LMFDB - Embedded newform 29.18.a.a.1.7

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:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 1610997 x^{16} - 28978880 x^{15} + 1054878119348 x^{14} + 33471007935200 x^{13} + \cdots - 13\!\cdots\!24 $ x^18 - 1610997x^16 - 28978880x^15 + 1054878119348x^14 + 33471007935200x^13 - 361118629330503872x^12 - 14867597249727884800x^11 + 69075461759211999549440x^10 + 3136429534292709271797760x^9 - 7293684107327839501793427456x^8 - 310705174164268019482139033600x^7 + 392089226833876108917621043232768x^6 + 11987811702756552456984769970831360x^5 - 8875073388959894229615422940880306176x^4 - 110123126416280653106554268008725872640x^3 + 38261887665727248243207924189998746697728x^2 - 570869901591701973911550639846099485982720x - 1366002559879573583573099965753694433050624
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{14}\cdot 17 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-235.315$ of defining polynomial
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)

$f(q)$	$=$	$q-235.315 q^{2} +964.844 q^{3} -75699.1 q^{4} +864499. q^{5} -227042. q^{6} +6.42601e6 q^{7} +4.86562e7 q^{8} -1.28209e8 q^{9} +O(q^{10})$	\(q-235.315 q^{2} +964.844 q^{3} -75699.1 q^{4} +864499. q^{5} -227042. q^{6} +6.42601e6 q^{7} +4.86562e7 q^{8} -1.28209e8 q^{9} -2.03429e8 q^{10} -1.22622e9 q^{11} -7.30378e7 q^{12} +3.51464e9 q^{13} -1.51213e9 q^{14} +8.34106e8 q^{15} -1.52749e9 q^{16} +2.92416e10 q^{17} +3.01695e10 q^{18} -1.20021e11 q^{19} -6.54417e10 q^{20} +6.20010e9 q^{21} +2.88547e11 q^{22} +6.15733e11 q^{23} +4.69457e10 q^{24} -1.55816e10 q^{25} -8.27046e11 q^{26} -2.48302e11 q^{27} -4.86443e11 q^{28} -5.00246e11 q^{29} -1.96277e11 q^{30} +7.49036e12 q^{31} -6.01803e12 q^{32} -1.18311e12 q^{33} -6.88099e12 q^{34} +5.55528e12 q^{35} +9.70532e12 q^{36} +1.39489e13 q^{37} +2.82428e13 q^{38} +3.39108e12 q^{39} +4.20633e13 q^{40} -1.24069e13 q^{41} -1.45897e12 q^{42} -5.66242e13 q^{43} +9.28234e13 q^{44} -1.10837e14 q^{45} -1.44891e14 q^{46} -1.16597e14 q^{47} -1.47379e12 q^{48} -1.91337e14 q^{49} +3.66657e12 q^{50} +2.82136e13 q^{51} -2.66055e14 q^{52} +1.72106e14 q^{53} +5.84291e13 q^{54} -1.06006e15 q^{55} +3.12666e14 q^{56} -1.15802e14 q^{57} +1.17715e14 q^{58} -1.37053e15 q^{59} -6.31410e13 q^{60} -4.28372e14 q^{61} -1.76259e15 q^{62} -8.23874e14 q^{63} +1.61634e15 q^{64} +3.03840e15 q^{65} +2.78402e14 q^{66} -5.49067e15 q^{67} -2.21357e15 q^{68} +5.94086e14 q^{69} -1.30724e15 q^{70} -7.52839e15 q^{71} -6.23818e15 q^{72} -1.29545e15 q^{73} -3.28239e15 q^{74} -1.50338e13 q^{75} +9.08551e15 q^{76} -7.87969e15 q^{77} -7.97970e14 q^{78} +1.35498e16 q^{79} -1.32052e15 q^{80} +1.63174e16 q^{81} +2.91952e15 q^{82} -3.76750e16 q^{83} -4.69342e14 q^{84} +2.52794e16 q^{85} +1.33245e16 q^{86} -4.82660e14 q^{87} -5.96631e16 q^{88} -2.31223e16 q^{89} +2.60815e16 q^{90} +2.25851e16 q^{91} -4.66104e16 q^{92} +7.22703e15 q^{93} +2.74370e16 q^{94} -1.03758e17 q^{95} -5.80646e15 q^{96} -6.79954e16 q^{97} +4.50243e16 q^{98} +1.57212e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) $ 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9} - 1301706588 q^{10} + 414318256 q^{11} + 4613809340 q^{12} - 1708529620 q^{13} - 10178671680 q^{14} - 35937136948 q^{15} + 13408243234 q^{16} - 31137019060 q^{17} - 216144895280 q^{18} - 236294644572 q^{19} - 343491571178 q^{20} + 292681980344 q^{21} + 237072099770 q^{22} + 448660830360 q^{23} + 1331075294514 q^{24} + 3016314845934 q^{25} + 4625052436620 q^{26} - 3633286593580 q^{27} - 5255043772340 q^{28} - 9004435433298 q^{29} + 11322123726866 q^{30} + 4286667897456 q^{31} + 20489566928480 q^{32} + 12272773628920 q^{33} - 29135914295852 q^{34} - 34335586657384 q^{35} - 34363200450796 q^{36} - 33745027570060 q^{37} - 96773461186360 q^{38} - 104536576294796 q^{39} - 136020881729180 q^{40} - 62894681812676 q^{41} - 363718470035260 q^{42} + 43558449431040 q^{43} - 49608048285572 q^{44} + 133812803620916 q^{45} - 219540697042836 q^{46} - 141597817069240 q^{47} - 267256681151460 q^{48} + 453054608269810 q^{49} - 13\!\cdots\!40 q^{50}+ \cdots + 11\!\cdots\!56 q^{99}+O(q^{100}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9 - 1301706588 * q^10 + 414318256 * q^11 + 4613809340 * q^12 - 1708529620 * q^13 - 10178671680 * q^14 - 35937136948 * q^15 + 13408243234 * q^16 - 31137019060 * q^17 - 216144895280 * q^18 - 236294644572 * q^19 - 343491571178 * q^20 + 292681980344 * q^21 + 237072099770 * q^22 + 448660830360 * q^23 + 1331075294514 * q^24 + 3016314845934 * q^25 + 4625052436620 * q^26 - 3633286593580 * q^27 - 5255043772340 * q^28 - 9004435433298 * q^29 + 11322123726866 * q^30 + 4286667897456 * q^31 + 20489566928480 * q^32 + 12272773628920 * q^33 - 29135914295852 * q^34 - 34335586657384 * q^35 - 34363200450796 * q^36 - 33745027570060 * q^37 - 96773461186360 * q^38 - 104536576294796 * q^39 - 136020881729180 * q^40 - 62894681812676 * q^41 - 363718470035260 * q^42 + 43558449431040 * q^43 - 49608048285572 * q^44 + 133812803620916 * q^45 - 219540697042836 * q^46 - 141597817069240 * q^47 - 267256681151460 * q^48 + 453054608269810 * q^49 - 1348659632272640 * q^50 - 1366163894523096 * q^51 - 1312273323620630 * q^52 - 485951074130100 * q^53 - 1795598060978246 * q^54 - 3426804650590972 * q^55 - 5564818824556288 * q^56 - 5205401672025040 * q^57 - 4547356113106800 * q^59 - 13819026055113000 * q^60 - 6121039899052148 * q^61 - 10199136673985490 * q^62 - 14641672030091800 * q^63 - 9962823646631806 * q^64 - 13420652091655824 * q^65 - 27721841054867288 * q^66 - 17715742779810920 * q^67 - 24471819430698220 * q^68 - 17159735572757960 * q^69 + 9006543780480744 * q^70 - 18877957007949512 * q^71 - 44531687124196680 * q^72 - 11641701802444700 * q^73 - 53655919274849056 * q^74 - 21032918050227748 * q^75 - 66122191206313032 * q^76 - 8842889451812280 * q^77 - 28799653307053650 * q^78 - 44197796400782136 * q^79 - 157325108946937442 * q^80 - 41532487375317502 * q^81 - 65440892426610260 * q^82 - 9547427423528400 * q^83 - 54796688181105048 * q^84 - 34123627920307712 * q^85 - 119642903919749046 * q^86 + 7703794759599400 * q^87 - 114332767598176050 * q^88 - 48534239108944036 * q^89 + 56810599078278752 * q^90 - 104774225723277192 * q^91 - 3343093822255980 * q^92 + 128149288210966200 * q^93 + 83032272917645478 * q^94 + 200021462885519192 * q^95 + 140361624410708610 * q^96 + 53343624485398380 * q^97 + 448366099002416160 * q^98 + 117966192294311356 * 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 $

$2$	−235.315	−0.649971	−0.324985	−	0.945719i	$-0.605359\pi$
$2$	−235.315	−0.649971	−0.324985	+	0.945719i	$0.605359\pi$
$3$	964.844	0.0849036	0.0424518	−	0.999099i	$-0.486483\pi$
$3$	964.844	0.0849036	0.0424518	+	0.999099i	$0.486483\pi$
$4$	−75699.1	−0.577538
$5$	864499.	0.989736	0.494868	−	0.868968i	$-0.335216\pi$
$5$	864499.	0.989736	0.494868	+	0.868968i	$0.335216\pi$
$6$	−227042.	−0.0551849
$7$	6.42601e6	0.421316	0.210658	−	0.977560i	$-0.432439\pi$
$7$	6.42601e6	0.421316	0.210658	+	0.977560i	$0.432439\pi$
$8$	4.86562e7	1.02535
$9$	−1.28209e8	−0.992791
$10$	−2.03429e8	−0.643299
$11$	−1.22622e9	−1.72476	−0.862381	−	0.506259i	$-0.831028\pi$
$11$	−1.22622e9	−1.72476	−0.862381	+	0.506259i	$0.831028\pi$
$12$	−7.30378e7	−0.0490351
$13$	3.51464e9	1.19498	0.597492	−	0.801875i	$-0.296164\pi$
$13$	3.51464e9	1.19498	0.597492	+	0.801875i	$0.296164\pi$
$14$	−1.51213e9	−0.273843
$15$	8.34106e8	0.0840322
$16$	−1.52749e9	−0.0889119
$17$	2.92416e10	1.01668	0.508342	−	0.861155i	$-0.330259\pi$
$17$	2.92416e10	1.01668	0.508342	+	0.861155i	$0.330259\pi$
$18$	3.01695e10	0.645285
$19$	−1.20021e11	−1.62126	−0.810631	−	0.585557i	$-0.800876\pi$
$19$	−1.20021e11	−1.62126	−0.810631	+	0.585557i	$0.800876\pi$
$20$	−6.54417e10	−0.571610
$21$	6.20010e9	0.0357713
$22$	2.88547e11	1.12105
$23$	6.15733e11	1.63948	0.819739	−	0.572738i	$-0.194119\pi$
$23$	6.15733e11	1.63948	0.819739	+	0.572738i	$0.194119\pi$
$24$	4.69457e10	0.0870563
$25$	−1.55816e10	−0.0204231
$26$	−8.27046e11	−0.776705
$27$	−2.48302e11	−0.169195
$28$	−4.86443e11	−0.243326
$29$	−5.00246e11	−0.185695
$29$	−5.00246e11	−0.185695
$30$	−1.96277e11	−0.0546185
$31$	7.49036e12	1.57735	0.788675	−	0.614810i	$-0.210767\pi$
$31$	7.49036e12	1.57735	0.788675	+	0.614810i	$0.210767\pi$
$32$	−6.01803e12	−0.967563
$33$	−1.18311e12	−0.146439
$34$	−6.88099e12	−0.660815
$35$	5.55528e12	0.416992
$36$	9.70532e12	0.573375
$37$	1.39489e13	0.652870	0.326435	−	0.945220i	$-0.394153\pi$
$37$	1.39489e13	0.652870	0.326435	+	0.945220i	$0.394153\pi$
$38$	2.82428e13	1.05377
$39$	3.39108e12	0.101459
$40$	4.20633e13	1.01483
$41$	−1.24069e13	−0.242661	−0.121330	−	0.992612i	$-0.538716\pi$
$41$	−1.24069e13	−0.242661	−0.121330	+	0.992612i	$0.538716\pi$
$42$	−1.45897e12	−0.0232503
$43$	−5.66242e13	−0.738789	−0.369394	−	0.929273i	$-0.620435\pi$
$43$	−5.66242e13	−0.738789	−0.369394	+	0.929273i	$0.620435\pi$
$44$	9.28234e13	0.996116
$45$	−1.10837e14	−0.982601
$46$	−1.44891e14	−1.06561
$47$	−1.16597e14	−0.714260	−0.357130	−	0.934055i	$-0.616245\pi$
$47$	−1.16597e14	−0.714260	−0.357130	+	0.934055i	$0.616245\pi$
$48$	−1.47379e12	−0.00754895
$49$	−1.91337e14	−0.822493
$50$	3.66657e12	0.0132744
$51$	2.82136e13	0.0863202
$52$	−2.66055e14	−0.690149
$53$	1.72106e14	0.379709	0.189854	−	0.981812i	$-0.439198\pi$
$53$	1.72106e14	0.379709	0.189854	+	0.981812i	$0.439198\pi$
$54$	5.84291e13	0.109972
$55$	−1.06006e15	−1.70706
$56$	3.12666e14	0.431998
$57$	−1.15802e14	−0.137651
$58$	1.17715e14	0.120697
$59$	−1.37053e15	−1.21520	−0.607599	−	0.794244i	$-0.707867\pi$
$59$	−1.37053e15	−1.21520	−0.607599	+	0.794244i	$0.707867\pi$
$60$	−6.31410e13	−0.0485318
$61$	−4.28372e14	−0.286100	−0.143050	−	0.989715i	$-0.545691\pi$
$61$	−4.28372e14	−0.286100	−0.143050	+	0.989715i	$0.545691\pi$
$62$	−1.76259e15	−1.02523
$63$	−8.23874e14	−0.418279
$64$	1.61634e15	0.717800
$65$	3.03840e15	1.18272
$66$	2.78402e14	0.0951808
$67$	−5.49067e15	−1.65192	−0.825960	−	0.563728i	$-0.809367\pi$
$67$	−5.49067e15	−1.65192	−0.825960	+	0.563728i	$0.809367\pi$
$68$	−2.21357e15	−0.587174
$69$	5.94086e14	0.139198
$70$	−1.30724e15	−0.271033
$71$	−7.52839e15	−1.38359	−0.691793	−	0.722096i	$-0.743179\pi$
$71$	−7.52839e15	−1.38359	−0.691793	+	0.722096i	$0.743179\pi$
$72$	−6.23818e15	−1.01796
$73$	−1.29545e15	−0.188008	−0.0940042	−	0.995572i	$-0.529967\pi$
$73$	−1.29545e15	−0.188008	−0.0940042	+	0.995572i	$0.529967\pi$
$74$	−3.28239e15	−0.424346
$75$	−1.50338e13	−0.00173399
$76$	9.08551e15	0.936341
$77$	−7.87969e15	−0.726671
$78$	−7.97970e14	−0.0659451
$79$	1.35498e16	1.00485	0.502427	−	0.864620i	$-0.332440\pi$
$79$	1.35498e16	1.00485	0.502427	+	0.864620i	$0.332440\pi$
$80$	−1.32052e15	−0.0879993
$81$	1.63174e16	0.978426
$82$	2.91952e15	0.157722
$83$	−3.76750e16	−1.83607	−0.918035	−	0.396499i	$-0.870225\pi$
$83$	−3.76750e16	−1.83607	−0.918035	+	0.396499i	$0.870225\pi$
$84$	−4.69342e14	−0.0206593
$85$	2.52794e16	1.00625
$86$	1.33245e16	0.480191
$87$	−4.82660e14	−0.0157662
$88$	−5.96631e16	−1.76849
$89$	−2.31223e16	−0.622610	−0.311305	−	0.950310i	$-0.600766\pi$
$89$	−2.31223e16	−0.622610	−0.311305	+	0.950310i	$0.600766\pi$
$90$	2.60815e16	0.638662
$91$	2.25851e16	0.503467
$92$	−4.66104e16	−0.946861
$93$	7.22703e15	0.133923
$94$	2.74370e16	0.464248
$95$	−1.03758e17	−1.60462
$96$	−5.80646e15	−0.0821497
$97$	−6.79954e16	−0.880886	−0.440443	−	0.897781i	$-0.645179\pi$
$97$	−6.79954e16	−0.880886	−0.440443	+	0.897781i	$0.645179\pi$
$98$	4.50243e16	0.534596
$99$	1.57212e17	1.71233
$100$	1.17951e15	0.0117951
$101$	1.01451e17	0.932230	0.466115	−	0.884724i	$-0.345653\pi$
$101$	1.01451e17	0.932230	0.466115	+	0.884724i	$0.345653\pi$
$102$	−6.63908e15	−0.0561056
$103$	−4.64446e16	−0.361259	−0.180630	−	0.983551i	$-0.557814\pi$
$103$	−4.64446e16	−0.361259	−0.180630	+	0.983551i	$0.557814\pi$
$104$	1.71009e17	1.22528
$105$	5.35998e15	0.0354041
$106$	−4.04990e16	−0.246800
$107$	−1.52685e17	−0.859083	−0.429542	−	0.903047i	$-0.641325\pi$
$107$	−1.52685e17	−0.859083	−0.429542	+	0.903047i	$0.641325\pi$
$108$	1.87962e16	0.0977167
$109$	−2.04411e16	−0.0982607	−0.0491303	−	0.998792i	$-0.515645\pi$
$109$	−2.04411e16	−0.0982607	−0.0491303	+	0.998792i	$0.515645\pi$
$110$	2.49448e17	1.10954
$111$	1.34586e16	0.0554310
$112$	−9.81570e15	−0.0374600
$113$	1.45317e17	0.514221	0.257110	−	0.966382i	$-0.417230\pi$
$113$	1.45317e17	0.514221	0.257110	+	0.966382i	$0.417230\pi$
$114$	2.72499e16	0.0894692
$115$	5.32300e17	1.62265
$116$	3.78682e16	0.107246
$117$	−4.50609e17	−1.18637
$118$	3.22506e17	0.789844
$119$	1.87907e17	0.428346
$120$	4.05845e16	0.0861627
$121$	9.98160e17	1.97481
$122$	1.00802e17	0.185957
$123$	−1.19707e16	−0.0206028
$124$	−5.67013e17	−0.910980
$125$	−6.73030e17	−1.00995
$126$	1.93870e17	0.271869
$127$	9.17335e17	1.20281	0.601404	−	0.798945i	$-0.294608\pi$
$127$	9.17335e17	1.20281	0.601404	+	0.798945i	$0.294608\pi$
$128$	4.08446e17	0.501014
$129$	−5.46335e16	−0.0627259
$130$	−7.14980e17	−0.768733
$131$	−1.07047e18	−1.07837	−0.539186	−	0.842186i	$-0.681268\pi$
$131$	−1.07047e18	−1.07837	−0.539186	+	0.842186i	$0.681268\pi$
$132$	8.95601e16	0.0845739
$133$	−7.71260e17	−0.683064
$134$	1.29203e18	1.07370
$135$	−2.14657e17	−0.167459
$136$	1.42279e18	1.04246
$137$	2.61631e17	0.180121	0.0900604	−	0.995936i	$-0.471294\pi$
$137$	2.61631e17	0.180121	0.0900604	+	0.995936i	$0.471294\pi$
$138$	−1.39797e17	−0.0904744
$139$	−2.12047e18	−1.29064	−0.645322	−	0.763910i	$-0.723277\pi$
$139$	−2.12047e18	−1.29064	−0.645322	+	0.763910i	$0.723277\pi$
$140$	−4.20530e17	−0.240829
$141$	−1.12498e17	−0.0606433
$142$	1.77154e18	0.899290
$143$	−4.30971e18	−2.06107
$144$	1.95839e17	0.0882710
$145$	−4.32462e17	−0.183789
$146$	3.04839e17	0.122200
$147$	−1.84610e17	−0.0698326
$148$	−1.05592e18	−0.377057
$149$	−5.56945e18	−1.87814	−0.939072	−	0.343721i	$-0.888313\pi$
$149$	−5.56945e18	−1.87814	−0.939072	+	0.343721i	$0.888313\pi$
$150$	3.53766e15	0.00112704
$151$	4.34938e18	1.30955	0.654777	−	0.755822i	$-0.272762\pi$
$151$	4.34938e18	1.30955	0.654777	+	0.755822i	$0.272762\pi$
$152$	−5.83979e18	−1.66237
$153$	−3.74905e18	−1.00936
$154$	1.85420e18	0.472315
$155$	6.47541e18	1.56116
$156$	−2.56701e17	−0.0585962
$157$	−3.33153e18	−0.720271	−0.360136	−	0.932900i	$-0.617270\pi$
$157$	−3.33153e18	−0.720271	−0.360136	+	0.932900i	$0.617270\pi$
$158$	−3.18847e18	−0.653126
$159$	1.66055e17	0.0322387
$160$	−5.20258e18	−0.957632
$161$	3.95671e18	0.690739
$162$	−3.83972e18	−0.635948
$163$	−3.07172e18	−0.482822	−0.241411	−	0.970423i	$-0.577610\pi$
$163$	−3.07172e18	−0.482822	−0.241411	+	0.970423i	$0.577610\pi$
$164$	9.39188e17	0.140146
$165$	−1.02279e18	−0.144936
$166$	8.86547e18	1.19339
$167$	−1.97071e16	−0.00252076	−0.00126038	−	0.999999i	$-0.500401\pi$
$167$	−1.97071e16	−0.00252076	−0.00126038	+	0.999999i	$0.500401\pi$
$168$	3.01674e17	0.0366782
$169$	3.70228e18	0.427989
$170$	−5.94860e18	−0.654032
$171$	1.53879e19	1.60958
$172$	4.28640e18	0.426679
$173$	−5.55314e18	−0.526195	−0.263098	−	0.964769i	$-0.584744\pi$
$173$	−5.55314e18	−0.526195	−0.263098	+	0.964769i	$0.584744\pi$
$174$	1.13577e17	0.0102476
$175$	−1.00127e17	−0.00860457
$176$	1.87304e18	0.153352
$177$	−1.32235e18	−0.103175
$178$	5.44102e18	0.404679
$179$	−8.82921e18	−0.626139	−0.313070	−	0.949730i	$-0.601357\pi$
$179$	−8.82921e18	−0.626139	−0.313070	+	0.949730i	$0.601357\pi$
$180$	8.39023e18	0.567489
$181$	−2.48836e19	−1.60563	−0.802815	−	0.596228i	$-0.796666\pi$
$181$	−2.48836e19	−1.60563	−0.802815	+	0.596228i	$0.796666\pi$
$182$	−5.31461e18	−0.327239
$183$	−4.13312e17	−0.0242909
$184$	2.99592e19	1.68104
$185$	1.20588e19	0.646169
$186$	−1.70062e18	−0.0870459
$187$	−3.58566e19	−1.75354
$188$	8.82629e18	0.412512
$189$	−1.59559e18	−0.0712847
$190$	2.44159e19	1.04296
$191$	3.09045e19	1.26252	0.631260	−	0.775571i	$-0.282538\pi$
$191$	3.09045e19	1.26252	0.631260	+	0.775571i	$0.282538\pi$
$192$	1.55952e18	0.0609438
$193$	3.91480e19	1.46377	0.731884	−	0.681429i	$-0.238641\pi$
$193$	3.91480e19	1.46377	0.731884	+	0.681429i	$0.238641\pi$
$194$	1.60003e19	0.572550
$195$	2.93158e18	0.100417
$196$	1.44840e19	0.475021
$197$	4.36031e19	1.36948	0.684738	−	0.728789i	$-0.259917\pi$
$197$	4.36031e19	1.36948	0.684738	+	0.728789i	$0.259917\pi$
$198$	−3.69943e19	−1.11296
$199$	−4.62733e19	−1.33377	−0.666883	−	0.745162i	$-0.732372\pi$
$199$	−4.62733e19	−1.33377	−0.666883	+	0.745162i	$0.732372\pi$
$200$	−7.58140e17	−0.0209409
$201$	−5.29764e18	−0.140254
$202$	−2.38728e19	−0.605922
$203$	−3.21459e18	−0.0782365
$204$	−2.13574e18	−0.0498532
$205$	−1.07257e19	−0.240170
$206$	1.09291e19	0.234808
$207$	−7.89426e19	−1.62766
$208$	−5.36860e18	−0.106248
$209$	1.47172e20	2.79629
$210$	−1.26128e18	−0.0230117
$211$	−1.03447e20	−1.81267	−0.906333	−	0.422565i	$-0.861130\pi$
$211$	−1.03447e20	−1.81267	−0.906333	+	0.422565i	$0.861130\pi$
$212$	−1.30283e19	−0.219296
$213$	−7.26372e18	−0.117471
$214$	3.59291e19	0.558379
$215$	−4.89516e19	−0.731206
$216$	−1.20814e19	−0.173485
$217$	4.81332e19	0.664564
$218$	4.81010e18	0.0638666
$219$	−1.24991e18	−0.0159626
$220$	8.02457e19	0.985892
$221$	1.02774e20	1.21492
$222$	−3.16699e18	−0.0360286
$223$	1.04390e20	1.14306	0.571528	−	0.820583i	$-0.306351\pi$
$223$	1.04390e20	1.14306	0.571528	+	0.820583i	$0.306351\pi$
$224$	−3.86719e19	−0.407650
$225$	1.99770e18	0.0202758
$226$	−3.41952e19	−0.334228
$227$	3.80934e19	0.358616	0.179308	−	0.983793i	$-0.442614\pi$
$227$	3.80934e19	0.358616	0.179308	+	0.983793i	$0.442614\pi$
$228$	8.76610e18	0.0794987
$229$	−1.14534e20	−1.00077	−0.500385	−	0.865803i	$-0.666808\pi$
$229$	−1.14534e20	−1.00077	−0.500385	+	0.865803i	$0.666808\pi$
$230$	−1.25258e20	−1.05467
$231$	−7.60267e18	−0.0616970
$232$	−2.43401e19	−0.190403
$233$	−1.69099e20	−1.27531	−0.637656	−	0.770321i	$-0.720096\pi$
$233$	−1.69099e20	−1.27531	−0.637656	+	0.770321i	$0.720096\pi$
$234$	1.06035e20	0.771106
$235$	−1.00798e20	−0.706928
$236$	1.03748e20	0.701823
$237$	1.30735e19	0.0853158
$238$	−4.42173e19	−0.278412
$239$	1.06921e20	0.649655	0.324827	−	0.945773i	$-0.394694\pi$
$239$	1.06921e20	0.649655	0.324827	+	0.945773i	$0.394694\pi$
$240$	−1.27409e18	−0.00747146
$241$	1.34869e20	0.763426	0.381713	−	0.924281i	$-0.375334\pi$
$241$	1.34869e20	0.763426	0.381713	+	0.924281i	$0.375334\pi$
$242$	−2.34882e20	−1.28357
$243$	4.78095e19	0.252267
$244$	3.24274e19	0.165234
$245$	−1.65410e20	−0.814050
$246$	2.81688e18	0.0133912
$247$	−4.21832e20	−1.93738
$248$	3.64453e20	1.61734
$249$	−3.63505e19	−0.155889
$250$	1.58374e20	0.656437
$251$	−2.96558e20	−1.18818	−0.594090	−	0.804399i	$-0.702488\pi$
$251$	−2.96558e20	−1.18818	−0.594090	+	0.804399i	$0.702488\pi$
$252$	6.23665e19	0.241572
$253$	−7.55021e20	−2.82771
$254$	−2.15862e20	−0.781790
$255$	2.43906e19	0.0854342
$256$	−3.07971e20	−1.04344
$257$	1.93754e20	0.635065	0.317532	−	0.948247i	$-0.397146\pi$
$257$	1.93754e20	0.635065	0.317532	+	0.948247i	$0.397146\pi$
$258$	1.28561e19	0.0407700
$259$	8.96361e19	0.275065
$260$	−2.30004e20	−0.683065
$261$	6.41362e19	0.184357
$262$	2.51897e20	0.700911
$263$	3.72142e20	1.00250	0.501250	−	0.865302i	$-0.332874\pi$
$263$	3.72142e20	1.00250	0.501250	+	0.865302i	$0.332874\pi$
$264$	−5.75656e19	−0.150151
$265$	1.48785e20	0.375811
$266$	1.81489e20	0.443972
$267$	−2.23094e19	−0.0528619
$268$	4.15638e20	0.954047
$269$	5.83680e18	0.0129802	0.00649008	−	0.999979i	$-0.497934\pi$
$269$	5.83680e18	0.0129802	0.00649008	+	0.999979i	$0.497934\pi$
$270$	5.05118e19	0.108843
$271$	1.13848e20	0.237731	0.118865	−	0.992910i	$-0.462074\pi$
$271$	1.13848e20	0.237731	0.118865	+	0.992910i	$0.462074\pi$
$272$	−4.46665e19	−0.0903953
$273$	2.17911e19	0.0427462
$274$	−6.15655e19	−0.117073
$275$	1.91064e19	0.0352249
$276$	−4.49717e19	−0.0803919
$277$	2.37600e20	0.411877	0.205939	−	0.978565i	$-0.433975\pi$
$277$	2.37600e20	0.411877	0.205939	+	0.978565i	$0.433975\pi$
$278$	4.98978e20	0.838881
$279$	−9.60333e20	−1.56598
$280$	2.70299e20	0.427564
$281$	−5.22791e20	−0.802277	−0.401139	−	0.916017i	$-0.631385\pi$
$281$	−5.22791e20	−0.802277	−0.401139	+	0.916017i	$0.631385\pi$
$282$	2.64724e19	0.0394163
$283$	2.73182e19	0.0394700	0.0197350	−	0.999805i	$-0.493718\pi$
$283$	2.73182e19	0.0394700	0.0197350	+	0.999805i	$0.493718\pi$
$284$	5.69892e20	0.799073
$285$	−1.00111e20	−0.136238
$286$	1.01414e21	1.33963
$287$	−7.97267e19	−0.102237
$288$	7.71567e20	0.960589
$289$	2.78337e19	0.0336464
$290$	1.01765e20	0.119458
$291$	−6.56049e19	−0.0747904
$292$	9.80645e19	0.108582
$293$	−5.36491e20	−0.577016	−0.288508	−	0.957477i	$-0.593159\pi$
$293$	−5.36491e20	−0.577016	−0.288508	+	0.957477i	$0.593159\pi$
$294$	4.34415e19	0.0453892
$295$	−1.18482e21	−1.20273
$296$	6.78703e20	0.669423
$297$	3.04472e20	0.291822
$298$	1.31057e21	1.22074
$299$	2.16408e21	1.95915
$300$	1.13804e18	0.00100145
$301$	−3.63868e20	−0.311264
$302$	−1.02347e21	−0.851172
$303$	9.78840e19	0.0791497
$304$	1.83332e20	0.144150
$305$	−3.70327e20	−0.283163
$306$	8.82206e20	0.656051
$307$	−1.77509e20	−0.128394	−0.0641968	−	0.997937i	$-0.520449\pi$
$307$	−1.77509e20	−0.128394	−0.0641968	+	0.997937i	$0.520449\pi$
$308$	5.96485e20	0.419680
$309$	−4.48118e19	−0.0306722
$310$	−1.52376e21	−1.01471
$311$	1.30986e21	0.848717	0.424359	−	0.905494i	$-0.360500\pi$
$311$	1.30986e21	0.848717	0.424359	+	0.905494i	$0.360500\pi$
$312$	1.64997e20	0.104031
$313$	−1.25353e21	−0.769143	−0.384572	−	0.923095i	$-0.625651\pi$
$313$	−1.25353e21	−0.769143	−0.384572	+	0.923095i	$0.625651\pi$
$314$	7.83956e20	0.468155
$315$	−7.12238e20	−0.413986
$316$	−1.02571e21	−0.580342
$317$	2.93174e21	1.61481	0.807406	−	0.589996i	$-0.200871\pi$
$317$	2.93174e21	1.61481	0.807406	+	0.589996i	$0.200871\pi$
$318$	−3.90752e19	−0.0209542
$319$	6.13410e20	0.320280
$320$	1.39733e21	0.710432
$321$	−1.47318e20	−0.0729393
$322$	−9.31071e20	−0.448960
$323$	−3.50963e21	−1.64831
$324$	−1.23521e21	−0.565078
$325$	−5.47636e19	−0.0244052
$326$	7.22821e20	0.313820
$327$	−1.97225e19	−0.00834269
$328$	−6.03671e20	−0.248813
$329$	−7.49255e20	−0.300929
$330$	2.40678e20	0.0942039
$331$	2.10501e21	0.803002	0.401501	−	0.915859i	$-0.368489\pi$
$331$	2.10501e21	0.803002	0.401501	+	0.915859i	$0.368489\pi$
$332$	2.85196e21	1.06040
$333$	−1.78838e21	−0.648164
$334$	4.63736e18	0.00163842
$335$	−4.74667e21	−1.63497
$336$	−9.47062e18	−0.00318049
$337$	−3.13923e21	−1.02794	−0.513971	−	0.857807i	$-0.671826\pi$
$337$	−3.13923e21	−1.02794	−0.513971	+	0.857807i	$0.671826\pi$
$338$	−8.71201e20	−0.278180
$339$	1.40208e20	0.0436592
$340$	−1.91362e21	−0.581147
$341$	−9.18480e21	−2.72056
$342$	−3.62099e21	−1.04618
$343$	−2.72442e21	−0.767846
$344$	−2.75512e21	−0.757520
$345$	5.13586e20	0.137769
$346$	1.30673e21	0.342011
$347$	4.55274e21	1.16271	0.581357	−	0.813649i	$-0.302522\pi$
$347$	4.55274e21	1.16271	0.581357	+	0.813649i	$0.302522\pi$
$348$	3.65369e19	0.00910559
$349$	−2.59082e21	−0.630117	−0.315059	−	0.949072i	$-0.602024\pi$
$349$	−2.59082e21	−0.630117	−0.315059	+	0.949072i	$0.602024\pi$
$350$	2.35614e19	0.00559272
$351$	−8.72692e20	−0.202186
$352$	7.37941e21	1.66882
$353$	6.99625e21	1.54447	0.772237	−	0.635335i	$-0.219138\pi$
$353$	6.99625e21	1.54447	0.772237	+	0.635335i	$0.219138\pi$
$354$	3.11168e20	0.0670606
$355$	−6.50828e21	−1.36938
$356$	1.75034e21	0.359581
$357$	1.81301e20	0.0363681
$358$	2.07764e21	0.406972
$359$	5.91939e21	1.13233	0.566166	−	0.824291i	$-0.308426\pi$
$359$	5.91939e21	1.13233	0.566166	+	0.824291i	$0.308426\pi$
$360$	−5.39290e21	−1.00751
$361$	8.92477e21	1.62849
$362$	5.85548e21	1.04361
$363$	9.63069e20	0.167668
$364$	−1.70967e21	−0.290771
$365$	−1.11992e21	−0.186079
$366$	9.72584e19	0.0157884
$367$	−4.79957e21	−0.761274	−0.380637	−	0.924725i	$-0.624295\pi$
$367$	−4.79957e21	−0.761274	−0.380637	+	0.924725i	$0.624295\pi$
$368$	−9.40528e20	−0.145769
$369$	1.59067e21	0.240911
$370$	−2.83762e21	−0.419991
$371$	1.10595e21	0.159978
$372$	−5.47079e20	−0.0773455
$373$	−8.28472e21	−1.14486	−0.572430	−	0.819953i	$-0.693999\pi$
$373$	−8.28472e21	−1.14486	−0.572430	+	0.819953i	$0.693999\pi$
$374$	8.43758e21	1.13975
$375$	−6.49369e20	−0.0857484
$376$	−5.67318e21	−0.732369
$377$	−1.75819e21	−0.221903
$378$	3.75466e20	0.0463330
$379$	6.88259e21	0.830460	0.415230	−	0.909716i	$-0.363701\pi$
$379$	6.88259e21	0.830460	0.415230	+	0.909716i	$0.363701\pi$
$380$	7.85441e21	0.926730
$381$	8.85085e20	0.102123
$382$	−7.27228e21	−0.820601
$383$	−3.03935e21	−0.335421	−0.167711	−	0.985836i	$-0.553637\pi$
$383$	−3.03935e21	−0.335421	−0.167711	+	0.985836i	$0.553637\pi$
$384$	3.94087e20	0.0425380
$385$	−6.81198e21	−0.719212
$386$	−9.21210e21	−0.951407
$387$	7.25975e21	0.733463
$388$	5.14719e21	0.508745
$389$	7.07580e21	0.684233	0.342117	−	0.939658i	$-0.388856\pi$
$389$	7.07580e21	0.684233	0.342117	+	0.939658i	$0.388856\pi$
$390$	−6.89844e20	−0.0652682
$391$	1.80050e22	1.66683
$392$	−9.30973e21	−0.843346
$393$	−1.03284e21	−0.0915578
$394$	−1.02604e22	−0.890120
$395$	1.17138e22	0.994540
$396$	−1.19008e22	−0.988935
$397$	1.89047e22	1.53762	0.768812	−	0.639475i	$-0.220848\pi$
$397$	1.89047e22	1.53762	0.768812	+	0.639475i	$0.220848\pi$
$398$	1.08888e22	0.866909
$399$	−7.44145e20	−0.0579947
$400$	2.38007e19	0.00181585
$401$	−9.59201e20	−0.0716445	−0.0358222	−	0.999358i	$-0.511405\pi$
$401$	−9.59201e20	−0.0716445	−0.0358222	+	0.999358i	$0.511405\pi$
$402$	1.24661e21	0.0911611
$403$	2.63259e22	1.88491
$404$	−7.67972e21	−0.538398
$405$	1.41064e22	0.968383
$406$	7.56440e20	0.0508514
$407$	−1.71044e22	−1.12605
$408$	1.37277e21	0.0885087
$409$	−7.85959e21	−0.496309	−0.248154	−	0.968720i	$-0.579824\pi$
$409$	−7.85959e21	−0.496309	−0.248154	+	0.968720i	$0.579824\pi$
$410$	2.52392e21	0.156103
$411$	2.52433e20	0.0152929
$412$	3.51581e21	0.208641
$413$	−8.80706e21	−0.511983
$414$	1.85763e22	1.05793
$415$	−3.25700e22	−1.81722
$416$	−2.11512e22	−1.15622
$417$	−2.04592e21	−0.109580
$418$	−3.46318e22	−1.81751
$419$	3.28453e22	1.68910	0.844548	−	0.535480i	$-0.179869\pi$
$419$	3.28453e22	1.68910	0.844548	+	0.535480i	$0.179869\pi$
$420$	−4.05745e20	−0.0204472
$421$	2.80009e21	0.138285	0.0691424	−	0.997607i	$-0.477974\pi$
$421$	2.80009e21	0.138285	0.0691424	+	0.997607i	$0.477974\pi$
$422$	2.43426e22	1.17818
$423$	1.49488e22	0.709111
$424$	8.37402e21	0.389336
$425$	−4.55630e20	−0.0207638
$426$	1.70926e21	0.0763530
$427$	−2.75273e21	−0.120539
$428$	1.15581e22	0.496153
$429$	−4.15820e21	−0.174992
$430$	1.15190e22	0.475262
$431$	4.20967e21	0.170291	0.0851454	−	0.996369i	$-0.472865\pi$
$431$	4.20967e21	0.170291	0.0851454	+	0.996369i	$0.472865\pi$
$432$	3.79280e20	0.0150435
$433$	4.48779e22	1.74536	0.872681	−	0.488291i	$-0.162380\pi$
$433$	4.48779e22	1.74536	0.872681	+	0.488291i	$0.162380\pi$
$434$	−1.13264e22	−0.431947
$435$	−4.17259e20	−0.0156044
$436$	1.54737e21	0.0567493
$437$	−7.39011e22	−2.65802
$438$	2.94122e20	0.0103752
$439$	−2.79414e22	−0.966717	−0.483359	−	0.875422i	$-0.660583\pi$
$439$	−2.79414e22	−0.966717	−0.483359	+	0.875422i	$0.660583\pi$
$440$	−5.15787e22	−1.75034
$441$	2.45312e22	0.816563
$442$	−2.41842e22	−0.789664
$443$	3.84278e22	1.23088	0.615438	−	0.788186i	$-0.288979\pi$
$443$	3.84278e22	1.23088	0.615438	+	0.788186i	$0.288979\pi$
$444$	−1.01880e21	−0.0320135
$445$	−1.99892e22	−0.616220
$446$	−2.45645e22	−0.742953
$447$	−5.37365e21	−0.159461
$448$	1.03866e22	0.302421
$449$	4.38984e22	1.25416	0.627082	−	0.778953i	$-0.284249\pi$
$449$	4.38984e22	1.25416	0.627082	+	0.778953i	$0.284249\pi$
$450$	−4.70088e20	−0.0131787
$451$	1.52135e22	0.418532
$452$	−1.10004e22	−0.296982
$453$	4.19648e21	0.111186
$454$	−8.96393e21	−0.233090
$455$	1.95248e22	0.498299
$456$	−5.63449e21	−0.141141
$457$	−2.51207e22	−0.617653	−0.308826	−	0.951118i	$-0.599936\pi$
$457$	−2.51207e22	−0.617653	−0.308826	+	0.951118i	$0.599936\pi$
$458$	2.69516e22	0.650472
$459$	−7.26076e21	−0.172018
$460$	−4.02946e22	−0.937142
$461$	3.98800e22	0.910536	0.455268	−	0.890354i	$-0.349543\pi$
$461$	3.98800e22	0.910536	0.455268	+	0.890354i	$0.349543\pi$
$462$	1.78902e21	0.0401012
$463$	−4.42518e22	−0.973852	−0.486926	−	0.873443i	$-0.661882\pi$
$463$	−4.42518e22	−0.973852	−0.486926	+	0.873443i	$0.661882\pi$
$464$	7.64124e20	0.0165105
$465$	6.24775e21	0.132548
$466$	3.97915e22	0.828915
$467$	−7.28749e22	−1.49068	−0.745341	−	0.666684i	$-0.767713\pi$
$467$	−7.28749e22	−1.49068	−0.745341	+	0.666684i	$0.767713\pi$
$468$	3.41107e22	0.685174
$469$	−3.52831e22	−0.695981
$470$	2.37193e22	0.459483
$471$	−3.21440e21	−0.0611537
$472$	−6.66850e22	−1.24601
$473$	6.94335e22	1.27424
$474$	−3.07637e21	−0.0554528
$475$	1.87012e21	0.0331111
$476$	−1.42244e22	−0.247386
$477$	−2.20656e22	−0.376972
$478$	−2.51602e22	−0.422257
$479$	−1.04057e22	−0.171561	−0.0857806	−	0.996314i	$-0.527338\pi$
$479$	−1.04057e22	−0.171561	−0.0857806	+	0.996314i	$0.527338\pi$
$480$	−5.01967e21	−0.0813065
$481$	4.90255e22	0.780170
$482$	−3.17366e22	−0.496205
$483$	3.81760e21	0.0586462
$484$	−7.55598e22	−1.14053
$485$	−5.87819e22	−0.871844
$486$	−1.12503e22	−0.163966
$487$	−4.22490e22	−0.605091	−0.302546	−	0.953135i	$-0.597836\pi$
$487$	−4.22490e22	−0.605091	−0.302546	+	0.953135i	$0.597836\pi$
$488$	−2.08430e22	−0.293353
$489$	−2.96373e21	−0.0409934
$490$	3.89235e22	0.529109
$491$	−4.11409e22	−0.549644	−0.274822	−	0.961495i	$-0.588619\pi$
$491$	−4.11409e22	−0.549644	−0.274822	+	0.961495i	$0.588619\pi$
$492$	9.06169e20	0.0118989
$493$	−1.46280e22	−0.188793
$494$	9.92633e22	1.25924
$495$	1.35910e23	1.69475
$496$	−1.14415e22	−0.140245
$497$	−4.83775e22	−0.582927
$498$	8.55380e21	0.101323
$499$	−5.15763e22	−0.600614	−0.300307	−	0.953843i	$-0.597089\pi$
$499$	−5.15763e22	−0.600614	−0.300307	+	0.953843i	$0.597089\pi$
$500$	5.09478e22	0.583284
$501$	−1.90142e19	−0.000214022 0
$502$	6.97843e22	0.772282
$503$	−1.59058e23	−1.73073	−0.865363	−	0.501145i	$-0.832912\pi$
$503$	−1.59058e23	−1.73073	−0.865363	+	0.501145i	$0.832912\pi$
$504$	−4.00866e22	−0.428884
$505$	8.77039e22	0.922661
$506$	1.77668e23	1.83793
$507$	3.57212e21	0.0363378
$508$	−6.94414e22	−0.694667
$509$	3.10306e22	0.305273	0.152637	−	0.988282i	$-0.451224\pi$
$509$	3.10306e22	0.305273	0.152637	+	0.988282i	$0.451224\pi$
$510$	−5.73947e21	−0.0555297
$511$	−8.32460e21	−0.0792110
$512$	1.89341e22	0.177194
$513$	2.98016e22	0.274310
$514$	−4.55930e22	−0.412774
$515$	−4.01513e22	−0.357551
$516$	4.13571e21	0.0362266
$517$	1.42973e23	1.23193
$518$	−2.10927e22	−0.178784
$519$	−5.35791e21	−0.0446759
$520$	1.47837e23	1.21271
$521$	6.79497e22	0.548361	0.274181	−	0.961678i	$-0.411593\pi$
$521$	6.79497e22	0.548361	0.274181	+	0.961678i	$0.411593\pi$
$522$	−1.50922e22	−0.119826
$523$	−6.38219e22	−0.498546	−0.249273	−	0.968433i	$-0.580192\pi$
$523$	−6.38219e22	−0.498546	−0.249273	+	0.968433i	$0.580192\pi$
$524$	8.10337e22	0.622801
$525$	−9.66072e19	−0.000730559 0
$526$	−8.75704e22	−0.651596
$527$	2.19030e23	1.60367
$528$	1.80719e21	0.0130201
$529$	2.38076e23	1.68789
$530$	−3.50113e22	−0.244266
$531$	1.75715e23	1.20644
$532$	5.83836e22	0.394496
$533$	−4.36057e22	−0.289976
$534$	5.24973e21	0.0343587
$535$	−1.31996e23	−0.850265
$536$	−2.67155e23	−1.69380
$537$	−8.51880e21	−0.0531615
$538$	−1.37348e21	−0.00843673
$539$	2.34620e23	1.41860
$540$	1.62493e22	0.0967137
$541$	−4.78999e22	−0.280646	−0.140323	−	0.990106i	$-0.544814\pi$
$541$	−4.78999e22	−0.280646	−0.140323	+	0.990106i	$0.544814\pi$
$542$	−2.67900e22	−0.154518
$543$	−2.40088e22	−0.136324
$544$	−1.75977e23	−0.983706
$545$	−1.76713e22	−0.0972521
$546$	−5.12777e21	−0.0277838
$547$	5.73447e22	0.305915	0.152958	−	0.988233i	$-0.451120\pi$
$547$	5.73447e22	0.305915	0.152958	+	0.988233i	$0.451120\pi$
$548$	−1.98052e22	−0.104027
$549$	5.49213e22	0.284037
$550$	−4.49600e21	−0.0228952
$551$	6.00403e22	0.301061
$552$	2.89060e22	0.142727
$553$	8.70713e22	0.423362
$554$	−5.59107e22	−0.267708
$555$	1.16349e22	0.0548621
$556$	1.60518e23	0.745396
$557$	5.19429e22	0.237551	0.118776	−	0.992921i	$-0.462103\pi$
$557$	5.19429e22	0.237551	0.118776	+	0.992921i	$0.462103\pi$
$558$	2.25980e23	1.01784
$559$	−1.99014e23	−0.882841
$560$	−8.48566e21	−0.0370755
$561$	−3.45960e22	−0.148882
$562$	1.23020e23	0.521457
$563$	−2.59945e23	−1.08532	−0.542662	−	0.839951i	$-0.682584\pi$
$563$	−2.59945e23	−1.08532	−0.542662	+	0.839951i	$0.682584\pi$
$564$	8.51600e21	0.0350238
$565$	1.25626e23	0.508942
$566$	−6.42837e21	−0.0256544
$567$	1.04856e23	0.412227
$568$	−3.66303e23	−1.41866
$569$	−3.53531e23	−1.34888	−0.674441	−	0.738329i	$-0.735615\pi$
$569$	−3.53531e23	−1.34888	−0.674441	+	0.738329i	$0.735615\pi$
$570$	2.35575e22	0.0885509
$571$	−3.29571e23	−1.22051	−0.610256	−	0.792204i	$-0.708934\pi$
$571$	−3.29571e23	−1.22051	−0.610256	+	0.792204i	$0.708934\pi$
$572$	3.26241e23	1.19034
$573$	2.98180e22	0.107193
$574$	1.87608e22	0.0664510
$575$	−9.59407e21	−0.0334831
$576$	−2.07230e23	−0.712626
$577$	−8.02263e22	−0.271846	−0.135923	−	0.990719i	$-0.543400\pi$
$577$	−8.02263e22	−0.271846	−0.135923	+	0.990719i	$0.543400\pi$
$578$	−6.54967e21	−0.0218692
$579$	3.77717e22	0.124279
$580$	3.27370e22	0.106145
$581$	−2.42100e23	−0.773567
$582$	1.54378e22	0.0486116
$583$	−2.11039e23	−0.654908
$584$	−6.30318e22	−0.192775
$585$	−3.89551e23	−1.17419
$586$	1.26244e23	0.375044
$587$	−3.79522e23	−1.11125	−0.555627	−	0.831432i	$-0.687522\pi$
$587$	−3.79522e23	−1.11125	−0.555627	+	0.831432i	$0.687522\pi$
$588$	1.39748e22	0.0403310
$589$	−8.99004e23	−2.55730
$590$	2.78806e23	0.781737
$591$	4.20702e22	0.116274
$592$	−2.13069e22	−0.0580479
$593$	−2.51484e23	−0.675377	−0.337688	−	0.941258i	$-0.609645\pi$
$593$	−2.51484e23	−0.675377	−0.337688	+	0.941258i	$0.609645\pi$
$594$	−7.16467e22	−0.189676
$595$	1.62446e23	0.423949
$596$	4.21602e23	1.08470
$597$	−4.46465e22	−0.113242
$598$	−5.09239e23	−1.27339
$599$	6.24492e23	1.53957	0.769784	−	0.638304i	$-0.220364\pi$
$599$	6.24492e23	1.53957	0.769784	+	0.638304i	$0.220364\pi$
$600$	−7.31486e20	−0.00177795
$601$	−4.50141e23	−1.07874	−0.539368	−	0.842070i	$-0.681337\pi$
$601$	−4.50141e23	−1.07874	−0.539368	+	0.842070i	$0.681337\pi$
$602$	8.56234e22	0.202312
$603$	7.03954e23	1.64001
$604$	−3.29244e23	−0.756318
$605$	8.62908e23	1.95454
$606$	−2.30335e22	−0.0514450
$607$	−5.98965e23	−1.31916	−0.659580	−	0.751634i	$-0.729266\pi$
$607$	−5.98965e23	−1.31916	−0.659580	+	0.751634i	$0.729266\pi$
$608$	7.22293e23	1.56867
$609$	−3.10158e21	−0.00664256
$610$	8.71434e22	0.184048
$611$	−4.09797e23	−0.853530
$612$	2.83800e23	0.582941
$613$	5.50490e23	1.11515	0.557577	−	0.830125i	$-0.311731\pi$
$613$	5.50490e23	1.11515	0.557577	+	0.830125i	$0.311731\pi$
$614$	4.17704e22	0.0834521
$615$	−1.03486e22	−0.0203913
$616$	−3.83396e23	−0.745095
$617$	−3.67385e23	−0.704203	−0.352102	−	0.935962i	$-0.614533\pi$
$617$	−3.67385e23	−0.704203	−0.352102	+	0.935962i	$0.614533\pi$
$618$	1.05449e22	0.0199360
$619$	−4.39601e22	−0.0819762	−0.0409881	−	0.999160i	$-0.513051\pi$
$619$	−4.39601e22	−0.0819762	−0.0409881	+	0.999160i	$0.513051\pi$
$620$	−4.90182e23	−0.901629
$621$	−1.52888e23	−0.277392
$622$	−3.08230e23	−0.551641
$623$	−1.48584e23	−0.262316
$624$	−5.17986e21	−0.00902088
$625$	−5.69946e23	−0.979160
$626$	2.94973e23	0.499921
$627$	1.41998e23	0.237415
$628$	2.52193e23	0.415984
$629$	4.07890e23	0.663763
$630$	1.67600e23	0.269079
$631$	5.79938e23	0.918612	0.459306	−	0.888278i	$-0.348098\pi$
$631$	5.79938e23	0.918612	0.459306	+	0.888278i	$0.348098\pi$
$632$	6.59283e23	1.03033
$633$	−9.98103e22	−0.153902
$634$	−6.89882e23	−1.04958
$635$	7.93035e23	1.19046
$636$	−1.25702e22	−0.0186191
$637$	−6.72480e23	−0.982866
$638$	−1.44344e23	−0.208173
$639$	9.65209e23	1.37361
$640$	3.53101e23	0.495872
$641$	−2.92002e23	−0.404662	−0.202331	−	0.979317i	$-0.564852\pi$
$641$	−2.92002e23	−0.404662	−0.202331	+	0.979317i	$0.564852\pi$
$642$	3.46660e22	0.0474084
$643$	6.45613e21	0.00871322	0.00435661	−	0.999991i	$-0.498613\pi$
$643$	6.45613e21	0.00871322	0.00435661	+	0.999991i	$0.498613\pi$
$644$	−2.99519e23	−0.398928
$645$	−4.72306e22	−0.0620820
$646$	8.25866e23	1.07135
$647$	−9.54333e23	−1.22184	−0.610919	−	0.791693i	$-0.709200\pi$
$647$	−9.54333e23	−1.22184	−0.610919	+	0.791693i	$0.709200\pi$
$648$	7.93943e23	1.00323
$649$	1.68057e24	2.09593
$650$	1.28867e22	0.0158627
$651$	4.64410e22	0.0564239
$652$	2.32526e23	0.278848
$653$	8.47649e23	1.00335	0.501677	−	0.865055i	$-0.332717\pi$
$653$	8.47649e23	1.00335	0.501677	+	0.865055i	$0.332717\pi$
$654$	4.64099e21	0.00542250
$655$	−9.25421e23	−1.06730
$656$	1.89514e22	0.0215754
$657$	1.66089e23	0.186653
$658$	1.76311e23	0.195595
$659$	−2.39162e23	−0.261918	−0.130959	−	0.991388i	$-0.541806\pi$
$659$	−2.39162e23	−0.261918	−0.130959	+	0.991388i	$0.541806\pi$
$660$	7.74246e22	0.0837058
$661$	−5.26345e23	−0.561769	−0.280885	−	0.959742i	$-0.590628\pi$
$661$	−5.26345e23	−0.561769	−0.280885	+	0.959742i	$0.590628\pi$
$662$	−4.95340e23	−0.521928
$663$	9.91607e22	0.103151
$664$	−1.83312e24	−1.88262
$665$	−6.66753e23	−0.676053
$666$	4.20833e23	0.421288
$667$	−3.08018e23	−0.304443
$668$	1.49181e21	0.00145584
$669$	1.00720e23	0.0970496
$670$	1.11696e24	1.06268
$671$	5.25277e23	0.493454
$672$	−3.73124e22	−0.0346110
$673$	−1.06102e24	−0.971838	−0.485919	−	0.874004i	$-0.661515\pi$
$673$	−1.06102e24	−0.971838	−0.485919	+	0.874004i	$0.661515\pi$
$674$	7.38707e23	0.668133
$675$	3.86893e21	0.00345548
$676$	−2.80259e23	−0.247180
$677$	9.30173e23	0.810140	0.405070	−	0.914286i	$-0.367247\pi$
$677$	9.30173e23	0.810140	0.405070	+	0.914286i	$0.367247\pi$
$678$	−3.29930e22	−0.0283772
$679$	−4.36939e23	−0.371132
$680$	1.23000e24	1.03176
$681$	3.67542e22	0.0304478
$682$	2.16132e24	1.76828
$683$	−9.10142e23	−0.735416	−0.367708	−	0.929941i	$-0.619857\pi$
$683$	−9.10142e23	−0.735416	−0.367708	+	0.929941i	$0.619857\pi$
$684$	−1.16485e24	−0.929591
$685$	2.26179e23	0.178272
$686$	6.41096e23	0.499077
$687$	−1.10508e23	−0.0849691
$688$	8.64932e22	0.0656871
$689$	6.04890e23	0.453746
$690$	−1.20854e23	−0.0895457
$691$	1.95993e24	1.43442	0.717210	−	0.696857i	$-0.245419\pi$
$691$	1.95993e24	1.43442	0.717210	+	0.696857i	$0.245419\pi$
$692$	4.20367e23	0.303898
$693$	1.01025e24	0.721432
$694$	−1.07133e24	−0.755730
$695$	−1.83315e24	−1.27740
$696$	−2.34844e22	−0.0161659
$697$	−3.62797e23	−0.246709
$698$	6.09658e23	0.409558
$699$	−1.63154e23	−0.108279
$700$	7.57954e21	0.00496946
$701$	6.91848e23	0.448134	0.224067	−	0.974574i	$-0.428067\pi$
$701$	6.91848e23	0.448134	0.224067	+	0.974574i	$0.428067\pi$
$702$	2.05357e23	0.131415
$703$	−1.67417e24	−1.05847
$704$	−1.98198e24	−1.23803
$705$	−9.72544e22	−0.0600208
$706$	−1.64632e24	−1.00386
$707$	6.51923e23	0.392764
$708$	1.00101e23	0.0595874
$709$	−1.46504e24	−0.861700	−0.430850	−	0.902424i	$-0.641786\pi$
$709$	−1.46504e24	−0.861700	−0.430850	+	0.902424i	$0.641786\pi$
$710$	1.53149e24	0.890060
$711$	−1.73721e24	−0.997611
$712$	−1.12505e24	−0.638396
$713$	4.61206e24	2.58603
$714$	−4.26628e22	−0.0236382
$715$	−3.72574e24	−2.03991
$716$	6.68363e23	0.361619
$717$	1.03163e23	0.0551581
$718$	−1.39292e24	−0.735983
$719$	1.80596e23	0.0943002	0.0471501	−	0.998888i	$-0.484986\pi$
$719$	1.80596e23	0.0943002	0.0471501	+	0.998888i	$0.484986\pi$
$720$	1.69303e23	0.0873649
$721$	−2.98454e23	−0.152204
$722$	−2.10013e24	−1.05847
$723$	1.30127e23	0.0648177
$724$	1.88367e24	0.927313
$725$	7.79462e21	0.00379247
$726$	−2.26624e23	−0.108979
$727$	−1.81529e24	−0.862787	−0.431393	−	0.902164i	$-0.641978\pi$
$727$	−1.81529e24	−0.862787	−0.431393	+	0.902164i	$0.641978\pi$
$728$	1.09891e24	0.516231
$729$	−2.06110e24	−0.957008
$730$	2.63533e23	0.120946
$731$	−1.65579e24	−0.751115
$732$	3.12873e22	0.0140289
$733$	−5.65132e23	−0.250476	−0.125238	−	0.992127i	$-0.539969\pi$
$733$	−5.65132e23	−0.250476	−0.125238	+	0.992127i	$0.539969\pi$
$734$	1.12941e24	0.494806
$735$	−1.59595e23	−0.0691158
$736$	−3.70550e24	−1.58630
$737$	6.73275e24	2.84917
$738$	−3.74309e23	−0.156585
$739$	−1.02681e24	−0.424632	−0.212316	−	0.977201i	$-0.568101\pi$
$739$	−1.02681e24	−0.424632	−0.212316	+	0.977201i	$0.568101\pi$
$740$	−9.12843e23	−0.373187
$741$	−4.07002e23	−0.164491
$742$	−2.60247e23	−0.103981
$743$	3.82303e23	0.151009	0.0755044	−	0.997145i	$-0.475943\pi$
$743$	3.82303e23	0.151009	0.0755044	+	0.997145i	$0.475943\pi$
$744$	3.51640e23	0.137318
$745$	−4.81478e24	−1.85887
$746$	1.94951e24	0.744126
$747$	4.83028e24	1.82283
$748$	2.71431e24	1.01274
$749$	−9.81158e23	−0.361946
$750$	1.52806e23	0.0557339
$751$	4.10876e24	1.48174	0.740869	−	0.671649i	$-0.234414\pi$
$751$	4.10876e24	1.48174	0.740869	+	0.671649i	$0.234414\pi$
$752$	1.78102e23	0.0635062
$753$	−2.86132e23	−0.100881
$754$	4.13727e23	0.144231
$755$	3.76004e24	1.29611
$756$	1.20785e23	0.0411696
$757$	−3.13286e23	−0.105591	−0.0527954	−	0.998605i	$-0.516813\pi$
$757$	−3.13286e23	−0.105591	−0.0527954	+	0.998605i	$0.516813\pi$
$758$	−1.61957e24	−0.539775
$759$	−7.28478e23	−0.240083
$760$	−5.04849e24	−1.64530
$761$	2.66344e24	0.858368	0.429184	−	0.903217i	$-0.358801\pi$
$761$	2.66344e24	0.858368	0.429184	+	0.903217i	$0.358801\pi$
$762$	−2.08273e23	−0.0663768
$763$	−1.31355e23	−0.0413988
$764$	−2.33944e24	−0.729153
$765$	−3.24105e24	−0.998995
$766$	7.15202e23	0.218014
$767$	−4.81693e24	−1.45214
$768$	−2.97143e23	−0.0885923
$769$	−2.07107e24	−0.610690	−0.305345	−	0.952242i	$-0.598772\pi$
$769$	−2.07107e24	−0.610690	−0.305345	+	0.952242i	$0.598772\pi$
$770$	1.60296e24	0.467467
$771$	1.86942e23	0.0539193
$772$	−2.96347e24	−0.845382
$773$	2.16123e24	0.609783	0.304892	−	0.952387i	$-0.401380\pi$
$773$	2.16123e24	0.609783	0.304892	+	0.952387i	$0.401380\pi$
$774$	−1.70832e24	−0.476730
$775$	−1.16711e23	−0.0322143
$776$	−3.30840e24	−0.903220
$777$	8.64849e22	0.0233540
$778$	−1.66504e24	−0.444732
$779$	1.48909e24	0.393416
$780$	−2.21918e23	−0.0579947
$781$	9.23143e24	2.38636
$782$	−4.23685e24	−1.08339
$783$	1.24212e23	0.0314188
$784$	2.92266e23	0.0731294
$785$	−2.88010e24	−0.712878
$786$	2.43042e23	0.0595099
$787$	5.71775e24	1.38497	0.692484	−	0.721433i	$-0.256516\pi$
$787$	5.71775e24	1.38497	0.692484	+	0.721433i	$0.256516\pi$
$788$	−3.30071e24	−0.790925
$789$	3.59059e23	0.0851159
$790$	−2.75643e24	−0.646422
$791$	9.33809e23	0.216650
$792$	7.64936e24	1.75574
$793$	−1.50557e24	−0.341885
$794$	−4.44855e24	−0.999410
$795$	1.43555e23	0.0319078
$796$	3.50285e24	0.770300
$797$	−4.28492e24	−0.932282	−0.466141	−	0.884710i	$-0.654356\pi$
$797$	−4.28492e24	−0.932282	−0.466141	+	0.884710i	$0.654356\pi$
$798$	1.75108e23	0.0376948
$799$	−3.40949e24	−0.726176
$800$	9.37702e22	0.0197606
$801$	2.96450e24	0.618122
$802$	2.25714e23	0.0465668
$803$	1.58851e24	0.324270
$804$	4.01026e23	0.0810021
$805$	3.42057e24	0.683649
$806$	−6.19487e24	−1.22514
$807$	5.63160e21	0.00110206
$808$	4.93621e24	0.955865
$809$	9.18980e24	1.76094	0.880468	−	0.474106i	$-0.157229\pi$
$809$	9.18980e24	1.76094	0.880468	+	0.474106i	$0.157229\pi$
$810$	−3.31943e24	−0.629421
$811$	7.75446e24	1.45504	0.727519	−	0.686088i	$-0.240674\pi$
$811$	7.75446e24	1.45504	0.727519	+	0.686088i	$0.240674\pi$
$812$	2.43341e23	0.0451845
$813$	1.09845e23	0.0201842
$814$	4.02492e24	0.731897
$815$	−2.65550e24	−0.477867
$816$	−4.30962e22	−0.00767489
$817$	6.79612e24	1.19777
$818$	1.84948e24	0.322586
$819$	−2.89562e24	−0.499837
$820$	8.11927e23	0.138707
$821$	9.98056e24	1.68748	0.843739	−	0.536754i	$-0.180350\pi$
$821$	9.98056e24	1.68748	0.843739	+	0.536754i	$0.180350\pi$
$822$	−5.94011e22	−0.00993995
$823$	5.04767e24	0.835973	0.417987	−	0.908453i	$-0.362736\pi$
$823$	5.04767e24	0.835973	0.417987	+	0.908453i	$0.362736\pi$
$824$	−2.25982e24	−0.370418
$825$	1.84347e22	0.00299072
$826$	2.07243e24	0.332774
$827$	−7.25183e24	−1.15253	−0.576263	−	0.817264i	$-0.695490\pi$
$827$	−7.25183e24	−1.15253	−0.576263	+	0.817264i	$0.695490\pi$
$828$	5.97588e24	0.940035
$829$	−4.40483e24	−0.685828	−0.342914	−	0.939367i	$-0.611414\pi$
$829$	−4.40483e24	−0.685828	−0.342914	+	0.939367i	$0.611414\pi$
$830$	7.66419e24	1.18114
$831$	2.29247e23	0.0349699
$832$	5.68086e24	0.857760
$833$	−5.59500e24	−0.836215
$834$	4.81436e23	0.0712241
$835$	−1.70367e22	−0.00249489
$836$	−1.11408e25	−1.61497
$837$	−1.85987e24	−0.266880
$838$	−7.72898e24	−1.09786
$839$	−1.59907e24	−0.224849	−0.112425	−	0.993660i	$-0.535862\pi$
$839$	−1.59907e24	−0.224849	−0.112425	+	0.993660i	$0.535862\pi$
$840$	2.60796e23	0.0363018
$841$	2.50246e23	0.0344828
$842$	−6.58902e23	−0.0898811
$843$	−5.04412e23	−0.0681163
$844$	7.83085e24	1.04688
$845$	3.20062e24	0.423596
$846$	−3.51768e24	−0.460901
$847$	6.41419e24	0.832018
$848$	−2.62891e23	−0.0337606
$849$	2.63578e22	0.00335115
$850$	1.07216e23	0.0134959
$851$	8.58882e24	1.07037
$852$	5.49857e23	0.0678442
$853$	1.86947e24	0.228377	0.114189	−	0.993459i	$-0.463573\pi$
$853$	1.86947e24	0.228377	0.114189	+	0.993459i	$0.463573\pi$
$854$	6.47756e23	0.0783465
$855$	1.33028e25	1.59305
$856$	−7.42910e24	−0.880864
$857$	4.77204e24	0.560230	0.280115	−	0.959966i	$-0.409627\pi$
$857$	4.77204e24	0.560230	0.280115	+	0.959966i	$0.409627\pi$
$858$	9.78484e23	0.113740
$859$	−1.60976e25	−1.85276	−0.926378	−	0.376595i	$-0.877095\pi$
$859$	−1.60976e25	−1.85276	−0.926378	+	0.376595i	$0.877095\pi$
$860$	3.70559e24	0.422299
$861$	−7.69238e22	−0.00868028
$862$	−9.90597e23	−0.110684
$863$	−1.08010e25	−1.19501	−0.597506	−	0.801865i	$-0.703841\pi$
$863$	−1.08010e25	−1.19501	−0.597506	+	0.801865i	$0.703841\pi$
$864$	1.49429e24	0.163707
$865$	−4.80068e24	−0.520794
$866$	−1.05604e25	−1.13443
$867$	2.68551e22	0.00285670
$868$	−3.64363e24	−0.383811
$869$	−1.66150e25	−1.73314
$870$	9.81870e22	0.0101424
$871$	−1.92977e25	−1.97402
$872$	−9.94589e23	−0.100752
$873$	8.71764e24	0.874536
$874$	1.73900e25	1.72764
$875$	−4.32490e24	−0.425508
$876$	9.46169e22	0.00921900
$877$	−6.44417e24	−0.621828	−0.310914	−	0.950438i	$-0.600635\pi$
$877$	−6.44417e24	−0.621828	−0.310914	+	0.950438i	$0.600635\pi$
$878$	6.57501e24	0.628338
$879$	−5.17630e23	−0.0489908
$880$	1.61924e24	0.151778
$881$	5.95119e24	0.552470	0.276235	−	0.961090i	$-0.410913\pi$
$881$	5.95119e24	0.552470	0.276235	+	0.961090i	$0.410913\pi$
$882$	−5.77254e24	−0.530742
$883$	3.41176e24	0.310679	0.155340	−	0.987861i	$-0.450353\pi$
$883$	3.41176e24	0.310679	0.155340	+	0.987861i	$0.450353\pi$
$884$	−7.77989e24	−0.701664
$885$	−1.14317e24	−0.102116
$886$	−9.04263e24	−0.800033
$887$	9.74652e24	0.854080	0.427040	−	0.904233i	$-0.359556\pi$
$887$	9.74652e24	0.854080	0.427040	+	0.904233i	$0.359556\pi$
$888$	6.54843e23	0.0568364
$889$	5.89481e24	0.506763
$890$	4.70375e24	0.400525
$891$	−2.00087e25	−1.68755
$892$	−7.90222e24	−0.660158
$893$	1.39942e25	1.15800
$894$	1.26450e24	0.103645
$895$	−7.63284e24	−0.619712
$896$	2.62468e24	0.211086
$897$	2.08800e24	0.166339
$898$	−1.03299e25	−0.815170
$899$	−3.74703e24	−0.292907
$900$	−1.51224e23	−0.0117101
$901$	5.03266e24	0.386044
$902$	−3.57996e24	−0.272033
$903$	−3.51076e23	−0.0264274
$904$	7.07058e24	0.527258
$905$	−2.15119e25	−1.58915
$906$	−9.87492e23	−0.0722676
$907$	−1.70606e25	−1.23689	−0.618447	−	0.785826i	$-0.712238\pi$
$907$	−1.70606e25	−1.23689	−0.618447	+	0.785826i	$0.712238\pi$
$908$	−2.88364e24	−0.207115
$909$	−1.30069e25	−0.925510
$910$	−4.59447e24	−0.323880
$911$	−1.04116e25	−0.727126	−0.363563	−	0.931570i	$-0.618440\pi$
$911$	−1.04116e25	−0.727126	−0.363563	+	0.931570i	$0.618440\pi$
$912$	1.76887e23	0.0122388
$913$	4.61977e25	3.16679
$914$	5.91127e24	0.401456
$915$	−3.57308e23	−0.0240416
$916$	8.67015e24	0.577983
$917$	−6.87886e24	−0.454336
$918$	1.70856e24	0.111807
$919$	−7.95051e24	−0.515482	−0.257741	−	0.966214i	$-0.582978\pi$
$919$	−7.95051e24	−0.515482	−0.257741	+	0.966214i	$0.582978\pi$
$920$	2.58997e25	1.66379
$921$	−1.71268e23	−0.0109011
$922$	−9.38434e24	−0.591822
$923$	−2.64596e25	−1.65336
$924$	5.75515e23	0.0356324
$925$	−2.17346e23	−0.0133336
$926$	1.04131e25	0.632975
$927$	5.95463e24	0.358655
$928$	3.01050e24	0.179672
$929$	−1.53623e25	−0.908492	−0.454246	−	0.890876i	$-0.650091\pi$
$929$	−1.53623e25	−0.908492	−0.454246	+	0.890876i	$0.650091\pi$
$930$	−1.47019e24	−0.0861525
$931$	2.29645e25	1.33348
$932$	1.28007e25	0.736541
$933$	1.26381e24	0.0720592
$934$	1.71485e25	0.968899
$935$	−3.09980e25	−1.73554
$936$	−2.19250e25	−1.21645
$937$	−1.55553e25	−0.855245	−0.427623	−	0.903957i	$-0.640649\pi$
$937$	−1.55553e25	−0.855245	−0.427623	+	0.903957i	$0.640649\pi$
$938$	8.30263e24	0.452368
$939$	−1.20946e24	−0.0653031
$940$	7.63032e24	0.408278
$941$	−8.19990e24	−0.434807	−0.217404	−	0.976082i	$-0.569759\pi$
$941$	−8.19990e24	−0.434807	−0.217404	+	0.976082i	$0.569759\pi$
$942$	7.56395e23	0.0397481
$943$	−7.63931e24	−0.397837
$944$	2.09348e24	0.108046
$945$	−1.37939e24	−0.0705530
$946$	−1.63387e25	−0.828216
$947$	7.94074e24	0.398920	0.199460	−	0.979906i	$-0.436081\pi$
$947$	7.94074e24	0.398920	0.199460	+	0.979906i	$0.436081\pi$
$948$	−9.89648e23	−0.0492731
$949$	−4.55305e24	−0.224667
$950$	−4.40067e23	−0.0215213
$951$	2.82867e24	0.137103
$952$	9.14286e24	0.439206
$953$	1.51723e25	0.722373	0.361187	−	0.932494i	$-0.382372\pi$
$953$	1.51723e25	0.722373	0.361187	+	0.932494i	$0.382372\pi$
$954$	5.19235e24	0.245021
$955$	2.67169e25	1.24956
$956$	−8.09385e24	−0.375200
$957$	5.91845e23	0.0271930
$958$	2.44861e24	0.111510
$959$	1.68124e24	0.0758878
$960$	1.34820e24	0.0603183
$961$	3.35554e25	1.48803
$962$	−1.15364e25	−0.507088
$963$	1.95757e25	0.852890
$964$	−1.02095e25	−0.440908
$965$	3.38434e25	1.44874
$966$	−8.98338e23	−0.0381183
$967$	4.91028e24	0.206529	0.103264	−	0.994654i	$-0.467071\pi$
$967$	4.91028e24	0.206529	0.103264	+	0.994654i	$0.467071\pi$
$968$	4.85667e25	2.02487
$969$	−3.38624e24	−0.139948
$970$	1.38322e25	0.566673
$971$	1.05347e25	0.427817	0.213909	−	0.976854i	$-0.431380\pi$
$971$	1.05347e25	0.427817	0.213909	+	0.976854i	$0.431380\pi$
$972$	−3.61913e24	−0.145694
$973$	−1.36262e25	−0.543770
$974$	9.94182e24	0.393291
$975$	−5.28383e22	−0.00207209
$976$	6.54336e23	0.0254377
$977$	−3.23139e25	−1.24533	−0.622667	−	0.782487i	$-0.713951\pi$
$977$	−3.23139e25	−1.24533	−0.622667	+	0.782487i	$0.713951\pi$
$978$	6.97409e23	0.0266445
$979$	2.83530e25	1.07386
$980$	1.25214e25	0.470145
$981$	2.62074e24	0.0975524
$982$	9.68105e24	0.357252
$983$	2.82841e25	1.03476	0.517378	−	0.855757i	$-0.326908\pi$
$983$	2.82841e25	1.03476	0.517378	+	0.855757i	$0.326908\pi$
$984$	−5.82448e23	−0.0211251
$985$	3.76948e25	1.35542
$986$	3.44219e24	0.122710
$987$	−7.22914e23	−0.0255500
$988$	3.19323e25	1.11891
$989$	−3.48654e25	−1.21123
$990$	−3.19816e25	−1.10154
$991$	−1.11768e25	−0.381673	−0.190837	−	0.981622i	$-0.561120\pi$
$991$	−1.11768e25	−0.381673	−0.190837	+	0.981622i	$0.561120\pi$
$992$	−4.50772e25	−1.52619
$993$	2.03101e24	0.0681778
$994$	1.13839e25	0.378886
$995$	−4.00032e25	−1.32008
$996$	2.75170e24	0.0900319
$997$	−4.54649e24	−0.147492	−0.0737458	−	0.997277i	$-0.523495\pi$
$997$	−4.54649e24	−0.147492	−0.0737458	+	0.997277i	$0.523495\pi$
$998$	1.21367e25	0.390382
$999$	−3.46355e24	−0.110463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.a.1.7	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.a.1.7	✓	18	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)

\(f(q)\)	\(=\)	\(q-235.315 q^{2} +964.844 q^{3} -75699.1 q^{4} +864499. q^{5} -227042. q^{6} +6.42601e6 q^{7} +4.86562e7 q^{8} -1.28209e8 q^{9} +O(q^{10})\)	\(q-235.315 q^{2} +964.844 q^{3} -75699.1 q^{4} +864499. q^{5} -227042. q^{6} +6.42601e6 q^{7} +4.86562e7 q^{8} -1.28209e8 q^{9} -2.03429e8 q^{10} -1.22622e9 q^{11} -7.30378e7 q^{12} +3.51464e9 q^{13} -1.51213e9 q^{14} +8.34106e8 q^{15} -1.52749e9 q^{16} +2.92416e10 q^{17} +3.01695e10 q^{18} -1.20021e11 q^{19} -6.54417e10 q^{20} +6.20010e9 q^{21} +2.88547e11 q^{22} +6.15733e11 q^{23} +4.69457e10 q^{24} -1.55816e10 q^{25} -8.27046e11 q^{26} -2.48302e11 q^{27} -4.86443e11 q^{28} -5.00246e11 q^{29} -1.96277e11 q^{30} +7.49036e12 q^{31} -6.01803e12 q^{32} -1.18311e12 q^{33} -6.88099e12 q^{34} +5.55528e12 q^{35} +9.70532e12 q^{36} +1.39489e13 q^{37} +2.82428e13 q^{38} +3.39108e12 q^{39} +4.20633e13 q^{40} -1.24069e13 q^{41} -1.45897e12 q^{42} -5.66242e13 q^{43} +9.28234e13 q^{44} -1.10837e14 q^{45} -1.44891e14 q^{46} -1.16597e14 q^{47} -1.47379e12 q^{48} -1.91337e14 q^{49} +3.66657e12 q^{50} +2.82136e13 q^{51} -2.66055e14 q^{52} +1.72106e14 q^{53} +5.84291e13 q^{54} -1.06006e15 q^{55} +3.12666e14 q^{56} -1.15802e14 q^{57} +1.17715e14 q^{58} -1.37053e15 q^{59} -6.31410e13 q^{60} -4.28372e14 q^{61} -1.76259e15 q^{62} -8.23874e14 q^{63} +1.61634e15 q^{64} +3.03840e15 q^{65} +2.78402e14 q^{66} -5.49067e15 q^{67} -2.21357e15 q^{68} +5.94086e14 q^{69} -1.30724e15 q^{70} -7.52839e15 q^{71} -6.23818e15 q^{72} -1.29545e15 q^{73} -3.28239e15 q^{74} -1.50338e13 q^{75} +9.08551e15 q^{76} -7.87969e15 q^{77} -7.97970e14 q^{78} +1.35498e16 q^{79} -1.32052e15 q^{80} +1.63174e16 q^{81} +2.91952e15 q^{82} -3.76750e16 q^{83} -4.69342e14 q^{84} +2.52794e16 q^{85} +1.33245e16 q^{86} -4.82660e14 q^{87} -5.96631e16 q^{88} -2.31223e16 q^{89} +2.60815e16 q^{90} +2.25851e16 q^{91} -4.66104e16 q^{92} +7.22703e15 q^{93} +2.74370e16 q^{94} -1.03758e17 q^{95} -5.80646e15 q^{96} -6.79954e16 q^{97} +4.50243e16 q^{98} +1.57212e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9} - 1301706588 q^{10} + 414318256 q^{11} + 4613809340 q^{12} - 1708529620 q^{13} - 10178671680 q^{14} - 35937136948 q^{15} + 13408243234 q^{16} - 31137019060 q^{17} - 216144895280 q^{18} - 236294644572 q^{19} - 343491571178 q^{20} + 292681980344 q^{21} + 237072099770 q^{22} + 448660830360 q^{23} + 1331075294514 q^{24} + 3016314845934 q^{25} + 4625052436620 q^{26} - 3633286593580 q^{27} - 5255043772340 q^{28} - 9004435433298 q^{29} + 11322123726866 q^{30} + 4286667897456 q^{31} + 20489566928480 q^{32} + 12272773628920 q^{33} - 29135914295852 q^{34} - 34335586657384 q^{35} - 34363200450796 q^{36} - 33745027570060 q^{37} - 96773461186360 q^{38} - 104536576294796 q^{39} - 136020881729180 q^{40} - 62894681812676 q^{41} - 363718470035260 q^{42} + 43558449431040 q^{43} - 49608048285572 q^{44} + 133812803620916 q^{45} - 219540697042836 q^{46} - 141597817069240 q^{47} - 267256681151460 q^{48} + 453054608269810 q^{49} - 13\!\cdots\!40 q^{50}+ \cdots + 11\!\cdots\!56 q^{99}+O(q^{100}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9 - 1301706588 * q^10 + 414318256 * q^11 + 4613809340 * q^12 - 1708529620 * q^13 - 10178671680 * q^14 - 35937136948 * q^15 + 13408243234 * q^16 - 31137019060 * q^17 - 216144895280 * q^18 - 236294644572 * q^19 - 343491571178 * q^20 + 292681980344 * q^21 + 237072099770 * q^22 + 448660830360 * q^23 + 1331075294514 * q^24 + 3016314845934 * q^25 + 4625052436620 * q^26 - 3633286593580 * q^27 - 5255043772340 * q^28 - 9004435433298 * q^29 + 11322123726866 * q^30 + 4286667897456 * q^31 + 20489566928480 * q^32 + 12272773628920 * q^33 - 29135914295852 * q^34 - 34335586657384 * q^35 - 34363200450796 * q^36 - 33745027570060 * q^37 - 96773461186360 * q^38 - 104536576294796 * q^39 - 136020881729180 * q^40 - 62894681812676 * q^41 - 363718470035260 * q^42 + 43558449431040 * q^43 - 49608048285572 * q^44 + 133812803620916 * q^45 - 219540697042836 * q^46 - 141597817069240 * q^47 - 267256681151460 * q^48 + 453054608269810 * q^49 - 1348659632272640 * q^50 - 1366163894523096 * q^51 - 1312273323620630 * q^52 - 485951074130100 * q^53 - 1795598060978246 * q^54 - 3426804650590972 * q^55 - 5564818824556288 * q^56 - 5205401672025040 * q^57 - 4547356113106800 * q^59 - 13819026055113000 * q^60 - 6121039899052148 * q^61 - 10199136673985490 * q^62 - 14641672030091800 * q^63 - 9962823646631806 * q^64 - 13420652091655824 * q^65 - 27721841054867288 * q^66 - 17715742779810920 * q^67 - 24471819430698220 * q^68 - 17159735572757960 * q^69 + 9006543780480744 * q^70 - 18877957007949512 * q^71 - 44531687124196680 * q^72 - 11641701802444700 * q^73 - 53655919274849056 * q^74 - 21032918050227748 * q^75 - 66122191206313032 * q^76 - 8842889451812280 * q^77 - 28799653307053650 * q^78 - 44197796400782136 * q^79 - 157325108946937442 * q^80 - 41532487375317502 * q^81 - 65440892426610260 * q^82 - 9547427423528400 * q^83 - 54796688181105048 * q^84 - 34123627920307712 * q^85 - 119642903919749046 * q^86 + 7703794759599400 * q^87 - 114332767598176050 * q^88 - 48534239108944036 * q^89 + 56810599078278752 * q^90 - 104774225723277192 * q^91 - 3343093822255980 * q^92 + 128149288210966200 * q^93 + 83032272917645478 * q^94 + 200021462885519192 * q^95 + 140361624410708610 * q^96 + 53343624485398380 * q^97 + 448366099002416160 * q^98 + 117966192294311356 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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