LMFDB - Embedded newform 3.24.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,24,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 24, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	3.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:	$10.0561211204$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{530401}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 132600 $ x^2 - x - 132600
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-363.643$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1563.86 q^{2} -177147. q^{3} -5.94295e6 q^{4} +1.13630e8 q^{5} -2.77033e8 q^{6} +7.85264e9 q^{7} -2.24125e10 q^{8} +3.13811e10 q^{9} +O(q^{10})$	\(q+1563.86 q^{2} -177147. q^{3} -5.94295e6 q^{4} +1.13630e8 q^{5} -2.77033e8 q^{6} +7.85264e9 q^{7} -2.24125e10 q^{8} +3.13811e10 q^{9} +1.77701e11 q^{10} +1.03137e12 q^{11} +1.05278e12 q^{12} +8.08921e12 q^{13} +1.22804e13 q^{14} -2.01292e13 q^{15} +1.48030e13 q^{16} -1.38649e14 q^{17} +4.90756e13 q^{18} -1.41905e14 q^{19} -6.75297e14 q^{20} -1.39107e15 q^{21} +1.61292e15 q^{22} +4.80770e15 q^{23} +3.97031e15 q^{24} +9.90836e14 q^{25} +1.26504e16 q^{26} -5.55906e15 q^{27} -4.66679e16 q^{28} -1.45614e16 q^{29} -3.14792e16 q^{30} -8.10883e16 q^{31} +2.11160e17 q^{32} -1.82704e17 q^{33} -2.16828e17 q^{34} +8.92295e17 q^{35} -1.86496e17 q^{36} +1.19418e18 q^{37} -2.21919e17 q^{38} -1.43298e18 q^{39} -2.54674e18 q^{40} +6.63767e18 q^{41} -2.17544e18 q^{42} -1.06144e19 q^{43} -6.12940e18 q^{44} +3.56583e18 q^{45} +7.51856e18 q^{46} +1.16951e19 q^{47} -2.62232e18 q^{48} +3.42952e19 q^{49} +1.54953e18 q^{50} +2.45613e19 q^{51} -4.80738e19 q^{52} -7.56809e19 q^{53} -8.69359e18 q^{54} +1.17195e20 q^{55} -1.75998e20 q^{56} +2.51380e19 q^{57} -2.27720e19 q^{58} -4.19627e19 q^{59} +1.19627e20 q^{60} +7.45869e19 q^{61} -1.26811e20 q^{62} +2.46424e20 q^{63} +2.06047e20 q^{64} +9.19177e20 q^{65} -2.85724e20 q^{66} -1.29554e21 q^{67} +8.23985e20 q^{68} -8.51670e20 q^{69} +1.39542e21 q^{70} -2.37787e21 q^{71} -7.03329e20 q^{72} -3.03208e21 q^{73} +1.86752e21 q^{74} -1.75524e20 q^{75} +8.43334e20 q^{76} +8.09899e21 q^{77} -2.24098e21 q^{78} +3.75756e20 q^{79} +1.68207e21 q^{80} +9.84771e20 q^{81} +1.03804e22 q^{82} -9.99994e21 q^{83} +8.26707e21 q^{84} -1.57547e22 q^{85} -1.65994e22 q^{86} +2.57951e21 q^{87} -2.31157e22 q^{88} -5.36043e21 q^{89} +5.57645e21 q^{90} +6.35217e22 q^{91} -2.85719e22 q^{92} +1.43645e22 q^{93} +1.82895e22 q^{94} -1.61246e22 q^{95} -3.74063e22 q^{96} +1.11058e22 q^{97} +5.36328e22 q^{98} +3.23655e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 1242 q^{2} - 354294 q^{3} - 6458716 q^{4} - 46808820 q^{5} + 220016574 q^{6} - 211963904 q^{7} + 2571869016 q^{8} + 62762119218 q^{9}+O(q^{10}) $ 2 * q - 1242 * q^2 - 354294 * q^3 - 6458716 * q^4 - 46808820 * q^5 + 220016574 * q^6 - 211963904 * q^7 + 2571869016 * q^8 + 62762119218 * q^9	$ 2 q - 1242 q^{2} - 354294 q^{3} - 6458716 q^{4} - 46808820 q^{5} + 220016574 q^{6} - 211963904 q^{7} + 2571869016 q^{8} + 62762119218 q^{9} + 627869790180 q^{10} + 1468972366488 q^{11} + 1144142163252 q^{12} + 10491654264748 q^{13} + 34908555004416 q^{14} + 8292042036540 q^{15} - 50973150676720 q^{16} - 210888011520828 q^{17} - 38975276034378 q^{18} - 907382448537944 q^{19} - 592549041758760 q^{20} + 37548769701888 q^{21} + 385075304370504 q^{22} + 10\!\cdots\!12 q^{23}+ \cdots + 46\!\cdots\!92 q^{99}+O(q^{100}) $ 2 * q - 1242 * q^2 - 354294 * q^3 - 6458716 * q^4 - 46808820 * q^5 + 220016574 * q^6 - 211963904 * q^7 + 2571869016 * q^8 + 62762119218 * q^9 + 627869790180 * q^10 + 1468972366488 * q^11 + 1144142163252 * q^12 + 10491654264748 * q^13 + 34908555004416 * q^14 + 8292042036540 * q^15 - 50973150676720 * q^16 - 210888011520828 * q^17 - 38975276034378 * q^18 - 907382448537944 * q^19 - 592549041758760 * q^20 + 37548769701888 * q^21 + 385075304370504 * q^22 + 10116923323892112 * q^23 - 455598880577352 * q^24 + 14810505797591150 * q^25 + 5909481699569604 * q^26 - 11118121133111046 * q^27 - 42508434042586112 * q^28 + 18478753545176892 * q^29 - 111225249721016460 * q^30 - 272793622592745488 * q^31 + 186134219136906336 * q^32 - 260224047806249736 * q^33 - 14135605903588212 * q^34 + 2186169652458823680 * q^35 - 202681351793602044 * q^36 - 478995036787364 * q^37 + 1925903087124629112 * q^38 - 1858565078037313956 * q^39 - 6555203866715785200 * q^40 + 5555714961308771412 * q^41 - 6183945793367281152 * q^42 - 1198322147609320040 * q^43 - 6355093136294718288 * q^44 - 1468910370646951380 * q^45 - 7378368693556745808 * q^46 + 26308565672855777280 * q^47 + 9029740722928917840 * q^48 + 71964232849356271890 * q^49 - 37226516336176411350 * q^50 + 37358178576880117716 * q^51 - 49312907988586886888 * q^52 - 41127501899415224628 * q^53 + 6904353223661959566 * q^54 + 46986672525187689360 * q^55 - 377486892221258373120 * q^56 + 160740078611151165768 * q^57 - 115477922638933597836 * q^58 - 307537061909444286696 * q^59 + 104968285100439057720 * q^60 + 594961179098503751020 * q^61 + 411087431199774869712 * q^62 - 6651651906380353536 * q^63 + 828036632782207954496 * q^64 + 533732415162776445960 * q^65 - 68214934943321672088 * q^66 - 1630225825126993264088 * q^67 + 861243436942941889224 * q^68 - 1792182616057515964464 * q^69 - 2235006928450834744320 * q^70 - 383942598581649272976 * q^71 + 80707974897636174744 * q^72 - 2812202351440561692428 * q^73 + 5219558875357315020756 * q^74 - 2623636670525879449050 * q^75 + 1238138884710050927056 * q^76 + 4569917579124061519872 * q^77 - 1046846954633656639788 * q^78 + 21069388575313284880 * q^79 + 12235121810092022582880 * q^80 + 1969541804367222465762 * q^81 + 13416177399661303790652 * q^82 - 14817262080324402696024 * q^83 + 7530241565342001982464 * q^84 - 4164778183840982876520 * q^85 - 43019621516128896935352 * q^86 - 3273455754267450887124 * q^87 - 12182478384106427357664 * q^88 - 43449805260884456557164 * q^89 + 19703219312328902839620 * q^90 + 44146945026523904417792 * q^91 - 31310234209098260658144 * q^92 + 48324571861437084962736 * q^93 - 22713687421447503614976 * q^94 + 106687644602844474428400 * q^95 - 32973118517445546703392 * q^96 + 107136573045242168450692 * q^97 - 52061241480597067368618 * q^98 + 46097909396733721983192 * 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 $

$2$	1563.86	0.539949	0.269974	−	0.962867i	$-0.412985\pi$
$2$	1563.86	0.539949	0.269974	+	0.962867i	$0.412985\pi$
$3$	−177147.	−0.577350
$3$	−177147.	−0.577350
$4$	−5.94295e6	−0.708455
$5$	1.13630e8	1.04073	0.520365	−	0.853944i	$-0.325796\pi$
$5$	1.13630e8	1.04073	0.520365	+	0.853944i	$0.325796\pi$
$6$	−2.77033e8	−0.311740
$7$	7.85264e9	1.50103	0.750513	−	0.660856i	$-0.229807\pi$
$7$	7.85264e9	1.50103	0.750513	+	0.660856i	$0.229807\pi$
$8$	−2.24125e10	−0.922478
$9$	3.13811e10	0.333333
$10$	1.77701e11	0.561941
$11$	1.03137e12	1.08993	0.544966	−	0.838458i	$-0.316543\pi$
$11$	1.03137e12	1.08993	0.544966	+	0.838458i	$0.316543\pi$
$12$	1.05278e12	0.409027
$13$	8.08921e12	1.25187	0.625933	−	0.779877i	$-0.284718\pi$
$13$	8.08921e12	1.25187	0.625933	+	0.779877i	$0.284718\pi$
$14$	1.22804e13	0.810477
$15$	−2.01292e13	−0.600865
$16$	1.48030e13	0.210364
$17$	−1.38649e14	−0.981193	−0.490597	−	0.871387i	$-0.663221\pi$
$17$	−1.38649e14	−0.981193	−0.490597	+	0.871387i	$0.663221\pi$
$18$	4.90756e13	0.179983
$19$	−1.41905e14	−0.279467	−0.139734	−	0.990189i	$-0.544625\pi$
$19$	−1.41905e14	−0.279467	−0.139734	+	0.990189i	$0.544625\pi$
$20$	−6.75297e14	−0.737310
$21$	−1.39107e15	−0.866618
$22$	1.61292e15	0.588508
$23$	4.80770e15	1.05212	0.526062	−	0.850446i	$-0.323668\pi$
$23$	4.80770e15	1.05212	0.526062	+	0.850446i	$0.323668\pi$
$24$	3.97031e15	0.532593
$25$	9.90836e14	0.0831174
$26$	1.26504e16	0.675944
$27$	−5.55906e15	−0.192450
$28$	−4.66679e16	−1.06341
$29$	−1.45614e16	−0.221629	−0.110814	−	0.993841i	$-0.535346\pi$
$29$	−1.45614e16	−0.221629	−0.110814	+	0.993841i	$0.535346\pi$
$30$	−3.14792e16	−0.324437
$31$	−8.10883e16	−0.573190	−0.286595	−	0.958052i	$-0.592523\pi$
$31$	−8.10883e16	−0.573190	−0.286595	+	0.958052i	$0.592523\pi$
$32$	2.11160e17	1.03606
$33$	−1.82704e17	−0.629273
$34$	−2.16828e17	−0.529794
$35$	8.92295e17	1.56216
$36$	−1.86496e17	−0.236152
$37$	1.19418e18	1.10344	0.551720	−	0.834029i	$-0.313972\pi$
$37$	1.19418e18	1.10344	0.551720	+	0.834029i	$0.313972\pi$
$38$	−2.21919e17	−0.150898
$39$	−1.43298e18	−0.722765
$40$	−2.54674e18	−0.960050
$41$	6.63767e18	1.88365	0.941827	−	0.336098i	$-0.109107\pi$
$41$	6.63767e18	1.88365	0.941827	+	0.336098i	$0.109107\pi$
$42$	−2.17544e18	−0.467929
$43$	−1.06144e19	−1.74184	−0.870920	−	0.491425i	$-0.836476\pi$
$43$	−1.06144e19	−1.74184	−0.870920	+	0.491425i	$0.836476\pi$
$44$	−6.12940e18	−0.772168
$45$	3.56583e18	0.346910
$46$	7.51856e18	0.568094
$47$	1.16951e19	0.690049	0.345024	−	0.938594i	$-0.387871\pi$
$47$	1.16951e19	0.690049	0.345024	+	0.938594i	$0.387871\pi$
$48$	−2.62232e18	−0.121454
$49$	3.42952e19	1.25308
$50$	1.54953e18	0.0448791
$51$	2.45613e19	0.566492
$52$	−4.80738e19	−0.886891
$53$	−7.56809e19	−1.12154	−0.560769	−	0.827972i	$-0.689494\pi$
$53$	−7.56809e19	−1.12154	−0.560769	+	0.827972i	$0.689494\pi$
$54$	−8.69359e18	−0.103913
$55$	1.17195e20	1.13432
$56$	−1.75998e20	−1.38466
$57$	2.51380e19	0.161350
$58$	−2.27720e19	−0.119668
$59$	−4.19627e19	−0.181161	−0.0905806	−	0.995889i	$-0.528872\pi$
$59$	−4.19627e19	−0.181161	−0.0905806	+	0.995889i	$0.528872\pi$
$60$	1.19627e20	0.425686
$61$	7.45869e19	0.219467	0.109734	−	0.993961i	$-0.465000\pi$
$61$	7.45869e19	0.219467	0.109734	+	0.993961i	$0.465000\pi$
$62$	−1.26811e20	−0.309493
$63$	2.46424e20	0.500342
$64$	2.06047e20	0.349058
$65$	9.19177e20	1.30285
$66$	−2.85724e20	−0.339775
$67$	−1.29554e21	−1.29595	−0.647976	−	0.761661i	$-0.724384\pi$
$67$	−1.29554e21	−1.29595	−0.647976	+	0.761661i	$0.724384\pi$
$68$	8.23985e20	0.695131
$69$	−8.51670e20	−0.607444
$70$	1.39542e21	0.843487
$71$	−2.37787e21	−1.22101	−0.610503	−	0.792014i	$-0.709033\pi$
$71$	−2.37787e21	−1.22101	−0.610503	+	0.792014i	$0.709033\pi$
$72$	−7.03329e20	−0.307493
$73$	−3.03208e21	−1.13117	−0.565585	−	0.824690i	$-0.691349\pi$
$73$	−3.03208e21	−1.13117	−0.565585	+	0.824690i	$0.691349\pi$
$74$	1.86752e21	0.595801
$75$	−1.75524e20	−0.0479878
$76$	8.43334e20	0.197990
$77$	8.09899e21	1.63602
$78$	−2.24098e21	−0.390256
$79$	3.75756e20	0.0565190	0.0282595	−	0.999601i	$-0.491004\pi$
$79$	3.75756e20	0.0565190	0.0282595	+	0.999601i	$0.491004\pi$
$80$	1.68207e21	0.218932
$81$	9.84771e20	0.111111
$82$	1.03804e22	1.01708
$83$	−9.99994e21	−0.852314	−0.426157	−	0.904649i	$-0.640133\pi$
$83$	−9.99994e21	−0.852314	−0.426157	+	0.904649i	$0.640133\pi$
$84$	8.26707e21	0.613960
$85$	−1.57547e22	−1.02116
$86$	−1.65994e22	−0.940505
$87$	2.57951e21	0.127957
$88$	−2.31157e22	−1.00544
$89$	−5.36043e21	−0.204746	−0.102373	−	0.994746i	$-0.532643\pi$
$89$	−5.36043e21	−0.204746	−0.102373	+	0.994746i	$0.532643\pi$
$90$	5.57645e21	0.187314
$91$	6.35217e22	1.87908
$92$	−2.85719e22	−0.745383
$93$	1.43645e22	0.330931
$94$	1.82895e22	0.372591
$95$	−1.61246e22	−0.290850
$96$	−3.74063e22	−0.598172
$97$	1.11058e22	0.157643	0.0788214	−	0.996889i	$-0.474884\pi$
$97$	1.11058e22	0.157643	0.0788214	+	0.996889i	$0.474884\pi$
$98$	5.36328e22	0.676598
$99$	3.23655e22	0.363311
$100$	−5.88849e21	−0.0588849
$101$	8.99589e22	0.802321	0.401160	−	0.916008i	$-0.368607\pi$
$101$	8.99589e22	0.802321	0.401160	+	0.916008i	$0.368607\pi$
$102$	3.84104e22	0.305877
$103$	−8.83460e22	−0.628867	−0.314434	−	0.949279i	$-0.601815\pi$
$103$	−8.83460e22	−0.628867	−0.314434	+	0.949279i	$0.601815\pi$
$104$	−1.81300e23	−1.15482
$105$	−1.58067e23	−0.901914
$106$	−1.18354e23	−0.605573
$107$	2.32082e23	1.06593	0.532963	−	0.846138i	$-0.321078\pi$
$107$	2.32082e23	1.06593	0.532963	+	0.846138i	$0.321078\pi$
$108$	3.30372e22	0.136342
$109$	−2.76863e23	−1.02768	−0.513842	−	0.857885i	$-0.671778\pi$
$109$	−2.76863e23	−1.02768	−0.513842	+	0.857885i	$0.671778\pi$
$110$	1.83276e23	0.612477
$111$	−2.11545e23	−0.637071
$112$	1.16243e23	0.315762
$113$	3.71795e23	0.911803	0.455901	−	0.890030i	$-0.349317\pi$
$113$	3.71795e23	0.911803	0.455901	+	0.890030i	$0.349317\pi$
$114$	3.93123e22	0.0871210
$115$	5.46299e23	1.09498
$116$	8.65376e22	0.157014
$117$	2.53848e23	0.417289
$118$	−6.56237e22	−0.0978178
$119$	−1.08876e24	−1.47280
$120$	4.51147e23	0.554285
$121$	1.68298e23	0.187952
$122$	1.16643e23	0.118501
$123$	−1.17584e24	−1.08753
$124$	4.81904e23	0.406080
$125$	−1.24199e24	−0.954227
$126$	3.85373e23	0.270159
$127$	−1.60553e24	−1.02772	−0.513861	−	0.857874i	$-0.671785\pi$
$127$	−1.60553e24	−1.02772	−0.513861	+	0.857874i	$0.671785\pi$
$128$	−1.44911e24	−0.847591
$129$	1.88031e24	1.00565
$130$	1.43746e24	0.703474
$131$	2.07814e24	0.931228	0.465614	−	0.884988i	$-0.345834\pi$
$131$	2.07814e24	0.931228	0.465614	+	0.884988i	$0.345834\pi$
$132$	1.08580e24	0.445811
$133$	−1.11433e24	−0.419487
$134$	−2.02603e24	−0.699748
$135$	−6.31676e23	−0.200288
$136$	3.10748e24	0.905130
$137$	4.86669e24	1.30301	0.651504	−	0.758645i	$-0.274138\pi$
$137$	4.86669e24	1.30301	0.651504	+	0.758645i	$0.274138\pi$
$138$	−1.33189e24	−0.327989
$139$	9.05962e23	0.205324	0.102662	−	0.994716i	$-0.467264\pi$
$139$	9.05962e23	0.205324	0.102662	+	0.994716i	$0.467264\pi$
$140$	−5.30287e24	−1.10672
$141$	−2.07176e24	−0.398400
$142$	−3.71866e24	−0.659281
$143$	8.34299e24	1.36445
$144$	4.64535e23	0.0701213
$145$	−1.65461e24	−0.230655
$146$	−4.74175e24	−0.610774
$147$	−6.07529e24	−0.723465
$148$	−7.09694e24	−0.781738
$149$	9.86509e24	1.00568	0.502839	−	0.864380i	$-0.332289\pi$
$149$	9.86509e24	1.00568	0.502839	+	0.864380i	$0.332289\pi$
$150$	−2.74494e23	−0.0259110
$151$	−4.82721e24	−0.422145	−0.211072	−	0.977470i	$-0.567696\pi$
$151$	−4.82721e24	−0.422145	−0.211072	+	0.977470i	$0.567696\pi$
$152$	3.18045e24	0.257802
$153$	−4.35096e24	−0.327064
$154$	1.26657e25	0.883365
$155$	−9.21406e24	−0.596536
$156$	8.51613e24	0.512047
$157$	1.87063e24	0.104506	0.0522529	−	0.998634i	$-0.483360\pi$
$157$	1.87063e24	0.104506	0.0522529	+	0.998634i	$0.483360\pi$
$158$	5.87629e23	0.0305174
$159$	1.34067e25	0.647520
$160$	2.39941e25	1.07826
$161$	3.77531e25	1.57927
$162$	1.54004e24	0.0599943
$163$	−3.92032e25	−1.42286	−0.711432	−	0.702755i	$-0.751953\pi$
$163$	−3.92032e25	−1.42286	−0.711432	+	0.702755i	$0.751953\pi$
$164$	−3.94473e25	−1.33448
$165$	−2.07607e25	−0.654902
$166$	−1.56385e25	−0.460206
$167$	−4.64021e25	−1.27438	−0.637188	−	0.770708i	$-0.719903\pi$
$167$	−4.64021e25	−1.27438	−0.637188	+	0.770708i	$0.719903\pi$
$168$	3.11774e25	0.799436
$169$	2.36815e25	0.567168
$170$	−2.46381e25	−0.551372
$171$	−4.45312e24	−0.0931557
$172$	6.30809e25	1.23402
$173$	−4.74788e25	−0.868900	−0.434450	−	0.900696i	$-0.643057\pi$
$173$	−4.74788e25	−0.868900	−0.434450	+	0.900696i	$0.643057\pi$
$174$	4.03398e24	0.0690904
$175$	7.78068e24	0.124761
$176$	1.52674e25	0.229282
$177$	7.43356e24	0.104593
$178$	−8.38295e24	−0.110552
$179$	5.97561e25	0.738878	0.369439	−	0.929255i	$-0.379550\pi$
$179$	5.97561e25	0.738878	0.369439	+	0.929255i	$0.379550\pi$
$180$	−2.11915e25	−0.245770
$181$	3.92753e25	0.427381	0.213691	−	0.976901i	$-0.431452\pi$
$181$	3.92753e25	0.427381	0.213691	+	0.976901i	$0.431452\pi$
$182$	9.93389e25	1.01461
$183$	−1.32128e25	−0.126709
$184$	−1.07753e26	−0.970562
$185$	1.35694e26	1.14838
$186$	2.24641e25	0.178686
$187$	−1.42999e26	−1.06943
$188$	−6.95036e25	−0.488869
$189$	−4.36533e25	−0.288873
$190$	−2.52167e25	−0.157044
$191$	−9.94591e25	−0.583124	−0.291562	−	0.956552i	$-0.594175\pi$
$191$	−9.94591e25	−0.583124	−0.291562	+	0.956552i	$0.594175\pi$
$192$	−3.65007e25	−0.201529
$193$	2.11752e26	1.10133	0.550667	−	0.834725i	$-0.314373\pi$
$193$	2.11752e26	1.10133	0.550667	+	0.834725i	$0.314373\pi$
$194$	1.73679e25	0.0851190
$195$	−1.62829e26	−0.752203
$196$	−2.03815e26	−0.887750
$197$	2.43182e26	0.999009	0.499505	−	0.866311i	$-0.333515\pi$
$197$	2.43182e26	0.999009	0.499505	+	0.866311i	$0.333515\pi$
$198$	5.06151e25	0.196169
$199$	−2.49955e26	−0.914220	−0.457110	−	0.889410i	$-0.651115\pi$
$199$	−2.49955e26	−0.914220	−0.457110	+	0.889410i	$0.651115\pi$
$200$	−2.22072e25	−0.0766740
$201$	2.29500e26	0.748218
$202$	1.40683e26	0.433212
$203$	−1.14345e26	−0.332670
$204$	−1.45967e26	−0.401334
$205$	7.54238e26	1.96037
$206$	−1.38161e26	−0.339556
$207$	1.50871e26	0.350708
$208$	1.19745e26	0.263347
$209$	−1.46357e26	−0.304600
$210$	−2.47195e26	−0.486988
$211$	−2.68608e26	−0.501038	−0.250519	−	0.968112i	$-0.580601\pi$
$211$	−2.68608e26	−0.501038	−0.250519	+	0.968112i	$0.580601\pi$
$212$	4.49768e26	0.794560
$213$	4.21233e26	0.704948
$214$	3.62943e26	0.575546
$215$	−1.20611e27	−1.81278
$216$	1.24593e26	0.177531
$217$	−6.36757e26	−0.860373
$218$	−4.32974e26	−0.554897
$219$	5.37124e26	0.653081
$220$	−6.96483e26	−0.803618
$221$	−1.12156e27	−1.22832
$222$	−3.30826e26	−0.343986
$223$	4.28148e25	0.0422754	0.0211377	−	0.999777i	$-0.493271\pi$
$223$	4.28148e25	0.0422754	0.0211377	+	0.999777i	$0.493271\pi$
$224$	1.65816e27	1.55516
$225$	3.10935e25	0.0277058
$226$	5.81434e26	0.492327
$227$	1.04141e27	0.838154	0.419077	−	0.907951i	$-0.362354\pi$
$227$	1.04141e27	0.838154	0.419077	+	0.907951i	$0.362354\pi$
$228$	−1.49394e26	−0.114310
$229$	3.17314e26	0.230877	0.115439	−	0.993315i	$-0.463173\pi$
$229$	3.17314e26	0.230877	0.115439	+	0.993315i	$0.463173\pi$
$230$	8.54334e26	0.591232
$231$	−1.43471e27	−0.944554
$232$	3.26358e26	0.204448
$233$	1.07463e27	0.640715	0.320357	−	0.947297i	$-0.396197\pi$
$233$	1.07463e27	0.640715	0.320357	+	0.947297i	$0.396197\pi$
$234$	3.96983e26	0.225315
$235$	1.32892e27	0.718154
$236$	2.49382e26	0.128345
$237$	−6.65640e25	−0.0326312
$238$	−1.70267e27	−0.795235
$239$	−2.91187e27	−1.29598	−0.647988	−	0.761651i	$-0.724389\pi$
$239$	−2.91187e27	−1.29598	−0.647988	+	0.761651i	$0.724389\pi$
$240$	−2.97974e26	−0.126400
$241$	−1.77639e27	−0.718362	−0.359181	−	0.933268i	$-0.616944\pi$
$241$	−1.77639e27	−0.718362	−0.359181	+	0.933268i	$0.616944\pi$
$242$	2.63194e26	0.101484
$243$	−1.74449e26	−0.0641500
$244$	−4.43266e26	−0.155483
$245$	3.89696e27	1.30411
$246$	−1.83885e27	−0.587210
$247$	−1.14790e27	−0.349855
$248$	1.81739e27	0.528756
$249$	1.77146e27	0.492084
$250$	−1.94229e27	−0.515234
$251$	−4.39892e27	−1.11455	−0.557274	−	0.830329i	$-0.688153\pi$
$251$	−4.39892e27	−1.11455	−0.557274	+	0.830329i	$0.688153\pi$
$252$	−1.46449e27	−0.354470
$253$	4.95853e27	1.14674
$254$	−2.51082e27	−0.554917
$255$	2.79090e27	0.589565
$256$	−3.99465e27	−0.806714
$257$	3.06305e27	0.591457	0.295729	−	0.955272i	$-0.404438\pi$
$257$	3.06305e27	0.591457	0.295729	+	0.955272i	$0.404438\pi$
$258$	2.94054e27	0.543001
$259$	9.37744e27	1.65629
$260$	−5.46263e27	−0.923013
$261$	−4.56952e26	−0.0738762
$262$	3.24992e27	0.502815
$263$	4.37920e27	0.648491	0.324246	−	0.945973i	$-0.394890\pi$
$263$	4.37920e27	0.648491	0.324246	+	0.945973i	$0.394890\pi$
$264$	4.09487e27	0.580490
$265$	−8.59962e27	−1.16722
$266$	−1.74265e27	−0.226502
$267$	9.49584e26	0.118210
$268$	7.69930e27	0.918124
$269$	−1.36648e28	−1.56118	−0.780588	−	0.625046i	$-0.785080\pi$
$269$	−1.36648e28	−1.56118	−0.780588	+	0.625046i	$0.785080\pi$
$270$	−9.87852e26	−0.108146
$271$	−7.06980e27	−0.741755	−0.370878	−	0.928682i	$-0.620943\pi$
$271$	−7.06980e27	−0.741755	−0.370878	+	0.928682i	$0.620943\pi$
$272$	−2.05243e27	−0.206408
$273$	−1.12527e28	−1.08489
$274$	7.61081e27	0.703558
$275$	1.02192e27	0.0905923
$276$	5.06143e27	0.430347
$277$	1.02188e28	0.833460	0.416730	−	0.909030i	$-0.363176\pi$
$277$	1.02188e28	0.833460	0.416730	+	0.909030i	$0.363176\pi$
$278$	1.41680e27	0.110865
$279$	−2.54464e27	−0.191063
$280$	−1.99986e28	−1.44106
$281$	−8.03841e26	−0.0555965	−0.0277983	−	0.999614i	$-0.508850\pi$
$281$	−8.03841e26	−0.0555965	−0.0277983	+	0.999614i	$0.508850\pi$
$282$	−3.23994e27	−0.215116
$283$	−2.15414e28	−1.37318	−0.686592	−	0.727043i	$-0.740894\pi$
$283$	−2.15414e28	−1.37318	−0.686592	+	0.727043i	$0.740894\pi$
$284$	1.41316e28	0.865028
$285$	2.85643e27	0.167922
$286$	1.30473e28	0.736733
$287$	5.21232e28	2.82741
$288$	6.62642e27	0.345355
$289$	−7.43986e26	−0.0372597
$290$	−2.58758e27	−0.124542
$291$	−1.96735e27	−0.0910151
$292$	1.80195e28	0.801383
$293$	−2.33106e28	−0.996725	−0.498363	−	0.866969i	$-0.666065\pi$
$293$	−2.33106e28	−0.996725	−0.498363	+	0.866969i	$0.666065\pi$
$294$	−9.50089e27	−0.390634
$295$	−4.76822e27	−0.188540
$296$	−2.67645e28	−1.01790
$297$	−5.73346e27	−0.209758
$298$	1.54276e28	0.543015
$299$	3.88905e28	1.31712
$300$	1.04313e27	0.0339972
$301$	−8.33511e28	−2.61455
$302$	−7.54907e27	−0.227936
$303$	−1.59359e28	−0.463220
$304$	−2.10062e27	−0.0587898
$305$	8.47531e27	0.228406
$306$	−6.80428e27	−0.176598
$307$	6.97395e28	1.74336	0.871681	−	0.490074i	$-0.163030\pi$
$307$	6.97395e28	1.74336	0.871681	+	0.490074i	$0.163030\pi$
$308$	−4.81319e28	−1.15904
$309$	1.56502e28	0.363077
$310$	−1.44095e28	−0.322099
$311$	−4.01460e28	−0.864765	−0.432382	−	0.901690i	$-0.642327\pi$
$311$	−4.01460e28	−0.864765	−0.432382	+	0.901690i	$0.642327\pi$
$312$	3.21167e28	0.666735
$313$	7.08075e28	1.41683	0.708417	−	0.705794i	$-0.249409\pi$
$313$	7.08075e28	1.41683	0.708417	+	0.705794i	$0.249409\pi$
$314$	2.92539e27	0.0564278
$315$	2.80012e28	0.520720
$316$	−2.23310e27	−0.0400412
$317$	−3.21150e28	−0.555298	−0.277649	−	0.960683i	$-0.589555\pi$
$317$	−3.21150e28	−0.555298	−0.277649	+	0.960683i	$0.589555\pi$
$318$	2.09661e28	0.349628
$319$	−1.50182e28	−0.241560
$320$	2.34132e28	0.363275
$321$	−4.11126e28	−0.615413
$322$	5.90406e28	0.852723
$323$	1.96750e28	0.274211
$324$	−5.85245e27	−0.0787172
$325$	8.01509e27	0.104052
$326$	−6.13082e28	−0.768274
$327$	4.90454e28	0.593333
$328$	−1.48767e29	−1.73763
$329$	9.18377e28	1.03578
$330$	−3.24668e28	−0.353614
$331$	8.40986e28	0.884640	0.442320	−	0.896857i	$-0.354155\pi$
$331$	8.40986e28	0.884640	0.442320	+	0.896857i	$0.354155\pi$
$332$	5.94292e28	0.603826
$333$	3.74745e28	0.367813
$334$	−7.25663e28	−0.688098
$335$	−1.47212e29	−1.34874
$336$	−2.05921e28	−0.182305
$337$	−1.63996e29	−1.40311	−0.701553	−	0.712618i	$-0.747510\pi$
$337$	−1.63996e29	−1.40311	−0.701553	+	0.712618i	$0.747510\pi$
$338$	3.70345e28	0.306242
$339$	−6.58623e28	−0.526430
$340$	9.36294e28	0.723444
$341$	−8.36322e28	−0.624738
$342$	−6.96406e27	−0.0502993
$343$	5.43907e28	0.379877
$344$	2.37896e29	1.60681
$345$	−9.67752e28	−0.632185
$346$	−7.42502e28	−0.469162
$347$	6.78465e28	0.414704	0.207352	−	0.978266i	$-0.433515\pi$
$347$	6.78465e28	0.414704	0.207352	+	0.978266i	$0.433515\pi$
$348$	−1.53299e28	−0.0906520
$349$	1.82821e29	1.04601	0.523003	−	0.852331i	$-0.324812\pi$
$349$	1.82821e29	1.04601	0.523003	+	0.852331i	$0.324812\pi$
$350$	1.21679e28	0.0673647
$351$	−4.49684e28	−0.240922
$352$	2.17784e29	1.12924
$353$	1.44105e29	0.723218	0.361609	−	0.932330i	$-0.382228\pi$
$353$	1.44105e29	0.723218	0.361609	+	0.932330i	$0.382228\pi$
$354$	1.16250e28	0.0564751
$355$	−2.70198e29	−1.27074
$356$	3.18568e28	0.145053
$357$	1.92871e29	0.850319
$358$	9.34501e28	0.398956
$359$	−3.54388e28	−0.146519	−0.0732593	−	0.997313i	$-0.523340\pi$
$359$	−3.54388e28	−0.146519	−0.0732593	+	0.997313i	$0.523340\pi$
$360$	−7.99193e28	−0.320017
$361$	−2.37693e29	−0.921898
$362$	6.14210e28	0.230764
$363$	−2.98135e28	−0.108514
$364$	−3.77506e29	−1.33125
$365$	−3.44535e29	−1.17724
$366$	−2.06630e28	−0.0684166
$367$	1.57063e29	0.503981	0.251990	−	0.967730i	$-0.418915\pi$
$367$	1.57063e29	0.503981	0.251990	+	0.967730i	$0.418915\pi$
$368$	7.11686e28	0.221329
$369$	2.08297e29	0.627885
$370$	2.12207e29	0.620068
$371$	−5.94295e29	−1.68346
$372$	−8.53678e28	−0.234450
$373$	4.68656e29	1.24796	0.623982	−	0.781438i	$-0.285514\pi$
$373$	4.68656e29	1.24796	0.623982	+	0.781438i	$0.285514\pi$
$374$	−2.23630e29	−0.577440
$375$	2.20014e29	0.550923
$376$	−2.62118e29	−0.636555
$377$	−1.17790e29	−0.277449
$378$	−6.82676e28	−0.155976
$379$	4.57537e28	0.101409	0.0507044	−	0.998714i	$-0.483853\pi$
$379$	4.57537e28	0.101409	0.0507044	+	0.998714i	$0.483853\pi$
$380$	9.58280e28	0.206054
$381$	2.84415e29	0.593355
$382$	−1.55540e29	−0.314857
$383$	4.53749e29	0.891312	0.445656	−	0.895204i	$-0.352970\pi$
$383$	4.53749e29	0.891312	0.445656	+	0.895204i	$0.352970\pi$
$384$	2.56705e29	0.489357
$385$	9.20288e29	1.70265
$386$	3.31151e29	0.594664
$387$	−3.33091e29	−0.580613
$388$	−6.60011e28	−0.111683
$389$	3.59874e29	0.591195	0.295597	−	0.955313i	$-0.404481\pi$
$389$	3.59874e29	0.591195	0.295597	+	0.955313i	$0.404481\pi$
$390$	−2.54642e29	−0.406151
$391$	−6.66583e29	−1.03234
$392$	−7.68642e29	−1.15594
$393$	−3.68137e29	−0.537644
$394$	3.80302e29	0.539414
$395$	4.26971e28	0.0588210
$396$	−1.92347e29	−0.257389
$397$	−9.62669e28	−0.125137	−0.0625686	−	0.998041i	$-0.519929\pi$
$397$	−9.62669e28	−0.125137	−0.0625686	+	0.998041i	$0.519929\pi$
$398$	−3.90894e29	−0.493632
$399$	1.97400e29	0.242191
$400$	1.46674e28	0.0174849
$401$	4.97920e29	0.576766	0.288383	−	0.957515i	$-0.406882\pi$
$401$	4.97920e29	0.576766	0.288383	+	0.957515i	$0.406882\pi$
$402$	3.58906e29	0.404000
$403$	−6.55941e29	−0.717557
$404$	−5.34621e29	−0.568408
$405$	1.11899e29	0.115637
$406$	−1.78820e29	−0.179625
$407$	1.23164e30	1.20267
$408$	−5.50481e29	−0.522577
$409$	−1.48649e30	−1.37197	−0.685985	−	0.727616i	$-0.740628\pi$
$409$	−1.48649e30	−1.37197	−0.685985	+	0.727616i	$0.740628\pi$
$410$	1.17952e30	1.05850
$411$	−8.62119e29	−0.752292
$412$	5.25036e29	0.445524
$413$	−3.29518e29	−0.271928
$414$	2.35941e29	0.189365
$415$	−1.13629e30	−0.887028
$416$	1.70812e30	1.29701
$417$	−1.60489e29	−0.118544
$418$	−2.28881e29	−0.164469
$419$	−5.07194e29	−0.354579	−0.177289	−	0.984159i	$-0.556733\pi$
$419$	−5.07194e29	−0.354579	−0.177289	+	0.984159i	$0.556733\pi$
$420$	9.39387e29	0.638966
$421$	2.56153e30	1.69533	0.847666	−	0.530531i	$-0.178007\pi$
$421$	2.56153e30	1.69533	0.847666	+	0.530531i	$0.178007\pi$
$422$	−4.20065e29	−0.270535
$423$	3.67006e29	0.230016
$424$	1.69620e30	1.03459
$425$	−1.37379e29	−0.0815542
$426$	6.58749e29	0.380636
$427$	5.85704e29	0.329426
$428$	−1.37925e30	−0.755161
$429$	−1.47794e30	−0.787765
$430$	−1.88619e30	−0.978811
$431$	−1.21646e30	−0.614625	−0.307312	−	0.951609i	$-0.599430\pi$
$431$	−1.21646e30	−0.614625	−0.307312	+	0.951609i	$0.599430\pi$
$432$	−8.22910e28	−0.0404846
$433$	1.79430e30	0.859577	0.429789	−	0.902930i	$-0.358588\pi$
$433$	1.79430e30	0.859577	0.429789	+	0.902930i	$0.358588\pi$
$434$	−9.95798e29	−0.464558
$435$	2.93109e29	0.133169
$436$	1.64538e30	0.728068
$437$	−6.82236e29	−0.294034
$438$	8.39986e29	0.352630
$439$	−3.97063e30	−1.62374	−0.811871	−	0.583837i	$-0.801551\pi$
$439$	−3.97063e30	−1.62374	−0.811871	+	0.583837i	$0.801551\pi$
$440$	−2.62663e30	−1.04639
$441$	1.07622e30	0.417693
$442$	−1.75397e30	−0.663231
$443$	−1.28735e30	−0.474301	−0.237151	−	0.971473i	$-0.576213\pi$
$443$	−1.28735e30	−0.474301	−0.237151	+	0.971473i	$0.576213\pi$
$444$	1.25720e30	0.451337
$445$	−6.09105e29	−0.213085
$446$	6.69562e28	0.0228265
$447$	−1.74757e30	−0.580628
$448$	1.61802e30	0.523945
$449$	3.17012e30	1.00056	0.500279	−	0.865864i	$-0.333231\pi$
$449$	3.17012e30	1.00056	0.500279	+	0.865864i	$0.333231\pi$
$450$	4.86258e28	0.0149597
$451$	6.84590e30	2.05305
$452$	−2.20956e30	−0.645971
$453$	8.55126e29	0.243725
$454$	1.62862e30	0.452560
$455$	7.21796e30	1.95562
$456$	−5.63407e29	−0.148842
$457$	−6.89795e30	−1.77699	−0.888493	−	0.458891i	$-0.848247\pi$
$457$	−6.89795e30	−1.77699	−0.888493	+	0.458891i	$0.848247\pi$
$458$	4.96234e29	0.124662
$459$	7.70759e29	0.188831
$460$	−3.24663e30	−0.775742
$461$	−1.25314e30	−0.292038	−0.146019	−	0.989282i	$-0.546646\pi$
$461$	−1.25314e30	−0.292038	−0.146019	+	0.989282i	$0.546646\pi$
$462$	−2.24369e30	−0.510011
$463$	4.87399e30	1.08070	0.540348	−	0.841442i	$-0.318293\pi$
$463$	4.87399e30	1.08070	0.540348	+	0.841442i	$0.318293\pi$
$464$	−2.15553e29	−0.0466227
$465$	1.63224e30	0.344410
$466$	1.68057e30	0.345953
$467$	4.35835e30	0.875343	0.437671	−	0.899135i	$-0.355803\pi$
$467$	4.35835e30	0.875343	0.437671	+	0.899135i	$0.355803\pi$
$468$	−1.50861e30	−0.295630
$469$	−1.01734e31	−1.94526
$470$	2.07824e30	0.387766
$471$	−3.31376e29	−0.0603365
$472$	9.40490e29	0.167117
$473$	−1.09474e31	−1.89849
$474$	−1.04097e29	−0.0176192
$475$	−1.40604e29	−0.0232286
$476$	6.47046e30	1.04341
$477$	−2.37495e30	−0.373846
$478$	−4.55376e30	−0.699760
$479$	4.80333e30	0.720582	0.360291	−	0.932840i	$-0.382677\pi$
$479$	4.80333e30	0.720582	0.360291	+	0.932840i	$0.382677\pi$
$480$	−4.25048e30	−0.622535
$481$	9.65995e30	1.38136
$482$	−2.77803e30	−0.387879
$483$	−6.68785e30	−0.911790
$484$	−1.00019e30	−0.133156
$485$	1.26195e30	0.164063
$486$	−2.72814e29	−0.0346377
$487$	−3.71714e30	−0.460920	−0.230460	−	0.973082i	$-0.574023\pi$
$487$	−3.71714e30	−0.460920	−0.230460	+	0.973082i	$0.574023\pi$
$488$	−1.67168e30	−0.202454
$489$	6.94472e30	0.821491
$490$	6.09429e30	0.704155
$491$	7.53933e30	0.850933	0.425466	−	0.904974i	$-0.360110\pi$
$491$	7.53933e30	0.850933	0.425466	+	0.904974i	$0.360110\pi$
$492$	6.98798e30	0.770465
$493$	2.01892e30	0.217460
$494$	−1.79515e30	−0.188904
$495$	3.67770e30	0.378108
$496$	−1.20035e30	−0.120579
$497$	−1.86726e31	−1.83276
$498$	2.77031e30	0.265700
$499$	3.09263e30	0.289849	0.144925	−	0.989443i	$-0.453706\pi$
$499$	3.09263e30	0.289849	0.144925	+	0.989443i	$0.453706\pi$
$500$	7.38106e30	0.676027
$501$	8.21999e30	0.735762
$502$	−6.87930e30	−0.601799
$503$	−4.43628e30	−0.379304	−0.189652	−	0.981851i	$-0.560736\pi$
$503$	−4.43628e30	−0.379304	−0.189652	+	0.981851i	$0.560736\pi$
$504$	−5.52299e30	−0.461555
$505$	1.02220e31	0.834999
$506$	7.75444e30	0.619183
$507$	−4.19510e30	−0.327455
$508$	9.54158e30	0.728094
$509$	−2.05052e31	−1.52971	−0.764855	−	0.644203i	$-0.777189\pi$
$509$	−2.05052e31	−1.52971	−0.764855	+	0.644203i	$0.777189\pi$
$510$	4.36457e30	0.318335
$511$	−2.38098e31	−1.69791
$512$	5.90893e30	0.412007
$513$	7.88858e29	0.0537835
$514$	4.79018e30	0.319357
$515$	−1.00388e31	−0.654481
$516$	−1.11746e31	−0.712459
$517$	1.20620e31	0.752106
$518$	1.46650e31	0.894313
$519$	8.41073e30	0.501660
$520$	−2.06011e31	−1.20185
$521$	−2.13126e31	−1.21620	−0.608098	−	0.793862i	$-0.708067\pi$
$521$	−2.13126e31	−1.21620	−0.608098	+	0.793862i	$0.708067\pi$
$522$	−7.14608e29	−0.0398894
$523$	5.37551e30	0.293528	0.146764	−	0.989172i	$-0.453114\pi$
$523$	5.37551e30	0.293528	0.146764	+	0.989172i	$0.453114\pi$
$524$	−1.23503e31	−0.659733
$525$	−1.37832e30	−0.0720310
$526$	6.84846e30	0.350152
$527$	1.12428e31	0.562410
$528$	−2.70458e30	−0.132376
$529$	2.23351e30	0.106966
$530$	−1.34486e31	−0.630238
$531$	−1.31683e30	−0.0603870
$532$	6.62240e30	0.297188
$533$	5.36935e31	2.35808
$534$	1.48502e30	0.0638273
$535$	2.63714e31	1.10934
$536$	2.90362e31	1.19549
$537$	−1.05856e31	−0.426591
$538$	−2.13698e31	−0.842955
$539$	3.53711e31	1.36577
$540$	3.75402e30	0.141895
$541$	−3.74692e30	−0.138646	−0.0693228	−	0.997594i	$-0.522084\pi$
$541$	−3.74692e30	−0.138646	−0.0693228	+	0.997594i	$0.522084\pi$
$542$	−1.10562e31	−0.400510
$543$	−6.95750e30	−0.246749
$544$	−2.92771e31	−1.01658
$545$	−3.14599e31	−1.06954
$546$	−1.75976e31	−0.585785
$547$	−3.43148e30	−0.111848	−0.0559239	−	0.998435i	$-0.517810\pi$
$547$	−3.43148e30	−0.111848	−0.0559239	+	0.998435i	$0.517810\pi$
$548$	−2.89225e31	−0.923123
$549$	2.34062e30	0.0731557
$550$	1.59814e30	0.0489152
$551$	2.06633e30	0.0619379
$552$	1.90881e31	0.560354
$553$	2.95068e30	0.0848364
$554$	1.59808e31	0.450026
$555$	−2.40378e31	−0.663019
$556$	−5.38409e30	−0.145463
$557$	3.40780e31	0.901860	0.450930	−	0.892559i	$-0.351092\pi$
$557$	3.40780e31	0.901860	0.450930	+	0.892559i	$0.351092\pi$
$558$	−3.97945e30	−0.103164
$559$	−8.58622e31	−2.18055
$560$	1.32087e31	0.328622
$561$	2.53318e31	0.617438
$562$	−1.25709e30	−0.0300193
$563$	−2.39242e31	−0.559747	−0.279873	−	0.960037i	$-0.590292\pi$
$563$	−2.39242e31	−0.559747	−0.279873	+	0.960037i	$0.590292\pi$
$564$	1.23124e31	0.282248
$565$	4.22470e31	0.948940
$566$	−3.36876e31	−0.741450
$567$	7.73305e30	0.166781
$568$	5.32942e31	1.12635
$569$	−1.92696e31	−0.399101	−0.199550	−	0.979888i	$-0.563948\pi$
$569$	−1.92696e31	−0.399101	−0.199550	+	0.979888i	$0.563948\pi$
$570$	4.46706e30	0.0906694
$571$	1.76715e31	0.351526	0.175763	−	0.984433i	$-0.443761\pi$
$571$	1.76715e31	0.351526	0.175763	+	0.984433i	$0.443761\pi$
$572$	−4.95820e31	−0.966651
$573$	1.76189e31	0.336667
$574$	8.15133e31	1.52666
$575$	4.76364e30	0.0874498
$576$	6.46598e30	0.116353
$577$	5.86874e31	1.03520	0.517599	−	0.855624i	$-0.326826\pi$
$577$	5.86874e31	1.03520	0.517599	+	0.855624i	$0.326826\pi$
$578$	−1.16349e30	−0.0201183
$579$	−3.75113e31	−0.635856
$580$	9.83327e30	0.163409
$581$	−7.85259e31	−1.27934
$582$	−3.07667e30	−0.0491435
$583$	−7.80552e31	−1.22240
$584$	6.79566e31	1.04348
$585$	2.88447e31	0.434284
$586$	−3.64545e31	−0.538181
$587$	6.89187e31	0.997697	0.498849	−	0.866689i	$-0.333756\pi$
$587$	6.89187e31	0.997697	0.498849	+	0.866689i	$0.333756\pi$
$588$	3.61051e31	0.512542
$589$	1.15068e31	0.160188
$590$	−7.45682e30	−0.101802
$591$	−4.30789e31	−0.576778
$592$	1.76775e31	0.232124
$593$	−7.35782e31	−0.947589	−0.473795	−	0.880635i	$-0.657116\pi$
$593$	−7.35782e31	−0.947589	−0.473795	+	0.880635i	$0.657116\pi$
$594$	−8.96632e30	−0.113258
$595$	−1.23716e32	−1.53278
$596$	−5.86278e31	−0.712478
$597$	4.42787e31	0.527825
$598$	6.08193e31	0.711177
$599$	1.35998e32	1.56000	0.779999	−	0.625780i	$-0.215219\pi$
$599$	1.35998e32	1.56000	0.779999	+	0.625780i	$0.215219\pi$
$600$	3.93393e30	0.0442677
$601$	−7.89659e31	−0.871732	−0.435866	−	0.900011i	$-0.643558\pi$
$601$	−7.89659e31	−0.871732	−0.435866	+	0.900011i	$0.643558\pi$
$602$	−1.30349e32	−1.41172
$603$	−4.06553e31	−0.431984
$604$	2.86879e31	0.299070
$605$	1.91237e31	0.195607
$606$	−2.49216e31	−0.250115
$607$	−4.65196e31	−0.458106	−0.229053	−	0.973414i	$-0.573563\pi$
$607$	−4.65196e31	−0.458106	−0.229053	+	0.973414i	$0.573563\pi$
$608$	−2.99646e31	−0.289546
$609$	2.02559e31	0.192067
$610$	1.32542e31	0.123327
$611$	9.46044e31	0.863849
$612$	2.58575e31	0.231710
$613$	1.41819e32	1.24721	0.623606	−	0.781739i	$-0.285667\pi$
$613$	1.41819e32	1.24721	0.623606	+	0.781739i	$0.285667\pi$
$614$	1.09063e32	0.941326
$615$	−1.33611e32	−1.13182
$616$	−1.81519e32	−1.50919
$617$	2.38519e32	1.94645	0.973227	−	0.229848i	$-0.0738228\pi$
$617$	2.38519e32	1.94645	0.973227	+	0.229848i	$0.0738228\pi$
$618$	2.44748e31	0.196043
$619$	1.46333e32	1.15054	0.575268	−	0.817965i	$-0.304898\pi$
$619$	1.46333e32	1.15054	0.575268	+	0.817965i	$0.304898\pi$
$620$	5.47587e31	0.422619
$621$	−2.67263e31	−0.202481
$622$	−6.27827e31	−0.466929
$623$	−4.20935e31	−0.307328
$624$	−2.12125e31	−0.152044
$625$	−1.52938e32	−1.07621
$626$	1.10733e32	0.765018
$627$	2.59266e31	0.175861
$628$	−1.11170e31	−0.0740377
$629$	−1.65572e32	−1.08269
$630$	4.37899e31	0.281162
$631$	2.57610e32	1.62414	0.812072	−	0.583557i	$-0.198339\pi$
$631$	2.57610e32	1.62414	0.812072	+	0.583557i	$0.198339\pi$
$632$	−8.42164e30	−0.0521375
$633$	4.75831e31	0.289274
$634$	−5.02233e31	−0.299833
$635$	−1.82436e32	−1.06958
$636$	−7.96751e31	−0.458739
$637$	2.77421e32	1.56869
$638$	−2.34864e31	−0.130430
$639$	−7.46202e31	−0.407002
$640$	−1.64662e32	−0.882113
$641$	−2.91189e32	−1.53217	−0.766086	−	0.642739i	$-0.777798\pi$
$641$	−2.91189e32	−1.53217	−0.766086	+	0.642739i	$0.777798\pi$
$642$	−6.42943e31	−0.332292
$643$	−3.58958e32	−1.82229	−0.911144	−	0.412088i	$-0.864800\pi$
$643$	−3.58958e32	−1.82229	−0.911144	+	0.412088i	$0.864800\pi$
$644$	−2.24365e32	−1.11884
$645$	2.13659e32	1.04661
$646$	3.07689e31	0.148060
$647$	3.52744e32	1.66748	0.833740	−	0.552157i	$-0.186195\pi$
$647$	3.52744e32	1.66748	0.833740	+	0.552157i	$0.186195\pi$
$648$	−2.20712e31	−0.102498
$649$	−4.32791e31	−0.197453
$650$	1.25345e31	0.0561827
$651$	1.12800e32	0.496737
$652$	2.32983e32	1.00804
$653$	−2.22542e32	−0.946041	−0.473021	−	0.881051i	$-0.656836\pi$
$653$	−2.22542e32	−0.946041	−0.473021	+	0.881051i	$0.656836\pi$
$654$	7.67000e31	0.320370
$655$	2.36139e32	0.969156
$656$	9.82577e31	0.396253
$657$	−9.51499e31	−0.377057
$658$	1.43621e32	0.559269
$659$	1.21818e31	0.0466152	0.0233076	−	0.999728i	$-0.492580\pi$
$659$	1.21818e31	0.0466152	0.0233076	+	0.999728i	$0.492580\pi$
$660$	1.23380e32	0.463969
$661$	−3.10145e32	−1.14617	−0.573084	−	0.819496i	$-0.694253\pi$
$661$	−3.10145e32	−1.14617	−0.573084	+	0.819496i	$0.694253\pi$
$662$	1.31518e32	0.477661
$663$	1.98681e32	0.709172
$664$	2.24124e32	0.786241
$665$	−1.26621e32	−0.436573
$666$	5.86049e31	0.198600
$667$	−7.00068e31	−0.233181
$668$	2.75765e32	0.902839
$669$	−7.58451e30	−0.0244077
$670$	−2.30218e32	−0.728248
$671$	7.69268e31	0.239204
$672$	−2.93738e32	−0.897872
$673$	1.82996e32	0.549880	0.274940	−	0.961461i	$-0.411342\pi$
$673$	1.82996e32	0.549880	0.274940	+	0.961461i	$0.411342\pi$
$674$	−2.56467e32	−0.757605
$675$	−5.50812e30	−0.0159959
$676$	−1.40738e32	−0.401813
$677$	−5.90638e32	−1.65788	−0.828938	−	0.559341i	$-0.811054\pi$
$677$	−5.90638e32	−1.65788	−0.828938	+	0.559341i	$0.811054\pi$
$678$	−1.02999e32	−0.284245
$679$	8.72096e31	0.236626
$680$	3.53103e32	0.941995
$681$	−1.84482e32	−0.483908
$682$	−1.30789e32	−0.337327
$683$	3.47709e32	0.881815	0.440907	−	0.897553i	$-0.354657\pi$
$683$	3.47709e32	0.881815	0.440907	+	0.897553i	$0.354657\pi$
$684$	2.64647e31	0.0659967
$685$	5.53001e32	1.35608
$686$	8.50594e31	0.205114
$687$	−5.62112e31	−0.133297
$688$	−1.57125e32	−0.366420
$689$	−6.12199e32	−1.40402
$690$	−1.51343e32	−0.341348
$691$	−4.28793e32	−0.951151	−0.475576	−	0.879675i	$-0.657760\pi$
$691$	−4.28793e32	−0.951151	−0.475576	+	0.879675i	$0.657760\pi$
$692$	2.82164e32	0.615577
$693$	2.54155e32	0.545339
$694$	1.06102e32	0.223919
$695$	1.02944e32	0.213687
$696$	−5.78133e31	−0.118038
$697$	−9.20307e32	−1.84823
$698$	2.85907e32	0.564790
$699$	−1.90367e32	−0.369917
$700$	−4.62402e31	−0.0883878
$701$	8.63465e32	1.62363	0.811816	−	0.583913i	$-0.198479\pi$
$701$	8.63465e32	1.62363	0.811816	+	0.583913i	$0.198479\pi$
$702$	−7.03243e31	−0.130085
$703$	−1.69459e32	−0.308375
$704$	2.12511e32	0.380449
$705$	−2.35414e32	−0.414626
$706$	2.25359e32	0.390501
$707$	7.06414e32	1.20430
$708$	−4.41773e31	−0.0740998
$709$	7.56772e32	1.24892	0.624458	−	0.781058i	$-0.285320\pi$
$709$	7.56772e32	1.24892	0.624458	+	0.781058i	$0.285320\pi$
$710$	−4.22551e32	−0.686133
$711$	1.17916e31	0.0188397
$712$	1.20141e32	0.188873
$713$	−3.89848e32	−0.603068
$714$	3.01623e32	0.459129
$715$	9.48013e32	1.42002
$716$	−3.55128e32	−0.523462
$717$	5.15830e32	0.748232
$718$	−5.54213e31	−0.0791126
$719$	−3.98801e32	−0.560240	−0.280120	−	0.959965i	$-0.590374\pi$
$719$	−3.98801e32	−0.560240	−0.280120	+	0.959965i	$0.590374\pi$
$720$	5.27851e31	0.0729773
$721$	−6.93749e32	−0.943946
$722$	−3.71718e32	−0.497778
$723$	3.14683e32	0.414746
$724$	−2.33411e32	−0.302781
$725$	−1.44279e31	−0.0184212
$726$	−4.66241e31	−0.0585921
$727$	−7.76270e32	−0.960211	−0.480106	−	0.877211i	$-0.659402\pi$
$727$	−7.76270e32	−0.960211	−0.480106	+	0.877211i	$0.659402\pi$
$728$	−1.42368e33	−1.73341
$729$	3.09032e31	0.0370370
$730$	−5.38804e32	−0.635650
$731$	1.47168e33	1.70908
$732$	7.85233e31	0.0897679
$733$	8.56762e32	0.964195	0.482097	−	0.876118i	$-0.339875\pi$
$733$	8.56762e32	0.964195	0.482097	+	0.876118i	$0.339875\pi$
$734$	2.45624e32	0.272124
$735$	−6.90335e32	−0.752931
$736$	1.01519e33	1.09007
$737$	−1.33618e33	−1.41250
$738$	3.25747e32	0.339026
$739$	−5.55833e32	−0.569552	−0.284776	−	0.958594i	$-0.591919\pi$
$739$	−5.55833e32	−0.569552	−0.284776	+	0.958594i	$0.591919\pi$
$740$	−8.06424e32	−0.813577
$741$	2.03347e32	0.201989
$742$	−9.29394e32	−0.908981
$743$	−1.55682e33	−1.49923	−0.749613	−	0.661876i	$-0.769760\pi$
$743$	−1.55682e33	−1.49923	−0.749613	+	0.661876i	$0.769760\pi$
$744$	−3.21946e32	−0.305277
$745$	1.12097e33	1.04664
$746$	7.32911e32	0.673837
$747$	−3.13809e32	−0.284105
$748$	8.49835e32	0.757646
$749$	1.82245e33	1.59998
$750$	3.44071e32	0.297470
$751$	1.66899e33	1.42100	0.710501	−	0.703696i	$-0.248468\pi$
$751$	1.66899e33	1.42100	0.710501	+	0.703696i	$0.248468\pi$
$752$	1.73124e32	0.145161
$753$	7.79256e32	0.643484
$754$	−1.84207e32	−0.149808
$755$	−5.48515e32	−0.439338
$756$	2.59429e32	0.204653
$757$	−7.88666e31	−0.0612760	−0.0306380	−	0.999531i	$-0.509754\pi$
$757$	−7.88666e31	−0.0612760	−0.0306380	+	0.999531i	$0.509754\pi$
$758$	7.15524e31	0.0547556
$759$	−8.78388e32	−0.662073
$760$	3.61394e32	0.268303
$761$	7.62229e32	0.557394	0.278697	−	0.960379i	$-0.410098\pi$
$761$	7.62229e32	0.557394	0.278697	+	0.960379i	$0.410098\pi$
$762$	4.44784e32	0.320381
$763$	−2.17410e33	−1.54258
$764$	5.91081e32	0.413117
$765$	−4.94399e32	−0.340386
$766$	7.09600e32	0.481263
$767$	−3.39445e32	−0.226789
$768$	7.07641e32	0.465756
$769$	−2.24557e33	−1.45604	−0.728020	−	0.685556i	$-0.759559\pi$
$769$	−2.24557e33	−1.45604	−0.728020	+	0.685556i	$0.759559\pi$
$770$	1.43920e33	0.919344
$771$	−5.42610e32	−0.341478
$772$	−1.25843e33	−0.780246
$773$	1.77063e33	1.08159	0.540795	−	0.841154i	$-0.318123\pi$
$773$	1.77063e33	1.08159	0.540795	+	0.841154i	$0.318123\pi$
$774$	−5.20908e32	−0.313502
$775$	−8.03452e31	−0.0476421
$776$	−2.48909e32	−0.145422
$777$	−1.66118e33	−0.956260
$778$	5.62793e32	0.319215
$779$	−9.41917e32	−0.526419
$780$	9.67688e32	0.532902
$781$	−2.45247e33	−1.33081
$782$	−1.04244e33	−0.557410
$783$	8.09476e31	0.0426524
$784$	5.07673e32	0.263602
$785$	2.12559e32	0.108762
$786$	−5.75714e32	−0.290301
$787$	1.41877e33	0.705024	0.352512	−	0.935807i	$-0.385328\pi$
$787$	1.41877e33	0.705024	0.352512	+	0.935807i	$0.385328\pi$
$788$	−1.44522e33	−0.707753
$789$	−7.75763e32	−0.374406
$790$	6.67723e31	0.0317603
$791$	2.91957e33	1.36864
$792$	−7.25394e32	−0.335146
$793$	6.03349e32	0.274743
$794$	−1.50548e32	−0.0675676
$795$	1.52340e33	0.673893
$796$	1.48547e33	0.647684
$797$	2.58083e33	1.10915	0.554573	−	0.832135i	$-0.312882\pi$
$797$	2.58083e33	1.10915	0.554573	+	0.832135i	$0.312882\pi$
$798$	3.08705e32	0.130771
$799$	−1.62152e33	−0.677071
$800$	2.09225e32	0.0861149
$801$	−1.68216e32	−0.0682485
$802$	7.78677e32	0.311424
$803$	−3.12720e33	−1.23290
$804$	−1.36391e33	−0.530079
$805$	4.28989e33	1.64359
$806$	−1.02580e33	−0.387444
$807$	2.42068e33	0.901345
$808$	−2.01621e33	−0.740124
$809$	−1.24432e33	−0.450323	−0.225161	−	0.974321i	$-0.572291\pi$
$809$	−1.24432e33	−0.450323	−0.225161	+	0.974321i	$0.572291\pi$
$810$	1.74995e32	0.0624378
$811$	1.55059e32	0.0545453	0.0272727	−	0.999628i	$-0.491318\pi$
$811$	1.55059e32	0.0545453	0.0272727	+	0.999628i	$0.491318\pi$
$812$	6.79549e32	0.235682
$813$	1.25239e33	0.428253
$814$	1.92611e33	0.649383
$815$	−4.45465e33	−1.48082
$816$	3.63582e32	0.119170
$817$	1.50624e33	0.486787
$818$	−2.32466e33	−0.740793
$819$	1.99338e33	0.626361
$820$	−4.48240e33	−1.38884
$821$	5.00186e33	1.52822	0.764108	−	0.645088i	$-0.223179\pi$
$821$	5.00186e33	1.52822	0.764108	+	0.645088i	$0.223179\pi$
$822$	−1.34823e33	−0.406199
$823$	2.77022e33	0.823030	0.411515	−	0.911403i	$-0.365000\pi$
$823$	2.77022e33	0.823030	0.411515	+	0.911403i	$0.365000\pi$
$824$	1.98006e33	0.580116
$825$	−1.81030e32	−0.0523035
$826$	−5.15319e32	−0.146827
$827$	−2.81604e33	−0.791270	−0.395635	−	0.918408i	$-0.629475\pi$
$827$	−2.81604e33	−0.791270	−0.395635	+	0.918408i	$0.629475\pi$
$828$	−8.96618e32	−0.248461
$829$	−6.05152e32	−0.165382	−0.0826908	−	0.996575i	$-0.526351\pi$
$829$	−6.05152e32	−0.165382	−0.0826908	+	0.996575i	$0.526351\pi$
$830$	−1.77700e33	−0.478950
$831$	−1.81024e33	−0.481198
$832$	1.66676e33	0.436974
$833$	−4.75500e33	−1.22951
$834$	−2.50981e32	−0.0640077
$835$	−5.27266e33	−1.32628
$836$	8.69791e32	0.215796
$837$	4.50775e32	0.110310
$838$	−7.93180e32	−0.191454
$839$	−2.21831e33	−0.528152	−0.264076	−	0.964502i	$-0.585067\pi$
$839$	−2.21831e33	−0.528152	−0.264076	+	0.964502i	$0.585067\pi$
$840$	3.54269e33	0.831996
$841$	−4.10469e33	−0.950881
$842$	4.00587e33	0.915392
$843$	1.42398e32	0.0320987
$844$	1.59632e33	0.354963
$845$	2.69093e33	0.590268
$846$	5.73945e32	0.124197
$847$	1.32158e33	0.282121
$848$	−1.12031e33	−0.235931
$849$	3.81599e33	0.792809
$850$	−2.14841e32	−0.0440351
$851$	5.74124e33	1.16096
$852$	−2.50337e33	−0.499424
$853$	9.69232e33	1.90772	0.953858	−	0.300257i	$-0.0970723\pi$
$853$	9.69232e33	1.90772	0.953858	+	0.300257i	$0.0970723\pi$
$854$	9.15958e32	0.177873
$855$	−5.06008e32	−0.0969499
$856$	−5.20154e33	−0.983295
$857$	−3.54610e33	−0.661411	−0.330705	−	0.943734i	$-0.607287\pi$
$857$	−3.54610e33	−0.661411	−0.330705	+	0.943734i	$0.607287\pi$
$858$	−2.31128e33	−0.425353
$859$	9.58348e33	1.74021	0.870105	−	0.492866i	$-0.164051\pi$
$859$	9.58348e33	1.74021	0.870105	+	0.492866i	$0.164051\pi$
$860$	7.16788e33	1.28428
$861$	−9.23347e33	−1.63241
$862$	−1.90238e33	−0.331866
$863$	3.43280e33	0.590915	0.295457	−	0.955356i	$-0.404528\pi$
$863$	3.43280e33	0.590915	0.295457	+	0.955356i	$0.404528\pi$
$864$	−1.17385e33	−0.199391
$865$	−5.39502e33	−0.904290
$866$	2.80604e33	0.464128
$867$	1.31795e32	0.0215119
$868$	3.78422e33	0.609536
$869$	3.87544e32	0.0616018
$870$	4.58381e32	0.0719044
$871$	−1.04799e34	−1.62236
$872$	6.20519e33	0.948016
$873$	3.48511e32	0.0525476
$874$	−1.06692e33	−0.158764
$875$	−9.75287e33	−1.43232
$876$	−3.19210e33	−0.462679
$877$	−8.57680e33	−1.22696	−0.613480	−	0.789711i	$-0.710231\pi$
$877$	−8.57680e33	−1.22696	−0.613480	+	0.789711i	$0.710231\pi$
$878$	−6.20950e33	−0.876738
$879$	4.12940e33	0.575460
$880$	1.73484e33	0.238621
$881$	−8.23643e33	−1.11819	−0.559096	−	0.829103i	$-0.688852\pi$
$881$	−8.23643e33	−1.11819	−0.559096	+	0.829103i	$0.688852\pi$
$882$	1.68305e33	0.225533
$883$	1.05626e34	1.39709	0.698545	−	0.715566i	$-0.253831\pi$
$883$	1.05626e34	1.39709	0.698545	+	0.715566i	$0.253831\pi$
$884$	6.66539e33	0.870211
$885$	8.44675e32	0.108853
$886$	−2.01324e33	−0.256098
$887$	6.30164e33	0.791283	0.395642	−	0.918405i	$-0.370522\pi$
$887$	6.30164e33	0.791283	0.395642	+	0.918405i	$0.370522\pi$
$888$	4.74126e33	0.587685
$889$	−1.26076e34	−1.54264
$890$	−9.52555e32	−0.115055
$891$	1.01567e33	0.121104
$892$	−2.54446e32	−0.0299502
$893$	−1.65960e33	−0.192846
$894$	−2.73295e33	−0.313510
$895$	6.79008e33	0.768972
$896$	−1.13793e34	−1.27226
$897$	−6.88934e33	−0.760439
$898$	4.95762e33	0.540250
$899$	1.18076e33	0.127035
$900$	−1.84787e32	−0.0196283
$901$	1.04931e34	1.10045
$902$	1.07060e34	1.10854
$903$	1.47654e34	1.50951
$904$	−8.33286e33	−0.841118
$905$	4.46285e33	0.444788
$906$	1.33730e33	0.131599
$907$	1.10592e34	1.07458	0.537292	−	0.843396i	$-0.319447\pi$
$907$	1.10592e34	1.07458	0.537292	+	0.843396i	$0.319447\pi$
$908$	−6.18904e33	−0.593795
$909$	2.82300e33	0.267440
$910$	1.12879e34	1.05593
$911$	−8.48544e33	−0.783814	−0.391907	−	0.920005i	$-0.628185\pi$
$911$	−8.48544e33	−0.783814	−0.391907	+	0.920005i	$0.628185\pi$
$912$	3.72119e32	0.0339423
$913$	−1.03137e34	−0.928964
$914$	−1.07874e34	−0.959481
$915$	−1.50138e33	−0.131870
$916$	−1.88578e33	−0.163566
$917$	1.63189e34	1.39780
$918$	1.20536e33	0.101959
$919$	2.82637e33	0.236102	0.118051	−	0.993008i	$-0.462335\pi$
$919$	2.82637e33	0.236102	0.118051	+	0.993008i	$0.462335\pi$
$920$	−1.22439e34	−1.01009
$921$	−1.23541e34	−1.00653
$922$	−1.95973e33	−0.157685
$923$	−1.92351e34	−1.52853
$924$	8.52643e33	0.669174
$925$	1.18323e33	0.0917150
$926$	7.62223e33	0.583520
$927$	−2.77239e33	−0.209622
$928$	−3.07478e33	−0.229621
$929$	2.09040e34	1.54187	0.770936	−	0.636913i	$-0.219789\pi$
$929$	2.09040e34	1.54187	0.770936	+	0.636913i	$0.219789\pi$
$930$	2.55260e33	0.185964
$931$	−4.86665e33	−0.350194
$932$	−6.38646e33	−0.453918
$933$	7.11175e33	0.499272
$934$	6.81585e33	0.472640
$935$	−1.62489e34	−1.11299
$936$	−5.68938e33	−0.384940
$937$	−9.77881e33	−0.653553	−0.326776	−	0.945102i	$-0.605962\pi$
$937$	−9.77881e33	−0.653553	−0.326776	+	0.945102i	$0.605962\pi$
$938$	−1.59097e34	−1.05034
$939$	−1.25433e34	−0.818010
$940$	−7.89769e33	−0.508780
$941$	2.28884e34	1.45658	0.728290	−	0.685270i	$-0.240316\pi$
$941$	2.28884e34	1.45658	0.728290	+	0.685270i	$0.240316\pi$
$942$	−5.18225e32	−0.0325786
$943$	3.19119e34	1.98184
$944$	−6.21175e32	−0.0381098
$945$	−4.96032e33	−0.300638
$946$	−1.71202e34	−1.02509
$947$	1.58194e34	0.935763	0.467882	−	0.883791i	$-0.345017\pi$
$947$	1.58194e34	0.935763	0.467882	+	0.883791i	$0.345017\pi$
$948$	3.95587e32	0.0231178
$949$	−2.45271e34	−1.41607
$950$	−2.19886e32	−0.0125422
$951$	5.68907e33	0.320601
$952$	2.44019e34	1.35862
$953$	−1.70079e34	−0.935582	−0.467791	−	0.883839i	$-0.654950\pi$
$953$	−1.70079e34	−0.935582	−0.467791	+	0.883839i	$0.654950\pi$
$954$	−3.71408e33	−0.201858
$955$	−1.13015e34	−0.606874
$956$	1.73051e34	0.918140
$957$	2.66043e33	0.139465
$958$	7.51172e33	0.389078
$959$	3.82163e34	1.95585
$960$	−4.14757e33	−0.209737
$961$	−1.34380e34	−0.671453
$962$	1.51068e34	0.745863
$963$	7.28297e33	0.355309
$964$	1.05570e34	0.508927
$965$	2.40614e34	1.14619
$966$	−1.04589e34	−0.492320
$967$	−3.44351e34	−1.60176	−0.800880	−	0.598825i	$-0.795634\pi$
$967$	−3.44351e34	−1.60176	−0.800880	+	0.598825i	$0.795634\pi$
$968$	−3.77198e33	−0.173382
$969$	−3.48536e33	−0.158316
$970$	1.97351e33	0.0885859
$971$	1.73462e33	0.0769456	0.0384728	−	0.999260i	$-0.487751\pi$
$971$	1.73462e33	0.0769456	0.0384728	+	0.999260i	$0.487751\pi$
$972$	1.03674e33	0.0454474
$973$	7.11419e33	0.308197
$974$	−5.81308e33	−0.248873
$975$	−1.41985e33	−0.0600743
$976$	1.10411e33	0.0461680
$977$	1.44173e33	0.0595794	0.0297897	−	0.999556i	$-0.490516\pi$
$977$	1.44173e33	0.0595794	0.0297897	+	0.999556i	$0.490516\pi$
$978$	1.08606e34	0.443563
$979$	−5.52859e33	−0.223159
$980$	−2.31594e34	−0.923907
$981$	−8.68824e33	−0.342561
$982$	1.17904e34	0.459460
$983$	−4.62857e34	−1.78271	−0.891357	−	0.453303i	$-0.850246\pi$
$983$	−4.62857e34	−1.78271	−0.891357	+	0.453303i	$0.850246\pi$
$984$	2.63536e34	1.00322
$985$	2.76327e34	1.03970
$986$	3.15731e33	0.117418
$987$	−1.62688e34	−0.598008
$988$	6.82191e33	0.247857
$989$	−5.10309e34	−1.83263
$990$	5.75140e33	0.204159
$991$	−1.68657e34	−0.591776	−0.295888	−	0.955223i	$-0.595615\pi$
$991$	−1.68657e34	−0.591776	−0.295888	+	0.955223i	$0.595615\pi$
$992$	−1.71226e34	−0.593862
$993$	−1.48978e34	−0.510747
$994$	−2.92013e34	−0.989597
$995$	−2.84023e34	−0.951455
$996$	−1.05277e34	−0.348619
$997$	2.01747e34	0.660410	0.330205	−	0.943909i	$-0.392882\pi$
$997$	2.01747e34	0.660410	0.330205	+	0.943909i	$0.392882\pi$
$998$	4.83644e33	0.156504
$999$	−6.63850e33	−0.212357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.24.a.b.1.2	✓	2
3.2	odd	2		9.24.a.c.1.1		2
4.3	odd	2		48.24.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.24.a.b.1.2	✓	2	1.1	even	1	trivial
9.24.a.c.1.1		2	3.2	odd	2
48.24.a.g.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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+1563.86 q^{2} -177147. q^{3} -5.94295e6 q^{4} +1.13630e8 q^{5} -2.77033e8 q^{6} +7.85264e9 q^{7} -2.24125e10 q^{8} +3.13811e10 q^{9} +O(q^{10})\)	\(q+1563.86 q^{2} -177147. q^{3} -5.94295e6 q^{4} +1.13630e8 q^{5} -2.77033e8 q^{6} +7.85264e9 q^{7} -2.24125e10 q^{8} +3.13811e10 q^{9} +1.77701e11 q^{10} +1.03137e12 q^{11} +1.05278e12 q^{12} +8.08921e12 q^{13} +1.22804e13 q^{14} -2.01292e13 q^{15} +1.48030e13 q^{16} -1.38649e14 q^{17} +4.90756e13 q^{18} -1.41905e14 q^{19} -6.75297e14 q^{20} -1.39107e15 q^{21} +1.61292e15 q^{22} +4.80770e15 q^{23} +3.97031e15 q^{24} +9.90836e14 q^{25} +1.26504e16 q^{26} -5.55906e15 q^{27} -4.66679e16 q^{28} -1.45614e16 q^{29} -3.14792e16 q^{30} -8.10883e16 q^{31} +2.11160e17 q^{32} -1.82704e17 q^{33} -2.16828e17 q^{34} +8.92295e17 q^{35} -1.86496e17 q^{36} +1.19418e18 q^{37} -2.21919e17 q^{38} -1.43298e18 q^{39} -2.54674e18 q^{40} +6.63767e18 q^{41} -2.17544e18 q^{42} -1.06144e19 q^{43} -6.12940e18 q^{44} +3.56583e18 q^{45} +7.51856e18 q^{46} +1.16951e19 q^{47} -2.62232e18 q^{48} +3.42952e19 q^{49} +1.54953e18 q^{50} +2.45613e19 q^{51} -4.80738e19 q^{52} -7.56809e19 q^{53} -8.69359e18 q^{54} +1.17195e20 q^{55} -1.75998e20 q^{56} +2.51380e19 q^{57} -2.27720e19 q^{58} -4.19627e19 q^{59} +1.19627e20 q^{60} +7.45869e19 q^{61} -1.26811e20 q^{62} +2.46424e20 q^{63} +2.06047e20 q^{64} +9.19177e20 q^{65} -2.85724e20 q^{66} -1.29554e21 q^{67} +8.23985e20 q^{68} -8.51670e20 q^{69} +1.39542e21 q^{70} -2.37787e21 q^{71} -7.03329e20 q^{72} -3.03208e21 q^{73} +1.86752e21 q^{74} -1.75524e20 q^{75} +8.43334e20 q^{76} +8.09899e21 q^{77} -2.24098e21 q^{78} +3.75756e20 q^{79} +1.68207e21 q^{80} +9.84771e20 q^{81} +1.03804e22 q^{82} -9.99994e21 q^{83} +8.26707e21 q^{84} -1.57547e22 q^{85} -1.65994e22 q^{86} +2.57951e21 q^{87} -2.31157e22 q^{88} -5.36043e21 q^{89} +5.57645e21 q^{90} +6.35217e22 q^{91} -2.85719e22 q^{92} +1.43645e22 q^{93} +1.82895e22 q^{94} -1.61246e22 q^{95} -3.74063e22 q^{96} +1.11058e22 q^{97} +5.36328e22 q^{98} +3.23655e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 1242 q^{2} - 354294 q^{3} - 6458716 q^{4} - 46808820 q^{5} + 220016574 q^{6} - 211963904 q^{7} + 2571869016 q^{8} + 62762119218 q^{9}+O(q^{10}) \) 2 * q - 1242 * q^2 - 354294 * q^3 - 6458716 * q^4 - 46808820 * q^5 + 220016574 * q^6 - 211963904 * q^7 + 2571869016 * q^8 + 62762119218 * q^9	\( 2 q - 1242 q^{2} - 354294 q^{3} - 6458716 q^{4} - 46808820 q^{5} + 220016574 q^{6} - 211963904 q^{7} + 2571869016 q^{8} + 62762119218 q^{9} + 627869790180 q^{10} + 1468972366488 q^{11} + 1144142163252 q^{12} + 10491654264748 q^{13} + 34908555004416 q^{14} + 8292042036540 q^{15} - 50973150676720 q^{16} - 210888011520828 q^{17} - 38975276034378 q^{18} - 907382448537944 q^{19} - 592549041758760 q^{20} + 37548769701888 q^{21} + 385075304370504 q^{22} + 10\!\cdots\!12 q^{23}+ \cdots + 46\!\cdots\!92 q^{99}+O(q^{100}) \) 2 * q - 1242 * q^2 - 354294 * q^3 - 6458716 * q^4 - 46808820 * q^5 + 220016574 * q^6 - 211963904 * q^7 + 2571869016 * q^8 + 62762119218 * q^9 + 627869790180 * q^10 + 1468972366488 * q^11 + 1144142163252 * q^12 + 10491654264748 * q^13 + 34908555004416 * q^14 + 8292042036540 * q^15 - 50973150676720 * q^16 - 210888011520828 * q^17 - 38975276034378 * q^18 - 907382448537944 * q^19 - 592549041758760 * q^20 + 37548769701888 * q^21 + 385075304370504 * q^22 + 10116923323892112 * q^23 - 455598880577352 * q^24 + 14810505797591150 * q^25 + 5909481699569604 * q^26 - 11118121133111046 * q^27 - 42508434042586112 * q^28 + 18478753545176892 * q^29 - 111225249721016460 * q^30 - 272793622592745488 * q^31 + 186134219136906336 * q^32 - 260224047806249736 * q^33 - 14135605903588212 * q^34 + 2186169652458823680 * q^35 - 202681351793602044 * q^36 - 478995036787364 * q^37 + 1925903087124629112 * q^38 - 1858565078037313956 * q^39 - 6555203866715785200 * q^40 + 5555714961308771412 * q^41 - 6183945793367281152 * q^42 - 1198322147609320040 * q^43 - 6355093136294718288 * q^44 - 1468910370646951380 * q^45 - 7378368693556745808 * q^46 + 26308565672855777280 * q^47 + 9029740722928917840 * q^48 + 71964232849356271890 * q^49 - 37226516336176411350 * q^50 + 37358178576880117716 * q^51 - 49312907988586886888 * q^52 - 41127501899415224628 * q^53 + 6904353223661959566 * q^54 + 46986672525187689360 * q^55 - 377486892221258373120 * q^56 + 160740078611151165768 * q^57 - 115477922638933597836 * q^58 - 307537061909444286696 * q^59 + 104968285100439057720 * q^60 + 594961179098503751020 * q^61 + 411087431199774869712 * q^62 - 6651651906380353536 * q^63 + 828036632782207954496 * q^64 + 533732415162776445960 * q^65 - 68214934943321672088 * q^66 - 1630225825126993264088 * q^67 + 861243436942941889224 * q^68 - 1792182616057515964464 * q^69 - 2235006928450834744320 * q^70 - 383942598581649272976 * q^71 + 80707974897636174744 * q^72 - 2812202351440561692428 * q^73 + 5219558875357315020756 * q^74 - 2623636670525879449050 * q^75 + 1238138884710050927056 * q^76 + 4569917579124061519872 * q^77 - 1046846954633656639788 * q^78 + 21069388575313284880 * q^79 + 12235121810092022582880 * q^80 + 1969541804367222465762 * q^81 + 13416177399661303790652 * q^82 - 14817262080324402696024 * q^83 + 7530241565342001982464 * q^84 - 4164778183840982876520 * q^85 - 43019621516128896935352 * q^86 - 3273455754267450887124 * q^87 - 12182478384106427357664 * q^88 - 43449805260884456557164 * q^89 + 19703219312328902839620 * q^90 + 44146945026523904417792 * q^91 - 31310234209098260658144 * q^92 + 48324571861437084962736 * q^93 - 22713687421447503614976 * q^94 + 106687644602844474428400 * q^95 - 32973118517445546703392 * q^96 + 107136573045242168450692 * q^97 - 52061241480597067368618 * q^98 + 46097909396733721983192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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