LMFDB - Embedded newform 6.28.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,28,Mod(1,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 28, names="a")

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

chi := DirichletCharacter("6.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	6.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:	$27.7113344903$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3386644380 $ x^2 - x - 3386644380
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-58194.4$ of defining polynomial
Character	$\chi$	$=$	6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8192.00 q^{2} -1.59432e6 q^{3} +6.71089e7 q^{4} +4.36927e9 q^{5} +1.30607e10 q^{6} +3.11219e11 q^{7} -5.49756e11 q^{8} +2.54187e12 q^{9} +O(q^{10})$	\(q-8192.00 q^{2} -1.59432e6 q^{3} +6.71089e7 q^{4} +4.36927e9 q^{5} +1.30607e10 q^{6} +3.11219e11 q^{7} -5.49756e11 q^{8} +2.54187e12 q^{9} -3.57931e13 q^{10} -6.06174e13 q^{11} -1.06993e14 q^{12} +6.46570e14 q^{13} -2.54951e15 q^{14} -6.96603e15 q^{15} +4.50360e15 q^{16} +2.78493e16 q^{17} -2.08230e16 q^{18} -3.23609e17 q^{19} +2.93217e17 q^{20} -4.96184e17 q^{21} +4.96578e17 q^{22} +2.77958e18 q^{23} +8.76488e17 q^{24} +1.16400e19 q^{25} -5.29670e18 q^{26} -4.05256e18 q^{27} +2.08856e19 q^{28} -4.40804e18 q^{29} +5.70657e19 q^{30} +1.35313e20 q^{31} -3.68935e19 q^{32} +9.66437e19 q^{33} -2.28142e20 q^{34} +1.35980e21 q^{35} +1.70582e20 q^{36} +2.42430e21 q^{37} +2.65101e21 q^{38} -1.03084e21 q^{39} -2.40203e21 q^{40} -1.00752e22 q^{41} +4.06474e21 q^{42} +6.87508e21 q^{43} -4.06796e21 q^{44} +1.11061e22 q^{45} -2.27703e22 q^{46} -7.32039e22 q^{47} -7.18019e21 q^{48} +3.11452e22 q^{49} -9.53546e22 q^{50} -4.44008e22 q^{51} +4.33906e22 q^{52} +2.25305e23 q^{53} +3.31985e22 q^{54} -2.64854e23 q^{55} -1.71095e23 q^{56} +5.15938e23 q^{57} +3.61107e22 q^{58} -6.81895e22 q^{59} -4.67482e23 q^{60} +2.06905e24 q^{61} -1.10849e24 q^{62} +7.91078e23 q^{63} +3.02231e23 q^{64} +2.82504e24 q^{65} -7.91705e23 q^{66} +5.18244e24 q^{67} +1.86894e24 q^{68} -4.43155e24 q^{69} -1.11395e25 q^{70} +9.12560e24 q^{71} -1.39741e24 q^{72} -6.99708e24 q^{73} -1.98599e25 q^{74} -1.85579e25 q^{75} -2.17171e25 q^{76} -1.88653e25 q^{77} +8.44466e24 q^{78} +3.46799e25 q^{79} +1.96775e25 q^{80} +6.46108e24 q^{81} +8.25364e25 q^{82} -5.24073e25 q^{83} -3.32984e25 q^{84} +1.21681e26 q^{85} -5.63207e25 q^{86} +7.02784e24 q^{87} +3.33248e25 q^{88} +2.05205e26 q^{89} -9.09812e25 q^{90} +2.01225e26 q^{91} +1.86534e26 q^{92} -2.15733e26 q^{93} +5.99686e26 q^{94} -1.41394e27 q^{95} +5.88201e25 q^{96} +3.43252e26 q^{97} -2.55141e26 q^{98} -1.54081e26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16384 q^{2} - 3188646 q^{3} + 134217728 q^{4} + 291441036 q^{5} + 26121388032 q^{6} + 121646295328 q^{7} - 1099511627776 q^{8} + 5083731656658 q^{9}+O(q^{10}) $ 2 * q - 16384 * q^2 - 3188646 * q^3 + 134217728 * q^4 + 291441036 * q^5 + 26121388032 * q^6 + 121646295328 * q^7 - 1099511627776 * q^8 + 5083731656658 * q^9	$ 2 q - 16384 q^{2} - 3188646 q^{3} + 134217728 q^{4} + 291441036 q^{5} + 26121388032 q^{6} + 121646295328 q^{7} - 1099511627776 q^{8} + 5083731656658 q^{9} - 2387484966912 q^{10} - 231807361766376 q^{11} - 213986410758144 q^{12} - 11\!\cdots\!64 q^{13}+ \cdots - 58\!\cdots\!04 q^{99}+O(q^{100}) $ 2 * q - 16384 * q^2 - 3188646 * q^3 + 134217728 * q^4 + 291441036 * q^5 + 26121388032 * q^6 + 121646295328 * q^7 - 1099511627776 * q^8 + 5083731656658 * q^9 - 2387484966912 * q^10 - 231807361766376 * q^11 - 213986410758144 * q^12 - 1155759271611764 * q^13 - 996526451326976 * q^14 - 464651146838628 * q^15 + 9007199254740992 * q^16 - 46125175777027452 * q^17 - 41645929731342336 * q^18 - 268519854753239000 * q^19 + 19558276848943104 * q^20 - 193943486506222944 * q^21 + 1898965907590152192 * q^22 + 1299561926005929936 * q^23 + 1752976676930715648 * q^24 + 20818087556919436046 * q^25 + 9467979953043570688 * q^26 - 8105110306037952534 * q^27 + 8163544689270587392 * q^28 + 60178362995785587900 * q^29 + 3806422194902040576 * q^30 + 203575085639304966544 * q^31 - 73786976294838206464 * q^32 + 369575808433453883448 * q^33 + 377857439965408886784 * q^34 + 2132849735738606710464 * q^35 + 341163456359156416512 * q^36 + 3022337597514982851388 * q^37 + 2199714650138533888000 * q^38 + 1842653589193882415772 * q^39 - 160221403946541907968 * q^40 - 10870375798082518905516 * q^41 + 1588785041458978357248 * q^42 - 1299568293415606314344 * q^43 - 15556328714978526756864 * q^44 + 740804010381201908844 * q^45 - 10646011297840578035712 * q^46 - 99372996476917699213632 * q^47 - 14360384937416422588416 * q^48 + 1370785920275118717906 * q^49 - 170541773266284020088832 * q^50 + 73538428620357738354996 * q^51 - 77561691775332931076096 * q^52 - 35770850049954566775924 * q^53 + 66397063627062907158528 * q^54 + 433229958906724722129552 * q^55 - 66875758094504651915264 * q^56 + 428107380389748262197000 * q^57 - 492981149661475536076800 * q^58 + 299672958231389705557080 * q^59 - 31182210620637516398592 * q^60 + 2165599091776519863171724 * q^61 - 1667687101557186285928448 * q^62 + 309208561237060882746912 * q^63 + 604462909807314587353088 * q^64 + 10174637395564415468537928 * q^65 - 3027565022686854213206016 * q^66 + 13568283837486181949525608 * q^67 - 3095408148196629600534528 * q^68 - 2071921468555552233353328 * q^69 - 17472305035170666172121088 * q^70 - 4319907418871433623040336 * q^71 - 2794811034494209364066304 * q^72 - 20032895180752990538485964 * q^73 - 24758989598842739518570496 * q^74 - 33190755808010466035166858 * q^75 - 18020062413934869610496000 * q^76 + 13587711578810985760484736 * q^77 - 15095018202676284750004224 * q^78 + 5633936436869082596599600 * q^79 + 1312533741130071310073856 * q^80 + 12922163778453346597864482 * q^81 + 89050118537891994873987072 * q^82 - 46762236922353070723154904 * q^83 - 13015327059631950702575616 * q^84 + 423336865613342459682869784 * q^85 + 10646063459660646927106048 * q^86 - 95943748226529865857491700 * q^87 + 127437444833104091192229888 * q^88 - 191930414076503127699406380 * q^89 - 6068666453042806037250048 * q^90 + 542898500680491813749530304 * q^91 + 87212124551910015268552704 * q^92 - 324564441261713612175329712 * q^93 + 814063587138909791958073344 * q^94 - 1638584179808499075287277840 * q^95 + 117640273407315333844303872 * q^96 + 544725669490755670759486468 * q^97 - 11229478258893772537085952 * q^98 - 589223211629049495820465704 * 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 $

$2$	−8192.00	−0.707107
$2$	−8192.00	−0.707107
$3$	−1.59432e6	−0.577350
$3$	−1.59432e6	−0.577350
$4$	6.71089e7	0.500000
$5$	4.36927e9	1.60072	0.800358	−	0.599523i	$-0.204643\pi$
$5$	4.36927e9	1.60072	0.800358	+	0.599523i	$0.204643\pi$
$6$	1.30607e10	0.408248
$7$	3.11219e11	1.21407	0.607034	−	0.794676i	$-0.292359\pi$
$7$	3.11219e11	1.21407	0.607034	+	0.794676i	$0.292359\pi$
$8$	−5.49756e11	−0.353553
$9$	2.54187e12	0.333333
$10$	−3.57931e13	−1.13188
$11$	−6.06174e13	−0.529415	−0.264707	−	0.964329i	$-0.585275\pi$
$11$	−6.06174e13	−0.529415	−0.264707	+	0.964329i	$0.585275\pi$
$12$	−1.06993e14	−0.288675
$13$	6.46570e14	0.592080	0.296040	−	0.955176i	$-0.404334\pi$
$13$	6.46570e14	0.592080	0.296040	+	0.955176i	$0.404334\pi$
$14$	−2.54951e15	−0.858476
$15$	−6.96603e15	−0.924173
$16$	4.50360e15	0.250000
$17$	2.78493e16	0.681953	0.340976	−	0.940072i	$-0.389242\pi$
$17$	2.78493e16	0.681953	0.340976	+	0.940072i	$0.389242\pi$
$18$	−2.08230e16	−0.235702
$19$	−3.23609e17	−1.76542	−0.882709	−	0.469920i	$-0.844283\pi$
$19$	−3.23609e17	−1.76542	−0.882709	+	0.469920i	$0.844283\pi$
$20$	2.93217e17	0.800358
$21$	−4.96184e17	−0.700943
$22$	4.96578e17	0.374353
$23$	2.77958e18	1.14988	0.574941	−	0.818195i	$-0.305025\pi$
$23$	2.77958e18	1.14988	0.574941	+	0.818195i	$0.305025\pi$
$24$	8.76488e17	0.204124
$25$	1.16400e19	1.56229
$26$	−5.29670e18	−0.418664
$27$	−4.05256e18	−0.192450
$28$	2.08856e19	0.607034
$29$	−4.40804e18	−0.0797761	−0.0398880	−	0.999204i	$-0.512700\pi$
$29$	−4.40804e18	−0.0797761	−0.0398880	+	0.999204i	$0.512700\pi$
$30$	5.70657e19	0.653489
$31$	1.35313e20	0.995309	0.497654	−	0.867375i	$-0.334195\pi$
$31$	1.35313e20	0.995309	0.497654	+	0.867375i	$0.334195\pi$
$32$	−3.68935e19	−0.176777
$33$	9.66437e19	0.305658
$34$	−2.28142e20	−0.482213
$35$	1.35980e21	1.94338
$36$	1.70582e20	0.166667
$37$	2.42430e21	1.63630	0.818150	−	0.575005i	$-0.195000\pi$
$37$	2.42430e21	1.63630	0.818150	+	0.575005i	$0.195000\pi$
$38$	2.65101e21	1.24834
$39$	−1.03084e21	−0.341838
$40$	−2.40203e21	−0.565938
$41$	−1.00752e22	−1.70088	−0.850439	−	0.526073i	$-0.823664\pi$
$41$	−1.00752e22	−1.70088	−0.850439	+	0.526073i	$0.823664\pi$
$42$	4.06474e21	0.495641
$43$	6.87508e21	0.610174	0.305087	−	0.952324i	$-0.401314\pi$
$43$	6.87508e21	0.610174	0.305087	+	0.952324i	$0.401314\pi$
$44$	−4.06796e21	−0.264707
$45$	1.11061e22	0.533572
$46$	−2.27703e22	−0.813090
$47$	−7.32039e22	−1.95530	−0.977650	−	0.210241i	$-0.932575\pi$
$47$	−7.32039e22	−1.95530	−0.977650	+	0.210241i	$0.932575\pi$
$48$	−7.18019e21	−0.144338
$49$	3.11452e22	0.473962
$50$	−9.53546e22	−1.10471
$51$	−4.44008e22	−0.393726
$52$	4.33906e22	0.296040
$53$	2.25305e23	1.18863	0.594316	−	0.804232i	$-0.297423\pi$
$53$	2.25305e23	1.18863	0.594316	+	0.804232i	$0.297423\pi$
$54$	3.31985e22	0.136083
$55$	−2.64854e23	−0.847442
$56$	−1.71095e23	−0.429238
$57$	5.15938e23	1.01926
$58$	3.61107e22	0.0564102
$59$	−6.81895e22	−0.0845698	−0.0422849	−	0.999106i	$-0.513464\pi$
$59$	−6.81895e22	−0.0845698	−0.0422849	+	0.999106i	$0.513464\pi$
$60$	−4.67482e23	−0.462087
$61$	2.06905e24	1.63613	0.818066	−	0.575124i	$-0.195046\pi$
$61$	2.06905e24	1.63613	0.818066	+	0.575124i	$0.195046\pi$
$62$	−1.10849e24	−0.703790
$63$	7.91078e23	0.404689
$64$	3.02231e23	0.125000
$65$	2.82504e24	0.947752
$66$	−7.91705e23	−0.216133
$67$	5.18244e24	1.15485	0.577424	−	0.816444i	$-0.304058\pi$
$67$	5.18244e24	1.15485	0.577424	+	0.816444i	$0.304058\pi$
$68$	1.86894e24	0.340976
$69$	−4.43155e24	−0.663885
$70$	−1.11395e25	−1.37418
$71$	9.12560e24	0.929552	0.464776	−	0.885428i	$-0.346135\pi$
$71$	9.12560e24	0.929552	0.464776	+	0.885428i	$0.346135\pi$
$72$	−1.39741e24	−0.117851
$73$	−6.99708e24	−0.489845	−0.244922	−	0.969543i	$-0.578762\pi$
$73$	−6.99708e24	−0.489845	−0.244922	+	0.969543i	$0.578762\pi$
$74$	−1.98599e25	−1.15704
$75$	−1.85579e25	−0.901988
$76$	−2.17171e25	−0.882709
$77$	−1.88653e25	−0.642746
$78$	8.44466e24	0.241716
$79$	3.46799e25	0.835818	0.417909	−	0.908489i	$-0.362763\pi$
$79$	3.46799e25	0.835818	0.417909	+	0.908489i	$0.362763\pi$
$80$	1.96775e25	0.400179
$81$	6.46108e24	0.111111
$82$	8.25364e25	1.20270
$83$	−5.24073e25	−0.648392	−0.324196	−	0.945990i	$-0.605094\pi$
$83$	−5.24073e25	−0.648392	−0.324196	+	0.945990i	$0.605094\pi$
$84$	−3.32984e25	−0.350471
$85$	1.21681e26	1.09161
$86$	−5.63207e25	−0.431458
$87$	7.02784e24	0.0460587
$88$	3.33248e25	0.187176
$89$	2.05205e26	0.989516	0.494758	−	0.869031i	$-0.335257\pi$
$89$	2.05205e26	0.989516	0.494758	+	0.869031i	$0.335257\pi$
$90$	−9.09812e25	−0.377292
$91$	2.01225e26	0.718826
$92$	1.86534e26	0.574941
$93$	−2.15733e26	−0.574642
$94$	5.99686e26	1.38261
$95$	−1.41394e27	−2.82593
$96$	5.88201e25	0.102062
$97$	3.43252e26	0.517839	0.258919	−	0.965899i	$-0.416634\pi$
$97$	3.43252e26	0.517839	0.258919	+	0.965899i	$0.416634\pi$
$98$	−2.55141e26	−0.335142
$99$	−1.54081e26	−0.176472
$100$	7.81144e26	0.781144
$101$	−5.43435e26	−0.475126	−0.237563	−	0.971372i	$-0.576349\pi$
$101$	−5.43435e26	−0.475126	−0.237563	+	0.971372i	$0.576349\pi$
$102$	3.63732e26	0.278406
$103$	5.07992e25	0.0340843	0.0170421	−	0.999855i	$-0.494575\pi$
$103$	5.07992e25	0.0340843	0.0170421	+	0.999855i	$0.494575\pi$
$104$	−3.55456e26	−0.209332
$105$	−2.16796e27	−1.12201
$106$	−1.84570e27	−0.840489
$107$	−1.31347e27	−0.526913	−0.263456	−	0.964671i	$-0.584862\pi$
$107$	−1.31347e27	−0.526913	−0.263456	+	0.964671i	$0.584862\pi$
$108$	−2.71962e26	−0.0962250
$109$	3.20537e27	1.00143	0.500715	−	0.865612i	$-0.333071\pi$
$109$	3.20537e27	1.00143	0.500715	+	0.865612i	$0.333071\pi$
$110$	2.16968e27	0.599232
$111$	−3.86512e27	−0.944718
$112$	1.40161e27	0.303517
$113$	1.64220e27	0.315403	0.157702	−	0.987487i	$-0.449592\pi$
$113$	1.64220e27	0.315403	0.157702	+	0.987487i	$0.449592\pi$
$114$	−4.22656e27	−0.720729
$115$	1.21447e28	1.84063
$116$	−2.95819e26	−0.0398880
$117$	1.64349e27	0.197360
$118$	5.58609e26	0.0597999
$119$	8.66725e27	0.827937
$120$	3.82962e27	0.326745
$121$	−9.43553e27	−0.719720
$122$	−1.69497e28	−1.15692
$123$	1.60632e28	0.982003
$124$	9.08073e27	0.497654
$125$	1.83045e28	0.900065
$126$	−6.48051e27	−0.286159
$127$	1.82085e28	0.722644	0.361322	−	0.932441i	$-0.382325\pi$
$127$	1.82085e28	0.722644	0.361322	+	0.932441i	$0.382325\pi$
$128$	−2.47588e27	−0.0883883
$129$	−1.09611e28	−0.352284
$130$	−2.31427e28	−0.670162
$131$	−4.91416e28	−1.28318	−0.641589	−	0.767049i	$-0.721725\pi$
$131$	−4.91416e28	−1.28318	−0.641589	+	0.767049i	$0.721725\pi$
$132$	6.48565e27	0.152829
$133$	−1.00714e29	−2.14334
$134$	−4.24546e28	−0.816601
$135$	−1.77067e28	−0.308058
$136$	−1.53103e28	−0.241107
$137$	5.37814e28	0.767193	0.383597	−	0.923501i	$-0.374685\pi$
$137$	5.37814e28	0.767193	0.383597	+	0.923501i	$0.374685\pi$
$138$	3.63033e28	0.469438
$139$	4.60592e28	0.540277	0.270138	−	0.962821i	$-0.412931\pi$
$139$	4.60592e28	0.540277	0.270138	+	0.962821i	$0.412931\pi$
$140$	9.12548e28	0.971689
$141$	1.16711e29	1.12889
$142$	−7.47569e28	−0.657293
$143$	−3.91934e28	−0.313456
$144$	1.14475e28	0.0833333
$145$	−1.92599e28	−0.127699
$146$	5.73201e28	0.346373
$147$	−4.96555e28	−0.273642
$148$	1.62692e29	0.818150
$149$	6.39934e28	0.293846	0.146923	−	0.989148i	$-0.453063\pi$
$149$	6.39934e28	0.293846	0.146923	+	0.989148i	$0.453063\pi$
$150$	1.52026e29	0.637802
$151$	−4.57912e29	−1.75628	−0.878139	−	0.478406i	$-0.841215\pi$
$151$	−4.57912e29	−1.75628	−0.878139	+	0.478406i	$0.841215\pi$
$152$	1.77906e29	0.624170
$153$	7.07893e28	0.227318
$154$	1.54545e29	0.454490
$155$	5.91221e29	1.59321
$156$	−6.91786e28	−0.170919
$157$	−7.23684e29	−1.64023	−0.820113	−	0.572202i	$-0.806089\pi$
$157$	−7.23684e29	−1.64023	−0.820113	+	0.572202i	$0.806089\pi$
$158$	−2.84098e29	−0.591013
$159$	−3.59209e29	−0.686256
$160$	−1.61198e29	−0.282969
$161$	8.65059e29	1.39604
$162$	−5.29292e28	−0.0785674
$163$	4.01419e29	0.548360	0.274180	−	0.961678i	$-0.411594\pi$
$163$	4.01419e29	0.548360	0.274180	+	0.961678i	$0.411594\pi$
$164$	−6.76138e29	−0.850439
$165$	4.22263e29	0.489271
$166$	4.29321e29	0.458483
$167$	−1.03017e30	−1.01447	−0.507233	−	0.861809i	$-0.669332\pi$
$167$	−1.03017e30	−1.01447	−0.507233	+	0.861809i	$0.669332\pi$
$168$	2.72780e29	0.247821
$169$	−7.74480e29	−0.649441
$170$	−9.96813e29	−0.771886
$171$	−8.22572e29	−0.588473
$172$	4.61379e29	0.305087
$173$	−2.68290e30	−1.64052	−0.820261	−	0.571989i	$-0.806172\pi$
$173$	−2.68290e30	−1.64052	−0.820261	+	0.571989i	$0.806172\pi$
$174$	−5.75721e28	−0.0325684
$175$	3.62258e30	1.89673
$176$	−2.72996e29	−0.132354
$177$	1.08716e29	0.0488264
$178$	−1.68104e30	−0.699693
$179$	2.21883e30	0.856264	0.428132	−	0.903716i	$-0.359172\pi$
$179$	2.21883e30	0.856264	0.428132	+	0.903716i	$0.359172\pi$
$180$	7.45318e29	0.266786
$181$	4.61780e30	1.53382	0.766911	−	0.641754i	$-0.221793\pi$
$181$	4.61780e30	1.53382	0.766911	+	0.641754i	$0.221793\pi$
$182$	−1.64844e30	−0.508287
$183$	−3.29874e30	−0.944622
$184$	−1.52809e30	−0.406545
$185$	1.05924e31	2.61925
$186$	1.76729e30	0.406333
$187$	−1.68815e30	−0.361036
$188$	−4.91263e30	−0.977650
$189$	−1.26123e30	−0.233648
$190$	1.15830e31	1.99824
$191$	−4.74656e30	−0.762831	−0.381415	−	0.924404i	$-0.624563\pi$
$191$	−4.74656e30	−0.762831	−0.381415	+	0.924404i	$0.624563\pi$
$192$	−4.81855e29	−0.0721688
$193$	2.52769e30	0.352940	0.176470	−	0.984306i	$-0.443532\pi$
$193$	2.52769e30	0.352940	0.176470	+	0.984306i	$0.443532\pi$
$194$	−2.81192e30	−0.366167
$195$	−4.50403e30	−0.547185
$196$	2.09012e30	0.236981
$197$	−2.31410e30	−0.244956	−0.122478	−	0.992471i	$-0.539084\pi$
$197$	−2.31410e30	−0.244956	−0.122478	+	0.992471i	$0.539084\pi$
$198$	1.26223e30	0.124784
$199$	−3.03480e30	−0.280294	−0.140147	−	0.990131i	$-0.544758\pi$
$199$	−3.03480e30	−0.280294	−0.140147	+	0.990131i	$0.544758\pi$
$200$	−6.39914e30	−0.552353
$201$	−8.26249e30	−0.666752
$202$	4.45182e30	0.335965
$203$	−1.37187e30	−0.0968536
$204$	−2.97969e30	−0.196863
$205$	−4.40215e31	−2.72262
$206$	−4.16147e29	−0.0241012
$207$	7.06532e30	0.383294
$208$	2.91189e30	0.148020
$209$	1.96164e31	0.934638
$210$	1.77600e31	0.793381
$211$	−1.95873e31	−0.820655	−0.410328	−	0.911938i	$-0.634586\pi$
$211$	−1.95873e31	−0.820655	−0.410328	+	0.911938i	$0.634586\pi$
$212$	1.51200e31	0.594316
$213$	−1.45492e31	−0.536677
$214$	1.07599e31	0.372583
$215$	3.00391e31	0.976715
$216$	2.22792e30	0.0680414
$217$	4.21122e31	1.20837
$218$	−2.62584e31	−0.708118
$219$	1.11556e31	0.282812
$220$	−1.77740e31	−0.423721
$221$	1.80065e31	0.403771
$222$	3.16630e31	0.668017
$223$	−2.74869e31	−0.545771	−0.272886	−	0.962047i	$-0.587978\pi$
$223$	−2.74869e31	−0.545771	−0.272886	+	0.962047i	$0.587978\pi$
$224$	−1.14820e31	−0.214619
$225$	2.95872e31	0.520763
$226$	−1.34529e31	−0.223024
$227$	−1.10085e30	−0.0171940	−0.00859701	−	0.999963i	$-0.502737\pi$
$227$	−1.10085e30	−0.0171940	−0.00859701	+	0.999963i	$0.502737\pi$
$228$	3.46240e31	0.509632
$229$	7.85209e31	1.08945	0.544724	−	0.838615i	$-0.316634\pi$
$229$	7.85209e31	1.08945	0.544724	+	0.838615i	$0.316634\pi$
$230$	−9.94897e31	−1.30153
$231$	3.00774e31	0.371089
$232$	2.42335e30	0.0282051
$233$	1.08140e32	1.18763	0.593817	−	0.804600i	$-0.297620\pi$
$233$	1.08140e32	1.18763	0.593817	+	0.804600i	$0.297620\pi$
$234$	−1.34635e31	−0.139555
$235$	−3.19848e32	−3.12988
$236$	−4.57612e30	−0.0422849
$237$	−5.52909e31	−0.482560
$238$	−7.10021e31	−0.585440
$239$	−3.85813e31	−0.300612	−0.150306	−	0.988640i	$-0.548026\pi$
$239$	−3.85813e31	−0.300612	−0.150306	+	0.988640i	$0.548026\pi$
$240$	−3.13722e31	−0.231043
$241$	2.43286e32	1.69389	0.846947	−	0.531677i	$-0.178438\pi$
$241$	2.43286e32	1.69389	0.846947	+	0.531677i	$0.178438\pi$
$242$	7.72958e31	0.508919
$243$	−1.03011e31	−0.0641500
$244$	1.38852e32	0.818066
$245$	1.36082e32	0.758678
$246$	−1.31590e32	−0.694381
$247$	−2.09236e32	−1.04527
$248$	−7.43893e31	−0.351895
$249$	8.35542e31	0.374349
$250$	−1.49951e32	−0.636442
$251$	1.35106e31	0.0543350	0.0271675	−	0.999631i	$-0.491351\pi$
$251$	1.35106e31	0.0543350	0.0271675	+	0.999631i	$0.491351\pi$
$252$	5.30883e31	0.202345
$253$	−1.68491e32	−0.608765
$254$	−1.49164e32	−0.510987
$255$	−1.93999e32	−0.630243
$256$	2.02824e31	0.0625000
$257$	−2.50576e32	−0.732559	−0.366280	−	0.930505i	$-0.619369\pi$
$257$	−2.50576e32	−0.732559	−0.366280	+	0.930505i	$0.619369\pi$
$258$	8.97934e31	0.249103
$259$	7.54489e32	1.98658
$260$	1.89585e32	0.473876
$261$	−1.12046e31	−0.0265920
$262$	4.02568e32	0.907344
$263$	−4.15757e32	−0.890096	−0.445048	−	0.895507i	$-0.646813\pi$
$263$	−4.15757e32	−0.890096	−0.445048	+	0.895507i	$0.646813\pi$
$264$	−5.31304e31	−0.108066
$265$	9.84420e32	1.90266
$266$	8.25045e32	1.51557
$267$	−3.27163e32	−0.571297
$268$	3.47788e32	0.577424
$269$	−1.81575e32	−0.286682	−0.143341	−	0.989673i	$-0.545785\pi$
$269$	−1.81575e32	−0.286682	−0.143341	+	0.989673i	$0.545785\pi$
$270$	1.45053e32	0.217830
$271$	−4.40915e32	−0.629897	−0.314949	−	0.949109i	$-0.601987\pi$
$271$	−4.40915e32	−0.629897	−0.314949	+	0.949109i	$0.601987\pi$
$272$	1.25422e32	0.170488
$273$	−3.20818e32	−0.415014
$274$	−4.40577e32	−0.542487
$275$	−7.05584e32	−0.827099
$276$	−2.97396e32	−0.331942
$277$	4.47660e32	0.475852	0.237926	−	0.971283i	$-0.423532\pi$
$277$	4.47660e32	0.475852	0.237926	+	0.971283i	$0.423532\pi$
$278$	−3.77317e32	−0.382033
$279$	3.43948e32	0.331770
$280$	−7.47559e32	−0.687088
$281$	−8.16751e32	−0.715409	−0.357704	−	0.933835i	$-0.616440\pi$
$281$	−8.16751e32	−0.715409	−0.357704	+	0.933835i	$0.616440\pi$
$282$	−9.56094e32	−0.798248
$283$	−3.19801e32	−0.254544	−0.127272	−	0.991868i	$-0.540622\pi$
$283$	−3.19801e32	−0.254544	−0.127272	+	0.991868i	$0.540622\pi$
$284$	6.12409e32	0.464776
$285$	2.25427e33	1.63155
$286$	3.21072e32	0.221647
$287$	−3.13561e33	−2.06498
$288$	−9.37783e31	−0.0589256
$289$	−8.92126e32	−0.534940
$290$	1.57777e32	0.0902966
$291$	−5.47255e32	−0.298974
$292$	−4.69566e32	−0.244922
$293$	2.58899e33	1.28949	0.644744	−	0.764399i	$-0.276964\pi$
$293$	2.58899e33	1.28949	0.644744	+	0.764399i	$0.276964\pi$
$294$	4.06778e32	0.193494
$295$	−2.97939e32	−0.135372
$296$	−1.33277e33	−0.578519
$297$	2.45655e32	0.101886
$298$	−5.24234e32	−0.207781
$299$	1.79719e33	0.680823
$300$	−1.24540e33	−0.450994
$301$	2.13966e33	0.740793
$302$	3.75121e33	1.24188
$303$	8.66410e32	0.274314
$304$	−1.45741e33	−0.441355
$305$	9.04025e33	2.61898
$306$	−5.79906e32	−0.160738
$307$	1.64496e33	0.436303	0.218152	−	0.975915i	$-0.429997\pi$
$307$	1.64496e33	0.436303	0.218152	+	0.975915i	$0.429997\pi$
$308$	−1.26603e33	−0.321373
$309$	−8.09903e31	−0.0196786
$310$	−4.84328e33	−1.12657
$311$	−6.49387e33	−1.44623	−0.723117	−	0.690725i	$-0.757291\pi$
$311$	−6.49387e33	−1.44623	−0.723117	+	0.690725i	$0.757291\pi$
$312$	5.66711e32	0.120858
$313$	−8.69247e33	−1.77539	−0.887697	−	0.460428i	$-0.847696\pi$
$313$	−8.69247e33	−1.77539	−0.887697	+	0.460428i	$0.847696\pi$
$314$	5.92842e33	1.15981
$315$	3.45644e33	0.647793
$316$	2.32733e33	0.417909
$317$	1.93111e33	0.332282	0.166141	−	0.986102i	$-0.446869\pi$
$317$	1.93111e33	0.332282	0.166141	+	0.986102i	$0.446869\pi$
$318$	2.94264e33	0.485257
$319$	2.67204e32	0.0422346
$320$	1.32053e33	0.200089
$321$	2.09409e33	0.304213
$322$	−7.08657e33	−0.987147
$323$	−9.01231e33	−1.20393
$324$	4.33596e32	0.0555556
$325$	7.52605e33	0.925000
$326$	−3.28843e33	−0.387749
$327$	−5.11039e33	−0.578176
$328$	5.53892e33	0.601351
$329$	−2.27825e34	−2.37387
$330$	−3.45918e33	−0.345967
$331$	−8.64145e33	−0.829676	−0.414838	−	0.909895i	$-0.636162\pi$
$331$	−8.64145e33	−0.829676	−0.414838	+	0.909895i	$0.636162\pi$
$332$	−3.51700e33	−0.324196
$333$	6.16224e33	0.545433
$334$	8.43917e33	0.717335
$335$	2.26435e34	1.84858
$336$	−2.23462e33	−0.175236
$337$	−2.03843e33	−0.153565	−0.0767826	−	0.997048i	$-0.524465\pi$
$337$	−2.03843e33	−0.153565	−0.0767826	+	0.997048i	$0.524465\pi$
$338$	6.34454e33	0.459224
$339$	−2.61819e33	−0.182098
$340$	8.16589e33	0.545806
$341$	−8.20234e33	−0.526931
$342$	6.73851e33	0.416113
$343$	−1.07580e34	−0.638646
$344$	−3.77962e33	−0.215729
$345$	−1.93626e34	−1.06269
$346$	2.19783e34	1.16002
$347$	8.12227e33	0.412315	0.206158	−	0.978519i	$-0.433904\pi$
$347$	8.12227e33	0.412315	0.206158	+	0.978519i	$0.433904\pi$
$348$	4.71630e32	0.0230294
$349$	4.94258e33	0.232172	0.116086	−	0.993239i	$-0.462965\pi$
$349$	4.94258e33	0.232172	0.116086	+	0.993239i	$0.462965\pi$
$350$	−2.96762e34	−1.34119
$351$	−2.62026e33	−0.113946
$352$	2.23639e33	0.0935882
$353$	1.97509e34	0.795478	0.397739	−	0.917499i	$-0.369795\pi$
$353$	1.97509e34	0.795478	0.397739	+	0.917499i	$0.369795\pi$
$354$	−8.90603e32	−0.0345255
$355$	3.98722e34	1.48795
$356$	1.37711e34	0.494758
$357$	−1.38184e34	−0.478010
$358$	−1.81766e34	−0.605470
$359$	1.80645e34	0.579495	0.289748	−	0.957103i	$-0.406429\pi$
$359$	1.80645e34	0.579495	0.289748	+	0.957103i	$0.406429\pi$
$360$	−6.10565e33	−0.188646
$361$	7.11225e34	2.11670
$362$	−3.78290e34	−1.08458
$363$	1.50433e34	0.415531
$364$	1.35040e34	0.359413
$365$	−3.05722e34	−0.784102
$366$	2.70233e34	0.667948
$367$	−2.27625e34	−0.542286	−0.271143	−	0.962539i	$-0.587402\pi$
$367$	−2.27625e34	−0.542286	−0.271143	+	0.962539i	$0.587402\pi$
$368$	1.25181e34	0.287471
$369$	−2.56099e34	−0.566960
$370$	−8.67731e34	−1.85209
$371$	7.01194e34	1.44308
$372$	−1.44776e34	−0.287321
$373$	−6.70992e34	−1.28425	−0.642123	−	0.766601i	$-0.721946\pi$
$373$	−6.70992e34	−1.28425	−0.642123	+	0.766601i	$0.721946\pi$
$374$	1.38294e34	0.255291
$375$	−2.91833e34	−0.519652
$376$	4.02443e34	0.691303
$377$	−2.85011e33	−0.0472338
$378$	1.03320e34	0.165214
$379$	−3.50560e34	−0.540921	−0.270460	−	0.962731i	$-0.587176\pi$
$379$	−3.50560e34	−0.540921	−0.270460	+	0.962731i	$0.587176\pi$
$380$	−9.48878e34	−1.41297
$381$	−2.90303e34	−0.417219
$382$	3.88838e34	0.539403
$383$	3.70361e33	0.0495955	0.0247978	−	0.999692i	$-0.492106\pi$
$383$	3.70361e33	0.0495955	0.0247978	+	0.999692i	$0.492106\pi$
$384$	3.94735e33	0.0510310
$385$	−8.24277e34	−1.02885
$386$	−2.07068e34	−0.249566
$387$	1.74755e34	0.203391
$388$	2.30353e34	0.258919
$389$	−7.02105e34	−0.762224	−0.381112	−	0.924529i	$-0.624459\pi$
$389$	−7.02105e34	−0.762224	−0.381112	+	0.924529i	$0.624459\pi$
$390$	3.68970e34	0.386918
$391$	7.74095e34	0.784166
$392$	−1.71222e34	−0.167571
$393$	7.83476e34	0.740843
$394$	1.89571e34	0.173210
$395$	1.51526e35	1.33791
$396$	−1.03402e34	−0.0882358
$397$	−1.30976e35	−1.08024	−0.540118	−	0.841589i	$-0.681620\pi$
$397$	−1.30976e35	−1.08024	−0.540118	+	0.841589i	$0.681620\pi$
$398$	2.48611e34	0.198198
$399$	1.60570e35	1.23746
$400$	5.24217e34	0.390572
$401$	1.32379e35	0.953612	0.476806	−	0.879009i	$-0.341794\pi$
$401$	1.32379e35	0.953612	0.476806	+	0.879009i	$0.341794\pi$
$402$	6.76863e34	0.471465
$403$	8.74896e34	0.589303
$404$	−3.64693e34	−0.237563
$405$	2.82302e34	0.177857
$406$	1.12383e34	0.0684858
$407$	−1.46955e35	−0.866281
$408$	2.44096e34	0.139203
$409$	−2.54536e35	−1.40438	−0.702190	−	0.711989i	$-0.747794\pi$
$409$	−2.54536e35	−1.40438	−0.702190	+	0.711989i	$0.747794\pi$
$410$	3.60624e35	1.92518
$411$	−8.57450e34	−0.442939
$412$	3.40908e33	0.0170421
$413$	−2.12219e34	−0.102674
$414$	−5.78791e34	−0.271030
$415$	−2.28982e35	−1.03789
$416$	−2.38542e34	−0.104666
$417$	−7.34332e34	−0.311929
$418$	−1.60697e35	−0.660889
$419$	−2.64873e35	−1.05475	−0.527373	−	0.849634i	$-0.676823\pi$
$419$	−2.64873e35	−1.05475	−0.527373	+	0.849634i	$0.676823\pi$
$420$	−1.45490e35	−0.561005
$421$	8.67841e34	0.324065	0.162032	−	0.986785i	$-0.448195\pi$
$421$	8.67841e34	0.324065	0.162032	+	0.986785i	$0.448195\pi$
$422$	1.60459e35	0.580291
$423$	−1.86075e35	−0.651766
$424$	−1.23863e35	−0.420245
$425$	3.24165e35	1.06541
$426$	1.19187e35	0.379488
$427$	6.43929e35	1.98638
$428$	−8.81454e34	−0.263456
$429$	6.24869e34	0.180974
$430$	−2.46080e35	−0.690642
$431$	−8.57490e34	−0.233231	−0.116615	−	0.993177i	$-0.537204\pi$
$431$	−8.57490e34	−0.233231	−0.116615	+	0.993177i	$0.537204\pi$
$432$	−1.82511e34	−0.0481125
$433$	−1.22839e35	−0.313870	−0.156935	−	0.987609i	$-0.550161\pi$
$433$	−1.22839e35	−0.313870	−0.156935	+	0.987609i	$0.550161\pi$
$434$	−3.44983e35	−0.854449
$435$	3.07065e34	0.0737269
$436$	2.15109e35	0.500715
$437$	−8.99499e35	−2.03002
$438$	−9.13868e34	−0.199978
$439$	−2.95742e34	−0.0627542	−0.0313771	−	0.999508i	$-0.509989\pi$
$439$	−2.95742e34	−0.0627542	−0.0313771	+	0.999508i	$0.509989\pi$
$440$	1.45605e35	0.299616
$441$	7.91669e34	0.157987
$442$	−1.47510e35	−0.285509
$443$	2.15913e35	0.405348	0.202674	−	0.979246i	$-0.435037\pi$
$443$	2.15913e35	0.405348	0.202674	+	0.979246i	$0.435037\pi$
$444$	−2.59384e35	−0.472359
$445$	8.96596e35	1.58393
$446$	2.25173e35	0.385918
$447$	−1.02026e35	−0.169652
$448$	9.40603e34	0.151759
$449$	2.22802e35	0.348813	0.174407	−	0.984674i	$-0.444199\pi$
$449$	2.22802e35	0.348813	0.174407	+	0.984674i	$0.444199\pi$
$450$	−2.42378e35	−0.368235
$451$	6.10735e35	0.900470
$452$	1.10206e35	0.157702
$453$	7.30060e35	1.01399
$454$	9.01813e33	0.0121580
$455$	8.79208e35	1.15064
$456$	−2.83640e35	−0.360365
$457$	−5.04203e35	−0.621923	−0.310961	−	0.950423i	$-0.600651\pi$
$457$	−5.04203e35	−0.621923	−0.310961	+	0.950423i	$0.600651\pi$
$458$	−6.43244e35	−0.770356
$459$	−1.12861e35	−0.131242
$460$	8.15020e35	0.920317
$461$	−1.02767e36	−1.12691	−0.563456	−	0.826146i	$-0.690529\pi$
$461$	−1.02767e36	−1.12691	−0.563456	+	0.826146i	$0.690529\pi$
$462$	−2.46394e35	−0.262400
$463$	1.28910e36	1.33335	0.666673	−	0.745350i	$-0.267718\pi$
$463$	1.28910e36	1.33335	0.666673	+	0.745350i	$0.267718\pi$
$464$	−1.98520e34	−0.0199440
$465$	−9.42597e35	−0.919838
$466$	−8.85885e35	−0.839784
$467$	−1.89841e36	−1.74829	−0.874143	−	0.485668i	$-0.838576\pi$
$467$	−1.89841e36	−1.74829	−0.874143	+	0.485668i	$0.838576\pi$
$468$	1.10293e35	0.0986800
$469$	1.61288e36	1.40206
$470$	2.62019e36	2.21316
$471$	1.15379e36	0.946985
$472$	3.74876e34	0.0299000
$473$	−4.16750e35	−0.323035
$474$	4.52943e35	0.341221
$475$	−3.76680e36	−2.75809
$476$	5.81649e35	0.413969
$477$	5.72696e35	0.396210
$478$	3.16058e35	0.212564
$479$	−1.33288e36	−0.871491	−0.435746	−	0.900070i	$-0.643515\pi$
$479$	−1.33288e36	−0.871491	−0.435746	+	0.900070i	$0.643515\pi$
$480$	2.57001e35	0.163372
$481$	1.56748e36	0.968821
$482$	−1.99300e36	−1.19776
$483$	−1.37918e36	−0.806002
$484$	−6.33207e35	−0.359860
$485$	1.49976e36	0.828913
$486$	8.43862e34	0.0453609
$487$	−3.24682e36	−1.69753	−0.848764	−	0.528772i	$-0.822653\pi$
$487$	−3.24682e36	−1.69753	−0.848764	+	0.528772i	$0.822653\pi$
$488$	−1.13747e36	−0.578460
$489$	−6.39992e35	−0.316596
$490$	−1.11478e36	−0.536467
$491$	5.80339e35	0.271695	0.135847	−	0.990730i	$-0.456624\pi$
$491$	5.80339e35	0.271695	0.135847	+	0.990730i	$0.456624\pi$
$492$	1.07798e36	0.491001
$493$	−1.22761e35	−0.0544035
$494$	1.71406e36	0.739117
$495$	−6.73223e35	−0.282481
$496$	6.09397e35	0.248827
$497$	2.84006e36	1.12854
$498$	−6.84476e35	−0.264705
$499$	−2.77354e36	−1.04394	−0.521972	−	0.852963i	$-0.674803\pi$
$499$	−2.77354e36	−1.04394	−0.521972	+	0.852963i	$0.674803\pi$
$500$	1.22840e36	0.450032
$501$	1.64243e36	0.585702
$502$	−1.10679e35	−0.0384207
$503$	1.25022e36	0.422491	0.211245	−	0.977433i	$-0.432248\pi$
$503$	1.25022e36	0.422491	0.211245	+	0.977433i	$0.432248\pi$
$504$	−4.34900e35	−0.143079
$505$	−2.37441e36	−0.760541
$506$	1.38028e36	0.430462
$507$	1.23477e36	0.374955
$508$	1.22195e36	0.361322
$509$	6.18070e36	1.77970	0.889852	−	0.456250i	$-0.150808\pi$
$509$	6.18070e36	1.77970	0.889852	+	0.456250i	$0.150808\pi$
$510$	1.58924e36	0.445649
$511$	−2.17763e36	−0.594705
$512$	−1.66153e35	−0.0441942
$513$	1.31145e36	0.339755
$514$	2.05272e36	0.517998
$515$	2.21955e35	0.0545592
$516$	−7.35587e35	−0.176142
$517$	4.43743e36	1.03516
$518$	−6.18077e36	−1.40472
$519$	4.27741e36	0.947156
$520$	−1.55308e36	−0.335081
$521$	−4.44502e36	−0.934468	−0.467234	−	0.884134i	$-0.654749\pi$
$521$	−4.44502e36	−0.934468	−0.467234	+	0.884134i	$0.654749\pi$
$522$	9.17885e34	0.0188034
$523$	7.64607e36	1.52639	0.763195	−	0.646169i	$-0.223630\pi$
$523$	7.64607e36	1.52639	0.763195	+	0.646169i	$0.223630\pi$
$524$	−3.29784e36	−0.641589
$525$	−5.77557e36	−1.09508
$526$	3.40588e36	0.629393
$527$	3.76839e36	0.678754
$528$	4.35245e35	0.0764144
$529$	1.88286e36	0.322230
$530$	−8.06437e36	−1.34538
$531$	−1.73329e35	−0.0281899
$532$	−6.75877e36	−1.07167
$533$	−6.51435e36	−1.00706
$534$	2.68012e36	0.403968
$535$	−5.73890e36	−0.843437
$536$	−2.84908e36	−0.408300
$537$	−3.53753e36	−0.494364
$538$	1.48746e36	0.202715
$539$	−1.88794e36	−0.250923
$540$	−1.18828e36	−0.154029
$541$	−1.30472e37	−1.64950	−0.824751	−	0.565495i	$-0.808685\pi$
$541$	−1.30472e37	−1.64950	−0.824751	+	0.565495i	$0.808685\pi$
$542$	3.61198e36	0.445405
$543$	−7.36227e36	−0.885552
$544$	−1.02746e36	−0.120553
$545$	1.40051e37	1.60300
$546$	2.62814e36	0.293459
$547$	1.03586e37	1.12843	0.564213	−	0.825629i	$-0.309180\pi$
$547$	1.03586e37	1.12843	0.564213	+	0.825629i	$0.309180\pi$
$548$	3.60921e36	0.383597
$549$	5.25925e36	0.545378
$550$	5.78014e36	0.584847
$551$	1.42648e36	0.140838
$552$	2.43627e36	0.234719
$553$	1.07931e37	1.01474
$554$	−3.66723e36	−0.336478
$555$	−1.68877e37	−1.51222
$556$	3.09098e36	0.270138
$557$	−1.07139e37	−0.913904	−0.456952	−	0.889491i	$-0.651059\pi$
$557$	−1.07139e37	−0.913904	−0.456952	+	0.889491i	$0.651059\pi$
$558$	−2.81763e36	−0.234597
$559$	4.44522e36	0.361272
$560$	6.12401e36	0.485844
$561$	2.69146e36	0.208444
$562$	6.69082e36	0.505870
$563$	−1.24198e37	−0.916749	−0.458374	−	0.888759i	$-0.651568\pi$
$563$	−1.24198e37	−0.916749	−0.458374	+	0.888759i	$0.651568\pi$
$564$	7.83232e36	0.564446
$565$	7.17521e36	0.504871
$566$	2.61981e36	0.179990
$567$	2.01081e36	0.134896
$568$	−5.01685e36	−0.328646
$569$	−6.72192e36	−0.430009	−0.215005	−	0.976613i	$-0.568977\pi$
$569$	−6.72192e36	−0.430009	−0.215005	+	0.976613i	$0.568977\pi$
$570$	−1.84670e37	−1.15368
$571$	6.75688e36	0.412248	0.206124	−	0.978526i	$-0.433915\pi$
$571$	6.75688e36	0.412248	0.206124	+	0.978526i	$0.433915\pi$
$572$	−2.63022e36	−0.156728
$573$	7.56754e36	0.440420
$574$	2.56869e37	1.46016
$575$	3.23542e37	1.79645
$576$	7.68232e35	0.0416667
$577$	−1.83494e37	−0.972184	−0.486092	−	0.873908i	$-0.661578\pi$
$577$	−1.83494e37	−0.972184	−0.486092	+	0.873908i	$0.661578\pi$
$578$	7.30830e36	0.378260
$579$	−4.02996e36	−0.203770
$580$	−1.29251e36	−0.0638494
$581$	−1.63102e37	−0.787193
$582$	4.48311e36	0.211407
$583$	−1.36574e37	−0.629279
$584$	3.84669e36	0.173186
$585$	7.18088e36	0.315917
$586$	−2.12090e37	−0.911805
$587$	1.38416e37	0.581528	0.290764	−	0.956795i	$-0.406090\pi$
$587$	1.38416e37	0.581528	0.290764	+	0.956795i	$0.406090\pi$
$588$	−3.33232e36	−0.136821
$589$	−4.37887e37	−1.75714
$590$	2.44071e36	0.0957226
$591$	3.68943e36	0.141426
$592$	1.09181e37	0.409075
$593$	−5.74168e36	−0.210281	−0.105141	−	0.994457i	$-0.533529\pi$
$593$	−5.74168e36	−0.210281	−0.105141	+	0.994457i	$0.533529\pi$
$594$	−2.01241e36	−0.0720442
$595$	3.78696e37	1.32529
$596$	4.29452e36	0.146923
$597$	4.83845e36	0.161828
$598$	−1.47226e37	−0.481414
$599$	9.06518e36	0.289811	0.144905	−	0.989446i	$-0.453712\pi$
$599$	9.06518e36	0.289811	0.144905	+	0.989446i	$0.453712\pi$
$600$	1.02023e37	0.318901
$601$	3.75922e36	0.114893	0.0574464	−	0.998349i	$-0.481704\pi$
$601$	3.75922e36	0.114893	0.0574464	+	0.998349i	$0.481704\pi$
$602$	−1.75281e37	−0.523820
$603$	1.31731e37	0.384949
$604$	−3.07300e37	−0.878139
$605$	−4.12264e37	−1.15207
$606$	−7.09763e36	−0.193969
$607$	−4.26047e37	−1.13870	−0.569351	−	0.822094i	$-0.692806\pi$
$607$	−4.26047e37	−1.13870	−0.569351	+	0.822094i	$0.692806\pi$
$608$	1.19391e37	0.312085
$609$	2.18720e36	0.0559184
$610$	−7.40577e37	−1.85190
$611$	−4.73315e37	−1.15769
$612$	4.75059e36	0.113659
$613$	5.38870e37	1.26115	0.630576	−	0.776127i	$-0.282819\pi$
$613$	5.38870e37	1.26115	0.630576	+	0.776127i	$0.282819\pi$
$614$	−1.34756e37	−0.308513
$615$	7.01844e37	1.57191
$616$	1.03713e37	0.227245
$617$	−3.49858e37	−0.749967	−0.374983	−	0.927031i	$-0.622352\pi$
$617$	−3.49858e37	−0.749967	−0.374983	+	0.927031i	$0.622352\pi$
$618$	6.63472e35	0.0139148
$619$	3.09916e37	0.635946	0.317973	−	0.948100i	$-0.396998\pi$
$619$	3.09916e37	0.635946	0.317973	+	0.948100i	$0.396998\pi$
$620$	3.96762e37	0.796603
$621$	−1.12644e37	−0.221295
$622$	5.31978e37	1.02264
$623$	6.38638e37	1.20134
$624$	−4.64250e36	−0.0854594
$625$	−6.74694e36	−0.121542
$626$	7.12087e37	1.25539
$627$	−3.12748e37	−0.539614
$628$	−4.85656e37	−0.820113
$629$	6.75151e37	1.11588
$630$	−2.83151e37	−0.458059
$631$	−7.75162e36	−0.122743	−0.0613714	−	0.998115i	$-0.519547\pi$
$631$	−7.75162e36	−0.122743	−0.0613714	+	0.998115i	$0.519547\pi$
$632$	−1.90655e37	−0.295506
$633$	3.12284e37	0.473806
$634$	−1.58196e37	−0.234959
$635$	7.95580e37	1.15675
$636$	−2.41061e37	−0.343128
$637$	2.01375e37	0.280624
$638$	−2.18893e36	−0.0298644
$639$	2.31961e37	0.309851
$640$	−1.08178e37	−0.141485
$641$	−7.99511e37	−1.02386	−0.511931	−	0.859027i	$-0.671070\pi$
$641$	−7.99511e37	−1.02386	−0.511931	+	0.859027i	$0.671070\pi$
$642$	−1.71548e37	−0.215111
$643$	2.47951e37	0.304451	0.152226	−	0.988346i	$-0.451356\pi$
$643$	2.47951e37	0.304451	0.152226	+	0.988346i	$0.451356\pi$
$644$	5.80532e37	0.698018
$645$	−4.78920e37	−0.563907
$646$	7.38288e37	0.851308
$647$	−3.52397e37	−0.397946	−0.198973	−	0.980005i	$-0.563761\pi$
$647$	−3.52397e37	−0.397946	−0.198973	+	0.980005i	$0.563761\pi$
$648$	−3.55202e36	−0.0392837
$649$	4.13347e36	0.0447725
$650$	−6.16534e37	−0.654074
$651$	−6.71404e37	−0.697655
$652$	2.69388e37	0.274180
$653$	1.58081e37	0.157599	0.0787993	−	0.996891i	$-0.474891\pi$
$653$	1.58081e37	0.157599	0.0787993	+	0.996891i	$0.474891\pi$
$654$	4.18643e37	0.408832
$655$	−2.14713e38	−2.05400
$656$	−4.53748e37	−0.425220
$657$	−1.77856e37	−0.163282
$658$	1.86634e38	1.67858
$659$	2.71928e37	0.239608	0.119804	−	0.992798i	$-0.461773\pi$
$659$	2.71928e37	0.239608	0.119804	+	0.992798i	$0.461773\pi$
$660$	2.83376e37	0.244635
$661$	8.48665e36	0.0717821	0.0358911	−	0.999356i	$-0.488573\pi$
$661$	8.48665e36	0.0717821	0.0358911	+	0.999356i	$0.488573\pi$
$662$	7.07907e37	0.586670
$663$	−2.87083e37	−0.233117
$664$	2.88112e37	0.229241
$665$	−4.40045e38	−3.43087
$666$	−5.04811e37	−0.385680
$667$	−1.22525e37	−0.0917331
$668$	−6.91337e37	−0.507233
$669$	4.38230e37	0.315101
$670$	−1.85496e38	−1.30715
$671$	−1.25421e38	−0.866193
$672$	1.83060e37	0.123910
$673$	2.46452e38	1.63504	0.817522	−	0.575898i	$-0.195347\pi$
$673$	2.46452e38	1.63504	0.817522	+	0.575898i	$0.195347\pi$
$674$	1.66989e37	0.108587
$675$	−4.71716e37	−0.300663
$676$	−5.19745e37	−0.324721
$677$	2.19397e38	1.34364	0.671822	−	0.740713i	$-0.265512\pi$
$677$	2.19397e38	1.34364	0.671822	+	0.740713i	$0.265512\pi$
$678$	2.14482e37	0.128763
$679$	1.06827e38	0.628692
$680$	−6.68950e37	−0.385943
$681$	1.75510e36	0.00992698
$682$	6.71936e37	0.372597
$683$	1.45078e38	0.788717	0.394358	−	0.918957i	$-0.370967\pi$
$683$	1.45078e38	0.788717	0.394358	+	0.918957i	$0.370967\pi$
$684$	−5.52019e37	−0.294236
$685$	2.34986e38	1.22806
$686$	8.81294e37	0.451591
$687$	−1.25188e38	−0.628993
$688$	3.09626e37	0.152544
$689$	1.45676e38	0.703765
$690$	1.58619e38	0.751436
$691$	4.04073e38	1.87718	0.938591	−	0.345031i	$-0.112131\pi$
$691$	4.04073e38	1.87718	0.938591	+	0.345031i	$0.112131\pi$
$692$	−1.80046e38	−0.820261
$693$	−4.79531e37	−0.214249
$694$	−6.65376e37	−0.291551
$695$	2.01245e38	0.864829
$696$	−3.86360e36	−0.0162842
$697$	−2.80589e38	−1.15992
$698$	−4.04896e37	−0.164171
$699$	−1.72411e38	−0.685681
$700$	2.43107e38	0.948363
$701$	6.40419e37	0.245059	0.122529	−	0.992465i	$-0.460899\pi$
$701$	6.40419e37	0.245059	0.122529	+	0.992465i	$0.460899\pi$
$702$	2.14652e37	0.0805719
$703$	−7.84526e38	−2.88875
$704$	−1.83205e37	−0.0661768
$705$	5.09941e38	1.80704
$706$	−1.61799e38	−0.562488
$707$	−1.69127e38	−0.576835
$708$	7.29582e36	0.0244132
$709$	7.71389e37	0.253250	0.126625	−	0.991951i	$-0.459586\pi$
$709$	7.71389e37	0.253250	0.126625	+	0.991951i	$0.459586\pi$
$710$	−3.26633e38	−1.05214
$711$	8.81516e37	0.278606
$712$	−1.12813e38	−0.349847
$713$	3.76114e38	1.14449
$714$	1.13200e38	0.338004
$715$	−1.71247e38	−0.501754
$716$	1.48903e38	0.428132
$717$	6.15111e37	0.173558
$718$	−1.47984e38	−0.409765
$719$	6.01226e38	1.63380	0.816898	−	0.576783i	$-0.195692\pi$
$719$	6.01226e38	1.63380	0.816898	+	0.576783i	$0.195692\pi$
$720$	5.00174e37	0.133393
$721$	1.58097e37	0.0413806
$722$	−5.82635e38	−1.49673
$723$	−3.87876e38	−0.977971
$724$	3.09896e38	0.766911
$725$	−5.13094e37	−0.124633
$726$	−1.23235e38	−0.293825
$727$	−5.96046e38	−1.39497	−0.697486	−	0.716599i	$-0.745698\pi$
$727$	−5.96046e38	−1.39497	−0.697486	+	0.716599i	$0.745698\pi$
$728$	−1.10625e38	−0.254143
$729$	1.64232e37	0.0370370
$730$	2.50447e38	0.554444
$731$	1.91466e38	0.416110
$732$	−2.21374e38	−0.472311
$733$	−3.15157e38	−0.660120	−0.330060	−	0.943960i	$-0.607069\pi$
$733$	−3.15157e38	−0.660120	−0.330060	+	0.943960i	$0.607069\pi$
$734$	1.86471e38	0.383454
$735$	−2.16958e38	−0.438023
$736$	−1.02548e38	−0.203272
$737$	−3.14146e38	−0.611393
$738$	2.09796e38	0.400901
$739$	−3.24282e38	−0.608447	−0.304223	−	0.952601i	$-0.598397\pi$
$739$	−3.24282e38	−0.608447	−0.304223	+	0.952601i	$0.598397\pi$
$740$	7.10845e38	1.30963
$741$	3.33590e38	0.603486
$742$	−5.74418e38	−1.02041
$743$	5.80289e38	1.01227	0.506134	−	0.862455i	$-0.331074\pi$
$743$	5.80289e38	1.01227	0.506134	+	0.862455i	$0.331074\pi$
$744$	1.18601e38	0.203167
$745$	2.79604e38	0.470364
$746$	5.49677e38	0.908099
$747$	−1.33212e38	−0.216131
$748$	−1.13290e38	−0.180518
$749$	−4.08777e38	−0.639708
$750$	2.39070e38	0.367450
$751$	2.21124e38	0.333808	0.166904	−	0.985973i	$-0.446623\pi$
$751$	2.21124e38	0.333808	0.166904	+	0.985973i	$0.446623\pi$
$752$	−3.29681e38	−0.488825
$753$	−2.15403e37	−0.0313703
$754$	2.33481e37	0.0333993
$755$	−2.00074e39	−2.81130
$756$	−8.46400e37	−0.116824
$757$	−2.01995e38	−0.273870	−0.136935	−	0.990580i	$-0.543725\pi$
$757$	−2.01995e38	−0.273870	−0.136935	+	0.990580i	$0.543725\pi$
$758$	2.87179e38	0.382489
$759$	2.68629e38	0.351470
$760$	7.77321e38	0.999118
$761$	6.78605e38	0.856888	0.428444	−	0.903568i	$-0.359062\pi$
$761$	6.78605e38	0.856888	0.428444	+	0.903568i	$0.359062\pi$
$762$	2.37816e38	0.295018
$763$	9.97573e38	1.21580
$764$	−3.18536e38	−0.381415
$765$	3.09298e38	0.363871
$766$	−3.03400e37	−0.0350693
$767$	−4.40893e37	−0.0500721
$768$	−3.23367e37	−0.0360844
$769$	9.79619e38	1.07412	0.537059	−	0.843545i	$-0.319535\pi$
$769$	9.79619e38	1.07412	0.537059	+	0.843545i	$0.319535\pi$
$770$	6.75247e38	0.727509
$771$	3.99500e38	0.422943
$772$	1.69631e38	0.176470
$773$	−1.58678e39	−1.62216	−0.811081	−	0.584934i	$-0.801120\pi$
$773$	−1.58678e39	−1.62216	−0.811081	+	0.584934i	$0.801120\pi$
$774$	−1.43160e38	−0.143819
$775$	1.57504e39	1.55496
$776$	−1.88705e38	−0.183084
$777$	−1.20290e39	−1.14695
$778$	5.75165e38	0.538974
$779$	3.26044e39	3.00276
$780$	−3.02260e38	−0.273592
$781$	−5.53170e38	−0.492119
$782$	−6.34138e38	−0.554489
$783$	1.78638e37	0.0153529
$784$	1.40265e38	0.118491
$785$	−3.16197e39	−2.62553
$786$	−6.41824e38	−0.523855
$787$	−1.82547e39	−1.46459	−0.732296	−	0.680987i	$-0.761551\pi$
$787$	−1.82547e39	−1.46459	−0.732296	+	0.680987i	$0.761551\pi$
$788$	−1.55297e38	−0.122478
$789$	6.62851e38	0.513897
$790$	−1.24130e39	−0.946043
$791$	5.11084e38	0.382921
$792$	8.47071e37	0.0623921
$793$	1.33779e39	0.968722
$794$	1.07295e39	0.763843
$795$	−1.56948e39	−1.09850
$796$	−2.03662e38	−0.140147
$797$	−6.64299e38	−0.449445	−0.224723	−	0.974423i	$-0.572148\pi$
$797$	−6.64299e38	−0.449445	−0.224723	+	0.974423i	$0.572148\pi$
$798$	−1.31539e39	−0.875014
$799$	−2.03868e39	−1.33342
$800$	−4.29439e38	−0.276176
$801$	5.21603e38	0.329839
$802$	−1.08445e39	−0.674305
$803$	4.24145e38	0.259331
$804$	−5.54486e38	−0.333376
$805$	3.77968e39	2.23466
$806$	−7.16715e38	−0.416700
$807$	2.89489e38	0.165516
$808$	2.98756e38	0.167982
$809$	−1.75085e39	−0.968150	−0.484075	−	0.875026i	$-0.660844\pi$
$809$	−1.75085e39	−0.968150	−0.484075	+	0.875026i	$0.660844\pi$
$810$	−2.31262e38	−0.125764
$811$	1.01209e39	0.541301	0.270651	−	0.962678i	$-0.412761\pi$
$811$	1.01209e39	0.541301	0.270651	+	0.962678i	$0.412761\pi$
$812$	−9.20645e37	−0.0484268
$813$	7.02961e38	0.363671
$814$	1.20385e39	0.612553
$815$	1.75391e39	0.877768
$816$	−1.99964e38	−0.0984314
$817$	−2.22484e39	−1.07721
$818$	2.08516e39	0.993047
$819$	5.11488e38	0.239609
$820$	−2.95423e39	−1.36131
$821$	−8.40933e38	−0.381179	−0.190589	−	0.981670i	$-0.561040\pi$
$821$	−8.40933e38	−0.381179	−0.190589	+	0.981670i	$0.561040\pi$
$822$	7.02423e38	0.313205
$823$	2.05478e39	0.901297	0.450649	−	0.892701i	$-0.351193\pi$
$823$	2.05478e39	0.901297	0.450649	+	0.892701i	$0.351193\pi$
$824$	−2.79271e37	−0.0120506
$825$	1.12493e39	0.477526
$826$	1.73850e38	0.0726012
$827$	−9.27685e38	−0.381133	−0.190566	−	0.981674i	$-0.561032\pi$
$827$	−9.27685e38	−0.381133	−0.190566	+	0.981674i	$0.561032\pi$
$828$	4.74146e38	0.191647
$829$	3.98790e39	1.58584	0.792918	−	0.609329i	$-0.208561\pi$
$829$	3.98790e39	1.58584	0.792918	+	0.609329i	$0.208561\pi$
$830$	1.87582e39	0.733900
$831$	−7.13715e38	−0.274733
$832$	1.95414e38	0.0740100
$833$	8.67372e38	0.323220
$834$	6.01565e38	0.220567
$835$	−4.50110e39	−1.62387
$836$	1.31643e39	0.467319
$837$	−5.48365e38	−0.191547
$838$	2.16984e39	0.745818
$839$	4.87871e39	1.65013	0.825066	−	0.565036i	$-0.191138\pi$
$839$	4.87871e39	1.65013	0.825066	+	0.565036i	$0.191138\pi$
$840$	1.19185e39	0.396690
$841$	−3.03370e39	−0.993636
$842$	−7.10935e38	−0.229148
$843$	1.30216e39	0.413042
$844$	−1.31448e39	−0.410328
$845$	−3.38391e39	−1.03957
$846$	1.52432e39	0.460868
$847$	−2.93652e39	−0.873789
$848$	1.01468e39	0.297158
$849$	5.09866e38	0.146961
$850$	−2.65556e39	−0.753357
$851$	6.73853e39	1.88155
$852$	−9.76377e38	−0.268339
$853$	4.52266e38	0.122344	0.0611720	−	0.998127i	$-0.480516\pi$
$853$	4.52266e38	0.122344	0.0611720	+	0.998127i	$0.480516\pi$
$854$	−5.27507e39	−1.40458
$855$	−3.59404e39	−0.941977
$856$	7.22087e38	0.186292
$857$	−7.11106e39	−1.80590	−0.902949	−	0.429748i	$-0.858602\pi$
$857$	−7.11106e39	−1.80590	−0.902949	+	0.429748i	$0.858602\pi$
$858$	−5.11893e38	−0.127968
$859$	3.37936e39	0.831624	0.415812	−	0.909451i	$-0.363497\pi$
$859$	3.37936e39	0.831624	0.415812	+	0.909451i	$0.363497\pi$
$860$	2.01589e39	0.488358
$861$	4.99918e39	1.19222
$862$	7.02456e38	0.164919
$863$	−4.33269e39	−1.00141	−0.500705	−	0.865618i	$-0.666926\pi$
$863$	−4.33269e39	−1.00141	−0.500705	+	0.865618i	$0.666926\pi$
$864$	1.49513e38	0.0340207
$865$	−1.17223e40	−2.62601
$866$	1.00630e39	0.221940
$867$	1.42234e39	0.308848
$868$	2.82610e39	0.604187
$869$	−2.10220e39	−0.442494
$870$	−2.51548e38	−0.0521328
$871$	3.35081e39	0.683763
$872$	−1.76217e39	−0.354059
$873$	8.72501e38	0.172613
$874$	7.36869e39	1.43544
$875$	5.69673e39	1.09274
$876$	7.48640e38	0.141406
$877$	−5.02589e39	−0.934800	−0.467400	−	0.884046i	$-0.654809\pi$
$877$	−5.02589e39	−0.934800	−0.467400	+	0.884046i	$0.654809\pi$
$878$	2.42272e38	0.0443739
$879$	−4.12768e39	−0.744486
$880$	−1.19280e39	−0.211861
$881$	−8.13080e39	−1.42219	−0.711097	−	0.703094i	$-0.751801\pi$
$881$	−8.13080e39	−1.42219	−0.711097	+	0.703094i	$0.751801\pi$
$882$	−6.48535e38	−0.111714
$883$	−8.35207e39	−1.41685	−0.708427	−	0.705784i	$-0.750595\pi$
$883$	−8.35207e39	−1.41685	−0.708427	+	0.705784i	$0.750595\pi$
$884$	1.20840e39	0.201885
$885$	4.75010e38	0.0781572
$886$	−1.76876e39	−0.286624
$887$	3.26135e39	0.520510	0.260255	−	0.965540i	$-0.416193\pi$
$887$	3.26135e39	0.520510	0.260255	+	0.965540i	$0.416193\pi$
$888$	2.12487e39	0.334008
$889$	5.66685e39	0.877339
$890$	−7.34492e39	−1.12001
$891$	−3.91654e38	−0.0588239
$892$	−1.84462e39	−0.272886
$893$	2.36895e40	3.45192
$894$	8.35798e38	0.119962
$895$	9.69467e39	1.37064
$896$	−7.70542e38	−0.107310
$897$	−2.86531e39	−0.393073
$898$	−1.82519e39	−0.246648
$899$	−5.96467e38	−0.0794018
$900$	1.98556e39	0.260381
$901$	6.27460e39	0.810590
$902$	−5.00314e39	−0.636728
$903$	−3.41131e39	−0.427697
$904$	−9.02807e38	−0.111512
$905$	2.01764e40	2.45521
$906$	−5.98065e39	−0.716997
$907$	−1.85496e39	−0.219096	−0.109548	−	0.993981i	$-0.534940\pi$
$907$	−1.85496e39	−0.219096	−0.109548	+	0.993981i	$0.534940\pi$
$908$	−7.38765e37	−0.00859701
$909$	−1.38134e39	−0.158375
$910$	−7.20247e39	−0.813622
$911$	−1.23539e40	−1.37501	−0.687503	−	0.726182i	$-0.741293\pi$
$911$	−1.23539e40	−1.37501	−0.687503	+	0.726182i	$0.741293\pi$
$912$	2.32358e39	0.254816
$913$	3.17680e39	0.343268
$914$	4.13043e39	0.439766
$915$	−1.44131e40	−1.51207
$916$	5.26945e39	0.544724
$917$	−1.52938e40	−1.55787
$918$	9.24557e38	0.0928020
$919$	9.73771e39	0.963157	0.481579	−	0.876403i	$-0.340064\pi$
$919$	9.73771e39	0.963157	0.481579	+	0.876403i	$0.340064\pi$
$920$	−6.67664e39	−0.650763
$921$	−2.62261e39	−0.251900
$922$	8.41865e39	0.796847
$923$	5.90034e39	0.550369
$924$	2.01846e39	0.185545
$925$	2.82187e40	2.55637
$926$	−1.05603e40	−0.942819
$927$	1.29125e38	0.0113614
$928$	1.62628e38	0.0141025
$929$	−6.31554e38	−0.0539757	−0.0269879	−	0.999636i	$-0.508592\pi$
$929$	−6.31554e38	−0.0539757	−0.0269879	+	0.999636i	$0.508592\pi$
$930$	7.72176e39	0.650424
$931$	−1.00789e40	−0.836741
$932$	7.25717e39	0.593817
$933$	1.03533e40	0.834984
$934$	1.55518e40	1.23623
$935$	−7.37600e39	−0.577916
$936$	−9.03521e38	−0.0697773
$937$	9.85113e38	0.0749897	0.0374948	−	0.999297i	$-0.488062\pi$
$937$	9.85113e38	0.0749897	0.0374948	+	0.999297i	$0.488062\pi$
$938$	−1.32127e40	−0.991409
$939$	1.38586e40	1.02502
$940$	−2.14646e40	−1.56494
$941$	−1.59948e40	−1.14953	−0.574763	−	0.818320i	$-0.694906\pi$
$941$	−1.59948e40	−1.14953	−0.574763	+	0.818320i	$0.694906\pi$
$942$	−9.45182e39	−0.669619
$943$	−2.80049e40	−1.95581
$944$	−3.07098e38	−0.0211425
$945$	−5.51067e39	−0.374003
$946$	3.41401e39	0.228420
$947$	−7.63606e38	−0.0503669	−0.0251834	−	0.999683i	$-0.508017\pi$
$947$	−7.63606e38	−0.0503669	−0.0251834	+	0.999683i	$0.508017\pi$
$948$	−3.71051e39	−0.241280
$949$	−4.52411e39	−0.290027
$950$	3.08576e40	1.95027
$951$	−3.07881e39	−0.191843
$952$	−4.76487e39	−0.292720
$953$	−2.87976e40	−1.74422	−0.872112	−	0.489307i	$-0.837250\pi$
$953$	−2.87976e40	−1.74422	−0.872112	+	0.489307i	$0.837250\pi$
$954$	−4.69152e39	−0.280163
$955$	−2.07390e40	−1.22107
$956$	−2.58915e39	−0.150306
$957$	−4.26009e38	−0.0243842
$958$	1.09190e40	0.616237
$959$	1.67378e40	0.931425
$960$	−2.10535e39	−0.115522
$961$	−1.73001e38	−0.00936016
$962$	−1.28408e40	−0.685060
$963$	−3.33866e39	−0.175638
$964$	1.63266e40	0.846947
$965$	1.10442e40	0.564956
$966$	1.12983e40	0.569929
$967$	2.00353e39	0.0996639	0.0498319	−	0.998758i	$-0.484131\pi$
$967$	2.00353e39	0.0996639	0.0498319	+	0.998758i	$0.484131\pi$
$968$	5.18724e39	0.254459
$969$	1.43685e40	0.695090
$970$	−1.22860e40	−0.586130
$971$	1.39930e40	0.658343	0.329172	−	0.944270i	$-0.393231\pi$
$971$	1.39930e40	0.658343	0.329172	+	0.944270i	$0.393231\pi$
$972$	−6.91292e38	−0.0320750
$973$	1.43345e40	0.655933
$974$	2.65979e40	1.20033
$975$	−1.19990e40	−0.534049
$976$	9.31818e39	0.409033
$977$	−1.69499e39	−0.0733824	−0.0366912	−	0.999327i	$-0.511682\pi$
$977$	−1.69499e39	−0.0733824	−0.0366912	+	0.999327i	$0.511682\pi$
$978$	5.24282e39	0.223867
$979$	−1.24390e40	−0.523864
$980$	9.13229e39	0.379339
$981$	8.14762e39	0.333810
$982$	−4.75414e39	−0.192117
$983$	1.61199e40	0.642526	0.321263	−	0.946990i	$-0.395893\pi$
$983$	1.61199e40	0.642526	0.321263	+	0.946990i	$0.395893\pi$
$984$	−8.83083e39	−0.347190
$985$	−1.01110e40	−0.392106
$986$	1.00566e39	0.0384691
$987$	3.63226e40	1.37055
$988$	−1.40416e40	−0.522635
$989$	1.91098e40	0.701629
$990$	5.51504e39	0.199744
$991$	6.12985e39	0.219006	0.109503	−	0.993986i	$-0.465074\pi$
$991$	6.12985e39	0.219006	0.109503	+	0.993986i	$0.465074\pi$
$992$	−4.99218e39	−0.175947
$993$	1.37773e40	0.479014
$994$	−2.32658e40	−0.797998
$995$	−1.32599e40	−0.448671
$996$	5.60723e39	0.187175
$997$	1.07857e40	0.355191	0.177596	−	0.984104i	$-0.443168\pi$
$997$	1.07857e40	0.355191	0.177596	+	0.984104i	$0.443168\pi$
$998$	2.27208e40	0.738180
$999$	−9.82461e39	−0.314906

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.28.a.d.1.2	✓	2
3.2	odd	2		18.28.a.g.1.1		2
4.3	odd	2		48.28.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.28.a.d.1.2	✓	2	1.1	even	1	trivial
18.28.a.g.1.1		2	3.2	odd	2
48.28.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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	6.a (trivial)

\(f(q)\)	\(=\)	\(q-8192.00 q^{2} -1.59432e6 q^{3} +6.71089e7 q^{4} +4.36927e9 q^{5} +1.30607e10 q^{6} +3.11219e11 q^{7} -5.49756e11 q^{8} +2.54187e12 q^{9} +O(q^{10})\)	\(q-8192.00 q^{2} -1.59432e6 q^{3} +6.71089e7 q^{4} +4.36927e9 q^{5} +1.30607e10 q^{6} +3.11219e11 q^{7} -5.49756e11 q^{8} +2.54187e12 q^{9} -3.57931e13 q^{10} -6.06174e13 q^{11} -1.06993e14 q^{12} +6.46570e14 q^{13} -2.54951e15 q^{14} -6.96603e15 q^{15} +4.50360e15 q^{16} +2.78493e16 q^{17} -2.08230e16 q^{18} -3.23609e17 q^{19} +2.93217e17 q^{20} -4.96184e17 q^{21} +4.96578e17 q^{22} +2.77958e18 q^{23} +8.76488e17 q^{24} +1.16400e19 q^{25} -5.29670e18 q^{26} -4.05256e18 q^{27} +2.08856e19 q^{28} -4.40804e18 q^{29} +5.70657e19 q^{30} +1.35313e20 q^{31} -3.68935e19 q^{32} +9.66437e19 q^{33} -2.28142e20 q^{34} +1.35980e21 q^{35} +1.70582e20 q^{36} +2.42430e21 q^{37} +2.65101e21 q^{38} -1.03084e21 q^{39} -2.40203e21 q^{40} -1.00752e22 q^{41} +4.06474e21 q^{42} +6.87508e21 q^{43} -4.06796e21 q^{44} +1.11061e22 q^{45} -2.27703e22 q^{46} -7.32039e22 q^{47} -7.18019e21 q^{48} +3.11452e22 q^{49} -9.53546e22 q^{50} -4.44008e22 q^{51} +4.33906e22 q^{52} +2.25305e23 q^{53} +3.31985e22 q^{54} -2.64854e23 q^{55} -1.71095e23 q^{56} +5.15938e23 q^{57} +3.61107e22 q^{58} -6.81895e22 q^{59} -4.67482e23 q^{60} +2.06905e24 q^{61} -1.10849e24 q^{62} +7.91078e23 q^{63} +3.02231e23 q^{64} +2.82504e24 q^{65} -7.91705e23 q^{66} +5.18244e24 q^{67} +1.86894e24 q^{68} -4.43155e24 q^{69} -1.11395e25 q^{70} +9.12560e24 q^{71} -1.39741e24 q^{72} -6.99708e24 q^{73} -1.98599e25 q^{74} -1.85579e25 q^{75} -2.17171e25 q^{76} -1.88653e25 q^{77} +8.44466e24 q^{78} +3.46799e25 q^{79} +1.96775e25 q^{80} +6.46108e24 q^{81} +8.25364e25 q^{82} -5.24073e25 q^{83} -3.32984e25 q^{84} +1.21681e26 q^{85} -5.63207e25 q^{86} +7.02784e24 q^{87} +3.33248e25 q^{88} +2.05205e26 q^{89} -9.09812e25 q^{90} +2.01225e26 q^{91} +1.86534e26 q^{92} -2.15733e26 q^{93} +5.99686e26 q^{94} -1.41394e27 q^{95} +5.88201e25 q^{96} +3.43252e26 q^{97} -2.55141e26 q^{98} -1.54081e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16384 q^{2} - 3188646 q^{3} + 134217728 q^{4} + 291441036 q^{5} + 26121388032 q^{6} + 121646295328 q^{7} - 1099511627776 q^{8} + 5083731656658 q^{9}+O(q^{10}) \) 2 * q - 16384 * q^2 - 3188646 * q^3 + 134217728 * q^4 + 291441036 * q^5 + 26121388032 * q^6 + 121646295328 * q^7 - 1099511627776 * q^8 + 5083731656658 * q^9	\( 2 q - 16384 q^{2} - 3188646 q^{3} + 134217728 q^{4} + 291441036 q^{5} + 26121388032 q^{6} + 121646295328 q^{7} - 1099511627776 q^{8} + 5083731656658 q^{9} - 2387484966912 q^{10} - 231807361766376 q^{11} - 213986410758144 q^{12} - 11\!\cdots\!64 q^{13}+ \cdots - 58\!\cdots\!04 q^{99}+O(q^{100}) \) 2 * q - 16384 * q^2 - 3188646 * q^3 + 134217728 * q^4 + 291441036 * q^5 + 26121388032 * q^6 + 121646295328 * q^7 - 1099511627776 * q^8 + 5083731656658 * q^9 - 2387484966912 * q^10 - 231807361766376 * q^11 - 213986410758144 * q^12 - 1155759271611764 * q^13 - 996526451326976 * q^14 - 464651146838628 * q^15 + 9007199254740992 * q^16 - 46125175777027452 * q^17 - 41645929731342336 * q^18 - 268519854753239000 * q^19 + 19558276848943104 * q^20 - 193943486506222944 * q^21 + 1898965907590152192 * q^22 + 1299561926005929936 * q^23 + 1752976676930715648 * q^24 + 20818087556919436046 * q^25 + 9467979953043570688 * q^26 - 8105110306037952534 * q^27 + 8163544689270587392 * q^28 + 60178362995785587900 * q^29 + 3806422194902040576 * q^30 + 203575085639304966544 * q^31 - 73786976294838206464 * q^32 + 369575808433453883448 * q^33 + 377857439965408886784 * q^34 + 2132849735738606710464 * q^35 + 341163456359156416512 * q^36 + 3022337597514982851388 * q^37 + 2199714650138533888000 * q^38 + 1842653589193882415772 * q^39 - 160221403946541907968 * q^40 - 10870375798082518905516 * q^41 + 1588785041458978357248 * q^42 - 1299568293415606314344 * q^43 - 15556328714978526756864 * q^44 + 740804010381201908844 * q^45 - 10646011297840578035712 * q^46 - 99372996476917699213632 * q^47 - 14360384937416422588416 * q^48 + 1370785920275118717906 * q^49 - 170541773266284020088832 * q^50 + 73538428620357738354996 * q^51 - 77561691775332931076096 * q^52 - 35770850049954566775924 * q^53 + 66397063627062907158528 * q^54 + 433229958906724722129552 * q^55 - 66875758094504651915264 * q^56 + 428107380389748262197000 * q^57 - 492981149661475536076800 * q^58 + 299672958231389705557080 * q^59 - 31182210620637516398592 * q^60 + 2165599091776519863171724 * q^61 - 1667687101557186285928448 * q^62 + 309208561237060882746912 * q^63 + 604462909807314587353088 * q^64 + 10174637395564415468537928 * q^65 - 3027565022686854213206016 * q^66 + 13568283837486181949525608 * q^67 - 3095408148196629600534528 * q^68 - 2071921468555552233353328 * q^69 - 17472305035170666172121088 * q^70 - 4319907418871433623040336 * q^71 - 2794811034494209364066304 * q^72 - 20032895180752990538485964 * q^73 - 24758989598842739518570496 * q^74 - 33190755808010466035166858 * q^75 - 18020062413934869610496000 * q^76 + 13587711578810985760484736 * q^77 - 15095018202676284750004224 * q^78 + 5633936436869082596599600 * q^79 + 1312533741130071310073856 * q^80 + 12922163778453346597864482 * q^81 + 89050118537891994873987072 * q^82 - 46762236922353070723154904 * q^83 - 13015327059631950702575616 * q^84 + 423336865613342459682869784 * q^85 + 10646063459660646927106048 * q^86 - 95943748226529865857491700 * q^87 + 127437444833104091192229888 * q^88 - 191930414076503127699406380 * q^89 - 6068666453042806037250048 * q^90 + 542898500680491813749530304 * q^91 + 87212124551910015268552704 * q^92 - 324564441261713612175329712 * q^93 + 814063587138909791958073344 * q^94 - 1638584179808499075287277840 * q^95 + 117640273407315333844303872 * q^96 + 544725669490755670759486468 * q^97 - 11229478258893772537085952 * q^98 - 589223211629049495820465704 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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