LMFDB - Embedded newform 177.8.a.c.1.2

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			1.2
Root			$-20.9857$ 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)

$f(q)$	$=$	$q-20.9857 q^{2} -27.0000 q^{3} +312.401 q^{4} -465.631 q^{5} +566.615 q^{6} +286.579 q^{7} -3869.79 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-20.9857 q^{2} -27.0000 q^{3} +312.401 q^{4} -465.631 q^{5} +566.615 q^{6} +286.579 q^{7} -3869.79 q^{8} +729.000 q^{9} +9771.60 q^{10} -3497.66 q^{11} -8434.83 q^{12} -4677.13 q^{13} -6014.07 q^{14} +12572.0 q^{15} +41223.0 q^{16} -1899.70 q^{17} -15298.6 q^{18} +6396.17 q^{19} -145463. q^{20} -7737.63 q^{21} +73400.9 q^{22} +9375.09 q^{23} +104484. q^{24} +138687. q^{25} +98153.0 q^{26} -19683.0 q^{27} +89527.5 q^{28} -160070. q^{29} -263833. q^{30} -272299. q^{31} -369763. q^{32} +94436.8 q^{33} +39866.7 q^{34} -133440. q^{35} +227740. q^{36} -35341.8 q^{37} -134228. q^{38} +126283. q^{39} +1.80189e6 q^{40} -727812. q^{41} +162380. q^{42} -712974. q^{43} -1.09267e6 q^{44} -339445. q^{45} -196743. q^{46} -476612. q^{47} -1.11302e6 q^{48} -741416. q^{49} -2.91045e6 q^{50} +51292.0 q^{51} -1.46114e6 q^{52} -1.49764e6 q^{53} +413062. q^{54} +1.62862e6 q^{55} -1.10900e6 q^{56} -172697. q^{57} +3.35919e6 q^{58} -205379. q^{59} +3.92751e6 q^{60} -1.04757e6 q^{61} +5.71439e6 q^{62} +208916. q^{63} +2.48319e6 q^{64} +2.17782e6 q^{65} -1.98182e6 q^{66} -2.56238e6 q^{67} -593470. q^{68} -253127. q^{69} +2.80033e6 q^{70} +3.16847e6 q^{71} -2.82108e6 q^{72} +1.62960e6 q^{73} +741674. q^{74} -3.74455e6 q^{75} +1.99817e6 q^{76} -1.00235e6 q^{77} -2.65013e6 q^{78} -2.11177e6 q^{79} -1.91947e7 q^{80} +531441. q^{81} +1.52737e7 q^{82} +5.43782e6 q^{83} -2.41724e6 q^{84} +884561. q^{85} +1.49623e7 q^{86} +4.32189e6 q^{87} +1.35352e7 q^{88} -2.27504e6 q^{89} +7.12350e6 q^{90} -1.34037e6 q^{91} +2.92879e6 q^{92} +7.35206e6 q^{93} +1.00021e7 q^{94} -2.97825e6 q^{95} +9.98359e6 q^{96} +1.00026e7 q^{97} +1.55591e7 q^{98} -2.54979e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−20.9857	−1.85489	−0.927447	−	0.373954i	$-0.878002\pi$
$2$	−20.9857	−1.85489	−0.927447	+	0.373954i	$0.878002\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	312.401	2.44063
$5$	−465.631	−1.66589	−0.832945	−	0.553355i	$-0.813347\pi$
$5$	−465.631	−1.66589	−0.832945	+	0.553355i	$0.813347\pi$
$6$	566.615	1.07092
$7$	286.579	0.315792	0.157896	−	0.987456i	$-0.449529\pi$
$7$	286.579	0.315792	0.157896	+	0.987456i	$0.449529\pi$
$8$	−3869.79	−2.67222
$9$	729.000	0.333333
$10$	9771.60	3.09005
$11$	−3497.66	−0.792324	−0.396162	−	0.918181i	$-0.629658\pi$
$11$	−3497.66	−0.792324	−0.396162	+	0.918181i	$0.629658\pi$
$12$	−8434.83	−1.40910
$13$	−4677.13	−0.590443	−0.295221	−	0.955429i	$-0.595393\pi$
$13$	−4677.13	−0.590443	−0.295221	+	0.955429i	$0.595393\pi$
$14$	−6014.07	−0.585761
$15$	12572.0	0.961802
$16$	41223.0	2.51605
$17$	−1899.70	−0.0937810	−0.0468905	−	0.998900i	$-0.514931\pi$
$17$	−1899.70	−0.0937810	−0.0468905	+	0.998900i	$0.514931\pi$
$18$	−15298.6	−0.618298
$19$	6396.17	0.213935	0.106968	−	0.994263i	$-0.465886\pi$
$19$	6396.17	0.213935	0.106968	+	0.994263i	$0.465886\pi$
$20$	−145463.	−4.06583
$21$	−7737.63	−0.182323
$22$	73400.9	1.46968
$23$	9375.09	0.160668	0.0803338	−	0.996768i	$-0.474401\pi$
$23$	9375.09	0.160668	0.0803338	+	0.996768i	$0.474401\pi$
$24$	104484.	1.54281
$25$	138687.	1.77519
$26$	98153.0	1.09521
$27$	−19683.0	−0.192450
$28$	89527.5	0.770732
$29$	−160070.	−1.21876	−0.609379	−	0.792879i	$-0.708581\pi$
$29$	−160070.	−1.21876	−0.609379	+	0.792879i	$0.708581\pi$
$30$	−263833.	−1.78404
$31$	−272299.	−1.64165	−0.820823	−	0.571183i	$-0.806485\pi$
$31$	−272299.	−1.64165	−0.820823	+	0.571183i	$0.806485\pi$
$32$	−369763.	−1.99479
$33$	94436.8	0.457449
$34$	39866.7	0.173954
$35$	−133440.	−0.526075
$36$	227740.	0.813544
$37$	−35341.8	−0.114705	−0.0573525	−	0.998354i	$-0.518266\pi$
$37$	−35341.8	−0.114705	−0.0573525	+	0.998354i	$0.518266\pi$
$38$	−134228.	−0.396827
$39$	126283.	0.340892
$40$	1.80189e6	4.45163
$41$	−727812.	−1.64921	−0.824605	−	0.565709i	$-0.808603\pi$
$41$	−727812.	−1.64921	−0.824605	+	0.565709i	$0.808603\pi$
$42$	162380.	0.338189
$43$	−712974.	−1.36752	−0.683761	−	0.729706i	$-0.739657\pi$
$43$	−712974.	−1.36752	−0.683761	+	0.729706i	$0.739657\pi$
$44$	−1.09267e6	−1.93377
$45$	−339445.	−0.555297
$46$	−196743.	−0.298021
$47$	−476612.	−0.669611	−0.334805	−	0.942287i	$-0.608671\pi$
$47$	−476612.	−0.669611	−0.334805	+	0.942287i	$0.608671\pi$
$48$	−1.11302e6	−1.45264
$49$	−741416.	−0.900275
$50$	−2.91045e6	−3.29279
$51$	51292.0	0.0541445
$52$	−1.46114e6	−1.44105
$53$	−1.49764e6	−1.38179	−0.690894	−	0.722956i	$-0.742783\pi$
$53$	−1.49764e6	−1.38179	−0.690894	+	0.722956i	$0.742783\pi$
$54$	413062.	0.356975
$55$	1.62862e6	1.31993
$56$	−1.10900e6	−0.843866
$57$	−172697.	−0.123516
$58$	3.35919e6	2.26067
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	3.92751e6	2.34741
$61$	−1.04757e6	−0.590919	−0.295460	−	0.955355i	$-0.595473\pi$
$61$	−1.04757e6	−0.590919	−0.295460	+	0.955355i	$0.595473\pi$
$62$	5.71439e6	3.04508
$63$	208916.	0.105264
$64$	2.48319e6	1.18408
$65$	2.17782e6	0.983613
$66$	−1.98182e6	−0.848519
$67$	−2.56238e6	−1.04083	−0.520416	−	0.853913i	$-0.674223\pi$
$67$	−2.56238e6	−1.04083	−0.520416	+	0.853913i	$0.674223\pi$
$68$	−593470.	−0.228885
$69$	−253127.	−0.0927614
$70$	2.80033e6	0.975813
$71$	3.16847e6	1.05062	0.525309	−	0.850912i	$-0.323950\pi$
$71$	3.16847e6	1.05062	0.525309	+	0.850912i	$0.323950\pi$
$72$	−2.82108e6	−0.890740
$73$	1.62960e6	0.490287	0.245144	−	0.969487i	$-0.421165\pi$
$73$	1.62960e6	0.490287	0.245144	+	0.969487i	$0.421165\pi$
$74$	741674.	0.212766
$75$	−3.74455e6	−1.02491
$76$	1.99817e6	0.522138
$77$	−1.00235e6	−0.250210
$78$	−2.65013e6	−0.632319
$79$	−2.11177e6	−0.481893	−0.240947	−	0.970538i	$-0.577458\pi$
$79$	−2.11177e6	−0.481893	−0.240947	+	0.970538i	$0.577458\pi$
$80$	−1.91947e7	−4.19147
$81$	531441.	0.111111
$82$	1.52737e7	3.05911
$83$	5.43782e6	1.04388	0.521941	−	0.852982i	$-0.325208\pi$
$83$	5.43782e6	1.04388	0.521941	+	0.852982i	$0.325208\pi$
$84$	−2.41724e6	−0.444982
$85$	884561.	0.156229
$86$	1.49623e7	2.53661
$87$	4.32189e6	0.703650
$88$	1.35352e7	2.11727
$89$	−2.27504e6	−0.342078	−0.171039	−	0.985264i	$-0.554712\pi$
$89$	−2.27504e6	−0.342078	−0.171039	+	0.985264i	$0.554712\pi$
$90$	7.12350e6	1.03002
$91$	−1.34037e6	−0.186457
$92$	2.92879e6	0.392130
$93$	7.35206e6	0.947805
$94$	1.00021e7	1.24206
$95$	−2.97825e6	−0.356393
$96$	9.98359e6	1.15170
$97$	1.00026e7	1.11279	0.556395	−	0.830918i	$-0.312184\pi$
$97$	1.00026e7	1.11279	0.556395	+	0.830918i	$0.312184\pi$
$98$	1.55591e7	1.66992
$99$	−2.54979e6	−0.264108
$100$	4.33259e7	4.33259
$101$	−4.08392e6	−0.394414	−0.197207	−	0.980362i	$-0.563187\pi$
$101$	−4.08392e6	−0.394414	−0.197207	+	0.980362i	$0.563187\pi$
$102$	−1.07640e6	−0.100432
$103$	−1.63687e7	−1.47599	−0.737996	−	0.674805i	$-0.764228\pi$
$103$	−1.63687e7	−1.47599	−0.737996	+	0.674805i	$0.764228\pi$
$104$	1.80995e7	1.57779
$105$	3.60288e6	0.303729
$106$	3.14290e7	2.56307
$107$	−1.43241e7	−1.13038	−0.565189	−	0.824961i	$-0.691197\pi$
$107$	−1.43241e7	−1.13038	−0.565189	+	0.824961i	$0.691197\pi$
$108$	−6.14899e6	−0.469700
$109$	−666192.	−0.0492728	−0.0246364	−	0.999696i	$-0.507843\pi$
$109$	−666192.	−0.0492728	−0.0246364	+	0.999696i	$0.507843\pi$
$110$	−3.41777e7	−2.44832
$111$	954229.	0.0662250
$112$	1.18137e7	0.794550
$113$	2.37986e7	1.55159	0.775795	−	0.630986i	$-0.217349\pi$
$113$	2.37986e7	1.55159	0.775795	+	0.630986i	$0.217349\pi$
$114$	3.62417e6	0.229108
$115$	−4.36533e6	−0.267655
$116$	−5.00060e7	−2.97454
$117$	−3.40963e6	−0.196814
$118$	4.31003e6	0.241487
$119$	−544415.	−0.0296153
$120$	−4.86511e7	−2.57015
$121$	−7.25356e6	−0.372222
$122$	2.19840e7	1.09609
$123$	1.96509e7	0.952172
$124$	−8.50663e7	−4.00665
$125$	−2.81995e7	−1.29139
$126$	−4.38426e6	−0.195254
$127$	7.78497e6	0.337244	0.168622	−	0.985681i	$-0.446068\pi$
$127$	7.78497e6	0.337244	0.168622	+	0.985681i	$0.446068\pi$
$128$	−4.78197e6	−0.201545
$129$	1.92503e7	0.789539
$130$	−4.57031e7	−1.82450
$131$	−2.68679e7	−1.04420	−0.522101	−	0.852884i	$-0.674852\pi$
$131$	−2.68679e7	−1.04420	−0.522101	+	0.852884i	$0.674852\pi$
$132$	2.95021e7	1.11646
$133$	1.83301e6	0.0675590
$134$	5.37733e7	1.93063
$135$	9.16501e6	0.320601
$136$	7.35146e6	0.250604
$137$	−5.02442e7	−1.66941	−0.834707	−	0.550695i	$-0.814363\pi$
$137$	−5.02442e7	−1.66941	−0.834707	+	0.550695i	$0.814363\pi$
$138$	5.31207e6	0.172063
$139$	−5.46930e7	−1.72735	−0.863675	−	0.504049i	$-0.831843\pi$
$139$	−5.46930e7	−1.72735	−0.863675	+	0.504049i	$0.831843\pi$
$140$	−4.16868e7	−1.28396
$141$	1.28685e7	0.386600
$142$	−6.64926e7	−1.94879
$143$	1.63590e7	0.467822
$144$	3.00516e7	0.838685
$145$	7.45335e7	2.03032
$146$	−3.41983e7	−0.909431
$147$	2.00182e7	0.519774
$148$	−1.10408e7	−0.279953
$149$	3.71390e7	0.919769	0.459884	−	0.887979i	$-0.347891\pi$
$149$	3.71390e7	0.919769	0.459884	+	0.887979i	$0.347891\pi$
$150$	7.85820e7	1.90110
$151$	1.36501e7	0.322639	0.161319	−	0.986902i	$-0.448425\pi$
$151$	1.36501e7	0.322639	0.161319	+	0.986902i	$0.448425\pi$
$152$	−2.47518e7	−0.571682
$153$	−1.38488e6	−0.0312603
$154$	2.10352e7	0.464112
$155$	1.26791e8	2.73480
$156$	3.94508e7	0.831993
$157$	3.77615e7	0.778755	0.389378	−	0.921078i	$-0.372690\pi$
$157$	3.77615e7	0.778755	0.389378	+	0.921078i	$0.372690\pi$
$158$	4.43169e7	0.893861
$159$	4.04362e7	0.797776
$160$	1.72173e8	3.32311
$161$	2.68670e6	0.0507375
$162$	−1.11527e7	−0.206099
$163$	4.92529e7	0.890790	0.445395	−	0.895334i	$-0.353063\pi$
$163$	4.92529e7	0.890790	0.445395	+	0.895334i	$0.353063\pi$
$164$	−2.27369e8	−4.02512
$165$	−4.39726e7	−0.762059
$166$	−1.14117e8	−1.93629
$167$	1.04186e8	1.73102	0.865508	−	0.500895i	$-0.166996\pi$
$167$	1.04186e8	1.73102	0.865508	+	0.500895i	$0.166996\pi$
$168$	2.99430e7	0.487206
$169$	−4.08730e7	−0.651377
$170$	−1.85632e7	−0.289788
$171$	4.66281e6	0.0713118
$172$	−2.22734e8	−3.33762
$173$	9.60679e7	1.41064	0.705321	−	0.708888i	$-0.250803\pi$
$173$	9.60679e7	1.41064	0.705321	+	0.708888i	$0.250803\pi$
$174$	−9.06981e7	−1.30520
$175$	3.97447e7	0.560591
$176$	−1.44184e8	−1.99353
$177$	5.54523e6	0.0751646
$178$	4.77435e7	0.634518
$179$	−8.54665e7	−1.11381	−0.556904	−	0.830577i	$-0.688011\pi$
$179$	−8.54665e7	−1.11381	−0.556904	+	0.830577i	$0.688011\pi$
$180$	−1.06043e8	−1.35528
$181$	4.14050e7	0.519012	0.259506	−	0.965741i	$-0.416440\pi$
$181$	4.14050e7	0.519012	0.259506	+	0.965741i	$0.416440\pi$
$182$	2.81286e7	0.345858
$183$	2.82844e7	0.341167
$184$	−3.62796e7	−0.429339
$185$	1.64562e7	0.191086
$186$	−1.54288e8	−1.75808
$187$	6.64452e6	0.0743050
$188$	−1.48894e8	−1.63427
$189$	−5.64073e6	−0.0607742
$190$	6.25008e7	0.661071
$191$	−8.00346e7	−0.831114	−0.415557	−	0.909567i	$-0.636413\pi$
$191$	−8.00346e7	−0.831114	−0.415557	+	0.909567i	$0.636413\pi$
$192$	−6.70462e7	−0.683628
$193$	1.36187e8	1.36360	0.681798	−	0.731540i	$-0.261198\pi$
$193$	1.36187e8	1.36360	0.681798	+	0.731540i	$0.261198\pi$
$194$	−2.09913e8	−2.06411
$195$	−5.88010e7	−0.567889
$196$	−2.31619e8	−2.19724
$197$	−1.36747e8	−1.27434	−0.637171	−	0.770723i	$-0.719895\pi$
$197$	−1.36747e8	−1.27434	−0.637171	+	0.770723i	$0.719895\pi$
$198$	5.35093e7	0.489893
$199$	−4.28301e7	−0.385268	−0.192634	−	0.981271i	$-0.561703\pi$
$199$	−4.28301e7	−0.385268	−0.192634	+	0.981271i	$0.561703\pi$
$200$	−5.36689e8	−4.74371
$201$	6.91841e7	0.600925
$202$	8.57040e7	0.731596
$203$	−4.58727e7	−0.384874
$204$	1.60237e7	0.132147
$205$	3.38892e8	2.74740
$206$	3.43509e8	2.73781
$207$	6.83444e6	0.0535558
$208$	−1.92806e8	−1.48559
$209$	−2.23716e7	−0.169506
$210$	−7.56090e7	−0.563386
$211$	−4.75756e7	−0.348655	−0.174327	−	0.984688i	$-0.555775\pi$
$211$	−4.75756e7	−0.348655	−0.174327	+	0.984688i	$0.555775\pi$
$212$	−4.67864e8	−3.37244
$213$	−8.55486e7	−0.606575
$214$	3.00602e8	2.09673
$215$	3.31982e8	2.27814
$216$	7.61691e7	0.514269
$217$	−7.80350e7	−0.518419
$218$	1.39805e7	0.0913958
$219$	−4.39992e7	−0.283067
$220$	5.08781e8	3.22145
$221$	8.88517e6	0.0553723
$222$	−2.00252e7	−0.122840
$223$	1.14043e8	0.688652	0.344326	−	0.938850i	$-0.388107\pi$
$223$	1.14043e8	0.688652	0.344326	+	0.938850i	$0.388107\pi$
$224$	−1.05966e8	−0.629940
$225$	1.01103e8	0.591731
$226$	−4.99431e8	−2.87803
$227$	5.49344e7	0.311712	0.155856	−	0.987780i	$-0.450186\pi$
$227$	5.49344e7	0.311712	0.155856	+	0.987780i	$0.450186\pi$
$228$	−5.39506e7	−0.301456
$229$	−5.39847e7	−0.297062	−0.148531	−	0.988908i	$-0.547454\pi$
$229$	−5.39847e7	−0.297062	−0.148531	+	0.988908i	$0.547454\pi$
$230$	9.16096e7	0.496471
$231$	2.70636e7	0.144459
$232$	6.19437e8	3.25679
$233$	−2.85964e8	−1.48104	−0.740518	−	0.672036i	$-0.765420\pi$
$233$	−2.85964e8	−1.48104	−0.740518	+	0.672036i	$0.765420\pi$
$234$	7.15536e7	0.365070
$235$	2.21925e8	1.11550
$236$	−6.41606e7	−0.317743
$237$	5.70177e7	0.278221
$238$	1.14250e7	0.0549332
$239$	−8.27309e7	−0.391990	−0.195995	−	0.980605i	$-0.562794\pi$
$239$	−8.27309e7	−0.391990	−0.195995	+	0.980605i	$0.562794\pi$
$240$	5.18257e8	2.41995
$241$	−2.15524e8	−0.991825	−0.495912	−	0.868373i	$-0.665166\pi$
$241$	−2.15524e8	−0.991825	−0.495912	+	0.868373i	$0.665166\pi$
$242$	1.52221e8	0.690433
$243$	−1.43489e7	−0.0641500
$244$	−3.27262e8	−1.44222
$245$	3.45226e8	1.49976
$246$	−4.12389e8	−1.76618
$247$	−2.99157e7	−0.126317
$248$	1.05374e9	4.38684
$249$	−1.46821e8	−0.602685
$250$	5.91786e8	2.39538
$251$	−3.78187e8	−1.50955	−0.754776	−	0.655982i	$-0.772255\pi$
$251$	−3.78187e8	−1.50955	−0.754776	+	0.655982i	$0.772255\pi$
$252$	6.52656e7	0.256911
$253$	−3.27909e7	−0.127301
$254$	−1.63373e8	−0.625551
$255$	−2.38831e7	−0.0901988
$256$	−2.17495e8	−0.810233
$257$	2.36018e8	0.867320	0.433660	−	0.901076i	$-0.357222\pi$
$257$	2.36018e8	0.867320	0.433660	+	0.901076i	$0.357222\pi$
$258$	−4.03982e8	−1.46451
$259$	−1.01282e7	−0.0362229
$260$	6.80352e8	2.40064
$261$	−1.16691e8	−0.406252
$262$	5.63843e8	1.93688
$263$	−3.99714e8	−1.35489	−0.677445	−	0.735573i	$-0.736913\pi$
$263$	−3.99714e8	−1.35489	−0.677445	+	0.735573i	$0.736913\pi$
$264$	−3.65450e8	−1.22240
$265$	6.97346e8	2.30191
$266$	−3.84670e7	−0.125315
$267$	6.14262e7	0.197499
$268$	−8.00489e8	−2.54029
$269$	3.97589e8	1.24538	0.622689	−	0.782470i	$-0.286040\pi$
$269$	3.97589e8	1.24538	0.622689	+	0.782470i	$0.286040\pi$
$270$	−1.92334e8	−0.594681
$271$	5.14541e8	1.57046	0.785232	−	0.619202i	$-0.212544\pi$
$271$	5.14541e8	1.57046	0.785232	+	0.619202i	$0.212544\pi$
$272$	−7.83116e7	−0.235958
$273$	3.61899e7	0.107651
$274$	1.05441e9	3.09658
$275$	−4.85079e8	−1.40653
$276$	−7.90773e7	−0.226397
$277$	−2.94631e8	−0.832911	−0.416455	−	0.909156i	$-0.636728\pi$
$277$	−2.94631e8	−0.832911	−0.416455	+	0.909156i	$0.636728\pi$
$278$	1.14777e9	3.20405
$279$	−1.98506e8	−0.547215
$280$	5.16384e8	1.40579
$281$	6.15936e8	1.65601	0.828006	−	0.560719i	$-0.189475\pi$
$281$	6.15936e8	1.65601	0.828006	+	0.560719i	$0.189475\pi$
$282$	−2.70055e8	−0.717102
$283$	−4.48859e6	−0.0117722	−0.00588609	−	0.999983i	$-0.501874\pi$
$283$	−4.48859e6	−0.0117722	−0.00588609	+	0.999983i	$0.501874\pi$
$284$	9.89832e8	2.56417
$285$	8.04128e7	0.205764
$286$	−3.43306e8	−0.867761
$287$	−2.08576e8	−0.520807
$288$	−2.69557e8	−0.664932
$289$	−4.06730e8	−0.991205
$290$	−1.56414e9	−3.76602
$291$	−2.70071e8	−0.642470
$292$	5.09088e8	1.19661
$293$	3.57368e8	0.830002	0.415001	−	0.909821i	$-0.363781\pi$
$293$	3.57368e8	0.830002	0.415001	+	0.909821i	$0.363781\pi$
$294$	−4.20097e8	−0.964126
$295$	9.56307e7	0.216880
$296$	1.36765e8	0.306517
$297$	6.88444e7	0.152483
$298$	−7.79390e8	−1.70607
$299$	−4.38485e7	−0.0948650
$300$	−1.16980e9	−2.50142
$301$	−2.04323e8	−0.431852
$302$	−2.86457e8	−0.598461
$303$	1.10266e8	0.227715
$304$	2.63670e8	0.538273
$305$	4.87780e8	0.984407
$306$	2.90628e7	0.0579846
$307$	−4.17291e8	−0.823105	−0.411552	−	0.911386i	$-0.635013\pi$
$307$	−4.17291e8	−0.823105	−0.411552	+	0.911386i	$0.635013\pi$
$308$	−3.13137e8	−0.610670
$309$	4.41955e8	0.852164
$310$	−2.66079e9	−5.07277
$311$	1.57129e8	0.296207	0.148103	−	0.988972i	$-0.452683\pi$
$311$	1.57129e8	0.296207	0.148103	+	0.988972i	$0.452683\pi$
$312$	−4.88687e8	−0.910940
$313$	8.52228e8	1.57091	0.785454	−	0.618920i	$-0.212430\pi$
$313$	8.52228e8	1.57091	0.785454	+	0.618920i	$0.212430\pi$
$314$	−7.92454e8	−1.44451
$315$	−9.72777e7	−0.175358
$316$	−6.59718e8	−1.17612
$317$	−7.40371e8	−1.30539	−0.652697	−	0.757619i	$-0.726363\pi$
$317$	−7.40371e8	−1.30539	−0.652697	+	0.757619i	$0.726363\pi$
$318$	−8.48584e8	−1.47979
$319$	5.59870e8	0.965651
$320$	−1.15625e9	−1.97254
$321$	3.86751e8	0.652625
$322$	−5.63824e7	−0.0941127
$323$	−1.21508e7	−0.0200631
$324$	1.66023e8	0.271181
$325$	−6.48657e8	−1.04815
$326$	−1.03361e9	−1.65232
$327$	1.79872e7	0.0284476
$328$	2.81648e9	4.40705
$329$	−1.36587e8	−0.211458
$330$	9.22798e8	1.41354
$331$	−2.16470e8	−0.328095	−0.164047	−	0.986452i	$-0.552455\pi$
$331$	−2.16470e8	−0.328095	−0.164047	+	0.986452i	$0.552455\pi$
$332$	1.69878e9	2.54773
$333$	−2.57642e7	−0.0382350
$334$	−2.18642e9	−3.21085
$335$	1.19312e9	1.73391
$336$	−3.18969e8	−0.458734
$337$	−1.73965e8	−0.247604	−0.123802	−	0.992307i	$-0.539509\pi$
$337$	−1.73965e8	−0.247604	−0.123802	+	0.992307i	$0.539509\pi$
$338$	8.57749e8	1.20824
$339$	−6.42562e8	−0.895810
$340$	2.76338e8	0.381297
$341$	9.52407e8	1.30072
$342$	−9.78525e7	−0.132276
$343$	−4.48484e8	−0.600092
$344$	2.75906e9	3.65432
$345$	1.17864e8	0.154530
$346$	−2.01606e9	−2.61659
$347$	−7.38996e7	−0.0949486	−0.0474743	−	0.998872i	$-0.515117\pi$
$347$	−7.38996e7	−0.0949486	−0.0474743	+	0.998872i	$0.515117\pi$
$348$	1.35016e9	1.71735
$349$	5.44309e8	0.685419	0.342710	−	0.939441i	$-0.388655\pi$
$349$	5.44309e8	0.685419	0.342710	+	0.939441i	$0.388655\pi$
$350$	−8.34072e8	−1.03984
$351$	9.20600e7	0.113631
$352$	1.29330e9	1.58052
$353$	1.58939e9	1.92317	0.961587	−	0.274499i	$-0.0885119\pi$
$353$	1.58939e9	1.92317	0.961587	+	0.274499i	$0.0885119\pi$
$354$	−1.16371e8	−0.139422
$355$	−1.47533e9	−1.75021
$356$	−7.10726e8	−0.834886
$357$	1.46992e7	0.0170984
$358$	1.79358e9	2.06599
$359$	1.69409e9	1.93244	0.966221	−	0.257713i	$-0.0829689\pi$
$359$	1.69409e9	1.93244	0.966221	+	0.257713i	$0.0829689\pi$
$360$	1.31358e9	1.48388
$361$	−8.52961e8	−0.954232
$362$	−8.68914e8	−0.962713
$363$	1.95846e8	0.214903
$364$	−4.18732e8	−0.455073
$365$	−7.58791e8	−0.816765
$366$	−5.93568e8	−0.632830
$367$	−1.50784e9	−1.59230	−0.796151	−	0.605098i	$-0.793134\pi$
$367$	−1.50784e9	−1.59230	−0.796151	+	0.605098i	$0.793134\pi$
$368$	3.86470e8	0.404248
$369$	−5.30575e8	−0.549737
$370$	−3.45346e8	−0.354445
$371$	−4.29192e8	−0.436358
$372$	2.29679e9	2.31324
$373$	−9.09574e8	−0.907522	−0.453761	−	0.891123i	$-0.649918\pi$
$373$	−9.09574e8	−0.907522	−0.453761	+	0.891123i	$0.649918\pi$
$374$	−1.39440e8	−0.137828
$375$	7.61385e8	0.745581
$376$	1.84439e9	1.78935
$377$	7.48669e8	0.719606
$378$	1.18375e8	0.112730
$379$	1.38013e9	1.30221	0.651106	−	0.758987i	$-0.274305\pi$
$379$	1.38013e9	1.30221	0.651106	+	0.758987i	$0.274305\pi$
$380$	−9.30409e8	−0.869824
$381$	−2.10194e8	−0.194708
$382$	1.67958e9	1.54163
$383$	−1.20160e9	−1.09286	−0.546430	−	0.837505i	$-0.684013\pi$
$383$	−1.20160e9	−1.09286	−0.546430	+	0.837505i	$0.684013\pi$
$384$	1.29113e8	0.116362
$385$	4.66727e8	0.416822
$386$	−2.85799e9	−2.52933
$387$	−5.19758e8	−0.455840
$388$	3.12483e9	2.71591
$389$	1.11547e9	0.960802	0.480401	−	0.877049i	$-0.340491\pi$
$389$	1.11547e9	0.960802	0.480401	+	0.877049i	$0.340491\pi$
$390$	1.23398e9	1.05337
$391$	−1.78099e7	−0.0150676
$392$	2.86912e9	2.40574
$393$	7.25434e8	0.602870
$394$	2.86973e9	2.36377
$395$	9.83303e8	0.802782
$396$	−7.96558e8	−0.644591
$397$	−1.21715e9	−0.976286	−0.488143	−	0.872764i	$-0.662325\pi$
$397$	−1.21715e9	−0.976286	−0.488143	+	0.872764i	$0.662325\pi$
$398$	8.98820e8	0.714631
$399$	−4.94912e7	−0.0390052
$400$	5.71709e9	4.46648
$401$	−9.38458e8	−0.726791	−0.363396	−	0.931635i	$-0.618383\pi$
$401$	−9.38458e8	−0.726791	−0.363396	+	0.931635i	$0.618383\pi$
$402$	−1.45188e9	−1.11465
$403$	1.27358e9	0.969298
$404$	−1.27582e9	−0.962620
$405$	−2.47455e8	−0.185099
$406$	9.62672e8	0.713900
$407$	1.23614e8	0.0908836
$408$	−1.98489e8	−0.144686
$409$	−2.00800e9	−1.45122	−0.725608	−	0.688108i	$-0.758441\pi$
$409$	−2.00800e9	−1.45122	−0.725608	+	0.688108i	$0.758441\pi$
$410$	−7.11189e9	−5.09614
$411$	1.35659e9	0.963836
$412$	−5.11360e9	−3.60235
$413$	−5.88573e7	−0.0411126
$414$	−1.43426e8	−0.0993404
$415$	−2.53201e9	−1.73899
$416$	1.72943e9	1.17781
$417$	1.47671e9	0.997286
$418$	4.69485e8	0.314416
$419$	−2.40847e9	−1.59953	−0.799765	−	0.600313i	$-0.795043\pi$
$419$	−2.40847e9	−1.59953	−0.799765	+	0.600313i	$0.795043\pi$
$420$	1.12554e9	0.741292
$421$	−5.54976e8	−0.362482	−0.181241	−	0.983439i	$-0.558011\pi$
$421$	−5.54976e8	−0.362482	−0.181241	+	0.983439i	$0.558011\pi$
$422$	9.98409e8	0.646718
$423$	−3.47450e8	−0.223204
$424$	5.79555e9	3.69244
$425$	−2.63464e8	−0.166479
$426$	1.79530e9	1.12513
$427$	−3.00211e8	−0.186608
$428$	−4.47486e9	−2.75884
$429$	−4.41693e8	−0.270097
$430$	−6.96690e9	−4.22571
$431$	−2.19055e9	−1.31790	−0.658951	−	0.752186i	$-0.728999\pi$
$431$	−2.19055e9	−1.31790	−0.658951	+	0.752186i	$0.728999\pi$
$432$	−8.11393e8	−0.484215
$433$	2.56663e8	0.151934	0.0759672	−	0.997110i	$-0.475796\pi$
$433$	2.56663e8	0.151934	0.0759672	+	0.997110i	$0.475796\pi$
$434$	1.63762e9	0.961611
$435$	−2.01241e9	−1.17220
$436$	−2.08119e8	−0.120257
$437$	5.99647e7	0.0343725
$438$	9.23355e8	0.525060
$439$	2.12343e9	1.19787	0.598937	−	0.800796i	$-0.295590\pi$
$439$	2.12343e9	1.19787	0.598937	+	0.800796i	$0.295590\pi$
$440$	−6.30240e9	−3.52713
$441$	−5.40492e8	−0.300092
$442$	−1.86462e8	−0.102710
$443$	3.50552e9	1.91575	0.957875	−	0.287185i	$-0.0927193\pi$
$443$	3.50552e9	1.91575	0.957875	+	0.287185i	$0.0927193\pi$
$444$	2.98102e8	0.161631
$445$	1.05933e9	0.569864
$446$	−2.39327e9	−1.27738
$447$	−1.00275e9	−0.531029
$448$	7.11630e8	0.373922
$449$	1.44417e9	0.752933	0.376467	−	0.926430i	$-0.377139\pi$
$449$	1.44417e9	0.752933	0.376467	+	0.926430i	$0.377139\pi$
$450$	−2.12171e9	−1.09760
$451$	2.54564e9	1.30671
$452$	7.43470e9	3.78686
$453$	−3.68553e8	−0.186276
$454$	−1.15284e9	−0.578193
$455$	6.24116e8	0.310617
$456$	6.68300e8	0.330061
$457$	−3.55204e7	−0.0174089	−0.00870445	−	0.999962i	$-0.502771\pi$
$457$	−3.55204e7	−0.0174089	−0.00870445	+	0.999962i	$0.502771\pi$
$458$	1.13291e9	0.551018
$459$	3.73919e7	0.0180482
$460$	−1.36373e9	−0.653246
$461$	−1.47773e9	−0.702491	−0.351245	−	0.936283i	$-0.614242\pi$
$461$	−1.47773e9	−0.702491	−0.351245	+	0.936283i	$0.614242\pi$
$462$	−5.67949e8	−0.267955
$463$	−1.25958e9	−0.589782	−0.294891	−	0.955531i	$-0.595283\pi$
$463$	−1.25958e9	−0.589782	−0.294891	+	0.955531i	$0.595283\pi$
$464$	−6.59858e9	−3.06646
$465$	−3.42335e9	−1.57894
$466$	6.00117e9	2.74717
$467$	1.25254e9	0.569090	0.284545	−	0.958663i	$-0.408157\pi$
$467$	1.25254e9	0.569090	0.284545	+	0.958663i	$0.408157\pi$
$468$	−1.06517e9	−0.480351
$469$	−7.34323e8	−0.328687
$470$	−4.65726e9	−2.06913
$471$	−1.01956e9	−0.449614
$472$	7.94773e8	0.347894
$473$	2.49374e9	1.08352
$474$	−1.19656e9	−0.516071
$475$	8.87065e8	0.379776
$476$	−1.70076e8	−0.0722800
$477$	−1.09178e9	−0.460596
$478$	1.73617e9	0.727100
$479$	3.28427e9	1.36541	0.682707	−	0.730693i	$-0.260803\pi$
$479$	3.28427e9	1.36541	0.682707	+	0.730693i	$0.260803\pi$
$480$	−4.64867e9	−1.91860
$481$	1.65298e8	0.0677268
$482$	4.52292e9	1.83973
$483$	−7.25410e7	−0.0292933
$484$	−2.26602e9	−0.908458
$485$	−4.65753e9	−1.85379
$486$	3.01122e8	0.118992
$487$	1.74837e8	0.0685935	0.0342968	−	0.999412i	$-0.489081\pi$
$487$	1.74837e8	0.0685935	0.0342968	+	0.999412i	$0.489081\pi$
$488$	4.05387e9	1.57907
$489$	−1.32983e9	−0.514298
$490$	−7.24482e9	−2.78190
$491$	−1.05796e9	−0.403353	−0.201676	−	0.979452i	$-0.564639\pi$
$491$	−1.05796e9	−0.403353	−0.201676	+	0.979452i	$0.564639\pi$
$492$	6.13897e9	2.32390
$493$	3.04086e8	0.114296
$494$	6.27804e8	0.234304
$495$	1.18726e9	0.439975
$496$	−1.12250e10	−4.13047
$497$	9.08015e8	0.331777
$498$	3.08115e9	1.11792
$499$	−7.20840e8	−0.259709	−0.129854	−	0.991533i	$-0.541451\pi$
$499$	−7.20840e8	−0.259709	−0.129854	+	0.991533i	$0.541451\pi$
$500$	−8.80954e9	−3.15180
$501$	−2.81302e9	−0.999402
$502$	7.93653e9	2.80006
$503$	5.82049e8	0.203925	0.101963	−	0.994788i	$-0.467488\pi$
$503$	5.82049e8	0.203925	0.101963	+	0.994788i	$0.467488\pi$
$504$	−8.08461e8	−0.281289
$505$	1.90160e9	0.657051
$506$	6.88140e8	0.236129
$507$	1.10357e9	0.376073
$508$	2.43203e9	0.823088
$509$	−5.21497e9	−1.75283	−0.876414	−	0.481558i	$-0.840071\pi$
$509$	−5.21497e9	−1.75283	−0.876414	+	0.481558i	$0.840071\pi$
$510$	5.01205e8	0.167309
$511$	4.67009e8	0.154829
$512$	5.17639e9	1.70444
$513$	−1.25896e8	−0.0411719
$514$	−4.95301e9	−1.60879
$515$	7.62177e9	2.45884
$516$	6.01381e9	1.92697
$517$	1.66703e9	0.530549
$518$	2.12548e8	0.0671897
$519$	−2.59383e9	−0.814435
$520$	−8.42769e9	−2.62843
$521$	4.72585e8	0.146402	0.0732011	−	0.997317i	$-0.476679\pi$
$521$	4.72585e8	0.146402	0.0732011	+	0.997317i	$0.476679\pi$
$522$	2.44885e9	0.753555
$523$	8.79553e8	0.268847	0.134424	−	0.990924i	$-0.457082\pi$
$523$	8.79553e8	0.268847	0.134424	+	0.990924i	$0.457082\pi$
$524$	−8.39357e9	−2.54851
$525$	−1.07311e9	−0.323658
$526$	8.38829e9	2.51318
$527$	5.17287e8	0.153955
$528$	3.89297e9	1.15097
$529$	−3.31693e9	−0.974186
$530$	−1.46343e10	−4.26980
$531$	−1.49721e8	−0.0433963
$532$	5.72633e8	0.164887
$533$	3.40407e9	0.973764
$534$	−1.28907e9	−0.366339
$535$	6.66974e9	1.88309
$536$	9.91585e9	2.78134
$537$	2.30759e9	0.643057
$538$	−8.34369e9	−2.31004
$539$	2.59322e9	0.713310
$540$	2.86316e9	0.782469
$541$	−1.83033e8	−0.0496981	−0.0248491	−	0.999691i	$-0.507911\pi$
$541$	−1.83033e8	−0.0496981	−0.0248491	+	0.999691i	$0.507911\pi$
$542$	−1.07980e10	−2.91304
$543$	−1.11793e9	−0.299652
$544$	7.02440e8	0.187074
$545$	3.10200e8	0.0820830
$546$	−7.59472e8	−0.199681
$547$	−2.64278e9	−0.690408	−0.345204	−	0.938528i	$-0.612190\pi$
$547$	−2.64278e9	−0.690408	−0.345204	+	0.938528i	$0.612190\pi$
$548$	−1.56963e10	−4.07442
$549$	−7.63678e8	−0.196973
$550$	1.01797e10	2.60896
$551$	−1.02384e9	−0.260735
$552$	9.79550e8	0.247879
$553$	−6.05187e8	−0.152178
$554$	6.18304e9	1.54496
$555$	−4.44318e8	−0.110324
$556$	−1.70862e10	−4.21583
$557$	2.28927e9	0.561313	0.280656	−	0.959808i	$-0.409448\pi$
$557$	2.28927e9	0.561313	0.280656	+	0.959808i	$0.409448\pi$
$558$	4.16579e9	1.01503
$559$	3.33467e9	0.807443
$560$	−5.50080e9	−1.32363
$561$	−1.79402e8	−0.0429000
$562$	−1.29259e10	−3.07173
$563$	1.07781e9	0.254543	0.127271	−	0.991868i	$-0.459378\pi$
$563$	1.07781e9	0.254543	0.127271	+	0.991868i	$0.459378\pi$
$564$	4.02014e9	0.943548
$565$	−1.10814e10	−2.58478
$566$	9.41963e7	0.0218362
$567$	1.52300e8	0.0350880
$568$	−1.22613e10	−2.80748
$569$	−1.08728e9	−0.247429	−0.123714	−	0.992318i	$-0.539481\pi$
$569$	−1.08728e9	−0.247429	−0.123714	+	0.992318i	$0.539481\pi$
$570$	−1.68752e9	−0.381670
$571$	2.15499e8	0.0484416	0.0242208	−	0.999707i	$-0.492290\pi$
$571$	2.15499e8	0.0484416	0.0242208	+	0.999707i	$0.492290\pi$
$572$	5.11057e9	1.14178
$573$	2.16093e9	0.479844
$574$	4.37711e9	0.966042
$575$	1.30020e9	0.285216
$576$	1.81025e9	0.394693
$577$	7.86457e9	1.70435	0.852176	−	0.523255i	$-0.175282\pi$
$577$	7.86457e9	1.70435	0.852176	+	0.523255i	$0.175282\pi$
$578$	8.53552e9	1.83858
$579$	−3.67705e9	−0.787273
$580$	2.32843e10	4.95526
$581$	1.55836e9	0.329649
$582$	5.66764e9	1.19171
$583$	5.23823e9	1.09482
$584$	−6.30620e9	−1.31016
$585$	1.58763e9	0.327871
$586$	−7.49963e9	−1.53957
$587$	7.86924e9	1.60583	0.802914	−	0.596094i	$-0.203282\pi$
$587$	7.86924e9	1.60583	0.802914	+	0.596094i	$0.203282\pi$
$588$	6.25371e9	1.26858
$589$	−1.74167e9	−0.351206
$590$	−2.00688e9	−0.402290
$591$	3.69217e9	0.735741
$592$	−1.45690e9	−0.288604
$593$	−9.64856e9	−1.90008	−0.950038	−	0.312134i	$-0.898956\pi$
$593$	−9.64856e9	−1.90008	−0.950038	+	0.312134i	$0.898956\pi$
$594$	−1.44475e9	−0.282840
$595$	2.53496e8	0.0493358
$596$	1.16023e10	2.24482
$597$	1.15641e9	0.222435
$598$	9.20194e8	0.175965
$599$	5.43654e9	1.03354	0.516772	−	0.856123i	$-0.327134\pi$
$599$	5.43654e9	1.03354	0.516772	+	0.856123i	$0.327134\pi$
$600$	1.44906e10	2.73878
$601$	−2.28199e9	−0.428798	−0.214399	−	0.976746i	$-0.568779\pi$
$601$	−2.28199e9	−0.428798	−0.214399	+	0.976746i	$0.568779\pi$
$602$	4.28787e9	0.801040
$603$	−1.86797e9	−0.346944
$604$	4.26431e9	0.787443
$605$	3.37748e9	0.620082
$606$	−2.31401e9	−0.422387
$607$	−2.22820e9	−0.404383	−0.202191	−	0.979346i	$-0.564806\pi$
$607$	−2.22820e9	−0.404383	−0.202191	+	0.979346i	$0.564806\pi$
$608$	−2.36507e9	−0.426757
$609$	1.23856e9	0.222207
$610$	−1.02364e10	−1.82597
$611$	2.22918e9	0.395367
$612$	−4.32639e8	−0.0762950
$613$	9.10899e8	0.159720	0.0798599	−	0.996806i	$-0.474553\pi$
$613$	9.10899e8	0.159720	0.0798599	+	0.996806i	$0.474553\pi$
$614$	8.75716e9	1.52677
$615$	−9.15008e9	−1.58621
$616$	3.87890e9	0.668615
$617$	6.17621e9	1.05858	0.529290	−	0.848441i	$-0.322458\pi$
$617$	6.17621e9	1.05858	0.529290	+	0.848441i	$0.322458\pi$
$618$	−9.27475e9	−1.58067
$619$	−9.92262e9	−1.68155	−0.840774	−	0.541387i	$-0.817900\pi$
$619$	−9.92262e9	−1.68155	−0.840774	+	0.541387i	$0.817900\pi$
$620$	3.96095e10	6.67465
$621$	−1.84530e8	−0.0309205
$622$	−3.29747e9	−0.549432
$623$	−6.51980e8	−0.108025
$624$	5.20575e9	0.857704
$625$	2.29562e9	0.376114
$626$	−1.78846e10	−2.91387
$627$	6.04034e8	0.0978644
$628$	1.17967e10	1.90066
$629$	6.71390e7	0.0107572
$630$	2.04144e9	0.325271
$631$	3.99548e9	0.633091	0.316546	−	0.948577i	$-0.397477\pi$
$631$	3.99548e9	0.633091	0.316546	+	0.948577i	$0.397477\pi$
$632$	8.17209e9	1.28773
$633$	1.28454e9	0.201296
$634$	1.55372e10	2.42137
$635$	−3.62492e9	−0.561811
$636$	1.26323e10	1.94708
$637$	3.46770e9	0.531561
$638$	−1.17493e10	−1.79118
$639$	2.30981e9	0.350206
$640$	2.22663e9	0.335752
$641$	−4.03744e9	−0.605485	−0.302742	−	0.953072i	$-0.597902\pi$
$641$	−4.03744e9	−0.605485	−0.302742	+	0.953072i	$0.597902\pi$
$642$	−8.11624e9	−1.21055
$643$	−8.64628e9	−1.28260	−0.641299	−	0.767291i	$-0.721604\pi$
$643$	−8.64628e9	−1.28260	−0.641299	+	0.767291i	$0.721604\pi$
$644$	8.39329e8	0.123832
$645$	−8.96353e9	−1.31529
$646$	2.54994e8	0.0372149
$647$	7.61025e9	1.10467	0.552337	−	0.833621i	$-0.313736\pi$
$647$	7.61025e9	1.10467	0.552337	+	0.833621i	$0.313736\pi$
$648$	−2.05656e9	−0.296913
$649$	7.18346e8	0.103152
$650$	1.36125e10	1.94421
$651$	2.10695e9	0.299309
$652$	1.53867e10	2.17409
$653$	−1.04681e10	−1.47120	−0.735599	−	0.677417i	$-0.763099\pi$
$653$	−1.04681e10	−1.47120	−0.735599	+	0.677417i	$0.763099\pi$
$654$	−3.77474e8	−0.0527674
$655$	1.25105e10	1.73953
$656$	−3.00026e10	−4.14950
$657$	1.18798e9	0.163429
$658$	2.86638e9	0.392232
$659$	3.31882e9	0.451737	0.225868	−	0.974158i	$-0.427478\pi$
$659$	3.31882e9	0.451737	0.225868	+	0.974158i	$0.427478\pi$
$660$	−1.37371e10	−1.85991
$661$	7.95737e9	1.07168	0.535839	−	0.844320i	$-0.319995\pi$
$661$	7.95737e9	1.07168	0.535839	+	0.844320i	$0.319995\pi$
$662$	4.54278e9	0.608581
$663$	−2.39900e8	−0.0319692
$664$	−2.10432e10	−2.78948
$665$	−8.53504e8	−0.112546
$666$	5.40680e8	0.0709219
$667$	−1.50067e9	−0.195815
$668$	3.25478e10	4.22477
$669$	−3.07915e9	−0.397593
$670$	−2.50385e10	−3.21623
$671$	3.66404e9	0.468200
$672$	2.86109e9	0.363696
$673$	−7.14650e9	−0.903734	−0.451867	−	0.892085i	$-0.649242\pi$
$673$	−7.14650e9	−0.903734	−0.451867	+	0.892085i	$0.649242\pi$
$674$	3.65079e9	0.459279
$675$	−2.72977e9	−0.341636
$676$	−1.27687e10	−1.58977
$677$	−7.35419e9	−0.910908	−0.455454	−	0.890259i	$-0.650523\pi$
$677$	−7.35419e9	−0.910908	−0.455454	+	0.890259i	$0.650523\pi$
$678$	1.34846e10	1.66163
$679$	2.86654e9	0.351410
$680$	−3.42306e9	−0.417478
$681$	−1.48323e9	−0.179967
$682$	−1.99870e10	−2.41269
$683$	4.04823e9	0.486175	0.243087	−	0.970004i	$-0.421840\pi$
$683$	4.04823e9	0.486175	0.243087	+	0.970004i	$0.421840\pi$
$684$	1.45667e9	0.174046
$685$	2.33952e10	2.78106
$686$	9.41177e9	1.11311
$687$	1.45759e9	0.171509
$688$	−2.93910e10	−3.44076
$689$	7.00465e9	0.815867
$690$	−2.47346e9	−0.286638
$691$	−1.70309e9	−0.196365	−0.0981823	−	0.995168i	$-0.531303\pi$
$691$	−1.70309e9	−0.196365	−0.0981823	+	0.995168i	$0.531303\pi$
$692$	3.00117e10	3.44286
$693$	−7.30717e8	−0.0834032
$694$	1.55084e9	0.176120
$695$	2.54668e10	2.87758
$696$	−1.67248e10	−1.88031
$697$	1.38263e9	0.154665
$698$	−1.14227e10	−1.27138
$699$	7.72103e9	0.855077
$700$	1.24163e10	1.36820
$701$	7.38709e9	0.809954	0.404977	−	0.914327i	$-0.367279\pi$
$701$	7.38709e9	0.809954	0.404977	+	0.914327i	$0.367279\pi$
$702$	−1.93195e9	−0.210773
$703$	−2.26052e8	−0.0245395
$704$	−8.68536e9	−0.938174
$705$	−5.99198e9	−0.644033
$706$	−3.33545e10	−3.56729
$707$	−1.17037e9	−0.124553
$708$	1.73234e9	0.183449
$709$	−3.00194e9	−0.316330	−0.158165	−	0.987413i	$-0.550558\pi$
$709$	−3.00194e9	−0.316330	−0.158165	+	0.987413i	$0.550558\pi$
$710$	3.09610e10	3.24646
$711$	−1.53948e9	−0.160631
$712$	8.80394e9	0.914108
$713$	−2.55282e9	−0.263759
$714$	−3.08474e8	−0.0317157
$715$	−7.61726e9	−0.779341
$716$	−2.66998e10	−2.71839
$717$	2.23373e9	0.226316
$718$	−3.55518e10	−3.58448
$719$	3.86807e9	0.388100	0.194050	−	0.980992i	$-0.437838\pi$
$719$	3.86807e9	0.388100	0.194050	+	0.980992i	$0.437838\pi$
$720$	−1.39929e10	−1.39716
$721$	−4.69092e9	−0.466106
$722$	1.79000e10	1.77000
$723$	5.81913e9	0.572630
$724$	1.29350e10	1.26672
$725$	−2.21996e10	−2.16353
$726$	−4.10997e9	−0.398622
$727$	1.88812e10	1.82247	0.911235	−	0.411887i	$-0.135130\pi$
$727$	1.88812e10	1.82247	0.911235	+	0.411887i	$0.135130\pi$
$728$	5.18694e9	0.498255
$729$	3.87420e8	0.0370370
$730$	1.59238e10	1.51501
$731$	1.35444e9	0.128247
$732$	8.83606e9	0.832665
$733$	−2.89464e9	−0.271476	−0.135738	−	0.990745i	$-0.543340\pi$
$733$	−2.89464e9	−0.271476	−0.135738	+	0.990745i	$0.543340\pi$
$734$	3.16432e10	2.95355
$735$	−9.32110e9	−0.865887
$736$	−3.46656e9	−0.320499
$737$	8.96231e9	0.824677
$738$	1.11345e10	1.01970
$739$	−4.83541e9	−0.440735	−0.220368	−	0.975417i	$-0.570726\pi$
$739$	−4.83541e9	−0.440735	−0.220368	+	0.975417i	$0.570726\pi$
$740$	5.14094e9	0.466371
$741$	8.07725e8	0.0729289
$742$	9.00690e9	0.809397
$743$	−1.65827e10	−1.48318	−0.741591	−	0.670852i	$-0.765929\pi$
$743$	−1.65827e10	−1.48318	−0.741591	+	0.670852i	$0.765929\pi$
$744$	−2.84509e10	−2.53274
$745$	−1.72931e10	−1.53223
$746$	1.90881e10	1.68336
$747$	3.96417e9	0.347961
$748$	2.07575e9	0.181351
$749$	−4.10498e9	−0.356965
$750$	−1.59782e10	−1.38297
$751$	1.94126e10	1.67242	0.836208	−	0.548413i	$-0.184768\pi$
$751$	1.94126e10	1.67242	0.836208	+	0.548413i	$0.184768\pi$
$752$	−1.96474e10	−1.68478
$753$	1.02110e10	0.871541
$754$	−1.57114e10	−1.33479
$755$	−6.35591e9	−0.537481
$756$	−1.76217e9	−0.148327
$757$	1.23613e10	1.03569	0.517843	−	0.855475i	$-0.326735\pi$
$757$	1.23613e10	1.03569	0.517843	+	0.855475i	$0.326735\pi$
$758$	−2.89630e10	−2.41547
$759$	8.85353e8	0.0734971
$760$	1.15252e10	0.952361
$761$	−1.27885e10	−1.05189	−0.525947	−	0.850517i	$-0.676289\pi$
$761$	−1.27885e10	−1.05189	−0.525947	+	0.850517i	$0.676289\pi$
$762$	4.41108e9	0.361162
$763$	−1.90917e8	−0.0155599
$764$	−2.50029e10	−2.02845
$765$	6.44845e8	0.0520763
$766$	2.52165e10	2.02714
$767$	9.60585e8	0.0768691
$768$	5.87238e9	0.467788
$769$	−6.74352e9	−0.534742	−0.267371	−	0.963594i	$-0.586155\pi$
$769$	−6.74352e9	−0.534742	−0.267371	+	0.963594i	$0.586155\pi$
$770$	−9.79461e9	−0.773160
$771$	−6.37249e9	−0.500748
$772$	4.25450e10	3.32804
$773$	3.73822e9	0.291096	0.145548	−	0.989351i	$-0.453505\pi$
$773$	3.73822e9	0.291096	0.145548	+	0.989351i	$0.453505\pi$
$774$	1.09075e10	0.845536
$775$	−3.77642e10	−2.91424
$776$	−3.87081e10	−2.97362
$777$	2.73462e8	0.0209133
$778$	−2.34089e10	−1.78219
$779$	−4.65521e9	−0.352824
$780$	−1.83695e10	−1.38601
$781$	−1.10822e10	−0.832430
$782$	3.73754e8	0.0279487
$783$	3.15066e9	0.234550
$784$	−3.05634e10	−2.26514
$785$	−1.75829e10	−1.29732
$786$	−1.52238e10	−1.11826
$787$	−1.47464e10	−1.07839	−0.539193	−	0.842182i	$-0.681271\pi$
$787$	−1.47464e10	−1.07839	−0.539193	+	0.842182i	$0.681271\pi$
$788$	−4.27199e10	−3.11020
$789$	1.07923e10	0.782246
$790$	−2.06353e10	−1.48907
$791$	6.82017e9	0.489979
$792$	9.86716e9	0.705755
$793$	4.89962e9	0.348904
$794$	2.55428e10	1.81091
$795$	−1.88284e10	−1.32901
$796$	−1.33802e10	−0.940298
$797$	−1.86115e10	−1.30220	−0.651099	−	0.758993i	$-0.725692\pi$
$797$	−1.86115e10	−1.30220	−0.651099	+	0.758993i	$0.725692\pi$
$798$	1.03861e9	0.0723506
$799$	9.05422e8	0.0627968
$800$	−5.12812e10	−3.54114
$801$	−1.65851e9	−0.114026
$802$	1.96942e10	1.34812
$803$	−5.69978e9	−0.388466
$804$	2.16132e10	1.46664
$805$	−1.25101e9	−0.0845231
$806$	−2.67269e10	−1.79795
$807$	−1.07349e10	−0.719019
$808$	1.58039e10	1.05396
$809$	4.53515e9	0.301143	0.150571	−	0.988599i	$-0.451889\pi$
$809$	4.53515e9	0.301143	0.150571	+	0.988599i	$0.451889\pi$
$810$	5.19303e9	0.343339
$811$	7.48809e9	0.492945	0.246472	−	0.969150i	$-0.420729\pi$
$811$	7.48809e9	0.492945	0.246472	+	0.969150i	$0.420729\pi$
$812$	−1.43307e10	−0.939335
$813$	−1.38926e10	−0.906707
$814$	−2.59412e9	−0.168579
$815$	−2.29337e10	−1.48396
$816$	2.11441e9	0.136230
$817$	−4.56030e9	−0.292561
$818$	4.21393e10	2.69185
$819$	−9.77128e8	−0.0621524
$820$	1.05870e11	6.70540
$821$	−1.66654e10	−1.05103	−0.525514	−	0.850785i	$-0.676127\pi$
$821$	−1.66654e10	−1.05103	−0.525514	+	0.850785i	$0.676127\pi$
$822$	−2.84691e10	−1.78781
$823$	1.72880e10	1.08105	0.540524	−	0.841328i	$-0.318226\pi$
$823$	1.72880e10	1.08105	0.540524	+	0.841328i	$0.318226\pi$
$824$	6.33434e10	3.94418
$825$	1.30971e10	0.812059
$826$	1.23516e9	0.0762595
$827$	−1.68089e10	−1.03341	−0.516703	−	0.856165i	$-0.672841\pi$
$827$	−1.68089e10	−1.03341	−0.516703	+	0.856165i	$0.672841\pi$
$828$	2.13509e9	0.130710
$829$	3.99422e9	0.243495	0.121748	−	0.992561i	$-0.461150\pi$
$829$	3.99422e9	0.243495	0.121748	+	0.992561i	$0.461150\pi$
$830$	5.31362e10	3.22565
$831$	7.95502e9	0.480881
$832$	−1.16142e10	−0.699130
$833$	1.40847e9	0.0844287
$834$	−3.09899e10	−1.84986
$835$	−4.85121e10	−2.88368
$836$	−6.98892e9	−0.413702
$837$	5.35965e9	0.315935
$838$	5.05435e10	2.96696
$839$	−1.32657e10	−0.775467	−0.387734	−	0.921771i	$-0.626742\pi$
$839$	−1.32657e10	−0.775467	−0.387734	+	0.921771i	$0.626742\pi$
$840$	−1.39424e10	−0.811632
$841$	8.37255e9	0.485369
$842$	1.16466e10	0.672367
$843$	−1.66303e10	−0.956099
$844$	−1.48627e10	−0.850938
$845$	1.90317e10	1.08512
$846$	7.29149e9	0.414019
$847$	−2.07872e9	−0.117545
$848$	−6.17372e10	−3.47665
$849$	1.21192e8	0.00679667
$850$	5.52899e9	0.308801
$851$	−3.31333e8	−0.0184294
$852$	−2.67255e10	−1.48043
$853$	3.06500e10	1.69087	0.845433	−	0.534082i	$-0.179343\pi$
$853$	3.06500e10	1.69087	0.845433	+	0.534082i	$0.179343\pi$
$854$	6.30015e9	0.346137
$855$	−2.17115e9	−0.118798
$856$	5.54312e10	3.02062
$857$	−5.05197e9	−0.274175	−0.137087	−	0.990559i	$-0.543774\pi$
$857$	−5.05197e9	−0.274175	−0.137087	+	0.990559i	$0.543774\pi$
$858$	9.26926e9	0.501002
$859$	−6.74004e7	−0.00362816	−0.00181408	−	0.999998i	$-0.500577\pi$
$859$	−6.74004e7	−0.00362816	−0.00181408	+	0.999998i	$0.500577\pi$
$860$	1.03712e11	5.56010
$861$	5.63154e9	0.300688
$862$	4.59703e10	2.44457
$863$	3.32493e10	1.76094	0.880471	−	0.474101i	$-0.157227\pi$
$863$	3.32493e10	1.76094	0.880471	+	0.474101i	$0.157227\pi$
$864$	7.27804e9	0.383898
$865$	−4.47322e10	−2.34998
$866$	−5.38627e9	−0.281822
$867$	1.09817e10	0.572273
$868$	−2.43782e10	−1.26527
$869$	7.38623e9	0.381816
$870$	4.22318e10	2.17431
$871$	1.19846e10	0.614552
$872$	2.57802e9	0.131668
$873$	7.29192e9	0.370930
$874$	−1.25840e9	−0.0637573
$875$	−8.08137e9	−0.407809
$876$	−1.37454e10	−0.690864
$877$	−3.04224e10	−1.52298	−0.761491	−	0.648176i	$-0.775532\pi$
$877$	−3.04224e10	−1.52298	−0.761491	+	0.648176i	$0.775532\pi$
$878$	−4.45616e10	−2.22193
$879$	−9.64893e9	−0.479202
$880$	6.71365e10	3.32101
$881$	1.67047e10	0.823044	0.411522	−	0.911400i	$-0.364997\pi$
$881$	1.67047e10	0.823044	0.411522	+	0.911400i	$0.364997\pi$
$882$	1.13426e10	0.556639
$883$	4.43529e9	0.216800	0.108400	−	0.994107i	$-0.465427\pi$
$883$	4.43529e9	0.216800	0.108400	+	0.994107i	$0.465427\pi$
$884$	2.77574e9	0.135144
$885$	−2.58203e9	−0.125216
$886$	−7.35658e10	−3.55351
$887$	3.65741e10	1.75971	0.879855	−	0.475242i	$-0.157640\pi$
$887$	3.65741e10	1.75971	0.879855	+	0.475242i	$0.157640\pi$
$888$	−3.69266e9	−0.176968
$889$	2.23101e9	0.106499
$890$	−2.22308e10	−1.05704
$891$	−1.85880e9	−0.0880360
$892$	3.56270e10	1.68075
$893$	−3.04849e9	−0.143253
$894$	2.10435e10	0.985002
$895$	3.97958e10	1.85548
$896$	−1.37041e9	−0.0636463
$897$	1.18391e9	0.0547703
$898$	−3.03070e10	−1.39661
$899$	4.35869e10	2.00077
$900$	3.15846e10	1.44420
$901$	2.84507e9	0.129585
$902$	−5.34221e10	−2.42381
$903$	5.51673e9	0.249330
$904$	−9.20955e10	−4.14619
$905$	−1.92794e10	−0.864618
$906$	7.73435e9	0.345522
$907$	1.91299e10	0.851307	0.425654	−	0.904886i	$-0.360044\pi$
$907$	1.91299e10	0.851307	0.425654	+	0.904886i	$0.360044\pi$
$908$	1.71616e10	0.760775
$909$	−2.97718e9	−0.131471
$910$	−1.30975e10	−0.576162
$911$	−3.39426e10	−1.48741	−0.743704	−	0.668509i	$-0.766933\pi$
$911$	−3.39426e10	−1.48741	−0.743704	+	0.668509i	$0.766933\pi$
$912$	−7.11908e9	−0.310772
$913$	−1.90196e10	−0.827093
$914$	7.45422e8	0.0322917
$915$	−1.31701e10	−0.568348
$916$	−1.68649e10	−0.725018
$917$	−7.69978e9	−0.329751
$918$	−7.84696e8	−0.0334774
$919$	−3.53345e10	−1.50174	−0.750870	−	0.660450i	$-0.770366\pi$
$919$	−3.53345e10	−1.50174	−0.750870	+	0.660450i	$0.770366\pi$
$920$	1.68929e10	0.715232
$921$	1.12669e10	0.475220
$922$	3.10111e10	1.30305
$923$	−1.48193e10	−0.620330
$924$	8.45469e9	0.352570
$925$	−4.90144e9	−0.203624
$926$	2.64332e10	1.09398
$927$	−1.19328e10	−0.491997
$928$	5.91879e10	2.43117
$929$	−3.23304e10	−1.32299	−0.661493	−	0.749951i	$-0.730077\pi$
$929$	−3.23304e10	−1.32299	−0.661493	+	0.749951i	$0.730077\pi$
$930$	7.18414e10	2.92876
$931$	−4.74222e9	−0.192601
$932$	−8.93354e10	−3.61467
$933$	−4.24249e9	−0.171015
$934$	−2.62854e10	−1.05560
$935$	−3.09389e9	−0.123784
$936$	1.31945e10	0.525931
$937$	9.18986e9	0.364939	0.182469	−	0.983212i	$-0.441591\pi$
$937$	9.18986e9	0.364939	0.182469	+	0.983212i	$0.441591\pi$
$938$	1.54103e10	0.609679
$939$	−2.30102e10	−0.906964
$940$	6.93296e10	2.72252
$941$	−1.09465e10	−0.428265	−0.214133	−	0.976805i	$-0.568693\pi$
$941$	−1.09465e10	−0.428265	−0.214133	+	0.976805i	$0.568693\pi$
$942$	2.13962e10	0.833987
$943$	−6.82331e9	−0.264974
$944$	−8.46635e9	−0.327562
$945$	2.62650e9	0.101243
$946$	−5.23329e10	−2.00982
$947$	−2.72786e10	−1.04375	−0.521875	−	0.853022i	$-0.674767\pi$
$947$	−2.72786e10	−1.04375	−0.521875	+	0.853022i	$0.674767\pi$
$948$	1.78124e10	0.679036
$949$	−7.62185e9	−0.289487
$950$	−1.86157e10	−0.704445
$951$	1.99900e10	0.753670
$952$	2.10677e9	0.0791386
$953$	−2.27671e10	−0.852085	−0.426043	−	0.904703i	$-0.640093\pi$
$953$	−2.27671e10	−0.852085	−0.426043	+	0.904703i	$0.640093\pi$
$954$	2.29118e10	0.854357
$955$	3.72665e10	1.38455
$956$	−2.58452e10	−0.956704
$957$	−1.51165e10	−0.557519
$958$	−6.89227e10	−2.53270
$959$	−1.43989e10	−0.527187
$960$	3.12188e10	1.13885
$961$	4.66339e10	1.69500
$962$	−3.46891e9	−0.125626
$963$	−1.04423e10	−0.376793
$964$	−6.73298e10	−2.42068
$965$	−6.34129e10	−2.27160
$966$	1.52233e9	0.0543360
$967$	−1.38243e10	−0.491645	−0.245822	−	0.969315i	$-0.579058\pi$
$967$	−1.38243e10	−0.491645	−0.245822	+	0.969315i	$0.579058\pi$
$968$	2.80697e10	0.994660
$969$	3.28073e8	0.0115834
$970$	9.77418e10	3.43858
$971$	1.62886e10	0.570973	0.285487	−	0.958383i	$-0.407845\pi$
$971$	1.62886e10	0.570973	0.285487	+	0.958383i	$0.407845\pi$
$972$	−4.48261e9	−0.156567
$973$	−1.56739e10	−0.545483
$974$	−3.66909e9	−0.127234
$975$	1.75137e10	0.605149
$976$	−4.31840e10	−1.48679
$977$	1.93224e10	0.662874	0.331437	−	0.943477i	$-0.392467\pi$
$977$	1.93224e10	0.662874	0.331437	+	0.943477i	$0.392467\pi$
$978$	2.79074e10	0.953968
$979$	7.95733e9	0.271037
$980$	1.07849e11	3.66036
$981$	−4.85654e8	−0.0164243
$982$	2.22021e10	0.748177
$983$	3.13862e10	1.05391	0.526953	−	0.849895i	$-0.323334\pi$
$983$	3.13862e10	1.05391	0.526953	+	0.849895i	$0.323334\pi$
$984$	−7.60450e10	−2.54441
$985$	6.36735e10	2.12291
$986$	−6.38146e9	−0.212007
$987$	3.68785e9	0.122085
$988$	−9.34571e9	−0.308292
$989$	−6.68420e9	−0.219716
$990$	−2.49156e10	−0.816107
$991$	−2.26508e9	−0.0739308	−0.0369654	−	0.999317i	$-0.511769\pi$
$991$	−2.26508e9	−0.0739308	−0.0369654	+	0.999317i	$0.511769\pi$
$992$	1.00686e11	3.27475
$993$	5.84469e9	0.189426
$994$	−1.90554e10	−0.615411
$995$	1.99430e10	0.641814
$996$	−4.58670e10	−1.47093
$997$	4.99508e10	1.59628	0.798140	−	0.602472i	$-0.205817\pi$
$997$	4.99508e10	1.59628	0.798140	+	0.602472i	$0.205817\pi$
$998$	1.51273e10	0.481732
$999$	6.95633e8	0.0220750

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.c.1.2	✓	17
3.2	odd	2		531.8.a.c.1.16		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.2	✓	17	1.1	even	1	trivial
531.8.a.c.1.16		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)

\(f(q)\)	\(=\)	\(q-20.9857 q^{2} -27.0000 q^{3} +312.401 q^{4} -465.631 q^{5} +566.615 q^{6} +286.579 q^{7} -3869.79 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-20.9857 q^{2} -27.0000 q^{3} +312.401 q^{4} -465.631 q^{5} +566.615 q^{6} +286.579 q^{7} -3869.79 q^{8} +729.000 q^{9} +9771.60 q^{10} -3497.66 q^{11} -8434.83 q^{12} -4677.13 q^{13} -6014.07 q^{14} +12572.0 q^{15} +41223.0 q^{16} -1899.70 q^{17} -15298.6 q^{18} +6396.17 q^{19} -145463. q^{20} -7737.63 q^{21} +73400.9 q^{22} +9375.09 q^{23} +104484. q^{24} +138687. q^{25} +98153.0 q^{26} -19683.0 q^{27} +89527.5 q^{28} -160070. q^{29} -263833. q^{30} -272299. q^{31} -369763. q^{32} +94436.8 q^{33} +39866.7 q^{34} -133440. q^{35} +227740. q^{36} -35341.8 q^{37} -134228. q^{38} +126283. q^{39} +1.80189e6 q^{40} -727812. q^{41} +162380. q^{42} -712974. q^{43} -1.09267e6 q^{44} -339445. q^{45} -196743. q^{46} -476612. q^{47} -1.11302e6 q^{48} -741416. q^{49} -2.91045e6 q^{50} +51292.0 q^{51} -1.46114e6 q^{52} -1.49764e6 q^{53} +413062. q^{54} +1.62862e6 q^{55} -1.10900e6 q^{56} -172697. q^{57} +3.35919e6 q^{58} -205379. q^{59} +3.92751e6 q^{60} -1.04757e6 q^{61} +5.71439e6 q^{62} +208916. q^{63} +2.48319e6 q^{64} +2.17782e6 q^{65} -1.98182e6 q^{66} -2.56238e6 q^{67} -593470. q^{68} -253127. q^{69} +2.80033e6 q^{70} +3.16847e6 q^{71} -2.82108e6 q^{72} +1.62960e6 q^{73} +741674. q^{74} -3.74455e6 q^{75} +1.99817e6 q^{76} -1.00235e6 q^{77} -2.65013e6 q^{78} -2.11177e6 q^{79} -1.91947e7 q^{80} +531441. q^{81} +1.52737e7 q^{82} +5.43782e6 q^{83} -2.41724e6 q^{84} +884561. q^{85} +1.49623e7 q^{86} +4.32189e6 q^{87} +1.35352e7 q^{88} -2.27504e6 q^{89} +7.12350e6 q^{90} -1.34037e6 q^{91} +2.92879e6 q^{92} +7.35206e6 q^{93} +1.00021e7 q^{94} -2.97825e6 q^{95} +9.98359e6 q^{96} +1.00026e7 q^{97} +1.55591e7 q^{98} -2.54979e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9}+O(q^{10}) \) 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

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