LMFDB - Embedded newform 38.10.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,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, 10, names="a")

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

chi := DirichletCharacter("38.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
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:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 34433x^{2} - 2723303x - 48270488 $ x^4 - x^3 - 34433x^2 - 2723303x - 48270488
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-67.1081$ 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)

$f(q)$	$=$	$q-16.0000 q^{2} +265.578 q^{3} +256.000 q^{4} -2367.11 q^{5} -4249.24 q^{6} +5859.40 q^{7} -4096.00 q^{8} +50848.5 q^{9} +O(q^{10})$	\(q-16.0000 q^{2} +265.578 q^{3} +256.000 q^{4} -2367.11 q^{5} -4249.24 q^{6} +5859.40 q^{7} -4096.00 q^{8} +50848.5 q^{9} +37873.7 q^{10} -38743.9 q^{11} +67987.9 q^{12} +179439. q^{13} -93750.4 q^{14} -628650. q^{15} +65536.0 q^{16} +184492. q^{17} -813576. q^{18} +130321. q^{19} -605979. q^{20} +1.55613e6 q^{21} +619902. q^{22} -115333. q^{23} -1.08781e6 q^{24} +3.65006e6 q^{25} -2.87102e6 q^{26} +8.27687e6 q^{27} +1.50001e6 q^{28} +569755. q^{29} +1.00584e7 q^{30} +5.80788e6 q^{31} -1.04858e6 q^{32} -1.02895e7 q^{33} -2.95187e6 q^{34} -1.38698e7 q^{35} +1.30172e7 q^{36} +3.15312e6 q^{37} -2.08514e6 q^{38} +4.76550e7 q^{39} +9.69566e6 q^{40} +54772.2 q^{41} -2.48980e7 q^{42} -1.63249e7 q^{43} -9.91844e6 q^{44} -1.20364e8 q^{45} +1.84533e6 q^{46} +2.84428e7 q^{47} +1.74049e7 q^{48} -6.02101e6 q^{49} -5.84010e7 q^{50} +4.89969e7 q^{51} +4.59363e7 q^{52} +7.33201e7 q^{53} -1.32430e8 q^{54} +9.17109e7 q^{55} -2.40001e7 q^{56} +3.46104e7 q^{57} -9.11608e6 q^{58} -1.45518e7 q^{59} -1.60935e8 q^{60} +9.96035e7 q^{61} -9.29260e7 q^{62} +2.97942e8 q^{63} +1.67772e7 q^{64} -4.24751e8 q^{65} +1.64632e8 q^{66} -2.49050e8 q^{67} +4.72299e7 q^{68} -3.06299e7 q^{69} +2.21917e8 q^{70} -1.33230e8 q^{71} -2.08276e8 q^{72} -2.28114e8 q^{73} -5.04499e7 q^{74} +9.69375e8 q^{75} +3.33622e7 q^{76} -2.27016e8 q^{77} -7.62479e8 q^{78} -6.65788e8 q^{79} -1.55131e8 q^{80} +1.19730e9 q^{81} -876356. q^{82} -3.48852e8 q^{83} +3.98368e8 q^{84} -4.36712e8 q^{85} +2.61199e8 q^{86} +1.51314e8 q^{87} +1.58695e8 q^{88} +2.61939e8 q^{89} +1.92582e9 q^{90} +1.05140e9 q^{91} -2.95252e7 q^{92} +1.54244e9 q^{93} -4.55084e8 q^{94} -3.08484e8 q^{95} -2.78478e8 q^{96} -1.10091e9 q^{97} +9.63361e7 q^{98} -1.97007e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9}+O(q^{10}) $ 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9	\( 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9} + 22320 q^{10} - 104249 q^{11} + 21504 q^{12} + 120486 q^{13} - 196912 q^{14} - 591090 q^{15} + 262144 q^{16} - 412139 q^{17} - 264608 q^{18} + 521284 q^{19} - 357120 q^{20} + 2437006 q^{21} + 1667984 q^{22} + 3010300 q^{23} - 344064 q^{24} + 9760585 q^{25} - 1927776 q^{26} + 12387978 q^{27} + 3150592 q^{28} + 6153240 q^{29} + 9457440 q^{30} + 12774024 q^{31} - 4194304 q^{32} - 3258022 q^{33} + 6594224 q^{34} + 9823425 q^{35} + 4233728 q^{36} + 20506048 q^{37} - 8340544 q^{38} + 69881444 q^{39} + 5713920 q^{40} + 11620300 q^{41} - 38992096 q^{42} + 7698327 q^{43} - 26687744 q^{44} - 124015815 q^{45} - 48164800 q^{46} - 31581083 q^{47} + 5505024 q^{48} + 18970383 q^{49} - 156169360 q^{50} - 8594812 q^{51} + 30844416 q^{52} + 72549422 q^{53} - 198207648 q^{54} + 21332505 q^{55} - 50409472 q^{56} + 10946964 q^{57} - 98451840 q^{58} - 149234120 q^{59} - 151319040 q^{60} + 129004373 q^{61} - 204384384 q^{62} + 102967551 q^{63} + 67108864 q^{64} + 124691700 q^{65} + 52128352 q^{66} + 132595266 q^{67} - 105507584 q^{68} - 45529972 q^{69} - 157174800 q^{70} - 47138482 q^{71} - 67739648 q^{72} - 39332795 q^{73} - 328096768 q^{74} + 824627010 q^{75} + 133448704 q^{76} - 165933719 q^{77} - 1118103104 q^{78} - 307010840 q^{79} - 91422720 q^{80} + 1305551744 q^{81} - 185924800 q^{82} - 746568232 q^{83} + 623873536 q^{84} - 105005985 q^{85} - 123173232 q^{86} - 82148208 q^{87} + 427003904 q^{88} + 286943482 q^{89} + 1984253040 q^{90} + 3155781114 q^{91} + 770636800 q^{92} + 1151901596 q^{93} + 505297328 q^{94} - 181797795 q^{95} - 88080384 q^{96} + 793519958 q^{97} - 303526128 q^{98} - 1681833809 q^{99}+O(q^{100}) \) 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9 + 22320 * q^10 - 104249 * q^11 + 21504 * q^12 + 120486 * q^13 - 196912 * q^14 - 591090 * q^15 + 262144 * q^16 - 412139 * q^17 - 264608 * q^18 + 521284 * q^19 - 357120 * q^20 + 2437006 * q^21 + 1667984 * q^22 + 3010300 * q^23 - 344064 * q^24 + 9760585 * q^25 - 1927776 * q^26 + 12387978 * q^27 + 3150592 * q^28 + 6153240 * q^29 + 9457440 * q^30 + 12774024 * q^31 - 4194304 * q^32 - 3258022 * q^33 + 6594224 * q^34 + 9823425 * q^35 + 4233728 * q^36 + 20506048 * q^37 - 8340544 * q^38 + 69881444 * q^39 + 5713920 * q^40 + 11620300 * q^41 - 38992096 * q^42 + 7698327 * q^43 - 26687744 * q^44 - 124015815 * q^45 - 48164800 * q^46 - 31581083 * q^47 + 5505024 * q^48 + 18970383 * q^49 - 156169360 * q^50 - 8594812 * q^51 + 30844416 * q^52 + 72549422 * q^53 - 198207648 * q^54 + 21332505 * q^55 - 50409472 * q^56 + 10946964 * q^57 - 98451840 * q^58 - 149234120 * q^59 - 151319040 * q^60 + 129004373 * q^61 - 204384384 * q^62 + 102967551 * q^63 + 67108864 * q^64 + 124691700 * q^65 + 52128352 * q^66 + 132595266 * q^67 - 105507584 * q^68 - 45529972 * q^69 - 157174800 * q^70 - 47138482 * q^71 - 67739648 * q^72 - 39332795 * q^73 - 328096768 * q^74 + 824627010 * q^75 + 133448704 * q^76 - 165933719 * q^77 - 1118103104 * q^78 - 307010840 * q^79 - 91422720 * q^80 + 1305551744 * q^81 - 185924800 * q^82 - 746568232 * q^83 + 623873536 * q^84 - 105005985 * q^85 - 123173232 * q^86 - 82148208 * q^87 + 427003904 * q^88 + 286943482 * q^89 + 1984253040 * q^90 + 3155781114 * q^91 + 770636800 * q^92 + 1151901596 * q^93 + 505297328 * q^94 - 181797795 * q^95 - 88080384 * q^96 + 793519958 * q^97 - 303526128 * q^98 - 1681833809 * 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 $

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	265.578	1.89298	0.946490	−	0.322733i	$-0.104602\pi$
$3$	265.578	1.89298	0.946490	+	0.322733i	$0.104602\pi$
$4$	256.000	0.500000
$5$	−2367.11	−1.69376	−0.846881	−	0.531782i	$-0.821523\pi$
$5$	−2367.11	−1.69376	−0.846881	+	0.531782i	$0.821523\pi$
$6$	−4249.24	−1.33854
$7$	5859.40	0.922385	0.461192	−	0.887300i	$-0.347422\pi$
$7$	5859.40	0.922385	0.461192	+	0.887300i	$0.347422\pi$
$8$	−4096.00	−0.353553
$9$	50848.5	2.58337
$10$	37873.7	1.19767
$11$	−38743.9	−0.797878	−0.398939	−	0.916978i	$-0.630621\pi$
$11$	−38743.9	−0.797878	−0.398939	+	0.916978i	$0.630621\pi$
$12$	67987.9	0.946490
$13$	179439.	1.74249	0.871247	−	0.490845i	$-0.163312\pi$
$13$	179439.	1.74249	0.871247	+	0.490845i	$0.163312\pi$
$14$	−93750.4	−0.652225
$15$	−628650.	−3.20626
$16$	65536.0	0.250000
$17$	184492.	0.535744	0.267872	−	0.963455i	$-0.413680\pi$
$17$	184492.	0.535744	0.267872	+	0.963455i	$0.413680\pi$
$18$	−813576.	−1.82672
$19$	130321.	0.229416
$19$	130321.	0.229416
$20$	−605979.	−0.846881
$21$	1.55613e6	1.74606
$22$	619902.	0.564185
$23$	−115333.	−0.0859366	−0.0429683	−	0.999076i	$-0.513681\pi$
$23$	−115333.	−0.0859366	−0.0429683	+	0.999076i	$0.513681\pi$
$24$	−1.08781e6	−0.669269
$25$	3.65006e6	1.86883
$26$	−2.87102e6	−1.23213
$27$	8.27687e6	2.99729
$28$	1.50001e6	0.461192
$29$	569755.	0.149588	0.0747941	−	0.997199i	$-0.476170\pi$
$29$	569755.	0.149588	0.0747941	+	0.997199i	$0.476170\pi$
$30$	1.00584e7	2.26717
$31$	5.80788e6	1.12951	0.564755	−	0.825259i	$-0.308971\pi$
$31$	5.80788e6	1.12951	0.564755	+	0.825259i	$0.308971\pi$
$32$	−1.04858e6	−0.176777
$33$	−1.02895e7	−1.51037
$34$	−2.95187e6	−0.378828
$35$	−1.38698e7	−1.56230
$36$	1.30172e7	1.29169
$37$	3.15312e6	0.276587	0.138294	−	0.990391i	$-0.455838\pi$
$37$	3.15312e6	0.276587	0.138294	+	0.990391i	$0.455838\pi$
$38$	−2.08514e6	−0.162221
$39$	4.76550e7	3.29851
$40$	9.69566e6	0.598836
$41$	54772.2	0.00302714	0.00151357	−	0.999999i	$-0.499518\pi$
$41$	54772.2	0.00302714	0.00151357	+	0.999999i	$0.499518\pi$
$42$	−2.48980e7	−1.23465
$43$	−1.63249e7	−0.728187	−0.364094	−	0.931362i	$-0.618621\pi$
$43$	−1.63249e7	−0.728187	−0.364094	+	0.931362i	$0.618621\pi$
$44$	−9.91844e6	−0.398939
$45$	−1.20364e8	−4.37562
$46$	1.84533e6	0.0607663
$47$	2.84428e7	0.850220	0.425110	−	0.905142i	$-0.360235\pi$
$47$	2.84428e7	0.850220	0.425110	+	0.905142i	$0.360235\pi$
$48$	1.74049e7	0.473245
$49$	−6.02101e6	−0.149206
$50$	−5.84010e7	−1.32146
$51$	4.89969e7	1.01415
$52$	4.59363e7	0.871247
$53$	7.33201e7	1.27639	0.638193	−	0.769877i	$-0.279682\pi$
$53$	7.33201e7	1.27639	0.638193	+	0.769877i	$0.279682\pi$
$54$	−1.32430e8	−2.11941
$55$	9.17109e7	1.35142
$56$	−2.40001e7	−0.326112
$57$	3.46104e7	0.434279
$58$	−9.11608e6	−0.105775
$59$	−1.45518e7	−0.156345	−0.0781725	−	0.996940i	$-0.524909\pi$
$59$	−1.45518e7	−0.156345	−0.0781725	+	0.996940i	$0.524909\pi$
$60$	−1.60935e8	−1.60313
$61$	9.96035e7	0.921065	0.460533	−	0.887643i	$-0.347658\pi$
$61$	9.96035e7	0.921065	0.460533	+	0.887643i	$0.347658\pi$
$62$	−9.29260e7	−0.798684
$63$	2.97942e8	2.38286
$64$	1.67772e7	0.125000
$65$	−4.24751e8	−2.95137
$66$	1.64632e8	1.06799
$67$	−2.49050e8	−1.50991	−0.754954	−	0.655778i	$-0.772341\pi$
$67$	−2.49050e8	−1.50991	−0.754954	+	0.655778i	$0.772341\pi$
$68$	4.72299e7	0.267872
$69$	−3.06299e7	−0.162676
$70$	2.21917e8	1.10471
$71$	−1.33230e8	−0.622215	−0.311108	−	0.950375i	$-0.600700\pi$
$71$	−1.33230e8	−0.622215	−0.311108	+	0.950375i	$0.600700\pi$
$72$	−2.08276e8	−0.913360
$73$	−2.28114e8	−0.940153	−0.470077	−	0.882626i	$-0.655774\pi$
$73$	−2.28114e8	−0.940153	−0.470077	+	0.882626i	$0.655774\pi$
$74$	−5.04499e7	−0.195577
$75$	9.69375e8	3.53766
$76$	3.33622e7	0.114708
$77$	−2.27016e8	−0.735950
$78$	−7.62479e8	−2.33240
$79$	−6.65788e8	−1.92315	−0.961577	−	0.274534i	$-0.911476\pi$
$79$	−6.65788e8	−1.92315	−0.961577	+	0.274534i	$0.911476\pi$
$80$	−1.55131e8	−0.423441
$81$	1.19730e9	3.09044
$82$	−876356.	−0.00214051
$83$	−3.48852e8	−0.806844	−0.403422	−	0.915014i	$-0.632179\pi$
$83$	−3.48852e8	−0.806844	−0.403422	+	0.915014i	$0.632179\pi$
$84$	3.98368e8	0.873028
$85$	−4.36712e8	−0.907422
$86$	2.61199e8	0.514906
$87$	1.51314e8	0.283167
$88$	1.58695e8	0.282092
$89$	2.61939e8	0.442533	0.221267	−	0.975213i	$-0.428981\pi$
$89$	2.61939e8	0.442533	0.221267	+	0.975213i	$0.428981\pi$
$90$	1.92582e9	3.09403
$91$	1.05140e9	1.60725
$92$	−2.95252e7	−0.0429683
$93$	1.54244e9	2.13814
$94$	−4.55084e8	−0.601197
$95$	−3.08484e8	−0.388576
$96$	−2.78478e8	−0.334635
$97$	−1.10091e9	−1.26264	−0.631321	−	0.775521i	$-0.717487\pi$
$97$	−1.10091e9	−1.26264	−0.631321	+	0.775521i	$0.717487\pi$
$98$	9.63361e7	0.105505
$99$	−1.97007e9	−2.06122
$100$	9.34416e8	0.934416
$101$	1.22467e9	1.17104	0.585521	−	0.810658i	$-0.300890\pi$
$101$	1.22467e9	1.17104	0.585521	+	0.810658i	$0.300890\pi$
$102$	−7.83951e8	−0.717114
$103$	1.37095e9	1.20020	0.600100	−	0.799925i	$-0.295128\pi$
$103$	1.37095e9	1.20020	0.600100	+	0.799925i	$0.295128\pi$
$104$	−7.34981e8	−0.616065
$105$	−3.68352e9	−2.95740
$106$	−1.17312e9	−0.902541
$107$	1.42672e9	1.05223	0.526115	−	0.850413i	$-0.323648\pi$
$107$	1.42672e9	1.05223	0.526115	+	0.850413i	$0.323648\pi$
$108$	2.11888e9	1.49865
$109$	−2.50340e9	−1.69868	−0.849340	−	0.527846i	$-0.823000\pi$
$109$	−2.50340e9	−1.69868	−0.849340	+	0.527846i	$0.823000\pi$
$110$	−1.46737e9	−0.955595
$111$	8.37398e8	0.523575
$112$	3.84002e8	0.230596
$113$	−3.27341e9	−1.88863	−0.944317	−	0.329036i	$-0.893276\pi$
$113$	−3.27341e9	−1.88863	−0.944317	+	0.329036i	$0.893276\pi$
$114$	−5.53766e8	−0.307082
$115$	2.73005e8	0.145556
$116$	1.45857e8	0.0747941
$117$	9.12420e9	4.50151
$118$	2.32830e8	0.110553
$119$	1.08101e9	0.494162
$120$	2.57495e9	1.13358
$121$	−8.56858e8	−0.363391
$122$	−1.59366e9	−0.651291
$123$	1.45463e7	0.00573032
$124$	1.48682e9	0.564755
$125$	−4.01683e9	−1.47160
$126$	−4.76707e9	−1.68494
$127$	−4.27729e9	−1.45899	−0.729494	−	0.683987i	$-0.760244\pi$
$127$	−4.27729e9	−1.45899	−0.729494	+	0.683987i	$0.760244\pi$
$128$	−2.68435e8	−0.0883883
$129$	−4.33554e9	−1.37844
$130$	6.79601e9	2.08693
$131$	3.80463e9	1.12873	0.564367	−	0.825524i	$-0.309120\pi$
$131$	3.80463e9	1.12873	0.564367	+	0.825524i	$0.309120\pi$
$132$	−2.63412e9	−0.755183
$133$	7.63603e8	0.211610
$134$	3.98481e9	1.06767
$135$	−1.95922e10	−5.07670
$136$	−7.55678e8	−0.189414
$137$	1.42380e8	0.0345308	0.0172654	−	0.999851i	$-0.494504\pi$
$137$	1.42380e8	0.0345308	0.0172654	+	0.999851i	$0.494504\pi$
$138$	4.90078e8	0.115029
$139$	2.12706e9	0.483295	0.241648	−	0.970364i	$-0.422312\pi$
$139$	2.12706e9	0.483295	0.241648	+	0.970364i	$0.422312\pi$
$140$	−3.55067e9	−0.781151
$141$	7.55377e9	1.60945
$142$	2.13169e9	0.439972
$143$	−6.95216e9	−1.39030
$144$	3.33241e9	0.645843
$145$	−1.34867e9	−0.253367
$146$	3.64982e9	0.664789
$147$	−1.59905e9	−0.282444
$148$	8.07198e8	0.138294
$149$	5.74897e9	0.955547	0.477773	−	0.878483i	$-0.341444\pi$
$149$	5.74897e9	0.955547	0.477773	+	0.878483i	$0.341444\pi$
$150$	−1.55100e10	−2.50150
$151$	3.66097e9	0.573059	0.286530	−	0.958071i	$-0.407498\pi$
$151$	3.66097e9	0.573059	0.286530	+	0.958071i	$0.407498\pi$
$152$	−5.33795e8	−0.0811107
$153$	9.38114e9	1.38403
$154$	3.63226e9	0.520395
$155$	−1.37479e10	−1.91312
$156$	1.21997e10	1.64925
$157$	−1.22861e9	−0.161386	−0.0806930	−	0.996739i	$-0.525713\pi$
$157$	−1.22861e9	−0.161386	−0.0806930	+	0.996739i	$0.525713\pi$
$158$	1.06526e10	1.35988
$159$	1.94722e10	2.41617
$160$	2.48209e9	0.299418
$161$	−6.75782e8	−0.0792666
$162$	−1.91568e10	−2.18527
$163$	−6.60342e8	−0.0732697	−0.0366349	−	0.999329i	$-0.511664\pi$
$163$	−6.60342e8	−0.0732697	−0.0366349	+	0.999329i	$0.511664\pi$
$164$	1.40217e7	0.00151357
$165$	2.43564e10	2.55820
$166$	5.58163e9	0.570525
$167$	−1.05713e10	−1.05173	−0.525865	−	0.850568i	$-0.676258\pi$
$167$	−1.05713e10	−1.05173	−0.525865	+	0.850568i	$0.676258\pi$
$168$	−6.37390e9	−0.617324
$169$	2.15938e10	2.03629
$170$	6.98738e9	0.641645
$171$	6.62663e9	0.592666
$172$	−4.17918e9	−0.364094
$173$	−1.23439e10	−1.04772	−0.523861	−	0.851804i	$-0.675509\pi$
$173$	−1.23439e10	−1.04772	−0.523861	+	0.851804i	$0.675509\pi$
$174$	−2.42103e9	−0.200230
$175$	2.13872e10	1.72378
$176$	−2.53912e9	−0.199469
$177$	−3.86465e9	−0.295958
$178$	−4.19103e9	−0.312918
$179$	3.15457e9	0.229669	0.114834	−	0.993385i	$-0.463366\pi$
$179$	3.15457e9	0.229669	0.114834	+	0.993385i	$0.463366\pi$
$180$	−3.08131e10	−2.18781
$181$	1.16218e10	0.804857	0.402429	−	0.915451i	$-0.368166\pi$
$181$	1.16218e10	0.804857	0.402429	+	0.915451i	$0.368166\pi$
$182$	−1.68225e10	−1.13650
$183$	2.64525e10	1.74356
$184$	4.72404e8	0.0303832
$185$	−7.46376e9	−0.468474
$186$	−2.46791e10	−1.51189
$187$	−7.14793e9	−0.427458
$188$	7.28135e9	0.425110
$189$	4.84975e10	2.76466
$190$	4.93574e9	0.274765
$191$	−3.25043e9	−0.176722	−0.0883610	−	0.996089i	$-0.528163\pi$
$191$	−3.25043e9	−0.176722	−0.0883610	+	0.996089i	$0.528163\pi$
$192$	4.45565e9	0.236622
$193$	2.45765e9	0.127501	0.0637503	−	0.997966i	$-0.479694\pi$
$193$	2.45765e9	0.127501	0.0637503	+	0.997966i	$0.479694\pi$
$194$	1.76146e10	0.892823
$195$	−1.12804e11	−5.58689
$196$	−1.54138e9	−0.0746031
$197$	−1.10866e10	−0.524445	−0.262223	−	0.965007i	$-0.584455\pi$
$197$	−1.10866e10	−0.524445	−0.262223	+	0.965007i	$0.584455\pi$
$198$	3.15211e10	1.45750
$199$	−1.66765e10	−0.753817	−0.376908	−	0.926251i	$-0.623013\pi$
$199$	−1.66765e10	−0.753817	−0.376908	+	0.926251i	$0.623013\pi$
$200$	−1.49507e10	−0.660732
$201$	−6.61422e10	−2.85823
$202$	−1.95947e10	−0.828051
$203$	3.33842e9	0.137978
$204$	1.25432e10	0.507076
$205$	−1.29652e8	−0.00512726
$206$	−2.19352e10	−0.848669
$207$	−5.86451e9	−0.222006
$208$	1.17597e10	0.435624
$209$	−5.04914e9	−0.183046
$210$	5.89363e10	2.09120
$211$	2.51893e10	0.874872	0.437436	−	0.899249i	$-0.355887\pi$
$211$	2.51893e10	0.874872	0.437436	+	0.899249i	$0.355887\pi$
$212$	1.87699e10	0.638193
$213$	−3.53830e10	−1.17784
$214$	−2.28275e10	−0.744039
$215$	3.86428e10	1.23338
$216$	−3.39021e10	−1.05970
$217$	3.40307e10	1.04184
$218$	4.00545e10	1.20115
$219$	−6.05819e10	−1.77969
$220$	2.34780e10	0.675708
$221$	3.31050e10	0.933530
$222$	−1.33984e10	−0.370223
$223$	4.72569e10	1.27966	0.639829	−	0.768518i	$-0.279005\pi$
$223$	4.72569e10	1.27966	0.639829	+	0.768518i	$0.279005\pi$
$224$	−6.14403e9	−0.163056
$225$	1.85600e11	4.82789
$226$	5.23746e10	1.33547
$227$	−3.66710e10	−0.916657	−0.458328	−	0.888783i	$-0.651552\pi$
$227$	−3.66710e10	−0.916657	−0.458328	+	0.888783i	$0.651552\pi$
$228$	8.86025e9	0.217140
$229$	1.94037e10	0.466258	0.233129	−	0.972446i	$-0.425104\pi$
$229$	1.94037e10	0.466258	0.233129	+	0.972446i	$0.425104\pi$
$230$	−4.36808e9	−0.102924
$231$	−6.02904e10	−1.39314
$232$	−2.33372e9	−0.0528874
$233$	−3.57852e10	−0.795430	−0.397715	−	0.917509i	$-0.630197\pi$
$233$	−3.57852e10	−0.795430	−0.397715	+	0.917509i	$0.630197\pi$
$234$	−1.45987e11	−3.18305
$235$	−6.73270e10	−1.44007
$236$	−3.72527e9	−0.0781725
$237$	−1.76819e11	−3.64049
$238$	−1.72962e10	−0.349425
$239$	5.18718e9	0.102835	0.0514174	−	0.998677i	$-0.483626\pi$
$239$	5.18718e9	0.102835	0.0514174	+	0.998677i	$0.483626\pi$
$240$	−4.11992e10	−0.801565
$241$	1.46244e10	0.279254	0.139627	−	0.990204i	$-0.455410\pi$
$241$	1.46244e10	0.279254	0.139627	+	0.990204i	$0.455410\pi$
$242$	1.37097e10	0.256957
$243$	1.55063e11	2.85285
$244$	2.54985e10	0.460533
$245$	1.42524e10	0.252720
$246$	−2.32741e8	−0.00405195
$247$	2.33846e10	0.399756
$248$	−2.37891e10	−0.399342
$249$	−9.26473e10	−1.52734
$250$	6.42693e10	1.04057
$251$	1.36902e8	0.00217710	0.00108855	−	0.999999i	$-0.499654\pi$
$251$	1.36902e8	0.00217710	0.00108855	+	0.999999i	$0.499654\pi$
$252$	7.62731e10	1.19143
$253$	4.46845e9	0.0685669
$254$	6.84366e10	1.03166
$255$	−1.15981e11	−1.71773
$256$	4.29497e9	0.0625000
$257$	5.04580e10	0.721491	0.360745	−	0.932664i	$-0.382522\pi$
$257$	5.04580e10	0.721491	0.360745	+	0.932664i	$0.382522\pi$
$258$	6.93686e10	0.974707
$259$	1.84754e10	0.255120
$260$	−1.08736e11	−1.47569
$261$	2.89712e10	0.386442
$262$	−6.08741e10	−0.798135
$263$	2.49089e10	0.321036	0.160518	−	0.987033i	$-0.448684\pi$
$263$	2.49089e10	0.321036	0.160518	+	0.987033i	$0.448684\pi$
$264$	4.21459e10	0.533995
$265$	−1.73556e11	−2.16189
$266$	−1.22177e10	−0.149631
$267$	6.95653e10	0.837706
$268$	−6.37569e10	−0.754954
$269$	1.21965e11	1.42020	0.710101	−	0.704100i	$-0.248649\pi$
$269$	1.21965e11	1.42020	0.710101	+	0.704100i	$0.248649\pi$
$270$	3.13476e11	3.58977
$271$	−1.00248e10	−0.112905	−0.0564524	−	0.998405i	$-0.517979\pi$
$271$	−1.00248e10	−0.112905	−0.0564524	+	0.998405i	$0.517979\pi$
$272$	1.20909e10	0.133936
$273$	2.79230e11	3.04249
$274$	−2.27808e9	−0.0244170
$275$	−1.41418e11	−1.49110
$276$	−7.84124e9	−0.0813381
$277$	4.21205e10	0.429868	0.214934	−	0.976629i	$-0.431046\pi$
$277$	4.21205e10	0.429868	0.214934	+	0.976629i	$0.431046\pi$
$278$	−3.40329e10	−0.341741
$279$	2.95322e11	2.91794
$280$	5.68108e10	0.552357
$281$	−1.07825e11	−1.03167	−0.515836	−	0.856687i	$-0.672519\pi$
$281$	−1.07825e11	−1.03167	−0.515836	+	0.856687i	$0.672519\pi$
$282$	−1.20860e11	−1.13805
$283$	4.94720e10	0.458480	0.229240	−	0.973370i	$-0.426376\pi$
$283$	4.94720e10	0.458480	0.229240	+	0.973370i	$0.426376\pi$
$284$	−3.41070e10	−0.311108
$285$	−8.19264e10	−0.735566
$286$	1.11235e11	0.983088
$287$	3.20933e8	0.00279219
$288$	−5.33185e10	−0.456680
$289$	−8.45506e10	−0.712979
$290$	2.15787e10	0.179157
$291$	−2.92378e11	−2.39016
$292$	−5.83971e10	−0.470077
$293$	−3.72945e9	−0.0295624	−0.0147812	−	0.999891i	$-0.504705\pi$
$293$	−3.72945e9	−0.0295624	−0.0147812	+	0.999891i	$0.504705\pi$
$294$	2.55847e10	0.199718
$295$	3.44458e10	0.264811
$296$	−1.29152e10	−0.0977884
$297$	−3.20678e11	−2.39147
$298$	−9.19835e10	−0.675674
$299$	−2.06952e10	−0.149744
$300$	2.48160e11	1.76883
$301$	−9.56543e10	−0.671669
$302$	−5.85755e10	−0.405214
$303$	3.25244e11	2.21676
$304$	8.54072e9	0.0573539
$305$	−2.35772e11	−1.56007
$306$	−1.50098e11	−0.978654
$307$	1.97134e11	1.26660	0.633300	−	0.773907i	$-0.281700\pi$
$307$	1.97134e11	1.26660	0.633300	+	0.773907i	$0.281700\pi$
$308$	−5.81161e10	−0.367975
$309$	3.64093e11	2.27195
$310$	2.19966e11	1.35278
$311$	−2.55635e11	−1.54953	−0.774763	−	0.632252i	$-0.782131\pi$
$311$	−2.55635e11	−1.54953	−0.774763	+	0.632252i	$0.782131\pi$
$312$	−1.95195e11	−1.16620
$313$	5.67565e10	0.334246	0.167123	−	0.985936i	$-0.446552\pi$
$313$	5.67565e10	0.334246	0.167123	+	0.985936i	$0.446552\pi$
$314$	1.96578e10	0.114117
$315$	−7.05260e11	−4.03601
$316$	−1.70442e11	−0.961577
$317$	1.17647e11	0.654354	0.327177	−	0.944963i	$-0.393903\pi$
$317$	1.17647e11	0.654354	0.327177	+	0.944963i	$0.393903\pi$
$318$	−3.11555e11	−1.70849
$319$	−2.20745e10	−0.119353
$320$	−3.97134e10	−0.211720
$321$	3.78904e11	1.99185
$322$	1.08125e10	0.0560500
$323$	2.40432e10	0.122908
$324$	3.06509e11	1.54522
$325$	6.54963e11	3.25643
$326$	1.05655e10	0.0518095
$327$	−6.64848e11	−3.21557
$328$	−2.24347e8	−0.00107026
$329$	1.66658e11	0.784230
$330$	−3.89702e11	−1.80892
$331$	−2.89438e11	−1.32535	−0.662673	−	0.748909i	$-0.730578\pi$
$331$	−2.89438e11	−1.32535	−0.662673	+	0.748909i	$0.730578\pi$
$332$	−8.93061e10	−0.403422
$333$	1.60331e11	0.714529
$334$	1.69141e11	0.743685
$335$	5.89528e11	2.55743
$336$	1.01982e11	0.436514
$337$	9.82619e10	0.415002	0.207501	−	0.978235i	$-0.433467\pi$
$337$	9.82619e10	0.415002	0.207501	+	0.978235i	$0.433467\pi$
$338$	−3.45501e11	−1.43987
$339$	−8.69346e11	−3.57515
$340$	−1.11798e11	−0.453711
$341$	−2.25020e11	−0.901210
$342$	−1.06026e11	−0.419078
$343$	−2.71728e11	−1.06001
$344$	6.68669e10	0.257453
$345$	7.25041e10	0.275535
$346$	1.97503e11	0.740852
$347$	−2.54903e11	−0.943827	−0.471914	−	0.881645i	$-0.656437\pi$
$347$	−2.54903e11	−0.943827	−0.471914	+	0.881645i	$0.656437\pi$
$348$	3.87364e10	0.141584
$349$	4.14692e11	1.49628	0.748138	−	0.663543i	$-0.230948\pi$
$349$	4.14692e11	1.49628	0.748138	+	0.663543i	$0.230948\pi$
$350$	−3.42195e11	−1.21890
$351$	1.48519e12	5.22277
$352$	4.06259e10	0.141046
$353$	−1.12437e11	−0.385410	−0.192705	−	0.981257i	$-0.561726\pi$
$353$	−1.12437e11	−0.385410	−0.192705	+	0.981257i	$0.561726\pi$
$354$	6.18344e10	0.209274
$355$	3.15370e11	1.05388
$356$	6.70565e10	0.221267
$357$	2.87093e11	0.935438
$358$	−5.04732e10	−0.162400
$359$	1.53457e11	0.487596	0.243798	−	0.969826i	$-0.421607\pi$
$359$	1.53457e11	0.487596	0.243798	+	0.969826i	$0.421607\pi$
$360$	4.93010e11	1.54702
$361$	1.69836e10	0.0526316
$362$	−1.85948e11	−0.569120
$363$	−2.27562e11	−0.687893
$364$	2.69160e11	0.803625
$365$	5.39969e11	1.59240
$366$	−4.23240e11	−1.23288
$367$	3.10410e11	0.893180	0.446590	−	0.894739i	$-0.352638\pi$
$367$	3.10410e11	0.893180	0.446590	+	0.894739i	$0.352638\pi$
$368$	−7.55846e9	−0.0214841
$369$	2.78509e9	0.00782024
$370$	1.19420e11	0.331261
$371$	4.29612e11	1.17732
$372$	3.94865e11	1.06907
$373$	−4.01840e11	−1.07489	−0.537444	−	0.843300i	$-0.680610\pi$
$373$	−4.01840e11	−1.07489	−0.537444	+	0.843300i	$0.680610\pi$
$374$	1.14367e11	0.302258
$375$	−1.06678e12	−2.78570
$376$	−1.16502e11	−0.300598
$377$	1.02236e11	0.260656
$378$	−7.75960e11	−1.95491
$379$	−4.14457e11	−1.03182	−0.515909	−	0.856644i	$-0.672546\pi$
$379$	−4.14457e11	−1.03182	−0.515909	+	0.856644i	$0.672546\pi$
$380$	−7.89718e10	−0.194288
$381$	−1.13595e12	−2.76184
$382$	5.20069e10	0.124961
$383$	2.40472e11	0.571044	0.285522	−	0.958372i	$-0.407833\pi$
$383$	2.40472e11	0.571044	0.285522	+	0.958372i	$0.407833\pi$
$384$	−7.12905e10	−0.167317
$385$	5.37371e11	1.24652
$386$	−3.93224e10	−0.0901565
$387$	−8.30098e11	−1.88118
$388$	−2.81834e11	−0.631321
$389$	−2.15388e11	−0.476923	−0.238461	−	0.971152i	$-0.576643\pi$
$389$	−2.15388e11	−0.476923	−0.238461	+	0.971152i	$0.576643\pi$
$390$	1.80487e12	3.95053
$391$	−2.12780e10	−0.0460400
$392$	2.46621e10	0.0527524
$393$	1.01042e12	2.13667
$394$	1.77385e11	0.370839
$395$	1.57599e12	3.25737
$396$	−5.04338e11	−1.03061
$397$	−9.46770e11	−1.91288	−0.956439	−	0.291932i	$-0.905702\pi$
$397$	−9.46770e11	−1.91288	−0.956439	+	0.291932i	$0.905702\pi$
$398$	2.66824e11	0.533029
$399$	2.02796e11	0.400573
$400$	2.39210e11	0.467208
$401$	2.94360e10	0.0568498	0.0284249	−	0.999596i	$-0.490951\pi$
$401$	2.94360e10	0.0568498	0.0284249	+	0.999596i	$0.490951\pi$
$402$	1.05828e12	2.02107
$403$	1.04216e12	1.96816
$404$	3.13515e11	0.585521
$405$	−2.83414e12	−5.23448
$406$	−5.34148e10	−0.0975650
$407$	−1.22164e11	−0.220683
$408$	−2.00691e11	−0.358557
$409$	−9.56914e11	−1.69090	−0.845450	−	0.534054i	$-0.820668\pi$
$409$	−9.56914e11	−1.69090	−0.845450	+	0.534054i	$0.820668\pi$
$410$	2.07443e9	0.00362552
$411$	3.78130e10	0.0653662
$412$	3.50963e11	0.600100
$413$	−8.52651e10	−0.144210
$414$	9.38322e10	0.156982
$415$	8.25769e11	1.36660
$416$	−1.88155e11	−0.308032
$417$	5.64899e11	0.914868
$418$	8.07863e10	0.129433
$419$	−8.06056e11	−1.27762	−0.638811	−	0.769364i	$-0.720573\pi$
$419$	−8.06056e11	−1.27762	−0.638811	+	0.769364i	$0.720573\pi$
$420$	−9.42980e11	−1.47870
$421$	−1.29752e11	−0.201300	−0.100650	−	0.994922i	$-0.532092\pi$
$421$	−1.29752e11	−0.201300	−0.100650	+	0.994922i	$0.532092\pi$
$422$	−4.03028e11	−0.618628
$423$	1.44627e12	2.19644
$424$	−3.00319e11	−0.451270
$425$	6.73407e11	1.00121
$426$	5.66128e11	0.832859
$427$	5.83617e11	0.849577
$428$	3.65239e11	0.526115
$429$	−1.84634e12	−2.63180
$430$	−6.18285e11	−0.872129
$431$	−1.30045e12	−1.81530	−0.907648	−	0.419732i	$-0.862124\pi$
$431$	−1.30045e12	−1.81530	−0.907648	+	0.419732i	$0.862124\pi$
$432$	5.42433e11	0.749323
$433$	−7.31189e11	−0.999618	−0.499809	−	0.866136i	$-0.666596\pi$
$433$	−7.31189e11	−0.999618	−0.499809	+	0.866136i	$0.666596\pi$
$434$	−5.44491e11	−0.736694
$435$	−3.58177e11	−0.479618
$436$	−6.40871e11	−0.849340
$437$	−1.50303e10	−0.0197152
$438$	9.69311e11	1.25843
$439$	1.03899e12	1.33513	0.667563	−	0.744553i	$-0.267337\pi$
$439$	1.03899e12	1.33513	0.667563	+	0.744553i	$0.267337\pi$
$440$	−3.75648e11	−0.477797
$441$	−3.06159e11	−0.385455
$442$	−5.29680e11	−0.660105
$443$	−4.22964e10	−0.0521779	−0.0260889	−	0.999660i	$-0.508305\pi$
$443$	−4.22964e10	−0.0521779	−0.0260889	+	0.999660i	$0.508305\pi$
$444$	2.14374e11	0.261787
$445$	−6.20038e11	−0.749546
$446$	−7.56111e11	−0.904854
$447$	1.52680e12	1.80883
$448$	9.83045e10	0.115298
$449$	−1.99335e11	−0.231459	−0.115730	−	0.993281i	$-0.536921\pi$
$449$	−1.99335e11	−0.231459	−0.115730	+	0.993281i	$0.536921\pi$
$450$	−2.96960e12	−3.41383
$451$	−2.12209e9	−0.00241529
$452$	−8.37994e11	−0.944317
$453$	9.72271e11	1.08479
$454$	5.86736e11	0.648174
$455$	−2.48878e12	−2.72230
$456$	−1.41764e11	−0.153541
$457$	6.57751e11	0.705405	0.352702	−	0.935736i	$-0.385263\pi$
$457$	6.57751e11	0.705405	0.352702	+	0.935736i	$0.385263\pi$
$458$	−3.10460e11	−0.329694
$459$	1.52701e12	1.60578
$460$	6.98893e10	0.0727781
$461$	8.30559e11	0.856478	0.428239	−	0.903665i	$-0.359134\pi$
$461$	8.30559e11	0.856478	0.428239	+	0.903665i	$0.359134\pi$
$462$	9.64647e11	0.985098
$463$	−1.09774e12	−1.11016	−0.555080	−	0.831797i	$-0.687312\pi$
$463$	−1.09774e12	−1.11016	−0.555080	+	0.831797i	$0.687312\pi$
$464$	3.73395e10	0.0373970
$465$	−3.65112e12	−3.62150
$466$	5.72564e11	0.562454
$467$	6.31199e11	0.614102	0.307051	−	0.951693i	$-0.400658\pi$
$467$	6.31199e11	0.614102	0.307051	+	0.951693i	$0.400658\pi$
$468$	2.33580e12	2.25076
$469$	−1.45929e12	−1.39272
$470$	1.07723e12	1.01828
$471$	−3.26292e11	−0.305500
$472$	5.96044e10	0.0552763
$473$	6.32491e11	0.581004
$474$	2.82910e12	2.57422
$475$	4.75680e11	0.428739
$476$	2.76739e11	0.247081
$477$	3.72822e12	3.29738
$478$	−8.29948e10	−0.0727152
$479$	−1.03045e12	−0.894370	−0.447185	−	0.894442i	$-0.647573\pi$
$479$	−1.03045e12	−0.894370	−0.447185	+	0.894442i	$0.647573\pi$
$480$	6.59188e11	0.566792
$481$	5.65792e11	0.481952
$482$	−2.33990e11	−0.197463
$483$	−1.79473e11	−0.150050
$484$	−2.19356e11	−0.181696
$485$	2.60598e12	2.13862
$486$	−2.48100e12	−2.01727
$487$	−6.97434e11	−0.561853	−0.280927	−	0.959729i	$-0.590642\pi$
$487$	−6.97434e11	−0.561853	−0.280927	+	0.959729i	$0.590642\pi$
$488$	−4.07976e11	−0.325646
$489$	−1.75372e11	−0.138698
$490$	−2.28038e11	−0.178700
$491$	1.25643e12	0.975600	0.487800	−	0.872955i	$-0.337799\pi$
$491$	1.25643e12	0.975600	0.487800	+	0.872955i	$0.337799\pi$
$492$	3.72385e9	0.00286516
$493$	1.05115e11	0.0801409
$494$	−3.74154e11	−0.282670
$495$	4.66336e12	3.49121
$496$	3.80625e11	0.282377
$497$	−7.80650e11	−0.573922
$498$	1.48236e12	1.07999
$499$	−7.26198e11	−0.524327	−0.262164	−	0.965023i	$-0.584436\pi$
$499$	−7.26198e11	−0.524327	−0.262164	+	0.965023i	$0.584436\pi$
$500$	−1.02831e12	−0.735798
$501$	−2.80750e12	−1.99090
$502$	−2.19044e9	−0.00153944
$503$	1.01445e12	0.706602	0.353301	−	0.935510i	$-0.385059\pi$
$503$	1.01445e12	0.706602	0.353301	+	0.935510i	$0.385059\pi$
$504$	−1.22037e12	−0.842470
$505$	−2.89892e12	−1.98347
$506$	−7.14952e10	−0.0484841
$507$	5.73483e12	3.85465
$508$	−1.09499e12	−0.729494
$509$	−1.88479e12	−1.24461	−0.622306	−	0.782774i	$-0.713804\pi$
$509$	−1.88479e12	−1.24461	−0.622306	+	0.782774i	$0.713804\pi$
$510$	1.85569e12	1.21462
$511$	−1.33661e12	−0.867183
$512$	−6.87195e10	−0.0441942
$513$	1.07865e12	0.687626
$514$	−8.07328e11	−0.510171
$515$	−3.24518e12	−2.03285
$516$	−1.10990e12	−0.689222
$517$	−1.10198e12	−0.678372
$518$	−2.95606e11	−0.180397
$519$	−3.27827e12	−1.98332
$520$	1.73978e12	1.04347
$521$	1.02179e12	0.607562	0.303781	−	0.952742i	$-0.401751\pi$
$521$	1.02179e12	0.607562	0.303781	+	0.952742i	$0.401751\pi$
$522$	−4.63539e11	−0.273256
$523$	−1.23513e12	−0.721862	−0.360931	−	0.932593i	$-0.617541\pi$
$523$	−1.23513e12	−0.721862	−0.360931	+	0.932593i	$0.617541\pi$
$524$	9.73985e11	0.564367
$525$	5.67996e12	3.26309
$526$	−3.98542e11	−0.227007
$527$	1.07151e12	0.605127
$528$	−6.74334e11	−0.377592
$529$	−1.78785e12	−0.992615
$530$	2.77690e12	1.52869
$531$	−7.39940e11	−0.403898
$532$	1.95482e11	0.105805
$533$	9.82827e9	0.00527478
$534$	−1.11304e12	−0.592348
$535$	−3.37719e12	−1.78223
$536$	1.02011e12	0.533833
$537$	8.37784e11	0.434758
$538$	−1.95144e12	−1.00423
$539$	2.33277e11	0.119048
$540$	−5.01561e12	−2.53835
$541$	−8.75167e11	−0.439241	−0.219621	−	0.975585i	$-0.570482\pi$
$541$	−8.75167e11	−0.439241	−0.219621	+	0.975585i	$0.570482\pi$
$542$	1.60396e11	0.0798358
$543$	3.08648e12	1.52358
$544$	−1.93454e11	−0.0947070
$545$	5.92582e12	2.87716
$546$	−4.46767e12	−2.15137
$547$	1.97687e12	0.944138	0.472069	−	0.881562i	$-0.343507\pi$
$547$	1.97687e12	0.944138	0.472069	+	0.881562i	$0.343507\pi$
$548$	3.64493e10	0.0172654
$549$	5.06469e12	2.37945
$550$	2.26268e12	1.05437
$551$	7.42510e10	0.0343179
$552$	1.25460e11	0.0575147
$553$	−3.90112e12	−1.77389
$554$	−6.73929e11	−0.303962
$555$	−1.98221e12	−0.886811
$556$	5.44526e11	0.241648
$557$	2.44569e12	1.07660	0.538298	−	0.842755i	$-0.319068\pi$
$557$	2.44569e12	1.07660	0.538298	+	0.842755i	$0.319068\pi$
$558$	−4.72515e12	−2.06330
$559$	−2.92933e12	−1.26886
$560$	−9.08973e11	−0.390575
$561$	−1.89833e12	−0.809169
$562$	1.72520e12	0.729503
$563$	−4.54810e11	−0.190784	−0.0953920	−	0.995440i	$-0.530410\pi$
$563$	−4.54810e11	−0.190784	−0.0953920	+	0.995440i	$0.530410\pi$
$564$	1.93376e12	0.804725
$565$	7.74852e12	3.19890
$566$	−7.91552e11	−0.324195
$567$	7.01547e12	2.85058
$568$	5.45711e11	0.219986
$569$	4.19643e12	1.67832	0.839160	−	0.543885i	$-0.183047\pi$
$569$	4.19643e12	1.67832	0.839160	+	0.543885i	$0.183047\pi$
$570$	1.31082e12	0.520124
$571$	3.03648e12	1.19539	0.597694	−	0.801725i	$-0.296084\pi$
$571$	3.03648e12	1.19539	0.597694	+	0.801725i	$0.296084\pi$
$572$	−1.77975e12	−0.695149
$573$	−8.63241e11	−0.334531
$574$	−5.13492e9	−0.00197438
$575$	−4.20972e11	−0.160601
$576$	8.53097e11	0.322922
$577$	−5.21026e12	−1.95690	−0.978449	−	0.206487i	$-0.933797\pi$
$577$	−5.21026e12	−1.95690	−0.978449	+	0.206487i	$0.933797\pi$
$578$	1.35281e12	0.504152
$579$	6.52697e11	0.241356
$580$	−3.45260e11	−0.126683
$581$	−2.04406e12	−0.744221
$582$	4.67805e12	1.69010
$583$	−2.84071e12	−1.01840
$584$	9.34354e11	0.332394
$585$	−2.15979e13	−7.62449
$586$	5.96712e10	0.0209038
$587$	−2.61266e12	−0.908264	−0.454132	−	0.890935i	$-0.650050\pi$
$587$	−2.61266e12	−0.908264	−0.454132	+	0.890935i	$0.650050\pi$
$588$	−4.09356e11	−0.141222
$589$	7.56888e11	0.259127
$590$	−5.51132e11	−0.187250
$591$	−2.94435e12	−0.992764
$592$	2.06643e11	0.0691469
$593$	3.90508e12	1.29683	0.648417	−	0.761286i	$-0.275431\pi$
$593$	3.90508e12	1.29683	0.648417	+	0.761286i	$0.275431\pi$
$594$	5.13085e12	1.69103
$595$	−2.55887e12	−0.836993
$596$	1.47174e12	0.477773
$597$	−4.42890e12	−1.42696
$598$	3.31123e11	0.105885
$599$	1.12506e12	0.357070	0.178535	−	0.983934i	$-0.442864\pi$
$599$	1.12506e12	0.357070	0.178535	+	0.983934i	$0.442864\pi$
$600$	−3.97056e12	−1.25075
$601$	−7.83252e11	−0.244887	−0.122444	−	0.992475i	$-0.539073\pi$
$601$	−7.83252e11	−0.244887	−0.122444	+	0.992475i	$0.539073\pi$
$602$	1.53047e12	0.474942
$603$	−1.26638e13	−3.90066
$604$	9.37207e11	0.286530
$605$	2.02827e12	0.615499
$606$	−5.20391e12	−1.56748
$607$	2.19285e12	0.655633	0.327816	−	0.944741i	$-0.393687\pi$
$607$	2.19285e12	0.655633	0.327816	+	0.944741i	$0.393687\pi$
$608$	−1.36651e11	−0.0405554
$609$	8.86611e11	0.261189
$610$	3.77235e12	1.10313
$611$	5.10374e12	1.48150
$612$	2.40157e12	0.692013
$613$	−6.85830e11	−0.196175	−0.0980877	−	0.995178i	$-0.531273\pi$
$613$	−6.85830e11	−0.196175	−0.0980877	+	0.995178i	$0.531273\pi$
$614$	−3.15415e12	−0.895621
$615$	−3.44326e10	−0.00970581
$616$	9.29858e11	0.260198
$617$	4.20809e12	1.16897	0.584483	−	0.811406i	$-0.301297\pi$
$617$	4.20809e12	1.16897	0.584483	+	0.811406i	$0.301297\pi$
$618$	−5.82549e12	−1.60651
$619$	−5.42304e12	−1.48469	−0.742344	−	0.670019i	$-0.766286\pi$
$619$	−5.42304e12	−1.48469	−0.742344	+	0.670019i	$0.766286\pi$
$620$	−3.51945e12	−0.956560
$621$	−9.54596e11	−0.257577
$622$	4.09016e12	1.09568
$623$	1.53481e12	0.408186
$624$	3.12312e12	0.824627
$625$	2.37923e12	0.623701
$626$	−9.08105e11	−0.236348
$627$	−1.34094e12	−0.346502
$628$	−3.14524e11	−0.0806930
$629$	5.81725e11	0.148180
$630$	1.12842e13	2.85389
$631$	−4.74716e12	−1.19207	−0.596035	−	0.802959i	$-0.703258\pi$
$631$	−4.74716e12	−1.19207	−0.596035	+	0.802959i	$0.703258\pi$
$632$	2.72707e12	0.679938
$633$	6.68971e12	1.65612
$634$	−1.88234e12	−0.462698
$635$	1.01248e13	2.47118
$636$	4.98488e12	1.20809
$637$	−1.08040e12	−0.259991
$638$	3.53192e11	0.0843953
$639$	−6.77457e12	−1.60741
$640$	6.35415e11	0.149709
$641$	−5.71232e12	−1.33645	−0.668223	−	0.743961i	$-0.732945\pi$
$641$	−5.71232e12	−1.33645	−0.668223	+	0.743961i	$0.732945\pi$
$642$	−6.06247e12	−1.40845
$643$	8.29997e12	1.91482	0.957409	−	0.288736i	$-0.0932350\pi$
$643$	8.29997e12	1.91482	0.957409	+	0.288736i	$0.0932350\pi$
$644$	−1.73000e11	−0.0396333
$645$	1.02627e13	2.33476
$646$	−3.84691e11	−0.0869091
$647$	−1.16040e12	−0.260339	−0.130169	−	0.991492i	$-0.541552\pi$
$647$	−1.16040e12	−0.260339	−0.130169	+	0.991492i	$0.541552\pi$
$648$	−4.90414e12	−1.09264
$649$	5.63795e11	0.124744
$650$	−1.04794e13	−2.30264
$651$	9.03779e12	1.97219
$652$	−1.69047e11	−0.0366349
$653$	−1.07293e12	−0.230921	−0.115461	−	0.993312i	$-0.536834\pi$
$653$	−1.07293e12	−0.230921	−0.115461	+	0.993312i	$0.536834\pi$
$654$	1.06376e13	2.27375
$655$	−9.00596e12	−1.91181
$656$	3.58955e9	0.000756786 0
$657$	−1.15992e13	−2.42877
$658$	−2.66652e12	−0.554535
$659$	−9.14394e12	−1.88864	−0.944319	−	0.329031i	$-0.893278\pi$
$659$	−9.14394e12	−1.88864	−0.944319	+	0.329031i	$0.893278\pi$
$660$	6.23523e12	1.27910
$661$	8.78371e12	1.78966	0.894832	−	0.446403i	$-0.147295\pi$
$661$	8.78371e12	1.78966	0.894832	+	0.446403i	$0.147295\pi$
$662$	4.63101e12	0.937161
$663$	8.79195e12	1.76715
$664$	1.42890e12	0.285262
$665$	−1.80753e12	−0.358416
$666$	−2.56530e12	−0.505248
$667$	−6.57115e10	−0.0128551
$668$	−2.70625e12	−0.525865
$669$	1.25504e13	2.42237
$670$	−9.43246e12	−1.80837
$671$	−3.85903e12	−0.734897
$672$	−1.63172e12	−0.308662
$673$	7.23901e12	1.36023	0.680114	−	0.733106i	$-0.261930\pi$
$673$	7.23901e12	1.36023	0.680114	+	0.733106i	$0.261930\pi$
$674$	−1.57219e12	−0.293451
$675$	3.02111e13	5.60144
$676$	5.52801e12	1.01814
$677$	−5.18390e12	−0.948435	−0.474218	−	0.880408i	$-0.657269\pi$
$677$	−5.18390e12	−0.948435	−0.474218	+	0.880408i	$0.657269\pi$
$678$	1.39095e13	2.52801
$679$	−6.45070e12	−1.16464
$680$	1.78877e12	0.320822
$681$	−9.73901e12	−1.73521
$682$	3.60032e12	0.637252
$683$	2.31773e12	0.407539	0.203769	−	0.979019i	$-0.434681\pi$
$683$	2.31773e12	0.407539	0.203769	+	0.979019i	$0.434681\pi$
$684$	1.69642e12	0.296333
$685$	−3.37029e11	−0.0584871
$686$	4.34764e12	0.749541
$687$	5.15320e12	0.882616
$688$	−1.06987e12	−0.182047
$689$	1.31565e13	2.22409
$690$	−1.16007e12	−0.194833
$691$	−2.82266e12	−0.470985	−0.235492	−	0.971876i	$-0.575670\pi$
$691$	−2.82266e12	−0.470985	−0.235492	+	0.971876i	$0.575670\pi$
$692$	−3.16005e12	−0.523861
$693$	−1.15434e13	−1.90123
$694$	4.07845e12	0.667387
$695$	−5.03497e12	−0.818587
$696$	−6.19783e11	−0.100115
$697$	1.01050e10	0.00162177
$698$	−6.63508e12	−1.05803
$699$	−9.50376e12	−1.50573
$700$	5.47512e12	0.861891
$701$	−9.84845e12	−1.54041	−0.770206	−	0.637795i	$-0.779847\pi$
$701$	−9.84845e12	−1.54041	−0.770206	+	0.637795i	$0.779847\pi$
$702$	−2.37631e13	−3.69305
$703$	4.10918e11	0.0634535
$704$	−6.50015e11	−0.0997347
$705$	−1.78806e13	−2.72603
$706$	1.79899e12	0.272526
$707$	7.17582e12	1.08015
$708$	−9.89350e11	−0.147979
$709$	4.56333e12	0.678225	0.339112	−	0.940746i	$-0.389873\pi$
$709$	4.56333e12	0.678225	0.339112	+	0.940746i	$0.389873\pi$
$710$	−5.04592e12	−0.745209
$711$	−3.38544e13	−4.96823
$712$	−1.07290e12	−0.156459
$713$	−6.69840e11	−0.0970662
$714$	−4.59348e12	−0.661455
$715$	1.64565e13	2.35483
$716$	8.07571e11	0.114834
$717$	1.37760e12	0.194664
$718$	−2.45530e12	−0.344783
$719$	−9.06278e12	−1.26468	−0.632341	−	0.774690i	$-0.717906\pi$
$719$	−9.06278e12	−1.26468	−0.632341	+	0.774690i	$0.717906\pi$
$720$	−7.88816e12	−1.09391
$721$	8.03293e12	1.10705
$722$	−2.71737e11	−0.0372161
$723$	3.88390e12	0.528623
$724$	2.97517e12	0.402429
$725$	2.07964e12	0.279555
$726$	3.64100e12	0.486414
$727$	−1.15554e11	−0.0153420	−0.00767100	−	0.999971i	$-0.502442\pi$
$727$	−1.15554e11	−0.0153420	−0.00767100	+	0.999971i	$0.502442\pi$
$728$	−4.30655e12	−0.568249
$729$	1.76147e13	2.30995
$730$	−8.63951e12	−1.12599
$731$	−3.01182e12	−0.390122
$732$	6.77183e12	0.871779
$733$	1.08986e13	1.39444	0.697222	−	0.716855i	$-0.254419\pi$
$733$	1.08986e13	1.39444	0.697222	+	0.716855i	$0.254419\pi$
$734$	−4.96657e12	−0.631574
$735$	3.78511e12	0.478394
$736$	1.20935e11	0.0151916
$737$	9.64918e12	1.20472
$738$	−4.45614e10	−0.00552975
$739$	−8.91416e12	−1.09946	−0.549731	−	0.835341i	$-0.685270\pi$
$739$	−8.91416e12	−1.09946	−0.549731	+	0.835341i	$0.685270\pi$
$740$	−1.91072e12	−0.234237
$741$	6.21044e12	0.756729
$742$	−6.87379e12	−0.832490
$743$	6.16929e12	0.742652	0.371326	−	0.928503i	$-0.378903\pi$
$743$	6.16929e12	0.742652	0.371326	+	0.928503i	$0.378903\pi$
$744$	−6.31785e12	−0.755946
$745$	−1.36084e13	−1.61847
$746$	6.42943e12	0.760060
$747$	−1.77386e13	−2.08438
$748$	−1.82987e12	−0.213729
$749$	8.35971e12	0.970561
$750$	1.70685e13	1.96979
$751$	6.30977e12	0.723826	0.361913	−	0.932212i	$-0.382124\pi$
$751$	6.30977e12	0.723826	0.361913	+	0.932212i	$0.382124\pi$
$752$	1.86403e12	0.212555
$753$	3.63582e10	0.00412121
$754$	−1.63578e12	−0.184312
$755$	−8.66589e12	−0.970626
$756$	1.24154e13	1.38233
$757$	−9.13291e12	−1.01083	−0.505414	−	0.862877i	$-0.668660\pi$
$757$	−9.13291e12	−1.01083	−0.505414	+	0.862877i	$0.668660\pi$
$758$	6.63131e12	0.729605
$759$	1.18672e12	0.129796
$760$	1.26355e12	0.137382
$761$	5.56499e12	0.601497	0.300748	−	0.953704i	$-0.402764\pi$
$761$	5.56499e12	0.601497	0.300748	+	0.953704i	$0.402764\pi$
$762$	1.81752e13	1.95291
$763$	−1.46684e13	−1.56684
$764$	−8.32110e11	−0.0883610
$765$	−2.22061e13	−2.34421
$766$	−3.84755e12	−0.403789
$767$	−2.61117e12	−0.272430
$768$	1.14065e12	0.118311
$769$	1.09213e13	1.12618	0.563089	−	0.826396i	$-0.309613\pi$
$769$	1.09213e13	1.12618	0.563089	+	0.826396i	$0.309613\pi$
$770$	−8.59794e12	−0.881426
$771$	1.34005e13	1.36577
$772$	6.29158e11	0.0637503
$773$	−1.06326e13	−1.07111	−0.535553	−	0.844502i	$-0.679897\pi$
$773$	−1.06326e13	−1.07111	−0.535553	+	0.844502i	$0.679897\pi$
$774$	1.32816e13	1.33019
$775$	2.11991e13	2.11086
$776$	4.50934e12	0.446412
$777$	4.90665e12	0.482937
$778$	3.44621e12	0.337235
$779$	7.13797e9	0.000694475 0
$780$	−2.88779e13	−2.79344
$781$	5.16186e12	0.496451
$782$	3.40448e11	0.0325552
$783$	4.71579e12	0.448359
$784$	−3.94593e11	−0.0373016
$785$	2.90825e12	0.273349
$786$	−1.61668e13	−1.51085
$787$	−2.50979e12	−0.233212	−0.116606	−	0.993178i	$-0.537202\pi$
$787$	−2.50979e12	−0.233212	−0.116606	+	0.993178i	$0.537202\pi$
$788$	−2.83817e12	−0.262223
$789$	6.61525e12	0.607715
$790$	−2.52159e13	−2.30331
$791$	−1.91803e13	−1.74205
$792$	8.06941e12	0.728750
$793$	1.78727e13	1.60495
$794$	1.51483e13	1.35261
$795$	−4.60927e13	−4.09242
$796$	−4.26918e12	−0.376908
$797$	−1.17969e13	−1.03563	−0.517815	−	0.855493i	$-0.673254\pi$
$797$	−1.17969e13	−1.03563	−0.517815	+	0.855493i	$0.673254\pi$
$798$	−3.24474e12	−0.283248
$799$	5.24746e12	0.455500
$800$	−3.82737e12	−0.330366
$801$	1.33192e13	1.14323
$802$	−4.70976e11	−0.0401989
$803$	8.83802e12	0.750127
$804$	−1.69324e13	−1.42911
$805$	1.59965e12	0.134259
$806$	−1.66745e13	−1.39170
$807$	3.23912e13	2.68841
$808$	−5.01624e12	−0.414026
$809$	−6.47962e12	−0.531840	−0.265920	−	0.963995i	$-0.585676\pi$
$809$	−6.47962e12	−0.531840	−0.265920	+	0.963995i	$0.585676\pi$
$810$	4.53462e13	3.70133
$811$	−5.08224e12	−0.412536	−0.206268	−	0.978496i	$-0.566132\pi$
$811$	−5.08224e12	−0.412536	−0.206268	+	0.978496i	$0.566132\pi$
$812$	8.54636e11	0.0689889
$813$	−2.66235e12	−0.213727
$814$	1.95463e12	0.156046
$815$	1.56310e12	0.124102
$816$	3.21106e12	0.253538
$817$	−2.12748e12	−0.167058
$818$	1.53106e13	1.19565
$819$	5.34624e13	4.15213
$820$	−3.31908e10	−0.00256363
$821$	8.99329e11	0.0690835	0.0345418	−	0.999403i	$-0.489003\pi$
$821$	8.99329e11	0.0690835	0.0345418	+	0.999403i	$0.489003\pi$
$822$	−6.05008e11	−0.0462209
$823$	−7.62233e12	−0.579147	−0.289573	−	0.957156i	$-0.593513\pi$
$823$	−7.62233e12	−0.579147	−0.289573	+	0.957156i	$0.593513\pi$
$824$	−5.61540e12	−0.424334
$825$	−3.75574e13	−2.82262
$826$	1.36424e12	0.101972
$827$	2.54111e12	0.188907	0.0944537	−	0.995529i	$-0.469890\pi$
$827$	2.54111e12	0.188907	0.0944537	+	0.995529i	$0.469890\pi$
$828$	−1.50131e12	−0.111003
$829$	2.04803e13	1.50605	0.753027	−	0.657990i	$-0.228593\pi$
$829$	2.04803e13	1.50605	0.753027	+	0.657990i	$0.228593\pi$
$830$	−1.32123e13	−0.966334
$831$	1.11863e13	0.813731
$832$	3.01048e12	0.217812
$833$	−1.11083e12	−0.0799363
$834$	−9.03838e12	−0.646909
$835$	2.50234e13	1.78138
$836$	−1.29258e12	−0.0915228
$837$	4.80710e13	3.38547
$838$	1.28969e13	0.903415
$839$	1.60416e13	1.11769	0.558843	−	0.829273i	$-0.311245\pi$
$839$	1.60416e13	1.11769	0.558843	+	0.829273i	$0.311245\pi$
$840$	1.50877e13	1.04560
$841$	−1.41825e13	−0.977623
$842$	2.07603e12	0.142340
$843$	−2.86360e13	−1.95294
$844$	6.44846e12	0.437436
$845$	−5.11148e13	−3.44899
$846$	−2.31404e13	−1.55312
$847$	−5.02068e12	−0.335187
$848$	4.80511e12	0.319096
$849$	1.31387e13	0.867894
$850$	−1.07745e13	−0.707966
$851$	−3.63658e11	−0.0237690
$852$	−9.05805e12	−0.588920
$853$	1.69954e13	1.09916	0.549581	−	0.835440i	$-0.314787\pi$
$853$	1.69954e13	1.09916	0.549581	+	0.835440i	$0.314787\pi$
$854$	−9.33787e12	−0.600741
$855$	−1.56859e13	−1.00384
$856$	−5.84383e12	−0.372019
$857$	−4.81872e12	−0.305153	−0.152577	−	0.988292i	$-0.548757\pi$
$857$	−4.81872e12	−0.305153	−0.152577	+	0.988292i	$0.548757\pi$
$858$	2.95414e13	1.86097
$859$	1.43473e13	0.899084	0.449542	−	0.893259i	$-0.351587\pi$
$859$	1.43473e13	0.899084	0.449542	+	0.893259i	$0.351587\pi$
$860$	9.89256e12	0.616688
$861$	8.52326e10	0.00528556
$862$	2.08073e13	1.28361
$863$	1.16081e13	0.712380	0.356190	−	0.934414i	$-0.384076\pi$
$863$	1.16081e13	0.712380	0.356190	+	0.934414i	$0.384076\pi$
$864$	−8.67893e12	−0.529852
$865$	2.92194e13	1.77459
$866$	1.16990e13	0.706837
$867$	−2.24548e13	−1.34965
$868$	8.71186e12	0.520921
$869$	2.57952e13	1.53444
$870$	5.73083e12	0.339141
$871$	−4.46893e13	−2.63101
$872$	1.02539e13	0.600574
$873$	−5.59798e13	−3.26188
$874$	2.40485e11	0.0139408
$875$	−2.35362e13	−1.35738
$876$	−1.55090e13	−0.889845
$877$	6.32859e11	0.0361251	0.0180625	−	0.999837i	$-0.494250\pi$
$877$	6.32859e11	0.0361251	0.0180625	+	0.999837i	$0.494250\pi$
$878$	−1.66239e13	−0.944077
$879$	−9.90458e11	−0.0559611
$880$	6.01036e12	0.337854
$881$	1.78534e13	0.998457	0.499229	−	0.866470i	$-0.333617\pi$
$881$	1.78534e13	0.998457	0.499229	+	0.866470i	$0.333617\pi$
$882$	4.89855e12	0.272558
$883$	−3.78633e12	−0.209602	−0.104801	−	0.994493i	$-0.533421\pi$
$883$	−3.78633e12	−0.209602	−0.104801	+	0.994493i	$0.533421\pi$
$884$	8.47488e12	0.466765
$885$	9.14803e12	0.501283
$886$	6.76742e11	0.0368953
$887$	−1.59149e13	−0.863274	−0.431637	−	0.902048i	$-0.642064\pi$
$887$	−1.59149e13	−0.863274	−0.431637	+	0.902048i	$0.642064\pi$
$888$	−3.42998e12	−0.185112
$889$	−2.50624e13	−1.34575
$890$	9.92061e12	0.530009
$891$	−4.63881e13	−2.46579
$892$	1.20978e13	0.639829
$893$	3.70669e12	0.195054
$894$	−2.44288e13	−1.27904
$895$	−7.46721e12	−0.389004
$896$	−1.57287e12	−0.0815281
$897$	−5.49619e12	−0.283462
$898$	3.18936e12	0.163666
$899$	3.30907e12	0.168961
$900$	4.75137e13	2.41394
$901$	1.35270e13	0.683815
$902$	3.39534e10	0.00170787
$903$	−2.54037e13	−1.27146
$904$	1.34079e13	0.667733
$905$	−2.75100e13	−1.36324
$906$	−1.55563e13	−0.767062
$907$	−8.91543e12	−0.437431	−0.218715	−	0.975789i	$-0.570187\pi$
$907$	−8.91543e12	−0.437431	−0.218715	+	0.975789i	$0.570187\pi$
$908$	−9.38778e12	−0.458328
$909$	6.22726e13	3.02524
$910$	3.98206e13	1.92496
$911$	−2.65789e13	−1.27851	−0.639256	−	0.768994i	$-0.720757\pi$
$911$	−2.65789e13	−1.27851	−0.639256	+	0.768994i	$0.720757\pi$
$912$	2.26822e12	0.108570
$913$	1.35159e13	0.643763
$914$	−1.05240e13	−0.498796
$915$	−6.26158e13	−2.95317
$916$	4.96736e12	0.233129
$917$	2.22928e13	1.04113
$918$	−2.44322e13	−1.13546
$919$	1.52684e13	0.706110	0.353055	−	0.935603i	$-0.385143\pi$
$919$	1.52684e13	0.706110	0.353055	+	0.935603i	$0.385143\pi$
$920$	−1.11823e12	−0.0514619
$921$	5.23545e13	2.39765
$922$	−1.32889e13	−0.605621
$923$	−2.39067e13	−1.08421
$924$	−1.54343e13	−0.696569
$925$	1.15091e13	0.516896
$926$	1.75639e13	0.785001
$927$	6.97107e13	3.10056
$928$	−5.97431e11	−0.0264437
$929$	−3.74604e13	−1.65007	−0.825033	−	0.565084i	$-0.808844\pi$
$929$	−3.74604e13	−1.65007	−0.825033	+	0.565084i	$0.808844\pi$
$930$	5.84180e13	2.56079
$931$	−7.84664e11	−0.0342303
$932$	−9.16102e12	−0.397715
$933$	−6.78910e13	−2.93322
$934$	−1.00992e13	−0.434235
$935$	1.69199e13	0.724012
$936$	−3.73727e13	−1.59152
$937$	−2.62942e13	−1.11438	−0.557188	−	0.830386i	$-0.688120\pi$
$937$	−2.62942e13	−1.11438	−0.557188	+	0.830386i	$0.688120\pi$
$938$	2.33486e13	0.984799
$939$	1.50733e13	0.632721
$940$	−1.72357e13	−0.720036
$941$	3.58875e13	1.49207	0.746036	−	0.665906i	$-0.231955\pi$
$941$	3.58875e13	1.49207	0.746036	+	0.665906i	$0.231955\pi$
$942$	5.22066e12	0.216021
$943$	−6.31704e9	−0.000260143 0
$944$	−9.53670e11	−0.0390863
$945$	−1.14799e14	−4.68267
$946$	−1.01199e13	−0.410832
$947$	3.11985e13	1.26054	0.630272	−	0.776374i	$-0.282943\pi$
$947$	3.11985e13	1.26054	0.630272	+	0.776374i	$0.282943\pi$
$948$	−4.52655e13	−1.82025
$949$	−4.09325e13	−1.63821
$950$	−7.61088e12	−0.303165
$951$	3.12443e13	1.23868
$952$	−4.42782e12	−0.174713
$953$	3.83515e13	1.50614	0.753068	−	0.657942i	$-0.228573\pi$
$953$	3.83515e13	1.50614	0.753068	+	0.657942i	$0.228573\pi$
$954$	−5.96515e13	−2.33160
$955$	7.69411e12	0.299325
$956$	1.32792e12	0.0514174
$957$	−5.86250e12	−0.225933
$958$	1.64872e13	0.632415
$959$	8.34263e11	0.0318507
$960$	−1.05470e13	−0.400782
$961$	7.29182e12	0.275791
$962$	−9.05267e12	−0.340792
$963$	7.25464e13	2.71830
$964$	3.74383e12	0.139627
$965$	−5.81751e12	−0.215956
$966$	2.87156e12	0.106101
$967$	2.52076e13	0.927071	0.463536	−	0.886078i	$-0.346581\pi$
$967$	2.52076e13	0.927071	0.463536	+	0.886078i	$0.346581\pi$
$968$	3.50969e12	0.128478
$969$	6.38533e12	0.232662
$970$	−4.16957e13	−1.51223
$971$	−9.11601e12	−0.329093	−0.164546	−	0.986369i	$-0.552616\pi$
$971$	−9.11601e12	−0.329093	−0.164546	+	0.986369i	$0.552616\pi$
$972$	3.96961e13	1.42643
$973$	1.24633e13	0.445784
$974$	1.11589e13	0.397290
$975$	1.73944e14	6.16435
$976$	6.52762e12	0.230266
$977$	4.10489e13	1.44137	0.720685	−	0.693262i	$-0.243827\pi$
$977$	4.10489e13	1.44137	0.720685	+	0.693262i	$0.243827\pi$
$978$	2.80595e12	0.0980744
$979$	−1.01486e13	−0.353087
$980$	3.64860e12	0.126360
$981$	−1.27294e14	−4.38832
$982$	−2.01029e13	−0.689854
$983$	3.76886e12	0.128742	0.0643708	−	0.997926i	$-0.479496\pi$
$983$	3.76886e12	0.128742	0.0643708	+	0.997926i	$0.479496\pi$
$984$	−5.95816e10	−0.00202598
$985$	2.62431e13	0.888286
$986$	−1.68184e12	−0.0566682
$987$	4.42606e13	1.48453
$988$	5.98647e12	0.199878
$989$	1.88280e12	0.0625779
$990$	−7.46138e13	−2.46866
$991$	−3.54987e13	−1.16918	−0.584590	−	0.811329i	$-0.698745\pi$
$991$	−3.54987e13	−1.16918	−0.584590	+	0.811329i	$0.698745\pi$
$992$	−6.09000e12	−0.199671
$993$	−7.68682e13	−2.50885
$994$	1.24904e13	0.405824
$995$	3.94750e13	1.27679
$996$	−2.37177e13	−0.763670
$997$	−3.48328e13	−1.11650	−0.558252	−	0.829672i	$-0.688528\pi$
$997$	−3.48328e13	−1.11650	−0.558252	+	0.829672i	$0.688528\pi$
$998$	1.16192e13	0.370755
$999$	2.60980e13	0.829014

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.a.d.1.4	✓	4
3.2	odd	2		342.10.a.l.1.3		4
4.3	odd	2		304.10.a.e.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.a.d.1.4	✓	4	1.1	even	1	trivial
304.10.a.e.1.1		4	4.3	odd	2
342.10.a.l.1.3		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +265.578 q^{3} +256.000 q^{4} -2367.11 q^{5} -4249.24 q^{6} +5859.40 q^{7} -4096.00 q^{8} +50848.5 q^{9} +O(q^{10})\)	\(q-16.0000 q^{2} +265.578 q^{3} +256.000 q^{4} -2367.11 q^{5} -4249.24 q^{6} +5859.40 q^{7} -4096.00 q^{8} +50848.5 q^{9} +37873.7 q^{10} -38743.9 q^{11} +67987.9 q^{12} +179439. q^{13} -93750.4 q^{14} -628650. q^{15} +65536.0 q^{16} +184492. q^{17} -813576. q^{18} +130321. q^{19} -605979. q^{20} +1.55613e6 q^{21} +619902. q^{22} -115333. q^{23} -1.08781e6 q^{24} +3.65006e6 q^{25} -2.87102e6 q^{26} +8.27687e6 q^{27} +1.50001e6 q^{28} +569755. q^{29} +1.00584e7 q^{30} +5.80788e6 q^{31} -1.04858e6 q^{32} -1.02895e7 q^{33} -2.95187e6 q^{34} -1.38698e7 q^{35} +1.30172e7 q^{36} +3.15312e6 q^{37} -2.08514e6 q^{38} +4.76550e7 q^{39} +9.69566e6 q^{40} +54772.2 q^{41} -2.48980e7 q^{42} -1.63249e7 q^{43} -9.91844e6 q^{44} -1.20364e8 q^{45} +1.84533e6 q^{46} +2.84428e7 q^{47} +1.74049e7 q^{48} -6.02101e6 q^{49} -5.84010e7 q^{50} +4.89969e7 q^{51} +4.59363e7 q^{52} +7.33201e7 q^{53} -1.32430e8 q^{54} +9.17109e7 q^{55} -2.40001e7 q^{56} +3.46104e7 q^{57} -9.11608e6 q^{58} -1.45518e7 q^{59} -1.60935e8 q^{60} +9.96035e7 q^{61} -9.29260e7 q^{62} +2.97942e8 q^{63} +1.67772e7 q^{64} -4.24751e8 q^{65} +1.64632e8 q^{66} -2.49050e8 q^{67} +4.72299e7 q^{68} -3.06299e7 q^{69} +2.21917e8 q^{70} -1.33230e8 q^{71} -2.08276e8 q^{72} -2.28114e8 q^{73} -5.04499e7 q^{74} +9.69375e8 q^{75} +3.33622e7 q^{76} -2.27016e8 q^{77} -7.62479e8 q^{78} -6.65788e8 q^{79} -1.55131e8 q^{80} +1.19730e9 q^{81} -876356. q^{82} -3.48852e8 q^{83} +3.98368e8 q^{84} -4.36712e8 q^{85} +2.61199e8 q^{86} +1.51314e8 q^{87} +1.58695e8 q^{88} +2.61939e8 q^{89} +1.92582e9 q^{90} +1.05140e9 q^{91} -2.95252e7 q^{92} +1.54244e9 q^{93} -4.55084e8 q^{94} -3.08484e8 q^{95} -2.78478e8 q^{96} -1.10091e9 q^{97} +9.63361e7 q^{98} -1.97007e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9}+O(q^{10}) \) 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9	\( 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9} + 22320 q^{10} - 104249 q^{11} + 21504 q^{12} + 120486 q^{13} - 196912 q^{14} - 591090 q^{15} + 262144 q^{16} - 412139 q^{17} - 264608 q^{18} + 521284 q^{19} - 357120 q^{20} + 2437006 q^{21} + 1667984 q^{22} + 3010300 q^{23} - 344064 q^{24} + 9760585 q^{25} - 1927776 q^{26} + 12387978 q^{27} + 3150592 q^{28} + 6153240 q^{29} + 9457440 q^{30} + 12774024 q^{31} - 4194304 q^{32} - 3258022 q^{33} + 6594224 q^{34} + 9823425 q^{35} + 4233728 q^{36} + 20506048 q^{37} - 8340544 q^{38} + 69881444 q^{39} + 5713920 q^{40} + 11620300 q^{41} - 38992096 q^{42} + 7698327 q^{43} - 26687744 q^{44} - 124015815 q^{45} - 48164800 q^{46} - 31581083 q^{47} + 5505024 q^{48} + 18970383 q^{49} - 156169360 q^{50} - 8594812 q^{51} + 30844416 q^{52} + 72549422 q^{53} - 198207648 q^{54} + 21332505 q^{55} - 50409472 q^{56} + 10946964 q^{57} - 98451840 q^{58} - 149234120 q^{59} - 151319040 q^{60} + 129004373 q^{61} - 204384384 q^{62} + 102967551 q^{63} + 67108864 q^{64} + 124691700 q^{65} + 52128352 q^{66} + 132595266 q^{67} - 105507584 q^{68} - 45529972 q^{69} - 157174800 q^{70} - 47138482 q^{71} - 67739648 q^{72} - 39332795 q^{73} - 328096768 q^{74} + 824627010 q^{75} + 133448704 q^{76} - 165933719 q^{77} - 1118103104 q^{78} - 307010840 q^{79} - 91422720 q^{80} + 1305551744 q^{81} - 185924800 q^{82} - 746568232 q^{83} + 623873536 q^{84} - 105005985 q^{85} - 123173232 q^{86} - 82148208 q^{87} + 427003904 q^{88} + 286943482 q^{89} + 1984253040 q^{90} + 3155781114 q^{91} + 770636800 q^{92} + 1151901596 q^{93} + 505297328 q^{94} - 181797795 q^{95} - 88080384 q^{96} + 793519958 q^{97} - 303526128 q^{98} - 1681833809 q^{99}+O(q^{100}) \) 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9 + 22320 * q^10 - 104249 * q^11 + 21504 * q^12 + 120486 * q^13 - 196912 * q^14 - 591090 * q^15 + 262144 * q^16 - 412139 * q^17 - 264608 * q^18 + 521284 * q^19 - 357120 * q^20 + 2437006 * q^21 + 1667984 * q^22 + 3010300 * q^23 - 344064 * q^24 + 9760585 * q^25 - 1927776 * q^26 + 12387978 * q^27 + 3150592 * q^28 + 6153240 * q^29 + 9457440 * q^30 + 12774024 * q^31 - 4194304 * q^32 - 3258022 * q^33 + 6594224 * q^34 + 9823425 * q^35 + 4233728 * q^36 + 20506048 * q^37 - 8340544 * q^38 + 69881444 * q^39 + 5713920 * q^40 + 11620300 * q^41 - 38992096 * q^42 + 7698327 * q^43 - 26687744 * q^44 - 124015815 * q^45 - 48164800 * q^46 - 31581083 * q^47 + 5505024 * q^48 + 18970383 * q^49 - 156169360 * q^50 - 8594812 * q^51 + 30844416 * q^52 + 72549422 * q^53 - 198207648 * q^54 + 21332505 * q^55 - 50409472 * q^56 + 10946964 * q^57 - 98451840 * q^58 - 149234120 * q^59 - 151319040 * q^60 + 129004373 * q^61 - 204384384 * q^62 + 102967551 * q^63 + 67108864 * q^64 + 124691700 * q^65 + 52128352 * q^66 + 132595266 * q^67 - 105507584 * q^68 - 45529972 * q^69 - 157174800 * q^70 - 47138482 * q^71 - 67739648 * q^72 - 39332795 * q^73 - 328096768 * q^74 + 824627010 * q^75 + 133448704 * q^76 - 165933719 * q^77 - 1118103104 * q^78 - 307010840 * q^79 - 91422720 * q^80 + 1305551744 * q^81 - 185924800 * q^82 - 746568232 * q^83 + 623873536 * q^84 - 105005985 * q^85 - 123173232 * q^86 - 82148208 * q^87 + 427003904 * q^88 + 286943482 * q^89 + 1984253040 * q^90 + 3155781114 * q^91 + 770636800 * q^92 + 1151901596 * q^93 + 505297328 * q^94 - 181797795 * q^95 - 88080384 * q^96 + 793519958 * q^97 - 303526128 * q^98 - 1681833809 * q^99

Introduction

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