LMFDB - Embedded newform 103.12.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [103,12,Mod(1,103)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(103, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("103.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 103 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	103.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:	$79.1393475976$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-74.2508 q^{2} -125.019 q^{3} +3465.19 q^{4} -2224.90 q^{5} +9282.79 q^{6} +36712.6 q^{7} -105227. q^{8} -161517. q^{9} +O(q^{10})$	\(q-74.2508 q^{2} -125.019 q^{3} +3465.19 q^{4} -2224.90 q^{5} +9282.79 q^{6} +36712.6 q^{7} -105227. q^{8} -161517. q^{9} +165201. q^{10} +97623.0 q^{11} -433216. q^{12} +36165.9 q^{13} -2.72594e6 q^{14} +278155. q^{15} +716521. q^{16} +7.49913e6 q^{17} +1.19928e7 q^{18} +1.27332e7 q^{19} -7.70969e6 q^{20} -4.58978e6 q^{21} -7.24859e6 q^{22} -6.88800e6 q^{23} +1.31555e7 q^{24} -4.38780e7 q^{25} -2.68535e6 q^{26} +4.23396e7 q^{27} +1.27216e8 q^{28} +1.98083e8 q^{29} -2.06533e7 q^{30} -1.95252e7 q^{31} +1.62304e8 q^{32} -1.22048e7 q^{33} -5.56817e8 q^{34} -8.16818e7 q^{35} -5.59687e8 q^{36} +6.25286e8 q^{37} -9.45454e8 q^{38} -4.52144e6 q^{39} +2.34120e8 q^{40} -8.06280e8 q^{41} +3.40795e8 q^{42} -1.10920e9 q^{43} +3.38282e8 q^{44} +3.59359e8 q^{45} +5.11440e8 q^{46} -2.03935e9 q^{47} -8.95790e7 q^{48} -6.29513e8 q^{49} +3.25798e9 q^{50} -9.37537e8 q^{51} +1.25322e8 q^{52} -2.64973e9 q^{53} -3.14375e9 q^{54} -2.17201e8 q^{55} -3.86317e9 q^{56} -1.59190e9 q^{57} -1.47078e10 q^{58} -4.32754e8 q^{59} +9.63861e8 q^{60} +1.95833e9 q^{61} +1.44976e9 q^{62} -5.92971e9 q^{63} -1.35186e10 q^{64} -8.04656e7 q^{65} +9.06214e8 q^{66} -1.66808e10 q^{67} +2.59859e10 q^{68} +8.61134e8 q^{69} +6.06494e9 q^{70} +2.18337e10 q^{71} +1.69960e10 q^{72} -2.52460e10 q^{73} -4.64280e10 q^{74} +5.48559e9 q^{75} +4.41231e10 q^{76} +3.58399e9 q^{77} +3.35721e8 q^{78} +2.87546e10 q^{79} -1.59419e9 q^{80} +2.33190e10 q^{81} +5.98670e10 q^{82} +5.22047e10 q^{83} -1.59045e10 q^{84} -1.66848e10 q^{85} +8.23592e10 q^{86} -2.47642e10 q^{87} -1.02726e10 q^{88} +8.66409e10 q^{89} -2.66827e10 q^{90} +1.32775e9 q^{91} -2.38682e10 q^{92} +2.44103e9 q^{93} +1.51424e11 q^{94} -2.83302e10 q^{95} -2.02911e10 q^{96} -9.45804e10 q^{97} +4.67419e10 q^{98} -1.57678e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q + 183 q^{2} + 466 q^{3} + 55743 q^{4} + 16065 q^{5} + 33631 q^{6} + 31238 q^{7} + 367572 q^{8} + 3580275 q^{9}+O(q^{10}) $ 49 * q + 183 * q^2 + 466 * q^3 + 55743 * q^4 + 16065 * q^5 + 33631 * q^6 + 31238 * q^7 + 367572 * q^8 + 3580275 * q^9	\( 49 q + 183 q^{2} + 466 q^{3} + 55743 q^{4} + 16065 q^{5} + 33631 q^{6} + 31238 q^{7} + 367572 q^{8} + 3580275 q^{9} + 750478 q^{10} + 727533 q^{11} + 2347431 q^{12} + 1686993 q^{13} + 1917175 q^{14} + 5732779 q^{15} + 63104603 q^{16} + 42447415 q^{17} + 38328816 q^{18} + 5625397 q^{19} + 23363733 q^{20} + 9056758 q^{21} + 35431841 q^{22} + 99653000 q^{23} + 60107634 q^{24} + 612692400 q^{25} - 287465619 q^{26} + 33237874 q^{27} + 94647576 q^{28} + 582553712 q^{29} + 2028243566 q^{30} + 574615536 q^{31} + 2461710524 q^{32} + 1398060597 q^{33} + 1095877670 q^{34} + 1224276663 q^{35} + 5178232888 q^{36} + 1054414698 q^{37} + 168008610 q^{38} - 682764349 q^{39} - 3058491845 q^{40} + 1814310718 q^{41} - 7019276677 q^{42} + 322591648 q^{43} - 1892602784 q^{44} - 4067379516 q^{45} - 11163159263 q^{46} + 15760013 q^{47} - 3956976183 q^{48} + 10317761631 q^{49} + 4788432202 q^{50} + 4167009909 q^{51} - 16558761537 q^{52} + 16561990335 q^{53} - 22053068789 q^{54} - 2528406158 q^{55} - 2175101045 q^{56} + 10578500421 q^{57} + 10570052770 q^{58} + 12504156727 q^{59} + 27219988055 q^{60} + 12858649383 q^{61} + 29953793573 q^{62} + 21928998164 q^{63} + 107776677998 q^{64} + 75670521263 q^{65} + 70097909751 q^{66} + 34656499990 q^{67} + 134555459108 q^{68} + 60441944808 q^{69} + 144324418256 q^{70} - 4976323973 q^{71} + 184674525846 q^{72} + 80843930205 q^{73} + 147160169907 q^{74} + 106406736723 q^{75} + 89376434340 q^{76} + 187650162769 q^{77} + 217624188512 q^{78} + 33073221431 q^{79} + 220351536446 q^{80} + 373198656177 q^{81} + 417339951569 q^{82} + 180678060299 q^{83} + 622749162897 q^{84} + 295945248373 q^{85} + 223228441021 q^{86} + 351128502358 q^{87} + 327529458125 q^{88} + 229672691360 q^{89} + 878270116936 q^{90} + 269714836479 q^{91} + 470788684476 q^{92} + 255181811376 q^{93} + 556696972040 q^{94} + 455878930472 q^{95} + 1296231412687 q^{96} + 248534514476 q^{97} + 747851098165 q^{98} + 465588303306 q^{99}+O(q^{100}) \) 49 * q + 183 * q^2 + 466 * q^3 + 55743 * q^4 + 16065 * q^5 + 33631 * q^6 + 31238 * q^7 + 367572 * q^8 + 3580275 * q^9 + 750478 * q^10 + 727533 * q^11 + 2347431 * q^12 + 1686993 * q^13 + 1917175 * q^14 + 5732779 * q^15 + 63104603 * q^16 + 42447415 * q^17 + 38328816 * q^18 + 5625397 * q^19 + 23363733 * q^20 + 9056758 * q^21 + 35431841 * q^22 + 99653000 * q^23 + 60107634 * q^24 + 612692400 * q^25 - 287465619 * q^26 + 33237874 * q^27 + 94647576 * q^28 + 582553712 * q^29 + 2028243566 * q^30 + 574615536 * q^31 + 2461710524 * q^32 + 1398060597 * q^33 + 1095877670 * q^34 + 1224276663 * q^35 + 5178232888 * q^36 + 1054414698 * q^37 + 168008610 * q^38 - 682764349 * q^39 - 3058491845 * q^40 + 1814310718 * q^41 - 7019276677 * q^42 + 322591648 * q^43 - 1892602784 * q^44 - 4067379516 * q^45 - 11163159263 * q^46 + 15760013 * q^47 - 3956976183 * q^48 + 10317761631 * q^49 + 4788432202 * q^50 + 4167009909 * q^51 - 16558761537 * q^52 + 16561990335 * q^53 - 22053068789 * q^54 - 2528406158 * q^55 - 2175101045 * q^56 + 10578500421 * q^57 + 10570052770 * q^58 + 12504156727 * q^59 + 27219988055 * q^60 + 12858649383 * q^61 + 29953793573 * q^62 + 21928998164 * q^63 + 107776677998 * q^64 + 75670521263 * q^65 + 70097909751 * q^66 + 34656499990 * q^67 + 134555459108 * q^68 + 60441944808 * q^69 + 144324418256 * q^70 - 4976323973 * q^71 + 184674525846 * q^72 + 80843930205 * q^73 + 147160169907 * q^74 + 106406736723 * q^75 + 89376434340 * q^76 + 187650162769 * q^77 + 217624188512 * q^78 + 33073221431 * q^79 + 220351536446 * q^80 + 373198656177 * q^81 + 417339951569 * q^82 + 180678060299 * q^83 + 622749162897 * q^84 + 295945248373 * q^85 + 223228441021 * q^86 + 351128502358 * q^87 + 327529458125 * q^88 + 229672691360 * q^89 + 878270116936 * q^90 + 269714836479 * q^91 + 470788684476 * q^92 + 255181811376 * q^93 + 556696972040 * q^94 + 455878930472 * q^95 + 1296231412687 * q^96 + 248534514476 * q^97 + 747851098165 * q^98 + 465588303306 * 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 $

$2$	−74.2508	−1.64073	−0.820364	−	0.571842i	$-0.806229\pi$
$2$	−74.2508	−1.64073	−0.820364	+	0.571842i	$0.806229\pi$
$3$	−125.019	−0.297037	−0.148518	−	0.988910i	$-0.547450\pi$
$3$	−125.019	−0.297037	−0.148518	+	0.988910i	$0.547450\pi$
$4$	3465.19	1.69199
$5$	−2224.90	−0.318402	−0.159201	−	0.987246i	$-0.550892\pi$
$5$	−2224.90	−0.318402	−0.159201	+	0.987246i	$0.550892\pi$
$6$	9282.79	0.487357
$7$	36712.6	0.825611	0.412806	−	0.910819i	$-0.364549\pi$
$7$	36712.6	0.825611	0.412806	+	0.910819i	$0.364549\pi$
$8$	−105227.	−1.13536
$9$	−161517.	−0.911769
$10$	165201.	0.522410
$11$	97623.0	0.182765	0.0913823	−	0.995816i	$-0.470871\pi$
$11$	97623.0	0.182765	0.0913823	+	0.995816i	$0.470871\pi$
$12$	−433216.	−0.502582
$13$	36165.9	0.0270154	0.0135077	−	0.999909i	$-0.495700\pi$
$13$	36165.9	0.0270154	0.0135077	+	0.999909i	$0.495700\pi$
$14$	−2.72594e6	−1.35460
$15$	278155.	0.0945770
$16$	716521.	0.170832
$17$	7.49913e6	1.28098	0.640489	−	0.767967i	$-0.278732\pi$
$17$	7.49913e6	1.28098	0.640489	+	0.767967i	$0.278732\pi$
$18$	1.19928e7	1.49596
$19$	1.27332e7	1.17976	0.589881	−	0.807490i	$-0.299175\pi$
$19$	1.27332e7	1.17976	0.589881	+	0.807490i	$0.299175\pi$
$20$	−7.70969e6	−0.538731
$21$	−4.58978e6	−0.245237
$22$	−7.24859e6	−0.299867
$23$	−6.88800e6	−0.223147	−0.111573	−	0.993756i	$-0.535589\pi$
$23$	−6.88800e6	−0.223147	−0.111573	+	0.993756i	$0.535589\pi$
$24$	1.31555e7	0.337244
$25$	−4.38780e7	−0.898620
$26$	−2.68535e6	−0.0443249
$27$	4.23396e7	0.567866
$28$	1.27216e8	1.39692
$29$	1.98083e8	1.79332	0.896661	−	0.442717i	$-0.145986\pi$
$29$	1.98083e8	1.79332	0.896661	+	0.442717i	$0.145986\pi$
$30$	−2.06533e7	−0.155175
$31$	−1.95252e7	−0.122492	−0.0612458	−	0.998123i	$-0.519507\pi$
$31$	−1.95252e7	−0.122492	−0.0612458	+	0.998123i	$0.519507\pi$
$32$	1.62304e8	0.855073
$33$	−1.22048e7	−0.0542879
$34$	−5.56817e8	−2.10174
$35$	−8.16818e7	−0.262876
$36$	−5.59687e8	−1.54270
$37$	6.25286e8	1.48241	0.741207	−	0.671277i	$-0.234254\pi$
$37$	6.25286e8	1.48241	0.741207	+	0.671277i	$0.234254\pi$
$38$	−9.45454e8	−1.93567
$39$	−4.52144e6	−0.00802457
$40$	2.34120e8	0.361501
$41$	−8.06280e8	−1.08686	−0.543431	−	0.839454i	$-0.682875\pi$
$41$	−8.06280e8	−1.08686	−0.543431	+	0.839454i	$0.682875\pi$
$42$	3.40795e8	0.402367
$43$	−1.10920e9	−1.15063	−0.575313	−	0.817933i	$-0.695120\pi$
$43$	−1.10920e9	−1.15063	−0.575313	+	0.817933i	$0.695120\pi$
$44$	3.38282e8	0.309235
$45$	3.59359e8	0.290309
$46$	5.11440e8	0.366123
$47$	−2.03935e9	−1.29704	−0.648522	−	0.761196i	$-0.724612\pi$
$47$	−2.03935e9	−1.29704	−0.648522	+	0.761196i	$0.724612\pi$
$48$	−8.95790e7	−0.0507434
$49$	−6.29513e8	−0.318366
$50$	3.25798e9	1.47439
$51$	−9.37537e8	−0.380498
$52$	1.25322e8	0.0457097
$53$	−2.64973e9	−0.870332	−0.435166	−	0.900350i	$-0.643310\pi$
$53$	−2.64973e9	−0.870332	−0.435166	+	0.900350i	$0.643310\pi$
$54$	−3.14375e9	−0.931713
$55$	−2.17201e8	−0.0581925
$56$	−3.86317e9	−0.937367
$57$	−1.59190e9	−0.350433
$58$	−1.47078e10	−2.94235
$59$	−4.32754e8	−0.0788052	−0.0394026	−	0.999223i	$-0.512545\pi$
$59$	−4.32754e8	−0.0788052	−0.0394026	+	0.999223i	$0.512545\pi$
$60$	9.63861e8	0.160023
$61$	1.95833e9	0.296874	0.148437	−	0.988922i	$-0.452576\pi$
$61$	1.95833e9	0.296874	0.148437	+	0.988922i	$0.452576\pi$
$62$	1.44976e9	0.200975
$63$	−5.92971e9	−0.752767
$64$	−1.35186e10	−1.57377
$65$	−8.04656e7	−0.00860174
$66$	9.06214e8	0.0890716
$67$	−1.66808e10	−1.50940	−0.754701	−	0.656069i	$-0.772218\pi$
$67$	−1.66808e10	−1.50940	−0.754701	+	0.656069i	$0.772218\pi$
$68$	2.59859e10	2.16740
$69$	8.61134e8	0.0662828
$70$	6.06494e9	0.431308
$71$	2.18337e10	1.43617	0.718085	−	0.695955i	$-0.245019\pi$
$71$	2.18337e10	1.43617	0.718085	+	0.695955i	$0.245019\pi$
$72$	1.69960e10	1.03519
$73$	−2.52460e10	−1.42533	−0.712667	−	0.701502i	$-0.752513\pi$
$73$	−2.52460e10	−1.42533	−0.712667	+	0.701502i	$0.752513\pi$
$74$	−4.64280e10	−2.43224
$75$	5.48559e9	0.266923
$76$	4.41231e10	1.99614
$77$	3.58399e9	0.150893
$78$	3.35721e8	0.0131661
$79$	2.87546e10	1.05138	0.525689	−	0.850677i	$-0.323808\pi$
$79$	2.87546e10	1.05138	0.525689	+	0.850677i	$0.323808\pi$
$80$	−1.59419e9	−0.0543931
$81$	2.33190e10	0.743092
$82$	5.98670e10	1.78325
$83$	5.22047e10	1.45472	0.727362	−	0.686254i	$-0.240746\pi$
$83$	5.22047e10	1.45472	0.727362	+	0.686254i	$0.240746\pi$
$84$	−1.59045e10	−0.414938
$85$	−1.66848e10	−0.407866
$86$	8.23592e10	1.88786
$87$	−2.47642e10	−0.532683
$88$	−1.02726e10	−0.207504
$89$	8.66409e10	1.64467	0.822334	−	0.569005i	$-0.192672\pi$
$89$	8.66409e10	1.64467	0.822334	+	0.569005i	$0.192672\pi$
$90$	−2.66827e10	−0.476317
$91$	1.32775e9	0.0223042
$92$	−2.38682e10	−0.377561
$93$	2.44103e9	0.0363845
$94$	1.51424e11	2.12809
$95$	−2.83302e10	−0.375638
$96$	−2.02911e10	−0.253988
$97$	−9.45804e10	−1.11830	−0.559148	−	0.829068i	$-0.688872\pi$
$97$	−9.45804e10	−1.11830	−0.559148	+	0.829068i	$0.688872\pi$
$98$	4.67419e10	0.522351
$99$	−1.57678e10	−0.166639
$100$	−1.52045e11	−1.52045
$101$	−2.84327e10	−0.269185	−0.134593	−	0.990901i	$-0.542973\pi$
$101$	−2.84327e10	−0.269185	−0.134593	+	0.990901i	$0.542973\pi$
$102$	6.96129e10	0.624293
$103$	−1.15927e10	−0.0985329
$103$	−1.15927e10	−0.0985329
$104$	−3.80565e9	−0.0306722
$105$	1.02118e10	0.0780839
$106$	1.96745e11	1.42798
$107$	1.48659e11	1.02466	0.512331	−	0.858788i	$-0.328782\pi$
$107$	1.48659e11	1.02466	0.512331	+	0.858788i	$0.328782\pi$
$108$	1.46715e11	0.960822
$109$	6.35639e10	0.395699	0.197849	−	0.980232i	$-0.436604\pi$
$109$	6.35639e10	0.395699	0.197849	+	0.980232i	$0.436604\pi$
$110$	1.61274e10	0.0954781
$111$	−7.81729e10	−0.440332
$112$	2.63053e10	0.141041
$113$	−2.14205e11	−1.09370	−0.546851	−	0.837230i	$-0.684174\pi$
$113$	−2.14205e11	−1.09370	−0.546851	+	0.837230i	$0.684174\pi$
$114$	1.18200e11	0.574965
$115$	1.53251e10	0.0710502
$116$	6.86395e11	3.03428
$117$	−5.84142e9	−0.0246318
$118$	3.21323e10	0.129298
$119$	2.75312e11	1.05759
$120$	−2.92696e10	−0.107379
$121$	−2.75781e11	−0.966597
$122$	−1.45408e11	−0.487089
$123$	1.00801e11	0.322838
$124$	−6.76585e10	−0.207254
$125$	2.06262e11	0.604524
$126$	4.40286e11	1.23509
$127$	3.48424e11	0.935810	0.467905	−	0.883779i	$-0.345009\pi$
$127$	3.48424e11	0.935810	0.467905	+	0.883779i	$0.345009\pi$
$128$	6.71371e11	1.72706
$129$	1.38672e11	0.341778
$130$	5.97464e9	0.0141131
$131$	−6.93946e11	−1.57157	−0.785784	−	0.618501i	$-0.787740\pi$
$131$	−6.93946e11	−1.57157	−0.785784	+	0.618501i	$0.787740\pi$
$132$	−4.22918e10	−0.0918543
$133$	4.67470e11	0.974025
$134$	1.23856e12	2.47652
$135$	−9.42013e10	−0.180809
$136$	−7.89114e11	−1.45437
$137$	7.05559e11	1.24902	0.624511	−	0.781016i	$-0.285298\pi$
$137$	7.05559e11	1.24902	0.624511	+	0.781016i	$0.285298\pi$
$138$	−6.39399e10	−0.108752
$139$	−7.91187e11	−1.29329	−0.646647	−	0.762789i	$-0.723829\pi$
$139$	−7.91187e11	−1.29329	−0.646647	+	0.762789i	$0.723829\pi$
$140$	−2.83043e11	−0.444783
$141$	2.54959e11	0.385270
$142$	−1.62117e12	−2.35636
$143$	3.53063e9	0.00493746
$144$	−1.15730e11	−0.155759
$145$	−4.40715e11	−0.570997
$146$	1.87454e12	2.33859
$147$	7.87013e10	0.0945664
$148$	2.16673e12	2.50822
$149$	−9.92060e11	−1.10666	−0.553329	−	0.832963i	$-0.686643\pi$
$149$	−9.92060e11	−1.10666	−0.553329	+	0.832963i	$0.686643\pi$
$150$	−4.07310e11	−0.437949
$151$	2.57255e11	0.266680	0.133340	−	0.991070i	$-0.457430\pi$
$151$	2.57255e11	0.266680	0.133340	+	0.991070i	$0.457430\pi$
$152$	−1.33989e12	−1.33946
$153$	−1.21124e12	−1.16796
$154$	−2.66114e11	−0.247574
$155$	4.34416e10	0.0390015
$156$	−1.56677e10	−0.0135775
$157$	2.26425e12	1.89442	0.947211	−	0.320611i	$-0.103888\pi$
$157$	2.26425e12	1.89442	0.947211	+	0.320611i	$0.103888\pi$
$158$	−2.13506e12	−1.72503
$159$	3.31268e11	0.258521
$160$	−3.61109e11	−0.272256
$161$	−2.52876e11	−0.184232
$162$	−1.73146e12	−1.21921
$163$	2.56181e12	1.74387	0.871936	−	0.489620i	$-0.162865\pi$
$163$	2.56181e12	1.74387	0.871936	+	0.489620i	$0.162865\pi$
$164$	−2.79391e12	−1.83896
$165$	2.71544e10	0.0172853
$166$	−3.87625e12	−2.38680
$167$	1.74747e12	1.04104	0.520522	−	0.853849i	$-0.325738\pi$
$167$	1.74747e12	1.04104	0.520522	+	0.853849i	$0.325738\pi$
$168$	4.82971e11	0.278433
$169$	−1.79085e12	−0.999270
$170$	1.23886e12	0.669196
$171$	−2.05664e12	−1.07567
$172$	−3.84359e12	−1.94684
$173$	3.80102e11	0.186486	0.0932430	−	0.995643i	$-0.470277\pi$
$173$	3.80102e11	0.186486	0.0932430	+	0.995643i	$0.470277\pi$
$174$	1.83876e12	0.873988
$175$	−1.61087e12	−0.741911
$176$	6.99489e10	0.0312220
$177$	5.41026e10	0.0234081
$178$	−6.43316e12	−2.69845
$179$	4.56947e12	1.85855	0.929274	−	0.369390i	$-0.120433\pi$
$179$	4.56947e12	1.85855	0.929274	+	0.369390i	$0.120433\pi$
$180$	1.24525e12	0.491198
$181$	4.54375e11	0.173853	0.0869265	−	0.996215i	$-0.472295\pi$
$181$	4.54375e11	0.173853	0.0869265	+	0.996215i	$0.472295\pi$
$182$	−9.85862e10	−0.0365952
$183$	−2.44829e11	−0.0881825
$184$	7.24807e11	0.253352
$185$	−1.39120e12	−0.472003
$186$	−1.81248e11	−0.0596971
$187$	7.32087e11	0.234118
$188$	−7.06675e12	−2.19458
$189$	1.55440e12	0.468837
$190$	2.10354e12	0.616319
$191$	−1.68867e12	−0.480687	−0.240343	−	0.970688i	$-0.577260\pi$
$191$	−1.68867e12	−0.480687	−0.240343	+	0.970688i	$0.577260\pi$
$192$	1.69009e12	0.467469
$193$	−5.20448e12	−1.39898	−0.699491	−	0.714641i	$-0.746590\pi$
$193$	−5.20448e12	−1.39898	−0.699491	+	0.714641i	$0.746590\pi$
$194$	7.02268e12	1.83482
$195$	1.00598e10	0.00255504
$196$	−2.18138e12	−0.538670
$197$	4.95183e12	1.18905	0.594526	−	0.804076i	$-0.297340\pi$
$197$	4.95183e12	1.18905	0.594526	+	0.804076i	$0.297340\pi$
$198$	1.17077e12	0.273409
$199$	1.80261e12	0.409459	0.204730	−	0.978819i	$-0.434368\pi$
$199$	1.80261e12	0.409459	0.204730	+	0.978819i	$0.434368\pi$
$200$	4.61716e12	1.02026
$201$	2.08542e12	0.448348
$202$	2.11115e12	0.441659
$203$	7.27214e12	1.48059
$204$	−3.24874e12	−0.643797
$205$	1.79389e12	0.346059
$206$	8.60771e11	0.161666
$207$	1.11253e12	0.203458
$208$	2.59137e10	0.00461509
$209$	1.24306e12	0.215619
$210$	−7.58235e11	−0.128114
$211$	8.38991e12	1.38103	0.690516	−	0.723317i	$-0.257383\pi$
$211$	8.38991e12	1.38103	0.690516	+	0.723317i	$0.257383\pi$
$212$	−9.18183e12	−1.47259
$213$	−2.72963e12	−0.426596
$214$	−1.10381e13	−1.68119
$215$	2.46786e12	0.366361
$216$	−4.45529e12	−0.644733
$217$	−7.16821e11	−0.101130
$218$	−4.71967e12	−0.649234
$219$	3.15624e12	0.423377
$220$	−7.52643e11	−0.0984610
$221$	2.71213e11	0.0346062
$222$	5.80440e12	0.722464
$223$	5.70322e12	0.692537	0.346269	−	0.938135i	$-0.387449\pi$
$223$	5.70322e12	0.692537	0.346269	+	0.938135i	$0.387449\pi$
$224$	5.95858e12	0.705958
$225$	7.08704e12	0.819334
$226$	1.59049e13	1.79447
$227$	5.03224e12	0.554140	0.277070	−	0.960850i	$-0.410637\pi$
$227$	5.03224e12	0.554140	0.277070	+	0.960850i	$0.410637\pi$
$228$	−5.51624e12	−0.592927
$229$	1.89417e12	0.198757	0.0993786	−	0.995050i	$-0.468315\pi$
$229$	1.89417e12	0.198757	0.0993786	+	0.995050i	$0.468315\pi$
$230$	−1.13790e12	−0.116574
$231$	−4.48068e11	−0.0448207
$232$	−2.08438e13	−2.03607
$233$	−1.66981e13	−1.59298	−0.796491	−	0.604651i	$-0.793313\pi$
$233$	−1.66981e13	−1.59298	−0.796491	+	0.604651i	$0.793313\pi$
$234$	4.33730e11	0.0404141
$235$	4.53736e12	0.412980
$236$	−1.49957e12	−0.133337
$237$	−3.59489e12	−0.312298
$238$	−2.04422e13	−1.73522
$239$	3.67245e12	0.304626	0.152313	−	0.988332i	$-0.451328\pi$
$239$	3.67245e12	0.304626	0.152313	+	0.988332i	$0.451328\pi$
$240$	1.99304e11	0.0161568
$241$	−1.67900e13	−1.33032	−0.665161	−	0.746700i	$-0.731637\pi$
$241$	−1.67900e13	−1.33032	−0.665161	+	0.746700i	$0.731637\pi$
$242$	2.04770e13	1.58592
$243$	−1.04157e13	−0.788592
$244$	6.78598e12	0.502306
$245$	1.40060e12	0.101368
$246$	−7.48453e12	−0.529690
$247$	4.60510e11	0.0318717
$248$	2.05459e12	0.139072
$249$	−6.52660e12	−0.432107
$250$	−1.53151e13	−0.991859
$251$	1.92130e12	0.121728	0.0608640	−	0.998146i	$-0.480614\pi$
$251$	1.92130e12	0.121728	0.0608640	+	0.998146i	$0.480614\pi$
$252$	−2.05476e13	−1.27367
$253$	−6.72427e11	−0.0407833
$254$	−2.58708e13	−1.53541
$255$	2.08592e12	0.121151
$256$	−2.21637e13	−1.25986
$257$	2.98489e10	0.00166072	0.000830360	−	1.00000i	$-0.499736\pi$
$257$	2.98489e10	0.00166072	0.000830360		1.00000i	$0.499736\pi$
$258$	−1.02965e13	−0.560765
$259$	2.29559e13	1.22390
$260$	−2.78828e11	−0.0145540
$261$	−3.19938e13	−1.63510
$262$	5.15260e13	2.57852
$263$	1.81252e13	0.888231	0.444116	−	0.895969i	$-0.353518\pi$
$263$	1.81252e13	0.888231	0.444116	+	0.895969i	$0.353518\pi$
$264$	1.28428e12	0.0616363
$265$	5.89539e12	0.277115
$266$	−3.47101e13	−1.59811
$267$	−1.08318e13	−0.488527
$268$	−5.78020e13	−2.55389
$269$	2.49369e13	1.07946	0.539728	−	0.841839i	$-0.318527\pi$
$269$	2.49369e13	1.07946	0.539728	+	0.841839i	$0.318527\pi$
$270$	6.99452e12	0.296659
$271$	1.86563e13	0.775343	0.387671	−	0.921798i	$-0.373280\pi$
$271$	1.86563e13	0.775343	0.387671	+	0.921798i	$0.373280\pi$
$272$	5.37329e12	0.218832
$273$	−1.65994e11	−0.00662518
$274$	−5.23883e13	−2.04930
$275$	−4.28350e12	−0.164236
$276$	2.98399e12	0.112150
$277$	5.11677e13	1.88520	0.942600	−	0.333925i	$-0.108373\pi$
$277$	5.11677e13	1.88520	0.942600	+	0.333925i	$0.108373\pi$
$278$	5.87463e13	2.12194
$279$	3.15366e12	0.111684
$280$	8.59516e12	0.298459
$281$	1.95709e13	0.666386	0.333193	−	0.942859i	$-0.391874\pi$
$281$	1.95709e13	0.666386	0.333193	+	0.942859i	$0.391874\pi$
$282$	−1.89309e13	−0.632122
$283$	−1.81516e13	−0.594414	−0.297207	−	0.954813i	$-0.596055\pi$
$283$	−1.81516e13	−0.594414	−0.297207	+	0.954813i	$0.596055\pi$
$284$	7.56578e13	2.42998
$285$	3.54182e12	0.111578
$286$	−2.62152e11	−0.00810103
$287$	−2.96006e13	−0.897327
$288$	−2.62148e13	−0.779629
$289$	2.19651e13	0.640906
$290$	3.27234e13	0.936850
$291$	1.18244e13	0.332175
$292$	−8.74822e13	−2.41165
$293$	7.09200e13	1.91865	0.959327	−	0.282296i	$-0.0910962\pi$
$293$	7.09200e13	1.91865	0.959327	+	0.282296i	$0.0910962\pi$
$294$	−5.84364e12	−0.155158
$295$	9.62834e11	0.0250917
$296$	−6.57973e13	−1.68307
$297$	4.13332e12	0.103786
$298$	7.36613e13	1.81572
$299$	−2.49111e11	−0.00602839
$300$	1.90086e13	0.451631
$301$	−4.07217e13	−0.949970
$302$	−1.91014e13	−0.437549
$303$	3.55464e12	0.0799579
$304$	9.12364e12	0.201541
$305$	−4.35709e12	−0.0945251
$306$	8.99355e13	1.91630
$307$	2.85362e13	0.597222	0.298611	−	0.954375i	$-0.403477\pi$
$307$	2.85362e13	0.597222	0.298611	+	0.954375i	$0.403477\pi$
$308$	1.24192e13	0.255308
$309$	1.44932e12	0.0292679
$310$	−3.22558e12	−0.0639909
$311$	1.73392e12	0.0337945	0.0168973	−	0.999857i	$-0.494621\pi$
$311$	1.73392e12	0.0337945	0.0168973	+	0.999857i	$0.494621\pi$
$312$	4.75780e11	0.00911079
$313$	−3.19303e13	−0.600772	−0.300386	−	0.953818i	$-0.597115\pi$
$313$	−3.19303e13	−0.600772	−0.300386	+	0.953818i	$0.597115\pi$
$314$	−1.68123e14	−3.10823
$315$	1.31930e13	0.239682
$316$	9.96403e13	1.77892
$317$	1.05908e14	1.85825	0.929124	−	0.369769i	$-0.120563\pi$
$317$	1.05908e14	1.85825	0.929124	+	0.369769i	$0.120563\pi$
$318$	−2.45969e13	−0.424162
$319$	1.93375e13	0.327756
$320$	3.00775e13	0.501092
$321$	−1.85852e13	−0.304362
$322$	1.87763e13	0.302275
$323$	9.54883e13	1.51125
$324$	8.08048e13	1.25730
$325$	−1.58689e12	−0.0242766
$326$	−1.90216e14	−2.86122
$327$	−7.94672e12	−0.117537
$328$	8.48428e13	1.23398
$329$	−7.48699e13	−1.07085
$330$	−2.01623e12	−0.0283605
$331$	4.90231e13	0.678183	0.339092	−	0.940753i	$-0.389880\pi$
$331$	4.90231e13	0.678183	0.339092	+	0.940753i	$0.389880\pi$
$332$	1.80899e14	2.46137
$333$	−1.00994e14	−1.35162
$334$	−1.29751e14	−1.70807
$335$	3.71130e13	0.480596
$336$	−3.28868e12	−0.0418943
$337$	1.02529e14	1.28494	0.642471	−	0.766310i	$-0.277909\pi$
$337$	1.02529e14	1.28494	0.642471	+	0.766310i	$0.277909\pi$
$338$	1.32972e14	1.63953
$339$	2.67798e13	0.324870
$340$	−5.78160e13	−0.690103
$341$	−1.90611e12	−0.0223871
$342$	1.52707e14	1.76488
$343$	−9.57038e13	−1.08846
$344$	1.16719e14	1.30638
$345$	−1.91594e12	−0.0211045
$346$	−2.82229e13	−0.305973
$347$	5.46090e13	0.582710	0.291355	−	0.956615i	$-0.405894\pi$
$347$	5.46090e13	0.582710	0.291355	+	0.956615i	$0.405894\pi$
$348$	−8.58127e13	−0.901292
$349$	−1.17773e14	−1.21760	−0.608801	−	0.793323i	$-0.708349\pi$
$349$	−1.17773e14	−1.21760	−0.608801	+	0.793323i	$0.708349\pi$
$350$	1.19609e14	1.21727
$351$	1.53125e12	0.0153411
$352$	1.58446e13	0.156277
$353$	1.69470e14	1.64563	0.822814	−	0.568310i	$-0.192403\pi$
$353$	1.69470e14	1.64563	0.822814	+	0.568310i	$0.192403\pi$
$354$	−4.01717e12	−0.0384062
$355$	−4.85777e13	−0.457279
$356$	3.00227e14	2.78276
$357$	−3.44194e13	−0.314143
$358$	−3.39287e14	−3.04937
$359$	−5.48090e13	−0.485101	−0.242550	−	0.970139i	$-0.577984\pi$
$359$	−5.48090e13	−0.485101	−0.242550	+	0.970139i	$0.577984\pi$
$360$	−3.78145e13	−0.329605
$361$	4.56452e13	0.391837
$362$	−3.37377e13	−0.285245
$363$	3.44780e13	0.287115
$364$	4.60089e12	0.0377384
$365$	5.61698e13	0.453829
$366$	1.81788e13	0.144683
$367$	−1.08462e14	−0.850382	−0.425191	−	0.905104i	$-0.639793\pi$
$367$	−1.08462e14	−0.850382	−0.425191	+	0.905104i	$0.639793\pi$
$368$	−4.93540e12	−0.0381206
$369$	1.30228e14	0.990968
$370$	1.03298e14	0.774428
$371$	−9.72786e13	−0.718556
$372$	8.45863e12	0.0615621
$373$	−1.58202e14	−1.13452	−0.567261	−	0.823538i	$-0.691997\pi$
$373$	−1.58202e14	−1.13452	−0.567261	+	0.823538i	$0.691997\pi$
$374$	−5.43581e13	−0.384123
$375$	−2.57867e13	−0.179566
$376$	2.14596e14	1.47261
$377$	7.16386e12	0.0484473
$378$	−1.15415e14	−0.769233
$379$	6.72598e13	0.441814	0.220907	−	0.975295i	$-0.429098\pi$
$379$	6.72598e13	0.441814	0.220907	+	0.975295i	$0.429098\pi$
$380$	−9.81694e13	−0.635574
$381$	−4.35598e13	−0.277970
$382$	1.25385e14	0.788676
$383$	−1.24584e14	−0.772448	−0.386224	−	0.922405i	$-0.626221\pi$
$383$	−1.24584e14	−0.772448	−0.386224	+	0.922405i	$0.626221\pi$
$384$	−8.39343e13	−0.513001
$385$	−7.97402e12	−0.0480444
$386$	3.86437e14	2.29535
$387$	1.79155e14	1.04911
$388$	−3.27739e14	−1.89214
$389$	−1.09005e14	−0.620473	−0.310236	−	0.950659i	$-0.600408\pi$
$389$	−1.09005e14	−0.620473	−0.310236	+	0.950659i	$0.600408\pi$
$390$	−7.46945e11	−0.00419212
$391$	−5.16540e13	−0.285846
$392$	6.62420e13	0.361460
$393$	8.67566e13	0.466814
$394$	−3.67677e14	−1.95091
$395$	−6.39762e13	−0.334760
$396$	−5.46383e13	−0.281951
$397$	−1.29463e14	−0.658867	−0.329433	−	0.944179i	$-0.606858\pi$
$397$	−1.29463e14	−0.658867	−0.329433	+	0.944179i	$0.606858\pi$
$398$	−1.33846e14	−0.671811
$399$	−5.84428e13	−0.289321
$400$	−3.14395e13	−0.153513
$401$	−2.12436e14	−1.02314	−0.511569	−	0.859242i	$-0.670936\pi$
$401$	−2.12436e14	−1.02314	−0.511569	+	0.859242i	$0.670936\pi$
$402$	−1.54844e14	−0.735617
$403$	−7.06148e11	−0.00330916
$404$	−9.85248e13	−0.455458
$405$	−5.18824e13	−0.236602
$406$	−5.39963e14	−2.42924
$407$	6.10423e13	0.270933
$408$	9.86546e13	0.432003
$409$	4.20525e14	1.81683	0.908413	−	0.418073i	$-0.137294\pi$
$409$	4.20525e14	1.81683	0.908413	+	0.418073i	$0.137294\pi$
$410$	−1.33198e14	−0.567788
$411$	−8.82085e13	−0.371006
$412$	−4.01710e13	−0.166716
$413$	−1.58875e13	−0.0650625
$414$	−8.26063e13	−0.333819
$415$	−1.16150e14	−0.463186
$416$	5.86986e12	0.0231001
$417$	9.89136e13	0.384156
$418$	−9.22980e13	−0.353772
$419$	−2.46200e14	−0.931344	−0.465672	−	0.884957i	$-0.654187\pi$
$419$	−2.46200e14	−0.931344	−0.465672	+	0.884957i	$0.654187\pi$
$420$	3.53858e13	0.132117
$421$	−5.71450e13	−0.210585	−0.105292	−	0.994441i	$-0.533578\pi$
$421$	−5.71450e13	−0.210585	−0.105292	+	0.994441i	$0.533578\pi$
$422$	−6.22958e14	−2.26590
$423$	3.29391e14	1.18260
$424$	2.78825e14	0.988141
$425$	−3.29047e14	−1.15111
$426$	2.02678e14	0.699927
$427$	7.18954e13	0.245102
$428$	5.15131e14	1.73371
$429$	−4.41397e11	−0.00146661
$430$	−1.83241e14	−0.601099
$431$	−5.35576e14	−1.73459	−0.867293	−	0.497798i	$-0.834142\pi$
$431$	−5.35576e14	−1.73459	−0.867293	+	0.497798i	$0.834142\pi$
$432$	3.03372e13	0.0970096
$433$	2.72944e14	0.861766	0.430883	−	0.902408i	$-0.358202\pi$
$433$	2.72944e14	0.861766	0.430883	+	0.902408i	$0.358202\pi$
$434$	5.32246e13	0.165928
$435$	5.50979e13	0.169607
$436$	2.20261e14	0.669517
$437$	−8.77066e13	−0.263260
$438$	−2.34353e14	−0.694646
$439$	4.97715e13	0.145689	0.0728444	−	0.997343i	$-0.476792\pi$
$439$	4.97715e13	0.145689	0.0728444	+	0.997343i	$0.476792\pi$
$440$	2.28555e13	0.0660696
$441$	1.01677e14	0.290276
$442$	−2.01378e13	−0.0567793
$443$	2.29800e14	0.639927	0.319964	−	0.947430i	$-0.396329\pi$
$443$	2.29800e14	0.639927	0.319964	+	0.947430i	$0.396329\pi$
$444$	−2.70884e14	−0.745035
$445$	−1.92767e14	−0.523665
$446$	−4.23469e14	−1.13627
$447$	1.24027e14	0.328718
$448$	−4.96303e14	−1.29933
$449$	−1.67192e14	−0.432375	−0.216187	−	0.976352i	$-0.569362\pi$
$449$	−1.67192e14	−0.432375	−0.216187	+	0.976352i	$0.569362\pi$
$450$	−5.26219e14	−1.34430
$451$	−7.87115e13	−0.198640
$452$	−7.42262e14	−1.85053
$453$	−3.21618e13	−0.0792137
$454$	−3.73648e14	−0.909193
$455$	−2.95410e12	−0.00710170
$456$	1.67512e14	0.397868
$457$	1.94617e14	0.456712	0.228356	−	0.973578i	$-0.426665\pi$
$457$	1.94617e14	0.456712	0.228356	+	0.973578i	$0.426665\pi$
$458$	−1.40643e14	−0.326106
$459$	3.17510e14	0.727424
$460$	5.31044e13	0.120216
$461$	2.41266e14	0.539685	0.269842	−	0.962905i	$-0.413028\pi$
$461$	2.41266e14	0.539685	0.269842	+	0.962905i	$0.413028\pi$
$462$	3.32695e13	0.0735385
$463$	−1.23175e13	−0.0269046	−0.0134523	−	0.999910i	$-0.504282\pi$
$463$	−1.23175e13	−0.0269046	−0.0134523	+	0.999910i	$0.504282\pi$
$464$	1.41931e14	0.306357
$465$	−5.43104e12	−0.0115849
$466$	1.23985e15	2.61365
$467$	−3.10141e14	−0.646125	−0.323062	−	0.946378i	$-0.604712\pi$
$467$	−3.10141e14	−0.646125	−0.323062	+	0.946378i	$0.604712\pi$
$468$	−2.02416e13	−0.0416767
$469$	−6.12394e14	−1.24618
$470$	−3.36902e14	−0.677588
$471$	−2.83075e14	−0.562713
$472$	4.55376e13	0.0894724
$473$	−1.08284e14	−0.210294
$474$	2.66923e14	0.512396
$475$	−5.58709e14	−1.06016
$476$	9.54010e14	1.78943
$477$	4.27977e14	0.793542
$478$	−2.72682e14	−0.499809
$479$	7.78601e14	1.41081	0.705407	−	0.708803i	$-0.250764\pi$
$479$	7.78601e14	1.41081	0.705407	+	0.708803i	$0.250764\pi$
$480$	4.51456e13	0.0808702
$481$	2.26141e13	0.0400480
$482$	1.24667e15	2.18270
$483$	3.16144e13	0.0547238
$484$	−9.55635e14	−1.63547
$485$	2.10432e14	0.356067
$486$	7.73371e14	1.29386
$487$	7.13562e14	1.18038	0.590191	−	0.807264i	$-0.299053\pi$
$487$	7.13562e14	1.18038	0.590191	+	0.807264i	$0.299053\pi$
$488$	−2.06070e14	−0.337059
$489$	−3.20275e14	−0.517994
$490$	−1.03996e14	−0.166317
$491$	3.64687e14	0.576729	0.288364	−	0.957521i	$-0.406889\pi$
$491$	3.64687e14	0.576729	0.288364	+	0.957521i	$0.406889\pi$
$492$	3.49293e14	0.546238
$493$	1.48545e15	2.29721
$494$	−3.41932e13	−0.0522928
$495$	3.50817e13	0.0530582
$496$	−1.39902e13	−0.0209255
$497$	8.01571e14	1.18572
$498$	4.84606e14	0.708969
$499$	2.20747e14	0.319406	0.159703	−	0.987165i	$-0.448946\pi$
$499$	2.20747e14	0.319406	0.159703	+	0.987165i	$0.448946\pi$
$500$	7.14735e14	1.02285
$501$	−2.18467e14	−0.309228
$502$	−1.42658e14	−0.199722
$503$	3.75693e14	0.520247	0.260123	−	0.965575i	$-0.416237\pi$
$503$	3.75693e14	0.520247	0.260123	+	0.965575i	$0.416237\pi$
$504$	6.23968e14	0.854663
$505$	6.32599e13	0.0857090
$506$	4.99283e13	0.0669143
$507$	2.23891e14	0.296820
$508$	1.20735e15	1.58338
$509$	1.04858e15	1.36035	0.680177	−	0.733048i	$-0.261903\pi$
$509$	1.04858e15	1.36035	0.680177	+	0.733048i	$0.261903\pi$
$510$	−1.54882e14	−0.198776
$511$	−9.26846e14	−1.17677
$512$	2.70708e14	0.340030
$513$	5.39120e14	0.669946
$514$	−2.21631e12	−0.00272479
$515$	2.57927e13	0.0313730
$516$	4.80524e14	0.578285
$517$	−1.99088e14	−0.237054
$518$	−1.70449e15	−2.00808
$519$	−4.75201e13	−0.0553932
$520$	8.46718e12	0.00976609
$521$	6.58622e14	0.751672	0.375836	−	0.926686i	$-0.377356\pi$
$521$	6.58622e14	0.751672	0.375836	+	0.926686i	$0.377356\pi$
$522$	2.37557e15	2.68275
$523$	−8.27061e14	−0.924226	−0.462113	−	0.886821i	$-0.652909\pi$
$523$	−8.27061e14	−0.924226	−0.462113	+	0.886821i	$0.652909\pi$
$524$	−2.40465e15	−2.65907
$525$	2.01390e14	0.220375
$526$	−1.34581e15	−1.45735
$527$	−1.46422e14	−0.156909
$528$	−8.74497e12	−0.00927410
$529$	−9.05365e14	−0.950206
$530$	−4.37738e14	−0.454670
$531$	6.98972e13	0.0718522
$532$	1.61987e15	1.64804
$533$	−2.91599e13	−0.0293620
$534$	8.04270e14	0.801540
$535$	−3.30751e14	−0.326254
$536$	1.75527e15	1.71372
$537$	−5.71272e14	−0.552058
$538$	−1.85159e15	−1.77109
$539$	−6.14549e13	−0.0581860
$540$	−3.26425e14	−0.305927
$541$	−6.57955e14	−0.610395	−0.305198	−	0.952289i	$-0.598723\pi$
$541$	−6.57955e14	−0.610395	−0.305198	+	0.952289i	$0.598723\pi$
$542$	−1.38524e15	−1.27213
$543$	−5.68056e13	−0.0516407
$544$	1.21714e15	1.09533
$545$	−1.41423e14	−0.125991
$546$	1.23252e13	0.0108701
$547$	−1.68639e15	−1.47240	−0.736201	−	0.676763i	$-0.763382\pi$
$547$	−1.68639e15	−1.47240	−0.736201	+	0.676763i	$0.763382\pi$
$548$	2.44489e15	2.11333
$549$	−3.16304e14	−0.270680
$550$	3.18053e14	0.269467
$551$	2.52224e15	2.11569
$552$	−9.06149e13	−0.0752549
$553$	1.05566e15	0.868030
$554$	−3.79925e15	−3.09310
$555$	1.73927e14	0.140202
$556$	−2.74161e15	−2.18824
$557$	−1.46483e15	−1.15767	−0.578833	−	0.815446i	$-0.696492\pi$
$557$	−1.46483e15	−1.15767	−0.578833	+	0.815446i	$0.696492\pi$
$558$	−2.34162e14	−0.183243
$559$	−4.01153e13	−0.0310846
$560$	−5.85267e13	−0.0449076
$561$	−9.15251e13	−0.0695416
$562$	−1.45315e15	−1.09336
$563$	9.78865e14	0.729334	0.364667	−	0.931138i	$-0.381183\pi$
$563$	9.78865e14	0.729334	0.364667	+	0.931138i	$0.381183\pi$
$564$	8.83480e14	0.651871
$565$	4.76585e14	0.348236
$566$	1.34777e15	0.975272
$567$	8.56101e14	0.613505
$568$	−2.29750e15	−1.63057
$569$	−1.32961e15	−0.934557	−0.467279	−	0.884110i	$-0.654766\pi$
$569$	−1.32961e15	−0.934557	−0.467279	+	0.884110i	$0.654766\pi$
$570$	−2.62983e14	−0.183070
$571$	−1.19787e15	−0.825872	−0.412936	−	0.910760i	$-0.635497\pi$
$571$	−1.19787e15	−0.825872	−0.412936	+	0.910760i	$0.635497\pi$
$572$	1.22343e13	0.00835412
$573$	2.11117e14	0.142782
$574$	2.19787e15	1.47227
$575$	3.02231e14	0.200524
$576$	2.18349e15	1.43492
$577$	2.69986e15	1.75741	0.878707	−	0.477361i	$-0.158407\pi$
$577$	2.69986e15	1.75741	0.878707	+	0.477361i	$0.158407\pi$
$578$	−1.63093e15	−1.05155
$579$	6.50661e14	0.415549
$580$	−1.52716e15	−0.966119
$581$	1.91657e15	1.20104
$582$	−8.77971e14	−0.545009
$583$	−2.58675e14	−0.159066
$584$	2.65657e15	1.61827
$585$	1.29966e13	0.00784280
$586$	−5.26587e15	−3.14799
$587$	5.12032e14	0.303241	0.151620	−	0.988439i	$-0.451551\pi$
$587$	5.12032e14	0.303241	0.151620	+	0.988439i	$0.451551\pi$
$588$	2.72715e14	0.160005
$589$	−2.48619e14	−0.144511
$590$	−7.14912e13	−0.0411686
$591$	−6.19074e14	−0.353193
$592$	4.48031e14	0.253244
$593$	1.38640e15	0.776402	0.388201	−	0.921575i	$-0.373097\pi$
$593$	1.38640e15	0.776402	0.388201	+	0.921575i	$0.373097\pi$
$594$	−3.06902e14	−0.170284
$595$	−6.12542e14	−0.336738
$596$	−3.43768e15	−1.87245
$597$	−2.25362e14	−0.121625
$598$	1.84967e13	0.00989095
$599$	1.87139e15	0.991553	0.495776	−	0.868450i	$-0.334884\pi$
$599$	1.87139e15	0.991553	0.495776	+	0.868450i	$0.334884\pi$
$600$	−5.77235e14	−0.303055
$601$	1.07164e15	0.557493	0.278746	−	0.960365i	$-0.410081\pi$
$601$	1.07164e15	0.557493	0.278746	+	0.960365i	$0.410081\pi$
$602$	3.02362e15	1.55864
$603$	2.69423e15	1.37623
$604$	8.91436e14	0.451218
$605$	6.13586e14	0.307766
$606$	−2.63935e14	−0.131189
$607$	−3.09134e15	−1.52268	−0.761341	−	0.648352i	$-0.775458\pi$
$607$	−3.09134e15	−1.52268	−0.761341	+	0.648352i	$0.775458\pi$
$608$	2.06665e15	1.00878
$609$	−9.09159e14	−0.439789
$610$	3.23517e14	0.155090
$611$	−7.37552e13	−0.0350401
$612$	−4.19717e15	−1.97617
$613$	−1.37626e15	−0.642197	−0.321098	−	0.947046i	$-0.604052\pi$
$613$	−1.37626e15	−0.642197	−0.321098	+	0.947046i	$0.604052\pi$
$614$	−2.11884e15	−0.979879
$615$	−2.24271e14	−0.102792
$616$	−3.77134e14	−0.171318
$617$	−6.80723e14	−0.306480	−0.153240	−	0.988189i	$-0.548971\pi$
$617$	−6.80723e14	−0.306480	−0.153240	+	0.988189i	$0.548971\pi$
$618$	−1.07613e14	−0.0480207
$619$	1.90542e15	0.842737	0.421368	−	0.906890i	$-0.361550\pi$
$619$	1.90542e15	0.842737	0.421368	+	0.906890i	$0.361550\pi$
$620$	1.50533e14	0.0659900
$621$	−2.91635e14	−0.126717
$622$	−1.28745e14	−0.0554476
$623$	3.18081e15	1.35786
$624$	−3.23971e12	−0.00137085
$625$	1.68357e15	0.706139
$626$	2.37085e15	0.985702
$627$	−1.55406e14	−0.0640467
$628$	7.84606e15	3.20534
$629$	4.68910e15	1.89894
$630$	−9.79592e14	−0.393253
$631$	−4.80602e14	−0.191260	−0.0956299	−	0.995417i	$-0.530487\pi$
$631$	−4.80602e14	−0.191260	−0.0956299	+	0.995417i	$0.530487\pi$
$632$	−3.02578e15	−1.19369
$633$	−1.04890e15	−0.410218
$634$	−7.86377e15	−3.04888
$635$	−7.75208e14	−0.297963
$636$	1.14791e15	0.437414
$637$	−2.27669e13	−0.00860078
$638$	−1.43582e15	−0.537758
$639$	−3.52651e15	−1.30946
$640$	−1.49373e15	−0.549899
$641$	−2.98917e15	−1.09102	−0.545508	−	0.838106i	$-0.683663\pi$
$641$	−2.98917e15	−1.09102	−0.545508	+	0.838106i	$0.683663\pi$
$642$	1.37997e15	0.499375
$643$	2.39422e14	0.0859021	0.0429511	−	0.999077i	$-0.486324\pi$
$643$	2.39422e14	0.0859021	0.0429511	+	0.999077i	$0.486324\pi$
$644$	−8.76264e14	−0.311719
$645$	−3.08531e14	−0.108823
$646$	−7.09008e15	−2.47955
$647$	1.57349e15	0.545622	0.272811	−	0.962068i	$-0.412047\pi$
$647$	1.57349e15	0.545622	0.272811	+	0.962068i	$0.412047\pi$
$648$	−2.45380e15	−0.843678
$649$	−4.22467e13	−0.0144028
$650$	1.17828e14	0.0398313
$651$	8.96165e13	0.0300395
$652$	8.87714e15	2.95061
$653$	1.03655e15	0.341641	0.170820	−	0.985302i	$-0.445358\pi$
$653$	1.03655e15	0.341641	0.170820	+	0.985302i	$0.445358\pi$
$654$	5.90051e14	0.192847
$655$	1.54396e15	0.500390
$656$	−5.77717e14	−0.185671
$657$	4.07766e15	1.29958
$658$	5.55916e15	1.75698
$659$	−1.96027e14	−0.0614393	−0.0307196	−	0.999528i	$-0.509780\pi$
$659$	−1.96027e14	−0.0614393	−0.0307196	+	0.999528i	$0.509780\pi$
$660$	9.40950e13	0.0292466
$661$	2.77323e15	0.854826	0.427413	−	0.904056i	$-0.359425\pi$
$661$	2.77323e15	0.854826	0.427413	+	0.904056i	$0.359425\pi$
$662$	−3.64001e15	−1.11271
$663$	−3.39069e13	−0.0102793
$664$	−5.49337e15	−1.65164
$665$	−1.04007e15	−0.310131
$666$	7.49892e15	2.21764
$667$	−1.36440e15	−0.400174
$668$	6.05531e15	1.76143
$669$	−7.13013e14	−0.205709
$670$	−2.75567e15	−0.788526
$671$	1.91178e14	0.0542580
$672$	−7.44938e14	−0.209696
$673$	−1.02611e15	−0.286491	−0.143246	−	0.989687i	$-0.545754\pi$
$673$	−1.02611e15	−0.286491	−0.143246	+	0.989687i	$0.545754\pi$
$674$	−7.61288e15	−2.10824
$675$	−1.85777e15	−0.510296
$676$	−6.20564e15	−1.69075
$677$	2.04307e15	0.552137	0.276068	−	0.961138i	$-0.410968\pi$
$677$	2.04307e15	0.552137	0.276068	+	0.961138i	$0.410968\pi$
$678$	−1.98842e15	−0.533023
$679$	−3.47229e15	−0.923278
$680$	1.75570e15	0.463075
$681$	−6.29128e14	−0.164600
$682$	1.41530e14	0.0367312
$683$	4.47444e15	1.15193	0.575963	−	0.817476i	$-0.304627\pi$
$683$	4.47444e15	1.15193	0.575963	+	0.817476i	$0.304627\pi$
$684$	−7.12664e15	−1.82002
$685$	−1.56980e15	−0.397691
$686$	7.10609e15	1.78586
$687$	−2.36807e14	−0.0590382
$688$	−7.94767e14	−0.196564
$689$	−9.58301e13	−0.0235124
$690$	1.42260e14	0.0346268
$691$	−5.42687e14	−0.131045	−0.0655225	−	0.997851i	$-0.520871\pi$
$691$	−5.42687e14	−0.131045	−0.0655225	+	0.997851i	$0.520871\pi$
$692$	1.31712e15	0.315532
$693$	−5.78876e14	−0.137579
$694$	−4.05477e15	−0.956068
$695$	1.76031e15	0.411787
$696$	2.60588e15	0.604788
$697$	−6.04640e15	−1.39225
$698$	8.74473e15	1.99775
$699$	2.08759e15	0.473174
$700$	−5.58198e15	−1.25530
$701$	4.22518e15	0.942749	0.471375	−	0.881933i	$-0.343758\pi$
$701$	4.22518e15	0.942749	0.471375	+	0.881933i	$0.343758\pi$
$702$	−1.13697e14	−0.0251706
$703$	7.96192e15	1.74889
$704$	−1.31973e15	−0.287630
$705$	−5.67257e14	−0.122670
$706$	−1.25833e16	−2.70003
$707$	−1.04384e15	−0.222242
$708$	1.87476e14	0.0396061
$709$	−5.82239e14	−0.122053	−0.0610263	−	0.998136i	$-0.519437\pi$
$709$	−5.82239e14	−0.122053	−0.0610263	+	0.998136i	$0.519437\pi$
$710$	3.60694e15	0.750270
$711$	−4.64437e15	−0.958614
$712$	−9.11700e15	−1.86729
$713$	1.34490e14	0.0273336
$714$	2.55567e15	0.515424
$715$	−7.85529e12	−0.00157209
$716$	1.58341e16	3.14464
$717$	−4.59127e14	−0.0904853
$718$	4.06961e15	0.795918
$719$	9.84105e14	0.191000	0.0954998	−	0.995429i	$-0.469555\pi$
$719$	9.84105e14	0.191000	0.0954998	+	0.995429i	$0.469555\pi$
$720$	2.57488e14	0.0495940
$721$	−4.25599e14	−0.0813499
$722$	−3.38920e15	−0.642898
$723$	2.09908e15	0.395155
$724$	1.57449e15	0.294157
$725$	−8.69148e15	−1.61152
$726$	−2.56002e15	−0.471077
$727$	−7.65034e15	−1.39714	−0.698572	−	0.715539i	$-0.746181\pi$
$727$	−7.65034e15	−1.39714	−0.698572	+	0.715539i	$0.746181\pi$
$728$	−1.39715e14	−0.0253234
$729$	−2.82873e15	−0.508851
$730$	−4.17065e15	−0.744609
$731$	−8.31805e15	−1.47393
$732$	−8.48379e14	−0.149204
$733$	9.36340e15	1.63441	0.817206	−	0.576346i	$-0.195522\pi$
$733$	9.36340e15	1.63441	0.817206	+	0.576346i	$0.195522\pi$
$734$	8.05339e15	1.39524
$735$	−1.75102e14	−0.0301101
$736$	−1.11795e15	−0.190807
$737$	−1.62843e15	−0.275865
$738$	−9.66955e15	−1.62591
$739$	−3.33351e15	−0.556362	−0.278181	−	0.960529i	$-0.589731\pi$
$739$	−3.33351e15	−0.556362	−0.278181	+	0.960529i	$0.589731\pi$
$740$	−4.82076e15	−0.798622
$741$	−5.75726e13	−0.00946708
$742$	7.22302e15	1.17895
$743$	1.01744e16	1.64843	0.824214	−	0.566278i	$-0.191617\pi$
$743$	1.01744e16	1.64843	0.824214	+	0.566278i	$0.191617\pi$
$744$	−2.56863e14	−0.0413096
$745$	2.20723e15	0.352362
$746$	1.17466e16	1.86144
$747$	−8.43196e15	−1.32637
$748$	2.53682e15	0.396124
$749$	5.45765e15	0.845972
$750$	1.91468e15	0.294619
$751$	3.55113e15	0.542433	0.271217	−	0.962518i	$-0.412574\pi$
$751$	3.55113e15	0.542433	0.271217	+	0.962518i	$0.412574\pi$
$752$	−1.46124e15	−0.221576
$753$	−2.40200e14	−0.0361577
$754$	−5.31923e14	−0.0794888
$755$	−5.72365e14	−0.0849112
$756$	5.38627e15	0.793265
$757$	6.53592e15	0.955607	0.477803	−	0.878467i	$-0.341433\pi$
$757$	6.53592e15	0.955607	0.477803	+	0.878467i	$0.341433\pi$
$758$	−4.99410e15	−0.724897
$759$	8.40664e13	0.0121141
$760$	2.98111e15	0.426485
$761$	−5.09380e15	−0.723479	−0.361739	−	0.932279i	$-0.617817\pi$
$761$	−5.09380e15	−0.723479	−0.361739	+	0.932279i	$0.617817\pi$
$762$	3.23435e15	0.456073
$763$	2.33360e15	0.326694
$764$	−5.85157e15	−0.813315
$765$	2.69488e15	0.371879
$766$	9.25047e15	1.26738
$767$	−1.56510e13	−0.00212895
$768$	2.77089e15	0.374225
$769$	−3.01083e15	−0.403730	−0.201865	−	0.979413i	$-0.564700\pi$
$769$	−3.01083e15	−0.403730	−0.201865	+	0.979413i	$0.564700\pi$
$770$	5.92077e14	0.0788278
$771$	−3.73169e12	−0.000493295 0
$772$	−1.80345e16	−2.36706
$773$	−1.21567e16	−1.58427	−0.792133	−	0.610348i	$-0.791029\pi$
$773$	−1.21567e16	−1.58427	−0.792133	+	0.610348i	$0.791029\pi$
$774$	−1.33024e16	−1.72130
$775$	8.56726e14	0.110073
$776$	9.95246e15	1.26967
$777$	−2.86993e15	−0.363543
$778$	8.09369e15	1.01803
$779$	−1.02666e16	−1.28224
$780$	3.48589e13	0.00432309
$781$	2.13147e15	0.262481
$782$	3.83536e15	0.468995
$783$	8.38675e15	1.01837
$784$	−4.51059e14	−0.0543870
$785$	−5.03773e15	−0.603187
$786$	−6.44175e15	−0.765914
$787$	−4.39746e15	−0.519208	−0.259604	−	0.965715i	$-0.583592\pi$
$787$	−4.39746e15	−0.519208	−0.259604	+	0.965715i	$0.583592\pi$
$788$	1.71590e16	2.01186
$789$	−2.26600e15	−0.263838
$790$	4.75028e15	0.549251
$791$	−7.86403e15	−0.902973
$792$	1.65920e15	0.189196
$793$	7.08249e13	0.00802016
$794$	9.61273e15	1.08102
$795$	−7.37038e14	−0.0823134
$796$	6.24639e15	0.692799
$797$	−1.42524e15	−0.156988	−0.0784939	−	0.996915i	$-0.525011\pi$
$797$	−1.42524e15	−0.156988	−0.0784939	+	0.996915i	$0.525011\pi$
$798$	4.33943e15	0.474697
$799$	−1.52934e16	−1.66148
$800$	−7.12155e15	−0.768386
$801$	−1.39940e16	−1.49956
$802$	1.57736e16	1.67869
$803$	−2.46459e15	−0.260501
$804$	7.22637e15	0.758599
$805$	5.62624e14	0.0586599
$806$	5.24321e13	0.00542943
$807$	−3.11760e15	−0.320638
$808$	2.99190e15	0.305622
$809$	−1.66750e16	−1.69180	−0.845901	−	0.533341i	$-0.820936\pi$
$809$	−1.66750e16	−1.69180	−0.845901	+	0.533341i	$0.820936\pi$
$810$	3.85231e15	0.388199
$811$	−1.38881e16	−1.39004	−0.695021	−	0.718990i	$-0.744605\pi$
$811$	−1.38881e16	−1.39004	−0.695021	+	0.718990i	$0.744605\pi$
$812$	2.51993e16	2.50513
$813$	−2.33239e15	−0.230305
$814$	−4.53244e15	−0.444527
$815$	−5.69976e15	−0.555251
$816$	−6.71765e14	−0.0650012
$817$	−1.41237e16	−1.35746
$818$	−3.12243e16	−2.98092
$819$	−2.14454e14	−0.0203363
$820$	6.21617e15	0.585527
$821$	1.90001e16	1.77774	0.888868	−	0.458163i	$-0.151492\pi$
$821$	1.90001e16	1.77774	0.888868	+	0.458163i	$0.151492\pi$
$822$	6.54956e15	0.608719
$823$	−7.81007e15	−0.721034	−0.360517	−	0.932753i	$-0.617400\pi$
$823$	−7.81007e15	−0.721034	−0.360517	+	0.932753i	$0.617400\pi$
$824$	1.21987e15	0.111870
$825$	5.35520e14	0.0487842
$826$	1.17966e15	0.106750
$827$	5.51553e15	0.495801	0.247900	−	0.968786i	$-0.420259\pi$
$827$	5.51553e15	0.495801	0.247900	+	0.968786i	$0.420259\pi$
$828$	3.85513e15	0.344248
$829$	9.99510e15	0.886619	0.443310	−	0.896368i	$-0.353804\pi$
$829$	9.99510e15	0.886619	0.443310	+	0.896368i	$0.353804\pi$
$830$	8.62425e15	0.759962
$831$	−6.39695e15	−0.559974
$832$	−4.88913e14	−0.0425161
$833$	−4.72080e15	−0.407820
$834$	−7.34442e15	−0.630296
$835$	−3.88794e15	−0.331470
$836$	4.30743e15	0.364824
$837$	−8.26689e14	−0.0695588
$838$	1.82805e16	1.52808
$839$	1.95569e16	1.62409	0.812045	−	0.583595i	$-0.198354\pi$
$839$	1.95569e16	1.62409	0.812045	+	0.583595i	$0.198354\pi$
$840$	−1.07456e15	−0.0886534
$841$	2.70364e16	2.21601
$842$	4.24306e15	0.345512
$843$	−2.44674e15	−0.197941
$844$	2.90726e16	2.33669
$845$	3.98446e15	0.318169
$846$	−2.44575e16	−1.94033
$847$	−1.01246e16	−0.798034
$848$	−1.89859e15	−0.148680
$849$	2.26930e15	0.176563
$850$	2.44320e16	1.88866
$851$	−4.30697e15	−0.330795
$852$	−9.45869e15	−0.721794
$853$	9.76526e15	0.740396	0.370198	−	0.928953i	$-0.379290\pi$
$853$	9.76526e15	0.740396	0.370198	+	0.928953i	$0.379290\pi$
$854$	−5.33829e15	−0.402146
$855$	4.57581e15	0.342495
$856$	−1.56430e16	−1.16336
$857$	3.22774e14	0.0238509	0.0119254	−	0.999929i	$-0.496204\pi$
$857$	3.22774e14	0.0238509	0.0119254	+	0.999929i	$0.496204\pi$
$858$	3.27741e13	0.00240630
$859$	−1.25952e16	−0.918843	−0.459421	−	0.888218i	$-0.651943\pi$
$859$	−1.25952e16	−0.918843	−0.459421	+	0.888218i	$0.651943\pi$
$860$	8.55161e15	0.619878
$861$	3.70065e15	0.266539
$862$	3.97670e16	2.84598
$863$	−1.82813e16	−1.30002	−0.650008	−	0.759927i	$-0.725235\pi$
$863$	−1.82813e16	−1.30002	−0.650008	+	0.759927i	$0.725235\pi$
$864$	6.87186e15	0.485567
$865$	−8.45688e14	−0.0593774
$866$	−2.02663e16	−1.41392
$867$	−2.74606e15	−0.190373
$868$	−2.48392e15	−0.171111
$869$	2.80711e15	0.192155
$870$	−4.09106e15	−0.278279
$871$	−6.03276e14	−0.0407771
$872$	−6.68867e15	−0.449261
$873$	1.52764e16	1.01963
$874$	6.51229e15	0.431937
$875$	7.57240e15	0.499102
$876$	1.09370e16	0.716348
$877$	1.62304e16	1.05641	0.528205	−	0.849117i	$-0.322865\pi$
$877$	1.62304e16	1.05641	0.528205	+	0.849117i	$0.322865\pi$
$878$	−3.69558e15	−0.239036
$879$	−8.86637e15	−0.569911
$880$	−1.55629e14	−0.00994114
$881$	1.03625e16	0.657806	0.328903	−	0.944364i	$-0.393321\pi$
$881$	1.03625e16	0.657806	0.328903	+	0.944364i	$0.393321\pi$
$882$	−7.54961e15	−0.476264
$883$	6.71508e15	0.420985	0.210493	−	0.977595i	$-0.432493\pi$
$883$	6.71508e15	0.420985	0.210493	+	0.977595i	$0.432493\pi$
$884$	9.39805e14	0.0585531
$885$	−1.20373e14	−0.00745316
$886$	−1.70629e16	−1.04995
$887$	2.09454e16	1.28088	0.640442	−	0.768007i	$-0.278751\pi$
$887$	2.09454e16	1.28088	0.640442	+	0.768007i	$0.278751\pi$
$888$	8.22593e15	0.499935
$889$	1.27915e16	0.772615
$890$	1.43131e16	0.859191
$891$	2.27647e15	0.135811
$892$	1.97627e16	1.17176
$893$	−2.59676e16	−1.53020
$894$	−9.20909e15	−0.539337
$895$	−1.01666e16	−0.591765
$896$	2.46477e16	1.42588
$897$	3.11437e13	0.00179066
$898$	1.24141e16	0.709410
$899$	−3.86761e15	−0.219667
$900$	2.45579e16	1.38630
$901$	−1.98707e16	−1.11488
$902$	5.84439e15	0.325914
$903$	5.09100e15	0.282176
$904$	2.25403e16	1.24175
$905$	−1.01094e15	−0.0553550
$906$	2.38804e15	0.129968
$907$	2.61064e16	1.41223	0.706117	−	0.708095i	$-0.250445\pi$
$907$	2.61064e16	1.41223	0.706117	+	0.708095i	$0.250445\pi$
$908$	1.74377e16	0.937597
$909$	4.59237e15	0.245435
$910$	2.19344e14	0.0116520
$911$	1.92057e16	1.01409	0.507047	−	0.861918i	$-0.330737\pi$
$911$	1.92057e16	1.01409	0.507047	+	0.861918i	$0.330737\pi$
$912$	−1.14063e15	−0.0598651
$913$	5.09638e15	0.265872
$914$	−1.44505e16	−0.749339
$915$	5.44720e14	0.0280774
$916$	6.56364e15	0.336295
$917$	−2.54765e16	−1.29750
$918$	−2.35754e16	−1.19350
$919$	−2.90113e16	−1.45993	−0.729966	−	0.683484i	$-0.760464\pi$
$919$	−2.90113e16	−1.45993	−0.729966	+	0.683484i	$0.760464\pi$
$920$	−1.61262e15	−0.0806677
$921$	−3.56758e15	−0.177397
$922$	−1.79142e16	−0.885476
$923$	7.89636e14	0.0387987
$924$	−1.55264e15	−0.0758360
$925$	−2.74363e16	−1.33213
$926$	9.14582e14	0.0441431
$927$	1.87243e15	0.0898393
$928$	3.21496e16	1.53342
$929$	−3.80977e16	−1.80639	−0.903196	−	0.429229i	$-0.858785\pi$
$929$	−3.80977e16	−1.80639	−0.903196	+	0.429229i	$0.858785\pi$
$930$	4.03259e14	0.0190076
$931$	−8.01574e15	−0.375596
$932$	−5.78622e16	−2.69530
$933$	−2.16773e14	−0.0100382
$934$	2.30282e16	1.06011
$935$	−1.62882e15	−0.0745434
$936$	6.14678e14	0.0279660
$937$	7.71204e15	0.348820	0.174410	−	0.984673i	$-0.444198\pi$
$937$	7.71204e15	0.348820	0.174410	+	0.984673i	$0.444198\pi$
$938$	4.54708e16	2.04464
$939$	3.99191e15	0.178451
$940$	1.57228e16	0.698757
$941$	8.23024e14	0.0363638	0.0181819	−	0.999835i	$-0.494212\pi$
$941$	8.23024e14	0.0363638	0.0181819	+	0.999835i	$0.494212\pi$
$942$	2.10186e16	0.923259
$943$	5.55366e15	0.242530
$944$	−3.10077e14	−0.0134624
$945$	−3.45837e15	−0.149278
$946$	8.04015e15	0.345035
$947$	1.05653e16	0.450771	0.225385	−	0.974270i	$-0.427636\pi$
$947$	1.05653e16	0.450771	0.225385	+	0.974270i	$0.427636\pi$
$948$	−1.24570e16	−0.528404
$949$	−9.13046e14	−0.0385060
$950$	4.14846e16	1.73943
$951$	−1.32406e16	−0.551968
$952$	−2.89704e16	−1.20075
$953$	−3.18167e16	−1.31113	−0.655563	−	0.755141i	$-0.727569\pi$
$953$	−3.18167e16	−1.31113	−0.655563	+	0.755141i	$0.727569\pi$
$954$	−3.17777e16	−1.30199
$955$	3.75713e15	0.153051
$956$	1.27257e16	0.515424
$957$	−2.41756e15	−0.0973556
$958$	−5.78118e16	−2.31476
$959$	2.59029e16	1.03121
$960$	−3.76027e15	−0.148843
$961$	−2.50272e16	−0.984996
$962$	−1.67911e15	−0.0657078
$963$	−2.40110e16	−0.934254
$964$	−5.81805e16	−2.25089
$965$	1.15794e16	0.445438
$966$	−2.34740e15	−0.0897869
$967$	2.07924e16	0.790785	0.395393	−	0.918512i	$-0.370609\pi$
$967$	2.07924e16	0.790785	0.395393	+	0.918512i	$0.370609\pi$
$968$	2.90198e16	1.09744
$969$	−1.19379e16	−0.448897
$970$	−1.56247e16	−0.584209
$971$	−1.45097e16	−0.539452	−0.269726	−	0.962937i	$-0.586933\pi$
$971$	−1.45097e16	−0.539452	−0.269726	+	0.962937i	$0.586933\pi$
$972$	−3.60922e16	−1.33429
$973$	−2.90465e16	−1.06776
$974$	−5.29826e16	−1.93668
$975$	1.98392e14	0.00721104
$976$	1.40318e15	0.0507155
$977$	−4.14107e16	−1.48831	−0.744153	−	0.668010i	$-0.767146\pi$
$977$	−4.14107e16	−1.48831	−0.744153	+	0.668010i	$0.767146\pi$
$978$	2.37807e16	0.849887
$979$	8.45815e15	0.300587
$980$	4.85335e15	0.171514
$981$	−1.02667e16	−0.360786
$982$	−2.70783e16	−0.946255
$983$	4.95997e16	1.72359	0.861797	−	0.507253i	$-0.169339\pi$
$983$	4.95997e16	1.72359	0.861797	+	0.507253i	$0.169339\pi$
$984$	−1.06070e16	−0.366538
$985$	−1.10173e16	−0.378596
$986$	−1.10296e17	−3.76909
$987$	9.36019e15	0.318083
$988$	1.59575e15	0.0539265
$989$	7.64019e15	0.256758
$990$	−2.60485e15	−0.0870540
$991$	1.65436e16	0.549825	0.274913	−	0.961469i	$-0.411351\pi$
$991$	1.65436e16	0.549825	0.274913	+	0.961469i	$0.411351\pi$
$992$	−3.16901e15	−0.104739
$993$	−6.12884e15	−0.201445
$994$	−5.95173e16	−1.94544
$995$	−4.01063e15	−0.130372
$996$	−2.26159e16	−0.731118
$997$	4.74273e16	1.52477	0.762387	−	0.647122i	$-0.224027\pi$
$997$	4.74273e16	1.52477	0.762387	+	0.647122i	$0.224027\pi$
$998$	−1.63907e16	−0.524058
$999$	2.64744e16	0.841812

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	103.12.a.b.1.5	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
103.12.a.b.1.5	✓	49	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:	\( N \)	\(=\)	\( 103 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	103.a (trivial)

\(f(q)\)	\(=\)	\(q-74.2508 q^{2} -125.019 q^{3} +3465.19 q^{4} -2224.90 q^{5} +9282.79 q^{6} +36712.6 q^{7} -105227. q^{8} -161517. q^{9} +O(q^{10})\)	\(q-74.2508 q^{2} -125.019 q^{3} +3465.19 q^{4} -2224.90 q^{5} +9282.79 q^{6} +36712.6 q^{7} -105227. q^{8} -161517. q^{9} +165201. q^{10} +97623.0 q^{11} -433216. q^{12} +36165.9 q^{13} -2.72594e6 q^{14} +278155. q^{15} +716521. q^{16} +7.49913e6 q^{17} +1.19928e7 q^{18} +1.27332e7 q^{19} -7.70969e6 q^{20} -4.58978e6 q^{21} -7.24859e6 q^{22} -6.88800e6 q^{23} +1.31555e7 q^{24} -4.38780e7 q^{25} -2.68535e6 q^{26} +4.23396e7 q^{27} +1.27216e8 q^{28} +1.98083e8 q^{29} -2.06533e7 q^{30} -1.95252e7 q^{31} +1.62304e8 q^{32} -1.22048e7 q^{33} -5.56817e8 q^{34} -8.16818e7 q^{35} -5.59687e8 q^{36} +6.25286e8 q^{37} -9.45454e8 q^{38} -4.52144e6 q^{39} +2.34120e8 q^{40} -8.06280e8 q^{41} +3.40795e8 q^{42} -1.10920e9 q^{43} +3.38282e8 q^{44} +3.59359e8 q^{45} +5.11440e8 q^{46} -2.03935e9 q^{47} -8.95790e7 q^{48} -6.29513e8 q^{49} +3.25798e9 q^{50} -9.37537e8 q^{51} +1.25322e8 q^{52} -2.64973e9 q^{53} -3.14375e9 q^{54} -2.17201e8 q^{55} -3.86317e9 q^{56} -1.59190e9 q^{57} -1.47078e10 q^{58} -4.32754e8 q^{59} +9.63861e8 q^{60} +1.95833e9 q^{61} +1.44976e9 q^{62} -5.92971e9 q^{63} -1.35186e10 q^{64} -8.04656e7 q^{65} +9.06214e8 q^{66} -1.66808e10 q^{67} +2.59859e10 q^{68} +8.61134e8 q^{69} +6.06494e9 q^{70} +2.18337e10 q^{71} +1.69960e10 q^{72} -2.52460e10 q^{73} -4.64280e10 q^{74} +5.48559e9 q^{75} +4.41231e10 q^{76} +3.58399e9 q^{77} +3.35721e8 q^{78} +2.87546e10 q^{79} -1.59419e9 q^{80} +2.33190e10 q^{81} +5.98670e10 q^{82} +5.22047e10 q^{83} -1.59045e10 q^{84} -1.66848e10 q^{85} +8.23592e10 q^{86} -2.47642e10 q^{87} -1.02726e10 q^{88} +8.66409e10 q^{89} -2.66827e10 q^{90} +1.32775e9 q^{91} -2.38682e10 q^{92} +2.44103e9 q^{93} +1.51424e11 q^{94} -2.83302e10 q^{95} -2.02911e10 q^{96} -9.45804e10 q^{97} +4.67419e10 q^{98} -1.57678e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q + 183 q^{2} + 466 q^{3} + 55743 q^{4} + 16065 q^{5} + 33631 q^{6} + 31238 q^{7} + 367572 q^{8} + 3580275 q^{9}+O(q^{10}) \) 49 * q + 183 * q^2 + 466 * q^3 + 55743 * q^4 + 16065 * q^5 + 33631 * q^6 + 31238 * q^7 + 367572 * q^8 + 3580275 * q^9	\( 49 q + 183 q^{2} + 466 q^{3} + 55743 q^{4} + 16065 q^{5} + 33631 q^{6} + 31238 q^{7} + 367572 q^{8} + 3580275 q^{9} + 750478 q^{10} + 727533 q^{11} + 2347431 q^{12} + 1686993 q^{13} + 1917175 q^{14} + 5732779 q^{15} + 63104603 q^{16} + 42447415 q^{17} + 38328816 q^{18} + 5625397 q^{19} + 23363733 q^{20} + 9056758 q^{21} + 35431841 q^{22} + 99653000 q^{23} + 60107634 q^{24} + 612692400 q^{25} - 287465619 q^{26} + 33237874 q^{27} + 94647576 q^{28} + 582553712 q^{29} + 2028243566 q^{30} + 574615536 q^{31} + 2461710524 q^{32} + 1398060597 q^{33} + 1095877670 q^{34} + 1224276663 q^{35} + 5178232888 q^{36} + 1054414698 q^{37} + 168008610 q^{38} - 682764349 q^{39} - 3058491845 q^{40} + 1814310718 q^{41} - 7019276677 q^{42} + 322591648 q^{43} - 1892602784 q^{44} - 4067379516 q^{45} - 11163159263 q^{46} + 15760013 q^{47} - 3956976183 q^{48} + 10317761631 q^{49} + 4788432202 q^{50} + 4167009909 q^{51} - 16558761537 q^{52} + 16561990335 q^{53} - 22053068789 q^{54} - 2528406158 q^{55} - 2175101045 q^{56} + 10578500421 q^{57} + 10570052770 q^{58} + 12504156727 q^{59} + 27219988055 q^{60} + 12858649383 q^{61} + 29953793573 q^{62} + 21928998164 q^{63} + 107776677998 q^{64} + 75670521263 q^{65} + 70097909751 q^{66} + 34656499990 q^{67} + 134555459108 q^{68} + 60441944808 q^{69} + 144324418256 q^{70} - 4976323973 q^{71} + 184674525846 q^{72} + 80843930205 q^{73} + 147160169907 q^{74} + 106406736723 q^{75} + 89376434340 q^{76} + 187650162769 q^{77} + 217624188512 q^{78} + 33073221431 q^{79} + 220351536446 q^{80} + 373198656177 q^{81} + 417339951569 q^{82} + 180678060299 q^{83} + 622749162897 q^{84} + 295945248373 q^{85} + 223228441021 q^{86} + 351128502358 q^{87} + 327529458125 q^{88} + 229672691360 q^{89} + 878270116936 q^{90} + 269714836479 q^{91} + 470788684476 q^{92} + 255181811376 q^{93} + 556696972040 q^{94} + 455878930472 q^{95} + 1296231412687 q^{96} + 248534514476 q^{97} + 747851098165 q^{98} + 465588303306 q^{99}+O(q^{100}) \) 49 * q + 183 * q^2 + 466 * q^3 + 55743 * q^4 + 16065 * q^5 + 33631 * q^6 + 31238 * q^7 + 367572 * q^8 + 3580275 * q^9 + 750478 * q^10 + 727533 * q^11 + 2347431 * q^12 + 1686993 * q^13 + 1917175 * q^14 + 5732779 * q^15 + 63104603 * q^16 + 42447415 * q^17 + 38328816 * q^18 + 5625397 * q^19 + 23363733 * q^20 + 9056758 * q^21 + 35431841 * q^22 + 99653000 * q^23 + 60107634 * q^24 + 612692400 * q^25 - 287465619 * q^26 + 33237874 * q^27 + 94647576 * q^28 + 582553712 * q^29 + 2028243566 * q^30 + 574615536 * q^31 + 2461710524 * q^32 + 1398060597 * q^33 + 1095877670 * q^34 + 1224276663 * q^35 + 5178232888 * q^36 + 1054414698 * q^37 + 168008610 * q^38 - 682764349 * q^39 - 3058491845 * q^40 + 1814310718 * q^41 - 7019276677 * q^42 + 322591648 * q^43 - 1892602784 * q^44 - 4067379516 * q^45 - 11163159263 * q^46 + 15760013 * q^47 - 3956976183 * q^48 + 10317761631 * q^49 + 4788432202 * q^50 + 4167009909 * q^51 - 16558761537 * q^52 + 16561990335 * q^53 - 22053068789 * q^54 - 2528406158 * q^55 - 2175101045 * q^56 + 10578500421 * q^57 + 10570052770 * q^58 + 12504156727 * q^59 + 27219988055 * q^60 + 12858649383 * q^61 + 29953793573 * q^62 + 21928998164 * q^63 + 107776677998 * q^64 + 75670521263 * q^65 + 70097909751 * q^66 + 34656499990 * q^67 + 134555459108 * q^68 + 60441944808 * q^69 + 144324418256 * q^70 - 4976323973 * q^71 + 184674525846 * q^72 + 80843930205 * q^73 + 147160169907 * q^74 + 106406736723 * q^75 + 89376434340 * q^76 + 187650162769 * q^77 + 217624188512 * q^78 + 33073221431 * q^79 + 220351536446 * q^80 + 373198656177 * q^81 + 417339951569 * q^82 + 180678060299 * q^83 + 622749162897 * q^84 + 295945248373 * q^85 + 223228441021 * q^86 + 351128502358 * q^87 + 327529458125 * q^88 + 229672691360 * q^89 + 878270116936 * q^90 + 269714836479 * q^91 + 470788684476 * q^92 + 255181811376 * q^93 + 556696972040 * q^94 + 455878930472 * q^95 + 1296231412687 * q^96 + 248534514476 * q^97 + 747851098165 * q^98 + 465588303306 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more