LMFDB - Embedded newform 29.10.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,10,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, 10, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 10 $
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:	$14.9360392488$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 4803 x^{10} + 14952 x^{9} + 8248476 x^{8} - 14809944 x^{7} - 6122244486 x^{6} + \cdots + 40\!\cdots\!38 $ x^12 - 4x^11 - 4803x^10 + 14952x^9 + 8248476x^8 - 14809944x^7 - 6122244486x^6 - 1026481216x^5 + 1899055440249x^4 + 3992697832188x^3 - 174144148490503x^2 - 282853247198664*x + 4071614738753338
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$9.20723$ 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)

$f(q)$	$=$	$q+10.2072 q^{2} -225.321 q^{3} -407.813 q^{4} -1619.94 q^{5} -2299.90 q^{6} -263.065 q^{7} -9388.73 q^{8} +31086.4 q^{9} +O(q^{10})$	\(q+10.2072 q^{2} -225.321 q^{3} -407.813 q^{4} -1619.94 q^{5} -2299.90 q^{6} -263.065 q^{7} -9388.73 q^{8} +31086.4 q^{9} -16535.1 q^{10} -15854.8 q^{11} +91888.6 q^{12} +37215.6 q^{13} -2685.16 q^{14} +365007. q^{15} +112967. q^{16} -249809. q^{17} +317306. q^{18} -73529.0 q^{19} +660634. q^{20} +59274.0 q^{21} -161833. q^{22} -1.69419e6 q^{23} +2.11548e6 q^{24} +671096. q^{25} +379868. q^{26} -2.56943e6 q^{27} +107281. q^{28} +707281. q^{29} +3.72571e6 q^{30} +8.52813e6 q^{31} +5.96011e6 q^{32} +3.57241e6 q^{33} -2.54986e6 q^{34} +426151. q^{35} -1.26774e7 q^{36} -1.01195e7 q^{37} -750527. q^{38} -8.38545e6 q^{39} +1.52092e7 q^{40} -2.51895e7 q^{41} +605023. q^{42} +1.42179e7 q^{43} +6.46577e6 q^{44} -5.03583e7 q^{45} -1.72930e7 q^{46} -2.94566e7 q^{47} -2.54538e7 q^{48} -4.02844e7 q^{49} +6.85003e6 q^{50} +5.62872e7 q^{51} -1.51770e7 q^{52} +1.04466e8 q^{53} -2.62268e7 q^{54} +2.56838e7 q^{55} +2.46985e6 q^{56} +1.65676e7 q^{57} +7.21938e6 q^{58} +4.40400e7 q^{59} -1.48855e8 q^{60} +1.29768e8 q^{61} +8.70486e7 q^{62} -8.17776e6 q^{63} +2.99708e6 q^{64} -6.02873e7 q^{65} +3.64644e7 q^{66} -3.03199e8 q^{67} +1.01875e8 q^{68} +3.81736e8 q^{69} +4.34982e6 q^{70} +2.30424e8 q^{71} -2.91862e8 q^{72} +3.68404e8 q^{73} -1.03292e8 q^{74} -1.51212e8 q^{75} +2.99861e7 q^{76} +4.17083e6 q^{77} -8.55922e7 q^{78} +1.14178e8 q^{79} -1.83000e8 q^{80} -3.29277e7 q^{81} -2.57115e8 q^{82} +6.43009e8 q^{83} -2.41727e7 q^{84} +4.04677e8 q^{85} +1.45125e8 q^{86} -1.59365e8 q^{87} +1.48856e8 q^{88} -2.06740e8 q^{89} -5.14019e8 q^{90} -9.79013e6 q^{91} +6.90911e8 q^{92} -1.92156e9 q^{93} -3.00670e8 q^{94} +1.19113e8 q^{95} -1.34294e9 q^{96} -9.20362e7 q^{97} -4.11192e8 q^{98} -4.92868e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9}+O(q^{10}) $ 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9	\( 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9} - 46678 q^{10} + 24474 q^{11} - 14210 q^{12} + 107722 q^{13} + 677768 q^{14} + 505426 q^{15} + 1656882 q^{16} + 982120 q^{17} + 2364102 q^{18} + 2084360 q^{19} + 4689410 q^{20} + 2911344 q^{21} + 2725230 q^{22} + 3004004 q^{23} + 7893170 q^{24} + 6339542 q^{25} + 6863698 q^{26} + 7881014 q^{27} + 5116944 q^{28} + 8487372 q^{29} + 10924626 q^{30} + 17872478 q^{31} + 5122946 q^{32} - 860442 q^{33} + 15662848 q^{34} - 22252312 q^{35} - 35199980 q^{36} + 452980 q^{37} - 68665276 q^{38} - 29528222 q^{39} - 61623214 q^{40} - 69039804 q^{41} - 150603216 q^{42} + 5379186 q^{43} - 58283762 q^{44} - 63687756 q^{45} - 76817844 q^{46} - 49104062 q^{47} - 99120062 q^{48} + 73113148 q^{49} - 281373726 q^{50} + 1578252 q^{51} - 49849646 q^{52} + 2253998 q^{53} - 166064634 q^{54} + 82907066 q^{55} + 119369464 q^{56} + 69024164 q^{57} + 11316496 q^{58} + 51587572 q^{59} - 107912622 q^{60} + 251179296 q^{61} + 2421010 q^{62} + 573206808 q^{63} + 460030950 q^{64} + 301434554 q^{65} + 305189958 q^{66} + 741046264 q^{67} + 503103116 q^{68} + 1480618500 q^{69} + 666826600 q^{70} + 488700124 q^{71} + 243154096 q^{72} + 1432375020 q^{73} - 208138340 q^{74} + 462882236 q^{75} - 253709644 q^{76} + 406327616 q^{77} - 1244370462 q^{78} + 400834638 q^{79} - 440320610 q^{80} + 207205984 q^{81} - 1992598260 q^{82} + 1525085236 q^{83} - 2191854376 q^{84} - 387675996 q^{85} - 3425646378 q^{86} + 171162002 q^{87} - 3147673814 q^{88} + 691159332 q^{89} - 2412410836 q^{90} + 1569278264 q^{91} - 2491626380 q^{92} + 270455138 q^{93} - 4397366402 q^{94} + 236293724 q^{95} - 1448270346 q^{96} + 2494422276 q^{97} - 3443098784 q^{98} + 2123567852 q^{99}+O(q^{100}) \) 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9 - 46678 * q^10 + 24474 * q^11 - 14210 * q^12 + 107722 * q^13 + 677768 * q^14 + 505426 * q^15 + 1656882 * q^16 + 982120 * q^17 + 2364102 * q^18 + 2084360 * q^19 + 4689410 * q^20 + 2911344 * q^21 + 2725230 * q^22 + 3004004 * q^23 + 7893170 * q^24 + 6339542 * q^25 + 6863698 * q^26 + 7881014 * q^27 + 5116944 * q^28 + 8487372 * q^29 + 10924626 * q^30 + 17872478 * q^31 + 5122946 * q^32 - 860442 * q^33 + 15662848 * q^34 - 22252312 * q^35 - 35199980 * q^36 + 452980 * q^37 - 68665276 * q^38 - 29528222 * q^39 - 61623214 * q^40 - 69039804 * q^41 - 150603216 * q^42 + 5379186 * q^43 - 58283762 * q^44 - 63687756 * q^45 - 76817844 * q^46 - 49104062 * q^47 - 99120062 * q^48 + 73113148 * q^49 - 281373726 * q^50 + 1578252 * q^51 - 49849646 * q^52 + 2253998 * q^53 - 166064634 * q^54 + 82907066 * q^55 + 119369464 * q^56 + 69024164 * q^57 + 11316496 * q^58 + 51587572 * q^59 - 107912622 * q^60 + 251179296 * q^61 + 2421010 * q^62 + 573206808 * q^63 + 460030950 * q^64 + 301434554 * q^65 + 305189958 * q^66 + 741046264 * q^67 + 503103116 * q^68 + 1480618500 * q^69 + 666826600 * q^70 + 488700124 * q^71 + 243154096 * q^72 + 1432375020 * q^73 - 208138340 * q^74 + 462882236 * q^75 - 253709644 * q^76 + 406327616 * q^77 - 1244370462 * q^78 + 400834638 * q^79 - 440320610 * q^80 + 207205984 * q^81 - 1992598260 * q^82 + 1525085236 * q^83 - 2191854376 * q^84 - 387675996 * q^85 - 3425646378 * q^86 + 171162002 * q^87 - 3147673814 * q^88 + 691159332 * q^89 - 2412410836 * q^90 + 1569278264 * q^91 - 2491626380 * q^92 + 270455138 * q^93 - 4397366402 * q^94 + 236293724 * q^95 - 1448270346 * q^96 + 2494422276 * q^97 - 3443098784 * q^98 + 2123567852 * 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 $

$2$	10.2072	0.451100	0.225550	−	0.974232i	$-0.427582\pi$
$2$	10.2072	0.451100	0.225550	+	0.974232i	$0.427582\pi$
$3$	−225.321	−1.60604	−0.803019	−	0.595954i	$-0.796774\pi$
$3$	−225.321	−1.60604	−0.803019	+	0.595954i	$0.796774\pi$
$4$	−407.813	−0.796509
$5$	−1619.94	−1.15914	−0.579569	−	0.814923i	$-0.696779\pi$
$5$	−1619.94	−1.15914	−0.579569	+	0.814923i	$0.696779\pi$
$6$	−2299.90	−0.724483
$7$	−263.065	−0.0414116	−0.0207058	−	0.999786i	$-0.506591\pi$
$7$	−263.065	−0.0414116	−0.0207058	+	0.999786i	$0.506591\pi$
$8$	−9388.73	−0.810405
$9$	31086.4	1.57936
$10$	−16535.1	−0.522887
$11$	−15854.8	−0.326507	−0.163254	−	0.986584i	$-0.552199\pi$
$11$	−15854.8	−0.326507	−0.163254	+	0.986584i	$0.552199\pi$
$12$	91888.6	1.27922
$13$	37215.6	0.361393	0.180697	−	0.983539i	$-0.442165\pi$
$13$	37215.6	0.361393	0.180697	+	0.983539i	$0.442165\pi$
$14$	−2685.16	−0.0186808
$15$	365007.	1.86162
$16$	112967.	0.430935
$17$	−249809.	−0.725417	−0.362709	−	0.931903i	$-0.618148\pi$
$17$	−249809.	−0.725417	−0.362709	+	0.931903i	$0.618148\pi$
$18$	317306.	0.712447
$19$	−73529.0	−0.129440	−0.0647199	−	0.997903i	$-0.520615\pi$
$19$	−73529.0	−0.129440	−0.0647199	+	0.997903i	$0.520615\pi$
$20$	660634.	0.923264
$21$	59274.0	0.0665086
$22$	−161833.	−0.147287
$23$	−1.69419e6	−1.26237	−0.631184	−	0.775633i	$-0.717431\pi$
$23$	−1.69419e6	−1.26237	−0.631184	+	0.775633i	$0.717431\pi$
$24$	2.11548e6	1.30154
$25$	671096.	0.343601
$26$	379868.	0.163025
$27$	−2.56943e6	−0.930466
$28$	107281.	0.0329847
$29$	707281.	0.185695
$29$	707281.	0.185695
$30$	3.72571e6	0.839776
$31$	8.52813e6	1.65854	0.829270	−	0.558847i	$-0.188756\pi$
$31$	8.52813e6	1.65854	0.829270	+	0.558847i	$0.188756\pi$
$32$	5.96011e6	1.00480
$33$	3.57241e6	0.524382
$34$	−2.54986e6	−0.327236
$35$	426151.	0.0480018
$36$	−1.26774e7	−1.25797
$37$	−1.01195e7	−0.887669	−0.443835	−	0.896109i	$-0.646382\pi$
$37$	−1.01195e7	−0.887669	−0.443835	+	0.896109i	$0.646382\pi$
$38$	−750527.	−0.0583903
$39$	−8.38545e6	−0.580411
$40$	1.52092e7	0.939371
$41$	−2.51895e7	−1.39217	−0.696086	−	0.717958i	$-0.745077\pi$
$41$	−2.51895e7	−1.39217	−0.696086	+	0.717958i	$0.745077\pi$
$42$	605023.	0.0300020
$43$	1.42179e7	0.634201	0.317101	−	0.948392i	$-0.397291\pi$
$43$	1.42179e7	0.634201	0.317101	+	0.948392i	$0.397291\pi$
$44$	6.46577e6	0.260066
$45$	−5.03583e7	−1.83069
$46$	−1.72930e7	−0.569454
$47$	−2.94566e7	−0.880526	−0.440263	−	0.897869i	$-0.645115\pi$
$47$	−2.94566e7	−0.880526	−0.440263	+	0.897869i	$0.645115\pi$
$48$	−2.54538e7	−0.692098
$49$	−4.02844e7	−0.998285
$50$	6.85003e6	0.154998
$51$	5.62872e7	1.16505
$52$	−1.51770e7	−0.287853
$53$	1.04466e8	1.81859	0.909294	−	0.416155i	$-0.136623\pi$
$53$	1.04466e8	1.81859	0.909294	+	0.416155i	$0.136623\pi$
$54$	−2.62268e7	−0.419733
$55$	2.56838e7	0.378467
$56$	2.46985e6	0.0335602
$57$	1.65676e7	0.207885
$58$	7.21938e6	0.0837672
$59$	4.40400e7	0.473165	0.236583	−	0.971611i	$-0.423973\pi$
$59$	4.40400e7	0.473165	0.236583	+	0.971611i	$0.423973\pi$
$60$	−1.48855e8	−1.48280
$61$	1.29768e8	1.20001	0.600005	−	0.799996i	$-0.295165\pi$
$61$	1.29768e8	1.20001	0.600005	+	0.799996i	$0.295165\pi$
$62$	8.70486e7	0.748168
$63$	−8.17776e6	−0.0654036
$64$	2.99708e6	0.0223300
$65$	−6.02873e7	−0.418905
$66$	3.64644e7	0.236549
$67$	−3.03199e8	−1.83820	−0.919098	−	0.394030i	$-0.871081\pi$
$67$	−3.03199e8	−1.83820	−0.919098	+	0.394030i	$0.871081\pi$
$68$	1.01875e8	0.577801
$69$	3.81736e8	2.02741
$70$	4.34982e6	0.0216536
$71$	2.30424e8	1.07613	0.538067	−	0.842902i	$-0.319155\pi$
$71$	2.30424e8	1.07613	0.538067	+	0.842902i	$0.319155\pi$
$72$	−2.91862e8	−1.27992
$73$	3.68404e8	1.51835	0.759175	−	0.650887i	$-0.225603\pi$
$73$	3.68404e8	1.51835	0.759175	+	0.650887i	$0.225603\pi$
$74$	−1.03292e8	−0.400427
$75$	−1.51212e8	−0.551836
$76$	2.99861e7	0.103100
$77$	4.17083e6	0.0135212
$78$	−8.55922e7	−0.261824
$79$	1.14178e8	0.329806	0.164903	−	0.986310i	$-0.447269\pi$
$79$	1.14178e8	0.329806	0.164903	+	0.986310i	$0.447269\pi$
$80$	−1.83000e8	−0.499513
$81$	−3.29277e7	−0.0849922
$82$	−2.57115e8	−0.628009
$83$	6.43009e8	1.48719	0.743594	−	0.668632i	$-0.233120\pi$
$83$	6.43009e8	1.48719	0.743594	+	0.668632i	$0.233120\pi$
$84$	−2.41727e7	−0.0529746
$85$	4.04677e8	0.840859
$86$	1.45125e8	0.286088
$87$	−1.59365e8	−0.298234
$88$	1.48856e8	0.264603
$89$	−2.06740e8	−0.349276	−0.174638	−	0.984633i	$-0.555876\pi$
$89$	−2.06740e8	−0.349276	−0.174638	+	0.984633i	$0.555876\pi$
$90$	−5.14019e8	−0.825825
$91$	−9.79013e6	−0.0149659
$92$	6.90911e8	1.00549
$93$	−1.92156e9	−2.66368
$94$	−3.00670e8	−0.397205
$95$	1.19113e8	0.150039
$96$	−1.34294e9	−1.61375
$97$	−9.20362e7	−0.105557	−0.0527784	−	0.998606i	$-0.516808\pi$
$97$	−9.20362e7	−0.105557	−0.0527784	+	0.998606i	$0.516808\pi$
$98$	−4.11192e8	−0.450326
$99$	−4.92868e8	−0.515671
$100$	−2.73681e8	−0.273681
$101$	−1.64802e8	−0.157585	−0.0787926	−	0.996891i	$-0.525107\pi$
$101$	−1.64802e8	−0.157585	−0.0787926	+	0.996891i	$0.525107\pi$
$102$	5.74536e8	0.525553
$103$	−1.40772e8	−0.123239	−0.0616194	−	0.998100i	$-0.519627\pi$
$103$	−1.40772e8	−0.123239	−0.0616194	+	0.998100i	$0.519627\pi$
$104$	−3.49408e8	−0.292875
$105$	−9.60206e7	−0.0770926
$106$	1.06631e9	0.820365
$107$	5.60091e8	0.413078	0.206539	−	0.978438i	$-0.433780\pi$
$107$	5.60091e8	0.413078	0.206539	+	0.978438i	$0.433780\pi$
$108$	1.04785e9	0.741124
$109$	1.02440e9	0.695107	0.347553	−	0.937660i	$-0.387013\pi$
$109$	1.02440e9	0.695107	0.347553	+	0.937660i	$0.387013\pi$
$110$	2.62161e8	0.170726
$111$	2.28013e9	1.42563
$112$	−2.97177e7	−0.0178457
$113$	−2.67026e9	−1.54064	−0.770318	−	0.637661i	$-0.779902\pi$
$113$	−2.67026e9	−1.54064	−0.770318	+	0.637661i	$0.779902\pi$
$114$	1.69109e8	0.0937769
$115$	2.74449e9	1.46326
$116$	−2.88438e8	−0.147908
$117$	1.15690e9	0.570769
$118$	4.49526e8	0.213445
$119$	6.57160e7	0.0300407
$120$	−3.42696e9	−1.50867
$121$	−2.10657e9	−0.893393
$122$	1.32458e9	0.541324
$123$	5.67573e9	2.23588
$124$	−3.47788e9	−1.32104
$125$	2.07682e9	0.760857
$126$	−8.34722e7	−0.0295036
$127$	−2.62235e8	−0.0894486	−0.0447243	−	0.998999i	$-0.514241\pi$
$127$	−2.62235e8	−0.0894486	−0.0447243	+	0.998999i	$0.514241\pi$
$128$	−3.02099e9	−0.994727
$129$	−3.20359e9	−1.01855
$130$	−6.15366e8	−0.188968
$131$	−3.72829e8	−0.110609	−0.0553043	−	0.998470i	$-0.517613\pi$
$131$	−3.72829e8	−0.110609	−0.0553043	+	0.998470i	$0.517613\pi$
$132$	−1.45687e9	−0.417675
$133$	1.93429e7	0.00536030
$134$	−3.09482e9	−0.829210
$135$	4.16234e9	1.07854
$136$	2.34539e9	0.587882
$137$	−5.53349e8	−0.134201	−0.0671006	−	0.997746i	$-0.521375\pi$
$137$	−5.53349e8	−0.134201	−0.0671006	+	0.997746i	$0.521375\pi$
$138$	3.89646e9	0.914565
$139$	3.41699e9	0.776384	0.388192	−	0.921578i	$-0.373100\pi$
$139$	3.41699e9	0.776384	0.388192	+	0.921578i	$0.373100\pi$
$140$	−1.73790e8	−0.0382338
$141$	6.63718e9	1.41416
$142$	2.35199e9	0.485444
$143$	−5.90045e8	−0.117998
$144$	3.51175e9	0.680600
$145$	−1.14576e9	−0.215247
$146$	3.76038e9	0.684927
$147$	9.07691e9	1.60328
$148$	4.12686e9	0.707036
$149$	−1.15778e10	−1.92437	−0.962186	−	0.272393i	$-0.912185\pi$
$149$	−1.15778e10	−1.92437	−0.962186	+	0.272393i	$0.912185\pi$
$150$	−1.54345e9	−0.248933
$151$	8.75265e8	0.137007	0.0685036	−	0.997651i	$-0.478178\pi$
$151$	8.75265e8	0.137007	0.0685036	+	0.997651i	$0.478178\pi$
$152$	6.90344e8	0.104899
$153$	−7.76568e9	−1.14569
$154$	4.25726e7	0.00609940
$155$	−1.38151e10	−1.92248
$156$	3.41969e9	0.462303
$157$	−1.12513e10	−1.47793	−0.738963	−	0.673746i	$-0.764684\pi$
$157$	−1.12513e10	−1.47793	−0.738963	+	0.673746i	$0.764684\pi$
$158$	1.16544e9	0.148776
$159$	−2.35384e10	−2.92072
$160$	−9.65505e9	−1.16470
$161$	4.45681e8	0.0522767
$162$	−3.36101e8	−0.0383400
$163$	1.02439e10	1.13663	0.568315	−	0.822811i	$-0.307595\pi$
$163$	1.02439e10	1.13663	0.568315	+	0.822811i	$0.307595\pi$
$164$	1.02726e10	1.10888
$165$	−5.78710e9	−0.607832
$166$	6.56334e9	0.670870
$167$	6.13852e9	0.610716	0.305358	−	0.952238i	$-0.401224\pi$
$167$	6.13852e9	0.610716	0.305358	+	0.952238i	$0.401224\pi$
$168$	−5.56508e8	−0.0538989
$169$	−9.21950e9	−0.869395
$170$	4.13063e9	0.379311
$171$	−2.28576e9	−0.204431
$172$	−5.79823e9	−0.505147
$173$	−1.51043e10	−1.28201	−0.641007	−	0.767535i	$-0.721483\pi$
$173$	−1.51043e10	−1.28201	−0.641007	+	0.767535i	$0.721483\pi$
$174$	−1.62668e9	−0.134533
$175$	−1.76542e8	−0.0142291
$176$	−1.79107e9	−0.140703
$177$	−9.92312e9	−0.759921
$178$	−2.11024e9	−0.157559
$179$	1.88721e10	1.37399	0.686993	−	0.726664i	$-0.258930\pi$
$179$	1.88721e10	1.37399	0.686993	+	0.726664i	$0.258930\pi$
$180$	2.05368e10	1.45816
$181$	2.42778e10	1.68134	0.840669	−	0.541549i	$-0.182162\pi$
$181$	2.42778e10	1.68134	0.840669	+	0.541549i	$0.182162\pi$
$182$	−9.99301e7	−0.00675111
$183$	−2.92395e10	−1.92726
$184$	1.59063e10	1.02303
$185$	1.63930e10	1.02893
$186$	−1.96138e10	−1.20159
$187$	3.96066e9	0.236854
$188$	1.20128e10	0.701347
$189$	6.75928e8	0.0385321
$190$	1.21581e9	0.0676824
$191$	−4.91504e8	−0.0267225	−0.0133613	−	0.999911i	$-0.504253\pi$
$191$	−4.91504e8	−0.0267225	−0.0133613	+	0.999911i	$0.504253\pi$
$192$	−6.75305e8	−0.0358628
$193$	1.21724e10	0.631495	0.315747	−	0.948843i	$-0.397745\pi$
$193$	1.21724e10	0.631495	0.315747	+	0.948843i	$0.397745\pi$
$194$	−9.39435e8	−0.0476167
$195$	1.35840e10	0.672777
$196$	1.64285e10	0.795143
$197$	−2.91630e10	−1.37954	−0.689770	−	0.724029i	$-0.742288\pi$
$197$	−2.91630e10	−1.37954	−0.689770	+	0.724029i	$0.742288\pi$
$198$	−5.03082e9	−0.232619
$199$	2.02050e10	0.913312	0.456656	−	0.889643i	$-0.349047\pi$
$199$	2.02050e10	0.913312	0.456656	+	0.889643i	$0.349047\pi$
$200$	−6.30074e9	−0.278456
$201$	6.83171e10	2.95221
$202$	−1.68217e9	−0.0710867
$203$	−1.86061e8	−0.00768994
$204$	−2.29546e10	−0.927970
$205$	4.08057e10	1.61372
$206$	−1.43689e9	−0.0555930
$207$	−5.26663e10	−1.99373
$208$	4.20414e9	0.155737
$209$	1.16578e9	0.0422630
$210$	−9.80104e8	−0.0347765
$211$	5.62206e10	1.95265	0.976325	−	0.216308i	$-0.0694014\pi$
$211$	5.62206e10	1.95265	0.976325	+	0.216308i	$0.0694014\pi$
$212$	−4.26026e10	−1.44852
$213$	−5.19194e10	−1.72831
$214$	5.71698e9	0.186339
$215$	−2.30322e10	−0.735127
$216$	2.41237e10	0.754054
$217$	−2.24345e9	−0.0686828
$218$	1.04563e10	0.313563
$219$	−8.30091e10	−2.43853
$220$	−1.04742e10	−0.301452
$221$	−9.29680e9	−0.262161
$222$	2.32738e10	0.643101
$223$	3.88952e10	1.05323	0.526616	−	0.850103i	$-0.323461\pi$
$223$	3.88952e10	1.05323	0.526616	+	0.850103i	$0.323461\pi$
$224$	−1.56790e9	−0.0416104
$225$	2.08620e10	0.542668
$226$	−2.72559e10	−0.694980
$227$	−2.62443e10	−0.656023	−0.328012	−	0.944674i	$-0.606378\pi$
$227$	−2.62443e10	−0.656023	−0.328012	+	0.944674i	$0.606378\pi$
$228$	−6.75648e9	−0.165582
$229$	2.41037e10	0.579194	0.289597	−	0.957149i	$-0.406479\pi$
$229$	2.41037e10	0.579194	0.289597	+	0.957149i	$0.406479\pi$
$230$	2.80136e10	0.660076
$231$	−9.39775e8	−0.0217155
$232$	−6.64047e9	−0.150488
$233$	−6.14784e10	−1.36653	−0.683267	−	0.730168i	$-0.739442\pi$
$233$	−6.14784e10	−1.36653	−0.683267	+	0.730168i	$0.739442\pi$
$234$	1.18088e10	0.257474
$235$	4.77181e10	1.02065
$236$	−1.79601e10	−0.376880
$237$	−2.57266e10	−0.529681
$238$	6.70778e8	0.0135514
$239$	−4.67931e10	−0.927665	−0.463832	−	0.885923i	$-0.653526\pi$
$239$	−4.67931e10	−0.927665	−0.463832	+	0.885923i	$0.653526\pi$
$240$	4.12338e10	0.802237
$241$	5.47331e10	1.04514	0.522569	−	0.852597i	$-0.324974\pi$
$241$	5.47331e10	1.04514	0.522569	+	0.852597i	$0.324974\pi$
$242$	−2.15023e10	−0.403010
$243$	5.79935e10	1.06697
$244$	−5.29212e10	−0.955819
$245$	6.52585e10	1.15715
$246$	5.79334e10	1.00861
$247$	−2.73643e9	−0.0467787
$248$	−8.00684e10	−1.34409
$249$	−1.44883e11	−2.38848
$250$	2.11985e10	0.343223
$251$	−3.22791e10	−0.513322	−0.256661	−	0.966501i	$-0.582622\pi$
$251$	−3.22791e10	−0.513322	−0.256661	+	0.966501i	$0.582622\pi$
$252$	3.33499e9	0.0520946
$253$	2.68609e10	0.412172
$254$	−2.67669e9	−0.0403503
$255$	−9.11821e10	−1.35045
$256$	−3.23704e10	−0.471051
$257$	5.86711e10	0.838929	0.419464	−	0.907772i	$-0.362218\pi$
$257$	5.86711e10	0.838929	0.419464	+	0.907772i	$0.362218\pi$
$258$	−3.26997e10	−0.459468
$259$	2.66209e9	0.0367598
$260$	2.45859e10	0.333661
$261$	2.19869e10	0.293279
$262$	−3.80555e9	−0.0498955
$263$	3.32432e10	0.428451	0.214226	−	0.976784i	$-0.431277\pi$
$263$	3.32432e10	0.428451	0.214226	+	0.976784i	$0.431277\pi$
$264$	−3.35404e10	−0.424962
$265$	−1.69229e11	−2.10799
$266$	1.97437e8	0.00241803
$267$	4.65828e10	0.560951
$268$	1.23648e11	1.46414
$269$	9.34482e10	1.08814	0.544071	−	0.839039i	$-0.316882\pi$
$269$	9.34482e10	1.08814	0.544071	+	0.839039i	$0.316882\pi$
$270$	4.24860e10	0.486529
$271$	−3.83342e10	−0.431742	−0.215871	−	0.976422i	$-0.569259\pi$
$271$	−3.83342e10	−0.431742	−0.215871	+	0.976422i	$0.569259\pi$
$272$	−2.82202e10	−0.312608
$273$	2.20592e9	0.0240358
$274$	−5.64815e9	−0.0605381
$275$	−1.06401e10	−0.112188
$276$	−1.55677e11	−1.61485
$277$	7.62266e10	0.777943	0.388971	−	0.921250i	$-0.372830\pi$
$277$	7.62266e10	0.777943	0.388971	+	0.921250i	$0.372830\pi$
$278$	3.48780e10	0.350227
$279$	2.65109e11	2.61943
$280$	−4.00102e9	−0.0389009
$281$	8.63697e10	0.826386	0.413193	−	0.910644i	$-0.364414\pi$
$281$	8.63697e10	0.826386	0.413193	+	0.910644i	$0.364414\pi$
$282$	6.77472e10	0.637927
$283$	6.39411e9	0.0592572	0.0296286	−	0.999561i	$-0.490568\pi$
$283$	6.39411e9	0.0592572	0.0296286	+	0.999561i	$0.490568\pi$
$284$	−9.39700e10	−0.857150
$285$	−2.68386e10	−0.240967
$286$	−6.02272e9	−0.0532287
$287$	6.62649e9	0.0576521
$288$	1.85279e11	1.58694
$289$	−5.61833e10	−0.473770
$290$	−1.16950e10	−0.0970977
$291$	2.07377e10	0.169528
$292$	−1.50240e11	−1.20938
$293$	1.60285e11	1.27054	0.635269	−	0.772291i	$-0.280889\pi$
$293$	1.60285e11	1.27054	0.635269	+	0.772291i	$0.280889\pi$
$294$	9.26501e10	0.723241
$295$	−7.13423e10	−0.548464
$296$	9.50093e10	0.719372
$297$	4.07378e10	0.303804
$298$	−1.18178e11	−0.868084
$299$	−6.30503e10	−0.456212
$300$	6.16661e10	0.439542
$301$	−3.74023e9	−0.0262633
$302$	8.93402e9	0.0618039
$303$	3.71333e10	0.253088
$304$	−8.30636e9	−0.0557801
$305$	−2.10218e11	−1.39098
$306$	−7.92660e10	−0.516821
$307$	2.32203e11	1.49192	0.745960	−	0.665991i	$-0.231991\pi$
$307$	2.32203e11	1.49192	0.745960	+	0.665991i	$0.231991\pi$
$308$	−1.70092e9	−0.0107697
$309$	3.17188e10	0.197926
$310$	−1.41014e11	−0.867230
$311$	2.02050e11	1.22472	0.612360	−	0.790579i	$-0.290220\pi$
$311$	2.02050e11	1.22472	0.612360	+	0.790579i	$0.290220\pi$
$312$	7.87288e10	0.470368
$313$	−1.56355e11	−0.920794	−0.460397	−	0.887713i	$-0.652293\pi$
$313$	−1.56355e11	−0.920794	−0.460397	+	0.887713i	$0.652293\pi$
$314$	−1.14844e11	−0.666692
$315$	1.32475e10	0.0758118
$316$	−4.65630e10	−0.262694
$317$	−1.36225e11	−0.757686	−0.378843	−	0.925461i	$-0.623678\pi$
$317$	−1.36225e11	−0.757686	−0.378843	+	0.925461i	$0.623678\pi$
$318$	−2.40262e11	−1.31754
$319$	−1.12138e10	−0.0606308
$320$	−4.85511e9	−0.0258835
$321$	−1.26200e11	−0.663418
$322$	4.54917e9	0.0235820
$323$	1.83682e10	0.0938978
$324$	1.34283e10	0.0676970
$325$	2.49753e10	0.124175
$326$	1.04561e11	0.512734
$327$	−2.30819e11	−1.11637
$328$	2.36498e11	1.12822
$329$	7.74900e9	0.0364640
$330$	−5.90703e10	−0.274193
$331$	−2.12969e10	−0.0975194	−0.0487597	−	0.998811i	$-0.515527\pi$
$331$	−2.12969e10	−0.0975194	−0.0487597	+	0.998811i	$0.515527\pi$
$332$	−2.62227e11	−1.18456
$333$	−3.14579e11	−1.40194
$334$	6.26573e10	0.275494
$335$	4.91166e11	2.13072
$336$	6.69601e9	0.0286609
$337$	2.23660e11	0.944614	0.472307	−	0.881434i	$-0.343421\pi$
$337$	2.23660e11	0.944614	0.472307	+	0.881434i	$0.343421\pi$
$338$	−9.41055e10	−0.392184
$339$	6.01664e11	2.47432
$340$	−1.65032e11	−0.669752
$341$	−1.35211e11	−0.541525
$342$	−2.33312e10	−0.0922190
$343$	2.12130e10	0.0827522
$344$	−1.33488e11	−0.513960
$345$	−6.18391e11	−2.35005
$346$	−1.54173e11	−0.578316
$347$	1.04985e11	0.388727	0.194364	−	0.980930i	$-0.437736\pi$
$347$	1.04985e11	0.388727	0.194364	+	0.980930i	$0.437736\pi$
$348$	6.49911e10	0.237546
$349$	1.37908e11	0.497596	0.248798	−	0.968555i	$-0.419965\pi$
$349$	1.37908e11	0.497596	0.248798	+	0.968555i	$0.419965\pi$
$350$	−1.80200e9	−0.00641873
$351$	−9.56231e10	−0.336264
$352$	−9.44962e10	−0.328074
$353$	−6.19034e10	−0.212192	−0.106096	−	0.994356i	$-0.533835\pi$
$353$	−6.19034e10	−0.212192	−0.106096	+	0.994356i	$0.533835\pi$
$354$	−1.01288e11	−0.342800
$355$	−3.73275e11	−1.24739
$356$	8.43111e10	0.278202
$357$	−1.48072e10	−0.0482465
$358$	1.92632e11	0.619805
$359$	5.14119e11	1.63357	0.816787	−	0.576939i	$-0.195753\pi$
$359$	5.14119e11	1.63357	0.816787	+	0.576939i	$0.195753\pi$
$360$	4.72801e11	1.48360
$361$	−3.17281e11	−0.983245
$362$	2.47809e11	0.758452
$363$	4.74655e11	1.43482
$364$	3.99254e9	0.0119205
$365$	−5.96794e11	−1.75998
$366$	−2.98454e11	−0.869387
$367$	2.84361e11	0.818224	0.409112	−	0.912484i	$-0.365838\pi$
$367$	2.84361e11	0.818224	0.409112	+	0.912484i	$0.365838\pi$
$368$	−1.91387e11	−0.543999
$369$	−7.83053e11	−2.19873
$370$	1.67327e11	0.464151
$371$	−2.74814e10	−0.0753106
$372$	7.83638e11	2.12164
$373$	−3.74821e11	−1.00261	−0.501307	−	0.865270i	$-0.667147\pi$
$373$	−3.74821e11	−1.00261	−0.501307	+	0.865270i	$0.667147\pi$
$374$	4.04274e10	0.106845
$375$	−4.67950e11	−1.22196
$376$	2.76560e11	0.713583
$377$	2.63219e10	0.0671091
$378$	6.89935e9	0.0173818
$379$	−2.36538e11	−0.588877	−0.294438	−	0.955670i	$-0.595133\pi$
$379$	−2.36538e11	−0.588877	−0.294438	+	0.955670i	$0.595133\pi$
$380$	−4.85758e10	−0.119507
$381$	5.90870e10	0.143658
$382$	−5.01690e9	−0.0120545
$383$	−2.89172e11	−0.686692	−0.343346	−	0.939209i	$-0.611560\pi$
$383$	−2.89172e11	−0.686692	−0.343346	+	0.939209i	$0.611560\pi$
$384$	6.80691e11	1.59757
$385$	−6.75652e9	−0.0156729
$386$	1.24247e11	0.284867
$387$	4.41984e11	1.00163
$388$	3.75335e10	0.0840769
$389$	4.37140e11	0.967938	0.483969	−	0.875085i	$-0.339195\pi$
$389$	4.37140e11	0.967938	0.483969	+	0.875085i	$0.339195\pi$
$390$	1.38655e11	0.303490
$391$	4.23223e11	0.915744
$392$	3.78220e11	0.809015
$393$	8.40061e10	0.177642
$394$	−2.97673e11	−0.622310
$395$	−1.84961e11	−0.382291
$396$	2.00998e11	0.410736
$397$	−3.73024e11	−0.753666	−0.376833	−	0.926281i	$-0.622987\pi$
$397$	−3.73024e11	−0.753666	−0.376833	+	0.926281i	$0.622987\pi$
$398$	2.06237e11	0.411995
$399$	−4.35836e9	−0.00860885
$400$	7.58117e10	0.148070
$401$	5.76534e11	1.11346	0.556731	−	0.830693i	$-0.312055\pi$
$401$	5.76534e11	1.11346	0.556731	+	0.830693i	$0.312055\pi$
$402$	6.97328e11	1.33174
$403$	3.17380e11	0.599386
$404$	6.72082e10	0.125518
$405$	5.33411e10	0.0985177
$406$	−1.89917e9	−0.00346893
$407$	1.60442e11	0.289830
$408$	−5.28465e11	−0.944160
$409$	2.17998e11	0.385209	0.192605	−	0.981276i	$-0.438306\pi$
$409$	2.17998e11	0.385209	0.192605	+	0.981276i	$0.438306\pi$
$410$	4.16513e11	0.727949
$411$	1.24681e11	0.215532
$412$	5.74084e10	0.0981608
$413$	−1.15854e10	−0.0195945
$414$	−5.37577e11	−0.899371
$415$	−1.04164e12	−1.72386
$416$	2.21809e11	0.363128
$417$	−7.69918e11	−1.24690
$418$	1.18994e10	0.0190648
$419$	−2.09524e11	−0.332101	−0.166051	−	0.986117i	$-0.553102\pi$
$419$	−2.09524e11	−0.332101	−0.166051	+	0.986117i	$0.553102\pi$
$420$	3.91584e10	0.0614049
$421$	1.21398e12	1.88339	0.941696	−	0.336465i	$-0.109231\pi$
$421$	1.21398e12	1.88339	0.941696	+	0.336465i	$0.109231\pi$
$422$	5.73857e11	0.880841
$423$	−9.15701e11	−1.39066
$424$	−9.80805e11	−1.47379
$425$	−1.67646e11	−0.249254
$426$	−5.29953e11	−0.779640
$427$	−3.41375e10	−0.0496943
$428$	−2.28412e11	−0.329020
$429$	1.32949e11	0.189508
$430$	−2.35095e11	−0.331616
$431$	−1.22643e12	−1.71197	−0.855986	−	0.516999i	$-0.827049\pi$
$431$	−1.22643e12	−1.71197	−0.855986	+	0.516999i	$0.827049\pi$
$432$	−2.90261e11	−0.400971
$433$	−1.20883e12	−1.65261	−0.826303	−	0.563226i	$-0.809560\pi$
$433$	−1.20883e12	−1.65261	−0.826303	+	0.563226i	$0.809560\pi$
$434$	−2.28994e10	−0.0309828
$435$	2.58163e11	0.345694
$436$	−4.17764e11	−0.553659
$437$	1.24572e11	0.163401
$438$	−8.47293e11	−1.10002
$439$	6.04563e11	0.776876	0.388438	−	0.921475i	$-0.373015\pi$
$439$	6.04563e11	0.776876	0.388438	+	0.921475i	$0.373015\pi$
$440$	−2.41139e11	−0.306711
$441$	−1.25230e12	−1.57665
$442$	−9.48945e10	−0.118261
$443$	1.17145e11	0.144513	0.0722566	−	0.997386i	$-0.476980\pi$
$443$	1.17145e11	0.144513	0.0722566	+	0.997386i	$0.476980\pi$
$444$	−9.29867e11	−1.13553
$445$	3.34907e11	0.404860
$446$	3.97012e11	0.475113
$447$	2.60873e12	3.09061
$448$	−7.88427e8	−0.000924721 0
$449$	−4.69249e11	−0.544872	−0.272436	−	0.962174i	$-0.587829\pi$
$449$	−4.69249e11	−0.544872	−0.272436	+	0.962174i	$0.587829\pi$
$450$	2.12943e11	0.244798
$451$	3.99374e11	0.454554
$452$	1.08896e12	1.22713
$453$	−1.97215e11	−0.220038
$454$	−2.67882e11	−0.295932
$455$	1.58595e10	0.0173475
$456$	−1.55549e11	−0.168471
$457$	−1.30024e12	−1.39444	−0.697220	−	0.716857i	$-0.745580\pi$
$457$	−1.30024e12	−1.39444	−0.697220	+	0.716857i	$0.745580\pi$
$458$	2.46032e11	0.261274
$459$	6.41868e11	0.674976
$460$	−1.11924e12	−1.16550
$461$	3.55584e11	0.366681	0.183341	−	0.983049i	$-0.441309\pi$
$461$	3.55584e11	0.366681	0.183341	+	0.983049i	$0.441309\pi$
$462$	−9.59250e9	−0.00979587
$463$	−5.18074e11	−0.523935	−0.261967	−	0.965077i	$-0.584371\pi$
$463$	−5.18074e11	−0.523935	−0.261967	+	0.965077i	$0.584371\pi$
$464$	7.98995e10	0.0800227
$465$	3.11283e12	3.08757
$466$	−6.27523e11	−0.616444
$467$	−8.16300e11	−0.794189	−0.397095	−	0.917778i	$-0.629982\pi$
$467$	−8.16300e11	−0.794189	−0.397095	+	0.917778i	$0.629982\pi$
$468$	−4.71799e11	−0.454622
$469$	7.97611e10	0.0761226
$470$	4.87069e11	0.460416
$471$	2.53514e12	2.37360
$472$	−4.13480e11	−0.383456
$473$	−2.25421e11	−0.207071
$474$	−2.62597e11	−0.238939
$475$	−4.93450e10	−0.0444756
$476$	−2.67998e10	−0.0239277
$477$	3.24748e12	2.87220
$478$	−4.77628e11	−0.418470
$479$	−4.44066e11	−0.385423	−0.192711	−	0.981255i	$-0.561728\pi$
$479$	−4.44066e11	−0.385423	−0.192711	+	0.981255i	$0.561728\pi$
$480$	2.17548e12	1.87055
$481$	−3.76603e11	−0.320798
$482$	5.58674e11	0.471462
$483$	−1.00421e11	−0.0839583
$484$	8.59087e11	0.711596
$485$	1.49094e11	0.122355
$486$	5.91952e11	0.481309
$487$	−1.54324e12	−1.24324	−0.621619	−	0.783320i	$-0.713525\pi$
$487$	−1.54324e12	−1.24324	−0.621619	+	0.783320i	$0.713525\pi$
$488$	−1.21836e12	−0.972494
$489$	−2.30815e12	−1.82547
$490$	6.66108e11	0.521990
$491$	−1.78888e12	−1.38904	−0.694518	−	0.719476i	$-0.744382\pi$
$491$	−1.78888e12	−1.38904	−0.694518	+	0.719476i	$0.744382\pi$
$492$	−2.31463e12	−1.78090
$493$	−1.76685e11	−0.134707
$494$	−2.79313e10	−0.0211019
$495$	7.98419e11	0.597734
$496$	9.63398e11	0.714724
$497$	−6.06166e10	−0.0445644
$498$	−1.47886e12	−1.07744
$499$	6.91441e11	0.499233	0.249616	−	0.968345i	$-0.419696\pi$
$499$	6.91441e11	0.499233	0.249616	+	0.968345i	$0.419696\pi$
$500$	−8.46952e11	−0.606029
$501$	−1.38314e12	−0.980833
$502$	−3.29480e11	−0.231560
$503$	−9.87253e11	−0.687658	−0.343829	−	0.939032i	$-0.611724\pi$
$503$	−9.87253e11	−0.687658	−0.343829	+	0.939032i	$0.611724\pi$
$504$	7.67788e10	0.0530034
$505$	2.66970e11	0.182663
$506$	2.74176e11	0.185931
$507$	2.07734e12	1.39628
$508$	1.06943e11	0.0712466
$509$	3.66579e11	0.242068	0.121034	−	0.992648i	$-0.461379\pi$
$509$	3.66579e11	0.242068	0.121034	+	0.992648i	$0.461379\pi$
$510$	−9.30716e11	−0.609188
$511$	−9.69142e10	−0.0628773
$512$	1.21633e12	0.782236
$513$	1.88928e11	0.120439
$514$	5.98869e11	0.378441
$515$	2.28042e11	0.142851
$516$	1.30646e12	0.811284
$517$	4.67027e11	0.287498
$518$	2.71725e10	0.0165823
$519$	3.40331e12	2.05896
$520$	5.66021e11	0.339483
$521$	1.28940e12	0.766689	0.383344	−	0.923605i	$-0.374772\pi$
$521$	1.28940e12	0.766689	0.383344	+	0.923605i	$0.374772\pi$
$522$	2.24425e11	0.132298
$523$	2.08788e12	1.22025	0.610125	−	0.792305i	$-0.291119\pi$
$523$	2.08788e12	1.22025	0.610125	+	0.792305i	$0.291119\pi$
$524$	1.52044e11	0.0881008
$525$	3.97785e10	0.0228524
$526$	3.39321e11	0.193274
$527$	−2.13040e12	−1.20313
$528$	4.03564e11	0.225975
$529$	1.06912e12	0.593575
$530$	−1.72736e12	−0.950916
$531$	1.36905e12	0.747296
$532$	−7.88828e9	−0.00426953
$533$	−9.37445e11	−0.503122
$534$	4.75481e11	0.253045
$535$	−9.07317e11	−0.478814
$536$	2.84666e12	1.48968
$537$	−4.25229e12	−2.20667
$538$	9.53847e11	0.490861
$539$	6.38700e11	0.325947
$540$	−1.69745e12	−0.859066
$541$	2.17780e12	1.09303	0.546513	−	0.837451i	$-0.315955\pi$
$541$	2.17780e12	1.09303	0.546513	+	0.837451i	$0.315955\pi$
$542$	−3.91286e11	−0.194759
$543$	−5.47029e12	−2.70029
$544$	−1.48889e12	−0.728899
$545$	−1.65948e12	−0.805725
$546$	2.25163e10	0.0108425
$547$	−1.31495e10	−0.00628012	−0.00314006	−	0.999995i	$-0.501000\pi$
$547$	−1.31495e10	−0.00628012	−0.00314006	+	0.999995i	$0.501000\pi$
$548$	2.25662e11	0.106892
$549$	4.03404e12	1.89524
$550$	−1.08606e11	−0.0506081
$551$	−5.20057e10	−0.0240364
$552$	−3.58401e12	−1.64302
$553$	−3.00361e10	−0.0136578
$554$	7.78062e11	0.350930
$555$	−3.69369e12	−1.65250
$556$	−1.39349e12	−0.618397
$557$	−1.30604e12	−0.574922	−0.287461	−	0.957792i	$-0.592811\pi$
$557$	−1.30604e12	−0.574922	−0.287461	+	0.957792i	$0.592811\pi$
$558$	2.70603e12	1.18162
$559$	5.29128e11	0.229196
$560$	4.81410e10	0.0206856
$561$	−8.92419e11	−0.380396
$562$	8.81595e11	0.372783
$563$	4.92098e11	0.206426	0.103213	−	0.994659i	$-0.467088\pi$
$563$	4.92098e11	0.206426	0.103213	+	0.994659i	$0.467088\pi$
$564$	−2.70673e12	−1.12639
$565$	4.32567e12	1.78581
$566$	6.52661e10	0.0267309
$567$	8.66213e9	0.00351966
$568$	−2.16339e12	−0.872104
$569$	1.30410e12	0.521562	0.260781	−	0.965398i	$-0.416020\pi$
$569$	1.30410e12	0.521562	0.260781	+	0.965398i	$0.416020\pi$
$570$	−2.73948e11	−0.108700
$571$	6.38900e11	0.251519	0.125759	−	0.992061i	$-0.459863\pi$
$571$	6.38900e11	0.251519	0.125759	+	0.992061i	$0.459863\pi$
$572$	2.40628e11	0.0939861
$573$	1.10746e11	0.0429173
$574$	6.76381e10	0.0260068
$575$	−1.13696e12	−0.433751
$576$	9.31686e10	0.0352670
$577$	−8.73015e11	−0.327892	−0.163946	−	0.986469i	$-0.552422\pi$
$577$	−8.73015e11	−0.327892	−0.163946	+	0.986469i	$0.552422\pi$
$578$	−5.73476e11	−0.213717
$579$	−2.74270e12	−1.01420
$580$	4.67254e11	0.171446
$581$	−1.69153e11	−0.0615868
$582$	2.11674e11	0.0764741
$583$	−1.65629e12	−0.593782
$584$	−3.45885e12	−1.23048
$585$	−1.87412e12	−0.661600
$586$	1.63606e12	0.573139
$587$	−1.70926e12	−0.594204	−0.297102	−	0.954846i	$-0.596020\pi$
$587$	−1.70926e12	−0.594204	−0.297102	+	0.954846i	$0.596020\pi$
$588$	−3.70168e12	−1.27703
$589$	−6.27065e11	−0.214681
$590$	−7.28207e11	−0.247412
$591$	6.57103e12	2.21559
$592$	−1.14317e12	−0.382528
$593$	3.83103e12	1.27224	0.636120	−	0.771590i	$-0.280538\pi$
$593$	3.83103e12	1.27224	0.636120	+	0.771590i	$0.280538\pi$
$594$	4.15820e11	0.137046
$595$	−1.06456e11	−0.0348213
$596$	4.72159e12	1.53278
$597$	−4.55260e12	−1.46681
$598$	−6.43568e11	−0.205797
$599$	3.31926e12	1.05347	0.526733	−	0.850031i	$-0.323417\pi$
$599$	3.31926e12	1.05347	0.526733	+	0.850031i	$0.323417\pi$
$600$	1.41969e12	0.447211
$601$	3.01812e12	0.943629	0.471815	−	0.881698i	$-0.343599\pi$
$601$	3.01812e12	0.943629	0.471815	+	0.881698i	$0.343599\pi$
$602$	−3.81774e10	−0.0118474
$603$	−9.42539e12	−2.90316
$604$	−3.56944e11	−0.109127
$605$	3.41253e12	1.03557
$606$	3.79028e11	0.114168
$607$	6.59775e12	1.97263	0.986317	−	0.164859i	$-0.0527169\pi$
$607$	6.59775e12	1.97263	0.986317	+	0.164859i	$0.0527169\pi$
$608$	−4.38241e11	−0.130061
$609$	4.19234e10	0.0123503
$610$	−2.14574e12	−0.627470
$611$	−1.09625e12	−0.318216
$612$	3.16694e12	0.912554
$613$	4.20132e12	1.20175	0.600874	−	0.799344i	$-0.294819\pi$
$613$	4.20132e12	1.20175	0.600874	+	0.799344i	$0.294819\pi$
$614$	2.37015e12	0.673005
$615$	−9.19436e12	−2.59169
$616$	−3.91588e10	−0.0109576
$617$	−7.83007e11	−0.217512	−0.108756	−	0.994068i	$-0.534687\pi$
$617$	−7.83007e11	−0.217512	−0.108756	+	0.994068i	$0.534687\pi$
$618$	3.23761e11	0.0892845
$619$	−1.65864e12	−0.454092	−0.227046	−	0.973884i	$-0.572907\pi$
$619$	−1.65864e12	−0.454092	−0.227046	+	0.973884i	$0.572907\pi$
$620$	5.63397e12	1.53127
$621$	4.35310e12	1.17459
$622$	2.06237e12	0.552471
$623$	5.43860e10	0.0144641
$624$	−9.47280e11	−0.250120
$625$	−4.67506e12	−1.22554
$626$	−1.59595e12	−0.415370
$627$	−2.62676e11	−0.0678759
$628$	4.58841e12	1.17718
$629$	2.52794e12	0.643931
$630$	1.35220e11	0.0341987
$631$	4.94831e12	1.24258	0.621291	−	0.783580i	$-0.286609\pi$
$631$	4.94831e12	1.24258	0.621291	+	0.783580i	$0.286609\pi$
$632$	−1.07198e12	−0.267277
$633$	−1.26677e13	−3.13603
$634$	−1.39048e12	−0.341792
$635$	4.24806e11	0.103683
$636$	9.59925e12	2.32638
$637$	−1.49921e12	−0.360774
$638$	−1.14461e11	−0.0273506
$639$	7.16308e12	1.69960
$640$	4.89383e12	1.15303
$641$	4.66360e12	1.09109	0.545544	−	0.838082i	$-0.316323\pi$
$641$	4.66360e12	1.09109	0.545544	+	0.838082i	$0.316323\pi$
$642$	−1.28815e12	−0.299268
$643$	3.87879e12	0.894844	0.447422	−	0.894323i	$-0.352342\pi$
$643$	3.87879e12	0.894844	0.447422	+	0.894323i	$0.352342\pi$
$644$	−1.81754e11	−0.0416389
$645$	5.18963e12	1.18064
$646$	1.87489e11	0.0423573
$647$	−8.34181e12	−1.87150	−0.935752	−	0.352658i	$-0.885278\pi$
$647$	−8.34181e12	−1.87150	−0.935752	+	0.352658i	$0.885278\pi$
$648$	3.09150e11	0.0688781
$649$	−6.98243e11	−0.154492
$650$	2.54928e11	0.0560154
$651$	5.05496e11	0.110307
$652$	−4.17757e12	−0.905336
$653$	−6.00532e12	−1.29249	−0.646244	−	0.763131i	$-0.723661\pi$
$653$	−6.00532e12	−1.29249	−0.646244	+	0.763131i	$0.723661\pi$
$654$	−2.35602e12	−0.503593
$655$	6.03963e11	0.128211
$656$	−2.84559e12	−0.599936
$657$	1.14524e13	2.39801
$658$	7.90958e10	0.0164489
$659$	−1.89964e12	−0.392363	−0.196181	−	0.980568i	$-0.562854\pi$
$659$	−1.89964e12	−0.392363	−0.196181	+	0.980568i	$0.562854\pi$
$660$	2.36005e12	0.484143
$661$	−6.58495e12	−1.34167	−0.670835	−	0.741607i	$-0.734064\pi$
$661$	−6.58495e12	−1.34167	−0.670835	+	0.741607i	$0.734064\pi$
$662$	−2.17383e11	−0.0439910
$663$	2.09476e12	0.421040
$664$	−6.03704e12	−1.20522
$665$	−3.13344e10	−0.00621333
$666$	−3.21098e12	−0.632417
$667$	−1.19827e12	−0.234416
$668$	−2.50337e12	−0.486441
$669$	−8.76390e12	−1.69153
$670$	5.01344e12	0.961169
$671$	−2.05745e12	−0.391812
$672$	3.53280e11	0.0668278
$673$	−4.60140e12	−0.864614	−0.432307	−	0.901727i	$-0.642300\pi$
$673$	−4.60140e12	−0.864614	−0.432307	+	0.901727i	$0.642300\pi$
$674$	2.28295e12	0.426115
$675$	−1.72434e12	−0.319709
$676$	3.75983e12	0.692481
$677$	5.81271e12	1.06348	0.531740	−	0.846908i	$-0.321538\pi$
$677$	5.81271e12	1.06348	0.531740	+	0.846908i	$0.321538\pi$
$678$	6.14132e12	1.11616
$679$	2.42115e10	0.00437127
$680$	−3.79940e12	−0.681436
$681$	5.91339e12	1.05360
$682$	−1.38013e12	−0.244282
$683$	−1.08160e13	−1.90184	−0.950918	−	0.309443i	$-0.899858\pi$
$683$	−1.08160e13	−1.90184	−0.950918	+	0.309443i	$0.899858\pi$
$684$	9.32160e11	0.162831
$685$	8.96394e11	0.155558
$686$	2.16526e11	0.0373295
$687$	−5.43106e12	−0.930207
$688$	1.60615e12	0.273300
$689$	3.88777e12	0.657225
$690$	−6.31205e12	−1.06011
$691$	2.03009e11	0.0338739	0.0169369	−	0.999857i	$-0.494609\pi$
$691$	2.03009e11	0.0338739	0.0169369	+	0.999857i	$0.494609\pi$
$692$	6.15971e12	1.02113
$693$	1.29656e11	0.0213547
$694$	1.07161e12	0.175355
$695$	−5.53533e12	−0.899937
$696$	1.49624e12	0.241690
$697$	6.29257e12	1.00991
$698$	1.40766e12	0.224465
$699$	1.38524e13	2.19471
$700$	7.19960e10	0.0113336
$701$	−8.41708e12	−1.31653	−0.658264	−	0.752787i	$-0.728709\pi$
$701$	−8.41708e12	−1.31653	−0.658264	+	0.752787i	$0.728709\pi$
$702$	−9.76047e11	−0.151689
$703$	7.44077e11	0.114900
$704$	−4.75180e10	−0.00729090
$705$	−1.07519e13	−1.63920
$706$	−6.31862e11	−0.0957196
$707$	4.33536e10	0.00652586
$708$	4.04677e12	0.605284
$709$	2.13274e12	0.316978	0.158489	−	0.987361i	$-0.449338\pi$
$709$	2.13274e12	0.316978	0.158489	+	0.987361i	$0.449338\pi$
$710$	−3.81010e12	−0.562696
$711$	3.54938e12	0.520881
$712$	1.94103e12	0.283055
$713$	−1.44483e13	−2.09369
$714$	−1.51140e11	−0.0217640
$715$	9.55840e11	0.136775
$716$	−7.69630e12	−1.09439
$717$	1.05435e13	1.48986
$718$	5.24773e12	0.736905
$719$	3.68760e12	0.514593	0.257296	−	0.966333i	$-0.417168\pi$
$719$	3.68760e12	0.514593	0.257296	+	0.966333i	$0.417168\pi$
$720$	−5.68883e12	−0.788909
$721$	3.70321e10	0.00510352
$722$	−3.23856e12	−0.443542
$723$	−1.23325e13	−1.67853
$724$	−9.90078e12	−1.33920
$725$	4.74653e11	0.0638051
$726$	4.84491e12	0.647248
$727$	−1.69842e12	−0.225497	−0.112748	−	0.993624i	$-0.535965\pi$
$727$	−1.69842e12	−0.225497	−0.112748	+	0.993624i	$0.535965\pi$
$728$	9.19169e10	0.0121284
$729$	−1.24190e13	−1.62860
$730$	−6.09162e12	−0.793925
$731$	−3.55176e12	−0.460060
$732$	1.19242e13	1.53508
$733$	−1.41276e13	−1.80760	−0.903799	−	0.427957i	$-0.859234\pi$
$733$	−1.41276e13	−1.80760	−0.903799	+	0.427957i	$0.859234\pi$
$734$	2.90253e12	0.369101
$735$	−1.47041e13	−1.85843
$736$	−1.00975e13	−1.26843
$737$	4.80715e12	0.600184
$738$	−7.99280e12	−0.991849
$739$	9.77087e12	1.20513	0.602564	−	0.798070i	$-0.294146\pi$
$739$	9.77087e12	1.20513	0.602564	+	0.798070i	$0.294146\pi$
$740$	−6.68528e12	−0.819553
$741$	6.16574e11	0.0751283
$742$	−2.80509e11	−0.0339726
$743$	1.27006e13	1.52889	0.764443	−	0.644691i	$-0.223014\pi$
$743$	1.27006e13	1.52889	0.764443	+	0.644691i	$0.223014\pi$
$744$	1.80411e13	2.15866
$745$	1.87554e13	2.23061
$746$	−3.82588e12	−0.452279
$747$	1.99889e13	2.34880
$748$	−1.61521e12	−0.188656
$749$	−1.47340e11	−0.0171062
$750$	−4.77647e12	−0.551228
$751$	1.32251e13	1.51712	0.758560	−	0.651603i	$-0.225903\pi$
$751$	1.32251e13	1.51712	0.758560	+	0.651603i	$0.225903\pi$
$752$	−3.32763e12	−0.379450
$753$	7.27316e12	0.824415
$754$	2.68674e11	0.0302729
$755$	−1.41788e12	−0.158810
$756$	−2.75652e11	−0.0306911
$757$	8.66873e12	0.959453	0.479727	−	0.877418i	$-0.340736\pi$
$757$	8.66873e12	0.959453	0.479727	+	0.877418i	$0.340736\pi$
$758$	−2.41440e12	−0.265642
$759$	−6.05233e12	−0.661964
$760$	−1.11832e12	−0.121592
$761$	7.59805e12	0.821242	0.410621	−	0.911806i	$-0.365312\pi$
$761$	7.59805e12	0.821242	0.410621	+	0.911806i	$0.365312\pi$
$762$	6.03114e11	0.0648040
$763$	−2.69485e11	−0.0287855
$764$	2.00442e11	0.0212847
$765$	1.25800e13	1.32801
$766$	−2.95165e12	−0.309767
$767$	1.63898e12	0.170999
$768$	7.29372e12	0.756526
$769$	6.90225e11	0.0711741	0.0355870	−	0.999367i	$-0.488670\pi$
$769$	6.90225e11	0.0711741	0.0355870	+	0.999367i	$0.488670\pi$
$770$	−6.89653e10	−0.00707005
$771$	−1.32198e13	−1.34735
$772$	−4.96407e12	−0.502991
$773$	4.45990e12	0.449280	0.224640	−	0.974442i	$-0.427879\pi$
$773$	4.45990e12	0.449280	0.224640	+	0.974442i	$0.427879\pi$
$774$	4.51143e12	0.451835
$775$	5.72319e12	0.569876
$776$	8.64104e11	0.0855437
$777$	−5.99823e11	−0.0590376
$778$	4.46199e12	0.436637
$779$	1.85216e12	0.180202
$780$	−5.53971e12	−0.535873
$781$	−3.65332e12	−0.351365
$782$	4.31994e12	0.413092
$783$	−1.81731e12	−0.172783
$784$	−4.55081e12	−0.430196
$785$	1.82264e13	1.71312
$786$	8.57470e11	0.0801341
$787$	−1.69889e13	−1.57863	−0.789313	−	0.613991i	$-0.789563\pi$
$787$	−1.69889e13	−1.57863	−0.789313	+	0.613991i	$0.789563\pi$
$788$	1.18930e13	1.09882
$789$	−7.49038e12	−0.688109
$790$	−1.88794e12	−0.172451
$791$	7.02451e11	0.0638001
$792$	4.62741e12	0.417902
$793$	4.82941e12	0.433676
$794$	−3.80754e12	−0.339979
$795$	3.81309e13	3.38552
$796$	−8.23983e12	−0.727461
$797$	3.44587e11	0.0302508	0.0151254	−	0.999886i	$-0.495185\pi$
$797$	3.44587e11	0.0302508	0.0151254	+	0.999886i	$0.495185\pi$
$798$	−4.44868e10	−0.00388345
$799$	7.35853e12	0.638749
$800$	3.99981e12	0.345250
$801$	−6.42681e12	−0.551632
$802$	5.88482e12	0.502283
$803$	−5.84096e12	−0.495752
$804$	−2.78606e13	−2.35146
$805$	−7.21979e11	−0.0605959
$806$	3.23957e12	0.270383
$807$	−2.10558e13	−1.74760
$808$	1.54728e12	0.127708
$809$	1.25397e12	0.102925	0.0514625	−	0.998675i	$-0.483612\pi$
$809$	1.25397e12	0.102925	0.0514625	+	0.998675i	$0.483612\pi$
$810$	5.44465e11	0.0444413
$811$	−1.94521e13	−1.57897	−0.789483	−	0.613772i	$-0.789651\pi$
$811$	−1.94521e13	−1.57897	−0.789483	+	0.613772i	$0.789651\pi$
$812$	7.58780e10	0.00612510
$813$	8.63749e12	0.693394
$814$	1.63767e12	0.130742
$815$	−1.65945e13	−1.31751
$816$	6.35860e12	0.502060
$817$	−1.04543e12	−0.0820908
$818$	2.22515e12	0.173768
$819$	−3.04340e11	−0.0236364
$820$	−1.66411e13	−1.28534
$821$	−2.37605e12	−0.182521	−0.0912604	−	0.995827i	$-0.529090\pi$
$821$	−2.37605e12	−0.182521	−0.0912604	+	0.995827i	$0.529090\pi$
$822$	1.27265e12	0.0972265
$823$	−1.88894e13	−1.43522	−0.717611	−	0.696444i	$-0.754764\pi$
$823$	−1.88894e13	−1.43522	−0.717611	+	0.696444i	$0.754764\pi$
$824$	1.32167e12	0.0998734
$825$	2.39743e12	0.180178
$826$	−1.18255e11	−0.00883909
$827$	9.51710e12	0.707506	0.353753	−	0.935339i	$-0.384905\pi$
$827$	9.51710e12	0.707506	0.353753	+	0.935339i	$0.384905\pi$
$828$	2.14780e13	1.58802
$829$	9.95255e12	0.731878	0.365939	−	0.930639i	$-0.380748\pi$
$829$	9.95255e12	0.731878	0.365939	+	0.930639i	$0.380748\pi$
$830$	−1.06322e13	−0.777631
$831$	−1.71754e13	−1.24941
$832$	1.11538e11	0.00806991
$833$	1.00634e13	0.724173
$834$	−7.85873e12	−0.562477
$835$	−9.94406e12	−0.707905
$836$	−4.75422e11	−0.0336628
$837$	−2.19125e13	−1.54322
$838$	−2.13866e12	−0.149811
$839$	4.51841e12	0.314816	0.157408	−	0.987534i	$-0.449686\pi$
$839$	4.51841e12	0.314816	0.157408	+	0.987534i	$0.449686\pi$
$840$	9.01512e11	0.0624762
$841$	5.00246e11	0.0344828
$842$	1.23913e13	0.849598
$843$	−1.94609e13	−1.32721
$844$	−2.29275e13	−1.55530
$845$	1.49351e13	1.00775
$846$	−9.34677e12	−0.627328
$847$	5.54166e11	0.0369968
$848$	1.18012e13	0.783693
$849$	−1.44073e12	−0.0951692
$850$	−1.71120e12	−0.112439
$851$	1.71443e13	1.12057
$852$	2.11734e13	1.37661
$853$	5.51677e12	0.356791	0.178395	−	0.983959i	$-0.442909\pi$
$853$	5.51677e12	0.356791	0.178395	+	0.983959i	$0.442909\pi$
$854$	−3.48450e11	−0.0224171
$855$	3.70280e12	0.236964
$856$	−5.25855e12	−0.334760
$857$	1.06020e13	0.671389	0.335694	−	0.941971i	$-0.391029\pi$
$857$	1.06020e13	0.671389	0.335694	+	0.941971i	$0.391029\pi$
$858$	1.35704e12	0.0854872
$859$	4.91496e12	0.308000	0.154000	−	0.988071i	$-0.450784\pi$
$859$	4.91496e12	0.308000	0.154000	+	0.988071i	$0.450784\pi$
$860$	9.39282e12	0.585535
$861$	−1.49309e12	−0.0925913
$862$	−1.25185e13	−0.772270
$863$	−1.97752e13	−1.21359	−0.606795	−	0.794859i	$-0.707545\pi$
$863$	−1.97752e13	−1.21359	−0.606795	+	0.794859i	$0.707545\pi$
$864$	−1.53141e13	−0.934932
$865$	2.44681e13	1.48603
$866$	−1.23388e13	−0.745490
$867$	1.26593e13	0.760892
$868$	9.14908e11	0.0547065
$869$	−1.81026e12	−0.107684
$870$	2.63512e12	0.155943
$871$	−1.12838e13	−0.664312
$872$	−9.61785e12	−0.563318
$873$	−2.86108e12	−0.166712
$874$	1.27153e12	0.0737100
$875$	−5.46338e11	−0.0315083
$876$	3.38522e13	1.94231
$877$	5.01602e12	0.286326	0.143163	−	0.989699i	$-0.454273\pi$
$877$	5.01602e12	0.286326	0.143163	+	0.989699i	$0.454273\pi$
$878$	6.17092e12	0.350449
$879$	−3.61154e13	−2.04053
$880$	2.90143e12	0.163095
$881$	3.37286e12	0.188628	0.0943140	−	0.995543i	$-0.469934\pi$
$881$	3.37286e12	0.188628	0.0943140	+	0.995543i	$0.469934\pi$
$882$	−1.27825e13	−0.711225
$883$	3.14645e13	1.74180	0.870899	−	0.491462i	$-0.163537\pi$
$883$	3.14645e13	1.74180	0.870899	+	0.491462i	$0.163537\pi$
$884$	3.79135e12	0.208814
$885$	1.60749e13	0.880854
$886$	1.19573e12	0.0651899
$887$	−8.34886e12	−0.452867	−0.226434	−	0.974027i	$-0.572707\pi$
$887$	−8.34886e12	−0.452867	−0.226434	+	0.974027i	$0.572707\pi$
$888$	−2.14076e13	−1.15534
$889$	6.89848e10	0.00370421
$890$	3.41847e12	0.182632
$891$	5.22061e11	0.0277506
$892$	−1.58620e13	−0.838909
$893$	2.16592e12	0.113975
$894$	2.66279e13	1.39418
$895$	−3.05718e13	−1.59264
$896$	7.94716e11	0.0411932
$897$	1.42065e13	0.732693
$898$	−4.78973e12	−0.245792
$899$	6.03178e12	0.307983
$900$	−8.50778e12	−0.432240
$901$	−2.60966e13	−1.31923
$902$	4.07650e12	0.205049
$903$	8.42751e11	0.0421798
$904$	2.50703e13	1.24854
$905$	−3.93286e13	−1.94890
$906$	−2.01302e12	−0.0992594
$907$	1.23189e13	0.604419	0.302210	−	0.953241i	$-0.402276\pi$
$907$	1.23189e13	0.604419	0.302210	+	0.953241i	$0.402276\pi$
$908$	1.07028e13	0.522528
$909$	−5.12310e12	−0.248883
$910$	1.61881e11	0.00782546
$911$	8.89925e12	0.428076	0.214038	−	0.976825i	$-0.431338\pi$
$911$	8.89925e12	0.428076	0.214038	+	0.976825i	$0.431338\pi$
$912$	1.87159e12	0.0895850
$913$	−1.01948e13	−0.485577
$914$	−1.32718e13	−0.629032
$915$	4.73664e13	2.23396
$916$	−9.82979e12	−0.461333
$917$	9.80783e10	0.00458048
$918$	6.55169e12	0.304482
$919$	−3.51364e13	−1.62494	−0.812471	−	0.583002i	$-0.801878\pi$
$919$	−3.51364e13	−1.62494	−0.812471	+	0.583002i	$0.801878\pi$
$920$	−2.57673e13	−1.18583
$921$	−5.23202e13	−2.39608
$922$	3.62953e12	0.165410
$923$	8.57539e12	0.388907
$924$	3.83252e11	0.0172966
$925$	−6.79115e12	−0.305004
$926$	−5.28810e12	−0.236347
$927$	−4.37609e12	−0.194638
$928$	4.21547e12	0.186587
$929$	3.62546e13	1.59695	0.798476	−	0.602026i	$-0.205640\pi$
$929$	3.62546e13	1.59695	0.798476	+	0.602026i	$0.205640\pi$
$930$	3.17733e13	1.39280
$931$	2.96207e12	0.129218
$932$	2.50716e13	1.08846
$933$	−4.55261e13	−1.96695
$934$	−8.33216e12	−0.358259
$935$	−6.41605e12	−0.274546
$936$	−1.08618e13	−0.462554
$937$	3.14201e13	1.33162	0.665809	−	0.746122i	$-0.268086\pi$
$937$	3.14201e13	1.33162	0.665809	+	0.746122i	$0.268086\pi$
$938$	8.14140e11	0.0343389
$939$	3.52300e13	1.47883
$940$	−1.94600e13	−0.812958
$941$	2.73264e13	1.13613	0.568065	−	0.822983i	$-0.307692\pi$
$941$	2.73264e13	1.13613	0.568065	+	0.822983i	$0.307692\pi$
$942$	2.58768e13	1.07073
$943$	4.26758e13	1.75743
$944$	4.97507e12	0.203904
$945$	−1.09497e12	−0.0446640
$946$	−2.30092e12	−0.0934098
$947$	−4.34735e13	−1.75650	−0.878252	−	0.478197i	$-0.841290\pi$
$947$	−4.34735e13	−1.75650	−0.878252	+	0.478197i	$0.841290\pi$
$948$	1.04916e13	0.421896
$949$	1.37104e13	0.548721
$950$	−5.03676e11	−0.0200630
$951$	3.06943e13	1.21687
$952$	−6.16990e11	−0.0243451
$953$	2.87676e13	1.12976	0.564878	−	0.825174i	$-0.308923\pi$
$953$	2.87676e13	1.12976	0.564878	+	0.825174i	$0.308923\pi$
$954$	3.31478e13	1.29565
$955$	7.96210e11	0.0309751
$956$	1.90828e13	0.738893
$957$	2.52670e12	0.0973754
$958$	−4.53268e12	−0.173864
$959$	1.45567e11	0.00555748
$960$	1.09396e12	0.0415699
$961$	4.62894e13	1.75076
$962$	−3.84408e12	−0.144712
$963$	1.74112e13	0.652397
$964$	−2.23209e13	−0.832462
$965$	−1.97187e13	−0.731990
$966$	−1.02502e12	−0.0378736
$967$	−3.31000e13	−1.21733	−0.608665	−	0.793427i	$-0.708295\pi$
$967$	−3.31000e13	−1.21733	−0.608665	+	0.793427i	$0.708295\pi$
$968$	1.97781e13	0.724010
$969$	−4.13874e12	−0.150803
$970$	1.52183e12	0.0551943
$971$	1.78447e13	0.644202	0.322101	−	0.946705i	$-0.395611\pi$
$971$	1.78447e13	0.644202	0.322101	+	0.946705i	$0.395611\pi$
$972$	−2.36505e13	−0.849848
$973$	−8.98890e11	−0.0321513
$974$	−1.57522e13	−0.560824
$975$	−5.62744e12	−0.199430
$976$	1.46596e13	0.517126
$977$	9.48552e12	0.333070	0.166535	−	0.986036i	$-0.446742\pi$
$977$	9.48552e12	0.333070	0.166535	+	0.986036i	$0.446742\pi$
$978$	−2.35598e13	−0.823469
$979$	3.27781e12	0.114041
$980$	−2.66132e13	−0.921680
$981$	3.18450e13	1.09782
$982$	−1.82595e13	−0.626594
$983$	−4.31263e12	−0.147316	−0.0736582	−	0.997284i	$-0.523467\pi$
$983$	−4.31263e12	−0.147316	−0.0736582	+	0.997284i	$0.523467\pi$
$984$	−5.32879e13	−1.81197
$985$	4.72424e13	1.59908
$986$	−1.80347e12	−0.0607662
$987$	−1.74601e12	−0.0585625
$988$	1.11595e12	0.0372596
$989$	−2.40878e13	−0.800596
$990$	8.14965e12	0.269638
$991$	−4.54332e13	−1.49638	−0.748189	−	0.663485i	$-0.769076\pi$
$991$	−4.54332e13	−1.49638	−0.748189	+	0.663485i	$0.769076\pi$
$992$	5.08286e13	1.66650
$993$	4.79864e12	0.156620
$994$	−6.18727e11	−0.0201030
$995$	−3.27309e13	−1.05865
$996$	5.90852e13	1.90244
$997$	−5.11822e13	−1.64055	−0.820277	−	0.571967i	$-0.806181\pi$
$997$	−5.11822e13	−1.64055	−0.820277	+	0.571967i	$0.806181\pi$
$998$	7.05770e12	0.225204
$999$	2.60014e13	0.825946

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.a.b.1.8	✓	12
3.2	odd	2		261.10.a.e.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.a.b.1.8	✓	12	1.1	even	1	trivial
261.10.a.e.1.5		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+10.2072 q^{2} -225.321 q^{3} -407.813 q^{4} -1619.94 q^{5} -2299.90 q^{6} -263.065 q^{7} -9388.73 q^{8} +31086.4 q^{9} +O(q^{10})\)	\(q+10.2072 q^{2} -225.321 q^{3} -407.813 q^{4} -1619.94 q^{5} -2299.90 q^{6} -263.065 q^{7} -9388.73 q^{8} +31086.4 q^{9} -16535.1 q^{10} -15854.8 q^{11} +91888.6 q^{12} +37215.6 q^{13} -2685.16 q^{14} +365007. q^{15} +112967. q^{16} -249809. q^{17} +317306. q^{18} -73529.0 q^{19} +660634. q^{20} +59274.0 q^{21} -161833. q^{22} -1.69419e6 q^{23} +2.11548e6 q^{24} +671096. q^{25} +379868. q^{26} -2.56943e6 q^{27} +107281. q^{28} +707281. q^{29} +3.72571e6 q^{30} +8.52813e6 q^{31} +5.96011e6 q^{32} +3.57241e6 q^{33} -2.54986e6 q^{34} +426151. q^{35} -1.26774e7 q^{36} -1.01195e7 q^{37} -750527. q^{38} -8.38545e6 q^{39} +1.52092e7 q^{40} -2.51895e7 q^{41} +605023. q^{42} +1.42179e7 q^{43} +6.46577e6 q^{44} -5.03583e7 q^{45} -1.72930e7 q^{46} -2.94566e7 q^{47} -2.54538e7 q^{48} -4.02844e7 q^{49} +6.85003e6 q^{50} +5.62872e7 q^{51} -1.51770e7 q^{52} +1.04466e8 q^{53} -2.62268e7 q^{54} +2.56838e7 q^{55} +2.46985e6 q^{56} +1.65676e7 q^{57} +7.21938e6 q^{58} +4.40400e7 q^{59} -1.48855e8 q^{60} +1.29768e8 q^{61} +8.70486e7 q^{62} -8.17776e6 q^{63} +2.99708e6 q^{64} -6.02873e7 q^{65} +3.64644e7 q^{66} -3.03199e8 q^{67} +1.01875e8 q^{68} +3.81736e8 q^{69} +4.34982e6 q^{70} +2.30424e8 q^{71} -2.91862e8 q^{72} +3.68404e8 q^{73} -1.03292e8 q^{74} -1.51212e8 q^{75} +2.99861e7 q^{76} +4.17083e6 q^{77} -8.55922e7 q^{78} +1.14178e8 q^{79} -1.83000e8 q^{80} -3.29277e7 q^{81} -2.57115e8 q^{82} +6.43009e8 q^{83} -2.41727e7 q^{84} +4.04677e8 q^{85} +1.45125e8 q^{86} -1.59365e8 q^{87} +1.48856e8 q^{88} -2.06740e8 q^{89} -5.14019e8 q^{90} -9.79013e6 q^{91} +6.90911e8 q^{92} -1.92156e9 q^{93} -3.00670e8 q^{94} +1.19113e8 q^{95} -1.34294e9 q^{96} -9.20362e7 q^{97} -4.11192e8 q^{98} -4.92868e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9}+O(q^{10}) \) 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9	\( 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9} - 46678 q^{10} + 24474 q^{11} - 14210 q^{12} + 107722 q^{13} + 677768 q^{14} + 505426 q^{15} + 1656882 q^{16} + 982120 q^{17} + 2364102 q^{18} + 2084360 q^{19} + 4689410 q^{20} + 2911344 q^{21} + 2725230 q^{22} + 3004004 q^{23} + 7893170 q^{24} + 6339542 q^{25} + 6863698 q^{26} + 7881014 q^{27} + 5116944 q^{28} + 8487372 q^{29} + 10924626 q^{30} + 17872478 q^{31} + 5122946 q^{32} - 860442 q^{33} + 15662848 q^{34} - 22252312 q^{35} - 35199980 q^{36} + 452980 q^{37} - 68665276 q^{38} - 29528222 q^{39} - 61623214 q^{40} - 69039804 q^{41} - 150603216 q^{42} + 5379186 q^{43} - 58283762 q^{44} - 63687756 q^{45} - 76817844 q^{46} - 49104062 q^{47} - 99120062 q^{48} + 73113148 q^{49} - 281373726 q^{50} + 1578252 q^{51} - 49849646 q^{52} + 2253998 q^{53} - 166064634 q^{54} + 82907066 q^{55} + 119369464 q^{56} + 69024164 q^{57} + 11316496 q^{58} + 51587572 q^{59} - 107912622 q^{60} + 251179296 q^{61} + 2421010 q^{62} + 573206808 q^{63} + 460030950 q^{64} + 301434554 q^{65} + 305189958 q^{66} + 741046264 q^{67} + 503103116 q^{68} + 1480618500 q^{69} + 666826600 q^{70} + 488700124 q^{71} + 243154096 q^{72} + 1432375020 q^{73} - 208138340 q^{74} + 462882236 q^{75} - 253709644 q^{76} + 406327616 q^{77} - 1244370462 q^{78} + 400834638 q^{79} - 440320610 q^{80} + 207205984 q^{81} - 1992598260 q^{82} + 1525085236 q^{83} - 2191854376 q^{84} - 387675996 q^{85} - 3425646378 q^{86} + 171162002 q^{87} - 3147673814 q^{88} + 691159332 q^{89} - 2412410836 q^{90} + 1569278264 q^{91} - 2491626380 q^{92} + 270455138 q^{93} - 4397366402 q^{94} + 236293724 q^{95} - 1448270346 q^{96} + 2494422276 q^{97} - 3443098784 q^{98} + 2123567852 q^{99}+O(q^{100}) \) 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9 - 46678 * q^10 + 24474 * q^11 - 14210 * q^12 + 107722 * q^13 + 677768 * q^14 + 505426 * q^15 + 1656882 * q^16 + 982120 * q^17 + 2364102 * q^18 + 2084360 * q^19 + 4689410 * q^20 + 2911344 * q^21 + 2725230 * q^22 + 3004004 * q^23 + 7893170 * q^24 + 6339542 * q^25 + 6863698 * q^26 + 7881014 * q^27 + 5116944 * q^28 + 8487372 * q^29 + 10924626 * q^30 + 17872478 * q^31 + 5122946 * q^32 - 860442 * q^33 + 15662848 * q^34 - 22252312 * q^35 - 35199980 * q^36 + 452980 * q^37 - 68665276 * q^38 - 29528222 * q^39 - 61623214 * q^40 - 69039804 * q^41 - 150603216 * q^42 + 5379186 * q^43 - 58283762 * q^44 - 63687756 * q^45 - 76817844 * q^46 - 49104062 * q^47 - 99120062 * q^48 + 73113148 * q^49 - 281373726 * q^50 + 1578252 * q^51 - 49849646 * q^52 + 2253998 * q^53 - 166064634 * q^54 + 82907066 * q^55 + 119369464 * q^56 + 69024164 * q^57 + 11316496 * q^58 + 51587572 * q^59 - 107912622 * q^60 + 251179296 * q^61 + 2421010 * q^62 + 573206808 * q^63 + 460030950 * q^64 + 301434554 * q^65 + 305189958 * q^66 + 741046264 * q^67 + 503103116 * q^68 + 1480618500 * q^69 + 666826600 * q^70 + 488700124 * q^71 + 243154096 * q^72 + 1432375020 * q^73 - 208138340 * q^74 + 462882236 * q^75 - 253709644 * q^76 + 406327616 * q^77 - 1244370462 * q^78 + 400834638 * q^79 - 440320610 * q^80 + 207205984 * q^81 - 1992598260 * q^82 + 1525085236 * q^83 - 2191854376 * q^84 - 387675996 * q^85 - 3425646378 * q^86 + 171162002 * q^87 - 3147673814 * q^88 + 691159332 * q^89 - 2412410836 * q^90 + 1569278264 * q^91 - 2491626380 * q^92 + 270455138 * q^93 - 4397366402 * q^94 + 236293724 * q^95 - 1448270346 * q^96 + 2494422276 * q^97 - 3443098784 * q^98 + 2123567852 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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