LMFDB - Embedded newform 177.10.a.a.1.4

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			1.4
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)

$f(q)$	$=$	$q-31.8892 q^{2} +81.0000 q^{3} +504.921 q^{4} -1889.12 q^{5} -2583.03 q^{6} +12272.3 q^{7} +225.735 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-31.8892 q^{2} +81.0000 q^{3} +504.921 q^{4} -1889.12 q^{5} -2583.03 q^{6} +12272.3 q^{7} +225.735 q^{8} +6561.00 q^{9} +60242.4 q^{10} -17051.0 q^{11} +40898.6 q^{12} +2771.93 q^{13} -391354. q^{14} -153018. q^{15} -265718. q^{16} -307419. q^{17} -209225. q^{18} +334845. q^{19} -953854. q^{20} +994057. q^{21} +543743. q^{22} -829855. q^{23} +18284.6 q^{24} +1.61563e6 q^{25} -88394.6 q^{26} +531441. q^{27} +6.19655e6 q^{28} -1.06708e6 q^{29} +4.87963e6 q^{30} -806611. q^{31} +8.35797e6 q^{32} -1.38113e6 q^{33} +9.80336e6 q^{34} -2.31838e7 q^{35} +3.31279e6 q^{36} -298636. q^{37} -1.06780e7 q^{38} +224526. q^{39} -426440. q^{40} +957358. q^{41} -3.16997e7 q^{42} -1.34324e7 q^{43} -8.60942e6 q^{44} -1.23945e7 q^{45} +2.64634e7 q^{46} +2.47451e6 q^{47} -2.15232e7 q^{48} +1.10256e8 q^{49} -5.15212e7 q^{50} -2.49010e7 q^{51} +1.39961e6 q^{52} -1.59804e7 q^{53} -1.69472e7 q^{54} +3.22113e7 q^{55} +2.77029e6 q^{56} +2.71225e7 q^{57} +3.40285e7 q^{58} +1.21174e7 q^{59} -7.72622e7 q^{60} +4.27262e7 q^{61} +2.57222e7 q^{62} +8.05186e7 q^{63} -1.30481e8 q^{64} -5.23649e6 q^{65} +4.40432e7 q^{66} -1.05151e8 q^{67} -1.55223e8 q^{68} -6.72183e7 q^{69} +7.39313e8 q^{70} -2.00930e6 q^{71} +1.48105e6 q^{72} +4.31697e8 q^{73} +9.52327e6 q^{74} +1.30866e8 q^{75} +1.69071e8 q^{76} -2.09255e8 q^{77} -7.15996e6 q^{78} -3.46731e8 q^{79} +5.01972e8 q^{80} +4.30467e7 q^{81} -3.05294e7 q^{82} +2.37127e8 q^{83} +5.01920e8 q^{84} +5.80750e8 q^{85} +4.28349e8 q^{86} -8.64338e7 q^{87} -3.84902e6 q^{88} +5.27887e8 q^{89} +3.95250e8 q^{90} +3.40180e7 q^{91} -4.19012e8 q^{92} -6.53355e7 q^{93} -7.89103e7 q^{94} -6.32561e8 q^{95} +6.76995e8 q^{96} +9.13439e8 q^{97} -3.51597e9 q^{98} -1.11872e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−31.8892	−1.40932	−0.704658	−	0.709547i	$-0.748900\pi$
$2$	−31.8892	−1.40932	−0.704658	+	0.709547i	$0.748900\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	504.921	0.986174
$5$	−1889.12	−1.35174	−0.675870	−	0.737021i	$-0.736232\pi$
$5$	−1889.12	−1.35174	−0.675870	+	0.737021i	$0.736232\pi$
$6$	−2583.03	−0.813670
$7$	12272.3	1.93190	0.965951	−	0.258726i	$-0.0833027\pi$
$7$	12272.3	1.93190	0.965951	+	0.258726i	$0.0833027\pi$
$8$	225.735	0.0194847
$9$	6561.00	0.333333
$10$	60242.4	1.90503
$11$	−17051.0	−0.351142	−0.175571	−	0.984467i	$-0.556177\pi$
$11$	−17051.0	−0.351142	−0.175571	+	0.984467i	$0.556177\pi$
$12$	40898.6	0.569368
$13$	2771.93	0.0269176	0.0134588	−	0.999909i	$-0.495716\pi$
$13$	2771.93	0.0269176	0.0134588	+	0.999909i	$0.495716\pi$
$14$	−391354.	−2.72266
$15$	−153018.	−0.780428
$16$	−265718.	−1.01363
$17$	−307419.	−0.892711	−0.446356	−	0.894856i	$-0.647278\pi$
$17$	−307419.	−0.892711	−0.446356	+	0.894856i	$0.647278\pi$
$18$	−209225.	−0.469772
$19$	334845.	0.589458	0.294729	−	0.955581i	$-0.404771\pi$
$19$	334845.	0.589458	0.294729	+	0.955581i	$0.404771\pi$
$20$	−953854.	−1.33305
$21$	994057.	1.11538
$22$	543743.	0.494871
$23$	−829855.	−0.618340	−0.309170	−	0.951007i	$-0.600051\pi$
$23$	−829855.	−0.618340	−0.309170	+	0.951007i	$0.600051\pi$
$24$	18284.6	0.0112495
$25$	1.61563e6	0.827203
$26$	−88394.6	−0.0379355
$27$	531441.	0.192450
$28$	6.19655e6	1.90519
$29$	−1.06708e6	−0.280161	−0.140081	−	0.990140i	$-0.544736\pi$
$29$	−1.06708e6	−0.280161	−0.140081	+	0.990140i	$0.544736\pi$
$30$	4.87963e6	1.09987
$31$	−806611.	−0.156869	−0.0784344	−	0.996919i	$-0.524992\pi$
$31$	−806611.	−0.156869	−0.0784344	+	0.996919i	$0.524992\pi$
$32$	8.35797e6	1.40905
$33$	−1.38113e6	−0.202732
$34$	9.80336e6	1.25811
$35$	−2.31838e7	−2.61143
$36$	3.31279e6	0.328725
$37$	−298636.	−0.0261960	−0.0130980	−	0.999914i	$-0.504169\pi$
$37$	−298636.	−0.0261960	−0.0130980	+	0.999914i	$0.504169\pi$
$38$	−1.06780e7	−0.830733
$39$	224526.	0.0155409
$40$	−426440.	−0.0263383
$41$	957358.	0.0529111	0.0264556	−	0.999650i	$-0.491578\pi$
$41$	957358.	0.0529111	0.0264556	+	0.999650i	$0.491578\pi$
$42$	−3.16997e7	−1.57193
$43$	−1.34324e7	−0.599164	−0.299582	−	0.954071i	$-0.596847\pi$
$43$	−1.34324e7	−0.599164	−0.299582	+	0.954071i	$0.596847\pi$
$44$	−8.60942e6	−0.346288
$45$	−1.23945e7	−0.450580
$46$	2.64634e7	0.871437
$47$	2.47451e6	0.0739690	0.0369845	−	0.999316i	$-0.488225\pi$
$47$	2.47451e6	0.0739690	0.0369845	+	0.999316i	$0.488225\pi$
$48$	−2.15232e7	−0.585222
$49$	1.10256e8	2.73224
$50$	−5.15212e7	−1.16579
$51$	−2.49010e7	−0.515407
$52$	1.39961e6	0.0265455
$53$	−1.59804e7	−0.278193	−0.139097	−	0.990279i	$-0.544420\pi$
$53$	−1.59804e7	−0.278193	−0.139097	+	0.990279i	$0.544420\pi$
$54$	−1.69472e7	−0.271223
$55$	3.22113e7	0.474653
$56$	2.77029e6	0.0376426
$57$	2.71225e7	0.340324
$58$	3.40285e7	0.394836
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−7.72622e7	−0.769638
$61$	4.27262e7	0.395102	0.197551	−	0.980293i	$-0.436701\pi$
$61$	4.27262e7	0.395102	0.197551	+	0.980293i	$0.436701\pi$
$62$	2.57222e7	0.221078
$63$	8.05186e7	0.643967
$64$	−1.30481e8	−0.972160
$65$	−5.23649e6	−0.0363857
$66$	4.40432e7	0.285714
$67$	−1.05151e8	−0.637498	−0.318749	−	0.947839i	$-0.603263\pi$
$67$	−1.05151e8	−0.637498	−0.318749	+	0.947839i	$0.603263\pi$
$68$	−1.55223e8	−0.880369
$69$	−6.72183e7	−0.356999
$70$	7.39313e8	3.68033
$71$	−2.00930e6	−0.00938386	−0.00469193	−	0.999989i	$-0.501493\pi$
$71$	−2.00930e6	−0.00938386	−0.00469193	+	0.999989i	$0.501493\pi$
$72$	1.48105e6	0.00649491
$73$	4.31697e8	1.77921	0.889603	−	0.456734i	$-0.150981\pi$
$73$	4.31697e8	1.77921	0.889603	+	0.456734i	$0.150981\pi$
$74$	9.52327e6	0.0369185
$75$	1.30866e8	0.477586
$76$	1.69071e8	0.581309
$77$	−2.09255e8	−0.678372
$78$	−7.15996e6	−0.0219021
$79$	−3.46731e8	−1.00154	−0.500772	−	0.865579i	$-0.666951\pi$
$79$	−3.46731e8	−1.00154	−0.500772	+	0.865579i	$0.666951\pi$
$80$	5.01972e8	1.37017
$81$	4.30467e7	0.111111
$82$	−3.05294e7	−0.0745686
$83$	2.37127e8	0.548440	0.274220	−	0.961667i	$-0.411580\pi$
$83$	2.37127e8	0.548440	0.274220	+	0.961667i	$0.411580\pi$
$84$	5.01920e8	1.09996
$85$	5.80750e8	1.20671
$86$	4.28349e8	0.844412
$87$	−8.64338e7	−0.161751
$88$	−3.84902e6	−0.00684192
$89$	5.27887e8	0.891837	0.445919	−	0.895073i	$-0.352877\pi$
$89$	5.27887e8	0.891837	0.445919	+	0.895073i	$0.352877\pi$
$90$	3.95250e8	0.635010
$91$	3.40180e7	0.0520022
$92$	−4.19012e8	−0.609791
$93$	−6.53355e7	−0.0905683
$94$	−7.89103e7	−0.104246
$95$	−6.32561e8	−0.796795
$96$	6.76995e8	0.813514
$97$	9.13439e8	1.04763	0.523814	−	0.851833i	$-0.324509\pi$
$97$	9.13439e8	1.04763	0.523814	+	0.851833i	$0.324509\pi$
$98$	−3.51597e9	−3.85060
$99$	−1.11872e8	−0.117047
$100$	8.15766e8	0.815766
$101$	−1.51441e9	−1.44810	−0.724050	−	0.689748i	$-0.757721\pi$
$101$	−1.51441e9	−1.44810	−0.724050	+	0.689748i	$0.757721\pi$
$102$	7.94072e8	0.726372
$103$	−1.02106e9	−0.893892	−0.446946	−	0.894561i	$-0.647488\pi$
$103$	−1.02106e9	−0.893892	−0.446946	+	0.894561i	$0.647488\pi$
$104$	625722.	0.000524483 0
$105$	−1.87789e9	−1.50771
$106$	5.09602e8	0.392062
$107$	8.43566e8	0.622146	0.311073	−	0.950386i	$-0.399312\pi$
$107$	8.43566e8	0.622146	0.311073	+	0.950386i	$0.399312\pi$
$108$	2.68336e8	0.189789
$109$	−2.50291e9	−1.69834	−0.849172	−	0.528117i	$-0.822898\pi$
$109$	−2.50291e9	−1.69834	−0.849172	+	0.528117i	$0.822898\pi$
$110$	−1.02719e9	−0.668937
$111$	−2.41895e7	−0.0151243
$112$	−3.26097e9	−1.95824
$113$	−1.87981e9	−1.08458	−0.542288	−	0.840192i	$-0.682442\pi$
$113$	−1.87981e9	−1.08458	−0.542288	+	0.840192i	$0.682442\pi$
$114$	−8.64914e8	−0.479624
$115$	1.56769e9	0.835835
$116$	−5.38794e8	−0.276288
$117$	1.81866e7	0.00897255
$118$	−3.86413e8	−0.183477
$119$	−3.77274e9	−1.72463
$120$	−3.45416e7	−0.0152064
$121$	−2.06721e9	−0.876699
$122$	−1.36250e9	−0.556824
$123$	7.75460e7	0.0305483
$124$	−4.07275e8	−0.154700
$125$	6.37566e8	0.233577
$126$	−2.56767e9	−0.907554
$127$	−3.26424e9	−1.11343	−0.556717	−	0.830702i	$-0.687939\pi$
$127$	−3.26424e9	−1.11343	−0.556717	+	0.830702i	$0.687939\pi$
$128$	−1.18339e8	−0.0389658
$129$	−1.08803e9	−0.345928
$130$	1.66988e8	0.0512789
$131$	1.77758e9	0.527363	0.263681	−	0.964610i	$-0.415063\pi$
$131$	1.77758e9	0.527363	0.263681	+	0.964610i	$0.415063\pi$
$132$	−6.97363e8	−0.199929
$133$	4.10932e9	1.13878
$134$	3.35319e9	0.898436
$135$	−1.00395e9	−0.260143
$136$	−6.93954e7	−0.0173942
$137$	−9.42311e8	−0.228535	−0.114267	−	0.993450i	$-0.536452\pi$
$137$	−9.42311e8	−0.228535	−0.114267	+	0.993450i	$0.536452\pi$
$138$	2.14354e9	0.503124
$139$	−3.94122e9	−0.895496	−0.447748	−	0.894160i	$-0.647774\pi$
$139$	−3.94122e9	−0.895496	−0.447748	+	0.894160i	$0.647774\pi$
$140$	−1.17060e10	−2.57533
$141$	2.00436e8	0.0427060
$142$	6.40749e7	0.0132248
$143$	−4.72642e7	−0.00945192
$144$	−1.74338e9	−0.337878
$145$	2.01585e9	0.378705
$146$	−1.37665e10	−2.50747
$147$	8.93073e9	1.57746
$148$	−1.50788e8	−0.0258338
$149$	8.74194e9	1.45301	0.726507	−	0.687159i	$-0.241143\pi$
$149$	8.74194e9	1.45301	0.726507	+	0.687159i	$0.241143\pi$
$150$	−4.17321e9	−0.673070
$151$	−6.56954e9	−1.02835	−0.514173	−	0.857687i	$-0.671901\pi$
$151$	−6.56954e9	−1.02835	−0.514173	+	0.857687i	$0.671901\pi$
$152$	7.55864e7	0.0114854
$153$	−2.01698e9	−0.297570
$154$	6.67298e9	0.956042
$155$	1.52378e9	0.212046
$156$	1.13368e8	0.0153260
$157$	1.03687e10	1.36200	0.681001	−	0.732282i	$-0.261545\pi$
$157$	1.03687e10	1.36200	0.681001	+	0.732282i	$0.261545\pi$
$158$	1.10570e10	1.41149
$159$	−1.29441e9	−0.160615
$160$	−1.57892e10	−1.90467
$161$	−1.01842e10	−1.19457
$162$	−1.37273e9	−0.156591
$163$	6.31177e9	0.700337	0.350168	−	0.936687i	$-0.386124\pi$
$163$	6.31177e9	0.700337	0.350168	+	0.936687i	$0.386124\pi$
$164$	4.83390e8	0.0521796
$165$	2.60912e9	0.274041
$166$	−7.56179e9	−0.772926
$167$	7.50187e8	0.0746355	0.0373177	−	0.999303i	$-0.488119\pi$
$167$	7.50187e8	0.0746355	0.0373177	+	0.999303i	$0.488119\pi$
$168$	2.24394e8	0.0217330
$169$	−1.05968e10	−0.999275
$170$	−1.85197e10	−1.70064
$171$	2.19692e9	0.196486
$172$	−6.78231e9	−0.590880
$173$	−1.26990e10	−1.07786	−0.538929	−	0.842351i	$-0.681171\pi$
$173$	−1.26990e10	−1.07786	−0.538929	+	0.842351i	$0.681171\pi$
$174$	2.75631e9	0.227959
$175$	1.98275e10	1.59807
$176$	4.53077e9	0.355930
$177$	9.81506e8	0.0751646
$178$	−1.68339e10	−1.25688
$179$	−1.79316e10	−1.30551	−0.652754	−	0.757570i	$-0.726387\pi$
$179$	−1.79316e10	−1.30551	−0.652754	+	0.757570i	$0.726387\pi$
$180$	−6.25824e9	−0.444351
$181$	−1.71696e10	−1.18907	−0.594534	−	0.804070i	$-0.702664\pi$
$181$	−1.71696e10	−1.18907	−0.594534	+	0.804070i	$0.702664\pi$
$182$	−1.08481e9	−0.0732876
$183$	3.46082e9	0.228112
$184$	−1.87328e8	−0.0120482
$185$	5.64158e8	0.0354102
$186$	2.08350e9	0.127639
$187$	5.24181e9	0.313469
$188$	1.24943e9	0.0729463
$189$	6.52201e9	0.371795
$190$	2.01719e10	1.12294
$191$	−2.64175e10	−1.43629	−0.718143	−	0.695895i	$-0.755008\pi$
$191$	−2.64175e10	−1.43629	−0.718143	+	0.695895i	$0.755008\pi$
$192$	−1.05690e10	−0.561277
$193$	−2.24534e10	−1.16486	−0.582431	−	0.812880i	$-0.697898\pi$
$193$	−2.24534e10	−1.16486	−0.582431	+	0.812880i	$0.697898\pi$
$194$	−2.91288e10	−1.47644
$195$	−4.24156e8	−0.0210073
$196$	5.56705e10	2.69447
$197$	2.52454e10	1.19422	0.597110	−	0.802160i	$-0.296316\pi$
$197$	2.52454e10	1.19422	0.597110	+	0.802160i	$0.296316\pi$
$198$	3.56750e9	0.164957
$199$	1.59249e10	0.719843	0.359922	−	0.932983i	$-0.382803\pi$
$199$	1.59249e10	0.719843	0.359922	+	0.932983i	$0.382803\pi$
$200$	3.64705e8	0.0161178
$201$	−8.51727e9	−0.368059
$202$	4.82934e10	2.04083
$203$	−1.30956e10	−0.541244
$204$	−1.25730e10	−0.508281
$205$	−1.80856e9	−0.0715221
$206$	3.25609e10	1.25978
$207$	−5.44468e9	−0.206113
$208$	−7.36552e8	−0.0272847
$209$	−5.70945e9	−0.206984
$210$	5.98843e10	2.12484
$211$	1.80597e10	0.627250	0.313625	−	0.949547i	$-0.398457\pi$
$211$	1.80597e10	0.627250	0.313625	+	0.949547i	$0.398457\pi$
$212$	−8.06885e9	−0.274347
$213$	−1.62753e8	−0.00541777
$214$	−2.69006e10	−0.876800
$215$	2.53754e10	0.809915
$216$	1.19965e8	0.00374984
$217$	−9.89898e9	−0.303055
$218$	7.98157e10	2.39350
$219$	3.49675e10	1.02723
$220$	1.62642e10	0.468091
$221$	−8.52144e8	−0.0240297
$222$	7.71385e8	0.0213149
$223$	−5.79827e10	−1.57010	−0.785048	−	0.619434i	$-0.787362\pi$
$223$	−5.79827e10	−1.57010	−0.785048	+	0.619434i	$0.787362\pi$
$224$	1.02572e11	2.72214
$225$	1.06002e10	0.275734
$226$	5.99456e10	1.52851
$227$	−1.84397e10	−0.460931	−0.230466	−	0.973080i	$-0.574025\pi$
$227$	−1.84397e10	−0.460931	−0.230466	+	0.973080i	$0.574025\pi$
$228$	1.36947e10	0.335619
$229$	3.07282e10	0.738376	0.369188	−	0.929355i	$-0.379636\pi$
$229$	3.07282e10	0.738376	0.369188	+	0.929355i	$0.379636\pi$
$230$	−4.99925e10	−1.17796
$231$	−1.69497e10	−0.391658
$232$	−2.40879e8	−0.00545887
$233$	−6.81886e10	−1.51569	−0.757845	−	0.652435i	$-0.773747\pi$
$233$	−6.81886e10	−1.51569	−0.757845	+	0.652435i	$0.773747\pi$
$234$	−5.79957e8	−0.0126452
$235$	−4.67464e9	−0.0999868
$236$	6.11831e9	0.128389
$237$	−2.80852e10	−0.578242
$238$	1.20310e11	2.43055
$239$	−7.97104e10	−1.58024	−0.790122	−	0.612949i	$-0.789983\pi$
$239$	−7.97104e10	−1.58024	−0.790122	+	0.612949i	$0.789983\pi$
$240$	4.06598e10	0.791069
$241$	−3.16837e10	−0.605005	−0.302503	−	0.953149i	$-0.597822\pi$
$241$	−3.16837e10	−0.605005	−0.302503	+	0.953149i	$0.597822\pi$
$242$	6.59217e10	1.23555
$243$	3.48678e9	0.0641500
$244$	2.15733e10	0.389640
$245$	−2.08286e11	−3.69328
$246$	−2.47288e9	−0.0430522
$247$	9.28167e8	0.0158668
$248$	−1.82081e8	−0.00305655
$249$	1.92073e10	0.316642
$250$	−2.03315e10	−0.329184
$251$	−1.06582e11	−1.69494	−0.847468	−	0.530846i	$-0.821874\pi$
$251$	−1.06582e11	−1.69494	−0.847468	+	0.530846i	$0.821874\pi$
$252$	4.06556e10	0.635064
$253$	1.41499e10	0.217125
$254$	1.04094e11	1.56918
$255$	4.70408e10	0.696697
$256$	7.05801e10	1.02708
$257$	−5.57546e10	−0.797227	−0.398613	−	0.917119i	$-0.630508\pi$
$257$	−5.57546e10	−0.797227	−0.398613	+	0.917119i	$0.630508\pi$
$258$	3.46963e10	0.487522
$259$	−3.66496e9	−0.0506081
$260$	−2.64402e9	−0.0358826
$261$	−7.00114e9	−0.0933870
$262$	−5.66857e10	−0.743221
$263$	−2.12500e10	−0.273879	−0.136939	−	0.990579i	$-0.543727\pi$
$263$	−2.12500e10	−0.273879	−0.136939	+	0.990579i	$0.543727\pi$
$264$	−3.11770e8	−0.00395018
$265$	3.01888e10	0.376045
$266$	−1.31043e11	−1.60490
$267$	4.27588e10	0.514903
$268$	−5.30932e10	−0.628684
$269$	2.74501e9	0.0319638	0.0159819	−	0.999872i	$-0.494913\pi$
$269$	2.74501e9	0.0319638	0.0159819	+	0.999872i	$0.494913\pi$
$270$	3.20153e10	0.366623
$271$	1.67543e11	1.88697	0.943485	−	0.331414i	$-0.107526\pi$
$271$	1.67543e11	1.88697	0.943485	+	0.331414i	$0.107526\pi$
$272$	8.16869e10	0.904883
$273$	2.75545e9	0.0300235
$274$	3.00496e10	0.322078
$275$	−2.75481e10	−0.290466
$276$	−3.39399e10	−0.352063
$277$	1.37791e11	1.40625	0.703123	−	0.711068i	$-0.251788\pi$
$277$	1.37791e11	1.40625	0.703123	+	0.711068i	$0.251788\pi$
$278$	1.25682e11	1.26204
$279$	−5.29218e9	−0.0522896
$280$	−5.23340e9	−0.0508830
$281$	−1.47914e11	−1.41524	−0.707622	−	0.706591i	$-0.750232\pi$
$281$	−1.47914e11	−1.41524	−0.707622	+	0.706591i	$0.750232\pi$
$282$	−6.39173e9	−0.0601863
$283$	4.45401e10	0.412774	0.206387	−	0.978470i	$-0.433829\pi$
$283$	4.45401e10	0.412774	0.206387	+	0.978470i	$0.433829\pi$
$284$	−1.01454e9	−0.00925412
$285$	−5.12375e10	−0.460030
$286$	1.50722e9	0.0133208
$287$	1.17490e10	0.102219
$288$	5.48366e10	0.469683
$289$	−2.40813e10	−0.203067
$290$	−6.42837e10	−0.533716
$291$	7.39886e10	0.604848
$292$	2.17973e11	1.75461
$293$	1.85472e11	1.47019	0.735097	−	0.677962i	$-0.237137\pi$
$293$	1.85472e11	1.47019	0.735097	+	0.677962i	$0.237137\pi$
$294$	−2.84794e11	−2.22314
$295$	−2.28911e10	−0.175982
$296$	−6.74128e7	−0.000510422 0
$297$	−9.06161e9	−0.0675774
$298$	−2.78774e11	−2.04776
$299$	−2.30030e9	−0.0166442
$300$	6.60771e10	0.470983
$301$	−1.64847e11	−1.15753
$302$	2.09497e11	1.44926
$303$	−1.22668e11	−0.836060
$304$	−8.89745e10	−0.597495
$305$	−8.07146e10	−0.534076
$306$	6.43198e10	0.419371
$307$	1.62747e11	1.04566	0.522830	−	0.852437i	$-0.324876\pi$
$307$	1.62747e11	1.04566	0.522830	+	0.852437i	$0.324876\pi$
$308$	−1.05657e11	−0.668993
$309$	−8.27061e10	−0.516089
$310$	−4.85922e10	−0.298840
$311$	−1.22720e10	−0.0743862	−0.0371931	−	0.999308i	$-0.511842\pi$
$311$	−1.22720e10	−0.0743862	−0.0371931	+	0.999308i	$0.511842\pi$
$312$	5.06835e7	0.000302811 0
$313$	−1.67219e11	−0.984776	−0.492388	−	0.870376i	$-0.663876\pi$
$313$	−1.67219e11	−0.984776	−0.492388	+	0.870376i	$0.663876\pi$
$314$	−3.30651e11	−1.91949
$315$	−1.52109e11	−0.870477
$316$	−1.75072e11	−0.987698
$317$	−2.57818e11	−1.43399	−0.716996	−	0.697078i	$-0.754483\pi$
$317$	−2.57818e11	−1.43399	−0.716996	+	0.697078i	$0.754483\pi$
$318$	4.12778e10	0.226357
$319$	1.81949e10	0.0983764
$320$	2.46494e11	1.31411
$321$	6.83288e10	0.359196
$322$	3.24767e11	1.68353
$323$	−1.02938e11	−0.526216
$324$	2.17352e10	0.109575
$325$	4.47841e9	0.0222663
$326$	−2.01277e11	−0.986996
$327$	−2.02736e11	−0.980539
$328$	2.16110e8	0.00103096
$329$	3.03680e10	0.142901
$330$	−8.32027e10	−0.386211
$331$	2.79741e11	1.28095	0.640473	−	0.767981i	$-0.278738\pi$
$331$	2.79741e11	1.28095	0.640473	+	0.767981i	$0.278738\pi$
$332$	1.19730e11	0.540858
$333$	−1.95935e9	−0.00873200
$334$	−2.39229e10	−0.105185
$335$	1.98643e11	0.861731
$336$	−2.64139e11	−1.13059
$337$	1.93079e11	0.815454	0.407727	−	0.913104i	$-0.366321\pi$
$337$	1.93079e11	0.815454	0.407727	+	0.913104i	$0.366321\pi$
$338$	3.37924e11	1.40830
$339$	−1.52264e11	−0.626181
$340$	2.93233e11	1.19003
$341$	1.37535e10	0.0550833
$342$	−7.00580e10	−0.276911
$343$	8.57862e11	3.34652
$344$	−3.03217e9	−0.0116746
$345$	1.26983e11	0.482570
$346$	4.04961e11	1.51904
$347$	4.07789e11	1.50992	0.754959	−	0.655773i	$-0.227657\pi$
$347$	4.07789e11	1.50992	0.754959	+	0.655773i	$0.227657\pi$
$348$	−4.36423e10	−0.159515
$349$	−1.82090e11	−0.657009	−0.328505	−	0.944502i	$-0.606545\pi$
$349$	−1.82090e11	−0.657009	−0.328505	+	0.944502i	$0.606545\pi$
$350$	−6.32284e11	−2.25219
$351$	1.47312e9	0.00518030
$352$	−1.42512e11	−0.494776
$353$	−5.32848e10	−0.182649	−0.0913245	−	0.995821i	$-0.529110\pi$
$353$	−5.32848e10	−0.182649	−0.0913245	+	0.995821i	$0.529110\pi$
$354$	−3.12995e10	−0.105931
$355$	3.79579e9	0.0126845
$356$	2.66541e11	0.879507
$357$	−3.05592e11	−0.995716
$358$	5.71824e11	1.83988
$359$	5.41580e11	1.72083	0.860414	−	0.509595i	$-0.170205\pi$
$359$	5.41580e11	1.72083	0.860414	+	0.509595i	$0.170205\pi$
$360$	−2.79787e9	−0.00877944
$361$	−2.10566e11	−0.652539
$362$	5.47525e11	1.67577
$363$	−1.67444e11	−0.506162
$364$	1.71764e10	0.0512833
$365$	−8.15526e11	−2.40503
$366$	−1.10363e11	−0.321483
$367$	−1.14857e11	−0.330492	−0.165246	−	0.986252i	$-0.552842\pi$
$367$	−1.14857e11	−0.330492	−0.165246	+	0.986252i	$0.552842\pi$
$368$	2.20508e11	0.626771
$369$	6.28123e9	0.0176370
$370$	−1.79906e10	−0.0499042
$371$	−1.96116e11	−0.537442
$372$	−3.29893e10	−0.0893161
$373$	−1.42587e11	−0.381409	−0.190705	−	0.981647i	$-0.561077\pi$
$373$	−1.42587e11	−0.381409	−0.190705	+	0.981647i	$0.561077\pi$
$374$	−1.67157e11	−0.441777
$375$	5.16428e10	0.134856
$376$	5.58585e8	0.00144127
$377$	−2.95788e9	−0.00754128
$378$	−2.07982e11	−0.523976
$379$	−7.82015e11	−1.94688	−0.973438	−	0.228949i	$-0.926471\pi$
$379$	−7.82015e11	−1.94688	−0.973438	+	0.228949i	$0.926471\pi$
$380$	−3.19394e11	−0.785778
$381$	−2.64403e11	−0.642842
$382$	8.42432e11	2.02418
$383$	3.21255e11	0.762878	0.381439	−	0.924394i	$-0.375429\pi$
$383$	3.21255e11	0.762878	0.381439	+	0.924394i	$0.375429\pi$
$384$	−9.58546e9	−0.0224969
$385$	3.95307e11	0.916984
$386$	7.16021e11	1.64166
$387$	−8.81300e10	−0.199721
$388$	4.61215e11	1.03314
$389$	1.78363e11	0.394939	0.197470	−	0.980309i	$-0.436728\pi$
$389$	1.78363e11	0.394939	0.197470	+	0.980309i	$0.436728\pi$
$390$	1.35260e10	0.0296059
$391$	2.55114e11	0.551999
$392$	2.48886e10	0.0532370
$393$	1.43984e11	0.304473
$394$	−8.05055e11	−1.68303
$395$	6.55014e11	1.35383
$396$	−5.64864e10	−0.115429
$397$	6.49654e11	1.31258	0.656289	−	0.754510i	$-0.272125\pi$
$397$	6.49654e11	1.31258	0.656289	+	0.754510i	$0.272125\pi$
$398$	−5.07833e11	−1.01449
$399$	3.32855e11	0.657472
$400$	−4.29302e11	−0.838481
$401$	−1.09019e11	−0.210550	−0.105275	−	0.994443i	$-0.533572\pi$
$401$	−1.09019e11	−0.210550	−0.105275	+	0.994443i	$0.533572\pi$
$402$	2.71609e11	0.518712
$403$	−2.23587e9	−0.00422254
$404$	−7.64660e11	−1.42808
$405$	−8.13202e10	−0.150193
$406$	4.17608e11	0.762784
$407$	5.09205e9	0.00919852
$408$	−5.62103e9	−0.0100426
$409$	−4.91552e11	−0.868590	−0.434295	−	0.900771i	$-0.643002\pi$
$409$	−4.91552e11	−0.868590	−0.434295	+	0.900771i	$0.643002\pi$
$410$	5.76735e10	0.100797
$411$	−7.63272e10	−0.131944
$412$	−5.15556e11	−0.881533
$413$	1.48708e11	0.251512
$414$	1.73627e11	0.290479
$415$	−4.47960e11	−0.741349
$416$	2.31677e10	0.0379282
$417$	−3.19239e11	−0.517015
$418$	1.82070e11	0.291706
$419$	1.82329e11	0.288997	0.144499	−	0.989505i	$-0.453843\pi$
$419$	1.82329e11	0.288997	0.144499	+	0.989505i	$0.453843\pi$
$420$	−9.48185e11	−1.48686
$421$	−1.14800e12	−1.78104	−0.890519	−	0.454947i	$-0.849658\pi$
$421$	−1.14800e12	−1.78104	−0.890519	+	0.454947i	$0.849658\pi$
$422$	−5.75911e11	−0.883994
$423$	1.62353e10	0.0246563
$424$	−3.60734e9	−0.00542052
$425$	−4.96676e11	−0.738453
$426$	5.19006e9	0.00763536
$427$	5.24348e11	0.763299
$428$	4.25934e11	0.613544
$429$	−3.82840e9	−0.00545707
$430$	−8.09200e11	−1.14143
$431$	9.10456e11	1.27090	0.635450	−	0.772142i	$-0.280815\pi$
$431$	9.10456e11	1.27090	0.635450	+	0.772142i	$0.280815\pi$
$432$	−1.41214e11	−0.195074
$433$	−1.35384e12	−1.85085	−0.925426	−	0.378929i	$-0.876292\pi$
$433$	−1.35384e12	−1.85085	−0.925426	+	0.378929i	$0.876292\pi$
$434$	3.15671e11	0.427101
$435$	1.63283e11	0.218646
$436$	−1.26377e12	−1.67486
$437$	−2.77873e11	−0.364485
$438$	−1.11508e12	−1.44769
$439$	−5.31193e11	−0.682593	−0.341297	−	0.939956i	$-0.610866\pi$
$439$	−5.31193e11	−0.682593	−0.341297	+	0.939956i	$0.610866\pi$
$440$	7.27124e9	0.00924850
$441$	7.23389e11	0.910748
$442$	2.71742e10	0.0338654
$443$	2.93695e11	0.362309	0.181155	−	0.983455i	$-0.442017\pi$
$443$	2.93695e11	0.362309	0.181155	+	0.983455i	$0.442017\pi$
$444$	−1.22138e10	−0.0149152
$445$	−9.97239e11	−1.20553
$446$	1.84902e12	2.21276
$447$	7.08097e11	0.838898
$448$	−1.60130e12	−1.87812
$449$	−2.96345e11	−0.344104	−0.172052	−	0.985088i	$-0.555040\pi$
$449$	−2.96345e11	−0.344104	−0.172052	+	0.985088i	$0.555040\pi$
$450$	−3.38030e11	−0.388597
$451$	−1.63239e10	−0.0185793
$452$	−9.49155e11	−1.06958
$453$	−5.32133e11	−0.593715
$454$	5.88026e11	0.649599
$455$	−6.42638e10	−0.0702935
$456$	6.12250e9	0.00663112
$457$	−1.56401e12	−1.67733	−0.838664	−	0.544650i	$-0.816663\pi$
$457$	−1.56401e12	−1.67733	−0.838664	+	0.544650i	$0.816663\pi$
$458$	−9.79898e11	−1.04061
$459$	−1.63375e11	−0.171802
$460$	7.91561e11	0.824279
$461$	−1.01947e12	−1.05128	−0.525642	−	0.850706i	$-0.676175\pi$
$461$	−1.01947e12	−1.05128	−0.525642	+	0.850706i	$0.676175\pi$
$462$	5.40512e11	0.551971
$463$	−3.45994e11	−0.349908	−0.174954	−	0.984577i	$-0.555978\pi$
$463$	−3.45994e11	−0.349908	−0.174954	+	0.984577i	$0.555978\pi$
$464$	2.83544e11	0.283981
$465$	1.23426e11	0.122425
$466$	2.17448e12	2.13609
$467$	5.45802e11	0.531018	0.265509	−	0.964108i	$-0.414460\pi$
$467$	5.45802e11	0.531018	0.265509	+	0.964108i	$0.414460\pi$
$468$	9.18281e9	0.00884850
$469$	−1.29045e12	−1.23158
$470$	1.49071e11	0.140913
$471$	8.39869e11	0.786353
$472$	2.73532e9	0.00253670
$473$	2.29036e11	0.210392
$474$	8.95614e11	0.814927
$475$	5.40986e11	0.487601
$476$	−1.90494e12	−1.70079
$477$	−1.04847e11	−0.0927311
$478$	2.54190e12	2.22706
$479$	−3.74861e11	−0.325357	−0.162679	−	0.986679i	$-0.552013\pi$
$479$	−3.74861e11	−0.325357	−0.162679	+	0.986679i	$0.552013\pi$
$480$	−1.27892e12	−1.09966
$481$	−8.27799e8	−0.000705134 0
$482$	1.01037e12	0.852644
$483$	−8.24923e11	−0.689686
$484$	−1.04378e12	−0.864578
$485$	−1.72559e12	−1.41612
$486$	−1.11191e11	−0.0904077
$487$	−1.96357e12	−1.58185	−0.790924	−	0.611914i	$-0.790400\pi$
$487$	−1.96357e12	−1.58185	−0.790924	+	0.611914i	$0.790400\pi$
$488$	9.64480e9	0.00769847
$489$	5.11253e11	0.404339
$490$	6.64208e12	5.20501
$491$	−1.40585e12	−1.09162	−0.545809	−	0.837910i	$-0.683778\pi$
$491$	−1.40585e12	−1.09162	−0.545809	+	0.837910i	$0.683778\pi$
$492$	3.91546e10	0.0301259
$493$	3.28042e11	0.250103
$494$	−2.95985e10	−0.0223614
$495$	2.11339e11	0.158218
$496$	2.14331e11	0.159008
$497$	−2.46587e10	−0.0181287
$498$	−6.12505e11	−0.446249
$499$	−1.21146e12	−0.874696	−0.437348	−	0.899292i	$-0.644082\pi$
$499$	−1.21146e12	−0.874696	−0.437348	+	0.899292i	$0.644082\pi$
$500$	3.21921e11	0.230348
$501$	6.07651e10	0.0430908
$502$	3.39882e12	2.38870
$503$	−1.83565e12	−1.27860	−0.639298	−	0.768959i	$-0.720775\pi$
$503$	−1.83565e12	−1.27860	−0.639298	+	0.768959i	$0.720775\pi$
$504$	1.81759e10	0.0125475
$505$	2.86090e12	1.95745
$506$	−4.51228e11	−0.305998
$507$	−8.58342e11	−0.576932
$508$	−1.64818e12	−1.09804
$509$	−7.98947e11	−0.527579	−0.263790	−	0.964580i	$-0.584972\pi$
$509$	−7.98947e11	−0.527579	−0.263790	+	0.964580i	$0.584972\pi$
$510$	−1.50009e12	−0.981866
$511$	5.29792e12	3.43725
$512$	−2.19015e12	−1.40851
$513$	1.77951e11	0.113441
$514$	1.77797e12	1.12354
$515$	1.92890e12	1.20831
$516$	−5.49367e11	−0.341145
$517$	−4.21930e10	−0.0259736
$518$	1.16873e11	0.0713228
$519$	−1.02862e12	−0.622302
$520$	−1.18206e9	−0.000708965 0
$521$	1.73968e12	1.03443	0.517214	−	0.855856i	$-0.326969\pi$
$521$	1.73968e12	1.03443	0.517214	+	0.855856i	$0.326969\pi$
$522$	2.23261e11	0.131612
$523$	1.07649e12	0.629150	0.314575	−	0.949233i	$-0.398138\pi$
$523$	1.07649e12	0.629150	0.314575	+	0.949233i	$0.398138\pi$
$524$	8.97540e11	0.520072
$525$	1.60603e12	0.922649
$526$	6.77647e11	0.385982
$527$	2.47968e11	0.140039
$528$	3.66992e11	0.205496
$529$	−1.11249e12	−0.617656
$530$	−9.62698e11	−0.529967
$531$	7.95020e10	0.0433963
$532$	2.07489e12	1.12303
$533$	2.65373e9	0.00142424
$534$	−1.36354e12	−0.725661
$535$	−1.59359e12	−0.840980
$536$	−2.37364e10	−0.0124215
$537$	−1.45246e12	−0.753736
$538$	−8.75362e10	−0.0450472
$539$	−1.87997e12	−0.959406
$540$	−5.06917e11	−0.256546
$541$	6.48663e11	0.325560	0.162780	−	0.986662i	$-0.447954\pi$
$541$	6.48663e11	0.325560	0.162780	+	0.986662i	$0.447954\pi$
$542$	−5.34282e12	−2.65934
$543$	−1.39074e12	−0.686509
$544$	−2.56940e12	−1.25787
$545$	4.72828e12	2.29572
$546$	−8.78693e10	−0.0423126
$547$	−3.36177e12	−1.60555	−0.802777	−	0.596279i	$-0.796645\pi$
$547$	−3.36177e12	−1.60555	−0.802777	+	0.596279i	$0.796645\pi$
$548$	−4.75793e11	−0.225375
$549$	2.80326e11	0.131701
$550$	8.78488e11	0.409359
$551$	−3.57308e11	−0.165143
$552$	−1.51735e10	−0.00695603
$553$	−4.25519e12	−1.93489
$554$	−4.39404e12	−1.98185
$555$	4.56968e10	0.0204441
$556$	−1.99000e12	−0.883116
$557$	−1.25211e12	−0.551180	−0.275590	−	0.961275i	$-0.588873\pi$
$557$	−1.25211e12	−0.551180	−0.275590	+	0.961275i	$0.588873\pi$
$558$	1.68763e11	0.0736927
$559$	−3.72337e10	−0.0161281
$560$	6.16036e12	2.64704
$561$	4.24587e11	0.180981
$562$	4.71687e12	1.99453
$563$	−8.31880e11	−0.348958	−0.174479	−	0.984661i	$-0.555824\pi$
$563$	−8.31880e11	−0.348958	−0.174479	+	0.984661i	$0.555824\pi$
$564$	1.01204e11	0.0421156
$565$	3.55117e12	1.46607
$566$	−1.42035e12	−0.581730
$567$	5.28283e11	0.214656
$568$	−4.53569e8	−0.000182842 0
$569$	1.53041e12	0.612071	0.306035	−	0.952020i	$-0.400997\pi$
$569$	1.53041e12	0.612071	0.306035	+	0.952020i	$0.400997\pi$
$570$	1.63392e12	0.648328
$571$	1.08360e12	0.426586	0.213293	−	0.976988i	$-0.431581\pi$
$571$	1.08360e12	0.426586	0.213293	+	0.976988i	$0.431581\pi$
$572$	−2.38647e10	−0.00932124
$573$	−2.13982e12	−0.829241
$574$	−3.74666e11	−0.144059
$575$	−1.34074e12	−0.511492
$576$	−8.56087e11	−0.324053
$577$	1.84892e12	0.694429	0.347215	−	0.937786i	$-0.387128\pi$
$577$	1.84892e12	0.694429	0.347215	+	0.937786i	$0.387128\pi$
$578$	7.67932e11	0.286185
$579$	−1.81873e12	−0.672533
$580$	1.01784e12	0.373469
$581$	2.91009e12	1.05953
$582$	−2.35944e12	−0.852423
$583$	2.72482e11	0.0976854
$584$	9.74493e10	0.0346674
$585$	−3.43566e10	−0.0121286
$586$	−5.91456e12	−2.07197
$587$	−1.65737e11	−0.0576168	−0.0288084	−	0.999585i	$-0.509171\pi$
$587$	−1.65737e11	−0.0576168	−0.0288084	+	0.999585i	$0.509171\pi$
$588$	4.50931e12	1.55565
$589$	−2.70090e11	−0.0924676
$590$	7.29979e11	0.248014
$591$	2.04488e12	0.689483
$592$	7.93531e10	0.0265532
$593$	−1.00017e12	−0.332146	−0.166073	−	0.986113i	$-0.553109\pi$
$593$	−1.00017e12	−0.332146	−0.166073	+	0.986113i	$0.553109\pi$
$594$	2.88967e11	0.0952379
$595$	7.12715e12	2.33125
$596$	4.41399e12	1.43292
$597$	1.28992e12	0.415602
$598$	7.33547e10	0.0234570
$599$	−3.62898e12	−1.15176	−0.575882	−	0.817533i	$-0.695341\pi$
$599$	−3.62898e12	−1.15176	−0.575882	+	0.817533i	$0.695341\pi$
$600$	2.95411e10	0.00930563
$601$	4.56853e12	1.42837	0.714186	−	0.699956i	$-0.246797\pi$
$601$	4.56853e12	1.42837	0.714186	+	0.699956i	$0.246797\pi$
$602$	5.25683e12	1.63132
$603$	−6.89898e11	−0.212499
$604$	−3.31710e12	−1.01413
$605$	3.90520e12	1.18507
$606$	3.91177e12	1.17827
$607$	3.24449e11	0.0970058	0.0485029	−	0.998823i	$-0.484555\pi$
$607$	3.24449e11	0.0970058	0.0485029	+	0.998823i	$0.484555\pi$
$608$	2.79863e12	0.830575
$609$	−1.06074e12	−0.312487
$610$	2.57393e12	0.752682
$611$	6.85918e9	0.00199107
$612$	−1.01842e12	−0.293456
$613$	−4.26225e12	−1.21918	−0.609588	−	0.792718i	$-0.708665\pi$
$613$	−4.26225e12	−1.21918	−0.609588	+	0.792718i	$0.708665\pi$
$614$	−5.18988e12	−1.47367
$615$	−1.46493e11	−0.0412933
$616$	−4.72363e10	−0.0132179
$617$	−4.33447e11	−0.120407	−0.0602037	−	0.998186i	$-0.519175\pi$
$617$	−4.33447e11	−0.120407	−0.0602037	+	0.998186i	$0.519175\pi$
$618$	2.63743e12	0.727332
$619$	1.15536e12	0.316306	0.158153	−	0.987415i	$-0.449446\pi$
$619$	1.15536e12	0.316306	0.158153	+	0.987415i	$0.449446\pi$
$620$	7.69390e11	0.209114
$621$	−4.41019e11	−0.119000
$622$	3.91343e11	0.104834
$623$	6.47839e12	1.72294
$624$	−5.96607e10	−0.0157528
$625$	−4.35996e12	−1.14294
$626$	5.33250e12	1.38786
$627$	−4.62466e11	−0.119502
$628$	5.23540e12	1.34317
$629$	9.18066e10	0.0233855
$630$	4.85063e12	1.22678
$631$	2.05136e12	0.515121	0.257560	−	0.966262i	$-0.417081\pi$
$631$	2.05136e12	0.515121	0.257560	+	0.966262i	$0.417081\pi$
$632$	−7.82694e10	−0.0195148
$633$	1.46284e12	0.362143
$634$	8.22161e12	2.02095
$635$	6.16652e12	1.50508
$636$	−6.53577e11	−0.158394
$637$	3.05621e11	0.0735455
$638$	−5.80220e11	−0.138644
$639$	−1.31830e10	−0.00312795
$640$	2.23556e11	0.0526716
$641$	7.24358e12	1.69470	0.847349	−	0.531036i	$-0.178197\pi$
$641$	7.24358e12	1.69470	0.847349	+	0.531036i	$0.178197\pi$
$642$	−2.17895e12	−0.506221
$643$	−9.75907e11	−0.225143	−0.112572	−	0.993644i	$-0.535909\pi$
$643$	−9.75907e11	−0.225143	−0.112572	+	0.993644i	$0.535909\pi$
$644$	−5.14224e12	−1.17806
$645$	2.05540e12	0.467604
$646$	3.28261e12	0.741605
$647$	−5.08148e12	−1.14004	−0.570021	−	0.821630i	$-0.693065\pi$
$647$	−5.08148e12	−1.14004	−0.570021	+	0.821630i	$0.693065\pi$
$648$	9.71717e9	0.00216497
$649$	−2.06613e11	−0.0457148
$650$	−1.42813e11	−0.0313803
$651$	−8.01818e11	−0.174969
$652$	3.18695e12	0.690654
$653$	2.74396e12	0.590565	0.295283	−	0.955410i	$-0.404586\pi$
$653$	2.74396e12	0.590565	0.295283	+	0.955410i	$0.404586\pi$
$654$	6.46507e12	1.38189
$655$	−3.35806e12	−0.712858
$656$	−2.54387e11	−0.0536326
$657$	2.83237e12	0.593069
$658$	−9.68411e11	−0.201392
$659$	−2.37620e12	−0.490793	−0.245396	−	0.969423i	$-0.578918\pi$
$659$	−2.37620e12	−0.490793	−0.245396	+	0.969423i	$0.578918\pi$
$660$	1.31740e12	0.270252
$661$	−3.46172e12	−0.705319	−0.352659	−	0.935752i	$-0.614723\pi$
$661$	−3.46172e12	−0.705319	−0.352659	+	0.935752i	$0.614723\pi$
$662$	−8.92073e12	−1.80526
$663$	−6.90237e10	−0.0138735
$664$	5.35279e10	0.0106862
$665$	−7.76299e12	−1.53933
$666$	6.24822e10	0.0123062
$667$	8.85526e11	0.173235
$668$	3.78785e11	0.0736036
$669$	−4.69660e12	−0.906496
$670$	−6.33457e12	−1.21445
$671$	−7.28524e11	−0.138737
$672$	8.30829e12	1.57163
$673$	−6.67858e12	−1.25492	−0.627461	−	0.778648i	$-0.715906\pi$
$673$	−6.67858e12	−1.25492	−0.627461	+	0.778648i	$0.715906\pi$
$674$	−6.15712e12	−1.14923
$675$	8.58612e11	0.159195
$676$	−5.35056e12	−0.985460
$677$	4.44582e11	0.0813398	0.0406699	−	0.999173i	$-0.487051\pi$
$677$	4.44582e11	0.0813398	0.0406699	+	0.999173i	$0.487051\pi$
$678$	4.85559e12	0.882487
$679$	1.12100e13	2.02391
$680$	1.31096e11	0.0235125
$681$	−1.49361e12	−0.266119
$682$	−4.38590e11	−0.0776298
$683$	9.48001e12	1.66692	0.833462	−	0.552577i	$-0.186355\pi$
$683$	9.48001e12	1.66692	0.833462	+	0.552577i	$0.186355\pi$
$684$	1.10927e12	0.193770
$685$	1.78013e12	0.308919
$686$	−2.73565e13	−4.71631
$687$	2.48899e12	0.426302
$688$	3.56924e12	0.607334
$689$	−4.42966e10	−0.00748830
$690$	−4.04939e12	−0.680093
$691$	−5.25166e12	−0.876284	−0.438142	−	0.898906i	$-0.644363\pi$
$691$	−5.25166e12	−0.876284	−0.438142	+	0.898906i	$0.644363\pi$
$692$	−6.41199e12	−1.06296
$693$	−1.37292e12	−0.226124
$694$	−1.30041e13	−2.12795
$695$	7.44541e12	1.21048
$696$	−1.95112e10	−0.00315168
$697$	−2.94310e11	−0.0472344
$698$	5.80670e12	0.925934
$699$	−5.52328e12	−0.875084
$700$	1.00113e13	1.57598
$701$	−9.50022e12	−1.48594	−0.742972	−	0.669323i	$-0.766584\pi$
$701$	−9.50022e12	−1.48594	−0.742972	+	0.669323i	$0.766584\pi$
$702$	−4.69765e10	−0.00730069
$703$	−9.99970e10	−0.0154414
$704$	2.22484e12	0.341367
$705$	−3.78646e11	−0.0577274
$706$	1.69921e12	0.257410
$707$	−1.85853e13	−2.79759
$708$	4.95583e11	0.0741254
$709$	3.80257e12	0.565158	0.282579	−	0.959244i	$-0.408810\pi$
$709$	3.80257e12	0.565158	0.282579	+	0.959244i	$0.408810\pi$
$710$	−1.21045e11	−0.0178765
$711$	−2.27490e12	−0.333848
$712$	1.19163e11	0.0173772
$713$	6.69371e11	0.0969983
$714$	9.74509e12	1.40328
$715$	8.92875e10	0.0127765
$716$	−9.05403e12	−1.28746
$717$	−6.45654e12	−0.912354
$718$	−1.72706e13	−2.42519
$719$	−4.75843e12	−0.664024	−0.332012	−	0.943275i	$-0.607727\pi$
$719$	−4.75843e12	−0.664024	−0.332012	+	0.943275i	$0.607727\pi$
$720$	3.29344e12	0.456724
$721$	−1.25308e13	−1.72691
$722$	6.71479e12	0.919634
$723$	−2.56638e12	−0.349300
$724$	−8.66930e12	−1.17263
$725$	−1.72401e12	−0.231750
$726$	5.33966e12	0.713343
$727$	−8.46722e11	−0.112418	−0.0562090	−	0.998419i	$-0.517901\pi$
$727$	−8.46722e11	−0.112418	−0.0562090	+	0.998419i	$0.517901\pi$
$728$	7.67906e9	0.00101325
$729$	2.82430e11	0.0370370
$730$	2.60065e13	3.38944
$731$	4.12938e12	0.534881
$732$	1.74744e12	0.224959
$733$	1.49200e13	1.90898	0.954490	−	0.298244i	$-0.0964009\pi$
$733$	1.49200e13	1.90898	0.954490	+	0.298244i	$0.0964009\pi$
$734$	3.66270e12	0.465767
$735$	−1.68712e13	−2.13232
$736$	−6.93590e12	−0.871270
$737$	1.79294e12	0.223852
$738$	−2.00303e11	−0.0248562
$739$	−1.33358e12	−0.164482	−0.0822409	−	0.996612i	$-0.526208\pi$
$739$	−1.33358e12	−0.164482	−0.0822409	+	0.996612i	$0.526208\pi$
$740$	2.84856e11	0.0349206
$741$	7.51816e10	0.00916072
$742$	6.25400e12	0.757426
$743$	1.73699e12	0.209097	0.104548	−	0.994520i	$-0.466660\pi$
$743$	1.73699e12	0.209097	0.104548	+	0.994520i	$0.466660\pi$
$744$	−1.47485e10	−0.00176470
$745$	−1.65145e13	−1.96410
$746$	4.54700e12	0.537527
$747$	1.55579e12	0.182813
$748$	2.64670e12	0.309135
$749$	1.03525e13	1.20192
$750$	−1.64685e12	−0.190054
$751$	−1.71628e12	−0.196883	−0.0984415	−	0.995143i	$-0.531386\pi$
$751$	−1.71628e12	−0.196883	−0.0984415	+	0.995143i	$0.531386\pi$
$752$	−6.57523e11	−0.0749775
$753$	−8.63317e12	−0.978572
$754$	9.43245e10	0.0106280
$755$	1.24106e13	1.39006
$756$	3.29310e12	0.366654
$757$	−1.73787e12	−0.192348	−0.0961739	−	0.995365i	$-0.530660\pi$
$757$	−1.73787e12	−0.192348	−0.0961739	+	0.995365i	$0.530660\pi$
$758$	2.49378e13	2.74377
$759$	1.14614e12	0.125357
$760$	−1.42791e11	−0.0155253
$761$	2.45314e12	0.265150	0.132575	−	0.991173i	$-0.457675\pi$
$761$	2.45314e12	0.265150	0.132575	+	0.991173i	$0.457675\pi$
$762$	8.43161e12	0.905968
$763$	−3.07164e13	−3.28103
$764$	−1.33387e13	−1.41643
$765$	3.81030e12	0.402238
$766$	−1.02446e13	−1.07514
$767$	3.35885e10	0.00350438
$768$	5.71699e12	0.592982
$769$	6.92178e12	0.713755	0.356878	−	0.934151i	$-0.383841\pi$
$769$	6.92178e12	0.713755	0.356878	+	0.934151i	$0.383841\pi$
$770$	−1.26060e13	−1.29232
$771$	−4.51612e12	−0.460279
$772$	−1.13372e13	−1.14876
$773$	7.14953e12	0.720228	0.360114	−	0.932908i	$-0.382738\pi$
$773$	7.14953e12	0.720228	0.360114	+	0.932908i	$0.382738\pi$
$774$	2.81040e12	0.281471
$775$	−1.30319e12	−0.129762
$776$	2.06196e11	0.0204127
$777$	−2.96861e11	−0.0292186
$778$	−5.68784e12	−0.556595
$779$	3.20567e11	0.0311889
$780$	−2.14165e11	−0.0207168
$781$	3.42605e10	0.00329507
$782$	−8.13537e12	−0.777941
$783$	−5.67092e11	−0.0539170
$784$	−2.92970e13	−2.76950
$785$	−1.95878e13	−1.84107
$786$	−4.59155e12	−0.429099
$787$	5.46600e12	0.507906	0.253953	−	0.967217i	$-0.418269\pi$
$787$	5.46600e12	0.507906	0.253953	+	0.967217i	$0.418269\pi$
$788$	1.27469e13	1.17771
$789$	−1.72125e12	−0.158124
$790$	−2.08879e13	−1.90797
$791$	−2.30696e13	−2.09530
$792$	−2.52534e10	−0.00228064
$793$	1.18434e11	0.0106352
$794$	−2.07170e13	−1.84984
$795$	2.44530e12	0.217110
$796$	8.04082e12	0.709891
$797$	−1.83343e13	−1.60954	−0.804770	−	0.593587i	$-0.797711\pi$
$797$	−1.83343e13	−1.60954	−0.804770	+	0.593587i	$0.797711\pi$
$798$	−1.06145e13	−0.926587
$799$	−7.60713e11	−0.0660329
$800$	1.35034e13	1.16557
$801$	3.46346e12	0.297279
$802$	3.47654e12	0.296731
$803$	−7.36088e12	−0.624755
$804$	−4.30055e12	−0.362971
$805$	1.92392e13	1.61475
$806$	7.13001e10	0.00595090
$807$	2.22346e11	0.0184543
$808$	−3.41857e11	−0.0282158
$809$	1.45650e13	1.19548	0.597741	−	0.801689i	$-0.296065\pi$
$809$	1.45650e13	1.19548	0.597741	+	0.801689i	$0.296065\pi$
$810$	2.59324e12	0.211670
$811$	−7.14300e12	−0.579811	−0.289906	−	0.957055i	$-0.593624\pi$
$811$	−7.14300e12	−0.579811	−0.289906	+	0.957055i	$0.593624\pi$
$812$	−6.61224e12	−0.533761
$813$	1.35710e13	1.08944
$814$	−1.62381e11	−0.0129636
$815$	−1.19237e13	−0.946673
$816$	6.61664e12	0.522434
$817$	−4.49778e12	−0.353182
$818$	1.56752e13	1.22412
$819$	2.23192e11	0.0173341
$820$	−9.13180e11	−0.0705333
$821$	1.86782e13	1.43480	0.717399	−	0.696663i	$-0.245333\pi$
$821$	1.86782e13	1.43480	0.717399	+	0.696663i	$0.245333\pi$
$822$	2.43401e12	0.185952
$823$	−1.64592e13	−1.25057	−0.625286	−	0.780395i	$-0.715018\pi$
$823$	−1.64592e13	−1.25057	−0.625286	+	0.780395i	$0.715018\pi$
$824$	−2.30490e11	−0.0174172
$825$	−2.23140e12	−0.167701
$826$	−4.74218e12	−0.354460
$827$	1.92951e13	1.43440	0.717202	−	0.696865i	$-0.245422\pi$
$827$	1.92951e13	1.43440	0.717202	+	0.696865i	$0.245422\pi$
$828$	−2.74914e12	−0.203264
$829$	−2.67671e12	−0.196836	−0.0984182	−	0.995145i	$-0.531378\pi$
$829$	−2.67671e12	−0.196836	−0.0984182	+	0.995145i	$0.531378\pi$
$830$	1.42851e13	1.04480
$831$	1.11611e13	0.811896
$832$	−3.61684e11	−0.0261683
$833$	−3.38948e13	−2.43910
$834$	1.01803e13	0.728638
$835$	−1.41719e12	−0.100888
$836$	−2.88282e12	−0.204122
$837$	−4.28666e11	−0.0301894
$838$	−5.81434e12	−0.407288
$839$	2.29406e13	1.59836	0.799182	−	0.601089i	$-0.205266\pi$
$839$	2.29406e13	1.59836	0.799182	+	0.601089i	$0.205266\pi$
$840$	−4.23906e11	−0.0293773
$841$	−1.33685e13	−0.921510
$842$	3.66088e13	2.51005
$843$	−1.19811e13	−0.817092
$844$	9.11875e12	0.618578
$845$	2.00186e13	1.35076
$846$	−5.17730e11	−0.0347486
$847$	−2.53694e13	−1.69370
$848$	4.24629e12	0.281986
$849$	3.60775e12	0.238315
$850$	1.58386e13	1.04071
$851$	2.47825e11	0.0161980
$852$	−8.21774e10	−0.00534287
$853$	2.67496e12	0.173000	0.0865001	−	0.996252i	$-0.472432\pi$
$853$	2.67496e12	0.173000	0.0865001	+	0.996252i	$0.472432\pi$
$854$	−1.67211e13	−1.07573
$855$	−4.15023e12	−0.265598
$856$	1.90423e11	0.0121223
$857$	9.53553e12	0.603853	0.301926	−	0.953331i	$-0.402370\pi$
$857$	9.53553e12	0.603853	0.301926	+	0.953331i	$0.402370\pi$
$858$	1.22085e11	0.00769074
$859$	2.42971e13	1.52260	0.761298	−	0.648402i	$-0.224562\pi$
$859$	2.42971e13	1.52260	0.761298	+	0.648402i	$0.224562\pi$
$860$	1.28126e13	0.798717
$861$	9.51668e11	0.0590162
$862$	−2.90337e13	−1.79110
$863$	5.09925e12	0.312938	0.156469	−	0.987683i	$-0.449989\pi$
$863$	5.09925e12	0.312938	0.156469	+	0.987683i	$0.449989\pi$
$864$	4.44177e12	0.271171
$865$	2.39899e13	1.45699
$866$	4.31729e13	2.60844
$867$	−1.95058e12	−0.117241
$868$	−4.99821e12	−0.298865
$869$	5.91211e12	0.351685
$870$	−5.20698e12	−0.308141
$871$	−2.91472e11	−0.0171599
$872$	−5.64995e11	−0.0330918
$873$	5.99307e12	0.349209
$874$	8.86116e12	0.513676
$875$	7.82440e12	0.451248
$876$	1.76558e13	1.01302
$877$	−1.18486e13	−0.676348	−0.338174	−	0.941084i	$-0.609809\pi$
$877$	−1.18486e13	−0.676348	−0.338174	+	0.941084i	$0.609809\pi$
$878$	1.69393e13	0.961990
$879$	1.50233e13	0.848817
$880$	−8.55914e12	−0.481125
$881$	−2.69059e13	−1.50472	−0.752360	−	0.658752i	$-0.771085\pi$
$881$	−2.69059e13	−1.50472	−0.752360	+	0.658752i	$0.771085\pi$
$882$	−2.30683e13	−1.28353
$883$	−2.48397e12	−0.137507	−0.0687534	−	0.997634i	$-0.521902\pi$
$883$	−2.48397e12	−0.137507	−0.0687534	+	0.997634i	$0.521902\pi$
$884$	−4.30266e11	−0.0236975
$885$	−1.85418e12	−0.101603
$886$	−9.36569e12	−0.510608
$887$	−1.74257e13	−0.945223	−0.472611	−	0.881271i	$-0.656689\pi$
$887$	−1.74257e13	−0.945223	−0.472611	+	0.881271i	$0.656689\pi$
$888$	−5.46043e9	−0.000294692 0
$889$	−4.00597e13	−2.15105
$890$	3.18011e13	1.69898
$891$	−7.33990e11	−0.0390158
$892$	−2.92767e13	−1.54839
$893$	8.28579e11	0.0436016
$894$	−2.25807e13	−1.18227
$895$	3.38748e13	1.76471
$896$	−1.45229e12	−0.0752780
$897$	−1.86324e11	−0.00960956
$898$	9.45022e12	0.484951
$899$	8.60723e11	0.0439486
$900$	5.35224e12	0.271922
$901$	4.91269e12	0.248346
$902$	5.20557e11	0.0261842
$903$	−1.33526e13	−0.668298
$904$	−4.24339e11	−0.0211327
$905$	3.24354e13	1.60731
$906$	1.69693e13	0.836733
$907$	−1.84102e13	−0.903286	−0.451643	−	0.892199i	$-0.649162\pi$
$907$	−1.84102e13	−0.903286	−0.451643	+	0.892199i	$0.649162\pi$
$908$	−9.31057e12	−0.454559
$909$	−9.93607e12	−0.482700
$910$	2.04932e12	0.0990659
$911$	2.95844e13	1.42308	0.711542	−	0.702644i	$-0.247997\pi$
$911$	2.95844e13	1.42308	0.711542	+	0.702644i	$0.247997\pi$
$912$	−7.20693e12	−0.344964
$913$	−4.04325e12	−0.192581
$914$	4.98752e13	2.36389
$915$	−6.53789e12	−0.308349
$916$	1.55153e13	0.728168
$917$	2.18151e13	1.01881
$918$	5.20991e12	0.242124
$919$	2.24233e13	1.03700	0.518501	−	0.855077i	$-0.326490\pi$
$919$	2.24233e13	1.03700	0.518501	+	0.855077i	$0.326490\pi$
$920$	3.53884e11	0.0162860
$921$	1.31825e13	0.603712
$922$	3.25101e13	1.48159
$923$	−5.56963e9	−0.000252591 0
$924$	−8.55825e12	−0.386244
$925$	−4.82486e11	−0.0216694
$926$	1.10335e13	0.493131
$927$	−6.69919e12	−0.297964
$928$	−8.91866e12	−0.394760
$929$	2.64278e13	1.16410	0.582050	−	0.813153i	$-0.302251\pi$
$929$	2.64278e13	1.16410	0.582050	+	0.813153i	$0.302251\pi$
$930$	−3.93597e12	−0.172535
$931$	3.69187e13	1.61054
$932$	−3.44299e13	−1.49473
$933$	−9.94029e11	−0.0429469
$934$	−1.74052e13	−0.748372
$935$	−9.90238e12	−0.423728
$936$	4.10536e9	0.000174828 0
$937$	4.85245e12	0.205652	0.102826	−	0.994699i	$-0.467212\pi$
$937$	4.85245e12	0.205652	0.102826	+	0.994699i	$0.467212\pi$
$938$	4.11514e13	1.73569
$939$	−1.35448e13	−0.568560
$940$	−2.36033e12	−0.0986045
$941$	2.17271e13	0.903336	0.451668	−	0.892186i	$-0.350829\pi$
$941$	2.17271e13	0.903336	0.451668	+	0.892186i	$0.350829\pi$
$942$	−2.67827e13	−1.10822
$943$	−7.94469e11	−0.0327171
$944$	−3.21980e12	−0.131964
$945$	−1.23208e13	−0.502570
$946$	−7.30378e12	−0.296509
$947$	2.12970e13	0.860486	0.430243	−	0.902713i	$-0.358428\pi$
$947$	2.12970e13	0.860486	0.430243	+	0.902713i	$0.358428\pi$
$948$	−1.41808e13	−0.570248
$949$	1.19663e12	0.0478920
$950$	−1.72516e13	−0.687185
$951$	−2.08833e13	−0.827915
$952$	−8.51642e11	−0.0336040
$953$	−8.67033e11	−0.0340500	−0.0170250	−	0.999855i	$-0.505419\pi$
$953$	−8.67033e11	−0.0340500	−0.0170250	+	0.999855i	$0.505419\pi$
$954$	3.34350e12	0.130687
$955$	4.99057e13	1.94149
$956$	−4.02475e13	−1.55840
$957$	1.47378e12	0.0567977
$958$	1.19540e13	0.458532
$959$	−1.15643e13	−0.441506
$960$	1.99660e13	0.758701
$961$	−2.57890e13	−0.975392
$962$	2.63978e10	0.000993758 0
$963$	5.53464e12	0.207382
$964$	−1.59978e13	−0.596641
$965$	4.24171e13	1.57459
$966$	2.63061e13	0.971986
$967$	−4.69969e12	−0.172842	−0.0864212	−	0.996259i	$-0.527543\pi$
$967$	−4.69969e12	−0.172842	−0.0864212	+	0.996259i	$0.527543\pi$
$968$	−4.66642e11	−0.0170823
$969$	−8.33797e12	−0.303811
$970$	5.50277e13	1.99576
$971$	4.65362e13	1.67998	0.839990	−	0.542602i	$-0.182561\pi$
$971$	4.65362e13	1.67998	0.839990	+	0.542602i	$0.182561\pi$
$972$	1.76055e12	0.0632631
$973$	−4.83678e13	−1.73001
$974$	6.26165e13	2.22933
$975$	3.62751e11	0.0128555
$976$	−1.13531e13	−0.400489
$977$	−6.68165e12	−0.234616	−0.117308	−	0.993096i	$-0.537427\pi$
$977$	−6.68165e12	−0.234616	−0.117308	+	0.993096i	$0.537427\pi$
$978$	−1.63035e13	−0.569842
$979$	−9.00100e12	−0.313162
$980$	−1.05168e14	−3.64222
$981$	−1.64216e13	−0.566115
$982$	4.48313e13	1.53844
$983$	−4.01992e13	−1.37318	−0.686589	−	0.727046i	$-0.740893\pi$
$983$	−4.01992e13	−1.37318	−0.686589	+	0.727046i	$0.740893\pi$
$984$	1.75049e10	0.000595225 0
$985$	−4.76914e13	−1.61427
$986$	−1.04610e13	−0.352474
$987$	2.45981e12	0.0825038
$988$	4.68651e11	0.0156475
$989$	1.11470e13	0.370487
$990$	−6.73942e12	−0.222979
$991$	1.10880e13	0.365191	0.182596	−	0.983188i	$-0.441550\pi$
$991$	1.10880e13	0.365191	0.182596	+	0.983188i	$0.441550\pi$
$992$	−6.74163e12	−0.221036
$993$	2.26591e13	0.739555
$994$	7.86346e11	0.0255491
$995$	−3.00840e13	−0.973042
$996$	9.69816e12	0.312264
$997$	−4.99784e13	−1.60197	−0.800985	−	0.598685i	$-0.795690\pi$
$997$	−4.99784e13	−1.60197	−0.800985	+	0.598685i	$0.795690\pi$
$998$	3.86325e13	1.23272
$999$	−1.58708e11	−0.00504142

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.4	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-31.8892 q^{2} +81.0000 q^{3} +504.921 q^{4} -1889.12 q^{5} -2583.03 q^{6} +12272.3 q^{7} +225.735 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-31.8892 q^{2} +81.0000 q^{3} +504.921 q^{4} -1889.12 q^{5} -2583.03 q^{6} +12272.3 q^{7} +225.735 q^{8} +6561.00 q^{9} +60242.4 q^{10} -17051.0 q^{11} +40898.6 q^{12} +2771.93 q^{13} -391354. q^{14} -153018. q^{15} -265718. q^{16} -307419. q^{17} -209225. q^{18} +334845. q^{19} -953854. q^{20} +994057. q^{21} +543743. q^{22} -829855. q^{23} +18284.6 q^{24} +1.61563e6 q^{25} -88394.6 q^{26} +531441. q^{27} +6.19655e6 q^{28} -1.06708e6 q^{29} +4.87963e6 q^{30} -806611. q^{31} +8.35797e6 q^{32} -1.38113e6 q^{33} +9.80336e6 q^{34} -2.31838e7 q^{35} +3.31279e6 q^{36} -298636. q^{37} -1.06780e7 q^{38} +224526. q^{39} -426440. q^{40} +957358. q^{41} -3.16997e7 q^{42} -1.34324e7 q^{43} -8.60942e6 q^{44} -1.23945e7 q^{45} +2.64634e7 q^{46} +2.47451e6 q^{47} -2.15232e7 q^{48} +1.10256e8 q^{49} -5.15212e7 q^{50} -2.49010e7 q^{51} +1.39961e6 q^{52} -1.59804e7 q^{53} -1.69472e7 q^{54} +3.22113e7 q^{55} +2.77029e6 q^{56} +2.71225e7 q^{57} +3.40285e7 q^{58} +1.21174e7 q^{59} -7.72622e7 q^{60} +4.27262e7 q^{61} +2.57222e7 q^{62} +8.05186e7 q^{63} -1.30481e8 q^{64} -5.23649e6 q^{65} +4.40432e7 q^{66} -1.05151e8 q^{67} -1.55223e8 q^{68} -6.72183e7 q^{69} +7.39313e8 q^{70} -2.00930e6 q^{71} +1.48105e6 q^{72} +4.31697e8 q^{73} +9.52327e6 q^{74} +1.30866e8 q^{75} +1.69071e8 q^{76} -2.09255e8 q^{77} -7.15996e6 q^{78} -3.46731e8 q^{79} +5.01972e8 q^{80} +4.30467e7 q^{81} -3.05294e7 q^{82} +2.37127e8 q^{83} +5.01920e8 q^{84} +5.80750e8 q^{85} +4.28349e8 q^{86} -8.64338e7 q^{87} -3.84902e6 q^{88} +5.27887e8 q^{89} +3.95250e8 q^{90} +3.40180e7 q^{91} -4.19012e8 q^{92} -6.53355e7 q^{93} -7.89103e7 q^{94} -6.32561e8 q^{95} +6.76995e8 q^{96} +9.13439e8 q^{97} -3.51597e9 q^{98} -1.11872e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) \) 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

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