LMFDB - Embedded newform 22.14.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,14,Mod(1,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("22.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	22.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:	$23.5908043694$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{100039}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 100039 $ x^2 - 100039
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$316.289$ of defining polynomial
Character	$\chi$	$=$	22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-64.0000 q^{2} +934.158 q^{3} +4096.00 q^{4} +8611.10 q^{5} -59786.1 q^{6} -145664. q^{7} -262144. q^{8} -721672. q^{9} +O(q^{10})$	\(q-64.0000 q^{2} +934.158 q^{3} +4096.00 q^{4} +8611.10 q^{5} -59786.1 q^{6} -145664. q^{7} -262144. q^{8} -721672. q^{9} -551110. q^{10} -1.77156e6 q^{11} +3.82631e6 q^{12} +4.86460e6 q^{13} +9.32252e6 q^{14} +8.04413e6 q^{15} +1.67772e7 q^{16} +5.51974e6 q^{17} +4.61870e7 q^{18} +3.91080e7 q^{19} +3.52711e7 q^{20} -1.36073e8 q^{21} +1.13380e8 q^{22} -2.88752e8 q^{23} -2.44884e8 q^{24} -1.14655e9 q^{25} -3.11335e8 q^{26} -2.16350e9 q^{27} -5.96641e8 q^{28} -3.82350e9 q^{29} -5.14824e8 q^{30} -4.38355e9 q^{31} -1.07374e9 q^{32} -1.65492e9 q^{33} -3.53263e8 q^{34} -1.25433e9 q^{35} -2.95597e9 q^{36} -4.15864e9 q^{37} -2.50291e9 q^{38} +4.54431e9 q^{39} -2.25735e9 q^{40} +9.40704e8 q^{41} +8.70870e9 q^{42} -3.96379e9 q^{43} -7.25631e9 q^{44} -6.21439e9 q^{45} +1.84801e10 q^{46} -9.39075e9 q^{47} +1.56726e10 q^{48} -7.56709e10 q^{49} +7.33793e10 q^{50} +5.15631e9 q^{51} +1.99254e10 q^{52} -2.79744e10 q^{53} +1.38464e11 q^{54} -1.52551e10 q^{55} +3.81850e10 q^{56} +3.65330e10 q^{57} +2.44704e11 q^{58} -3.28230e10 q^{59} +3.29487e10 q^{60} +2.84818e11 q^{61} +2.80547e11 q^{62} +1.05122e11 q^{63} +6.87195e10 q^{64} +4.18896e10 q^{65} +1.05915e11 q^{66} -2.51531e11 q^{67} +2.26088e10 q^{68} -2.69740e11 q^{69} +8.02771e10 q^{70} -1.27448e12 q^{71} +1.89182e11 q^{72} +2.44460e11 q^{73} +2.66153e11 q^{74} -1.07106e12 q^{75} +1.60186e11 q^{76} +2.58053e11 q^{77} -2.90836e11 q^{78} -8.92263e10 q^{79} +1.44470e11 q^{80} -8.70476e11 q^{81} -6.02051e10 q^{82} -2.75095e12 q^{83} -5.57357e11 q^{84} +4.75310e10 q^{85} +2.53683e11 q^{86} -3.57175e12 q^{87} +4.64404e11 q^{88} -4.62025e12 q^{89} +3.97721e11 q^{90} -7.08600e11 q^{91} -1.18273e12 q^{92} -4.09493e12 q^{93} +6.01008e11 q^{94} +3.36763e11 q^{95} -1.00304e12 q^{96} +8.68766e12 q^{97} +4.84294e12 q^{98} +1.27849e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 128 q^{2} - 662 q^{3} + 8192 q^{4} - 48566 q^{5} + 42368 q^{6} + 404508 q^{7} - 524288 q^{8} + 231724 q^{9}+O(q^{10}) $ 2 * q - 128 * q^2 - 662 * q^3 + 8192 * q^4 - 48566 * q^5 + 42368 * q^6 + 404508 * q^7 - 524288 * q^8 + 231724 * q^9	\( 2 q - 128 q^{2} - 662 q^{3} + 8192 q^{4} - 48566 q^{5} + 42368 q^{6} + 404508 q^{7} - 524288 q^{8} + 231724 q^{9} + 3108224 q^{10} - 3543122 q^{11} - 2711552 q^{12} + 28445952 q^{13} - 25888512 q^{14} + 99307794 q^{15} + 33554432 q^{16} + 107032052 q^{17} - 14830336 q^{18} - 73524568 q^{19} - 198926336 q^{20} - 1014235348 q^{21} + 226759808 q^{22} - 987164862 q^{23} + 173539328 q^{24} + 901965576 q^{25} - 1820540928 q^{26} - 1140484994 q^{27} + 1656864768 q^{28} - 9516399376 q^{29} - 6355698816 q^{30} - 6865940430 q^{31} - 2147483648 q^{32} + 1172773382 q^{33} - 6850051328 q^{34} - 32711590964 q^{35} + 949141504 q^{36} - 4145233266 q^{37} + 4705572352 q^{38} - 33095241568 q^{39} + 12731285504 q^{40} + 39451523656 q^{41} + 64911062272 q^{42} + 5532549228 q^{43} - 14512627712 q^{44} - 60726834468 q^{45} + 63178551168 q^{46} - 28411609744 q^{47} - 11106516992 q^{48} + 130129720218 q^{49} - 57725796864 q^{50} - 156873354588 q^{51} + 116514619392 q^{52} - 49178542972 q^{53} + 72991039616 q^{54} + 86037631526 q^{55} - 106039345152 q^{56} + 216312273320 q^{57} + 609049560064 q^{58} + 110326136718 q^{59} + 406764724224 q^{60} - 161816895480 q^{61} + 439420187520 q^{62} + 629654304296 q^{63} + 137438953472 q^{64} - 1306423470272 q^{65} - 75057496448 q^{66} - 483661746106 q^{67} + 438403284992 q^{68} + 845036821770 q^{69} + 2093541821696 q^{70} + 318713704774 q^{71} - 60745056256 q^{72} - 1073843539168 q^{73} + 265294929024 q^{74} - 4340817675224 q^{75} - 301156630528 q^{76} - 716610596988 q^{77} + 2118095460352 q^{78} - 742108796220 q^{79} - 814802272256 q^{80} - 4023398824910 q^{81} - 2524897513984 q^{82} - 6905249437156 q^{83} - 4154307985408 q^{84} - 5756648698492 q^{85} - 354083150592 q^{86} + 5515016618352 q^{87} + 928808173568 q^{88} - 8233927751362 q^{89} + 3886517405952 q^{90} + 12265206226208 q^{91} - 4043427274752 q^{92} - 132647408710 q^{93} + 1818343023616 q^{94} + 6776763758856 q^{95} + 710817087488 q^{96} - 4680888780654 q^{97} - 8328302093952 q^{98} - 410513201164 q^{99}+O(q^{100}) \) 2 * q - 128 * q^2 - 662 * q^3 + 8192 * q^4 - 48566 * q^5 + 42368 * q^6 + 404508 * q^7 - 524288 * q^8 + 231724 * q^9 + 3108224 * q^10 - 3543122 * q^11 - 2711552 * q^12 + 28445952 * q^13 - 25888512 * q^14 + 99307794 * q^15 + 33554432 * q^16 + 107032052 * q^17 - 14830336 * q^18 - 73524568 * q^19 - 198926336 * q^20 - 1014235348 * q^21 + 226759808 * q^22 - 987164862 * q^23 + 173539328 * q^24 + 901965576 * q^25 - 1820540928 * q^26 - 1140484994 * q^27 + 1656864768 * q^28 - 9516399376 * q^29 - 6355698816 * q^30 - 6865940430 * q^31 - 2147483648 * q^32 + 1172773382 * q^33 - 6850051328 * q^34 - 32711590964 * q^35 + 949141504 * q^36 - 4145233266 * q^37 + 4705572352 * q^38 - 33095241568 * q^39 + 12731285504 * q^40 + 39451523656 * q^41 + 64911062272 * q^42 + 5532549228 * q^43 - 14512627712 * q^44 - 60726834468 * q^45 + 63178551168 * q^46 - 28411609744 * q^47 - 11106516992 * q^48 + 130129720218 * q^49 - 57725796864 * q^50 - 156873354588 * q^51 + 116514619392 * q^52 - 49178542972 * q^53 + 72991039616 * q^54 + 86037631526 * q^55 - 106039345152 * q^56 + 216312273320 * q^57 + 609049560064 * q^58 + 110326136718 * q^59 + 406764724224 * q^60 - 161816895480 * q^61 + 439420187520 * q^62 + 629654304296 * q^63 + 137438953472 * q^64 - 1306423470272 * q^65 - 75057496448 * q^66 - 483661746106 * q^67 + 438403284992 * q^68 + 845036821770 * q^69 + 2093541821696 * q^70 + 318713704774 * q^71 - 60745056256 * q^72 - 1073843539168 * q^73 + 265294929024 * q^74 - 4340817675224 * q^75 - 301156630528 * q^76 - 716610596988 * q^77 + 2118095460352 * q^78 - 742108796220 * q^79 - 814802272256 * q^80 - 4023398824910 * q^81 - 2524897513984 * q^82 - 6905249437156 * q^83 - 4154307985408 * q^84 - 5756648698492 * q^85 - 354083150592 * q^86 + 5515016618352 * q^87 + 928808173568 * q^88 - 8233927751362 * q^89 + 3886517405952 * q^90 + 12265206226208 * q^91 - 4043427274752 * q^92 - 132647408710 * q^93 + 1818343023616 * q^94 + 6776763758856 * q^95 + 710817087488 * q^96 - 4680888780654 * q^97 - 8328302093952 * q^98 - 410513201164 * 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 $

$2$	−64.0000	−0.707107
$2$	−64.0000	−0.707107
$3$	934.158	0.739830	0.369915	−	0.929066i	$-0.379387\pi$
$3$	934.158	0.739830	0.369915	+	0.929066i	$0.379387\pi$
$4$	4096.00	0.500000
$5$	8611.10	0.246464	0.123232	−	0.992378i	$-0.460674\pi$
$5$	8611.10	0.246464	0.123232	+	0.992378i	$0.460674\pi$
$6$	−59786.1	−0.523139
$7$	−145664.	−0.467968	−0.233984	−	0.972240i	$-0.575176\pi$
$7$	−145664.	−0.467968	−0.233984	+	0.972240i	$0.575176\pi$
$8$	−262144.	−0.353553
$9$	−721672.	−0.452651
$10$	−551110.	−0.174276
$11$	−1.77156e6	−0.301511
$11$	−1.77156e6	−0.301511
$12$	3.82631e6	0.369915
$13$	4.86460e6	0.279522	0.139761	−	0.990185i	$-0.455367\pi$
$13$	4.86460e6	0.279522	0.139761	+	0.990185i	$0.455367\pi$
$14$	9.32252e6	0.330903
$15$	8.04413e6	0.182342
$16$	1.67772e7	0.250000
$17$	5.51974e6	0.0554626	0.0277313	−	0.999615i	$-0.491172\pi$
$17$	5.51974e6	0.0554626	0.0277313	+	0.999615i	$0.491172\pi$
$18$	4.61870e7	0.320073
$19$	3.91080e7	0.190707	0.0953535	−	0.995443i	$-0.469602\pi$
$19$	3.91080e7	0.190707	0.0953535	+	0.995443i	$0.469602\pi$
$20$	3.52711e7	0.123232
$21$	−1.36073e8	−0.346217
$22$	1.13380e8	0.213201
$23$	−2.88752e8	−0.406719	−0.203359	−	0.979104i	$-0.565186\pi$
$23$	−2.88752e8	−0.406719	−0.203359	+	0.979104i	$0.565186\pi$
$24$	−2.44884e8	−0.261569
$25$	−1.14655e9	−0.939255
$26$	−3.11335e8	−0.197652
$27$	−2.16350e9	−1.07472
$28$	−5.96641e8	−0.233984
$29$	−3.82350e9	−1.19364	−0.596821	−	0.802375i	$-0.703570\pi$
$29$	−3.82350e9	−1.19364	−0.596821	+	0.802375i	$0.703570\pi$
$30$	−5.14824e8	−0.128935
$31$	−4.38355e9	−0.887105	−0.443553	−	0.896248i	$-0.646282\pi$
$31$	−4.38355e9	−0.887105	−0.443553	+	0.896248i	$0.646282\pi$
$32$	−1.07374e9	−0.176777
$33$	−1.65492e9	−0.223067
$34$	−3.53263e8	−0.0392180
$35$	−1.25433e9	−0.115337
$36$	−2.95597e9	−0.226326
$37$	−4.15864e9	−0.266465	−0.133233	−	0.991085i	$-0.542536\pi$
$37$	−4.15864e9	−0.266465	−0.133233	+	0.991085i	$0.542536\pi$
$38$	−2.50291e9	−0.134850
$39$	4.54431e9	0.206799
$40$	−2.25735e9	−0.0871382
$41$	9.40704e8	0.0309284	0.0154642	−	0.999880i	$-0.495077\pi$
$41$	9.40704e8	0.0309284	0.0154642	+	0.999880i	$0.495077\pi$
$42$	8.70870e9	0.244812
$43$	−3.96379e9	−0.0956238	−0.0478119	−	0.998856i	$-0.515225\pi$
$43$	−3.96379e9	−0.0956238	−0.0478119	+	0.998856i	$0.515225\pi$
$44$	−7.25631e9	−0.150756
$45$	−6.21439e9	−0.111562
$46$	1.84801e10	0.287594
$47$	−9.39075e9	−0.127076	−0.0635381	−	0.997979i	$-0.520238\pi$
$47$	−9.39075e9	−0.127076	−0.0635381	+	0.997979i	$0.520238\pi$
$48$	1.56726e10	0.184958
$49$	−7.56709e10	−0.781006
$50$	7.33793e10	0.664154
$51$	5.15631e9	0.0410329
$52$	1.99254e10	0.139761
$53$	−2.79744e10	−0.173367	−0.0866836	−	0.996236i	$-0.527627\pi$
$53$	−2.79744e10	−0.173367	−0.0866836	+	0.996236i	$0.527627\pi$
$54$	1.38464e11	0.759938
$55$	−1.52551e10	−0.0743117
$56$	3.81850e10	0.165452
$57$	3.65330e10	0.141091
$58$	2.44704e11	0.844032
$59$	−3.28230e10	−0.101307	−0.0506536	−	0.998716i	$-0.516130\pi$
$59$	−3.28230e10	−0.101307	−0.0506536	+	0.998716i	$0.516130\pi$
$60$	3.29487e10	0.0911708
$61$	2.84818e11	0.707821	0.353910	−	0.935279i	$-0.384852\pi$
$61$	2.84818e11	0.707821	0.353910	+	0.935279i	$0.384852\pi$
$62$	2.80547e11	0.627278
$63$	1.05122e11	0.211826
$64$	6.87195e10	0.125000
$65$	4.18896e10	0.0688921
$66$	1.05915e11	0.157732
$67$	−2.51531e11	−0.339707	−0.169854	−	0.985469i	$-0.554330\pi$
$67$	−2.51531e11	−0.339707	−0.169854	+	0.985469i	$0.554330\pi$
$68$	2.26088e10	0.0277313
$69$	−2.69740e11	−0.300903
$70$	8.02771e10	0.0815558
$71$	−1.27448e12	−1.18074	−0.590370	−	0.807133i	$-0.701018\pi$
$71$	−1.27448e12	−1.18074	−0.590370	+	0.807133i	$0.701018\pi$
$72$	1.89182e11	0.160036
$73$	2.44460e11	0.189064	0.0945319	−	0.995522i	$-0.469865\pi$
$73$	2.44460e11	0.189064	0.0945319	+	0.995522i	$0.469865\pi$
$74$	2.66153e11	0.188419
$75$	−1.07106e12	−0.694890
$76$	1.60186e11	0.0953535
$77$	2.58053e11	0.141098
$78$	−2.90836e11	−0.146229
$79$	−8.92263e10	−0.0412969	−0.0206484	−	0.999787i	$-0.506573\pi$
$79$	−8.92263e10	−0.0412969	−0.0206484	+	0.999787i	$0.506573\pi$
$80$	1.44470e11	0.0616160
$81$	−8.70476e11	−0.342455
$82$	−6.02051e10	−0.0218697
$83$	−2.75095e12	−0.923581	−0.461791	−	0.886989i	$-0.652793\pi$
$83$	−2.75095e12	−0.923581	−0.461791	+	0.886989i	$0.652793\pi$
$84$	−5.57357e11	−0.173108
$85$	4.75310e10	0.0136695
$86$	2.53683e11	0.0676162
$87$	−3.57175e12	−0.883092
$88$	4.64404e11	0.106600
$89$	−4.62025e12	−0.985440	−0.492720	−	0.870188i	$-0.663997\pi$
$89$	−4.62025e12	−0.985440	−0.492720	+	0.870188i	$0.663997\pi$
$90$	3.97721e11	0.0788864
$91$	−7.08600e11	−0.130807
$92$	−1.18273e12	−0.203359
$93$	−4.09493e12	−0.656307
$94$	6.01008e11	0.0898564
$95$	3.36763e11	0.0470024
$96$	−1.00304e12	−0.130785
$97$	8.68766e12	1.05898	0.529489	−	0.848317i	$-0.322384\pi$
$97$	8.68766e12	1.05898	0.529489	+	0.848317i	$0.322384\pi$
$98$	4.84294e12	0.552255
$99$	1.27849e12	0.136480
$100$	−4.69628e12	−0.469628
$101$	1.61744e13	1.51614	0.758069	−	0.652174i	$-0.226143\pi$
$101$	1.61744e13	1.51614	0.758069	+	0.652174i	$0.226143\pi$
$102$	−3.30004e11	−0.0290147
$103$	1.96746e13	1.62354	0.811772	−	0.583974i	$-0.198503\pi$
$103$	1.96746e13	1.62354	0.811772	+	0.583974i	$0.198503\pi$
$104$	−1.27523e12	−0.0988259
$105$	−1.17174e12	−0.0853300
$106$	1.79036e12	0.122589
$107$	1.14083e13	0.734898	0.367449	−	0.930044i	$-0.380231\pi$
$107$	1.14083e13	0.734898	0.367449	+	0.930044i	$0.380231\pi$
$108$	−8.86172e12	−0.537358
$109$	2.54906e13	1.45582	0.727911	−	0.685672i	$-0.240492\pi$
$109$	2.54906e13	1.45582	0.727911	+	0.685672i	$0.240492\pi$
$110$	9.76326e11	0.0525463
$111$	−3.88483e12	−0.197139
$112$	−2.44384e12	−0.116992
$113$	4.30324e12	0.194440	0.0972201	−	0.995263i	$-0.469005\pi$
$113$	4.30324e12	0.194440	0.0972201	+	0.995263i	$0.469005\pi$
$114$	−2.33811e12	−0.0997663
$115$	−2.48647e12	−0.100242
$116$	−1.56611e13	−0.596821
$117$	−3.51065e12	−0.126526
$118$	2.10067e12	0.0716351
$119$	−8.04029e11	−0.0259547
$120$	−2.10872e12	−0.0644675
$121$	3.13843e12	0.0909091
$122$	−1.82283e13	−0.500505
$123$	8.78766e11	0.0228818
$124$	−1.79550e13	−0.443553
$125$	−2.03847e13	−0.477957
$126$	−6.72780e12	−0.149784
$127$	−4.05332e13	−0.857210	−0.428605	−	0.903492i	$-0.640995\pi$
$127$	−4.05332e13	−0.857210	−0.428605	+	0.903492i	$0.640995\pi$
$128$	−4.39805e12	−0.0883883
$129$	−3.70281e12	−0.0707454
$130$	−2.68093e12	−0.0487141
$131$	5.20688e13	0.900148	0.450074	−	0.892991i	$-0.351398\pi$
$131$	5.20688e13	0.900148	0.450074	+	0.892991i	$0.351398\pi$
$132$	−6.77854e12	−0.111534
$133$	−5.69664e12	−0.0892448
$134$	1.60980e13	0.240209
$135$	−1.86302e13	−0.264879
$136$	−1.44697e12	−0.0196090
$137$	−7.98050e13	−1.03121	−0.515604	−	0.856827i	$-0.672432\pi$
$137$	−7.98050e13	−1.03121	−0.515604	+	0.856827i	$0.672432\pi$
$138$	1.72634e13	0.212770
$139$	6.47898e13	0.761922	0.380961	−	0.924591i	$-0.375593\pi$
$139$	6.47898e13	0.761922	0.380961	+	0.924591i	$0.375593\pi$
$140$	−5.13774e12	−0.0576686
$141$	−8.77244e12	−0.0940148
$142$	8.15668e13	0.834909
$143$	−8.61794e12	−0.0842790
$144$	−1.21077e13	−0.113163
$145$	−3.29245e13	−0.294190
$146$	−1.56454e13	−0.133688
$147$	−7.06886e13	−0.577812
$148$	−1.70338e13	−0.133233
$149$	−1.96816e14	−1.47350	−0.736748	−	0.676167i	$-0.763640\pi$
$149$	−1.96816e14	−1.47350	−0.736748	+	0.676167i	$0.763640\pi$
$150$	6.85479e13	0.491361
$151$	7.64401e13	0.524772	0.262386	−	0.964963i	$-0.415491\pi$
$151$	7.64401e13	0.524772	0.262386	+	0.964963i	$0.415491\pi$
$152$	−1.02519e13	−0.0674251
$153$	−3.98344e12	−0.0251052
$154$	−1.65154e13	−0.0997711
$155$	−3.77472e13	−0.218640
$156$	1.86135e13	0.103399
$157$	−1.06579e13	−0.0567967	−0.0283983	−	0.999597i	$-0.509041\pi$
$157$	−1.06579e13	−0.0567967	−0.0283983	+	0.999597i	$0.509041\pi$
$158$	5.71049e12	0.0292013
$159$	−2.61325e13	−0.128262
$160$	−9.24610e12	−0.0435691
$161$	4.20609e13	0.190331
$162$	5.57105e13	0.242153
$163$	3.66961e14	1.53250	0.766251	−	0.642542i	$-0.222120\pi$
$163$	3.66961e14	1.53250	0.766251	+	0.642542i	$0.222120\pi$
$164$	3.85312e12	0.0154642
$165$	−1.42507e13	−0.0549780
$166$	1.76061e14	0.653071
$167$	6.96199e13	0.248357	0.124178	−	0.992260i	$-0.460370\pi$
$167$	6.96199e13	0.248357	0.124178	+	0.992260i	$0.460370\pi$
$168$	3.56708e13	0.122406
$169$	−2.79211e14	−0.921868
$170$	−3.04199e12	−0.00966583
$171$	−2.82231e13	−0.0863238
$172$	−1.62357e13	−0.0478119
$173$	1.51465e13	0.0429549	0.0214774	−	0.999769i	$-0.493163\pi$
$173$	1.51465e13	0.0429549	0.0214774	+	0.999769i	$0.493163\pi$
$174$	2.28592e14	0.624440
$175$	1.67012e14	0.439541
$176$	−2.97219e13	−0.0753778
$177$	−3.06619e13	−0.0749502
$178$	2.95696e14	0.696812
$179$	−5.93510e13	−0.134860	−0.0674301	−	0.997724i	$-0.521480\pi$
$179$	−5.93510e13	−0.134860	−0.0674301	+	0.997724i	$0.521480\pi$
$180$	−2.54542e13	−0.0557811
$181$	3.61796e14	0.764808	0.382404	−	0.923995i	$-0.375096\pi$
$181$	3.61796e14	0.764808	0.382404	+	0.923995i	$0.375096\pi$
$182$	4.53504e13	0.0924947
$183$	2.66065e14	0.523667
$184$	7.56946e13	0.143797
$185$	−3.58105e13	−0.0656741
$186$	2.62075e14	0.464079
$187$	−9.77855e12	−0.0167226
$188$	−3.84645e13	−0.0635381
$189$	3.15146e14	0.502932
$190$	−2.15528e13	−0.0332357
$191$	−9.97874e14	−1.48716	−0.743582	−	0.668645i	$-0.766875\pi$
$191$	−9.97874e14	−1.48716	−0.743582	+	0.668645i	$0.766875\pi$
$192$	6.41948e13	0.0924788
$193$	−4.43872e14	−0.618209	−0.309105	−	0.951028i	$-0.600029\pi$
$193$	−4.43872e14	−0.618209	−0.309105	+	0.951028i	$0.600029\pi$
$194$	−5.56010e14	−0.748810
$195$	3.91315e13	0.0509684
$196$	−3.09948e14	−0.390503
$197$	−9.57219e14	−1.16676	−0.583379	−	0.812200i	$-0.698270\pi$
$197$	−9.57219e14	−1.16676	−0.583379	+	0.812200i	$0.698270\pi$
$198$	−8.18231e13	−0.0965056
$199$	−1.82565e14	−0.208387	−0.104194	−	0.994557i	$-0.533226\pi$
$199$	−1.82565e14	−0.208387	−0.104194	+	0.994557i	$0.533226\pi$
$200$	3.00562e14	0.332077
$201$	−2.34969e14	−0.251326
$202$	−1.03516e15	−1.07207
$203$	5.56948e14	0.558586
$204$	2.11202e13	0.0205165
$205$	8.10050e12	0.00762275
$206$	−1.25918e15	−1.14802
$207$	2.08384e14	0.184102
$208$	8.16145e13	0.0698805
$209$	−6.92821e13	−0.0575003
$210$	7.49915e13	0.0603374
$211$	1.45274e15	1.13332	0.566658	−	0.823953i	$-0.308236\pi$
$211$	1.45274e15	1.13332	0.566658	+	0.823953i	$0.308236\pi$
$212$	−1.14583e14	−0.0866836
$213$	−1.19057e15	−0.873546
$214$	−7.30133e14	−0.519652
$215$	−3.41326e13	−0.0235678
$216$	5.67150e14	0.379969
$217$	6.38527e14	0.415137
$218$	−1.63140e15	−1.02942
$219$	2.28364e14	0.139875
$220$	−6.24848e13	−0.0371559
$221$	2.68513e13	0.0155030
$222$	2.48629e14	0.139398
$223$	1.81969e15	0.990866	0.495433	−	0.868646i	$-0.335009\pi$
$223$	1.81969e15	0.990866	0.495433	+	0.868646i	$0.335009\pi$
$224$	1.56406e14	0.0827258
$225$	8.27435e14	0.425155
$226$	−2.75408e14	−0.137490
$227$	−1.34324e14	−0.0651606	−0.0325803	−	0.999469i	$-0.510372\pi$
$227$	−1.34324e14	−0.0651606	−0.0325803	+	0.999469i	$0.510372\pi$
$228$	1.49639e14	0.0705454
$229$	4.03230e14	0.184766	0.0923830	−	0.995724i	$-0.470552\pi$
$229$	4.03230e14	0.184766	0.0923830	+	0.995724i	$0.470552\pi$
$230$	1.59134e14	0.0708815
$231$	2.41062e14	0.104388
$232$	1.00231e15	0.422016
$233$	9.69371e14	0.396896	0.198448	−	0.980111i	$-0.436410\pi$
$233$	9.69371e14	0.396896	0.198448	+	0.980111i	$0.436410\pi$
$234$	2.24682e14	0.0894673
$235$	−8.08647e13	−0.0313197
$236$	−1.34443e14	−0.0506536
$237$	−8.33515e13	−0.0305527
$238$	5.14579e13	0.0183528
$239$	4.47159e15	1.55194	0.775972	−	0.630768i	$-0.217260\pi$
$239$	4.47159e15	1.55194	0.775972	+	0.630768i	$0.217260\pi$
$240$	1.34958e14	0.0455854
$241$	−1.70701e15	−0.561210	−0.280605	−	0.959823i	$-0.590535\pi$
$241$	−1.70701e15	−0.561210	−0.280605	+	0.959823i	$0.590535\pi$
$242$	−2.00859e14	−0.0642824
$243$	2.63616e15	0.821356
$244$	1.16661e15	0.353910
$245$	−6.51610e14	−0.192490
$246$	−5.62410e13	−0.0161799
$247$	1.90245e14	0.0533068
$248$	1.14912e15	0.313639
$249$	−2.56982e15	−0.683293
$250$	1.30462e15	0.337966
$251$	3.53852e14	0.0893187	0.0446594	−	0.999002i	$-0.485780\pi$
$251$	3.53852e14	0.0893187	0.0446594	+	0.999002i	$0.485780\pi$
$252$	4.30580e14	0.105913
$253$	5.11542e14	0.122630
$254$	2.59413e15	0.606139
$255$	4.44015e13	0.0101131
$256$	2.81475e14	0.0625000
$257$	−6.09403e15	−1.31929	−0.659644	−	0.751578i	$-0.729293\pi$
$257$	−6.09403e15	−1.31929	−0.659644	+	0.751578i	$0.729293\pi$
$258$	2.36980e14	0.0500245
$259$	6.05766e14	0.124697
$260$	1.71580e14	0.0344460
$261$	2.75931e15	0.540303
$262$	−3.33240e15	−0.636501
$263$	−6.91274e14	−0.128807	−0.0644033	−	0.997924i	$-0.520514\pi$
$263$	−6.91274e14	−0.128807	−0.0644033	+	0.997924i	$0.520514\pi$
$264$	4.33827e14	0.0788662
$265$	−2.40890e14	−0.0427288
$266$	3.64585e14	0.0631056
$267$	−4.31604e15	−0.729059
$268$	−1.03027e15	−0.169854
$269$	−6.11656e15	−0.984278	−0.492139	−	0.870517i	$-0.663785\pi$
$269$	−6.11656e15	−0.984278	−0.492139	+	0.870517i	$0.663785\pi$
$270$	1.19233e15	0.187298
$271$	−5.84790e15	−0.896809	−0.448404	−	0.893831i	$-0.648008\pi$
$271$	−5.84790e15	−0.896809	−0.448404	+	0.893831i	$0.648008\pi$
$272$	9.26058e13	0.0138657
$273$	−6.61944e14	−0.0967752
$274$	5.10752e15	0.729174
$275$	2.03119e15	0.283196
$276$	−1.10486e15	−0.150451
$277$	−9.37891e15	−1.24748	−0.623741	−	0.781631i	$-0.714388\pi$
$277$	−9.37891e15	−1.24748	−0.623741	+	0.781631i	$0.714388\pi$
$278$	−4.14655e15	−0.538760
$279$	3.16349e15	0.401549
$280$	3.28815e14	0.0407779
$281$	−1.12496e16	−1.36316	−0.681578	−	0.731745i	$-0.738706\pi$
$281$	−1.12496e16	−1.36316	−0.681578	+	0.731745i	$0.738706\pi$
$282$	5.61436e14	0.0664785
$283$	1.23351e16	1.42735	0.713673	−	0.700479i	$-0.247030\pi$
$283$	1.23351e16	1.42735	0.713673	+	0.700479i	$0.247030\pi$
$284$	−5.22027e15	−0.590370
$285$	3.14589e14	0.0347738
$286$	5.51548e14	0.0595943
$287$	−1.37027e14	−0.0144735
$288$	7.74890e14	0.0800182
$289$	−9.87411e15	−0.996924
$290$	2.10717e15	0.208024
$291$	8.11564e15	0.783463
$292$	1.00131e15	0.0945319
$293$	−1.08912e16	−1.00562	−0.502811	−	0.864396i	$-0.667701\pi$
$293$	−1.08912e16	−1.00562	−0.502811	+	0.864396i	$0.667701\pi$
$294$	4.52407e15	0.408575
$295$	−2.82642e14	−0.0249686
$296$	1.09016e15	0.0942096
$297$	3.83278e15	0.324039
$298$	1.25962e16	1.04192
$299$	−1.40466e15	−0.113687
$300$	−4.38706e15	−0.347445
$301$	5.77383e14	0.0447489
$302$	−4.89216e15	−0.371070
$303$	1.51094e16	1.12169
$304$	6.56123e14	0.0476768
$305$	2.45259e15	0.174452
$306$	2.54940e14	0.0177521
$307$	1.24083e16	0.845886	0.422943	−	0.906156i	$-0.360997\pi$
$307$	1.24083e16	0.845886	0.422943	+	0.906156i	$0.360997\pi$
$308$	1.05699e15	0.0705488
$309$	1.83792e16	1.20115
$310$	2.41582e15	0.154602
$311$	−2.49878e16	−1.56597	−0.782987	−	0.622038i	$-0.786305\pi$
$311$	−2.49878e16	−1.56597	−0.782987	+	0.622038i	$0.786305\pi$
$312$	−1.19126e15	−0.0731144
$313$	3.37640e15	0.202963	0.101481	−	0.994837i	$-0.467642\pi$
$313$	3.37640e15	0.202963	0.101481	+	0.994837i	$0.467642\pi$
$314$	6.82104e14	0.0401613
$315$	9.05216e14	0.0522076
$316$	−3.65471e14	−0.0206484
$317$	−3.01769e16	−1.67028	−0.835139	−	0.550039i	$-0.814613\pi$
$317$	−3.01769e16	−1.67028	−0.835139	+	0.550039i	$0.814613\pi$
$318$	1.67248e15	0.0906952
$319$	6.77356e15	0.359896
$320$	5.91750e14	0.0308080
$321$	1.06572e16	0.543700
$322$	−2.69190e15	−0.134585
$323$	2.15866e14	0.0105771
$324$	−3.56547e15	−0.171228
$325$	−5.57752e15	−0.262542
$326$	−2.34855e16	−1.08364
$327$	2.38123e16	1.07706
$328$	−2.46600e14	−0.0109349
$329$	1.36790e15	0.0594676
$330$	9.12042e14	0.0388754
$331$	3.90278e16	1.63114	0.815572	−	0.578656i	$-0.196423\pi$
$331$	3.90278e16	1.63114	0.815572	+	0.578656i	$0.196423\pi$
$332$	−1.12679e16	−0.461791
$333$	3.00118e15	0.120616
$334$	−4.45567e15	−0.175615
$335$	−2.16596e15	−0.0837257
$336$	−2.28293e15	−0.0865542
$337$	−7.47633e15	−0.278032	−0.139016	−	0.990290i	$-0.544394\pi$
$337$	−7.47633e15	−0.278032	−0.139016	+	0.990290i	$0.544394\pi$
$338$	1.78695e16	0.651859
$339$	4.01991e15	0.143853
$340$	1.94687e14	0.00683477
$341$	7.76573e15	0.267472
$342$	1.80628e15	0.0610401
$343$	2.51358e16	0.833454
$344$	1.03908e15	0.0338081
$345$	−2.32276e15	−0.0741617
$346$	−9.69375e14	−0.0303737
$347$	4.23869e15	0.130344	0.0651719	−	0.997874i	$-0.479240\pi$
$347$	4.23869e15	0.130344	0.0651719	+	0.997874i	$0.479240\pi$
$348$	−1.46299e16	−0.441546
$349$	5.66695e16	1.67874	0.839372	−	0.543558i	$-0.182923\pi$
$349$	5.66695e16	1.67874	0.839372	+	0.543558i	$0.182923\pi$
$350$	−1.06888e16	−0.310803
$351$	−1.05246e16	−0.300406
$352$	1.90220e15	0.0533002
$353$	3.59013e16	0.987584	0.493792	−	0.869580i	$-0.335610\pi$
$353$	3.59013e16	0.987584	0.493792	+	0.869580i	$0.335610\pi$
$354$	1.96236e15	0.0529978
$355$	−1.09747e16	−0.291010
$356$	−1.89245e16	−0.492720
$357$	−7.51090e14	−0.0192021
$358$	3.79847e15	0.0953605
$359$	−4.43260e16	−1.09281	−0.546405	−	0.837521i	$-0.684004\pi$
$359$	−4.43260e16	−1.09281	−0.546405	+	0.837521i	$0.684004\pi$
$360$	1.62907e15	0.0394432
$361$	−4.05236e16	−0.963631
$362$	−2.31549e16	−0.540801
$363$	2.93179e15	0.0672573
$364$	−2.90242e15	−0.0654036
$365$	2.10507e15	0.0465975
$366$	−1.70281e16	−0.370289
$367$	−9.22924e16	−1.97168	−0.985840	−	0.167687i	$-0.946370\pi$
$367$	−9.22924e16	−1.97168	−0.985840	+	0.167687i	$0.946370\pi$
$368$	−4.84446e15	−0.101680
$369$	−6.78880e14	−0.0139998
$370$	2.29187e15	0.0464386
$371$	4.07487e15	0.0811303
$372$	−1.67728e16	−0.328154
$373$	−2.04883e16	−0.393911	−0.196955	−	0.980412i	$-0.563105\pi$
$373$	−2.04883e16	−0.393911	−0.196955	+	0.980412i	$0.563105\pi$
$374$	6.25827e14	0.0118247
$375$	−1.90425e16	−0.353607
$376$	2.46173e15	0.0449282
$377$	−1.85998e16	−0.333649
$378$	−2.01693e16	−0.355627
$379$	9.71876e15	0.168444	0.0842221	−	0.996447i	$-0.473159\pi$
$379$	9.71876e15	0.168444	0.0842221	+	0.996447i	$0.473159\pi$
$380$	1.37938e15	0.0235012
$381$	−3.78644e16	−0.634190
$382$	6.38639e16	1.05158
$383$	−7.59555e16	−1.22961	−0.614805	−	0.788679i	$-0.710765\pi$
$383$	−7.59555e16	−1.22961	−0.614805	+	0.788679i	$0.710765\pi$
$384$	−4.10847e15	−0.0653924
$385$	2.22212e15	0.0347755
$386$	2.84078e16	0.437140
$387$	2.86056e15	0.0432842
$388$	3.55847e16	0.529489
$389$	−5.47273e16	−0.800813	−0.400407	−	0.916338i	$-0.631131\pi$
$389$	−5.47273e16	−0.800813	−0.400407	+	0.916338i	$0.631131\pi$
$390$	−2.50442e15	−0.0360401
$391$	−1.59384e15	−0.0225577
$392$	1.98367e16	0.276127
$393$	4.86405e16	0.665957
$394$	6.12620e16	0.825023
$395$	−7.68337e14	−0.0101782
$396$	5.23668e15	0.0682398
$397$	5.64279e16	0.723362	0.361681	−	0.932302i	$-0.382203\pi$
$397$	5.64279e16	0.723362	0.361681	+	0.932302i	$0.382203\pi$
$398$	1.16841e16	0.147352
$399$	−5.32156e15	−0.0660260
$400$	−1.92360e16	−0.234814
$401$	5.24149e16	0.629530	0.314765	−	0.949170i	$-0.398074\pi$
$401$	5.24149e16	0.629530	0.314765	+	0.949170i	$0.398074\pi$
$402$	1.50380e16	0.177714
$403$	−2.13243e16	−0.247965
$404$	6.62503e16	0.758069
$405$	−7.49575e15	−0.0844030
$406$	−3.56446e16	−0.394980
$407$	7.36729e15	0.0803422
$408$	−1.35169e15	−0.0145073
$409$	1.67831e17	1.77285	0.886423	−	0.462876i	$-0.153183\pi$
$409$	1.67831e17	1.77285	0.886423	+	0.462876i	$0.153183\pi$
$410$	−5.18432e14	−0.00539010
$411$	−7.45504e16	−0.762919
$412$	8.05872e16	0.811772
$413$	4.78115e15	0.0474085
$414$	−1.33366e16	−0.130180
$415$	−2.36887e16	−0.227630
$416$	−5.22333e15	−0.0494129
$417$	6.05239e16	0.563693
$418$	4.43406e15	0.0406589
$419$	1.74041e17	1.57131	0.785654	−	0.618666i	$-0.212327\pi$
$419$	1.74041e17	1.57131	0.785654	+	0.618666i	$0.212327\pi$
$420$	−4.79946e15	−0.0426650
$421$	−2.35159e16	−0.205839	−0.102920	−	0.994690i	$-0.532818\pi$
$421$	−2.35159e16	−0.205839	−0.102920	+	0.994690i	$0.532818\pi$
$422$	−9.29752e16	−0.801376
$423$	6.77704e15	0.0575212
$424$	7.33331e15	0.0612946
$425$	−6.32867e15	−0.0520936
$426$	7.61962e16	0.617691
$427$	−4.14878e16	−0.331237
$428$	4.67285e16	0.367449
$429$	−8.05052e15	−0.0623522
$430$	2.18449e15	0.0166650
$431$	1.54643e17	1.16206	0.581031	−	0.813881i	$-0.302649\pi$
$431$	1.54643e17	1.16206	0.581031	+	0.813881i	$0.302649\pi$
$432$	−3.62976e16	−0.268679
$433$	−1.69876e17	−1.23868	−0.619341	−	0.785122i	$-0.712600\pi$
$433$	−1.69876e17	−1.23868	−0.619341	+	0.785122i	$0.712600\pi$
$434$	−4.08658e16	−0.293546
$435$	−3.07567e16	−0.217650
$436$	1.04410e17	0.727911
$437$	−1.12925e16	−0.0775641
$438$	−1.46153e16	−0.0989067
$439$	9.54322e14	0.00636320	0.00318160	−	0.999995i	$-0.498987\pi$
$439$	9.54322e14	0.00636320	0.00318160	+	0.999995i	$0.498987\pi$
$440$	3.99903e15	0.0262732
$441$	5.46096e16	0.353523
$442$	−1.71849e15	−0.0109623
$443$	−1.77761e17	−1.11741	−0.558706	−	0.829366i	$-0.688702\pi$
$443$	−1.77761e17	−1.11741	−0.558706	+	0.829366i	$0.688702\pi$
$444$	−1.59123e16	−0.0985694
$445$	−3.97854e16	−0.242876
$446$	−1.16460e17	−0.700648
$447$	−1.83857e17	−1.09014
$448$	−1.00100e16	−0.0584960
$449$	1.16968e17	0.673698	0.336849	−	0.941559i	$-0.390639\pi$
$449$	1.16968e17	0.673698	0.336849	+	0.941559i	$0.390639\pi$
$450$	−5.29558e16	−0.300630
$451$	−1.66651e15	−0.00932527
$452$	1.76261e16	0.0972201
$453$	7.14071e16	0.388242
$454$	8.59672e15	0.0460755
$455$	−6.10182e15	−0.0322393
$456$	−9.57691e15	−0.0498831
$457$	−3.07739e17	−1.58025	−0.790126	−	0.612944i	$-0.789985\pi$
$457$	−3.07739e17	−1.58025	−0.790126	+	0.612944i	$0.789985\pi$
$458$	−2.58067e16	−0.130649
$459$	−1.19420e16	−0.0596065
$460$	−1.01846e16	−0.0501208
$461$	3.02092e17	1.46583	0.732914	−	0.680321i	$-0.238160\pi$
$461$	3.02092e17	1.46583	0.732914	+	0.680321i	$0.238160\pi$
$462$	−1.54280e16	−0.0738137
$463$	−1.18806e17	−0.560482	−0.280241	−	0.959930i	$-0.590414\pi$
$463$	−1.18806e17	−0.560482	−0.280241	+	0.959930i	$0.590414\pi$
$464$	−6.41477e16	−0.298410
$465$	−3.52618e16	−0.161756
$466$	−6.20398e16	−0.280648
$467$	−6.99767e16	−0.312172	−0.156086	−	0.987743i	$-0.549888\pi$
$467$	−6.99767e16	−0.312172	−0.156086	+	0.987743i	$0.549888\pi$
$468$	−1.43796e16	−0.0632630
$469$	3.66391e16	0.158972
$470$	5.17534e15	0.0221464
$471$	−9.95614e15	−0.0420199
$472$	8.60436e15	0.0358175
$473$	7.02210e15	0.0288317
$474$	5.33449e15	0.0216040
$475$	−4.48393e16	−0.179123
$476$	−3.29330e15	−0.0129774
$477$	2.01883e16	0.0784749
$478$	−2.86182e17	−1.09739
$479$	8.97197e16	0.339396	0.169698	−	0.985496i	$-0.445721\pi$
$479$	8.97197e16	0.339396	0.169698	+	0.985496i	$0.445721\pi$
$480$	−8.63731e15	−0.0322337
$481$	−2.02301e16	−0.0744828
$482$	1.09249e17	0.396835
$483$	3.92915e16	0.140813
$484$	1.28550e16	0.0454545
$485$	7.48103e16	0.261000
$486$	−1.68714e17	−0.580787
$487$	−3.29378e17	−1.11881	−0.559405	−	0.828895i	$-0.688970\pi$
$487$	−3.29378e17	−1.11881	−0.559405	+	0.828895i	$0.688970\pi$
$488$	−7.46633e16	−0.250252
$489$	3.42800e17	1.13379
$490$	4.17030e16	0.136111
$491$	3.19805e17	1.03004	0.515022	−	0.857177i	$-0.327784\pi$
$491$	3.19805e17	1.03004	0.515022	+	0.857177i	$0.327784\pi$
$492$	3.59943e15	0.0114409
$493$	−2.11047e16	−0.0662025
$494$	−1.21757e16	−0.0376936
$495$	1.10092e16	0.0336373
$496$	−7.35438e16	−0.221776
$497$	1.85646e17	0.552548
$498$	1.64469e17	0.483161
$499$	−6.96209e15	−0.0201877	−0.0100938	−	0.999949i	$-0.503213\pi$
$499$	−6.96209e15	−0.0201877	−0.0100938	+	0.999949i	$0.503213\pi$
$500$	−8.34956e16	−0.238978
$501$	6.50359e16	0.183742
$502$	−2.26465e16	−0.0631579
$503$	2.25575e17	0.621011	0.310505	−	0.950572i	$-0.399502\pi$
$503$	2.25575e17	0.621011	0.310505	+	0.950572i	$0.399502\pi$
$504$	−2.75571e16	−0.0748919
$505$	1.39279e17	0.373674
$506$	−3.27387e16	−0.0867127
$507$	−2.60827e17	−0.682025
$508$	−1.66024e17	−0.428605
$509$	3.31280e17	0.844363	0.422182	−	0.906511i	$-0.361264\pi$
$509$	3.31280e17	0.844363	0.422182	+	0.906511i	$0.361264\pi$
$510$	−2.84169e15	−0.00715107
$511$	−3.56091e16	−0.0884758
$512$	−1.80144e16	−0.0441942
$513$	−8.46103e16	−0.204956
$514$	3.90018e17	0.932877
$515$	1.69420e17	0.400145
$516$	−1.51667e16	−0.0353727
$517$	1.66363e16	0.0383149
$518$	−3.87690e16	−0.0881742
$519$	1.41492e16	0.0317793
$520$	−1.09811e16	−0.0243570
$521$	6.60917e17	1.44778	0.723889	−	0.689917i	$-0.242353\pi$
$521$	6.60917e17	1.44778	0.723889	+	0.689917i	$0.242353\pi$
$522$	−1.76596e17	−0.382052
$523$	−4.66930e17	−0.997679	−0.498840	−	0.866694i	$-0.666240\pi$
$523$	−4.66930e17	−0.997679	−0.498840	+	0.866694i	$0.666240\pi$
$524$	2.13274e17	0.450074
$525$	1.56015e17	0.325186
$526$	4.42416e16	0.0910800
$527$	−2.41961e16	−0.0492012
$528$	−2.77649e16	−0.0557668
$529$	−4.20659e17	−0.834580
$530$	1.54170e16	0.0302138
$531$	2.36875e16	0.0458569
$532$	−2.33334e16	−0.0446224
$533$	4.57615e15	0.00864517
$534$	2.76227e17	0.515522
$535$	9.82382e16	0.181126
$536$	6.59373e16	0.120105
$537$	−5.54432e16	−0.0997736
$538$	3.91460e17	0.695990
$539$	1.34056e17	0.235482
$540$	−7.63091e16	−0.132439
$541$	−3.13603e17	−0.537772	−0.268886	−	0.963172i	$-0.586656\pi$
$541$	−3.13603e17	−0.537772	−0.268886	+	0.963172i	$0.586656\pi$
$542$	3.74266e17	0.634140
$543$	3.37974e17	0.565828
$544$	−5.92677e15	−0.00980450
$545$	2.19502e17	0.358808
$546$	4.23644e16	0.0684304
$547$	−1.08937e18	−1.73884	−0.869420	−	0.494074i	$-0.835507\pi$
$547$	−1.08937e18	−1.73884	−0.869420	+	0.494074i	$0.835507\pi$
$548$	−3.26881e17	−0.515604
$549$	−2.05545e17	−0.320396
$550$	−1.29996e17	−0.200250
$551$	−1.49529e17	−0.227636
$552$	7.07107e16	0.106385
$553$	1.29971e16	0.0193256
$554$	6.00251e17	0.882103
$555$	−3.34526e16	−0.0485877
$556$	2.65379e17	0.380961
$557$	−3.34492e17	−0.474599	−0.237299	−	0.971437i	$-0.576262\pi$
$557$	−3.34492e17	−0.474599	−0.237299	+	0.971437i	$0.576262\pi$
$558$	−2.02463e17	−0.283938
$559$	−1.92823e16	−0.0267289
$560$	−2.10442e16	−0.0288343
$561$	−9.13471e15	−0.0123719
$562$	7.19974e17	0.963897
$563$	−2.25034e17	−0.297814	−0.148907	−	0.988851i	$-0.547575\pi$
$563$	−2.25034e17	−0.297814	−0.148907	+	0.988851i	$0.547575\pi$
$564$	−3.59319e16	−0.0470074
$565$	3.70557e16	0.0479225
$566$	−7.89443e17	−1.00929
$567$	1.26797e17	0.160258
$568$	3.34097e17	0.417454
$569$	−1.08609e18	−1.34164	−0.670822	−	0.741618i	$-0.734059\pi$
$569$	−1.08609e18	−1.34164	−0.670822	+	0.741618i	$0.734059\pi$
$570$	−2.01337e16	−0.0245888
$571$	−1.01199e18	−1.22192	−0.610960	−	0.791662i	$-0.709216\pi$
$571$	−1.01199e18	−1.22192	−0.610960	+	0.791662i	$0.709216\pi$
$572$	−3.52991e16	−0.0421395
$573$	−9.32171e17	−1.10025
$574$	8.76973e15	0.0102343
$575$	3.31069e17	0.382013
$576$	−4.95929e16	−0.0565814
$577$	6.33312e17	0.714455	0.357227	−	0.934017i	$-0.383722\pi$
$577$	6.33312e17	0.714455	0.357227	+	0.934017i	$0.383722\pi$
$578$	6.31943e17	0.704932
$579$	−4.14647e17	−0.457370
$580$	−1.34859e17	−0.147095
$581$	4.00716e17	0.432206
$582$	−5.19401e17	−0.553992
$583$	4.95583e16	0.0522722
$584$	−6.40836e16	−0.0668442
$585$	−3.02306e16	−0.0311841
$586$	6.97035e17	0.711082
$587$	1.76669e18	1.78243	0.891216	−	0.453578i	$-0.149853\pi$
$587$	1.76669e18	1.78243	0.891216	+	0.453578i	$0.149853\pi$
$588$	−2.89540e17	−0.288906
$589$	−1.71432e17	−0.169177
$590$	1.80891e16	0.0176555
$591$	−8.94194e17	−0.863203
$592$	−6.97704e16	−0.0666163
$593$	−1.09484e18	−1.03394	−0.516970	−	0.856003i	$-0.672940\pi$
$593$	−1.09484e18	−1.03394	−0.516970	+	0.856003i	$0.672940\pi$
$594$	−2.45298e17	−0.229130
$595$	−6.92358e15	−0.00639691
$596$	−8.06158e17	−0.736748
$597$	−1.70544e17	−0.154171
$598$	8.98986e16	0.0803887
$599$	1.31291e18	1.16135	0.580673	−	0.814137i	$-0.302790\pi$
$599$	1.31291e18	1.16135	0.580673	+	0.814137i	$0.302790\pi$
$600$	2.80772e17	0.245681
$601$	−4.84449e16	−0.0419338	−0.0209669	−	0.999780i	$-0.506674\pi$
$601$	−4.84449e16	−0.0419338	−0.0209669	+	0.999780i	$0.506674\pi$
$602$	−3.69525e16	−0.0316422
$603$	1.81523e17	0.153769
$604$	3.13099e17	0.262386
$605$	2.70253e16	0.0224058
$606$	−9.67003e17	−0.793151
$607$	−2.68669e17	−0.218018	−0.109009	−	0.994041i	$-0.534768\pi$
$607$	−2.68669e17	−0.218018	−0.109009	+	0.994041i	$0.534768\pi$
$608$	−4.19919e16	−0.0337126
$609$	5.20277e17	0.413259
$610$	−1.56966e17	−0.123356
$611$	−4.56823e16	−0.0355206
$612$	−1.63162e16	−0.0125526
$613$	−2.37487e18	−1.80778	−0.903891	−	0.427763i	$-0.859302\pi$
$613$	−2.37487e18	−1.80778	−0.903891	+	0.427763i	$0.859302\pi$
$614$	−7.94129e17	−0.598132
$615$	7.56714e15	0.00563954
$616$	−6.76471e16	−0.0498855
$617$	−1.59521e17	−0.116403	−0.0582016	−	0.998305i	$-0.518537\pi$
$617$	−1.59521e17	−0.116403	−0.0582016	+	0.998305i	$0.518537\pi$
$618$	−1.17627e18	−0.849339
$619$	1.11648e18	0.797743	0.398872	−	0.917007i	$-0.369402\pi$
$619$	1.11648e18	0.797743	0.398872	+	0.917007i	$0.369402\pi$
$620$	−1.54613e17	−0.109320
$621$	6.24717e17	0.437107
$622$	1.59922e18	1.10731
$623$	6.73006e17	0.461154
$624$	7.62408e16	0.0516997
$625$	1.22407e18	0.821456
$626$	−2.16090e17	−0.143516
$627$	−6.47204e16	−0.0425405
$628$	−4.36547e16	−0.0283983
$629$	−2.29546e16	−0.0147789
$630$	−5.79338e16	−0.0369163
$631$	1.90484e18	1.20134	0.600671	−	0.799496i	$-0.294900\pi$
$631$	1.90484e18	1.20134	0.600671	+	0.799496i	$0.294900\pi$
$632$	2.33901e16	0.0146006
$633$	1.35709e18	0.838462
$634$	1.93132e18	1.18106
$635$	−3.49036e17	−0.211271
$636$	−1.07039e17	−0.0641312
$637$	−3.68109e17	−0.218308
$638$	−4.33508e17	−0.254485
$639$	9.19757e17	0.534463
$640$	−3.78720e16	−0.0217846
$641$	−4.48235e16	−0.0255228	−0.0127614	−	0.999919i	$-0.504062\pi$
$641$	−4.48235e16	−0.0255228	−0.0127614	+	0.999919i	$0.504062\pi$
$642$	−6.82059e17	−0.384454
$643$	2.79236e18	1.55812	0.779060	−	0.626950i	$-0.215697\pi$
$643$	2.79236e18	1.55812	0.779060	+	0.626950i	$0.215697\pi$
$644$	1.72281e17	0.0951657
$645$	−3.18852e16	−0.0174362
$646$	−1.38154e16	−0.00747915
$647$	2.44546e18	1.31064	0.655319	−	0.755352i	$-0.272534\pi$
$647$	2.44546e18	1.31064	0.655319	+	0.755352i	$0.272534\pi$
$648$	2.28190e17	0.121076
$649$	5.81480e16	0.0305453
$650$	3.56961e17	0.185646
$651$	5.96485e17	0.307131
$652$	1.50307e18	0.766251
$653$	1.15911e16	0.00585045	0.00292523	−	0.999996i	$-0.499069\pi$
$653$	1.15911e16	0.00585045	0.00292523	+	0.999996i	$0.499069\pi$
$654$	−1.52398e18	−0.761597
$655$	4.48370e17	0.221854
$656$	1.57824e16	0.00773211
$657$	−1.76420e17	−0.0855800
$658$	−8.75454e16	−0.0420499
$659$	−6.75265e17	−0.321158	−0.160579	−	0.987023i	$-0.551336\pi$
$659$	−6.75265e17	−0.321158	−0.160579	+	0.987023i	$0.551336\pi$
$660$	−5.83707e16	−0.0274890
$661$	−1.97459e18	−0.920802	−0.460401	−	0.887711i	$-0.652294\pi$
$661$	−1.97459e18	−0.920802	−0.460401	+	0.887711i	$0.652294\pi$
$662$	−2.49778e18	−1.15339
$663$	2.50834e16	0.0114696
$664$	7.21145e17	0.326535
$665$	−4.90543e16	−0.0219956
$666$	−1.92075e17	−0.0852882
$667$	1.10404e18	0.485477
$668$	2.85163e17	0.124178
$669$	1.69987e18	0.733073
$670$	1.38621e17	0.0592030
$671$	−5.04572e17	−0.213416
$672$	1.46108e17	0.0612031
$673$	−2.43594e18	−1.01058	−0.505288	−	0.862951i	$-0.668614\pi$
$673$	−2.43594e18	−1.01058	−0.505288	+	0.862951i	$0.668614\pi$
$674$	4.78485e17	0.196598
$675$	2.48057e18	1.00943
$676$	−1.14365e18	−0.460934
$677$	−3.95380e18	−1.57830	−0.789148	−	0.614203i	$-0.789477\pi$
$677$	−3.95380e18	−1.57830	−0.789148	+	0.614203i	$0.789477\pi$
$678$	−2.57274e17	−0.101719
$679$	−1.26548e18	−0.495567
$680$	−1.24600e16	−0.00483291
$681$	−1.25480e17	−0.0482078
$682$	−4.97007e17	−0.189132
$683$	−3.36873e18	−1.26979	−0.634895	−	0.772599i	$-0.718957\pi$
$683$	−3.36873e18	−1.26979	−0.634895	+	0.772599i	$0.718957\pi$
$684$	−1.15602e17	−0.0431619
$685$	−6.87209e17	−0.254156
$686$	−1.60869e18	−0.589341
$687$	3.76680e17	0.136695
$688$	−6.65014e16	−0.0239059
$689$	−1.36084e17	−0.0484599
$690$	1.48657e17	0.0524403
$691$	−2.27962e18	−0.796628	−0.398314	−	0.917249i	$-0.630405\pi$
$691$	−2.27962e18	−0.796628	−0.398314	+	0.917249i	$0.630405\pi$
$692$	6.20400e16	0.0214774
$693$	−1.86230e17	−0.0638680
$694$	−2.71276e17	−0.0921670
$695$	5.57911e17	0.187786
$696$	9.36313e17	0.312220
$697$	5.19244e15	0.00171537
$698$	−3.62685e18	−1.18705
$699$	9.05545e17	0.293636
$700$	6.84080e17	0.219771
$701$	−6.13061e18	−1.95136	−0.975679	−	0.219206i	$-0.929653\pi$
$701$	−6.13061e18	−1.95136	−0.975679	+	0.219206i	$0.929653\pi$
$702$	6.73574e17	0.212419
$703$	−1.62636e17	−0.0508168
$704$	−1.21741e17	−0.0376889
$705$	−7.55404e16	−0.0231713
$706$	−2.29768e18	−0.698328
$707$	−2.35603e18	−0.709504
$708$	−1.25591e17	−0.0374751
$709$	−1.93040e17	−0.0570752	−0.0285376	−	0.999593i	$-0.509085\pi$
$709$	−1.93040e17	−0.0570752	−0.0285376	+	0.999593i	$0.509085\pi$
$710$	7.02379e17	0.205775
$711$	6.43922e16	0.0186931
$712$	1.21117e18	0.348406
$713$	1.26576e18	0.360802
$714$	4.80698e16	0.0135779
$715$	−7.42100e16	−0.0207717
$716$	−2.43102e17	−0.0674301
$717$	4.17717e18	1.14817
$718$	2.83687e18	0.772734
$719$	2.65569e18	0.716867	0.358434	−	0.933555i	$-0.383311\pi$
$719$	2.65569e18	0.716867	0.358434	+	0.933555i	$0.383311\pi$
$720$	−1.04260e17	−0.0278906
$721$	−2.86589e18	−0.759767
$722$	2.59351e18	0.681390
$723$	−1.59462e18	−0.415200
$724$	1.48191e18	0.382404
$725$	4.38384e18	1.12113
$726$	−1.87634e17	−0.0475581
$727$	−2.86870e17	−0.0720628	−0.0360314	−	0.999351i	$-0.511472\pi$
$727$	−2.86870e17	−0.0720628	−0.0360314	+	0.999351i	$0.511472\pi$
$728$	1.85755e17	0.0462473
$729$	3.85041e18	0.950120
$730$	−1.34724e17	−0.0329494
$731$	−2.18791e16	−0.00530355
$732$	1.08980e18	0.261834
$733$	−1.96067e18	−0.466906	−0.233453	−	0.972368i	$-0.575002\pi$
$733$	−1.96067e18	−0.466906	−0.233453	+	0.972368i	$0.575002\pi$
$734$	5.90671e18	1.39419
$735$	−6.08706e17	−0.142410
$736$	3.10045e17	0.0718984
$737$	4.45602e17	0.102426
$738$	4.34483e16	0.00989935
$739$	4.93679e18	1.11495	0.557475	−	0.830194i	$-0.311770\pi$
$739$	4.93679e18	1.11495	0.557475	+	0.830194i	$0.311770\pi$
$740$	−1.46680e17	−0.0328370
$741$	1.77719e17	0.0394380
$742$	−2.60792e17	−0.0573678
$743$	−6.69842e18	−1.46065	−0.730323	−	0.683102i	$-0.760631\pi$
$743$	−6.69842e18	−1.46065	−0.730323	+	0.683102i	$0.760631\pi$
$744$	1.07346e18	0.232040
$745$	−1.69480e18	−0.363164
$746$	1.31125e18	0.278537
$747$	1.98529e18	0.418060
$748$	−4.00530e16	−0.00836131
$749$	−1.66179e18	−0.343909
$750$	1.21872e18	0.250038
$751$	−5.34477e18	−1.08710	−0.543550	−	0.839377i	$-0.682920\pi$
$751$	−5.34477e18	−1.08710	−0.543550	+	0.839377i	$0.682920\pi$
$752$	−1.57551e17	−0.0317690
$753$	3.30554e17	0.0660807
$754$	1.19039e18	0.235925
$755$	6.58233e17	0.129338
$756$	1.29084e18	0.251466
$757$	−2.75160e18	−0.531449	−0.265725	−	0.964049i	$-0.585611\pi$
$757$	−2.75160e18	−0.531449	−0.265725	+	0.964049i	$0.585611\pi$
$758$	−6.22001e17	−0.119108
$759$	4.77861e17	0.0907256
$760$	−8.82803e16	−0.0166179
$761$	4.18820e18	0.781676	0.390838	−	0.920459i	$-0.372185\pi$
$761$	4.18820e18	0.781676	0.390838	+	0.920459i	$0.372185\pi$
$762$	2.42332e18	0.448440
$763$	−3.71307e18	−0.681278
$764$	−4.08729e18	−0.743582
$765$	−3.43018e16	−0.00618754
$766$	4.86116e18	0.869466
$767$	−1.59671e17	−0.0283176
$768$	2.62942e17	0.0462394
$769$	8.92185e18	1.55573	0.777864	−	0.628433i	$-0.216303\pi$
$769$	8.92185e18	1.55573	0.777864	+	0.628433i	$0.216303\pi$
$770$	−1.42216e17	−0.0245900
$771$	−5.69279e18	−0.976049
$772$	−1.81810e18	−0.309105
$773$	−4.73291e18	−0.797924	−0.398962	−	0.916967i	$-0.630629\pi$
$773$	−4.73291e18	−0.797924	−0.398962	+	0.916967i	$0.630629\pi$
$774$	−1.83076e17	−0.0306066
$775$	5.02597e18	0.833219
$776$	−2.27742e18	−0.374405
$777$	5.65881e17	0.0922547
$778$	3.50254e18	0.566261
$779$	3.67890e16	0.00589827
$780$	1.60283e17	0.0254842
$781$	2.25782e18	0.356006
$782$	1.02006e17	0.0159507
$783$	8.27216e18	1.28282
$784$	−1.26955e18	−0.195252
$785$	−9.17761e16	−0.0139983
$786$	−3.11299e18	−0.470903
$787$	7.05561e17	0.105852	0.0529260	−	0.998598i	$-0.483145\pi$
$787$	7.05561e17	0.105852	0.0529260	+	0.998598i	$0.483145\pi$
$788$	−3.92077e18	−0.583379
$789$	−6.45759e17	−0.0952950
$790$	4.91736e16	0.00719707
$791$	−6.26829e17	−0.0909918
$792$	−3.35148e17	−0.0482528
$793$	1.38553e18	0.197851
$794$	−3.61138e18	−0.511494
$795$	−2.25029e17	−0.0316121
$796$	−7.47784e17	−0.104194
$797$	3.39436e18	0.469114	0.234557	−	0.972102i	$-0.424636\pi$
$797$	3.39436e18	0.469114	0.234557	+	0.972102i	$0.424636\pi$
$798$	3.40580e17	0.0466874
$799$	−5.18345e16	−0.00704798
$800$	1.23110e18	0.166038
$801$	3.33431e18	0.446061
$802$	−3.35456e18	−0.445145
$803$	−4.33075e17	−0.0570049
$804$	−9.62435e17	−0.125663
$805$	3.62191e17	0.0469098
$806$	1.36475e18	0.175338
$807$	−5.71384e18	−0.728199
$808$	−4.24002e18	−0.536036
$809$	5.49065e18	0.688586	0.344293	−	0.938862i	$-0.388119\pi$
$809$	5.49065e18	0.688586	0.344293	+	0.938862i	$0.388119\pi$
$810$	4.79728e17	0.0596819
$811$	3.62040e18	0.446808	0.223404	−	0.974726i	$-0.428283\pi$
$811$	3.62040e18	0.446808	0.223404	+	0.974726i	$0.428283\pi$
$812$	2.28126e18	0.279293
$813$	−5.46286e18	−0.663486
$814$	−4.71506e17	−0.0568105
$815$	3.15994e18	0.377706
$816$	8.65085e16	0.0102582
$817$	−1.55016e17	−0.0182361
$818$	−1.07412e19	−1.25359
$819$	5.11377e17	0.0592101
$820$	3.31796e16	0.00381137
$821$	−8.94485e18	−1.01940	−0.509698	−	0.860354i	$-0.670243\pi$
$821$	−8.94485e18	−1.01940	−0.509698	+	0.860354i	$0.670243\pi$
$822$	4.77123e18	0.539465
$823$	−4.31382e18	−0.483909	−0.241954	−	0.970288i	$-0.577788\pi$
$823$	−4.31382e18	−0.483909	−0.241954	+	0.970288i	$0.577788\pi$
$824$	−5.15758e18	−0.574010
$825$	1.89745e18	0.209517
$826$	−3.05993e17	−0.0335229
$827$	4.53811e17	0.0493275	0.0246638	−	0.999696i	$-0.492148\pi$
$827$	4.53811e17	0.0493275	0.0246638	+	0.999696i	$0.492148\pi$
$828$	8.53543e17	0.0920509
$829$	−3.77967e18	−0.404436	−0.202218	−	0.979341i	$-0.564815\pi$
$829$	−3.77967e18	−0.404436	−0.202218	+	0.979341i	$0.564815\pi$
$830$	1.51608e18	0.160958
$831$	−8.76139e18	−0.922924
$832$	3.34293e17	0.0349402
$833$	−4.17684e17	−0.0433167
$834$	−3.87353e18	−0.398591
$835$	5.99504e17	0.0612110
$836$	−2.83780e17	−0.0287502
$837$	9.48384e18	0.953386
$838$	−1.11386e19	−1.11108
$839$	−4.98543e18	−0.493458	−0.246729	−	0.969084i	$-0.579356\pi$
$839$	−4.98543e18	−0.493458	−0.246729	+	0.969084i	$0.579356\pi$
$840$	3.07165e17	0.0301687
$841$	4.35851e18	0.424780
$842$	1.50502e18	0.145550
$843$	−1.05089e19	−1.00850
$844$	5.95041e18	0.566658
$845$	−2.40431e18	−0.227207
$846$	−4.33731e17	−0.0406736
$847$	−4.57157e17	−0.0425425
$848$	−4.69332e17	−0.0433418
$849$	1.15229e19	1.05599
$850$	4.05035e17	0.0368357
$851$	1.20082e18	0.108376
$852$	−4.87656e18	−0.436773
$853$	−2.93026e17	−0.0260458	−0.0130229	−	0.999915i	$-0.504145\pi$
$853$	−2.93026e17	−0.0260458	−0.0130229	+	0.999915i	$0.504145\pi$
$854$	2.65522e18	0.234220
$855$	−2.43032e17	−0.0212757
$856$	−2.99062e18	−0.259826
$857$	2.40051e18	0.206980	0.103490	−	0.994630i	$-0.466999\pi$
$857$	2.40051e18	0.206980	0.103490	+	0.994630i	$0.466999\pi$
$858$	5.15233e17	0.0440896
$859$	1.72966e19	1.46895	0.734474	−	0.678637i	$-0.237429\pi$
$859$	1.72966e19	1.46895	0.734474	+	0.678637i	$0.237429\pi$
$860$	−1.39807e17	−0.0117839
$861$	−1.28005e17	−0.0107079
$862$	−9.89718e18	−0.821702
$863$	−1.10049e18	−0.0906809	−0.0453405	−	0.998972i	$-0.514437\pi$
$863$	−1.10049e18	−0.0906809	−0.0453405	+	0.998972i	$0.514437\pi$
$864$	2.32305e18	0.189985
$865$	1.30428e17	0.0105868
$866$	1.08720e19	0.875881
$867$	−9.22398e18	−0.737554
$868$	2.61541e18	0.207568
$869$	1.58070e17	0.0124515
$870$	1.96843e18	0.153902
$871$	−1.22360e18	−0.0949556
$872$	−6.68221e18	−0.514711
$873$	−6.26964e18	−0.479347
$874$	7.22720e17	0.0548461
$875$	2.96932e18	0.223668
$876$	9.35378e17	0.0699376
$877$	1.78397e18	0.132400	0.0662002	−	0.997806i	$-0.478912\pi$
$877$	1.78397e18	0.132400	0.0662002	+	0.997806i	$0.478912\pi$
$878$	−6.10766e16	−0.00449946
$879$	−1.01741e19	−0.743990
$880$	−2.55938e17	−0.0185779
$881$	2.35963e19	1.70020	0.850102	−	0.526617i	$-0.176540\pi$
$881$	2.35963e19	1.70020	0.850102	+	0.526617i	$0.176540\pi$
$882$	−3.49501e18	−0.249979
$883$	−1.83145e19	−1.30032	−0.650161	−	0.759796i	$-0.725299\pi$
$883$	−1.83145e19	−1.30032	−0.650161	+	0.759796i	$0.725299\pi$
$884$	1.09983e17	0.00775151
$885$	−2.64033e17	−0.0184725
$886$	1.13767e19	0.790129
$887$	−4.59129e18	−0.316542	−0.158271	−	0.987396i	$-0.550592\pi$
$887$	−4.59129e18	−0.316542	−0.158271	+	0.987396i	$0.550592\pi$
$888$	1.01838e18	0.0696991
$889$	5.90425e18	0.401147
$890$	2.54627e18	0.171739
$891$	1.54210e18	0.103254
$892$	7.45344e18	0.495433
$893$	−3.67253e17	−0.0242343
$894$	1.17668e19	0.770844
$895$	−5.11078e17	−0.0332382
$896$	6.40639e17	0.0413629
$897$	−1.31218e18	−0.0841089
$898$	−7.48594e18	−0.476376
$899$	1.67605e19	1.05889
$900$	3.38917e18	0.212578
$901$	−1.54411e17	−0.00961541
$902$	1.06657e17	0.00659397
$903$	5.39367e17	0.0331066
$904$	−1.12807e18	−0.0687450
$905$	3.11546e18	0.188498
$906$	−4.57005e18	−0.274529
$907$	2.66383e19	1.58876	0.794381	−	0.607419i	$-0.207795\pi$
$907$	2.66383e19	1.58876	0.794381	+	0.607419i	$0.207795\pi$
$908$	−5.50190e17	−0.0325803
$909$	−1.16726e19	−0.686282
$910$	3.90517e17	0.0227966
$911$	−9.97557e18	−0.578187	−0.289094	−	0.957301i	$-0.593354\pi$
$911$	−9.97557e18	−0.578187	−0.289094	+	0.957301i	$0.593354\pi$
$912$	6.12922e17	0.0352727
$913$	4.87348e18	0.278470
$914$	1.96953e19	1.11741
$915$	2.29111e18	0.129065
$916$	1.65163e18	0.0923830
$917$	−7.58457e18	−0.421241
$918$	7.64287e17	0.0421482
$919$	9.74115e18	0.533408	0.266704	−	0.963779i	$-0.414065\pi$
$919$	9.74115e18	0.533408	0.266704	+	0.963779i	$0.414065\pi$
$920$	6.51814e17	0.0354407
$921$	1.15913e19	0.625812
$922$	−1.93339e19	−1.03650
$923$	−6.19984e18	−0.330042
$924$	9.87392e17	0.0521941
$925$	4.76810e18	0.250279
$926$	7.60357e18	0.396320
$927$	−1.41986e19	−0.734900
$928$	4.10545e18	0.211008
$929$	2.55447e19	1.30376	0.651880	−	0.758322i	$-0.273980\pi$
$929$	2.55447e19	1.30376	0.651880	+	0.758322i	$0.273980\pi$
$930$	2.25676e18	0.114379
$931$	−2.95933e18	−0.148943
$932$	3.97054e18	0.198448
$933$	−2.33425e19	−1.15856
$934$	4.47851e18	0.220739
$935$	−8.42041e16	−0.00412152
$936$	9.20296e17	0.0447337
$937$	−8.48715e18	−0.409689	−0.204845	−	0.978795i	$-0.565669\pi$
$937$	−8.48715e18	−0.409689	−0.204845	+	0.978795i	$0.565669\pi$
$938$	−2.34490e18	−0.112410
$939$	3.15409e18	0.150158
$940$	−3.31222e17	−0.0156599
$941$	−7.75658e18	−0.364198	−0.182099	−	0.983280i	$-0.558289\pi$
$941$	−7.75658e18	−0.364198	−0.182099	+	0.983280i	$0.558289\pi$
$942$	6.37193e17	0.0297126
$943$	−2.71630e17	−0.0125792
$944$	−5.50679e17	−0.0253268
$945$	2.71375e18	0.123955
$946$	−4.49414e17	−0.0203871
$947$	1.02868e17	0.00463453	0.00231726	−	0.999997i	$-0.499262\pi$
$947$	1.02868e17	0.00463453	0.00231726	+	0.999997i	$0.499262\pi$
$948$	−3.41408e17	−0.0152763
$949$	1.18920e18	0.0528475
$950$	2.86972e18	0.126659
$951$	−2.81899e19	−1.23572
$952$	2.10771e17	0.00917638
$953$	−2.51081e19	−1.08570	−0.542849	−	0.839830i	$-0.682654\pi$
$953$	−2.51081e19	−1.08570	−0.542849	+	0.839830i	$0.682654\pi$
$954$	−1.29205e18	−0.0554901
$955$	−8.59279e18	−0.366532
$956$	1.83156e19	0.775972
$957$	6.32757e18	0.266262
$958$	−5.74206e18	−0.239989
$959$	1.16247e19	0.482572
$960$	5.52788e17	0.0227927
$961$	−5.20201e18	−0.213044
$962$	1.29473e18	0.0526673
$963$	−8.23307e18	−0.332653
$964$	−6.99191e18	−0.280605
$965$	−3.82223e18	−0.152366
$966$	−2.51466e18	−0.0995697
$967$	−2.03388e19	−0.799934	−0.399967	−	0.916529i	$-0.630978\pi$
$967$	−2.03388e19	−0.799934	−0.399967	+	0.916529i	$0.630978\pi$
$968$	−8.22720e17	−0.0321412
$969$	2.01653e17	0.00782527
$970$	−4.78786e18	−0.184555
$971$	−4.04038e19	−1.54702	−0.773512	−	0.633782i	$-0.781502\pi$
$971$	−4.04038e19	−1.54702	−0.773512	+	0.633782i	$0.781502\pi$
$972$	1.07977e19	0.410678
$973$	−9.43757e18	−0.356555
$974$	2.10802e19	0.791118
$975$	−5.21029e18	−0.194237
$976$	4.77845e18	0.176955
$977$	1.43938e19	0.529494	0.264747	−	0.964318i	$-0.414712\pi$
$977$	1.43938e19	0.529494	0.264747	+	0.964318i	$0.414712\pi$
$978$	−2.19392e19	−0.801711
$979$	8.18505e18	0.297121
$980$	−2.66899e18	−0.0962450
$981$	−1.83959e19	−0.658979
$982$	−2.04675e19	−0.728351
$983$	−6.97609e17	−0.0246612	−0.0123306	−	0.999924i	$-0.503925\pi$
$983$	−6.97609e17	−0.0246612	−0.0123306	+	0.999924i	$0.503925\pi$
$984$	−2.30363e17	−0.00808993
$985$	−8.24271e18	−0.287564
$986$	1.35070e18	0.0468122
$987$	1.27783e18	0.0439959
$988$	7.79242e17	0.0266534
$989$	1.14455e18	0.0388920
$990$	−7.04587e17	−0.0237852
$991$	−1.49887e19	−0.502673	−0.251336	−	0.967900i	$-0.580870\pi$
$991$	−1.49887e19	−0.502673	−0.251336	+	0.967900i	$0.580870\pi$
$992$	4.70680e18	0.156820
$993$	3.64581e19	1.20677
$994$	−1.18814e19	−0.390710
$995$	−1.57208e18	−0.0513600
$996$	−1.05260e19	−0.341647
$997$	−3.37660e19	−1.08883	−0.544417	−	0.838815i	$-0.683249\pi$
$997$	−3.37660e19	−1.08883	−0.544417	+	0.838815i	$0.683249\pi$
$998$	4.45574e17	0.0142748
$999$	8.99724e18	0.286374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.14.a.a.1.2	✓	2
3.2	odd	2		198.14.a.e.1.1		2
4.3	odd	2		176.14.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.14.a.a.1.2	✓	2	1.1	even	1	trivial
176.14.a.b.1.1		2	4.3	odd	2
198.14.a.e.1.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	22.a (trivial)

\(f(q)\)	\(=\)	\(q-64.0000 q^{2} +934.158 q^{3} +4096.00 q^{4} +8611.10 q^{5} -59786.1 q^{6} -145664. q^{7} -262144. q^{8} -721672. q^{9} +O(q^{10})\)	\(q-64.0000 q^{2} +934.158 q^{3} +4096.00 q^{4} +8611.10 q^{5} -59786.1 q^{6} -145664. q^{7} -262144. q^{8} -721672. q^{9} -551110. q^{10} -1.77156e6 q^{11} +3.82631e6 q^{12} +4.86460e6 q^{13} +9.32252e6 q^{14} +8.04413e6 q^{15} +1.67772e7 q^{16} +5.51974e6 q^{17} +4.61870e7 q^{18} +3.91080e7 q^{19} +3.52711e7 q^{20} -1.36073e8 q^{21} +1.13380e8 q^{22} -2.88752e8 q^{23} -2.44884e8 q^{24} -1.14655e9 q^{25} -3.11335e8 q^{26} -2.16350e9 q^{27} -5.96641e8 q^{28} -3.82350e9 q^{29} -5.14824e8 q^{30} -4.38355e9 q^{31} -1.07374e9 q^{32} -1.65492e9 q^{33} -3.53263e8 q^{34} -1.25433e9 q^{35} -2.95597e9 q^{36} -4.15864e9 q^{37} -2.50291e9 q^{38} +4.54431e9 q^{39} -2.25735e9 q^{40} +9.40704e8 q^{41} +8.70870e9 q^{42} -3.96379e9 q^{43} -7.25631e9 q^{44} -6.21439e9 q^{45} +1.84801e10 q^{46} -9.39075e9 q^{47} +1.56726e10 q^{48} -7.56709e10 q^{49} +7.33793e10 q^{50} +5.15631e9 q^{51} +1.99254e10 q^{52} -2.79744e10 q^{53} +1.38464e11 q^{54} -1.52551e10 q^{55} +3.81850e10 q^{56} +3.65330e10 q^{57} +2.44704e11 q^{58} -3.28230e10 q^{59} +3.29487e10 q^{60} +2.84818e11 q^{61} +2.80547e11 q^{62} +1.05122e11 q^{63} +6.87195e10 q^{64} +4.18896e10 q^{65} +1.05915e11 q^{66} -2.51531e11 q^{67} +2.26088e10 q^{68} -2.69740e11 q^{69} +8.02771e10 q^{70} -1.27448e12 q^{71} +1.89182e11 q^{72} +2.44460e11 q^{73} +2.66153e11 q^{74} -1.07106e12 q^{75} +1.60186e11 q^{76} +2.58053e11 q^{77} -2.90836e11 q^{78} -8.92263e10 q^{79} +1.44470e11 q^{80} -8.70476e11 q^{81} -6.02051e10 q^{82} -2.75095e12 q^{83} -5.57357e11 q^{84} +4.75310e10 q^{85} +2.53683e11 q^{86} -3.57175e12 q^{87} +4.64404e11 q^{88} -4.62025e12 q^{89} +3.97721e11 q^{90} -7.08600e11 q^{91} -1.18273e12 q^{92} -4.09493e12 q^{93} +6.01008e11 q^{94} +3.36763e11 q^{95} -1.00304e12 q^{96} +8.68766e12 q^{97} +4.84294e12 q^{98} +1.27849e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 128 q^{2} - 662 q^{3} + 8192 q^{4} - 48566 q^{5} + 42368 q^{6} + 404508 q^{7} - 524288 q^{8} + 231724 q^{9}+O(q^{10}) \) 2 * q - 128 * q^2 - 662 * q^3 + 8192 * q^4 - 48566 * q^5 + 42368 * q^6 + 404508 * q^7 - 524288 * q^8 + 231724 * q^9	\( 2 q - 128 q^{2} - 662 q^{3} + 8192 q^{4} - 48566 q^{5} + 42368 q^{6} + 404508 q^{7} - 524288 q^{8} + 231724 q^{9} + 3108224 q^{10} - 3543122 q^{11} - 2711552 q^{12} + 28445952 q^{13} - 25888512 q^{14} + 99307794 q^{15} + 33554432 q^{16} + 107032052 q^{17} - 14830336 q^{18} - 73524568 q^{19} - 198926336 q^{20} - 1014235348 q^{21} + 226759808 q^{22} - 987164862 q^{23} + 173539328 q^{24} + 901965576 q^{25} - 1820540928 q^{26} - 1140484994 q^{27} + 1656864768 q^{28} - 9516399376 q^{29} - 6355698816 q^{30} - 6865940430 q^{31} - 2147483648 q^{32} + 1172773382 q^{33} - 6850051328 q^{34} - 32711590964 q^{35} + 949141504 q^{36} - 4145233266 q^{37} + 4705572352 q^{38} - 33095241568 q^{39} + 12731285504 q^{40} + 39451523656 q^{41} + 64911062272 q^{42} + 5532549228 q^{43} - 14512627712 q^{44} - 60726834468 q^{45} + 63178551168 q^{46} - 28411609744 q^{47} - 11106516992 q^{48} + 130129720218 q^{49} - 57725796864 q^{50} - 156873354588 q^{51} + 116514619392 q^{52} - 49178542972 q^{53} + 72991039616 q^{54} + 86037631526 q^{55} - 106039345152 q^{56} + 216312273320 q^{57} + 609049560064 q^{58} + 110326136718 q^{59} + 406764724224 q^{60} - 161816895480 q^{61} + 439420187520 q^{62} + 629654304296 q^{63} + 137438953472 q^{64} - 1306423470272 q^{65} - 75057496448 q^{66} - 483661746106 q^{67} + 438403284992 q^{68} + 845036821770 q^{69} + 2093541821696 q^{70} + 318713704774 q^{71} - 60745056256 q^{72} - 1073843539168 q^{73} + 265294929024 q^{74} - 4340817675224 q^{75} - 301156630528 q^{76} - 716610596988 q^{77} + 2118095460352 q^{78} - 742108796220 q^{79} - 814802272256 q^{80} - 4023398824910 q^{81} - 2524897513984 q^{82} - 6905249437156 q^{83} - 4154307985408 q^{84} - 5756648698492 q^{85} - 354083150592 q^{86} + 5515016618352 q^{87} + 928808173568 q^{88} - 8233927751362 q^{89} + 3886517405952 q^{90} + 12265206226208 q^{91} - 4043427274752 q^{92} - 132647408710 q^{93} + 1818343023616 q^{94} + 6776763758856 q^{95} + 710817087488 q^{96} - 4680888780654 q^{97} - 8328302093952 q^{98} - 410513201164 q^{99}+O(q^{100}) \) 2 * q - 128 * q^2 - 662 * q^3 + 8192 * q^4 - 48566 * q^5 + 42368 * q^6 + 404508 * q^7 - 524288 * q^8 + 231724 * q^9 + 3108224 * q^10 - 3543122 * q^11 - 2711552 * q^12 + 28445952 * q^13 - 25888512 * q^14 + 99307794 * q^15 + 33554432 * q^16 + 107032052 * q^17 - 14830336 * q^18 - 73524568 * q^19 - 198926336 * q^20 - 1014235348 * q^21 + 226759808 * q^22 - 987164862 * q^23 + 173539328 * q^24 + 901965576 * q^25 - 1820540928 * q^26 - 1140484994 * q^27 + 1656864768 * q^28 - 9516399376 * q^29 - 6355698816 * q^30 - 6865940430 * q^31 - 2147483648 * q^32 + 1172773382 * q^33 - 6850051328 * q^34 - 32711590964 * q^35 + 949141504 * q^36 - 4145233266 * q^37 + 4705572352 * q^38 - 33095241568 * q^39 + 12731285504 * q^40 + 39451523656 * q^41 + 64911062272 * q^42 + 5532549228 * q^43 - 14512627712 * q^44 - 60726834468 * q^45 + 63178551168 * q^46 - 28411609744 * q^47 - 11106516992 * q^48 + 130129720218 * q^49 - 57725796864 * q^50 - 156873354588 * q^51 + 116514619392 * q^52 - 49178542972 * q^53 + 72991039616 * q^54 + 86037631526 * q^55 - 106039345152 * q^56 + 216312273320 * q^57 + 609049560064 * q^58 + 110326136718 * q^59 + 406764724224 * q^60 - 161816895480 * q^61 + 439420187520 * q^62 + 629654304296 * q^63 + 137438953472 * q^64 - 1306423470272 * q^65 - 75057496448 * q^66 - 483661746106 * q^67 + 438403284992 * q^68 + 845036821770 * q^69 + 2093541821696 * q^70 + 318713704774 * q^71 - 60745056256 * q^72 - 1073843539168 * q^73 + 265294929024 * q^74 - 4340817675224 * q^75 - 301156630528 * q^76 - 716610596988 * q^77 + 2118095460352 * q^78 - 742108796220 * q^79 - 814802272256 * q^80 - 4023398824910 * q^81 - 2524897513984 * q^82 - 6905249437156 * q^83 - 4154307985408 * q^84 - 5756648698492 * q^85 - 354083150592 * q^86 + 5515016618352 * q^87 + 928808173568 * q^88 - 8233927751362 * q^89 + 3886517405952 * q^90 + 12265206226208 * q^91 - 4043427274752 * q^92 - 132647408710 * q^93 + 1818343023616 * q^94 + 6776763758856 * q^95 + 710817087488 * q^96 - 4680888780654 * q^97 - 8328302093952 * q^98 - 410513201164 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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