LMFDB - Embedded newform 177.10.a.a.1.1

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			1.1
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)

$f(q)$	$=$	$q-43.9134 q^{2} +81.0000 q^{3} +1416.39 q^{4} -993.635 q^{5} -3556.99 q^{6} +3425.90 q^{7} -39714.8 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-43.9134 q^{2} +81.0000 q^{3} +1416.39 q^{4} -993.635 q^{5} -3556.99 q^{6} +3425.90 q^{7} -39714.8 q^{8} +6561.00 q^{9} +43633.9 q^{10} -75091.5 q^{11} +114727. q^{12} +66893.5 q^{13} -150443. q^{14} -80484.4 q^{15} +1.01882e6 q^{16} +199427. q^{17} -288116. q^{18} +79861.8 q^{19} -1.40737e6 q^{20} +277498. q^{21} +3.29753e6 q^{22} +2.06317e6 q^{23} -3.21690e6 q^{24} -965814. q^{25} -2.93752e6 q^{26} +531441. q^{27} +4.85241e6 q^{28} -5.68682e6 q^{29} +3.53435e6 q^{30} +1.44520e6 q^{31} -2.44059e7 q^{32} -6.08241e6 q^{33} -8.75750e6 q^{34} -3.40410e6 q^{35} +9.29292e6 q^{36} -6.74414e6 q^{37} -3.50700e6 q^{38} +5.41837e6 q^{39} +3.94620e7 q^{40} -3.10309e7 q^{41} -1.21859e7 q^{42} +3.99027e7 q^{43} -1.06359e8 q^{44} -6.51924e6 q^{45} -9.06009e7 q^{46} +1.76289e7 q^{47} +8.25245e7 q^{48} -2.86168e7 q^{49} +4.24122e7 q^{50} +1.61536e7 q^{51} +9.47471e7 q^{52} +9.14817e7 q^{53} -2.33374e7 q^{54} +7.46136e7 q^{55} -1.36059e8 q^{56} +6.46880e6 q^{57} +2.49728e8 q^{58} +1.21174e7 q^{59} -1.13997e8 q^{60} -3.45269e7 q^{61} -6.34637e7 q^{62} +2.24773e7 q^{63} +5.50112e8 q^{64} -6.64677e7 q^{65} +2.67100e8 q^{66} +4.20121e7 q^{67} +2.82465e8 q^{68} +1.67117e8 q^{69} +1.49485e8 q^{70} +2.88238e8 q^{71} -2.60569e8 q^{72} -4.61767e8 q^{73} +2.96158e8 q^{74} -7.82309e7 q^{75} +1.13115e8 q^{76} -2.57256e8 q^{77} -2.37939e8 q^{78} -3.32943e6 q^{79} -1.01234e9 q^{80} +4.30467e7 q^{81} +1.36267e9 q^{82} +4.97533e8 q^{83} +3.93045e8 q^{84} -1.98157e8 q^{85} -1.75226e9 q^{86} -4.60632e8 q^{87} +2.98224e9 q^{88} +5.53405e8 q^{89} +2.86282e8 q^{90} +2.29170e8 q^{91} +2.92225e9 q^{92} +1.17061e8 q^{93} -7.74147e8 q^{94} -7.93535e7 q^{95} -1.97688e9 q^{96} -4.40860e8 q^{97} +1.25666e9 q^{98} -4.92675e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−43.9134	−1.94072	−0.970359	−	0.241670i	$-0.922305\pi$
$2$	−43.9134	−1.94072	−0.970359	+	0.241670i	$0.922305\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	1416.39	2.76638
$5$	−993.635	−0.710987	−0.355494	−	0.934679i	$-0.615687\pi$
$5$	−993.635	−0.710987	−0.355494	+	0.934679i	$0.615687\pi$
$6$	−3556.99	−1.12047
$7$	3425.90	0.539304	0.269652	−	0.962958i	$-0.413091\pi$
$7$	3425.90	0.539304	0.269652	+	0.962958i	$0.413091\pi$
$8$	−39714.8	−3.42805
$9$	6561.00	0.333333
$10$	43633.9	1.37983
$11$	−75091.5	−1.54641	−0.773204	−	0.634158i	$-0.781347\pi$
$11$	−75091.5	−1.54641	−0.773204	+	0.634158i	$0.781347\pi$
$12$	114727.	1.59717
$13$	66893.5	0.649589	0.324794	−	0.945785i	$-0.394705\pi$
$13$	66893.5	0.649589	0.324794	+	0.945785i	$0.394705\pi$
$14$	−150443.	−1.04664
$15$	−80484.4	−0.410489
$16$	1.01882e6	3.88649
$17$	199427.	0.579112	0.289556	−	0.957161i	$-0.406492\pi$
$17$	199427.	0.579112	0.289556	+	0.957161i	$0.406492\pi$
$18$	−288116.	−0.646906
$19$	79861.8	0.140588	0.0702939	−	0.997526i	$-0.477606\pi$
$19$	79861.8	0.140588	0.0702939	+	0.997526i	$0.477606\pi$
$20$	−1.40737e6	−1.96686
$21$	277498.	0.311367
$22$	3.29753e6	3.00114
$23$	2.06317e6	1.53731	0.768653	−	0.639666i	$-0.220928\pi$
$23$	2.06317e6	1.53731	0.768653	+	0.639666i	$0.220928\pi$
$24$	−3.21690e6	−1.97919
$25$	−965814.	−0.494497
$26$	−2.93752e6	−1.26067
$27$	531441.	0.192450
$28$	4.85241e6	1.49192
$29$	−5.68682e6	−1.49306	−0.746532	−	0.665349i	$-0.768283\pi$
$29$	−5.68682e6	−1.49306	−0.746532	+	0.665349i	$0.768283\pi$
$30$	3.53435e6	0.796643
$31$	1.44520e6	0.281061	0.140531	−	0.990076i	$-0.455119\pi$
$31$	1.44520e6	0.281061	0.140531	+	0.990076i	$0.455119\pi$
$32$	−2.44059e7	−4.11453
$33$	−6.08241e6	−0.892819
$34$	−8.75750e6	−1.12389
$35$	−3.40410e6	−0.383438
$36$	9.29292e6	0.922128
$37$	−6.74414e6	−0.591588	−0.295794	−	0.955252i	$-0.595584\pi$
$37$	−6.74414e6	−0.591588	−0.295794	+	0.955252i	$0.595584\pi$
$38$	−3.50700e6	−0.272841
$39$	5.41837e6	0.375040
$40$	3.94620e7	2.43730
$41$	−3.10309e7	−1.71501	−0.857507	−	0.514472i	$-0.827988\pi$
$41$	−3.10309e7	−1.71501	−0.857507	+	0.514472i	$0.827988\pi$
$42$	−1.21859e7	−0.604276
$43$	3.99027e7	1.77989	0.889947	−	0.456065i	$-0.150741\pi$
$43$	3.99027e7	1.77989	0.889947	+	0.456065i	$0.150741\pi$
$44$	−1.06359e8	−4.27795
$45$	−6.51924e6	−0.236996
$46$	−9.06009e7	−2.98347
$47$	1.76289e7	0.526970	0.263485	−	0.964663i	$-0.415128\pi$
$47$	1.76289e7	0.526970	0.263485	+	0.964663i	$0.415128\pi$
$48$	8.25245e7	2.24387
$49$	−2.86168e7	−0.709151
$50$	4.24122e7	0.959678
$51$	1.61536e7	0.334351
$52$	9.47471e7	1.79701
$53$	9.14817e7	1.59255	0.796274	−	0.604936i	$-0.206801\pi$
$53$	9.14817e7	1.59255	0.796274	+	0.604936i	$0.206801\pi$
$54$	−2.33374e7	−0.373491
$55$	7.46136e7	1.09948
$56$	−1.36059e8	−1.84876
$57$	6.46880e6	0.0811684
$58$	2.49728e8	2.89762
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−1.13997e8	−1.13557
$61$	−3.45269e7	−0.319281	−0.159640	−	0.987175i	$-0.551033\pi$
$61$	−3.45269e7	−0.319281	−0.159640	+	0.987175i	$0.551033\pi$
$62$	−6.34637e7	−0.545460
$63$	2.24773e7	0.179768
$64$	5.50112e8	4.09865
$65$	−6.64677e7	−0.461850
$66$	2.67100e8	1.73271
$67$	4.20121e7	0.254705	0.127353	−	0.991857i	$-0.459352\pi$
$67$	4.20121e7	0.254705	0.127353	+	0.991857i	$0.459352\pi$
$68$	2.82465e8	1.60205
$69$	1.67117e8	0.887564
$70$	1.49485e8	0.744145
$71$	2.88238e8	1.34613	0.673067	−	0.739582i	$-0.264977\pi$
$71$	2.88238e8	1.34613	0.673067	+	0.739582i	$0.264977\pi$
$72$	−2.60569e8	−1.14268
$73$	−4.61767e8	−1.90313	−0.951567	−	0.307440i	$-0.900528\pi$
$73$	−4.61767e8	−1.90313	−0.951567	+	0.307440i	$0.900528\pi$
$74$	2.96158e8	1.14810
$75$	−7.82309e7	−0.285498
$76$	1.13115e8	0.388920
$77$	−2.57256e8	−0.833984
$78$	−2.37939e8	−0.727847
$79$	−3.32943e6	−0.00961718	−0.00480859	−	0.999988i	$-0.501531\pi$
$79$	−3.32943e6	−0.00961718	−0.00480859	+	0.999988i	$0.501531\pi$
$80$	−1.01234e9	−2.76325
$81$	4.30467e7	0.111111
$82$	1.36267e9	3.32836
$83$	4.97533e8	1.15072	0.575361	−	0.817900i	$-0.304862\pi$
$83$	4.97533e8	1.15072	0.575361	+	0.817900i	$0.304862\pi$
$84$	3.93045e8	0.861361
$85$	−1.98157e8	−0.411742
$86$	−1.75226e9	−3.45427
$87$	−4.60632e8	−0.862021
$88$	2.98224e9	5.30116
$89$	5.53405e8	0.934949	0.467474	−	0.884007i	$-0.345164\pi$
$89$	5.53405e8	0.934949	0.467474	+	0.884007i	$0.345164\pi$
$90$	2.86282e8	0.459942
$91$	2.29170e8	0.350326
$92$	2.92225e9	4.25278
$93$	1.17061e8	0.162271
$94$	−7.74147e8	−1.02270
$95$	−7.93535e7	−0.0999562
$96$	−1.97688e9	−2.37553
$97$	−4.40860e8	−0.505624	−0.252812	−	0.967515i	$-0.581355\pi$
$97$	−4.40860e8	−0.505624	−0.252812	+	0.967515i	$0.581355\pi$
$98$	1.25666e9	1.37626
$99$	−4.92675e8	−0.515469
$100$	−1.36797e9	−1.36797
$101$	−1.27590e7	−0.0122003	−0.00610017	−	0.999981i	$-0.501942\pi$
$101$	−1.27590e7	−0.0122003	−0.00610017	+	0.999981i	$0.501942\pi$
$102$	−7.09358e8	−0.648880
$103$	−3.19147e8	−0.279398	−0.139699	−	0.990194i	$-0.544613\pi$
$103$	−3.19147e8	−0.279398	−0.139699	+	0.990194i	$0.544613\pi$
$104$	−2.65666e9	−2.22682
$105$	−2.75732e8	−0.221378
$106$	−4.01727e9	−3.09069
$107$	−1.82659e9	−1.34715	−0.673573	−	0.739121i	$-0.735241\pi$
$107$	−1.82659e9	−1.34715	−0.673573	+	0.739121i	$0.735241\pi$
$108$	7.52727e8	0.532391
$109$	−1.41497e9	−0.960125	−0.480062	−	0.877234i	$-0.659386\pi$
$109$	−1.41497e9	−0.960125	−0.480062	+	0.877234i	$0.659386\pi$
$110$	−3.27654e9	−2.13377
$111$	−5.46276e8	−0.341553
$112$	3.49038e9	2.09600
$113$	−9.45147e8	−0.545314	−0.272657	−	0.962111i	$-0.587902\pi$
$113$	−9.45147e8	−0.545314	−0.272657	+	0.962111i	$0.587902\pi$
$114$	−2.84067e8	−0.157525
$115$	−2.05004e9	−1.09300
$116$	−8.05474e9	−4.13039
$117$	4.38888e8	0.216530
$118$	−5.32115e8	−0.252660
$119$	6.83216e8	0.312318
$120$	3.19642e9	1.40718
$121$	3.28079e9	1.39137
$122$	1.51619e9	0.619634
$123$	−2.51351e9	−0.990164
$124$	2.04697e9	0.777523
$125$	2.90036e9	1.06257
$126$	−9.87057e8	−0.348879
$127$	1.86091e9	0.634758	0.317379	−	0.948299i	$-0.397197\pi$
$127$	1.86091e9	0.634758	0.317379	+	0.948299i	$0.397197\pi$
$128$	−1.16614e10	−3.83979
$129$	3.23212e9	1.02762
$130$	2.91882e9	0.896319
$131$	−4.14751e9	−1.23046	−0.615228	−	0.788349i	$-0.710936\pi$
$131$	−4.14751e9	−1.23046	−0.615228	+	0.788349i	$0.710936\pi$
$132$	−8.61506e9	−2.46988
$133$	2.73599e8	0.0758196
$134$	−1.84490e9	−0.494311
$135$	−5.28058e8	−0.136830
$136$	−7.92018e9	−1.98523
$137$	−4.07295e9	−0.987794	−0.493897	−	0.869521i	$-0.664428\pi$
$137$	−4.07295e9	−0.987794	−0.493897	+	0.869521i	$0.664428\pi$
$138$	−7.33867e9	−1.72251
$139$	5.43583e9	1.23509	0.617546	−	0.786535i	$-0.288127\pi$
$139$	5.43583e9	1.23509	0.617546	+	0.786535i	$0.288127\pi$
$140$	−4.82152e9	−1.06074
$141$	1.42794e9	0.304246
$142$	−1.26575e10	−2.61246
$143$	−5.02313e9	−1.00453
$144$	6.68448e9	1.29550
$145$	5.65062e9	1.06155
$146$	2.02777e10	3.69345
$147$	−2.31796e9	−0.409429
$148$	−9.55233e9	−1.63656
$149$	1.22909e8	0.0204289	0.0102145	−	0.999948i	$-0.496749\pi$
$149$	1.22909e8	0.0204289	0.0102145	+	0.999948i	$0.496749\pi$
$150$	3.43539e9	0.554071
$151$	9.58481e9	1.50033	0.750166	−	0.661250i	$-0.229974\pi$
$151$	9.58481e9	1.50033	0.750166	+	0.661250i	$0.229974\pi$
$152$	−3.17169e9	−0.481942
$153$	1.30844e9	0.193037
$154$	1.12970e10	1.61853
$155$	−1.43600e9	−0.199831
$156$	7.67452e9	1.03751
$157$	6.23709e9	0.819283	0.409641	−	0.912247i	$-0.365654\pi$
$157$	6.23709e9	0.819283	0.409641	+	0.912247i	$0.365654\pi$
$158$	1.46207e8	0.0186642
$159$	7.41001e9	0.919458
$160$	2.42506e10	2.92538
$161$	7.06822e9	0.829075
$162$	−1.89033e9	−0.215635
$163$	−1.19932e10	−1.33073	−0.665366	−	0.746517i	$-0.731725\pi$
$163$	−1.19932e10	−1.33073	−0.665366	+	0.746517i	$0.731725\pi$
$164$	−4.39519e10	−4.74439
$165$	6.04370e9	0.634783
$166$	−2.18484e10	−2.23323
$167$	−1.20055e9	−0.119442	−0.0597209	−	0.998215i	$-0.519021\pi$
$167$	−1.20055e9	−0.119442	−0.0597209	+	0.998215i	$0.519021\pi$
$168$	−1.10208e10	−1.06738
$169$	−6.12976e9	−0.578034
$170$	8.70176e9	0.799074
$171$	5.23973e8	0.0468626
$172$	5.65177e10	4.92387
$173$	−7.45260e8	−0.0632558	−0.0316279	−	0.999500i	$-0.510069\pi$
$173$	−7.45260e8	−0.0632558	−0.0316279	+	0.999500i	$0.510069\pi$
$174$	2.02279e10	1.67294
$175$	−3.30878e9	−0.266684
$176$	−7.65048e10	−6.01010
$177$	9.81506e8	0.0751646
$178$	−2.43019e10	−1.81447
$179$	−7.16883e9	−0.521927	−0.260963	−	0.965349i	$-0.584040\pi$
$179$	−7.16883e9	−0.521927	−0.260963	+	0.965349i	$0.584040\pi$
$180$	−9.23377e9	−0.655621
$181$	1.17303e9	0.0812376	0.0406188	−	0.999175i	$-0.487067\pi$
$181$	1.17303e9	0.0812376	0.0406188	+	0.999175i	$0.487067\pi$
$182$	−1.00637e10	−0.679883
$183$	−2.79668e9	−0.184337
$184$	−8.19384e10	−5.26996
$185$	6.70122e9	0.420611
$186$	−5.14056e9	−0.314921
$187$	−1.49752e10	−0.895544
$188$	2.49694e10	1.45780
$189$	1.82066e9	0.103789
$190$	3.48468e9	0.193987
$191$	4.15563e9	0.225936	0.112968	−	0.993599i	$-0.463964\pi$
$191$	4.15563e9	0.225936	0.112968	+	0.993599i	$0.463964\pi$
$192$	4.45590e10	2.36636
$193$	−2.61187e10	−1.35501	−0.677506	−	0.735517i	$-0.736939\pi$
$193$	−2.61187e10	−1.35501	−0.677506	+	0.735517i	$0.736939\pi$
$194$	1.93597e10	0.981273
$195$	−5.38388e9	−0.266649
$196$	−4.05325e10	−1.96178
$197$	−2.92561e10	−1.38394	−0.691972	−	0.721925i	$-0.743258\pi$
$197$	−2.92561e10	−1.38394	−0.691972	+	0.721925i	$0.743258\pi$
$198$	2.16351e10	1.00038
$199$	−1.80017e10	−0.813721	−0.406861	−	0.913490i	$-0.633377\pi$
$199$	−1.80017e10	−0.813721	−0.406861	+	0.913490i	$0.633377\pi$
$200$	3.83571e10	1.69516
$201$	3.40298e9	0.147054
$202$	5.60293e8	0.0236774
$203$	−1.94825e10	−0.805216
$204$	2.28797e10	0.924942
$205$	3.08334e10	1.21935
$206$	1.40148e10	0.542232
$207$	1.35365e10	0.512435
$208$	6.81524e10	2.52462
$209$	−5.99694e9	−0.217406
$210$	1.21083e10	0.429633
$211$	−1.97777e10	−0.686919	−0.343459	−	0.939168i	$-0.611599\pi$
$211$	−1.97777e10	−0.686919	−0.343459	+	0.939168i	$0.611599\pi$
$212$	1.29574e11	4.40560
$213$	2.33472e10	0.777190
$214$	8.02119e10	2.61443
$215$	−3.96487e10	−1.26548
$216$	−2.11061e10	−0.659729
$217$	4.95112e9	0.151577
$218$	6.21361e10	1.86333
$219$	−3.74031e10	−1.09878
$220$	1.05682e11	3.04157
$221$	1.33403e10	0.376185
$222$	2.39888e10	0.662858
$223$	−5.70225e10	−1.54410	−0.772048	−	0.635565i	$-0.780767\pi$
$223$	−5.70225e10	−1.54410	−0.772048	+	0.635565i	$0.780767\pi$
$224$	−8.36123e10	−2.21898
$225$	−6.33671e9	−0.164832
$226$	4.15046e10	1.05830
$227$	1.51234e10	0.378035	0.189018	−	0.981974i	$-0.439470\pi$
$227$	1.51234e10	0.378035	0.189018	+	0.981974i	$0.439470\pi$
$228$	9.16234e9	0.224543
$229$	−1.70590e10	−0.409915	−0.204958	−	0.978771i	$-0.565706\pi$
$229$	−1.70590e10	−0.409915	−0.204958	+	0.978771i	$0.565706\pi$
$230$	9.00243e10	2.12121
$231$	−2.08377e10	−0.481501
$232$	2.25851e11	5.11830
$233$	−1.69879e10	−0.377605	−0.188802	−	0.982015i	$-0.560461\pi$
$233$	−1.69879e10	−0.377605	−0.188802	+	0.982015i	$0.560461\pi$
$234$	−1.92731e10	−0.420223
$235$	−1.75167e10	−0.374669
$236$	1.71629e10	0.360152
$237$	−2.69684e8	−0.00555248
$238$	−3.00023e10	−0.606120
$239$	6.50543e10	1.28969	0.644845	−	0.764314i	$-0.276922\pi$
$239$	6.50543e10	1.28969	0.644845	+	0.764314i	$0.276922\pi$
$240$	−8.19992e10	−1.59536
$241$	−1.97716e10	−0.377542	−0.188771	−	0.982021i	$-0.560450\pi$
$241$	−1.97716e10	−0.377542	−0.188771	+	0.982021i	$0.560450\pi$
$242$	−1.44071e11	−2.70026
$243$	3.48678e9	0.0641500
$244$	−4.89034e10	−0.883253
$245$	2.84347e10	0.504198
$246$	1.10377e11	1.92163
$247$	5.34223e9	0.0913243
$248$	−5.73958e10	−0.963491
$249$	4.03002e10	0.664370
$250$	−1.27365e11	−2.06214
$251$	−5.38268e10	−0.855987	−0.427993	−	0.903782i	$-0.640779\pi$
$251$	−5.38268e10	−0.855987	−0.427993	+	0.903782i	$0.640779\pi$
$252$	3.18366e10	0.497307
$253$	−1.54927e11	−2.37730
$254$	−8.17189e10	−1.23189
$255$	−1.60507e10	−0.237719
$256$	2.30437e11	3.35330
$257$	−1.17069e11	−1.67396	−0.836978	−	0.547236i	$-0.815680\pi$
$257$	−1.17069e11	−1.67396	−0.836978	+	0.547236i	$0.815680\pi$
$258$	−1.41933e11	−1.99432
$259$	−2.31048e10	−0.319046
$260$	−9.41441e10	−1.27765
$261$	−3.73112e10	−0.497688
$262$	1.82131e11	2.38797
$263$	2.07653e10	0.267631	0.133816	−	0.991006i	$-0.457277\pi$
$263$	2.07653e10	0.267631	0.133816	+	0.991006i	$0.457277\pi$
$264$	2.41562e11	3.06063
$265$	−9.08994e10	−1.13228
$266$	−1.20146e10	−0.147144
$267$	4.48258e10	0.539793
$268$	5.95055e10	0.704613
$269$	−1.57983e11	−1.83961	−0.919805	−	0.392375i	$-0.871654\pi$
$269$	−1.57983e11	−1.83961	−0.919805	+	0.392375i	$0.871654\pi$
$270$	2.31889e10	0.265548
$271$	−7.82662e10	−0.881480	−0.440740	−	0.897635i	$-0.645284\pi$
$271$	−7.82662e10	−0.881480	−0.440740	+	0.897635i	$0.645284\pi$
$272$	2.03180e11	2.25072
$273$	1.85628e10	0.202261
$274$	1.78857e11	1.91703
$275$	7.25245e10	0.764693
$276$	2.36702e11	2.45534
$277$	1.45137e11	1.48122	0.740611	−	0.671934i	$-0.234536\pi$
$277$	1.45137e11	1.48122	0.740611	+	0.671934i	$0.234536\pi$
$278$	−2.38706e11	−2.39696
$279$	9.48196e9	0.0936870
$280$	1.35193e11	1.31445
$281$	−9.06795e10	−0.867622	−0.433811	−	0.901004i	$-0.642831\pi$
$281$	−9.06795e10	−0.867622	−0.433811	+	0.901004i	$0.642831\pi$
$282$	−6.27059e10	−0.590456
$283$	6.43589e10	0.596444	0.298222	−	0.954497i	$-0.403607\pi$
$283$	6.43589e10	0.596444	0.298222	+	0.954497i	$0.403607\pi$
$284$	4.08256e11	3.72392
$285$	−6.42763e9	−0.0577097
$286$	2.20583e11	1.94951
$287$	−1.06309e11	−0.924914
$288$	−1.60127e11	−1.37151
$289$	−7.88169e10	−0.664629
$290$	−2.48138e11	−2.06017
$291$	−3.57097e10	−0.291922
$292$	−6.54041e11	−5.26480
$293$	−2.18801e11	−1.73438	−0.867190	−	0.497977i	$-0.834076\pi$
$293$	−2.18801e11	−1.73438	−0.867190	+	0.497977i	$0.834076\pi$
$294$	1.01790e11	0.794585
$295$	−1.20402e10	−0.0925627
$296$	2.67842e11	2.02799
$297$	−3.99067e10	−0.297606
$298$	−5.39736e9	−0.0396468
$299$	1.38013e11	0.998616
$300$	−1.10805e11	−0.789797
$301$	1.36703e11	0.959904
$302$	−4.20902e11	−2.91172
$303$	−1.03348e9	−0.00704386
$304$	8.13648e10	0.546393
$305$	3.43071e10	0.227005
$306$	−5.74580e10	−0.374631
$307$	−2.89373e10	−0.185924	−0.0929618	−	0.995670i	$-0.529633\pi$
$307$	−2.89373e10	−0.185924	−0.0929618	+	0.995670i	$0.529633\pi$
$308$	−3.64375e11	−2.30712
$309$	−2.58509e10	−0.161310
$310$	6.30598e10	0.387815
$311$	−7.72235e10	−0.468088	−0.234044	−	0.972226i	$-0.575196\pi$
$311$	−7.72235e10	−0.468088	−0.234044	+	0.972226i	$0.575196\pi$
$312$	−2.15189e11	−1.28566
$313$	1.62389e11	0.956330	0.478165	−	0.878270i	$-0.341302\pi$
$313$	1.62389e11	0.956330	0.478165	+	0.878270i	$0.341302\pi$
$314$	−2.73892e11	−1.59000
$315$	−2.23343e10	−0.127813
$316$	−4.71576e9	−0.0266048
$317$	−3.15230e10	−0.175332	−0.0876660	−	0.996150i	$-0.527941\pi$
$317$	−3.15230e10	−0.175332	−0.0876660	+	0.996150i	$0.527941\pi$
$318$	−3.25399e11	−1.78441
$319$	4.27032e11	2.30888
$320$	−5.46610e11	−2.91409
$321$	−1.47954e11	−0.777775
$322$	−3.10390e11	−1.60900
$323$	1.59266e10	0.0814162
$324$	6.09709e10	0.307376
$325$	−6.46066e10	−0.321220
$326$	5.26662e11	2.58257
$327$	−1.14612e11	−0.554328
$328$	1.23239e12	5.87915
$329$	6.03950e10	0.284197
$330$	−2.65399e11	−1.23193
$331$	1.25675e11	0.575468	0.287734	−	0.957710i	$-0.407098\pi$
$331$	1.25675e11	0.575468	0.287734	+	0.957710i	$0.407098\pi$
$332$	7.04700e11	3.18334
$333$	−4.42483e10	−0.197196
$334$	5.27203e10	0.231803
$335$	−4.17447e10	−0.181092
$336$	2.82721e11	1.21013
$337$	7.04245e9	0.0297433	0.0148717	−	0.999889i	$-0.495266\pi$
$337$	7.04245e9	0.0297433	0.0148717	+	0.999889i	$0.495266\pi$
$338$	2.69179e11	1.12180
$339$	−7.65569e10	−0.314837
$340$	−2.80668e11	−1.13904
$341$	−1.08522e11	−0.434635
$342$	−2.30094e10	−0.0909471
$343$	−2.36286e11	−0.921752
$344$	−1.58473e12	−6.10156
$345$	−1.66053e11	−0.631047
$346$	3.27269e10	0.122762
$347$	6.16137e10	0.228136	0.114068	−	0.993473i	$-0.463612\pi$
$347$	6.16137e10	0.228136	0.114068	+	0.993473i	$0.463612\pi$
$348$	−6.52434e11	−2.38468
$349$	−3.69141e11	−1.33192	−0.665960	−	0.745988i	$-0.731978\pi$
$349$	−3.69141e11	−1.33192	−0.665960	+	0.745988i	$0.731978\pi$
$350$	1.45300e11	0.517558
$351$	3.55499e10	0.125013
$352$	1.83268e12	6.36274
$353$	−8.47433e10	−0.290482	−0.145241	−	0.989396i	$-0.546396\pi$
$353$	−8.47433e10	−0.290482	−0.145241	+	0.989396i	$0.546396\pi$
$354$	−4.31013e10	−0.145873
$355$	−2.86403e11	−0.957084
$356$	7.83836e11	2.58643
$357$	5.53405e10	0.180317
$358$	3.14808e11	1.01291
$359$	−4.96385e11	−1.57722	−0.788612	−	0.614891i	$-0.789200\pi$
$359$	−4.96385e11	−1.57722	−0.788612	+	0.614891i	$0.789200\pi$
$360$	2.58910e11	0.812434
$361$	−3.16310e11	−0.980235
$362$	−5.15119e10	−0.157659
$363$	2.65744e11	0.803311
$364$	3.24594e11	0.969136
$365$	4.58827e11	1.35311
$366$	1.22812e11	0.357746
$367$	3.02132e10	0.0869359	0.0434680	−	0.999055i	$-0.486159\pi$
$367$	3.02132e10	0.0869359	0.0434680	+	0.999055i	$0.486159\pi$
$368$	2.10200e12	5.97472
$369$	−2.03594e11	−0.571671
$370$	−2.94273e11	−0.816288
$371$	3.13407e11	0.858868
$372$	1.65804e11	0.448903
$373$	−9.04302e10	−0.241893	−0.120947	−	0.992659i	$-0.538593\pi$
$373$	−9.04302e10	−0.241893	−0.120947	+	0.992659i	$0.538593\pi$
$374$	6.57614e11	1.73800
$375$	2.34929e11	0.613474
$376$	−7.00130e11	−1.80648
$377$	−3.80411e11	−0.969878
$378$	−7.99516e10	−0.201425
$379$	−2.02163e11	−0.503299	−0.251650	−	0.967818i	$-0.580973\pi$
$379$	−2.02163e11	−0.503299	−0.251650	+	0.967818i	$0.580973\pi$
$380$	−1.12395e11	−0.276517
$381$	1.50734e11	0.366478
$382$	−1.82488e11	−0.438479
$383$	−6.62686e10	−0.157367	−0.0786835	−	0.996900i	$-0.525072\pi$
$383$	−6.62686e10	−0.157367	−0.0786835	+	0.996900i	$0.525072\pi$
$384$	−9.44577e11	−2.21690
$385$	2.55619e11	0.592952
$386$	1.14696e12	2.62969
$387$	2.61801e11	0.593298
$388$	−6.24429e11	−1.39875
$389$	7.03704e11	1.55818	0.779088	−	0.626914i	$-0.215682\pi$
$389$	7.03704e11	1.55818	0.779088	+	0.626914i	$0.215682\pi$
$390$	2.36425e11	0.517490
$391$	4.11451e11	0.890273
$392$	1.13651e12	2.43101
$393$	−3.35948e11	−0.710405
$394$	1.28473e12	2.68584
$395$	3.30824e9	0.00683770
$396$	−6.97820e11	−1.42598
$397$	−5.59407e11	−1.13024	−0.565120	−	0.825009i	$-0.691170\pi$
$397$	−5.59407e11	−1.13024	−0.565120	+	0.825009i	$0.691170\pi$
$398$	7.90518e11	1.57920
$399$	2.21615e10	0.0437745
$400$	−9.83991e11	−1.92186
$401$	4.71707e11	0.911010	0.455505	−	0.890233i	$-0.349459\pi$
$401$	4.71707e11	0.911010	0.455505	+	0.890233i	$0.349459\pi$
$402$	−1.49437e11	−0.285391
$403$	9.66745e10	0.182574
$404$	−1.80717e10	−0.0337508
$405$	−4.27727e10	−0.0789986
$406$	8.55542e11	1.56270
$407$	5.06428e11	0.914835
$408$	−6.41535e11	−1.14617
$409$	−8.77400e11	−1.55040	−0.775198	−	0.631718i	$-0.782350\pi$
$409$	−8.77400e11	−1.55040	−0.775198	+	0.631718i	$0.782350\pi$
$410$	−1.35400e12	−2.36642
$411$	−3.29909e11	−0.570303
$412$	−4.52035e11	−0.772921
$413$	4.15129e10	0.0702114
$414$	−5.94433e11	−0.994492
$415$	−4.94366e11	−0.818149
$416$	−1.63260e12	−2.67275
$417$	4.40302e11	0.713081
$418$	2.63346e11	0.421924
$419$	−2.19302e11	−0.347599	−0.173800	−	0.984781i	$-0.555604\pi$
$419$	−2.19302e11	−0.347599	−0.173800	+	0.984781i	$0.555604\pi$
$420$	−3.90543e11	−0.612417
$421$	5.11479e11	0.793521	0.396761	−	0.917922i	$-0.370134\pi$
$421$	5.11479e11	0.793521	0.396761	+	0.917922i	$0.370134\pi$
$422$	8.68508e11	1.33311
$423$	1.15664e11	0.175657
$424$	−3.63317e12	−5.45933
$425$	−1.92609e11	−0.286369
$426$	−1.02526e12	−1.50831
$427$	−1.18286e11	−0.172189
$428$	−2.58716e12	−3.72672
$429$	−4.06874e11	−0.579965
$430$	1.74111e12	2.45594
$431$	8.61585e11	1.20268	0.601340	−	0.798993i	$-0.294634\pi$
$431$	8.61585e11	1.20268	0.601340	+	0.798993i	$0.294634\pi$
$432$	5.41443e11	0.747956
$433$	−9.73320e11	−1.33064	−0.665319	−	0.746559i	$-0.731705\pi$
$433$	−9.73320e11	−1.33064	−0.665319	+	0.746559i	$0.731705\pi$
$434$	−2.17420e11	−0.294169
$435$	4.57701e11	0.612886
$436$	−2.00415e12	−2.65607
$437$	1.64769e11	0.216126
$438$	1.64250e12	2.13241
$439$	4.35557e11	0.559699	0.279849	−	0.960044i	$-0.409715\pi$
$439$	4.35557e11	0.559699	0.279849	+	0.960044i	$0.409715\pi$
$440$	−2.96326e12	−3.76906
$441$	−1.87755e11	−0.236384
$442$	−5.85820e11	−0.730069
$443$	−6.79092e11	−0.837745	−0.418873	−	0.908045i	$-0.637575\pi$
$443$	−6.79092e11	−0.837745	−0.418873	+	0.908045i	$0.637575\pi$
$444$	−7.73738e11	−0.944867
$445$	−5.49882e11	−0.664737
$446$	2.50405e12	2.99665
$447$	9.95563e9	0.0117946
$448$	1.88463e12	2.21042
$449$	−7.23578e11	−0.840188	−0.420094	−	0.907481i	$-0.638003\pi$
$449$	−7.23578e11	−0.840188	−0.420094	+	0.907481i	$0.638003\pi$
$450$	2.78266e11	0.319893
$451$	2.33016e12	2.65211
$452$	−1.33870e12	−1.50855
$453$	7.76370e11	0.866217
$454$	−6.64119e11	−0.733660
$455$	−2.27712e11	−0.249077
$456$	−2.56907e11	−0.278249
$457$	6.67676e10	0.0716049	0.0358025	−	0.999359i	$-0.488601\pi$
$457$	6.67676e10	0.0716049	0.0358025	+	0.999359i	$0.488601\pi$
$458$	7.49119e11	0.795530
$459$	1.05983e11	0.111450
$460$	−2.90365e12	−3.02367
$461$	1.20243e12	1.23995	0.619975	−	0.784622i	$-0.287143\pi$
$461$	1.20243e12	1.23995	0.619975	+	0.784622i	$0.287143\pi$
$462$	9.15057e11	0.934457
$463$	−2.35427e11	−0.238090	−0.119045	−	0.992889i	$-0.537983\pi$
$463$	−2.35427e11	−0.238090	−0.119045	+	0.992889i	$0.537983\pi$
$464$	−5.79385e12	−5.80278
$465$	−1.16316e11	−0.115372
$466$	7.45996e11	0.732824
$467$	1.35968e12	1.32285	0.661424	−	0.750012i	$-0.269952\pi$
$467$	1.35968e12	1.32285	0.661424	+	0.750012i	$0.269952\pi$
$468$	6.21636e11	0.599004
$469$	1.43929e11	0.137364
$470$	7.69220e11	0.727127
$471$	5.05204e11	0.473013
$472$	−4.81238e11	−0.446294
$473$	−2.99635e12	−2.75244
$474$	1.18427e10	0.0107758
$475$	−7.71316e10	−0.0695202
$476$	9.67699e11	0.863990
$477$	6.00211e11	0.530849
$478$	−2.85675e12	−2.50292
$479$	−1.19605e12	−1.03811	−0.519053	−	0.854742i	$-0.673715\pi$
$479$	−1.19605e12	−1.03811	−0.519053	+	0.854742i	$0.673715\pi$
$480$	1.96430e12	1.68897
$481$	−4.51139e11	−0.384289
$482$	8.68238e11	0.732702
$483$	5.72526e11	0.478667
$484$	4.64687e12	3.84908
$485$	4.38054e11	0.359492
$486$	−1.53117e11	−0.124497
$487$	4.71067e11	0.379492	0.189746	−	0.981833i	$-0.439234\pi$
$487$	4.71067e11	0.379492	0.189746	+	0.981833i	$0.439234\pi$
$488$	1.37123e12	1.09451
$489$	−9.71449e11	−0.768299
$490$	−1.24866e12	−0.978505
$491$	−1.37541e12	−1.06798	−0.533991	−	0.845490i	$-0.679308\pi$
$491$	−1.37541e12	−1.06798	−0.533991	+	0.845490i	$0.679308\pi$
$492$	−3.56010e12	−2.73917
$493$	−1.13410e12	−0.864652
$494$	−2.34596e11	−0.177235
$495$	4.89540e11	0.366492
$496$	1.47240e12	1.09234
$497$	9.87474e11	0.725975
$498$	−1.76972e12	−1.28935
$499$	−1.67648e12	−1.21044	−0.605222	−	0.796057i	$-0.706916\pi$
$499$	−1.67648e12	−1.21044	−0.605222	+	0.796057i	$0.706916\pi$
$500$	4.10804e12	2.93947
$501$	−9.72447e10	−0.0689598
$502$	2.36372e12	1.66123
$503$	8.76570e11	0.610563	0.305282	−	0.952262i	$-0.401249\pi$
$503$	8.76570e11	0.610563	0.305282	+	0.952262i	$0.401249\pi$
$504$	−8.92682e11	−0.616254
$505$	1.26778e10	0.00867428
$506$	6.80336e12	4.61367
$507$	−4.96511e11	−0.333728
$508$	2.63577e12	1.75598
$509$	−1.40681e12	−0.928976	−0.464488	−	0.885579i	$-0.653762\pi$
$509$	−1.40681e12	−0.928976	−0.464488	+	0.885579i	$0.653762\pi$
$510$	7.04843e11	0.461346
$511$	−1.58197e12	−1.02637
$512$	−4.14860e12	−2.66801
$513$	4.24418e10	0.0270561
$514$	5.14091e12	3.24868
$515$	3.17115e11	0.198648
$516$	4.57793e12	2.84280
$517$	−1.32378e12	−0.814910
$518$	1.01461e12	0.619177
$519$	−6.03661e10	−0.0365208
$520$	2.63975e12	1.58324
$521$	2.24585e12	1.33540	0.667700	−	0.744430i	$-0.267279\pi$
$521$	2.24585e12	1.33540	0.667700	+	0.744430i	$0.267279\pi$
$522$	1.63846e12	0.965872
$523$	−2.36065e12	−1.37967	−0.689833	−	0.723969i	$-0.742316\pi$
$523$	−2.36065e12	−1.37967	−0.689833	+	0.723969i	$0.742316\pi$
$524$	−5.87448e12	−3.40391
$525$	−2.68011e11	−0.153970
$526$	−9.11875e11	−0.519397
$527$	2.88212e11	0.162766
$528$	−6.19689e12	−3.46993
$529$	2.45552e12	1.36331
$530$	3.99170e12	2.19744
$531$	7.95020e10	0.0433963
$532$	3.87522e11	0.209746
$533$	−2.07577e12	−1.11405
$534$	−1.96845e12	−1.04759
$535$	1.81497e12	0.957804
$536$	−1.66850e12	−0.873143
$537$	−5.80675e11	−0.301335
$538$	6.93759e12	3.57016
$539$	2.14888e12	1.09664
$540$	−7.47936e11	−0.378523
$541$	−1.15338e12	−0.578874	−0.289437	−	0.957197i	$-0.593468\pi$
$541$	−1.15338e12	−0.578874	−0.289437	+	0.957197i	$0.593468\pi$
$542$	3.43694e12	1.71070
$543$	9.50157e10	0.0469025
$544$	−4.86719e12	−2.38278
$545$	1.40596e12	0.682637
$546$	−8.15156e11	−0.392531
$547$	−2.92047e12	−1.39479	−0.697397	−	0.716685i	$-0.745659\pi$
$547$	−2.92047e12	−1.39479	−0.697397	+	0.716685i	$0.745659\pi$
$548$	−5.76887e12	−2.73262
$549$	−2.26531e11	−0.106427
$550$	−3.18480e12	−1.48405
$551$	−4.54159e11	−0.209907
$552$	−6.63701e12	−3.04261
$553$	−1.14063e10	−0.00518659
$554$	−6.37348e12	−2.87463
$555$	5.42799e11	0.242840
$556$	7.69925e12	3.41674
$557$	4.06498e11	0.178941	0.0894706	−	0.995989i	$-0.471482\pi$
$557$	4.06498e11	0.178941	0.0894706	+	0.995989i	$0.471482\pi$
$558$	−4.16385e11	−0.181820
$559$	2.66923e12	1.15620
$560$	−3.46816e12	−1.49023
$561$	−1.21299e12	−0.517042
$562$	3.98205e12	1.68381
$563$	−3.37014e12	−1.41371	−0.706854	−	0.707359i	$-0.749886\pi$
$563$	−3.37014e12	−1.41371	−0.706854	+	0.707359i	$0.749886\pi$
$564$	2.02252e12	0.841662
$565$	9.39131e11	0.387711
$566$	−2.82622e12	−1.15753
$567$	1.47474e11	0.0599227
$568$	−1.14473e13	−4.61461
$569$	3.49409e12	1.39742	0.698712	−	0.715403i	$-0.253757\pi$
$569$	3.49409e12	1.39742	0.698712	+	0.715403i	$0.253757\pi$
$570$	2.82259e11	0.111998
$571$	4.63108e12	1.82314	0.911569	−	0.411147i	$-0.134872\pi$
$571$	4.63108e12	1.82314	0.911569	+	0.411147i	$0.134872\pi$
$572$	−7.11470e12	−2.77891
$573$	3.36606e11	0.130444
$574$	4.66839e12	1.79500
$575$	−1.99264e12	−0.760193
$576$	3.60928e12	1.36622
$577$	−4.42077e12	−1.66038	−0.830188	−	0.557483i	$-0.811767\pi$
$577$	−4.42077e12	−1.66038	−0.830188	+	0.557483i	$0.811767\pi$
$578$	3.46112e12	1.28986
$579$	−2.11561e12	−0.782316
$580$	8.00348e12	2.93665
$581$	1.70450e12	0.620589
$582$	1.56813e12	0.566539
$583$	−6.86950e12	−2.46273
$584$	1.83390e13	6.52404
$585$	−4.36095e11	−0.153950
$586$	9.60828e12	3.36594
$587$	3.53913e12	1.23034	0.615170	−	0.788394i	$-0.289087\pi$
$587$	3.53913e12	1.23034	0.615170	+	0.788394i	$0.289087\pi$
$588$	−3.28313e12	−1.13264
$589$	1.15416e11	0.0395138
$590$	5.28728e11	0.179638
$591$	−2.36974e12	−0.799020
$592$	−6.87107e12	−2.29920
$593$	4.75888e12	1.58037	0.790185	−	0.612868i	$-0.209984\pi$
$593$	4.75888e12	1.58037	0.790185	+	0.612868i	$0.209984\pi$
$594$	1.75244e12	0.577569
$595$	−6.78867e11	−0.222054
$596$	1.74087e11	0.0565142
$597$	−1.45814e12	−0.469802
$598$	−6.06061e12	−1.93803
$599$	−3.24559e12	−1.03009	−0.515043	−	0.857164i	$-0.672224\pi$
$599$	−3.24559e12	−1.03009	−0.515043	+	0.857164i	$0.672224\pi$
$600$	3.10692e12	0.978701
$601$	−3.78568e12	−1.18361	−0.591805	−	0.806081i	$-0.701585\pi$
$601$	−3.78568e12	−1.18361	−0.591805	+	0.806081i	$0.701585\pi$
$602$	−6.00308e12	−1.86290
$603$	2.75642e11	0.0849018
$604$	1.35758e13	4.15049
$605$	−3.25991e12	−0.989250
$606$	4.53837e10	0.0136701
$607$	4.14733e12	1.23999	0.619997	−	0.784604i	$-0.287134\pi$
$607$	4.14733e12	1.23999	0.619997	+	0.784604i	$0.287134\pi$
$608$	−1.94910e12	−0.578453
$609$	−1.57808e12	−0.464891
$610$	−1.50654e12	−0.440552
$611$	1.17926e12	0.342314
$612$	1.85326e12	0.534016
$613$	6.39011e12	1.82783	0.913916	−	0.405904i	$-0.133043\pi$
$613$	6.39011e12	1.82783	0.913916	+	0.405904i	$0.133043\pi$
$614$	1.27073e12	0.360825
$615$	2.49751e12	0.703994
$616$	1.02169e13	2.85894
$617$	5.61739e12	1.56045	0.780227	−	0.625496i	$-0.215103\pi$
$617$	5.61739e12	1.56045	0.780227	+	0.625496i	$0.215103\pi$
$618$	1.13520e12	0.313058
$619$	−1.48141e12	−0.405573	−0.202786	−	0.979223i	$-0.565000\pi$
$619$	−1.48141e12	−0.405573	−0.202786	+	0.979223i	$0.565000\pi$
$620$	−2.03394e12	−0.552809
$621$	1.09645e12	0.295855
$622$	3.39115e12	0.908427
$623$	1.89591e12	0.504222
$624$	5.52035e12	1.45759
$625$	−9.95545e11	−0.260976
$626$	−7.13107e12	−1.85597
$627$	−4.85752e11	−0.125519
$628$	8.83414e12	2.26645
$629$	−1.34496e12	−0.342596
$630$	9.80774e11	0.248048
$631$	2.81353e12	0.706511	0.353256	−	0.935527i	$-0.385075\pi$
$631$	2.81353e12	0.706511	0.353256	+	0.935527i	$0.385075\pi$
$632$	1.32228e11	0.0329682
$633$	−1.60200e12	−0.396593
$634$	1.38428e12	0.340270
$635$	−1.84906e12	−0.451305
$636$	1.04955e13	2.54357
$637$	−1.91428e12	−0.460657
$638$	−1.87524e13	−4.48089
$639$	1.89113e12	0.448711
$640$	1.15872e13	2.73004
$641$	2.06430e12	0.482961	0.241481	−	0.970406i	$-0.422367\pi$
$641$	2.06430e12	0.482961	0.241481	+	0.970406i	$0.422367\pi$
$642$	6.49717e12	1.50944
$643$	3.21655e12	0.742063	0.371031	−	0.928620i	$-0.379004\pi$
$643$	3.21655e12	0.742063	0.371031	+	0.928620i	$0.379004\pi$
$644$	1.00113e13	2.29354
$645$	−3.21155e12	−0.730626
$646$	−6.99390e11	−0.158006
$647$	1.60571e12	0.360245	0.180122	−	0.983644i	$-0.442351\pi$
$647$	1.60571e12	0.360245	0.180122	+	0.983644i	$0.442351\pi$
$648$	−1.70959e12	−0.380894
$649$	−9.09911e11	−0.201325
$650$	2.83710e12	0.623396
$651$	4.01040e11	0.0875132
$652$	−1.69870e13	−3.68131
$653$	5.16633e12	1.11192	0.555959	−	0.831210i	$-0.312351\pi$
$653$	5.16633e12	1.11192	0.555959	+	0.831210i	$0.312351\pi$
$654$	5.03303e12	1.07579
$655$	4.12111e12	0.874839
$656$	−3.16150e13	−6.66539
$657$	−3.02965e12	−0.634378
$658$	−2.65215e12	−0.551546
$659$	7.28418e12	1.50451	0.752257	−	0.658870i	$-0.228965\pi$
$659$	7.28418e12	1.50451	0.752257	+	0.658870i	$0.228965\pi$
$660$	8.56022e12	1.75605
$661$	2.45718e12	0.500645	0.250323	−	0.968162i	$-0.419463\pi$
$661$	2.45718e12	0.500645	0.250323	+	0.968162i	$0.419463\pi$
$662$	−5.51880e12	−1.11682
$663$	1.08057e12	0.217191
$664$	−1.97594e13	−3.94473
$665$	−2.71857e11	−0.0539068
$666$	1.94310e12	0.382701
$667$	−1.17329e13	−2.29530
$668$	−1.70045e12	−0.330422
$669$	−4.61882e12	−0.891484
$670$	1.83315e12	0.351449
$671$	2.59268e12	0.493738
$672$	−6.77260e12	−1.28113
$673$	−4.76030e12	−0.894471	−0.447236	−	0.894416i	$-0.647591\pi$
$673$	−4.76030e12	−0.894471	−0.447236	+	0.894416i	$0.647591\pi$
$674$	−3.09258e11	−0.0577233
$675$	−5.13273e11	−0.0951660
$676$	−8.68213e12	−1.59906
$677$	1.06786e12	0.195373	0.0976865	−	0.995217i	$-0.468856\pi$
$677$	1.06786e12	0.195373	0.0976865	+	0.995217i	$0.468856\pi$
$678$	3.36188e12	0.611010
$679$	−1.51034e12	−0.272685
$680$	7.86977e12	1.41147
$681$	1.22499e12	0.218259
$682$	4.76559e12	0.843503
$683$	−7.12649e12	−1.25309	−0.626545	−	0.779385i	$-0.715532\pi$
$683$	−7.12649e12	−1.25309	−0.626545	+	0.779385i	$0.715532\pi$
$684$	7.42149e11	0.129640
$685$	4.04702e12	0.702309
$686$	1.03761e13	1.78886
$687$	−1.38178e12	−0.236665
$688$	4.06537e13	6.91754
$689$	6.11952e12	1.03450
$690$	7.29196e12	1.22468
$691$	1.91579e12	0.319666	0.159833	−	0.987144i	$-0.448904\pi$
$691$	1.91579e12	0.319666	0.159833	+	0.987144i	$0.448904\pi$
$692$	−1.05558e12	−0.174990
$693$	−1.68786e12	−0.277995
$694$	−2.70567e12	−0.442748
$695$	−5.40123e12	−0.878135
$696$	1.82939e13	2.95505
$697$	−6.18840e12	−0.993186
$698$	1.62102e13	2.58488
$699$	−1.37602e12	−0.218010
$700$	−4.68652e12	−0.737750
$701$	−9.03925e12	−1.41384	−0.706922	−	0.707292i	$-0.749917\pi$
$701$	−9.03925e12	−1.41384	−0.706922	+	0.707292i	$0.749917\pi$
$702$	−1.56112e12	−0.242616
$703$	−5.38599e11	−0.0831700
$704$	−4.13087e13	−6.33818
$705$	−1.41886e12	−0.216315
$706$	3.72137e12	0.563743
$707$	−4.37112e10	−0.00657969
$708$	1.39019e12	0.207934
$709$	1.12846e13	1.67717	0.838586	−	0.544769i	$-0.183383\pi$
$709$	1.12846e13	1.67717	0.838586	+	0.544769i	$0.183383\pi$
$710$	1.25769e13	1.85743
$711$	−2.18444e10	−0.00320573
$712$	−2.19783e13	−3.20505
$713$	2.98170e12	0.432077
$714$	−2.43019e12	−0.349944
$715$	4.99116e12	0.714207
$716$	−1.01538e13	−1.44385
$717$	5.26939e12	0.744603
$718$	2.17980e13	3.06095
$719$	2.15065e12	0.300116	0.150058	−	0.988677i	$-0.452054\pi$
$719$	2.15065e12	0.300116	0.150058	+	0.988677i	$0.452054\pi$
$720$	−6.64194e12	−0.921082
$721$	−1.09336e12	−0.150680
$722$	1.38902e13	1.90236
$723$	−1.60150e12	−0.217974
$724$	1.66147e12	0.224734
$725$	5.49241e12	0.738316
$726$	−1.16697e13	−1.55900
$727$	−3.66096e12	−0.486061	−0.243030	−	0.970019i	$-0.578141\pi$
$727$	−3.66096e12	−0.486061	−0.243030	+	0.970019i	$0.578141\pi$
$728$	−9.10145e12	−1.20093
$729$	2.82430e11	0.0370370
$730$	−2.01487e13	−2.62599
$731$	7.95766e12	1.03076
$732$	−3.96118e12	−0.509947
$733$	−8.51645e12	−1.08966	−0.544829	−	0.838547i	$-0.683406\pi$
$733$	−8.51645e12	−1.08966	−0.544829	+	0.838547i	$0.683406\pi$
$734$	−1.32676e12	−0.168718
$735$	2.30321e12	0.291099
$736$	−5.03536e13	−6.32529
$737$	−3.15475e12	−0.393878
$738$	8.94051e12	1.10945
$739$	−1.04799e13	−1.29258	−0.646291	−	0.763091i	$-0.723681\pi$
$739$	−1.04799e13	−1.29258	−0.646291	+	0.763091i	$0.723681\pi$
$740$	9.49153e12	1.16357
$741$	4.32721e11	0.0527261
$742$	−1.37628e13	−1.66682
$743$	−9.83152e12	−1.18351	−0.591754	−	0.806119i	$-0.701564\pi$
$743$	−9.83152e12	−1.18351	−0.591754	+	0.806119i	$0.701564\pi$
$744$	−4.64906e12	−0.556272
$745$	−1.22127e11	−0.0145247
$746$	3.97110e12	0.469446
$747$	3.26431e12	0.383574
$748$	−2.12108e13	−2.47742
$749$	−6.25773e12	−0.726521
$750$	−1.03165e13	−1.19058
$751$	8.73479e12	1.00201	0.501006	−	0.865444i	$-0.332964\pi$
$751$	8.73479e12	1.00201	0.501006	+	0.865444i	$0.332964\pi$
$752$	1.79607e13	2.04807
$753$	−4.35997e12	−0.494204
$754$	1.67051e13	1.88226
$755$	−9.52381e12	−1.06672
$756$	2.57877e12	0.287120
$757$	8.83748e12	0.978130	0.489065	−	0.872247i	$-0.337338\pi$
$757$	8.83748e12	0.978130	0.489065	+	0.872247i	$0.337338\pi$
$758$	8.87769e12	0.976761
$759$	−1.25491e13	−1.37253
$760$	3.15150e12	0.342655
$761$	−1.34581e13	−1.45463	−0.727314	−	0.686305i	$-0.759232\pi$
$761$	−1.34581e13	−1.45463	−0.727314	+	0.686305i	$0.759232\pi$
$762$	−6.61923e12	−0.711230
$763$	−4.84754e12	−0.517799
$764$	5.88598e12	0.625027
$765$	−1.30011e12	−0.137247
$766$	2.91008e12	0.305405
$767$	8.10572e11	0.0845693
$768$	1.86654e13	1.93603
$769$	2.86965e12	0.295911	0.147955	−	0.988994i	$-0.452731\pi$
$769$	2.86965e12	0.295911	0.147955	+	0.988994i	$0.452731\pi$
$770$	−1.12251e13	−1.15075
$771$	−9.48262e12	−0.966459
$772$	−3.69942e13	−3.74848
$773$	1.77419e13	1.78728	0.893640	−	0.448786i	$-0.148143\pi$
$773$	1.77419e13	1.78728	0.893640	+	0.448786i	$0.148143\pi$
$774$	−1.14966e13	−1.15142
$775$	−1.39580e12	−0.138984
$776$	1.75087e13	1.73330
$777$	−1.87149e12	−0.184201
$778$	−3.09020e13	−3.02398
$779$	−2.47819e12	−0.241110
$780$	−7.62567e12	−0.737653
$781$	−2.16442e13	−2.08167
$782$	−1.80682e13	−1.72777
$783$	−3.02221e12	−0.287340
$784$	−2.91554e13	−2.75611
$785$	−6.19739e12	−0.582500
$786$	1.47526e13	1.37869
$787$	−1.14046e13	−1.05973	−0.529864	−	0.848082i	$-0.677757\pi$
$787$	−1.14046e13	−1.05973	−0.529864	+	0.848082i	$0.677757\pi$
$788$	−4.14380e13	−3.82852
$789$	1.68199e12	0.154517
$790$	−1.45276e11	−0.0132700
$791$	−3.23798e12	−0.294090
$792$	1.95665e13	1.76705
$793$	−2.30962e12	−0.207401
$794$	2.45655e13	2.19348
$795$	−7.36285e12	−0.653723
$796$	−2.54975e13	−2.25106
$797$	1.37607e13	1.20803	0.604015	−	0.796973i	$-0.293567\pi$
$797$	1.37607e13	1.20803	0.604015	+	0.796973i	$0.293567\pi$
$798$	−9.73186e11	−0.0849538
$799$	3.51568e12	0.305175
$800$	2.35716e13	2.03462
$801$	3.63089e12	0.311650
$802$	−2.07143e13	−1.76801
$803$	3.46747e13	2.94302
$804$	4.81994e12	0.406808
$805$	−7.02323e12	−0.589462
$806$	−4.24531e12	−0.354325
$807$	−1.27966e13	−1.06210
$808$	5.06722e11	0.0418233
$809$	−2.09569e13	−1.72012	−0.860061	−	0.510192i	$-0.829574\pi$
$809$	−2.09569e13	−1.72012	−0.860061	+	0.510192i	$0.829574\pi$
$810$	1.87830e12	0.153314
$811$	1.71895e13	1.39531	0.697654	−	0.716435i	$-0.254228\pi$
$811$	1.71895e13	1.39531	0.697654	+	0.716435i	$0.254228\pi$
$812$	−2.75948e13	−2.22753
$813$	−6.33957e12	−0.508923
$814$	−2.22390e13	−1.77544
$815$	1.19169e13	0.946134
$816$	1.64576e13	1.29945
$817$	3.18670e12	0.250231
$818$	3.85296e13	3.00888
$819$	1.50359e12	0.116775
$820$	4.36721e13	3.37320
$821$	5.60147e11	0.0430286	0.0215143	−	0.999769i	$-0.493151\pi$
$821$	5.60147e11	0.0430286	0.0215143	+	0.999769i	$0.493151\pi$
$822$	1.44874e13	1.10680
$823$	−6.40278e12	−0.486485	−0.243243	−	0.969965i	$-0.578211\pi$
$823$	−6.40278e12	−0.486485	−0.243243	+	0.969965i	$0.578211\pi$
$824$	1.26748e13	0.957789
$825$	5.87448e12	0.441496
$826$	−1.82297e12	−0.136260
$827$	1.23366e13	0.917110	0.458555	−	0.888666i	$-0.348367\pi$
$827$	1.23366e13	0.917110	0.458555	+	0.888666i	$0.348367\pi$
$828$	1.91729e13	1.41759
$829$	−1.37312e13	−1.00975	−0.504873	−	0.863194i	$-0.668460\pi$
$829$	−1.37312e13	−1.00975	−0.504873	+	0.863194i	$0.668460\pi$
$830$	2.17093e13	1.58780
$831$	1.17561e13	0.855184
$832$	3.67989e13	2.66244
$833$	−5.70695e12	−0.410678
$834$	−1.93352e13	−1.38389
$835$	1.19291e12	0.0849217
$836$	−8.49400e12	−0.601428
$837$	7.68039e11	0.0540902
$838$	9.63028e12	0.674592
$839$	−9.04675e12	−0.630324	−0.315162	−	0.949038i	$-0.602059\pi$
$839$	−9.04675e12	−0.630324	−0.315162	+	0.949038i	$0.602059\pi$
$840$	1.09506e13	0.758896
$841$	1.78328e13	1.22924
$842$	−2.24608e13	−1.54000
$843$	−7.34504e12	−0.500922
$844$	−2.80129e13	−1.90028
$845$	6.09075e12	0.410975
$846$	−5.07918e12	−0.340900
$847$	1.12397e13	0.750374
$848$	9.32034e13	6.18943
$849$	5.21307e12	0.344357
$850$	8.45812e12	0.555762
$851$	−1.39143e13	−0.909451
$852$	3.30688e13	2.15001
$853$	−1.99730e13	−1.29174	−0.645868	−	0.763449i	$-0.723504\pi$
$853$	−1.99730e13	−1.29174	−0.645868	+	0.763449i	$0.723504\pi$
$854$	5.19433e12	0.334171
$855$	−5.20638e11	−0.0333187
$856$	7.25427e13	4.61808
$857$	−8.24335e12	−0.522023	−0.261012	−	0.965336i	$-0.584056\pi$
$857$	−8.24335e12	−0.522023	−0.261012	+	0.965336i	$0.584056\pi$
$858$	1.78672e13	1.12555
$859$	2.68595e12	0.168317	0.0841586	−	0.996452i	$-0.473180\pi$
$859$	2.68595e12	0.168317	0.0841586	+	0.996452i	$0.473180\pi$
$860$	−5.61580e13	−3.50081
$861$	−8.61103e12	−0.533999
$862$	−3.78351e13	−2.33406
$863$	−1.84104e13	−1.12984	−0.564918	−	0.825147i	$-0.691092\pi$
$863$	−1.84104e13	−1.12984	−0.564918	+	0.825147i	$0.691092\pi$
$864$	−1.29703e13	−0.791842
$865$	7.40517e11	0.0449741
$866$	4.27418e13	2.58239
$867$	−6.38417e12	−0.383724
$868$	7.01270e12	0.419321
$869$	2.50012e11	0.0148721
$870$	−2.00992e13	−1.18944
$871$	2.81034e12	0.165454
$872$	5.61952e13	3.29136
$873$	−2.89248e12	−0.168541
$874$	−7.23555e12	−0.419440
$875$	9.93635e12	0.573047
$876$	−5.29773e13	−3.03963
$877$	2.63357e13	1.50331	0.751653	−	0.659559i	$-0.229257\pi$
$877$	2.63357e13	1.50331	0.751653	+	0.659559i	$0.229257\pi$
$878$	−1.91268e13	−1.08622
$879$	−1.77229e13	−1.00134
$880$	7.60178e13	4.27310
$881$	−2.53338e13	−1.41680	−0.708401	−	0.705810i	$-0.750583\pi$
$881$	−2.53338e13	−1.41680	−0.708401	+	0.705810i	$0.750583\pi$
$882$	8.24496e12	0.458754
$883$	3.23574e13	1.79122	0.895612	−	0.444837i	$-0.146738\pi$
$883$	3.23574e13	1.79122	0.895612	+	0.444837i	$0.146738\pi$
$884$	1.88951e13	1.04067
$885$	−9.75259e11	−0.0534411
$886$	2.98213e13	1.62583
$887$	9.07362e12	0.492180	0.246090	−	0.969247i	$-0.420854\pi$
$887$	9.07362e12	0.492180	0.246090	+	0.969247i	$0.420854\pi$
$888$	2.16952e13	1.17086
$889$	6.37529e12	0.342328
$890$	2.41472e13	1.29007
$891$	−3.23244e12	−0.171823
$892$	−8.07659e13	−4.27156
$893$	1.40788e12	0.0740856
$894$	−4.37186e11	−0.0228901
$895$	7.12320e12	0.371083
$896$	−3.99510e13	−2.07081
$897$	1.11790e13	0.576551
$898$	3.17748e13	1.63057
$899$	−8.21860e12	−0.419642
$900$	−8.97524e12	−0.455989
$901$	1.82439e13	0.922265
$902$	−1.02325e14	−5.14700
$903$	1.10729e13	0.554201
$904$	3.75363e13	1.86936
$905$	−1.16557e12	−0.0577589
$906$	−3.40930e13	−1.68108
$907$	−8.04078e12	−0.394517	−0.197258	−	0.980352i	$-0.563204\pi$
$907$	−8.04078e12	−0.394517	−0.197258	+	0.980352i	$0.563204\pi$
$908$	2.14206e13	1.04579
$909$	−8.37120e10	−0.00406678
$910$	9.99960e12	0.483389
$911$	1.44263e13	0.693942	0.346971	−	0.937876i	$-0.387210\pi$
$911$	1.44263e13	0.693942	0.346971	+	0.937876i	$0.387210\pi$
$912$	6.59055e12	0.315460
$913$	−3.73605e13	−1.77948
$914$	−2.93199e12	−0.138965
$915$	2.77888e12	0.131061
$916$	−2.41622e13	−1.13398
$917$	−1.42090e13	−0.663590
$918$	−4.65410e12	−0.216293
$919$	−1.26368e13	−0.584408	−0.292204	−	0.956356i	$-0.594389\pi$
$919$	−1.26368e13	−0.584408	−0.292204	+	0.956356i	$0.594389\pi$
$920$	8.14169e13	3.74687
$921$	−2.34392e12	−0.107343
$922$	−5.28026e13	−2.40639
$923$	1.92812e13	0.874433
$924$	−2.95143e13	−1.33202
$925$	6.51359e12	0.292538
$926$	1.03384e13	0.462066
$927$	−2.09392e12	−0.0931325
$928$	1.38792e14	6.14326
$929$	3.76990e13	1.66058	0.830290	−	0.557332i	$-0.188175\pi$
$929$	3.76990e13	1.66058	0.830290	+	0.557332i	$0.188175\pi$
$930$	5.10784e12	0.223905
$931$	−2.28539e12	−0.0996980
$932$	−2.40614e13	−1.04460
$933$	−6.25511e12	−0.270251
$934$	−5.97081e13	−2.56727
$935$	1.48799e13	0.636720
$936$	−1.74303e13	−0.742274
$937$	−3.01281e13	−1.27686	−0.638430	−	0.769680i	$-0.720416\pi$
$937$	−3.01281e13	−1.27686	−0.638430	+	0.769680i	$0.720416\pi$
$938$	−6.32043e12	−0.266584
$939$	1.31535e13	0.552138
$940$	−2.48105e13	−1.03648
$941$	−3.31424e12	−0.137794	−0.0688972	−	0.997624i	$-0.521948\pi$
$941$	−3.31424e12	−0.137794	−0.0688972	+	0.997624i	$0.521948\pi$
$942$	−2.21853e13	−0.917984
$943$	−6.40222e13	−2.63650
$944$	1.23454e13	0.505978
$945$	−1.80908e12	−0.0737928
$946$	1.31580e14	5.34171
$947$	1.29122e13	0.521705	0.260853	−	0.965379i	$-0.415996\pi$
$947$	1.29122e13	0.521705	0.260853	+	0.965379i	$0.415996\pi$
$948$	−3.81977e11	−0.0153603
$949$	−3.08892e13	−1.23626
$950$	3.38711e12	0.134919
$951$	−2.55336e12	−0.101228
$952$	−2.71338e13	−1.07064
$953$	−3.68198e13	−1.44598	−0.722992	−	0.690857i	$-0.757234\pi$
$953$	−3.68198e13	−1.44598	−0.722992	+	0.690857i	$0.757234\pi$
$954$	−2.63573e13	−1.03023
$955$	−4.12918e12	−0.160638
$956$	9.21421e13	3.56778
$957$	3.45896e13	1.33304
$958$	5.25229e13	2.01467
$959$	−1.39535e13	−0.532721
$960$	−4.42754e13	−1.68245
$961$	−2.43510e13	−0.921005
$962$	1.98111e13	0.745796
$963$	−1.19843e13	−0.449049
$964$	−2.80042e13	−1.04442
$965$	2.59524e13	0.963396
$966$	−2.51416e13	−0.928957
$967$	2.42967e13	0.893569	0.446784	−	0.894642i	$-0.352569\pi$
$967$	2.42967e13	0.893569	0.446784	+	0.894642i	$0.352569\pi$
$968$	−1.30296e14	−4.76970
$969$	1.29005e12	0.0470056
$970$	−1.92364e13	−0.697673
$971$	3.70876e13	1.33888	0.669442	−	0.742865i	$-0.266533\pi$
$971$	3.70876e13	1.33888	0.669442	+	0.742865i	$0.266533\pi$
$972$	4.93864e12	0.177464
$973$	1.86226e13	0.666090
$974$	−2.06862e13	−0.736487
$975$	−5.23314e12	−0.185456
$976$	−3.51767e13	−1.24088
$977$	−3.37506e13	−1.18510	−0.592551	−	0.805533i	$-0.701879\pi$
$977$	−3.37506e13	−1.18510	−0.592551	+	0.805533i	$0.701879\pi$
$978$	4.26596e13	1.49105
$979$	−4.15560e13	−1.44581
$980$	4.02745e13	1.39480
$981$	−9.28361e12	−0.320042
$982$	6.03987e13	2.07265
$983$	1.32805e13	0.453652	0.226826	−	0.973935i	$-0.427165\pi$
$983$	1.32805e13	0.453652	0.226826	+	0.973935i	$0.427165\pi$
$984$	9.98234e13	3.39433
$985$	2.90699e13	0.983966
$986$	4.98023e13	1.67805
$987$	4.89200e12	0.164081
$988$	7.56667e12	0.252638
$989$	8.23261e13	2.73624
$990$	−2.14974e13	−0.711257
$991$	−2.92040e12	−0.0961857	−0.0480928	−	0.998843i	$-0.515314\pi$
$991$	−2.92040e12	−0.0961857	−0.0480928	+	0.998843i	$0.515314\pi$
$992$	−3.52715e13	−1.15643
$993$	1.01796e13	0.332247
$994$	−4.33633e13	−1.40891
$995$	1.78872e13	0.578546
$996$	5.70807e13	1.83790
$997$	−6.86175e12	−0.219941	−0.109971	−	0.993935i	$-0.535076\pi$
$997$	−6.86175e12	−0.219941	−0.109971	+	0.993935i	$0.535076\pi$
$998$	7.36197e13	2.34913
$999$	−3.58411e12	−0.113851

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-43.9134 q^{2} +81.0000 q^{3} +1416.39 q^{4} -993.635 q^{5} -3556.99 q^{6} +3425.90 q^{7} -39714.8 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-43.9134 q^{2} +81.0000 q^{3} +1416.39 q^{4} -993.635 q^{5} -3556.99 q^{6} +3425.90 q^{7} -39714.8 q^{8} +6561.00 q^{9} +43633.9 q^{10} -75091.5 q^{11} +114727. q^{12} +66893.5 q^{13} -150443. q^{14} -80484.4 q^{15} +1.01882e6 q^{16} +199427. q^{17} -288116. q^{18} +79861.8 q^{19} -1.40737e6 q^{20} +277498. q^{21} +3.29753e6 q^{22} +2.06317e6 q^{23} -3.21690e6 q^{24} -965814. q^{25} -2.93752e6 q^{26} +531441. q^{27} +4.85241e6 q^{28} -5.68682e6 q^{29} +3.53435e6 q^{30} +1.44520e6 q^{31} -2.44059e7 q^{32} -6.08241e6 q^{33} -8.75750e6 q^{34} -3.40410e6 q^{35} +9.29292e6 q^{36} -6.74414e6 q^{37} -3.50700e6 q^{38} +5.41837e6 q^{39} +3.94620e7 q^{40} -3.10309e7 q^{41} -1.21859e7 q^{42} +3.99027e7 q^{43} -1.06359e8 q^{44} -6.51924e6 q^{45} -9.06009e7 q^{46} +1.76289e7 q^{47} +8.25245e7 q^{48} -2.86168e7 q^{49} +4.24122e7 q^{50} +1.61536e7 q^{51} +9.47471e7 q^{52} +9.14817e7 q^{53} -2.33374e7 q^{54} +7.46136e7 q^{55} -1.36059e8 q^{56} +6.46880e6 q^{57} +2.49728e8 q^{58} +1.21174e7 q^{59} -1.13997e8 q^{60} -3.45269e7 q^{61} -6.34637e7 q^{62} +2.24773e7 q^{63} +5.50112e8 q^{64} -6.64677e7 q^{65} +2.67100e8 q^{66} +4.20121e7 q^{67} +2.82465e8 q^{68} +1.67117e8 q^{69} +1.49485e8 q^{70} +2.88238e8 q^{71} -2.60569e8 q^{72} -4.61767e8 q^{73} +2.96158e8 q^{74} -7.82309e7 q^{75} +1.13115e8 q^{76} -2.57256e8 q^{77} -2.37939e8 q^{78} -3.32943e6 q^{79} -1.01234e9 q^{80} +4.30467e7 q^{81} +1.36267e9 q^{82} +4.97533e8 q^{83} +3.93045e8 q^{84} -1.98157e8 q^{85} -1.75226e9 q^{86} -4.60632e8 q^{87} +2.98224e9 q^{88} +5.53405e8 q^{89} +2.86282e8 q^{90} +2.29170e8 q^{91} +2.92225e9 q^{92} +1.17061e8 q^{93} -7.74147e8 q^{94} -7.93535e7 q^{95} -1.97688e9 q^{96} -4.40860e8 q^{97} +1.25666e9 q^{98} -4.92675e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) \) 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

L-functions

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