LMFDB - Embedded newform 121.10.a.i.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,10,Mod(1,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, 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("121.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	121.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:	$62.3193361758$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5809 x^{14} - 4272 x^{13} + 13066060 x^{12} + 16497800 x^{11} - 14560551456 x^{10} + \cdots + 24\!\cdots\!44 $ x^16 - 5809x^14 - 4272x^13 + 13066060x^12 + 16497800x^11 - 14560551456x^10 - 23195020992x^9 + 8610494517504x^8 + 17243789456256x^7 - 2678625538125824x^6 - 7333691570889728x^5 + 407745151492356096x^4 + 1471911449728821248x^3 - 24138375758574923776x^2 - 94475289166645297152x + 244256059909199314944
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{4}\cdot 11^{9} $
Twist minimal:	no (minimal twist has level 11)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-8.64074$ of defining polynomial
Character	$\chi$	$=$	121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+13.8768 q^{2} -68.3315 q^{3} -319.434 q^{4} -768.757 q^{5} -948.222 q^{6} +11279.4 q^{7} -11537.7 q^{8} -15013.8 q^{9} +O(q^{10})$	\(q+13.8768 q^{2} -68.3315 q^{3} -319.434 q^{4} -768.757 q^{5} -948.222 q^{6} +11279.4 q^{7} -11537.7 q^{8} -15013.8 q^{9} -10667.9 q^{10} +21827.4 q^{12} -191299. q^{13} +156521. q^{14} +52530.3 q^{15} +3444.55 q^{16} +263199. q^{17} -208344. q^{18} -256607. q^{19} +245567. q^{20} -770734. q^{21} -61217.9 q^{23} +788385. q^{24} -1.36214e6 q^{25} -2.65462e6 q^{26} +2.37088e6 q^{27} -3.60301e6 q^{28} -6.10177e6 q^{29} +728952. q^{30} +1.84785e6 q^{31} +5.95508e6 q^{32} +3.65236e6 q^{34} -8.67108e6 q^{35} +4.79593e6 q^{36} +8.27552e6 q^{37} -3.56088e6 q^{38} +1.30717e7 q^{39} +8.86965e6 q^{40} +1.15281e7 q^{41} -1.06953e7 q^{42} +7.83354e6 q^{43} +1.15420e7 q^{45} -849508. q^{46} +1.66571e7 q^{47} -235371. q^{48} +8.68702e7 q^{49} -1.89021e7 q^{50} -1.79848e7 q^{51} +6.11074e7 q^{52} +5.98897e7 q^{53} +3.29003e7 q^{54} -1.30137e8 q^{56} +1.75343e7 q^{57} -8.46731e7 q^{58} -5.86736e7 q^{59} -1.67800e7 q^{60} +1.08653e8 q^{61} +2.56423e7 q^{62} -1.69346e8 q^{63} +8.08739e7 q^{64} +1.47062e8 q^{65} +1.16650e8 q^{67} -8.40748e7 q^{68} +4.18311e6 q^{69} -1.20327e8 q^{70} +1.52456e8 q^{71} +1.73224e8 q^{72} +2.46323e8 q^{73} +1.14838e8 q^{74} +9.30769e7 q^{75} +8.19690e7 q^{76} +1.81394e8 q^{78} +5.52487e7 q^{79} -2.64802e6 q^{80} +1.33511e8 q^{81} +1.59973e8 q^{82} +3.69940e8 q^{83} +2.46199e8 q^{84} -2.02336e8 q^{85} +1.08705e8 q^{86} +4.16943e8 q^{87} -4.85830e8 q^{89} +1.60166e8 q^{90} -2.15773e9 q^{91} +1.95551e7 q^{92} -1.26266e8 q^{93} +2.31147e8 q^{94} +1.97268e8 q^{95} -4.06919e8 q^{96} -2.85657e8 q^{97} +1.20548e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 48 q^{2} + 222 q^{3} + 3670 q^{4} - 1875 q^{5} + 6191 q^{6} + 12575 q^{7} + 41046 q^{8} + 78904 q^{9}+O(q^{10}) $ 16 * q + 48 * q^2 + 222 * q^3 + 3670 * q^4 - 1875 * q^5 + 6191 * q^6 + 12575 * q^7 + 41046 * q^8 + 78904 * q^9	\( 16 q + 48 q^{2} + 222 q^{3} + 3670 q^{4} - 1875 q^{5} + 6191 q^{6} + 12575 q^{7} + 41046 q^{8} + 78904 q^{9} + 8136 q^{10} + 169811 q^{12} + 119783 q^{13} - 150396 q^{14} + 128978 q^{15} + 1706770 q^{16} + 570930 q^{17} + 1377185 q^{18} + 708062 q^{19} - 2134062 q^{20} + 1713601 q^{21} - 2022726 q^{23} + 5319405 q^{24} - 222677 q^{25} - 4839084 q^{26} + 6603192 q^{27} + 4933520 q^{28} + 12196593 q^{29} + 20118540 q^{30} - 1920467 q^{31} + 28274430 q^{32} + 4257577 q^{34} + 17645076 q^{35} + 10442417 q^{36} + 8193077 q^{37} + 17969289 q^{38} + 26233656 q^{39} - 78857762 q^{40} + 27052578 q^{41} + 126693168 q^{42} + 2191717 q^{43} - 82573010 q^{45} - 82764586 q^{46} + 61772571 q^{47} + 26253395 q^{48} - 35102109 q^{49} + 162127428 q^{50} + 27137348 q^{51} + 174822050 q^{52} + 230906967 q^{53} + 168706262 q^{54} - 163593804 q^{56} + 68054133 q^{57} - 373835684 q^{58} - 92927886 q^{59} + 190895818 q^{60} + 463219765 q^{61} + 573749574 q^{62} + 784007783 q^{63} + 1128452290 q^{64} + 434503197 q^{65} - 473101677 q^{67} + 1073658963 q^{68} - 975630076 q^{69} + 524415506 q^{70} + 374085717 q^{71} + 3278349663 q^{72} + 1061898004 q^{73} + 1887418362 q^{74} + 1708808113 q^{75} + 2116654933 q^{76} - 2149007830 q^{78} + 1193641695 q^{79} - 2800403982 q^{80} - 160274720 q^{81} + 406045707 q^{82} + 3036904890 q^{83} + 3741117150 q^{84} + 2067806293 q^{85} + 4258123329 q^{86} + 2016430701 q^{87} - 779711079 q^{89} + 2671912588 q^{90} - 2737301136 q^{91} + 211938438 q^{92} - 2375160030 q^{93} + 8271211980 q^{94} + 3152016348 q^{95} + 7750699293 q^{96} + 6028874386 q^{97} + 3685530690 q^{98}+O(q^{100}) \) 16 * q + 48 * q^2 + 222 * q^3 + 3670 * q^4 - 1875 * q^5 + 6191 * q^6 + 12575 * q^7 + 41046 * q^8 + 78904 * q^9 + 8136 * q^10 + 169811 * q^12 + 119783 * q^13 - 150396 * q^14 + 128978 * q^15 + 1706770 * q^16 + 570930 * q^17 + 1377185 * q^18 + 708062 * q^19 - 2134062 * q^20 + 1713601 * q^21 - 2022726 * q^23 + 5319405 * q^24 - 222677 * q^25 - 4839084 * q^26 + 6603192 * q^27 + 4933520 * q^28 + 12196593 * q^29 + 20118540 * q^30 - 1920467 * q^31 + 28274430 * q^32 + 4257577 * q^34 + 17645076 * q^35 + 10442417 * q^36 + 8193077 * q^37 + 17969289 * q^38 + 26233656 * q^39 - 78857762 * q^40 + 27052578 * q^41 + 126693168 * q^42 + 2191717 * q^43 - 82573010 * q^45 - 82764586 * q^46 + 61772571 * q^47 + 26253395 * q^48 - 35102109 * q^49 + 162127428 * q^50 + 27137348 * q^51 + 174822050 * q^52 + 230906967 * q^53 + 168706262 * q^54 - 163593804 * q^56 + 68054133 * q^57 - 373835684 * q^58 - 92927886 * q^59 + 190895818 * q^60 + 463219765 * q^61 + 573749574 * q^62 + 784007783 * q^63 + 1128452290 * q^64 + 434503197 * q^65 - 473101677 * q^67 + 1073658963 * q^68 - 975630076 * q^69 + 524415506 * q^70 + 374085717 * q^71 + 3278349663 * q^72 + 1061898004 * q^73 + 1887418362 * q^74 + 1708808113 * q^75 + 2116654933 * q^76 - 2149007830 * q^78 + 1193641695 * q^79 - 2800403982 * q^80 - 160274720 * q^81 + 406045707 * q^82 + 3036904890 * q^83 + 3741117150 * q^84 + 2067806293 * q^85 + 4258123329 * q^86 + 2016430701 * q^87 - 779711079 * q^89 + 2671912588 * q^90 - 2737301136 * q^91 + 211938438 * q^92 - 2375160030 * q^93 + 8271211980 * q^94 + 3152016348 * q^95 + 7750699293 * q^96 + 6028874386 * q^97 + 3685530690 * q^98

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 $

$2$	13.8768	0.613274	0.306637	−	0.951827i	$-0.400796\pi$
$2$	13.8768	0.613274	0.306637	+	0.951827i	$0.400796\pi$
$3$	−68.3315	−0.487052	−0.243526	−	0.969894i	$-0.578304\pi$
$3$	−68.3315	−0.487052	−0.243526	+	0.969894i	$0.578304\pi$
$4$	−319.434	−0.623895
$5$	−768.757	−0.550077	−0.275039	−	0.961433i	$-0.588691\pi$
$5$	−768.757	−0.550077	−0.275039	+	0.961433i	$0.588691\pi$
$6$	−948.222	−0.298696
$7$	11279.4	1.77559	0.887796	−	0.460238i	$-0.152236\pi$
$7$	11279.4	1.77559	0.887796	+	0.460238i	$0.152236\pi$
$8$	−11537.7	−0.995893
$9$	−15013.8	−0.762781
$10$	−10667.9	−0.337348
$11$	0	0
$11$	0	0
$12$	21827.4	0.303869
$13$	−191299.	−1.85766	−0.928832	−	0.370501i	$-0.879186\pi$
$13$	−191299.	−1.85766	−0.928832	+	0.370501i	$0.879186\pi$
$14$	156521.	1.08892
$15$	52530.3	0.267916
$16$	3444.55	0.0131399
$17$	263199.	0.764300	0.382150	−	0.924100i	$-0.375184\pi$
$17$	263199.	0.764300	0.382150	+	0.924100i	$0.375184\pi$
$18$	−208344.	−0.467794
$19$	−256607.	−0.451728	−0.225864	−	0.974159i	$-0.572520\pi$
$19$	−256607.	−0.451728	−0.225864	+	0.974159i	$0.572520\pi$
$20$	245567.	0.343191
$21$	−770734.	−0.864805
$22$	0	0
$23$	−61217.9	−0.0456145	−0.0228072	−	0.999740i	$-0.507260\pi$
$23$	−61217.9	−0.0456145	−0.0228072	+	0.999740i	$0.507260\pi$
$24$	788385.	0.485051
$25$	−1.36214e6	−0.697415
$26$	−2.65462e6	−1.13926
$27$	2.37088e6	0.858565
$28$	−3.60301e6	−1.10778
$29$	−6.10177e6	−1.60201	−0.801005	−	0.598658i	$-0.795701\pi$
$29$	−6.10177e6	−1.60201	−0.801005	+	0.598658i	$0.795701\pi$
$30$	728952.	0.164306
$31$	1.84785e6	0.359368	0.179684	−	0.983724i	$-0.442492\pi$
$31$	1.84785e6	0.359368	0.179684	+	0.983724i	$0.442492\pi$
$32$	5.95508e6	1.00395
$33$	0	0
$34$	3.65236e6	0.468726
$35$	−8.67108e6	−0.976713
$36$	4.79593e6	0.475895
$37$	8.27552e6	0.725918	0.362959	−	0.931805i	$-0.381766\pi$
$37$	8.27552e6	0.725918	0.362959	+	0.931805i	$0.381766\pi$
$38$	−3.56088e6	−0.277033
$39$	1.30717e7	0.904778
$40$	8.86965e6	0.547818
$41$	1.15281e7	0.637131	0.318565	−	0.947901i	$-0.396799\pi$
$41$	1.15281e7	0.637131	0.318565	+	0.947901i	$0.396799\pi$
$42$	−1.06953e7	−0.530362
$43$	7.83354e6	0.349422	0.174711	−	0.984620i	$-0.444101\pi$
$43$	7.83354e6	0.349422	0.174711	+	0.984620i	$0.444101\pi$
$44$	0	0
$45$	1.15420e7	0.419588
$46$	−849508.	−0.0279742
$47$	1.66571e7	0.497918	0.248959	−	0.968514i	$-0.419912\pi$
$47$	1.66571e7	0.497918	0.248959	+	0.968514i	$0.419912\pi$
$48$	−235371.	−0.00639981
$49$	8.68702e7	2.15272
$50$	−1.89021e7	−0.427706
$51$	−1.79848e7	−0.372254
$52$	6.11074e7	1.15899
$53$	5.98897e7	1.04258	0.521291	−	0.853379i	$-0.325451\pi$
$53$	5.98897e7	1.04258	0.521291	+	0.853379i	$0.325451\pi$
$54$	3.29003e7	0.526536
$55$	0	0
$56$	−1.30137e8	−1.76830
$57$	1.75343e7	0.220015
$58$	−8.46731e7	−0.982471
$59$	−5.86736e7	−0.630389	−0.315194	−	0.949027i	$-0.602070\pi$
$59$	−5.86736e7	−0.630389	−0.315194	+	0.949027i	$0.602070\pi$
$60$	−1.67800e7	−0.167152
$61$	1.08653e8	1.00475	0.502374	−	0.864651i	$-0.332460\pi$
$61$	1.08653e8	1.00475	0.502374	+	0.864651i	$0.332460\pi$
$62$	2.56423e7	0.220391
$63$	−1.69346e8	−1.35439
$64$	8.08739e7	0.602557
$65$	1.47062e8	1.02186
$66$	0	0
$67$	1.16650e8	0.707212	0.353606	−	0.935394i	$-0.384955\pi$
$67$	1.16650e8	0.707212	0.353606	+	0.935394i	$0.384955\pi$
$68$	−8.40748e7	−0.476843
$69$	4.18311e6	0.0222166
$70$	−1.20327e8	−0.598992
$71$	1.52456e8	0.712003	0.356002	−	0.934485i	$-0.384140\pi$
$71$	1.52456e8	0.712003	0.356002	+	0.934485i	$0.384140\pi$
$72$	1.73224e8	0.759648
$73$	2.46323e8	1.01520	0.507601	−	0.861592i	$-0.330532\pi$
$73$	2.46323e8	1.01520	0.507601	+	0.861592i	$0.330532\pi$
$74$	1.14838e8	0.445187
$75$	9.30769e7	0.339677
$76$	8.19690e7	0.281831
$77$	0	0
$78$	1.81394e8	0.554877
$79$	5.52487e7	0.159588	0.0797940	−	0.996811i	$-0.474574\pi$
$79$	5.52487e7	0.159588	0.0797940	+	0.996811i	$0.474574\pi$
$80$	−2.64802e6	−0.00722797
$81$	1.33511e8	0.344615
$82$	1.59973e8	0.390736
$83$	3.69940e8	0.855618	0.427809	−	0.903869i	$-0.359286\pi$
$83$	3.69940e8	0.855618	0.427809	+	0.903869i	$0.359286\pi$
$84$	2.46199e8	0.539547
$85$	−2.02336e8	−0.420424
$86$	1.08705e8	0.214291
$87$	4.16943e8	0.780261
$88$	0	0
$89$	−4.85830e8	−0.820784	−0.410392	−	0.911909i	$-0.634608\pi$
$89$	−4.85830e8	−0.820784	−0.410392	+	0.911909i	$0.634608\pi$
$90$	1.60166e8	0.257323
$91$	−2.15773e9	−3.29845
$92$	1.95551e7	0.0284587
$93$	−1.26266e8	−0.175031
$94$	2.31147e8	0.305360
$95$	1.97268e8	0.248485
$96$	−4.06919e8	−0.488976
$97$	−2.85657e8	−0.327621	−0.163811	−	0.986492i	$-0.552379\pi$
$97$	−2.85657e8	−0.327621	−0.163811	+	0.986492i	$0.552379\pi$
$98$	1.20548e9	1.32021
$99$	0	0
$100$	4.35114e8	0.435114
$101$	−8.87737e8	−0.848864	−0.424432	−	0.905460i	$-0.639526\pi$
$101$	−8.87737e8	−0.848864	−0.424432	+	0.905460i	$0.639526\pi$
$102$	−2.49571e8	−0.228294
$103$	−1.33107e9	−1.16528	−0.582642	−	0.812729i	$-0.697981\pi$
$103$	−1.33107e9	−1.16528	−0.582642	+	0.812729i	$0.697981\pi$
$104$	2.20714e9	1.85003
$105$	5.92507e8	0.475710
$106$	8.31077e8	0.639389
$107$	4.81845e8	0.355370	0.177685	−	0.984087i	$-0.443139\pi$
$107$	4.81845e8	0.355370	0.177685	+	0.984087i	$0.443139\pi$
$108$	−7.57341e8	−0.535655
$109$	9.36787e8	0.635655	0.317828	−	0.948149i	$-0.397047\pi$
$109$	9.36787e8	0.635655	0.317828	+	0.948149i	$0.397047\pi$
$110$	0	0
$111$	−5.65478e8	−0.353560
$112$	3.88523e7	0.0233311
$113$	5.84705e8	0.337352	0.168676	−	0.985672i	$-0.446051\pi$
$113$	5.84705e8	0.337352	0.168676	+	0.985672i	$0.446051\pi$
$114$	2.43320e8	0.134929
$115$	4.70616e7	0.0250915
$116$	1.94911e9	0.999485
$117$	2.87212e9	1.41699
$118$	−8.14202e8	−0.386601
$119$	2.96871e9	1.35708
$120$	−6.06076e8	−0.266816
$121$	0	0
$122$	1.50775e9	0.616185
$123$	−7.87729e8	−0.310316
$124$	−5.90268e8	−0.224208
$125$	2.54863e9	0.933710
$126$	−2.34998e9	−0.830610
$127$	4.53889e8	0.154822	0.0774110	−	0.996999i	$-0.475335\pi$
$127$	4.53889e8	0.154822	0.0774110	+	0.996999i	$0.475335\pi$
$128$	−1.92673e9	−0.634418
$129$	−5.35278e8	−0.170187
$130$	2.04075e9	0.626680
$131$	1.84813e9	0.548293	0.274146	−	0.961688i	$-0.411605\pi$
$131$	1.84813e9	0.548293	0.274146	+	0.961688i	$0.411605\pi$
$132$	0	0
$133$	−2.89436e9	−0.802084
$134$	1.61874e9	0.433715
$135$	−1.82263e9	−0.472277
$136$	−3.03670e9	−0.761161
$137$	6.75964e9	1.63938	0.819692	−	0.572804i	$-0.194144\pi$
$137$	6.75964e9	1.63938	0.819692	+	0.572804i	$0.194144\pi$
$138$	5.80482e7	0.0136249
$139$	−5.06814e9	−1.15155	−0.575773	−	0.817609i	$-0.695299\pi$
$139$	−5.06814e9	−1.15155	−0.575773	+	0.817609i	$0.695299\pi$
$140$	2.76984e9	0.609366
$141$	−1.13820e9	−0.242512
$142$	2.11560e9	0.436653
$143$	0	0
$144$	−5.17158e7	−0.0100229
$145$	4.69078e9	0.881229
$146$	3.41818e9	0.622597
$147$	−5.93596e9	−1.04849
$148$	−2.64349e9	−0.452897
$149$	−2.76548e9	−0.459656	−0.229828	−	0.973231i	$-0.573816\pi$
$149$	−2.76548e9	−0.459656	−0.229828	+	0.973231i	$0.573816\pi$
$150$	1.29161e9	0.208315
$151$	6.13082e8	0.0959671	0.0479835	−	0.998848i	$-0.484721\pi$
$151$	6.13082e8	0.0959671	0.0479835	+	0.998848i	$0.484721\pi$
$152$	2.96064e9	0.449873
$153$	−3.95162e9	−0.582994
$154$	0	0
$155$	−1.42055e9	−0.197680
$156$	−4.17556e9	−0.564487
$157$	5.12341e9	0.672993	0.336497	−	0.941685i	$-0.390758\pi$
$157$	5.12341e9	0.672993	0.336497	+	0.941685i	$0.390758\pi$
$158$	7.66676e8	0.0978712
$159$	−4.09235e9	−0.507792
$160$	−4.57801e9	−0.552251
$161$	−6.90498e8	−0.0809927
$162$	1.85271e9	0.211343
$163$	−1.35972e10	−1.50870	−0.754351	−	0.656471i	$-0.772048\pi$
$163$	−1.35972e10	−1.50870	−0.754351	+	0.656471i	$0.772048\pi$
$164$	−3.68245e9	−0.397503
$165$	0	0
$166$	5.13358e9	0.524728
$167$	−9.00710e9	−0.896109	−0.448054	−	0.894006i	$-0.647883\pi$
$167$	−9.00710e9	−0.896109	−0.448054	+	0.894006i	$0.647883\pi$
$168$	8.89247e9	0.861252
$169$	2.59907e10	2.45092
$170$	−2.80778e9	−0.257835
$171$	3.85265e9	0.344569
$172$	−2.50230e9	−0.218003
$173$	2.64952e9	0.224884	0.112442	−	0.993658i	$-0.464133\pi$
$173$	2.64952e9	0.224884	0.112442	+	0.993658i	$0.464133\pi$
$174$	5.78584e9	0.478514
$175$	−1.53640e10	−1.23832
$176$	0	0
$177$	4.00925e9	0.307032
$178$	−6.74176e9	−0.503366
$179$	3.13939e9	0.228564	0.114282	−	0.993448i	$-0.463543\pi$
$179$	3.13939e9	0.228564	0.114282	+	0.993448i	$0.463543\pi$
$180$	−3.68690e9	−0.261779
$181$	−2.65675e9	−0.183991	−0.0919957	−	0.995759i	$-0.529325\pi$
$181$	−2.65675e9	−0.183991	−0.0919957	+	0.995759i	$0.529325\pi$
$182$	−2.99424e10	−2.02285
$183$	−7.42441e9	−0.489364
$184$	7.06310e8	0.0454271
$185$	−6.36186e9	−0.399311
$186$	−1.75218e9	−0.107342
$187$	0	0
$188$	−5.32083e9	−0.310649
$189$	2.67420e10	1.52446
$190$	2.73745e9	0.152390
$191$	−9.31950e9	−0.506690	−0.253345	−	0.967376i	$-0.581531\pi$
$191$	−9.31950e9	−0.506690	−0.253345	+	0.967376i	$0.581531\pi$
$192$	−5.52623e9	−0.293476
$193$	−3.16102e9	−0.163991	−0.0819954	−	0.996633i	$-0.526129\pi$
$193$	−3.16102e9	−0.163991	−0.0819954	+	0.996633i	$0.526129\pi$
$194$	−3.96401e9	−0.200922
$195$	−1.00490e10	−0.497698
$196$	−2.77493e10	−1.34307
$197$	−2.27534e10	−1.07634	−0.538169	−	0.842837i	$-0.680884\pi$
$197$	−2.27534e10	−1.07634	−0.538169	+	0.842837i	$0.680884\pi$
$198$	0	0
$199$	1.10008e10	0.497264	0.248632	−	0.968598i	$-0.420019\pi$
$199$	1.10008e10	0.497264	0.248632	+	0.968598i	$0.420019\pi$
$200$	1.57159e10	0.694550
$201$	−7.97089e9	−0.344449
$202$	−1.23189e10	−0.520586
$203$	−6.88240e10	−2.84451
$204$	5.74495e9	0.232247
$205$	−8.86227e9	−0.350471
$206$	−1.84709e10	−0.714638
$207$	9.19114e8	0.0347939
$208$	−6.58938e8	−0.0244095
$209$	0	0
$210$	8.22211e9	0.291740
$211$	−9.28711e9	−0.322559	−0.161280	−	0.986909i	$-0.551562\pi$
$211$	−9.28711e9	−0.322559	−0.161280	+	0.986909i	$0.551562\pi$
$212$	−1.91308e10	−0.650462
$213$	−1.04175e10	−0.346782
$214$	6.68647e9	0.217939
$215$	−6.02209e9	−0.192209
$216$	−2.73544e10	−0.855039
$217$	2.08426e10	0.638091
$218$	1.29996e10	0.389831
$219$	−1.68316e10	−0.494456
$220$	0	0
$221$	−5.03497e10	−1.41981
$222$	−7.84704e9	−0.216829
$223$	6.31352e10	1.70962	0.854810	−	0.518941i	$-0.173673\pi$
$223$	6.31352e10	1.70962	0.854810	+	0.518941i	$0.173673\pi$
$224$	6.71694e10	1.78261
$225$	2.04509e10	0.531975
$226$	8.11383e9	0.206889
$227$	6.21531e10	1.55363	0.776813	−	0.629731i	$-0.216835\pi$
$227$	6.21531e10	1.55363	0.776813	+	0.629731i	$0.216835\pi$
$228$	−5.60106e9	−0.137266
$229$	4.19844e10	1.00885	0.504426	−	0.863455i	$-0.331704\pi$
$229$	4.19844e10	1.00885	0.504426	+	0.863455i	$0.331704\pi$
$230$	6.53065e8	0.0153880
$231$	0	0
$232$	7.04001e10	1.59543
$233$	1.18933e10	0.264364	0.132182	−	0.991225i	$-0.457802\pi$
$233$	1.18933e10	0.264364	0.132182	+	0.991225i	$0.457802\pi$
$234$	3.98559e10	0.869003
$235$	−1.28052e10	−0.273894
$236$	1.87423e10	0.393296
$237$	−3.77522e9	−0.0777276
$238$	4.11963e10	0.832265
$239$	−3.52268e10	−0.698364	−0.349182	−	0.937055i	$-0.613541\pi$
$239$	−3.52268e10	−0.698364	−0.349182	+	0.937055i	$0.613541\pi$
$240$	1.80943e8	0.00352039
$241$	−2.50205e10	−0.477771	−0.238886	−	0.971048i	$-0.576782\pi$
$241$	−2.50205e10	−0.477771	−0.238886	+	0.971048i	$0.576782\pi$
$242$	0	0
$243$	−5.57891e10	−1.02641
$244$	−3.47074e10	−0.626857
$245$	−6.67820e10	−1.18416
$246$	−1.09312e10	−0.190308
$247$	4.90886e10	0.839159
$248$	−2.13199e10	−0.357892
$249$	−2.52785e10	−0.416730
$250$	3.53669e10	0.572620
$251$	−8.32744e10	−1.32428	−0.662140	−	0.749380i	$-0.730351\pi$
$251$	−8.32744e10	−1.32428	−0.662140	+	0.749380i	$0.730351\pi$
$252$	5.40949e10	0.844995
$253$	0	0
$254$	6.29852e9	0.0949483
$255$	1.38259e10	0.204768
$256$	−6.81443e10	−0.991629
$257$	−4.86914e10	−0.696230	−0.348115	−	0.937452i	$-0.613178\pi$
$257$	−4.86914e10	−0.696230	−0.348115	+	0.937452i	$0.613178\pi$
$258$	−7.42794e9	−0.104371
$259$	9.33425e10	1.28893
$260$	−4.69767e10	−0.637533
$261$	9.16109e10	1.22198
$262$	2.56462e10	0.336254
$263$	1.39894e11	1.80301	0.901506	−	0.432768i	$-0.142463\pi$
$263$	1.39894e11	1.80301	0.901506	+	0.432768i	$0.142463\pi$
$264$	0	0
$265$	−4.60406e10	−0.573501
$266$	−4.01644e10	−0.491897
$267$	3.31974e10	0.399764
$268$	−3.72621e10	−0.441226
$269$	8.02007e10	0.933884	0.466942	−	0.884288i	$-0.345356\pi$
$269$	8.02007e10	0.933884	0.466942	+	0.884288i	$0.345356\pi$
$270$	−2.52923e10	−0.289635
$271$	−5.88345e10	−0.662629	−0.331314	−	0.943520i	$-0.607492\pi$
$271$	−5.88345e10	−0.662629	−0.331314	+	0.943520i	$0.607492\pi$
$272$	9.06602e8	0.0100428
$273$	1.47441e11	1.60652
$274$	9.38022e10	1.00539
$275$	0	0
$276$	−1.33623e9	−0.0138608
$277$	5.27203e10	0.538045	0.269023	−	0.963134i	$-0.413299\pi$
$277$	5.27203e10	0.538045	0.269023	+	0.963134i	$0.413299\pi$
$278$	−7.03295e10	−0.706214
$279$	−2.77433e10	−0.274119
$280$	1.00044e11	0.972701
$281$	1.29483e11	1.23889	0.619447	−	0.785038i	$-0.287357\pi$
$281$	1.29483e11	1.23889	0.619447	+	0.785038i	$0.287357\pi$
$282$	−1.57946e10	−0.148726
$283$	−1.51762e10	−0.140645	−0.0703225	−	0.997524i	$-0.522403\pi$
$283$	−1.51762e10	−0.140645	−0.0703225	+	0.997524i	$0.522403\pi$
$284$	−4.86997e10	−0.444215
$285$	−1.34796e10	−0.121025
$286$	0	0
$287$	1.30029e11	1.13128
$288$	−8.94084e10	−0.765794
$289$	−4.93142e10	−0.415845
$290$	6.50930e10	0.540435
$291$	1.95194e10	0.159568
$292$	−7.86840e10	−0.633379
$293$	2.13791e11	1.69467	0.847336	−	0.531058i	$-0.178205\pi$
$293$	2.13791e11	1.69467	0.847336	+	0.531058i	$0.178205\pi$
$294$	−8.23722e10	−0.643010
$295$	4.51057e10	0.346763
$296$	−9.54801e10	−0.722937
$297$	0	0
$298$	−3.83761e10	−0.281895
$299$	1.17109e10	0.0847364
$300$	−2.97319e10	−0.211923
$301$	8.83573e10	0.620431
$302$	8.50762e9	0.0588541
$303$	6.06603e10	0.413440
$304$	−8.83894e8	−0.00593566
$305$	−8.35276e10	−0.552689
$306$	−5.48359e10	−0.357535
$307$	1.51741e11	0.974947	0.487473	−	0.873138i	$-0.337919\pi$
$307$	1.51741e11	0.974947	0.487473	+	0.873138i	$0.337919\pi$
$308$	0	0
$309$	9.09536e10	0.567554
$310$	−1.97127e10	−0.121232
$311$	−2.16783e9	−0.0131402	−0.00657012	−	0.999978i	$-0.502091\pi$
$311$	−2.16783e9	−0.0131402	−0.00657012	+	0.999978i	$0.502091\pi$
$312$	−1.50817e11	−0.901062
$313$	1.48160e10	0.0872535	0.0436267	−	0.999048i	$-0.486109\pi$
$313$	1.48160e10	0.0872535	0.0436267	+	0.999048i	$0.486109\pi$
$314$	7.10966e10	0.412729
$315$	1.30186e11	0.745018
$316$	−1.76483e10	−0.0995662
$317$	2.52933e11	1.40682	0.703412	−	0.710783i	$-0.251659\pi$
$317$	2.52933e11	1.40682	0.703412	+	0.710783i	$0.251659\pi$
$318$	−5.67887e10	−0.311415
$319$	0	0
$320$	−6.21723e10	−0.331453
$321$	−3.29252e10	−0.173083
$322$	−9.58190e9	−0.0496707
$323$	−6.75387e10	−0.345256
$324$	−4.26480e10	−0.215004
$325$	2.60575e11	1.29556
$326$	−1.88685e11	−0.925248
$327$	−6.40120e10	−0.309597
$328$	−1.33007e11	−0.634514
$329$	1.87881e11	0.884099
$330$	0	0
$331$	−3.45634e11	−1.58267	−0.791336	−	0.611382i	$-0.790614\pi$
$331$	−3.45634e11	−1.58267	−0.791336	+	0.611382i	$0.790614\pi$
$332$	−1.18171e11	−0.533816
$333$	−1.24247e11	−0.553716
$334$	−1.24990e11	−0.549560
$335$	−8.96758e10	−0.389021
$336$	−2.65483e9	−0.0113635
$337$	2.92919e11	1.23712	0.618561	−	0.785737i	$-0.287716\pi$
$337$	2.92919e11	1.23712	0.618561	+	0.785737i	$0.287716\pi$
$338$	3.60668e11	1.50308
$339$	−3.99537e10	−0.164308
$340$	6.46330e10	0.262301
$341$	0	0
$342$	5.34624e10	0.211315
$343$	5.24676e11	2.04677
$344$	−9.03807e10	−0.347987
$345$	−3.21579e9	−0.0122209
$346$	3.67668e10	0.137916
$347$	−4.33381e11	−1.60468	−0.802338	−	0.596870i	$-0.796411\pi$
$347$	−4.33381e11	−1.60468	−0.802338	+	0.596870i	$0.796411\pi$
$348$	−1.33186e11	−0.486801
$349$	−4.58324e11	−1.65371	−0.826853	−	0.562417i	$-0.809871\pi$
$349$	−4.58324e11	−1.65371	−0.826853	+	0.562417i	$0.809871\pi$
$350$	−2.13204e11	−0.759432
$351$	−4.53547e11	−1.59493
$352$	0	0
$353$	−1.21912e11	−0.417888	−0.208944	−	0.977928i	$-0.567003\pi$
$353$	−1.21912e11	−0.417888	−0.208944	+	0.977928i	$0.567003\pi$
$354$	5.56356e10	0.188295
$355$	−1.17202e11	−0.391657
$356$	1.55191e11	0.512083
$357$	−2.02857e11	−0.660970
$358$	4.35648e10	0.140172
$359$	2.40212e11	0.763255	0.381627	−	0.924316i	$-0.375364\pi$
$359$	2.40212e11	0.763255	0.381627	+	0.924316i	$0.375364\pi$
$360$	−1.33167e11	−0.417865
$361$	−2.56841e11	−0.795942
$362$	−3.68672e10	−0.112837
$363$	0	0
$364$	6.89252e11	2.05789
$365$	−1.89363e11	−0.558440
$366$	−1.03027e11	−0.300114
$367$	5.38647e11	1.54991	0.774956	−	0.632016i	$-0.217772\pi$
$367$	5.38647e11	1.54991	0.774956	+	0.632016i	$0.217772\pi$
$368$	−2.10868e8	−0.000599370 0
$369$	−1.73080e11	−0.485991
$370$	−8.82823e10	−0.244887
$371$	6.75516e11	1.85120
$372$	4.03338e10	0.109201
$373$	−2.43275e11	−0.650741	−0.325371	−	0.945587i	$-0.605489\pi$
$373$	−2.43275e11	−0.650741	−0.325371	+	0.945587i	$0.605489\pi$
$374$	0	0
$375$	−1.74152e11	−0.454765
$376$	−1.92183e11	−0.495873
$377$	1.16726e12	2.97599
$378$	3.71094e11	0.934912
$379$	−2.90138e11	−0.722317	−0.361159	−	0.932504i	$-0.617619\pi$
$379$	−2.90138e11	−0.722317	−0.361159	+	0.932504i	$0.617619\pi$
$380$	−6.30142e10	−0.155029
$381$	−3.10149e10	−0.0754063
$382$	−1.29325e11	−0.310740
$383$	5.63325e11	1.33772	0.668859	−	0.743389i	$-0.266783\pi$
$383$	5.63325e11	1.33772	0.668859	+	0.743389i	$0.266783\pi$
$384$	1.31656e11	0.308994
$385$	0	0
$386$	−4.38649e10	−0.100571
$387$	−1.17611e11	−0.266532
$388$	9.12486e10	0.204401
$389$	−6.36994e11	−1.41047	−0.705233	−	0.708976i	$-0.749157\pi$
$389$	−6.36994e11	−1.41047	−0.705233	+	0.708976i	$0.749157\pi$
$390$	−1.39448e11	−0.305225
$391$	−1.61125e10	−0.0348632
$392$	−1.00228e12	−2.14388
$393$	−1.26286e11	−0.267047
$394$	−3.15745e11	−0.660090
$395$	−4.24728e10	−0.0877858
$396$	0	0
$397$	−2.58745e10	−0.0522775	−0.0261387	−	0.999658i	$-0.508321\pi$
$397$	−2.58745e10	−0.0522775	−0.0261387	+	0.999658i	$0.508321\pi$
$398$	1.52657e11	0.304959
$399$	1.97776e11	0.390656
$400$	−4.69195e9	−0.00916397
$401$	−3.00445e11	−0.580250	−0.290125	−	0.956989i	$-0.593697\pi$
$401$	−3.00445e11	−0.580250	−0.290125	+	0.956989i	$0.593697\pi$
$402$	−1.10611e11	−0.211242
$403$	−3.53492e11	−0.667586
$404$	2.83573e11	0.529602
$405$	−1.02637e11	−0.189565
$406$	−9.55058e11	−1.74447
$407$	0	0
$408$	2.07502e11	0.370725
$409$	−1.50133e11	−0.265291	−0.132646	−	0.991164i	$-0.542347\pi$
$409$	−1.50133e11	−0.265291	−0.132646	+	0.991164i	$0.542347\pi$
$410$	−1.22980e11	−0.214935
$411$	−4.61896e11	−0.798465
$412$	4.25188e11	0.727015
$413$	−6.61800e11	−1.11931
$414$	1.27544e10	0.0213382
$415$	−2.84394e11	−0.470656
$416$	−1.13920e12	−1.86500
$417$	3.46313e11	0.560863
$418$	0	0
$419$	1.81835e11	0.288213	0.144107	−	0.989562i	$-0.453969\pi$
$419$	1.81835e11	0.288213	0.144107	+	0.989562i	$0.453969\pi$
$420$	−1.89267e11	−0.296793
$421$	6.03517e10	0.0936310	0.0468155	−	0.998904i	$-0.485093\pi$
$421$	6.03517e10	0.0936310	0.0468155	+	0.998904i	$0.485093\pi$
$422$	−1.28875e11	−0.197817
$423$	−2.50086e11	−0.379802
$424$	−6.90986e11	−1.03830
$425$	−3.58513e11	−0.533034
$426$	−1.44562e11	−0.212673
$427$	1.22553e12	1.78402
$428$	−1.53918e11	−0.221713
$429$	0	0
$430$	−8.35674e10	−0.117877
$431$	1.07701e12	1.50340	0.751699	−	0.659507i	$-0.229235\pi$
$431$	1.07701e12	1.50340	0.751699	+	0.659507i	$0.229235\pi$
$432$	8.16662e9	0.0112815
$433$	2.88525e11	0.394447	0.197223	−	0.980359i	$-0.436808\pi$
$433$	2.88525e11	0.394447	0.197223	+	0.980359i	$0.436808\pi$
$434$	2.89229e11	0.391325
$435$	−3.20528e11	−0.429204
$436$	−2.99242e11	−0.396582
$437$	1.57089e10	0.0206053
$438$	−2.33569e11	−0.303237
$439$	−6.95114e11	−0.893235	−0.446618	−	0.894725i	$-0.647372\pi$
$439$	−6.95114e11	−0.893235	−0.446618	+	0.894725i	$0.647372\pi$
$440$	0	0
$441$	−1.30425e12	−1.64206
$442$	−6.98692e11	−0.870735
$443$	3.03242e11	0.374087	0.187043	−	0.982352i	$-0.440109\pi$
$443$	3.03242e11	0.374087	0.187043	+	0.982352i	$0.440109\pi$
$444$	1.80633e11	0.220584
$445$	3.73485e11	0.451495
$446$	8.76115e11	1.04847
$447$	1.88969e11	0.223876
$448$	9.12205e11	1.06990
$449$	4.65136e11	0.540096	0.270048	−	0.962847i	$-0.412960\pi$
$449$	4.65136e11	0.540096	0.270048	+	0.962847i	$0.412960\pi$
$450$	2.83793e11	0.326246
$451$	0	0
$452$	−1.86775e11	−0.210472
$453$	−4.18928e10	−0.0467409
$454$	8.62487e11	0.952798
$455$	1.65877e12	1.81440
$456$	−2.02305e11	−0.219111
$457$	1.19905e12	1.28593	0.642963	−	0.765897i	$-0.277705\pi$
$457$	1.19905e12	1.28593	0.642963	+	0.765897i	$0.277705\pi$
$458$	5.82609e11	0.618703
$459$	6.24014e11	0.656202
$460$	−1.50331e10	−0.0156545
$461$	2.79855e11	0.288589	0.144294	−	0.989535i	$-0.453909\pi$
$461$	2.79855e11	0.288589	0.144294	+	0.989535i	$0.453909\pi$
$462$	0	0
$463$	1.56289e12	1.58057	0.790284	−	0.612741i	$-0.209933\pi$
$463$	1.56289e12	1.58057	0.790284	+	0.612741i	$0.209933\pi$
$464$	−2.10178e10	−0.0210503
$465$	9.70682e10	0.0962806
$466$	1.65042e11	0.162127
$467$	−1.02384e12	−0.996109	−0.498054	−	0.867146i	$-0.665952\pi$
$467$	−1.02384e12	−0.996109	−0.498054	+	0.867146i	$0.665952\pi$
$468$	−9.17455e11	−0.884053
$469$	1.31574e12	1.25572
$470$	−1.77696e11	−0.167972
$471$	−3.50090e11	−0.327782
$472$	6.76955e11	0.627800
$473$	0	0
$474$	−5.23881e10	−0.0476683
$475$	3.49534e11	0.315042
$476$	−9.48309e11	−0.846678
$477$	−8.99172e11	−0.795262
$478$	−4.88835e11	−0.428289
$479$	1.23559e12	1.07242	0.536208	−	0.844086i	$-0.319856\pi$
$479$	1.23559e12	1.07242	0.536208	+	0.844086i	$0.319856\pi$
$480$	3.12822e11	0.268975
$481$	−1.58310e12	−1.34851
$482$	−3.47205e11	−0.293005
$483$	4.71827e10	0.0394476
$484$	0	0
$485$	2.19601e11	0.180217
$486$	−7.74175e11	−0.629471
$487$	−6.29197e11	−0.506881	−0.253441	−	0.967351i	$-0.581562\pi$
$487$	−6.29197e11	−0.506881	−0.253441	+	0.967351i	$0.581562\pi$
$488$	−1.25360e12	−1.00062
$489$	9.29113e11	0.734816
$490$	−9.26721e11	−0.726217
$491$	1.63049e12	1.26605	0.633025	−	0.774132i	$-0.281813\pi$
$491$	1.63049e12	1.26605	0.633025	+	0.774132i	$0.281813\pi$
$492$	2.51627e11	0.193604
$493$	−1.60598e12	−1.22442
$494$	6.81193e11	0.514634
$495$	0	0
$496$	6.36502e9	0.00472207
$497$	1.71960e12	1.26423
$498$	−3.50785e11	−0.255570
$499$	−6.91033e11	−0.498938	−0.249469	−	0.968383i	$-0.580256\pi$
$499$	−6.91033e11	−0.498938	−0.249469	+	0.968383i	$0.580256\pi$
$500$	−8.14120e11	−0.582537
$501$	6.15468e11	0.436451
$502$	−1.15558e12	−0.812146
$503$	−9.17643e11	−0.639172	−0.319586	−	0.947557i	$-0.603544\pi$
$503$	−9.17643e11	−0.639172	−0.319586	+	0.947557i	$0.603544\pi$
$504$	1.95386e12	1.34882
$505$	6.82453e11	0.466941
$506$	0	0
$507$	−1.77598e12	−1.19372
$508$	−1.44988e11	−0.0965926
$509$	−2.69346e12	−1.77861	−0.889306	−	0.457313i	$-0.848812\pi$
$509$	−2.69346e12	−1.77861	−0.889306	+	0.457313i	$0.848812\pi$
$510$	1.91860e11	0.125579
$511$	2.77837e12	1.80258
$512$	4.08605e10	0.0262778
$513$	−6.08385e11	−0.387838
$514$	−6.75681e11	−0.426980
$515$	1.02327e12	0.640997
$516$	1.70986e11	0.106179
$517$	0	0
$518$	1.29530e12	0.790470
$519$	−1.81045e11	−0.109530
$520$	−1.69675e12	−1.01766
$521$	−1.07054e12	−0.636550	−0.318275	−	0.947999i	$-0.603103\pi$
$521$	−1.07054e12	−0.636550	−0.318275	+	0.947999i	$0.603103\pi$
$522$	1.27127e12	0.749410
$523$	2.01115e12	1.17540	0.587701	−	0.809078i	$-0.300033\pi$
$523$	2.01115e12	1.17540	0.587701	+	0.809078i	$0.300033\pi$
$524$	−5.90357e11	−0.342077
$525$	1.04985e12	0.603127
$526$	1.94128e12	1.10574
$527$	4.86353e11	0.274665
$528$	0	0
$529$	−1.79741e12	−0.997919
$530$	−6.38896e11	−0.351713
$531$	8.80914e11	0.480848
$532$	9.24557e11	0.500416
$533$	−2.20530e12	−1.18357
$534$	4.60675e11	0.245165
$535$	−3.70422e11	−0.195481
$536$	−1.34587e12	−0.704307
$537$	−2.14519e11	−0.111322
$538$	1.11293e12	0.572727
$539$	0	0
$540$	5.82211e11	0.294652
$541$	−2.72255e12	−1.36643	−0.683217	−	0.730215i	$-0.739420\pi$
$541$	−2.72255e12	−1.36643	−0.683217	+	0.730215i	$0.739420\pi$
$542$	−8.16435e11	−0.406373
$543$	1.81540e11	0.0896133
$544$	1.56737e12	0.767320
$545$	−7.20161e11	−0.349660
$546$	2.04600e12	0.985235
$547$	−8.69202e10	−0.0415124	−0.0207562	−	0.999785i	$-0.506607\pi$
$547$	−8.69202e10	−0.0415124	−0.0207562	+	0.999785i	$0.506607\pi$
$548$	−2.15926e12	−1.02280
$549$	−1.63129e12	−0.766402
$550$	0	0
$551$	1.56576e12	0.723672
$552$	−4.82632e10	−0.0221254
$553$	6.23170e11	0.283363
$554$	7.31589e11	0.329969
$555$	4.34715e11	0.194485
$556$	1.61894e12	0.718444
$557$	2.89783e12	1.27563	0.637815	−	0.770190i	$-0.279838\pi$
$557$	2.89783e12	1.27563	0.637815	+	0.770190i	$0.279838\pi$
$558$	−3.84989e11	−0.168110
$559$	−1.49855e12	−0.649109
$560$	−2.98679e10	−0.0128339
$561$	0	0
$562$	1.79681e12	0.759782
$563$	4.95036e11	0.207658	0.103829	−	0.994595i	$-0.466890\pi$
$563$	4.95036e11	0.207658	0.103829	+	0.994595i	$0.466890\pi$
$564$	3.63580e11	0.151302
$565$	−4.49496e11	−0.185570
$566$	−2.10597e11	−0.0862539
$567$	1.50592e12	0.611895
$568$	−1.75898e12	−0.709079
$569$	3.73556e12	1.49400	0.747001	−	0.664823i	$-0.231493\pi$
$569$	3.73556e12	1.49400	0.747001	+	0.664823i	$0.231493\pi$
$570$	−1.87054e11	−0.0742216
$571$	3.67472e12	1.44665	0.723323	−	0.690510i	$-0.242614\pi$
$571$	3.67472e12	1.44665	0.723323	+	0.690510i	$0.242614\pi$
$572$	0	0
$573$	6.36815e11	0.246784
$574$	1.80439e12	0.693787
$575$	8.33872e10	0.0318122
$576$	−1.21422e12	−0.459619
$577$	3.03109e12	1.13843	0.569216	−	0.822188i	$-0.307247\pi$
$577$	3.03109e12	1.13843	0.569216	+	0.822188i	$0.307247\pi$
$578$	−6.84323e11	−0.255027
$579$	2.15997e11	0.0798720
$580$	−1.49839e12	−0.549794
$581$	4.17268e12	1.51923
$582$	2.70866e11	0.0978592
$583$	0	0
$584$	−2.84199e12	−1.01103
$585$	−2.20796e12	−0.779454
$586$	2.96674e12	1.03930
$587$	−1.02429e12	−0.356082	−0.178041	−	0.984023i	$-0.556976\pi$
$587$	−1.02429e12	−0.356082	−0.178041	+	0.984023i	$0.556976\pi$
$588$	1.89615e12	0.654146
$589$	−4.74172e11	−0.162337
$590$	6.25923e11	0.212661
$591$	1.55477e12	0.524232
$592$	2.85054e10	0.00953850
$593$	2.72056e12	0.903466	0.451733	−	0.892153i	$-0.350806\pi$
$593$	2.72056e12	0.903466	0.451733	+	0.892153i	$0.350806\pi$
$594$	0	0
$595$	−2.28222e12	−0.746502
$596$	8.83389e11	0.286777
$597$	−7.51704e11	−0.242193
$598$	1.62510e11	0.0519666
$599$	−2.57228e12	−0.816390	−0.408195	−	0.912895i	$-0.633842\pi$
$599$	−2.57228e12	−0.816390	−0.408195	+	0.912895i	$0.633842\pi$
$600$	−1.07389e12	−0.338282
$601$	−3.89797e12	−1.21872	−0.609360	−	0.792894i	$-0.708573\pi$
$601$	−3.89797e12	−1.21872	−0.609360	+	0.792894i	$0.708573\pi$
$602$	1.22612e12	0.380494
$603$	−1.75137e12	−0.539448
$604$	−1.95839e11	−0.0598734
$605$	0	0
$606$	8.41772e11	0.253552
$607$	9.22491e11	0.275812	0.137906	−	0.990445i	$-0.455963\pi$
$607$	9.22491e11	0.275812	0.137906	+	0.990445i	$0.455963\pi$
$608$	−1.52811e12	−0.453513
$609$	4.70285e12	1.38542
$610$	−1.15910e12	−0.338950
$611$	−3.18648e12	−0.924965
$612$	1.26228e12	0.363727
$613$	3.33932e11	0.0955181	0.0477591	−	0.998859i	$-0.484792\pi$
$613$	3.33932e11	0.0955181	0.0477591	+	0.998859i	$0.484792\pi$
$614$	2.10568e12	0.597909
$615$	6.05572e11	0.170698
$616$	0	0
$617$	−6.48062e10	−0.0180025	−0.00900126	−	0.999959i	$-0.502865\pi$
$617$	−6.48062e10	−0.0180025	−0.00900126	+	0.999959i	$0.502865\pi$
$618$	1.26215e12	0.348066
$619$	−3.31283e12	−0.906967	−0.453484	−	0.891265i	$-0.649819\pi$
$619$	−3.31283e12	−0.906967	−0.453484	+	0.891265i	$0.649819\pi$
$620$	4.53772e11	0.123332
$621$	−1.45140e11	−0.0391630
$622$	−3.00825e10	−0.00805856
$623$	−5.47984e12	−1.45738
$624$	4.50262e10	0.0118887
$625$	7.01149e11	0.183802
$626$	2.05599e11	0.0535103
$627$	0	0
$628$	−1.63659e12	−0.419877
$629$	2.17811e12	0.554820
$630$	1.80656e12	0.456900
$631$	−5.35257e12	−1.34410	−0.672048	−	0.740507i	$-0.734585\pi$
$631$	−5.35257e12	−1.34410	−0.672048	+	0.740507i	$0.734585\pi$
$632$	−6.37440e11	−0.158933
$633$	6.34602e11	0.157103
$634$	3.50991e12	0.862768
$635$	−3.48930e11	−0.0851641
$636$	1.30724e12	0.316809
$637$	−1.66182e13	−3.99904
$638$	0	0
$639$	−2.28895e12	−0.543102
$640$	1.48119e12	0.348979
$641$	7.61469e12	1.78152	0.890761	−	0.454473i	$-0.150172\pi$
$641$	7.61469e12	1.78152	0.890761	+	0.454473i	$0.150172\pi$
$642$	−4.56896e11	−0.106148
$643$	−2.65473e12	−0.612450	−0.306225	−	0.951959i	$-0.599066\pi$
$643$	−2.65473e12	−0.612450	−0.306225	+	0.951959i	$0.599066\pi$
$644$	2.20569e11	0.0505309
$645$	4.11498e11	0.0936158
$646$	−9.37221e11	−0.211736
$647$	−6.98331e12	−1.56672	−0.783361	−	0.621567i	$-0.786496\pi$
$647$	−6.98331e12	−1.56672	−0.783361	+	0.621567i	$0.786496\pi$
$648$	−1.54040e12	−0.343200
$649$	0	0
$650$	3.61595e12	0.794535
$651$	−1.42420e12	−0.310783
$652$	4.34340e12	0.941272
$653$	7.33087e12	1.57778	0.788889	−	0.614536i	$-0.210657\pi$
$653$	7.33087e12	1.57778	0.788889	+	0.614536i	$0.210657\pi$
$654$	−8.88283e11	−0.189868
$655$	−1.42077e12	−0.301604
$656$	3.97089e10	0.00837184
$657$	−3.69825e12	−0.774376
$658$	2.60719e12	0.542195
$659$	4.71087e12	0.973009	0.486505	−	0.873678i	$-0.338272\pi$
$659$	4.71087e12	0.973009	0.486505	+	0.873678i	$0.338272\pi$
$660$	0	0
$661$	4.41493e12	0.899533	0.449767	−	0.893146i	$-0.351507\pi$
$661$	4.41493e12	0.899533	0.449767	+	0.893146i	$0.351507\pi$
$662$	−4.79630e12	−0.970611
$663$	3.44047e12	0.691522
$664$	−4.26824e12	−0.852103
$665$	2.22506e12	0.441208
$666$	−1.72415e12	−0.339580
$667$	3.73537e11	0.0730748
$668$	2.87718e12	0.559078
$669$	−4.31412e12	−0.832673
$670$	−1.24441e12	−0.238577
$671$	0	0
$672$	−4.58978e12	−0.868221
$673$	−1.63808e12	−0.307798	−0.153899	−	0.988087i	$-0.549183\pi$
$673$	−1.63808e12	−0.307798	−0.153899	+	0.988087i	$0.549183\pi$
$674$	4.06478e12	0.758695
$675$	−3.22947e12	−0.598776
$676$	−8.30233e12	−1.52911
$677$	−3.20440e12	−0.586270	−0.293135	−	0.956071i	$-0.594698\pi$
$677$	−3.20440e12	−0.586270	−0.293135	+	0.956071i	$0.594698\pi$
$678$	−5.54430e11	−0.100766
$679$	−3.22203e12	−0.581721
$680$	2.33448e12	0.418698
$681$	−4.24701e12	−0.756696
$682$	0	0
$683$	1.07312e13	1.88693	0.943466	−	0.331470i	$-0.107545\pi$
$683$	1.07312e13	1.88693	0.943466	+	0.331470i	$0.107545\pi$
$684$	−1.23067e12	−0.214975
$685$	−5.19652e12	−0.901789
$686$	7.28083e12	1.25523
$687$	−2.86885e12	−0.491363
$688$	2.69830e10	0.00459137
$689$	−1.14568e13	−1.93677
$690$	−4.46249e10	−0.00749474
$691$	−4.16657e12	−0.695229	−0.347614	−	0.937638i	$-0.613008\pi$
$691$	−4.16657e12	−0.695229	−0.347614	+	0.937638i	$0.613008\pi$
$692$	−8.46346e11	−0.140304
$693$	0	0
$694$	−6.01395e12	−0.984106
$695$	3.89616e12	0.633440
$696$	−4.81054e12	−0.777056
$697$	3.03417e12	0.486959
$698$	−6.36008e12	−1.01418
$699$	−8.12689e11	−0.128759
$700$	4.90780e12	0.772584
$701$	−6.26352e12	−0.979687	−0.489843	−	0.871810i	$-0.662946\pi$
$701$	−6.26352e12	−0.979687	−0.489843	+	0.871810i	$0.662946\pi$
$702$	−6.29379e12	−0.978126
$703$	−2.12356e12	−0.327918
$704$	0	0
$705$	8.75000e11	0.133400
$706$	−1.69175e12	−0.256280
$707$	−1.00131e13	−1.50723
$708$	−1.28069e12	−0.191556
$709$	−3.53915e12	−0.526006	−0.263003	−	0.964795i	$-0.584713\pi$
$709$	−3.53915e12	−0.526006	−0.263003	+	0.964795i	$0.584713\pi$
$710$	−1.62638e12	−0.240193
$711$	−8.29494e11	−0.121731
$712$	5.60533e12	0.817413
$713$	−1.13122e11	−0.0163924
$714$	−2.81500e12	−0.405356
$715$	0	0
$716$	−1.00283e12	−0.142600
$717$	2.40710e12	0.340140
$718$	3.33337e12	0.468084
$719$	7.43884e11	0.103807	0.0519033	−	0.998652i	$-0.483471\pi$
$719$	7.43884e11	0.103807	0.0519033	+	0.998652i	$0.483471\pi$
$720$	3.97569e10	0.00551335
$721$	−1.50136e13	−2.06907
$722$	−3.56413e12	−0.488130
$723$	1.70969e12	0.232699
$724$	8.48658e11	0.114791
$725$	8.31146e12	1.11726
$726$	0	0
$727$	−7.69490e11	−0.102164	−0.0510820	−	0.998694i	$-0.516267\pi$
$727$	−7.69490e11	−0.102164	−0.0510820	+	0.998694i	$0.516267\pi$
$728$	2.48951e13	3.28490
$729$	1.18425e12	0.155300
$730$	−2.62775e12	−0.342477
$731$	2.06178e12	0.267063
$732$	2.37161e12	0.305312
$733$	7.31027e12	0.935331	0.467666	−	0.883905i	$-0.345095\pi$
$733$	7.31027e12	0.935331	0.467666	+	0.883905i	$0.345095\pi$
$734$	7.47470e12	0.950520
$735$	4.56331e12	0.576749
$736$	−3.64557e11	−0.0457947
$737$	0	0
$738$	−2.40180e12	−0.298046
$739$	−1.50006e13	−1.85016	−0.925078	−	0.379778i	$-0.876000\pi$
$739$	−1.50006e13	−1.85016	−0.925078	+	0.379778i	$0.876000\pi$
$740$	2.03220e12	0.249128
$741$	−3.35429e12	−0.408714
$742$	9.37401e12	1.13529
$743$	2.70788e11	0.0325971	0.0162986	−	0.999867i	$-0.494812\pi$
$743$	2.70788e11	0.0325971	0.0162986	+	0.999867i	$0.494812\pi$
$744$	1.45682e12	0.174312
$745$	2.12598e12	0.252846
$746$	−3.37588e12	−0.399083
$747$	−5.55421e12	−0.652649
$748$	0	0
$749$	5.43490e12	0.630991
$750$	−2.41667e12	−0.278895
$751$	1.21944e13	1.39888	0.699438	−	0.714693i	$-0.253434\pi$
$751$	1.21944e13	1.39888	0.699438	+	0.714693i	$0.253434\pi$
$752$	5.73760e10	0.00654260
$753$	5.69026e12	0.644992
$754$	1.61979e13	1.82510
$755$	−4.71311e11	−0.0527893
$756$	−8.54232e12	−0.951103
$757$	3.63171e11	0.0401957	0.0200979	−	0.999798i	$-0.493602\pi$
$757$	3.63171e11	0.0401957	0.0200979	+	0.999798i	$0.493602\pi$
$758$	−4.02619e12	−0.442978
$759$	0	0
$760$	−2.27601e12	−0.247465
$761$	−7.27502e12	−0.786327	−0.393163	−	0.919469i	$-0.628619\pi$
$761$	−7.27502e12	−0.786327	−0.393163	+	0.919469i	$0.628619\pi$
$762$	−4.30387e11	−0.0462447
$763$	1.05664e13	1.12866
$764$	2.97697e12	0.316121
$765$	3.03783e12	0.320692
$766$	7.81716e12	0.820388
$767$	1.12242e13	1.17105
$768$	4.65640e12	0.482975
$769$	1.18338e13	1.22027	0.610134	−	0.792298i	$-0.291116\pi$
$769$	1.18338e13	1.22027	0.610134	+	0.792298i	$0.291116\pi$
$770$	0	0
$771$	3.32715e12	0.339100
$772$	1.00974e12	0.102313
$773$	−1.01635e13	−1.02385	−0.511926	−	0.859030i	$-0.671068\pi$
$773$	−1.01635e13	−1.02385	−0.511926	+	0.859030i	$0.671068\pi$
$774$	−1.63207e12	−0.163457
$775$	−2.51703e12	−0.250629
$776$	3.29581e12	0.326276
$777$	−6.37823e12	−0.627777
$778$	−8.83945e12	−0.865002
$779$	−2.95818e12	−0.287810
$780$	3.20999e12	0.310511
$781$	0	0
$782$	−2.23590e11	−0.0213807
$783$	−1.44666e13	−1.37543
$784$	2.99228e11	0.0282866
$785$	−3.93865e12	−0.370198
$786$	−1.75244e12	−0.163773
$787$	6.02245e12	0.559612	0.279806	−	0.960057i	$-0.409730\pi$
$787$	6.02245e12	0.559612	0.279806	+	0.960057i	$0.409730\pi$
$788$	7.26822e12	0.671522
$789$	−9.55916e12	−0.878160
$790$	−5.89387e11	−0.0538367
$791$	6.59509e12	0.599000
$792$	0	0
$793$	−2.07852e13	−1.86648
$794$	−3.59055e11	−0.0320604
$795$	3.14602e12	0.279325
$796$	−3.51405e12	−0.310241
$797$	−1.04447e13	−0.916926	−0.458463	−	0.888713i	$-0.651600\pi$
$797$	−1.04447e13	−0.916926	−0.458463	+	0.888713i	$0.651600\pi$
$798$	2.74450e12	0.239579
$799$	4.38412e12	0.380559
$800$	−8.11164e12	−0.700170
$801$	7.29416e12	0.626078
$802$	−4.16922e12	−0.355852
$803$	0	0
$804$	2.54618e12	0.214900
$805$	5.30825e11	0.0445523
$806$	−4.90534e12	−0.409413
$807$	−5.48023e12	−0.454850
$808$	1.02424e13	0.845377
$809$	1.58004e12	0.129688	0.0648442	−	0.997895i	$-0.479345\pi$
$809$	1.58004e12	0.129688	0.0648442	+	0.997895i	$0.479345\pi$
$810$	−1.42428e12	−0.116255
$811$	1.15277e13	0.935730	0.467865	−	0.883800i	$-0.345023\pi$
$811$	1.15277e13	0.935730	0.467865	+	0.883800i	$0.345023\pi$
$812$	2.19847e13	1.77468
$813$	4.02025e12	0.322734
$814$	0	0
$815$	1.04529e13	0.829903
$816$	−6.19494e10	−0.00489138
$817$	−2.01014e12	−0.157844
$818$	−2.08337e12	−0.162696
$819$	3.23957e13	2.51599
$820$	2.83091e12	0.218657
$821$	8.50850e11	0.0653595	0.0326797	−	0.999466i	$-0.489596\pi$
$821$	8.50850e11	0.0653595	0.0326797	+	0.999466i	$0.489596\pi$
$822$	−6.40964e12	−0.489678
$823$	1.33769e13	1.01638	0.508189	−	0.861246i	$-0.330315\pi$
$823$	1.33769e13	1.01638	0.508189	+	0.861246i	$0.330315\pi$
$824$	1.53574e13	1.16050
$825$	0	0
$826$	−9.18367e12	−0.686445
$827$	2.51389e13	1.86883	0.934417	−	0.356180i	$-0.115921\pi$
$827$	2.51389e13	1.86883	0.934417	+	0.356180i	$0.115921\pi$
$828$	−2.93596e11	−0.0217077
$829$	−1.46242e13	−1.07542	−0.537708	−	0.843131i	$-0.680710\pi$
$829$	−1.46242e13	−1.07542	−0.537708	+	0.843131i	$0.680710\pi$
$830$	−3.94648e12	−0.288641
$831$	−3.60245e12	−0.262056
$832$	−1.54711e13	−1.11935
$833$	2.28641e13	1.64533
$834$	4.80572e12	0.343963
$835$	6.92427e12	0.492929
$836$	0	0
$837$	4.38104e12	0.308541
$838$	2.52329e12	0.176754
$839$	−1.58896e13	−1.10710	−0.553548	−	0.832817i	$-0.686726\pi$
$839$	−1.58896e13	−1.10710	−0.553548	+	0.832817i	$0.686726\pi$
$840$	−6.83614e12	−0.473756
$841$	2.27245e13	1.56643
$842$	8.37488e11	0.0574215
$843$	−8.84776e12	−0.603406
$844$	2.96662e12	0.201243
$845$	−1.99805e13	−1.34819
$846$	−3.47039e12	−0.232923
$847$	0	0
$848$	2.06293e11	0.0136994
$849$	1.03701e12	0.0685014
$850$	−4.97502e12	−0.326896
$851$	−5.06610e11	−0.0331124
$852$	3.32772e12	0.216356
$853$	−1.24747e13	−0.806786	−0.403393	−	0.915027i	$-0.632169\pi$
$853$	−1.24747e13	−0.806786	−0.403393	+	0.915027i	$0.632169\pi$
$854$	1.70065e13	1.09409
$855$	−2.96175e12	−0.189540
$856$	−5.55936e12	−0.353910
$857$	2.79236e13	1.76830	0.884152	−	0.467199i	$-0.154737\pi$
$857$	2.79236e13	1.76830	0.884152	+	0.467199i	$0.154737\pi$
$858$	0	0
$859$	6.50558e12	0.407678	0.203839	−	0.979004i	$-0.434658\pi$
$859$	6.50558e12	0.407678	0.203839	+	0.979004i	$0.434658\pi$
$860$	1.92366e12	0.119918
$861$	−8.88507e12	−0.550994
$862$	1.49455e13	0.921995
$863$	−2.30774e13	−1.41625	−0.708123	−	0.706089i	$-0.750458\pi$
$863$	−2.30774e13	−1.41625	−0.708123	+	0.706089i	$0.750458\pi$
$864$	1.41188e13	0.861957
$865$	−2.03683e12	−0.123704
$866$	4.00381e12	0.241904
$867$	3.36971e12	0.202538
$868$	−6.65783e12	−0.398102
$869$	0	0
$870$	−4.44790e12	−0.263220
$871$	−2.23151e13	−1.31376
$872$	−1.08083e13	−0.633044
$873$	4.28880e12	0.249903
$874$	2.17990e11	0.0126367
$875$	2.87469e13	1.65789
$876$	5.37660e12	0.308488
$877$	−2.61610e13	−1.49333	−0.746666	−	0.665199i	$-0.768347\pi$
$877$	−2.61610e13	−1.49333	−0.746666	+	0.665199i	$0.768347\pi$
$878$	−9.64596e12	−0.547798
$879$	−1.46087e13	−0.825392
$880$	0	0
$881$	2.89685e13	1.62007	0.810037	−	0.586379i	$-0.199447\pi$
$881$	2.89685e13	1.62007	0.810037	+	0.586379i	$0.199447\pi$
$882$	−1.80989e13	−1.00703
$883$	1.43673e13	0.795336	0.397668	−	0.917529i	$-0.369820\pi$
$883$	1.43673e13	0.795336	0.397668	+	0.917529i	$0.369820\pi$
$884$	1.60834e13	0.885814
$885$	−3.08214e12	−0.168891
$886$	4.20803e12	0.229418
$887$	1.85270e13	1.00496	0.502481	−	0.864588i	$-0.332421\pi$
$887$	1.85270e13	1.00496	0.502481	+	0.864588i	$0.332421\pi$
$888$	6.52429e12	0.352107
$889$	5.11957e12	0.274900
$890$	5.18278e12	0.276890
$891$	0	0
$892$	−2.01675e13	−1.06662
$893$	−4.27431e12	−0.224924
$894$	2.62229e12	0.137297
$895$	−2.41343e12	−0.125728
$896$	−2.17323e13	−1.12647
$897$	−8.00223e11	−0.0412710
$898$	6.45460e12	0.331227
$899$	−1.12752e13	−0.575711
$900$	−6.53271e12	−0.331896
$901$	1.57629e13	0.796846
$902$	0	0
$903$	−6.03758e12	−0.302182
$904$	−6.74612e12	−0.335967
$905$	2.04240e12	0.101210
$906$	−5.81338e11	−0.0286650
$907$	9.08355e12	0.445679	0.222840	−	0.974855i	$-0.428467\pi$
$907$	9.08355e12	0.445679	0.222840	+	0.974855i	$0.428467\pi$
$908$	−1.98538e13	−0.969299
$909$	1.33283e13	0.647497
$910$	2.30184e13	1.11273
$911$	−2.39767e13	−1.15334	−0.576668	−	0.816978i	$-0.695648\pi$
$911$	−2.39767e13	−1.15334	−0.576668	+	0.816978i	$0.695648\pi$
$912$	6.03978e10	0.00289097
$913$	0	0
$914$	1.66390e13	0.788625
$915$	5.70756e12	0.269188
$916$	−1.34112e13	−0.629418
$917$	2.08457e13	0.973544
$918$	8.65933e12	0.402432
$919$	−2.41539e13	−1.11704	−0.558518	−	0.829492i	$-0.688630\pi$
$919$	−2.41539e13	−1.11704	−0.558518	+	0.829492i	$0.688630\pi$
$920$	−5.42981e11	−0.0249884
$921$	−1.03687e13	−0.474849
$922$	3.88350e12	0.176984
$923$	−2.91647e13	−1.32266
$924$	0	0
$925$	−1.12724e13	−0.506266
$926$	2.16879e13	0.969321
$927$	1.99844e13	0.888856
$928$	−3.63365e13	−1.60834
$929$	1.08190e13	0.476560	0.238280	−	0.971196i	$-0.423416\pi$
$929$	1.08190e13	0.476560	0.238280	+	0.971196i	$0.423416\pi$
$930$	1.34700e12	0.0590464
$931$	−2.22915e13	−0.972445
$932$	−3.79914e12	−0.164935
$933$	1.48131e11	0.00639997
$934$	−1.42077e13	−0.610888
$935$	0	0
$936$	−3.31376e13	−1.41117
$937$	−2.14465e13	−0.908926	−0.454463	−	0.890765i	$-0.650169\pi$
$937$	−2.14465e13	−0.908926	−0.454463	+	0.890765i	$0.650169\pi$
$938$	1.82583e13	0.770100
$939$	−1.01240e12	−0.0424970
$940$	4.09043e12	0.170881
$941$	2.61262e13	1.08623	0.543117	−	0.839657i	$-0.317244\pi$
$941$	2.61262e13	1.08623	0.543117	+	0.839657i	$0.317244\pi$
$942$	−4.85813e12	−0.201020
$943$	−7.05723e11	−0.0290624
$944$	−2.02104e11	−0.00828325
$945$	−2.05581e13	−0.838572
$946$	0	0
$947$	1.50614e13	0.608543	0.304271	−	0.952585i	$-0.401587\pi$
$947$	1.50614e13	0.608543	0.304271	+	0.952585i	$0.401587\pi$
$948$	1.20594e12	0.0484939
$949$	−4.71213e13	−1.88590
$950$	4.85041e12	0.193207
$951$	−1.72833e13	−0.685196
$952$	−3.42520e13	−1.35151
$953$	−9.23874e12	−0.362823	−0.181411	−	0.983407i	$-0.558067\pi$
$953$	−9.23874e12	−0.362823	−0.181411	+	0.983407i	$0.558067\pi$
$954$	−1.24776e13	−0.487713
$955$	7.16443e12	0.278719
$956$	1.12526e13	0.435706
$957$	0	0
$958$	1.71460e13	0.657685
$959$	7.62443e13	2.91088
$960$	4.24832e12	0.161435
$961$	−2.30251e13	−0.870854
$962$	−2.19683e13	−0.827007
$963$	−7.23433e12	−0.271069
$964$	7.99241e12	0.298079
$965$	2.43006e12	0.0902077
$966$	6.54745e11	0.0241922
$967$	−3.40625e13	−1.25273	−0.626364	−	0.779531i	$-0.715458\pi$
$967$	−3.40625e13	−1.25273	−0.626364	+	0.779531i	$0.715458\pi$
$968$	0	0
$969$	4.61501e12	0.168157
$970$	3.04736e12	0.110522
$971$	5.34673e12	0.193020	0.0965098	−	0.995332i	$-0.469232\pi$
$971$	5.34673e12	0.193020	0.0965098	+	0.995332i	$0.469232\pi$
$972$	1.78209e13	0.640372
$973$	−5.71653e13	−2.04468
$974$	−8.73124e12	−0.310857
$975$	−1.78055e13	−0.631006
$976$	3.74260e11	0.0132023
$977$	2.42794e13	0.852534	0.426267	−	0.904597i	$-0.359828\pi$
$977$	2.42794e13	0.852534	0.426267	+	0.904597i	$0.359828\pi$
$978$	1.28931e13	0.450644
$979$	0	0
$980$	2.13325e13	0.738794
$981$	−1.40647e13	−0.484866
$982$	2.26260e13	0.776435
$983$	4.45778e12	0.152275	0.0761373	−	0.997097i	$-0.475741\pi$
$983$	4.45778e12	0.152275	0.0761373	+	0.997097i	$0.475741\pi$
$984$	9.08854e12	0.309041
$985$	1.74918e13	0.592069
$986$	−2.22859e13	−0.750903
$987$	−1.28382e13	−0.430602
$988$	−1.56806e13	−0.523547
$989$	−4.79553e11	−0.0159387
$990$	0	0
$991$	−5.08157e13	−1.67366	−0.836829	−	0.547465i	$-0.815593\pi$
$991$	−5.08157e13	−1.67366	−0.836829	+	0.547465i	$0.815593\pi$
$992$	1.10041e13	0.360788
$993$	2.36177e13	0.770843
$994$	2.38626e13	0.775317
$995$	−8.45697e12	−0.273534
$996$	8.07483e12	0.259996
$997$	1.41700e13	0.454194	0.227097	−	0.973872i	$-0.427077\pi$
$997$	1.41700e13	0.454194	0.227097	+	0.973872i	$0.427077\pi$
$998$	−9.58933e12	−0.305985
$999$	1.96203e13	0.623248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.10.a.i.1.10		16
11.7	odd	10		11.10.c.a.5.4	✓	32
11.8	odd	10		11.10.c.a.9.4	yes	32
11.10	odd	2		121.10.a.h.1.7		16
33.8	even	10		99.10.f.a.64.5		32
33.29	even	10		99.10.f.a.82.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.10.c.a.5.4	✓	32	11.7	odd	10
11.10.c.a.9.4	yes	32	11.8	odd	10
99.10.f.a.64.5		32	33.8	even	10
99.10.f.a.82.5		32	33.29	even	10
121.10.a.h.1.7		16	11.10	odd	2
121.10.a.i.1.10		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)

\(f(q)\)	\(=\)	\(q+13.8768 q^{2} -68.3315 q^{3} -319.434 q^{4} -768.757 q^{5} -948.222 q^{6} +11279.4 q^{7} -11537.7 q^{8} -15013.8 q^{9} +O(q^{10})\)	\(q+13.8768 q^{2} -68.3315 q^{3} -319.434 q^{4} -768.757 q^{5} -948.222 q^{6} +11279.4 q^{7} -11537.7 q^{8} -15013.8 q^{9} -10667.9 q^{10} +21827.4 q^{12} -191299. q^{13} +156521. q^{14} +52530.3 q^{15} +3444.55 q^{16} +263199. q^{17} -208344. q^{18} -256607. q^{19} +245567. q^{20} -770734. q^{21} -61217.9 q^{23} +788385. q^{24} -1.36214e6 q^{25} -2.65462e6 q^{26} +2.37088e6 q^{27} -3.60301e6 q^{28} -6.10177e6 q^{29} +728952. q^{30} +1.84785e6 q^{31} +5.95508e6 q^{32} +3.65236e6 q^{34} -8.67108e6 q^{35} +4.79593e6 q^{36} +8.27552e6 q^{37} -3.56088e6 q^{38} +1.30717e7 q^{39} +8.86965e6 q^{40} +1.15281e7 q^{41} -1.06953e7 q^{42} +7.83354e6 q^{43} +1.15420e7 q^{45} -849508. q^{46} +1.66571e7 q^{47} -235371. q^{48} +8.68702e7 q^{49} -1.89021e7 q^{50} -1.79848e7 q^{51} +6.11074e7 q^{52} +5.98897e7 q^{53} +3.29003e7 q^{54} -1.30137e8 q^{56} +1.75343e7 q^{57} -8.46731e7 q^{58} -5.86736e7 q^{59} -1.67800e7 q^{60} +1.08653e8 q^{61} +2.56423e7 q^{62} -1.69346e8 q^{63} +8.08739e7 q^{64} +1.47062e8 q^{65} +1.16650e8 q^{67} -8.40748e7 q^{68} +4.18311e6 q^{69} -1.20327e8 q^{70} +1.52456e8 q^{71} +1.73224e8 q^{72} +2.46323e8 q^{73} +1.14838e8 q^{74} +9.30769e7 q^{75} +8.19690e7 q^{76} +1.81394e8 q^{78} +5.52487e7 q^{79} -2.64802e6 q^{80} +1.33511e8 q^{81} +1.59973e8 q^{82} +3.69940e8 q^{83} +2.46199e8 q^{84} -2.02336e8 q^{85} +1.08705e8 q^{86} +4.16943e8 q^{87} -4.85830e8 q^{89} +1.60166e8 q^{90} -2.15773e9 q^{91} +1.95551e7 q^{92} -1.26266e8 q^{93} +2.31147e8 q^{94} +1.97268e8 q^{95} -4.06919e8 q^{96} -2.85657e8 q^{97} +1.20548e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 48 q^{2} + 222 q^{3} + 3670 q^{4} - 1875 q^{5} + 6191 q^{6} + 12575 q^{7} + 41046 q^{8} + 78904 q^{9}+O(q^{10}) \) 16 * q + 48 * q^2 + 222 * q^3 + 3670 * q^4 - 1875 * q^5 + 6191 * q^6 + 12575 * q^7 + 41046 * q^8 + 78904 * q^9	\( 16 q + 48 q^{2} + 222 q^{3} + 3670 q^{4} - 1875 q^{5} + 6191 q^{6} + 12575 q^{7} + 41046 q^{8} + 78904 q^{9} + 8136 q^{10} + 169811 q^{12} + 119783 q^{13} - 150396 q^{14} + 128978 q^{15} + 1706770 q^{16} + 570930 q^{17} + 1377185 q^{18} + 708062 q^{19} - 2134062 q^{20} + 1713601 q^{21} - 2022726 q^{23} + 5319405 q^{24} - 222677 q^{25} - 4839084 q^{26} + 6603192 q^{27} + 4933520 q^{28} + 12196593 q^{29} + 20118540 q^{30} - 1920467 q^{31} + 28274430 q^{32} + 4257577 q^{34} + 17645076 q^{35} + 10442417 q^{36} + 8193077 q^{37} + 17969289 q^{38} + 26233656 q^{39} - 78857762 q^{40} + 27052578 q^{41} + 126693168 q^{42} + 2191717 q^{43} - 82573010 q^{45} - 82764586 q^{46} + 61772571 q^{47} + 26253395 q^{48} - 35102109 q^{49} + 162127428 q^{50} + 27137348 q^{51} + 174822050 q^{52} + 230906967 q^{53} + 168706262 q^{54} - 163593804 q^{56} + 68054133 q^{57} - 373835684 q^{58} - 92927886 q^{59} + 190895818 q^{60} + 463219765 q^{61} + 573749574 q^{62} + 784007783 q^{63} + 1128452290 q^{64} + 434503197 q^{65} - 473101677 q^{67} + 1073658963 q^{68} - 975630076 q^{69} + 524415506 q^{70} + 374085717 q^{71} + 3278349663 q^{72} + 1061898004 q^{73} + 1887418362 q^{74} + 1708808113 q^{75} + 2116654933 q^{76} - 2149007830 q^{78} + 1193641695 q^{79} - 2800403982 q^{80} - 160274720 q^{81} + 406045707 q^{82} + 3036904890 q^{83} + 3741117150 q^{84} + 2067806293 q^{85} + 4258123329 q^{86} + 2016430701 q^{87} - 779711079 q^{89} + 2671912588 q^{90} - 2737301136 q^{91} + 211938438 q^{92} - 2375160030 q^{93} + 8271211980 q^{94} + 3152016348 q^{95} + 7750699293 q^{96} + 6028874386 q^{97} + 3685530690 q^{98}+O(q^{100}) \) 16 * q + 48 * q^2 + 222 * q^3 + 3670 * q^4 - 1875 * q^5 + 6191 * q^6 + 12575 * q^7 + 41046 * q^8 + 78904 * q^9 + 8136 * q^10 + 169811 * q^12 + 119783 * q^13 - 150396 * q^14 + 128978 * q^15 + 1706770 * q^16 + 570930 * q^17 + 1377185 * q^18 + 708062 * q^19 - 2134062 * q^20 + 1713601 * q^21 - 2022726 * q^23 + 5319405 * q^24 - 222677 * q^25 - 4839084 * q^26 + 6603192 * q^27 + 4933520 * q^28 + 12196593 * q^29 + 20118540 * q^30 - 1920467 * q^31 + 28274430 * q^32 + 4257577 * q^34 + 17645076 * q^35 + 10442417 * q^36 + 8193077 * q^37 + 17969289 * q^38 + 26233656 * q^39 - 78857762 * q^40 + 27052578 * q^41 + 126693168 * q^42 + 2191717 * q^43 - 82573010 * q^45 - 82764586 * q^46 + 61772571 * q^47 + 26253395 * q^48 - 35102109 * q^49 + 162127428 * q^50 + 27137348 * q^51 + 174822050 * q^52 + 230906967 * q^53 + 168706262 * q^54 - 163593804 * q^56 + 68054133 * q^57 - 373835684 * q^58 - 92927886 * q^59 + 190895818 * q^60 + 463219765 * q^61 + 573749574 * q^62 + 784007783 * q^63 + 1128452290 * q^64 + 434503197 * q^65 - 473101677 * q^67 + 1073658963 * q^68 - 975630076 * q^69 + 524415506 * q^70 + 374085717 * q^71 + 3278349663 * q^72 + 1061898004 * q^73 + 1887418362 * q^74 + 1708808113 * q^75 + 2116654933 * q^76 - 2149007830 * q^78 + 1193641695 * q^79 - 2800403982 * q^80 - 160274720 * q^81 + 406045707 * q^82 + 3036904890 * q^83 + 3741117150 * q^84 + 2067806293 * q^85 + 4258123329 * q^86 + 2016430701 * q^87 - 779711079 * q^89 + 2671912588 * q^90 - 2737301136 * q^91 + 211938438 * q^92 - 2375160030 * q^93 + 8271211980 * q^94 + 3152016348 * q^95 + 7750699293 * q^96 + 6028874386 * q^97 + 3685530690 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more