LMFDB - Embedded newform 29.12.a.b.1.5

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			1.5
Root			$-55.2092$ 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)

$f(q)$	$=$	$q-55.2092 q^{2} -283.770 q^{3} +1000.05 q^{4} +5132.07 q^{5} +15666.7 q^{6} -31764.7 q^{7} +57856.2 q^{8} -96621.5 q^{9} +O(q^{10})$	\(q-55.2092 q^{2} -283.770 q^{3} +1000.05 q^{4} +5132.07 q^{5} +15666.7 q^{6} -31764.7 q^{7} +57856.2 q^{8} -96621.5 q^{9} -283337. q^{10} -180170. q^{11} -283786. q^{12} -2.59617e6 q^{13} +1.75370e6 q^{14} -1.45633e6 q^{15} -5.24231e6 q^{16} +5.77750e6 q^{17} +5.33440e6 q^{18} -1.08083e7 q^{19} +5.13235e6 q^{20} +9.01387e6 q^{21} +9.94702e6 q^{22} +4.47086e6 q^{23} -1.64179e7 q^{24} -2.24900e7 q^{25} +1.43333e8 q^{26} +7.76873e7 q^{27} -3.17664e7 q^{28} -2.05111e7 q^{29} +8.04027e7 q^{30} +2.76138e8 q^{31} +1.70934e8 q^{32} +5.11268e7 q^{33} -3.18971e8 q^{34} -1.63019e8 q^{35} -9.66268e7 q^{36} +6.00935e8 q^{37} +5.96716e8 q^{38} +7.36716e8 q^{39} +2.96922e8 q^{40} -1.56523e8 q^{41} -4.97649e8 q^{42} -1.36728e9 q^{43} -1.80180e8 q^{44} -4.95868e8 q^{45} -2.46833e8 q^{46} -2.06833e9 q^{47} +1.48761e9 q^{48} -9.68330e8 q^{49} +1.24165e9 q^{50} -1.63948e9 q^{51} -2.59631e9 q^{52} +4.30204e9 q^{53} -4.28905e9 q^{54} -9.24644e8 q^{55} -1.83779e9 q^{56} +3.06706e9 q^{57} +1.13240e9 q^{58} +8.75599e9 q^{59} -1.45641e9 q^{60} +3.83225e9 q^{61} -1.52454e10 q^{62} +3.06915e9 q^{63} +1.29912e9 q^{64} -1.33237e10 q^{65} -2.82267e9 q^{66} +6.61153e9 q^{67} +5.77782e9 q^{68} -1.26870e9 q^{69} +9.00013e9 q^{70} +1.75093e10 q^{71} -5.59015e9 q^{72} -1.99968e10 q^{73} -3.31772e10 q^{74} +6.38199e9 q^{75} -1.08089e10 q^{76} +5.72304e9 q^{77} -4.06735e10 q^{78} +4.13459e10 q^{79} -2.69039e10 q^{80} -4.92913e9 q^{81} +8.64150e9 q^{82} +9.08317e9 q^{83} +9.01437e9 q^{84} +2.96505e10 q^{85} +7.54866e10 q^{86} +5.82045e9 q^{87} -1.04239e10 q^{88} +5.85488e10 q^{89} +2.73765e10 q^{90} +8.24666e10 q^{91} +4.47111e9 q^{92} -7.83598e10 q^{93} +1.14191e11 q^{94} -5.54688e10 q^{95} -4.85060e10 q^{96} +7.42488e10 q^{97} +5.34607e10 q^{98} +1.74083e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−55.2092	−1.21996	−0.609981	−	0.792416i	$-0.708823\pi$
$2$	−55.2092	−1.21996	−0.609981	+	0.792416i	$0.708823\pi$
$3$	−283.770	−0.674217	−0.337109	−	0.941466i	$-0.609449\pi$
$3$	−283.770	−0.674217	−0.337109	+	0.941466i	$0.609449\pi$
$4$	1000.05	0.488308
$5$	5132.07	0.734442	0.367221	−	0.930134i	$-0.380309\pi$
$5$	5132.07	0.734442	0.367221	+	0.930134i	$0.380309\pi$
$6$	15666.7	0.822519
$7$	−31764.7	−0.714341	−0.357171	−	0.934039i	$-0.616259\pi$
$7$	−31764.7	−0.714341	−0.357171	+	0.934039i	$0.616259\pi$
$8$	57856.2	0.624245
$9$	−96621.5	−0.545431
$10$	−283337.	−0.895992
$11$	−180170.	−0.337304	−0.168652	−	0.985676i	$-0.553941\pi$
$11$	−180170.	−0.337304	−0.168652	+	0.985676i	$0.553941\pi$
$12$	−283786.	−0.329226
$13$	−2.59617e6	−1.93930	−0.969650	−	0.244498i	$-0.921377\pi$
$13$	−2.59617e6	−1.93930	−0.969650	+	0.244498i	$0.921377\pi$
$14$	1.75370e6	0.871469
$15$	−1.45633e6	−0.495173
$16$	−5.24231e6	−1.24986
$17$	5.77750e6	0.986895	0.493448	−	0.869775i	$-0.335736\pi$
$17$	5.77750e6	0.986895	0.493448	+	0.869775i	$0.335736\pi$
$18$	5.33440e6	0.665406
$19$	−1.08083e7	−1.00141	−0.500704	−	0.865618i	$-0.666926\pi$
$19$	−1.08083e7	−1.00141	−0.500704	+	0.865618i	$0.666926\pi$
$20$	5.13235e6	0.358634
$21$	9.01387e6	0.481621
$22$	9.94702e6	0.411499
$23$	4.47086e6	0.144840	0.0724200	−	0.997374i	$-0.476928\pi$
$23$	4.47086e6	0.144840	0.0724200	+	0.997374i	$0.476928\pi$
$24$	−1.64179e7	−0.420877
$25$	−2.24900e7	−0.460595
$26$	1.43333e8	2.36587
$27$	7.76873e7	1.04196
$28$	−3.17664e7	−0.348818
$29$	−2.05111e7	−0.185695
$29$	−2.05111e7	−0.185695
$30$	8.04027e7	0.604093
$31$	2.76138e8	1.73236	0.866178	−	0.499735i	$-0.166569\pi$
$31$	2.76138e8	1.73236	0.866178	+	0.499735i	$0.166569\pi$
$32$	1.70934e8	0.900541
$33$	5.11268e7	0.227416
$34$	−3.18971e8	−1.20398
$35$	−1.63019e8	−0.524642
$36$	−9.66268e7	−0.266338
$37$	6.00935e8	1.42468	0.712342	−	0.701833i	$-0.247635\pi$
$37$	6.00935e8	1.42468	0.712342	+	0.701833i	$0.247635\pi$
$38$	5.96716e8	1.22168
$39$	7.36716e8	1.30751
$40$	2.96922e8	0.458472
$41$	−1.56523e8	−0.210992	−0.105496	−	0.994420i	$-0.533643\pi$
$41$	−1.56523e8	−0.210992	−0.105496	+	0.994420i	$0.533643\pi$
$42$	−4.97649e8	−0.587559
$43$	−1.36728e9	−1.41834	−0.709172	−	0.705035i	$-0.750931\pi$
$43$	−1.36728e9	−1.41834	−0.709172	+	0.705035i	$0.750931\pi$
$44$	−1.80180e8	−0.164708
$45$	−4.95868e8	−0.400588
$46$	−2.46833e8	−0.176699
$47$	−2.06833e9	−1.31547	−0.657736	−	0.753249i	$-0.728486\pi$
$47$	−2.06833e9	−1.31547	−0.657736	+	0.753249i	$0.728486\pi$
$48$	1.48761e9	0.842679
$49$	−9.68330e8	−0.489717
$50$	1.24165e9	0.561908
$51$	−1.63948e9	−0.665382
$52$	−2.59631e9	−0.946975
$53$	4.30204e9	1.41305	0.706524	−	0.707689i	$-0.250262\pi$
$53$	4.30204e9	1.41305	0.706524	+	0.707689i	$0.250262\pi$
$54$	−4.28905e9	−1.27115
$55$	−9.24644e8	−0.247731
$56$	−1.83779e9	−0.445924
$57$	3.06706e9	0.675167
$58$	1.13240e9	0.226541
$59$	8.75599e9	1.59448	0.797240	−	0.603662i	$-0.206292\pi$
$59$	8.75599e9	1.59448	0.797240	+	0.603662i	$0.206292\pi$
$60$	−1.45641e9	−0.241797
$61$	3.83225e9	0.580951	0.290476	−	0.956882i	$-0.406186\pi$
$61$	3.83225e9	0.580951	0.290476	+	0.956882i	$0.406186\pi$
$62$	−1.52454e10	−2.11341
$63$	3.06915e9	0.389624
$64$	1.29912e9	0.151237
$65$	−1.33237e10	−1.42430
$66$	−2.82267e9	−0.277439
$67$	6.61153e9	0.598261	0.299130	−	0.954212i	$-0.403303\pi$
$67$	6.61153e9	0.598261	0.299130	+	0.954212i	$0.403303\pi$
$68$	5.77782e9	0.481909
$69$	−1.26870e9	−0.0976536
$70$	9.00013e9	0.640044
$71$	1.75093e10	1.15172	0.575860	−	0.817548i	$-0.304667\pi$
$71$	1.75093e10	1.15172	0.575860	+	0.817548i	$0.304667\pi$
$72$	−5.59015e9	−0.340483
$73$	−1.99968e10	−1.12898	−0.564488	−	0.825441i	$-0.690926\pi$
$73$	−1.99968e10	−1.12898	−0.564488	+	0.825441i	$0.690926\pi$
$74$	−3.31772e10	−1.73806
$75$	6.38199e9	0.310541
$76$	−1.08089e10	−0.488996
$77$	5.72304e9	0.240950
$78$	−4.06735e10	−1.59511
$79$	4.13459e10	1.51176	0.755880	−	0.654710i	$-0.227209\pi$
$79$	4.13459e10	1.51176	0.755880	+	0.654710i	$0.227209\pi$
$80$	−2.69039e10	−0.917952
$81$	−4.92913e9	−0.157073
$82$	8.64150e9	0.257403
$83$	9.08317e9	0.253109	0.126555	−	0.991960i	$-0.459608\pi$
$83$	9.08317e9	0.253109	0.126555	+	0.991960i	$0.459608\pi$
$84$	9.01437e9	0.235179
$85$	2.96505e10	0.724817
$86$	7.54866e10	1.73033
$87$	5.82045e9	0.125199
$88$	−1.04239e10	−0.210561
$89$	5.85488e10	1.11141	0.555703	−	0.831381i	$-0.312449\pi$
$89$	5.85488e10	1.11141	0.555703	+	0.831381i	$0.312449\pi$
$90$	2.73765e10	0.488702
$91$	8.24666e10	1.38532
$92$	4.47111e9	0.0707265
$93$	−7.83598e10	−1.16798
$94$	1.14191e11	1.60483
$95$	−5.54688e10	−0.735477
$96$	−4.85060e10	−0.607160
$97$	7.42488e10	0.877900	0.438950	−	0.898512i	$-0.355351\pi$
$97$	7.42488e10	0.877900	0.438950	+	0.898512i	$0.355351\pi$
$98$	5.34607e10	0.597436
$99$	1.74083e10	0.183976
$100$	−2.24912e10	−0.224912
$101$	−9.86172e10	−0.933652	−0.466826	−	0.884349i	$-0.654603\pi$
$101$	−9.86172e10	−0.933652	−0.466826	+	0.884349i	$0.654603\pi$
$102$	9.05145e10	0.811741
$103$	9.15348e9	0.0778003	0.0389002	−	0.999243i	$-0.487615\pi$
$103$	9.15348e9	0.0778003	0.0389002	+	0.999243i	$0.487615\pi$
$104$	−1.50205e11	−1.21060
$105$	4.62598e10	0.353723
$106$	−2.37512e11	−1.72386
$107$	7.21944e10	0.497614	0.248807	−	0.968553i	$-0.419962\pi$
$107$	7.21944e10	0.497614	0.248807	+	0.968553i	$0.419962\pi$
$108$	7.76916e10	0.508796
$109$	−5.99817e10	−0.373399	−0.186699	−	0.982417i	$-0.559779\pi$
$109$	−5.99817e10	−0.373399	−0.186699	+	0.982417i	$0.559779\pi$
$110$	5.10488e10	0.302222
$111$	−1.70528e11	−0.960546
$112$	1.66520e11	0.892829
$113$	−1.92348e11	−0.982099	−0.491050	−	0.871132i	$-0.663387\pi$
$113$	−1.92348e11	−0.982099	−0.491050	+	0.871132i	$0.663387\pi$
$114$	−1.69330e11	−0.823678
$115$	2.29448e10	0.106377
$116$	−2.05123e10	−0.0906765
$117$	2.50846e11	1.05775
$118$	−4.83411e11	−1.94521
$119$	−1.83521e11	−0.704980
$120$	−8.42576e10	−0.309109
$121$	−2.52851e11	−0.886226
$122$	−2.11575e11	−0.708739
$123$	4.44165e10	0.142255
$124$	2.76153e11	0.845924
$125$	−3.66010e11	−1.07272
$126$	−1.69446e11	−0.475327
$127$	4.66587e10	0.125318	0.0626588	−	0.998035i	$-0.480042\pi$
$127$	4.66587e10	0.125318	0.0626588	+	0.998035i	$0.480042\pi$
$128$	−4.21796e11	−1.08504
$129$	3.87994e11	0.956272
$130$	7.35592e11	1.73760
$131$	2.44957e11	0.554749	0.277375	−	0.960762i	$-0.410536\pi$
$131$	2.44957e11	0.554749	0.277375	+	0.960762i	$0.410536\pi$
$132$	5.11296e10	0.111049
$133$	3.43322e11	0.715348
$134$	−3.65017e11	−0.729856
$135$	3.98697e11	0.765256
$136$	3.34264e11	0.616064
$137$	−5.49156e11	−0.972148	−0.486074	−	0.873918i	$-0.661572\pi$
$137$	−5.49156e11	−0.972148	−0.486074	+	0.873918i	$0.661572\pi$
$138$	7.00438e10	0.119134
$139$	6.72642e11	1.09952	0.549759	−	0.835323i	$-0.314720\pi$
$139$	6.72642e11	1.09952	0.549759	+	0.835323i	$0.314720\pi$
$140$	−1.63028e11	−0.256187
$141$	5.86930e11	0.886913
$142$	−9.66672e11	−1.40505
$143$	4.67751e11	0.654134
$144$	5.06520e11	0.681715
$145$	−1.05265e11	−0.136382
$146$	1.10401e12	1.37731
$147$	2.74783e11	0.330175
$148$	6.00968e11	0.695684
$149$	2.13043e11	0.237652	0.118826	−	0.992915i	$-0.462087\pi$
$149$	2.13043e11	0.237652	0.118826	+	0.992915i	$0.462087\pi$
$150$	−3.52344e11	−0.378848
$151$	−5.95297e11	−0.617107	−0.308553	−	0.951207i	$-0.599845\pi$
$151$	−5.95297e11	−0.617107	−0.308553	+	0.951207i	$0.599845\pi$
$152$	−6.25326e11	−0.625124
$153$	−5.58231e11	−0.538284
$154$	−3.15964e11	−0.293950
$155$	1.41716e12	1.27232
$156$	7.36756e11	0.638467
$157$	−6.01302e11	−0.503088	−0.251544	−	0.967846i	$-0.580938\pi$
$157$	−6.01302e11	−0.503088	−0.251544	+	0.967846i	$0.580938\pi$
$158$	−2.28267e12	−1.84429
$159$	−1.22079e12	−0.952701
$160$	8.77245e11	0.661395
$161$	−1.42016e11	−0.103465
$162$	2.72133e11	0.191624
$163$	1.21944e12	0.830099	0.415049	−	0.909799i	$-0.363764\pi$
$163$	1.21944e12	0.830099	0.415049	+	0.909799i	$0.363764\pi$
$164$	−1.56531e11	−0.103029
$165$	2.62386e11	0.167024
$166$	−5.01475e11	−0.308784
$167$	−1.39765e11	−0.0832642	−0.0416321	−	0.999133i	$-0.513256\pi$
$167$	−1.39765e11	−0.0832642	−0.0416321	+	0.999133i	$0.513256\pi$
$168$	5.21509e11	0.300649
$169$	4.94794e12	2.76088
$170$	−1.63698e12	−0.884250
$171$	1.04431e12	0.546200
$172$	−1.36736e12	−0.692589
$173$	3.55880e11	0.174602	0.0873010	−	0.996182i	$-0.472176\pi$
$173$	3.55880e11	0.174602	0.0873010	+	0.996182i	$0.472176\pi$
$174$	−3.21342e11	−0.152738
$175$	7.14388e11	0.329022
$176$	9.44505e11	0.421584
$177$	−2.48469e12	−1.07503
$178$	−3.23243e12	−1.35587
$179$	−2.22178e12	−0.903670	−0.451835	−	0.892102i	$-0.649230\pi$
$179$	−2.22178e12	−0.903670	−0.451835	+	0.892102i	$0.649230\pi$
$180$	−4.95896e11	−0.195610
$181$	1.72574e12	0.660301	0.330151	−	0.943928i	$-0.392900\pi$
$181$	1.72574e12	0.660301	0.330151	+	0.943928i	$0.392900\pi$
$182$	−4.55292e12	−1.69004
$183$	−1.08748e12	−0.391687
$184$	2.58667e11	0.0904156
$185$	3.08404e12	1.04635
$186$	4.32618e12	1.42490
$187$	−1.04093e12	−0.332884
$188$	−2.06844e12	−0.642355
$189$	−2.46772e12	−0.744312
$190$	3.06239e12	0.897254
$191$	5.04167e11	0.143513	0.0717565	−	0.997422i	$-0.477140\pi$
$191$	5.04167e11	0.143513	0.0717565	+	0.997422i	$0.477140\pi$
$192$	−3.68651e11	−0.101967
$193$	−2.67955e12	−0.720273	−0.360137	−	0.932900i	$-0.617270\pi$
$193$	−2.67955e12	−0.720273	−0.360137	+	0.932900i	$0.617270\pi$
$194$	−4.09922e12	−1.07100
$195$	3.78088e12	0.960290
$196$	−9.68383e11	−0.239133
$197$	−2.06337e12	−0.495465	−0.247733	−	0.968828i	$-0.579685\pi$
$197$	−2.06337e12	−0.495465	−0.247733	+	0.968828i	$0.579685\pi$
$198$	−9.61097e11	−0.224444
$199$	2.60929e12	0.592694	0.296347	−	0.955080i	$-0.404232\pi$
$199$	2.60929e12	0.592694	0.296347	+	0.955080i	$0.404232\pi$
$200$	−1.30119e12	−0.287524
$201$	−1.87615e12	−0.403358
$202$	5.44457e12	1.13902
$203$	6.51531e11	0.132650
$204$	−1.63957e12	−0.324911
$205$	−8.03287e11	−0.154962
$206$	−5.05356e11	−0.0949135
$207$	−4.31982e11	−0.0790002
$208$	1.36099e13	2.42386
$209$	1.94732e12	0.337780
$210$	−2.55397e12	−0.431528
$211$	−7.67957e12	−1.26411	−0.632053	−	0.774925i	$-0.717788\pi$
$211$	−7.67957e12	−1.26411	−0.632053	+	0.774925i	$0.717788\pi$
$212$	4.30227e12	0.690002
$213$	−4.96860e12	−0.776509
$214$	−3.98579e12	−0.607070
$215$	−7.01699e12	−1.04169
$216$	4.49469e12	0.650436
$217$	−8.77145e12	−1.23749
$218$	3.31154e12	0.455533
$219$	5.67450e12	0.761175
$220$	−9.24694e11	−0.120969
$221$	−1.49994e13	−1.91389
$222$	9.41469e12	1.17183
$223$	5.72026e11	0.0694606	0.0347303	−	0.999397i	$-0.488943\pi$
$223$	5.72026e11	0.0694606	0.0347303	+	0.999397i	$0.488943\pi$
$224$	−5.42967e12	−0.643294
$225$	2.17302e12	0.251223
$226$	1.06194e13	1.19812
$227$	1.06237e12	0.116986	0.0584928	−	0.998288i	$-0.481371\pi$
$227$	1.06237e12	0.116986	0.0584928	+	0.998288i	$0.481371\pi$
$228$	3.06723e12	0.329689
$229$	8.18231e12	0.858580	0.429290	−	0.903167i	$-0.358764\pi$
$229$	8.18231e12	0.858580	0.429290	+	0.903167i	$0.358764\pi$
$230$	−1.26676e12	−0.129775
$231$	−1.62403e12	−0.162453
$232$	−1.18670e12	−0.115919
$233$	1.03457e13	0.986964	0.493482	−	0.869756i	$-0.335724\pi$
$233$	1.03457e13	0.986964	0.493482	+	0.869756i	$0.335724\pi$
$234$	−1.38490e13	−1.29042
$235$	−1.06148e13	−0.966137
$236$	8.75647e12	0.778598
$237$	−1.17327e13	−1.01925
$238$	1.01320e13	0.860049
$239$	2.12800e13	1.76516	0.882580	−	0.470162i	$-0.155805\pi$
$239$	2.12800e13	1.76516	0.882580	+	0.470162i	$0.155805\pi$
$240$	7.63452e12	0.618899
$241$	−2.96664e12	−0.235056	−0.117528	−	0.993070i	$-0.537497\pi$
$241$	−2.96664e12	−0.235056	−0.117528	+	0.993070i	$0.537497\pi$
$242$	1.39597e13	1.08116
$243$	−1.23633e13	−0.936055
$244$	3.83246e12	0.283683
$245$	−4.96954e12	−0.359669
$246$	−2.45220e12	−0.173545
$247$	2.80601e13	1.94203
$248$	1.59763e13	1.08141
$249$	−2.57753e12	−0.170651
$250$	2.02071e13	1.30868
$251$	2.66256e11	0.0168692	0.00843460	−	0.999964i	$-0.497315\pi$
$251$	2.66256e11	0.0168692	0.00843460	+	0.999964i	$0.497315\pi$
$252$	3.06932e12	0.190256
$253$	−8.05514e11	−0.0488552
$254$	−2.57599e12	−0.152883
$255$	−8.41394e12	−0.488684
$256$	2.06264e13	1.17248
$257$	−3.50604e13	−1.95067	−0.975336	−	0.220724i	$-0.929158\pi$
$257$	−3.50604e13	−1.95067	−0.975336	+	0.220724i	$0.929158\pi$
$258$	−2.14208e13	−1.16662
$259$	−1.90885e13	−1.01771
$260$	−1.33245e13	−0.695499
$261$	1.98182e12	0.101284
$262$	−1.35239e13	−0.676773
$263$	3.22483e13	1.58034	0.790169	−	0.612890i	$-0.209993\pi$
$263$	3.22483e13	1.58034	0.790169	+	0.612890i	$0.209993\pi$
$264$	2.95800e12	0.141964
$265$	2.20783e13	1.03780
$266$	−1.89545e13	−0.872697
$267$	−1.66144e13	−0.749329
$268$	6.61189e12	0.292136
$269$	4.44943e13	1.92605	0.963023	−	0.269419i	$-0.0868315\pi$
$269$	4.44943e13	1.92605	0.963023	+	0.269419i	$0.0868315\pi$
$270$	−2.20117e13	−0.933584
$271$	−3.31612e13	−1.37816	−0.689078	−	0.724687i	$-0.741984\pi$
$271$	−3.31612e13	−1.37816	−0.689078	+	0.724687i	$0.741984\pi$
$272$	−3.02874e13	−1.23348
$273$	−2.34016e13	−0.934007
$274$	3.03185e13	1.18598
$275$	4.05201e12	0.155361
$276$	−1.26877e12	−0.0476850
$277$	−1.64457e13	−0.605916	−0.302958	−	0.953004i	$-0.597974\pi$
$277$	−1.64457e13	−0.605916	−0.302958	+	0.953004i	$0.597974\pi$
$278$	−3.71360e13	−1.34137
$279$	−2.66809e13	−0.944881
$280$	−9.43164e12	−0.327505
$281$	3.83056e13	1.30430	0.652150	−	0.758090i	$-0.273867\pi$
$281$	3.83056e13	1.30430	0.652150	+	0.758090i	$0.273867\pi$
$282$	−3.24039e13	−1.08200
$283$	−5.02772e13	−1.64644	−0.823220	−	0.567723i	$-0.807825\pi$
$283$	−5.02772e13	−1.64644	−0.823220	+	0.567723i	$0.807825\pi$
$284$	1.75102e13	0.562394
$285$	1.57404e13	0.495871
$286$	−2.58242e13	−0.798019
$287$	4.97190e12	0.150721
$288$	−1.65159e13	−0.491183
$289$	−8.92360e11	−0.0260377
$290$	5.81158e12	0.166381
$291$	−2.10696e13	−0.591895
$292$	−1.99979e13	−0.551288
$293$	−3.07537e13	−0.832004	−0.416002	−	0.909364i	$-0.636569\pi$
$293$	−3.07537e13	−0.832004	−0.416002	+	0.909364i	$0.636569\pi$
$294$	−1.51706e13	−0.402802
$295$	4.49364e13	1.17105
$296$	3.47678e13	0.889351
$297$	−1.39969e13	−0.351456
$298$	−1.17619e13	−0.289927
$299$	−1.16071e13	−0.280888
$300$	6.38234e12	0.151640
$301$	4.34313e13	1.01318
$302$	3.28659e13	0.752847
$303$	2.79846e13	0.629484
$304$	5.66603e13	1.25162
$305$	1.96674e13	0.426675
$306$	3.08195e13	0.656686
$307$	6.52000e13	1.36454	0.682270	−	0.731100i	$-0.260993\pi$
$307$	6.52000e13	1.36454	0.682270	+	0.731100i	$0.260993\pi$
$308$	5.72335e12	0.117658
$309$	−2.59748e12	−0.0524543
$310$	−7.82403e13	−1.55218
$311$	4.28860e13	0.835860	0.417930	−	0.908479i	$-0.362756\pi$
$311$	4.28860e13	0.835860	0.417930	+	0.908479i	$0.362756\pi$
$312$	4.26236e13	0.816206
$313$	−2.53027e13	−0.476073	−0.238036	−	0.971256i	$-0.576504\pi$
$313$	−2.53027e13	−0.476073	−0.238036	+	0.971256i	$0.576504\pi$
$314$	3.31974e13	0.613749
$315$	1.57511e13	0.286156
$316$	4.13481e13	0.738205
$317$	−5.50395e13	−0.965715	−0.482857	−	0.875699i	$-0.660401\pi$
$317$	−5.50395e13	−0.965715	−0.482857	+	0.875699i	$0.660401\pi$
$318$	6.73988e13	1.16226
$319$	3.69549e12	0.0626359
$320$	6.66716e12	0.111075
$321$	−2.04866e13	−0.335500
$322$	7.84057e12	0.126224
$323$	−6.24448e13	−0.988286
$324$	−4.92940e12	−0.0767002
$325$	5.83879e13	0.893231
$326$	−6.73245e13	−1.01269
$327$	1.70210e13	0.251752
$328$	−9.05582e12	−0.131711
$329$	6.56999e13	0.939695
$330$	−1.44861e13	−0.203763
$331$	1.36316e14	1.88578	0.942892	−	0.333099i	$-0.108094\pi$
$331$	1.36316e14	1.88578	0.942892	+	0.333099i	$0.108094\pi$
$332$	9.08367e12	0.123595
$333$	−5.80633e13	−0.777067
$334$	7.71632e12	0.101579
$335$	3.39308e13	0.439388
$336$	−4.72535e13	−0.601960
$337$	1.04469e14	1.30925	0.654627	−	0.755952i	$-0.272826\pi$
$337$	1.04469e14	1.30925	0.654627	+	0.755952i	$0.272826\pi$
$338$	−2.73172e14	−3.36817
$339$	5.45825e13	0.662148
$340$	2.96522e13	0.353934
$341$	−4.97518e13	−0.584332
$342$	−5.76556e13	−0.666343
$343$	9.35679e13	1.06417
$344$	−7.91058e13	−0.885395
$345$	−6.51104e12	−0.0717209
$346$	−1.96478e13	−0.213008
$347$	−1.14715e13	−0.122407	−0.0612035	−	0.998125i	$-0.519494\pi$
$347$	−1.14715e13	−0.122407	−0.0612035	+	0.998125i	$0.519494\pi$
$348$	5.82077e12	0.0611357
$349$	−4.63142e12	−0.0478822	−0.0239411	−	0.999713i	$-0.507621\pi$
$349$	−4.63142e12	−0.0478822	−0.0239411	+	0.999713i	$0.507621\pi$
$350$	−3.94408e13	−0.401394
$351$	−2.01690e14	−2.02067
$352$	−3.07971e13	−0.303757
$353$	−1.10731e14	−1.07525	−0.537625	−	0.843184i	$-0.680678\pi$
$353$	−1.10731e14	−1.07525	−0.537625	+	0.843184i	$0.680678\pi$
$354$	1.37178e14	1.31149
$355$	8.98587e13	0.845871
$356$	5.85520e13	0.542709
$357$	5.20777e13	0.475309
$358$	1.22663e14	1.10244
$359$	6.13375e13	0.542883	0.271442	−	0.962455i	$-0.412500\pi$
$359$	6.13375e13	0.542883	0.271442	+	0.962455i	$0.412500\pi$
$360$	−2.86891e13	−0.250065
$361$	3.28472e11	0.00281974
$362$	−9.52765e13	−0.805543
$363$	7.17514e13	0.597509
$364$	8.24711e13	0.676463
$365$	−1.02625e14	−0.829168
$366$	6.00388e13	0.477844
$367$	−4.65753e13	−0.365168	−0.182584	−	0.983190i	$-0.558446\pi$
$367$	−4.65753e13	−0.365168	−0.182584	+	0.983190i	$0.558446\pi$
$368$	−2.34376e13	−0.181030
$369$	1.51235e13	0.115082
$370$	−1.70268e14	−1.27650
$371$	−1.36653e14	−1.00940
$372$	−7.83641e13	−0.570336
$373$	−1.11726e14	−0.801225	−0.400612	−	0.916248i	$-0.631203\pi$
$373$	−1.11726e14	−0.801225	−0.400612	+	0.916248i	$0.631203\pi$
$374$	5.74690e13	0.406106
$375$	1.03863e14	0.723248
$376$	−1.19666e14	−0.821176
$377$	5.32505e13	0.360119
$378$	1.36241e14	0.908033
$379$	−1.39890e14	−0.918904	−0.459452	−	0.888203i	$-0.651954\pi$
$379$	−1.39890e14	−0.918904	−0.459452	+	0.888203i	$0.651954\pi$
$380$	−5.54718e13	−0.359139
$381$	−1.32403e13	−0.0844913
$382$	−2.78347e13	−0.175080
$383$	7.01459e13	0.434919	0.217460	−	0.976069i	$-0.430223\pi$
$383$	7.01459e13	0.434919	0.217460	+	0.976069i	$0.430223\pi$
$384$	1.19693e14	0.731556
$385$	2.93710e13	0.176964
$386$	1.47936e14	0.878706
$387$	1.32109e14	0.773610
$388$	7.42529e13	0.428685
$389$	−2.15723e14	−1.22793	−0.613966	−	0.789333i	$-0.710427\pi$
$389$	−2.15723e14	−1.22793	−0.613966	+	0.789333i	$0.710427\pi$
$390$	−2.08739e14	−1.17152
$391$	2.58304e13	0.142942
$392$	−5.60239e13	−0.305703
$393$	−6.95113e13	−0.374022
$394$	1.13917e14	0.604449
$395$	2.12190e14	1.11030
$396$	1.74092e13	0.0898371
$397$	2.53053e14	1.28784	0.643922	−	0.765091i	$-0.277306\pi$
$397$	2.53053e14	1.28784	0.643922	+	0.765091i	$0.277306\pi$
$398$	−1.44057e14	−0.723064
$399$	−9.74244e13	−0.482300
$400$	1.17899e14	0.575681
$401$	2.18806e14	1.05382	0.526909	−	0.849922i	$-0.323351\pi$
$401$	2.18806e14	1.05382	0.526909	+	0.849922i	$0.323351\pi$
$402$	1.03581e14	0.492081
$403$	−7.16902e14	−3.35956
$404$	−9.86226e13	−0.455910
$405$	−2.52966e13	−0.115361
$406$	−3.59705e13	−0.161828
$407$	−1.08270e14	−0.480552
$408$	−9.48543e13	−0.415361
$409$	2.64970e14	1.14477	0.572385	−	0.819985i	$-0.306018\pi$
$409$	2.64970e14	1.14477	0.572385	+	0.819985i	$0.306018\pi$
$410$	4.43488e13	0.189047
$411$	1.55834e14	0.655439
$412$	9.15398e12	0.0379905
$413$	−2.78131e14	−1.13900
$414$	2.38494e13	0.0963773
$415$	4.66155e13	0.185894
$416$	−4.43774e14	−1.74642
$417$	−1.90876e14	−0.741314
$418$	−1.07510e14	−0.412078
$419$	1.92160e14	0.726918	0.363459	−	0.931610i	$-0.381596\pi$
$419$	1.92160e14	0.726918	0.363459	+	0.931610i	$0.381596\pi$
$420$	4.62624e13	0.172726
$421$	2.25537e14	0.831126	0.415563	−	0.909564i	$-0.363585\pi$
$421$	2.25537e14	0.831126	0.415563	+	0.909564i	$0.363585\pi$
$422$	4.23983e14	1.54216
$423$	1.99845e14	0.717499
$424$	2.48900e14	0.882088
$425$	−1.29936e14	−0.454559
$426$	2.74313e14	0.947312
$427$	−1.21730e14	−0.414997
$428$	7.21983e13	0.242989
$429$	−1.32734e14	−0.441029
$430$	3.87402e14	1.27083
$431$	6.96736e13	0.225654	0.112827	−	0.993615i	$-0.464009\pi$
$431$	6.96736e13	0.225654	0.112827	+	0.993615i	$0.464009\pi$
$432$	−4.07261e14	−1.30230
$433$	−5.25052e14	−1.65775	−0.828875	−	0.559434i	$-0.811018\pi$
$433$	−5.25052e14	−1.65775	−0.828875	+	0.559434i	$0.811018\pi$
$434$	4.84265e14	1.50970
$435$	2.98710e13	0.0919514
$436$	−5.99850e13	−0.182334
$437$	−4.83223e13	−0.145044
$438$	−3.13284e14	−0.928605
$439$	−1.10308e14	−0.322889	−0.161445	−	0.986882i	$-0.551615\pi$
$439$	−1.10308e14	−0.322889	−0.161445	+	0.986882i	$0.551615\pi$
$440$	−5.34964e13	−0.154645
$441$	9.35615e13	0.267107
$442$	8.28104e14	2.33487
$443$	3.82986e14	1.06650	0.533251	−	0.845957i	$-0.320970\pi$
$443$	3.82986e14	1.06650	0.533251	+	0.845957i	$0.320970\pi$
$444$	−1.70537e14	−0.469042
$445$	3.00477e14	0.816264
$446$	−3.15811e13	−0.0847393
$447$	−6.04552e13	−0.160229
$448$	−4.12661e13	−0.108035
$449$	−1.72376e14	−0.445782	−0.222891	−	0.974843i	$-0.571549\pi$
$449$	−1.72376e14	−0.445782	−0.222891	+	0.974843i	$0.571549\pi$
$450$	−1.19970e14	−0.306482
$451$	2.82007e13	0.0711687
$452$	−1.92358e14	−0.479567
$453$	1.68927e14	0.416064
$454$	−5.86525e13	−0.142718
$455$	4.23224e14	1.01744
$456$	1.77449e14	0.421470
$457$	−2.16113e14	−0.507156	−0.253578	−	0.967315i	$-0.581607\pi$
$457$	−2.16113e14	−0.507156	−0.253578	+	0.967315i	$0.581607\pi$
$458$	−4.51738e14	−1.04743
$459$	4.48839e14	1.02830
$460$	2.29460e13	0.0519445
$461$	−5.90412e14	−1.32069	−0.660344	−	0.750963i	$-0.729589\pi$
$461$	−5.90412e14	−1.32069	−0.660344	+	0.750963i	$0.729589\pi$
$462$	8.96612e13	0.198186
$463$	3.94036e14	0.860678	0.430339	−	0.902667i	$-0.358394\pi$
$463$	3.94036e14	0.860678	0.430339	+	0.902667i	$0.358394\pi$
$464$	1.07526e14	0.232094
$465$	−4.02148e14	−0.857817
$466$	−5.71177e14	−1.20406
$467$	6.34366e14	1.32159	0.660796	−	0.750566i	$-0.270219\pi$
$467$	6.34366e14	1.32159	0.660796	+	0.750566i	$0.270219\pi$
$468$	2.50860e14	0.516510
$469$	−2.10013e14	−0.427362
$470$	5.86035e14	1.17865
$471$	1.70631e14	0.339191
$472$	5.06588e14	0.995346
$473$	2.46343e14	0.478414
$474$	6.47754e14	1.24345
$475$	2.43078e14	0.461244
$476$	−1.83531e14	−0.344247
$477$	−4.15669e14	−0.770720
$478$	−1.17485e15	−2.15343
$479$	5.45021e14	0.987571	0.493785	−	0.869584i	$-0.335613\pi$
$479$	5.45021e14	0.987571	0.493785	+	0.869584i	$0.335613\pi$
$480$	−2.48936e14	−0.445924
$481$	−1.56013e15	−2.76289
$482$	1.63786e14	0.286759
$483$	4.02998e13	0.0697580
$484$	−2.52864e14	−0.432751
$485$	3.81050e14	0.644766
$486$	6.82570e14	1.14195
$487$	−8.85153e14	−1.46423	−0.732114	−	0.681182i	$-0.761466\pi$
$487$	−8.85153e14	−1.46423	−0.732114	+	0.681182i	$0.761466\pi$
$488$	2.21719e14	0.362656
$489$	−3.46042e14	−0.559667
$490$	2.74364e14	0.438782
$491$	2.00204e14	0.316610	0.158305	−	0.987390i	$-0.449397\pi$
$491$	2.00204e14	0.316610	0.158305	+	0.987390i	$0.449397\pi$
$492$	4.44190e13	0.0694641
$493$	−1.18503e14	−0.183262
$494$	−1.54918e15	−2.36921
$495$	8.93405e13	0.135120
$496$	−1.44760e15	−2.16521
$497$	−5.56176e14	−0.822721
$498$	1.42304e14	0.208187
$499$	5.17136e14	0.748259	0.374129	−	0.927377i	$-0.377942\pi$
$499$	5.17136e14	0.748259	0.374129	+	0.927377i	$0.377942\pi$
$500$	−3.66030e14	−0.523819
$501$	3.96612e13	0.0561382
$502$	−1.46998e13	−0.0205798
$503$	−4.67807e14	−0.647803	−0.323901	−	0.946091i	$-0.604995\pi$
$503$	−4.67807e14	−0.647803	−0.323901	+	0.946091i	$0.604995\pi$
$504$	1.77570e14	0.243221
$505$	−5.06110e14	−0.685713
$506$	4.44718e13	0.0596014
$507$	−1.40408e15	−1.86143
$508$	4.66613e13	0.0611936
$509$	5.04923e14	0.655054	0.327527	−	0.944842i	$-0.393785\pi$
$509$	5.04923e14	0.655054	0.327527	+	0.944842i	$0.393785\pi$
$510$	4.64527e14	0.596176
$511$	6.35193e14	0.806474
$512$	−2.74930e14	−0.345332
$513$	−8.39666e14	−1.04342
$514$	1.93566e15	2.37975
$515$	4.69763e13	0.0571398
$516$	3.88015e14	0.466955
$517$	3.72650e14	0.443714
$518$	1.05386e15	1.24157
$519$	−1.00988e14	−0.117720
$520$	−7.70861e14	−0.889114
$521$	−3.92631e14	−0.448103	−0.224051	−	0.974577i	$-0.571928\pi$
$521$	−3.92631e14	−0.448103	−0.224051	+	0.974577i	$0.571928\pi$
$522$	−1.09415e14	−0.123563
$523$	1.57451e15	1.75948	0.879741	−	0.475453i	$-0.157716\pi$
$523$	1.57451e15	1.75948	0.879741	+	0.475453i	$0.157716\pi$
$524$	2.44970e14	0.270889
$525$	−2.02722e14	−0.221832
$526$	−1.78040e15	−1.92795
$527$	1.59539e15	1.70965
$528$	−2.68022e14	−0.284239
$529$	−9.32821e14	−0.979021
$530$	−1.21893e15	−1.26608
$531$	−8.46017e14	−0.869680
$532$	3.43340e14	0.349310
$533$	4.06360e14	0.409177
$534$	9.17268e14	0.914154
$535$	3.70507e14	0.365469
$536$	3.82518e14	0.373461
$537$	6.30475e14	0.609270
$538$	−2.45649e15	−2.34970
$539$	1.74464e14	0.165184
$540$	3.98719e14	0.373681
$541$	9.49366e13	0.0880742	0.0440371	−	0.999030i	$-0.485978\pi$
$541$	9.49366e13	0.0880742	0.0440371	+	0.999030i	$0.485978\pi$
$542$	1.83080e15	1.68130
$543$	−4.89712e14	−0.445187
$544$	9.87572e14	0.888740
$545$	−3.07830e14	−0.274240
$546$	1.29198e15	1.13945
$547$	−5.16732e14	−0.451165	−0.225582	−	0.974224i	$-0.572428\pi$
$547$	−5.16732e14	−0.451165	−0.225582	+	0.974224i	$0.572428\pi$
$548$	−5.49186e14	−0.474708
$549$	−3.70278e14	−0.316869
$550$	−2.23708e14	−0.189534
$551$	2.21690e14	0.185957
$552$	−7.34020e13	−0.0609597
$553$	−1.31334e15	−1.07991
$554$	9.07952e14	0.739195
$555$	−8.75159e14	−0.705465
$556$	6.72678e14	0.536903
$557$	2.37108e15	1.87389	0.936943	−	0.349483i	$-0.113643\pi$
$557$	2.37108e15	1.87389	0.936943	+	0.349483i	$0.113643\pi$
$558$	1.47303e15	1.15272
$559$	3.54970e15	2.75060
$560$	8.54594e14	0.655731
$561$	2.95385e14	0.224436
$562$	−2.11482e15	−1.59120
$563$	−1.59742e15	−1.19021	−0.595105	−	0.803648i	$-0.702890\pi$
$563$	−1.59742e15	−1.19021	−0.595105	+	0.803648i	$0.702890\pi$
$564$	5.86962e14	0.433087
$565$	−9.87141e14	−0.721295
$566$	2.77576e15	2.00859
$567$	1.56572e14	0.112204
$568$	1.01302e15	0.718955
$569$	1.98282e15	1.39369	0.696844	−	0.717223i	$-0.254587\pi$
$569$	1.98282e15	1.39369	0.696844	+	0.717223i	$0.254587\pi$
$570$	−8.69014e14	−0.604944
$571$	−6.72623e14	−0.463738	−0.231869	−	0.972747i	$-0.574484\pi$
$571$	−6.72623e14	−0.463738	−0.231869	+	0.972747i	$0.574484\pi$
$572$	4.67777e14	0.319419
$573$	−1.43068e14	−0.0967589
$574$	−2.74495e14	−0.183873
$575$	−1.00550e14	−0.0667125
$576$	−1.25523e14	−0.0824894
$577$	−4.58722e14	−0.298595	−0.149298	−	0.988792i	$-0.547701\pi$
$577$	−4.58722e14	−0.298595	−0.149298	+	0.988792i	$0.547701\pi$
$578$	4.92665e13	0.0317650
$579$	7.60377e14	0.485621
$580$	−1.05270e14	−0.0665966
$581$	−2.88524e14	−0.180806
$582$	1.16323e15	0.722089
$583$	−7.75097e14	−0.476627
$584$	−1.15694e15	−0.704758
$585$	1.28736e15	0.776859
$586$	1.69789e15	1.01501
$587$	1.05166e15	0.622824	0.311412	−	0.950275i	$-0.399198\pi$
$587$	1.05166e15	0.622824	0.311412	+	0.950275i	$0.399198\pi$
$588$	2.74798e14	0.161227
$589$	−2.98458e15	−1.73480
$590$	−2.48090e15	−1.42864
$591$	5.85523e14	0.334051
$592$	−3.15029e15	−1.78066
$593$	−3.86942e14	−0.216693	−0.108347	−	0.994113i	$-0.534556\pi$
$593$	−3.86942e14	−0.216693	−0.108347	+	0.994113i	$0.534556\pi$
$594$	7.72758e14	0.428764
$595$	−9.41841e14	−0.517767
$596$	2.13054e14	0.116048
$597$	−7.40438e14	−0.399604
$598$	6.40820e14	0.342673
$599$	−2.83245e15	−1.50077	−0.750385	−	0.661001i	$-0.770132\pi$
$599$	−2.83245e15	−1.50077	−0.750385	+	0.661001i	$0.770132\pi$
$600$	3.69238e14	0.193854
$601$	−1.93832e15	−1.00836	−0.504181	−	0.863598i	$-0.668206\pi$
$601$	−1.93832e15	−1.00836	−0.504181	+	0.863598i	$0.668206\pi$
$602$	−2.39781e15	−1.23604
$603$	−6.38816e14	−0.326310
$604$	−5.95329e14	−0.301338
$605$	−1.29765e15	−0.650881
$606$	−1.54501e15	−0.767947
$607$	5.80866e14	0.286113	0.143057	−	0.989714i	$-0.454307\pi$
$607$	5.80866e14	0.286113	0.143057	+	0.989714i	$0.454307\pi$
$608$	−1.84750e15	−0.901810
$609$	−1.84885e14	−0.0894348
$610$	−1.08582e15	−0.520527
$611$	5.36974e15	2.55109
$612$	−5.58262e14	−0.262848
$613$	4.60071e14	0.214680	0.107340	−	0.994222i	$-0.465767\pi$
$613$	4.60071e14	0.214680	0.107340	+	0.994222i	$0.465767\pi$
$614$	−3.59964e15	−1.66469
$615$	2.27949e14	0.104478
$616$	3.31113e14	0.150412
$617$	2.08386e15	0.938211	0.469106	−	0.883142i	$-0.344576\pi$
$617$	2.08386e15	0.938211	0.469106	+	0.883142i	$0.344576\pi$
$618$	1.43405e14	0.0639923
$619$	−6.03555e14	−0.266943	−0.133471	−	0.991053i	$-0.542612\pi$
$619$	−6.03555e14	−0.266943	−0.133471	+	0.991053i	$0.542612\pi$
$620$	1.41724e15	0.621282
$621$	3.47329e14	0.150917
$622$	−2.36770e15	−1.01972
$623$	−1.85979e15	−0.793923
$624$	−3.86209e15	−1.63421
$625$	−7.80243e14	−0.327257
$626$	1.39694e15	0.580791
$627$	−5.52592e14	−0.227737
$628$	−6.01335e14	−0.245662
$629$	3.47191e15	1.40601
$630$	−8.69606e14	−0.349100
$631$	4.40133e15	1.75155	0.875775	−	0.482719i	$-0.160351\pi$
$631$	4.40133e15	1.75155	0.875775	+	0.482719i	$0.160351\pi$
$632$	2.39211e15	0.943709
$633$	2.17923e15	0.852282
$634$	3.03869e15	1.17814
$635$	2.39456e14	0.0920385
$636$	−1.22086e15	−0.465211
$637$	2.51395e15	0.949708
$638$	−2.04025e14	−0.0764134
$639$	−1.69177e15	−0.628184
$640$	−2.16469e15	−0.796902
$641$	−1.97734e15	−0.721709	−0.360854	−	0.932622i	$-0.617515\pi$
$641$	−1.97734e15	−0.721709	−0.360854	+	0.932622i	$0.617515\pi$
$642$	1.13105e15	0.409297
$643$	−2.74931e15	−0.986423	−0.493212	−	0.869909i	$-0.664177\pi$
$643$	−2.74931e15	−0.986423	−0.493212	+	0.869909i	$0.664177\pi$
$644$	−1.42023e14	−0.0505228
$645$	1.99121e15	0.702327
$646$	3.44753e15	1.20567
$647$	1.26875e15	0.439948	0.219974	−	0.975506i	$-0.429403\pi$
$647$	1.26875e15	0.439948	0.219974	+	0.975506i	$0.429403\pi$
$648$	−2.85181e14	−0.0980523
$649$	−1.57756e15	−0.537825
$650$	−3.22355e15	−1.08971
$651$	2.48908e15	0.834339
$652$	1.21951e15	0.405344
$653$	−1.09306e15	−0.360264	−0.180132	−	0.983642i	$-0.557653\pi$
$653$	−1.09306e15	−0.360264	−0.180132	+	0.983642i	$0.557653\pi$
$654$	−9.39717e14	−0.307128
$655$	1.25713e15	0.407431
$656$	8.20541e14	0.263712
$657$	1.93212e15	0.615779
$658$	−3.62724e15	−1.14639
$659$	1.63177e15	0.511434	0.255717	−	0.966752i	$-0.417689\pi$
$659$	1.63177e15	0.511434	0.255717	+	0.966752i	$0.417689\pi$
$660$	2.62401e14	0.0815592
$661$	5.50155e15	1.69581	0.847905	−	0.530148i	$-0.177863\pi$
$661$	5.50155e15	1.69581	0.847905	+	0.530148i	$0.177863\pi$
$662$	−7.52588e15	−2.30058
$663$	4.25638e15	1.29037
$664$	5.25518e14	0.158002
$665$	1.76195e15	0.525381
$666$	3.20563e15	0.947992
$667$	−9.17026e13	−0.0268961
$668$	−1.39773e14	−0.0406586
$669$	−1.62324e14	−0.0468315
$670$	−1.87329e15	−0.536037
$671$	−6.90455e14	−0.195957
$672$	1.54078e15	0.433720
$673$	−1.00349e15	−0.280176	−0.140088	−	0.990139i	$-0.544739\pi$
$673$	−1.00349e15	−0.280176	−0.140088	+	0.990139i	$0.544739\pi$
$674$	−5.76767e15	−1.59724
$675$	−1.74719e15	−0.479920
$676$	4.94822e15	1.34816
$677$	−3.92864e13	−0.0106171	−0.00530854	−	0.999986i	$-0.501690\pi$
$677$	−3.92864e13	−0.0106171	−0.00530854	+	0.999986i	$0.501690\pi$
$678$	−3.01346e15	−0.807796
$679$	−2.35849e15	−0.627120
$680$	1.71547e15	0.452464
$681$	−3.01468e14	−0.0788737
$682$	2.74675e15	0.712862
$683$	2.79041e14	0.0718381	0.0359190	−	0.999355i	$-0.488564\pi$
$683$	2.79041e14	0.0718381	0.0359190	+	0.999355i	$0.488564\pi$
$684$	1.04437e15	0.266714
$685$	−2.81831e15	−0.713987
$686$	−5.16581e15	−1.29824
$687$	−2.32189e15	−0.578869
$688$	7.16772e15	1.77274
$689$	−1.11688e16	−2.74032
$690$	3.59469e14	0.0874968
$691$	2.90138e15	0.700607	0.350304	−	0.936636i	$-0.386078\pi$
$691$	2.90138e15	0.700607	0.350304	+	0.936636i	$0.386078\pi$
$692$	3.55899e14	0.0852596
$693$	−5.52969e14	−0.131422
$694$	6.33330e14	0.149332
$695$	3.45204e15	0.807532
$696$	3.36749e14	0.0781548
$697$	−9.04312e14	−0.208227
$698$	2.55697e14	0.0584145
$699$	−2.93580e15	−0.665428
$700$	7.14427e14	0.160664
$701$	5.25552e15	1.17265	0.586323	−	0.810077i	$-0.300575\pi$
$701$	5.25552e15	1.17265	0.586323	+	0.810077i	$0.300575\pi$
$702$	1.11351e16	2.46514
$703$	−6.49507e15	−1.42669
$704$	−2.34062e14	−0.0510129
$705$	3.01217e15	0.651386
$706$	6.11338e15	1.31176
$707$	3.13255e15	0.666946
$708$	−2.48482e15	−0.524944
$709$	5.95286e15	1.24788	0.623938	−	0.781474i	$-0.285532\pi$
$709$	5.95286e15	1.24788	0.623938	+	0.781474i	$0.285532\pi$
$710$	−4.96103e15	−1.03193
$711$	−3.99490e15	−0.824562
$712$	3.38741e15	0.693790
$713$	1.23458e15	0.250914
$714$	−2.87517e15	−0.579860
$715$	2.40053e15	0.480424
$716$	−2.22190e15	−0.441269
$717$	−6.03864e15	−1.19010
$718$	−3.38639e15	−0.662297
$719$	−2.59634e15	−0.503909	−0.251955	−	0.967739i	$-0.581073\pi$
$719$	−2.59634e15	−0.503909	−0.251955	+	0.967739i	$0.581073\pi$
$720$	2.59949e15	0.500680
$721$	−2.90758e14	−0.0555760
$722$	−1.81347e13	−0.00343997
$723$	8.41844e14	0.158479
$724$	1.72583e15	0.322430
$725$	4.61295e14	0.0855303
$726$	−3.96134e15	−0.728938
$727$	3.10394e15	0.566858	0.283429	−	0.958993i	$-0.408528\pi$
$727$	3.10394e15	0.566858	0.283429	+	0.958993i	$0.408528\pi$
$728$	4.77121e15	0.864780
$729$	4.38153e15	0.788177
$730$	5.66584e15	1.01155
$731$	−7.89948e15	−1.39976
$732$	−1.08754e15	−0.191264
$733$	−6.21570e15	−1.08497	−0.542486	−	0.840065i	$-0.682517\pi$
$733$	−6.21570e15	−1.08497	−0.542486	+	0.840065i	$0.682517\pi$
$734$	2.57139e15	0.445491
$735$	1.41021e15	0.242495
$736$	7.64223e14	0.130434
$737$	−1.19120e15	−0.201796
$738$	−8.34955e14	−0.140395
$739$	4.90042e15	0.817878	0.408939	−	0.912562i	$-0.365899\pi$
$739$	4.90042e15	0.817878	0.408939	+	0.912562i	$0.365899\pi$
$740$	3.08421e15	0.510940
$741$	−7.96262e15	−1.30935
$742$	7.54450e15	1.23143
$743$	2.64186e15	0.428028	0.214014	−	0.976831i	$-0.431346\pi$
$743$	2.64186e15	0.428028	0.214014	+	0.976831i	$0.431346\pi$
$744$	−4.53360e15	−0.729108
$745$	1.09335e15	0.174542
$746$	6.16829e15	0.977464
$747$	−8.77630e14	−0.138054
$748$	−1.04099e15	−0.162550
$749$	−2.29323e15	−0.355466
$750$	−5.73417e15	−0.882335
$751$	8.64855e15	1.32106	0.660532	−	0.750798i	$-0.270331\pi$
$751$	8.64855e15	1.32106	0.660532	+	0.750798i	$0.270331\pi$
$752$	1.08428e16	1.64416
$753$	−7.55556e13	−0.0113735
$754$	−2.93991e15	−0.439331
$755$	−3.05510e15	−0.453229
$756$	−2.46785e15	−0.363454
$757$	−6.61424e14	−0.0967058	−0.0483529	−	0.998830i	$-0.515397\pi$
$757$	−6.61424e14	−0.0967058	−0.0483529	+	0.998830i	$0.515397\pi$
$758$	7.72320e15	1.12103
$759$	2.28581e14	0.0329390
$760$	−3.20921e15	−0.459118
$761$	−9.70066e15	−1.37780	−0.688899	−	0.724857i	$-0.741906\pi$
$761$	−9.70066e15	−1.37780	−0.688899	+	0.724857i	$0.741906\pi$
$762$	7.30989e14	0.103076
$763$	1.90530e15	0.266734
$764$	5.04195e14	0.0700785
$765$	−2.86488e15	−0.395338
$766$	−3.87270e15	−0.530585
$767$	−2.27321e16	−3.09218
$768$	−5.85316e15	−0.790504
$769$	−6.63840e15	−0.890161	−0.445080	−	0.895491i	$-0.646825\pi$
$769$	−6.63840e15	−0.890161	−0.445080	+	0.895491i	$0.646825\pi$
$770$	−1.62155e15	−0.215890
$771$	9.94909e15	1.31518
$772$	−2.67970e15	−0.351715
$773$	−4.24738e15	−0.553521	−0.276760	−	0.960939i	$-0.589261\pi$
$773$	−4.24738e15	−0.553521	−0.276760	+	0.960939i	$0.589261\pi$
$774$	−7.29363e15	−0.943775
$775$	−6.21035e15	−0.797915
$776$	4.29575e15	0.548024
$777$	5.41676e15	0.686157
$778$	1.19099e16	1.49803
$779$	1.69174e15	0.211290
$780$	3.78108e15	0.468917
$781$	−3.15464e15	−0.388480
$782$	−1.42608e15	−0.174384
$783$	−1.59346e15	−0.193486
$784$	5.07628e15	0.612079
$785$	−3.08592e15	−0.369489
$786$	3.83767e15	0.456292
$787$	1.18637e16	1.40075	0.700375	−	0.713775i	$-0.253016\pi$
$787$	1.18637e16	1.40075	0.700375	+	0.713775i	$0.253016\pi$
$788$	−2.06348e15	−0.241940
$789$	−9.15109e15	−1.06549
$790$	−1.17148e16	−1.35452
$791$	6.10986e15	0.701554
$792$	1.00718e15	0.114846
$793$	−9.94918e15	−1.12664
$794$	−1.39708e16	−1.57112
$795$	−6.26518e15	−0.699704
$796$	2.60943e15	0.289417
$797$	−9.75125e15	−1.07409	−0.537044	−	0.843554i	$-0.680459\pi$
$797$	−9.75125e15	−1.07409	−0.537044	+	0.843554i	$0.680459\pi$
$798$	5.37872e15	0.588387
$799$	−1.19498e16	−1.29823
$800$	−3.84430e15	−0.414785
$801$	−5.65707e15	−0.606196
$802$	−1.20801e16	−1.28562
$803$	3.60282e15	0.380809
$804$	−1.87626e15	−0.196963
$805$	−7.28834e14	−0.0759891
$806$	3.95796e16	4.09853
$807$	−1.26261e16	−1.29857
$808$	−5.70562e15	−0.582828
$809$	1.02093e16	1.03581	0.517906	−	0.855437i	$-0.326712\pi$
$809$	1.02093e16	1.03581	0.517906	+	0.855437i	$0.326712\pi$
$810$	1.39661e15	0.140736
$811$	8.01250e15	0.801962	0.400981	−	0.916086i	$-0.368669\pi$
$811$	8.01250e15	0.801962	0.400981	+	0.916086i	$0.368669\pi$
$812$	6.51566e14	0.0647740
$813$	9.41014e15	0.929177
$814$	5.97752e15	0.586255
$815$	6.25827e15	0.609659
$816$	8.59467e15	0.831636
$817$	1.47780e16	1.42034
$818$	−1.46288e16	−1.39658
$819$	−7.96805e15	−0.755598
$820$	−8.03331e14	−0.0756690
$821$	2.39145e15	0.223756	0.111878	−	0.993722i	$-0.464313\pi$
$821$	2.39145e15	0.223756	0.111878	+	0.993722i	$0.464313\pi$
$822$	−8.60347e15	−0.799611
$823$	−2.30714e15	−0.212998	−0.106499	−	0.994313i	$-0.533964\pi$
$823$	−2.30714e15	−0.212998	−0.106499	+	0.994313i	$0.533964\pi$
$824$	5.29586e14	0.0485665
$825$	−1.14984e15	−0.104747
$826$	1.53554e16	1.38954
$827$	7.76497e15	0.698007	0.349003	−	0.937121i	$-0.386520\pi$
$827$	7.76497e15	0.698007	0.349003	+	0.937121i	$0.386520\pi$
$828$	−4.32005e14	−0.0385764
$829$	1.98592e16	1.76162	0.880811	−	0.473468i	$-0.156998\pi$
$829$	1.98592e16	1.76162	0.880811	+	0.473468i	$0.156998\pi$
$830$	−2.57360e15	−0.226784
$831$	4.66679e15	0.408519
$832$	−3.37273e15	−0.293294
$833$	−5.59453e15	−0.483299
$834$	1.05381e16	0.904375
$835$	−7.17285e14	−0.0611527
$836$	1.94743e15	0.164940
$837$	2.14524e16	1.80504
$838$	−1.06090e16	−0.886813
$839$	−2.25499e16	−1.87264	−0.936318	−	0.351154i	$-0.885789\pi$
$839$	−2.25499e16	−1.87264	−0.936318	+	0.351154i	$0.885789\pi$
$840$	2.67642e15	0.220810
$841$	4.20707e14	0.0344828
$842$	−1.24517e16	−1.01394
$843$	−1.08700e16	−0.879382
$844$	−7.67999e15	−0.617273
$845$	2.53932e16	2.02771
$846$	−1.10333e16	−0.875322
$847$	8.03172e15	0.633067
$848$	−2.25526e16	−1.76612
$849$	1.42672e16	1.11006
$850$	7.17366e15	0.554545
$851$	2.68670e15	0.206351
$852$	−4.96888e15	−0.379176
$853$	1.48398e16	1.12515	0.562574	−	0.826747i	$-0.309811\pi$
$853$	1.48398e16	1.12515	0.562574	+	0.826747i	$0.309811\pi$
$854$	6.72063e15	0.506281
$855$	5.35948e15	0.401152
$856$	4.17689e15	0.310633
$857$	1.51233e16	1.11751	0.558756	−	0.829332i	$-0.311279\pi$
$857$	1.51233e16	1.11751	0.558756	+	0.829332i	$0.311279\pi$
$858$	7.32813e15	0.538038
$859$	1.87916e15	0.137088	0.0685442	−	0.997648i	$-0.478165\pi$
$859$	1.87916e15	0.137088	0.0685442	+	0.997648i	$0.478165\pi$
$860$	−7.01738e15	−0.508667
$861$	−1.41088e15	−0.101618
$862$	−3.84662e15	−0.275289
$863$	1.33355e16	0.948310	0.474155	−	0.880441i	$-0.342754\pi$
$863$	1.33355e16	0.948310	0.474155	+	0.880441i	$0.342754\pi$
$864$	1.32794e16	0.938324
$865$	1.82640e15	0.128235
$866$	2.89877e16	2.02239
$867$	2.53225e14	0.0175550
$868$	−8.77193e15	−0.604278
$869$	−7.44927e15	−0.509924
$870$	−1.64915e15	−0.112177
$871$	−1.71647e16	−1.16021
$872$	−3.47031e15	−0.233092
$873$	−7.17403e15	−0.478834
$874$	2.66784e15	0.176948
$875$	1.16262e16	0.766290
$876$	5.67481e15	0.371688
$877$	−4.71771e15	−0.307067	−0.153534	−	0.988143i	$-0.549065\pi$
$877$	−4.71771e15	−0.307067	−0.153534	+	0.988143i	$0.549065\pi$
$878$	6.09004e15	0.393913
$879$	8.72698e15	0.560951
$880$	4.84727e15	0.309629
$881$	−2.95153e16	−1.87361	−0.936805	−	0.349853i	$-0.886231\pi$
$881$	−2.95153e16	−1.87361	−0.936805	+	0.349853i	$0.886231\pi$
$882$	−5.16546e15	−0.325860
$883$	8.98369e14	0.0563211	0.0281605	−	0.999603i	$-0.491035\pi$
$883$	8.98369e14	0.0563211	0.0281605	+	0.999603i	$0.491035\pi$
$884$	−1.50002e16	−0.934566
$885$	−1.27516e16	−0.789544
$886$	−2.11443e16	−1.30109
$887$	1.80081e16	1.10126	0.550628	−	0.834751i	$-0.314388\pi$
$887$	1.80081e16	1.10126	0.550628	+	0.834751i	$0.314388\pi$
$888$	−9.86608e15	−0.599616
$889$	−1.48210e15	−0.0895195
$890$	−1.65891e16	−0.995811
$891$	8.88080e14	0.0529816
$892$	5.72057e14	0.0339182
$893$	2.23551e16	1.31732
$894$	3.33768e15	0.195474
$895$	−1.14023e16	−0.663693
$896$	1.33982e16	0.775092
$897$	3.29376e15	0.189380
$898$	9.51675e15	0.543837
$899$	−5.66391e15	−0.321691
$900$	2.17314e15	0.122674
$901$	2.48550e16	1.39453
$902$	−1.55694e15	−0.0868231
$903$	−1.23245e16	−0.683105
$904$	−1.11285e16	−0.613070
$905$	8.85660e15	0.484953
$906$	−9.32635e15	−0.507582
$907$	−1.39176e16	−0.752880	−0.376440	−	0.926441i	$-0.622852\pi$
$907$	−1.39176e16	−0.752880	−0.376440	+	0.926441i	$0.622852\pi$
$908$	1.06243e15	0.0571250
$909$	9.52854e15	0.509243
$910$	−2.33659e16	−1.24124
$911$	−1.12330e15	−0.0593121	−0.0296560	−	0.999560i	$-0.509441\pi$
$911$	−1.12330e15	−0.0593121	−0.0296560	+	0.999560i	$0.509441\pi$
$912$	−1.60785e16	−0.843866
$913$	−1.63651e15	−0.0853749
$914$	1.19314e16	0.618711
$915$	−5.58101e15	−0.287672
$916$	8.18275e15	0.419251
$917$	−7.78097e15	−0.396280
$918$	−2.47800e16	−1.25449
$919$	−3.51858e16	−1.77065	−0.885324	−	0.464975i	$-0.846063\pi$
$919$	−3.51858e16	−1.77065	−0.885324	+	0.464975i	$0.846063\pi$
$920$	1.32750e15	0.0664050
$921$	−1.85018e16	−0.919996
$922$	3.25962e16	1.61119
$923$	−4.54570e16	−2.23353
$924$	−1.62412e15	−0.0793270
$925$	−1.35150e16	−0.656202
$926$	−2.17544e16	−1.04999
$927$	−8.84423e14	−0.0424347
$928$	−3.50605e15	−0.167226
$929$	3.05140e16	1.44682	0.723408	−	0.690421i	$-0.242575\pi$
$929$	3.05140e16	1.44682	0.723408	+	0.690421i	$0.242575\pi$
$930$	2.22023e16	1.04650
$931$	1.04660e16	0.490407
$932$	1.03462e16	0.481943
$933$	−1.21698e16	−0.563551
$934$	−3.50228e16	−1.61229
$935$	−5.34213e15	−0.244484
$936$	1.45130e16	0.660298
$937$	3.05900e16	1.38360	0.691802	−	0.722087i	$-0.256817\pi$
$937$	3.05900e16	1.38360	0.691802	+	0.722087i	$0.256817\pi$
$938$	1.15947e16	0.521366
$939$	7.18015e15	0.320976
$940$	−1.06154e16	−0.471773
$941$	−3.24871e16	−1.43538	−0.717691	−	0.696362i	$-0.754801\pi$
$941$	−3.24871e16	−1.43538	−0.717691	+	0.696362i	$0.754801\pi$
$942$	−9.42042e15	−0.413800
$943$	−6.99793e14	−0.0305601
$944$	−4.59016e16	−1.99288
$945$	−1.26645e16	−0.546654
$946$	−1.36004e16	−0.583647
$947$	1.36690e16	0.583191	0.291596	−	0.956542i	$-0.405814\pi$
$947$	1.36690e16	0.583191	0.291596	+	0.956542i	$0.405814\pi$
$948$	−1.17334e16	−0.497710
$949$	5.19151e16	2.18942
$950$	−1.34201e16	−0.562700
$951$	1.56186e16	0.651101
$952$	−1.06178e16	−0.440080
$953$	−3.16059e14	−0.0130244	−0.00651218	−	0.999979i	$-0.502073\pi$
$953$	−3.16059e14	−0.0130244	−0.00651218	+	0.999979i	$0.502073\pi$
$954$	2.29488e16	0.940250
$955$	2.58742e15	0.105402
$956$	2.12812e16	0.861942
$957$	−1.04867e15	−0.0422302
$958$	−3.00902e16	−1.20480
$959$	1.74438e16	0.694445
$960$	−1.89194e15	−0.0748886
$961$	5.08439e16	2.00106
$962$	8.61336e16	3.37062
$963$	−6.97553e15	−0.271414
$964$	−2.96680e15	−0.114780
$965$	−1.37517e16	−0.528999
$966$	−2.22492e15	−0.0851021
$967$	2.19424e16	0.834525	0.417262	−	0.908786i	$-0.362990\pi$
$967$	2.19424e16	0.834525	0.417262	+	0.908786i	$0.362990\pi$
$968$	−1.46290e16	−0.553222
$969$	1.77200e16	0.666319
$970$	−2.10375e16	−0.786591
$971$	−1.10258e16	−0.409926	−0.204963	−	0.978770i	$-0.565707\pi$
$971$	−1.10258e16	−0.409926	−0.204963	+	0.978770i	$0.565707\pi$
$972$	−1.23640e16	−0.457083
$973$	−2.13663e16	−0.785431
$974$	4.88686e16	1.78630
$975$	−1.65687e16	−0.602232
$976$	−2.00898e16	−0.726110
$977$	−3.06639e15	−0.110207	−0.0551033	−	0.998481i	$-0.517549\pi$
$977$	−3.06639e15	−0.110207	−0.0551033	+	0.998481i	$0.517549\pi$
$978$	1.91047e16	0.682772
$979$	−1.05487e16	−0.374882
$980$	−4.96981e15	−0.175629
$981$	5.79552e15	0.203663
$982$	−1.10531e16	−0.386252
$983$	−2.16527e15	−0.0752431	−0.0376216	−	0.999292i	$-0.511978\pi$
$983$	−2.16527e15	−0.0752431	−0.0376216	+	0.999292i	$0.511978\pi$
$984$	2.56977e15	0.0888018
$985$	−1.05894e16	−0.363891
$986$	6.54247e15	0.223573
$987$	−1.86437e16	−0.633559
$988$	2.80617e16	0.948310
$989$	−6.11294e15	−0.205433
$990$	−4.93241e15	−0.164841
$991$	1.79045e16	0.595055	0.297528	−	0.954713i	$-0.403838\pi$
$991$	1.79045e16	0.595055	0.297528	+	0.954713i	$0.403838\pi$
$992$	4.72014e16	1.56006
$993$	−3.86823e16	−1.27143
$994$	3.07060e16	1.00369
$995$	1.33911e16	0.435299
$996$	−2.57767e15	−0.0833301
$997$	−5.53122e14	−0.0177827	−0.00889134	−	0.999960i	$-0.502830\pi$
$997$	−5.53122e14	−0.0177827	−0.00889134	+	0.999960i	$0.502830\pi$
$998$	−2.85507e16	−0.912847
$999$	4.66851e16	1.48446

Twists

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

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

\(f(q)\)	\(=\)	\(q-55.2092 q^{2} -283.770 q^{3} +1000.05 q^{4} +5132.07 q^{5} +15666.7 q^{6} -31764.7 q^{7} +57856.2 q^{8} -96621.5 q^{9} +O(q^{10})\)	\(q-55.2092 q^{2} -283.770 q^{3} +1000.05 q^{4} +5132.07 q^{5} +15666.7 q^{6} -31764.7 q^{7} +57856.2 q^{8} -96621.5 q^{9} -283337. q^{10} -180170. q^{11} -283786. q^{12} -2.59617e6 q^{13} +1.75370e6 q^{14} -1.45633e6 q^{15} -5.24231e6 q^{16} +5.77750e6 q^{17} +5.33440e6 q^{18} -1.08083e7 q^{19} +5.13235e6 q^{20} +9.01387e6 q^{21} +9.94702e6 q^{22} +4.47086e6 q^{23} -1.64179e7 q^{24} -2.24900e7 q^{25} +1.43333e8 q^{26} +7.76873e7 q^{27} -3.17664e7 q^{28} -2.05111e7 q^{29} +8.04027e7 q^{30} +2.76138e8 q^{31} +1.70934e8 q^{32} +5.11268e7 q^{33} -3.18971e8 q^{34} -1.63019e8 q^{35} -9.66268e7 q^{36} +6.00935e8 q^{37} +5.96716e8 q^{38} +7.36716e8 q^{39} +2.96922e8 q^{40} -1.56523e8 q^{41} -4.97649e8 q^{42} -1.36728e9 q^{43} -1.80180e8 q^{44} -4.95868e8 q^{45} -2.46833e8 q^{46} -2.06833e9 q^{47} +1.48761e9 q^{48} -9.68330e8 q^{49} +1.24165e9 q^{50} -1.63948e9 q^{51} -2.59631e9 q^{52} +4.30204e9 q^{53} -4.28905e9 q^{54} -9.24644e8 q^{55} -1.83779e9 q^{56} +3.06706e9 q^{57} +1.13240e9 q^{58} +8.75599e9 q^{59} -1.45641e9 q^{60} +3.83225e9 q^{61} -1.52454e10 q^{62} +3.06915e9 q^{63} +1.29912e9 q^{64} -1.33237e10 q^{65} -2.82267e9 q^{66} +6.61153e9 q^{67} +5.77782e9 q^{68} -1.26870e9 q^{69} +9.00013e9 q^{70} +1.75093e10 q^{71} -5.59015e9 q^{72} -1.99968e10 q^{73} -3.31772e10 q^{74} +6.38199e9 q^{75} -1.08089e10 q^{76} +5.72304e9 q^{77} -4.06735e10 q^{78} +4.13459e10 q^{79} -2.69039e10 q^{80} -4.92913e9 q^{81} +8.64150e9 q^{82} +9.08317e9 q^{83} +9.01437e9 q^{84} +2.96505e10 q^{85} +7.54866e10 q^{86} +5.82045e9 q^{87} -1.04239e10 q^{88} +5.85488e10 q^{89} +2.73765e10 q^{90} +8.24666e10 q^{91} +4.47111e9 q^{92} -7.83598e10 q^{93} +1.14191e11 q^{94} -5.54688e10 q^{95} -4.85060e10 q^{96} +7.42488e10 q^{97} +5.34607e10 q^{98} +1.74083e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9}+O(q^{10}) \) 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

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