LMFDB - Embedded newform 22.14.a.b.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:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{55441}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 13860 $ x^2 - x - 13860
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-117.230$ 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)

$f(q)$	$=$	$q-64.0000 q^{2} +2225.75 q^{3} +4096.00 q^{4} -31956.8 q^{5} -142448. q^{6} +302984. q^{7} -262144. q^{8} +3.35966e6 q^{9} +O(q^{10})$	\(q-64.0000 q^{2} +2225.75 q^{3} +4096.00 q^{4} -31956.8 q^{5} -142448. q^{6} +302984. q^{7} -262144. q^{8} +3.35966e6 q^{9} +2.04523e6 q^{10} +1.77156e6 q^{11} +9.11669e6 q^{12} +2.00440e6 q^{13} -1.93910e7 q^{14} -7.11280e7 q^{15} +1.67772e7 q^{16} +5.06208e7 q^{17} -2.15018e8 q^{18} -1.58421e8 q^{19} -1.30895e8 q^{20} +6.74367e8 q^{21} -1.13380e8 q^{22} +9.79828e8 q^{23} -5.83468e8 q^{24} -1.99467e8 q^{25} -1.28281e8 q^{26} +3.92921e9 q^{27} +1.24102e9 q^{28} +5.86890e9 q^{29} +4.55219e9 q^{30} +1.21733e9 q^{31} -1.07374e9 q^{32} +3.94306e9 q^{33} -3.23973e9 q^{34} -9.68239e9 q^{35} +1.37612e10 q^{36} -2.66600e10 q^{37} +1.01390e10 q^{38} +4.46130e9 q^{39} +8.37728e9 q^{40} +4.14199e10 q^{41} -4.31595e10 q^{42} +5.82119e10 q^{43} +7.25631e9 q^{44} -1.07364e11 q^{45} -6.27090e10 q^{46} +1.16586e11 q^{47} +3.73420e10 q^{48} -5.08989e9 q^{49} +1.27659e10 q^{50} +1.12669e11 q^{51} +8.21002e9 q^{52} +4.45431e10 q^{53} -2.51469e11 q^{54} -5.66134e10 q^{55} -7.94254e10 q^{56} -3.52607e11 q^{57} -3.75610e11 q^{58} -6.41456e10 q^{59} -2.91340e11 q^{60} -4.11413e11 q^{61} -7.79089e10 q^{62} +1.01792e12 q^{63} +6.87195e10 q^{64} -6.40541e10 q^{65} -2.52356e11 q^{66} +3.99596e11 q^{67} +2.07343e11 q^{68} +2.18086e12 q^{69} +6.19673e11 q^{70} -1.61668e12 q^{71} -8.80715e11 q^{72} -2.11220e12 q^{73} +1.70624e12 q^{74} -4.43964e11 q^{75} -6.48893e11 q^{76} +5.36754e11 q^{77} -2.85523e11 q^{78} +2.00404e12 q^{79} -5.36146e11 q^{80} +3.38907e12 q^{81} -2.65087e12 q^{82} +1.16354e12 q^{83} +2.76221e12 q^{84} -1.61768e12 q^{85} -3.72556e12 q^{86} +1.30627e13 q^{87} -4.64404e11 q^{88} -5.55579e12 q^{89} +6.87129e12 q^{90} +6.07300e11 q^{91} +4.01338e12 q^{92} +2.70947e12 q^{93} -7.46152e12 q^{94} +5.06263e12 q^{95} -2.38989e12 q^{96} -9.32760e12 q^{97} +3.25753e11 q^{98} +5.95184e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 128 q^{2} + 1626 q^{3} + 8192 q^{4} + 7666 q^{5} - 104064 q^{6} + 637048 q^{7} - 524288 q^{8} + 2125044 q^{9}+O(q^{10}) $ 2 * q - 128 * q^2 + 1626 * q^3 + 8192 * q^4 + 7666 * q^5 - 104064 * q^6 + 637048 * q^7 - 524288 * q^8 + 2125044 * q^9	\( 2 q - 128 q^{2} + 1626 q^{3} + 8192 q^{4} + 7666 q^{5} - 104064 q^{6} + 637048 q^{7} - 524288 q^{8} + 2125044 q^{9} - 490624 q^{10} + 3543122 q^{11} + 6660096 q^{12} - 3788668 q^{13} - 40771072 q^{14} - 94891926 q^{15} + 33554432 q^{16} + 37137304 q^{17} - 136002816 q^{18} - 102460596 q^{19} + 31399936 q^{20} + 474010752 q^{21} - 226759808 q^{22} + 1352747042 q^{23} - 426246144 q^{24} + 149795256 q^{25} + 242474752 q^{26} + 5625880326 q^{27} + 2609348608 q^{28} + 7425318120 q^{29} + 6073083264 q^{30} + 8163482594 q^{31} - 2147483648 q^{32} + 2880558186 q^{33} - 2376787456 q^{34} + 3554173208 q^{35} + 8704180224 q^{36} - 12073195594 q^{37} + 6557478144 q^{38} + 7935717852 q^{39} - 2009595904 q^{40} + 73792259580 q^{41} - 30336688128 q^{42} + 20450919684 q^{43} + 14512627712 q^{44} - 156282954732 q^{45} - 86575810688 q^{46} + 71306154600 q^{47} + 27279753216 q^{48} + 9620058330 q^{49} - 9586896384 q^{50} + 120756166944 q^{51} - 15518384128 q^{52} + 309577967404 q^{53} - 360056340864 q^{54} + 13580786626 q^{55} - 166998310912 q^{56} - 386169325212 q^{57} - 475220359680 q^{58} - 403802069082 q^{59} - 388677328896 q^{60} - 81219577008 q^{61} - 522462886016 q^{62} + 605481038784 q^{63} + 137438953472 q^{64} - 293591556156 q^{65} - 184355723904 q^{66} + 229155633102 q^{67} + 152114397184 q^{68} + 1957197038322 q^{69} - 227467085312 q^{70} - 1161878914578 q^{71} - 557067534336 q^{72} + 456037317380 q^{73} + 772684518016 q^{74} - 653435984616 q^{75} - 419678601216 q^{76} + 1128569391928 q^{77} - 507885942528 q^{78} + 5041088907052 q^{79} + 128614137856 q^{80} + 4339865129850 q^{81} - 4722704613120 q^{82} + 5610906244940 q^{83} + 1941548040192 q^{84} - 2151929029832 q^{85} - 1308858859776 q^{86} + 12129274956600 q^{87} - 928808173568 q^{88} - 3239330626042 q^{89} + 10002109102848 q^{90} - 1327956640328 q^{91} + 5540851884032 q^{92} - 1456518848238 q^{93} - 4563593894400 q^{94} + 7279946339020 q^{95} - 1745904205824 q^{96} - 20541366120174 q^{97} - 615683733120 q^{98} + 3764645073684 q^{99}+O(q^{100}) \) 2 * q - 128 * q^2 + 1626 * q^3 + 8192 * q^4 + 7666 * q^5 - 104064 * q^6 + 637048 * q^7 - 524288 * q^8 + 2125044 * q^9 - 490624 * q^10 + 3543122 * q^11 + 6660096 * q^12 - 3788668 * q^13 - 40771072 * q^14 - 94891926 * q^15 + 33554432 * q^16 + 37137304 * q^17 - 136002816 * q^18 - 102460596 * q^19 + 31399936 * q^20 + 474010752 * q^21 - 226759808 * q^22 + 1352747042 * q^23 - 426246144 * q^24 + 149795256 * q^25 + 242474752 * q^26 + 5625880326 * q^27 + 2609348608 * q^28 + 7425318120 * q^29 + 6073083264 * q^30 + 8163482594 * q^31 - 2147483648 * q^32 + 2880558186 * q^33 - 2376787456 * q^34 + 3554173208 * q^35 + 8704180224 * q^36 - 12073195594 * q^37 + 6557478144 * q^38 + 7935717852 * q^39 - 2009595904 * q^40 + 73792259580 * q^41 - 30336688128 * q^42 + 20450919684 * q^43 + 14512627712 * q^44 - 156282954732 * q^45 - 86575810688 * q^46 + 71306154600 * q^47 + 27279753216 * q^48 + 9620058330 * q^49 - 9586896384 * q^50 + 120756166944 * q^51 - 15518384128 * q^52 + 309577967404 * q^53 - 360056340864 * q^54 + 13580786626 * q^55 - 166998310912 * q^56 - 386169325212 * q^57 - 475220359680 * q^58 - 403802069082 * q^59 - 388677328896 * q^60 - 81219577008 * q^61 - 522462886016 * q^62 + 605481038784 * q^63 + 137438953472 * q^64 - 293591556156 * q^65 - 184355723904 * q^66 + 229155633102 * q^67 + 152114397184 * q^68 + 1957197038322 * q^69 - 227467085312 * q^70 - 1161878914578 * q^71 - 557067534336 * q^72 + 456037317380 * q^73 + 772684518016 * q^74 - 653435984616 * q^75 - 419678601216 * q^76 + 1128569391928 * q^77 - 507885942528 * q^78 + 5041088907052 * q^79 + 128614137856 * q^80 + 4339865129850 * q^81 - 4722704613120 * q^82 + 5610906244940 * q^83 + 1941548040192 * q^84 - 2151929029832 * q^85 - 1308858859776 * q^86 + 12129274956600 * q^87 - 928808173568 * q^88 - 3239330626042 * q^89 + 10002109102848 * q^90 - 1327956640328 * q^91 + 5540851884032 * q^92 - 1456518848238 * q^93 - 4563593894400 * q^94 + 7279946339020 * q^95 - 1745904205824 * q^96 - 20541366120174 * q^97 - 615683733120 * q^98 + 3764645073684 * 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
$3$	2225.75	1.76274	0.881372	−	0.472423i	$-0.156621\pi$
$3$	2225.75	1.76274	0.881372	+	0.472423i	$0.156621\pi$
$4$	4096.00	0.500000
$5$	−31956.8	−0.914657	−0.457328	−	0.889298i	$-0.651194\pi$
$5$	−31956.8	−0.914657	−0.457328	+	0.889298i	$0.651194\pi$
$6$	−142448.	−1.24645
$7$	302984.	0.973379	0.486690	−	0.873575i	$-0.338204\pi$
$7$	302984.	0.973379	0.486690	+	0.873575i	$0.338204\pi$
$8$	−262144.	−0.353553
$9$	3.35966e6	2.10727
$10$	2.04523e6	0.646760
$11$	1.77156e6	0.301511
$11$	1.77156e6	0.301511
$12$	9.11669e6	0.881372
$13$	2.00440e6	0.115173	0.0575867	−	0.998341i	$-0.481659\pi$
$13$	2.00440e6	0.115173	0.0575867	+	0.998341i	$0.481659\pi$
$14$	−1.93910e7	−0.688283
$15$	−7.11280e7	−1.61231
$16$	1.67772e7	0.250000
$17$	5.06208e7	0.508640	0.254320	−	0.967120i	$-0.418148\pi$
$17$	5.06208e7	0.508640	0.254320	+	0.967120i	$0.418148\pi$
$18$	−2.15018e8	−1.49006
$19$	−1.58421e8	−0.772529	−0.386265	−	0.922388i	$-0.626235\pi$
$19$	−1.58421e8	−0.772529	−0.386265	+	0.922388i	$0.626235\pi$
$20$	−1.30895e8	−0.457328
$21$	6.74367e8	1.71582
$22$	−1.13380e8	−0.213201
$23$	9.79828e8	1.38013	0.690063	−	0.723749i	$-0.257583\pi$
$23$	9.79828e8	1.38013	0.690063	+	0.723749i	$0.257583\pi$
$24$	−5.83468e8	−0.623224
$25$	−1.99467e8	−0.163403
$26$	−1.28281e8	−0.0814399
$27$	3.92921e9	1.95182
$28$	1.24102e9	0.486690
$29$	5.86890e9	1.83219	0.916094	−	0.400964i	$-0.131325\pi$
$29$	5.86890e9	1.83219	0.916094	+	0.400964i	$0.131325\pi$
$30$	4.55219e9	1.14007
$31$	1.21733e9	0.246352	0.123176	−	0.992385i	$-0.460692\pi$
$31$	1.21733e9	0.246352	0.123176	+	0.992385i	$0.460692\pi$
$32$	−1.07374e9	−0.176777
$33$	3.94306e9	0.531487
$34$	−3.23973e9	−0.359663
$35$	−9.68239e9	−0.890308
$36$	1.37612e10	1.05363
$37$	−2.66600e10	−1.70824	−0.854121	−	0.520074i	$-0.825904\pi$
$37$	−2.66600e10	−1.70824	−0.854121	+	0.520074i	$0.825904\pi$
$38$	1.01390e10	0.546261
$39$	4.46130e9	0.203021
$40$	8.37728e9	0.323380
$41$	4.14199e10	1.36180	0.680900	−	0.732376i	$-0.261589\pi$
$41$	4.14199e10	1.36180	0.680900	+	0.732376i	$0.261589\pi$
$42$	−4.31595e10	−1.21327
$43$	5.82119e10	1.40432	0.702161	−	0.712018i	$-0.252219\pi$
$43$	5.82119e10	1.40432	0.702161	+	0.712018i	$0.252219\pi$
$44$	7.25631e9	0.150756
$45$	−1.07364e11	−1.92742
$46$	−6.27090e10	−0.975897
$47$	1.16586e11	1.57765	0.788826	−	0.614616i	$-0.210689\pi$
$47$	1.16586e11	1.57765	0.788826	+	0.614616i	$0.210689\pi$
$48$	3.73420e10	0.440686
$49$	−5.08989e9	−0.0525332
$50$	1.27659e10	0.115544
$51$	1.12669e11	0.896602
$52$	8.21002e9	0.0575867
$53$	4.45431e10	0.276050	0.138025	−	0.990429i	$-0.455925\pi$
$53$	4.45431e10	0.276050	0.138025	+	0.990429i	$0.455925\pi$
$54$	−2.51469e11	−1.38015
$55$	−5.66134e10	−0.275779
$56$	−7.94254e10	−0.344141
$57$	−3.52607e11	−1.36177
$58$	−3.75610e11	−1.29555
$59$	−6.41456e10	−0.197984	−0.0989918	−	0.995088i	$-0.531562\pi$
$59$	−6.41456e10	−0.197984	−0.0989918	+	0.995088i	$0.531562\pi$
$60$	−2.91340e11	−0.806153
$61$	−4.11413e11	−1.02243	−0.511215	−	0.859453i	$-0.670805\pi$
$61$	−4.11413e11	−1.02243	−0.511215	+	0.859453i	$0.670805\pi$
$62$	−7.79089e10	−0.174197
$63$	1.01792e12	2.05117
$64$	6.87195e10	0.125000
$65$	−6.40541e10	−0.105344
$66$	−2.52356e11	−0.375818
$67$	3.99596e11	0.539678	0.269839	−	0.962906i	$-0.413030\pi$
$67$	3.99596e11	0.539678	0.269839	+	0.962906i	$0.413030\pi$
$68$	2.07343e11	0.254320
$69$	2.18086e12	2.43281
$70$	6.19673e11	0.629543
$71$	−1.61668e12	−1.49777	−0.748885	−	0.662700i	$-0.769411\pi$
$71$	−1.61668e12	−1.49777	−0.748885	+	0.662700i	$0.769411\pi$
$72$	−8.80715e11	−0.745031
$73$	−2.11220e12	−1.63356	−0.816781	−	0.576948i	$-0.804243\pi$
$73$	−2.11220e12	−1.63356	−0.816781	+	0.576948i	$0.804243\pi$
$74$	1.70624e12	1.20791
$75$	−4.43964e11	−0.288038
$76$	−6.48893e11	−0.386265
$77$	5.36754e11	0.293485
$78$	−2.85523e11	−0.143558
$79$	2.00404e12	0.927534	0.463767	−	0.885957i	$-0.346497\pi$
$79$	2.00404e12	0.927534	0.463767	+	0.885957i	$0.346497\pi$
$80$	−5.36146e11	−0.228664
$81$	3.38907e12	1.33330
$82$	−2.65087e12	−0.962938
$83$	1.16354e12	0.390638	0.195319	−	0.980740i	$-0.437426\pi$
$83$	1.16354e12	0.390638	0.195319	+	0.980740i	$0.437426\pi$
$84$	2.76221e12	0.857909
$85$	−1.61768e12	−0.465231
$86$	−3.72556e12	−0.993006
$87$	1.30627e13	3.22968
$88$	−4.64404e11	−0.106600
$89$	−5.55579e12	−1.18498	−0.592490	−	0.805578i	$-0.701855\pi$
$89$	−5.55579e12	−1.18498	−0.592490	+	0.805578i	$0.701855\pi$
$90$	6.87129e12	1.36289
$91$	6.07300e11	0.112107
$92$	4.01338e12	0.690063
$93$	2.70947e12	0.434256
$94$	−7.46152e12	−1.11557
$95$	5.06263e12	0.706599
$96$	−2.38989e12	−0.311612
$97$	−9.32760e12	−1.13698	−0.568491	−	0.822689i	$-0.692473\pi$
$97$	−9.32760e12	−1.13698	−0.568491	+	0.822689i	$0.692473\pi$
$98$	3.25753e11	0.0371466
$99$	5.95184e12	0.635364
$100$	−8.17016e11	−0.0817016
$101$	−1.66214e13	−1.55804	−0.779019	−	0.627000i	$-0.784283\pi$
$101$	−1.66214e13	−1.55804	−0.779019	+	0.627000i	$0.784283\pi$
$102$	−7.21084e12	−0.633994
$103$	−4.44191e12	−0.366545	−0.183273	−	0.983062i	$-0.558669\pi$
$103$	−4.44191e12	−0.366545	−0.183273	+	0.983062i	$0.558669\pi$
$104$	−5.25441e11	−0.0407199
$105$	−2.15506e13	−1.56938
$106$	−2.85076e12	−0.195196
$107$	−6.44502e12	−0.415174	−0.207587	−	0.978217i	$-0.566561\pi$
$107$	−6.44502e12	−0.415174	−0.207587	+	0.978217i	$0.566561\pi$
$108$	1.60940e13	0.975912
$109$	2.37258e13	1.35503	0.677515	−	0.735509i	$-0.263057\pi$
$109$	2.37258e13	1.35503	0.677515	+	0.735509i	$0.263057\pi$
$110$	3.62326e12	0.195005
$111$	−5.93387e13	−3.01119
$112$	5.08322e12	0.243345
$113$	−4.13825e13	−1.86985	−0.934926	−	0.354843i	$-0.884534\pi$
$113$	−4.13825e13	−1.86985	−0.934926	+	0.354843i	$0.884534\pi$
$114$	2.25668e13	0.962917
$115$	−3.13122e13	−1.26234
$116$	2.40390e13	0.916094
$117$	6.73410e12	0.242701
$118$	4.10532e12	0.139995
$119$	1.53373e13	0.495100
$120$	1.86458e13	0.570036
$121$	3.13843e12	0.0909091
$122$	2.63304e13	0.722968
$123$	9.21904e13	2.40051
$124$	4.98617e12	0.123176
$125$	4.53841e13	1.06411
$126$	−6.51470e13	−1.45039
$127$	−3.90066e13	−0.824925	−0.412462	−	0.910975i	$-0.635331\pi$
$127$	−3.90066e13	−0.824925	−0.412462	+	0.910975i	$0.635331\pi$
$128$	−4.39805e12	−0.0883883
$129$	1.29565e14	2.47546
$130$	4.09946e12	0.0744895
$131$	3.58886e13	0.620431	0.310215	−	0.950666i	$-0.399599\pi$
$131$	3.58886e13	0.620431	0.310215	+	0.950666i	$0.399599\pi$
$132$	1.61508e13	0.265744
$133$	−4.79990e13	−0.751964
$134$	−2.55741e13	−0.381610
$135$	−1.25565e14	−1.78525
$136$	−1.32699e13	−0.179831
$137$	−1.20138e14	−1.55238	−0.776189	−	0.630500i	$-0.782850\pi$
$137$	−1.20138e14	−1.55238	−0.776189	+	0.630500i	$0.782850\pi$
$138$	−1.39575e14	−1.72026
$139$	4.26646e13	0.501732	0.250866	−	0.968022i	$-0.419285\pi$
$139$	4.26646e13	0.501732	0.250866	+	0.968022i	$0.419285\pi$
$140$	−3.96591e13	−0.445154
$141$	2.59492e14	2.78100
$142$	1.03468e14	1.05908
$143$	3.55091e12	0.0347261
$144$	5.63658e13	0.526816
$145$	−1.87551e14	−1.67582
$146$	1.35180e14	1.15510
$147$	−1.13288e13	−0.0926026
$148$	−1.09200e14	−0.854121
$149$	6.61821e13	0.495484	0.247742	−	0.968826i	$-0.420311\pi$
$149$	6.61821e13	0.495484	0.247742	+	0.968826i	$0.420311\pi$
$150$	2.84137e13	0.203674
$151$	8.83140e13	0.606288	0.303144	−	0.952945i	$-0.401964\pi$
$151$	8.83140e13	0.606288	0.303144	+	0.952945i	$0.401964\pi$
$152$	4.15292e13	0.273130
$153$	1.70069e14	1.07184
$154$	−3.43523e13	−0.207525
$155$	−3.89019e13	−0.225328
$156$	1.82735e13	0.101511
$157$	5.56936e13	0.296796	0.148398	−	0.988928i	$-0.452588\pi$
$157$	5.56936e13	0.296796	0.148398	+	0.988928i	$0.452588\pi$
$158$	−1.28258e14	−0.655866
$159$	9.91419e13	0.486605
$160$	3.43133e13	0.161690
$161$	2.96872e14	1.34339
$162$	−2.16901e14	−0.942786
$163$	−4.48055e14	−1.87116	−0.935582	−	0.353110i	$-0.885124\pi$
$163$	−4.48055e14	−1.87116	−0.935582	+	0.353110i	$0.885124\pi$
$164$	1.69656e14	0.680900
$165$	−1.26008e14	−0.486128
$166$	−7.44666e13	−0.276223
$167$	8.22217e11	0.00293312	0.00146656	−	0.999999i	$-0.499533\pi$
$167$	8.22217e11	0.00293312	0.00146656	+	0.999999i	$0.499533\pi$
$168$	−1.76781e14	−0.606633
$169$	−2.98857e14	−0.986735
$170$	1.03531e14	0.328968
$171$	−5.32242e14	−1.62792
$172$	2.38436e14	0.702161
$173$	2.61534e14	0.741701	0.370851	−	0.928692i	$-0.379066\pi$
$173$	2.61534e14	0.741701	0.370851	+	0.928692i	$0.379066\pi$
$174$	−8.36015e14	−2.28373
$175$	−6.04352e13	−0.159053
$176$	2.97219e13	0.0753778
$177$	−1.42772e14	−0.348994
$178$	3.55571e14	0.837907
$179$	2.92171e14	0.663883	0.331942	−	0.943300i	$-0.392296\pi$
$179$	2.92171e14	0.663883	0.331942	+	0.943300i	$0.392296\pi$
$180$	−4.39763e14	−0.963712
$181$	5.39955e14	1.14142	0.570711	−	0.821151i	$-0.306667\pi$
$181$	5.39955e14	1.14142	0.570711	+	0.821151i	$0.306667\pi$
$182$	−3.88672e13	−0.0792719
$183$	−9.15704e14	−1.80228
$184$	−2.56856e14	−0.487948
$185$	8.51969e14	1.56246
$186$	−1.73406e14	−0.307065
$187$	8.96778e13	0.153361
$188$	4.77537e14	0.788826
$189$	1.19049e15	1.89987
$190$	−3.24008e14	−0.499641
$191$	−7.11944e14	−1.06103	−0.530517	−	0.847674i	$-0.678002\pi$
$191$	−7.11944e14	−1.06103	−0.530517	+	0.847674i	$0.678002\pi$
$192$	1.52953e14	0.220343
$193$	−9.22178e13	−0.128438	−0.0642188	−	0.997936i	$-0.520456\pi$
$193$	−9.22178e13	−0.128438	−0.0642188	+	0.997936i	$0.520456\pi$
$194$	5.96966e14	0.803968
$195$	−1.42569e14	−0.185695
$196$	−2.08482e13	−0.0262666
$197$	−7.85606e14	−0.957578	−0.478789	−	0.877930i	$-0.658924\pi$
$197$	−7.85606e14	−0.957578	−0.478789	+	0.877930i	$0.658924\pi$
$198$	−3.80918e14	−0.449270
$199$	2.60788e14	0.297675	0.148838	−	0.988862i	$-0.452447\pi$
$199$	2.60788e14	0.297675	0.148838	+	0.988862i	$0.452447\pi$
$200$	5.22890e13	0.0577718
$201$	8.89402e14	0.951313
$202$	1.06377e15	1.10170
$203$	1.77818e15	1.78341
$204$	4.61494e14	0.448301
$205$	−1.32365e15	−1.24558
$206$	2.84282e14	0.259187
$207$	3.29189e15	2.90829
$208$	3.36282e13	0.0287934
$209$	−2.80653e14	−0.232926
$210$	1.37924e15	1.10972
$211$	2.54912e14	0.198863	0.0994316	−	0.995044i	$-0.468298\pi$
$211$	2.54912e14	0.198863	0.0994316	+	0.995044i	$0.468298\pi$
$212$	1.82448e14	0.138025
$213$	−3.59834e15	−2.64019
$214$	4.12481e14	0.293572
$215$	−1.86027e15	−1.28447
$216$	−1.03002e15	−0.690074
$217$	3.68830e14	0.239794
$218$	−1.51845e15	−0.958151
$219$	−4.70123e15	−2.87955
$220$	−2.31888e14	−0.137890
$221$	1.01464e14	0.0585818
$222$	3.79768e15	2.12924
$223$	9.64193e14	0.525028	0.262514	−	0.964928i	$-0.415448\pi$
$223$	9.64193e14	0.525028	0.262514	+	0.964928i	$0.415448\pi$
$224$	−3.25326e14	−0.172071
$225$	−6.70141e14	−0.344334
$226$	2.64848e15	1.32218
$227$	2.34314e15	1.13666	0.568329	−	0.822801i	$-0.307590\pi$
$227$	2.34314e15	1.13666	0.568329	+	0.822801i	$0.307590\pi$
$228$	−1.44428e15	−0.680885
$229$	−1.03175e15	−0.472765	−0.236383	−	0.971660i	$-0.575962\pi$
$229$	−1.03175e15	−0.472765	−0.236383	+	0.971660i	$0.575962\pi$
$230$	2.00398e15	0.892611
$231$	1.19468e15	0.517339
$232$	−1.53850e15	−0.647776
$233$	−1.75359e15	−0.717983	−0.358992	−	0.933341i	$-0.616879\pi$
$233$	−1.75359e15	−0.717983	−0.358992	+	0.933341i	$0.616879\pi$
$234$	−4.30982e14	−0.171615
$235$	−3.72572e15	−1.44301
$236$	−2.62741e14	−0.0989918
$237$	4.46050e15	1.63501
$238$	−9.81585e14	−0.350088
$239$	1.66633e13	0.00578328	0.00289164	−	0.999996i	$-0.499080\pi$
$239$	1.66633e13	0.00578328	0.00289164	+	0.999996i	$0.499080\pi$
$240$	−1.19333e15	−0.403076
$241$	−2.51640e15	−0.827311	−0.413656	−	0.910433i	$-0.635748\pi$
$241$	−2.51640e15	−0.827311	−0.413656	+	0.910433i	$0.635748\pi$
$242$	−2.00859e14	−0.0642824
$243$	1.27881e15	0.398444
$244$	−1.68515e15	−0.511215
$245$	1.62657e14	0.0480498
$246$	−5.90019e15	−1.69741
$247$	−3.17539e14	−0.0889748
$248$	−3.19115e14	−0.0870986
$249$	2.58976e15	0.688594
$250$	−2.90458e15	−0.752443
$251$	−3.99769e15	−1.00909	−0.504545	−	0.863386i	$-0.668340\pi$
$251$	−3.99769e15	−1.00909	−0.504545	+	0.863386i	$0.668340\pi$
$252$	4.16941e15	1.02558
$253$	1.73583e15	0.416124
$254$	2.49642e15	0.583310
$255$	−3.60055e15	−0.820083
$256$	2.81475e14	0.0625000
$257$	2.21945e15	0.480486	0.240243	−	0.970713i	$-0.422773\pi$
$257$	2.21945e15	0.480486	0.240243	+	0.970713i	$0.422773\pi$
$258$	−8.29219e15	−1.75042
$259$	−8.07756e15	−1.66277
$260$	−2.62366e14	−0.0526721
$261$	1.97175e16	3.86091
$262$	−2.29687e15	−0.438711
$263$	1.18636e15	0.221058	0.110529	−	0.993873i	$-0.464746\pi$
$263$	1.18636e15	0.221058	0.110529	+	0.993873i	$0.464746\pi$
$264$	−1.03365e15	−0.187909
$265$	−1.42345e15	−0.252491
$266$	3.07194e15	0.531719
$267$	−1.23658e16	−2.08882
$268$	1.63674e15	0.269839
$269$	7.34739e15	1.18234	0.591171	−	0.806546i	$-0.298666\pi$
$269$	7.34739e15	1.18234	0.591171	+	0.806546i	$0.298666\pi$
$270$	8.03616e15	1.26236
$271$	6.00216e15	0.920464	0.460232	−	0.887799i	$-0.347766\pi$
$271$	6.00216e15	0.920464	0.460232	+	0.887799i	$0.347766\pi$
$272$	8.49275e14	0.127160
$273$	1.35170e15	0.197617
$274$	7.68885e15	1.09770
$275$	−3.53368e14	−0.0492679
$276$	8.93279e15	1.21640
$277$	4.15267e15	0.552343	0.276172	−	0.961108i	$-0.410934\pi$
$277$	4.15267e15	0.552343	0.276172	+	0.961108i	$0.410934\pi$
$278$	−2.73054e15	−0.354778
$279$	4.08981e15	0.519129
$280$	2.53818e15	0.314771
$281$	5.59808e15	0.678341	0.339171	−	0.940725i	$-0.389854\pi$
$281$	5.59808e15	0.678341	0.339171	+	0.940725i	$0.389854\pi$
$282$	−1.66075e16	−1.96646
$283$	1.15285e15	0.133402	0.0667008	−	0.997773i	$-0.478753\pi$
$283$	1.15285e15	0.133402	0.0667008	+	0.997773i	$0.478753\pi$
$284$	−6.62193e15	−0.748885
$285$	1.12682e16	1.24555
$286$	−2.27258e14	−0.0245551
$287$	1.25495e16	1.32555
$288$	−3.60741e15	−0.372515
$289$	−7.34212e15	−0.741285
$290$	1.20033e16	1.18499
$291$	−2.07609e16	−2.00421
$292$	−8.65155e15	−0.816781
$293$	−1.77531e16	−1.63921	−0.819604	−	0.572931i	$-0.805806\pi$
$293$	−1.77531e16	−1.63921	−0.819604	+	0.572931i	$0.805806\pi$
$294$	7.25046e14	0.0654799
$295$	2.04989e15	0.181087
$296$	6.98877e15	0.603955
$297$	6.96084e15	0.588497
$298$	−4.23565e15	−0.350360
$299$	1.96397e15	0.158954
$300$	−1.81848e15	−0.144019
$301$	1.76373e16	1.36694
$302$	−5.65209e15	−0.428711
$303$	−3.69951e16	−2.74642
$304$	−2.65787e15	−0.193132
$305$	1.31474e16	0.935173
$306$	−1.08844e16	−0.757905
$307$	−1.16775e16	−0.796069	−0.398035	−	0.917370i	$-0.630308\pi$
$307$	−1.16775e16	−0.796069	−0.398035	+	0.917370i	$0.630308\pi$
$308$	2.19854e15	0.146742
$309$	−9.88659e15	−0.646125
$310$	2.48972e15	0.159331
$311$	1.92297e16	1.20512	0.602559	−	0.798074i	$-0.294148\pi$
$311$	1.92297e16	1.20512	0.602559	+	0.798074i	$0.294148\pi$
$312$	−1.16950e15	−0.0717788
$313$	1.98065e16	1.19061	0.595305	−	0.803500i	$-0.297031\pi$
$313$	1.98065e16	1.19061	0.595305	+	0.803500i	$0.297031\pi$
$314$	−3.56439e15	−0.209866
$315$	−3.25295e16	−1.87611
$316$	8.20854e15	0.463767
$317$	2.45901e16	1.36105	0.680525	−	0.732724i	$-0.261752\pi$
$317$	2.45901e16	1.36105	0.680525	+	0.732724i	$0.261752\pi$
$318$	−6.34508e15	−0.344081
$319$	1.03971e16	0.552425
$320$	−2.19605e15	−0.114332
$321$	−1.43450e16	−0.731845
$322$	−1.89998e16	−0.949918
$323$	−8.01940e15	−0.392939
$324$	1.38816e16	0.666651
$325$	−3.99811e14	−0.0188197
$326$	2.86755e16	1.32311
$327$	5.28079e16	2.38857
$328$	−1.08580e16	−0.481469
$329$	3.53237e16	1.53565
$330$	8.06448e15	0.343745
$331$	2.56591e16	1.07241	0.536204	−	0.844088i	$-0.319858\pi$
$331$	2.56591e16	1.07241	0.536204	+	0.844088i	$0.319858\pi$
$332$	4.76586e15	0.195319
$333$	−8.95687e16	−3.59972
$334$	−5.26219e13	−0.00207403
$335$	−1.27698e16	−0.493620
$336$	1.13140e16	0.428954
$337$	−4.07046e16	−1.51373	−0.756866	−	0.653570i	$-0.773271\pi$
$337$	−4.07046e16	−1.51373	−0.756866	+	0.653570i	$0.773271\pi$
$338$	1.91269e16	0.697727
$339$	−9.21074e16	−3.29607
$340$	−6.62600e15	−0.232616
$341$	2.15657e15	0.0742779
$342$	3.40635e16	1.15112
$343$	−3.08979e16	−1.02451
$344$	−1.52599e16	−0.496503
$345$	−6.96932e16	−2.22519
$346$	−1.67382e16	−0.524462
$347$	1.94355e16	0.597661	0.298831	−	0.954306i	$-0.403403\pi$
$347$	1.94355e16	0.597661	0.298831	+	0.954306i	$0.403403\pi$
$348$	5.35050e16	1.61484
$349$	−2.60862e16	−0.772761	−0.386381	−	0.922339i	$-0.626275\pi$
$349$	−2.60862e16	−0.772761	−0.386381	+	0.922339i	$0.626275\pi$
$350$	3.86785e15	0.112468
$351$	7.87570e15	0.224798
$352$	−1.90220e15	−0.0533002
$353$	1.76103e16	0.484431	0.242215	−	0.970223i	$-0.422126\pi$
$353$	1.76103e16	0.484431	0.242215	+	0.970223i	$0.422126\pi$
$354$	9.13744e15	0.246776
$355$	5.16640e16	1.36995
$356$	−2.27565e16	−0.592490
$357$	3.41370e16	0.872734
$358$	−1.86989e16	−0.469436
$359$	2.08965e16	0.515180	0.257590	−	0.966254i	$-0.417072\pi$
$359$	2.08965e16	0.515180	0.257590	+	0.966254i	$0.417072\pi$
$360$	2.81448e16	0.681447
$361$	−1.69557e16	−0.403199
$362$	−3.45571e16	−0.807108
$363$	6.98537e15	0.160249
$364$	2.48750e15	0.0560537
$365$	6.74990e16	1.49415
$366$	5.86051e16	1.27441
$367$	5.14989e15	0.110019	0.0550096	−	0.998486i	$-0.482481\pi$
$367$	5.14989e15	0.110019	0.0550096	+	0.998486i	$0.482481\pi$
$368$	1.64388e16	0.345032
$369$	1.39157e17	2.86967
$370$	−5.45260e16	−1.10482
$371$	1.34958e16	0.268701
$372$	1.10980e16	0.217128
$373$	−4.41999e16	−0.849794	−0.424897	−	0.905242i	$-0.639690\pi$
$373$	−4.41999e16	−0.849794	−0.424897	+	0.905242i	$0.639690\pi$
$374$	−5.73938e15	−0.108442
$375$	1.01014e17	1.87576
$376$	−3.05624e16	−0.557784
$377$	1.17636e16	0.211019
$378$	−7.61911e16	−1.34341
$379$	−4.50046e16	−0.780014	−0.390007	−	0.920812i	$-0.627527\pi$
$379$	−4.50046e16	−0.780014	−0.390007	+	0.920812i	$0.627527\pi$
$380$	2.07365e16	0.353299
$381$	−8.68192e16	−1.45413
$382$	4.55644e16	0.750264
$383$	2.56640e16	0.415462	0.207731	−	0.978186i	$-0.433392\pi$
$383$	2.56640e16	0.415462	0.207731	+	0.978186i	$0.433392\pi$
$384$	−9.78897e15	−0.155806
$385$	−1.71529e16	−0.268438
$386$	5.90194e15	0.0908191
$387$	1.95572e17	2.95928
$388$	−3.82058e16	−0.568491
$389$	−8.40261e16	−1.22954	−0.614769	−	0.788707i	$-0.710751\pi$
$389$	−8.40261e16	−1.22954	−0.614769	+	0.788707i	$0.710751\pi$
$390$	9.12440e15	0.131306
$391$	4.95996e16	0.701988
$392$	1.33428e15	0.0185733
$393$	7.98793e16	1.09366
$394$	5.02788e16	0.677110
$395$	−6.40426e16	−0.848375
$396$	2.43788e16	0.317682
$397$	6.39508e16	0.819799	0.409900	−	0.912131i	$-0.365564\pi$
$397$	6.39508e16	0.819799	0.409900	+	0.912131i	$0.365564\pi$
$398$	−1.66904e16	−0.210488
$399$	−1.06834e17	−1.32552
$400$	−3.34650e15	−0.0408508
$401$	−8.71566e16	−1.04680	−0.523398	−	0.852088i	$-0.675336\pi$
$401$	−8.71566e16	−1.04680	−0.523398	+	0.852088i	$0.675336\pi$
$402$	−5.69217e16	−0.672680
$403$	2.44001e15	0.0283732
$404$	−6.80812e16	−0.779019
$405$	−1.08304e17	−1.21951
$406$	−1.13804e17	−1.26106
$407$	−4.72299e16	−0.515055
$408$	−2.95356e16	−0.316997
$409$	7.46992e15	0.0789068	0.0394534	−	0.999221i	$-0.487438\pi$
$409$	7.46992e15	0.0789068	0.0394534	+	0.999221i	$0.487438\pi$
$410$	8.47133e16	0.880758
$411$	−2.67398e17	−2.73645
$412$	−1.81940e16	−0.183273
$413$	−1.94351e16	−0.192713
$414$	−2.10681e17	−2.05647
$415$	−3.71830e16	−0.357299
$416$	−2.15221e15	−0.0203600
$417$	9.49610e16	0.884424
$418$	1.79618e16	0.164704
$419$	1.31046e17	1.18313	0.591564	−	0.806258i	$-0.298511\pi$
$419$	1.31046e17	1.18313	0.591564	+	0.806258i	$0.298511\pi$
$420$	−8.82713e16	−0.784692
$421$	−5.70341e16	−0.499230	−0.249615	−	0.968345i	$-0.580304\pi$
$421$	−5.70341e16	−0.499230	−0.249615	+	0.968345i	$0.580304\pi$
$422$	−1.63144e16	−0.140617
$423$	3.91690e17	3.32453
$424$	−1.16767e16	−0.0975982
$425$	−1.00972e16	−0.0831135
$426$	2.30294e17	1.86689
$427$	−1.24651e17	−0.995213
$428$	−2.63988e16	−0.207587
$429$	7.90346e15	0.0612132
$430$	1.19057e17	0.908260
$431$	1.02108e17	0.767289	0.383644	−	0.923481i	$-0.374669\pi$
$431$	1.02108e17	0.767289	0.383644	+	0.923481i	$0.374669\pi$
$432$	6.59212e16	0.487956
$433$	2.87322e16	0.209506	0.104753	−	0.994498i	$-0.466595\pi$
$433$	2.87322e16	0.209506	0.104753	+	0.994498i	$0.466595\pi$
$434$	−2.36051e16	−0.169560
$435$	−4.17443e17	−2.95405
$436$	9.71810e16	0.677515
$437$	−1.55226e17	−1.06619
$438$	3.00879e17	2.03615
$439$	1.60593e17	1.07080	0.535399	−	0.844599i	$-0.320161\pi$
$439$	1.60593e17	1.07080	0.535399	+	0.844599i	$0.320161\pi$
$440$	1.48409e16	0.0975027
$441$	−1.71003e16	−0.110701
$442$	−6.49371e15	−0.0414236
$443$	2.34828e15	0.0147613	0.00738066	−	0.999973i	$-0.497651\pi$
$443$	2.34828e15	0.0147613	0.00738066	+	0.999973i	$0.497651\pi$
$444$	−2.43051e17	−1.50560
$445$	1.77545e17	1.08385
$446$	−6.17084e16	−0.371251
$447$	1.47305e17	0.873411
$448$	2.08209e16	0.121672
$449$	−2.75009e17	−1.58397	−0.791984	−	0.610542i	$-0.790952\pi$
$449$	−2.75009e17	−1.58397	−0.791984	+	0.610542i	$0.790952\pi$
$450$	4.28890e16	0.243481
$451$	7.33778e16	0.410598
$452$	−1.69503e17	−0.934926
$453$	1.96565e17	1.06873
$454$	−1.49961e17	−0.803739
$455$	−1.94074e16	−0.102540
$456$	9.24337e16	0.481459
$457$	6.26245e16	0.321580	0.160790	−	0.986989i	$-0.448596\pi$
$457$	6.26245e16	0.321580	0.160790	+	0.986989i	$0.448596\pi$
$458$	6.60323e16	0.334295
$459$	1.98900e17	0.992776
$460$	−1.28255e17	−0.631171
$461$	−1.55426e17	−0.754167	−0.377084	−	0.926179i	$-0.623073\pi$
$461$	−1.55426e17	−0.754167	−0.377084	+	0.926179i	$0.623073\pi$
$462$	−7.64597e16	−0.365814
$463$	−2.59848e16	−0.122587	−0.0612933	−	0.998120i	$-0.519522\pi$
$463$	−2.59848e16	−0.122587	−0.0612933	+	0.998120i	$0.519522\pi$
$464$	9.84639e16	0.458047
$465$	−8.65860e16	−0.397195
$466$	1.12230e17	0.507691
$467$	−2.83872e16	−0.126638	−0.0633188	−	0.997993i	$-0.520168\pi$
$467$	−2.83872e16	−0.126638	−0.0633188	+	0.997993i	$0.520168\pi$
$468$	2.75829e16	0.121350
$469$	1.21071e17	0.525311
$470$	2.38446e17	1.02036
$471$	1.23960e17	0.523175
$472$	1.68154e16	0.0699977
$473$	1.03126e17	0.423419
$474$	−2.85472e17	−1.15612
$475$	3.15998e16	0.126234
$476$	6.28214e16	0.247550
$477$	1.49650e17	0.581709
$478$	−1.06645e15	−0.00408939
$479$	−2.68756e17	−1.01666	−0.508332	−	0.861161i	$-0.669738\pi$
$479$	−2.68756e17	−1.01666	−0.508332	+	0.861161i	$0.669738\pi$
$480$	7.63731e16	0.285018
$481$	−5.34373e16	−0.196744
$482$	1.61050e17	0.584997
$483$	6.60764e17	2.36805
$484$	1.28550e16	0.0454545
$485$	2.98080e17	1.03995
$486$	−8.18441e16	−0.281742
$487$	−1.45677e16	−0.0494825	−0.0247413	−	0.999694i	$-0.507876\pi$
$487$	−1.45677e16	−0.0494825	−0.0247413	+	0.999694i	$0.507876\pi$
$488$	1.07849e17	0.361484
$489$	−9.97260e17	−3.29838
$490$	−1.04100e16	−0.0339764
$491$	−3.14764e17	−1.01381	−0.506903	−	0.862003i	$-0.669210\pi$
$491$	−3.14764e17	−1.01381	−0.506903	+	0.862003i	$0.669210\pi$
$492$	3.77612e17	1.20025
$493$	2.97088e17	0.931924
$494$	2.03225e16	0.0629147
$495$	−1.90202e17	−0.581140
$496$	2.04234e16	0.0615880
$497$	−4.89828e17	−1.45790
$498$	−1.65744e17	−0.486910
$499$	4.36329e17	1.26520	0.632602	−	0.774477i	$-0.281987\pi$
$499$	4.36329e17	1.26520	0.632602	+	0.774477i	$0.281987\pi$
$500$	1.85893e17	0.532057
$501$	1.83005e15	0.00517033
$502$	2.55852e17	0.713534
$503$	−4.94500e17	−1.36136	−0.680682	−	0.732579i	$-0.738317\pi$
$503$	−4.94500e17	−1.36136	−0.680682	+	0.732579i	$0.738317\pi$
$504$	−2.66842e17	−0.725197
$505$	5.31166e17	1.42507
$506$	−1.11093e17	−0.294244
$507$	−6.65183e17	−1.73936
$508$	−1.59771e17	−0.412462
$509$	−1.86644e17	−0.475716	−0.237858	−	0.971300i	$-0.576445\pi$
$509$	−1.86644e17	−0.475716	−0.237858	+	0.971300i	$0.576445\pi$
$510$	2.30435e17	0.579886
$511$	−6.39961e17	−1.59007
$512$	−1.80144e16	−0.0441942
$513$	−6.22470e17	−1.50784
$514$	−1.42045e17	−0.339755
$515$	1.41949e17	0.335263
$516$	5.30700e17	1.23773
$517$	2.06540e17	0.475680
$518$	5.16964e17	1.17575
$519$	5.82111e17	1.30743
$520$	1.67914e16	0.0372448
$521$	−6.78256e17	−1.48576	−0.742880	−	0.669425i	$-0.766541\pi$
$521$	−6.78256e17	−1.48576	−0.742880	+	0.669425i	$0.766541\pi$
$522$	−1.26192e18	−2.73007
$523$	1.42018e17	0.303446	0.151723	−	0.988423i	$-0.451518\pi$
$523$	1.42018e17	0.303446	0.151723	+	0.988423i	$0.451518\pi$
$524$	1.47000e17	0.310215
$525$	−1.34514e17	−0.280370
$526$	−7.59273e16	−0.156311
$527$	6.16220e16	0.125305
$528$	6.61536e16	0.132872
$529$	4.56027e17	0.904750
$530$	9.11010e16	0.178538
$531$	−2.15508e17	−0.417204
$532$	−1.96604e17	−0.375982
$533$	8.30219e16	0.156843
$534$	7.91413e17	1.47702
$535$	2.05962e17	0.379741
$536$	−1.04752e17	−0.190805
$537$	6.50300e17	1.17026
$538$	−4.70233e17	−0.836042
$539$	−9.01705e15	−0.0158394
$540$	−5.14314e17	−0.892625
$541$	−5.04702e17	−0.865471	−0.432736	−	0.901521i	$-0.642452\pi$
$541$	−5.04702e17	−0.865471	−0.432736	+	0.901521i	$0.642452\pi$
$542$	−3.84138e17	−0.650867
$543$	1.20181e18	2.01204
$544$	−5.43536e16	−0.0899157
$545$	−7.58201e17	−1.23939
$546$	−8.65089e16	−0.139736
$547$	1.04995e18	1.67591	0.837955	−	0.545739i	$-0.183751\pi$
$547$	1.04995e18	1.67591	0.837955	+	0.545739i	$0.183751\pi$
$548$	−4.92086e17	−0.776189
$549$	−1.38221e18	−2.15453
$550$	2.26155e16	0.0348377
$551$	−9.29759e17	−1.41542
$552$	−5.71699e17	−0.860128
$553$	6.07191e17	0.902843
$554$	−2.65771e17	−0.390566
$555$	1.89627e18	2.75421
$556$	1.74754e17	0.250866
$557$	1.37236e18	1.94719	0.973594	−	0.228287i	$-0.0733126\pi$
$557$	1.37236e18	1.94719	0.973594	+	0.228287i	$0.0733126\pi$
$558$	−2.61748e17	−0.367080
$559$	1.16680e17	0.161741
$560$	−1.62443e17	−0.222577
$561$	1.99601e17	0.270336
$562$	−3.58277e17	−0.479660
$563$	7.33324e17	0.970490	0.485245	−	0.874378i	$-0.338730\pi$
$563$	7.33324e17	0.970490	0.485245	+	0.874378i	$0.338730\pi$
$564$	1.06288e18	1.39050
$565$	1.32245e18	1.71027
$566$	−7.37824e16	−0.0943292
$567$	1.02683e18	1.29781
$568$	4.23803e17	0.529542
$569$	−1.23495e18	−1.52553	−0.762764	−	0.646677i	$-0.776158\pi$
$569$	−1.23495e18	−1.52553	−0.762764	+	0.646677i	$0.776158\pi$
$570$	−7.21163e17	−0.880739
$571$	−7.32931e17	−0.884970	−0.442485	−	0.896776i	$-0.645903\pi$
$571$	−7.32931e17	−0.884970	−0.442485	+	0.896776i	$0.645903\pi$
$572$	1.45445e16	0.0173630
$573$	−1.58461e18	−1.87033
$574$	−8.03171e17	−0.937304
$575$	−1.95443e17	−0.225517
$576$	2.30874e17	0.263408
$577$	1.27135e18	1.43424	0.717121	−	0.696948i	$-0.245459\pi$
$577$	1.27135e18	1.43424	0.717121	+	0.696948i	$0.245459\pi$
$578$	4.69895e17	0.524168
$579$	−2.05254e17	−0.226403
$580$	−7.68210e17	−0.837911
$581$	3.52534e17	0.380239
$582$	1.32870e18	1.41719
$583$	7.89108e16	0.0832321
$584$	5.53699e17	0.577551
$585$	−2.15200e17	−0.221988
$586$	1.13620e18	1.15909
$587$	−7.70319e17	−0.777182	−0.388591	−	0.921410i	$-0.627038\pi$
$587$	−7.70319e17	−0.777182	−0.388591	+	0.921410i	$0.627038\pi$
$588$	−4.64030e16	−0.0463013
$589$	−1.92850e17	−0.190314
$590$	−1.31193e17	−0.128048
$591$	−1.74857e18	−1.68796
$592$	−4.47281e17	−0.427061
$593$	−1.15827e18	−1.09384	−0.546922	−	0.837184i	$-0.684201\pi$
$593$	−1.15827e18	−1.09384	−0.546922	+	0.837184i	$0.684201\pi$
$594$	−4.45493e17	−0.416130
$595$	−4.90130e17	−0.452846
$596$	2.71082e17	0.247742
$597$	5.80450e17	0.524725
$598$	−1.25694e17	−0.112397
$599$	1.08015e18	0.955455	0.477728	−	0.878508i	$-0.341461\pi$
$599$	1.08015e18	0.955455	0.477728	+	0.878508i	$0.341461\pi$
$600$	1.16383e17	0.101837
$601$	−1.22457e17	−0.105999	−0.0529993	−	0.998595i	$-0.516878\pi$
$601$	−1.22457e17	−0.105999	−0.0529993	+	0.998595i	$0.516878\pi$
$602$	−1.12878e18	−0.966571
$603$	1.34251e18	1.13724
$604$	3.61734e17	0.303144
$605$	−1.00294e17	−0.0831506
$606$	2.36769e18	1.94201
$607$	−1.52192e18	−1.23500	−0.617499	−	0.786572i	$-0.711854\pi$
$607$	−1.52192e18	−1.23500	−0.617499	+	0.786572i	$0.711854\pi$
$608$	1.70103e17	0.136565
$609$	3.95780e18	3.14370
$610$	−8.41436e17	−0.661267
$611$	2.33685e17	0.181704
$612$	6.96601e17	0.535920
$613$	−4.10708e17	−0.312636	−0.156318	−	0.987707i	$-0.549963\pi$
$613$	−4.10708e17	−0.312636	−0.156318	+	0.987707i	$0.549963\pi$
$614$	7.47361e17	0.562906
$615$	−2.94611e18	−2.19564
$616$	−1.40707e17	−0.103763
$617$	2.15777e18	1.57453	0.787265	−	0.616615i	$-0.211496\pi$
$617$	2.15777e18	1.57453	0.787265	+	0.616615i	$0.211496\pi$
$618$	6.32742e17	0.456879
$619$	−1.14512e18	−0.818201	−0.409101	−	0.912489i	$-0.634157\pi$
$619$	−1.14512e18	−0.818201	−0.409101	+	0.912489i	$0.634157\pi$
$620$	−1.59342e17	−0.112664
$621$	3.84995e18	2.69377
$622$	−1.23070e18	−0.852148
$623$	−1.68331e18	−1.15343
$624$	7.48482e16	0.0507553
$625$	−1.20684e18	−0.809896
$626$	−1.26762e18	−0.841889
$627$	−6.24664e17	−0.410589
$628$	2.28121e17	0.148398
$629$	−1.34955e18	−0.868881
$630$	2.08189e18	1.32661
$631$	−1.90253e18	−1.19989	−0.599945	−	0.800041i	$-0.704811\pi$
$631$	−1.90253e18	−1.19989	−0.599945	+	0.800041i	$0.704811\pi$
$632$	−5.25347e17	−0.327933
$633$	5.67372e17	0.350545
$634$	−1.57376e18	−0.962408
$635$	1.24653e18	0.754523
$636$	4.06085e17	0.243302
$637$	−1.02022e16	−0.00605043
$638$	−6.65416e17	−0.390624
$639$	−5.43150e18	−3.15620
$640$	1.40547e17	0.0808450
$641$	2.38321e18	1.35702	0.678508	−	0.734593i	$-0.262627\pi$
$641$	2.38321e18	1.35702	0.678508	+	0.734593i	$0.262627\pi$
$642$	9.18082e17	0.517492
$643$	−6.83533e17	−0.381406	−0.190703	−	0.981648i	$-0.561077\pi$
$643$	−6.83533e17	−0.381406	−0.190703	+	0.981648i	$0.561077\pi$
$644$	1.21599e18	0.671693
$645$	−4.14050e18	−2.26420
$646$	5.13242e17	0.277850
$647$	1.09106e18	0.584753	0.292376	−	0.956303i	$-0.405554\pi$
$647$	1.09106e18	0.584753	0.292376	+	0.956303i	$0.405554\pi$
$648$	−8.88425e17	−0.471393
$649$	−1.13638e17	−0.0596943
$650$	2.55879e16	0.0133075
$651$	8.20926e17	0.422695
$652$	−1.83523e18	−0.935582
$653$	−1.44931e17	−0.0731518	−0.0365759	−	0.999331i	$-0.511645\pi$
$653$	−1.44931e17	−0.0731518	−0.0365759	+	0.999331i	$0.511645\pi$
$654$	−3.37970e18	−1.68897
$655$	−1.14689e18	−0.567481
$656$	6.94910e17	0.340450
$657$	−7.09626e18	−3.44235
$658$	−2.26072e18	−1.08587
$659$	−1.73620e18	−0.825744	−0.412872	−	0.910789i	$-0.635474\pi$
$659$	−1.73620e18	−0.825744	−0.412872	+	0.910789i	$0.635474\pi$
$660$	−5.16127e17	−0.243064
$661$	2.37669e18	1.10831	0.554157	−	0.832412i	$-0.313041\pi$
$661$	2.37669e18	1.10831	0.554157	+	0.832412i	$0.313041\pi$
$662$	−1.64219e18	−0.758307
$663$	2.25834e17	0.103265
$664$	−3.05015e17	−0.138111
$665$	1.53389e18	0.687789
$666$	5.73240e18	2.54539
$667$	5.75052e18	2.52865
$668$	3.36780e15	0.00146656
$669$	2.14606e18	0.925490
$670$	8.17267e17	0.349042
$671$	−7.28843e17	−0.308274
$672$	−7.24096e17	−0.303317
$673$	2.96597e17	0.123047	0.0615233	−	0.998106i	$-0.480404\pi$
$673$	2.96597e17	0.123047	0.0615233	+	0.998106i	$0.480404\pi$
$674$	2.60509e18	1.07037
$675$	−7.83747e17	−0.318935
$676$	−1.22412e18	−0.493368
$677$	1.15857e18	0.462483	0.231242	−	0.972896i	$-0.425721\pi$
$677$	1.15857e18	0.462483	0.231242	+	0.972896i	$0.425721\pi$
$678$	5.89487e18	2.33067
$679$	−2.82611e18	−1.10671
$680$	4.24064e17	0.164484
$681$	5.21525e18	2.00364
$682$	−1.38020e17	−0.0525224
$683$	2.86942e18	1.08158	0.540790	−	0.841157i	$-0.318125\pi$
$683$	2.86942e18	1.08158	0.540790	+	0.841157i	$0.318125\pi$
$684$	−2.18006e18	−0.813962
$685$	3.83923e18	1.41989
$686$	1.97747e18	0.724441
$687$	−2.29643e18	−0.833364
$688$	9.76634e17	0.351081
$689$	8.92820e16	0.0317936
$690$	4.46036e18	1.57344
$691$	1.23360e18	0.431089	0.215544	−	0.976494i	$-0.430847\pi$
$691$	1.23360e18	0.431089	0.215544	+	0.976494i	$0.430847\pi$
$692$	1.07124e18	0.370851
$693$	1.80331e18	0.618450
$694$	−1.24387e18	−0.422610
$695$	−1.36342e18	−0.458912
$696$	−3.42432e18	−1.14186
$697$	2.09670e18	0.692666
$698$	1.66952e18	0.546425
$699$	−3.90306e18	−1.26562
$700$	−2.47543e17	−0.0795267
$701$	3.02492e18	0.962823	0.481411	−	0.876495i	$-0.340124\pi$
$701$	3.02492e18	0.962823	0.481411	+	0.876495i	$0.340124\pi$
$702$	−5.04045e17	−0.158956
$703$	4.22351e18	1.31967
$704$	1.21741e17	0.0376889
$705$	−8.29254e18	−2.54366
$706$	−1.12706e18	−0.342544
$707$	−5.03601e18	−1.51656
$708$	−5.84796e17	−0.174497
$709$	−2.10385e17	−0.0622033	−0.0311016	−	0.999516i	$-0.509902\pi$
$709$	−2.10385e17	−0.0622033	−0.0311016	+	0.999516i	$0.509902\pi$
$710$	−3.30649e18	−0.968698
$711$	6.73289e18	1.95456
$712$	1.45642e18	0.418954
$713$	1.19277e18	0.339997
$714$	−2.18477e18	−0.617116
$715$	−1.13476e17	−0.0317624
$716$	1.19673e18	0.331942
$717$	3.70884e16	0.0101944
$718$	−1.33737e18	−0.364287
$719$	4.76095e18	1.28516	0.642578	−	0.766220i	$-0.277865\pi$
$719$	4.76095e18	1.28516	0.642578	+	0.766220i	$0.277865\pi$
$720$	−1.80127e18	−0.481856
$721$	−1.34583e18	−0.356787
$722$	1.08517e18	0.285105
$723$	−5.60089e18	−1.45834
$724$	2.21165e18	0.570711
$725$	−1.17065e18	−0.299386
$726$	−4.47064e17	−0.113313
$727$	5.66362e16	0.0142272	0.00711361	−	0.999975i	$-0.497736\pi$
$727$	5.66362e16	0.0142272	0.00711361	+	0.999975i	$0.497736\pi$
$728$	−1.59200e17	−0.0396359
$729$	−2.55695e18	−0.630947
$730$	−4.31993e18	−1.05652
$731$	2.94673e18	0.714295
$732$	−3.75072e18	−0.901142
$733$	−1.05951e18	−0.252308	−0.126154	−	0.992011i	$-0.540263\pi$
$733$	−1.05951e18	−0.252308	−0.126154	+	0.992011i	$0.540263\pi$
$734$	−3.29593e17	−0.0777953
$735$	3.62034e17	0.0846995
$736$	−1.05208e18	−0.243974
$737$	7.07908e17	0.162719
$738$	−8.90603e18	−2.02917
$739$	6.68141e18	1.50897	0.754483	−	0.656319i	$-0.227888\pi$
$739$	6.68141e18	1.50897	0.754483	+	0.656319i	$0.227888\pi$
$740$	3.48967e18	0.781228
$741$	−7.06764e17	−0.156840
$742$	−8.63733e17	−0.190000
$743$	−6.55576e17	−0.142954	−0.0714769	−	0.997442i	$-0.522771\pi$
$743$	−6.55576e17	−0.142954	−0.0714769	+	0.997442i	$0.522771\pi$
$744$	−7.10272e17	−0.153533
$745$	−2.11497e18	−0.453198
$746$	2.82879e18	0.600895
$747$	3.90910e18	0.823177
$748$	3.67320e17	0.0766804
$749$	−1.95274e18	−0.404121
$750$	−6.46488e18	−1.32636
$751$	−7.63114e18	−1.55214	−0.776068	−	0.630649i	$-0.782789\pi$
$751$	−7.63114e18	−1.55214	−0.776068	+	0.630649i	$0.782789\pi$
$752$	1.95599e18	0.394413
$753$	−8.89787e18	−1.77877
$754$	−7.52872e17	−0.149213
$755$	−2.82223e18	−0.554546
$756$	4.87623e18	0.949933
$757$	5.67987e18	1.09702	0.548511	−	0.836143i	$-0.315195\pi$
$757$	5.67987e18	1.09702	0.548511	+	0.836143i	$0.315195\pi$
$758$	2.88030e18	0.551553
$759$	3.86352e18	0.733520
$760$	−1.32714e18	−0.249820
$761$	9.65147e18	1.80133	0.900665	−	0.434514i	$-0.143080\pi$
$761$	9.65147e18	1.80133	0.900665	+	0.434514i	$0.143080\pi$
$762$	5.55643e18	1.02823
$763$	7.18854e18	1.31896
$764$	−2.91612e18	−0.530517
$765$	−5.43485e18	−0.980365
$766$	−1.64249e18	−0.293776
$767$	−1.28573e17	−0.0228024
$768$	6.26494e17	0.110171
$769$	8.91220e18	1.55405	0.777023	−	0.629472i	$-0.216729\pi$
$769$	8.91220e18	1.55405	0.777023	+	0.629472i	$0.216729\pi$
$770$	1.09779e18	0.189814
$771$	4.93996e18	0.846974
$772$	−3.77724e17	−0.0642188
$773$	4.38027e18	0.738472	0.369236	−	0.929336i	$-0.379619\pi$
$773$	4.38027e18	0.738472	0.369236	+	0.929336i	$0.379619\pi$
$774$	−1.25166e19	−2.09253
$775$	−2.42816e17	−0.0402547
$776$	2.44517e18	0.401984
$777$	−1.79787e19	−2.93103
$778$	5.37767e18	0.869414
$779$	−6.56178e18	−1.05203
$780$	−5.83962e17	−0.0928473
$781$	−2.86405e18	−0.451595
$782$	−3.17438e18	−0.496380
$783$	2.30602e19	3.57611
$784$	−8.53942e16	−0.0131333
$785$	−1.77979e18	−0.271466
$786$	−5.11227e18	−0.773335
$787$	−1.26153e19	−1.89261	−0.946304	−	0.323278i	$-0.895215\pi$
$787$	−1.26153e19	−1.89261	−0.946304	+	0.323278i	$0.895215\pi$
$788$	−3.21784e18	−0.478789
$789$	2.64055e18	0.389668
$790$	4.09873e18	0.599892
$791$	−1.25382e19	−1.82007
$792$	−1.56024e18	−0.224635
$793$	−8.24635e17	−0.117757
$794$	−4.09285e18	−0.579685
$795$	−3.16826e18	−0.445076
$796$	1.06819e18	0.148838
$797$	1.35971e18	0.187918	0.0939590	−	0.995576i	$-0.470048\pi$
$797$	1.35971e18	0.187918	0.0939590	+	0.995576i	$0.470048\pi$
$798$	6.83738e18	0.937284
$799$	5.90169e18	0.802457
$800$	2.14176e17	0.0288859
$801$	−1.86656e19	−2.49707
$802$	5.57802e18	0.740197
$803$	−3.74188e18	−0.492537
$804$	3.64299e18	0.475657
$805$	−9.48707e18	−1.22874
$806$	−1.56160e17	−0.0200629
$807$	1.63535e19	2.08417
$808$	4.35720e18	0.550850
$809$	−2.04137e18	−0.256009	−0.128005	−	0.991774i	$-0.540857\pi$
$809$	−2.04137e18	−0.256009	−0.128005	+	0.991774i	$0.540857\pi$
$810$	6.93145e18	0.862326
$811$	−1.01171e19	−1.24859	−0.624297	−	0.781187i	$-0.714614\pi$
$811$	−1.01171e19	−1.24859	−0.624297	+	0.781187i	$0.714614\pi$
$812$	7.28343e18	0.891707
$813$	1.33593e19	1.62254
$814$	3.02271e18	0.364199
$815$	1.43184e19	1.71147
$816$	1.89028e18	0.224151
$817$	−9.22200e18	−1.08488
$818$	−4.78075e17	−0.0557955
$819$	2.04032e18	0.236240
$820$	−5.42165e18	−0.622790
$821$	7.64549e17	0.0871314	0.0435657	−	0.999051i	$-0.486128\pi$
$821$	7.64549e17	0.0871314	0.0435657	+	0.999051i	$0.486128\pi$
$822$	1.71135e19	1.93496
$823$	−8.95169e18	−1.00417	−0.502084	−	0.864819i	$-0.667433\pi$
$823$	−8.95169e18	−1.00417	−0.502084	+	0.864819i	$0.667433\pi$
$824$	1.16442e18	0.129593
$825$	−7.86510e17	−0.0868467
$826$	1.24385e18	0.136269
$827$	−1.61706e17	−0.0175768	−0.00878841	−	0.999961i	$-0.502797\pi$
$827$	−1.61706e17	−0.0175768	−0.00878841	+	0.999961i	$0.502797\pi$
$828$	1.34836e19	1.45415
$829$	−1.73777e19	−1.85947	−0.929733	−	0.368234i	$-0.879963\pi$
$829$	−1.73777e19	−1.85947	−0.929733	+	0.368234i	$0.879963\pi$
$830$	2.37971e18	0.252649
$831$	9.24283e18	0.973640
$832$	1.37741e17	0.0143967
$833$	−2.57654e17	−0.0267205
$834$	−6.07750e18	−0.625383
$835$	−2.62754e16	−0.00268280
$836$	−1.14955e18	−0.116463
$837$	4.78313e18	0.480836
$838$	−8.38693e18	−0.836598
$839$	−1.45687e19	−1.44201	−0.721007	−	0.692928i	$-0.756320\pi$
$839$	−1.45687e19	−1.44201	−0.721007	+	0.692928i	$0.756320\pi$
$840$	5.64936e18	0.554861
$841$	2.41834e19	2.35691
$842$	3.65018e18	0.353009
$843$	1.24600e19	1.19574
$844$	1.04412e18	0.0994316
$845$	9.55053e18	0.902524
$846$	−2.50682e19	−2.35080
$847$	9.50893e17	0.0884890
$848$	7.47309e17	0.0690124
$849$	2.56596e18	0.235153
$850$	6.46219e17	0.0587701
$851$	−2.61223e19	−2.35759
$852$	−1.47388e19	−1.32009
$853$	1.16789e19	1.03809	0.519045	−	0.854747i	$-0.326288\pi$
$853$	1.16789e19	1.03809	0.519045	+	0.854747i	$0.326288\pi$
$854$	7.97769e18	0.703722
$855$	1.70087e19	1.48899
$856$	1.68952e18	0.146786
$857$	1.64916e19	1.42196	0.710978	−	0.703214i	$-0.248253\pi$
$857$	1.64916e19	1.42196	0.710978	+	0.703214i	$0.248253\pi$
$858$	−5.05822e17	−0.0432843
$859$	−1.50935e19	−1.28184	−0.640921	−	0.767607i	$-0.721447\pi$
$859$	−1.50935e19	−1.28184	−0.640921	+	0.767607i	$0.721447\pi$
$860$	−7.61965e18	−0.642237
$861$	2.79322e19	2.33660
$862$	−6.53493e18	−0.542555
$863$	7.85715e18	0.647433	0.323717	−	0.946154i	$-0.395068\pi$
$863$	7.85715e18	0.647433	0.323717	+	0.946154i	$0.395068\pi$
$864$	−4.21896e18	−0.345037
$865$	−8.35780e18	−0.678402
$866$	−1.83886e18	−0.148143
$867$	−1.63418e19	−1.30670
$868$	1.51073e18	0.119897
$869$	3.55028e18	0.279662
$870$	2.67164e19	2.08883
$871$	8.00949e17	0.0621565
$872$	−6.21958e18	−0.479076
$873$	−3.13376e19	−2.39592
$874$	9.93443e18	0.753909
$875$	1.37506e19	1.03579
$876$	−1.92562e19	−1.43977
$877$	−4.78591e18	−0.355195	−0.177598	−	0.984103i	$-0.556833\pi$
$877$	−4.78591e18	−0.355195	−0.177598	+	0.984103i	$0.556833\pi$
$878$	−1.02780e19	−0.757168
$879$	−3.95140e19	−2.88950
$880$	−9.49815e17	−0.0689448
$881$	1.97848e19	1.42557	0.712785	−	0.701383i	$-0.247434\pi$
$881$	1.97848e19	1.42557	0.712785	+	0.701383i	$0.247434\pi$
$882$	1.09442e18	0.0782777
$883$	−2.83743e18	−0.201456	−0.100728	−	0.994914i	$-0.532117\pi$
$883$	−2.83743e18	−0.201456	−0.100728	+	0.994914i	$0.532117\pi$
$884$	4.15597e17	0.0292909
$885$	4.56255e18	0.319210
$886$	−1.50290e17	−0.0104378
$887$	−1.07901e19	−0.743915	−0.371957	−	0.928250i	$-0.621313\pi$
$887$	−1.07901e19	−0.743915	−0.371957	+	0.928250i	$0.621313\pi$
$888$	1.55553e19	1.06462
$889$	−1.18184e19	−0.802964
$890$	−1.13629e19	−0.766397
$891$	6.00395e18	0.402005
$892$	3.94934e18	0.262514
$893$	−1.84697e19	−1.21878
$894$	−9.42752e18	−0.617595
$895$	−9.33683e18	−0.607225
$896$	−1.33254e18	−0.0860354
$897$	4.37131e18	0.280195
$898$	1.76006e19	1.12003
$899$	7.14437e18	0.451363
$900$	−2.74490e18	−0.172167
$901$	2.25480e18	0.140410
$902$	−4.69618e18	−0.290337
$903$	3.92562e19	2.40956
$904$	1.08482e19	0.661092
$905$	−1.72552e19	−1.04401
$906$	−1.25802e19	−0.755707
$907$	−2.12586e18	−0.126791	−0.0633954	−	0.997988i	$-0.520193\pi$
$907$	−2.12586e18	−0.126791	−0.0633954	+	0.997988i	$0.520193\pi$
$908$	9.59750e18	0.568329
$909$	−5.58422e19	−3.28320
$910$	1.24207e18	0.0725066
$911$	1.04891e19	0.607953	0.303976	−	0.952680i	$-0.401686\pi$
$911$	1.04891e19	0.607953	0.303976	+	0.952680i	$0.401686\pi$
$912$	−5.91576e18	−0.340443
$913$	2.06128e18	0.117782
$914$	−4.00797e18	−0.227391
$915$	2.92630e19	1.64847
$916$	−4.22606e18	−0.236383
$917$	1.08737e19	0.603914
$918$	−1.27296e19	−0.701999
$919$	3.00252e18	0.164412	0.0822062	−	0.996615i	$-0.473803\pi$
$919$	3.00252e18	0.164412	0.0822062	+	0.996615i	$0.473803\pi$
$920$	8.20829e18	0.446305
$921$	−2.59913e19	−1.40327
$922$	9.94727e18	0.533277
$923$	−3.24047e18	−0.172503
$924$	4.89342e18	0.258669
$925$	5.31779e18	0.279132
$926$	1.66303e18	0.0866818
$927$	−1.49233e19	−0.772408
$928$	−6.30169e18	−0.323888
$929$	5.64203e17	0.0287961	0.0143980	−	0.999896i	$-0.495417\pi$
$929$	5.64203e17	0.0287961	0.0143980	+	0.999896i	$0.495417\pi$
$930$	5.54150e18	0.280859
$931$	8.06346e17	0.0405834
$932$	−7.18270e18	−0.358992
$933$	4.28006e19	2.12432
$934$	1.81678e18	0.0895463
$935$	−2.86581e18	−0.140272
$936$	−1.76530e18	−0.0858077
$937$	−1.93769e19	−0.935356	−0.467678	−	0.883899i	$-0.654909\pi$
$937$	−1.93769e19	−0.935356	−0.467678	+	0.883899i	$0.654909\pi$
$938$	−7.74854e18	−0.371451
$939$	4.40844e19	2.09874
$940$	−1.52606e19	−0.721505
$941$	−9.15670e18	−0.429938	−0.214969	−	0.976621i	$-0.568965\pi$
$941$	−9.15670e18	−0.429938	−0.214969	+	0.976621i	$0.568965\pi$
$942$	−7.93346e18	−0.369940
$943$	4.05843e19	1.87946
$944$	−1.07619e18	−0.0494959
$945$	−3.80441e19	−1.73772
$946$	−6.60006e18	−0.299403
$947$	−1.21946e19	−0.549405	−0.274702	−	0.961529i	$-0.588579\pi$
$947$	−1.21946e19	−0.549405	−0.274702	+	0.961529i	$0.588579\pi$
$948$	1.82702e19	0.817503
$949$	−4.23368e18	−0.188143
$950$	−2.02239e18	−0.0892608
$951$	5.47314e19	2.39918
$952$	−4.02057e18	−0.175044
$953$	−2.30251e19	−0.995630	−0.497815	−	0.867283i	$-0.665864\pi$
$953$	−2.30251e19	−0.995630	−0.497815	+	0.867283i	$0.665864\pi$
$954$	−9.57758e18	−0.411331
$955$	2.27515e19	0.970482
$956$	6.82528e16	0.00289164
$957$	2.31414e19	0.973784
$958$	1.72004e19	0.718889
$959$	−3.63999e19	−1.51105
$960$	−4.88788e18	−0.201538
$961$	−2.29357e19	−0.939311
$962$	3.41999e18	0.139119
$963$	−2.16531e19	−0.874881
$964$	−1.03072e19	−0.413656
$965$	2.94699e18	0.117476
$966$	−4.22889e19	−1.67446
$967$	4.12343e19	1.62176	0.810880	−	0.585212i	$-0.198989\pi$
$967$	4.12343e19	1.62176	0.810880	+	0.585212i	$0.198989\pi$
$968$	−8.22720e17	−0.0321412
$969$	−1.78492e19	−0.692651
$970$	−1.90771e19	−0.735354
$971$	−3.43700e19	−1.31600	−0.657998	−	0.753019i	$-0.728597\pi$
$971$	−3.43700e19	−1.31600	−0.657998	+	0.753019i	$0.728597\pi$
$972$	5.23802e18	0.199222
$973$	1.29267e19	0.488375
$974$	9.32331e17	0.0349894
$975$	−8.89881e17	−0.0331743
$976$	−6.90236e18	−0.255608
$977$	−1.47268e19	−0.541744	−0.270872	−	0.962615i	$-0.587312\pi$
$977$	−1.47268e19	−0.541744	−0.270872	+	0.962615i	$0.587312\pi$
$978$	6.38247e19	2.33231
$979$	−9.84242e18	−0.357285
$980$	6.66241e17	0.0240249
$981$	7.97107e19	2.85541
$982$	2.01449e19	0.716869
$983$	4.37259e19	1.54576	0.772878	−	0.634555i	$-0.218816\pi$
$983$	4.37259e19	1.54576	0.772878	+	0.634555i	$0.218816\pi$
$984$	−2.41672e19	−0.848707
$985$	2.51054e19	0.875855
$986$	−1.90137e19	−0.658970
$987$	7.86220e19	2.70696
$988$	−1.30064e18	−0.0444874
$989$	5.70377e19	1.93814
$990$	1.21729e19	0.410928
$991$	1.10764e19	0.371465	0.185733	−	0.982600i	$-0.440534\pi$
$991$	1.10764e19	0.371465	0.185733	+	0.982600i	$0.440534\pi$
$992$	−1.30709e18	−0.0435493
$993$	5.71110e19	1.89038
$994$	3.13490e19	1.03089
$995$	−8.33394e18	−0.272270
$996$	1.06076e19	0.344297
$997$	5.42011e19	1.74779	0.873895	−	0.486114i	$-0.161586\pi$
$997$	5.42011e19	1.74779	0.873895	+	0.486114i	$0.161586\pi$
$998$	−2.79251e19	−0.894635
$999$	−1.04753e20	−3.33419

Twists

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

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

\(f(q)\)	\(=\)	\(q-64.0000 q^{2} +2225.75 q^{3} +4096.00 q^{4} -31956.8 q^{5} -142448. q^{6} +302984. q^{7} -262144. q^{8} +3.35966e6 q^{9} +O(q^{10})\)	\(q-64.0000 q^{2} +2225.75 q^{3} +4096.00 q^{4} -31956.8 q^{5} -142448. q^{6} +302984. q^{7} -262144. q^{8} +3.35966e6 q^{9} +2.04523e6 q^{10} +1.77156e6 q^{11} +9.11669e6 q^{12} +2.00440e6 q^{13} -1.93910e7 q^{14} -7.11280e7 q^{15} +1.67772e7 q^{16} +5.06208e7 q^{17} -2.15018e8 q^{18} -1.58421e8 q^{19} -1.30895e8 q^{20} +6.74367e8 q^{21} -1.13380e8 q^{22} +9.79828e8 q^{23} -5.83468e8 q^{24} -1.99467e8 q^{25} -1.28281e8 q^{26} +3.92921e9 q^{27} +1.24102e9 q^{28} +5.86890e9 q^{29} +4.55219e9 q^{30} +1.21733e9 q^{31} -1.07374e9 q^{32} +3.94306e9 q^{33} -3.23973e9 q^{34} -9.68239e9 q^{35} +1.37612e10 q^{36} -2.66600e10 q^{37} +1.01390e10 q^{38} +4.46130e9 q^{39} +8.37728e9 q^{40} +4.14199e10 q^{41} -4.31595e10 q^{42} +5.82119e10 q^{43} +7.25631e9 q^{44} -1.07364e11 q^{45} -6.27090e10 q^{46} +1.16586e11 q^{47} +3.73420e10 q^{48} -5.08989e9 q^{49} +1.27659e10 q^{50} +1.12669e11 q^{51} +8.21002e9 q^{52} +4.45431e10 q^{53} -2.51469e11 q^{54} -5.66134e10 q^{55} -7.94254e10 q^{56} -3.52607e11 q^{57} -3.75610e11 q^{58} -6.41456e10 q^{59} -2.91340e11 q^{60} -4.11413e11 q^{61} -7.79089e10 q^{62} +1.01792e12 q^{63} +6.87195e10 q^{64} -6.40541e10 q^{65} -2.52356e11 q^{66} +3.99596e11 q^{67} +2.07343e11 q^{68} +2.18086e12 q^{69} +6.19673e11 q^{70} -1.61668e12 q^{71} -8.80715e11 q^{72} -2.11220e12 q^{73} +1.70624e12 q^{74} -4.43964e11 q^{75} -6.48893e11 q^{76} +5.36754e11 q^{77} -2.85523e11 q^{78} +2.00404e12 q^{79} -5.36146e11 q^{80} +3.38907e12 q^{81} -2.65087e12 q^{82} +1.16354e12 q^{83} +2.76221e12 q^{84} -1.61768e12 q^{85} -3.72556e12 q^{86} +1.30627e13 q^{87} -4.64404e11 q^{88} -5.55579e12 q^{89} +6.87129e12 q^{90} +6.07300e11 q^{91} +4.01338e12 q^{92} +2.70947e12 q^{93} -7.46152e12 q^{94} +5.06263e12 q^{95} -2.38989e12 q^{96} -9.32760e12 q^{97} +3.25753e11 q^{98} +5.95184e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 128 q^{2} + 1626 q^{3} + 8192 q^{4} + 7666 q^{5} - 104064 q^{6} + 637048 q^{7} - 524288 q^{8} + 2125044 q^{9}+O(q^{10}) \) 2 * q - 128 * q^2 + 1626 * q^3 + 8192 * q^4 + 7666 * q^5 - 104064 * q^6 + 637048 * q^7 - 524288 * q^8 + 2125044 * q^9	\( 2 q - 128 q^{2} + 1626 q^{3} + 8192 q^{4} + 7666 q^{5} - 104064 q^{6} + 637048 q^{7} - 524288 q^{8} + 2125044 q^{9} - 490624 q^{10} + 3543122 q^{11} + 6660096 q^{12} - 3788668 q^{13} - 40771072 q^{14} - 94891926 q^{15} + 33554432 q^{16} + 37137304 q^{17} - 136002816 q^{18} - 102460596 q^{19} + 31399936 q^{20} + 474010752 q^{21} - 226759808 q^{22} + 1352747042 q^{23} - 426246144 q^{24} + 149795256 q^{25} + 242474752 q^{26} + 5625880326 q^{27} + 2609348608 q^{28} + 7425318120 q^{29} + 6073083264 q^{30} + 8163482594 q^{31} - 2147483648 q^{32} + 2880558186 q^{33} - 2376787456 q^{34} + 3554173208 q^{35} + 8704180224 q^{36} - 12073195594 q^{37} + 6557478144 q^{38} + 7935717852 q^{39} - 2009595904 q^{40} + 73792259580 q^{41} - 30336688128 q^{42} + 20450919684 q^{43} + 14512627712 q^{44} - 156282954732 q^{45} - 86575810688 q^{46} + 71306154600 q^{47} + 27279753216 q^{48} + 9620058330 q^{49} - 9586896384 q^{50} + 120756166944 q^{51} - 15518384128 q^{52} + 309577967404 q^{53} - 360056340864 q^{54} + 13580786626 q^{55} - 166998310912 q^{56} - 386169325212 q^{57} - 475220359680 q^{58} - 403802069082 q^{59} - 388677328896 q^{60} - 81219577008 q^{61} - 522462886016 q^{62} + 605481038784 q^{63} + 137438953472 q^{64} - 293591556156 q^{65} - 184355723904 q^{66} + 229155633102 q^{67} + 152114397184 q^{68} + 1957197038322 q^{69} - 227467085312 q^{70} - 1161878914578 q^{71} - 557067534336 q^{72} + 456037317380 q^{73} + 772684518016 q^{74} - 653435984616 q^{75} - 419678601216 q^{76} + 1128569391928 q^{77} - 507885942528 q^{78} + 5041088907052 q^{79} + 128614137856 q^{80} + 4339865129850 q^{81} - 4722704613120 q^{82} + 5610906244940 q^{83} + 1941548040192 q^{84} - 2151929029832 q^{85} - 1308858859776 q^{86} + 12129274956600 q^{87} - 928808173568 q^{88} - 3239330626042 q^{89} + 10002109102848 q^{90} - 1327956640328 q^{91} + 5540851884032 q^{92} - 1456518848238 q^{93} - 4563593894400 q^{94} + 7279946339020 q^{95} - 1745904205824 q^{96} - 20541366120174 q^{97} - 615683733120 q^{98} + 3764645073684 q^{99}+O(q^{100}) \) 2 * q - 128 * q^2 + 1626 * q^3 + 8192 * q^4 + 7666 * q^5 - 104064 * q^6 + 637048 * q^7 - 524288 * q^8 + 2125044 * q^9 - 490624 * q^10 + 3543122 * q^11 + 6660096 * q^12 - 3788668 * q^13 - 40771072 * q^14 - 94891926 * q^15 + 33554432 * q^16 + 37137304 * q^17 - 136002816 * q^18 - 102460596 * q^19 + 31399936 * q^20 + 474010752 * q^21 - 226759808 * q^22 + 1352747042 * q^23 - 426246144 * q^24 + 149795256 * q^25 + 242474752 * q^26 + 5625880326 * q^27 + 2609348608 * q^28 + 7425318120 * q^29 + 6073083264 * q^30 + 8163482594 * q^31 - 2147483648 * q^32 + 2880558186 * q^33 - 2376787456 * q^34 + 3554173208 * q^35 + 8704180224 * q^36 - 12073195594 * q^37 + 6557478144 * q^38 + 7935717852 * q^39 - 2009595904 * q^40 + 73792259580 * q^41 - 30336688128 * q^42 + 20450919684 * q^43 + 14512627712 * q^44 - 156282954732 * q^45 - 86575810688 * q^46 + 71306154600 * q^47 + 27279753216 * q^48 + 9620058330 * q^49 - 9586896384 * q^50 + 120756166944 * q^51 - 15518384128 * q^52 + 309577967404 * q^53 - 360056340864 * q^54 + 13580786626 * q^55 - 166998310912 * q^56 - 386169325212 * q^57 - 475220359680 * q^58 - 403802069082 * q^59 - 388677328896 * q^60 - 81219577008 * q^61 - 522462886016 * q^62 + 605481038784 * q^63 + 137438953472 * q^64 - 293591556156 * q^65 - 184355723904 * q^66 + 229155633102 * q^67 + 152114397184 * q^68 + 1957197038322 * q^69 - 227467085312 * q^70 - 1161878914578 * q^71 - 557067534336 * q^72 + 456037317380 * q^73 + 772684518016 * q^74 - 653435984616 * q^75 - 419678601216 * q^76 + 1128569391928 * q^77 - 507885942528 * q^78 + 5041088907052 * q^79 + 128614137856 * q^80 + 4339865129850 * q^81 - 4722704613120 * q^82 + 5610906244940 * q^83 + 1941548040192 * q^84 - 2151929029832 * q^85 - 1308858859776 * q^86 + 12129274956600 * q^87 - 928808173568 * q^88 - 3239330626042 * q^89 + 10002109102848 * q^90 - 1327956640328 * q^91 + 5540851884032 * q^92 - 1456518848238 * q^93 - 4563593894400 * q^94 + 7279946339020 * q^95 - 1745904205824 * q^96 - 20541366120174 * q^97 - 615683733120 * q^98 + 3764645073684 * q^99

Introduction

L-functions

Modular forms

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Database

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