LMFDB - Embedded newform 197.10.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,10,Mod(1,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, 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("197.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	197.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:	$101.462059724$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-38.2269 q^{2} -153.641 q^{3} +949.295 q^{4} +2107.84 q^{5} +5873.22 q^{6} +5202.74 q^{7} -16716.4 q^{8} +3922.60 q^{9} +O(q^{10})$	\(q-38.2269 q^{2} -153.641 q^{3} +949.295 q^{4} +2107.84 q^{5} +5873.22 q^{6} +5202.74 q^{7} -16716.4 q^{8} +3922.60 q^{9} -80576.2 q^{10} +14459.1 q^{11} -145851. q^{12} -27160.2 q^{13} -198885. q^{14} -323851. q^{15} +152978. q^{16} +305985. q^{17} -149949. q^{18} +750970. q^{19} +2.00096e6 q^{20} -799355. q^{21} -552727. q^{22} +30312.0 q^{23} +2.56833e6 q^{24} +2.48987e6 q^{25} +1.03825e6 q^{26} +2.42145e6 q^{27} +4.93893e6 q^{28} +3.93647e6 q^{29} +1.23798e7 q^{30} +952075. q^{31} +2.71094e6 q^{32} -2.22152e6 q^{33} -1.16969e7 q^{34} +1.09665e7 q^{35} +3.72371e6 q^{36} -267723. q^{37} -2.87072e7 q^{38} +4.17293e6 q^{39} -3.52356e7 q^{40} +1.05316e7 q^{41} +3.05568e7 q^{42} +8.50472e6 q^{43} +1.37260e7 q^{44} +8.26822e6 q^{45} -1.15873e6 q^{46} +7.59559e6 q^{47} -2.35037e7 q^{48} -1.32851e7 q^{49} -9.51799e7 q^{50} -4.70120e7 q^{51} -2.57831e7 q^{52} +4.98917e7 q^{53} -9.25643e7 q^{54} +3.04775e7 q^{55} -8.69712e7 q^{56} -1.15380e8 q^{57} -1.50479e8 q^{58} +6.81953e6 q^{59} -3.07430e8 q^{60} +1.19460e8 q^{61} -3.63949e7 q^{62} +2.04083e7 q^{63} -1.81955e8 q^{64} -5.72495e7 q^{65} +8.49217e7 q^{66} -5.06638e7 q^{67} +2.90470e8 q^{68} -4.65716e6 q^{69} -4.19217e8 q^{70} -2.45300e8 q^{71} -6.55719e7 q^{72} +1.17975e8 q^{73} +1.02342e7 q^{74} -3.82546e8 q^{75} +7.12892e8 q^{76} +7.52270e7 q^{77} -1.59518e8 q^{78} +5.16564e8 q^{79} +3.22454e8 q^{80} -4.49242e8 q^{81} -4.02589e8 q^{82} +3.97742e7 q^{83} -7.58824e8 q^{84} +6.44969e8 q^{85} -3.25109e8 q^{86} -6.04804e8 q^{87} -2.41705e8 q^{88} +1.21044e8 q^{89} -3.16068e8 q^{90} -1.41308e8 q^{91} +2.87750e7 q^{92} -1.46278e8 q^{93} -2.90356e8 q^{94} +1.58293e9 q^{95} -4.16511e8 q^{96} -5.64314e7 q^{97} +5.07849e8 q^{98} +5.67174e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9}+O(q^{10}) $ 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9	\( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9} + 121093 q^{10} + 120464 q^{11} + 415744 q^{12} + 480131 q^{13} + 330849 q^{14} + 544874 q^{15} + 5963776 q^{16} + 942582 q^{17} + 1483945 q^{18} + 3097319 q^{19} + 3237739 q^{20} + 889076 q^{21} + 3791921 q^{22} + 5139200 q^{23} + 1999533 q^{24} + 34080519 q^{25} + 2791454 q^{26} + 24386486 q^{27} + 20891166 q^{28} + 6886818 q^{29} + 14171083 q^{30} + 28002851 q^{31} + 16857332 q^{32} + 30921422 q^{33} + 33506194 q^{34} + 16271736 q^{35} + 151430458 q^{36} + 55950976 q^{37} + 62370882 q^{38} - 11569592 q^{39} + 129854766 q^{40} + 14990859 q^{41} + 82216531 q^{42} + 169867467 q^{43} + 41872434 q^{44} + 205007649 q^{45} + 144032301 q^{46} + 78743342 q^{47} + 156250562 q^{48} + 533861890 q^{49} + 626841163 q^{50} + 477099244 q^{51} + 560784114 q^{52} + 188670216 q^{53} + 525901687 q^{54} + 298497914 q^{55} + 56575048 q^{56} + 213972590 q^{57} + 338315251 q^{58} + 208222151 q^{59} - 615921507 q^{60} - 233556134 q^{61} - 399368105 q^{62} + 329825056 q^{63} + 876517017 q^{64} - 840557006 q^{65} - 2482481592 q^{66} + 1210808414 q^{67} - 1266757099 q^{68} + 327801786 q^{69} - 546384313 q^{70} + 345300221 q^{71} - 1549481681 q^{72} + 1192286460 q^{73} - 1471133595 q^{74} + 761630676 q^{75} - 398699826 q^{76} - 101106252 q^{77} - 2609825943 q^{78} + 955627631 q^{79} + 1059617770 q^{80} + 3387041436 q^{81} + 1062705523 q^{82} + 1538917201 q^{83} + 1394513218 q^{84} + 225481100 q^{85} + 701644810 q^{86} + 1758812842 q^{87} + 3151474875 q^{88} + 855413630 q^{89} + 6070671455 q^{90} + 4652436248 q^{91} + 8082863606 q^{92} + 3462095982 q^{93} + 2660342117 q^{94} + 1036805508 q^{95} + 12370989029 q^{96} + 6393874545 q^{97} + 7510976010 q^{98} + 8731109606 q^{99}+O(q^{100}) \) 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9 + 121093 * q^10 + 120464 * q^11 + 415744 * q^12 + 480131 * q^13 + 330849 * q^14 + 544874 * q^15 + 5963776 * q^16 + 942582 * q^17 + 1483945 * q^18 + 3097319 * q^19 + 3237739 * q^20 + 889076 * q^21 + 3791921 * q^22 + 5139200 * q^23 + 1999533 * q^24 + 34080519 * q^25 + 2791454 * q^26 + 24386486 * q^27 + 20891166 * q^28 + 6886818 * q^29 + 14171083 * q^30 + 28002851 * q^31 + 16857332 * q^32 + 30921422 * q^33 + 33506194 * q^34 + 16271736 * q^35 + 151430458 * q^36 + 55950976 * q^37 + 62370882 * q^38 - 11569592 * q^39 + 129854766 * q^40 + 14990859 * q^41 + 82216531 * q^42 + 169867467 * q^43 + 41872434 * q^44 + 205007649 * q^45 + 144032301 * q^46 + 78743342 * q^47 + 156250562 * q^48 + 533861890 * q^49 + 626841163 * q^50 + 477099244 * q^51 + 560784114 * q^52 + 188670216 * q^53 + 525901687 * q^54 + 298497914 * q^55 + 56575048 * q^56 + 213972590 * q^57 + 338315251 * q^58 + 208222151 * q^59 - 615921507 * q^60 - 233556134 * q^61 - 399368105 * q^62 + 329825056 * q^63 + 876517017 * q^64 - 840557006 * q^65 - 2482481592 * q^66 + 1210808414 * q^67 - 1266757099 * q^68 + 327801786 * q^69 - 546384313 * q^70 + 345300221 * q^71 - 1549481681 * q^72 + 1192286460 * q^73 - 1471133595 * q^74 + 761630676 * q^75 - 398699826 * q^76 - 101106252 * q^77 - 2609825943 * q^78 + 955627631 * q^79 + 1059617770 * q^80 + 3387041436 * q^81 + 1062705523 * q^82 + 1538917201 * q^83 + 1394513218 * q^84 + 225481100 * q^85 + 701644810 * q^86 + 1758812842 * q^87 + 3151474875 * q^88 + 855413630 * q^89 + 6070671455 * q^90 + 4652436248 * q^91 + 8082863606 * q^92 + 3462095982 * q^93 + 2660342117 * q^94 + 1036805508 * q^95 + 12370989029 * q^96 + 6393874545 * q^97 + 7510976010 * q^98 + 8731109606 * 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 $

$2$	−38.2269	−1.68941	−0.844703	−	0.535235i	$-0.820223\pi$
$2$	−38.2269	−1.68941	−0.844703	+	0.535235i	$0.820223\pi$
$3$	−153.641	−1.09512	−0.547560	−	0.836766i	$-0.684443\pi$
$3$	−153.641	−1.09512	−0.547560	+	0.836766i	$0.684443\pi$
$4$	949.295	1.85409
$5$	2107.84	1.50825	0.754124	−	0.656732i	$-0.228062\pi$
$5$	2107.84	1.50825	0.754124	+	0.656732i	$0.228062\pi$
$6$	5873.22	1.85010
$7$	5202.74	0.819013	0.409507	−	0.912307i	$-0.365701\pi$
$7$	5202.74	0.819013	0.409507	+	0.912307i	$0.365701\pi$
$8$	−16716.4	−1.44291
$9$	3922.60	0.199289
$10$	−80576.2	−2.54804
$11$	14459.1	0.297766	0.148883	−	0.988855i	$-0.452432\pi$
$11$	14459.1	0.297766	0.148883	+	0.988855i	$0.452432\pi$
$12$	−145851.	−2.03045
$13$	−27160.2	−0.263748	−0.131874	−	0.991267i	$-0.542099\pi$
$13$	−27160.2	−0.263748	−0.131874	+	0.991267i	$0.542099\pi$
$14$	−198885.	−1.38365
$15$	−323851.	−1.65171
$16$	152978.	0.583565
$17$	305985.	0.888547	0.444274	−	0.895891i	$-0.353462\pi$
$17$	305985.	0.888547	0.444274	+	0.895891i	$0.353462\pi$
$18$	−149949.	−0.336680
$19$	750970.	1.32200	0.661000	−	0.750386i	$-0.270132\pi$
$19$	750970.	1.32200	0.661000	+	0.750386i	$0.270132\pi$
$20$	2.00096e6	2.79643
$21$	−799355.	−0.896918
$22$	−552727.	−0.503047
$23$	30312.0	0.0225860	0.0112930	−	0.999936i	$-0.496405\pi$
$23$	30312.0	0.0225860	0.0112930	+	0.999936i	$0.496405\pi$
$24$	2.56833e6	1.58016
$25$	2.48987e6	1.27481
$26$	1.03825e6	0.445577
$27$	2.42145e6	0.876875
$28$	4.93893e6	1.51853
$29$	3.93647e6	1.03351	0.516757	−	0.856132i	$-0.327139\pi$
$29$	3.93647e6	1.03351	0.516757	+	0.856132i	$0.327139\pi$
$30$	1.23798e7	2.79041
$31$	952075.	0.185158	0.0925792	−	0.995705i	$-0.470489\pi$
$31$	952075.	0.185158	0.0925792	+	0.995705i	$0.470489\pi$
$32$	2.71094e6	0.457029
$33$	−2.22152e6	−0.326089
$34$	−1.16969e7	−1.50112
$35$	1.09665e7	1.23527
$36$	3.72371e6	0.369500
$37$	−267723.	−0.0234843	−0.0117422	−	0.999931i	$-0.503738\pi$
$37$	−267723.	−0.0234843	−0.0117422	+	0.999931i	$0.503738\pi$
$38$	−2.87072e7	−2.23339
$39$	4.17293e6	0.288835
$40$	−3.52356e7	−2.17626
$41$	1.05316e7	0.582056	0.291028	−	0.956714i	$-0.406003\pi$
$41$	1.05316e7	0.582056	0.291028	+	0.956714i	$0.406003\pi$
$42$	3.05568e7	1.51526
$43$	8.50472e6	0.379360	0.189680	−	0.981846i	$-0.439255\pi$
$43$	8.50472e6	0.379360	0.189680	+	0.981846i	$0.439255\pi$
$44$	1.37260e7	0.552085
$45$	8.26822e6	0.300577
$46$	−1.15873e6	−0.0381569
$47$	7.59559e6	0.227050	0.113525	−	0.993535i	$-0.463786\pi$
$47$	7.59559e6	0.227050	0.113525	+	0.993535i	$0.463786\pi$
$48$	−2.35037e7	−0.639074
$49$	−1.32851e7	−0.329218
$50$	−9.51799e7	−2.15367
$51$	−4.70120e7	−0.973066
$52$	−2.57831e7	−0.489012
$53$	4.98917e7	0.868534	0.434267	−	0.900784i	$-0.357007\pi$
$53$	4.98917e7	0.868534	0.434267	+	0.900784i	$0.357007\pi$
$54$	−9.25643e7	−1.48140
$55$	3.04775e7	0.449105
$56$	−8.69712e7	−1.18176
$57$	−1.15380e8	−1.44775
$58$	−1.50479e8	−1.74602
$59$	6.81953e6	0.0732690	0.0366345	−	0.999329i	$-0.488336\pi$
$59$	6.81953e6	0.0732690	0.0366345	+	0.999329i	$0.488336\pi$
$60$	−3.07430e8	−3.06243
$61$	1.19460e8	1.10469	0.552343	−	0.833617i	$-0.313734\pi$
$61$	1.19460e8	1.10469	0.552343	+	0.833617i	$0.313734\pi$
$62$	−3.63949e7	−0.312808
$63$	2.04083e7	0.163220
$64$	−1.81955e8	−1.35567
$65$	−5.72495e7	−0.397797
$66$	8.49217e7	0.550897
$67$	−5.06638e7	−0.307157	−0.153579	−	0.988136i	$-0.549080\pi$
$67$	−5.06638e7	−0.307157	−0.153579	+	0.988136i	$0.549080\pi$
$68$	2.90470e8	1.64745
$69$	−4.65716e6	−0.0247344
$70$	−4.19217e8	−2.08688
$71$	−2.45300e8	−1.14560	−0.572802	−	0.819694i	$-0.694144\pi$
$71$	−2.45300e8	−1.14560	−0.572802	+	0.819694i	$0.694144\pi$
$72$	−6.55719e7	−0.287555
$73$	1.17975e8	0.486225	0.243112	−	0.969998i	$-0.421832\pi$
$73$	1.17975e8	0.486225	0.243112	+	0.969998i	$0.421832\pi$
$74$	1.02342e7	0.0396745
$75$	−3.82546e8	−1.39607
$76$	7.12892e8	2.45111
$77$	7.52270e7	0.243874
$78$	−1.59518e8	−0.487960
$79$	5.16564e8	1.49212	0.746058	−	0.665882i	$-0.231944\pi$
$79$	5.16564e8	1.49212	0.746058	+	0.665882i	$0.231944\pi$
$80$	3.22454e8	0.880161
$81$	−4.49242e8	−1.15957
$82$	−4.02589e8	−0.983330
$83$	3.97742e7	0.0919919	0.0459960	−	0.998942i	$-0.485354\pi$
$83$	3.97742e7	0.0919919	0.0459960	+	0.998942i	$0.485354\pi$
$84$	−7.58824e8	−1.66297
$85$	6.44969e8	1.34015
$86$	−3.25109e8	−0.640893
$87$	−6.04804e8	−1.13182
$88$	−2.41705e8	−0.429649
$89$	1.21044e8	0.204498	0.102249	−	0.994759i	$-0.467396\pi$
$89$	1.21044e8	0.204498	0.102249	+	0.994759i	$0.467396\pi$
$90$	−3.16068e8	−0.507796
$91$	−1.41308e8	−0.216013
$92$	2.87750e7	0.0418765
$93$	−1.46278e8	−0.202771
$94$	−2.90356e8	−0.383579
$95$	1.58293e9	1.99390
$96$	−4.16511e8	−0.500502
$97$	−5.64314e7	−0.0647214	−0.0323607	−	0.999476i	$-0.510303\pi$
$97$	−5.64314e7	−0.0647214	−0.0323607	+	0.999476i	$0.510303\pi$
$98$	5.07849e8	0.556182
$99$	5.67174e7	0.0593414
$100$	2.36362e9	2.36362
$101$	−4.08268e8	−0.390391	−0.195195	−	0.980764i	$-0.562534\pi$
$101$	−4.08268e8	−0.390391	−0.195195	+	0.980764i	$0.562534\pi$
$102$	1.79712e9	1.64390
$103$	−6.99257e8	−0.612166	−0.306083	−	0.952005i	$-0.599018\pi$
$103$	−6.99257e8	−0.612166	−0.306083	+	0.952005i	$0.599018\pi$
$104$	4.54022e8	0.380564
$105$	−1.68491e9	−1.35277
$106$	−1.90720e9	−1.46731
$107$	−9.08297e8	−0.669886	−0.334943	−	0.942238i	$-0.608717\pi$
$107$	−9.08297e8	−0.669886	−0.334943	+	0.942238i	$0.608717\pi$
$108$	2.29867e9	1.62581
$109$	1.34403e7	0.00911989	0.00455994	−	0.999990i	$-0.498549\pi$
$109$	1.34403e7	0.00911989	0.00455994	+	0.999990i	$0.498549\pi$
$110$	−1.16506e9	−0.758720
$111$	4.11333e7	0.0257181
$112$	7.95905e8	0.477948
$113$	−2.36910e7	−0.0136688	−0.00683440	−	0.999977i	$-0.502175\pi$
$113$	−2.36910e7	−0.0136688	−0.00683440	+	0.999977i	$0.502175\pi$
$114$	4.41061e9	2.44584
$115$	6.38928e7	0.0340652
$116$	3.73687e9	1.91623
$117$	−1.06539e8	−0.0525619
$118$	−2.60689e8	−0.123781
$119$	1.59196e9	0.727732
$120$	5.41363e9	2.38327
$121$	−2.14888e9	−0.911335
$122$	−4.56659e9	−1.86626
$123$	−1.61808e9	−0.637422
$124$	9.03800e8	0.343301
$125$	1.13137e9	0.414484
$126$	−7.80144e8	−0.275745
$127$	1.36484e8	0.0465547	0.0232774	−	0.999729i	$-0.492590\pi$
$127$	1.36484e8	0.0465547	0.0232774	+	0.999729i	$0.492590\pi$
$128$	5.56759e9	1.83325
$129$	−1.30667e9	−0.415445
$130$	2.18847e9	0.672040
$131$	−1.63921e9	−0.486310	−0.243155	−	0.969987i	$-0.578182\pi$
$131$	−1.63921e9	−0.486310	−0.243155	+	0.969987i	$0.578182\pi$
$132$	−2.10887e9	−0.604600
$133$	3.90710e9	1.08274
$134$	1.93672e9	0.518913
$135$	5.10402e9	1.32255
$136$	−5.11499e9	−1.28209
$137$	2.43866e9	0.591438	0.295719	−	0.955275i	$-0.404441\pi$
$137$	2.43866e9	0.591438	0.295719	+	0.955275i	$0.404441\pi$
$138$	1.78029e8	0.0417864
$139$	−4.13325e9	−0.939128	−0.469564	−	0.882899i	$-0.655589\pi$
$139$	−4.13325e9	−0.939128	−0.469564	+	0.882899i	$0.655589\pi$
$140$	1.04105e10	2.29031
$141$	−1.16700e9	−0.248647
$142$	9.37704e9	1.93539
$143$	−3.92713e8	−0.0785351
$144$	6.00072e8	0.116298
$145$	8.29745e9	1.55879
$146$	−4.50982e9	−0.821431
$147$	2.04114e9	0.360533
$148$	−2.54148e8	−0.0435421
$149$	−6.01056e9	−0.999025	−0.499513	−	0.866307i	$-0.666488\pi$
$149$	−6.01056e9	−0.999025	−0.499513	+	0.866307i	$0.666488\pi$
$150$	1.46235e10	2.35853
$151$	1.06469e10	1.66658	0.833291	−	0.552834i	$-0.186454\pi$
$151$	1.06469e10	1.66658	0.833291	+	0.552834i	$0.186454\pi$
$152$	−1.25535e10	−1.90752
$153$	1.20026e9	0.177077
$154$	−2.87570e9	−0.412002
$155$	2.00682e9	0.279265
$156$	3.96134e9	0.535528
$157$	−6.94726e9	−0.912567	−0.456284	−	0.889834i	$-0.650820\pi$
$157$	−6.94726e9	−0.912567	−0.456284	+	0.889834i	$0.650820\pi$
$158$	−1.97466e10	−2.52079
$159$	−7.66542e9	−0.951149
$160$	5.71422e9	0.689314
$161$	1.57705e8	0.0184982
$162$	1.71731e10	1.95899
$163$	−9.81379e9	−1.08891	−0.544455	−	0.838790i	$-0.683264\pi$
$163$	−9.81379e9	−1.08891	−0.544455	+	0.838790i	$0.683264\pi$
$164$	9.99755e9	1.07919
$165$	−4.68260e9	−0.491824
$166$	−1.52044e9	−0.155412
$167$	1.52995e10	1.52213	0.761067	−	0.648673i	$-0.224676\pi$
$167$	1.52995e10	1.52213	0.761067	+	0.648673i	$0.224676\pi$
$168$	1.33624e10	1.29417
$169$	−9.86682e9	−0.930437
$170$	−2.46551e10	−2.26406
$171$	2.94576e9	0.263460
$172$	8.07349e9	0.703369
$173$	1.50390e10	1.27647	0.638235	−	0.769842i	$-0.279665\pi$
$173$	1.50390e10	1.27647	0.638235	+	0.769842i	$0.279665\pi$
$174$	2.31198e10	1.91211
$175$	1.29541e10	1.04409
$176$	2.21193e9	0.173766
$177$	−1.04776e9	−0.0802384
$178$	−4.62715e9	−0.345480
$179$	2.77580e8	0.0202092	0.0101046	−	0.999949i	$-0.496784\pi$
$179$	2.77580e8	0.0202092	0.0101046	+	0.999949i	$0.496784\pi$
$180$	7.84898e9	0.557297
$181$	−1.00484e10	−0.695897	−0.347948	−	0.937514i	$-0.613122\pi$
$181$	−1.00484e10	−0.695897	−0.347948	+	0.937514i	$0.613122\pi$
$182$	5.40175e9	0.364933
$183$	−1.83540e10	−1.20976
$184$	−5.06708e8	−0.0325895
$185$	−5.64317e8	−0.0354202
$186$	5.59175e9	0.342562
$187$	4.42428e9	0.264579
$188$	7.21046e9	0.420971
$189$	1.25981e10	0.718172
$190$	−6.05103e10	−3.36851
$191$	−1.52351e10	−0.828315	−0.414158	−	0.910205i	$-0.635924\pi$
$191$	−1.52351e10	−0.828315	−0.414158	+	0.910205i	$0.635924\pi$
$192$	2.79558e10	1.48463
$193$	−3.17609e9	−0.164772	−0.0823862	−	0.996600i	$-0.526254\pi$
$193$	−3.17609e9	−0.164772	−0.0823862	+	0.996600i	$0.526254\pi$
$194$	2.15720e9	0.109341
$195$	8.79587e9	0.435636
$196$	−1.26115e10	−0.610400
$197$	1.50614e9	0.0712470
$197$	1.50614e9	0.0712470
$198$	−2.16813e9	−0.100252
$199$	1.28543e10	0.581044	0.290522	−	0.956868i	$-0.406171\pi$
$199$	1.28543e10	0.581044	0.290522	+	0.956868i	$0.406171\pi$
$200$	−4.16217e10	−1.83944
$201$	7.78404e9	0.336374
$202$	1.56068e10	0.659529
$203$	2.04804e10	0.846461
$204$	−4.46282e10	−1.80415
$205$	2.21988e10	0.877885
$206$	2.67304e10	1.03420
$207$	1.18902e8	0.00450113
$208$	−4.15492e9	−0.153914
$209$	1.08584e10	0.393646
$210$	6.44090e10	2.28539
$211$	3.19945e10	1.11123	0.555616	−	0.831439i	$-0.312482\pi$
$211$	3.19945e10	1.11123	0.555616	+	0.831439i	$0.312482\pi$
$212$	4.73619e10	1.61034
$213$	3.76881e10	1.25457
$214$	3.47214e10	1.13171
$215$	1.79266e10	0.572169
$216$	−4.04779e10	−1.26525
$217$	4.95340e9	0.151647
$218$	−5.13781e8	−0.0154072
$219$	−1.81258e10	−0.532475
$220$	2.89322e10	0.832682
$221$	−8.31064e9	−0.234352
$222$	−1.57240e9	−0.0434484
$223$	6.58160e10	1.78221	0.891107	−	0.453793i	$-0.149929\pi$
$223$	6.58160e10	1.78221	0.891107	+	0.453793i	$0.149929\pi$
$224$	1.41043e10	0.374313
$225$	9.76675e9	0.254056
$226$	9.05634e8	0.0230922
$227$	−5.91660e10	−1.47896	−0.739479	−	0.673179i	$-0.764928\pi$
$227$	−5.91660e10	−1.47896	−0.739479	+	0.673179i	$0.764928\pi$
$228$	−1.09530e11	−2.68426
$229$	−3.32122e10	−0.798065	−0.399033	−	0.916937i	$-0.630654\pi$
$229$	−3.32122e10	−0.798065	−0.399033	+	0.916937i	$0.630654\pi$
$230$	−2.44242e9	−0.0575500
$231$	−1.15580e10	−0.267072
$232$	−6.58038e10	−1.49126
$233$	−1.36784e9	−0.0304041	−0.0152021	−	0.999884i	$-0.504839\pi$
$233$	−1.36784e9	−0.0304041	−0.0152021	+	0.999884i	$0.504839\pi$
$234$	4.07265e9	0.0887985
$235$	1.60103e10	0.342447
$236$	6.47375e9	0.135847
$237$	−7.93655e10	−1.63405
$238$	−6.08558e10	−1.22943
$239$	−8.40292e10	−1.66586	−0.832932	−	0.553375i	$-0.813339\pi$
$239$	−8.40292e10	−1.66586	−0.832932	+	0.553375i	$0.813339\pi$
$240$	−4.95421e10	−0.963882
$241$	5.38143e9	0.102759	0.0513796	−	0.998679i	$-0.483638\pi$
$241$	5.38143e9	0.102759	0.0513796	+	0.998679i	$0.483638\pi$
$242$	8.21451e10	1.53962
$243$	2.13608e10	0.392997
$244$	1.13403e11	2.04819
$245$	−2.80029e10	−0.496542
$246$	6.18542e10	1.07686
$247$	−2.03965e10	−0.348674
$248$	−1.59153e10	−0.267167
$249$	−6.11095e9	−0.100742
$250$	−4.32486e10	−0.700232
$251$	−5.96891e10	−0.949212	−0.474606	−	0.880198i	$-0.657409\pi$
$251$	−5.96891e10	−0.949212	−0.474606	+	0.880198i	$0.657409\pi$
$252$	1.93735e10	0.302625
$253$	4.38284e8	0.00672533
$254$	−5.21734e9	−0.0786498
$255$	−9.90937e10	−1.46763
$256$	−1.19671e11	−1.74144
$257$	−1.06712e11	−1.52585	−0.762926	−	0.646486i	$-0.776238\pi$
$257$	−1.06712e11	−1.52585	−0.762926	+	0.646486i	$0.776238\pi$
$258$	4.99501e10	0.701855
$259$	−1.39289e9	−0.0192340
$260$	−5.43466e10	−0.737552
$261$	1.54412e10	0.205968
$262$	6.26619e10	0.821576
$263$	1.62217e10	0.209072	0.104536	−	0.994521i	$-0.466664\pi$
$263$	1.62217e10	0.209072	0.104536	+	0.994521i	$0.466664\pi$
$264$	3.71358e10	0.470517
$265$	1.05164e11	1.30996
$266$	−1.49356e11	−1.82918
$267$	−1.85974e10	−0.223950
$268$	−4.80949e10	−0.569498
$269$	−1.05738e11	−1.23125	−0.615624	−	0.788040i	$-0.711096\pi$
$269$	−1.05738e11	−1.23125	−0.615624	+	0.788040i	$0.711096\pi$
$270$	−1.95111e11	−2.23432
$271$	1.03622e11	1.16705	0.583527	−	0.812094i	$-0.301672\pi$
$271$	1.03622e11	1.16705	0.583527	+	0.812094i	$0.301672\pi$
$272$	4.68091e10	0.518525
$273$	2.17107e10	0.236560
$274$	−9.32225e10	−0.999179
$275$	3.60013e10	0.379595
$276$	−4.42102e9	−0.0458598
$277$	1.03616e11	1.05747	0.528734	−	0.848788i	$-0.322667\pi$
$277$	1.03616e11	1.05747	0.528734	+	0.848788i	$0.322667\pi$
$278$	1.58001e11	1.58657
$279$	3.73461e9	0.0369000
$280$	−1.83321e11	−1.78239
$281$	−4.10264e10	−0.392541	−0.196271	−	0.980550i	$-0.562883\pi$
$281$	−4.10264e10	−0.392541	−0.196271	+	0.980550i	$0.562883\pi$
$282$	4.46106e10	0.420066
$283$	8.45522e9	0.0783584	0.0391792	−	0.999232i	$-0.487526\pi$
$283$	8.45522e9	0.0783584	0.0391792	+	0.999232i	$0.487526\pi$
$284$	−2.32862e11	−2.12405
$285$	−2.43202e11	−2.18356
$286$	1.50122e10	0.132678
$287$	5.47929e10	0.476712
$288$	1.06339e10	0.0910808
$289$	−2.49608e10	−0.210483
$290$	−3.17186e11	−2.63344
$291$	8.67018e9	0.0708777
$292$	1.11993e11	0.901505
$293$	7.16759e10	0.568158	0.284079	−	0.958801i	$-0.408312\pi$
$293$	7.16759e10	0.568158	0.284079	+	0.958801i	$0.408312\pi$
$294$	−7.80265e10	−0.609086
$295$	1.43745e10	0.110508
$296$	4.47537e9	0.0338857
$297$	3.50120e10	0.261104
$298$	2.29765e11	1.68776
$299$	−8.23280e8	−0.00595700
$300$	−3.63149e11	−2.58845
$301$	4.42478e10	0.310701
$302$	−4.06998e11	−2.81553
$303$	6.27268e10	0.427525
$304$	1.14882e11	0.771473
$305$	2.51803e11	1.66614
$306$	−4.58822e10	−0.299156
$307$	1.84404e11	1.18481	0.592404	−	0.805641i	$-0.298179\pi$
$307$	1.84404e11	1.18481	0.592404	+	0.805641i	$0.298179\pi$
$308$	7.14127e10	0.452165
$309$	1.07435e11	0.670395
$310$	−7.67146e10	−0.471792
$311$	−6.53057e9	−0.0395849	−0.0197924	−	0.999804i	$-0.506301\pi$
$311$	−6.53057e9	−0.0395849	−0.0197924	+	0.999804i	$0.506301\pi$
$312$	−6.97565e10	−0.416763
$313$	2.62007e11	1.54299	0.771495	−	0.636235i	$-0.219509\pi$
$313$	2.62007e11	1.54299	0.771495	+	0.636235i	$0.219509\pi$
$314$	2.65572e11	1.54170
$315$	4.30174e10	0.246176
$316$	4.90372e11	2.76652
$317$	−1.33176e11	−0.740727	−0.370363	−	0.928887i	$-0.620767\pi$
$317$	−1.33176e11	−0.740727	−0.370363	+	0.928887i	$0.620767\pi$
$318$	2.93025e11	1.60688
$319$	5.69179e10	0.307745
$320$	−3.83533e11	−2.04469
$321$	1.39552e11	0.733606
$322$	−6.02858e9	−0.0312510
$323$	2.29786e11	1.17466
$324$	−4.26463e11	−2.14995
$325$	−6.76254e10	−0.336229
$326$	3.75151e11	1.83961
$327$	−2.06498e9	−0.00998738
$328$	−1.76050e11	−0.839854
$329$	3.95179e10	0.185957
$330$	1.79001e11	0.830890
$331$	2.27005e11	1.03946	0.519732	−	0.854329i	$-0.326032\pi$
$331$	2.27005e11	1.03946	0.519732	+	0.854329i	$0.326032\pi$
$332$	3.77574e10	0.170561
$333$	−1.05017e9	−0.00468016
$334$	−5.84852e11	−2.57150
$335$	−1.06791e11	−0.463269
$336$	−1.22284e11	−0.523410
$337$	−7.17572e9	−0.0303062	−0.0151531	−	0.999885i	$-0.504824\pi$
$337$	−7.17572e9	−0.0303062	−0.0151531	+	0.999885i	$0.504824\pi$
$338$	3.77178e11	1.57189
$339$	3.63991e9	0.0149690
$340$	6.12265e11	2.48476
$341$	1.37662e10	0.0551339
$342$	−1.12607e11	−0.445090
$343$	−2.79068e11	−1.08865
$344$	−1.42169e11	−0.547382
$345$	−9.81656e9	−0.0373055
$346$	−5.74893e11	−2.15648
$347$	8.58364e10	0.317826	0.158913	−	0.987293i	$-0.449201\pi$
$347$	8.58364e10	0.317826	0.158913	+	0.987293i	$0.449201\pi$
$348$	−5.74137e11	−2.09850
$349$	1.96745e11	0.709888	0.354944	−	0.934888i	$-0.384500\pi$
$349$	1.96745e11	0.709888	0.354944	+	0.934888i	$0.384500\pi$
$350$	−4.95196e11	−1.76389
$351$	−6.57671e10	−0.231274
$352$	3.91977e10	0.136088
$353$	5.13579e11	1.76044	0.880219	−	0.474567i	$-0.157395\pi$
$353$	5.13579e11	1.76044	0.880219	+	0.474567i	$0.157395\pi$
$354$	4.00526e10	0.135555
$355$	−5.17053e11	−1.72785
$356$	1.14907e11	0.379159
$357$	−2.44591e11	−0.796954
$358$	−1.06110e10	−0.0341416
$359$	1.92052e11	0.610229	0.305115	−	0.952316i	$-0.401305\pi$
$359$	1.92052e11	0.610229	0.305115	+	0.952316i	$0.401305\pi$
$360$	−1.38215e11	−0.433705
$361$	2.41268e11	0.747684
$362$	3.84120e11	1.17565
$363$	3.30157e11	0.998022
$364$	−1.34143e11	−0.400508
$365$	2.48672e11	0.733347
$366$	7.01616e11	2.04378
$367$	−7.10357e10	−0.204399	−0.102200	−	0.994764i	$-0.532588\pi$
$367$	−7.10357e10	−0.204399	−0.102200	+	0.994764i	$0.532588\pi$
$368$	4.63707e9	0.0131804
$369$	4.13111e10	0.115997
$370$	2.15721e10	0.0598390
$371$	2.59573e11	0.711341
$372$	−1.38861e11	−0.375956
$373$	5.97727e11	1.59887	0.799435	−	0.600753i	$-0.205132\pi$
$373$	5.97727e11	1.59887	0.799435	+	0.600753i	$0.205132\pi$
$374$	−1.69127e11	−0.446981
$375$	−1.73824e11	−0.453910
$376$	−1.26971e11	−0.327612
$377$	−1.06916e11	−0.272587
$378$	−4.81588e11	−1.21328
$379$	6.94367e11	1.72867	0.864336	−	0.502914i	$-0.167739\pi$
$379$	6.94367e11	1.72867	0.864336	+	0.502914i	$0.167739\pi$
$380$	1.50266e12	3.69688
$381$	−2.09695e10	−0.0509830
$382$	5.82391e11	1.39936
$383$	−2.01772e11	−0.479145	−0.239572	−	0.970879i	$-0.577007\pi$
$383$	−2.01772e11	−0.479145	−0.239572	+	0.970879i	$0.577007\pi$
$384$	−8.55411e11	−2.00763
$385$	1.58567e11	0.367823
$386$	1.21412e11	0.278367
$387$	3.33606e10	0.0756022
$388$	−5.35701e10	−0.119999
$389$	3.61861e9	0.00801250	0.00400625	−	0.999992i	$-0.498725\pi$
$389$	3.61861e9	0.00801250	0.00400625	+	0.999992i	$0.498725\pi$
$390$	−3.36239e11	−0.735965
$391$	9.27502e9	0.0200687
$392$	2.22080e11	0.475031
$393$	2.51850e11	0.532569
$394$	−5.75750e10	−0.120365
$395$	1.08883e12	2.25048
$396$	5.38415e10	0.110024
$397$	5.85838e11	1.18364	0.591821	−	0.806069i	$-0.298409\pi$
$397$	5.85838e11	1.18364	0.591821	+	0.806069i	$0.298409\pi$
$398$	−4.91379e11	−0.981619
$399$	−6.00291e11	−1.18573
$400$	3.80895e11	0.743936
$401$	5.63448e11	1.08819	0.544094	−	0.839024i	$-0.316873\pi$
$401$	5.63448e11	1.08819	0.544094	+	0.839024i	$0.316873\pi$
$402$	−2.97560e11	−0.568272
$403$	−2.58586e10	−0.0488351
$404$	−3.87567e11	−0.723821
$405$	−9.46931e11	−1.74892
$406$	−7.82903e11	−1.43002
$407$	−3.87104e9	−0.00699283
$408$	7.85872e11	1.40405
$409$	−1.05392e12	−1.86232	−0.931161	−	0.364608i	$-0.881203\pi$
$409$	−1.05392e12	−1.86232	−0.931161	+	0.364608i	$0.881203\pi$
$410$	−8.48592e11	−1.48310
$411$	−3.74679e11	−0.647696
$412$	−6.63801e11	−1.13501
$413$	3.54802e10	0.0600083
$414$	−4.54524e9	−0.00760423
$415$	8.38376e10	0.138747
$416$	−7.36297e10	−0.120540
$417$	6.35037e11	1.02846
$418$	−4.15082e11	−0.665029
$419$	3.21361e11	0.509367	0.254683	−	0.967025i	$-0.418029\pi$
$419$	3.21361e11	0.509367	0.254683	+	0.967025i	$0.418029\pi$
$420$	−1.59948e12	−2.50817
$421$	−9.38143e11	−1.45546	−0.727729	−	0.685865i	$-0.759424\pi$
$421$	−9.38143e11	−1.45546	−0.727729	+	0.685865i	$0.759424\pi$
$422$	−1.22305e12	−1.87732
$423$	2.97945e10	0.0452485
$424$	−8.34011e11	−1.25321
$425$	7.61863e11	1.13273
$426$	−1.44070e12	−2.11948
$427$	6.21520e11	0.904752
$428$	−8.62242e11	−1.24203
$429$	6.03369e10	0.0860054
$430$	−6.85278e11	−0.966626
$431$	9.37611e11	1.30881	0.654403	−	0.756146i	$-0.272920\pi$
$431$	9.37611e11	1.30881	0.654403	+	0.756146i	$0.272920\pi$
$432$	3.70428e11	0.511714
$433$	7.64066e11	1.04456	0.522282	−	0.852773i	$-0.325081\pi$
$433$	7.64066e11	1.04456	0.522282	+	0.852773i	$0.325081\pi$
$434$	−1.89353e11	−0.256194
$435$	−1.27483e12	−1.70707
$436$	1.27588e10	0.0169091
$437$	2.27634e10	0.0298586
$438$	6.92893e11	0.899566
$439$	−2.67401e10	−0.0343616	−0.0171808	−	0.999852i	$-0.505469\pi$
$439$	−2.67401e10	−0.0343616	−0.0171808	+	0.999852i	$0.505469\pi$
$440$	−5.09476e11	−0.648017
$441$	−5.21122e10	−0.0656094
$442$	3.17690e11	0.395916
$443$	−2.85059e10	−0.0351656	−0.0175828	−	0.999845i	$-0.505597\pi$
$443$	−2.85059e10	−0.0351656	−0.0175828	+	0.999845i	$0.505597\pi$
$444$	3.90476e10	0.0476838
$445$	2.55142e11	0.308434
$446$	−2.51594e12	−3.01088
$447$	9.23469e11	1.09405
$448$	−9.46666e11	−1.11031
$449$	−1.51978e12	−1.76471	−0.882353	−	0.470589i	$-0.844042\pi$
$449$	−1.51978e12	−1.76471	−0.882353	+	0.470589i	$0.844042\pi$
$450$	−3.73353e11	−0.429203
$451$	1.52277e11	0.173317
$452$	−2.24898e10	−0.0253432
$453$	−1.63580e12	−1.82511
$454$	2.26173e12	2.49856
$455$	−2.97854e11	−0.325801
$456$	1.92874e12	2.08897
$457$	5.95490e11	0.638633	0.319317	−	0.947648i	$-0.396547\pi$
$457$	5.95490e11	0.638633	0.319317	+	0.947648i	$0.396547\pi$
$458$	1.26960e12	1.34826
$459$	7.40927e11	0.779145
$460$	6.06531e10	0.0631601
$461$	−1.24624e12	−1.28513	−0.642565	−	0.766231i	$-0.722130\pi$
$461$	−1.24624e12	−1.28513	−0.642565	+	0.766231i	$0.722130\pi$
$462$	4.41825e11	0.451192
$463$	1.26834e12	1.28269	0.641346	−	0.767252i	$-0.278376\pi$
$463$	1.26834e12	1.28269	0.641346	+	0.767252i	$0.278376\pi$
$464$	6.02194e11	0.603122
$465$	−3.08330e11	−0.305829
$466$	5.22881e10	0.0513649
$467$	−7.05768e11	−0.686651	−0.343325	−	0.939217i	$-0.611553\pi$
$467$	−7.05768e11	−0.686651	−0.343325	+	0.939217i	$0.611553\pi$
$468$	−1.01137e11	−0.0974547
$469$	−2.63590e11	−0.251566
$470$	−6.12024e11	−0.578533
$471$	1.06738e12	0.999371
$472$	−1.13998e11	−0.105720
$473$	1.22971e11	0.112961
$474$	3.03390e12	2.76057
$475$	1.86982e12	1.68530
$476$	1.51124e12	1.34928
$477$	1.95705e11	0.173089
$478$	3.21217e12	2.81432
$479$	1.12193e12	0.973768	0.486884	−	0.873467i	$-0.338133\pi$
$479$	1.12193e12	0.973768	0.486884	+	0.873467i	$0.338133\pi$
$480$	−8.77939e11	−0.754882
$481$	7.27142e9	0.00619393
$482$	−2.05715e11	−0.173602
$483$	−2.42300e10	−0.0202578
$484$	−2.03992e12	−1.68970
$485$	−1.18948e11	−0.0976159
$486$	−8.16556e11	−0.663931
$487$	8.32354e11	0.670545	0.335272	−	0.942121i	$-0.391172\pi$
$487$	8.32354e11	0.670545	0.335272	+	0.942121i	$0.391172\pi$
$488$	−1.99695e12	−1.59396
$489$	1.50780e12	1.19249
$490$	1.07046e12	0.838861
$491$	1.54507e12	1.19973	0.599863	−	0.800103i	$-0.295222\pi$
$491$	1.54507e12	1.19973	0.599863	+	0.800103i	$0.295222\pi$
$492$	−1.53604e12	−1.18184
$493$	1.20450e12	0.918326
$494$	7.79696e11	0.589053
$495$	1.19551e11	0.0895015
$496$	1.45647e11	0.108052
$497$	−1.27623e12	−0.938264
$498$	2.33603e11	0.170194
$499$	1.13614e12	0.820310	0.410155	−	0.912016i	$-0.365475\pi$
$499$	1.13614e12	0.820310	0.410155	+	0.912016i	$0.365475\pi$
$500$	1.07400e12	0.768492
$501$	−2.35063e12	−1.66692
$502$	2.28173e12	1.60360
$503$	−1.29522e12	−0.902170	−0.451085	−	0.892481i	$-0.648963\pi$
$503$	−1.29522e12	−0.902170	−0.451085	+	0.892481i	$0.648963\pi$
$504$	−3.41153e11	−0.235512
$505$	−8.60565e11	−0.588806
$506$	−1.67542e10	−0.0113618
$507$	1.51595e12	1.01894
$508$	1.29563e11	0.0863167
$509$	−9.48803e11	−0.626536	−0.313268	−	0.949665i	$-0.601424\pi$
$509$	−9.48803e11	−0.626536	−0.313268	+	0.949665i	$0.601424\pi$
$510$	3.78804e12	2.47942
$511$	6.13793e11	0.398224
$512$	1.72403e12	1.10874
$513$	1.81843e12	1.15923
$514$	4.07925e12	2.57778
$515$	−1.47392e12	−0.923298
$516$	−1.24042e12	−0.770274
$517$	1.09826e11	0.0676077
$518$	5.32459e10	0.0324940
$519$	−2.31060e12	−1.39789
$520$	9.57007e11	0.573984
$521$	−2.46207e12	−1.46396	−0.731981	−	0.681325i	$-0.761404\pi$
$521$	−2.46207e12	−1.46396	−0.731981	+	0.681325i	$0.761404\pi$
$522$	−5.90269e11	−0.347963
$523$	2.42753e12	1.41875	0.709377	−	0.704829i	$-0.248976\pi$
$523$	2.42753e12	1.41875	0.709377	+	0.704829i	$0.248976\pi$
$524$	−1.55609e12	−0.901664
$525$	−1.99029e12	−1.14340
$526$	−6.20106e11	−0.353208
$527$	2.91321e11	0.164522
$528$	−3.39843e11	−0.190295
$529$	−1.80023e12	−0.999490
$530$	−4.02008e12	−2.21306
$531$	2.67503e10	0.0146017
$532$	3.70899e12	2.00749
$533$	−2.86040e11	−0.153516
$534$	7.10921e11	0.378343
$535$	−1.91455e12	−1.01035
$536$	8.46917e11	0.443200
$537$	−4.26477e10	−0.0221315
$538$	4.04203e12	2.08008
$539$	−1.92091e11	−0.0980298
$540$	4.84522e12	2.45212
$541$	−3.08748e12	−1.54959	−0.774795	−	0.632213i	$-0.782147\pi$
$541$	−3.08748e12	−1.54959	−0.774795	+	0.632213i	$0.782147\pi$
$542$	−3.96115e12	−1.97163
$543$	1.54385e12	0.762091
$544$	8.29507e11	0.406092
$545$	2.83300e10	0.0137551
$546$	−8.29931e11	−0.399646
$547$	7.65281e11	0.365492	0.182746	−	0.983160i	$-0.441501\pi$
$547$	7.65281e11	0.365492	0.182746	+	0.983160i	$0.441501\pi$
$548$	2.31501e12	1.09658
$549$	4.68594e11	0.220151
$550$	−1.37622e12	−0.641291
$551$	2.95617e12	1.36630
$552$	7.78512e10	0.0356894
$553$	2.68755e12	1.22206
$554$	−3.96091e12	−1.78649
$555$	8.67023e10	0.0387893
$556$	−3.92367e12	−1.74123
$557$	−1.37829e12	−0.606727	−0.303364	−	0.952875i	$-0.598110\pi$
$557$	−1.37829e12	−0.606727	−0.303364	+	0.952875i	$0.598110\pi$
$558$	−1.42762e11	−0.0623390
$559$	−2.30990e11	−0.100055
$560$	1.67764e12	0.720863
$561$	−6.79752e11	−0.289746
$562$	1.56831e12	0.663161
$563$	2.62254e12	1.10011	0.550054	−	0.835129i	$-0.314607\pi$
$563$	2.62254e12	1.10011	0.550054	+	0.835129i	$0.314607\pi$
$564$	−1.10782e12	−0.461014
$565$	−4.99369e10	−0.0206160
$566$	−3.23217e11	−0.132379
$567$	−2.33729e12	−0.949705
$568$	4.10054e12	1.65300
$569$	9.63896e11	0.385501	0.192750	−	0.981248i	$-0.438259\pi$
$569$	9.63896e11	0.385501	0.192750	+	0.981248i	$0.438259\pi$
$570$	9.29687e12	3.68893
$571$	−2.36629e12	−0.931550	−0.465775	−	0.884903i	$-0.654224\pi$
$571$	−2.36629e12	−0.931550	−0.465775	+	0.884903i	$0.654224\pi$
$572$	−3.72801e11	−0.145611
$573$	2.34074e12	0.907105
$574$	−2.09456e12	−0.805360
$575$	7.54727e10	0.0287929
$576$	−7.13738e11	−0.270170
$577$	−3.34486e11	−0.125628	−0.0628140	−	0.998025i	$-0.520008\pi$
$577$	−3.34486e11	−0.125628	−0.0628140	+	0.998025i	$0.520008\pi$
$578$	9.54173e11	0.355592
$579$	4.87977e11	0.180446
$580$	7.87673e12	2.89015
$581$	2.06935e11	0.0753426
$582$	−3.31434e11	−0.119741
$583$	7.21390e11	0.258620
$584$	−1.97212e12	−0.701578
$585$	−2.24567e11	−0.0792764
$586$	−2.73995e12	−0.959849
$587$	2.97724e12	1.03501	0.517503	−	0.855682i	$-0.326862\pi$
$587$	2.97724e12	1.03501	0.517503	+	0.855682i	$0.326862\pi$
$588$	1.93765e12	0.668461
$589$	7.14980e11	0.244779
$590$	−5.49492e11	−0.186693
$591$	−2.31405e11	−0.0780241
$592$	−4.09558e10	−0.0137046
$593$	−2.95484e12	−0.981269	−0.490634	−	0.871366i	$-0.663235\pi$
$593$	−2.95484e12	−0.981269	−0.490634	+	0.871366i	$0.663235\pi$
$594$	−1.33840e12	−0.441110
$595$	3.35560e12	1.09760
$596$	−5.70579e12	−1.85228
$597$	−1.97495e12	−0.636313
$598$	3.14714e10	0.0100638
$599$	−2.19881e12	−0.697857	−0.348929	−	0.937149i	$-0.613454\pi$
$599$	−2.19881e12	−0.697857	−0.348929	+	0.937149i	$0.613454\pi$
$600$	6.39480e12	2.01440
$601$	1.04958e12	0.328156	0.164078	−	0.986447i	$-0.447535\pi$
$601$	1.04958e12	0.328156	0.164078	+	0.986447i	$0.447535\pi$
$602$	−1.69146e12	−0.524900
$603$	−1.98734e11	−0.0612130
$604$	1.01070e13	3.09000
$605$	−4.52950e12	−1.37452
$606$	−2.39785e12	−0.722263
$607$	4.96644e11	0.148490	0.0742449	−	0.997240i	$-0.476345\pi$
$607$	4.96644e11	0.148490	0.0742449	+	0.997240i	$0.476345\pi$
$608$	2.03583e12	0.604193
$609$	−3.14664e12	−0.926977
$610$	−9.62564e12	−2.81479
$611$	−2.06298e11	−0.0598839
$612$	1.13940e12	0.328318
$613$	−2.11053e11	−0.0603699	−0.0301849	−	0.999544i	$-0.509610\pi$
$613$	−2.11053e11	−0.0603699	−0.0301849	+	0.999544i	$0.509610\pi$
$614$	−7.04919e12	−2.00162
$615$	−3.41065e12	−0.961390
$616$	−1.25753e12	−0.351888
$617$	−3.15337e12	−0.875974	−0.437987	−	0.898981i	$-0.644308\pi$
$617$	−3.15337e12	−0.875974	−0.437987	+	0.898981i	$0.644308\pi$
$618$	−4.10689e12	−1.13257
$619$	1.40671e12	0.385121	0.192561	−	0.981285i	$-0.438321\pi$
$619$	1.40671e12	0.385121	0.192561	+	0.981285i	$0.438321\pi$
$620$	1.90507e12	0.517783
$621$	7.33988e10	0.0198051
$622$	2.49643e11	0.0668749
$623$	6.29762e11	0.167487
$624$	6.38367e11	0.168554
$625$	−2.47828e12	−0.649667
$626$	−1.00157e13	−2.60674
$627$	−1.66829e12	−0.431090
$628$	−6.59500e12	−1.69198
$629$	−8.19193e10	−0.0208669
$630$	−1.64442e12	−0.415892
$631$	4.63510e12	1.16393	0.581966	−	0.813213i	$-0.302284\pi$
$631$	4.63510e12	1.16393	0.581966	+	0.813213i	$0.302284\pi$
$632$	−8.63511e12	−2.15298
$633$	−4.91568e12	−1.21693
$634$	5.09089e12	1.25139
$635$	2.87686e11	0.0702160
$636$	−7.27674e12	−1.76352
$637$	3.60827e11	0.0868304
$638$	−2.17580e12	−0.519906
$639$	−9.62213e11	−0.228306
$640$	1.17356e13	2.76500
$641$	2.74470e12	0.642145	0.321073	−	0.947055i	$-0.395957\pi$
$641$	2.74470e12	0.642145	0.321073	+	0.947055i	$0.395957\pi$
$642$	−5.33463e12	−1.23936
$643$	−4.81477e12	−1.11078	−0.555388	−	0.831591i	$-0.687430\pi$
$643$	−4.81477e12	−1.11078	−0.555388	+	0.831591i	$0.687430\pi$
$644$	1.49709e11	0.0342974
$645$	−2.75426e12	−0.626594
$646$	−8.78400e12	−1.98448
$647$	−7.31467e12	−1.64106	−0.820531	−	0.571602i	$-0.806322\pi$
$647$	−7.31467e12	−1.64106	−0.820531	+	0.571602i	$0.806322\pi$
$648$	7.50973e12	1.67316
$649$	9.86044e10	0.0218170
$650$	2.58511e12	0.568027
$651$	−7.61045e11	−0.166072
$652$	−9.31618e12	−2.01894
$653$	−4.80438e12	−1.03402	−0.517009	−	0.855980i	$-0.672955\pi$
$653$	−4.80438e12	−1.03402	−0.517009	+	0.855980i	$0.672955\pi$
$654$	7.89379e10	0.0168727
$655$	−3.45519e12	−0.733477
$656$	1.61110e12	0.339668
$657$	4.62769e11	0.0968991
$658$	−1.51065e12	−0.314156
$659$	−3.89676e12	−0.804858	−0.402429	−	0.915451i	$-0.631834\pi$
$659$	−3.89676e12	−0.804858	−0.402429	+	0.915451i	$0.631834\pi$
$660$	−4.44517e12	−0.911887
$661$	3.64506e12	0.742673	0.371336	−	0.928498i	$-0.378900\pi$
$661$	3.64506e12	0.742673	0.371336	+	0.928498i	$0.378900\pi$
$662$	−8.67769e12	−1.75608
$663$	1.27686e12	0.256644
$664$	−6.64882e11	−0.132736
$665$	8.23555e12	1.63303
$666$	4.01447e10	0.00790669
$667$	1.19322e11	0.0233429
$668$	1.45237e13	2.82218
$669$	−1.01121e13	−1.95174
$670$	4.08229e12	0.782650
$671$	1.72729e12	0.328938
$672$	−2.16700e12	−0.409918
$673$	5.49056e12	1.03169	0.515844	−	0.856682i	$-0.327478\pi$
$673$	5.49056e12	1.03169	0.515844	+	0.856682i	$0.327478\pi$
$674$	2.74306e11	0.0511994
$675$	6.02908e12	1.11785
$676$	−9.36652e12	−1.72512
$677$	−1.69761e12	−0.310591	−0.155296	−	0.987868i	$-0.549633\pi$
$677$	−1.69761e12	−0.310591	−0.155296	+	0.987868i	$0.549633\pi$
$678$	−1.39143e11	−0.0252887
$679$	−2.93598e11	−0.0530077
$680$	−1.07816e13	−1.93371
$681$	9.09033e12	1.61964
$682$	−5.26238e11	−0.0931435
$683$	−7.52172e9	−0.00132259	−0.000661293	−	1.00000i	$-0.500210\pi$
$683$	−7.52172e9	−0.00132259	−0.000661293		1.00000i	$0.500210\pi$
$684$	2.79639e12	0.488478
$685$	5.14031e12	0.892036
$686$	1.06679e13	1.83917
$687$	5.10277e12	0.873978
$688$	1.30104e12	0.221381
$689$	−1.35507e12	−0.229074
$690$	3.75256e11	0.0630242
$691$	−3.24633e12	−0.541679	−0.270840	−	0.962625i	$-0.587301\pi$
$691$	−3.24633e12	−0.541679	−0.270840	+	0.962625i	$0.587301\pi$
$692$	1.42764e13	2.36669
$693$	2.95086e11	0.0486014
$694$	−3.28126e12	−0.536937
$695$	−8.71222e12	−1.41644
$696$	1.01102e13	1.63311
$697$	3.22250e12	0.517185
$698$	−7.52096e12	−1.19929
$699$	2.10156e11	0.0332962
$700$	1.22973e13	1.93583
$701$	1.14756e12	0.179492	0.0897462	−	0.995965i	$-0.471394\pi$
$701$	1.14756e12	0.179492	0.0897462	+	0.995965i	$0.471394\pi$
$702$	2.51407e12	0.390715
$703$	−2.01052e11	−0.0310463
$704$	−2.63092e12	−0.403673
$705$	−2.45984e12	−0.375021
$706$	−1.96325e13	−2.97410
$707$	−2.12411e12	−0.319735
$708$	−9.94634e11	−0.148769
$709$	−1.08250e13	−1.60886	−0.804432	−	0.594044i	$-0.797530\pi$
$709$	−1.08250e13	−1.60886	−0.804432	+	0.594044i	$0.797530\pi$
$710$	1.97653e13	2.91905
$711$	2.02627e12	0.297362
$712$	−2.02343e12	−0.295072
$713$	2.88592e10	0.00418198
$714$	9.34995e12	1.34638
$715$	−8.27777e11	−0.118450
$716$	2.63505e11	0.0374698
$717$	1.29103e13	1.82432
$718$	−7.34154e12	−1.03093
$719$	−7.26303e12	−1.01353	−0.506766	−	0.862083i	$-0.669159\pi$
$719$	−7.26303e12	−1.01353	−0.506766	+	0.862083i	$0.669159\pi$
$720$	1.26486e12	0.175406
$721$	−3.63805e12	−0.501372
$722$	−9.22294e12	−1.26314
$723$	−8.26809e11	−0.112534
$724$	−9.53893e12	−1.29026
$725$	9.80129e12	1.31753
$726$	−1.26209e13	−1.68606
$727$	−7.97647e11	−0.105902	−0.0529512	−	0.998597i	$-0.516863\pi$
$727$	−7.97647e11	−0.105902	−0.0529512	+	0.998597i	$0.516863\pi$
$728$	2.36216e12	0.311687
$729$	5.56054e12	0.729194
$730$	−9.50597e12	−1.23892
$731$	2.60232e12	0.337080
$732$	−1.74234e13	−2.24301
$733$	−3.30785e12	−0.423232	−0.211616	−	0.977353i	$-0.567873\pi$
$733$	−3.30785e12	−0.423232	−0.211616	+	0.977353i	$0.567873\pi$
$734$	2.71547e12	0.345313
$735$	4.30240e12	0.543773
$736$	8.21737e10	0.0103225
$737$	−7.32554e11	−0.0914609
$738$	−1.57919e12	−0.195966
$739$	9.17440e12	1.13156	0.565780	−	0.824556i	$-0.308575\pi$
$739$	9.17440e12	1.13156	0.565780	+	0.824556i	$0.308575\pi$
$740$	−5.35704e11	−0.0656722
$741$	3.13375e12	0.381840
$742$	−9.92269e12	−1.20174
$743$	1.29134e13	1.55451	0.777253	−	0.629189i	$-0.216613\pi$
$743$	1.29134e13	1.55451	0.777253	+	0.629189i	$0.216613\pi$
$744$	2.44524e12	0.292580
$745$	−1.26693e13	−1.50678
$746$	−2.28492e13	−2.70114
$747$	1.56018e11	0.0183329
$748$	4.19995e12	0.490554
$749$	−4.72563e12	−0.548645
$750$	6.64477e12	0.766839
$751$	1.13700e13	1.30431	0.652153	−	0.758087i	$-0.273866\pi$
$751$	1.13700e13	1.30431	0.652153	+	0.758087i	$0.273866\pi$
$752$	1.16196e12	0.132498
$753$	9.17070e12	1.03950
$754$	4.08705e12	0.460510
$755$	2.24420e13	2.51362
$756$	1.19594e13	1.33156
$757$	6.02655e12	0.667017	0.333509	−	0.942747i	$-0.391767\pi$
$757$	6.02655e12	0.667017	0.333509	+	0.942747i	$0.391767\pi$
$758$	−2.65435e13	−2.92043
$759$	−6.73385e10	−0.00736505
$760$	−2.64609e13	−2.87702
$761$	−9.14307e11	−0.0988237	−0.0494119	−	0.998778i	$-0.515735\pi$
$761$	−9.14307e11	−0.0988237	−0.0494119	+	0.998778i	$0.515735\pi$
$762$	8.01598e11	0.0861310
$763$	6.99263e10	0.00746931
$764$	−1.44626e13	−1.53577
$765$	2.52995e12	0.267077
$766$	7.71312e12	0.809470
$767$	−1.85220e11	−0.0193245
$768$	1.83863e13	1.90708
$769$	3.48454e12	0.359316	0.179658	−	0.983729i	$-0.442501\pi$
$769$	3.48454e12	0.359316	0.179658	+	0.983729i	$0.442501\pi$
$770$	−6.06151e12	−0.621402
$771$	1.63953e13	1.67099
$772$	−3.01504e12	−0.305503
$773$	−9.06972e12	−0.913663	−0.456832	−	0.889553i	$-0.651016\pi$
$773$	−9.06972e12	−0.913663	−0.456832	+	0.889553i	$0.651016\pi$
$774$	−1.27527e12	−0.127723
$775$	2.37054e12	0.236042
$776$	9.43332e11	0.0933871
$777$	2.14006e11	0.0210635
$778$	−1.38328e11	−0.0135364
$779$	7.90888e12	0.769479
$780$	8.34988e12	0.807708
$781$	−3.54682e12	−0.341122
$782$	−3.54555e11	−0.0339042
$783$	9.53195e12	0.906262
$784$	−2.03233e12	−0.192120
$785$	−1.46437e13	−1.37638
$786$	−9.62744e12	−0.899724
$787$	−2.91276e12	−0.270657	−0.135328	−	0.990801i	$-0.543209\pi$
$787$	−2.91276e12	−0.270657	−0.135328	+	0.990801i	$0.543209\pi$
$788$	1.42977e12	0.132099
$789$	−2.49232e12	−0.228959
$790$	−4.16228e13	−3.80197
$791$	−1.23258e11	−0.0111949
$792$	−9.48112e11	−0.0856242
$793$	−3.24457e12	−0.291358
$794$	−2.23948e13	−1.99965
$795$	−1.61575e13	−1.43457
$796$	1.22025e13	1.07731
$797$	1.37467e13	1.20680	0.603400	−	0.797439i	$-0.293812\pi$
$797$	1.37467e13	1.20680	0.603400	+	0.797439i	$0.293812\pi$
$798$	2.29473e13	2.00317
$799$	2.32414e12	0.201745
$800$	6.74987e12	0.582627
$801$	4.74809e11	0.0407542
$802$	−2.15389e13	−1.83839
$803$	1.70582e12	0.144781
$804$	7.38935e12	0.623669
$805$	3.32417e11	0.0278999
$806$	9.88493e11	0.0825023
$807$	1.62457e13	1.34837
$808$	6.82479e12	0.563298
$809$	2.09640e13	1.72070	0.860352	−	0.509700i	$-0.170244\pi$
$809$	2.09640e13	1.72070	0.860352	+	0.509700i	$0.170244\pi$
$810$	3.61982e13	2.95464
$811$	1.80143e13	1.46226	0.731130	−	0.682238i	$-0.238993\pi$
$811$	1.80143e13	1.46226	0.731130	+	0.682238i	$0.238993\pi$
$812$	1.94420e13	1.56942
$813$	−1.59206e13	−1.27806
$814$	1.47978e11	0.0118137
$815$	−2.06859e13	−1.64235
$816$	−7.19180e12	−0.567848
$817$	6.38679e12	0.501514
$818$	4.02883e13	3.14622
$819$	−5.54294e11	−0.0430489
$820$	2.10732e13	1.62768
$821$	−1.41619e13	−1.08787	−0.543934	−	0.839128i	$-0.683066\pi$
$821$	−1.41619e13	−1.08787	−0.543934	+	0.839128i	$0.683066\pi$
$822$	1.43228e13	1.09422
$823$	1.99084e13	1.51264	0.756321	−	0.654201i	$-0.226995\pi$
$823$	1.99084e13	1.51264	0.756321	+	0.654201i	$0.226995\pi$
$824$	1.16891e13	0.883299
$825$	−5.53128e12	−0.415703
$826$	−1.35630e12	−0.101378
$827$	−1.21535e12	−0.0903497	−0.0451749	−	0.998979i	$-0.514385\pi$
$827$	−1.21535e12	−0.0903497	−0.0451749	+	0.998979i	$0.514385\pi$
$828$	1.12873e11	0.00834551
$829$	1.43806e13	1.05750	0.528752	−	0.848777i	$-0.322660\pi$
$829$	1.43806e13	1.05750	0.528752	+	0.848777i	$0.322660\pi$
$830$	−3.20485e12	−0.234399
$831$	−1.59196e13	−1.15805
$832$	4.94195e12	0.357556
$833$	−4.06505e12	−0.292525
$834$	−2.42755e13	−1.73748
$835$	3.22489e13	2.29576
$836$	1.03078e13	0.729857
$837$	2.30540e12	0.162361
$838$	−1.22846e13	−0.860527
$839$	1.95134e11	0.0135958	0.00679790	−	0.999977i	$-0.497836\pi$
$839$	1.95134e11	0.0135958	0.00679790	+	0.999977i	$0.497836\pi$
$840$	2.81657e13	1.95193
$841$	9.88657e11	0.0681497
$842$	3.58623e13	2.45886
$843$	6.30335e12	0.429880
$844$	3.03723e13	2.06033
$845$	−2.07977e13	−1.40333
$846$	−1.13895e12	−0.0764430
$847$	−1.11801e13	−0.746396
$848$	7.63234e12	0.506846
$849$	−1.29907e12	−0.0858119
$850$	−2.91237e13	−1.91364
$851$	−8.11520e9	−0.000530416 0
$852$	3.57772e13	2.32610
$853$	−1.61260e13	−1.04293	−0.521467	−	0.853271i	$-0.674615\pi$
$853$	−1.61260e13	−1.04293	−0.521467	+	0.853271i	$0.674615\pi$
$854$	−2.37588e13	−1.52849
$855$	6.20918e12	0.397363
$856$	1.51835e13	0.966584
$857$	2.32841e13	1.47450	0.737252	−	0.675618i	$-0.236123\pi$
$857$	2.32841e13	1.47450	0.737252	+	0.675618i	$0.236123\pi$
$858$	−2.30649e12	−0.145298
$859$	−2.80294e13	−1.75649	−0.878244	−	0.478212i	$-0.841285\pi$
$859$	−2.80294e13	−1.75649	−0.878244	+	0.478212i	$0.841285\pi$
$860$	1.70176e13	1.06085
$861$	−8.41845e12	−0.522057
$862$	−3.58420e13	−2.21110
$863$	1.95516e13	1.19987	0.599933	−	0.800050i	$-0.295194\pi$
$863$	1.95516e13	1.19987	0.599933	+	0.800050i	$0.295194\pi$
$864$	6.56438e12	0.400758
$865$	3.16997e13	1.92523
$866$	−2.92079e13	−1.76469
$867$	3.83500e12	0.230505
$868$	4.70223e12	0.281168
$869$	7.46906e12	0.444301
$870$	4.87328e13	2.88393
$871$	1.37604e12	0.0810120
$872$	−2.24674e11	−0.0131592
$873$	−2.21358e11	−0.0128982
$874$	−8.70173e11	−0.0504434
$875$	5.88620e12	0.339468
$876$	−1.72067e13	−0.987257
$877$	−2.28721e13	−1.30560	−0.652798	−	0.757532i	$-0.726405\pi$
$877$	−2.28721e13	−1.30560	−0.652798	+	0.757532i	$0.726405\pi$
$878$	1.02219e12	0.0580506
$879$	−1.10124e13	−0.622201
$880$	4.66240e12	0.262082
$881$	−1.32499e13	−0.741007	−0.370504	−	0.928831i	$-0.620815\pi$
$881$	−1.32499e13	−0.741007	−0.370504	+	0.928831i	$0.620815\pi$
$882$	1.99209e12	0.110841
$883$	4.12981e12	0.228616	0.114308	−	0.993445i	$-0.463535\pi$
$883$	4.12981e12	0.228616	0.114308	+	0.993445i	$0.463535\pi$
$884$	−7.88925e12	−0.434511
$885$	−2.20851e12	−0.121019
$886$	1.08969e12	0.0594089
$887$	2.42722e13	1.31660	0.658298	−	0.752757i	$-0.271277\pi$
$887$	2.42722e13	1.31660	0.658298	+	0.752757i	$0.271277\pi$
$888$	−6.87601e11	−0.0371089
$889$	7.10088e11	0.0381289
$890$	−9.75329e12	−0.521070
$891$	−6.49565e12	−0.345281
$892$	6.24788e13	3.30439
$893$	5.70406e12	0.300160
$894$	−3.53013e13	−1.84830
$895$	5.85094e11	0.0304805
$896$	2.89667e13	1.50146
$897$	1.26490e11	0.00652363
$898$	5.80965e13	2.98130
$899$	3.74781e12	0.191364
$900$	9.27153e12	0.471043
$901$	1.52661e13	0.771734
$902$	−5.82108e12	−0.292802
$903$	−6.79829e12	−0.340255
$904$	3.96029e11	0.0197228
$905$	−2.11805e13	−1.04958
$906$	6.25316e13	3.08335
$907$	3.60325e12	0.176792	0.0883958	−	0.996085i	$-0.471826\pi$
$907$	3.60325e12	0.176792	0.0883958	+	0.996085i	$0.471826\pi$
$908$	−5.61660e13	−2.74212
$909$	−1.60147e12	−0.0778005
$910$	1.13860e13	0.550410
$911$	1.38844e12	0.0667872	0.0333936	−	0.999442i	$-0.489369\pi$
$911$	1.38844e12	0.0667872	0.0333936	+	0.999442i	$0.489369\pi$
$912$	−1.76506e13	−0.844856
$913$	5.75100e11	0.0273920
$914$	−2.27637e13	−1.07891
$915$	−3.86873e13	−1.82462
$916$	−3.15282e13	−1.47969
$917$	−8.52838e12	−0.398295
$918$	−2.83233e13	−1.31629
$919$	1.30682e13	0.604361	0.302180	−	0.953251i	$-0.402285\pi$
$919$	1.30682e13	0.604361	0.302180	+	0.953251i	$0.402285\pi$
$920$	−1.06806e12	−0.0491530
$921$	−2.83320e13	−1.29751
$922$	4.76398e13	2.17111
$923$	6.66240e12	0.302150
$924$	−1.09719e13	−0.495175
$925$	−6.66594e11	−0.0299381
$926$	−4.84848e13	−2.16699
$927$	−2.74290e12	−0.121998
$928$	1.06715e13	0.472346
$929$	−2.19012e13	−0.964709	−0.482354	−	0.875976i	$-0.660218\pi$
$929$	−2.19012e13	−0.964709	−0.482354	+	0.875976i	$0.660218\pi$
$930$	1.17865e13	0.516669
$931$	−9.97673e12	−0.435226
$932$	−1.29848e12	−0.0563720
$933$	1.00336e12	0.0433502
$934$	2.69793e13	1.16003
$935$	9.32568e12	0.399051
$936$	1.78095e12	0.0758421
$937$	1.20196e13	0.509403	0.254701	−	0.967020i	$-0.418023\pi$
$937$	1.20196e13	0.509403	0.254701	+	0.967020i	$0.418023\pi$
$938$	1.00762e13	0.424997
$939$	−4.02550e13	−1.68976
$940$	1.51985e13	0.634929
$941$	2.50039e13	1.03957	0.519786	−	0.854297i	$-0.326012\pi$
$941$	2.50039e13	1.03957	0.519786	+	0.854297i	$0.326012\pi$
$942$	−4.08028e13	−1.68834
$943$	3.19232e11	0.0131463
$944$	1.04324e12	0.0427573
$945$	2.65549e13	1.08318
$946$	−4.70079e12	−0.190836
$947$	3.96314e13	1.60127	0.800636	−	0.599151i	$-0.204495\pi$
$947$	3.96314e13	1.60127	0.800636	+	0.599151i	$0.204495\pi$
$948$	−7.53413e13	−3.02967
$949$	−3.20423e12	−0.128241
$950$	−7.14772e13	−2.84716
$951$	2.04613e13	0.811185
$952$	−2.66119e13	−1.05005
$953$	−6.42157e12	−0.252187	−0.126094	−	0.992018i	$-0.540244\pi$
$953$	−6.42157e12	−0.252187	−0.126094	+	0.992018i	$0.540244\pi$
$954$	−7.48120e12	−0.292418
$955$	−3.21132e13	−1.24930
$956$	−7.97685e13	−3.08866
$957$	−8.74494e12	−0.337018
$958$	−4.28878e13	−1.64509
$959$	1.26877e13	0.484396
$960$	5.89265e13	2.23918
$961$	−2.55332e13	−0.965716
$962$	−2.77964e11	−0.0104641
$963$	−3.56289e12	−0.133501
$964$	5.10857e12	0.190525
$965$	−6.69468e12	−0.248518
$966$	9.26238e11	0.0342236
$967$	3.50542e13	1.28920	0.644600	−	0.764520i	$-0.277024\pi$
$967$	3.50542e13	1.28920	0.644600	+	0.764520i	$0.277024\pi$
$968$	3.59216e13	1.31497
$969$	−3.53046e13	−1.28639
$970$	4.54703e12	0.164913
$971$	−5.00924e13	−1.80836	−0.904181	−	0.427150i	$-0.859517\pi$
$971$	−5.00924e13	−1.80836	−0.904181	+	0.427150i	$0.859517\pi$
$972$	2.02777e13	0.728652
$973$	−2.15042e13	−0.769158
$974$	−3.18183e13	−1.13282
$975$	1.03900e13	0.368211
$976$	1.82748e13	0.644656
$977$	−3.04571e13	−1.06946	−0.534728	−	0.845024i	$-0.679586\pi$
$977$	−3.04571e13	−1.06946	−0.534728	+	0.845024i	$0.679586\pi$
$978$	−5.76386e13	−2.01460
$979$	1.75020e12	0.0608926
$980$	−2.65830e13	−0.920634
$981$	5.27209e10	0.00181749
$982$	−5.90633e13	−2.02682
$983$	−4.68733e13	−1.60116	−0.800579	−	0.599227i	$-0.795475\pi$
$983$	−4.68733e13	−1.60116	−0.800579	+	0.599227i	$0.795475\pi$
$984$	2.70485e13	0.919741
$985$	3.17470e12	0.107458
$986$	−4.60444e13	−1.55142
$987$	−6.07157e12	−0.203645
$988$	−1.93623e13	−0.646474
$989$	2.57795e11	0.00856822
$990$	−4.57007e12	−0.151204
$991$	−1.75561e13	−0.578224	−0.289112	−	0.957295i	$-0.593360\pi$
$991$	−1.75561e13	−0.578224	−0.289112	+	0.957295i	$0.593360\pi$
$992$	2.58101e12	0.0846228
$993$	−3.48773e13	−1.13834
$994$	4.87863e13	1.58511
$995$	2.70948e13	0.876358
$996$	−5.80109e12	−0.186785
$997$	2.86332e13	0.917787	0.458893	−	0.888491i	$-0.348246\pi$
$997$	2.86332e13	0.917787	0.458893	+	0.888491i	$0.348246\pi$
$998$	−4.34310e13	−1.38584
$999$	−6.48277e11	−0.0205928

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.10.a.b.1.8	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.10.a.b.1.8	✓	76	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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-38.2269 q^{2} -153.641 q^{3} +949.295 q^{4} +2107.84 q^{5} +5873.22 q^{6} +5202.74 q^{7} -16716.4 q^{8} +3922.60 q^{9} +O(q^{10})\)	\(q-38.2269 q^{2} -153.641 q^{3} +949.295 q^{4} +2107.84 q^{5} +5873.22 q^{6} +5202.74 q^{7} -16716.4 q^{8} +3922.60 q^{9} -80576.2 q^{10} +14459.1 q^{11} -145851. q^{12} -27160.2 q^{13} -198885. q^{14} -323851. q^{15} +152978. q^{16} +305985. q^{17} -149949. q^{18} +750970. q^{19} +2.00096e6 q^{20} -799355. q^{21} -552727. q^{22} +30312.0 q^{23} +2.56833e6 q^{24} +2.48987e6 q^{25} +1.03825e6 q^{26} +2.42145e6 q^{27} +4.93893e6 q^{28} +3.93647e6 q^{29} +1.23798e7 q^{30} +952075. q^{31} +2.71094e6 q^{32} -2.22152e6 q^{33} -1.16969e7 q^{34} +1.09665e7 q^{35} +3.72371e6 q^{36} -267723. q^{37} -2.87072e7 q^{38} +4.17293e6 q^{39} -3.52356e7 q^{40} +1.05316e7 q^{41} +3.05568e7 q^{42} +8.50472e6 q^{43} +1.37260e7 q^{44} +8.26822e6 q^{45} -1.15873e6 q^{46} +7.59559e6 q^{47} -2.35037e7 q^{48} -1.32851e7 q^{49} -9.51799e7 q^{50} -4.70120e7 q^{51} -2.57831e7 q^{52} +4.98917e7 q^{53} -9.25643e7 q^{54} +3.04775e7 q^{55} -8.69712e7 q^{56} -1.15380e8 q^{57} -1.50479e8 q^{58} +6.81953e6 q^{59} -3.07430e8 q^{60} +1.19460e8 q^{61} -3.63949e7 q^{62} +2.04083e7 q^{63} -1.81955e8 q^{64} -5.72495e7 q^{65} +8.49217e7 q^{66} -5.06638e7 q^{67} +2.90470e8 q^{68} -4.65716e6 q^{69} -4.19217e8 q^{70} -2.45300e8 q^{71} -6.55719e7 q^{72} +1.17975e8 q^{73} +1.02342e7 q^{74} -3.82546e8 q^{75} +7.12892e8 q^{76} +7.52270e7 q^{77} -1.59518e8 q^{78} +5.16564e8 q^{79} +3.22454e8 q^{80} -4.49242e8 q^{81} -4.02589e8 q^{82} +3.97742e7 q^{83} -7.58824e8 q^{84} +6.44969e8 q^{85} -3.25109e8 q^{86} -6.04804e8 q^{87} -2.41705e8 q^{88} +1.21044e8 q^{89} -3.16068e8 q^{90} -1.41308e8 q^{91} +2.87750e7 q^{92} -1.46278e8 q^{93} -2.90356e8 q^{94} +1.58293e9 q^{95} -4.16511e8 q^{96} -5.64314e7 q^{97} +5.07849e8 q^{98} +5.67174e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9}+O(q^{10}) \) 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9	\( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9} + 121093 q^{10} + 120464 q^{11} + 415744 q^{12} + 480131 q^{13} + 330849 q^{14} + 544874 q^{15} + 5963776 q^{16} + 942582 q^{17} + 1483945 q^{18} + 3097319 q^{19} + 3237739 q^{20} + 889076 q^{21} + 3791921 q^{22} + 5139200 q^{23} + 1999533 q^{24} + 34080519 q^{25} + 2791454 q^{26} + 24386486 q^{27} + 20891166 q^{28} + 6886818 q^{29} + 14171083 q^{30} + 28002851 q^{31} + 16857332 q^{32} + 30921422 q^{33} + 33506194 q^{34} + 16271736 q^{35} + 151430458 q^{36} + 55950976 q^{37} + 62370882 q^{38} - 11569592 q^{39} + 129854766 q^{40} + 14990859 q^{41} + 82216531 q^{42} + 169867467 q^{43} + 41872434 q^{44} + 205007649 q^{45} + 144032301 q^{46} + 78743342 q^{47} + 156250562 q^{48} + 533861890 q^{49} + 626841163 q^{50} + 477099244 q^{51} + 560784114 q^{52} + 188670216 q^{53} + 525901687 q^{54} + 298497914 q^{55} + 56575048 q^{56} + 213972590 q^{57} + 338315251 q^{58} + 208222151 q^{59} - 615921507 q^{60} - 233556134 q^{61} - 399368105 q^{62} + 329825056 q^{63} + 876517017 q^{64} - 840557006 q^{65} - 2482481592 q^{66} + 1210808414 q^{67} - 1266757099 q^{68} + 327801786 q^{69} - 546384313 q^{70} + 345300221 q^{71} - 1549481681 q^{72} + 1192286460 q^{73} - 1471133595 q^{74} + 761630676 q^{75} - 398699826 q^{76} - 101106252 q^{77} - 2609825943 q^{78} + 955627631 q^{79} + 1059617770 q^{80} + 3387041436 q^{81} + 1062705523 q^{82} + 1538917201 q^{83} + 1394513218 q^{84} + 225481100 q^{85} + 701644810 q^{86} + 1758812842 q^{87} + 3151474875 q^{88} + 855413630 q^{89} + 6070671455 q^{90} + 4652436248 q^{91} + 8082863606 q^{92} + 3462095982 q^{93} + 2660342117 q^{94} + 1036805508 q^{95} + 12370989029 q^{96} + 6393874545 q^{97} + 7510976010 q^{98} + 8731109606 q^{99}+O(q^{100}) \) 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9 + 121093 * q^10 + 120464 * q^11 + 415744 * q^12 + 480131 * q^13 + 330849 * q^14 + 544874 * q^15 + 5963776 * q^16 + 942582 * q^17 + 1483945 * q^18 + 3097319 * q^19 + 3237739 * q^20 + 889076 * q^21 + 3791921 * q^22 + 5139200 * q^23 + 1999533 * q^24 + 34080519 * q^25 + 2791454 * q^26 + 24386486 * q^27 + 20891166 * q^28 + 6886818 * q^29 + 14171083 * q^30 + 28002851 * q^31 + 16857332 * q^32 + 30921422 * q^33 + 33506194 * q^34 + 16271736 * q^35 + 151430458 * q^36 + 55950976 * q^37 + 62370882 * q^38 - 11569592 * q^39 + 129854766 * q^40 + 14990859 * q^41 + 82216531 * q^42 + 169867467 * q^43 + 41872434 * q^44 + 205007649 * q^45 + 144032301 * q^46 + 78743342 * q^47 + 156250562 * q^48 + 533861890 * q^49 + 626841163 * q^50 + 477099244 * q^51 + 560784114 * q^52 + 188670216 * q^53 + 525901687 * q^54 + 298497914 * q^55 + 56575048 * q^56 + 213972590 * q^57 + 338315251 * q^58 + 208222151 * q^59 - 615921507 * q^60 - 233556134 * q^61 - 399368105 * q^62 + 329825056 * q^63 + 876517017 * q^64 - 840557006 * q^65 - 2482481592 * q^66 + 1210808414 * q^67 - 1266757099 * q^68 + 327801786 * q^69 - 546384313 * q^70 + 345300221 * q^71 - 1549481681 * q^72 + 1192286460 * q^73 - 1471133595 * q^74 + 761630676 * q^75 - 398699826 * q^76 - 101106252 * q^77 - 2609825943 * q^78 + 955627631 * q^79 + 1059617770 * q^80 + 3387041436 * q^81 + 1062705523 * q^82 + 1538917201 * q^83 + 1394513218 * q^84 + 225481100 * q^85 + 701644810 * q^86 + 1758812842 * q^87 + 3151474875 * q^88 + 855413630 * q^89 + 6070671455 * q^90 + 4652436248 * q^91 + 8082863606 * q^92 + 3462095982 * q^93 + 2660342117 * q^94 + 1036805508 * q^95 + 12370989029 * q^96 + 6393874545 * q^97 + 7510976010 * q^98 + 8731109606 * q^99

Introduction

L-functions

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