LMFDB - Embedded newform 177.12.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,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, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
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:	$135.996742959$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-5.21206 q^{2} +243.000 q^{3} -2020.83 q^{4} -8551.43 q^{5} -1266.53 q^{6} -16524.4 q^{7} +21207.0 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-5.21206 q^{2} +243.000 q^{3} -2020.83 q^{4} -8551.43 q^{5} -1266.53 q^{6} -16524.4 q^{7} +21207.0 q^{8} +59049.0 q^{9} +44570.6 q^{10} -89297.0 q^{11} -491063. q^{12} -114841. q^{13} +86126.0 q^{14} -2.07800e6 q^{15} +4.02814e6 q^{16} -2.27567e6 q^{17} -307767. q^{18} -1.31943e7 q^{19} +1.72810e7 q^{20} -4.01542e6 q^{21} +465421. q^{22} -2.62891e7 q^{23} +5.15331e6 q^{24} +2.42989e7 q^{25} +598558. q^{26} +1.43489e7 q^{27} +3.33930e7 q^{28} -1.02740e8 q^{29} +1.08307e7 q^{30} -2.81409e8 q^{31} -6.44269e7 q^{32} -2.16992e7 q^{33} +1.18609e7 q^{34} +1.41307e8 q^{35} -1.19328e8 q^{36} -9.42260e7 q^{37} +6.87696e7 q^{38} -2.79063e7 q^{39} -1.81350e8 q^{40} -1.20015e9 q^{41} +2.09286e7 q^{42} -6.09679e8 q^{43} +1.80454e8 q^{44} -5.04954e8 q^{45} +1.37020e8 q^{46} -2.59230e9 q^{47} +9.78837e8 q^{48} -1.70427e9 q^{49} -1.26647e8 q^{50} -5.52988e8 q^{51} +2.32074e8 q^{52} +5.94524e9 q^{53} -7.47874e7 q^{54} +7.63617e8 q^{55} -3.50433e8 q^{56} -3.20622e9 q^{57} +5.35486e8 q^{58} +7.14924e8 q^{59} +4.19929e9 q^{60} +4.54803e9 q^{61} +1.46672e9 q^{62} -9.75747e8 q^{63} -7.91383e9 q^{64} +9.82054e8 q^{65} +1.13097e8 q^{66} +9.68563e9 q^{67} +4.59875e9 q^{68} -6.38824e9 q^{69} -7.36501e8 q^{70} +1.70954e10 q^{71} +1.25225e9 q^{72} -8.07569e9 q^{73} +4.91112e8 q^{74} +5.90463e9 q^{75} +2.66635e10 q^{76} +1.47557e9 q^{77} +1.45450e8 q^{78} +3.36701e10 q^{79} -3.44463e10 q^{80} +3.48678e9 q^{81} +6.25527e9 q^{82} -2.87180e10 q^{83} +8.11450e9 q^{84} +1.94602e10 q^{85} +3.17769e9 q^{86} -2.49657e10 q^{87} -1.89372e9 q^{88} -2.72935e9 q^{89} +2.63185e9 q^{90} +1.89767e9 q^{91} +5.31258e10 q^{92} -6.83823e10 q^{93} +1.35113e10 q^{94} +1.12830e11 q^{95} -1.56557e10 q^{96} +1.22050e11 q^{97} +8.88278e9 q^{98} -5.27290e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) $ 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * 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 $

$2$	−5.21206	−0.115171	−0.0575857	−	0.998341i	$-0.518340\pi$
$2$	−5.21206	−0.115171	−0.0575857	+	0.998341i	$0.518340\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−2020.83	−0.986736
$5$	−8551.43	−1.22378	−0.611891	−	0.790942i	$-0.709591\pi$
$5$	−8551.43	−1.22378	−0.611891	+	0.790942i	$0.709591\pi$
$6$	−1266.53	−0.0664943
$7$	−16524.4	−0.371608	−0.185804	−	0.982587i	$-0.559489\pi$
$7$	−16524.4	−0.371608	−0.185804	+	0.982587i	$0.559489\pi$
$8$	21207.0	0.228815
$9$	59049.0	0.333333
$10$	44570.6	0.140945
$11$	−89297.0	−0.167177	−0.0835886	−	0.996500i	$-0.526638\pi$
$11$	−89297.0	−0.167177	−0.0835886	+	0.996500i	$0.526638\pi$
$12$	−491063.	−0.569692
$13$	−114841.	−0.0857843	−0.0428922	−	0.999080i	$-0.513657\pi$
$13$	−114841.	−0.0857843	−0.0428922	+	0.999080i	$0.513657\pi$
$14$	86126.0	0.0427987
$15$	−2.07800e6	−0.706551
$16$	4.02814e6	0.960383
$17$	−2.27567e6	−0.388723	−0.194361	−	0.980930i	$-0.562263\pi$
$17$	−2.27567e6	−0.388723	−0.194361	+	0.980930i	$0.562263\pi$
$18$	−307767.	−0.0383905
$19$	−1.31943e7	−1.22248	−0.611240	−	0.791445i	$-0.709329\pi$
$19$	−1.31943e7	−1.22248	−0.611240	+	0.791445i	$0.709329\pi$
$20$	1.72810e7	1.20755
$21$	−4.01542e6	−0.214548
$22$	465421.	0.0192540
$23$	−2.62891e7	−0.851671	−0.425836	−	0.904801i	$-0.640020\pi$
$23$	−2.62891e7	−0.851671	−0.425836	+	0.904801i	$0.640020\pi$
$24$	5.15331e6	0.132107
$25$	2.42989e7	0.497641
$26$	598558.	0.00987990
$27$	1.43489e7	0.192450
$28$	3.33930e7	0.366679
$29$	−1.02740e8	−0.930142	−0.465071	−	0.885273i	$-0.653971\pi$
$29$	−1.02740e8	−0.930142	−0.465071	+	0.885273i	$0.653971\pi$
$30$	1.08307e7	0.0813745
$31$	−2.81409e8	−1.76542	−0.882710	−	0.469918i	$-0.844284\pi$
$31$	−2.81409e8	−1.76542	−0.882710	+	0.469918i	$0.844284\pi$
$32$	−6.44269e7	−0.339424
$33$	−2.16992e7	−0.0965198
$34$	1.18609e7	0.0447698
$35$	1.41307e8	0.454767
$36$	−1.19328e8	−0.328912
$37$	−9.42260e7	−0.223389	−0.111694	−	0.993743i	$-0.535628\pi$
$37$	−9.42260e7	−0.223389	−0.111694	+	0.993743i	$0.535628\pi$
$38$	6.87696e7	0.140795
$39$	−2.79063e7	−0.0495276
$40$	−1.81350e8	−0.280020
$41$	−1.20015e9	−1.61780	−0.808901	−	0.587945i	$-0.799937\pi$
$41$	−1.20015e9	−1.61780	−0.808901	+	0.587945i	$0.799937\pi$
$42$	2.09286e7	0.0247098
$43$	−6.09679e8	−0.632448	−0.316224	−	0.948685i	$-0.602415\pi$
$43$	−6.09679e8	−0.632448	−0.316224	+	0.948685i	$0.602415\pi$
$44$	1.80454e8	0.164960
$45$	−5.04954e8	−0.407927
$46$	1.37020e8	0.0980882
$47$	−2.59230e9	−1.64872	−0.824362	−	0.566064i	$-0.808466\pi$
$47$	−2.59230e9	−1.64872	−0.824362	+	0.566064i	$0.808466\pi$
$48$	9.78837e8	0.554477
$49$	−1.70427e9	−0.861907
$50$	−1.26647e8	−0.0573141
$51$	−5.52988e8	−0.224429
$52$	2.32074e8	0.0846464
$53$	5.94524e9	1.95277	0.976387	−	0.216031i	$-0.0693112\pi$
$53$	5.94524e9	1.95277	0.976387	+	0.216031i	$0.0693112\pi$
$54$	−7.47874e7	−0.0221648
$55$	7.63617e8	0.204588
$56$	−3.50433e8	−0.0850296
$57$	−3.20622e9	−0.705799
$58$	5.35486e8	0.107126
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	4.19929e9	0.697179
$61$	4.54803e9	0.689460	0.344730	−	0.938702i	$-0.387970\pi$
$61$	4.54803e9	0.689460	0.344730	+	0.938702i	$0.387970\pi$
$62$	1.46672e9	0.203326
$63$	−9.75747e8	−0.123869
$64$	−7.91383e9	−0.921291
$65$	9.82054e8	0.104981
$66$	1.13097e8	0.0111163
$67$	9.68563e9	0.876428	0.438214	−	0.898871i	$-0.355611\pi$
$67$	9.68563e9	0.876428	0.438214	+	0.898871i	$0.355611\pi$
$68$	4.59875e9	0.383567
$69$	−6.38824e9	−0.491713
$70$	−7.36501e8	−0.0523762
$71$	1.70954e10	1.12450	0.562248	−	0.826968i	$-0.309937\pi$
$71$	1.70954e10	1.12450	0.562248	+	0.826968i	$0.309937\pi$
$72$	1.25225e9	0.0762717
$73$	−8.07569e9	−0.455936	−0.227968	−	0.973669i	$-0.573208\pi$
$73$	−8.07569e9	−0.455936	−0.227968	+	0.973669i	$0.573208\pi$
$74$	4.91112e8	0.0257280
$75$	5.90463e9	0.287313
$76$	2.66635e10	1.20626
$77$	1.47557e9	0.0621244
$78$	1.45450e8	0.00570416
$79$	3.36701e10	1.23111	0.615554	−	0.788095i	$-0.288932\pi$
$79$	3.36701e10	1.23111	0.615554	+	0.788095i	$0.288932\pi$
$80$	−3.44463e10	−1.17530
$81$	3.48678e9	0.111111
$82$	6.25527e9	0.186325
$83$	−2.87180e10	−0.800247	−0.400123	−	0.916461i	$-0.631033\pi$
$83$	−2.87180e10	−0.800247	−0.400123	+	0.916461i	$0.631033\pi$
$84$	8.11450e9	0.211702
$85$	1.94602e10	0.475712
$86$	3.17769e9	0.0728400
$87$	−2.49657e10	−0.537018
$88$	−1.89372e9	−0.0382527
$89$	−2.72935e9	−0.0518102	−0.0259051	−	0.999664i	$-0.508247\pi$
$89$	−2.72935e9	−0.0518102	−0.0259051	+	0.999664i	$0.508247\pi$
$90$	2.63185e9	0.0469816
$91$	1.89767e9	0.0318782
$92$	5.31258e10	0.840374
$93$	−6.83823e10	−1.01927
$94$	1.35113e10	0.189886
$95$	1.12830e11	1.49605
$96$	−1.56557e10	−0.195966
$97$	1.22050e11	1.44309	0.721545	−	0.692368i	$-0.243432\pi$
$97$	1.22050e11	1.44309	0.721545	+	0.692368i	$0.243432\pi$
$98$	8.88278e9	0.0992671
$99$	−5.27290e9	−0.0557257
$100$	−4.91041e10	−0.491041
$101$	9.32657e10	0.882987	0.441493	−	0.897265i	$-0.354449\pi$
$101$	9.32657e10	0.882987	0.441493	+	0.897265i	$0.354449\pi$
$102$	2.88221e9	0.0258478
$103$	−1.62092e11	−1.37770	−0.688852	−	0.724902i	$-0.741885\pi$
$103$	−1.62092e11	−1.37770	−0.688852	+	0.724902i	$0.741885\pi$
$104$	−2.43543e9	−0.0196288
$105$	3.43376e10	0.262560
$106$	−3.09869e10	−0.224904
$107$	1.14640e10	0.0790180	0.0395090	−	0.999219i	$-0.487421\pi$
$107$	1.14640e10	0.0790180	0.0395090	+	0.999219i	$0.487421\pi$
$108$	−2.89968e10	−0.189897
$109$	−1.94706e11	−1.21208	−0.606042	−	0.795433i	$-0.707244\pi$
$109$	−1.94706e11	−1.21208	−0.606042	+	0.795433i	$0.707244\pi$
$110$	−3.98002e9	−0.0235627
$111$	−2.28969e10	−0.128974
$112$	−6.65624e10	−0.356886
$113$	−3.50109e11	−1.78761	−0.893804	−	0.448458i	$-0.851973\pi$
$113$	−3.50109e11	−1.78761	−0.893804	+	0.448458i	$0.851973\pi$
$114$	1.67110e10	0.0812879
$115$	2.24809e11	1.04226
$116$	2.07620e11	0.917804
$117$	−6.78124e9	−0.0285948
$118$	−3.72623e9	−0.0149940
$119$	3.76040e10	0.144453
$120$	−4.40682e10	−0.161670
$121$	−2.77338e11	−0.972052
$122$	−2.37046e10	−0.0794061
$123$	−2.91637e11	−0.934038
$124$	5.68680e11	1.74200
$125$	2.09760e11	0.614777
$126$	5.08566e9	0.0142662
$127$	−4.12670e11	−1.10836	−0.554182	−	0.832396i	$-0.686969\pi$
$127$	−4.12670e11	−1.10836	−0.554182	+	0.832396i	$0.686969\pi$
$128$	1.73194e11	0.445530
$129$	−1.48152e11	−0.365144
$130$	−5.11853e9	−0.0120908
$131$	−1.90011e11	−0.430316	−0.215158	−	0.976579i	$-0.569027\pi$
$131$	−1.90011e11	−0.430316	−0.215158	+	0.976579i	$0.569027\pi$
$132$	4.38504e10	0.0952395
$133$	2.18027e11	0.454284
$134$	−5.04821e10	−0.100940
$135$	−1.22704e11	−0.235517
$136$	−4.82602e10	−0.0889457
$137$	3.59136e11	0.635764	0.317882	−	0.948130i	$-0.397028\pi$
$137$	3.59136e11	0.635764	0.317882	+	0.948130i	$0.397028\pi$
$138$	3.32959e10	0.0566312
$139$	8.45010e11	1.38128	0.690638	−	0.723201i	$-0.257330\pi$
$139$	8.45010e11	1.38128	0.690638	+	0.723201i	$0.257330\pi$
$140$	−2.85558e11	−0.448735
$141$	−6.29930e11	−0.951891
$142$	−8.91023e10	−0.129510
$143$	1.02549e10	0.0143412
$144$	2.37857e11	0.320128
$145$	8.78572e11	1.13829
$146$	4.20910e10	0.0525108
$147$	−4.14138e11	−0.497622
$148$	1.90415e11	0.220426
$149$	−6.07518e11	−0.677695	−0.338848	−	0.940841i	$-0.610037\pi$
$149$	−6.07518e11	−0.677695	−0.338848	+	0.940841i	$0.610037\pi$
$150$	−3.07753e10	−0.0330903
$151$	5.39506e11	0.559272	0.279636	−	0.960106i	$-0.409786\pi$
$151$	5.39506e11	0.559272	0.279636	+	0.960106i	$0.409786\pi$
$152$	−2.79812e11	−0.279722
$153$	−1.34376e11	−0.129574
$154$	−7.69079e9	−0.00715496
$155$	2.40645e12	2.16049
$156$	5.63940e10	0.0488706
$157$	−4.28284e11	−0.358331	−0.179165	−	0.983819i	$-0.557340\pi$
$157$	−4.28284e11	−0.358331	−0.179165	+	0.983819i	$0.557340\pi$
$158$	−1.75491e11	−0.141788
$159$	1.44469e12	1.12743
$160$	5.50942e11	0.415381
$161$	4.34410e11	0.316488
$162$	−1.81733e10	−0.0127968
$163$	1.99661e12	1.35913	0.679567	−	0.733613i	$-0.262168\pi$
$163$	1.99661e12	1.35913	0.679567	+	0.733613i	$0.262168\pi$
$164$	2.42531e12	1.59634
$165$	1.85559e11	0.118119
$166$	1.49680e11	0.0921656
$167$	2.56504e12	1.52810	0.764052	−	0.645155i	$-0.223207\pi$
$167$	2.56504e12	1.52810	0.764052	+	0.645155i	$0.223207\pi$
$168$	−8.51551e10	−0.0490919
$169$	−1.77897e12	−0.992641
$170$	−1.01428e11	−0.0547884
$171$	−7.79110e11	−0.407493
$172$	1.23206e12	0.624059
$173$	−2.30931e12	−1.13300	−0.566500	−	0.824062i	$-0.691703\pi$
$173$	−2.30931e12	−1.13300	−0.566500	+	0.824062i	$0.691703\pi$
$174$	1.30123e11	0.0618491
$175$	−4.01524e11	−0.184928
$176$	−3.59700e11	−0.160554
$177$	1.73727e11	0.0751646
$178$	1.42256e10	0.00596705
$179$	1.60705e12	0.653638	0.326819	−	0.945087i	$-0.394023\pi$
$179$	1.60705e12	0.653638	0.326819	+	0.945087i	$0.394023\pi$
$180$	1.02043e12	0.402516
$181$	3.40265e12	1.30192	0.650961	−	0.759111i	$-0.274366\pi$
$181$	3.40265e12	1.30192	0.650961	+	0.759111i	$0.274366\pi$
$182$	−9.89078e9	−0.00367145
$183$	1.10517e12	0.398060
$184$	−5.57513e11	−0.194875
$185$	8.05767e11	0.273379
$186$	3.56413e11	0.117390
$187$	2.03210e11	0.0649856
$188$	5.23862e12	1.62685
$189$	−2.37107e11	−0.0715161
$190$	−5.88078e11	−0.172302
$191$	−5.66849e12	−1.61355	−0.806777	−	0.590856i	$-0.798790\pi$
$191$	−5.66849e12	−1.61355	−0.806777	+	0.590856i	$0.798790\pi$
$192$	−1.92306e12	−0.531907
$193$	1.68647e12	0.453330	0.226665	−	0.973973i	$-0.427218\pi$
$193$	1.68647e12	0.453330	0.226665	+	0.973973i	$0.427218\pi$
$194$	−6.36132e11	−0.166203
$195$	2.38639e11	0.0606110
$196$	3.44405e12	0.850475
$197$	−5.21431e11	−0.125208	−0.0626041	−	0.998038i	$-0.519941\pi$
$197$	−5.21431e11	−0.125208	−0.0626041	+	0.998038i	$0.519941\pi$
$198$	2.74827e10	0.00641801
$199$	−9.64663e11	−0.219121	−0.109560	−	0.993980i	$-0.534944\pi$
$199$	−9.64663e11	−0.219121	−0.109560	+	0.993980i	$0.534944\pi$
$200$	5.15307e11	0.113868
$201$	2.35361e12	0.506006
$202$	−4.86107e11	−0.101695
$203$	1.69771e12	0.345649
$204$	1.11750e12	0.221452
$205$	1.02630e13	1.97984
$206$	8.44832e11	0.158672
$207$	−1.55234e12	−0.283890
$208$	−4.62594e11	−0.0823858
$209$	1.17821e12	0.204371
$210$	−1.78970e11	−0.0302394
$211$	1.06069e13	1.74595	0.872977	−	0.487760i	$-0.162186\pi$
$211$	1.06069e13	1.74595	0.872977	+	0.487760i	$0.162186\pi$
$212$	−1.20143e13	−1.92687
$213$	4.15418e12	0.649228
$214$	−5.97512e10	−0.00910061
$215$	5.21363e12	0.773978
$216$	3.04298e11	0.0440355
$217$	4.65010e12	0.656045
$218$	1.01482e12	0.139597
$219$	−1.96239e12	−0.263235
$220$	−1.54314e12	−0.201875
$221$	2.61340e11	0.0333463
$222$	1.19340e11	0.0148541
$223$	−4.74343e12	−0.575991	−0.287995	−	0.957632i	$-0.592989\pi$
$223$	−4.74343e12	−0.575991	−0.287995	+	0.957632i	$0.592989\pi$
$224$	1.06461e12	0.126133
$225$	1.43483e12	0.165880
$226$	1.82479e12	0.205881
$227$	−1.00024e13	−1.10144	−0.550719	−	0.834691i	$-0.685646\pi$
$227$	−1.00024e13	−1.10144	−0.550719	+	0.834691i	$0.685646\pi$
$228$	6.47923e12	0.696437
$229$	−1.55990e13	−1.63682	−0.818412	−	0.574632i	$-0.805145\pi$
$229$	−1.55990e13	−1.63682	−0.818412	+	0.574632i	$0.805145\pi$
$230$	−1.17172e12	−0.120039
$231$	3.58565e11	0.0358675
$232$	−2.17880e12	−0.212831
$233$	−3.16513e12	−0.301949	−0.150975	−	0.988538i	$-0.548241\pi$
$233$	−3.16513e12	−0.301949	−0.150975	+	0.988538i	$0.548241\pi$
$234$	3.53442e10	0.00329330
$235$	2.21679e13	2.01768
$236$	−1.44474e12	−0.128462
$237$	8.18184e12	0.710780
$238$	−1.95994e11	−0.0166368
$239$	−4.40436e12	−0.365337	−0.182669	−	0.983175i	$-0.558474\pi$
$239$	−4.40436e12	−0.365337	−0.182669	+	0.983175i	$0.558474\pi$
$240$	−8.37046e12	−0.678559
$241$	−1.99297e12	−0.157909	−0.0789545	−	0.996878i	$-0.525158\pi$
$241$	−1.99297e12	−0.157909	−0.0789545	+	0.996878i	$0.525158\pi$
$242$	1.44550e12	0.111953
$243$	8.47289e11	0.0641500
$244$	−9.19081e12	−0.680315
$245$	1.45740e13	1.05479
$246$	1.52003e12	0.107575
$247$	1.51524e12	0.104870
$248$	−5.96784e12	−0.403955
$249$	−6.97846e12	−0.462023
$250$	−1.09328e12	−0.0708048
$251$	1.99837e13	1.26611	0.633053	−	0.774108i	$-0.281801\pi$
$251$	1.99837e13	1.26611	0.633053	+	0.774108i	$0.281801\pi$
$252$	1.97182e12	0.122226
$253$	2.34753e12	0.142380
$254$	2.15086e12	0.127652
$255$	4.72884e12	0.274652
$256$	1.53048e13	0.869978
$257$	3.10791e13	1.72917	0.864583	−	0.502491i	$-0.167583\pi$
$257$	3.10791e13	1.72917	0.864583	+	0.502491i	$0.167583\pi$
$258$	7.72178e11	0.0420542
$259$	1.55702e12	0.0830131
$260$	−1.98457e12	−0.103589
$261$	−6.06668e12	−0.310047
$262$	9.90352e11	0.0495601
$263$	1.67030e12	0.0818535	0.0409268	−	0.999162i	$-0.486969\pi$
$263$	1.67030e12	0.0818535	0.0409268	+	0.999162i	$0.486969\pi$
$264$	−4.60175e11	−0.0220852
$265$	−5.08403e13	−2.38977
$266$	−1.13637e12	−0.0523205
$267$	−6.63233e11	−0.0299126
$268$	−1.95731e13	−0.864803
$269$	4.16327e13	1.80217	0.901087	−	0.433638i	$-0.142770\pi$
$269$	4.16327e13	1.80217	0.901087	+	0.433638i	$0.142770\pi$
$270$	6.39540e11	0.0271248
$271$	−2.71374e13	−1.12782	−0.563908	−	0.825838i	$-0.690703\pi$
$271$	−2.71374e13	−1.12782	−0.563908	+	0.825838i	$0.690703\pi$
$272$	−9.16671e12	−0.373323
$273$	4.61134e11	0.0184049
$274$	−1.87184e12	−0.0732219
$275$	−2.16982e12	−0.0831943
$276$	1.29096e13	0.485190
$277$	−2.19871e13	−0.810082	−0.405041	−	0.914299i	$-0.632743\pi$
$277$	−2.19871e13	−0.810082	−0.405041	+	0.914299i	$0.632743\pi$
$278$	−4.40425e12	−0.159083
$279$	−1.66169e13	−0.588474
$280$	2.99670e12	0.104058
$281$	−2.21421e13	−0.753934	−0.376967	−	0.926227i	$-0.623033\pi$
$281$	−2.21421e13	−0.753934	−0.376967	+	0.926227i	$0.623033\pi$
$282$	3.28324e12	0.109631
$283$	3.42500e11	0.0112159	0.00560796	−	0.999984i	$-0.498215\pi$
$283$	3.42500e11	0.0112159	0.00560796	+	0.999984i	$0.498215\pi$
$284$	−3.45470e13	−1.10958
$285$	2.74177e13	0.863744
$286$	−5.34494e10	−0.00165169
$287$	1.98318e13	0.601189
$288$	−3.80434e12	−0.113141
$289$	−2.90932e13	−0.848894
$290$	−4.57917e12	−0.131099
$291$	2.96581e13	0.833168
$292$	1.63196e13	0.449888
$293$	4.84850e13	1.31170	0.655851	−	0.754890i	$-0.272310\pi$
$293$	4.84850e13	1.31170	0.655851	+	0.754890i	$0.272310\pi$
$294$	2.15851e12	0.0573119
$295$	−6.11363e12	−0.159323
$296$	−1.99825e12	−0.0511147
$297$	−1.28131e12	−0.0321733
$298$	3.16642e12	0.0780511
$299$	3.01906e12	0.0730600
$300$	−1.19323e13	−0.283502
$301$	1.00746e13	0.235023
$302$	−2.81194e12	−0.0644121
$303$	2.26636e13	0.509793
$304$	−5.31485e13	−1.17405
$305$	−3.88922e13	−0.843748
$306$	7.00376e11	0.0149233
$307$	7.50703e13	1.57111	0.785556	−	0.618791i	$-0.212377\pi$
$307$	7.50703e13	1.57111	0.785556	+	0.618791i	$0.212377\pi$
$308$	−2.98189e12	−0.0613004
$309$	−3.93883e13	−0.795418
$310$	−1.25426e13	−0.248827
$311$	−2.70953e13	−0.528094	−0.264047	−	0.964510i	$-0.585057\pi$
$311$	−2.70953e13	−0.528094	−0.264047	+	0.964510i	$0.585057\pi$
$312$	−5.91810e11	−0.0113327
$313$	5.44038e13	1.02361	0.511806	−	0.859101i	$-0.328977\pi$
$313$	5.44038e13	1.02361	0.511806	+	0.859101i	$0.328977\pi$
$314$	2.23225e12	0.0412695
$315$	8.34404e12	0.151589
$316$	−6.80418e13	−1.21478
$317$	6.63376e13	1.16395	0.581974	−	0.813207i	$-0.302280\pi$
$317$	6.63376e13	1.16395	0.581974	+	0.813207i	$0.302280\pi$
$318$	−7.52983e12	−0.129848
$319$	9.17434e12	0.155498
$320$	6.76746e13	1.12746
$321$	2.78575e12	0.0456210
$322$	−2.26417e12	−0.0364504
$323$	3.00259e13	0.475206
$324$	−7.04621e12	−0.109637
$325$	−2.79051e12	−0.0426898
$326$	−1.04065e13	−0.156533
$327$	−4.73135e13	−0.699797
$328$	−2.54517e13	−0.370178
$329$	4.28362e13	0.612679
$330$	−9.67145e11	−0.0136039
$331$	7.23224e13	1.00050	0.500252	−	0.865880i	$-0.333241\pi$
$331$	7.23224e13	1.00050	0.500252	+	0.865880i	$0.333241\pi$
$332$	5.80342e13	0.789632
$333$	−5.56395e12	−0.0744629
$334$	−1.33691e13	−0.175994
$335$	−8.28260e13	−1.07256
$336$	−1.61747e13	−0.206048
$337$	−1.52367e14	−1.90954	−0.954768	−	0.297353i	$-0.903896\pi$
$337$	−1.52367e14	−1.90954	−0.954768	+	0.297353i	$0.903896\pi$
$338$	9.27212e12	0.114324
$339$	−8.50766e13	−1.03208
$340$	−3.93259e13	−0.469402
$341$	2.51289e13	0.295138
$342$	4.06077e12	0.0469316
$343$	6.08361e13	0.691900
$344$	−1.29295e13	−0.144714
$345$	5.46286e13	0.601749
$346$	1.20363e13	0.130489
$347$	−1.14214e14	−1.21873	−0.609363	−	0.792891i	$-0.708575\pi$
$347$	−1.14214e14	−1.21873	−0.609363	+	0.792891i	$0.708575\pi$
$348$	5.04516e13	0.529895
$349$	−6.78528e13	−0.701500	−0.350750	−	0.936469i	$-0.614073\pi$
$349$	−6.78528e13	−0.701500	−0.350750	+	0.936469i	$0.614073\pi$
$350$	2.09277e12	0.0212984
$351$	−1.64784e12	−0.0165092
$352$	5.75313e12	0.0567439
$353$	−7.72969e13	−0.750588	−0.375294	−	0.926906i	$-0.622458\pi$
$353$	−7.72969e13	−0.750588	−0.375294	+	0.926906i	$0.622458\pi$
$354$	−9.05474e11	−0.00865682
$355$	−1.46190e14	−1.37614
$356$	5.51557e12	0.0511229
$357$	9.13777e12	0.0833998
$358$	−8.37603e12	−0.0752804
$359$	1.37432e14	1.21638	0.608190	−	0.793792i	$-0.291896\pi$
$359$	1.37432e14	1.21638	0.608190	+	0.793792i	$0.291896\pi$
$360$	−1.07086e13	−0.0933399
$361$	5.75994e13	0.494457
$362$	−1.77348e13	−0.149944
$363$	−6.73931e13	−0.561214
$364$	−3.83488e12	−0.0314553
$365$	6.90587e13	0.557966
$366$	−5.76022e12	−0.0458451
$367$	−1.97753e14	−1.55045	−0.775227	−	0.631683i	$-0.782364\pi$
$367$	−1.97753e14	−1.55045	−0.775227	+	0.631683i	$0.782364\pi$
$368$	−1.05896e14	−0.817930
$369$	−7.08678e13	−0.539267
$370$	−4.19971e12	−0.0314855
$371$	−9.82412e13	−0.725667
$372$	1.38189e14	1.00575
$373$	−1.38885e14	−0.995997	−0.497998	−	0.867178i	$-0.665931\pi$
$373$	−1.38885e14	−0.995997	−0.497998	+	0.867178i	$0.665931\pi$
$374$	−1.05915e12	−0.00748448
$375$	5.09717e13	0.354942
$376$	−5.49751e13	−0.377253
$377$	1.17987e13	0.0797916
$378$	1.23581e12	0.00823661
$379$	−6.00439e13	−0.394415	−0.197207	−	0.980362i	$-0.563187\pi$
$379$	−6.00439e13	−0.394415	−0.197207	+	0.980362i	$0.563187\pi$
$380$	−2.28011e14	−1.47620
$381$	−1.00279e14	−0.639914
$382$	2.95445e13	0.185835
$383$	1.50750e14	0.934684	0.467342	−	0.884077i	$-0.345212\pi$
$383$	1.50750e14	0.934684	0.467342	+	0.884077i	$0.345212\pi$
$384$	4.20861e13	0.257227
$385$	−1.26183e13	−0.0760267
$386$	−8.79001e12	−0.0522106
$387$	−3.60010e13	−0.210816
$388$	−2.46643e14	−1.42395
$389$	1.37224e14	0.781098	0.390549	−	0.920582i	$-0.372285\pi$
$389$	1.37224e14	0.781098	0.390549	+	0.920582i	$0.372285\pi$
$390$	−1.24380e12	−0.00698065
$391$	5.98252e13	0.331064
$392$	−3.61425e13	−0.197217
$393$	−4.61728e13	−0.248443
$394$	2.71773e12	0.0144204
$395$	−2.87928e14	−1.50661
$396$	1.06556e13	0.0549865
$397$	1.01916e14	0.518674	0.259337	−	0.965787i	$-0.416496\pi$
$397$	1.01916e14	0.518674	0.259337	+	0.965787i	$0.416496\pi$
$398$	5.02789e12	0.0252365
$399$	5.29807e13	0.262281
$400$	9.78793e13	0.477926
$401$	−3.55470e14	−1.71202	−0.856009	−	0.516960i	$-0.827063\pi$
$401$	−3.55470e14	−1.71202	−0.856009	+	0.516960i	$0.827063\pi$
$402$	−1.22672e13	−0.0582775
$403$	3.23172e13	0.151445
$404$	−1.88474e14	−0.871274
$405$	−2.98170e13	−0.135976
$406$	−8.84856e12	−0.0398088
$407$	8.41409e12	0.0373455
$408$	−1.17272e13	−0.0513528
$409$	1.58196e14	0.683469	0.341734	−	0.939797i	$-0.388986\pi$
$409$	1.58196e14	0.683469	0.341734	+	0.939797i	$0.388986\pi$
$410$	−5.34916e13	−0.228021
$411$	8.72701e13	0.367059
$412$	3.27560e14	1.35943
$413$	−1.18137e13	−0.0483793
$414$	8.09091e12	0.0326961
$415$	2.45580e14	0.979327
$416$	7.39884e12	0.0291172
$417$	2.05337e14	0.797480
$418$	−6.14091e12	−0.0235377
$419$	−4.16354e14	−1.57502	−0.787510	−	0.616302i	$-0.788630\pi$
$419$	−4.16354e14	−1.57502	−0.787510	+	0.616302i	$0.788630\pi$
$420$	−6.93906e13	−0.259077
$421$	−4.53385e14	−1.67077	−0.835383	−	0.549668i	$-0.814754\pi$
$421$	−4.53385e14	−1.67077	−0.835383	+	0.549668i	$0.814754\pi$
$422$	−5.52836e13	−0.201084
$423$	−1.53073e14	−0.549574
$424$	1.26081e14	0.446824
$425$	−5.52963e13	−0.193445
$426$	−2.16519e13	−0.0747726
$427$	−7.51533e13	−0.256209
$428$	−2.31669e13	−0.0779698
$429$	2.49195e12	0.00827988
$430$	−2.71738e13	−0.0891402
$431$	5.47784e14	1.77412	0.887062	−	0.461650i	$-0.152742\pi$
$431$	5.47784e14	1.77412	0.887062	+	0.461650i	$0.152742\pi$
$432$	5.77994e13	0.184826
$433$	−3.13894e14	−0.991059	−0.495530	−	0.868591i	$-0.665026\pi$
$433$	−3.13894e14	−0.991059	−0.495530	+	0.868591i	$0.665026\pi$
$434$	−2.42366e13	−0.0755576
$435$	2.13493e14	0.657192
$436$	3.93468e14	1.19601
$437$	3.46866e14	1.04115
$438$	1.02281e13	0.0303171
$439$	7.60946e13	0.222740	0.111370	−	0.993779i	$-0.464476\pi$
$439$	7.60946e13	0.222740	0.111370	+	0.993779i	$0.464476\pi$
$440$	1.61940e13	0.0468129
$441$	−1.00636e14	−0.287302
$442$	−1.36212e12	−0.00384054
$443$	−1.57927e14	−0.439780	−0.219890	−	0.975525i	$-0.570570\pi$
$443$	−1.57927e14	−0.439780	−0.219890	+	0.975525i	$0.570570\pi$
$444$	4.62709e13	0.127263
$445$	2.33399e13	0.0634043
$446$	2.47230e13	0.0663377
$447$	−1.47627e14	−0.391268
$448$	1.30771e14	0.342359
$449$	5.86221e13	0.151602	0.0758012	−	0.997123i	$-0.475849\pi$
$449$	5.86221e13	0.151602	0.0758012	+	0.997123i	$0.475849\pi$
$450$	−7.47840e12	−0.0191047
$451$	1.07170e14	0.270460
$452$	7.07513e14	1.76390
$453$	1.31100e14	0.322896
$454$	5.21329e13	0.126854
$455$	−1.62278e13	−0.0390119
$456$	−6.79943e13	−0.161498
$457$	−2.69689e13	−0.0632883	−0.0316441	−	0.999499i	$-0.510074\pi$
$457$	−2.69689e13	−0.0632883	−0.0316441	+	0.999499i	$0.510074\pi$
$458$	8.13031e13	0.188515
$459$	−3.26534e13	−0.0748098
$460$	−4.54302e14	−1.02843
$461$	7.62958e14	1.70665	0.853327	−	0.521376i	$-0.174581\pi$
$461$	7.62958e14	1.70665	0.853327	+	0.521376i	$0.174581\pi$
$462$	−1.86886e12	−0.00413092
$463$	−1.72470e14	−0.376720	−0.188360	−	0.982100i	$-0.560317\pi$
$463$	−1.72470e14	−0.376720	−0.188360	+	0.982100i	$0.560317\pi$
$464$	−4.13849e14	−0.893292
$465$	5.84767e14	1.24736
$466$	1.64969e13	0.0347759
$467$	4.90313e14	1.02148	0.510741	−	0.859735i	$-0.329371\pi$
$467$	4.90313e14	1.02148	0.510741	+	0.859735i	$0.329371\pi$
$468$	1.37038e13	0.0282155
$469$	−1.60049e14	−0.325688
$470$	−1.15541e14	−0.232379
$471$	−1.04073e14	−0.206882
$472$	1.51614e13	0.0297892
$473$	5.44425e13	0.105731
$474$	−4.26443e13	−0.0818616
$475$	−3.20607e14	−0.608357
$476$	−7.59914e13	−0.142537
$477$	3.51060e14	0.650924
$478$	2.29558e13	0.0420764
$479$	7.87631e14	1.42718	0.713588	−	0.700566i	$-0.247069\pi$
$479$	7.87631e14	1.42718	0.713588	+	0.700566i	$0.247069\pi$
$480$	1.33879e14	0.239820
$481$	1.08210e13	0.0191632
$482$	1.03875e13	0.0181866
$483$	1.05562e14	0.182724
$484$	5.60454e14	0.959158
$485$	−1.04370e15	−1.76603
$486$	−4.41612e12	−0.00738825
$487$	−6.23331e14	−1.03112	−0.515560	−	0.856853i	$-0.672416\pi$
$487$	−6.23331e14	−1.03112	−0.515560	+	0.856853i	$0.672416\pi$
$488$	9.64502e13	0.157759
$489$	4.85177e14	0.784696
$490$	−7.59605e13	−0.121481
$491$	3.47269e13	0.0549184	0.0274592	−	0.999623i	$-0.491258\pi$
$491$	3.47269e13	0.0549184	0.0274592	+	0.999623i	$0.491258\pi$
$492$	5.89350e14	0.921649
$493$	2.33802e14	0.361568
$494$	−7.89755e12	−0.0120780
$495$	4.50908e13	0.0681961
$496$	−1.13355e15	−1.69548
$497$	−2.82490e14	−0.417872
$498$	3.63722e13	0.0532118
$499$	−1.72369e14	−0.249405	−0.124703	−	0.992194i	$-0.539798\pi$
$499$	−1.72369e14	−0.249405	−0.124703	+	0.992194i	$0.539798\pi$
$500$	−4.23890e14	−0.606622
$501$	6.23304e14	0.882251
$502$	−1.04156e14	−0.145819
$503$	−1.52985e14	−0.211848	−0.105924	−	0.994374i	$-0.533780\pi$
$503$	−1.52985e14	−0.211848	−0.105924	+	0.994374i	$0.533780\pi$
$504$	−2.06927e13	−0.0283432
$505$	−7.97555e14	−1.08058
$506$	−1.22355e13	−0.0163981
$507$	−4.32290e14	−0.573102
$508$	8.33937e14	1.09366
$509$	3.75714e14	0.487427	0.243714	−	0.969847i	$-0.421634\pi$
$509$	3.75714e14	0.487427	0.243714	+	0.969847i	$0.421634\pi$
$510$	−2.46470e13	−0.0316321
$511$	1.33446e14	0.169430
$512$	−4.34470e14	−0.545727
$513$	−1.89324e14	−0.235266
$514$	−1.61986e14	−0.199150
$515$	1.38612e15	1.68601
$516$	2.99391e14	0.360301
$517$	2.31485e14	0.275629
$518$	−8.11531e12	−0.00956074
$519$	−5.61163e14	−0.654137
$520$	2.08264e13	0.0240213
$521$	1.37663e13	0.0157112	0.00785560	−	0.999969i	$-0.497499\pi$
$521$	1.37663e13	0.0157112	0.00785560	+	0.999969i	$0.497499\pi$
$522$	3.16199e13	0.0357086
$523$	−4.65180e14	−0.519831	−0.259915	−	0.965631i	$-0.583695\pi$
$523$	−4.65180e14	−0.519831	−0.259915	+	0.965631i	$0.583695\pi$
$524$	3.83982e14	0.424608
$525$	−9.75703e13	−0.106768
$526$	−8.70570e12	−0.00942719
$527$	6.40393e14	0.686260
$528$	−8.74072e13	−0.0926959
$529$	−2.61695e14	−0.274656
$530$	2.64983e14	0.275233
$531$	4.22156e13	0.0433963
$532$	−4.40597e14	−0.448258
$533$	1.37827e14	0.138782
$534$	3.45681e12	0.00344508
$535$	−9.80337e13	−0.0967007
$536$	2.05403e14	0.200540
$537$	3.90512e14	0.377378
$538$	−2.16992e14	−0.207559
$539$	1.52186e14	0.144091
$540$	2.47964e14	0.232393
$541$	−8.31910e14	−0.771776	−0.385888	−	0.922546i	$-0.626105\pi$
$541$	−8.31910e14	−0.771776	−0.385888	+	0.922546i	$0.626105\pi$
$542$	1.41442e14	0.129892
$543$	8.26843e14	0.751665
$544$	1.46614e14	0.131942
$545$	1.66501e15	1.48333
$546$	−2.40346e12	−0.00211971
$547$	−1.37546e15	−1.20093	−0.600466	−	0.799651i	$-0.705018\pi$
$547$	−1.37546e15	−1.20093	−0.600466	+	0.799651i	$0.705018\pi$
$548$	−7.25755e14	−0.627331
$549$	2.68557e14	0.229820
$550$	1.13092e13	0.00958160
$551$	1.35558e15	1.13708
$552$	−1.35476e14	−0.112511
$553$	−5.56378e14	−0.457490
$554$	1.14598e14	0.0932983
$555$	1.95801e14	0.157835
$556$	−1.70762e15	−1.36295
$557$	1.83778e15	1.45241	0.726206	−	0.687477i	$-0.241282\pi$
$557$	1.83778e15	1.45241	0.726206	+	0.687477i	$0.241282\pi$
$558$	8.66084e13	0.0677753
$559$	7.00161e13	0.0542541
$560$	5.69204e14	0.436751
$561$	4.93801e13	0.0375194
$562$	1.15406e14	0.0868316
$563$	1.22975e15	0.916262	0.458131	−	0.888885i	$-0.348519\pi$
$563$	1.22975e15	0.916262	0.458131	+	0.888885i	$0.348519\pi$
$564$	1.27298e15	0.939264
$565$	2.99394e15	2.18764
$566$	−1.78513e12	−0.00129175
$567$	−5.76169e13	−0.0412898
$568$	3.62542e14	0.257302
$569$	−7.10444e14	−0.499358	−0.249679	−	0.968329i	$-0.580325\pi$
$569$	−7.10444e14	−0.499358	−0.249679	+	0.968329i	$0.580325\pi$
$570$	−1.42903e14	−0.0994786
$571$	−2.86714e15	−1.97675	−0.988373	−	0.152048i	$-0.951413\pi$
$571$	−2.86714e15	−1.97675	−0.988373	+	0.152048i	$0.951413\pi$
$572$	−2.07235e13	−0.0141509
$573$	−1.37744e15	−0.931586
$574$	−1.03364e14	−0.0692398
$575$	−6.38795e14	−0.423827
$576$	−4.67304e14	−0.307097
$577$	1.78351e15	1.16094	0.580468	−	0.814283i	$-0.302869\pi$
$577$	1.78351e15	1.16094	0.580468	+	0.814283i	$0.302869\pi$
$578$	1.51636e14	0.0977684
$579$	4.09813e14	0.261730
$580$	−1.77545e15	−1.12319
$581$	4.74546e14	0.297378
$582$	−1.54580e14	−0.0959572
$583$	−5.30891e14	−0.326459
$584$	−1.71261e14	−0.104325
$585$	5.79893e13	0.0349938
$586$	−2.52707e14	−0.151071
$587$	−9.89640e14	−0.586095	−0.293047	−	0.956098i	$-0.594669\pi$
$587$	−9.89640e14	−0.586095	−0.293047	+	0.956098i	$0.594669\pi$
$588$	8.36905e14	0.491022
$589$	3.71299e15	2.15819
$590$	3.18646e13	0.0183494
$591$	−1.26708e14	−0.0722890
$592$	−3.79555e14	−0.214539
$593$	3.41739e15	1.91379	0.956894	−	0.290437i	$-0.0938008\pi$
$593$	3.41739e15	1.91379	0.956894	+	0.290437i	$0.0938008\pi$
$594$	6.67829e12	0.00370544
$595$	−3.21568e14	−0.176779
$596$	1.22769e15	0.668706
$597$	−2.34413e14	−0.126509
$598$	−1.57355e13	−0.00841443
$599$	−1.53010e15	−0.810725	−0.405362	−	0.914156i	$-0.632855\pi$
$599$	−1.53010e15	−0.810725	−0.405362	+	0.914156i	$0.632855\pi$
$600$	1.25220e14	0.0657417
$601$	7.71695e14	0.401454	0.200727	−	0.979647i	$-0.435670\pi$
$601$	7.71695e14	0.401454	0.200727	+	0.979647i	$0.435670\pi$
$602$	−5.25093e13	−0.0270679
$603$	5.71927e14	0.292143
$604$	−1.09025e15	−0.551853
$605$	2.37164e15	1.18958
$606$	−1.18124e14	−0.0587136
$607$	−1.94990e15	−0.960451	−0.480225	−	0.877145i	$-0.659445\pi$
$607$	−1.94990e15	−0.960451	−0.480225	+	0.877145i	$0.659445\pi$
$608$	8.50068e14	0.414939
$609$	4.12543e14	0.199560
$610$	2.02708e14	0.0971757
$611$	2.97702e14	0.141435
$612$	2.71552e14	0.127856
$613$	−2.81617e15	−1.31409	−0.657047	−	0.753850i	$-0.728195\pi$
$613$	−2.81617e15	−1.31409	−0.657047	+	0.753850i	$0.728195\pi$
$614$	−3.91271e14	−0.180947
$615$	2.49392e15	1.14306
$616$	3.12926e13	0.0142150
$617$	3.74732e15	1.68715	0.843573	−	0.537014i	$-0.180448\pi$
$617$	3.74732e15	1.68715	0.843573	+	0.537014i	$0.180448\pi$
$618$	2.05294e14	0.0916094
$619$	9.40230e14	0.415849	0.207924	−	0.978145i	$-0.433329\pi$
$619$	9.40230e14	0.415849	0.207924	+	0.978145i	$0.433329\pi$
$620$	−4.86303e15	−2.13183
$621$	−3.77219e14	−0.163904
$622$	1.41222e14	0.0608213
$623$	4.51008e13	0.0192531
$624$	−1.12410e14	−0.0475654
$625$	−2.98022e15	−1.24999
$626$	−2.83556e14	−0.117891
$627$	2.86305e14	0.117993
$628$	8.65492e14	0.353578
$629$	2.14427e14	0.0868363
$630$	−4.34897e13	−0.0174587
$631$	4.12374e15	1.64108	0.820540	−	0.571589i	$-0.193673\pi$
$631$	4.12374e15	1.64108	0.820540	+	0.571589i	$0.193673\pi$
$632$	7.14044e14	0.281696
$633$	2.57747e15	1.00803
$634$	−3.45756e14	−0.134054
$635$	3.52892e15	1.35639
$636$	−2.91948e15	−1.11248
$637$	1.95720e14	0.0739381
$638$	−4.78173e13	−0.0179090
$639$	1.00947e15	0.374832
$640$	−1.48105e15	−0.545232
$641$	−7.38983e14	−0.269721	−0.134861	−	0.990865i	$-0.543059\pi$
$641$	−7.38983e14	−0.269721	−0.134861	+	0.990865i	$0.543059\pi$
$642$	−1.45195e13	−0.00525424
$643$	−5.39380e15	−1.93524	−0.967620	−	0.252412i	$-0.918776\pi$
$643$	−5.39380e15	−1.93524	−0.967620	+	0.252412i	$0.918776\pi$
$644$	−8.77870e14	−0.312290
$645$	1.26691e15	0.446857
$646$	−1.56497e14	−0.0547302
$647$	−2.67699e14	−0.0928268	−0.0464134	−	0.998922i	$-0.514779\pi$
$647$	−2.67699e14	−0.0928268	−0.0464134	+	0.998922i	$0.514779\pi$
$648$	7.39443e13	0.0254239
$649$	−6.38406e13	−0.0217646
$650$	1.45443e13	0.00491665
$651$	1.12997e15	0.378768
$652$	−4.03483e15	−1.34111
$653$	4.11687e14	0.135689	0.0678445	−	0.997696i	$-0.478388\pi$
$653$	4.11687e14	0.135689	0.0678445	+	0.997696i	$0.478388\pi$
$654$	2.46601e14	0.0805966
$655$	1.62487e15	0.526613
$656$	−4.83438e15	−1.55371
$657$	−4.76861e14	−0.151979
$658$	−2.23265e14	−0.0705631
$659$	−1.67225e15	−0.524121	−0.262061	−	0.965051i	$-0.584402\pi$
$659$	−1.67225e15	−0.524121	−0.262061	+	0.965051i	$0.584402\pi$
$660$	−3.74984e14	−0.116552
$661$	−7.32781e14	−0.225874	−0.112937	−	0.993602i	$-0.536026\pi$
$661$	−7.32781e14	−0.225874	−0.112937	+	0.993602i	$0.536026\pi$
$662$	−3.76949e14	−0.115229
$663$	6.35056e13	0.0192525
$664$	−6.09022e14	−0.183109
$665$	−1.86445e15	−0.555944
$666$	2.89997e13	0.00857600
$667$	2.70093e15	0.792175
$668$	−5.18351e15	−1.50783
$669$	−1.15265e15	−0.332548
$670$	4.31695e14	0.123528
$671$	−4.06125e14	−0.115262
$672$	2.58701e14	0.0728228
$673$	−5.90906e15	−1.64982	−0.824908	−	0.565267i	$-0.808773\pi$
$673$	−5.90906e15	−1.64982	−0.824908	+	0.565267i	$0.808773\pi$
$674$	7.94149e14	0.219924
$675$	3.48663e14	0.0957711
$676$	3.59501e15	0.979474
$677$	−2.93415e15	−0.792949	−0.396474	−	0.918046i	$-0.629766\pi$
$677$	−2.93415e15	−0.792949	−0.396474	+	0.918046i	$0.629766\pi$
$678$	4.43425e14	0.118866
$679$	−2.01680e15	−0.536264
$680$	4.12694e14	0.108850
$681$	−2.43057e15	−0.635915
$682$	−1.30974e14	−0.0339915
$683$	−2.31821e15	−0.596815	−0.298407	−	0.954439i	$-0.596455\pi$
$683$	−2.31821e15	−0.596815	−0.298407	+	0.954439i	$0.596455\pi$
$684$	1.57445e15	0.402088
$685$	−3.07113e15	−0.778037
$686$	−3.17082e14	−0.0796871
$687$	−3.79056e15	−0.945021
$688$	−2.45587e15	−0.607392
$689$	−6.82756e14	−0.167517
$690$	−2.84728e14	−0.0693043
$691$	5.28556e15	1.27633	0.638163	−	0.769901i	$-0.279695\pi$
$691$	5.28556e15	1.27633	0.638163	+	0.769901i	$0.279695\pi$
$692$	4.66674e15	1.11797
$693$	8.71312e13	0.0207081
$694$	5.95289e14	0.140362
$695$	−7.22605e15	−1.69038
$696$	−5.29449e14	−0.122878
$697$	2.73115e15	0.628877
$698$	3.53653e14	0.0807928
$699$	−7.69127e14	−0.174331
$700$	8.11413e14	0.182475
$701$	5.74005e15	1.28076	0.640378	−	0.768060i	$-0.278778\pi$
$701$	5.74005e15	1.28076	0.640378	+	0.768060i	$0.278778\pi$
$702$	8.58865e12	0.00190139
$703$	1.24325e15	0.273088
$704$	7.06681e14	0.154019
$705$	5.38680e15	1.16491
$706$	4.02877e14	0.0864462
$707$	−1.54116e15	−0.328125
$708$	−3.51073e14	−0.0741676
$709$	−7.44495e14	−0.156066	−0.0780328	−	0.996951i	$-0.524864\pi$
$709$	−7.44495e14	−0.156066	−0.0780328	+	0.996951i	$0.524864\pi$
$710$	7.61952e14	0.158492
$711$	1.98819e15	0.410369
$712$	−5.78815e13	−0.0118550
$713$	7.39797e15	1.50356
$714$	−4.76266e13	−0.00960527
$715$	−8.76944e13	−0.0175505
$716$	−3.24758e15	−0.644967
$717$	−1.07026e15	−0.210928
$718$	−7.16306e14	−0.140092
$719$	−6.85041e15	−1.32956	−0.664779	−	0.747040i	$-0.731474\pi$
$719$	−6.85041e15	−1.32956	−0.664779	+	0.747040i	$0.731474\pi$
$720$	−2.03402e15	−0.391766
$721$	2.67846e15	0.511966
$722$	−3.00212e14	−0.0569473
$723$	−4.84291e14	−0.0911688
$724$	−6.87619e15	−1.28465
$725$	−2.49646e15	−0.462877
$726$	3.51257e14	0.0646359
$727$	−5.98546e15	−1.09310	−0.546548	−	0.837428i	$-0.684058\pi$
$727$	−5.98546e15	−1.09310	−0.546548	+	0.837428i	$0.684058\pi$
$728$	4.02440e13	0.00729421
$729$	2.05891e14	0.0370370
$730$	−3.59939e14	−0.0642618
$731$	1.38743e15	0.245847
$732$	−2.23337e15	−0.392780
$733$	−6.65829e15	−1.16223	−0.581113	−	0.813823i	$-0.697383\pi$
$733$	−6.65829e15	−1.16223	−0.581113	+	0.813823i	$0.697383\pi$
$734$	1.03070e15	0.178568
$735$	3.54148e15	0.608981
$736$	1.69372e15	0.289077
$737$	−8.64897e14	−0.146519
$738$	3.69368e14	0.0621082
$739$	−8.08499e15	−1.34938	−0.674692	−	0.738100i	$-0.735723\pi$
$739$	−8.08499e15	−1.34938	−0.674692	+	0.738100i	$0.735723\pi$
$740$	−1.62832e15	−0.269753
$741$	3.68204e14	0.0605465
$742$	5.12040e14	0.0835761
$743$	−8.56884e15	−1.38830	−0.694150	−	0.719830i	$-0.744220\pi$
$743$	−8.56884e15	−1.38830	−0.694150	+	0.719830i	$0.744220\pi$
$744$	−1.45019e15	−0.233224
$745$	5.19515e15	0.829351
$746$	7.23879e14	0.114710
$747$	−1.69577e15	−0.266749
$748$	−4.10655e14	−0.0641236
$749$	−1.89435e14	−0.0293637
$750$	−2.65668e14	−0.0408792
$751$	−4.53331e15	−0.692462	−0.346231	−	0.938149i	$-0.612539\pi$
$751$	−4.53331e15	−0.692462	−0.346231	+	0.938149i	$0.612539\pi$
$752$	−1.04422e16	−1.58340
$753$	4.85604e15	0.730987
$754$	−6.14956e13	−0.00918971
$755$	−4.61355e15	−0.684426
$756$	4.79153e14	0.0705674
$757$	2.66059e15	0.389001	0.194501	−	0.980902i	$-0.437691\pi$
$757$	2.66059e15	0.389001	0.194501	+	0.980902i	$0.437691\pi$
$758$	3.12953e14	0.0454253
$759$	5.70450e14	0.0822031
$760$	2.39279e15	0.342319
$761$	5.68425e15	0.807342	0.403671	−	0.914904i	$-0.367734\pi$
$761$	5.68425e15	0.807342	0.403671	+	0.914904i	$0.367734\pi$
$762$	5.22659e14	0.0736998
$763$	3.21739e15	0.450420
$764$	1.14551e16	1.59215
$765$	1.14911e15	0.158571
$766$	−7.85720e14	−0.107649
$767$	−8.21025e13	−0.0111682
$768$	3.71907e15	0.502282
$769$	1.54022e15	0.206532	0.103266	−	0.994654i	$-0.467071\pi$
$769$	1.54022e15	0.206532	0.103266	+	0.994654i	$0.467071\pi$
$770$	6.57673e13	0.00875611
$771$	7.55223e15	0.998334
$772$	−3.40808e15	−0.447317
$773$	−7.67995e14	−0.100086	−0.0500428	−	0.998747i	$-0.515936\pi$
$773$	−7.67995e14	−0.100086	−0.0500428	+	0.998747i	$0.515936\pi$
$774$	1.87639e14	0.0242800
$775$	−6.83792e15	−0.878547
$776$	2.58832e15	0.330201
$777$	3.78357e14	0.0479276
$778$	−7.15218e14	−0.0899602
$779$	1.58352e16	1.97773
$780$	−4.82250e14	−0.0598070
$781$	−1.52657e15	−0.187990
$782$	−3.11813e14	−0.0381291
$783$	−1.47420e15	−0.179006
$784$	−6.86504e15	−0.827761
$785$	3.66245e15	0.438519
$786$	2.40656e14	0.0286136
$787$	5.07026e15	0.598645	0.299322	−	0.954152i	$-0.403239\pi$
$787$	5.07026e15	0.598645	0.299322	+	0.954152i	$0.403239\pi$
$788$	1.05373e15	0.123547
$789$	4.05883e14	0.0472582
$790$	1.50070e15	0.173518
$791$	5.78533e15	0.664290
$792$	−1.11822e14	−0.0127509
$793$	−5.22299e14	−0.0591448
$794$	−5.31193e14	−0.0597364
$795$	−1.23542e16	−1.37973
$796$	1.94942e15	0.216214
$797$	7.88311e15	0.868314	0.434157	−	0.900837i	$-0.357046\pi$
$797$	7.88311e15	0.868314	0.434157	+	0.900837i	$0.357046\pi$
$798$	−2.76139e14	−0.0302073
$799$	5.89923e15	0.640896
$800$	−1.56550e15	−0.168911
$801$	−1.61166e14	−0.0172701
$802$	1.85273e15	0.197176
$803$	7.21134e14	0.0762221
$804$	−4.75625e15	−0.499294
$805$	−3.71483e15	−0.387312
$806$	−1.68439e14	−0.0174422
$807$	1.01167e16	1.04049
$808$	1.97789e15	0.202041
$809$	−9.15896e15	−0.929243	−0.464622	−	0.885509i	$-0.653810\pi$
$809$	−9.15896e15	−0.929243	−0.464622	+	0.885509i	$0.653810\pi$
$810$	1.55408e14	0.0156605
$811$	1.35494e16	1.35615	0.678073	−	0.734994i	$-0.262815\pi$
$811$	1.35494e16	1.35615	0.678073	+	0.734994i	$0.262815\pi$
$812$	−3.43079e15	−0.341064
$813$	−6.59440e15	−0.651144
$814$	−4.38548e13	−0.00430113
$815$	−1.70739e16	−1.66328
$816$	−2.22751e15	−0.215538
$817$	8.04429e15	0.773155
$818$	−8.24530e14	−0.0787161
$819$	1.12056e14	0.0106261
$820$	−2.07399e16	−1.95358
$821$	−1.53313e15	−0.143447	−0.0717237	−	0.997425i	$-0.522850\pi$
$821$	−1.53313e15	−0.143447	−0.0717237	+	0.997425i	$0.522850\pi$
$822$	−4.54858e14	−0.0422747
$823$	−1.19210e16	−1.10056	−0.550279	−	0.834981i	$-0.685479\pi$
$823$	−1.19210e16	−1.10056	−0.550279	+	0.834981i	$0.685479\pi$
$824$	−3.43748e15	−0.315240
$825$	−5.27266e14	−0.0480322
$826$	6.15736e13	0.00557191
$827$	−4.09891e15	−0.368459	−0.184229	−	0.982883i	$-0.558979\pi$
$827$	−4.09891e15	−0.368459	−0.184229	+	0.982883i	$0.558979\pi$
$828$	3.13703e15	0.280125
$829$	−3.92677e15	−0.348326	−0.174163	−	0.984717i	$-0.555722\pi$
$829$	−3.92677e15	−0.348326	−0.174163	+	0.984717i	$0.555722\pi$
$830$	−1.27998e15	−0.112791
$831$	−5.34286e15	−0.467701
$832$	9.08830e14	0.0790323
$833$	3.87836e15	0.335043
$834$	−1.07023e15	−0.0918469
$835$	−2.19347e16	−1.87006
$836$	−2.38097e15	−0.201660
$837$	−4.03791e15	−0.339755
$838$	2.17007e15	0.181397
$839$	6.60581e15	0.548574	0.274287	−	0.961648i	$-0.411558\pi$
$839$	6.60581e15	0.548574	0.274287	+	0.961648i	$0.411558\pi$
$840$	7.28198e14	0.0600777
$841$	−1.64507e15	−0.134836
$842$	2.36307e15	0.192425
$843$	−5.38052e15	−0.435284
$844$	−2.14347e16	−1.72280
$845$	1.52128e16	1.21478
$846$	7.97826e14	0.0632953
$847$	4.58283e15	0.361223
$848$	2.39482e16	1.87541
$849$	8.32275e13	0.00647552
$850$	2.88208e14	0.0222793
$851$	2.47711e15	0.190254
$852$	−8.39491e15	−0.640617
$853$	1.19891e16	0.909007	0.454503	−	0.890745i	$-0.349817\pi$
$853$	1.19891e16	0.909007	0.454503	+	0.890745i	$0.349817\pi$
$854$	3.91704e14	0.0295080
$855$	6.66251e15	0.498683
$856$	2.43118e14	0.0180805
$857$	−9.30733e15	−0.687750	−0.343875	−	0.939015i	$-0.611740\pi$
$857$	−9.30733e15	−0.687750	−0.343875	+	0.939015i	$0.611740\pi$
$858$	−1.29882e13	−0.000953606 0
$859$	2.79249e15	0.203718	0.101859	−	0.994799i	$-0.467521\pi$
$859$	2.79249e15	0.203718	0.101859	+	0.994799i	$0.467521\pi$
$860$	−1.05359e16	−0.763712
$861$	4.81912e15	0.347096
$862$	−2.85508e15	−0.204328
$863$	4.56386e15	0.324544	0.162272	−	0.986746i	$-0.448118\pi$
$863$	4.56386e15	0.324544	0.162272	+	0.986746i	$0.448118\pi$
$864$	−9.24456e14	−0.0653221
$865$	1.97480e16	1.38654
$866$	1.63604e15	0.114142
$867$	−7.06965e15	−0.490109
$868$	−9.39708e15	−0.647343
$869$	−3.00664e15	−0.205813
$870$	−1.11274e15	−0.0756898
$871$	−1.11231e15	−0.0751838
$872$	−4.12913e15	−0.277343
$873$	7.20693e15	0.481030
$874$	−1.80789e15	−0.119911
$875$	−3.46615e15	−0.228456
$876$	3.96567e15	0.259743
$877$	3.01027e16	1.95933	0.979667	−	0.200633i	$-0.0642997\pi$
$877$	3.01027e16	1.95933	0.979667	+	0.200633i	$0.0642997\pi$
$878$	−3.96610e14	−0.0256533
$879$	1.17818e16	0.757311
$880$	3.07595e15	0.196483
$881$	1.13358e15	0.0719592	0.0359796	−	0.999353i	$-0.488545\pi$
$881$	1.13358e15	0.0719592	0.0359796	+	0.999353i	$0.488545\pi$
$882$	5.24519e14	0.0330890
$883$	−1.68216e16	−1.05459	−0.527295	−	0.849682i	$-0.676794\pi$
$883$	−1.68216e16	−1.05459	−0.527295	+	0.849682i	$0.676794\pi$
$884$	−5.28124e14	−0.0329040
$885$	−1.48561e15	−0.0919851
$886$	8.23125e14	0.0506501
$887$	2.54107e16	1.55395	0.776974	−	0.629533i	$-0.216754\pi$
$887$	2.54107e16	1.55395	0.776974	+	0.629533i	$0.216754\pi$
$888$	−4.85575e14	−0.0295111
$889$	6.81910e15	0.411877
$890$	−1.21649e14	−0.00730237
$891$	−3.11359e14	−0.0185752
$892$	9.58568e15	0.568350
$893$	3.42036e16	2.01553
$894$	7.69440e14	0.0450628
$895$	−1.37426e16	−0.799910
$896$	−2.86191e15	−0.165563
$897$	7.33631e14	0.0421812
$898$	−3.05542e14	−0.0174603
$899$	2.89118e16	1.64209
$900$	−2.89955e15	−0.163680
$901$	−1.35294e16	−0.759088
$902$	−5.58577e14	−0.0311492
$903$	2.44812e15	0.135691
$904$	−7.42478e15	−0.409032
$905$	−2.90975e16	−1.59327
$906$	−6.83301e14	−0.0371884
$907$	−8.67146e15	−0.469086	−0.234543	−	0.972106i	$-0.575359\pi$
$907$	−8.67146e15	−0.469086	−0.234543	+	0.972106i	$0.575359\pi$
$908$	2.02131e16	1.08683
$909$	5.50724e15	0.294329
$910$	8.45804e13	0.00449306
$911$	1.89333e14	0.00999713	0.00499856	−	0.999988i	$-0.498409\pi$
$911$	1.89333e14	0.00999713	0.00499856	+	0.999988i	$0.498409\pi$
$912$	−1.29151e16	−0.677837
$913$	2.56443e15	0.133783
$914$	1.40563e14	0.00728900
$915$	−9.45080e15	−0.487138
$916$	3.15230e16	1.61511
$917$	3.13982e15	0.159909
$918$	1.70191e14	0.00861595
$919$	2.69305e16	1.35522	0.677610	−	0.735421i	$-0.263016\pi$
$919$	2.69305e16	1.35522	0.677610	+	0.735421i	$0.263016\pi$
$920$	4.76753e15	0.238485
$921$	1.82421e16	0.907081
$922$	−3.97659e15	−0.196558
$923$	−1.96325e15	−0.0964642
$924$	−7.24600e14	−0.0353918
$925$	−2.28959e15	−0.111167
$926$	8.98925e14	0.0433874
$927$	−9.57135e15	−0.459235
$928$	6.61920e15	0.315712
$929$	2.50400e14	0.0118727	0.00593633	−	0.999982i	$-0.498110\pi$
$929$	2.50400e14	0.0118727	0.00593633	+	0.999982i	$0.498110\pi$
$930$	−3.04784e15	−0.143660
$931$	2.24867e16	1.05366
$932$	6.39620e15	0.297944
$933$	−6.58415e15	−0.304895
$934$	−2.55554e15	−0.117646
$935$	−1.73774e15	−0.0795282
$936$	−1.43810e14	−0.00654292
$937$	1.27295e16	0.575764	0.287882	−	0.957666i	$-0.407049\pi$
$937$	1.27295e16	0.575764	0.287882	+	0.957666i	$0.407049\pi$
$938$	8.34185e14	0.0375100
$939$	1.32201e16	0.590982
$940$	−4.47977e16	−1.99091
$941$	4.30849e15	0.190363	0.0951815	−	0.995460i	$-0.469657\pi$
$941$	4.30849e15	0.190363	0.0951815	+	0.995460i	$0.469657\pi$
$942$	5.42436e14	0.0238269
$943$	3.15509e16	1.37784
$944$	2.87981e15	0.125031
$945$	2.02760e15	0.0875200
$946$	−2.83758e14	−0.0121772
$947$	−8.23320e15	−0.351272	−0.175636	−	0.984455i	$-0.556198\pi$
$947$	−8.23320e15	−0.351272	−0.175636	+	0.984455i	$0.556198\pi$
$948$	−1.65342e16	−0.701352
$949$	9.27419e14	0.0391122
$950$	1.67102e15	0.0700653
$951$	1.61200e16	0.672006
$952$	7.97469e14	0.0330530
$953$	−1.84384e15	−0.0759821	−0.0379911	−	0.999278i	$-0.512096\pi$
$953$	−1.84384e15	−0.0759821	−0.0379911	+	0.999278i	$0.512096\pi$
$954$	−1.82975e15	−0.0749679
$955$	4.84737e16	1.97464
$956$	8.90047e15	0.360491
$957$	2.22936e15	0.0897771
$958$	−4.10518e15	−0.164370
$959$	−5.93450e15	−0.236255
$960$	1.64449e16	0.650938
$961$	5.37824e16	2.11671
$962$	−5.63997e13	−0.00220706
$963$	6.76938e14	0.0263393
$964$	4.02746e15	0.155814
$965$	−1.44218e16	−0.554777
$966$	−5.50194e14	−0.0210446
$967$	3.36559e16	1.28002	0.640009	−	0.768368i	$-0.278931\pi$
$967$	3.36559e16	1.28002	0.640009	+	0.768368i	$0.278931\pi$
$968$	−5.88151e15	−0.222420
$969$	7.29629e15	0.274360
$970$	5.43984e15	0.203396
$971$	−2.08661e15	−0.0775775	−0.0387888	−	0.999247i	$-0.512350\pi$
$971$	−2.08661e15	−0.0775775	−0.0387888	+	0.999247i	$0.512350\pi$
$972$	−1.71223e15	−0.0632991
$973$	−1.39632e16	−0.513293
$974$	3.24884e15	0.118756
$975$	−6.78093e14	−0.0246470
$976$	1.83201e16	0.662145
$977$	−4.70144e15	−0.168970	−0.0844851	−	0.996425i	$-0.526925\pi$
$977$	−4.70144e15	−0.168970	−0.0844851	+	0.996425i	$0.526925\pi$
$978$	−2.52877e15	−0.0903746
$979$	2.43723e14	0.00866147
$980$	−2.94516e16	−1.04080
$981$	−1.14972e16	−0.404028
$982$	−1.80999e14	−0.00632503
$983$	2.49311e16	0.866358	0.433179	−	0.901308i	$-0.357392\pi$
$983$	2.49311e16	0.866358	0.433179	+	0.901308i	$0.357392\pi$
$984$	−6.18476e15	−0.213722
$985$	4.45899e15	0.153228
$986$	−1.21859e15	−0.0416423
$987$	1.04092e16	0.353731
$988$	−3.06206e15	−0.103479
$989$	1.60279e16	0.538638
$990$	−2.35016e14	−0.00785424
$991$	1.15949e16	0.385357	0.192678	−	0.981262i	$-0.438283\pi$
$991$	1.15949e16	0.385357	0.192678	+	0.981262i	$0.438283\pi$
$992$	1.81303e16	0.599226
$993$	1.75743e16	0.577641
$994$	1.47236e15	0.0481270
$995$	8.24925e15	0.268156
$996$	1.41023e16	0.455894
$997$	6.17929e16	1.98662	0.993311	−	0.115467i	$-0.0368366\pi$
$997$	6.17929e16	1.98662	0.993311	+	0.115467i	$0.0368366\pi$
$998$	8.98397e14	0.0287244
$999$	−1.35204e15	−0.0429912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.14	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.14	✓	28	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-5.21206 q^{2} +243.000 q^{3} -2020.83 q^{4} -8551.43 q^{5} -1266.53 q^{6} -16524.4 q^{7} +21207.0 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-5.21206 q^{2} +243.000 q^{3} -2020.83 q^{4} -8551.43 q^{5} -1266.53 q^{6} -16524.4 q^{7} +21207.0 q^{8} +59049.0 q^{9} +44570.6 q^{10} -89297.0 q^{11} -491063. q^{12} -114841. q^{13} +86126.0 q^{14} -2.07800e6 q^{15} +4.02814e6 q^{16} -2.27567e6 q^{17} -307767. q^{18} -1.31943e7 q^{19} +1.72810e7 q^{20} -4.01542e6 q^{21} +465421. q^{22} -2.62891e7 q^{23} +5.15331e6 q^{24} +2.42989e7 q^{25} +598558. q^{26} +1.43489e7 q^{27} +3.33930e7 q^{28} -1.02740e8 q^{29} +1.08307e7 q^{30} -2.81409e8 q^{31} -6.44269e7 q^{32} -2.16992e7 q^{33} +1.18609e7 q^{34} +1.41307e8 q^{35} -1.19328e8 q^{36} -9.42260e7 q^{37} +6.87696e7 q^{38} -2.79063e7 q^{39} -1.81350e8 q^{40} -1.20015e9 q^{41} +2.09286e7 q^{42} -6.09679e8 q^{43} +1.80454e8 q^{44} -5.04954e8 q^{45} +1.37020e8 q^{46} -2.59230e9 q^{47} +9.78837e8 q^{48} -1.70427e9 q^{49} -1.26647e8 q^{50} -5.52988e8 q^{51} +2.32074e8 q^{52} +5.94524e9 q^{53} -7.47874e7 q^{54} +7.63617e8 q^{55} -3.50433e8 q^{56} -3.20622e9 q^{57} +5.35486e8 q^{58} +7.14924e8 q^{59} +4.19929e9 q^{60} +4.54803e9 q^{61} +1.46672e9 q^{62} -9.75747e8 q^{63} -7.91383e9 q^{64} +9.82054e8 q^{65} +1.13097e8 q^{66} +9.68563e9 q^{67} +4.59875e9 q^{68} -6.38824e9 q^{69} -7.36501e8 q^{70} +1.70954e10 q^{71} +1.25225e9 q^{72} -8.07569e9 q^{73} +4.91112e8 q^{74} +5.90463e9 q^{75} +2.66635e10 q^{76} +1.47557e9 q^{77} +1.45450e8 q^{78} +3.36701e10 q^{79} -3.44463e10 q^{80} +3.48678e9 q^{81} +6.25527e9 q^{82} -2.87180e10 q^{83} +8.11450e9 q^{84} +1.94602e10 q^{85} +3.17769e9 q^{86} -2.49657e10 q^{87} -1.89372e9 q^{88} -2.72935e9 q^{89} +2.63185e9 q^{90} +1.89767e9 q^{91} +5.31258e10 q^{92} -6.83823e10 q^{93} +1.35113e10 q^{94} +1.12830e11 q^{95} -1.56557e10 q^{96} +1.22050e11 q^{97} +8.88278e9 q^{98} -5.27290e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * q^99

Introduction

L-functions

Modular forms

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