LMFDB - Embedded newform 22.14.a.b.1.1

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			1.1
Root			$118.230$ 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)

$f(q)$	$=$	$q-64.0000 q^{2} -599.755 q^{3} +4096.00 q^{4} +39622.8 q^{5} +38384.3 q^{6} +334064. q^{7} -262144. q^{8} -1.23462e6 q^{9} +O(q^{10})$	\(q-64.0000 q^{2} -599.755 q^{3} +4096.00 q^{4} +39622.8 q^{5} +38384.3 q^{6} +334064. q^{7} -262144. q^{8} -1.23462e6 q^{9} -2.53586e6 q^{10} +1.77156e6 q^{11} -2.45660e6 q^{12} -5.79307e6 q^{13} -2.13801e7 q^{14} -2.37640e7 q^{15} +1.67772e7 q^{16} -1.34835e7 q^{17} +7.90155e7 q^{18} +5.59606e7 q^{19} +1.62295e8 q^{20} -2.00357e8 q^{21} -1.13380e8 q^{22} +3.72919e8 q^{23} +1.57222e8 q^{24} +3.49262e8 q^{25} +3.70756e8 q^{26} +1.69667e9 q^{27} +1.36833e9 q^{28} +1.55641e9 q^{29} +1.52089e9 q^{30} +6.94616e9 q^{31} -1.07374e9 q^{32} -1.06250e9 q^{33} +8.62941e8 q^{34} +1.32366e10 q^{35} -5.05699e9 q^{36} +1.45868e10 q^{37} -3.58148e9 q^{38} +3.47442e9 q^{39} -1.03869e10 q^{40} +3.23724e10 q^{41} +1.28228e10 q^{42} -3.77610e10 q^{43} +7.25631e9 q^{44} -4.89190e10 q^{45} -2.38668e10 q^{46} -4.52801e10 q^{47} -1.00622e10 q^{48} +1.47099e10 q^{49} -2.23528e10 q^{50} +8.08677e9 q^{51} -2.37284e10 q^{52} +2.65035e11 q^{53} -1.08587e11 q^{54} +7.01942e10 q^{55} -8.75730e10 q^{56} -3.35626e10 q^{57} -9.96105e10 q^{58} -3.39656e11 q^{59} -9.73372e10 q^{60} +3.30193e11 q^{61} -4.44554e11 q^{62} -4.12442e11 q^{63} +6.87195e10 q^{64} -2.29537e11 q^{65} +6.80001e10 q^{66} -1.70440e11 q^{67} -5.52282e10 q^{68} -2.23660e11 q^{69} -8.47140e11 q^{70} +4.54803e11 q^{71} +3.23647e11 q^{72} +2.56823e12 q^{73} -9.33558e11 q^{74} -2.09472e11 q^{75} +2.29215e11 q^{76} +5.91815e11 q^{77} -2.22363e11 q^{78} +3.03705e12 q^{79} +6.64760e11 q^{80} +9.50793e11 q^{81} -2.07183e12 q^{82} +4.44737e12 q^{83} -8.20661e11 q^{84} -5.34252e11 q^{85} +2.41670e12 q^{86} -9.33467e11 q^{87} -4.64404e11 q^{88} +2.31646e12 q^{89} +3.13081e12 q^{90} -1.93526e12 q^{91} +1.52748e12 q^{92} -4.16599e12 q^{93} +2.89793e12 q^{94} +2.21731e12 q^{95} +6.43982e11 q^{96} -1.12138e13 q^{97} -9.41437e11 q^{98} -2.18720e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−599.755	−0.474991	−0.237496	−	0.971389i	$-0.576327\pi$
$3$	−599.755	−0.474991	−0.237496	+	0.971389i	$0.576327\pi$
$4$	4096.00	0.500000
$5$	39622.8	1.13407	0.567035	−	0.823694i	$-0.308090\pi$
$5$	39622.8	1.13407	0.567035	+	0.823694i	$0.308090\pi$
$6$	38384.3	0.335869
$7$	334064.	1.07323	0.536615	−	0.843827i	$-0.319703\pi$
$7$	334064.	1.07323	0.536615	+	0.843827i	$0.319703\pi$
$8$	−262144.	−0.353553
$9$	−1.23462e6	−0.774383
$10$	−2.53586e6	−0.801909
$11$	1.77156e6	0.301511
$11$	1.77156e6	0.301511
$12$	−2.45660e6	−0.237496
$13$	−5.79307e6	−0.332872	−0.166436	−	0.986052i	$-0.553226\pi$
$13$	−5.79307e6	−0.332872	−0.166436	+	0.986052i	$0.553226\pi$
$14$	−2.13801e7	−0.758888
$15$	−2.37640e7	−0.538673
$16$	1.67772e7	0.250000
$17$	−1.34835e7	−0.135483	−0.0677413	−	0.997703i	$-0.521579\pi$
$17$	−1.34835e7	−0.135483	−0.0677413	+	0.997703i	$0.521579\pi$
$18$	7.90155e7	0.547572
$19$	5.59606e7	0.272888	0.136444	−	0.990648i	$-0.456433\pi$
$19$	5.59606e7	0.272888	0.136444	+	0.990648i	$0.456433\pi$
$20$	1.62295e8	0.567035
$21$	−2.00357e8	−0.509775
$22$	−1.13380e8	−0.213201
$23$	3.72919e8	0.525271	0.262636	−	0.964895i	$-0.415408\pi$
$23$	3.72919e8	0.525271	0.262636	+	0.964895i	$0.415408\pi$
$24$	1.57222e8	0.167935
$25$	3.49262e8	0.286116
$26$	3.70756e8	0.235376
$27$	1.69667e9	0.842816
$28$	1.36833e9	0.536615
$29$	1.55641e9	0.485890	0.242945	−	0.970040i	$-0.421887\pi$
$29$	1.55641e9	0.485890	0.242945	+	0.970040i	$0.421887\pi$
$30$	1.52089e9	0.380900
$31$	6.94616e9	1.40570	0.702851	−	0.711337i	$-0.251910\pi$
$31$	6.94616e9	1.40570	0.702851	+	0.711337i	$0.251910\pi$
$32$	−1.07374e9	−0.176777
$33$	−1.06250e9	−0.143215
$34$	8.62941e8	0.0958006
$35$	1.32366e10	1.21712
$36$	−5.05699e9	−0.387192
$37$	1.45868e10	0.934652	0.467326	−	0.884085i	$-0.345217\pi$
$37$	1.45868e10	0.934652	0.467326	+	0.884085i	$0.345217\pi$
$38$	−3.58148e9	−0.192961
$39$	3.47442e9	0.158111
$40$	−1.03869e10	−0.400954
$41$	3.23724e10	1.06434	0.532169	−	0.846638i	$-0.321377\pi$
$41$	3.23724e10	1.06434	0.532169	+	0.846638i	$0.321377\pi$
$42$	1.28228e10	0.360465
$43$	−3.77610e10	−0.910958	−0.455479	−	0.890246i	$-0.650532\pi$
$43$	−3.77610e10	−0.910958	−0.455479	+	0.890246i	$0.650532\pi$
$44$	7.25631e9	0.150756
$45$	−4.89190e10	−0.878205
$46$	−2.38668e10	−0.371423
$47$	−4.52801e10	−0.612733	−0.306367	−	0.951914i	$-0.599113\pi$
$47$	−4.52801e10	−0.612733	−0.306367	+	0.951914i	$0.599113\pi$
$48$	−1.00622e10	−0.118748
$49$	1.47099e10	0.151823
$50$	−2.23528e10	−0.202314
$51$	8.08677e9	0.0643530
$52$	−2.37284e10	−0.166436
$53$	2.65035e11	1.64252	0.821259	−	0.570556i	$-0.193272\pi$
$53$	2.65035e11	1.64252	0.821259	+	0.570556i	$0.193272\pi$
$54$	−1.08587e11	−0.595961
$55$	7.01942e10	0.341935
$56$	−8.75730e10	−0.379444
$57$	−3.35626e10	−0.129619
$58$	−9.96105e10	−0.343576
$59$	−3.39656e11	−1.04834	−0.524170	−	0.851614i	$-0.675624\pi$
$59$	−3.39656e11	−1.04834	−0.524170	+	0.851614i	$0.675624\pi$
$60$	−9.73372e10	−0.269337
$61$	3.30193e11	0.820586	0.410293	−	0.911954i	$-0.365426\pi$
$61$	3.30193e11	0.820586	0.410293	+	0.911954i	$0.365426\pi$
$62$	−4.44554e11	−0.993982
$63$	−4.12442e11	−0.831091
$64$	6.87195e10	0.125000
$65$	−2.29537e11	−0.377500
$66$	6.80001e10	0.101268
$67$	−1.70440e11	−0.230189	−0.115095	−	0.993355i	$-0.536717\pi$
$67$	−1.70440e11	−0.230189	−0.115095	+	0.993355i	$0.536717\pi$
$68$	−5.52282e10	−0.0677413
$69$	−2.23660e11	−0.249499
$70$	−8.47140e11	−0.860633
$71$	4.54803e11	0.421351	0.210675	−	0.977556i	$-0.432434\pi$
$71$	4.54803e11	0.421351	0.210675	+	0.977556i	$0.432434\pi$
$72$	3.23647e11	0.273786
$73$	2.56823e12	1.98626	0.993129	−	0.117023i	$-0.0373353\pi$
$73$	2.56823e12	1.98626	0.993129	+	0.117023i	$0.0373353\pi$
$74$	−9.33558e11	−0.660899
$75$	−2.09472e11	−0.135902
$76$	2.29215e11	0.136444
$77$	5.91815e11	0.323591
$78$	−2.22363e11	−0.111801
$79$	3.03705e12	1.40565	0.702823	−	0.711365i	$-0.251923\pi$
$79$	3.03705e12	1.40565	0.702823	+	0.711365i	$0.251923\pi$
$80$	6.64760e11	0.283518
$81$	9.50793e11	0.374053
$82$	−2.07183e12	−0.752601
$83$	4.44737e12	1.49312	0.746561	−	0.665317i	$-0.231704\pi$
$83$	4.44737e12	1.49312	0.746561	+	0.665317i	$0.231704\pi$
$84$	−8.20661e11	−0.254887
$85$	−5.34252e11	−0.153647
$86$	2.41670e12	0.644145
$87$	−9.33467e11	−0.230794
$88$	−4.64404e11	−0.106600
$89$	2.31646e12	0.494072	0.247036	−	0.969006i	$-0.420543\pi$
$89$	2.31646e12	0.494072	0.247036	+	0.969006i	$0.420543\pi$
$90$	3.13081e12	0.620985
$91$	−1.93526e12	−0.357248
$92$	1.52748e12	0.262636
$93$	−4.16599e12	−0.667696
$94$	2.89793e12	0.433268
$95$	2.21731e12	0.309474
$96$	6.43982e11	0.0839674
$97$	−1.12138e13	−1.36690	−0.683448	−	0.730000i	$-0.739520\pi$
$97$	−1.12138e13	−1.36690	−0.683448	+	0.730000i	$0.739520\pi$
$98$	−9.41437e11	−0.107355
$99$	−2.18720e12	−0.233485
$100$	1.43058e12	0.143058
$101$	1.99542e12	0.187045	0.0935224	−	0.995617i	$-0.470187\pi$
$101$	1.99542e12	0.187045	0.0935224	+	0.995617i	$0.470187\pi$
$102$	−5.17553e11	−0.0455044
$103$	−1.73226e13	−1.42946	−0.714729	−	0.699402i	$-0.753450\pi$
$103$	−1.73226e13	−1.42946	−0.714729	+	0.699402i	$0.753450\pi$
$104$	1.51862e12	0.117688
$105$	−7.93869e12	−0.578120
$106$	−1.69622e13	−1.16144
$107$	−9.04861e12	−0.582891	−0.291445	−	0.956587i	$-0.594136\pi$
$107$	−9.04861e12	−0.582891	−0.291445	+	0.956587i	$0.594136\pi$
$108$	6.94956e12	0.421408
$109$	−1.73142e13	−0.988851	−0.494426	−	0.869220i	$-0.664622\pi$
$109$	−1.73142e13	−0.988851	−0.494426	+	0.869220i	$0.664622\pi$
$110$	−4.49243e12	−0.241785
$111$	−8.74853e12	−0.443952
$112$	5.60467e12	0.268308
$113$	3.03174e13	1.36988	0.684940	−	0.728599i	$-0.259828\pi$
$113$	3.03174e13	1.36988	0.684940	+	0.728599i	$0.259828\pi$
$114$	2.14801e12	0.0916546
$115$	1.47761e13	0.595694
$116$	6.37507e12	0.242945
$117$	7.15222e12	0.257770
$118$	2.17380e13	0.741288
$119$	−4.50434e12	−0.145404
$120$	6.22958e12	0.190450
$121$	3.13843e12	0.0909091
$122$	−2.11324e13	−0.580242
$123$	−1.94155e13	−0.505552
$124$	2.84515e13	0.702851
$125$	−3.45289e13	−0.809595
$126$	2.63963e13	0.587670
$127$	−8.28887e13	−1.75296	−0.876478	−	0.481441i	$-0.840113\pi$
$127$	−8.28887e13	−1.75296	−0.876478	+	0.481441i	$0.840113\pi$
$128$	−4.39805e12	−0.0883883
$129$	2.26473e13	0.432697
$130$	1.46904e13	0.266933
$131$	1.40030e13	0.242079	0.121040	−	0.992648i	$-0.461377\pi$
$131$	1.40030e13	0.242079	0.121040	+	0.992648i	$0.461377\pi$
$132$	−4.35201e12	−0.0716076
$133$	1.86944e13	0.292871
$134$	1.09082e13	0.162768
$135$	6.72268e13	0.955813
$136$	3.53461e12	0.0479003
$137$	7.44048e13	0.961429	0.480714	−	0.876877i	$-0.340377\pi$
$137$	7.44048e13	0.961429	0.480714	+	0.876877i	$0.340377\pi$
$138$	1.43142e13	0.176423
$139$	6.03007e13	0.709131	0.354565	−	0.935031i	$-0.384629\pi$
$139$	6.03007e13	0.709131	0.354565	+	0.935031i	$0.384629\pi$
$140$	5.42169e13	0.608559
$141$	2.71570e13	0.291043
$142$	−2.91074e13	−0.297940
$143$	−1.02628e13	−0.100365
$144$	−2.07134e13	−0.193596
$145$	6.16695e13	0.551034
$146$	−1.64367e14	−1.40450
$147$	−8.82236e12	−0.0721144
$148$	5.97477e13	0.467326
$149$	−7.28617e13	−0.545492	−0.272746	−	0.962086i	$-0.587932\pi$
$149$	−7.28617e13	−0.545492	−0.272746	+	0.962086i	$0.587932\pi$
$150$	1.34062e13	0.0960975
$151$	−1.40176e14	−0.962326	−0.481163	−	0.876631i	$-0.659786\pi$
$151$	−1.40176e14	−0.962326	−0.481163	+	0.876631i	$0.659786\pi$
$152$	−1.46697e13	−0.0964803
$153$	1.66469e13	0.104915
$154$	−3.78762e13	−0.228813
$155$	2.75226e14	1.59417
$156$	1.42312e13	0.0790555
$157$	−5.49793e13	−0.292989	−0.146495	−	0.989211i	$-0.546799\pi$
$157$	−5.49793e13	−0.292989	−0.146495	+	0.989211i	$0.546799\pi$
$158$	−1.94371e14	−0.993942
$159$	−1.58956e14	−0.780181
$160$	−4.25446e13	−0.200477
$161$	1.24579e14	0.563737
$162$	−6.08507e13	−0.264495
$163$	1.03711e14	0.433118	0.216559	−	0.976270i	$-0.430517\pi$
$163$	1.03711e14	0.433118	0.216559	+	0.976270i	$0.430517\pi$
$164$	1.32597e14	0.532169
$165$	−4.20993e13	−0.162416
$166$	−2.84631e14	−1.05580
$167$	3.44703e14	1.22967	0.614834	−	0.788656i	$-0.289223\pi$
$167$	3.44703e14	1.22967	0.614834	+	0.788656i	$0.289223\pi$
$168$	5.25223e13	0.180233
$169$	−2.69315e14	−0.889197
$170$	3.41921e13	0.108645
$171$	−6.90899e13	−0.211320
$172$	−1.54669e14	−0.455479
$173$	−1.06953e14	−0.303315	−0.151658	−	0.988433i	$-0.548461\pi$
$173$	−1.06953e14	−0.303315	−0.151658	+	0.988433i	$0.548461\pi$
$174$	5.97419e13	0.163196
$175$	1.16676e14	0.307068
$176$	2.97219e13	0.0753778
$177$	2.03711e14	0.497952
$178$	−1.48253e14	−0.349361
$179$	−4.49285e14	−1.02089	−0.510443	−	0.859912i	$-0.670518\pi$
$179$	−4.49285e14	−1.02089	−0.510443	+	0.859912i	$0.670518\pi$
$180$	−2.00372e14	−0.439103
$181$	−8.33325e14	−1.76159	−0.880793	−	0.473502i	$-0.842990\pi$
$181$	−8.33325e14	−1.76159	−0.880793	+	0.473502i	$0.842990\pi$
$182$	1.23856e14	0.252612
$183$	−1.98035e14	−0.389771
$184$	−9.77585e13	−0.185711
$185$	5.77971e14	1.05996
$186$	2.66623e14	0.472133
$187$	−2.38868e13	−0.0408495
$188$	−1.85467e14	−0.306367
$189$	5.66797e14	0.904536
$190$	−1.41908e14	−0.218831
$191$	−5.21923e14	−0.777839	−0.388919	−	0.921272i	$-0.627152\pi$
$191$	−5.21923e14	−0.777839	−0.388919	+	0.921272i	$0.627152\pi$
$192$	−4.12148e13	−0.0593739
$193$	8.46686e13	0.117923	0.0589617	−	0.998260i	$-0.481221\pi$
$193$	8.46686e13	0.117923	0.0589617	+	0.998260i	$0.481221\pi$
$194$	7.17681e14	0.966541
$195$	1.37666e14	0.179309
$196$	6.02519e13	0.0759113
$197$	1.22404e15	1.49198	0.745991	−	0.665956i	$-0.231976\pi$
$197$	1.22404e15	1.49198	0.745991	+	0.665956i	$0.231976\pi$
$198$	1.39981e14	0.165099
$199$	−8.59631e14	−0.981221	−0.490611	−	0.871379i	$-0.663226\pi$
$199$	−8.59631e14	−0.981221	−0.490611	+	0.871379i	$0.663226\pi$
$200$	−9.15570e13	−0.101157
$201$	1.02222e14	0.109338
$202$	−1.27707e14	−0.132261
$203$	5.19942e14	0.521472
$204$	3.31234e13	0.0321765
$205$	1.28269e15	1.20704
$206$	1.10865e15	1.01078
$207$	−4.60412e14	−0.406761
$208$	−9.71915e13	−0.0832179
$209$	9.91376e13	0.0822787
$210$	5.08076e14	0.408793
$211$	2.68642e14	0.209574	0.104787	−	0.994495i	$-0.466584\pi$
$211$	2.68642e14	0.209574	0.104787	+	0.994495i	$0.466584\pi$
$212$	1.08558e15	0.821259
$213$	−2.72770e14	−0.200138
$214$	5.79111e14	0.412166
$215$	−1.49620e15	−1.03309
$216$	−4.44772e14	−0.297981
$217$	2.32046e15	1.50864
$218$	1.10811e15	0.699224
$219$	−1.54031e15	−0.943455
$220$	2.87515e14	0.170968
$221$	7.81106e13	0.0450983
$222$	5.59906e14	0.313921
$223$	−6.60257e14	−0.359527	−0.179763	−	0.983710i	$-0.557533\pi$
$223$	−6.60257e14	−0.359527	−0.179763	+	0.983710i	$0.557533\pi$
$224$	−3.58699e14	−0.189722
$225$	−4.31205e14	−0.221563
$226$	−1.94032e15	−0.968652
$227$	−2.20485e15	−1.06958	−0.534788	−	0.844986i	$-0.679608\pi$
$227$	−2.20485e15	−1.06958	−0.534788	+	0.844986i	$0.679608\pi$
$228$	−1.37473e14	−0.0648096
$229$	−2.26106e15	−1.03605	−0.518026	−	0.855365i	$-0.673333\pi$
$229$	−2.26106e15	−1.03605	−0.518026	+	0.855365i	$0.673333\pi$
$230$	−9.45670e14	−0.421220
$231$	−3.54944e14	−0.153703
$232$	−4.08005e14	−0.171788
$233$	1.85391e15	0.759059	0.379530	−	0.925180i	$-0.376086\pi$
$233$	1.85391e15	0.759059	0.379530	+	0.925180i	$0.376086\pi$
$234$	−4.57742e14	−0.182271
$235$	−1.79412e15	−0.694882
$236$	−1.39123e15	−0.524170
$237$	−1.82149e15	−0.667669
$238$	2.88278e14	0.102816
$239$	8.58657e14	0.298012	0.149006	−	0.988836i	$-0.452393\pi$
$239$	8.58657e14	0.298012	0.149006	+	0.988836i	$0.452393\pi$
$240$	−3.98693e14	−0.134668
$241$	1.99748e15	0.656707	0.328354	−	0.944555i	$-0.393506\pi$
$241$	1.99748e15	0.656707	0.328354	+	0.944555i	$0.393506\pi$
$242$	−2.00859e14	−0.0642824
$243$	−3.27528e15	−1.02049
$244$	1.35247e15	0.410293
$245$	5.82849e14	0.172178
$246$	1.24259e15	0.357479
$247$	−3.24183e14	−0.0908365
$248$	−1.82089e15	−0.496991
$249$	−2.66733e15	−0.709220
$250$	2.20985e15	0.572470
$251$	−4.93558e15	−1.24583	−0.622916	−	0.782289i	$-0.714052\pi$
$251$	−4.93558e15	−1.24583	−0.622916	+	0.782289i	$0.714052\pi$
$252$	−1.68936e15	−0.415546
$253$	6.60649e14	0.158375
$254$	5.30488e15	1.23953
$255$	3.20420e14	0.0729808
$256$	2.81475e14	0.0625000
$257$	1.09465e15	0.236980	0.118490	−	0.992955i	$-0.462195\pi$
$257$	1.09465e15	0.236980	0.118490	+	0.992955i	$0.462195\pi$
$258$	−1.44943e15	−0.305963
$259$	4.87294e15	1.00310
$260$	−9.40185e14	−0.188750
$261$	−1.92158e15	−0.376265
$262$	−8.96192e14	−0.171176
$263$	1.03726e16	1.93275	0.966374	−	0.257142i	$-0.0827808\pi$
$263$	1.03726e16	1.93275	0.966374	+	0.257142i	$0.0827808\pi$
$264$	2.78529e14	0.0506342
$265$	1.05014e16	1.86273
$266$	−1.19644e15	−0.207091
$267$	−1.38931e15	−0.234680
$268$	−6.98122e14	−0.115095
$269$	8.01732e15	1.29015	0.645073	−	0.764121i	$-0.276827\pi$
$269$	8.01732e15	1.29015	0.645073	+	0.764121i	$0.276827\pi$
$270$	−4.30252e15	−0.675862
$271$	−8.31361e15	−1.27494	−0.637470	−	0.770476i	$-0.720019\pi$
$271$	−8.31361e15	−1.27494	−0.637470	+	0.770476i	$0.720019\pi$
$272$	−2.26215e14	−0.0338706
$273$	1.16068e15	0.169690
$274$	−4.76190e15	−0.679833
$275$	6.18739e14	0.0862671
$276$	−9.16111e14	−0.124750
$277$	4.46648e14	0.0594083	0.0297042	−	0.999559i	$-0.490543\pi$
$277$	4.46648e14	0.0594083	0.0297042	+	0.999559i	$0.490543\pi$
$278$	−3.85925e15	−0.501431
$279$	−8.57584e15	−1.08855
$280$	−3.46988e15	−0.430316
$281$	1.35012e16	1.63600	0.817999	−	0.575220i	$-0.195084\pi$
$281$	1.35012e16	1.63600	0.817999	+	0.575220i	$0.195084\pi$
$282$	−1.73805e15	−0.205798
$283$	9.97911e15	1.15473	0.577364	−	0.816487i	$-0.304081\pi$
$283$	9.97911e15	1.15473	0.577364	+	0.816487i	$0.304081\pi$
$284$	1.86287e15	0.210675
$285$	−1.32984e15	−0.146997
$286$	6.56817e14	0.0709685
$287$	1.08145e16	1.14228
$288$	1.32566e15	0.136893
$289$	−9.72277e15	−0.981644
$290$	−3.94685e15	−0.389640
$291$	6.72551e15	0.649263
$292$	1.05195e16	0.993129
$293$	8.46068e15	0.781207	0.390603	−	0.920559i	$-0.372266\pi$
$293$	8.46068e15	0.781207	0.390603	+	0.920559i	$0.372266\pi$
$294$	5.64631e14	0.0509926
$295$	−1.34581e16	−1.18889
$296$	−3.82385e15	−0.330450
$297$	3.00576e15	0.254119
$298$	4.66315e15	0.385721
$299$	−2.16034e15	−0.174848
$300$	−8.57996e14	−0.0679512
$301$	−1.26146e16	−0.977668
$302$	8.97124e15	0.680467
$303$	−1.19676e15	−0.0888447
$304$	9.38863e14	0.0682219
$305$	1.30832e16	0.930603
$306$	−1.06540e15	−0.0741864
$307$	−2.07716e16	−1.41602	−0.708011	−	0.706202i	$-0.750407\pi$
$307$	−2.07716e16	−1.41602	−0.708011	+	0.706202i	$0.750407\pi$
$308$	2.42408e15	0.161796
$309$	1.03893e16	0.678979
$310$	−1.76145e16	−1.12725
$311$	−2.06802e16	−1.29602	−0.648010	−	0.761632i	$-0.724398\pi$
$311$	−2.06802e16	−1.29602	−0.648010	+	0.761632i	$0.724398\pi$
$312$	−9.10798e14	−0.0559007
$313$	−1.65799e16	−0.996653	−0.498327	−	0.866989i	$-0.666052\pi$
$313$	−1.65799e16	−0.996653	−0.498327	+	0.866989i	$0.666052\pi$
$314$	3.51868e15	0.207175
$315$	−1.63421e16	−0.942516
$316$	1.24398e16	0.702823
$317$	1.08785e16	0.602123	0.301061	−	0.953605i	$-0.402659\pi$
$317$	1.08785e16	0.602123	0.301061	+	0.953605i	$0.402659\pi$
$318$	1.01732e16	0.551671
$319$	2.75728e15	0.146501
$320$	2.72286e15	0.141759
$321$	5.42695e15	0.276868
$322$	−7.97305e15	−0.398622
$323$	−7.54542e14	−0.0369715
$324$	3.89445e15	0.187026
$325$	−2.02330e15	−0.0952397
$326$	−6.63752e15	−0.306261
$327$	1.03843e16	0.469696
$328$	−8.48623e15	−0.376301
$329$	−1.51265e16	−0.657604
$330$	2.69435e15	0.114846
$331$	2.58146e16	1.07891	0.539453	−	0.842016i	$-0.318631\pi$
$331$	2.58146e16	1.07891	0.539453	+	0.842016i	$0.318631\pi$
$332$	1.82164e16	0.746561
$333$	−1.80092e16	−0.723779
$334$	−2.20610e16	−0.869507
$335$	−6.75330e15	−0.261051
$336$	−3.36143e15	−0.127444
$337$	−3.07345e16	−1.14296	−0.571482	−	0.820615i	$-0.693631\pi$
$337$	−3.07345e16	−1.14296	−0.571482	+	0.820615i	$0.693631\pi$
$338$	1.72362e16	0.628757
$339$	−1.81830e16	−0.650681
$340$	−2.18830e15	−0.0768234
$341$	1.23055e16	0.423835
$342$	4.42175e15	0.149426
$343$	−2.74531e16	−0.910289
$344$	9.89882e15	0.322072
$345$	−8.86203e15	−0.282950
$346$	6.84501e15	0.214476
$347$	−2.13816e16	−0.657504	−0.328752	−	0.944416i	$-0.606628\pi$
$347$	−2.13816e16	−0.657504	−0.328752	+	0.944416i	$0.606628\pi$
$348$	−3.82348e15	−0.115397
$349$	2.13547e16	0.632599	0.316299	−	0.948659i	$-0.397560\pi$
$349$	2.13547e16	0.632599	0.316299	+	0.948659i	$0.397560\pi$
$350$	−7.46726e15	−0.217130
$351$	−9.82892e15	−0.280550
$352$	−1.90220e15	−0.0533002
$353$	5.84295e16	1.60730	0.803649	−	0.595104i	$-0.202889\pi$
$353$	5.84295e16	1.60730	0.803649	+	0.595104i	$0.202889\pi$
$354$	−1.30375e16	−0.352105
$355$	1.80206e16	0.477842
$356$	9.48822e15	0.247036
$357$	2.70150e15	0.0690656
$358$	2.87542e16	0.721875
$359$	−6.18101e16	−1.52386	−0.761931	−	0.647658i	$-0.775748\pi$
$359$	−6.18101e16	−1.52386	−0.761931	+	0.647658i	$0.775748\pi$
$360$	1.28238e16	0.310492
$361$	−3.89214e16	−0.925532
$362$	5.33328e16	1.24563
$363$	−1.88229e15	−0.0431810
$364$	−7.92681e15	−0.178624
$365$	1.01761e17	2.25256
$366$	1.26742e16	0.275610
$367$	3.20355e16	0.684388	0.342194	−	0.939629i	$-0.388830\pi$
$367$	3.20355e16	0.684388	0.342194	+	0.939629i	$0.388830\pi$
$368$	6.25654e15	0.131318
$369$	−3.99675e16	−0.824206
$370$	−3.69902e16	−0.749506
$371$	8.85387e16	1.76280
$372$	−1.70639e16	−0.333848
$373$	1.53277e16	0.294693	0.147347	−	0.989085i	$-0.452927\pi$
$373$	1.53277e16	0.294693	0.147347	+	0.989085i	$0.452927\pi$
$374$	1.52875e15	0.0288850
$375$	2.07089e16	0.384551
$376$	1.18699e16	0.216634
$377$	−9.01641e15	−0.161739
$378$	−3.62750e16	−0.639603
$379$	4.83237e16	0.837540	0.418770	−	0.908092i	$-0.362461\pi$
$379$	4.83237e16	0.837540	0.418770	+	0.908092i	$0.362461\pi$
$380$	9.08212e15	0.154737
$381$	4.97129e16	0.832639
$382$	3.34031e16	0.550015
$383$	−1.02436e17	−1.65829	−0.829144	−	0.559035i	$-0.811172\pi$
$383$	−1.02436e17	−1.65829	−0.829144	+	0.559035i	$0.811172\pi$
$384$	2.63775e15	0.0419837
$385$	2.34494e16	0.366975
$386$	−5.41879e15	−0.0833844
$387$	4.66204e16	0.705431
$388$	−4.59316e16	−0.683448
$389$	−1.14101e17	−1.66962	−0.834809	−	0.550540i	$-0.814422\pi$
$389$	−1.14101e17	−1.66962	−0.834809	+	0.550540i	$0.814422\pi$
$390$	−8.81063e15	−0.126791
$391$	−5.02824e15	−0.0711651
$392$	−3.85612e15	−0.0536774
$393$	−8.39837e15	−0.114986
$394$	−7.83382e16	−1.05499
$395$	1.20336e17	1.59410
$396$	−8.95877e15	−0.116743
$397$	3.03086e16	0.388532	0.194266	−	0.980949i	$-0.437767\pi$
$397$	3.03086e16	0.388532	0.194266	+	0.980949i	$0.437767\pi$
$398$	5.50164e16	0.693828
$399$	−1.12121e16	−0.139111
$400$	5.85965e15	0.0715289
$401$	−6.58499e16	−0.790892	−0.395446	−	0.918489i	$-0.629410\pi$
$401$	−6.58499e16	−0.790892	−0.395446	+	0.918489i	$0.629410\pi$
$402$	−6.54222e15	−0.0773135
$403$	−4.02395e16	−0.467918
$404$	8.17325e15	0.0935224
$405$	3.76731e16	0.424202
$406$	−3.32763e16	−0.368736
$407$	2.58415e16	0.281808
$408$	−2.11990e15	−0.0227522
$409$	−3.79254e16	−0.400616	−0.200308	−	0.979733i	$-0.564194\pi$
$409$	−3.79254e16	−0.400616	−0.200308	+	0.979733i	$0.564194\pi$
$410$	−8.20918e16	−0.853503
$411$	−4.46246e16	−0.456670
$412$	−7.09534e16	−0.714729
$413$	−1.13467e17	−1.12511
$414$	2.94664e16	0.287624
$415$	1.76217e17	1.69330
$416$	6.22026e15	0.0588439
$417$	−3.61657e16	−0.336831
$418$	−6.34481e15	−0.0581798
$419$	−7.22078e16	−0.651918	−0.325959	−	0.945384i	$-0.605687\pi$
$419$	−7.22078e16	−0.651918	−0.325959	+	0.945384i	$0.605687\pi$
$420$	−3.25169e16	−0.289060
$421$	−1.46245e17	−1.28011	−0.640054	−	0.768330i	$-0.721088\pi$
$421$	−1.46245e17	−1.28011	−0.640054	+	0.768330i	$0.721088\pi$
$422$	−1.71931e16	−0.148191
$423$	5.59036e16	0.474490
$424$	−6.94773e16	−0.580718
$425$	−4.70926e15	−0.0387637
$426$	1.74573e16	0.141519
$427$	1.10306e17	0.880678
$428$	−3.70631e16	−0.291445
$429$	6.15515e15	0.0476723
$430$	9.57565e16	0.730505
$431$	7.06813e16	0.531132	0.265566	−	0.964093i	$-0.414441\pi$
$431$	7.06813e16	0.531132	0.265566	+	0.964093i	$0.414441\pi$
$432$	2.84654e16	0.210704
$433$	−2.32905e17	−1.69827	−0.849136	−	0.528174i	$-0.822877\pi$
$433$	−2.32905e17	−1.69827	−0.849136	+	0.528174i	$0.822877\pi$
$434$	−1.48510e17	−1.06677
$435$	−3.69865e16	−0.261736
$436$	−7.09191e16	−0.494426
$437$	2.08688e16	0.143340
$438$	9.85798e16	0.667124
$439$	−3.39801e16	−0.226571	−0.113286	−	0.993562i	$-0.536138\pi$
$439$	−3.39801e16	−0.226571	−0.113286	+	0.993562i	$0.536138\pi$
$440$	−1.84010e16	−0.120892
$441$	−1.81612e16	−0.117569
$442$	−4.99908e15	−0.0318893
$443$	−2.53590e16	−0.159407	−0.0797037	−	0.996819i	$-0.525397\pi$
$443$	−2.53590e16	−0.159407	−0.0797037	+	0.996819i	$0.525397\pi$
$444$	−3.58340e16	−0.221976
$445$	9.17846e16	0.560312
$446$	4.22564e16	0.254224
$447$	4.36991e16	0.259104
$448$	2.29567e16	0.134154
$449$	1.71031e17	0.985087	0.492544	−	0.870288i	$-0.336067\pi$
$449$	1.71031e17	0.985087	0.492544	+	0.870288i	$0.336067\pi$
$450$	2.75971e16	0.156669
$451$	5.73497e16	0.320910
$452$	1.24180e17	0.684940
$453$	8.40710e16	0.457096
$454$	1.41111e17	0.756304
$455$	−7.66803e16	−0.405144
$456$	8.79824e15	0.0458273
$457$	2.59067e17	1.33032	0.665162	−	0.746699i	$-0.268362\pi$
$457$	2.59067e17	1.33032	0.665162	+	0.746699i	$0.268362\pi$
$458$	1.44708e17	0.732599
$459$	−2.28770e16	−0.114187
$460$	6.05229e16	0.297847
$461$	1.40771e17	0.683057	0.341528	−	0.939871i	$-0.389055\pi$
$461$	1.40771e17	0.683057	0.341528	+	0.939871i	$0.389055\pi$
$462$	2.27164e16	0.108684
$463$	2.64867e17	1.24954	0.624771	−	0.780808i	$-0.285192\pi$
$463$	2.64867e17	1.24954	0.624771	+	0.780808i	$0.285192\pi$
$464$	2.61123e16	0.121473
$465$	−1.65068e17	−0.757215
$466$	−1.18650e17	−0.536736
$467$	7.37372e16	0.328948	0.164474	−	0.986381i	$-0.447407\pi$
$467$	7.37372e16	0.328948	0.164474	+	0.986381i	$0.447407\pi$
$468$	2.92955e16	0.128885
$469$	−5.69379e16	−0.247046
$470$	1.14824e17	0.491356
$471$	3.29741e16	0.139167
$472$	8.90389e16	0.370644
$473$	−6.68959e16	−0.274664
$474$	1.16575e17	0.472113
$475$	1.95449e16	0.0780774
$476$	−1.84498e16	−0.0727020
$477$	−3.27217e17	−1.27194
$478$	−5.49540e16	−0.210726
$479$	−2.80724e17	−1.06194	−0.530968	−	0.847392i	$-0.678172\pi$
$479$	−2.80724e17	−1.06194	−0.530968	+	0.847392i	$0.678172\pi$
$480$	2.55164e16	0.0952249
$481$	−8.45025e16	−0.311119
$482$	−1.27839e17	−0.464362
$483$	−7.47168e16	−0.267770
$484$	1.28550e16	0.0454545
$485$	−4.44321e17	−1.55016
$486$	2.09618e17	0.721594
$487$	8.30275e16	0.282022	0.141011	−	0.990008i	$-0.454965\pi$
$487$	8.30275e16	0.282022	0.141011	+	0.990008i	$0.454965\pi$
$488$	−8.65582e16	−0.290121
$489$	−6.22013e16	−0.205727
$490$	−3.73023e16	−0.121748
$491$	−2.64183e17	−0.850893	−0.425446	−	0.904984i	$-0.639883\pi$
$491$	−2.64183e17	−0.850893	−0.425446	+	0.904984i	$0.639883\pi$
$492$	−7.95259e16	−0.252776
$493$	−2.09858e16	−0.0658296
$494$	2.07477e16	0.0642311
$495$	−8.66629e16	−0.264789
$496$	1.16537e17	0.351426
$497$	1.51933e17	0.452207
$498$	1.70709e17	0.501494
$499$	5.54636e17	1.60825	0.804126	−	0.594458i	$-0.202633\pi$
$499$	5.54636e17	1.60825	0.804126	+	0.594458i	$0.202633\pi$
$500$	−1.41430e17	−0.404798
$501$	−2.06737e17	−0.584082
$502$	3.15877e17	0.880936
$503$	−1.57515e17	−0.433641	−0.216821	−	0.976211i	$-0.569569\pi$
$503$	−1.57515e17	−0.433641	−0.216821	+	0.976211i	$0.569569\pi$
$504$	1.08119e17	0.293835
$505$	7.90642e16	0.212122
$506$	−4.22815e16	−0.111988
$507$	1.61523e17	0.422361
$508$	−3.39512e17	−0.876478
$509$	−5.22539e17	−1.33184	−0.665922	−	0.746022i	$-0.731962\pi$
$509$	−5.22539e17	−1.33184	−0.665922	+	0.746022i	$0.731962\pi$
$510$	−2.05069e16	−0.0516052
$511$	8.57955e17	2.13171
$512$	−1.80144e16	−0.0441942
$513$	9.49467e16	0.229994
$514$	−7.00579e16	−0.167570
$515$	−6.86370e17	−1.62110
$516$	9.27635e16	0.216349
$517$	−8.02165e16	−0.184746
$518$	−3.11868e17	−0.709297
$519$	6.41457e16	0.144072
$520$	6.01719e16	0.133466
$521$	−2.90970e16	−0.0637386	−0.0318693	−	0.999492i	$-0.510146\pi$
$521$	−2.90970e16	−0.0637386	−0.0318693	+	0.999492i	$0.510146\pi$
$522$	1.22981e17	0.266060
$523$	4.29087e17	0.916821	0.458410	−	0.888741i	$-0.348419\pi$
$523$	4.29087e17	0.916821	0.458410	+	0.888741i	$0.348419\pi$
$524$	5.73563e16	0.121040
$525$	−6.99770e16	−0.145854
$526$	−6.63846e17	−1.36666
$527$	−9.36582e16	−0.190448
$528$	−1.78258e16	−0.0358038
$529$	−3.64968e17	−0.724090
$530$	−6.72091e17	−1.31715
$531$	4.19346e17	0.811816
$532$	7.65724e16	0.146436
$533$	−1.87536e17	−0.354288
$534$	8.89157e16	0.165944
$535$	−3.58531e17	−0.661039
$536$	4.46798e16	0.0813842
$537$	2.69461e17	0.484912
$538$	−5.13108e17	−0.912272
$539$	2.60596e16	0.0457763
$540$	2.75361e17	0.477907
$541$	7.38907e17	1.26709	0.633545	−	0.773706i	$-0.281599\pi$
$541$	7.38907e17	1.26709	0.633545	+	0.773706i	$0.281599\pi$
$542$	5.32071e17	0.901518
$543$	4.99791e17	0.836738
$544$	1.44778e16	0.0239502
$545$	−6.86038e17	−1.12143
$546$	−7.42835e16	−0.119989
$547$	−7.66836e17	−1.22401	−0.612005	−	0.790854i	$-0.709637\pi$
$547$	−7.66836e17	−1.22401	−0.612005	+	0.790854i	$0.709637\pi$
$548$	3.04762e17	0.480714
$549$	−4.07662e17	−0.635448
$550$	−3.95993e16	−0.0610000
$551$	8.70978e16	0.132593
$552$	5.86311e16	0.0882113
$553$	1.01457e18	1.50858
$554$	−2.85855e16	−0.0420080
$555$	−3.46641e17	−0.503472
$556$	2.46992e17	0.354565
$557$	−8.11846e16	−0.115190	−0.0575950	−	0.998340i	$-0.518343\pi$
$557$	−8.11846e16	−0.115190	−0.0575950	+	0.998340i	$0.518343\pi$
$558$	5.48854e17	0.769723
$559$	2.18752e17	0.303232
$560$	2.22073e17	0.304280
$561$	1.43262e16	0.0194032
$562$	−8.64079e17	−1.15682
$563$	−6.63649e17	−0.878282	−0.439141	−	0.898418i	$-0.644717\pi$
$563$	−6.63649e17	−0.878282	−0.439141	+	0.898418i	$0.644717\pi$
$564$	1.11235e17	0.145521
$565$	1.20126e18	1.55354
$566$	−6.38663e17	−0.816517
$567$	3.17626e17	0.401445
$568$	−1.19224e17	−0.148970
$569$	−6.11631e17	−0.755544	−0.377772	−	0.925899i	$-0.623310\pi$
$569$	−6.11631e17	−0.755544	−0.377772	+	0.925899i	$0.623310\pi$
$570$	8.51101e16	0.103943
$571$	−6.46687e17	−0.780835	−0.390418	−	0.920638i	$-0.627669\pi$
$571$	−6.46687e17	−0.780835	−0.390418	+	0.920638i	$0.627669\pi$
$572$	−4.20363e16	−0.0501823
$573$	3.13026e17	0.369466
$574$	−6.92126e17	−0.807714
$575$	1.30246e17	0.150288
$576$	−8.48423e16	−0.0967979
$577$	9.60666e17	1.08375	0.541875	−	0.840459i	$-0.317714\pi$
$577$	9.60666e17	1.08375	0.541875	+	0.840459i	$0.317714\pi$
$578$	6.22258e17	0.694127
$579$	−5.07804e16	−0.0560126
$580$	2.52598e17	0.275517
$581$	1.48571e18	1.60246
$582$	−4.30433e17	−0.459098
$583$	4.69525e17	0.495238
$584$	−6.73247e17	−0.702248
$585$	2.83391e17	0.292330
$586$	−5.41484e17	−0.552397
$587$	1.88001e18	1.89677	0.948383	−	0.317128i	$-0.102718\pi$
$587$	1.88001e18	1.89677	0.948383	+	0.317128i	$0.102718\pi$
$588$	−3.61364e16	−0.0360572
$589$	3.88711e17	0.383599
$590$	8.61321e17	0.840672
$591$	−7.34121e17	−0.708678
$592$	2.44727e17	0.233663
$593$	1.26273e18	1.19249	0.596245	−	0.802802i	$-0.296659\pi$
$593$	1.26273e18	1.19249	0.596245	+	0.802802i	$0.296659\pi$
$594$	−1.92368e17	−0.179689
$595$	−1.78475e17	−0.164898
$596$	−2.98441e17	−0.272746
$597$	5.15568e17	0.466071
$598$	1.38262e17	0.123636
$599$	−1.29018e18	−1.14124	−0.570618	−	0.821215i	$-0.693296\pi$
$599$	−1.29018e18	−1.14124	−0.570618	+	0.821215i	$0.693296\pi$
$600$	5.49117e16	0.0480487
$601$	1.06087e18	0.918283	0.459141	−	0.888363i	$-0.348157\pi$
$601$	1.06087e18	0.918283	0.459141	+	0.888363i	$0.348157\pi$
$602$	8.07334e17	0.691315
$603$	2.10428e17	0.178255
$604$	−5.74159e17	−0.481163
$605$	1.24353e17	0.103097
$606$	7.65929e16	0.0628227
$607$	−1.57867e18	−1.28104	−0.640522	−	0.767939i	$-0.721282\pi$
$607$	−1.57867e18	−1.28104	−0.640522	+	0.767939i	$0.721282\pi$
$608$	−6.00872e16	−0.0482402
$609$	−3.11838e17	−0.247695
$610$	−8.37323e17	−0.658035
$611$	2.62311e17	0.203961
$612$	6.81857e16	0.0524577
$613$	−1.96716e18	−1.49743	−0.748715	−	0.662892i	$-0.769329\pi$
$613$	−1.96716e18	−1.49743	−0.748715	+	0.662892i	$0.769329\pi$
$614$	1.32938e18	1.00128
$615$	−7.69296e17	−0.573331
$616$	−1.55141e17	−0.114407
$617$	−1.84848e18	−1.34884	−0.674421	−	0.738347i	$-0.735607\pi$
$617$	−1.84848e18	−1.34884	−0.674421	+	0.738347i	$0.735607\pi$
$618$	−6.64916e17	−0.480111
$619$	−1.50881e18	−1.07806	−0.539032	−	0.842285i	$-0.681210\pi$
$619$	−1.50881e18	−1.07806	−0.539032	+	0.842285i	$0.681210\pi$
$620$	1.12733e18	0.797083
$621$	6.32721e17	0.442707
$622$	1.32353e18	0.916424
$623$	7.73847e17	0.530253
$624$	5.82911e16	0.0395278
$625$	−1.79448e18	−1.20425
$626$	1.06111e18	0.704740
$627$	−5.94582e16	−0.0390817
$628$	−2.25195e17	−0.146495
$629$	−1.96681e17	−0.126629
$630$	1.04589e18	0.666460
$631$	9.91571e17	0.625364	0.312682	−	0.949858i	$-0.398773\pi$
$631$	9.91571e17	0.625364	0.312682	+	0.949858i	$0.398773\pi$
$632$	−7.96144e17	−0.496971
$633$	−1.61119e17	−0.0995458
$634$	−6.96226e17	−0.425765
$635$	−3.28428e18	−1.98798
$636$	−6.51084e17	−0.390091
$637$	−8.52157e16	−0.0505374
$638$	−1.76466e17	−0.103592
$639$	−5.61508e17	−0.326287
$640$	−1.74263e17	−0.100239
$641$	−2.19269e18	−1.24853	−0.624266	−	0.781212i	$-0.714602\pi$
$641$	−2.19269e18	−1.24853	−0.624266	+	0.781212i	$0.714602\pi$
$642$	−3.47325e17	−0.195775
$643$	1.41146e18	0.787583	0.393792	−	0.919200i	$-0.371163\pi$
$643$	1.41146e18	0.787583	0.393792	+	0.919200i	$0.371163\pi$
$644$	5.10275e17	0.281868
$645$	8.97351e17	0.490709
$646$	4.82907e16	0.0261428
$647$	−7.57404e17	−0.405929	−0.202964	−	0.979186i	$-0.565058\pi$
$647$	−7.57404e17	−0.405929	−0.202964	+	0.979186i	$0.565058\pi$
$648$	−2.49245e17	−0.132248
$649$	−6.01722e17	−0.316086
$650$	1.29491e17	0.0673447
$651$	−1.39171e18	−0.716592
$652$	4.24801e17	0.216559
$653$	3.44024e18	1.73641	0.868207	−	0.496202i	$-0.165273\pi$
$653$	3.44024e18	1.73641	0.868207	+	0.496202i	$0.165273\pi$
$654$	−6.64595e17	−0.332125
$655$	5.54838e17	0.274535
$656$	5.43119e17	0.266085
$657$	−3.17078e18	−1.53813
$658$	9.68094e17	0.464996
$659$	2.41946e17	0.115070	0.0575351	−	0.998343i	$-0.481676\pi$
$659$	2.41946e17	0.115070	0.0575351	+	0.998343i	$0.481676\pi$
$660$	−1.72439e17	−0.0812081
$661$	−1.03317e18	−0.481797	−0.240898	−	0.970550i	$-0.577442\pi$
$661$	−1.03317e18	−0.481797	−0.240898	+	0.970550i	$0.577442\pi$
$662$	−1.65214e18	−0.762902
$663$	−4.68472e16	−0.0214213
$664$	−1.16585e18	−0.527898
$665$	7.40726e17	0.332137
$666$	1.15259e18	0.511789
$667$	5.80416e17	0.255224
$668$	1.41190e18	0.614834
$669$	3.95992e17	0.170772
$670$	4.32211e17	0.184591
$671$	5.84957e17	0.247416
$672$	2.15131e17	0.0901163
$673$	3.43036e18	1.42312	0.711561	−	0.702624i	$-0.247989\pi$
$673$	3.43036e18	1.42312	0.711561	+	0.702624i	$0.247989\pi$
$674$	1.96701e18	0.808197
$675$	5.92583e17	0.241143
$676$	−1.10312e18	−0.444598
$677$	−2.62921e18	−1.04954	−0.524769	−	0.851245i	$-0.675848\pi$
$677$	−2.62921e18	−1.04954	−0.524769	+	0.851245i	$0.675848\pi$
$678$	1.16371e18	0.460101
$679$	−3.74612e18	−1.46699
$680$	1.40051e17	0.0543223
$681$	1.32237e18	0.508039
$682$	−7.87554e17	−0.299697
$683$	−5.36104e17	−0.202076	−0.101038	−	0.994883i	$-0.532216\pi$
$683$	−5.36104e17	−0.202076	−0.101038	+	0.994883i	$0.532216\pi$
$684$	−2.82992e17	−0.105660
$685$	2.94812e18	1.09033
$686$	1.75700e18	0.643672
$687$	1.35608e18	0.492115
$688$	−6.33524e17	−0.227740
$689$	−1.53536e18	−0.546747
$690$	5.67170e17	0.200076
$691$	3.77227e18	1.31824	0.659121	−	0.752037i	$-0.270928\pi$
$691$	3.77227e18	1.31824	0.659121	+	0.752037i	$0.270928\pi$
$692$	−4.38080e17	−0.151658
$693$	−7.30665e17	−0.250584
$694$	1.36842e18	0.464925
$695$	2.38928e18	0.804204
$696$	2.44703e17	0.0815978
$697$	−4.36492e17	−0.144199
$698$	−1.36670e18	−0.447315
$699$	−1.11189e18	−0.360546
$700$	4.77905e17	0.153534
$701$	6.07722e18	1.93436	0.967181	−	0.254088i	$-0.0817754\pi$
$701$	6.07722e18	1.93436	0.967181	+	0.254088i	$0.0817754\pi$
$702$	6.29051e17	0.198379
$703$	8.16288e17	0.255055
$704$	1.21741e17	0.0376889
$705$	1.07603e18	0.330063
$706$	−3.73949e18	−1.13653
$707$	6.66599e17	0.200742
$708$	8.34398e17	0.248976
$709$	5.95192e18	1.75977	0.879886	−	0.475185i	$-0.157619\pi$
$709$	5.95192e18	1.75977	0.879886	+	0.475185i	$0.157619\pi$
$710$	−1.15332e18	−0.337885
$711$	−3.74959e18	−1.08851
$712$	−6.07246e17	−0.174681
$713$	2.59035e18	0.738375
$714$	−1.72896e17	−0.0488367
$715$	−4.06640e17	−0.113820
$716$	−1.84027e18	−0.510443
$717$	−5.14984e17	−0.141553
$718$	3.95585e18	1.07753
$719$	2.03429e18	0.549130	0.274565	−	0.961568i	$-0.411466\pi$
$719$	2.03429e18	0.549130	0.274565	+	0.961568i	$0.411466\pi$
$720$	−8.20724e17	−0.219551
$721$	−5.78686e18	−1.53414
$722$	2.49097e18	0.654450
$723$	−1.19800e18	−0.311930
$724$	−3.41330e18	−0.880793
$725$	5.43596e17	0.139021
$726$	1.20466e17	0.0305336
$727$	−4.66467e18	−1.17178	−0.585892	−	0.810389i	$-0.699256\pi$
$727$	−4.66467e18	−1.17178	−0.585892	+	0.810389i	$0.699256\pi$
$728$	5.07316e17	0.126306
$729$	4.48496e17	0.110670
$730$	−6.51267e18	−1.59280
$731$	5.09149e17	0.123419
$732$	−8.11151e17	−0.194886
$733$	4.20871e18	1.00224	0.501122	−	0.865377i	$-0.332921\pi$
$733$	4.20871e18	1.00224	0.501122	+	0.865377i	$0.332921\pi$
$734$	−2.05027e18	−0.483935
$735$	−3.49567e17	−0.0817828
$736$	−4.00419e17	−0.0928557
$737$	−3.01945e17	−0.0694047
$738$	2.55792e18	0.582802
$739$	1.45417e18	0.328418	0.164209	−	0.986426i	$-0.447493\pi$
$739$	1.45417e18	0.328418	0.164209	+	0.986426i	$0.447493\pi$
$740$	2.36737e18	0.529981
$741$	1.94431e17	0.0431466
$742$	−5.66648e18	−1.24649
$743$	1.61923e18	0.353086	0.176543	−	0.984293i	$-0.443509\pi$
$743$	1.61923e18	0.353086	0.176543	+	0.984293i	$0.443509\pi$
$744$	1.09209e18	0.236066
$745$	−2.88698e18	−0.618626
$746$	−9.80973e17	−0.208379
$747$	−5.49079e18	−1.15625
$748$	−9.78402e16	−0.0204248
$749$	−3.02282e18	−0.625576
$750$	−1.32537e18	−0.271918
$751$	−3.74420e17	−0.0761552	−0.0380776	−	0.999275i	$-0.512123\pi$
$751$	−3.74420e17	−0.0761552	−0.0380776	+	0.999275i	$0.512123\pi$
$752$	−7.59674e17	−0.153183
$753$	2.96014e18	0.591759
$754$	5.77050e17	0.114367
$755$	−5.55415e18	−1.09135
$756$	2.32160e18	0.452268
$757$	2.97462e18	0.574524	0.287262	−	0.957852i	$-0.407255\pi$
$757$	2.97462e18	0.574524	0.287262	+	0.957852i	$0.407255\pi$
$758$	−3.09272e18	−0.592230
$759$	−3.96227e17	−0.0752268
$760$	−5.81256e17	−0.109415
$761$	7.10686e18	1.32641	0.663205	−	0.748438i	$-0.269196\pi$
$761$	7.10686e18	1.32641	0.663205	+	0.748438i	$0.269196\pi$
$762$	−3.18163e18	−0.588765
$763$	−5.78407e18	−1.06126
$764$	−2.13780e18	−0.388919
$765$	6.59597e17	0.118981
$766$	6.55590e18	1.17259
$767$	1.96765e18	0.348962
$768$	−1.68816e17	−0.0296869
$769$	−7.35326e18	−1.28221	−0.641104	−	0.767454i	$-0.721523\pi$
$769$	−7.35326e18	−1.28221	−0.641104	+	0.767454i	$0.721523\pi$
$770$	−1.50076e18	−0.259490
$771$	−6.56524e17	−0.112563
$772$	3.46803e17	0.0589617
$773$	−1.74050e18	−0.293432	−0.146716	−	0.989179i	$-0.546870\pi$
$773$	−1.74050e18	−0.293432	−0.146716	+	0.989179i	$0.546870\pi$
$774$	−2.98370e18	−0.498815
$775$	2.42603e18	0.402193
$776$	2.93962e18	0.483270
$777$	−2.92257e18	−0.476462
$778$	7.30246e18	1.18060
$779$	1.81158e18	0.290445
$780$	5.63881e17	0.0896545
$781$	8.05711e17	0.127042
$782$	3.21807e17	0.0503213
$783$	2.64072e18	0.409516
$784$	2.46792e17	0.0379557
$785$	−2.17843e18	−0.332271
$786$	5.37496e17	0.0813071
$787$	5.86640e18	0.880108	0.440054	−	0.897971i	$-0.354959\pi$
$787$	5.86640e18	0.880108	0.440054	+	0.897971i	$0.354959\pi$
$788$	5.01365e18	0.745991
$789$	−6.22101e18	−0.918038
$790$	−7.70153e18	−1.12720
$791$	1.01280e19	1.47020
$792$	5.73361e17	0.0825495
$793$	−1.91283e18	−0.273150
$794$	−1.93975e18	−0.274734
$795$	−6.29828e18	−0.884780
$796$	−3.52105e18	−0.490611
$797$	−1.56766e18	−0.216657	−0.108328	−	0.994115i	$-0.534550\pi$
$797$	−1.56766e18	−0.216657	−0.108328	+	0.994115i	$0.534550\pi$
$798$	7.17573e17	0.0983665
$799$	6.10532e17	0.0830146
$800$	−3.75017e17	−0.0505786
$801$	−2.85994e18	−0.382601
$802$	4.21440e18	0.559245
$803$	4.54978e18	0.598879
$804$	4.18702e17	0.0546689
$805$	4.93616e18	0.639317
$806$	2.57533e18	0.330868
$807$	−4.80842e18	−0.612808
$808$	−5.23088e17	−0.0661303
$809$	−6.06191e18	−0.760228	−0.380114	−	0.924940i	$-0.624115\pi$
$809$	−6.06191e18	−0.760228	−0.380114	+	0.924940i	$0.624115\pi$
$810$	−2.41108e18	−0.299956
$811$	1.52062e18	0.187665	0.0938326	−	0.995588i	$-0.470088\pi$
$811$	1.52062e18	0.187665	0.0938326	+	0.995588i	$0.470088\pi$
$812$	2.12968e18	0.260736
$813$	4.98613e18	0.605585
$814$	−1.65385e18	−0.199269
$815$	4.10933e18	0.491186
$816$	1.35673e17	0.0160883
$817$	−2.11313e18	−0.248589
$818$	2.42722e18	0.283278
$819$	2.38930e18	0.276647
$820$	5.25388e18	0.603518
$821$	−2.30108e18	−0.262242	−0.131121	−	0.991366i	$-0.541858\pi$
$821$	−2.30108e18	−0.262242	−0.131121	+	0.991366i	$0.541858\pi$
$822$	2.85597e18	0.322915
$823$	6.99638e18	0.784828	0.392414	−	0.919789i	$-0.371640\pi$
$823$	6.99638e18	0.784828	0.392414	+	0.919789i	$0.371640\pi$
$824$	4.54102e18	0.505389
$825$	−3.71092e17	−0.0409761
$826$	7.26189e18	0.795572
$827$	1.07394e19	1.16734	0.583668	−	0.811993i	$-0.301617\pi$
$827$	1.07394e19	1.16734	0.583668	+	0.811993i	$0.301617\pi$
$828$	−1.88585e18	−0.203381
$829$	−9.93092e18	−1.06264	−0.531319	−	0.847172i	$-0.678303\pi$
$829$	−9.93092e18	−1.06264	−0.531319	+	0.847172i	$0.678303\pi$
$830$	−1.12779e19	−1.19735
$831$	−2.67879e17	−0.0282184
$832$	−3.98096e17	−0.0416089
$833$	−1.98341e17	−0.0205693
$834$	2.31460e18	0.238175
$835$	1.36581e19	1.39453
$836$	4.06068e17	0.0411394
$837$	1.17853e19	1.18475
$838$	4.62130e18	0.460976
$839$	−1.23974e19	−1.22710	−0.613548	−	0.789658i	$-0.710258\pi$
$839$	−1.23974e19	−1.22710	−0.613548	+	0.789658i	$0.710258\pi$
$840$	2.08108e18	0.204396
$841$	−7.83820e18	−0.763911
$842$	9.35967e18	0.905173
$843$	−8.09743e18	−0.777084
$844$	1.10036e18	0.104787
$845$	−1.06710e19	−1.00841
$846$	−3.57783e18	−0.335515
$847$	1.04844e18	0.0975664
$848$	4.44655e18	0.410629
$849$	−5.98502e18	−0.548486
$850$	3.01393e17	0.0274100
$851$	5.43971e18	0.490946
$852$	−1.11727e18	−0.100069
$853$	−1.06856e19	−0.949796	−0.474898	−	0.880041i	$-0.657515\pi$
$853$	−1.06856e19	−0.949796	−0.474898	+	0.880041i	$0.657515\pi$
$854$	−7.05957e18	−0.622733
$855$	−2.73753e18	−0.239651
$856$	2.37204e18	0.206083
$857$	−1.71851e19	−1.48175	−0.740876	−	0.671642i	$-0.765589\pi$
$857$	−1.71851e19	−1.48175	−0.740876	+	0.671642i	$0.765589\pi$
$858$	−3.93929e17	−0.0337094
$859$	4.76230e18	0.404446	0.202223	−	0.979339i	$-0.435183\pi$
$859$	4.76230e18	0.404446	0.202223	+	0.979339i	$0.435183\pi$
$860$	−6.12842e18	−0.516545
$861$	−6.48603e18	−0.542573
$862$	−4.52360e18	−0.375567
$863$	1.32697e19	1.09343	0.546714	−	0.837319i	$-0.315878\pi$
$863$	1.32697e19	1.09343	0.546714	+	0.837319i	$0.315878\pi$
$864$	−1.82179e18	−0.148990
$865$	−4.23778e18	−0.343981
$866$	1.49059e19	1.20086
$867$	5.83128e18	0.466272
$868$	9.50462e18	0.754321
$869$	5.38032e18	0.423818
$870$	2.36714e18	0.185075
$871$	9.87370e17	0.0766235
$872$	4.53882e18	0.349612
$873$	1.38447e19	1.05850
$874$	−1.33560e18	−0.101357
$875$	−1.15349e19	−0.868882
$876$	−6.30911e18	−0.471728
$877$	2.00056e19	1.48476	0.742378	−	0.669982i	$-0.233698\pi$
$877$	2.00056e19	1.48476	0.742378	+	0.669982i	$0.233698\pi$
$878$	2.17472e18	0.160210
$879$	−5.07434e18	−0.371066
$880$	1.17766e18	0.0854838
$881$	8.52994e18	0.614614	0.307307	−	0.951610i	$-0.400572\pi$
$881$	8.52994e18	0.614614	0.307307	+	0.951610i	$0.400572\pi$
$882$	1.16231e18	0.0831338
$883$	6.68791e18	0.474838	0.237419	−	0.971407i	$-0.423699\pi$
$883$	6.68791e18	0.474838	0.237419	+	0.971407i	$0.423699\pi$
$884$	3.19941e17	0.0225491
$885$	8.07158e18	0.564712
$886$	1.62298e18	0.112718
$887$	2.68437e18	0.185072	0.0925358	−	0.995709i	$-0.470503\pi$
$887$	2.68437e18	0.185072	0.0925358	+	0.995709i	$0.470503\pi$
$888$	2.29337e18	0.156961
$889$	−2.76902e19	−1.88133
$890$	−5.87422e18	−0.396200
$891$	1.68439e18	0.112781
$892$	−2.70441e18	−0.179763
$893$	−2.53390e18	−0.167207
$894$	−2.79674e18	−0.183214
$895$	−1.78019e19	−1.15776
$896$	−1.46923e18	−0.0948610
$897$	1.29568e18	0.0830512
$898$	−1.09460e19	−0.696562
$899$	1.08111e19	0.683017
$900$	−1.76622e18	−0.110782
$901$	−3.57359e18	−0.222532
$902$	−3.67038e18	−0.226918
$903$	7.56567e18	0.464384
$904$	−7.94754e18	−0.484326
$905$	−3.30187e19	−1.99776
$906$	−5.38054e18	−0.323216
$907$	1.22355e19	0.729753	0.364877	−	0.931056i	$-0.381111\pi$
$907$	1.22355e19	0.729753	0.364877	+	0.931056i	$0.381111\pi$
$908$	−9.03107e18	−0.534788
$909$	−2.46358e18	−0.144844
$910$	4.90754e18	0.286480
$911$	−1.55168e19	−0.899358	−0.449679	−	0.893190i	$-0.648462\pi$
$911$	−1.55168e19	−0.899358	−0.449679	+	0.893190i	$0.648462\pi$
$912$	−5.63087e17	−0.0324048
$913$	7.87878e18	0.450193
$914$	−1.65803e19	−0.940681
$915$	−7.84670e18	−0.442028
$916$	−9.26130e18	−0.518026
$917$	4.67790e18	0.259807
$918$	1.46413e18	0.0807423
$919$	−3.07679e19	−1.68480	−0.842399	−	0.538855i	$-0.818857\pi$
$919$	−3.07679e19	−1.68480	−0.842399	+	0.538855i	$0.818857\pi$
$920$	−3.87346e18	−0.210610
$921$	1.24578e19	0.672598
$922$	−9.00934e18	−0.482994
$923$	−2.63470e18	−0.140256
$924$	−1.45385e18	−0.0768514
$925$	5.09463e18	0.267419
$926$	−1.69515e19	−0.883559
$927$	2.13868e19	1.10695
$928$	−1.67119e18	−0.0858941
$929$	8.48806e17	0.0433218	0.0216609	−	0.999765i	$-0.493105\pi$
$929$	8.48806e17	0.0433218	0.0216609	+	0.999765i	$0.493105\pi$
$930$	1.05644e19	0.535432
$931$	8.23177e17	0.0414305
$932$	7.59362e18	0.379530
$933$	1.24030e19	0.615598
$934$	−4.71918e18	−0.232601
$935$	−9.46460e17	−0.0463262
$936$	−1.87491e18	−0.0911355
$937$	−1.14995e19	−0.555098	−0.277549	−	0.960711i	$-0.589522\pi$
$937$	−1.14995e19	−0.555098	−0.277549	+	0.960711i	$0.589522\pi$
$938$	3.64402e18	0.174688
$939$	9.94388e18	0.473401
$940$	−7.34873e18	−0.347441
$941$	1.99127e19	0.934970	0.467485	−	0.884001i	$-0.345160\pi$
$941$	1.99127e19	0.934970	0.467485	+	0.884001i	$0.345160\pi$
$942$	−2.11034e18	−0.0984062
$943$	1.20723e19	0.559067
$944$	−5.69849e18	−0.262085
$945$	2.24581e19	1.02581
$946$	4.28134e18	0.194217
$947$	3.75213e19	1.69045	0.845226	−	0.534409i	$-0.179466\pi$
$947$	3.75213e19	1.69045	0.845226	+	0.534409i	$0.179466\pi$
$948$	−7.46080e18	−0.333835
$949$	−1.48779e19	−0.661169
$950$	−1.25087e18	−0.0552091
$951$	−6.52445e18	−0.286003
$952$	1.18079e18	0.0514080
$953$	−2.27161e19	−0.982269	−0.491135	−	0.871084i	$-0.663418\pi$
$953$	−2.27161e19	−0.982269	−0.491135	+	0.871084i	$0.663418\pi$
$954$	2.09419e19	0.899396
$955$	−2.06800e19	−0.882124
$956$	3.51706e18	0.149006
$957$	−1.65369e18	−0.0695869
$958$	1.79663e19	0.750902
$959$	2.48560e19	1.03183
$960$	−1.63305e18	−0.0673342
$961$	2.38315e19	0.976000
$962$	5.40816e18	0.219994
$963$	1.11716e19	0.451381
$964$	8.18168e18	0.328354
$965$	3.35481e18	0.133733
$966$	4.78188e18	0.189342
$967$	6.36616e18	0.250383	0.125192	−	0.992133i	$-0.460045\pi$
$967$	6.36616e18	0.250383	0.125192	+	0.992133i	$0.460045\pi$
$968$	−8.22720e17	−0.0321412
$969$	4.52540e17	0.0175611
$970$	2.84365e19	1.09613
$971$	1.73822e19	0.665547	0.332773	−	0.943007i	$-0.392016\pi$
$971$	1.73822e19	0.665547	0.332773	+	0.943007i	$0.392016\pi$
$972$	−1.34156e19	−0.510244
$973$	2.01443e19	0.761061
$974$	−5.31376e18	−0.199420
$975$	1.21348e18	0.0452380
$976$	5.53972e18	0.205147
$977$	−2.66963e19	−0.982057	−0.491028	−	0.871144i	$-0.663379\pi$
$977$	−2.66963e19	−0.982057	−0.491028	+	0.871144i	$0.663379\pi$
$978$	3.98088e18	0.145471
$979$	4.10375e18	0.148968
$980$	2.38735e18	0.0860888
$981$	2.13765e19	0.765750
$982$	1.69077e19	0.601672
$983$	−4.35486e19	−1.53949	−0.769745	−	0.638352i	$-0.779617\pi$
$983$	−4.35486e19	−1.53949	−0.769745	+	0.638352i	$0.779617\pi$
$984$	5.08966e18	0.178739
$985$	4.84997e19	1.69201
$986$	1.34309e18	0.0465486
$987$	9.07217e18	0.312356
$988$	−1.32786e18	−0.0454183
$989$	−1.40818e19	−0.478500
$990$	5.54643e18	0.187234
$991$	−2.53375e19	−0.849739	−0.424869	−	0.905255i	$-0.639680\pi$
$991$	−2.53375e19	−0.849739	−0.424869	+	0.905255i	$0.639680\pi$
$992$	−7.45838e18	−0.248495
$993$	−1.54824e19	−0.512471
$994$	−9.72374e18	−0.319758
$995$	−3.40610e19	−1.11277
$996$	−1.09254e19	−0.354610
$997$	−1.14171e19	−0.368160	−0.184080	−	0.982911i	$-0.558931\pi$
$997$	−1.14171e19	−0.368160	−0.184080	+	0.982911i	$0.558931\pi$
$998$	−3.54967e19	−1.13721
$999$	2.47491e19	0.787740

Twists

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

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

\(f(q)\)	\(=\)	\(q-64.0000 q^{2} -599.755 q^{3} +4096.00 q^{4} +39622.8 q^{5} +38384.3 q^{6} +334064. q^{7} -262144. q^{8} -1.23462e6 q^{9} +O(q^{10})\)	\(q-64.0000 q^{2} -599.755 q^{3} +4096.00 q^{4} +39622.8 q^{5} +38384.3 q^{6} +334064. q^{7} -262144. q^{8} -1.23462e6 q^{9} -2.53586e6 q^{10} +1.77156e6 q^{11} -2.45660e6 q^{12} -5.79307e6 q^{13} -2.13801e7 q^{14} -2.37640e7 q^{15} +1.67772e7 q^{16} -1.34835e7 q^{17} +7.90155e7 q^{18} +5.59606e7 q^{19} +1.62295e8 q^{20} -2.00357e8 q^{21} -1.13380e8 q^{22} +3.72919e8 q^{23} +1.57222e8 q^{24} +3.49262e8 q^{25} +3.70756e8 q^{26} +1.69667e9 q^{27} +1.36833e9 q^{28} +1.55641e9 q^{29} +1.52089e9 q^{30} +6.94616e9 q^{31} -1.07374e9 q^{32} -1.06250e9 q^{33} +8.62941e8 q^{34} +1.32366e10 q^{35} -5.05699e9 q^{36} +1.45868e10 q^{37} -3.58148e9 q^{38} +3.47442e9 q^{39} -1.03869e10 q^{40} +3.23724e10 q^{41} +1.28228e10 q^{42} -3.77610e10 q^{43} +7.25631e9 q^{44} -4.89190e10 q^{45} -2.38668e10 q^{46} -4.52801e10 q^{47} -1.00622e10 q^{48} +1.47099e10 q^{49} -2.23528e10 q^{50} +8.08677e9 q^{51} -2.37284e10 q^{52} +2.65035e11 q^{53} -1.08587e11 q^{54} +7.01942e10 q^{55} -8.75730e10 q^{56} -3.35626e10 q^{57} -9.96105e10 q^{58} -3.39656e11 q^{59} -9.73372e10 q^{60} +3.30193e11 q^{61} -4.44554e11 q^{62} -4.12442e11 q^{63} +6.87195e10 q^{64} -2.29537e11 q^{65} +6.80001e10 q^{66} -1.70440e11 q^{67} -5.52282e10 q^{68} -2.23660e11 q^{69} -8.47140e11 q^{70} +4.54803e11 q^{71} +3.23647e11 q^{72} +2.56823e12 q^{73} -9.33558e11 q^{74} -2.09472e11 q^{75} +2.29215e11 q^{76} +5.91815e11 q^{77} -2.22363e11 q^{78} +3.03705e12 q^{79} +6.64760e11 q^{80} +9.50793e11 q^{81} -2.07183e12 q^{82} +4.44737e12 q^{83} -8.20661e11 q^{84} -5.34252e11 q^{85} +2.41670e12 q^{86} -9.33467e11 q^{87} -4.64404e11 q^{88} +2.31646e12 q^{89} +3.13081e12 q^{90} -1.93526e12 q^{91} +1.52748e12 q^{92} -4.16599e12 q^{93} +2.89793e12 q^{94} +2.21731e12 q^{95} +6.43982e11 q^{96} -1.12138e13 q^{97} -9.41437e11 q^{98} -2.18720e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 128 q^{2} + 1626 q^{3} + 8192 q^{4} + 7666 q^{5} - 104064 q^{6} + 637048 q^{7} - 524288 q^{8} + 2125044 q^{9}+O(q^{10}) \) 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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