LMFDB - Embedded newform 37.10.a.b.1.8

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			1.8
Root			$1.40540$ 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)

$f(q)$	$=$	$q+4.40540 q^{2} +198.342 q^{3} -492.592 q^{4} +2557.54 q^{5} +873.778 q^{6} +499.386 q^{7} -4425.63 q^{8} +19656.7 q^{9} +O(q^{10})$	\(q+4.40540 q^{2} +198.342 q^{3} -492.592 q^{4} +2557.54 q^{5} +873.778 q^{6} +499.386 q^{7} -4425.63 q^{8} +19656.7 q^{9} +11267.0 q^{10} +66654.7 q^{11} -97701.9 q^{12} -101907. q^{13} +2200.00 q^{14} +507269. q^{15} +232711. q^{16} +83920.5 q^{17} +86595.6 q^{18} -260637. q^{19} -1.25983e6 q^{20} +99049.4 q^{21} +293641. q^{22} -212587. q^{23} -877791. q^{24} +4.58790e6 q^{25} -448942. q^{26} -5220.39 q^{27} -245994. q^{28} +4.96493e6 q^{29} +2.23472e6 q^{30} +5.82154e6 q^{31} +3.29111e6 q^{32} +1.32205e7 q^{33} +369704. q^{34} +1.27720e6 q^{35} -9.68273e6 q^{36} +1.87416e6 q^{37} -1.14821e6 q^{38} -2.02125e7 q^{39} -1.13187e7 q^{40} -7.82814e6 q^{41} +436352. q^{42} +1.45520e6 q^{43} -3.28336e7 q^{44} +5.02728e7 q^{45} -936530. q^{46} -3.98083e7 q^{47} +4.61564e7 q^{48} -4.01042e7 q^{49} +2.02115e7 q^{50} +1.66450e7 q^{51} +5.01987e7 q^{52} -6.68199e7 q^{53} -22997.9 q^{54} +1.70472e8 q^{55} -2.21010e6 q^{56} -5.16954e7 q^{57} +2.18725e7 q^{58} -8.48603e7 q^{59} -2.49877e8 q^{60} -1.65067e8 q^{61} +2.56462e7 q^{62} +9.81627e6 q^{63} -1.04649e8 q^{64} -2.60632e8 q^{65} +5.82414e7 q^{66} +2.49940e8 q^{67} -4.13386e7 q^{68} -4.21650e7 q^{69} +5.62658e6 q^{70} -3.60899e8 q^{71} -8.69933e7 q^{72} +3.87465e8 q^{73} +8.25643e6 q^{74} +9.09974e8 q^{75} +1.28388e8 q^{76} +3.32864e7 q^{77} -8.90442e7 q^{78} -3.48676e8 q^{79} +5.95167e8 q^{80} -3.87938e8 q^{81} -3.44861e7 q^{82} -8.29492e7 q^{83} -4.87910e7 q^{84} +2.14630e8 q^{85} +6.41074e6 q^{86} +9.84757e8 q^{87} -2.94990e8 q^{88} +1.02047e8 q^{89} +2.21472e8 q^{90} -5.08910e7 q^{91} +1.04719e8 q^{92} +1.15466e9 q^{93} -1.75372e8 q^{94} -6.66591e8 q^{95} +6.52766e8 q^{96} -1.41077e9 q^{97} -1.76675e8 q^{98} +1.31021e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.40540	0.194693	0.0973466	−	0.995251i	$-0.468964\pi$
$2$	4.40540	0.194693	0.0973466	+	0.995251i	$0.468964\pi$
$3$	198.342	1.41374	0.706870	−	0.707343i	$-0.250106\pi$
$3$	198.342	1.41374	0.706870	+	0.707343i	$0.250106\pi$
$4$	−492.592	−0.962095
$5$	2557.54	1.83003	0.915014	−	0.403422i	$-0.132179\pi$
$5$	2557.54	1.83003	0.915014	+	0.403422i	$0.132179\pi$
$6$	873.778	0.275246
$7$	499.386	0.0786131	0.0393066	−	0.999227i	$-0.487485\pi$
$7$	499.386	0.0786131	0.0393066	+	0.999227i	$0.487485\pi$
$8$	−4425.63	−0.382006
$9$	19656.7	0.998663
$10$	11267.0	0.356294
$11$	66654.7	1.37266	0.686332	−	0.727289i	$-0.259220\pi$
$11$	66654.7	1.37266	0.686332	+	0.727289i	$0.259220\pi$
$12$	−97701.9	−1.36015
$13$	−101907.	−0.989600	−0.494800	−	0.869007i	$-0.664759\pi$
$13$	−101907.	−0.989600	−0.494800	+	0.869007i	$0.664759\pi$
$14$	2200.00	0.0153054
$15$	507269.	2.58719
$16$	232711.	0.887721
$17$	83920.5	0.243696	0.121848	−	0.992549i	$-0.461118\pi$
$17$	83920.5	0.243696	0.121848	+	0.992549i	$0.461118\pi$
$18$	86595.6	0.194433
$19$	−260637.	−0.458823	−0.229412	−	0.973330i	$-0.573680\pi$
$19$	−260637.	−0.458823	−0.229412	+	0.973330i	$0.573680\pi$
$20$	−1.25983e6	−1.76066
$21$	99049.4	0.111139
$22$	293641.	0.267248
$23$	−212587.	−0.158402	−0.0792011	−	0.996859i	$-0.525237\pi$
$23$	−212587.	−0.158402	−0.0792011	+	0.996859i	$0.525237\pi$
$24$	−877791.	−0.540058
$25$	4.58790e6	2.34900
$26$	−448942.	−0.192668
$27$	−5220.39	−0.00189045
$28$	−245994.	−0.0756333
$29$	4.96493e6	1.30353	0.651767	−	0.758419i	$-0.274028\pi$
$29$	4.96493e6	1.30353	0.651767	+	0.758419i	$0.274028\pi$
$30$	2.23472e6	0.503707
$31$	5.82154e6	1.13217	0.566083	−	0.824348i	$-0.308458\pi$
$31$	5.82154e6	1.13217	0.566083	+	0.824348i	$0.308458\pi$
$32$	3.29111e6	0.554839
$33$	1.32205e7	1.94059
$34$	369704.	0.0474459
$35$	1.27720e6	0.143864
$36$	−9.68273e6	−0.960808
$37$	1.87416e6	0.164399
$37$	1.87416e6	0.164399
$38$	−1.14821e6	−0.0893297
$39$	−2.02125e7	−1.39904
$40$	−1.13187e7	−0.699082
$41$	−7.82814e6	−0.432644	−0.216322	−	0.976322i	$-0.569406\pi$
$41$	−7.82814e6	−0.432644	−0.216322	+	0.976322i	$0.569406\pi$
$42$	436352.	0.0216379
$43$	1.45520e6	0.0649105	0.0324552	−	0.999473i	$-0.489667\pi$
$43$	1.45520e6	0.0649105	0.0324552	+	0.999473i	$0.489667\pi$
$44$	−3.28336e7	−1.32063
$45$	5.02728e7	1.82758
$46$	−936530.	−0.0308398
$47$	−3.98083e7	−1.18996	−0.594981	−	0.803739i	$-0.702841\pi$
$47$	−3.98083e7	−1.18996	−0.594981	+	0.803739i	$0.702841\pi$
$48$	4.61564e7	1.25501
$49$	−4.01042e7	−0.993820
$50$	2.02115e7	0.457335
$51$	1.66450e7	0.344523
$52$	5.01987e7	0.952088
$53$	−6.68199e7	−1.16323	−0.581613	−	0.813466i	$-0.697578\pi$
$53$	−6.68199e7	−1.16323	−0.581613	+	0.813466i	$0.697578\pi$
$54$	−22997.9	−0.000368058 0
$55$	1.70472e8	2.51201
$56$	−2.21010e6	−0.0300307
$57$	−5.16954e7	−0.648657
$58$	2.18725e7	0.253789
$59$	−8.48603e7	−0.911738	−0.455869	−	0.890047i	$-0.650672\pi$
$59$	−8.48603e7	−0.911738	−0.455869	+	0.890047i	$0.650672\pi$
$60$	−2.49877e8	−2.48912
$61$	−1.65067e8	−1.52643	−0.763216	−	0.646144i	$-0.776381\pi$
$61$	−1.65067e8	−1.52643	−0.763216	+	0.646144i	$0.776381\pi$
$62$	2.56462e7	0.220425
$63$	9.81627e6	0.0785080
$64$	−1.04649e8	−0.779697
$65$	−2.60632e8	−1.81100
$66$	5.82414e7	0.377819
$67$	2.49940e8	1.51530	0.757652	−	0.652659i	$-0.226347\pi$
$67$	2.49940e8	1.51530	0.757652	+	0.652659i	$0.226347\pi$
$68$	−4.13386e7	−0.234458
$69$	−4.21650e7	−0.223940
$70$	5.62658e6	0.0280094
$71$	−3.60899e8	−1.68548	−0.842739	−	0.538323i	$-0.819058\pi$
$71$	−3.60899e8	−1.68548	−0.842739	+	0.538323i	$0.819058\pi$
$72$	−8.69933e7	−0.381495
$73$	3.87465e8	1.59691	0.798454	−	0.602056i	$-0.205652\pi$
$73$	3.87465e8	1.59691	0.798454	+	0.602056i	$0.205652\pi$
$74$	8.25643e6	0.0320074
$75$	9.09974e8	3.32088
$76$	1.28388e8	0.441431
$77$	3.32864e7	0.107909
$78$	−8.90442e7	−0.272383
$79$	−3.48676e8	−1.00716	−0.503582	−	0.863947i	$-0.667985\pi$
$79$	−3.48676e8	−1.00716	−0.503582	+	0.863947i	$0.667985\pi$
$80$	5.95167e8	1.62455
$81$	−3.87938e8	−1.00134
$82$	−3.44861e7	−0.0842329
$83$	−8.29492e7	−0.191850	−0.0959248	−	0.995389i	$-0.530581\pi$
$83$	−8.29492e7	−0.191850	−0.0959248	+	0.995389i	$0.530581\pi$
$84$	−4.87910e7	−0.106926
$85$	2.14630e8	0.445970
$86$	6.41074e6	0.0126376
$87$	9.84757e8	1.84286
$88$	−2.94990e8	−0.524366
$89$	1.02047e8	0.172403	0.0862017	−	0.996278i	$-0.472527\pi$
$89$	1.02047e8	0.172403	0.0862017	+	0.996278i	$0.472527\pi$
$90$	2.21472e8	0.355817
$91$	−5.08910e7	−0.0777955
$92$	1.04719e8	0.152398
$93$	1.15466e9	1.60059
$94$	−1.75372e8	−0.231678
$95$	−6.66591e8	−0.839659
$96$	6.52766e8	0.784399
$97$	−1.41077e9	−1.61801	−0.809007	−	0.587799i	$-0.799995\pi$
$97$	−1.41077e9	−1.61801	−0.809007	+	0.587799i	$0.799995\pi$
$98$	−1.76675e8	−0.193490
$99$	1.31021e9	1.37083
$100$	−2.25996e9	−2.25996
$101$	1.37046e9	1.31045	0.655227	−	0.755432i	$-0.272573\pi$
$101$	1.37046e9	1.31045	0.655227	+	0.755432i	$0.272573\pi$
$102$	7.33279e7	0.0670762
$103$	−9.62916e8	−0.842987	−0.421494	−	0.906831i	$-0.638494\pi$
$103$	−9.62916e8	−0.842987	−0.421494	+	0.906831i	$0.638494\pi$
$104$	4.51004e8	0.378033
$105$	2.53323e8	0.203387
$106$	−2.94368e8	−0.226472
$107$	−1.15626e9	−0.852765	−0.426383	−	0.904543i	$-0.640212\pi$
$107$	−1.15626e9	−0.852765	−0.426383	+	0.904543i	$0.640212\pi$
$108$	2.57152e6	0.00181880
$109$	9.54304e8	0.647542	0.323771	−	0.946136i	$-0.395049\pi$
$109$	9.54304e8	0.647542	0.323771	+	0.946136i	$0.395049\pi$
$110$	7.50999e8	0.489072
$111$	3.71725e8	0.232418
$112$	1.16212e8	0.0697865
$113$	−6.47520e8	−0.373594	−0.186797	−	0.982399i	$-0.559811\pi$
$113$	−6.47520e8	−0.373594	−0.186797	+	0.982399i	$0.559811\pi$
$114$	−2.27739e8	−0.126289
$115$	−5.43700e8	−0.289880
$116$	−2.44569e9	−1.25412
$117$	−2.00316e9	−0.988276
$118$	−3.73844e8	−0.177509
$119$	4.19087e7	0.0191577
$120$	−2.24499e9	−0.988321
$121$	2.08491e9	0.884204
$122$	−7.27189e8	−0.297186
$123$	−1.55265e9	−0.611647
$124$	−2.86765e9	−1.08925
$125$	6.73855e9	2.46872
$126$	4.32446e7	0.0152850
$127$	4.72592e9	1.61202	0.806009	−	0.591903i	$-0.201623\pi$
$127$	4.72592e9	1.61202	0.806009	+	0.591903i	$0.201623\pi$
$128$	−2.14607e9	−0.706641
$129$	2.88628e8	0.0917665
$130$	−1.14819e9	−0.352588
$131$	6.55072e9	1.94343	0.971714	−	0.236160i	$-0.0758891\pi$
$131$	6.55072e9	1.94343	0.971714	+	0.236160i	$0.0758891\pi$
$132$	−6.51230e9	−1.86703
$133$	−1.30159e8	−0.0360695
$134$	1.10109e9	0.295019
$135$	−1.33514e7	−0.00345958
$136$	−3.71401e8	−0.0930933
$137$	−4.17583e8	−0.101274	−0.0506372	−	0.998717i	$-0.516125\pi$
$137$	−4.17583e8	−0.101274	−0.0506372	+	0.998717i	$0.516125\pi$
$138$	−1.85754e8	−0.0435995
$139$	−4.06730e9	−0.924143	−0.462072	−	0.886843i	$-0.652894\pi$
$139$	−4.06730e9	−0.924143	−0.462072	+	0.886843i	$0.652894\pi$
$140$	−6.29139e8	−0.138411
$141$	−7.89567e9	−1.68230
$142$	−1.58990e9	−0.328151
$143$	−6.79259e9	−1.35839
$144$	4.57432e9	0.886534
$145$	1.26980e10	2.38550
$146$	1.70694e9	0.310907
$147$	−7.95436e9	−1.40500
$148$	−9.23198e8	−0.158167
$149$	−6.86429e9	−1.14093	−0.570463	−	0.821323i	$-0.693236\pi$
$149$	−6.86429e9	−1.14093	−0.570463	+	0.821323i	$0.693236\pi$
$150$	4.00880e9	0.646553
$151$	2.64929e8	0.0414699	0.0207350	−	0.999785i	$-0.493399\pi$
$151$	2.64929e8	0.0414699	0.0207350	+	0.999785i	$0.493399\pi$
$152$	1.15349e9	0.175273
$153$	1.64960e9	0.243370
$154$	1.46640e8	0.0210092
$155$	1.48888e10	2.07190
$156$	9.95652e9	1.34601
$157$	−3.36015e9	−0.441378	−0.220689	−	0.975344i	$-0.570831\pi$
$157$	−3.36015e9	−0.441378	−0.220689	+	0.975344i	$0.570831\pi$
$158$	−1.53606e9	−0.196088
$159$	−1.32532e10	−1.64450
$160$	8.41715e9	1.01537
$161$	−1.06163e8	−0.0124525
$162$	−1.70902e9	−0.194953
$163$	1.14252e9	0.126771	0.0633854	−	0.997989i	$-0.479810\pi$
$163$	1.14252e9	0.126771	0.0633854	+	0.997989i	$0.479810\pi$
$164$	3.85608e9	0.416245
$165$	3.38119e10	3.55133
$166$	−3.65425e8	−0.0373518
$167$	8.02748e9	0.798648	0.399324	−	0.916810i	$-0.369245\pi$
$167$	8.02748e9	0.798648	0.399324	+	0.916810i	$0.369245\pi$
$168$	−4.38356e8	−0.0424556
$169$	−2.19435e8	−0.0206926
$170$	9.45533e8	0.0868273
$171$	−5.12326e9	−0.458210
$172$	−7.16820e8	−0.0624500
$173$	−1.16440e10	−0.988317	−0.494158	−	0.869372i	$-0.664524\pi$
$173$	−1.16440e10	−0.988317	−0.494158	+	0.869372i	$0.664524\pi$
$174$	4.33825e9	0.358792
$175$	2.29113e9	0.184663
$176$	1.55113e10	1.21854
$177$	−1.68314e10	−1.28896
$178$	4.49559e8	0.0335657
$179$	−8.22772e9	−0.599019	−0.299510	−	0.954093i	$-0.596823\pi$
$179$	−8.22772e9	−0.599019	−0.299510	+	0.954093i	$0.596823\pi$
$180$	−2.47640e10	−1.75831
$181$	2.20989e10	1.53044	0.765220	−	0.643769i	$-0.222630\pi$
$181$	2.20989e10	1.53044	0.765220	+	0.643769i	$0.222630\pi$
$182$	−2.24195e8	−0.0151463
$183$	−3.27399e10	−2.15798
$184$	9.40831e8	0.0605106
$185$	4.79325e9	0.300855
$186$	5.08673e9	0.311624
$187$	5.59370e9	0.334512
$188$	1.96093e10	1.14486
$189$	−2.60699e6	−0.000148614 0
$190$	−2.93660e9	−0.163476
$191$	−1.16533e10	−0.633577	−0.316788	−	0.948496i	$-0.602604\pi$
$191$	−1.16533e10	−0.633577	−0.316788	+	0.948496i	$0.602604\pi$
$192$	−2.07564e10	−1.10229
$193$	−5.79075e9	−0.300419	−0.150209	−	0.988654i	$-0.547995\pi$
$193$	−5.79075e9	−0.300419	−0.150209	+	0.988654i	$0.547995\pi$
$194$	−6.21499e9	−0.315016
$195$	−5.16943e10	−2.56028
$196$	1.97550e10	0.956149
$197$	4.00616e10	1.89509	0.947546	−	0.319620i	$-0.103555\pi$
$197$	4.00616e10	1.89509	0.947546	+	0.319620i	$0.103555\pi$
$198$	5.77201e9	0.266891
$199$	−2.59069e10	−1.17105	−0.585526	−	0.810654i	$-0.699112\pi$
$199$	−2.59069e10	−1.17105	−0.585526	+	0.810654i	$0.699112\pi$
$200$	−2.03044e10	−0.897334
$201$	4.95737e10	2.14225
$202$	6.03745e9	0.255136
$203$	2.47942e9	0.102475
$204$	−8.19920e9	−0.331463
$205$	−2.00208e10	−0.791751
$206$	−4.24203e9	−0.164124
$207$	−4.17875e9	−0.158190
$208$	−2.37149e10	−0.878488
$209$	−1.73727e10	−0.629810
$210$	1.11599e9	0.0395980
$211$	1.89498e10	0.658165	0.329082	−	0.944301i	$-0.393261\pi$
$211$	1.89498e10	0.658165	0.329082	+	0.944301i	$0.393261\pi$
$212$	3.29150e10	1.11913
$213$	−7.15815e10	−2.38283
$214$	−5.09380e9	−0.166027
$215$	3.72174e9	0.118788
$216$	2.31035e7	0.000722165 0
$217$	2.90720e9	0.0890032
$218$	4.20410e9	0.126072
$219$	7.68508e10	2.25761
$220$	−8.39734e10	−2.41679
$221$	−8.55210e9	−0.241161
$222$	1.63760e9	0.0452501
$223$	8.08003e9	0.218797	0.109398	−	0.993998i	$-0.465108\pi$
$223$	8.08003e9	0.218797	0.109398	+	0.993998i	$0.465108\pi$
$224$	1.64353e9	0.0436177
$225$	9.01829e10	2.34586
$226$	−2.85259e9	−0.0727362
$227$	2.57349e9	0.0643288	0.0321644	−	0.999483i	$-0.489760\pi$
$227$	2.57349e9	0.0643288	0.0321644	+	0.999483i	$0.489760\pi$
$228$	2.54648e10	0.624069
$229$	−7.03039e10	−1.68935	−0.844675	−	0.535279i	$-0.820206\pi$
$229$	−7.03039e10	−1.68935	−0.844675	+	0.535279i	$0.820206\pi$
$230$	−2.39522e9	−0.0564377
$231$	6.60211e9	0.152556
$232$	−2.19730e10	−0.497958
$233$	6.52553e10	1.45049	0.725244	−	0.688491i	$-0.241727\pi$
$233$	6.52553e10	1.45049	0.725244	+	0.688491i	$0.241727\pi$
$234$	−8.82471e9	−0.192411
$235$	−1.01811e11	−2.17767
$236$	4.18015e10	0.877179
$237$	−6.91573e10	−1.42387
$238$	1.84625e8	0.00372987
$239$	9.32645e10	1.84895	0.924477	−	0.381238i	$-0.124502\pi$
$239$	9.32645e10	1.84895	0.924477	+	0.381238i	$0.124502\pi$
$240$	1.18047e11	2.29670
$241$	−1.76488e9	−0.0337006	−0.0168503	−	0.999858i	$-0.505364\pi$
$241$	−1.76488e9	−0.0337006	−0.0168503	+	0.999858i	$0.505364\pi$
$242$	9.18486e9	0.172149
$243$	−7.68417e10	−1.41374
$244$	8.13110e10	1.46857
$245$	−1.02568e11	−1.81872
$246$	−6.84005e9	−0.119083
$247$	2.65608e10	0.454051
$248$	−2.57640e10	−0.432495
$249$	−1.64523e10	−0.271226
$250$	2.96860e10	0.480642
$251$	−2.62757e10	−0.417852	−0.208926	−	0.977931i	$-0.566997\pi$
$251$	−2.62757e10	−0.417852	−0.208926	+	0.977931i	$0.566997\pi$
$252$	−4.83542e9	−0.0755321
$253$	−1.41699e10	−0.217433
$254$	2.08196e10	0.313849
$255$	4.25703e10	0.630486
$256$	4.41261e10	0.642119
$257$	2.74299e10	0.392216	0.196108	−	0.980582i	$-0.437170\pi$
$257$	2.74299e10	0.392216	0.196108	+	0.980582i	$0.437170\pi$
$258$	1.27152e9	0.0178663
$259$	9.35930e8	0.0129239
$260$	1.28385e11	1.74235
$261$	9.75941e10	1.30179
$262$	2.88586e10	0.378372
$263$	−1.07202e11	−1.38166	−0.690832	−	0.723015i	$-0.742756\pi$
$263$	−1.07202e11	−1.38166	−0.690832	+	0.723015i	$0.742756\pi$
$264$	−5.85089e10	−0.741318
$265$	−1.70895e11	−2.12874
$266$	−5.73401e8	−0.00702249
$267$	2.02403e10	0.243734
$268$	−1.23119e11	−1.45786
$269$	2.73350e10	0.318298	0.159149	−	0.987255i	$-0.449125\pi$
$269$	2.73350e10	0.318298	0.159149	+	0.987255i	$0.449125\pi$
$270$	−5.88182e7	−0.000673557 0
$271$	1.55233e11	1.74832	0.874160	−	0.485638i	$-0.161413\pi$
$271$	1.55233e11	1.74832	0.874160	+	0.485638i	$0.161413\pi$
$272$	1.95292e10	0.216334
$273$	−1.00938e10	−0.109983
$274$	−1.83962e9	−0.0197174
$275$	3.05805e11	3.22439
$276$	2.07701e10	0.215451
$277$	5.49776e10	0.561083	0.280541	−	0.959842i	$-0.409486\pi$
$277$	5.49776e10	0.561083	0.280541	+	0.959842i	$0.409486\pi$
$278$	−1.79181e10	−0.179924
$279$	1.14432e11	1.13065
$280$	−5.65242e9	−0.0549571
$281$	−6.92975e10	−0.663039	−0.331519	−	0.943448i	$-0.607561\pi$
$281$	−6.92975e10	−0.663039	−0.331519	+	0.943448i	$0.607561\pi$
$282$	−3.47836e10	−0.327532
$283$	9.97985e10	0.924879	0.462440	−	0.886651i	$-0.346974\pi$
$283$	9.97985e10	0.924879	0.462440	+	0.886651i	$0.346974\pi$
$284$	1.77776e11	1.62159
$285$	−1.32213e11	−1.18706
$286$	−2.99241e10	−0.264469
$287$	−3.90926e9	−0.0340115
$288$	6.46923e10	0.554097
$289$	−1.11545e11	−0.940612
$290$	5.59399e10	0.464441
$291$	−2.79815e11	−2.28745
$292$	−1.90862e11	−1.53638
$293$	−1.35171e11	−1.07147	−0.535733	−	0.844387i	$-0.679965\pi$
$293$	−1.35171e11	−1.07147	−0.535733	+	0.844387i	$0.679965\pi$
$294$	−3.50422e10	−0.273545
$295$	−2.17034e11	−1.66851
$296$	−8.29435e9	−0.0628014
$297$	−3.47964e8	−0.00259496
$298$	−3.02400e10	−0.222130
$299$	2.16641e10	0.156755
$300$	−4.48247e11	−3.19500
$301$	7.26706e8	0.00510281
$302$	1.16712e9	0.00807391
$303$	2.71821e11	1.85264
$304$	−6.06531e10	−0.407307
$305$	−4.22167e11	−2.79341
$306$	7.26715e9	0.0473824
$307$	8.47271e10	0.544377	0.272188	−	0.962244i	$-0.412253\pi$
$307$	8.47271e10	0.544377	0.272188	+	0.962244i	$0.412253\pi$
$308$	−1.63966e10	−0.103819
$309$	−1.90987e11	−1.19177
$310$	6.55913e10	0.403384
$311$	2.03917e11	1.23604	0.618019	−	0.786163i	$-0.287935\pi$
$311$	2.03917e11	1.23604	0.618019	+	0.786163i	$0.287935\pi$
$312$	8.94531e10	0.534441
$313$	1.75892e11	1.03585	0.517923	−	0.855427i	$-0.326705\pi$
$313$	1.75892e11	1.03585	0.517923	+	0.855427i	$0.326705\pi$
$314$	−1.48028e10	−0.0859332
$315$	2.51055e10	0.143672
$316$	1.71755e11	0.968988
$317$	1.26532e11	0.703773	0.351887	−	0.936043i	$-0.385540\pi$
$317$	1.26532e11	0.703773	0.351887	+	0.936043i	$0.385540\pi$
$318$	−5.83857e10	−0.320173
$319$	3.30936e11	1.78931
$320$	−2.67645e11	−1.42687
$321$	−2.29336e11	−1.20559
$322$	−4.67690e8	−0.00242441
$323$	−2.18728e10	−0.111813
$324$	1.91095e11	0.963379
$325$	−4.67540e11	−2.32457
$326$	5.03325e9	0.0246814
$327$	1.89279e11	0.915456
$328$	3.46445e10	0.165273
$329$	−1.98797e10	−0.0935467
$330$	1.48955e11	0.691420
$331$	1.24844e11	0.571667	0.285833	−	0.958279i	$-0.407730\pi$
$331$	1.24844e11	0.571667	0.285833	+	0.958279i	$0.407730\pi$
$332$	4.08602e10	0.184577
$333$	3.68398e10	0.164179
$334$	3.53643e10	0.155491
$335$	6.39233e11	2.77305
$336$	2.30498e10	0.0986600
$337$	2.33786e11	0.987377	0.493689	−	0.869639i	$-0.335648\pi$
$337$	2.33786e11	0.987377	0.493689	+	0.869639i	$0.335648\pi$
$338$	−9.66699e8	−0.00402871
$339$	−1.28431e11	−0.528165
$340$	−1.05725e11	−0.429065
$341$	3.88033e11	1.55408
$342$	−2.25700e10	−0.0892103
$343$	−4.01795e10	−0.156740
$344$	−6.44018e9	−0.0247962
$345$	−1.07839e11	−0.409816
$346$	−5.12967e10	−0.192418
$347$	−5.95058e10	−0.220332	−0.110166	−	0.993913i	$-0.535138\pi$
$347$	−5.95058e10	−0.220332	−0.110166	+	0.993913i	$0.535138\pi$
$348$	−4.85084e11	−1.77301
$349$	6.64621e10	0.239806	0.119903	−	0.992786i	$-0.461742\pi$
$349$	6.64621e10	0.239806	0.119903	+	0.992786i	$0.461742\pi$
$350$	1.00934e10	0.0359525
$351$	5.31995e8	0.00187079
$352$	2.19368e11	0.761608
$353$	1.32534e11	0.454298	0.227149	−	0.973860i	$-0.427060\pi$
$353$	1.32534e11	0.454298	0.227149	+	0.973860i	$0.427060\pi$
$354$	−7.41490e10	−0.250952
$355$	−9.23014e11	−3.08447
$356$	−5.02676e10	−0.165868
$357$	8.31227e9	0.0270840
$358$	−3.62464e10	−0.116625
$359$	−5.99056e11	−1.90345	−0.951726	−	0.306948i	$-0.900692\pi$
$359$	−5.99056e11	−1.90345	−0.951726	+	0.306948i	$0.900692\pi$
$360$	−2.22489e11	−0.698148
$361$	−2.54756e11	−0.789481
$362$	9.73543e10	0.297966
$363$	4.13525e11	1.25004
$364$	2.50685e10	0.0748466
$365$	9.90959e11	2.92239
$366$	−1.44232e11	−0.420143
$367$	3.52657e11	1.01474	0.507370	−	0.861728i	$-0.330618\pi$
$367$	3.52657e11	1.01474	0.507370	+	0.861728i	$0.330618\pi$
$368$	−4.94712e10	−0.140617
$369$	−1.53875e11	−0.432066
$370$	2.11162e10	0.0585744
$371$	−3.33689e10	−0.0914449
$372$	−5.68776e11	−1.53992
$373$	−4.28575e10	−0.114640	−0.0573201	−	0.998356i	$-0.518256\pi$
$373$	−4.28575e10	−0.114640	−0.0573201	+	0.998356i	$0.518256\pi$
$374$	2.46425e10	0.0651272
$375$	1.33654e12	3.49012
$376$	1.76177e11	0.454573
$377$	−5.05962e11	−1.28998
$378$	−1.14848e7	−2.89342e−5 0
$379$	−1.08446e11	−0.269984	−0.134992	−	0.990847i	$-0.543101\pi$
$379$	−1.08446e11	−0.269984	−0.134992	+	0.990847i	$0.543101\pi$
$380$	3.28358e11	0.807832
$381$	9.37350e11	2.27898
$382$	−5.13375e10	−0.123353
$383$	−9.25653e10	−0.219813	−0.109907	−	0.993942i	$-0.535055\pi$
$383$	−9.25653e10	−0.219813	−0.109907	+	0.993942i	$0.535055\pi$
$384$	−4.25656e11	−0.999007
$385$	8.51315e10	0.197477
$386$	−2.55106e10	−0.0584894
$387$	2.86044e10	0.0648237
$388$	6.94933e11	1.55668
$389$	3.61923e11	0.801388	0.400694	−	0.916212i	$-0.368769\pi$
$389$	3.61923e11	0.801388	0.400694	+	0.916212i	$0.368769\pi$
$390$	−2.27734e11	−0.498468
$391$	−1.78404e10	−0.0386019
$392$	1.77487e11	0.379645
$393$	1.29929e12	2.74750
$394$	1.76487e11	0.368961
$395$	−8.91755e11	−1.84314
$396$	−6.45400e11	−1.31887
$397$	−4.67683e11	−0.944919	−0.472459	−	0.881352i	$-0.656634\pi$
$397$	−4.67683e11	−0.944919	−0.472459	+	0.881352i	$0.656634\pi$
$398$	−1.14130e11	−0.227996
$399$	−2.58160e10	−0.0509930
$400$	1.06765e12	2.08526
$401$	6.23544e10	0.120425	0.0602126	−	0.998186i	$-0.480822\pi$
$401$	6.23544e10	0.120425	0.0602126	+	0.998186i	$0.480822\pi$
$402$	2.18392e11	0.417080
$403$	−5.93257e11	−1.12039
$404$	−6.75081e11	−1.26078
$405$	−9.92168e11	−1.83247
$406$	1.09228e10	0.0199512
$407$	1.24922e11	0.225664
$408$	−7.36646e10	−0.131610
$409$	−7.12180e10	−0.125845	−0.0629224	−	0.998018i	$-0.520042\pi$
$409$	−7.12180e10	−0.125845	−0.0629224	+	0.998018i	$0.520042\pi$
$410$	−8.81996e10	−0.154149
$411$	−8.28243e10	−0.143176
$412$	4.74325e11	0.811034
$413$	−4.23780e10	−0.0716746
$414$	−1.84091e10	−0.0307986
$415$	−2.12146e11	−0.351090
$416$	−3.35387e11	−0.549069
$417$	−8.06717e11	−1.30650
$418$	−7.65338e10	−0.122620
$419$	1.25210e11	0.198461	0.0992303	−	0.995064i	$-0.468362\pi$
$419$	1.25210e11	0.198461	0.0992303	+	0.995064i	$0.468362\pi$
$420$	−1.24785e11	−0.195677
$421$	−1.09381e12	−1.69696	−0.848482	−	0.529224i	$-0.822483\pi$
$421$	−1.09381e12	−1.69696	−0.848482	+	0.529224i	$0.822483\pi$
$422$	8.34817e10	0.128140
$423$	−7.82499e11	−1.18837
$424$	2.95720e11	0.444360
$425$	3.85019e11	0.572442
$426$	−3.15345e11	−0.463920
$427$	−8.24324e10	−0.119998
$428$	5.69566e11	0.820441
$429$	−1.34726e12	−1.92041
$430$	1.63957e10	0.0231272
$431$	−5.59711e11	−0.781297	−0.390648	−	0.920540i	$-0.627749\pi$
$431$	−5.59711e11	−0.781297	−0.390648	+	0.920540i	$0.627749\pi$
$432$	−1.21484e9	−0.00167819
$433$	6.05301e11	0.827514	0.413757	−	0.910387i	$-0.364216\pi$
$433$	6.05301e11	0.827514	0.413757	+	0.910387i	$0.364216\pi$
$434$	1.28074e10	0.0173283
$435$	2.51856e12	3.37249
$436$	−4.70083e11	−0.622996
$437$	5.54080e10	0.0726786
$438$	3.38558e11	0.439542
$439$	1.05287e12	1.35295	0.676477	−	0.736464i	$-0.263506\pi$
$439$	1.05287e12	1.35295	0.676477	+	0.736464i	$0.263506\pi$
$440$	−7.54448e11	−0.959605
$441$	−7.88316e11	−0.992491
$442$	−3.76754e10	−0.0469524
$443$	−4.34039e11	−0.535441	−0.267720	−	0.963497i	$-0.586270\pi$
$443$	−4.34039e11	−0.535441	−0.267720	+	0.963497i	$0.586270\pi$
$444$	−1.83109e11	−0.223608
$445$	2.60990e11	0.315503
$446$	3.55958e10	0.0425982
$447$	−1.36148e12	−1.61297
$448$	−5.22603e10	−0.0612944
$449$	−5.67782e11	−0.659285	−0.329642	−	0.944106i	$-0.606928\pi$
$449$	−5.67782e11	−0.659285	−0.329642	+	0.944106i	$0.606928\pi$
$450$	3.97292e11	0.456723
$451$	−5.21782e11	−0.593875
$452$	3.18963e11	0.359433
$453$	5.25466e10	0.0586277
$454$	1.13372e10	0.0125244
$455$	−1.30156e11	−0.142368
$456$	2.28785e11	0.247791
$457$	−7.14742e11	−0.766525	−0.383262	−	0.923639i	$-0.625200\pi$
$457$	−7.14742e11	−0.766525	−0.383262	+	0.923639i	$0.625200\pi$
$458$	−3.09717e11	−0.328905
$459$	−4.38098e8	−0.000460696 0
$460$	2.67822e11	0.278892
$461$	−1.20830e12	−1.24600	−0.623002	−	0.782220i	$-0.714087\pi$
$461$	−1.20830e12	−1.24600	−0.623002	+	0.782220i	$0.714087\pi$
$462$	2.90850e10	0.0297016
$463$	1.45853e12	1.47503	0.737516	−	0.675329i	$-0.235999\pi$
$463$	1.45853e12	1.47503	0.737516	+	0.675329i	$0.235999\pi$
$464$	1.15539e12	1.15717
$465$	2.95309e12	2.92913
$466$	2.87476e11	0.282400
$467$	6.00408e10	0.0584145	0.0292072	−	0.999573i	$-0.490702\pi$
$467$	6.00408e10	0.0584145	0.0292072	+	0.999573i	$0.490702\pi$
$468$	9.86739e11	0.950815
$469$	1.24817e11	0.119123
$470$	−4.48520e11	−0.423977
$471$	−6.66460e11	−0.623994
$472$	3.75560e11	0.348290
$473$	9.69960e10	0.0891002
$474$	−3.04666e11	−0.277218
$475$	−1.19578e12	−1.07778
$476$	−2.06439e10	−0.0184315
$477$	−1.31346e12	−1.16167
$478$	4.10868e11	0.359979
$479$	1.41389e12	1.22718	0.613588	−	0.789627i	$-0.289726\pi$
$479$	1.41389e12	1.22718	0.613588	+	0.789627i	$0.289726\pi$
$480$	1.66948e12	1.43547
$481$	−1.90990e11	−0.162689
$482$	−7.77499e9	−0.00656127
$483$	−2.10566e10	−0.0176046
$484$	−1.02701e12	−0.850688
$485$	−3.60810e12	−2.96101
$486$	−3.38519e11	−0.275245
$487$	6.88922e11	0.554996	0.277498	−	0.960726i	$-0.410495\pi$
$487$	6.88922e11	0.554996	0.277498	+	0.960726i	$0.410495\pi$
$488$	7.30528e11	0.583106
$489$	2.26610e11	0.179221
$490$	−4.51854e11	−0.354092
$491$	1.41867e12	1.10158	0.550788	−	0.834645i	$-0.314327\pi$
$491$	1.41867e12	1.10158	0.550788	+	0.834645i	$0.314327\pi$
$492$	7.64824e11	0.588462
$493$	4.16660e11	0.317666
$494$	1.17011e11	0.0884006
$495$	3.35092e12	2.50865
$496$	1.35473e12	1.00505
$497$	−1.80228e11	−0.132501
$498$	−7.24792e10	−0.0528057
$499$	8.11800e11	0.586134	0.293067	−	0.956092i	$-0.405324\pi$
$499$	8.11800e11	0.586134	0.293067	+	0.956092i	$0.405324\pi$
$500$	−3.31936e12	−2.37514
$501$	1.59219e12	1.12908
$502$	−1.15755e11	−0.0813529
$503$	1.41752e12	0.987355	0.493677	−	0.869645i	$-0.335652\pi$
$503$	1.41752e12	0.987355	0.493677	+	0.869645i	$0.335652\pi$
$504$	−4.34432e10	−0.0299906
$505$	3.50502e12	2.39817
$506$	−6.24242e10	−0.0423327
$507$	−4.35232e10	−0.0292540
$508$	−2.32795e12	−1.55091
$509$	−6.65269e11	−0.439306	−0.219653	−	0.975578i	$-0.570493\pi$
$509$	−6.65269e11	−0.439306	−0.219653	+	0.975578i	$0.570493\pi$
$510$	1.87539e11	0.122751
$511$	1.93495e11	0.125538
$512$	1.29318e12	0.831657
$513$	1.36063e9	0.000867384 0
$514$	1.20840e11	0.0763618
$515$	−2.46270e12	−1.54269
$516$	−1.42176e11	−0.0882881
$517$	−2.65341e12	−1.63342
$518$	4.12315e9	0.00251620
$519$	−2.30951e12	−1.39722
$520$	1.15346e12	0.691812
$521$	2.12682e12	1.26462	0.632310	−	0.774715i	$-0.282107\pi$
$521$	2.12682e12	1.26462	0.632310	+	0.774715i	$0.282107\pi$
$522$	4.29941e11	0.253450
$523$	1.01067e12	0.590680	0.295340	−	0.955392i	$-0.404567\pi$
$523$	1.01067e12	0.590680	0.295340	+	0.955392i	$0.404567\pi$
$524$	−3.22684e12	−1.86976
$525$	4.54428e11	0.261065
$526$	−4.72268e11	−0.269000
$527$	4.88547e11	0.275904
$528$	3.07654e12	1.72270
$529$	−1.75596e12	−0.974909
$530$	−7.52860e11	−0.414450
$531$	−1.66807e12	−0.910519
$532$	6.41151e10	0.0347023
$533$	7.97743e11	0.428145
$534$	8.91665e10	0.0474533
$535$	−2.95719e12	−1.56058
$536$	−1.10614e12	−0.578855
$537$	−1.63190e12	−0.846858
$538$	1.20422e11	0.0619704
$539$	−2.67314e12	−1.36418
$540$	6.57678e9	0.00332845
$541$	−7.20703e11	−0.361717	−0.180858	−	0.983509i	$-0.557888\pi$
$541$	−7.20703e11	−0.361717	−0.180858	+	0.983509i	$0.557888\pi$
$542$	6.83862e11	0.340386
$543$	4.38314e12	2.16364
$544$	2.76191e11	0.135212
$545$	2.44067e12	1.18502
$546$	−4.44674e10	−0.0214129
$547$	−1.14887e11	−0.0548689	−0.0274345	−	0.999624i	$-0.508734\pi$
$547$	−1.14887e11	−0.0548689	−0.0274345	+	0.999624i	$0.508734\pi$
$548$	2.05698e11	0.0974356
$549$	−3.24468e12	−1.52439
$550$	1.34720e12	0.627767
$551$	−1.29405e12	−0.598092
$552$	1.86607e11	0.0855463
$553$	−1.74124e11	−0.0791764
$554$	2.42198e11	0.109239
$555$	9.50704e11	0.425331
$556$	2.00352e12	0.889113
$557$	−4.19852e12	−1.84820	−0.924098	−	0.382155i	$-0.875182\pi$
$557$	−4.19852e12	−1.84820	−0.924098	+	0.382155i	$0.875182\pi$
$558$	5.04120e11	0.220130
$559$	−1.48295e11	−0.0642354
$560$	2.97218e11	0.127711
$561$	1.10947e12	0.472914
$562$	−3.05283e11	−0.129089
$563$	1.94743e12	0.816911	0.408455	−	0.912778i	$-0.366068\pi$
$563$	1.94743e12	0.816911	0.408455	+	0.912778i	$0.366068\pi$
$564$	3.88935e12	1.61853
$565$	−1.65606e12	−0.683688
$566$	4.39652e11	0.180068
$567$	−1.93731e11	−0.0787181
$568$	1.59721e12	0.643863
$569$	−1.69043e12	−0.676071	−0.338035	−	0.941133i	$-0.609762\pi$
$569$	−1.69043e12	−0.676071	−0.338035	+	0.941133i	$0.609762\pi$
$570$	−5.82452e11	−0.231113
$571$	5.99518e11	0.236015	0.118008	−	0.993013i	$-0.462349\pi$
$571$	5.99518e11	0.236015	0.118008	+	0.993013i	$0.462349\pi$
$572$	3.34598e12	1.30690
$573$	−2.31135e12	−0.895713
$574$	−1.72219e10	−0.00662181
$575$	−9.75327e11	−0.372087
$576$	−2.05706e12	−0.778655
$577$	4.28030e12	1.60762	0.803810	−	0.594886i	$-0.202803\pi$
$577$	4.28030e12	1.60762	0.803810	+	0.594886i	$0.202803\pi$
$578$	−4.91402e11	−0.183131
$579$	−1.14855e12	−0.424714
$580$	−6.25495e12	−2.29508
$581$	−4.14237e10	−0.0150819
$582$	−1.23270e12	−0.445351
$583$	−4.45386e12	−1.59672
$584$	−1.71478e12	−0.610029
$585$	−5.12316e12	−1.80857
$586$	−5.95481e11	−0.208607
$587$	−1.30746e12	−0.454523	−0.227262	−	0.973834i	$-0.572977\pi$
$587$	−1.30746e12	−0.454523	−0.227262	+	0.973834i	$0.572977\pi$
$588$	3.91826e12	1.35175
$589$	−1.51731e12	−0.519464
$590$	−9.56121e11	−0.324847
$591$	7.94591e12	2.67917
$592$	4.36137e11	0.145940
$593$	−3.68528e12	−1.22384	−0.611919	−	0.790920i	$-0.709602\pi$
$593$	−3.68528e12	−1.22384	−0.611919	+	0.790920i	$0.709602\pi$
$594$	−1.53292e9	−0.000505220 0
$595$	1.07183e11	0.0350591
$596$	3.38130e12	1.09768
$597$	−5.13843e12	−1.65556
$598$	9.54391e10	0.0305191
$599$	−3.00946e12	−0.955143	−0.477572	−	0.878593i	$-0.658483\pi$
$599$	−3.00946e12	−0.955143	−0.477572	+	0.878593i	$0.658483\pi$
$600$	−4.02721e12	−1.26860
$601$	3.43141e11	0.107285	0.0536424	−	0.998560i	$-0.482917\pi$
$601$	3.43141e11	0.107285	0.0536424	+	0.998560i	$0.482917\pi$
$602$	3.20143e9	0.000993483 0
$603$	4.91299e12	1.51328
$604$	−1.30502e11	−0.0398980
$605$	5.33224e12	1.61812
$606$	1.19748e12	0.360697
$607$	4.80372e12	1.43625	0.718123	−	0.695917i	$-0.245002\pi$
$607$	4.80372e12	1.43625	0.718123	+	0.695917i	$0.245002\pi$
$608$	−8.57786e11	−0.254573
$609$	4.91773e11	0.144873
$610$	−1.85982e12	−0.543858
$611$	4.05675e12	1.17759
$612$	−8.12580e11	−0.234145
$613$	1.07655e12	0.307939	0.153969	−	0.988076i	$-0.450794\pi$
$613$	1.07655e12	0.307939	0.153969	+	0.988076i	$0.450794\pi$
$614$	3.73257e11	0.105986
$615$	−3.97097e12	−1.11933
$616$	−1.47314e11	−0.0412221
$617$	−1.69084e12	−0.469700	−0.234850	−	0.972032i	$-0.575460\pi$
$617$	−1.69084e12	−0.469700	−0.234850	+	0.972032i	$0.575460\pi$
$618$	−8.41375e11	−0.232029
$619$	4.16958e12	1.14152	0.570761	−	0.821116i	$-0.306648\pi$
$619$	4.16958e12	1.14152	0.570761	+	0.821116i	$0.306648\pi$
$620$	−7.33413e12	−1.99336
$621$	1.10979e9	0.000299452 0
$622$	8.98337e11	0.240648
$623$	5.09609e10	0.0135532
$624$	−4.70366e12	−1.24195
$625$	8.27338e12	2.16882
$626$	7.74873e11	0.201672
$627$	−3.44574e12	−0.890388
$628$	1.65519e12	0.424647
$629$	1.57281e11	0.0400633
$630$	1.10600e11	0.0279719
$631$	3.40860e12	0.855940	0.427970	−	0.903793i	$-0.359229\pi$
$631$	3.40860e12	0.855940	0.427970	+	0.903793i	$0.359229\pi$
$632$	1.54311e12	0.384743
$633$	3.75856e12	0.930474
$634$	5.57423e11	0.137020
$635$	1.20867e13	2.95004
$636$	6.52843e12	1.58216
$637$	4.08691e12	0.983484
$638$	1.45791e12	0.348367
$639$	−7.09407e12	−1.68322
$640$	−5.48866e12	−1.29317
$641$	6.08634e12	1.42395	0.711976	−	0.702204i	$-0.247801\pi$
$641$	6.08634e12	1.42395	0.711976	+	0.702204i	$0.247801\pi$
$642$	−1.01032e12	−0.234720
$643$	2.50278e12	0.577396	0.288698	−	0.957420i	$-0.406778\pi$
$643$	2.50278e12	0.577396	0.288698	+	0.957420i	$0.406778\pi$
$644$	5.22950e10	0.0119805
$645$	7.38178e11	0.167935
$646$	−9.63585e10	−0.0217693
$647$	1.01313e12	0.227298	0.113649	−	0.993521i	$-0.463746\pi$
$647$	1.01313e12	0.227298	0.113649	+	0.993521i	$0.463746\pi$
$648$	1.71687e12	0.382516
$649$	−5.65634e12	−1.25151
$650$	−2.05970e12	−0.452578
$651$	5.76620e11	0.125827
$652$	−5.62796e11	−0.121965
$653$	−7.52694e12	−1.61998	−0.809989	−	0.586445i	$-0.800527\pi$
$653$	−7.52694e12	−1.61998	−0.809989	+	0.586445i	$0.800527\pi$
$654$	8.33850e11	0.178233
$655$	1.67538e13	3.55653
$656$	−1.82169e12	−0.384067
$657$	7.61628e12	1.59477
$658$	−8.75781e10	−0.0182129
$659$	3.78116e12	0.780982	0.390491	−	0.920607i	$-0.372305\pi$
$659$	3.78116e12	0.780982	0.390491	+	0.920607i	$0.372305\pi$
$660$	−1.66555e13	−3.41672
$661$	−4.63730e12	−0.944841	−0.472421	−	0.881373i	$-0.656620\pi$
$661$	−4.63730e12	−0.944841	−0.472421	+	0.881373i	$0.656620\pi$
$662$	5.49990e11	0.111300
$663$	−1.69624e12	−0.340939
$664$	3.67103e11	0.0732878
$665$	−3.32886e11	−0.0660083
$666$	1.62294e11	0.0319646
$667$	−1.05548e12	−0.206483
$668$	−3.95428e12	−0.768375
$669$	1.60261e12	0.309322
$670$	2.81608e12	0.539893
$671$	−1.10025e13	−2.09528
$672$	3.25982e11	0.0616641
$673$	−2.13350e12	−0.400889	−0.200445	−	0.979705i	$-0.564239\pi$
$673$	−2.13350e12	−0.400889	−0.200445	+	0.979705i	$0.564239\pi$
$674$	1.02992e12	0.192236
$675$	−2.39506e10	−0.00444068
$676$	1.08092e11	0.0199083
$677$	−1.38993e12	−0.254298	−0.127149	−	0.991884i	$-0.540583\pi$
$677$	−1.38993e12	−0.254298	−0.127149	+	0.991884i	$0.540583\pi$
$678$	−5.65789e11	−0.102830
$679$	−7.04517e11	−0.127197
$680$	−9.49875e11	−0.170363
$681$	5.10431e11	0.0909442
$682$	1.70944e12	0.302569
$683$	1.06036e13	1.86449	0.932244	−	0.361831i	$-0.117848\pi$
$683$	1.06036e13	1.86449	0.932244	+	0.361831i	$0.117848\pi$
$684$	2.52368e12	0.440841
$685$	−1.06799e12	−0.185335
$686$	−1.77007e11	−0.0305163
$687$	−1.39442e13	−2.38830
$688$	3.38640e11	0.0576223
$689$	6.80942e12	1.15113
$690$	−4.75073e11	−0.0797883
$691$	−1.00909e12	−0.168375	−0.0841877	−	0.996450i	$-0.526830\pi$
$691$	−1.00909e12	−0.168375	−0.0841877	+	0.996450i	$0.526830\pi$
$692$	5.73576e12	0.950854
$693$	6.54301e11	0.107765
$694$	−2.62147e11	−0.0428970
$695$	−1.04023e13	−1.69121
$696$	−4.35817e12	−0.703984
$697$	−6.56941e11	−0.105434
$698$	2.92792e11	0.0466885
$699$	1.29429e13	2.05062
$700$	−1.12859e12	−0.177663
$701$	4.71197e12	0.737007	0.368504	−	0.929626i	$-0.379870\pi$
$701$	4.71197e12	0.737007	0.368504	+	0.929626i	$0.379870\pi$
$702$	2.34365e9	0.000364230 0
$703$	−4.88476e11	−0.0754301
$704$	−6.97537e12	−1.07026
$705$	−2.01935e13	−3.07865
$706$	5.83865e11	0.0884487
$707$	6.84391e11	0.103019
$708$	8.29101e12	1.24010
$709$	−5.65043e12	−0.839796	−0.419898	−	0.907571i	$-0.637934\pi$
$709$	−5.65043e12	−0.839796	−0.419898	+	0.907571i	$0.637934\pi$
$710$	−4.06625e12	−0.600525
$711$	−6.85382e12	−1.00582
$712$	−4.51623e11	−0.0658592
$713$	−1.23758e12	−0.179338
$714$	3.66189e10	0.00527307
$715$	−1.73723e13	−2.48589
$716$	4.05291e12	0.576313
$717$	1.84983e13	2.61394
$718$	−2.63908e12	−0.370589
$719$	−5.36008e12	−0.747982	−0.373991	−	0.927432i	$-0.622011\pi$
$719$	−5.36008e12	−0.747982	−0.373991	+	0.927432i	$0.622011\pi$
$720$	1.16990e13	1.62238
$721$	−4.80867e11	−0.0662699
$722$	−1.12230e12	−0.153707
$723$	−3.50050e11	−0.0476439
$724$	−1.08857e13	−1.47243
$725$	2.27786e13	3.06201
$726$	1.82175e12	0.243373
$727$	9.87402e12	1.31096	0.655480	−	0.755213i	$-0.272466\pi$
$727$	9.87402e12	1.31096	0.655480	+	0.755213i	$0.272466\pi$
$728$	2.25225e11	0.0297184
$729$	−7.60519e12	−0.997324
$730$	4.36557e12	0.568969
$731$	1.22121e11	0.0158184
$732$	1.61274e13	2.07618
$733$	−8.91508e12	−1.14066	−0.570331	−	0.821415i	$-0.693185\pi$
$733$	−8.91508e12	−1.14066	−0.570331	+	0.821415i	$0.693185\pi$
$734$	1.55359e12	0.197563
$735$	−2.03436e13	−2.57120
$736$	−6.99646e11	−0.0878877
$737$	1.66597e13	2.08000
$738$	−6.77882e11	−0.0841202
$739$	2.33267e12	0.287708	0.143854	−	0.989599i	$-0.454050\pi$
$739$	2.33267e12	0.287708	0.143854	+	0.989599i	$0.454050\pi$
$740$	−2.36112e12	−0.289451
$741$	5.26813e12	0.641911
$742$	−1.47003e11	−0.0178037
$743$	−7.75609e12	−0.933669	−0.466835	−	0.884345i	$-0.654606\pi$
$743$	−7.75609e12	−0.933669	−0.466835	+	0.884345i	$0.654606\pi$
$744$	−5.11009e12	−0.611436
$745$	−1.75557e13	−2.08793
$746$	−1.88805e11	−0.0223197
$747$	−1.63051e12	−0.191593
$748$	−2.75541e12	−0.321832
$749$	−5.77421e11	−0.0670385
$750$	5.88799e12	0.679503
$751$	−1.01065e12	−0.115936	−0.0579681	−	0.998318i	$-0.518462\pi$
$751$	−1.01065e12	−0.115936	−0.0579681	+	0.998318i	$0.518462\pi$
$752$	−9.26382e12	−1.05635
$753$	−5.21158e12	−0.590734
$754$	−2.22897e12	−0.251150
$755$	6.77567e11	0.0758912
$756$	1.28418e9	0.000142981 0
$757$	−1.62756e13	−1.80138	−0.900689	−	0.434465i	$-0.856938\pi$
$757$	−1.62756e13	−1.80138	−0.900689	+	0.434465i	$0.856938\pi$
$758$	−4.77749e11	−0.0525640
$759$	−2.81049e12	−0.307394
$760$	2.95009e12	0.320755
$761$	8.46614e12	0.915070	0.457535	−	0.889192i	$-0.348732\pi$
$761$	8.46614e12	0.915070	0.457535	+	0.889192i	$0.348732\pi$
$762$	4.12941e12	0.443701
$763$	4.76566e11	0.0509053
$764$	5.74033e12	0.609561
$765$	4.21892e12	0.445374
$766$	−4.07787e11	−0.0427961
$767$	8.64787e12	0.902256
$768$	8.75207e12	0.907790
$769$	−8.85213e12	−0.912807	−0.456404	−	0.889773i	$-0.650863\pi$
$769$	−8.85213e12	−0.912807	−0.456404	+	0.889773i	$0.650863\pi$
$770$	3.75038e11	0.0384474
$771$	5.44051e12	0.554492
$772$	2.85248e12	0.289031
$773$	1.26705e12	0.127640	0.0638198	−	0.997961i	$-0.479672\pi$
$773$	1.26705e12	0.127640	0.0638198	+	0.997961i	$0.479672\pi$
$774$	1.26014e11	0.0126207
$775$	2.67086e13	2.65946
$776$	6.24354e12	0.618092
$777$	1.85634e11	0.0182711
$778$	1.59442e12	0.156025
$779$	2.04030e12	0.198507
$780$	2.54642e13	2.46323
$781$	−2.40556e13	−2.31359
$782$	−7.85941e10	−0.00751553
$783$	−2.59189e10	−0.00246427
$784$	−9.33268e12	−0.882234
$785$	−8.59373e12	−0.807734
$786$	5.72388e12	0.534920
$787$	9.11402e12	0.846884	0.423442	−	0.905923i	$-0.360822\pi$
$787$	9.11402e12	0.846884	0.423442	+	0.905923i	$0.360822\pi$
$788$	−1.97340e13	−1.82326
$789$	−2.12627e13	−1.95331
$790$	−3.92854e12	−0.358847
$791$	−3.23362e11	−0.0293694
$792$	−5.79851e12	−0.523665
$793$	1.68216e13	1.51056
$794$	−2.06033e12	−0.183969
$795$	−3.38956e13	−3.00948
$796$	1.27615e13	1.12666
$797$	−1.10430e13	−0.969446	−0.484723	−	0.874668i	$-0.661080\pi$
$797$	−1.10430e13	−0.969446	−0.484723	+	0.874668i	$0.661080\pi$
$798$	−1.13730e11	−0.00992798
$799$	−3.34073e12	−0.289989
$800$	1.50993e13	1.30332
$801$	2.00591e12	0.172173
$802$	2.74696e11	0.0234459
$803$	2.58264e13	2.19202
$804$	−2.44196e13	−2.06104
$805$	−2.71516e11	−0.0227884
$806$	−2.61353e12	−0.218133
$807$	5.42168e12	0.449990
$808$	−6.06518e12	−0.500602
$809$	5.49563e12	0.451075	0.225538	−	0.974234i	$-0.427586\pi$
$809$	5.49563e12	0.451075	0.225538	+	0.974234i	$0.427586\pi$
$810$	−4.37090e12	−0.356770
$811$	−9.90610e12	−0.804098	−0.402049	−	0.915618i	$-0.631702\pi$
$811$	−9.90610e12	−0.804098	−0.402049	+	0.915618i	$0.631702\pi$
$812$	−1.22134e12	−0.0985906
$813$	3.07892e13	2.47167
$814$	5.50330e11	0.0439353
$815$	2.92204e12	0.231994
$816$	3.87347e12	0.305840
$817$	−3.79279e11	−0.0297824
$818$	−3.13744e11	−0.0245011
$819$	−1.00035e12	−0.0776915
$820$	9.86209e12	0.761740
$821$	1.10284e13	0.847164	0.423582	−	0.905858i	$-0.360773\pi$
$821$	1.10284e13	0.847164	0.423582	+	0.905858i	$0.360773\pi$
$822$	−3.64874e11	−0.0278753
$823$	−3.74832e12	−0.284798	−0.142399	−	0.989809i	$-0.545482\pi$
$823$	−3.74832e12	−0.284798	−0.142399	+	0.989809i	$0.545482\pi$
$824$	4.26151e12	0.322026
$825$	6.06541e13	4.55845
$826$	−1.86692e11	−0.0139546
$827$	−1.61307e13	−1.19917	−0.599583	−	0.800312i	$-0.704667\pi$
$827$	−1.61307e13	−1.19917	−0.599583	+	0.800312i	$0.704667\pi$
$828$	2.05842e12	0.152194
$829$	1.02440e13	0.753312	0.376656	−	0.926353i	$-0.377074\pi$
$829$	1.02440e13	0.753312	0.376656	+	0.926353i	$0.377074\pi$
$830$	−9.34589e11	−0.0683548
$831$	1.09044e13	0.793225
$832$	1.06645e13	0.771588
$833$	−3.36557e12	−0.242190
$834$	−3.55391e12	−0.254366
$835$	2.05306e13	1.46155
$836$	8.55767e12	0.605937
$837$	−3.03907e10	−0.00214031
$838$	5.51599e11	0.0386389
$839$	−1.93059e13	−1.34512	−0.672559	−	0.740044i	$-0.734805\pi$
$839$	−1.93059e13	−1.34512	−0.672559	+	0.740044i	$0.734805\pi$
$840$	−1.12111e12	−0.0776950
$841$	1.01434e13	0.699202
$842$	−4.81868e12	−0.330387
$843$	−1.37446e13	−0.937365
$844$	−9.33455e12	−0.633217
$845$	−5.61214e11	−0.0378681
$846$	−3.44722e12	−0.231368
$847$	1.04117e12	0.0695101
$848$	−1.55497e13	−1.03262
$849$	1.97943e13	1.30754
$850$	1.69616e12	0.111451
$851$	−3.98422e11	−0.0260411
$852$	3.52605e13	2.29251
$853$	−1.06746e13	−0.690370	−0.345185	−	0.938535i	$-0.612184\pi$
$853$	−1.06746e13	−0.690370	−0.345185	+	0.938535i	$0.612184\pi$
$854$	−3.63148e11	−0.0233627
$855$	−1.31030e13	−0.838537
$856$	5.11719e12	0.325762
$857$	5.54831e12	0.351356	0.175678	−	0.984448i	$-0.443788\pi$
$857$	5.54831e12	0.351356	0.175678	+	0.984448i	$0.443788\pi$
$858$	−5.93522e12	−0.373890
$859$	−4.80064e12	−0.300836	−0.150418	−	0.988622i	$-0.548062\pi$
$859$	−4.80064e12	−0.300836	−0.150418	+	0.988622i	$0.548062\pi$
$860$	−1.83330e12	−0.114285
$861$	−7.75372e11	−0.0480835
$862$	−2.46575e12	−0.152113
$863$	4.23745e12	0.260050	0.130025	−	0.991511i	$-0.458494\pi$
$863$	4.23745e12	0.260050	0.130025	+	0.991511i	$0.458494\pi$
$864$	−1.71809e10	−0.00104890
$865$	−2.97801e13	−1.80865
$866$	2.66659e12	0.161111
$867$	−2.21241e13	−1.32978
$868$	−1.43206e12	−0.0856295
$869$	−2.32409e13	−1.38250
$870$	1.10953e13	0.656600
$871$	−2.54707e13	−1.49954
$872$	−4.22340e12	−0.247365
$873$	−2.77310e13	−1.61585
$874$	2.44095e11	0.0141500
$875$	3.36513e12	0.194073
$876$	−3.78561e13	−2.17204
$877$	−1.89201e13	−1.08000	−0.540002	−	0.841664i	$-0.681576\pi$
$877$	−1.89201e13	−1.08000	−0.540002	+	0.841664i	$0.681576\pi$
$878$	4.63830e12	0.263411
$879$	−2.68101e13	−1.51478
$880$	3.96707e13	2.22997
$881$	2.35557e13	1.31736	0.658680	−	0.752423i	$-0.271115\pi$
$881$	2.35557e13	1.31736	0.658680	+	0.752423i	$0.271115\pi$
$882$	−3.47285e12	−0.193231
$883$	2.62625e13	1.45382	0.726912	−	0.686730i	$-0.240955\pi$
$883$	2.62625e13	1.45382	0.726912	+	0.686730i	$0.240955\pi$
$884$	4.21270e12	0.232020
$885$	−4.30470e13	−2.35884
$886$	−1.91211e12	−0.104247
$887$	−2.19345e13	−1.18979	−0.594897	−	0.803802i	$-0.702807\pi$
$887$	−2.19345e13	−1.18979	−0.594897	+	0.803802i	$0.702807\pi$
$888$	−1.64512e12	−0.0887850
$889$	2.36006e12	0.126726
$890$	1.14977e12	0.0614263
$891$	−2.58579e13	−1.37450
$892$	−3.98016e12	−0.210503
$893$	1.03755e13	0.545983
$894$	−5.99787e12	−0.314035
$895$	−2.10427e13	−1.09622
$896$	−1.07172e12	−0.0555513
$897$	4.29691e12	0.221610
$898$	−2.50131e12	−0.128358
$899$	2.89036e13	1.47582
$900$	−4.44234e13	−2.25694
$901$	−5.60756e12	−0.283473
$902$	−2.29866e12	−0.115623
$903$	1.44137e11	0.00721406
$904$	2.86569e12	0.142715
$905$	5.65188e13	2.80075
$906$	2.31489e11	0.0114144
$907$	9.60810e12	0.471417	0.235708	−	0.971824i	$-0.424259\pi$
$907$	9.60810e12	0.471417	0.235708	+	0.971824i	$0.424259\pi$
$908$	−1.26768e12	−0.0618904
$909$	2.69388e13	1.30870
$910$	−5.73389e11	−0.0277181
$911$	1.39517e13	0.671112	0.335556	−	0.942020i	$-0.391076\pi$
$911$	1.39517e13	0.671112	0.335556	+	0.942020i	$0.391076\pi$
$912$	−1.20301e13	−0.575826
$913$	−5.52896e12	−0.263345
$914$	−3.14872e12	−0.149237
$915$	−8.37336e13	−3.94916
$916$	3.46312e13	1.62531
$917$	3.27134e12	0.152779
$918$	−1.93000e9	−8.96942e−5 0
$919$	1.23641e13	0.571797	0.285898	−	0.958260i	$-0.407708\pi$
$919$	1.23641e13	0.571797	0.285898	+	0.958260i	$0.407708\pi$
$920$	2.40622e12	0.110736
$921$	1.68050e13	0.769608
$922$	−5.32303e12	−0.242588
$923$	3.67782e13	1.66795
$924$	−3.25215e12	−0.146773
$925$	8.59846e12	0.386174
$926$	6.42542e12	0.287179
$927$	−1.89277e13	−0.841860
$928$	1.63401e13	0.723252
$929$	−1.21014e13	−0.533048	−0.266524	−	0.963828i	$-0.585875\pi$
$929$	−1.21014e13	−0.533048	−0.266524	+	0.963828i	$0.585875\pi$
$930$	1.30095e13	0.570281
$931$	1.04527e13	0.455988
$932$	−3.21443e13	−1.39551
$933$	4.04454e13	1.74744
$934$	2.64504e11	0.0113729
$935$	1.43061e13	0.612167
$936$	8.86523e12	0.377528
$937$	−2.95588e13	−1.25273	−0.626367	−	0.779528i	$-0.715459\pi$
$937$	−2.95588e13	−1.25273	−0.626367	+	0.779528i	$0.715459\pi$
$938$	5.49867e11	0.0231924
$939$	3.48867e13	1.46442
$940$	5.01515e13	2.09512
$941$	6.41446e12	0.266690	0.133345	−	0.991070i	$-0.457428\pi$
$941$	6.41446e12	0.266690	0.133345	+	0.991070i	$0.457428\pi$
$942$	−2.93603e12	−0.121487
$943$	1.66416e12	0.0685318
$944$	−1.97479e13	−0.809369
$945$	−6.66749e9	−0.000271969 0
$946$	4.27306e11	0.0173472
$947$	5.03344e12	0.203372	0.101686	−	0.994817i	$-0.467576\pi$
$947$	5.03344e12	0.203372	0.101686	+	0.994817i	$0.467576\pi$
$948$	3.40664e13	1.36990
$949$	−3.94855e13	−1.58030
$950$	−5.26788e12	−0.209836
$951$	2.50966e13	0.994953
$952$	−1.85473e11	−0.00731836
$953$	1.56069e13	0.612913	0.306456	−	0.951885i	$-0.400857\pi$
$953$	1.56069e13	0.612913	0.306456	+	0.951885i	$0.400857\pi$
$954$	−5.78631e12	−0.226169
$955$	−2.98038e13	−1.15946
$956$	−4.59414e13	−1.77887
$957$	6.56387e13	2.52963
$958$	6.22877e12	0.238923
$959$	−2.08535e11	−0.00796150
$960$	−5.30853e13	−2.01722
$961$	7.45072e12	0.281801
$962$	−8.41389e11	−0.0316745
$963$	−2.27283e13	−0.851625
$964$	8.69365e11	0.0324232
$965$	−1.48101e13	−0.549774
$966$	−9.27627e10	−0.00342749
$967$	4.60413e12	0.169328	0.0846639	−	0.996410i	$-0.473018\pi$
$967$	4.60413e12	0.169328	0.0846639	+	0.996410i	$0.473018\pi$
$968$	−9.22704e12	−0.337772
$969$	−4.33830e12	−0.158075
$970$	−1.58951e13	−0.576489
$971$	−2.07356e13	−0.748567	−0.374283	−	0.927314i	$-0.622111\pi$
$971$	−2.07356e13	−0.748567	−0.374283	+	0.927314i	$0.622111\pi$
$972$	3.78517e13	1.36015
$973$	−2.03115e12	−0.0726498
$974$	3.03498e12	0.108054
$975$	−9.27329e13	−3.28634
$976$	−3.84130e13	−1.35504
$977$	−2.00968e13	−0.705671	−0.352835	−	0.935685i	$-0.614782\pi$
$977$	−2.00968e13	−0.705671	−0.352835	+	0.935685i	$0.614782\pi$
$978$	9.98307e11	0.0348931
$979$	6.80192e12	0.236652
$980$	5.05243e13	1.74978
$981$	1.87585e13	0.646676
$982$	6.24981e12	0.214469
$983$	7.18742e11	0.0245517	0.0122759	−	0.999925i	$-0.496092\pi$
$983$	7.18742e11	0.0245517	0.0122759	+	0.999925i	$0.496092\pi$
$984$	6.87146e12	0.233653
$985$	1.02459e14	3.46807
$986$	1.83555e12	0.0618473
$987$	−3.94299e12	−0.132251
$988$	−1.30836e13	−0.436840
$989$	−3.09356e11	−0.0102820
$990$	1.47622e13	0.488418
$991$	−4.69128e13	−1.54511	−0.772556	−	0.634947i	$-0.781022\pi$
$991$	−4.69128e13	−1.54511	−0.772556	+	0.634947i	$0.781022\pi$
$992$	1.91593e13	0.628171
$993$	2.47619e13	0.808189
$994$	−7.93976e11	−0.0257970
$995$	−6.62579e13	−2.14306
$996$	8.10430e12	0.260945
$997$	−2.97530e13	−0.953679	−0.476839	−	0.878990i	$-0.658218\pi$
$997$	−2.97530e13	−0.953679	−0.476839	+	0.878990i	$0.658218\pi$
$998$	3.57631e12	0.114116
$999$	−9.78385e9	−0.000310789 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.a.b.1.8	✓	14
3.2	odd	2		333.10.a.d.1.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.a.b.1.8	✓	14	1.1	even	1	trivial
333.10.a.d.1.7		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)

\(f(q)\)	\(=\)	\(q+4.40540 q^{2} +198.342 q^{3} -492.592 q^{4} +2557.54 q^{5} +873.778 q^{6} +499.386 q^{7} -4425.63 q^{8} +19656.7 q^{9} +O(q^{10})\)	\(q+4.40540 q^{2} +198.342 q^{3} -492.592 q^{4} +2557.54 q^{5} +873.778 q^{6} +499.386 q^{7} -4425.63 q^{8} +19656.7 q^{9} +11267.0 q^{10} +66654.7 q^{11} -97701.9 q^{12} -101907. q^{13} +2200.00 q^{14} +507269. q^{15} +232711. q^{16} +83920.5 q^{17} +86595.6 q^{18} -260637. q^{19} -1.25983e6 q^{20} +99049.4 q^{21} +293641. q^{22} -212587. q^{23} -877791. q^{24} +4.58790e6 q^{25} -448942. q^{26} -5220.39 q^{27} -245994. q^{28} +4.96493e6 q^{29} +2.23472e6 q^{30} +5.82154e6 q^{31} +3.29111e6 q^{32} +1.32205e7 q^{33} +369704. q^{34} +1.27720e6 q^{35} -9.68273e6 q^{36} +1.87416e6 q^{37} -1.14821e6 q^{38} -2.02125e7 q^{39} -1.13187e7 q^{40} -7.82814e6 q^{41} +436352. q^{42} +1.45520e6 q^{43} -3.28336e7 q^{44} +5.02728e7 q^{45} -936530. q^{46} -3.98083e7 q^{47} +4.61564e7 q^{48} -4.01042e7 q^{49} +2.02115e7 q^{50} +1.66450e7 q^{51} +5.01987e7 q^{52} -6.68199e7 q^{53} -22997.9 q^{54} +1.70472e8 q^{55} -2.21010e6 q^{56} -5.16954e7 q^{57} +2.18725e7 q^{58} -8.48603e7 q^{59} -2.49877e8 q^{60} -1.65067e8 q^{61} +2.56462e7 q^{62} +9.81627e6 q^{63} -1.04649e8 q^{64} -2.60632e8 q^{65} +5.82414e7 q^{66} +2.49940e8 q^{67} -4.13386e7 q^{68} -4.21650e7 q^{69} +5.62658e6 q^{70} -3.60899e8 q^{71} -8.69933e7 q^{72} +3.87465e8 q^{73} +8.25643e6 q^{74} +9.09974e8 q^{75} +1.28388e8 q^{76} +3.32864e7 q^{77} -8.90442e7 q^{78} -3.48676e8 q^{79} +5.95167e8 q^{80} -3.87938e8 q^{81} -3.44861e7 q^{82} -8.29492e7 q^{83} -4.87910e7 q^{84} +2.14630e8 q^{85} +6.41074e6 q^{86} +9.84757e8 q^{87} -2.94990e8 q^{88} +1.02047e8 q^{89} +2.21472e8 q^{90} -5.08910e7 q^{91} +1.04719e8 q^{92} +1.15466e9 q^{93} -1.75372e8 q^{94} -6.66591e8 q^{95} +6.52766e8 q^{96} -1.41077e9 q^{97} -1.76675e8 q^{98} +1.31021e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9}+O(q^{10}) \) 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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