LMFDB - Embedded newform 23.16.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,16,Mod(1,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("23.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	23.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:	$32.8195061730$
Analytic rank:	$1$
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} - 4 x^{11} - 68942 x^{10} - 977032 x^{9} + 1644150380 x^{8} + 50352376602 x^{7} + \cdots + 34\!\cdots\!76 $ x^12 - 4x^11 - 68942x^10 - 977032x^9 + 1644150380x^8 + 50352376602x^7 - 15614385123802x^6 - 702635376772966x^5 + 50805039593451715x^4 + 3084648153192808082x^3 + 3701665188552036536x^2 - 1120833250638227525562*x + 3479819676773674797376
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{22}\cdot 3^{6}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$3.23741$ of defining polynomial
Character	$\chi$	$=$	23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-15.5252 q^{2} -2381.89 q^{3} -32527.0 q^{4} +172933. q^{5} +36979.3 q^{6} -570604. q^{7} +1.01372e6 q^{8} -8.67549e6 q^{9} +O(q^{10})$	\(q-15.5252 q^{2} -2381.89 q^{3} -32527.0 q^{4} +172933. q^{5} +36979.3 q^{6} -570604. q^{7} +1.01372e6 q^{8} -8.67549e6 q^{9} -2.68481e6 q^{10} +7.47818e7 q^{11} +7.74758e7 q^{12} +2.00125e8 q^{13} +8.85874e6 q^{14} -4.11907e8 q^{15} +1.05011e9 q^{16} +1.04444e9 q^{17} +1.34689e8 q^{18} -4.82221e9 q^{19} -5.62498e9 q^{20} +1.35912e9 q^{21} -1.16100e9 q^{22} +3.40483e9 q^{23} -2.41457e9 q^{24} -6.11864e8 q^{25} -3.10698e9 q^{26} +5.48417e10 q^{27} +1.85600e10 q^{28} -9.04593e10 q^{29} +6.39494e9 q^{30} -1.68751e11 q^{31} -4.95205e10 q^{32} -1.78122e11 q^{33} -1.62151e10 q^{34} -9.86762e10 q^{35} +2.82187e11 q^{36} -5.36118e11 q^{37} +7.48658e10 q^{38} -4.76677e11 q^{39} +1.75305e11 q^{40} -1.56473e12 q^{41} -2.11006e10 q^{42} +2.10123e12 q^{43} -2.43243e12 q^{44} -1.50028e12 q^{45} -5.28605e10 q^{46} -2.98427e12 q^{47} -2.50124e12 q^{48} -4.42197e12 q^{49} +9.49930e9 q^{50} -2.48775e12 q^{51} -6.50947e12 q^{52} +5.68091e11 q^{53} -8.51427e11 q^{54} +1.29322e13 q^{55} -5.78431e11 q^{56} +1.14860e13 q^{57} +1.40440e12 q^{58} -2.01143e13 q^{59} +1.33981e13 q^{60} +2.55334e13 q^{61} +2.61989e12 q^{62} +4.95027e12 q^{63} -3.36410e13 q^{64} +3.46082e13 q^{65} +2.76538e12 q^{66} -3.39102e13 q^{67} -3.39725e13 q^{68} -8.10993e12 q^{69} +1.53197e12 q^{70} +1.82564e13 q^{71} -8.79449e12 q^{72} +1.58901e14 q^{73} +8.32333e12 q^{74} +1.45739e12 q^{75} +1.56852e14 q^{76} -4.26708e13 q^{77} +7.40050e12 q^{78} +1.90999e14 q^{79} +1.81598e14 q^{80} -6.14326e12 q^{81} +2.42927e13 q^{82} -2.14018e14 q^{83} -4.42080e13 q^{84} +1.80618e14 q^{85} -3.26220e13 q^{86} +2.15465e14 q^{87} +7.58075e13 q^{88} -7.76950e14 q^{89} +2.32921e13 q^{90} -1.14192e14 q^{91} -1.10749e14 q^{92} +4.01947e14 q^{93} +4.63313e13 q^{94} -8.33918e14 q^{95} +1.17953e14 q^{96} -7.97824e14 q^{97} +6.86519e13 q^{98} -6.48769e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 256 q^{2} - 1745 q^{3} + 163840 q^{4} - 204476 q^{5} - 199430 q^{6} - 5717328 q^{7} + 10323168 q^{8} + 32660341 q^{9}+O(q^{10}) $ 12 * q - 256 * q^2 - 1745 * q^3 + 163840 * q^4 - 204476 * q^5 - 199430 * q^6 - 5717328 * q^7 + 10323168 * q^8 + 32660341 * q^9	\( 12 q - 256 q^{2} - 1745 q^{3} + 163840 q^{4} - 204476 q^{5} - 199430 q^{6} - 5717328 q^{7} + 10323168 q^{8} + 32660341 q^{9} - 137846540 q^{10} - 87636002 q^{11} - 398208076 q^{12} - 292496079 q^{13} + 415954912 q^{14} + 548079030 q^{15} + 4273503168 q^{16} - 2462528162 q^{17} + 7261215718 q^{18} + 175321758 q^{19} + 2660811480 q^{20} + 205665472 q^{21} - 21718153768 q^{22} + 40857905364 q^{23} - 63413289624 q^{24} + 20443225284 q^{25} - 137268652810 q^{26} - 151915208903 q^{27} - 325638721712 q^{28} - 164667697193 q^{29} - 356944003956 q^{30} + 20222384151 q^{31} - 369109524032 q^{32} + 132365097022 q^{33} - 582887018988 q^{34} - 1578083373112 q^{35} - 1903913944516 q^{36} - 869669414912 q^{37} - 5525312078376 q^{38} - 5762413466499 q^{39} - 4733269274576 q^{40} - 7510147709883 q^{41} - 7436463221624 q^{42} - 5682603487020 q^{43} - 11849381658176 q^{44} - 10780493432442 q^{45} - 871635314432 q^{46} - 5828073094301 q^{47} - 29418911592496 q^{48} - 6518780198860 q^{49} - 16781003942456 q^{50} - 771327642584 q^{51} - 3841511618340 q^{52} + 1452974784324 q^{53} - 32167598069522 q^{54} - 14882020037092 q^{55} + 416192984288 q^{56} - 12135794354818 q^{57} - 60065613521022 q^{58} - 11503084624084 q^{59} - 6378557828664 q^{60} - 23587566667200 q^{61} + 49359974806402 q^{62} + 87886039196104 q^{63} + 80321007324160 q^{64} + 54548135308138 q^{65} + 316922278045948 q^{66} + 61525019345122 q^{67} + 45114528974104 q^{68} - 5941420405015 q^{69} + 374016699556320 q^{70} + 197895887067063 q^{71} + 439014895837656 q^{72} - 22888563242709 q^{73} + 694696716227036 q^{74} + 612085940395201 q^{75} + 301381886149904 q^{76} + 209007839834200 q^{77} + 350406148895766 q^{78} + 229938065096294 q^{79} + 555529032250016 q^{80} + 37596523177660 q^{81} - 414508112727306 q^{82} + 369402590629184 q^{83} + 559863541234208 q^{84} - 343366303925348 q^{85} + 12\!\cdots\!08 q^{86}+ \cdots - 32\!\cdots\!24 q^{99}+O(q^{100}) \) 12 * q - 256 * q^2 - 1745 * q^3 + 163840 * q^4 - 204476 * q^5 - 199430 * q^6 - 5717328 * q^7 + 10323168 * q^8 + 32660341 * q^9 - 137846540 * q^10 - 87636002 * q^11 - 398208076 * q^12 - 292496079 * q^13 + 415954912 * q^14 + 548079030 * q^15 + 4273503168 * q^16 - 2462528162 * q^17 + 7261215718 * q^18 + 175321758 * q^19 + 2660811480 * q^20 + 205665472 * q^21 - 21718153768 * q^22 + 40857905364 * q^23 - 63413289624 * q^24 + 20443225284 * q^25 - 137268652810 * q^26 - 151915208903 * q^27 - 325638721712 * q^28 - 164667697193 * q^29 - 356944003956 * q^30 + 20222384151 * q^31 - 369109524032 * q^32 + 132365097022 * q^33 - 582887018988 * q^34 - 1578083373112 * q^35 - 1903913944516 * q^36 - 869669414912 * q^37 - 5525312078376 * q^38 - 5762413466499 * q^39 - 4733269274576 * q^40 - 7510147709883 * q^41 - 7436463221624 * q^42 - 5682603487020 * q^43 - 11849381658176 * q^44 - 10780493432442 * q^45 - 871635314432 * q^46 - 5828073094301 * q^47 - 29418911592496 * q^48 - 6518780198860 * q^49 - 16781003942456 * q^50 - 771327642584 * q^51 - 3841511618340 * q^52 + 1452974784324 * q^53 - 32167598069522 * q^54 - 14882020037092 * q^55 + 416192984288 * q^56 - 12135794354818 * q^57 - 60065613521022 * q^58 - 11503084624084 * q^59 - 6378557828664 * q^60 - 23587566667200 * q^61 + 49359974806402 * q^62 + 87886039196104 * q^63 + 80321007324160 * q^64 + 54548135308138 * q^65 + 316922278045948 * q^66 + 61525019345122 * q^67 + 45114528974104 * q^68 - 5941420405015 * q^69 + 374016699556320 * q^70 + 197895887067063 * q^71 + 439014895837656 * q^72 - 22888563242709 * q^73 + 694696716227036 * q^74 + 612085940395201 * q^75 + 301381886149904 * q^76 + 209007839834200 * q^77 + 350406148895766 * q^78 + 229938065096294 * q^79 + 555529032250016 * q^80 + 37596523177660 * q^81 - 414508112727306 * q^82 + 369402590629184 * q^83 + 559863541234208 * q^84 - 343366303925348 * q^85 + 1273071253885508 * q^86 - 725794048127953 * q^87 - 2461430290350720 * q^88 - 85082918654478 * q^89 + 125194382337864 * q^90 - 180251669559688 * q^91 + 557846601236480 * q^92 + 190758447044005 * q^93 + 640973603901258 * q^94 + 462985554800484 * q^95 - 2815189465233952 * q^96 - 5046858838511686 * q^97 - 3547540222626416 * q^98 - 3251416762282424 * 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 $

$2$	−15.5252	−0.0857653	−0.0428827	−	0.999080i	$-0.513654\pi$
$2$	−15.5252	−0.0857653	−0.0428827	+	0.999080i	$0.513654\pi$
$3$	−2381.89	−0.628801	−0.314400	−	0.949290i	$-0.601803\pi$
$3$	−2381.89	−0.628801	−0.314400	+	0.949290i	$0.601803\pi$
$4$	−32527.0	−0.992644
$5$	172933.	0.989924	0.494962	−	0.868914i	$-0.335182\pi$
$5$	172933.	0.989924	0.494962	+	0.868914i	$0.335182\pi$
$6$	36979.3	0.0539293
$7$	−570604.	−0.261879	−0.130939	−	0.991390i	$-0.541799\pi$
$7$	−570604.	−0.261879	−0.130939	+	0.991390i	$0.541799\pi$
$8$	1.01372e6	0.170900
$9$	−8.67549e6	−0.604610
$10$	−2.68481e6	−0.0849012
$11$	7.47818e7	1.15705	0.578523	−	0.815666i	$-0.303629\pi$
$11$	7.47818e7	1.15705	0.578523	+	0.815666i	$0.303629\pi$
$12$	7.74758e7	0.624175
$13$	2.00125e8	0.884559	0.442279	−	0.896877i	$-0.354170\pi$
$13$	2.00125e8	0.884559	0.442279	+	0.896877i	$0.354170\pi$
$14$	8.85874e6	0.0224601
$15$	−4.11907e8	−0.622465
$16$	1.05011e9	0.977987
$17$	1.04444e9	0.617329	0.308665	−	0.951171i	$-0.400118\pi$
$17$	1.04444e9	0.617329	0.308665	+	0.951171i	$0.400118\pi$
$18$	1.34689e8	0.0518546
$19$	−4.82221e9	−1.23764	−0.618820	−	0.785533i	$-0.712389\pi$
$19$	−4.82221e9	−1.23764	−0.618820	+	0.785533i	$0.712389\pi$
$20$	−5.62498e9	−0.982643
$21$	1.35912e9	0.164669
$22$	−1.16100e9	−0.0992345
$23$	3.40483e9	0.208514
$23$	3.40483e9	0.208514
$24$	−2.41457e9	−0.107462
$25$	−6.11864e8	−0.0200496
$26$	−3.10698e9	−0.0758645
$27$	5.48417e10	1.00898
$28$	1.85600e10	0.259952
$29$	−9.04593e10	−0.973797	−0.486899	−	0.873459i	$-0.661872\pi$
$29$	−9.04593e10	−0.973797	−0.486899	+	0.873459i	$0.661872\pi$
$30$	6.39494e9	0.0533859
$31$	−1.68751e11	−1.10163	−0.550813	−	0.834629i	$-0.685682\pi$
$31$	−1.68751e11	−1.10163	−0.550813	+	0.834629i	$0.685682\pi$
$32$	−4.95205e10	−0.254777
$33$	−1.78122e11	−0.727551
$34$	−1.62151e10	−0.0529454
$35$	−9.86762e10	−0.259240
$36$	2.82187e11	0.600162
$37$	−5.36118e11	−0.928426	−0.464213	−	0.885724i	$-0.653663\pi$
$37$	−5.36118e11	−0.928426	−0.464213	+	0.885724i	$0.653663\pi$
$38$	7.48658e10	0.106147
$39$	−4.76677e11	−0.556211
$40$	1.75305e11	0.169178
$41$	−1.56473e12	−1.25476	−0.627380	−	0.778713i	$-0.715873\pi$
$41$	−1.56473e12	−1.25476	−0.627380	+	0.778713i	$0.715873\pi$
$42$	−2.11006e10	−0.0141229
$43$	2.10123e12	1.17886	0.589428	−	0.807821i	$-0.299353\pi$
$43$	2.10123e12	1.17886	0.589428	+	0.807821i	$0.299353\pi$
$44$	−2.43243e12	−1.14854
$45$	−1.50028e12	−0.598518
$46$	−5.28605e10	−0.0178833
$47$	−2.98427e12	−0.859219	−0.429609	−	0.903015i	$-0.641349\pi$
$47$	−2.98427e12	−0.859219	−0.429609	+	0.903015i	$0.641349\pi$
$48$	−2.50124e12	−0.614959
$49$	−4.42197e12	−0.931420
$50$	9.49930e9	0.00171956
$51$	−2.48775e12	−0.388177
$52$	−6.50947e12	−0.878052
$53$	5.68091e11	0.0664277	0.0332138	−	0.999448i	$-0.489426\pi$
$53$	5.68091e11	0.0664277	0.0332138	+	0.999448i	$0.489426\pi$
$54$	−8.51427e11	−0.0865355
$55$	1.29322e13	1.14539
$56$	−5.78431e11	−0.0447550
$57$	1.14860e13	0.778229
$58$	1.40440e12	0.0835180
$59$	−2.01143e13	−1.05224	−0.526119	−	0.850411i	$-0.676353\pi$
$59$	−2.01143e13	−1.05224	−0.526119	+	0.850411i	$0.676353\pi$
$60$	1.33981e13	0.617887
$61$	2.55334e13	1.04024	0.520122	−	0.854092i	$-0.325886\pi$
$61$	2.55334e13	1.04024	0.520122	+	0.854092i	$0.325886\pi$
$62$	2.61989e12	0.0944813
$63$	4.95027e12	0.158334
$64$	−3.36410e13	−0.956136
$65$	3.46082e13	0.875646
$66$	2.76538e12	0.0623987
$67$	−3.39102e13	−0.683548	−0.341774	−	0.939782i	$-0.611028\pi$
$67$	−3.39102e13	−0.683548	−0.341774	+	0.939782i	$0.611028\pi$
$68$	−3.39725e13	−0.612788
$69$	−8.10993e12	−0.131114
$70$	1.53197e12	0.0222338
$71$	1.82564e13	0.238220	0.119110	−	0.992881i	$-0.461996\pi$
$71$	1.82564e13	0.238220	0.119110	+	0.992881i	$0.461996\pi$
$72$	−8.79449e12	−0.103328
$73$	1.58901e14	1.68347	0.841735	−	0.539892i	$-0.181535\pi$
$73$	1.58901e14	1.68347	0.841735	+	0.539892i	$0.181535\pi$
$74$	8.32333e12	0.0796268
$75$	1.45739e12	0.0126072
$76$	1.56852e14	1.22854
$77$	−4.26708e13	−0.303006
$78$	7.40050e12	0.0477036
$79$	1.90999e14	1.11899	0.559496	−	0.828833i	$-0.310995\pi$
$79$	1.90999e14	1.11899	0.559496	+	0.828833i	$0.310995\pi$
$80$	1.81598e14	0.968133
$81$	−6.14326e12	−0.0298374
$82$	2.42927e13	0.107615
$83$	−2.14018e14	−0.865695	−0.432848	−	0.901467i	$-0.642491\pi$
$83$	−2.14018e14	−0.865695	−0.432848	+	0.901467i	$0.642491\pi$
$84$	−4.42080e13	−0.163458
$85$	1.80618e14	0.611109
$86$	−3.26220e13	−0.101105
$87$	2.15465e14	0.612324
$88$	7.58075e13	0.197739
$89$	−7.76950e14	−1.86195	−0.930975	−	0.365084i	$-0.881040\pi$
$89$	−7.76950e14	−1.86195	−0.930975	+	0.365084i	$0.881040\pi$
$90$	2.32921e13	0.0513321
$91$	−1.14192e14	−0.231647
$92$	−1.10749e14	−0.206981
$93$	4.01947e14	0.692703
$94$	4.63313e13	0.0736912
$95$	−8.33918e14	−1.22517
$96$	1.17953e14	0.160204
$97$	−7.97824e14	−1.00258	−0.501290	−	0.865279i	$-0.667141\pi$
$97$	−7.97824e14	−1.00258	−0.501290	+	0.865279i	$0.667141\pi$
$98$	6.86519e13	0.0798835
$99$	−6.48769e14	−0.699561
$100$	1.99021e13	0.0199021
$101$	−9.70709e14	−0.900905	−0.450452	−	0.892800i	$-0.648737\pi$
$101$	−9.70709e14	−0.900905	−0.450452	+	0.892800i	$0.648737\pi$
$102$	3.86227e13	0.0332921
$103$	2.39616e14	0.191972	0.0959859	−	0.995383i	$-0.469400\pi$
$103$	2.39616e14	0.191972	0.0959859	+	0.995383i	$0.469400\pi$
$104$	2.02870e14	0.151171
$105$	2.35036e14	0.163010
$106$	−8.81972e12	−0.00569719
$107$	1.70714e15	1.02776	0.513879	−	0.857863i	$-0.328208\pi$
$107$	1.70714e15	1.02776	0.513879	+	0.857863i	$0.328208\pi$
$108$	−1.78383e15	−1.00156
$109$	−8.74027e14	−0.457959	−0.228979	−	0.973431i	$-0.573539\pi$
$109$	−8.74027e14	−0.457959	−0.228979	+	0.973431i	$0.573539\pi$
$110$	−2.00775e14	−0.0982346
$111$	1.27698e15	0.583795
$112$	−5.99195e14	−0.256114
$113$	−2.25991e15	−0.903656	−0.451828	−	0.892105i	$-0.649228\pi$
$113$	−2.25991e15	−0.903656	−0.451828	+	0.892105i	$0.649228\pi$
$114$	−1.78322e14	−0.0667451
$115$	5.88806e14	0.206414
$116$	2.94237e15	0.966634
$117$	−1.73618e15	−0.534813
$118$	3.12278e14	0.0902456
$119$	−5.95962e14	−0.161665
$120$	−4.17557e14	−0.106379
$121$	1.41507e15	0.338756
$122$	−3.96411e14	−0.0892169
$123$	3.72702e15	0.788994
$124$	5.48896e15	1.09352
$125$	−5.38330e15	−1.00977
$126$	−7.68539e13	−0.0135796
$127$	−3.80340e15	−0.633350	−0.316675	−	0.948534i	$-0.602566\pi$
$127$	−3.80340e15	−0.633350	−0.316675	+	0.948534i	$0.602566\pi$
$128$	2.14497e15	0.336781
$129$	−5.00491e15	−0.741265
$130$	−5.37299e14	−0.0751001
$131$	5.34775e15	0.705727	0.352863	−	0.935675i	$-0.385208\pi$
$131$	5.34775e15	0.705727	0.352863	+	0.935675i	$0.385208\pi$
$132$	5.79378e15	0.722200
$133$	2.75158e15	0.324111
$134$	5.26461e14	0.0586247
$135$	9.48392e15	0.998814
$136$	1.05877e15	0.105501
$137$	8.22313e15	0.775591	0.387795	−	0.921745i	$-0.373237\pi$
$137$	8.22313e15	0.775591	0.387795	+	0.921745i	$0.373237\pi$
$138$	1.25908e14	0.0112450
$139$	−1.63224e14	−0.0138093	−0.00690465	−	0.999976i	$-0.502198\pi$
$139$	−1.63224e14	−0.0138093	−0.00690465	+	0.999976i	$0.502198\pi$
$140$	3.20964e15	0.257333
$141$	7.10821e15	0.540277
$142$	−2.83434e14	−0.0204310
$143$	1.49657e16	1.02348
$144$	−9.11018e15	−0.591300
$145$	−1.56434e16	−0.963986
$146$	−2.46697e15	−0.144383
$147$	1.05327e16	0.585677
$148$	1.74383e16	0.921597
$149$	−9.68363e15	−0.486565	−0.243283	−	0.969955i	$-0.578224\pi$
$149$	−9.68363e15	−0.486565	−0.243283	+	0.969955i	$0.578224\pi$
$150$	−2.26263e13	−0.00108126
$151$	−3.03297e16	−1.37893	−0.689463	−	0.724321i	$-0.742153\pi$
$151$	−3.03297e16	−1.37893	−0.689463	+	0.724321i	$0.742153\pi$
$152$	−4.88836e15	−0.211513
$153$	−9.06103e15	−0.373243
$154$	6.62473e14	0.0259874
$155$	−2.91826e16	−1.09053
$156$	1.55049e16	0.552120
$157$	−5.68272e15	−0.192890	−0.0964448	−	0.995338i	$-0.530747\pi$
$157$	−5.68272e15	−0.192890	−0.0964448	+	0.995338i	$0.530747\pi$
$158$	−2.96529e15	−0.0959708
$159$	−1.35313e15	−0.0417698
$160$	−8.56372e15	−0.252210
$161$	−1.94281e15	−0.0546054
$162$	9.53753e13	0.00255902
$163$	−3.94644e16	−1.01111	−0.505555	−	0.862794i	$-0.668712\pi$
$163$	−3.94644e16	−1.01111	−0.505555	+	0.862794i	$0.668712\pi$
$164$	5.08960e16	1.24553
$165$	−3.08032e16	−0.720221
$166$	3.32267e15	0.0742467
$167$	−1.05277e16	−0.224885	−0.112442	−	0.993658i	$-0.535867\pi$
$167$	−1.05277e16	−0.224885	−0.112442	+	0.993658i	$0.535867\pi$
$168$	1.37776e15	0.0281420
$169$	−1.11358e16	−0.217556
$170$	−2.80413e15	−0.0524120
$171$	4.18351e16	0.748289
$172$	−6.83467e16	−1.17018
$173$	−5.36034e16	−0.878712	−0.439356	−	0.898313i	$-0.644793\pi$
$173$	−5.36034e16	−0.878712	−0.439356	+	0.898313i	$0.644793\pi$
$174$	−3.34513e15	−0.0525162
$175$	3.49132e14	0.00525055
$176$	7.85288e16	1.13158
$177$	4.79101e16	0.661648
$178$	1.20623e16	0.159691
$179$	−2.43147e16	−0.308654	−0.154327	−	0.988020i	$-0.549321\pi$
$179$	−2.43147e16	−0.308654	−0.154327	+	0.988020i	$0.549321\pi$
$180$	4.87994e16	0.594115
$181$	−1.06707e17	−1.24624	−0.623120	−	0.782126i	$-0.714135\pi$
$181$	−1.06707e17	−1.24624	−0.623120	+	0.782126i	$0.714135\pi$
$182$	1.77286e15	0.0198673
$183$	−6.08179e16	−0.654106
$184$	3.45153e15	0.0356351
$185$	−9.27123e16	−0.919071
$186$	−6.24031e15	−0.0594099
$187$	7.81051e16	0.714278
$188$	9.70692e16	0.852899
$189$	−3.12929e16	−0.264230
$190$	1.29467e16	0.105077
$191$	−1.81713e17	−1.41787	−0.708935	−	0.705274i	$-0.750824\pi$
$191$	−1.81713e17	−1.41787	−0.708935	+	0.705274i	$0.750824\pi$
$192$	8.01294e16	0.601219
$193$	4.67137e15	0.0337105	0.0168552	−	0.999858i	$-0.494635\pi$
$193$	4.67137e15	0.0337105	0.0168552	+	0.999858i	$0.494635\pi$
$194$	1.23864e16	0.0859867
$195$	−8.24331e16	−0.550607
$196$	1.43833e17	0.924568
$197$	2.49874e17	1.54605	0.773026	−	0.634375i	$-0.218742\pi$
$197$	2.49874e17	1.54605	0.773026	+	0.634375i	$0.218742\pi$
$198$	1.00723e16	0.0599981
$199$	3.28526e17	1.88439	0.942196	−	0.335061i	$-0.108757\pi$
$199$	3.28526e17	1.88439	0.942196	+	0.335061i	$0.108757\pi$
$200$	−6.20256e14	−0.00342647
$201$	8.07704e16	0.429815
$202$	1.50704e16	0.0772664
$203$	5.16165e16	0.255017
$204$	8.09188e16	0.385322
$205$	−2.70593e17	−1.24212
$206$	−3.72009e15	−0.0164645
$207$	−2.95385e16	−0.126070
$208$	2.10153e17	0.865087
$209$	−3.60614e17	−1.43201
$210$	−3.64898e15	−0.0139806
$211$	1.08856e17	0.402470	0.201235	−	0.979543i	$-0.435505\pi$
$211$	1.08856e17	0.402470	0.201235	+	0.979543i	$0.435505\pi$
$212$	−1.84783e16	−0.0659390
$213$	−4.34848e16	−0.149793
$214$	−2.65037e16	−0.0881460
$215$	3.63372e17	1.16698
$216$	5.55939e16	0.172434
$217$	9.62901e16	0.288492
$218$	1.35694e16	0.0392770
$219$	−3.78485e17	−1.05857
$220$	−4.20646e17	−1.13696
$221$	2.09019e17	0.546064
$222$	−1.98253e16	−0.0500694
$223$	7.33179e17	1.79029	0.895146	−	0.445774i	$-0.147071\pi$
$223$	7.33179e17	1.79029	0.895146	+	0.445774i	$0.147071\pi$
$224$	2.82566e16	0.0667207
$225$	5.30822e15	0.0121222
$226$	3.50856e16	0.0775024
$227$	−6.76599e17	−1.44590	−0.722949	−	0.690902i	$-0.757214\pi$
$227$	−6.76599e17	−1.44590	−0.722949	+	0.690902i	$0.757214\pi$
$228$	−3.73605e17	−0.772505
$229$	−2.90156e17	−0.580585	−0.290293	−	0.956938i	$-0.593753\pi$
$229$	−2.90156e17	−0.580585	−0.290293	+	0.956938i	$0.593753\pi$
$230$	−9.14132e15	−0.0177031
$231$	1.01637e17	0.190530
$232$	−9.17001e16	−0.166422
$233$	1.06724e18	1.87539	0.937696	−	0.347455i	$-0.112954\pi$
$233$	1.06724e18	1.87539	0.937696	+	0.347455i	$0.112954\pi$
$234$	2.69546e16	0.0458684
$235$	−5.16077e17	−0.850562
$236$	6.54256e17	1.04450
$237$	−4.54939e17	−0.703623
$238$	9.25243e15	0.0138653
$239$	4.98155e17	0.723403	0.361702	−	0.932294i	$-0.382196\pi$
$239$	4.98155e17	0.723403	0.361702	+	0.932294i	$0.382196\pi$
$240$	−4.32546e17	−0.608763
$241$	−5.05627e17	−0.689767	−0.344883	−	0.938646i	$-0.612082\pi$
$241$	−5.05627e17	−0.689767	−0.344883	+	0.938646i	$0.612082\pi$
$242$	−2.19692e16	−0.0290535
$243$	−7.72285e17	−0.990218
$244$	−8.30525e17	−1.03259
$245$	−7.64704e17	−0.922035
$246$	−5.78627e16	−0.0676684
$247$	−9.65047e17	−1.09477
$248$	−1.71066e17	−0.188268
$249$	5.09769e17	0.544350
$250$	8.35767e16	0.0866034
$251$	−1.04844e18	−1.05437	−0.527183	−	0.849752i	$-0.676752\pi$
$251$	−1.04844e18	−1.05437	−0.527183	+	0.849752i	$0.676752\pi$
$252$	−1.61017e17	−0.157170
$253$	2.54619e17	0.241261
$254$	5.90484e16	0.0543195
$255$	−4.30213e17	−0.384266
$256$	1.06905e18	0.927252
$257$	3.40668e17	0.286968	0.143484	−	0.989653i	$-0.454169\pi$
$257$	3.40668e17	0.286968	0.143484	+	0.989653i	$0.454169\pi$
$258$	7.77022e16	0.0635749
$259$	3.05911e17	0.243135
$260$	−1.12570e18	−0.869205
$261$	7.84779e17	0.588767
$262$	−8.30249e16	−0.0605269
$263$	1.73688e18	1.23056	0.615278	−	0.788310i	$-0.289044\pi$
$263$	1.73688e18	1.23056	0.615278	+	0.788310i	$0.289044\pi$
$264$	−1.80566e17	−0.124338
$265$	9.82415e16	0.0657584
$266$	−4.27187e16	−0.0277975
$267$	1.85061e18	1.17080
$268$	1.10299e18	0.678520
$269$	−6.92293e17	−0.414141	−0.207070	−	0.978326i	$-0.566393\pi$
$269$	−6.92293e17	−0.414141	−0.207070	+	0.978326i	$0.566393\pi$
$270$	−1.47240e17	−0.0856636
$271$	1.90030e18	1.07536	0.537678	−	0.843151i	$-0.319302\pi$
$271$	1.90030e18	1.07536	0.537678	+	0.843151i	$0.319302\pi$
$272$	1.09677e18	0.603740
$273$	2.71994e17	0.145660
$274$	−1.27666e17	−0.0665188
$275$	−4.57563e16	−0.0231983
$276$	2.63792e17	0.130150
$277$	−2.34953e18	−1.12819	−0.564097	−	0.825709i	$-0.690776\pi$
$277$	−2.34953e18	−1.12819	−0.564097	+	0.825709i	$0.690776\pi$
$278$	2.53408e15	0.00118436
$279$	1.46400e18	0.666053
$280$	−1.00030e17	−0.0443041
$281$	3.08483e17	0.133025	0.0665125	−	0.997786i	$-0.478813\pi$
$281$	3.08483e17	0.133025	0.0665125	+	0.997786i	$0.478813\pi$
$282$	−1.10356e17	−0.0463371
$283$	−1.17091e17	−0.0478767	−0.0239384	−	0.999713i	$-0.507621\pi$
$283$	−1.17091e17	−0.0478767	−0.0239384	+	0.999713i	$0.507621\pi$
$284$	−5.93825e17	−0.236467
$285$	1.98631e18	0.770388
$286$	−2.32346e17	−0.0877787
$287$	8.92843e17	0.328595
$288$	4.29615e17	0.154041
$289$	−1.77157e18	−0.618905
$290$	2.42866e17	0.0826766
$291$	1.90033e18	0.630423
$292$	−5.16857e18	−1.67109
$293$	6.96748e17	0.219568	0.109784	−	0.993955i	$-0.464984\pi$
$293$	6.96748e17	0.219568	0.109784	+	0.993955i	$0.464984\pi$
$294$	−1.63522e17	−0.0502308
$295$	−3.47841e18	−1.04164
$296$	−5.43471e17	−0.158668
$297$	4.10116e18	1.16744
$298$	1.50340e17	0.0417304
$299$	6.81392e17	0.184443
$300$	−4.74046e16	−0.0125144
$301$	−1.19897e18	−0.308717
$302$	4.70874e17	0.118264
$303$	2.31213e18	0.566490
$304$	−5.06383e18	−1.21040
$305$	4.41556e18	1.02976
$306$	1.40674e17	0.0320113
$307$	8.47663e18	1.88228	0.941142	−	0.338010i	$-0.109754\pi$
$307$	8.47663e18	1.88228	0.941142	+	0.338010i	$0.109754\pi$
$308$	1.38795e18	0.300777
$309$	−5.70741e17	−0.120712
$310$	4.53065e17	0.0935293
$311$	3.27749e18	0.660448	0.330224	−	0.943903i	$-0.392876\pi$
$311$	3.27749e18	0.660448	0.330224	+	0.943903i	$0.392876\pi$
$312$	−4.83215e17	−0.0950564
$313$	4.42356e18	0.849550	0.424775	−	0.905299i	$-0.360353\pi$
$313$	4.42356e18	0.849550	0.424775	+	0.905299i	$0.360353\pi$
$314$	8.82253e16	0.0165432
$315$	8.56064e17	0.156739
$316$	−6.21261e18	−1.11076
$317$	−7.25075e18	−1.26601	−0.633007	−	0.774146i	$-0.718180\pi$
$317$	−7.25075e18	−1.26601	−0.633007	+	0.774146i	$0.718180\pi$
$318$	2.10076e16	0.00358240
$319$	−6.76471e18	−1.12673
$320$	−5.81764e18	−0.946502
$321$	−4.06623e18	−0.646255
$322$	3.01625e16	0.00468326
$323$	−5.03652e18	−0.764032
$324$	1.99822e17	0.0296180
$325$	−1.22449e17	−0.0177350
$326$	6.12693e17	0.0867183
$327$	2.08184e18	0.287965
$328$	−1.58619e18	−0.214438
$329$	1.70284e18	0.225011
$330$	4.78225e17	0.0617700
$331$	−9.59736e18	−1.21183	−0.605915	−	0.795529i	$-0.707193\pi$
$331$	−9.59736e18	−1.21183	−0.605915	+	0.795529i	$0.707193\pi$
$332$	6.96136e18	0.859327
$333$	4.65108e18	0.561335
$334$	1.63444e17	0.0192873
$335$	−5.86417e18	−0.676661
$336$	1.42722e18	0.161045
$337$	−1.63390e19	−1.80302	−0.901511	−	0.432757i	$-0.857541\pi$
$337$	−1.63390e19	−1.80302	−0.901511	+	0.432757i	$0.857541\pi$
$338$	1.72885e17	0.0186587
$339$	5.38287e18	0.568220
$340$	−5.87495e18	−0.606614
$341$	−1.26195e19	−1.27463
$342$	−6.49497e17	−0.0641773
$343$	5.23218e18	0.505797
$344$	2.13005e18	0.201466
$345$	−1.40247e18	−0.129793
$346$	8.32202e17	0.0753630
$347$	3.61515e18	0.320372	0.160186	−	0.987087i	$-0.448791\pi$
$347$	3.61515e18	0.320372	0.160186	+	0.987087i	$0.448791\pi$
$348$	−7.00841e18	−0.607820
$349$	5.70564e18	0.484299	0.242150	−	0.970239i	$-0.422148\pi$
$349$	5.70564e18	0.484299	0.242150	+	0.970239i	$0.422148\pi$
$350$	−5.42034e15	−0.000450315 0
$351$	1.09752e19	0.892502
$352$	−3.70324e18	−0.294789
$353$	9.02400e18	0.703216	0.351608	−	0.936147i	$-0.385635\pi$
$353$	9.02400e18	0.703216	0.351608	+	0.936147i	$0.385635\pi$
$354$	−7.43813e17	−0.0567465
$355$	3.15713e18	0.235819
$356$	2.52718e19	1.84825
$357$	1.41952e18	0.101655
$358$	3.77491e17	0.0264718
$359$	−1.22515e19	−0.841360	−0.420680	−	0.907209i	$-0.638208\pi$
$359$	−1.22515e19	−0.841360	−0.420680	+	0.907209i	$0.638208\pi$
$360$	−1.52085e18	−0.102287
$361$	8.07262e18	0.531754
$362$	1.65664e18	0.106884
$363$	−3.37054e18	−0.213010
$364$	3.71433e18	0.229943
$365$	2.74792e19	1.66651
$366$	9.44209e17	0.0560996
$367$	−8.77650e18	−0.510888	−0.255444	−	0.966824i	$-0.582222\pi$
$367$	−8.77650e18	−0.510888	−0.255444	+	0.966824i	$0.582222\pi$
$368$	3.57543e18	0.203924
$369$	1.35748e19	0.758640
$370$	1.43938e18	0.0788245
$371$	−3.24155e17	−0.0173960
$372$	−1.30741e19	−0.687607
$373$	−2.91891e19	−1.50454	−0.752272	−	0.658852i	$-0.771042\pi$
$373$	−2.91891e19	−1.50454	−0.752272	+	0.658852i	$0.771042\pi$
$374$	−1.21260e18	−0.0612603
$375$	1.28224e19	0.634945
$376$	−3.02520e18	−0.146840
$377$	−1.81032e19	−0.861381
$378$	4.85828e17	0.0226618
$379$	3.02442e18	0.138308	0.0691541	−	0.997606i	$-0.477970\pi$
$379$	3.02442e18	0.138308	0.0691541	+	0.997606i	$0.477970\pi$
$380$	2.71248e19	1.21616
$381$	9.05928e18	0.398251
$382$	2.82113e18	0.121604
$383$	7.88658e18	0.333348	0.166674	−	0.986012i	$-0.446697\pi$
$383$	7.88658e18	0.333348	0.166674	+	0.986012i	$0.446697\pi$
$384$	−5.10910e18	−0.211768
$385$	−7.37918e18	−0.299953
$386$	−7.25240e16	−0.00289119
$387$	−1.82292e19	−0.712747
$388$	2.59508e19	0.995206
$389$	3.05090e19	1.14764	0.573820	−	0.818982i	$-0.305461\pi$
$389$	3.05090e19	1.14764	0.573820	+	0.818982i	$0.305461\pi$
$390$	1.27979e18	0.0472230
$391$	3.55614e18	0.128722
$392$	−4.48263e18	−0.159179
$393$	−1.27378e19	−0.443762
$394$	−3.87934e18	−0.132598
$395$	3.30299e19	1.10772
$396$	2.11025e19	0.694416
$397$	−3.26053e19	−1.05283	−0.526417	−	0.850227i	$-0.676465\pi$
$397$	−3.26053e19	−1.05283	−0.526417	+	0.850227i	$0.676465\pi$
$398$	−5.10042e18	−0.161616
$399$	−6.55396e18	−0.203802
$400$	−6.42522e17	−0.0196082
$401$	−2.53256e19	−0.758536	−0.379268	−	0.925287i	$-0.623824\pi$
$401$	−2.53256e19	−0.758536	−0.379268	+	0.925287i	$0.623824\pi$
$402$	−1.25398e18	−0.0368633
$403$	−3.37714e19	−0.974452
$404$	3.15742e19	0.894278
$405$	−1.06237e18	−0.0295368
$406$	−8.01356e17	−0.0218716
$407$	−4.00918e19	−1.07423
$408$	−2.52187e18	−0.0663394
$409$	4.20753e19	1.08668	0.543340	−	0.839512i	$-0.317159\pi$
$409$	4.20753e19	1.08668	0.543340	+	0.839512i	$0.317159\pi$
$410$	4.20101e18	0.106531
$411$	−1.95866e19	−0.487692
$412$	−7.79399e18	−0.190560
$413$	1.14773e19	0.275559
$414$	4.58591e17	0.0108124
$415$	−3.70107e19	−0.856973
$416$	−9.91031e18	−0.225365
$417$	3.88781e17	0.00868330
$418$	5.59860e18	0.122817
$419$	1.65077e19	0.355698	0.177849	−	0.984058i	$-0.443086\pi$
$419$	1.65077e19	0.355698	0.177849	+	0.984058i	$0.443086\pi$
$420$	−7.64501e18	−0.161811
$421$	−6.68850e18	−0.139063	−0.0695317	−	0.997580i	$-0.522150\pi$
$421$	−6.68850e18	−0.139063	−0.0695317	+	0.997580i	$0.522150\pi$
$422$	−1.69001e18	−0.0345180
$423$	2.58900e19	0.519492
$424$	5.75883e17	0.0113525
$425$	−6.39055e17	−0.0123772
$426$	6.75109e17	0.0128470
$427$	−1.45695e19	−0.272418
$428$	−5.55281e19	−1.02020
$429$	−3.56468e19	−0.643562
$430$	−5.64141e18	−0.100086
$431$	−2.77311e19	−0.483490	−0.241745	−	0.970340i	$-0.577720\pi$
$431$	−2.77311e19	−0.483490	−0.241745	+	0.970340i	$0.577720\pi$
$432$	5.75895e19	0.986769
$433$	−9.57361e19	−1.61219	−0.806095	−	0.591786i	$-0.798423\pi$
$433$	−9.57361e19	−1.61219	−0.806095	+	0.591786i	$0.798423\pi$
$434$	−1.49492e18	−0.0247426
$435$	3.72609e19	0.606155
$436$	2.84295e19	0.454590
$437$	−1.64188e19	−0.258066
$438$	5.87605e18	0.0907883
$439$	−3.44721e19	−0.523580	−0.261790	−	0.965125i	$-0.584313\pi$
$439$	−3.44721e19	−0.523580	−0.261790	+	0.965125i	$0.584313\pi$
$440$	1.31096e19	0.195747
$441$	3.83628e19	0.563145
$442$	−3.24506e18	−0.0468334
$443$	−5.95698e19	−0.845276	−0.422638	−	0.906299i	$-0.638896\pi$
$443$	−5.95698e19	−0.845276	−0.422638	+	0.906299i	$0.638896\pi$
$444$	−4.15361e19	−0.579501
$445$	−1.34360e20	−1.84319
$446$	−1.13827e19	−0.153545
$447$	2.30654e19	0.305953
$448$	1.91957e19	0.250391
$449$	8.94789e19	1.14782	0.573909	−	0.818919i	$-0.305426\pi$
$449$	8.94789e19	1.14782	0.573909	+	0.818919i	$0.305426\pi$
$450$	−8.24111e16	−0.00103966
$451$	−1.17013e20	−1.45182
$452$	7.35081e19	0.897009
$453$	7.22421e19	0.867070
$454$	1.05043e19	0.124008
$455$	−1.97476e19	−0.229313
$456$	1.16436e19	0.132999
$457$	5.79286e19	0.650911	0.325456	−	0.945557i	$-0.394482\pi$
$457$	5.79286e19	0.650911	0.325456	+	0.945557i	$0.394482\pi$
$458$	4.50473e18	0.0497941
$459$	5.72789e19	0.622873
$460$	−1.91521e19	−0.204895
$461$	8.38609e19	0.882678	0.441339	−	0.897340i	$-0.354504\pi$
$461$	8.38609e19	0.882678	0.441339	+	0.897340i	$0.354504\pi$
$462$	−1.57794e18	−0.0163409
$463$	2.95297e18	0.0300886	0.0150443	−	0.999887i	$-0.495211\pi$
$463$	2.95297e18	0.0300886	0.0150443	+	0.999887i	$0.495211\pi$
$464$	−9.49919e19	−0.952361
$465$	6.95098e19	0.685723
$466$	−1.65691e19	−0.160844
$467$	5.77022e19	0.551209	0.275604	−	0.961271i	$-0.411122\pi$
$467$	5.77022e19	0.551209	0.275604	+	0.961271i	$0.411122\pi$
$468$	5.64728e19	0.530879
$469$	1.93493e19	0.179006
$470$	8.01220e18	0.0729487
$471$	1.35356e19	0.121289
$472$	−2.03902e19	−0.179827
$473$	1.57134e20	1.36399
$474$	7.06301e18	0.0603465
$475$	2.95054e18	0.0248141
$476$	1.93849e19	0.160476
$477$	−4.92847e18	−0.0401628
$478$	−7.73395e18	−0.0620429
$479$	2.01251e20	1.58936	0.794679	−	0.607030i	$-0.207639\pi$
$479$	2.01251e20	1.58936	0.794679	+	0.607030i	$0.207639\pi$
$480$	2.03979e19	0.158590
$481$	−1.07291e20	−0.821247
$482$	7.84995e18	0.0591581
$483$	4.62756e18	0.0343359
$484$	−4.60279e19	−0.336264
$485$	−1.37970e20	−0.992479
$486$	1.19899e19	0.0849264
$487$	9.71386e19	0.677524	0.338762	−	0.940872i	$-0.389992\pi$
$487$	9.71386e19	0.677524	0.338762	+	0.940872i	$0.389992\pi$
$488$	2.58837e19	0.177778
$489$	9.40001e19	0.635787
$490$	1.18722e19	0.0790787
$491$	2.68546e19	0.176160	0.0880801	−	0.996113i	$-0.471927\pi$
$491$	2.68546e19	0.176160	0.0880801	+	0.996113i	$0.471927\pi$
$492$	−1.21229e20	−0.783191
$493$	−9.44794e19	−0.601153
$494$	1.49825e19	0.0938930
$495$	−1.12193e20	−0.692513
$496$	−1.77206e20	−1.07738
$497$	−1.04172e19	−0.0623846
$498$	−7.91425e18	−0.0466863
$499$	2.95204e20	1.71541	0.857707	−	0.514139i	$-0.171889\pi$
$499$	2.95204e20	1.71541	0.857707	+	0.514139i	$0.171889\pi$
$500$	1.75102e20	1.00234
$501$	2.50758e19	0.141408
$502$	1.62772e19	0.0904280
$503$	2.01194e19	0.110117	0.0550585	−	0.998483i	$-0.482465\pi$
$503$	2.01194e19	0.110117	0.0550585	+	0.998483i	$0.482465\pi$
$504$	5.01817e18	0.0270593
$505$	−1.67867e20	−0.891828
$506$	−3.95301e18	−0.0206918
$507$	2.65242e19	0.136799
$508$	1.23713e20	0.628691
$509$	−1.85913e20	−0.930949	−0.465475	−	0.885061i	$-0.654116\pi$
$509$	−1.85913e20	−0.930949	−0.465475	+	0.885061i	$0.654116\pi$
$510$	6.67913e18	0.0329567
$511$	−9.06696e19	−0.440864
$512$	−8.68836e19	−0.416307
$513$	−2.64458e20	−1.24875
$514$	−5.28893e18	−0.0246119
$515$	4.14375e19	0.190037
$516$	1.62795e20	0.735813
$517$	−2.23169e20	−0.994156
$518$	−4.74933e18	−0.0208525
$519$	1.27678e20	0.552534
$520$	3.50829e19	0.149648
$521$	3.26698e20	1.37361	0.686806	−	0.726841i	$-0.259012\pi$
$521$	3.26698e20	1.37361	0.686806	+	0.726841i	$0.259012\pi$
$522$	−1.21838e19	−0.0504958
$523$	3.03905e19	0.124158	0.0620791	−	0.998071i	$-0.480227\pi$
$523$	3.03905e19	0.124158	0.0620791	+	0.998071i	$0.480227\pi$
$524$	−1.73946e20	−0.700536
$525$	−8.31596e17	−0.00330155
$526$	−2.69654e19	−0.105539
$527$	−1.76250e20	−0.680065
$528$	−1.87047e20	−0.711536
$529$	1.15928e19	0.0434783
$530$	−1.52522e18	−0.00563979
$531$	1.74501e20	0.636194
$532$	−8.95005e19	−0.321727
$533$	−3.13142e20	−1.10991
$534$	−2.87311e19	−0.100414
$535$	2.95220e20	1.01740
$536$	−3.43753e19	−0.116818
$537$	5.79151e19	0.194082
$538$	1.07480e19	0.0355189
$539$	−3.30683e20	−1.07770
$540$	−3.08483e20	−0.991467
$541$	−3.97691e20	−1.26057	−0.630285	−	0.776364i	$-0.717062\pi$
$541$	−3.97691e20	−1.26057	−0.630285	+	0.776364i	$0.717062\pi$
$542$	−2.95025e19	−0.0922282
$543$	2.54164e20	0.783637
$544$	−5.17213e19	−0.157281
$545$	−1.51148e20	−0.453344
$546$	−4.22276e18	−0.0124926
$547$	2.73763e20	0.798860	0.399430	−	0.916764i	$-0.369208\pi$
$547$	2.73763e20	0.798860	0.399430	+	0.916764i	$0.369208\pi$
$548$	−2.67473e20	−0.769886
$549$	−2.21515e20	−0.628942
$550$	7.10375e17	0.00198961
$551$	4.36214e20	1.20521
$552$	−8.22117e18	−0.0224074
$553$	−1.08985e20	−0.293040
$554$	3.64770e19	0.0967599
$555$	2.20831e20	0.577913
$556$	5.30917e18	0.0137077
$557$	2.85130e20	0.726322	0.363161	−	0.931726i	$-0.381698\pi$
$557$	2.85130e20	0.726322	0.363161	+	0.931726i	$0.381698\pi$
$558$	−2.27288e19	−0.0571243
$559$	4.20510e20	1.04277
$560$	−1.03620e20	−0.253533
$561$	−1.86038e20	−0.449139
$562$	−4.78925e18	−0.0114089
$563$	2.79342e20	0.656635	0.328317	−	0.944567i	$-0.393518\pi$
$563$	2.79342e20	0.656635	0.328317	+	0.944567i	$0.393518\pi$
$564$	−2.31208e20	−0.536303
$565$	−3.90813e20	−0.894551
$566$	1.81786e18	0.00410617
$567$	3.50537e18	0.00781378
$568$	1.85068e19	0.0407117
$569$	−4.50453e20	−0.977929	−0.488964	−	0.872304i	$-0.662625\pi$
$569$	−4.50453e20	−0.977929	−0.488964	+	0.872304i	$0.662625\pi$
$570$	−3.08378e19	−0.0660726
$571$	5.91705e20	1.25122	0.625611	−	0.780135i	$-0.284850\pi$
$571$	5.91705e20	1.25122	0.625611	+	0.780135i	$0.284850\pi$
$572$	−4.86790e20	−1.01595
$573$	4.32822e20	0.891557
$574$	−1.38615e19	−0.0281820
$575$	−2.08329e18	−0.00418062
$576$	2.91852e20	0.578089
$577$	6.28034e20	1.22790	0.613952	−	0.789343i	$-0.289579\pi$
$577$	6.28034e20	1.22790	0.613952	+	0.789343i	$0.289579\pi$
$578$	2.75039e19	0.0530806
$579$	−1.11267e19	−0.0211972
$580$	5.08832e20	0.956895
$581$	1.22120e20	0.226707
$582$	−2.95030e19	−0.0540685
$583$	4.24829e19	0.0768599
$584$	1.61081e20	0.287705
$585$	−3.00243e20	−0.529424
$586$	−1.08171e19	−0.0188313
$587$	6.47715e20	1.11326	0.556632	−	0.830759i	$-0.312093\pi$
$587$	6.47715e20	1.11326	0.556632	+	0.830759i	$0.312093\pi$
$588$	−3.42596e20	−0.581369
$589$	8.13754e20	1.36342
$590$	5.40030e19	0.0893363
$591$	−5.95173e20	−0.972158
$592$	−5.62980e20	−0.907988
$593$	−6.72773e20	−1.07142	−0.535708	−	0.844403i	$-0.679955\pi$
$593$	−6.72773e20	−1.07142	−0.535708	+	0.844403i	$0.679955\pi$
$594$	−6.36712e19	−0.100126
$595$	−1.03061e20	−0.160036
$596$	3.14979e20	0.482986
$597$	−7.82514e20	−1.18491
$598$	−1.05787e19	−0.0158188
$599$	−1.08185e21	−1.59759	−0.798793	−	0.601607i	$-0.794528\pi$
$599$	−1.08185e21	−1.59759	−0.798793	+	0.601607i	$0.794528\pi$
$600$	1.47739e18	0.00215456
$601$	9.33536e20	1.34454	0.672268	−	0.740308i	$-0.265320\pi$
$601$	9.33536e20	1.34454	0.672268	+	0.740308i	$0.265320\pi$
$602$	1.86143e19	0.0264772
$603$	2.94187e20	0.413280
$604$	9.86533e20	1.36878
$605$	2.44712e20	0.335343
$606$	−3.58962e19	−0.0485852
$607$	1.17377e21	1.56916	0.784578	−	0.620030i	$-0.212879\pi$
$607$	1.17377e21	1.56916	0.784578	+	0.620030i	$0.212879\pi$
$608$	2.38799e20	0.315323
$609$	−1.22945e20	−0.160355
$610$	−6.85524e19	−0.0883180
$611$	−5.97227e20	−0.760030
$612$	2.94728e20	0.370498
$613$	1.00029e20	0.124215	0.0621073	−	0.998069i	$-0.480218\pi$
$613$	1.00029e20	0.124215	0.0621073	+	0.998069i	$0.480218\pi$
$614$	−1.31601e20	−0.161435
$615$	6.44524e20	0.781045
$616$	−4.32561e19	−0.0517836
$617$	1.34327e21	1.58864	0.794321	−	0.607498i	$-0.207827\pi$
$617$	1.34327e21	1.58864	0.794321	+	0.607498i	$0.207827\pi$
$618$	8.86086e18	0.0103529
$619$	−1.02245e21	−1.18022	−0.590109	−	0.807324i	$-0.700915\pi$
$619$	−1.02245e21	−1.18022	−0.590109	+	0.807324i	$0.700915\pi$
$620$	9.49221e20	1.08250
$621$	1.86726e20	0.210387
$622$	−5.08837e19	−0.0566436
$623$	4.43331e20	0.487605
$624$	−5.00561e20	−0.543967
$625$	−9.12276e20	−0.979548
$626$	−6.86765e19	−0.0728619
$627$	8.58944e20	0.900447
$628$	1.84842e20	0.191471
$629$	−5.59943e20	−0.573144
$630$	−1.32906e19	−0.0134428
$631$	−1.08624e21	−1.08569	−0.542843	−	0.839834i	$-0.682652\pi$
$631$	−1.08624e21	−1.08569	−0.542843	+	0.839834i	$0.682652\pi$
$632$	1.93618e20	0.191236
$633$	−2.59283e20	−0.253073
$634$	1.12569e20	0.108580
$635$	−6.57731e20	−0.626968
$636$	4.40133e19	0.0414625
$637$	−8.84948e20	−0.823895
$638$	1.05023e20	0.0966342
$639$	−1.58383e20	−0.144030
$640$	3.70936e20	0.333387
$641$	1.60485e20	0.142561	0.0712805	−	0.997456i	$-0.477291\pi$
$641$	1.60485e20	0.142561	0.0712805	+	0.997456i	$0.477291\pi$
$642$	6.31289e19	0.0554263
$643$	−2.74963e19	−0.0238611	−0.0119306	−	0.999929i	$-0.503798\pi$
$643$	−2.74963e19	−0.0238611	−0.0119306	+	0.999929i	$0.503798\pi$
$644$	6.31937e19	0.0542038
$645$	−8.65513e20	−0.733796
$646$	7.81928e19	0.0655274
$647$	−1.81886e21	−1.50667	−0.753335	−	0.657638i	$-0.771556\pi$
$647$	−1.81886e21	−1.50667	−0.753335	+	0.657638i	$0.771556\pi$
$648$	−6.22753e18	−0.00509921
$649$	−1.50418e21	−1.21749
$650$	1.90105e18	0.00152105
$651$	−2.29353e20	−0.181404
$652$	1.28366e21	1.00367
$653$	−2.24645e21	−1.73639	−0.868196	−	0.496222i	$-0.834720\pi$
$653$	−2.24645e21	−1.73639	−0.868196	+	0.496222i	$0.834720\pi$
$654$	−3.23209e19	−0.0246974
$655$	9.24801e20	0.698616
$656$	−1.64313e21	−1.22714
$657$	−1.37854e21	−1.01784
$658$	−2.64369e19	−0.0192981
$659$	−2.35248e20	−0.169779	−0.0848897	−	0.996390i	$-0.527054\pi$
$659$	−2.35248e20	−0.169779	−0.0848897	+	0.996390i	$0.527054\pi$
$660$	1.00193e21	0.714923
$661$	3.81833e20	0.269378	0.134689	−	0.990888i	$-0.456996\pi$
$661$	3.81833e20	0.269378	0.134689	+	0.990888i	$0.456996\pi$
$662$	1.49001e20	0.103933
$663$	−4.97861e20	−0.343365
$664$	−2.16954e20	−0.147947
$665$	4.75838e20	0.320846
$666$	−7.22089e19	−0.0481431
$667$	−3.07998e20	−0.203051
$668$	3.42434e20	0.223230
$669$	−1.74636e21	−1.12574
$670$	9.10424e19	0.0580340
$671$	1.90943e21	1.20361
$672$	−6.73043e19	−0.0419540
$673$	5.34419e20	0.329435	0.164717	−	0.986341i	$-0.447329\pi$
$673$	5.34419e20	0.329435	0.164717	+	0.986341i	$0.447329\pi$
$674$	2.53666e20	0.154637
$675$	−3.35556e19	−0.0202296
$676$	3.62213e20	0.215955
$677$	−1.66665e21	−0.982719	−0.491360	−	0.870957i	$-0.663500\pi$
$677$	−1.66665e21	−0.982719	−0.491360	+	0.870957i	$0.663500\pi$
$678$	−8.35701e19	−0.0487336
$679$	4.55242e20	0.262554
$680$	1.83095e20	0.104438
$681$	1.61159e21	0.909181
$682$	1.95920e20	0.109319
$683$	1.71560e21	0.946804	0.473402	−	0.880846i	$-0.343026\pi$
$683$	1.71560e21	0.946804	0.473402	+	0.880846i	$0.343026\pi$
$684$	−1.36077e21	−0.742785
$685$	1.42205e21	0.767776
$686$	−8.12305e19	−0.0433799
$687$	6.91122e20	0.365072
$688$	2.20652e21	1.15291
$689$	1.13689e20	0.0587592
$690$	2.17736e19	0.0111317
$691$	6.30779e20	0.319001	0.159500	−	0.987198i	$-0.449012\pi$
$691$	6.30779e20	0.319001	0.159500	+	0.987198i	$0.449012\pi$
$692$	1.74356e21	0.872248
$693$	3.70190e20	0.183200
$694$	−5.61258e19	−0.0274768
$695$	−2.82267e19	−0.0136702
$696$	2.18420e20	0.104646
$697$	−1.63427e21	−0.774600
$698$	−8.85811e19	−0.0415361
$699$	−2.54205e21	−1.17925
$700$	−1.13562e19	−0.00521193
$701$	1.03695e21	0.470841	0.235421	−	0.971894i	$-0.424353\pi$
$701$	1.03695e21	0.470841	0.235421	+	0.971894i	$0.424353\pi$
$702$	−1.70392e20	−0.0765457
$703$	2.58527e21	1.14906
$704$	−2.51574e21	−1.10629
$705$	1.22924e21	0.534834
$706$	−1.40099e20	−0.0603115
$707$	5.53891e20	0.235928
$708$	−1.55837e21	−0.656781
$709$	−2.16562e21	−0.903100	−0.451550	−	0.892246i	$-0.649129\pi$
$709$	−2.16562e21	−0.903100	−0.451550	+	0.892246i	$0.649129\pi$
$710$	−4.90150e19	−0.0202251
$711$	−1.65701e21	−0.676554
$712$	−7.87607e20	−0.318207
$713$	−5.74568e20	−0.229705
$714$	−2.20383e19	−0.00871850
$715$	2.58806e21	1.01316
$716$	7.90884e20	0.306383
$717$	−1.18655e21	−0.454876
$718$	1.90207e20	0.0721595
$719$	−5.96459e19	−0.0223931	−0.0111965	−	0.999937i	$-0.503564\pi$
$719$	−5.96459e19	−0.0223931	−0.0111965	+	0.999937i	$0.503564\pi$
$720$	−1.57545e21	−0.585343
$721$	−1.36726e20	−0.0502733
$722$	−1.25329e20	−0.0456061
$723$	1.20435e21	0.433726
$724$	3.47084e21	1.23707
$725$	5.53488e19	0.0195242
$726$	5.23283e19	0.0182689
$727$	−1.44311e21	−0.498646	−0.249323	−	0.968420i	$-0.580208\pi$
$727$	−1.44311e21	−0.498646	−0.249323	+	0.968420i	$0.580208\pi$
$728$	−1.15759e20	−0.0395884
$729$	1.92765e21	0.652487
$730$	−4.26619e20	−0.142929
$731$	2.19461e21	0.727742
$732$	1.97822e21	0.649295
$733$	1.99977e21	0.649682	0.324841	−	0.945769i	$-0.394689\pi$
$733$	1.99977e21	0.649682	0.324841	+	0.945769i	$0.394689\pi$
$734$	1.36257e20	0.0438165
$735$	1.82144e21	0.579776
$736$	−1.68609e20	−0.0531247
$737$	−2.53586e21	−0.790896
$738$	−2.10751e20	−0.0650650
$739$	4.98840e21	1.52450	0.762252	−	0.647281i	$-0.224094\pi$
$739$	4.98840e21	1.52450	0.762252	+	0.647281i	$0.224094\pi$
$740$	3.01565e21	0.912311
$741$	2.29864e21	0.688390
$742$	5.03257e18	0.00149197
$743$	−3.33069e21	−0.977502	−0.488751	−	0.872423i	$-0.662547\pi$
$743$	−3.33069e21	−0.977502	−0.488751	+	0.872423i	$0.662547\pi$
$744$	4.07461e20	0.118383
$745$	−1.67462e21	−0.481663
$746$	4.53167e20	0.129038
$747$	1.85671e21	0.523408
$748$	−2.54052e21	−0.709024
$749$	−9.74101e20	−0.269148
$750$	−1.99071e20	−0.0544563
$751$	5.76438e21	1.56118	0.780591	−	0.625042i	$-0.214918\pi$
$751$	5.76438e21	1.56118	0.780591	+	0.625042i	$0.214918\pi$
$752$	−3.13380e21	−0.840305
$753$	2.49728e21	0.662986
$754$	2.81056e20	0.0738766
$755$	−5.24500e21	−1.36503
$756$	1.01786e21	0.262287
$757$	2.54721e21	0.649899	0.324949	−	0.945731i	$-0.394653\pi$
$757$	2.54721e21	0.649899	0.324949	+	0.945731i	$0.394653\pi$
$758$	−4.69547e19	−0.0118620
$759$	−6.06475e20	−0.151705
$760$	−8.45357e20	−0.209381
$761$	−7.84587e21	−1.92423	−0.962114	−	0.272649i	$-0.912100\pi$
$761$	−7.84587e21	−1.92423	−0.962114	+	0.272649i	$0.912100\pi$
$762$	−1.40647e20	−0.0341561
$763$	4.98724e20	0.119930
$764$	5.91058e21	1.40744
$765$	−1.56695e21	−0.369483
$766$	−1.22441e20	−0.0285897
$767$	−4.02537e21	−0.930767
$768$	−2.54636e21	−0.583057
$769$	−2.63103e21	−0.596594	−0.298297	−	0.954473i	$-0.596419\pi$
$769$	−2.63103e21	−0.596594	−0.298297	+	0.954473i	$0.596419\pi$
$770$	1.14563e20	0.0257255
$771$	−8.11435e20	−0.180445
$772$	−1.51946e20	−0.0334625
$773$	−6.36115e21	−1.38736	−0.693680	−	0.720283i	$-0.744012\pi$
$773$	−6.36115e21	−1.38736	−0.693680	+	0.720283i	$0.744012\pi$
$774$	2.83012e20	0.0611290
$775$	1.03253e20	0.0220871
$776$	−8.08768e20	−0.171341
$777$	−7.28648e20	−0.152883
$778$	−4.73657e20	−0.0984277
$779$	7.54547e21	1.55294
$780$	2.68130e21	0.546557
$781$	1.36525e21	0.275631
$782$	−5.52097e19	−0.0110399
$783$	−4.96094e21	−0.982541
$784$	−4.64354e21	−0.910916
$785$	−9.82728e20	−0.190946
$786$	1.97756e20	0.0380594
$787$	−3.24939e21	−0.619429	−0.309715	−	0.950830i	$-0.600234\pi$
$787$	−3.24939e21	−0.619429	−0.309715	+	0.950830i	$0.600234\pi$
$788$	−8.12764e21	−1.53468
$789$	−4.13706e21	−0.773775
$790$	−5.12795e20	−0.0950038
$791$	1.28952e21	0.236648
$792$	−6.57667e20	−0.119555
$793$	5.10988e21	0.920157
$794$	5.06204e20	0.0902966
$795$	−2.34001e20	−0.0413489
$796$	−1.06859e22	−1.87053
$797$	−4.07921e21	−0.707356	−0.353678	−	0.935367i	$-0.615069\pi$
$797$	−4.07921e21	−0.707356	−0.353678	+	0.935367i	$0.615069\pi$
$798$	1.01752e20	0.0174791
$799$	−3.11689e21	−0.530421
$800$	3.02998e19	0.00510817
$801$	6.74042e21	1.12575
$802$	3.93184e20	0.0650561
$803$	1.18829e22	1.94785
$804$	−2.62722e21	−0.426654
$805$	−3.35975e20	−0.0540553
$806$	5.24307e20	0.0835743
$807$	1.64897e21	0.260412
$808$	−9.84024e20	−0.153964
$809$	1.06709e22	1.65419	0.827096	−	0.562060i	$-0.189991\pi$
$809$	1.06709e22	1.65419	0.827096	+	0.562060i	$0.189991\pi$
$810$	1.64935e19	0.00253323
$811$	9.04661e21	1.37667	0.688334	−	0.725394i	$-0.258342\pi$
$811$	9.04661e21	1.37667	0.688334	+	0.725394i	$0.258342\pi$
$812$	−1.67893e21	−0.253141
$813$	−4.52631e21	−0.676184
$814$	6.22433e20	0.0921318
$815$	−6.82469e21	−1.00092
$816$	−2.61240e21	−0.379632
$817$	−1.01326e22	−1.45900
$818$	−6.53226e20	−0.0931996
$819$	9.90675e20	0.140056
$820$	8.80157e21	1.23298
$821$	4.88369e21	0.677914	0.338957	−	0.940802i	$-0.389926\pi$
$821$	4.88369e21	0.677914	0.338957	+	0.940802i	$0.389926\pi$
$822$	3.04086e20	0.0418271
$823$	3.41416e21	0.465355	0.232678	−	0.972554i	$-0.425251\pi$
$823$	3.41416e21	0.465355	0.232678	+	0.972554i	$0.425251\pi$
$824$	2.42903e20	0.0328079
$825$	1.08987e20	0.0145871
$826$	−1.78187e20	−0.0236334
$827$	1.19362e22	1.56882	0.784411	−	0.620242i	$-0.212965\pi$
$827$	1.19362e22	1.56882	0.784411	+	0.620242i	$0.212965\pi$
$828$	9.60799e20	0.125143
$829$	−1.04497e22	−1.34879	−0.674396	−	0.738370i	$-0.735596\pi$
$829$	−1.04497e22	−1.34879	−0.674396	+	0.738370i	$0.735596\pi$
$830$	5.74599e20	0.0734986
$831$	5.59634e21	0.709409
$832$	−6.73242e21	−0.845759
$833$	−4.61849e21	−0.574992
$834$	−6.03590e18	−0.000744726 0
$835$	−1.82058e21	−0.222619
$836$	1.17297e22	1.42147
$837$	−9.25459e21	−1.11152
$838$	−2.56285e20	−0.0305065
$839$	1.58332e22	1.86790	0.933949	−	0.357406i	$-0.116339\pi$
$839$	1.58332e22	1.86790	0.933949	+	0.357406i	$0.116339\pi$
$840$	2.38260e20	0.0278584
$841$	−4.46295e20	−0.0517193
$842$	1.03840e20	0.0119268
$843$	−7.34773e20	−0.0836462
$844$	−3.54075e21	−0.399509
$845$	−1.92574e21	−0.215364
$846$	−4.01947e20	−0.0445544
$847$	−8.07444e20	−0.0887129
$848$	5.96556e20	0.0649654
$849$	2.78898e20	0.0301049
$850$	9.92145e18	0.00106153
$851$	−1.82539e21	−0.193590
$852$	1.41443e21	0.148691
$853$	1.41353e21	0.147295	0.0736476	−	0.997284i	$-0.476536\pi$
$853$	1.41353e21	0.147295	0.0736476	+	0.997284i	$0.476536\pi$
$854$	2.26194e20	0.0233640
$855$	7.23465e21	0.740750
$856$	1.73056e21	0.175644
$857$	1.52956e22	1.53890	0.769450	−	0.638707i	$-0.220531\pi$
$857$	1.52956e22	1.53890	0.769450	+	0.638707i	$0.220531\pi$
$858$	5.53423e20	0.0551953
$859$	1.10126e22	1.08878	0.544391	−	0.838831i	$-0.316761\pi$
$859$	1.10126e22	1.08878	0.544391	+	0.838831i	$0.316761\pi$
$860$	−1.18194e22	−1.15839
$861$	−2.12666e21	−0.206621
$862$	4.30531e20	0.0414667
$863$	−8.37870e21	−0.800011	−0.400005	−	0.916513i	$-0.630992\pi$
$863$	−8.37870e21	−0.800011	−0.400005	+	0.916513i	$0.630992\pi$
$864$	−2.71579e21	−0.257065
$865$	−9.26977e21	−0.869858
$866$	1.48632e21	0.138270
$867$	4.21969e21	0.389168
$868$	−3.13203e21	−0.286370
$869$	1.42832e22	1.29473
$870$	−5.78482e20	−0.0519871
$871$	−6.78628e21	−0.604638
$872$	−8.86016e20	−0.0782650
$873$	6.92152e21	0.606170
$874$	2.54905e20	0.0221331
$875$	3.07173e21	0.264438
$876$	1.23110e22	1.05078
$877$	3.30841e21	0.279977	0.139989	−	0.990153i	$-0.455293\pi$
$877$	3.30841e21	0.279977	0.139989	+	0.990153i	$0.455293\pi$
$878$	5.35185e20	0.0449051
$879$	−1.65958e21	−0.138064
$880$	1.35802e22	1.12018
$881$	−1.49480e22	−1.22254	−0.611272	−	0.791421i	$-0.709342\pi$
$881$	−1.49480e22	−1.22254	−0.611272	+	0.791421i	$0.709342\pi$
$882$	−5.95589e20	−0.0482984
$883$	−1.27760e21	−0.102728	−0.0513641	−	0.998680i	$-0.516357\pi$
$883$	−1.27760e21	−0.102728	−0.0513641	+	0.998680i	$0.516357\pi$
$884$	−6.79875e21	−0.542047
$885$	8.28521e21	0.654982
$886$	9.24833e20	0.0724954
$887$	−1.50330e22	−1.16848	−0.584238	−	0.811582i	$-0.698607\pi$
$887$	−1.50330e22	−1.16848	−0.584238	+	0.811582i	$0.698607\pi$
$888$	1.29449e21	0.0997704
$889$	2.17023e21	0.165861
$890$	2.08596e21	0.158082
$891$	−4.59404e20	−0.0345233
$892$	−2.38481e22	−1.77712
$893$	1.43908e22	1.06340
$894$	−3.58094e20	−0.0262401
$895$	−4.20481e21	−0.305544
$896$	−1.22393e21	−0.0881956
$897$	−1.62300e21	−0.115978
$898$	−1.38918e21	−0.0984430
$899$	1.52651e22	1.07276
$900$	−1.72660e20	−0.0120330
$901$	5.93337e20	0.0410077
$902$	1.81665e21	0.124515
$903$	2.85582e21	0.194121
$904$	−2.29091e21	−0.154435
$905$	−1.84531e22	−1.23368
$906$	−1.12157e21	−0.0743645
$907$	−2.51696e22	−1.65509	−0.827545	−	0.561399i	$-0.810263\pi$
$907$	−2.51696e22	−1.65509	−0.827545	+	0.561399i	$0.810263\pi$
$908$	2.20077e22	1.43526
$909$	8.42138e21	0.544696
$910$	3.06585e20	0.0196671
$911$	2.89389e22	1.84117	0.920585	−	0.390541i	$-0.127712\pi$
$911$	2.89389e22	1.84117	0.920585	+	0.390541i	$0.127712\pi$
$912$	1.20615e22	0.761098
$913$	−1.60047e22	−1.00165
$914$	−8.99353e20	−0.0558256
$915$	−1.05174e22	−0.647516
$916$	9.43791e21	0.576315
$917$	−3.05145e21	−0.184815
$918$	−8.89265e20	−0.0534209
$919$	−3.07511e22	−1.83229	−0.916144	−	0.400849i	$-0.868715\pi$
$919$	−3.07511e22	−1.83229	−0.916144	+	0.400849i	$0.868715\pi$
$920$	5.96882e20	0.0352760
$921$	−2.01904e22	−1.18358
$922$	−1.30196e21	−0.0757032
$923$	3.65357e21	0.210719
$924$	−3.30596e21	−0.189129
$925$	3.28031e20	0.0186145
$926$	−4.58454e19	−0.00258056
$927$	−2.07879e21	−0.116068
$928$	4.47960e21	0.248101
$929$	−1.69923e22	−0.933545	−0.466772	−	0.884377i	$-0.654583\pi$
$929$	−1.69923e22	−0.933545	−0.466772	+	0.884377i	$0.654583\pi$
$930$	−1.07915e21	−0.0588113
$931$	2.13237e22	1.15276
$932$	−3.47140e22	−1.86160
$933$	−7.80664e21	−0.415290
$934$	−8.95838e20	−0.0472746
$935$	1.35069e22	0.707082
$936$	−1.76000e21	−0.0913994
$937$	−9.96605e21	−0.513424	−0.256712	−	0.966488i	$-0.582639\pi$
$937$	−9.96605e21	−0.513424	−0.256712	+	0.966488i	$0.582639\pi$
$938$	−3.00401e20	−0.0153525
$939$	−1.05364e22	−0.534198
$940$	1.67864e22	0.844305
$941$	2.15280e22	1.07419	0.537096	−	0.843521i	$-0.319521\pi$
$941$	2.15280e22	1.07419	0.537096	+	0.843521i	$0.319521\pi$
$942$	−2.10143e20	−0.0104024
$943$	−5.32764e21	−0.261636
$944$	−2.11221e22	−1.02908
$945$	−5.41157e21	−0.261568
$946$	−2.43953e21	−0.116983
$947$	−1.10896e22	−0.527585	−0.263793	−	0.964579i	$-0.584973\pi$
$947$	−1.10896e22	−0.527585	−0.263793	+	0.964579i	$0.584973\pi$
$948$	1.47978e22	0.698448
$949$	3.18001e22	1.48913
$950$	−4.58077e19	−0.00212819
$951$	1.72705e22	0.796071
$952$	−6.04137e20	−0.0276286
$953$	−3.73381e22	−1.69416	−0.847082	−	0.531462i	$-0.821643\pi$
$953$	−3.73381e22	−1.69416	−0.847082	+	0.531462i	$0.821643\pi$
$954$	7.65154e19	0.00344458
$955$	−3.14242e22	−1.40358
$956$	−1.62035e22	−0.718082
$957$	1.61128e22	0.708488
$958$	−3.12446e21	−0.136312
$959$	−4.69215e21	−0.203111
$960$	1.38570e22	0.595161
$961$	5.01167e21	0.213578
$962$	1.66571e21	0.0704346
$963$	−1.48103e22	−0.621392
$964$	1.64465e22	0.684693
$965$	8.07833e20	0.0333708
$966$	−7.18438e19	−0.00294483
$967$	−4.24664e22	−1.72722	−0.863608	−	0.504164i	$-0.831801\pi$
$967$	−4.24664e22	−1.72722	−0.863608	+	0.504164i	$0.831801\pi$
$968$	1.43448e21	0.0578934
$969$	1.19964e22	0.480424
$970$	2.14201e21	0.0851203
$971$	1.13659e22	0.448188	0.224094	−	0.974568i	$-0.428058\pi$
$971$	1.13659e22	0.448188	0.224094	+	0.974568i	$0.428058\pi$
$972$	2.51201e22	0.982934
$973$	9.31361e19	0.00361636
$974$	−1.50809e21	−0.0581080
$975$	2.91661e20	0.0111518
$976$	2.68128e22	1.01735
$977$	−2.55841e22	−0.963299	−0.481650	−	0.876364i	$-0.659962\pi$
$977$	−2.55841e22	−0.963299	−0.481650	+	0.876364i	$0.659962\pi$
$978$	−1.45937e21	−0.0545285
$979$	−5.81017e22	−2.15436
$980$	2.48735e22	0.915253
$981$	7.58261e21	0.276886
$982$	−4.16923e20	−0.0151084
$983$	6.67644e21	0.240101	0.120050	−	0.992768i	$-0.461694\pi$
$983$	6.67644e21	0.240101	0.120050	+	0.992768i	$0.461694\pi$
$984$	3.77815e21	0.134839
$985$	4.32113e22	1.53047
$986$	1.46681e21	0.0515581
$987$	−4.05598e21	−0.141487
$988$	3.13900e22	1.08671
$989$	7.15433e21	0.245808
$990$	1.74182e21	0.0593936
$991$	4.23576e22	1.43344	0.716719	−	0.697362i	$-0.245643\pi$
$991$	4.23576e22	1.43344	0.716719	+	0.697362i	$0.245643\pi$
$992$	8.35665e21	0.280669
$993$	2.28599e22	0.761999
$994$	1.61729e20	0.00535044
$995$	5.68128e22	1.86541
$996$	−1.65812e22	−0.540346
$997$	−3.16161e22	−1.02257	−0.511287	−	0.859410i	$-0.670831\pi$
$997$	−3.16161e22	−1.02257	−0.511287	+	0.859410i	$0.670831\pi$
$998$	−4.58310e21	−0.147123
$999$	−2.94016e22	−0.936763

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.16.a.a.1.7	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.16.a.a.1.7	✓	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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

\(f(q)\)	\(=\)	\(q-15.5252 q^{2} -2381.89 q^{3} -32527.0 q^{4} +172933. q^{5} +36979.3 q^{6} -570604. q^{7} +1.01372e6 q^{8} -8.67549e6 q^{9} +O(q^{10})\)	\(q-15.5252 q^{2} -2381.89 q^{3} -32527.0 q^{4} +172933. q^{5} +36979.3 q^{6} -570604. q^{7} +1.01372e6 q^{8} -8.67549e6 q^{9} -2.68481e6 q^{10} +7.47818e7 q^{11} +7.74758e7 q^{12} +2.00125e8 q^{13} +8.85874e6 q^{14} -4.11907e8 q^{15} +1.05011e9 q^{16} +1.04444e9 q^{17} +1.34689e8 q^{18} -4.82221e9 q^{19} -5.62498e9 q^{20} +1.35912e9 q^{21} -1.16100e9 q^{22} +3.40483e9 q^{23} -2.41457e9 q^{24} -6.11864e8 q^{25} -3.10698e9 q^{26} +5.48417e10 q^{27} +1.85600e10 q^{28} -9.04593e10 q^{29} +6.39494e9 q^{30} -1.68751e11 q^{31} -4.95205e10 q^{32} -1.78122e11 q^{33} -1.62151e10 q^{34} -9.86762e10 q^{35} +2.82187e11 q^{36} -5.36118e11 q^{37} +7.48658e10 q^{38} -4.76677e11 q^{39} +1.75305e11 q^{40} -1.56473e12 q^{41} -2.11006e10 q^{42} +2.10123e12 q^{43} -2.43243e12 q^{44} -1.50028e12 q^{45} -5.28605e10 q^{46} -2.98427e12 q^{47} -2.50124e12 q^{48} -4.42197e12 q^{49} +9.49930e9 q^{50} -2.48775e12 q^{51} -6.50947e12 q^{52} +5.68091e11 q^{53} -8.51427e11 q^{54} +1.29322e13 q^{55} -5.78431e11 q^{56} +1.14860e13 q^{57} +1.40440e12 q^{58} -2.01143e13 q^{59} +1.33981e13 q^{60} +2.55334e13 q^{61} +2.61989e12 q^{62} +4.95027e12 q^{63} -3.36410e13 q^{64} +3.46082e13 q^{65} +2.76538e12 q^{66} -3.39102e13 q^{67} -3.39725e13 q^{68} -8.10993e12 q^{69} +1.53197e12 q^{70} +1.82564e13 q^{71} -8.79449e12 q^{72} +1.58901e14 q^{73} +8.32333e12 q^{74} +1.45739e12 q^{75} +1.56852e14 q^{76} -4.26708e13 q^{77} +7.40050e12 q^{78} +1.90999e14 q^{79} +1.81598e14 q^{80} -6.14326e12 q^{81} +2.42927e13 q^{82} -2.14018e14 q^{83} -4.42080e13 q^{84} +1.80618e14 q^{85} -3.26220e13 q^{86} +2.15465e14 q^{87} +7.58075e13 q^{88} -7.76950e14 q^{89} +2.32921e13 q^{90} -1.14192e14 q^{91} -1.10749e14 q^{92} +4.01947e14 q^{93} +4.63313e13 q^{94} -8.33918e14 q^{95} +1.17953e14 q^{96} -7.97824e14 q^{97} +6.86519e13 q^{98} -6.48769e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 256 q^{2} - 1745 q^{3} + 163840 q^{4} - 204476 q^{5} - 199430 q^{6} - 5717328 q^{7} + 10323168 q^{8} + 32660341 q^{9}+O(q^{10}) \) 12 * q - 256 * q^2 - 1745 * q^3 + 163840 * q^4 - 204476 * q^5 - 199430 * q^6 - 5717328 * q^7 + 10323168 * q^8 + 32660341 * q^9	\( 12 q - 256 q^{2} - 1745 q^{3} + 163840 q^{4} - 204476 q^{5} - 199430 q^{6} - 5717328 q^{7} + 10323168 q^{8} + 32660341 q^{9} - 137846540 q^{10} - 87636002 q^{11} - 398208076 q^{12} - 292496079 q^{13} + 415954912 q^{14} + 548079030 q^{15} + 4273503168 q^{16} - 2462528162 q^{17} + 7261215718 q^{18} + 175321758 q^{19} + 2660811480 q^{20} + 205665472 q^{21} - 21718153768 q^{22} + 40857905364 q^{23} - 63413289624 q^{24} + 20443225284 q^{25} - 137268652810 q^{26} - 151915208903 q^{27} - 325638721712 q^{28} - 164667697193 q^{29} - 356944003956 q^{30} + 20222384151 q^{31} - 369109524032 q^{32} + 132365097022 q^{33} - 582887018988 q^{34} - 1578083373112 q^{35} - 1903913944516 q^{36} - 869669414912 q^{37} - 5525312078376 q^{38} - 5762413466499 q^{39} - 4733269274576 q^{40} - 7510147709883 q^{41} - 7436463221624 q^{42} - 5682603487020 q^{43} - 11849381658176 q^{44} - 10780493432442 q^{45} - 871635314432 q^{46} - 5828073094301 q^{47} - 29418911592496 q^{48} - 6518780198860 q^{49} - 16781003942456 q^{50} - 771327642584 q^{51} - 3841511618340 q^{52} + 1452974784324 q^{53} - 32167598069522 q^{54} - 14882020037092 q^{55} + 416192984288 q^{56} - 12135794354818 q^{57} - 60065613521022 q^{58} - 11503084624084 q^{59} - 6378557828664 q^{60} - 23587566667200 q^{61} + 49359974806402 q^{62} + 87886039196104 q^{63} + 80321007324160 q^{64} + 54548135308138 q^{65} + 316922278045948 q^{66} + 61525019345122 q^{67} + 45114528974104 q^{68} - 5941420405015 q^{69} + 374016699556320 q^{70} + 197895887067063 q^{71} + 439014895837656 q^{72} - 22888563242709 q^{73} + 694696716227036 q^{74} + 612085940395201 q^{75} + 301381886149904 q^{76} + 209007839834200 q^{77} + 350406148895766 q^{78} + 229938065096294 q^{79} + 555529032250016 q^{80} + 37596523177660 q^{81} - 414508112727306 q^{82} + 369402590629184 q^{83} + 559863541234208 q^{84} - 343366303925348 q^{85} + 12\!\cdots\!08 q^{86}+ \cdots - 32\!\cdots\!24 q^{99}+O(q^{100}) \) 12 * q - 256 * q^2 - 1745 * q^3 + 163840 * q^4 - 204476 * q^5 - 199430 * q^6 - 5717328 * q^7 + 10323168 * q^8 + 32660341 * q^9 - 137846540 * q^10 - 87636002 * q^11 - 398208076 * q^12 - 292496079 * q^13 + 415954912 * q^14 + 548079030 * q^15 + 4273503168 * q^16 - 2462528162 * q^17 + 7261215718 * q^18 + 175321758 * q^19 + 2660811480 * q^20 + 205665472 * q^21 - 21718153768 * q^22 + 40857905364 * q^23 - 63413289624 * q^24 + 20443225284 * q^25 - 137268652810 * q^26 - 151915208903 * q^27 - 325638721712 * q^28 - 164667697193 * q^29 - 356944003956 * q^30 + 20222384151 * q^31 - 369109524032 * q^32 + 132365097022 * q^33 - 582887018988 * q^34 - 1578083373112 * q^35 - 1903913944516 * q^36 - 869669414912 * q^37 - 5525312078376 * q^38 - 5762413466499 * q^39 - 4733269274576 * q^40 - 7510147709883 * q^41 - 7436463221624 * q^42 - 5682603487020 * q^43 - 11849381658176 * q^44 - 10780493432442 * q^45 - 871635314432 * q^46 - 5828073094301 * q^47 - 29418911592496 * q^48 - 6518780198860 * q^49 - 16781003942456 * q^50 - 771327642584 * q^51 - 3841511618340 * q^52 + 1452974784324 * q^53 - 32167598069522 * q^54 - 14882020037092 * q^55 + 416192984288 * q^56 - 12135794354818 * q^57 - 60065613521022 * q^58 - 11503084624084 * q^59 - 6378557828664 * q^60 - 23587566667200 * q^61 + 49359974806402 * q^62 + 87886039196104 * q^63 + 80321007324160 * q^64 + 54548135308138 * q^65 + 316922278045948 * q^66 + 61525019345122 * q^67 + 45114528974104 * q^68 - 5941420405015 * q^69 + 374016699556320 * q^70 + 197895887067063 * q^71 + 439014895837656 * q^72 - 22888563242709 * q^73 + 694696716227036 * q^74 + 612085940395201 * q^75 + 301381886149904 * q^76 + 209007839834200 * q^77 + 350406148895766 * q^78 + 229938065096294 * q^79 + 555529032250016 * q^80 + 37596523177660 * q^81 - 414508112727306 * q^82 + 369402590629184 * q^83 + 559863541234208 * q^84 - 343366303925348 * q^85 + 1273071253885508 * q^86 - 725794048127953 * q^87 - 2461430290350720 * q^88 - 85082918654478 * q^89 + 125194382337864 * q^90 - 180251669559688 * q^91 + 557846601236480 * q^92 + 190758447044005 * q^93 + 640973603901258 * q^94 + 462985554800484 * q^95 - 2815189465233952 * q^96 - 5046858838511686 * q^97 - 3547540222626416 * q^98 - 3251416762282424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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