LMFDB - Embedded newform 49.26.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,26,Mod(1,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, 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("49.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	49.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:	$194.038422177$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 212249190 x^{5} + 97966970896 x^{4} + \cdots + 48\!\cdots\!56 $ x^7 - x^6 - 212249190x^5 + 97966970896x^4 + 13490510525162432x^3 - 12908535655668027648x^2 - 247876261380147473323520*x + 486739593081059559316115456
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{10}\cdot 5^{4}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-8028.26$ of defining polynomial
Character	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6832.26 q^{2} -1.31327e6 q^{3} +1.31253e7 q^{4} +4.35962e8 q^{5} +8.97259e9 q^{6} +1.39577e11 q^{8} +8.77387e11 q^{9} +O(q^{10})$	\(q-6832.26 q^{2} -1.31327e6 q^{3} +1.31253e7 q^{4} +4.35962e8 q^{5} +8.97259e9 q^{6} +1.39577e11 q^{8} +8.77387e11 q^{9} -2.97861e12 q^{10} -3.69609e12 q^{11} -1.72371e13 q^{12} -2.73802e13 q^{13} -5.72536e14 q^{15} -1.39404e15 q^{16} +1.00004e15 q^{17} -5.99453e15 q^{18} +9.34899e13 q^{19} +5.72214e15 q^{20} +2.52526e16 q^{22} +1.63865e17 q^{23} -1.83302e17 q^{24} -1.07960e17 q^{25} +1.87069e17 q^{26} -3.95270e16 q^{27} +2.33477e18 q^{29} +3.91171e18 q^{30} +1.72495e18 q^{31} +4.84100e18 q^{32} +4.85396e18 q^{33} -6.83256e18 q^{34} +1.15160e19 q^{36} +7.75006e19 q^{37} -6.38747e17 q^{38} +3.59576e19 q^{39} +6.08503e19 q^{40} -2.64987e20 q^{41} +4.16758e20 q^{43} -4.85124e19 q^{44} +3.82507e20 q^{45} -1.11956e21 q^{46} +1.02507e21 q^{47} +1.83075e21 q^{48} +7.37612e20 q^{50} -1.31333e21 q^{51} -3.59374e20 q^{52} +4.73494e21 q^{53} +2.70058e20 q^{54} -1.61136e21 q^{55} -1.22777e20 q^{57} -1.59518e22 q^{58} -1.19792e22 q^{59} -7.51471e21 q^{60} -1.58632e21 q^{61} -1.17853e22 q^{62} +1.37012e22 q^{64} -1.19367e22 q^{65} -3.31635e22 q^{66} -4.39528e22 q^{67} +1.31259e22 q^{68} -2.15198e23 q^{69} +8.51750e22 q^{71} +1.22463e23 q^{72} +2.00446e23 q^{73} -5.29504e23 q^{74} +1.41781e23 q^{75} +1.22708e21 q^{76} -2.45671e23 q^{78} +9.52870e22 q^{79} -6.07748e23 q^{80} -6.91490e23 q^{81} +1.81046e24 q^{82} -1.17292e24 q^{83} +4.35982e23 q^{85} -2.84740e24 q^{86} -3.06618e24 q^{87} -5.15889e23 q^{88} -4.82938e23 q^{89} -2.61339e24 q^{90} +2.15077e24 q^{92} -2.26532e24 q^{93} -7.00352e24 q^{94} +4.07580e22 q^{95} -6.35754e24 q^{96} -1.25190e24 q^{97} -3.24290e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 8373 q^{2} + 599172 q^{3} + 199632661 q^{4} - 485320794 q^{5} - 548762130 q^{6} + 679913241639 q^{8} + 2499178495563 q^{9}+O(q^{10}) $ 7 * q + 8373 * q^2 + 599172 * q^3 + 199632661 * q^4 - 485320794 * q^5 - 548762130 * q^6 + 679913241639 * q^8 + 2499178495563 * q^9	$ 7 q + 8373 q^{2} + 599172 q^{3} + 199632661 q^{4} - 485320794 q^{5} - 548762130 q^{6} + 679913241639 q^{8} + 2499178495563 q^{9} + 876704815140 q^{10} - 7845139606524 q^{11} + 83731581305106 q^{12} + 75871445642734 q^{13} + 12\!\cdots\!84 q^{15}+ \cdots + 29\!\cdots\!00 q^{99}+O(q^{100}) $ 7 * q + 8373 * q^2 + 599172 * q^3 + 199632661 * q^4 - 485320794 * q^5 - 548762130 * q^6 + 679913241639 * q^8 + 2499178495563 * q^9 + 876704815140 * q^10 - 7845139606524 * q^11 + 83731581305106 * q^12 + 75871445642734 * q^13 + 1250450093573784 * q^15 + 2533333214129041 * q^16 - 4930179049331550 * q^17 + 6108218172751149 * q^18 + 8822108307937204 * q^19 + 35797888210439208 * q^20 + 122308015837411896 * q^22 + 260380318250119992 * q^23 - 280838923324398306 * q^24 + 442974124902943561 * q^25 - 525030062154247104 * q^26 + 508138451607400488 * q^27 + 3074121146906357394 * q^29 + 20693674849314206160 * q^30 - 17867964278742490304 * q^31 + 41524963168122393471 * q^32 - 18631713362079899088 * q^33 - 76530595013021124150 * q^34 + 120686738791924632357 * q^36 + 37537195275383667242 * q^37 - 133898980332930749790 * q^38 + 160680068588101330968 * q^39 - 260261018010811048560 * q^40 - 349555665716732087718 * q^41 - 188918130006461199484 * q^43 - 866635019544130150704 * q^44 + 2875914312455481795918 * q^45 - 1056444907691638473648 * q^46 + 577519309883773958064 * q^47 + 1705636002072738200514 * q^48 - 3108044078925178785 * q^50 - 8568497654252614793448 * q^51 + 21223967127059853562252 * q^52 + 724118360265623334330 * q^53 + 23525683999565788877508 * q^54 + 3874297214249814234792 * q^55 + 21002099147408968606176 * q^57 - 6571075616758407948534 * q^58 + 29388013065202679743548 * q^59 + 131210151872269358361312 * q^60 - 24863323230677092393442 * q^61 - 178098511159147000538004 * q^62 + 185730465159694629378817 * q^64 - 28642507689771657088260 * q^65 + 182488465275344339797728 * q^66 + 87288896332559907446444 * q^67 - 236561584649915083645422 * q^68 + 38736311524504328113344 * q^69 + 507749245951454445426264 * q^71 - 136846012456831244000985 * q^72 + 384451815193432683470074 * q^73 - 180156332882615168418510 * q^74 + 917728597534517928543804 * q^75 + 1802955096706900507996366 * q^76 - 2701299412149008608565208 * q^78 - 512089643024553543168400 * q^79 - 1072829383400652355143456 * q^80 - 1711055088184234765637889 * q^81 + 328793973025384284153498 * q^82 - 683613625271699866065420 * q^83 - 4106127272649214828366668 * q^85 + 6352668961585470034751760 * q^86 - 6810779334667612471104168 * q^87 - 1678346430445345786597824 * q^88 - 7785138614078665124468694 * q^89 + 6907385334351120772566420 * q^90 + 4229143913695999872649632 * q^92 + 9311007684860974346150688 * q^93 - 16094575705640558287782684 * q^94 + 8670853765297953493275288 * q^95 - 20458763379770390869400514 * q^96 - 16735236191051483252826350 * q^97 + 29494988134999515624453300 * 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 $

$2$	−6832.26	−1.17948	−0.589738	−	0.807594i	$-0.700769\pi$
$2$	−6832.26	−1.17948	−0.589738	+	0.807594i	$0.700769\pi$
$3$	−1.31327e6	−1.42672	−0.713359	−	0.700799i	$-0.752827\pi$
$3$	−1.31327e6	−1.42672	−0.713359	+	0.700799i	$0.752827\pi$
$4$	1.31253e7	0.391165
$5$	4.35962e8	0.798590	0.399295	−	0.916823i	$-0.369255\pi$
$5$	4.35962e8	0.798590	0.399295	+	0.916823i	$0.369255\pi$
$6$	8.97259e9	1.68278
$7$	0	0
$7$	0	0
$8$	1.39577e11	0.718107
$9$	8.77387e11	1.03552
$10$	−2.97861e12	−0.941918
$11$	−3.69609e12	−0.355086	−0.177543	−	0.984113i	$-0.556815\pi$
$11$	−3.69609e12	−0.355086	−0.177543	+	0.984113i	$0.556815\pi$
$12$	−1.72371e13	−0.558082
$13$	−2.73802e13	−0.325945	−0.162973	−	0.986631i	$-0.552108\pi$
$13$	−2.73802e13	−0.325945	−0.162973	+	0.986631i	$0.552108\pi$
$14$	0	0
$15$	−5.72536e14	−1.13936
$16$	−1.39404e15	−1.23815
$17$	1.00004e15	0.416301	0.208151	−	0.978097i	$-0.433256\pi$
$17$	1.00004e15	0.416301	0.208151	+	0.978097i	$0.433256\pi$
$18$	−5.99453e15	−1.22137
$19$	9.34899e13	0.00969046	0.00484523	−	0.999988i	$-0.498458\pi$
$19$	9.34899e13	0.00969046	0.00484523	+	0.999988i	$0.498458\pi$
$20$	5.72214e15	0.312380
$21$	0	0
$22$	2.52526e16	0.418816
$23$	1.63865e17	1.55915	0.779573	−	0.626311i	$-0.215436\pi$
$23$	1.63865e17	1.55915	0.779573	+	0.626311i	$0.215436\pi$
$24$	−1.83302e17	−1.02454
$25$	−1.07960e17	−0.362254
$26$	1.87069e17	0.384445
$27$	−3.95270e16	−0.0506812
$28$	0	0
$29$	2.33477e18	1.22538	0.612688	−	0.790325i	$-0.290088\pi$
$29$	2.33477e18	1.22538	0.612688	+	0.790325i	$0.290088\pi$
$30$	3.91171e18	1.34385
$31$	1.72495e18	0.393328	0.196664	−	0.980471i	$-0.436989\pi$
$31$	1.72495e18	0.393328	0.196664	+	0.980471i	$0.436989\pi$
$32$	4.84100e18	0.742268
$33$	4.85396e18	0.506608
$34$	−6.83256e18	−0.491018
$35$	0	0
$36$	1.15160e19	0.405060
$37$	7.75006e19	1.93546	0.967729	−	0.251994i	$-0.0810863\pi$
$37$	7.75006e19	1.93546	0.967729	+	0.251994i	$0.0810863\pi$
$38$	−6.38747e17	−0.0114297
$39$	3.59576e19	0.465032
$40$	6.08503e19	0.573473
$41$	−2.64987e20	−1.83412	−0.917058	−	0.398755i	$-0.869443\pi$
$41$	−2.64987e20	−1.83412	−0.917058	+	0.398755i	$0.869443\pi$
$42$	0	0
$43$	4.16758e20	1.59048	0.795239	−	0.606295i	$-0.207345\pi$
$43$	4.16758e20	1.59048	0.795239	+	0.606295i	$0.207345\pi$
$44$	−4.85124e19	−0.138897
$45$	3.82507e20	0.826958
$46$	−1.11956e21	−1.83898
$47$	1.02507e21	1.28685	0.643427	−	0.765508i	$-0.277512\pi$
$47$	1.02507e21	1.28685	0.643427	+	0.765508i	$0.277512\pi$
$48$	1.83075e21	1.76650
$49$	0	0
$50$	7.37612e20	0.427271
$51$	−1.31333e21	−0.593944
$52$	−3.59374e20	−0.127498
$53$	4.73494e21	1.32393	0.661967	−	0.749533i	$-0.269722\pi$
$53$	4.73494e21	1.32393	0.661967	+	0.749533i	$0.269722\pi$
$54$	2.70058e20	0.0597772
$55$	−1.61136e21	−0.283568
$56$	0	0
$57$	−1.22777e20	−0.0138256
$58$	−1.59518e22	−1.44530
$59$	−1.19792e22	−0.876551	−0.438275	−	0.898841i	$-0.644411\pi$
$59$	−1.19792e22	−0.876551	−0.438275	+	0.898841i	$0.644411\pi$
$60$	−7.51471e21	−0.445678
$61$	−1.58632e21	−0.0765190	−0.0382595	−	0.999268i	$-0.512181\pi$
$61$	−1.58632e21	−0.0765190	−0.0382595	+	0.999268i	$0.512181\pi$
$62$	−1.17853e22	−0.463921
$63$	0	0
$64$	1.37012e22	0.362667
$65$	−1.19367e22	−0.260297
$66$	−3.31635e22	−0.597532
$67$	−4.39528e22	−0.656223	−0.328112	−	0.944639i	$-0.606412\pi$
$67$	−4.39528e22	−0.656223	−0.328112	+	0.944639i	$0.606412\pi$
$68$	1.31259e22	0.162842
$69$	−2.15198e23	−2.22446
$70$	0	0
$71$	8.51750e22	0.616003	0.308002	−	0.951386i	$-0.400340\pi$
$71$	8.51750e22	0.616003	0.308002	+	0.951386i	$0.400340\pi$
$72$	1.22463e23	0.743616
$73$	2.00446e23	1.02438	0.512191	−	0.858872i	$-0.328834\pi$
$73$	2.00446e23	1.02438	0.512191	+	0.858872i	$0.328834\pi$
$74$	−5.29504e23	−2.28283
$75$	1.41781e23	0.516835
$76$	1.22708e21	0.00379057
$77$	0	0
$78$	−2.45671e23	−0.548494
$79$	9.52870e22	0.181424	0.0907120	−	0.995877i	$-0.471086\pi$
$79$	9.52870e22	0.181424	0.0907120	+	0.995877i	$0.471086\pi$
$80$	−6.07748e23	−0.988778
$81$	−6.91490e23	−0.963215
$82$	1.81046e24	2.16330
$83$	−1.17292e24	−1.20446	−0.602229	−	0.798324i	$-0.705720\pi$
$83$	−1.17292e24	−1.20446	−0.602229	+	0.798324i	$0.705720\pi$
$84$	0	0
$85$	4.35982e23	0.332454
$86$	−2.84740e24	−1.87593
$87$	−3.06618e24	−1.74827
$88$	−5.15889e23	−0.254990
$89$	−4.82938e23	−0.207261	−0.103630	−	0.994616i	$-0.533046\pi$
$89$	−4.82938e23	−0.207261	−0.103630	+	0.994616i	$0.533046\pi$
$90$	−2.61339e24	−0.975378
$91$	0	0
$92$	2.15077e24	0.609883
$93$	−2.26532e24	−0.561167
$94$	−7.00352e24	−1.51781
$95$	4.07580e22	0.00773870
$96$	−6.35754e24	−1.05901
$97$	−1.25190e24	−0.183198	−0.0915991	−	0.995796i	$-0.529198\pi$
$97$	−1.25190e24	−0.183198	−0.0915991	+	0.995796i	$0.529198\pi$
$98$	0	0
$99$	−3.24290e24	−0.367700
$100$	−1.41701e24	−0.141701
$101$	1.68007e25	1.48358	0.741788	−	0.670634i	$-0.233978\pi$
$101$	1.68007e25	1.48358	0.741788	+	0.670634i	$0.233978\pi$
$102$	8.97299e24	0.700543
$103$	2.10384e25	1.45394	0.726971	−	0.686669i	$-0.240928\pi$
$103$	2.10384e25	1.45394	0.726971	+	0.686669i	$0.240928\pi$
$104$	−3.82165e24	−0.234064
$105$	0	0
$106$	−3.23504e25	−1.56155
$107$	−1.29699e24	−0.0556723	−0.0278361	−	0.999612i	$-0.508862\pi$
$107$	−1.29699e24	−0.0556723	−0.0278361	+	0.999612i	$0.508862\pi$
$108$	−5.18804e23	−0.0198247
$109$	3.94597e25	1.34376	0.671882	−	0.740658i	$-0.265486\pi$
$109$	3.94597e25	1.34376	0.671882	+	0.740658i	$0.265486\pi$
$110$	1.10092e25	0.334462
$111$	−1.01779e26	−2.76135
$112$	0	0
$113$	−3.74857e25	−0.813551	−0.406775	−	0.913528i	$-0.633347\pi$
$113$	−3.74857e25	−0.813551	−0.406775	+	0.913528i	$0.633347\pi$
$114$	8.38846e23	0.0163069
$115$	7.14387e25	1.24512
$116$	3.06446e25	0.479324
$117$	−2.40230e25	−0.337524
$118$	8.18449e25	1.03387
$119$	0	0
$120$	−7.99128e25	−0.818183
$121$	−9.46860e25	−0.873914
$122$	1.08382e25	0.0902523
$123$	3.47999e26	2.61676
$124$	2.26405e25	0.153856
$125$	−1.76993e26	−1.08788
$126$	0	0
$127$	−6.66455e25	−0.335911	−0.167955	−	0.985795i	$-0.553716\pi$
$127$	−6.66455e25	−0.335911	−0.167955	+	0.985795i	$0.553716\pi$
$128$	−2.56047e26	−1.17003
$129$	−5.47315e26	−2.26916
$130$	8.15548e25	0.307014
$131$	−4.22940e26	−1.44673	−0.723366	−	0.690465i	$-0.757406\pi$
$131$	−4.22940e26	−1.44673	−0.723366	+	0.690465i	$0.757406\pi$
$132$	6.37098e25	0.198167
$133$	0	0
$134$	3.00297e26	0.774000
$135$	−1.72323e25	−0.0404735
$136$	1.39583e26	0.298949
$137$	−1.98436e26	−0.387805	−0.193903	−	0.981021i	$-0.562115\pi$
$137$	−1.98436e26	−0.387805	−0.193903	+	0.981021i	$0.562115\pi$
$138$	1.47029e27	2.62370
$139$	−7.78481e26	−1.26930	−0.634648	−	0.772801i	$-0.718855\pi$
$139$	−7.78481e26	−1.26930	−0.634648	+	0.772801i	$0.718855\pi$
$140$	0	0
$141$	−1.34619e27	−1.83598
$142$	−5.81938e26	−0.726561
$143$	1.01200e26	0.115739
$144$	−1.22311e27	−1.28214
$145$	1.01787e27	0.978572
$146$	−1.36950e27	−1.20823
$147$	0	0
$148$	1.01722e27	0.757083
$149$	2.10273e27	1.43865	0.719326	−	0.694673i	$-0.244451\pi$
$149$	2.10273e27	1.43865	0.719326	+	0.694673i	$0.244451\pi$
$150$	−9.68683e26	−0.609594
$151$	−1.56862e27	−0.908458	−0.454229	−	0.890885i	$-0.650085\pi$
$151$	−1.56862e27	−0.908458	−0.454229	+	0.890885i	$0.650085\pi$
$152$	1.30490e25	0.00695879
$153$	8.77426e26	0.431090
$154$	0	0
$155$	7.52011e26	0.314107
$156$	4.71954e26	0.181904
$157$	1.70727e27	0.607514	0.303757	−	0.952750i	$-0.401759\pi$
$157$	1.70727e27	0.607514	0.303757	+	0.952750i	$0.401759\pi$
$158$	−6.51025e26	−0.213985
$159$	−6.21826e27	−1.88888
$160$	2.11049e27	0.592768
$161$	0	0
$162$	4.72444e27	1.13609
$163$	−5.56782e26	−0.123977	−0.0619883	−	0.998077i	$-0.519744\pi$
$163$	−5.56782e26	−0.123977	−0.0619883	+	0.998077i	$0.519744\pi$
$164$	−3.47804e27	−0.717442
$165$	2.11614e27	0.404572
$166$	8.01368e27	1.42063
$167$	8.04806e26	0.132353	0.0661767	−	0.997808i	$-0.478920\pi$
$167$	8.04806e26	0.132353	0.0661767	+	0.997808i	$0.478920\pi$
$168$	0	0
$169$	−6.30673e27	−0.893760
$170$	−2.97874e27	−0.392122
$171$	8.20268e25	0.0100347
$172$	5.47008e27	0.622140
$173$	−1.19467e27	−0.126378	−0.0631892	−	0.998002i	$-0.520127\pi$
$173$	−1.19467e27	−0.126378	−0.0631892	+	0.998002i	$0.520127\pi$
$174$	2.09489e28	2.06204
$175$	0	0
$176$	5.15249e27	0.439652
$177$	1.57319e28	1.25059
$178$	3.29956e27	0.244459
$179$	5.56239e27	0.384236	0.192118	−	0.981372i	$-0.438464\pi$
$179$	5.56239e27	0.384236	0.192118	+	0.981372i	$0.438464\pi$
$180$	5.02053e27	0.323477
$181$	3.02910e28	1.82109	0.910546	−	0.413408i	$-0.135662\pi$
$181$	3.02910e28	1.82109	0.910546	+	0.413408i	$0.135662\pi$
$182$	0	0
$183$	2.08327e27	0.109171
$184$	2.28717e28	1.11963
$185$	3.37873e28	1.54564
$186$	1.54772e28	0.661884
$187$	−3.69625e27	−0.147823
$188$	1.34543e28	0.503372
$189$	0	0
$190$	−2.78469e26	−0.00912762
$191$	5.66244e28	1.73815	0.869074	−	0.494683i	$-0.164716\pi$
$191$	5.66244e28	1.73815	0.869074	+	0.494683i	$0.164716\pi$
$192$	−1.79933e28	−0.517424
$193$	6.19204e27	0.166866	0.0834328	−	0.996513i	$-0.473412\pi$
$193$	6.19204e27	0.166866	0.0834328	+	0.996513i	$0.473412\pi$
$194$	8.55327e27	0.216078
$195$	1.56761e28	0.371370
$196$	0	0
$197$	−6.82060e28	−1.42231	−0.711156	−	0.703034i	$-0.751828\pi$
$197$	−6.82060e28	−1.42231	−0.711156	+	0.703034i	$0.751828\pi$
$198$	2.21563e28	0.433694
$199$	−6.64928e26	−0.0122211	−0.00611056	−	0.999981i	$-0.501945\pi$
$199$	−6.64928e26	−0.0122211	−0.00611056	+	0.999981i	$0.501945\pi$
$200$	−1.50688e28	−0.260137
$201$	5.77219e28	0.936245
$202$	−1.14787e29	−1.74984
$203$	0	0
$204$	−1.72378e28	−0.232330
$205$	−1.15524e29	−1.46471
$206$	−1.43740e29	−1.71489
$207$	1.43773e29	1.61453
$208$	3.81691e28	0.403571
$209$	−3.45547e26	−0.00344095
$210$	0	0
$211$	2.65231e28	0.234473	0.117236	−	0.993104i	$-0.462596\pi$
$211$	2.65231e28	0.234473	0.117236	+	0.993104i	$0.462596\pi$
$212$	6.21476e28	0.517877
$213$	−1.11858e29	−0.878862
$214$	8.86136e27	0.0656642
$215$	1.81691e29	1.27014
$216$	−5.51706e27	−0.0363945
$217$	0	0
$218$	−2.69599e29	−1.58494
$219$	−2.63240e29	−1.46150
$220$	−2.11496e28	−0.110922
$221$	−2.73814e28	−0.135691
$222$	6.95382e29	3.25695
$223$	−5.44528e28	−0.241107	−0.120553	−	0.992707i	$-0.538467\pi$
$223$	−5.44528e28	−0.241107	−0.120553	+	0.992707i	$0.538467\pi$
$224$	0	0
$225$	−9.47229e28	−0.375123
$226$	2.56112e29	0.959564
$227$	−9.52227e28	−0.337611	−0.168806	−	0.985649i	$-0.553991\pi$
$227$	−9.52227e28	−0.337611	−0.168806	+	0.985649i	$0.553991\pi$
$228$	−1.61149e27	−0.00540807
$229$	3.16948e29	1.00703	0.503517	−	0.863985i	$-0.332039\pi$
$229$	3.16948e29	1.00703	0.503517	+	0.863985i	$0.332039\pi$
$230$	−4.88088e29	−1.46859
$231$	0	0
$232$	3.25880e29	0.879951
$233$	1.09215e29	0.279468	0.139734	−	0.990189i	$-0.455375\pi$
$233$	1.09215e29	0.279468	0.139734	+	0.990189i	$0.455375\pi$
$234$	1.64132e29	0.398101
$235$	4.46890e29	1.02767
$236$	−1.57231e29	−0.342876
$237$	−1.25137e29	−0.258841
$238$	0	0
$239$	6.15796e28	0.114673	0.0573367	−	0.998355i	$-0.481739\pi$
$239$	6.15796e28	0.114673	0.0573367	+	0.998355i	$0.481739\pi$
$240$	7.98137e29	1.41071
$241$	−1.03638e30	−1.73902	−0.869509	−	0.493916i	$-0.835565\pi$
$241$	−1.03638e30	−1.73902	−0.869509	+	0.493916i	$0.835565\pi$
$242$	6.46919e29	1.03076
$243$	9.41603e29	1.42492
$244$	−2.08210e28	−0.0299315
$245$	0	0
$246$	−2.37762e30	−3.08641
$247$	−2.55977e27	−0.00315856
$248$	2.40763e29	0.282451
$249$	1.54036e30	1.71842
$250$	1.20926e30	1.28313
$251$	8.96423e29	0.904881	0.452441	−	0.891795i	$-0.350553\pi$
$251$	8.96423e29	0.904881	0.452441	+	0.891795i	$0.350553\pi$
$252$	0	0
$253$	−6.05658e29	−0.553632
$254$	4.55339e29	0.396199
$255$	−5.72561e29	−0.474318
$256$	1.28964e30	1.01735
$257$	−2.27003e30	−1.70556	−0.852782	−	0.522267i	$-0.825087\pi$
$257$	−2.27003e30	−1.70556	−0.852782	+	0.522267i	$0.825087\pi$
$258$	3.73940e30	2.67643
$259$	0	0
$260$	−1.56673e29	−0.101819
$261$	2.04850e30	1.26890
$262$	2.88964e30	1.70639
$263$	−2.83015e29	−0.159354	−0.0796770	−	0.996821i	$-0.525389\pi$
$263$	−2.83015e29	−0.159354	−0.0796770	+	0.996821i	$0.525389\pi$
$264$	6.77501e29	0.363799
$265$	2.06426e30	1.05728
$266$	0	0
$267$	6.34228e29	0.295702
$268$	−5.76895e29	−0.256692
$269$	−1.97761e30	−0.839917	−0.419959	−	0.907543i	$-0.637955\pi$
$269$	−1.97761e30	−0.839917	−0.419959	+	0.907543i	$0.637955\pi$
$270$	1.17735e29	0.0477375
$271$	2.31167e30	0.894973	0.447486	−	0.894291i	$-0.352319\pi$
$271$	2.31167e30	0.894973	0.447486	+	0.894291i	$0.352319\pi$
$272$	−1.39410e30	−0.515445
$273$	0	0
$274$	1.35577e30	0.457407
$275$	3.99031e29	0.128632
$276$	−2.82454e30	−0.870131
$277$	−3.49642e30	−1.02950	−0.514750	−	0.857340i	$-0.672115\pi$
$277$	−3.49642e30	−1.02950	−0.514750	+	0.857340i	$0.672115\pi$
$278$	5.31878e30	1.49711
$279$	1.51345e30	0.407300
$280$	0	0
$281$	3.91418e30	0.963413	0.481706	−	0.876333i	$-0.340017\pi$
$281$	3.91418e30	0.963413	0.481706	+	0.876333i	$0.340017\pi$
$282$	9.19751e30	2.16549
$283$	6.37116e30	1.43512	0.717559	−	0.696498i	$-0.245259\pi$
$283$	6.37116e30	1.43512	0.717559	+	0.696498i	$0.245259\pi$
$284$	1.11795e30	0.240959
$285$	−5.35263e28	−0.0110409
$286$	−6.91422e29	−0.136511
$287$	0	0
$288$	4.24743e30	0.768635
$289$	−4.77054e30	−0.826693
$290$	−6.95436e30	−1.15420
$291$	1.64408e30	0.261372
$292$	2.63092e30	0.400702
$293$	−3.51950e30	−0.513612	−0.256806	−	0.966463i	$-0.582670\pi$
$293$	−3.51950e30	−0.513612	−0.256806	+	0.966463i	$0.582670\pi$
$294$	0	0
$295$	−5.22247e30	−0.700004
$296$	1.08173e31	1.38987
$297$	1.46095e29	0.0179962
$298$	−1.43664e31	−1.69686
$299$	−4.48664e30	−0.508196
$300$	1.86092e30	0.202168
$301$	0	0
$302$	1.07172e31	1.07150
$303$	−2.20638e31	−2.11664
$304$	−1.30328e29	−0.0119983
$305$	−6.91577e29	−0.0611073
$306$	−5.99480e30	−0.508460
$307$	−2.24006e30	−0.182402	−0.0912012	−	0.995832i	$-0.529071\pi$
$307$	−2.24006e30	−0.182402	−0.0912012	+	0.995832i	$0.529071\pi$
$308$	0	0
$309$	−2.76290e31	−2.07436
$310$	−5.13794e30	−0.370482
$311$	−2.65869e31	−1.84146	−0.920730	−	0.390200i	$-0.872406\pi$
$311$	−2.65869e31	−1.84146	−0.920730	+	0.390200i	$0.872406\pi$
$312$	5.01885e30	0.333943
$313$	−3.26609e30	−0.208797	−0.104398	−	0.994536i	$-0.533292\pi$
$313$	−3.26609e30	−0.208797	−0.104398	+	0.994536i	$0.533292\pi$
$314$	−1.16645e31	−0.716548
$315$	0	0
$316$	1.25067e30	0.0709667
$317$	−2.47602e31	−1.35056	−0.675279	−	0.737562i	$-0.735977\pi$
$317$	−2.47602e31	−1.35056	−0.675279	+	0.737562i	$0.735977\pi$
$318$	4.24847e31	2.22789
$319$	−8.62952e30	−0.435114
$320$	5.97320e30	0.289622
$321$	1.70330e30	0.0794286
$322$	0	0
$323$	9.34940e28	0.00403415
$324$	−9.07603e30	−0.376776
$325$	2.95597e30	0.118075
$326$	3.80408e30	0.146228
$327$	−5.18213e31	−1.91717
$328$	−3.69861e31	−1.31709
$329$	0	0
$330$	−1.44580e31	−0.477183
$331$	2.28809e31	0.727149	0.363575	−	0.931565i	$-0.381556\pi$
$331$	2.28809e31	0.727149	0.363575	+	0.931565i	$0.381556\pi$
$332$	−1.53949e31	−0.471141
$333$	6.79980e31	2.00421
$334$	−5.49864e30	−0.156108
$335$	−1.91618e31	−0.524053
$336$	0	0
$337$	3.34473e31	0.849156	0.424578	−	0.905391i	$-0.360423\pi$
$337$	3.34473e31	0.849156	0.424578	+	0.905391i	$0.360423\pi$
$338$	4.30892e31	1.05417
$339$	4.92287e31	1.16071
$340$	5.72239e30	0.130044
$341$	−6.37556e30	−0.139665
$342$	−5.60428e29	−0.0118357
$343$	0	0
$344$	5.81698e31	1.14213
$345$	−9.38183e31	−1.77643
$346$	8.16232e30	0.149060
$347$	−9.88058e30	−0.174046	−0.0870230	−	0.996206i	$-0.527735\pi$
$347$	−9.88058e30	−0.174046	−0.0870230	+	0.996206i	$0.527735\pi$
$348$	−4.02446e31	−0.683860
$349$	1.73865e31	0.285033	0.142516	−	0.989792i	$-0.454481\pi$
$349$	1.73865e31	0.285033	0.142516	+	0.989792i	$0.454481\pi$
$350$	0	0
$351$	1.08226e30	0.0165193
$352$	−1.78928e31	−0.263569
$353$	2.74753e31	0.390623	0.195312	−	0.980741i	$-0.437428\pi$
$353$	2.74753e31	0.390623	0.195312	+	0.980741i	$0.437428\pi$
$354$	−1.07484e32	−1.47504
$355$	3.71331e31	0.491934
$356$	−6.33872e30	−0.0810731
$357$	0	0
$358$	−3.80037e31	−0.453198
$359$	−1.23068e32	−1.41731	−0.708656	−	0.705554i	$-0.750698\pi$
$359$	−1.23068e32	−1.41731	−0.708656	+	0.705554i	$0.750698\pi$
$360$	5.33892e31	0.593844
$361$	−9.30678e31	−0.999906
$362$	−2.06956e32	−2.14793
$363$	1.24348e32	1.24683
$364$	0	0
$365$	8.73869e31	0.818061
$366$	−1.42334e31	−0.128765
$367$	−1.29688e32	−1.13390	−0.566951	−	0.823751i	$-0.691877\pi$
$367$	−1.29688e32	−1.13390	−0.566951	+	0.823751i	$0.691877\pi$
$368$	−2.28433e32	−1.93046
$369$	−2.32496e32	−1.89927
$370$	−2.30844e32	−1.82304
$371$	0	0
$372$	−2.97330e31	−0.219509
$373$	−2.66744e31	−0.190429	−0.0952147	−	0.995457i	$-0.530354\pi$
$373$	−2.66744e31	−0.190429	−0.0952147	+	0.995457i	$0.530354\pi$
$374$	2.52538e31	0.174354
$375$	2.32440e32	1.55210
$376$	1.43076e32	0.924098
$377$	−6.39265e31	−0.399405
$378$	0	0
$379$	1.44112e32	0.842773	0.421386	−	0.906881i	$-0.361544\pi$
$379$	1.44112e32	0.842773	0.421386	+	0.906881i	$0.361544\pi$
$380$	5.34962e29	0.00302711
$381$	8.75234e31	0.479250
$382$	−3.86873e32	−2.05010
$383$	1.47096e32	0.754424	0.377212	−	0.926127i	$-0.376883\pi$
$383$	1.47096e32	0.754424	0.377212	+	0.926127i	$0.376883\pi$
$384$	3.36259e32	1.66930
$385$	0	0
$386$	−4.23056e31	−0.196814
$387$	3.65658e32	1.64698
$388$	−1.64315e31	−0.0716607
$389$	−1.96677e32	−0.830586	−0.415293	−	0.909688i	$-0.636321\pi$
$389$	−1.96677e32	−0.830586	−0.415293	+	0.909688i	$0.636321\pi$
$390$	−1.07103e32	−0.438022
$391$	1.63872e32	0.649075
$392$	0	0
$393$	5.55434e32	2.06408
$394$	4.66001e32	1.67758
$395$	4.15415e31	0.144883
$396$	−4.25641e31	−0.143831
$397$	−1.54454e32	−0.505728	−0.252864	−	0.967502i	$-0.581373\pi$
$397$	−1.54454e32	−0.505728	−0.252864	+	0.967502i	$0.581373\pi$
$398$	4.54296e30	0.0144145
$399$	0	0
$400$	1.50501e32	0.448527
$401$	−1.76329e32	−0.509352	−0.254676	−	0.967026i	$-0.581969\pi$
$401$	−1.76329e32	−0.509352	−0.254676	+	0.967026i	$0.581969\pi$
$402$	−3.94371e32	−1.10428
$403$	−4.72294e31	−0.128203
$404$	2.20514e32	0.580323
$405$	−3.01464e32	−0.769214
$406$	0	0
$407$	−2.86449e32	−0.687255
$408$	−1.83310e32	−0.426515
$409$	5.32009e32	1.20054	0.600271	−	0.799796i	$-0.295059\pi$
$409$	5.32009e32	1.20054	0.600271	+	0.799796i	$0.295059\pi$
$410$	7.89292e32	1.72759
$411$	2.60600e32	0.553288
$412$	2.76135e32	0.568731
$413$	0	0
$414$	−9.82291e32	−1.90430
$415$	−5.11348e32	−0.961867
$416$	−1.32548e32	−0.241939
$417$	1.02235e33	1.81093
$418$	2.36087e30	0.00405852
$419$	5.37913e32	0.897506	0.448753	−	0.893656i	$-0.351868\pi$
$419$	5.37913e32	0.897506	0.448753	+	0.893656i	$0.351868\pi$
$420$	0	0
$421$	−3.44392e32	−0.541411	−0.270705	−	0.962662i	$-0.587257\pi$
$421$	−3.44392e32	−0.541411	−0.270705	+	0.962662i	$0.587257\pi$
$422$	−1.81212e32	−0.276555
$423$	8.99380e32	1.33257
$424$	6.60889e32	0.950726
$425$	−1.07965e32	−0.150807
$426$	7.64241e32	1.03660
$427$	0	0
$428$	−1.70234e31	−0.0217770
$429$	−1.32902e32	−0.165126
$430$	−1.24136e33	−1.49810
$431$	−3.24792e32	−0.380749	−0.190375	−	0.981712i	$-0.560970\pi$
$431$	−3.24792e32	−0.380749	−0.190375	+	0.981712i	$0.560970\pi$
$432$	5.51021e31	0.0627511
$433$	−1.52868e33	−1.69129	−0.845647	−	0.533743i	$-0.820785\pi$
$433$	−1.52868e33	−1.69129	−0.845647	+	0.533743i	$0.820785\pi$
$434$	0	0
$435$	−1.33674e33	−1.39615
$436$	5.17922e32	0.525633
$437$	1.53197e31	0.0151089
$438$	1.79852e33	1.72381
$439$	2.11036e33	1.96585	0.982926	−	0.184002i	$-0.0589052\pi$
$439$	2.11036e33	1.96585	0.982926	+	0.184002i	$0.0589052\pi$
$440$	−2.24908e32	−0.203632
$441$	0	0
$442$	1.87077e32	0.160045
$443$	9.63813e32	0.801579	0.400789	−	0.916170i	$-0.368736\pi$
$443$	9.63813e32	0.801579	0.400789	+	0.916170i	$0.368736\pi$
$444$	−1.33588e33	−1.08014
$445$	−2.10543e32	−0.165516
$446$	3.72035e32	0.284380
$447$	−2.76145e33	−2.05255
$448$	0	0
$449$	−5.73187e32	−0.402918	−0.201459	−	0.979497i	$-0.564568\pi$
$449$	−5.73187e32	−0.402918	−0.201459	+	0.979497i	$0.564568\pi$
$450$	6.47171e32	0.442448
$451$	9.79417e32	0.651269
$452$	−4.92011e32	−0.318232
$453$	2.06001e33	1.29611
$454$	6.50586e32	0.398205
$455$	0	0
$456$	−1.71369e31	−0.00992822
$457$	3.27954e33	1.84867	0.924336	−	0.381580i	$-0.124620\pi$
$457$	3.27954e33	1.84867	0.924336	+	0.381580i	$0.124620\pi$
$458$	−2.16547e33	−1.18777
$459$	−3.95287e31	−0.0210986
$460$	9.37656e32	0.487047
$461$	4.27163e31	0.0215939	0.0107970	−	0.999942i	$-0.496563\pi$
$461$	4.27163e31	0.0215939	0.0107970	+	0.999942i	$0.496563\pi$
$462$	0	0
$463$	7.24193e32	0.346810	0.173405	−	0.984851i	$-0.444523\pi$
$463$	7.24193e32	0.346810	0.173405	+	0.984851i	$0.444523\pi$
$464$	−3.25476e33	−1.51720
$465$	−9.87593e32	−0.448142
$466$	−7.46182e32	−0.329626
$467$	3.44173e33	1.48018	0.740092	−	0.672505i	$-0.234782\pi$
$467$	3.44173e33	1.48018	0.740092	+	0.672505i	$0.234782\pi$
$468$	−3.15310e32	−0.132027
$469$	0	0
$470$	−3.05327e33	−1.21211
$471$	−2.24210e33	−0.866751
$472$	−1.67202e33	−0.629457
$473$	−1.54037e33	−0.564757
$474$	8.54971e32	0.305297
$475$	−1.00932e31	−0.00351041
$476$	0	0
$477$	4.15438e33	1.37096
$478$	−4.20727e32	−0.135255
$479$	4.50751e33	1.41170	0.705850	−	0.708361i	$-0.250565\pi$
$479$	4.50751e33	1.41170	0.705850	+	0.708361i	$0.250565\pi$
$480$	−2.77165e33	−0.845712
$481$	−2.12198e33	−0.630853
$482$	7.08079e33	2.05113
$483$	0	0
$484$	−1.24278e33	−0.341844
$485$	−5.45779e32	−0.146300
$486$	−6.43328e33	−1.68066
$487$	5.13187e33	1.30666	0.653332	−	0.757072i	$-0.273371\pi$
$487$	5.13187e33	1.30666	0.653332	+	0.757072i	$0.273371\pi$
$488$	−2.21414e32	−0.0549488
$489$	7.31204e32	0.176880
$490$	0	0
$491$	6.79071e33	1.56098	0.780489	−	0.625170i	$-0.214970\pi$
$491$	6.79071e33	1.56098	0.780489	+	0.625170i	$0.214970\pi$
$492$	4.56760e33	1.02359
$493$	2.33487e33	0.510126
$494$	1.74890e31	0.00372545
$495$	−1.41378e33	−0.293642
$496$	−2.40464e33	−0.487000
$497$	0	0
$498$	−1.05241e34	−2.02684
$499$	4.87122e33	0.914915	0.457458	−	0.889231i	$-0.348760\pi$
$499$	4.87122e33	0.914915	0.457458	+	0.889231i	$0.348760\pi$
$500$	−2.32309e33	−0.425541
$501$	−1.05693e33	−0.188831
$502$	−6.12459e33	−1.06729
$503$	9.10336e33	1.54740	0.773698	−	0.633554i	$-0.218405\pi$
$503$	9.10336e33	1.54740	0.773698	+	0.633554i	$0.218405\pi$
$504$	0	0
$505$	7.32447e33	1.18477
$506$	4.13801e33	0.652996
$507$	8.28244e33	1.27514
$508$	−8.74743e32	−0.131397
$509$	−5.91504e33	−0.866932	−0.433466	−	0.901170i	$-0.642710\pi$
$509$	−5.91504e33	−0.866932	−0.433466	+	0.901170i	$0.642710\pi$
$510$	3.91188e33	0.559447
$511$	0	0
$512$	−2.19669e32	−0.0299154
$513$	−3.69537e30	−0.000491124 0
$514$	1.55095e34	2.01167
$515$	9.17193e33	1.16110
$516$	−7.18368e33	−0.887617
$517$	−3.78874e33	−0.456944
$518$	0	0
$519$	1.56893e33	0.180306
$520$	−1.66609e33	−0.186921
$521$	8.99179e33	0.984861	0.492430	−	0.870352i	$-0.336109\pi$
$521$	8.99179e33	0.984861	0.492430	+	0.870352i	$0.336109\pi$
$522$	−1.39959e34	−1.49664
$523$	7.49051e33	0.782060	0.391030	−	0.920378i	$-0.372119\pi$
$523$	7.49051e33	0.782060	0.391030	+	0.920378i	$0.372119\pi$
$524$	−5.55123e33	−0.565911
$525$	0	0
$526$	1.93363e33	0.187954
$527$	1.72502e33	0.163743
$528$	−6.76661e33	−0.627259
$529$	1.58058e34	1.43094
$530$	−1.41035e34	−1.24704
$531$	−1.05104e34	−0.907688
$532$	0	0
$533$	7.25540e33	0.597821
$534$	−4.33321e33	−0.348774
$535$	−5.65438e32	−0.0444593
$536$	−6.13480e33	−0.471238
$537$	−7.30491e33	−0.548197
$538$	1.35115e34	0.990662
$539$	0	0
$540$	−2.26179e32	−0.0158318
$541$	−1.85625e34	−1.26961	−0.634805	−	0.772672i	$-0.718920\pi$
$541$	−1.85625e34	−1.26961	−0.634805	+	0.772672i	$0.718920\pi$
$542$	−1.57939e34	−1.05560
$543$	−3.97803e34	−2.59818
$544$	4.84122e33	0.309007
$545$	1.72030e34	1.07312
$546$	0	0
$547$	−1.74455e34	−1.03954	−0.519772	−	0.854305i	$-0.673983\pi$
$547$	−1.74455e34	−1.03954	−0.519772	+	0.854305i	$0.673983\pi$
$548$	−2.60454e33	−0.151696
$549$	−1.39182e33	−0.0792371
$550$	−2.72628e33	−0.151718
$551$	2.18277e32	0.0118745
$552$	−3.00367e34	−1.59740
$553$	0	0
$554$	2.38884e34	1.21427
$555$	−4.43719e34	−2.20519
$556$	−1.02178e34	−0.496504
$557$	1.71435e34	0.814536	0.407268	−	0.913309i	$-0.366482\pi$
$557$	1.71435e34	0.814536	0.407268	+	0.913309i	$0.366482\pi$
$558$	−1.03402e34	−0.480400
$559$	−1.14109e34	−0.518409
$560$	0	0
$561$	4.85418e33	0.210902
$562$	−2.67427e34	−1.13632
$563$	−6.86857e33	−0.285438	−0.142719	−	0.989763i	$-0.545584\pi$
$563$	−6.86857e33	−0.285438	−0.142719	+	0.989763i	$0.545584\pi$
$564$	−1.76691e34	−0.718169
$565$	−1.63423e34	−0.649693
$566$	−4.35294e34	−1.69269
$567$	0	0
$568$	1.18885e34	0.442356
$569$	1.99060e34	0.724570	0.362285	−	0.932067i	$-0.381997\pi$
$569$	1.99060e34	0.724570	0.362285	+	0.932067i	$0.381997\pi$
$570$	3.65705e32	0.0130225
$571$	−2.53519e33	−0.0883201	−0.0441601	−	0.999024i	$-0.514061\pi$
$571$	−2.53519e33	−0.0883201	−0.0441601	+	0.999024i	$0.514061\pi$
$572$	1.32828e33	0.0452729
$573$	−7.43631e34	−2.47985
$574$	0	0
$575$	−1.76908e34	−0.564808
$576$	1.20212e34	0.375550
$577$	−2.59025e34	−0.791852	−0.395926	−	0.918282i	$-0.629576\pi$
$577$	−2.59025e34	−0.791852	−0.395926	+	0.918282i	$0.629576\pi$
$578$	3.25936e34	0.975065
$579$	−8.13181e33	−0.238070
$580$	1.33599e34	0.382783
$581$	0	0
$582$	−1.12327e34	−0.308282
$583$	−1.75008e34	−0.470111
$584$	2.79777e34	0.735615
$585$	−1.04731e34	−0.269543
$586$	2.40461e34	0.605794
$587$	1.97255e34	0.486465	0.243233	−	0.969968i	$-0.421792\pi$
$587$	1.97255e34	0.486465	0.243233	+	0.969968i	$0.421792\pi$
$588$	0	0
$589$	1.61265e32	0.00381153
$590$	3.56813e34	0.825639
$591$	8.95729e34	2.02924
$592$	−1.08039e35	−2.39640
$593$	−1.50116e34	−0.326018	−0.163009	−	0.986625i	$-0.552120\pi$
$593$	−1.50116e34	−0.326018	−0.163009	+	0.986625i	$0.552120\pi$
$594$	−9.98161e32	−0.0212261
$595$	0	0
$596$	2.75990e34	0.562750
$597$	8.73229e32	0.0174361
$598$	3.06539e34	0.599406
$599$	−4.95679e34	−0.949216	−0.474608	−	0.880197i	$-0.657410\pi$
$599$	−4.95679e34	−0.949216	−0.474608	+	0.880197i	$0.657410\pi$
$600$	1.97893e34	0.371142
$601$	3.45063e34	0.633823	0.316911	−	0.948455i	$-0.397354\pi$
$601$	3.45063e34	0.633823	0.316911	+	0.948455i	$0.397354\pi$
$602$	0	0
$603$	−3.85636e34	−0.679534
$604$	−2.05886e34	−0.355357
$605$	−4.12795e34	−0.697898
$606$	1.50746e35	2.49653
$607$	−2.78899e34	−0.452469	−0.226234	−	0.974073i	$-0.572641\pi$
$607$	−2.78899e34	−0.452469	−0.226234	+	0.974073i	$0.572641\pi$
$608$	4.52585e32	0.00719292
$609$	0	0
$610$	4.72503e33	0.0720746
$611$	−2.80665e34	−0.419444
$612$	1.15165e34	0.168627
$613$	1.22663e35	1.75978	0.879891	−	0.475176i	$-0.157616\pi$
$613$	1.22663e35	1.75978	0.879891	+	0.475176i	$0.157616\pi$
$614$	1.53047e34	0.215139
$615$	1.51715e35	2.08972
$616$	0	0
$617$	1.52700e34	0.201964	0.100982	−	0.994888i	$-0.467801\pi$
$617$	1.52700e34	0.201964	0.100982	+	0.994888i	$0.467801\pi$
$618$	1.88769e35	2.44666
$619$	−7.94048e34	−1.00859	−0.504294	−	0.863532i	$-0.668247\pi$
$619$	−7.94048e34	−1.00859	−0.504294	+	0.863532i	$0.668247\pi$
$620$	9.87039e33	0.122868
$621$	−6.47707e33	−0.0790194
$622$	1.81648e35	2.17196
$623$	0	0
$624$	−5.01262e34	−0.575781
$625$	−4.49878e34	−0.506517
$626$	2.23147e34	0.246271
$627$	4.53796e32	0.00490927
$628$	2.24084e34	0.237638
$629$	7.75041e34	0.805734
$630$	0	0
$631$	8.76252e34	0.875512	0.437756	−	0.899094i	$-0.355773\pi$
$631$	8.76252e34	0.875512	0.437756	+	0.899094i	$0.355773\pi$
$632$	1.32999e34	0.130282
$633$	−3.48319e34	−0.334527
$634$	1.69168e35	1.59295
$635$	−2.90549e34	−0.268255
$636$	−8.16166e34	−0.738864
$637$	0	0
$638$	5.89591e34	0.513207
$639$	7.47314e34	0.637885
$640$	−1.11627e35	−0.934370
$641$	−5.60022e34	−0.459706	−0.229853	−	0.973225i	$-0.573825\pi$
$641$	−5.60022e34	−0.459706	−0.229853	+	0.973225i	$0.573825\pi$
$642$	−1.16374e34	−0.0936842
$643$	−8.71276e34	−0.687890	−0.343945	−	0.938990i	$-0.611763\pi$
$643$	−8.71276e34	−0.687890	−0.343945	+	0.938990i	$0.611763\pi$
$644$	0	0
$645$	−2.38609e35	−1.81213
$646$	−6.38775e32	−0.00475819
$647$	−5.29085e34	−0.386564	−0.193282	−	0.981143i	$-0.561913\pi$
$647$	−5.29085e34	−0.386564	−0.193282	+	0.981143i	$0.561913\pi$
$648$	−9.65161e34	−0.691691
$649$	4.42761e34	0.311251
$650$	−2.01960e34	−0.139267
$651$	0	0
$652$	−7.30794e33	−0.0484953
$653$	1.16032e35	0.755378	0.377689	−	0.925933i	$-0.376719\pi$
$653$	1.16032e35	0.755378	0.377689	+	0.925933i	$0.376719\pi$
$654$	3.54056e35	2.26126
$655$	−1.84386e35	−1.15534
$656$	3.69402e35	2.27092
$657$	1.75869e35	1.06077
$658$	0	0
$659$	2.99940e35	1.74168	0.870838	−	0.491571i	$-0.163577\pi$
$659$	2.99940e35	1.74168	0.870838	+	0.491571i	$0.163577\pi$
$660$	2.77750e34	0.158254
$661$	−2.99712e35	−1.67566	−0.837829	−	0.545932i	$-0.816176\pi$
$661$	−2.99712e35	−1.67566	−0.837829	+	0.545932i	$0.816176\pi$
$662$	−1.56328e35	−0.857655
$663$	3.59592e34	0.193593
$664$	−1.63712e35	−0.864929
$665$	0	0
$666$	−4.64580e35	−2.36392
$667$	3.82586e35	1.91054
$668$	1.05633e34	0.0517720
$669$	7.15111e34	0.343991
$670$	1.30918e35	0.618108
$671$	5.86320e33	0.0271708
$672$	0	0
$673$	2.23827e35	0.999365	0.499683	−	0.866209i	$-0.333450\pi$
$673$	2.23827e35	0.999365	0.499683	+	0.866209i	$0.333450\pi$
$674$	−2.28521e35	−1.00156
$675$	4.26734e33	0.0183595
$676$	−8.27779e34	−0.349607
$677$	4.16477e35	1.72676	0.863381	−	0.504552i	$-0.168342\pi$
$677$	4.16477e35	1.72676	0.863381	+	0.504552i	$0.168342\pi$
$678$	−3.36343e35	−1.36903
$679$	0	0
$680$	6.08530e34	0.238737
$681$	1.25053e35	0.481676
$682$	4.35595e34	0.164732
$683$	3.10089e35	1.15140	0.575702	−	0.817660i	$-0.304729\pi$
$683$	3.10089e35	1.15140	0.575702	+	0.817660i	$0.304729\pi$
$684$	1.07663e33	0.00392522
$685$	−8.65106e34	−0.309697
$686$	0	0
$687$	−4.16238e35	−1.43675
$688$	−5.80976e35	−1.96926
$689$	−1.29644e35	−0.431530
$690$	6.40991e35	2.09526
$691$	1.14581e35	0.367822	0.183911	−	0.982943i	$-0.441124\pi$
$691$	1.14581e35	0.367822	0.183911	+	0.982943i	$0.441124\pi$
$692$	−1.56805e34	−0.0494348
$693$	0	0
$694$	6.75066e34	0.205283
$695$	−3.39388e35	−1.01365
$696$	−4.27968e35	−1.25544
$697$	−2.64999e35	−0.763545
$698$	−1.18789e35	−0.336189
$699$	−1.43428e35	−0.398722
$700$	0	0
$701$	−3.31730e35	−0.889834	−0.444917	−	0.895572i	$-0.646767\pi$
$701$	−3.31730e35	−0.889834	−0.444917	+	0.895572i	$0.646767\pi$
$702$	−7.39426e33	−0.0194841
$703$	7.24552e33	0.0187555
$704$	−5.06408e34	−0.128778
$705$	−5.86887e35	−1.46619
$706$	−1.87718e35	−0.460731
$707$	0	0
$708$	2.06486e35	0.489187
$709$	−4.87259e35	−1.13418	−0.567090	−	0.823656i	$-0.691931\pi$
$709$	−4.87259e35	−1.13418	−0.567090	+	0.823656i	$0.691931\pi$
$710$	−2.53703e35	−0.580224
$711$	8.36035e34	0.187869
$712$	−6.74071e34	−0.148835
$713$	2.82657e35	0.613255
$714$	0	0
$715$	4.41192e34	0.0924278
$716$	7.30081e34	0.150300
$717$	−8.08705e34	−0.163607
$718$	8.40834e35	1.67169
$719$	6.33760e35	1.23827	0.619133	−	0.785286i	$-0.287484\pi$
$719$	6.33760e35	1.23827	0.619133	+	0.785286i	$0.287484\pi$
$720$	−5.33230e35	−1.02390
$721$	0	0
$722$	6.35863e35	1.17937
$723$	1.36104e36	2.48109
$724$	3.97579e35	0.712347
$725$	−2.52062e35	−0.443898
$726$	−8.49579e35	−1.47060
$727$	4.98956e35	0.848950	0.424475	−	0.905440i	$-0.360459\pi$
$727$	4.98956e35	0.848950	0.424475	+	0.905440i	$0.360459\pi$
$728$	0	0
$729$	−6.50687e35	−1.06974
$730$	−5.97050e35	−0.964883
$731$	4.16776e35	0.662118
$732$	2.73436e34	0.0427038
$733$	−6.11009e35	−0.938097	−0.469049	−	0.883172i	$-0.655403\pi$
$733$	−6.11009e35	−0.938097	−0.469049	+	0.883172i	$0.655403\pi$
$734$	8.86065e35	1.33741
$735$	0	0
$736$	7.93269e35	1.15730
$737$	1.62454e35	0.233016
$738$	1.58847e36	2.24014
$739$	−9.92910e35	−1.37675	−0.688374	−	0.725356i	$-0.741675\pi$
$739$	−9.92910e35	−1.37675	−0.688374	+	0.725356i	$0.741675\pi$
$740$	4.43470e35	0.604599
$741$	3.36167e33	0.00450637
$742$	0	0
$743$	−8.23996e35	−1.06798	−0.533992	−	0.845489i	$-0.679309\pi$
$743$	−8.23996e35	−1.06798	−0.533992	+	0.845489i	$0.679309\pi$
$744$	−3.16186e35	−0.402978
$745$	9.16712e35	1.14889
$746$	1.82246e35	0.224607
$747$	−1.02910e36	−1.24724
$748$	−4.85145e34	−0.0578231
$749$	0	0
$750$	−1.58809e36	−1.83067
$751$	7.87144e35	0.892390	0.446195	−	0.894936i	$-0.352779\pi$
$751$	7.87144e35	0.892390	0.446195	+	0.894936i	$0.352779\pi$
$752$	−1.42898e36	−1.59332
$753$	−1.17724e36	−1.29101
$754$	4.36762e35	0.471089
$755$	−6.83857e35	−0.725485
$756$	0	0
$757$	1.22159e36	1.25380	0.626900	−	0.779099i	$-0.284323\pi$
$757$	1.22159e36	1.25380	0.626900	+	0.779099i	$0.284323\pi$
$758$	−9.84611e35	−0.994031
$759$	7.95392e35	0.789876
$760$	5.68888e33	0.00555721
$761$	−1.12157e36	−1.07775	−0.538876	−	0.842385i	$-0.681151\pi$
$761$	−1.12157e36	−1.07775	−0.538876	+	0.842385i	$0.681151\pi$
$762$	−5.97983e35	−0.565264
$763$	0	0
$764$	7.43213e35	0.679902
$765$	3.82524e35	0.344264
$766$	−1.00500e36	−0.889826
$767$	3.27992e35	0.285708
$768$	−1.69365e36	−1.45147
$769$	1.27803e36	1.07761	0.538805	−	0.842430i	$-0.318876\pi$
$769$	1.27803e36	1.07761	0.538805	+	0.842430i	$0.318876\pi$
$770$	0	0
$771$	2.98116e36	2.43336
$772$	8.12724e34	0.0652720
$773$	−1.77689e35	−0.140416	−0.0702082	−	0.997532i	$-0.522366\pi$
$773$	−1.77689e35	−0.140416	−0.0702082	+	0.997532i	$0.522366\pi$
$774$	−2.49827e36	−1.94257
$775$	−1.86226e35	−0.142485
$776$	−1.74736e35	−0.131556
$777$	0	0
$778$	1.34375e36	0.979656
$779$	−2.47736e34	−0.0177734
$780$	2.05754e35	0.145267
$781$	−3.14815e35	−0.218734
$782$	−1.11961e36	−0.765568
$783$	−9.22864e34	−0.0621035
$784$	0	0
$785$	7.44305e35	0.485154
$786$	−3.79487e36	−2.43453
$787$	−1.34339e36	−0.848236	−0.424118	−	0.905607i	$-0.639416\pi$
$787$	−1.34339e36	−0.848236	−0.424118	+	0.905607i	$0.639416\pi$
$788$	−8.95226e35	−0.556359
$789$	3.71675e35	0.227353
$790$	−2.83822e35	−0.170887
$791$	0	0
$792$	−4.52634e35	−0.264048
$793$	4.34339e34	0.0249410
$794$	1.05527e36	0.596495
$795$	−2.71092e36	−1.50844
$796$	−8.72739e33	−0.00478047
$797$	1.56302e36	0.842822	0.421411	−	0.906870i	$-0.361535\pi$
$797$	1.56302e36	0.842822	0.421411	+	0.906870i	$0.361535\pi$
$798$	0	0
$799$	1.02511e36	0.535719
$800$	−5.22636e35	−0.268890
$801$	−4.23724e35	−0.214623
$802$	1.20472e36	0.600769
$803$	−7.40867e35	−0.363744
$804$	7.57618e35	0.366226
$805$	0	0
$806$	3.22683e35	0.151213
$807$	2.59713e36	1.19832
$808$	2.34499e36	1.06537
$809$	2.88433e35	0.129029	0.0645146	−	0.997917i	$-0.479450\pi$
$809$	2.88433e35	0.129029	0.0645146	+	0.997917i	$0.479450\pi$
$810$	2.05968e36	0.907270
$811$	−2.93205e35	−0.127178	−0.0635888	−	0.997976i	$-0.520255\pi$
$811$	−2.93205e35	−0.127178	−0.0635888	+	0.997976i	$0.520255\pi$
$812$	0	0
$813$	−3.03585e36	−1.27687
$814$	1.95710e36	0.810601
$815$	−2.42736e35	−0.0990065
$816$	1.83083e36	0.735395
$817$	3.89626e34	0.0154125
$818$	−3.63482e36	−1.41601
$819$	0	0
$820$	−1.51629e36	−0.572941
$821$	−1.25135e36	−0.465683	−0.232842	−	0.972515i	$-0.574802\pi$
$821$	−1.25135e36	−0.465683	−0.232842	+	0.972515i	$0.574802\pi$
$822$	−1.78049e36	−0.652591
$823$	−9.52069e35	−0.343693	−0.171846	−	0.985124i	$-0.554973\pi$
$823$	−9.52069e35	−0.343693	−0.171846	+	0.985124i	$0.554973\pi$
$824$	2.93647e36	1.04408
$825$	−5.24035e35	−0.183521
$826$	0	0
$827$	1.59835e36	0.543067	0.271533	−	0.962429i	$-0.412469\pi$
$827$	1.59835e36	0.543067	0.271533	+	0.962429i	$0.412469\pi$
$828$	1.88706e36	0.631548
$829$	2.81042e36	0.926488	0.463244	−	0.886231i	$-0.346685\pi$
$829$	2.81042e36	0.926488	0.463244	+	0.886231i	$0.346685\pi$
$830$	3.49366e36	1.13450
$831$	4.59174e36	1.46881
$832$	−3.75141e35	−0.118210
$833$	0	0
$834$	−6.98499e36	−2.13595
$835$	3.50865e35	0.105696
$836$	−4.53541e33	−0.00134598
$837$	−6.81819e34	−0.0199343
$838$	−3.67516e36	−1.05859
$839$	7.31568e35	0.207601	0.103801	−	0.994598i	$-0.466900\pi$
$839$	7.31568e35	0.207601	0.103801	+	0.994598i	$0.466900\pi$
$840$	0	0
$841$	1.82079e36	0.501546
$842$	2.35298e36	0.638581
$843$	−5.14038e36	−1.37452
$844$	3.48123e35	0.0917176
$845$	−2.74950e36	−0.713747
$846$	−6.14480e36	−1.57173
$847$	0	0
$848$	−6.60069e36	−1.63924
$849$	−8.36704e36	−2.04751
$850$	7.37645e35	0.177873
$851$	1.26996e37	3.01766
$852$	−1.46817e36	−0.343780
$853$	2.11845e36	0.488827	0.244414	−	0.969671i	$-0.421405\pi$
$853$	2.11845e36	0.488827	0.244414	+	0.969671i	$0.421405\pi$
$854$	0	0
$855$	3.57606e34	0.00801360
$856$	−1.81030e35	−0.0399786
$857$	1.44989e36	0.315556	0.157778	−	0.987475i	$-0.449567\pi$
$857$	1.44989e36	0.315556	0.157778	+	0.987475i	$0.449567\pi$
$858$	9.08024e35	0.194763
$859$	−2.33156e36	−0.492870	−0.246435	−	0.969159i	$-0.579259\pi$
$859$	−2.33156e36	−0.492870	−0.246435	+	0.969159i	$0.579259\pi$
$860$	2.38475e36	0.496834
$861$	0	0
$862$	2.21906e36	0.449085
$863$	2.68218e36	0.535000	0.267500	−	0.963558i	$-0.413803\pi$
$863$	2.68218e36	0.535000	0.267500	+	0.963558i	$0.413803\pi$
$864$	−1.91350e35	−0.0376190
$865$	−5.20832e35	−0.100925
$866$	1.04444e37	1.99484
$867$	6.26500e36	1.17946
$868$	0	0
$869$	−3.52189e35	−0.0644212
$870$	9.13295e36	1.64672
$871$	1.20344e36	0.213893
$872$	5.50767e36	0.964966
$873$	−1.09840e36	−0.189706
$874$	−1.04668e35	−0.0178205
$875$	0	0
$876$	−3.45510e36	−0.571689
$877$	−1.01194e37	−1.65066	−0.825331	−	0.564649i	$-0.809012\pi$
$877$	−1.01194e37	−1.65066	−0.825331	+	0.564649i	$0.809012\pi$
$878$	−1.44185e37	−2.31868
$879$	4.62205e36	0.732780
$880$	2.24629e36	0.351102
$881$	6.03146e36	0.929444	0.464722	−	0.885457i	$-0.346154\pi$
$881$	6.03146e36	0.929444	0.464722	+	0.885457i	$0.346154\pi$
$882$	0	0
$883$	−2.16384e36	−0.324128	−0.162064	−	0.986780i	$-0.551815\pi$
$883$	−2.16384e36	−0.324128	−0.162064	+	0.986780i	$0.551815\pi$
$884$	−3.59390e35	−0.0530777
$885$	6.85851e36	0.998708
$886$	−6.58502e36	−0.945443
$887$	8.81117e36	1.24735	0.623675	−	0.781684i	$-0.285639\pi$
$887$	8.81117e36	1.24735	0.623675	+	0.781684i	$0.285639\pi$
$888$	−1.42060e37	−1.98295
$889$	0	0
$890$	1.43848e36	0.195222
$891$	2.55581e36	0.342025
$892$	−7.14710e35	−0.0943124
$893$	9.58334e34	0.0124702
$894$	1.88670e37	2.42093
$895$	2.42499e36	0.306847
$896$	0	0
$897$	5.89217e36	0.725053
$898$	3.91616e36	0.475233
$899$	4.02735e36	0.481974
$900$	−1.24327e36	−0.146735
$901$	4.73515e36	0.551156
$902$	−6.69163e36	−0.768157
$903$	0	0
$904$	−5.23213e36	−0.584216
$905$	1.32057e37	1.45430
$906$	−1.40745e37	−1.52873
$907$	−1.52125e37	−1.62971	−0.814854	−	0.579667i	$-0.803183\pi$
$907$	−1.52125e37	−1.62971	−0.814854	+	0.579667i	$0.803183\pi$
$908$	−1.24983e36	−0.132062
$909$	1.47407e37	1.53628
$910$	0	0
$911$	1.85608e37	1.88199	0.940993	−	0.338425i	$-0.109894\pi$
$911$	1.85608e37	1.88199	0.940993	+	0.338425i	$0.109894\pi$
$912$	1.71156e35	0.0171182
$913$	4.33521e36	0.427686
$914$	−2.24066e37	−2.18046
$915$	9.08227e35	0.0871828
$916$	4.16004e36	0.393916
$917$	0	0
$918$	2.70070e35	0.0248853
$919$	−3.03365e36	−0.275754	−0.137877	−	0.990449i	$-0.544028\pi$
$919$	−3.03365e36	−0.275754	−0.137877	+	0.990449i	$0.544028\pi$
$920$	9.97120e36	0.894128
$921$	2.94181e36	0.260237
$922$	−2.91849e35	−0.0254695
$923$	−2.33211e36	−0.200783
$924$	0	0
$925$	−8.36699e36	−0.701128
$926$	−4.94787e36	−0.409054
$927$	1.84588e37	1.50559
$928$	1.13026e37	0.909557
$929$	−1.62463e37	−1.28991	−0.644954	−	0.764222i	$-0.723123\pi$
$929$	−1.62463e37	−1.28991	−0.644954	+	0.764222i	$0.723123\pi$
$930$	6.74749e36	0.528574
$931$	0	0
$932$	1.43348e36	0.109318
$933$	3.49157e37	2.62724
$934$	−2.35148e37	−1.74584
$935$	−1.61143e36	−0.118050
$936$	−3.35306e36	−0.242378
$937$	−1.05950e37	−0.755714	−0.377857	−	0.925864i	$-0.623339\pi$
$937$	−1.05950e37	−0.755714	−0.377857	+	0.925864i	$0.623339\pi$
$938$	0	0
$939$	4.28925e36	0.297894
$940$	5.86558e36	0.401988
$941$	−2.16180e37	−1.46199	−0.730995	−	0.682383i	$-0.760944\pi$
$941$	−2.16180e37	−1.46199	−0.730995	+	0.682383i	$0.760944\pi$
$942$	1.53186e37	1.02231
$943$	−4.34220e37	−2.85965
$944$	1.66994e37	1.08531
$945$	0	0
$946$	1.05242e37	0.666118
$947$	−7.39738e36	−0.462065	−0.231033	−	0.972946i	$-0.574210\pi$
$947$	−7.39738e36	−0.462065	−0.231033	+	0.972946i	$0.574210\pi$
$948$	−1.64247e36	−0.101249
$949$	−5.48825e36	−0.333892
$950$	6.89593e34	0.00414045
$951$	3.25168e37	1.92686
$952$	0	0
$953$	−2.77523e37	−1.60191	−0.800955	−	0.598725i	$-0.795674\pi$
$953$	−2.77523e37	−1.60191	−0.800955	+	0.598725i	$0.795674\pi$
$954$	−2.83838e37	−1.61702
$955$	2.46861e37	1.38807
$956$	8.08251e35	0.0448562
$957$	1.13329e37	0.620785
$958$	−3.07964e37	−1.66507
$959$	0	0
$960$	−7.84441e36	−0.413209
$961$	−1.62574e37	−0.845293
$962$	1.44979e37	0.744077
$963$	−1.13796e36	−0.0576499
$964$	−1.36028e37	−0.680243
$965$	2.69949e36	0.133257
$966$	0	0
$967$	2.79266e37	1.34334	0.671672	−	0.740849i	$-0.265576\pi$
$967$	2.79266e37	1.34334	0.671672	+	0.740849i	$0.265576\pi$
$968$	−1.32160e37	−0.627563
$969$	−1.22783e35	−0.00575560
$970$	3.72890e36	0.172558
$971$	3.26358e37	1.49092	0.745460	−	0.666550i	$-0.232230\pi$
$971$	3.26358e37	1.49092	0.745460	+	0.666550i	$0.232230\pi$
$972$	1.23588e37	0.557378
$973$	0	0
$974$	−3.50623e37	−1.54118
$975$	−3.88199e36	−0.168460
$976$	2.21140e36	0.0947423
$977$	−7.36801e35	−0.0311651	−0.0155825	−	0.999879i	$-0.504960\pi$
$977$	−7.36801e35	−0.0311651	−0.0155825	+	0.999879i	$0.504960\pi$
$978$	−4.99578e36	−0.208625
$979$	1.78498e36	0.0735954
$980$	0	0
$981$	3.46215e37	1.39150
$982$	−4.63959e37	−1.84114
$983$	2.16750e37	0.849261	0.424630	−	0.905367i	$-0.360404\pi$
$983$	2.16750e37	0.849261	0.424630	+	0.905367i	$0.360404\pi$
$984$	4.85727e37	1.87912
$985$	−2.97353e37	−1.13584
$986$	−1.59525e37	−0.601681
$987$	0	0
$988$	−3.35978e34	−0.00123552
$989$	6.82918e37	2.47979
$990$	9.65932e36	0.346343
$991$	−2.99183e37	−1.05929	−0.529646	−	0.848219i	$-0.677675\pi$
$991$	−2.99183e37	−1.05929	−0.529646	+	0.848219i	$0.677675\pi$
$992$	8.35047e36	0.291954
$993$	−3.00488e37	−1.03744
$994$	0	0
$995$	−2.89883e35	−0.00975966
$996$	2.02177e37	0.672186
$997$	9.07116e36	0.297834	0.148917	−	0.988850i	$-0.452421\pi$
$997$	9.07116e36	0.297834	0.148917	+	0.988850i	$0.452421\pi$
$998$	−3.32814e37	−1.07912
$999$	−3.06337e36	−0.0980912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.26.a.d.1.2		7
7.6	odd	2		7.26.a.b.1.2	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.26.a.b.1.2	✓	7	7.6	odd	2
49.26.a.d.1.2		7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q-6832.26 q^{2} -1.31327e6 q^{3} +1.31253e7 q^{4} +4.35962e8 q^{5} +8.97259e9 q^{6} +1.39577e11 q^{8} +8.77387e11 q^{9} +O(q^{10})\)	\(q-6832.26 q^{2} -1.31327e6 q^{3} +1.31253e7 q^{4} +4.35962e8 q^{5} +8.97259e9 q^{6} +1.39577e11 q^{8} +8.77387e11 q^{9} -2.97861e12 q^{10} -3.69609e12 q^{11} -1.72371e13 q^{12} -2.73802e13 q^{13} -5.72536e14 q^{15} -1.39404e15 q^{16} +1.00004e15 q^{17} -5.99453e15 q^{18} +9.34899e13 q^{19} +5.72214e15 q^{20} +2.52526e16 q^{22} +1.63865e17 q^{23} -1.83302e17 q^{24} -1.07960e17 q^{25} +1.87069e17 q^{26} -3.95270e16 q^{27} +2.33477e18 q^{29} +3.91171e18 q^{30} +1.72495e18 q^{31} +4.84100e18 q^{32} +4.85396e18 q^{33} -6.83256e18 q^{34} +1.15160e19 q^{36} +7.75006e19 q^{37} -6.38747e17 q^{38} +3.59576e19 q^{39} +6.08503e19 q^{40} -2.64987e20 q^{41} +4.16758e20 q^{43} -4.85124e19 q^{44} +3.82507e20 q^{45} -1.11956e21 q^{46} +1.02507e21 q^{47} +1.83075e21 q^{48} +7.37612e20 q^{50} -1.31333e21 q^{51} -3.59374e20 q^{52} +4.73494e21 q^{53} +2.70058e20 q^{54} -1.61136e21 q^{55} -1.22777e20 q^{57} -1.59518e22 q^{58} -1.19792e22 q^{59} -7.51471e21 q^{60} -1.58632e21 q^{61} -1.17853e22 q^{62} +1.37012e22 q^{64} -1.19367e22 q^{65} -3.31635e22 q^{66} -4.39528e22 q^{67} +1.31259e22 q^{68} -2.15198e23 q^{69} +8.51750e22 q^{71} +1.22463e23 q^{72} +2.00446e23 q^{73} -5.29504e23 q^{74} +1.41781e23 q^{75} +1.22708e21 q^{76} -2.45671e23 q^{78} +9.52870e22 q^{79} -6.07748e23 q^{80} -6.91490e23 q^{81} +1.81046e24 q^{82} -1.17292e24 q^{83} +4.35982e23 q^{85} -2.84740e24 q^{86} -3.06618e24 q^{87} -5.15889e23 q^{88} -4.82938e23 q^{89} -2.61339e24 q^{90} +2.15077e24 q^{92} -2.26532e24 q^{93} -7.00352e24 q^{94} +4.07580e22 q^{95} -6.35754e24 q^{96} -1.25190e24 q^{97} -3.24290e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 8373 q^{2} + 599172 q^{3} + 199632661 q^{4} - 485320794 q^{5} - 548762130 q^{6} + 679913241639 q^{8} + 2499178495563 q^{9}+O(q^{10}) \) 7 * q + 8373 * q^2 + 599172 * q^3 + 199632661 * q^4 - 485320794 * q^5 - 548762130 * q^6 + 679913241639 * q^8 + 2499178495563 * q^9	\( 7 q + 8373 q^{2} + 599172 q^{3} + 199632661 q^{4} - 485320794 q^{5} - 548762130 q^{6} + 679913241639 q^{8} + 2499178495563 q^{9} + 876704815140 q^{10} - 7845139606524 q^{11} + 83731581305106 q^{12} + 75871445642734 q^{13} + 12\!\cdots\!84 q^{15}+ \cdots + 29\!\cdots\!00 q^{99}+O(q^{100}) \) 7 * q + 8373 * q^2 + 599172 * q^3 + 199632661 * q^4 - 485320794 * q^5 - 548762130 * q^6 + 679913241639 * q^8 + 2499178495563 * q^9 + 876704815140 * q^10 - 7845139606524 * q^11 + 83731581305106 * q^12 + 75871445642734 * q^13 + 1250450093573784 * q^15 + 2533333214129041 * q^16 - 4930179049331550 * q^17 + 6108218172751149 * q^18 + 8822108307937204 * q^19 + 35797888210439208 * q^20 + 122308015837411896 * q^22 + 260380318250119992 * q^23 - 280838923324398306 * q^24 + 442974124902943561 * q^25 - 525030062154247104 * q^26 + 508138451607400488 * q^27 + 3074121146906357394 * q^29 + 20693674849314206160 * q^30 - 17867964278742490304 * q^31 + 41524963168122393471 * q^32 - 18631713362079899088 * q^33 - 76530595013021124150 * q^34 + 120686738791924632357 * q^36 + 37537195275383667242 * q^37 - 133898980332930749790 * q^38 + 160680068588101330968 * q^39 - 260261018010811048560 * q^40 - 349555665716732087718 * q^41 - 188918130006461199484 * q^43 - 866635019544130150704 * q^44 + 2875914312455481795918 * q^45 - 1056444907691638473648 * q^46 + 577519309883773958064 * q^47 + 1705636002072738200514 * q^48 - 3108044078925178785 * q^50 - 8568497654252614793448 * q^51 + 21223967127059853562252 * q^52 + 724118360265623334330 * q^53 + 23525683999565788877508 * q^54 + 3874297214249814234792 * q^55 + 21002099147408968606176 * q^57 - 6571075616758407948534 * q^58 + 29388013065202679743548 * q^59 + 131210151872269358361312 * q^60 - 24863323230677092393442 * q^61 - 178098511159147000538004 * q^62 + 185730465159694629378817 * q^64 - 28642507689771657088260 * q^65 + 182488465275344339797728 * q^66 + 87288896332559907446444 * q^67 - 236561584649915083645422 * q^68 + 38736311524504328113344 * q^69 + 507749245951454445426264 * q^71 - 136846012456831244000985 * q^72 + 384451815193432683470074 * q^73 - 180156332882615168418510 * q^74 + 917728597534517928543804 * q^75 + 1802955096706900507996366 * q^76 - 2701299412149008608565208 * q^78 - 512089643024553543168400 * q^79 - 1072829383400652355143456 * q^80 - 1711055088184234765637889 * q^81 + 328793973025384284153498 * q^82 - 683613625271699866065420 * q^83 - 4106127272649214828366668 * q^85 + 6352668961585470034751760 * q^86 - 6810779334667612471104168 * q^87 - 1678346430445345786597824 * q^88 - 7785138614078665124468694 * q^89 + 6907385334351120772566420 * q^90 + 4229143913695999872649632 * q^92 + 9311007684860974346150688 * q^93 - 16094575705640558287782684 * q^94 + 8670853765297953493275288 * q^95 - 20458763379770390869400514 * q^96 - 16735236191051483252826350 * q^97 + 29494988134999515624453300 * q^99

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