LMFDB - Embedded newform 177.14.a.b.1.14

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			1.14
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-42.0742 q^{2} -729.000 q^{3} -6421.76 q^{4} -29646.8 q^{5} +30672.1 q^{6} +519485. q^{7} +614862. q^{8} +531441. q^{9} +O(q^{10})$	\(q-42.0742 q^{2} -729.000 q^{3} -6421.76 q^{4} -29646.8 q^{5} +30672.1 q^{6} +519485. q^{7} +614862. q^{8} +531441. q^{9} +1.24737e6 q^{10} +5.17537e6 q^{11} +4.68146e6 q^{12} -1.50807e7 q^{13} -2.18569e7 q^{14} +2.16125e7 q^{15} +2.67372e7 q^{16} -4.83523e7 q^{17} -2.23600e7 q^{18} -1.21451e8 q^{19} +1.90385e8 q^{20} -3.78705e8 q^{21} -2.17750e8 q^{22} +1.03178e6 q^{23} -4.48235e8 q^{24} -3.41770e8 q^{25} +6.34508e8 q^{26} -3.87420e8 q^{27} -3.33601e9 q^{28} -2.75011e9 q^{29} -9.09329e8 q^{30} -7.52220e8 q^{31} -6.16190e9 q^{32} -3.77285e9 q^{33} +2.03438e9 q^{34} -1.54011e10 q^{35} -3.41279e9 q^{36} +2.97989e10 q^{37} +5.10997e9 q^{38} +1.09938e10 q^{39} -1.82287e10 q^{40} -2.00571e10 q^{41} +1.59337e10 q^{42} -4.09695e10 q^{43} -3.32350e10 q^{44} -1.57555e10 q^{45} -4.34111e7 q^{46} +1.04296e11 q^{47} -1.94915e10 q^{48} +1.72976e11 q^{49} +1.43797e10 q^{50} +3.52488e10 q^{51} +9.68446e10 q^{52} +2.07363e11 q^{53} +1.63004e10 q^{54} -1.53433e11 q^{55} +3.19412e11 q^{56} +8.85381e10 q^{57} +1.15709e11 q^{58} -4.21805e10 q^{59} -1.38790e11 q^{60} -1.41464e11 q^{61} +3.16490e10 q^{62} +2.76076e11 q^{63} +4.02254e10 q^{64} +4.47094e11 q^{65} +1.58739e11 q^{66} +7.07112e11 q^{67} +3.10507e11 q^{68} -7.52164e8 q^{69} +6.47988e11 q^{70} +1.32663e9 q^{71} +3.26763e11 q^{72} +6.69188e11 q^{73} -1.25376e12 q^{74} +2.49151e11 q^{75} +7.79932e11 q^{76} +2.68853e12 q^{77} -4.62556e11 q^{78} -3.83781e11 q^{79} -7.92674e11 q^{80} +2.82430e11 q^{81} +8.43888e11 q^{82} -3.96671e12 q^{83} +2.43195e12 q^{84} +1.43349e12 q^{85} +1.72376e12 q^{86} +2.00483e12 q^{87} +3.18214e12 q^{88} -2.74811e12 q^{89} +6.62901e11 q^{90} -7.83420e12 q^{91} -6.62582e9 q^{92} +5.48368e11 q^{93} -4.38816e12 q^{94} +3.60065e12 q^{95} +4.49202e12 q^{96} -1.54618e13 q^{97} -7.27783e12 q^{98} +2.75040e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−42.0742	−0.464859	−0.232429	−	0.972613i	$-0.574667\pi$
$2$	−42.0742	−0.464859	−0.232429	+	0.972613i	$0.574667\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	−6421.76	−0.783907
$5$	−29646.8	−0.848541	−0.424270	−	0.905536i	$-0.639469\pi$
$5$	−29646.8	−0.848541	−0.424270	+	0.905536i	$0.639469\pi$
$6$	30672.1	0.268386
$7$	519485.	1.66892	0.834461	−	0.551067i	$-0.185779\pi$
$7$	519485.	1.66892	0.834461	+	0.551067i	$0.185779\pi$
$8$	614862.	0.829264
$9$	531441.	0.333333
$10$	1.24737e6	0.394452
$11$	5.17537e6	0.880824	0.440412	−	0.897796i	$-0.354832\pi$
$11$	5.17537e6	0.880824	0.440412	+	0.897796i	$0.354832\pi$
$12$	4.68146e6	0.452589
$13$	−1.50807e7	−0.866542	−0.433271	−	0.901264i	$-0.642641\pi$
$13$	−1.50807e7	−0.866542	−0.433271	+	0.901264i	$0.642641\pi$
$14$	−2.18569e7	−0.775813
$15$	2.16125e7	0.489905
$16$	2.67372e7	0.398416
$17$	−4.83523e7	−0.485847	−0.242923	−	0.970045i	$-0.578106\pi$
$17$	−4.83523e7	−0.485847	−0.242923	+	0.970045i	$0.578106\pi$
$18$	−2.23600e7	−0.154953
$19$	−1.21451e8	−0.592249	−0.296124	−	0.955149i	$-0.595694\pi$
$19$	−1.21451e8	−0.592249	−0.296124	+	0.955149i	$0.595694\pi$
$20$	1.90385e8	0.665177
$21$	−3.78705e8	−0.963553
$22$	−2.17750e8	−0.409458
$23$	1.03178e6	0.00145330	0.000726648	−	1.00000i	$-0.499769\pi$
$23$	1.03178e6	0.00145330	0.000726648		1.00000i	$0.499769\pi$
$24$	−4.48235e8	−0.478776
$25$	−3.41770e8	−0.279978
$26$	6.34508e8	0.402819
$27$	−3.87420e8	−0.192450
$28$	−3.33601e9	−1.30828
$29$	−2.75011e9	−0.858545	−0.429272	−	0.903175i	$-0.641230\pi$
$29$	−2.75011e9	−0.858545	−0.429272	+	0.903175i	$0.641230\pi$
$30$	−9.09329e8	−0.227737
$31$	−7.52220e8	−0.152228	−0.0761139	−	0.997099i	$-0.524251\pi$
$31$	−7.52220e8	−0.152228	−0.0761139	+	0.997099i	$0.524251\pi$
$32$	−6.16190e9	−1.01447
$33$	−3.77285e9	−0.508544
$34$	2.03438e9	0.225850
$35$	−1.54011e10	−1.41615
$36$	−3.41279e9	−0.261302
$37$	2.97989e10	1.90936	0.954681	−	0.297631i	$-0.0961964\pi$
$37$	2.97989e10	1.90936	0.954681	+	0.297631i	$0.0961964\pi$
$38$	5.10997e9	0.275312
$39$	1.09938e10	0.500298
$40$	−1.82287e10	−0.703665
$41$	−2.00571e10	−0.659438	−0.329719	−	0.944079i	$-0.606954\pi$
$41$	−2.00571e10	−0.659438	−0.329719	+	0.944079i	$0.606954\pi$
$42$	1.59337e10	0.447916
$43$	−4.09695e10	−0.988362	−0.494181	−	0.869359i	$-0.664532\pi$
$43$	−4.09695e10	−0.988362	−0.494181	+	0.869359i	$0.664532\pi$
$44$	−3.32350e10	−0.690483
$45$	−1.57555e10	−0.282847
$46$	−4.34111e7	−0.000675577 0
$47$	1.04296e11	1.41134	0.705668	−	0.708543i	$-0.250647\pi$
$47$	1.04296e11	1.41134	0.705668	+	0.708543i	$0.250647\pi$
$48$	−1.94915e10	−0.230026
$49$	1.72976e11	1.78530
$50$	1.43797e10	0.130150
$51$	3.52488e10	0.280504
$52$	9.68446e10	0.679288
$53$	2.07363e11	1.28510	0.642551	−	0.766243i	$-0.277876\pi$
$53$	2.07363e11	1.28510	0.642551	+	0.766243i	$0.277876\pi$
$54$	1.63004e10	0.0894621
$55$	−1.53433e11	−0.747415
$56$	3.19412e11	1.38398
$57$	8.85381e10	0.341935
$58$	1.15709e11	0.399102
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−1.38790e11	−0.384040
$61$	−1.41464e11	−0.351561	−0.175781	−	0.984429i	$-0.556245\pi$
$61$	−1.41464e11	−0.351561	−0.175781	+	0.984429i	$0.556245\pi$
$62$	3.16490e10	0.0707644
$63$	2.76076e11	0.556307
$64$	4.02254e10	0.0731696
$65$	4.47094e11	0.735296
$66$	1.58739e11	0.236401
$67$	7.07112e11	0.954997	0.477499	−	0.878633i	$-0.341544\pi$
$67$	7.07112e11	0.954997	0.477499	+	0.878633i	$0.341544\pi$
$68$	3.10507e11	0.380858
$69$	−7.52164e8	−0.000839061 0
$70$	6.47988e11	0.658309
$71$	1.32663e9	0.00122905	0.000614525	−	1.00000i	$-0.499804\pi$
$71$	1.32663e9	0.00122905	0.000614525		1.00000i	$0.499804\pi$
$72$	3.26763e11	0.276421
$73$	6.69188e11	0.517547	0.258774	−	0.965938i	$-0.416682\pi$
$73$	6.69188e11	0.517547	0.258774	+	0.965938i	$0.416682\pi$
$74$	−1.25376e12	−0.887583
$75$	2.49151e11	0.161646
$76$	7.79932e11	0.464268
$77$	2.68853e12	1.47003
$78$	−4.62556e11	−0.232568
$79$	−3.83781e11	−0.177626	−0.0888132	−	0.996048i	$-0.528307\pi$
$79$	−3.83781e11	−0.177626	−0.0888132	+	0.996048i	$0.528307\pi$
$80$	−7.92674e11	−0.338072
$81$	2.82430e11	0.111111
$82$	8.43888e11	0.306545
$83$	−3.96671e12	−1.33175	−0.665875	−	0.746063i	$-0.731942\pi$
$83$	−3.96671e12	−1.33175	−0.665875	+	0.746063i	$0.731942\pi$
$84$	2.43195e12	0.755335
$85$	1.43349e12	0.412261
$86$	1.72376e12	0.459449
$87$	2.00483e12	0.495681
$88$	3.18214e12	0.730436
$89$	−2.74811e12	−0.586138	−0.293069	−	0.956091i	$-0.594676\pi$
$89$	−2.74811e12	−0.586138	−0.293069	+	0.956091i	$0.594676\pi$
$90$	6.62901e11	0.131484
$91$	−7.83420e12	−1.44619
$92$	−6.62582e9	−0.00113925
$93$	5.48368e11	0.0878887
$94$	−4.38816e12	−0.656071
$95$	3.60065e12	0.502547
$96$	4.49202e12	0.585705
$97$	−1.54618e13	−1.88471	−0.942353	−	0.334621i	$-0.891392\pi$
$97$	−1.54618e13	−1.88471	−0.942353	+	0.334621i	$0.891392\pi$
$98$	−7.27783e12	−0.829913
$99$	2.75040e12	0.293608
$100$	2.19477e12	0.219477
$101$	−2.70633e12	−0.253683	−0.126841	−	0.991923i	$-0.540484\pi$
$101$	−2.70633e12	−0.253683	−0.126841	+	0.991923i	$0.540484\pi$
$102$	−1.48307e12	−0.130395
$103$	−1.35987e13	−1.12216	−0.561079	−	0.827762i	$-0.689614\pi$
$103$	−1.35987e13	−1.12216	−0.561079	+	0.827762i	$0.689614\pi$
$104$	−9.27255e12	−0.718592
$105$	1.12274e13	0.817614
$106$	−8.72462e12	−0.597391
$107$	2.39297e13	1.54149	0.770747	−	0.637141i	$-0.219883\pi$
$107$	2.39297e13	1.54149	0.770747	+	0.637141i	$0.219883\pi$
$108$	2.48792e12	0.150863
$109$	1.35576e13	0.774305	0.387152	−	0.922016i	$-0.373459\pi$
$109$	1.35576e13	0.774305	0.387152	+	0.922016i	$0.373459\pi$
$110$	6.45558e12	0.347442
$111$	−2.17234e13	−1.10237
$112$	1.38896e13	0.664925
$113$	8.03222e12	0.362933	0.181466	−	0.983397i	$-0.441916\pi$
$113$	8.03222e12	0.362933	0.181466	+	0.983397i	$0.441916\pi$
$114$	−3.72517e12	−0.158951
$115$	−3.05888e10	−0.00123318
$116$	1.76605e13	0.673019
$117$	−8.01450e12	−0.288847
$118$	1.77471e12	0.0605194
$119$	−2.51183e13	−0.810840
$120$	1.32887e13	0.406261
$121$	−7.73825e12	−0.224150
$122$	5.95197e12	0.163426
$123$	1.46217e13	0.380727
$124$	4.83058e12	0.119332
$125$	4.63223e13	1.08611
$126$	−1.16157e13	−0.258604
$127$	4.69736e13	0.993413	0.496707	−	0.867919i	$-0.334543\pi$
$127$	4.69736e13	0.993413	0.496707	+	0.867919i	$0.334543\pi$
$128$	4.87858e13	0.980458
$129$	2.98668e13	0.570631
$130$	−1.88111e13	−0.341809
$131$	8.75068e13	1.51279	0.756394	−	0.654116i	$-0.226959\pi$
$131$	8.75068e13	1.51279	0.756394	+	0.654116i	$0.226959\pi$
$132$	2.42283e13	0.398651
$133$	−6.30923e13	−0.988417
$134$	−2.97512e13	−0.443939
$135$	1.14858e13	0.163302
$136$	−2.97300e13	−0.402895
$137$	3.36875e13	0.435297	0.217648	−	0.976027i	$-0.430161\pi$
$137$	3.36875e13	0.435297	0.217648	+	0.976027i	$0.430161\pi$
$138$	3.16467e10	0.000390045 0
$139$	−1.32566e14	−1.55896	−0.779482	−	0.626424i	$-0.784518\pi$
$139$	−1.32566e14	−1.55896	−0.779482	+	0.626424i	$0.784518\pi$
$140$	9.89021e13	1.11013
$141$	−7.60316e13	−0.814835
$142$	−5.58167e10	−0.000571334 0
$143$	−7.80482e13	−0.763271
$144$	1.42093e13	0.132805
$145$	8.15319e13	0.728510
$146$	−2.81556e13	−0.240586
$147$	−1.26100e14	−1.03074
$148$	−1.91361e14	−1.49676
$149$	−9.98894e13	−0.747840	−0.373920	−	0.927461i	$-0.621986\pi$
$149$	−9.98894e13	−0.747840	−0.373920	+	0.927461i	$0.621986\pi$
$150$	−1.04828e13	−0.0751423
$151$	2.35342e14	1.61566	0.807828	−	0.589418i	$-0.200643\pi$
$151$	2.35342e14	1.61566	0.807828	+	0.589418i	$0.200643\pi$
$152$	−7.46759e13	−0.491131
$153$	−2.56964e13	−0.161949
$154$	−1.13118e14	−0.683354
$155$	2.23009e13	0.129171
$156$	−7.05997e13	−0.392187
$157$	−1.47239e14	−0.784649	−0.392325	−	0.919827i	$-0.628329\pi$
$157$	−1.47239e14	−0.784649	−0.392325	+	0.919827i	$0.628329\pi$
$158$	1.61473e13	0.0825712
$159$	−1.51168e14	−0.741954
$160$	1.82681e14	0.860820
$161$	5.35992e11	0.00242544
$162$	−1.18830e13	−0.0516509
$163$	4.04430e14	1.68898	0.844489	−	0.535573i	$-0.179904\pi$
$163$	4.04430e14	1.68898	0.844489	+	0.535573i	$0.179904\pi$
$164$	1.28802e14	0.516938
$165$	1.11853e14	0.431520
$166$	1.66896e14	0.619076
$167$	1.05281e14	0.375572	0.187786	−	0.982210i	$-0.439869\pi$
$167$	1.05281e14	0.375572	0.187786	+	0.982210i	$0.439869\pi$
$168$	−2.32851e14	−0.799040
$169$	−7.54478e13	−0.249105
$170$	−6.03130e13	−0.191643
$171$	−6.45443e13	−0.197416
$172$	2.63097e14	0.774783
$173$	−4.71850e14	−1.33815	−0.669075	−	0.743195i	$-0.733309\pi$
$173$	−4.71850e14	−1.33815	−0.669075	+	0.743195i	$0.733309\pi$
$174$	−8.43516e13	−0.230422
$175$	−1.77545e14	−0.467262
$176$	1.38375e14	0.350934
$177$	3.07496e13	0.0751646
$178$	1.15625e14	0.272471
$179$	−2.39788e14	−0.544858	−0.272429	−	0.962176i	$-0.587827\pi$
$179$	−2.39788e14	−0.544858	−0.272429	+	0.962176i	$0.587827\pi$
$180$	1.01178e14	0.221726
$181$	−9.22930e13	−0.195100	−0.0975502	−	0.995231i	$-0.531101\pi$
$181$	−9.22930e13	−0.195100	−0.0975502	+	0.995231i	$0.531101\pi$
$182$	3.29618e14	0.672274
$183$	1.03127e14	0.202974
$184$	6.34400e11	0.00120517
$185$	−8.83441e14	−1.62017
$186$	−2.30722e13	−0.0408558
$187$	−2.50241e14	−0.427945
$188$	−6.69762e14	−1.10636
$189$	−2.01259e14	−0.321184
$190$	−1.51494e14	−0.233613
$191$	7.45616e14	1.11122	0.555608	−	0.831444i	$-0.312485\pi$
$191$	7.45616e14	1.11122	0.555608	+	0.831444i	$0.312485\pi$
$192$	−2.93243e13	−0.0422445
$193$	−1.17016e14	−0.162975	−0.0814877	−	0.996674i	$-0.525967\pi$
$193$	−1.17016e14	−0.162975	−0.0814877	+	0.996674i	$0.525967\pi$
$194$	6.50542e14	0.876122
$195$	−3.25932e14	−0.424524
$196$	−1.11081e15	−1.39951
$197$	4.65777e14	0.567737	0.283869	−	0.958863i	$-0.408382\pi$
$197$	4.65777e14	0.567737	0.283869	+	0.958863i	$0.408382\pi$
$198$	−1.15721e14	−0.136486
$199$	1.14963e15	1.31224	0.656118	−	0.754659i	$-0.272197\pi$
$199$	1.14963e15	1.31224	0.656118	+	0.754659i	$0.272197\pi$
$200$	−2.10142e14	−0.232176
$201$	−5.15485e14	−0.551368
$202$	1.13866e14	0.117927
$203$	−1.42864e15	−1.43284
$204$	−2.26360e14	−0.219889
$205$	5.94630e14	0.559560
$206$	5.72153e14	0.521645
$207$	5.48328e11	0.000484432 0
$208$	−4.03216e14	−0.345244
$209$	−6.28556e14	−0.521667
$210$	−4.72383e14	−0.380075
$211$	2.89074e14	0.225514	0.112757	−	0.993623i	$-0.464032\pi$
$211$	2.89074e14	0.225514	0.112757	+	0.993623i	$0.464032\pi$
$212$	−1.33163e15	−1.00740
$213$	−9.67110e11	−0.000709592 0
$214$	−1.00682e15	−0.716577
$215$	1.21462e15	0.838666
$216$	−2.38210e14	−0.159592
$217$	−3.90767e14	−0.254056
$218$	−5.70427e14	−0.359942
$219$	−4.87838e14	−0.298806
$220$	9.85311e14	0.585904
$221$	7.29186e14	0.421006
$222$	9.13993e14	0.512446
$223$	1.08863e15	0.592785	0.296393	−	0.955066i	$-0.404216\pi$
$223$	1.08863e15	0.592785	0.296393	+	0.955066i	$0.404216\pi$
$224$	−3.20102e15	−1.69307
$225$	−1.81631e14	−0.0933261
$226$	−3.37949e14	−0.168712
$227$	2.58105e15	1.25207	0.626034	−	0.779796i	$-0.284677\pi$
$227$	2.58105e15	1.25207	0.626034	+	0.779796i	$0.284677\pi$
$228$	−5.68571e14	−0.268045
$229$	7.44687e14	0.341227	0.170613	−	0.985338i	$-0.445425\pi$
$229$	7.44687e14	0.341227	0.170613	+	0.985338i	$0.445425\pi$
$230$	1.28700e12	0.000573255 0
$231$	−1.95994e15	−0.848720
$232$	−1.69094e15	−0.711960
$233$	−8.04669e14	−0.329461	−0.164730	−	0.986339i	$-0.552675\pi$
$233$	−8.04669e14	−0.329461	−0.164730	+	0.986339i	$0.552675\pi$
$234$	3.37204e14	0.134273
$235$	−3.09203e15	−1.19758
$236$	2.70873e14	0.102056
$237$	2.79777e14	0.102553
$238$	1.05683e15	0.376926
$239$	−3.27505e15	−1.13666	−0.568332	−	0.822799i	$-0.692411\pi$
$239$	−3.27505e15	−1.13666	−0.568332	+	0.822799i	$0.692411\pi$
$240$	5.77859e14	0.195186
$241$	−4.16019e15	−1.36774	−0.683868	−	0.729606i	$-0.739703\pi$
$241$	−4.16019e15	−1.36774	−0.683868	+	0.729606i	$0.739703\pi$
$242$	3.25581e14	0.104198
$243$	−2.05891e14	−0.0641500
$244$	9.08447e14	0.275591
$245$	−5.12819e15	−1.51490
$246$	−6.15194e14	−0.176984
$247$	1.83157e15	0.513209
$248$	−4.62512e14	−0.126237
$249$	2.89173e15	0.768887
$250$	−1.94898e15	−0.504889
$251$	−4.91997e15	−1.24189	−0.620945	−	0.783854i	$-0.713251\pi$
$251$	−4.91997e15	−1.24189	−0.620945	+	0.783854i	$0.713251\pi$
$252$	−1.77289e15	−0.436093
$253$	5.33982e12	0.00128010
$254$	−1.97638e15	−0.461797
$255$	−1.04502e15	−0.238019
$256$	−2.38215e15	−0.528944
$257$	−5.09014e15	−1.10196	−0.550979	−	0.834519i	$-0.685745\pi$
$257$	−5.09014e15	−1.10196	−0.550979	+	0.834519i	$0.685745\pi$
$258$	−1.25662e15	−0.265263
$259$	1.54801e16	3.18658
$260$	−2.87113e15	−0.576404
$261$	−1.46152e15	−0.286182
$262$	−3.68178e15	−0.703233
$263$	1.12234e15	0.209129	0.104564	−	0.994518i	$-0.466655\pi$
$263$	1.12234e15	0.209129	0.104564	+	0.994518i	$0.466655\pi$
$264$	−2.31978e15	−0.421717
$265$	−6.14765e15	−1.09046
$266$	2.65456e15	0.459474
$267$	2.00337e15	0.338407
$268$	−4.54091e15	−0.748628
$269$	7.55630e15	1.21596	0.607980	−	0.793953i	$-0.291980\pi$
$269$	7.55630e15	1.21596	0.607980	+	0.793953i	$0.291980\pi$
$270$	−4.83255e14	−0.0759122
$271$	1.30920e15	0.200773	0.100387	−	0.994948i	$-0.467992\pi$
$271$	1.30920e15	0.200773	0.100387	+	0.994948i	$0.467992\pi$
$272$	−1.29281e15	−0.193569
$273$	5.71113e15	0.834959
$274$	−1.41738e15	−0.202351
$275$	−1.76879e15	−0.246611
$276$	4.83022e12	0.000657746 0
$277$	−4.81062e15	−0.639856	−0.319928	−	0.947442i	$-0.603659\pi$
$277$	−4.81062e15	−0.639856	−0.319928	+	0.947442i	$0.603659\pi$
$278$	5.57761e15	0.724698
$279$	−3.99761e14	−0.0507426
$280$	−9.46954e15	−1.17436
$281$	−7.61790e15	−0.923090	−0.461545	−	0.887117i	$-0.652705\pi$
$281$	−7.61790e15	−0.923090	−0.461545	+	0.887117i	$0.652705\pi$
$282$	3.19897e15	0.378783
$283$	−3.79838e15	−0.439528	−0.219764	−	0.975553i	$-0.570529\pi$
$283$	−3.79838e15	−0.439528	−0.219764	+	0.975553i	$0.570529\pi$
$284$	−8.51928e12	−0.000963460 0
$285$	−2.62487e15	−0.290146
$286$	3.28381e15	0.354813
$287$	−1.04194e16	−1.10055
$288$	−3.27469e15	−0.338157
$289$	−7.56663e15	−0.763953
$290$	−3.43039e15	−0.338654
$291$	1.12716e16	1.08814
$292$	−4.29737e15	−0.405709
$293$	−8.76568e14	−0.0809368	−0.0404684	−	0.999181i	$-0.512885\pi$
$293$	−8.76568e14	−0.0809368	−0.0404684	+	0.999181i	$0.512885\pi$
$294$	5.30554e15	0.479150
$295$	1.25052e15	0.110471
$296$	1.83222e16	1.58337
$297$	−2.00504e15	−0.169515
$298$	4.20276e15	0.347640
$299$	−1.55599e13	−0.00125934
$300$	−1.59999e15	−0.126715
$301$	−2.12831e16	−1.64950
$302$	−9.90182e15	−0.751052
$303$	1.97291e15	0.146464
$304$	−3.24728e15	−0.235961
$305$	4.19395e15	0.298314
$306$	1.08116e15	0.0752833
$307$	−6.06330e15	−0.413342	−0.206671	−	0.978410i	$-0.566263\pi$
$307$	−6.06330e15	−0.413342	−0.206671	+	0.978410i	$0.566263\pi$
$308$	−1.72651e16	−1.15236
$309$	9.91342e15	0.647878
$310$	−9.38293e14	−0.0600465
$311$	−1.63509e16	−1.02471	−0.512354	−	0.858774i	$-0.671227\pi$
$311$	−1.63509e16	−1.02471	−0.512354	+	0.858774i	$0.671227\pi$
$312$	6.75969e15	0.414879
$313$	−1.57463e16	−0.946541	−0.473271	−	0.880917i	$-0.656927\pi$
$313$	−1.57463e16	−0.946541	−0.473271	+	0.880917i	$0.656927\pi$
$314$	6.19497e15	0.364751
$315$	−8.18477e15	−0.472050
$316$	2.46455e15	0.139243
$317$	2.70870e16	1.49926	0.749628	−	0.661860i	$-0.230233\pi$
$317$	2.70870e16	1.49926	0.749628	+	0.661860i	$0.230233\pi$
$318$	6.36025e15	0.344904
$319$	−1.42328e16	−0.756226
$320$	−1.19256e15	−0.0620874
$321$	−1.74447e16	−0.889982
$322$	−2.25514e13	−0.00112749
$323$	5.87246e15	0.287742
$324$	−1.81370e15	−0.0871007
$325$	5.15413e15	0.242613
$326$	−1.70161e16	−0.785136
$327$	−9.88352e15	−0.447045
$328$	−1.23324e16	−0.546848
$329$	5.41801e16	2.35541
$330$	−4.70612e15	−0.200596
$331$	3.49968e15	0.146267	0.0731335	−	0.997322i	$-0.476700\pi$
$331$	3.49968e15	0.146267	0.0731335	+	0.997322i	$0.476700\pi$
$332$	2.54733e16	1.04397
$333$	1.58363e16	0.636454
$334$	−4.42962e15	−0.174588
$335$	−2.09636e16	−0.810354
$336$	−1.01255e16	−0.383895
$337$	−7.30781e15	−0.271764	−0.135882	−	0.990725i	$-0.543387\pi$
$337$	−7.30781e15	−0.271764	−0.135882	+	0.990725i	$0.543387\pi$
$338$	3.17440e15	0.115799
$339$	−5.85549e15	−0.209539
$340$	−9.20554e15	−0.323174
$341$	−3.89302e15	−0.134086
$342$	2.71565e15	0.0917707
$343$	3.95261e16	1.31061
$344$	−2.51906e16	−0.819613
$345$	2.22993e13	0.000711978 0
$346$	1.98527e16	0.622050
$347$	1.04858e16	0.322449	0.161224	−	0.986918i	$-0.448456\pi$
$347$	1.04858e16	0.322449	0.161224	+	0.986918i	$0.448456\pi$
$348$	−1.28745e16	−0.388568
$349$	−5.48359e16	−1.62442	−0.812212	−	0.583362i	$-0.801737\pi$
$349$	−5.48359e16	−1.62442	−0.812212	+	0.583362i	$0.801737\pi$
$350$	7.47005e15	0.217211
$351$	5.84257e15	0.166766
$352$	−3.18901e16	−0.893570
$353$	−4.50440e16	−1.23909	−0.619543	−	0.784963i	$-0.712682\pi$
$353$	−4.50440e16	−1.23909	−0.619543	+	0.784963i	$0.712682\pi$
$354$	−1.29376e15	−0.0349409
$355$	−3.93302e13	−0.00104290
$356$	1.76477e16	0.459477
$357$	1.83113e16	0.468139
$358$	1.00889e16	0.253282
$359$	4.67877e16	1.15350	0.576750	−	0.816921i	$-0.304321\pi$
$359$	4.67877e16	1.15350	0.576750	+	0.816921i	$0.304321\pi$
$360$	−9.68748e15	−0.234555
$361$	−2.73025e16	−0.649241
$362$	3.88316e15	0.0906941
$363$	5.64118e15	0.129413
$364$	5.03094e16	1.13368
$365$	−1.98393e16	−0.439160
$366$	−4.33899e15	−0.0943542
$367$	8.30206e16	1.77360	0.886802	−	0.462150i	$-0.152922\pi$
$367$	8.30206e16	1.77360	0.886802	+	0.462150i	$0.152922\pi$
$368$	2.75868e13	0.000579017 0
$369$	−1.06592e16	−0.219813
$370$	3.71700e16	0.753151
$371$	1.07722e17	2.14474
$372$	−3.52149e15	−0.0688966
$373$	−1.23123e16	−0.236719	−0.118359	−	0.992971i	$-0.537763\pi$
$373$	−1.23123e16	−0.236719	−0.118359	+	0.992971i	$0.537763\pi$
$374$	1.05287e16	0.198934
$375$	−3.37690e16	−0.627068
$376$	6.41275e16	1.17037
$377$	4.14735e16	0.743965
$378$	8.46782e15	0.149305
$379$	−8.67394e16	−1.50336	−0.751678	−	0.659530i	$-0.770755\pi$
$379$	−8.67394e16	−1.50336	−0.751678	+	0.659530i	$0.770755\pi$
$380$	−2.31225e16	−0.393950
$381$	−3.42438e16	−0.573547
$382$	−3.13712e16	−0.516558
$383$	−9.33161e15	−0.151065	−0.0755326	−	0.997143i	$-0.524066\pi$
$383$	−9.33161e15	−0.151065	−0.0755326	+	0.997143i	$0.524066\pi$
$384$	−3.55649e16	−0.566068
$385$	−7.97063e16	−1.24738
$386$	4.92335e15	0.0757605
$387$	−2.17729e16	−0.329454
$388$	9.92920e16	1.47743
$389$	3.33207e16	0.487575	0.243787	−	0.969829i	$-0.421610\pi$
$389$	3.33207e16	0.487575	0.243787	+	0.969829i	$0.421610\pi$
$390$	1.37133e16	0.197343
$391$	−4.98887e13	−0.000706079 0
$392$	1.06356e17	1.48049
$393$	−6.37924e16	−0.873409
$394$	−1.95972e16	−0.263918
$395$	1.13779e16	0.150723
$396$	−1.76624e16	−0.230161
$397$	−8.45703e16	−1.08413	−0.542063	−	0.840338i	$-0.682356\pi$
$397$	−8.45703e16	−1.08413	−0.542063	+	0.840338i	$0.682356\pi$
$398$	−4.83696e16	−0.610004
$399$	4.59943e16	0.570663
$400$	−9.13800e15	−0.111548
$401$	−1.34825e17	−1.61931	−0.809657	−	0.586903i	$-0.800347\pi$
$401$	−1.34825e17	−1.61931	−0.809657	+	0.586903i	$0.800347\pi$
$402$	2.16886e16	0.256308
$403$	1.13440e16	0.131912
$404$	1.73794e16	0.198864
$405$	−8.37313e15	−0.0942823
$406$	6.01089e16	0.666070
$407$	1.54220e17	1.68181
$408$	2.16732e16	0.232612
$409$	−9.46427e16	−0.999736	−0.499868	−	0.866102i	$-0.666618\pi$
$409$	−9.46427e16	−0.999736	−0.499868	+	0.866102i	$0.666618\pi$
$410$	−2.50186e16	−0.260116
$411$	−2.45582e16	−0.251319
$412$	8.73274e16	0.879667
$413$	−2.19122e16	−0.217275
$414$	−2.30705e13	−0.000225192 0
$415$	1.17600e17	1.13005
$416$	9.29257e16	0.879082
$417$	9.66407e16	0.900069
$418$	2.64460e16	0.242501
$419$	8.90865e16	0.804305	0.402153	−	0.915573i	$-0.368262\pi$
$419$	8.90865e16	0.804305	0.402153	+	0.915573i	$0.368262\pi$
$420$	−7.20996e16	−0.640933
$421$	2.41521e16	0.211408	0.105704	−	0.994398i	$-0.466290\pi$
$421$	2.41521e16	0.211408	0.105704	+	0.994398i	$0.466290\pi$
$422$	−1.21626e16	−0.104832
$423$	5.54270e16	0.470445
$424$	1.27500e17	1.06569
$425$	1.65254e16	0.136026
$426$	4.06904e13	0.000329860 0
$427$	−7.34884e16	−0.586729
$428$	−1.53671e17	−1.20839
$429$	5.68971e16	0.440675
$430$	−5.11040e16	−0.389861
$431$	−1.59848e17	−1.20117	−0.600584	−	0.799561i	$-0.705065\pi$
$431$	−1.59848e17	−1.20117	−0.600584	+	0.799561i	$0.705065\pi$
$432$	−1.03586e16	−0.0766752
$433$	1.98866e17	1.45007	0.725035	−	0.688712i	$-0.241824\pi$
$433$	1.98866e17	1.45007	0.725035	+	0.688712i	$0.241824\pi$
$434$	1.64412e16	0.118100
$435$	−5.94368e16	−0.420606
$436$	−8.70639e16	−0.606982
$437$	−1.25311e14	−0.000860714 0
$438$	2.05254e16	0.138902
$439$	−2.64129e17	−1.76115	−0.880576	−	0.473904i	$-0.842844\pi$
$439$	−2.64129e17	−1.76115	−0.880576	+	0.473904i	$0.842844\pi$
$440$	−9.43403e16	−0.619805
$441$	9.19266e16	0.595101
$442$	−3.06799e16	−0.195708
$443$	1.74987e17	1.09997	0.549987	−	0.835173i	$-0.314633\pi$
$443$	1.74987e17	1.09997	0.549987	+	0.835173i	$0.314633\pi$
$444$	1.39502e17	0.864156
$445$	8.14728e16	0.497362
$446$	−4.58031e16	−0.275561
$447$	7.28194e16	0.431765
$448$	2.08965e16	0.122114
$449$	4.30946e16	0.248211	0.124106	−	0.992269i	$-0.460394\pi$
$449$	4.30946e16	0.248211	0.124106	+	0.992269i	$0.460394\pi$
$450$	7.64197e15	0.0433834
$451$	−1.03803e17	−0.580849
$452$	−5.15810e16	−0.284505
$453$	−1.71564e17	−0.932800
$454$	−1.08595e17	−0.582034
$455$	2.32259e17	1.22715
$456$	5.44387e16	0.283555
$457$	−3.34947e17	−1.71997	−0.859984	−	0.510322i	$-0.829526\pi$
$457$	−3.34947e17	−1.71997	−0.859984	+	0.510322i	$0.829526\pi$
$458$	−3.13321e16	−0.158622
$459$	1.87327e16	0.0935012
$460$	1.96434e14	0.000966699 0
$461$	2.87280e17	1.39395	0.696977	−	0.717093i	$-0.254528\pi$
$461$	2.87280e17	1.39395	0.696977	+	0.717093i	$0.254528\pi$
$462$	8.24628e16	0.394535
$463$	4.24478e16	0.200253	0.100126	−	0.994975i	$-0.468075\pi$
$463$	4.24478e16	0.200253	0.100126	+	0.994975i	$0.468075\pi$
$464$	−7.35303e16	−0.342058
$465$	−1.62574e16	−0.0745772
$466$	3.38558e16	0.153153
$467$	3.42928e16	0.152983	0.0764915	−	0.997070i	$-0.475628\pi$
$467$	3.42928e16	0.152983	0.0764915	+	0.997070i	$0.475628\pi$
$468$	5.14672e16	0.226429
$469$	3.67334e17	1.59382
$470$	1.30095e17	0.556703
$471$	1.07337e17	0.453018
$472$	−2.59352e16	−0.107961
$473$	−2.12033e17	−0.870573
$474$	−1.17714e16	−0.0476725
$475$	4.15085e16	0.165817
$476$	1.61304e17	0.635623
$477$	1.10201e17	0.428368
$478$	1.37795e17	0.528388
$479$	4.39963e17	1.66431	0.832157	−	0.554540i	$-0.187106\pi$
$479$	4.39963e17	1.66431	0.832157	+	0.554540i	$0.187106\pi$
$480$	−1.33174e17	−0.496995
$481$	−4.49387e17	−1.65454
$482$	1.75037e17	0.635804
$483$	−3.90738e14	−0.00140033
$484$	4.96932e16	0.175712
$485$	4.58393e17	1.59925
$486$	8.66270e15	0.0298207
$487$	−1.14430e17	−0.388687	−0.194343	−	0.980934i	$-0.562258\pi$
$487$	−1.14430e17	−0.388687	−0.194343	+	0.980934i	$0.562258\pi$
$488$	−8.69807e16	−0.291537
$489$	−2.94830e17	−0.975132
$490$	2.15764e17	0.704215
$491$	−3.51378e17	−1.13173	−0.565867	−	0.824496i	$-0.691458\pi$
$491$	−3.51378e17	−1.13173	−0.565867	+	0.824496i	$0.691458\pi$
$492$	−9.38968e16	−0.298454
$493$	1.32974e17	0.417121
$494$	−7.70619e16	−0.238569
$495$	−8.15407e16	−0.249138
$496$	−2.01123e16	−0.0606500
$497$	6.89163e14	0.00205119
$498$	−1.21667e17	−0.357424
$499$	−3.75672e17	−1.08932	−0.544659	−	0.838658i	$-0.683341\pi$
$499$	−3.75672e17	−1.08932	−0.544659	+	0.838658i	$0.683341\pi$
$500$	−2.97471e17	−0.851412
$501$	−7.67499e16	−0.216837
$502$	2.07004e17	0.577304
$503$	6.23517e16	0.171655	0.0858275	−	0.996310i	$-0.472647\pi$
$503$	6.23517e16	0.171655	0.0858275	+	0.996310i	$0.472647\pi$
$504$	1.69749e17	0.461326
$505$	8.02339e16	0.215260
$506$	−2.24669e14	−0.000595065 0
$507$	5.50014e16	0.143821
$508$	−3.01653e17	−0.778743
$509$	4.79539e17	1.22224	0.611122	−	0.791536i	$-0.290718\pi$
$509$	4.79539e17	1.22224	0.611122	+	0.791536i	$0.290718\pi$
$510$	4.39682e16	0.110645
$511$	3.47634e17	0.863746
$512$	−2.99426e17	−0.734574
$513$	4.70528e16	0.113978
$514$	2.14164e17	0.512254
$515$	4.03157e17	0.952197
$516$	−1.91797e17	−0.447321
$517$	5.39769e17	1.24314
$518$	−6.51311e17	−1.48131
$519$	3.43979e17	0.772581
$520$	2.74901e17	0.609755
$521$	2.02174e17	0.442875	0.221437	−	0.975175i	$-0.428925\pi$
$521$	2.02174e17	0.442875	0.221437	+	0.975175i	$0.428925\pi$
$522$	6.14923e16	0.133034
$523$	−6.54643e17	−1.39876	−0.699380	−	0.714750i	$-0.746541\pi$
$523$	−6.54643e17	−1.39876	−0.699380	+	0.714750i	$0.746541\pi$
$524$	−5.61948e17	−1.18588
$525$	1.29430e17	0.269774
$526$	−4.72217e16	−0.0972153
$527$	3.63716e16	0.0739594
$528$	−1.00875e17	−0.202612
$529$	−5.04035e17	−0.999998
$530$	2.58657e17	0.506911
$531$	−2.24165e16	−0.0433963
$532$	4.05163e17	0.774827
$533$	3.02476e17	0.571431
$534$	−8.42904e16	−0.157311
$535$	−7.09438e17	−1.30802
$536$	4.34777e17	0.791945
$537$	1.74806e17	0.314574
$538$	−3.17925e17	−0.565249
$539$	8.95215e17	1.57254
$540$	−7.37589e16	−0.128013
$541$	−1.59102e17	−0.272830	−0.136415	−	0.990652i	$-0.543558\pi$
$541$	−1.59102e17	−0.272830	−0.136415	+	0.990652i	$0.543558\pi$
$542$	−5.50836e16	−0.0933312
$543$	6.72816e16	0.112641
$544$	2.97942e17	0.492878
$545$	−4.01941e17	−0.657029
$546$	−2.40291e17	−0.388138
$547$	1.62299e17	0.259059	0.129529	−	0.991576i	$-0.458653\pi$
$547$	1.62299e17	0.259059	0.129529	+	0.991576i	$0.458653\pi$
$548$	−2.16333e17	−0.341232
$549$	−7.51796e16	−0.117187
$550$	7.44203e16	0.114639
$551$	3.34005e17	0.508472
$552$	−4.62478e14	−0.000695804 0
$553$	−1.99369e17	−0.296445
$554$	2.02403e17	0.297443
$555$	6.44028e17	0.935407
$556$	8.51308e17	1.22208
$557$	2.97528e17	0.422152	0.211076	−	0.977470i	$-0.432303\pi$
$557$	2.97528e17	0.422152	0.211076	+	0.977470i	$0.432303\pi$
$558$	1.68196e16	0.0235881
$559$	6.17849e17	0.856457
$560$	−4.11782e17	−0.564216
$561$	1.82426e17	0.247074
$562$	3.20517e17	0.429106
$563$	−6.10404e17	−0.807817	−0.403909	−	0.914799i	$-0.632349\pi$
$563$	−6.10404e17	−0.807817	−0.403909	+	0.914799i	$0.632349\pi$
$564$	4.88257e17	0.638754
$565$	−2.38130e17	−0.307963
$566$	1.59814e17	0.204318
$567$	1.46718e17	0.185436
$568$	8.15692e14	0.00101921
$569$	−2.91779e17	−0.360433	−0.180217	−	0.983627i	$-0.557680\pi$
$569$	−2.91779e17	−0.360433	−0.180217	+	0.983627i	$0.557680\pi$
$570$	1.10439e17	0.134877
$571$	6.49232e17	0.783908	0.391954	−	0.919985i	$-0.371799\pi$
$571$	6.49232e17	0.783908	0.391954	+	0.919985i	$0.371799\pi$
$572$	5.01207e17	0.598333
$573$	−5.43554e17	−0.641561
$574$	4.38388e17	0.511601
$575$	−3.52630e14	−0.000406891 0
$576$	2.13774e16	0.0243899
$577$	−3.50407e17	−0.395303	−0.197652	−	0.980272i	$-0.563331\pi$
$577$	−3.50407e17	−0.395303	−0.197652	+	0.980272i	$0.563331\pi$
$578$	3.18360e17	0.355130
$579$	8.53046e16	0.0940939
$580$	−5.23579e17	−0.571084
$581$	−2.06065e18	−2.22259
$582$	−4.74245e17	−0.505829
$583$	1.07318e18	1.13195
$584$	4.11459e17	0.429183
$585$	2.37604e17	0.245099
$586$	3.68809e16	0.0376242
$587$	−7.37728e17	−0.744301	−0.372150	−	0.928172i	$-0.621379\pi$
$587$	−7.37728e17	−0.744301	−0.372150	+	0.928172i	$0.621379\pi$
$588$	8.09782e17	0.808007
$589$	9.13582e16	0.0901567
$590$	−5.26145e16	−0.0513532
$591$	−3.39551e17	−0.327783
$592$	7.96739e17	0.760720
$593$	−7.46191e17	−0.704684	−0.352342	−	0.935871i	$-0.614615\pi$
$593$	−7.46191e17	−0.704684	−0.352342	+	0.935871i	$0.614615\pi$
$594$	8.43606e16	0.0788003
$595$	7.44678e17	0.688031
$596$	6.41466e17	0.586236
$597$	−8.38078e17	−0.757619
$598$	6.54670e14	0.000585416 0
$599$	2.57448e17	0.227727	0.113863	−	0.993496i	$-0.463677\pi$
$599$	2.57448e17	0.227727	0.113863	+	0.993496i	$0.463677\pi$
$600$	1.53193e17	0.134047
$601$	−4.42336e17	−0.382885	−0.191442	−	0.981504i	$-0.561317\pi$
$601$	−4.42336e17	−0.382885	−0.191442	+	0.981504i	$0.561317\pi$
$602$	8.95468e17	0.766784
$603$	3.75788e17	0.318332
$604$	−1.51131e18	−1.26652
$605$	2.29414e17	0.190200
$606$	−8.30087e16	−0.0680850
$607$	−1.20369e18	−0.976762	−0.488381	−	0.872630i	$-0.662412\pi$
$607$	−1.20369e18	−0.976762	−0.488381	+	0.872630i	$0.662412\pi$
$608$	7.48372e17	0.600820
$609$	1.04148e18	0.827253
$610$	−1.76457e17	−0.138674
$611$	−1.57285e18	−1.22298
$612$	1.65016e17	0.126953
$613$	−2.42900e18	−1.84899	−0.924495	−	0.381194i	$-0.875513\pi$
$613$	−2.42900e18	−1.84899	−0.924495	+	0.381194i	$0.875513\pi$
$614$	2.55109e17	0.192146
$615$	−4.33485e17	−0.323062
$616$	1.65308e18	1.21904
$617$	1.65295e18	1.20616	0.603082	−	0.797679i	$-0.293939\pi$
$617$	1.65295e18	1.20616	0.603082	+	0.797679i	$0.293939\pi$
$618$	−4.17099e17	−0.301172
$619$	−1.73811e17	−0.124190	−0.0620951	−	0.998070i	$-0.519778\pi$
$619$	−1.73811e17	−0.124190	−0.0620951	+	0.998070i	$0.519778\pi$
$620$	−1.43211e17	−0.101258
$621$	−3.99731e14	−0.000279687 0
$622$	6.87953e17	0.476345
$623$	−1.42760e18	−0.978218
$624$	2.93945e17	0.199327
$625$	−9.56109e17	−0.641634
$626$	6.62512e17	0.440008
$627$	4.58218e17	0.301185
$628$	9.45535e17	0.615092
$629$	−1.44084e18	−0.927657
$630$	3.44367e17	0.219436
$631$	−6.50398e17	−0.410193	−0.205097	−	0.978742i	$-0.565751\pi$
$631$	−6.50398e17	−0.410193	−0.205097	+	0.978742i	$0.565751\pi$
$632$	−2.35973e17	−0.147299
$633$	−2.10735e17	−0.130200
$634$	−1.13966e18	−0.696942
$635$	−1.39262e18	−0.842952
$636$	9.70762e17	0.581623
$637$	−2.60860e18	−1.54704
$638$	5.98835e17	0.351538
$639$	7.05023e14	0.000409683 0
$640$	−1.44634e18	−0.831959
$641$	−1.96015e18	−1.11612	−0.558062	−	0.829799i	$-0.688455\pi$
$641$	−1.96015e18	−1.11612	−0.558062	+	0.829799i	$0.688455\pi$
$642$	7.33972e17	0.413716
$643$	−1.03447e18	−0.577226	−0.288613	−	0.957446i	$-0.593194\pi$
$643$	−1.03447e18	−0.577226	−0.288613	+	0.957446i	$0.593194\pi$
$644$	−3.44202e15	−0.00190132
$645$	−8.85455e17	−0.484204
$646$	−2.47079e17	−0.133759
$647$	1.32889e18	0.712214	0.356107	−	0.934445i	$-0.384104\pi$
$647$	1.32889e18	0.712214	0.356107	+	0.934445i	$0.384104\pi$
$648$	1.73655e17	0.0921405
$649$	−2.18300e17	−0.114673
$650$	−2.16856e17	−0.112781
$651$	2.84869e17	0.146679
$652$	−2.59715e18	−1.32400
$653$	−2.51128e18	−1.26753	−0.633767	−	0.773524i	$-0.718492\pi$
$653$	−2.51128e18	−1.26753	−0.633767	+	0.773524i	$0.718492\pi$
$654$	4.15841e17	0.207813
$655$	−2.59430e18	−1.28366
$656$	−5.36273e17	−0.262731
$657$	3.55634e17	0.172516
$658$	−2.27958e18	−1.09493
$659$	5.35629e16	0.0254747	0.0127373	−	0.999919i	$-0.495945\pi$
$659$	5.35629e16	0.0254747	0.0127373	+	0.999919i	$0.495945\pi$
$660$	−7.18292e17	−0.338272
$661$	−4.15725e18	−1.93864	−0.969318	−	0.245811i	$-0.920946\pi$
$661$	−4.15725e18	−1.93864	−0.969318	+	0.245811i	$0.920946\pi$
$662$	−1.47246e17	−0.0679935
$663$	−5.31577e17	−0.243068
$664$	−2.43898e18	−1.10437
$665$	1.87048e18	0.838713
$666$	−6.66301e17	−0.295861
$667$	−2.83750e15	−0.00124772
$668$	−6.76090e17	−0.294414
$669$	−7.93609e17	−0.342245
$670$	8.82027e17	0.376700
$671$	−7.32127e17	−0.309664
$672$	2.33354e18	0.977497
$673$	−3.25282e17	−0.134947	−0.0674733	−	0.997721i	$-0.521494\pi$
$673$	−3.25282e17	−0.134947	−0.0674733	+	0.997721i	$0.521494\pi$
$674$	3.07470e17	0.126332
$675$	1.32409e17	0.0538818
$676$	4.84508e17	0.195275
$677$	−6.07475e17	−0.242495	−0.121247	−	0.992622i	$-0.538689\pi$
$677$	−6.07475e17	−0.242495	−0.121247	+	0.992622i	$0.538689\pi$
$678$	2.46365e17	0.0974061
$679$	−8.03218e18	−3.14543
$680$	8.81400e17	0.341873
$681$	−1.88158e18	−0.722882
$682$	1.63796e17	0.0623309
$683$	−2.15000e17	−0.0810408	−0.0405204	−	0.999179i	$-0.512902\pi$
$683$	−2.15000e17	−0.0810408	−0.0405204	+	0.999179i	$0.512902\pi$
$684$	4.14488e17	0.154756
$685$	−9.98727e17	−0.369367
$686$	−1.66303e18	−0.609247
$687$	−5.42877e17	−0.197007
$688$	−1.09541e18	−0.393779
$689$	−3.12718e18	−1.11360
$690$	−9.38224e14	−0.000330969 0
$691$	1.89309e18	0.661552	0.330776	−	0.943709i	$-0.392689\pi$
$691$	1.89309e18	0.661552	0.330776	+	0.943709i	$0.392689\pi$
$692$	3.03011e18	1.04898
$693$	1.42879e18	0.490009
$694$	−4.41182e17	−0.149893
$695$	3.93016e18	1.32285
$696$	1.23269e18	0.411050
$697$	9.69809e17	0.320386
$698$	2.30717e18	0.755127
$699$	5.86604e17	0.190214
$700$	1.14015e18	0.366290
$701$	2.71417e18	0.863913	0.431956	−	0.901895i	$-0.357823\pi$
$701$	2.71417e18	0.863913	0.431956	+	0.901895i	$0.357823\pi$
$702$	−2.45821e17	−0.0775226
$703$	−3.61911e18	−1.13082
$704$	2.08182e17	0.0644496
$705$	2.25409e18	0.691421
$706$	1.89519e18	0.576000
$707$	−1.40590e18	−0.423377
$708$	−1.97467e17	−0.0589220
$709$	−2.89163e18	−0.854953	−0.427476	−	0.904027i	$-0.640597\pi$
$709$	−2.89163e18	−0.854953	−0.427476	+	0.904027i	$0.640597\pi$
$710$	1.65479e15	0.000484800 0
$711$	−2.03957e17	−0.0592088
$712$	−1.68971e18	−0.486063
$713$	−7.76122e14	−0.000221232 0
$714$	−7.70431e17	−0.217618
$715$	2.31388e18	0.647666
$716$	1.53986e18	0.427117
$717$	2.38751e18	0.656253
$718$	−1.96855e18	−0.536215
$719$	−1.40046e18	−0.378037	−0.189019	−	0.981974i	$-0.560531\pi$
$719$	−1.40046e18	−0.378037	−0.189019	+	0.981974i	$0.560531\pi$
$720$	−4.21259e17	−0.112691
$721$	−7.06431e18	−1.87280
$722$	1.14873e18	0.301805
$723$	3.03278e18	0.789662
$724$	5.92684e17	0.152941
$725$	9.39905e17	0.240374
$726$	−2.37348e17	−0.0601586
$727$	2.30094e18	0.578006	0.289003	−	0.957328i	$-0.406676\pi$
$727$	2.30094e18	0.578006	0.289003	+	0.957328i	$0.406676\pi$
$728$	−4.81695e18	−1.19927
$729$	1.50095e17	0.0370370
$730$	8.34722e17	0.204147
$731$	1.98097e18	0.480192
$732$	−6.62258e17	−0.159113
$733$	5.18870e17	0.123561	0.0617807	−	0.998090i	$-0.480322\pi$
$733$	5.18870e17	0.123561	0.0617807	+	0.998090i	$0.480322\pi$
$734$	−3.49302e18	−0.824475
$735$	3.73845e18	0.874629
$736$	−6.35770e15	−0.00147433
$737$	3.65957e18	0.841184
$738$	4.48477e17	0.102182
$739$	4.45497e18	1.00613	0.503067	−	0.864247i	$-0.332205\pi$
$739$	4.45497e18	1.00613	0.503067	+	0.864247i	$0.332205\pi$
$740$	5.67325e18	1.27006
$741$	−1.33522e18	−0.296301
$742$	−4.53232e18	−0.996999
$743$	4.91263e18	1.07124	0.535620	−	0.844459i	$-0.320078\pi$
$743$	4.91263e18	1.07124	0.535620	+	0.844459i	$0.320078\pi$
$744$	3.37171e17	0.0728830
$745$	2.96140e18	0.634573
$746$	5.18031e17	0.110041
$747$	−2.10807e18	−0.443917
$748$	1.60699e18	0.335469
$749$	1.24311e19	2.57263
$750$	1.42080e18	0.291498
$751$	8.42095e16	0.0171278	0.00856390	−	0.999963i	$-0.497274\pi$
$751$	8.42095e16	0.0171278	0.00856390	+	0.999963i	$0.497274\pi$
$752$	2.78858e18	0.562299
$753$	3.58666e18	0.717006
$754$	−1.74497e18	−0.345838
$755$	−6.97713e18	−1.37095
$756$	1.29244e18	0.251778
$757$	−3.82632e18	−0.739022	−0.369511	−	0.929226i	$-0.620475\pi$
$757$	−3.82632e18	−0.739022	−0.369511	+	0.929226i	$0.620475\pi$
$758$	3.64949e18	0.698848
$759$	−3.89273e15	−0.000739065 0
$760$	2.21390e18	0.416745
$761$	−7.67763e18	−1.43294	−0.716468	−	0.697620i	$-0.754242\pi$
$761$	−7.67763e18	−1.43294	−0.716468	+	0.697620i	$0.754242\pi$
$762$	1.44078e18	0.266618
$763$	7.04300e18	1.29225
$764$	−4.78817e18	−0.871090
$765$	7.61816e17	0.137420
$766$	3.92620e17	0.0702240
$767$	6.36112e17	0.112814
$768$	1.73659e18	0.305386
$769$	−3.01793e18	−0.526246	−0.263123	−	0.964762i	$-0.584752\pi$
$769$	−3.01793e18	−0.526246	−0.263123	+	0.964762i	$0.584752\pi$
$770$	3.35358e18	0.579854
$771$	3.71071e18	0.636215
$772$	7.51448e17	0.127758
$773$	3.04317e18	0.513050	0.256525	−	0.966538i	$-0.417422\pi$
$773$	3.04317e18	0.513050	0.256525	+	0.966538i	$0.417422\pi$
$774$	9.16077e17	0.153150
$775$	2.57086e17	0.0426205
$776$	−9.50687e18	−1.56292
$777$	−1.12850e19	−1.83977
$778$	−1.40194e18	−0.226653
$779$	2.43597e18	0.390552
$780$	2.09306e18	0.332787
$781$	6.86578e15	0.00108258
$782$	2.09903e15	0.000328227 0
$783$	1.06545e18	0.165227
$784$	4.62490e18	0.711293
$785$	4.36517e18	0.665807
$786$	2.68401e18	0.406012
$787$	4.82693e18	0.724161	0.362081	−	0.932147i	$-0.382067\pi$
$787$	4.82693e18	0.724161	0.362081	+	0.932147i	$0.382067\pi$
$788$	−2.99111e18	−0.445053
$789$	−8.18189e17	−0.120741
$790$	−4.78715e17	−0.0700650
$791$	4.17262e18	0.605706
$792$	1.69112e18	0.243479
$793$	2.13337e18	0.304643
$794$	3.55823e18	0.503965
$795$	4.48163e18	0.629579
$796$	−7.38263e18	−1.02867
$797$	−5.54998e18	−0.767029	−0.383515	−	0.923535i	$-0.625286\pi$
$797$	−5.54998e18	−0.767029	−0.383515	+	0.923535i	$0.625286\pi$
$798$	−1.93517e18	−0.265278
$799$	−5.04294e18	−0.685693
$800$	2.10595e18	0.284030
$801$	−1.46046e18	−0.195379
$802$	5.67264e18	0.752752
$803$	3.46330e18	0.455868
$804$	3.31032e18	0.432221
$805$	−1.58905e16	−0.00205808
$806$	−4.77290e17	−0.0613203
$807$	−5.50854e18	−0.702035
$808$	−1.66402e18	−0.210370
$809$	−8.09954e18	−1.01577	−0.507885	−	0.861425i	$-0.669572\pi$
$809$	−8.09954e18	−1.01577	−0.507885	+	0.861425i	$0.669572\pi$
$810$	3.52293e17	0.0438279
$811$	1.04477e19	1.28939	0.644697	−	0.764438i	$-0.276983\pi$
$811$	1.04477e19	1.28939	0.644697	+	0.764438i	$0.276983\pi$
$812$	9.17440e18	1.12322
$813$	−9.54408e17	−0.115917
$814$	−6.48869e18	−0.781804
$815$	−1.19901e19	−1.43317
$816$	9.42457e17	0.111757
$817$	4.97581e18	0.585356
$818$	3.98201e18	0.464736
$819$	−4.16342e18	−0.482064
$820$	−3.81857e18	−0.438643
$821$	−5.88504e18	−0.670686	−0.335343	−	0.942096i	$-0.608852\pi$
$821$	−5.88504e18	−0.670686	−0.335343	+	0.942096i	$0.608852\pi$
$822$	1.03327e18	0.116828
$823$	1.26926e19	1.42381	0.711904	−	0.702276i	$-0.247833\pi$
$823$	1.26926e19	1.42381	0.711904	+	0.702276i	$0.247833\pi$
$824$	−8.36130e18	−0.930566
$825$	1.28945e18	0.142381
$826$	9.21937e17	0.101002
$827$	5.76038e17	0.0626131	0.0313065	−	0.999510i	$-0.490033\pi$
$827$	5.76038e17	0.0626131	0.0313065	+	0.999510i	$0.490033\pi$
$828$	−3.52123e15	−0.000379750 0
$829$	−1.73735e19	−1.85901	−0.929506	−	0.368808i	$-0.879766\pi$
$829$	−1.73735e19	−1.85901	−0.929506	+	0.368808i	$0.879766\pi$
$830$	−4.94794e18	−0.525311
$831$	3.50694e18	0.369421
$832$	−6.06628e17	−0.0634046
$833$	−8.36379e18	−0.867383
$834$	−4.06608e18	−0.418405
$835$	−3.12125e18	−0.318688
$836$	4.03644e18	0.408938
$837$	2.91425e17	0.0292962
$838$	−3.74824e18	−0.373888
$839$	−6.92308e18	−0.685246	−0.342623	−	0.939473i	$-0.611315\pi$
$839$	−6.92308e18	−0.685246	−0.342623	+	0.939473i	$0.611315\pi$
$840$	6.90330e18	0.678018
$841$	−2.69753e18	−0.262901
$842$	−1.01618e18	−0.0982748
$843$	5.55345e18	0.532946
$844$	−1.85636e18	−0.176782
$845$	2.23678e18	0.211376
$846$	−2.33205e18	−0.218690
$847$	−4.01991e18	−0.374088
$848$	5.54431e18	0.512005
$849$	2.76902e18	0.253761
$850$	−6.95292e17	−0.0632331
$851$	3.07457e16	0.00277487
$852$	6.21055e15	0.000556254 0
$853$	1.47745e19	1.31324	0.656619	−	0.754222i	$-0.271986\pi$
$853$	1.47745e19	1.31324	0.656619	+	0.754222i	$0.271986\pi$
$854$	3.09196e18	0.272746
$855$	1.91353e18	0.167516
$856$	1.47134e19	1.27831
$857$	−1.53348e19	−1.32222	−0.661108	−	0.750291i	$-0.729914\pi$
$857$	−1.53348e19	−1.32222	−0.661108	+	0.750291i	$0.729914\pi$
$858$	−2.39390e18	−0.204851
$859$	−1.65089e18	−0.140205	−0.0701023	−	0.997540i	$-0.522333\pi$
$859$	−1.65089e18	−0.140205	−0.0701023	+	0.997540i	$0.522333\pi$
$860$	−7.79997e18	−0.657435
$861$	7.59574e18	0.635403
$862$	6.72546e18	0.558373
$863$	1.77571e19	1.46319	0.731596	−	0.681738i	$-0.238776\pi$
$863$	1.77571e19	1.46319	0.731596	+	0.681738i	$0.238776\pi$
$864$	2.38725e18	0.195235
$865$	1.39889e19	1.13547
$866$	−8.36712e18	−0.674077
$867$	5.51607e18	0.441068
$868$	2.50941e18	0.199156
$869$	−1.98621e18	−0.156458
$870$	2.50075e18	0.195522
$871$	−1.06637e19	−0.827545
$872$	8.33608e18	0.642103
$873$	−8.21703e18	−0.628235
$874$	5.27234e15	0.000400110 0
$875$	2.40638e19	1.81264
$876$	3.13278e18	0.234236
$877$	1.31264e19	0.974204	0.487102	−	0.873345i	$-0.338054\pi$
$877$	1.31264e19	0.974204	0.487102	+	0.873345i	$0.338054\pi$
$878$	1.11130e19	0.818687
$879$	6.39018e17	0.0467289
$880$	−4.10238e18	−0.297782
$881$	1.27348e19	0.917594	0.458797	−	0.888541i	$-0.348281\pi$
$881$	1.27348e19	0.917594	0.458797	+	0.888541i	$0.348281\pi$
$882$	−3.86774e18	−0.276638
$883$	4.63386e17	0.0329002	0.0164501	−	0.999865i	$-0.494764\pi$
$883$	4.63386e17	0.0329002	0.0164501	+	0.999865i	$0.494764\pi$
$884$	−4.68266e18	−0.330030
$885$	−9.11628e17	−0.0637802
$886$	−7.36245e18	−0.511332
$887$	6.90504e18	0.476061	0.238030	−	0.971258i	$-0.423498\pi$
$887$	6.90504e18	0.476061	0.238030	+	0.971258i	$0.423498\pi$
$888$	−1.33569e19	−0.914157
$889$	2.44021e19	1.65793
$890$	−3.42790e18	−0.231203
$891$	1.46168e18	0.0978693
$892$	−6.99090e18	−0.464688
$893$	−1.26669e19	−0.835862
$894$	−3.06382e18	−0.200710
$895$	7.10895e18	0.462334
$896$	2.53435e19	1.63631
$897$	1.13432e16	0.000727082 0
$898$	−1.81317e18	−0.115383
$899$	2.06869e18	0.130694
$900$	1.16639e18	0.0731589
$901$	−1.00265e19	−0.624363
$902$	4.36743e18	0.270012
$903$	1.55154e19	0.952339
$904$	4.93871e18	0.300967
$905$	2.73619e18	0.165551
$906$	7.21843e18	0.433620
$907$	−1.26250e19	−0.752979	−0.376490	−	0.926421i	$-0.622869\pi$
$907$	−1.26250e19	−0.752979	−0.376490	+	0.926421i	$0.622869\pi$
$908$	−1.65749e19	−0.981504
$909$	−1.43825e18	−0.0845610
$910$	−9.77211e18	−0.570452
$911$	1.04074e19	0.603217	0.301608	−	0.953432i	$-0.402477\pi$
$911$	1.04074e19	0.603217	0.301608	+	0.953432i	$0.402477\pi$
$912$	2.36726e18	0.136232
$913$	−2.05292e19	−1.17304
$914$	1.40926e19	0.799542
$915$	−3.05739e18	−0.172232
$916$	−4.78220e18	−0.267490
$917$	4.54585e19	2.52473
$918$	−7.88162e17	−0.0434648
$919$	−3.88121e18	−0.212528	−0.106264	−	0.994338i	$-0.533889\pi$
$919$	−3.88121e18	−0.212528	−0.106264	+	0.994338i	$0.533889\pi$
$920$	−1.88079e16	−0.00102263
$921$	4.42015e18	0.238643
$922$	−1.20871e19	−0.647992
$923$	−2.00064e16	−0.00106502
$924$	1.25863e19	0.665317
$925$	−1.01844e19	−0.534580
$926$	−1.78596e18	−0.0930893
$927$	−7.22689e18	−0.374053
$928$	1.69459e19	0.870969
$929$	−1.37647e19	−0.702528	−0.351264	−	0.936277i	$-0.614248\pi$
$929$	−1.37647e19	−0.702528	−0.351264	+	0.936277i	$0.614248\pi$
$930$	6.84016e17	0.0346678
$931$	−2.10082e19	−1.05734
$932$	5.16740e18	0.258267
$933$	1.19198e19	0.591616
$934$	−1.44284e18	−0.0711154
$935$	7.41885e18	0.363129
$936$	−4.92781e18	−0.239531
$937$	2.77960e18	0.134176	0.0670881	−	0.997747i	$-0.478629\pi$
$937$	2.77960e18	0.134176	0.0670881	+	0.997747i	$0.478629\pi$
$938$	−1.54553e19	−0.740899
$939$	1.14790e19	0.546486
$940$	1.98563e19	0.938788
$941$	−1.79211e19	−0.841457	−0.420729	−	0.907187i	$-0.638225\pi$
$941$	−1.79211e19	−0.841457	−0.420729	+	0.907187i	$0.638225\pi$
$942$	−4.51613e18	−0.210589
$943$	−2.06945e16	−0.000958359 0
$944$	−1.12779e18	−0.0518693
$945$	5.96669e18	0.272538
$946$	8.92110e18	0.404693
$947$	2.78571e19	1.25505	0.627526	−	0.778596i	$-0.284068\pi$
$947$	2.78571e19	1.25505	0.627526	+	0.778596i	$0.284068\pi$
$948$	−1.79666e18	−0.0803917
$949$	−1.00918e19	−0.448476
$950$	−1.74644e18	−0.0770814
$951$	−1.97464e19	−0.865595
$952$	−1.54443e19	−0.672401
$953$	4.26175e19	1.84282	0.921412	−	0.388586i	$-0.127036\pi$
$953$	4.26175e19	1.84282	0.921412	+	0.388586i	$0.127036\pi$
$954$	−4.63662e18	−0.199130
$955$	−2.21051e19	−0.942913
$956$	2.10316e19	0.891038
$957$	1.03757e19	0.436608
$958$	−1.85111e19	−0.773671
$959$	1.75002e19	0.726476
$960$	8.69373e17	0.0358462
$961$	−2.38517e19	−0.976827
$962$	1.89076e19	0.769128
$963$	1.27172e19	0.513831
$964$	2.67157e19	1.07218
$965$	3.46915e18	0.138291
$966$	1.64400e16	0.000650954 0
$967$	−4.36536e19	−1.71691	−0.858455	−	0.512889i	$-0.828575\pi$
$967$	−4.36536e19	−1.71691	−0.858455	+	0.512889i	$0.828575\pi$
$968$	−4.75796e18	−0.185879
$969$	−4.28102e18	−0.166128
$970$	−1.92865e19	−0.743425
$971$	2.50166e19	0.957864	0.478932	−	0.877852i	$-0.341024\pi$
$971$	2.50166e19	0.957864	0.478932	+	0.877852i	$0.341024\pi$
$972$	1.32218e18	0.0502876
$973$	−6.88662e19	−2.60179
$974$	4.81453e18	0.180684
$975$	−3.75736e18	−0.140073
$976$	−3.78235e18	−0.140068
$977$	2.16619e19	0.796858	0.398429	−	0.917199i	$-0.369555\pi$
$977$	2.16619e19	0.796858	0.398429	+	0.917199i	$0.369555\pi$
$978$	1.24047e19	0.453298
$979$	−1.42225e19	−0.516284
$980$	3.29320e19	1.18754
$981$	7.20508e18	0.258102
$982$	1.47839e19	0.526096
$983$	−4.85622e19	−1.71672	−0.858362	−	0.513045i	$-0.828517\pi$
$983$	−4.85622e19	−1.71672	−0.858362	+	0.513045i	$0.828517\pi$
$984$	8.99031e18	0.315723
$985$	−1.38088e19	−0.481748
$986$	−5.59478e18	−0.193902
$987$	−3.94973e19	−1.35990
$988$	−1.17619e19	−0.402308
$989$	−4.22714e16	−0.00143638
$990$	3.43076e18	0.115814
$991$	−4.20059e19	−1.40874	−0.704370	−	0.709833i	$-0.748771\pi$
$991$	−4.20059e19	−1.40874	−0.704370	+	0.709833i	$0.748771\pi$
$992$	4.63510e18	0.154431
$993$	−2.55127e18	−0.0844473
$994$	−2.89960e16	−0.000953512 0
$995$	−3.40827e19	−1.11349
$996$	−1.85700e19	−0.602735
$997$	3.88938e19	1.25419	0.627094	−	0.778944i	$-0.284244\pi$
$997$	3.88938e19	1.25419	0.627094	+	0.778944i	$0.284244\pi$
$998$	1.58061e19	0.506379
$999$	−1.15447e19	−0.367457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.14	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-42.0742 q^{2} -729.000 q^{3} -6421.76 q^{4} -29646.8 q^{5} +30672.1 q^{6} +519485. q^{7} +614862. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-42.0742 q^{2} -729.000 q^{3} -6421.76 q^{4} -29646.8 q^{5} +30672.1 q^{6} +519485. q^{7} +614862. q^{8} +531441. q^{9} +1.24737e6 q^{10} +5.17537e6 q^{11} +4.68146e6 q^{12} -1.50807e7 q^{13} -2.18569e7 q^{14} +2.16125e7 q^{15} +2.67372e7 q^{16} -4.83523e7 q^{17} -2.23600e7 q^{18} -1.21451e8 q^{19} +1.90385e8 q^{20} -3.78705e8 q^{21} -2.17750e8 q^{22} +1.03178e6 q^{23} -4.48235e8 q^{24} -3.41770e8 q^{25} +6.34508e8 q^{26} -3.87420e8 q^{27} -3.33601e9 q^{28} -2.75011e9 q^{29} -9.09329e8 q^{30} -7.52220e8 q^{31} -6.16190e9 q^{32} -3.77285e9 q^{33} +2.03438e9 q^{34} -1.54011e10 q^{35} -3.41279e9 q^{36} +2.97989e10 q^{37} +5.10997e9 q^{38} +1.09938e10 q^{39} -1.82287e10 q^{40} -2.00571e10 q^{41} +1.59337e10 q^{42} -4.09695e10 q^{43} -3.32350e10 q^{44} -1.57555e10 q^{45} -4.34111e7 q^{46} +1.04296e11 q^{47} -1.94915e10 q^{48} +1.72976e11 q^{49} +1.43797e10 q^{50} +3.52488e10 q^{51} +9.68446e10 q^{52} +2.07363e11 q^{53} +1.63004e10 q^{54} -1.53433e11 q^{55} +3.19412e11 q^{56} +8.85381e10 q^{57} +1.15709e11 q^{58} -4.21805e10 q^{59} -1.38790e11 q^{60} -1.41464e11 q^{61} +3.16490e10 q^{62} +2.76076e11 q^{63} +4.02254e10 q^{64} +4.47094e11 q^{65} +1.58739e11 q^{66} +7.07112e11 q^{67} +3.10507e11 q^{68} -7.52164e8 q^{69} +6.47988e11 q^{70} +1.32663e9 q^{71} +3.26763e11 q^{72} +6.69188e11 q^{73} -1.25376e12 q^{74} +2.49151e11 q^{75} +7.79932e11 q^{76} +2.68853e12 q^{77} -4.62556e11 q^{78} -3.83781e11 q^{79} -7.92674e11 q^{80} +2.82430e11 q^{81} +8.43888e11 q^{82} -3.96671e12 q^{83} +2.43195e12 q^{84} +1.43349e12 q^{85} +1.72376e12 q^{86} +2.00483e12 q^{87} +3.18214e12 q^{88} -2.74811e12 q^{89} +6.62901e11 q^{90} -7.83420e12 q^{91} -6.62582e9 q^{92} +5.48368e11 q^{93} -4.38816e12 q^{94} +3.60065e12 q^{95} +4.49202e12 q^{96} -1.54618e13 q^{97} -7.27783e12 q^{98} +2.75040e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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