LMFDB - Embedded newform 29.18.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,18,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	29.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:	$53.1344053299$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+59.1674 q^{2} +15524.2 q^{3} -127571. q^{4} +1.59085e6 q^{5} +918527. q^{6} -2.66210e7 q^{7} -1.53032e7 q^{8} +1.11861e8 q^{9} +O(q^{10})$	\(q+59.1674 q^{2} +15524.2 q^{3} -127571. q^{4} +1.59085e6 q^{5} +918527. q^{6} -2.66210e7 q^{7} -1.53032e7 q^{8} +1.11861e8 q^{9} +9.41262e7 q^{10} -1.84119e7 q^{11} -1.98044e9 q^{12} +2.82255e9 q^{13} -1.57509e9 q^{14} +2.46966e10 q^{15} +1.58156e10 q^{16} -1.97108e10 q^{17} +6.61853e9 q^{18} +1.30823e11 q^{19} -2.02946e11 q^{20} -4.13270e11 q^{21} -1.08938e9 q^{22} +5.53754e11 q^{23} -2.37571e11 q^{24} +1.76785e12 q^{25} +1.67003e11 q^{26} -2.68243e11 q^{27} +3.39607e12 q^{28} +5.00246e11 q^{29} +1.46124e12 q^{30} +3.77753e12 q^{31} +2.94159e12 q^{32} -2.85830e11 q^{33} -1.16624e12 q^{34} -4.23499e13 q^{35} -1.42703e13 q^{36} +2.05179e12 q^{37} +7.74046e12 q^{38} +4.38179e13 q^{39} -2.43451e13 q^{40} -8.70274e13 q^{41} -2.44521e13 q^{42} +1.89137e13 q^{43} +2.34883e12 q^{44} +1.77954e14 q^{45} +3.27642e13 q^{46} +3.80579e13 q^{47} +2.45524e14 q^{48} +4.76047e14 q^{49} +1.04599e14 q^{50} -3.05995e14 q^{51} -3.60077e14 q^{52} +6.28417e14 q^{53} -1.58712e13 q^{54} -2.92905e13 q^{55} +4.07388e14 q^{56} +2.03093e15 q^{57} +2.95983e13 q^{58} -6.10432e14 q^{59} -3.15058e15 q^{60} +2.98009e14 q^{61} +2.23507e14 q^{62} -2.97786e15 q^{63} -1.89893e15 q^{64} +4.49025e15 q^{65} -1.69118e13 q^{66} +4.16516e15 q^{67} +2.51453e15 q^{68} +8.59660e15 q^{69} -2.50573e15 q^{70} -2.48533e15 q^{71} -1.71184e15 q^{72} +1.08197e16 q^{73} +1.21399e14 q^{74} +2.74445e16 q^{75} -1.66893e16 q^{76} +4.90143e14 q^{77} +2.59259e15 q^{78} +7.02687e15 q^{79} +2.51601e16 q^{80} -1.86100e16 q^{81} -5.14918e15 q^{82} -1.19821e16 q^{83} +5.27214e16 q^{84} -3.13568e16 q^{85} +1.11907e15 q^{86} +7.76593e15 q^{87} +2.81762e14 q^{88} -1.76958e16 q^{89} +1.05291e16 q^{90} -7.51392e16 q^{91} -7.06431e16 q^{92} +5.86433e16 q^{93} +2.25179e15 q^{94} +2.08119e17 q^{95} +4.56659e16 q^{96} -8.49829e16 q^{97} +2.81665e16 q^{98} -2.05958e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) $ 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9} - 224469478 q^{10} + 1203139534 q^{11} - 5164251122 q^{12} + 3854339312 q^{13} + 25262272904 q^{14} + 28324474306 q^{15} + 196520815922 q^{16} + 76444714794 q^{17} + 75758949126 q^{18} + 246497292428 q^{19} - 46900976670 q^{20} + 360937126704 q^{21} - 275001533522 q^{22} + 213498528140 q^{23} - 451123453870 q^{24} + 3898884886997 q^{25} - 3609347694206 q^{26} - 2718903745978 q^{27} - 5946174617200 q^{28} + 10505174672181 q^{29} - 20237658929454 q^{30} + 16670029895798 q^{31} - 42141001912046 q^{32} - 7157109761394 q^{33} + 12785761151136 q^{34} + 46677934312888 q^{35} + 132137824374868 q^{36} + 53445659988410 q^{37} + 76581637956388 q^{38} + 79233849032530 q^{39} + 193617444734146 q^{40} - 20814769309298 q^{41} + 76690667258352 q^{42} + 185498647364454 q^{43} + 315429066899678 q^{44} - 486270821438526 q^{45} + 261474367677132 q^{46} + 389503471719450 q^{47} - 101509672247630 q^{48} + 730079062141437 q^{49} + 14\!\cdots\!54 q^{50}+ \cdots - 95\!\cdots\!64 q^{99}+O(q^{100}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9 - 224469478 * q^10 + 1203139534 * q^11 - 5164251122 * q^12 + 3854339312 * q^13 + 25262272904 * q^14 + 28324474306 * q^15 + 196520815922 * q^16 + 76444714794 * q^17 + 75758949126 * q^18 + 246497292428 * q^19 - 46900976670 * q^20 + 360937126704 * q^21 - 275001533522 * q^22 + 213498528140 * q^23 - 451123453870 * q^24 + 3898884886997 * q^25 - 3609347694206 * q^26 - 2718903745978 * q^27 - 5946174617200 * q^28 + 10505174672181 * q^29 - 20237658929454 * q^30 + 16670029895798 * q^31 - 42141001912046 * q^32 - 7157109761394 * q^33 + 12785761151136 * q^34 + 46677934312888 * q^35 + 132137824374868 * q^36 + 53445659988410 * q^37 + 76581637956388 * q^38 + 79233849032530 * q^39 + 193617444734146 * q^40 - 20814769309298 * q^41 + 76690667258352 * q^42 + 185498647364454 * q^43 + 315429066899678 * q^44 - 486270821438526 * q^45 + 261474367677132 * q^46 + 389503471719450 * q^47 - 101509672247630 * q^48 + 730079062141437 * q^49 + 1482269666368354 * q^50 + 718238208473988 * q^51 + 1966802817157170 * q^52 + 747441265526156 * q^53 + 5692893333117030 * q^54 + 1639109418219546 * q^55 + 5657219329125240 * q^56 + 4694352396864932 * q^57 + 128063081718016 * q^58 + 5280258638332960 * q^59 + 15251367906033378 * q^60 + 5813675353074254 * q^61 + 6242066590947250 * q^62 + 10947760075450368 * q^63 + 24583792057508902 * q^64 + 19190799243789974 * q^65 + 41877805444482390 * q^66 + 13420580230958268 * q^67 + 24771837384165388 * q^68 + 30973047049935252 * q^69 + 8505088080182440 * q^70 + 4824462822979508 * q^71 + 1180071997284592 * q^72 + 11228916281304662 * q^73 - 89132715356772 * q^74 + 59161419576630296 * q^75 + 57466858643173460 * q^76 + 58741564492720064 * q^77 + 142050530910210210 * q^78 + 71718598015696758 * q^79 + 48350023652407550 * q^80 + 75805931446703569 * q^81 + 188661890754420812 * q^82 + 50769377111735608 * q^83 + 198832046985593048 * q^84 + 53422044849490784 * q^85 + 35014892323844118 * q^86 + 11988905533023326 * q^87 + 37459283979085258 * q^88 - 70981414576978018 * q^89 + 57211029866143724 * q^90 + 112933943315157320 * q^91 - 103019729095759724 * q^92 - 350358290646906646 * q^93 - 150286322409612578 * q^94 - 102561321856584476 * q^95 - 213770098354021866 * q^96 - 130930167251505210 * q^97 - 537387515497557296 * q^98 - 95267700931431064 * 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 $

$2$	59.1674	0.163428	0.0817142	−	0.996656i	$-0.473961\pi$
$2$	59.1674	0.163428	0.0817142	+	0.996656i	$0.473961\pi$
$3$	15524.2	1.36609	0.683045	−	0.730377i	$-0.260655\pi$
$3$	15524.2	1.36609	0.683045	+	0.730377i	$0.260655\pi$
$4$	−127571.	−0.973291
$5$	1.59085e6	1.82131	0.910654	−	0.413171i	$-0.135579\pi$
$5$	1.59085e6	1.82131	0.910654	+	0.413171i	$0.135579\pi$
$6$	918527.	0.223258
$7$	−2.66210e7	−1.74538	−0.872692	−	0.488271i	$-0.837628\pi$
$7$	−2.66210e7	−1.74538	−0.872692	+	0.488271i	$0.837628\pi$
$8$	−1.53032e7	−0.322492
$9$	1.11861e8	0.866200
$10$	9.41262e7	0.297653
$11$	−1.84119e7	−0.0258977	−0.0129488	−	0.999916i	$-0.504122\pi$
$11$	−1.84119e7	−0.0258977	−0.0129488	+	0.999916i	$0.504122\pi$
$12$	−1.98044e9	−1.32960
$13$	2.82255e9	0.959674	0.479837	−	0.877358i	$-0.340696\pi$
$13$	2.82255e9	0.959674	0.479837	+	0.877358i	$0.340696\pi$
$14$	−1.57509e9	−0.285245
$15$	2.46966e10	2.48807
$16$	1.58156e10	0.920587
$17$	−1.97108e10	−0.685312	−0.342656	−	0.939461i	$-0.611326\pi$
$17$	−1.97108e10	−0.685312	−0.342656	+	0.939461i	$0.611326\pi$
$18$	6.61853e9	0.141562
$19$	1.30823e11	1.76717	0.883586	−	0.468269i	$-0.155122\pi$
$19$	1.30823e11	1.76717	0.883586	+	0.468269i	$0.155122\pi$
$20$	−2.02946e11	−1.77266
$21$	−4.13270e11	−2.38435
$22$	−1.08938e9	−0.00423241
$23$	5.53754e11	1.47445	0.737226	−	0.675646i	$-0.236135\pi$
$23$	5.53754e11	1.47445	0.737226	+	0.675646i	$0.236135\pi$
$24$	−2.37571e11	−0.440552
$25$	1.76785e12	2.31716
$26$	1.67003e11	0.156838
$27$	−2.68243e11	−0.182783
$28$	3.39607e12	1.69877
$29$	5.00246e11	0.185695
$29$	5.00246e11	0.185695
$30$	1.46124e12	0.406621
$31$	3.77753e12	0.795489	0.397744	−	0.917496i	$-0.369793\pi$
$31$	3.77753e12	0.795489	0.397744	+	0.917496i	$0.369793\pi$
$32$	2.94159e12	0.472942
$33$	−2.85830e11	−0.0353785
$34$	−1.16624e12	−0.111999
$35$	−4.23499e13	−3.17888
$36$	−1.42703e13	−0.843065
$37$	2.05179e12	0.0960323	0.0480162	−	0.998847i	$-0.484710\pi$
$37$	2.05179e12	0.0960323	0.0480162	+	0.998847i	$0.484710\pi$
$38$	7.74046e12	0.288806
$39$	4.38179e13	1.31100
$40$	−2.43451e13	−0.587356
$41$	−8.70274e13	−1.70213	−0.851066	−	0.525059i	$-0.824043\pi$
$41$	−8.70274e13	−1.70213	−0.851066	+	0.525059i	$0.824043\pi$
$42$	−2.44521e13	−0.389670
$43$	1.89137e13	0.246772	0.123386	−	0.992359i	$-0.460625\pi$
$43$	1.89137e13	0.246772	0.123386	+	0.992359i	$0.460625\pi$
$44$	2.34883e12	0.0252060
$45$	1.77954e14	1.57762
$46$	3.27642e13	0.240967
$47$	3.80579e13	0.233138	0.116569	−	0.993183i	$-0.462810\pi$
$47$	3.80579e13	0.233138	0.116569	+	0.993183i	$0.462810\pi$
$48$	2.45524e14	1.25760
$49$	4.76047e14	2.04637
$50$	1.04599e14	0.378690
$51$	−3.05995e14	−0.936197
$52$	−3.60077e14	−0.934042
$53$	6.28417e14	1.38645	0.693223	−	0.720723i	$-0.256190\pi$
$53$	6.28417e14	1.38645	0.693223	+	0.720723i	$0.256190\pi$
$54$	−1.58712e13	−0.0298719
$55$	−2.92905e13	−0.0471676
$56$	4.07388e14	0.562872
$57$	2.03093e15	2.41412
$58$	2.95983e13	0.0303479
$59$	−6.10432e14	−0.541247	−0.270623	−	0.962685i	$-0.587230\pi$
$59$	−6.10432e14	−0.541247	−0.270623	+	0.962685i	$0.587230\pi$
$60$	−3.15058e15	−2.42161
$61$	2.98009e14	0.199033	0.0995165	−	0.995036i	$-0.468270\pi$
$61$	2.98009e14	0.199033	0.0995165	+	0.995036i	$0.468270\pi$
$62$	2.23507e14	0.130005
$63$	−2.97786e15	−1.51185
$64$	−1.89893e15	−0.843295
$65$	4.49025e15	1.74786
$66$	−1.69118e13	−0.00578185
$67$	4.16516e15	1.25313	0.626564	−	0.779370i	$-0.284461\pi$
$67$	4.16516e15	1.25313	0.626564	+	0.779370i	$0.284461\pi$
$68$	2.51453e15	0.667008
$69$	8.59660e15	2.01423
$70$	−2.50573e15	−0.519519
$71$	−2.48533e15	−0.456760	−0.228380	−	0.973572i	$-0.573343\pi$
$71$	−2.48533e15	−0.456760	−0.228380	+	0.973572i	$0.573343\pi$
$72$	−1.71184e15	−0.279342
$73$	1.08197e16	1.57026	0.785132	−	0.619329i	$-0.212595\pi$
$73$	1.08197e16	1.57026	0.785132	+	0.619329i	$0.212595\pi$
$74$	1.21399e14	0.0156944
$75$	2.74445e16	3.16545
$76$	−1.66893e16	−1.71997
$77$	4.90143e14	0.0452014
$78$	2.59259e15	0.214255
$79$	7.02687e15	0.521112	0.260556	−	0.965459i	$-0.416094\pi$
$79$	7.02687e15	0.521112	0.260556	+	0.965459i	$0.416094\pi$
$80$	2.51601e16	1.67667
$81$	−1.86100e16	−1.11590
$82$	−5.14918e15	−0.278176
$83$	−1.19821e16	−0.583941	−0.291971	−	0.956427i	$-0.594311\pi$
$83$	−1.19821e16	−0.583941	−0.291971	+	0.956427i	$0.594311\pi$
$84$	5.27214e16	2.32067
$85$	−3.13568e16	−1.24816
$86$	1.11907e15	0.0403294
$87$	7.76593e15	0.253676
$88$	2.81762e14	0.00835178
$89$	−1.76958e16	−0.476491	−0.238246	−	0.971205i	$-0.576572\pi$
$89$	−1.76958e16	−0.476491	−0.238246	+	0.971205i	$0.576572\pi$
$90$	1.05291e16	0.257827
$91$	−7.51392e16	−1.67500
$92$	−7.06431e16	−1.43507
$93$	5.86433e16	1.08671
$94$	2.25179e15	0.0381014
$95$	2.08119e17	3.21856
$96$	4.56659e16	0.646080
$97$	−8.49829e16	−1.10096	−0.550480	−	0.834848i	$-0.685555\pi$
$97$	−8.49829e16	−1.10096	−0.550480	+	0.834848i	$0.685555\pi$
$98$	2.81665e16	0.334434
$99$	−2.05958e15	−0.0224326
$100$	−2.25527e17	−2.25527
$101$	6.28965e16	0.577956	0.288978	−	0.957336i	$-0.406685\pi$
$101$	6.28965e16	0.577956	0.288978	+	0.957336i	$0.406685\pi$
$102$	−1.81049e16	−0.153001
$103$	−1.26651e17	−0.985126	−0.492563	−	0.870277i	$-0.663940\pi$
$103$	−1.26651e17	−0.985126	−0.492563	+	0.870277i	$0.663940\pi$
$104$	−4.31942e16	−0.309487
$105$	−6.57449e17	−4.34263
$106$	3.71818e16	0.226585
$107$	1.40747e17	0.791914	0.395957	−	0.918269i	$-0.370413\pi$
$107$	1.40747e17	0.791914	0.395957	+	0.918269i	$0.370413\pi$
$108$	3.42200e16	0.177901
$109$	1.63223e17	0.784616	0.392308	−	0.919834i	$-0.371677\pi$
$109$	1.63223e17	0.784616	0.392308	+	0.919834i	$0.371677\pi$
$110$	−1.73304e15	−0.00770853
$111$	3.18524e16	0.131189
$112$	−4.21026e17	−1.60678
$113$	−1.59606e17	−0.564785	−0.282392	−	0.959299i	$-0.591128\pi$
$113$	−1.59606e17	−0.564785	−0.282392	+	0.959299i	$0.591128\pi$
$114$	1.20165e17	0.394535
$115$	8.80938e17	2.68543
$116$	−6.38170e16	−0.180736
$117$	3.15734e17	0.831270
$118$	−3.61177e16	−0.0884551
$119$	5.24721e17	1.19613
$120$	−3.77939e17	−0.802381
$121$	−5.05108e17	−0.999329
$122$	1.76324e16	0.0325276
$123$	−1.35103e18	−2.32526
$124$	−4.81905e17	−0.774242
$125$	1.59866e18	2.39895
$126$	−1.76192e17	−0.247079
$127$	6.82923e16	0.0895447	0.0447724	−	0.998997i	$-0.485744\pi$
$127$	6.82923e16	0.0895447	0.0447724	+	0.998997i	$0.485744\pi$
$128$	−4.97915e17	−0.610760
$129$	2.93621e17	0.337112
$130$	2.65676e17	0.285650
$131$	−2.13898e17	−0.215477	−0.107739	−	0.994179i	$-0.534361\pi$
$131$	−2.13898e17	−0.215477	−0.107739	+	0.994179i	$0.534361\pi$
$132$	3.64637e16	0.0344336
$133$	−3.48264e18	−3.08439
$134$	2.46441e17	0.204797
$135$	−4.26733e17	−0.332904
$136$	3.01639e17	0.221007
$137$	−1.48225e18	−1.02046	−0.510231	−	0.860037i	$-0.670440\pi$
$137$	−1.48225e18	−1.02046	−0.510231	+	0.860037i	$0.670440\pi$
$138$	5.08638e17	0.329183
$139$	−1.02984e18	−0.626823	−0.313411	−	0.949617i	$-0.601472\pi$
$139$	−1.02984e18	−0.626823	−0.313411	+	0.949617i	$0.601472\pi$
$140$	5.40263e18	3.09398
$141$	5.90820e17	0.318488
$142$	−1.47050e17	−0.0746475
$143$	−5.19686e16	−0.0248533
$144$	1.76915e18	0.797412
$145$	7.95815e17	0.338208
$146$	6.40176e17	0.256626
$147$	7.39026e18	2.79552
$148$	−2.61749e17	−0.0934674
$149$	−3.67744e18	−1.24012	−0.620059	−	0.784556i	$-0.712891\pi$
$149$	−3.67744e18	−1.24012	−0.620059	+	0.784556i	$0.712891\pi$
$150$	1.62382e18	0.517324
$151$	−9.45989e17	−0.284828	−0.142414	−	0.989807i	$-0.545486\pi$
$151$	−9.45989e17	−0.284828	−0.142414	+	0.989807i	$0.545486\pi$
$152$	−2.00202e18	−0.569898
$153$	−2.20487e18	−0.593617
$154$	2.90005e16	0.00738719
$155$	6.00948e18	1.44883
$156$	−5.58991e18	−1.27599
$157$	3.77632e18	0.816434	0.408217	−	0.912885i	$-0.366151\pi$
$157$	3.77632e18	0.816434	0.408217	+	0.912885i	$0.366151\pi$
$158$	4.15761e17	0.0851645
$159$	9.75568e18	1.89401
$160$	4.67962e18	0.861372
$161$	−1.47415e19	−2.57348
$162$	−1.10111e18	−0.182369
$163$	5.94198e18	0.933978	0.466989	−	0.884263i	$-0.345339\pi$
$163$	5.94198e18	0.933978	0.466989	+	0.884263i	$0.345339\pi$
$164$	1.11022e19	1.65667
$165$	−4.54712e17	−0.0644352
$166$	−7.08950e17	−0.0954326
$167$	−5.85064e18	−0.748365	−0.374182	−	0.927355i	$-0.622077\pi$
$167$	−5.85064e18	−0.748365	−0.374182	+	0.927355i	$0.622077\pi$
$168$	6.32437e18	0.768933
$169$	−6.83603e17	−0.0790254
$170$	−1.85530e18	−0.203985
$171$	1.46340e19	1.53072
$172$	−2.41285e18	−0.240181
$173$	8.45038e18	0.800727	0.400363	−	0.916356i	$-0.368884\pi$
$173$	8.45038e18	0.800727	0.400363	+	0.916356i	$0.368884\pi$
$174$	4.59490e17	0.0414579
$175$	−4.70620e19	−4.04433
$176$	−2.91195e17	−0.0238411
$177$	−9.47649e18	−0.739392
$178$	−1.04701e18	−0.0778722
$179$	1.05247e19	0.746378	0.373189	−	0.927755i	$-0.378264\pi$
$179$	1.05247e19	0.746378	0.373189	+	0.927755i	$0.378264\pi$
$180$	−2.27018e19	−1.53548
$181$	1.60547e19	1.03594	0.517968	−	0.855400i	$-0.326688\pi$
$181$	1.60547e19	1.03594	0.517968	+	0.855400i	$0.326688\pi$
$182$	−4.44579e18	−0.273742
$183$	4.62635e18	0.271897
$184$	−8.47424e18	−0.475498
$185$	3.26408e18	0.174904
$186$	3.46977e18	0.177599
$187$	3.62913e17	0.0177480
$188$	−4.85510e18	−0.226911
$189$	7.14088e18	0.319026
$190$	1.23139e19	0.526004
$191$	−1.32467e19	−0.541157	−0.270578	−	0.962698i	$-0.587215\pi$
$191$	−1.32467e19	−0.541157	−0.270578	+	0.962698i	$0.587215\pi$
$192$	−2.94794e19	−1.15202
$193$	−8.70826e18	−0.325608	−0.162804	−	0.986658i	$-0.552054\pi$
$193$	−8.70826e18	−0.325608	−0.162804	+	0.986658i	$0.552054\pi$
$194$	−5.02821e18	−0.179928
$195$	6.97076e19	2.38773
$196$	−6.07299e19	−1.99171
$197$	−4.32460e19	−1.35826	−0.679130	−	0.734018i	$-0.737643\pi$
$197$	−4.32460e19	−1.35826	−0.679130	+	0.734018i	$0.737643\pi$
$198$	−1.21860e17	−0.00366612
$199$	2.37786e19	0.685385	0.342692	−	0.939448i	$-0.388661\pi$
$199$	2.37786e19	0.685385	0.342692	+	0.939448i	$0.388661\pi$
$200$	−2.70539e19	−0.747265
$201$	6.46608e19	1.71188
$202$	3.72142e18	0.0944544
$203$	−1.33171e19	−0.324110
$204$	3.90361e19	0.911192
$205$	−1.38447e20	−3.10010
$206$	−7.49360e18	−0.160997
$207$	6.19436e19	1.27717
$208$	4.46403e19	0.883464
$209$	−2.40870e18	−0.0457657
$210$	−3.88996e19	−0.709709
$211$	7.89946e19	1.38419	0.692096	−	0.721805i	$-0.256687\pi$
$211$	7.89946e19	1.38419	0.692096	+	0.721805i	$0.256687\pi$
$212$	−8.01679e19	−1.34942
$213$	−3.85828e19	−0.623974
$214$	8.32765e18	0.129421
$215$	3.00888e19	0.449447
$216$	4.10498e18	0.0589460
$217$	−1.00562e20	−1.38843
$218$	9.65750e18	0.128228
$219$	1.67968e20	2.14512
$220$	3.73663e18	0.0459078
$221$	−5.56348e19	−0.657676
$222$	1.88462e18	0.0214400
$223$	−1.58681e19	−0.173754	−0.0868768	−	0.996219i	$-0.527689\pi$
$223$	−1.58681e19	−0.173754	−0.0868768	+	0.996219i	$0.527689\pi$
$224$	−7.83081e19	−0.825465
$225$	1.97754e20	2.00712
$226$	−9.44348e18	−0.0923018
$227$	−1.91160e20	−1.79961	−0.899804	−	0.436295i	$-0.856290\pi$
$227$	−1.91160e20	−1.79961	−0.899804	+	0.436295i	$0.856290\pi$
$228$	−2.59088e20	−2.34964
$229$	1.13641e20	0.992964	0.496482	−	0.868047i	$-0.334625\pi$
$229$	1.13641e20	0.992964	0.496482	+	0.868047i	$0.334625\pi$
$230$	5.21228e19	0.438875
$231$	7.60909e18	0.0617491
$232$	−7.65539e18	−0.0598852
$233$	−9.84570e19	−0.742543	−0.371271	−	0.928524i	$-0.621078\pi$
$233$	−9.84570e19	−0.742543	−0.371271	+	0.928524i	$0.621078\pi$
$234$	1.86812e19	0.135853
$235$	6.05444e19	0.424616
$236$	7.78736e19	0.526791
$237$	1.09087e20	0.711886
$238$	3.10463e19	0.195482
$239$	−3.69133e18	−0.0224285	−0.0112143	−	0.999937i	$-0.503570\pi$
$239$	−3.69133e18	−0.0224285	−0.0112143	+	0.999937i	$0.503570\pi$
$240$	3.90591e20	2.29048
$241$	4.49702e19	0.254554	0.127277	−	0.991867i	$-0.459376\pi$
$241$	4.49702e19	0.254554	0.127277	+	0.991867i	$0.459376\pi$
$242$	−2.98859e19	−0.163319
$243$	−2.54265e20	−1.34163
$244$	−3.80173e19	−0.193717
$245$	7.57318e20	3.72706
$246$	−7.99370e19	−0.380014
$247$	3.69255e20	1.69591
$248$	−5.78085e19	−0.256539
$249$	−1.86013e20	−0.797716
$250$	9.45887e19	0.392057
$251$	2.08042e20	0.833534	0.416767	−	0.909013i	$-0.363163\pi$
$251$	2.08042e20	0.833534	0.416767	+	0.909013i	$0.363163\pi$
$252$	3.79889e20	1.47147
$253$	−1.01957e19	−0.0381849
$254$	4.04067e18	0.0146341
$255$	−4.86790e20	−1.70510
$256$	2.19436e20	0.743479
$257$	1.67937e20	0.550446	0.275223	−	0.961380i	$-0.411248\pi$
$257$	1.67937e20	0.550446	0.275223	+	0.961380i	$0.411248\pi$
$258$	1.73728e19	0.0550936
$259$	−5.46206e19	−0.167613
$260$	−5.72827e20	−1.70118
$261$	5.59582e19	0.160849
$262$	−1.26558e19	−0.0352151
$263$	8.28653e19	0.223228	0.111614	−	0.993752i	$-0.464398\pi$
$263$	8.28653e19	0.223228	0.111614	+	0.993752i	$0.464398\pi$
$264$	4.37413e18	0.0114093
$265$	9.99715e20	2.52515
$266$	−2.06059e20	−0.504077
$267$	−2.74713e20	−0.650930
$268$	−5.31354e20	−1.21966
$269$	−8.63620e20	−1.92056	−0.960281	−	0.279035i	$-0.909985\pi$
$269$	−8.63620e20	−1.92056	−0.960281	+	0.279035i	$0.909985\pi$
$270$	−2.52486e19	−0.0544059
$271$	−5.03901e20	−1.05222	−0.526109	−	0.850417i	$-0.676350\pi$
$271$	−5.03901e20	−1.05222	−0.526109	+	0.850417i	$0.676350\pi$
$272$	−3.11737e20	−0.630889
$273$	−1.16648e21	−2.28820
$274$	−8.77009e19	−0.166773
$275$	−3.25495e19	−0.0600091
$276$	−1.09668e21	−1.96044
$277$	−8.35573e20	−1.44846	−0.724230	−	0.689558i	$-0.757805\pi$
$277$	−8.35573e20	−1.44846	−0.724230	+	0.689558i	$0.757805\pi$
$278$	−6.09330e19	−0.102441
$279$	4.22560e20	0.689052
$280$	6.48091e20	1.02516
$281$	−5.15605e20	−0.791250	−0.395625	−	0.918412i	$-0.629472\pi$
$281$	−5.15605e20	−0.791250	−0.395625	+	0.918412i	$0.629472\pi$
$282$	3.49573e19	0.0520499
$283$	−2.13361e20	−0.308270	−0.154135	−	0.988050i	$-0.549259\pi$
$283$	−2.13361e20	−0.308270	−0.154135	+	0.988050i	$0.549259\pi$
$284$	3.17056e20	0.444560
$285$	3.23089e21	4.39685
$286$	−3.07484e18	−0.00406174
$287$	2.31676e21	2.97087
$288$	3.29050e20	0.409662
$289$	−4.38725e20	−0.530348
$290$	4.70863e19	0.0552728
$291$	−1.31929e21	−1.50401
$292$	−1.38029e21	−1.52832
$293$	1.45005e21	1.55958	0.779789	−	0.626042i	$-0.215326\pi$
$293$	1.45005e21	1.55958	0.779789	+	0.626042i	$0.215326\pi$
$294$	4.37262e20	0.456867
$295$	−9.71104e20	−0.985777
$296$	−3.13990e19	−0.0309696
$297$	4.93885e18	0.00473365
$298$	−2.17585e20	−0.202670
$299$	1.56300e21	1.41499
$300$	−3.50113e21	−3.08090
$301$	−5.03502e20	−0.430711
$302$	−5.59717e19	−0.0465489
$303$	9.76419e20	0.789540
$304$	2.06904e21	1.62684
$305$	4.74086e20	0.362500
$306$	−1.30456e20	−0.0970138
$307$	4.76376e20	0.344567	0.172284	−	0.985047i	$-0.444885\pi$
$307$	4.76376e20	0.344567	0.172284	+	0.985047i	$0.444885\pi$
$308$	−6.25282e19	−0.0439941
$309$	−1.96615e21	−1.34577
$310$	3.55565e20	0.236780
$311$	−4.29205e20	−0.278100	−0.139050	−	0.990285i	$-0.544405\pi$
$311$	−4.29205e20	−0.278100	−0.139050	+	0.990285i	$0.544405\pi$
$312$	−6.70557e20	−0.422787
$313$	−2.40731e21	−1.47708	−0.738542	−	0.674207i	$-0.764485\pi$
$313$	−2.40731e21	−1.47708	−0.738542	+	0.674207i	$0.764485\pi$
$314$	2.23435e20	0.133428
$315$	−4.73731e21	−2.75355
$316$	−8.96426e20	−0.507194
$317$	5.89868e20	0.324901	0.162451	−	0.986717i	$-0.448060\pi$
$317$	5.89868e20	0.324901	0.162451	+	0.986717i	$0.448060\pi$
$318$	5.77218e20	0.309535
$319$	−9.21049e18	−0.00480908
$320$	−3.02091e21	−1.53590
$321$	2.18499e21	1.08182
$322$	−8.72216e20	−0.420580
$323$	−2.57863e21	−1.21106
$324$	2.37410e21	1.08609
$325$	4.98986e21	2.22372
$326$	3.51571e20	0.152638
$327$	2.53392e21	1.07186
$328$	1.33180e21	0.548923
$329$	−1.01314e21	−0.406916
$330$	−2.69041e19	−0.0105305
$331$	3.64847e21	1.39179	0.695893	−	0.718145i	$-0.255009\pi$
$331$	3.64847e21	1.39179	0.695893	+	0.718145i	$0.255009\pi$
$332$	1.52857e21	0.568345
$333$	2.29515e20	0.0831832
$334$	−3.46167e20	−0.122304
$335$	6.62612e21	2.28233
$336$	−6.53610e21	−2.19500
$337$	−6.21191e20	−0.203409	−0.101705	−	0.994815i	$-0.532430\pi$
$337$	−6.21191e20	−0.203409	−0.101705	+	0.994815i	$0.532430\pi$
$338$	−4.04470e19	−0.0129150
$339$	−2.47776e21	−0.771547
$340$	4.00023e21	1.21483
$341$	−6.95516e19	−0.0206013
$342$	8.65857e20	0.250164
$343$	−6.47999e21	−1.82631
$344$	−2.89441e20	−0.0795817
$345$	1.36759e22	3.66854
$346$	4.99987e20	0.130861
$347$	2.77510e21	0.708726	0.354363	−	0.935108i	$-0.384698\pi$
$347$	2.77510e21	0.708726	0.354363	+	0.935108i	$0.384698\pi$
$348$	−9.90710e20	−0.246901
$349$	−1.89304e21	−0.460408	−0.230204	−	0.973142i	$-0.573939\pi$
$349$	−1.89304e21	−0.460408	−0.230204	+	0.973142i	$0.573939\pi$
$350$	−2.78454e21	−0.660959
$351$	−7.57129e20	−0.175412
$352$	−5.41603e19	−0.0122481
$353$	−1.28568e21	−0.283823	−0.141912	−	0.989879i	$-0.545325\pi$
$353$	−1.28568e21	−0.283823	−0.141912	+	0.989879i	$0.545325\pi$
$354$	−5.60699e20	−0.120838
$355$	−3.95377e21	−0.831900
$356$	2.25747e21	0.463765
$357$	8.14588e21	1.63402
$358$	6.22719e20	0.121979
$359$	−8.93665e21	−1.70951	−0.854756	−	0.519031i	$-0.826293\pi$
$359$	−8.93665e21	−1.70951	−0.854756	+	0.519031i	$0.826293\pi$
$360$	−2.72327e21	−0.508768
$361$	1.16343e22	2.12290
$362$	9.49912e20	0.169301
$363$	−7.84141e21	−1.36517
$364$	9.58560e21	1.63026
$365$	1.72125e22	2.85993
$366$	2.73729e20	0.0444356
$367$	−3.41667e21	−0.541928	−0.270964	−	0.962589i	$-0.587342\pi$
$367$	−3.41667e21	−0.541928	−0.270964	+	0.962589i	$0.587342\pi$
$368$	8.75794e21	1.35736
$369$	−9.73498e21	−1.47439
$370$	1.93127e20	0.0285843
$371$	−1.67291e22	−2.41988
$372$	−7.48119e21	−1.05768
$373$	−8.64667e21	−1.19488	−0.597439	−	0.801914i	$-0.703815\pi$
$373$	−8.64667e21	−1.19488	−0.597439	+	0.801914i	$0.703815\pi$
$374$	2.14726e19	0.00290052
$375$	2.48180e22	3.27718
$376$	−5.82410e20	−0.0751851
$377$	1.41197e21	0.178207
$378$	4.22507e20	0.0521379
$379$	−1.75979e21	−0.212338	−0.106169	−	0.994348i	$-0.533858\pi$
$379$	−1.75979e21	−0.212338	−0.106169	+	0.994348i	$0.533858\pi$
$380$	−2.65501e22	−3.13260
$381$	1.06018e21	0.122326
$382$	−7.83771e20	−0.0884403
$383$	−2.50692e21	−0.276663	−0.138331	−	0.990386i	$-0.544174\pi$
$383$	−2.50692e21	−0.276663	−0.138331	+	0.990386i	$0.544174\pi$
$384$	−7.72974e21	−0.834352
$385$	7.79743e20	0.0823256
$386$	−5.15245e20	−0.0532135
$387$	2.11571e21	0.213753
$388$	1.08414e22	1.07156
$389$	−2.31724e21	−0.224078	−0.112039	−	0.993704i	$-0.535738\pi$
$389$	−2.31724e21	−0.224078	−0.112039	+	0.993704i	$0.535738\pi$
$390$	4.12442e21	0.390223
$391$	−1.09149e22	−1.01046
$392$	−7.28506e21	−0.659936
$393$	−3.32061e21	−0.294361
$394$	−2.55875e21	−0.221978
$395$	1.11787e22	0.949106
$396$	2.62743e20	0.0218334
$397$	1.85394e22	1.50791	0.753957	−	0.656924i	$-0.228143\pi$
$397$	1.85394e22	1.50791	0.753957	+	0.656924i	$0.228143\pi$
$398$	1.40691e21	0.112011
$399$	−5.40653e22	−4.21356
$400$	2.79596e22	2.13315
$401$	1.97408e21	0.147448	0.0737239	−	0.997279i	$-0.476512\pi$
$401$	1.97408e21	0.147448	0.0737239	+	0.997279i	$0.476512\pi$
$402$	3.82581e21	0.279770
$403$	1.06623e22	0.763410
$404$	−8.02378e21	−0.562520
$405$	−2.96057e22	−2.03239
$406$	−7.87935e20	−0.0529687
$407$	−3.77773e19	−0.00248701
$408$	4.68271e21	0.301916
$409$	−2.11407e22	−1.33497	−0.667484	−	0.744624i	$-0.732629\pi$
$409$	−2.11407e22	−1.33497	−0.667484	+	0.744624i	$0.732629\pi$
$410$	−8.19155e21	−0.506645
$411$	−2.30108e22	−1.39404
$412$	1.61570e22	0.958814
$413$	1.62503e22	0.944684
$414$	3.66504e21	0.208726
$415$	−1.90617e22	−1.06354
$416$	8.30280e21	0.453870
$417$	−1.59875e22	−0.856296
$418$	−1.42517e20	−0.00747940
$419$	7.93337e21	0.407980	0.203990	−	0.978973i	$-0.434609\pi$
$419$	7.93337e21	0.407980	0.203990	+	0.978973i	$0.434609\pi$
$420$	8.38716e22	4.22665
$421$	−2.31921e22	−1.14536	−0.572679	−	0.819779i	$-0.694096\pi$
$421$	−2.31921e22	−1.14536	−0.572679	+	0.819779i	$0.694096\pi$
$422$	4.67390e21	0.226216
$423$	4.25721e21	0.201944
$424$	−9.61682e21	−0.447117
$425$	−3.48458e22	−1.58798
$426$	−2.28284e21	−0.101975
$427$	−7.93329e21	−0.347389
$428$	−1.79553e22	−0.770763
$429$	−8.06772e20	−0.0339519
$430$	1.78028e21	0.0734523
$431$	−3.99208e21	−0.161489	−0.0807445	−	0.996735i	$-0.525730\pi$
$431$	−3.99208e21	−0.161489	−0.0807445	+	0.996735i	$0.525730\pi$
$432$	−4.24241e21	−0.168268
$433$	1.66552e22	0.647744	0.323872	−	0.946101i	$-0.395015\pi$
$433$	1.66552e22	0.647744	0.323872	+	0.946101i	$0.395015\pi$
$434$	−5.94997e21	−0.226909
$435$	1.23544e22	0.462023
$436$	−2.08226e22	−0.763660
$437$	7.24439e22	2.60561
$438$	9.93823e21	0.350573
$439$	3.41737e22	1.18234	0.591171	−	0.806546i	$-0.298666\pi$
$439$	3.41737e22	1.18234	0.591171	+	0.806546i	$0.298666\pi$
$440$	4.48240e20	0.0152112
$441$	5.32512e22	1.77256
$442$	−3.29176e21	−0.107483
$443$	3.12316e22	1.00037	0.500187	−	0.865918i	$-0.333265\pi$
$443$	3.12316e22	1.00037	0.500187	+	0.865918i	$0.333265\pi$
$444$	−4.06345e21	−0.127685
$445$	−2.81513e22	−0.867837
$446$	−9.38874e20	−0.0283963
$447$	−5.70894e22	−1.69411
$448$	5.05514e22	1.47187
$449$	4.55042e22	1.30004	0.650021	−	0.759916i	$-0.274760\pi$
$449$	4.55042e22	1.30004	0.650021	+	0.759916i	$0.274760\pi$
$450$	1.17006e22	0.328021
$451$	1.60234e21	0.0440812
$452$	2.03612e22	0.549700
$453$	−1.46857e22	−0.389100
$454$	−1.13104e22	−0.294107
$455$	−1.19535e23	−3.05069
$456$	−3.10798e22	−0.778532
$457$	−4.65466e22	−1.14446	−0.572229	−	0.820094i	$-0.693921\pi$
$457$	−4.65466e22	−1.14446	−0.572229	+	0.820094i	$0.693921\pi$
$458$	6.72384e21	0.162278
$459$	5.28727e21	0.125263
$460$	−1.12382e23	−2.61371
$461$	1.13842e22	0.259922	0.129961	−	0.991519i	$-0.458515\pi$
$461$	1.13842e22	0.259922	0.129961	+	0.991519i	$0.458515\pi$
$462$	4.50210e20	0.0100916
$463$	7.44899e22	1.63930	0.819651	−	0.572863i	$-0.194167\pi$
$463$	7.44899e22	1.63930	0.819651	+	0.572863i	$0.194167\pi$
$464$	7.91168e21	0.170949
$465$	9.32924e22	1.97923
$466$	−5.82544e21	−0.121352
$467$	6.41847e22	1.31292	0.656460	−	0.754361i	$-0.272053\pi$
$467$	6.41847e22	1.31292	0.656460	+	0.754361i	$0.272053\pi$
$468$	−4.02786e22	−0.809067
$469$	−1.10881e23	−2.18719
$470$	3.58225e21	0.0693943
$471$	5.86243e22	1.11532
$472$	9.34159e21	0.174548
$473$	−3.48237e20	−0.00639081
$474$	6.45437e21	0.116342
$475$	2.31276e23	4.09482
$476$	−6.69393e22	−1.16418
$477$	7.02955e22	1.20094
$478$	−2.18406e20	−0.00366546
$479$	−2.45057e18	−4.04031e−5 0	−2.02015e−5	−	1.00000i	$-0.500006\pi$
$479$	−2.45057e18	−4.04031e−5 0	−2.02015e−5		1.00000i	$0.500006\pi$
$480$	7.26474e22	1.17671
$481$	5.79128e21	0.0921597
$482$	2.66077e21	0.0416014
$483$	−2.28850e23	−3.51561
$484$	6.44372e22	0.972638
$485$	−1.35195e23	−2.00519
$486$	−1.50442e22	−0.219261
$487$	3.84472e22	0.550641	0.275321	−	0.961352i	$-0.411216\pi$
$487$	3.84472e22	0.550641	0.275321	+	0.961352i	$0.411216\pi$
$488$	−4.56050e21	−0.0641865
$489$	9.22446e22	1.27590
$490$	4.48085e22	0.609107
$491$	−1.80938e22	−0.241734	−0.120867	−	0.992669i	$-0.538567\pi$
$491$	−1.80938e22	−0.241734	−0.120867	+	0.992669i	$0.538567\pi$
$492$	1.72353e23	2.26316
$493$	−9.86025e21	−0.127259
$494$	2.18479e22	0.277160
$495$	−3.27647e21	−0.0408566
$496$	5.97438e22	0.732317
$497$	6.61619e22	0.797221
$498$	−1.10059e22	−0.130369
$499$	1.60429e22	0.186822	0.0934111	−	0.995628i	$-0.470223\pi$
$499$	1.60429e22	0.186822	0.0934111	+	0.995628i	$0.470223\pi$
$500$	−2.03943e23	−2.33488
$501$	−9.08266e22	−1.02233
$502$	1.23093e22	0.136223
$503$	−1.07175e23	−1.16618	−0.583088	−	0.812409i	$-0.698156\pi$
$503$	−1.07175e23	−1.16618	−0.583088	+	0.812409i	$0.698156\pi$
$504$	4.55709e22	0.487559
$505$	1.00059e23	1.05264
$506$	−6.03251e20	−0.00624049
$507$	−1.06124e22	−0.107956
$508$	−8.71213e21	−0.0871531
$509$	−4.45153e21	−0.0437933	−0.0218967	−	0.999760i	$-0.506970\pi$
$509$	−4.45153e21	−0.0437933	−0.0218967	+	0.999760i	$0.506970\pi$
$510$	−2.88021e22	−0.278662
$511$	−2.88032e23	−2.74071
$512$	7.82462e22	0.732265
$513$	−3.50923e22	−0.323009
$514$	9.93638e21	0.0899584
$515$	−2.01482e23	−1.79422
$516$	−3.74575e22	−0.328108
$517$	−7.00719e20	−0.00603774
$518$	−3.23176e21	−0.0273928
$519$	1.31186e23	1.09386
$520$	−6.87154e22	−0.563671
$521$	−1.67517e23	−1.35188	−0.675942	−	0.736955i	$-0.736263\pi$
$521$	−1.67517e23	−1.35188	−0.675942	+	0.736955i	$0.736263\pi$
$522$	3.31090e21	0.0262873
$523$	1.57104e23	1.22722	0.613611	−	0.789608i	$-0.289716\pi$
$523$	1.57104e23	1.22722	0.613611	+	0.789608i	$0.289716\pi$
$524$	2.72873e22	0.209722
$525$	−7.30601e23	−5.52492
$526$	4.90292e21	0.0364818
$527$	−7.44582e22	−0.545158
$528$	−4.52057e21	−0.0325690
$529$	1.65594e23	1.17401
$530$	5.91505e22	0.412680
$531$	−6.82837e22	−0.468828
$532$	4.44285e23	3.00201
$533$	−2.45639e23	−1.63349
$534$	−1.62541e22	−0.106380
$535$	2.23907e23	1.44232
$536$	−6.37404e22	−0.404123
$537$	1.63388e23	1.01962
$538$	−5.10981e22	−0.313874
$539$	−8.76493e21	−0.0529961
$540$	5.44388e22	0.324012
$541$	−7.10836e22	−0.416479	−0.208239	−	0.978078i	$-0.566773\pi$
$541$	−7.10836e22	−0.416479	−0.208239	+	0.978078i	$0.566773\pi$
$542$	−2.98145e22	−0.171962
$543$	2.49236e23	1.41518
$544$	−5.79811e22	−0.324112
$545$	2.59663e23	1.42903
$546$	−6.90174e22	−0.373957
$547$	−9.59019e22	−0.511605	−0.255803	−	0.966729i	$-0.582340\pi$
$547$	−9.59019e22	−0.511605	−0.255803	+	0.966729i	$0.582340\pi$
$548$	1.89093e23	0.993208
$549$	3.33356e22	0.172402
$550$	−1.92587e21	−0.00980718
$551$	6.54438e22	0.328156
$552$	−1.31556e23	−0.649573
$553$	−1.87062e23	−0.909541
$554$	−4.94387e22	−0.236719
$555$	5.06722e22	0.238935
$556$	1.31378e23	0.610081
$557$	−1.06132e23	−0.485377	−0.242689	−	0.970104i	$-0.578029\pi$
$557$	−1.06132e23	−0.485377	−0.242689	+	0.970104i	$0.578029\pi$
$558$	2.50017e22	0.112611
$559$	5.33850e22	0.236820
$560$	−6.69788e23	−2.92644
$561$	5.63394e21	0.0242453
$562$	−3.05070e22	−0.129313
$563$	3.93150e23	1.64148	0.820742	−	0.571299i	$-0.193560\pi$
$563$	3.93150e23	1.64148	0.820742	+	0.571299i	$0.193560\pi$
$564$	−7.53716e22	−0.309981
$565$	−2.53909e23	−1.02865
$566$	−1.26240e22	−0.0503800
$567$	4.95418e23	1.94767
$568$	3.80336e22	0.147301
$569$	−3.79766e22	−0.144898	−0.0724489	−	0.997372i	$-0.523081\pi$
$569$	−3.79766e22	−0.144898	−0.0724489	+	0.997372i	$0.523081\pi$
$570$	1.91163e23	0.718569
$571$	1.57694e23	0.583994	0.291997	−	0.956419i	$-0.405680\pi$
$571$	1.57694e23	0.583994	0.291997	+	0.956419i	$0.405680\pi$
$572$	6.62970e21	0.0241895
$573$	−2.05644e23	−0.739268
$574$	1.37076e23	0.485525
$575$	9.78956e23	3.41654
$576$	−2.12417e23	−0.730462
$577$	−2.40199e23	−0.813910	−0.406955	−	0.913448i	$-0.633409\pi$
$577$	−2.40199e23	−0.813910	−0.406955	+	0.913448i	$0.633409\pi$
$578$	−2.59582e22	−0.0866739
$579$	−1.35189e23	−0.444809
$580$	−1.01523e23	−0.329175
$581$	3.18976e23	1.01920
$582$	−7.80591e22	−0.245798
$583$	−1.15704e22	−0.0359057
$584$	−1.65577e23	−0.506397
$585$	5.02285e23	1.51400
$586$	8.57955e22	0.254879
$587$	1.07951e23	0.316085	0.158043	−	0.987432i	$-0.449482\pi$
$587$	1.07951e23	0.316085	0.158043	+	0.987432i	$0.449482\pi$
$588$	−9.42784e23	−2.72085
$589$	4.94189e23	1.40577
$590$	−5.74577e22	−0.161104
$591$	−6.71360e23	−1.85550
$592$	3.24502e22	0.0884061
$593$	−2.63694e23	−0.708166	−0.354083	−	0.935214i	$-0.615207\pi$
$593$	−2.63694e23	−0.708166	−0.354083	+	0.935214i	$0.615207\pi$
$594$	2.92219e20	0.000773613 0
$595$	8.34750e23	2.17852
$596$	4.69136e23	1.20700
$597$	3.69144e23	0.936297
$598$	9.24787e22	0.231250
$599$	4.26526e23	1.05152	0.525760	−	0.850633i	$-0.323781\pi$
$599$	4.26526e23	1.05152	0.525760	+	0.850633i	$0.323781\pi$
$600$	−4.19990e23	−1.02083
$601$	−3.50391e23	−0.839693	−0.419846	−	0.907595i	$-0.637916\pi$
$601$	−3.50391e23	−0.839693	−0.419846	+	0.907595i	$0.637916\pi$
$602$	−2.97909e22	−0.0703904
$603$	4.65919e23	1.08546
$604$	1.20681e23	0.277220
$605$	−8.03549e23	−1.82009
$606$	5.77722e22	0.129033
$607$	−6.94105e21	−0.0152870	−0.00764349	−	0.999971i	$-0.502433\pi$
$607$	−6.94105e21	−0.0152870	−0.00764349	+	0.999971i	$0.502433\pi$
$608$	3.84828e23	0.835769
$609$	−2.06737e23	−0.442763
$610$	2.80504e22	0.0592428
$611$	1.07421e23	0.223737
$612$	2.81278e23	0.577762
$613$	6.32634e23	1.28156	0.640779	−	0.767725i	$-0.278611\pi$
$613$	6.32634e23	1.28156	0.640779	+	0.767725i	$0.278611\pi$
$614$	2.81859e22	0.0563120
$615$	−2.14928e24	−4.23502
$616$	−7.50078e21	−0.0145771
$617$	−7.12003e22	−0.136477	−0.0682383	−	0.997669i	$-0.521738\pi$
$617$	−7.12003e22	−0.136477	−0.0682383	+	0.997669i	$0.521738\pi$
$618$	−1.16332e23	−0.219937
$619$	−5.76920e23	−1.07583	−0.537917	−	0.842998i	$-0.680789\pi$
$619$	−5.76920e23	−1.07583	−0.537917	+	0.842998i	$0.680789\pi$
$620$	−7.66636e23	−1.41013
$621$	−1.48540e23	−0.269505
$622$	−2.53949e22	−0.0454495
$623$	4.71080e23	0.831660
$624$	6.93006e23	1.20689
$625$	1.19446e24	2.05207
$626$	−1.42434e23	−0.241397
$627$	−3.73932e22	−0.0625200
$628$	−4.81749e23	−0.794628
$629$	−4.04423e22	−0.0658121
$630$	−2.80294e23	−0.450007
$631$	6.09733e23	0.965807	0.482903	−	0.875674i	$-0.339582\pi$
$631$	6.09733e23	0.965807	0.482903	+	0.875674i	$0.339582\pi$
$632$	−1.07534e23	−0.168054
$633$	1.22633e24	1.89093
$634$	3.49010e22	0.0530981
$635$	1.08643e23	0.163088
$636$	−1.24454e24	−1.84342
$637$	1.34367e24	1.96384
$638$	−5.44960e20	−0.000785939 0
$639$	−2.78012e23	−0.395645
$640$	−7.92106e23	−1.11238
$641$	−2.25448e22	−0.0312430	−0.0156215	−	0.999878i	$-0.504973\pi$
$641$	−2.25448e22	−0.0312430	−0.0156215	+	0.999878i	$0.504973\pi$
$642$	1.29280e23	0.176801
$643$	−1.12241e23	−0.151481	−0.0757407	−	0.997128i	$-0.524132\pi$
$643$	−1.12241e23	−0.151481	−0.0757407	+	0.997128i	$0.524132\pi$
$644$	1.88059e24	2.50475
$645$	4.67105e23	0.613984
$646$	−1.52571e23	−0.197922
$647$	6.05485e23	0.775206	0.387603	−	0.921826i	$-0.373303\pi$
$647$	6.05485e23	0.775206	0.387603	+	0.921826i	$0.373303\pi$
$648$	2.84794e23	0.359868
$649$	1.12392e22	0.0140170
$650$	2.95237e23	0.363419
$651$	−1.56114e24	−1.89672
$652$	−7.58025e23	−0.909032
$653$	9.28141e23	1.09863	0.549315	−	0.835615i	$-0.314889\pi$
$653$	9.28141e23	1.09863	0.549315	+	0.835615i	$0.314889\pi$
$654$	1.49925e23	0.175172
$655$	−3.40279e23	−0.392450
$656$	−1.37639e24	−1.56696
$657$	1.21031e24	1.36016
$658$	−5.99449e22	−0.0665016
$659$	−1.22388e24	−1.34034	−0.670168	−	0.742210i	$-0.733778\pi$
$659$	−1.22388e24	−1.34034	−0.670168	+	0.742210i	$0.733778\pi$
$660$	5.80082e22	0.0627142
$661$	1.17784e24	1.25711	0.628557	−	0.777763i	$-0.283646\pi$
$661$	1.17784e24	1.25711	0.628557	+	0.777763i	$0.283646\pi$
$662$	2.15870e23	0.227457
$663$	−8.63686e23	−0.898444
$664$	1.83365e23	0.188316
$665$	−5.54035e24	−5.61763
$666$	1.35798e22	0.0135945
$667$	2.77014e23	0.273799
$668$	7.46373e23	0.728377
$669$	−2.46340e23	−0.237363
$670$	3.92050e23	0.372998
$671$	−5.48690e21	−0.00515449
$672$	−1.21567e24	−1.12766
$673$	−8.60875e21	−0.00788518	−0.00394259	−	0.999992i	$-0.501255\pi$
$673$	−8.60875e21	−0.00788518	−0.00394259	+	0.999992i	$0.501255\pi$
$674$	−3.67542e22	−0.0332429
$675$	−4.74213e23	−0.423537
$676$	8.72081e22	0.0769148
$677$	−2.10499e24	−1.83336	−0.916679	−	0.399624i	$-0.869141\pi$
$677$	−2.10499e24	−1.83336	−0.916679	+	0.399624i	$0.869141\pi$
$678$	−1.46603e23	−0.126093
$679$	2.26233e24	1.92160
$680$	4.79861e23	0.402522
$681$	−2.96761e24	−2.45842
$682$	−4.11519e21	−0.00336684
$683$	−1.08078e24	−0.873292	−0.436646	−	0.899633i	$-0.643834\pi$
$683$	−1.08078e24	−0.873292	−0.436646	+	0.899633i	$0.643834\pi$
$684$	−1.86688e24	−1.48984
$685$	−2.35804e24	−1.85858
$686$	−3.83404e23	−0.298471
$687$	1.76419e24	1.35648
$688$	2.99131e23	0.227175
$689$	1.77374e24	1.33054
$690$	8.09166e23	0.599543
$691$	2.26445e24	1.65729	0.828647	−	0.559771i	$-0.189111\pi$
$691$	2.26445e24	1.65729	0.828647	+	0.559771i	$0.189111\pi$
$692$	−1.07803e24	−0.779340
$693$	5.48280e22	0.0391534
$694$	1.64196e23	0.115826
$695$	−1.63832e24	−1.14164
$696$	−1.18844e23	−0.0818085
$697$	1.71538e24	1.16649
$698$	−1.12006e23	−0.0752437
$699$	−1.52847e24	−1.01438
$700$	6.00376e24	3.93631
$701$	2.23912e23	0.145035	0.0725177	−	0.997367i	$-0.476897\pi$
$701$	2.23912e23	0.145035	0.0725177	+	0.997367i	$0.476897\pi$
$702$	−4.47973e22	−0.0286673
$703$	2.68421e23	0.169706
$704$	3.49629e22	0.0218394
$705$	9.39904e23	0.580064
$706$	−7.60703e22	−0.0463847
$707$	−1.67437e24	−1.00876
$708$	1.20893e24	0.719643
$709$	3.61327e23	0.212524	0.106262	−	0.994338i	$-0.466112\pi$
$709$	3.61327e23	0.212524	0.106262	+	0.994338i	$0.466112\pi$
$710$	−2.33934e23	−0.135956
$711$	7.86034e23	0.451388
$712$	2.70803e23	0.153664
$713$	2.09183e24	1.17291
$714$	4.81970e23	0.267046
$715$	−8.26740e22	−0.0452656
$716$	−1.34265e24	−0.726443
$717$	−5.73050e22	−0.0306394
$718$	−5.28758e23	−0.279383
$719$	1.32038e24	0.689449	0.344724	−	0.938704i	$-0.387972\pi$
$719$	1.32038e24	0.689449	0.344724	+	0.938704i	$0.387972\pi$
$720$	2.81444e24	1.45233
$721$	3.37157e24	1.71942
$722$	6.88371e23	0.346942
$723$	6.98128e23	0.347744
$724$	−2.04811e24	−1.00827
$725$	8.84362e23	0.430286
$726$	−4.63955e23	−0.223108
$727$	−4.02236e24	−1.91178	−0.955890	−	0.293723i	$-0.905106\pi$
$727$	−4.02236e24	−1.91178	−0.955890	+	0.293723i	$0.905106\pi$
$728$	1.14987e24	0.540174
$729$	−1.54397e24	−0.716893
$730$	1.01842e24	0.467394
$731$	−3.72804e23	−0.169115
$732$	−5.90189e23	−0.264635
$733$	−4.15571e24	−1.84188	−0.920941	−	0.389702i	$-0.872578\pi$
$733$	−4.15571e24	−1.84188	−0.920941	+	0.389702i	$0.872578\pi$
$734$	−2.02155e23	−0.0885664
$735$	1.17568e25	5.09150
$736$	1.62892e24	0.697330
$737$	−7.66884e22	−0.0324531
$738$	−5.75993e23	−0.240956
$739$	7.97183e23	0.329671	0.164835	−	0.986321i	$-0.447291\pi$
$739$	7.97183e23	0.329671	0.164835	+	0.986321i	$0.447291\pi$
$740$	−4.16402e23	−0.170233
$741$	5.73240e24	2.31676
$742$	−9.89816e23	−0.395477
$743$	2.60488e24	1.02892	0.514461	−	0.857514i	$-0.327992\pi$
$743$	2.60488e24	1.02892	0.514461	+	0.857514i	$0.327992\pi$
$744$	−8.97432e23	−0.350454
$745$	−5.85025e24	−2.25863
$746$	−5.11600e23	−0.195277
$747$	−1.34033e24	−0.505810
$748$	−4.62973e22	−0.0172740
$749$	−3.74683e24	−1.38219
$750$	1.46842e24	0.535585
$751$	−3.60447e24	−1.29988	−0.649938	−	0.759988i	$-0.725205\pi$
$751$	−3.60447e24	−1.29988	−0.649938	+	0.759988i	$0.725205\pi$
$752$	6.01908e23	0.214624
$753$	3.22968e24	1.13868
$754$	8.35427e22	0.0291241
$755$	−1.50492e24	−0.518759
$756$	−9.10971e23	−0.310506
$757$	−3.02689e24	−1.02019	−0.510095	−	0.860118i	$-0.670390\pi$
$757$	−3.02689e24	−1.02019	−0.510095	+	0.860118i	$0.670390\pi$
$758$	−1.04122e23	−0.0347020
$759$	−1.58280e23	−0.0521640
$760$	−3.18490e24	−1.03796
$761$	−2.73578e24	−0.881682	−0.440841	−	0.897585i	$-0.645320\pi$
$761$	−2.73578e24	−0.881682	−0.440841	+	0.897585i	$0.645320\pi$
$762$	6.27283e22	0.0199915
$763$	−4.34517e24	−1.36946
$764$	1.68989e24	0.526703
$765$	−3.50761e24	−1.08116
$766$	−1.48328e23	−0.0452146
$767$	−1.72298e24	−0.519421
$768$	3.40658e24	1.01566
$769$	6.17127e24	1.81970	0.909851	−	0.414934i	$-0.136195\pi$
$769$	6.17127e24	1.81970	0.909851	+	0.414934i	$0.136195\pi$
$770$	4.61353e22	0.0134543
$771$	2.60709e24	0.751958
$772$	1.11092e24	0.316911
$773$	−5.91266e24	−1.66824	−0.834118	−	0.551586i	$-0.814023\pi$
$773$	−5.91266e24	−1.66824	−0.834118	+	0.551586i	$0.814023\pi$
$774$	1.25181e23	0.0349334
$775$	6.67813e24	1.84327
$776$	1.30051e24	0.355051
$777$	−8.47942e23	−0.228975
$778$	−1.37105e23	−0.0366207
$779$	−1.13852e25	−3.00796
$780$	−8.89269e24	−2.32396
$781$	4.57596e22	0.0118290
$782$	−6.45808e23	−0.165138
$783$	−1.34187e23	−0.0339419
$784$	7.52895e24	1.88386
$785$	6.00754e24	1.48698
$786$	−1.96471e23	−0.0481070
$787$	5.94715e24	1.44053	0.720267	−	0.693697i	$-0.244019\pi$
$787$	5.94715e24	1.44053	0.720267	+	0.693697i	$0.244019\pi$
$788$	5.51694e24	1.32198
$789$	1.28642e24	0.304949
$790$	6.61412e23	0.155111
$791$	4.24888e24	0.985767
$792$	3.15182e22	0.00723431
$793$	8.41145e23	0.191007
$794$	1.09693e24	0.246436
$795$	1.55198e25	3.44957
$796$	−3.03346e24	−0.667079
$797$	1.84492e24	0.401403	0.200702	−	0.979652i	$-0.435678\pi$
$797$	1.84492e24	0.401403	0.200702	+	0.979652i	$0.435678\pi$
$798$	−3.19890e24	−0.688615
$799$	−7.50152e23	−0.159772
$800$	5.20030e24	1.09588
$801$	−1.97947e24	−0.412737
$802$	1.16801e23	0.0240972
$803$	−1.99212e23	−0.0406662
$804$	−8.24886e24	−1.66616
$805$	−2.34515e25	−4.68711
$806$	6.30860e23	0.124763
$807$	−1.34070e25	−2.62366
$808$	−9.62520e23	−0.186386
$809$	6.87807e24	1.31797	0.658983	−	0.752158i	$-0.270987\pi$
$809$	6.87807e24	1.31797	0.658983	+	0.752158i	$0.270987\pi$
$810$	−1.75169e24	−0.332150
$811$	−6.97932e24	−1.30959	−0.654796	−	0.755806i	$-0.727246\pi$
$811$	−6.97932e24	−1.30959	−0.654796	+	0.755806i	$0.727246\pi$
$812$	1.69887e24	0.315453
$813$	−7.82266e24	−1.43742
$814$	−2.23518e21	−0.000406449 0
$815$	9.45277e24	1.70106
$816$	−4.83948e24	−0.861851
$817$	2.47435e24	0.436088
$818$	−1.25084e24	−0.218172
$819$	−8.40516e24	−1.45088
$820$	1.76619e25	3.01730
$821$	5.77311e24	0.976097	0.488048	−	0.872817i	$-0.337709\pi$
$821$	5.77311e24	0.976097	0.488048	+	0.872817i	$0.337709\pi$
$822$	−1.36149e24	−0.227826
$823$	1.07494e25	1.78026	0.890131	−	0.455704i	$-0.150612\pi$
$823$	1.07494e25	1.78026	0.890131	+	0.455704i	$0.150612\pi$
$824$	1.93817e24	0.317695
$825$	−5.05306e23	−0.0819777
$826$	9.61489e23	0.154388
$827$	9.47498e23	0.150585	0.0752924	−	0.997161i	$-0.476011\pi$
$827$	9.47498e23	0.150585	0.0752924	+	0.997161i	$0.476011\pi$
$828$	−7.90222e24	−1.24306
$829$	−3.22721e24	−0.502475	−0.251237	−	0.967926i	$-0.580837\pi$
$829$	−3.22721e24	−0.502475	−0.251237	+	0.967926i	$0.580837\pi$
$830$	−1.12783e24	−0.173812
$831$	−1.29716e25	−1.97873
$832$	−5.35984e24	−0.809288
$833$	−9.38326e24	−1.40240
$834$	−9.45937e23	−0.139943
$835$	−9.30747e24	−1.36300
$836$	3.07281e23	0.0445433
$837$	−1.01330e24	−0.145402
$838$	4.69396e23	0.0666754
$839$	−1.27649e25	−1.79491	−0.897454	−	0.441109i	$-0.854585\pi$
$839$	−1.27649e25	−1.79491	−0.897454	+	0.441109i	$0.854585\pi$
$840$	1.00611e25	1.40046
$841$	2.50246e23	0.0344828
$842$	−1.37221e24	−0.187184
$843$	−8.00437e24	−1.08092
$844$	−1.00774e25	−1.34722
$845$	−1.08751e24	−0.143930
$846$	2.51888e23	0.0330034
$847$	1.34465e25	1.74421
$848$	9.93877e24	1.27634
$849$	−3.31227e24	−0.421124
$850$	−2.06173e24	−0.259520
$851$	1.13619e24	0.141595
$852$	4.92205e24	0.607309
$853$	−4.06027e24	−0.496007	−0.248004	−	0.968759i	$-0.579774\pi$
$853$	−4.06027e24	−0.496007	−0.248004	+	0.968759i	$0.579774\pi$
$854$	−4.69392e23	−0.0567732
$855$	2.32805e25	2.78792
$856$	−2.15389e24	−0.255386
$857$	−7.75663e23	−0.0910617	−0.0455309	−	0.998963i	$-0.514498\pi$
$857$	−7.75663e23	−0.0910617	−0.0455309	+	0.998963i	$0.514498\pi$
$858$	−4.77346e22	−0.00554870
$859$	1.11921e25	1.28816	0.644078	−	0.764960i	$-0.277241\pi$
$859$	1.11921e25	1.28816	0.644078	+	0.764960i	$0.277241\pi$
$860$	−3.83847e24	−0.437443
$861$	3.59658e25	4.05848
$862$	−2.36201e23	−0.0263919
$863$	1.10256e25	1.21986	0.609932	−	0.792454i	$-0.291197\pi$
$863$	1.10256e25	1.21986	0.609932	+	0.792454i	$0.291197\pi$
$864$	−7.89060e23	−0.0864456
$865$	1.34433e25	1.45837
$866$	9.85446e23	0.105860
$867$	−6.81087e24	−0.724503
$868$	1.28288e25	1.35135
$869$	−1.29378e23	−0.0134956
$870$	7.30978e23	0.0755076
$871$	1.17564e25	1.20259
$872$	−2.49785e24	−0.253032
$873$	−9.50629e24	−0.953652
$874$	4.28631e24	0.425831
$875$	−4.25580e25	−4.18709
$876$	−2.14279e25	−2.08783
$877$	−1.80437e25	−1.74112	−0.870559	−	0.492063i	$-0.836243\pi$
$877$	−1.80437e25	−1.74112	−0.870559	+	0.492063i	$0.836243\pi$
$878$	2.02197e24	0.193228
$879$	2.25108e25	2.13052
$880$	−4.63246e23	−0.0434219
$881$	2.00681e24	0.186299	0.0931496	−	0.995652i	$-0.470307\pi$
$881$	2.00681e24	0.186299	0.0931496	+	0.995652i	$0.470307\pi$
$882$	3.15073e24	0.289687
$883$	−1.20389e25	−1.09628	−0.548141	−	0.836386i	$-0.684664\pi$
$883$	−1.20389e25	−1.09628	−0.548141	+	0.836386i	$0.684664\pi$
$884$	7.09739e24	0.640110
$885$	−1.50756e25	−1.34666
$886$	1.84789e24	0.163489
$887$	−4.13882e24	−0.362682	−0.181341	−	0.983420i	$-0.558044\pi$
$887$	−4.13882e24	−0.362682	−0.181341	+	0.983420i	$0.558044\pi$
$888$	−4.87445e23	−0.0423073
$889$	−1.81801e24	−0.156290
$890$	−1.66564e24	−0.141829
$891$	3.42646e23	0.0288992
$892$	2.02431e24	0.169113
$893$	4.97886e24	0.411996
$894$	−3.37783e24	−0.276866
$895$	1.67432e25	1.35938
$896$	1.32550e25	1.06601
$897$	2.42644e25	1.93301
$898$	2.69236e24	0.212464
$899$	1.88970e24	0.147719
$900$	−2.52277e25	−1.95352
$901$	−1.23866e25	−0.950148
$902$	9.48062e22	0.00720412
$903$	−7.81648e24	−0.588390
$904$	2.44249e24	0.182138
$905$	2.55405e25	1.88676
$906$	−8.68917e23	−0.0635899
$907$	2.16092e24	0.156666	0.0783332	−	0.996927i	$-0.475040\pi$
$907$	2.16092e24	0.156666	0.0783332	+	0.996927i	$0.475040\pi$
$908$	2.43865e25	1.75154
$909$	7.03568e24	0.500626
$910$	−7.07257e24	−0.498569
$911$	−1.11145e25	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$911$	−1.11145e25	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$912$	3.21202e25	2.22240
$913$	2.20613e23	0.0151227
$914$	−2.75404e24	−0.187037
$915$	7.35981e24	0.495208
$916$	−1.44973e25	−0.966443
$917$	5.69419e24	0.376091
$918$	3.12834e23	0.0204716
$919$	−3.44814e24	−0.223565	−0.111782	−	0.993733i	$-0.535656\pi$
$919$	−3.44814e24	−0.223565	−0.111782	+	0.993733i	$0.535656\pi$
$920$	−1.34812e25	−0.866029
$921$	7.39537e24	0.470710
$922$	6.73571e23	0.0424786
$923$	−7.01497e24	−0.438340
$924$	−9.70701e23	−0.0600999
$925$	3.62726e24	0.222522
$926$	4.40737e24	0.267908
$927$	−1.41673e25	−0.853316
$928$	1.47152e24	0.0878231
$929$	−2.51649e24	−0.148820	−0.0744101	−	0.997228i	$-0.523707\pi$
$929$	−2.51649e24	−0.148820	−0.0744101	+	0.997228i	$0.523707\pi$
$930$	5.51987e24	0.323462
$931$	6.22780e25	3.61628
$932$	1.25603e25	0.722710
$933$	−6.66308e24	−0.379910
$934$	3.79764e24	0.214568
$935$	5.77339e23	0.0323245
$936$	−4.83176e24	−0.268078
$937$	−2.55821e25	−1.40653	−0.703267	−	0.710926i	$-0.748276\pi$
$937$	−2.55821e25	−1.40653	−0.703267	+	0.710926i	$0.748276\pi$
$938$	−6.56052e24	−0.357449
$939$	−3.73716e25	−2.01783
$940$	−7.72372e24	−0.413275
$941$	3.16049e25	1.67588	0.837940	−	0.545762i	$-0.183760\pi$
$941$	3.16049e25	1.67588	0.837940	+	0.545762i	$0.183760\pi$
$942$	3.46865e24	0.182275
$943$	−4.81918e25	−2.50971
$944$	−9.65433e24	−0.498265
$945$	1.13600e25	0.581045
$946$	−2.06043e22	−0.00104444
$947$	−2.58946e25	−1.30087	−0.650435	−	0.759562i	$-0.725413\pi$
$947$	−2.58946e25	−1.30087	−0.650435	+	0.759562i	$0.725413\pi$
$948$	−1.39163e25	−0.692873
$949$	3.05393e25	1.50694
$950$	1.36840e25	0.669210
$951$	9.15724e24	0.443844
$952$	−8.02993e24	−0.385743
$953$	−2.44252e25	−1.16292	−0.581459	−	0.813576i	$-0.697518\pi$
$953$	−2.44252e25	−1.16292	−0.581459	+	0.813576i	$0.697518\pi$
$954$	4.15920e24	0.196268
$955$	−2.10734e25	−0.985613
$956$	4.70908e23	0.0218295
$957$	−1.42986e23	−0.00656963
$958$	−1.44994e20	−6.60301e−6 0
$959$	3.94590e25	1.78110
$960$	−4.68972e25	−2.09818
$961$	−8.28035e24	−0.367198
$962$	3.42655e23	0.0150615
$963$	1.57442e25	0.685956
$964$	−5.73691e24	−0.247755
$965$	−1.38535e25	−0.593031
$966$	−1.35405e25	−0.574550
$967$	−4.18195e25	−1.75895	−0.879475	−	0.475944i	$-0.842106\pi$
$967$	−4.18195e25	−1.75895	−0.879475	+	0.475944i	$0.842106\pi$
$968$	7.72979e24	0.322275
$969$	−4.00312e25	−1.65442
$970$	−7.99912e24	−0.327704
$971$	−1.31711e25	−0.534882	−0.267441	−	0.963574i	$-0.586178\pi$
$971$	−1.31711e25	−0.534882	−0.267441	+	0.963574i	$0.586178\pi$
$972$	3.24369e25	1.30580
$973$	2.74154e25	1.09405
$974$	2.27482e24	0.0899904
$975$	7.74637e25	3.03780
$976$	4.71317e24	0.183227
$977$	−2.75909e25	−1.06331	−0.531657	−	0.846960i	$-0.678430\pi$
$977$	−2.75909e25	−1.06331	−0.531657	+	0.846960i	$0.678430\pi$
$978$	5.45787e24	0.208518
$979$	3.25813e23	0.0123400
$980$	−9.66120e25	−3.62752
$981$	1.82584e25	0.679634
$982$	−1.07056e24	−0.0395062
$983$	−5.61356e24	−0.205368	−0.102684	−	0.994714i	$-0.532743\pi$
$983$	−5.61356e24	−0.205368	−0.102684	+	0.994714i	$0.532743\pi$
$984$	2.06752e25	0.749878
$985$	−6.87977e25	−2.47381
$986$	−5.83405e23	−0.0207978
$987$	−1.57282e25	−0.555883
$988$	−4.71064e25	−1.65061
$989$	1.04736e25	0.363853
$990$	−1.93860e23	−0.00667712
$991$	4.46423e25	1.52448	0.762238	−	0.647297i	$-0.224101\pi$
$991$	4.46423e25	1.52448	0.762238	+	0.647297i	$0.224101\pi$
$992$	1.11120e25	0.376220
$993$	5.66396e25	1.90130
$994$	3.91463e24	0.130288
$995$	3.78280e25	1.24830
$996$	2.37299e25	0.776410
$997$	5.26797e24	0.170897	0.0854485	−	0.996343i	$-0.472768\pi$
$997$	5.26797e24	0.170897	0.0854485	+	0.996343i	$0.472768\pi$
$998$	9.49217e23	0.0305320
$999$	−5.50376e23	−0.0175531

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.b.1.12	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.b.1.12	✓	21	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+59.1674 q^{2} +15524.2 q^{3} -127571. q^{4} +1.59085e6 q^{5} +918527. q^{6} -2.66210e7 q^{7} -1.53032e7 q^{8} +1.11861e8 q^{9} +O(q^{10})\)	\(q+59.1674 q^{2} +15524.2 q^{3} -127571. q^{4} +1.59085e6 q^{5} +918527. q^{6} -2.66210e7 q^{7} -1.53032e7 q^{8} +1.11861e8 q^{9} +9.41262e7 q^{10} -1.84119e7 q^{11} -1.98044e9 q^{12} +2.82255e9 q^{13} -1.57509e9 q^{14} +2.46966e10 q^{15} +1.58156e10 q^{16} -1.97108e10 q^{17} +6.61853e9 q^{18} +1.30823e11 q^{19} -2.02946e11 q^{20} -4.13270e11 q^{21} -1.08938e9 q^{22} +5.53754e11 q^{23} -2.37571e11 q^{24} +1.76785e12 q^{25} +1.67003e11 q^{26} -2.68243e11 q^{27} +3.39607e12 q^{28} +5.00246e11 q^{29} +1.46124e12 q^{30} +3.77753e12 q^{31} +2.94159e12 q^{32} -2.85830e11 q^{33} -1.16624e12 q^{34} -4.23499e13 q^{35} -1.42703e13 q^{36} +2.05179e12 q^{37} +7.74046e12 q^{38} +4.38179e13 q^{39} -2.43451e13 q^{40} -8.70274e13 q^{41} -2.44521e13 q^{42} +1.89137e13 q^{43} +2.34883e12 q^{44} +1.77954e14 q^{45} +3.27642e13 q^{46} +3.80579e13 q^{47} +2.45524e14 q^{48} +4.76047e14 q^{49} +1.04599e14 q^{50} -3.05995e14 q^{51} -3.60077e14 q^{52} +6.28417e14 q^{53} -1.58712e13 q^{54} -2.92905e13 q^{55} +4.07388e14 q^{56} +2.03093e15 q^{57} +2.95983e13 q^{58} -6.10432e14 q^{59} -3.15058e15 q^{60} +2.98009e14 q^{61} +2.23507e14 q^{62} -2.97786e15 q^{63} -1.89893e15 q^{64} +4.49025e15 q^{65} -1.69118e13 q^{66} +4.16516e15 q^{67} +2.51453e15 q^{68} +8.59660e15 q^{69} -2.50573e15 q^{70} -2.48533e15 q^{71} -1.71184e15 q^{72} +1.08197e16 q^{73} +1.21399e14 q^{74} +2.74445e16 q^{75} -1.66893e16 q^{76} +4.90143e14 q^{77} +2.59259e15 q^{78} +7.02687e15 q^{79} +2.51601e16 q^{80} -1.86100e16 q^{81} -5.14918e15 q^{82} -1.19821e16 q^{83} +5.27214e16 q^{84} -3.13568e16 q^{85} +1.11907e15 q^{86} +7.76593e15 q^{87} +2.81762e14 q^{88} -1.76958e16 q^{89} +1.05291e16 q^{90} -7.51392e16 q^{91} -7.06431e16 q^{92} +5.86433e16 q^{93} +2.25179e15 q^{94} +2.08119e17 q^{95} +4.56659e16 q^{96} -8.49829e16 q^{97} +2.81665e16 q^{98} -2.05958e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9} - 224469478 q^{10} + 1203139534 q^{11} - 5164251122 q^{12} + 3854339312 q^{13} + 25262272904 q^{14} + 28324474306 q^{15} + 196520815922 q^{16} + 76444714794 q^{17} + 75758949126 q^{18} + 246497292428 q^{19} - 46900976670 q^{20} + 360937126704 q^{21} - 275001533522 q^{22} + 213498528140 q^{23} - 451123453870 q^{24} + 3898884886997 q^{25} - 3609347694206 q^{26} - 2718903745978 q^{27} - 5946174617200 q^{28} + 10505174672181 q^{29} - 20237658929454 q^{30} + 16670029895798 q^{31} - 42141001912046 q^{32} - 7157109761394 q^{33} + 12785761151136 q^{34} + 46677934312888 q^{35} + 132137824374868 q^{36} + 53445659988410 q^{37} + 76581637956388 q^{38} + 79233849032530 q^{39} + 193617444734146 q^{40} - 20814769309298 q^{41} + 76690667258352 q^{42} + 185498647364454 q^{43} + 315429066899678 q^{44} - 486270821438526 q^{45} + 261474367677132 q^{46} + 389503471719450 q^{47} - 101509672247630 q^{48} + 730079062141437 q^{49} + 14\!\cdots\!54 q^{50}+ \cdots - 95\!\cdots\!64 q^{99}+O(q^{100}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9 - 224469478 * q^10 + 1203139534 * q^11 - 5164251122 * q^12 + 3854339312 * q^13 + 25262272904 * q^14 + 28324474306 * q^15 + 196520815922 * q^16 + 76444714794 * q^17 + 75758949126 * q^18 + 246497292428 * q^19 - 46900976670 * q^20 + 360937126704 * q^21 - 275001533522 * q^22 + 213498528140 * q^23 - 451123453870 * q^24 + 3898884886997 * q^25 - 3609347694206 * q^26 - 2718903745978 * q^27 - 5946174617200 * q^28 + 10505174672181 * q^29 - 20237658929454 * q^30 + 16670029895798 * q^31 - 42141001912046 * q^32 - 7157109761394 * q^33 + 12785761151136 * q^34 + 46677934312888 * q^35 + 132137824374868 * q^36 + 53445659988410 * q^37 + 76581637956388 * q^38 + 79233849032530 * q^39 + 193617444734146 * q^40 - 20814769309298 * q^41 + 76690667258352 * q^42 + 185498647364454 * q^43 + 315429066899678 * q^44 - 486270821438526 * q^45 + 261474367677132 * q^46 + 389503471719450 * q^47 - 101509672247630 * q^48 + 730079062141437 * q^49 + 1482269666368354 * q^50 + 718238208473988 * q^51 + 1966802817157170 * q^52 + 747441265526156 * q^53 + 5692893333117030 * q^54 + 1639109418219546 * q^55 + 5657219329125240 * q^56 + 4694352396864932 * q^57 + 128063081718016 * q^58 + 5280258638332960 * q^59 + 15251367906033378 * q^60 + 5813675353074254 * q^61 + 6242066590947250 * q^62 + 10947760075450368 * q^63 + 24583792057508902 * q^64 + 19190799243789974 * q^65 + 41877805444482390 * q^66 + 13420580230958268 * q^67 + 24771837384165388 * q^68 + 30973047049935252 * q^69 + 8505088080182440 * q^70 + 4824462822979508 * q^71 + 1180071997284592 * q^72 + 11228916281304662 * q^73 - 89132715356772 * q^74 + 59161419576630296 * q^75 + 57466858643173460 * q^76 + 58741564492720064 * q^77 + 142050530910210210 * q^78 + 71718598015696758 * q^79 + 48350023652407550 * q^80 + 75805931446703569 * q^81 + 188661890754420812 * q^82 + 50769377111735608 * q^83 + 198832046985593048 * q^84 + 53422044849490784 * q^85 + 35014892323844118 * q^86 + 11988905533023326 * q^87 + 37459283979085258 * q^88 - 70981414576978018 * q^89 + 57211029866143724 * q^90 + 112933943315157320 * q^91 - 103019729095759724 * q^92 - 350358290646906646 * q^93 - 150286322409612578 * q^94 - 102561321856584476 * q^95 - 213770098354021866 * q^96 - 130930167251505210 * q^97 - 537387515497557296 * q^98 - 95267700931431064 * q^99

Introduction

L-functions

Modular forms

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