LMFDB - Embedded newform 177.8.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,8,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, 8, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
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:	$55.2921495107$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + \cdots + 24\!\cdots\!16 $ x^17 - 2x^16 - 1669x^15 + 2385x^14 + 1108684x^13 - 848131x^12 - 377920980x^11 + 12724944x^10 + 71331230512x^9 + 50741131904x^8 - 7480805165760x^7 - 10751966150272x^6 + 413177144536320x^5 + 886760582981376x^4 - 10454479722123264x^3 - 29180140031461376x^2 + 79787300207378432x + 248723246810300416
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-12.3679$ of defining polynomial
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)

$f(q)$	$=$	$q-12.3679 q^{2} -27.0000 q^{3} +24.9655 q^{4} -477.980 q^{5} +333.934 q^{6} +1344.57 q^{7} +1274.32 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-12.3679 q^{2} -27.0000 q^{3} +24.9655 q^{4} -477.980 q^{5} +333.934 q^{6} +1344.57 q^{7} +1274.32 q^{8} +729.000 q^{9} +5911.62 q^{10} +6221.77 q^{11} -674.068 q^{12} +10930.7 q^{13} -16629.5 q^{14} +12905.5 q^{15} -18956.3 q^{16} -31807.5 q^{17} -9016.21 q^{18} -36490.6 q^{19} -11933.0 q^{20} -36303.3 q^{21} -76950.3 q^{22} +38312.8 q^{23} -34406.7 q^{24} +150340. q^{25} -135190. q^{26} -19683.0 q^{27} +33567.7 q^{28} -138973. q^{29} -159614. q^{30} +256427. q^{31} +71336.8 q^{32} -167988. q^{33} +393392. q^{34} -642676. q^{35} +18199.8 q^{36} +22109.8 q^{37} +451313. q^{38} -295128. q^{39} -609101. q^{40} +316134. q^{41} +448996. q^{42} +148255. q^{43} +155329. q^{44} -348448. q^{45} -473850. q^{46} +748870. q^{47} +511820. q^{48} +984312. q^{49} -1.85940e6 q^{50} +858802. q^{51} +272890. q^{52} -1.94662e6 q^{53} +243438. q^{54} -2.97388e6 q^{55} +1.71341e6 q^{56} +985246. q^{57} +1.71880e6 q^{58} -205379. q^{59} +322191. q^{60} +1.76648e6 q^{61} -3.17147e6 q^{62} +980188. q^{63} +1.54412e6 q^{64} -5.22465e6 q^{65} +2.07766e6 q^{66} -425592. q^{67} -794089. q^{68} -1.03445e6 q^{69} +7.94856e6 q^{70} -3.19791e6 q^{71} +928981. q^{72} -4.35846e6 q^{73} -273452. q^{74} -4.05918e6 q^{75} -911006. q^{76} +8.36557e6 q^{77} +3.65013e6 q^{78} -2.91855e6 q^{79} +9.06074e6 q^{80} +531441. q^{81} -3.90993e6 q^{82} -1.97344e6 q^{83} -906328. q^{84} +1.52033e7 q^{85} -1.83361e6 q^{86} +3.75226e6 q^{87} +7.92854e6 q^{88} +7.72572e6 q^{89} +4.30957e6 q^{90} +1.46970e7 q^{91} +956499. q^{92} -6.92352e6 q^{93} -9.26197e6 q^{94} +1.74418e7 q^{95} -1.92609e6 q^{96} +9.26843e6 q^{97} -1.21739e7 q^{98} +4.53567e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9}+O(q^{10}) $ 17 * q + 2 * q^2 - 459 * q^3 + 1166 * q^4 - 318 * q^5 - 54 * q^6 + 3145 * q^7 + 2355 * q^8 + 12393 * q^9	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9} + 6521 q^{10} - 1764 q^{11} - 31482 q^{12} + 18192 q^{13} - 7827 q^{14} + 8586 q^{15} + 139226 q^{16} - 15507 q^{17} + 1458 q^{18} + 52083 q^{19} + 721 q^{20} - 84915 q^{21} - 234434 q^{22} + 63823 q^{23} - 63585 q^{24} + 202153 q^{25} - 367956 q^{26} - 334611 q^{27} + 182306 q^{28} - 502955 q^{29} - 176067 q^{30} + 347531 q^{31} - 243908 q^{32} + 47628 q^{33} - 330872 q^{34} + 92641 q^{35} + 850014 q^{36} + 447615 q^{37} + 775669 q^{38} - 491184 q^{39} + 2203270 q^{40} + 940335 q^{41} + 211329 q^{42} + 478562 q^{43} - 596924 q^{44} - 231822 q^{45} - 3078663 q^{46} + 703121 q^{47} - 3759102 q^{48} + 1895082 q^{49} - 876967 q^{50} + 418689 q^{51} + 6278296 q^{52} - 1005974 q^{53} - 39366 q^{54} + 5212846 q^{55} + 3425294 q^{56} - 1406241 q^{57} + 6710166 q^{58} - 3491443 q^{59} - 19467 q^{60} + 11510749 q^{61} + 5996234 q^{62} + 2292705 q^{63} + 29496941 q^{64} + 11094180 q^{65} + 6329718 q^{66} + 14007144 q^{67} + 19688159 q^{68} - 1723221 q^{69} + 30909708 q^{70} + 5229074 q^{71} + 1716795 q^{72} + 5452211 q^{73} + 12819662 q^{74} - 5458131 q^{75} + 41929340 q^{76} + 9930777 q^{77} + 9934812 q^{78} + 15275654 q^{79} + 36576105 q^{80} + 9034497 q^{81} + 32025935 q^{82} + 7826609 q^{83} - 4922262 q^{84} + 11836945 q^{85} + 51649136 q^{86} + 13579785 q^{87} + 30223741 q^{88} - 6436185 q^{89} + 4753809 q^{90} + 11633535 q^{91} + 43357972 q^{92} - 9383337 q^{93} - 4494252 q^{94} + 23741055 q^{95} + 6585516 q^{96} + 26377540 q^{97} + 26517816 q^{98} - 1285956 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 459 * q^3 + 1166 * q^4 - 318 * q^5 - 54 * q^6 + 3145 * q^7 + 2355 * q^8 + 12393 * q^9 + 6521 * q^10 - 1764 * q^11 - 31482 * q^12 + 18192 * q^13 - 7827 * q^14 + 8586 * q^15 + 139226 * q^16 - 15507 * q^17 + 1458 * q^18 + 52083 * q^19 + 721 * q^20 - 84915 * q^21 - 234434 * q^22 + 63823 * q^23 - 63585 * q^24 + 202153 * q^25 - 367956 * q^26 - 334611 * q^27 + 182306 * q^28 - 502955 * q^29 - 176067 * q^30 + 347531 * q^31 - 243908 * q^32 + 47628 * q^33 - 330872 * q^34 + 92641 * q^35 + 850014 * q^36 + 447615 * q^37 + 775669 * q^38 - 491184 * q^39 + 2203270 * q^40 + 940335 * q^41 + 211329 * q^42 + 478562 * q^43 - 596924 * q^44 - 231822 * q^45 - 3078663 * q^46 + 703121 * q^47 - 3759102 * q^48 + 1895082 * q^49 - 876967 * q^50 + 418689 * q^51 + 6278296 * q^52 - 1005974 * q^53 - 39366 * q^54 + 5212846 * q^55 + 3425294 * q^56 - 1406241 * q^57 + 6710166 * q^58 - 3491443 * q^59 - 19467 * q^60 + 11510749 * q^61 + 5996234 * q^62 + 2292705 * q^63 + 29496941 * q^64 + 11094180 * q^65 + 6329718 * q^66 + 14007144 * q^67 + 19688159 * q^68 - 1723221 * q^69 + 30909708 * q^70 + 5229074 * q^71 + 1716795 * q^72 + 5452211 * q^73 + 12819662 * q^74 - 5458131 * q^75 + 41929340 * q^76 + 9930777 * q^77 + 9934812 * q^78 + 15275654 * q^79 + 36576105 * q^80 + 9034497 * q^81 + 32025935 * q^82 + 7826609 * q^83 - 4922262 * q^84 + 11836945 * q^85 + 51649136 * q^86 + 13579785 * q^87 + 30223741 * q^88 - 6436185 * q^89 + 4753809 * q^90 + 11633535 * q^91 + 43357972 * q^92 - 9383337 * q^93 - 4494252 * q^94 + 23741055 * q^95 + 6585516 * q^96 + 26377540 * q^97 + 26517816 * q^98 - 1285956 * 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 $

$2$	−12.3679	−1.09318	−0.546590	−	0.837400i	$-0.684074\pi$
$2$	−12.3679	−1.09318	−0.546590	+	0.837400i	$0.684074\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	24.9655	0.195043
$5$	−477.980	−1.71007	−0.855037	−	0.518567i	$-0.826466\pi$
$5$	−477.980	−1.71007	−0.855037	+	0.518567i	$0.826466\pi$
$6$	333.934	0.631148
$7$	1344.57	1.48163	0.740813	−	0.671711i	$-0.234440\pi$
$7$	1344.57	1.48163	0.740813	+	0.671711i	$0.234440\pi$
$8$	1274.32	0.879963
$9$	729.000	0.333333
$10$	5911.62	1.86942
$11$	6221.77	1.40942	0.704708	−	0.709497i	$-0.251078\pi$
$11$	6221.77	1.40942	0.704708	+	0.709497i	$0.251078\pi$
$12$	−674.068	−0.112608
$13$	10930.7	1.37989	0.689947	−	0.723860i	$-0.257634\pi$
$13$	10930.7	1.37989	0.689947	+	0.723860i	$0.257634\pi$
$14$	−16629.5	−1.61968
$15$	12905.5	0.987312
$16$	−18956.3	−1.15700
$17$	−31807.5	−1.57021	−0.785105	−	0.619362i	$-0.787391\pi$
$17$	−31807.5	−1.57021	−0.785105	+	0.619362i	$0.787391\pi$
$18$	−9016.21	−0.364393
$19$	−36490.6	−1.22052	−0.610258	−	0.792203i	$-0.708934\pi$
$19$	−36490.6	−1.22052	−0.610258	+	0.792203i	$0.708934\pi$
$20$	−11933.0	−0.333538
$21$	−36303.3	−0.855417
$22$	−76950.3	−1.54075
$23$	38312.8	0.656594	0.328297	−	0.944575i	$-0.393525\pi$
$23$	38312.8	0.656594	0.328297	+	0.944575i	$0.393525\pi$
$24$	−34406.7	−0.508047
$25$	150340.	1.92435
$26$	−135190.	−1.50847
$27$	−19683.0	−0.192450
$28$	33567.7	0.288981
$29$	−138973.	−1.05812	−0.529062	−	0.848583i	$-0.677456\pi$
$29$	−138973.	−1.05812	−0.529062	+	0.848583i	$0.677456\pi$
$30$	−159614.	−1.07931
$31$	256427.	1.54596	0.772979	−	0.634432i	$-0.218766\pi$
$31$	256427.	1.54596	0.772979	+	0.634432i	$0.218766\pi$
$32$	71336.8	0.384847
$33$	−167988.	−0.813727
$34$	393392.	1.71652
$35$	−642676.	−2.53369
$36$	18199.8	0.0650143
$37$	22109.8	0.0717594	0.0358797	−	0.999356i	$-0.488577\pi$
$37$	22109.8	0.0717594	0.0358797	+	0.999356i	$0.488577\pi$
$38$	451313.	1.33424
$39$	−295128.	−0.796682
$40$	−609101.	−1.50480
$41$	316134.	0.716355	0.358178	−	0.933653i	$-0.383398\pi$
$41$	316134.	0.716355	0.358178	+	0.933653i	$0.383398\pi$
$42$	448996.	0.935125
$43$	148255.	0.284361	0.142181	−	0.989841i	$-0.454589\pi$
$43$	148255.	0.284361	0.142181	+	0.989841i	$0.454589\pi$
$44$	155329.	0.274897
$45$	−348448.	−0.570025
$46$	−473850.	−0.717776
$47$	748870.	1.05212	0.526058	−	0.850448i	$-0.323669\pi$
$47$	748870.	1.05212	0.526058	+	0.850448i	$0.323669\pi$
$48$	511820.	0.667995
$49$	984312.	1.19522
$50$	−1.85940e6	−2.10367
$51$	858802.	0.906562
$52$	272890.	0.269138
$53$	−1.94662e6	−1.79604	−0.898021	−	0.439953i	$-0.854995\pi$
$53$	−1.94662e6	−1.79604	−0.898021	+	0.439953i	$0.854995\pi$
$54$	243438.	0.210383
$55$	−2.97388e6	−2.41021
$56$	1.71341e6	1.30378
$57$	985246.	0.704665
$58$	1.71880e6	1.15672
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	322191.	0.192568
$61$	1.76648e6	0.996445	0.498222	−	0.867049i	$-0.333986\pi$
$61$	1.76648e6	0.996445	0.498222	+	0.867049i	$0.333986\pi$
$62$	−3.17147e6	−1.69001
$63$	980188.	0.493875
$64$	1.54412e6	0.736294
$65$	−5.22465e6	−2.35972
$66$	2.07766e6	0.889550
$67$	−425592.	−0.172875	−0.0864374	−	0.996257i	$-0.527548\pi$
$67$	−425592.	−0.172875	−0.0864374	+	0.996257i	$0.527548\pi$
$68$	−794089.	−0.306258
$69$	−1.03445e6	−0.379085
$70$	7.94856e6	2.76978
$71$	−3.19791e6	−1.06038	−0.530191	−	0.847878i	$-0.677880\pi$
$71$	−3.19791e6	−1.06038	−0.530191	+	0.847878i	$0.677880\pi$
$72$	928981.	0.293321
$73$	−4.35846e6	−1.31130	−0.655651	−	0.755064i	$-0.727606\pi$
$73$	−4.35846e6	−1.31130	−0.655651	+	0.755064i	$0.727606\pi$
$74$	−273452.	−0.0784459
$75$	−4.05918e6	−1.11103
$76$	−911006.	−0.238053
$77$	8.36557e6	2.08823
$78$	3.65013e6	0.870917
$79$	−2.91855e6	−0.665996	−0.332998	−	0.942928i	$-0.608060\pi$
$79$	−2.91855e6	−0.665996	−0.332998	+	0.942928i	$0.608060\pi$
$80$	9.06074e6	1.97856
$81$	531441.	0.111111
$82$	−3.90993e6	−0.783105
$83$	−1.97344e6	−0.378835	−0.189418	−	0.981897i	$-0.560660\pi$
$83$	−1.97344e6	−0.378835	−0.189418	+	0.981897i	$0.560660\pi$
$84$	−906328.	−0.166843
$85$	1.52033e7	2.68518
$86$	−1.83361e6	−0.310858
$87$	3.75226e6	0.610908
$88$	7.92854e6	1.24023
$89$	7.72572e6	1.16165	0.580823	−	0.814030i	$-0.302731\pi$
$89$	7.72572e6	1.16165	0.580823	+	0.814030i	$0.302731\pi$
$90$	4.30957e6	0.623140
$91$	1.46970e7	2.04449
$92$	956499.	0.128064
$93$	−6.92352e6	−0.892559
$94$	−9.26197e6	−1.15015
$95$	1.74418e7	2.08717
$96$	−1.92609e6	−0.222192
$97$	9.26843e6	1.03111	0.515555	−	0.856857i	$-0.327586\pi$
$97$	9.26843e6	1.03111	0.515555	+	0.856857i	$0.327586\pi$
$98$	−1.21739e7	−1.30659
$99$	4.53567e6	0.469805
$100$	3.75331e6	0.375331
$101$	5.77631e6	0.557861	0.278930	−	0.960311i	$-0.410020\pi$
$101$	5.77631e6	0.557861	0.278930	+	0.960311i	$0.410020\pi$
$102$	−1.06216e7	−0.991035
$103$	−1.72461e7	−1.55511	−0.777555	−	0.628815i	$-0.783540\pi$
$103$	−1.72461e7	−1.55511	−0.777555	+	0.628815i	$0.783540\pi$
$104$	1.39292e7	1.21426
$105$	1.73522e7	1.46283
$106$	2.40757e7	1.96340
$107$	5.41952e6	0.427679	0.213839	−	0.976869i	$-0.431403\pi$
$107$	5.41952e6	0.427679	0.213839	+	0.976869i	$0.431403\pi$
$108$	−491396.	−0.0375360
$109$	4.21169e6	0.311504	0.155752	−	0.987796i	$-0.450220\pi$
$109$	4.21169e6	0.311504	0.155752	+	0.987796i	$0.450220\pi$
$110$	3.67807e7	2.63479
$111$	−596965.	−0.0414303
$112$	−2.54880e7	−1.71424
$113$	−1.72308e7	−1.12339	−0.561695	−	0.827345i	$-0.689850\pi$
$113$	−1.72308e7	−1.12339	−0.561695	+	0.827345i	$0.689850\pi$
$114$	−1.21855e7	−0.770326
$115$	−1.83128e7	−1.12282
$116$	−3.46952e6	−0.206379
$117$	7.96847e6	0.459965
$118$	2.54011e6	0.142320
$119$	−4.27672e7	−2.32647
$120$	1.64457e7	0.868798
$121$	1.92232e7	0.986455
$122$	−2.18476e7	−1.08929
$123$	−8.53563e6	−0.413588
$124$	6.40182e6	0.301528
$125$	−3.45174e7	−1.58071
$126$	−1.21229e7	−0.539895
$127$	1.99947e7	0.866169	0.433085	−	0.901353i	$-0.357425\pi$
$127$	1.99947e7	0.866169	0.433085	+	0.901353i	$0.357425\pi$
$128$	−2.82287e7	−1.18975
$129$	−4.00289e6	−0.164176
$130$	6.46181e7	2.57960
$131$	1.04080e6	0.0404501	0.0202251	−	0.999795i	$-0.493562\pi$
$131$	1.04080e6	0.0404501	0.0202251	+	0.999795i	$0.493562\pi$
$132$	−4.19389e6	−0.158712
$133$	−4.90640e7	−1.80835
$134$	5.26369e6	0.188983
$135$	9.40809e6	0.329104
$136$	−4.05330e7	−1.38173
$137$	4.65153e7	1.54552	0.772759	−	0.634699i	$-0.218876\pi$
$137$	4.65153e7	1.54552	0.772759	+	0.634699i	$0.218876\pi$
$138$	1.27940e7	0.414408
$139$	−1.91042e7	−0.603360	−0.301680	−	0.953409i	$-0.597547\pi$
$139$	−1.91042e7	−0.603360	−0.301680	+	0.953409i	$0.597547\pi$
$140$	−1.60447e7	−0.494178
$141$	−2.02195e7	−0.607440
$142$	3.95515e7	1.15919
$143$	6.80082e7	1.94484
$144$	−1.38191e7	−0.385667
$145$	6.64262e7	1.80947
$146$	5.39050e7	1.43349
$147$	−2.65764e7	−0.690059
$148$	551982.	0.0139962
$149$	−5.31787e7	−1.31700	−0.658500	−	0.752580i	$-0.728809\pi$
$149$	−5.31787e7	−1.31700	−0.658500	+	0.752580i	$0.728809\pi$
$150$	5.02037e7	1.21455
$151$	4.97786e7	1.17658	0.588292	−	0.808648i	$-0.299800\pi$
$151$	4.97786e7	1.17658	0.588292	+	0.808648i	$0.299800\pi$
$152$	−4.65008e7	−1.07401
$153$	−2.31876e7	−0.523404
$154$	−1.03465e8	−2.28281
$155$	−1.22567e8	−2.64370
$156$	−7.36802e6	−0.155387
$157$	7.17256e7	1.47920	0.739598	−	0.673049i	$-0.235016\pi$
$157$	7.17256e7	1.47920	0.739598	+	0.673049i	$0.235016\pi$
$158$	3.60963e7	0.728054
$159$	5.25588e7	1.03694
$160$	−3.40976e7	−0.658118
$161$	5.15141e7	0.972827
$162$	−6.57282e6	−0.121464
$163$	−6.67080e7	−1.20648	−0.603241	−	0.797559i	$-0.706124\pi$
$163$	−6.67080e7	−1.20648	−0.603241	+	0.797559i	$0.706124\pi$
$164$	7.89245e6	0.139720
$165$	8.02948e7	1.39153
$166$	2.44073e7	0.414135
$167$	−3.70110e7	−0.614927	−0.307463	−	0.951560i	$-0.599480\pi$
$167$	−3.70110e7	−0.614927	−0.307463	+	0.951560i	$0.599480\pi$
$168$	−4.62621e7	−0.752736
$169$	5.67313e7	0.904106
$170$	−1.88034e8	−2.93538
$171$	−2.66017e7	−0.406839
$172$	3.70127e6	0.0554627
$173$	3.73146e7	0.547920	0.273960	−	0.961741i	$-0.411666\pi$
$173$	3.73146e7	0.547920	0.273960	+	0.961741i	$0.411666\pi$
$174$	−4.64077e7	−0.667832
$175$	2.02142e8	2.85117
$176$	−1.17942e8	−1.63070
$177$	5.54523e6	0.0751646
$178$	−9.55511e7	−1.26989
$179$	7.93461e7	1.03405	0.517023	−	0.855972i	$-0.327040\pi$
$179$	7.93461e7	1.03405	0.517023	+	0.855972i	$0.327040\pi$
$180$	−8.69916e6	−0.111179
$181$	8.73656e7	1.09513	0.547565	−	0.836763i	$-0.315555\pi$
$181$	8.73656e7	1.09513	0.547565	+	0.836763i	$0.315555\pi$
$182$	−1.81772e8	−2.23499
$183$	−4.76948e7	−0.575298
$184$	4.88229e7	0.577779
$185$	−1.05680e7	−0.122714
$186$	8.56296e7	0.975727
$187$	−1.97899e8	−2.21308
$188$	1.86959e7	0.205208
$189$	−2.64651e7	−0.285139
$190$	−2.15719e8	−2.28166
$191$	−1.36478e8	−1.41725	−0.708625	−	0.705586i	$-0.750684\pi$
$191$	−1.36478e8	−1.41725	−0.708625	+	0.705586i	$0.750684\pi$
$192$	−4.16912e7	−0.425099
$193$	1.59359e8	1.59561	0.797804	−	0.602917i	$-0.205995\pi$
$193$	1.59359e8	1.59561	0.797804	+	0.602917i	$0.205995\pi$
$194$	−1.14631e8	−1.12719
$195$	1.41066e8	1.36239
$196$	2.45738e7	0.233118
$197$	−2.20118e7	−0.205127	−0.102564	−	0.994726i	$-0.532705\pi$
$197$	−2.20118e7	−0.205127	−0.102564	+	0.994726i	$0.532705\pi$
$198$	−5.60968e7	−0.513582
$199$	7.23177e7	0.650517	0.325259	−	0.945625i	$-0.394549\pi$
$199$	7.23177e7	0.650517	0.325259	+	0.945625i	$0.394549\pi$
$200$	1.91582e8	1.69336
$201$	1.14910e7	0.0998093
$202$	−7.14410e7	−0.609842
$203$	−1.86858e8	−1.56774
$204$	2.14404e7	0.176818
$205$	−1.51106e8	−1.22502
$206$	2.13299e8	1.70001
$207$	2.79301e7	0.218865
$208$	−2.07205e8	−1.59654
$209$	−2.27036e8	−1.72022
$210$	−2.14611e8	−1.59913
$211$	1.37262e8	1.00592	0.502959	−	0.864310i	$-0.332245\pi$
$211$	1.37262e8	1.00592	0.502959	+	0.864310i	$0.332245\pi$
$212$	−4.85984e7	−0.350305
$213$	8.63437e7	0.612212
$214$	−6.70282e7	−0.467530
$215$	−7.08631e7	−0.486279
$216$	−2.50825e7	−0.169349
$217$	3.44782e8	2.29053
$218$	−5.20899e7	−0.340530
$219$	1.17678e8	0.757080
$220$	−7.42444e7	−0.470094
$221$	−3.47677e8	−2.16672
$222$	7.38321e6	0.0452908
$223$	5.13329e7	0.309977	0.154988	−	0.987916i	$-0.450466\pi$
$223$	5.13329e7	0.309977	0.154988	+	0.987916i	$0.450466\pi$
$224$	9.59170e7	0.570200
$225$	1.09598e8	0.641451
$226$	2.13109e8	1.22807
$227$	2.24268e8	1.27256	0.636278	−	0.771459i	$-0.280473\pi$
$227$	2.24268e8	1.27256	0.636278	+	0.771459i	$0.280473\pi$
$228$	2.45972e7	0.137440
$229$	1.09514e8	0.602625	0.301313	−	0.953525i	$-0.402575\pi$
$229$	1.09514e8	0.602625	0.301313	+	0.953525i	$0.402575\pi$
$230$	2.26491e8	1.22745
$231$	−2.25870e8	−1.20564
$232$	−1.77096e8	−0.931110
$233$	1.49211e8	0.772779	0.386390	−	0.922336i	$-0.373722\pi$
$233$	1.49211e8	0.772779	0.386390	+	0.922336i	$0.373722\pi$
$234$	−9.85534e7	−0.502824
$235$	−3.57945e8	−1.79920
$236$	−5.12739e6	−0.0253924
$237$	7.88007e7	0.384513
$238$	5.28942e8	2.54325
$239$	−1.38832e8	−0.657804	−0.328902	−	0.944364i	$-0.606679\pi$
$239$	−1.38832e8	−0.657804	−0.328902	+	0.944364i	$0.606679\pi$
$240$	−2.44640e8	−1.14232
$241$	2.34611e8	1.07966	0.539831	−	0.841773i	$-0.318488\pi$
$241$	2.34611e8	1.07966	0.539831	+	0.841773i	$0.318488\pi$
$242$	−2.37751e8	−1.07837
$243$	−1.43489e7	−0.0641500
$244$	4.41009e7	0.194349
$245$	−4.70482e8	−2.04391
$246$	1.05568e8	0.452126
$247$	−3.98867e8	−1.68418
$248$	3.26770e8	1.36039
$249$	5.32828e7	0.218721
$250$	4.26909e8	1.72800
$251$	2.52396e8	1.00745	0.503725	−	0.863864i	$-0.331962\pi$
$251$	2.52396e8	1.00745	0.503725	+	0.863864i	$0.331962\pi$
$252$	2.44709e7	0.0963269
$253$	2.38374e8	0.925414
$254$	−2.47293e8	−0.946879
$255$	−4.10490e8	−1.55029
$256$	1.51483e8	0.564316
$257$	4.59969e8	1.69029	0.845147	−	0.534534i	$-0.179513\pi$
$257$	4.59969e8	1.69029	0.845147	+	0.534534i	$0.179513\pi$
$258$	4.95075e7	0.179474
$259$	2.97281e7	0.106321
$260$	−1.30436e8	−0.460247
$261$	−1.01311e8	−0.352708
$262$	−1.28726e7	−0.0442193
$263$	3.87682e8	1.31411	0.657053	−	0.753844i	$-0.271803\pi$
$263$	3.87682e8	1.31411	0.657053	+	0.753844i	$0.271803\pi$
$264$	−2.14071e8	−0.716050
$265$	9.30447e8	3.07136
$266$	6.06820e8	1.97685
$267$	−2.08594e8	−0.670677
$268$	−1.06251e7	−0.0337180
$269$	2.41785e7	0.0757351	0.0378675	−	0.999283i	$-0.487944\pi$
$269$	2.41785e7	0.0757351	0.0378675	+	0.999283i	$0.487944\pi$
$270$	−1.16358e8	−0.359770
$271$	−2.33181e7	−0.0711707	−0.0355853	−	0.999367i	$-0.511330\pi$
$271$	−2.33181e7	−0.0711707	−0.0355853	+	0.999367i	$0.511330\pi$
$272$	6.02952e8	1.81674
$273$	−3.96819e8	−1.18038
$274$	−5.75298e8	−1.68953
$275$	9.35381e8	2.71222
$276$	−2.58255e7	−0.0739378
$277$	3.40111e7	0.0961482	0.0480741	−	0.998844i	$-0.484692\pi$
$277$	3.40111e7	0.0961482	0.0480741	+	0.998844i	$0.484692\pi$
$278$	2.36279e8	0.659581
$279$	1.86935e8	0.515319
$280$	−8.18976e8	−2.22955
$281$	−9.09433e7	−0.244511	−0.122256	−	0.992499i	$-0.539013\pi$
$281$	−9.09433e7	−0.244511	−0.122256	+	0.992499i	$0.539013\pi$
$282$	2.50073e8	0.664041
$283$	−1.54868e8	−0.406171	−0.203085	−	0.979161i	$-0.565097\pi$
$283$	−1.54868e8	−0.406171	−0.203085	+	0.979161i	$0.565097\pi$
$284$	−7.98374e7	−0.206820
$285$	−4.70928e8	−1.20503
$286$	−8.41120e8	−2.12607
$287$	4.25063e8	1.06137
$288$	5.20045e7	0.128282
$289$	6.01377e8	1.46556
$290$	−8.21554e8	−1.97808
$291$	−2.50247e8	−0.595311
$292$	−1.08811e8	−0.255760
$293$	−2.68346e8	−0.623245	−0.311623	−	0.950206i	$-0.600872\pi$
$293$	−2.68346e8	−0.623245	−0.311623	+	0.950206i	$0.600872\pi$
$294$	3.28695e8	0.754358
$295$	9.81671e7	0.222633
$296$	2.81750e7	0.0631456
$297$	−1.22463e8	−0.271242
$298$	6.57710e8	1.43972
$299$	4.18786e8	0.906030
$300$	−1.01339e8	−0.216698
$301$	1.99339e8	0.421317
$302$	−6.15658e8	−1.28622
$303$	−1.55960e8	−0.322081
$304$	6.91727e8	1.41214
$305$	−8.44340e8	−1.70399
$306$	2.86783e8	0.572174
$307$	−8.22676e8	−1.62272	−0.811362	−	0.584544i	$-0.801273\pi$
$307$	−8.22676e8	−1.62272	−0.811362	+	0.584544i	$0.801273\pi$
$308$	2.08850e8	0.407294
$309$	4.65645e8	0.897843
$310$	1.51590e9	2.89004
$311$	−8.75600e8	−1.65061	−0.825305	−	0.564687i	$-0.808997\pi$
$311$	−8.75600e8	−1.65061	−0.825305	+	0.564687i	$0.808997\pi$
$312$	−3.76089e8	−0.701051
$313$	−4.06490e8	−0.749280	−0.374640	−	0.927170i	$-0.622234\pi$
$313$	−4.06490e8	−0.749280	−0.374640	+	0.927170i	$0.622234\pi$
$314$	−8.87097e8	−1.61703
$315$	−4.68510e8	−0.844564
$316$	−7.28629e7	−0.129898
$317$	−6.46224e8	−1.13940	−0.569699	−	0.821853i	$-0.692940\pi$
$317$	−6.46224e8	−1.13940	−0.569699	+	0.821853i	$0.692940\pi$
$318$	−6.50043e8	−1.13357
$319$	−8.64655e8	−1.49134
$320$	−7.38059e8	−1.25912
$321$	−1.46327e8	−0.246921
$322$	−6.37122e8	−1.06348
$323$	1.16067e9	1.91647
$324$	1.32677e7	0.0216714
$325$	1.64332e9	2.65540
$326$	8.25039e8	1.31890
$327$	−1.13716e8	−0.179847
$328$	4.02857e8	0.630366
$329$	1.00690e9	1.55884
$330$	−9.93080e8	−1.52120
$331$	−7.67395e8	−1.16311	−0.581555	−	0.813507i	$-0.697556\pi$
$331$	−7.67395e8	−1.16311	−0.581555	+	0.813507i	$0.697556\pi$
$332$	−4.92678e7	−0.0738891
$333$	1.61180e7	0.0239198
$334$	4.57749e8	0.672226
$335$	2.03425e8	0.295629
$336$	6.88176e8	0.989719
$337$	6.41971e8	0.913715	0.456858	−	0.889540i	$-0.348975\pi$
$337$	6.41971e8	0.913715	0.456858	+	0.889540i	$0.348975\pi$
$338$	−7.01649e8	−0.988351
$339$	4.65231e8	0.648589
$340$	3.79559e8	0.523725
$341$	1.59543e9	2.17890
$342$	3.29007e8	0.444748
$343$	2.16165e8	0.289238
$344$	1.88925e8	0.250228
$345$	4.94445e8	0.648263
$346$	−4.61504e8	−0.598976
$347$	6.85227e8	0.880403	0.440201	−	0.897899i	$-0.354907\pi$
$347$	6.85227e8	0.880403	0.440201	+	0.897899i	$0.354907\pi$
$348$	9.36770e7	0.119153
$349$	−3.31439e8	−0.417363	−0.208682	−	0.977984i	$-0.566917\pi$
$349$	−3.31439e8	−0.417363	−0.208682	+	0.977984i	$0.566917\pi$
$350$	−2.50008e9	−3.11685
$351$	−2.15149e8	−0.265561
$352$	4.43841e8	0.542410
$353$	1.17646e9	1.42353	0.711766	−	0.702416i	$-0.247896\pi$
$353$	1.17646e9	1.42353	0.711766	+	0.702416i	$0.247896\pi$
$354$	−6.85830e7	−0.0821685
$355$	1.52854e9	1.81333
$356$	1.92876e8	0.226571
$357$	1.15471e9	1.34319
$358$	−9.81346e8	−1.13040
$359$	−5.67306e8	−0.647123	−0.323562	−	0.946207i	$-0.604880\pi$
$359$	−5.67306e8	−0.647123	−0.323562	+	0.946207i	$0.604880\pi$
$360$	−4.44035e8	−0.501601
$361$	4.37693e8	0.489660
$362$	−1.08053e9	−1.19717
$363$	−5.19027e8	−0.569530
$364$	3.66918e8	0.398762
$365$	2.08326e9	2.24242
$366$	5.89886e8	0.628904
$367$	1.09692e8	0.115836	0.0579182	−	0.998321i	$-0.481554\pi$
$367$	1.09692e8	0.115836	0.0579182	+	0.998321i	$0.481554\pi$
$368$	−7.26270e8	−0.759680
$369$	2.30462e8	0.238785
$370$	1.30705e8	0.134148
$371$	−2.61736e9	−2.66106
$372$	−1.72849e8	−0.174087
$373$	−1.29535e9	−1.29243	−0.646214	−	0.763156i	$-0.723649\pi$
$373$	−1.29535e9	−1.29243	−0.646214	+	0.763156i	$0.723649\pi$
$374$	2.44760e9	2.41930
$375$	9.31970e8	0.912625
$376$	9.54302e8	0.925824
$377$	−1.51907e9	−1.46010
$378$	3.27318e8	0.311708
$379$	−3.39868e8	−0.320681	−0.160341	−	0.987062i	$-0.551259\pi$
$379$	−3.39868e8	−0.320681	−0.160341	+	0.987062i	$0.551259\pi$
$380$	4.35443e8	0.407088
$381$	−5.39858e8	−0.500083
$382$	1.68795e9	1.54931
$383$	1.07778e9	0.980246	0.490123	−	0.871653i	$-0.336952\pi$
$383$	1.07778e9	0.980246	0.490123	+	0.871653i	$0.336952\pi$
$384$	7.62174e8	0.686902
$385$	−3.99858e9	−3.57103
$386$	−1.97094e9	−1.74429
$387$	1.08078e8	0.0947872
$388$	2.31391e8	0.201111
$389$	7.02547e8	0.605134	0.302567	−	0.953128i	$-0.402156\pi$
$389$	7.02547e8	0.605134	0.302567	+	0.953128i	$0.402156\pi$
$390$	−1.74469e9	−1.48933
$391$	−1.21863e9	−1.03099
$392$	1.25433e9	1.05175
$393$	−2.81017e7	−0.0233539
$394$	2.72240e8	0.224241
$395$	1.39501e9	1.13890
$396$	1.13235e8	0.0916322
$397$	−4.23518e7	−0.0339708	−0.0169854	−	0.999856i	$-0.505407\pi$
$397$	−4.23518e7	−0.0339708	−0.0169854	+	0.999856i	$0.505407\pi$
$398$	−8.94419e8	−0.711132
$399$	1.32473e9	1.04405
$400$	−2.84989e9	−2.22648
$401$	1.82357e9	1.41227	0.706133	−	0.708079i	$-0.250438\pi$
$401$	1.82357e9	1.41227	0.706133	+	0.708079i	$0.250438\pi$
$402$	−1.42120e8	−0.109110
$403$	2.80292e9	2.13326
$404$	1.44208e8	0.108807
$405$	−2.54018e8	−0.190008
$406$	2.31104e9	1.71383
$407$	1.37562e8	0.101139
$408$	1.09439e9	0.797741
$409$	−3.94853e8	−0.285367	−0.142684	−	0.989768i	$-0.545573\pi$
$409$	−3.94853e8	−0.285367	−0.142684	+	0.989768i	$0.545573\pi$
$410$	1.86887e9	1.33917
$411$	−1.25591e9	−0.892306
$412$	−4.30558e8	−0.303313
$413$	−2.76145e8	−0.192891
$414$	−3.45437e8	−0.239259
$415$	9.43265e8	0.647836
$416$	7.79760e8	0.531049
$417$	5.15813e8	0.348350
$418$	2.80796e9	1.88051
$419$	1.27926e9	0.849591	0.424795	−	0.905289i	$-0.360346\pi$
$419$	1.27926e9	0.849591	0.424795	+	0.905289i	$0.360346\pi$
$420$	4.33207e8	0.285314
$421$	−4.37766e8	−0.285926	−0.142963	−	0.989728i	$-0.545663\pi$
$421$	−4.37766e8	−0.285926	−0.142963	+	0.989728i	$0.545663\pi$
$422$	−1.69765e9	−1.09965
$423$	5.45926e8	0.350706
$424$	−2.48063e9	−1.58045
$425$	−4.78194e9	−3.02164
$426$	−1.06789e9	−0.669258
$427$	2.37514e9	1.47636
$428$	1.35301e8	0.0834157
$429$	−1.83622e9	−1.12286
$430$	8.76430e8	0.531591
$431$	2.13470e9	1.28430	0.642150	−	0.766579i	$-0.278043\pi$
$431$	2.13470e9	1.28430	0.642150	+	0.766579i	$0.278043\pi$
$432$	3.73117e8	0.222665
$433$	−2.81072e9	−1.66383	−0.831917	−	0.554900i	$-0.812757\pi$
$433$	−2.81072e9	−1.66383	−0.831917	+	0.554900i	$0.812757\pi$
$434$	−4.26424e9	−2.50396
$435$	−1.79351e9	−1.04470
$436$	1.05147e8	0.0607567
$437$	−1.39806e9	−0.801384
$438$	−1.45544e9	−0.827625
$439$	2.30629e9	1.30103	0.650516	−	0.759493i	$-0.274553\pi$
$439$	2.30629e9	1.30103	0.650516	+	0.759493i	$0.274553\pi$
$440$	−3.78969e9	−2.12089
$441$	7.17564e8	0.398405
$442$	4.30005e9	2.36862
$443$	9.88032e8	0.539956	0.269978	−	0.962867i	$-0.412984\pi$
$443$	9.88032e8	0.539956	0.269978	+	0.962867i	$0.412984\pi$
$444$	−1.49035e7	−0.00808068
$445$	−3.69274e9	−1.98650
$446$	−6.34882e8	−0.338860
$447$	1.43583e9	0.760371
$448$	2.07617e9	1.09091
$449$	−3.41363e8	−0.177973	−0.0889866	−	0.996033i	$-0.528363\pi$
$449$	−3.41363e8	−0.177973	−0.0889866	+	0.996033i	$0.528363\pi$
$450$	−1.35550e9	−0.701222
$451$	1.96692e9	1.00964
$452$	−4.30175e8	−0.219109
$453$	−1.34402e9	−0.679302
$454$	−2.77373e9	−1.39113
$455$	−7.02488e9	−3.49622
$456$	1.25552e9	0.620080
$457$	−2.86701e6	−0.00140515	−0.000702575	−	1.00000i	$-0.500224\pi$
$457$	−2.86701e6	−0.00140515	−0.000702575		1.00000i	$0.500224\pi$
$458$	−1.35447e9	−0.658778
$459$	6.26067e8	0.302187
$460$	−4.57187e8	−0.218999
$461$	2.81859e9	1.33992	0.669959	−	0.742398i	$-0.266312\pi$
$461$	2.81859e9	1.33992	0.669959	+	0.742398i	$0.266312\pi$
$462$	2.79355e9	1.31798
$463$	1.30688e9	0.611932	0.305966	−	0.952042i	$-0.401021\pi$
$463$	1.30688e9	0.611932	0.305966	+	0.952042i	$0.401021\pi$
$464$	2.63441e9	1.22425
$465$	3.30931e9	1.52634
$466$	−1.84543e9	−0.844787
$467$	−1.72823e9	−0.785221	−0.392611	−	0.919705i	$-0.628428\pi$
$467$	−1.72823e9	−0.785221	−0.392611	+	0.919705i	$0.628428\pi$
$468$	1.98937e8	0.0897128
$469$	−5.72236e8	−0.256136
$470$	4.42704e9	1.96685
$471$	−1.93659e9	−0.854014
$472$	−2.61719e8	−0.114561
$473$	9.22410e8	0.400784
$474$	−9.74601e8	−0.420342
$475$	−5.48600e9	−2.34870
$476$	−1.06770e9	−0.453760
$477$	−1.41909e9	−0.598680
$478$	1.71706e9	0.719099
$479$	2.64444e9	1.09941	0.549705	−	0.835359i	$-0.314740\pi$
$479$	2.64444e9	1.09941	0.549705	+	0.835359i	$0.314740\pi$
$480$	9.20635e8	0.379964
$481$	2.41675e8	0.0990203
$482$	−2.90165e9	−1.18027
$483$	−1.39088e9	−0.561662
$484$	4.79917e8	0.192401
$485$	−4.43012e9	−1.76327
$486$	1.77466e8	0.0701275
$487$	2.49943e9	0.980594	0.490297	−	0.871556i	$-0.336888\pi$
$487$	2.49943e9	0.980594	0.490297	+	0.871556i	$0.336888\pi$
$488$	2.25106e9	0.876835
$489$	1.80112e9	0.696563
$490$	5.81888e9	2.23436
$491$	−1.41128e9	−0.538057	−0.269029	−	0.963132i	$-0.586703\pi$
$491$	−1.41128e9	−0.538057	−0.269029	+	0.963132i	$0.586703\pi$
$492$	−2.13096e8	−0.0806673
$493$	4.42037e9	1.66148
$494$	4.93316e9	1.84111
$495$	−2.16796e9	−0.803402
$496$	−4.86090e9	−1.78867
$497$	−4.29980e9	−1.57109
$498$	−6.58998e8	−0.239101
$499$	2.12697e8	0.0766319	0.0383159	−	0.999266i	$-0.487801\pi$
$499$	2.12697e8	0.0766319	0.0383159	+	0.999266i	$0.487801\pi$
$500$	−8.61744e8	−0.308307
$501$	9.99298e8	0.355028
$502$	−3.12161e9	−1.10133
$503$	−2.85799e7	−0.0100132	−0.00500660	−	0.999987i	$-0.501594\pi$
$503$	−2.85799e7	−0.0100132	−0.00500660	+	0.999987i	$0.501594\pi$
$504$	1.24908e9	0.434592
$505$	−2.76096e9	−0.953984
$506$	−2.94819e9	−1.01164
$507$	−1.53175e9	−0.521986
$508$	4.99178e8	0.168940
$509$	−1.91356e9	−0.643178	−0.321589	−	0.946879i	$-0.604217\pi$
$509$	−1.91356e9	−0.643178	−0.321589	+	0.946879i	$0.604217\pi$
$510$	5.07691e9	1.69474
$511$	−5.86023e9	−1.94286
$512$	1.73974e9	0.572849
$513$	7.18245e8	0.234888
$514$	−5.68885e9	−1.84780
$515$	8.24330e9	2.65935
$516$	−9.99342e7	−0.0320214
$517$	4.65929e9	1.48287
$518$	−3.67674e8	−0.116228
$519$	−1.00749e9	−0.316342
$520$	−6.65789e9	−2.07647
$521$	1.49555e9	0.463306	0.231653	−	0.972798i	$-0.425587\pi$
$521$	1.49555e9	0.463306	0.231653	+	0.972798i	$0.425587\pi$
$522$	1.25301e9	0.385573
$523$	2.48258e9	0.758835	0.379417	−	0.925226i	$-0.376124\pi$
$523$	2.48258e9	0.758835	0.379417	+	0.925226i	$0.376124\pi$
$524$	2.59842e7	0.00788951
$525$	−5.45784e9	−1.64613
$526$	−4.79482e9	−1.43656
$527$	−8.15629e9	−2.42748
$528$	3.18443e9	0.941483
$529$	−1.93695e9	−0.568884
$530$	−1.15077e10	−3.35755
$531$	−1.49721e8	−0.0433963
$532$	−1.22491e9	−0.352705
$533$	3.45557e9	0.988494
$534$	2.57988e9	0.733171
$535$	−2.59043e9	−0.731363
$536$	−5.42342e8	−0.152124
$537$	−2.14234e9	−0.597007
$538$	−2.99038e8	−0.0827921
$539$	6.12416e9	1.68456
$540$	2.34877e8	0.0641894
$541$	−6.44103e9	−1.74890	−0.874450	−	0.485115i	$-0.838778\pi$
$541$	−6.44103e9	−1.74890	−0.874450	+	0.485115i	$0.838778\pi$
$542$	2.88397e8	0.0778024
$543$	−2.35887e9	−0.632273
$544$	−2.26904e9	−0.604292
$545$	−2.01311e9	−0.532695
$546$	4.90783e9	1.29037
$547$	−5.40495e8	−0.141200	−0.0706002	−	0.997505i	$-0.522491\pi$
$547$	−5.40495e8	−0.141200	−0.0706002	+	0.997505i	$0.522491\pi$
$548$	1.16128e9	0.301442
$549$	1.28776e9	0.332148
$550$	−1.15687e10	−2.96494
$551$	5.07120e9	1.29146
$552$	−1.31822e9	−0.333581
$553$	−3.92417e9	−0.986757
$554$	−4.20646e8	−0.105107
$555$	2.85337e8	0.0708489
$556$	−4.76945e8	−0.117681
$557$	2.83692e9	0.695591	0.347795	−	0.937570i	$-0.386930\pi$
$557$	2.83692e9	0.695591	0.347795	+	0.937570i	$0.386930\pi$
$558$	−2.31200e9	−0.563337
$559$	1.62053e9	0.392389
$560$	1.21828e10	2.93148
$561$	5.34326e9	1.27772
$562$	1.12478e9	0.267295
$563$	7.86504e9	1.85747	0.928734	−	0.370747i	$-0.120898\pi$
$563$	7.86504e9	1.85747	0.928734	+	0.370747i	$0.120898\pi$
$564$	−5.04789e8	−0.118477
$565$	8.23597e9	1.92108
$566$	1.91539e9	0.444018
$567$	7.14557e8	0.164625
$568$	−4.07517e9	−0.933097
$569$	6.12820e9	1.39457	0.697285	−	0.716794i	$-0.254391\pi$
$569$	6.12820e9	1.39457	0.697285	+	0.716794i	$0.254391\pi$
$570$	5.82441e9	1.31731
$571$	7.88550e9	1.77257	0.886284	−	0.463142i	$-0.153278\pi$
$571$	7.88550e9	1.77257	0.886284	+	0.463142i	$0.153278\pi$
$572$	1.69786e9	0.379328
$573$	3.68491e9	0.818249
$574$	−5.25715e9	−1.16027
$575$	5.75996e9	1.26352
$576$	1.12566e9	0.245431
$577$	4.87423e9	1.05631	0.528154	−	0.849149i	$-0.322884\pi$
$577$	4.87423e9	1.05631	0.528154	+	0.849149i	$0.322884\pi$
$578$	−7.43778e9	−1.60212
$579$	−4.30269e9	−0.921224
$580$	1.65836e9	0.352924
$581$	−2.65342e9	−0.561292
$582$	3.09504e9	0.650783
$583$	−1.21114e10	−2.53137
$584$	−5.55408e9	−1.15390
$585$	−3.80877e9	−0.786573
$586$	3.31889e9	0.681319
$587$	1.45833e9	0.297593	0.148796	−	0.988868i	$-0.452460\pi$
$587$	1.45833e9	0.297593	0.148796	+	0.988868i	$0.452460\pi$
$588$	−6.63493e8	−0.134591
$589$	−9.35717e9	−1.88687
$590$	−1.21412e9	−0.243378
$591$	5.94318e8	0.118430
$592$	−4.19120e8	−0.0830257
$593$	2.71973e9	0.535592	0.267796	−	0.963476i	$-0.413705\pi$
$593$	2.71973e9	0.535592	0.267796	+	0.963476i	$0.413705\pi$
$594$	1.51461e9	0.296517
$595$	2.04419e10	3.97843
$596$	−1.32763e9	−0.256872
$597$	−1.95258e9	−0.375576
$598$	−5.17951e9	−0.990454
$599$	−8.04358e9	−1.52917	−0.764584	−	0.644524i	$-0.777056\pi$
$599$	−8.04358e9	−1.52917	−0.764584	+	0.644524i	$0.777056\pi$
$600$	−5.17271e9	−0.977662
$601$	3.08370e9	0.579444	0.289722	−	0.957111i	$-0.406437\pi$
$601$	3.08370e9	0.579444	0.289722	+	0.957111i	$0.406437\pi$
$602$	−2.46541e9	−0.460576
$603$	−3.10257e8	−0.0576250
$604$	1.24275e9	0.229484
$605$	−9.18832e9	−1.68691
$606$	1.92891e9	0.352093
$607$	5.53440e9	1.00441	0.502204	−	0.864749i	$-0.332523\pi$
$607$	5.53440e9	1.00441	0.502204	+	0.864749i	$0.332523\pi$
$608$	−2.60312e9	−0.469713
$609$	5.04516e9	0.905137
$610$	1.04427e10	1.86277
$611$	8.18566e9	1.45181
$612$	−5.78891e8	−0.102086
$613$	−1.57182e9	−0.275608	−0.137804	−	0.990460i	$-0.544004\pi$
$613$	−1.57182e9	−0.275608	−0.137804	+	0.990460i	$0.544004\pi$
$614$	1.01748e10	1.77393
$615$	4.07986e9	0.707266
$616$	1.06604e10	1.83756
$617$	−3.83210e9	−0.656809	−0.328404	−	0.944537i	$-0.606511\pi$
$617$	−3.83210e9	−0.656809	−0.328404	+	0.944537i	$0.606511\pi$
$618$	−5.75906e9	−0.981504
$619$	−5.03030e9	−0.852465	−0.426233	−	0.904614i	$-0.640159\pi$
$619$	−5.03030e9	−0.852465	−0.426233	+	0.904614i	$0.640159\pi$
$620$	−3.05994e9	−0.515635
$621$	−7.54112e8	−0.126362
$622$	1.08294e10	1.80441
$623$	1.03877e10	1.72113
$624$	5.59455e9	0.921762
$625$	4.75332e9	0.778784
$626$	5.02743e9	0.819098
$627$	6.12997e9	0.993167
$628$	1.79066e9	0.288506
$629$	−7.03257e8	−0.112677
$630$	5.79450e9	0.923260
$631$	5.76799e9	0.913949	0.456974	−	0.889480i	$-0.348933\pi$
$631$	5.76799e9	0.913949	0.456974	+	0.889480i	$0.348933\pi$
$632$	−3.71917e9	−0.586052
$633$	−3.70608e9	−0.580767
$634$	7.99244e9	1.24557
$635$	−9.55709e9	−1.48121
$636$	1.31216e9	0.202249
$637$	1.07592e10	1.64927
$638$	1.06940e10	1.63030
$639$	−2.33128e9	−0.353461
$640$	1.34927e10	2.03456
$641$	−1.37617e9	−0.206381	−0.103191	−	0.994662i	$-0.532905\pi$
$641$	−1.37617e9	−0.206381	−0.103191	+	0.994662i	$0.532905\pi$
$642$	1.80976e9	0.269929
$643$	8.74856e9	1.29777	0.648886	−	0.760886i	$-0.275235\pi$
$643$	8.74856e9	1.29777	0.648886	+	0.760886i	$0.275235\pi$
$644$	1.28607e9	0.189743
$645$	1.91330e9	0.280753
$646$	−1.43551e10	−2.09504
$647$	8.82702e9	1.28130	0.640648	−	0.767835i	$-0.278666\pi$
$647$	8.82702e9	1.28130	0.640648	+	0.767835i	$0.278666\pi$
$648$	6.77227e8	0.0977737
$649$	−1.27782e9	−0.183490
$650$	−2.03245e10	−2.90283
$651$	−9.30913e9	−1.32244
$652$	−1.66540e9	−0.235316
$653$	−2.39631e9	−0.336780	−0.168390	−	0.985720i	$-0.553857\pi$
$653$	−2.39631e9	−0.336780	−0.168390	+	0.985720i	$0.553857\pi$
$654$	1.40643e9	0.196605
$655$	−4.97484e8	−0.0691727
$656$	−5.99274e9	−0.828824
$657$	−3.17731e9	−0.437101
$658$	−1.24533e10	−1.70410
$659$	−3.92961e9	−0.534873	−0.267437	−	0.963575i	$-0.586177\pi$
$659$	−3.92961e9	−0.534873	−0.267437	+	0.963575i	$0.586177\pi$
$660$	2.00460e9	0.271409
$661$	6.16515e9	0.830307	0.415153	−	0.909751i	$-0.363728\pi$
$661$	6.16515e9	0.830307	0.415153	+	0.909751i	$0.363728\pi$
$662$	9.49108e9	1.27149
$663$	9.38729e9	1.25096
$664$	−2.51480e9	−0.333361
$665$	2.34516e10	3.09241
$666$	−1.99347e8	−0.0261486
$667$	−5.32444e9	−0.694757
$668$	−9.23998e8	−0.119937
$669$	−1.38599e9	−0.178965
$670$	−2.51594e9	−0.323176
$671$	1.09906e10	1.40441
$672$	−2.58976e9	−0.329205
$673$	−8.84954e9	−1.11910	−0.559549	−	0.828798i	$-0.689025\pi$
$673$	−8.84954e9	−1.11910	−0.559549	+	0.828798i	$0.689025\pi$
$674$	−7.93985e9	−0.998856
$675$	−2.95914e9	−0.370342
$676$	1.41633e9	0.176339
$677$	5.42902e9	0.672452	0.336226	−	0.941781i	$-0.390849\pi$
$677$	5.42902e9	0.672452	0.336226	+	0.941781i	$0.390849\pi$
$678$	−5.75394e9	−0.709025
$679$	1.24620e10	1.52772
$680$	1.93740e10	2.36286
$681$	−6.05524e9	−0.734711
$682$	−1.97321e10	−2.38193
$683$	5.65530e9	0.679178	0.339589	−	0.940574i	$-0.389712\pi$
$683$	5.65530e9	0.679178	0.339589	+	0.940574i	$0.389712\pi$
$684$	−6.64123e8	−0.0793510
$685$	−2.22334e10	−2.64295
$686$	−2.67351e9	−0.316189
$687$	−2.95689e9	−0.347926
$688$	−2.81037e9	−0.329007
$689$	−2.12779e10	−2.47835
$690$	−6.11526e9	−0.708668
$691$	−6.11832e9	−0.705439	−0.352719	−	0.935729i	$-0.614743\pi$
$691$	−6.11832e9	−0.705439	−0.352719	+	0.935729i	$0.614743\pi$
$692$	9.31577e8	0.106868
$693$	6.09850e9	0.696076
$694$	−8.47484e9	−0.962439
$695$	9.13142e9	1.03179
$696$	4.78159e9	0.537576
$697$	−1.00554e10	−1.12483
$698$	4.09921e9	0.456253
$699$	−4.02870e9	−0.446164
$700$	5.04657e9	0.556101
$701$	−1.75688e9	−0.192632	−0.0963160	−	0.995351i	$-0.530706\pi$
$701$	−1.75688e9	−0.192632	−0.0963160	+	0.995351i	$0.530706\pi$
$702$	2.66094e9	0.290306
$703$	−8.06800e8	−0.0875835
$704$	9.60715e9	1.03774
$705$	9.66452e9	1.03877
$706$	−1.45504e10	−1.55618
$707$	7.76663e9	0.826541
$708$	1.38439e8	0.0146603
$709$	−9.00661e9	−0.949072	−0.474536	−	0.880236i	$-0.657384\pi$
$709$	−9.00661e9	−0.949072	−0.474536	+	0.880236i	$0.657384\pi$
$710$	−1.89049e10	−1.98230
$711$	−2.12762e9	−0.221999
$712$	9.84506e9	1.02221
$713$	9.82444e9	1.01507
$714$	−1.42814e10	−1.46834
$715$	−3.25066e10	−3.32583
$716$	1.98091e9	0.201683
$717$	3.74846e9	0.379784
$718$	7.01640e9	0.707422
$719$	3.19207e8	0.0320274	0.0160137	−	0.999872i	$-0.494902\pi$
$719$	3.19207e8	0.0320274	0.0160137	+	0.999872i	$0.494902\pi$
$720$	6.60528e9	0.659519
$721$	−2.31885e10	−2.30409
$722$	−5.41335e9	−0.535286
$723$	−6.33449e9	−0.623344
$724$	2.18112e9	0.213597
$725$	−2.08932e10	−2.03620
$726$	6.41928e9	0.622599
$727$	7.47713e9	0.721713	0.360856	−	0.932621i	$-0.382484\pi$
$727$	7.47713e9	0.721713	0.360856	+	0.932621i	$0.382484\pi$
$728$	1.87287e10	1.79907
$729$	3.87420e8	0.0370370
$730$	−2.57655e10	−2.45137
$731$	−4.71563e9	−0.446507
$732$	−1.19072e9	−0.112208
$733$	−7.27192e9	−0.682002	−0.341001	−	0.940063i	$-0.610766\pi$
$733$	−7.27192e9	−0.682002	−0.341001	+	0.940063i	$0.610766\pi$
$734$	−1.35667e9	−0.126630
$735$	1.27030e10	1.18005
$736$	2.73312e9	0.252689
$737$	−2.64794e9	−0.243653
$738$	−2.85034e9	−0.261035
$739$	6.36734e8	0.0580367	0.0290183	−	0.999579i	$-0.490762\pi$
$739$	6.36734e8	0.0580367	0.0290183	+	0.999579i	$0.490762\pi$
$740$	−2.63836e8	−0.0239345
$741$	1.07694e10	0.972363
$742$	3.23713e10	2.90902
$743$	1.53224e10	1.37045	0.685227	−	0.728329i	$-0.259703\pi$
$743$	1.53224e10	1.37045	0.685227	+	0.728329i	$0.259703\pi$
$744$	−8.82280e9	−0.785419
$745$	2.54184e10	2.25217
$746$	1.60208e10	1.41286
$747$	−1.43864e9	−0.126278
$748$	−4.94064e9	−0.431646
$749$	7.28690e9	0.633660
$750$	−1.15265e10	−0.997664
$751$	−1.47426e10	−1.27009	−0.635045	−	0.772475i	$-0.719018\pi$
$751$	−1.47426e10	−1.27009	−0.635045	+	0.772475i	$0.719018\pi$
$752$	−1.41958e10	−1.21730
$753$	−6.81468e9	−0.581652
$754$	1.87877e10	1.59615
$755$	−2.37932e10	−2.01205
$756$	−6.60713e8	−0.0556143
$757$	1.03556e10	0.867643	0.433822	−	0.900999i	$-0.357165\pi$
$757$	1.03556e10	0.867643	0.433822	+	0.900999i	$0.357165\pi$
$758$	4.20347e9	0.350562
$759$	−6.43609e9	−0.534288
$760$	2.22265e10	1.83664
$761$	4.05993e9	0.333943	0.166971	−	0.985962i	$-0.446601\pi$
$761$	4.05993e9	0.333943	0.166971	+	0.985962i	$0.446601\pi$
$762$	6.67692e9	0.546681
$763$	5.66289e9	0.461533
$764$	−3.40724e9	−0.276424
$765$	1.10832e10	0.895059
$766$	−1.33299e10	−1.07159
$767$	−2.24493e9	−0.179647
$768$	−4.09003e9	−0.325808
$769$	−2.02272e10	−1.60396	−0.801981	−	0.597349i	$-0.796221\pi$
$769$	−2.02272e10	−1.60396	−0.801981	+	0.597349i	$0.796221\pi$
$770$	4.94541e10	3.90377
$771$	−1.24192e10	−0.975892
$772$	3.97847e9	0.311212
$773$	1.26500e10	0.985062	0.492531	−	0.870295i	$-0.336072\pi$
$773$	1.26500e10	0.985062	0.492531	+	0.870295i	$0.336072\pi$
$774$	−1.33670e9	−0.103619
$775$	3.85512e10	2.97497
$776$	1.18110e10	0.907339
$777$	−8.02658e8	−0.0613842
$778$	−8.68905e9	−0.661521
$779$	−1.15359e10	−0.874323
$780$	3.52177e9	0.265723
$781$	−1.98967e10	−1.49452
$782$	1.50720e10	1.12706
$783$	2.73540e9	0.203636
$784$	−1.86589e10	−1.38287
$785$	−3.42834e10	−2.52953
$786$	3.47560e8	0.0255300
$787$	−2.58438e9	−0.188992	−0.0944962	−	0.995525i	$-0.530124\pi$
$787$	−2.58438e9	−0.188992	−0.0944962	+	0.995525i	$0.530124\pi$
$788$	−5.49535e8	−0.0400086
$789$	−1.04674e10	−0.758700
$790$	−1.72533e10	−1.24503
$791$	−2.31679e10	−1.66444
$792$	5.77991e9	0.413412
$793$	1.93088e10	1.37499
$794$	5.23804e8	0.0371362
$795$	−2.51221e10	−1.77325
$796$	1.80545e9	0.126879
$797$	2.54750e10	1.78242	0.891209	−	0.453593i	$-0.149858\pi$
$797$	2.54750e10	1.78242	0.891209	+	0.453593i	$0.149858\pi$
$798$	−1.63841e10	−1.14134
$799$	−2.38197e10	−1.65205
$800$	1.07248e10	0.740583
$801$	5.63205e9	0.387215
$802$	−2.25537e10	−1.54386
$803$	−2.71173e10	−1.84817
$804$	2.86878e8	0.0194671
$805$	−2.46227e10	−1.66361
$806$	−3.46663e10	−2.33203
$807$	−6.52820e8	−0.0437257
$808$	7.36089e9	0.490897
$809$	2.50645e10	1.66433	0.832163	−	0.554531i	$-0.187102\pi$
$809$	2.50645e10	1.66433	0.832163	+	0.554531i	$0.187102\pi$
$810$	3.14168e9	0.207713
$811$	−9.63538e9	−0.634301	−0.317151	−	0.948375i	$-0.602726\pi$
$811$	−9.63538e9	−0.634301	−0.317151	+	0.948375i	$0.602726\pi$
$812$	−4.66499e9	−0.305777
$813$	6.29589e8	0.0410904
$814$	−1.70136e9	−0.110563
$815$	3.18851e10	2.06317
$816$	−1.62797e10	−1.04889
$817$	−5.40993e9	−0.347068
$818$	4.88351e9	0.311958
$819$	1.07141e10	0.681496
$820$	−3.77244e9	−0.238931
$821$	−2.27996e10	−1.43789	−0.718946	−	0.695066i	$-0.755375\pi$
$821$	−2.27996e10	−1.43789	−0.718946	+	0.695066i	$0.755375\pi$
$822$	1.55331e10	0.975451
$823$	7.33439e9	0.458632	0.229316	−	0.973352i	$-0.426351\pi$
$823$	7.33439e9	0.458632	0.229316	+	0.973352i	$0.426351\pi$
$824$	−2.19771e10	−1.36844
$825$	−2.52553e10	−1.56590
$826$	3.41534e9	0.210865
$827$	1.34883e9	0.0829252	0.0414626	−	0.999140i	$-0.486798\pi$
$827$	1.34883e9	0.0829252	0.0414626	+	0.999140i	$0.486798\pi$
$828$	6.97287e8	0.0426880
$829$	1.61073e10	0.981932	0.490966	−	0.871179i	$-0.336644\pi$
$829$	1.61073e10	0.981932	0.490966	+	0.871179i	$0.336644\pi$
$830$	−1.16662e10	−0.708202
$831$	−9.18299e8	−0.0555112
$832$	1.68783e10	1.01601
$833$	−3.13085e10	−1.87674
$834$	−6.37953e9	−0.380810
$835$	1.76905e10	1.05157
$836$	−5.66806e9	−0.335516
$837$	−5.04725e9	−0.297520
$838$	−1.58218e10	−0.928756
$839$	−1.49944e10	−0.876523	−0.438261	−	0.898848i	$-0.644406\pi$
$839$	−1.49944e10	−0.876523	−0.438261	+	0.898848i	$0.644406\pi$
$840$	2.21124e10	1.28723
$841$	2.06352e9	0.119625
$842$	5.41425e9	0.312569
$843$	2.45547e9	0.141169
$844$	3.42682e9	0.196197
$845$	−2.71165e10	−1.54609
$846$	−6.75197e9	−0.383384
$847$	2.58469e10	1.46156
$848$	3.69008e10	2.07802
$849$	4.18143e9	0.234503
$850$	5.91427e10	3.30320
$851$	8.47089e8	0.0471168
$852$	2.15561e9	0.119408
$853$	−2.48117e9	−0.136879	−0.0684393	−	0.997655i	$-0.521802\pi$
$853$	−2.48117e9	−0.136879	−0.0684393	+	0.997655i	$0.521802\pi$
$854$	−2.93756e10	−1.61393
$855$	1.27151e10	0.695724
$856$	6.90622e9	0.376342
$857$	1.30344e10	0.707388	0.353694	−	0.935361i	$-0.384925\pi$
$857$	1.30344e10	0.707388	0.353694	+	0.935361i	$0.384925\pi$
$858$	2.27102e10	1.22748
$859$	−3.01941e10	−1.62535	−0.812673	−	0.582720i	$-0.801989\pi$
$859$	−3.01941e10	−1.62535	−0.812673	+	0.582720i	$0.801989\pi$
$860$	−1.76913e9	−0.0948453
$861$	−1.14767e10	−0.612783
$862$	−2.64018e10	−1.40397
$863$	4.40460e9	0.233275	0.116638	−	0.993175i	$-0.462788\pi$
$863$	4.40460e9	0.233275	0.116638	+	0.993175i	$0.462788\pi$
$864$	−1.40412e9	−0.0740639
$865$	−1.78356e10	−0.936984
$866$	3.47628e10	1.81887
$867$	−1.62372e10	−0.846143
$868$	8.60766e9	0.446752
$869$	−1.81585e10	−0.938666
$870$	2.21820e10	1.14204
$871$	−4.65201e9	−0.238549
$872$	5.36706e9	0.274112
$873$	6.75668e9	0.343703
$874$	1.72911e10	0.876057
$875$	−4.64109e10	−2.34203
$876$	2.93790e9	0.147663
$877$	1.87680e10	0.939549	0.469775	−	0.882786i	$-0.344335\pi$
$877$	1.87680e10	0.939549	0.469775	+	0.882786i	$0.344335\pi$
$878$	−2.85240e10	−1.42226
$879$	7.24535e9	0.359831
$880$	5.63738e10	2.78861
$881$	2.99234e10	1.47433	0.737165	−	0.675713i	$-0.236164\pi$
$881$	2.99234e10	1.47433	0.737165	+	0.675713i	$0.236164\pi$
$882$	−8.87477e9	−0.435529
$883$	3.52933e10	1.72516	0.862582	−	0.505918i	$-0.168846\pi$
$883$	3.52933e10	1.72516	0.862582	+	0.505918i	$0.168846\pi$
$884$	−8.67994e9	−0.422604
$885$	−2.65051e9	−0.128537
$886$	−1.22199e10	−0.590269
$887$	−1.25706e10	−0.604818	−0.302409	−	0.953178i	$-0.597791\pi$
$887$	−1.25706e10	−0.604818	−0.302409	+	0.953178i	$0.597791\pi$
$888$	−7.60726e8	−0.0364571
$889$	2.68842e10	1.28334
$890$	4.56715e10	2.17160
$891$	3.30650e9	0.156602
$892$	1.28155e9	0.0604587
$893$	−2.73267e10	−1.28413
$894$	−1.77582e10	−0.831222
$895$	−3.79258e10	−1.76829
$896$	−3.79553e10	−1.76276
$897$	−1.13072e10	−0.523097
$898$	4.22196e9	0.194557
$899$	−3.56363e10	−1.63581
$900$	2.73617e9	0.125110
$901$	6.19172e10	2.82016
$902$	−2.43267e10	−1.10372
$903$	−5.38215e9	−0.243248
$904$	−2.19576e10	−0.988541
$905$	−4.17590e10	−1.87275
$906$	1.66228e10	0.742599
$907$	−1.02215e10	−0.454874	−0.227437	−	0.973793i	$-0.573035\pi$
$907$	−1.02215e10	−0.454874	−0.227437	+	0.973793i	$0.573035\pi$
$908$	5.59896e9	0.248203
$909$	4.21093e9	0.185954
$910$	8.68832e10	3.82200
$911$	−3.10518e9	−0.136073	−0.0680366	−	0.997683i	$-0.521673\pi$
$911$	−3.10518e9	−0.136073	−0.0680366	+	0.997683i	$0.521673\pi$
$912$	−1.86766e10	−0.815299
$913$	−1.22783e10	−0.533936
$914$	3.54590e7	0.00153608
$915$	2.27972e10	0.983801
$916$	2.73408e9	0.117538
$917$	1.39943e9	0.0599320
$918$	−7.74314e9	−0.330345
$919$	2.97646e10	1.26501	0.632507	−	0.774554i	$-0.282026\pi$
$919$	2.97646e10	1.26501	0.632507	+	0.774554i	$0.282026\pi$
$920$	−2.33364e10	−0.988044
$921$	2.22123e10	0.936880
$922$	−3.48601e10	−1.46477
$923$	−3.49554e10	−1.46321
$924$	−5.63896e9	−0.235151
$925$	3.32399e9	0.138090
$926$	−1.61634e10	−0.668952
$927$	−1.25724e10	−0.518370
$928$	−9.91386e9	−0.407216
$929$	3.44435e10	1.40946	0.704729	−	0.709477i	$-0.251069\pi$
$929$	3.44435e10	1.40946	0.704729	+	0.709477i	$0.251069\pi$
$930$	−4.09293e10	−1.66857
$931$	−3.59182e10	−1.45878
$932$	3.72513e9	0.150725
$933$	2.36412e10	0.952980
$934$	2.13746e10	0.858388
$935$	9.45917e10	3.78453
$936$	1.01544e10	0.404752
$937$	2.41950e10	0.960807	0.480404	−	0.877048i	$-0.340490\pi$
$937$	2.41950e10	0.960807	0.480404	+	0.877048i	$0.340490\pi$
$938$	7.07737e9	0.280003
$939$	1.09752e10	0.432597
$940$	−8.93627e9	−0.350921
$941$	−3.24324e10	−1.26886	−0.634432	−	0.772979i	$-0.718766\pi$
$941$	−3.24324e10	−1.26886	−0.634432	+	0.772979i	$0.718766\pi$
$942$	2.39516e10	0.933591
$943$	1.21120e10	0.470355
$944$	3.89323e9	0.150629
$945$	1.26498e10	0.487609
$946$	−1.14083e10	−0.438129
$947$	−4.68426e9	−0.179232	−0.0896162	−	0.995976i	$-0.528564\pi$
$947$	−4.68426e9	−0.179232	−0.0896162	+	0.995976i	$0.528564\pi$
$948$	1.96730e9	0.0749965
$949$	−4.76409e10	−1.80946
$950$	6.78505e10	2.56756
$951$	1.74480e10	0.657832
$952$	−5.44992e10	−2.04720
$953$	−3.34959e10	−1.25362	−0.626811	−	0.779171i	$-0.715640\pi$
$953$	−3.34959e10	−1.25362	−0.626811	+	0.779171i	$0.715640\pi$
$954$	1.75512e10	0.654466
$955$	6.52338e10	2.42360
$956$	−3.46601e9	−0.128300
$957$	2.33457e10	0.861023
$958$	−3.27063e10	−1.20185
$959$	6.25429e10	2.28988
$960$	1.99276e10	0.726951
$961$	3.82421e10	1.38998
$962$	−2.98902e9	−0.108247
$963$	3.95083e9	0.142560
$964$	5.85717e9	0.210580
$965$	−7.61705e10	−2.72861
$966$	1.72023e10	0.613998
$967$	4.48458e10	1.59489	0.797443	−	0.603395i	$-0.206186\pi$
$967$	4.48458e10	1.59489	0.797443	+	0.603395i	$0.206186\pi$
$968$	2.44966e10	0.868044
$969$	−3.13382e10	−1.10647
$970$	5.47914e10	1.92758
$971$	−3.33761e10	−1.16995	−0.584977	−	0.811050i	$-0.698896\pi$
$971$	−3.33761e10	−1.16995	−0.584977	+	0.811050i	$0.698896\pi$
$972$	−3.58227e8	−0.0125120
$973$	−2.56868e10	−0.893954
$974$	−3.09127e10	−1.07197
$975$	−4.43697e10	−1.53310
$976$	−3.34858e10	−1.15289
$977$	−2.05126e10	−0.703705	−0.351853	−	0.936055i	$-0.614448\pi$
$977$	−2.05126e10	−0.703705	−0.351853	+	0.936055i	$0.614448\pi$
$978$	−2.22761e10	−0.761469
$979$	4.80676e10	1.63724
$980$	−1.17458e10	−0.398650
$981$	3.07032e9	0.103835
$982$	1.74546e10	0.588193
$983$	−1.39469e9	−0.0468317	−0.0234158	−	0.999726i	$-0.507454\pi$
$983$	−1.39469e9	−0.0468317	−0.0234158	+	0.999726i	$0.507454\pi$
$984$	−1.08771e10	−0.363942
$985$	1.05212e10	0.350783
$986$	−5.46708e10	−1.81629
$987$	−2.71864e10	−0.899999
$988$	−9.95792e9	−0.328488
$989$	5.68008e9	0.186710
$990$	2.68132e10	0.878263
$991$	−5.58431e10	−1.82268	−0.911342	−	0.411650i	$-0.864953\pi$
$991$	−5.58431e10	−1.82268	−0.911342	+	0.411650i	$0.864953\pi$
$992$	1.82927e10	0.594958
$993$	2.07197e10	0.671522
$994$	5.31796e10	1.71748
$995$	−3.45664e10	−1.11243
$996$	1.33023e9	0.0426599
$997$	−3.23901e9	−0.103509	−0.0517546	−	0.998660i	$-0.516481\pi$
$997$	−3.23901e9	−0.103509	−0.0517546	+	0.998660i	$0.516481\pi$
$998$	−2.63062e9	−0.0837725
$999$	−4.35187e8	−0.0138101

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.c.1.5	✓	17
3.2	odd	2		531.8.a.c.1.13		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.5	✓	17	1.1	even	1	trivial
531.8.a.c.1.13		17	3.2	odd	2

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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-12.3679 q^{2} -27.0000 q^{3} +24.9655 q^{4} -477.980 q^{5} +333.934 q^{6} +1344.57 q^{7} +1274.32 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-12.3679 q^{2} -27.0000 q^{3} +24.9655 q^{4} -477.980 q^{5} +333.934 q^{6} +1344.57 q^{7} +1274.32 q^{8} +729.000 q^{9} +5911.62 q^{10} +6221.77 q^{11} -674.068 q^{12} +10930.7 q^{13} -16629.5 q^{14} +12905.5 q^{15} -18956.3 q^{16} -31807.5 q^{17} -9016.21 q^{18} -36490.6 q^{19} -11933.0 q^{20} -36303.3 q^{21} -76950.3 q^{22} +38312.8 q^{23} -34406.7 q^{24} +150340. q^{25} -135190. q^{26} -19683.0 q^{27} +33567.7 q^{28} -138973. q^{29} -159614. q^{30} +256427. q^{31} +71336.8 q^{32} -167988. q^{33} +393392. q^{34} -642676. q^{35} +18199.8 q^{36} +22109.8 q^{37} +451313. q^{38} -295128. q^{39} -609101. q^{40} +316134. q^{41} +448996. q^{42} +148255. q^{43} +155329. q^{44} -348448. q^{45} -473850. q^{46} +748870. q^{47} +511820. q^{48} +984312. q^{49} -1.85940e6 q^{50} +858802. q^{51} +272890. q^{52} -1.94662e6 q^{53} +243438. q^{54} -2.97388e6 q^{55} +1.71341e6 q^{56} +985246. q^{57} +1.71880e6 q^{58} -205379. q^{59} +322191. q^{60} +1.76648e6 q^{61} -3.17147e6 q^{62} +980188. q^{63} +1.54412e6 q^{64} -5.22465e6 q^{65} +2.07766e6 q^{66} -425592. q^{67} -794089. q^{68} -1.03445e6 q^{69} +7.94856e6 q^{70} -3.19791e6 q^{71} +928981. q^{72} -4.35846e6 q^{73} -273452. q^{74} -4.05918e6 q^{75} -911006. q^{76} +8.36557e6 q^{77} +3.65013e6 q^{78} -2.91855e6 q^{79} +9.06074e6 q^{80} +531441. q^{81} -3.90993e6 q^{82} -1.97344e6 q^{83} -906328. q^{84} +1.52033e7 q^{85} -1.83361e6 q^{86} +3.75226e6 q^{87} +7.92854e6 q^{88} +7.72572e6 q^{89} +4.30957e6 q^{90} +1.46970e7 q^{91} +956499. q^{92} -6.92352e6 q^{93} -9.26197e6 q^{94} +1.74418e7 q^{95} -1.92609e6 q^{96} +9.26843e6 q^{97} -1.21739e7 q^{98} +4.53567e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9}+O(q^{10}) \) 17 * q + 2 * q^2 - 459 * q^3 + 1166 * q^4 - 318 * q^5 - 54 * q^6 + 3145 * q^7 + 2355 * q^8 + 12393 * q^9	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9} + 6521 q^{10} - 1764 q^{11} - 31482 q^{12} + 18192 q^{13} - 7827 q^{14} + 8586 q^{15} + 139226 q^{16} - 15507 q^{17} + 1458 q^{18} + 52083 q^{19} + 721 q^{20} - 84915 q^{21} - 234434 q^{22} + 63823 q^{23} - 63585 q^{24} + 202153 q^{25} - 367956 q^{26} - 334611 q^{27} + 182306 q^{28} - 502955 q^{29} - 176067 q^{30} + 347531 q^{31} - 243908 q^{32} + 47628 q^{33} - 330872 q^{34} + 92641 q^{35} + 850014 q^{36} + 447615 q^{37} + 775669 q^{38} - 491184 q^{39} + 2203270 q^{40} + 940335 q^{41} + 211329 q^{42} + 478562 q^{43} - 596924 q^{44} - 231822 q^{45} - 3078663 q^{46} + 703121 q^{47} - 3759102 q^{48} + 1895082 q^{49} - 876967 q^{50} + 418689 q^{51} + 6278296 q^{52} - 1005974 q^{53} - 39366 q^{54} + 5212846 q^{55} + 3425294 q^{56} - 1406241 q^{57} + 6710166 q^{58} - 3491443 q^{59} - 19467 q^{60} + 11510749 q^{61} + 5996234 q^{62} + 2292705 q^{63} + 29496941 q^{64} + 11094180 q^{65} + 6329718 q^{66} + 14007144 q^{67} + 19688159 q^{68} - 1723221 q^{69} + 30909708 q^{70} + 5229074 q^{71} + 1716795 q^{72} + 5452211 q^{73} + 12819662 q^{74} - 5458131 q^{75} + 41929340 q^{76} + 9930777 q^{77} + 9934812 q^{78} + 15275654 q^{79} + 36576105 q^{80} + 9034497 q^{81} + 32025935 q^{82} + 7826609 q^{83} - 4922262 q^{84} + 11836945 q^{85} + 51649136 q^{86} + 13579785 q^{87} + 30223741 q^{88} - 6436185 q^{89} + 4753809 q^{90} + 11633535 q^{91} + 43357972 q^{92} - 9383337 q^{93} - 4494252 q^{94} + 23741055 q^{95} + 6585516 q^{96} + 26377540 q^{97} + 26517816 q^{98} - 1285956 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 459 * q^3 + 1166 * q^4 - 318 * q^5 - 54 * q^6 + 3145 * q^7 + 2355 * q^8 + 12393 * q^9 + 6521 * q^10 - 1764 * q^11 - 31482 * q^12 + 18192 * q^13 - 7827 * q^14 + 8586 * q^15 + 139226 * q^16 - 15507 * q^17 + 1458 * q^18 + 52083 * q^19 + 721 * q^20 - 84915 * q^21 - 234434 * q^22 + 63823 * q^23 - 63585 * q^24 + 202153 * q^25 - 367956 * q^26 - 334611 * q^27 + 182306 * q^28 - 502955 * q^29 - 176067 * q^30 + 347531 * q^31 - 243908 * q^32 + 47628 * q^33 - 330872 * q^34 + 92641 * q^35 + 850014 * q^36 + 447615 * q^37 + 775669 * q^38 - 491184 * q^39 + 2203270 * q^40 + 940335 * q^41 + 211329 * q^42 + 478562 * q^43 - 596924 * q^44 - 231822 * q^45 - 3078663 * q^46 + 703121 * q^47 - 3759102 * q^48 + 1895082 * q^49 - 876967 * q^50 + 418689 * q^51 + 6278296 * q^52 - 1005974 * q^53 - 39366 * q^54 + 5212846 * q^55 + 3425294 * q^56 - 1406241 * q^57 + 6710166 * q^58 - 3491443 * q^59 - 19467 * q^60 + 11510749 * q^61 + 5996234 * q^62 + 2292705 * q^63 + 29496941 * q^64 + 11094180 * q^65 + 6329718 * q^66 + 14007144 * q^67 + 19688159 * q^68 - 1723221 * q^69 + 30909708 * q^70 + 5229074 * q^71 + 1716795 * q^72 + 5452211 * q^73 + 12819662 * q^74 - 5458131 * q^75 + 41929340 * q^76 + 9930777 * q^77 + 9934812 * q^78 + 15275654 * q^79 + 36576105 * q^80 + 9034497 * q^81 + 32025935 * q^82 + 7826609 * q^83 - 4922262 * q^84 + 11836945 * q^85 + 51649136 * q^86 + 13579785 * q^87 + 30223741 * q^88 - 6436185 * q^89 + 4753809 * q^90 + 11633535 * q^91 + 43357972 * q^92 - 9383337 * q^93 - 4494252 * q^94 + 23741055 * q^95 + 6585516 * q^96 + 26377540 * q^97 + 26517816 * q^98 - 1285956 * q^99

Introduction

L-functions

Modular forms

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