LMFDB - Embedded newform 29.12.a.b.1.10

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			1.10
Root			$35.2896$ 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)

$f(q)$	$=$	$q+35.2896 q^{2} +118.146 q^{3} -802.642 q^{4} -5887.06 q^{5} +4169.31 q^{6} +66890.4 q^{7} -100598. q^{8} -163189. q^{9} +O(q^{10})$	\(q+35.2896 q^{2} +118.146 q^{3} -802.642 q^{4} -5887.06 q^{5} +4169.31 q^{6} +66890.4 q^{7} -100598. q^{8} -163189. q^{9} -207752. q^{10} +1.04288e6 q^{11} -94828.6 q^{12} +2.13068e6 q^{13} +2.36054e6 q^{14} -695530. q^{15} -1.90626e6 q^{16} +2.02683e6 q^{17} -5.75887e6 q^{18} +1.77301e6 q^{19} +4.72520e6 q^{20} +7.90280e6 q^{21} +3.68028e7 q^{22} +1.34834e7 q^{23} -1.18852e7 q^{24} -1.41706e7 q^{25} +7.51909e7 q^{26} -4.02091e7 q^{27} -5.36891e7 q^{28} -2.05111e7 q^{29} -2.45450e7 q^{30} +2.63758e8 q^{31} +1.38754e8 q^{32} +1.23211e8 q^{33} +7.15262e7 q^{34} -3.93788e8 q^{35} +1.30982e8 q^{36} +3.19353e8 q^{37} +6.25688e7 q^{38} +2.51730e8 q^{39} +5.92227e8 q^{40} -3.78469e8 q^{41} +2.78887e8 q^{42} +3.37307e8 q^{43} -8.37059e8 q^{44} +9.60702e8 q^{45} +4.75823e8 q^{46} -1.25964e9 q^{47} -2.25216e8 q^{48} +2.49700e9 q^{49} -5.00076e8 q^{50} +2.39461e8 q^{51} -1.71017e9 q^{52} +2.43349e9 q^{53} -1.41897e9 q^{54} -6.13949e9 q^{55} -6.72905e9 q^{56} +2.09473e8 q^{57} -7.23831e8 q^{58} -7.96316e9 q^{59} +5.58262e8 q^{60} +4.28172e9 q^{61} +9.30791e9 q^{62} -1.09158e10 q^{63} +8.80059e9 q^{64} -1.25434e10 q^{65} +4.34809e9 q^{66} -2.09117e10 q^{67} -1.62682e9 q^{68} +1.59300e9 q^{69} -1.38966e10 q^{70} +1.27122e10 q^{71} +1.64165e10 q^{72} -6.43549e9 q^{73} +1.12699e10 q^{74} -1.67420e9 q^{75} -1.42309e9 q^{76} +6.97586e10 q^{77} +8.88346e9 q^{78} +3.72736e9 q^{79} +1.12223e10 q^{80} +2.41578e10 q^{81} -1.33560e10 q^{82} -1.79731e10 q^{83} -6.34312e9 q^{84} -1.19321e10 q^{85} +1.19034e10 q^{86} -2.42330e9 q^{87} -1.04912e11 q^{88} -1.69946e10 q^{89} +3.39028e10 q^{90} +1.42522e11 q^{91} -1.08223e10 q^{92} +3.11618e10 q^{93} -4.44523e10 q^{94} -1.04378e10 q^{95} +1.63931e10 q^{96} +9.11305e10 q^{97} +8.81183e10 q^{98} -1.70186e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	35.2896	0.779798	0.389899	−	0.920858i	$-0.372510\pi$
$2$	35.2896	0.779798	0.389899	+	0.920858i	$0.372510\pi$
$3$	118.146	0.280705	0.140353	−	0.990102i	$-0.455176\pi$
$3$	118.146	0.280705	0.140353	+	0.990102i	$0.455176\pi$
$4$	−802.642	−0.391915
$5$	−5887.06	−0.842488	−0.421244	−	0.906947i	$-0.638406\pi$
$5$	−5887.06	−0.842488	−0.421244	+	0.906947i	$0.638406\pi$
$6$	4169.31	0.218893
$7$	66890.4	1.50427	0.752133	−	0.659011i	$-0.229025\pi$
$7$	66890.4	1.50427	0.752133	+	0.659011i	$0.229025\pi$
$8$	−100598.	−1.08541
$9$	−163189.	−0.921205
$10$	−207752.	−0.656970
$11$	1.04288e6	1.95242	0.976212	−	0.216818i	$-0.0695677\pi$
$11$	1.04288e6	1.95242	0.976212	+	0.216818i	$0.0695677\pi$
$12$	−94828.6	−0.110013
$13$	2.13068e6	1.59158	0.795792	−	0.605570i	$-0.207055\pi$
$13$	2.13068e6	1.59158	0.795792	+	0.605570i	$0.207055\pi$
$14$	2.36054e6	1.17302
$15$	−695530.	−0.236491
$16$	−1.90626e6	−0.454487
$17$	2.02683e6	0.346218	0.173109	−	0.984903i	$-0.444619\pi$
$17$	2.02683e6	0.346218	0.173109	+	0.984903i	$0.444619\pi$
$18$	−5.75887e6	−0.718354
$19$	1.77301e6	0.164273	0.0821364	−	0.996621i	$-0.473826\pi$
$19$	1.77301e6	0.164273	0.0821364	+	0.996621i	$0.473826\pi$
$20$	4.72520e6	0.330184
$21$	7.90280e6	0.422255
$22$	3.68028e7	1.52250
$23$	1.34834e7	0.436812	0.218406	−	0.975858i	$-0.429914\pi$
$23$	1.34834e7	0.436812	0.218406	+	0.975858i	$0.429914\pi$
$24$	−1.18852e7	−0.304681
$25$	−1.41706e7	−0.290214
$26$	7.51909e7	1.24111
$27$	−4.02091e7	−0.539292
$28$	−5.36891e7	−0.589545
$29$	−2.05111e7	−0.185695
$29$	−2.05111e7	−0.185695
$30$	−2.45450e7	−0.184415
$31$	2.63758e8	1.65469	0.827343	−	0.561697i	$-0.189851\pi$
$31$	2.63758e8	1.65469	0.827343	+	0.561697i	$0.189851\pi$
$32$	1.38754e8	0.731004
$33$	1.23211e8	0.548055
$34$	7.15262e7	0.269980
$35$	−3.93788e8	−1.26733
$36$	1.30982e8	0.361034
$37$	3.19353e8	0.757116	0.378558	−	0.925578i	$-0.376420\pi$
$37$	3.19353e8	0.757116	0.378558	+	0.925578i	$0.376420\pi$
$38$	6.25688e7	0.128100
$39$	2.51730e8	0.446766
$40$	5.92227e8	0.914447
$41$	−3.78469e8	−0.510175	−0.255087	−	0.966918i	$-0.582104\pi$
$41$	−3.78469e8	−0.510175	−0.255087	+	0.966918i	$0.582104\pi$
$42$	2.78887e8	0.329274
$43$	3.37307e8	0.349904	0.174952	−	0.984577i	$-0.444023\pi$
$43$	3.37307e8	0.349904	0.174952	+	0.984577i	$0.444023\pi$
$44$	−8.37059e8	−0.765185
$45$	9.60702e8	0.776104
$46$	4.75823e8	0.340625
$47$	−1.25964e9	−0.801141	−0.400571	−	0.916266i	$-0.631188\pi$
$47$	−1.25964e9	−0.801141	−0.400571	+	0.916266i	$0.631188\pi$
$48$	−2.25216e8	−0.127577
$49$	2.49700e9	1.26282
$50$	−5.00076e8	−0.226309
$51$	2.39461e8	0.0971851
$52$	−1.71017e9	−0.623766
$53$	2.43349e9	0.799304	0.399652	−	0.916667i	$-0.369131\pi$
$53$	2.43349e9	0.799304	0.399652	+	0.916667i	$0.369131\pi$
$54$	−1.41897e9	−0.420539
$55$	−6.13949e9	−1.64489
$56$	−6.72905e9	−1.63275
$57$	2.09473e8	0.0461122
$58$	−7.23831e8	−0.144805
$59$	−7.96316e9	−1.45010	−0.725052	−	0.688694i	$-0.758184\pi$
$59$	−7.96316e9	−1.45010	−0.725052	+	0.688694i	$0.758184\pi$
$60$	5.58262e8	0.0926843
$61$	4.28172e9	0.649088	0.324544	−	0.945871i	$-0.394789\pi$
$61$	4.28172e9	0.649088	0.324544	+	0.945871i	$0.394789\pi$
$62$	9.30791e9	1.29032
$63$	−1.09158e10	−1.38574
$64$	8.80059e9	1.02452
$65$	−1.25434e10	−1.34089
$66$	4.34809e9	0.427373
$67$	−2.09117e10	−1.89224	−0.946122	−	0.323812i	$-0.895036\pi$
$67$	−2.09117e10	−1.89224	−0.946122	+	0.323812i	$0.895036\pi$
$68$	−1.62682e9	−0.135688
$69$	1.59300e9	0.122615
$70$	−1.38966e10	−0.988258
$71$	1.27122e10	0.836183	0.418092	−	0.908405i	$-0.362699\pi$
$71$	1.27122e10	0.836183	0.418092	+	0.908405i	$0.362699\pi$
$72$	1.64165e10	0.999887
$73$	−6.43549e9	−0.363334	−0.181667	−	0.983360i	$-0.558149\pi$
$73$	−6.43549e9	−0.363334	−0.181667	+	0.983360i	$0.558149\pi$
$74$	1.12699e10	0.590397
$75$	−1.67420e9	−0.0814647
$76$	−1.42309e9	−0.0643810
$77$	6.97586e10	2.93697
$78$	8.88346e9	0.348387
$79$	3.72736e9	0.136286	0.0681432	−	0.997676i	$-0.478293\pi$
$79$	3.72736e9	0.136286	0.0681432	+	0.997676i	$0.478293\pi$
$80$	1.12223e10	0.382900
$81$	2.41578e10	0.769823
$82$	−1.33560e10	−0.397833
$83$	−1.79731e10	−0.500833	−0.250416	−	0.968138i	$-0.580567\pi$
$83$	−1.79731e10	−0.500833	−0.250416	+	0.968138i	$0.580567\pi$
$84$	−6.34312e9	−0.165488
$85$	−1.19321e10	−0.291684
$86$	1.19034e10	0.272855
$87$	−2.42330e9	−0.0521256
$88$	−1.04912e11	−2.11919
$89$	−1.69946e10	−0.322602	−0.161301	−	0.986905i	$-0.551569\pi$
$89$	−1.69946e10	−0.322602	−0.161301	+	0.986905i	$0.551569\pi$
$90$	3.39028e10	0.605204
$91$	1.42522e11	2.39417
$92$	−1.08223e10	−0.171193
$93$	3.11618e10	0.464479
$94$	−4.44523e10	−0.624728
$95$	−1.04378e10	−0.138398
$96$	1.63931e10	0.205197
$97$	9.11305e10	1.07750	0.538752	−	0.842464i	$-0.318896\pi$
$97$	9.11305e10	1.07750	0.538752	+	0.842464i	$0.318896\pi$
$98$	8.81183e10	0.984742
$99$	−1.70186e11	−1.79858
$100$	1.13739e10	0.113739
$101$	−6.69466e10	−0.633813	−0.316906	−	0.948457i	$-0.602644\pi$
$101$	−6.69466e10	−0.633813	−0.316906	+	0.948457i	$0.602644\pi$
$102$	8.45050e9	0.0757847
$103$	1.51444e11	1.28721	0.643603	−	0.765360i	$-0.277439\pi$
$103$	1.51444e11	1.28721	0.643603	+	0.765360i	$0.277439\pi$
$104$	−2.14342e11	−1.72752
$105$	−4.65243e10	−0.355745
$106$	8.58769e10	0.623295
$107$	1.17360e11	0.808927	0.404464	−	0.914554i	$-0.367458\pi$
$107$	1.17360e11	0.808927	0.404464	+	0.914554i	$0.367458\pi$
$108$	3.22735e10	0.211357
$109$	−1.76213e11	−1.09697	−0.548483	−	0.836162i	$-0.684794\pi$
$109$	−1.76213e11	−1.09697	−0.548483	+	0.836162i	$0.684794\pi$
$110$	−2.16660e11	−1.28268
$111$	3.77302e10	0.212526
$112$	−1.27510e11	−0.683670
$113$	2.00301e11	1.02271	0.511355	−	0.859370i	$-0.329144\pi$
$113$	2.00301e11	1.02271	0.511355	+	0.859370i	$0.329144\pi$
$114$	7.39222e9	0.0359582
$115$	−7.93773e10	−0.368009
$116$	1.64631e10	0.0727768
$117$	−3.47703e11	−1.46617
$118$	−2.81017e11	−1.13079
$119$	1.35576e11	0.520804
$120$	6.99690e10	0.256690
$121$	8.02285e11	2.81196
$122$	1.51100e11	0.506158
$123$	−4.47144e10	−0.143209
$124$	−2.11703e11	−0.648497
$125$	3.70878e11	1.08699
$126$	−3.85213e11	−1.08059
$127$	−4.31013e11	−1.15763	−0.578816	−	0.815458i	$-0.696485\pi$
$127$	−4.31013e11	−1.15763	−0.578816	+	0.815458i	$0.696485\pi$
$128$	2.64017e10	0.0679167
$129$	3.98513e10	0.0982199
$130$	−4.42653e11	−1.04562
$131$	−5.77134e9	−0.0130703	−0.00653514	−	0.999979i	$-0.502080\pi$
$131$	−5.77134e9	−0.0130703	−0.00653514	+	0.999979i	$0.502080\pi$
$132$	−9.88947e10	−0.214791
$133$	1.18597e11	0.247110
$134$	−7.37964e11	−1.47557
$135$	2.36714e11	0.454347
$136$	−2.03896e11	−0.375789
$137$	−2.23844e11	−0.396262	−0.198131	−	0.980176i	$-0.563487\pi$
$137$	−2.23844e11	−0.396262	−0.198131	+	0.980176i	$0.563487\pi$
$138$	5.62163e10	0.0956153
$139$	−8.20484e11	−1.34118	−0.670592	−	0.741826i	$-0.733960\pi$
$139$	−8.20484e11	−1.34118	−0.670592	+	0.741826i	$0.733960\pi$
$140$	3.16071e11	0.496684
$141$	−1.48821e11	−0.224884
$142$	4.48611e11	0.652054
$143$	2.22204e12	3.10745
$144$	3.11080e11	0.418676
$145$	1.20750e11	0.156446
$146$	−2.27106e11	−0.283327
$147$	2.95010e11	0.354479
$148$	−2.56327e11	−0.296725
$149$	6.51970e11	0.727282	0.363641	−	0.931539i	$-0.381534\pi$
$149$	6.51970e11	0.727282	0.363641	+	0.931539i	$0.381534\pi$
$150$	−5.90817e10	−0.0635260
$151$	−5.81231e11	−0.602526	−0.301263	−	0.953541i	$-0.597408\pi$
$151$	−5.81231e11	−0.602526	−0.301263	+	0.953541i	$0.597408\pi$
$152$	−1.78361e11	−0.178304
$153$	−3.30756e11	−0.318937
$154$	2.46176e12	2.29024
$155$	−1.55276e12	−1.39405
$156$	−2.02049e11	−0.175094
$157$	5.29592e11	0.443091	0.221546	−	0.975150i	$-0.428890\pi$
$157$	5.29592e11	0.443091	0.221546	+	0.975150i	$0.428890\pi$
$158$	1.31537e11	0.106276
$159$	2.87506e11	0.224369
$160$	−8.16852e11	−0.615862
$161$	9.01907e11	0.657082
$162$	8.52522e11	0.600306
$163$	2.77475e12	1.88883	0.944414	−	0.328758i	$-0.106630\pi$
$163$	2.77475e12	1.88883	0.944414	+	0.328758i	$0.106630\pi$
$164$	3.03775e11	0.199945
$165$	−7.25354e11	−0.461730
$166$	−6.34263e11	−0.390548
$167$	7.87027e11	0.468866	0.234433	−	0.972132i	$-0.424677\pi$
$167$	7.87027e11	0.468866	0.234433	+	0.972132i	$0.424677\pi$
$168$	−7.95007e11	−0.458321
$169$	2.74763e12	1.53314
$170$	−4.21079e11	−0.227455
$171$	−2.89335e11	−0.151329
$172$	−2.70737e11	−0.137133
$173$	−2.47176e12	−1.21270	−0.606348	−	0.795199i	$-0.707366\pi$
$173$	−2.47176e12	−1.21270	−0.606348	+	0.795199i	$0.707366\pi$
$174$	−8.55174e10	−0.0406475
$175$	−9.47879e11	−0.436560
$176$	−1.98800e12	−0.887352
$177$	−9.40811e11	−0.407052
$178$	−5.99735e11	−0.251564
$179$	−3.62898e12	−1.47602	−0.738011	−	0.674789i	$-0.764235\pi$
$179$	−3.62898e12	−1.47602	−0.738011	+	0.674789i	$0.764235\pi$
$180$	−7.71100e11	−0.304167
$181$	−9.59864e11	−0.367263	−0.183632	−	0.982995i	$-0.558785\pi$
$181$	−9.59864e11	−0.367263	−0.183632	+	0.982995i	$0.558785\pi$
$182$	5.02955e12	1.86697
$183$	5.05866e11	0.182202
$184$	−1.35640e12	−0.474122
$185$	−1.88005e12	−0.637861
$186$	1.09969e12	0.362200
$187$	2.11374e12	0.675964
$188$	1.01104e12	0.313979
$189$	−2.68961e12	−0.811239
$190$	−3.68346e11	−0.107922
$191$	−1.65817e11	−0.0472005	−0.0236002	−	0.999721i	$-0.507513\pi$
$191$	−1.65817e11	−0.0472005	−0.0236002	+	0.999721i	$0.507513\pi$
$192$	1.03975e12	0.287589
$193$	−6.01609e12	−1.61714	−0.808572	−	0.588397i	$-0.799759\pi$
$193$	−6.01609e12	−1.61714	−0.808572	+	0.588397i	$0.799759\pi$
$194$	3.21596e12	0.840236
$195$	−1.48195e12	−0.376395
$196$	−2.00420e12	−0.494917
$197$	−8.50856e11	−0.204311	−0.102155	−	0.994768i	$-0.532574\pi$
$197$	−8.50856e11	−0.204311	−0.102155	+	0.994768i	$0.532574\pi$
$198$	−6.00580e12	−1.40253
$199$	3.55570e12	0.807669	0.403835	−	0.914832i	$-0.367677\pi$
$199$	3.55570e12	0.807669	0.403835	+	0.914832i	$0.367677\pi$
$200$	1.42554e12	0.315002
$201$	−2.47062e12	−0.531162
$202$	−2.36252e12	−0.494246
$203$	−1.37200e12	−0.279335
$204$	−1.92202e11	−0.0380883
$205$	2.22807e12	0.429816
$206$	5.34441e12	1.00376
$207$	−2.20033e12	−0.402394
$208$	−4.06162e12	−0.723355
$209$	1.84903e12	0.320730
$210$	−1.64183e12	−0.277409
$211$	−3.49492e12	−0.575286	−0.287643	−	0.957738i	$-0.592872\pi$
$211$	−3.49492e12	−0.575286	−0.287643	+	0.957738i	$0.592872\pi$
$212$	−1.95322e12	−0.313259
$213$	1.50190e12	0.234721
$214$	4.14159e12	0.630800
$215$	−1.98575e12	−0.294790
$216$	4.04496e12	0.585354
$217$	1.76429e13	2.48909
$218$	−6.21850e12	−0.855411
$219$	−7.60325e11	−0.101990
$220$	4.92782e12	0.644659
$221$	4.31853e12	0.551034
$222$	1.33148e12	0.165728
$223$	4.29867e12	0.521985	0.260992	−	0.965341i	$-0.415950\pi$
$223$	4.29867e12	0.521985	0.260992	+	0.965341i	$0.415950\pi$
$224$	9.28130e12	1.09962
$225$	2.31248e12	0.267347
$226$	7.06856e12	0.797507
$227$	−1.60784e13	−1.77052	−0.885262	−	0.465092i	$-0.846021\pi$
$227$	−1.60784e13	−1.77052	−0.885262	+	0.465092i	$0.846021\pi$
$228$	−1.68132e11	−0.0180721
$229$	3.80096e11	0.0398840	0.0199420	−	0.999801i	$-0.493652\pi$
$229$	3.80096e11	0.0398840	0.0199420	+	0.999801i	$0.493652\pi$
$230$	−2.80120e12	−0.286973
$231$	8.24167e12	0.824421
$232$	2.06338e12	0.201556
$233$	7.18682e12	0.685613	0.342807	−	0.939406i	$-0.388622\pi$
$233$	7.18682e12	0.685613	0.342807	+	0.939406i	$0.388622\pi$
$234$	−1.22703e13	−1.14332
$235$	7.41559e12	0.674952
$236$	6.39157e12	0.568318
$237$	4.40371e11	0.0382563
$238$	4.78442e12	0.406122
$239$	−1.29966e13	−1.07806	−0.539028	−	0.842288i	$-0.681208\pi$
$239$	−1.29966e13	−1.07806	−0.539028	+	0.842288i	$0.681208\pi$
$240$	1.32586e12	0.107482
$241$	−1.44593e13	−1.14565	−0.572827	−	0.819677i	$-0.694153\pi$
$241$	−1.44593e13	−1.14565	−0.572827	+	0.819677i	$0.694153\pi$
$242$	2.83123e13	2.19276
$243$	9.97707e12	0.755385
$244$	−3.43669e12	−0.254388
$245$	−1.47000e13	−1.06391
$246$	−1.57795e12	−0.111674
$247$	3.77771e12	0.261454
$248$	−2.65335e13	−1.79602
$249$	−2.12344e12	−0.140586
$250$	1.30881e13	0.847632
$251$	−2.28996e13	−1.45085	−0.725424	−	0.688302i	$-0.758356\pi$
$251$	−2.28996e13	−1.45085	−0.725424	+	0.688302i	$0.758356\pi$
$252$	8.76145e12	0.543091
$253$	1.40615e13	0.852843
$254$	−1.52103e13	−0.902718
$255$	−1.40972e12	−0.0818772
$256$	−1.70919e13	−0.971562
$257$	−3.18355e13	−1.77125	−0.885624	−	0.464404i	$-0.846269\pi$
$257$	−3.18355e13	−1.77125	−0.885624	+	0.464404i	$0.846269\pi$
$258$	1.40634e12	0.0765917
$259$	2.13617e13	1.13890
$260$	1.00679e13	0.525515
$261$	3.34719e12	0.171063
$262$	−2.03668e11	−0.0101922
$263$	3.69614e13	1.81131	0.905654	−	0.424017i	$-0.139380\pi$
$263$	3.69614e13	1.81131	0.905654	+	0.424017i	$0.139380\pi$
$264$	−1.23948e13	−0.594866
$265$	−1.43261e13	−0.673404
$266$	4.18525e12	0.192696
$267$	−2.00784e12	−0.0905560
$268$	1.67846e13	0.741599
$269$	−1.69926e12	−0.0735567	−0.0367784	−	0.999323i	$-0.511710\pi$
$269$	−1.69926e12	−0.0735567	−0.0367784	+	0.999323i	$0.511710\pi$
$270$	8.35354e12	0.354299
$271$	−7.40491e12	−0.307743	−0.153872	−	0.988091i	$-0.549174\pi$
$271$	−7.40491e12	−0.307743	−0.153872	+	0.988091i	$0.549174\pi$
$272$	−3.86367e12	−0.157352
$273$	1.68383e13	0.672055
$274$	−7.89938e12	−0.309005
$275$	−1.47782e13	−0.566622
$276$	−1.27861e12	−0.0480549
$277$	−1.62155e13	−0.597435	−0.298717	−	0.954342i	$-0.596559\pi$
$277$	−1.62155e13	−0.597435	−0.298717	+	0.954342i	$0.596559\pi$
$278$	−2.89546e13	−1.04585
$279$	−4.30422e13	−1.52430
$280$	3.96143e13	1.37557
$281$	−4.32901e13	−1.47402	−0.737010	−	0.675882i	$-0.763763\pi$
$281$	−4.32901e13	−1.47402	−0.737010	+	0.675882i	$0.763763\pi$
$282$	−5.25184e12	−0.175364
$283$	1.52025e13	0.497841	0.248921	−	0.968524i	$-0.419924\pi$
$283$	1.52025e13	0.497841	0.248921	+	0.968524i	$0.419924\pi$
$284$	−1.02034e13	−0.327713
$285$	−1.23318e12	−0.0388490
$286$	7.84150e13	2.42318
$287$	−2.53159e13	−0.767439
$288$	−2.26430e13	−0.673404
$289$	−3.01638e13	−0.880133
$290$	4.26124e12	0.121996
$291$	1.07667e13	0.302461
$292$	5.16540e12	0.142396
$293$	2.98268e13	0.806928	0.403464	−	0.914996i	$-0.367806\pi$
$293$	2.98268e13	0.806928	0.403464	+	0.914996i	$0.367806\pi$
$294$	1.04108e13	0.276422
$295$	4.68796e13	1.22170
$296$	−3.21264e13	−0.821783
$297$	−4.19333e13	−1.05293
$298$	2.30078e13	0.567133
$299$	2.87287e13	0.695223
$300$	1.34378e12	0.0319272
$301$	2.25626e13	0.526349
$302$	−2.05114e13	−0.469848
$303$	−7.90944e12	−0.177915
$304$	−3.37981e12	−0.0746600
$305$	−2.52067e13	−0.546849
$306$	−1.16723e13	−0.248707
$307$	6.98858e13	1.46261	0.731304	−	0.682052i	$-0.238912\pi$
$307$	6.98858e13	1.46261	0.731304	+	0.682052i	$0.238912\pi$
$308$	−5.59912e13	−1.15104
$309$	1.78925e13	0.361325
$310$	−5.47962e13	−1.08708
$311$	−9.69941e13	−1.89044	−0.945220	−	0.326433i	$-0.894153\pi$
$311$	−9.69941e13	−1.89044	−0.945220	+	0.326433i	$0.894153\pi$
$312$	−2.53236e13	−0.484925
$313$	2.70556e13	0.509053	0.254527	−	0.967066i	$-0.418080\pi$
$313$	2.70556e13	0.509053	0.254527	+	0.967066i	$0.418080\pi$
$314$	1.86891e13	0.345522
$315$	6.42617e13	1.16747
$316$	−2.99174e12	−0.0534127
$317$	8.31995e13	1.45980	0.729902	−	0.683552i	$-0.239566\pi$
$317$	8.31995e13	1.45980	0.729902	+	0.683552i	$0.239566\pi$
$318$	1.01460e13	0.174962
$319$	−2.13906e13	−0.362556
$320$	−5.18096e13	−0.863148
$321$	1.38656e13	0.227070
$322$	3.18280e13	0.512391
$323$	3.59359e12	0.0568742
$324$	−1.93901e13	−0.301705
$325$	−3.01930e13	−0.461900
$326$	9.79200e13	1.47290
$327$	−2.08188e13	−0.307924
$328$	3.80732e13	0.553750
$329$	−8.42580e13	−1.20513
$330$	−2.55975e13	−0.360056
$331$	7.73861e13	1.07056	0.535278	−	0.844676i	$-0.320207\pi$
$331$	7.73861e13	1.07056	0.535278	+	0.844676i	$0.320207\pi$
$332$	1.44259e13	0.196284
$333$	−5.21149e13	−0.697458
$334$	2.77739e13	0.365621
$335$	1.23108e14	1.59419
$336$	−1.50648e13	−0.191910
$337$	2.22962e13	0.279425	0.139713	−	0.990192i	$-0.455382\pi$
$337$	2.22962e13	0.279425	0.139713	+	0.990192i	$0.455382\pi$
$338$	9.69629e13	1.19554
$339$	2.36647e13	0.287080
$340$	9.57721e12	0.114315
$341$	2.75067e14	3.23065
$342$	−1.02105e13	−0.118006
$343$	3.47613e13	0.395347
$344$	−3.39325e13	−0.379790
$345$	−9.37808e12	−0.103302
$346$	−8.72273e13	−0.945658
$347$	−1.15059e14	−1.22775	−0.613874	−	0.789404i	$-0.710390\pi$
$347$	−1.15059e14	−1.22775	−0.613874	+	0.789404i	$0.710390\pi$
$348$	1.94504e12	0.0204288
$349$	−1.87548e13	−0.193898	−0.0969490	−	0.995289i	$-0.530908\pi$
$349$	−1.87548e13	−0.193898	−0.0969490	+	0.995289i	$0.530908\pi$
$350$	−3.34503e13	−0.340428
$351$	−8.56727e13	−0.858328
$352$	1.44703e14	1.42723
$353$	3.42634e13	0.332713	0.166356	−	0.986066i	$-0.446800\pi$
$353$	3.42634e13	0.332713	0.166356	+	0.986066i	$0.446800\pi$
$354$	−3.32009e13	−0.317418
$355$	−7.48378e13	−0.704474
$356$	1.36406e13	0.126433
$357$	1.60177e13	0.146192
$358$	−1.28065e14	−1.15100
$359$	−1.18934e14	−1.05265	−0.526327	−	0.850282i	$-0.676431\pi$
$359$	−1.18934e14	−1.05265	−0.526327	+	0.850282i	$0.676431\pi$
$360$	−9.66448e13	−0.842393
$361$	−1.13347e14	−0.973014
$362$	−3.38732e13	−0.286391
$363$	9.47864e13	0.789332
$364$	−1.14394e14	−0.938310
$365$	3.78862e13	0.306105
$366$	1.78518e13	0.142081
$367$	6.79151e13	0.532480	0.266240	−	0.963907i	$-0.414219\pi$
$367$	6.79151e13	0.532480	0.266240	+	0.963907i	$0.414219\pi$
$368$	−2.57028e13	−0.198526
$369$	6.17618e13	0.469975
$370$	−6.63464e13	−0.497402
$371$	1.62777e14	1.20237
$372$	−2.50118e13	−0.182036
$373$	−4.93278e13	−0.353747	−0.176874	−	0.984234i	$-0.556598\pi$
$373$	−4.93278e13	−0.353747	−0.176874	+	0.984234i	$0.556598\pi$
$374$	7.45932e13	0.527115
$375$	4.38175e13	0.305124
$376$	1.26718e14	0.869569
$377$	−4.37027e13	−0.295550
$378$	−9.49152e13	−0.632602
$379$	3.90697e13	0.256640	0.128320	−	0.991733i	$-0.459042\pi$
$379$	3.90697e13	0.256640	0.128320	+	0.991733i	$0.459042\pi$
$380$	8.37783e12	0.0542402
$381$	−5.09223e13	−0.324953
$382$	−5.85163e12	−0.0368069
$383$	4.92689e12	0.0305477	0.0152739	−	0.999883i	$-0.495138\pi$
$383$	4.92689e12	0.0305477	0.0152739	+	0.999883i	$0.495138\pi$
$384$	3.11924e12	0.0190646
$385$	−4.10673e14	−2.47436
$386$	−2.12305e14	−1.26105
$387$	−5.50447e13	−0.322333
$388$	−7.31452e13	−0.422290
$389$	−1.85263e14	−1.05454	−0.527272	−	0.849697i	$-0.676785\pi$
$389$	−1.85263e14	−1.05454	−0.527272	+	0.849697i	$0.676785\pi$
$390$	−5.22975e13	−0.293512
$391$	2.73285e13	0.151232
$392$	−2.51194e14	−1.37068
$393$	−6.81858e11	−0.00366889
$394$	−3.00264e13	−0.159321
$395$	−2.19432e13	−0.114820
$396$	1.36598e14	0.704892
$397$	2.53580e14	1.29053	0.645263	−	0.763960i	$-0.276748\pi$
$397$	2.53580e14	1.29053	0.645263	+	0.763960i	$0.276748\pi$
$398$	1.25479e14	0.629819
$399$	1.40117e13	0.0693651
$400$	2.70129e13	0.131899
$401$	−2.02543e14	−0.975491	−0.487746	−	0.872986i	$-0.662181\pi$
$401$	−2.02543e14	−0.975491	−0.487746	+	0.872986i	$0.662181\pi$
$402$	−8.71872e13	−0.414199
$403$	5.61983e14	2.63357
$404$	5.37342e13	0.248401
$405$	−1.42219e14	−0.648566
$406$	−4.84173e13	−0.217825
$407$	3.33047e14	1.47821
$408$	−2.40894e13	−0.105486
$409$	4.48649e14	1.93833	0.969167	−	0.246404i	$-0.0792490\pi$
$409$	4.48649e14	1.93833	0.969167	+	0.246404i	$0.0792490\pi$
$410$	7.86278e13	0.335170
$411$	−2.64462e13	−0.111233
$412$	−1.21556e14	−0.504475
$413$	−5.32659e14	−2.18134
$414$	−7.76488e13	−0.313786
$415$	1.05809e14	0.421945
$416$	2.95640e14	1.16345
$417$	−9.69365e13	−0.376477
$418$	6.52517e13	0.250105
$419$	8.59820e13	0.325260	0.162630	−	0.986687i	$-0.448002\pi$
$419$	8.59820e13	0.325260	0.162630	+	0.986687i	$0.448002\pi$
$420$	3.73424e13	0.139422
$421$	−2.91547e13	−0.107438	−0.0537188	−	0.998556i	$-0.517107\pi$
$421$	−2.91547e13	−0.107438	−0.0537188	+	0.998556i	$0.517107\pi$
$422$	−1.23334e14	−0.448607
$423$	2.05559e14	0.738015
$424$	−2.44804e14	−0.867574
$425$	−2.87215e13	−0.100477
$426$	5.30013e13	0.183035
$427$	2.86406e14	0.976402
$428$	−9.41981e13	−0.317031
$429$	2.62524e14	0.872276
$430$	−7.00763e13	−0.229877
$431$	9.74570e13	0.315637	0.157819	−	0.987468i	$-0.449554\pi$
$431$	9.74570e13	0.315637	0.157819	+	0.987468i	$0.449554\pi$
$432$	7.66490e13	0.245101
$433$	−2.30721e14	−0.728456	−0.364228	−	0.931310i	$-0.618667\pi$
$433$	−2.30721e14	−0.728456	−0.364228	+	0.931310i	$0.618667\pi$
$434$	6.22610e14	1.94099
$435$	1.42661e13	0.0439152
$436$	1.41436e14	0.429917
$437$	2.39061e13	0.0717564
$438$	−2.68316e13	−0.0795314
$439$	−3.45189e14	−1.01042	−0.505210	−	0.862997i	$-0.668585\pi$
$439$	−3.45189e14	−1.01042	−0.505210	+	0.862997i	$0.668585\pi$
$440$	6.17621e14	1.78539
$441$	−4.07482e14	−1.16331
$442$	1.52399e14	0.429696
$443$	7.05116e13	0.196354	0.0981771	−	0.995169i	$-0.468699\pi$
$443$	7.05116e13	0.196354	0.0981771	+	0.995169i	$0.468699\pi$
$444$	−3.02838e13	−0.0832922
$445$	1.00049e14	0.271788
$446$	1.51699e14	0.407043
$447$	7.70273e13	0.204152
$448$	5.88675e14	1.54116
$449$	6.58137e14	1.70201	0.851003	−	0.525160i	$-0.175995\pi$
$449$	6.58137e14	1.70201	0.851003	+	0.525160i	$0.175995\pi$
$450$	8.16067e13	0.208476
$451$	−3.94697e14	−0.996078
$452$	−1.60770e14	−0.400815
$453$	−6.86698e13	−0.169132
$454$	−5.67403e14	−1.38065
$455$	−8.39036e14	−2.01706
$456$	−2.10726e13	−0.0500508
$457$	−6.02229e14	−1.41326	−0.706630	−	0.707583i	$-0.749786\pi$
$457$	−6.02229e14	−1.41326	−0.706630	+	0.707583i	$0.749786\pi$
$458$	1.34135e13	0.0311014
$459$	−8.14973e13	−0.186712
$460$	6.37116e13	0.144228
$461$	1.62146e14	0.362704	0.181352	−	0.983418i	$-0.441953\pi$
$461$	1.62146e14	0.362704	0.181352	+	0.983418i	$0.441953\pi$
$462$	2.90845e14	0.642882
$463$	−1.42179e14	−0.310555	−0.155278	−	0.987871i	$-0.549627\pi$
$463$	−1.42179e14	−0.310555	−0.155278	+	0.987871i	$0.549627\pi$
$464$	3.90995e13	0.0843962
$465$	−1.83451e14	−0.391318
$466$	2.53620e14	0.534640
$467$	−3.19272e14	−0.665147	−0.332573	−	0.943077i	$-0.607917\pi$
$467$	−3.19272e14	−0.665147	−0.332573	+	0.943077i	$0.607917\pi$
$468$	2.79081e14	0.574616
$469$	−1.39879e15	−2.84644
$470$	2.61694e14	0.526326
$471$	6.25689e13	0.124378
$472$	8.01079e14	1.57396
$473$	3.51771e14	0.683162
$474$	1.55405e13	0.0298322
$475$	−2.51246e13	−0.0476743
$476$	−1.08819e14	−0.204111
$477$	−3.97117e14	−0.736322
$478$	−4.58645e14	−0.840666
$479$	−6.75270e14	−1.22358	−0.611789	−	0.791021i	$-0.709550\pi$
$479$	−6.75270e14	−1.22358	−0.611789	+	0.791021i	$0.709550\pi$
$480$	−9.65074e13	−0.172876
$481$	6.80440e14	1.20501
$482$	−5.10263e14	−0.893378
$483$	1.06556e14	0.184446
$484$	−6.43948e14	−1.10205
$485$	−5.36491e14	−0.907785
$486$	3.52087e14	0.589048
$487$	8.91285e14	1.47437	0.737186	−	0.675690i	$-0.236154\pi$
$487$	8.91285e14	1.47437	0.737186	+	0.675690i	$0.236154\pi$
$488$	−4.30732e14	−0.704529
$489$	3.27825e14	0.530204
$490$	−5.18758e14	−0.829633
$491$	7.16236e14	1.13268	0.566341	−	0.824171i	$-0.308359\pi$
$491$	7.16236e14	1.13268	0.566341	+	0.824171i	$0.308359\pi$
$492$	3.58897e13	0.0561256
$493$	−4.15727e13	−0.0642910
$494$	1.33314e14	0.203881
$495$	1.00190e15	1.51528
$496$	−5.02790e14	−0.752034
$497$	8.50328e14	1.25784
$498$	−7.49353e13	−0.109629
$499$	−8.29953e14	−1.20088	−0.600441	−	0.799669i	$-0.705008\pi$
$499$	−8.29953e14	−1.20088	−0.600441	+	0.799669i	$0.705008\pi$
$500$	−2.97682e14	−0.426008
$501$	9.29837e13	0.131613
$502$	−8.08118e14	−1.13137
$503$	−7.94411e14	−1.10007	−0.550036	−	0.835141i	$-0.685386\pi$
$503$	−7.94411e14	−1.10007	−0.550036	+	0.835141i	$0.685386\pi$
$504$	1.09810e15	1.50410
$505$	3.94119e14	0.533980
$506$	4.96225e14	0.665045
$507$	3.24620e14	0.430360
$508$	3.45949e14	0.453693
$509$	−3.19810e14	−0.414900	−0.207450	−	0.978246i	$-0.566516\pi$
$509$	−3.19810e14	−0.414900	−0.207450	+	0.978246i	$0.566516\pi$
$510$	−4.97486e13	−0.0638477
$511$	−4.30473e14	−0.546551
$512$	−6.57237e14	−0.825539
$513$	−7.12911e13	−0.0885911
$514$	−1.12346e15	−1.38121
$515$	−8.91562e14	−1.08446
$516$	−3.19864e13	−0.0384939
$517$	−1.31365e15	−1.56417
$518$	7.53846e14	0.888115
$519$	−2.92027e14	−0.340410
$520$	1.26185e15	1.45542
$521$	−4.06638e14	−0.464088	−0.232044	−	0.972705i	$-0.574541\pi$
$521$	−4.06638e14	−0.464088	−0.232044	+	0.972705i	$0.574541\pi$
$522$	1.18121e14	0.133395
$523$	1.85108e14	0.206855	0.103427	−	0.994637i	$-0.467019\pi$
$523$	1.85108e14	0.206855	0.103427	+	0.994637i	$0.467019\pi$
$524$	4.63232e12	0.00512244
$525$	−1.11988e14	−0.122545
$526$	1.30436e15	1.41245
$527$	5.34593e14	0.572882
$528$	−2.34873e14	−0.249084
$529$	−7.71009e14	−0.809195
$530$	−5.05562e14	−0.525119
$531$	1.29950e15	1.33584
$532$	−9.51912e13	−0.0968462
$533$	−8.06395e14	−0.811986
$534$	−7.08559e13	−0.0706154
$535$	−6.90906e14	−0.681511
$536$	2.10367e15	2.05386
$537$	−4.28747e14	−0.414327
$538$	−5.99663e13	−0.0573594
$539$	2.60407e15	2.46555
$540$	−1.89996e14	−0.178065
$541$	−4.75602e14	−0.441223	−0.220612	−	0.975362i	$-0.570805\pi$
$541$	−4.75602e14	−0.441223	−0.220612	+	0.975362i	$0.570805\pi$
$542$	−2.61316e14	−0.239977
$543$	−1.13404e14	−0.103093
$544$	2.81231e14	0.253087
$545$	1.03738e15	0.924180
$546$	5.94218e14	0.524067
$547$	1.25492e15	1.09568	0.547841	−	0.836583i	$-0.315450\pi$
$547$	1.25492e15	1.09568	0.547841	+	0.836583i	$0.315450\pi$
$548$	1.79667e14	0.155301
$549$	−6.98727e14	−0.597943
$550$	−5.21519e14	−0.441850
$551$	−3.63664e13	−0.0305047
$552$	−1.60253e14	−0.133088
$553$	2.49325e14	0.205011
$554$	−5.72237e14	−0.465878
$555$	−2.22120e14	−0.179051
$556$	6.58555e14	0.525631
$557$	1.26707e15	1.00137	0.500687	−	0.865629i	$-0.333081\pi$
$557$	1.26707e15	1.00137	0.500687	+	0.865629i	$0.333081\pi$
$558$	−1.51894e15	−1.18865
$559$	7.18693e14	0.556902
$560$	7.50662e14	0.575984
$561$	2.49729e14	0.189747
$562$	−1.52769e15	−1.14944
$563$	−1.11847e15	−0.833354	−0.416677	−	0.909055i	$-0.636805\pi$
$563$	−1.11847e15	−0.833354	−0.416677	+	0.909055i	$0.636805\pi$
$564$	1.19450e14	0.0881356
$565$	−1.17919e15	−0.861621
$566$	5.36492e14	0.388216
$567$	1.61593e15	1.15802
$568$	−1.27883e15	−0.907604
$569$	−5.81851e14	−0.408972	−0.204486	−	0.978869i	$-0.565552\pi$
$569$	−5.81851e14	−0.408972	−0.204486	+	0.978869i	$0.565552\pi$
$570$	−4.35185e13	−0.0302944
$571$	8.19590e14	0.565064	0.282532	−	0.959258i	$-0.408826\pi$
$571$	8.19590e14	0.565064	0.282532	+	0.959258i	$0.408826\pi$
$572$	−1.78350e15	−1.21786
$573$	−1.95906e13	−0.0132494
$574$	−8.93390e14	−0.598447
$575$	−1.91068e14	−0.126769
$576$	−1.43616e15	−0.943795
$577$	2.89704e15	1.88576	0.942881	−	0.333129i	$-0.108104\pi$
$577$	2.89704e15	1.88576	0.942881	+	0.333129i	$0.108104\pi$
$578$	−1.06447e15	−0.686326
$579$	−7.10774e14	−0.453941
$580$	−9.69194e13	−0.0613136
$581$	−1.20223e15	−0.753386
$582$	3.79951e14	0.235859
$583$	2.53783e15	1.56058
$584$	6.47398e14	0.394367
$585$	2.04695e15	1.23523
$586$	1.05258e15	0.629241
$587$	2.08142e15	1.23268	0.616338	−	0.787481i	$-0.288615\pi$
$587$	2.08142e15	1.23268	0.616338	+	0.787481i	$0.288615\pi$
$588$	−2.36787e14	−0.138926
$589$	4.67644e14	0.271820
$590$	1.65436e15	0.952676
$591$	−1.00525e14	−0.0573511
$592$	−6.08770e14	−0.344099
$593$	−1.61615e15	−0.905067	−0.452533	−	0.891747i	$-0.649480\pi$
$593$	−1.61615e15	−0.905067	−0.452533	+	0.891747i	$0.649480\pi$
$594$	−1.47981e15	−0.821070
$595$	−7.98143e14	−0.438771
$596$	−5.23298e14	−0.285033
$597$	4.20090e14	0.226717
$598$	1.01382e15	0.542134
$599$	1.29668e15	0.687047	0.343524	−	0.939144i	$-0.388379\pi$
$599$	1.29668e15	0.687047	0.343524	+	0.939144i	$0.388379\pi$
$600$	1.68421e14	0.0884228
$601$	2.93134e15	1.52495	0.762476	−	0.647016i	$-0.223983\pi$
$601$	2.93134e15	1.52495	0.762476	+	0.647016i	$0.223983\pi$
$602$	7.96227e14	0.410446
$603$	3.41254e15	1.74314
$604$	4.66520e14	0.236139
$605$	−4.72310e15	−2.36904
$606$	−2.79121e14	−0.138737
$607$	−1.66177e15	−0.818527	−0.409264	−	0.912416i	$-0.634214\pi$
$607$	−1.66177e15	−0.818527	−0.409264	+	0.912416i	$0.634214\pi$
$608$	2.46012e14	0.120084
$609$	−1.62096e14	−0.0784108
$610$	−8.89536e14	−0.426432
$611$	−2.68389e15	−1.27508
$612$	2.65479e14	0.124996
$613$	−1.17050e14	−0.0546186	−0.0273093	−	0.999627i	$-0.508694\pi$
$613$	−1.17050e14	−0.0546186	−0.0273093	+	0.999627i	$0.508694\pi$
$614$	2.46624e15	1.14054
$615$	2.63236e14	0.120652
$616$	−7.01758e15	−3.18782
$617$	−2.73172e15	−1.22989	−0.614947	−	0.788568i	$-0.710823\pi$
$617$	−2.73172e15	−1.22989	−0.614947	+	0.788568i	$0.710823\pi$
$618$	6.31418e14	0.281761
$619$	2.14864e14	0.0950307	0.0475154	−	0.998871i	$-0.484870\pi$
$619$	2.14864e14	0.0950307	0.0475154	+	0.998871i	$0.484870\pi$
$620$	1.24631e15	0.546351
$621$	−5.42154e14	−0.235569
$622$	−3.42288e15	−1.47416
$623$	−1.13678e15	−0.485279
$624$	−4.79863e14	−0.203049
$625$	−1.49145e15	−0.625561
$626$	9.54781e14	0.396959
$627$	2.18455e14	0.0900307
$628$	−4.25073e14	−0.173654
$629$	6.47277e14	0.262127
$630$	2.26777e15	0.910388
$631$	−3.58105e14	−0.142511	−0.0712555	−	0.997458i	$-0.522701\pi$
$631$	−3.58105e14	−0.142511	−0.0712555	+	0.997458i	$0.522701\pi$
$632$	−3.74965e14	−0.147927
$633$	−4.12909e14	−0.161486
$634$	2.93608e15	1.13835
$635$	2.53740e15	0.975290
$636$	−2.30764e14	−0.0879335
$637$	5.32031e15	2.00988
$638$	−7.54868e14	−0.282720
$639$	−2.07449e15	−0.770296
$640$	−1.55428e14	−0.0572190
$641$	−2.86723e15	−1.04651	−0.523256	−	0.852176i	$-0.675283\pi$
$641$	−2.86723e15	−1.04651	−0.523256	+	0.852176i	$0.675283\pi$
$642$	4.89311e14	0.177069
$643$	−4.89266e15	−1.75543	−0.877717	−	0.479179i	$-0.840935\pi$
$643$	−4.89266e15	−1.75543	−0.877717	+	0.479179i	$0.840935\pi$
$644$	−7.23909e14	−0.257520
$645$	−2.34607e14	−0.0827491
$646$	1.26817e14	0.0443504
$647$	3.01143e15	1.04424	0.522118	−	0.852873i	$-0.325142\pi$
$647$	3.01143e15	1.04424	0.522118	+	0.852873i	$0.325142\pi$
$648$	−2.43023e15	−0.835575
$649$	−8.30461e15	−2.83122
$650$	−1.06550e15	−0.360189
$651$	2.08442e15	0.698700
$652$	−2.22713e15	−0.740260
$653$	−2.94129e15	−0.969429	−0.484715	−	0.874672i	$-0.661077\pi$
$653$	−2.94129e15	−0.969429	−0.484715	+	0.874672i	$0.661077\pi$
$654$	−7.34688e14	−0.240118
$655$	3.39762e13	0.0110115
$656$	7.21459e14	0.231868
$657$	1.05020e15	0.334705
$658$	−2.97343e15	−0.939758
$659$	4.13211e15	1.29510	0.647548	−	0.762025i	$-0.275795\pi$
$659$	4.13211e15	1.29510	0.647548	+	0.762025i	$0.275795\pi$
$660$	5.82199e14	0.180959
$661$	1.72957e15	0.533128	0.266564	−	0.963817i	$-0.414112\pi$
$661$	1.72957e15	0.533128	0.266564	+	0.963817i	$0.414112\pi$
$662$	2.73093e15	0.834817
$663$	5.10215e14	0.154678
$664$	1.80806e15	0.543610
$665$	−6.98189e14	−0.208187
$666$	−1.83911e15	−0.543877
$667$	−2.76559e14	−0.0811140
$668$	−6.31701e14	−0.183756
$669$	5.07869e14	0.146524
$670$	4.34444e15	1.24315
$671$	4.46531e15	1.26730
$672$	1.09654e15	0.308670
$673$	−1.26135e15	−0.352170	−0.176085	−	0.984375i	$-0.556343\pi$
$673$	−1.26135e15	−0.352170	−0.176085	+	0.984375i	$0.556343\pi$
$674$	7.86824e14	0.217895
$675$	5.69788e14	0.156510
$676$	−2.20536e15	−0.600860
$677$	−4.79653e14	−0.129625	−0.0648125	−	0.997897i	$-0.520645\pi$
$677$	−4.79653e14	−0.129625	−0.0648125	+	0.997897i	$0.520645\pi$
$678$	8.35119e14	0.223864
$679$	6.09576e15	1.62085
$680$	1.20035e15	0.316598
$681$	−1.89960e15	−0.496995
$682$	9.70702e15	2.51925
$683$	−4.53770e15	−1.16821	−0.584107	−	0.811677i	$-0.698555\pi$
$683$	−4.53770e15	−1.16821	−0.584107	+	0.811677i	$0.698555\pi$
$684$	2.32232e14	0.0593081
$685$	1.31778e15	0.333846
$686$	1.22671e15	0.308290
$687$	4.49067e13	0.0111956
$688$	−6.42995e14	−0.159027
$689$	5.18498e15	1.27216
$690$	−3.30949e14	−0.0805547
$691$	4.63998e15	1.12044	0.560218	−	0.828345i	$-0.310717\pi$
$691$	4.63998e15	1.12044	0.560218	+	0.828345i	$0.310717\pi$
$692$	1.98394e15	0.475274
$693$	−1.13838e16	−2.70555
$694$	−4.06040e15	−0.957395
$695$	4.83024e15	1.12993
$696$	2.43779e14	0.0565778
$697$	−7.67094e14	−0.176632
$698$	−6.61851e14	−0.151201
$699$	8.49091e14	0.192455
$700$	7.60808e14	0.171094
$701$	4.35445e15	0.971593	0.485797	−	0.874072i	$-0.338530\pi$
$701$	4.35445e15	0.971593	0.485797	+	0.874072i	$0.338530\pi$
$702$	−3.02336e15	−0.669323
$703$	5.66216e14	0.124374
$704$	9.17795e15	2.00030
$705$	8.76119e14	0.189462
$706$	1.20914e15	0.259449
$707$	−4.47809e15	−0.953423
$708$	7.55135e14	0.159530
$709$	4.43145e15	0.928948	0.464474	−	0.885587i	$-0.346243\pi$
$709$	4.43145e15	0.928948	0.464474	+	0.885587i	$0.346243\pi$
$710$	−2.64100e15	−0.549348
$711$	−6.08263e14	−0.125548
$712$	1.70963e15	0.350156
$713$	3.55634e15	0.722787
$714$	5.65258e14	0.114000
$715$	−1.30813e16	−2.61799
$716$	2.91277e15	0.578475
$717$	−1.53549e15	−0.302616
$718$	−4.19713e15	−0.820858
$719$	4.19195e15	0.813594	0.406797	−	0.913519i	$-0.366646\pi$
$719$	4.19195e15	0.813594	0.406797	+	0.913519i	$0.366646\pi$
$720$	−1.83135e15	−0.352729
$721$	1.01302e16	1.93630
$722$	−3.99996e15	−0.758755
$723$	−1.70830e15	−0.321591
$724$	7.70427e14	0.143936
$725$	2.90656e14	0.0538915
$726$	3.34498e15	0.615519
$727$	1.09105e15	0.199253	0.0996266	−	0.995025i	$-0.468235\pi$
$727$	1.09105e15	0.199253	0.0996266	+	0.995025i	$0.468235\pi$
$728$	−1.43374e16	−2.59866
$729$	−3.10074e15	−0.557782
$730$	1.33699e15	0.238700
$731$	6.83666e14	0.121143
$732$	−4.06029e14	−0.0714079
$733$	8.14746e15	1.42217	0.711083	−	0.703108i	$-0.248205\pi$
$733$	8.14746e15	1.42217	0.711083	+	0.703108i	$0.248205\pi$
$734$	2.39670e15	0.415226
$735$	−1.73674e15	−0.298644
$736$	1.87087e15	0.319312
$737$	−2.18083e16	−3.69446
$738$	2.17955e15	0.366486
$739$	−3.21859e15	−0.537182	−0.268591	−	0.963254i	$-0.586558\pi$
$739$	−3.21859e15	−0.537182	−0.268591	+	0.963254i	$0.586558\pi$
$740$	1.50901e15	0.249987
$741$	4.46320e14	0.0733915
$742$	5.74434e15	0.937602
$743$	−2.98371e15	−0.483412	−0.241706	−	0.970349i	$-0.577707\pi$
$743$	−2.98371e15	−0.483412	−0.241706	+	0.970349i	$0.577707\pi$
$744$	−3.13482e15	−0.504151
$745$	−3.83819e15	−0.612726
$746$	−1.74076e15	−0.275851
$747$	2.93300e15	0.461369
$748$	−1.69658e15	−0.264920
$749$	7.85026e15	1.21684
$750$	1.54630e15	0.237935
$751$	−6.72656e15	−1.02748	−0.513740	−	0.857946i	$-0.671740\pi$
$751$	−6.72656e15	−1.02748	−0.513740	+	0.857946i	$0.671740\pi$
$752$	2.40120e15	0.364109
$753$	−2.70548e15	−0.407261
$754$	−1.54225e15	−0.230469
$755$	3.42174e15	0.507620
$756$	2.15879e15	0.317937
$757$	6.08693e15	0.889961	0.444981	−	0.895540i	$-0.353211\pi$
$757$	6.08693e15	0.889961	0.444981	+	0.895540i	$0.353211\pi$
$758$	1.37875e15	0.200127
$759$	1.66130e15	0.239397
$760$	1.05002e15	0.150219
$761$	5.36699e15	0.762281	0.381141	−	0.924517i	$-0.375531\pi$
$761$	5.36699e15	0.762281	0.381141	+	0.924517i	$0.375531\pi$
$762$	−1.79703e15	−0.253398
$763$	−1.17870e16	−1.65013
$764$	1.33092e14	0.0184986
$765$	1.94718e15	0.268701
$766$	1.73868e14	0.0238211
$767$	−1.69669e16	−2.30796
$768$	−2.01933e15	−0.272722
$769$	6.68797e15	0.896808	0.448404	−	0.893831i	$-0.351993\pi$
$769$	6.68797e15	0.896808	0.448404	+	0.893831i	$0.351993\pi$
$770$	−1.44925e16	−1.92950
$771$	−3.76122e15	−0.497198
$772$	4.82876e15	0.633783
$773$	−1.00049e16	−1.30385	−0.651925	−	0.758283i	$-0.726038\pi$
$773$	−1.00049e16	−1.30385	−0.651925	+	0.758283i	$0.726038\pi$
$774$	−1.94251e15	−0.251355
$775$	−3.73761e15	−0.480214
$776$	−9.16756e15	−1.16954
$777$	2.52379e15	0.319696
$778$	−6.53785e15	−0.822331
$779$	−6.71028e14	−0.0838079
$780$	1.18948e15	0.147515
$781$	1.32573e16	1.63258
$782$	9.64414e14	0.117931
$783$	8.24735e14	0.100144
$784$	−4.75993e15	−0.573934
$785$	−3.11774e15	−0.373299
$786$	−2.40625e13	−0.00286099
$787$	−3.79413e15	−0.447972	−0.223986	−	0.974592i	$-0.571907\pi$
$787$	−3.79413e15	−0.447972	−0.223986	+	0.974592i	$0.571907\pi$
$788$	6.82933e14	0.0800726
$789$	4.36683e15	0.508444
$790$	−7.74367e14	−0.0895361
$791$	1.33982e16	1.53843
$792$	1.71204e16	1.95220
$793$	9.12296e15	1.03308
$794$	8.94874e15	1.00635
$795$	−1.69256e15	−0.189028
$796$	−2.85396e15	−0.316538
$797$	1.00861e14	0.0111097	0.00555483	−	0.999985i	$-0.498232\pi$
$797$	1.00861e14	0.0111097	0.00555483	+	0.999985i	$0.498232\pi$
$798$	4.94469e14	0.0540908
$799$	−2.55309e15	−0.277369
$800$	−1.96623e15	−0.212148
$801$	2.77333e15	0.297182
$802$	−7.14767e15	−0.760686
$803$	−6.71144e15	−0.709382
$804$	1.98302e15	0.208171
$805$	−5.30958e15	−0.553584
$806$	1.98322e16	2.05365
$807$	−2.00760e14	−0.0206478
$808$	6.73470e15	0.687949
$809$	−8.11460e13	−0.00823285	−0.00411643	−	0.999992i	$-0.501310\pi$
$809$	−8.11460e13	−0.00823285	−0.00411643	+	0.999992i	$0.501310\pi$
$810$	−5.01885e15	−0.505751
$811$	1.57478e16	1.57618	0.788088	−	0.615563i	$-0.211071\pi$
$811$	1.57478e16	1.57618	0.788088	+	0.615563i	$0.211071\pi$
$812$	1.10122e15	0.109476
$813$	−8.74856e14	−0.0863851
$814$	1.17531e16	1.15271
$815$	−1.63351e16	−1.59131
$816$	−4.56475e14	−0.0441694
$817$	5.98049e14	0.0574798
$818$	1.58327e16	1.51151
$819$	−2.32580e16	−2.20552
$820$	−1.78834e15	−0.168451
$821$	−6.05019e15	−0.566085	−0.283043	−	0.959107i	$-0.591344\pi$
$821$	−6.05019e15	−0.566085	−0.283043	+	0.959107i	$0.591344\pi$
$822$	−9.33276e14	−0.0867391
$823$	2.94991e15	0.272339	0.136170	−	0.990686i	$-0.456521\pi$
$823$	2.94991e15	0.272339	0.136170	+	0.990686i	$0.456521\pi$
$824$	−1.52350e16	−1.39715
$825$	−1.74598e15	−0.159054
$826$	−1.87973e16	−1.70101
$827$	−8.24061e14	−0.0740763	−0.0370381	−	0.999314i	$-0.511792\pi$
$827$	−8.24061e14	−0.0740763	−0.0370381	+	0.999314i	$0.511792\pi$
$828$	1.76608e15	0.157704
$829$	1.91429e16	1.69808	0.849038	−	0.528332i	$-0.177182\pi$
$829$	1.91429e16	1.69808	0.849038	+	0.528332i	$0.177182\pi$
$830$	3.73394e15	0.329032
$831$	−1.91578e15	−0.167703
$832$	1.87512e16	1.63061
$833$	5.06101e15	0.437210
$834$	−3.42085e15	−0.293576
$835$	−4.63328e15	−0.395014
$836$	−1.48411e15	−0.125699
$837$	−1.06055e16	−0.892359
$838$	3.03427e15	0.253637
$839$	−7.68261e15	−0.637996	−0.318998	−	0.947755i	$-0.603346\pi$
$839$	−7.68261e15	−0.637996	−0.318998	+	0.947755i	$0.603346\pi$
$840$	4.68026e15	0.386130
$841$	4.20707e14	0.0344828
$842$	−1.02886e15	−0.0837796
$843$	−5.11453e15	−0.413765
$844$	2.80517e15	0.225463
$845$	−1.61755e16	−1.29165
$846$	7.25411e15	0.575503
$847$	5.36652e16	4.22994
$848$	−4.63886e15	−0.363273
$849$	1.79611e15	0.139747
$850$	−1.01357e15	−0.0783520
$851$	4.30596e15	0.330717
$852$	−1.20548e15	−0.0919907
$853$	−8.47059e15	−0.642235	−0.321118	−	0.947039i	$-0.604058\pi$
$853$	−8.47059e15	−0.642235	−0.321118	+	0.947039i	$0.604058\pi$
$854$	1.01072e16	0.761396
$855$	1.70333e15	0.127493
$856$	−1.18062e16	−0.878020
$857$	7.38562e15	0.545748	0.272874	−	0.962050i	$-0.412026\pi$
$857$	7.38562e15	0.545748	0.272874	+	0.962050i	$0.412026\pi$
$858$	9.26438e15	0.680199
$859$	2.36806e16	1.72755	0.863774	−	0.503880i	$-0.168094\pi$
$859$	2.36806e16	1.72755	0.863774	+	0.503880i	$0.168094\pi$
$860$	1.59385e15	0.115533
$861$	−2.99096e15	−0.215424
$862$	3.43922e15	0.246133
$863$	−7.38744e15	−0.525333	−0.262667	−	0.964887i	$-0.584602\pi$
$863$	−7.38744e15	−0.525333	−0.262667	+	0.964887i	$0.584602\pi$
$864$	−5.57917e15	−0.394225
$865$	1.45514e16	1.02168
$866$	−8.14205e15	−0.568049
$867$	−3.56372e15	−0.247058
$868$	−1.41609e16	−0.975512
$869$	3.88719e15	0.266089
$870$	5.03446e14	0.0342450
$871$	−4.45560e16	−3.01166
$872$	1.77267e16	1.19066
$873$	−1.48715e16	−0.992602
$874$	8.43637e14	0.0559555
$875$	2.48082e16	1.63512
$876$	6.10269e14	0.0399713
$877$	−5.66931e15	−0.369005	−0.184503	−	0.982832i	$-0.559067\pi$
$877$	−5.66931e15	−0.369005	−0.184503	+	0.982832i	$0.559067\pi$
$878$	−1.21816e16	−0.787923
$879$	3.52390e15	0.226509
$880$	1.17035e16	0.747583
$881$	−4.58653e14	−0.0291150	−0.0145575	−	0.999894i	$-0.504634\pi$
$881$	−4.58653e14	−0.0291150	−0.0145575	+	0.999894i	$0.504634\pi$
$882$	−1.43799e16	−0.907149
$883$	−3.87610e15	−0.243002	−0.121501	−	0.992591i	$-0.538771\pi$
$883$	−3.87610e15	−0.243002	−0.121501	+	0.992591i	$0.538771\pi$
$884$	−3.46624e15	−0.215959
$885$	5.53862e15	0.342936
$886$	2.48833e15	0.153117
$887$	−4.58824e15	−0.280586	−0.140293	−	0.990110i	$-0.544804\pi$
$887$	−4.58824e15	−0.280586	−0.140293	+	0.990110i	$0.544804\pi$
$888$	−3.79558e15	−0.230679
$889$	−2.88307e16	−1.74139
$890$	3.53067e15	0.211940
$891$	2.51937e16	1.50302
$892$	−3.45030e15	−0.204574
$893$	−2.23336e15	−0.131606
$894$	2.71826e15	0.159197
$895$	2.13640e16	1.24353
$896$	1.76602e15	0.102165
$897$	3.39417e15	0.195153
$898$	2.32254e16	1.32722
$899$	−5.40997e15	−0.307268
$900$	−1.85610e15	−0.104777
$901$	4.93228e15	0.276733
$902$	−1.39287e16	−0.776739
$903$	2.66567e15	0.147749
$904$	−2.01499e16	−1.11006
$905$	5.65078e15	0.309415
$906$	−2.42333e15	−0.131889
$907$	2.47879e16	1.34091	0.670454	−	0.741951i	$-0.266099\pi$
$907$	2.47879e16	1.34091	0.670454	+	0.741951i	$0.266099\pi$
$908$	1.29052e16	0.693895
$909$	1.09249e16	0.583871
$910$	−2.96093e16	−1.57290
$911$	−3.34296e16	−1.76514	−0.882572	−	0.470178i	$-0.844190\pi$
$911$	−3.34296e16	−1.76514	−0.882572	+	0.470178i	$0.844190\pi$
$912$	−3.99310e14	−0.0209574
$913$	−1.87437e16	−0.977838
$914$	−2.12524e16	−1.10206
$915$	−2.97806e15	−0.153503
$916$	−3.05081e14	−0.0156311
$917$	−3.86047e14	−0.0196612
$918$	−2.87601e15	−0.145598
$919$	5.65963e15	0.284808	0.142404	−	0.989809i	$-0.454517\pi$
$919$	5.65963e15	0.284808	0.142404	+	0.989809i	$0.454517\pi$
$920$	7.98521e15	0.399442
$921$	8.25669e15	0.410561
$922$	5.72209e15	0.282836
$923$	2.70857e16	1.33086
$924$	−6.61511e15	−0.323103
$925$	−4.52544e15	−0.219726
$926$	−5.01743e15	−0.242170
$927$	−2.47140e16	−1.18578
$928$	−2.84600e15	−0.135744
$929$	−4.70851e15	−0.223253	−0.111627	−	0.993750i	$-0.535606\pi$
$929$	−4.70851e15	−0.223253	−0.111627	+	0.993750i	$0.535606\pi$
$930$	−6.47393e15	−0.305149
$931$	4.42720e15	0.207447
$932$	−5.76845e15	−0.268702
$933$	−1.14594e16	−0.530656
$934$	−1.12670e16	−0.518680
$935$	−1.24437e16	−0.569491
$936$	3.49782e16	1.59140
$937$	3.72927e16	1.68677	0.843385	−	0.537309i	$-0.180559\pi$
$937$	3.72927e16	1.68677	0.843385	+	0.537309i	$0.180559\pi$
$938$	−4.93627e16	−2.21965
$939$	3.19650e15	0.142894
$940$	−5.95207e15	−0.264524
$941$	4.47904e16	1.97898	0.989490	−	0.144598i	$-0.0461889\pi$
$941$	4.47904e16	1.97898	0.989490	+	0.144598i	$0.0461889\pi$
$942$	2.20803e15	0.0969897
$943$	−5.10303e15	−0.222851
$944$	1.51798e16	0.659054
$945$	1.58339e16	0.683459
$946$	1.24139e16	0.532728
$947$	−2.37450e16	−1.01309	−0.506543	−	0.862215i	$-0.669077\pi$
$947$	−2.37450e16	−1.01309	−0.506543	+	0.862215i	$0.669077\pi$
$948$	−3.53460e14	−0.0149932
$949$	−1.37120e16	−0.578277
$950$	−8.86639e14	−0.0371764
$951$	9.82964e15	0.409774
$952$	−1.36387e16	−0.565287
$953$	−1.51068e16	−0.622533	−0.311266	−	0.950323i	$-0.600753\pi$
$953$	−1.51068e16	−0.622533	−0.311266	+	0.950323i	$0.600753\pi$
$954$	−1.40141e16	−0.574183
$955$	9.76177e14	0.0397658
$956$	1.04316e16	0.422507
$957$	−2.52721e15	−0.101771
$958$	−2.38300e16	−0.954144
$959$	−1.49730e16	−0.596084
$960$	−6.12107e15	−0.242290
$961$	4.41596e16	1.73799
$962$	2.40125e16	0.939667
$963$	−1.91518e16	−0.745188
$964$	1.16056e16	0.448999
$965$	3.54171e16	1.36242
$966$	3.76033e15	0.143831
$967$	−4.03014e16	−1.53276	−0.766381	−	0.642387i	$-0.777944\pi$
$967$	−4.03014e16	−1.53276	−0.766381	+	0.642387i	$0.777944\pi$
$968$	−8.07084e16	−3.05214
$969$	4.24567e14	0.0159649
$970$	−1.89326e16	−0.707889
$971$	−2.66454e16	−0.990642	−0.495321	−	0.868710i	$-0.664950\pi$
$971$	−2.66454e16	−0.990642	−0.495321	+	0.868710i	$0.664950\pi$
$972$	−8.00802e15	−0.296047
$973$	−5.48825e16	−2.01750
$974$	3.14531e16	1.14971
$975$	−3.56717e15	−0.129658
$976$	−8.16206e15	−0.295002
$977$	6.22626e15	0.223773	0.111886	−	0.993721i	$-0.464311\pi$
$977$	6.22626e15	0.223773	0.111886	+	0.993721i	$0.464311\pi$
$978$	1.15688e16	0.413452
$979$	−1.77234e16	−0.629856
$980$	1.17988e16	0.416962
$981$	2.87560e16	1.01053
$982$	2.52757e16	0.883263
$983$	1.34179e16	0.466272	0.233136	−	0.972444i	$-0.425101\pi$
$983$	1.34179e16	0.466272	0.233136	+	0.972444i	$0.425101\pi$
$984$	4.49818e15	0.155440
$985$	5.00904e15	0.172130
$986$	−1.46709e15	−0.0501340
$987$	−9.95471e15	−0.338286
$988$	−3.03215e15	−0.102468
$989$	4.54803e15	0.152842
$990$	3.53565e16	1.18162
$991$	1.43337e16	0.476380	0.238190	−	0.971219i	$-0.423446\pi$
$991$	1.43337e16	0.476380	0.238190	+	0.971219i	$0.423446\pi$
$992$	3.65974e16	1.20958
$993$	9.14282e15	0.300510
$994$	3.00077e16	0.980863
$995$	−2.09326e16	−0.680451
$996$	1.70436e15	0.0550979
$997$	−1.33142e16	−0.428047	−0.214024	−	0.976829i	$-0.568657\pi$
$997$	−1.33142e16	−0.428047	−0.214024	+	0.976829i	$0.568657\pi$
$998$	−2.92887e16	−0.936445
$999$	−1.28409e16	−0.408306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.12.a.b.1.10	✓	14
3.2	odd	2		261.12.a.e.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.b.1.10	✓	14	1.1	even	1	trivial
261.12.a.e.1.5		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)

\(f(q)\)	\(=\)	\(q+35.2896 q^{2} +118.146 q^{3} -802.642 q^{4} -5887.06 q^{5} +4169.31 q^{6} +66890.4 q^{7} -100598. q^{8} -163189. q^{9} +O(q^{10})\)	\(q+35.2896 q^{2} +118.146 q^{3} -802.642 q^{4} -5887.06 q^{5} +4169.31 q^{6} +66890.4 q^{7} -100598. q^{8} -163189. q^{9} -207752. q^{10} +1.04288e6 q^{11} -94828.6 q^{12} +2.13068e6 q^{13} +2.36054e6 q^{14} -695530. q^{15} -1.90626e6 q^{16} +2.02683e6 q^{17} -5.75887e6 q^{18} +1.77301e6 q^{19} +4.72520e6 q^{20} +7.90280e6 q^{21} +3.68028e7 q^{22} +1.34834e7 q^{23} -1.18852e7 q^{24} -1.41706e7 q^{25} +7.51909e7 q^{26} -4.02091e7 q^{27} -5.36891e7 q^{28} -2.05111e7 q^{29} -2.45450e7 q^{30} +2.63758e8 q^{31} +1.38754e8 q^{32} +1.23211e8 q^{33} +7.15262e7 q^{34} -3.93788e8 q^{35} +1.30982e8 q^{36} +3.19353e8 q^{37} +6.25688e7 q^{38} +2.51730e8 q^{39} +5.92227e8 q^{40} -3.78469e8 q^{41} +2.78887e8 q^{42} +3.37307e8 q^{43} -8.37059e8 q^{44} +9.60702e8 q^{45} +4.75823e8 q^{46} -1.25964e9 q^{47} -2.25216e8 q^{48} +2.49700e9 q^{49} -5.00076e8 q^{50} +2.39461e8 q^{51} -1.71017e9 q^{52} +2.43349e9 q^{53} -1.41897e9 q^{54} -6.13949e9 q^{55} -6.72905e9 q^{56} +2.09473e8 q^{57} -7.23831e8 q^{58} -7.96316e9 q^{59} +5.58262e8 q^{60} +4.28172e9 q^{61} +9.30791e9 q^{62} -1.09158e10 q^{63} +8.80059e9 q^{64} -1.25434e10 q^{65} +4.34809e9 q^{66} -2.09117e10 q^{67} -1.62682e9 q^{68} +1.59300e9 q^{69} -1.38966e10 q^{70} +1.27122e10 q^{71} +1.64165e10 q^{72} -6.43549e9 q^{73} +1.12699e10 q^{74} -1.67420e9 q^{75} -1.42309e9 q^{76} +6.97586e10 q^{77} +8.88346e9 q^{78} +3.72736e9 q^{79} +1.12223e10 q^{80} +2.41578e10 q^{81} -1.33560e10 q^{82} -1.79731e10 q^{83} -6.34312e9 q^{84} -1.19321e10 q^{85} +1.19034e10 q^{86} -2.42330e9 q^{87} -1.04912e11 q^{88} -1.69946e10 q^{89} +3.39028e10 q^{90} +1.42522e11 q^{91} -1.08223e10 q^{92} +3.11618e10 q^{93} -4.44523e10 q^{94} -1.04378e10 q^{95} +1.63931e10 q^{96} +9.11305e10 q^{97} +8.81183e10 q^{98} -1.70186e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9}+O(q^{10}) \) 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

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Groups

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