	−0.919284	−	0.393594i	$-0.871232\pi$
$911$	−4.60549e7	−1.83857	−0.919284	+	0.393594i	$0.871232\pi$
$912$	1.89270e6	0.0753521
$913$	−1.80970e7	−0.718506
$914$	2.57764e7	1.02060
$915$	2.64291e7	1.04359
$916$	−6.93906e6	−0.273251
$917$	−360828.	−0.0141702
$918$	1.20940e6	0.0473656
$919$	−6.67836e6	−0.260844	−0.130422	−	0.991459i	$-0.541633\pi$
$919$	−6.67836e6	−0.260844	−0.130422	+	0.991459i	$0.541633\pi$
$920$	1.46022e6	0.0568785
$921$	−2.53631e7	−0.985264
$922$	1.64043e7	0.635522
$923$	−5.10717e6	−0.197322
$924$	−2.16682e6	−0.0834915
$925$	−3.83772e6	−0.147475
$926$	−3.59473e7	−1.37765
$927$	1.63498e7	0.624903
$928$	7.39254e6	0.281789
$929$	−84737.5	−0.00322134	−0.00161067	−	0.999999i	$-0.500513\pi$
$929$	−84737.5	−0.00322134	−0.00161067	+	0.999999i	$0.500513\pi$
$930$	−1.52576e7	−0.578466
$931$	−5.93809e6	−0.224529
$932$	6.19477e6	0.233607
$933$	−3.65706e7	−1.37540
$934$	3.53763e7	1.32692
$935$	2.66970e6	0.0998695
$936$	−8.03552e6	−0.299795
$937$	−3.12820e7	−1.16398	−0.581989	−	0.813196i	$-0.697725\pi$
$937$	−3.12820e7	−1.16398	−0.581989	+	0.813196i	$0.697725\pi$
$938$	−4.15924e6	−0.154350
$939$	−6.17701e7	−2.28620
$940$	−1.50109e7	−0.554100
$941$	2.88841e7	1.06337	0.531685	−	0.846942i	$-0.321559\pi$
$941$	2.88841e7	1.06337	0.531685	+	0.846942i	$0.321559\pi$
$942$	−3.56320e7	−1.30832
$943$	2.06101e6	0.0754746
$944$	−9.70367e6	−0.354410
$945$	888302.	0.0323580
$946$	−444607.	−0.0161528
$947$	1.99925e7	0.724422	0.362211	−	0.932096i	$-0.382022\pi$
$947$	1.99925e7	0.724422	0.362211	+	0.932096i	$0.382022\pi$
$948$	1.18308e7	0.427557
$949$	4.60732e7	1.66067
$950$	2.79968e6	0.100647
$951$	1.05645e7	0.378790
$952$	268591.	0.00960502
$953$	5.22187e7	1.86249	0.931244	−	0.364396i	$-0.118724\pi$
$953$	5.22187e7	1.86249	0.931244	+	0.364396i	$0.118724\pi$
$954$	786666.	0.0279846
$955$	−9.83573e6	−0.348978
$956$	−9.95941e6	−0.352443
$957$	−5.16716e7	−1.82378
$958$	−1.15728e7	−0.407403
$959$	5.04580e6	0.177167
$960$	2.88914e6	0.101179
$961$	614716.	0.0214717
$962$	−5.63414e6	−0.196286
$963$	−8.32029e6	−0.289116
$964$	−5.94327e6	−0.205984
$965$	−1.84913e6	−0.0639218
$966$	−1.02684e6	−0.0354047
$967$	2.66303e7	0.915818	0.457909	−	0.888999i	$-0.348598\pi$
$967$	2.66303e7	0.915818	0.457909	+	0.888999i	$0.348598\pi$
$968$	2.49053e6	0.0854287
$969$	1.63987e6	0.0561047
$970$	−5.44340e6	−0.185755
$971$	1.04206e7	0.354686	0.177343	−	0.984149i	$-0.443250\pi$
$971$	1.04206e7	0.354686	0.177343	+	0.984149i	$0.443250\pi$
$972$	−1.78977e7	−0.607620
$973$	5.57959e6	0.188938
$974$	1.27267e7	0.429850
$975$	−2.82560e7	−0.951918
$976$	9.59212e6	0.322322
$977$	1.82795e7	0.612673	0.306336	−	0.951923i	$-0.400897\pi$
$977$	1.82795e7	0.612673	0.306336	+	0.951923i	$0.400897\pi$
$978$	2.08966e7	0.698601
$979$	5.07633e7	1.69275
$980$	−9.06425e6	−0.301486
$981$	9.25433e6	0.307024
$982$	1.78204e7	0.589709
$983$	2.25159e7	0.743199	0.371600	−	0.928393i	$-0.378809\pi$
$983$	2.25159e7	0.743199	0.371600	+	0.928393i	$0.378809\pi$
$984$	4.07785e6	0.134259
$985$	500730.	0.0164442
$986$	6.40502e6	0.209811
$987$	1.05559e7	0.344907
$988$	4.11019e6	0.133958
$989$	−210697.	−0.00684964
$990$	−8.49482e6	−0.275465
$991$	3.42068e7	1.10644	0.553221	−	0.833034i	$-0.313398\pi$
$991$	3.42068e7	1.10644	0.553221	+	0.833034i	$0.313398\pi$
$992$	−5.53755e6	−0.178664
$993$	−4.61726e7	−1.48597
$994$	−543187.	−0.0174375
$995$	−4.94914e6	−0.158479
$996$	−1.69684e7	−0.541990
$997$	−1.12682e7	−0.359018	−0.179509	−	0.983756i	$-0.557451\pi$
$997$	−1.12682e7	−0.359018	−0.179509	+	0.983756i	$0.557451\pi$
$998$	−3.72589e7	−1.18414
$999$	−2.69821e6	−0.0855387

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.a.c.1.2	✓	2
3.2	odd	2		342.6.a.i.1.1		2
4.3	odd	2		304.6.a.f.1.1		2
5.4	even	2		950.6.a.d.1.1		2
19.18	odd	2		722.6.a.c.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.a.c.1.2	✓	2	1.1	even	1	trivial
304.6.a.f.1.1		2	4.3	odd	2
342.6.a.i.1.1		2	3.2	odd	2
722.6.a.c.1.1		2	19.18	odd	2
950.6.a.d.1.1		2	5.4	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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +20.4803 q^{3} +16.0000 q^{4} +34.4408 q^{5} -81.9210 q^{6} -18.9210 q^{7} -64.0000 q^{8} +176.441 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +20.4803 q^{3} +16.0000 q^{4} +34.4408 q^{5} -81.9210 q^{6} -18.9210 q^{7} -64.0000 q^{8} +176.441 q^{9} -137.763 q^{10} +349.480 q^{11} +327.684 q^{12} +711.599 q^{13} +75.6840 q^{14} +705.355 q^{15} +256.000 q^{16} +221.803 q^{17} -705.763 q^{18} +361.000 q^{19} +551.052 q^{20} -387.507 q^{21} -1397.92 q^{22} -662.468 q^{23} -1310.74 q^{24} -1938.83 q^{25} -2846.39 q^{26} -1363.15 q^{27} -302.736 q^{28} -7219.28 q^{29} -2821.42 q^{30} +5407.76 q^{31} -1024.00 q^{32} +7157.44 q^{33} -887.210 q^{34} -651.654 q^{35} +2823.05 q^{36} +1979.40 q^{37} -1444.00 q^{38} +14573.7 q^{39} -2204.21 q^{40} -3111.11 q^{41} +1550.03 q^{42} +318.049 q^{43} +5591.68 q^{44} +6076.75 q^{45} +2649.87 q^{46} -27240.5 q^{47} +5242.94 q^{48} -16449.0 q^{49} +7755.34 q^{50} +4542.57 q^{51} +11385.6 q^{52} -1114.63 q^{53} +5452.60 q^{54} +12036.4 q^{55} +1210.94 q^{56} +7393.37 q^{57} +28877.1 q^{58} -37904.9 q^{59} +11285.7 q^{60} +37469.2 q^{61} -21631.0 q^{62} -3338.44 q^{63} +4096.00 q^{64} +24508.0 q^{65} -28629.8 q^{66} -54955.3 q^{67} +3548.84 q^{68} -13567.5 q^{69} +2606.62 q^{70} -7177.04 q^{71} -11292.2 q^{72} +64746.1 q^{73} -7917.59 q^{74} -39707.8 q^{75} +5776.00 q^{76} -6612.52 q^{77} -58294.9 q^{78} +36104.4 q^{79} +8816.83 q^{80} -70792.8 q^{81} +12444.4 q^{82} -51782.7 q^{83} -6200.11 q^{84} +7639.05 q^{85} -1272.20 q^{86} -147853. q^{87} -22366.7 q^{88} +145254. q^{89} -24307.0 q^{90} -13464.2 q^{91} -10599.5 q^{92} +110752. q^{93} +108962. q^{94} +12433.1 q^{95} -20971.8 q^{96} +39512.8 q^{97} +65796.0 q^{98} +61662.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} + 3 q^{3} + 32 q^{4} - 45 q^{5} - 12 q^{6} + 114 q^{7} - 128 q^{8} + 239 q^{9}+O(q^{10}) \) 2 * q - 8 * q^2 + 3 * q^3 + 32 * q^4 - 45 * q^5 - 12 * q^6 + 114 * q^7 - 128 * q^8 + 239 * q^9	\( 2 q - 8 q^{2} + 3 q^{3} + 32 q^{4} - 45 q^{5} - 12 q^{6} + 114 q^{7} - 128 q^{8} + 239 q^{9} + 180 q^{10} + 661 q^{11} + 48 q^{12} + 1613 q^{13} - 456 q^{14} + 2094 q^{15} + 512 q^{16} + 64 q^{17} - 956 q^{18} + 722 q^{19} - 720 q^{20} - 2711 q^{21} - 2644 q^{22} - 3185 q^{23} - 192 q^{24} + 1247 q^{25} - 6452 q^{26} + 1791 q^{27} + 1824 q^{28} - 2481 q^{29} - 8376 q^{30} - 1180 q^{31} - 2048 q^{32} + 1712 q^{33} - 256 q^{34} - 11211 q^{35} + 3824 q^{36} + 10488 q^{37} - 2888 q^{38} - 1183 q^{39} + 2880 q^{40} + 16630 q^{41} + 10844 q^{42} + 11303 q^{43} + 10576 q^{44} + 1107 q^{45} + 12740 q^{46} - 12155 q^{47} + 768 q^{48} - 15588 q^{49} - 4988 q^{50} + 7301 q^{51} + 25808 q^{52} + 20585 q^{53} - 7164 q^{54} - 12711 q^{55} - 7296 q^{56} + 1083 q^{57} + 9924 q^{58} - 78581 q^{59} + 33504 q^{60} + 43621 q^{61} + 4720 q^{62} + 4977 q^{63} + 8192 q^{64} - 47100 q^{65} - 6848 q^{66} + 7805 q^{67} + 1024 q^{68} + 30527 q^{69} + 44844 q^{70} - 62488 q^{71} - 15296 q^{72} + 16218 q^{73} - 41952 q^{74} - 95397 q^{75} + 11552 q^{76} + 34795 q^{77} + 4732 q^{78} + 67122 q^{79} - 11520 q^{80} - 141130 q^{81} - 66520 q^{82} - 10714 q^{83} - 43376 q^{84} + 20175 q^{85} - 45212 q^{86} - 230679 q^{87} - 42304 q^{88} + 128188 q^{89} - 4428 q^{90} + 106351 q^{91} - 50960 q^{92} + 225908 q^{93} + 48620 q^{94} - 16245 q^{95} - 3072 q^{96} + 178558 q^{97} + 62352 q^{98} + 81151 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 + 3 * q^3 + 32 * q^4 - 45 * q^5 - 12 * q^6 + 114 * q^7 - 128 * q^8 + 239 * q^9 + 180 * q^10 + 661 * q^11 + 48 * q^12 + 1613 * q^13 - 456 * q^14 + 2094 * q^15 + 512 * q^16 + 64 * q^17 - 956 * q^18 + 722 * q^19 - 720 * q^20 - 2711 * q^21 - 2644 * q^22 - 3185 * q^23 - 192 * q^24 + 1247 * q^25 - 6452 * q^26 + 1791 * q^27 + 1824 * q^28 - 2481 * q^29 - 8376 * q^30 - 1180 * q^31 - 2048 * q^32 + 1712 * q^33 - 256 * q^34 - 11211 * q^35 + 3824 * q^36 + 10488 * q^37 - 2888 * q^38 - 1183 * q^39 + 2880 * q^40 + 16630 * q^41 + 10844 * q^42 + 11303 * q^43 + 10576 * q^44 + 1107 * q^45 + 12740 * q^46 - 12155 * q^47 + 768 * q^48 - 15588 * q^49 - 4988 * q^50 + 7301 * q^51 + 25808 * q^52 + 20585 * q^53 - 7164 * q^54 - 12711 * q^55 - 7296 * q^56 + 1083 * q^57 + 9924 * q^58 - 78581 * q^59 + 33504 * q^60 + 43621 * q^61 + 4720 * q^62 + 4977 * q^63 + 8192 * q^64 - 47100 * q^65 - 6848 * q^66 + 7805 * q^67 + 1024 * q^68 + 30527 * q^69 + 44844 * q^70 - 62488 * q^71 - 15296 * q^72 + 16218 * q^73 - 41952 * q^74 - 95397 * q^75 + 11552 * q^76 + 34795 * q^77 + 4732 * q^78 + 67122 * q^79 - 11520 * q^80 - 141130 * q^81 - 66520 * q^82 - 10714 * q^83 - 43376 * q^84 + 20175 * q^85 - 45212 * q^86 - 230679 * q^87 - 42304 * q^88 + 128188 * q^89 - 4428 * q^90 + 106351 * q^91 - 50960 * q^92 + 225908 * q^93 + 48620 * q^94 - 16245 * q^95 - 3072 * q^96 + 178558 * q^97 + 62352 * q^98 + 81151 * q^99

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