LMFDB - Embedded newform 3.26.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,26,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, 26, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 26 $
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:	$11.8799033986$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1287001}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 321750 $ x^2 - x - 321750
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-566.730$ 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)

$f(q)$	$=$	$q+6644.76 q^{2} -531441. q^{3} +1.05985e7 q^{4} +1.29474e8 q^{5} -3.53130e9 q^{6} -4.99182e10 q^{7} -1.52537e11 q^{8} +2.82430e11 q^{9} +O(q^{10})$	\(q+6644.76 q^{2} -531441. q^{3} +1.05985e7 q^{4} +1.29474e8 q^{5} -3.53130e9 q^{6} -4.99182e10 q^{7} -1.52537e11 q^{8} +2.82430e11 q^{9} +8.60326e11 q^{10} -2.40245e12 q^{11} -5.63245e12 q^{12} -1.10132e14 q^{13} -3.31695e14 q^{14} -6.88080e13 q^{15} -1.36920e15 q^{16} +1.88823e15 q^{17} +1.87668e15 q^{18} -5.16785e15 q^{19} +1.37223e15 q^{20} +2.65286e16 q^{21} -1.59637e16 q^{22} +2.07157e17 q^{23} +8.10644e16 q^{24} -2.81260e17 q^{25} -7.31801e17 q^{26} -1.50095e17 q^{27} -5.29056e17 q^{28} -3.91886e17 q^{29} -4.57213e17 q^{30} +7.70306e18 q^{31} -3.97970e18 q^{32} +1.27676e18 q^{33} +1.25469e19 q^{34} -6.46313e18 q^{35} +2.99332e18 q^{36} -2.99716e18 q^{37} -3.43391e19 q^{38} +5.85287e19 q^{39} -1.97496e19 q^{40} -2.45123e20 q^{41} +1.76276e20 q^{42} -2.88038e20 q^{43} -2.54623e19 q^{44} +3.65674e19 q^{45} +1.37651e21 q^{46} -3.01578e20 q^{47} +7.27648e20 q^{48} +1.15076e21 q^{49} -1.86890e21 q^{50} -1.00348e21 q^{51} -1.16723e21 q^{52} -4.35340e21 q^{53} -9.97343e20 q^{54} -3.11056e20 q^{55} +7.61438e21 q^{56} +2.74641e21 q^{57} -2.60399e21 q^{58} +6.92162e21 q^{59} -7.29258e20 q^{60} -2.89150e22 q^{61} +5.11850e22 q^{62} -1.40984e22 q^{63} +1.94985e22 q^{64} -1.42593e22 q^{65} +8.48379e21 q^{66} -1.41680e22 q^{67} +2.00123e22 q^{68} -1.10092e23 q^{69} -4.29460e22 q^{70} -6.66992e22 q^{71} -4.30810e22 q^{72} +1.33600e23 q^{73} -1.99154e22 q^{74} +1.49473e23 q^{75} -5.47712e22 q^{76} +1.19926e23 q^{77} +3.88909e23 q^{78} +8.16786e23 q^{79} -1.77276e23 q^{80} +7.97664e22 q^{81} -1.62878e24 q^{82} -7.24814e23 q^{83} +2.81162e23 q^{84} +2.44478e23 q^{85} -1.91394e24 q^{86} +2.08265e23 q^{87} +3.66463e23 q^{88} +1.55091e23 q^{89} +2.42982e23 q^{90} +5.49760e24 q^{91} +2.19554e24 q^{92} -4.09372e24 q^{93} -2.00391e24 q^{94} -6.69104e23 q^{95} +2.11498e24 q^{96} -2.30974e24 q^{97} +7.64654e24 q^{98} -6.78524e23 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 324 q^{2} - 1062882 q^{3} + 25607696 q^{4} + 570861756 q^{5} + 172186884 q^{6} - 29687385728 q^{7} - 23299970112 q^{8} + 564859072962 q^{9}+O(q^{10}) $ 2 * q - 324 * q^2 - 1062882 * q^3 + 25607696 * q^4 + 570861756 * q^5 + 172186884 * q^6 - 29687385728 * q^7 - 23299970112 * q^8 + 564859072962 * q^9	$ 2 q - 324 q^{2} - 1062882 q^{3} + 25607696 q^{4} + 570861756 q^{5} + 172186884 q^{6} - 29687385728 q^{7} - 23299970112 q^{8} + 564859072962 q^{9} - 2215598822136 q^{10} - 18187785618552 q^{11} - 13608979569936 q^{12} - 105143636679236 q^{13} - 472678969464576 q^{14} - 303379342470396 q^{15} - 27\!\cdots\!40 q^{16}+ \cdots - 51\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 324 * q^2 - 1062882 * q^3 + 25607696 * q^4 + 570861756 * q^5 + 172186884 * q^6 - 29687385728 * q^7 - 23299970112 * q^8 + 564859072962 * q^9 - 2215598822136 * q^10 - 18187785618552 * q^11 - 13608979569936 * q^12 - 105143636679236 * q^13 - 472678969464576 * q^14 - 303379342470396 * q^15 - 2773446956957440 * q^16 - 456987364349436 * q^17 - 91507169819844 * q^18 + 13897438495347064 * q^19 + 7997117779360224 * q^20 + 15777093958674048 * q^21 + 94040499983248368 * q^22 + 139342298900353776 * q^23 + 12382559416291392 * q^24 - 384459968007086914 * q^25 - 766564464131074296 * q^26 - 300189270593998242 * q^27 - 225406556770067456 * q^28 - 2502033490260709812 * q^29 + 1177460053634777976 * q^30 + 1075472102492455312 * q^31 + 1469701790817795072 * q^32 + 9665734976908893432 * q^33 + 28890135735526240632 * q^34 + 2466515950356245760 * q^35 + 7232369711626357776 * q^36 - 1971470949238312628 * q^37 - 167200626490209687024 * q^38 + 55877639420449859076 * q^39 + 37293994460212449408 * q^40 - 419163355703989597068 * q^41 + 251200984211223734016 * q^42 + 38930395898259827080 * q^43 - 262388124019551701952 * q^44 + 161228221141809720636 * q^45 + 1849090502383427845152 * q^46 - 738406177844949815040 * q^47 + 1473923424252418871040 * q^48 + 218980881200994518130 * q^49 - 1149725049975869177916 * q^50 + 242861821897228617276 * q^51 - 1092357476627674689056 * q^52 - 8494002801961842724164 * q^53 + 48630661836227715204 * q^54 - 7278503149452310381584 * q^55 + 10228956809527292497920 * q^56 - 7385668611405739039224 * q^57 + 12101124135433085546472 * q^58 + 8432077474426193999496 * q^59 - 4249996269780976802784 * q^60 - 24279127983741126331460 * q^61 + 97371085084960544796384 * q^62 - 8384594590491694743168 * q^63 + 28641639605810268606464 * q^64 - 12057449268713827431672 * q^65 - 49976977351597495938288 * q^66 - 135686108042078517042056 * q^67 - 15187614376581326197728 * q^68 - 74052210669902911071216 * q^69 - 105174558114673018728960 * q^70 + 120403069132729999155984 * q^71 - 6580599758753313655872 * q^72 + 84978009597861904797076 * q^73 - 27063264550565974651416 * q^74 + 204317789857654276663074 * q^75 + 231384244314856676602816 * q^76 - 199424410226061985552896 * q^77 + 407383785382282254940536 * q^78 + 1260761953277708216756080 * q^79 - 797093885216644267516416 * q^80 + 159532886153745019726722 * q^81 - 415932720534797186451816 * q^82 - 877480501829850785701512 * q^83 + 119790285936441418884096 * q^84 - 790672874505842808668808 * q^85 - 4192505892879917618487312 * q^86 + 1329683180097641883199092 * q^87 - 1673586555576256790675712 * q^88 + 2130788092375875828694644 * q^89 - 625750548363720042343416 * q^90 + 5598517474862662217460992 * q^91 + 1177698493733784503306112 * q^92 - 571549969620692943464592 * q^93 + 1040238523552479859385856 * q^94 + 7746075091871122248616464 * q^95 - 781059789413999830858752 * q^96 - 5594117297299805221393916 * q^97 + 14139905210414655642611676 * q^98 - 5136767861863439234395512 * 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 $

$2$	6644.76	1.14711	0.573554	−	0.819167i	$-0.305564\pi$
$2$	6644.76	1.14711	0.573554	+	0.819167i	$0.305564\pi$
$3$	−531441.	−0.577350
$3$	−531441.	−0.577350
$4$	1.05985e7	0.315859
$5$	1.29474e8	0.237169	0.118585	−	0.992944i	$-0.462164\pi$
$5$	1.29474e8	0.237169	0.118585	+	0.992944i	$0.462164\pi$
$6$	−3.53130e9	−0.662284
$7$	−4.99182e10	−1.36312	−0.681559	−	0.731763i	$-0.738698\pi$
$7$	−4.99182e10	−1.36312	−0.681559	+	0.731763i	$0.738698\pi$
$8$	−1.52537e11	−0.784785
$9$	2.82430e11	0.333333
$10$	8.60326e11	0.272059
$11$	−2.40245e12	−0.230806	−0.115403	−	0.993319i	$-0.536816\pi$
$11$	−2.40245e12	−0.230806	−0.115403	+	0.993319i	$0.536816\pi$
$12$	−5.63245e12	−0.182361
$13$	−1.10132e14	−1.31106	−0.655529	−	0.755170i	$-0.727554\pi$
$13$	−1.10132e14	−1.31106	−0.655529	+	0.755170i	$0.727554\pi$
$14$	−3.31695e14	−1.56365
$15$	−6.88080e13	−0.136930
$16$	−1.36920e15	−1.21609
$17$	1.88823e15	0.786039	0.393019	−	0.919530i	$-0.371431\pi$
$17$	1.88823e15	0.786039	0.393019	+	0.919530i	$0.371431\pi$
$18$	1.87668e15	0.382370
$19$	−5.16785e15	−0.535661	−0.267830	−	0.963466i	$-0.586307\pi$
$19$	−5.16785e15	−0.535661	−0.267830	+	0.963466i	$0.586307\pi$
$20$	1.37223e15	0.0749120
$21$	2.65286e16	0.786997
$22$	−1.59637e16	−0.264759
$23$	2.07157e17	1.97107	0.985533	−	0.169484i	$-0.0542102\pi$
$23$	2.07157e17	1.97107	0.985533	+	0.169484i	$0.0542102\pi$
$24$	8.10644e16	0.453096
$25$	−2.81260e17	−0.943751
$26$	−7.31801e17	−1.50393
$27$	−1.50095e17	−0.192450
$28$	−5.29056e17	−0.430553
$29$	−3.91886e17	−0.205677	−0.102838	−	0.994698i	$-0.532792\pi$
$29$	−3.91886e17	−0.205677	−0.102838	+	0.994698i	$0.532792\pi$
$30$	−4.57213e17	−0.157073
$31$	7.70306e18	1.75648	0.878238	−	0.478225i	$-0.158720\pi$
$31$	7.70306e18	1.75648	0.878238	+	0.478225i	$0.158720\pi$
$32$	−3.97970e18	−0.610205
$33$	1.27676e18	0.133256
$34$	1.25469e19	0.901672
$35$	−6.46313e18	−0.323290
$36$	2.99332e18	0.105286
$37$	−2.99716e18	−0.0748495	−0.0374248	−	0.999299i	$-0.511915\pi$
$37$	−2.99716e18	−0.0748495	−0.0374248	+	0.999299i	$0.511915\pi$
$38$	−3.43391e19	−0.614461
$39$	5.85287e19	0.756939
$40$	−1.97496e19	−0.186127
$41$	−2.45123e20	−1.69662	−0.848311	−	0.529498i	$-0.822380\pi$
$41$	−2.45123e20	−1.69662	−0.848311	+	0.529498i	$0.822380\pi$
$42$	1.76276e20	0.902771
$43$	−2.88038e20	−1.09924	−0.549621	−	0.835414i	$-0.685228\pi$
$43$	−2.88038e20	−1.09924	−0.549621	+	0.835414i	$0.685228\pi$
$44$	−2.54623e19	−0.0729020
$45$	3.65674e19	0.0790564
$46$	1.37651e21	2.26103
$47$	−3.01578e20	−0.378596	−0.189298	−	0.981920i	$-0.560621\pi$
$47$	−3.01578e20	−0.378596	−0.189298	+	0.981920i	$0.560621\pi$
$48$	7.27648e20	0.702111
$49$	1.15076e21	0.858093
$50$	−1.86890e21	−1.08258
$51$	−1.00348e21	−0.453820
$52$	−1.16723e21	−0.414109
$53$	−4.35340e21	−1.21725	−0.608626	−	0.793457i	$-0.708279\pi$
$53$	−4.35340e21	−1.21725	−0.608626	+	0.793457i	$0.708279\pi$
$54$	−9.97343e20	−0.220761
$55$	−3.11056e20	−0.0547400
$56$	7.61438e21	1.06975
$57$	2.74641e21	0.309264
$58$	−2.60399e21	−0.235934
$59$	6.92162e21	0.506475	0.253237	−	0.967404i	$-0.418505\pi$
$59$	6.92162e21	0.506475	0.253237	+	0.967404i	$0.418505\pi$
$60$	−7.29258e20	−0.0432504
$61$	−2.89150e22	−1.39476	−0.697381	−	0.716701i	$-0.745651\pi$
$61$	−2.89150e22	−1.39476	−0.697381	+	0.716701i	$0.745651\pi$
$62$	5.11850e22	2.01487
$63$	−1.40984e22	−0.454373
$64$	1.94985e22	0.516120
$65$	−1.42593e22	−0.310943
$66$	8.48379e21	0.152859
$67$	−1.41680e22	−0.211530	−0.105765	−	0.994391i	$-0.533729\pi$
$67$	−1.41680e22	−0.211530	−0.105765	+	0.994391i	$0.533729\pi$
$68$	2.00123e22	0.248277
$69$	−1.10092e23	−1.13800
$70$	−4.29460e22	−0.370849
$71$	−6.66992e22	−0.482382	−0.241191	−	0.970478i	$-0.577538\pi$
$71$	−6.66992e22	−0.482382	−0.241191	+	0.970478i	$0.577538\pi$
$72$	−4.30810e22	−0.261595
$73$	1.33600e23	0.682764	0.341382	−	0.939925i	$-0.389105\pi$
$73$	1.33600e23	0.682764	0.341382	+	0.939925i	$0.389105\pi$
$74$	−1.99154e22	−0.0858605
$75$	1.49473e23	0.544875
$76$	−5.47712e22	−0.169193
$77$	1.19926e23	0.314616
$78$	3.88909e23	0.868292
$79$	8.16786e23	1.55514	0.777570	−	0.628796i	$-0.216452\pi$
$79$	8.16786e23	1.55514	0.777570	+	0.628796i	$0.216452\pi$
$80$	−1.77276e23	−0.288420
$81$	7.97664e22	0.111111
$82$	−1.62878e24	−1.94621
$83$	−7.24814e23	−0.744304	−0.372152	−	0.928172i	$-0.621380\pi$
$83$	−7.24814e23	−0.744304	−0.372152	+	0.928172i	$0.621380\pi$
$84$	2.81162e23	0.248580
$85$	2.44478e23	0.186424
$86$	−1.91394e24	−1.26095
$87$	2.08265e23	0.118748
$88$	3.66463e23	0.181133
$89$	1.55091e23	0.0665596	0.0332798	−	0.999446i	$-0.489405\pi$
$89$	1.55091e23	0.0665596	0.0332798	+	0.999446i	$0.489405\pi$
$90$	2.42982e23	0.0906863
$91$	5.49760e24	1.78713
$92$	2.19554e24	0.622578
$93$	−4.09372e24	−1.01410
$94$	−2.00391e24	−0.434291
$95$	−6.69104e23	−0.127042
$96$	2.11498e24	0.352302
$97$	−2.30974e24	−0.337999	−0.169000	−	0.985616i	$-0.554054\pi$
$97$	−2.30974e24	−0.337999	−0.169000	+	0.985616i	$0.554054\pi$
$98$	7.64654e24	0.984326
$99$	−6.78524e23	−0.0769353
$100$	−2.98092e24	−0.298092
$101$	5.98206e24	0.528243	0.264121	−	0.964489i	$-0.414918\pi$
$101$	5.98206e24	0.528243	0.264121	+	0.964489i	$0.414918\pi$
$102$	−6.66791e24	−0.520580
$103$	−1.62280e25	−1.12150	−0.560749	−	0.827986i	$-0.689487\pi$
$103$	−1.62280e25	−1.12150	−0.560749	+	0.827986i	$0.689487\pi$
$104$	1.67992e25	1.02890
$105$	3.43477e24	0.186652
$106$	−2.89273e25	−1.39632
$107$	−2.21061e25	−0.948889	−0.474445	−	0.880285i	$-0.657351\pi$
$107$	−2.21061e25	−0.948889	−0.474445	+	0.880285i	$0.657351\pi$
$108$	−1.59077e24	−0.0607870
$109$	1.78900e25	0.609228	0.304614	−	0.952476i	$-0.401472\pi$
$109$	1.78900e25	0.609228	0.304614	+	0.952476i	$0.401472\pi$
$110$	−2.06689e24	−0.0627928
$111$	1.59282e24	0.0432144
$112$	6.83479e25	1.65768
$113$	1.77379e25	0.384965	0.192483	−	0.981300i	$-0.438346\pi$
$113$	1.77379e25	0.384965	0.192483	+	0.981300i	$0.438346\pi$
$114$	1.82492e25	0.354759
$115$	2.68215e25	0.467476
$116$	−4.15339e24	−0.0649648
$117$	−3.11045e25	−0.437019
$118$	4.59925e25	0.580982
$119$	−9.42572e25	−1.07146
$120$	1.04958e25	0.107460
$121$	−1.02575e26	−0.946729
$122$	−1.92133e26	−1.59994
$123$	1.30268e26	0.979545
$124$	8.16405e25	0.554798
$125$	−7.50022e25	−0.460998
$126$	−9.36804e25	−0.521215
$127$	−1.71063e26	−0.862205	−0.431103	−	0.902303i	$-0.641875\pi$
$127$	−1.71063e26	−0.862205	−0.431103	+	0.902303i	$0.641875\pi$
$128$	2.63099e26	1.20225
$129$	1.53075e26	0.634648
$130$	−9.47495e25	−0.356685
$131$	3.60318e26	1.23252	0.616261	−	0.787542i	$-0.288647\pi$
$131$	3.60318e26	1.23252	0.616261	+	0.787542i	$0.288647\pi$
$132$	1.35317e25	0.0420900
$133$	2.57970e26	0.730169
$134$	−9.41429e25	−0.242648
$135$	−1.94334e25	−0.0456433
$136$	−2.88025e26	−0.616871
$137$	1.72015e26	0.336171	0.168085	−	0.985772i	$-0.446242\pi$
$137$	1.72015e26	0.336171	0.168085	+	0.985772i	$0.446242\pi$
$138$	−7.31533e26	−1.30540
$139$	4.70812e26	0.767648	0.383824	−	0.923406i	$-0.374607\pi$
$139$	4.70812e26	0.767648	0.383824	+	0.923406i	$0.374607\pi$
$140$	−6.84992e25	−0.102114
$141$	1.60271e26	0.218583
$142$	−4.43200e26	−0.553345
$143$	2.64587e26	0.302600
$144$	−3.86702e26	−0.405364
$145$	−5.07392e25	−0.0487802
$146$	8.87740e26	0.783205
$147$	−6.11562e26	−0.495420
$148$	−3.17653e25	−0.0236419
$149$	−2.21239e27	−1.51368	−0.756840	−	0.653600i	$-0.773258\pi$
$149$	−2.21239e27	−1.51368	−0.756840	+	0.653600i	$0.773258\pi$
$150$	9.93212e26	0.625031
$151$	−1.13447e27	−0.657022	−0.328511	−	0.944500i	$-0.606547\pi$
$151$	−1.13447e27	−0.657022	−0.328511	+	0.944500i	$0.606547\pi$
$152$	7.88288e26	0.420378
$153$	5.33292e26	0.262013
$154$	7.96882e26	0.360898
$155$	9.97348e26	0.416582
$156$	6.20314e26	0.239086
$157$	1.14663e27	0.408015	0.204008	−	0.978969i	$-0.434603\pi$
$157$	1.14663e27	0.408015	0.204008	+	0.978969i	$0.434603\pi$
$158$	5.42735e27	1.78392
$159$	2.31358e27	0.702781
$160$	−5.15269e26	−0.144722
$161$	−1.03409e28	−2.68680
$162$	5.30029e26	0.127457
$163$	3.61041e27	0.803918	0.401959	−	0.915658i	$-0.368329\pi$
$163$	3.61041e27	0.803918	0.401959	+	0.915658i	$0.368329\pi$
$164$	−2.59792e27	−0.535893
$165$	1.65308e26	0.0316042
$166$	−4.81622e27	−0.853798
$167$	−9.25891e27	−1.52266	−0.761332	−	0.648362i	$-0.775454\pi$
$167$	−9.25891e27	−1.52266	−0.761332	+	0.648362i	$0.775454\pi$
$168$	−4.04659e27	−0.617623
$169$	5.07266e27	0.718872
$170$	1.62450e27	0.213849
$171$	−1.45955e27	−0.178554
$172$	−3.05275e27	−0.347205
$173$	1.49540e28	1.58191	0.790956	−	0.611874i	$-0.209584\pi$
$173$	1.49540e28	1.58191	0.790956	+	0.611874i	$0.209584\pi$
$174$	1.38387e27	0.136216
$175$	1.40400e28	1.28644
$176$	3.28944e27	0.280681
$177$	−3.67843e27	−0.292413
$178$	1.03054e27	0.0763511
$179$	−9.77909e27	−0.675516	−0.337758	−	0.941233i	$-0.609668\pi$
$179$	−9.77909e27	−0.675516	−0.337758	+	0.941233i	$0.609668\pi$
$180$	3.87558e26	0.0249707
$181$	−1.56087e28	−0.938391	−0.469196	−	0.883094i	$-0.655456\pi$
$181$	−1.56087e28	−0.938391	−0.469196	+	0.883094i	$0.655456\pi$
$182$	3.65302e28	2.05003
$183$	1.53666e28	0.805266
$184$	−3.15991e28	−1.54686
$185$	−3.88056e26	−0.0177520
$186$	−2.72018e28	−1.16328
$187$	−4.53639e27	−0.181422
$188$	−3.19626e27	−0.119583
$189$	7.49246e27	0.262332
$190$	−4.44604e27	−0.145731
$191$	2.17845e28	0.668698	0.334349	−	0.942449i	$-0.391484\pi$
$191$	2.17845e28	0.668698	0.334349	+	0.942449i	$0.391484\pi$
$192$	−1.03623e28	−0.297982
$193$	3.41420e27	0.0920074	0.0460037	−	0.998941i	$-0.485351\pi$
$193$	3.41420e27	0.0920074	0.0460037	+	0.998941i	$0.485351\pi$
$194$	−1.53476e28	−0.387722
$195$	7.57796e27	0.179523
$196$	1.21963e28	0.271036
$197$	−8.35320e28	−1.74191	−0.870953	−	0.491366i	$-0.836498\pi$
$197$	−8.35320e28	−1.74191	−0.870953	+	0.491366i	$0.836498\pi$
$198$	−4.50863e27	−0.0882531
$199$	5.55661e28	1.02128	0.510642	−	0.859794i	$-0.329408\pi$
$199$	5.55661e28	1.02128	0.510642	+	0.859794i	$0.329408\pi$
$200$	4.29025e28	0.740641
$201$	7.52944e27	0.122127
$202$	3.97494e28	0.605952
$203$	1.95623e28	0.280362
$204$	−1.06354e28	−0.143343
$205$	−3.17371e28	−0.402387
$206$	−1.07831e29	−1.28648
$207$	5.85072e28	0.657022
$208$	1.50793e29	1.59437
$209$	1.24155e28	0.123634
$210$	2.28232e28	0.214110
$211$	1.28099e28	0.113244	0.0566218	−	0.998396i	$-0.481967\pi$
$211$	1.28099e28	0.113244	0.0566218	+	0.998396i	$0.481967\pi$
$212$	−4.61394e28	−0.384480
$213$	3.54467e28	0.278503
$214$	−1.46890e29	−1.08848
$215$	−3.72935e28	−0.260707
$216$	2.28950e28	0.151032
$217$	−3.84523e29	−2.39428
$218$	1.18875e29	0.698851
$219$	−7.10005e28	−0.394194
$220$	−3.29672e27	−0.0172901
$221$	−2.07955e29	−1.03054
$222$	1.05839e28	0.0495716
$223$	2.22695e29	0.986052	0.493026	−	0.870015i	$-0.335891\pi$
$223$	2.22695e29	0.986052	0.493026	+	0.870015i	$0.335891\pi$
$224$	1.98660e29	0.831782
$225$	−7.94360e28	−0.314584
$226$	1.17864e29	0.441597
$227$	4.35654e29	1.54461	0.772304	−	0.635254i	$-0.219104\pi$
$227$	4.35654e29	1.54461	0.772304	+	0.635254i	$0.219104\pi$
$228$	2.91077e28	0.0976837
$229$	2.49870e29	0.793907	0.396954	−	0.917839i	$-0.370067\pi$
$229$	2.49870e29	0.793907	0.396954	+	0.917839i	$0.370067\pi$
$230$	1.78222e29	0.536246
$231$	−6.37338e28	−0.181643
$232$	5.97772e28	0.161412
$233$	−3.53889e29	−0.905561	−0.452780	−	0.891622i	$-0.649568\pi$
$233$	−3.53889e29	−0.905561	−0.452780	+	0.891622i	$0.649568\pi$
$234$	−2.06682e29	−0.501309
$235$	−3.90466e28	−0.0897914
$236$	7.33585e28	0.159974
$237$	−4.34074e29	−0.897861
$238$	−6.26317e29	−1.22909
$239$	5.49570e29	1.02341	0.511704	−	0.859162i	$-0.329014\pi$
$239$	5.49570e29	1.02341	0.511704	+	0.859162i	$0.329014\pi$
$240$	9.42117e28	0.166519
$241$	4.54972e28	0.0763435	0.0381717	−	0.999271i	$-0.487847\pi$
$241$	4.54972e28	0.0763435	0.0381717	+	0.999271i	$0.487847\pi$
$242$	−6.81588e29	−1.08600
$243$	−4.23912e28	−0.0641500
$244$	−3.06454e29	−0.440547
$245$	1.48994e29	0.203513
$246$	8.65601e29	1.12364
$247$	5.69146e29	0.702282
$248$	−1.17500e30	−1.37845
$249$	3.85196e29	0.429724
$250$	−4.98372e29	−0.528815
$251$	1.51777e30	1.53210	0.766048	−	0.642784i	$-0.222221\pi$
$251$	1.51777e30	1.53210	0.766048	+	0.642784i	$0.222221\pi$
$252$	−1.49421e29	−0.143518
$253$	−4.97685e29	−0.454933
$254$	−1.13668e30	−0.989043
$255$	−1.29925e29	−0.107632
$256$	1.09397e30	0.862993
$257$	2.06529e29	0.155173	0.0775866	−	0.996986i	$-0.475279\pi$
$257$	2.06529e29	0.155173	0.0775866	+	0.996986i	$0.475279\pi$
$258$	1.01715e30	0.728010
$259$	1.49613e29	0.102029
$260$	−1.51126e29	−0.0982139
$261$	−1.10680e29	−0.0685589
$262$	2.39423e30	1.41384
$263$	−2.18186e30	−1.22851	−0.614256	−	0.789107i	$-0.710544\pi$
$263$	−2.18186e30	−1.22851	−0.614256	+	0.789107i	$0.710544\pi$
$264$	−1.94754e29	−0.104577
$265$	−5.63654e29	−0.288695
$266$	1.71415e30	0.837584
$267$	−8.24216e28	−0.0384282
$268$	−1.50159e29	−0.0668137
$269$	−1.09180e30	−0.463701	−0.231850	−	0.972751i	$-0.574478\pi$
$269$	−1.09180e30	−0.463701	−0.231850	+	0.972751i	$0.574478\pi$
$270$	−1.29130e29	−0.0523578
$271$	2.29128e29	0.0887080	0.0443540	−	0.999016i	$-0.485877\pi$
$271$	2.29128e29	0.0887080	0.0443540	+	0.999016i	$0.485877\pi$
$272$	−2.58536e30	−0.955895
$273$	−2.92165e30	−1.03180
$274$	1.14300e30	0.385625
$275$	6.75714e29	0.217823
$276$	−1.16680e30	−0.359446
$277$	−6.57654e30	−1.93642	−0.968212	−	0.250130i	$-0.919527\pi$
$277$	−6.57654e30	−1.93642	−0.968212	+	0.250130i	$0.919527\pi$
$278$	3.12843e30	0.880576
$279$	2.17557e30	0.585492
$280$	9.85867e29	0.253713
$281$	3.73125e30	0.918387	0.459193	−	0.888336i	$-0.348139\pi$
$281$	3.73125e30	0.918387	0.459193	+	0.888336i	$0.348139\pi$
$282$	1.06496e30	0.250738
$283$	−1.55938e30	−0.351255	−0.175627	−	0.984457i	$-0.556195\pi$
$283$	−1.55938e30	−0.351255	−0.175627	+	0.984457i	$0.556195\pi$
$284$	−7.06908e29	−0.152364
$285$	3.55589e29	0.0733479
$286$	1.75812e30	0.347115
$287$	1.22361e31	2.31270
$288$	−1.12399e30	−0.203402
$289$	−2.20521e30	−0.382143
$290$	−3.37150e29	−0.0559562
$291$	1.22749e30	0.195144
$292$	1.41595e30	0.215657
$293$	1.50675e30	0.219885	0.109942	−	0.993938i	$-0.464933\pi$
$293$	1.50675e30	0.219885	0.109942	+	0.993938i	$0.464933\pi$
$294$	−4.06369e30	−0.568301
$295$	8.96172e29	0.120120
$296$	4.57179e29	0.0587407
$297$	3.60596e29	0.0444186
$298$	−1.47008e31	−1.73636
$299$	−2.28146e31	−2.58418
$300$	1.58418e30	0.172103
$301$	1.43783e31	1.49840
$302$	−7.53826e30	−0.753676
$303$	−3.17911e30	−0.304981
$304$	7.07581e30	0.651413
$305$	−3.74375e30	−0.330795
$306$	3.54360e30	0.300557
$307$	2.27795e30	0.185487	0.0927437	−	0.995690i	$-0.470436\pi$
$307$	2.27795e30	0.185487	0.0927437	+	0.995690i	$0.470436\pi$
$308$	1.27103e30	0.0993741
$309$	8.62421e30	0.647498
$310$	6.62714e30	0.477865
$311$	6.14144e30	0.425369	0.212684	−	0.977121i	$-0.431779\pi$
$311$	6.14144e30	0.425369	0.212684	+	0.977121i	$0.431779\pi$
$312$	−8.92779e30	−0.594034
$313$	8.21019e30	0.524866	0.262433	−	0.964950i	$-0.415475\pi$
$313$	8.21019e30	0.524866	0.262433	+	0.964950i	$0.415475\pi$
$314$	7.61906e30	0.468038
$315$	−1.82538e30	−0.107763
$316$	8.65667e30	0.491204
$317$	−1.66055e31	−0.905755	−0.452877	−	0.891573i	$-0.649602\pi$
$317$	−1.66055e31	−0.905755	−0.452877	+	0.891573i	$0.649602\pi$
$318$	1.53732e31	0.806166
$319$	9.41489e29	0.0474714
$320$	2.52455e30	0.122408
$321$	1.17481e31	0.547841
$322$	−6.87128e31	−3.08205
$323$	−9.75810e30	−0.421050
$324$	8.45401e29	0.0350954
$325$	3.09757e31	1.23731
$326$	2.39903e31	0.922182
$327$	−9.50750e30	−0.351738
$328$	3.73903e31	1.33148
$329$	1.50542e31	0.516072
$330$	1.09843e30	0.0362534
$331$	−3.03050e31	−0.963085	−0.481543	−	0.876423i	$-0.659923\pi$
$331$	−3.03050e31	−0.963085	−0.481543	+	0.876423i	$0.659923\pi$
$332$	−7.68191e30	−0.235095
$333$	−8.46488e29	−0.0249498
$334$	−6.15233e31	−1.74666
$335$	−1.83439e30	−0.0501685
$336$	−3.63229e31	−0.957061
$337$	2.72642e30	0.0692179	0.0346090	−	0.999401i	$-0.488981\pi$
$337$	2.72642e30	0.0692179	0.0346090	+	0.999401i	$0.488981\pi$
$338$	3.37066e31	0.824625
$339$	−9.42664e30	−0.222260
$340$	2.59108e30	0.0588837
$341$	−1.85062e31	−0.405405
$342$	−9.69839e30	−0.204820
$343$	9.49977e30	0.193436
$344$	4.39364e31	0.862669
$345$	−1.42540e31	−0.269898
$346$	9.93660e31	1.81462
$347$	−1.01187e32	−1.78240	−0.891199	−	0.453612i	$-0.850135\pi$
$347$	−1.01187e32	−1.78240	−0.891199	+	0.453612i	$0.850135\pi$
$348$	2.20728e30	0.0375074
$349$	8.38211e30	0.137415	0.0687077	−	0.997637i	$-0.478112\pi$
$349$	8.38211e30	0.137415	0.0687077	+	0.997637i	$0.478112\pi$
$350$	9.32924e31	1.47569
$351$	1.65302e31	0.252313
$352$	9.56106e30	0.140839
$353$	1.08262e32	1.53919	0.769593	−	0.638535i	$-0.220459\pi$
$353$	1.08262e32	1.53919	0.769593	+	0.638535i	$0.220459\pi$
$354$	−2.44423e31	−0.335430
$355$	−8.63583e30	−0.114406
$356$	1.64372e30	0.0210234
$357$	5.00921e31	0.618610
$358$	−6.49797e31	−0.774890
$359$	−1.17867e32	−1.35741	−0.678704	−	0.734412i	$-0.737458\pi$
$359$	−1.17867e32	−1.35741	−0.678704	+	0.734412i	$0.737458\pi$
$360$	−5.57788e30	−0.0620423
$361$	−6.63698e31	−0.713068
$362$	−1.03716e32	−1.07644
$363$	5.45127e31	0.546594
$364$	5.82661e31	0.564480
$365$	1.72978e31	0.161931
$366$	1.02107e32	0.923727
$367$	−1.52999e32	−1.33771	−0.668854	−	0.743393i	$-0.733215\pi$
$367$	−1.52999e32	−1.33771	−0.668854	+	0.743393i	$0.733215\pi$
$368$	−2.83639e32	−2.39700
$369$	−6.92299e31	−0.565541
$370$	−2.57854e30	−0.0203635
$371$	2.17314e32	1.65926
$372$	−4.33871e31	−0.320313
$373$	1.30496e32	0.931617	0.465809	−	0.884885i	$-0.345763\pi$
$373$	1.30496e32	0.931617	0.465809	+	0.884885i	$0.345763\pi$
$374$	−3.01433e31	−0.208111
$375$	3.98593e31	0.266157
$376$	4.60018e31	0.297117
$377$	4.31593e31	0.269654
$378$	4.97856e31	0.300924
$379$	1.05862e32	0.619082	0.309541	−	0.950886i	$-0.399825\pi$
$379$	1.05862e32	0.619082	0.309541	+	0.950886i	$0.399825\pi$
$380$	−7.09147e30	−0.0401274
$381$	9.09101e31	0.497794
$382$	1.44753e32	0.767069
$383$	1.36570e31	0.0700439	0.0350220	−	0.999387i	$-0.488850\pi$
$383$	1.36570e31	0.0700439	0.0350220	+	0.999387i	$0.488850\pi$
$384$	−1.39822e32	−0.694120
$385$	1.55274e31	0.0746172
$386$	2.26866e31	0.105543
$387$	−8.13504e31	−0.366414
$388$	−2.44796e31	−0.106760
$389$	−7.76945e31	−0.328111	−0.164055	−	0.986451i	$-0.552458\pi$
$389$	−7.76945e31	−0.328111	−0.164055	+	0.986451i	$0.552458\pi$
$390$	5.03538e31	0.205932
$391$	3.91160e32	1.54933
$392$	−1.75534e32	−0.673418
$393$	−1.91488e32	−0.711597
$394$	−5.55050e32	−1.99816
$395$	1.05753e32	0.368832
$396$	−7.19131e30	−0.0243007
$397$	−3.93664e32	−1.28897	−0.644487	−	0.764616i	$-0.722929\pi$
$397$	−3.93664e32	−1.28897	−0.644487	+	0.764616i	$0.722929\pi$
$398$	3.69223e32	1.17152
$399$	−1.37096e32	−0.421563
$400$	3.85100e32	1.14769
$401$	4.19501e32	1.21179	0.605896	−	0.795544i	$-0.292815\pi$
$401$	4.19501e32	1.21179	0.605896	+	0.795544i	$0.292815\pi$
$402$	5.00314e31	0.140093
$403$	−8.48354e32	−2.30284
$404$	6.34006e31	0.166850
$405$	1.03277e31	0.0263521
$406$	1.29987e32	0.321606
$407$	7.20055e30	0.0172757
$408$	1.53068e32	0.356151
$409$	1.78800e32	0.403485	0.201742	−	0.979439i	$-0.435340\pi$
$409$	1.78800e32	0.403485	0.201742	+	0.979439i	$0.435340\pi$
$410$	−2.10885e32	−0.461581
$411$	−9.14160e31	−0.194088
$412$	−1.71991e32	−0.354235
$413$	−3.45515e32	−0.690385
$414$	3.88766e32	0.753676
$415$	−9.38448e31	−0.176526
$416$	4.38293e32	0.800014
$417$	−2.50209e32	−0.443202
$418$	8.24982e31	0.141821
$419$	1.92588e32	0.321332	0.160666	−	0.987009i	$-0.448636\pi$
$419$	1.92588e32	0.321332	0.160666	+	0.987009i	$0.448636\pi$
$420$	3.64033e31	0.0589555
$421$	3.35557e32	0.527522	0.263761	−	0.964588i	$-0.415037\pi$
$421$	3.35557e32	0.527522	0.263761	+	0.964588i	$0.415037\pi$
$422$	8.51185e31	0.129903
$423$	−8.51745e31	−0.126199
$424$	6.64055e32	0.955281
$425$	−5.31083e32	−0.741824
$426$	2.35535e32	0.319474
$427$	1.44338e33	1.90123
$428$	−2.34291e32	−0.299715
$429$	−1.40613e32	−0.174706
$430$	−2.47806e32	−0.299059
$431$	3.67557e32	0.430883	0.215441	−	0.976517i	$-0.430881\pi$
$431$	3.67557e32	0.430883	0.215441	+	0.976517i	$0.430881\pi$
$432$	2.05509e32	0.234037
$433$	−1.07010e33	−1.18393	−0.591966	−	0.805963i	$-0.701648\pi$
$433$	−1.07010e33	−1.18393	−0.591966	+	0.805963i	$0.701648\pi$
$434$	−2.55507e33	−2.74650
$435$	2.69649e31	0.0281633
$436$	1.89607e32	0.192430
$437$	−1.07055e33	−1.05582
$438$	−4.71782e32	−0.452183
$439$	6.22601e32	0.579967	0.289983	−	0.957032i	$-0.406350\pi$
$439$	6.22601e32	0.579967	0.289983	+	0.957032i	$0.406350\pi$
$440$	4.74476e31	0.0429591
$441$	3.25009e32	0.286031
$442$	−1.38181e33	−1.18214
$443$	3.00547e32	0.249957	0.124979	−	0.992159i	$-0.460114\pi$
$443$	3.00547e32	0.249957	0.124979	+	0.992159i	$0.460114\pi$
$444$	1.68814e31	0.0136496
$445$	2.00803e31	0.0157859
$446$	1.47976e33	1.13111
$447$	1.17576e33	0.873923
$448$	−9.73329e32	−0.703533
$449$	1.53124e33	1.07638	0.538188	−	0.842825i	$-0.319109\pi$
$449$	1.53124e33	1.07638	0.538188	+	0.842825i	$0.319109\pi$
$450$	−5.27834e32	−0.360862
$451$	5.88896e32	0.391590
$452$	1.87994e32	0.121595
$453$	6.02902e32	0.379332
$454$	2.89482e33	1.77183
$455$	7.11798e32	0.423852
$456$	−4.18929e32	−0.242706
$457$	−2.43126e33	−1.37050	−0.685250	−	0.728308i	$-0.740307\pi$
$457$	−2.43126e33	−1.37050	−0.685250	+	0.728308i	$0.740307\pi$
$458$	1.66032e33	0.910698
$459$	−2.83413e32	−0.151273
$460$	2.84266e32	0.147656
$461$	−1.28433e33	−0.649253	−0.324627	−	0.945842i	$-0.605239\pi$
$461$	−1.28433e33	−0.649253	−0.324627	+	0.945842i	$0.605239\pi$
$462$	−4.23496e32	−0.208365
$463$	−1.44154e33	−0.690342	−0.345171	−	0.938540i	$-0.612179\pi$
$463$	−1.44154e33	−0.690342	−0.345171	+	0.938540i	$0.612179\pi$
$464$	5.36570e32	0.250122
$465$	−5.30032e32	−0.240514
$466$	−2.35151e33	−1.03878
$467$	1.43360e33	0.616547	0.308274	−	0.951298i	$-0.400249\pi$
$467$	1.43360e33	0.616547	0.308274	+	0.951298i	$0.400249\pi$
$468$	−3.29660e32	−0.138036
$469$	7.07240e32	0.288341
$470$	−2.59455e32	−0.103001
$471$	−6.09364e32	−0.235568
$472$	−1.05580e33	−0.397473
$473$	6.91998e32	0.253712
$474$	−2.88432e33	−1.02994
$475$	1.45351e33	0.505530
$476$	−9.98981e32	−0.338431
$477$	−1.22953e33	−0.405751
$478$	3.65176e33	1.17396
$479$	−4.48751e33	−1.40544	−0.702719	−	0.711467i	$-0.748031\pi$
$479$	−4.48751e33	−1.40544	−0.702719	+	0.711467i	$0.748031\pi$
$480$	2.73835e32	0.0835553
$481$	3.30084e32	0.0981320
$482$	3.02318e32	0.0875743
$483$	5.49558e33	1.55122
$484$	−1.08714e33	−0.299032
$485$	−2.99051e32	−0.0801630
$486$	−2.81679e32	−0.0735871
$487$	2.85084e33	0.725872	0.362936	−	0.931814i	$-0.381774\pi$
$487$	2.85084e33	0.725872	0.362936	+	0.931814i	$0.381774\pi$
$488$	4.41060e33	1.09459
$489$	−1.91872e33	−0.464142
$490$	9.90031e32	0.233452
$491$	−5.52771e33	−1.27065	−0.635326	−	0.772244i	$-0.719134\pi$
$491$	−5.52771e33	−1.27065	−0.635326	+	0.772244i	$0.719134\pi$
$492$	1.38064e33	0.309398
$493$	−7.39972e32	−0.161670
$494$	3.78184e33	0.805594
$495$	−8.78514e31	−0.0182467
$496$	−1.05470e34	−2.13604
$497$	3.32951e33	0.657544
$498$	2.55954e33	0.492941
$499$	1.75201e33	0.329063	0.164531	−	0.986372i	$-0.447389\pi$
$499$	1.75201e33	0.329063	0.164531	+	0.986372i	$0.447389\pi$
$500$	−7.94908e32	−0.145610
$501$	4.92057e33	0.879111
$502$	1.00853e34	1.75748
$503$	−7.18569e33	−1.22143	−0.610715	−	0.791851i	$-0.709118\pi$
$503$	−7.18569e33	−1.22143	−0.610715	+	0.791851i	$0.709118\pi$
$504$	2.15053e33	0.356585
$505$	7.74523e32	0.125283
$506$	−3.30700e33	−0.521858
$507$	−2.69582e33	−0.415041
$508$	−1.81301e33	−0.272335
$509$	−5.15790e32	−0.0755964	−0.0377982	−	0.999285i	$-0.512034\pi$
$509$	−5.15790e32	−0.0755964	−0.0377982	+	0.999285i	$0.512034\pi$
$510$	−8.63323e32	−0.123466
$511$	−6.66908e33	−0.930689
$512$	−1.55896e33	−0.212305
$513$	7.75666e32	0.103088
$514$	1.37234e33	0.178001
$515$	−2.10110e33	−0.265985
$516$	1.62236e33	0.200459
$517$	7.24527e32	0.0873822
$518$	9.94144e32	0.117038
$519$	−7.94719e33	−0.913317
$520$	2.17507e33	0.244023
$521$	−8.53974e33	−0.935348	−0.467674	−	0.883901i	$-0.654908\pi$
$521$	−8.53974e33	−0.935348	−0.467674	+	0.883901i	$0.654908\pi$
$522$	−7.35444e32	−0.0786445
$523$	−1.91349e33	−0.199782	−0.0998909	−	0.994998i	$-0.531849\pi$
$523$	−1.91349e33	−0.199782	−0.0998909	+	0.994998i	$0.531849\pi$
$524$	3.81881e33	0.389303
$525$	−7.46142e33	−0.742729
$526$	−1.44979e34	−1.40924
$527$	1.45452e34	1.38066
$528$	−1.74814e33	−0.162051
$529$	3.18681e34	2.88510
$530$	−3.74535e33	−0.331164
$531$	1.95487e33	0.168825
$532$	2.73408e33	0.230630
$533$	2.69959e34	2.22437
$534$	−5.47672e32	−0.0440813
$535$	−2.86218e33	−0.225047
$536$	2.16114e33	0.166006
$537$	5.19701e33	0.390009
$538$	−7.25472e33	−0.531915
$539$	−2.76465e33	−0.198053
$540$	−2.05964e32	−0.0144168
$541$	−6.22140e33	−0.425522	−0.212761	−	0.977104i	$-0.568246\pi$
$541$	−6.22140e33	−0.425522	−0.212761	+	0.977104i	$0.568246\pi$
$542$	1.52250e33	0.101758
$543$	8.29509e33	0.541780
$544$	−7.51460e33	−0.479645
$545$	2.31630e33	0.144490
$546$	−1.94137e34	−1.18359
$547$	−2.04660e34	−1.21953	−0.609764	−	0.792583i	$-0.708736\pi$
$547$	−2.04660e34	−1.21953	−0.609764	+	0.792583i	$0.708736\pi$
$548$	1.82310e33	0.106183
$549$	−8.16644e33	−0.464920
$550$	4.48996e33	0.249867
$551$	2.02521e33	0.110173
$552$	1.67930e34	0.893081
$553$	−4.07725e34	−2.11984
$554$	−4.36996e34	−2.22129
$555$	2.06229e32	0.0102491
$556$	4.98988e33	0.242468
$557$	1.35440e34	0.643513	0.321756	−	0.946823i	$-0.395727\pi$
$557$	1.35440e34	0.643513	0.321756	+	0.946823i	$0.395727\pi$
$558$	1.44562e34	0.671623
$559$	3.17222e34	1.44117
$560$	8.84930e33	0.393150
$561$	2.41082e33	0.104744
$562$	2.47933e34	1.05349
$563$	−1.17943e34	−0.490136	−0.245068	−	0.969506i	$-0.578810\pi$
$563$	−1.17943e34	−0.490136	−0.245068	+	0.969506i	$0.578810\pi$
$564$	1.69862e33	0.0690412
$565$	2.29660e33	0.0913019
$566$	−1.03617e34	−0.402927
$567$	−3.98180e33	−0.151458
$568$	1.01741e34	0.378566
$569$	1.74485e34	0.635118	0.317559	−	0.948239i	$-0.397137\pi$
$569$	1.74485e34	0.635118	0.317559	+	0.948239i	$0.397137\pi$
$570$	2.36281e33	0.0841380
$571$	−2.25243e34	−0.784693	−0.392346	−	0.919818i	$-0.628337\pi$
$571$	−2.25243e34	−0.784693	−0.392346	+	0.919818i	$0.628337\pi$
$572$	2.80422e33	0.0955787
$573$	−1.15772e34	−0.386073
$574$	8.13059e34	2.65292
$575$	−5.82648e34	−1.86019
$576$	5.50694e33	0.172040
$577$	−1.13350e34	−0.346518	−0.173259	−	0.984876i	$-0.555430\pi$
$577$	−1.13350e34	−0.346518	−0.173259	+	0.984876i	$0.555430\pi$
$578$	−1.46531e34	−0.438360
$579$	−1.81445e33	−0.0531205
$580$	−5.37757e32	−0.0154077
$581$	3.61815e34	1.01458
$582$	8.15637e33	0.223851
$583$	1.04589e34	0.280949
$584$	−2.03789e34	−0.535823
$585$	−4.02724e33	−0.103648
$586$	1.00120e34	0.252232
$587$	−2.66748e34	−0.657847	−0.328923	−	0.944357i	$-0.606686\pi$
$587$	−2.66748e34	−0.657847	−0.328923	+	0.944357i	$0.606686\pi$
$588$	−6.48161e33	−0.156483
$589$	−3.98082e34	−0.940875
$590$	5.95485e33	0.137791
$591$	4.43923e34	1.00569
$592$	4.10371e33	0.0910239
$593$	4.96310e34	1.07788	0.538939	−	0.842345i	$-0.318825\pi$
$593$	4.96310e34	1.07788	0.538939	+	0.842345i	$0.318825\pi$
$594$	2.39607e33	0.0509530
$595$	−1.22039e34	−0.254118
$596$	−2.34480e34	−0.478109
$597$	−2.95301e34	−0.589638
$598$	−1.51598e35	−2.96434
$599$	5.49894e33	0.105304	0.0526519	−	0.998613i	$-0.483233\pi$
$599$	5.49894e33	0.105304	0.0526519	+	0.998613i	$0.483233\pi$
$600$	−2.28002e34	−0.427609
$601$	3.39406e34	0.623431	0.311716	−	0.950175i	$-0.399096\pi$
$601$	3.39406e34	0.623431	0.311716	+	0.950175i	$0.399096\pi$
$602$	9.55406e34	1.71883
$603$	−4.00146e33	−0.0705101
$604$	−1.20236e34	−0.207526
$605$	−1.32809e34	−0.224535
$606$	−2.11244e34	−0.349846
$607$	4.05995e34	0.658661	0.329331	−	0.944215i	$-0.393177\pi$
$607$	4.05995e34	0.658661	0.329331	+	0.944215i	$0.393177\pi$
$608$	2.05665e34	0.326863
$609$	−1.03962e34	−0.161867
$610$	−2.48763e34	−0.379457
$611$	3.32134e34	0.496362
$612$	5.65208e33	0.0827590
$613$	−4.07586e34	−0.584740	−0.292370	−	0.956305i	$-0.594444\pi$
$613$	−4.07586e34	−0.584740	−0.292370	+	0.956305i	$0.594444\pi$
$614$	1.51364e34	0.212774
$615$	1.68664e34	0.232318
$616$	−1.82932e34	−0.246906
$617$	−1.48447e32	−0.00196340	−0.000981698	−	1.00000i	$-0.500312\pi$
$617$	−1.48447e32	−0.00196340	−0.000981698		1.00000i	$0.500312\pi$
$618$	5.73058e34	0.742750
$619$	1.37639e35	1.74827	0.874135	−	0.485683i	$-0.161429\pi$
$619$	1.37639e35	1.74827	0.874135	+	0.485683i	$0.161429\pi$
$620$	1.05704e34	0.131581
$621$	−3.10931e34	−0.379332
$622$	4.08084e34	0.487944
$623$	−7.74186e33	−0.0907287
$624$	−8.01373e34	−0.920508
$625$	7.41110e34	0.834416
$626$	5.45548e34	0.602079
$627$	−6.59812e33	−0.0713799
$628$	1.21525e34	0.128875
$629$	−5.65934e33	−0.0588346
$630$	−1.21292e34	−0.123616
$631$	2.02543e34	0.202372	0.101186	−	0.994868i	$-0.467736\pi$
$631$	2.02543e34	0.202372	0.101186	+	0.994868i	$0.467736\pi$
$632$	−1.24590e35	−1.22045
$633$	−6.80768e33	−0.0653812
$634$	−1.10340e35	−1.03900
$635$	−2.21483e34	−0.204489
$636$	2.45203e34	0.221979
$637$	−1.26736e35	−1.12501
$638$	6.25597e33	0.0544548
$639$	−1.88378e34	−0.160794
$640$	3.40646e34	0.285137
$641$	−2.21421e35	−1.81758	−0.908789	−	0.417255i	$-0.862992\pi$
$641$	−2.21421e35	−1.81758	−0.908789	+	0.417255i	$0.862992\pi$
$642$	7.80634e34	0.628434
$643$	9.55888e34	0.754692	0.377346	−	0.926072i	$-0.376837\pi$
$643$	9.55888e34	0.754692	0.377346	+	0.926072i	$0.376837\pi$
$644$	−1.09598e35	−0.848648
$645$	1.98193e34	0.150519
$646$	−6.48403e34	−0.482990
$647$	−1.46531e35	−1.07059	−0.535297	−	0.844664i	$-0.679800\pi$
$647$	−1.46531e35	−1.07059	−0.535297	+	0.844664i	$0.679800\pi$
$648$	−1.21673e34	−0.0871983
$649$	−1.66289e34	−0.116897
$650$	2.05826e35	1.41933
$651$	2.04351e35	1.38234
$652$	3.82648e34	0.253925
$653$	9.72520e34	0.633117	0.316558	−	0.948573i	$-0.397473\pi$
$653$	9.72520e34	0.633117	0.316558	+	0.948573i	$0.397473\pi$
$654$	−6.31751e34	−0.403482
$655$	4.66519e34	0.292316
$656$	3.35621e35	2.06325
$657$	3.77326e34	0.227588
$658$	1.00032e35	0.591991
$659$	−7.79784e34	−0.452800	−0.226400	−	0.974034i	$-0.572696\pi$
$659$	−7.79784e34	−0.452800	−0.226400	+	0.974034i	$0.572696\pi$
$660$	1.75201e33	0.00998245
$661$	−9.49959e34	−0.531113	−0.265556	−	0.964095i	$-0.585556\pi$
$661$	−9.49959e34	−0.531113	−0.265556	+	0.964095i	$0.585556\pi$
$662$	−2.01370e35	−1.10476
$663$	1.10516e35	0.594984
$664$	1.10561e35	0.584119
$665$	3.34005e34	0.173174
$666$	−5.62471e33	−0.0286202
$667$	−8.11819e34	−0.405402
$668$	−9.81302e34	−0.480947
$669$	−1.18349e35	−0.569297
$670$	−1.21891e34	−0.0575488
$671$	6.94669e34	0.321919
$672$	−1.05576e35	−0.480230
$673$	−1.65562e35	−0.739218	−0.369609	−	0.929187i	$-0.620508\pi$
$673$	−1.65562e35	−0.739218	−0.369609	+	0.929187i	$0.620508\pi$
$674$	1.81164e34	0.0794005
$675$	4.22156e34	0.181625
$676$	5.37623e34	0.227062
$677$	5.11450e34	0.212053	0.106027	−	0.994363i	$-0.466187\pi$
$677$	5.11450e34	0.212053	0.106027	+	0.994363i	$0.466187\pi$
$678$	−6.26378e34	−0.254956
$679$	1.15298e35	0.460733
$680$	−3.72919e34	−0.146303
$681$	−2.31524e35	−0.891779
$682$	−1.22970e35	−0.465043
$683$	−2.15770e35	−0.801185	−0.400592	−	0.916256i	$-0.631196\pi$
$683$	−2.15770e35	−0.801185	−0.400592	+	0.916256i	$0.631196\pi$
$684$	−1.54690e34	−0.0563977
$685$	2.22716e34	0.0797294
$686$	6.31237e34	0.221892
$687$	−1.32791e35	−0.458363
$688$	3.94381e35	1.33678
$689$	4.79449e35	1.59589
$690$	−9.47147e34	−0.309602
$691$	9.90059e34	0.317823	0.158912	−	0.987293i	$-0.449202\pi$
$691$	9.90059e34	0.317823	0.158912	+	0.987293i	$0.449202\pi$
$692$	1.58490e35	0.499660
$693$	3.38707e34	0.104872
$694$	−6.72361e35	−2.04460
$695$	6.09580e34	0.182063
$696$	−3.17681e34	−0.0931912
$697$	−4.62848e35	−1.33361
$698$	5.56971e34	0.157630
$699$	1.88071e35	0.522826
$700$	1.48802e35	0.406335
$701$	−2.67422e35	−0.717335	−0.358667	−	0.933465i	$-0.616769\pi$
$701$	−2.67422e35	−0.717335	−0.358667	+	0.933465i	$0.616769\pi$
$702$	1.09839e35	0.289431
$703$	1.54889e34	0.0400939
$704$	−4.68442e34	−0.119124
$705$	2.07510e34	0.0518411
$706$	7.19373e35	1.76561
$707$	−2.98614e35	−0.720058
$708$	−3.89857e34	−0.0923613
$709$	−1.75635e35	−0.408821	−0.204410	−	0.978885i	$-0.565528\pi$
$709$	−1.75635e35	−0.408821	−0.204410	+	0.978885i	$0.565528\pi$
$710$	−5.73830e34	−0.131236
$711$	2.30684e35	0.518380
$712$	−2.36571e34	−0.0522350
$713$	1.59574e36	3.46213
$714$	3.32851e35	0.709613
$715$	3.42572e34	0.0717674
$716$	−1.03643e35	−0.213367
$717$	−2.92064e35	−0.590865
$718$	−7.83196e35	−1.55709
$719$	−6.42805e35	−1.25594	−0.627969	−	0.778239i	$-0.716113\pi$
$719$	−6.42805e35	−1.25594	−0.627969	+	0.778239i	$0.716113\pi$
$720$	−5.00680e34	−0.0961399
$721$	8.10071e35	1.52874
$722$	−4.41012e35	−0.817966
$723$	−2.41791e34	−0.0440769
$724$	−1.65428e35	−0.296399
$725$	1.10222e35	0.194108
$726$	3.62224e35	0.627003
$727$	−3.58991e35	−0.610806	−0.305403	−	0.952223i	$-0.598791\pi$
$727$	−3.58991e35	−0.610806	−0.305403	+	0.952223i	$0.598791\pi$
$728$	−8.38587e35	−1.40251
$729$	2.25284e34	0.0370370
$730$	1.14940e35	0.185752
$731$	−5.43882e35	−0.864047
$732$	1.62862e35	0.254350
$733$	7.09081e35	1.08867	0.544335	−	0.838868i	$-0.316782\pi$
$733$	7.09081e35	1.08867	0.544335	+	0.838868i	$0.316782\pi$
$734$	−1.01664e36	−1.53450
$735$	−7.91816e34	−0.117499
$736$	−8.24422e35	−1.20275
$737$	3.40379e34	0.0488224
$738$	−4.60016e35	−0.648737
$739$	4.60446e35	0.638445	0.319222	−	0.947680i	$-0.396578\pi$
$739$	4.60446e35	0.638445	0.319222	+	0.947680i	$0.396578\pi$
$740$	−4.11279e33	−0.00560713
$741$	−3.02467e35	−0.405463
$742$	1.44400e36	1.90335
$743$	−6.33352e35	−0.820889	−0.410445	−	0.911885i	$-0.634627\pi$
$743$	−6.33352e35	−0.820889	−0.410445	+	0.911885i	$0.634627\pi$
$744$	6.24444e35	0.795851
$745$	−2.86448e35	−0.358998
$746$	8.67117e35	1.06867
$747$	−2.04709e35	−0.248101
$748$	−4.80788e34	−0.0573038
$749$	1.10350e36	1.29345
$750$	2.64855e35	0.305311
$751$	8.97236e35	1.01720	0.508601	−	0.861002i	$-0.330163\pi$
$751$	8.97236e35	1.01720	0.508601	+	0.861002i	$0.330163\pi$
$752$	4.12920e35	0.460408
$753$	−8.06608e35	−0.884556
$754$	2.86783e35	0.309323
$755$	−1.46884e35	−0.155825
$756$	7.94085e34	0.0828599
$757$	−1.65635e36	−1.70002	−0.850008	−	0.526769i	$-0.823403\pi$
$757$	−1.65635e36	−1.70002	−0.850008	+	0.526769i	$0.823403\pi$
$758$	7.03426e35	0.710155
$759$	2.64490e35	0.262656
$760$	1.02063e35	0.0997008
$761$	1.56563e36	1.50447	0.752233	−	0.658898i	$-0.228977\pi$
$761$	1.56563e36	1.50447	0.752233	+	0.658898i	$0.228977\pi$
$762$	6.04076e35	0.571024
$763$	−8.93039e35	−0.830451
$764$	2.30882e35	0.211214
$765$	6.90477e34	0.0621414
$766$	9.07475e34	0.0803480
$767$	−7.62292e35	−0.664017
$768$	−5.81382e35	−0.498249
$769$	−7.73859e35	−0.652503	−0.326252	−	0.945283i	$-0.605786\pi$
$769$	−7.73859e35	−0.652503	−0.326252	+	0.945283i	$0.605786\pi$
$770$	1.03176e35	0.0855940
$771$	−1.09758e35	−0.0895893
$772$	3.61853e34	0.0290613
$773$	−2.09014e36	−1.65171	−0.825853	−	0.563886i	$-0.809306\pi$
$773$	−2.09014e36	−1.65171	−0.825853	+	0.563886i	$0.809306\pi$
$774$	−5.40554e35	−0.420317
$775$	−2.16656e36	−1.65767
$776$	3.52320e35	0.265257
$777$	−7.95106e34	−0.0589064
$778$	−5.16262e35	−0.376379
$779$	1.26676e36	0.908814
$780$	8.03147e34	0.0567038
$781$	1.60242e35	0.111337
$782$	2.59917e36	1.77725
$783$	5.88200e34	0.0395825
$784$	−1.57562e36	−1.04352
$785$	1.48459e35	0.0967687
$786$	−1.27239e36	−0.816279
$787$	2.18782e36	1.38143	0.690714	−	0.723128i	$-0.257297\pi$
$787$	2.18782e36	1.38143	0.690714	+	0.723128i	$0.257297\pi$
$788$	−8.85310e35	−0.550196
$789$	1.15953e36	0.709282
$790$	7.02702e35	0.423090
$791$	−8.85444e35	−0.524753
$792$	1.03500e35	0.0603776
$793$	3.18447e36	1.82861
$794$	−2.61580e36	−1.47859
$795$	2.99549e35	0.166678
$796$	5.88915e35	0.322581
$797$	9.03430e35	0.487153	0.243577	−	0.969882i	$-0.421679\pi$
$797$	9.03430e35	0.487153	0.243577	+	0.969882i	$0.421679\pi$
$798$	−9.10969e35	−0.483579
$799$	−5.69449e35	−0.297591
$800$	1.11933e36	0.575882
$801$	4.38022e34	0.0221865
$802$	2.78748e36	1.39006
$803$	−3.20968e35	−0.157586
$804$	7.98005e34	0.0385749
$805$	−1.33888e36	−0.637226
$806$	−5.63711e36	−2.64161
$807$	5.80225e35	0.267718
$808$	−9.12485e35	−0.414557
$809$	3.54875e36	1.58752	0.793759	−	0.608232i	$-0.208121\pi$
$809$	3.54875e36	1.58752	0.793759	+	0.608232i	$0.208121\pi$
$810$	6.86252e34	0.0302288
$811$	−1.70178e35	−0.0738148	−0.0369074	−	0.999319i	$-0.511751\pi$
$811$	−1.70178e35	−0.0738148	−0.0369074	+	0.999319i	$0.511751\pi$
$812$	2.07330e35	0.0885547
$813$	−1.21768e35	−0.0512156
$814$	4.78460e34	0.0198171
$815$	4.67456e35	0.190665
$816$	1.37397e36	0.551886
$817$	1.48854e36	0.588821
$818$	1.18809e36	0.462841
$819$	1.55268e36	0.595709
$820$	−3.36364e35	−0.127097
$821$	−5.18640e36	−1.93009	−0.965043	−	0.262093i	$-0.915587\pi$
$821$	−5.18640e36	−1.93009	−0.965043	+	0.262093i	$0.915587\pi$
$822$	−6.07438e35	−0.222641
$823$	3.28317e36	1.18521	0.592605	−	0.805493i	$-0.298100\pi$
$823$	3.28317e36	1.18521	0.592605	+	0.805493i	$0.298100\pi$
$824$	2.47537e36	0.880135
$825$	−3.59102e35	−0.125760
$826$	−2.29587e36	−0.791947
$827$	−4.89130e36	−1.66190	−0.830952	−	0.556345i	$-0.812203\pi$
$827$	−4.89130e36	−1.66190	−0.830952	+	0.556345i	$0.812203\pi$
$828$	6.20086e35	0.207526
$829$	−4.62258e36	−1.52389	−0.761944	−	0.647643i	$-0.775755\pi$
$829$	−4.62258e36	−1.52389	−0.761944	+	0.647643i	$0.775755\pi$
$830$	−6.23577e35	−0.202495
$831$	3.49504e36	1.11800
$832$	−2.14741e36	−0.676663
$833$	2.17291e36	0.674494
$834$	−1.66258e36	−0.508401
$835$	−1.19879e36	−0.361129
$836$	1.31585e35	0.0390507
$837$	−1.15619e36	−0.338034
$838$	1.27970e36	0.368603
$839$	−4.20124e35	−0.119221	−0.0596105	−	0.998222i	$-0.518986\pi$
$839$	−4.20124e35	−0.119221	−0.0596105	+	0.998222i	$0.518986\pi$
$840$	−5.23930e35	−0.146481
$841$	−3.47679e36	−0.957697
$842$	2.22970e36	0.605125
$843$	−1.98294e36	−0.530231
$844$	1.35765e35	0.0357690
$845$	6.56779e35	0.170494
$846$	−5.65965e35	−0.144764
$847$	5.12038e36	1.29050
$848$	5.96067e36	1.48029
$849$	8.28720e35	0.202797
$850$	−3.52892e36	−0.850953
$851$	−6.20883e35	−0.147533
$852$	3.75680e35	0.0879677
$853$	4.26648e36	0.984479	0.492239	−	0.870460i	$-0.336178\pi$
$853$	4.26648e36	0.984479	0.492239	+	0.870460i	$0.336178\pi$
$854$	9.59095e36	2.18091
$855$	−1.88975e35	−0.0423474
$856$	3.37200e36	0.744674
$857$	−2.20636e36	−0.480193	−0.240097	−	0.970749i	$-0.577179\pi$
$857$	−2.20636e36	−0.480193	−0.240097	+	0.970749i	$0.577179\pi$
$858$	−9.34337e35	−0.200407
$859$	2.43164e36	0.514025	0.257012	−	0.966408i	$-0.417262\pi$
$859$	2.43164e36	0.514025	0.257012	+	0.966408i	$0.417262\pi$
$860$	−3.95253e35	−0.0823464
$861$	−6.50276e36	−1.33524
$862$	2.44233e36	0.494269
$863$	1.12630e34	0.00224657	0.00112328	−	0.999999i	$-0.499642\pi$
$863$	1.12630e34	0.00224657	0.00112328	+	0.999999i	$0.499642\pi$
$864$	5.97332e35	0.117434
$865$	1.93616e36	0.375181
$866$	−7.11058e36	−1.35810
$867$	1.17194e36	0.220631
$868$	−4.07535e36	−0.756255
$869$	−1.96229e36	−0.358935
$870$	1.79175e35	0.0323063
$871$	1.56035e36	0.277329
$872$	−2.72889e36	−0.478113
$873$	−6.52338e35	−0.112666
$874$	−7.11358e36	−1.21114
$875$	3.74398e36	0.628395
$876$	−7.52496e35	−0.124510
$877$	−1.12815e37	−1.84023	−0.920113	−	0.391654i	$-0.871903\pi$
$877$	−1.12815e37	−1.84023	−0.920113	+	0.391654i	$0.871903\pi$
$878$	4.13703e36	0.665285
$879$	−8.00748e35	−0.126951
$880$	4.25897e35	0.0665689
$881$	−4.10947e36	−0.633267	−0.316634	−	0.948548i	$-0.602553\pi$
$881$	−4.10947e36	−0.633267	−0.316634	+	0.948548i	$0.602553\pi$
$882$	2.15961e36	0.328109
$883$	−4.82914e36	−0.723370	−0.361685	−	0.932300i	$-0.617798\pi$
$883$	−4.82914e36	−0.723370	−0.361685	+	0.932300i	$0.617798\pi$
$884$	−2.20400e36	−0.325506
$885$	−4.76263e35	−0.0693515
$886$	1.99706e36	0.286728
$887$	7.49526e36	1.06106	0.530532	−	0.847665i	$-0.321992\pi$
$887$	7.49526e36	1.06106	0.530532	+	0.847665i	$0.321992\pi$
$888$	−2.42963e35	−0.0339140
$889$	8.53918e36	1.17529
$890$	1.33429e35	0.0181081
$891$	−1.91635e35	−0.0256451
$892$	2.36022e36	0.311453
$893$	1.55851e36	0.202799
$894$	7.81262e36	1.00249
$895$	−1.26614e36	−0.160212
$896$	−1.31335e37	−1.63881
$897$	1.21246e37	1.49198
$898$	1.01747e37	1.23472
$899$	−3.01872e36	−0.361266
$900$	−8.41899e35	−0.0993639
$901$	−8.22024e36	−0.956807
$902$	3.91307e36	0.449197
$903$	−7.64124e36	−0.865101
$904$	−2.70569e36	−0.302115
$905$	−2.02092e36	−0.222558
$906$	4.00614e36	0.435135
$907$	5.98111e36	0.640753	0.320377	−	0.947290i	$-0.396191\pi$
$907$	5.98111e36	0.640753	0.320377	+	0.947290i	$0.396191\pi$
$908$	4.61726e36	0.487878
$909$	1.68951e36	0.176081
$910$	4.72973e36	0.486204
$911$	1.45805e37	1.47841	0.739203	−	0.673483i	$-0.235202\pi$
$911$	1.45805e37	1.47841	0.739203	+	0.673483i	$0.235202\pi$
$912$	−3.76037e36	−0.376093
$913$	1.74133e36	0.171790
$914$	−1.61552e37	−1.57211
$915$	1.98958e36	0.190984
$916$	2.64823e36	0.250762
$917$	−1.79864e37	−1.68007
$918$	−1.88322e36	−0.173527
$919$	7.22313e36	0.656570	0.328285	−	0.944579i	$-0.393529\pi$
$919$	7.22313e36	0.656570	0.328285	+	0.944579i	$0.393529\pi$
$920$	−4.09127e36	−0.366868
$921$	−1.21060e36	−0.107091
$922$	−8.53405e36	−0.744764
$923$	7.34572e36	0.632431
$924$	−6.75479e35	−0.0573737
$925$	8.42981e35	0.0706393
$926$	−9.57869e36	−0.791897
$927$	−4.58326e36	−0.373833
$928$	1.55959e36	0.125505
$929$	9.78808e36	0.777143	0.388572	−	0.921419i	$-0.372969\pi$
$929$	9.78808e36	0.777143	0.388572	+	0.921419i	$0.372969\pi$
$930$	−3.52194e36	−0.275895
$931$	−5.94696e36	−0.459647
$932$	−3.75067e36	−0.286029
$933$	−3.26382e36	−0.245587
$934$	9.52592e36	0.707247
$935$	−5.87346e35	−0.0430278
$936$	4.74459e36	0.342966
$937$	1.56917e37	1.11924	0.559622	−	0.828748i	$-0.310946\pi$
$937$	1.56917e37	1.11924	0.559622	+	0.828748i	$0.310946\pi$
$938$	4.69945e36	0.330759
$939$	−4.36323e36	−0.303032
$940$	−4.13834e35	−0.0283614
$941$	1.53917e37	1.04092	0.520460	−	0.853886i	$-0.325760\pi$
$941$	1.53917e37	1.04092	0.520460	+	0.853886i	$0.325760\pi$
$942$	−4.04908e36	−0.270222
$943$	−5.07788e37	−3.34415
$944$	−9.47707e36	−0.615920
$945$	9.70081e35	0.0622172
$946$	4.59816e36	0.291035
$947$	1.08264e37	0.676254	0.338127	−	0.941100i	$-0.390207\pi$
$947$	1.08264e37	0.676254	0.338127	+	0.941100i	$0.390207\pi$
$948$	−4.60051e36	−0.283597
$949$	−1.47136e37	−0.895143
$950$	9.65821e36	0.579898
$951$	8.82483e36	0.522938
$952$	1.43777e37	0.840868
$953$	2.72401e37	1.57234	0.786172	−	0.618008i	$-0.212060\pi$
$953$	2.72401e37	1.57234	0.786172	+	0.618008i	$0.212060\pi$
$954$	−8.16993e36	−0.465440
$955$	2.82053e36	0.158595
$956$	5.82459e36	0.323252
$957$	−5.00346e35	−0.0274076
$958$	−2.98185e37	−1.61219
$959$	−8.58671e36	−0.458241
$960$	−1.34165e36	−0.0706722
$961$	4.01043e37	2.08520
$962$	2.19333e36	0.112568
$963$	−6.24342e36	−0.316296
$964$	4.82200e35	0.0241137
$965$	4.42051e35	0.0218213
$966$	3.65168e37	1.77942
$967$	−7.44297e36	−0.358027	−0.179013	−	0.983847i	$-0.557291\pi$
$967$	−7.44297e36	−0.358027	−0.179013	+	0.983847i	$0.557291\pi$
$968$	1.56465e37	0.742978
$969$	5.18585e36	0.243093
$970$	−1.98713e36	−0.0919557
$971$	−8.79733e36	−0.401893	−0.200947	−	0.979602i	$-0.564402\pi$
$971$	−8.79733e36	−0.401893	−0.200947	+	0.979602i	$0.564402\pi$
$972$	−4.49281e35	−0.0202623
$973$	−2.35021e37	−1.04640
$974$	1.89431e37	0.832655
$975$	−1.64618e37	−0.714362
$976$	3.95903e37	1.69616
$977$	−1.99766e37	−0.844965	−0.422482	−	0.906371i	$-0.638841\pi$
$977$	−1.99766e37	−0.844965	−0.422482	+	0.906371i	$0.638841\pi$
$978$	−1.27495e37	−0.532422
$979$	−3.72599e35	−0.0153623
$980$	1.57911e36	0.0642815
$981$	5.05268e36	0.203076
$982$	−3.67303e37	−1.45758
$983$	−3.17907e37	−1.24561	−0.622804	−	0.782378i	$-0.714006\pi$
$983$	−3.17907e37	−1.24561	−0.622804	+	0.782378i	$0.714006\pi$
$984$	−1.98707e37	−0.768732
$985$	−1.08152e37	−0.413127
$986$	−4.91694e36	−0.185453
$987$	−8.00044e36	−0.297954
$988$	6.03207e36	0.221822
$989$	−5.96689e37	−2.16668
$990$	−5.83752e35	−0.0209309
$991$	2.16363e37	0.766059	0.383029	−	0.923736i	$-0.374881\pi$
$991$	2.16363e37	0.766059	0.383029	+	0.923736i	$0.374881\pi$
$992$	−3.06559e37	−1.07181
$993$	1.61053e37	0.556038
$994$	2.21238e37	0.754275
$995$	7.19438e36	0.242217
$996$	4.08248e36	0.135732
$997$	4.01728e37	1.31899	0.659496	−	0.751708i	$-0.270770\pi$
$997$	4.01728e37	1.31899	0.659496	+	0.751708i	$0.270770\pi$
$998$	1.16417e37	0.377471
$999$	4.49858e35	0.0144048

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.26.a.a.1.2	✓	2
3.2	odd	2		9.26.a.b.1.1		2
4.3	odd	2		48.26.a.f.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.26.a.a.1.2	✓	2	1.1	even	1	trivial
9.26.a.b.1.1		2	3.2	odd	2
48.26.a.f.1.1		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:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+6644.76 q^{2} -531441. q^{3} +1.05985e7 q^{4} +1.29474e8 q^{5} -3.53130e9 q^{6} -4.99182e10 q^{7} -1.52537e11 q^{8} +2.82430e11 q^{9} +O(q^{10})\)	\(q+6644.76 q^{2} -531441. q^{3} +1.05985e7 q^{4} +1.29474e8 q^{5} -3.53130e9 q^{6} -4.99182e10 q^{7} -1.52537e11 q^{8} +2.82430e11 q^{9} +8.60326e11 q^{10} -2.40245e12 q^{11} -5.63245e12 q^{12} -1.10132e14 q^{13} -3.31695e14 q^{14} -6.88080e13 q^{15} -1.36920e15 q^{16} +1.88823e15 q^{17} +1.87668e15 q^{18} -5.16785e15 q^{19} +1.37223e15 q^{20} +2.65286e16 q^{21} -1.59637e16 q^{22} +2.07157e17 q^{23} +8.10644e16 q^{24} -2.81260e17 q^{25} -7.31801e17 q^{26} -1.50095e17 q^{27} -5.29056e17 q^{28} -3.91886e17 q^{29} -4.57213e17 q^{30} +7.70306e18 q^{31} -3.97970e18 q^{32} +1.27676e18 q^{33} +1.25469e19 q^{34} -6.46313e18 q^{35} +2.99332e18 q^{36} -2.99716e18 q^{37} -3.43391e19 q^{38} +5.85287e19 q^{39} -1.97496e19 q^{40} -2.45123e20 q^{41} +1.76276e20 q^{42} -2.88038e20 q^{43} -2.54623e19 q^{44} +3.65674e19 q^{45} +1.37651e21 q^{46} -3.01578e20 q^{47} +7.27648e20 q^{48} +1.15076e21 q^{49} -1.86890e21 q^{50} -1.00348e21 q^{51} -1.16723e21 q^{52} -4.35340e21 q^{53} -9.97343e20 q^{54} -3.11056e20 q^{55} +7.61438e21 q^{56} +2.74641e21 q^{57} -2.60399e21 q^{58} +6.92162e21 q^{59} -7.29258e20 q^{60} -2.89150e22 q^{61} +5.11850e22 q^{62} -1.40984e22 q^{63} +1.94985e22 q^{64} -1.42593e22 q^{65} +8.48379e21 q^{66} -1.41680e22 q^{67} +2.00123e22 q^{68} -1.10092e23 q^{69} -4.29460e22 q^{70} -6.66992e22 q^{71} -4.30810e22 q^{72} +1.33600e23 q^{73} -1.99154e22 q^{74} +1.49473e23 q^{75} -5.47712e22 q^{76} +1.19926e23 q^{77} +3.88909e23 q^{78} +8.16786e23 q^{79} -1.77276e23 q^{80} +7.97664e22 q^{81} -1.62878e24 q^{82} -7.24814e23 q^{83} +2.81162e23 q^{84} +2.44478e23 q^{85} -1.91394e24 q^{86} +2.08265e23 q^{87} +3.66463e23 q^{88} +1.55091e23 q^{89} +2.42982e23 q^{90} +5.49760e24 q^{91} +2.19554e24 q^{92} -4.09372e24 q^{93} -2.00391e24 q^{94} -6.69104e23 q^{95} +2.11498e24 q^{96} -2.30974e24 q^{97} +7.64654e24 q^{98} -6.78524e23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 324 q^{2} - 1062882 q^{3} + 25607696 q^{4} + 570861756 q^{5} + 172186884 q^{6} - 29687385728 q^{7} - 23299970112 q^{8} + 564859072962 q^{9}+O(q^{10}) \) 2 * q - 324 * q^2 - 1062882 * q^3 + 25607696 * q^4 + 570861756 * q^5 + 172186884 * q^6 - 29687385728 * q^7 - 23299970112 * q^8 + 564859072962 * q^9	\( 2 q - 324 q^{2} - 1062882 q^{3} + 25607696 q^{4} + 570861756 q^{5} + 172186884 q^{6} - 29687385728 q^{7} - 23299970112 q^{8} + 564859072962 q^{9} - 2215598822136 q^{10} - 18187785618552 q^{11} - 13608979569936 q^{12} - 105143636679236 q^{13} - 472678969464576 q^{14} - 303379342470396 q^{15} - 27\!\cdots\!40 q^{16}+ \cdots - 51\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 324 * q^2 - 1062882 * q^3 + 25607696 * q^4 + 570861756 * q^5 + 172186884 * q^6 - 29687385728 * q^7 - 23299970112 * q^8 + 564859072962 * q^9 - 2215598822136 * q^10 - 18187785618552 * q^11 - 13608979569936 * q^12 - 105143636679236 * q^13 - 472678969464576 * q^14 - 303379342470396 * q^15 - 2773446956957440 * q^16 - 456987364349436 * q^17 - 91507169819844 * q^18 + 13897438495347064 * q^19 + 7997117779360224 * q^20 + 15777093958674048 * q^21 + 94040499983248368 * q^22 + 139342298900353776 * q^23 + 12382559416291392 * q^24 - 384459968007086914 * q^25 - 766564464131074296 * q^26 - 300189270593998242 * q^27 - 225406556770067456 * q^28 - 2502033490260709812 * q^29 + 1177460053634777976 * q^30 + 1075472102492455312 * q^31 + 1469701790817795072 * q^32 + 9665734976908893432 * q^33 + 28890135735526240632 * q^34 + 2466515950356245760 * q^35 + 7232369711626357776 * q^36 - 1971470949238312628 * q^37 - 167200626490209687024 * q^38 + 55877639420449859076 * q^39 + 37293994460212449408 * q^40 - 419163355703989597068 * q^41 + 251200984211223734016 * q^42 + 38930395898259827080 * q^43 - 262388124019551701952 * q^44 + 161228221141809720636 * q^45 + 1849090502383427845152 * q^46 - 738406177844949815040 * q^47 + 1473923424252418871040 * q^48 + 218980881200994518130 * q^49 - 1149725049975869177916 * q^50 + 242861821897228617276 * q^51 - 1092357476627674689056 * q^52 - 8494002801961842724164 * q^53 + 48630661836227715204 * q^54 - 7278503149452310381584 * q^55 + 10228956809527292497920 * q^56 - 7385668611405739039224 * q^57 + 12101124135433085546472 * q^58 + 8432077474426193999496 * q^59 - 4249996269780976802784 * q^60 - 24279127983741126331460 * q^61 + 97371085084960544796384 * q^62 - 8384594590491694743168 * q^63 + 28641639605810268606464 * q^64 - 12057449268713827431672 * q^65 - 49976977351597495938288 * q^66 - 135686108042078517042056 * q^67 - 15187614376581326197728 * q^68 - 74052210669902911071216 * q^69 - 105174558114673018728960 * q^70 + 120403069132729999155984 * q^71 - 6580599758753313655872 * q^72 + 84978009597861904797076 * q^73 - 27063264550565974651416 * q^74 + 204317789857654276663074 * q^75 + 231384244314856676602816 * q^76 - 199424410226061985552896 * q^77 + 407383785382282254940536 * q^78 + 1260761953277708216756080 * q^79 - 797093885216644267516416 * q^80 + 159532886153745019726722 * q^81 - 415932720534797186451816 * q^82 - 877480501829850785701512 * q^83 + 119790285936441418884096 * q^84 - 790672874505842808668808 * q^85 - 4192505892879917618487312 * q^86 + 1329683180097641883199092 * q^87 - 1673586555576256790675712 * q^88 + 2130788092375875828694644 * q^89 - 625750548363720042343416 * q^90 + 5598517474862662217460992 * q^91 + 1177698493733784503306112 * q^92 - 571549969620692943464592 * q^93 + 1040238523552479859385856 * q^94 + 7746075091871122248616464 * q^95 - 781059789413999830858752 * q^96 - 5594117297299805221393916 * q^97 + 14139905210414655642611676 * q^98 - 5136767861863439234395512 * q^99

Introduction

L-functions

Modular forms

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