LMFDB - Embedded newform 177.14.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,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, 14, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
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:	$189.798744245$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q+20.8810 q^{2} -729.000 q^{3} -7755.98 q^{4} +27865.9 q^{5} -15222.2 q^{6} +61118.3 q^{7} -333010. q^{8} +531441. q^{9} +O(q^{10})$	\(q+20.8810 q^{2} -729.000 q^{3} -7755.98 q^{4} +27865.9 q^{5} -15222.2 q^{6} +61118.3 q^{7} -333010. q^{8} +531441. q^{9} +581867. q^{10} -3.53045e6 q^{11} +5.65411e6 q^{12} +2.05403e7 q^{13} +1.27621e6 q^{14} -2.03142e7 q^{15} +5.65834e7 q^{16} -1.17268e8 q^{17} +1.10970e7 q^{18} +3.76293e6 q^{19} -2.16127e8 q^{20} -4.45552e7 q^{21} -7.37192e7 q^{22} -6.80717e8 q^{23} +2.42764e8 q^{24} -4.44197e8 q^{25} +4.28902e8 q^{26} -3.87420e8 q^{27} -4.74032e8 q^{28} +3.42738e9 q^{29} -4.24181e8 q^{30} -1.83633e9 q^{31} +3.90954e9 q^{32} +2.57370e9 q^{33} -2.44867e9 q^{34} +1.70311e9 q^{35} -4.12185e9 q^{36} +1.49290e10 q^{37} +7.85738e7 q^{38} -1.49739e10 q^{39} -9.27960e9 q^{40} +2.74461e10 q^{41} -9.30357e8 q^{42} -4.39208e10 q^{43} +2.73821e10 q^{44} +1.48091e10 q^{45} -1.42141e10 q^{46} +4.98609e10 q^{47} -4.12493e10 q^{48} -9.31536e10 q^{49} -9.27528e9 q^{50} +8.54883e10 q^{51} -1.59310e11 q^{52} +1.99807e11 q^{53} -8.08973e9 q^{54} -9.83789e10 q^{55} -2.03530e10 q^{56} -2.74318e9 q^{57} +7.15672e10 q^{58} -4.21805e10 q^{59} +1.57557e11 q^{60} +2.57022e11 q^{61} -3.83444e10 q^{62} +3.24807e10 q^{63} -3.81897e11 q^{64} +5.72374e11 q^{65} +5.37413e10 q^{66} +1.02262e11 q^{67} +9.09528e11 q^{68} +4.96243e11 q^{69} +3.55627e10 q^{70} -1.55726e12 q^{71} -1.76975e11 q^{72} +2.32473e12 q^{73} +3.11732e11 q^{74} +3.23820e11 q^{75} -2.91853e10 q^{76} -2.15775e11 q^{77} -3.12670e11 q^{78} -3.36486e11 q^{79} +1.57675e12 q^{80} +2.82430e11 q^{81} +5.73103e11 q^{82} +1.25533e12 q^{83} +3.45569e11 q^{84} -3.26777e12 q^{85} -9.17110e11 q^{86} -2.49856e12 q^{87} +1.17567e12 q^{88} +4.64185e12 q^{89} +3.09228e11 q^{90} +1.25539e12 q^{91} +5.27963e12 q^{92} +1.33868e12 q^{93} +1.04115e12 q^{94} +1.04857e11 q^{95} -2.85005e12 q^{96} +1.27449e12 q^{97} -1.94514e12 q^{98} -1.87622e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) $ 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9} - 3854663 q^{10} + 3943968 q^{11} - 92499894 q^{12} - 48510022 q^{13} - 51427459 q^{14} - 24411294 q^{15} + 370110498 q^{16} + 83288419 q^{17} - 27634932 q^{18} - 180425297 q^{19} + 753620445 q^{20} + 827807931 q^{21} + 2300196142 q^{22} - 1305810279 q^{23} + 1107897021 q^{24} + 8070954867 q^{25} + 464550322 q^{26} - 12010035159 q^{27} - 9887169562 q^{28} + 6248352277 q^{29} + 2810049327 q^{30} - 26730150789 q^{31} - 24001343230 q^{32} - 2875152672 q^{33} - 36571033348 q^{34} + 10255900979 q^{35} + 67432422726 q^{36} - 43284776933 q^{37} - 36293696947 q^{38} + 35363806038 q^{39} - 105980683856 q^{40} - 9961079285 q^{41} + 37490617611 q^{42} - 51755851288 q^{43} - 59623729442 q^{44} + 17795833326 q^{45} - 202287132683 q^{46} - 82747063727 q^{47} - 269810553042 q^{48} + 535277836542 q^{49} + 526974390461 q^{50} - 60717257451 q^{51} + 544982341446 q^{52} + 561701818494 q^{53} + 20145865428 q^{54} - 521861534450 q^{55} - 228056576664 q^{56} + 131530041513 q^{57} + 10555409160 q^{58} - 1307596542871 q^{59} - 549389304405 q^{60} + 618193248201 q^{61} - 1486611437386 q^{62} - 603471981699 q^{63} + 679062548045 q^{64} - 1130583307122 q^{65} - 1676842987518 q^{66} - 4137387490592 q^{67} - 3901389300295 q^{68} + 951935693391 q^{69} - 819291947844 q^{70} - 3766439869810 q^{71} - 807656928309 q^{72} - 2386775553523 q^{73} + 3060770694642 q^{74} - 5883726098043 q^{75} - 847741068784 q^{76} + 1650423006137 q^{77} - 338657184738 q^{78} + 787155757766 q^{79} + 13999832121779 q^{80} + 8755315630911 q^{81} + 10083281915577 q^{82} + 8743877051639 q^{83} + 7207746610698 q^{84} + 15373177520565 q^{85} + 18939443838984 q^{86} - 4555048809933 q^{87} + 39713314506713 q^{88} + 11026795445259 q^{89} - 2048525959383 q^{90} + 23285721962531 q^{91} + 40411079823254 q^{92} + 19486279925181 q^{93} + 35237377585624 q^{94} + 13730236994039 q^{95} + 17496979214670 q^{96} + 10134565481560 q^{97} + 70916776240976 q^{98} + 2095986297888 q^{99}+O(q^{100}) \) 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9 - 3854663 * q^10 + 3943968 * q^11 - 92499894 * q^12 - 48510022 * q^13 - 51427459 * q^14 - 24411294 * q^15 + 370110498 * q^16 + 83288419 * q^17 - 27634932 * q^18 - 180425297 * q^19 + 753620445 * q^20 + 827807931 * q^21 + 2300196142 * q^22 - 1305810279 * q^23 + 1107897021 * q^24 + 8070954867 * q^25 + 464550322 * q^26 - 12010035159 * q^27 - 9887169562 * q^28 + 6248352277 * q^29 + 2810049327 * q^30 - 26730150789 * q^31 - 24001343230 * q^32 - 2875152672 * q^33 - 36571033348 * q^34 + 10255900979 * q^35 + 67432422726 * q^36 - 43284776933 * q^37 - 36293696947 * q^38 + 35363806038 * q^39 - 105980683856 * q^40 - 9961079285 * q^41 + 37490617611 * q^42 - 51755851288 * q^43 - 59623729442 * q^44 + 17795833326 * q^45 - 202287132683 * q^46 - 82747063727 * q^47 - 269810553042 * q^48 + 535277836542 * q^49 + 526974390461 * q^50 - 60717257451 * q^51 + 544982341446 * q^52 + 561701818494 * q^53 + 20145865428 * q^54 - 521861534450 * q^55 - 228056576664 * q^56 + 131530041513 * q^57 + 10555409160 * q^58 - 1307596542871 * q^59 - 549389304405 * q^60 + 618193248201 * q^61 - 1486611437386 * q^62 - 603471981699 * q^63 + 679062548045 * q^64 - 1130583307122 * q^65 - 1676842987518 * q^66 - 4137387490592 * q^67 - 3901389300295 * q^68 + 951935693391 * q^69 - 819291947844 * q^70 - 3766439869810 * q^71 - 807656928309 * q^72 - 2386775553523 * q^73 + 3060770694642 * q^74 - 5883726098043 * q^75 - 847741068784 * q^76 + 1650423006137 * q^77 - 338657184738 * q^78 + 787155757766 * q^79 + 13999832121779 * q^80 + 8755315630911 * q^81 + 10083281915577 * q^82 + 8743877051639 * q^83 + 7207746610698 * q^84 + 15373177520565 * q^85 + 18939443838984 * q^86 - 4555048809933 * q^87 + 39713314506713 * q^88 + 11026795445259 * q^89 - 2048525959383 * q^90 + 23285721962531 * q^91 + 40411079823254 * q^92 + 19486279925181 * q^93 + 35237377585624 * q^94 + 13730236994039 * q^95 + 17496979214670 * q^96 + 10134565481560 * q^97 + 70916776240976 * q^98 + 2095986297888 * 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 $

$2$	20.8810	0.230705	0.115352	−	0.993325i	$-0.463200\pi$
$2$	20.8810	0.230705	0.115352	+	0.993325i	$0.463200\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	−7755.98	−0.946775
$5$	27865.9	0.797567	0.398784	−	0.917045i	$-0.369432\pi$
$5$	27865.9	0.797567	0.398784	+	0.917045i	$0.369432\pi$
$6$	−15222.2	−0.133197
$7$	61118.3	0.196351	0.0981756	−	0.995169i	$-0.468699\pi$
$7$	61118.3	0.196351	0.0981756	+	0.995169i	$0.468699\pi$
$8$	−333010.	−0.449130
$9$	531441.	0.333333
$10$	581867.	0.184002
$11$	−3.53045e6	−0.600865	−0.300433	−	0.953803i	$-0.597131\pi$
$11$	−3.53045e6	−0.600865	−0.300433	+	0.953803i	$0.597131\pi$
$12$	5.65411e6	0.546621
$13$	2.05403e7	1.18025	0.590127	−	0.807311i	$-0.299078\pi$
$13$	2.05403e7	1.18025	0.590127	+	0.807311i	$0.299078\pi$
$14$	1.27621e6	0.0452991
$15$	−2.03142e7	−0.460476
$16$	5.65834e7	0.843159
$17$	−1.17268e8	−1.17831	−0.589157	−	0.808018i	$-0.700540\pi$
$17$	−1.17268e8	−1.17831	−0.589157	+	0.808018i	$0.700540\pi$
$18$	1.10970e7	0.0769015
$19$	3.76293e6	0.0183497	0.00917483	−	0.999958i	$-0.497080\pi$
$19$	3.76293e6	0.0183497	0.00917483	+	0.999958i	$0.497080\pi$
$20$	−2.16127e8	−0.755117
$21$	−4.45552e7	−0.113363
$22$	−7.37192e7	−0.138622
$23$	−6.80717e8	−0.958818	−0.479409	−	0.877592i	$-0.659149\pi$
$23$	−6.80717e8	−0.958818	−0.479409	+	0.877592i	$0.659149\pi$
$24$	2.42764e8	0.259305
$25$	−4.44197e8	−0.363886
$26$	4.28902e8	0.272290
$27$	−3.87420e8	−0.192450
$28$	−4.74032e8	−0.185901
$29$	3.42738e9	1.06998	0.534990	−	0.844859i	$-0.320315\pi$
$29$	3.42738e9	1.06998	0.534990	+	0.844859i	$0.320315\pi$
$30$	−4.24181e8	−0.106234
$31$	−1.83633e9	−0.371620	−0.185810	−	0.982586i	$-0.559491\pi$
$31$	−1.83633e9	−0.371620	−0.185810	+	0.982586i	$0.559491\pi$
$32$	3.90954e9	0.643651
$33$	2.57370e9	0.346910
$34$	−2.44867e9	−0.271843
$35$	1.70311e9	0.156603
$36$	−4.12185e9	−0.315592
$37$	1.49290e10	0.956573	0.478287	−	0.878204i	$-0.341258\pi$
$37$	1.49290e10	0.956573	0.478287	+	0.878204i	$0.341258\pi$
$38$	7.85738e7	0.00423335
$39$	−1.49739e10	−0.681420
$40$	−9.27960e9	−0.358211
$41$	2.74461e10	0.902373	0.451186	−	0.892430i	$-0.351001\pi$
$41$	2.74461e10	0.902373	0.451186	+	0.892430i	$0.351001\pi$
$42$	−9.30357e8	−0.0261535
$43$	−4.39208e10	−1.05956	−0.529780	−	0.848135i	$-0.677725\pi$
$43$	−4.39208e10	−1.05956	−0.529780	+	0.848135i	$0.677725\pi$
$44$	2.73821e10	0.568885
$45$	1.48091e10	0.265856
$46$	−1.42141e10	−0.221204
$47$	4.98609e10	0.674721	0.337361	−	0.941375i	$-0.390466\pi$
$47$	4.98609e10	0.674721	0.337361	+	0.941375i	$0.390466\pi$
$48$	−4.12493e10	−0.486798
$49$	−9.31536e10	−0.961446
$50$	−9.27528e9	−0.0839502
$51$	8.54883e10	0.680300
$52$	−1.59310e11	−1.11744
$53$	1.99807e11	1.23828	0.619139	−	0.785282i	$-0.287482\pi$
$53$	1.99807e11	1.23828	0.619139	+	0.785282i	$0.287482\pi$
$54$	−8.08973e9	−0.0443991
$55$	−9.83789e10	−0.479231
$56$	−2.03530e10	−0.0881873
$57$	−2.74318e9	−0.0105942
$58$	7.15672e10	0.246849
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	1.57557e11	0.435967
$61$	2.57022e11	0.638743	0.319372	−	0.947630i	$-0.396528\pi$
$61$	2.57022e11	0.638743	0.319372	+	0.947630i	$0.396528\pi$
$62$	−3.83444e10	−0.0857345
$63$	3.24807e10	0.0654504
$64$	−3.81897e11	−0.694666
$65$	5.72374e11	0.941332
$66$	5.37413e10	0.0800337
$67$	1.02262e11	0.138111	0.0690555	−	0.997613i	$-0.478001\pi$
$67$	1.02262e11	0.138111	0.0690555	+	0.997613i	$0.478001\pi$
$68$	9.09528e11	1.11560
$69$	4.96243e11	0.553574
$70$	3.55627e10	0.0361291
$71$	−1.55726e12	−1.44272	−0.721361	−	0.692560i	$-0.756483\pi$
$71$	−1.55726e12	−1.44272	−0.721361	+	0.692560i	$0.756483\pi$
$72$	−1.76975e11	−0.149710
$73$	2.32473e12	1.79793	0.898967	−	0.438017i	$-0.144319\pi$
$73$	2.32473e12	1.79793	0.898967	+	0.438017i	$0.144319\pi$
$74$	3.11732e11	0.220686
$75$	3.23820e11	0.210090
$76$	−2.91853e10	−0.0173730
$77$	−2.15775e11	−0.117981
$78$	−3.12670e11	−0.157207
$79$	−3.36486e11	−0.155737	−0.0778684	−	0.996964i	$-0.524811\pi$
$79$	−3.36486e11	−0.155737	−0.0778684	+	0.996964i	$0.524811\pi$
$80$	1.57675e12	0.672476
$81$	2.82430e11	0.111111
$82$	5.73103e11	0.208182
$83$	1.25533e12	0.421454	0.210727	−	0.977545i	$-0.432417\pi$
$83$	1.25533e12	0.421454	0.210727	+	0.977545i	$0.432417\pi$
$84$	3.45569e11	0.107330
$85$	−3.26777e12	−0.939785
$86$	−9.17110e11	−0.244445
$87$	−2.49856e12	−0.617753
$88$	1.17567e12	0.269867
$89$	4.64185e12	0.990048	0.495024	−	0.868879i	$-0.335159\pi$
$89$	4.64185e12	0.990048	0.495024	+	0.868879i	$0.335159\pi$
$90$	3.09228e11	0.0613342
$91$	1.25539e12	0.231744
$92$	5.27963e12	0.907785
$93$	1.33868e12	0.214555
$94$	1.04115e12	0.155661
$95$	1.04857e11	0.0146351
$96$	−2.85005e12	−0.371612
$97$	1.27449e12	0.155353	0.0776766	−	0.996979i	$-0.475250\pi$
$97$	1.27449e12	0.155353	0.0776766	+	0.996979i	$0.475250\pi$
$98$	−1.94514e12	−0.221810
$99$	−1.87622e12	−0.200288
$100$	3.44519e12	0.344519
$101$	1.32306e12	0.124020	0.0620098	−	0.998076i	$-0.480249\pi$
$101$	1.32306e12	0.124020	0.0620098	+	0.998076i	$0.480249\pi$
$102$	1.78508e12	0.156948
$103$	6.96661e12	0.574883	0.287442	−	0.957798i	$-0.407195\pi$
$103$	6.96661e12	0.574883	0.287442	+	0.957798i	$0.407195\pi$
$104$	−6.84013e12	−0.530087
$105$	−1.24157e12	−0.0904150
$106$	4.17217e12	0.285676
$107$	−4.60780e12	−0.296824	−0.148412	−	0.988926i	$-0.547416\pi$
$107$	−4.60780e12	−0.296824	−0.148412	+	0.988926i	$0.547416\pi$
$108$	3.00483e12	0.182207
$109$	1.77365e11	0.0101297	0.00506484	−	0.999987i	$-0.498388\pi$
$109$	1.77365e11	0.0101297	0.00506484	+	0.999987i	$0.498388\pi$
$110$	−2.05425e12	−0.110561
$111$	−1.08832e13	−0.552278
$112$	3.45828e12	0.165555
$113$	1.41676e12	0.0640155	0.0320077	−	0.999488i	$-0.489810\pi$
$113$	1.41676e12	0.0640155	0.0320077	+	0.999488i	$0.489810\pi$
$114$	−5.72803e10	−0.00244413
$115$	−1.89688e13	−0.764722
$116$	−2.65827e13	−1.01303
$117$	1.09160e13	0.393418
$118$	−8.80772e11	−0.0300352
$119$	−7.16721e12	−0.231364
$120$	6.76483e12	0.206814
$121$	−2.20587e13	−0.638961
$122$	5.36687e12	0.147361
$123$	−2.00082e13	−0.520985
$124$	1.42425e13	0.351841
$125$	−4.63939e13	−1.08779
$126$	6.78230e11	0.0150997
$127$	−7.29322e13	−1.54239	−0.771197	−	0.636597i	$-0.780342\pi$
$127$	−7.29322e13	−1.54239	−0.771197	+	0.636597i	$0.780342\pi$
$128$	−4.00013e13	−0.803913
$129$	3.20183e13	0.611737
$130$	1.19517e13	0.217170
$131$	−2.71938e13	−0.470118	−0.235059	−	0.971981i	$-0.575528\pi$
$131$	−2.71938e13	−0.470118	−0.235059	+	0.971981i	$0.575528\pi$
$132$	−1.99615e13	−0.328446
$133$	2.29984e11	0.00360298
$134$	2.13533e12	0.0318629
$135$	−1.07958e13	−0.153492
$136$	3.90514e13	0.529216
$137$	−7.63322e12	−0.0986334	−0.0493167	−	0.998783i	$-0.515704\pi$
$137$	−7.63322e12	−0.0986334	−0.0493167	+	0.998783i	$0.515704\pi$
$138$	1.03620e13	0.127712
$139$	−3.56919e12	−0.0419733	−0.0209867	−	0.999780i	$-0.506681\pi$
$139$	−3.56919e12	−0.0419733	−0.0209867	+	0.999780i	$0.506681\pi$
$140$	−1.32093e13	−0.148268
$141$	−3.63486e13	−0.389551
$142$	−3.25172e13	−0.332842
$143$	−7.25165e13	−0.709174
$144$	3.00708e13	0.281053
$145$	9.55069e13	0.853381
$146$	4.85426e13	0.414792
$147$	6.79090e13	0.555091
$148$	−1.15789e14	−0.905660
$149$	−3.99812e13	−0.299327	−0.149663	−	0.988737i	$-0.547819\pi$
$149$	−3.99812e13	−0.299327	−0.149663	+	0.988737i	$0.547819\pi$
$150$	6.76168e12	0.0484687
$151$	−6.86589e13	−0.471353	−0.235677	−	0.971832i	$-0.575731\pi$
$151$	−6.86589e13	−0.471353	−0.235677	+	0.971832i	$0.575731\pi$
$152$	−1.25309e12	−0.00824139
$153$	−6.23210e13	−0.392771
$154$	−4.50559e12	−0.0272187
$155$	−5.11709e13	−0.296392
$156$	1.16137e14	0.645151
$157$	3.38824e14	1.80562	0.902811	−	0.430037i	$-0.141500\pi$
$157$	3.38824e14	1.80562	0.902811	+	0.430037i	$0.141500\pi$
$158$	−7.02617e12	−0.0359292
$159$	−1.45659e14	−0.714920
$160$	1.08943e14	0.513355
$161$	−4.16043e13	−0.188265
$162$	5.89741e12	0.0256338
$163$	−8.86561e13	−0.370245	−0.185122	−	0.982715i	$-0.559268\pi$
$163$	−8.86561e13	−0.370245	−0.185122	+	0.982715i	$0.559268\pi$
$164$	−2.12872e14	−0.854344
$165$	7.17182e13	0.276684
$166$	2.62125e13	0.0972314
$167$	−1.70881e14	−0.609590	−0.304795	−	0.952418i	$-0.598588\pi$
$167$	−1.70881e14	−0.609590	−0.304795	+	0.952418i	$0.598588\pi$
$168$	1.48373e13	0.0509149
$169$	1.19029e14	0.392999
$170$	−6.82343e13	−0.216813
$171$	1.99978e12	0.00611655
$172$	3.40649e14	1.00316
$173$	−3.02308e14	−0.857333	−0.428666	−	0.903463i	$-0.641016\pi$
$173$	−3.02308e14	−0.857333	−0.428666	+	0.903463i	$0.641016\pi$
$174$	−5.21725e13	−0.142518
$175$	−2.71486e13	−0.0714495
$176$	−1.99765e14	−0.506625
$177$	3.07496e13	0.0751646
$178$	9.69265e13	0.228409
$179$	−2.07521e14	−0.471539	−0.235769	−	0.971809i	$-0.575761\pi$
$179$	−2.07521e14	−0.471539	−0.235769	+	0.971809i	$0.575761\pi$
$180$	−1.14859e14	−0.251706
$181$	−6.71548e14	−1.41960	−0.709801	−	0.704402i	$-0.751215\pi$
$181$	−6.71548e14	−1.41960	−0.709801	+	0.704402i	$0.751215\pi$
$182$	2.62138e13	0.0534645
$183$	−1.87369e14	−0.368778
$184$	2.26686e14	0.430634
$185$	4.16008e14	0.762932
$186$	2.79531e13	0.0494989
$187$	4.14008e14	0.708008
$188$	−3.86721e14	−0.638810
$189$	−2.36785e13	−0.0377878
$190$	2.18953e12	0.00337638
$191$	1.16600e15	1.73772	0.868861	−	0.495056i	$-0.164853\pi$
$191$	1.16600e15	1.73772	0.868861	+	0.495056i	$0.164853\pi$
$192$	2.78403e14	0.401065
$193$	−1.23038e15	−1.71363	−0.856814	−	0.515625i	$-0.827560\pi$
$193$	−1.23038e15	−1.71363	−0.856814	+	0.515625i	$0.827560\pi$
$194$	2.66126e13	0.0358407
$195$	−4.17260e14	−0.543478
$196$	7.22498e14	0.910274
$197$	−1.51806e15	−1.85037	−0.925184	−	0.379520i	$-0.876089\pi$
$197$	−1.51806e15	−1.85037	−0.925184	+	0.379520i	$0.876089\pi$
$198$	−3.91774e13	−0.0462075
$199$	3.24648e12	0.00370567	0.00185284	−	0.999998i	$-0.499410\pi$
$199$	3.24648e12	0.00370567	0.00185284	+	0.999998i	$0.499410\pi$
$200$	1.47922e14	0.163432
$201$	−7.45491e13	−0.0797385
$202$	2.76268e13	0.0286119
$203$	2.09476e14	0.210092
$204$	−6.63046e14	−0.644091
$205$	7.64810e14	0.719703
$206$	1.45470e14	0.132628
$207$	−3.61761e14	−0.319606
$208$	1.16224e15	0.995141
$209$	−1.32848e13	−0.0110257
$210$	−2.59252e13	−0.0208592
$211$	1.45830e15	1.13765	0.568827	−	0.822457i	$-0.307397\pi$
$211$	1.45830e15	1.13765	0.568827	+	0.822457i	$0.307397\pi$
$212$	−1.54970e15	−1.17237
$213$	1.13524e15	0.832955
$214$	−9.62155e13	−0.0684787
$215$	−1.22389e15	−0.845070
$216$	1.29015e14	0.0864351
$217$	−1.12233e14	−0.0729681
$218$	3.70356e12	0.00233696
$219$	−1.69473e15	−1.03804
$220$	7.63025e14	0.453724
$221$	−2.40872e15	−1.39071
$222$	−2.27252e14	−0.127413
$223$	−3.58918e15	−1.95440	−0.977199	−	0.212324i	$-0.931897\pi$
$223$	−3.58918e15	−1.95440	−0.977199	+	0.212324i	$0.931897\pi$
$224$	2.38944e14	0.126382
$225$	−2.36065e14	−0.121295
$226$	2.95833e13	0.0147687
$227$	−2.73313e14	−0.132584	−0.0662922	−	0.997800i	$-0.521117\pi$
$227$	−2.73313e14	−0.132584	−0.0662922	+	0.997800i	$0.521117\pi$
$228$	2.12760e13	0.0100303
$229$	−3.13250e15	−1.43536	−0.717679	−	0.696374i	$-0.754795\pi$
$229$	−3.13250e15	−1.43536	−0.717679	+	0.696374i	$0.754795\pi$
$230$	−3.96087e14	−0.176425
$231$	1.57300e14	0.0681162
$232$	−1.14135e15	−0.480560
$233$	9.46506e14	0.387534	0.193767	−	0.981048i	$-0.437929\pi$
$233$	9.46506e14	0.387534	0.193767	+	0.981048i	$0.437929\pi$
$234$	2.27936e14	0.0907633
$235$	1.38942e15	0.538136
$236$	3.27152e14	0.123260
$237$	2.45299e14	0.0899147
$238$	−1.49659e14	−0.0533766
$239$	−2.20035e15	−0.763670	−0.381835	−	0.924231i	$-0.624708\pi$
$239$	−2.20035e15	−0.763670	−0.381835	+	0.924231i	$0.624708\pi$
$240$	−1.14945e15	−0.388254
$241$	−2.93638e15	−0.965388	−0.482694	−	0.875789i	$-0.660342\pi$
$241$	−2.93638e15	−0.965388	−0.482694	+	0.875789i	$0.660342\pi$
$242$	−4.60607e14	−0.147411
$243$	−2.05891e14	−0.0641500
$244$	−1.99346e15	−0.604746
$245$	−2.59580e15	−0.766818
$246$	−4.17792e14	−0.120194
$247$	7.72918e13	0.0216573
$248$	6.11516e14	0.166906
$249$	−9.15135e14	−0.243327
$250$	−9.68750e14	−0.250958
$251$	−1.95179e15	−0.492667	−0.246334	−	0.969185i	$-0.579226\pi$
$251$	−1.95179e15	−0.492667	−0.246334	+	0.969185i	$0.579226\pi$
$252$	−2.51920e14	−0.0619668
$253$	2.40324e15	0.576120
$254$	−1.52290e15	−0.355837
$255$	2.38220e15	0.542585
$256$	2.29323e15	0.509199
$257$	3.36927e15	0.729408	0.364704	−	0.931124i	$-0.381170\pi$
$257$	3.36927e15	0.729408	0.364704	+	0.931124i	$0.381170\pi$
$258$	6.68573e14	0.141131
$259$	9.12432e14	0.187824
$260$	−4.43932e15	−0.891230
$261$	1.82145e15	0.356660
$262$	−5.67834e14	−0.108458
$263$	3.60306e15	0.671366	0.335683	−	0.941975i	$-0.391033\pi$
$263$	3.60306e15	0.671366	0.335683	+	0.941975i	$0.391033\pi$
$264$	−8.57066e14	−0.155808
$265$	5.56780e15	0.987610
$266$	4.80229e12	0.000831224 0
$267$	−3.38391e15	−0.571605
$268$	−7.93143e14	−0.130760
$269$	1.04709e16	1.68498	0.842488	−	0.538715i	$-0.181090\pi$
$269$	1.04709e16	1.68498	0.842488	+	0.538715i	$0.181090\pi$
$270$	−2.25427e14	−0.0354113
$271$	−9.34514e14	−0.143313	−0.0716565	−	0.997429i	$-0.522829\pi$
$271$	−9.34514e14	−0.143313	−0.0716565	+	0.997429i	$0.522829\pi$
$272$	−6.63542e15	−0.993506
$273$	−9.15178e14	−0.133798
$274$	−1.59389e14	−0.0227552
$275$	1.56821e15	0.218647
$276$	−3.84885e15	−0.524110
$277$	−2.36833e15	−0.315009	−0.157504	−	0.987518i	$-0.550345\pi$
$277$	−2.36833e15	−0.315009	−0.157504	+	0.987518i	$0.550345\pi$
$278$	−7.45283e13	−0.00968344
$279$	−9.75901e14	−0.123873
$280$	−5.67153e14	−0.0703353
$281$	3.80118e15	0.460604	0.230302	−	0.973119i	$-0.426029\pi$
$281$	3.80118e15	0.460604	0.230302	+	0.973119i	$0.426029\pi$
$282$	−7.58996e14	−0.0898711
$283$	−1.32742e16	−1.53602	−0.768009	−	0.640439i	$-0.778753\pi$
$283$	−1.32742e16	−1.53602	−0.768009	+	0.640439i	$0.778753\pi$
$284$	1.20781e16	1.36593
$285$	−7.64410e13	−0.00844958
$286$	−1.51422e15	−0.163610
$287$	1.67746e15	0.177182
$288$	2.07769e15	0.214550
$289$	3.84718e15	0.388425
$290$	1.99428e15	0.196879
$291$	−9.29103e14	−0.0896932
$292$	−1.80306e16	−1.70224
$293$	−1.34267e16	−1.23973	−0.619867	−	0.784707i	$-0.712814\pi$
$293$	−1.34267e16	−1.23973	−0.619867	+	0.784707i	$0.712814\pi$
$294$	1.41801e15	0.128062
$295$	−1.17540e15	−0.103834
$296$	−4.97149e15	−0.429626
$297$	1.36777e15	0.115637
$298$	−8.34848e14	−0.0690560
$299$	−1.39822e16	−1.13165
$300$	−2.51154e15	−0.198908
$301$	−2.68436e15	−0.208046
$302$	−1.43367e15	−0.108743
$303$	−9.64510e14	−0.0716027
$304$	2.12920e14	0.0154717
$305$	7.16214e15	0.509441
$306$	−1.30132e15	−0.0906142
$307$	−1.64480e16	−1.12128	−0.560640	−	0.828060i	$-0.689445\pi$
$307$	−1.64480e16	−1.12128	−0.560640	+	0.828060i	$0.689445\pi$
$308$	1.67355e15	0.111701
$309$	−5.07866e15	−0.331909
$310$	−1.06850e15	−0.0683791
$311$	−2.51091e15	−0.157358	−0.0786788	−	0.996900i	$-0.525070\pi$
$311$	−2.51091e15	−0.157358	−0.0786788	+	0.996900i	$0.525070\pi$
$312$	4.98645e15	0.306046
$313$	−1.97719e16	−1.18853	−0.594264	−	0.804270i	$-0.702556\pi$
$313$	−1.97719e16	−1.18853	−0.594264	+	0.804270i	$0.702556\pi$
$314$	7.07499e15	0.416565
$315$	9.05104e14	0.0522011
$316$	2.60978e15	0.147448
$317$	−3.53817e16	−1.95837	−0.979183	−	0.202979i	$-0.934938\pi$
$317$	−3.53817e16	−1.95837	−0.979183	+	0.202979i	$0.934938\pi$
$318$	−3.04151e15	−0.164935
$319$	−1.21002e16	−0.642914
$320$	−1.06419e16	−0.554043
$321$	3.35909e15	0.171372
$322$	−8.68739e14	−0.0434336
$323$	−4.41271e14	−0.0216217
$324$	−2.19052e15	−0.105197
$325$	−9.12395e15	−0.429478
$326$	−1.85123e15	−0.0854172
$327$	−1.29299e14	−0.00584837
$328$	−9.13983e15	−0.405283
$329$	3.04741e15	0.132482
$330$	1.49755e15	0.0638323
$331$	1.42799e16	0.596818	0.298409	−	0.954438i	$-0.403544\pi$
$331$	1.42799e16	0.596818	0.298409	+	0.954438i	$0.403544\pi$
$332$	−9.73632e15	−0.399022
$333$	7.93386e15	0.318858
$334$	−3.56817e15	−0.140635
$335$	2.84962e15	0.110153
$336$	−2.52109e15	−0.0955834
$337$	4.09546e15	0.152303	0.0761514	−	0.997096i	$-0.475737\pi$
$337$	4.09546e15	0.152303	0.0761514	+	0.997096i	$0.475737\pi$
$338$	2.48545e15	0.0906666
$339$	−1.03281e15	−0.0369594
$340$	2.53448e16	0.889765
$341$	6.48306e15	0.223294
$342$	4.17573e13	0.00141112
$343$	−1.16151e16	−0.385132
$344$	1.46261e16	0.475880
$345$	1.38282e16	0.441512
$346$	−6.31249e15	−0.197791
$347$	−5.20554e16	−1.60075	−0.800377	−	0.599497i	$-0.795367\pi$
$347$	−5.20554e16	−1.60075	−0.800377	+	0.599497i	$0.795367\pi$
$348$	1.93788e16	0.584873
$349$	1.93726e16	0.573882	0.286941	−	0.957948i	$-0.407362\pi$
$349$	1.93726e16	0.573882	0.286941	+	0.957948i	$0.407362\pi$
$350$	−5.66889e14	−0.0164837
$351$	−7.95774e15	−0.227140
$352$	−1.38024e16	−0.386747
$353$	−3.79937e16	−1.04514	−0.522572	−	0.852595i	$-0.675027\pi$
$353$	−3.79937e16	−1.04514	−0.522572	+	0.852595i	$0.675027\pi$
$354$	6.42083e14	0.0173408
$355$	−4.33944e16	−1.15067
$356$	−3.60021e16	−0.937353
$357$	5.22490e15	0.133578
$358$	−4.33325e15	−0.108786
$359$	−2.18276e15	−0.0538136	−0.0269068	−	0.999638i	$-0.508566\pi$
$359$	−2.18276e15	−0.0538136	−0.0269068	+	0.999638i	$0.508566\pi$
$360$	−4.93156e15	−0.119404
$361$	−4.20388e16	−0.999663
$362$	−1.40226e16	−0.327509
$363$	1.60808e16	0.368904
$364$	−9.73677e15	−0.219410
$365$	6.47805e16	1.43397
$366$	−3.91245e15	−0.0850789
$367$	4.35444e16	0.930256	0.465128	−	0.885243i	$-0.346008\pi$
$367$	4.35444e16	0.930256	0.465128	+	0.885243i	$0.346008\pi$
$368$	−3.85173e16	−0.808436
$369$	1.45860e16	0.300791
$370$	8.68667e15	0.176012
$371$	1.22119e16	0.243137
$372$	−1.03828e16	−0.203136
$373$	5.44789e16	1.04742	0.523710	−	0.851896i	$-0.324547\pi$
$373$	5.44789e16	1.04742	0.523710	+	0.851896i	$0.324547\pi$
$374$	8.64490e15	0.163341
$375$	3.38211e16	0.628037
$376$	−1.66042e16	−0.303038
$377$	7.03995e16	1.26285
$378$	−4.94430e14	−0.00871782
$379$	5.34271e15	0.0925991	0.0462995	−	0.998928i	$-0.485257\pi$
$379$	5.34271e15	0.0925991	0.0462995	+	0.998928i	$0.485257\pi$
$380$	−8.13272e14	−0.0138561
$381$	5.31676e16	0.890501
$382$	2.43472e16	0.400900
$383$	9.80659e16	1.58754	0.793772	−	0.608215i	$-0.208114\pi$
$383$	9.80659e16	1.58754	0.793772	+	0.608215i	$0.208114\pi$
$384$	2.91609e16	0.464140
$385$	−6.01275e15	−0.0940975
$386$	−2.56916e16	−0.395342
$387$	−2.33413e16	−0.353187
$388$	−9.88492e15	−0.147085
$389$	9.92135e16	1.45177	0.725886	−	0.687815i	$-0.241430\pi$
$389$	9.92135e16	1.45177	0.725886	+	0.687815i	$0.241430\pi$
$390$	−8.71281e15	−0.125383
$391$	7.98263e16	1.12979
$392$	3.10211e16	0.431814
$393$	1.98243e16	0.271422
$394$	−3.16986e16	−0.426888
$395$	−9.37648e15	−0.124211
$396$	1.45520e16	0.189628
$397$	1.17008e17	1.49995	0.749974	−	0.661467i	$-0.230066\pi$
$397$	1.17008e17	1.49995	0.749974	+	0.661467i	$0.230066\pi$
$398$	6.77897e13	0.000854916 0
$399$	−1.67658e14	−0.00208018
$400$	−2.51342e16	−0.306814
$401$	−3.54991e16	−0.426362	−0.213181	−	0.977013i	$-0.568382\pi$
$401$	−3.54991e16	−0.426362	−0.213181	+	0.977013i	$0.568382\pi$
$402$	−1.55666e15	−0.0183960
$403$	−3.77188e16	−0.438606
$404$	−1.02616e16	−0.117419
$405$	7.87014e15	0.0886186
$406$	4.37406e15	0.0484692
$407$	−5.27059e16	−0.574772
$408$	−2.84684e16	−0.305543
$409$	1.03752e17	1.09596	0.547981	−	0.836491i	$-0.315396\pi$
$409$	1.03752e17	1.09596	0.547981	+	0.836491i	$0.315396\pi$
$410$	1.59700e16	0.166039
$411$	5.56462e15	0.0569460
$412$	−5.40329e16	−0.544285
$413$	−2.57800e15	−0.0255628
$414$	−7.55393e15	−0.0737345
$415$	3.49808e16	0.336138
$416$	8.03031e16	0.759671
$417$	2.60194e15	0.0242333
$418$	−2.77401e14	−0.00254367
$419$	−8.02079e16	−0.724146	−0.362073	−	0.932150i	$-0.617931\pi$
$419$	−8.02079e16	−0.724146	−0.362073	+	0.932150i	$0.617931\pi$
$420$	9.62959e15	0.0856027
$421$	−9.31693e16	−0.815529	−0.407765	−	0.913087i	$-0.633692\pi$
$421$	−9.31693e16	−0.815529	−0.407765	+	0.913087i	$0.633692\pi$
$422$	3.04507e16	0.262462
$423$	2.64982e16	0.224907
$424$	−6.65378e16	−0.556148
$425$	5.20901e16	0.428772
$426$	2.37050e16	0.192167
$427$	1.57087e16	0.125418
$428$	3.57381e16	0.281026
$429$	5.28645e16	0.409442
$430$	−2.55561e16	−0.194962
$431$	−9.15688e15	−0.0688090	−0.0344045	−	0.999408i	$-0.510953\pi$
$431$	−9.15688e15	−0.0688090	−0.0344045	+	0.999408i	$0.510953\pi$
$432$	−2.19216e16	−0.162266
$433$	2.30944e17	1.68397	0.841985	−	0.539500i	$-0.181387\pi$
$433$	2.30944e17	1.68397	0.841985	+	0.539500i	$0.181387\pi$
$434$	−2.34354e15	−0.0168341
$435$	−6.96246e16	−0.492700
$436$	−1.37564e15	−0.00959053
$437$	−2.56149e15	−0.0175940
$438$	−3.53876e16	−0.239480
$439$	1.64700e16	0.109818	0.0549089	−	0.998491i	$-0.482513\pi$
$439$	1.64700e16	0.109818	0.0549089	+	0.998491i	$0.482513\pi$
$440$	3.27611e16	0.215237
$441$	−4.95056e16	−0.320482
$442$	−5.02965e16	−0.320843
$443$	6.01390e15	0.0378035	0.0189017	−	0.999821i	$-0.493983\pi$
$443$	6.01390e15	0.0378035	0.0189017	+	0.999821i	$0.493983\pi$
$444$	8.44100e16	0.522883
$445$	1.29349e17	0.789630
$446$	−7.49456e16	−0.450889
$447$	2.91463e16	0.172816
$448$	−2.33409e16	−0.136399
$449$	−3.81409e16	−0.219680	−0.109840	−	0.993949i	$-0.535034\pi$
$449$	−3.81409e16	−0.219680	−0.109840	+	0.993949i	$0.535034\pi$
$450$	−4.92926e15	−0.0279834
$451$	−9.68971e16	−0.542205
$452$	−1.09883e16	−0.0606083
$453$	5.00523e16	0.272136
$454$	−5.70705e15	−0.0305878
$455$	3.49825e16	0.184832
$456$	9.13505e14	0.00475817
$457$	−7.74185e16	−0.397548	−0.198774	−	0.980045i	$-0.563696\pi$
$457$	−7.74185e16	−0.397548	−0.198774	+	0.980045i	$0.563696\pi$
$458$	−6.54097e16	−0.331144
$459$	4.54320e16	0.226767
$460$	1.47122e17	0.724020
$461$	−1.57961e17	−0.766466	−0.383233	−	0.923652i	$-0.625189\pi$
$461$	−1.57961e17	−0.766466	−0.383233	+	0.923652i	$0.625189\pi$
$462$	3.28458e15	0.0157147
$463$	2.66714e17	1.25826	0.629129	−	0.777301i	$-0.283412\pi$
$463$	2.66714e17	1.25826	0.629129	+	0.777301i	$0.283412\pi$
$464$	1.93933e17	0.902163
$465$	3.73036e16	0.171122
$466$	1.97640e16	0.0894059
$467$	2.59454e17	1.15745	0.578724	−	0.815524i	$-0.303551\pi$
$467$	2.59454e17	1.15745	0.578724	+	0.815524i	$0.303551\pi$
$468$	−8.46641e16	−0.372478
$469$	6.25008e15	0.0271183
$470$	2.90124e16	0.124150
$471$	−2.47003e17	−1.04248
$472$	1.40465e16	0.0584718
$473$	1.55060e17	0.636653
$474$	5.12208e15	0.0207437
$475$	−1.67148e15	−0.00667719
$476$	5.55888e16	0.219049
$477$	1.06186e17	0.412759
$478$	−4.59455e16	−0.176182
$479$	−4.56981e17	−1.72869	−0.864345	−	0.502900i	$-0.832267\pi$
$479$	−4.56981e17	−1.72869	−0.864345	+	0.502900i	$0.832267\pi$
$480$	−7.94191e16	−0.296386
$481$	3.06646e17	1.12900
$482$	−6.13146e16	−0.222719
$483$	3.03295e16	0.108695
$484$	1.71087e17	0.604952
$485$	3.55148e16	0.123905
$486$	−4.29921e15	−0.0147997
$487$	−1.94911e17	−0.662062	−0.331031	−	0.943620i	$-0.607396\pi$
$487$	−1.94911e17	−0.662062	−0.331031	+	0.943620i	$0.607396\pi$
$488$	−8.55908e16	−0.286879
$489$	6.46303e16	0.213761
$490$	−5.42030e16	−0.176908
$491$	−1.70429e17	−0.548926	−0.274463	−	0.961598i	$-0.588500\pi$
$491$	−1.70429e17	−0.548926	−0.274463	+	0.961598i	$0.588500\pi$
$492$	1.55183e17	0.493256
$493$	−4.01922e17	−1.26077
$494$	1.61393e15	0.00499643
$495$	−5.22826e16	−0.159744
$496$	−1.03906e17	−0.313335
$497$	−9.51771e16	−0.283280
$498$	−1.91089e16	−0.0561366
$499$	−1.61294e17	−0.467698	−0.233849	−	0.972273i	$-0.575132\pi$
$499$	−1.61294e17	−0.467698	−0.233849	+	0.972273i	$0.575132\pi$
$500$	3.59830e17	1.02989
$501$	1.24573e17	0.351947
$502$	−4.07553e16	−0.113661
$503$	3.85274e17	1.06066	0.530332	−	0.847790i	$-0.322067\pi$
$503$	3.85274e17	1.06066	0.530332	+	0.847790i	$0.322067\pi$
$504$	−1.08164e16	−0.0293958
$505$	3.68682e16	0.0989140
$506$	5.01820e16	0.132914
$507$	−8.67725e16	−0.226898
$508$	5.65661e17	1.46030
$509$	−3.52611e17	−0.898732	−0.449366	−	0.893348i	$-0.648350\pi$
$509$	−3.52611e17	−0.898732	−0.449366	+	0.893348i	$0.648350\pi$
$510$	4.97428e16	0.125177
$511$	1.42083e17	0.353027
$512$	3.75576e17	0.921388
$513$	−1.45784e15	−0.00353139
$514$	7.03537e16	0.168278
$515$	1.94131e17	0.458508
$516$	−2.48333e17	−0.579178
$517$	−1.76031e17	−0.405417
$518$	1.90525e16	0.0433320
$519$	2.20382e17	0.494981
$520$	−1.90606e17	−0.422780
$521$	−6.82893e16	−0.149592	−0.0747959	−	0.997199i	$-0.523831\pi$
$521$	−6.82893e16	−0.149592	−0.0747959	+	0.997199i	$0.523831\pi$
$522$	3.80337e16	0.0822831
$523$	4.17689e17	0.892466	0.446233	−	0.894917i	$-0.352765\pi$
$523$	4.17689e17	0.892466	0.446233	+	0.894917i	$0.352765\pi$
$524$	2.10915e17	0.445096
$525$	1.97913e16	0.0412514
$526$	7.52356e16	0.154887
$527$	2.15343e17	0.437886
$528$	1.45629e17	0.292500
$529$	−4.06601e16	−0.0806690
$530$	1.16261e17	0.227846
$531$	−2.24165e16	−0.0433963
$532$	−1.78375e15	−0.00341121
$533$	5.63752e17	1.06503
$534$	−7.06594e16	−0.131872
$535$	−1.28400e17	−0.236737
$536$	−3.40543e16	−0.0620298
$537$	1.51283e17	0.272243
$538$	2.18643e17	0.388732
$539$	3.28874e17	0.577700
$540$	8.37321e16	0.145322
$541$	−2.16614e17	−0.371454	−0.185727	−	0.982601i	$-0.559464\pi$
$541$	−2.16614e17	−0.371454	−0.185727	+	0.982601i	$0.559464\pi$
$542$	−1.95136e16	−0.0330630
$543$	4.89559e17	0.819607
$544$	−4.58463e17	−0.758423
$545$	4.94243e15	0.00807910
$546$	−1.91098e16	−0.0308677
$547$	−3.36177e17	−0.536600	−0.268300	−	0.963335i	$-0.586462\pi$
$547$	−3.36177e17	−0.536600	−0.268300	+	0.963335i	$0.586462\pi$
$548$	5.92031e16	0.0933837
$549$	1.36592e17	0.212914
$550$	3.27459e16	0.0504428
$551$	1.28970e16	0.0196338
$552$	−1.65254e17	−0.248627
$553$	−2.05655e16	−0.0305791
$554$	−4.94530e16	−0.0726740
$555$	−3.03270e17	−0.440479
$556$	2.76826e16	0.0397393
$557$	−9.72448e17	−1.37977	−0.689886	−	0.723918i	$-0.742339\pi$
$557$	−9.72448e17	−1.37977	−0.689886	+	0.723918i	$0.742339\pi$
$558$	−2.03778e16	−0.0285782
$559$	−9.02147e17	−1.25055
$560$	9.63680e16	0.132042
$561$	−3.01812e17	−0.408769
$562$	7.93724e16	0.106263
$563$	1.04329e18	1.38070	0.690352	−	0.723474i	$-0.257456\pi$
$563$	1.04329e18	1.38070	0.690352	+	0.723474i	$0.257456\pi$
$564$	2.81919e17	0.368817
$565$	3.94791e16	0.0510567
$566$	−2.77179e17	−0.354367
$567$	1.72616e16	0.0218168
$568$	5.18584e17	0.647969
$569$	−6.01984e17	−0.743627	−0.371813	−	0.928308i	$-0.621264\pi$
$569$	−6.01984e17	−0.743627	−0.371813	+	0.928308i	$0.621264\pi$
$570$	−1.59616e15	−0.00194936
$571$	6.04687e17	0.730123	0.365061	−	0.930983i	$-0.381048\pi$
$571$	6.04687e17	0.730123	0.365061	+	0.930983i	$0.381048\pi$
$572$	5.62437e17	0.671428
$573$	−8.50011e17	−1.00327
$574$	3.50270e16	0.0408767
$575$	3.02373e17	0.348901
$576$	−2.02955e17	−0.231555
$577$	−4.15422e17	−0.468648	−0.234324	−	0.972159i	$-0.575288\pi$
$577$	−4.15422e17	−0.468648	−0.234324	+	0.972159i	$0.575288\pi$
$578$	8.03330e16	0.0896114
$579$	8.96947e17	0.989364
$580$	−7.40750e17	−0.807960
$581$	7.67236e16	0.0827530
$582$	−1.94006e16	−0.0206926
$583$	−7.05409e17	−0.744038
$584$	−7.74157e17	−0.807506
$585$	3.04183e17	0.313777
$586$	−2.80362e17	−0.286013
$587$	−3.35130e17	−0.338116	−0.169058	−	0.985606i	$-0.554072\pi$
$587$	−3.35130e17	−0.338116	−0.169058	+	0.985606i	$0.554072\pi$
$588$	−5.26701e17	−0.525547
$589$	−6.90999e15	−0.00681911
$590$	−2.45435e16	−0.0239551
$591$	1.10666e18	1.06831
$592$	8.44732e17	0.806543
$593$	1.79338e17	0.169363	0.0846814	−	0.996408i	$-0.473013\pi$
$593$	1.79338e17	0.169363	0.0846814	+	0.996408i	$0.473013\pi$
$594$	2.85603e16	0.0266779
$595$	−1.99720e17	−0.184528
$596$	3.10094e17	0.283395
$597$	−2.36668e15	−0.00213947
$598$	−2.91961e17	−0.261076
$599$	−5.06562e17	−0.448083	−0.224042	−	0.974580i	$-0.571925\pi$
$599$	−5.06562e17	−0.448083	−0.224042	+	0.974580i	$0.571925\pi$
$600$	−1.07835e17	−0.0943577
$601$	2.32054e17	0.200865	0.100433	−	0.994944i	$-0.467977\pi$
$601$	2.32054e17	0.200865	0.100433	+	0.994944i	$0.467977\pi$
$602$	−5.60522e16	−0.0479971
$603$	5.43463e16	0.0460370
$604$	5.32517e17	0.446266
$605$	−6.14683e17	−0.509614
$606$	−2.01399e16	−0.0165191
$607$	−6.05840e17	−0.491622	−0.245811	−	0.969318i	$-0.579054\pi$
$607$	−6.05840e17	−0.491622	−0.245811	+	0.969318i	$0.579054\pi$
$608$	1.47113e16	0.0118108
$609$	−1.52708e17	−0.121297
$610$	1.49553e17	0.117530
$611$	1.02416e18	0.796342
$612$	4.83360e17	0.371866
$613$	−8.95906e17	−0.681976	−0.340988	−	0.940068i	$-0.610762\pi$
$613$	−8.95906e17	−0.681976	−0.340988	+	0.940068i	$0.610762\pi$
$614$	−3.43451e17	−0.258684
$615$	−5.57546e17	−0.415521
$616$	7.18551e16	0.0529887
$617$	1.60375e18	1.17026	0.585132	−	0.810938i	$-0.301043\pi$
$617$	1.60375e18	1.17026	0.585132	+	0.810938i	$0.301043\pi$
$618$	−1.06047e17	−0.0765729
$619$	−2.18879e18	−1.56392	−0.781961	−	0.623328i	$-0.785780\pi$
$619$	−2.18879e18	−1.56392	−0.781961	+	0.623328i	$0.785780\pi$
$620$	3.96881e17	0.280617
$621$	2.63724e17	0.184525
$622$	−5.24302e16	−0.0363031
$623$	2.83702e17	0.194397
$624$	−8.47274e17	−0.574545
$625$	−7.50572e17	−0.503701
$626$	−4.12856e17	−0.274199
$627$	9.68464e15	0.00636568
$628$	−2.62792e18	−1.70952
$629$	−1.75069e18	−1.12714
$630$	1.88995e16	0.0120430
$631$	3.75058e17	0.236541	0.118271	−	0.992981i	$-0.462265\pi$
$631$	3.75058e17	0.236541	0.118271	+	0.992981i	$0.462265\pi$
$632$	1.12053e17	0.0699461
$633$	−1.06310e18	−0.656825
$634$	−7.38806e17	−0.451804
$635$	−2.03232e18	−1.23016
$636$	1.12973e18	0.676868
$637$	−1.91340e18	−1.13475
$638$	−2.52664e17	−0.148323
$639$	−8.27593e17	−0.480907
$640$	−1.11467e18	−0.641175
$641$	−4.07307e17	−0.231924	−0.115962	−	0.993254i	$-0.536995\pi$
$641$	−4.07307e17	−0.231924	−0.115962	+	0.993254i	$0.536995\pi$
$642$	7.01411e16	0.0395362
$643$	−1.69566e18	−0.946169	−0.473084	−	0.881017i	$-0.656859\pi$
$643$	−1.69566e18	−0.946169	−0.473084	+	0.881017i	$0.656859\pi$
$644$	3.22682e17	0.178245
$645$	8.92217e17	0.487901
$646$	−9.21419e15	−0.00498822
$647$	6.79188e16	0.0364009	0.0182004	−	0.999834i	$-0.494206\pi$
$647$	6.79188e16	0.0364009	0.0182004	+	0.999834i	$0.494206\pi$
$648$	−9.40518e16	−0.0499033
$649$	1.48916e17	0.0782260
$650$	−1.90517e17	−0.0990826
$651$	8.18180e16	0.0421282
$652$	6.87615e17	0.350539
$653$	4.22685e17	0.213345	0.106672	−	0.994294i	$-0.465980\pi$
$653$	4.22685e17	0.213345	0.106672	+	0.994294i	$0.465980\pi$
$654$	−2.69989e15	−0.00134925
$655$	−7.57779e17	−0.374950
$656$	1.55300e18	0.760844
$657$	1.23546e18	0.599311
$658$	6.36330e16	0.0305643
$659$	−3.92987e18	−1.86906	−0.934529	−	0.355888i	$-0.884179\pi$
$659$	−3.92987e18	−1.86906	−0.934529	+	0.355888i	$0.884179\pi$
$660$	−5.56245e17	−0.261958
$661$	−1.79698e18	−0.837981	−0.418990	−	0.907991i	$-0.637616\pi$
$661$	−1.79698e18	−0.837981	−0.418990	+	0.907991i	$0.637616\pi$
$662$	2.98178e17	0.137689
$663$	1.75596e18	0.802927
$664$	−4.18037e17	−0.189288
$665$	6.40870e15	0.00287362
$666$	1.65667e17	0.0735620
$667$	−2.33308e18	−1.02592
$668$	1.32535e18	0.577145
$669$	2.61651e18	1.12837
$670$	5.95029e16	0.0254128
$671$	−9.07402e17	−0.383799
$672$	−1.74190e17	−0.0729665
$673$	−1.61201e18	−0.668760	−0.334380	−	0.942438i	$-0.608527\pi$
$673$	−1.61201e18	−0.668760	−0.334380	+	0.942438i	$0.608527\pi$
$674$	8.55172e16	0.0351370
$675$	1.72091e17	0.0700299
$676$	−9.23191e17	−0.372081
$677$	4.87247e17	0.194502	0.0972508	−	0.995260i	$-0.468995\pi$
$677$	4.87247e17	0.194502	0.0972508	+	0.995260i	$0.468995\pi$
$678$	−2.15662e16	−0.00852670
$679$	7.78946e16	0.0305038
$680$	1.08820e18	0.422086
$681$	1.99245e17	0.0765477
$682$	1.35373e17	0.0515149
$683$	−2.76053e18	−1.04054	−0.520268	−	0.854003i	$-0.674168\pi$
$683$	−2.76053e18	−1.04054	−0.520268	+	0.854003i	$0.674168\pi$
$684$	−1.55102e16	−0.00579100
$685$	−2.12706e17	−0.0786668
$686$	−2.42534e17	−0.0888518
$687$	2.28359e18	0.828704
$688$	−2.48519e18	−0.893377
$689$	4.10410e18	1.46148
$690$	2.88747e17	0.101859
$691$	2.87559e17	0.100489	0.0502447	−	0.998737i	$-0.484000\pi$
$691$	2.87559e17	0.100489	0.0502447	+	0.998737i	$0.484000\pi$
$692$	2.34469e18	0.811702
$693$	−1.14672e17	−0.0393269
$694$	−1.08697e18	−0.369301
$695$	−9.94586e16	−0.0334766
$696$	8.32045e17	0.277451
$697$	−3.21855e18	−1.06328
$698$	4.04519e17	0.132397
$699$	−6.90003e17	−0.223743
$700$	2.10564e17	0.0676467
$701$	−2.75660e17	−0.0877418	−0.0438709	−	0.999037i	$-0.513969\pi$
$701$	−2.75660e17	−0.0877418	−0.0438709	+	0.999037i	$0.513969\pi$
$702$	−1.66166e17	−0.0524022
$703$	5.61767e16	0.0175528
$704$	1.34827e18	0.417401
$705$	−1.01289e18	−0.310693
$706$	−7.93347e17	−0.241120
$707$	8.08630e16	0.0243514
$708$	−2.38493e17	−0.0711640
$709$	−2.00180e18	−0.591862	−0.295931	−	0.955209i	$-0.595630\pi$
$709$	−2.00180e18	−0.591862	−0.295931	+	0.955209i	$0.595630\pi$
$710$	−9.06119e17	−0.265464
$711$	−1.78823e17	−0.0519123
$712$	−1.54578e18	−0.444660
$713$	1.25002e18	0.356316
$714$	1.09101e17	0.0308170
$715$	−2.02073e18	−0.565614
$716$	1.60953e18	0.446441
$717$	1.60406e18	0.440905
$718$	−4.55782e16	−0.0124151
$719$	2.24291e18	0.605444	0.302722	−	0.953079i	$-0.402105\pi$
$719$	2.24291e18	0.605444	0.302722	+	0.953079i	$0.402105\pi$
$720$	8.37948e17	0.224159
$721$	4.25787e17	0.112879
$722$	−8.77813e17	−0.230627
$723$	2.14062e18	0.557367
$724$	5.20852e18	1.34404
$725$	−1.52243e18	−0.389351
$726$	3.35782e17	0.0851079
$727$	7.17739e18	1.80299	0.901494	−	0.432792i	$-0.142472\pi$
$727$	7.17739e18	1.80299	0.901494	+	0.432792i	$0.142472\pi$
$728$	−4.18057e17	−0.104083
$729$	1.50095e17	0.0370370
$730$	1.35268e18	0.330824
$731$	5.15050e18	1.24849
$732$	1.45323e18	0.349150
$733$	−3.13330e18	−0.746150	−0.373075	−	0.927801i	$-0.621697\pi$
$733$	−3.13330e18	−0.746150	−0.373075	+	0.927801i	$0.621697\pi$
$734$	9.09250e17	0.214614
$735$	1.89234e18	0.442723
$736$	−2.66129e18	−0.617144
$737$	−3.61031e17	−0.0829862
$738$	3.04570e17	0.0693939
$739$	−6.97251e18	−1.57471	−0.787354	−	0.616501i	$-0.788550\pi$
$739$	−6.97251e18	−1.57471	−0.787354	+	0.616501i	$0.788550\pi$
$740$	−3.22655e18	−0.722325
$741$	−5.63458e16	−0.0125038
$742$	2.54996e17	0.0560929
$743$	−1.09913e18	−0.239674	−0.119837	−	0.992794i	$-0.538237\pi$
$743$	−1.09913e18	−0.239674	−0.119837	+	0.992794i	$0.538237\pi$
$744$	−4.45795e17	−0.0963632
$745$	−1.11411e18	−0.238733
$746$	1.13757e18	0.241645
$747$	6.67134e17	0.140485
$748$	−3.21104e18	−0.670325
$749$	−2.81621e17	−0.0582818
$750$	7.06219e17	0.144891
$751$	5.70536e17	0.116044	0.0580221	−	0.998315i	$-0.481521\pi$
$751$	5.70536e17	0.116044	0.0580221	+	0.998315i	$0.481521\pi$
$752$	2.82130e18	0.568897
$753$	1.42285e18	0.284442
$754$	1.47001e18	0.291345
$755$	−1.91324e18	−0.375936
$756$	1.83650e17	0.0357766
$757$	−7.79524e18	−1.50559	−0.752794	−	0.658256i	$-0.771295\pi$
$757$	−7.79524e18	−1.50559	−0.752794	+	0.658256i	$0.771295\pi$
$758$	1.11561e17	0.0213630
$759$	−1.75196e18	−0.332623
$760$	−3.49185e16	−0.00657306
$761$	−6.74460e18	−1.25880	−0.629398	−	0.777083i	$-0.716699\pi$
$761$	−6.74460e18	−1.25880	−0.629398	+	0.777083i	$0.716699\pi$
$762$	1.11019e18	0.205443
$763$	1.08402e16	0.00198898
$764$	−9.04345e18	−1.64523
$765$	−1.73663e18	−0.313262
$766$	2.04771e18	0.366254
$767$	−8.66402e17	−0.153656
$768$	−1.67176e18	−0.293986
$769$	5.75544e17	0.100359	0.0501796	−	0.998740i	$-0.484021\pi$
$769$	5.75544e17	0.100359	0.0501796	+	0.998740i	$0.484021\pi$
$770$	−1.25552e17	−0.0217087
$771$	−2.45620e18	−0.421124
$772$	9.54281e18	1.62242
$773$	9.29101e18	1.56638	0.783188	−	0.621785i	$-0.213592\pi$
$773$	9.29101e18	1.56638	0.783188	+	0.621785i	$0.213592\pi$
$774$	−4.87390e17	−0.0814818
$775$	8.15692e17	0.135228
$776$	−4.24418e17	−0.0697738
$777$	−6.65163e17	−0.108440
$778$	2.07168e18	0.334931
$779$	1.03278e17	0.0165582
$780$	3.23626e18	0.514552
$781$	5.49783e18	0.866881
$782$	1.66685e18	0.260647
$783$	−1.32784e18	−0.205918
$784$	−5.27095e18	−0.810652
$785$	9.44163e18	1.44011
$786$	4.13951e17	0.0626184
$787$	4.83303e18	0.725076	0.362538	−	0.931969i	$-0.381910\pi$
$787$	4.83303e18	0.725076	0.362538	+	0.931969i	$0.381910\pi$
$788$	1.17740e19	1.75188
$789$	−2.62663e18	−0.387614
$790$	−1.95790e17	−0.0286560
$791$	8.65896e16	0.0125695
$792$	6.24801e17	0.0899556
$793$	5.27931e18	0.753879
$794$	2.44324e18	0.346045
$795$	−4.05893e18	−0.570197
$796$	−2.51796e16	−0.00350844
$797$	6.31421e18	0.872649	0.436325	−	0.899789i	$-0.356280\pi$
$797$	6.31421e18	0.872649	0.436325	+	0.899789i	$0.356280\pi$
$798$	−3.50087e15	−0.000479907 0
$799$	−5.84709e18	−0.795034
$800$	−1.73660e18	−0.234216
$801$	2.46687e18	0.330016
$802$	−7.41257e17	−0.0983638
$803$	−8.20733e18	−1.08032
$804$	5.78201e17	0.0754944
$805$	−1.15934e18	−0.150154
$806$	−7.87606e17	−0.101189
$807$	−7.63328e18	−0.972821
$808$	−4.40592e17	−0.0557009
$809$	−4.14704e18	−0.520083	−0.260042	−	0.965597i	$-0.583736\pi$
$809$	−4.14704e18	−0.520083	−0.260042	+	0.965597i	$0.583736\pi$
$810$	1.64336e17	0.0204447
$811$	−5.45234e18	−0.672895	−0.336447	−	0.941702i	$-0.609225\pi$
$811$	−5.45234e18	−0.672895	−0.336447	+	0.941702i	$0.609225\pi$
$812$	−1.62469e18	−0.198910
$813$	6.81261e17	0.0827417
$814$	−1.10055e18	−0.132603
$815$	−2.47048e18	−0.295295
$816$	4.83722e18	0.573601
$817$	−1.65271e17	−0.0194426
$818$	2.16645e18	0.252844
$819$	6.67165e17	0.0772481
$820$	−5.93185e18	−0.681397
$821$	1.06447e19	1.21311	0.606557	−	0.795040i	$-0.292550\pi$
$821$	1.06447e19	1.21311	0.606557	+	0.795040i	$0.292550\pi$
$822$	1.16195e17	0.0131377
$823$	3.57380e17	0.0400895	0.0200448	−	0.999799i	$-0.493619\pi$
$823$	3.57380e17	0.0400895	0.0200448	+	0.999799i	$0.493619\pi$
$824$	−2.31995e18	−0.258197
$825$	−1.14323e18	−0.126236
$826$	−5.38312e16	−0.00589745
$827$	6.30493e18	0.685322	0.342661	−	0.939459i	$-0.388672\pi$
$827$	6.30493e18	0.685322	0.342661	+	0.939459i	$0.388672\pi$
$828$	2.80581e18	0.302595
$829$	5.39659e18	0.577451	0.288726	−	0.957412i	$-0.406768\pi$
$829$	5.39659e18	0.577451	0.288726	+	0.957412i	$0.406768\pi$
$830$	7.30435e17	0.0775486
$831$	1.72651e18	0.181871
$832$	−7.84428e18	−0.819882
$833$	1.09239e19	1.13289
$834$	5.43311e16	0.00559074
$835$	−4.76176e18	−0.486189
$836$	1.03037e17	0.0104388
$837$	7.11432e17	0.0715184
$838$	−1.67482e18	−0.167064
$839$	9.98977e18	0.988787	0.494393	−	0.869238i	$-0.335390\pi$
$839$	9.98977e18	0.988787	0.494393	+	0.869238i	$0.335390\pi$
$840$	4.13455e17	0.0406081
$841$	1.48632e18	0.144856
$842$	−1.94547e18	−0.188146
$843$	−2.77106e18	−0.265930
$844$	−1.13105e19	−1.07710
$845$	3.31686e18	0.313443
$846$	5.53308e17	0.0518871
$847$	−1.34819e18	−0.125461
$848$	1.13058e19	1.04406
$849$	9.67689e18	0.886821
$850$	1.08769e18	0.0989198
$851$	−1.01624e19	−0.917179
$852$	−8.80493e18	−0.788622
$853$	−1.07605e19	−0.956457	−0.478229	−	0.878235i	$-0.658721\pi$
$853$	−1.07605e19	−0.956457	−0.478229	+	0.878235i	$0.658721\pi$
$854$	3.28014e17	0.0289345
$855$	5.57255e16	0.00487836
$856$	1.53444e18	0.133313
$857$	1.67522e19	1.44443	0.722214	−	0.691670i	$-0.243125\pi$
$857$	1.67522e19	1.44443	0.722214	+	0.691670i	$0.243125\pi$
$858$	1.10386e18	0.0944600
$859$	7.92902e18	0.673385	0.336693	−	0.941615i	$-0.390692\pi$
$859$	7.92902e18	0.673385	0.336693	+	0.941615i	$0.390692\pi$
$860$	9.49248e18	0.800092
$861$	−1.22287e18	−0.102296
$862$	−1.91205e17	−0.0158746
$863$	−2.18196e19	−1.79795	−0.898973	−	0.438003i	$-0.855686\pi$
$863$	−2.18196e19	−1.79795	−0.898973	+	0.438003i	$0.855686\pi$
$864$	−1.51463e18	−0.123871
$865$	−8.42406e18	−0.683781
$866$	4.82233e18	0.388500
$867$	−2.80460e18	−0.224257
$868$	8.70479e17	0.0690844
$869$	1.18795e18	0.0935769
$870$	−1.45383e18	−0.113668
$871$	2.10050e18	0.163006
$872$	−5.90643e16	−0.00454954
$873$	6.77316e17	0.0517844
$874$	−5.34866e16	−0.00405901
$875$	−2.83551e18	−0.213589
$876$	1.31443e19	0.982788
$877$	9.66319e18	0.717171	0.358586	−	0.933497i	$-0.383259\pi$
$877$	9.66319e18	0.717171	0.358586	+	0.933497i	$0.383259\pi$
$878$	3.43909e17	0.0253355
$879$	9.78804e18	0.715761
$880$	−5.56662e18	−0.404068
$881$	1.64352e19	1.18422	0.592109	−	0.805858i	$-0.298295\pi$
$881$	1.64352e19	1.18422	0.592109	+	0.805858i	$0.298295\pi$
$882$	−1.03373e18	−0.0739367
$883$	−1.84658e19	−1.31106	−0.655530	−	0.755169i	$-0.727555\pi$
$883$	−1.84658e19	−1.31106	−0.655530	+	0.755169i	$0.727555\pi$
$884$	1.86820e19	1.31669
$885$	8.56864e17	0.0599488
$886$	1.25576e17	0.00872144
$887$	−7.06988e18	−0.487426	−0.243713	−	0.969847i	$-0.578365\pi$
$887$	−7.06988e18	−0.487426	−0.243713	+	0.969847i	$0.578365\pi$
$888$	3.62422e18	0.248045
$889$	−4.45749e18	−0.302851
$890$	2.70094e18	0.182171
$891$	−9.97102e17	−0.0667628
$892$	2.78376e19	1.85038
$893$	1.87623e17	0.0123809
$894$	6.08604e17	0.0398695
$895$	−5.78275e18	−0.376084
$896$	−2.44481e18	−0.157849
$897$	1.01930e19	0.653357
$898$	−7.96420e17	−0.0506811
$899$	−6.29380e18	−0.397626
$900$	1.83091e18	0.114840
$901$	−2.34310e19	−1.45908
$902$	−2.02331e18	−0.125089
$903$	1.95690e18	0.120115
$904$	−4.71794e17	−0.0287513
$905$	−1.87133e19	−1.13223
$906$	1.04514e18	0.0627830
$907$	−1.27508e19	−0.760485	−0.380243	−	0.924887i	$-0.624160\pi$
$907$	−1.27508e19	−0.760485	−0.380243	+	0.924887i	$0.624160\pi$
$908$	2.11981e18	0.125528
$909$	7.03128e17	0.0413399
$910$	7.30469e17	0.0426415
$911$	4.48067e18	0.259701	0.129850	−	0.991534i	$-0.458550\pi$
$911$	4.48067e18	0.259701	0.129850	+	0.991534i	$0.458550\pi$
$912$	−1.55218e17	−0.00893258
$913$	−4.43187e18	−0.253237
$914$	−1.61658e18	−0.0917161
$915$	−5.22120e18	−0.294126
$916$	2.42956e19	1.35896
$917$	−1.66204e18	−0.0923082
$918$	9.48665e17	0.0523161
$919$	2.04324e19	1.11884	0.559420	−	0.828885i	$-0.311024\pi$
$919$	2.04324e19	1.11884	0.559420	+	0.828885i	$0.311024\pi$
$920$	6.31679e18	0.343459
$921$	1.19906e19	0.647371
$922$	−3.29838e18	−0.176827
$923$	−3.19867e19	−1.70278
$924$	−1.22001e18	−0.0644907
$925$	−6.63140e18	−0.348084
$926$	5.56926e18	0.290286
$927$	3.70234e18	0.191628
$928$	1.33995e19	0.688693
$929$	−2.01468e19	−1.02826	−0.514132	−	0.857711i	$-0.671886\pi$
$929$	−2.01468e19	−1.02826	−0.514132	+	0.857711i	$0.671886\pi$
$930$	7.78936e17	0.0394787
$931$	−3.50531e17	−0.0176422
$932$	−7.34108e18	−0.366908
$933$	1.83045e18	0.0908505
$934$	5.41767e18	0.267029
$935$	1.15367e19	0.564684
$936$	−3.63512e18	−0.176696
$937$	1.03671e18	0.0500436	0.0250218	−	0.999687i	$-0.492034\pi$
$937$	1.03671e18	0.0500436	0.0250218	+	0.999687i	$0.492034\pi$
$938$	1.30508e17	0.00625631
$939$	1.44137e19	0.686197
$940$	−1.07763e19	−0.509494
$941$	1.67806e19	0.787908	0.393954	−	0.919130i	$-0.371107\pi$
$941$	1.67806e19	0.787908	0.393954	+	0.919130i	$0.371107\pi$
$942$	−5.15767e18	−0.240504
$943$	−1.86831e19	−0.865211
$944$	−2.38672e18	−0.109770
$945$	−6.59821e17	−0.0301383
$946$	3.23781e18	0.146879
$947$	−1.59447e19	−0.718361	−0.359180	−	0.933268i	$-0.616944\pi$
$947$	−1.59447e19	−0.718361	−0.359180	+	0.933268i	$0.616944\pi$
$948$	−1.90253e18	−0.0851290
$949$	4.77507e19	2.12202
$950$	−3.49023e16	−0.00154046
$951$	2.57933e19	1.13066
$952$	2.38675e18	0.103912
$953$	2.88095e19	1.24575	0.622877	−	0.782320i	$-0.285964\pi$
$953$	2.88095e19	1.24575	0.622877	+	0.782320i	$0.285964\pi$
$954$	2.21726e18	0.0952254
$955$	3.24915e19	1.38595
$956$	1.70659e19	0.723024
$957$	8.82104e18	0.371186
$958$	−9.54221e18	−0.398817
$959$	−4.66529e17	−0.0193668
$960$	7.75793e18	0.319877
$961$	−2.10454e19	−0.861898
$962$	6.40306e18	0.260465
$963$	−2.44878e18	−0.0989414
$964$	2.27745e19	0.914006
$965$	−3.42856e19	−1.36673
$966$	6.33310e17	0.0250764
$967$	2.32383e19	0.913972	0.456986	−	0.889474i	$-0.348929\pi$
$967$	2.32383e19	0.913972	0.456986	+	0.889474i	$0.348929\pi$
$968$	7.34575e18	0.286977
$969$	3.21687e17	0.0124833
$970$	7.41584e17	0.0285854
$971$	1.73052e19	0.662599	0.331299	−	0.943526i	$-0.392513\pi$
$971$	1.73052e19	0.662599	0.331299	+	0.943526i	$0.392513\pi$
$972$	1.59689e18	0.0607357
$973$	−2.18143e17	−0.00824152
$974$	−4.06994e18	−0.152741
$975$	6.65136e18	0.247959
$976$	1.45432e19	0.538562
$977$	2.76119e18	0.101574	0.0507868	−	0.998710i	$-0.483827\pi$
$977$	2.76119e18	0.101574	0.0507868	+	0.998710i	$0.483827\pi$
$978$	1.34954e18	0.0493157
$979$	−1.63878e19	−0.594886
$980$	2.01330e19	0.726005
$981$	9.42590e16	0.00337656
$982$	−3.55873e18	−0.126640
$983$	2.26212e19	0.799682	0.399841	−	0.916585i	$-0.369065\pi$
$983$	2.26212e19	0.799682	0.399841	+	0.916585i	$0.369065\pi$
$984$	6.66294e18	0.233990
$985$	−4.23020e19	−1.47579
$986$	−8.39253e18	−0.290866
$987$	−2.22156e18	−0.0764887
$988$	−5.99474e17	−0.0205046
$989$	2.98977e19	1.01592
$990$	−1.09171e18	−0.0368536
$991$	−4.68696e19	−1.57186	−0.785928	−	0.618318i	$-0.787814\pi$
$991$	−4.68696e19	−1.57186	−0.785928	+	0.618318i	$0.787814\pi$
$992$	−7.17919e18	−0.239194
$993$	−1.04100e19	−0.344573
$994$	−1.98739e18	−0.0653540
$995$	9.04659e16	0.00295553
$996$	7.09778e18	0.230376
$997$	−3.16586e19	−1.02087	−0.510437	−	0.859915i	$-0.670517\pi$
$997$	−3.16586e19	−1.02087	−0.510437	+	0.859915i	$0.670517\pi$
$998$	−3.36799e18	−0.107900
$999$	−5.78378e18	−0.184093

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.17	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.17	✓	31	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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+20.8810 q^{2} -729.000 q^{3} -7755.98 q^{4} +27865.9 q^{5} -15222.2 q^{6} +61118.3 q^{7} -333010. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+20.8810 q^{2} -729.000 q^{3} -7755.98 q^{4} +27865.9 q^{5} -15222.2 q^{6} +61118.3 q^{7} -333010. q^{8} +531441. q^{9} +581867. q^{10} -3.53045e6 q^{11} +5.65411e6 q^{12} +2.05403e7 q^{13} +1.27621e6 q^{14} -2.03142e7 q^{15} +5.65834e7 q^{16} -1.17268e8 q^{17} +1.10970e7 q^{18} +3.76293e6 q^{19} -2.16127e8 q^{20} -4.45552e7 q^{21} -7.37192e7 q^{22} -6.80717e8 q^{23} +2.42764e8 q^{24} -4.44197e8 q^{25} +4.28902e8 q^{26} -3.87420e8 q^{27} -4.74032e8 q^{28} +3.42738e9 q^{29} -4.24181e8 q^{30} -1.83633e9 q^{31} +3.90954e9 q^{32} +2.57370e9 q^{33} -2.44867e9 q^{34} +1.70311e9 q^{35} -4.12185e9 q^{36} +1.49290e10 q^{37} +7.85738e7 q^{38} -1.49739e10 q^{39} -9.27960e9 q^{40} +2.74461e10 q^{41} -9.30357e8 q^{42} -4.39208e10 q^{43} +2.73821e10 q^{44} +1.48091e10 q^{45} -1.42141e10 q^{46} +4.98609e10 q^{47} -4.12493e10 q^{48} -9.31536e10 q^{49} -9.27528e9 q^{50} +8.54883e10 q^{51} -1.59310e11 q^{52} +1.99807e11 q^{53} -8.08973e9 q^{54} -9.83789e10 q^{55} -2.03530e10 q^{56} -2.74318e9 q^{57} +7.15672e10 q^{58} -4.21805e10 q^{59} +1.57557e11 q^{60} +2.57022e11 q^{61} -3.83444e10 q^{62} +3.24807e10 q^{63} -3.81897e11 q^{64} +5.72374e11 q^{65} +5.37413e10 q^{66} +1.02262e11 q^{67} +9.09528e11 q^{68} +4.96243e11 q^{69} +3.55627e10 q^{70} -1.55726e12 q^{71} -1.76975e11 q^{72} +2.32473e12 q^{73} +3.11732e11 q^{74} +3.23820e11 q^{75} -2.91853e10 q^{76} -2.15775e11 q^{77} -3.12670e11 q^{78} -3.36486e11 q^{79} +1.57675e12 q^{80} +2.82430e11 q^{81} +5.73103e11 q^{82} +1.25533e12 q^{83} +3.45569e11 q^{84} -3.26777e12 q^{85} -9.17110e11 q^{86} -2.49856e12 q^{87} +1.17567e12 q^{88} +4.64185e12 q^{89} +3.09228e11 q^{90} +1.25539e12 q^{91} +5.27963e12 q^{92} +1.33868e12 q^{93} +1.04115e12 q^{94} +1.04857e11 q^{95} -2.85005e12 q^{96} +1.27449e12 q^{97} -1.94514e12 q^{98} -1.87622e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9} - 3854663 q^{10} + 3943968 q^{11} - 92499894 q^{12} - 48510022 q^{13} - 51427459 q^{14} - 24411294 q^{15} + 370110498 q^{16} + 83288419 q^{17} - 27634932 q^{18} - 180425297 q^{19} + 753620445 q^{20} + 827807931 q^{21} + 2300196142 q^{22} - 1305810279 q^{23} + 1107897021 q^{24} + 8070954867 q^{25} + 464550322 q^{26} - 12010035159 q^{27} - 9887169562 q^{28} + 6248352277 q^{29} + 2810049327 q^{30} - 26730150789 q^{31} - 24001343230 q^{32} - 2875152672 q^{33} - 36571033348 q^{34} + 10255900979 q^{35} + 67432422726 q^{36} - 43284776933 q^{37} - 36293696947 q^{38} + 35363806038 q^{39} - 105980683856 q^{40} - 9961079285 q^{41} + 37490617611 q^{42} - 51755851288 q^{43} - 59623729442 q^{44} + 17795833326 q^{45} - 202287132683 q^{46} - 82747063727 q^{47} - 269810553042 q^{48} + 535277836542 q^{49} + 526974390461 q^{50} - 60717257451 q^{51} + 544982341446 q^{52} + 561701818494 q^{53} + 20145865428 q^{54} - 521861534450 q^{55} - 228056576664 q^{56} + 131530041513 q^{57} + 10555409160 q^{58} - 1307596542871 q^{59} - 549389304405 q^{60} + 618193248201 q^{61} - 1486611437386 q^{62} - 603471981699 q^{63} + 679062548045 q^{64} - 1130583307122 q^{65} - 1676842987518 q^{66} - 4137387490592 q^{67} - 3901389300295 q^{68} + 951935693391 q^{69} - 819291947844 q^{70} - 3766439869810 q^{71} - 807656928309 q^{72} - 2386775553523 q^{73} + 3060770694642 q^{74} - 5883726098043 q^{75} - 847741068784 q^{76} + 1650423006137 q^{77} - 338657184738 q^{78} + 787155757766 q^{79} + 13999832121779 q^{80} + 8755315630911 q^{81} + 10083281915577 q^{82} + 8743877051639 q^{83} + 7207746610698 q^{84} + 15373177520565 q^{85} + 18939443838984 q^{86} - 4555048809933 q^{87} + 39713314506713 q^{88} + 11026795445259 q^{89} - 2048525959383 q^{90} + 23285721962531 q^{91} + 40411079823254 q^{92} + 19486279925181 q^{93} + 35237377585624 q^{94} + 13730236994039 q^{95} + 17496979214670 q^{96} + 10134565481560 q^{97} + 70916776240976 q^{98} + 2095986297888 q^{99}+O(q^{100}) \) 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9 - 3854663 * q^10 + 3943968 * q^11 - 92499894 * q^12 - 48510022 * q^13 - 51427459 * q^14 - 24411294 * q^15 + 370110498 * q^16 + 83288419 * q^17 - 27634932 * q^18 - 180425297 * q^19 + 753620445 * q^20 + 827807931 * q^21 + 2300196142 * q^22 - 1305810279 * q^23 + 1107897021 * q^24 + 8070954867 * q^25 + 464550322 * q^26 - 12010035159 * q^27 - 9887169562 * q^28 + 6248352277 * q^29 + 2810049327 * q^30 - 26730150789 * q^31 - 24001343230 * q^32 - 2875152672 * q^33 - 36571033348 * q^34 + 10255900979 * q^35 + 67432422726 * q^36 - 43284776933 * q^37 - 36293696947 * q^38 + 35363806038 * q^39 - 105980683856 * q^40 - 9961079285 * q^41 + 37490617611 * q^42 - 51755851288 * q^43 - 59623729442 * q^44 + 17795833326 * q^45 - 202287132683 * q^46 - 82747063727 * q^47 - 269810553042 * q^48 + 535277836542 * q^49 + 526974390461 * q^50 - 60717257451 * q^51 + 544982341446 * q^52 + 561701818494 * q^53 + 20145865428 * q^54 - 521861534450 * q^55 - 228056576664 * q^56 + 131530041513 * q^57 + 10555409160 * q^58 - 1307596542871 * q^59 - 549389304405 * q^60 + 618193248201 * q^61 - 1486611437386 * q^62 - 603471981699 * q^63 + 679062548045 * q^64 - 1130583307122 * q^65 - 1676842987518 * q^66 - 4137387490592 * q^67 - 3901389300295 * q^68 + 951935693391 * q^69 - 819291947844 * q^70 - 3766439869810 * q^71 - 807656928309 * q^72 - 2386775553523 * q^73 + 3060770694642 * q^74 - 5883726098043 * q^75 - 847741068784 * q^76 + 1650423006137 * q^77 - 338657184738 * q^78 + 787155757766 * q^79 + 13999832121779 * q^80 + 8755315630911 * q^81 + 10083281915577 * q^82 + 8743877051639 * q^83 + 7207746610698 * q^84 + 15373177520565 * q^85 + 18939443838984 * q^86 - 4555048809933 * q^87 + 39713314506713 * q^88 + 11026795445259 * q^89 - 2048525959383 * q^90 + 23285721962531 * q^91 + 40411079823254 * q^92 + 19486279925181 * q^93 + 35237377585624 * q^94 + 13730236994039 * q^95 + 17496979214670 * q^96 + 10134565481560 * q^97 + 70916776240976 * q^98 + 2095986297888 * q^99

Introduction

L-functions

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