LMFDB - Embedded newform 37.10.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,10,Mod(1,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("37.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	37.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:	$19.0563259381$
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} - 6 x^{13} - 5234 x^{12} + 33102 x^{11} + 10421899 x^{10} - 66002244 x^{9} + \cdots + 51\!\cdots\!20 $ x^14 - 6x^13 - 5234x^12 + 33102x^11 + 10421899x^10 - 66002244x^9 - 9839334124x^8 + 60512691564x^7 + 4405897359639x^6 - 25392014044254x^5 - 798948725725074x^4 + 3805427076948774x^3 + 41503424166638973x^2 - 100457651820986424*x + 51865911118483920
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$16.7224$ of defining polynomial
Character	$\chi$	$=$	37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+19.7224 q^{2} -4.59450 q^{3} -123.026 q^{4} +1294.63 q^{5} -90.6146 q^{6} +10932.2 q^{7} -12524.3 q^{8} -19661.9 q^{9} +O(q^{10})$	\(q+19.7224 q^{2} -4.59450 q^{3} -123.026 q^{4} +1294.63 q^{5} -90.6146 q^{6} +10932.2 q^{7} -12524.3 q^{8} -19661.9 q^{9} +25533.2 q^{10} -12106.9 q^{11} +565.245 q^{12} +131031. q^{13} +215610. q^{14} -5948.18 q^{15} -184019. q^{16} +559798. q^{17} -387780. q^{18} +834235. q^{19} -159274. q^{20} -50228.2 q^{21} -238778. q^{22} +1.31118e6 q^{23} +57542.7 q^{24} -277059. q^{25} +2.58424e6 q^{26} +180770. q^{27} -1.34496e6 q^{28} +868358. q^{29} -117312. q^{30} -7.91306e6 q^{31} +2.78312e6 q^{32} +55625.3 q^{33} +1.10406e7 q^{34} +1.41532e7 q^{35} +2.41893e6 q^{36} +1.87416e6 q^{37} +1.64531e7 q^{38} -602021. q^{39} -1.62143e7 q^{40} -1.44997e7 q^{41} -990621. q^{42} -9.44607e6 q^{43} +1.48947e6 q^{44} -2.54549e7 q^{45} +2.58596e7 q^{46} -575498. q^{47} +845475. q^{48} +7.91604e7 q^{49} -5.46426e6 q^{50} -2.57199e6 q^{51} -1.61202e7 q^{52} -2.25201e7 q^{53} +3.56522e6 q^{54} -1.56740e7 q^{55} -1.36918e8 q^{56} -3.83289e6 q^{57} +1.71261e7 q^{58} -1.47467e8 q^{59} +731783. q^{60} -2.95734e7 q^{61} -1.56065e8 q^{62} -2.14949e8 q^{63} +1.49108e8 q^{64} +1.69636e8 q^{65} +1.09707e6 q^{66} -3.13628e8 q^{67} -6.88699e7 q^{68} -6.02421e6 q^{69} +2.79136e8 q^{70} +1.99072e8 q^{71} +2.46251e8 q^{72} +1.66018e8 q^{73} +3.69630e7 q^{74} +1.27295e6 q^{75} -1.02633e8 q^{76} -1.32356e8 q^{77} -1.18733e7 q^{78} +1.16930e8 q^{79} -2.38236e8 q^{80} +3.86174e8 q^{81} -2.85968e8 q^{82} +6.63907e8 q^{83} +6.17940e6 q^{84} +7.24731e8 q^{85} -1.86299e8 q^{86} -3.98967e6 q^{87} +1.51630e8 q^{88} -7.14990e8 q^{89} -5.02031e8 q^{90} +1.43246e9 q^{91} -1.61310e8 q^{92} +3.63565e7 q^{93} -1.13502e7 q^{94} +1.08003e9 q^{95} -1.27870e7 q^{96} -1.19344e9 q^{97} +1.56123e9 q^{98} +2.38045e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9}+O(q^{10}) $ 14 * q + 48 * q^2 + 397 * q^3 + 3498 * q^4 + 2841 * q^5 + 3375 * q^6 + 6632 * q^7 + 41046 * q^8 + 101917 * q^9	\( 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9} + 129003 q^{10} + 44949 q^{11} - 123661 q^{12} + 38913 q^{13} + 16434 q^{14} + 119816 q^{15} + 859962 q^{16} + 893196 q^{17} + 1833339 q^{18} + 1532124 q^{19} + 4974963 q^{20} + 1851132 q^{21} + 3195323 q^{22} + 5911773 q^{23} + 7885413 q^{24} + 9978791 q^{25} + 10634475 q^{26} + 13105312 q^{27} + 9469678 q^{28} + 8764377 q^{29} + 21804216 q^{30} + 13188927 q^{31} + 23982750 q^{32} + 9398618 q^{33} + 29914960 q^{34} + 29633556 q^{35} + 24297333 q^{36} + 26238254 q^{37} + 23342796 q^{38} + 40855861 q^{39} + 42889049 q^{40} + 22153785 q^{41} + 6999662 q^{42} + 1779790 q^{43} - 83674089 q^{44} - 45101798 q^{45} - 23239663 q^{46} + 40080072 q^{47} - 141884869 q^{48} - 170457752 q^{49} - 89214633 q^{50} - 127867462 q^{51} - 276889277 q^{52} - 102088122 q^{53} - 356745582 q^{54} - 206797385 q^{55} - 294922194 q^{56} - 141710762 q^{57} - 527059089 q^{58} + 56191266 q^{59} - 283393416 q^{60} - 178507397 q^{61} - 27353505 q^{62} - 291948734 q^{63} - 242330062 q^{64} - 174258810 q^{65} - 1153895008 q^{66} + 287062499 q^{67} + 308827572 q^{68} - 80094823 q^{69} - 672888452 q^{70} + 224382678 q^{71} + 105778731 q^{72} + 271440727 q^{73} + 89959728 q^{74} + 1017561832 q^{75} - 229522980 q^{76} + 671279994 q^{77} - 119785879 q^{78} + 379128625 q^{79} + 1999017183 q^{80} + 2367007018 q^{81} + 551153781 q^{82} + 1664083206 q^{83} + 1344035042 q^{84} + 1982056546 q^{85} + 520253082 q^{86} + 3606452357 q^{87} + 684092585 q^{88} + 3293434692 q^{89} + 892602798 q^{90} + 1715813946 q^{91} + 3729310881 q^{92} + 2573139250 q^{93} + 998499458 q^{94} + 878402766 q^{95} - 1221963827 q^{96} + 2385468336 q^{97} - 3234447132 q^{98} + 4029218638 q^{99}+O(q^{100}) \) 14 * q + 48 * q^2 + 397 * q^3 + 3498 * q^4 + 2841 * q^5 + 3375 * q^6 + 6632 * q^7 + 41046 * q^8 + 101917 * q^9 + 129003 * q^10 + 44949 * q^11 - 123661 * q^12 + 38913 * q^13 + 16434 * q^14 + 119816 * q^15 + 859962 * q^16 + 893196 * q^17 + 1833339 * q^18 + 1532124 * q^19 + 4974963 * q^20 + 1851132 * q^21 + 3195323 * q^22 + 5911773 * q^23 + 7885413 * q^24 + 9978791 * q^25 + 10634475 * q^26 + 13105312 * q^27 + 9469678 * q^28 + 8764377 * q^29 + 21804216 * q^30 + 13188927 * q^31 + 23982750 * q^32 + 9398618 * q^33 + 29914960 * q^34 + 29633556 * q^35 + 24297333 * q^36 + 26238254 * q^37 + 23342796 * q^38 + 40855861 * q^39 + 42889049 * q^40 + 22153785 * q^41 + 6999662 * q^42 + 1779790 * q^43 - 83674089 * q^44 - 45101798 * q^45 - 23239663 * q^46 + 40080072 * q^47 - 141884869 * q^48 - 170457752 * q^49 - 89214633 * q^50 - 127867462 * q^51 - 276889277 * q^52 - 102088122 * q^53 - 356745582 * q^54 - 206797385 * q^55 - 294922194 * q^56 - 141710762 * q^57 - 527059089 * q^58 + 56191266 * q^59 - 283393416 * q^60 - 178507397 * q^61 - 27353505 * q^62 - 291948734 * q^63 - 242330062 * q^64 - 174258810 * q^65 - 1153895008 * q^66 + 287062499 * q^67 + 308827572 * q^68 - 80094823 * q^69 - 672888452 * q^70 + 224382678 * q^71 + 105778731 * q^72 + 271440727 * q^73 + 89959728 * q^74 + 1017561832 * q^75 - 229522980 * q^76 + 671279994 * q^77 - 119785879 * q^78 + 379128625 * q^79 + 1999017183 * q^80 + 2367007018 * q^81 + 551153781 * q^82 + 1664083206 * q^83 + 1344035042 * q^84 + 1982056546 * q^85 + 520253082 * q^86 + 3606452357 * q^87 + 684092585 * q^88 + 3293434692 * q^89 + 892602798 * q^90 + 1715813946 * q^91 + 3729310881 * q^92 + 2573139250 * q^93 + 998499458 * q^94 + 878402766 * q^95 - 1221963827 * q^96 + 2385468336 * q^97 - 3234447132 * q^98 + 4029218638 * 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 $

$2$	19.7224	0.871616	0.435808	−	0.900040i	$-0.356463\pi$
$2$	19.7224	0.871616	0.435808	+	0.900040i	$0.356463\pi$
$3$	−4.59450	−0.0327486	−0.0163743	−	0.999866i	$-0.505212\pi$
$3$	−4.59450	−0.0327486	−0.0163743	+	0.999866i	$0.505212\pi$
$4$	−123.026	−0.240286
$5$	1294.63	0.926362	0.463181	−	0.886264i	$-0.346708\pi$
$5$	1294.63	0.926362	0.463181	+	0.886264i	$0.346708\pi$
$6$	−90.6146	−0.0285442
$7$	10932.2	1.72095	0.860475	−	0.509493i	$-0.170167\pi$
$7$	10932.2	1.72095	0.860475	+	0.509493i	$0.170167\pi$
$8$	−12524.3	−1.08105
$9$	−19661.9	−0.998928
$10$	25533.2	0.807431
$11$	−12106.9	−0.249326	−0.124663	−	0.992199i	$-0.539785\pi$
$11$	−12106.9	−0.249326	−0.124663	+	0.992199i	$0.539785\pi$
$12$	565.245	0.00786903
$13$	131031.	1.27241	0.636207	−	0.771519i	$-0.280503\pi$
$13$	131031.	1.27241	0.636207	+	0.771519i	$0.280503\pi$
$14$	215610.	1.50001
$15$	−5948.18	−0.0303370
$16$	−184019.	−0.701977
$17$	559798.	1.62559	0.812795	−	0.582550i	$-0.197945\pi$
$17$	559798.	1.62559	0.812795	+	0.582550i	$0.197945\pi$
$18$	−387780.	−0.870681
$19$	834235.	1.46858	0.734289	−	0.678837i	$-0.237516\pi$
$19$	834235.	1.46858	0.734289	+	0.678837i	$0.237516\pi$
$20$	−159274.	−0.222592
$21$	−50228.2	−0.0563587
$22$	−238778.	−0.217316
$23$	1.31118e6	0.976983	0.488491	−	0.872569i	$-0.337547\pi$
$23$	1.31118e6	0.976983	0.488491	+	0.872569i	$0.337547\pi$
$24$	57542.7	0.0354029
$25$	−277059.	−0.141854
$26$	2.58424e6	1.10906
$27$	180770.	0.0654620
$28$	−1.34496e6	−0.413520
$29$	868358.	0.227986	0.113993	−	0.993482i	$-0.463636\pi$
$29$	868358.	0.227986	0.113993	+	0.993482i	$0.463636\pi$
$30$	−117312.	−0.0264422
$31$	−7.91306e6	−1.53892	−0.769461	−	0.638694i	$-0.779475\pi$
$31$	−7.91306e6	−1.53892	−0.769461	+	0.638694i	$0.779475\pi$
$32$	2.78312e6	0.469199
$33$	55625.3	0.00816507
$34$	1.10406e7	1.41689
$35$	1.41532e7	1.59422
$36$	2.41893e6	0.240028
$37$	1.87416e6	0.164399
$37$	1.87416e6	0.164399
$38$	1.64531e7	1.28004
$39$	−602021.	−0.0416697
$40$	−1.62143e7	−1.00145
$41$	−1.44997e7	−0.801365	−0.400682	−	0.916217i	$-0.631227\pi$
$41$	−1.44997e7	−0.801365	−0.400682	+	0.916217i	$0.631227\pi$
$42$	−990621.	−0.0491231
$43$	−9.44607e6	−0.421350	−0.210675	−	0.977556i	$-0.567566\pi$
$43$	−9.44607e6	−0.421350	−0.210675	+	0.977556i	$0.567566\pi$
$44$	1.48947e6	0.0599095
$45$	−2.54549e7	−0.925368
$46$	2.58596e7	0.851553
$47$	−575498.	−0.0172030	−0.00860149	−	0.999963i	$-0.502738\pi$
$47$	−575498.	−0.0172030	−0.00860149	+	0.999963i	$0.502738\pi$
$48$	845475.	0.0229887
$49$	7.91604e7	1.96167
$50$	−5.46426e6	−0.123642
$51$	−2.57199e6	−0.0532358
$52$	−1.61202e7	−0.305743
$53$	−2.25201e7	−0.392038	−0.196019	−	0.980600i	$-0.562801\pi$
$53$	−2.25201e7	−0.392038	−0.196019	+	0.980600i	$0.562801\pi$
$54$	3.56522e6	0.0570577
$55$	−1.56740e7	−0.230966
$56$	−1.36918e8	−1.86044
$57$	−3.83289e6	−0.0480939
$58$	1.71261e7	0.198716
$59$	−1.47467e8	−1.58439	−0.792194	−	0.610269i	$-0.791061\pi$
$59$	−1.47467e8	−1.58439	−0.792194	+	0.610269i	$0.791061\pi$
$60$	731783.	0.00728956
$61$	−2.95734e7	−0.273474	−0.136737	−	0.990607i	$-0.543662\pi$
$61$	−2.95734e7	−0.273474	−0.136737	+	0.990607i	$0.543662\pi$
$62$	−1.56065e8	−1.34135
$63$	−2.14949e8	−1.71910
$64$	1.49108e8	1.11094
$65$	1.69636e8	1.17872
$66$	1.09707e6	0.00711680
$67$	−3.13628e8	−1.90142	−0.950711	−	0.310077i	$-0.899645\pi$
$67$	−3.13628e8	−1.90142	−0.950711	+	0.310077i	$0.899645\pi$
$68$	−6.88699e7	−0.390606
$69$	−6.02421e6	−0.0319948
$70$	2.79136e8	1.38955
$71$	1.99072e8	0.929712	0.464856	−	0.885386i	$-0.346106\pi$
$71$	1.99072e8	0.929712	0.464856	+	0.885386i	$0.346106\pi$
$72$	2.46251e8	1.07989
$73$	1.66018e8	0.684231	0.342115	−	0.939658i	$-0.388857\pi$
$73$	1.66018e8	0.684231	0.342115	+	0.939658i	$0.388857\pi$
$74$	3.69630e7	0.143293
$75$	1.27295e6	0.00464552
$76$	−1.02633e8	−0.352879
$77$	−1.32356e8	−0.429077
$78$	−1.18733e7	−0.0363200
$79$	1.16930e8	0.337756	0.168878	−	0.985637i	$-0.445986\pi$
$79$	1.16930e8	0.337756	0.168878	+	0.985637i	$0.445986\pi$
$80$	−2.38236e8	−0.650284
$81$	3.86174e8	0.996784
$82$	−2.85968e8	−0.698482
$83$	6.63907e8	1.53552	0.767761	−	0.640737i	$-0.221371\pi$
$83$	6.63907e8	1.53552	0.767761	+	0.640737i	$0.221371\pi$
$84$	6.17940e6	0.0135422
$85$	7.24731e8	1.50588
$86$	−1.86299e8	−0.367255
$87$	−3.98967e6	−0.00746621
$88$	1.51630e8	0.269534
$89$	−7.14990e8	−1.20794	−0.603969	−	0.797008i	$-0.706415\pi$
$89$	−7.14990e8	−1.20794	−0.603969	+	0.797008i	$0.706415\pi$
$90$	−5.02031e8	−0.806566
$91$	1.43246e9	2.18976
$92$	−1.61310e8	−0.234755
$93$	3.63565e7	0.0503975
$94$	−1.13502e7	−0.0149944
$95$	1.08003e9	1.36044
$96$	−1.27870e7	−0.0153656
$97$	−1.19344e9	−1.36876	−0.684380	−	0.729126i	$-0.739927\pi$
$97$	−1.19344e9	−1.36876	−0.684380	+	0.729126i	$0.739927\pi$
$98$	1.56123e9	1.70982
$99$	2.38045e8	0.249059
$100$	3.40855e7	0.0340855
$101$	−4.67384e8	−0.446918	−0.223459	−	0.974713i	$-0.571735\pi$
$101$	−4.67384e8	−0.446918	−0.223459	+	0.974713i	$0.571735\pi$
$102$	−5.07259e7	−0.0464011
$103$	−1.20613e9	−1.05591	−0.527954	−	0.849273i	$-0.677041\pi$
$103$	−1.20613e9	−1.05591	−0.527954	+	0.849273i	$0.677041\pi$
$104$	−1.64106e9	−1.37555
$105$	−6.50269e7	−0.0522085
$106$	−4.44150e8	−0.341707
$107$	−1.14065e9	−0.841249	−0.420624	−	0.907235i	$-0.638189\pi$
$107$	−1.14065e9	−0.841249	−0.420624	+	0.907235i	$0.638189\pi$
$108$	−2.22395e7	−0.0157296
$109$	9.36138e8	0.635215	0.317607	−	0.948222i	$-0.397121\pi$
$109$	9.36138e8	0.635215	0.317607	+	0.948222i	$0.397121\pi$
$110$	−3.09129e8	−0.201314
$111$	−8.61083e6	−0.00538383
$112$	−2.01174e9	−1.20807
$113$	2.21205e9	1.27627	0.638134	−	0.769925i	$-0.279707\pi$
$113$	2.21205e9	1.27627	0.638134	+	0.769925i	$0.279707\pi$
$114$	−7.55939e7	−0.0419194
$115$	1.69749e9	0.905039
$116$	−1.06831e8	−0.0547818
$117$	−2.57631e9	−1.27105
$118$	−2.90841e9	−1.38098
$119$	6.11985e9	2.79756
$120$	7.44965e7	0.0327959
$121$	−2.21137e9	−0.937837
$122$	−5.83258e8	−0.238365
$123$	6.66186e7	0.0262436
$124$	9.73515e8	0.369782
$125$	−2.88726e9	−1.05777
$126$	−4.23931e9	−1.49840
$127$	−2.04987e9	−0.699213	−0.349606	−	0.936897i	$-0.613685\pi$
$127$	−2.04987e9	−0.699213	−0.349606	+	0.936897i	$0.613685\pi$
$128$	1.51580e9	0.499112
$129$	4.34000e7	0.0137986
$130$	3.34564e9	1.02739
$131$	7.60721e8	0.225686	0.112843	−	0.993613i	$-0.464004\pi$
$131$	7.60721e8	0.225686	0.112843	+	0.993613i	$0.464004\pi$
$132$	−6.84339e6	−0.00196195
$133$	9.12006e9	2.52735
$134$	−6.18551e9	−1.65731
$135$	2.34030e8	0.0606415
$136$	−7.01105e9	−1.75735
$137$	−7.55403e8	−0.183205	−0.0916023	−	0.995796i	$-0.529199\pi$
$137$	−7.55403e8	−0.183205	−0.0916023	+	0.995796i	$0.529199\pi$
$138$	−1.18812e8	−0.0278872
$139$	5.70778e9	1.29688	0.648441	−	0.761265i	$-0.275421\pi$
$139$	5.70778e9	1.29688	0.648441	+	0.761265i	$0.275421\pi$
$140$	−1.74122e9	−0.383069
$141$	2.64412e6	0.000563373 0
$142$	3.92619e9	0.810352
$143$	−1.58638e9	−0.317246
$144$	3.61816e9	0.701224
$145$	1.12420e9	0.211197
$146$	3.27428e9	0.596386
$147$	−3.63702e8	−0.0642419
$148$	−2.30571e8	−0.0395028
$149$	−1.73790e9	−0.288859	−0.144430	−	0.989515i	$-0.546135\pi$
$149$	−1.73790e9	−0.288859	−0.144430	+	0.989515i	$0.546135\pi$
$150$	2.51056e7	0.00404911
$151$	6.57538e9	1.02926	0.514629	−	0.857413i	$-0.327930\pi$
$151$	6.57538e9	1.02926	0.514629	+	0.857413i	$0.327930\pi$
$152$	−1.04482e10	−1.58761
$153$	−1.10067e10	−1.62385
$154$	−2.61038e9	−0.373991
$155$	−1.02445e10	−1.42560
$156$	7.40645e7	0.0100127
$157$	4.27094e9	0.561015	0.280508	−	0.959852i	$-0.409497\pi$
$157$	4.27094e9	0.561015	0.280508	+	0.959852i	$0.409497\pi$
$158$	2.30614e9	0.294394
$159$	1.03468e8	0.0128387
$160$	3.60311e9	0.434648
$161$	1.43341e10	1.68134
$162$	7.61629e9	0.868812
$163$	−5.79182e9	−0.642644	−0.321322	−	0.946970i	$-0.604127\pi$
$163$	−5.79182e9	−0.642644	−0.321322	+	0.946970i	$0.604127\pi$
$164$	1.78384e9	0.192557
$165$	7.20142e7	0.00756381
$166$	1.30939e10	1.33838
$167$	1.73516e10	1.72630	0.863151	−	0.504947i	$-0.168488\pi$
$167$	1.73516e10	1.72630	0.863151	+	0.504947i	$0.168488\pi$
$168$	6.29071e8	0.0609267
$169$	6.56457e9	0.619036
$170$	1.42934e10	1.31255
$171$	−1.64026e10	−1.46700
$172$	1.16212e9	0.101245
$173$	−9.59737e9	−0.814600	−0.407300	−	0.913294i	$-0.633530\pi$
$173$	−9.59737e9	−0.814600	−0.407300	+	0.913294i	$0.633530\pi$
$174$	−7.86859e7	−0.00650767
$175$	−3.02887e9	−0.244124
$176$	2.22791e9	0.175021
$177$	6.77538e8	0.0518865
$178$	−1.41013e10	−1.05286
$179$	−1.87832e10	−1.36751	−0.683754	−	0.729712i	$-0.739654\pi$
$179$	−1.87832e10	−1.36751	−0.683754	+	0.729712i	$0.739654\pi$
$180$	3.13162e9	0.222353
$181$	9.26134e9	0.641387	0.320694	−	0.947183i	$-0.396084\pi$
$181$	9.26134e9	0.641387	0.320694	+	0.947183i	$0.396084\pi$
$182$	2.82516e10	1.90863
$183$	1.35875e8	0.00895590
$184$	−1.64215e10	−1.05617
$185$	2.42634e9	0.152293
$186$	7.17039e8	0.0439273
$187$	−6.77744e9	−0.405302
$188$	7.08015e7	0.00413363
$189$	1.97622e9	0.112657
$190$	2.13007e10	1.18578
$191$	−6.14215e9	−0.333941	−0.166971	−	0.985962i	$-0.553399\pi$
$191$	−6.14215e9	−0.333941	−0.166971	+	0.985962i	$0.553399\pi$
$192$	−6.85074e8	−0.0363816
$193$	−2.41383e10	−1.25227	−0.626136	−	0.779714i	$-0.715365\pi$
$193$	−2.41383e10	−1.25227	−0.626136	+	0.779714i	$0.715365\pi$
$194$	−2.35375e10	−1.19303
$195$	−7.79394e8	−0.0386012
$196$	−9.73882e9	−0.471362
$197$	3.11518e10	1.47362	0.736809	−	0.676101i	$-0.236332\pi$
$197$	3.11518e10	1.47362	0.736809	+	0.676101i	$0.236332\pi$
$198$	4.69483e9	0.217083
$199$	2.78368e10	1.25829	0.629146	−	0.777287i	$-0.283405\pi$
$199$	2.78368e10	1.25829	0.629146	+	0.777287i	$0.283405\pi$
$200$	3.46995e9	0.153352
$201$	1.44097e9	0.0622689
$202$	−9.21794e9	−0.389541
$203$	9.49311e9	0.392352
$204$	3.16423e8	0.0127918
$205$	−1.87717e10	−0.742354
$206$	−2.37878e10	−0.920346
$207$	−2.57803e10	−0.975935
$208$	−2.41121e10	−0.893205
$209$	−1.01000e10	−0.366155
$210$	−1.28249e9	−0.0455058
$211$	−3.98071e10	−1.38258	−0.691289	−	0.722579i	$-0.742957\pi$
$211$	−3.98071e10	−1.38258	−0.691289	+	0.722579i	$0.742957\pi$
$212$	2.77056e9	0.0942013
$213$	−9.14638e8	−0.0304468
$214$	−2.24963e10	−0.733246
$215$	−1.22292e10	−0.390323
$216$	−2.26401e9	−0.0707679
$217$	−8.65075e10	−2.64841
$218$	1.84629e10	0.553663
$219$	−7.62770e8	−0.0224076
$220$	1.92832e9	0.0554979
$221$	7.33507e10	2.06842
$222$	−1.69826e8	−0.00469263
$223$	−9.86531e9	−0.267140	−0.133570	−	0.991039i	$-0.542644\pi$
$223$	−9.86531e9	−0.267140	−0.133570	+	0.991039i	$0.542644\pi$
$224$	3.04258e10	0.807468
$225$	5.44749e9	0.141702
$226$	4.36269e10	1.11242
$227$	−2.56627e10	−0.641483	−0.320742	−	0.947167i	$-0.603932\pi$
$227$	−2.56627e10	−0.641483	−0.320742	+	0.947167i	$0.603932\pi$
$228$	4.71547e8	0.0115563
$229$	−1.18702e10	−0.285232	−0.142616	−	0.989778i	$-0.545551\pi$
$229$	−1.18702e10	−0.285232	−0.142616	+	0.989778i	$0.545551\pi$
$230$	3.34786e10	0.788846
$231$	6.08110e8	0.0140517
$232$	−1.08755e10	−0.246465
$233$	3.18641e9	0.0708272	0.0354136	−	0.999373i	$-0.488725\pi$
$233$	3.18641e9	0.0708272	0.0354136	+	0.999373i	$0.488725\pi$
$234$	−5.08111e10	−1.10787
$235$	−7.45057e8	−0.0159362
$236$	1.81424e10	0.380706
$237$	−5.37234e8	−0.0110610
$238$	1.20698e11	2.43840
$239$	6.79003e10	1.34611	0.673056	−	0.739591i	$-0.264981\pi$
$239$	6.79003e10	1.34611	0.673056	+	0.739591i	$0.264981\pi$
$240$	1.09458e9	0.0212959
$241$	−9.06780e10	−1.73151	−0.865755	−	0.500468i	$-0.833161\pi$
$241$	−9.06780e10	−1.73151	−0.865755	+	0.500468i	$0.833161\pi$
$242$	−4.36135e10	−0.817433
$243$	−5.33238e9	−0.0981053
$244$	3.63831e9	0.0657121
$245$	1.02483e11	1.81722
$246$	1.31388e9	0.0228743
$247$	1.09310e11	1.86864
$248$	9.91051e10	1.66366
$249$	−3.05032e9	−0.0502862
$250$	−5.69438e10	−0.921969
$251$	4.03360e10	0.641448	0.320724	−	0.947173i	$-0.396074\pi$
$251$	4.03360e10	0.641448	0.320724	+	0.947173i	$0.396074\pi$
$252$	2.64444e10	0.413077
$253$	−1.58744e10	−0.243587
$254$	−4.04284e10	−0.609445
$255$	−3.32978e9	−0.0493156
$256$	−4.64478e10	−0.675904
$257$	−9.00158e10	−1.28712	−0.643561	−	0.765395i	$-0.722544\pi$
$257$	−9.00158e10	−1.28712	−0.643561	+	0.765395i	$0.722544\pi$
$258$	8.55952e8	0.0120271
$259$	2.04888e10	0.282922
$260$	−2.08698e10	−0.283229
$261$	−1.70736e10	−0.227741
$262$	1.50033e10	0.196712
$263$	1.12736e10	0.145298	0.0726492	−	0.997358i	$-0.476855\pi$
$263$	1.12736e10	0.145298	0.0726492	+	0.997358i	$0.476855\pi$
$264$	−6.96666e8	−0.00882687
$265$	−2.91552e10	−0.363169
$266$	1.79870e11	2.20288
$267$	3.28502e9	0.0395583
$268$	3.85846e10	0.456885
$269$	−2.66417e8	−0.00310225	−0.00155112	−	0.999999i	$-0.500494\pi$
$269$	−2.66417e8	−0.00310225	−0.00155112	+	0.999999i	$0.500494\pi$
$270$	4.61564e9	0.0528561
$271$	6.71510e10	0.756294	0.378147	−	0.925746i	$-0.376561\pi$
$271$	6.71510e10	0.756294	0.378147	+	0.925746i	$0.376561\pi$
$272$	−1.03013e11	−1.14113
$273$	−6.58144e9	−0.0717115
$274$	−1.48984e10	−0.159684
$275$	3.35433e9	0.0353679
$276$	7.41137e8	0.00768790
$277$	−6.01488e10	−0.613858	−0.306929	−	0.951732i	$-0.599301\pi$
$277$	−6.01488e10	−0.613858	−0.306929	+	0.951732i	$0.599301\pi$
$278$	1.12571e11	1.13038
$279$	1.55586e11	1.53727
$280$	−1.77258e11	−1.72344
$281$	−6.86869e10	−0.657197	−0.328598	−	0.944470i	$-0.606576\pi$
$281$	−6.86869e10	−0.657197	−0.328598	+	0.944470i	$0.606576\pi$
$282$	5.21485e7	0.000491045 0
$283$	−1.10859e11	−1.02738	−0.513689	−	0.857977i	$-0.671721\pi$
$283$	−1.10859e11	−1.02738	−0.513689	+	0.857977i	$0.671721\pi$
$284$	−2.44912e10	−0.223397
$285$	−4.96218e9	−0.0445523
$286$	−3.12873e10	−0.276516
$287$	−1.58514e11	−1.37911
$288$	−5.47214e10	−0.468696
$289$	1.94786e11	1.64254
$290$	2.21720e10	0.184083
$291$	5.48325e9	0.0448249
$292$	−2.04246e10	−0.164411
$293$	−4.79500e10	−0.380088	−0.190044	−	0.981776i	$-0.560863\pi$
$293$	−4.79500e10	−0.380088	−0.190044	+	0.981776i	$0.560863\pi$
$294$	−7.17309e9	−0.0559942
$295$	−1.90915e11	−1.46772
$296$	−2.34725e10	−0.177724
$297$	−2.18857e9	−0.0163214
$298$	−3.42756e10	−0.251774
$299$	1.71805e11	1.24313
$300$	−1.56606e8	−0.00111625
$301$	−1.03267e11	−0.725122
$302$	1.29682e11	0.897118
$303$	2.14740e9	0.0146359
$304$	−1.53515e11	−1.03091
$305$	−3.82866e10	−0.253336
$306$	−2.17078e11	−1.41537
$307$	1.25995e11	0.809528	0.404764	−	0.914421i	$-0.367354\pi$
$307$	1.25995e11	0.809528	0.404764	+	0.914421i	$0.367354\pi$
$308$	1.62833e10	0.103101
$309$	5.54155e9	0.0345795
$310$	−2.02046e11	−1.24257
$311$	1.93710e11	1.17417	0.587084	−	0.809526i	$-0.300276\pi$
$311$	1.93710e11	1.17417	0.587084	+	0.809526i	$0.300276\pi$
$312$	7.53986e9	0.0450472
$313$	−1.27977e11	−0.753671	−0.376835	−	0.926280i	$-0.622988\pi$
$313$	−1.27977e11	−0.753671	−0.376835	+	0.926280i	$0.622988\pi$
$314$	8.42332e10	0.488990
$315$	−2.78279e11	−1.59251
$316$	−1.43855e10	−0.0811581
$317$	−9.76563e10	−0.543167	−0.271584	−	0.962415i	$-0.587547\pi$
$317$	−9.76563e10	−0.543167	−0.271584	+	0.962415i	$0.587547\pi$
$318$	2.04065e9	0.0111904
$319$	−1.05132e10	−0.0568428
$320$	1.93039e11	1.02913
$321$	5.24070e9	0.0275497
$322$	2.82704e11	1.46548
$323$	4.67003e11	2.38731
$324$	−4.75097e10	−0.239513
$325$	−3.63032e10	−0.180497
$326$	−1.14229e11	−0.560139
$327$	−4.30108e9	−0.0208024
$328$	1.81597e11	0.866318
$329$	−6.29149e9	−0.0296055
$330$	1.42029e9	0.00659273
$331$	1.55365e11	0.711422	0.355711	−	0.934596i	$-0.384239\pi$
$331$	1.55365e11	0.711422	0.355711	+	0.934596i	$0.384239\pi$
$332$	−8.16781e10	−0.368964
$333$	−3.68495e10	−0.164223
$334$	3.42216e11	1.50467
$335$	−4.06033e11	−1.76141
$336$	9.24294e9	0.0395625
$337$	−3.66763e11	−1.54900	−0.774500	−	0.632574i	$-0.781999\pi$
$337$	−3.66763e11	−1.54900	−0.774500	+	0.632574i	$0.781999\pi$
$338$	1.29469e11	0.539562
$339$	−1.01633e10	−0.0417960
$340$	−8.91611e10	−0.361843
$341$	9.58029e10	0.383693
$342$	−3.23500e11	−1.27866
$343$	4.24246e11	1.65498
$344$	1.18305e11	0.455502
$345$	−7.79912e9	−0.0296388
$346$	−1.89283e11	−0.710018
$347$	−5.27051e10	−0.195151	−0.0975753	−	0.995228i	$-0.531109\pi$
$347$	−5.27051e10	−0.195151	−0.0975753	+	0.995228i	$0.531109\pi$
$348$	4.90835e8	0.00179403
$349$	−1.62721e11	−0.587124	−0.293562	−	0.955940i	$-0.594841\pi$
$349$	−1.62721e11	−0.587124	−0.293562	+	0.955940i	$0.594841\pi$
$350$	−5.97367e10	−0.212782
$351$	2.36864e10	0.0832948
$352$	−3.36951e10	−0.116983
$353$	3.54670e10	0.121573	0.0607866	−	0.998151i	$-0.480639\pi$
$353$	3.54670e10	0.121573	0.0607866	+	0.998151i	$0.480639\pi$
$354$	1.33627e10	0.0452251
$355$	2.57725e11	0.861250
$356$	8.79626e10	0.290251
$357$	−2.81176e10	−0.0916161
$358$	−3.70449e11	−1.19194
$359$	1.48868e11	0.473016	0.236508	−	0.971630i	$-0.423997\pi$
$359$	1.48868e11	0.473016	0.236508	+	0.971630i	$0.423997\pi$
$360$	3.18803e11	1.00037
$361$	3.73260e11	1.15672
$362$	1.82656e11	0.559043
$363$	1.01601e10	0.0307128
$364$	−1.76231e11	−0.526169
$365$	2.14932e11	0.633845
$366$	2.67978e9	0.00780610
$367$	−3.54977e11	−1.02142	−0.510708	−	0.859754i	$-0.670617\pi$
$367$	−3.54977e11	−1.02142	−0.510708	+	0.859754i	$0.670617\pi$
$368$	−2.41282e11	−0.685819
$369$	2.85091e11	0.800505
$370$	4.78534e10	0.132741
$371$	−2.46195e11	−0.674678
$372$	−4.47281e9	−0.0121098
$373$	2.89668e11	0.774838	0.387419	−	0.921904i	$-0.373367\pi$
$373$	2.89668e11	0.774838	0.387419	+	0.921904i	$0.373367\pi$
$374$	−1.33667e11	−0.353267
$375$	1.32655e10	0.0346405
$376$	7.20768e9	0.0185973
$377$	1.13782e11	0.290092
$378$	3.89759e10	0.0981935
$379$	7.70971e10	0.191938	0.0959692	−	0.995384i	$-0.469405\pi$
$379$	7.70971e10	0.191938	0.0959692	+	0.995384i	$0.469405\pi$
$380$	−1.32872e11	−0.326893
$381$	9.41812e9	0.0228982
$382$	−1.21138e11	−0.291068
$383$	3.66015e11	0.869170	0.434585	−	0.900631i	$-0.356895\pi$
$383$	3.66015e11	0.869170	0.434585	+	0.900631i	$0.356895\pi$
$384$	−6.96436e9	−0.0163452
$385$	−1.71352e11	−0.397481
$386$	−4.76066e11	−1.09150
$387$	1.85728e11	0.420898
$388$	1.46824e11	0.328894
$389$	5.16898e11	1.14454	0.572271	−	0.820065i	$-0.306063\pi$
$389$	5.16898e11	1.14454	0.572271	+	0.820065i	$0.306063\pi$
$390$	−1.53715e10	−0.0336455
$391$	7.33995e11	1.58817
$392$	−9.91425e11	−2.12067
$393$	−3.49513e9	−0.00739090
$394$	6.14388e11	1.28443
$395$	1.51381e11	0.312884
$396$	−2.92859e10	−0.0598453
$397$	2.05972e11	0.416152	0.208076	−	0.978113i	$-0.433280\pi$
$397$	2.05972e11	0.416152	0.208076	+	0.978113i	$0.433280\pi$
$398$	5.49010e11	1.09675
$399$	−4.19021e10	−0.0827671
$400$	5.09840e10	0.0995782
$401$	−2.99634e11	−0.578684	−0.289342	−	0.957226i	$-0.593437\pi$
$401$	−2.99634e11	−0.578684	−0.289342	+	0.957226i	$0.593437\pi$
$402$	2.84193e10	0.0542746
$403$	−1.03685e12	−1.95815
$404$	5.75006e10	0.107388
$405$	4.99953e11	0.923382
$406$	1.87227e11	0.341980
$407$	−2.26904e10	−0.0409889
$408$	3.22123e10	0.0575507
$409$	−2.28781e11	−0.404264	−0.202132	−	0.979358i	$-0.564787\pi$
$409$	−2.28781e11	−0.404264	−0.202132	+	0.979358i	$0.564787\pi$
$410$	−3.70223e11	−0.647047
$411$	3.47070e9	0.00599969
$412$	1.48386e11	0.253720
$413$	−1.61215e12	−2.72665
$414$	−5.08449e11	−0.850640
$415$	8.59514e11	1.42245
$416$	3.64674e11	0.597015
$417$	−2.62244e10	−0.0424710
$418$	−1.99197e11	−0.319146
$419$	−5.81778e11	−0.922134	−0.461067	−	0.887365i	$-0.652533\pi$
$419$	−5.81778e11	−0.922134	−0.461067	+	0.887365i	$0.652533\pi$
$420$	8.00003e9	0.0125450
$421$	9.50730e11	1.47499	0.737493	−	0.675355i	$-0.236010\pi$
$421$	9.50730e11	1.47499	0.737493	+	0.675355i	$0.236010\pi$
$422$	−7.85092e11	−1.20508
$423$	1.13154e10	0.0171845
$424$	2.82047e11	0.423814
$425$	−1.55097e11	−0.230596
$426$	−1.80389e10	−0.0265379
$427$	−3.23304e11	−0.470636
$428$	1.40330e11	0.202140
$429$	7.28863e9	0.0103893
$430$	−2.41189e11	−0.340211
$431$	4.81790e11	0.672527	0.336264	−	0.941768i	$-0.390837\pi$
$431$	4.81790e11	0.672527	0.336264	+	0.941768i	$0.390837\pi$
$432$	−3.32651e10	−0.0459528
$433$	−8.98817e11	−1.22878	−0.614392	−	0.789001i	$-0.710599\pi$
$433$	−8.98817e11	−1.22878	−0.614392	+	0.789001i	$0.710599\pi$
$434$	−1.70614e12	−2.30839
$435$	−5.16515e9	−0.00691641
$436$	−1.15170e11	−0.152633
$437$	1.09383e12	1.43478
$438$	−1.50437e10	−0.0195308
$439$	−1.54786e12	−1.98903	−0.994517	−	0.104574i	$-0.966652\pi$
$439$	−1.54786e12	−1.98903	−0.994517	+	0.104574i	$0.966652\pi$
$440$	1.96305e11	0.249686
$441$	−1.55644e12	−1.95957
$442$	1.44665e12	1.80287
$443$	7.12269e11	0.878673	0.439337	−	0.898323i	$-0.355214\pi$
$443$	7.12269e11	0.878673	0.439337	+	0.898323i	$0.355214\pi$
$444$	1.05936e9	0.00129366
$445$	−9.25647e11	−1.11899
$446$	−1.94568e11	−0.232844
$447$	7.98478e9	0.00945973
$448$	1.63008e12	1.91187
$449$	9.09336e11	1.05588	0.527941	−	0.849281i	$-0.322964\pi$
$449$	9.09336e11	1.05588	0.527941	+	0.849281i	$0.322964\pi$
$450$	1.07438e11	0.123510
$451$	1.75546e11	0.199801
$452$	−2.72141e11	−0.306669
$453$	−3.02106e10	−0.0337068
$454$	−5.06129e11	−0.559127
$455$	1.85451e12	2.02851
$456$	4.80041e10	0.0519920
$457$	−6.91667e11	−0.741778	−0.370889	−	0.928677i	$-0.620947\pi$
$457$	−6.91667e11	−0.741778	−0.370889	+	0.928677i	$0.620947\pi$
$458$	−2.34109e11	−0.248613
$459$	1.01195e11	0.106414
$460$	−2.08836e11	−0.217468
$461$	−1.48746e12	−1.53388	−0.766939	−	0.641720i	$-0.778221\pi$
$461$	−1.48746e12	−1.53388	−0.766939	+	0.641720i	$0.778221\pi$
$462$	1.19934e10	0.0122477
$463$	1.05707e12	1.06903	0.534514	−	0.845160i	$-0.320495\pi$
$463$	1.05707e12	1.06903	0.534514	+	0.845160i	$0.320495\pi$
$464$	−1.59794e11	−0.160041
$465$	4.70683e10	0.0466863
$466$	6.28437e10	0.0617341
$467$	−2.12127e11	−0.206381	−0.103191	−	0.994662i	$-0.532905\pi$
$467$	−2.12127e11	−0.206381	−0.103191	+	0.994662i	$0.532905\pi$
$468$	3.16955e11	0.305415
$469$	−3.42866e12	−3.27225
$470$	−1.46943e10	−0.0138902
$471$	−1.96228e10	−0.0183725
$472$	1.84692e12	1.71281
$473$	1.14363e11	0.105053
$474$	−1.05956e10	−0.00964098
$475$	−2.31132e11	−0.208324
$476$	−7.52903e11	−0.672214
$477$	4.42787e11	0.391618
$478$	1.33916e12	1.17329
$479$	7.07578e11	0.614136	0.307068	−	0.951688i	$-0.400652\pi$
$479$	7.07578e11	0.614136	0.307068	+	0.951688i	$0.400652\pi$
$480$	−1.65545e10	−0.0142341
$481$	2.45573e11	0.209183
$482$	−1.78839e12	−1.50921
$483$	−6.58582e10	−0.0550614
$484$	2.72057e11	0.225349
$485$	−1.54506e12	−1.26797
$486$	−1.05167e11	−0.0855101
$487$	3.98529e11	0.321056	0.160528	−	0.987031i	$-0.448680\pi$
$487$	3.98529e11	0.321056	0.160528	+	0.987031i	$0.448680\pi$
$488$	3.70385e11	0.295640
$489$	2.66105e10	0.0210457
$490$	2.02122e12	1.58391
$491$	1.88715e12	1.46534	0.732671	−	0.680583i	$-0.238273\pi$
$491$	1.88715e12	1.46534	0.732671	+	0.680583i	$0.238273\pi$
$492$	−8.19585e9	−0.00630596
$493$	4.86105e11	0.370612
$494$	2.15587e12	1.62874
$495$	3.08181e11	0.230718
$496$	1.45615e12	1.08029
$497$	2.17631e12	1.59999
$498$	−6.01597e10	−0.0438302
$499$	1.09346e12	0.789495	0.394747	−	0.918790i	$-0.370832\pi$
$499$	1.09346e12	0.789495	0.394747	+	0.918790i	$0.370832\pi$
$500$	3.55210e11	0.254167
$501$	−7.97221e10	−0.0565339
$502$	7.95524e11	0.559096
$503$	6.83512e11	0.476091	0.238046	−	0.971254i	$-0.423493\pi$
$503$	6.83512e11	0.476091	0.238046	+	0.971254i	$0.423493\pi$
$504$	2.69207e12	1.85844
$505$	−6.05089e11	−0.414008
$506$	−3.13081e11	−0.212314
$507$	−3.01609e10	−0.0202726
$508$	2.52188e11	0.168011
$509$	−2.01887e12	−1.33315	−0.666573	−	0.745440i	$-0.732239\pi$
$509$	−2.01887e12	−1.33315	−0.666573	+	0.745440i	$0.732239\pi$
$510$	−6.56712e10	−0.0429842
$511$	1.81495e12	1.17753
$512$	−1.69215e12	−1.08824
$513$	1.50805e11	0.0961362
$514$	−1.77533e12	−1.12188
$515$	−1.56149e12	−0.978152
$516$	−5.33934e9	−0.00331561
$517$	6.96752e9	0.00428915
$518$	4.04088e11	0.246600
$519$	4.40951e10	0.0266770
$520$	−2.12457e12	−1.27425
$521$	−2.25407e12	−1.34029	−0.670145	−	0.742231i	$-0.733768\pi$
$521$	−2.25407e12	−1.34029	−0.670145	+	0.742231i	$0.733768\pi$
$522$	−3.36732e11	−0.198503
$523$	1.23017e12	0.718966	0.359483	−	0.933152i	$-0.382953\pi$
$523$	1.23017e12	0.718966	0.359483	+	0.933152i	$0.382953\pi$
$524$	−9.35888e10	−0.0542292
$525$	1.39162e10	0.00799470
$526$	2.22342e11	0.126644
$527$	−4.42971e12	−2.50166
$528$	−1.02361e10	−0.00573169
$529$	−8.19615e10	−0.0455050
$530$	−5.75010e11	−0.316544
$531$	2.89948e12	1.58269
$532$	−1.12201e12	−0.607287
$533$	−1.89990e12	−1.01967
$534$	6.47885e10	0.0344796
$535$	−1.47672e12	−0.779301
$536$	3.92796e12	2.05554
$537$	8.62992e10	0.0447840
$538$	−5.25439e9	−0.00270397
$539$	−9.58391e11	−0.489095
$540$	−2.87919e10	−0.0145713
$541$	−2.93951e12	−1.47532	−0.737661	−	0.675171i	$-0.764070\pi$
$541$	−2.93951e12	−1.47532	−0.737661	+	0.675171i	$0.764070\pi$
$542$	1.32438e12	0.659197
$543$	−4.25512e10	−0.0210045
$544$	1.55798e12	0.762725
$545$	1.21195e12	0.588438
$546$	−1.29802e11	−0.0625049
$547$	−3.05804e12	−1.46049	−0.730247	−	0.683184i	$-0.760595\pi$
$547$	−3.05804e12	−1.46049	−0.730247	+	0.683184i	$0.760595\pi$
$548$	9.29346e10	0.0440215
$549$	5.81469e11	0.273181
$550$	6.61555e10	0.0308272
$551$	7.24415e11	0.334815
$552$	7.54488e10	0.0345881
$553$	1.27831e12	0.581262
$554$	−1.18628e12	−0.535048
$555$	−1.11478e10	−0.00498738
$556$	−7.02207e11	−0.311622
$557$	−3.13656e12	−1.38072	−0.690359	−	0.723467i	$-0.742547\pi$
$557$	−3.13656e12	−1.38072	−0.690359	+	0.723467i	$0.742547\pi$
$558$	3.06852e12	1.33991
$559$	−1.23773e12	−0.536132
$560$	−2.60446e12	−1.11911
$561$	3.11389e10	0.0132731
$562$	−1.35467e12	−0.572823
$563$	−2.51159e12	−1.05356	−0.526782	−	0.850000i	$-0.676602\pi$
$563$	−2.51159e12	−1.05356	−0.526782	+	0.850000i	$0.676602\pi$
$564$	−3.25297e8	−0.000135371 0
$565$	2.86379e12	1.18229
$566$	−2.18640e12	−0.895479
$567$	4.22175e12	1.71542
$568$	−2.49323e12	−1.00507
$569$	2.98788e12	1.19497	0.597487	−	0.801879i	$-0.296166\pi$
$569$	2.98788e12	1.19497	0.597487	+	0.801879i	$0.296166\pi$
$570$	−9.78661e10	−0.0388325
$571$	−1.80331e12	−0.709916	−0.354958	−	0.934882i	$-0.615505\pi$
$571$	−1.80331e12	−0.709916	−0.354958	+	0.934882i	$0.615505\pi$
$572$	1.95167e11	0.0762297
$573$	2.82201e10	0.0109361
$574$	−3.12627e12	−1.20205
$575$	−3.63273e11	−0.138589
$576$	−2.93174e12	−1.10975
$577$	−2.37500e12	−0.892017	−0.446009	−	0.895029i	$-0.647155\pi$
$577$	−2.37500e12	−0.892017	−0.446009	+	0.895029i	$0.647155\pi$
$578$	3.84164e12	1.43167
$579$	1.10903e11	0.0410102
$580$	−1.38307e11	−0.0507478
$581$	7.25800e12	2.64256
$582$	1.08143e11	0.0390701
$583$	2.72649e11	0.0977453
$584$	−2.07925e12	−0.739689
$585$	−3.33537e12	−1.17745
$586$	−9.45690e11	−0.331291
$587$	−1.17269e12	−0.407673	−0.203837	−	0.979005i	$-0.565341\pi$
$587$	−1.17269e12	−0.407673	−0.203837	+	0.979005i	$0.565341\pi$
$588$	4.47450e10	0.0154364
$589$	−6.60135e12	−2.26003
$590$	−3.76531e12	−1.27928
$591$	−1.43127e11	−0.0482589
$592$	−3.44881e11	−0.115404
$593$	3.73697e12	1.24100	0.620502	−	0.784205i	$-0.286929\pi$
$593$	3.73697e12	1.24100	0.620502	+	0.784205i	$0.286929\pi$
$594$	−4.31639e10	−0.0142260
$595$	7.92294e12	2.59155
$596$	2.13808e11	0.0694089
$597$	−1.27896e11	−0.0412073
$598$	3.38841e12	1.08353
$599$	1.36337e12	0.432705	0.216353	−	0.976315i	$-0.430584\pi$
$599$	1.36337e12	0.432705	0.216353	+	0.976315i	$0.430584\pi$
$600$	−1.59427e10	−0.00502205
$601$	3.27549e11	0.102410	0.0512049	−	0.998688i	$-0.483694\pi$
$601$	3.27549e11	0.102410	0.0512049	+	0.998688i	$0.483694\pi$
$602$	−2.03667e12	−0.632028
$603$	6.16653e12	1.89938
$604$	−8.08945e11	−0.247316
$605$	−2.86291e12	−0.868776
$606$	4.23518e10	0.0127569
$607$	6.13245e12	1.83352	0.916759	−	0.399441i	$-0.130796\pi$
$607$	6.13245e12	1.83352	0.916759	+	0.399441i	$0.130796\pi$
$608$	2.32178e12	0.689056
$609$	−4.36161e10	−0.0128490
$610$	−7.55104e11	−0.220812
$611$	−7.54080e10	−0.0218893
$612$	1.35411e12	0.390188
$613$	−4.41524e12	−1.26294	−0.631470	−	0.775400i	$-0.717548\pi$
$613$	−4.41524e12	−1.26294	−0.631470	+	0.775400i	$0.717548\pi$
$614$	2.48493e12	0.705598
$615$	8.62465e10	0.0243110
$616$	1.65766e12	0.463855
$617$	4.59382e12	1.27612	0.638059	−	0.769988i	$-0.279738\pi$
$617$	4.59382e12	1.27612	0.638059	+	0.769988i	$0.279738\pi$
$618$	1.09293e11	0.0301400
$619$	3.30623e12	0.905159	0.452580	−	0.891724i	$-0.350504\pi$
$619$	3.30623e12	0.905159	0.452580	+	0.891724i	$0.350504\pi$
$620$	1.26034e12	0.342551
$621$	2.37022e11	0.0639553
$622$	3.82043e12	1.02342
$623$	−7.81645e12	−2.07880
$624$	1.10783e11	0.0292512
$625$	−3.19681e12	−0.838023
$626$	−2.52401e12	−0.656911
$627$	4.64046e10	0.0119910
$628$	−5.25438e11	−0.134804
$629$	1.04915e12	0.267245
$630$	−5.48833e12	−1.38806
$631$	−1.85941e12	−0.466920	−0.233460	−	0.972366i	$-0.575005\pi$
$631$	−1.85941e12	−0.466920	−0.233460	+	0.972366i	$0.575005\pi$
$632$	−1.46446e12	−0.365132
$633$	1.82894e11	0.0452774
$634$	−1.92602e12	−0.473433
$635$	−2.65382e12	−0.647724
$636$	−1.27294e10	−0.00308496
$637$	1.03725e13	2.49605
$638$	−2.07345e11	−0.0495451
$639$	−3.91414e12	−0.928715
$640$	1.96240e12	0.462358
$641$	−2.74825e12	−0.642978	−0.321489	−	0.946913i	$-0.604183\pi$
$641$	−2.74825e12	−0.642978	−0.321489	+	0.946913i	$0.604183\pi$
$642$	1.03359e11	0.0240128
$643$	4.78059e12	1.10289	0.551445	−	0.834211i	$-0.314077\pi$
$643$	4.78059e12	1.10289	0.551445	+	0.834211i	$0.314077\pi$
$644$	−1.76348e12	−0.404002
$645$	5.61869e10	0.0127825
$646$	9.21042e12	2.08081
$647$	−8.42031e11	−0.188912	−0.0944559	−	0.995529i	$-0.530111\pi$
$647$	−8.42031e11	−0.188912	−0.0944559	+	0.995529i	$0.530111\pi$
$648$	−4.83655e12	−1.07758
$649$	1.78538e12	0.395029
$650$	−7.15987e11	−0.157324
$651$	3.97459e11	0.0867316
$652$	7.12547e11	0.154418
$653$	4.45590e12	0.959016	0.479508	−	0.877538i	$-0.340815\pi$
$653$	4.45590e12	0.959016	0.479508	+	0.877538i	$0.340815\pi$
$654$	−8.48277e10	−0.0181317
$655$	9.84853e11	0.209067
$656$	2.66821e12	0.562539
$657$	−3.26423e12	−0.683497
$658$	−1.24083e11	−0.0258046
$659$	1.15312e12	0.238171	0.119086	−	0.992884i	$-0.462004\pi$
$659$	1.15312e12	0.238171	0.119086	+	0.992884i	$0.462004\pi$
$660$	−8.85965e9	−0.00181748
$661$	−2.83247e12	−0.577110	−0.288555	−	0.957463i	$-0.593175\pi$
$661$	−2.83247e12	−0.577110	−0.288555	+	0.957463i	$0.593175\pi$
$662$	3.06418e12	0.620087
$663$	−3.37010e11	−0.0677379
$664$	−8.31494e12	−1.65998
$665$	1.18071e13	2.34124
$666$	−7.26762e11	−0.143139
$667$	1.13857e12	0.222738
$668$	−2.13471e12	−0.414806
$669$	4.53262e10	0.00874846
$670$	−8.00794e12	−1.53527
$671$	3.58043e11	0.0681843
$672$	−1.39791e11	−0.0264434
$673$	8.28135e12	1.55608	0.778042	−	0.628212i	$-0.216213\pi$
$673$	8.28135e12	1.55608	0.778042	+	0.628212i	$0.216213\pi$
$674$	−7.23346e12	−1.35013
$675$	−5.00839e10	−0.00928605
$676$	−8.07615e11	−0.148746
$677$	8.27912e12	1.51473	0.757364	−	0.652992i	$-0.226487\pi$
$677$	8.27912e12	1.51473	0.757364	+	0.652992i	$0.226487\pi$
$678$	−2.00444e11	−0.0364300
$679$	−1.30470e13	−2.35557
$680$	−9.07671e12	−1.62794
$681$	1.17907e11	0.0210077
$682$	1.88947e12	0.334433
$683$	−2.32298e12	−0.408463	−0.204231	−	0.978923i	$-0.565469\pi$
$683$	−2.32298e12	−0.408463	−0.204231	+	0.978923i	$0.565469\pi$
$684$	2.01796e12	0.352500
$685$	−9.77967e11	−0.169714
$686$	8.36715e12	1.44251
$687$	5.45376e10	0.00934094
$688$	1.73826e12	0.295778
$689$	−2.95082e12	−0.498835
$690$	−1.53818e11	−0.0258336
$691$	3.96850e12	0.662179	0.331090	−	0.943599i	$-0.392584\pi$
$691$	3.96850e12	0.662179	0.331090	+	0.943599i	$0.392584\pi$
$692$	1.18073e12	0.195737
$693$	2.60237e12	0.428617
$694$	−1.03947e12	−0.170096
$695$	7.38946e12	1.20138
$696$	4.99676e10	0.00807137
$697$	−8.11687e12	−1.30269
$698$	−3.20925e12	−0.511746
$699$	−1.46400e10	−0.00231949
$700$	3.72631e11	0.0586595
$701$	6.25925e12	0.979020	0.489510	−	0.871998i	$-0.337176\pi$
$701$	6.25925e12	0.979020	0.489510	+	0.871998i	$0.337176\pi$
$702$	4.67154e11	0.0726010
$703$	1.56349e12	0.241433
$704$	−1.80524e12	−0.276986
$705$	3.42316e9	0.000521887 0
$706$	6.99494e11	0.105965
$707$	−5.10956e12	−0.769123
$708$	−8.33551e10	−0.0124676
$709$	−9.53378e12	−1.41696	−0.708479	−	0.705732i	$-0.750618\pi$
$709$	−9.53378e12	−1.41696	−0.708479	+	0.705732i	$0.750618\pi$
$710$	5.08296e12	0.750679
$711$	−2.29906e12	−0.337394
$712$	8.95471e12	1.30585
$713$	−1.03754e13	−1.50350
$714$	−5.54548e11	−0.0798540
$715$	−2.05378e12	−0.293884
$716$	2.31082e12	0.328593
$717$	−3.11968e11	−0.0440833
$718$	2.93603e12	0.412288
$719$	4.56349e12	0.636821	0.318411	−	0.947953i	$-0.396851\pi$
$719$	4.56349e12	0.636821	0.318411	+	0.947953i	$0.396851\pi$
$720$	4.68418e12	0.649587
$721$	−1.31857e13	−1.81716
$722$	7.36160e12	1.00822
$723$	4.16620e11	0.0567045
$724$	−1.13939e12	−0.154116
$725$	−2.40586e11	−0.0323407
$726$	2.00382e11	0.0267698
$727$	6.62877e12	0.880092	0.440046	−	0.897975i	$-0.354962\pi$
$727$	6.62877e12	0.880092	0.440046	+	0.897975i	$0.354962\pi$
$728$	−1.79405e13	−2.36725
$729$	−7.57657e12	−0.993571
$730$	4.23898e12	0.552469
$731$	−5.28789e12	−0.684942
$732$	−1.67162e10	−0.00215198
$733$	4.55378e12	0.582645	0.291322	−	0.956625i	$-0.405905\pi$
$733$	4.55378e12	0.582645	0.291322	+	0.956625i	$0.405905\pi$
$734$	−7.00100e12	−0.890282
$735$	−4.70860e11	−0.0595112
$736$	3.64917e12	0.458399
$737$	3.79708e12	0.474074
$738$	5.62267e12	0.697733
$739$	−1.49732e12	−0.184678	−0.0923391	−	0.995728i	$-0.529434\pi$
$739$	−1.49732e12	−0.184678	−0.0923391	+	0.995728i	$0.529434\pi$
$740$	−2.98505e11	−0.0365939
$741$	−5.02227e11	−0.0611953
$742$	−4.85556e12	−0.588060
$743$	5.33929e12	0.642737	0.321369	−	0.946954i	$-0.395857\pi$
$743$	5.33929e12	0.642737	0.321369	+	0.946954i	$0.395857\pi$
$744$	−4.55338e11	−0.0544824
$745$	−2.24994e12	−0.267588
$746$	5.71295e12	0.675361
$747$	−1.30537e13	−1.53387
$748$	8.33804e11	0.0973883
$749$	−1.24698e13	−1.44775
$750$	2.61628e11	0.0301932
$751$	−1.49392e12	−0.171375	−0.0856874	−	0.996322i	$-0.527309\pi$
$751$	−1.49392e12	−0.171375	−0.0856874	+	0.996322i	$0.527309\pi$
$752$	1.05903e11	0.0120761
$753$	−1.85324e11	−0.0210065
$754$	2.24405e12	0.252849
$755$	8.51268e12	0.953466
$756$	−2.43128e11	−0.0270699
$757$	5.31090e12	0.587809	0.293905	−	0.955835i	$-0.405045\pi$
$757$	5.31090e12	0.587809	0.293905	+	0.955835i	$0.405045\pi$
$758$	1.52054e12	0.167297
$759$	7.29348e10	0.00797713
$760$	−1.35265e13	−1.47070
$761$	−1.72437e12	−0.186380	−0.0931902	−	0.995648i	$-0.529706\pi$
$761$	−1.72437e12	−0.186380	−0.0931902	+	0.995648i	$0.529706\pi$
$762$	1.85748e11	0.0199585
$763$	1.02341e13	1.09317
$764$	7.55646e11	0.0802414
$765$	−1.42496e13	−1.50427
$766$	7.21870e12	0.757582
$767$	−1.93227e13	−2.01600
$768$	2.13404e11	0.0221349
$769$	−1.72572e13	−1.77951	−0.889757	−	0.456434i	$-0.849127\pi$
$769$	−1.72572e13	−1.77951	−0.889757	+	0.456434i	$0.849127\pi$
$770$	−3.37948e12	−0.346451
$771$	4.13577e11	0.0421514
$772$	2.96965e12	0.300904
$773$	1.63336e13	1.64541	0.822705	−	0.568468i	$-0.192464\pi$
$773$	1.63336e13	1.64541	0.822705	+	0.568468i	$0.192464\pi$
$774$	3.66300e12	0.366862
$775$	2.19238e12	0.218302
$776$	1.49469e13	1.47970
$777$	−9.41357e10	−0.00926531
$778$	1.01945e13	0.997601
$779$	−1.20961e13	−1.17687
$780$	9.58861e10	0.00927534
$781$	−2.41016e12	−0.231801
$782$	1.44762e13	1.38428
$783$	1.56973e11	0.0149244
$784$	−1.45670e13	−1.37705
$785$	5.52928e12	0.519703
$786$	−6.89325e10	−0.00644203
$787$	1.77862e13	1.65271	0.826354	−	0.563151i	$-0.190411\pi$
$787$	1.77862e13	1.65271	0.826354	+	0.563151i	$0.190411\pi$
$788$	−3.83249e12	−0.354090
$789$	−5.17964e10	−0.00475832
$790$	2.98560e12	0.272715
$791$	2.41827e13	2.19639
$792$	−2.98134e12	−0.269245
$793$	−3.87502e12	−0.347973
$794$	4.06227e12	0.362724
$795$	1.33953e11	0.0118933
$796$	−3.42467e12	−0.302350
$797$	1.16034e13	1.01864	0.509322	−	0.860576i	$-0.329896\pi$
$797$	1.16034e13	1.01864	0.509322	+	0.860576i	$0.329896\pi$
$798$	−8.26411e11	−0.0721412
$799$	−3.22162e11	−0.0279650
$800$	−7.71087e11	−0.0665577
$801$	1.40581e13	1.20664
$802$	−5.90951e12	−0.504390
$803$	−2.00997e12	−0.170596
$804$	−1.77277e11	−0.0149623
$805$	1.85574e13	1.55753
$806$	−2.04493e13	−1.70675
$807$	1.22405e9	0.000101594 0
$808$	5.85364e12	0.483142
$809$	9.23142e12	0.757705	0.378853	−	0.925457i	$-0.376319\pi$
$809$	9.23142e12	0.757705	0.378853	+	0.925457i	$0.376319\pi$
$810$	9.86028e12	0.804835
$811$	−8.92855e12	−0.724748	−0.362374	−	0.932033i	$-0.618034\pi$
$811$	−8.92855e12	−0.724748	−0.362374	+	0.932033i	$0.618034\pi$
$812$	−1.16790e12	−0.0942768
$813$	−3.08525e11	−0.0247675
$814$	−4.47509e11	−0.0357266
$815$	−7.49826e12	−0.595321
$816$	4.73295e11	0.0373703
$817$	−7.88024e12	−0.618786
$818$	−4.51211e12	−0.352363
$819$	−2.81649e13	−2.18741
$820$	2.30941e12	0.178377
$821$	−1.39735e13	−1.07340	−0.536700	−	0.843773i	$-0.680329\pi$
$821$	−1.39735e13	−1.07340	−0.536700	+	0.843773i	$0.680329\pi$
$822$	6.84506e10	0.00522942
$823$	−7.35797e12	−0.559061	−0.279530	−	0.960137i	$-0.590179\pi$
$823$	−7.35797e12	−0.559061	−0.279530	+	0.960137i	$0.590179\pi$
$824$	1.51059e13	1.14149
$825$	−1.54115e10	−0.00115825
$826$	−3.17955e13	−2.37659
$827$	1.62383e13	1.20716	0.603582	−	0.797301i	$-0.293740\pi$
$827$	1.62383e13	1.20716	0.603582	+	0.797301i	$0.293740\pi$
$828$	3.17165e12	0.234503
$829$	9.63996e12	0.708892	0.354446	−	0.935077i	$-0.384670\pi$
$829$	9.63996e12	0.708892	0.354446	+	0.935077i	$0.384670\pi$
$830$	1.69517e13	1.23983
$831$	2.76353e11	0.0201030
$832$	1.95377e13	1.41357
$833$	4.43138e13	3.18887
$834$	−5.17208e11	−0.0370184
$835$	2.24640e13	1.59918
$836$	1.24257e12	0.0879818
$837$	−1.43044e12	−0.100741
$838$	−1.14741e13	−0.803746
$839$	1.71074e10	0.00119194	0.000595970	−	1.00000i	$-0.499810\pi$
$839$	1.71074e10	0.00119194	0.000595970		1.00000i	$0.499810\pi$
$840$	8.14414e11	0.0564402
$841$	−1.37531e13	−0.948022
$842$	1.87507e13	1.28562
$843$	3.15582e11	0.0215223
$844$	4.89732e12	0.332214
$845$	8.49868e12	0.573451
$846$	2.23167e11	0.0149783
$847$	−2.41752e13	−1.61397
$848$	4.14412e12	0.275202
$849$	5.09339e11	0.0336452
$850$	−3.05888e12	−0.200991
$851$	2.45736e12	0.160615
$852$	1.12525e11	0.00731593
$853$	8.09585e12	0.523590	0.261795	−	0.965123i	$-0.415685\pi$
$853$	8.09585e12	0.523590	0.261795	+	0.965123i	$0.415685\pi$
$854$	−6.37633e12	−0.410214
$855$	−2.12353e13	−1.35898
$856$	1.42858e13	0.909435
$857$	2.29474e13	1.45318	0.726589	−	0.687072i	$-0.241104\pi$
$857$	2.29474e13	1.45318	0.726589	+	0.687072i	$0.241104\pi$
$858$	1.43749e11	0.00905552
$859$	−1.20700e13	−0.756375	−0.378187	−	0.925729i	$-0.623453\pi$
$859$	−1.20700e13	−0.756375	−0.378187	+	0.925729i	$0.623453\pi$
$860$	1.50451e12	0.0937891
$861$	7.28291e11	0.0451639
$862$	9.50206e12	0.586185
$863$	−7.20862e12	−0.442388	−0.221194	−	0.975230i	$-0.570995\pi$
$863$	−7.20862e12	−0.442388	−0.221194	+	0.975230i	$0.570995\pi$
$864$	5.03105e11	0.0307147
$865$	−1.24250e13	−0.754615
$866$	−1.77268e13	−1.07103
$867$	−8.94942e11	−0.0537909
$868$	1.06427e13	0.636376
$869$	−1.41566e12	−0.0842114
$870$	−1.01869e11	−0.00602846
$871$	−4.10950e13	−2.41940
$872$	−1.17244e13	−0.686700
$873$	2.34653e13	1.36729
$874$	2.15730e13	1.25057
$875$	−3.15643e13	−1.82037
$876$	9.38409e10	0.00538423
$877$	4.07949e12	0.232867	0.116433	−	0.993198i	$-0.462854\pi$
$877$	4.07949e12	0.232867	0.116433	+	0.993198i	$0.462854\pi$
$878$	−3.05276e13	−1.73367
$879$	2.20306e11	0.0124474
$880$	2.88431e12	0.162133
$881$	−2.90992e13	−1.62738	−0.813692	−	0.581296i	$-0.802546\pi$
$881$	−2.90992e13	−1.62738	−0.813692	+	0.581296i	$0.802546\pi$
$882$	−3.06968e13	−1.70799
$883$	3.20864e12	0.177623	0.0888113	−	0.996048i	$-0.471693\pi$
$883$	3.20864e12	0.177623	0.0888113	+	0.996048i	$0.471693\pi$
$884$	−9.02408e12	−0.497013
$885$	8.77161e11	0.0480656
$886$	1.40477e13	0.765865
$887$	−6.68851e12	−0.362805	−0.181402	−	0.983409i	$-0.558064\pi$
$887$	−6.68851e12	−0.362805	−0.181402	+	0.983409i	$0.558064\pi$
$888$	1.07844e11	0.00582021
$889$	−2.24097e13	−1.20331
$890$	−1.82560e13	−0.975328
$891$	−4.67539e12	−0.248524
$892$	1.21369e12	0.0641900
$893$	−4.80101e11	−0.0252639
$894$	1.57479e11	0.00824525
$895$	−2.43172e13	−1.26681
$896$	1.65711e13	0.858947
$897$	−7.89357e11	−0.0407106
$898$	1.79343e13	0.920324
$899$	−6.87137e12	−0.350853
$900$	−6.70186e11	−0.0340490
$901$	−1.26067e13	−0.637293
$902$	3.46220e12	0.174150
$903$	4.74459e11	0.0237467
$904$	−2.77043e13	−1.37971
$905$	1.19900e13	0.594156
$906$	−5.95825e11	−0.0293793
$907$	−2.37853e13	−1.16702	−0.583508	−	0.812108i	$-0.698320\pi$
$907$	−2.37853e13	−1.16702	−0.583508	+	0.812108i	$0.698320\pi$
$908$	3.15718e12	0.154139
$909$	9.18965e12	0.446439
$910$	3.65753e13	1.76808
$911$	3.26697e13	1.57149	0.785746	−	0.618549i	$-0.212279\pi$
$911$	3.26697e13	1.57149	0.785746	+	0.618549i	$0.212279\pi$
$912$	7.05325e11	0.0337608
$913$	−8.03789e12	−0.382845
$914$	−1.36413e13	−0.646545
$915$	1.75908e11	0.00829640
$916$	1.46035e12	0.0685372
$917$	8.31640e12	0.388395
$918$	1.99580e12	0.0927525
$919$	8.41847e12	0.389326	0.194663	−	0.980870i	$-0.437639\pi$
$919$	8.41847e12	0.389326	0.194663	+	0.980870i	$0.437639\pi$
$920$	−2.12598e13	−0.978395
$921$	−5.78886e11	−0.0265109
$922$	−2.93363e13	−1.33695
$923$	2.60846e13	1.18298
$924$	−7.48136e10	−0.00337642
$925$	−5.19252e11	−0.0233206
$926$	2.08480e13	0.931781
$927$	2.37148e13	1.05478
$928$	2.41674e12	0.106971
$929$	1.09081e13	0.480483	0.240242	−	0.970713i	$-0.422773\pi$
$929$	1.09081e13	0.480483	0.240242	+	0.970713i	$0.422773\pi$
$930$	9.28300e11	0.0406925
$931$	6.60384e13	2.88087
$932$	−3.92013e11	−0.0170188
$933$	−8.90000e11	−0.0384523
$934$	−4.18366e12	−0.179885
$935$	−8.77427e12	−0.375456
$936$	3.22664e13	1.37407
$937$	−3.93081e13	−1.66592	−0.832960	−	0.553334i	$-0.813356\pi$
$937$	−3.93081e13	−1.66592	−0.832960	+	0.553334i	$0.813356\pi$
$938$	−6.76215e13	−2.85215
$939$	5.87989e11	0.0246816
$940$	9.16617e10	0.00382924
$941$	1.37658e13	0.572333	0.286167	−	0.958180i	$-0.407619\pi$
$941$	1.37658e13	0.572333	0.286167	+	0.958180i	$0.407619\pi$
$942$	−3.87009e11	−0.0160137
$943$	−1.90116e13	−0.782919
$944$	2.71368e13	1.11220
$945$	2.55848e12	0.104361
$946$	2.25551e12	0.0915663
$947$	5.10471e12	0.206251	0.103126	−	0.994668i	$-0.467116\pi$
$947$	5.10471e12	0.206251	0.103126	+	0.994668i	$0.467116\pi$
$948$	6.60940e10	0.00265781
$949$	2.17535e13	0.870624
$950$	−4.55848e12	−0.181578
$951$	4.48682e11	0.0177880
$952$	−7.66465e13	−3.02431
$953$	−6.26857e12	−0.246178	−0.123089	−	0.992396i	$-0.539280\pi$
$953$	−6.26857e12	−0.246178	−0.123089	+	0.992396i	$0.539280\pi$
$954$	8.73283e12	0.341340
$955$	−7.95181e12	−0.309350
$956$	−8.35353e12	−0.323452
$957$	4.83027e10	0.00186152
$958$	1.39551e13	0.535291
$959$	−8.25825e12	−0.315286
$960$	−8.86918e11	−0.0337026
$961$	3.61769e13	1.36828
$962$	4.84329e12	0.182328
$963$	2.24273e13	0.840347
$964$	1.11558e13	0.416058
$965$	−3.12502e13	−1.16006
$966$	−1.29888e12	−0.0479924
$967$	−1.52494e13	−0.560834	−0.280417	−	0.959878i	$-0.590473\pi$
$967$	−1.52494e13	−0.560834	−0.280417	+	0.959878i	$0.590473\pi$
$968$	2.76958e13	1.01385
$969$	−2.14564e12	−0.0781809
$970$	−3.04723e13	−1.10518
$971$	4.25045e13	1.53443	0.767216	−	0.641388i	$-0.221641\pi$
$971$	4.25045e13	1.53443	0.767216	+	0.641388i	$0.221641\pi$
$972$	6.56023e11	0.0235733
$973$	6.23988e13	2.23187
$974$	7.85996e12	0.279837
$975$	1.66795e11	0.00591102
$976$	5.44206e12	0.191973
$977$	4.42319e13	1.55314	0.776570	−	0.630031i	$-0.216958\pi$
$977$	4.42319e13	1.55314	0.776570	+	0.630031i	$0.216958\pi$
$978$	5.24823e11	0.0183438
$979$	8.65634e12	0.301170
$980$	−1.26082e13	−0.436651
$981$	−1.84062e13	−0.634533
$982$	3.72191e13	1.27722
$983$	−2.40486e13	−0.821483	−0.410742	−	0.911752i	$-0.634730\pi$
$983$	−2.40486e13	−0.821483	−0.410742	+	0.911752i	$0.634730\pi$
$984$	−8.34349e11	−0.0283707
$985$	4.03300e13	1.36510
$986$	9.58716e12	0.323031
$987$	2.89062e10	0.000969537 0
$988$	−1.34481e13	−0.449008
$989$	−1.23855e13	−0.411652
$990$	6.07807e12	0.201098
$991$	−3.39491e13	−1.11814	−0.559071	−	0.829120i	$-0.688842\pi$
$991$	−3.39491e13	−1.11814	−0.559071	+	0.829120i	$0.688842\pi$
$992$	−2.20230e13	−0.722061
$993$	−7.13825e11	−0.0232981
$994$	4.29221e13	1.39457
$995$	3.60384e13	1.16563
$996$	3.75270e11	0.0120831
$997$	−6.80150e12	−0.218010	−0.109005	−	0.994041i	$-0.534766\pi$
$997$	−6.80150e12	−0.218010	−0.109005	+	0.994041i	$0.534766\pi$
$998$	2.15656e13	0.688136
$999$	3.38792e11	0.0107619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.a.b.1.10	✓	14
3.2	odd	2		333.10.a.d.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.a.b.1.10	✓	14	1.1	even	1	trivial
333.10.a.d.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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	37.a (trivial)

\(f(q)\)	\(=\)	\(q+19.7224 q^{2} -4.59450 q^{3} -123.026 q^{4} +1294.63 q^{5} -90.6146 q^{6} +10932.2 q^{7} -12524.3 q^{8} -19661.9 q^{9} +O(q^{10})\)	\(q+19.7224 q^{2} -4.59450 q^{3} -123.026 q^{4} +1294.63 q^{5} -90.6146 q^{6} +10932.2 q^{7} -12524.3 q^{8} -19661.9 q^{9} +25533.2 q^{10} -12106.9 q^{11} +565.245 q^{12} +131031. q^{13} +215610. q^{14} -5948.18 q^{15} -184019. q^{16} +559798. q^{17} -387780. q^{18} +834235. q^{19} -159274. q^{20} -50228.2 q^{21} -238778. q^{22} +1.31118e6 q^{23} +57542.7 q^{24} -277059. q^{25} +2.58424e6 q^{26} +180770. q^{27} -1.34496e6 q^{28} +868358. q^{29} -117312. q^{30} -7.91306e6 q^{31} +2.78312e6 q^{32} +55625.3 q^{33} +1.10406e7 q^{34} +1.41532e7 q^{35} +2.41893e6 q^{36} +1.87416e6 q^{37} +1.64531e7 q^{38} -602021. q^{39} -1.62143e7 q^{40} -1.44997e7 q^{41} -990621. q^{42} -9.44607e6 q^{43} +1.48947e6 q^{44} -2.54549e7 q^{45} +2.58596e7 q^{46} -575498. q^{47} +845475. q^{48} +7.91604e7 q^{49} -5.46426e6 q^{50} -2.57199e6 q^{51} -1.61202e7 q^{52} -2.25201e7 q^{53} +3.56522e6 q^{54} -1.56740e7 q^{55} -1.36918e8 q^{56} -3.83289e6 q^{57} +1.71261e7 q^{58} -1.47467e8 q^{59} +731783. q^{60} -2.95734e7 q^{61} -1.56065e8 q^{62} -2.14949e8 q^{63} +1.49108e8 q^{64} +1.69636e8 q^{65} +1.09707e6 q^{66} -3.13628e8 q^{67} -6.88699e7 q^{68} -6.02421e6 q^{69} +2.79136e8 q^{70} +1.99072e8 q^{71} +2.46251e8 q^{72} +1.66018e8 q^{73} +3.69630e7 q^{74} +1.27295e6 q^{75} -1.02633e8 q^{76} -1.32356e8 q^{77} -1.18733e7 q^{78} +1.16930e8 q^{79} -2.38236e8 q^{80} +3.86174e8 q^{81} -2.85968e8 q^{82} +6.63907e8 q^{83} +6.17940e6 q^{84} +7.24731e8 q^{85} -1.86299e8 q^{86} -3.98967e6 q^{87} +1.51630e8 q^{88} -7.14990e8 q^{89} -5.02031e8 q^{90} +1.43246e9 q^{91} -1.61310e8 q^{92} +3.63565e7 q^{93} -1.13502e7 q^{94} +1.08003e9 q^{95} -1.27870e7 q^{96} -1.19344e9 q^{97} +1.56123e9 q^{98} +2.38045e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9}+O(q^{10}) \) 14 * q + 48 * q^2 + 397 * q^3 + 3498 * q^4 + 2841 * q^5 + 3375 * q^6 + 6632 * q^7 + 41046 * q^8 + 101917 * q^9	\( 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9} + 129003 q^{10} + 44949 q^{11} - 123661 q^{12} + 38913 q^{13} + 16434 q^{14} + 119816 q^{15} + 859962 q^{16} + 893196 q^{17} + 1833339 q^{18} + 1532124 q^{19} + 4974963 q^{20} + 1851132 q^{21} + 3195323 q^{22} + 5911773 q^{23} + 7885413 q^{24} + 9978791 q^{25} + 10634475 q^{26} + 13105312 q^{27} + 9469678 q^{28} + 8764377 q^{29} + 21804216 q^{30} + 13188927 q^{31} + 23982750 q^{32} + 9398618 q^{33} + 29914960 q^{34} + 29633556 q^{35} + 24297333 q^{36} + 26238254 q^{37} + 23342796 q^{38} + 40855861 q^{39} + 42889049 q^{40} + 22153785 q^{41} + 6999662 q^{42} + 1779790 q^{43} - 83674089 q^{44} - 45101798 q^{45} - 23239663 q^{46} + 40080072 q^{47} - 141884869 q^{48} - 170457752 q^{49} - 89214633 q^{50} - 127867462 q^{51} - 276889277 q^{52} - 102088122 q^{53} - 356745582 q^{54} - 206797385 q^{55} - 294922194 q^{56} - 141710762 q^{57} - 527059089 q^{58} + 56191266 q^{59} - 283393416 q^{60} - 178507397 q^{61} - 27353505 q^{62} - 291948734 q^{63} - 242330062 q^{64} - 174258810 q^{65} - 1153895008 q^{66} + 287062499 q^{67} + 308827572 q^{68} - 80094823 q^{69} - 672888452 q^{70} + 224382678 q^{71} + 105778731 q^{72} + 271440727 q^{73} + 89959728 q^{74} + 1017561832 q^{75} - 229522980 q^{76} + 671279994 q^{77} - 119785879 q^{78} + 379128625 q^{79} + 1999017183 q^{80} + 2367007018 q^{81} + 551153781 q^{82} + 1664083206 q^{83} + 1344035042 q^{84} + 1982056546 q^{85} + 520253082 q^{86} + 3606452357 q^{87} + 684092585 q^{88} + 3293434692 q^{89} + 892602798 q^{90} + 1715813946 q^{91} + 3729310881 q^{92} + 2573139250 q^{93} + 998499458 q^{94} + 878402766 q^{95} - 1221963827 q^{96} + 2385468336 q^{97} - 3234447132 q^{98} + 4029218638 q^{99}+O(q^{100}) \) 14 * q + 48 * q^2 + 397 * q^3 + 3498 * q^4 + 2841 * q^5 + 3375 * q^6 + 6632 * q^7 + 41046 * q^8 + 101917 * q^9 + 129003 * q^10 + 44949 * q^11 - 123661 * q^12 + 38913 * q^13 + 16434 * q^14 + 119816 * q^15 + 859962 * q^16 + 893196 * q^17 + 1833339 * q^18 + 1532124 * q^19 + 4974963 * q^20 + 1851132 * q^21 + 3195323 * q^22 + 5911773 * q^23 + 7885413 * q^24 + 9978791 * q^25 + 10634475 * q^26 + 13105312 * q^27 + 9469678 * q^28 + 8764377 * q^29 + 21804216 * q^30 + 13188927 * q^31 + 23982750 * q^32 + 9398618 * q^33 + 29914960 * q^34 + 29633556 * q^35 + 24297333 * q^36 + 26238254 * q^37 + 23342796 * q^38 + 40855861 * q^39 + 42889049 * q^40 + 22153785 * q^41 + 6999662 * q^42 + 1779790 * q^43 - 83674089 * q^44 - 45101798 * q^45 - 23239663 * q^46 + 40080072 * q^47 - 141884869 * q^48 - 170457752 * q^49 - 89214633 * q^50 - 127867462 * q^51 - 276889277 * q^52 - 102088122 * q^53 - 356745582 * q^54 - 206797385 * q^55 - 294922194 * q^56 - 141710762 * q^57 - 527059089 * q^58 + 56191266 * q^59 - 283393416 * q^60 - 178507397 * q^61 - 27353505 * q^62 - 291948734 * q^63 - 242330062 * q^64 - 174258810 * q^65 - 1153895008 * q^66 + 287062499 * q^67 + 308827572 * q^68 - 80094823 * q^69 - 672888452 * q^70 + 224382678 * q^71 + 105778731 * q^72 + 271440727 * q^73 + 89959728 * q^74 + 1017561832 * q^75 - 229522980 * q^76 + 671279994 * q^77 - 119785879 * q^78 + 379128625 * q^79 + 1999017183 * q^80 + 2367007018 * q^81 + 551153781 * q^82 + 1664083206 * q^83 + 1344035042 * q^84 + 1982056546 * q^85 + 520253082 * q^86 + 3606452357 * q^87 + 684092585 * q^88 + 3293434692 * q^89 + 892602798 * q^90 + 1715813946 * q^91 + 3729310881 * q^92 + 2573139250 * q^93 + 998499458 * q^94 + 878402766 * q^95 - 1221963827 * q^96 + 2385468336 * q^97 - 3234447132 * q^98 + 4029218638 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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