LMFDB - Embedded newform 529.8.a.k.1.44

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,8,Mod(1,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("529.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	529.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:	$165.251678481$
Analytic rank:	$0$
Dimension:	$65$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.44
Character	$\chi$	$=$	529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.66710 q^{2} -19.3654 q^{3} -52.8813 q^{4} +542.126 q^{5} -167.842 q^{6} +1044.51 q^{7} -1567.72 q^{8} -1811.98 q^{9} +O(q^{10})$	\(q+8.66710 q^{2} -19.3654 q^{3} -52.8813 q^{4} +542.126 q^{5} -167.842 q^{6} +1044.51 q^{7} -1567.72 q^{8} -1811.98 q^{9} +4698.67 q^{10} -4270.15 q^{11} +1024.07 q^{12} +1016.32 q^{13} +9052.88 q^{14} -10498.5 q^{15} -6818.76 q^{16} -11703.9 q^{17} -15704.6 q^{18} -17254.9 q^{19} -28668.4 q^{20} -20227.3 q^{21} -37009.9 q^{22} +30359.4 q^{24} +215776. q^{25} +8808.52 q^{26} +77441.8 q^{27} -55235.1 q^{28} -35744.3 q^{29} -90991.5 q^{30} -15701.8 q^{31} +141569. q^{32} +82693.2 q^{33} -101439. q^{34} +566257. q^{35} +95820.0 q^{36} +412271. q^{37} -149550. q^{38} -19681.4 q^{39} -849901. q^{40} +221831. q^{41} -175312. q^{42} +832497. q^{43} +225811. q^{44} -982323. q^{45} -61012.0 q^{47} +132048. q^{48} +267459. q^{49} +1.87015e6 q^{50} +226650. q^{51} -53744.2 q^{52} -1.83416e6 q^{53} +671196. q^{54} -2.31496e6 q^{55} -1.63750e6 q^{56} +334149. q^{57} -309800. q^{58} +1.77618e6 q^{59} +555174. q^{60} +2.06411e6 q^{61} -136089. q^{62} -1.89263e6 q^{63} +2.09979e6 q^{64} +550972. q^{65} +716710. q^{66} +2.00346e6 q^{67} +618917. q^{68} +4.90780e6 q^{70} -3.96423e6 q^{71} +2.84067e6 q^{72} +2.91355e6 q^{73} +3.57320e6 q^{74} -4.17859e6 q^{75} +912464. q^{76} -4.46022e6 q^{77} -170580. q^{78} +1.94364e6 q^{79} -3.69663e6 q^{80} +2.46311e6 q^{81} +1.92263e6 q^{82} +5.11107e6 q^{83} +1.06965e6 q^{84} -6.34498e6 q^{85} +7.21533e6 q^{86} +692202. q^{87} +6.69439e6 q^{88} -3.19926e6 q^{89} -8.51390e6 q^{90} +1.06155e6 q^{91} +304071. q^{93} -528797. q^{94} -9.35436e6 q^{95} -2.74154e6 q^{96} -1.17293e7 q^{97} +2.31809e6 q^{98} +7.73744e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 65 q + 8 q^{2} + 14 q^{3} + 3776 q^{4} + 1181 q^{5} + 1082 q^{6} + 3628 q^{7} - 5757 q^{8} + 38263 q^{9}+O(q^{10}) $ 65 * q + 8 * q^2 + 14 * q^3 + 3776 * q^4 + 1181 * q^5 + 1082 * q^6 + 3628 * q^7 - 5757 * q^8 + 38263 * q^9	\( 65 q + 8 q^{2} + 14 q^{3} + 3776 q^{4} + 1181 q^{5} + 1082 q^{6} + 3628 q^{7} - 5757 q^{8} + 38263 q^{9} + 6879 q^{10} + 26147 q^{11} + 35689 q^{12} - 100 q^{13} + 55020 q^{14} + 92935 q^{15} + 176888 q^{16} + 89552 q^{17} + 190670 q^{18} + 169530 q^{19} + 210098 q^{20} + 190951 q^{21} + 218663 q^{22} + 190835 q^{24} + 721210 q^{25} + 186894 q^{26} - 670321 q^{27} + 366019 q^{28} + 340963 q^{29} + 671873 q^{30} - 175163 q^{31} - 406068 q^{32} + 726837 q^{33} + 1110895 q^{34} - 596883 q^{35} + 361164 q^{36} + 790283 q^{37} + 1963838 q^{38} - 21993 q^{39} + 1600645 q^{40} - 623859 q^{41} + 2696872 q^{42} + 1189188 q^{43} + 3885217 q^{44} + 2158369 q^{45} + 1365507 q^{47} + 1218748 q^{48} + 5854235 q^{49} - 2728396 q^{50} + 4554663 q^{51} + 7887791 q^{52} + 4362562 q^{53} + 5072916 q^{54} - 3989544 q^{55} + 12949007 q^{56} + 551326 q^{57} - 7443768 q^{58} + 13201460 q^{59} + 19296285 q^{60} + 8838644 q^{61} - 14615728 q^{62} + 12479203 q^{63} - 9711751 q^{64} + 13544545 q^{65} + 4907285 q^{66} + 5760553 q^{67} + 17044359 q^{68} + 6122411 q^{70} + 4531745 q^{71} + 10759455 q^{72} - 2535486 q^{73} + 21404597 q^{74} + 22917428 q^{75} + 21958812 q^{76} + 11733492 q^{77} - 35437508 q^{78} + 27234683 q^{79} + 28932289 q^{80} + 3995985 q^{81} - 11682773 q^{82} + 39797339 q^{83} + 33971997 q^{84} - 19766357 q^{85} + 43836707 q^{86} - 13972389 q^{87} + 33099818 q^{88} + 41235321 q^{89} + 17210275 q^{90} + 30292506 q^{91} + 47965734 q^{93} - 9981701 q^{94} - 5998448 q^{95} - 48738628 q^{96} + 13984256 q^{97} + 56728191 q^{98} + 81303822 q^{99}+O(q^{100}) \) 65 * q + 8 * q^2 + 14 * q^3 + 3776 * q^4 + 1181 * q^5 + 1082 * q^6 + 3628 * q^7 - 5757 * q^8 + 38263 * q^9 + 6879 * q^10 + 26147 * q^11 + 35689 * q^12 - 100 * q^13 + 55020 * q^14 + 92935 * q^15 + 176888 * q^16 + 89552 * q^17 + 190670 * q^18 + 169530 * q^19 + 210098 * q^20 + 190951 * q^21 + 218663 * q^22 + 190835 * q^24 + 721210 * q^25 + 186894 * q^26 - 670321 * q^27 + 366019 * q^28 + 340963 * q^29 + 671873 * q^30 - 175163 * q^31 - 406068 * q^32 + 726837 * q^33 + 1110895 * q^34 - 596883 * q^35 + 361164 * q^36 + 790283 * q^37 + 1963838 * q^38 - 21993 * q^39 + 1600645 * q^40 - 623859 * q^41 + 2696872 * q^42 + 1189188 * q^43 + 3885217 * q^44 + 2158369 * q^45 + 1365507 * q^47 + 1218748 * q^48 + 5854235 * q^49 - 2728396 * q^50 + 4554663 * q^51 + 7887791 * q^52 + 4362562 * q^53 + 5072916 * q^54 - 3989544 * q^55 + 12949007 * q^56 + 551326 * q^57 - 7443768 * q^58 + 13201460 * q^59 + 19296285 * q^60 + 8838644 * q^61 - 14615728 * q^62 + 12479203 * q^63 - 9711751 * q^64 + 13544545 * q^65 + 4907285 * q^66 + 5760553 * q^67 + 17044359 * q^68 + 6122411 * q^70 + 4531745 * q^71 + 10759455 * q^72 - 2535486 * q^73 + 21404597 * q^74 + 22917428 * q^75 + 21958812 * q^76 + 11733492 * q^77 - 35437508 * q^78 + 27234683 * q^79 + 28932289 * q^80 + 3995985 * q^81 - 11682773 * q^82 + 39797339 * q^83 + 33971997 * q^84 - 19766357 * q^85 + 43836707 * q^86 - 13972389 * q^87 + 33099818 * q^88 + 41235321 * q^89 + 17210275 * q^90 + 30292506 * q^91 + 47965734 * q^93 - 9981701 * q^94 - 5998448 * q^95 - 48738628 * q^96 + 13984256 * q^97 + 56728191 * q^98 + 81303822 * 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 $

$2$	8.66710	0.766071	0.383035	−	0.923734i	$-0.374879\pi$
$2$	8.66710	0.766071	0.383035	+	0.923734i	$0.374879\pi$
$3$	−19.3654	−0.414097	−0.207048	−	0.978331i	$-0.566386\pi$
$3$	−19.3654	−0.414097	−0.207048	+	0.978331i	$0.566386\pi$
$4$	−52.8813	−0.413135
$5$	542.126	1.93957	0.969785	−	0.243960i	$-0.0784467\pi$
$5$	542.126	1.93957	0.969785	+	0.243960i	$0.0784467\pi$
$6$	−167.842	−0.317227
$7$	1044.51	1.15098	0.575492	−	0.817807i	$-0.304810\pi$
$7$	1044.51	1.15098	0.575492	+	0.817807i	$0.304810\pi$
$8$	−1567.72	−1.08256
$9$	−1811.98	−0.828524
$10$	4698.67	1.48585
$11$	−4270.15	−0.967317	−0.483659	−	0.875257i	$-0.660692\pi$
$11$	−4270.15	−0.967317	−0.483659	+	0.875257i	$0.660692\pi$
$12$	1024.07	0.171078
$13$	1016.32	0.128300	0.0641501	−	0.997940i	$-0.479566\pi$
$13$	1016.32	0.128300	0.0641501	+	0.997940i	$0.479566\pi$
$14$	9052.88	0.881736
$15$	−10498.5	−0.803170
$16$	−6818.76	−0.416184
$17$	−11703.9	−0.577775	−0.288887	−	0.957363i	$-0.593285\pi$
$17$	−11703.9	−0.577775	−0.288887	+	0.957363i	$0.593285\pi$
$18$	−15704.6	−0.634708
$19$	−17254.9	−0.577133	−0.288566	−	0.957460i	$-0.593179\pi$
$19$	−17254.9	−0.577133	−0.288566	+	0.957460i	$0.593179\pi$
$20$	−28668.4	−0.801305
$21$	−20227.3	−0.476619
$22$	−37009.9	−0.741034
$23$	0	0
$23$	0	0
$24$	30359.4	0.448285
$25$	215776.	2.76193
$26$	8808.52	0.0982871
$27$	77441.8	0.757186
$28$	−55235.1	−0.475513
$29$	−35744.3	−0.272154	−0.136077	−	0.990698i	$-0.543449\pi$
$29$	−35744.3	−0.272154	−0.136077	+	0.990698i	$0.543449\pi$
$30$	−90991.5	−0.615285
$31$	−15701.8	−0.0946635	−0.0473318	−	0.998879i	$-0.515072\pi$
$31$	−15701.8	−0.0946635	−0.0473318	+	0.998879i	$0.515072\pi$
$32$	141569.	0.763736
$33$	82693.2	0.400563
$34$	−101439.	−0.442616
$35$	566257.	2.23242
$36$	95820.0	0.342293
$37$	412271.	1.33807	0.669033	−	0.743233i	$-0.266709\pi$
$37$	412271.	1.33807	0.669033	+	0.743233i	$0.266709\pi$
$38$	−149550.	−0.442125
$39$	−19681.4	−0.0531287
$40$	−849901.	−2.09970
$41$	221831.	0.502665	0.251332	−	0.967901i	$-0.419131\pi$
$41$	221831.	0.502665	0.251332	+	0.967901i	$0.419131\pi$
$42$	−175312.	−0.365124
$43$	832497.	1.59677	0.798386	−	0.602146i	$-0.205688\pi$
$43$	832497.	1.59677	0.798386	+	0.602146i	$0.205688\pi$
$44$	225811.	0.399633
$45$	−982323.	−1.60698
$46$	0	0
$47$	−61012.0	−0.0857181	−0.0428590	−	0.999081i	$-0.513647\pi$
$47$	−61012.0	−0.0857181	−0.0428590	+	0.999081i	$0.513647\pi$
$48$	132048.	0.172340
$49$	267459.	0.324766
$50$	1.87015e6	2.11584
$51$	226650.	0.239255
$52$	−53744.2	−0.0530054
$53$	−1.83416e6	−1.69228	−0.846138	−	0.532965i	$-0.821078\pi$
$53$	−1.83416e6	−1.69228	−0.846138	+	0.532965i	$0.821078\pi$
$54$	671196.	0.580058
$55$	−2.31496e6	−1.87618
$56$	−1.63750e6	−1.24601
$57$	334149.	0.238989
$58$	−309800.	−0.208489
$59$	1.77618e6	1.12592	0.562958	−	0.826485i	$-0.309663\pi$
$59$	1.77618e6	1.12592	0.562958	+	0.826485i	$0.309663\pi$
$60$	555174.	0.331818
$61$	2.06411e6	1.16434	0.582168	−	0.813069i	$-0.302205\pi$
$61$	2.06411e6	1.16434	0.582168	+	0.813069i	$0.302205\pi$
$62$	−136089.	−0.0725190
$63$	−1.89263e6	−0.953619
$64$	2.09979e6	1.00126
$65$	550972.	0.248847
$66$	716710.	0.306860
$67$	2.00346e6	0.813804	0.406902	−	0.913472i	$-0.366609\pi$
$67$	2.00346e6	0.813804	0.406902	+	0.913472i	$0.366609\pi$
$68$	618917.	0.238699
$69$	0	0
$70$	4.90780e6	1.71019
$71$	−3.96423e6	−1.31448	−0.657241	−	0.753681i	$-0.728277\pi$
$71$	−3.96423e6	−1.31448	−0.657241	+	0.753681i	$0.728277\pi$
$72$	2.84067e6	0.896928
$73$	2.91355e6	0.876582	0.438291	−	0.898833i	$-0.355584\pi$
$73$	2.91355e6	0.876582	0.438291	+	0.898833i	$0.355584\pi$
$74$	3.57320e6	1.02505
$75$	−4.17859e6	−1.14371
$76$	912464.	0.238434
$77$	−4.46022e6	−1.11337
$78$	−170580.	−0.0407004
$79$	1.94364e6	0.443527	0.221763	−	0.975101i	$-0.428819\pi$
$79$	1.94364e6	0.443527	0.221763	+	0.975101i	$0.428819\pi$
$80$	−3.69663e6	−0.807218
$81$	2.46311e6	0.514976
$82$	1.92263e6	0.385077
$83$	5.11107e6	0.981157	0.490579	−	0.871397i	$-0.336785\pi$
$83$	5.11107e6	0.981157	0.490579	+	0.871397i	$0.336785\pi$
$84$	1.06965e6	0.196908
$85$	−6.34498e6	−1.12063
$86$	7.21533e6	1.22324
$87$	692202.	0.112698
$88$	6.69439e6	1.04718
$89$	−3.19926e6	−0.481044	−0.240522	−	0.970644i	$-0.577319\pi$
$89$	−3.19926e6	−0.481044	−0.240522	+	0.970644i	$0.577319\pi$
$90$	−8.51390e6	−1.23106
$91$	1.06155e6	0.147672
$92$	0	0
$93$	304071.	0.0391999
$94$	−528797.	−0.0656661
$95$	−9.35436e6	−1.11939
$96$	−2.74154e6	−0.316260
$97$	−1.17293e7	−1.30488	−0.652440	−	0.757841i	$-0.726254\pi$
$97$	−1.17293e7	−1.30488	−0.652440	+	0.757841i	$0.726254\pi$
$98$	2.31809e6	0.248794
$99$	7.73744e6	0.801446
$100$	−1.14105e7	−1.14105
$101$	1.61926e7	1.56384	0.781921	−	0.623377i	$-0.214240\pi$
$101$	1.61926e7	1.56384	0.781921	+	0.623377i	$0.214240\pi$
$102$	1.96440e6	0.183286
$103$	−6.68202e6	−0.602529	−0.301264	−	0.953541i	$-0.597409\pi$
$103$	−6.68202e6	−0.602529	−0.301264	+	0.953541i	$0.597409\pi$
$104$	−1.59330e6	−0.138893
$105$	−1.09658e7	−0.924436
$106$	−1.58968e7	−1.29640
$107$	−1.66690e7	−1.31542	−0.657711	−	0.753270i	$-0.728475\pi$
$107$	−1.66690e7	−1.31542	−0.657711	+	0.753270i	$0.728475\pi$
$108$	−4.09523e6	−0.312820
$109$	−5.23503e6	−0.387192	−0.193596	−	0.981081i	$-0.562015\pi$
$109$	−5.23503e6	−0.387192	−0.193596	+	0.981081i	$0.562015\pi$
$110$	−2.00640e7	−1.43729
$111$	−7.98380e6	−0.554088
$112$	−7.12226e6	−0.479021
$113$	2.60194e7	1.69638	0.848191	−	0.529691i	$-0.177692\pi$
$113$	2.60194e7	1.69638	0.848191	+	0.529691i	$0.177692\pi$
$114$	2.89610e6	0.183082
$115$	0	0
$116$	1.89021e6	0.112436
$117$	−1.84155e6	−0.106300
$118$	1.53944e7	0.862532
$119$	−1.22248e7	−0.665010
$120$	1.64587e7	0.869481
$121$	−1.25296e6	−0.0642969
$122$	1.78898e7	0.891963
$123$	−4.29584e6	−0.208152
$124$	830331.	0.0391089
$125$	7.46243e7	3.41739
$126$	−1.64037e7	−0.730539
$127$	1.38622e7	0.600509	0.300255	−	0.953859i	$-0.402928\pi$
$127$	1.38622e7	0.600509	0.300255	+	0.953859i	$0.402928\pi$
$128$	78299.6	0.00330008
$129$	−1.61216e7	−0.661218
$130$	4.77533e6	0.190635
$131$	4.67361e7	1.81636	0.908182	−	0.418576i	$-0.137471\pi$
$131$	4.67361e7	1.81636	0.908182	+	0.418576i	$0.137471\pi$
$132$	−4.37292e6	−0.165487
$133$	−1.80230e7	−0.664271
$134$	1.73642e7	0.623432
$135$	4.19833e7	1.46861
$136$	1.83484e7	0.625477
$137$	−2.59833e7	−0.863321	−0.431660	−	0.902036i	$-0.642072\pi$
$137$	−2.59833e7	−0.863321	−0.431660	+	0.902036i	$0.642072\pi$
$138$	0	0
$139$	2.26041e6	0.0713895	0.0356948	−	0.999363i	$-0.488636\pi$
$139$	2.26041e6	0.0713895	0.0356948	+	0.999363i	$0.488636\pi$
$140$	−2.99444e7	−0.922290
$141$	1.18152e6	0.0354956
$142$	−3.43584e7	−1.00699
$143$	−4.33983e6	−0.124107
$144$	1.23555e7	0.344818
$145$	−1.93779e7	−0.527861
$146$	2.52520e7	0.671524
$147$	−5.17945e6	−0.134485
$148$	−2.18015e7	−0.552802
$149$	−2.97046e6	−0.0735652	−0.0367826	−	0.999323i	$-0.511711\pi$
$149$	−2.97046e6	−0.0735652	−0.0367826	+	0.999323i	$0.511711\pi$
$150$	−3.62162e7	−0.876161
$151$	−1.91688e7	−0.453082	−0.226541	−	0.974002i	$-0.572742\pi$
$151$	−1.91688e7	−0.453082	−0.226541	+	0.974002i	$0.572742\pi$
$152$	2.70509e7	0.624782
$153$	2.12072e7	0.478700
$154$	−3.86572e7	−0.852919
$155$	−8.51235e6	−0.183607
$156$	1.04078e6	0.0219493
$157$	1.97736e7	0.407791	0.203896	−	0.978993i	$-0.434640\pi$
$157$	1.97736e7	0.407791	0.203896	+	0.978993i	$0.434640\pi$
$158$	1.68457e7	0.339773
$159$	3.55192e7	0.700766
$160$	7.67483e7	1.48132
$161$	0	0
$162$	2.13481e7	0.394508
$163$	5.63782e7	1.01966	0.509829	−	0.860276i	$-0.329709\pi$
$163$	5.63782e7	1.01966	0.509829	+	0.860276i	$0.329709\pi$
$164$	−1.17307e7	−0.207669
$165$	4.48301e7	0.776920
$166$	4.42982e7	0.751636
$167$	2.23754e7	0.371760	0.185880	−	0.982572i	$-0.440486\pi$
$167$	2.23754e7	0.371760	0.185880	+	0.982572i	$0.440486\pi$
$168$	3.17108e7	0.515970
$169$	−6.17156e7	−0.983539
$170$	−5.49926e7	−0.858486
$171$	3.12656e7	0.478168
$172$	−4.40235e7	−0.659683
$173$	9.07470e7	1.33251	0.666256	−	0.745723i	$-0.267896\pi$
$173$	9.07470e7	1.33251	0.666256	+	0.745723i	$0.267896\pi$
$174$	5.99939e6	0.0863346
$175$	2.25380e8	3.17894
$176$	2.91171e7	0.402582
$177$	−3.43965e7	−0.466238
$178$	−2.77283e7	−0.368513
$179$	1.08366e8	1.41224	0.706120	−	0.708092i	$-0.250444\pi$
$179$	1.08366e8	1.41224	0.706120	+	0.708092i	$0.250444\pi$
$180$	5.19466e7	0.663900
$181$	9.27210e7	1.16226	0.581130	−	0.813811i	$-0.302611\pi$
$181$	9.27210e7	1.16226	0.581130	+	0.813811i	$0.302611\pi$
$182$	9.20059e6	0.113127
$183$	−3.99722e7	−0.482147
$184$	0	0
$185$	2.23503e8	2.59527
$186$	2.63541e6	0.0300299
$187$	4.99773e7	0.558892
$188$	3.22639e6	0.0354132
$189$	8.08888e7	0.871509
$190$	−8.10752e7	−0.857532
$191$	2.87240e7	0.298283	0.149141	−	0.988816i	$-0.452349\pi$
$191$	2.87240e7	0.298283	0.149141	+	0.988816i	$0.452349\pi$
$192$	−4.06633e7	−0.414618
$193$	2.74078e7	0.274425	0.137213	−	0.990542i	$-0.456186\pi$
$193$	2.74078e7	0.274425	0.137213	+	0.990542i	$0.456186\pi$
$194$	−1.01659e8	−0.999630
$195$	−1.06698e7	−0.103047
$196$	−1.41436e7	−0.134172
$197$	7.03755e7	0.655828	0.327914	−	0.944708i	$-0.393654\pi$
$197$	7.03755e7	0.655828	0.327914	+	0.944708i	$0.393654\pi$
$198$	6.70612e7	0.613964
$199$	−6.70213e7	−0.602874	−0.301437	−	0.953486i	$-0.597466\pi$
$199$	−6.70213e7	−0.602874	−0.301437	+	0.953486i	$0.597466\pi$
$200$	−3.38276e8	−2.98996
$201$	−3.87979e7	−0.336994
$202$	1.40343e8	1.19801
$203$	−3.73353e7	−0.313245
$204$	−1.19856e7	−0.0988445
$205$	1.20260e8	0.974954
$206$	−5.79138e7	−0.461580
$207$	0	0
$208$	−6.93002e6	−0.0533965
$209$	7.36812e7	0.558271
$210$	−9.50415e7	−0.708184
$211$	−4.66279e7	−0.341710	−0.170855	−	0.985296i	$-0.554653\pi$
$211$	−4.66279e7	−0.341710	−0.170855	+	0.985296i	$0.554653\pi$
$212$	9.69927e7	0.699139
$213$	7.67688e7	0.544322
$214$	−1.44472e8	−1.00771
$215$	4.51318e8	3.09705
$216$	−1.21407e8	−0.819700
$217$	−1.64007e7	−0.108956
$218$	−4.53725e7	−0.296616
$219$	−5.64220e7	−0.362990
$220$	1.22418e8	0.775116
$221$	−1.18948e7	−0.0741286
$222$	−6.91964e7	−0.424471
$223$	9.81490e7	0.592678	0.296339	−	0.955083i	$-0.404234\pi$
$223$	9.81490e7	0.592678	0.296339	+	0.955083i	$0.404234\pi$
$224$	1.47870e8	0.879048
$225$	−3.90982e8	−2.28833
$226$	2.25513e8	1.29955
$227$	2.25604e8	1.28014	0.640069	−	0.768317i	$-0.278906\pi$
$227$	2.25604e8	1.28014	0.640069	+	0.768317i	$0.278906\pi$
$228$	−1.76702e7	−0.0987347
$229$	−1.90712e8	−1.04943	−0.524715	−	0.851278i	$-0.675828\pi$
$229$	−1.90712e8	−1.04943	−0.524715	+	0.851278i	$0.675828\pi$
$230$	0	0
$231$	8.63739e7	0.461042
$232$	5.60370e7	0.294623
$233$	7.83459e7	0.405761	0.202881	−	0.979203i	$-0.434970\pi$
$233$	7.83459e7	0.405761	0.202881	+	0.979203i	$0.434970\pi$
$234$	−1.59609e7	−0.0814332
$235$	−3.30762e7	−0.166256
$236$	−9.39270e7	−0.465156
$237$	−3.76392e7	−0.183663
$238$	−1.05954e8	−0.509445
$239$	7.41144e7	0.351164	0.175582	−	0.984465i	$-0.443819\pi$
$239$	7.41144e7	0.351164	0.175582	+	0.984465i	$0.443819\pi$
$240$	7.15866e7	0.334266
$241$	−1.40501e8	−0.646578	−0.323289	−	0.946300i	$-0.604789\pi$
$241$	−1.40501e8	−0.646578	−0.323289	+	0.946300i	$0.604789\pi$
$242$	−1.08596e7	−0.0492560
$243$	−2.17064e8	−0.970436
$244$	−1.09153e8	−0.481028
$245$	1.44997e8	0.629907
$246$	−3.72325e7	−0.159459
$247$	−1.75365e7	−0.0740463
$248$	2.46159e7	0.102479
$249$	−9.89779e7	−0.406294
$250$	6.46776e8	2.61797
$251$	3.20516e8	1.27936	0.639679	−	0.768642i	$-0.279067\pi$
$251$	3.20516e8	1.27936	0.639679	+	0.768642i	$0.279067\pi$
$252$	1.00085e8	0.393974
$253$	0	0
$254$	1.20145e8	0.460033
$255$	1.22873e8	0.464051
$256$	−2.68095e8	−0.998731
$257$	−2.76645e8	−1.01662	−0.508309	−	0.861175i	$-0.669729\pi$
$257$	−2.76645e8	−1.01662	−0.508309	+	0.861175i	$0.669729\pi$
$258$	−1.39728e8	−0.506540
$259$	4.30622e8	1.54009
$260$	−2.91361e7	−0.102808
$261$	6.47680e7	0.225486
$262$	4.05067e8	1.39146
$263$	3.55901e8	1.20638	0.603190	−	0.797598i	$-0.293896\pi$
$263$	3.55901e8	1.20638	0.603190	+	0.797598i	$0.293896\pi$
$264$	−1.29639e8	−0.433634
$265$	−9.94345e8	−3.28229
$266$	−1.56207e8	−0.508879
$267$	6.19549e7	0.199199
$268$	−1.05946e8	−0.336211
$269$	4.54487e7	0.142360	0.0711801	−	0.997463i	$-0.477323\pi$
$269$	4.54487e7	0.142360	0.0711801	+	0.997463i	$0.477323\pi$
$270$	3.63873e8	1.12506
$271$	−2.28063e8	−0.696086	−0.348043	−	0.937479i	$-0.613154\pi$
$271$	−2.28063e8	−0.696086	−0.348043	+	0.937479i	$0.613154\pi$
$272$	7.98059e7	0.240460
$273$	−2.05574e7	−0.0611503
$274$	−2.25200e8	−0.661365
$275$	−9.21397e8	−2.67167
$276$	0	0
$277$	1.54555e8	0.436921	0.218460	−	0.975846i	$-0.429897\pi$
$277$	1.54555e8	0.436921	0.218460	+	0.975846i	$0.429897\pi$
$278$	1.95912e7	0.0546895
$279$	2.84513e7	0.0784310
$280$	−8.87730e8	−2.41673
$281$	−3.05796e8	−0.822167	−0.411083	−	0.911598i	$-0.634850\pi$
$281$	−3.05796e8	−0.822167	−0.411083	+	0.911598i	$0.634850\pi$
$282$	1.02404e7	0.0271921
$283$	−2.21869e8	−0.581893	−0.290947	−	0.956739i	$-0.593970\pi$
$283$	−2.21869e8	−0.581893	−0.290947	+	0.956739i	$0.593970\pi$
$284$	2.09634e8	0.543059
$285$	1.81151e8	0.463536
$286$	−3.76137e7	−0.0950748
$287$	2.31705e8	0.578560
$288$	−2.56520e8	−0.632773
$289$	−2.73358e8	−0.666176
$290$	−1.67951e8	−0.404379
$291$	2.27142e8	0.540346
$292$	−1.54072e8	−0.362147
$293$	6.55948e8	1.52347	0.761733	−	0.647890i	$-0.224349\pi$
$293$	6.55948e8	1.52347	0.761733	+	0.647890i	$0.224349\pi$
$294$	−4.48908e7	−0.103025
$295$	9.62916e8	2.18379
$296$	−6.46325e8	−1.44854
$297$	−3.30688e8	−0.732439
$298$	−2.57453e7	−0.0563562
$299$	0	0
$300$	2.20969e8	0.472506
$301$	8.69551e8	1.83786
$302$	−1.66138e8	−0.347093
$303$	−3.13577e8	−0.647582
$304$	1.17657e8	0.240193
$305$	1.11901e9	2.25831
$306$	1.83805e8	0.366718
$307$	−4.05008e7	−0.0798876	−0.0399438	−	0.999202i	$-0.512718\pi$
$307$	−4.05008e7	−0.0798876	−0.0399438	+	0.999202i	$0.512718\pi$
$308$	2.35862e8	0.459972
$309$	1.29400e8	0.249505
$310$	−7.37774e7	−0.140656
$311$	−4.05100e8	−0.763662	−0.381831	−	0.924232i	$-0.624706\pi$
$311$	−4.05100e8	−0.763662	−0.381831	+	0.924232i	$0.624706\pi$
$312$	3.08548e7	0.0575151
$313$	6.40725e8	1.18104	0.590522	−	0.807021i	$-0.298922\pi$
$313$	6.40725e8	1.18104	0.590522	+	0.807021i	$0.298922\pi$
$314$	1.71380e8	0.312397
$315$	−1.02605e9	−1.84961
$316$	−1.02782e8	−0.183237
$317$	−1.49994e8	−0.264464	−0.132232	−	0.991219i	$-0.542214\pi$
$317$	−1.49994e8	−0.264464	−0.132232	+	0.991219i	$0.542214\pi$
$318$	3.07848e8	0.536836
$319$	1.52634e8	0.263259
$320$	1.13835e9	1.94201
$321$	3.22801e8	0.544712
$322$	0	0
$323$	2.01950e8	0.333453
$324$	−1.30253e8	−0.212755
$325$	2.19297e8	0.354357
$326$	4.88636e8	0.781130
$327$	1.01378e8	0.160335
$328$	−3.47768e8	−0.544166
$329$	−6.37276e7	−0.0986602
$330$	3.88547e8	0.595176
$331$	−2.80642e7	−0.0425359	−0.0212679	−	0.999774i	$-0.506770\pi$
$331$	−2.80642e7	−0.0425359	−0.0212679	+	0.999774i	$0.506770\pi$
$332$	−2.70280e8	−0.405351
$333$	−7.47028e8	−1.10862
$334$	1.93930e8	0.284795
$335$	1.08613e9	1.57843
$336$	1.37925e8	0.198361
$337$	−1.05585e9	−1.50279	−0.751393	−	0.659855i	$-0.770618\pi$
$337$	−1.05585e9	−1.50279	−0.751393	+	0.659855i	$0.770618\pi$
$338$	−5.34896e8	−0.753461
$339$	−5.03877e8	−0.702466
$340$	3.35531e8	0.462974
$341$	6.70490e7	0.0915697
$342$	2.70982e8	0.366311
$343$	−5.80836e8	−0.777184
$344$	−1.30512e9	−1.72860
$345$	0	0
$346$	7.86514e8	1.02080
$347$	−8.15616e8	−1.04793	−0.523965	−	0.851740i	$-0.675548\pi$
$347$	−8.15616e8	−1.04793	−0.523965	+	0.851740i	$0.675548\pi$
$348$	−3.66046e7	−0.0465595
$349$	−4.40661e8	−0.554901	−0.277451	−	0.960740i	$-0.589490\pi$
$349$	−4.40661e8	−0.554901	−0.277451	+	0.960740i	$0.589490\pi$
$350$	1.95339e9	2.43530
$351$	7.87054e7	0.0971471
$352$	−6.04521e8	−0.738775
$353$	5.83734e8	0.706323	0.353161	−	0.935562i	$-0.385107\pi$
$353$	5.83734e8	0.706323	0.353161	+	0.935562i	$0.385107\pi$
$354$	−2.98118e8	−0.357171
$355$	−2.14911e9	−2.54953
$356$	1.69181e8	0.198736
$357$	2.36738e8	0.275378
$358$	9.39221e8	1.08188
$359$	5.95420e7	0.0679192	0.0339596	−	0.999423i	$-0.489188\pi$
$359$	5.95420e7	0.0679192	0.0339596	+	0.999423i	$0.489188\pi$
$360$	1.54000e9	1.73966
$361$	−5.96139e8	−0.666918
$362$	8.03623e8	0.890373
$363$	2.42641e7	0.0266251
$364$	−5.61364e7	−0.0610084
$365$	1.57951e9	1.70019
$366$	−3.46444e8	−0.369359
$367$	−1.63164e8	−0.172304	−0.0861518	−	0.996282i	$-0.527457\pi$
$367$	−1.63164e8	−0.172304	−0.0861518	+	0.996282i	$0.527457\pi$
$368$	0	0
$369$	−4.01954e8	−0.416470
$370$	1.93713e9	1.98816
$371$	−1.91580e9	−1.94778
$372$	−1.60797e7	−0.0161949
$373$	1.74801e8	0.174406	0.0872032	−	0.996191i	$-0.472207\pi$
$373$	1.74801e8	0.174406	0.0872032	+	0.996191i	$0.472207\pi$
$374$	4.33159e8	0.428151
$375$	−1.44513e9	−1.41513
$376$	9.56495e7	0.0927951
$377$	−3.63275e7	−0.0349174
$378$	7.01071e8	0.667638
$379$	1.02119e9	0.963536	0.481768	−	0.876299i	$-0.339995\pi$
$379$	1.02119e9	0.963536	0.481768	+	0.876299i	$0.339995\pi$
$380$	4.94671e8	0.462460
$381$	−2.68447e8	−0.248669
$382$	2.48954e8	0.228506
$383$	8.41599e8	0.765437	0.382719	−	0.923865i	$-0.374988\pi$
$383$	8.41599e8	0.765437	0.382719	+	0.923865i	$0.374988\pi$
$384$	−1.51630e6	−0.00136655
$385$	−2.41800e9	−2.15946
$386$	2.37546e8	0.210229
$387$	−1.50847e9	−1.32296
$388$	6.20260e8	0.539092
$389$	1.18066e9	1.01695	0.508477	−	0.861076i	$-0.330209\pi$
$389$	1.18066e9	1.01695	0.508477	+	0.861076i	$0.330209\pi$
$390$	−9.24762e7	−0.0789412
$391$	0	0
$392$	−4.19300e8	−0.351580
$393$	−9.05062e8	−0.752150
$394$	6.09952e8	0.502411
$395$	1.05370e9	0.860251
$396$	−4.09166e8	−0.331106
$397$	−2.31701e9	−1.85849	−0.929246	−	0.369462i	$-0.879542\pi$
$397$	−2.31701e9	−1.85849	−0.929246	+	0.369462i	$0.879542\pi$
$398$	−5.80880e8	−0.461845
$399$	3.49022e8	0.275073
$400$	−1.47132e9	−1.14947
$401$	8.28620e8	0.641727	0.320863	−	0.947125i	$-0.396027\pi$
$401$	8.28620e8	0.641727	0.320863	+	0.947125i	$0.396027\pi$
$402$	−3.36265e8	−0.258161
$403$	−1.59580e7	−0.0121454
$404$	−8.56289e8	−0.646079
$405$	1.33532e9	0.998832
$406$	−3.23589e8	−0.239968
$407$	−1.76046e9	−1.29433
$408$	−3.55323e8	−0.259008
$409$	−1.23844e8	−0.0895043	−0.0447521	−	0.998998i	$-0.514250\pi$
$409$	−1.23844e8	−0.0895043	−0.0447521	+	0.998998i	$0.514250\pi$
$410$	1.04231e9	0.746884
$411$	5.03176e8	0.357498
$412$	3.53354e8	0.248926
$413$	1.85524e9	1.29591
$414$	0	0
$415$	2.77085e9	1.90302
$416$	1.43879e8	0.0979874
$417$	−4.37736e7	−0.0295622
$418$	6.38603e8	0.427675
$419$	−1.56753e9	−1.04104	−0.520519	−	0.853850i	$-0.674261\pi$
$419$	−1.56753e9	−1.04104	−0.520519	+	0.853850i	$0.674261\pi$
$420$	5.79885e8	0.381917
$421$	2.33555e9	1.52546	0.762732	−	0.646715i	$-0.223858\pi$
$421$	2.33555e9	1.52546	0.762732	+	0.646715i	$0.223858\pi$
$422$	−4.04129e8	−0.261774
$423$	1.10553e8	0.0710195
$424$	2.87544e9	1.83199
$425$	−2.52542e9	−1.59577
$426$	6.65363e8	0.416990
$427$	2.15598e9	1.34013
$428$	8.81477e8	0.543448
$429$	8.40425e7	0.0513923
$430$	3.91162e9	2.37256
$431$	2.30436e8	0.138637	0.0693186	−	0.997595i	$-0.477917\pi$
$431$	2.30436e8	0.138637	0.0693186	+	0.997595i	$0.477917\pi$
$432$	−5.28057e8	−0.315128
$433$	6.14017e8	0.363473	0.181737	−	0.983347i	$-0.441828\pi$
$433$	6.14017e8	0.363473	0.181737	+	0.983347i	$0.441828\pi$
$434$	−1.42146e8	−0.0834683
$435$	3.75261e8	0.218585
$436$	2.76835e8	0.159963
$437$	0	0
$438$	−4.89015e8	−0.278076
$439$	5.15540e8	0.290828	0.145414	−	0.989371i	$-0.453549\pi$
$439$	5.15540e8	0.290828	0.145414	+	0.989371i	$0.453549\pi$
$440$	3.62921e9	2.03108
$441$	−4.84631e8	−0.269077
$442$	−1.03094e8	−0.0567878
$443$	1.46631e9	0.801333	0.400667	−	0.916224i	$-0.368779\pi$
$443$	1.46631e9	0.801333	0.400667	+	0.916224i	$0.368779\pi$
$444$	4.22194e8	0.228914
$445$	−1.73440e9	−0.933018
$446$	8.50667e8	0.454033
$447$	5.75242e7	0.0304631
$448$	2.19326e9	1.15243
$449$	5.09881e7	0.0265831	0.0132916	−	0.999912i	$-0.495769\pi$
$449$	5.09881e7	0.0265831	0.0132916	+	0.999912i	$0.495769\pi$
$450$	−3.38868e9	−1.75302
$451$	−9.47252e8	−0.486237
$452$	−1.37594e9	−0.700835
$453$	3.71212e8	0.187620
$454$	1.95534e9	0.980677
$455$	5.75496e8	0.286419
$456$	−5.23850e8	−0.258720
$457$	−1.46590e9	−0.718454	−0.359227	−	0.933250i	$-0.616960\pi$
$457$	−1.46590e9	−0.718454	−0.359227	+	0.933250i	$0.616960\pi$
$458$	−1.65292e9	−0.803938
$459$	−9.06370e8	−0.437483
$460$	0	0
$461$	−2.45533e9	−1.16723	−0.583615	−	0.812031i	$-0.698362\pi$
$461$	−2.45533e9	−1.16723	−0.583615	+	0.812031i	$0.698362\pi$
$462$	7.48611e8	0.353191
$463$	6.43422e7	0.0301275	0.0150637	−	0.999887i	$-0.495205\pi$
$463$	6.43422e7	0.0301275	0.0150637	+	0.999887i	$0.495205\pi$
$464$	2.43732e8	0.113266
$465$	1.64845e8	0.0760309
$466$	6.79032e8	0.310842
$467$	4.26933e9	1.93977	0.969885	−	0.243562i	$-0.0783161\pi$
$467$	4.26933e9	1.93977	0.969885	+	0.243562i	$0.0783161\pi$
$468$	9.73835e7	0.0439162
$469$	2.09264e9	0.936676
$470$	−2.86675e8	−0.127364
$471$	−3.82924e8	−0.168865
$472$	−2.78455e9	−1.21887
$473$	−3.55489e9	−1.54459
$474$	−3.26223e8	−0.140699
$475$	−3.72320e9	−1.59400
$476$	6.46465e8	0.274739
$477$	3.32346e9	1.40209
$478$	6.42357e8	0.269017
$479$	−1.34238e9	−0.558088	−0.279044	−	0.960278i	$-0.590018\pi$
$479$	−1.34238e9	−0.558088	−0.279044	+	0.960278i	$0.590018\pi$
$480$	−1.48626e9	−0.613409
$481$	4.18998e8	0.171674
$482$	−1.21774e9	−0.495325
$483$	0	0
$484$	6.62584e7	0.0265633
$485$	−6.35875e9	−2.53090
$486$	−1.88132e9	−0.743422
$487$	−1.20665e9	−0.473403	−0.236702	−	0.971582i	$-0.576066\pi$
$487$	−1.20665e9	−0.473403	−0.236702	+	0.971582i	$0.576066\pi$
$488$	−3.23594e9	−1.26046
$489$	−1.09179e9	−0.422237
$490$	1.25670e9	0.482553
$491$	−9.30374e8	−0.354709	−0.177355	−	0.984147i	$-0.556754\pi$
$491$	−9.30374e8	−0.354709	−0.177355	+	0.984147i	$0.556754\pi$
$492$	2.27170e8	0.0859949
$493$	4.18347e8	0.157243
$494$	−1.51991e8	−0.0567247
$495$	4.19467e9	1.55446
$496$	1.07067e8	0.0393974
$497$	−4.14068e9	−1.51295
$498$	−8.57851e8	−0.311250
$499$	4.02502e9	1.45016	0.725081	−	0.688664i	$-0.241802\pi$
$499$	4.02502e9	1.45016	0.725081	+	0.688664i	$0.241802\pi$
$500$	−3.94623e9	−1.41185
$501$	−4.33308e8	−0.153945
$502$	2.77795e9	0.980079
$503$	−4.09549e9	−1.43489	−0.717443	−	0.696617i	$-0.754688\pi$
$503$	−4.09549e9	−1.43489	−0.717443	+	0.696617i	$0.754688\pi$
$504$	2.96711e9	1.03235
$505$	8.77846e9	3.03318
$506$	0	0
$507$	1.19515e9	0.407280
$508$	−7.33052e8	−0.248092
$509$	3.37336e9	1.13384	0.566918	−	0.823774i	$-0.308135\pi$
$509$	3.37336e9	1.13384	0.566918	+	0.823774i	$0.308135\pi$
$510$	1.06495e9	0.355496
$511$	3.04323e9	1.00893
$512$	−2.33363e9	−0.768399
$513$	−1.33625e9	−0.436997
$514$	−2.39771e9	−0.778801
$515$	−3.62250e9	−1.16865
$516$	8.52533e8	0.273173
$517$	2.60530e8	0.0829166
$518$	3.73224e9	1.17982
$519$	−1.75735e9	−0.551789
$520$	−8.63769e8	−0.269393
$521$	1.49524e9	0.463210	0.231605	−	0.972810i	$-0.425602\pi$
$521$	1.49524e9	0.463210	0.231605	+	0.972810i	$0.425602\pi$
$522$	5.61351e8	0.172738
$523$	2.52482e9	0.771747	0.385874	−	0.922552i	$-0.373900\pi$
$523$	2.52482e9	0.771747	0.385874	+	0.922552i	$0.373900\pi$
$524$	−2.47147e9	−0.750404
$525$	−4.36458e9	−1.31639
$526$	3.08463e9	0.924173
$527$	1.83772e8	0.0546942
$528$	−5.63864e8	−0.166708
$529$	0	0
$530$	−8.61809e9	−2.51446
$531$	−3.21841e9	−0.932848
$532$	9.53078e8	0.274434
$533$	2.25451e8	0.0644920
$534$	5.36969e8	0.152600
$535$	−9.03669e9	−2.55136
$536$	−3.14087e9	−0.880993
$537$	−2.09855e9	−0.584804
$538$	3.93909e8	0.109058
$539$	−1.14209e9	−0.314152
$540$	−2.22013e9	−0.606737
$541$	−2.50718e9	−0.680761	−0.340380	−	0.940288i	$-0.610556\pi$
$541$	−2.50718e9	−0.680761	−0.340380	+	0.940288i	$0.610556\pi$
$542$	−1.97665e9	−0.533251
$543$	−1.79558e9	−0.481288
$544$	−1.65691e9	−0.441267
$545$	−2.83805e9	−0.750986
$546$	−1.78173e8	−0.0468455
$547$	2.05372e9	0.536519	0.268260	−	0.963347i	$-0.413552\pi$
$547$	2.05372e9	0.536519	0.268260	+	0.963347i	$0.413552\pi$
$548$	1.37403e9	0.356668
$549$	−3.74013e9	−0.964680
$550$	−7.98584e9	−2.04669
$551$	6.16766e8	0.157069
$552$	0	0
$553$	2.03015e9	0.510493
$554$	1.33954e9	0.334712
$555$	−4.32823e9	−1.07469
$556$	−1.19533e8	−0.0294935
$557$	−1.96653e9	−0.482179	−0.241089	−	0.970503i	$-0.577505\pi$
$557$	−1.96653e9	−0.482179	−0.241089	+	0.970503i	$0.577505\pi$
$558$	2.46591e8	0.0600837
$559$	8.46080e8	0.204866
$560$	−3.86117e9	−0.929095
$561$	−9.67831e8	−0.231435
$562$	−2.65037e9	−0.629838
$563$	3.90604e8	0.0922481	0.0461241	−	0.998936i	$-0.485313\pi$
$563$	3.90604e8	0.0922481	0.0461241	+	0.998936i	$0.485313\pi$
$564$	−6.24804e7	−0.0146645
$565$	1.41058e10	3.29025
$566$	−1.92296e9	−0.445771
$567$	2.57275e9	0.592729
$568$	6.21479e9	1.42301
$569$	−7.32372e9	−1.66663	−0.833314	−	0.552800i	$-0.813559\pi$
$569$	−7.32372e9	−1.66663	−0.833314	+	0.552800i	$0.813559\pi$
$570$	1.57005e9	0.355101
$571$	−8.71682e9	−1.95944	−0.979720	−	0.200372i	$-0.935785\pi$
$571$	−8.71682e9	−1.95944	−0.979720	+	0.200372i	$0.935785\pi$
$572$	2.29496e8	0.0512730
$573$	−5.56252e8	−0.123518
$574$	2.00821e9	0.443218
$575$	0	0
$576$	−3.80479e9	−0.829567
$577$	2.99923e6	0.000649971 0	0.000324986	−	1.00000i	$-0.499897\pi$
$577$	2.99923e6	0.000649971 0	0.000324986		1.00000i	$0.499897\pi$
$578$	−2.36922e9	−0.510338
$579$	−5.30763e8	−0.113639
$580$	1.02473e9	0.218078
$581$	5.33857e9	1.12930
$582$	1.96866e9	0.413943
$583$	7.83213e9	1.63697
$584$	−4.56762e9	−0.948954
$585$	−9.98352e8	−0.206176
$586$	5.68517e9	1.16708
$587$	4.53865e9	0.926177	0.463088	−	0.886312i	$-0.346741\pi$
$587$	4.53865e9	0.926177	0.463088	+	0.886312i	$0.346741\pi$
$588$	2.73896e8	0.0555604
$589$	2.70933e8	0.0546334
$590$	8.34570e9	1.67294
$591$	−1.36285e9	−0.271576
$592$	−2.81118e9	−0.556881
$593$	−2.03647e9	−0.401039	−0.200520	−	0.979690i	$-0.564263\pi$
$593$	−2.03647e9	−0.401039	−0.200520	+	0.979690i	$0.564263\pi$
$594$	−2.86611e9	−0.561100
$595$	−6.62740e9	−1.28983
$596$	1.57082e8	0.0303924
$597$	1.29789e9	0.249648
$598$	0	0
$599$	4.66482e9	0.886832	0.443416	−	0.896316i	$-0.353767\pi$
$599$	4.66482e9	0.886832	0.443416	+	0.896316i	$0.353767\pi$
$600$	6.55084e9	1.23813
$601$	2.16736e9	0.407259	0.203630	−	0.979048i	$-0.434726\pi$
$601$	2.16736e9	0.407259	0.203630	+	0.979048i	$0.434726\pi$
$602$	7.53649e9	1.40793
$603$	−3.63024e9	−0.674256
$604$	1.01367e9	0.187184
$605$	−6.79265e8	−0.124708
$606$	−2.71780e9	−0.496094
$607$	6.26353e9	1.13673	0.568367	−	0.822775i	$-0.307576\pi$
$607$	6.26353e9	1.13673	0.568367	+	0.822775i	$0.307576\pi$
$608$	−2.44276e9	−0.440777
$609$	7.23013e8	0.129714
$610$	9.69855e9	1.73003
$611$	−6.20075e7	−0.0109976
$612$	−1.12147e9	−0.197768
$613$	−2.31401e9	−0.405746	−0.202873	−	0.979205i	$-0.565028\pi$
$613$	−2.31401e9	−0.405746	−0.202873	+	0.979205i	$0.565028\pi$
$614$	−3.51025e8	−0.0611996
$615$	−2.32889e9	−0.403725
$616$	6.99236e9	1.20529
$617$	2.83897e9	0.486590	0.243295	−	0.969952i	$-0.421772\pi$
$617$	2.83897e9	0.486590	0.243295	+	0.969952i	$0.421772\pi$
$618$	1.12152e9	0.191139
$619$	−3.66984e9	−0.621913	−0.310956	−	0.950424i	$-0.600649\pi$
$619$	−3.66984e9	−0.621913	−0.310956	+	0.950424i	$0.600649\pi$
$620$	4.50144e8	0.0758544
$621$	0	0
$622$	−3.51105e9	−0.585019
$623$	−3.34166e9	−0.553674
$624$	1.34202e8	0.0221113
$625$	2.35983e10	3.86634
$626$	5.55323e9	0.904764
$627$	−1.42687e9	−0.231178
$628$	−1.04566e9	−0.168473
$629$	−4.82517e9	−0.773100
$630$	−8.89285e9	−1.41693
$631$	6.90058e8	0.109341	0.0546705	−	0.998504i	$-0.482589\pi$
$631$	6.90058e8	0.109341	0.0546705	+	0.998504i	$0.482589\pi$
$632$	−3.04707e9	−0.480145
$633$	9.02968e8	0.141501
$634$	−1.30001e9	−0.202598
$635$	7.51507e9	1.16473
$636$	−1.87830e9	−0.289511
$637$	2.71823e8	0.0416676
$638$	1.32289e9	0.201675
$639$	7.18311e9	1.08908
$640$	4.24483e7	0.00640074
$641$	−4.66391e9	−0.699435	−0.349718	−	0.936855i	$-0.613722\pi$
$641$	−4.66391e9	−0.699435	−0.349718	+	0.936855i	$0.613722\pi$
$642$	2.79775e9	0.417288
$643$	−4.09785e9	−0.607879	−0.303940	−	0.952691i	$-0.598302\pi$
$643$	−4.09785e9	−0.607879	−0.303940	+	0.952691i	$0.598302\pi$
$644$	0	0
$645$	−8.73995e9	−1.28248
$646$	1.75032e9	0.255448
$647$	−2.96565e9	−0.430481	−0.215241	−	0.976561i	$-0.569054\pi$
$647$	−2.96565e9	−0.430481	−0.215241	+	0.976561i	$0.569054\pi$
$648$	−3.86146e9	−0.557493
$649$	−7.58458e9	−1.08912
$650$	1.90067e9	0.271462
$651$	3.17605e8	0.0451185
$652$	−2.98135e9	−0.421257
$653$	7.89168e9	1.10911	0.554553	−	0.832148i	$-0.312889\pi$
$653$	7.89168e9	1.10911	0.554553	+	0.832148i	$0.312889\pi$
$654$	8.78656e8	0.122828
$655$	2.53369e10	3.52297
$656$	−1.51261e9	−0.209201
$657$	−5.27930e9	−0.726269
$658$	−5.52334e8	−0.0755807
$659$	2.12909e9	0.289798	0.144899	−	0.989446i	$-0.453714\pi$
$659$	2.12909e9	0.289798	0.144899	+	0.989446i	$0.453714\pi$
$660$	−2.37068e9	−0.320973
$661$	−7.19461e9	−0.968952	−0.484476	−	0.874804i	$-0.660990\pi$
$661$	−7.19461e9	−0.968952	−0.484476	+	0.874804i	$0.660990\pi$
$662$	−2.43236e8	−0.0325855
$663$	2.30348e8	0.0306964
$664$	−8.01271e9	−1.06216
$665$	−9.77072e9	−1.28840
$666$	−6.47457e9	−0.849281
$667$	0	0
$668$	−1.18324e9	−0.153587
$669$	−1.90069e9	−0.245426
$670$	9.41361e9	1.20919
$671$	−8.81406e9	−1.12628
$672$	−2.86356e9	−0.364011
$673$	1.40355e10	1.77491	0.887456	−	0.460893i	$-0.152471\pi$
$673$	1.40355e10	1.77491	0.887456	+	0.460893i	$0.152471\pi$
$674$	−9.15115e9	−1.15124
$675$	1.67101e10	2.09130
$676$	3.26360e9	0.406335
$677$	−8.73683e9	−1.08216	−0.541082	−	0.840970i	$-0.681985\pi$
$677$	−8.73683e9	−1.08216	−0.541082	+	0.840970i	$0.681985\pi$
$678$	−4.36715e9	−0.538139
$679$	−1.22514e10	−1.50190
$680$	9.94713e9	1.21316
$681$	−4.36892e9	−0.530101
$682$	5.81120e8	0.0701489
$683$	1.18837e10	1.42718	0.713591	−	0.700562i	$-0.247067\pi$
$683$	1.18837e10	1.42718	0.713591	+	0.700562i	$0.247067\pi$
$684$	−1.65337e9	−0.197548
$685$	−1.40862e10	−1.67447
$686$	−5.03416e9	−0.595378
$687$	3.69321e9	0.434566
$688$	−5.67659e9	−0.664551
$689$	−1.86408e9	−0.217119
$690$	0	0
$691$	−9.16684e9	−1.05693	−0.528465	−	0.848955i	$-0.677232\pi$
$691$	−9.16684e9	−1.05693	−0.528465	+	0.848955i	$0.677232\pi$
$692$	−4.79882e9	−0.550508
$693$	8.08184e9	0.922452
$694$	−7.06903e9	−0.802789
$695$	1.22543e9	0.138465
$696$	−1.08518e9	−0.122002
$697$	−2.59628e9	−0.290427
$698$	−3.81926e9	−0.425094
$699$	−1.51720e9	−0.168024
$700$	−1.19184e10	−1.31333
$701$	4.19200e9	0.459629	0.229815	−	0.973234i	$-0.426188\pi$
$701$	4.19200e9	0.459629	0.229815	+	0.973234i	$0.426188\pi$
$702$	6.82148e8	0.0744216
$703$	−7.11372e9	−0.772241
$704$	−8.96644e9	−0.968536
$705$	6.40533e8	0.0688462
$706$	5.05928e9	0.541093
$707$	1.69134e10	1.79996
$708$	1.81893e9	0.192619
$709$	−1.03587e9	−0.109155	−0.0545777	−	0.998510i	$-0.517381\pi$
$709$	−1.03587e9	−0.109155	−0.0545777	+	0.998510i	$0.517381\pi$
$710$	−1.86266e10	−1.95312
$711$	−3.52183e9	−0.367473
$712$	5.01553e9	0.520759
$713$	0	0
$714$	2.05184e9	0.210959
$715$	−2.35274e9	−0.240714
$716$	−5.73055e9	−0.583446
$717$	−1.43525e9	−0.145416
$718$	5.16056e8	0.0520309
$719$	−1.68901e10	−1.69466	−0.847329	−	0.531068i	$-0.821791\pi$
$719$	−1.68901e10	−1.69466	−0.847329	+	0.531068i	$0.821791\pi$
$720$	6.69822e9	0.668799
$721$	−6.97944e9	−0.693501
$722$	−5.16680e9	−0.510906
$723$	2.72086e9	0.267746
$724$	−4.90321e9	−0.480171
$725$	−7.71277e9	−0.751670
$726$	2.10300e8	0.0203967
$727$	−8.72966e9	−0.842611	−0.421305	−	0.906919i	$-0.638428\pi$
$727$	−8.72966e9	−0.842611	−0.421305	+	0.906919i	$0.638428\pi$
$728$	−1.66422e9	−0.159864
$729$	−1.18329e9	−0.113122
$730$	1.36898e10	1.30247
$731$	−9.74344e9	−0.922574
$732$	2.11379e9	0.199192
$733$	1.63552e10	1.53389	0.766943	−	0.641715i	$-0.221777\pi$
$733$	1.63552e10	1.53389	0.766943	+	0.641715i	$0.221777\pi$
$734$	−1.41416e9	−0.131997
$735$	−2.80791e9	−0.260842
$736$	0	0
$737$	−8.55510e9	−0.787207
$738$	−3.48377e9	−0.319045
$739$	−1.54400e10	−1.40732	−0.703660	−	0.710537i	$-0.748452\pi$
$739$	−1.54400e10	−1.40732	−0.703660	+	0.710537i	$0.748452\pi$
$740$	−1.18191e10	−1.07220
$741$	3.39601e8	0.0306623
$742$	−1.66044e10	−1.49214
$743$	−3.46427e8	−0.0309850	−0.0154925	−	0.999880i	$-0.504932\pi$
$743$	−3.46427e8	−0.0309850	−0.0154925	+	0.999880i	$0.504932\pi$
$744$	−4.76697e8	−0.0424363
$745$	−1.61037e9	−0.142685
$746$	1.51502e9	0.133608
$747$	−9.26117e9	−0.812912
$748$	−2.64287e9	−0.230898
$749$	−1.74109e10	−1.51403
$750$	−1.25251e10	−1.08409
$751$	−4.24477e9	−0.365691	−0.182845	−	0.983142i	$-0.558531\pi$
$751$	−4.24477e9	−0.365691	−0.182845	+	0.983142i	$0.558531\pi$
$752$	4.16026e8	0.0356745
$753$	−6.20692e9	−0.529778
$754$	−3.14855e8	−0.0267492
$755$	−1.03919e10	−0.878784
$756$	−4.27751e9	−0.360051
$757$	1.05096e10	0.880540	0.440270	−	0.897865i	$-0.354883\pi$
$757$	1.05096e10	0.880540	0.440270	+	0.897865i	$0.354883\pi$
$758$	8.85073e9	0.738137
$759$	0	0
$760$	1.46650e10	1.21181
$761$	1.08964e10	0.896265	0.448133	−	0.893967i	$-0.352089\pi$
$761$	1.08964e10	0.896265	0.448133	+	0.893967i	$0.352089\pi$
$762$	−2.32666e9	−0.190498
$763$	−5.46804e9	−0.445652
$764$	−1.51896e9	−0.123231
$765$	1.14970e10	0.928473
$766$	7.29422e9	0.586379
$767$	1.80517e9	0.144455
$768$	5.19176e9	0.413571
$769$	1.05679e10	0.838007	0.419004	−	0.907985i	$-0.362379\pi$
$769$	1.05679e10	0.838007	0.419004	+	0.907985i	$0.362379\pi$
$770$	−2.09571e10	−1.65430
$771$	5.35735e9	0.420978
$772$	−1.44936e9	−0.113375
$773$	−5.98162e9	−0.465791	−0.232895	−	0.972502i	$-0.574820\pi$
$773$	−5.98162e9	−0.465791	−0.232895	+	0.972502i	$0.574820\pi$
$774$	−1.30741e10	−1.01348
$775$	−3.38807e9	−0.261454
$776$	1.83882e10	1.41261
$777$	−8.33916e9	−0.637747
$778$	1.02329e10	0.779058
$779$	−3.82768e9	−0.290104
$780$	5.64233e8	0.0425723
$781$	1.69279e10	1.27152
$782$	0	0
$783$	−2.76810e9	−0.206071
$784$	−1.82374e9	−0.135162
$785$	1.07198e10	0.790939
$786$	−7.84427e9	−0.576200
$787$	−2.33391e10	−1.70676	−0.853382	−	0.521286i	$-0.825452\pi$
$787$	−2.33391e10	−1.70676	−0.853382	+	0.521286i	$0.825452\pi$
$788$	−3.72155e9	−0.270946
$789$	−6.89216e9	−0.499558
$790$	9.13249e9	0.659014
$791$	2.71776e10	1.95251
$792$	−1.21301e10	−0.867615
$793$	2.09779e9	0.149384
$794$	−2.00817e10	−1.42374
$795$	1.92559e10	1.35918
$796$	3.54417e9	0.249069
$797$	1.22501e9	0.0857106	0.0428553	−	0.999081i	$-0.486355\pi$
$797$	1.22501e9	0.0857106	0.0428553	+	0.999081i	$0.486355\pi$
$798$	3.02501e9	0.210725
$799$	7.14076e8	0.0495257
$800$	3.05472e10	2.10939
$801$	5.79700e9	0.398556
$802$	7.18174e9	0.491608
$803$	−1.24413e10	−0.847933
$804$	2.05168e9	0.139224
$805$	0	0
$806$	−1.38309e8	−0.00930420
$807$	−8.80132e8	−0.0589509
$808$	−2.53855e10	−1.69296
$809$	−3.24093e9	−0.215204	−0.107602	−	0.994194i	$-0.534317\pi$
$809$	−3.24093e9	−0.215204	−0.107602	+	0.994194i	$0.534317\pi$
$810$	1.15733e10	0.765176
$811$	2.70263e10	1.77915	0.889577	−	0.456786i	$-0.150999\pi$
$811$	2.70263e10	1.77915	0.889577	+	0.456786i	$0.150999\pi$
$812$	1.97434e9	0.129412
$813$	4.41653e9	0.288247
$814$	−1.52581e10	−0.991551
$815$	3.05641e10	1.97770
$816$	−1.54547e9	−0.0995739
$817$	−1.43647e10	−0.921550
$818$	−1.07337e9	−0.0685666
$819$	−1.92352e9	−0.122349
$820$	−6.35953e9	−0.402788
$821$	−2.11616e10	−1.33459	−0.667294	−	0.744794i	$-0.732548\pi$
$821$	−2.11616e10	−1.33459	−0.667294	+	0.744794i	$0.732548\pi$
$822$	4.36108e9	0.273869
$823$	3.92486e9	0.245428	0.122714	−	0.992442i	$-0.460840\pi$
$823$	3.92486e9	0.245428	0.122714	+	0.992442i	$0.460840\pi$
$824$	1.04755e10	0.652274
$825$	1.78432e10	1.10633
$826$	1.60796e10	0.992761
$827$	−2.54703e10	−1.56591	−0.782953	−	0.622081i	$-0.786287\pi$
$827$	−2.54703e10	−1.56591	−0.782953	+	0.622081i	$0.786287\pi$
$828$	0	0
$829$	−6.33950e9	−0.386468	−0.193234	−	0.981153i	$-0.561898\pi$
$829$	−6.33950e9	−0.386468	−0.193234	+	0.981153i	$0.561898\pi$
$830$	2.40152e10	1.45785
$831$	−2.99301e9	−0.180927
$832$	2.13406e9	0.128462
$833$	−3.13031e9	−0.187642
$834$	−3.79391e8	−0.0226467
$835$	1.21303e10	0.721055
$836$	−3.89636e9	−0.230641
$837$	−1.21597e9	−0.0716779
$838$	−1.35859e10	−0.797509
$839$	2.56356e10	1.49857	0.749284	−	0.662248i	$-0.230398\pi$
$839$	2.56356e10	1.49857	0.749284	+	0.662248i	$0.230398\pi$
$840$	1.71912e10	1.00076
$841$	−1.59722e10	−0.925932
$842$	2.02425e10	1.16861
$843$	5.92186e9	0.340457
$844$	2.46575e9	0.141172
$845$	−3.34577e10	−1.90764
$846$	9.58170e8	0.0544060
$847$	−1.30873e9	−0.0740047
$848$	1.25067e10	0.704297
$849$	4.29657e9	0.240960
$850$	−2.18880e10	−1.22248
$851$	0	0
$852$	−4.05964e9	−0.224879
$853$	−1.12411e10	−0.620139	−0.310069	−	0.950714i	$-0.600352\pi$
$853$	−1.12411e10	−0.620139	−0.310069	+	0.950714i	$0.600352\pi$
$854$	1.86861e10	1.02664
$855$	1.69499e10	0.927441
$856$	2.61322e10	1.42403
$857$	−8.09752e9	−0.439460	−0.219730	−	0.975561i	$-0.570518\pi$
$857$	−8.09752e9	−0.439460	−0.219730	+	0.975561i	$0.570518\pi$
$858$	7.28405e8	0.0393702
$859$	−1.02929e10	−0.554068	−0.277034	−	0.960860i	$-0.589351\pi$
$859$	−1.02929e10	−0.554068	−0.277034	+	0.960860i	$0.589351\pi$
$860$	−2.38663e10	−1.27950
$861$	−4.48705e9	−0.239580
$862$	1.99721e9	0.106206
$863$	3.60482e10	1.90918	0.954588	−	0.297930i	$-0.0962961\pi$
$863$	3.60482e10	1.90918	0.954588	+	0.297930i	$0.0962961\pi$
$864$	1.09634e10	0.578290
$865$	4.91964e10	2.58450
$866$	5.32175e9	0.278446
$867$	5.29368e9	0.275861
$868$	8.67289e8	0.0450137
$869$	−8.29962e9	−0.429031
$870$	3.25243e9	0.167452
$871$	2.03615e9	0.104411
$872$	8.20704e9	0.419159
$873$	2.12532e10	1.08112
$874$	0	0
$875$	7.79458e10	3.93337
$876$	2.98367e9	0.149964
$877$	2.72918e10	1.36626	0.683130	−	0.730297i	$-0.260618\pi$
$877$	2.72918e10	1.36626	0.683130	+	0.730297i	$0.260618\pi$
$878$	4.46824e9	0.222795
$879$	−1.27027e10	−0.630863
$880$	1.57852e10	0.780836
$881$	1.33573e10	0.658117	0.329058	−	0.944310i	$-0.393269\pi$
$881$	1.33573e10	0.658117	0.329058	+	0.944310i	$0.393269\pi$
$882$	−4.20034e9	−0.206132
$883$	−1.66840e9	−0.0815527	−0.0407763	−	0.999168i	$-0.512983\pi$
$883$	−1.66840e9	−0.0815527	−0.0407763	+	0.999168i	$0.512983\pi$
$884$	6.29015e8	0.0306252
$885$	−1.86472e10	−0.904302
$886$	1.27087e10	0.613878
$887$	−4.54692e9	−0.218769	−0.109384	−	0.994000i	$-0.534888\pi$
$887$	−4.54692e9	−0.218769	−0.109384	+	0.994000i	$0.534888\pi$
$888$	1.25163e10	0.599835
$889$	1.44792e10	0.691177
$890$	−1.50322e10	−0.714758
$891$	−1.05179e10	−0.498145
$892$	−5.19025e9	−0.244856
$893$	1.05276e9	0.0494707
$894$	4.98568e8	0.0233369
$895$	5.87482e10	2.73914
$896$	8.17847e7	0.00379834
$897$	0	0
$898$	4.41919e8	0.0203646
$899$	5.61249e8	0.0257630
$900$	2.06757e10	0.945389
$901$	2.14667e10	0.977754
$902$	−8.20993e9	−0.372492
$903$	−1.68392e10	−0.761052
$904$	−4.07911e10	−1.83644
$905$	5.02665e10	2.25428
$906$	3.21733e9	0.143730
$907$	2.70866e10	1.20539	0.602697	−	0.797970i	$-0.294093\pi$
$907$	2.70866e10	1.20539	0.602697	+	0.797970i	$0.294093\pi$
$908$	−1.19303e10	−0.528871
$909$	−2.93408e10	−1.29568
$910$	4.98788e9	0.219418
$911$	1.72237e10	0.754764	0.377382	−	0.926058i	$-0.376824\pi$
$911$	1.72237e10	0.754764	0.377382	+	0.926058i	$0.376824\pi$
$912$	−2.27848e9	−0.0994633
$913$	−2.18251e10	−0.949091
$914$	−1.27051e10	−0.550387
$915$	−2.16700e10	−0.935159
$916$	1.00851e10	0.433557
$917$	4.88163e10	2.09061
$918$	−7.85560e9	−0.335143
$919$	−3.58011e10	−1.52157	−0.760785	−	0.649004i	$-0.775186\pi$
$919$	−3.58011e10	−1.52157	−0.760785	+	0.649004i	$0.775186\pi$
$920$	0	0
$921$	7.84314e8	0.0330812
$922$	−2.12806e10	−0.894180
$923$	−4.02891e9	−0.168648
$924$	−4.56756e9	−0.190473
$925$	8.89583e10	3.69565
$926$	5.57661e8	0.0230798
$927$	1.21077e10	0.499209
$928$	−5.06028e9	−0.207853
$929$	−1.63750e10	−0.670078	−0.335039	−	0.942204i	$-0.608750\pi$
$929$	−1.63750e10	−0.670078	−0.335039	+	0.942204i	$0.608750\pi$
$930$	1.42873e9	0.0582451
$931$	−4.61499e9	−0.187433
$932$	−4.14304e9	−0.167634
$933$	7.84492e9	0.316230
$934$	3.70027e10	1.48600
$935$	2.70940e10	1.08401
$936$	2.88703e9	0.115076
$937$	6.48254e9	0.257428	0.128714	−	0.991682i	$-0.458915\pi$
$937$	6.48254e9	0.257428	0.128714	+	0.991682i	$0.458915\pi$
$938$	1.81371e10	0.717560
$939$	−1.24079e10	−0.489067
$940$	1.74911e9	0.0686863
$941$	−4.11357e10	−1.60937	−0.804683	−	0.593705i	$-0.797665\pi$
$941$	−4.11357e10	−1.60937	−0.804683	+	0.593705i	$0.797665\pi$
$942$	−3.31884e9	−0.129363
$943$	0	0
$944$	−1.21114e10	−0.468588
$945$	4.38519e10	1.69035
$946$	−3.08106e10	−1.18326
$947$	8.70120e9	0.332931	0.166466	−	0.986047i	$-0.446765\pi$
$947$	8.70120e9	0.332931	0.166466	+	0.986047i	$0.446765\pi$
$948$	1.99041e9	0.0758777
$949$	2.96109e9	0.112466
$950$	−3.22694e10	−1.22112
$951$	2.90469e9	0.109514
$952$	1.91651e10	0.719914
$953$	−1.32812e9	−0.0497063	−0.0248532	−	0.999691i	$-0.507912\pi$
$953$	−1.32812e9	−0.0497063	−0.0248532	+	0.999691i	$0.507912\pi$
$954$	2.88048e10	1.07410
$955$	1.55720e10	0.578541
$956$	−3.91927e9	−0.145078
$957$	−2.95581e9	−0.109015
$958$	−1.16346e10	−0.427535
$959$	−2.71398e10	−0.993669
$960$	−2.20447e10	−0.804181
$961$	−2.72661e10	−0.991039
$962$	3.63150e9	0.131515
$963$	3.02039e10	1.08986
$964$	7.42990e9	0.267124
$965$	1.48585e10	0.532267
$966$	0	0
$967$	1.71240e10	0.608993	0.304497	−	0.952513i	$-0.401512\pi$
$967$	1.71240e10	0.608993	0.304497	+	0.952513i	$0.401512\pi$
$968$	1.96429e9	0.0696054
$969$	−3.91083e9	−0.138082
$970$	−5.51120e10	−1.93885
$971$	2.55589e10	0.895932	0.447966	−	0.894051i	$-0.352149\pi$
$971$	2.55589e10	0.895932	0.447966	+	0.894051i	$0.352149\pi$
$972$	1.14787e10	0.400921
$973$	2.36102e9	0.0821683
$974$	−1.04582e10	−0.362661
$975$	−4.24677e9	−0.146738
$976$	−1.40746e10	−0.484577
$977$	−4.43825e9	−0.152258	−0.0761291	−	0.997098i	$-0.524256\pi$
$977$	−4.43825e9	−0.152258	−0.0761291	+	0.997098i	$0.524256\pi$
$978$	−9.46262e9	−0.323463
$979$	1.36613e10	0.465322
$980$	−7.66761e9	−0.260237
$981$	9.48577e9	0.320798
$982$	−8.06365e9	−0.271732
$983$	3.95151e10	1.32686	0.663430	−	0.748238i	$-0.269100\pi$
$983$	3.95151e10	1.32686	0.663430	+	0.748238i	$0.269100\pi$
$984$	6.73466e9	0.225337
$985$	3.81524e10	1.27202
$986$	3.62586e9	0.120460
$987$	1.23411e9	0.0408549
$988$	9.27353e8	0.0305911
$989$	0	0
$990$	3.63556e10	1.19083
$991$	−3.72174e10	−1.21475	−0.607377	−	0.794414i	$-0.707778\pi$
$991$	−3.72174e10	−1.21475	−0.607377	+	0.794414i	$0.707778\pi$
$992$	−2.22288e9	−0.0722979
$993$	5.43475e8	0.0176140
$994$	−3.58877e10	−1.15903
$995$	−3.63340e10	−1.16932
$996$	5.23408e9	0.167854
$997$	−5.13840e10	−1.64208	−0.821040	−	0.570870i	$-0.806606\pi$
$997$	−5.13840e10	−1.64208	−0.821040	+	0.570870i	$0.806606\pi$
$998$	3.48853e10	1.11093
$999$	3.19271e10	1.01316

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.8.a.k.1.44		65
23.9	even	11		23.8.c.a.12.9	yes	130
23.18	even	11		23.8.c.a.2.9	✓	130
23.22	odd	2		529.8.a.j.1.44		65

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.8.c.a.2.9	✓	130	23.18	even	11
23.8.c.a.12.9	yes	130	23.9	even	11
529.8.a.j.1.44		65	23.22	odd	2
529.8.a.k.1.44		65	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:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q+8.66710 q^{2} -19.3654 q^{3} -52.8813 q^{4} +542.126 q^{5} -167.842 q^{6} +1044.51 q^{7} -1567.72 q^{8} -1811.98 q^{9} +O(q^{10})\)	\(q+8.66710 q^{2} -19.3654 q^{3} -52.8813 q^{4} +542.126 q^{5} -167.842 q^{6} +1044.51 q^{7} -1567.72 q^{8} -1811.98 q^{9} +4698.67 q^{10} -4270.15 q^{11} +1024.07 q^{12} +1016.32 q^{13} +9052.88 q^{14} -10498.5 q^{15} -6818.76 q^{16} -11703.9 q^{17} -15704.6 q^{18} -17254.9 q^{19} -28668.4 q^{20} -20227.3 q^{21} -37009.9 q^{22} +30359.4 q^{24} +215776. q^{25} +8808.52 q^{26} +77441.8 q^{27} -55235.1 q^{28} -35744.3 q^{29} -90991.5 q^{30} -15701.8 q^{31} +141569. q^{32} +82693.2 q^{33} -101439. q^{34} +566257. q^{35} +95820.0 q^{36} +412271. q^{37} -149550. q^{38} -19681.4 q^{39} -849901. q^{40} +221831. q^{41} -175312. q^{42} +832497. q^{43} +225811. q^{44} -982323. q^{45} -61012.0 q^{47} +132048. q^{48} +267459. q^{49} +1.87015e6 q^{50} +226650. q^{51} -53744.2 q^{52} -1.83416e6 q^{53} +671196. q^{54} -2.31496e6 q^{55} -1.63750e6 q^{56} +334149. q^{57} -309800. q^{58} +1.77618e6 q^{59} +555174. q^{60} +2.06411e6 q^{61} -136089. q^{62} -1.89263e6 q^{63} +2.09979e6 q^{64} +550972. q^{65} +716710. q^{66} +2.00346e6 q^{67} +618917. q^{68} +4.90780e6 q^{70} -3.96423e6 q^{71} +2.84067e6 q^{72} +2.91355e6 q^{73} +3.57320e6 q^{74} -4.17859e6 q^{75} +912464. q^{76} -4.46022e6 q^{77} -170580. q^{78} +1.94364e6 q^{79} -3.69663e6 q^{80} +2.46311e6 q^{81} +1.92263e6 q^{82} +5.11107e6 q^{83} +1.06965e6 q^{84} -6.34498e6 q^{85} +7.21533e6 q^{86} +692202. q^{87} +6.69439e6 q^{88} -3.19926e6 q^{89} -8.51390e6 q^{90} +1.06155e6 q^{91} +304071. q^{93} -528797. q^{94} -9.35436e6 q^{95} -2.74154e6 q^{96} -1.17293e7 q^{97} +2.31809e6 q^{98} +7.73744e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 65 q + 8 q^{2} + 14 q^{3} + 3776 q^{4} + 1181 q^{5} + 1082 q^{6} + 3628 q^{7} - 5757 q^{8} + 38263 q^{9}+O(q^{10}) \) 65 * q + 8 * q^2 + 14 * q^3 + 3776 * q^4 + 1181 * q^5 + 1082 * q^6 + 3628 * q^7 - 5757 * q^8 + 38263 * q^9	\( 65 q + 8 q^{2} + 14 q^{3} + 3776 q^{4} + 1181 q^{5} + 1082 q^{6} + 3628 q^{7} - 5757 q^{8} + 38263 q^{9} + 6879 q^{10} + 26147 q^{11} + 35689 q^{12} - 100 q^{13} + 55020 q^{14} + 92935 q^{15} + 176888 q^{16} + 89552 q^{17} + 190670 q^{18} + 169530 q^{19} + 210098 q^{20} + 190951 q^{21} + 218663 q^{22} + 190835 q^{24} + 721210 q^{25} + 186894 q^{26} - 670321 q^{27} + 366019 q^{28} + 340963 q^{29} + 671873 q^{30} - 175163 q^{31} - 406068 q^{32} + 726837 q^{33} + 1110895 q^{34} - 596883 q^{35} + 361164 q^{36} + 790283 q^{37} + 1963838 q^{38} - 21993 q^{39} + 1600645 q^{40} - 623859 q^{41} + 2696872 q^{42} + 1189188 q^{43} + 3885217 q^{44} + 2158369 q^{45} + 1365507 q^{47} + 1218748 q^{48} + 5854235 q^{49} - 2728396 q^{50} + 4554663 q^{51} + 7887791 q^{52} + 4362562 q^{53} + 5072916 q^{54} - 3989544 q^{55} + 12949007 q^{56} + 551326 q^{57} - 7443768 q^{58} + 13201460 q^{59} + 19296285 q^{60} + 8838644 q^{61} - 14615728 q^{62} + 12479203 q^{63} - 9711751 q^{64} + 13544545 q^{65} + 4907285 q^{66} + 5760553 q^{67} + 17044359 q^{68} + 6122411 q^{70} + 4531745 q^{71} + 10759455 q^{72} - 2535486 q^{73} + 21404597 q^{74} + 22917428 q^{75} + 21958812 q^{76} + 11733492 q^{77} - 35437508 q^{78} + 27234683 q^{79} + 28932289 q^{80} + 3995985 q^{81} - 11682773 q^{82} + 39797339 q^{83} + 33971997 q^{84} - 19766357 q^{85} + 43836707 q^{86} - 13972389 q^{87} + 33099818 q^{88} + 41235321 q^{89} + 17210275 q^{90} + 30292506 q^{91} + 47965734 q^{93} - 9981701 q^{94} - 5998448 q^{95} - 48738628 q^{96} + 13984256 q^{97} + 56728191 q^{98} + 81303822 q^{99}+O(q^{100}) \) 65 * q + 8 * q^2 + 14 * q^3 + 3776 * q^4 + 1181 * q^5 + 1082 * q^6 + 3628 * q^7 - 5757 * q^8 + 38263 * q^9 + 6879 * q^10 + 26147 * q^11 + 35689 * q^12 - 100 * q^13 + 55020 * q^14 + 92935 * q^15 + 176888 * q^16 + 89552 * q^17 + 190670 * q^18 + 169530 * q^19 + 210098 * q^20 + 190951 * q^21 + 218663 * q^22 + 190835 * q^24 + 721210 * q^25 + 186894 * q^26 - 670321 * q^27 + 366019 * q^28 + 340963 * q^29 + 671873 * q^30 - 175163 * q^31 - 406068 * q^32 + 726837 * q^33 + 1110895 * q^34 - 596883 * q^35 + 361164 * q^36 + 790283 * q^37 + 1963838 * q^38 - 21993 * q^39 + 1600645 * q^40 - 623859 * q^41 + 2696872 * q^42 + 1189188 * q^43 + 3885217 * q^44 + 2158369 * q^45 + 1365507 * q^47 + 1218748 * q^48 + 5854235 * q^49 - 2728396 * q^50 + 4554663 * q^51 + 7887791 * q^52 + 4362562 * q^53 + 5072916 * q^54 - 3989544 * q^55 + 12949007 * q^56 + 551326 * q^57 - 7443768 * q^58 + 13201460 * q^59 + 19296285 * q^60 + 8838644 * q^61 - 14615728 * q^62 + 12479203 * q^63 - 9711751 * q^64 + 13544545 * q^65 + 4907285 * q^66 + 5760553 * q^67 + 17044359 * q^68 + 6122411 * q^70 + 4531745 * q^71 + 10759455 * q^72 - 2535486 * q^73 + 21404597 * q^74 + 22917428 * q^75 + 21958812 * q^76 + 11733492 * q^77 - 35437508 * q^78 + 27234683 * q^79 + 28932289 * q^80 + 3995985 * q^81 - 11682773 * q^82 + 39797339 * q^83 + 33971997 * q^84 - 19766357 * q^85 + 43836707 * q^86 - 13972389 * q^87 + 33099818 * q^88 + 41235321 * q^89 + 17210275 * q^90 + 30292506 * q^91 + 47965734 * q^93 - 9981701 * q^94 - 5998448 * q^95 - 48738628 * q^96 + 13984256 * q^97 + 56728191 * q^98 + 81303822 * q^99

Introduction

L-functions

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