LMFDB - Embedded newform 17.18.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,18,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, 18, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("17.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 18 $
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:	$31.1477548486$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 1187158 x^{10} - 42381124 x^{9} + 516627945000 x^{8} + 35391783973088 x^{7} + \cdots + 61\!\cdots\!00 $ x^12 - x^11 - 1187158x^10 - 42381124x^9 + 516627945000x^8 + 35391783973088x^7 - 99087971288891648x^6 - 9479954937590448128x^5 + 7601386522170057295872x^4 + 823950667366006189842432x^3 - 113725321550829675696881664x^2 - 61769149550929485409812480x + 6146035964769577099434393600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{34}\cdot 3^{8} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-472.034$ 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)

$f(q)$	$=$	$q+516.034 q^{2} +15990.3 q^{3} +135219. q^{4} +1.06954e6 q^{5} +8.25154e6 q^{6} +2.48734e7 q^{7} +2.13988e6 q^{8} +1.26550e8 q^{9} +O(q^{10})$	\(q+516.034 q^{2} +15990.3 q^{3} +135219. q^{4} +1.06954e6 q^{5} +8.25154e6 q^{6} +2.48734e7 q^{7} +2.13988e6 q^{8} +1.26550e8 q^{9} +5.51917e8 q^{10} -1.01257e9 q^{11} +2.16219e9 q^{12} -1.98879e9 q^{13} +1.28355e10 q^{14} +1.71022e10 q^{15} -1.66191e10 q^{16} +6.97576e9 q^{17} +6.53039e10 q^{18} -1.19709e11 q^{19} +1.44621e11 q^{20} +3.97734e11 q^{21} -5.22518e11 q^{22} +5.69153e11 q^{23} +3.42174e10 q^{24} +3.80970e11 q^{25} -1.02628e12 q^{26} -4.14228e10 q^{27} +3.36335e12 q^{28} -3.32350e12 q^{29} +8.82532e12 q^{30} +3.32753e11 q^{31} -8.85652e12 q^{32} -1.61912e13 q^{33} +3.59973e12 q^{34} +2.66030e13 q^{35} +1.71119e13 q^{36} +2.58461e13 q^{37} -6.17737e13 q^{38} -3.18014e13 q^{39} +2.28868e12 q^{40} +2.80628e13 q^{41} +2.05244e14 q^{42} +6.82637e13 q^{43} -1.36918e14 q^{44} +1.35350e14 q^{45} +2.93702e14 q^{46} +7.06795e13 q^{47} -2.65745e14 q^{48} +3.86057e14 q^{49} +1.96593e14 q^{50} +1.11544e14 q^{51} -2.68922e14 q^{52} +2.91013e14 q^{53} -2.13756e13 q^{54} -1.08298e15 q^{55} +5.32262e13 q^{56} -1.91418e15 q^{57} -1.71504e15 q^{58} -8.60211e14 q^{59} +2.31254e15 q^{60} -1.78874e15 q^{61} +1.71712e14 q^{62} +3.14772e15 q^{63} -2.39196e15 q^{64} -2.12709e15 q^{65} -8.35522e15 q^{66} +3.38692e15 q^{67} +9.43253e14 q^{68} +9.10093e15 q^{69} +1.37281e16 q^{70} -3.42363e15 q^{71} +2.70801e14 q^{72} -7.14682e15 q^{73} +1.33375e16 q^{74} +6.09182e15 q^{75} -1.61869e16 q^{76} -2.51860e16 q^{77} -1.64106e16 q^{78} +2.01204e15 q^{79} -1.77748e16 q^{80} -1.70050e16 q^{81} +1.44814e16 q^{82} +9.29633e15 q^{83} +5.37811e16 q^{84} +7.46083e15 q^{85} +3.52264e16 q^{86} -5.31438e16 q^{87} -2.16677e15 q^{88} +6.47554e16 q^{89} +6.98449e16 q^{90} -4.94681e16 q^{91} +7.69602e16 q^{92} +5.32082e15 q^{93} +3.64730e16 q^{94} -1.28033e17 q^{95} -1.41618e17 q^{96} +2.22579e16 q^{97} +1.99218e17 q^{98} -1.28140e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 527 q^{2} + 21484 q^{3} + 824597 q^{4} + 1770512 q^{5} - 3292232 q^{6} + 22379060 q^{7} + 45571509 q^{8} + 746877740 q^{9}+O(q^{10}) $ 12 * q + 527 * q^2 + 21484 * q^3 + 824597 * q^4 + 1770512 * q^5 - 3292232 * q^6 + 22379060 * q^7 + 45571509 * q^8 + 746877740 * q^9	\( 12 q + 527 q^{2} + 21484 q^{3} + 824597 q^{4} + 1770512 q^{5} - 3292232 q^{6} + 22379060 q^{7} + 45571509 q^{8} + 746877740 q^{9} + 824176946 q^{10} + 1508850220 q^{11} + 4380824560 q^{12} + 2071135824 q^{13} - 9581529548 q^{14} - 15603628992 q^{15} + 20409782305 q^{16} + 83709089292 q^{17} - 195058406893 q^{18} - 1108652840 q^{19} + 304149438198 q^{20} + 711976780056 q^{21} + 350258857160 q^{22} + 816663191324 q^{23} - 118287259488 q^{24} + 841645606900 q^{25} + 1135562035330 q^{26} + 2668523518384 q^{27} + 7745458522756 q^{28} - 4667447777712 q^{29} + 15034204946608 q^{30} + 23367156664948 q^{31} + 16779331087925 q^{32} + 25952886361216 q^{33} + 3676224171407 q^{34} + 52808829544064 q^{35} + 178683325289537 q^{36} + 45103867774096 q^{37} + 141942362802260 q^{38} + 187488571444048 q^{39} + 231489638087062 q^{40} + 106534751749128 q^{41} + 82630767165312 q^{42} + 350248430413232 q^{43} + 468477290587728 q^{44} + 238676787528480 q^{45} + 587080431637364 q^{46} + 419195348129576 q^{47} + 10\!\cdots\!72 q^{48}+ \cdots - 11\!\cdots\!24 q^{99}+O(q^{100}) \) 12 * q + 527 * q^2 + 21484 * q^3 + 824597 * q^4 + 1770512 * q^5 - 3292232 * q^6 + 22379060 * q^7 + 45571509 * q^8 + 746877740 * q^9 + 824176946 * q^10 + 1508850220 * q^11 + 4380824560 * q^12 + 2071135824 * q^13 - 9581529548 * q^14 - 15603628992 * q^15 + 20409782305 * q^16 + 83709089292 * q^17 - 195058406893 * q^18 - 1108652840 * q^19 + 304149438198 * q^20 + 711976780056 * q^21 + 350258857160 * q^22 + 816663191324 * q^23 - 118287259488 * q^24 + 841645606900 * q^25 + 1135562035330 * q^26 + 2668523518384 * q^27 + 7745458522756 * q^28 - 4667447777712 * q^29 + 15034204946608 * q^30 + 23367156664948 * q^31 + 16779331087925 * q^32 + 25952886361216 * q^33 + 3676224171407 * q^34 + 52808829544064 * q^35 + 178683325289537 * q^36 + 45103867774096 * q^37 + 141942362802260 * q^38 + 187488571444048 * q^39 + 231489638087062 * q^40 + 106534751749128 * q^41 + 82630767165312 * q^42 + 350248430413232 * q^43 + 468477290587728 * q^44 + 238676787528480 * q^45 + 587080431637364 * q^46 + 419195348129576 * q^47 + 1093472072556672 * q^48 + 794411575895372 * q^49 + 1412694936225137 * q^50 + 149867172862444 * q^51 + 642014932833750 * q^52 + 56947812536104 * q^53 - 1392308314286000 * q^54 - 1412881301128432 * q^55 - 3203817872304204 * q^56 - 2707439010959184 * q^57 - 1529508580613878 * q^58 - 3177686539773696 * q^59 - 10022838941748448 * q^60 - 3392964491871408 * q^61 - 12114194581567516 * q^62 + 1635686752578012 * q^63 - 8465772367878263 * q^64 - 3660813322103328 * q^65 - 11453990779029568 * q^66 - 2857880476265040 * q^67 + 5752188658576277 * q^68 - 12630398353679160 * q^69 + 3399395009377720 * q^70 - 1862686563242532 * q^71 - 36929264963425119 * q^72 - 15078079303572472 * q^73 + 542093202855346 * q^74 - 20330126181611628 * q^75 + 6303255557523596 * q^76 - 20295555037512648 * q^77 - 53192869717439760 * q^78 + 19398131823479964 * q^79 - 7257576275928962 * q^80 + 37457071423573532 * q^81 + 127570037419772678 * q^82 + 50819373739336784 * q^83 + 179493786749097600 * q^84 + 12350662258379792 * q^85 + 22727028430696588 * q^86 + 102295071486477840 * q^87 + 194000133114521056 * q^88 + 40280615281839032 * q^89 + 223872567241318058 * q^90 + 169549572827745440 * q^91 + 116206299681681348 * q^92 + 32924009888402024 * q^93 + 130371382365284928 * q^94 + 106757515750638208 * q^95 - 16033015771117248 * q^96 + 173995685961333528 * q^97 - 246436513972691449 * q^98 - 112553818797736924 * 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 $

$2$	516.034	1.42536	0.712678	−	0.701492i	$-0.247482\pi$
$2$	516.034	1.42536	0.712678	+	0.701492i	$0.247482\pi$
$3$	15990.3	1.40710	0.703552	−	0.710644i	$-0.251596\pi$
$3$	15990.3	1.40710	0.703552	+	0.710644i	$0.251596\pi$
$4$	135219.	1.03164
$5$	1.06954e6	1.22448	0.612239	−	0.790673i	$-0.290269\pi$
$5$	1.06954e6	1.22448	0.612239	+	0.790673i	$0.290269\pi$
$6$	8.25154e6	2.00562
$7$	2.48734e7	1.63081	0.815403	−	0.578894i	$-0.196516\pi$
$7$	2.48734e7	1.63081	0.815403	+	0.578894i	$0.196516\pi$
$8$	2.13988e6	0.0450947
$9$	1.26550e8	0.979940
$10$	5.51917e8	1.74531
$11$	−1.01257e9	−1.42425	−0.712124	−	0.702054i	$-0.752267\pi$
$11$	−1.01257e9	−1.42425	−0.712124	+	0.702054i	$0.752267\pi$
$12$	2.16219e9	1.45162
$13$	−1.98879e9	−0.676194	−0.338097	−	0.941111i	$-0.609783\pi$
$13$	−1.98879e9	−0.676194	−0.338097	+	0.941111i	$0.609783\pi$
$14$	1.28355e10	2.32448
$15$	1.71022e10	1.72297
$16$	−1.66191e10	−0.967362
$17$	6.97576e9	0.242536
$17$	6.97576e9	0.242536
$18$	6.53039e10	1.39676
$19$	−1.19709e11	−1.61704	−0.808519	−	0.588470i	$-0.799730\pi$
$19$	−1.19709e11	−1.61704	−0.808519	+	0.588470i	$0.799730\pi$
$20$	1.44621e11	1.26322
$21$	3.97734e11	2.29471
$22$	−5.22518e11	−2.03006
$23$	5.69153e11	1.51545	0.757726	−	0.652573i	$-0.226310\pi$
$23$	5.69153e11	1.51545	0.757726	+	0.652573i	$0.226310\pi$
$24$	3.42174e10	0.0634529
$25$	3.80970e11	0.499344
$26$	−1.02628e12	−0.963816
$27$	−4.14228e10	−0.0282259
$28$	3.36335e12	1.68240
$29$	−3.32350e12	−1.23371	−0.616854	−	0.787077i	$-0.711593\pi$
$29$	−3.32350e12	−1.23371	−0.616854	+	0.787077i	$0.711593\pi$
$30$	8.82532e12	2.45584
$31$	3.32753e11	0.0700725	0.0350362	−	0.999386i	$-0.488845\pi$
$31$	3.32753e11	0.0700725	0.0350362	+	0.999386i	$0.488845\pi$
$32$	−8.85652e12	−1.42393
$33$	−1.61912e13	−2.00406
$34$	3.59973e12	0.345699
$35$	2.66030e13	1.99688
$36$	1.71119e13	1.01094
$37$	2.58461e13	1.20971	0.604854	−	0.796336i	$-0.293232\pi$
$37$	2.58461e13	1.20971	0.604854	+	0.796336i	$0.293232\pi$
$38$	−6.17737e13	−2.30485
$39$	−3.18014e13	−0.951475
$40$	2.28868e12	0.0552174
$41$	2.80628e13	0.548868	0.274434	−	0.961606i	$-0.411509\pi$
$41$	2.80628e13	0.548868	0.274434	+	0.961606i	$0.411509\pi$
$42$	2.05244e14	3.27078
$43$	6.82637e13	0.890652	0.445326	−	0.895369i	$-0.353088\pi$
$43$	6.82637e13	0.890652	0.445326	+	0.895369i	$0.353088\pi$
$44$	−1.36918e14	−1.46931
$45$	1.35350e14	1.19991
$46$	2.93702e14	2.16006
$47$	7.06795e13	0.432974	0.216487	−	0.976285i	$-0.430540\pi$
$47$	7.06795e13	0.432974	0.216487	+	0.976285i	$0.430540\pi$
$48$	−2.65745e14	−1.36118
$49$	3.86057e14	1.65953
$50$	1.96593e14	0.711743
$51$	1.11544e14	0.341273
$52$	−2.68922e14	−0.697587
$53$	2.91013e14	0.642047	0.321024	−	0.947071i	$-0.395973\pi$
$53$	2.91013e14	0.642047	0.321024	+	0.947071i	$0.395973\pi$
$54$	−2.13756e13	−0.0402319
$55$	−1.08298e15	−1.74396
$56$	5.32262e13	0.0735406
$57$	−1.91418e15	−2.27534
$58$	−1.71504e15	−1.75847
$59$	−8.60211e14	−0.762716	−0.381358	−	0.924427i	$-0.624543\pi$
$59$	−8.60211e14	−0.762716	−0.381358	+	0.924427i	$0.624543\pi$
$60$	2.31254e15	1.77748
$61$	−1.78874e15	−1.19466	−0.597328	−	0.801997i	$-0.703771\pi$
$61$	−1.78874e15	−1.19466	−0.597328	+	0.801997i	$0.703771\pi$
$62$	1.71712e14	0.0998782
$63$	3.14772e15	1.59809
$64$	−2.39196e15	−1.06224
$65$	−2.12709e15	−0.827984
$66$	−8.35522e15	−2.85650
$67$	3.38692e15	1.01899	0.509494	−	0.860474i	$-0.329833\pi$
$67$	3.38692e15	1.01899	0.509494	+	0.860474i	$0.329833\pi$
$68$	9.43253e14	0.250209
$69$	9.10093e15	2.13240
$70$	1.37281e16	2.84627
$71$	−3.42363e15	−0.629204	−0.314602	−	0.949224i	$-0.601871\pi$
$71$	−3.42363e15	−0.629204	−0.314602	+	0.949224i	$0.601871\pi$
$72$	2.70801e14	0.0441901
$73$	−7.14682e15	−1.03721	−0.518607	−	0.855013i	$-0.673549\pi$
$73$	−7.14682e15	−1.03721	−0.518607	+	0.855013i	$0.673549\pi$
$74$	1.33375e16	1.72426
$75$	6.09182e15	0.702629
$76$	−1.61869e16	−1.66820
$77$	−2.51860e16	−2.32267
$78$	−1.64106e16	−1.35619
$79$	2.01204e15	0.149213	0.0746066	−	0.997213i	$-0.476230\pi$
$79$	2.01204e15	0.149213	0.0746066	+	0.997213i	$0.476230\pi$
$80$	−1.77748e16	−1.18451
$81$	−1.70050e16	−1.01966
$82$	1.44814e16	0.782332
$83$	9.29633e15	0.453052	0.226526	−	0.974005i	$-0.427263\pi$
$83$	9.29633e15	0.453052	0.226526	+	0.974005i	$0.427263\pi$
$84$	5.37811e16	2.36731
$85$	7.46083e15	0.296979
$86$	3.52264e16	1.26950
$87$	−5.31438e16	−1.73596
$88$	−2.16677e15	−0.0642260
$89$	6.47554e16	1.74366	0.871828	−	0.489813i	$-0.162935\pi$
$89$	6.47554e16	1.74366	0.871828	+	0.489813i	$0.162935\pi$
$90$	6.98449e16	1.71030
$91$	−4.94681e16	−1.10274
$92$	7.69602e16	1.56340
$93$	5.32082e15	0.0985992
$94$	3.64730e16	0.617142
$95$	−1.28033e17	−1.98003
$96$	−1.41618e17	−2.00361
$97$	2.22579e16	0.288353	0.144176	−	0.989552i	$-0.453947\pi$
$97$	2.22579e16	0.288353	0.144176	+	0.989552i	$0.453947\pi$
$98$	1.99218e17	2.36542
$99$	−1.28140e17	−1.39568
$100$	5.15142e16	0.515142
$101$	−9.40854e16	−0.864551	−0.432275	−	0.901742i	$-0.642289\pi$
$101$	−9.40854e16	−0.864551	−0.432275	+	0.901742i	$0.642289\pi$
$102$	5.75607e16	0.486435
$103$	−2.55193e16	−0.198496	−0.0992480	−	0.995063i	$-0.531644\pi$
$103$	−2.55193e16	−0.198496	−0.0992480	+	0.995063i	$0.531644\pi$
$104$	−4.25579e15	−0.0304927
$105$	4.25391e17	2.80982
$106$	1.50172e17	0.915146
$107$	−4.56740e16	−0.256984	−0.128492	−	0.991711i	$-0.541014\pi$
$107$	−4.56740e16	−0.256984	−0.128492	+	0.991711i	$0.541014\pi$
$108$	−5.60114e15	−0.0291189
$109$	−4.53641e16	−0.218066	−0.109033	−	0.994038i	$-0.534775\pi$
$109$	−4.53641e16	−0.218066	−0.109033	+	0.994038i	$0.534775\pi$
$110$	−5.58852e17	−2.48576
$111$	4.13287e17	1.70218
$112$	−4.13375e17	−1.57758
$113$	−1.11166e17	−0.393375	−0.196688	−	0.980466i	$-0.563018\pi$
$113$	−1.11166e17	−0.393375	−0.196688	+	0.980466i	$0.563018\pi$
$114$	−9.87781e17	−3.24317
$115$	6.08730e17	1.85564
$116$	−4.49400e17	−1.27274
$117$	−2.51681e17	−0.662630
$118$	−4.43898e17	−1.08714
$119$	1.73511e17	0.395528
$120$	3.65967e16	0.0776966
$121$	5.19843e17	1.02848
$122$	−9.23049e17	−1.70281
$123$	4.48733e17	0.772315
$124$	4.49944e16	0.0722894
$125$	−4.08531e17	−0.613041
$126$	1.62433e18	2.27785
$127$	6.76045e17	0.886429	0.443214	−	0.896416i	$-0.353838\pi$
$127$	6.76045e17	0.886429	0.443214	+	0.896416i	$0.353838\pi$
$128$	−7.34890e16	−0.0901442
$129$	1.09156e18	1.25324
$130$	−1.09765e18	−1.18017
$131$	−5.54410e17	−0.558502	−0.279251	−	0.960218i	$-0.590086\pi$
$131$	−5.54410e17	−0.558502	−0.279251	+	0.960218i	$0.590086\pi$
$132$	−2.18936e18	−2.06747
$133$	−2.97757e18	−2.63707
$134$	1.74777e18	1.45242
$135$	−4.43032e16	−0.0345620
$136$	1.49273e16	0.0109371
$137$	2.71743e18	1.87083	0.935415	−	0.353552i	$-0.115026\pi$
$137$	2.71743e18	1.87083	0.935415	+	0.353552i	$0.115026\pi$
$138$	4.69639e18	3.03943
$139$	1.64614e18	1.00194	0.500971	−	0.865464i	$-0.332977\pi$
$139$	1.64614e18	1.00194	0.500971	+	0.865464i	$0.332977\pi$
$140$	3.59723e18	2.06006
$141$	1.13019e18	0.609239
$142$	−1.76671e18	−0.896839
$143$	2.01378e18	0.963067
$144$	−2.10315e18	−0.947957
$145$	−3.55461e18	−1.51065
$146$	−3.68800e18	−1.47840
$147$	6.17316e18	2.33513
$148$	3.49488e18	1.24798
$149$	−1.91602e18	−0.646126	−0.323063	−	0.946378i	$-0.604713\pi$
$149$	−1.91602e18	−0.646126	−0.323063	+	0.946378i	$0.604713\pi$
$150$	3.14358e18	1.00150
$151$	−6.22642e18	−1.87471	−0.937356	−	0.348373i	$-0.886734\pi$
$151$	−6.22642e18	−1.87471	−0.937356	+	0.348373i	$0.886734\pi$
$152$	−2.56163e17	−0.0729198
$153$	8.82780e17	0.237670
$154$	−1.29968e19	−3.31063
$155$	3.55891e17	0.0858021
$156$	−4.30015e18	−0.981577
$157$	2.57744e18	0.557240	0.278620	−	0.960401i	$-0.410123\pi$
$157$	2.57744e18	0.557240	0.278620	+	0.960401i	$0.410123\pi$
$158$	1.03828e18	0.212682
$159$	4.65338e18	0.903427
$160$	−9.47237e18	−1.74357
$161$	1.41568e19	2.47141
$162$	−8.77516e18	−1.45337
$163$	3.82135e18	0.600651	0.300325	−	0.953837i	$-0.402905\pi$
$163$	3.82135e18	0.600651	0.300325	+	0.953837i	$0.402905\pi$
$164$	3.79462e18	0.566233
$165$	−1.73171e19	−2.45393
$166$	4.79722e18	0.645759
$167$	1.46342e18	0.187189	0.0935945	−	0.995610i	$-0.470164\pi$
$167$	1.46342e18	0.187189	0.0935945	+	0.995610i	$0.470164\pi$
$168$	8.51103e17	0.103479
$169$	−4.69512e18	−0.542762
$170$	3.85004e18	0.423301
$171$	−1.51491e19	−1.58460
$172$	9.23054e18	0.918830
$173$	1.89287e19	1.79361	0.896805	−	0.442426i	$-0.145882\pi$
$173$	1.89287e19	1.79361	0.896805	+	0.442426i	$0.145882\pi$
$174$	−2.74240e19	−2.47435
$175$	9.47602e18	0.814334
$176$	1.68280e19	1.37776
$177$	−1.37550e19	−1.07322
$178$	3.34159e19	2.48533
$179$	−5.47699e18	−0.388411	−0.194205	−	0.980961i	$-0.562213\pi$
$179$	−5.47699e18	−0.388411	−0.194205	+	0.980961i	$0.562213\pi$
$180$	1.83018e19	1.23788
$181$	−1.05579e18	−0.0681252	−0.0340626	−	0.999420i	$-0.510845\pi$
$181$	−1.05579e18	−0.0681252	−0.0340626	+	0.999420i	$0.510845\pi$
$182$	−2.55272e19	−1.57180
$183$	−2.86025e19	−1.68101
$184$	1.21792e18	0.0683388
$185$	2.76434e19	1.48126
$186$	2.74572e18	0.140539
$187$	−7.06341e18	−0.345431
$188$	9.55720e18	0.446672
$189$	−1.03033e18	−0.0460309
$190$	−6.60693e19	−2.82224
$191$	−2.96658e18	−0.121192	−0.0605958	−	0.998162i	$-0.519300\pi$
$191$	−2.96658e18	−0.121192	−0.0605958	+	0.998162i	$0.519300\pi$
$192$	−3.82481e19	−1.49469
$193$	4.91545e19	1.83792	0.918959	−	0.394353i	$-0.129031\pi$
$193$	4.91545e19	1.83792	0.918959	+	0.394353i	$0.129031\pi$
$194$	1.14858e19	0.411005
$195$	−3.40128e19	−1.16506
$196$	5.22021e19	1.71203
$197$	1.85317e19	0.582039	0.291020	−	0.956717i	$-0.406006\pi$
$197$	1.85317e19	0.582039	0.291020	+	0.956717i	$0.406006\pi$
$198$	−6.61245e19	−1.98934
$199$	2.31783e19	0.668082	0.334041	−	0.942559i	$-0.391588\pi$
$199$	2.31783e19	0.668082	0.334041	+	0.942559i	$0.391588\pi$
$200$	8.15230e17	0.0225178
$201$	5.41579e19	1.43382
$202$	−4.85512e19	−1.23229
$203$	−8.26668e19	−2.01194
$204$	1.50829e19	0.352070
$205$	3.00142e19	0.672077
$206$	−1.31688e19	−0.282927
$207$	7.20261e19	1.48505
$208$	3.30520e19	0.654124
$209$	1.21213e20	2.30306
$210$	2.19516e20	4.00500
$211$	−7.57721e19	−1.32773	−0.663863	−	0.747854i	$-0.731084\pi$
$211$	−7.57721e19	−1.32773	−0.663863	+	0.747854i	$0.731084\pi$
$212$	3.93504e19	0.662360
$213$	−5.47450e19	−0.885355
$214$	−2.35693e19	−0.366294
$215$	7.30106e19	1.09058
$216$	−8.86400e16	−0.00127284
$217$	8.27670e18	0.114275
$218$	−2.34094e19	−0.310821
$219$	−1.14280e20	−1.45947
$220$	−1.46439e20	−1.79913
$221$	−1.38733e19	−0.164001
$222$	2.13270e20	2.42622
$223$	8.83224e19	0.967118	0.483559	−	0.875312i	$-0.339344\pi$
$223$	8.83224e19	0.967118	0.483559	+	0.875312i	$0.339344\pi$
$224$	−2.20292e20	−2.32215
$225$	4.82116e19	0.489328
$226$	−5.73657e19	−0.560700
$227$	−2.80685e19	−0.264240	−0.132120	−	0.991234i	$-0.542178\pi$
$227$	−2.80685e19	−0.264240	−0.132120	+	0.991234i	$0.542178\pi$
$228$	−2.58833e20	−2.34733
$229$	6.81095e19	0.595122	0.297561	−	0.954703i	$-0.403827\pi$
$229$	6.81095e19	0.595122	0.297561	+	0.954703i	$0.403827\pi$
$230$	3.14125e20	2.64494
$231$	−4.02731e20	−3.26824
$232$	−7.11190e18	−0.0556337
$233$	−1.08527e20	−0.818487	−0.409244	−	0.912425i	$-0.634207\pi$
$233$	−1.08527e20	−0.818487	−0.409244	+	0.912425i	$0.634207\pi$
$234$	−1.29876e20	−0.944483
$235$	7.55944e19	0.530167
$236$	−1.16317e20	−0.786846
$237$	3.21732e19	0.209958
$238$	8.95375e19	0.563769
$239$	−2.45578e20	−1.49213	−0.746066	−	0.665872i	$-0.768060\pi$
$239$	−2.45578e20	−1.49213	−0.746066	+	0.665872i	$0.768060\pi$
$240$	−2.84224e20	−1.66673
$241$	7.25277e19	0.410543	0.205272	−	0.978705i	$-0.434192\pi$
$241$	7.25277e19	0.410543	0.205272	+	0.978705i	$0.434192\pi$
$242$	2.68256e20	1.46595
$243$	−2.66566e20	−1.40654
$244$	−2.41871e20	−1.23245
$245$	4.12902e20	2.03205
$246$	2.31561e20	1.10082
$247$	2.38076e20	1.09343
$248$	7.12052e17	0.00315989
$249$	1.48651e20	0.637490
$250$	−2.10816e20	−0.873802
$251$	−2.13249e20	−0.854397	−0.427199	−	0.904158i	$-0.640500\pi$
$251$	−2.13249e20	−0.854397	−0.427199	+	0.904158i	$0.640500\pi$
$252$	4.25631e20	1.64865
$253$	−5.76305e20	−2.15838
$254$	3.48862e20	1.26348
$255$	1.19301e20	0.417881
$256$	2.75596e20	0.933755
$257$	−1.70498e20	−0.558842	−0.279421	−	0.960169i	$-0.590142\pi$
$257$	−1.70498e20	−0.558842	−0.279421	+	0.960169i	$0.590142\pi$
$258$	5.63280e20	1.78631
$259$	6.42881e20	1.97280
$260$	−2.87622e20	−0.854179
$261$	−4.20588e20	−1.20896
$262$	−2.86094e20	−0.796064
$263$	2.07754e20	0.559661	0.279831	−	0.960049i	$-0.409722\pi$
$263$	2.07754e20	0.559661	0.279831	+	0.960049i	$0.409722\pi$
$264$	−3.46474e19	−0.0903726
$265$	3.11249e20	0.786172
$266$	−1.53652e21	−3.75877
$267$	1.03546e21	2.45350
$268$	4.57975e20	1.05123
$269$	1.12637e20	0.250487	0.125243	−	0.992126i	$-0.460029\pi$
$269$	1.12637e20	0.250487	0.125243	+	0.992126i	$0.460029\pi$
$270$	−2.28620e19	−0.0492631
$271$	−6.41241e20	−1.33900	−0.669502	−	0.742810i	$-0.733493\pi$
$271$	−6.41241e20	−1.33900	−0.669502	+	0.742810i	$0.733493\pi$
$272$	−1.15931e20	−0.234620
$273$	−7.91010e20	−1.55167
$274$	1.40229e21	2.66660
$275$	−3.85757e20	−0.711190
$276$	1.23062e21	2.19986
$277$	−4.11234e20	−0.712872	−0.356436	−	0.934320i	$-0.616008\pi$
$277$	−4.11234e20	−0.712872	−0.356436	+	0.934320i	$0.616008\pi$
$278$	8.49466e20	1.42812
$279$	4.21098e19	0.0686668
$280$	5.69274e19	0.0900488
$281$	1.16485e21	1.78758	0.893791	−	0.448483i	$-0.148036\pi$
$281$	1.16485e21	1.78758	0.893791	+	0.448483i	$0.148036\pi$
$282$	5.83215e20	0.868383
$283$	−6.36279e20	−0.919311	−0.459656	−	0.888097i	$-0.652027\pi$
$283$	−6.36279e20	−0.919311	−0.459656	+	0.888097i	$0.652027\pi$
$284$	−4.62940e20	−0.649110
$285$	−2.04729e21	−2.78610
$286$	1.03918e21	1.37271
$287$	6.98018e20	0.895098
$288$	−1.12079e21	−1.39537
$289$	4.86612e19	0.0588235
$290$	−1.83430e21	−2.15321
$291$	3.55910e20	0.405742
$292$	−9.66384e20	−1.07003
$293$	−5.52767e20	−0.594521	−0.297261	−	0.954796i	$-0.596073\pi$
$293$	−5.52767e20	−0.594521	−0.297261	+	0.954796i	$0.596073\pi$
$294$	3.18556e21	3.32838
$295$	−9.20027e20	−0.933928
$296$	5.53076e19	0.0545514
$297$	4.19433e19	0.0402007
$298$	−9.88731e20	−0.920959
$299$	−1.13193e21	−1.02474
$300$	8.23728e20	0.724859
$301$	1.69795e21	1.45248
$302$	−3.21304e21	−2.67213
$303$	−1.50445e21	−1.21651
$304$	1.98946e21	1.56426
$305$	−1.91312e21	−1.46283
$306$	4.55544e20	0.338765
$307$	−9.85477e20	−0.712804	−0.356402	−	0.934333i	$-0.615997\pi$
$307$	−9.85477e20	−0.712804	−0.356402	+	0.934333i	$0.615997\pi$
$308$	−3.40562e21	−2.39615
$309$	−4.08061e20	−0.279305
$310$	1.83652e20	0.122299
$311$	3.13417e20	0.203076	0.101538	−	0.994832i	$-0.467624\pi$
$311$	3.13417e20	0.203076	0.101538	+	0.994832i	$0.467624\pi$
$312$	−6.80513e19	−0.0429064
$313$	1.80275e21	1.10613	0.553067	−	0.833137i	$-0.313457\pi$
$313$	1.80275e21	1.10613	0.553067	+	0.833137i	$0.313457\pi$
$314$	1.33005e21	0.794265
$315$	3.36661e21	1.95683
$316$	2.72066e20	0.153934
$317$	−1.43187e21	−0.788677	−0.394338	−	0.918965i	$-0.629026\pi$
$317$	−1.43187e21	−0.788677	−0.394338	+	0.918965i	$0.629026\pi$
$318$	2.40130e21	1.28770
$319$	3.36526e21	1.75711
$320$	−2.55829e21	−1.30069
$321$	−7.30341e20	−0.361604
$322$	7.30538e21	3.52263
$323$	−8.35059e20	−0.392189
$324$	−2.29940e21	−1.05192
$325$	−7.57670e20	−0.337654
$326$	1.97194e21	0.856141
$327$	−7.25386e20	−0.306841
$328$	6.00511e19	0.0247510
$329$	1.75804e21	0.706097
$330$	−8.93622e21	−3.49772
$331$	2.84453e20	0.108511	0.0542554	−	0.998527i	$-0.482721\pi$
$331$	2.84453e20	0.108511	0.0542554	+	0.998527i	$0.482721\pi$
$332$	1.25704e21	0.467385
$333$	3.27082e21	1.18544
$334$	7.55176e20	0.266811
$335$	3.62244e21	1.24773
$336$	−6.60999e21	−2.21982
$337$	−5.55418e21	−1.81872	−0.909360	−	0.416011i	$-0.863428\pi$
$337$	−5.55418e21	−1.81872	−0.909360	+	0.416011i	$0.863428\pi$
$338$	−2.42284e21	−0.773629
$339$	−1.77759e21	−0.553520
$340$	1.00884e21	0.306375
$341$	−3.36934e20	−0.0998005
$342$	−7.81745e21	−2.25862
$343$	3.81623e21	1.07556
$344$	1.46076e20	0.0401636
$345$	9.73378e21	2.61107
$346$	9.76783e21	2.55653
$347$	−4.09219e21	−1.04509	−0.522547	−	0.852610i	$-0.675018\pi$
$347$	−4.09219e21	−1.04509	−0.522547	+	0.852610i	$0.675018\pi$
$348$	−7.18604e21	−1.79088
$349$	−1.34789e21	−0.327823	−0.163912	−	0.986475i	$-0.552411\pi$
$349$	−1.34789e21	−0.327823	−0.163912	+	0.986475i	$0.552411\pi$
$350$	4.88994e21	1.16071
$351$	8.23814e19	0.0190862
$352$	8.96781e21	2.02803
$353$	−2.54504e19	−0.00561837	−0.00280918	−	0.999996i	$-0.500894\pi$
$353$	−2.54504e19	−0.00561837	−0.00280918	+	0.999996i	$0.500894\pi$
$354$	−7.09806e21	−1.52972
$355$	−3.66170e21	−0.770446
$356$	8.75614e21	1.79882
$357$	2.77449e21	0.556550
$358$	−2.82631e21	−0.553624
$359$	8.60051e21	1.64521	0.822605	−	0.568613i	$-0.192520\pi$
$359$	8.60051e21	1.64521	0.822605	+	0.568613i	$0.192520\pi$
$360$	2.89632e20	0.0541098
$361$	8.84979e21	1.61481
$362$	−5.44821e20	−0.0971026
$363$	8.31244e21	1.44718
$364$	−6.68902e21	−1.13763
$365$	−7.64379e21	−1.27005
$366$	−1.47598e22	−2.39603
$367$	3.89368e20	0.0617587	0.0308794	−	0.999523i	$-0.490169\pi$
$367$	3.89368e20	0.0617587	0.0308794	+	0.999523i	$0.490169\pi$
$368$	−9.45883e21	−1.46599
$369$	3.55134e21	0.537858
$370$	1.42649e22	2.11132
$371$	7.23848e21	1.04705
$372$	7.19475e20	0.101719
$373$	−6.59456e21	−0.911299	−0.455649	−	0.890159i	$-0.650593\pi$
$373$	−6.59456e21	−0.911299	−0.455649	+	0.890159i	$0.650593\pi$
$374$	−3.64496e21	−0.492362
$375$	−6.53253e21	−0.862613
$376$	1.51246e20	0.0195248
$377$	6.60975e21	0.834226
$378$	−5.31684e20	−0.0656104
$379$	5.52278e21	0.666384	0.333192	−	0.942859i	$-0.391874\pi$
$379$	5.52278e21	0.666384	0.333192	+	0.942859i	$0.391874\pi$
$380$	−1.73125e22	−2.04267
$381$	1.08102e22	1.24730
$382$	−1.53086e21	−0.172741
$383$	1.03281e22	1.13981	0.569903	−	0.821712i	$-0.306981\pi$
$383$	1.03281e22	1.13981	0.569903	+	0.821712i	$0.306981\pi$
$384$	−1.17511e21	−0.126842
$385$	−2.69373e22	−2.84406
$386$	2.53654e22	2.61969
$387$	8.63875e21	0.872786
$388$	3.00968e21	0.297475
$389$	−1.28750e22	−1.24501	−0.622507	−	0.782614i	$-0.713886\pi$
$389$	−1.28750e22	−1.24501	−0.622507	+	0.782614i	$0.713886\pi$
$390$	−1.75517e22	−1.66062
$391$	3.97027e21	0.367551
$392$	8.26116e20	0.0748358
$393$	−8.86518e21	−0.785870
$394$	9.56298e21	0.829613
$395$	2.15196e21	0.182708
$396$	−1.73269e22	−1.43983
$397$	−1.14903e22	−0.934574	−0.467287	−	0.884106i	$-0.654768\pi$
$397$	−1.14903e22	−0.934574	−0.467287	+	0.884106i	$0.654768\pi$
$398$	1.19608e22	0.952254
$399$	−4.76122e22	−3.71064
$400$	−6.33139e21	−0.483047
$401$	2.77540e21	0.207300	0.103650	−	0.994614i	$-0.466948\pi$
$401$	2.77540e21	0.207300	0.103650	+	0.994614i	$0.466948\pi$
$402$	2.79473e22	2.04371
$403$	−6.61777e20	−0.0473826
$404$	−1.27221e22	−0.891903
$405$	−1.81875e22	−1.24855
$406$	−4.26589e22	−2.86773
$407$	−2.61709e22	−1.72292
$408$	2.38692e20	0.0153896
$409$	−2.53447e22	−1.60044	−0.800218	−	0.599709i	$-0.795283\pi$
$409$	−2.53447e22	−1.60044	−0.800218	+	0.599709i	$0.795283\pi$
$410$	1.54883e22	0.957948
$411$	4.34526e22	2.63245
$412$	−3.45069e21	−0.204776
$413$	−2.13964e22	−1.24384
$414$	3.71679e22	2.11673
$415$	9.94276e21	0.554751
$416$	1.76138e22	0.962852
$417$	2.63224e22	1.40983
$418$	6.25500e22	3.28268
$419$	3.75097e22	1.92896	0.964481	−	0.264151i	$-0.0850916\pi$
$419$	3.75097e22	1.92896	0.964481	+	0.264151i	$0.0850916\pi$
$420$	5.75208e22	2.89872
$421$	2.77360e22	1.36976	0.684881	−	0.728655i	$-0.259854\pi$
$421$	2.77360e22	1.36976	0.684881	+	0.728655i	$0.259854\pi$
$422$	−3.91009e22	−1.89248
$423$	8.94447e21	0.424289
$424$	6.22733e20	0.0289529
$425$	2.65755e21	0.121109
$426$	−2.82502e22	−1.26195
$427$	−4.44920e22	−1.94825
$428$	−6.17598e21	−0.265115
$429$	3.22010e22	1.35514
$430$	3.76759e22	1.55447
$431$	1.91176e21	0.0773351	0.0386675	−	0.999252i	$-0.487689\pi$
$431$	1.91176e21	0.0773351	0.0386675	+	0.999252i	$0.487689\pi$
$432$	6.88412e20	0.0273046
$433$	3.57490e22	1.39032	0.695162	−	0.718853i	$-0.255332\pi$
$433$	3.57490e22	1.39032	0.695162	+	0.718853i	$0.255332\pi$
$434$	4.27106e21	0.162882
$435$	−5.68392e22	−2.12564
$436$	−6.13408e21	−0.224965
$437$	−6.81326e22	−2.45054
$438$	−5.89722e22	−2.08026
$439$	3.78888e22	1.31088	0.655439	−	0.755248i	$-0.272484\pi$
$439$	3.78888e22	1.31088	0.655439	+	0.755248i	$0.272484\pi$
$440$	−2.31744e21	−0.0786432
$441$	4.88553e22	1.62624
$442$	−7.15911e21	−0.233760
$443$	7.50792e21	0.240485	0.120242	−	0.992745i	$-0.461633\pi$
$443$	7.50792e21	0.240485	0.120242	+	0.992745i	$0.461633\pi$
$444$	5.58842e22	1.75604
$445$	6.92582e22	2.13507
$446$	4.55773e22	1.37849
$447$	−3.06378e22	−0.909166
$448$	−5.94962e22	−1.73231
$449$	−4.77034e22	−1.36287	−0.681437	−	0.731877i	$-0.738645\pi$
$449$	−4.77034e22	−1.36287	−0.681437	+	0.731877i	$0.738645\pi$
$450$	2.48788e22	0.697466
$451$	−2.84154e22	−0.781725
$452$	−1.50318e22	−0.405821
$453$	−9.95624e22	−2.63791
$454$	−1.44843e22	−0.376636
$455$	−5.29080e22	−1.35028
$456$	−4.09612e21	−0.102606
$457$	5.15436e22	1.26732	0.633661	−	0.773611i	$-0.281551\pi$
$457$	5.15436e22	1.26732	0.633661	+	0.773611i	$0.281551\pi$
$458$	3.51468e22	0.848261
$459$	−2.88956e20	−0.00684578
$460$	8.23117e22	1.91434
$461$	−1.20883e22	−0.275998	−0.137999	−	0.990432i	$-0.544067\pi$
$461$	−1.20883e22	−0.275998	−0.137999	+	0.990432i	$0.544067\pi$
$462$	−2.07823e23	−4.65840
$463$	8.66647e21	0.190723	0.0953616	−	0.995443i	$-0.469599\pi$
$463$	8.66647e21	0.190723	0.0953616	+	0.995443i	$0.469599\pi$
$464$	5.52337e22	1.19344
$465$	5.69081e21	0.120732
$466$	−5.60035e22	−1.16663
$467$	5.82081e22	1.19067	0.595333	−	0.803479i	$-0.297020\pi$
$467$	5.82081e22	1.19067	0.595333	+	0.803479i	$0.297020\pi$
$468$	−3.40320e22	−0.683594
$469$	8.42443e22	1.66177
$470$	3.90092e22	0.755676
$471$	4.12141e22	0.784094
$472$	−1.84075e21	−0.0343944
$473$	−6.91215e22	−1.26851
$474$	1.66025e22	0.299265
$475$	−4.56054e22	−0.807459
$476$	2.34619e22	0.408042
$477$	3.68276e22	0.629168
$478$	−1.26726e23	−2.12682
$479$	−9.64561e22	−1.59030	−0.795148	−	0.606416i	$-0.792607\pi$
$479$	−9.64561e22	−1.59030	−0.795148	+	0.606416i	$0.792607\pi$
$480$	−1.51466e23	−2.45338
$481$	−5.14026e22	−0.817997
$482$	3.74267e22	0.585170
$483$	2.26371e23	3.47753
$484$	7.02925e22	1.06102
$485$	2.38056e22	0.353081
$486$	−1.37557e23	−2.00482
$487$	−4.05214e22	−0.580348	−0.290174	−	0.956974i	$-0.593713\pi$
$487$	−4.05214e22	−0.580348	−0.290174	+	0.956974i	$0.593713\pi$
$488$	−3.82769e21	−0.0538726
$489$	6.11045e22	0.845178
$490$	2.13071e23	2.89640
$491$	1.06929e23	1.42857	0.714286	−	0.699854i	$-0.246751\pi$
$491$	1.06929e23	1.42857	0.714286	+	0.699854i	$0.246751\pi$
$492$	6.06771e22	0.796749
$493$	−2.31839e22	−0.299218
$494$	1.22855e23	1.55853
$495$	−1.37050e23	−1.70898
$496$	−5.53007e21	−0.0677854
$497$	−8.51575e22	−1.02611
$498$	7.67090e22	0.908650
$499$	7.75398e22	0.902963	0.451481	−	0.892281i	$-0.350896\pi$
$499$	7.75398e22	0.902963	0.451481	+	0.892281i	$0.350896\pi$
$500$	−5.52410e22	−0.632436
$501$	2.34006e22	0.263394
$502$	−1.10044e23	−1.21782
$503$	2.54893e22	0.277351	0.138675	−	0.990338i	$-0.455716\pi$
$503$	2.54893e22	0.277351	0.138675	+	0.990338i	$0.455716\pi$
$504$	6.73576e21	0.0720654
$505$	−1.00628e23	−1.05862
$506$	−2.97393e23	−3.07646
$507$	−7.50763e22	−0.763722
$508$	9.14139e22	0.914473
$509$	−1.10772e23	−1.08976	−0.544879	−	0.838515i	$-0.683424\pi$
$509$	−1.10772e23	−1.08976	−0.544879	+	0.838515i	$0.683424\pi$
$510$	6.15633e22	0.595628
$511$	−1.77766e23	−1.69149
$512$	1.51849e23	1.42108
$513$	4.95867e21	0.0456423
$514$	−8.79829e22	−0.796548
$515$	−2.72938e22	−0.243054
$516$	1.47599e23	1.29289
$517$	−7.15677e22	−0.616662
$518$	3.31748e23	2.81194
$519$	3.02675e23	2.52379
$520$	−4.55172e21	−0.0373377
$521$	−1.19603e23	−0.965212	−0.482606	−	0.875838i	$-0.660310\pi$
$521$	−1.19603e23	−0.965212	−0.482606	+	0.875838i	$0.660310\pi$
$522$	−2.17037e23	−1.72320
$523$	1.03131e23	0.805608	0.402804	−	0.915286i	$-0.368036\pi$
$523$	1.03131e23	0.805608	0.402804	+	0.915286i	$0.368036\pi$
$524$	−7.49666e22	−0.576172
$525$	1.51524e23	1.14585
$526$	1.07208e23	0.797716
$527$	2.32120e21	0.0169951
$528$	2.69085e23	1.93865
$529$	1.82885e23	1.29660
$530$	1.60615e23	1.12057
$531$	−1.08859e23	−0.747416
$532$	−4.02623e23	−2.72051
$533$	−5.58111e22	−0.371141
$534$	5.34331e23	3.49711
$535$	−4.88500e22	−0.314672
$536$	7.24761e21	0.0459509
$537$	−8.75788e22	−0.546534
$538$	5.81243e22	0.357033
$539$	−3.90908e23	−2.36358
$540$	−5.99063e21	−0.0356554
$541$	2.04030e23	1.19541	0.597704	−	0.801717i	$-0.296080\pi$
$541$	2.04030e23	1.19541	0.597704	+	0.801717i	$0.296080\pi$
$542$	−3.30902e23	−1.90856
$543$	−1.68823e22	−0.0958592
$544$	−6.17809e22	−0.345353
$545$	−4.85186e22	−0.267016
$546$	−4.08188e23	−2.21168
$547$	−1.12034e23	−0.597665	−0.298833	−	0.954306i	$-0.596597\pi$
$547$	−1.12034e23	−0.597665	−0.298833	+	0.954306i	$0.596597\pi$
$548$	3.67448e23	1.93002
$549$	−2.26364e23	−1.17069
$550$	−1.99064e23	−1.01370
$551$	3.97852e23	1.99495
$552$	1.94749e22	0.0961598
$553$	5.00464e22	0.243338
$554$	−2.12211e23	−1.01610
$555$	4.42026e23	2.08429
$556$	2.22590e23	1.03364
$557$	−4.76195e22	−0.217779	−0.108889	−	0.994054i	$-0.534729\pi$
$557$	−4.76195e22	−0.217779	−0.108889	+	0.994054i	$0.534729\pi$
$558$	2.17301e22	0.0978746
$559$	−1.35762e23	−0.602253
$560$	−4.42120e23	−1.93171
$561$	−1.12946e23	−0.486057
$562$	6.01102e23	2.54794
$563$	3.73269e23	1.55848	0.779238	−	0.626728i	$-0.215606\pi$
$563$	3.73269e23	1.55848	0.779238	+	0.626728i	$0.215606\pi$
$564$	1.52823e23	0.628514
$565$	−1.18897e23	−0.481679
$566$	−3.28341e23	−1.31035
$567$	−4.22973e23	−1.66286
$568$	−7.32618e21	−0.0283737
$569$	3.51840e23	1.34243	0.671213	−	0.741264i	$-0.265773\pi$
$569$	3.51840e23	1.34243	0.671213	+	0.741264i	$0.265773\pi$
$570$	−1.05647e24	−3.97118
$571$	1.09677e23	0.406172	0.203086	−	0.979161i	$-0.434903\pi$
$571$	1.09677e23	0.406172	0.203086	+	0.979161i	$0.434903\pi$
$572$	2.72302e23	0.993536
$573$	−4.74365e22	−0.170529
$574$	3.60201e23	1.27583
$575$	2.16830e23	0.756733
$576$	−3.02701e23	−1.04093
$577$	−9.47325e22	−0.321000	−0.160500	−	0.987036i	$-0.551311\pi$
$577$	−9.47325e22	−0.321000	−0.160500	+	0.987036i	$0.551311\pi$
$578$	2.51108e22	0.0838444
$579$	7.85996e23	2.58614
$580$	−4.80649e23	−1.55844
$581$	2.31231e23	0.738839
$582$	1.83662e23	0.578326
$583$	−2.94670e23	−0.914434
$584$	−1.52934e22	−0.0467728
$585$	−2.69182e23	−0.811375
$586$	−2.85246e23	−0.847404
$587$	−4.70936e23	−1.37892	−0.689458	−	0.724325i	$-0.742151\pi$
$587$	−4.70936e23	−1.37892	−0.689458	+	0.724325i	$0.742151\pi$
$588$	8.34728e23	2.40900
$589$	−3.98334e22	−0.113310
$590$	−4.74765e23	−1.33118
$591$	2.96327e23	0.818989
$592$	−4.29540e23	−1.17022
$593$	−3.44197e23	−0.924362	−0.462181	−	0.886786i	$-0.652933\pi$
$593$	−3.44197e23	−0.924362	−0.462181	+	0.886786i	$0.652933\pi$
$594$	2.16442e22	0.0573002
$595$	1.85576e23	0.484316
$596$	−2.59082e23	−0.666567
$597$	3.70627e23	0.940060
$598$	−5.84113e23	−1.46062
$599$	−5.77593e23	−1.42395	−0.711973	−	0.702207i	$-0.752198\pi$
$599$	−5.77593e23	−1.42395	−0.711973	+	0.702207i	$0.752198\pi$
$600$	1.30358e22	0.0316848
$601$	3.72643e23	0.893017	0.446508	−	0.894780i	$-0.352667\pi$
$601$	3.72643e23	0.893017	0.446508	+	0.894780i	$0.352667\pi$
$602$	8.76200e23	2.07030
$603$	4.28614e23	0.998548
$604$	−8.41929e23	−1.93402
$605$	5.55991e23	1.25935
$606$	−7.76349e23	−1.73396
$607$	7.01152e23	1.54422	0.772109	−	0.635490i	$-0.219202\pi$
$607$	7.01152e23	1.54422	0.772109	+	0.635490i	$0.219202\pi$
$608$	1.06020e24	2.30255
$609$	−1.32187e24	−2.83101
$610$	−9.87235e23	−2.08505
$611$	−1.40567e23	−0.292774
$612$	1.19368e23	0.245190
$613$	−4.94331e23	−1.00139	−0.500695	−	0.865624i	$-0.666922\pi$
$613$	−4.94331e23	−1.00139	−0.500695	+	0.865624i	$0.666922\pi$
$614$	−5.08539e23	−1.01600
$615$	4.79936e23	0.945682
$616$	−5.38951e22	−0.104740
$617$	−2.96368e23	−0.568077	−0.284038	−	0.958813i	$-0.591674\pi$
$617$	−2.96368e23	−0.568077	−0.284038	+	0.958813i	$0.591674\pi$
$618$	−2.10573e23	−0.398108
$619$	5.66382e23	1.05618	0.528091	−	0.849188i	$-0.322908\pi$
$619$	5.66382e23	1.05618	0.528091	+	0.849188i	$0.322908\pi$
$620$	4.81232e22	0.0885167
$621$	−2.35759e22	−0.0427750
$622$	1.61734e23	0.289456
$623$	1.61069e24	2.84356
$624$	5.28512e23	0.920420
$625$	−7.27596e23	−1.25000
$626$	9.30278e23	1.57663
$627$	1.93823e24	3.24065
$628$	3.48519e23	0.574870
$629$	1.80296e23	0.293397
$630$	1.73728e24	2.78917
$631$	−4.32094e23	−0.684429	−0.342215	−	0.939622i	$-0.611177\pi$
$631$	−4.32094e23	−0.684429	−0.342215	+	0.939622i	$0.611177\pi$
$632$	4.30554e21	0.00672872
$633$	−1.21162e24	−1.86825
$634$	−7.38892e23	−1.12414
$635$	7.23055e23	1.08541
$636$	6.29225e23	0.932009
$637$	−7.67787e23	−1.12216
$638$	1.73659e24	2.50450
$639$	−4.33260e23	−0.616582
$640$	−7.85992e22	−0.110380
$641$	−6.35471e23	−0.880648	−0.440324	−	0.897839i	$-0.645136\pi$
$641$	−6.35471e23	−0.880648	−0.440324	+	0.897839i	$0.645136\pi$
$642$	−3.76880e23	−0.515414
$643$	−5.99371e23	−0.808915	−0.404457	−	0.914557i	$-0.632540\pi$
$643$	−5.99371e23	−0.808915	−0.404457	+	0.914557i	$0.632540\pi$
$644$	1.91426e24	2.54960
$645$	1.16746e24	1.53456
$646$	−4.30919e23	−0.559009
$647$	−7.52873e23	−0.963908	−0.481954	−	0.876197i	$-0.660073\pi$
$647$	−7.52873e23	−0.963908	−0.481954	+	0.876197i	$0.660073\pi$
$648$	−3.63887e22	−0.0459811
$649$	8.71020e23	1.08630
$650$	−3.90983e23	−0.481276
$651$	1.32347e23	0.160796
$652$	5.16718e23	0.619654
$653$	−7.52618e23	−0.890867	−0.445433	−	0.895315i	$-0.646950\pi$
$653$	−7.52618e23	−0.890867	−0.445433	+	0.895315i	$0.646950\pi$
$654$	−3.74324e23	−0.437357
$655$	−5.92961e23	−0.683873
$656$	−4.66380e23	−0.530954
$657$	−9.04428e23	−1.01641
$658$	9.07209e23	1.00644
$659$	−1.81940e23	−0.199252	−0.0996258	−	0.995025i	$-0.531765\pi$
$659$	−1.81940e23	−0.199252	−0.0996258	+	0.995025i	$0.531765\pi$
$660$	−2.34160e24	−2.53157
$661$	−1.14840e24	−1.22569	−0.612846	−	0.790203i	$-0.709975\pi$
$661$	−1.14840e24	−1.22569	−0.612846	+	0.790203i	$0.709975\pi$
$662$	1.46788e23	0.154666
$663$	−2.21839e23	−0.230767
$664$	1.98931e22	0.0204302
$665$	−3.18462e24	−3.22904
$666$	1.68785e24	1.68968
$667$	−1.89158e24	−1.86963
$668$	1.97882e23	0.193111
$669$	1.41230e24	1.36084
$670$	1.86930e24	1.77846
$671$	1.81122e24	1.70149
$672$	−3.52253e24	−3.26751
$673$	9.96208e22	0.0912477	0.0456238	−	0.998959i	$-0.485472\pi$
$673$	9.96208e22	0.0912477	0.0456238	+	0.998959i	$0.485472\pi$
$674$	−2.86614e24	−2.59232
$675$	−1.57808e22	−0.0140944
$676$	−6.34868e23	−0.559934
$677$	−5.30805e23	−0.462308	−0.231154	−	0.972917i	$-0.574250\pi$
$677$	−5.30805e23	−0.462308	−0.231154	+	0.972917i	$0.574250\pi$
$678$	−9.17294e23	−0.788962
$679$	5.53629e23	0.470247
$680$	1.59653e22	0.0133922
$681$	−4.48824e23	−0.371814
$682$	−1.73869e23	−0.142251
$683$	−1.36346e24	−1.10171	−0.550856	−	0.834601i	$-0.685699\pi$
$683$	−1.36346e24	−1.10171	−0.550856	+	0.834601i	$0.685699\pi$
$684$	−2.04844e24	−1.63473
$685$	2.90640e24	2.29079
$686$	1.96930e24	1.53306
$687$	1.08909e24	0.837399
$688$	−1.13448e24	−0.861582
$689$	−5.78764e23	−0.434148
$690$	5.02296e24	3.72171
$691$	1.70516e24	1.24796	0.623982	−	0.781439i	$-0.285514\pi$
$691$	1.70516e24	1.24796	0.623982	+	0.781439i	$0.285514\pi$
$692$	2.55951e24	1.85035
$693$	−3.18728e24	−2.27608
$694$	−2.11171e24	−1.48963
$695$	1.76061e24	1.22685
$696$	−1.13721e23	−0.0782824
$697$	1.95759e23	0.133120
$698$	−6.95559e23	−0.467264
$699$	−1.73538e24	−1.15170
$700$	1.28134e24	0.840097
$701$	2.03504e24	1.31816	0.659082	−	0.752071i	$-0.270945\pi$
$701$	2.03504e24	1.31816	0.659082	+	0.752071i	$0.270945\pi$
$702$	4.25116e22	0.0272046
$703$	−3.09400e24	−1.95614
$704$	2.42201e24	1.51290
$705$	1.20878e24	0.746000
$706$	−1.31333e22	−0.00800817
$707$	−2.34023e24	−1.40991
$708$	−1.85994e24	−1.10717
$709$	2.52653e24	1.48604	0.743021	−	0.669268i	$-0.233392\pi$
$709$	2.52653e24	1.48604	0.743021	+	0.669268i	$0.233392\pi$
$710$	−1.88956e24	−1.09816
$711$	2.54624e23	0.146220
$712$	1.38569e23	0.0786296
$713$	1.89387e23	0.106191
$714$	1.43173e24	0.793281
$715$	2.15382e24	1.17925
$716$	−7.40592e23	−0.400699
$717$	−3.92687e24	−2.09958
$718$	4.43815e24	2.34501
$719$	1.51759e24	0.792424	0.396212	−	0.918159i	$-0.370325\pi$
$719$	1.51759e24	0.792424	0.396212	+	0.918159i	$0.370325\pi$
$720$	−2.24939e24	−1.16075
$721$	−6.34752e23	−0.323708
$722$	4.56679e24	2.30168
$723$	1.15974e24	0.577677
$724$	−1.42762e23	−0.0702805
$725$	−1.26615e24	−0.616046
$726$	4.28950e24	2.06274
$727$	2.91188e23	0.138398	0.0691992	−	0.997603i	$-0.477956\pi$
$727$	2.91188e23	0.138398	0.0691992	+	0.997603i	$0.477956\pi$
$728$	−1.05856e23	−0.0497277
$729$	−2.06644e24	−0.959487
$730$	−3.94445e24	−1.81027
$731$	4.76191e23	0.216015
$732$	−3.86759e24	−1.73419
$733$	3.51195e23	0.155655	0.0778277	−	0.996967i	$-0.475202\pi$
$733$	3.51195e23	0.155655	0.0778277	+	0.996967i	$0.475202\pi$
$734$	2.00927e23	0.0880281
$735$	6.60242e24	2.85931
$736$	−5.04071e24	−2.15790
$737$	−3.42948e24	−1.45129
$738$	1.83261e24	0.766639
$739$	9.61540e23	0.397640	0.198820	−	0.980036i	$-0.436289\pi$
$739$	9.61540e23	0.397640	0.198820	+	0.980036i	$0.436289\pi$
$740$	3.73790e24	1.52812
$741$	3.80691e24	1.53857
$742$	3.73530e24	1.49242
$743$	−1.13776e24	−0.449415	−0.224707	−	0.974426i	$-0.572143\pi$
$743$	−1.13776e24	−0.449415	−0.224707	+	0.974426i	$0.572143\pi$
$744$	1.13859e22	0.00444630
$745$	−2.04925e24	−0.791166
$746$	−3.40301e24	−1.29892
$747$	1.17645e24	0.443964
$748$	−9.55106e23	−0.356359
$749$	−1.13607e24	−0.419092
$750$	−3.37101e24	−1.22953
$751$	2.65648e24	0.958004	0.479002	−	0.877814i	$-0.340999\pi$
$751$	2.65648e24	0.958004	0.479002	+	0.877814i	$0.340999\pi$
$752$	−1.17463e24	−0.418843
$753$	−3.40991e24	−1.20223
$754$	3.41086e24	1.18907
$755$	−6.65939e24	−2.29554
$756$	−1.39320e23	−0.0474873
$757$	2.90900e23	0.0980459	0.0490229	−	0.998798i	$-0.484389\pi$
$757$	2.90900e23	0.0980459	0.0490229	+	0.998798i	$0.484389\pi$
$758$	2.84994e24	0.949835
$759$	−9.21529e24	−3.03706
$760$	−2.73975e23	−0.0892886
$761$	−6.95154e23	−0.224033	−0.112016	−	0.993706i	$-0.535731\pi$
$761$	−6.95154e23	−0.224033	−0.112016	+	0.993706i	$0.535731\pi$
$762$	5.57841e24	1.77784
$763$	−1.12836e24	−0.355623
$764$	−4.01137e23	−0.125026
$765$	9.44165e23	0.291022
$766$	5.32965e24	1.62463
$767$	1.71078e24	0.515744
$768$	4.40686e24	1.31389
$769$	3.27579e24	0.965924	0.482962	−	0.875641i	$-0.339561\pi$
$769$	3.27579e24	0.965924	0.482962	+	0.875641i	$0.339561\pi$
$770$	−1.39006e25	−4.05379
$771$	−2.72632e24	−0.786348
$772$	6.64661e24	1.89607
$773$	2.32427e24	0.655784	0.327892	−	0.944715i	$-0.393662\pi$
$773$	2.32427e24	0.655784	0.327892	+	0.944715i	$0.393662\pi$
$774$	4.45789e24	1.24403
$775$	1.26769e23	0.0349903
$776$	4.76292e22	0.0130032
$777$	1.02799e25	2.77593
$778$	−6.64392e24	−1.77459
$779$	−3.35936e24	−0.887541
$780$	−4.59917e24	−1.20192
$781$	3.46666e24	0.896142
$782$	2.04879e24	0.523891
$783$	1.37669e23	0.0348225
$784$	−6.41593e24	−1.60536
$785$	2.75667e24	0.682328
$786$	−4.57473e24	−1.12014
$787$	4.71881e24	1.14300	0.571502	−	0.820601i	$-0.306361\pi$
$787$	4.71881e24	1.14300	0.571502	+	0.820601i	$0.306361\pi$
$788$	2.50583e24	0.600453
$789$	3.32205e24	0.787501
$790$	1.11048e24	0.260424
$791$	−2.76509e24	−0.641519
$792$	−2.74204e23	−0.0629376
$793$	3.55743e24	0.807820
$794$	−5.92940e24	−1.33210
$795$	4.97696e24	1.10623
$796$	3.13414e24	0.689218
$797$	4.02895e23	0.0876590	0.0438295	−	0.999039i	$-0.486044\pi$
$797$	4.02895e23	0.0876590	0.0438295	+	0.999039i	$0.486044\pi$
$798$	−2.45695e25	−5.28898
$799$	4.93043e23	0.105012
$800$	−3.37406e24	−0.711031
$801$	8.19477e24	1.70868
$802$	1.43220e24	0.295475
$803$	7.23663e24	1.47725
$804$	7.32316e24	1.47918
$805$	1.51412e25	3.02618
$806$	−3.41499e23	−0.0675370
$807$	1.80109e24	0.352461
$808$	−2.01332e23	−0.0389866
$809$	−9.96086e24	−1.90869	−0.954343	−	0.298713i	$-0.903443\pi$
$809$	−9.96086e24	−1.90869	−0.954343	+	0.298713i	$0.903443\pi$
$810$	−9.38535e24	−1.77962
$811$	−4.67036e24	−0.876341	−0.438170	−	0.898892i	$-0.644373\pi$
$811$	−4.67036e24	−0.876341	−0.438170	+	0.898892i	$0.644373\pi$
$812$	−1.11781e25	−2.07559
$813$	−1.02536e25	−1.88412
$814$	−1.35051e25	−2.45578
$815$	4.08707e24	0.735483
$816$	−1.85377e24	−0.330134
$817$	−8.17176e24	−1.44022
$818$	−1.30787e25	−2.28119
$819$	−6.26017e24	−1.08062
$820$	4.05848e24	0.693340
$821$	3.67946e23	0.0622110	0.0311055	−	0.999516i	$-0.490097\pi$
$821$	3.67946e23	0.0622110	0.0311055	+	0.999516i	$0.490097\pi$
$822$	2.24230e25	3.75218
$823$	9.04629e24	1.49821	0.749104	−	0.662453i	$-0.230484\pi$
$823$	9.04629e24	1.49821	0.749104	+	0.662453i	$0.230484\pi$
$824$	−5.46083e22	−0.00895111
$825$	−6.16837e24	−1.00072
$826$	−1.10413e25	−1.77292
$827$	−3.85087e24	−0.612015	−0.306007	−	0.952029i	$-0.598993\pi$
$827$	−3.85087e24	−0.612015	−0.306007	+	0.952029i	$0.598993\pi$
$828$	9.73928e24	1.53204
$829$	−9.85001e24	−1.53364	−0.766819	−	0.641863i	$-0.778162\pi$
$829$	−9.85001e24	−1.53364	−0.766819	+	0.641863i	$0.778162\pi$
$830$	5.13080e24	0.790718
$831$	−6.57576e24	−1.00308
$832$	4.75711e24	0.718282
$833$	2.69304e24	0.402494
$834$	1.35832e25	2.00952
$835$	1.56519e24	0.229209
$836$	1.63903e25	2.37593
$837$	−1.37836e22	−0.00197786
$838$	1.93562e25	2.74946
$839$	−1.08693e25	−1.52836	−0.764182	−	0.645001i	$-0.776857\pi$
$839$	−1.08693e25	−1.52836	−0.764182	+	0.645001i	$0.776857\pi$
$840$	9.10286e23	0.126708
$841$	3.78850e24	0.522037
$842$	1.43127e25	1.95240
$843$	1.86263e25	2.51531
$844$	−1.02458e25	−1.36973
$845$	−5.02160e24	−0.664600
$846$	4.61565e24	0.604762
$847$	1.29303e25	1.67725
$848$	−4.83638e24	−0.621092
$849$	−1.01743e25	−1.29357
$850$	1.37139e24	0.172623
$851$	1.47104e25	1.83325
$852$	−7.40255e24	−0.913365
$853$	−1.47561e25	−1.80262	−0.901312	−	0.433171i	$-0.857395\pi$
$853$	−1.47561e25	−1.80262	−0.901312	+	0.433171i	$0.857395\pi$
$854$	−2.29594e25	−2.77695
$855$	−1.62025e25	−1.94031
$856$	−9.77370e22	−0.0115886
$857$	−7.81735e24	−0.917746	−0.458873	−	0.888502i	$-0.651747\pi$
$857$	−7.81735e24	−0.917746	−0.458873	+	0.888502i	$0.651747\pi$
$858$	1.66168e25	1.93155
$859$	−1.64830e24	−0.189712	−0.0948560	−	0.995491i	$-0.530239\pi$
$859$	−1.64830e24	−0.189712	−0.0948560	+	0.995491i	$0.530239\pi$
$860$	9.87240e24	1.12509
$861$	1.11615e25	1.25950
$862$	9.86532e23	0.110230
$863$	5.54240e24	0.613206	0.306603	−	0.951838i	$-0.400808\pi$
$863$	5.54240e24	0.613206	0.306603	+	0.951838i	$0.400808\pi$
$864$	3.66862e23	0.0401917
$865$	2.02449e25	2.19623
$866$	1.84477e25	1.98171
$867$	7.78107e23	0.0827708
$868$	1.11917e24	0.117890
$869$	−2.03733e24	−0.212517
$870$	−2.93310e25	−3.02979
$871$	−6.73589e24	−0.689034
$872$	−9.70739e22	−0.00983360
$873$	2.81673e24	0.282568
$874$	−3.51587e25	−3.49290
$875$	−1.01616e25	−0.999751
$876$	−1.54528e25	−1.50564
$877$	6.16193e24	0.594594	0.297297	−	0.954785i	$-0.403915\pi$
$877$	6.16193e24	0.594594	0.297297	+	0.954785i	$0.403915\pi$
$878$	1.95519e25	1.86847
$879$	−8.83891e24	−0.836553
$880$	1.79981e25	1.68704
$881$	−8.72958e24	−0.810397	−0.405199	−	0.914229i	$-0.632798\pi$
$881$	−8.72958e24	−0.810397	−0.405199	+	0.914229i	$0.632798\pi$
$882$	2.52110e25	2.31797
$883$	4.74587e24	0.432165	0.216083	−	0.976375i	$-0.430672\pi$
$883$	4.74587e24	0.432165	0.216083	+	0.976375i	$0.430672\pi$
$884$	−1.87594e24	−0.169190
$885$	−1.47115e25	−1.31413
$886$	3.87434e24	0.342776
$887$	2.01695e25	1.76744	0.883719	−	0.468017i	$-0.155032\pi$
$887$	2.01695e25	1.76744	0.883719	+	0.468017i	$0.155032\pi$
$888$	8.84386e23	0.0767594
$889$	1.68155e25	1.44559
$890$	3.57396e25	3.04323
$891$	1.72187e25	1.45224
$892$	1.19428e25	0.997715
$893$	−8.46096e24	−0.700136
$894$	−1.58101e25	−1.29588
$895$	−5.85785e24	−0.475600
$896$	−1.82792e24	−0.147008
$897$	−1.80999e25	−1.44191
$898$	−2.46166e25	−1.94258
$899$	−1.10590e24	−0.0864490
$900$	6.51911e24	0.504809
$901$	2.03003e24	0.155719
$902$	−1.46633e25	−1.11424
$903$	2.71508e25	2.04379
$904$	−2.37883e23	−0.0177391
$905$	−1.12920e24	−0.0834177
$906$	−5.13776e25	−3.75996
$907$	−1.86626e25	−1.35304	−0.676519	−	0.736425i	$-0.736512\pi$
$907$	−1.86626e25	−1.35304	−0.676519	+	0.736425i	$0.736512\pi$
$908$	−3.79539e24	−0.272600
$909$	−1.19065e25	−0.847208
$910$	−2.73023e25	−1.92463
$911$	7.97898e24	0.557239	0.278619	−	0.960402i	$-0.410123\pi$
$911$	7.97898e24	0.557239	0.278619	+	0.960402i	$0.410123\pi$
$912$	3.18120e25	2.20108
$913$	−9.41314e24	−0.645258
$914$	2.65982e25	1.80638
$915$	−3.05914e25	−2.05835
$916$	9.20969e24	0.613951
$917$	−1.37901e25	−0.910808
$918$	−1.49111e23	−0.00975768
$919$	1.28717e25	0.834555	0.417278	−	0.908779i	$-0.362984\pi$
$919$	1.28717e25	0.834555	0.417278	+	0.908779i	$0.362984\pi$
$920$	1.30261e24	0.0836793
$921$	−1.57581e25	−1.00299
$922$	−6.23796e24	−0.393396
$923$	6.80890e24	0.425464
$924$	−5.44569e25	−3.37164
$925$	9.84658e24	0.604061
$926$	4.47219e24	0.271848
$927$	−3.22946e24	−0.194514
$928$	2.94346e25	1.75671
$929$	2.34114e23	0.0138450	0.00692250	−	0.999976i	$-0.497796\pi$
$929$	2.34114e23	0.0138450	0.00692250	+	0.999976i	$0.497796\pi$
$930$	2.93665e24	0.172087
$931$	−4.62143e25	−2.68352
$932$	−1.46749e25	−0.844382
$933$	5.01163e24	0.285749
$934$	3.00373e25	1.69712
$935$	−7.55458e24	−0.422972
$936$	−5.38568e23	−0.0298811
$937$	−2.57730e25	−1.41703	−0.708515	−	0.705696i	$-0.750635\pi$
$937$	−2.57730e25	−1.41703	−0.708515	+	0.705696i	$0.750635\pi$
$938$	4.34729e25	2.36862
$939$	2.88265e25	1.55644
$940$	1.02218e25	0.546940
$941$	−1.47062e25	−0.779807	−0.389904	−	0.920856i	$-0.627492\pi$
$941$	−1.47062e25	−0.779807	−0.389904	+	0.920856i	$0.627492\pi$
$942$	2.12679e25	1.11761
$943$	1.59720e25	0.831784
$944$	1.42960e25	0.737822
$945$	−1.10197e24	−0.0563638
$946$	−3.56690e25	−1.80808
$947$	−2.29031e25	−1.15059	−0.575293	−	0.817947i	$-0.695112\pi$
$947$	−2.29031e25	−1.15059	−0.575293	+	0.817947i	$0.695112\pi$
$948$	4.35042e24	0.216601
$949$	1.42135e25	0.701358
$950$	−2.35339e25	−1.15092
$951$	−2.28960e25	−1.10975
$952$	3.71293e23	0.0178362
$953$	−6.24291e24	−0.297233	−0.148617	−	0.988895i	$-0.547482\pi$
$953$	−6.24291e24	−0.297233	−0.148617	+	0.988895i	$0.547482\pi$
$954$	1.90043e25	0.896788
$955$	−3.17287e24	−0.148396
$956$	−3.32067e25	−1.53934
$957$	5.38116e25	2.47243
$958$	−4.97746e25	−2.26674
$959$	6.75919e25	3.05096
$960$	−4.09078e25	−1.83021
$961$	−2.24394e25	−0.995090
$962$	−2.65255e25	−1.16594
$963$	−5.78003e24	−0.251829
$964$	9.80711e24	0.423532
$965$	5.25726e25	2.25049
$966$	1.16815e26	4.95671
$967$	1.59167e25	0.669464	0.334732	−	0.942313i	$-0.391354\pi$
$967$	1.59167e25	0.669464	0.334732	+	0.942313i	$0.391354\pi$
$968$	1.11240e24	0.0463790
$969$	−1.33528e25	−0.551851
$970$	1.22845e25	0.503266
$971$	−4.26073e24	−0.173029	−0.0865147	−	0.996251i	$-0.527573\pi$
$971$	−4.26073e24	−0.173029	−0.0865147	+	0.996251i	$0.527573\pi$
$972$	−3.60447e25	−1.45104
$973$	4.09452e25	1.63397
$974$	−2.09104e25	−0.827202
$975$	−1.21154e25	−0.475114
$976$	2.97273e25	1.15567
$977$	−1.69745e25	−0.654172	−0.327086	−	0.944995i	$-0.606067\pi$
$977$	−1.69745e25	−0.654172	−0.327086	+	0.944995i	$0.606067\pi$
$978$	3.15320e25	1.20468
$979$	−6.55691e25	−2.48340
$980$	5.58321e25	2.09634
$981$	−5.74081e24	−0.213691
$982$	5.51789e25	2.03622
$983$	−1.99194e25	−0.728738	−0.364369	−	0.931255i	$-0.618715\pi$
$983$	−1.99194e25	−0.728738	−0.364369	+	0.931255i	$0.618715\pi$
$984$	9.60236e23	0.0348273
$985$	1.98203e25	0.712694
$986$	−1.19637e25	−0.426492
$987$	2.81116e25	0.993551
$988$	3.21923e25	1.12802
$989$	3.88525e25	1.34974
$990$	−7.07226e25	−2.43590
$991$	−8.16714e24	−0.278897	−0.139449	−	0.990229i	$-0.544533\pi$
$991$	−8.16714e24	−0.278897	−0.139449	+	0.990229i	$0.544533\pi$
$992$	−2.94703e24	−0.0997782
$993$	4.54850e24	0.152686
$994$	−4.39441e25	−1.46257
$995$	2.47900e25	0.818051
$996$	2.01004e25	0.657659
$997$	4.33491e25	1.40628	0.703139	−	0.711052i	$-0.251781\pi$
$997$	4.33491e25	1.40628	0.703139	+	0.711052i	$0.251781\pi$
$998$	4.00131e25	1.28704
$999$	−1.07062e24	−0.0341451

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.18.a.b.1.10	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.18.a.b.1.10	✓	12	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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

\(f(q)\)	\(=\)	\(q+516.034 q^{2} +15990.3 q^{3} +135219. q^{4} +1.06954e6 q^{5} +8.25154e6 q^{6} +2.48734e7 q^{7} +2.13988e6 q^{8} +1.26550e8 q^{9} +O(q^{10})\)	\(q+516.034 q^{2} +15990.3 q^{3} +135219. q^{4} +1.06954e6 q^{5} +8.25154e6 q^{6} +2.48734e7 q^{7} +2.13988e6 q^{8} +1.26550e8 q^{9} +5.51917e8 q^{10} -1.01257e9 q^{11} +2.16219e9 q^{12} -1.98879e9 q^{13} +1.28355e10 q^{14} +1.71022e10 q^{15} -1.66191e10 q^{16} +6.97576e9 q^{17} +6.53039e10 q^{18} -1.19709e11 q^{19} +1.44621e11 q^{20} +3.97734e11 q^{21} -5.22518e11 q^{22} +5.69153e11 q^{23} +3.42174e10 q^{24} +3.80970e11 q^{25} -1.02628e12 q^{26} -4.14228e10 q^{27} +3.36335e12 q^{28} -3.32350e12 q^{29} +8.82532e12 q^{30} +3.32753e11 q^{31} -8.85652e12 q^{32} -1.61912e13 q^{33} +3.59973e12 q^{34} +2.66030e13 q^{35} +1.71119e13 q^{36} +2.58461e13 q^{37} -6.17737e13 q^{38} -3.18014e13 q^{39} +2.28868e12 q^{40} +2.80628e13 q^{41} +2.05244e14 q^{42} +6.82637e13 q^{43} -1.36918e14 q^{44} +1.35350e14 q^{45} +2.93702e14 q^{46} +7.06795e13 q^{47} -2.65745e14 q^{48} +3.86057e14 q^{49} +1.96593e14 q^{50} +1.11544e14 q^{51} -2.68922e14 q^{52} +2.91013e14 q^{53} -2.13756e13 q^{54} -1.08298e15 q^{55} +5.32262e13 q^{56} -1.91418e15 q^{57} -1.71504e15 q^{58} -8.60211e14 q^{59} +2.31254e15 q^{60} -1.78874e15 q^{61} +1.71712e14 q^{62} +3.14772e15 q^{63} -2.39196e15 q^{64} -2.12709e15 q^{65} -8.35522e15 q^{66} +3.38692e15 q^{67} +9.43253e14 q^{68} +9.10093e15 q^{69} +1.37281e16 q^{70} -3.42363e15 q^{71} +2.70801e14 q^{72} -7.14682e15 q^{73} +1.33375e16 q^{74} +6.09182e15 q^{75} -1.61869e16 q^{76} -2.51860e16 q^{77} -1.64106e16 q^{78} +2.01204e15 q^{79} -1.77748e16 q^{80} -1.70050e16 q^{81} +1.44814e16 q^{82} +9.29633e15 q^{83} +5.37811e16 q^{84} +7.46083e15 q^{85} +3.52264e16 q^{86} -5.31438e16 q^{87} -2.16677e15 q^{88} +6.47554e16 q^{89} +6.98449e16 q^{90} -4.94681e16 q^{91} +7.69602e16 q^{92} +5.32082e15 q^{93} +3.64730e16 q^{94} -1.28033e17 q^{95} -1.41618e17 q^{96} +2.22579e16 q^{97} +1.99218e17 q^{98} -1.28140e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 527 q^{2} + 21484 q^{3} + 824597 q^{4} + 1770512 q^{5} - 3292232 q^{6} + 22379060 q^{7} + 45571509 q^{8} + 746877740 q^{9}+O(q^{10}) \) 12 * q + 527 * q^2 + 21484 * q^3 + 824597 * q^4 + 1770512 * q^5 - 3292232 * q^6 + 22379060 * q^7 + 45571509 * q^8 + 746877740 * q^9	\( 12 q + 527 q^{2} + 21484 q^{3} + 824597 q^{4} + 1770512 q^{5} - 3292232 q^{6} + 22379060 q^{7} + 45571509 q^{8} + 746877740 q^{9} + 824176946 q^{10} + 1508850220 q^{11} + 4380824560 q^{12} + 2071135824 q^{13} - 9581529548 q^{14} - 15603628992 q^{15} + 20409782305 q^{16} + 83709089292 q^{17} - 195058406893 q^{18} - 1108652840 q^{19} + 304149438198 q^{20} + 711976780056 q^{21} + 350258857160 q^{22} + 816663191324 q^{23} - 118287259488 q^{24} + 841645606900 q^{25} + 1135562035330 q^{26} + 2668523518384 q^{27} + 7745458522756 q^{28} - 4667447777712 q^{29} + 15034204946608 q^{30} + 23367156664948 q^{31} + 16779331087925 q^{32} + 25952886361216 q^{33} + 3676224171407 q^{34} + 52808829544064 q^{35} + 178683325289537 q^{36} + 45103867774096 q^{37} + 141942362802260 q^{38} + 187488571444048 q^{39} + 231489638087062 q^{40} + 106534751749128 q^{41} + 82630767165312 q^{42} + 350248430413232 q^{43} + 468477290587728 q^{44} + 238676787528480 q^{45} + 587080431637364 q^{46} + 419195348129576 q^{47} + 10\!\cdots\!72 q^{48}+ \cdots - 11\!\cdots\!24 q^{99}+O(q^{100}) \) 12 * q + 527 * q^2 + 21484 * q^3 + 824597 * q^4 + 1770512 * q^5 - 3292232 * q^6 + 22379060 * q^7 + 45571509 * q^8 + 746877740 * q^9 + 824176946 * q^10 + 1508850220 * q^11 + 4380824560 * q^12 + 2071135824 * q^13 - 9581529548 * q^14 - 15603628992 * q^15 + 20409782305 * q^16 + 83709089292 * q^17 - 195058406893 * q^18 - 1108652840 * q^19 + 304149438198 * q^20 + 711976780056 * q^21 + 350258857160 * q^22 + 816663191324 * q^23 - 118287259488 * q^24 + 841645606900 * q^25 + 1135562035330 * q^26 + 2668523518384 * q^27 + 7745458522756 * q^28 - 4667447777712 * q^29 + 15034204946608 * q^30 + 23367156664948 * q^31 + 16779331087925 * q^32 + 25952886361216 * q^33 + 3676224171407 * q^34 + 52808829544064 * q^35 + 178683325289537 * q^36 + 45103867774096 * q^37 + 141942362802260 * q^38 + 187488571444048 * q^39 + 231489638087062 * q^40 + 106534751749128 * q^41 + 82630767165312 * q^42 + 350248430413232 * q^43 + 468477290587728 * q^44 + 238676787528480 * q^45 + 587080431637364 * q^46 + 419195348129576 * q^47 + 1093472072556672 * q^48 + 794411575895372 * q^49 + 1412694936225137 * q^50 + 149867172862444 * q^51 + 642014932833750 * q^52 + 56947812536104 * q^53 - 1392308314286000 * q^54 - 1412881301128432 * q^55 - 3203817872304204 * q^56 - 2707439010959184 * q^57 - 1529508580613878 * q^58 - 3177686539773696 * q^59 - 10022838941748448 * q^60 - 3392964491871408 * q^61 - 12114194581567516 * q^62 + 1635686752578012 * q^63 - 8465772367878263 * q^64 - 3660813322103328 * q^65 - 11453990779029568 * q^66 - 2857880476265040 * q^67 + 5752188658576277 * q^68 - 12630398353679160 * q^69 + 3399395009377720 * q^70 - 1862686563242532 * q^71 - 36929264963425119 * q^72 - 15078079303572472 * q^73 + 542093202855346 * q^74 - 20330126181611628 * q^75 + 6303255557523596 * q^76 - 20295555037512648 * q^77 - 53192869717439760 * q^78 + 19398131823479964 * q^79 - 7257576275928962 * q^80 + 37457071423573532 * q^81 + 127570037419772678 * q^82 + 50819373739336784 * q^83 + 179493786749097600 * q^84 + 12350662258379792 * q^85 + 22727028430696588 * q^86 + 102295071486477840 * q^87 + 194000133114521056 * q^88 + 40280615281839032 * q^89 + 223872567241318058 * q^90 + 169549572827745440 * q^91 + 116206299681681348 * q^92 + 32924009888402024 * q^93 + 130371382365284928 * q^94 + 106757515750638208 * q^95 - 16033015771117248 * q^96 + 173995685961333528 * q^97 - 246436513972691449 * q^98 - 112553818797736924 * q^99

Introduction

L-functions

Modular forms

Varieties

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