LMFDB - Embedded newform 29.12.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,12,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, 12, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 12 $
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:	$22.2819522362$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 23517 x^{12} - 42196 x^{11} + 214206700 x^{10} + 532863376 x^{9} - 951901011680 x^{8} + \cdots + 30\!\cdots\!04 $ x^14 - 23517x^12 - 42196x^11 + 214206700x^10 + 532863376x^9 - 951901011680x^8 - 1439668569088x^7 + 2125122050961664x^6 - 3617975849298944x^5 - 2179155305696991232x^4 + 15507015861824716800x^3 + 709645914927917694976x^2 - 9478460460037847384064x + 30797548279705794248704
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$6.06439$ 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)

$f(q)$	$=$	$q+6.06439 q^{2} -282.467 q^{3} -2011.22 q^{4} -8656.32 q^{5} -1712.99 q^{6} -42605.5 q^{7} -24616.7 q^{8} -97359.2 q^{9} +O(q^{10})$	\(q+6.06439 q^{2} -282.467 q^{3} -2011.22 q^{4} -8656.32 q^{5} -1712.99 q^{6} -42605.5 q^{7} -24616.7 q^{8} -97359.2 q^{9} -52495.3 q^{10} -84741.1 q^{11} +568105. q^{12} -184065. q^{13} -258376. q^{14} +2.44513e6 q^{15} +3.96970e6 q^{16} -3.55936e6 q^{17} -590424. q^{18} -5.58101e6 q^{19} +1.74098e7 q^{20} +1.20346e7 q^{21} -513903. q^{22} -9.75888e6 q^{23} +6.95342e6 q^{24} +2.61038e7 q^{25} -1.11624e6 q^{26} +7.75390e7 q^{27} +8.56891e7 q^{28} -2.05111e7 q^{29} +1.48282e7 q^{30} -1.20297e8 q^{31} +7.44888e7 q^{32} +2.39366e7 q^{33} -2.15854e7 q^{34} +3.68807e8 q^{35} +1.95811e8 q^{36} +2.53231e8 q^{37} -3.38454e7 q^{38} +5.19923e7 q^{39} +2.13090e8 q^{40} +7.41898e8 q^{41} +7.29828e7 q^{42} -6.80255e8 q^{43} +1.70433e8 q^{44} +8.42773e8 q^{45} -5.91817e7 q^{46} -1.58428e9 q^{47} -1.12131e9 q^{48} -1.62102e8 q^{49} +1.58304e8 q^{50} +1.00540e9 q^{51} +3.70195e8 q^{52} -5.78978e9 q^{53} +4.70227e8 q^{54} +7.33546e8 q^{55} +1.04881e9 q^{56} +1.57645e9 q^{57} -1.24388e8 q^{58} -4.38718e9 q^{59} -4.91770e9 q^{60} -9.17122e9 q^{61} -7.29528e8 q^{62} +4.14803e9 q^{63} -7.67822e9 q^{64} +1.59332e9 q^{65} +1.45161e8 q^{66} -6.71176e8 q^{67} +7.15867e9 q^{68} +2.75656e9 q^{69} +2.23659e9 q^{70} +3.09080e9 q^{71} +2.39666e9 q^{72} +4.55826e9 q^{73} +1.53569e9 q^{74} -7.37347e9 q^{75} +1.12246e10 q^{76} +3.61043e9 q^{77} +3.15301e8 q^{78} +6.82377e9 q^{79} -3.43630e10 q^{80} -4.65534e9 q^{81} +4.49916e9 q^{82} +2.79923e10 q^{83} -2.42044e10 q^{84} +3.08110e10 q^{85} -4.12533e9 q^{86} +5.79373e9 q^{87} +2.08605e9 q^{88} +6.74688e10 q^{89} +5.11090e9 q^{90} +7.84216e9 q^{91} +1.96273e10 q^{92} +3.39800e10 q^{93} -9.60768e9 q^{94} +4.83110e10 q^{95} -2.10407e10 q^{96} +6.18052e10 q^{97} -9.83050e8 q^{98} +8.25033e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9}+O(q^{10}) $ 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9} + 713576 q^{10} + 398020 q^{11} - 4026800 q^{12} + 2272440 q^{13} - 7199712 q^{14} - 4763864 q^{15} + 19015138 q^{16} + 5623508 q^{17} - 204156 q^{18} + 29803300 q^{19} + 65161006 q^{20} + 51227832 q^{21} + 167334266 q^{22} + 52654304 q^{23} + 221514842 q^{24} + 194970462 q^{25} + 373581536 q^{26} + 397348256 q^{27} + 319501772 q^{28} - 287156086 q^{29} + 423014226 q^{30} + 634041348 q^{31} + 1260290884 q^{32} + 1180833420 q^{33} + 1316105060 q^{34} + 1599853768 q^{35} + 3198076132 q^{36} + 488665204 q^{37} + 1892845072 q^{38} + 1972619104 q^{39} + 1826486880 q^{40} + 198215164 q^{41} + 1011384468 q^{42} + 2193188100 q^{43} + 26522720 q^{44} - 1129321956 q^{45} - 1567525268 q^{46} - 4175934476 q^{47} - 15582938120 q^{48} + 1105222462 q^{49} - 6630582612 q^{50} + 3297462720 q^{51} - 4557341374 q^{52} - 13223081840 q^{53} - 8946135054 q^{54} - 2726359424 q^{55} - 27538267872 q^{56} - 24477013312 q^{57} + 352219640 q^{59} - 36042747924 q^{60} - 7658546476 q^{61} - 10024135594 q^{62} - 23037581736 q^{63} + 14721327762 q^{64} + 1152802884 q^{65} - 99505241364 q^{66} + 21781534280 q^{67} - 104178000188 q^{68} - 14601399408 q^{69} - 67948872984 q^{70} - 5573287168 q^{71} - 24062143544 q^{72} + 39661511924 q^{73} + 28506052056 q^{74} + 81845109044 q^{75} + 166950090320 q^{76} + 38773567192 q^{77} + 54249159006 q^{78} + 105565209020 q^{79} + 146242150550 q^{80} + 170581084750 q^{81} + 47345182756 q^{82} + 127846064024 q^{83} + 215311861496 q^{84} + 83883234552 q^{85} - 103162039382 q^{86} - 9763306924 q^{87} + 418253082102 q^{88} + 187826099404 q^{89} + 96335639960 q^{90} + 58390389864 q^{91} - 259645875396 q^{92} + 394641636020 q^{93} + 117694719934 q^{94} + 69935059424 q^{95} + 12533631786 q^{96} + 137285937500 q^{97} - 484896369168 q^{98} + 235419947204 q^{99}+O(q^{100}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9 + 713576 * q^10 + 398020 * q^11 - 4026800 * q^12 + 2272440 * q^13 - 7199712 * q^14 - 4763864 * q^15 + 19015138 * q^16 + 5623508 * q^17 - 204156 * q^18 + 29803300 * q^19 + 65161006 * q^20 + 51227832 * q^21 + 167334266 * q^22 + 52654304 * q^23 + 221514842 * q^24 + 194970462 * q^25 + 373581536 * q^26 + 397348256 * q^27 + 319501772 * q^28 - 287156086 * q^29 + 423014226 * q^30 + 634041348 * q^31 + 1260290884 * q^32 + 1180833420 * q^33 + 1316105060 * q^34 + 1599853768 * q^35 + 3198076132 * q^36 + 488665204 * q^37 + 1892845072 * q^38 + 1972619104 * q^39 + 1826486880 * q^40 + 198215164 * q^41 + 1011384468 * q^42 + 2193188100 * q^43 + 26522720 * q^44 - 1129321956 * q^45 - 1567525268 * q^46 - 4175934476 * q^47 - 15582938120 * q^48 + 1105222462 * q^49 - 6630582612 * q^50 + 3297462720 * q^51 - 4557341374 * q^52 - 13223081840 * q^53 - 8946135054 * q^54 - 2726359424 * q^55 - 27538267872 * q^56 - 24477013312 * q^57 + 352219640 * q^59 - 36042747924 * q^60 - 7658546476 * q^61 - 10024135594 * q^62 - 23037581736 * q^63 + 14721327762 * q^64 + 1152802884 * q^65 - 99505241364 * q^66 + 21781534280 * q^67 - 104178000188 * q^68 - 14601399408 * q^69 - 67948872984 * q^70 - 5573287168 * q^71 - 24062143544 * q^72 + 39661511924 * q^73 + 28506052056 * q^74 + 81845109044 * q^75 + 166950090320 * q^76 + 38773567192 * q^77 + 54249159006 * q^78 + 105565209020 * q^79 + 146242150550 * q^80 + 170581084750 * q^81 + 47345182756 * q^82 + 127846064024 * q^83 + 215311861496 * q^84 + 83883234552 * q^85 - 103162039382 * q^86 - 9763306924 * q^87 + 418253082102 * q^88 + 187826099404 * q^89 + 96335639960 * q^90 + 58390389864 * q^91 - 259645875396 * q^92 + 394641636020 * q^93 + 117694719934 * q^94 + 69935059424 * q^95 + 12533631786 * q^96 + 137285937500 * q^97 - 484896369168 * q^98 + 235419947204 * 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 $

$2$	6.06439	0.134005	0.0670027	−	0.997753i	$-0.478656\pi$
$2$	6.06439	0.134005	0.0670027	+	0.997753i	$0.478656\pi$
$3$	−282.467	−0.671122	−0.335561	−	0.942019i	$-0.608926\pi$
$3$	−282.467	−0.671122	−0.335561	+	0.942019i	$0.608926\pi$
$4$	−2011.22	−0.982043
$5$	−8656.32	−1.23879	−0.619396	−	0.785079i	$-0.712622\pi$
$5$	−8656.32	−1.23879	−0.619396	+	0.785079i	$0.712622\pi$
$6$	−1712.99	−0.0899339
$7$	−42605.5	−0.958133	−0.479067	−	0.877779i	$-0.659025\pi$
$7$	−42605.5	−0.958133	−0.479067	+	0.877779i	$0.659025\pi$
$8$	−24616.7	−0.265604
$9$	−97359.2	−0.549596
$10$	−52495.3	−0.166005
$11$	−84741.1	−0.158648	−0.0793239	−	0.996849i	$-0.525276\pi$
$11$	−84741.1	−0.158648	−0.0793239	+	0.996849i	$0.525276\pi$
$12$	568105.	0.659070
$13$	−184065.	−0.137493	−0.0687467	−	0.997634i	$-0.521900\pi$
$13$	−184065.	−0.137493	−0.0687467	+	0.997634i	$0.521900\pi$
$14$	−258376.	−0.128395
$15$	2.44513e6	0.831380
$16$	3.96970e6	0.946450
$17$	−3.55936e6	−0.608000	−0.304000	−	0.952672i	$-0.598322\pi$
$17$	−3.55936e6	−0.608000	−0.304000	+	0.952672i	$0.598322\pi$
$18$	−590424.	−0.0736488
$19$	−5.58101e6	−0.517092	−0.258546	−	0.965999i	$-0.583243\pi$
$19$	−5.58101e6	−0.517092	−0.258546	+	0.965999i	$0.583243\pi$
$20$	1.74098e7	1.21655
$21$	1.20346e7	0.643024
$22$	−513903.	−0.0212597
$23$	−9.75888e6	−0.316153	−0.158076	−	0.987427i	$-0.550529\pi$
$23$	−9.75888e6	−0.316153	−0.158076	+	0.987427i	$0.550529\pi$
$24$	6.95342e6	0.178253
$25$	2.61038e7	0.534606
$26$	−1.11624e6	−0.0184249
$27$	7.75390e7	1.03997
$28$	8.56891e7	0.940928
$29$	−2.05111e7	−0.185695
$29$	−2.05111e7	−0.185695
$30$	1.48282e7	0.111409
$31$	−1.20297e8	−0.754685	−0.377343	−	0.926074i	$-0.623162\pi$
$31$	−1.20297e8	−0.754685	−0.377343	+	0.926074i	$0.623162\pi$
$32$	7.44888e7	0.392434
$33$	2.39366e7	0.106472
$34$	−2.15854e7	−0.0814752
$35$	3.68807e8	1.18693
$36$	1.95811e8	0.539726
$37$	2.53231e8	0.600353	0.300177	−	0.953884i	$-0.402954\pi$
$37$	2.53231e8	0.600353	0.300177	+	0.953884i	$0.402954\pi$
$38$	−3.38454e7	−0.0692931
$39$	5.19923e7	0.0922748
$40$	2.13090e8	0.329029
$41$	7.41898e8	1.00008	0.500038	−	0.866003i	$-0.333319\pi$
$41$	7.41898e8	1.00008	0.500038	+	0.866003i	$0.333319\pi$
$42$	7.29828e7	0.0861687
$43$	−6.80255e8	−0.705660	−0.352830	−	0.935688i	$-0.614781\pi$
$43$	−6.80255e8	−0.705660	−0.352830	+	0.935688i	$0.614781\pi$
$44$	1.70433e8	0.155799
$45$	8.42773e8	0.680835
$46$	−5.91817e7	−0.0423662
$47$	−1.58428e9	−1.00761	−0.503806	−	0.863817i	$-0.668067\pi$
$47$	−1.58428e9	−1.00761	−0.503806	+	0.863817i	$0.668067\pi$
$48$	−1.12131e9	−0.635183
$49$	−1.62102e8	−0.0819804
$50$	1.58304e8	0.0716401
$51$	1.00540e9	0.408042
$52$	3.70195e8	0.135024
$53$	−5.78978e9	−1.90171	−0.950856	−	0.309632i	$-0.899794\pi$
$53$	−5.78978e9	−1.90171	−0.950856	+	0.309632i	$0.899794\pi$
$54$	4.70227e8	0.139361
$55$	7.33546e8	0.196532
$56$	1.04881e9	0.254484
$57$	1.57645e9	0.347031
$58$	−1.24388e8	−0.0248842
$59$	−4.38718e9	−0.798914	−0.399457	−	0.916752i	$-0.630801\pi$
$59$	−4.38718e9	−0.798914	−0.399457	+	0.916752i	$0.630801\pi$
$60$	−4.91770e9	−0.816451
$61$	−9.17122e9	−1.39031	−0.695157	−	0.718857i	$-0.744665\pi$
$61$	−9.17122e9	−1.39031	−0.695157	+	0.718857i	$0.744665\pi$
$62$	−7.29528e8	−0.101132
$63$	4.14803e9	0.526586
$64$	−7.67822e9	−0.893862
$65$	1.59332e9	0.170326
$66$	1.45161e8	0.0142678
$67$	−6.71176e8	−0.0607330	−0.0303665	−	0.999539i	$-0.509667\pi$
$67$	−6.71176e8	−0.0607330	−0.0303665	+	0.999539i	$0.509667\pi$
$68$	7.15867e9	0.597081
$69$	2.75656e9	0.212177
$70$	2.23659e9	0.159055
$71$	3.09080e9	0.203306	0.101653	−	0.994820i	$-0.467587\pi$
$71$	3.09080e9	0.203306	0.101653	+	0.994820i	$0.467587\pi$
$72$	2.39666e9	0.145975
$73$	4.55826e9	0.257349	0.128675	−	0.991687i	$-0.458928\pi$
$73$	4.55826e9	0.257349	0.128675	+	0.991687i	$0.458928\pi$
$74$	1.53569e9	0.0804505
$75$	−7.37347e9	−0.358786
$76$	1.12246e10	0.507806
$77$	3.61043e9	0.152006
$78$	3.15301e8	0.0123653
$79$	6.82377e9	0.249503	0.124751	−	0.992188i	$-0.460187\pi$
$79$	6.82377e9	0.249503	0.124751	+	0.992188i	$0.460187\pi$
$80$	−3.43630e10	−1.17246
$81$	−4.65534e9	−0.148349
$82$	4.49916e9	0.134016
$83$	2.79923e10	0.780025	0.390012	−	0.920810i	$-0.372471\pi$
$83$	2.79923e10	0.780025	0.390012	+	0.920810i	$0.372471\pi$
$84$	−2.42044e10	−0.631477
$85$	3.08110e10	0.753185
$86$	−4.12533e9	−0.0945621
$87$	5.79373e9	0.124624
$88$	2.08605e9	0.0421376
$89$	6.74688e10	1.28073	0.640365	−	0.768071i	$-0.278783\pi$
$89$	6.74688e10	1.28073	0.640365	+	0.768071i	$0.278783\pi$
$90$	5.11090e9	0.0912355
$91$	7.84216e9	0.131737
$92$	1.96273e10	0.310475
$93$	3.39800e10	0.506486
$94$	−9.60768e9	−0.135025
$95$	4.83110e10	0.640569
$96$	−2.10407e10	−0.263371
$97$	6.18052e10	0.730770	0.365385	−	0.930856i	$-0.380937\pi$
$97$	6.18052e10	0.730770	0.365385	+	0.930856i	$0.380937\pi$
$98$	−9.83050e8	−0.0109858
$99$	8.25033e9	0.0871922
$100$	−5.25006e10	−0.525006
$101$	1.36218e11	1.28964	0.644820	−	0.764335i	$-0.276933\pi$
$101$	1.36218e11	1.28964	0.644820	+	0.764335i	$0.276933\pi$
$102$	6.09716e9	0.0546798
$103$	−9.04576e10	−0.768847	−0.384424	−	0.923157i	$-0.625600\pi$
$103$	−9.04576e10	−0.768847	−0.384424	+	0.923157i	$0.625600\pi$
$104$	4.53107e9	0.0365189
$105$	−1.04176e11	−0.796573
$106$	−3.51115e10	−0.254840
$107$	−5.21129e10	−0.359198	−0.179599	−	0.983740i	$-0.557480\pi$
$107$	−5.21129e10	−0.359198	−0.179599	+	0.983740i	$0.557480\pi$
$108$	−1.55948e11	−1.02129
$109$	−9.39985e10	−0.585161	−0.292580	−	0.956241i	$-0.594514\pi$
$109$	−9.39985e10	−0.585161	−0.292580	+	0.956241i	$0.594514\pi$
$110$	4.44851e9	0.0263363
$111$	−7.15294e10	−0.402910
$112$	−1.69131e11	−0.906826
$113$	−1.04962e11	−0.535921	−0.267960	−	0.963430i	$-0.586350\pi$
$113$	−1.04962e11	−0.535921	−0.267960	+	0.963430i	$0.586350\pi$
$114$	9.56021e9	0.0465041
$115$	8.44760e10	0.391648
$116$	4.12525e10	0.182361
$117$	1.79204e10	0.0755658
$118$	−2.66056e10	−0.107059
$119$	1.51648e11	0.582545
$120$	−6.01910e10	−0.220818
$121$	−2.78131e11	−0.974831
$122$	−5.56179e10	−0.186310
$123$	−2.09562e11	−0.671173
$124$	2.41944e11	0.741133
$125$	1.96709e11	0.576526
$126$	2.51553e10	0.0705653
$127$	6.82121e11	1.83207	0.916033	−	0.401103i	$-0.131373\pi$
$127$	6.82121e11	1.83207	0.916033	+	0.401103i	$0.131373\pi$
$128$	−1.99117e11	−0.512216
$129$	1.92150e11	0.473583
$130$	9.66253e9	0.0228246
$131$	−4.20774e11	−0.952922	−0.476461	−	0.879196i	$-0.658081\pi$
$131$	−4.20774e11	−0.952922	−0.476461	+	0.879196i	$0.658081\pi$
$132$	−4.81418e10	−0.104560
$133$	2.37781e11	0.495443
$134$	−4.07027e9	−0.00813855
$135$	−6.71203e11	−1.28830
$136$	8.76198e10	0.161487
$137$	−6.50277e10	−0.115116	−0.0575579	−	0.998342i	$-0.518331\pi$
$137$	−6.50277e10	−0.115116	−0.0575579	+	0.998342i	$0.518331\pi$
$138$	1.67169e10	0.0284328
$139$	−1.55269e11	−0.253808	−0.126904	−	0.991915i	$-0.540504\pi$
$139$	−1.55269e11	−0.253808	−0.126904	+	0.991915i	$0.540504\pi$
$140$	−7.41752e11	−1.16561
$141$	4.47507e11	0.676230
$142$	1.87438e10	0.0272441
$143$	1.55978e10	0.0218130
$144$	−3.86487e11	−0.520165
$145$	1.77551e11	0.230038
$146$	2.76430e10	0.0344862
$147$	4.57885e10	0.0550188
$148$	−5.09303e11	−0.589572
$149$	8.25236e11	0.920564	0.460282	−	0.887773i	$-0.347748\pi$
$149$	8.25236e11	0.920564	0.460282	+	0.887773i	$0.347748\pi$
$150$	−4.47156e10	−0.0480792
$151$	1.67135e12	1.73258	0.866292	−	0.499538i	$-0.166497\pi$
$151$	1.67135e12	1.73258	0.866292	+	0.499538i	$0.166497\pi$
$152$	1.37386e11	0.137342
$153$	3.46537e11	0.334154
$154$	2.18951e10	0.0203696
$155$	1.04133e12	0.934898
$156$	−1.04568e11	−0.0906178
$157$	1.44245e12	1.20685	0.603423	−	0.797421i	$-0.293803\pi$
$157$	1.44245e12	1.20685	0.603423	+	0.797421i	$0.293803\pi$
$158$	4.13820e10	0.0334347
$159$	1.63542e12	1.27628
$160$	−6.44799e11	−0.486144
$161$	4.15782e11	0.302916
$162$	−2.82318e10	−0.0198795
$163$	2.11140e12	1.43727	0.718637	−	0.695386i	$-0.244766\pi$
$163$	2.11140e12	1.43727	0.718637	+	0.695386i	$0.244766\pi$
$164$	−1.49212e12	−0.982117
$165$	−2.07203e11	−0.131897
$166$	1.69756e11	0.104527
$167$	−2.49060e12	−1.48376	−0.741878	−	0.670535i	$-0.766065\pi$
$167$	−2.49060e12	−1.48376	−0.741878	+	0.670535i	$0.766065\pi$
$168$	−2.96253e11	−0.170790
$169$	−1.75828e12	−0.981096
$170$	1.86850e11	0.100931
$171$	5.43362e11	0.284191
$172$	1.36814e12	0.692988
$173$	−2.24630e12	−1.10208	−0.551041	−	0.834478i	$-0.685769\pi$
$173$	−2.24630e12	−1.10208	−0.551041	+	0.834478i	$0.685769\pi$
$174$	3.51354e10	0.0167003
$175$	−1.11216e12	−0.512224
$176$	−3.36397e11	−0.150152
$177$	1.23924e12	0.536168
$178$	4.09157e11	0.171625
$179$	−8.99862e11	−0.366003	−0.183001	−	0.983113i	$-0.558581\pi$
$179$	−8.99862e11	−0.366003	−0.183001	+	0.983113i	$0.558581\pi$
$180$	−1.69500e12	−0.668609
$181$	−3.58658e12	−1.37230	−0.686148	−	0.727462i	$-0.740700\pi$
$181$	−3.58658e12	−1.37230	−0.686148	+	0.727462i	$0.740700\pi$
$182$	4.75579e10	0.0176535
$183$	2.59057e12	0.933070
$184$	2.40232e11	0.0839715
$185$	−2.19205e12	−0.743713
$186$	2.06068e11	0.0678718
$187$	3.01624e11	0.0964578
$188$	3.18634e12	0.989517
$189$	−3.30359e12	−0.996427
$190$	2.92977e11	0.0858397
$191$	3.03829e12	0.864859	0.432429	−	0.901668i	$-0.357656\pi$
$191$	3.03829e12	0.864859	0.432429	+	0.901668i	$0.357656\pi$
$192$	2.16884e12	0.599890
$193$	−3.08891e12	−0.830309	−0.415155	−	0.909751i	$-0.636273\pi$
$193$	−3.08891e12	−0.830309	−0.415155	+	0.909751i	$0.636273\pi$
$194$	3.74811e11	0.0979271
$195$	−4.50062e11	−0.114309
$196$	3.26023e11	0.0805083
$197$	−4.53679e12	−1.08939	−0.544696	−	0.838634i	$-0.683355\pi$
$197$	−4.53679e12	−1.08939	−0.544696	+	0.838634i	$0.683355\pi$
$198$	5.00332e10	0.0116842
$199$	−7.26504e12	−1.65024	−0.825118	−	0.564960i	$-0.808891\pi$
$199$	−7.26504e12	−1.65024	−0.825118	+	0.564960i	$0.808891\pi$
$200$	−6.42590e11	−0.141994
$201$	1.89585e11	0.0407592
$202$	8.26081e11	0.172819
$203$	8.73887e11	0.177921
$204$	−2.02209e12	−0.400714
$205$	−6.42211e12	−1.23889
$206$	−5.48570e11	−0.103030
$207$	9.50117e11	0.173756
$208$	−7.30682e11	−0.130131
$209$	4.72940e11	0.0820355
$210$	−6.31763e11	−0.106745
$211$	7.09681e12	1.16818	0.584090	−	0.811689i	$-0.301451\pi$
$211$	7.09681e12	1.16818	0.584090	+	0.811689i	$0.301451\pi$
$212$	1.16445e13	1.86756
$213$	−8.73051e11	−0.136443
$214$	−3.16033e11	−0.0481345
$215$	5.88851e12	0.874166
$216$	−1.90876e12	−0.276220
$217$	5.12531e12	0.723089
$218$	−5.70044e11	−0.0784147
$219$	−1.28756e12	−0.172713
$220$	−1.47533e12	−0.193003
$221$	6.55153e11	0.0835960
$222$	−4.33782e11	−0.0539921
$223$	1.22941e13	1.49286	0.746432	−	0.665462i	$-0.231765\pi$
$223$	1.22941e13	1.49286	0.746432	+	0.665462i	$0.231765\pi$
$224$	−3.17363e12	−0.376004
$225$	−2.54145e12	−0.293817
$226$	−6.36530e11	−0.0718162
$227$	3.72145e11	0.0409798	0.0204899	−	0.999790i	$-0.493477\pi$
$227$	3.72145e11	0.0409798	0.0204899	+	0.999790i	$0.493477\pi$
$228$	−3.17060e12	−0.340800
$229$	4.71023e12	0.494250	0.247125	−	0.968984i	$-0.420514\pi$
$229$	4.71023e12	0.494250	0.247125	+	0.968984i	$0.420514\pi$
$230$	5.12296e11	0.0524829
$231$	−1.01983e12	−0.102014
$232$	5.04917e11	0.0493215
$233$	−8.84711e12	−0.844002	−0.422001	−	0.906595i	$-0.638672\pi$
$233$	−8.84711e12	−0.844002	−0.422001	+	0.906595i	$0.638672\pi$
$234$	1.08676e11	0.0101262
$235$	1.37140e13	1.24822
$236$	8.82361e12	0.784567
$237$	−1.92749e12	−0.167447
$238$	9.19654e11	0.0780641
$239$	−1.79346e13	−1.48766	−0.743829	−	0.668369i	$-0.766993\pi$
$239$	−1.79346e13	−1.48766	−0.743829	+	0.668369i	$0.766993\pi$
$240$	9.70642e12	0.786860
$241$	1.12617e13	0.892295	0.446147	−	0.894960i	$-0.352796\pi$
$241$	1.12617e13	0.892295	0.446147	+	0.894960i	$0.352796\pi$
$242$	−1.68669e12	−0.130633
$243$	−1.24208e13	−0.940407
$244$	1.84454e13	1.36535
$245$	1.40321e12	0.101557
$246$	−1.27086e12	−0.0899407
$247$	1.02727e12	0.0710967
$248$	2.96132e12	0.200448
$249$	−7.90690e12	−0.523491
$250$	1.19292e12	0.0772576
$251$	−4.83970e12	−0.306629	−0.153314	−	0.988177i	$-0.548995\pi$
$251$	−4.83970e12	−0.306629	−0.153314	+	0.988177i	$0.548995\pi$
$252$	−8.34262e12	−0.517130
$253$	8.26978e11	0.0501570
$254$	4.13665e12	0.245507
$255$	−8.70310e12	−0.505479
$256$	1.45175e13	0.825222
$257$	6.11418e12	0.340178	0.170089	−	0.985429i	$-0.445594\pi$
$257$	6.11418e12	0.340178	0.170089	+	0.985429i	$0.445594\pi$
$258$	1.16527e12	0.0634627
$259$	−1.07890e13	−0.575218
$260$	−3.20453e12	−0.167267
$261$	1.99695e12	0.102057
$262$	−2.55174e12	−0.127697
$263$	−3.46978e13	−1.70038	−0.850190	−	0.526477i	$-0.823513\pi$
$263$	−3.46978e13	−1.70038	−0.850190	+	0.526477i	$0.823513\pi$
$264$	−5.89240e11	−0.0282794
$265$	5.01182e13	2.35583
$266$	1.44200e12	0.0663920
$267$	−1.90577e13	−0.859526
$268$	1.34988e12	0.0596424
$269$	−3.26301e13	−1.41248	−0.706238	−	0.707974i	$-0.749609\pi$
$269$	−3.26301e13	−1.41248	−0.706238	+	0.707974i	$0.749609\pi$
$270$	−4.07044e12	−0.172640
$271$	1.70050e13	0.706719	0.353359	−	0.935488i	$-0.385039\pi$
$271$	1.70050e13	0.706719	0.353359	+	0.935488i	$0.385039\pi$
$272$	−1.41296e13	−0.575441
$273$	−2.21515e12	−0.0884116
$274$	−3.94353e11	−0.0154261
$275$	−2.21207e12	−0.0848141
$276$	−5.54407e12	−0.208367
$277$	1.59300e13	0.586917	0.293459	−	0.955972i	$-0.405194\pi$
$277$	1.59300e13	0.586917	0.293459	+	0.955972i	$0.405194\pi$
$278$	−9.41614e11	−0.0340116
$279$	1.17120e13	0.414772
$280$	−9.07880e12	−0.315253
$281$	−3.07678e13	−1.04764	−0.523820	−	0.851829i	$-0.675494\pi$
$281$	−3.07678e13	−1.04764	−0.523820	+	0.851829i	$0.675494\pi$
$282$	2.71385e12	0.0906184
$283$	−3.00744e11	−0.00984853	−0.00492427	−	0.999988i	$-0.501567\pi$
$283$	−3.00744e11	−0.00984853	−0.00492427	+	0.999988i	$0.501567\pi$
$284$	−6.21630e12	−0.199655
$285$	−1.36463e13	−0.429900
$286$	9.45914e10	0.00292306
$287$	−3.16089e13	−0.958206
$288$	−7.25217e12	−0.215680
$289$	−2.16028e13	−0.630337
$290$	1.07674e12	0.0308263
$291$	−1.74580e13	−0.490436
$292$	−9.16767e12	−0.252728
$293$	9.55992e11	0.0258632	0.0129316	−	0.999916i	$-0.495884\pi$
$293$	9.55992e11	0.0258632	0.0129316	+	0.999916i	$0.495884\pi$
$294$	2.77679e11	0.00737282
$295$	3.79769e13	0.989688
$296$	−6.23370e12	−0.159456
$297$	−6.57074e12	−0.164989
$298$	5.00456e12	0.123360
$299$	1.79627e12	0.0434689
$300$	1.48297e13	0.352343
$301$	2.89826e13	0.676116
$302$	1.01357e13	0.232176
$303$	−3.84772e13	−0.865505
$304$	−2.21549e13	−0.489402
$305$	7.93891e13	1.72231
$306$	2.10153e12	0.0447784
$307$	2.19777e13	0.459961	0.229980	−	0.973195i	$-0.426134\pi$
$307$	2.19777e13	0.459961	0.229980	+	0.973195i	$0.426134\pi$
$308$	−7.26139e12	−0.149276
$309$	2.55513e13	0.515990
$310$	6.31503e12	0.125281
$311$	5.46018e12	0.106420	0.0532102	−	0.998583i	$-0.483055\pi$
$311$	5.46018e12	0.106420	0.0532102	+	0.998583i	$0.483055\pi$
$312$	−1.27988e12	−0.0245086
$313$	7.56153e13	1.42271	0.711354	−	0.702833i	$-0.248082\pi$
$313$	7.56153e13	1.42271	0.711354	+	0.702833i	$0.248082\pi$
$314$	8.74756e12	0.161724
$315$	−3.59067e13	−0.652331
$316$	−1.37241e13	−0.245022
$317$	−9.20495e13	−1.61509	−0.807543	−	0.589809i	$-0.799203\pi$
$317$	−9.20495e13	−1.61509	−0.807543	+	0.589809i	$0.799203\pi$
$318$	9.91785e12	0.171028
$319$	1.73814e12	0.0294602
$320$	6.64651e13	1.10731
$321$	1.47202e13	0.241066
$322$	2.52146e12	0.0405924
$323$	1.98648e13	0.314392
$324$	9.36293e12	0.145685
$325$	−4.80479e12	−0.0735048
$326$	1.28044e13	0.192602
$327$	2.65515e13	0.392714
$328$	−1.82631e13	−0.265624
$329$	6.74989e13	0.965426
$330$	−1.25656e12	−0.0176749
$331$	1.00259e14	1.38698	0.693488	−	0.720468i	$-0.256073\pi$
$331$	1.00259e14	1.38698	0.693488	+	0.720468i	$0.256073\pi$
$332$	−5.62987e13	−0.766017
$333$	−2.46543e13	−0.329951
$334$	−1.51039e13	−0.198831
$335$	5.80991e12	0.0752356
$336$	4.77739e13	0.608590
$337$	−1.34580e14	−1.68661	−0.843307	−	0.537432i	$-0.819394\pi$
$337$	−1.34580e14	−1.68661	−0.843307	+	0.537432i	$0.819394\pi$
$338$	−1.06629e13	−0.131472
$339$	2.96483e13	0.359668
$340$	−6.19678e13	−0.739660
$341$	1.01941e13	0.119729
$342$	3.29516e12	0.0380832
$343$	9.11513e13	1.03668
$344$	1.67456e13	0.187426
$345$	−2.38617e13	−0.262843
$346$	−1.36224e13	−0.147685
$347$	9.91474e13	1.05796	0.528980	−	0.848634i	$-0.322575\pi$
$347$	9.91474e13	1.05796	0.528980	+	0.848634i	$0.322575\pi$
$348$	−1.16525e13	−0.122386
$349$	1.35366e14	1.39949	0.699744	−	0.714394i	$-0.253297\pi$
$349$	1.35366e14	1.39949	0.699744	+	0.714394i	$0.253297\pi$
$350$	−6.74460e12	−0.0686407
$351$	−1.42722e13	−0.142989
$352$	−6.31226e12	−0.0622588
$353$	−8.59497e13	−0.834610	−0.417305	−	0.908767i	$-0.637025\pi$
$353$	−8.59497e13	−0.834610	−0.417305	+	0.908767i	$0.637025\pi$
$354$	7.51521e12	0.0718494
$355$	−2.67550e13	−0.251854
$356$	−1.35695e14	−1.25773
$357$	−4.28357e13	−0.390958
$358$	−5.45712e12	−0.0490463
$359$	−1.51516e13	−0.134103	−0.0670517	−	0.997750i	$-0.521359\pi$
$359$	−1.51516e13	−0.134103	−0.0670517	+	0.997750i	$0.521359\pi$
$360$	−2.07463e13	−0.180833
$361$	−8.53426e13	−0.732616
$362$	−2.17504e13	−0.183895
$363$	7.85628e13	0.654230
$364$	−1.57723e13	−0.129371
$365$	−3.94577e13	−0.318802
$366$	1.57102e13	0.125036
$367$	−2.57851e13	−0.202164	−0.101082	−	0.994878i	$-0.532231\pi$
$367$	−2.57851e13	−0.202164	−0.101082	+	0.994878i	$0.532231\pi$
$368$	−3.87398e13	−0.299223
$369$	−7.22306e13	−0.549637
$370$	−1.32934e13	−0.0996615
$371$	2.46676e14	1.82209
$372$	−6.83414e13	−0.497390
$373$	4.65411e13	0.333763	0.166882	−	0.985977i	$-0.446630\pi$
$373$	4.65411e13	0.333763	0.166882	+	0.985977i	$0.446630\pi$
$374$	1.82917e12	0.0129259
$375$	−5.55639e13	−0.386919
$376$	3.89997e13	0.267626
$377$	3.77538e12	0.0255319
$378$	−2.00342e13	−0.133527
$379$	2.01562e14	1.32401	0.662006	−	0.749498i	$-0.269705\pi$
$379$	2.01562e14	1.32401	0.662006	+	0.749498i	$0.269705\pi$
$380$	−9.71642e13	−0.629066
$381$	−1.92677e14	−1.22954
$382$	1.84254e13	0.115896
$383$	−1.54072e14	−0.955280	−0.477640	−	0.878556i	$-0.658508\pi$
$383$	−1.54072e14	−0.955280	−0.477640	+	0.878556i	$0.658508\pi$
$384$	5.62440e13	0.343759
$385$	−3.12531e13	−0.188304
$386$	−1.87323e13	−0.111266
$387$	6.62291e13	0.387827
$388$	−1.24304e14	−0.717647
$389$	−8.79423e13	−0.500582	−0.250291	−	0.968171i	$-0.580526\pi$
$389$	−8.79423e13	−0.500582	−0.250291	+	0.968171i	$0.580526\pi$
$390$	−2.72935e12	−0.0153181
$391$	3.47354e13	0.192221
$392$	3.99042e12	0.0217743
$393$	1.18855e14	0.639526
$394$	−2.75128e13	−0.145984
$395$	−5.90688e13	−0.309082
$396$	−1.65933e13	−0.0856265
$397$	−1.83769e14	−0.935242	−0.467621	−	0.883929i	$-0.654889\pi$
$397$	−1.83769e14	−0.935242	−0.467621	+	0.883929i	$0.654889\pi$
$398$	−4.40580e13	−0.221140
$399$	−6.71654e13	−0.332502
$400$	1.03624e14	0.505978
$401$	1.30329e14	0.627691	0.313845	−	0.949474i	$-0.398383\pi$
$401$	1.30329e14	0.627691	0.313845	+	0.949474i	$0.398383\pi$
$402$	1.14972e12	0.00546196
$403$	2.21425e13	0.103764
$404$	−2.73966e14	−1.26648
$405$	4.02982e13	0.183773
$406$	5.29959e12	0.0238424
$407$	−2.14590e13	−0.0952447
$408$	−2.47497e13	−0.108378
$409$	−3.12991e14	−1.35224	−0.676119	−	0.736793i	$-0.736339\pi$
$409$	−3.12991e14	−1.35224	−0.676119	+	0.736793i	$0.736339\pi$
$410$	−3.89462e13	−0.166017
$411$	1.83682e13	0.0772568
$412$	1.81930e14	0.755041
$413$	1.86918e14	0.765466
$414$	5.76188e12	0.0232843
$415$	−2.42310e14	−0.966288
$416$	−1.37108e13	−0.0539571
$417$	4.38585e13	0.170336
$418$	2.86810e12	0.0109932
$419$	2.54220e14	0.961685	0.480843	−	0.876807i	$-0.340331\pi$
$419$	2.54220e14	0.961685	0.480843	+	0.876807i	$0.340331\pi$
$420$	2.09521e14	0.782269
$421$	4.22441e13	0.155674	0.0778368	−	0.996966i	$-0.475199\pi$
$421$	4.22441e13	0.155674	0.0778368	+	0.996966i	$0.475199\pi$
$422$	4.30378e13	0.156542
$423$	1.54244e14	0.553779
$424$	1.42525e14	0.505103
$425$	−9.29130e13	−0.325040
$426$	−5.29452e12	−0.0182841
$427$	3.90744e14	1.33211
$428$	1.04811e14	0.352748
$429$	−4.40588e12	−0.0146392
$430$	3.57102e13	0.117143
$431$	3.94529e13	0.127777	0.0638886	−	0.997957i	$-0.479650\pi$
$431$	3.94529e13	0.127777	0.0638886	+	0.997957i	$0.479650\pi$
$432$	3.07807e14	0.984277
$433$	4.46872e14	1.41091	0.705456	−	0.708754i	$-0.250742\pi$
$433$	4.46872e14	1.41091	0.705456	+	0.708754i	$0.250742\pi$
$434$	3.10819e13	0.0968978
$435$	−5.01524e13	−0.154383
$436$	1.89052e14	0.574653
$437$	5.44644e13	0.163480
$438$	−7.80825e12	−0.0231444
$439$	4.94771e14	1.44827	0.724135	−	0.689658i	$-0.242239\pi$
$439$	4.94771e14	1.44827	0.724135	+	0.689658i	$0.242239\pi$
$440$	−1.80575e13	−0.0521997
$441$	1.57821e13	0.0450561
$442$	3.97310e12	0.0112023
$443$	1.00814e12	0.00280738	0.00140369	−	0.999999i	$-0.499553\pi$
$443$	1.00814e12	0.00280738	0.00140369	+	0.999999i	$0.499553\pi$
$444$	1.43862e14	0.395675
$445$	−5.84031e14	−1.58656
$446$	7.45562e13	0.200052
$447$	−2.33102e14	−0.617810
$448$	3.27134e14	0.856439
$449$	−4.80074e14	−1.24152	−0.620759	−	0.784002i	$-0.713175\pi$
$449$	−4.80074e14	−1.24152	−0.620759	+	0.784002i	$0.713175\pi$
$450$	−1.54123e13	−0.0393731
$451$	−6.28692e13	−0.158660
$452$	2.11102e14	0.526297
$453$	−4.72102e14	−1.16277
$454$	2.25683e12	0.00549151
$455$	−6.78843e13	−0.163195
$456$	−3.88070e13	−0.0921730
$457$	−6.63448e14	−1.55693	−0.778463	−	0.627691i	$-0.784000\pi$
$457$	−6.63448e14	−1.55693	−0.778463	+	0.627691i	$0.784000\pi$
$458$	2.85646e13	0.0662321
$459$	−2.75990e14	−0.632300
$460$	−1.69900e14	−0.384615
$461$	4.42404e14	0.989609	0.494804	−	0.869004i	$-0.335240\pi$
$461$	4.42404e14	0.989609	0.494804	+	0.869004i	$0.335240\pi$
$462$	−6.18464e12	−0.0136705
$463$	−2.59461e14	−0.566730	−0.283365	−	0.959012i	$-0.591451\pi$
$463$	−2.59461e14	−0.566730	−0.283365	+	0.959012i	$0.591451\pi$
$464$	−8.14231e13	−0.175751
$465$	−2.94142e14	−0.627430
$466$	−5.36523e13	−0.113101
$467$	3.95171e14	0.823271	0.411635	−	0.911349i	$-0.364958\pi$
$467$	3.95171e14	0.823271	0.411635	+	0.911349i	$0.364958\pi$
$468$	−3.60419e13	−0.0742089
$469$	2.85957e13	0.0581903
$470$	8.31672e13	0.167268
$471$	−4.07444e14	−0.809940
$472$	1.07998e14	0.212195
$473$	5.76455e13	0.111951
$474$	−1.16891e13	−0.0224388
$475$	−1.45686e14	−0.276440
$476$	−3.04999e14	−0.572084
$477$	5.63689e14	1.04517
$478$	−1.08762e14	−0.199354
$479$	1.45131e14	0.262975	0.131488	−	0.991318i	$-0.458025\pi$
$479$	1.45131e14	0.262975	0.131488	+	0.991318i	$0.458025\pi$
$480$	1.82135e14	0.326262
$481$	−4.66108e13	−0.0825446
$482$	6.82950e13	0.119572
$483$	−1.17445e14	−0.203294
$484$	5.59383e14	0.957325
$485$	−5.35006e14	−0.905272
$486$	−7.53247e13	−0.126020
$487$	−4.31810e14	−0.714304	−0.357152	−	0.934046i	$-0.616252\pi$
$487$	−4.31810e14	−0.714304	−0.357152	+	0.934046i	$0.616252\pi$
$488$	2.25765e14	0.369274
$489$	−5.96402e14	−0.964585
$490$	8.50960e12	0.0136091
$491$	1.04625e15	1.65458	0.827288	−	0.561778i	$-0.189883\pi$
$491$	1.04625e15	1.65458	0.827288	+	0.561778i	$0.189883\pi$
$492$	4.21476e14	0.659120
$493$	7.30066e13	0.112903
$494$	6.22974e12	0.00952734
$495$	−7.14175e13	−0.108013
$496$	−4.77543e14	−0.714272
$497$	−1.31685e14	−0.194794
$498$	−4.79505e13	−0.0701506
$499$	3.50648e14	0.507363	0.253681	−	0.967288i	$-0.418359\pi$
$499$	3.50648e14	0.507363	0.253681	+	0.967288i	$0.418359\pi$
$500$	−3.95626e14	−0.566173
$501$	7.03512e14	0.995781
$502$	−2.93498e13	−0.0410899
$503$	−1.61952e14	−0.224266	−0.112133	−	0.993693i	$-0.535768\pi$
$503$	−1.61952e14	−0.224266	−0.112133	+	0.993693i	$0.535768\pi$
$504$	−1.02111e14	−0.139863
$505$	−1.17915e15	−1.59759
$506$	5.01512e12	0.00672130
$507$	4.96657e14	0.658434
$508$	−1.37190e15	−1.79917
$509$	−8.18227e14	−1.06152	−0.530758	−	0.847524i	$-0.678093\pi$
$509$	−8.18227e14	−1.06152	−0.530758	+	0.847524i	$0.678093\pi$
$510$	−5.27790e13	−0.0677369
$511$	−1.94207e14	−0.246575
$512$	4.95831e14	0.622800
$513$	−4.32746e14	−0.537758
$514$	3.70788e13	0.0455857
$515$	7.83030e14	0.952442
$516$	−3.86456e14	−0.465079
$517$	1.34253e14	0.159855
$518$	−6.54287e13	−0.0770823
$519$	6.34506e14	0.739631
$520$	−3.92224e13	−0.0452393
$521$	−1.99937e14	−0.228184	−0.114092	−	0.993470i	$-0.536396\pi$
$521$	−1.99937e14	−0.228184	−0.114092	+	0.993470i	$0.536396\pi$
$522$	1.21103e13	0.0136762
$523$	−1.57766e15	−1.76300	−0.881501	−	0.472182i	$-0.843467\pi$
$523$	−1.57766e15	−1.76300	−0.881501	+	0.472182i	$0.843467\pi$
$524$	8.46271e14	0.935810
$525$	3.14150e14	0.343765
$526$	−2.10421e14	−0.227860
$527$	4.28181e14	0.458848
$528$	9.50211e13	0.100770
$529$	−8.57574e14	−0.900047
$530$	3.03936e14	0.315693
$531$	4.27133e14	0.439080
$532$	−4.78231e14	−0.486546
$533$	−1.36557e14	−0.137504
$534$	−1.15573e14	−0.115181
$535$	4.51106e14	0.444972
$536$	1.65221e13	0.0161309
$537$	2.54182e14	0.245632
$538$	−1.97882e14	−0.189279
$539$	1.37367e13	0.0130060
$540$	1.34994e15	1.26517
$541$	−9.82170e14	−0.911175	−0.455587	−	0.890191i	$-0.650571\pi$
$541$	−9.82170e14	−0.911175	−0.455587	+	0.890191i	$0.650571\pi$
$542$	1.03125e14	0.0947041
$543$	1.01309e15	0.920978
$544$	−2.65133e14	−0.238599
$545$	8.13682e14	0.724893
$546$	−1.34336e13	−0.0118476
$547$	1.64553e15	1.43673	0.718365	−	0.695667i	$-0.244891\pi$
$547$	1.64553e15	1.43673	0.718365	+	0.695667i	$0.244891\pi$
$548$	1.30785e14	0.113049
$549$	8.92903e14	0.764111
$550$	−1.34148e13	−0.0113655
$551$	1.14473e14	0.0960215
$552$	−6.78576e13	−0.0563551
$553$	−2.90730e14	−0.239057
$554$	9.66057e13	0.0786500
$555$	6.19181e14	0.499122
$556$	3.12281e14	0.249250
$557$	−8.26165e12	−0.00652925	−0.00326463	−	0.999995i	$-0.501039\pi$
$557$	−8.26165e12	−0.00652925	−0.00326463	+	0.999995i	$0.501039\pi$
$558$	7.10263e13	0.0555816
$559$	1.25211e14	0.0970236
$560$	1.46405e15	1.12337
$561$	−8.51990e13	−0.0647349
$562$	−1.86588e14	−0.140389
$563$	−4.57235e14	−0.340677	−0.170339	−	0.985386i	$-0.554486\pi$
$563$	−4.57235e14	−0.340677	−0.170339	+	0.985386i	$0.554486\pi$
$564$	−9.00036e14	−0.664087
$565$	9.08584e14	0.663894
$566$	−1.82383e12	−0.00131976
$567$	1.98343e14	0.142138
$568$	−7.60854e13	−0.0539990
$569$	4.99442e14	0.351049	0.175524	−	0.984475i	$-0.443838\pi$
$569$	4.99442e14	0.351049	0.175524	+	0.984475i	$0.443838\pi$
$570$	−8.27563e13	−0.0576089
$571$	1.97175e14	0.135942	0.0679711	−	0.997687i	$-0.478347\pi$
$571$	1.97175e14	0.135942	0.0679711	+	0.997687i	$0.478347\pi$
$572$	−3.13707e13	−0.0214213
$573$	−8.58217e14	−0.580425
$574$	−1.91689e14	−0.128405
$575$	−2.54744e14	−0.169017
$576$	7.47545e14	0.491263
$577$	−1.19531e15	−0.778063	−0.389031	−	0.921225i	$-0.627190\pi$
$577$	−1.19531e15	−0.778063	−0.389031	+	0.921225i	$0.627190\pi$
$578$	−1.31008e14	−0.0844685
$579$	8.72516e14	0.557238
$580$	−3.57095e14	−0.225907
$581$	−1.19262e15	−0.747368
$582$	−1.05872e14	−0.0657210
$583$	4.90632e14	0.301703
$584$	−1.12209e14	−0.0683531
$585$	−1.55125e14	−0.0936104
$586$	5.79751e12	0.00346581
$587$	−4.69690e14	−0.278165	−0.139082	−	0.990281i	$-0.544415\pi$
$587$	−4.69690e14	−0.278165	−0.139082	+	0.990281i	$0.544415\pi$
$588$	−9.20910e13	−0.0540308
$589$	6.71379e14	0.390242
$590$	2.30307e14	0.132623
$591$	1.28149e15	0.731114
$592$	1.00525e15	0.568204
$593$	−2.84374e15	−1.59254	−0.796269	−	0.604943i	$-0.793196\pi$
$593$	−2.84374e15	−1.59254	−0.796269	+	0.604943i	$0.793196\pi$
$594$	−3.98475e13	−0.0221094
$595$	−1.31272e15	−0.721652
$596$	−1.65973e15	−0.904033
$597$	2.05214e15	1.10751
$598$	1.08933e13	0.00582507
$599$	−5.84678e13	−0.0309791	−0.0154896	−	0.999880i	$-0.504931\pi$
$599$	−5.84678e13	−0.0309791	−0.0154896	+	0.999880i	$0.504931\pi$
$600$	1.81511e14	0.0952950
$601$	3.04063e14	0.158181	0.0790904	−	0.996867i	$-0.474798\pi$
$601$	3.04063e14	0.158181	0.0790904	+	0.996867i	$0.474798\pi$
$602$	1.75762e14	0.0906031
$603$	6.53452e13	0.0333786
$604$	−3.36146e15	−1.70147
$605$	2.40759e15	1.20761
$606$	−2.33341e14	−0.115982
$607$	7.54775e14	0.371775	0.185887	−	0.982571i	$-0.440484\pi$
$607$	7.54775e14	0.371775	0.185887	+	0.982571i	$0.440484\pi$
$608$	−4.15723e14	−0.202924
$609$	−2.46844e14	−0.119407
$610$	4.81446e14	0.230799
$611$	2.91610e14	0.138540
$612$	−6.96963e14	−0.328153
$613$	−1.14265e15	−0.533187	−0.266593	−	0.963809i	$-0.585898\pi$
$613$	−1.14265e15	−0.533187	−0.266593	+	0.963809i	$0.585898\pi$
$614$	1.33281e14	0.0616372
$615$	1.81404e15	0.831443
$616$	−8.88770e13	−0.0403734
$617$	2.03761e15	0.917388	0.458694	−	0.888594i	$-0.348317\pi$
$617$	2.03761e15	0.917388	0.458694	+	0.888594i	$0.348317\pi$
$618$	1.54953e14	0.0691454
$619$	1.99627e15	0.882918	0.441459	−	0.897282i	$-0.354461\pi$
$619$	1.99627e15	0.882918	0.441459	+	0.897282i	$0.354461\pi$
$620$	−2.09435e15	−0.918110
$621$	−7.56694e14	−0.328788
$622$	3.31126e13	0.0142609
$623$	−2.87454e15	−1.22711
$624$	2.06394e14	0.0873335
$625$	−2.97738e15	−1.24880
$626$	4.58561e14	0.190651
$627$	−1.33590e14	−0.0550558
$628$	−2.90108e15	−1.18517
$629$	−9.01340e14	−0.365014
$630$	−2.17752e14	−0.0874158
$631$	4.17643e15	1.66205	0.831024	−	0.556236i	$-0.187755\pi$
$631$	4.17643e15	1.66205	0.831024	+	0.556236i	$0.187755\pi$
$632$	−1.67979e14	−0.0662690
$633$	−2.00462e15	−0.783991
$634$	−5.58224e14	−0.216430
$635$	−5.90466e15	−2.26955
$636$	−3.28920e15	−1.25336
$637$	2.98373e13	0.0112718
$638$	1.05407e13	0.00394782
$639$	−3.00918e14	−0.111736
$640$	1.72362e15	0.634529
$641$	2.09304e15	0.763938	0.381969	−	0.924175i	$-0.375246\pi$
$641$	2.09304e15	0.763938	0.381969	+	0.924175i	$0.375246\pi$
$642$	8.92689e13	0.0323041
$643$	1.49982e15	0.538118	0.269059	−	0.963124i	$-0.413287\pi$
$643$	1.49982e15	0.538118	0.269059	+	0.963124i	$0.413287\pi$
$644$	−8.36230e14	−0.297477
$645$	−1.66331e15	−0.586671
$646$	1.20468e14	0.0421301
$647$	−7.66777e14	−0.265886	−0.132943	−	0.991124i	$-0.542443\pi$
$647$	−7.66777e14	−0.265886	−0.132943	+	0.991124i	$0.542443\pi$
$648$	1.14599e14	0.0394021
$649$	3.71775e14	0.126746
$650$	−2.91381e13	−0.00985004
$651$	−1.44773e15	−0.485281
$652$	−4.24650e15	−1.41146
$653$	1.87656e15	0.618501	0.309251	−	0.950981i	$-0.399922\pi$
$653$	1.87656e15	0.618501	0.309251	+	0.950981i	$0.399922\pi$
$654$	1.61019e14	0.0526258
$655$	3.64236e15	1.18047
$656$	2.94511e15	0.946522
$657$	−4.43788e14	−0.141438
$658$	4.09339e14	0.129372
$659$	3.76632e15	1.18045	0.590224	−	0.807239i	$-0.299039\pi$
$659$	3.76632e15	1.18045	0.590224	+	0.807239i	$0.299039\pi$
$660$	4.16731e14	0.129528
$661$	5.61989e15	1.73229	0.866144	−	0.499795i	$-0.166591\pi$
$661$	5.61989e15	1.73229	0.866144	+	0.499795i	$0.166591\pi$
$662$	6.08009e14	0.185862
$663$	−1.85059e14	−0.0561031
$664$	−6.89077e14	−0.207178
$665$	−2.05831e15	−0.613751
$666$	−1.49513e14	−0.0442153
$667$	2.00166e14	0.0587081
$668$	5.00914e15	1.45711
$669$	−3.47268e15	−1.00189
$670$	3.52336e13	0.0100820
$671$	7.77180e14	0.220571
$672$	8.96447e14	0.252344
$673$	−1.30083e15	−0.363195	−0.181597	−	0.983373i	$-0.558127\pi$
$673$	−1.30083e15	−0.363195	−0.181597	+	0.983373i	$0.558127\pi$
$674$	−8.16145e14	−0.226015
$675$	2.02406e15	0.555973
$676$	3.53629e15	0.963478
$677$	3.38162e15	0.913877	0.456938	−	0.889498i	$-0.348946\pi$
$677$	3.38162e15	0.913877	0.456938	+	0.889498i	$0.348946\pi$
$678$	1.79799e14	0.0481974
$679$	−2.63324e15	−0.700175
$680$	−7.58465e14	−0.200049
$681$	−1.05119e14	−0.0275024
$682$	6.18210e13	0.0160444
$683$	−4.97782e15	−1.28152	−0.640760	−	0.767741i	$-0.721381\pi$
$683$	−4.97782e15	−1.28152	−0.640760	+	0.767741i	$0.721381\pi$
$684$	−1.09282e15	−0.279088
$685$	5.62901e14	0.142605
$686$	5.52777e14	0.138921
$687$	−1.33048e15	−0.331702
$688$	−2.70041e15	−0.667872
$689$	1.06569e15	0.261473
$690$	−1.44707e14	−0.0352224
$691$	6.04340e15	1.45933	0.729663	−	0.683807i	$-0.239677\pi$
$691$	6.04340e15	1.45933	0.729663	+	0.683807i	$0.239677\pi$
$692$	4.51781e15	1.08229
$693$	−3.51509e14	−0.0835418
$694$	6.01269e14	0.141772
$695$	1.34406e15	0.314415
$696$	−1.42623e14	−0.0331007
$697$	−2.64068e15	−0.608046
$698$	8.20911e14	0.187539
$699$	2.49902e15	0.566428
$700$	2.23681e15	0.503026
$701$	4.71422e15	1.05187	0.525933	−	0.850526i	$-0.323716\pi$
$701$	4.71422e15	1.05187	0.525933	+	0.850526i	$0.323716\pi$
$702$	−8.65522e13	−0.0191612
$703$	−1.41328e15	−0.310438
$704$	6.50660e14	0.141809
$705$	−3.87376e15	−0.837708
$706$	−5.21232e14	−0.111842
$707$	−5.80365e15	−1.23565
$708$	−2.49238e15	−0.526540
$709$	−7.60301e15	−1.59379	−0.796896	−	0.604117i	$-0.793526\pi$
$709$	−7.60301e15	−1.59379	−0.796896	+	0.604117i	$0.793526\pi$
$710$	−1.62253e14	−0.0337498
$711$	−6.64357e14	−0.137126
$712$	−1.66086e15	−0.340167
$713$	1.17397e15	0.238596
$714$	−2.59772e14	−0.0523905
$715$	−1.35020e14	−0.0270218
$716$	1.80982e15	0.359430
$717$	5.06594e15	0.998400
$718$	−9.18854e13	−0.0179706
$719$	6.82779e15	1.32517	0.662584	−	0.748987i	$-0.269460\pi$
$719$	6.82779e15	1.32517	0.662584	+	0.748987i	$0.269460\pi$
$720$	3.34556e15	0.644376
$721$	3.85399e15	0.736658
$722$	−5.17551e14	−0.0981745
$723$	−3.18105e15	−0.598838
$724$	7.21341e15	1.34765
$725$	−5.35419e14	−0.0992739
$726$	4.76435e14	0.0876703
$727$	2.03779e15	0.372152	0.186076	−	0.982535i	$-0.440423\pi$
$727$	2.03779e15	0.372152	0.186076	+	0.982535i	$0.440423\pi$
$728$	−1.93048e14	−0.0349899
$729$	4.33316e15	0.779476
$730$	−2.39287e14	−0.0427212
$731$	2.42127e15	0.429041
$732$	−5.21022e15	−0.916315
$733$	2.10283e15	0.367056	0.183528	−	0.983015i	$-0.441248\pi$
$733$	2.10283e15	0.367056	0.183528	+	0.983015i	$0.441248\pi$
$734$	−1.56371e14	−0.0270911
$735$	−3.96360e14	−0.0681569
$736$	−7.26928e14	−0.124069
$737$	5.68762e13	0.00963516
$738$	−4.38035e14	−0.0736543
$739$	−4.77238e15	−0.796509	−0.398254	−	0.917275i	$-0.630384\pi$
$739$	−4.77238e15	−0.796509	−0.398254	+	0.917275i	$0.630384\pi$
$740$	4.40869e15	0.730357
$741$	−2.90169e14	−0.0477146
$742$	1.49594e15	0.244170
$743$	−6.05561e15	−0.981114	−0.490557	−	0.871409i	$-0.663207\pi$
$743$	−6.05561e15	−0.981114	−0.490557	+	0.871409i	$0.663207\pi$
$744$	−8.36476e14	−0.134525
$745$	−7.14351e15	−1.14039
$746$	2.82244e14	0.0447260
$747$	−2.72530e15	−0.428698
$748$	−6.06634e14	−0.0947257
$749$	2.22029e15	0.344160
$750$	−3.36961e14	−0.0518493
$751$	2.82413e15	0.431385	0.215693	−	0.976461i	$-0.430799\pi$
$751$	2.82413e15	0.431385	0.215693	+	0.976461i	$0.430799\pi$
$752$	−6.28911e15	−0.953654
$753$	1.36706e15	0.205785
$754$	2.28954e13	0.00342141
$755$	−1.44678e16	−2.14631
$756$	6.64425e15	0.978534
$757$	−7.58115e15	−1.10843	−0.554214	−	0.832374i	$-0.686981\pi$
$757$	−7.58115e15	−1.10843	−0.554214	+	0.832374i	$0.686981\pi$
$758$	1.22235e15	0.177425
$759$	−2.33594e14	−0.0336614
$760$	−1.18926e15	−0.170138
$761$	−3.85386e15	−0.547369	−0.273684	−	0.961820i	$-0.588242\pi$
$761$	−3.85386e15	−0.547369	−0.273684	+	0.961820i	$0.588242\pi$
$762$	−1.16847e15	−0.164765
$763$	4.00485e15	0.560662
$764$	−6.11067e15	−0.849328
$765$	−2.99974e15	−0.413947
$766$	−9.34353e14	−0.128013
$767$	8.07526e14	0.109845
$768$	−4.10071e15	−0.553825
$769$	1.24679e16	1.67186	0.835929	−	0.548838i	$-0.184930\pi$
$769$	1.24679e16	1.67186	0.835929	+	0.548838i	$0.184930\pi$
$770$	−1.89531e14	−0.0252337
$771$	−1.72706e15	−0.228301
$772$	6.21248e15	0.815399
$773$	−1.49691e16	−1.95078	−0.975388	−	0.220494i	$-0.929233\pi$
$773$	−1.49691e16	−1.95078	−0.975388	+	0.220494i	$0.929233\pi$
$774$	4.01639e14	0.0519710
$775$	−3.14021e15	−0.403459
$776$	−1.52144e15	−0.194096
$777$	3.04754e15	0.386041
$778$	−5.33317e14	−0.0670807
$779$	−4.14054e15	−0.517131
$780$	9.05175e14	0.112257
$781$	−2.61918e14	−0.0322541
$782$	2.10649e14	0.0257586
$783$	−1.59041e15	−0.193117
$784$	−6.43497e14	−0.0775904
$785$	−1.24863e16	−1.49503
$786$	7.20783e14	0.0856999
$787$	−1.18935e14	−0.0140426	−0.00702129	−	0.999975i	$-0.502235\pi$
$787$	−1.18935e14	−0.0140426	−0.00702129	+	0.999975i	$0.502235\pi$
$788$	9.12449e15	1.06983
$789$	9.80100e15	1.14116
$790$	−3.58216e14	−0.0414187
$791$	4.47195e15	0.513483
$792$	−2.03096e14	−0.0231586
$793$	1.68810e15	0.191159
$794$	−1.11445e15	−0.125327
$795$	−1.41568e16	−1.58105
$796$	1.46116e16	1.62060
$797$	−7.06274e15	−0.777951	−0.388976	−	0.921248i	$-0.627171\pi$
$797$	−7.06274e15	−0.777951	−0.388976	+	0.921248i	$0.627171\pi$
$798$	−4.07317e14	−0.0445571
$799$	5.63902e15	0.612627
$800$	1.94444e15	0.209797
$801$	−6.56871e15	−0.703884
$802$	7.90364e14	0.0841139
$803$	−3.86272e14	−0.0408279
$804$	−3.81298e14	−0.0400273
$805$	−3.59914e15	−0.375251
$806$	1.34280e14	0.0139050
$807$	9.21694e15	0.947944
$808$	−3.35325e15	−0.342534
$809$	4.44463e15	0.450940	0.225470	−	0.974250i	$-0.427608\pi$
$809$	4.44463e15	0.450940	0.225470	+	0.974250i	$0.427608\pi$
$810$	2.44384e14	0.0246266
$811$	1.17179e16	1.17283	0.586414	−	0.810012i	$-0.300539\pi$
$811$	1.17179e16	1.17283	0.586414	+	0.810012i	$0.300539\pi$
$812$	−1.75758e15	−0.174726
$813$	−4.80337e15	−0.474294
$814$	−1.30136e14	−0.0127633
$815$	−1.82770e16	−1.78048
$816$	3.99115e15	0.386191
$817$	3.79651e15	0.364891
$818$	−1.89810e15	−0.181207
$819$	−7.63507e14	−0.0724021
$820$	1.29163e16	1.21664
$821$	1.65246e16	1.54612	0.773062	−	0.634331i	$-0.218724\pi$
$821$	1.65246e16	1.54612	0.773062	+	0.634331i	$0.218724\pi$
$822$	1.11392e14	0.0103528
$823$	−1.42171e16	−1.31254	−0.656270	−	0.754526i	$-0.727867\pi$
$823$	−1.42171e16	−1.31254	−0.656270	+	0.754526i	$0.727867\pi$
$824$	2.22677e15	0.204209
$825$	6.24836e14	0.0569206
$826$	1.13354e15	0.102577
$827$	−3.70660e15	−0.333193	−0.166596	−	0.986025i	$-0.553278\pi$
$827$	−3.70660e15	−0.333193	−0.166596	+	0.986025i	$0.553278\pi$
$828$	−1.91090e15	−0.170636
$829$	2.12551e16	1.88544	0.942721	−	0.333582i	$-0.108258\pi$
$829$	2.12551e16	1.88544	0.942721	+	0.333582i	$0.108258\pi$
$830$	−1.46946e15	−0.129488
$831$	−4.49970e15	−0.393893
$832$	1.41329e15	0.122900
$833$	5.76980e14	0.0498441
$834$	2.65975e14	0.0228259
$835$	2.15594e16	1.83807
$836$	−9.51189e14	−0.0805624
$837$	−9.32772e15	−0.784848
$838$	1.54169e15	0.128871
$839$	1.90879e16	1.58514	0.792571	−	0.609779i	$-0.208742\pi$
$839$	1.90879e16	1.58514	0.792571	+	0.609779i	$0.208742\pi$
$840$	2.56447e15	0.211573
$841$	4.20707e14	0.0344828
$842$	2.56185e14	0.0208611
$843$	8.69091e15	0.703094
$844$	−1.42733e16	−1.14720
$845$	1.52202e16	1.21537
$846$	9.35396e14	0.0742093
$847$	1.18499e16	0.934018
$848$	−2.29837e16	−1.79988
$849$	8.49503e13	0.00660956
$850$	−5.63460e14	−0.0435571
$851$	−2.47125e15	−0.189803
$852$	1.75590e15	0.133993
$853$	−2.15560e16	−1.63436	−0.817181	−	0.576381i	$-0.804465\pi$
$853$	−2.15560e16	−1.63436	−0.817181	+	0.576381i	$0.804465\pi$
$854$	2.36962e15	0.178509
$855$	−4.70352e15	−0.352054
$856$	1.28285e15	0.0954046
$857$	1.64901e16	1.21851	0.609256	−	0.792974i	$-0.291468\pi$
$857$	1.64901e16	1.21851	0.609256	+	0.792974i	$0.291468\pi$
$858$	−2.67190e13	−0.00196173
$859$	3.06095e14	0.0223302	0.0111651	−	0.999938i	$-0.496446\pi$
$859$	3.06095e14	0.0223302	0.0111651	+	0.999938i	$0.496446\pi$
$860$	−1.18431e16	−0.858468
$861$	8.92848e15	0.643073
$862$	2.39258e14	0.0171228
$863$	−2.41816e16	−1.71959	−0.859796	−	0.510637i	$-0.829410\pi$
$863$	−2.41816e16	−1.71959	−0.859796	+	0.510637i	$0.829410\pi$
$864$	5.77579e15	0.408118
$865$	1.94447e16	1.36525
$866$	2.71001e15	0.189070
$867$	6.10209e15	0.423033
$868$	−1.03081e16	−0.710104
$869$	−5.78254e14	−0.0395831
$870$	−3.04144e14	−0.0206882
$871$	1.23540e14	0.00835039
$872$	2.31393e15	0.155421
$873$	−6.01731e15	−0.401628
$874$	3.30293e14	0.0219072
$875$	−8.38088e15	−0.552389
$876$	2.58957e15	0.169611
$877$	−2.72200e15	−0.177170	−0.0885849	−	0.996069i	$-0.528234\pi$
$877$	−2.72200e15	−0.177170	−0.0885849	+	0.996069i	$0.528234\pi$
$878$	3.00049e15	0.194076
$879$	−2.70036e14	−0.0173574
$880$	2.91196e15	0.186008
$881$	−1.19185e16	−0.756579	−0.378290	−	0.925687i	$-0.623488\pi$
$881$	−1.19185e16	−0.756579	−0.378290	+	0.925687i	$0.623488\pi$
$882$	9.57090e13	0.00603776
$883$	4.27269e15	0.267866	0.133933	−	0.990990i	$-0.457239\pi$
$883$	4.27269e15	0.267866	0.133933	+	0.990990i	$0.457239\pi$
$884$	−1.31766e15	−0.0820948
$885$	−1.07272e16	−0.664201
$886$	6.11377e12	0.000376204 0
$887$	3.17935e16	1.94428	0.972140	−	0.234402i	$-0.0753132\pi$
$887$	3.17935e16	1.94428	0.972140	+	0.234402i	$0.0753132\pi$
$888$	1.76082e15	0.107015
$889$	−2.90621e16	−1.75536
$890$	−3.54179e15	−0.212607
$891$	3.94499e14	0.0235352
$892$	−2.47262e16	−1.46606
$893$	8.84186e15	0.521028
$894$	−1.41362e15	−0.0827899
$895$	7.78950e15	0.453401
$896$	8.48346e15	0.490771
$897$	−5.07386e14	−0.0291729
$898$	−2.91135e15	−0.166370
$899$	2.46743e15	0.140142
$900$	5.11142e15	0.288541
$901$	2.06079e16	1.15624
$902$	−3.81264e14	−0.0212613
$903$	−8.18663e15	−0.453756
$904$	2.58382e15	0.142343
$905$	3.10466e16	1.69999
$906$	−2.86301e15	−0.155818
$907$	2.05145e16	1.10974	0.554868	−	0.831938i	$-0.312769\pi$
$907$	2.05145e16	1.10974	0.554868	+	0.831938i	$0.312769\pi$
$908$	−7.48466e14	−0.0402439
$909$	−1.32621e16	−0.708780
$910$	−4.11677e14	−0.0218690
$911$	−2.66210e16	−1.40564	−0.702818	−	0.711370i	$-0.748075\pi$
$911$	−2.66210e16	−1.40564	−0.702818	+	0.711370i	$0.748075\pi$
$912$	6.25804e15	0.328448
$913$	−2.37209e15	−0.123749
$914$	−4.02341e15	−0.208636
$915$	−2.24248e16	−1.15588
$916$	−9.47332e15	−0.485374
$917$	1.79273e16	0.913026
$918$	−1.67371e15	−0.0847315
$919$	−2.94199e16	−1.48049	−0.740245	−	0.672337i	$-0.765291\pi$
$919$	−2.94199e16	−1.48049	−0.740245	+	0.672337i	$0.765291\pi$
$920$	−2.07952e15	−0.104023
$921$	−6.20797e15	−0.308690
$922$	2.68291e15	0.132613
$923$	−5.68908e14	−0.0279533
$924$	2.05110e15	0.100182
$925$	6.61028e15	0.320952
$926$	−1.57347e15	−0.0759449
$927$	8.80688e15	0.422555
$928$	−1.52785e15	−0.0728731
$929$	−9.85760e15	−0.467396	−0.233698	−	0.972309i	$-0.575083\pi$
$929$	−9.85760e15	−0.467396	−0.233698	+	0.972309i	$0.575083\pi$
$930$	−1.78379e15	−0.0840790
$931$	9.04692e14	0.0423914
$932$	1.77935e16	0.828846
$933$	−1.54232e15	−0.0714210
$934$	2.39647e15	0.110323
$935$	−2.61096e15	−0.119491
$936$	−4.41141e14	−0.0200706
$937$	4.73140e15	0.214004	0.107002	−	0.994259i	$-0.465875\pi$
$937$	4.73140e15	0.214004	0.107002	+	0.994259i	$0.465875\pi$
$938$	1.73416e14	0.00779781
$939$	−2.13589e16	−0.954811
$940$	−2.75820e16	−1.22581
$941$	−1.65035e16	−0.729179	−0.364589	−	0.931168i	$-0.618791\pi$
$941$	−1.65035e16	−0.729179	−0.364589	+	0.931168i	$0.618791\pi$
$942$	−2.47090e15	−0.108536
$943$	−7.24009e15	−0.316177
$944$	−1.74158e16	−0.756132
$945$	2.85969e16	1.23437
$946$	3.49585e14	0.0150021
$947$	−4.39296e16	−1.87427	−0.937134	−	0.348969i	$-0.886532\pi$
$947$	−4.39296e16	−1.87427	−0.937134	+	0.348969i	$0.886532\pi$
$948$	3.87662e15	0.164440
$949$	−8.39014e14	−0.0353838
$950$	−8.83494e14	−0.0370445
$951$	2.60010e16	1.08392
$952$	−3.73308e15	−0.154726
$953$	−3.29937e15	−0.135963	−0.0679815	−	0.997687i	$-0.521656\pi$
$953$	−3.29937e15	−0.135963	−0.0679815	+	0.997687i	$0.521656\pi$
$954$	3.41843e15	0.140059
$955$	−2.63004e16	−1.07138
$956$	3.60705e16	1.46094
$957$	−4.90967e14	−0.0197714
$958$	8.80131e14	0.0352401
$959$	2.77053e15	0.110296
$960$	−1.87742e16	−0.743139
$961$	−1.09371e16	−0.430450
$962$	−2.82666e14	−0.0110614
$963$	5.07367e15	0.197414
$964$	−2.26497e16	−0.876271
$965$	2.67386e16	1.02858
$966$	−7.12230e14	−0.0272425
$967$	9.31732e15	0.354360	0.177180	−	0.984178i	$-0.443302\pi$
$967$	9.31732e15	0.354360	0.177180	+	0.984178i	$0.443302\pi$
$968$	6.84666e15	0.258919
$969$	−5.61116e15	−0.210995
$970$	−3.24449e15	−0.121311
$971$	−6.05444e15	−0.225096	−0.112548	−	0.993646i	$-0.535901\pi$
$971$	−6.05444e15	−0.225096	−0.112548	+	0.993646i	$0.535901\pi$
$972$	2.49811e16	0.923520
$973$	6.61532e15	0.243181
$974$	−2.61866e15	−0.0957205
$975$	1.35720e15	0.0493307
$976$	−3.64070e16	−1.31586
$977$	8.47458e15	0.304578	0.152289	−	0.988336i	$-0.451336\pi$
$977$	8.47458e15	0.304578	0.152289	+	0.988336i	$0.451336\pi$
$978$	−3.61682e15	−0.129260
$979$	−5.71738e15	−0.203185
$980$	−2.82216e15	−0.0997330
$981$	9.15162e15	0.321602
$982$	6.34486e15	0.221722
$983$	−4.27180e16	−1.48445	−0.742227	−	0.670148i	$-0.766230\pi$
$983$	−4.27180e16	−1.48445	−0.742227	+	0.670148i	$0.766230\pi$
$984$	5.15872e15	0.178266
$985$	3.92719e16	1.34953
$986$	4.42741e14	0.0151296
$987$	−1.90662e16	−0.647918
$988$	−2.06606e15	−0.0698200
$989$	6.63853e15	0.223096
$990$	−4.33104e14	−0.0144743
$991$	1.29684e16	0.431003	0.215501	−	0.976504i	$-0.430861\pi$
$991$	1.29684e16	0.431003	0.215501	+	0.976504i	$0.430861\pi$
$992$	−8.96079e15	−0.296164
$993$	−2.83199e16	−0.930829
$994$	−7.98590e14	−0.0261035
$995$	6.28885e16	2.04430
$996$	1.59025e16	0.514091
$997$	3.83044e16	1.23147	0.615736	−	0.787952i	$-0.288859\pi$
$997$	3.83044e16	1.23147	0.615736	+	0.787952i	$0.288859\pi$
$998$	2.12647e15	0.0679893
$999$	1.96353e16	0.624347

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.12.a.b.1.7	✓	14
3.2	odd	2		261.12.a.e.1.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.b.1.7	✓	14	1.1	even	1	trivial
261.12.a.e.1.8		14	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+6.06439 q^{2} -282.467 q^{3} -2011.22 q^{4} -8656.32 q^{5} -1712.99 q^{6} -42605.5 q^{7} -24616.7 q^{8} -97359.2 q^{9} +O(q^{10})\)	\(q+6.06439 q^{2} -282.467 q^{3} -2011.22 q^{4} -8656.32 q^{5} -1712.99 q^{6} -42605.5 q^{7} -24616.7 q^{8} -97359.2 q^{9} -52495.3 q^{10} -84741.1 q^{11} +568105. q^{12} -184065. q^{13} -258376. q^{14} +2.44513e6 q^{15} +3.96970e6 q^{16} -3.55936e6 q^{17} -590424. q^{18} -5.58101e6 q^{19} +1.74098e7 q^{20} +1.20346e7 q^{21} -513903. q^{22} -9.75888e6 q^{23} +6.95342e6 q^{24} +2.61038e7 q^{25} -1.11624e6 q^{26} +7.75390e7 q^{27} +8.56891e7 q^{28} -2.05111e7 q^{29} +1.48282e7 q^{30} -1.20297e8 q^{31} +7.44888e7 q^{32} +2.39366e7 q^{33} -2.15854e7 q^{34} +3.68807e8 q^{35} +1.95811e8 q^{36} +2.53231e8 q^{37} -3.38454e7 q^{38} +5.19923e7 q^{39} +2.13090e8 q^{40} +7.41898e8 q^{41} +7.29828e7 q^{42} -6.80255e8 q^{43} +1.70433e8 q^{44} +8.42773e8 q^{45} -5.91817e7 q^{46} -1.58428e9 q^{47} -1.12131e9 q^{48} -1.62102e8 q^{49} +1.58304e8 q^{50} +1.00540e9 q^{51} +3.70195e8 q^{52} -5.78978e9 q^{53} +4.70227e8 q^{54} +7.33546e8 q^{55} +1.04881e9 q^{56} +1.57645e9 q^{57} -1.24388e8 q^{58} -4.38718e9 q^{59} -4.91770e9 q^{60} -9.17122e9 q^{61} -7.29528e8 q^{62} +4.14803e9 q^{63} -7.67822e9 q^{64} +1.59332e9 q^{65} +1.45161e8 q^{66} -6.71176e8 q^{67} +7.15867e9 q^{68} +2.75656e9 q^{69} +2.23659e9 q^{70} +3.09080e9 q^{71} +2.39666e9 q^{72} +4.55826e9 q^{73} +1.53569e9 q^{74} -7.37347e9 q^{75} +1.12246e10 q^{76} +3.61043e9 q^{77} +3.15301e8 q^{78} +6.82377e9 q^{79} -3.43630e10 q^{80} -4.65534e9 q^{81} +4.49916e9 q^{82} +2.79923e10 q^{83} -2.42044e10 q^{84} +3.08110e10 q^{85} -4.12533e9 q^{86} +5.79373e9 q^{87} +2.08605e9 q^{88} +6.74688e10 q^{89} +5.11090e9 q^{90} +7.84216e9 q^{91} +1.96273e10 q^{92} +3.39800e10 q^{93} -9.60768e9 q^{94} +4.83110e10 q^{95} -2.10407e10 q^{96} +6.18052e10 q^{97} -9.83050e8 q^{98} +8.25033e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9}+O(q^{10}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9} + 713576 q^{10} + 398020 q^{11} - 4026800 q^{12} + 2272440 q^{13} - 7199712 q^{14} - 4763864 q^{15} + 19015138 q^{16} + 5623508 q^{17} - 204156 q^{18} + 29803300 q^{19} + 65161006 q^{20} + 51227832 q^{21} + 167334266 q^{22} + 52654304 q^{23} + 221514842 q^{24} + 194970462 q^{25} + 373581536 q^{26} + 397348256 q^{27} + 319501772 q^{28} - 287156086 q^{29} + 423014226 q^{30} + 634041348 q^{31} + 1260290884 q^{32} + 1180833420 q^{33} + 1316105060 q^{34} + 1599853768 q^{35} + 3198076132 q^{36} + 488665204 q^{37} + 1892845072 q^{38} + 1972619104 q^{39} + 1826486880 q^{40} + 198215164 q^{41} + 1011384468 q^{42} + 2193188100 q^{43} + 26522720 q^{44} - 1129321956 q^{45} - 1567525268 q^{46} - 4175934476 q^{47} - 15582938120 q^{48} + 1105222462 q^{49} - 6630582612 q^{50} + 3297462720 q^{51} - 4557341374 q^{52} - 13223081840 q^{53} - 8946135054 q^{54} - 2726359424 q^{55} - 27538267872 q^{56} - 24477013312 q^{57} + 352219640 q^{59} - 36042747924 q^{60} - 7658546476 q^{61} - 10024135594 q^{62} - 23037581736 q^{63} + 14721327762 q^{64} + 1152802884 q^{65} - 99505241364 q^{66} + 21781534280 q^{67} - 104178000188 q^{68} - 14601399408 q^{69} - 67948872984 q^{70} - 5573287168 q^{71} - 24062143544 q^{72} + 39661511924 q^{73} + 28506052056 q^{74} + 81845109044 q^{75} + 166950090320 q^{76} + 38773567192 q^{77} + 54249159006 q^{78} + 105565209020 q^{79} + 146242150550 q^{80} + 170581084750 q^{81} + 47345182756 q^{82} + 127846064024 q^{83} + 215311861496 q^{84} + 83883234552 q^{85} - 103162039382 q^{86} - 9763306924 q^{87} + 418253082102 q^{88} + 187826099404 q^{89} + 96335639960 q^{90} + 58390389864 q^{91} - 259645875396 q^{92} + 394641636020 q^{93} + 117694719934 q^{94} + 69935059424 q^{95} + 12533631786 q^{96} + 137285937500 q^{97} - 484896369168 q^{98} + 235419947204 q^{99}+O(q^{100}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9 + 713576 * q^10 + 398020 * q^11 - 4026800 * q^12 + 2272440 * q^13 - 7199712 * q^14 - 4763864 * q^15 + 19015138 * q^16 + 5623508 * q^17 - 204156 * q^18 + 29803300 * q^19 + 65161006 * q^20 + 51227832 * q^21 + 167334266 * q^22 + 52654304 * q^23 + 221514842 * q^24 + 194970462 * q^25 + 373581536 * q^26 + 397348256 * q^27 + 319501772 * q^28 - 287156086 * q^29 + 423014226 * q^30 + 634041348 * q^31 + 1260290884 * q^32 + 1180833420 * q^33 + 1316105060 * q^34 + 1599853768 * q^35 + 3198076132 * q^36 + 488665204 * q^37 + 1892845072 * q^38 + 1972619104 * q^39 + 1826486880 * q^40 + 198215164 * q^41 + 1011384468 * q^42 + 2193188100 * q^43 + 26522720 * q^44 - 1129321956 * q^45 - 1567525268 * q^46 - 4175934476 * q^47 - 15582938120 * q^48 + 1105222462 * q^49 - 6630582612 * q^50 + 3297462720 * q^51 - 4557341374 * q^52 - 13223081840 * q^53 - 8946135054 * q^54 - 2726359424 * q^55 - 27538267872 * q^56 - 24477013312 * q^57 + 352219640 * q^59 - 36042747924 * q^60 - 7658546476 * q^61 - 10024135594 * q^62 - 23037581736 * q^63 + 14721327762 * q^64 + 1152802884 * q^65 - 99505241364 * q^66 + 21781534280 * q^67 - 104178000188 * q^68 - 14601399408 * q^69 - 67948872984 * q^70 - 5573287168 * q^71 - 24062143544 * q^72 + 39661511924 * q^73 + 28506052056 * q^74 + 81845109044 * q^75 + 166950090320 * q^76 + 38773567192 * q^77 + 54249159006 * q^78 + 105565209020 * q^79 + 146242150550 * q^80 + 170581084750 * q^81 + 47345182756 * q^82 + 127846064024 * q^83 + 215311861496 * q^84 + 83883234552 * q^85 - 103162039382 * q^86 - 9763306924 * q^87 + 418253082102 * q^88 + 187826099404 * q^89 + 96335639960 * q^90 + 58390389864 * q^91 - 259645875396 * q^92 + 394641636020 * q^93 + 117694719934 * q^94 + 69935059424 * q^95 + 12533631786 * q^96 + 137285937500 * q^97 - 484896369168 * q^98 + 235419947204 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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