LMFDB - Embedded newform 177.10.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	177.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:	$91.1613430010$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.57853 q^{2} +81.0000 q^{3} -420.252 q^{4} +279.985 q^{5} -775.861 q^{6} +7953.06 q^{7} +8929.60 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-9.57853 q^{2} +81.0000 q^{3} -420.252 q^{4} +279.985 q^{5} -775.861 q^{6} +7953.06 q^{7} +8929.60 q^{8} +6561.00 q^{9} -2681.84 q^{10} -24455.7 q^{11} -34040.4 q^{12} -4184.11 q^{13} -76178.7 q^{14} +22678.8 q^{15} +129636. q^{16} +164024. q^{17} -62844.7 q^{18} +826643. q^{19} -117664. q^{20} +644198. q^{21} +234249. q^{22} +840452. q^{23} +723298. q^{24} -1.87473e6 q^{25} +40077.6 q^{26} +531441. q^{27} -3.34229e6 q^{28} +6.86036e6 q^{29} -217229. q^{30} -1.00194e7 q^{31} -5.81368e6 q^{32} -1.98091e6 q^{33} -1.57111e6 q^{34} +2.22674e6 q^{35} -2.75727e6 q^{36} +2.02637e6 q^{37} -7.91803e6 q^{38} -338913. q^{39} +2.50015e6 q^{40} -2.68086e7 q^{41} -6.17047e6 q^{42} +3.41186e7 q^{43} +1.02775e7 q^{44} +1.83698e6 q^{45} -8.05029e6 q^{46} -1.02082e7 q^{47} +1.05006e7 q^{48} +2.28976e7 q^{49} +1.79572e7 q^{50} +1.32859e7 q^{51} +1.75838e6 q^{52} -1.18232e7 q^{53} -5.09042e6 q^{54} -6.84722e6 q^{55} +7.10177e7 q^{56} +6.69581e7 q^{57} -6.57122e7 q^{58} -1.21174e7 q^{59} -9.53080e6 q^{60} +2.71179e7 q^{61} +9.59710e7 q^{62} +5.21801e7 q^{63} -1.06874e7 q^{64} -1.17149e6 q^{65} +1.89742e7 q^{66} -5.94366e7 q^{67} -6.89314e7 q^{68} +6.80766e7 q^{69} -2.13289e7 q^{70} -8.70465e7 q^{71} +5.85871e7 q^{72} +5.93796e7 q^{73} -1.94096e7 q^{74} -1.51853e8 q^{75} -3.47398e8 q^{76} -1.94497e8 q^{77} +3.24628e6 q^{78} +4.90761e8 q^{79} +3.62963e7 q^{80} +4.30467e7 q^{81} +2.56787e8 q^{82} -8.27340e7 q^{83} -2.70725e8 q^{84} +4.59243e7 q^{85} -3.26806e8 q^{86} +5.55689e8 q^{87} -2.18379e8 q^{88} +6.23380e8 q^{89} -1.75956e7 q^{90} -3.32765e7 q^{91} -3.53201e8 q^{92} -8.11570e8 q^{93} +9.77792e7 q^{94} +2.31448e8 q^{95} -4.70908e8 q^{96} +1.98677e8 q^{97} -2.19326e8 q^{98} -1.60454e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) $ 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * 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 $

$2$	−9.57853	−0.423315	−0.211658	−	0.977344i	$-0.567886\pi$
$2$	−9.57853	−0.423315	−0.211658	+	0.977344i	$0.567886\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−420.252	−0.820804
$5$	279.985	0.200341	0.100170	−	0.994970i	$-0.468061\pi$
$5$	279.985	0.200341	0.100170	+	0.994970i	$0.468061\pi$
$6$	−775.861	−0.244401
$7$	7953.06	1.25197	0.625984	−	0.779836i	$-0.284697\pi$
$7$	7953.06	1.25197	0.625984	+	0.779836i	$0.284697\pi$
$8$	8929.60	0.770774
$9$	6561.00	0.333333
$10$	−2681.84	−0.0848074
$11$	−24455.7	−0.503631	−0.251815	−	0.967775i	$-0.581028\pi$
$11$	−24455.7	−0.503631	−0.251815	+	0.967775i	$0.581028\pi$
$12$	−34040.4	−0.473892
$13$	−4184.11	−0.0406310	−0.0203155	−	0.999794i	$-0.506467\pi$
$13$	−4184.11	−0.0406310	−0.0203155	+	0.999794i	$0.506467\pi$
$14$	−76178.7	−0.529977
$15$	22678.8	0.115667
$16$	129636.	0.494524
$17$	164024.	0.476307	0.238154	−	0.971227i	$-0.423458\pi$
$17$	164024.	0.476307	0.238154	+	0.971227i	$0.423458\pi$
$18$	−62844.7	−0.141105
$19$	826643.	1.45521	0.727607	−	0.685994i	$-0.240632\pi$
$19$	826643.	1.45521	0.727607	+	0.685994i	$0.240632\pi$
$20$	−117664.	−0.164441
$21$	644198.	0.722824
$22$	234249.	0.213195
$23$	840452.	0.626235	0.313118	−	0.949714i	$-0.398627\pi$
$23$	840452.	0.626235	0.313118	+	0.949714i	$0.398627\pi$
$24$	723298.	0.445007
$25$	−1.87473e6	−0.959863
$26$	40077.6	0.0171997
$27$	531441.	0.192450
$28$	−3.34229e6	−1.02762
$29$	6.86036e6	1.80118	0.900588	−	0.434674i	$-0.143136\pi$
$29$	6.86036e6	1.80118	0.900588	+	0.434674i	$0.143136\pi$
$30$	−217229.	−0.0489636
$31$	−1.00194e7	−1.94856	−0.974279	−	0.225344i	$-0.927649\pi$
$31$	−1.00194e7	−1.94856	−0.974279	+	0.225344i	$0.927649\pi$
$32$	−5.81368e6	−0.980114
$33$	−1.98091e6	−0.290771
$34$	−1.57111e6	−0.201628
$35$	2.22674e6	0.250821
$36$	−2.75727e6	−0.273601
$37$	2.02637e6	0.177751	0.0888753	−	0.996043i	$-0.471673\pi$
$37$	2.02637e6	0.177751	0.0888753	+	0.996043i	$0.471673\pi$
$38$	−7.91803e6	−0.616014
$39$	−338913.	−0.0234583
$40$	2.50015e6	0.154418
$41$	−2.68086e7	−1.48165	−0.740827	−	0.671696i	$-0.765566\pi$
$41$	−2.68086e7	−1.48165	−0.740827	+	0.671696i	$0.765566\pi$
$42$	−6.17047e6	−0.305982
$43$	3.41186e7	1.52189	0.760944	−	0.648818i	$-0.224736\pi$
$43$	3.41186e7	1.52189	0.760944	+	0.648818i	$0.224736\pi$
$44$	1.02775e7	0.413382
$45$	1.83698e6	0.0667803
$46$	−8.05029e6	−0.265095
$47$	−1.02082e7	−0.305146	−0.152573	−	0.988292i	$-0.548756\pi$
$47$	−1.02082e7	−0.305146	−0.152573	+	0.988292i	$0.548756\pi$
$48$	1.05006e7	0.285514
$49$	2.28976e7	0.567425
$50$	1.79572e7	0.406325
$51$	1.32859e7	0.274996
$52$	1.75838e6	0.0333501
$53$	−1.18232e7	−0.205823	−0.102911	−	0.994691i	$-0.532816\pi$
$53$	−1.18232e7	−0.205823	−0.102911	+	0.994691i	$0.532816\pi$
$54$	−5.09042e6	−0.0814670
$55$	−6.84722e6	−0.100898
$56$	7.10177e7	0.964985
$57$	6.69581e7	0.840169
$58$	−6.57122e7	−0.762465
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−9.53080e6	−0.0949399
$61$	2.71179e7	0.250768	0.125384	−	0.992108i	$-0.459984\pi$
$61$	2.71179e7	0.250768	0.125384	+	0.992108i	$0.459984\pi$
$62$	9.59710e7	0.824854
$63$	5.21801e7	0.417323
$64$	−1.06874e7	−0.0796271
$65$	−1.17149e6	−0.00814006
$66$	1.89742e7	0.123088
$67$	−5.94366e7	−0.360344	−0.180172	−	0.983635i	$-0.557665\pi$
$67$	−5.94366e7	−0.360344	−0.180172	+	0.983635i	$0.557665\pi$
$68$	−6.89314e7	−0.390955
$69$	6.80766e7	0.361557
$70$	−2.13289e7	−0.106176
$71$	−8.70465e7	−0.406527	−0.203263	−	0.979124i	$-0.565155\pi$
$71$	−8.70465e7	−0.406527	−0.203263	+	0.979124i	$0.565155\pi$
$72$	5.85871e7	0.256925
$73$	5.93796e7	0.244728	0.122364	−	0.992485i	$-0.460952\pi$
$73$	5.93796e7	0.244728	0.122364	+	0.992485i	$0.460952\pi$
$74$	−1.94096e7	−0.0752445
$75$	−1.51853e8	−0.554177
$76$	−3.47398e8	−1.19445
$77$	−1.94497e8	−0.630530
$78$	3.24628e6	0.00993027
$79$	4.90761e8	1.41758	0.708791	−	0.705418i	$-0.249241\pi$
$79$	4.90761e8	1.41758	0.708791	+	0.705418i	$0.249241\pi$
$80$	3.62963e7	0.0990734
$81$	4.30467e7	0.111111
$82$	2.56787e8	0.627206
$83$	−8.27340e7	−0.191352	−0.0956759	−	0.995413i	$-0.530501\pi$
$83$	−8.27340e7	−0.191352	−0.0956759	+	0.995413i	$0.530501\pi$
$84$	−2.70725e8	−0.593297
$85$	4.59243e7	0.0954239
$86$	−3.26806e8	−0.644238
$87$	5.55689e8	1.03991
$88$	−2.18379e8	−0.388185
$89$	6.23380e8	1.05317	0.526584	−	0.850123i	$-0.323473\pi$
$89$	6.23380e8	1.05317	0.526584	+	0.850123i	$0.323473\pi$
$90$	−1.75956e7	−0.0282691
$91$	−3.32765e7	−0.0508687
$92$	−3.53201e8	−0.514017
$93$	−8.11570e8	−1.12500
$94$	9.77792e7	0.129173
$95$	2.31448e8	0.291539
$96$	−4.70908e8	−0.565869
$97$	1.98677e8	0.227864	0.113932	−	0.993489i	$-0.463655\pi$
$97$	1.98677e8	0.227864	0.113932	+	0.993489i	$0.463655\pi$
$98$	−2.19326e8	−0.240199
$99$	−1.60454e8	−0.167877
$100$	7.87860e8	0.787860
$101$	3.04753e8	0.291408	0.145704	−	0.989328i	$-0.453455\pi$
$101$	3.04753e8	0.291408	0.145704	+	0.989328i	$0.453455\pi$
$102$	−1.27260e8	−0.116410
$103$	3.83311e8	0.335570	0.167785	−	0.985824i	$-0.446339\pi$
$103$	3.83311e8	0.335570	0.167785	+	0.985824i	$0.446339\pi$
$104$	−3.73624e7	−0.0313173
$105$	1.80366e8	0.144811
$106$	1.13249e8	0.0871280
$107$	1.92857e9	1.42236	0.711178	−	0.703012i	$-0.248162\pi$
$107$	1.92857e9	1.42236	0.711178	+	0.703012i	$0.248162\pi$
$108$	−2.23339e8	−0.157964
$109$	9.41013e8	0.638523	0.319261	−	0.947667i	$-0.396565\pi$
$109$	9.41013e8	0.638523	0.319261	+	0.947667i	$0.396565\pi$
$110$	6.55863e7	0.0427116
$111$	1.64136e8	0.102624
$112$	1.03101e9	0.619128
$113$	1.25727e9	0.725398	0.362699	−	0.931906i	$-0.381855\pi$
$113$	1.25727e9	0.725398	0.362699	+	0.931906i	$0.381855\pi$
$114$	−6.41360e8	−0.355656
$115$	2.35314e8	0.125461
$116$	−2.88308e9	−1.47841
$117$	−2.74519e7	−0.0135437
$118$	1.16066e8	0.0551109
$119$	1.30449e9	0.596322
$120$	2.02513e8	0.0891531
$121$	−1.75987e9	−0.746356
$122$	−2.59750e8	−0.106154
$123$	−2.17150e9	−0.855433
$124$	4.21066e9	1.59939
$125$	−1.07174e9	−0.392641
$126$	−4.99808e8	−0.176659
$127$	2.25881e8	0.0770483	0.0385242	−	0.999258i	$-0.487734\pi$
$127$	2.25881e8	0.0770483	0.0385242	+	0.999258i	$0.487734\pi$
$128$	3.07897e9	1.01382
$129$	2.76360e9	0.878662
$130$	1.12211e7	0.00344581
$131$	8.52863e8	0.253022	0.126511	−	0.991965i	$-0.459622\pi$
$131$	8.52863e8	0.253022	0.126511	+	0.991965i	$0.459622\pi$
$132$	8.32480e8	0.238666
$133$	6.57435e9	1.82188
$134$	5.69315e8	0.152539
$135$	1.48796e8	0.0385556
$136$	1.46467e9	0.367125
$137$	4.73702e9	1.14885	0.574424	−	0.818558i	$-0.305226\pi$
$137$	4.73702e9	1.14885	0.574424	+	0.818558i	$0.305226\pi$
$138$	−6.52073e8	−0.153053
$139$	8.40208e8	0.190906	0.0954531	−	0.995434i	$-0.469570\pi$
$139$	8.40208e8	0.190906	0.0954531	+	0.995434i	$0.469570\pi$
$140$	−9.35791e8	−0.205875
$141$	−8.26862e8	−0.176176
$142$	8.33778e8	0.172089
$143$	1.02325e8	0.0204630
$144$	8.50545e8	0.164841
$145$	1.92080e9	0.360849
$146$	−5.68769e8	−0.103597
$147$	1.85471e9	0.327603
$148$	−8.51585e8	−0.145898
$149$	4.22892e9	0.702896	0.351448	−	0.936207i	$-0.385689\pi$
$149$	4.22892e9	0.702896	0.351448	+	0.936207i	$0.385689\pi$
$150$	1.45453e9	0.234592
$151$	−1.20936e9	−0.189304	−0.0946520	−	0.995510i	$-0.530174\pi$
$151$	−1.20936e9	−0.189304	−0.0946520	+	0.995510i	$0.530174\pi$
$152$	7.38160e9	1.12164
$153$	1.07616e9	0.158769
$154$	1.86300e9	0.266913
$155$	−2.80528e9	−0.390376
$156$	1.42429e8	0.0192547
$157$	9.30072e9	1.22171	0.610855	−	0.791742i	$-0.290826\pi$
$157$	9.30072e9	1.22171	0.610855	+	0.791742i	$0.290826\pi$
$158$	−4.70077e9	−0.600084
$159$	−9.57680e8	−0.118832
$160$	−1.62774e9	−0.196357
$161$	6.68417e9	0.784027
$162$	−4.12324e8	−0.0470350
$163$	1.77937e10	1.97434	0.987169	−	0.159676i	$-0.0510450\pi$
$163$	1.77937e10	1.97434	0.987169	+	0.159676i	$0.0510450\pi$
$164$	1.12664e10	1.21615
$165$	−5.54625e8	−0.0582534
$166$	7.92470e8	0.0810021
$167$	4.36596e9	0.434366	0.217183	−	0.976131i	$-0.430313\pi$
$167$	4.36596e9	0.434366	0.217183	+	0.976131i	$0.430313\pi$
$168$	5.75243e9	0.557134
$169$	−1.05870e10	−0.998349
$170$	−4.39887e8	−0.0403944
$171$	5.42361e9	0.485072
$172$	−1.43384e10	−1.24917
$173$	2.07485e10	1.76108	0.880540	−	0.473971i	$-0.157180\pi$
$173$	2.07485e10	1.76108	0.880540	+	0.473971i	$0.157180\pi$
$174$	−5.32269e9	−0.440209
$175$	−1.49099e10	−1.20172
$176$	−3.17035e9	−0.249057
$177$	−9.81506e8	−0.0751646
$178$	−5.97106e9	−0.445822
$179$	−1.25662e10	−0.914881	−0.457441	−	0.889240i	$-0.651234\pi$
$179$	−1.25662e10	−0.914881	−0.457441	+	0.889240i	$0.651234\pi$
$180$	−7.71995e8	−0.0548136
$181$	−1.09358e8	−0.00757349	−0.00378674	−	0.999993i	$-0.501205\pi$
$181$	−1.09358e8	−0.00757349	−0.00378674	+	0.999993i	$0.501205\pi$
$182$	3.18740e8	0.0215335
$183$	2.19655e9	0.144781
$184$	7.50490e9	0.482686
$185$	5.67353e8	0.0356107
$186$	7.77365e9	0.476230
$187$	−4.01131e9	−0.239883
$188$	4.29000e9	0.250465
$189$	4.22658e9	0.240941
$190$	−2.21693e9	−0.123413
$191$	1.10145e10	0.598845	0.299423	−	0.954121i	$-0.403206\pi$
$191$	1.10145e10	0.598845	0.299423	+	0.954121i	$0.403206\pi$
$192$	−8.65677e8	−0.0459727
$193$	−2.89225e10	−1.50047	−0.750237	−	0.661169i	$-0.770061\pi$
$193$	−2.89225e10	−1.50047	−0.750237	+	0.661169i	$0.770061\pi$
$194$	−1.90303e9	−0.0964581
$195$	−9.48905e7	−0.00469966
$196$	−9.62277e9	−0.465745
$197$	−1.80535e10	−0.854010	−0.427005	−	0.904249i	$-0.640431\pi$
$197$	−1.80535e10	−0.854010	−0.427005	+	0.904249i	$0.640431\pi$
$198$	1.53691e9	0.0710648
$199$	−2.31277e10	−1.04543	−0.522713	−	0.852509i	$-0.675080\pi$
$199$	−2.31277e10	−1.04543	−0.522713	+	0.852509i	$0.675080\pi$
$200$	−1.67406e10	−0.739838
$201$	−4.81436e9	−0.208045
$202$	−2.91908e9	−0.123357
$203$	5.45609e10	2.25501
$204$	−5.58344e9	−0.225718
$205$	−7.50600e9	−0.296836
$206$	−3.67155e9	−0.142052
$207$	5.51420e9	0.208745
$208$	−5.42413e8	−0.0200930
$209$	−2.02161e10	−0.732891
$210$	−1.72764e9	−0.0613008
$211$	2.93108e9	0.101802	0.0509010	−	0.998704i	$-0.483791\pi$
$211$	2.93108e9	0.101802	0.0509010	+	0.998704i	$0.483791\pi$
$212$	4.96872e9	0.168940
$213$	−7.05077e9	−0.234708
$214$	−1.84729e10	−0.602105
$215$	9.55269e9	0.304897
$216$	4.74556e9	0.148336
$217$	−7.96848e10	−2.43953
$218$	−9.01352e9	−0.270296
$219$	4.80975e9	0.141294
$220$	2.87756e9	0.0828174
$221$	−6.86294e8	−0.0193529
$222$	−1.57218e9	−0.0434424
$223$	−3.19223e10	−0.864414	−0.432207	−	0.901774i	$-0.642265\pi$
$223$	−3.19223e10	−0.864414	−0.432207	+	0.901774i	$0.642265\pi$
$224$	−4.62366e10	−1.22707
$225$	−1.23001e10	−0.319954
$226$	−1.20428e10	−0.307072
$227$	4.18184e10	1.04532	0.522662	−	0.852540i	$-0.324939\pi$
$227$	4.18184e10	1.04532	0.522662	+	0.852540i	$0.324939\pi$
$228$	−2.81393e10	−0.689614
$229$	7.18309e10	1.72604	0.863022	−	0.505167i	$-0.168569\pi$
$229$	7.18309e10	1.72604	0.863022	+	0.505167i	$0.168569\pi$
$230$	−2.25396e9	−0.0531094
$231$	−1.57543e10	−0.364036
$232$	6.12603e10	1.38830
$233$	2.46588e10	0.548113	0.274057	−	0.961714i	$-0.411634\pi$
$233$	2.46588e10	0.548113	0.274057	+	0.961714i	$0.411634\pi$
$234$	2.62949e8	0.00573324
$235$	−2.85813e9	−0.0611332
$236$	5.09234e9	0.106860
$237$	3.97517e10	0.818442
$238$	−1.24951e10	−0.252432
$239$	3.63090e10	0.719820	0.359910	−	0.932987i	$-0.382807\pi$
$239$	3.63090e10	0.719820	0.359910	+	0.932987i	$0.382807\pi$
$240$	2.94000e9	0.0572001
$241$	2.69176e10	0.513996	0.256998	−	0.966412i	$-0.417267\pi$
$241$	2.69176e10	0.513996	0.256998	+	0.966412i	$0.417267\pi$
$242$	1.68570e10	0.315944
$243$	3.48678e9	0.0641500
$244$	−1.13964e10	−0.205832
$245$	6.41099e9	0.113678
$246$	2.07997e10	0.362118
$247$	−3.45876e9	−0.0591268
$248$	−8.94691e10	−1.50190
$249$	−6.70146e9	−0.110477
$250$	1.02657e10	0.166211
$251$	8.57174e10	1.36313	0.681565	−	0.731758i	$-0.261300\pi$
$251$	8.57174e10	1.36313	0.681565	+	0.731758i	$0.261300\pi$
$252$	−2.19288e10	−0.342540
$253$	−2.05538e10	−0.315391
$254$	−2.16361e9	−0.0326157
$255$	3.71987e9	0.0550930
$256$	−2.40201e10	−0.349539
$257$	−5.60139e10	−0.800934	−0.400467	−	0.916311i	$-0.631152\pi$
$257$	−5.60139e10	−0.800934	−0.400467	+	0.916311i	$0.631152\pi$
$258$	−2.64713e10	−0.371951
$259$	1.61158e10	0.222538
$260$	4.92320e8	0.00668139
$261$	4.50108e10	0.600392
$262$	−8.16917e9	−0.107108
$263$	−5.53871e10	−0.713852	−0.356926	−	0.934133i	$-0.616175\pi$
$263$	−5.53871e10	−0.713852	−0.356926	+	0.934133i	$0.616175\pi$
$264$	−1.76887e10	−0.224119
$265$	−3.31032e9	−0.0412348
$266$	−6.29726e10	−0.771230
$267$	5.04937e10	0.608047
$268$	2.49783e10	0.295772
$269$	1.29810e11	1.51155	0.755777	−	0.654829i	$-0.227259\pi$
$269$	1.29810e11	1.51155	0.755777	+	0.654829i	$0.227259\pi$
$270$	−1.42524e9	−0.0163212
$271$	−3.87526e10	−0.436455	−0.218227	−	0.975898i	$-0.570027\pi$
$271$	−3.87526e10	−0.436455	−0.218227	+	0.975898i	$0.570027\pi$
$272$	2.12635e10	0.235545
$273$	−2.69539e9	−0.0293691
$274$	−4.53736e10	−0.486324
$275$	4.58478e10	0.483417
$276$	−2.86093e10	−0.296768
$277$	−7.14595e10	−0.729292	−0.364646	−	0.931146i	$-0.618810\pi$
$277$	−7.14595e10	−0.729292	−0.364646	+	0.931146i	$0.618810\pi$
$278$	−8.04796e9	−0.0808135
$279$	−6.57372e10	−0.649519
$280$	1.98839e10	0.193326
$281$	−1.06795e10	−0.102182	−0.0510910	−	0.998694i	$-0.516270\pi$
$281$	−1.06795e10	−0.102182	−0.0510910	+	0.998694i	$0.516270\pi$
$282$	7.92012e9	0.0745780
$283$	−1.74567e11	−1.61779	−0.808895	−	0.587953i	$-0.799934\pi$
$283$	−1.74567e11	−1.61779	−0.808895	+	0.587953i	$0.799934\pi$
$284$	3.65815e10	0.333679
$285$	1.87473e10	0.168320
$286$	−9.80124e8	−0.00866231
$287$	−2.13210e11	−1.85498
$288$	−3.81436e10	−0.326705
$289$	−9.16840e10	−0.773131
$290$	−1.83984e10	−0.152753
$291$	1.60928e10	0.131557
$292$	−2.49544e10	−0.200874
$293$	−8.31117e10	−0.658806	−0.329403	−	0.944189i	$-0.606848\pi$
$293$	−8.31117e10	−0.658806	−0.329403	+	0.944189i	$0.606848\pi$
$294$	−1.77654e10	−0.138679
$295$	−3.39268e9	−0.0260822
$296$	1.80947e10	0.137005
$297$	−1.29967e10	−0.0969238
$298$	−4.05068e10	−0.297547
$299$	−3.51654e9	−0.0254446
$300$	6.38167e10	0.454871
$301$	2.71347e11	1.90536
$302$	1.15839e10	0.0801353
$303$	2.46850e10	0.168244
$304$	1.07163e11	0.719638
$305$	7.59262e9	0.0502391
$306$	−1.03080e10	−0.0672094
$307$	−2.41303e11	−1.55039	−0.775194	−	0.631724i	$-0.782348\pi$
$307$	−2.41303e11	−1.55039	−0.775194	+	0.631724i	$0.782348\pi$
$308$	8.17379e10	0.517541
$309$	3.10482e10	0.193742
$310$	2.68704e10	0.165252
$311$	−3.16050e11	−1.91573	−0.957864	−	0.287224i	$-0.907268\pi$
$311$	−3.16050e11	−1.91573	−0.957864	+	0.287224i	$0.907268\pi$
$312$	−3.02635e9	−0.0180811
$313$	2.18895e11	1.28910	0.644550	−	0.764562i	$-0.277045\pi$
$313$	2.18895e11	1.28910	0.644550	+	0.764562i	$0.277045\pi$
$314$	−8.90872e10	−0.517168
$315$	1.46096e10	0.0836069
$316$	−2.06243e11	−1.16356
$317$	−4.19690e10	−0.233433	−0.116716	−	0.993165i	$-0.537237\pi$
$317$	−4.19690e10	−0.233433	−0.116716	+	0.993165i	$0.537237\pi$
$318$	9.17316e9	0.0503034
$319$	−1.67775e11	−0.907127
$320$	−2.99230e9	−0.0159526
$321$	1.56214e11	0.821198
$322$	−6.40245e10	−0.331890
$323$	1.35589e11	0.693129
$324$	−1.80905e10	−0.0912005
$325$	7.84408e9	0.0390002
$326$	−1.70437e11	−0.835768
$327$	7.62221e10	0.368651
$328$	−2.39390e11	−1.14202
$329$	−8.11862e10	−0.382033
$330$	5.31249e9	0.0246596
$331$	−6.43346e9	−0.0294590	−0.0147295	−	0.999892i	$-0.504689\pi$
$331$	−6.43346e9	−0.0294590	−0.0147295	+	0.999892i	$0.504689\pi$
$332$	3.47691e10	0.157062
$333$	1.32950e10	0.0592502
$334$	−4.18195e10	−0.183874
$335$	−1.66414e10	−0.0721917
$336$	8.35116e10	0.357454
$337$	−1.98819e11	−0.839698	−0.419849	−	0.907594i	$-0.637917\pi$
$337$	−1.98819e11	−0.839698	−0.419849	+	0.907594i	$0.637917\pi$
$338$	1.01408e11	0.422616
$339$	1.01839e11	0.418809
$340$	−1.92998e10	−0.0783243
$341$	2.45031e11	0.981354
$342$	−5.19502e10	−0.205338
$343$	−1.38829e11	−0.541571
$344$	3.04665e11	1.17303
$345$	1.90604e10	0.0724347
$346$	−1.98740e11	−0.745492
$347$	3.33397e11	1.23447	0.617233	−	0.786780i	$-0.288254\pi$
$347$	3.33397e11	1.23447	0.617233	+	0.786780i	$0.288254\pi$
$348$	−2.33529e11	−0.853562
$349$	2.25022e10	0.0811916	0.0405958	−	0.999176i	$-0.487074\pi$
$349$	2.25022e10	0.0811916	0.0405958	+	0.999176i	$0.487074\pi$
$350$	1.42815e11	0.508706
$351$	−2.22361e9	−0.00781944
$352$	1.42177e11	0.493615
$353$	3.24247e11	1.11145	0.555725	−	0.831366i	$-0.312441\pi$
$353$	3.24247e11	1.11145	0.555725	+	0.831366i	$0.312441\pi$
$354$	9.40139e9	0.0318183
$355$	−2.43717e10	−0.0814439
$356$	−2.61976e11	−0.864445
$357$	1.05664e11	0.344286
$358$	1.20366e11	0.387283
$359$	5.14941e11	1.63618	0.818092	−	0.575087i	$-0.195032\pi$
$359$	5.14941e11	1.63618	0.818092	+	0.575087i	$0.195032\pi$
$360$	1.64035e10	0.0514725
$361$	3.60652e11	1.11765
$362$	1.04749e9	0.00320597
$363$	−1.42549e11	−0.430909
$364$	1.39845e10	0.0417533
$365$	1.66254e10	0.0490291
$366$	−2.10397e10	−0.0612880
$367$	−4.75270e11	−1.36755	−0.683775	−	0.729693i	$-0.739663\pi$
$367$	−4.75270e11	−1.36755	−0.683775	+	0.729693i	$0.739663\pi$
$368$	1.08953e11	0.309688
$369$	−1.75891e11	−0.493884
$370$	−5.43441e9	−0.0150746
$371$	−9.40307e10	−0.257684
$372$	3.41064e11	0.923405
$373$	−3.17239e11	−0.848587	−0.424294	−	0.905525i	$-0.639478\pi$
$373$	−3.17239e11	−0.848587	−0.424294	+	0.905525i	$0.639478\pi$
$374$	3.84225e10	0.101546
$375$	−8.68112e10	−0.226691
$376$	−9.11549e10	−0.235199
$377$	−2.87045e10	−0.0731836
$378$	−4.04845e10	−0.101994
$379$	2.91888e11	0.726674	0.363337	−	0.931658i	$-0.381637\pi$
$379$	2.91888e11	0.726674	0.363337	+	0.931658i	$0.381637\pi$
$380$	−9.72664e10	−0.239297
$381$	1.82964e10	0.0444839
$382$	−1.05503e11	−0.253500
$383$	−1.63564e11	−0.388413	−0.194207	−	0.980961i	$-0.562213\pi$
$383$	−1.63564e11	−0.388413	−0.194207	+	0.980961i	$0.562213\pi$
$384$	2.49397e11	0.585330
$385$	−5.44564e10	−0.126321
$386$	2.77035e11	0.635173
$387$	2.23852e11	0.507296
$388$	−8.34944e10	−0.187031
$389$	−4.14721e11	−0.918297	−0.459148	−	0.888360i	$-0.651845\pi$
$389$	−4.14721e11	−0.918297	−0.459148	+	0.888360i	$0.651845\pi$
$390$	9.08911e8	0.00198944
$391$	1.37854e11	0.298280
$392$	2.04467e11	0.437356
$393$	6.90819e10	0.146082
$394$	1.72926e11	0.361515
$395$	1.37406e11	0.284000
$396$	6.74309e10	0.137794
$397$	−4.15700e10	−0.0839890	−0.0419945	−	0.999118i	$-0.513371\pi$
$397$	−4.15700e10	−0.0839890	−0.0419945	+	0.999118i	$0.513371\pi$
$398$	2.21529e11	0.442545
$399$	5.32522e11	1.05186
$400$	−2.43034e11	−0.474676
$401$	−4.54725e11	−0.878212	−0.439106	−	0.898435i	$-0.644705\pi$
$401$	−4.54725e11	−0.878212	−0.439106	+	0.898435i	$0.644705\pi$
$402$	4.61145e10	0.0880685
$403$	4.19222e10	0.0791719
$404$	−1.28073e11	−0.239189
$405$	1.20524e10	0.0222601
$406$	−5.22613e11	−0.954582
$407$	−4.95562e10	−0.0895206
$408$	1.18638e11	0.211960
$409$	6.69144e11	1.18240	0.591200	−	0.806525i	$-0.298654\pi$
$409$	6.69144e11	1.18240	0.591200	+	0.806525i	$0.298654\pi$
$410$	7.18965e10	0.125655
$411$	3.83698e11	0.663287
$412$	−1.61087e11	−0.275438
$413$	−9.63702e10	−0.162992
$414$	−5.28180e10	−0.0883649
$415$	−2.31643e10	−0.0383356
$416$	2.43251e10	0.0398230
$417$	6.80568e10	0.110220
$418$	1.93641e11	0.310244
$419$	4.40416e11	0.698071	0.349036	−	0.937109i	$-0.386509\pi$
$419$	4.40416e11	0.698071	0.349036	+	0.937109i	$0.386509\pi$
$420$	−7.57991e10	−0.118862
$421$	6.33252e11	0.982442	0.491221	−	0.871035i	$-0.336551\pi$
$421$	6.33252e11	0.982442	0.491221	+	0.871035i	$0.336551\pi$
$422$	−2.80754e10	−0.0430943
$423$	−6.69758e10	−0.101715
$424$	−1.05576e11	−0.158643
$425$	−3.07501e11	−0.457190
$426$	6.75360e10	0.0993555
$427$	2.15671e11	0.313954
$428$	−8.10485e11	−1.16748
$429$	8.28833e9	0.0118143
$430$	−9.15007e10	−0.129067
$431$	9.74440e11	1.36021	0.680107	−	0.733113i	$-0.261933\pi$
$431$	9.74440e11	1.36021	0.680107	+	0.733113i	$0.261933\pi$
$432$	6.88941e10	0.0951712
$433$	1.90387e11	0.260281	0.130141	−	0.991496i	$-0.458457\pi$
$433$	1.90387e11	0.260281	0.130141	+	0.991496i	$0.458457\pi$
$434$	7.63263e11	1.03269
$435$	1.55585e11	0.208336
$436$	−3.95463e11	−0.524102
$437$	6.94754e11	0.911307
$438$	−4.60703e10	−0.0598119
$439$	−1.27826e12	−1.64259	−0.821297	−	0.570501i	$-0.806749\pi$
$439$	−1.27826e12	−1.64259	−0.821297	+	0.570501i	$0.806749\pi$
$440$	−6.11429e10	−0.0777695
$441$	1.50231e11	0.189142
$442$	6.57369e9	0.00819236
$443$	−1.09736e12	−1.35374	−0.676868	−	0.736105i	$-0.736663\pi$
$443$	−1.09736e12	−1.35374	−0.676868	+	0.736105i	$0.736663\pi$
$444$	−6.89784e10	−0.0842345
$445$	1.74537e11	0.210993
$446$	3.05768e11	0.365920
$447$	3.42542e11	0.405817
$448$	−8.49973e10	−0.0996906
$449$	1.35831e12	1.57722	0.788609	−	0.614895i	$-0.210802\pi$
$449$	1.35831e12	1.57722	0.788609	+	0.614895i	$0.210802\pi$
$450$	1.17817e11	0.135442
$451$	6.55622e11	0.746206
$452$	−5.28371e11	−0.595410
$453$	−9.79583e10	−0.109295
$454$	−4.00558e11	−0.442501
$455$	−9.31691e9	−0.0101911
$456$	5.97909e11	0.647580
$457$	4.51819e11	0.484554	0.242277	−	0.970207i	$-0.422106\pi$
$457$	4.51819e11	0.484554	0.242277	+	0.970207i	$0.422106\pi$
$458$	−6.88035e11	−0.730660
$459$	8.71691e10	0.0916654
$460$	−9.88911e10	−0.102979
$461$	1.06027e12	1.09336	0.546678	−	0.837343i	$-0.315892\pi$
$461$	1.06027e12	1.09336	0.546678	+	0.837343i	$0.315892\pi$
$462$	1.50903e11	0.154102
$463$	7.93160e11	0.802133	0.401067	−	0.916049i	$-0.368640\pi$
$463$	7.93160e11	0.802133	0.401067	+	0.916049i	$0.368640\pi$
$464$	8.89353e11	0.890725
$465$	−2.27228e11	−0.225384
$466$	−2.36195e11	−0.232025
$467$	1.10323e12	1.07335	0.536675	−	0.843789i	$-0.319680\pi$
$467$	1.10323e12	1.07335	0.536675	+	0.843789i	$0.319680\pi$
$468$	1.15367e10	0.0111167
$469$	−4.72703e11	−0.451139
$470$	2.73767e10	0.0258786
$471$	7.53358e11	0.705355
$472$	−1.08203e11	−0.100346
$473$	−8.34392e11	−0.766469
$474$	−3.80762e11	−0.346459
$475$	−1.54974e12	−1.39681
$476$	−5.48216e11	−0.489463
$477$	−7.75720e10	−0.0686076
$478$	−3.47787e11	−0.304711
$479$	−6.09570e11	−0.529071	−0.264535	−	0.964376i	$-0.585219\pi$
$479$	−6.09570e11	−0.529071	−0.264535	+	0.964376i	$0.585219\pi$
$480$	−1.31847e11	−0.113367
$481$	−8.47855e9	−0.00722218
$482$	−2.57831e11	−0.217582
$483$	5.41417e11	0.452658
$484$	7.39588e11	0.612612
$485$	5.56266e10	0.0456504
$486$	−3.33983e10	−0.0271557
$487$	−2.37201e12	−1.91090	−0.955448	−	0.295161i	$-0.904627\pi$
$487$	−2.37201e12	−1.91090	−0.955448	+	0.295161i	$0.904627\pi$
$488$	2.42152e11	0.193286
$489$	1.44129e12	1.13989
$490$	−6.14079e10	−0.0481218
$491$	−4.27405e11	−0.331874	−0.165937	−	0.986136i	$-0.553065\pi$
$491$	−4.27405e11	−0.331874	−0.165937	+	0.986136i	$0.553065\pi$
$492$	9.12575e11	0.702143
$493$	1.12526e12	0.857913
$494$	3.31299e10	0.0250293
$495$	−4.49246e10	−0.0336326
$496$	−1.29888e12	−0.963609
$497$	−6.92287e11	−0.508958
$498$	6.41901e10	0.0467666
$499$	−9.86003e11	−0.711911	−0.355956	−	0.934503i	$-0.615845\pi$
$499$	−9.86003e11	−0.711911	−0.355956	+	0.934503i	$0.615845\pi$
$500$	4.50402e11	0.322281
$501$	3.53643e11	0.250781
$502$	−8.21046e11	−0.577033
$503$	2.34755e12	1.63516	0.817579	−	0.575817i	$-0.195316\pi$
$503$	2.34755e12	1.63516	0.817579	+	0.575817i	$0.195316\pi$
$504$	4.65947e11	0.321662
$505$	8.53262e10	0.0583810
$506$	1.96875e11	0.133510
$507$	−8.57546e11	−0.576397
$508$	−9.49269e10	−0.0632416
$509$	2.11552e12	1.39697	0.698483	−	0.715626i	$-0.253859\pi$
$509$	2.11552e12	1.39697	0.698483	+	0.715626i	$0.253859\pi$
$510$	−3.56308e10	−0.0233217
$511$	4.72250e11	0.306392
$512$	−1.34636e12	−0.865856
$513$	4.39312e11	0.280056
$514$	5.36531e11	0.339048
$515$	1.07321e11	0.0672285
$516$	−1.16141e12	−0.721210
$517$	2.49647e11	0.153681
$518$	−1.54366e11	−0.0942037
$519$	1.68063e12	1.01676
$520$	−1.04609e10	−0.00627415
$521$	1.32436e12	0.787474	0.393737	−	0.919223i	$-0.371182\pi$
$521$	1.32436e12	0.787474	0.393737	+	0.919223i	$0.371182\pi$
$522$	−4.31138e11	−0.254155
$523$	−2.18959e11	−0.127969	−0.0639845	−	0.997951i	$-0.520381\pi$
$523$	−2.18959e11	−0.127969	−0.0639845	+	0.997951i	$0.520381\pi$
$524$	−3.58417e11	−0.207682
$525$	−1.20770e12	−0.693813
$526$	5.30527e11	0.302184
$527$	−1.64342e12	−0.928113
$528$	−2.56798e11	−0.143793
$529$	−1.09479e12	−0.607830
$530$	3.17080e10	0.0174553
$531$	−7.95020e10	−0.0433963
$532$	−2.76288e12	−1.49541
$533$	1.12170e11	0.0602011
$534$	−4.83656e11	−0.257395
$535$	5.39971e11	0.284956
$536$	−5.30745e11	−0.277744
$537$	−1.01786e12	−0.528207
$538$	−1.24339e12	−0.639864
$539$	−5.59977e11	−0.285772
$540$	−6.25316e10	−0.0316466
$541$	−1.87971e12	−0.943416	−0.471708	−	0.881755i	$-0.656362\pi$
$541$	−1.87971e12	−0.943416	−0.471708	+	0.881755i	$0.656362\pi$
$542$	3.71193e11	0.184758
$543$	−8.85798e9	−0.00437256
$544$	−9.53583e11	−0.466835
$545$	2.63470e11	0.127922
$546$	2.58179e10	0.0124324
$547$	1.45627e12	0.695502	0.347751	−	0.937587i	$-0.386946\pi$
$547$	1.45627e12	0.695502	0.347751	+	0.937587i	$0.386946\pi$
$548$	−1.99074e12	−0.942979
$549$	1.77921e11	0.0835894
$550$	−4.39155e11	−0.204638
$551$	5.67107e12	2.62110
$552$	6.07897e11	0.278679
$553$	3.90306e12	1.77477
$554$	6.84477e11	0.308720
$555$	4.59556e10	0.0205599
$556$	−3.53099e11	−0.156697
$557$	1.34465e11	0.0591919	0.0295959	−	0.999562i	$-0.490578\pi$
$557$	1.34465e11	0.0591919	0.0295959	+	0.999562i	$0.490578\pi$
$558$	6.29665e11	0.274951
$559$	−1.42756e11	−0.0618358
$560$	2.88667e11	0.124037
$561$	−3.24916e11	−0.138497
$562$	1.02294e11	0.0432552
$563$	−3.82201e12	−1.60326	−0.801630	−	0.597820i	$-0.796034\pi$
$563$	−3.82201e12	−1.60326	−0.801630	+	0.597820i	$0.796034\pi$
$564$	3.47490e11	0.144606
$565$	3.52018e11	0.145327
$566$	1.67209e12	0.684835
$567$	3.42353e11	0.139108
$568$	−7.77291e11	−0.313340
$569$	−2.55907e12	−1.02348	−0.511738	−	0.859142i	$-0.670998\pi$
$569$	−2.55907e12	−1.02348	−0.511738	+	0.859142i	$0.670998\pi$
$570$	−1.79571e11	−0.0712525
$571$	3.38712e11	0.133342	0.0666712	−	0.997775i	$-0.478762\pi$
$571$	3.38712e11	0.133342	0.0666712	+	0.997775i	$0.478762\pi$
$572$	−4.30023e10	−0.0167961
$573$	8.92175e11	0.345744
$574$	2.04224e12	0.785242
$575$	−1.57562e12	−0.601100
$576$	−7.01198e10	−0.0265424
$577$	−1.31031e12	−0.492134	−0.246067	−	0.969253i	$-0.579138\pi$
$577$	−1.31031e12	−0.492134	−0.246067	+	0.969253i	$0.579138\pi$
$578$	8.78198e11	0.327278
$579$	−2.34272e12	−0.866299
$580$	−8.07219e11	−0.296187
$581$	−6.57989e11	−0.239566
$582$	−1.54146e11	−0.0556901
$583$	2.89144e11	0.103659
$584$	5.30236e11	0.188630
$585$	−7.68613e9	−0.00271335
$586$	7.96088e11	0.278883
$587$	−1.73713e12	−0.603893	−0.301946	−	0.953325i	$-0.597636\pi$
$587$	−1.73713e12	−0.603893	−0.301946	+	0.953325i	$0.597636\pi$
$588$	−7.79444e11	−0.268898
$589$	−8.28246e12	−2.83557
$590$	3.24969e10	0.0110410
$591$	−1.46233e12	−0.493063
$592$	2.62691e11	0.0879019
$593$	1.03177e11	0.0342640	0.0171320	−	0.999853i	$-0.494546\pi$
$593$	1.03177e11	0.0342640	0.0171320	+	0.999853i	$0.494546\pi$
$594$	1.24490e11	0.0410293
$595$	3.65239e11	0.119468
$596$	−1.77721e12	−0.576940
$597$	−1.87334e12	−0.603577
$598$	3.36833e10	0.0107711
$599$	2.06669e11	0.0655926	0.0327963	−	0.999462i	$-0.489559\pi$
$599$	2.06669e11	0.0655926	0.0327963	+	0.999462i	$0.489559\pi$
$600$	−1.35599e12	−0.427146
$601$	−4.41366e12	−1.37995	−0.689975	−	0.723833i	$-0.742379\pi$
$601$	−4.41366e12	−1.37995	−0.689975	+	0.723833i	$0.742379\pi$
$602$	−2.59911e12	−0.806566
$603$	−3.89964e11	−0.120115
$604$	5.08236e11	0.155382
$605$	−4.92737e11	−0.149526
$606$	−2.36446e11	−0.0712204
$607$	3.52761e12	1.05471	0.527354	−	0.849646i	$-0.323184\pi$
$607$	3.52761e12	1.05471	0.527354	+	0.849646i	$0.323184\pi$
$608$	−4.80584e12	−1.42628
$609$	4.41943e12	1.30193
$610$	−7.27261e10	−0.0212670
$611$	4.27121e10	0.0123984
$612$	−4.52259e11	−0.130318
$613$	−1.61053e11	−0.0460677	−0.0230339	−	0.999735i	$-0.507333\pi$
$613$	−1.61053e11	−0.0460677	−0.0230339	+	0.999735i	$0.507333\pi$
$614$	2.31133e12	0.656303
$615$	−6.07986e11	−0.171378
$616$	−1.73678e12	−0.485996
$617$	−4.10818e12	−1.14121	−0.570606	−	0.821224i	$-0.693292\pi$
$617$	−4.10818e12	−1.14121	−0.570606	+	0.821224i	$0.693292\pi$
$618$	−2.97396e11	−0.0820138
$619$	3.36299e12	0.920698	0.460349	−	0.887738i	$-0.347724\pi$
$619$	3.36299e12	0.920698	0.460349	+	0.887738i	$0.347724\pi$
$620$	1.17892e12	0.320422
$621$	4.46650e11	0.120519
$622$	3.02729e12	0.810956
$623$	4.95778e12	1.31853
$624$	−4.39354e10	−0.0116007
$625$	3.36152e12	0.881201
$626$	−2.09669e12	−0.545696
$627$	−1.63750e12	−0.423135
$628$	−3.90864e12	−1.00278
$629$	3.32373e11	0.0846639
$630$	−1.39939e11	−0.0353920
$631$	−4.90415e12	−1.23149	−0.615747	−	0.787944i	$-0.711145\pi$
$631$	−4.90415e12	−1.23149	−0.615747	+	0.787944i	$0.711145\pi$
$632$	4.38230e12	1.09264
$633$	2.37417e11	0.0587754
$634$	4.02001e11	0.0988156
$635$	6.32433e10	0.0154359
$636$	4.02467e11	0.0975378
$637$	−9.58061e10	−0.0230550
$638$	1.60703e12	0.384001
$639$	−5.71112e11	−0.135509
$640$	8.62067e11	0.203110
$641$	9.35863e11	0.218953	0.109477	−	0.993989i	$-0.465083\pi$
$641$	9.35863e11	0.218953	0.109477	+	0.993989i	$0.465083\pi$
$642$	−1.49630e12	−0.347625
$643$	7.78616e11	0.179628	0.0898140	−	0.995959i	$-0.471373\pi$
$643$	7.78616e11	0.179628	0.0898140	+	0.995959i	$0.471373\pi$
$644$	−2.80903e12	−0.643532
$645$	7.73768e11	0.176032
$646$	−1.29875e12	−0.293412
$647$	1.37091e12	0.307568	0.153784	−	0.988104i	$-0.450854\pi$
$647$	1.37091e12	0.307568	0.153784	+	0.988104i	$0.450854\pi$
$648$	3.84390e11	0.0856416
$649$	2.96338e11	0.0655671
$650$	−7.51348e10	−0.0165094
$651$	−6.45447e12	−1.40847
$652$	−7.47783e12	−1.62055
$653$	−7.64528e12	−1.64545	−0.822724	−	0.568441i	$-0.807547\pi$
$653$	−7.64528e12	−1.64545	−0.822724	+	0.568441i	$0.807547\pi$
$654$	−7.30095e11	−0.156056
$655$	2.38789e11	0.0506907
$656$	−3.47537e12	−0.732713
$657$	3.89589e11	0.0815761
$658$	7.77645e11	0.161720
$659$	1.26763e12	0.261823	0.130911	−	0.991394i	$-0.458210\pi$
$659$	1.26763e12	0.261823	0.130911	+	0.991394i	$0.458210\pi$
$660$	2.33082e11	0.0478147
$661$	5.08848e12	1.03677	0.518384	−	0.855148i	$-0.326534\pi$
$661$	5.08848e12	1.03677	0.518384	+	0.855148i	$0.326534\pi$
$662$	6.16231e10	0.0124705
$663$	−5.55898e10	−0.0111734
$664$	−7.38782e11	−0.147489
$665$	1.84072e12	0.364998
$666$	−1.27347e11	−0.0250815
$667$	5.76580e12	1.12796
$668$	−1.83480e12	−0.356529
$669$	−2.58570e12	−0.499070
$670$	1.59400e11	0.0305598
$671$	−6.63187e11	−0.126295
$672$	−3.74516e12	−0.708450
$673$	1.67350e12	0.314455	0.157227	−	0.987562i	$-0.449744\pi$
$673$	1.67350e12	0.314455	0.157227	+	0.987562i	$0.449744\pi$
$674$	1.90439e12	0.355457
$675$	−9.96310e11	−0.184726
$676$	4.44920e12	0.819449
$677$	−1.45172e12	−0.265603	−0.132802	−	0.991143i	$-0.542397\pi$
$677$	−1.45172e12	−0.265603	−0.132802	+	0.991143i	$0.542397\pi$
$678$	−9.75469e11	−0.177288
$679$	1.58009e12	0.285278
$680$	4.10085e11	0.0735503
$681$	3.38729e12	0.603518
$682$	−2.34703e12	−0.415422
$683$	5.62955e12	0.989876	0.494938	−	0.868928i	$-0.335191\pi$
$683$	5.62955e12	0.989876	0.494938	+	0.868928i	$0.335191\pi$
$684$	−2.27928e12	−0.398149
$685$	1.32629e12	0.230161
$686$	1.32977e12	0.229255
$687$	5.81830e12	0.996532
$688$	4.42301e12	0.752610
$689$	4.94695e10	0.00836280
$690$	−1.82571e11	−0.0306627
$691$	7.22348e12	1.20530	0.602650	−	0.798005i	$-0.294111\pi$
$691$	7.22348e12	1.20530	0.602650	+	0.798005i	$0.294111\pi$
$692$	−8.71960e12	−1.44550
$693$	−1.27610e12	−0.210177
$694$	−3.19345e12	−0.522568
$695$	2.35246e11	0.0382464
$696$	4.96208e12	0.801535
$697$	−4.39725e12	−0.705722
$698$	−2.15538e11	−0.0343696
$699$	1.99736e12	0.316453
$700$	6.26590e12	0.986376
$701$	1.16867e13	1.82793	0.913967	−	0.405789i	$-0.133003\pi$
$701$	1.16867e13	1.82793	0.913967	+	0.405789i	$0.133003\pi$
$702$	2.12989e10	0.00331009
$703$	1.67509e12	0.258665
$704$	2.61367e11	0.0401026
$705$	−2.31509e11	−0.0352953
$706$	−3.10581e12	−0.470493
$707$	2.42372e12	0.364834
$708$	4.12480e11	0.0616954
$709$	1.02089e13	1.51730	0.758652	−	0.651496i	$-0.225858\pi$
$709$	1.02089e13	1.51730	0.758652	+	0.651496i	$0.225858\pi$
$710$	2.33445e11	0.0344764
$711$	3.21988e12	0.472528
$712$	5.56653e12	0.811754
$713$	−8.42081e12	−1.22026
$714$	−1.01211e12	−0.145742
$715$	2.86495e10	0.00409958
$716$	5.28096e12	0.750938
$717$	2.94103e12	0.415588
$718$	−4.93237e12	−0.692622
$719$	8.61256e12	1.20186	0.600928	−	0.799303i	$-0.294798\pi$
$719$	8.61256e12	1.20186	0.600928	+	0.799303i	$0.294798\pi$
$720$	2.38140e11	0.0330245
$721$	3.04850e12	0.420123
$722$	−3.45451e12	−0.473118
$723$	2.18032e12	0.296756
$724$	4.59578e10	0.00621635
$725$	−1.28613e13	−1.72888
$726$	1.36541e12	0.182410
$727$	−1.13796e13	−1.51086	−0.755428	−	0.655231i	$-0.772571\pi$
$727$	−1.13796e13	−1.51086	−0.755428	+	0.655231i	$0.772571\pi$
$728$	−2.97146e11	−0.0392083
$729$	2.82430e11	0.0370370
$730$	−1.59247e11	−0.0207548
$731$	5.59626e12	0.724886
$732$	−9.23105e11	−0.118837
$733$	−1.07252e12	−0.137226	−0.0686131	−	0.997643i	$-0.521857\pi$
$733$	−1.07252e12	−0.137226	−0.0686131	+	0.997643i	$0.521857\pi$
$734$	4.55239e12	0.578905
$735$	5.19291e11	0.0656323
$736$	−4.88612e12	−0.613782
$737$	1.45356e12	0.181480
$738$	1.68478e12	0.209069
$739$	−1.10892e13	−1.36773	−0.683865	−	0.729609i	$-0.739702\pi$
$739$	−1.10892e13	−1.36773	−0.683865	+	0.729609i	$0.739702\pi$
$740$	−2.38431e11	−0.0292294
$741$	−2.80160e11	−0.0341369
$742$	9.00676e11	0.109081
$743$	−5.45647e12	−0.656843	−0.328422	−	0.944531i	$-0.606517\pi$
$743$	−5.45647e12	−0.656843	−0.328422	+	0.944531i	$0.606517\pi$
$744$	−7.24700e12	−0.867121
$745$	1.18403e12	0.140819
$746$	3.03868e12	0.359220
$747$	−5.42818e11	−0.0637840
$748$	1.68576e12	0.196897
$749$	1.53380e13	1.78074
$750$	8.31523e11	0.0959619
$751$	−1.27661e13	−1.46447	−0.732234	−	0.681053i	$-0.761522\pi$
$751$	−1.27661e13	−1.46447	−0.732234	+	0.681053i	$0.761522\pi$
$752$	−1.32335e12	−0.150902
$753$	6.94311e12	0.787003
$754$	2.74947e11	0.0309797
$755$	−3.38603e11	−0.0379254
$756$	−1.77623e12	−0.197766
$757$	−5.42850e12	−0.600826	−0.300413	−	0.953809i	$-0.597124\pi$
$757$	−5.42850e12	−0.600826	−0.300413	+	0.953809i	$0.597124\pi$
$758$	−2.79586e12	−0.307612
$759$	−1.66486e12	−0.182091
$760$	2.06674e12	0.224711
$761$	1.16683e13	1.26118	0.630591	−	0.776116i	$-0.282813\pi$
$761$	1.16683e13	1.26118	0.630591	+	0.776116i	$0.282813\pi$
$762$	−1.75252e11	−0.0188307
$763$	7.48394e12	0.799411
$764$	−4.62886e12	−0.491535
$765$	3.01309e11	0.0318080
$766$	1.56671e12	0.164421
$767$	5.07003e10	0.00528971
$768$	−1.94563e12	−0.201806
$769$	7.33122e11	0.0755976	0.0377988	−	0.999285i	$-0.487965\pi$
$769$	7.33122e11	0.0755976	0.0377988	+	0.999285i	$0.487965\pi$
$770$	5.21612e11	0.0534736
$771$	−4.53713e12	−0.462420
$772$	1.21547e13	1.23160
$773$	1.97291e13	1.98746	0.993732	−	0.111789i	$-0.0356580\pi$
$773$	1.97291e13	1.98746	0.993732	+	0.111789i	$0.0356580\pi$
$774$	−2.14417e12	−0.214746
$775$	1.87837e13	1.87035
$776$	1.77411e12	0.175631
$777$	1.30538e12	0.128482
$778$	3.97242e12	0.388729
$779$	−2.21611e13	−2.15612
$780$	3.98779e10	0.00385750
$781$	2.12878e12	0.204739
$782$	−1.32044e12	−0.126267
$783$	3.64588e12	0.346636
$784$	2.96837e12	0.280605
$785$	2.60406e12	0.244759
$786$	−6.61703e11	−0.0618389
$787$	−7.76348e12	−0.721390	−0.360695	−	0.932684i	$-0.617460\pi$
$787$	−7.76348e12	−0.721390	−0.360695	+	0.932684i	$0.617460\pi$
$788$	7.58701e12	0.700975
$789$	−4.48636e12	−0.412143
$790$	−1.31615e12	−0.120221
$791$	9.99917e12	0.908176
$792$	−1.43279e12	−0.129395
$793$	−1.13464e11	−0.0101890
$794$	3.98179e11	0.0355538
$795$	−2.68136e11	−0.0238069
$796$	9.71945e12	0.858090
$797$	−9.48983e12	−0.833098	−0.416549	−	0.909113i	$-0.636761\pi$
$797$	−9.48983e12	−0.833098	−0.416549	+	0.909113i	$0.636761\pi$
$798$	−5.10078e12	−0.445270
$799$	−1.67438e12	−0.145343
$800$	1.08991e13	0.940775
$801$	4.08999e12	0.351056
$802$	4.35560e12	0.371760
$803$	−1.45217e12	−0.123253
$804$	2.02325e12	0.170764
$805$	1.87147e12	0.157073
$806$	−4.01553e11	−0.0335147
$807$	1.05146e13	0.872697
$808$	2.72132e12	0.224610
$809$	−2.02032e13	−1.65826	−0.829128	−	0.559059i	$-0.811163\pi$
$809$	−2.02032e13	−1.65826	−0.829128	+	0.559059i	$0.811163\pi$
$810$	−1.15445e11	−0.00942304
$811$	1.33725e13	1.08547	0.542735	−	0.839904i	$-0.317389\pi$
$811$	1.33725e13	1.08547	0.542735	+	0.839904i	$0.317389\pi$
$812$	−2.29293e13	−1.85093
$813$	−3.13896e12	−0.251987
$814$	4.74675e11	0.0378954
$815$	4.98197e12	0.395541
$816$	1.72234e12	0.135992
$817$	2.82039e13	2.21467
$818$	−6.40941e12	−0.500528
$819$	−2.18327e11	−0.0169562
$820$	3.15441e12	0.243644
$821$	−6.30233e12	−0.484124	−0.242062	−	0.970261i	$-0.577824\pi$
$821$	−6.30233e12	−0.484124	−0.242062	+	0.970261i	$0.577824\pi$
$822$	−3.67526e12	−0.280780
$823$	−1.10580e13	−0.840190	−0.420095	−	0.907480i	$-0.638003\pi$
$823$	−1.10580e13	−0.840190	−0.420095	+	0.907480i	$0.638003\pi$
$824$	3.42281e12	0.258649
$825$	3.71367e12	0.279101
$826$	9.23084e11	0.0689971
$827$	9.48648e12	0.705229	0.352614	−	0.935769i	$-0.385293\pi$
$827$	9.48648e12	0.705229	0.352614	+	0.935769i	$0.385293\pi$
$828$	−2.31735e12	−0.171339
$829$	1.42896e13	1.05081	0.525406	−	0.850852i	$-0.323913\pi$
$829$	1.42896e13	1.05081	0.525406	+	0.850852i	$0.323913\pi$
$830$	2.21880e11	0.0162280
$831$	−5.78822e12	−0.421057
$832$	4.47171e10	0.00323533
$833$	3.75576e12	0.270269
$834$	−6.51884e11	−0.0466577
$835$	1.22240e12	0.0870213
$836$	8.49586e12	0.601560
$837$	−5.32471e12	−0.375000
$838$	−4.21854e12	−0.295504
$839$	2.21256e13	1.54158	0.770789	−	0.637091i	$-0.219862\pi$
$839$	2.21256e13	1.54158	0.770789	+	0.637091i	$0.219862\pi$
$840$	1.61060e12	0.111617
$841$	3.25574e13	2.24423
$842$	−6.06562e12	−0.415883
$843$	−8.65043e11	−0.0589948
$844$	−1.23179e12	−0.0835595
$845$	−2.96420e12	−0.200010
$846$	6.41530e11	0.0430576
$847$	−1.39963e13	−0.934414
$848$	−1.53272e12	−0.101784
$849$	−1.41399e13	−0.934031
$850$	2.94541e12	0.193535
$851$	1.70307e12	0.111314
$852$	2.96310e12	0.192650
$853$	−2.45669e13	−1.58884	−0.794418	−	0.607371i	$-0.792224\pi$
$853$	−2.45669e13	−1.58884	−0.794418	+	0.607371i	$0.792224\pi$
$854$	−2.06581e12	−0.132901
$855$	1.51853e12	0.0971797
$856$	1.72214e13	1.09631
$857$	1.18349e12	0.0749467	0.0374734	−	0.999298i	$-0.488069\pi$
$857$	1.18349e12	0.0749467	0.0374734	+	0.999298i	$0.488069\pi$
$858$	−7.93900e10	−0.00500119
$859$	−7.80900e12	−0.489357	−0.244679	−	0.969604i	$-0.578682\pi$
$859$	−7.80900e12	−0.489357	−0.244679	+	0.969604i	$0.578682\pi$
$860$	−4.01453e12	−0.250260
$861$	−1.72700e13	−1.07097
$862$	−9.33370e12	−0.575799
$863$	−2.60230e13	−1.59701	−0.798507	−	0.601986i	$-0.794376\pi$
$863$	−2.60230e13	−1.59701	−0.798507	+	0.601986i	$0.794376\pi$
$864$	−3.08963e12	−0.188623
$865$	5.80927e12	0.352817
$866$	−1.82363e12	−0.110181
$867$	−7.42640e12	−0.446368
$868$	3.34877e13	2.00238
$869$	−1.20019e13	−0.713938
$870$	−1.49027e12	−0.0881920
$871$	2.48689e11	0.0146411
$872$	8.40287e12	0.492157
$873$	1.30352e12	0.0759546
$874$	−6.65472e12	−0.385770
$875$	−8.52364e12	−0.491574
$876$	−2.02130e12	−0.115975
$877$	2.23145e13	1.27377	0.636883	−	0.770961i	$-0.280224\pi$
$877$	2.23145e13	1.27377	0.636883	+	0.770961i	$0.280224\pi$
$878$	1.22439e13	0.695335
$879$	−6.73205e12	−0.380362
$880$	−8.87649e11	−0.0498964
$881$	−4.12977e12	−0.230958	−0.115479	−	0.993310i	$-0.536840\pi$
$881$	−4.12977e12	−0.230958	−0.115479	+	0.993310i	$0.536840\pi$
$882$	−1.43900e12	−0.0800665
$883$	1.42470e13	0.788682	0.394341	−	0.918964i	$-0.370973\pi$
$883$	1.42470e13	0.788682	0.394341	+	0.918964i	$0.370973\pi$
$884$	2.88416e11	0.0158849
$885$	−2.74807e11	−0.0150586
$886$	1.05111e13	0.573057
$887$	−1.91200e13	−1.03712	−0.518562	−	0.855040i	$-0.673532\pi$
$887$	−1.91200e13	−1.03712	−0.518562	+	0.855040i	$0.673532\pi$
$888$	1.46567e12	0.0791002
$889$	1.79645e12	0.0964620
$890$	−1.67181e12	−0.0893164
$891$	−1.05274e12	−0.0559590
$892$	1.34154e13	0.709515
$893$	−8.43852e12	−0.444053
$894$	−3.28105e12	−0.171789
$895$	−3.51834e12	−0.183288
$896$	2.44873e13	1.26927
$897$	−2.84840e11	−0.0146904
$898$	−1.30106e13	−0.667660
$899$	−6.87366e13	−3.50970
$900$	5.16915e12	0.262620
$901$	−1.93929e12	−0.0980350
$902$	−6.27989e12	−0.315880
$903$	2.19791e13	1.10006
$904$	1.12269e13	0.559118
$905$	−3.06185e10	−0.00151728
$906$	9.38296e11	0.0462661
$907$	2.51088e12	0.123195	0.0615974	−	0.998101i	$-0.480381\pi$
$907$	2.51088e12	0.123195	0.0615974	+	0.998101i	$0.480381\pi$
$908$	−1.75742e13	−0.858006
$909$	1.99948e12	0.0971360
$910$	8.92423e10	0.00431404
$911$	−9.38760e12	−0.451567	−0.225783	−	0.974178i	$-0.572494\pi$
$911$	−9.38760e12	−0.451567	−0.225783	+	0.974178i	$0.572494\pi$
$912$	8.68022e12	0.415483
$913$	2.02331e12	0.0963707
$914$	−4.32777e12	−0.205119
$915$	6.15002e11	0.0290056
$916$	−3.01871e13	−1.41674
$917$	6.78288e12	0.316776
$918$	−8.34952e11	−0.0388033
$919$	−1.67433e13	−0.774320	−0.387160	−	0.922013i	$-0.626544\pi$
$919$	−1.67433e13	−0.774320	−0.387160	+	0.922013i	$0.626544\pi$
$920$	2.10126e12	0.0967018
$921$	−1.95456e13	−0.895117
$922$	−1.01558e13	−0.462834
$923$	3.64212e11	0.0165176
$924$	6.62077e12	0.298803
$925$	−3.79890e12	−0.170616
$926$	−7.59731e12	−0.339555
$927$	2.51490e12	0.111857
$928$	−3.98840e13	−1.76536
$929$	−2.28909e13	−1.00830	−0.504152	−	0.863615i	$-0.668195\pi$
$929$	−2.28909e13	−1.00830	−0.504152	+	0.863615i	$0.668195\pi$
$930$	2.17651e12	0.0954084
$931$	1.89282e13	0.825725
$932$	−1.03629e13	−0.449894
$933$	−2.56000e13	−1.10605
$934$	−1.05673e13	−0.454365
$935$	−1.12311e12	−0.0480584
$936$	−2.45135e11	−0.0104391
$937$	1.00934e13	0.427770	0.213885	−	0.976859i	$-0.431388\pi$
$937$	1.00934e13	0.427770	0.213885	+	0.976859i	$0.431388\pi$
$938$	4.52780e12	0.190974
$939$	1.77305e13	0.744263
$940$	1.20114e12	0.0501784
$941$	−1.00404e13	−0.417444	−0.208722	−	0.977975i	$-0.566930\pi$
$941$	−1.00404e13	−0.417444	−0.208722	+	0.977975i	$0.566930\pi$
$942$	−7.21606e12	−0.298587
$943$	−2.25313e13	−0.927863
$944$	−1.57085e12	−0.0643815
$945$	1.18338e12	0.0482704
$946$	7.99224e12	0.324458
$947$	1.08513e13	0.438438	0.219219	−	0.975676i	$-0.429649\pi$
$947$	1.08513e13	0.438438	0.219219	+	0.975676i	$0.429649\pi$
$948$	−1.67057e13	−0.671781
$949$	−2.48450e11	−0.00994356
$950$	1.48442e13	0.591290
$951$	−3.39949e12	−0.134773
$952$	1.16486e13	0.459629
$953$	−4.63187e13	−1.81902	−0.909511	−	0.415680i	$-0.863544\pi$
$953$	−4.63187e13	−1.81902	−0.909511	+	0.415680i	$0.863544\pi$
$954$	7.43026e11	0.0290427
$955$	3.08390e12	0.119973
$956$	−1.52589e13	−0.590831
$957$	−1.35897e13	−0.523730
$958$	5.83878e12	0.223964
$959$	3.76738e13	1.43832
$960$	−2.42377e11	−0.00921022
$961$	7.39485e13	2.79688
$962$	8.12120e10	0.00305726
$963$	1.26533e13	0.474119
$964$	−1.13122e13	−0.421890
$965$	−8.09788e12	−0.300606
$966$	−5.18598e12	−0.191617
$967$	1.75311e13	0.644748	0.322374	−	0.946612i	$-0.395519\pi$
$967$	1.75311e13	0.644748	0.322374	+	0.946612i	$0.395519\pi$
$968$	−1.57149e13	−0.575272
$969$	1.09827e13	0.400178
$970$	−5.32821e11	−0.0193245
$971$	−5.17404e13	−1.86786	−0.933928	−	0.357462i	$-0.883642\pi$
$971$	−5.17404e13	−1.86786	−0.933928	+	0.357462i	$0.883642\pi$
$972$	−1.46533e12	−0.0526546
$973$	6.68223e12	0.239009
$974$	2.27204e13	0.808911
$975$	6.35371e11	0.0225168
$976$	3.51547e12	0.124011
$977$	3.99723e13	1.40357	0.701785	−	0.712389i	$-0.252387\pi$
$977$	3.99723e13	1.40357	0.701785	+	0.712389i	$0.252387\pi$
$978$	−1.38054e13	−0.482531
$979$	−1.52452e13	−0.530408
$980$	−2.69423e12	−0.0933077
$981$	6.17399e12	0.212841
$982$	4.09391e12	0.140487
$983$	8.61081e12	0.294140	0.147070	−	0.989126i	$-0.453016\pi$
$983$	8.61081e12	0.294140	0.147070	+	0.989126i	$0.453016\pi$
$984$	−1.93906e13	−0.659345
$985$	−5.05470e12	−0.171093
$986$	−1.07784e13	−0.363168
$987$	−6.57608e12	−0.220567
$988$	1.45355e12	0.0485316
$989$	2.86750e13	0.953060
$990$	4.30311e11	0.0142372
$991$	−3.90846e13	−1.28728	−0.643642	−	0.765326i	$-0.722578\pi$
$991$	−3.90846e13	−1.28728	−0.643642	+	0.765326i	$0.722578\pi$
$992$	5.82495e13	1.90981
$993$	−5.21110e11	−0.0170082
$994$	6.63109e12	0.215450
$995$	−6.47541e12	−0.209442
$996$	2.81630e12	0.0906800
$997$	4.21821e12	0.135207	0.0676037	−	0.997712i	$-0.478465\pi$
$997$	4.21821e12	0.135207	0.0676037	+	0.997712i	$0.478465\pi$
$998$	9.44446e12	0.301363
$999$	1.07690e12	0.0342081

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.9	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.9	✓	22	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-9.57853 q^{2} +81.0000 q^{3} -420.252 q^{4} +279.985 q^{5} -775.861 q^{6} +7953.06 q^{7} +8929.60 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-9.57853 q^{2} +81.0000 q^{3} -420.252 q^{4} +279.985 q^{5} -775.861 q^{6} +7953.06 q^{7} +8929.60 q^{8} +6561.00 q^{9} -2681.84 q^{10} -24455.7 q^{11} -34040.4 q^{12} -4184.11 q^{13} -76178.7 q^{14} +22678.8 q^{15} +129636. q^{16} +164024. q^{17} -62844.7 q^{18} +826643. q^{19} -117664. q^{20} +644198. q^{21} +234249. q^{22} +840452. q^{23} +723298. q^{24} -1.87473e6 q^{25} +40077.6 q^{26} +531441. q^{27} -3.34229e6 q^{28} +6.86036e6 q^{29} -217229. q^{30} -1.00194e7 q^{31} -5.81368e6 q^{32} -1.98091e6 q^{33} -1.57111e6 q^{34} +2.22674e6 q^{35} -2.75727e6 q^{36} +2.02637e6 q^{37} -7.91803e6 q^{38} -338913. q^{39} +2.50015e6 q^{40} -2.68086e7 q^{41} -6.17047e6 q^{42} +3.41186e7 q^{43} +1.02775e7 q^{44} +1.83698e6 q^{45} -8.05029e6 q^{46} -1.02082e7 q^{47} +1.05006e7 q^{48} +2.28976e7 q^{49} +1.79572e7 q^{50} +1.32859e7 q^{51} +1.75838e6 q^{52} -1.18232e7 q^{53} -5.09042e6 q^{54} -6.84722e6 q^{55} +7.10177e7 q^{56} +6.69581e7 q^{57} -6.57122e7 q^{58} -1.21174e7 q^{59} -9.53080e6 q^{60} +2.71179e7 q^{61} +9.59710e7 q^{62} +5.21801e7 q^{63} -1.06874e7 q^{64} -1.17149e6 q^{65} +1.89742e7 q^{66} -5.94366e7 q^{67} -6.89314e7 q^{68} +6.80766e7 q^{69} -2.13289e7 q^{70} -8.70465e7 q^{71} +5.85871e7 q^{72} +5.93796e7 q^{73} -1.94096e7 q^{74} -1.51853e8 q^{75} -3.47398e8 q^{76} -1.94497e8 q^{77} +3.24628e6 q^{78} +4.90761e8 q^{79} +3.62963e7 q^{80} +4.30467e7 q^{81} +2.56787e8 q^{82} -8.27340e7 q^{83} -2.70725e8 q^{84} +4.59243e7 q^{85} -3.26806e8 q^{86} +5.55689e8 q^{87} -2.18379e8 q^{88} +6.23380e8 q^{89} -1.75956e7 q^{90} -3.32765e7 q^{91} -3.53201e8 q^{92} -8.11570e8 q^{93} +9.77792e7 q^{94} +2.31448e8 q^{95} -4.70908e8 q^{96} +1.98677e8 q^{97} -2.19326e8 q^{98} -1.60454e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * q^99

Introduction

L-functions

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