LMFDB - Embedded newform 177.10.a.a.1.18

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:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q+30.4984 q^{2} +81.0000 q^{3} +418.150 q^{4} +1050.93 q^{5} +2470.37 q^{6} -5890.68 q^{7} -2862.26 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+30.4984 q^{2} +81.0000 q^{3} +418.150 q^{4} +1050.93 q^{5} +2470.37 q^{6} -5890.68 q^{7} -2862.26 q^{8} +6561.00 q^{9} +32051.7 q^{10} +26388.8 q^{11} +33870.2 q^{12} -71180.0 q^{13} -179656. q^{14} +85125.4 q^{15} -301387. q^{16} -660629. q^{17} +200100. q^{18} -713962. q^{19} +439447. q^{20} -477145. q^{21} +804816. q^{22} +1.72289e6 q^{23} -231843. q^{24} -848670. q^{25} -2.17087e6 q^{26} +531441. q^{27} -2.46319e6 q^{28} -882627. q^{29} +2.59619e6 q^{30} +8.02994e6 q^{31} -7.72634e6 q^{32} +2.13749e6 q^{33} -2.01481e7 q^{34} -6.19069e6 q^{35} +2.74348e6 q^{36} -1.38423e7 q^{37} -2.17747e7 q^{38} -5.76558e6 q^{39} -3.00804e6 q^{40} -1.60785e7 q^{41} -1.45521e7 q^{42} -1.63480e7 q^{43} +1.10345e7 q^{44} +6.89516e6 q^{45} +5.25454e7 q^{46} +4.25996e7 q^{47} -2.44124e7 q^{48} -5.65355e6 q^{49} -2.58830e7 q^{50} -5.35109e7 q^{51} -2.97639e7 q^{52} +5.47396e6 q^{53} +1.62081e7 q^{54} +2.77328e7 q^{55} +1.68607e7 q^{56} -5.78309e7 q^{57} -2.69187e7 q^{58} +1.21174e7 q^{59} +3.55952e7 q^{60} -1.55390e8 q^{61} +2.44900e8 q^{62} -3.86487e7 q^{63} -8.13305e7 q^{64} -7.48053e7 q^{65} +6.51901e7 q^{66} +1.19205e8 q^{67} -2.76242e8 q^{68} +1.39554e8 q^{69} -1.88806e8 q^{70} +5.29891e7 q^{71} -1.87793e7 q^{72} -1.44959e8 q^{73} -4.22167e8 q^{74} -6.87422e7 q^{75} -2.98543e8 q^{76} -1.55448e8 q^{77} -1.75841e8 q^{78} +3.12409e8 q^{79} -3.16737e8 q^{80} +4.30467e7 q^{81} -4.90367e8 q^{82} +5.07060e7 q^{83} -1.99518e8 q^{84} -6.94275e8 q^{85} -4.98587e8 q^{86} -7.14928e7 q^{87} -7.55317e7 q^{88} +6.65499e8 q^{89} +2.10291e8 q^{90} +4.19298e8 q^{91} +7.20428e8 q^{92} +6.50425e8 q^{93} +1.29922e9 q^{94} -7.50324e8 q^{95} -6.25834e8 q^{96} -1.11643e9 q^{97} -1.72424e8 q^{98} +1.73137e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) $ 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9} - 54663 q^{10} - 151769 q^{11} + 421686 q^{12} - 153611 q^{13} - 286771 q^{14} - 240084 q^{15} + 805530 q^{16} - 723621 q^{17} - 433026 q^{18} - 549388 q^{19} - 527311 q^{20} - 2492775 q^{21} + 2973158 q^{22} + 169962 q^{23} - 1994301 q^{24} + 8035779 q^{25} - 2337392 q^{26} + 11160261 q^{27} - 22659054 q^{28} - 16845442 q^{29} - 4427703 q^{30} - 19307976 q^{31} - 44923568 q^{32} - 12293289 q^{33} - 35547496 q^{34} - 34882596 q^{35} + 34156566 q^{36} - 41561129 q^{37} - 52335371 q^{38} - 12442491 q^{39} - 125735038 q^{40} - 68169291 q^{41} - 23228451 q^{42} - 25719587 q^{43} - 126277032 q^{44} - 19446804 q^{45} - 292814271 q^{46} - 174095332 q^{47} + 65247930 q^{48} + 7479350 q^{49} - 227877439 q^{50} - 58613301 q^{51} - 232397708 q^{52} - 228390500 q^{53} - 35075106 q^{54} - 29426208 q^{55} + 326778474 q^{56} - 44500428 q^{57} + 480343762 q^{58} + 254464581 q^{59} - 42712191 q^{60} - 183928964 q^{61} - 21753862 q^{62} - 201914775 q^{63} + 310571245 q^{64} + 5308466 q^{65} + 240825798 q^{66} - 82724114 q^{67} - 138336205 q^{68} + 13766922 q^{69} + 1030274876 q^{70} - 404721965 q^{71} - 161538381 q^{72} + 154162574 q^{73} + 36352054 q^{74} + 650898099 q^{75} + 1068940636 q^{76} - 448535481 q^{77} - 189328752 q^{78} + 272529635 q^{79} - 345587859 q^{80} + 903981141 q^{81} - 38412637 q^{82} + 432518643 q^{83} - 1835383374 q^{84} - 126211490 q^{85} - 3699273072 q^{86} - 1364480802 q^{87} + 170111045 q^{88} - 1255621070 q^{89} - 358643943 q^{90} + 1448885849 q^{91} + 1568933320 q^{92} - 1563946056 q^{93} - 1908445164 q^{94} - 2896546490 q^{95} - 3638809008 q^{96} + 1007235486 q^{97} - 9506868248 q^{98} - 995756409 q^{99}+O(q^{100}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9 - 54663 * q^10 - 151769 * q^11 + 421686 * q^12 - 153611 * q^13 - 286771 * q^14 - 240084 * q^15 + 805530 * q^16 - 723621 * q^17 - 433026 * q^18 - 549388 * q^19 - 527311 * q^20 - 2492775 * q^21 + 2973158 * q^22 + 169962 * q^23 - 1994301 * q^24 + 8035779 * q^25 - 2337392 * q^26 + 11160261 * q^27 - 22659054 * q^28 - 16845442 * q^29 - 4427703 * q^30 - 19307976 * q^31 - 44923568 * q^32 - 12293289 * q^33 - 35547496 * q^34 - 34882596 * q^35 + 34156566 * q^36 - 41561129 * q^37 - 52335371 * q^38 - 12442491 * q^39 - 125735038 * q^40 - 68169291 * q^41 - 23228451 * q^42 - 25719587 * q^43 - 126277032 * q^44 - 19446804 * q^45 - 292814271 * q^46 - 174095332 * q^47 + 65247930 * q^48 + 7479350 * q^49 - 227877439 * q^50 - 58613301 * q^51 - 232397708 * q^52 - 228390500 * q^53 - 35075106 * q^54 - 29426208 * q^55 + 326778474 * q^56 - 44500428 * q^57 + 480343762 * q^58 + 254464581 * q^59 - 42712191 * q^60 - 183928964 * q^61 - 21753862 * q^62 - 201914775 * q^63 + 310571245 * q^64 + 5308466 * q^65 + 240825798 * q^66 - 82724114 * q^67 - 138336205 * q^68 + 13766922 * q^69 + 1030274876 * q^70 - 404721965 * q^71 - 161538381 * q^72 + 154162574 * q^73 + 36352054 * q^74 + 650898099 * q^75 + 1068940636 * q^76 - 448535481 * q^77 - 189328752 * q^78 + 272529635 * q^79 - 345587859 * q^80 + 903981141 * q^81 - 38412637 * q^82 + 432518643 * q^83 - 1835383374 * q^84 - 126211490 * q^85 - 3699273072 * q^86 - 1364480802 * q^87 + 170111045 * q^88 - 1255621070 * q^89 - 358643943 * q^90 + 1448885849 * q^91 + 1568933320 * q^92 - 1563946056 * q^93 - 1908445164 * q^94 - 2896546490 * q^95 - 3638809008 * q^96 + 1007235486 * q^97 - 9506868248 * q^98 - 995756409 * 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 $

$2$	30.4984	1.34785	0.673925	−	0.738800i	$-0.264607\pi$
$2$	30.4984	1.34785	0.673925	+	0.738800i	$0.264607\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	418.150	0.816700
$5$	1050.93	0.751985	0.375992	−	0.926623i	$-0.377302\pi$
$5$	1050.93	0.751985	0.375992	+	0.926623i	$0.377302\pi$
$6$	2470.37	0.778182
$7$	−5890.68	−0.927308	−0.463654	−	0.886016i	$-0.653462\pi$
$7$	−5890.68	−0.927308	−0.463654	+	0.886016i	$0.653462\pi$
$8$	−2862.26	−0.247061
$9$	6561.00	0.333333
$10$	32051.7	1.01356
$11$	26388.8	0.543442	0.271721	−	0.962376i	$-0.412407\pi$
$11$	26388.8	0.543442	0.271721	+	0.962376i	$0.412407\pi$
$12$	33870.2	0.471522
$13$	−71180.0	−0.691215	−0.345607	−	0.938379i	$-0.612327\pi$
$13$	−71180.0	−0.691215	−0.345607	+	0.938379i	$0.612327\pi$
$14$	−179656.	−1.24987
$15$	85125.4	0.434159
$16$	−301387.	−1.14970
$17$	−660629.	−1.91839	−0.959196	−	0.282742i	$-0.908756\pi$
$17$	−660629.	−1.91839	−0.959196	+	0.282742i	$0.908756\pi$
$18$	200100.	0.449283
$19$	−713962.	−1.25685	−0.628425	−	0.777870i	$-0.716300\pi$
$19$	−713962.	−1.25685	−0.628425	+	0.777870i	$0.716300\pi$
$20$	439447.	0.614146
$21$	−477145.	−0.535381
$22$	804816.	0.732478
$23$	1.72289e6	1.28376	0.641878	−	0.766806i	$-0.278155\pi$
$23$	1.72289e6	1.28376	0.641878	+	0.766806i	$0.278155\pi$
$24$	−231843.	−0.142641
$25$	−848670.	−0.434519
$26$	−2.17087e6	−0.931654
$27$	531441.	0.192450
$28$	−2.46319e6	−0.757332
$29$	−882627.	−0.231732	−0.115866	−	0.993265i	$-0.536964\pi$
$29$	−882627.	−0.231732	−0.115866	+	0.993265i	$0.536964\pi$
$30$	2.59619e6	0.585181
$31$	8.02994e6	1.56165	0.780827	−	0.624748i	$-0.214798\pi$
$31$	8.02994e6	1.56165	0.780827	+	0.624748i	$0.214798\pi$
$32$	−7.72634e6	−1.30256
$33$	2.13749e6	0.313756
$34$	−2.01481e7	−2.58570
$35$	−6.19069e6	−0.697321
$36$	2.74348e6	0.272233
$37$	−1.38423e7	−1.21423	−0.607113	−	0.794615i	$-0.707673\pi$
$37$	−1.38423e7	−1.21423	−0.607113	+	0.794615i	$0.707673\pi$
$38$	−2.17747e7	−1.69405
$39$	−5.76558e6	−0.399073
$40$	−3.00804e6	−0.185786
$41$	−1.60785e7	−0.888623	−0.444311	−	0.895872i	$-0.646552\pi$
$41$	−1.60785e7	−0.888623	−0.444311	+	0.895872i	$0.646552\pi$
$42$	−1.45521e7	−0.721614
$43$	−1.63480e7	−0.729216	−0.364608	−	0.931161i	$-0.618797\pi$
$43$	−1.63480e7	−0.729216	−0.364608	+	0.931161i	$0.618797\pi$
$44$	1.10345e7	0.443829
$45$	6.89516e6	0.250662
$46$	5.25454e7	1.73031
$47$	4.25996e7	1.27340	0.636701	−	0.771111i	$-0.280299\pi$
$47$	4.25996e7	1.27340	0.636701	+	0.771111i	$0.280299\pi$
$48$	−2.44124e7	−0.663780
$49$	−5.65355e6	−0.140100
$50$	−2.58830e7	−0.585666
$51$	−5.35109e7	−1.10758
$52$	−2.97639e7	−0.564515
$53$	5.47396e6	0.0952928	0.0476464	−	0.998864i	$-0.484828\pi$
$53$	5.47396e6	0.0952928	0.0476464	+	0.998864i	$0.484828\pi$
$54$	1.62081e7	0.259394
$55$	2.77328e7	0.408660
$56$	1.68607e7	0.229102
$57$	−5.78309e7	−0.725643
$58$	−2.69187e7	−0.312340
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	3.55952e7	0.354577
$61$	−1.55390e8	−1.43694	−0.718471	−	0.695557i	$-0.755158\pi$
$61$	−1.55390e8	−1.43694	−0.718471	+	0.695557i	$0.755158\pi$
$62$	2.44900e8	2.10487
$63$	−3.86487e7	−0.309103
$64$	−8.13305e7	−0.605959
$65$	−7.48053e7	−0.519783
$66$	6.51901e7	0.422896
$67$	1.19205e8	0.722702	0.361351	−	0.932430i	$-0.382316\pi$
$67$	1.19205e8	0.722702	0.361351	+	0.932430i	$0.382316\pi$
$68$	−2.76242e8	−1.56675
$69$	1.39554e8	0.741177
$70$	−1.88806e8	−0.939885
$71$	5.29891e7	0.247471	0.123736	−	0.992315i	$-0.460513\pi$
$71$	5.29891e7	0.247471	0.123736	+	0.992315i	$0.460513\pi$
$72$	−1.87793e7	−0.0823537
$73$	−1.44959e8	−0.597437	−0.298719	−	0.954341i	$-0.596559\pi$
$73$	−1.44959e8	−0.597437	−0.298719	+	0.954341i	$0.596559\pi$
$74$	−4.22167e8	−1.63660
$75$	−6.87422e7	−0.250870
$76$	−2.98543e8	−1.02647
$77$	−1.55448e8	−0.503938
$78$	−1.75841e8	−0.537891
$79$	3.12409e8	0.902406	0.451203	−	0.892421i	$-0.350995\pi$
$79$	3.12409e8	0.902406	0.451203	+	0.892421i	$0.350995\pi$
$80$	−3.16737e8	−0.864558
$81$	4.30467e7	0.111111
$82$	−4.90367e8	−1.19773
$83$	5.07060e7	0.117276	0.0586379	−	0.998279i	$-0.481324\pi$
$83$	5.07060e7	0.117276	0.0586379	+	0.998279i	$0.481324\pi$
$84$	−1.99518e8	−0.437246
$85$	−6.94275e8	−1.44260
$86$	−4.98587e8	−0.982874
$87$	−7.14928e7	−0.133791
$88$	−7.55317e7	−0.134263
$89$	6.65499e8	1.12433	0.562163	−	0.827026i	$-0.309969\pi$
$89$	6.65499e8	1.12433	0.562163	+	0.827026i	$0.309969\pi$
$90$	2.10291e8	0.337854
$91$	4.19298e8	0.640969
$92$	7.20428e8	1.04844
$93$	6.50425e8	0.901621
$94$	1.29922e9	1.71635
$95$	−7.50324e8	−0.945132
$96$	−6.25834e8	−0.752036
$97$	−1.11643e9	−1.28044	−0.640221	−	0.768191i	$-0.721157\pi$
$97$	−1.11643e9	−1.28044	−0.640221	+	0.768191i	$0.721157\pi$
$98$	−1.72424e8	−0.188834
$99$	1.73137e8	0.181147
$100$	−3.54872e8	−0.354872
$101$	−7.41591e8	−0.709118	−0.354559	−	0.935034i	$-0.615369\pi$
$101$	−7.41591e8	−0.709118	−0.354559	+	0.935034i	$0.615369\pi$
$102$	−1.63200e9	−1.49286
$103$	1.65068e7	0.0144509	0.00722547	−	0.999974i	$-0.497700\pi$
$103$	1.65068e7	0.0144509	0.00722547	+	0.999974i	$0.497700\pi$
$104$	2.03736e8	0.170772
$105$	−5.01446e8	−0.402599
$106$	1.66947e8	0.128440
$107$	2.51369e9	1.85389	0.926945	−	0.375197i	$-0.122425\pi$
$107$	2.51369e9	1.85389	0.926945	+	0.375197i	$0.122425\pi$
$108$	2.22222e8	0.157174
$109$	−1.57567e9	−1.06917	−0.534583	−	0.845116i	$-0.679531\pi$
$109$	−1.57567e9	−1.06917	−0.534583	+	0.845116i	$0.679531\pi$
$110$	8.45806e8	0.550812
$111$	−1.12122e9	−0.701034
$112$	1.77537e9	1.06613
$113$	−4.34260e8	−0.250551	−0.125276	−	0.992122i	$-0.539982\pi$
$113$	−4.34260e8	−0.250551	−0.125276	+	0.992122i	$0.539982\pi$
$114$	−1.76375e9	−0.978058
$115$	1.81064e9	0.965366
$116$	−3.69071e8	−0.189256
$117$	−4.67012e8	−0.230405
$118$	3.69560e8	0.175475
$119$	3.89155e9	1.77894
$120$	−2.43651e8	−0.107264
$121$	−1.66158e9	−0.704671
$122$	−4.73915e9	−1.93678
$123$	−1.30236e9	−0.513046
$124$	3.35772e9	1.27540
$125$	−2.94449e9	−1.07874
$126$	−1.17872e9	−0.416624
$127$	−2.00644e9	−0.684400	−0.342200	−	0.939627i	$-0.611172\pi$
$127$	−2.00644e9	−0.684400	−0.342200	+	0.939627i	$0.611172\pi$
$128$	1.47544e9	0.485821
$129$	−1.32419e9	−0.421013
$130$	−2.28144e9	−0.700590
$131$	−5.58693e9	−1.65750	−0.828748	−	0.559621i	$-0.810947\pi$
$131$	−5.58693e9	−1.65750	−0.828748	+	0.559621i	$0.810947\pi$
$132$	8.93794e8	0.256245
$133$	4.20572e9	1.16549
$134$	3.63557e9	0.974094
$135$	5.58508e8	0.144720
$136$	1.89089e9	0.473960
$137$	1.77995e9	0.431683	0.215841	−	0.976428i	$-0.430751\pi$
$137$	1.77995e9	0.431683	0.215841	+	0.976428i	$0.430751\pi$
$138$	4.25618e9	0.998996
$139$	−3.20102e9	−0.727313	−0.363656	−	0.931533i	$-0.618472\pi$
$139$	−3.20102e9	−0.727313	−0.363656	+	0.931533i	$0.618472\pi$
$140$	−2.58864e9	−0.569502
$141$	3.45057e9	0.735199
$142$	1.61608e9	0.333554
$143$	−1.87836e9	−0.375635
$144$	−1.97740e9	−0.383234
$145$	−9.27580e8	−0.174259
$146$	−4.42101e9	−0.805256
$147$	−4.57938e8	−0.0808870
$148$	−5.78815e9	−0.991659
$149$	2.75929e8	0.0458626	0.0229313	−	0.999737i	$-0.492700\pi$
$149$	2.75929e8	0.0458626	0.0229313	+	0.999737i	$0.492700\pi$
$150$	−2.09653e9	−0.338135
$151$	2.26643e9	0.354770	0.177385	−	0.984142i	$-0.443236\pi$
$151$	2.26643e9	0.354770	0.177385	+	0.984142i	$0.443236\pi$
$152$	2.04354e9	0.310519
$153$	−4.33439e9	−0.639464
$154$	−4.74091e9	−0.679232
$155$	8.43891e9	1.17434
$156$	−2.41088e9	−0.325923
$157$	5.86242e9	0.770067	0.385033	−	0.922903i	$-0.374190\pi$
$157$	5.86242e9	0.770067	0.385033	+	0.922903i	$0.374190\pi$
$158$	9.52798e9	1.21631
$159$	4.43391e8	0.0550173
$160$	−8.11985e9	−0.979508
$161$	−1.01490e10	−1.19044
$162$	1.31285e9	0.149761
$163$	−4.17928e8	−0.0463722	−0.0231861	−	0.999731i	$-0.507381\pi$
$163$	−4.17928e8	−0.0463722	−0.0231861	+	0.999731i	$0.507381\pi$
$164$	−6.72322e9	−0.725738
$165$	2.24636e9	0.235940
$166$	1.54645e9	0.158070
$167$	9.44876e9	0.940049	0.470025	−	0.882653i	$-0.344245\pi$
$167$	9.44876e9	0.940049	0.470025	+	0.882653i	$0.344245\pi$
$168$	1.36571e9	0.132272
$169$	−5.53790e9	−0.522222
$170$	−2.11743e10	−1.94441
$171$	−4.68430e9	−0.418950
$172$	−6.83592e9	−0.595551
$173$	1.95277e10	1.65746	0.828732	−	0.559645i	$-0.189063\pi$
$173$	1.95277e10	1.65746	0.828732	+	0.559645i	$0.189063\pi$
$174$	−2.18041e9	−0.180330
$175$	4.99924e9	0.402933
$176$	−7.95325e9	−0.624795
$177$	9.81506e8	0.0751646
$178$	2.02966e10	1.51542
$179$	1.59226e10	1.15924	0.579621	−	0.814886i	$-0.303201\pi$
$179$	1.59226e10	1.15924	0.579621	+	0.814886i	$0.303201\pi$
$180$	2.88321e9	0.204715
$181$	−1.76554e10	−1.22271	−0.611357	−	0.791355i	$-0.709376\pi$
$181$	−1.76554e10	−1.22271	−0.611357	+	0.791355i	$0.709376\pi$
$182$	1.27879e10	0.863930
$183$	−1.25866e10	−0.829619
$184$	−4.93137e9	−0.317166
$185$	−1.45473e10	−0.913080
$186$	1.98369e10	1.21525
$187$	−1.74332e10	−1.04253
$188$	1.78130e10	1.03999
$189$	−3.13055e9	−0.178460
$190$	−2.28837e10	−1.27390
$191$	1.53998e10	0.837271	0.418635	−	0.908154i	$-0.362509\pi$
$191$	1.53998e10	0.837271	0.418635	+	0.908154i	$0.362509\pi$
$192$	−6.58777e9	−0.349851
$193$	−2.04849e10	−1.06274	−0.531368	−	0.847141i	$-0.678322\pi$
$193$	−2.04849e10	−1.06274	−0.531368	+	0.847141i	$0.678322\pi$
$194$	−3.40494e10	−1.72584
$195$	−6.05923e9	−0.300097
$196$	−2.36404e9	−0.114420
$197$	3.47341e10	1.64308	0.821539	−	0.570152i	$-0.193116\pi$
$197$	3.47341e10	1.64308	0.821539	+	0.570152i	$0.193116\pi$
$198$	5.28040e9	0.244159
$199$	−3.86058e10	−1.74507	−0.872536	−	0.488549i	$-0.837526\pi$
$199$	−3.86058e10	−1.74507	−0.872536	+	0.488549i	$0.837526\pi$
$200$	2.42911e9	0.107353
$201$	9.65564e9	0.417252
$202$	−2.26173e10	−0.955785
$203$	5.19927e9	0.214887
$204$	−2.23756e10	−0.904564
$205$	−1.68974e10	−0.668231
$206$	5.03431e8	0.0194777
$207$	1.13039e10	0.427919
$208$	2.14528e10	0.794690
$209$	−1.88406e10	−0.683025
$210$	−1.52933e10	−0.542643
$211$	−4.41749e10	−1.53428	−0.767139	−	0.641480i	$-0.778321\pi$
$211$	−4.41749e10	−1.53428	−0.767139	+	0.641480i	$0.778321\pi$
$212$	2.28894e9	0.0778256
$213$	4.29212e9	0.142877
$214$	7.66633e10	2.49877
$215$	−1.71806e10	−0.548359
$216$	−1.52112e9	−0.0475469
$217$	−4.73018e10	−1.44813
$218$	−4.80552e10	−1.44107
$219$	−1.17417e10	−0.344930
$220$	1.15965e10	0.333752
$221$	4.70236e10	1.32602
$222$	−3.41955e10	−0.944889
$223$	6.94229e9	0.187988	0.0939942	−	0.995573i	$-0.470036\pi$
$223$	6.94229e9	0.187988	0.0939942	+	0.995573i	$0.470036\pi$
$224$	4.55134e10	1.20788
$225$	−5.56812e9	−0.144840
$226$	−1.32442e10	−0.337706
$227$	−8.88310e9	−0.222049	−0.111024	−	0.993818i	$-0.535413\pi$
$227$	−8.88310e9	−0.222049	−0.111024	+	0.993818i	$0.535413\pi$
$228$	−2.41820e10	−0.592632
$229$	3.07383e10	0.738619	0.369310	−	0.929306i	$-0.379594\pi$
$229$	3.07383e10	0.738619	0.369310	+	0.929306i	$0.379594\pi$
$230$	5.52216e10	1.30117
$231$	−1.25913e10	−0.290948
$232$	2.52631e9	0.0572520
$233$	2.08242e10	0.462879	0.231440	−	0.972849i	$-0.425656\pi$
$233$	2.08242e10	0.462879	0.231440	+	0.972849i	$0.425656\pi$
$234$	−1.42431e10	−0.310551
$235$	4.47692e10	0.957578
$236$	5.06688e9	0.106325
$237$	2.53052e10	0.521005
$238$	1.18686e11	2.39774
$239$	8.52149e10	1.68937	0.844686	−	0.535263i	$-0.179787\pi$
$239$	8.52149e10	1.68937	0.844686	+	0.535263i	$0.179787\pi$
$240$	−2.56557e10	−0.499153
$241$	−8.04735e9	−0.153665	−0.0768327	−	0.997044i	$-0.524481\pi$
$241$	−8.04735e9	−0.153665	−0.0768327	+	0.997044i	$0.524481\pi$
$242$	−5.06754e10	−0.949791
$243$	3.48678e9	0.0641500
$244$	−6.49765e10	−1.17355
$245$	−5.94149e9	−0.105353
$246$	−3.97197e10	−0.691510
$247$	5.08198e10	0.868754
$248$	−2.29838e10	−0.385824
$249$	4.10719e9	0.0677092
$250$	−8.98022e10	−1.45397
$251$	6.99285e10	1.11205	0.556023	−	0.831167i	$-0.312327\pi$
$251$	6.99285e10	1.11205	0.556023	+	0.831167i	$0.312327\pi$
$252$	−1.61610e10	−0.252444
$253$	4.54651e10	0.697647
$254$	−6.11932e10	−0.922468
$255$	−5.62363e10	−0.832886
$256$	8.66397e10	1.26077
$257$	5.86319e10	0.838369	0.419184	−	0.907901i	$-0.362316\pi$
$257$	5.86319e10	0.838369	0.419184	+	0.907901i	$0.362316\pi$
$258$	−4.03855e10	−0.567463
$259$	8.15403e10	1.12596
$260$	−3.12798e10	−0.424507
$261$	−5.79092e9	−0.0772441
$262$	−1.70392e11	−2.23406
$263$	−8.46098e10	−1.09048	−0.545242	−	0.838278i	$-0.683562\pi$
$263$	−8.46098e10	−1.09048	−0.545242	+	0.838278i	$0.683562\pi$
$264$	−6.11807e9	−0.0775169
$265$	5.75275e9	0.0716587
$266$	1.28267e11	1.57090
$267$	5.39054e10	0.649130
$268$	4.98458e10	0.590231
$269$	1.49829e11	1.74466	0.872329	−	0.488919i	$-0.162609\pi$
$269$	1.49829e11	1.74466	0.872329	+	0.488919i	$0.162609\pi$
$270$	1.70336e10	0.195060
$271$	−5.86333e10	−0.660362	−0.330181	−	0.943918i	$-0.607110\pi$
$271$	−5.86333e10	−0.660362	−0.330181	+	0.943918i	$0.607110\pi$
$272$	1.99105e11	2.20558
$273$	3.39632e10	0.370064
$274$	5.42855e10	0.581844
$275$	−2.23954e10	−0.236136
$276$	5.83547e10	0.605319
$277$	1.55859e11	1.59064	0.795321	−	0.606189i	$-0.207303\pi$
$277$	1.55859e11	1.59064	0.795321	+	0.606189i	$0.207303\pi$
$278$	−9.76258e10	−0.980309
$279$	5.26844e10	0.520551
$280$	1.77194e10	0.172281
$281$	−9.66239e9	−0.0924499	−0.0462249	−	0.998931i	$-0.514719\pi$
$281$	−9.66239e9	−0.0924499	−0.0462249	+	0.998931i	$0.514719\pi$
$282$	1.05237e11	0.990938
$283$	−6.44213e10	−0.597023	−0.298511	−	0.954406i	$-0.596490\pi$
$283$	−6.44213e10	−0.597023	−0.298511	+	0.954406i	$0.596490\pi$
$284$	2.21574e10	0.202110
$285$	−6.07762e10	−0.545672
$286$	−5.72868e10	−0.506299
$287$	9.47130e10	0.824027
$288$	−5.06925e10	−0.434188
$289$	3.17843e11	2.68023
$290$	−2.82897e10	−0.234875
$291$	−9.04310e10	−0.739263
$292$	−6.06146e10	−0.487927
$293$	−6.96073e10	−0.551760	−0.275880	−	0.961192i	$-0.588969\pi$
$293$	−6.96073e10	−0.551760	−0.275880	+	0.961192i	$0.588969\pi$
$294$	−1.39664e10	−0.109024
$295$	1.27345e10	0.0979001
$296$	3.96202e10	0.299988
$297$	1.40241e10	0.104585
$298$	8.41538e9	0.0618159
$299$	−1.22635e11	−0.887352
$300$	−2.87446e10	−0.204885
$301$	9.63007e10	0.676208
$302$	6.91225e10	0.478177
$303$	−6.00689e10	−0.409409
$304$	2.15179e11	1.44500
$305$	−1.63304e11	−1.08056
$306$	−1.32192e11	−0.861902
$307$	1.21751e11	0.782255	0.391128	−	0.920336i	$-0.372085\pi$
$307$	1.21751e11	0.782255	0.391128	+	0.920336i	$0.372085\pi$
$308$	−6.50006e10	−0.411566
$309$	1.33705e9	0.00834326
$310$	2.57373e11	1.58283
$311$	−1.26038e11	−0.763979	−0.381989	−	0.924167i	$-0.624761\pi$
$311$	−1.26038e11	−0.763979	−0.381989	+	0.924167i	$0.624761\pi$
$312$	1.65026e10	0.0985954
$313$	−5.96233e10	−0.351129	−0.175564	−	0.984468i	$-0.556175\pi$
$313$	−5.96233e10	−0.351129	−0.175564	+	0.984468i	$0.556175\pi$
$314$	1.78794e11	1.03793
$315$	−4.06171e10	−0.232440
$316$	1.30634e11	0.736995
$317$	1.37551e11	0.765064	0.382532	−	0.923942i	$-0.375052\pi$
$317$	1.37551e11	0.765064	0.382532	+	0.923942i	$0.375052\pi$
$318$	1.35227e10	0.0741551
$319$	−2.32915e10	−0.125933
$320$	−8.54727e10	−0.455672
$321$	2.03609e11	1.07034
$322$	−3.09528e11	−1.60453
$323$	4.71664e11	2.41113
$324$	1.80000e10	0.0907444
$325$	6.04083e10	0.300346
$326$	−1.27461e10	−0.0625027
$327$	−1.27629e11	−0.617283
$328$	4.60208e10	0.219544
$329$	−2.50940e11	−1.18083
$330$	6.85103e10	0.318012
$331$	−3.56768e11	−1.63365	−0.816827	−	0.576882i	$-0.804269\pi$
$331$	−3.56768e11	−1.63365	−0.816827	+	0.576882i	$0.804269\pi$
$332$	2.12027e10	0.0957791
$333$	−9.08192e10	−0.404742
$334$	2.88172e11	1.26705
$335$	1.25277e11	0.543461
$336$	1.43805e11	0.615529
$337$	−3.33498e10	−0.140851	−0.0704253	−	0.997517i	$-0.522436\pi$
$337$	−3.33498e10	−0.140851	−0.0704253	+	0.997517i	$0.522436\pi$
$338$	−1.68897e11	−0.703877
$339$	−3.51750e10	−0.144656
$340$	−2.90311e11	−1.17817
$341$	2.11901e11	0.848667
$342$	−1.42864e11	−0.564682
$343$	2.71013e11	1.05722
$344$	4.67922e10	0.180161
$345$	1.46662e11	0.557354
$346$	5.95564e11	2.23401
$347$	−4.01239e11	−1.48567	−0.742833	−	0.669477i	$-0.766518\pi$
$347$	−4.01239e11	−1.48567	−0.742833	+	0.669477i	$0.766518\pi$
$348$	−2.98947e10	−0.109267
$349$	4.22628e11	1.52491	0.762455	−	0.647042i	$-0.223994\pi$
$349$	4.22628e11	1.52491	0.762455	+	0.647042i	$0.223994\pi$
$350$	1.52469e11	0.543093
$351$	−3.78280e10	−0.133024
$352$	−2.03889e11	−0.707867
$353$	−5.37777e11	−1.84338	−0.921692	−	0.387923i	$-0.873193\pi$
$353$	−5.37777e11	−1.84338	−0.921692	+	0.387923i	$0.873193\pi$
$354$	2.99343e10	0.101311
$355$	5.56879e10	0.186094
$356$	2.78279e11	0.918237
$357$	3.15216e11	1.02707
$358$	4.85612e11	1.56248
$359$	−2.09495e11	−0.665654	−0.332827	−	0.942988i	$-0.608003\pi$
$359$	−2.09495e11	−0.665654	−0.332827	+	0.942988i	$0.608003\pi$
$360$	−1.97357e10	−0.0619287
$361$	1.87053e11	0.579673
$362$	−5.38462e11	−1.64803
$363$	−1.34588e11	−0.406842
$364$	1.75330e11	0.523479
$365$	−1.52342e11	−0.449264
$366$	−3.83871e11	−1.11820
$367$	−1.37201e11	−0.394783	−0.197392	−	0.980325i	$-0.563247\pi$
$367$	−1.37201e11	−0.394783	−0.197392	+	0.980325i	$0.563247\pi$
$368$	−5.19258e11	−1.47594
$369$	−1.05491e11	−0.296208
$370$	−4.43668e11	−1.23069
$371$	−3.22453e10	−0.0883657
$372$	2.71975e11	0.736354
$373$	3.50710e11	0.938119	0.469060	−	0.883166i	$-0.344593\pi$
$373$	3.50710e11	0.938119	0.469060	+	0.883166i	$0.344593\pi$
$374$	−5.31684e11	−1.40518
$375$	−2.38504e11	−0.622809
$376$	−1.21931e11	−0.314608
$377$	6.28254e10	0.160177
$378$	−9.54765e10	−0.240538
$379$	−3.57636e11	−0.890358	−0.445179	−	0.895442i	$-0.646860\pi$
$379$	−3.57636e11	−0.890358	−0.445179	+	0.895442i	$0.646860\pi$
$380$	−3.13748e11	−0.771890
$381$	−1.62522e11	−0.395138
$382$	4.69670e11	1.12852
$383$	1.83871e10	0.0436635	0.0218318	−	0.999762i	$-0.493050\pi$
$383$	1.83871e10	0.0436635	0.0218318	+	0.999762i	$0.493050\pi$
$384$	1.19511e11	0.280489
$385$	−1.63365e11	−0.378953
$386$	−6.24755e11	−1.43241
$387$	−1.07259e11	−0.243072
$388$	−4.66837e11	−1.04574
$389$	−5.36462e11	−1.18786	−0.593931	−	0.804516i	$-0.702425\pi$
$389$	−5.36462e11	−1.18786	−0.593931	+	0.804516i	$0.702425\pi$
$390$	−1.84797e11	−0.404486
$391$	−1.13819e12	−2.46275
$392$	1.61819e10	0.0346133
$393$	−4.52542e11	−0.956956
$394$	1.05933e12	2.21462
$395$	3.28321e11	0.678596
$396$	7.23973e10	0.147943
$397$	1.88055e11	0.379951	0.189976	−	0.981789i	$-0.439159\pi$
$397$	1.88055e11	0.379951	0.189976	+	0.981789i	$0.439159\pi$
$398$	−1.17741e12	−2.35210
$399$	3.40663e11	0.672894
$400$	2.55778e11	0.499567
$401$	2.08200e11	0.402097	0.201048	−	0.979581i	$-0.435565\pi$
$401$	2.08200e11	0.402097	0.201048	+	0.979581i	$0.435565\pi$
$402$	2.94481e11	0.562394
$403$	−5.71571e11	−1.07944
$404$	−3.10097e11	−0.579137
$405$	4.52391e10	0.0835539
$406$	1.58569e11	0.289636
$407$	−3.65281e11	−0.659861
$408$	1.53162e11	0.273641
$409$	−9.77641e10	−0.172753	−0.0863763	−	0.996263i	$-0.527529\pi$
$409$	−9.77641e10	−0.172753	−0.0863763	+	0.996263i	$0.527529\pi$
$410$	−5.15342e11	−0.900675
$411$	1.44176e11	0.249232
$412$	6.90234e9	0.0118021
$413$	−7.13794e10	−0.120725
$414$	3.44750e11	0.576771
$415$	5.32885e10	0.0881896
$416$	5.49961e11	0.900351
$417$	−2.59282e11	−0.419914
$418$	−5.74608e11	−0.920615
$419$	−6.06783e11	−0.961767	−0.480884	−	0.876784i	$-0.659684\pi$
$419$	−6.06783e11	−0.961767	−0.480884	+	0.876784i	$0.659684\pi$
$420$	−2.09680e11	−0.328802
$421$	9.96114e11	1.54540	0.772698	−	0.634774i	$-0.218907\pi$
$421$	9.96114e11	1.54540	0.772698	+	0.634774i	$0.218907\pi$
$422$	−1.34726e12	−2.06798
$423$	2.79496e11	0.424467
$424$	−1.56679e10	−0.0235431
$425$	5.60656e11	0.833578
$426$	1.30903e11	0.192577
$427$	9.15353e11	1.33249
$428$	1.05110e12	1.51407
$429$	−1.52147e11	−0.216873
$430$	−5.23980e11	−0.739106
$431$	9.84981e11	1.37493	0.687465	−	0.726218i	$-0.258724\pi$
$431$	9.84981e11	1.37493	0.687465	+	0.726218i	$0.258724\pi$
$432$	−1.60170e11	−0.221260
$433$	−5.50407e11	−0.752468	−0.376234	−	0.926525i	$-0.622781\pi$
$433$	−5.50407e11	−0.752468	−0.376234	+	0.926525i	$0.622781\pi$
$434$	−1.44263e12	−1.95187
$435$	−7.51340e10	−0.100609
$436$	−6.58865e11	−0.873187
$437$	−1.23008e12	−1.61349
$438$	−3.58102e11	−0.464915
$439$	−4.59045e10	−0.0589882	−0.0294941	−	0.999565i	$-0.509390\pi$
$439$	−4.59045e10	−0.0589882	−0.0294941	+	0.999565i	$0.509390\pi$
$440$	−7.93786e10	−0.100964
$441$	−3.70930e10	−0.0467001
$442$	1.43414e12	1.78728
$443$	−6.41010e11	−0.790766	−0.395383	−	0.918516i	$-0.629388\pi$
$443$	−6.41010e11	−0.790766	−0.395383	+	0.918516i	$0.629388\pi$
$444$	−4.68840e11	−0.572534
$445$	6.99393e11	0.845476
$446$	2.11729e11	0.253380
$447$	2.23502e10	0.0264788
$448$	4.79092e11	0.561911
$449$	−1.04339e11	−0.121154	−0.0605771	−	0.998164i	$-0.519294\pi$
$449$	−1.04339e11	−0.121154	−0.0605771	+	0.998164i	$0.519294\pi$
$450$	−1.69819e11	−0.195222
$451$	−4.24292e11	−0.482914
$452$	−1.81586e11	−0.204625
$453$	1.83581e11	0.204827
$454$	−2.70920e11	−0.299288
$455$	4.40654e11	0.481999
$456$	1.65527e11	0.179278
$457$	−9.29917e11	−0.997289	−0.498645	−	0.866807i	$-0.666169\pi$
$457$	−9.29917e11	−0.997289	−0.498645	+	0.866807i	$0.666169\pi$
$458$	9.37469e11	0.995548
$459$	−3.51085e11	−0.369195
$460$	7.57120e11	0.788414
$461$	−1.57666e12	−1.62586	−0.812931	−	0.582361i	$-0.802129\pi$
$461$	−1.57666e12	−1.62586	−0.812931	+	0.582361i	$0.802129\pi$
$462$	−3.84014e11	−0.392155
$463$	−1.49875e12	−1.51571	−0.757853	−	0.652426i	$-0.773751\pi$
$463$	−1.49875e12	−1.51571	−0.757853	+	0.652426i	$0.773751\pi$
$464$	2.66013e11	0.266423
$465$	6.83552e11	0.678005
$466$	6.35106e11	0.623892
$467$	−1.06084e12	−1.03210	−0.516050	−	0.856558i	$-0.672598\pi$
$467$	−1.06084e12	−1.03210	−0.516050	+	0.856558i	$0.672598\pi$
$468$	−1.95281e11	−0.188172
$469$	−7.02201e11	−0.670168
$470$	1.36539e12	1.29067
$471$	4.74856e11	0.444598
$472$	−3.46831e10	−0.0321646
$473$	−4.31404e11	−0.396286
$474$	7.71766e11	0.702236
$475$	6.05918e11	0.546125
$476$	1.62725e12	1.45286
$477$	3.59146e10	0.0317643
$478$	2.59892e12	2.27702
$479$	1.62236e12	1.40811	0.704056	−	0.710144i	$-0.251370\pi$
$479$	1.62236e12	1.40811	0.704056	+	0.710144i	$0.251370\pi$
$480$	−6.57708e11	−0.565519
$481$	9.85293e11	0.839291
$482$	−2.45431e11	−0.207118
$483$	−8.22069e11	−0.687300
$484$	−6.94789e11	−0.575505
$485$	−1.17329e12	−0.962872
$486$	1.06341e11	0.0864646
$487$	9.85769e11	0.794136	0.397068	−	0.917789i	$-0.370028\pi$
$487$	9.85769e11	0.794136	0.397068	+	0.917789i	$0.370028\pi$
$488$	4.44767e11	0.355013
$489$	−3.38522e10	−0.0267730
$490$	−1.81206e11	−0.142000
$491$	1.97389e12	1.53270	0.766348	−	0.642425i	$-0.222072\pi$
$491$	1.97389e12	1.53270	0.766348	+	0.642425i	$0.222072\pi$
$492$	−5.44581e11	−0.419005
$493$	5.83089e11	0.444553
$494$	1.54992e12	1.17095
$495$	1.81955e11	0.136220
$496$	−2.42012e12	−1.79543
$497$	−3.12142e11	−0.229482
$498$	1.25263e11	0.0912618
$499$	−9.09868e11	−0.656941	−0.328470	−	0.944514i	$-0.606533\pi$
$499$	−9.09868e11	−0.656941	−0.328470	+	0.944514i	$0.606533\pi$
$500$	−1.23124e12	−0.881004
$501$	7.65349e11	0.542738
$502$	2.13271e12	1.49887
$503$	3.29409e11	0.229446	0.114723	−	0.993398i	$-0.463402\pi$
$503$	3.29409e11	0.229446	0.114723	+	0.993398i	$0.463402\pi$
$504$	1.10623e11	0.0763672
$505$	−7.79361e11	−0.533246
$506$	1.38661e12	0.940323
$507$	−4.48570e11	−0.301505
$508$	−8.38995e11	−0.558949
$509$	−1.73073e12	−1.14288	−0.571440	−	0.820644i	$-0.693615\pi$
$509$	−1.73073e12	−1.14288	−0.571440	+	0.820644i	$0.693615\pi$
$510$	−1.71511e12	−1.12261
$511$	8.53906e11	0.554008
$512$	1.88694e12	1.21351
$513$	−3.79428e11	−0.241881
$514$	1.78818e12	1.13000
$515$	1.73475e10	0.0108669
$516$	−5.53709e11	−0.343841
$517$	1.12415e12	0.692019
$518$	2.48685e12	1.51763
$519$	1.58175e12	0.956938
$520$	2.14112e11	0.128418
$521$	−7.85423e11	−0.467018	−0.233509	−	0.972355i	$-0.575021\pi$
$521$	−7.85423e11	−0.467018	−0.233509	+	0.972355i	$0.575021\pi$
$522$	−1.76614e11	−0.104113
$523$	1.11757e12	0.653155	0.326577	−	0.945170i	$-0.394105\pi$
$523$	1.11757e12	0.653155	0.326577	+	0.945170i	$0.394105\pi$
$524$	−2.33618e12	−1.35368
$525$	4.04938e11	0.232633
$526$	−2.58046e12	−1.46981
$527$	−5.30481e12	−2.99586
$528$	−6.44214e11	−0.360726
$529$	1.16720e12	0.648032
$530$	1.75449e11	0.0965852
$531$	7.95020e10	0.0433963
$532$	1.75862e12	0.951853
$533$	1.14447e12	0.614229
$534$	1.64403e12	0.874930
$535$	2.64171e12	1.39410
$536$	−3.41197e11	−0.178552
$537$	1.28973e12	0.669289
$538$	4.56954e12	2.35154
$539$	−1.49191e11	−0.0761363
$540$	2.33540e11	0.118192
$541$	2.85930e12	1.43507	0.717534	−	0.696523i	$-0.245271\pi$
$541$	2.85930e12	1.43507	0.717534	+	0.696523i	$0.245271\pi$
$542$	−1.78822e12	−0.890070
$543$	−1.43009e12	−0.705934
$544$	5.10424e12	2.49883
$545$	−1.65592e12	−0.803996
$546$	1.03582e12	0.498790
$547$	−1.85565e12	−0.886244	−0.443122	−	0.896461i	$-0.646129\pi$
$547$	−1.85565e12	−0.886244	−0.443122	+	0.896461i	$0.646129\pi$
$548$	7.44286e11	0.352555
$549$	−1.01951e12	−0.478981
$550$	−6.83023e11	−0.318275
$551$	6.30162e11	0.291253
$552$	−3.99441e11	−0.183116
$553$	−1.84030e12	−0.836809
$554$	4.75344e12	2.14395
$555$	−1.17833e12	−0.527167
$556$	−1.33851e12	−0.593996
$557$	7.86874e10	0.0346383	0.0173192	−	0.999850i	$-0.494487\pi$
$557$	7.86874e10	0.0346383	0.0173192	+	0.999850i	$0.494487\pi$
$558$	1.60679e12	0.701625
$559$	1.16365e12	0.504045
$560$	1.86580e12	0.801711
$561$	−1.41209e12	−0.601907
$562$	−2.94687e11	−0.124609
$563$	−1.24500e12	−0.522253	−0.261127	−	0.965305i	$-0.584094\pi$
$563$	−1.24500e12	−0.522253	−0.261127	+	0.965305i	$0.584094\pi$
$564$	1.44286e12	0.600437
$565$	−4.56377e11	−0.188411
$566$	−1.96475e12	−0.804697
$567$	−2.53574e11	−0.103034
$568$	−1.51669e11	−0.0611405
$569$	4.98949e11	0.199550	0.0997748	−	0.995010i	$-0.468188\pi$
$569$	4.98949e11	0.199550	0.0997748	+	0.995010i	$0.468188\pi$
$570$	−1.85358e12	−0.735485
$571$	−4.33571e12	−1.70686	−0.853430	−	0.521207i	$-0.825482\pi$
$571$	−4.33571e12	−1.70686	−0.853430	+	0.521207i	$0.825482\pi$
$572$	−7.85435e11	−0.306781
$573$	1.24739e12	0.483398
$574$	2.88859e12	1.11066
$575$	−1.46217e12	−0.557817
$576$	−5.33609e11	−0.201986
$577$	−2.90292e12	−1.09029	−0.545146	−	0.838341i	$-0.683526\pi$
$577$	−2.90292e12	−1.09029	−0.545146	+	0.838341i	$0.683526\pi$
$578$	9.69368e12	3.61255
$579$	−1.65927e12	−0.613571
$580$	−3.87868e11	−0.142317
$581$	−2.98693e11	−0.108751
$582$	−2.75800e12	−0.996416
$583$	1.44451e11	0.0517861
$584$	4.14910e11	0.147603
$585$	−4.90797e11	−0.173261
$586$	−2.12291e12	−0.743690
$587$	−5.13323e11	−0.178451	−0.0892256	−	0.996011i	$-0.528439\pi$
$587$	−5.13323e11	−0.178451	−0.0892256	+	0.996011i	$0.528439\pi$
$588$	−1.91487e11	−0.0660604
$589$	−5.73307e12	−1.96276
$590$	3.88382e11	0.131955
$591$	2.81346e12	0.948632
$592$	4.17189e12	1.39600
$593$	−3.36316e12	−1.11687	−0.558434	−	0.829549i	$-0.688598\pi$
$593$	−3.36316e12	−1.11687	−0.558434	+	0.829549i	$0.688598\pi$
$594$	4.27712e11	0.140965
$595$	4.08975e12	1.33774
$596$	1.15380e11	0.0374560
$597$	−3.12707e12	−1.00752
$598$	−3.74018e12	−1.19602
$599$	−2.69284e12	−0.854654	−0.427327	−	0.904097i	$-0.640545\pi$
$599$	−2.69284e12	−0.854654	−0.427327	+	0.904097i	$0.640545\pi$
$600$	1.96758e11	0.0619801
$601$	−2.40549e12	−0.752087	−0.376044	−	0.926602i	$-0.622716\pi$
$601$	−2.40549e12	−0.752087	−0.376044	+	0.926602i	$0.622716\pi$
$602$	2.93701e12	0.911427
$603$	7.82107e11	0.240901
$604$	9.47710e11	0.289741
$605$	−1.74620e12	−0.529902
$606$	−1.83200e12	−0.551823
$607$	−5.07434e12	−1.51716	−0.758578	−	0.651582i	$-0.774106\pi$
$607$	−5.07434e12	−1.51716	−0.758578	+	0.651582i	$0.774106\pi$
$608$	5.51631e12	1.63713
$609$	4.21141e11	0.124065
$610$	−4.98051e12	−1.45643
$611$	−3.03224e12	−0.880194
$612$	−1.81242e12	−0.522250
$613$	−6.48764e12	−1.85573	−0.927865	−	0.372917i	$-0.878358\pi$
$613$	−6.48764e12	−1.85573	−0.927865	+	0.372917i	$0.878358\pi$
$614$	3.71320e12	1.05436
$615$	−1.36869e12	−0.385803
$616$	4.44933e11	0.124503
$617$	−3.61489e12	−1.00418	−0.502090	−	0.864815i	$-0.667435\pi$
$617$	−3.61489e12	−1.00418	−0.502090	+	0.864815i	$0.667435\pi$
$618$	4.07779e10	0.0112455
$619$	4.35188e12	1.19143	0.595715	−	0.803196i	$-0.296869\pi$
$619$	4.35188e12	1.19143	0.595715	+	0.803196i	$0.296869\pi$
$620$	3.52873e12	0.959083
$621$	9.15615e11	0.247059
$622$	−3.84397e12	−1.02973
$623$	−3.92024e12	−1.04260
$624$	1.73767e12	0.458815
$625$	−1.43690e12	−0.376674
$626$	−1.81841e12	−0.473269
$627$	−1.52609e12	−0.394345
$628$	2.45137e12	0.628913
$629$	9.14461e12	2.32936
$630$	−1.23876e12	−0.313295
$631$	4.90105e12	1.23071	0.615356	−	0.788249i	$-0.289012\pi$
$631$	4.90105e12	1.23071	0.615356	+	0.788249i	$0.289012\pi$
$632$	−8.94197e11	−0.222950
$633$	−3.57816e12	−0.885816
$634$	4.19509e12	1.03119
$635$	−2.10863e12	−0.514658
$636$	1.85404e11	0.0449326
$637$	4.02420e11	0.0968394
$638$	−7.10353e11	−0.169739
$639$	3.47662e11	0.0824903
$640$	1.55058e12	0.365330
$641$	3.31638e12	0.775895	0.387947	−	0.921681i	$-0.373184\pi$
$641$	3.31638e12	0.775895	0.387947	+	0.921681i	$0.373184\pi$
$642$	6.20973e12	1.44266
$643$	3.46709e12	0.799864	0.399932	−	0.916545i	$-0.369034\pi$
$643$	3.46709e12	0.799864	0.399932	+	0.916545i	$0.369034\pi$
$644$	−4.24381e12	−0.972230
$645$	−1.39163e12	−0.316595
$646$	1.43850e13	3.24984
$647$	−4.53182e11	−0.101672	−0.0508362	−	0.998707i	$-0.516189\pi$
$647$	−4.53182e11	−0.101672	−0.0508362	+	0.998707i	$0.516189\pi$
$648$	−1.23211e11	−0.0274512
$649$	3.19763e11	0.0707501
$650$	1.84236e12	0.404821
$651$	−3.83144e12	−0.836080
$652$	−1.74757e11	−0.0378721
$653$	−6.66887e12	−1.43530	−0.717651	−	0.696403i	$-0.754783\pi$
$653$	−6.66887e12	−1.43530	−0.717651	+	0.696403i	$0.754783\pi$
$654$	−3.89247e12	−0.832005
$655$	−5.87148e12	−1.24641
$656$	4.84585e12	1.02165
$657$	−9.51076e11	−0.199146
$658$	−7.65327e12	−1.59159
$659$	−1.64690e12	−0.340160	−0.170080	−	0.985430i	$-0.554403\pi$
$659$	−1.64690e12	−0.340160	−0.170080	+	0.985430i	$0.554403\pi$
$660$	9.39315e11	0.192692
$661$	3.47144e12	0.707298	0.353649	−	0.935378i	$-0.384941\pi$
$661$	3.47144e12	0.707298	0.353649	+	0.935378i	$0.384941\pi$
$662$	−1.08808e13	−2.20192
$663$	3.80891e12	0.765578
$664$	−1.45134e11	−0.0289743
$665$	4.41992e12	0.876429
$666$	−2.76984e12	−0.545532
$667$	−1.52067e12	−0.297488
$668$	3.95100e12	0.767738
$669$	5.62326e11	0.108535
$670$	3.82073e12	0.732504
$671$	−4.10056e12	−0.780894
$672$	3.68658e12	0.697368
$673$	−9.62726e12	−1.80898	−0.904492	−	0.426490i	$-0.859750\pi$
$673$	−9.62726e12	−1.80898	−0.904492	+	0.426490i	$0.859750\pi$
$674$	−1.01711e12	−0.189846
$675$	−4.51018e11	−0.0836232
$676$	−2.31568e12	−0.426499
$677$	5.03997e12	0.922101	0.461051	−	0.887374i	$-0.347473\pi$
$677$	5.03997e12	0.922101	0.461051	+	0.887374i	$0.347473\pi$
$678$	−1.07278e12	−0.194974
$679$	6.57654e12	1.18736
$680$	1.98720e12	0.356411
$681$	−7.19531e11	−0.128200
$682$	6.46262e12	1.14388
$683$	−2.29099e11	−0.0402837	−0.0201419	−	0.999797i	$-0.506412\pi$
$683$	−2.29099e11	−0.0402837	−0.0201419	+	0.999797i	$0.506412\pi$
$684$	−1.95874e12	−0.342157
$685$	1.87060e12	0.324619
$686$	8.26546e12	1.42498
$687$	2.48980e12	0.426442
$688$	4.92708e12	0.838381
$689$	−3.89636e11	−0.0658678
$690$	4.47295e12	0.751230
$691$	3.62693e12	0.605184	0.302592	−	0.953120i	$-0.402148\pi$
$691$	3.62693e12	0.605184	0.302592	+	0.953120i	$0.402148\pi$
$692$	8.16553e12	1.35365
$693$	−1.01989e12	−0.167979
$694$	−1.22371e13	−2.00245
$695$	−3.36405e12	−0.546928
$696$	2.04631e11	0.0330545
$697$	1.06219e13	1.70473
$698$	1.28895e13	2.05535
$699$	1.68676e12	0.267243
$700$	2.09043e12	0.329075
$701$	−5.66301e12	−0.885760	−0.442880	−	0.896581i	$-0.646043\pi$
$701$	−5.66301e12	−0.885760	−0.442880	+	0.896581i	$0.646043\pi$
$702$	−1.15369e12	−0.179297
$703$	9.88285e12	1.52610
$704$	−2.14622e12	−0.329304
$705$	3.62631e12	0.552858
$706$	−1.64013e13	−2.48460
$707$	4.36847e12	0.657571
$708$	4.10417e11	0.0613869
$709$	−5.22597e12	−0.776710	−0.388355	−	0.921510i	$-0.626957\pi$
$709$	−5.22597e12	−0.776710	−0.388355	+	0.921510i	$0.626957\pi$
$710$	1.69839e12	0.250827
$711$	2.04972e12	0.300802
$712$	−1.90483e12	−0.277777
$713$	1.38347e13	2.00478
$714$	9.61356e12	1.38434
$715$	−1.97402e12	−0.282472
$716$	6.65802e12	0.946753
$717$	6.90241e12	0.975359
$718$	−6.38925e12	−0.897202
$719$	1.17100e13	1.63409	0.817047	−	0.576571i	$-0.195610\pi$
$719$	1.17100e13	1.63409	0.817047	+	0.576571i	$0.195610\pi$
$720$	−2.07811e12	−0.288186
$721$	−9.72364e10	−0.0134005
$722$	5.70482e12	0.781312
$723$	−6.51835e11	−0.0887187
$724$	−7.38262e12	−0.998590
$725$	7.49059e11	0.100692
$726$	−4.10471e12	−0.548362
$727$	−1.35866e13	−1.80388	−0.901938	−	0.431866i	$-0.857855\pi$
$727$	−1.35866e13	−1.80388	−0.901938	+	0.431866i	$0.857855\pi$
$728$	−1.20014e12	−0.158358
$729$	2.82430e11	0.0370370
$730$	−4.64618e12	−0.605540
$731$	1.08000e13	1.39892
$732$	−5.26309e12	−0.677550
$733$	−1.02246e13	−1.30822	−0.654110	−	0.756400i	$-0.726956\pi$
$733$	−1.02246e13	−1.30822	−0.654110	+	0.756400i	$0.726956\pi$
$734$	−4.18439e12	−0.532108
$735$	−4.81261e11	−0.0608258
$736$	−1.33117e13	−1.67218
$737$	3.14569e12	0.392747
$738$	−3.21730e12	−0.399243
$739$	−1.29123e13	−1.59259	−0.796293	−	0.604912i	$-0.793208\pi$
$739$	−1.29123e13	−1.59259	−0.796293	+	0.604912i	$0.793208\pi$
$740$	−6.08295e12	−0.745712
$741$	4.11640e12	0.501575
$742$	−9.83429e11	−0.119104
$743$	−5.53690e11	−0.0666526	−0.0333263	−	0.999445i	$-0.510610\pi$
$743$	−5.53690e11	−0.0666526	−0.0333263	+	0.999445i	$0.510610\pi$
$744$	−1.86169e12	−0.222755
$745$	2.89982e11	0.0344880
$746$	1.06961e13	1.26444
$747$	3.32682e11	0.0390919
$748$	−7.28970e12	−0.851437
$749$	−1.48073e13	−1.71913
$750$	−7.27398e12	−0.839453
$751$	1.51274e13	1.73534	0.867668	−	0.497145i	$-0.165618\pi$
$751$	1.51274e13	1.73534	0.867668	+	0.497145i	$0.165618\pi$
$752$	−1.28390e13	−1.46403
$753$	5.66421e12	0.642040
$754$	1.91607e12	0.215894
$755$	2.38187e12	0.266782
$756$	−1.30904e12	−0.145749
$757$	−2.24958e12	−0.248983	−0.124492	−	0.992221i	$-0.539730\pi$
$757$	−2.24958e12	−0.248983	−0.124492	+	0.992221i	$0.539730\pi$
$758$	−1.09073e13	−1.20007
$759$	3.68267e12	0.402787
$760$	2.14762e12	0.233505
$761$	7.95249e12	0.859552	0.429776	−	0.902936i	$-0.358593\pi$
$761$	7.95249e12	0.859552	0.429776	+	0.902936i	$0.358593\pi$
$762$	−4.95665e12	−0.532587
$763$	9.28173e12	0.991445
$764$	6.43945e12	0.683799
$765$	−4.55514e12	−0.480867
$766$	5.60777e11	0.0588519
$767$	−8.62514e11	−0.0899885
$768$	7.01782e12	0.727908
$769$	−6.25524e12	−0.645023	−0.322512	−	0.946565i	$-0.604527\pi$
$769$	−6.25524e12	−0.645023	−0.322512	+	0.946565i	$0.604527\pi$
$770$	−4.98237e12	−0.510772
$771$	4.74918e12	0.484032
$772$	−8.56576e12	−0.867936
$773$	−1.29802e13	−1.30760	−0.653799	−	0.756668i	$-0.726826\pi$
$773$	−1.29802e13	−1.30760	−0.653799	+	0.756668i	$0.726826\pi$
$774$	−3.27123e12	−0.327625
$775$	−6.81477e12	−0.678568
$776$	3.19552e12	0.316347
$777$	6.60477e12	0.650074
$778$	−1.63612e13	−1.60106
$779$	1.14794e13	1.11687
$780$	−2.53367e12	−0.245089
$781$	1.39832e12	0.134486
$782$	−3.47130e13	−3.31942
$783$	−4.69064e11	−0.0445969
$784$	1.70391e12	0.161074
$785$	6.16100e12	0.579079
$786$	−1.38018e13	−1.28983
$787$	−3.91811e12	−0.364074	−0.182037	−	0.983292i	$-0.558269\pi$
$787$	−3.91811e12	−0.364074	−0.182037	+	0.983292i	$0.558269\pi$
$788$	1.45241e13	1.34190
$789$	−6.85339e12	−0.629592
$790$	1.00132e13	0.914646
$791$	2.55808e12	0.232338
$792$	−4.95563e11	−0.0447544
$793$	1.10607e13	0.993236
$794$	5.73538e12	0.512118
$795$	4.65973e11	0.0413722
$796$	−1.61430e13	−1.42520
$797$	−1.59762e13	−1.40253	−0.701265	−	0.712901i	$-0.747381\pi$
$797$	−1.59762e13	−1.40253	−0.701265	+	0.712901i	$0.747381\pi$
$798$	1.03897e13	0.906961
$799$	−2.81425e13	−2.44288
$800$	6.55711e12	0.565989
$801$	4.36634e12	0.374775
$802$	6.34975e12	0.541966
$803$	−3.82530e12	−0.324672
$804$	4.03751e12	0.340770
$805$	−1.06659e13	−0.895191
$806$	−1.74320e13	−1.45492
$807$	1.21361e13	1.00728
$808$	2.12263e12	0.175195
$809$	−2.07097e13	−1.69983	−0.849916	−	0.526918i	$-0.823348\pi$
$809$	−2.07097e13	−1.69983	−0.849916	+	0.526918i	$0.823348\pi$
$810$	1.37972e12	0.112618
$811$	1.63462e13	1.32685	0.663426	−	0.748242i	$-0.269102\pi$
$811$	1.63462e13	1.32685	0.663426	+	0.748242i	$0.269102\pi$
$812$	2.17408e12	0.175498
$813$	−4.74930e12	−0.381260
$814$	−1.11405e13	−0.889394
$815$	−4.39213e11	−0.0348712
$816$	1.61275e13	1.27339
$817$	1.16718e13	0.916516
$818$	−2.98165e12	−0.232845
$819$	2.75102e12	0.213656
$820$	−7.06564e12	−0.545744
$821$	−7.95905e12	−0.611388	−0.305694	−	0.952130i	$-0.598888\pi$
$821$	−7.95905e12	−0.611388	−0.305694	+	0.952130i	$0.598888\pi$
$822$	4.39713e12	0.335928
$823$	−7.99086e12	−0.607148	−0.303574	−	0.952808i	$-0.598180\pi$
$823$	−7.99086e12	−0.607148	−0.303574	+	0.952808i	$0.598180\pi$
$824$	−4.72469e10	−0.00357027
$825$	−1.81403e12	−0.136333
$826$	−2.17696e12	−0.162719
$827$	−1.49770e13	−1.11339	−0.556697	−	0.830715i	$-0.687932\pi$
$827$	−1.49770e13	−1.11339	−0.556697	+	0.830715i	$0.687932\pi$
$828$	4.72673e12	0.349481
$829$	1.45469e13	1.06973	0.534865	−	0.844937i	$-0.320362\pi$
$829$	1.45469e13	1.06973	0.534865	+	0.844937i	$0.320362\pi$
$830$	1.62521e12	0.118866
$831$	1.26246e13	0.918357
$832$	5.78911e12	0.418848
$833$	3.73490e12	0.268767
$834$	−7.90769e12	−0.565981
$835$	9.92999e12	0.706903
$836$	−7.87820e12	−0.557826
$837$	4.26744e12	0.300540
$838$	−1.85059e13	−1.29632
$839$	−1.37194e13	−0.955886	−0.477943	−	0.878391i	$-0.658617\pi$
$839$	−1.37194e13	−0.955886	−0.477943	+	0.878391i	$0.658617\pi$
$840$	1.43527e12	0.0994665
$841$	−1.37281e13	−0.946300
$842$	3.03799e13	2.08296
$843$	−7.82654e11	−0.0533760
$844$	−1.84717e13	−1.25305
$845$	−5.81995e12	−0.392703
$846$	8.52417e12	0.572118
$847$	9.78782e12	0.653447
$848$	−1.64978e12	−0.109558
$849$	−5.21813e12	−0.344691
$850$	1.70991e13	1.12354
$851$	−2.38487e13	−1.55877
$852$	1.79475e12	0.116688
$853$	1.65135e13	1.06799	0.533997	−	0.845486i	$-0.320689\pi$
$853$	1.65135e13	1.06799	0.533997	+	0.845486i	$0.320689\pi$
$854$	2.79168e13	1.79599
$855$	−4.92288e12	−0.315044
$856$	−7.19483e12	−0.458024
$857$	−1.96681e12	−0.124551	−0.0622756	−	0.998059i	$-0.519836\pi$
$857$	−1.96681e12	−0.124551	−0.0622756	+	0.998059i	$0.519836\pi$
$858$	−4.64023e12	−0.292312
$859$	2.16110e13	1.35427	0.677136	−	0.735858i	$-0.263221\pi$
$859$	2.16110e13	1.35427	0.677136	+	0.735858i	$0.263221\pi$
$860$	−7.18408e12	−0.447845
$861$	7.67176e12	0.475752
$862$	3.00403e13	1.85320
$863$	−7.52982e12	−0.462100	−0.231050	−	0.972942i	$-0.574216\pi$
$863$	−7.52982e12	−0.462100	−0.231050	+	0.972942i	$0.574216\pi$
$864$	−4.10609e12	−0.250679
$865$	2.05223e13	1.24639
$866$	−1.67865e13	−1.01421
$867$	2.57452e13	1.54743
$868$	−1.97792e13	−1.18269
$869$	8.24411e12	0.490405
$870$	−2.29146e12	−0.135605
$871$	−8.48505e12	−0.499543
$872$	4.50997e12	0.264149
$873$	−7.32491e12	−0.426814
$874$	−3.75154e13	−2.17474
$875$	1.73450e13	1.00032
$876$	−4.90979e12	−0.281705
$877$	1.51055e13	0.862259	0.431129	−	0.902290i	$-0.358115\pi$
$877$	1.51055e13	0.862259	0.431129	+	0.902290i	$0.358115\pi$
$878$	−1.40001e12	−0.0795073
$879$	−5.63819e12	−0.318559
$880$	−8.35832e12	−0.469837
$881$	−2.32110e13	−1.29808	−0.649042	−	0.760752i	$-0.724830\pi$
$881$	−2.32110e13	−1.29808	−0.649042	+	0.760752i	$0.724830\pi$
$882$	−1.13127e12	−0.0629447
$883$	1.44144e13	0.797947	0.398974	−	0.916962i	$-0.369367\pi$
$883$	1.44144e13	0.797947	0.398974	+	0.916962i	$0.369367\pi$
$884$	1.96629e13	1.08296
$885$	1.03150e12	0.0565226
$886$	−1.95498e13	−1.06583
$887$	8.64043e12	0.468683	0.234341	−	0.972154i	$-0.424707\pi$
$887$	8.64043e12	0.468683	0.234341	+	0.972154i	$0.424707\pi$
$888$	3.20924e12	0.173198
$889$	1.18193e13	0.634649
$890$	2.13303e13	1.13957
$891$	1.13595e12	0.0603824
$892$	2.90292e12	0.153530
$893$	−3.04145e13	−1.60048
$894$	6.81645e11	0.0356894
$895$	1.67335e13	0.871733
$896$	−8.69133e12	−0.450506
$897$	−9.93347e12	−0.512313
$898$	−3.18217e12	−0.163298
$899$	−7.08744e12	−0.361885
$900$	−2.32831e12	−0.118291
$901$	−3.61625e12	−0.182809
$902$	−1.29402e13	−0.650896
$903$	7.80036e12	0.390409
$904$	1.24297e12	0.0619015
$905$	−1.85546e13	−0.919462
$906$	5.59893e12	0.276075
$907$	−2.82043e12	−0.138383	−0.0691915	−	0.997603i	$-0.522042\pi$
$907$	−2.82043e12	−0.138383	−0.0691915	+	0.997603i	$0.522042\pi$
$908$	−3.71447e12	−0.181347
$909$	−4.86558e12	−0.236373
$910$	1.34392e13	0.649662
$911$	1.47354e13	0.708807	0.354404	−	0.935093i	$-0.384684\pi$
$911$	1.47354e13	0.708807	0.354404	+	0.935093i	$0.384684\pi$
$912$	1.74295e13	0.834273
$913$	1.33807e12	0.0637325
$914$	−2.83609e13	−1.34420
$915$	−1.32276e13	−0.623861
$916$	1.28532e13	0.603230
$917$	3.29108e13	1.53701
$918$	−1.07075e13	−0.497619
$919$	−9.13825e12	−0.422613	−0.211307	−	0.977420i	$-0.567772\pi$
$919$	−9.13825e12	−0.422613	−0.211307	+	0.977420i	$0.567772\pi$
$920$	−5.18253e12	−0.238504
$921$	9.86180e12	0.451635
$922$	−4.80855e13	−2.19142
$923$	−3.77177e12	−0.171056
$924$	−5.26505e12	−0.237618
$925$	1.17475e13	0.527604
$926$	−4.57094e13	−2.04294
$927$	1.08301e11	0.00481698
$928$	6.81948e12	0.301846
$929$	2.70772e13	1.19271	0.596354	−	0.802722i	$-0.296616\pi$
$929$	2.70772e13	1.19271	0.596354	+	0.802722i	$0.296616\pi$
$930$	2.08472e13	0.913849
$931$	4.03642e12	0.176085
$932$	8.70767e12	0.378033
$933$	−1.02091e13	−0.441083
$934$	−3.23538e13	−1.39112
$935$	−1.83211e13	−0.783970
$936$	1.33671e12	0.0569241
$937$	−4.22187e9	−0.000178927 0	−8.94637e−5	−	1.00000i	$-0.500028\pi$
$937$	−4.22187e9	−0.000178927 0	−8.94637e−5		1.00000i	$0.500028\pi$
$938$	−2.14160e13	−0.903285
$939$	−4.82949e12	−0.202724
$940$	1.87203e13	0.782054
$941$	−1.65925e13	−0.689857	−0.344929	−	0.938629i	$-0.612097\pi$
$941$	−1.65925e13	−0.689857	−0.344929	+	0.938629i	$0.612097\pi$
$942$	1.44823e13	0.599252
$943$	−2.77015e13	−1.14078
$944$	−3.65202e12	−0.149678
$945$	−3.28999e12	−0.134200
$946$	−1.31571e13	−0.534135
$947$	1.81520e13	0.733415	0.366708	−	0.930336i	$-0.380485\pi$
$947$	1.81520e13	0.733415	0.366708	+	0.930336i	$0.380485\pi$
$948$	1.05814e13	0.425504
$949$	1.03182e13	0.412957
$950$	1.84795e13	0.736095
$951$	1.11417e13	0.441710
$952$	−1.11386e13	−0.439507
$953$	4.04715e13	1.58939	0.794696	−	0.607008i	$-0.207630\pi$
$953$	4.04715e13	1.58939	0.794696	+	0.607008i	$0.207630\pi$
$954$	1.09534e12	0.0428135
$955$	1.61842e13	0.629615
$956$	3.56326e13	1.37971
$957$	−1.88661e12	−0.0727074
$958$	4.94793e13	1.89793
$959$	−1.04851e13	−0.400303
$960$	−6.92329e12	−0.263083
$961$	3.80403e13	1.43876
$962$	3.00498e13	1.13124
$963$	1.64923e13	0.617963
$964$	−3.36500e12	−0.125498
$965$	−2.15282e13	−0.799161
$966$	−2.50718e13	−0.926377
$967$	−8.58992e12	−0.315915	−0.157957	−	0.987446i	$-0.550491\pi$
$967$	−8.58992e12	−0.315915	−0.157957	+	0.987446i	$0.550491\pi$
$968$	4.75587e12	0.174097
$969$	3.82047e13	1.39207
$970$	−3.57835e13	−1.29781
$971$	1.58363e13	0.571697	0.285849	−	0.958275i	$-0.407725\pi$
$971$	1.58363e13	0.571697	0.285849	+	0.958275i	$0.407725\pi$
$972$	1.45800e12	0.0523913
$973$	1.88561e13	0.674443
$974$	3.00643e13	1.07038
$975$	4.89307e12	0.173405
$976$	4.68326e13	1.65205
$977$	−2.81128e13	−0.987141	−0.493571	−	0.869706i	$-0.664309\pi$
$977$	−2.81128e13	−0.987141	−0.493571	+	0.869706i	$0.664309\pi$
$978$	−1.03244e12	−0.0360860
$979$	1.75617e13	0.611005
$980$	−2.48444e12	−0.0860420
$981$	−1.03379e13	−0.356388
$982$	6.02004e13	2.06585
$983$	−7.66030e11	−0.0261671	−0.0130835	−	0.999914i	$-0.504165\pi$
$983$	−7.66030e11	−0.0261671	−0.0130835	+	0.999914i	$0.504165\pi$
$984$	3.72768e12	0.126754
$985$	3.65032e13	1.23557
$986$	1.77833e13	0.599191
$987$	−2.03262e13	−0.681755
$988$	2.12503e13	0.709511
$989$	−2.81658e13	−0.936136
$990$	5.54933e12	0.183604
$991$	−3.40219e13	−1.12054	−0.560270	−	0.828310i	$-0.689303\pi$
$991$	−3.40219e13	−1.12054	−0.560270	+	0.828310i	$0.689303\pi$
$992$	−6.20420e13	−2.03415
$993$	−2.88982e13	−0.943191
$994$	−9.51982e12	−0.309307
$995$	−4.05720e13	−1.31227
$996$	1.71742e12	0.0552981
$997$	−2.09508e13	−0.671540	−0.335770	−	0.941944i	$-0.608996\pi$
$997$	−2.09508e13	−0.671540	−0.335770	+	0.941944i	$0.608996\pi$
$998$	−2.77495e13	−0.885457
$999$	−7.35635e12	−0.233678

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.18	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.18	✓	21	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)

\(f(q)\)	\(=\)	\(q+30.4984 q^{2} +81.0000 q^{3} +418.150 q^{4} +1050.93 q^{5} +2470.37 q^{6} -5890.68 q^{7} -2862.26 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+30.4984 q^{2} +81.0000 q^{3} +418.150 q^{4} +1050.93 q^{5} +2470.37 q^{6} -5890.68 q^{7} -2862.26 q^{8} +6561.00 q^{9} +32051.7 q^{10} +26388.8 q^{11} +33870.2 q^{12} -71180.0 q^{13} -179656. q^{14} +85125.4 q^{15} -301387. q^{16} -660629. q^{17} +200100. q^{18} -713962. q^{19} +439447. q^{20} -477145. q^{21} +804816. q^{22} +1.72289e6 q^{23} -231843. q^{24} -848670. q^{25} -2.17087e6 q^{26} +531441. q^{27} -2.46319e6 q^{28} -882627. q^{29} +2.59619e6 q^{30} +8.02994e6 q^{31} -7.72634e6 q^{32} +2.13749e6 q^{33} -2.01481e7 q^{34} -6.19069e6 q^{35} +2.74348e6 q^{36} -1.38423e7 q^{37} -2.17747e7 q^{38} -5.76558e6 q^{39} -3.00804e6 q^{40} -1.60785e7 q^{41} -1.45521e7 q^{42} -1.63480e7 q^{43} +1.10345e7 q^{44} +6.89516e6 q^{45} +5.25454e7 q^{46} +4.25996e7 q^{47} -2.44124e7 q^{48} -5.65355e6 q^{49} -2.58830e7 q^{50} -5.35109e7 q^{51} -2.97639e7 q^{52} +5.47396e6 q^{53} +1.62081e7 q^{54} +2.77328e7 q^{55} +1.68607e7 q^{56} -5.78309e7 q^{57} -2.69187e7 q^{58} +1.21174e7 q^{59} +3.55952e7 q^{60} -1.55390e8 q^{61} +2.44900e8 q^{62} -3.86487e7 q^{63} -8.13305e7 q^{64} -7.48053e7 q^{65} +6.51901e7 q^{66} +1.19205e8 q^{67} -2.76242e8 q^{68} +1.39554e8 q^{69} -1.88806e8 q^{70} +5.29891e7 q^{71} -1.87793e7 q^{72} -1.44959e8 q^{73} -4.22167e8 q^{74} -6.87422e7 q^{75} -2.98543e8 q^{76} -1.55448e8 q^{77} -1.75841e8 q^{78} +3.12409e8 q^{79} -3.16737e8 q^{80} +4.30467e7 q^{81} -4.90367e8 q^{82} +5.07060e7 q^{83} -1.99518e8 q^{84} -6.94275e8 q^{85} -4.98587e8 q^{86} -7.14928e7 q^{87} -7.55317e7 q^{88} +6.65499e8 q^{89} +2.10291e8 q^{90} +4.19298e8 q^{91} +7.20428e8 q^{92} +6.50425e8 q^{93} +1.29922e9 q^{94} -7.50324e8 q^{95} -6.25834e8 q^{96} -1.11643e9 q^{97} -1.72424e8 q^{98} +1.73137e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9} - 54663 q^{10} - 151769 q^{11} + 421686 q^{12} - 153611 q^{13} - 286771 q^{14} - 240084 q^{15} + 805530 q^{16} - 723621 q^{17} - 433026 q^{18} - 549388 q^{19} - 527311 q^{20} - 2492775 q^{21} + 2973158 q^{22} + 169962 q^{23} - 1994301 q^{24} + 8035779 q^{25} - 2337392 q^{26} + 11160261 q^{27} - 22659054 q^{28} - 16845442 q^{29} - 4427703 q^{30} - 19307976 q^{31} - 44923568 q^{32} - 12293289 q^{33} - 35547496 q^{34} - 34882596 q^{35} + 34156566 q^{36} - 41561129 q^{37} - 52335371 q^{38} - 12442491 q^{39} - 125735038 q^{40} - 68169291 q^{41} - 23228451 q^{42} - 25719587 q^{43} - 126277032 q^{44} - 19446804 q^{45} - 292814271 q^{46} - 174095332 q^{47} + 65247930 q^{48} + 7479350 q^{49} - 227877439 q^{50} - 58613301 q^{51} - 232397708 q^{52} - 228390500 q^{53} - 35075106 q^{54} - 29426208 q^{55} + 326778474 q^{56} - 44500428 q^{57} + 480343762 q^{58} + 254464581 q^{59} - 42712191 q^{60} - 183928964 q^{61} - 21753862 q^{62} - 201914775 q^{63} + 310571245 q^{64} + 5308466 q^{65} + 240825798 q^{66} - 82724114 q^{67} - 138336205 q^{68} + 13766922 q^{69} + 1030274876 q^{70} - 404721965 q^{71} - 161538381 q^{72} + 154162574 q^{73} + 36352054 q^{74} + 650898099 q^{75} + 1068940636 q^{76} - 448535481 q^{77} - 189328752 q^{78} + 272529635 q^{79} - 345587859 q^{80} + 903981141 q^{81} - 38412637 q^{82} + 432518643 q^{83} - 1835383374 q^{84} - 126211490 q^{85} - 3699273072 q^{86} - 1364480802 q^{87} + 170111045 q^{88} - 1255621070 q^{89} - 358643943 q^{90} + 1448885849 q^{91} + 1568933320 q^{92} - 1563946056 q^{93} - 1908445164 q^{94} - 2896546490 q^{95} - 3638809008 q^{96} + 1007235486 q^{97} - 9506868248 q^{98} - 995756409 q^{99}+O(q^{100}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9 - 54663 * q^10 - 151769 * q^11 + 421686 * q^12 - 153611 * q^13 - 286771 * q^14 - 240084 * q^15 + 805530 * q^16 - 723621 * q^17 - 433026 * q^18 - 549388 * q^19 - 527311 * q^20 - 2492775 * q^21 + 2973158 * q^22 + 169962 * q^23 - 1994301 * q^24 + 8035779 * q^25 - 2337392 * q^26 + 11160261 * q^27 - 22659054 * q^28 - 16845442 * q^29 - 4427703 * q^30 - 19307976 * q^31 - 44923568 * q^32 - 12293289 * q^33 - 35547496 * q^34 - 34882596 * q^35 + 34156566 * q^36 - 41561129 * q^37 - 52335371 * q^38 - 12442491 * q^39 - 125735038 * q^40 - 68169291 * q^41 - 23228451 * q^42 - 25719587 * q^43 - 126277032 * q^44 - 19446804 * q^45 - 292814271 * q^46 - 174095332 * q^47 + 65247930 * q^48 + 7479350 * q^49 - 227877439 * q^50 - 58613301 * q^51 - 232397708 * q^52 - 228390500 * q^53 - 35075106 * q^54 - 29426208 * q^55 + 326778474 * q^56 - 44500428 * q^57 + 480343762 * q^58 + 254464581 * q^59 - 42712191 * q^60 - 183928964 * q^61 - 21753862 * q^62 - 201914775 * q^63 + 310571245 * q^64 + 5308466 * q^65 + 240825798 * q^66 - 82724114 * q^67 - 138336205 * q^68 + 13766922 * q^69 + 1030274876 * q^70 - 404721965 * q^71 - 161538381 * q^72 + 154162574 * q^73 + 36352054 * q^74 + 650898099 * q^75 + 1068940636 * q^76 - 448535481 * q^77 - 189328752 * q^78 + 272529635 * q^79 - 345587859 * q^80 + 903981141 * q^81 - 38412637 * q^82 + 432518643 * q^83 - 1835383374 * q^84 - 126211490 * q^85 - 3699273072 * q^86 - 1364480802 * q^87 + 170111045 * q^88 - 1255621070 * q^89 - 358643943 * q^90 + 1448885849 * q^91 + 1568933320 * q^92 - 1563946056 * q^93 - 1908445164 * q^94 - 2896546490 * q^95 - 3638809008 * q^96 + 1007235486 * q^97 - 9506868248 * q^98 - 995756409 * q^99

Introduction

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