LMFDB - Embedded newform 37.10.a.b.1.11

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			1.11
Root			$27.2642$ 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)

$f(q)$	$=$	$q+30.2642 q^{2} +264.228 q^{3} +403.920 q^{4} +600.015 q^{5} +7996.64 q^{6} -145.658 q^{7} -3270.94 q^{8} +50133.3 q^{9} +O(q^{10})$	\(q+30.2642 q^{2} +264.228 q^{3} +403.920 q^{4} +600.015 q^{5} +7996.64 q^{6} -145.658 q^{7} -3270.94 q^{8} +50133.3 q^{9} +18159.0 q^{10} -66081.7 q^{11} +106727. q^{12} +195642. q^{13} -4408.22 q^{14} +158541. q^{15} -305800. q^{16} -90589.5 q^{17} +1.51724e6 q^{18} -912070. q^{19} +242358. q^{20} -38486.9 q^{21} -1.99991e6 q^{22} +414179. q^{23} -864273. q^{24} -1.59311e6 q^{25} +5.92096e6 q^{26} +8.04582e6 q^{27} -58834.3 q^{28} -591572. q^{29} +4.79810e6 q^{30} +3.55042e6 q^{31} -7.58005e6 q^{32} -1.74606e7 q^{33} -2.74162e6 q^{34} -87397.1 q^{35} +2.02499e7 q^{36} +1.87416e6 q^{37} -2.76030e7 q^{38} +5.16941e7 q^{39} -1.96261e6 q^{40} +1.38491e7 q^{41} -1.16478e6 q^{42} -9.55458e6 q^{43} -2.66918e7 q^{44} +3.00807e7 q^{45} +1.25348e7 q^{46} +3.81802e7 q^{47} -8.08007e7 q^{48} -4.03324e7 q^{49} -4.82141e7 q^{50} -2.39363e7 q^{51} +7.90240e7 q^{52} -4.13773e7 q^{53} +2.43500e8 q^{54} -3.96500e7 q^{55} +476439. q^{56} -2.40994e8 q^{57} -1.79034e7 q^{58} -9.05072e7 q^{59} +6.40378e7 q^{60} -1.58361e8 q^{61} +1.07450e8 q^{62} -7.30233e6 q^{63} -7.28347e7 q^{64} +1.17388e8 q^{65} -5.28432e8 q^{66} +1.54266e8 q^{67} -3.65910e7 q^{68} +1.09437e8 q^{69} -2.64500e6 q^{70} -4.66352e7 q^{71} -1.63983e8 q^{72} -1.96666e8 q^{73} +5.67199e7 q^{74} -4.20943e8 q^{75} -3.68404e8 q^{76} +9.62534e6 q^{77} +1.56448e9 q^{78} +2.94979e8 q^{79} -1.83484e8 q^{80} +1.13916e9 q^{81} +4.19132e8 q^{82} +4.20535e8 q^{83} -1.55457e7 q^{84} -5.43551e7 q^{85} -2.89161e8 q^{86} -1.56310e8 q^{87} +2.16149e8 q^{88} -3.67127e7 q^{89} +9.10369e8 q^{90} -2.84969e7 q^{91} +1.67295e8 q^{92} +9.38119e8 q^{93} +1.15549e9 q^{94} -5.47256e8 q^{95} -2.00286e9 q^{96} +8.10863e8 q^{97} -1.22063e9 q^{98} -3.31290e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	30.2642	1.33750	0.668750	−	0.743487i	$-0.266830\pi$
$2$	30.2642	1.33750	0.668750	+	0.743487i	$0.266830\pi$
$3$	264.228	1.88336	0.941679	−	0.336513i	$-0.109248\pi$
$3$	264.228	1.88336	0.941679	+	0.336513i	$0.109248\pi$
$4$	403.920	0.788907
$5$	600.015	0.429336	0.214668	−	0.976687i	$-0.431133\pi$
$5$	600.015	0.429336	0.214668	+	0.976687i	$0.431133\pi$
$6$	7996.64	2.51899
$7$	−145.658	−0.0229295	−0.0114647	−	0.999934i	$-0.503649\pi$
$7$	−145.658	−0.0229295	−0.0114647	+	0.999934i	$0.503649\pi$
$8$	−3270.94	−0.282337
$9$	50133.3	2.54704
$10$	18159.0	0.574237
$11$	−66081.7	−1.36086	−0.680431	−	0.732812i	$-0.738208\pi$
$11$	−66081.7	−1.36086	−0.680431	+	0.732812i	$0.738208\pi$
$12$	106727.	1.48579
$13$	195642.	1.89984	0.949922	−	0.312488i	$-0.101162\pi$
$13$	195642.	1.89984	0.949922	+	0.312488i	$0.101162\pi$
$14$	−4408.22	−0.0306681
$15$	158541.	0.808593
$16$	−305800.	−1.16653
$17$	−90589.5	−0.263062	−0.131531	−	0.991312i	$-0.541989\pi$
$17$	−90589.5	−0.263062	−0.131531	+	0.991312i	$0.541989\pi$
$18$	1.51724e6	3.40666
$19$	−912070.	−1.60560	−0.802799	−	0.596250i	$-0.796657\pi$
$19$	−912070.	−1.60560	−0.802799	+	0.596250i	$0.796657\pi$
$20$	242358.	0.338706
$21$	−38486.9	−0.0431844
$22$	−1.99991e6	−1.82015
$23$	414179.	0.308612	0.154306	−	0.988023i	$-0.450686\pi$
$23$	414179.	0.308612	0.154306	+	0.988023i	$0.450686\pi$
$24$	−864273.	−0.531741
$25$	−1.59311e6	−0.815671
$26$	5.92096e6	2.54104
$27$	8.04582e6	2.91362
$28$	−58834.3	−0.0180892
$29$	−591572.	−0.155316	−0.0776580	−	0.996980i	$-0.524744\pi$
$29$	−591572.	−0.155316	−0.0776580	+	0.996980i	$0.524744\pi$
$30$	4.79810e6	1.08149
$31$	3.55042e6	0.690481	0.345241	−	0.938514i	$-0.387797\pi$
$31$	3.55042e6	0.690481	0.345241	+	0.938514i	$0.387797\pi$
$32$	−7.58005e6	−1.27790
$33$	−1.74606e7	−2.56299
$34$	−2.74162e6	−0.351845
$35$	−87397.1	−0.00984444
$36$	2.02499e7	2.00938
$37$	1.87416e6	0.164399
$37$	1.87416e6	0.164399
$38$	−2.76030e7	−2.14749
$39$	5.16941e7	3.57808
$40$	−1.96261e6	−0.121217
$41$	1.38491e7	0.765410	0.382705	−	0.923871i	$-0.374993\pi$
$41$	1.38491e7	0.765410	0.382705	+	0.923871i	$0.374993\pi$
$42$	−1.16478e6	−0.0577591
$43$	−9.55458e6	−0.426190	−0.213095	−	0.977031i	$-0.568354\pi$
$43$	−9.55458e6	−0.426190	−0.213095	+	0.977031i	$0.568354\pi$
$44$	−2.66918e7	−1.07359
$45$	3.00807e7	1.09353
$46$	1.25348e7	0.412768
$47$	3.81802e7	1.14129	0.570647	−	0.821195i	$-0.306692\pi$
$47$	3.81802e7	1.14129	0.570647	+	0.821195i	$0.306692\pi$
$48$	−8.08007e7	−2.19700
$49$	−4.03324e7	−0.999474
$50$	−4.82141e7	−1.09096
$51$	−2.39363e7	−0.495439
$52$	7.90240e7	1.49880
$53$	−4.13773e7	−0.720311	−0.360156	−	0.932892i	$-0.617276\pi$
$53$	−4.13773e7	−0.720311	−0.360156	+	0.932892i	$0.617276\pi$
$54$	2.43500e8	3.89697
$55$	−3.96500e7	−0.584267
$56$	476439.	0.00647383
$57$	−2.40994e8	−3.02392
$58$	−1.79034e7	−0.207735
$59$	−9.05072e7	−0.972409	−0.486204	−	0.873845i	$-0.661619\pi$
$59$	−9.05072e7	−0.972409	−0.486204	+	0.873845i	$0.661619\pi$
$60$	6.40378e7	0.637905
$61$	−1.58361e8	−1.46441	−0.732206	−	0.681083i	$-0.761509\pi$
$61$	−1.58361e8	−1.46441	−0.732206	+	0.681083i	$0.761509\pi$
$62$	1.07450e8	0.923519
$63$	−7.30233e6	−0.0584021
$64$	−7.28347e7	−0.542660
$65$	1.17388e8	0.815671
$66$	−5.28432e8	−3.42800
$67$	1.54266e8	0.935265	0.467632	−	0.883923i	$-0.345107\pi$
$67$	1.54266e8	0.935265	0.467632	+	0.883923i	$0.345107\pi$
$68$	−3.65910e7	−0.207531
$69$	1.09437e8	0.581226
$70$	−2.64500e6	−0.0131669
$71$	−4.66352e7	−0.217797	−0.108898	−	0.994053i	$-0.534732\pi$
$71$	−4.66352e7	−0.217797	−0.108898	+	0.994053i	$0.534732\pi$
$72$	−1.63983e8	−0.719122
$73$	−1.96666e8	−0.810543	−0.405272	−	0.914196i	$-0.632823\pi$
$73$	−1.96666e8	−0.810543	−0.405272	+	0.914196i	$0.632823\pi$
$74$	5.67199e7	0.219884
$75$	−4.20943e8	−1.53620
$76$	−3.68404e8	−1.26667
$77$	9.62534e6	0.0312038
$78$	1.56448e9	4.78569
$79$	2.94979e8	0.852059	0.426030	−	0.904709i	$-0.359912\pi$
$79$	2.94979e8	0.852059	0.426030	+	0.904709i	$0.359912\pi$
$80$	−1.83484e8	−0.500834
$81$	1.13916e9	2.94036
$82$	4.19132e8	1.02374
$83$	4.20535e8	0.972638	0.486319	−	0.873781i	$-0.338339\pi$
$83$	4.20535e8	0.972638	0.486319	+	0.873781i	$0.338339\pi$
$84$	−1.55457e7	−0.0340684
$85$	−5.43551e7	−0.112942
$86$	−2.89161e8	−0.570030
$87$	−1.56310e8	−0.292516
$88$	2.16149e8	0.384222
$89$	−3.67127e7	−0.0620242	−0.0310121	−	0.999519i	$-0.509873\pi$
$89$	−3.67127e7	−0.0620242	−0.0310121	+	0.999519i	$0.509873\pi$
$90$	9.10369e8	1.46260
$91$	−2.84969e7	−0.0435624
$92$	1.67295e8	0.243466
$93$	9.38119e8	1.30042
$94$	1.15549e9	1.52648
$95$	−5.47256e8	−0.689341
$96$	−2.00286e9	−2.40674
$97$	8.10863e8	0.929982	0.464991	−	0.885315i	$-0.346058\pi$
$97$	8.10863e8	0.929982	0.464991	+	0.885315i	$0.346058\pi$
$98$	−1.22063e9	−1.33680
$99$	−3.31290e9	−3.46617
$100$	−6.43488e8	−0.643488
$101$	6.23959e8	0.596637	0.298318	−	0.954466i	$-0.403574\pi$
$101$	6.23959e8	0.596637	0.298318	+	0.954466i	$0.403574\pi$
$102$	−7.24411e8	−0.662650
$103$	−3.04029e6	−0.00266163	−0.00133082	−	0.999999i	$-0.500424\pi$
$103$	−3.04029e6	−0.00266163	−0.00133082	+	0.999999i	$0.500424\pi$
$104$	−6.39934e8	−0.536396
$105$	−2.30927e7	−0.0185406
$106$	−1.25225e9	−0.963417
$107$	2.26313e9	1.66910	0.834549	−	0.550933i	$-0.185728\pi$
$107$	2.26313e9	1.66910	0.834549	+	0.550933i	$0.185728\pi$
$108$	3.24987e9	2.29858
$109$	−2.94736e8	−0.199993	−0.0999963	−	0.994988i	$-0.531883\pi$
$109$	−2.94736e8	−0.199993	−0.0999963	+	0.994988i	$0.531883\pi$
$110$	−1.19998e9	−0.781457
$111$	4.95205e8	0.309622
$112$	4.45422e7	0.0267480
$113$	−1.99177e9	−1.14918	−0.574588	−	0.818443i	$-0.694838\pi$
$113$	−1.99177e9	−1.14918	−0.574588	+	0.818443i	$0.694838\pi$
$114$	−7.29349e9	−4.04449
$115$	2.48513e8	0.132498
$116$	−2.38948e8	−0.122530
$117$	9.80820e9	4.83897
$118$	−2.73913e9	−1.30060
$119$	1.31951e7	0.00603186
$120$	−5.18577e8	−0.228296
$121$	2.00885e9	0.851947
$122$	−4.79266e9	−1.95865
$123$	3.65932e9	1.44154
$124$	1.43409e9	0.544726
$125$	−2.12779e9	−0.779533
$126$	−2.20999e8	−0.0781129
$127$	2.52353e9	0.860780	0.430390	−	0.902643i	$-0.358376\pi$
$127$	2.52353e9	0.860780	0.430390	+	0.902643i	$0.358376\pi$
$128$	1.67671e9	0.552093
$129$	−2.52459e9	−0.802669
$130$	3.55266e9	1.09096
$131$	4.25243e9	1.26158	0.630792	−	0.775952i	$-0.282730\pi$
$131$	4.25243e9	1.26158	0.630792	+	0.775952i	$0.282730\pi$
$132$	−7.05270e9	−2.02196
$133$	1.32850e8	0.0368155
$134$	4.66874e9	1.25092
$135$	4.82761e9	1.25092
$136$	2.96313e8	0.0742720
$137$	−7.66156e9	−1.85812	−0.929062	−	0.369925i	$-0.879383\pi$
$137$	−7.66156e9	−1.85812	−0.929062	+	0.369925i	$0.879383\pi$
$138$	3.31204e9	0.777390
$139$	−2.65515e9	−0.603284	−0.301642	−	0.953421i	$-0.597535\pi$
$139$	−2.65515e9	−0.603284	−0.301642	+	0.953421i	$0.597535\pi$
$140$	−3.53015e7	−0.00776635
$141$	1.00883e10	2.14947
$142$	−1.41138e9	−0.291303
$143$	−1.29284e10	−2.58543
$144$	−1.53307e10	−2.97120
$145$	−3.54952e8	−0.0666827
$146$	−5.95193e9	−1.08410
$147$	−1.06569e10	−1.88237
$148$	7.57012e8	0.129696
$149$	8.29744e9	1.37913	0.689566	−	0.724223i	$-0.257801\pi$
$149$	8.29744e9	1.37913	0.689566	+	0.724223i	$0.257801\pi$
$150$	−1.27395e10	−2.05467
$151$	4.81034e9	0.752973	0.376486	−	0.926422i	$-0.377132\pi$
$151$	4.81034e9	0.752973	0.376486	+	0.926422i	$0.377132\pi$
$152$	2.98332e9	0.453319
$153$	−4.54155e9	−0.670028
$154$	2.91303e8	0.0417351
$155$	2.13030e9	0.296448
$156$	2.08803e10	2.82278
$157$	6.25505e9	0.821642	0.410821	−	0.911716i	$-0.365242\pi$
$157$	6.25505e9	0.821642	0.410821	+	0.911716i	$0.365242\pi$
$158$	8.92731e9	1.13963
$159$	−1.09330e10	−1.35660
$160$	−4.54815e9	−0.548649
$161$	−6.03285e7	−0.00707630
$162$	3.44756e10	3.93273
$163$	1.54066e10	1.70948	0.854738	−	0.519060i	$-0.173718\pi$
$163$	1.54066e10	1.70948	0.854738	+	0.519060i	$0.173718\pi$
$164$	5.59393e9	0.603837
$165$	−1.04766e10	−1.10038
$166$	1.27272e10	1.30090
$167$	1.42870e9	0.142141	0.0710703	−	0.997471i	$-0.477359\pi$
$167$	1.42870e9	0.142141	0.0710703	+	0.997471i	$0.477359\pi$
$168$	1.25888e8	0.0121925
$169$	2.76714e10	2.60941
$170$	−1.64501e9	−0.151060
$171$	−4.57251e10	−4.08952
$172$	−3.85929e9	−0.336225
$173$	1.34393e10	1.14070	0.570349	−	0.821403i	$-0.306808\pi$
$173$	1.34393e10	1.14070	0.570349	+	0.821403i	$0.306808\pi$
$174$	−4.73058e9	−0.391240
$175$	2.32049e8	0.0187029
$176$	2.02078e10	1.58749
$177$	−2.39145e10	−1.83139
$178$	−1.11108e9	−0.0829574
$179$	−1.01581e9	−0.0739561	−0.0369781	−	0.999316i	$-0.511773\pi$
$179$	−1.01581e9	−0.0739561	−0.0369781	+	0.999316i	$0.511773\pi$
$180$	1.21502e10	0.862697
$181$	−1.96698e10	−1.36222	−0.681108	−	0.732183i	$-0.738501\pi$
$181$	−1.96698e10	−1.36222	−0.681108	+	0.732183i	$0.738501\pi$
$182$	−8.62435e8	−0.0582647
$183$	−4.18433e10	−2.75801
$184$	−1.35475e9	−0.0871324
$185$	1.12452e9	0.0705824
$186$	2.83914e10	1.73932
$187$	5.98631e9	0.357991
$188$	1.54218e10	0.900375
$189$	−1.17194e9	−0.0668078
$190$	−1.65622e10	−0.921993
$191$	2.43763e10	1.32531	0.662655	−	0.748925i	$-0.269430\pi$
$191$	2.43763e10	1.32531	0.662655	+	0.748925i	$0.269430\pi$
$192$	−1.92449e10	−1.02202
$193$	1.03785e10	0.538427	0.269213	−	0.963081i	$-0.413236\pi$
$193$	1.03785e10	0.538427	0.269213	+	0.963081i	$0.413236\pi$
$194$	2.45401e10	1.24385
$195$	3.10173e10	1.53620
$196$	−1.62911e10	−0.788492
$197$	−2.89108e10	−1.36761	−0.683806	−	0.729664i	$-0.739676\pi$
$197$	−2.89108e10	−1.36761	−0.683806	+	0.729664i	$0.739676\pi$
$198$	−1.00262e11	−4.63600
$199$	−3.25676e10	−1.47213	−0.736067	−	0.676908i	$-0.763319\pi$
$199$	−3.25676e10	−1.47213	−0.736067	+	0.676908i	$0.763319\pi$
$200$	5.21095e9	0.230294
$201$	4.07614e10	1.76144
$202$	1.88836e10	0.798002
$203$	8.61672e7	0.00356131
$204$	−9.66835e9	−0.390856
$205$	8.30967e9	0.328618
$206$	−9.20119e7	−0.00355993
$207$	2.07641e10	0.786045
$208$	−5.98273e10	−2.21623
$209$	6.02711e10	2.18500
$210$	−6.98883e8	−0.0247981
$211$	6.13266e9	0.212999	0.106500	−	0.994313i	$-0.466036\pi$
$211$	6.13266e9	0.212999	0.106500	+	0.994313i	$0.466036\pi$
$212$	−1.67131e10	−0.568259
$213$	−1.23223e10	−0.410189
$214$	6.84917e10	2.23242
$215$	−5.73289e9	−0.182979
$216$	−2.63174e10	−0.822623
$217$	−5.17147e8	−0.0158324
$218$	−8.91994e9	−0.267490
$219$	−5.19646e10	−1.52654
$220$	−1.60155e10	−0.460933
$221$	−1.77231e10	−0.499776
$222$	1.49870e10	0.414120
$223$	−4.44779e10	−1.20441	−0.602203	−	0.798343i	$-0.705710\pi$
$223$	−4.44779e10	−1.20441	−0.602203	+	0.798343i	$0.705710\pi$
$224$	1.10410e9	0.0293016
$225$	−7.98677e10	−2.07754
$226$	−6.02793e10	−1.53702
$227$	5.45228e10	1.36289	0.681447	−	0.731868i	$-0.261351\pi$
$227$	5.45228e10	1.36289	0.681447	+	0.731868i	$0.261351\pi$
$228$	−9.73425e10	−2.38559
$229$	−1.14619e10	−0.275422	−0.137711	−	0.990472i	$-0.543974\pi$
$229$	−1.14619e10	−0.275422	−0.137711	+	0.990472i	$0.543974\pi$
$230$	7.52105e9	0.177216
$231$	2.54328e9	0.0587680
$232$	1.93499e9	0.0438514
$233$	4.18178e10	0.929521	0.464761	−	0.885436i	$-0.346140\pi$
$233$	4.18178e10	0.929521	0.464761	+	0.885436i	$0.346140\pi$
$234$	2.96837e11	6.47212
$235$	2.29087e10	0.489999
$236$	−3.65577e10	−0.767140
$237$	7.79418e10	1.60473
$238$	3.99339e8	0.00806762
$239$	1.09336e10	0.216756	0.108378	−	0.994110i	$-0.465434\pi$
$239$	1.09336e10	0.216756	0.108378	+	0.994110i	$0.465434\pi$
$240$	−4.84817e10	−0.943250
$241$	−8.20140e10	−1.56607	−0.783035	−	0.621978i	$-0.786329\pi$
$241$	−8.20140e10	−1.56607	−0.783035	+	0.621978i	$0.786329\pi$
$242$	6.07961e10	1.13948
$243$	1.42631e11	2.62412
$244$	−6.39652e10	−1.15529
$245$	−2.42000e10	−0.429110
$246$	1.10746e11	1.92806
$247$	−1.78439e11	−3.05038
$248$	−1.16132e10	−0.194948
$249$	1.11117e11	1.83182
$250$	−6.43959e10	−1.04263
$251$	3.67155e10	0.583872	0.291936	−	0.956438i	$-0.405701\pi$
$251$	3.67155e10	0.583872	0.291936	+	0.956438i	$0.405701\pi$
$252$	−2.94956e9	−0.0460739
$253$	−2.73696e10	−0.419978
$254$	7.63726e10	1.15129
$255$	−1.43621e10	−0.212710
$256$	8.80354e10	1.28108
$257$	−8.85674e10	−1.26641	−0.633206	−	0.773984i	$-0.718261\pi$
$257$	−8.85674e10	−1.26641	−0.633206	+	0.773984i	$0.718261\pi$
$258$	−7.64045e10	−1.07357
$259$	−2.72987e8	−0.00376958
$260$	4.74156e10	0.643489
$261$	−2.96574e10	−0.395596
$262$	1.28696e11	1.68737
$263$	1.01698e10	0.131072	0.0655361	−	0.997850i	$-0.479124\pi$
$263$	1.01698e10	0.131072	0.0655361	+	0.997850i	$0.479124\pi$
$264$	5.71126e10	0.723627
$265$	−2.48270e10	−0.309256
$266$	4.02061e9	0.0492407
$267$	−9.70052e9	−0.116814
$268$	6.23113e10	0.737837
$269$	−1.18297e11	−1.37749	−0.688747	−	0.725002i	$-0.741839\pi$
$269$	−1.18297e11	−1.37749	−0.688747	+	0.725002i	$0.741839\pi$
$270$	1.46104e11	1.67311
$271$	−1.64339e10	−0.185088	−0.0925439	−	0.995709i	$-0.529500\pi$
$271$	−1.64339e10	−0.185088	−0.0925439	+	0.995709i	$0.529500\pi$
$272$	2.77022e10	0.306870
$273$	−7.52967e9	−0.0820435
$274$	−2.31871e11	−2.48524
$275$	1.05275e11	1.11002
$276$	4.42040e10	0.458533
$277$	1.33557e11	1.36304	0.681521	−	0.731799i	$-0.261319\pi$
$277$	1.33557e11	1.36304	0.681521	+	0.731799i	$0.261319\pi$
$278$	−8.03558e10	−0.806892
$279$	1.77994e11	1.75868
$280$	2.85871e8	0.00277945
$281$	2.56040e10	0.244979	0.122490	−	0.992470i	$-0.460912\pi$
$281$	2.56040e10	0.244979	0.122490	+	0.992470i	$0.460912\pi$
$282$	3.05313e11	2.87491
$283$	−1.73577e10	−0.160862	−0.0804309	−	0.996760i	$-0.525630\pi$
$283$	−1.73577e10	−0.160862	−0.0804309	+	0.996760i	$0.525630\pi$
$284$	−1.88369e10	−0.171821
$285$	−1.44600e11	−1.29828
$286$	−3.91267e11	−3.45801
$287$	−2.01723e9	−0.0175504
$288$	−3.80013e11	−3.25486
$289$	−1.10381e11	−0.930799
$290$	−1.07423e10	−0.0891882
$291$	2.14252e11	1.75149
$292$	−7.94374e10	−0.639443
$293$	−4.35953e10	−0.345570	−0.172785	−	0.984960i	$-0.555277\pi$
$293$	−4.35953e10	−0.345570	−0.172785	+	0.984960i	$0.555277\pi$
$294$	−3.22523e11	−2.51767
$295$	−5.43057e10	−0.417490
$296$	−6.13027e9	−0.0464159
$297$	−5.31682e11	−3.96504
$298$	2.51115e11	1.84459
$299$	8.10309e10	0.586314
$300$	−1.70028e11	−1.21192
$301$	1.39170e9	0.00977231
$302$	1.45581e11	1.00710
$303$	1.64867e11	1.12368
$304$	2.78910e11	1.87298
$305$	−9.50189e10	−0.628725
$306$	−1.37446e11	−0.896162
$307$	−1.13081e10	−0.0726551	−0.0363276	−	0.999340i	$-0.511566\pi$
$307$	−1.13081e10	−0.0726551	−0.0363276	+	0.999340i	$0.511566\pi$
$308$	3.88787e9	0.0246169
$309$	−8.03330e8	−0.00501280
$310$	6.44719e10	0.396500
$311$	1.95094e11	1.18256	0.591278	−	0.806468i	$-0.298624\pi$
$311$	1.95094e11	1.18256	0.591278	+	0.806468i	$0.298624\pi$
$312$	−1.69088e11	−1.01022
$313$	−1.04305e11	−0.614267	−0.307133	−	0.951666i	$-0.599370\pi$
$313$	−1.04305e11	−0.614267	−0.307133	+	0.951666i	$0.599370\pi$
$314$	1.89304e11	1.09895
$315$	−4.38151e9	−0.0250741
$316$	1.19148e11	0.672196
$317$	−1.90469e11	−1.05940	−0.529698	−	0.848186i	$-0.677695\pi$
$317$	−1.90469e11	−1.05940	−0.529698	+	0.848186i	$0.677695\pi$
$318$	−3.30879e11	−1.81446
$319$	3.90921e10	0.211364
$320$	−4.37019e10	−0.232984
$321$	5.97981e11	3.14351
$322$	−1.82579e9	−0.00946455
$323$	8.26239e10	0.422371
$324$	4.60128e11	2.31967
$325$	−3.11679e11	−1.54965
$326$	4.66269e11	2.28642
$327$	−7.78774e10	−0.376658
$328$	−4.52995e10	−0.216103
$329$	−5.56126e9	−0.0261693
$330$	−3.17067e11	−1.47176
$331$	2.87995e11	1.31874	0.659369	−	0.751819i	$-0.270823\pi$
$331$	2.87995e11	1.31874	0.659369	+	0.751819i	$0.270823\pi$
$332$	1.69863e11	0.767321
$333$	9.39579e10	0.418730
$334$	4.32385e10	0.190113
$335$	9.25621e10	0.401543
$336$	1.17693e10	0.0503760
$337$	−2.87184e11	−1.21290	−0.606450	−	0.795122i	$-0.707407\pi$
$337$	−2.87184e11	−1.21290	−0.606450	+	0.795122i	$0.707407\pi$
$338$	8.37453e11	3.49008
$339$	−5.26281e11	−2.16431
$340$	−2.19551e10	−0.0891006
$341$	−2.34618e11	−0.939650
$342$	−1.38383e12	−5.46973
$343$	1.17526e10	0.0458468
$344$	3.12524e10	0.120329
$345$	6.56641e10	0.249541
$346$	4.06730e11	1.52568
$347$	−4.00865e11	−1.48428	−0.742139	−	0.670246i	$-0.766189\pi$
$347$	−4.00865e11	−1.48428	−0.742139	+	0.670246i	$0.766189\pi$
$348$	−6.31367e10	−0.230768
$349$	−2.02871e11	−0.731990	−0.365995	−	0.930617i	$-0.619271\pi$
$349$	−2.02871e11	−0.731990	−0.365995	+	0.930617i	$0.619271\pi$
$350$	7.02277e9	0.0250151
$351$	1.57410e12	5.53543
$352$	5.00903e11	1.73905
$353$	2.77118e11	0.949903	0.474952	−	0.880012i	$-0.342466\pi$
$353$	2.77118e11	0.949903	0.474952	+	0.880012i	$0.342466\pi$
$354$	−7.23753e11	−2.44949
$355$	−2.79818e10	−0.0935080
$356$	−1.48290e10	−0.0489314
$357$	3.48651e9	0.0113602
$358$	−3.07427e10	−0.0989163
$359$	−1.85627e11	−0.589815	−0.294908	−	0.955526i	$-0.595289\pi$
$359$	−1.85627e11	−0.589815	−0.294908	+	0.955526i	$0.595289\pi$
$360$	−9.83923e10	−0.308745
$361$	5.09183e11	1.57794
$362$	−5.95290e11	−1.82196
$363$	5.30793e11	1.60452
$364$	−1.15105e10	−0.0343667
$365$	−1.18002e11	−0.347995
$366$	−1.26635e12	−3.68884
$367$	−1.75278e11	−0.504346	−0.252173	−	0.967682i	$-0.581145\pi$
$367$	−1.75278e11	−0.504346	−0.252173	+	0.967682i	$0.581145\pi$
$368$	−1.26656e11	−0.360006
$369$	6.94301e11	1.94953
$370$	3.40328e10	0.0944040
$371$	6.02694e9	0.0165163
$372$	3.78925e11	1.02591
$373$	−7.47050e11	−1.99830	−0.999148	−	0.0412732i	$-0.986859\pi$
$373$	−7.47050e11	−1.99830	−0.999148	+	0.0412732i	$0.986859\pi$
$374$	1.81171e11	0.478813
$375$	−5.62222e11	−1.46814
$376$	−1.24885e11	−0.322229
$377$	−1.15736e11	−0.295076
$378$	−3.54678e10	−0.0893554
$379$	4.53099e10	0.112802	0.0564009	−	0.998408i	$-0.482037\pi$
$379$	4.53099e10	0.112802	0.0564009	+	0.998408i	$0.482037\pi$
$380$	−2.21048e11	−0.543826
$381$	6.66787e11	1.62116
$382$	7.37728e11	1.77260
$383$	6.39288e10	0.151811	0.0759053	−	0.997115i	$-0.475815\pi$
$383$	6.39288e10	0.151811	0.0759053	+	0.997115i	$0.475815\pi$
$384$	4.43032e11	1.03979
$385$	5.77535e9	0.0133969
$386$	3.14097e11	0.720146
$387$	−4.79003e11	−1.08552
$388$	3.27524e11	0.733669
$389$	9.89182e10	0.219030	0.109515	−	0.993985i	$-0.465070\pi$
$389$	9.89182e10	0.219030	0.109515	+	0.993985i	$0.465070\pi$
$390$	9.38712e11	2.05467
$391$	−3.75202e10	−0.0811839
$392$	1.31925e11	0.282188
$393$	1.12361e12	2.37602
$394$	−8.74963e11	−1.82918
$395$	1.76992e11	0.365820
$396$	−1.33815e12	−2.73448
$397$	−4.52208e11	−0.913652	−0.456826	−	0.889556i	$-0.651014\pi$
$397$	−4.52208e11	−0.913652	−0.456826	+	0.889556i	$0.651014\pi$
$398$	−9.85633e11	−1.96898
$399$	3.51028e10	0.0693367
$400$	4.87171e11	0.951507
$401$	−1.02424e10	−0.0197811	−0.00989055	−	0.999951i	$-0.503148\pi$
$401$	−1.02424e10	−0.0197811	−0.00989055	+	0.999951i	$0.503148\pi$
$402$	1.23361e12	2.35592
$403$	6.94612e11	1.31181
$404$	2.52030e11	0.470691
$405$	6.83510e11	1.26240
$406$	2.60778e9	0.00476326
$407$	−1.23848e11	−0.223724
$408$	7.82940e10	0.139881
$409$	−1.46363e11	−0.258628	−0.129314	−	0.991604i	$-0.541278\pi$
$409$	−1.46363e11	−0.258628	−0.129314	+	0.991604i	$0.541278\pi$
$410$	2.51485e11	0.439527
$411$	−2.02440e12	−3.49951
$412$	−1.22804e9	−0.00209978
$413$	1.31831e10	0.0222968
$414$	6.28410e11	1.05134
$415$	2.52328e11	0.417588
$416$	−1.48298e12	−2.42781
$417$	−7.01563e11	−1.13620
$418$	1.82406e12	2.92244
$419$	6.64776e10	0.105369	0.0526844	−	0.998611i	$-0.483222\pi$
$419$	6.64776e10	0.105369	0.0526844	+	0.998611i	$0.483222\pi$
$420$	−9.32763e9	−0.0146268
$421$	4.46135e11	0.692144	0.346072	−	0.938208i	$-0.387515\pi$
$421$	4.46135e11	0.692144	0.346072	+	0.938208i	$0.387515\pi$
$422$	1.85600e11	0.284887
$423$	1.91410e12	2.90692
$424$	1.35342e11	0.203370
$425$	1.44319e11	0.214572
$426$	−3.72925e11	−0.548628
$427$	2.30665e10	0.0335782
$428$	9.14124e11	1.31676
$429$	−3.41604e12	−4.86928
$430$	−1.73501e11	−0.244734
$431$	8.08879e11	1.12911	0.564554	−	0.825396i	$-0.309048\pi$
$431$	8.08879e11	1.12911	0.564554	+	0.825396i	$0.309048\pi$
$432$	−2.46041e12	−3.39884
$433$	−1.06908e12	−1.46155	−0.730775	−	0.682618i	$-0.760841\pi$
$433$	−1.06908e12	−1.46155	−0.730775	+	0.682618i	$0.760841\pi$
$434$	−1.56510e10	−0.0211758
$435$	−9.37881e10	−0.125587
$436$	−1.19050e11	−0.157776
$437$	−3.77760e11	−0.495506
$438$	−1.57267e12	−2.04175
$439$	−3.51205e11	−0.451306	−0.225653	−	0.974208i	$-0.572451\pi$
$439$	−3.51205e11	−0.451306	−0.225653	+	0.974208i	$0.572451\pi$
$440$	1.29693e11	0.164960
$441$	−2.02200e12	−2.54570
$442$	−5.36376e11	−0.668451
$443$	−6.75971e11	−0.833895	−0.416947	−	0.908931i	$-0.636900\pi$
$443$	−6.75971e11	−0.833895	−0.416947	+	0.908931i	$0.636900\pi$
$444$	2.00024e11	0.244263
$445$	−2.20282e10	−0.0266292
$446$	−1.34609e12	−1.61089
$447$	2.19241e12	2.59740
$448$	1.06090e10	0.0124429
$449$	6.40975e11	0.744273	0.372137	−	0.928178i	$-0.378625\pi$
$449$	6.40975e11	0.744273	0.372137	+	0.928178i	$0.378625\pi$
$450$	−2.41713e12	−2.77871
$451$	−9.15172e11	−1.04162
$452$	−8.04517e11	−0.906593
$453$	1.27102e12	1.41812
$454$	1.65009e12	1.82287
$455$	−1.70986e10	−0.0187029
$456$	7.88277e11	0.853762
$457$	1.27528e12	1.36767	0.683837	−	0.729635i	$-0.260310\pi$
$457$	1.27528e12	1.36767	0.683837	+	0.729635i	$0.260310\pi$
$458$	−3.46886e11	−0.368377
$459$	−7.28867e11	−0.766463
$460$	1.00380e11	0.104529
$461$	−3.25176e11	−0.335323	−0.167662	−	0.985845i	$-0.553622\pi$
$461$	−3.25176e11	−0.335323	−0.167662	+	0.985845i	$0.553622\pi$
$462$	7.69704e10	0.0786022
$463$	2.32530e11	0.235160	0.117580	−	0.993063i	$-0.462486\pi$
$463$	2.32530e11	0.235160	0.117580	+	0.993063i	$0.462486\pi$
$464$	1.80902e11	0.181181
$465$	5.62886e11	0.558318
$466$	1.26558e12	1.24324
$467$	−8.50334e11	−0.827301	−0.413651	−	0.910436i	$-0.635747\pi$
$467$	−8.50334e11	−0.827301	−0.413651	+	0.910436i	$0.635747\pi$
$468$	3.96173e12	3.81750
$469$	−2.24701e10	−0.0214451
$470$	6.93313e11	0.655373
$471$	1.65276e12	1.54745
$472$	2.96043e11	0.274547
$473$	6.31383e11	0.579986
$474$	2.35884e12	2.14633
$475$	1.45302e12	1.30964
$476$	5.32977e9	0.00475858
$477$	−2.07438e12	−1.83466
$478$	3.30896e11	0.289912
$479$	−3.41895e11	−0.296745	−0.148372	−	0.988932i	$-0.547403\pi$
$479$	−3.41895e11	−0.296745	−0.148372	+	0.988932i	$0.547403\pi$
$480$	−1.20175e12	−1.03330
$481$	3.66665e11	0.312332
$482$	−2.48208e12	−2.09462
$483$	−1.59405e10	−0.0133272
$484$	8.11414e11	0.672107
$485$	4.86530e11	0.399275
$486$	4.31660e12	3.50977
$487$	−2.09280e12	−1.68596	−0.842981	−	0.537943i	$-0.819201\pi$
$487$	−2.09280e12	−1.68596	−0.842981	+	0.537943i	$0.819201\pi$
$488$	5.17989e11	0.413458
$489$	4.07086e12	3.21955
$490$	−7.32394e11	−0.573935
$491$	−2.22502e12	−1.72769	−0.863847	−	0.503755i	$-0.831952\pi$
$491$	−2.22502e12	−1.72769	−0.863847	+	0.503755i	$0.831952\pi$
$492$	1.47807e12	1.13724
$493$	5.35902e10	0.0408577
$494$	−5.40032e12	−4.07989
$495$	−1.98779e12	−1.48815
$496$	−1.08572e12	−0.805469
$497$	6.79280e9	0.00499396
$498$	3.36287e12	2.45007
$499$	−1.23529e12	−0.891900	−0.445950	−	0.895058i	$-0.647134\pi$
$499$	−1.23529e12	−0.891900	−0.445950	+	0.895058i	$0.647134\pi$
$500$	−8.59459e11	−0.614979
$501$	3.77503e11	0.267702
$502$	1.11116e12	0.780929
$503$	−1.12859e12	−0.786103	−0.393051	−	0.919516i	$-0.628581\pi$
$503$	−1.12859e12	−0.786103	−0.393051	+	0.919516i	$0.628581\pi$
$504$	2.38855e10	0.0164891
$505$	3.74385e11	0.256157
$506$	−8.28319e11	−0.561721
$507$	7.31156e12	4.91444
$508$	1.01931e12	0.679075
$509$	2.94301e12	1.94340	0.971698	−	0.236227i	$-0.0759109\pi$
$509$	2.94301e12	1.94340	0.971698	+	0.236227i	$0.0759109\pi$
$510$	−4.34658e11	−0.284500
$511$	2.86460e10	0.0185853
$512$	1.80585e12	1.16136
$513$	−7.33835e12	−4.67811
$514$	−2.68042e12	−1.69383
$515$	−1.82422e9	−0.00114273
$516$	−1.01973e12	−0.633231
$517$	−2.52301e12	−1.55315
$518$	−8.26172e9	−0.00504181
$519$	3.55105e12	2.14834
$520$	−3.83970e11	−0.230294
$521$	5.75677e11	0.342302	0.171151	−	0.985245i	$-0.445251\pi$
$521$	5.75677e11	0.342302	0.171151	+	0.985245i	$0.445251\pi$
$522$	−8.97558e11	−0.529109
$523$	−1.79678e12	−1.05011	−0.525057	−	0.851067i	$-0.675956\pi$
$523$	−1.79678e12	−1.05011	−0.525057	+	0.851067i	$0.675956\pi$
$524$	1.71764e12	0.995273
$525$	6.13138e10	0.0352242
$526$	3.07780e11	0.175309
$527$	−3.21631e11	−0.181639
$528$	5.33945e12	2.98981
$529$	−1.62961e12	−0.904759
$530$	−7.51368e11	−0.413629
$531$	−4.53743e12	−2.47676
$532$	5.36610e10	0.0290440
$533$	2.70947e12	1.45416
$534$	−2.93578e11	−0.156238
$535$	1.35791e12	0.716604
$536$	−5.04596e11	−0.264060
$537$	−2.68405e11	−0.139286
$538$	−3.58017e12	−1.84240
$539$	2.66523e12	1.36015
$540$	1.94997e12	0.986862
$541$	−5.51533e11	−0.276811	−0.138406	−	0.990376i	$-0.544198\pi$
$541$	−5.51533e11	−0.276811	−0.138406	+	0.990376i	$0.544198\pi$
$542$	−4.97357e11	−0.247555
$543$	−5.19730e12	−2.56554
$544$	6.86673e11	0.336167
$545$	−1.76846e11	−0.0858640
$546$	−2.27879e11	−0.109733
$547$	−1.19064e12	−0.568639	−0.284320	−	0.958730i	$-0.591768\pi$
$547$	−1.19064e12	−0.568639	−0.284320	+	0.958730i	$0.591768\pi$
$548$	−3.09466e12	−1.46589
$549$	−7.93915e12	−3.72991
$550$	3.18607e12	1.48465
$551$	5.39554e11	0.249375
$552$	−3.57963e11	−0.164102
$553$	−4.29662e10	−0.0195373
$554$	4.04201e12	1.82307
$555$	2.97131e11	0.132932
$556$	−1.07247e12	−0.475935
$557$	−2.96543e12	−1.30539	−0.652695	−	0.757621i	$-0.726361\pi$
$557$	−2.96543e12	−1.30539	−0.652695	+	0.757621i	$0.726361\pi$
$558$	5.38685e12	2.35224
$559$	−1.86928e12	−0.809695
$560$	2.67260e10	0.0114839
$561$	1.58175e12	0.674225
$562$	7.74883e11	0.327660
$563$	8.35493e11	0.350473	0.175237	−	0.984526i	$-0.443931\pi$
$563$	8.35493e11	0.350473	0.175237	+	0.984526i	$0.443931\pi$
$564$	4.07486e12	1.69573
$565$	−1.19509e12	−0.493382
$566$	−5.25316e11	−0.215153
$567$	−1.65927e11	−0.0674208
$568$	1.52541e11	0.0614920
$569$	1.84629e12	0.738405	0.369203	−	0.929349i	$-0.379631\pi$
$569$	1.84629e12	0.738405	0.369203	+	0.929349i	$0.379631\pi$
$570$	−4.37620e12	−1.73644
$571$	1.20489e12	0.474335	0.237167	−	0.971469i	$-0.423781\pi$
$571$	1.20489e12	0.474335	0.237167	+	0.971469i	$0.423781\pi$
$572$	−5.22204e12	−2.03966
$573$	6.44089e12	2.49603
$574$	−6.10499e10	−0.0234737
$575$	−6.59831e11	−0.251725
$576$	−3.65144e12	−1.38218
$577$	−6.55037e11	−0.246022	−0.123011	−	0.992405i	$-0.539255\pi$
$577$	−6.55037e11	−0.246022	−0.123011	+	0.992405i	$0.539255\pi$
$578$	−3.34060e12	−1.24494
$579$	2.74229e12	1.01405
$580$	−1.43372e11	−0.0526065
$581$	−6.12544e10	−0.0223020
$582$	6.48417e12	2.34262
$583$	2.73428e12	0.980245
$584$	6.43282e11	0.228846
$585$	5.88507e12	2.07754
$586$	−1.31938e12	−0.462200
$587$	−9.24536e11	−0.321405	−0.160702	−	0.987003i	$-0.551376\pi$
$587$	−9.24536e11	−0.321405	−0.160702	+	0.987003i	$0.551376\pi$
$588$	−4.30456e12	−1.48501
$589$	−3.23823e12	−1.10864
$590$	−1.64352e12	−0.558393
$591$	−7.63905e12	−2.57570
$592$	−5.73118e11	−0.191777
$593$	1.47452e12	0.489670	0.244835	−	0.969565i	$-0.421266\pi$
$593$	1.47452e12	0.489670	0.244835	+	0.969565i	$0.421266\pi$
$594$	−1.60909e13	−5.30324
$595$	7.91726e9	0.00258969
$596$	3.35151e12	1.08801
$597$	−8.60528e12	−2.77256
$598$	2.45233e12	0.784195
$599$	−8.35093e11	−0.265042	−0.132521	−	0.991180i	$-0.542307\pi$
$599$	−8.35093e11	−0.265042	−0.132521	+	0.991180i	$0.542307\pi$
$600$	1.37688e12	0.433726
$601$	2.80777e12	0.877861	0.438931	−	0.898521i	$-0.355357\pi$
$601$	2.80777e12	0.877861	0.438931	+	0.898521i	$0.355357\pi$
$602$	4.21187e10	0.0130705
$603$	7.73388e12	2.38215
$604$	1.94299e12	0.594026
$605$	1.20534e12	0.365771
$606$	4.98957e12	1.50292
$607$	−1.65202e11	−0.0493932	−0.0246966	−	0.999695i	$-0.507862\pi$
$607$	−1.65202e11	−0.0493932	−0.0246966	+	0.999695i	$0.507862\pi$
$608$	6.91353e12	2.05180
$609$	2.27678e10	0.00670722
$610$	−2.87567e12	−0.840920
$611$	7.46966e12	2.16828
$612$	−1.83443e12	−0.528590
$613$	−3.34796e12	−0.957652	−0.478826	−	0.877910i	$-0.658937\pi$
$613$	−3.34796e12	−0.957652	−0.478826	+	0.877910i	$0.658937\pi$
$614$	−3.42230e11	−0.0971762
$615$	2.19564e12	0.618905
$616$	−3.14839e10	−0.00880999
$617$	−1.04652e12	−0.290712	−0.145356	−	0.989379i	$-0.546433\pi$
$617$	−1.04652e12	−0.290712	−0.145356	+	0.989379i	$0.546433\pi$
$618$	−2.43121e10	−0.00670462
$619$	6.98655e12	1.91274	0.956368	−	0.292166i	$-0.0943760\pi$
$619$	6.98655e12	1.91274	0.956368	+	0.292166i	$0.0943760\pi$
$620$	8.60474e11	0.233870
$621$	3.33241e12	0.899178
$622$	5.90435e12	1.58167
$623$	5.34750e9	0.00142218
$624$	−1.58080e13	−4.17395
$625$	1.83483e12	0.480989
$626$	−3.15671e12	−0.821582
$627$	1.59253e13	4.11513
$628$	2.52654e12	0.648199
$629$	−1.69779e11	−0.0432471
$630$	−1.32603e11	−0.0335367
$631$	−3.98579e12	−1.00088	−0.500440	−	0.865771i	$-0.666828\pi$
$631$	−3.98579e12	−1.00088	−0.500440	+	0.865771i	$0.666828\pi$
$632$	−9.64860e11	−0.240568
$633$	1.62042e12	0.401154
$634$	−5.76440e12	−1.41694
$635$	1.51416e12	0.369564
$636$	−4.41607e12	−1.07023
$637$	−7.89072e12	−1.89884
$638$	1.18309e12	0.282699
$639$	−2.33798e12	−0.554736
$640$	1.00605e12	0.237033
$641$	−1.85369e11	−0.0433686	−0.0216843	−	0.999765i	$-0.506903\pi$
$641$	−1.85369e11	−0.0433686	−0.0216843	+	0.999765i	$0.506903\pi$
$642$	1.80974e13	4.20445
$643$	6.07454e12	1.40141	0.700703	−	0.713453i	$-0.252870\pi$
$643$	6.07454e12	1.40141	0.700703	+	0.713453i	$0.252870\pi$
$644$	−2.43679e10	−0.00558254
$645$	−1.51479e12	−0.344614
$646$	2.50055e12	0.564922
$647$	8.64572e12	1.93969	0.969845	−	0.243724i	$-0.0783692\pi$
$647$	8.64572e12	1.93969	0.969845	+	0.243724i	$0.0783692\pi$
$648$	−3.72611e12	−0.830171
$649$	5.98087e12	1.32332
$650$	−9.43271e12	−2.07265
$651$	−1.36645e11	−0.0298180
$652$	6.22305e12	1.34862
$653$	−3.03713e11	−0.0653663	−0.0326831	−	0.999466i	$-0.510405\pi$
$653$	−3.03713e11	−0.0653663	−0.0326831	+	0.999466i	$0.510405\pi$
$654$	−2.35690e12	−0.503780
$655$	2.55152e12	0.541644
$656$	−4.23505e12	−0.892876
$657$	−9.85951e12	−2.06448
$658$	−1.68307e11	−0.0350014
$659$	−5.32280e12	−1.09940	−0.549700	−	0.835362i	$-0.685258\pi$
$659$	−5.32280e12	−1.09940	−0.549700	+	0.835362i	$0.685258\pi$
$660$	−4.23173e12	−0.868101
$661$	2.57132e12	0.523901	0.261950	−	0.965081i	$-0.415634\pi$
$661$	2.57132e12	0.523901	0.261950	+	0.965081i	$0.415634\pi$
$662$	8.71592e12	1.76381
$663$	−4.68295e12	−0.941257
$664$	−1.37555e12	−0.274611
$665$	7.97122e10	0.0158062
$666$	2.84356e12	0.560052
$667$	−2.45016e11	−0.0479323
$668$	5.77083e11	0.112136
$669$	−1.17523e13	−2.26833
$670$	2.80132e12	0.537063
$671$	1.04648e13	1.99286
$672$	2.91733e11	0.0551853
$673$	4.35627e12	0.818554	0.409277	−	0.912410i	$-0.365781\pi$
$673$	4.35627e12	0.818554	0.409277	+	0.912410i	$0.365781\pi$
$674$	−8.69138e12	−1.62225
$675$	−1.28179e13	−2.37656
$676$	1.11771e13	2.05858
$677$	−6.14723e12	−1.12468	−0.562342	−	0.826905i	$-0.690099\pi$
$677$	−6.14723e12	−1.12468	−0.562342	+	0.826905i	$0.690099\pi$
$678$	−1.59275e13	−2.89476
$679$	−1.18109e11	−0.0213240
$680$	1.77792e11	0.0318876
$681$	1.44064e13	2.56682
$682$	−7.10051e12	−1.25678
$683$	−2.51421e12	−0.442088	−0.221044	−	0.975264i	$-0.570946\pi$
$683$	−2.51421e12	−0.442088	−0.221044	+	0.975264i	$0.570946\pi$
$684$	−1.84693e13	−3.22625
$685$	−4.59705e12	−0.797759
$686$	3.55682e11	0.0613202
$687$	−3.02856e12	−0.518718
$688$	2.92179e12	0.497165
$689$	−8.09514e12	−1.36848
$690$	1.98727e12	0.333761
$691$	2.14470e12	0.357862	0.178931	−	0.983862i	$-0.442736\pi$
$691$	2.14470e12	0.357862	0.178931	+	0.983862i	$0.442736\pi$
$692$	5.42842e12	0.899904
$693$	4.82550e11	0.0794773
$694$	−1.21318e13	−1.98522
$695$	−1.59313e12	−0.259011
$696$	5.11279e11	0.0825879
$697$	−1.25458e12	−0.201350
$698$	−6.13972e12	−0.979036
$699$	1.10494e13	1.75062
$700$	9.37293e10	0.0147548
$701$	7.67507e12	1.20047	0.600235	−	0.799824i	$-0.295074\pi$
$701$	7.67507e12	1.20047	0.600235	+	0.799824i	$0.295074\pi$
$702$	4.76389e13	7.40364
$703$	−1.70937e12	−0.263959
$704$	4.81304e12	0.738486
$705$	6.05311e12	0.922843
$706$	8.38676e12	1.27050
$707$	−9.08847e10	−0.0136805
$708$	−9.65956e12	−1.44480
$709$	3.12348e12	0.464227	0.232114	−	0.972689i	$-0.425436\pi$
$709$	3.12348e12	0.464227	0.232114	+	0.972689i	$0.425436\pi$
$710$	−8.46847e11	−0.125067
$711$	1.47883e13	2.17023
$712$	1.20085e11	0.0175117
$713$	1.47051e12	0.213091
$714$	1.05516e11	0.0151942
$715$	−7.75723e12	−1.11002
$716$	−4.10307e11	−0.0583445
$717$	2.88896e12	0.408230
$718$	−5.61785e12	−0.788878
$719$	−5.15721e12	−0.719673	−0.359836	−	0.933015i	$-0.617168\pi$
$719$	−5.15721e12	−0.719673	−0.359836	+	0.933015i	$0.617168\pi$
$720$	−9.19868e12	−1.27564
$721$	4.42843e8	6.10297e−5 0
$722$	1.54100e13	2.11050
$723$	−2.16704e13	−2.94947
$724$	−7.94502e12	−1.07466
$725$	9.42437e11	0.126687
$726$	1.60640e13	2.14605
$727$	−7.14105e12	−0.948107	−0.474053	−	0.880496i	$-0.657210\pi$
$727$	−7.14105e12	−0.948107	−0.474053	+	0.880496i	$0.657210\pi$
$728$	9.32116e10	0.0122993
$729$	1.52650e13	2.00181
$730$	−3.57125e12	−0.465444
$731$	8.65544e11	0.112114
$732$	−1.69014e13	−2.17582
$733$	3.16277e12	0.404669	0.202335	−	0.979316i	$-0.435147\pi$
$733$	3.16277e12	0.404669	0.202335	+	0.979316i	$0.435147\pi$
$734$	−5.30463e12	−0.674564
$735$	−6.39432e12	−0.808168
$736$	−3.13949e12	−0.394375
$737$	−1.01942e13	−1.27277
$738$	2.10125e13	2.60749
$739$	−1.79699e12	−0.221639	−0.110819	−	0.993841i	$-0.535348\pi$
$739$	−1.79699e12	−0.221639	−0.110819	+	0.993841i	$0.535348\pi$
$740$	4.54219e11	0.0556829
$741$	−4.71487e13	−5.74497
$742$	1.82400e11	0.0220906
$743$	9.21252e12	1.10899	0.554496	−	0.832186i	$-0.312911\pi$
$743$	9.21252e12	1.10899	0.554496	+	0.832186i	$0.312911\pi$
$744$	−3.06853e12	−0.367157
$745$	4.97859e12	0.592111
$746$	−2.26088e13	−2.67272
$747$	2.10828e13	2.47734
$748$	2.41799e12	0.282422
$749$	−3.29643e11	−0.0382715
$750$	−1.70152e13	−1.96364
$751$	5.67356e12	0.650843	0.325421	−	0.945569i	$-0.394494\pi$
$751$	5.67356e12	0.650843	0.325421	+	0.945569i	$0.394494\pi$
$752$	−1.16755e13	−1.33136
$753$	9.70125e12	1.09964
$754$	−3.50267e12	−0.394664
$755$	2.88628e12	0.323278
$756$	−4.73370e11	−0.0527051
$757$	5.41977e12	0.599859	0.299929	−	0.953961i	$-0.403037\pi$
$757$	5.41977e12	0.599859	0.299929	+	0.953961i	$0.403037\pi$
$758$	1.37127e12	0.150873
$759$	−7.23182e12	−0.790969
$760$	1.79004e12	0.194626
$761$	2.15873e12	0.233328	0.116664	−	0.993171i	$-0.462780\pi$
$761$	2.15873e12	0.233328	0.116664	+	0.993171i	$0.462780\pi$
$762$	2.01798e13	2.16830
$763$	4.29307e10	0.00458572
$764$	9.84608e12	1.04555
$765$	−2.72500e12	−0.287667
$766$	1.93475e12	0.203047
$767$	−1.77070e13	−1.84742
$768$	2.32614e13	2.41274
$769$	−4.28032e12	−0.441375	−0.220688	−	0.975345i	$-0.570830\pi$
$769$	−4.28032e12	−0.441375	−0.220688	+	0.975345i	$0.570830\pi$
$770$	1.74786e11	0.0179184
$771$	−2.34020e13	−2.38511
$772$	4.19209e12	0.424769
$773$	1.20590e13	1.21480	0.607400	−	0.794396i	$-0.292212\pi$
$773$	1.20590e13	1.21480	0.607400	+	0.794396i	$0.292212\pi$
$774$	−1.44966e13	−1.45189
$775$	−5.65620e12	−0.563205
$776$	−2.65228e12	−0.262568
$777$	−7.21307e10	−0.00709946
$778$	2.99368e12	0.292952
$779$	−1.26313e13	−1.22894
$780$	1.25285e13	1.21192
$781$	3.08174e12	0.296391
$782$	−1.13552e12	−0.108584
$783$	−4.75968e12	−0.452532
$784$	1.23336e13	1.16592
$785$	3.75313e12	0.352760
$786$	3.40051e13	3.17792
$787$	−8.78555e12	−0.816362	−0.408181	−	0.912901i	$-0.633837\pi$
$787$	−8.78555e12	−0.816362	−0.408181	+	0.912901i	$0.633837\pi$
$788$	−1.16777e13	−1.07892
$789$	2.68714e12	0.246856
$790$	5.35652e12	0.489284
$791$	2.90118e11	0.0263500
$792$	1.08363e13	0.978626
$793$	−3.09821e13	−2.78215
$794$	−1.36857e13	−1.22201
$795$	−6.55998e12	−0.582439
$796$	−1.31547e13	−1.16138
$797$	5.07818e12	0.445806	0.222903	−	0.974841i	$-0.428447\pi$
$797$	5.07818e12	0.445806	0.222903	+	0.974841i	$0.428447\pi$
$798$	1.06236e12	0.0927379
$799$	−3.45872e12	−0.300231
$800$	1.20758e13	1.04235
$801$	−1.84053e12	−0.157978
$802$	−3.09977e11	−0.0264572
$803$	1.29960e13	1.10304
$804$	1.64644e13	1.38961
$805$	−3.61980e10	−0.00303811
$806$	2.10219e13	1.75454
$807$	−3.12574e13	−2.59431
$808$	−2.04093e12	−0.168452
$809$	1.90437e13	1.56308	0.781542	−	0.623852i	$-0.214433\pi$
$809$	1.90437e13	1.56308	0.781542	+	0.623852i	$0.214433\pi$
$810$	2.06859e13	1.68846
$811$	4.93947e12	0.400947	0.200473	−	0.979699i	$-0.435752\pi$
$811$	4.93947e12	0.400947	0.200473	+	0.979699i	$0.435752\pi$
$812$	3.48047e10	0.00280954
$813$	−4.34228e12	−0.348586
$814$	−3.74815e12	−0.299232
$815$	9.24420e12	0.733939
$816$	7.31970e12	0.577946
$817$	8.71444e12	0.684290
$818$	−4.42956e12	−0.345916
$819$	−1.42864e12	−0.110955
$820$	3.35644e12	0.259249
$821$	6.16249e11	0.0473382	0.0236691	−	0.999720i	$-0.492465\pi$
$821$	6.16249e11	0.0473382	0.0236691	+	0.999720i	$0.492465\pi$
$822$	−6.12667e13	−4.68060
$823$	−1.09076e13	−0.828763	−0.414382	−	0.910103i	$-0.636002\pi$
$823$	−1.09076e13	−0.828763	−0.414382	+	0.910103i	$0.636002\pi$
$824$	9.94461e9	0.000751476 0
$825$	2.78166e13	2.09056
$826$	3.98976e11	0.0298220
$827$	1.53397e13	1.14036	0.570180	−	0.821520i	$-0.306874\pi$
$827$	1.53397e13	1.14036	0.570180	+	0.821520i	$0.306874\pi$
$828$	8.38706e12	0.620117
$829$	1.86138e13	1.36880	0.684398	−	0.729109i	$-0.260065\pi$
$829$	1.86138e13	1.36880	0.684398	+	0.729109i	$0.260065\pi$
$830$	7.63649e12	0.558524
$831$	3.52896e13	2.56710
$832$	−1.42495e13	−1.03097
$833$	3.65369e12	0.262923
$834$	−2.12322e13	−1.51967
$835$	8.57244e11	0.0610260
$836$	2.43447e13	1.72376
$837$	2.85660e13	2.01180
$838$	2.01189e12	0.140931
$839$	1.61742e12	0.112692	0.0563462	−	0.998411i	$-0.482055\pi$
$839$	1.61742e12	0.112692	0.0563462	+	0.998411i	$0.482055\pi$
$840$	7.55349e10	0.00523469
$841$	−1.41572e13	−0.975877
$842$	1.35019e13	0.925743
$843$	6.76528e12	0.461383
$844$	2.47711e12	0.168037
$845$	1.66033e13	1.12031
$846$	5.79287e13	3.88801
$847$	−2.92605e11	−0.0195347
$848$	1.26531e13	0.840267
$849$	−4.58638e12	−0.302960
$850$	4.36769e12	0.286990
$851$	7.76237e11	0.0507354
$852$	−4.97724e12	−0.323601
$853$	−1.32159e13	−0.854722	−0.427361	−	0.904081i	$-0.640557\pi$
$853$	−1.32159e13	−0.854722	−0.427361	+	0.904081i	$0.640557\pi$
$854$	6.98090e11	0.0449108
$855$	−2.74357e13	−1.75578
$856$	−7.40255e12	−0.471248
$857$	1.80486e13	1.14296	0.571478	−	0.820617i	$-0.306370\pi$
$857$	1.80486e13	1.14296	0.571478	+	0.820617i	$0.306370\pi$
$858$	−1.03384e14	−6.51267
$859$	4.76460e12	0.298578	0.149289	−	0.988794i	$-0.452302\pi$
$859$	4.76460e12	0.298578	0.149289	+	0.988794i	$0.452302\pi$
$860$	−2.31563e12	−0.144353
$861$	−5.33009e11	−0.0330537
$862$	2.44800e13	1.51018
$863$	2.58565e13	1.58680	0.793399	−	0.608702i	$-0.208310\pi$
$863$	2.58565e13	1.58680	0.793399	+	0.608702i	$0.208310\pi$
$864$	−6.09877e13	−3.72332
$865$	8.06380e12	0.489742
$866$	−3.23548e13	−1.95482
$867$	−2.91658e13	−1.75303
$868$	−2.08886e11	−0.0124903
$869$	−1.94928e13	−1.15954
$870$	−2.83842e12	−0.167973
$871$	3.01810e13	1.77686
$872$	9.64063e11	0.0564653
$873$	4.06512e13	2.36870
$874$	−1.14326e13	−0.662740
$875$	3.09930e11	0.0178743
$876$	−2.09896e13	−1.20430
$877$	4.98151e12	0.284356	0.142178	−	0.989841i	$-0.454589\pi$
$877$	4.98151e12	0.284356	0.142178	+	0.989841i	$0.454589\pi$
$878$	−1.06289e13	−0.603621
$879$	−1.15191e13	−0.650832
$880$	1.21250e13	0.681567
$881$	1.02559e12	0.0573567	0.0286783	−	0.999589i	$-0.490870\pi$
$881$	1.02559e12	0.0573567	0.0286783	+	0.999589i	$0.490870\pi$
$882$	−6.11941e13	−3.40487
$883$	−2.77027e13	−1.53355	−0.766776	−	0.641915i	$-0.778140\pi$
$883$	−2.77027e13	−1.53355	−0.766776	+	0.641915i	$0.778140\pi$
$884$	−7.15874e12	−0.394277
$885$	−1.43491e13	−0.786283
$886$	−2.04577e13	−1.11533
$887$	2.56421e13	1.39090	0.695452	−	0.718572i	$-0.255204\pi$
$887$	2.56421e13	1.39090	0.695452	+	0.718572i	$0.255204\pi$
$888$	−1.61979e12	−0.0874177
$889$	−3.67573e11	−0.0197372
$890$	−6.66665e11	−0.0356166
$891$	−7.52773e13	−4.00142
$892$	−1.79656e13	−0.950164
$893$	−3.48230e13	−1.83246
$894$	6.63516e13	3.47402
$895$	−6.09502e11	−0.0317520
$896$	−2.44226e11	−0.0126592
$897$	2.14106e13	1.10424
$898$	1.93986e13	0.995466
$899$	−2.10033e12	−0.107243
$900$	−3.22602e13	−1.63899
$901$	3.74835e12	0.189486
$902$	−2.76969e13	−1.39316
$903$	3.67726e11	0.0184048
$904$	6.51496e12	0.324455
$905$	−1.18022e13	−0.584848
$906$	3.84665e13	1.89673
$907$	−2.92105e13	−1.43320	−0.716599	−	0.697485i	$-0.754302\pi$
$907$	−2.92105e13	−1.43320	−0.716599	+	0.697485i	$0.754302\pi$
$908$	2.20229e13	1.07520
$909$	3.12811e13	1.51966
$910$	−5.17474e11	−0.0250151
$911$	−2.51001e13	−1.20738	−0.603688	−	0.797221i	$-0.706303\pi$
$911$	−2.51001e13	−1.20738	−0.603688	+	0.797221i	$0.706303\pi$
$912$	7.36959e13	3.52750
$913$	−2.77897e13	−1.32363
$914$	3.85953e13	1.82927
$915$	−2.51066e13	−1.18411
$916$	−4.62971e12	−0.217282
$917$	−6.19401e11	−0.0289274
$918$	−2.20586e13	−1.02514
$919$	2.38576e13	1.10333	0.551667	−	0.834065i	$-0.313992\pi$
$919$	2.38576e13	1.10333	0.551667	+	0.834065i	$0.313992\pi$
$920$	−8.12872e11	−0.0374091
$921$	−2.98791e12	−0.136836
$922$	−9.84117e12	−0.448495
$923$	−9.12382e12	−0.413780
$924$	1.02728e12	0.0463625
$925$	−2.98574e12	−0.134095
$926$	7.03732e12	0.314527
$927$	−1.52420e11	−0.00677927
$928$	4.48414e12	0.198479
$929$	−2.47859e13	−1.09178	−0.545888	−	0.837858i	$-0.683808\pi$
$929$	−2.47859e13	−1.09178	−0.545888	+	0.837858i	$0.683808\pi$
$930$	1.70353e13	0.746751
$931$	3.67859e13	1.60475
$932$	1.68911e13	0.733306
$933$	5.15492e13	2.22717
$934$	−2.57347e13	−1.10652
$935$	3.59188e12	0.153698
$936$	−3.20820e13	−1.36622
$937$	2.19643e13	0.930870	0.465435	−	0.885082i	$-0.345898\pi$
$937$	2.19643e13	0.930870	0.465435	+	0.885082i	$0.345898\pi$
$938$	−6.80041e11	−0.0286828
$939$	−2.75604e13	−1.15688
$940$	9.25329e12	0.386563
$941$	1.69142e13	0.703231	0.351616	−	0.936144i	$-0.385632\pi$
$941$	1.69142e13	0.703231	0.351616	+	0.936144i	$0.385632\pi$
$942$	5.00194e13	2.06971
$943$	5.73600e12	0.236214
$944$	2.76771e13	1.13435
$945$	−7.03181e11	−0.0286830
$946$	1.91083e13	0.775732
$947$	−3.75974e13	−1.51909	−0.759544	−	0.650455i	$-0.774578\pi$
$947$	−3.75974e13	−1.51909	−0.759544	+	0.650455i	$0.774578\pi$
$948$	3.14823e13	1.26599
$949$	−3.84762e13	−1.53991
$950$	4.39746e13	1.75164
$951$	−5.03273e13	−1.99522
$952$	−4.31604e10	−0.00170302
$953$	2.47537e13	0.972126	0.486063	−	0.873924i	$-0.338433\pi$
$953$	2.47537e13	0.972126	0.486063	+	0.873924i	$0.338433\pi$
$954$	−6.27794e13	−2.45386
$955$	1.46261e13	0.569003
$956$	4.41630e12	0.171001
$957$	1.03292e13	0.398074
$958$	−1.03472e13	−0.396896
$959$	1.11597e12	0.0426058
$960$	−1.15473e13	−0.438791
$961$	−1.38342e13	−0.523236
$962$	1.10968e13	0.417745
$963$	1.13458e14	4.25126
$964$	−3.31271e13	−1.23548
$965$	6.22726e12	0.231166
$966$	−4.82425e11	−0.0178251
$967$	2.81613e13	1.03570	0.517849	−	0.855472i	$-0.326733\pi$
$967$	2.81613e13	1.03570	0.517849	+	0.855472i	$0.326733\pi$
$968$	−6.57081e12	−0.240536
$969$	2.18315e13	0.795476
$970$	1.47244e13	0.534030
$971$	2.69137e13	0.971599	0.485800	−	0.874070i	$-0.338528\pi$
$971$	2.69137e13	0.971599	0.485800	+	0.874070i	$0.338528\pi$
$972$	5.76114e13	2.07019
$973$	3.86744e11	0.0138330
$974$	−6.33369e13	−2.25497
$975$	−8.23543e13	−2.91854
$976$	4.84267e13	1.70829
$977$	−2.48025e13	−0.870905	−0.435452	−	0.900212i	$-0.643412\pi$
$977$	−2.48025e13	−0.870905	−0.435452	+	0.900212i	$0.643412\pi$
$978$	1.23201e14	4.30616
$979$	2.42604e12	0.0844064
$980$	−9.77489e12	−0.338528
$981$	−1.47761e13	−0.509388
$982$	−6.73383e13	−2.31079
$983$	8.03233e12	0.274379	0.137190	−	0.990545i	$-0.456193\pi$
$983$	8.03233e12	0.274379	0.137190	+	0.990545i	$0.456193\pi$
$984$	−1.19694e13	−0.407000
$985$	−1.73469e13	−0.587165
$986$	1.62186e12	0.0546472
$987$	−1.46944e12	−0.0492861
$988$	−7.20753e13	−2.40647
$989$	−3.95730e12	−0.131527
$990$	−6.01588e13	−1.99040
$991$	−5.11207e13	−1.68370	−0.841850	−	0.539711i	$-0.818534\pi$
$991$	−5.11207e13	−1.68370	−0.841850	+	0.539711i	$0.818534\pi$
$992$	−2.69124e13	−0.882367
$993$	7.60962e13	2.48366
$994$	2.05579e11	0.00667942
$995$	−1.95411e13	−0.632040
$996$	4.48825e13	1.44514
$997$	−2.04571e13	−0.655717	−0.327859	−	0.944727i	$-0.606327\pi$
$997$	−2.04571e13	−0.655717	−0.327859	+	0.944727i	$0.606327\pi$
$998$	−3.73850e13	−1.19292
$999$	1.50792e13	0.478997

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.a.b.1.11	✓	14
3.2	odd	2		333.10.a.d.1.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.a.b.1.11	✓	14	1.1	even	1	trivial
333.10.a.d.1.4		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)

\(f(q)\)	\(=\)	\(q+30.2642 q^{2} +264.228 q^{3} +403.920 q^{4} +600.015 q^{5} +7996.64 q^{6} -145.658 q^{7} -3270.94 q^{8} +50133.3 q^{9} +O(q^{10})\)	\(q+30.2642 q^{2} +264.228 q^{3} +403.920 q^{4} +600.015 q^{5} +7996.64 q^{6} -145.658 q^{7} -3270.94 q^{8} +50133.3 q^{9} +18159.0 q^{10} -66081.7 q^{11} +106727. q^{12} +195642. q^{13} -4408.22 q^{14} +158541. q^{15} -305800. q^{16} -90589.5 q^{17} +1.51724e6 q^{18} -912070. q^{19} +242358. q^{20} -38486.9 q^{21} -1.99991e6 q^{22} +414179. q^{23} -864273. q^{24} -1.59311e6 q^{25} +5.92096e6 q^{26} +8.04582e6 q^{27} -58834.3 q^{28} -591572. q^{29} +4.79810e6 q^{30} +3.55042e6 q^{31} -7.58005e6 q^{32} -1.74606e7 q^{33} -2.74162e6 q^{34} -87397.1 q^{35} +2.02499e7 q^{36} +1.87416e6 q^{37} -2.76030e7 q^{38} +5.16941e7 q^{39} -1.96261e6 q^{40} +1.38491e7 q^{41} -1.16478e6 q^{42} -9.55458e6 q^{43} -2.66918e7 q^{44} +3.00807e7 q^{45} +1.25348e7 q^{46} +3.81802e7 q^{47} -8.08007e7 q^{48} -4.03324e7 q^{49} -4.82141e7 q^{50} -2.39363e7 q^{51} +7.90240e7 q^{52} -4.13773e7 q^{53} +2.43500e8 q^{54} -3.96500e7 q^{55} +476439. q^{56} -2.40994e8 q^{57} -1.79034e7 q^{58} -9.05072e7 q^{59} +6.40378e7 q^{60} -1.58361e8 q^{61} +1.07450e8 q^{62} -7.30233e6 q^{63} -7.28347e7 q^{64} +1.17388e8 q^{65} -5.28432e8 q^{66} +1.54266e8 q^{67} -3.65910e7 q^{68} +1.09437e8 q^{69} -2.64500e6 q^{70} -4.66352e7 q^{71} -1.63983e8 q^{72} -1.96666e8 q^{73} +5.67199e7 q^{74} -4.20943e8 q^{75} -3.68404e8 q^{76} +9.62534e6 q^{77} +1.56448e9 q^{78} +2.94979e8 q^{79} -1.83484e8 q^{80} +1.13916e9 q^{81} +4.19132e8 q^{82} +4.20535e8 q^{83} -1.55457e7 q^{84} -5.43551e7 q^{85} -2.89161e8 q^{86} -1.56310e8 q^{87} +2.16149e8 q^{88} -3.67127e7 q^{89} +9.10369e8 q^{90} -2.84969e7 q^{91} +1.67295e8 q^{92} +9.38119e8 q^{93} +1.15549e9 q^{94} -5.47256e8 q^{95} -2.00286e9 q^{96} +8.10863e8 q^{97} -1.22063e9 q^{98} -3.31290e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9}+O(q^{10}) \) 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

Properties

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