LMFDB - Embedded newform 17.10.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,10,Mod(1,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, 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("17.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	17.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:	$8.75560921479$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 1596x^{3} + 5754x^{2} + 488987x - 2711704 $ x^5 - 2x^4 - 1596x^3 + 5754x^2 + 488987x - 2711704
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-35.0613$ of defining polynomial
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-42.0613 q^{2} -256.773 q^{3} +1257.15 q^{4} +1407.25 q^{5} +10800.2 q^{6} -5138.64 q^{7} -31342.2 q^{8} +46249.6 q^{9} +O(q^{10})$	\(q-42.0613 q^{2} -256.773 q^{3} +1257.15 q^{4} +1407.25 q^{5} +10800.2 q^{6} -5138.64 q^{7} -31342.2 q^{8} +46249.6 q^{9} -59190.7 q^{10} +26560.4 q^{11} -322804. q^{12} +71402.0 q^{13} +216138. q^{14} -361344. q^{15} +674631. q^{16} -83521.0 q^{17} -1.94532e6 q^{18} -548715. q^{19} +1.76913e6 q^{20} +1.31947e6 q^{21} -1.11716e6 q^{22} +1.15988e6 q^{23} +8.04785e6 q^{24} +27218.8 q^{25} -3.00326e6 q^{26} -6.82160e6 q^{27} -6.46007e6 q^{28} +1.44199e6 q^{29} +1.51986e7 q^{30} -6.05781e6 q^{31} -1.23287e7 q^{32} -6.82000e6 q^{33} +3.51300e6 q^{34} -7.23134e6 q^{35} +5.81429e7 q^{36} -9.50334e6 q^{37} +2.30797e7 q^{38} -1.83341e7 q^{39} -4.41062e7 q^{40} +1.75776e7 q^{41} -5.54985e7 q^{42} -2.06503e7 q^{43} +3.33905e7 q^{44} +6.50846e7 q^{45} -4.87861e7 q^{46} +3.15997e7 q^{47} -1.73227e8 q^{48} -1.39480e7 q^{49} -1.14486e6 q^{50} +2.14460e7 q^{51} +8.97634e7 q^{52} -1.02011e8 q^{53} +2.86925e8 q^{54} +3.73770e7 q^{55} +1.61056e8 q^{56} +1.40895e8 q^{57} -6.06520e7 q^{58} -5.95270e7 q^{59} -4.54265e8 q^{60} +5.34058e7 q^{61} +2.54799e8 q^{62} -2.37660e8 q^{63} +1.73149e8 q^{64} +1.00480e8 q^{65} +2.86858e8 q^{66} -6.45107e7 q^{67} -1.04999e8 q^{68} -2.97827e8 q^{69} +3.04160e8 q^{70} -2.71132e8 q^{71} -1.44956e9 q^{72} +2.75443e8 q^{73} +3.99723e8 q^{74} -6.98908e6 q^{75} -6.89819e8 q^{76} -1.36484e8 q^{77} +7.71158e8 q^{78} -4.33372e8 q^{79} +9.49373e8 q^{80} +8.41275e8 q^{81} -7.39337e8 q^{82} +1.23703e8 q^{83} +1.65877e9 q^{84} -1.17535e8 q^{85} +8.68579e8 q^{86} -3.70264e8 q^{87} -8.32461e8 q^{88} -8.87168e8 q^{89} -2.73755e9 q^{90} -3.66909e8 q^{91} +1.45815e9 q^{92} +1.55548e9 q^{93} -1.32912e9 q^{94} -7.72177e8 q^{95} +3.16568e9 q^{96} -4.41697e8 q^{97} +5.86670e8 q^{98} +1.22841e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 33 q^{2} - 236 q^{3} + 853 q^{4} + 1480 q^{5} + 7578 q^{6} - 13202 q^{7} - 42423 q^{8} + 10981 q^{9}+O(q^{10}) $ 5 * q - 33 * q^2 - 236 * q^3 + 853 * q^4 + 1480 * q^5 + 7578 * q^6 - 13202 * q^7 - 42423 * q^8 + 10981 * q^9	\( 5 q - 33 q^{2} - 236 q^{3} + 853 q^{4} + 1480 q^{5} + 7578 q^{6} - 13202 q^{7} - 42423 q^{8} + 10981 q^{9} - 89328 q^{10} - 68036 q^{11} - 406010 q^{12} - 158862 q^{13} - 84700 q^{14} - 687324 q^{15} + 350225 q^{16} - 417605 q^{17} - 1911585 q^{18} - 370992 q^{19} + 1632640 q^{20} + 1783880 q^{21} + 122290 q^{22} + 1645870 q^{23} + 9678702 q^{24} + 3270239 q^{25} + 734846 q^{26} - 2998268 q^{27} + 183372 q^{28} + 3668616 q^{29} + 17048544 q^{30} - 7262362 q^{31} - 5605919 q^{32} - 11334900 q^{33} + 2756193 q^{34} - 26503988 q^{35} + 49782133 q^{36} - 31420708 q^{37} + 18513700 q^{38} - 42449884 q^{39} - 53930464 q^{40} - 7996938 q^{41} - 44519496 q^{42} - 56908268 q^{43} + 43323054 q^{44} + 12799536 q^{45} - 32063472 q^{46} - 16903336 q^{47} - 102794498 q^{48} - 11784059 q^{49} + 85921093 q^{50} + 19710956 q^{51} + 173619082 q^{52} - 83362982 q^{53} + 386329164 q^{54} + 6363364 q^{55} + 317409372 q^{56} + 136615904 q^{57} + 64577488 q^{58} - 37946604 q^{59} - 223158912 q^{60} - 77685452 q^{61} + 324855300 q^{62} - 191945278 q^{63} + 131623105 q^{64} - 40321288 q^{65} + 298037676 q^{66} - 304503600 q^{67} - 71243413 q^{68} - 333409272 q^{69} - 122787392 q^{70} - 476602922 q^{71} - 1301701911 q^{72} - 289980486 q^{73} + 262289012 q^{74} - 153685772 q^{75} - 1031276084 q^{76} - 143385648 q^{77} + 691646196 q^{78} - 828240610 q^{79} + 912750944 q^{80} + 891328609 q^{81} - 1109615654 q^{82} + 194681148 q^{83} + 1541719592 q^{84} - 123611080 q^{85} + 1164707144 q^{86} + 158149884 q^{87} - 1017979978 q^{88} + 376848106 q^{89} - 2240087472 q^{90} + 194543664 q^{91} + 2506713088 q^{92} + 3494835920 q^{93} - 2244811104 q^{94} + 1498679864 q^{95} + 2935047582 q^{96} + 692035246 q^{97} + 871744055 q^{98} + 2027106408 q^{99}+O(q^{100}) \) 5 * q - 33 * q^2 - 236 * q^3 + 853 * q^4 + 1480 * q^5 + 7578 * q^6 - 13202 * q^7 - 42423 * q^8 + 10981 * q^9 - 89328 * q^10 - 68036 * q^11 - 406010 * q^12 - 158862 * q^13 - 84700 * q^14 - 687324 * q^15 + 350225 * q^16 - 417605 * q^17 - 1911585 * q^18 - 370992 * q^19 + 1632640 * q^20 + 1783880 * q^21 + 122290 * q^22 + 1645870 * q^23 + 9678702 * q^24 + 3270239 * q^25 + 734846 * q^26 - 2998268 * q^27 + 183372 * q^28 + 3668616 * q^29 + 17048544 * q^30 - 7262362 * q^31 - 5605919 * q^32 - 11334900 * q^33 + 2756193 * q^34 - 26503988 * q^35 + 49782133 * q^36 - 31420708 * q^37 + 18513700 * q^38 - 42449884 * q^39 - 53930464 * q^40 - 7996938 * q^41 - 44519496 * q^42 - 56908268 * q^43 + 43323054 * q^44 + 12799536 * q^45 - 32063472 * q^46 - 16903336 * q^47 - 102794498 * q^48 - 11784059 * q^49 + 85921093 * q^50 + 19710956 * q^51 + 173619082 * q^52 - 83362982 * q^53 + 386329164 * q^54 + 6363364 * q^55 + 317409372 * q^56 + 136615904 * q^57 + 64577488 * q^58 - 37946604 * q^59 - 223158912 * q^60 - 77685452 * q^61 + 324855300 * q^62 - 191945278 * q^63 + 131623105 * q^64 - 40321288 * q^65 + 298037676 * q^66 - 304503600 * q^67 - 71243413 * q^68 - 333409272 * q^69 - 122787392 * q^70 - 476602922 * q^71 - 1301701911 * q^72 - 289980486 * q^73 + 262289012 * q^74 - 153685772 * q^75 - 1031276084 * q^76 - 143385648 * q^77 + 691646196 * q^78 - 828240610 * q^79 + 912750944 * q^80 + 891328609 * q^81 - 1109615654 * q^82 + 194681148 * q^83 + 1541719592 * q^84 - 123611080 * q^85 + 1164707144 * q^86 + 158149884 * q^87 - 1017979978 * q^88 + 376848106 * q^89 - 2240087472 * q^90 + 194543664 * q^91 + 2506713088 * q^92 + 3494835920 * q^93 - 2244811104 * q^94 + 1498679864 * q^95 + 2935047582 * q^96 + 692035246 * q^97 + 871744055 * q^98 + 2027106408 * 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 $

$2$	−42.0613	−1.85887	−0.929433	−	0.368992i	$-0.879703\pi$
$2$	−42.0613	−1.85887	−0.929433	+	0.368992i	$0.879703\pi$
$3$	−256.773	−1.83022	−0.915112	−	0.403199i	$-0.867898\pi$
$3$	−256.773	−1.83022	−0.915112	+	0.403199i	$0.867898\pi$
$4$	1257.15	2.45538
$5$	1407.25	1.00694	0.503472	−	0.864012i	$-0.332056\pi$
$5$	1407.25	1.00694	0.503472	+	0.864012i	$0.332056\pi$
$6$	10800.2	3.40214
$7$	−5138.64	−0.808923	−0.404461	−	0.914555i	$-0.632541\pi$
$7$	−5138.64	−0.808923	−0.404461	+	0.914555i	$0.632541\pi$
$8$	−31342.2	−2.70536
$9$	46249.6	2.34972
$10$	−59190.7	−1.87177
$11$	26560.4	0.546975	0.273487	−	0.961876i	$-0.411823\pi$
$11$	26560.4	0.546975	0.273487	+	0.961876i	$0.411823\pi$
$12$	−322804.	−4.49390
$13$	71402.0	0.693371	0.346685	−	0.937981i	$-0.387307\pi$
$13$	71402.0	0.693371	0.346685	+	0.937981i	$0.387307\pi$
$14$	216138.	1.50368
$15$	−361344.	−1.84293
$16$	674631.	2.57351
$17$	−83521.0	−0.242536
$17$	−83521.0	−0.242536
$18$	−1.94532e6	−4.36782
$19$	−548715.	−0.965951	−0.482976	−	0.875634i	$-0.660444\pi$
$19$	−548715.	−0.965951	−0.482976	+	0.875634i	$0.660444\pi$
$20$	1.76913e6	2.47243
$21$	1.31947e6	1.48051
$22$	−1.11716e6	−1.01675
$23$	1.15988e6	0.864247	0.432124	−	0.901814i	$-0.357764\pi$
$23$	1.15988e6	0.864247	0.432124	+	0.901814i	$0.357764\pi$
$24$	8.04785e6	4.95141
$25$	27218.8	0.0139360
$26$	−3.00326e6	−1.28888
$27$	−6.82160e6	−2.47030
$28$	−6.46007e6	−1.98621
$29$	1.44199e6	0.378592	0.189296	−	0.981920i	$-0.439380\pi$
$29$	1.44199e6	0.378592	0.189296	+	0.981920i	$0.439380\pi$
$30$	1.51986e7	3.42577
$31$	−6.05781e6	−1.17812	−0.589058	−	0.808091i	$-0.700501\pi$
$31$	−6.05781e6	−1.17812	−0.589058	+	0.808091i	$0.700501\pi$
$32$	−1.23287e7	−2.07846
$33$	−6.82000e6	−1.00109
$34$	3.51300e6	0.450841
$35$	−7.23134e6	−0.814540
$36$	5.81429e7	5.76947
$37$	−9.50334e6	−0.833621	−0.416810	−	0.908993i	$-0.636852\pi$
$37$	−9.50334e6	−0.833621	−0.416810	+	0.908993i	$0.636852\pi$
$38$	2.30797e7	1.79557
$39$	−1.83341e7	−1.26902
$40$	−4.41062e7	−2.72414
$41$	1.75776e7	0.971476	0.485738	−	0.874104i	$-0.338551\pi$
$41$	1.75776e7	0.971476	0.485738	+	0.874104i	$0.338551\pi$
$42$	−5.54985e7	−2.75207
$43$	−2.06503e7	−0.921125	−0.460562	−	0.887627i	$-0.652352\pi$
$43$	−2.06503e7	−0.921125	−0.460562	+	0.887627i	$0.652352\pi$
$44$	3.33905e7	1.34303
$45$	6.50846e7	2.36604
$46$	−4.87861e7	−1.60652
$47$	3.15997e7	0.944587	0.472294	−	0.881441i	$-0.343426\pi$
$47$	3.15997e7	0.944587	0.472294	+	0.881441i	$0.343426\pi$
$48$	−1.73227e8	−4.71011
$49$	−1.39480e7	−0.345644
$50$	−1.14486e6	−0.0259052
$51$	2.14460e7	0.443895
$52$	8.97634e7	1.70249
$53$	−1.02011e8	−1.77585	−0.887924	−	0.459990i	$-0.847853\pi$
$53$	−1.02011e8	−1.77585	−0.887924	+	0.459990i	$0.847853\pi$
$54$	2.86925e8	4.59195
$55$	3.73770e7	0.550773
$56$	1.61056e8	2.18842
$57$	1.40895e8	1.76791
$58$	−6.06520e7	−0.703751
$59$	−5.95270e7	−0.639558	−0.319779	−	0.947492i	$-0.603609\pi$
$59$	−5.95270e7	−0.639558	−0.319779	+	0.947492i	$0.603609\pi$
$60$	−4.54265e8	−4.52510
$61$	5.34058e7	0.493860	0.246930	−	0.969033i	$-0.420578\pi$
$61$	5.34058e7	0.493860	0.246930	+	0.969033i	$0.420578\pi$
$62$	2.54799e8	2.18996
$63$	−2.37660e8	−1.90074
$64$	1.73149e8	1.29006
$65$	1.00480e8	0.698185
$66$	2.86858e8	1.86089
$67$	−6.45107e7	−0.391107	−0.195553	−	0.980693i	$-0.562650\pi$
$67$	−6.45107e7	−0.391107	−0.195553	+	0.980693i	$0.562650\pi$
$68$	−1.04999e8	−0.595517
$69$	−2.97827e8	−1.58177
$70$	3.04160e8	1.51412
$71$	−2.71132e8	−1.26625	−0.633123	−	0.774051i	$-0.718227\pi$
$71$	−2.71132e8	−1.26625	−0.633123	+	0.774051i	$0.718227\pi$
$72$	−1.44956e9	−6.35684
$73$	2.75443e8	1.13522	0.567609	−	0.823298i	$-0.307868\pi$
$73$	2.75443e8	1.13522	0.567609	+	0.823298i	$0.307868\pi$
$74$	3.99723e8	1.54959
$75$	−6.98908e6	−0.0255061
$76$	−6.89819e8	−2.37178
$77$	−1.36484e8	−0.442460
$78$	7.71158e8	2.35895
$79$	−4.33372e8	−1.25181	−0.625906	−	0.779898i	$-0.715271\pi$
$79$	−4.33372e8	−1.25181	−0.625906	+	0.779898i	$0.715271\pi$
$80$	9.49373e8	2.59138
$81$	8.41275e8	2.17148
$82$	−7.39337e8	−1.80584
$83$	1.23703e8	0.286106	0.143053	−	0.989715i	$-0.454308\pi$
$83$	1.23703e8	0.286106	0.143053	+	0.989715i	$0.454308\pi$
$84$	1.65877e9	3.63522
$85$	−1.17535e8	−0.244220
$86$	8.68579e8	1.71225
$87$	−3.70264e8	−0.692908
$88$	−8.32461e8	−1.47976
$89$	−8.87168e8	−1.49882	−0.749412	−	0.662104i	$-0.769664\pi$
$89$	−8.87168e8	−1.49882	−0.749412	+	0.662104i	$0.769664\pi$
$90$	−2.73755e9	−4.39815
$91$	−3.66909e8	−0.560883
$92$	1.45815e9	2.12206
$93$	1.55548e9	2.15622
$94$	−1.32912e9	−1.75586
$95$	−7.72177e8	−0.972659
$96$	3.16568e9	3.80405
$97$	−4.41697e8	−0.506585	−0.253292	−	0.967390i	$-0.581513\pi$
$97$	−4.41697e8	−0.506585	−0.253292	+	0.967390i	$0.581513\pi$
$98$	5.86670e8	0.642506
$99$	1.22841e9	1.28524
$100$	3.42183e7	0.0342183
$101$	−1.14036e9	−1.09042	−0.545212	−	0.838298i	$-0.683551\pi$
$101$	−1.14036e9	−1.09042	−0.545212	+	0.838298i	$0.683551\pi$
$102$	−9.02046e8	−0.825141
$103$	8.49153e8	0.743393	0.371696	−	0.928354i	$-0.378776\pi$
$103$	8.49153e8	0.743393	0.371696	+	0.928354i	$0.378776\pi$
$104$	−2.23790e9	−1.87582
$105$	1.85682e9	1.49079
$106$	4.29072e9	3.30106
$107$	2.23234e9	1.64639	0.823196	−	0.567758i	$-0.192189\pi$
$107$	2.23234e9	1.64639	0.823196	+	0.567758i	$0.192189\pi$
$108$	−8.57581e9	−6.06552
$109$	1.34014e9	0.909352	0.454676	−	0.890657i	$-0.349755\pi$
$109$	1.34014e9	0.909352	0.454676	+	0.890657i	$0.349755\pi$
$110$	−1.57213e9	−1.02381
$111$	2.44021e9	1.52571
$112$	−3.46669e9	−2.08177
$113$	−2.00028e9	−1.15408	−0.577042	−	0.816715i	$-0.695793\pi$
$113$	−2.00028e9	−1.15408	−0.577042	+	0.816715i	$0.695793\pi$
$114$	−5.92624e9	−3.28630
$115$	1.63224e9	0.870248
$116$	1.81280e9	0.929586
$117$	3.30232e9	1.62923
$118$	2.50379e9	1.18885
$119$	4.29184e8	0.196193
$120$	1.13253e10	4.98579
$121$	−1.65249e9	−0.700819
$122$	−2.24632e9	−0.918020
$123$	−4.51346e9	−1.77802
$124$	−7.61560e9	−2.89272
$125$	−2.71023e9	−0.992911
$126$	9.99630e9	3.53323
$127$	−3.35970e9	−1.14600	−0.572999	−	0.819556i	$-0.694220\pi$
$127$	−3.35970e9	−1.14600	−0.572999	+	0.819556i	$0.694220\pi$
$128$	−9.70602e8	−0.319592
$129$	5.30245e9	1.68587
$130$	−4.22633e9	−1.29783
$131$	−2.27481e8	−0.0674876	−0.0337438	−	0.999431i	$-0.510743\pi$
$131$	−2.27481e8	−0.0674876	−0.0337438	+	0.999431i	$0.510743\pi$
$132$	−8.57380e9	−2.45805
$133$	2.81965e9	0.781380
$134$	2.71341e9	0.727014
$135$	−9.59967e9	−2.48745
$136$	2.61773e9	0.656145
$137$	−3.72862e9	−0.904285	−0.452142	−	0.891946i	$-0.649340\pi$
$137$	−3.72862e9	−0.904285	−0.452142	+	0.891946i	$0.649340\pi$
$138$	1.25270e10	2.94029
$139$	−8.72554e8	−0.198256	−0.0991279	−	0.995075i	$-0.531605\pi$
$139$	−8.72554e8	−0.198256	−0.0991279	+	0.995075i	$0.531605\pi$
$140$	−9.09091e9	−2.00001
$141$	−8.11395e9	−1.72881
$142$	1.14042e10	2.35378
$143$	1.89647e9	0.379256
$144$	3.12014e10	6.04705
$145$	2.02923e9	0.381220
$146$	−1.15855e10	−2.11022
$147$	3.58147e9	0.632606
$148$	−1.19472e10	−2.04686
$149$	5.86193e9	0.974323	0.487161	−	0.873312i	$-0.338032\pi$
$149$	5.86193e9	0.974323	0.487161	+	0.873312i	$0.338032\pi$
$150$	2.93970e8	0.0474124
$151$	1.01489e10	1.58864	0.794318	−	0.607502i	$-0.207828\pi$
$151$	1.01489e10	1.58864	0.794318	+	0.607502i	$0.207828\pi$
$152$	1.71979e10	2.61324
$153$	−3.86281e9	−0.569892
$154$	5.74071e9	0.822474
$155$	−8.52483e9	−1.18630
$156$	−2.30489e10	−3.11594
$157$	−5.31929e9	−0.698723	−0.349362	−	0.936988i	$-0.613601\pi$
$157$	−5.31929e9	−0.698723	−0.349362	+	0.936988i	$0.613601\pi$
$158$	1.82282e10	2.32695
$159$	2.61937e10	3.25020
$160$	−1.73495e10	−2.09289
$161$	−5.96021e9	−0.699109
$162$	−3.53851e10	−4.03648
$163$	−1.08994e10	−1.20937	−0.604685	−	0.796465i	$-0.706701\pi$
$163$	−1.08994e10	−1.20937	−0.604685	+	0.796465i	$0.706701\pi$
$164$	2.20978e10	2.38534
$165$	−9.59743e9	−1.00804
$166$	−5.20309e9	−0.531833
$167$	−5.90585e9	−0.587569	−0.293784	−	0.955872i	$-0.594915\pi$
$167$	−5.90585e9	−0.587569	−0.293784	+	0.955872i	$0.594915\pi$
$168$	−4.13550e10	−4.00531
$169$	−5.50625e9	−0.519237
$170$	4.94366e9	0.453972
$171$	−2.53778e10	−2.26972
$172$	−2.59606e10	−2.26171
$173$	1.33412e10	1.13237	0.566183	−	0.824280i	$-0.308420\pi$
$173$	1.33412e10	1.13237	0.566183	+	0.824280i	$0.308420\pi$
$174$	1.55738e10	1.28802
$175$	−1.39868e8	−0.0112732
$176$	1.79185e10	1.40765
$177$	1.52850e10	1.17054
$178$	3.73154e10	2.78611
$179$	1.62530e10	1.18330	0.591651	−	0.806194i	$-0.298476\pi$
$179$	1.62530e10	1.18330	0.591651	+	0.806194i	$0.298476\pi$
$180$	8.18214e10	5.80953
$181$	−4.03320e9	−0.279316	−0.139658	−	0.990200i	$-0.544600\pi$
$181$	−4.03320e9	−0.279316	−0.139658	+	0.990200i	$0.544600\pi$
$182$	1.54327e10	1.04261
$183$	−1.37132e10	−0.903875
$184$	−3.63532e10	−2.33810
$185$	−1.33735e10	−0.839409
$186$	−6.54257e10	−4.00812
$187$	−2.21835e9	−0.132661
$188$	3.97257e10	2.31932
$189$	3.50537e10	1.99828
$190$	3.24788e10	1.80804
$191$	−1.09015e10	−0.592700	−0.296350	−	0.955079i	$-0.595769\pi$
$191$	−1.09015e10	−0.592700	−0.296350	+	0.955079i	$0.595769\pi$
$192$	−4.44601e10	−2.36110
$193$	1.29615e10	0.672428	0.336214	−	0.941786i	$-0.390853\pi$
$193$	1.29615e10	0.672428	0.336214	+	0.941786i	$0.390853\pi$
$194$	1.85784e10	0.941673
$195$	−2.58007e10	−1.27784
$196$	−1.75348e10	−0.848687
$197$	7.15882e9	0.338644	0.169322	−	0.985561i	$-0.445842\pi$
$197$	7.15882e9	0.338644	0.169322	+	0.985561i	$0.445842\pi$
$198$	−5.16684e10	−2.38909
$199$	3.03762e9	0.137307	0.0686537	−	0.997641i	$-0.478130\pi$
$199$	3.03762e9	0.137307	0.0686537	+	0.997641i	$0.478130\pi$
$200$	−8.53098e8	−0.0377020
$201$	1.65646e10	0.715813
$202$	4.79650e10	2.02695
$203$	−7.40986e9	−0.306251
$204$	2.69609e10	1.08993
$205$	2.47360e10	0.978222
$206$	−3.57165e10	−1.38187
$207$	5.36440e10	2.03074
$208$	4.81700e10	1.78440
$209$	−1.45741e10	−0.528351
$210$	−7.81001e10	−2.77118
$211$	−3.30011e10	−1.14619	−0.573097	−	0.819488i	$-0.694258\pi$
$211$	−3.30011e10	−1.14619	−0.573097	+	0.819488i	$0.694258\pi$
$212$	−1.28244e11	−4.36038
$213$	6.96195e10	2.31752
$214$	−9.38951e10	−3.06042
$215$	−2.90601e10	−0.927521
$216$	2.13804e11	6.68304
$217$	3.11289e10	0.953004
$218$	−5.63682e10	−1.69036
$219$	−7.07266e10	−2.07771
$220$	4.69887e10	1.35236
$221$	−5.96357e9	−0.168167
$222$	−1.02638e11	−2.83610
$223$	−3.03057e10	−0.820640	−0.410320	−	0.911942i	$-0.634583\pi$
$223$	−3.03057e10	−0.820640	−0.410320	+	0.911942i	$0.634583\pi$
$224$	6.33526e10	1.68131
$225$	1.25886e9	0.0327459
$226$	8.41343e10	2.14529
$227$	−4.49193e10	−1.12284	−0.561418	−	0.827532i	$-0.689744\pi$
$227$	−4.49193e10	−1.12284	−0.561418	+	0.827532i	$0.689744\pi$
$228$	1.77127e11	4.34089
$229$	4.68022e10	1.12462	0.562311	−	0.826926i	$-0.309913\pi$
$229$	4.68022e10	1.12462	0.562311	+	0.826926i	$0.309913\pi$
$230$	−6.86541e10	−1.61767
$231$	3.50455e10	0.809802
$232$	−4.51951e10	−1.02423
$233$	−2.08143e10	−0.462658	−0.231329	−	0.972876i	$-0.574307\pi$
$233$	−2.08143e10	−0.462658	−0.231329	+	0.972876i	$0.574307\pi$
$234$	−1.38900e11	−3.02852
$235$	4.44685e10	0.951146
$236$	−7.48347e10	−1.57036
$237$	1.11279e11	2.29110
$238$	−1.80521e10	−0.364696
$239$	1.23779e9	0.0245390	0.0122695	−	0.999925i	$-0.496094\pi$
$239$	1.23779e9	0.0245390	0.0122695	+	0.999925i	$0.496094\pi$
$240$	−2.43774e11	−4.74282
$241$	−3.29491e10	−0.629167	−0.314584	−	0.949230i	$-0.601865\pi$
$241$	−3.29491e10	−0.629167	−0.314584	+	0.949230i	$0.601865\pi$
$242$	6.95061e10	1.30273
$243$	−8.17474e10	−1.50399
$244$	6.71394e10	1.21262
$245$	−1.96283e10	−0.348044
$246$	1.89842e11	3.30510
$247$	−3.91793e10	−0.669762
$248$	1.89865e11	3.18722
$249$	−3.17635e10	−0.523638
$250$	1.13996e11	1.84569
$251$	−3.15140e10	−0.501154	−0.250577	−	0.968097i	$-0.580620\pi$
$251$	−3.15140e10	−0.501154	−0.250577	+	0.968097i	$0.580620\pi$
$252$	−2.98776e11	−4.66705
$253$	3.08069e10	0.472721
$254$	1.41313e11	2.13026
$255$	3.01798e10	0.446977
$256$	−4.78276e10	−0.695983
$257$	−7.36840e10	−1.05360	−0.526798	−	0.849991i	$-0.676607\pi$
$257$	−7.36840e10	−1.05360	−0.526798	+	0.849991i	$0.676607\pi$
$258$	−2.23028e11	−3.13380
$259$	4.88342e10	0.674335
$260$	1.26319e11	1.71431
$261$	6.66914e10	0.889585
$262$	9.56814e9	0.125450
$263$	−5.81832e10	−0.749888	−0.374944	−	0.927047i	$-0.622338\pi$
$263$	−5.81832e10	−0.749888	−0.374944	+	0.927047i	$0.622338\pi$
$264$	2.13754e11	2.70830
$265$	−1.43555e11	−1.78818
$266$	−1.18598e11	−1.45248
$267$	2.27801e11	2.74318
$268$	−8.10999e10	−0.960315
$269$	1.32703e11	1.54523	0.772617	−	0.634872i	$-0.218947\pi$
$269$	1.32703e11	1.54523	0.772617	+	0.634872i	$0.218947\pi$
$270$	4.03775e11	4.62384
$271$	−1.25505e11	−1.41351	−0.706757	−	0.707456i	$-0.749843\pi$
$271$	−1.25505e11	−1.41351	−0.706757	+	0.707456i	$0.749843\pi$
$272$	−5.63459e10	−0.624169
$273$	9.42126e10	1.02654
$274$	1.56831e11	1.68094
$275$	7.22943e8	0.00762267
$276$	−3.74414e11	−3.88384
$277$	−1.08560e11	−1.10792	−0.553961	−	0.832542i	$-0.686884\pi$
$277$	−1.08560e11	−1.10792	−0.553961	+	0.832542i	$0.686884\pi$
$278$	3.67008e10	0.368531
$279$	−2.80171e11	−2.76825
$280$	2.26646e11	2.20362
$281$	−1.21647e11	−1.16392	−0.581961	−	0.813216i	$-0.697714\pi$
$281$	−1.21647e11	−1.16392	−0.581961	+	0.813216i	$0.697714\pi$
$282$	3.41284e11	3.21362
$283$	1.97694e11	1.83212	0.916060	−	0.401041i	$-0.131352\pi$
$283$	1.97694e11	1.83212	0.916060	+	0.401041i	$0.131352\pi$
$284$	−3.40855e11	−3.10912
$285$	1.98275e11	1.78018
$286$	−7.97678e10	−0.704986
$287$	−9.03249e10	−0.785849
$288$	−5.70196e11	−4.88380
$289$	6.97576e9	0.0588235
$290$	−8.53523e10	−0.708637
$291$	1.13416e11	0.927164
$292$	3.46275e11	2.78739
$293$	−5.29206e10	−0.419489	−0.209745	−	0.977756i	$-0.567263\pi$
$293$	−5.29206e10	−0.419489	−0.209745	+	0.977756i	$0.567263\pi$
$294$	−1.50641e11	−1.17593
$295$	−8.37692e10	−0.643999
$296$	2.97856e11	2.25524
$297$	−1.81184e11	−1.35119
$298$	−2.46561e11	−1.81113
$299$	8.28178e10	0.599244
$300$	−8.78635e9	−0.0626272
$301$	1.06115e11	0.745119
$302$	−4.26878e11	−2.95306
$303$	2.92814e11	1.99572
$304$	−3.70180e11	−2.48589
$305$	7.51551e10	0.497290
$306$	1.62475e11	1.05935
$307$	6.66906e10	0.428491	0.214246	−	0.976780i	$-0.431271\pi$
$307$	6.66906e10	0.428491	0.214246	+	0.976780i	$0.431271\pi$
$308$	−1.71582e11	−1.08641
$309$	−2.18040e11	−1.36058
$310$	3.58566e11	2.20516
$311$	2.16895e11	1.31470	0.657352	−	0.753584i	$-0.271676\pi$
$311$	2.16895e11	1.31470	0.657352	+	0.753584i	$0.271676\pi$
$312$	5.74633e11	3.43316
$313$	2.03438e11	1.19807	0.599034	−	0.800723i	$-0.295551\pi$
$313$	2.03438e11	1.19807	0.599034	+	0.800723i	$0.295551\pi$
$314$	2.23736e11	1.29883
$315$	−3.34446e11	−1.91394
$316$	−5.44816e11	−3.07368
$317$	2.27635e11	1.26611	0.633056	−	0.774106i	$-0.281800\pi$
$317$	2.27635e11	1.26611	0.633056	+	0.774106i	$0.281800\pi$
$318$	−1.10174e12	−6.04169
$319$	3.82998e10	0.207080
$320$	2.43664e11	1.29902
$321$	−5.73205e11	−3.01327
$322$	2.50694e11	1.29955
$323$	4.58292e10	0.234278
$324$	1.05761e12	5.33180
$325$	1.94348e9	0.00966285
$326$	4.58444e11	2.24806
$327$	−3.44113e11	−1.66432
$328$	−5.50921e11	−2.62819
$329$	−1.62379e11	−0.764098
$330$	4.03680e11	1.87381
$331$	1.97602e11	0.904828	0.452414	−	0.891808i	$-0.350563\pi$
$331$	1.97602e11	0.904828	0.452414	+	0.891808i	$0.350563\pi$
$332$	1.55513e11	0.702499
$333$	−4.39526e11	−1.95878
$334$	2.48408e11	1.09221
$335$	−9.07825e10	−0.393822
$336$	8.90153e11	3.81011
$337$	4.61396e9	0.0194867	0.00974337	−	0.999953i	$-0.496899\pi$
$337$	4.61396e9	0.0194867	0.00974337	+	0.999953i	$0.496899\pi$
$338$	2.31600e11	0.965192
$339$	5.13618e11	2.11223
$340$	−1.47759e11	−0.599653
$341$	−1.60898e11	−0.644399
$342$	1.06743e12	4.21910
$343$	2.79036e11	1.08852
$344$	6.47226e11	2.49197
$345$	−4.19115e11	−1.59275
$346$	−5.61148e11	−2.10492
$347$	−3.34855e11	−1.23987	−0.619933	−	0.784655i	$-0.712840\pi$
$347$	−3.34855e11	−1.23987	−0.619933	+	0.784655i	$0.712840\pi$
$348$	−4.65480e11	−1.70135
$349$	−1.38047e11	−0.498095	−0.249048	−	0.968491i	$-0.580118\pi$
$349$	−1.38047e11	−0.498095	−0.249048	+	0.968491i	$0.580118\pi$
$350$	5.88303e9	0.0209553
$351$	−4.87076e11	−1.71283
$352$	−3.27454e11	−1.13686
$353$	3.22524e11	1.10554	0.552771	−	0.833333i	$-0.313570\pi$
$353$	3.22524e11	1.10554	0.552771	+	0.833333i	$0.313570\pi$
$354$	−6.42906e11	−2.17587
$355$	−3.81550e11	−1.27504
$356$	−1.11531e12	−3.68018
$357$	−1.10203e11	−0.359077
$358$	−6.83624e11	−2.19960
$359$	1.09669e11	0.348465	0.174232	−	0.984705i	$-0.444256\pi$
$359$	1.09669e11	0.348465	0.174232	+	0.984705i	$0.444256\pi$
$360$	−2.03990e12	−6.40098
$361$	−2.16000e10	−0.0669378
$362$	1.69642e11	0.519212
$363$	4.24316e11	1.28266
$364$	−4.61262e11	−1.37718
$365$	3.87617e11	1.14310
$366$	5.76795e11	1.68018
$367$	1.91239e11	0.550273	0.275137	−	0.961405i	$-0.411277\pi$
$367$	1.91239e11	0.550273	0.275137	+	0.961405i	$0.411277\pi$
$368$	7.82492e11	2.22415
$369$	8.12957e11	2.28270
$370$	5.62509e11	1.56035
$371$	5.24198e11	1.43652
$372$	1.95548e12	5.29433
$373$	1.18077e11	0.315846	0.157923	−	0.987451i	$-0.449520\pi$
$373$	1.18077e11	0.315846	0.157923	+	0.987451i	$0.449520\pi$
$374$	9.33067e10	0.246599
$375$	6.95914e11	1.81725
$376$	−9.90403e11	−2.55545
$377$	1.02961e11	0.262504
$378$	−1.47441e12	−3.71453
$379$	−1.76959e11	−0.440551	−0.220276	−	0.975438i	$-0.570696\pi$
$379$	−1.76959e11	−0.440551	−0.220276	+	0.975438i	$0.570696\pi$
$380$	−9.70746e11	−2.38825
$381$	8.62682e11	2.09743
$382$	4.58530e11	1.10175
$383$	1.29043e11	0.306436	0.153218	−	0.988192i	$-0.451036\pi$
$383$	1.29043e11	0.306436	0.153218	+	0.988192i	$0.451036\pi$
$384$	2.49225e11	0.584926
$385$	−1.92067e11	−0.445533
$386$	−5.45176e11	−1.24995
$387$	−9.55069e11	−2.16439
$388$	−5.55282e11	−1.24386
$389$	6.86269e10	0.151957	0.0759785	−	0.997109i	$-0.475792\pi$
$389$	6.86269e10	0.151957	0.0759785	+	0.997109i	$0.475792\pi$
$390$	1.08521e12	2.37533
$391$	−9.68744e10	−0.209611
$392$	4.37160e11	0.935090
$393$	5.84110e10	0.123517
$394$	−3.01110e11	−0.629494
$395$	−6.09862e11	−1.26051
$396$	1.54430e12	3.15575
$397$	7.83412e11	1.58283	0.791413	−	0.611282i	$-0.209346\pi$
$397$	7.83412e11	1.58283	0.791413	+	0.611282i	$0.209346\pi$
$398$	−1.27766e11	−0.255236
$399$	−7.24011e11	−1.43010
$400$	1.83627e10	0.0358646
$401$	1.06747e11	0.206161	0.103080	−	0.994673i	$-0.467130\pi$
$401$	1.06747e11	0.206161	0.103080	+	0.994673i	$0.467130\pi$
$402$	−6.96730e11	−1.33060
$403$	−4.32540e11	−0.816871
$404$	−1.43361e12	−2.67741
$405$	1.18388e12	2.18656
$406$	3.11669e11	0.569280
$407$	−2.52412e11	−0.455969
$408$	−6.72164e11	−1.20089
$409$	−1.08641e12	−1.91973	−0.959863	−	0.280469i	$-0.909510\pi$
$409$	−1.08641e12	−1.91973	−0.959863	+	0.280469i	$0.909510\pi$
$410$	−1.04043e12	−1.81838
$411$	9.57410e11	1.65504
$412$	1.06752e12	1.82531
$413$	3.05888e11	0.517353
$414$	−2.25634e12	−3.77488
$415$	1.74080e11	0.288093
$416$	−8.80292e11	−1.44114
$417$	2.24049e11	0.362853
$418$	6.13005e11	0.982134
$419$	6.48628e11	1.02809	0.514047	−	0.857762i	$-0.328146\pi$
$419$	6.48628e11	1.02809	0.514047	+	0.857762i	$0.328146\pi$
$420$	2.33430e12	3.66046
$421$	−8.74376e11	−1.35653	−0.678264	−	0.734818i	$-0.737267\pi$
$421$	−8.74376e11	−1.35653	−0.678264	+	0.734818i	$0.737267\pi$
$422$	1.38807e12	2.13062
$423$	1.46147e12	2.21952
$424$	3.19725e12	4.80430
$425$	−2.27334e9	−0.00337999
$426$	−2.92829e12	−4.30795
$427$	−2.74433e11	−0.399495
$428$	2.80640e12	4.04252
$429$	−4.86962e11	−0.694124
$430$	1.22231e12	1.72414
$431$	2.93756e10	0.0410052	0.0205026	−	0.999790i	$-0.493473\pi$
$431$	2.93756e10	0.0410052	0.0205026	+	0.999790i	$0.493473\pi$
$432$	−4.60206e12	−6.35734
$433$	−1.33717e12	−1.82806	−0.914029	−	0.405648i	$-0.867046\pi$
$433$	−1.33717e12	−1.82806	−0.914029	+	0.405648i	$0.867046\pi$
$434$	−1.30932e12	−1.77151
$435$	−5.21053e11	−0.697719
$436$	1.68477e12	2.23280
$437$	−6.36443e11	−0.834821
$438$	2.97485e12	3.86218
$439$	7.90604e11	1.01594	0.507971	−	0.861374i	$-0.330396\pi$
$439$	7.90604e11	1.01594	0.507971	+	0.861374i	$0.330396\pi$
$440$	−1.17148e12	−1.49004
$441$	−6.45089e11	−0.812168
$442$	2.50836e11	0.312600
$443$	1.18811e12	1.46569	0.732843	−	0.680398i	$-0.238193\pi$
$443$	1.18811e12	1.46569	0.732843	+	0.680398i	$0.238193\pi$
$444$	3.06772e12	3.74621
$445$	−1.24846e12	−1.50923
$446$	1.27470e12	1.52546
$447$	−1.50519e12	−1.78323
$448$	−8.89751e11	−1.04356
$449$	6.04411e11	0.701817	0.350909	−	0.936410i	$-0.385873\pi$
$449$	6.04411e11	0.701817	0.350909	+	0.936410i	$0.385873\pi$
$450$	−5.29493e10	−0.0608701
$451$	4.66868e11	0.531373
$452$	−2.51466e12	−2.83371
$453$	−2.60598e12	−2.90756
$454$	1.88936e12	2.08720
$455$	−5.16332e11	−0.564778
$456$	−4.41597e12	−4.78282
$457$	−9.65513e11	−1.03546	−0.517732	−	0.855543i	$-0.673224\pi$
$457$	−9.65513e11	−1.03546	−0.517732	+	0.855543i	$0.673224\pi$
$458$	−1.96856e12	−2.09052
$459$	5.69747e11	0.599135
$460$	2.05198e12	2.13679
$461$	5.15082e10	0.0531156	0.0265578	−	0.999647i	$-0.491545\pi$
$461$	5.15082e10	0.0531156	0.0265578	+	0.999647i	$0.491545\pi$
$462$	−1.47406e12	−1.50531
$463$	−7.66043e11	−0.774709	−0.387355	−	0.921931i	$-0.626611\pi$
$463$	−7.66043e11	−0.774709	−0.387355	+	0.921931i	$0.626611\pi$
$464$	9.72811e11	0.974310
$465$	2.18895e12	2.17119
$466$	8.75477e11	0.860019
$467$	−1.55842e12	−1.51621	−0.758104	−	0.652133i	$-0.773874\pi$
$467$	−1.55842e12	−1.51621	−0.758104	+	0.652133i	$0.773874\pi$
$468$	4.15152e12	4.00038
$469$	3.31497e11	0.316375
$470$	−1.87041e12	−1.76805
$471$	1.36585e12	1.27882
$472$	1.86571e12	1.73023
$473$	−5.48480e11	−0.503832
$474$	−4.68052e12	−4.25885
$475$	−1.49354e10	−0.0134615
$476$	5.39551e11	0.481728
$477$	−4.71797e12	−4.17275
$478$	−5.20632e10	−0.0456147
$479$	1.36399e12	1.18386	0.591931	−	0.805989i	$-0.298366\pi$
$479$	1.36399e12	1.18386	0.591931	+	0.805989i	$0.298366\pi$
$480$	4.45489e12	3.83046
$481$	−6.78558e11	−0.578008
$482$	1.38588e12	1.16954
$483$	1.53042e12	1.27953
$484$	−2.07744e12	−1.72078
$485$	−6.21577e11	−0.510102
$486$	3.43841e12	2.79572
$487$	−9.00584e11	−0.725511	−0.362755	−	0.931884i	$-0.618164\pi$
$487$	−9.00584e11	−0.725511	−0.362755	+	0.931884i	$0.618164\pi$
$488$	−1.67386e12	−1.33607
$489$	2.79868e12	2.21342
$490$	8.25590e11	0.646967
$491$	2.39477e12	1.85950	0.929751	−	0.368189i	$-0.120022\pi$
$491$	2.39477e12	1.85950	0.929751	+	0.368189i	$0.120022\pi$
$492$	−5.67412e12	−4.36572
$493$	−1.20436e11	−0.0918219
$494$	1.64793e12	1.24500
$495$	1.72867e12	1.29416
$496$	−4.08679e12	−3.03190
$497$	1.39325e12	1.02430
$498$	1.33602e12	0.973373
$499$	−1.19891e12	−0.865637	−0.432819	−	0.901481i	$-0.642481\pi$
$499$	−1.19891e12	−0.865637	−0.432819	+	0.901481i	$0.642481\pi$
$500$	−3.40717e12	−2.43797
$501$	1.51647e12	1.07538
$502$	1.32552e12	0.931579
$503$	−3.61742e11	−0.251967	−0.125983	−	0.992032i	$-0.540209\pi$
$503$	−3.61742e11	−0.251967	−0.125983	+	0.992032i	$0.540209\pi$
$504$	7.44879e12	5.14219
$505$	−1.60477e12	−1.09800
$506$	−1.29578e12	−0.878725
$507$	1.41386e12	0.950321
$508$	−4.22366e12	−2.81386
$509$	1.61404e12	1.06582	0.532910	−	0.846172i	$-0.321098\pi$
$509$	1.61404e12	1.06582	0.532910	+	0.846172i	$0.321098\pi$
$510$	−1.26940e12	−0.830870
$511$	−1.41541e12	−0.918304
$512$	2.50864e12	1.61333
$513$	3.74311e12	2.38619
$514$	3.09924e12	1.95849
$515$	1.19497e12	0.748555
$516$	6.66600e12	4.13944
$517$	8.39299e11	0.516665
$518$	−2.05403e12	−1.25350
$519$	−3.42566e12	−2.07248
$520$	−3.14927e12	−1.88884
$521$	−2.86199e12	−1.70176	−0.850881	−	0.525358i	$-0.823931\pi$
$521$	−2.86199e12	−1.70176	−0.850881	+	0.525358i	$0.823931\pi$
$522$	−2.80513e12	−1.65362
$523$	1.01799e12	0.594957	0.297479	−	0.954728i	$-0.403854\pi$
$523$	1.01799e12	0.594957	0.297479	+	0.954728i	$0.403854\pi$
$524$	−2.85979e11	−0.165708
$525$	3.59143e10	0.0206325
$526$	2.44726e12	1.39394
$527$	5.05954e11	0.285735
$528$	−4.60099e12	−2.57631
$529$	−4.55830e11	−0.253077
$530$	6.03810e12	3.32399
$531$	−2.75310e12	−1.50278
$532$	3.54473e12	1.91859
$533$	1.25508e12	0.673593
$534$	−9.58161e12	−5.09921
$535$	3.14145e12	1.65782
$536$	2.02191e12	1.05808
$537$	−4.17335e12	−2.16571
$538$	−5.58165e12	−2.87238
$539$	−3.70464e11	−0.189058
$540$	−1.20683e13	−6.10764
$541$	−1.10637e12	−0.555283	−0.277642	−	0.960685i	$-0.589553\pi$
$541$	−1.10637e12	−0.555283	−0.277642	+	0.960685i	$0.589553\pi$
$542$	5.27892e12	2.62753
$543$	1.03562e12	0.511212
$544$	1.02970e12	0.504100
$545$	1.88591e12	0.915666
$546$	−3.96271e12	−1.90820
$547$	−1.37273e12	−0.655605	−0.327803	−	0.944746i	$-0.606308\pi$
$547$	−1.37273e12	−0.655605	−0.327803	+	0.944746i	$0.606308\pi$
$548$	−4.68745e12	−2.22036
$549$	2.47000e12	1.16044
$550$	−3.04079e10	−0.0141695
$551$	−7.91240e11	−0.365701
$552$	9.33454e12	4.27924
$553$	2.22695e12	1.01262
$554$	4.56616e12	2.05948
$555$	3.43397e12	1.53631
$556$	−1.09694e12	−0.486793
$557$	−2.29710e12	−1.01119	−0.505594	−	0.862771i	$-0.668727\pi$
$557$	−2.29710e12	−1.01119	−0.505594	+	0.862771i	$0.668727\pi$
$558$	1.17844e13	5.14580
$559$	−1.47447e12	−0.638681
$560$	−4.87849e12	−2.09623
$561$	5.69613e11	0.242799
$562$	5.11665e12	2.16358
$563$	−1.84812e11	−0.0775250	−0.0387625	−	0.999248i	$-0.512342\pi$
$563$	−1.84812e11	−0.0775250	−0.0387625	+	0.999248i	$0.512342\pi$
$564$	−1.02005e13	−4.24488
$565$	−2.81488e12	−1.16210
$566$	−8.31526e12	−3.40566
$567$	−4.32301e12	−1.75656
$568$	8.49788e12	3.42565
$569$	−2.10912e11	−0.0843523	−0.0421761	−	0.999110i	$-0.513429\pi$
$569$	−2.10912e11	−0.0843523	−0.0421761	+	0.999110i	$0.513429\pi$
$570$	−8.33969e12	−3.30912
$571$	2.37391e12	0.934548	0.467274	−	0.884112i	$-0.345236\pi$
$571$	2.37391e12	0.934548	0.467274	+	0.884112i	$0.345236\pi$
$572$	2.38415e12	0.931219
$573$	2.79921e12	1.08477
$574$	3.79919e12	1.46079
$575$	3.15706e10	0.0120442
$576$	8.00808e12	3.03129
$577$	1.71792e12	0.645225	0.322613	−	0.946531i	$-0.395439\pi$
$577$	1.71792e12	0.645225	0.322613	+	0.946531i	$0.395439\pi$
$578$	−2.93410e11	−0.109345
$579$	−3.32816e12	−1.23070
$580$	2.55106e12	0.936041
$581$	−6.35663e11	−0.231438
$582$	−4.77043e12	−1.72347
$583$	−2.70945e12	−0.971344
$584$	−8.63301e12	−3.07117
$585$	4.64717e12	1.64054
$586$	2.22591e12	0.779774
$587$	2.32455e12	0.808103	0.404052	−	0.914736i	$-0.367602\pi$
$587$	2.32455e12	0.808103	0.404052	+	0.914736i	$0.367602\pi$
$588$	4.50246e12	1.55329
$589$	3.32401e12	1.13800
$590$	3.52344e12	1.19711
$591$	−1.83820e12	−0.619795
$592$	−6.41125e12	−2.14533
$593$	2.36534e12	0.785503	0.392751	−	0.919645i	$-0.371523\pi$
$593$	2.36534e12	0.785503	0.392751	+	0.919645i	$0.371523\pi$
$594$	7.62085e12	2.51168
$595$	6.03968e11	0.197555
$596$	7.36936e12	2.39233
$597$	−7.79979e11	−0.251303
$598$	−3.48343e12	−1.11391
$599$	1.14807e12	0.364375	0.182188	−	0.983264i	$-0.441682\pi$
$599$	1.14807e12	0.364375	0.182188	+	0.983264i	$0.441682\pi$
$600$	2.19053e11	0.0690031
$601$	−3.38041e12	−1.05690	−0.528451	−	0.848964i	$-0.677227\pi$
$601$	−3.38041e12	−1.05690	−0.528451	+	0.848964i	$0.677227\pi$
$602$	−4.46332e12	−1.38508
$603$	−2.98359e12	−0.918992
$604$	1.27588e13	3.90071
$605$	−2.32547e12	−0.705685
$606$	−1.23161e13	−3.70978
$607$	2.57549e12	0.770036	0.385018	−	0.922909i	$-0.374195\pi$
$607$	2.57549e12	0.770036	0.385018	+	0.922909i	$0.374195\pi$
$608$	6.76492e12	2.00769
$609$	1.90266e12	0.560509
$610$	−3.16112e12	−0.924395
$611$	2.25628e12	0.654949
$612$	−4.85615e12	−1.39930
$613$	−1.91477e12	−0.547701	−0.273851	−	0.961772i	$-0.588297\pi$
$613$	−1.91477e12	−0.547701	−0.273851	+	0.961772i	$0.588297\pi$
$614$	−2.80509e12	−0.796507
$615$	−6.35155e12	−1.79037
$616$	4.27772e12	1.19701
$617$	5.24069e12	1.45581	0.727907	−	0.685676i	$-0.240493\pi$
$617$	5.24069e12	1.45581	0.727907	+	0.685676i	$0.240493\pi$
$618$	9.17105e12	2.52913
$619$	−5.64576e10	−0.0154566	−0.00772831	−	0.999970i	$-0.502460\pi$
$619$	−5.64576e10	−0.0154566	−0.00772831	+	0.999970i	$0.502460\pi$
$620$	−1.07170e13	−2.91281
$621$	−7.91224e12	−2.13495
$622$	−9.12290e12	−2.44386
$623$	4.55884e12	1.21243
$624$	−1.23688e13	−3.26585
$625$	−3.86712e12	−1.01374
$626$	−8.55685e12	−2.22705
$627$	3.74223e12	0.967001
$628$	−6.68717e12	−1.71563
$629$	7.93728e11	0.202183
$630$	1.40673e13	3.55776
$631$	3.44629e12	0.865405	0.432703	−	0.901537i	$-0.357560\pi$
$631$	3.44629e12	0.865405	0.432703	+	0.901537i	$0.357560\pi$
$632$	1.35828e13	3.38660
$633$	8.47382e12	2.09779
$634$	−9.57462e12	−2.35353
$635$	−4.72793e12	−1.15396
$636$	3.29296e13	7.98048
$637$	−9.95914e11	−0.239659
$638$	−1.61094e12	−0.384934
$639$	−1.25398e13	−2.97533
$640$	−1.36588e12	−0.321811
$641$	−5.50971e12	−1.28904	−0.644522	−	0.764586i	$-0.722943\pi$
$641$	−5.50971e12	−1.28904	−0.644522	+	0.764586i	$0.722943\pi$
$642$	2.41098e13	5.60126
$643$	5.98753e11	0.138133	0.0690667	−	0.997612i	$-0.477998\pi$
$643$	5.98753e11	0.138133	0.0690667	+	0.997612i	$0.477998\pi$
$644$	−7.49291e12	−1.71658
$645$	7.46186e12	1.69757
$646$	−1.92764e12	−0.435491
$647$	−2.84687e12	−0.638701	−0.319351	−	0.947637i	$-0.603465\pi$
$647$	−2.84687e12	−0.638701	−0.319351	+	0.947637i	$0.603465\pi$
$648$	−2.63674e13	−5.87462
$649$	−1.58106e12	−0.349822
$650$	−8.17454e10	−0.0179619
$651$	−7.99307e12	−1.74421
$652$	−1.37023e13	−2.96946
$653$	−1.82215e12	−0.392170	−0.196085	−	0.980587i	$-0.562823\pi$
$653$	−1.82215e12	−0.392170	−0.196085	+	0.980587i	$0.562823\pi$
$654$	1.44739e13	3.09374
$655$	−3.20122e11	−0.0679562
$656$	1.18584e13	2.50011
$657$	1.27392e13	2.66745
$658$	6.82989e12	1.42036
$659$	−3.55378e12	−0.734017	−0.367008	−	0.930218i	$-0.619618\pi$
$659$	−3.55378e12	−0.734017	−0.367008	+	0.930218i	$0.619618\pi$
$660$	−1.20655e13	−2.47512
$661$	4.80541e12	0.979093	0.489546	−	0.871977i	$-0.337162\pi$
$661$	4.80541e12	0.979093	0.489546	+	0.871977i	$0.337162\pi$
$662$	−8.31141e12	−1.68195
$663$	1.53129e12	0.307784
$664$	−3.87711e12	−0.774019
$665$	3.96794e12	0.786806
$666$	1.84870e13	3.64110
$667$	1.67253e12	0.327197
$668$	−7.42457e12	−1.44270
$669$	7.78170e12	1.50196
$670$	3.81843e12	0.732063
$671$	1.41848e12	0.270129
$672$	−1.62673e13	−3.07718
$673$	5.10315e12	0.958894	0.479447	−	0.877571i	$-0.340837\pi$
$673$	5.10315e12	0.958894	0.479447	+	0.877571i	$0.340837\pi$
$674$	−1.94069e11	−0.0362232
$675$	−1.85676e11	−0.0344262
$676$	−6.92221e12	−1.27492
$677$	2.66255e12	0.487134	0.243567	−	0.969884i	$-0.421682\pi$
$677$	2.66255e12	0.487134	0.243567	+	0.969884i	$0.421682\pi$
$678$	−2.16035e13	−3.92636
$679$	2.26972e12	0.409788
$680$	3.68380e12	0.660702
$681$	1.15341e13	2.05504
$682$	6.76757e12	1.19785
$683$	−3.15981e12	−0.555607	−0.277804	−	0.960638i	$-0.589606\pi$
$683$	−3.15981e12	−0.555607	−0.277804	+	0.960638i	$0.589606\pi$
$684$	−3.19039e13	−5.57302
$685$	−5.24708e12	−0.910564
$686$	−1.17366e13	−2.02342
$687$	−1.20176e13	−2.05831
$688$	−1.39313e13	−2.37053
$689$	−7.28380e12	−1.23132
$690$	1.76286e13	2.96071
$691$	−7.41599e12	−1.23742	−0.618711	−	0.785619i	$-0.712345\pi$
$691$	−7.41599e12	−1.23742	−0.618711	+	0.785619i	$0.712345\pi$
$692$	1.67719e13	2.78039
$693$	−6.31234e12	−1.03966
$694$	1.40845e13	2.30474
$695$	−1.22790e12	−0.199632
$696$	1.16049e13	1.87456
$697$	−1.46810e12	−0.235618
$698$	5.80644e12	0.925892
$699$	5.34456e12	0.846768
$700$	−1.75836e11	−0.0276800
$701$	−9.39002e12	−1.46871	−0.734354	−	0.678767i	$-0.762515\pi$
$701$	−9.39002e12	−1.46871	−0.734354	+	0.678767i	$0.762515\pi$
$702$	2.04871e13	3.18392
$703$	5.21462e12	0.805237
$704$	4.59891e12	0.705631
$705$	−1.14183e13	−1.74081
$706$	−1.35658e13	−2.05505
$707$	5.85989e12	0.882069
$708$	1.92156e13	2.87411
$709$	4.58730e11	0.0681788	0.0340894	−	0.999419i	$-0.489147\pi$
$709$	4.58730e11	0.0681788	0.0340894	+	0.999419i	$0.489147\pi$
$710$	1.60485e13	2.37013
$711$	−2.00433e13	−2.94141
$712$	2.78058e13	4.05485
$713$	−7.02633e12	−1.01818
$714$	4.63529e12	0.667475
$715$	2.66880e12	0.381890
$716$	2.04326e13	2.90546
$717$	−3.17832e11	−0.0449119
$718$	−4.61282e12	−0.647749
$719$	4.10035e12	0.572191	0.286096	−	0.958201i	$-0.407643\pi$
$719$	4.10035e12	0.572191	0.286096	+	0.958201i	$0.407643\pi$
$720$	4.39081e13	6.08904
$721$	−4.36349e12	−0.601347
$722$	9.08525e11	0.124428
$723$	8.46044e12	1.15152
$724$	−5.07036e12	−0.685828
$725$	3.92493e10	0.00527607
$726$	−1.78473e13	−2.38428
$727$	3.64967e12	0.484561	0.242280	−	0.970206i	$-0.422105\pi$
$727$	3.64967e12	0.484561	0.242280	+	0.970206i	$0.422105\pi$
$728$	1.14997e13	1.51739
$729$	4.43176e12	0.581169
$730$	−1.63037e13	−2.12487
$731$	1.72473e12	0.223406
$732$	−1.72396e13	−2.21936
$733$	−2.77480e11	−0.0355029	−0.0177514	−	0.999842i	$-0.505651\pi$
$733$	−2.77480e11	−0.0355029	−0.0177514	+	0.999842i	$0.505651\pi$
$734$	−8.04375e12	−1.02288
$735$	5.04001e12	0.636999
$736$	−1.42998e13	−1.79630
$737$	−1.71343e12	−0.213925
$738$	−3.41940e13	−4.24323
$739$	1.15877e13	1.42922	0.714608	−	0.699525i	$-0.246605\pi$
$739$	1.15877e13	1.42922	0.714608	+	0.699525i	$0.246605\pi$
$740$	−1.68126e13	−2.06107
$741$	1.00602e13	1.22582
$742$	−2.20485e13	−2.67031
$743$	4.79681e12	0.577434	0.288717	−	0.957414i	$-0.406771\pi$
$743$	4.79681e12	0.577434	0.288717	+	0.957414i	$0.406771\pi$
$744$	−4.87523e13	−5.83333
$745$	8.24919e12	0.981088
$746$	−4.96648e12	−0.587116
$747$	5.72119e12	0.672270
$748$	−2.78881e12	−0.325733
$749$	−1.14712e13	−1.33180
$750$	−2.92711e13	−3.37802
$751$	−2.32776e12	−0.267029	−0.133515	−	0.991047i	$-0.542626\pi$
$751$	−2.32776e12	−0.267029	−0.133515	+	0.991047i	$0.542626\pi$
$752$	2.13181e13	2.43091
$753$	8.09196e12	0.917225
$754$	−4.33067e12	−0.487960
$755$	1.42821e13	1.59967
$756$	4.40680e13	4.90654
$757$	−6.01494e12	−0.665732	−0.332866	−	0.942974i	$-0.608016\pi$
$757$	−6.01494e12	−0.665732	−0.332866	+	0.942974i	$0.608016\pi$
$758$	7.44314e12	0.818926
$759$	−7.91039e12	−0.865187
$760$	2.42017e13	2.63139
$761$	−1.12427e13	−1.21518	−0.607589	−	0.794252i	$-0.707863\pi$
$761$	−1.12427e13	−1.21518	−0.607589	+	0.794252i	$0.707863\pi$
$762$	−3.62855e13	−3.89885
$763$	−6.88651e12	−0.735595
$764$	−1.37048e13	−1.45530
$765$	−5.43593e12	−0.573849
$766$	−5.42772e12	−0.569623
$767$	−4.25035e12	−0.443451
$768$	1.22809e13	1.27381
$769$	1.35036e13	1.39246	0.696230	−	0.717819i	$-0.254860\pi$
$769$	1.35036e13	1.39246	0.696230	+	0.717819i	$0.254860\pi$
$770$	8.07860e12	0.828185
$771$	1.89201e13	1.92832
$772$	1.62946e13	1.65107
$773$	2.43055e12	0.244848	0.122424	−	0.992478i	$-0.460933\pi$
$773$	2.43055e12	0.244848	0.122424	+	0.992478i	$0.460933\pi$
$774$	4.01715e13	4.02331
$775$	−1.64886e11	−0.0164183
$776$	1.38438e13	1.37049
$777$	−1.25393e13	−1.23418
$778$	−2.88654e12	−0.282468
$779$	−9.64508e12	−0.938399
$780$	−3.24354e13	−3.13757
$781$	−7.20137e12	−0.692605
$782$	4.07466e12	0.389638
$783$	−9.83667e12	−0.935234
$784$	−9.40974e12	−0.889519
$785$	−7.48555e12	−0.703575
$786$	−2.45684e12	−0.229602
$787$	−3.78714e12	−0.351905	−0.175953	−	0.984399i	$-0.556301\pi$
$787$	−3.78714e12	−0.351905	−0.175953	+	0.984399i	$0.556301\pi$
$788$	8.99975e12	0.831501
$789$	1.49399e13	1.37246
$790$	2.56516e13	2.34311
$791$	1.02787e13	0.933565
$792$	−3.85010e13	−3.47703
$793$	3.81328e12	0.342428
$794$	−3.29514e13	−2.94226
$795$	3.68611e13	3.27277
$796$	3.81875e12	0.337142
$797$	2.23878e12	0.196539	0.0982694	−	0.995160i	$-0.468669\pi$
$797$	2.23878e12	0.196539	0.0982694	+	0.995160i	$0.468669\pi$
$798$	3.04528e13	2.65837
$799$	−2.63924e12	−0.229096
$800$	−3.35572e11	−0.0289655
$801$	−4.10311e13	−3.52182
$802$	−4.48992e12	−0.383225
$803$	7.31588e12	0.620936
$804$	2.08243e13	1.75759
$805$	−8.38749e12	−0.703964
$806$	1.81932e13	1.51845
$807$	−3.40745e13	−2.82813
$808$	3.57414e13	2.94999
$809$	−6.77107e12	−0.555762	−0.277881	−	0.960615i	$-0.589632\pi$
$809$	−6.77107e12	−0.555762	−0.277881	+	0.960615i	$0.589632\pi$
$810$	−4.97956e13	−4.06451
$811$	1.26099e13	1.02357	0.511785	−	0.859113i	$-0.328984\pi$
$811$	1.26099e13	1.02357	0.511785	+	0.859113i	$0.328984\pi$
$812$	−9.31534e12	−0.751964
$813$	3.22264e13	2.58705
$814$	1.06168e13	0.847586
$815$	−1.53382e13	−1.21777
$816$	1.44681e13	1.14237
$817$	1.13311e13	0.889762
$818$	4.56959e13	3.56851
$819$	−1.69694e13	−1.31792
$820$	3.10970e13	2.40191
$821$	1.40858e13	1.08203	0.541013	−	0.841014i	$-0.318041\pi$
$821$	1.40858e13	1.08203	0.541013	+	0.841014i	$0.318041\pi$
$822$	−4.02699e13	−3.07650
$823$	−1.62081e13	−1.23150	−0.615748	−	0.787943i	$-0.711146\pi$
$823$	−1.62081e13	−1.23150	−0.615748	+	0.787943i	$0.711146\pi$
$824$	−2.66143e13	−2.01114
$825$	−1.85633e11	−0.0139512
$826$	−1.28661e13	−0.961690
$827$	8.84797e12	0.657762	0.328881	−	0.944371i	$-0.393329\pi$
$827$	8.84797e12	0.657762	0.328881	+	0.944371i	$0.393329\pi$
$828$	6.74388e13	4.98624
$829$	9.64554e12	0.709302	0.354651	−	0.934999i	$-0.384600\pi$
$829$	9.64554e12	0.709302	0.354651	+	0.934999i	$0.384600\pi$
$830$	−7.32203e12	−0.535526
$831$	2.78752e13	2.02775
$832$	1.23632e13	0.894491
$833$	1.16495e12	0.0838310
$834$	−9.42379e12	−0.674494
$835$	−8.31099e12	−0.591649
$836$	−1.83219e13	−1.29730
$837$	4.13239e13	2.91030
$838$	−2.72822e13	−1.91109
$839$	1.77288e13	1.23524	0.617618	−	0.786478i	$-0.288098\pi$
$839$	1.77288e13	1.23524	0.617618	+	0.786478i	$0.288098\pi$
$840$	−5.81967e13	−4.03312
$841$	−1.24278e13	−0.856668
$842$	3.67774e13	2.52160
$843$	3.12358e13	2.13024
$844$	−4.14876e13	−2.81434
$845$	−7.74865e12	−0.522843
$846$	−6.14714e13	−4.12579
$847$	8.49157e12	0.566908
$848$	−6.88198e13	−4.57017
$849$	−5.07625e13	−3.35319
$850$	9.56199e10	0.00628294
$851$	−1.10227e13	−0.720454
$852$	8.75225e13	5.69039
$853$	1.82317e13	1.17911	0.589557	−	0.807727i	$-0.299303\pi$
$853$	1.82317e13	1.17911	0.589557	+	0.807727i	$0.299303\pi$
$854$	1.15430e13	0.742607
$855$	−3.57129e13	−2.28548
$856$	−6.99664e13	−4.45408
$857$	−4.46174e12	−0.282547	−0.141273	−	0.989971i	$-0.545120\pi$
$857$	−4.46174e12	−0.282547	−0.141273	+	0.989971i	$0.545120\pi$
$858$	2.04823e13	1.29028
$859$	2.49571e13	1.56395	0.781977	−	0.623307i	$-0.214211\pi$
$859$	2.49571e13	1.56395	0.781977	+	0.623307i	$0.214211\pi$
$860$	−3.65330e13	−2.27742
$861$	2.31930e13	1.43828
$862$	−1.23558e12	−0.0762231
$863$	−4.92247e12	−0.302089	−0.151044	−	0.988527i	$-0.548264\pi$
$863$	−4.92247e12	−0.302089	−0.151044	+	0.988527i	$0.548264\pi$
$864$	8.41013e13	5.13441
$865$	1.87743e13	1.14023
$866$	5.62430e13	3.39812
$867$	−1.79119e12	−0.107660
$868$	3.91338e13	2.33999
$869$	−1.15105e13	−0.684710
$870$	2.19162e13	1.29697
$871$	−4.60619e12	−0.271182
$872$	−4.20030e13	−2.46012
$873$	−2.04283e13	−1.19033
$874$	2.67696e13	1.55182
$875$	1.39269e13	0.803188
$876$	−8.89143e13	−5.10156
$877$	−1.68831e13	−0.963725	−0.481863	−	0.876247i	$-0.660040\pi$
$877$	−1.68831e13	−0.963725	−0.481863	+	0.876247i	$0.660040\pi$
$878$	−3.32539e13	−1.88850
$879$	1.35886e13	0.767760
$880$	2.52157e13	1.41742
$881$	−1.26880e13	−0.709583	−0.354792	−	0.934945i	$-0.615448\pi$
$881$	−1.26880e13	−0.709583	−0.354792	+	0.934945i	$0.615448\pi$
$882$	2.71333e13	1.50971
$883$	−2.65648e13	−1.47056	−0.735281	−	0.677762i	$-0.762950\pi$
$883$	−2.65648e13	−1.47056	−0.735281	+	0.677762i	$0.762950\pi$
$884$	−7.49713e12	−0.412914
$885$	2.15097e13	1.17866
$886$	−4.99736e13	−2.72451
$887$	−5.71289e11	−0.0309885	−0.0154942	−	0.999880i	$-0.504932\pi$
$887$	−5.71289e11	−0.0309885	−0.0154942	+	0.999880i	$0.504932\pi$
$888$	−7.64814e13	−4.12760
$889$	1.72643e13	0.927023
$890$	5.25120e13	2.80546
$891$	2.23446e13	1.18774
$892$	−3.80990e13	−2.01498
$893$	−1.73392e13	−0.912425
$894$	6.33103e13	3.31478
$895$	2.28720e13	1.19152
$896$	4.98757e12	0.258525
$897$	−2.12654e13	−1.09675
$898$	−2.54223e13	−1.30458
$899$	−8.73529e12	−0.446025
$900$	1.58258e12	0.0804035
$901$	8.52007e12	0.430706
$902$	−1.96371e13	−0.987751
$903$	−2.72474e13	−1.36374
$904$	6.26931e13	3.12221
$905$	−5.67571e12	−0.281256
$906$	1.09611e14	5.40477
$907$	3.29210e12	0.161525	0.0807625	−	0.996733i	$-0.474264\pi$
$907$	3.29210e12	0.161525	0.0807625	+	0.996733i	$0.474264\pi$
$908$	−5.64705e13	−2.75699
$909$	−5.27411e13	−2.56219
$910$	2.17176e13	1.04985
$911$	−1.27945e13	−0.615445	−0.307723	−	0.951476i	$-0.599567\pi$
$911$	−1.27945e13	−0.615445	−0.307723	+	0.951476i	$0.599567\pi$
$912$	9.50524e13	4.54974
$913$	3.28559e12	0.156493
$914$	4.06107e13	1.92479
$915$	−1.92978e13	−0.910152
$916$	5.88376e13	2.76137
$917$	1.16894e12	0.0545922
$918$	−2.39643e13	−1.11371
$919$	−3.16626e13	−1.46429	−0.732146	−	0.681148i	$-0.761481\pi$
$919$	−3.16626e13	−1.46429	−0.732146	+	0.681148i	$0.761481\pi$
$920$	−5.11579e13	−2.35433
$921$	−1.71244e13	−0.784235
$922$	−2.16650e12	−0.0987348
$923$	−1.93594e13	−0.877979
$924$	4.40577e13	1.98837
$925$	−2.58670e11	−0.0116174
$926$	3.22208e13	1.44008
$927$	3.92730e13	1.74677
$928$	−1.77778e13	−0.786887
$929$	−1.31826e13	−0.580673	−0.290336	−	0.956925i	$-0.593767\pi$
$929$	−1.31826e13	−0.580673	−0.290336	+	0.956925i	$0.593767\pi$
$930$	−9.20701e13	−4.03595
$931$	7.65346e12	0.333875
$932$	−2.61668e13	−1.13600
$933$	−5.56929e13	−2.40620
$934$	6.55493e13	2.81843
$935$	−3.12177e12	−0.133582
$936$	−1.03502e14	−4.40765
$937$	−2.06204e13	−0.873916	−0.436958	−	0.899482i	$-0.643944\pi$
$937$	−2.06204e13	−0.873916	−0.436958	+	0.899482i	$0.643944\pi$
$938$	−1.39432e13	−0.588099
$939$	−5.22374e13	−2.19273
$940$	5.59038e13	2.33543
$941$	2.43975e13	1.01436	0.507180	−	0.861840i	$-0.330688\pi$
$941$	2.43975e13	1.01436	0.507180	+	0.861840i	$0.330688\pi$
$942$	−5.74495e13	−2.37715
$943$	2.03879e13	0.839596
$944$	−4.01588e13	−1.64591
$945$	4.93293e13	2.01216
$946$	2.30698e13	0.936556
$947$	−4.10278e13	−1.65769	−0.828845	−	0.559478i	$-0.811002\pi$
$947$	−4.10278e13	−1.65769	−0.828845	+	0.559478i	$0.811002\pi$
$948$	1.39894e14	5.62552
$949$	1.96672e13	0.787128
$950$	6.28202e11	0.0250232
$951$	−5.84506e13	−2.31727
$952$	−1.34516e13	−0.530771
$953$	4.09880e13	1.60968	0.804839	−	0.593494i	$-0.202252\pi$
$953$	4.09880e13	1.60968	0.804839	+	0.593494i	$0.202252\pi$
$954$	1.98444e14	7.75659
$955$	−1.53410e13	−0.596815
$956$	1.55610e12	0.0602527
$957$	−9.83437e12	−0.379003
$958$	−5.73711e13	−2.20064
$959$	1.91600e13	0.731496
$960$	−6.25663e13	−2.37750
$961$	1.02574e13	0.387956
$962$	2.85410e13	1.07444
$963$	1.03245e14	3.86856
$964$	−4.14221e13	−1.54485
$965$	1.82400e13	0.677098
$966$	−6.43716e13	−2.37847
$967$	−4.45707e12	−0.163919	−0.0819597	−	0.996636i	$-0.526118\pi$
$967$	−4.45707e12	−0.163919	−0.0819597	+	0.996636i	$0.526118\pi$
$968$	5.17928e13	1.89596
$969$	−1.17677e13	−0.428781
$970$	2.61444e13	0.948211
$971$	3.69975e13	1.33563	0.667815	−	0.744327i	$-0.267230\pi$
$971$	3.69975e13	1.33563	0.667815	+	0.744327i	$0.267230\pi$
$972$	−1.02769e14	−3.69288
$973$	4.48374e12	0.160374
$974$	3.78797e13	1.34863
$975$	−4.99034e11	−0.0176852
$976$	3.60292e13	1.27096
$977$	4.72608e13	1.65949	0.829746	−	0.558141i	$-0.188485\pi$
$977$	4.72608e13	1.65949	0.829746	+	0.558141i	$0.188485\pi$
$978$	−1.17716e14	−4.11445
$979$	−2.35635e13	−0.819819
$980$	−2.46758e13	−0.854581
$981$	6.19811e13	2.13673
$982$	−1.00727e14	−3.45656
$983$	−1.37629e13	−0.470130	−0.235065	−	0.971980i	$-0.575530\pi$
$983$	−1.37629e13	−0.470130	−0.235065	+	0.971980i	$0.575530\pi$
$984$	1.41462e14	4.81018
$985$	1.00742e13	0.340996
$986$	5.06571e12	0.170685
$987$	4.16947e13	1.39847
$988$	−4.92545e13	−1.64452
$989$	−2.39519e13	−0.796080
$990$	−7.27102e13	−2.40568
$991$	−3.34745e13	−1.10251	−0.551255	−	0.834337i	$-0.685851\pi$
$991$	−3.34745e13	−1.10251	−0.551255	+	0.834337i	$0.685851\pi$
$992$	7.46847e13	2.44866
$993$	−5.07390e13	−1.65604
$994$	−5.86020e13	−1.90403
$995$	4.27468e12	0.138261
$996$	−3.99317e13	−1.28573
$997$	−4.78709e13	−1.53442	−0.767209	−	0.641398i	$-0.778355\pi$
$997$	−4.78709e13	−1.53442	−0.767209	+	0.641398i	$0.778355\pi$
$998$	5.04279e13	1.60910
$999$	6.48280e13	2.05929

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.a.a.1.1	✓	5
3.2	odd	2		153.10.a.c.1.5		5
4.3	odd	2		272.10.a.f.1.5		5
17.16	even	2		289.10.a.a.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.a.1.1	✓	5	1.1	even	1	trivial
153.10.a.c.1.5		5	3.2	odd	2
272.10.a.f.1.5		5	4.3	odd	2
289.10.a.a.1.1		5	17.16	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

\(f(q)\)	\(=\)	\(q-42.0613 q^{2} -256.773 q^{3} +1257.15 q^{4} +1407.25 q^{5} +10800.2 q^{6} -5138.64 q^{7} -31342.2 q^{8} +46249.6 q^{9} +O(q^{10})\)	\(q-42.0613 q^{2} -256.773 q^{3} +1257.15 q^{4} +1407.25 q^{5} +10800.2 q^{6} -5138.64 q^{7} -31342.2 q^{8} +46249.6 q^{9} -59190.7 q^{10} +26560.4 q^{11} -322804. q^{12} +71402.0 q^{13} +216138. q^{14} -361344. q^{15} +674631. q^{16} -83521.0 q^{17} -1.94532e6 q^{18} -548715. q^{19} +1.76913e6 q^{20} +1.31947e6 q^{21} -1.11716e6 q^{22} +1.15988e6 q^{23} +8.04785e6 q^{24} +27218.8 q^{25} -3.00326e6 q^{26} -6.82160e6 q^{27} -6.46007e6 q^{28} +1.44199e6 q^{29} +1.51986e7 q^{30} -6.05781e6 q^{31} -1.23287e7 q^{32} -6.82000e6 q^{33} +3.51300e6 q^{34} -7.23134e6 q^{35} +5.81429e7 q^{36} -9.50334e6 q^{37} +2.30797e7 q^{38} -1.83341e7 q^{39} -4.41062e7 q^{40} +1.75776e7 q^{41} -5.54985e7 q^{42} -2.06503e7 q^{43} +3.33905e7 q^{44} +6.50846e7 q^{45} -4.87861e7 q^{46} +3.15997e7 q^{47} -1.73227e8 q^{48} -1.39480e7 q^{49} -1.14486e6 q^{50} +2.14460e7 q^{51} +8.97634e7 q^{52} -1.02011e8 q^{53} +2.86925e8 q^{54} +3.73770e7 q^{55} +1.61056e8 q^{56} +1.40895e8 q^{57} -6.06520e7 q^{58} -5.95270e7 q^{59} -4.54265e8 q^{60} +5.34058e7 q^{61} +2.54799e8 q^{62} -2.37660e8 q^{63} +1.73149e8 q^{64} +1.00480e8 q^{65} +2.86858e8 q^{66} -6.45107e7 q^{67} -1.04999e8 q^{68} -2.97827e8 q^{69} +3.04160e8 q^{70} -2.71132e8 q^{71} -1.44956e9 q^{72} +2.75443e8 q^{73} +3.99723e8 q^{74} -6.98908e6 q^{75} -6.89819e8 q^{76} -1.36484e8 q^{77} +7.71158e8 q^{78} -4.33372e8 q^{79} +9.49373e8 q^{80} +8.41275e8 q^{81} -7.39337e8 q^{82} +1.23703e8 q^{83} +1.65877e9 q^{84} -1.17535e8 q^{85} +8.68579e8 q^{86} -3.70264e8 q^{87} -8.32461e8 q^{88} -8.87168e8 q^{89} -2.73755e9 q^{90} -3.66909e8 q^{91} +1.45815e9 q^{92} +1.55548e9 q^{93} -1.32912e9 q^{94} -7.72177e8 q^{95} +3.16568e9 q^{96} -4.41697e8 q^{97} +5.86670e8 q^{98} +1.22841e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 33 q^{2} - 236 q^{3} + 853 q^{4} + 1480 q^{5} + 7578 q^{6} - 13202 q^{7} - 42423 q^{8} + 10981 q^{9}+O(q^{10}) \) 5 * q - 33 * q^2 - 236 * q^3 + 853 * q^4 + 1480 * q^5 + 7578 * q^6 - 13202 * q^7 - 42423 * q^8 + 10981 * q^9	\( 5 q - 33 q^{2} - 236 q^{3} + 853 q^{4} + 1480 q^{5} + 7578 q^{6} - 13202 q^{7} - 42423 q^{8} + 10981 q^{9} - 89328 q^{10} - 68036 q^{11} - 406010 q^{12} - 158862 q^{13} - 84700 q^{14} - 687324 q^{15} + 350225 q^{16} - 417605 q^{17} - 1911585 q^{18} - 370992 q^{19} + 1632640 q^{20} + 1783880 q^{21} + 122290 q^{22} + 1645870 q^{23} + 9678702 q^{24} + 3270239 q^{25} + 734846 q^{26} - 2998268 q^{27} + 183372 q^{28} + 3668616 q^{29} + 17048544 q^{30} - 7262362 q^{31} - 5605919 q^{32} - 11334900 q^{33} + 2756193 q^{34} - 26503988 q^{35} + 49782133 q^{36} - 31420708 q^{37} + 18513700 q^{38} - 42449884 q^{39} - 53930464 q^{40} - 7996938 q^{41} - 44519496 q^{42} - 56908268 q^{43} + 43323054 q^{44} + 12799536 q^{45} - 32063472 q^{46} - 16903336 q^{47} - 102794498 q^{48} - 11784059 q^{49} + 85921093 q^{50} + 19710956 q^{51} + 173619082 q^{52} - 83362982 q^{53} + 386329164 q^{54} + 6363364 q^{55} + 317409372 q^{56} + 136615904 q^{57} + 64577488 q^{58} - 37946604 q^{59} - 223158912 q^{60} - 77685452 q^{61} + 324855300 q^{62} - 191945278 q^{63} + 131623105 q^{64} - 40321288 q^{65} + 298037676 q^{66} - 304503600 q^{67} - 71243413 q^{68} - 333409272 q^{69} - 122787392 q^{70} - 476602922 q^{71} - 1301701911 q^{72} - 289980486 q^{73} + 262289012 q^{74} - 153685772 q^{75} - 1031276084 q^{76} - 143385648 q^{77} + 691646196 q^{78} - 828240610 q^{79} + 912750944 q^{80} + 891328609 q^{81} - 1109615654 q^{82} + 194681148 q^{83} + 1541719592 q^{84} - 123611080 q^{85} + 1164707144 q^{86} + 158149884 q^{87} - 1017979978 q^{88} + 376848106 q^{89} - 2240087472 q^{90} + 194543664 q^{91} + 2506713088 q^{92} + 3494835920 q^{93} - 2244811104 q^{94} + 1498679864 q^{95} + 2935047582 q^{96} + 692035246 q^{97} + 871744055 q^{98} + 2027106408 q^{99}+O(q^{100}) \) 5 * q - 33 * q^2 - 236 * q^3 + 853 * q^4 + 1480 * q^5 + 7578 * q^6 - 13202 * q^7 - 42423 * q^8 + 10981 * q^9 - 89328 * q^10 - 68036 * q^11 - 406010 * q^12 - 158862 * q^13 - 84700 * q^14 - 687324 * q^15 + 350225 * q^16 - 417605 * q^17 - 1911585 * q^18 - 370992 * q^19 + 1632640 * q^20 + 1783880 * q^21 + 122290 * q^22 + 1645870 * q^23 + 9678702 * q^24 + 3270239 * q^25 + 734846 * q^26 - 2998268 * q^27 + 183372 * q^28 + 3668616 * q^29 + 17048544 * q^30 - 7262362 * q^31 - 5605919 * q^32 - 11334900 * q^33 + 2756193 * q^34 - 26503988 * q^35 + 49782133 * q^36 - 31420708 * q^37 + 18513700 * q^38 - 42449884 * q^39 - 53930464 * q^40 - 7996938 * q^41 - 44519496 * q^42 - 56908268 * q^43 + 43323054 * q^44 + 12799536 * q^45 - 32063472 * q^46 - 16903336 * q^47 - 102794498 * q^48 - 11784059 * q^49 + 85921093 * q^50 + 19710956 * q^51 + 173619082 * q^52 - 83362982 * q^53 + 386329164 * q^54 + 6363364 * q^55 + 317409372 * q^56 + 136615904 * q^57 + 64577488 * q^58 - 37946604 * q^59 - 223158912 * q^60 - 77685452 * q^61 + 324855300 * q^62 - 191945278 * q^63 + 131623105 * q^64 - 40321288 * q^65 + 298037676 * q^66 - 304503600 * q^67 - 71243413 * q^68 - 333409272 * q^69 - 122787392 * q^70 - 476602922 * q^71 - 1301701911 * q^72 - 289980486 * q^73 + 262289012 * q^74 - 153685772 * q^75 - 1031276084 * q^76 - 143385648 * q^77 + 691646196 * q^78 - 828240610 * q^79 + 912750944 * q^80 + 891328609 * q^81 - 1109615654 * q^82 + 194681148 * q^83 + 1541719592 * q^84 - 123611080 * q^85 + 1164707144 * q^86 + 158149884 * q^87 - 1017979978 * q^88 + 376848106 * q^89 - 2240087472 * q^90 + 194543664 * q^91 + 2506713088 * q^92 + 3494835920 * q^93 - 2244811104 * q^94 + 1498679864 * q^95 + 2935047582 * q^96 + 692035246 * q^97 + 871744055 * q^98 + 2027106408 * q^99

Introduction

L-functions

Modular forms

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