LMFDB - Embedded newform 21.10.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,10,Mod(1,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("21.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	21.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:	$10.8157525594$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{2353}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 588 $ x^2 - x - 588
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$24.7539$ of defining polynomial
Character	$\chi$	$=$	21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-19.7539 q^{2} -81.0000 q^{3} -121.785 q^{4} +2282.77 q^{5} +1600.06 q^{6} -2401.00 q^{7} +12519.7 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-19.7539 q^{2} -81.0000 q^{3} -121.785 q^{4} +2282.77 q^{5} +1600.06 q^{6} -2401.00 q^{7} +12519.7 q^{8} +6561.00 q^{9} -45093.5 q^{10} -59533.4 q^{11} +9864.57 q^{12} +40644.6 q^{13} +47429.0 q^{14} -184904. q^{15} -184959. q^{16} -664562. q^{17} -129605. q^{18} -117597. q^{19} -278007. q^{20} +194481. q^{21} +1.17601e6 q^{22} -878334. q^{23} -1.01410e6 q^{24} +3.25792e6 q^{25} -802888. q^{26} -531441. q^{27} +292405. q^{28} +4.29526e6 q^{29} +3.65258e6 q^{30} -4.59898e6 q^{31} -2.75644e6 q^{32} +4.82220e6 q^{33} +1.31277e7 q^{34} -5.48093e6 q^{35} -799030. q^{36} -8.36034e6 q^{37} +2.32300e6 q^{38} -3.29221e6 q^{39} +2.85796e7 q^{40} -2.74739e7 q^{41} -3.84175e6 q^{42} -2.81850e7 q^{43} +7.25026e6 q^{44} +1.49773e7 q^{45} +1.73505e7 q^{46} -7.05802e6 q^{47} +1.49817e7 q^{48} +5.76480e6 q^{49} -6.43564e7 q^{50} +5.38295e7 q^{51} -4.94989e6 q^{52} -1.83901e6 q^{53} +1.04980e7 q^{54} -1.35901e8 q^{55} -3.00598e7 q^{56} +9.52537e6 q^{57} -8.48479e7 q^{58} -1.47578e8 q^{59} +2.25185e7 q^{60} +1.03231e8 q^{61} +9.08477e7 q^{62} -1.57530e7 q^{63} +1.49149e8 q^{64} +9.27823e7 q^{65} -9.52572e7 q^{66} +3.01386e8 q^{67} +8.09336e7 q^{68} +7.11451e7 q^{69} +1.08270e8 q^{70} -2.79118e8 q^{71} +8.21417e7 q^{72} +1.48537e8 q^{73} +1.65149e8 q^{74} -2.63891e8 q^{75} +1.43215e7 q^{76} +1.42940e8 q^{77} +6.50339e7 q^{78} -7.91332e7 q^{79} -4.22218e8 q^{80} +4.30467e7 q^{81} +5.42717e8 q^{82} +4.46149e8 q^{83} -2.36848e7 q^{84} -1.51704e9 q^{85} +5.56762e8 q^{86} -3.47916e8 q^{87} -7.45340e8 q^{88} -5.24499e8 q^{89} -2.95859e8 q^{90} -9.75876e7 q^{91} +1.06968e8 q^{92} +3.72517e8 q^{93} +1.39423e8 q^{94} -2.68447e8 q^{95} +2.23271e8 q^{96} +2.83183e8 q^{97} -1.13877e8 q^{98} -3.90598e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 9 q^{2} - 162 q^{3} + 193 q^{4} + 1170 q^{5} - 729 q^{6} - 4802 q^{7} + 6849 q^{8} + 13122 q^{9}+O(q^{10}) $ 2 * q + 9 * q^2 - 162 * q^3 + 193 * q^4 + 1170 * q^5 - 729 * q^6 - 4802 * q^7 + 6849 * q^8 + 13122 * q^9	\( 2 q + 9 q^{2} - 162 q^{3} + 193 q^{4} + 1170 q^{5} - 729 q^{6} - 4802 q^{7} + 6849 q^{8} + 13122 q^{9} - 77090 q^{10} - 145746 q^{11} - 15633 q^{12} + 86528 q^{13} - 21609 q^{14} - 94770 q^{15} - 509183 q^{16} - 229842 q^{17} + 59049 q^{18} - 221224 q^{19} - 628290 q^{20} + 388962 q^{21} - 1302932 q^{22} - 2035782 q^{23} - 554769 q^{24} + 2543050 q^{25} + 516438 q^{26} - 1062882 q^{27} - 463393 q^{28} + 9756252 q^{29} + 6244290 q^{30} + 204000 q^{31} - 9175743 q^{32} + 11805426 q^{33} + 25627554 q^{34} - 2809170 q^{35} + 1266273 q^{36} - 13959816 q^{37} - 656676 q^{38} - 7008768 q^{39} + 34889790 q^{40} - 42362550 q^{41} + 1750329 q^{42} - 4763912 q^{43} - 19888164 q^{44} + 7676370 q^{45} - 15930600 q^{46} - 48278484 q^{47} + 41243823 q^{48} + 11529602 q^{49} - 84911625 q^{50} + 18617202 q^{51} + 9493510 q^{52} - 108980352 q^{53} - 4782969 q^{54} - 39966160 q^{55} - 16444449 q^{56} + 17919144 q^{57} + 72176782 q^{58} - 188376804 q^{59} + 50891490 q^{60} + 19722092 q^{61} + 228951936 q^{62} - 31505922 q^{63} + 130572161 q^{64} + 41724540 q^{65} + 105537492 q^{66} + 70274396 q^{67} + 217776834 q^{68} + 164898342 q^{69} + 185093090 q^{70} - 382044186 q^{71} + 44936289 q^{72} + 191785896 q^{73} + 4142502 q^{74} - 205987050 q^{75} - 18298628 q^{76} + 349936146 q^{77} - 41831478 q^{78} - 72592148 q^{79} - 61430850 q^{80} + 86093442 q^{81} + 114611450 q^{82} + 187994232 q^{83} + 37534833 q^{84} - 2000786580 q^{85} + 1230207804 q^{86} - 790256412 q^{87} - 256454052 q^{88} + 42930954 q^{89} - 505787490 q^{90} - 207753728 q^{91} - 257379192 q^{92} - 16524000 q^{93} - 1045824480 q^{94} - 153134280 q^{95} + 743235183 q^{96} + 1726854096 q^{97} + 51883209 q^{98} - 956239506 q^{99}+O(q^{100}) \) 2 * q + 9 * q^2 - 162 * q^3 + 193 * q^4 + 1170 * q^5 - 729 * q^6 - 4802 * q^7 + 6849 * q^8 + 13122 * q^9 - 77090 * q^10 - 145746 * q^11 - 15633 * q^12 + 86528 * q^13 - 21609 * q^14 - 94770 * q^15 - 509183 * q^16 - 229842 * q^17 + 59049 * q^18 - 221224 * q^19 - 628290 * q^20 + 388962 * q^21 - 1302932 * q^22 - 2035782 * q^23 - 554769 * q^24 + 2543050 * q^25 + 516438 * q^26 - 1062882 * q^27 - 463393 * q^28 + 9756252 * q^29 + 6244290 * q^30 + 204000 * q^31 - 9175743 * q^32 + 11805426 * q^33 + 25627554 * q^34 - 2809170 * q^35 + 1266273 * q^36 - 13959816 * q^37 - 656676 * q^38 - 7008768 * q^39 + 34889790 * q^40 - 42362550 * q^41 + 1750329 * q^42 - 4763912 * q^43 - 19888164 * q^44 + 7676370 * q^45 - 15930600 * q^46 - 48278484 * q^47 + 41243823 * q^48 + 11529602 * q^49 - 84911625 * q^50 + 18617202 * q^51 + 9493510 * q^52 - 108980352 * q^53 - 4782969 * q^54 - 39966160 * q^55 - 16444449 * q^56 + 17919144 * q^57 + 72176782 * q^58 - 188376804 * q^59 + 50891490 * q^60 + 19722092 * q^61 + 228951936 * q^62 - 31505922 * q^63 + 130572161 * q^64 + 41724540 * q^65 + 105537492 * q^66 + 70274396 * q^67 + 217776834 * q^68 + 164898342 * q^69 + 185093090 * q^70 - 382044186 * q^71 + 44936289 * q^72 + 191785896 * q^73 + 4142502 * q^74 - 205987050 * q^75 - 18298628 * q^76 + 349936146 * q^77 - 41831478 * q^78 - 72592148 * q^79 - 61430850 * q^80 + 86093442 * q^81 + 114611450 * q^82 + 187994232 * q^83 + 37534833 * q^84 - 2000786580 * q^85 + 1230207804 * q^86 - 790256412 * q^87 - 256454052 * q^88 + 42930954 * q^89 - 505787490 * q^90 - 207753728 * q^91 - 257379192 * q^92 - 16524000 * q^93 - 1045824480 * q^94 - 153134280 * q^95 + 743235183 * q^96 + 1726854096 * q^97 + 51883209 * q^98 - 956239506 * 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 $

$2$	−19.7539	−0.873006	−0.436503	−	0.899703i	$-0.643783\pi$
$2$	−19.7539	−0.873006	−0.436503	+	0.899703i	$0.643783\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−121.785	−0.237861
$5$	2282.77	1.63342	0.816709	−	0.577050i	$-0.195796\pi$
$5$	2282.77	1.63342	0.816709	+	0.577050i	$0.195796\pi$
$6$	1600.06	0.504030
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	12519.7	1.08066
$9$	6561.00	0.333333
$10$	−45093.5	−1.42598
$11$	−59533.4	−1.22601	−0.613004	−	0.790080i	$-0.710039\pi$
$11$	−59533.4	−1.22601	−0.613004	+	0.790080i	$0.710039\pi$
$12$	9864.57	0.137329
$13$	40644.6	0.394691	0.197346	−	0.980334i	$-0.436768\pi$
$13$	40644.6	0.394691	0.197346	+	0.980334i	$0.436768\pi$
$14$	47429.0	0.329965
$15$	−184904.	−0.943054
$16$	−184959.	−0.705561
$17$	−664562.	−1.92981	−0.964907	−	0.262592i	$-0.915423\pi$
$17$	−664562.	−1.92981	−0.964907	+	0.262592i	$0.915423\pi$
$18$	−129605.	−0.291002
$19$	−117597.	−0.207017	−0.103508	−	0.994629i	$-0.533007\pi$
$19$	−117597.	−0.207017	−0.103508	+	0.994629i	$0.533007\pi$
$20$	−278007.	−0.388526
$21$	194481.	0.218218
$22$	1.17601e6	1.07031
$23$	−878334.	−0.654462	−0.327231	−	0.944944i	$-0.606116\pi$
$23$	−878334.	−0.654462	−0.327231	+	0.944944i	$0.606116\pi$
$24$	−1.01410e6	−0.623919
$25$	3.25792e6	1.66805
$26$	−802888.	−0.344568
$27$	−531441.	−0.192450
$28$	292405.	0.0899030
$29$	4.29526e6	1.12771	0.563856	−	0.825873i	$-0.309317\pi$
$29$	4.29526e6	1.12771	0.563856	+	0.825873i	$0.309317\pi$
$30$	3.65258e6	0.823292
$31$	−4.59898e6	−0.894405	−0.447202	−	0.894433i	$-0.647580\pi$
$31$	−4.59898e6	−0.894405	−0.447202	+	0.894433i	$0.647580\pi$
$32$	−2.75644e6	−0.464701
$33$	4.82220e6	0.707836
$34$	1.31277e7	1.68474
$35$	−5.48093e6	−0.617374
$36$	−799030.	−0.0792870
$37$	−8.36034e6	−0.733358	−0.366679	−	0.930347i	$-0.619505\pi$
$37$	−8.36034e6	−0.733358	−0.366679	+	0.930347i	$0.619505\pi$
$38$	2.32300e6	0.180727
$39$	−3.29221e6	−0.227875
$40$	2.85796e7	1.76517
$41$	−2.74739e7	−1.51843	−0.759213	−	0.650842i	$-0.774416\pi$
$41$	−2.74739e7	−1.51843	−0.759213	+	0.650842i	$0.774416\pi$
$42$	−3.84175e6	−0.190505
$43$	−2.81850e7	−1.25721	−0.628607	−	0.777723i	$-0.716375\pi$
$43$	−2.81850e7	−1.25721	−0.628607	+	0.777723i	$0.716375\pi$
$44$	7.25026e6	0.291619
$45$	1.49773e7	0.544473
$46$	1.73505e7	0.571349
$47$	−7.05802e6	−0.210981	−0.105490	−	0.994420i	$-0.533641\pi$
$47$	−7.05802e6	−0.210981	−0.105490	+	0.994420i	$0.533641\pi$
$48$	1.49817e7	0.407356
$49$	5.76480e6	0.142857
$50$	−6.43564e7	−1.45622
$51$	5.38295e7	1.11418
$52$	−4.94989e6	−0.0938816
$53$	−1.83901e6	−0.0320142	−0.0160071	−	0.999872i	$-0.505095\pi$
$53$	−1.83901e6	−0.0320142	−0.0160071	+	0.999872i	$0.505095\pi$
$54$	1.04980e7	0.168010
$55$	−1.35901e8	−2.00258
$56$	−3.00598e7	−0.408451
$57$	9.52537e6	0.119521
$58$	−8.48479e7	−0.984499
$59$	−1.47578e8	−1.58558	−0.792790	−	0.609495i	$-0.791372\pi$
$59$	−1.47578e8	−1.58558	−0.792790	+	0.609495i	$0.791372\pi$
$60$	2.25185e7	0.224316
$61$	1.03231e8	0.954610	0.477305	−	0.878738i	$-0.341614\pi$
$61$	1.03231e8	0.954610	0.477305	+	0.878738i	$0.341614\pi$
$62$	9.08477e7	0.780820
$63$	−1.57530e7	−0.125988
$64$	1.49149e8	1.11125
$65$	9.27823e7	0.644696
$66$	−9.52572e7	−0.617945
$67$	3.01386e8	1.82720	0.913601	−	0.406611i	$-0.133290\pi$
$67$	3.01386e8	1.82720	0.913601	+	0.406611i	$0.133290\pi$
$68$	8.09336e7	0.459027
$69$	7.11451e7	0.377854
$70$	1.08270e8	0.538971
$71$	−2.79118e8	−1.30354	−0.651772	−	0.758415i	$-0.725974\pi$
$71$	−2.79118e8	−1.30354	−0.651772	+	0.758415i	$0.725974\pi$
$72$	8.21417e7	0.360220
$73$	1.48537e8	0.612184	0.306092	−	0.952002i	$-0.400978\pi$
$73$	1.48537e8	0.612184	0.306092	+	0.952002i	$0.400978\pi$
$74$	1.65149e8	0.640226
$75$	−2.63891e8	−0.963051
$76$	1.43215e7	0.0492412
$77$	1.42940e8	0.463388
$78$	6.50339e7	0.198936
$79$	−7.91332e7	−0.228579	−0.114290	−	0.993447i	$-0.536459\pi$
$79$	−7.91332e7	−0.228579	−0.114290	+	0.993447i	$0.536459\pi$
$80$	−4.22218e8	−1.15248
$81$	4.30467e7	0.111111
$82$	5.42717e8	1.32559
$83$	4.46149e8	1.03188	0.515940	−	0.856625i	$-0.327443\pi$
$83$	4.46149e8	1.03188	0.515940	+	0.856625i	$0.327443\pi$
$84$	−2.36848e7	−0.0519055
$85$	−1.51704e9	−3.15219
$86$	5.56762e8	1.09756
$87$	−3.47916e8	−0.651085
$88$	−7.45340e8	−1.32490
$89$	−5.24499e8	−0.886113	−0.443057	−	0.896494i	$-0.646106\pi$
$89$	−5.24499e8	−0.886113	−0.443057	+	0.896494i	$0.646106\pi$
$90$	−2.95859e8	−0.475328
$91$	−9.75876e7	−0.149179
$92$	1.06968e8	0.155671
$93$	3.72517e8	0.516385
$94$	1.39423e8	0.184187
$95$	−2.68447e8	−0.338145
$96$	2.23271e8	0.268295
$97$	2.83183e8	0.324784	0.162392	−	0.986726i	$-0.448079\pi$
$97$	2.83183e8	0.324784	0.162392	+	0.986726i	$0.448079\pi$
$98$	−1.13877e8	−0.124715
$99$	−3.90598e8	−0.408669
$100$	−3.96765e8	−0.396765
$101$	1.52969e9	1.46271	0.731355	−	0.681997i	$-0.238888\pi$
$101$	1.52969e9	1.46271	0.731355	+	0.681997i	$0.238888\pi$
$102$	−1.06334e9	−0.972684
$103$	7.25190e8	0.634869	0.317435	−	0.948280i	$-0.397179\pi$
$103$	7.25190e8	0.634869	0.317435	+	0.948280i	$0.397179\pi$
$104$	5.08858e8	0.426527
$105$	4.43956e8	0.356441
$106$	3.63276e7	0.0279486
$107$	3.08449e8	0.227487	0.113743	−	0.993510i	$-0.463716\pi$
$107$	3.08449e8	0.227487	0.113743	+	0.993510i	$0.463716\pi$
$108$	6.47214e7	0.0457764
$109$	−2.19394e9	−1.48869	−0.744347	−	0.667793i	$-0.767239\pi$
$109$	−2.19394e9	−1.48869	−0.744347	+	0.667793i	$0.767239\pi$
$110$	2.68457e9	1.74827
$111$	6.77188e8	0.423405
$112$	4.44086e8	0.266677
$113$	−7.34737e8	−0.423915	−0.211958	−	0.977279i	$-0.567984\pi$
$113$	−7.34737e8	−0.423915	−0.211958	+	0.977279i	$0.567984\pi$
$114$	−1.88163e8	−0.104343
$115$	−2.00504e9	−1.06901
$116$	−5.23097e8	−0.268239
$117$	2.66669e8	0.131564
$118$	2.91524e9	1.38422
$119$	1.59561e9	0.729401
$120$	−2.31495e9	−1.01912
$121$	1.18627e9	0.503096
$122$	−2.03921e9	−0.833380
$123$	2.22539e9	0.876664
$124$	5.60086e8	0.212744
$125$	2.97854e9	1.09121
$126$	3.11182e8	0.109988
$127$	1.61072e9	0.549420	0.274710	−	0.961527i	$-0.411418\pi$
$127$	1.61072e9	0.549420	0.274710	+	0.961527i	$0.411418\pi$
$128$	−1.53498e9	−0.505425
$129$	2.28298e9	0.725853
$130$	−1.83281e9	−0.562823
$131$	−1.95305e9	−0.579419	−0.289710	−	0.957115i	$-0.593559\pi$
$131$	−1.95305e9	−0.579419	−0.289710	+	0.957115i	$0.593559\pi$
$132$	−5.87271e8	−0.168367
$133$	2.82351e8	0.0782450
$134$	−5.95354e9	−1.59516
$135$	−1.21316e9	−0.314351
$136$	−8.32012e9	−2.08547
$137$	−4.50559e8	−0.109272	−0.0546361	−	0.998506i	$-0.517400\pi$
$137$	−4.50559e8	−0.109272	−0.0546361	+	0.998506i	$0.517400\pi$
$138$	−1.40539e9	−0.329869
$139$	6.05262e9	1.37524	0.687618	−	0.726073i	$-0.258656\pi$
$139$	6.05262e9	1.37524	0.687618	+	0.726073i	$0.258656\pi$
$140$	6.67494e8	0.146849
$141$	5.71700e8	0.121810
$142$	5.51366e9	1.13800
$143$	−2.41971e9	−0.483895
$144$	−1.21351e9	−0.235187
$145$	9.80509e9	1.84202
$146$	−2.93418e9	−0.534440
$147$	−4.66949e8	−0.0824786
$148$	1.01816e9	0.174437
$149$	−5.73416e9	−0.953084	−0.476542	−	0.879152i	$-0.658110\pi$
$149$	−5.73416e9	−0.953084	−0.476542	+	0.879152i	$0.658110\pi$
$150$	5.21287e9	0.840749
$151$	−3.15569e9	−0.493967	−0.246984	−	0.969020i	$-0.579439\pi$
$151$	−3.15569e9	−0.493967	−0.246984	+	0.969020i	$0.579439\pi$
$152$	−1.47228e9	−0.223715
$153$	−4.36019e9	−0.643271
$154$	−2.82361e9	−0.404540
$155$	−1.04984e10	−1.46094
$156$	4.00941e8	0.0542026
$157$	4.33763e9	0.569776	0.284888	−	0.958561i	$-0.408044\pi$
$157$	4.33763e9	0.569776	0.284888	+	0.958561i	$0.408044\pi$
$158$	1.56319e9	0.199551
$159$	1.48960e8	0.0184834
$160$	−6.29232e9	−0.759050
$161$	2.10888e9	0.247363
$162$	−8.50339e8	−0.0970006
$163$	6.14747e8	0.0682106	0.0341053	−	0.999418i	$-0.489142\pi$
$163$	6.14747e8	0.0682106	0.0341053	+	0.999418i	$0.489142\pi$
$164$	3.34591e9	0.361174
$165$	1.10080e10	1.15619
$166$	−8.81317e9	−0.900836
$167$	−9.79513e9	−0.974510	−0.487255	−	0.873260i	$-0.662002\pi$
$167$	−9.79513e9	−0.974510	−0.487255	+	0.873260i	$0.662002\pi$
$168$	2.43484e9	0.235819
$169$	−8.95252e9	−0.844219
$170$	2.99675e10	2.75188
$171$	−7.71555e8	−0.0690056
$172$	3.43250e9	0.299042
$173$	−2.30438e9	−0.195590	−0.0977950	−	0.995207i	$-0.531179\pi$
$173$	−2.30438e9	−0.195590	−0.0977950	+	0.995207i	$0.531179\pi$
$174$	6.87268e9	0.568401
$175$	−7.82226e9	−0.630465
$176$	1.10112e10	0.865024
$177$	1.19538e10	0.915435
$178$	1.03609e10	0.773582
$179$	1.29453e10	0.942481	0.471241	−	0.882005i	$-0.343806\pi$
$179$	1.29453e10	0.942481	0.471241	+	0.882005i	$0.343806\pi$
$180$	−1.82400e9	−0.129509
$181$	7.07259e9	0.489807	0.244903	−	0.969548i	$-0.421244\pi$
$181$	7.07259e9	0.489807	0.244903	+	0.969548i	$0.421244\pi$
$182$	1.92773e9	0.130234
$183$	−8.36172e9	−0.551145
$184$	−1.09965e10	−0.707251
$185$	−1.90847e10	−1.19788
$186$	−7.35866e9	−0.450807
$187$	3.95636e10	2.36597
$188$	8.59560e8	0.0501840
$189$	1.27599e9	0.0727393
$190$	5.30287e9	0.295202
$191$	−3.43999e10	−1.87028	−0.935141	−	0.354275i	$-0.884728\pi$
$191$	−3.43999e10	−1.87028	−0.935141	+	0.354275i	$0.884728\pi$
$192$	−1.20811e10	−0.641579
$193$	−7.69676e9	−0.399301	−0.199650	−	0.979867i	$-0.563981\pi$
$193$	−7.69676e9	−0.399301	−0.199650	+	0.979867i	$0.563981\pi$
$194$	−5.59396e9	−0.283538
$195$	−7.51536e9	−0.372215
$196$	−7.02065e8	−0.0339801
$197$	4.11021e10	1.94431	0.972155	−	0.234337i	$-0.0752920\pi$
$197$	4.11021e10	1.94431	0.972155	+	0.234337i	$0.0752920\pi$
$198$	7.71583e9	0.356771
$199$	−4.55641e9	−0.205960	−0.102980	−	0.994683i	$-0.532838\pi$
$199$	−4.55641e9	−0.205960	−0.102980	+	0.994683i	$0.532838\pi$
$200$	4.07881e10	1.80260
$201$	−2.44123e10	−1.05494
$202$	−3.02173e10	−1.27695
$203$	−1.03129e10	−0.426235
$204$	−6.55562e9	−0.265020
$205$	−6.27167e10	−2.48022
$206$	−1.43253e10	−0.554244
$207$	−5.76275e9	−0.218154
$208$	−7.51757e9	−0.278479
$209$	7.00095e9	0.253804
$210$	−8.76984e9	−0.311175
$211$	1.50665e10	0.523288	0.261644	−	0.965165i	$-0.415735\pi$
$211$	1.50665e10	0.523288	0.261644	+	0.965165i	$0.415735\pi$
$212$	2.23964e8	0.00761493
$213$	2.26086e10	0.752601
$214$	−6.09306e9	−0.198597
$215$	−6.43398e10	−2.05356
$216$	−6.65348e9	−0.207973
$217$	1.10422e10	0.338053
$218$	4.33388e10	1.29964
$219$	−1.20315e10	−0.353445
$220$	1.65507e10	0.476336
$221$	−2.70108e10	−0.761681
$222$	−1.33771e10	−0.369635
$223$	−1.57308e10	−0.425969	−0.212985	−	0.977056i	$-0.568318\pi$
$223$	−1.57308e10	−0.425969	−0.212985	+	0.977056i	$0.568318\pi$
$224$	6.61821e9	0.175640
$225$	2.13752e10	0.556018
$226$	1.45139e10	0.370081
$227$	5.79336e10	1.44815	0.724076	−	0.689720i	$-0.242266\pi$
$227$	5.79336e10	1.44815	0.724076	+	0.689720i	$0.242266\pi$
$228$	−1.16004e9	−0.0284294
$229$	3.89790e10	0.936637	0.468318	−	0.883560i	$-0.344860\pi$
$229$	3.89790e10	0.936637	0.468318	+	0.883560i	$0.344860\pi$
$230$	3.96072e10	0.933252
$231$	−1.15781e10	−0.267537
$232$	5.37753e10	1.21867
$233$	3.27047e10	0.726957	0.363479	−	0.931603i	$-0.381589\pi$
$233$	3.27047e10	0.726957	0.363479	+	0.931603i	$0.381589\pi$
$234$	−5.26775e9	−0.114856
$235$	−1.61118e10	−0.344619
$236$	1.79728e10	0.377148
$237$	6.40979e9	0.131970
$238$	−3.15195e10	−0.636771
$239$	−1.02805e10	−0.203810	−0.101905	−	0.994794i	$-0.532494\pi$
$239$	−1.02805e10	−0.203810	−0.101905	+	0.994794i	$0.532494\pi$
$240$	3.41997e10	0.665382
$241$	7.00691e10	1.33798	0.668991	−	0.743271i	$-0.266727\pi$
$241$	7.00691e10	1.33798	0.668991	+	0.743271i	$0.266727\pi$
$242$	−2.34335e10	−0.439206
$243$	−3.48678e9	−0.0641500
$244$	−1.25720e10	−0.227064
$245$	1.31597e10	0.233345
$246$	−4.39600e10	−0.765332
$247$	−4.77969e9	−0.0817077
$248$	−5.75779e10	−0.966547
$249$	−3.61381e10	−0.595756
$250$	−5.88377e10	−0.952633
$251$	−5.08170e10	−0.808122	−0.404061	−	0.914732i	$-0.632402\pi$
$251$	−5.08170e10	−0.808122	−0.404061	+	0.914732i	$0.632402\pi$
$252$	1.91847e9	0.0299677
$253$	5.22902e10	0.802376
$254$	−3.18180e10	−0.479647
$255$	1.22880e11	1.81992
$256$	−4.60427e10	−0.670009
$257$	−6.17671e9	−0.0883199	−0.0441599	−	0.999024i	$-0.514061\pi$
$257$	−6.17671e9	−0.0883199	−0.0441599	+	0.999024i	$0.514061\pi$
$258$	−4.50977e10	−0.633674
$259$	2.00732e10	0.277183
$260$	−1.12995e10	−0.153348
$261$	2.81812e10	0.375904
$262$	3.85803e10	0.505837
$263$	5.49689e10	0.708461	0.354231	−	0.935158i	$-0.384743\pi$
$263$	5.49689e10	0.708461	0.354231	+	0.935158i	$0.384743\pi$
$264$	6.03725e10	0.764930
$265$	−4.19804e9	−0.0522926
$266$	−5.57752e9	−0.0683083
$267$	4.24844e10	0.511598
$268$	−3.67042e10	−0.434620
$269$	−4.81391e10	−0.560548	−0.280274	−	0.959920i	$-0.590425\pi$
$269$	−4.81391e10	−0.560548	−0.280274	+	0.959920i	$0.590425\pi$
$270$	2.39646e10	0.274431
$271$	−1.53993e11	−1.73436	−0.867179	−	0.497996i	$-0.834069\pi$
$271$	−1.53993e11	−1.73436	−0.867179	+	0.497996i	$0.834069\pi$
$272$	1.22917e11	1.36160
$273$	7.90460e9	0.0861287
$274$	8.90029e9	0.0953952
$275$	−1.93955e11	−2.04505
$276$	−8.66439e9	−0.0898767
$277$	2.52011e10	0.257194	0.128597	−	0.991697i	$-0.458953\pi$
$277$	2.52011e10	0.257194	0.128597	+	0.991697i	$0.458953\pi$
$278$	−1.19563e11	−1.20059
$279$	−3.01739e10	−0.298135
$280$	−6.86196e10	−0.667171
$281$	1.43216e11	1.37029	0.685144	−	0.728407i	$-0.259739\pi$
$281$	1.43216e11	1.37029	0.685144	+	0.728407i	$0.259739\pi$
$282$	−1.12933e10	−0.106341
$283$	−5.05373e10	−0.468353	−0.234177	−	0.972194i	$-0.575239\pi$
$283$	−5.05373e10	−0.468353	−0.234177	+	0.972194i	$0.575239\pi$
$284$	3.39924e10	0.310062
$285$	2.17442e10	0.195228
$286$	4.77986e10	0.422443
$287$	6.59649e10	0.573911
$288$	−1.80850e10	−0.154900
$289$	3.23055e11	2.72418
$290$	−1.93688e11	−1.60810
$291$	−2.29378e10	−0.187514
$292$	−1.80896e10	−0.145615
$293$	−1.63219e11	−1.29380	−0.646898	−	0.762577i	$-0.723934\pi$
$293$	−1.63219e11	−1.29380	−0.646898	+	0.762577i	$0.723934\pi$
$294$	9.22405e9	0.0720043
$295$	−3.36887e11	−2.58992
$296$	−1.04669e11	−0.792511
$297$	3.16385e10	0.235945
$298$	1.13272e11	0.832048
$299$	−3.56995e10	−0.258311
$300$	3.21379e10	0.229072
$301$	6.76721e10	0.475182
$302$	6.23371e10	0.431236
$303$	−1.23905e11	−0.844496
$304$	2.17506e10	0.146063
$305$	2.35653e11	1.55928
$306$	8.61306e10	0.561580
$307$	1.87774e11	1.20646	0.603230	−	0.797567i	$-0.293880\pi$
$307$	1.87774e11	1.20646	0.603230	+	0.797567i	$0.293880\pi$
$308$	−1.74079e10	−0.110222
$309$	−5.87404e10	−0.366542
$310$	2.07384e11	1.27541
$311$	−2.05749e11	−1.24714	−0.623571	−	0.781766i	$-0.714319\pi$
$311$	−2.05749e11	−1.24714	−0.623571	+	0.781766i	$0.714319\pi$
$312$	−4.12175e10	−0.246255
$313$	2.49276e11	1.46802	0.734008	−	0.679141i	$-0.237647\pi$
$313$	2.49276e11	1.46802	0.734008	+	0.679141i	$0.237647\pi$
$314$	−8.56850e10	−0.497418
$315$	−3.59604e10	−0.205791
$316$	9.63721e9	0.0543700
$317$	−8.23810e10	−0.458205	−0.229103	−	0.973402i	$-0.573579\pi$
$317$	−8.23810e10	−0.458205	−0.229103	+	0.973402i	$0.573579\pi$
$318$	−2.94253e9	−0.0161361
$319$	−2.55711e11	−1.38258
$320$	3.40473e11	1.81513
$321$	−2.49844e10	−0.131340
$322$	−4.16585e10	−0.215950
$323$	7.81506e10	0.399504
$324$	−5.24244e9	−0.0264290
$325$	1.32417e11	0.658366
$326$	−1.21436e10	−0.0595483
$327$	1.77709e11	0.859498
$328$	−3.43965e11	−1.64090
$329$	1.69463e10	0.0797432
$330$	−2.17450e11	−1.00936
$331$	4.58028e10	0.209733	0.104866	−	0.994486i	$-0.466558\pi$
$331$	4.58028e10	0.209733	0.104866	+	0.994486i	$0.466558\pi$
$332$	−5.43342e10	−0.245444
$333$	−5.48522e10	−0.244453
$334$	1.93492e11	0.850753
$335$	6.87995e11	2.98458
$336$	−3.59709e10	−0.153966
$337$	−2.97513e11	−1.25653	−0.628263	−	0.778001i	$-0.716234\pi$
$337$	−2.97513e11	−1.25653	−0.628263	+	0.778001i	$0.716234\pi$
$338$	1.76847e11	0.737008
$339$	5.95137e10	0.244748
$340$	1.84753e11	0.749783
$341$	2.73793e11	1.09655
$342$	1.52412e10	0.0602423
$343$	−1.38413e10	−0.0539949
$344$	−3.52867e11	−1.35862
$345$	1.62408e11	0.617193
$346$	4.55204e10	0.170751
$347$	1.23999e10	0.0459129	0.0229564	−	0.999736i	$-0.492692\pi$
$347$	1.23999e10	0.0459129	0.0229564	+	0.999736i	$0.492692\pi$
$348$	4.23709e10	0.154868
$349$	−4.72713e11	−1.70562	−0.852811	−	0.522219i	$-0.825104\pi$
$349$	−4.72713e11	−1.70562	−0.852811	+	0.522219i	$0.825104\pi$
$350$	1.54520e11	0.550399
$351$	−2.16002e10	−0.0759584
$352$	1.64100e11	0.569727
$353$	−3.61017e11	−1.23749	−0.618745	−	0.785592i	$-0.712359\pi$
$353$	−3.61017e11	−1.23749	−0.618745	+	0.785592i	$0.712359\pi$
$354$	−2.36135e11	−0.799180
$355$	−6.37163e11	−2.12923
$356$	6.38760e10	0.210772
$357$	−1.29245e11	−0.421120
$358$	−2.55719e11	−0.822791
$359$	1.26560e10	0.0402134	0.0201067	−	0.999798i	$-0.493599\pi$
$359$	1.26560e10	0.0402134	0.0201067	+	0.999798i	$0.493599\pi$
$360$	1.87511e11	0.588390
$361$	−3.08859e11	−0.957144
$362$	−1.39711e11	−0.427604
$363$	−9.60883e10	−0.290463
$364$	1.18847e10	0.0354839
$365$	3.39076e11	0.999953
$366$	1.65176e11	0.481152
$367$	2.47524e11	0.712231	0.356115	−	0.934442i	$-0.384101\pi$
$367$	2.47524e11	0.712231	0.356115	+	0.934442i	$0.384101\pi$
$368$	1.62456e11	0.461763
$369$	−1.80257e11	−0.506142
$370$	3.76997e11	1.04576
$371$	4.41547e9	0.0121002
$372$	−4.53670e10	−0.122828
$373$	−4.21588e11	−1.12771	−0.563857	−	0.825873i	$-0.690683\pi$
$373$	−4.21588e11	−1.12771	−0.563857	+	0.825873i	$0.690683\pi$
$374$	−7.81535e11	−2.06550
$375$	−2.41262e11	−0.630010
$376$	−8.83643e10	−0.227998
$377$	1.74579e11	0.445098
$378$	−2.52057e10	−0.0635018
$379$	−2.75764e11	−0.686534	−0.343267	−	0.939238i	$-0.611534\pi$
$379$	−2.75764e11	−0.686534	−0.343267	+	0.939238i	$0.611534\pi$
$380$	3.26928e10	0.0804314
$381$	−1.30469e11	−0.317208
$382$	6.79531e11	1.63277
$383$	3.61139e11	0.857592	0.428796	−	0.903401i	$-0.358938\pi$
$383$	3.61139e11	0.857592	0.428796	+	0.903401i	$0.358938\pi$
$384$	1.24333e11	0.291807
$385$	3.26298e11	0.756905
$386$	1.52041e11	0.348592
$387$	−1.84922e11	−0.419072
$388$	−3.44874e10	−0.0772535
$389$	−8.08747e11	−1.79077	−0.895384	−	0.445294i	$-0.853099\pi$
$389$	−8.08747e11	−1.79077	−0.895384	+	0.445294i	$0.853099\pi$
$390$	1.48457e11	0.324946
$391$	5.83708e11	1.26299
$392$	7.21736e10	0.154380
$393$	1.58197e11	0.334528
$394$	−8.11925e11	−1.69739
$395$	−1.80643e11	−0.373365
$396$	4.75690e10	0.0972065
$397$	7.20360e11	1.45543	0.727717	−	0.685878i	$-0.240582\pi$
$397$	7.20360e11	1.45543	0.727717	+	0.685878i	$0.240582\pi$
$398$	9.00067e10	0.179805
$399$	−2.28704e10	−0.0451748
$400$	−6.02580e11	−1.17691
$401$	6.65589e10	0.128545	0.0642727	−	0.997932i	$-0.479527\pi$
$401$	6.65589e10	0.128545	0.0642727	+	0.997932i	$0.479527\pi$
$402$	4.82237e11	0.920965
$403$	−1.86924e11	−0.353014
$404$	−1.86293e11	−0.347921
$405$	9.82658e10	0.181491
$406$	2.03720e11	0.372106
$407$	4.97719e11	0.899103
$408$	6.73930e11	1.20405
$409$	1.67239e11	0.295517	0.147758	−	0.989023i	$-0.452794\pi$
$409$	1.67239e11	0.295517	0.147758	+	0.989023i	$0.452794\pi$
$410$	1.23890e12	2.16525
$411$	3.64953e10	0.0630883
$412$	−8.83171e10	−0.151011
$413$	3.54335e11	0.599293
$414$	1.13837e11	0.190450
$415$	1.01846e12	1.68549
$416$	−1.12034e11	−0.183413
$417$	−4.90263e11	−0.793993
$418$	−1.38296e11	−0.221573
$419$	5.26765e11	0.834937	0.417468	−	0.908691i	$-0.362917\pi$
$419$	5.26765e11	0.834937	0.417468	+	0.908691i	$0.362917\pi$
$420$	−5.40670e10	−0.0847834
$421$	6.35836e11	0.986451	0.493226	−	0.869901i	$-0.335818\pi$
$421$	6.35836e11	0.986451	0.493226	+	0.869901i	$0.335818\pi$
$422$	−2.97621e11	−0.456833
$423$	−4.63077e10	−0.0703269
$424$	−2.30239e10	−0.0345965
$425$	−2.16509e12	−3.21903
$426$	−4.46607e11	−0.657025
$427$	−2.47858e11	−0.360809
$428$	−3.75644e10	−0.0541102
$429$	1.95996e11	0.279377
$430$	1.27096e12	1.79277
$431$	−8.51820e11	−1.18905	−0.594525	−	0.804077i	$-0.702660\pi$
$431$	−8.51820e11	−1.18905	−0.594525	+	0.804077i	$0.702660\pi$
$432$	9.82946e10	0.135785
$433$	−3.41951e11	−0.467486	−0.233743	−	0.972298i	$-0.575097\pi$
$433$	−3.41951e11	−0.467486	−0.233743	+	0.972298i	$0.575097\pi$
$434$	−2.18125e11	−0.295122
$435$	−7.94212e11	−1.06349
$436$	2.67188e11	0.354102
$437$	1.03290e11	0.135485
$438$	2.37669e11	0.308559
$439$	−2.09164e11	−0.268780	−0.134390	−	0.990929i	$-0.542908\pi$
$439$	−2.09164e11	−0.268780	−0.134390	+	0.990929i	$0.542908\pi$
$440$	−1.70144e12	−2.16411
$441$	3.78229e10	0.0476190
$442$	5.33569e11	0.664952
$443$	−1.29400e12	−1.59630	−0.798152	−	0.602456i	$-0.794189\pi$
$443$	−1.29400e12	−1.59630	−0.798152	+	0.602456i	$0.794189\pi$
$444$	−8.24712e10	−0.100711
$445$	−1.19731e12	−1.44739
$446$	3.10744e11	0.371874
$447$	4.64467e11	0.550264
$448$	−3.58107e11	−0.420012
$449$	8.29311e11	0.962961	0.481481	−	0.876457i	$-0.340099\pi$
$449$	8.29311e11	0.962961	0.481481	+	0.876457i	$0.340099\pi$
$450$	−4.22243e11	−0.485407
$451$	1.63562e12	1.86160
$452$	8.94798e10	0.100833
$453$	2.55611e11	0.285192
$454$	−1.14441e12	−1.26425
$455$	−2.22770e11	−0.243672
$456$	1.19255e11	0.129162
$457$	3.02462e11	0.324376	0.162188	−	0.986760i	$-0.448145\pi$
$457$	3.02462e11	0.324376	0.162188	+	0.986760i	$0.448145\pi$
$458$	−7.69986e11	−0.817689
$459$	3.53176e11	0.371393
$460$	2.44183e11	0.254276
$461$	1.33590e12	1.37759	0.688796	−	0.724955i	$-0.258139\pi$
$461$	1.33590e12	1.37759	0.688796	+	0.724955i	$0.258139\pi$
$462$	2.28712e11	0.233561
$463$	1.86794e11	0.188907	0.0944536	−	0.995529i	$-0.469890\pi$
$463$	1.86794e11	0.188907	0.0944536	+	0.995529i	$0.469890\pi$
$464$	−7.94445e11	−0.795670
$465$	8.50372e11	0.843472
$466$	−6.46045e11	−0.634638
$467$	2.44048e11	0.237438	0.118719	−	0.992928i	$-0.462121\pi$
$467$	2.44048e11	0.237438	0.118719	+	0.992928i	$0.462121\pi$
$468$	−3.24762e10	−0.0312939
$469$	−7.23628e11	−0.690618
$470$	3.18271e11	0.300855
$471$	−3.51348e11	−0.328960
$472$	−1.84764e12	−1.71347
$473$	1.67795e12	1.54136
$474$	−1.26618e11	−0.115211
$475$	−3.83122e11	−0.345315
$476$	−1.94321e11	−0.173496
$477$	−1.20658e10	−0.0106714
$478$	2.03080e11	0.177927
$479$	1.35721e12	1.17798	0.588988	−	0.808142i	$-0.299526\pi$
$479$	1.35721e12	1.17798	0.588988	+	0.808142i	$0.299526\pi$
$480$	5.09678e11	0.438238
$481$	−3.39803e11	−0.289450
$482$	−1.38414e12	−1.16807
$483$	−1.70819e11	−0.142815
$484$	−1.44470e11	−0.119667
$485$	6.46442e11	0.530508
$486$	6.88775e10	0.0560033
$487$	9.55017e11	0.769362	0.384681	−	0.923049i	$-0.374311\pi$
$487$	9.55017e11	0.769362	0.384681	+	0.923049i	$0.374311\pi$
$488$	1.29242e12	1.03161
$489$	−4.97945e10	−0.0393814
$490$	−2.59955e11	−0.203712
$491$	−4.08713e11	−0.317360	−0.158680	−	0.987330i	$-0.550724\pi$
$491$	−4.08713e11	−0.317360	−0.158680	+	0.987330i	$0.550724\pi$
$492$	−2.71019e11	−0.208524
$493$	−2.85447e12	−2.17627
$494$	9.44173e10	0.0713313
$495$	−8.91647e11	−0.667528
$496$	8.50621e11	0.631057
$497$	6.70163e11	0.492693
$498$	7.13867e11	0.520098
$499$	−6.74812e11	−0.487226	−0.243613	−	0.969872i	$-0.578333\pi$
$499$	−6.74812e11	−0.487226	−0.243613	+	0.969872i	$0.578333\pi$
$500$	−3.62741e11	−0.259556
$501$	7.93406e11	0.562634
$502$	1.00383e12	0.705495
$503$	1.38580e12	0.965262	0.482631	−	0.875824i	$-0.339681\pi$
$503$	1.38580e12	0.965262	0.482631	+	0.875824i	$0.339681\pi$
$504$	−1.97222e11	−0.136150
$505$	3.49194e12	2.38922
$506$	−1.03293e12	−0.700479
$507$	7.25154e11	0.487410
$508$	−1.96162e11	−0.130686
$509$	−1.48591e12	−0.981212	−0.490606	−	0.871381i	$-0.663225\pi$
$509$	−1.48591e12	−0.981212	−0.490606	+	0.871381i	$0.663225\pi$
$510$	−2.42736e12	−1.58880
$511$	−3.56638e11	−0.231384
$512$	1.69543e12	1.09035
$513$	6.24959e10	0.0398404
$514$	1.22014e11	0.0771038
$515$	1.65544e12	1.03701
$516$	−2.78033e11	−0.172652
$517$	4.20188e11	0.258664
$518$	−3.96523e11	−0.241983
$519$	1.86655e11	0.112924
$520$	1.16161e12	0.696697
$521$	−9.52393e11	−0.566300	−0.283150	−	0.959076i	$-0.591379\pi$
$521$	−9.52393e11	−0.566300	−0.283150	+	0.959076i	$0.591379\pi$
$522$	−5.56687e11	−0.328166
$523$	−1.43789e12	−0.840367	−0.420183	−	0.907439i	$-0.638034\pi$
$523$	−1.43789e12	−0.840367	−0.420183	+	0.907439i	$0.638034\pi$
$524$	2.37852e11	0.137821
$525$	6.33603e11	0.363999
$526$	−1.08585e12	−0.618491
$527$	3.05631e12	1.72603
$528$	−8.91908e11	−0.499422
$529$	−1.02968e12	−0.571679
$530$	8.29275e10	0.0456517
$531$	−9.68261e11	−0.528527
$532$	−3.43860e10	−0.0186114
$533$	−1.11667e12	−0.599310
$534$	−8.39231e11	−0.446628
$535$	7.04118e11	0.371581
$536$	3.77326e12	1.97458
$537$	−1.04857e12	−0.544142
$538$	9.50933e11	0.489361
$539$	−3.43198e11	−0.175144
$540$	1.47744e11	0.0747719
$541$	−2.73289e12	−1.37162	−0.685811	−	0.727780i	$-0.740552\pi$
$541$	−2.73289e12	−1.37162	−0.685811	+	0.727780i	$0.740552\pi$
$542$	3.04195e12	1.51410
$543$	−5.72879e11	−0.282790
$544$	1.83182e12	0.896786
$545$	−5.00826e12	−2.43166
$546$	−1.56146e11	−0.0751909
$547$	3.20466e12	1.53052	0.765261	−	0.643720i	$-0.222610\pi$
$547$	3.20466e12	1.53052	0.765261	+	0.643720i	$0.222610\pi$
$548$	5.48713e10	0.0259916
$549$	6.77299e11	0.318203
$550$	3.83136e12	1.78534
$551$	−5.05110e11	−0.233455
$552$	8.90715e11	0.408332
$553$	1.89999e11	0.0863948
$554$	−4.97819e11	−0.224532
$555$	1.54586e12	0.691597
$556$	−7.37118e11	−0.327115
$557$	−4.30481e12	−1.89499	−0.947493	−	0.319777i	$-0.896392\pi$
$557$	−4.30481e12	−1.89499	−0.947493	+	0.319777i	$0.896392\pi$
$558$	5.96051e11	0.260273
$559$	−1.14557e12	−0.496212
$560$	1.01375e12	0.435595
$561$	−3.20465e12	−1.36599
$562$	−2.82906e12	−1.19627
$563$	1.55389e12	0.651826	0.325913	−	0.945400i	$-0.394328\pi$
$563$	1.55389e12	0.651826	0.325913	+	0.945400i	$0.394328\pi$
$564$	−6.96243e10	−0.0289738
$565$	−1.67724e12	−0.692431
$566$	9.98308e11	0.408875
$567$	−1.03355e11	−0.0419961
$568$	−3.49448e12	−1.40869
$569$	−1.90192e12	−0.760655	−0.380328	−	0.924852i	$-0.624189\pi$
$569$	−1.90192e12	−0.760655	−0.380328	+	0.924852i	$0.624189\pi$
$570$	−4.29533e11	−0.170435
$571$	−3.88730e12	−1.53033	−0.765166	−	0.643833i	$-0.777343\pi$
$571$	−3.88730e12	−1.53033	−0.765166	+	0.643833i	$0.777343\pi$
$572$	2.94684e11	0.115100
$573$	2.78639e12	1.07981
$574$	−1.30306e12	−0.501028
$575$	−2.86154e12	−1.09168
$576$	9.78567e11	0.370416
$577$	5.36782e11	0.201608	0.100804	−	0.994906i	$-0.467859\pi$
$577$	5.36782e11	0.201608	0.100804	+	0.994906i	$0.467859\pi$
$578$	−6.38158e12	−2.37823
$579$	6.23438e11	0.230536
$580$	−1.19411e12	−0.438146
$581$	−1.07120e12	−0.390014
$582$	4.53111e11	0.163701
$583$	1.09483e11	0.0392497
$584$	1.85964e12	0.661563
$585$	6.08744e11	0.214899
$586$	3.22420e12	1.12949
$587$	1.54883e12	0.538435	0.269217	−	0.963079i	$-0.413235\pi$
$587$	1.54883e12	0.538435	0.269217	+	0.963079i	$0.413235\pi$
$588$	5.68673e10	0.0196184
$589$	5.40827e11	0.185157
$590$	6.65483e12	2.26101
$591$	−3.32927e12	−1.12255
$592$	1.54632e12	0.517429
$593$	−9.53692e11	−0.316710	−0.158355	−	0.987382i	$-0.550619\pi$
$593$	−9.53692e11	−0.316710	−0.158355	+	0.987382i	$0.550619\pi$
$594$	−6.24982e11	−0.205982
$595$	3.64242e12	1.19142
$596$	6.98333e11	0.226702
$597$	3.69069e11	0.118911
$598$	7.05204e11	0.225507
$599$	8.23573e11	0.261385	0.130693	−	0.991423i	$-0.458280\pi$
$599$	8.23573e11	0.261385	0.130693	+	0.991423i	$0.458280\pi$
$600$	−3.30384e12	−1.04073
$601$	2.75024e12	0.859875	0.429937	−	0.902859i	$-0.358536\pi$
$601$	2.75024e12	0.859875	0.429937	+	0.902859i	$0.358536\pi$
$602$	−1.33679e12	−0.414837
$603$	1.97739e12	0.609067
$604$	3.84315e11	0.117496
$605$	2.70799e12	0.821766
$606$	2.44761e12	0.737250
$607$	2.95853e12	0.884559	0.442279	−	0.896877i	$-0.354170\pi$
$607$	2.95853e12	0.884559	0.442279	+	0.896877i	$0.354170\pi$
$608$	3.24149e11	0.0962008
$609$	8.35346e11	0.246087
$610$	−4.65505e12	−1.36126
$611$	−2.86870e11	−0.0832722
$612$	5.31005e11	0.153009
$613$	−2.00607e12	−0.573817	−0.286909	−	0.957958i	$-0.592628\pi$
$613$	−2.00607e12	−0.573817	−0.286909	+	0.957958i	$0.592628\pi$
$614$	−3.70927e12	−1.05325
$615$	5.08005e12	1.43196
$616$	1.78956e12	0.500764
$617$	−5.93637e12	−1.64907	−0.824533	−	0.565814i	$-0.808562\pi$
$617$	−5.93637e12	−1.64907	−0.824533	+	0.565814i	$0.808562\pi$
$618$	1.16035e12	0.319993
$619$	6.33621e11	0.173469	0.0867344	−	0.996231i	$-0.472357\pi$
$619$	6.33621e11	0.173469	0.0867344	+	0.996231i	$0.472357\pi$
$620$	1.27855e12	0.347500
$621$	4.66783e11	0.125951
$622$	4.06434e12	1.08876
$623$	1.25932e12	0.334919
$624$	6.08923e11	0.160780
$625$	4.36205e11	0.114349
$626$	−4.92416e12	−1.28159
$627$	−5.67077e11	−0.146534
$628$	−5.28258e11	−0.135527
$629$	5.55597e12	1.41525
$630$	7.10357e11	0.179657
$631$	1.20654e12	0.302978	0.151489	−	0.988459i	$-0.451593\pi$
$631$	1.20654e12	0.302978	0.151489	+	0.988459i	$0.451593\pi$
$632$	−9.90723e11	−0.247016
$633$	−1.22038e12	−0.302120
$634$	1.62734e12	0.400016
$635$	3.67691e12	0.897432
$636$	−1.81411e10	−0.00439648
$637$	2.34308e11	0.0563845
$638$	5.05128e12	1.20700
$639$	−1.83129e12	−0.434515
$640$	−3.50400e12	−0.825570
$641$	−6.50909e12	−1.52286	−0.761429	−	0.648248i	$-0.775502\pi$
$641$	−6.50909e12	−1.52286	−0.761429	+	0.648248i	$0.775502\pi$
$642$	4.93538e11	0.114660
$643$	−4.92189e12	−1.13549	−0.567744	−	0.823205i	$-0.692183\pi$
$643$	−4.92189e12	−1.13549	−0.567744	+	0.823205i	$0.692183\pi$
$644$	−2.56830e11	−0.0588381
$645$	5.21152e12	1.18562
$646$	−1.54378e12	−0.348769
$647$	−1.78384e12	−0.400209	−0.200105	−	0.979775i	$-0.564128\pi$
$647$	−1.78384e12	−0.400209	−0.200105	+	0.979775i	$0.564128\pi$
$648$	5.38932e11	0.120073
$649$	8.78583e12	1.94393
$650$	−2.61574e12	−0.574757
$651$	−8.94414e11	−0.195175
$652$	−7.48668e10	−0.0162246
$653$	−4.17059e12	−0.897611	−0.448806	−	0.893629i	$-0.648150\pi$
$653$	−4.17059e12	−0.897611	−0.448806	+	0.893629i	$0.648150\pi$
$654$	−3.51044e12	−0.750346
$655$	−4.45837e12	−0.946434
$656$	5.08154e12	1.07134
$657$	9.74552e11	0.204061
$658$	−3.34755e11	−0.0696163
$659$	1.42327e11	0.0293970	0.0146985	−	0.999892i	$-0.495321\pi$
$659$	1.42327e11	0.0293970	0.0146985	+	0.999892i	$0.495321\pi$
$660$	−1.34061e12	−0.275013
$661$	2.64976e10	0.00539883	0.00269942	−	0.999996i	$-0.499141\pi$
$661$	2.64976e10	0.00539883	0.00269942	+	0.999996i	$0.499141\pi$
$662$	−9.04783e11	−0.183098
$663$	2.18788e12	0.439757
$664$	5.58565e12	1.11511
$665$	6.44542e11	0.127807
$666$	1.08354e12	0.213409
$667$	−3.77267e12	−0.738045
$668$	1.19290e12	0.231798
$669$	1.27419e12	0.245934
$670$	−1.35906e13	−2.60556
$671$	−6.14569e12	−1.17036
$672$	−5.36075e11	−0.101406
$673$	7.87384e11	0.147951	0.0739757	−	0.997260i	$-0.476431\pi$
$673$	7.87384e11	0.147951	0.0739757	+	0.997260i	$0.476431\pi$
$674$	5.87704e12	1.09695
$675$	−1.73139e12	−0.321017
$676$	1.09028e12	0.200807
$677$	4.37732e12	0.800865	0.400433	−	0.916326i	$-0.368860\pi$
$677$	4.37732e12	0.800865	0.400433	+	0.916326i	$0.368860\pi$
$678$	−1.17563e12	−0.213666
$679$	−6.79923e11	−0.122757
$680$	−1.89929e13	−3.40645
$681$	−4.69262e12	−0.836091
$682$	−5.40847e12	−0.957292
$683$	−3.54722e12	−0.623727	−0.311864	−	0.950127i	$-0.600953\pi$
$683$	−3.54722e12	−0.623727	−0.311864	+	0.950127i	$0.600953\pi$
$684$	9.39636e10	0.0164137
$685$	−1.02852e12	−0.178487
$686$	2.73419e11	0.0471379
$687$	−3.15730e12	−0.540768
$688$	5.21305e12	0.887042
$689$	−7.47458e10	−0.0126357
$690$	−3.20818e12	−0.538813
$691$	−1.27365e12	−0.212520	−0.106260	−	0.994338i	$-0.533888\pi$
$691$	−1.27365e12	−0.212520	−0.106260	+	0.994338i	$0.533888\pi$
$692$	2.80639e11	0.0465232
$693$	9.37827e11	0.154463
$694$	−2.44945e11	−0.0400822
$695$	1.38168e13	2.24633
$696$	−4.35580e12	−0.703601
$697$	1.82581e13	2.93028
$698$	9.33791e12	1.48902
$699$	−2.64908e12	−0.419709
$700$	9.52632e11	0.149963
$701$	−9.81590e12	−1.53532	−0.767660	−	0.640857i	$-0.778579\pi$
$701$	−9.81590e12	−1.53532	−0.767660	+	0.640857i	$0.778579\pi$
$702$	4.26687e11	0.0663121
$703$	9.83152e11	0.151817
$704$	−8.87935e12	−1.36240
$705$	1.30506e12	0.198966
$706$	7.13149e12	1.08034
$707$	−3.67279e12	−0.552852
$708$	−1.45580e12	−0.217746
$709$	1.18706e13	1.76426	0.882132	−	0.471003i	$-0.156108\pi$
$709$	1.18706e13	1.76426	0.882132	+	0.471003i	$0.156108\pi$
$710$	1.25864e13	1.85883
$711$	−5.19193e11	−0.0761930
$712$	−6.56656e12	−0.957587
$713$	4.03944e12	0.585354
$714$	2.55308e12	0.367640
$715$	−5.52364e12	−0.790402
$716$	−1.57654e12	−0.224179
$717$	8.32723e11	0.117670
$718$	−2.50004e11	−0.0351065
$719$	3.19559e12	0.445935	0.222967	−	0.974826i	$-0.428426\pi$
$719$	3.19559e12	0.445935	0.222967	+	0.974826i	$0.428426\pi$
$720$	−2.77017e12	−0.384159
$721$	−1.74118e12	−0.239958
$722$	6.10115e12	0.835592
$723$	−5.67560e12	−0.772484
$724$	−8.61333e11	−0.116506
$725$	1.39936e13	1.88108
$726$	1.89811e12	0.253576
$727$	−6.52980e12	−0.866951	−0.433476	−	0.901165i	$-0.642713\pi$
$727$	−6.52980e12	−0.866951	−0.433476	+	0.901165i	$0.642713\pi$
$728$	−1.22177e12	−0.161212
$729$	2.82430e11	0.0370370
$730$	−6.69807e12	−0.872964
$731$	1.87307e13	2.42619
$732$	1.01833e12	0.131096
$733$	−2.97869e12	−0.381116	−0.190558	−	0.981676i	$-0.561030\pi$
$733$	−2.97869e12	−0.381116	−0.190558	+	0.981676i	$0.561030\pi$
$734$	−4.88956e12	−0.621781
$735$	−1.06594e12	−0.134722
$736$	2.42107e12	0.304129
$737$	−1.79425e13	−2.24017
$738$	3.56076e12	0.441865
$739$	−3.71384e12	−0.458061	−0.229031	−	0.973419i	$-0.573556\pi$
$739$	−3.71384e12	−0.458061	−0.229031	+	0.973419i	$0.573556\pi$
$740$	2.32423e12	0.284929
$741$	3.87155e11	0.0471740
$742$	−8.72225e10	−0.0105636
$743$	1.18837e13	1.43055	0.715275	−	0.698843i	$-0.246301\pi$
$743$	1.18837e13	1.43055	0.715275	+	0.698843i	$0.246301\pi$
$744$	4.66381e12	0.558036
$745$	−1.30898e13	−1.55678
$746$	8.32800e12	0.984501
$747$	2.92719e12	0.343960
$748$	−4.81825e12	−0.562771
$749$	−7.40586e11	−0.0859819
$750$	4.76585e12	0.550003
$751$	9.67262e12	1.10959	0.554797	−	0.831986i	$-0.312796\pi$
$751$	9.67262e12	1.10959	0.554797	+	0.831986i	$0.312796\pi$
$752$	1.30544e12	0.148860
$753$	4.11617e12	0.466569
$754$	−3.44861e12	−0.388573
$755$	−7.20372e12	−0.806855
$756$	−1.55396e11	−0.0173018
$757$	−4.65776e12	−0.515520	−0.257760	−	0.966209i	$-0.582984\pi$
$757$	−4.65776e12	−0.515520	−0.257760	+	0.966209i	$0.582984\pi$
$758$	5.44741e12	0.599348
$759$	−4.23551e12	−0.463252
$760$	−3.36088e12	−0.365419
$761$	−2.58075e12	−0.278942	−0.139471	−	0.990226i	$-0.544540\pi$
$761$	−2.58075e12	−0.278942	−0.139471	+	0.990226i	$0.544540\pi$
$762$	2.57726e12	0.276924
$763$	5.26765e12	0.562673
$764$	4.18939e12	0.444867
$765$	−9.95332e12	−1.05073
$766$	−7.13390e12	−0.748682
$767$	−5.99826e12	−0.625815
$768$	3.72945e12	0.386830
$769$	−4.17055e11	−0.0430056	−0.0215028	−	0.999769i	$-0.506845\pi$
$769$	−4.17055e11	−0.0430056	−0.0215028	+	0.999769i	$0.506845\pi$
$770$	−6.44565e12	−0.660783
$771$	5.00314e11	0.0509915
$772$	9.37349e11	0.0949781
$773$	4.80469e12	0.484013	0.242007	−	0.970275i	$-0.422194\pi$
$773$	4.80469e12	0.484013	0.242007	+	0.970275i	$0.422194\pi$
$774$	3.65292e12	0.365852
$775$	−1.49831e13	−1.49191
$776$	3.54537e12	0.350981
$777$	−1.62593e12	−0.160032
$778$	1.59759e13	1.56335
$779$	3.23086e12	0.314340
$780$	9.15257e11	0.0885355
$781$	1.66168e13	1.59816
$782$	−1.15305e13	−1.10260
$783$	−2.28268e12	−0.217028
$784$	−1.06625e12	−0.100794
$785$	9.90182e12	0.930682
$786$	−3.12501e12	−0.292045
$787$	−8.88345e12	−0.825458	−0.412729	−	0.910854i	$-0.635424\pi$
$787$	−8.88345e12	−0.825458	−0.412729	+	0.910854i	$0.635424\pi$
$788$	−5.00561e12	−0.462476
$789$	−4.45248e12	−0.409030
$790$	3.56839e12	0.325950
$791$	1.76410e12	0.160225
$792$	−4.89018e12	−0.441633
$793$	4.19578e12	0.376776
$794$	−1.42299e13	−1.27060
$795$	3.40041e11	0.0301911
$796$	5.54901e11	0.0489899
$797$	−7.88653e12	−0.692347	−0.346173	−	0.938171i	$-0.612519\pi$
$797$	−7.88653e12	−0.692347	−0.346173	+	0.938171i	$0.612519\pi$
$798$	4.51779e11	0.0394378
$799$	4.69049e12	0.407153
$800$	−8.98024e12	−0.775145
$801$	−3.44124e12	−0.295371
$802$	−1.31480e12	−0.112221
$803$	−8.84292e12	−0.750543
$804$	2.97304e12	0.250928
$805$	4.81409e12	0.404048
$806$	3.69247e12	0.308183
$807$	3.89927e12	0.323632
$808$	1.91513e13	1.58069
$809$	4.64943e12	0.381620	0.190810	−	0.981627i	$-0.438889\pi$
$809$	4.64943e12	0.381620	0.190810	+	0.981627i	$0.438889\pi$
$810$	−1.94113e12	−0.158443
$811$	−1.25525e13	−1.01891	−0.509457	−	0.860496i	$-0.670154\pi$
$811$	−1.25525e13	−1.01891	−0.509457	+	0.860496i	$0.670154\pi$
$812$	1.25596e12	0.101385
$813$	1.24734e13	1.00133
$814$	−9.83188e12	−0.784922
$815$	1.40333e12	0.111416
$816$	−9.95624e12	−0.786121
$817$	3.31447e12	0.260264
$818$	−3.30361e12	−0.257988
$819$	−6.40273e11	−0.0497264
$820$	7.63794e12	0.589948
$821$	2.80521e12	0.215487	0.107743	−	0.994179i	$-0.465638\pi$
$821$	2.80521e12	0.215487	0.107743	+	0.994179i	$0.465638\pi$
$822$	−7.20924e11	−0.0550765
$823$	−1.18020e13	−0.896723	−0.448361	−	0.893852i	$-0.647992\pi$
$823$	−1.18020e13	−0.896723	−0.448361	+	0.893852i	$0.647992\pi$
$824$	9.07916e12	0.686078
$825$	1.57103e13	1.18071
$826$	−6.99949e12	−0.523186
$827$	−1.90585e13	−1.41682	−0.708409	−	0.705803i	$-0.750587\pi$
$827$	−1.90585e13	−1.41682	−0.708409	+	0.705803i	$0.750587\pi$
$828$	7.01815e11	0.0518903
$829$	1.12313e13	0.825913	0.412957	−	0.910751i	$-0.364496\pi$
$829$	1.12313e13	0.825913	0.412957	+	0.910751i	$0.364496\pi$
$830$	−2.01185e13	−1.47144
$831$	−2.04129e12	−0.148491
$832$	6.06210e12	0.438600
$833$	−3.83107e12	−0.275688
$834$	9.68458e12	0.693160
$835$	−2.23600e13	−1.59178
$836$	−8.52610e11	−0.0603701
$837$	2.44409e12	0.172128
$838$	−1.04056e13	−0.728905
$839$	2.93349e12	0.204388	0.102194	−	0.994764i	$-0.467414\pi$
$839$	2.93349e12	0.204388	0.102194	+	0.994764i	$0.467414\pi$
$840$	5.55819e12	0.385191
$841$	3.94209e12	0.271734
$842$	−1.25602e13	−0.861177
$843$	−1.16005e13	−0.791137
$844$	−1.83487e12	−0.124470
$845$	−2.04365e13	−1.37896
$846$	9.14756e11	0.0613958
$847$	−2.84825e12	−0.190153
$848$	3.40141e11	0.0225880
$849$	4.09352e12	0.270404
$850$	4.27689e13	2.81023
$851$	7.34317e12	0.479955
$852$	−2.75338e12	−0.179014
$853$	−1.18903e13	−0.768993	−0.384497	−	0.923126i	$-0.625625\pi$
$853$	−1.18903e13	−0.768993	−0.384497	+	0.923126i	$0.625625\pi$
$854$	4.89615e12	0.314988
$855$	−1.76128e12	−0.112715
$856$	3.86169e12	0.245836
$857$	6.38332e12	0.404234	0.202117	−	0.979361i	$-0.435218\pi$
$857$	6.38332e12	0.404234	0.202117	+	0.979361i	$0.435218\pi$
$858$	−3.87169e12	−0.243898
$859$	1.96326e13	1.23029	0.615147	−	0.788412i	$-0.289097\pi$
$859$	1.96326e13	1.23029	0.615147	+	0.788412i	$0.289097\pi$
$860$	7.83561e12	0.488461
$861$	−5.34316e12	−0.331348
$862$	1.68267e13	1.03805
$863$	1.11673e13	0.685328	0.342664	−	0.939458i	$-0.388671\pi$
$863$	1.11673e13	0.685328	0.342664	+	0.939458i	$0.388671\pi$
$864$	1.46488e12	0.0894317
$865$	−5.26037e12	−0.319480
$866$	6.75486e12	0.408118
$867$	−2.61674e13	−1.57281
$868$	−1.34477e12	−0.0804096
$869$	4.71106e12	0.280240
$870$	1.56888e13	0.928436
$871$	1.22497e13	0.721181
$872$	−2.74675e13	−1.60877
$873$	1.85797e12	0.108261
$874$	−2.04037e12	−0.118279
$875$	−7.15147e12	−0.412439
$876$	1.46525e12	0.0840707
$877$	−1.61862e13	−0.923948	−0.461974	−	0.886894i	$-0.652859\pi$
$877$	−1.61862e13	−0.923948	−0.461974	+	0.886894i	$0.652859\pi$
$878$	4.13180e12	0.234647
$879$	1.32207e13	0.746974
$880$	2.51361e13	1.41295
$881$	2.22815e13	1.24610	0.623049	−	0.782183i	$-0.285894\pi$
$881$	2.22815e13	1.24610	0.623049	+	0.782183i	$0.285894\pi$
$882$	−7.47148e11	−0.0415717
$883$	−8.45851e12	−0.468242	−0.234121	−	0.972207i	$-0.575221\pi$
$883$	−8.45851e12	−0.468242	−0.234121	+	0.972207i	$0.575221\pi$
$884$	3.28951e12	0.181174
$885$	2.72879e13	1.49529
$886$	2.55614e13	1.39358
$887$	7.51066e12	0.407401	0.203700	−	0.979033i	$-0.434703\pi$
$887$	7.51066e12	0.407401	0.203700	+	0.979033i	$0.434703\pi$
$888$	8.47819e12	0.457556
$889$	−3.86735e12	−0.207661
$890$	2.36515e13	1.26358
$891$	−2.56272e12	−0.136223
$892$	1.91577e12	0.101321
$893$	8.30003e11	0.0436765
$894$	−9.17501e12	−0.480383
$895$	2.95511e13	1.53947
$896$	3.68548e12	0.191033
$897$	2.89166e12	0.149136
$898$	−1.63821e13	−0.840671
$899$	−1.97538e13	−1.00863
$900$	−2.60317e12	−0.132255
$901$	1.22214e12	0.0617815
$902$	−3.23097e13	−1.62519
$903$	−5.48144e12	−0.274347
$904$	−9.19869e12	−0.458108
$905$	1.61451e13	0.800059
$906$	−5.04931e12	−0.248974
$907$	−2.06584e13	−1.01360	−0.506798	−	0.862065i	$-0.669171\pi$
$907$	−2.06584e13	−1.01360	−0.506798	+	0.862065i	$0.669171\pi$
$908$	−7.05543e12	−0.344459
$909$	1.00363e13	0.487570
$910$	4.40057e12	0.212727
$911$	1.25513e13	0.603746	0.301873	−	0.953348i	$-0.402388\pi$
$911$	1.25513e13	0.603746	0.301873	+	0.953348i	$0.402388\pi$
$912$	−1.76180e12	−0.0843295
$913$	−2.65608e13	−1.26509
$914$	−5.97480e12	−0.283182
$915$	−1.90879e13	−0.900249
$916$	−4.74705e12	−0.222789
$917$	4.68928e12	0.219000
$918$	−6.97658e12	−0.324228
$919$	6.79883e12	0.314423	0.157211	−	0.987565i	$-0.449750\pi$
$919$	6.79883e12	0.314423	0.157211	+	0.987565i	$0.449750\pi$
$920$	−2.51024e13	−1.15524
$921$	−1.52097e13	−0.696550
$922$	−2.63893e13	−1.20265
$923$	−1.13446e13	−0.514497
$924$	1.41004e12	0.0636366
$925$	−2.72373e13	−1.22328
$926$	−3.68990e12	−0.164917
$927$	4.75797e12	0.211623
$928$	−1.18396e13	−0.524048
$929$	−2.45313e13	−1.08056	−0.540281	−	0.841484i	$-0.681682\pi$
$929$	−2.45313e13	−1.08056	−0.540281	+	0.841484i	$0.681682\pi$
$930$	−1.67981e13	−0.736356
$931$	−6.77924e11	−0.0295738
$932$	−3.98294e12	−0.172915
$933$	1.66657e13	0.720038
$934$	−4.82090e12	−0.207285
$935$	9.03147e13	3.86461
$936$	3.33862e12	0.142176
$937$	−1.61956e13	−0.686385	−0.343192	−	0.939265i	$-0.611508\pi$
$937$	−1.61956e13	−0.686385	−0.343192	+	0.939265i	$0.611508\pi$
$938$	1.42945e13	0.602913
$939$	−2.01913e13	−0.847559
$940$	1.96218e12	0.0819715
$941$	1.16583e13	0.484711	0.242356	−	0.970188i	$-0.422080\pi$
$941$	1.16583e13	0.484711	0.242356	+	0.970188i	$0.422080\pi$
$942$	6.94048e12	0.287184
$943$	2.41313e13	0.993752
$944$	2.72959e13	1.11872
$945$	2.91279e12	0.118814
$946$	−3.31459e13	−1.34561
$947$	−1.49581e13	−0.604366	−0.302183	−	0.953250i	$-0.597715\pi$
$947$	−1.49581e13	−0.604366	−0.302183	+	0.953250i	$0.597715\pi$
$948$	−7.80614e11	−0.0313906
$949$	6.03723e12	0.241624
$950$	7.56813e12	0.301462
$951$	6.67286e12	0.264545
$952$	1.99766e13	0.788234
$953$	−5.60549e12	−0.220138	−0.110069	−	0.993924i	$-0.535107\pi$
$953$	−5.60549e12	−0.220138	−0.110069	+	0.993924i	$0.535107\pi$
$954$	2.38345e11	0.00931620
$955$	−7.85271e13	−3.05495
$956$	1.25201e12	0.0484784
$957$	2.07126e13	0.798235
$958$	−2.68101e13	−1.02838
$959$	1.08179e12	0.0413010
$960$	−2.75783e13	−1.04797
$961$	−5.28899e12	−0.200040
$962$	6.71241e12	0.252692
$963$	2.02373e12	0.0758290
$964$	−8.53336e12	−0.318253
$965$	−1.75699e13	−0.652225
$966$	3.37434e12	0.124679
$967$	3.74282e13	1.37651	0.688256	−	0.725468i	$-0.258376\pi$
$967$	3.74282e13	1.37651	0.688256	+	0.725468i	$0.258376\pi$
$968$	1.48518e13	0.543676
$969$	−6.33020e12	−0.230654
$970$	−1.27697e13	−0.463137
$971$	−2.43843e12	−0.0880287	−0.0440143	−	0.999031i	$-0.514015\pi$
$971$	−2.43843e12	−0.0880287	−0.0440143	+	0.999031i	$0.514015\pi$
$972$	4.24637e11	0.0152588
$973$	−1.45324e13	−0.519790
$974$	−1.88653e13	−0.671658
$975$	−1.07257e13	−0.380108
$976$	−1.90935e13	−0.673536
$977$	−5.85191e12	−0.205481	−0.102741	−	0.994708i	$-0.532761\pi$
$977$	−5.85191e12	−0.205481	−0.102741	+	0.994708i	$0.532761\pi$
$978$	9.83633e11	0.0343802
$979$	3.12252e13	1.08638
$980$	−1.60265e12	−0.0555037
$981$	−1.43944e13	−0.496231
$982$	8.07366e12	0.277057
$983$	−2.35337e13	−0.803895	−0.401947	−	0.915663i	$-0.631666\pi$
$983$	−2.35337e13	−0.803895	−0.401947	+	0.915663i	$0.631666\pi$
$984$	2.78612e13	0.947375
$985$	9.38266e13	3.17587
$986$	5.63867e13	1.89990
$987$	−1.37265e12	−0.0460397
$988$	5.82093e11	0.0194351
$989$	2.47558e13	0.822799
$990$	1.76135e13	0.582756
$991$	−2.84698e13	−0.937677	−0.468839	−	0.883284i	$-0.655327\pi$
$991$	−2.84698e13	−0.937677	−0.468839	+	0.883284i	$0.655327\pi$
$992$	1.26768e13	0.415630
$993$	−3.71003e12	−0.121089
$994$	−1.32383e13	−0.430124
$995$	−1.04012e13	−0.336419
$996$	4.40107e12	0.141707
$997$	2.36797e13	0.759009	0.379505	−	0.925190i	$-0.376094\pi$
$997$	2.36797e13	0.759009	0.379505	+	0.925190i	$0.376094\pi$
$998$	1.33302e13	0.425351
$999$	4.44303e12	0.141135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.10.a.b.1.1	✓	2
3.2	odd	2		63.10.a.c.1.2		2
4.3	odd	2		336.10.a.m.1.2		2
7.6	odd	2		147.10.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.10.a.b.1.1	✓	2	1.1	even	1	trivial
63.10.a.c.1.2		2	3.2	odd	2
147.10.a.d.1.1		2	7.6	odd	2
336.10.a.m.1.2		2	4.3	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	21.a (trivial)

\(f(q)\)	\(=\)	\(q-19.7539 q^{2} -81.0000 q^{3} -121.785 q^{4} +2282.77 q^{5} +1600.06 q^{6} -2401.00 q^{7} +12519.7 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-19.7539 q^{2} -81.0000 q^{3} -121.785 q^{4} +2282.77 q^{5} +1600.06 q^{6} -2401.00 q^{7} +12519.7 q^{8} +6561.00 q^{9} -45093.5 q^{10} -59533.4 q^{11} +9864.57 q^{12} +40644.6 q^{13} +47429.0 q^{14} -184904. q^{15} -184959. q^{16} -664562. q^{17} -129605. q^{18} -117597. q^{19} -278007. q^{20} +194481. q^{21} +1.17601e6 q^{22} -878334. q^{23} -1.01410e6 q^{24} +3.25792e6 q^{25} -802888. q^{26} -531441. q^{27} +292405. q^{28} +4.29526e6 q^{29} +3.65258e6 q^{30} -4.59898e6 q^{31} -2.75644e6 q^{32} +4.82220e6 q^{33} +1.31277e7 q^{34} -5.48093e6 q^{35} -799030. q^{36} -8.36034e6 q^{37} +2.32300e6 q^{38} -3.29221e6 q^{39} +2.85796e7 q^{40} -2.74739e7 q^{41} -3.84175e6 q^{42} -2.81850e7 q^{43} +7.25026e6 q^{44} +1.49773e7 q^{45} +1.73505e7 q^{46} -7.05802e6 q^{47} +1.49817e7 q^{48} +5.76480e6 q^{49} -6.43564e7 q^{50} +5.38295e7 q^{51} -4.94989e6 q^{52} -1.83901e6 q^{53} +1.04980e7 q^{54} -1.35901e8 q^{55} -3.00598e7 q^{56} +9.52537e6 q^{57} -8.48479e7 q^{58} -1.47578e8 q^{59} +2.25185e7 q^{60} +1.03231e8 q^{61} +9.08477e7 q^{62} -1.57530e7 q^{63} +1.49149e8 q^{64} +9.27823e7 q^{65} -9.52572e7 q^{66} +3.01386e8 q^{67} +8.09336e7 q^{68} +7.11451e7 q^{69} +1.08270e8 q^{70} -2.79118e8 q^{71} +8.21417e7 q^{72} +1.48537e8 q^{73} +1.65149e8 q^{74} -2.63891e8 q^{75} +1.43215e7 q^{76} +1.42940e8 q^{77} +6.50339e7 q^{78} -7.91332e7 q^{79} -4.22218e8 q^{80} +4.30467e7 q^{81} +5.42717e8 q^{82} +4.46149e8 q^{83} -2.36848e7 q^{84} -1.51704e9 q^{85} +5.56762e8 q^{86} -3.47916e8 q^{87} -7.45340e8 q^{88} -5.24499e8 q^{89} -2.95859e8 q^{90} -9.75876e7 q^{91} +1.06968e8 q^{92} +3.72517e8 q^{93} +1.39423e8 q^{94} -2.68447e8 q^{95} +2.23271e8 q^{96} +2.83183e8 q^{97} -1.13877e8 q^{98} -3.90598e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 9 q^{2} - 162 q^{3} + 193 q^{4} + 1170 q^{5} - 729 q^{6} - 4802 q^{7} + 6849 q^{8} + 13122 q^{9}+O(q^{10}) \) 2 * q + 9 * q^2 - 162 * q^3 + 193 * q^4 + 1170 * q^5 - 729 * q^6 - 4802 * q^7 + 6849 * q^8 + 13122 * q^9	\( 2 q + 9 q^{2} - 162 q^{3} + 193 q^{4} + 1170 q^{5} - 729 q^{6} - 4802 q^{7} + 6849 q^{8} + 13122 q^{9} - 77090 q^{10} - 145746 q^{11} - 15633 q^{12} + 86528 q^{13} - 21609 q^{14} - 94770 q^{15} - 509183 q^{16} - 229842 q^{17} + 59049 q^{18} - 221224 q^{19} - 628290 q^{20} + 388962 q^{21} - 1302932 q^{22} - 2035782 q^{23} - 554769 q^{24} + 2543050 q^{25} + 516438 q^{26} - 1062882 q^{27} - 463393 q^{28} + 9756252 q^{29} + 6244290 q^{30} + 204000 q^{31} - 9175743 q^{32} + 11805426 q^{33} + 25627554 q^{34} - 2809170 q^{35} + 1266273 q^{36} - 13959816 q^{37} - 656676 q^{38} - 7008768 q^{39} + 34889790 q^{40} - 42362550 q^{41} + 1750329 q^{42} - 4763912 q^{43} - 19888164 q^{44} + 7676370 q^{45} - 15930600 q^{46} - 48278484 q^{47} + 41243823 q^{48} + 11529602 q^{49} - 84911625 q^{50} + 18617202 q^{51} + 9493510 q^{52} - 108980352 q^{53} - 4782969 q^{54} - 39966160 q^{55} - 16444449 q^{56} + 17919144 q^{57} + 72176782 q^{58} - 188376804 q^{59} + 50891490 q^{60} + 19722092 q^{61} + 228951936 q^{62} - 31505922 q^{63} + 130572161 q^{64} + 41724540 q^{65} + 105537492 q^{66} + 70274396 q^{67} + 217776834 q^{68} + 164898342 q^{69} + 185093090 q^{70} - 382044186 q^{71} + 44936289 q^{72} + 191785896 q^{73} + 4142502 q^{74} - 205987050 q^{75} - 18298628 q^{76} + 349936146 q^{77} - 41831478 q^{78} - 72592148 q^{79} - 61430850 q^{80} + 86093442 q^{81} + 114611450 q^{82} + 187994232 q^{83} + 37534833 q^{84} - 2000786580 q^{85} + 1230207804 q^{86} - 790256412 q^{87} - 256454052 q^{88} + 42930954 q^{89} - 505787490 q^{90} - 207753728 q^{91} - 257379192 q^{92} - 16524000 q^{93} - 1045824480 q^{94} - 153134280 q^{95} + 743235183 q^{96} + 1726854096 q^{97} + 51883209 q^{98} - 956239506 q^{99}+O(q^{100}) \) 2 * q + 9 * q^2 - 162 * q^3 + 193 * q^4 + 1170 * q^5 - 729 * q^6 - 4802 * q^7 + 6849 * q^8 + 13122 * q^9 - 77090 * q^10 - 145746 * q^11 - 15633 * q^12 + 86528 * q^13 - 21609 * q^14 - 94770 * q^15 - 509183 * q^16 - 229842 * q^17 + 59049 * q^18 - 221224 * q^19 - 628290 * q^20 + 388962 * q^21 - 1302932 * q^22 - 2035782 * q^23 - 554769 * q^24 + 2543050 * q^25 + 516438 * q^26 - 1062882 * q^27 - 463393 * q^28 + 9756252 * q^29 + 6244290 * q^30 + 204000 * q^31 - 9175743 * q^32 + 11805426 * q^33 + 25627554 * q^34 - 2809170 * q^35 + 1266273 * q^36 - 13959816 * q^37 - 656676 * q^38 - 7008768 * q^39 + 34889790 * q^40 - 42362550 * q^41 + 1750329 * q^42 - 4763912 * q^43 - 19888164 * q^44 + 7676370 * q^45 - 15930600 * q^46 - 48278484 * q^47 + 41243823 * q^48 + 11529602 * q^49 - 84911625 * q^50 + 18617202 * q^51 + 9493510 * q^52 - 108980352 * q^53 - 4782969 * q^54 - 39966160 * q^55 - 16444449 * q^56 + 17919144 * q^57 + 72176782 * q^58 - 188376804 * q^59 + 50891490 * q^60 + 19722092 * q^61 + 228951936 * q^62 - 31505922 * q^63 + 130572161 * q^64 + 41724540 * q^65 + 105537492 * q^66 + 70274396 * q^67 + 217776834 * q^68 + 164898342 * q^69 + 185093090 * q^70 - 382044186 * q^71 + 44936289 * q^72 + 191785896 * q^73 + 4142502 * q^74 - 205987050 * q^75 - 18298628 * q^76 + 349936146 * q^77 - 41831478 * q^78 - 72592148 * q^79 - 61430850 * q^80 + 86093442 * q^81 + 114611450 * q^82 + 187994232 * q^83 + 37534833 * q^84 - 2000786580 * q^85 + 1230207804 * q^86 - 790256412 * q^87 - 256454052 * q^88 + 42930954 * q^89 - 505787490 * q^90 - 207753728 * q^91 - 257379192 * q^92 - 16524000 * q^93 - 1045824480 * q^94 - 153134280 * q^95 + 743235183 * q^96 + 1726854096 * q^97 + 51883209 * q^98 - 956239506 * q^99

Introduction

L-functions

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