LMFDB - Embedded newform 177.14.a.b.1.11

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			1.11
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)

$f(q)$	$=$	$q-66.2972 q^{2} -729.000 q^{3} -3796.68 q^{4} +24188.3 q^{5} +48330.7 q^{6} -395052. q^{7} +794816. q^{8} +531441. q^{9} +O(q^{10})$	\(q-66.2972 q^{2} -729.000 q^{3} -3796.68 q^{4} +24188.3 q^{5} +48330.7 q^{6} -395052. q^{7} +794816. q^{8} +531441. q^{9} -1.60362e6 q^{10} +9.00651e6 q^{11} +2.76778e6 q^{12} -3.09760e7 q^{13} +2.61909e7 q^{14} -1.76333e7 q^{15} -2.15917e7 q^{16} +5.93547e7 q^{17} -3.52331e7 q^{18} +1.66261e8 q^{19} -9.18353e7 q^{20} +2.87993e8 q^{21} -5.97107e8 q^{22} -1.38955e9 q^{23} -5.79421e8 q^{24} -6.35628e8 q^{25} +2.05362e9 q^{26} -3.87420e8 q^{27} +1.49989e9 q^{28} +2.71580e9 q^{29} +1.16904e9 q^{30} +4.57411e9 q^{31} -5.07966e9 q^{32} -6.56575e9 q^{33} -3.93505e9 q^{34} -9.55565e9 q^{35} -2.01771e9 q^{36} -9.75563e9 q^{37} -1.10227e10 q^{38} +2.25815e10 q^{39} +1.92253e10 q^{40} -1.59783e10 q^{41} -1.90931e10 q^{42} +6.97849e7 q^{43} -3.41949e10 q^{44} +1.28547e10 q^{45} +9.21231e10 q^{46} +1.45482e11 q^{47} +1.57403e10 q^{48} +5.91774e10 q^{49} +4.21404e10 q^{50} -4.32695e10 q^{51} +1.17606e11 q^{52} -3.12070e11 q^{53} +2.56849e10 q^{54} +2.17852e11 q^{55} -3.13994e11 q^{56} -1.21205e11 q^{57} -1.80050e11 q^{58} -4.21805e10 q^{59} +6.69479e10 q^{60} -3.14234e11 q^{61} -3.03251e11 q^{62} -2.09947e11 q^{63} +5.13647e11 q^{64} -7.49258e11 q^{65} +4.35291e11 q^{66} +1.17389e12 q^{67} -2.25351e11 q^{68} +1.01298e12 q^{69} +6.33513e11 q^{70} -9.67396e11 q^{71} +4.22398e11 q^{72} +2.15669e12 q^{73} +6.46771e11 q^{74} +4.63373e11 q^{75} -6.31241e11 q^{76} -3.55805e12 q^{77} -1.49709e12 q^{78} +2.07035e12 q^{79} -5.22266e11 q^{80} +2.82430e11 q^{81} +1.05932e12 q^{82} +3.77349e12 q^{83} -1.09342e12 q^{84} +1.43569e12 q^{85} -4.62654e9 q^{86} -1.97982e12 q^{87} +7.15852e12 q^{88} +1.92476e12 q^{89} -8.52228e11 q^{90} +1.22372e13 q^{91} +5.27567e12 q^{92} -3.33453e12 q^{93} -9.64504e12 q^{94} +4.02158e12 q^{95} +3.70308e12 q^{96} -7.77732e12 q^{97} -3.92330e12 q^{98} +4.78643e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−66.2972	−0.732488	−0.366244	−	0.930519i	$-0.619356\pi$
$2$	−66.2972	−0.732488	−0.366244	+	0.930519i	$0.619356\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	−3796.68	−0.463462
$5$	24188.3	0.692310	0.346155	−	0.938177i	$-0.387487\pi$
$5$	24188.3	0.692310	0.346155	+	0.938177i	$0.387487\pi$
$6$	48330.7	0.422902
$7$	−395052.	−1.26916	−0.634582	−	0.772856i	$-0.718828\pi$
$7$	−395052.	−1.26916	−0.634582	+	0.772856i	$0.718828\pi$
$8$	794816.	1.07197
$9$	531441.	0.333333
$10$	−1.60362e6	−0.507109
$11$	9.00651e6	1.53287	0.766433	−	0.642324i	$-0.222030\pi$
$11$	9.00651e6	1.53287	0.766433	+	0.642324i	$0.222030\pi$
$12$	2.76778e6	0.267580
$13$	−3.09760e7	−1.77989	−0.889947	−	0.456065i	$-0.849259\pi$
$13$	−3.09760e7	−1.77989	−0.889947	+	0.456065i	$0.849259\pi$
$14$	2.61909e7	0.929646
$15$	−1.76333e7	−0.399705
$16$	−2.15917e7	−0.321741
$17$	5.93547e7	0.596399	0.298199	−	0.954504i	$-0.403614\pi$
$17$	5.93547e7	0.596399	0.298199	+	0.954504i	$0.403614\pi$
$18$	−3.52331e7	−0.244163
$19$	1.66261e8	0.810761	0.405381	−	0.914148i	$-0.367139\pi$
$19$	1.66261e8	0.810761	0.405381	+	0.914148i	$0.367139\pi$
$20$	−9.18353e7	−0.320859
$21$	2.87993e8	0.732752
$22$	−5.97107e8	−1.12281
$23$	−1.38955e9	−1.95723	−0.978617	−	0.205693i	$-0.934055\pi$
$23$	−1.38955e9	−1.95723	−0.978617	+	0.205693i	$0.934055\pi$
$24$	−5.79421e8	−0.618901
$25$	−6.35628e8	−0.520707
$26$	2.05362e9	1.30375
$27$	−3.87420e8	−0.192450
$28$	1.49989e9	0.588209
$29$	2.71580e9	0.847833	0.423916	−	0.905701i	$-0.360655\pi$
$29$	2.71580e9	0.847833	0.423916	+	0.905701i	$0.360655\pi$
$30$	1.16904e9	0.292779
$31$	4.57411e9	0.925669	0.462834	−	0.886445i	$-0.346832\pi$
$31$	4.57411e9	0.925669	0.462834	+	0.886445i	$0.346832\pi$
$32$	−5.07966e9	−0.836296
$33$	−6.56575e9	−0.885001
$34$	−3.93505e9	−0.436855
$35$	−9.55565e9	−0.878654
$36$	−2.01771e9	−0.154487
$37$	−9.75563e9	−0.625092	−0.312546	−	0.949903i	$-0.601182\pi$
$37$	−9.75563e9	−0.625092	−0.312546	+	0.949903i	$0.601182\pi$
$38$	−1.10227e10	−0.593873
$39$	2.25815e10	1.02762
$40$	1.92253e10	0.742134
$41$	−1.59783e10	−0.525333	−0.262667	−	0.964887i	$-0.584602\pi$
$41$	−1.59783e10	−0.525333	−0.262667	+	0.964887i	$0.584602\pi$
$42$	−1.90931e10	−0.536732
$43$	6.97849e7	0.00168351	0.000841756	−	1.00000i	$-0.499732\pi$
$43$	6.97849e7	0.00168351	0.000841756		1.00000i	$0.499732\pi$
$44$	−3.41949e10	−0.710425
$45$	1.28547e10	0.230770
$46$	9.21231e10	1.43365
$47$	1.45482e11	1.96867	0.984334	−	0.176311i	$-0.0564165\pi$
$47$	1.45482e11	1.96867	0.984334	+	0.176311i	$0.0564165\pi$
$48$	1.57403e10	0.185757
$49$	5.91774e10	0.610775
$50$	4.21404e10	0.381411
$51$	−4.32695e10	−0.344331
$52$	1.17606e11	0.824913
$53$	−3.12070e11	−1.93401	−0.967004	−	0.254760i	$-0.918003\pi$
$53$	−3.12070e11	−1.93401	−0.967004	+	0.254760i	$0.918003\pi$
$54$	2.56849e10	0.140967
$55$	2.17852e11	1.06122
$56$	−3.13994e11	−1.36050
$57$	−1.21205e11	−0.468093
$58$	−1.80050e11	−0.621027
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	6.69479e10	0.185248
$61$	−3.14234e11	−0.780925	−0.390463	−	0.920619i	$-0.627685\pi$
$61$	−3.14234e11	−0.780925	−0.390463	+	0.920619i	$0.627685\pi$
$62$	−3.03251e11	−0.678041
$63$	−2.09947e11	−0.423054
$64$	5.13647e11	0.934318
$65$	−7.49258e11	−1.23224
$66$	4.35291e11	0.648252
$67$	1.17389e12	1.58541	0.792704	−	0.609607i	$-0.208673\pi$
$67$	1.17389e12	1.58541	0.792704	+	0.609607i	$0.208673\pi$
$68$	−2.25351e11	−0.276408
$69$	1.01298e12	1.13001
$70$	6.33513e11	0.643604
$71$	−9.67396e11	−0.896242	−0.448121	−	0.893973i	$-0.647907\pi$
$71$	−9.67396e11	−0.896242	−0.448121	+	0.893973i	$0.647907\pi$
$72$	4.22398e11	0.357323
$73$	2.15669e12	1.66797	0.833986	−	0.551785i	$-0.186053\pi$
$73$	2.15669e12	1.66797	0.833986	+	0.551785i	$0.186053\pi$
$74$	6.46771e11	0.457872
$75$	4.63373e11	0.300630
$76$	−6.31241e11	−0.375757
$77$	−3.55805e12	−1.94546
$78$	−1.49709e12	−0.752720
$79$	2.07035e12	0.958224	0.479112	−	0.877754i	$-0.340959\pi$
$79$	2.07035e12	0.958224	0.479112	+	0.877754i	$0.340959\pi$
$80$	−5.22266e11	−0.222745
$81$	2.82430e11	0.111111
$82$	1.05932e12	0.384800
$83$	3.77349e12	1.26688	0.633440	−	0.773791i	$-0.281642\pi$
$83$	3.77349e12	1.26688	0.633440	+	0.773791i	$0.281642\pi$
$84$	−1.09342e12	−0.339603
$85$	1.43569e12	0.412893
$86$	−4.62654e9	−0.00123315
$87$	−1.97982e12	−0.489496
$88$	7.15852e12	1.64318
$89$	1.92476e12	0.410527	0.205264	−	0.978707i	$-0.434195\pi$
$89$	1.92476e12	0.410527	0.205264	+	0.978707i	$0.434195\pi$
$90$	−8.52228e11	−0.169036
$91$	1.22372e13	2.25898
$92$	5.27567e12	0.907103
$93$	−3.33453e12	−0.534435
$94$	−9.64504e12	−1.44203
$95$	4.02158e12	0.561298
$96$	3.70308e12	0.482836
$97$	−7.77732e12	−0.948011	−0.474006	−	0.880522i	$-0.657192\pi$
$97$	−7.77732e12	−0.948011	−0.474006	+	0.880522i	$0.657192\pi$
$98$	−3.92330e12	−0.447385
$99$	4.78643e12	0.510955
$100$	2.41328e12	0.241328
$101$	1.79650e13	1.68398	0.841992	−	0.539490i	$-0.181383\pi$
$101$	1.79650e13	1.68398	0.841992	+	0.539490i	$0.181383\pi$
$102$	2.86865e12	0.252218
$103$	−1.68871e12	−0.139352	−0.0696760	−	0.997570i	$-0.522197\pi$
$103$	−1.68871e12	−0.139352	−0.0696760	+	0.997570i	$0.522197\pi$
$104$	−2.46202e13	−1.90799
$105$	6.96607e12	0.507291
$106$	2.06893e13	1.41664
$107$	8.61080e12	0.554688	0.277344	−	0.960771i	$-0.410546\pi$
$107$	8.61080e12	0.554688	0.277344	+	0.960771i	$0.410546\pi$
$108$	1.47091e12	0.0891933
$109$	−1.80048e12	−0.102829	−0.0514146	−	0.998677i	$-0.516373\pi$
$109$	−1.80048e12	−0.102829	−0.0514146	+	0.998677i	$0.516373\pi$
$110$	−1.44430e13	−0.777330
$111$	7.11186e12	0.360897
$112$	8.52985e12	0.408342
$113$	6.79997e11	0.0307254	0.0153627	−	0.999882i	$-0.495110\pi$
$113$	6.79997e11	0.0307254	0.0153627	+	0.999882i	$0.495110\pi$
$114$	8.03552e12	0.342873
$115$	−3.36108e13	−1.35501
$116$	−1.03110e13	−0.392938
$117$	−1.64619e13	−0.593298
$118$	2.79645e12	0.0953618
$119$	−2.34482e13	−0.756927
$120$	−1.40152e13	−0.428471
$121$	4.65946e13	1.34968
$122$	2.08328e13	0.572018
$123$	1.16482e13	0.303301
$124$	−1.73664e13	−0.429012
$125$	−4.49015e13	−1.05280
$126$	1.39189e13	0.309882
$127$	1.58988e13	0.336233	0.168116	−	0.985767i	$-0.446232\pi$
$127$	1.58988e13	0.336233	0.168116	+	0.985767i	$0.446232\pi$
$128$	7.55927e12	0.151920
$129$	−5.08732e10	−0.000971976 0
$130$	4.96737e13	0.902599
$131$	7.45244e13	1.28835	0.644177	−	0.764876i	$-0.277200\pi$
$131$	7.45244e13	1.28835	0.644177	+	0.764876i	$0.277200\pi$
$132$	2.49280e13	0.410164
$133$	−6.56820e13	−1.02899
$134$	−7.78256e13	−1.16129
$135$	−9.37105e12	−0.133235
$136$	4.71760e13	0.639320
$137$	−6.74566e12	−0.0871647	−0.0435823	−	0.999050i	$-0.513877\pi$
$137$	−6.74566e12	−0.0871647	−0.0435823	+	0.999050i	$0.513877\pi$
$138$	−6.71578e13	−0.827718
$139$	2.71419e13	0.319186	0.159593	−	0.987183i	$-0.448982\pi$
$139$	2.71419e13	0.319186	0.159593	+	0.987183i	$0.448982\pi$
$140$	3.62798e13	0.407223
$141$	−1.06056e14	−1.13661
$142$	6.41357e13	0.656486
$143$	−2.78986e14	−2.72834
$144$	−1.14747e13	−0.107247
$145$	6.56905e13	0.586963
$146$	−1.42982e14	−1.22177
$147$	−4.31403e13	−0.352631
$148$	3.70390e13	0.289707
$149$	1.25880e14	0.942423	0.471211	−	0.882020i	$-0.343817\pi$
$149$	1.25880e14	0.942423	0.471211	+	0.882020i	$0.343817\pi$
$150$	−3.07203e13	−0.220208
$151$	−1.69344e14	−1.16257	−0.581285	−	0.813700i	$-0.697450\pi$
$151$	−1.69344e14	−1.16257	−0.581285	+	0.813700i	$0.697450\pi$
$152$	1.32147e14	0.869110
$153$	3.15435e13	0.198800
$154$	2.35888e14	1.42502
$155$	1.10640e14	0.640850
$156$	−8.57348e13	−0.476264
$157$	7.46180e13	0.397645	0.198823	−	0.980035i	$-0.436288\pi$
$157$	7.46180e13	0.397645	0.198823	+	0.980035i	$0.436288\pi$
$158$	−1.37258e14	−0.701888
$159$	2.27499e14	1.11660
$160$	−1.22869e14	−0.578976
$161$	5.48944e14	2.48405
$162$	−1.87243e13	−0.0813875
$163$	−1.71344e14	−0.715564	−0.357782	−	0.933805i	$-0.616467\pi$
$163$	−1.71344e14	−0.715564	−0.357782	+	0.933805i	$0.616467\pi$
$164$	6.06644e13	0.243472
$165$	−1.58814e14	−0.612695
$166$	−2.50172e14	−0.927975
$167$	−3.04444e13	−0.108605	−0.0543025	−	0.998525i	$-0.517294\pi$
$167$	−3.04444e13	−0.108605	−0.0543025	+	0.998525i	$0.517294\pi$
$168$	2.28902e14	0.785486
$169$	6.56639e14	2.16802
$170$	−9.51822e13	−0.302439
$171$	8.83581e13	0.270254
$172$	−2.64951e11	−0.000780244 0
$173$	2.75315e14	0.780784	0.390392	−	0.920649i	$-0.372340\pi$
$173$	2.75315e14	0.780784	0.390392	+	0.920649i	$0.372340\pi$
$174$	1.31256e14	0.358550
$175$	2.51107e14	0.660862
$176$	−1.94466e14	−0.493186
$177$	3.07496e13	0.0751646
$178$	−1.27606e14	−0.300706
$179$	−1.16652e14	−0.265063	−0.132531	−	0.991179i	$-0.542311\pi$
$179$	−1.16652e14	−0.265063	−0.132531	+	0.991179i	$0.542311\pi$
$180$	−4.88050e13	−0.106953
$181$	4.23209e14	0.894631	0.447316	−	0.894376i	$-0.352380\pi$
$181$	4.23209e14	0.894631	0.447316	+	0.894376i	$0.352380\pi$
$182$	−8.11289e14	−1.65467
$183$	2.29077e14	0.450867
$184$	−1.10443e15	−2.09809
$185$	−2.35972e14	−0.432758
$186$	2.21070e14	0.391467
$187$	5.34579e14	0.914200
$188$	−5.52348e14	−0.912403
$189$	1.53051e14	0.244251
$190$	−2.66620e14	−0.411144
$191$	3.91423e13	0.0583350	0.0291675	−	0.999575i	$-0.490714\pi$
$191$	3.91423e13	0.0583350	0.0291675	+	0.999575i	$0.490714\pi$
$192$	−3.74448e14	−0.539429
$193$	−1.27389e15	−1.77423	−0.887114	−	0.461550i	$-0.847294\pi$
$193$	−1.27389e15	−1.77423	−0.887114	+	0.461550i	$0.847294\pi$
$194$	5.15614e14	0.694407
$195$	5.46209e14	0.711433
$196$	−2.24678e14	−0.283071
$197$	−1.36196e15	−1.66010	−0.830052	−	0.557686i	$-0.811689\pi$
$197$	−1.36196e15	−1.66010	−0.830052	+	0.557686i	$0.811689\pi$
$198$	−3.17327e14	−0.374269
$199$	−1.74517e13	−0.0199202	−0.00996010	−	0.999950i	$-0.503170\pi$
$199$	−1.74517e13	−0.0199202	−0.00996010	+	0.999950i	$0.503170\pi$
$200$	−5.05208e14	−0.558181
$201$	−8.55765e14	−0.915336
$202$	−1.19103e15	−1.23350
$203$	−1.07288e15	−1.07604
$204$	1.64281e14	0.159584
$205$	−3.86488e14	−0.363694
$206$	1.11957e14	0.102074
$207$	−7.38463e14	−0.652411
$208$	6.68825e14	0.572665
$209$	1.49744e15	1.24279
$210$	−4.61831e14	−0.371585
$211$	−1.31001e15	−1.02197	−0.510986	−	0.859589i	$-0.670720\pi$
$211$	−1.31001e15	−1.02197	−0.510986	+	0.859589i	$0.670720\pi$
$212$	1.18483e15	0.896339
$213$	7.05232e14	0.517445
$214$	−5.70872e14	−0.406302
$215$	1.68798e12	0.00116551
$216$	−3.07928e14	−0.206300
$217$	−1.80701e15	−1.17482
$218$	1.19367e14	0.0753211
$219$	−1.57223e15	−0.963004
$220$	−8.27116e14	−0.491834
$221$	−1.83857e15	−1.06153
$222$	−4.71496e14	−0.264353
$223$	−2.50006e15	−1.36135	−0.680675	−	0.732586i	$-0.738313\pi$
$223$	−2.50006e15	−1.36135	−0.680675	+	0.732586i	$0.738313\pi$
$224$	2.00673e15	1.06140
$225$	−3.37799e14	−0.173569
$226$	−4.50819e13	−0.0225060
$227$	−3.09622e15	−1.50198	−0.750990	−	0.660313i	$-0.770424\pi$
$227$	−3.09622e15	−1.50198	−0.750990	+	0.660313i	$0.770424\pi$
$228$	4.60175e14	0.216943
$229$	2.26959e15	1.03996	0.519980	−	0.854179i	$-0.325940\pi$
$229$	2.26959e15	1.03996	0.519980	+	0.854179i	$0.325940\pi$
$230$	2.22830e15	0.992530
$231$	2.59381e15	1.12321
$232$	2.15856e15	0.908849
$233$	−6.15223e14	−0.251895	−0.125947	−	0.992037i	$-0.540197\pi$
$233$	−6.15223e14	−0.251895	−0.125947	+	0.992037i	$0.540197\pi$
$234$	1.09138e15	0.434583
$235$	3.51896e15	1.36293
$236$	1.60146e14	0.0603376
$237$	−1.50928e15	−0.553231
$238$	1.55455e15	0.554440
$239$	−1.81888e15	−0.631272	−0.315636	−	0.948880i	$-0.602218\pi$
$239$	−1.81888e15	−0.631272	−0.315636	+	0.948880i	$0.602218\pi$
$240$	3.80732e14	0.128602
$241$	4.87508e15	1.60277	0.801384	−	0.598150i	$-0.204097\pi$
$241$	4.87508e15	1.60277	0.801384	+	0.598150i	$0.204097\pi$
$242$	−3.08909e15	−0.988623
$243$	−2.05891e14	−0.0641500
$244$	1.19305e15	0.361929
$245$	1.43140e15	0.422846
$246$	−7.72241e14	−0.222165
$247$	−5.15012e15	−1.44307
$248$	3.63558e15	0.992287
$249$	−2.75088e15	−0.731434
$250$	2.97685e15	0.771163
$251$	−3.95345e15	−0.997922	−0.498961	−	0.866624i	$-0.666285\pi$
$251$	−3.95345e15	−0.997922	−0.498961	+	0.866624i	$0.666285\pi$
$252$	7.97102e14	0.196070
$253$	−1.25150e16	−3.00018
$254$	−1.05405e15	−0.246286
$255$	−1.04662e15	−0.238384
$256$	−4.70895e15	−1.04560
$257$	−3.43727e15	−0.744130	−0.372065	−	0.928207i	$-0.621350\pi$
$257$	−3.43727e15	−0.744130	−0.372065	+	0.928207i	$0.621350\pi$
$258$	3.37275e12	0.000711960 0
$259$	3.85399e15	0.793344
$260$	2.84469e15	0.571095
$261$	1.44329e15	0.282611
$262$	−4.94076e15	−0.943704
$263$	−9.04159e15	−1.68474	−0.842369	−	0.538901i	$-0.818840\pi$
$263$	−9.04159e15	−1.68474	−0.842369	+	0.538901i	$0.818840\pi$
$264$	−5.21856e15	−0.948692
$265$	−7.54844e15	−1.33893
$266$	4.35453e15	0.753721
$267$	−1.40315e15	−0.237018
$268$	−4.45688e15	−0.734776
$269$	−9.00168e15	−1.44855	−0.724275	−	0.689511i	$-0.757826\pi$
$269$	−9.00168e15	−1.44855	−0.724275	+	0.689511i	$0.757826\pi$
$270$	6.21274e14	0.0975931
$271$	5.02090e14	0.0769984	0.0384992	−	0.999259i	$-0.487742\pi$
$271$	5.02090e14	0.0769984	0.0384992	+	0.999259i	$0.487742\pi$
$272$	−1.28157e15	−0.191886
$273$	−8.92089e15	−1.30422
$274$	4.47218e14	0.0638470
$275$	−5.72480e15	−0.798174
$276$	−3.84596e15	−0.523716
$277$	8.16380e15	1.08586	0.542930	−	0.839778i	$-0.317315\pi$
$277$	8.16380e15	1.08586	0.542930	+	0.839778i	$0.317315\pi$
$278$	−1.79943e15	−0.233800
$279$	2.43087e15	0.308556
$280$	−7.59499e15	−0.941889
$281$	3.10827e15	0.376641	0.188320	−	0.982108i	$-0.439696\pi$
$281$	3.10827e15	0.376641	0.188320	+	0.982108i	$0.439696\pi$
$282$	7.03123e15	0.832554
$283$	1.18849e15	0.137525	0.0687626	−	0.997633i	$-0.478095\pi$
$283$	1.18849e15	0.137525	0.0687626	+	0.997633i	$0.478095\pi$
$284$	3.67289e15	0.415374
$285$	−2.93173e15	−0.324066
$286$	1.84960e16	1.99847
$287$	6.31226e15	0.666734
$288$	−2.69954e15	−0.278765
$289$	−6.38160e15	−0.644308
$290$	−4.35510e15	−0.429943
$291$	5.66966e15	0.547335
$292$	−8.18826e15	−0.773042
$293$	−1.32316e16	−1.22172	−0.610862	−	0.791737i	$-0.709177\pi$
$293$	−1.32316e16	−1.22172	−0.610862	+	0.791737i	$0.709177\pi$
$294$	2.86008e15	0.258298
$295$	−1.02028e15	−0.0901311
$296$	−7.75393e15	−0.670079
$297$	−3.48931e15	−0.295000
$298$	−8.34549e15	−0.690313
$299$	4.30427e16	3.48367
$300$	−1.75928e15	−0.139331
$301$	−2.75687e13	−0.00213665
$302$	1.12270e16	0.851568
$303$	−1.30965e16	−0.972249
$304$	−3.58986e15	−0.260855
$305$	−7.60079e15	−0.540642
$306$	−2.09125e15	−0.145618
$307$	6.62499e15	0.451633	0.225817	−	0.974170i	$-0.427495\pi$
$307$	6.62499e15	0.451633	0.225817	+	0.974170i	$0.427495\pi$
$308$	1.35088e16	0.901645
$309$	1.23107e15	0.0804549
$310$	−7.33512e15	−0.469414
$311$	−1.17605e16	−0.737029	−0.368514	−	0.929622i	$-0.620133\pi$
$311$	−1.17605e16	−0.737029	−0.368514	+	0.929622i	$0.620133\pi$
$312$	1.79482e16	1.10158
$313$	−2.09100e15	−0.125695	−0.0628473	−	0.998023i	$-0.520018\pi$
$313$	−2.09100e15	−0.125695	−0.0628473	+	0.998023i	$0.520018\pi$
$314$	−4.94696e15	−0.291270
$315$	−5.07827e15	−0.292885
$316$	−7.86045e15	−0.444101
$317$	9.00659e15	0.498512	0.249256	−	0.968438i	$-0.419814\pi$
$317$	9.00659e15	0.498512	0.249256	+	0.968438i	$0.419814\pi$
$318$	−1.50825e16	−0.817896
$319$	2.44599e16	1.29961
$320$	1.24242e16	0.646838
$321$	−6.27728e15	−0.320250
$322$	−3.63935e16	−1.81953
$323$	9.86839e15	0.483537
$324$	−1.07229e15	−0.0514958
$325$	1.96892e16	0.926802
$326$	1.13596e16	0.524141
$327$	1.31255e15	0.0593685
$328$	−1.26998e16	−0.563140
$329$	−5.74730e16	−2.49856
$330$	1.05290e16	0.448791
$331$	−1.49381e16	−0.624330	−0.312165	−	0.950028i	$-0.601054\pi$
$331$	−1.49381e16	−0.624330	−0.312165	+	0.950028i	$0.601054\pi$
$332$	−1.43267e16	−0.587151
$333$	−5.18454e15	−0.208364
$334$	2.01838e15	0.0795518
$335$	2.83944e16	1.09759
$336$	−6.21826e15	−0.235756
$337$	−7.32859e15	−0.272537	−0.136269	−	0.990672i	$-0.543511\pi$
$337$	−7.32859e15	−0.272537	−0.136269	+	0.990672i	$0.543511\pi$
$338$	−4.35334e16	−1.58805
$339$	−4.95718e14	−0.0177393
$340$	−5.45085e15	−0.191360
$341$	4.11968e16	1.41893
$342$	−5.85790e15	−0.197958
$343$	1.48981e16	0.493990
$344$	5.54661e13	0.00180467
$345$	2.45023e16	0.782317
$346$	−1.82526e16	−0.571914
$347$	5.06850e16	1.55861	0.779306	−	0.626643i	$-0.215572\pi$
$347$	5.06850e16	1.55861	0.779306	+	0.626643i	$0.215572\pi$
$348$	7.51672e15	0.226863
$349$	−4.77340e15	−0.141404	−0.0707022	−	0.997497i	$-0.522524\pi$
$349$	−4.77340e15	−0.141404	−0.0707022	+	0.997497i	$0.522524\pi$
$350$	−1.66477e16	−0.484073
$351$	1.20007e16	0.342541
$352$	−4.57501e16	−1.28193
$353$	2.66414e16	0.732860	0.366430	−	0.930446i	$-0.380580\pi$
$353$	2.66414e16	0.732860	0.366430	+	0.930446i	$0.380580\pi$
$354$	−2.03861e15	−0.0550571
$355$	−2.33997e16	−0.620477
$356$	−7.30771e15	−0.190264
$357$	1.70937e16	0.437012
$358$	7.73372e15	0.194155
$359$	2.90946e16	0.717296	0.358648	−	0.933473i	$-0.383238\pi$
$359$	2.90946e16	0.717296	0.358648	+	0.933473i	$0.383238\pi$
$360$	1.02171e16	0.247378
$361$	−1.44101e16	−0.342666
$362$	−2.80576e16	−0.655306
$363$	−3.39674e16	−0.779238
$364$	−4.64606e16	−1.04695
$365$	5.21667e16	1.15475
$366$	−1.51871e16	−0.330255
$367$	4.94440e16	1.05629	0.528147	−	0.849153i	$-0.322887\pi$
$367$	4.94440e16	1.05629	0.528147	+	0.849153i	$0.322887\pi$
$368$	3.00027e16	0.629722
$369$	−8.49151e15	−0.175111
$370$	1.56443e16	0.316990
$371$	1.23284e17	2.45457
$372$	1.26601e16	0.247690
$373$	−1.42386e16	−0.273754	−0.136877	−	0.990588i	$-0.543707\pi$
$373$	−1.42386e16	−0.273754	−0.136877	+	0.990588i	$0.543707\pi$
$374$	−3.54411e16	−0.669640
$375$	3.27332e16	0.607835
$376$	1.15631e17	2.11035
$377$	−8.41246e16	−1.50905
$378$	−1.01469e16	−0.178911
$379$	−1.01224e17	−1.75440	−0.877201	−	0.480123i	$-0.840592\pi$
$379$	−1.01224e17	−1.75440	−0.877201	+	0.480123i	$0.840592\pi$
$380$	−1.52687e16	−0.260140
$381$	−1.15902e16	−0.194124
$382$	−2.59502e15	−0.0427297
$383$	−1.79418e15	−0.0290452	−0.0145226	−	0.999895i	$-0.504623\pi$
$383$	−1.79418e15	−0.0290452	−0.0145226	+	0.999895i	$0.504623\pi$
$384$	−5.51071e15	−0.0877111
$385$	−8.60631e16	−1.34686
$386$	8.44554e16	1.29960
$387$	3.70865e13	0.000561171 0
$388$	2.95280e16	0.439367
$389$	6.66866e16	0.975812	0.487906	−	0.872896i	$-0.337761\pi$
$389$	6.66866e16	0.975812	0.487906	+	0.872896i	$0.337761\pi$
$390$	−3.62121e16	−0.521116
$391$	−8.24761e16	−1.16729
$392$	4.70352e16	0.654731
$393$	−5.43283e16	−0.743832
$394$	9.02944e16	1.21601
$395$	5.00782e16	0.663388
$396$	−1.81725e16	−0.236808
$397$	1.14660e17	1.46985	0.734927	−	0.678146i	$-0.237216\pi$
$397$	1.14660e17	1.46985	0.734927	+	0.678146i	$0.237216\pi$
$398$	1.15700e15	0.0145913
$399$	4.78822e16	0.594087
$400$	1.37243e16	0.167533
$401$	−1.18945e17	−1.42859	−0.714295	−	0.699845i	$-0.753252\pi$
$401$	−1.18945e17	−1.42859	−0.714295	+	0.699845i	$0.753252\pi$
$402$	5.67349e16	0.670472
$403$	−1.41688e17	−1.64759
$404$	−6.82073e16	−0.780462
$405$	6.83150e15	0.0769233
$406$	7.11291e16	0.788185
$407$	−8.78642e16	−0.958183
$408$	−3.43913e16	−0.369112
$409$	9.34144e16	0.986762	0.493381	−	0.869813i	$-0.335761\pi$
$409$	9.34144e16	0.986762	0.493381	+	0.869813i	$0.335761\pi$
$410$	2.56231e16	0.266401
$411$	4.91758e15	0.0503245
$412$	6.41149e15	0.0645843
$413$	1.66635e16	0.165231
$414$	4.89580e16	0.477883
$415$	9.12744e16	0.877074
$416$	1.57348e17	1.48852
$417$	−1.97864e16	−0.184282
$418$	−9.92758e16	−0.910327
$419$	−3.90001e16	−0.352107	−0.176053	−	0.984381i	$-0.556333\pi$
$419$	−3.90001e16	−0.352107	−0.176053	+	0.984381i	$0.556333\pi$
$420$	−2.64479e16	−0.235110
$421$	8.00151e16	0.700388	0.350194	−	0.936677i	$-0.386116\pi$
$421$	8.00151e16	0.700388	0.350194	+	0.936677i	$0.386116\pi$
$422$	8.68501e16	0.748582
$423$	7.73150e16	0.656223
$424$	−2.48038e17	−2.07319
$425$	−3.77275e16	−0.310549
$426$	−4.67549e16	−0.379022
$427$	1.24139e17	0.991121
$428$	−3.26925e16	−0.257077
$429$	2.03381e17	1.57521
$430$	−1.11908e14	−0.000853723 0
$431$	−2.40571e16	−0.180776	−0.0903881	−	0.995907i	$-0.528811\pi$
$431$	−2.40571e16	−0.180776	−0.0903881	+	0.995907i	$0.528811\pi$
$432$	8.36506e15	0.0619191
$433$	7.32442e16	0.534075	0.267037	−	0.963686i	$-0.413955\pi$
$433$	7.32442e16	0.534075	0.267037	+	0.963686i	$0.413955\pi$
$434$	1.19800e17	0.860544
$435$	−4.78884e16	−0.338883
$436$	6.83586e15	0.0476574
$437$	−2.31028e17	−1.58685
$438$	1.04234e17	0.705389
$439$	1.59228e16	0.106169	0.0530847	−	0.998590i	$-0.483095\pi$
$439$	1.59228e16	0.106169	0.0530847	+	0.998590i	$0.483095\pi$
$440$	1.73153e17	1.13759
$441$	3.14493e16	0.203592
$442$	1.21892e17	0.777555
$443$	1.43251e16	0.0900480	0.0450240	−	0.998986i	$-0.485664\pi$
$443$	1.43251e16	0.0900480	0.0450240	+	0.998986i	$0.485664\pi$
$444$	−2.70014e16	−0.167262
$445$	4.65568e16	0.284212
$446$	1.65747e17	0.997171
$447$	−9.17665e16	−0.544108
$448$	−2.02917e17	−1.18580
$449$	−2.20473e17	−1.26986	−0.634928	−	0.772572i	$-0.718970\pi$
$449$	−2.20473e17	−1.26986	−0.634928	+	0.772572i	$0.718970\pi$
$450$	2.23951e16	0.127137
$451$	−1.43909e17	−0.805266
$452$	−2.58173e15	−0.0142400
$453$	1.23452e17	0.671210
$454$	2.05271e17	1.10018
$455$	2.95996e17	1.56391
$456$	−9.63353e16	−0.501781
$457$	−1.42337e17	−0.730906	−0.365453	−	0.930830i	$-0.619086\pi$
$457$	−1.42337e17	−0.730906	−0.365453	+	0.930830i	$0.619086\pi$
$458$	−1.50467e17	−0.761757
$459$	−2.29952e16	−0.114777
$460$	1.27610e17	0.627997
$461$	1.91520e17	0.929302	0.464651	−	0.885494i	$-0.346180\pi$
$461$	1.91520e17	0.929302	0.464651	+	0.885494i	$0.346180\pi$
$462$	−1.71963e17	−0.822738
$463$	−2.76794e16	−0.130581	−0.0652904	−	0.997866i	$-0.520797\pi$
$463$	−2.76794e16	−0.130581	−0.0652904	+	0.997866i	$0.520797\pi$
$464$	−5.86386e16	−0.272783
$465$	−8.06566e16	−0.369995
$466$	4.07876e16	0.184510
$467$	−5.95978e16	−0.265871	−0.132935	−	0.991125i	$-0.542440\pi$
$467$	−5.95978e16	−0.265871	−0.132935	+	0.991125i	$0.542440\pi$
$468$	6.25007e16	0.274971
$469$	−4.63748e17	−2.01214
$470$	−2.33297e17	−0.998329
$471$	−5.43965e16	−0.229581
$472$	−3.35258e16	−0.139558
$473$	6.28518e14	0.00258060
$474$	1.00061e17	0.405235
$475$	−1.05680e17	−0.422169
$476$	8.90253e16	0.350807
$477$	−1.65847e17	−0.644669
$478$	1.20586e17	0.462399
$479$	−1.29801e17	−0.491019	−0.245509	−	0.969394i	$-0.578955\pi$
$479$	−1.29801e17	−0.491019	−0.245509	+	0.969394i	$0.578955\pi$
$480$	8.95712e16	0.334272
$481$	3.02191e17	1.11260
$482$	−3.23204e17	−1.17401
$483$	−4.00180e17	−1.43417
$484$	−1.76905e17	−0.625525
$485$	−1.88120e17	−0.656318
$486$	1.36500e16	0.0469891
$487$	−1.65002e17	−0.560469	−0.280235	−	0.959932i	$-0.590412\pi$
$487$	−1.65002e17	−0.560469	−0.280235	+	0.959932i	$0.590412\pi$
$488$	−2.49758e17	−0.837127
$489$	1.24909e17	0.413131
$490$	−9.48980e16	−0.309729
$491$	3.60927e17	1.16249	0.581245	−	0.813729i	$-0.302566\pi$
$491$	3.60927e17	1.16249	0.581245	+	0.813729i	$0.302566\pi$
$492$	−4.42244e16	−0.140569
$493$	1.61195e17	0.505646
$494$	3.41438e17	1.05703
$495$	1.15776e17	0.353740
$496$	−9.87627e16	−0.297826
$497$	3.82172e17	1.13748
$498$	1.82375e17	0.535766
$499$	−1.29018e16	−0.0374109	−0.0187054	−	0.999825i	$-0.505954\pi$
$499$	−1.29018e16	−0.0374109	−0.0187054	+	0.999825i	$0.505954\pi$
$500$	1.70477e17	0.487933
$501$	2.21939e16	0.0627031
$502$	2.62103e17	0.730966
$503$	5.41825e17	1.49165	0.745825	−	0.666142i	$-0.232056\pi$
$503$	5.41825e17	1.49165	0.745825	+	0.666142i	$0.232056\pi$
$504$	−1.66869e17	−0.453501
$505$	4.34543e17	1.16584
$506$	8.29708e17	2.19759
$507$	−4.78690e17	−1.25171
$508$	−6.03626e16	−0.155831
$509$	−9.65207e16	−0.246011	−0.123006	−	0.992406i	$-0.539253\pi$
$509$	−9.65207e16	−0.246011	−0.123006	+	0.992406i	$0.539253\pi$
$510$	6.93878e16	0.174613
$511$	−8.52005e17	−2.11693
$512$	2.50265e17	0.613967
$513$	−6.44131e16	−0.156031
$514$	2.27882e17	0.545066
$515$	−4.08470e16	−0.0964748
$516$	1.93149e14	0.000450474 0
$517$	1.31028e18	3.01771
$518$	−2.55509e17	−0.581115
$519$	−2.00705e17	−0.450786
$520$	−5.95522e17	−1.32092
$521$	−2.36741e17	−0.518596	−0.259298	−	0.965797i	$-0.583491\pi$
$521$	−2.36741e17	−0.518596	−0.259298	+	0.965797i	$0.583491\pi$
$522$	−9.56858e16	−0.207009
$523$	−9.65494e16	−0.206295	−0.103148	−	0.994666i	$-0.532891\pi$
$523$	−9.65494e16	−0.206295	−0.103148	+	0.994666i	$0.532891\pi$
$524$	−2.82945e17	−0.597103
$525$	−1.83057e17	−0.381549
$526$	5.99432e17	1.23405
$527$	2.71495e17	0.552068
$528$	1.41766e17	0.284741
$529$	1.42681e18	2.83076
$530$	5.00440e17	0.980752
$531$	−2.24165e16	−0.0433963
$532$	2.49373e17	0.476897
$533$	4.94944e17	0.935037
$534$	9.30250e16	0.173613
$535$	2.08281e17	0.384016
$536$	9.33026e17	1.69951
$537$	8.50395e16	0.153034
$538$	5.96786e17	1.06105
$539$	5.32982e17	0.936237
$540$	3.55789e16	0.0617494
$541$	−5.17097e17	−0.886727	−0.443363	−	0.896342i	$-0.646215\pi$
$541$	−5.17097e17	−0.886727	−0.443363	+	0.896342i	$0.646215\pi$
$542$	−3.32872e16	−0.0564003
$543$	−3.08519e17	−0.516516
$544$	−3.01502e17	−0.498766
$545$	−4.35506e16	−0.0711897
$546$	5.91430e17	0.955325
$547$	−1.17641e18	−1.87776	−0.938879	−	0.344246i	$-0.888135\pi$
$547$	−1.17641e18	−1.87776	−0.938879	+	0.344246i	$0.888135\pi$
$548$	2.56111e16	0.0403975
$549$	−1.66997e17	−0.260308
$550$	3.79538e17	0.584652
$551$	4.51532e17	0.687390
$552$	8.05133e17	1.21133
$553$	−8.17896e17	−1.21614
$554$	−5.41237e17	−0.795379
$555$	1.72024e17	0.249853
$556$	−1.03049e17	−0.147930
$557$	−6.58364e17	−0.934130	−0.467065	−	0.884223i	$-0.654689\pi$
$557$	−6.58364e17	−0.934130	−0.467065	+	0.884223i	$0.654689\pi$
$558$	−1.61160e17	−0.226014
$559$	−2.16166e15	−0.00299647
$560$	2.06323e17	0.282699
$561$	−3.89708e17	−0.527813
$562$	−2.06069e17	−0.275885
$563$	7.46468e16	0.0987885	0.0493943	−	0.998779i	$-0.484271\pi$
$563$	7.46468e16	0.0987885	0.0493943	+	0.998779i	$0.484271\pi$
$564$	4.02662e17	0.526776
$565$	1.64480e16	0.0212715
$566$	−7.87933e16	−0.100736
$567$	−1.11574e17	−0.141018
$568$	−7.68902e17	−0.960742
$569$	−1.32614e16	−0.0163818	−0.00819088	−	0.999966i	$-0.502607\pi$
$569$	−1.32614e16	−0.0163818	−0.00819088	+	0.999966i	$0.502607\pi$
$570$	1.94366e17	0.237374
$571$	−8.32634e17	−1.00535	−0.502677	−	0.864474i	$-0.667652\pi$
$571$	−8.32634e17	−1.00535	−0.502677	+	0.864474i	$0.667652\pi$
$572$	1.05922e18	1.26448
$573$	−2.85347e16	−0.0336797
$574$	−4.18485e17	−0.488374
$575$	8.83236e17	1.01914
$576$	2.72973e17	0.311439
$577$	1.45763e18	1.64439	0.822196	−	0.569205i	$-0.192749\pi$
$577$	1.45763e18	1.64439	0.822196	+	0.569205i	$0.192749\pi$
$578$	4.23082e17	0.471948
$579$	9.28666e17	1.02435
$580$	−2.49406e17	−0.272035
$581$	−1.49073e18	−1.60788
$582$	−3.75883e17	−0.400916
$583$	−2.81066e18	−2.96458
$584$	1.71417e18	1.78801
$585$	−3.98186e17	−0.410746
$586$	8.77219e17	0.894898
$587$	−1.61649e18	−1.63089	−0.815444	−	0.578836i	$-0.803507\pi$
$587$	−1.61649e18	−1.63089	−0.815444	+	0.578836i	$0.803507\pi$
$588$	1.63790e17	0.163431
$589$	7.60498e17	0.750496
$590$	6.76415e16	0.0660199
$591$	9.92872e17	0.958461
$592$	2.10641e17	0.201118
$593$	1.67586e18	1.58264	0.791321	−	0.611401i	$-0.209394\pi$
$593$	1.67586e18	1.58264	0.791321	+	0.611401i	$0.209394\pi$
$594$	2.31331e17	0.216084
$595$	−5.67173e17	−0.524029
$596$	−4.77926e17	−0.436777
$597$	1.27223e16	0.0115009
$598$	−2.85361e18	−2.55174
$599$	−1.11637e18	−0.987490	−0.493745	−	0.869607i	$-0.664372\pi$
$599$	−1.11637e18	−0.987490	−0.493745	+	0.869607i	$0.664372\pi$
$600$	3.68296e17	0.322266
$601$	−1.51121e18	−1.30810	−0.654050	−	0.756451i	$-0.726931\pi$
$601$	−1.51121e18	−1.30810	−0.654050	+	0.756451i	$0.726931\pi$
$602$	1.82773e15	0.00156507
$603$	6.23853e17	0.528469
$604$	6.42944e17	0.538807
$605$	1.12704e18	0.934396
$606$	8.68260e17	0.712160
$607$	−1.94403e18	−1.57753	−0.788765	−	0.614695i	$-0.789279\pi$
$607$	−1.94403e18	−1.57753	−0.788765	+	0.614695i	$0.789279\pi$
$608$	−8.44552e17	−0.678037
$609$	7.82131e17	0.621251
$610$	5.03911e17	0.396014
$611$	−4.50645e18	−3.50402
$612$	−1.19761e17	−0.0921360
$613$	−1.24029e18	−0.944124	−0.472062	−	0.881565i	$-0.656490\pi$
$613$	−1.24029e18	−0.944124	−0.472062	+	0.881565i	$0.656490\pi$
$614$	−4.39219e17	−0.330816
$615$	2.81750e17	0.209979
$616$	−2.82799e18	−2.08547
$617$	4.04176e15	0.00294929	0.00147464	−	0.999999i	$-0.499531\pi$
$617$	4.04176e15	0.00294929	0.00147464	+	0.999999i	$0.499531\pi$
$618$	−8.16165e16	−0.0589322
$619$	3.05627e17	0.218374	0.109187	−	0.994021i	$-0.465175\pi$
$619$	3.05627e17	0.218374	0.109187	+	0.994021i	$0.465175\pi$
$620$	−4.20065e17	−0.297009
$621$	5.38339e17	0.376670
$622$	7.79690e17	0.539864
$623$	−7.60382e17	−0.521026
$624$	−4.87573e17	−0.330628
$625$	−3.10179e17	−0.208158
$626$	1.38628e17	0.0920697
$627$	−1.09163e18	−0.717524
$628$	−2.83301e17	−0.184293
$629$	−5.79042e17	−0.372804
$630$	3.36675e17	0.214535
$631$	1.46562e18	0.924337	0.462168	−	0.886792i	$-0.347072\pi$
$631$	1.46562e18	0.924337	0.462168	+	0.886792i	$0.347072\pi$
$632$	1.64555e18	1.02719
$633$	9.54999e17	0.590036
$634$	−5.97112e17	−0.365154
$635$	3.84565e17	0.232777
$636$	−8.63740e17	−0.517502
$637$	−1.83308e18	−1.08711
$638$	−1.62162e18	−0.951951
$639$	−5.14114e17	−0.298747
$640$	1.82846e17	0.105176
$641$	−1.04197e18	−0.593307	−0.296653	−	0.954985i	$-0.595871\pi$
$641$	−1.04197e18	−0.593307	−0.296653	+	0.954985i	$0.595871\pi$
$642$	4.16166e17	0.234579
$643$	3.04390e17	0.169847	0.0849237	−	0.996387i	$-0.472935\pi$
$643$	3.04390e17	0.169847	0.0849237	+	0.996387i	$0.472935\pi$
$644$	−2.08417e18	−1.15126
$645$	−1.23054e15	−0.000672909 0
$646$	−6.54247e17	−0.354185
$647$	−2.96662e18	−1.58995	−0.794976	−	0.606641i	$-0.792517\pi$
$647$	−2.96662e18	−1.58995	−0.794976	+	0.606641i	$0.792517\pi$
$648$	2.24480e17	0.119108
$649$	−3.79900e17	−0.199562
$650$	−1.30534e18	−0.678871
$651$	1.31731e18	0.678285
$652$	6.50537e17	0.331636
$653$	−1.67294e18	−0.844394	−0.422197	−	0.906504i	$-0.638741\pi$
$653$	−1.67294e18	−0.844394	−0.422197	+	0.906504i	$0.638741\pi$
$654$	−8.70185e16	−0.0434867
$655$	1.80262e18	0.891941
$656$	3.44998e17	0.169021
$657$	1.14615e18	0.555991
$658$	3.81030e18	1.83017
$659$	−2.51358e18	−1.19547	−0.597733	−	0.801695i	$-0.703932\pi$
$659$	−2.51358e18	−1.19547	−0.597733	+	0.801695i	$0.703932\pi$
$660$	6.02968e17	0.283961
$661$	2.08332e18	0.971507	0.485753	−	0.874096i	$-0.338545\pi$
$661$	2.08332e18	0.971507	0.485753	+	0.874096i	$0.338545\pi$
$662$	9.90356e17	0.457314
$663$	1.34032e18	0.612872
$664$	2.99923e18	1.35806
$665$	−1.58874e18	−0.712379
$666$	3.43721e17	0.152624
$667$	−3.77373e18	−1.65941
$668$	1.15587e17	0.0503343
$669$	1.82255e18	0.785975
$670$	−1.88247e18	−0.803974
$671$	−2.83015e18	−1.19705
$672$	−1.46291e18	−0.612798
$673$	1.90322e18	0.789570	0.394785	−	0.918774i	$-0.370819\pi$
$673$	1.90322e18	0.789570	0.394785	+	0.918774i	$0.370819\pi$
$674$	4.85865e17	0.199630
$675$	2.46255e17	0.100210
$676$	−2.49305e18	−1.00479
$677$	2.04877e18	0.817838	0.408919	−	0.912571i	$-0.365906\pi$
$677$	2.04877e18	0.817838	0.408919	+	0.912571i	$0.365906\pi$
$678$	3.28647e16	0.0129938
$679$	3.07245e18	1.20318
$680$	1.14111e18	0.442608
$681$	2.25715e18	0.867169
$682$	−2.73123e18	−1.03935
$683$	−1.53611e18	−0.579012	−0.289506	−	0.957176i	$-0.593491\pi$
$683$	−1.53611e18	−0.579012	−0.289506	+	0.957176i	$0.593491\pi$
$684$	−3.35468e17	−0.125252
$685$	−1.63166e17	−0.0603450
$686$	−9.87700e17	−0.361841
$687$	−1.65453e18	−0.600421
$688$	−1.50677e15	−0.000541655 0
$689$	9.66668e18	3.44233
$690$	−1.62443e18	−0.573037
$691$	7.30668e17	0.255336	0.127668	−	0.991817i	$-0.459251\pi$
$691$	7.30668e17	0.255336	0.127668	+	0.991817i	$0.459251\pi$
$692$	−1.04528e18	−0.361863
$693$	−1.89089e18	−0.648486
$694$	−3.36028e18	−1.14166
$695$	6.56516e17	0.220976
$696$	−1.57359e18	−0.524724
$697$	−9.48385e17	−0.313308
$698$	3.16463e17	0.103577
$699$	4.48498e17	0.145431
$700$	−9.53371e17	−0.306284
$701$	−5.29959e18	−1.68684	−0.843422	−	0.537251i	$-0.819463\pi$
$701$	−5.29959e18	−1.68684	−0.843422	+	0.537251i	$0.819463\pi$
$702$	−7.95616e17	−0.250907
$703$	−1.62199e18	−0.506801
$704$	4.62617e18	1.43218
$705$	−2.56532e18	−0.786888
$706$	−1.76625e18	−0.536811
$707$	−7.09711e18	−2.13725
$708$	−1.16746e17	−0.0348359
$709$	−3.40661e17	−0.100722	−0.0503608	−	0.998731i	$-0.516037\pi$
$709$	−3.40661e17	−0.100722	−0.0503608	+	0.998731i	$0.516037\pi$
$710$	1.55133e18	0.454492
$711$	1.10027e18	0.319408
$712$	1.52983e18	0.440072
$713$	−6.35594e18	−1.81175
$714$	−1.13327e18	−0.320106
$715$	−6.74820e18	−1.88886
$716$	4.42892e17	0.122846
$717$	1.32596e18	0.364465
$718$	−1.92889e18	−0.525411
$719$	3.22541e18	0.870656	0.435328	−	0.900272i	$-0.356632\pi$
$719$	3.22541e18	0.870656	0.435328	+	0.900272i	$0.356632\pi$
$720$	−2.77554e17	−0.0742482
$721$	6.67129e17	0.176860
$722$	9.55352e17	0.250999
$723$	−3.55393e18	−0.925359
$724$	−1.60679e18	−0.414628
$725$	−1.72624e18	−0.441472
$726$	2.25195e18	0.570782
$727$	−4.66127e18	−1.17093	−0.585465	−	0.810698i	$-0.699088\pi$
$727$	−4.66127e18	−1.17093	−0.585465	+	0.810698i	$0.699088\pi$
$728$	9.72629e18	2.42155
$729$	1.50095e17	0.0370370
$730$	−3.45850e18	−0.845843
$731$	4.14206e15	0.00100404
$732$	−8.69731e17	−0.208960
$733$	−3.40711e18	−0.811355	−0.405677	−	0.914016i	$-0.632964\pi$
$733$	−3.40711e18	−0.811355	−0.405677	+	0.914016i	$0.632964\pi$
$734$	−3.27800e18	−0.773722
$735$	−1.04349e18	−0.244130
$736$	7.05844e18	1.63683
$737$	1.05727e19	2.43022
$738$	5.62964e17	0.128267
$739$	2.73641e18	0.618005	0.309003	−	0.951061i	$-0.400005\pi$
$739$	2.73641e18	0.618005	0.309003	+	0.951061i	$0.400005\pi$
$740$	8.95912e17	0.200567
$741$	3.75444e18	0.833156
$742$	−8.17338e18	−1.79794
$743$	1.64585e18	0.358892	0.179446	−	0.983768i	$-0.442569\pi$
$743$	1.64585e18	0.358892	0.179446	+	0.983768i	$0.442569\pi$
$744$	−2.65033e18	−0.572897
$745$	3.04482e18	0.652449
$746$	9.43982e17	0.200522
$747$	2.00539e18	0.422294
$748$	−2.02962e18	−0.423697
$749$	−3.40172e18	−0.703990
$750$	−2.17012e18	−0.445231
$751$	−8.27237e18	−1.68256	−0.841280	−	0.540600i	$-0.818197\pi$
$751$	−8.27237e18	−1.68256	−0.841280	+	0.540600i	$0.818197\pi$
$752$	−3.14120e18	−0.633402
$753$	2.88206e18	0.576151
$754$	5.57722e18	1.10536
$755$	−4.09614e18	−0.804859
$756$	−5.81087e17	−0.113201
$757$	−7.54897e18	−1.45802	−0.729012	−	0.684501i	$-0.760020\pi$
$757$	−7.54897e18	−1.45802	−0.729012	+	0.684501i	$0.760020\pi$
$758$	6.71088e18	1.28508
$759$	9.12342e18	1.73215
$760$	3.19642e18	0.601694
$761$	7.12996e18	1.33072	0.665360	−	0.746522i	$-0.268278\pi$
$761$	7.12996e18	1.33072	0.665360	+	0.746522i	$0.268278\pi$
$762$	7.68399e17	0.142193
$763$	7.11285e17	0.130507
$764$	−1.48611e17	−0.0270361
$765$	7.62984e17	0.137631
$766$	1.18949e17	0.0212752
$767$	1.30659e18	0.231722
$768$	3.43283e18	0.603676
$769$	7.42916e18	1.29544	0.647722	−	0.761877i	$-0.275722\pi$
$769$	7.42916e18	1.29544	0.647722	+	0.761877i	$0.275722\pi$
$770$	5.70575e18	0.986558
$771$	2.50577e18	0.429624
$772$	4.83655e18	0.822287
$773$	−5.54036e18	−0.934052	−0.467026	−	0.884244i	$-0.654675\pi$
$773$	−5.54036e18	−0.934052	−0.467026	+	0.884244i	$0.654675\pi$
$774$	−2.45873e15	−0.000411051 0
$775$	−2.90743e18	−0.482002
$776$	−6.18154e18	−1.01624
$777$	−2.80956e18	−0.458038
$778$	−4.42114e18	−0.714771
$779$	−2.65657e18	−0.425920
$780$	−2.07378e18	−0.329722
$781$	−8.71287e18	−1.37382
$782$	5.46794e18	0.855027
$783$	−1.05215e18	−0.163165
$784$	−1.27774e18	−0.196512
$785$	1.80488e18	0.275294
$786$	3.60182e18	0.544848
$787$	−4.81562e18	−0.722465	−0.361232	−	0.932476i	$-0.617644\pi$
$787$	−4.81562e18	−0.722465	−0.361232	+	0.932476i	$0.617644\pi$
$788$	5.17094e18	0.769395
$789$	6.59132e18	0.972684
$790$	−3.32005e18	−0.485924
$791$	−2.68635e17	−0.0389955
$792$	3.80433e18	0.547728
$793$	9.73373e18	1.38996
$794$	−7.60165e18	−1.07665
$795$	5.50281e18	0.773034
$796$	6.62586e16	0.00923225
$797$	−8.01513e18	−1.10772	−0.553862	−	0.832608i	$-0.686847\pi$
$797$	−8.01513e18	−1.10772	−0.553862	+	0.832608i	$0.686847\pi$
$798$	−3.17445e18	−0.435161
$799$	8.63502e18	1.17411
$800$	3.22878e18	0.435465
$801$	1.02290e18	0.136842
$802$	7.88572e18	1.04642
$803$	1.94242e19	2.55678
$804$	3.24907e18	0.424223
$805$	1.32780e19	1.71973
$806$	9.39350e18	1.20684
$807$	6.56222e18	0.836321
$808$	1.42789e19	1.80518
$809$	−9.80201e18	−1.22928	−0.614638	−	0.788809i	$-0.710698\pi$
$809$	−9.80201e18	−1.22928	−0.614638	+	0.788809i	$0.710698\pi$
$810$	−4.52909e17	−0.0563454
$811$	−5.22975e18	−0.645425	−0.322712	−	0.946497i	$-0.604595\pi$
$811$	−5.22975e18	−0.645425	−0.322712	+	0.946497i	$0.604595\pi$
$812$	4.07339e18	0.498703
$813$	−3.66024e17	−0.0444550
$814$	5.82515e18	0.701857
$815$	−4.14451e18	−0.495392
$816$	9.34262e17	0.110785
$817$	1.16025e16	0.00136493
$818$	−6.19312e18	−0.722791
$819$	6.50333e18	0.752992
$820$	1.46737e18	0.168558
$821$	2.56010e18	0.291761	0.145880	−	0.989302i	$-0.453399\pi$
$821$	2.56010e18	0.291761	0.145880	+	0.989302i	$0.453399\pi$
$822$	−3.26022e17	−0.0368621
$823$	−8.71139e18	−0.977211	−0.488605	−	0.872505i	$-0.662494\pi$
$823$	−8.71139e18	−0.977211	−0.488605	+	0.872505i	$0.662494\pi$
$824$	−1.34221e18	−0.149381
$825$	4.17338e18	0.460826
$826$	−1.10475e18	−0.121030
$827$	1.03968e19	1.13009	0.565043	−	0.825061i	$-0.308859\pi$
$827$	1.03968e19	1.13009	0.565043	+	0.825061i	$0.308859\pi$
$828$	2.80371e18	0.302368
$829$	−1.16199e19	−1.24336	−0.621682	−	0.783270i	$-0.713550\pi$
$829$	−1.16199e19	−1.24336	−0.621682	+	0.783270i	$0.713550\pi$
$830$	−6.05124e18	−0.642446
$831$	−5.95141e18	−0.626922
$832$	−1.59107e19	−1.66299
$833$	3.51245e18	0.364266
$834$	1.31178e18	0.134984
$835$	−7.36398e17	−0.0751883
$836$	−5.68528e18	−0.575985
$837$	−1.77210e18	−0.178145
$838$	2.58560e18	0.257914
$839$	−1.03399e19	−1.02344	−0.511720	−	0.859152i	$-0.670991\pi$
$839$	−1.03399e19	−1.02344	−0.511720	+	0.859152i	$0.670991\pi$
$840$	5.53675e18	0.543800
$841$	−2.88508e18	−0.281180
$842$	−5.30478e18	−0.513025
$843$	−2.26593e18	−0.217454
$844$	4.97370e18	0.473645
$845$	1.58830e19	1.50094
$846$	−5.12577e18	−0.480675
$847$	−1.84073e19	−1.71296
$848$	6.73811e18	0.622250
$849$	−8.66407e17	−0.0794002
$850$	2.50123e18	0.227473
$851$	1.35559e19	1.22345
$852$	−2.67754e18	−0.239816
$853$	−1.83597e19	−1.63192	−0.815958	−	0.578111i	$-0.803790\pi$
$853$	−1.83597e19	−1.63192	−0.815958	+	0.578111i	$0.803790\pi$
$854$	−8.23007e18	−0.725984
$855$	2.13723e18	0.187099
$856$	6.84400e18	0.594608
$857$	−7.25793e18	−0.625802	−0.312901	−	0.949786i	$-0.601301\pi$
$857$	−7.25793e18	−0.625802	−0.312901	+	0.949786i	$0.601301\pi$
$858$	−1.34836e19	−1.15382
$859$	−3.54601e18	−0.301151	−0.150576	−	0.988599i	$-0.548113\pi$
$859$	−3.54601e18	−0.301151	−0.150576	+	0.988599i	$0.548113\pi$
$860$	−6.40871e15	−0.000540171 0
$861$	−4.60164e18	−0.384939
$862$	1.59492e18	0.132416
$863$	−2.11515e18	−0.174289	−0.0871446	−	0.996196i	$-0.527774\pi$
$863$	−2.11515e18	−0.174289	−0.0871446	+	0.996196i	$0.527774\pi$
$864$	1.96797e18	0.160945
$865$	6.65941e18	0.540544
$866$	−4.85589e18	−0.391203
$867$	4.65219e18	0.371992
$868$	6.86065e18	0.544486
$869$	1.86466e19	1.46883
$870$	3.17487e18	0.248228
$871$	−3.63624e19	−2.82186
$872$	−1.43105e18	−0.110230
$873$	−4.13319e18	−0.316004
$874$	1.53165e19	1.16235
$875$	1.77385e19	1.33618
$876$	5.96924e18	0.446316
$877$	9.33642e18	0.692920	0.346460	−	0.938065i	$-0.387384\pi$
$877$	9.33642e18	0.692920	0.346460	+	0.938065i	$0.387384\pi$
$878$	−1.05563e18	−0.0777677
$879$	9.64585e18	0.705363
$880$	−4.70380e18	−0.341438
$881$	3.84401e18	0.276975	0.138488	−	0.990364i	$-0.455776\pi$
$881$	3.84401e18	0.276975	0.138488	+	0.990364i	$0.455776\pi$
$882$	−2.08500e18	−0.149128
$883$	−4.87356e17	−0.0346020	−0.0173010	−	0.999850i	$-0.505507\pi$
$883$	−4.87356e17	−0.0346020	−0.0173010	+	0.999850i	$0.505507\pi$
$884$	6.98047e18	0.491977
$885$	7.43781e17	0.0520372
$886$	−9.49716e17	−0.0659591
$887$	2.16616e19	1.49344	0.746718	−	0.665140i	$-0.231628\pi$
$887$	2.16616e19	1.49344	0.746718	+	0.665140i	$0.231628\pi$
$888$	5.65262e18	0.386870
$889$	−6.28085e18	−0.426734
$890$	−3.08658e18	−0.208182
$891$	2.54371e18	0.170318
$892$	9.49194e18	0.630934
$893$	2.41880e19	1.59612
$894$	6.08386e18	0.398552
$895$	−2.82162e18	−0.183506
$896$	−2.98631e18	−0.192811
$897$	−3.13781e19	−2.01130
$898$	1.46167e19	0.930153
$899$	1.24223e19	0.784812
$900$	1.28251e18	0.0804426
$901$	−1.85228e19	−1.15344
$902$	9.54074e18	0.589847
$903$	2.00976e16	0.00123360
$904$	5.40473e17	0.0329366
$905$	1.02367e19	0.619362
$906$	−8.18450e18	−0.491653
$907$	2.90941e19	1.73523	0.867616	−	0.497235i	$-0.165651\pi$
$907$	2.90941e19	1.73523	0.867616	+	0.497235i	$0.165651\pi$
$908$	1.17554e19	0.696111
$909$	9.54733e18	0.561328
$910$	−1.96237e19	−1.14555
$911$	−9.46913e18	−0.548834	−0.274417	−	0.961611i	$-0.588485\pi$
$911$	−9.46913e18	−0.548834	−0.274417	+	0.961611i	$0.588485\pi$
$912$	2.61701e18	0.150605
$913$	3.39860e19	1.94196
$914$	9.43652e18	0.535379
$915$	5.54098e18	0.312140
$916$	−8.61690e18	−0.481981
$917$	−2.94411e19	−1.63513
$918$	1.52452e18	0.0840727
$919$	2.29731e19	1.25797	0.628984	−	0.777419i	$-0.283471\pi$
$919$	2.29731e19	1.25797	0.628984	+	0.777419i	$0.283471\pi$
$920$	−2.67144e19	−1.45253
$921$	−4.82962e18	−0.260751
$922$	−1.26972e19	−0.680702
$923$	2.99661e19	1.59521
$924$	−9.84789e18	−0.520565
$925$	6.20096e18	0.325490
$926$	1.83506e18	0.0956489
$927$	−8.97450e17	−0.0464506
$928$	−1.37953e19	−0.709039
$929$	−2.32058e19	−1.18439	−0.592194	−	0.805796i	$-0.701738\pi$
$929$	−2.32058e19	−1.18439	−0.592194	+	0.805796i	$0.701738\pi$
$930$	5.34731e18	0.271017
$931$	9.83892e18	0.495193
$932$	2.33581e18	0.116744
$933$	8.57343e18	0.425524
$934$	3.95117e18	0.194747
$935$	1.29306e19	0.632910
$936$	−1.30842e19	−0.635996
$937$	−1.05355e19	−0.508568	−0.254284	−	0.967130i	$-0.581840\pi$
$937$	−1.05355e19	−0.508568	−0.254284	+	0.967130i	$0.581840\pi$
$938$	3.07452e19	1.47387
$939$	1.52434e18	0.0725698
$940$	−1.33604e19	−0.631666
$941$	−9.40380e18	−0.441541	−0.220770	−	0.975326i	$-0.570857\pi$
$941$	−9.40380e18	−0.441541	−0.220770	+	0.975326i	$0.570857\pi$
$942$	3.60634e18	0.168165
$943$	2.22026e19	1.02820
$944$	9.10749e17	0.0418871
$945$	3.70206e18	0.169097
$946$	−4.16690e16	−0.00189026
$947$	−4.17865e19	−1.88261	−0.941307	−	0.337551i	$-0.890402\pi$
$947$	−4.17865e19	−1.88261	−0.941307	+	0.337551i	$0.890402\pi$
$948$	5.73027e18	0.256402
$949$	−6.68056e19	−2.96881
$950$	7.00632e18	0.309233
$951$	−6.56581e18	−0.287816
$952$	−1.86370e19	−0.811402
$953$	−1.17614e18	−0.0508576	−0.0254288	−	0.999677i	$-0.508095\pi$
$953$	−1.17614e18	−0.0508576	−0.0254288	+	0.999677i	$0.508095\pi$
$954$	1.09952e19	0.472212
$955$	9.46786e17	0.0403859
$956$	6.90569e18	0.292571
$957$	−1.78312e19	−0.750333
$958$	8.60546e18	0.359665
$959$	2.66489e18	0.110626
$960$	−9.05728e18	−0.373452
$961$	−3.49507e18	−0.143138
$962$	−2.00344e19	−0.814964
$963$	4.57613e18	0.184896
$964$	−1.85091e19	−0.742822
$965$	−3.08133e19	−1.22832
$966$	2.65308e19	1.05051
$967$	−1.96858e19	−0.774248	−0.387124	−	0.922028i	$-0.626531\pi$
$967$	−1.96858e19	−0.774248	−0.387124	+	0.922028i	$0.626531\pi$
$968$	3.70341e19	1.44681
$969$	−7.19405e18	−0.279170
$970$	1.24718e19	0.480745
$971$	−1.81593e19	−0.695302	−0.347651	−	0.937624i	$-0.613021\pi$
$971$	−1.81593e19	−0.695302	−0.347651	+	0.937624i	$0.613021\pi$
$972$	7.81703e17	0.0297311
$973$	−1.07225e19	−0.405099
$974$	1.09392e19	0.410537
$975$	−1.43535e19	−0.535090
$976$	6.78484e18	0.251256
$977$	3.12787e19	1.15062	0.575312	−	0.817934i	$-0.304881\pi$
$977$	3.12787e19	1.15062	0.575312	+	0.817934i	$0.304881\pi$
$978$	−8.28115e18	−0.302613
$979$	1.73354e19	0.629283
$980$	−5.43458e18	−0.195973
$981$	−9.56850e17	−0.0342764
$982$	−2.39284e19	−0.851509
$983$	1.23581e19	0.436872	0.218436	−	0.975851i	$-0.429904\pi$
$983$	1.23581e19	0.436872	0.218436	+	0.975851i	$0.429904\pi$
$984$	9.25815e18	0.325129
$985$	−3.29436e19	−1.14931
$986$	−1.06868e19	−0.370380
$987$	4.18978e19	1.44255
$988$	1.95533e19	0.668807
$989$	−9.69694e16	−0.00329503
$990$	−7.67561e18	−0.259110
$991$	−2.03024e18	−0.0680875	−0.0340438	−	0.999420i	$-0.510839\pi$
$991$	−2.03024e18	−0.0680875	−0.0340438	+	0.999420i	$0.510839\pi$
$992$	−2.32349e19	−0.774133
$993$	1.08899e19	0.360457
$994$	−2.53370e19	−0.833188
$995$	−4.22128e17	−0.0137910
$996$	1.04442e19	0.338992
$997$	−3.18071e19	−1.02566	−0.512832	−	0.858489i	$-0.671404\pi$
$997$	−3.18071e19	−1.02566	−0.512832	+	0.858489i	$0.671404\pi$
$998$	8.55356e17	0.0274030
$999$	3.77953e18	0.120299

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.11	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-66.2972 q^{2} -729.000 q^{3} -3796.68 q^{4} +24188.3 q^{5} +48330.7 q^{6} -395052. q^{7} +794816. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-66.2972 q^{2} -729.000 q^{3} -3796.68 q^{4} +24188.3 q^{5} +48330.7 q^{6} -395052. q^{7} +794816. q^{8} +531441. q^{9} -1.60362e6 q^{10} +9.00651e6 q^{11} +2.76778e6 q^{12} -3.09760e7 q^{13} +2.61909e7 q^{14} -1.76333e7 q^{15} -2.15917e7 q^{16} +5.93547e7 q^{17} -3.52331e7 q^{18} +1.66261e8 q^{19} -9.18353e7 q^{20} +2.87993e8 q^{21} -5.97107e8 q^{22} -1.38955e9 q^{23} -5.79421e8 q^{24} -6.35628e8 q^{25} +2.05362e9 q^{26} -3.87420e8 q^{27} +1.49989e9 q^{28} +2.71580e9 q^{29} +1.16904e9 q^{30} +4.57411e9 q^{31} -5.07966e9 q^{32} -6.56575e9 q^{33} -3.93505e9 q^{34} -9.55565e9 q^{35} -2.01771e9 q^{36} -9.75563e9 q^{37} -1.10227e10 q^{38} +2.25815e10 q^{39} +1.92253e10 q^{40} -1.59783e10 q^{41} -1.90931e10 q^{42} +6.97849e7 q^{43} -3.41949e10 q^{44} +1.28547e10 q^{45} +9.21231e10 q^{46} +1.45482e11 q^{47} +1.57403e10 q^{48} +5.91774e10 q^{49} +4.21404e10 q^{50} -4.32695e10 q^{51} +1.17606e11 q^{52} -3.12070e11 q^{53} +2.56849e10 q^{54} +2.17852e11 q^{55} -3.13994e11 q^{56} -1.21205e11 q^{57} -1.80050e11 q^{58} -4.21805e10 q^{59} +6.69479e10 q^{60} -3.14234e11 q^{61} -3.03251e11 q^{62} -2.09947e11 q^{63} +5.13647e11 q^{64} -7.49258e11 q^{65} +4.35291e11 q^{66} +1.17389e12 q^{67} -2.25351e11 q^{68} +1.01298e12 q^{69} +6.33513e11 q^{70} -9.67396e11 q^{71} +4.22398e11 q^{72} +2.15669e12 q^{73} +6.46771e11 q^{74} +4.63373e11 q^{75} -6.31241e11 q^{76} -3.55805e12 q^{77} -1.49709e12 q^{78} +2.07035e12 q^{79} -5.22266e11 q^{80} +2.82430e11 q^{81} +1.05932e12 q^{82} +3.77349e12 q^{83} -1.09342e12 q^{84} +1.43569e12 q^{85} -4.62654e9 q^{86} -1.97982e12 q^{87} +7.15852e12 q^{88} +1.92476e12 q^{89} -8.52228e11 q^{90} +1.22372e13 q^{91} +5.27567e12 q^{92} -3.33453e12 q^{93} -9.64504e12 q^{94} +4.02158e12 q^{95} +3.70308e12 q^{96} -7.77732e12 q^{97} -3.92330e12 q^{98} +4.78643e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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