LMFDB - Embedded newform 177.8.a.c.1.8

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			1.8
Root			$-3.88629$ 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)

$f(q)$	$=$	$q-3.88629 q^{2} -27.0000 q^{3} -112.897 q^{4} -26.2639 q^{5} +104.930 q^{6} -644.460 q^{7} +936.194 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-3.88629 q^{2} -27.0000 q^{3} -112.897 q^{4} -26.2639 q^{5} +104.930 q^{6} -644.460 q^{7} +936.194 q^{8} +729.000 q^{9} +102.069 q^{10} -5692.26 q^{11} +3048.21 q^{12} -606.275 q^{13} +2504.56 q^{14} +709.124 q^{15} +10812.5 q^{16} -39283.3 q^{17} -2833.10 q^{18} -34062.8 q^{19} +2965.10 q^{20} +17400.4 q^{21} +22121.8 q^{22} -21244.4 q^{23} -25277.2 q^{24} -77435.2 q^{25} +2356.16 q^{26} -19683.0 q^{27} +72757.5 q^{28} +26193.7 q^{29} -2755.86 q^{30} -310358. q^{31} -161853. q^{32} +153691. q^{33} +152666. q^{34} +16926.0 q^{35} -82301.7 q^{36} -330264. q^{37} +132378. q^{38} +16369.4 q^{39} -24588.1 q^{40} +318533. q^{41} -67623.0 q^{42} +16755.2 q^{43} +642638. q^{44} -19146.3 q^{45} +82562.0 q^{46} +764733. q^{47} -291937. q^{48} -408214. q^{49} +300935. q^{50} +1.06065e6 q^{51} +68446.5 q^{52} -1.38308e6 q^{53} +76493.8 q^{54} +149501. q^{55} -603340. q^{56} +919695. q^{57} -101796. q^{58} -205379. q^{59} -80057.8 q^{60} -354332. q^{61} +1.20614e6 q^{62} -469811. q^{63} -754988. q^{64} +15923.1 q^{65} -597287. q^{66} +4.54645e6 q^{67} +4.43496e6 q^{68} +573600. q^{69} -65779.3 q^{70} -367019. q^{71} +682485. q^{72} -1.13809e6 q^{73} +1.28350e6 q^{74} +2.09075e6 q^{75} +3.84558e6 q^{76} +3.66843e6 q^{77} -63616.3 q^{78} +3.04988e6 q^{79} -283977. q^{80} +531441. q^{81} -1.23791e6 q^{82} -8.39695e6 q^{83} -1.96445e6 q^{84} +1.03173e6 q^{85} -65115.7 q^{86} -707229. q^{87} -5.32906e6 q^{88} -3.28661e6 q^{89} +74408.2 q^{90} +390720. q^{91} +2.39843e6 q^{92} +8.37967e6 q^{93} -2.97197e6 q^{94} +894620. q^{95} +4.37004e6 q^{96} +8.46055e6 q^{97} +1.58644e6 q^{98} -4.14966e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.88629	−0.343503	−0.171751	−	0.985140i	$-0.554943\pi$
$2$	−3.88629	−0.343503	−0.171751	+	0.985140i	$0.554943\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−112.897	−0.882006
$5$	−26.2639	−0.0939644	−0.0469822	−	0.998896i	$-0.514960\pi$
$5$	−26.2639	−0.0939644	−0.0469822	+	0.998896i	$0.514960\pi$
$6$	104.930	0.198321
$7$	−644.460	−0.710155	−0.355077	−	0.934837i	$-0.615545\pi$
$7$	−644.460	−0.710155	−0.355077	+	0.934837i	$0.615545\pi$
$8$	936.194	0.646474
$9$	729.000	0.333333
$10$	102.069	0.0322770
$11$	−5692.26	−1.28947	−0.644734	−	0.764407i	$-0.723032\pi$
$11$	−5692.26	−1.28947	−0.644734	+	0.764407i	$0.723032\pi$
$12$	3048.21	0.509226
$13$	−606.275	−0.0765364	−0.0382682	−	0.999268i	$-0.512184\pi$
$13$	−606.275	−0.0765364	−0.0382682	+	0.999268i	$0.512184\pi$
$14$	2504.56	0.243940
$15$	709.124	0.0542504
$16$	10812.5	0.659941
$17$	−39283.3	−1.93926	−0.969632	−	0.244570i	$-0.921353\pi$
$17$	−39283.3	−1.93926	−0.969632	+	0.244570i	$0.921353\pi$
$18$	−2833.10	−0.114501
$19$	−34062.8	−1.13931	−0.569656	−	0.821883i	$-0.692923\pi$
$19$	−34062.8	−1.13931	−0.569656	+	0.821883i	$0.692923\pi$
$20$	2965.10	0.0828772
$21$	17400.4	0.410008
$22$	22121.8	0.442935
$23$	−21244.4	−0.364081	−0.182040	−	0.983291i	$-0.558270\pi$
$23$	−21244.4	−0.364081	−0.182040	+	0.983291i	$0.558270\pi$
$24$	−25277.2	−0.373242
$25$	−77435.2	−0.991171
$26$	2356.16	0.0262905
$27$	−19683.0	−0.192450
$28$	72757.5	0.626361
$29$	26193.7	0.199436	0.0997179	−	0.995016i	$-0.468206\pi$
$29$	26193.7	0.199436	0.0997179	+	0.995016i	$0.468206\pi$
$30$	−2755.86	−0.0186351
$31$	−310358.	−1.87110	−0.935551	−	0.353193i	$-0.885096\pi$
$31$	−310358.	−1.87110	−0.935551	+	0.353193i	$0.885096\pi$
$32$	−161853.	−0.873165
$33$	153691.	0.744474
$34$	152666.	0.666142
$35$	16926.0	0.0667292
$36$	−82301.7	−0.294002
$37$	−330264.	−1.07190	−0.535951	−	0.844249i	$-0.680047\pi$
$37$	−330264.	−1.07190	−0.535951	+	0.844249i	$0.680047\pi$
$38$	132378.	0.391356
$39$	16369.4	0.0441883
$40$	−24588.1	−0.0607455
$41$	318533.	0.721790	0.360895	−	0.932607i	$-0.382471\pi$
$41$	318533.	0.721790	0.360895	+	0.932607i	$0.382471\pi$
$42$	−67623.0	−0.140839
$43$	16755.2	0.0321374	0.0160687	−	0.999871i	$-0.494885\pi$
$43$	16755.2	0.0321374	0.0160687	+	0.999871i	$0.494885\pi$
$44$	642638.	1.13732
$45$	−19146.3	−0.0313215
$46$	82562.0	0.125063
$47$	764733.	1.07440	0.537202	−	0.843454i	$-0.319481\pi$
$47$	764733.	1.07440	0.537202	+	0.843454i	$0.319481\pi$
$48$	−291937.	−0.381017
$49$	−408214.	−0.495681
$50$	300935.	0.340470
$51$	1.06065e6	1.11963
$52$	68446.5	0.0675056
$53$	−1.38308e6	−1.27609	−0.638046	−	0.769998i	$-0.720257\pi$
$53$	−1.38308e6	−1.27609	−0.638046	+	0.769998i	$0.720257\pi$
$54$	76493.8	0.0661071
$55$	149501.	0.121164
$56$	−603340.	−0.459096
$57$	919695.	0.657782
$58$	−101796.	−0.0685067
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−80057.8	−0.0478492
$61$	−354332.	−0.199874	−0.0999371	−	0.994994i	$-0.531864\pi$
$61$	−354332.	−0.199874	−0.0999371	+	0.994994i	$0.531864\pi$
$62$	1.20614e6	0.642728
$63$	−469811.	−0.236718
$64$	−754988.	−0.360006
$65$	15923.1	0.00719170
$66$	−597287.	−0.255729
$67$	4.54645e6	1.84676	0.923380	−	0.383887i	$-0.125415\pi$
$67$	4.54645e6	1.84676	0.923380	+	0.383887i	$0.125415\pi$
$68$	4.43496e6	1.71044
$69$	573600.	0.210202
$70$	−65779.3	−0.0229217
$71$	−367019.	−0.121698	−0.0608491	−	0.998147i	$-0.519381\pi$
$71$	−367019.	−0.121698	−0.0608491	+	0.998147i	$0.519381\pi$
$72$	682485.	0.215491
$73$	−1.13809e6	−0.342411	−0.171205	−	0.985235i	$-0.554766\pi$
$73$	−1.13809e6	−0.342411	−0.171205	+	0.985235i	$0.554766\pi$
$74$	1.28350e6	0.368201
$75$	2.09075e6	0.572253
$76$	3.84558e6	1.00488
$77$	3.66843e6	0.915721
$78$	−63616.3	−0.0151788
$79$	3.04988e6	0.695967	0.347983	−	0.937501i	$-0.386867\pi$
$79$	3.04988e6	0.695967	0.347983	+	0.937501i	$0.386867\pi$
$80$	−283977.	−0.0620109
$81$	531441.	0.111111
$82$	−1.23791e6	−0.247937
$83$	−8.39695e6	−1.61194	−0.805969	−	0.591958i	$-0.798355\pi$
$83$	−8.39695e6	−1.61194	−0.805969	+	0.591958i	$0.798355\pi$
$84$	−1.96445e6	−0.361629
$85$	1.03173e6	0.182222
$86$	−65115.7	−0.0110393
$87$	−707229.	−0.115144
$88$	−5.32906e6	−0.833607
$89$	−3.28661e6	−0.494177	−0.247089	−	0.968993i	$-0.579474\pi$
$89$	−3.28661e6	−0.494177	−0.247089	+	0.968993i	$0.579474\pi$
$90$	74408.2	0.0107590
$91$	390720.	0.0543527
$92$	2.39843e6	0.321121
$93$	8.37967e6	1.08028
$94$	−2.97197e6	−0.369060
$95$	894620.	0.107055
$96$	4.37004e6	0.504122
$97$	8.46055e6	0.941234	0.470617	−	0.882338i	$-0.344031\pi$
$97$	8.46055e6	0.941234	0.470617	+	0.882338i	$0.344031\pi$
$98$	1.58644e6	0.170268
$99$	−4.14966e6	−0.429822
$100$	8.74219e6	0.874219
$101$	7.61349e6	0.735290	0.367645	−	0.929966i	$-0.380164\pi$
$101$	7.61349e6	0.735290	0.367645	+	0.929966i	$0.380164\pi$
$102$	−4.12199e6	−0.384597
$103$	4.15554e6	0.374712	0.187356	−	0.982292i	$-0.440008\pi$
$103$	4.15554e6	0.374712	0.187356	+	0.982292i	$0.440008\pi$
$104$	−567591.	−0.0494788
$105$	−457002.	−0.0385262
$106$	5.37505e6	0.438341
$107$	1.11011e7	0.876038	0.438019	−	0.898966i	$-0.355680\pi$
$107$	1.11011e7	0.876038	0.438019	+	0.898966i	$0.355680\pi$
$108$	2.22215e6	0.169742
$109$	8.22798e6	0.608556	0.304278	−	0.952583i	$-0.401585\pi$
$109$	8.22798e6	0.608556	0.304278	+	0.952583i	$0.401585\pi$
$110$	−581002.	−0.0416201
$111$	8.91712e6	0.618863
$112$	−6.96820e6	−0.468660
$113$	−1.87058e7	−1.21956	−0.609779	−	0.792571i	$-0.708742\pi$
$113$	−1.87058e7	−1.21956	−0.609779	+	0.792571i	$0.708742\pi$
$114$	−3.57420e6	−0.225950
$115$	557961.	0.0342106
$116$	−2.95718e6	−0.175904
$117$	−441975.	−0.0255121
$118$	798162.	0.0447202
$119$	2.53165e7	1.37718
$120$	663878.	0.0350714
$121$	1.29146e7	0.662725
$122$	1.37704e6	0.0686573
$123$	−8.60039e6	−0.416725
$124$	3.50384e7	1.65032
$125$	4.08561e6	0.187099
$126$	1.82582e6	0.0813133
$127$	1.39760e7	0.605437	0.302718	−	0.953080i	$-0.402106\pi$
$127$	1.39760e7	0.605437	0.302718	+	0.953080i	$0.402106\pi$
$128$	2.36513e7	0.996828
$129$	−452392.	−0.0185546
$130$	−61881.8	−0.00247037
$131$	1.69407e7	0.658387	0.329193	−	0.944263i	$-0.393223\pi$
$131$	1.69407e7	0.658387	0.329193	+	0.944263i	$0.393223\pi$
$132$	−1.73512e7	−0.656631
$133$	2.19521e7	0.809087
$134$	−1.76688e7	−0.634367
$135$	516951.	0.0180835
$136$	−3.67768e7	−1.25368
$137$	−2.48882e7	−0.826935	−0.413467	−	0.910519i	$-0.635682\pi$
$137$	−2.48882e7	−0.826935	−0.413467	+	0.910519i	$0.635682\pi$
$138$	−2.22917e6	−0.0722049
$139$	−5.91087e7	−1.86681	−0.933404	−	0.358826i	$-0.883177\pi$
$139$	−5.91087e7	−1.86681	−0.933404	+	0.358826i	$0.883177\pi$
$140$	−1.91089e6	−0.0588556
$141$	−2.06478e7	−0.620307
$142$	1.42634e6	0.0418036
$143$	3.45108e6	0.0986912
$144$	7.88229e6	0.219980
$145$	−687946.	−0.0187399
$146$	4.42295e6	0.117619
$147$	1.10218e7	0.286181
$148$	3.72857e7	0.945424
$149$	−4.77206e7	−1.18183	−0.590914	−	0.806735i	$-0.701233\pi$
$149$	−4.77206e7	−1.18183	−0.590914	+	0.806735i	$0.701233\pi$
$150$	−8.12526e6	−0.196570
$151$	1.71936e7	0.406393	0.203197	−	0.979138i	$-0.434867\pi$
$151$	1.71936e7	0.406393	0.203197	+	0.979138i	$0.434867\pi$
$152$	−3.18894e7	−0.736535
$153$	−2.86375e7	−0.646421
$154$	−1.42566e7	−0.314552
$155$	8.15120e6	0.175817
$156$	−1.84806e6	−0.0389744
$157$	−2.53780e7	−0.523371	−0.261685	−	0.965153i	$-0.584278\pi$
$157$	−2.53780e7	−0.523371	−0.261685	+	0.965153i	$0.584278\pi$
$158$	−1.18527e7	−0.239066
$159$	3.73432e7	0.736752
$160$	4.25089e6	0.0820464
$161$	1.36912e7	0.258554
$162$	−2.06533e6	−0.0381669
$163$	6.34001e7	1.14666	0.573328	−	0.819326i	$-0.305652\pi$
$163$	6.34001e7	1.14666	0.573328	+	0.819326i	$0.305652\pi$
$164$	−3.59613e7	−0.636623
$165$	−4.03652e6	−0.0699541
$166$	3.26330e7	0.553705
$167$	−3.68194e7	−0.611743	−0.305872	−	0.952073i	$-0.598948\pi$
$167$	−3.68194e7	−0.611743	−0.305872	+	0.952073i	$0.598948\pi$
$168$	1.62902e7	0.265059
$169$	−6.23809e7	−0.994142
$170$	−4.00960e6	−0.0625936
$171$	−2.48318e7	−0.379771
$172$	−1.89161e6	−0.0283454
$173$	−6.29918e7	−0.924959	−0.462480	−	0.886630i	$-0.653040\pi$
$173$	−6.29918e7	−0.924959	−0.462480	+	0.886630i	$0.653040\pi$
$174$	2.74849e6	0.0395524
$175$	4.99039e7	0.703884
$176$	−6.15474e7	−0.850972
$177$	5.54523e6	0.0751646
$178$	1.27727e7	0.169751
$179$	−1.68796e7	−0.219977	−0.109989	−	0.993933i	$-0.535081\pi$
$179$	−1.68796e7	−0.219977	−0.109989	+	0.993933i	$0.535081\pi$
$180$	2.16156e6	0.0276257
$181$	5.41326e7	0.678554	0.339277	−	0.940687i	$-0.389818\pi$
$181$	5.41326e7	0.678554	0.339277	+	0.940687i	$0.389818\pi$
$182$	−1.51845e6	−0.0186703
$183$	9.56698e6	0.115397
$184$	−1.98889e7	−0.235369
$185$	8.67400e6	0.100721
$186$	−3.25658e7	−0.371079
$187$	2.23611e8	2.50062
$188$	−8.63359e7	−0.947630
$189$	1.26849e7	0.136669
$190$	−3.47675e6	−0.0367736
$191$	−8.74794e7	−0.908425	−0.454213	−	0.890893i	$-0.650079\pi$
$191$	−8.74794e7	−0.908425	−0.454213	+	0.890893i	$0.650079\pi$
$192$	2.03847e7	0.207850
$193$	−8.18019e7	−0.819054	−0.409527	−	0.912298i	$-0.634306\pi$
$193$	−8.18019e7	−0.819054	−0.409527	+	0.912298i	$0.634306\pi$
$194$	−3.28801e7	−0.323316
$195$	−429924.	−0.00415213
$196$	4.60861e7	0.437193
$197$	−1.92295e8	−1.79199	−0.895996	−	0.444061i	$-0.853537\pi$
$197$	−1.92295e8	−1.79199	−0.895996	+	0.444061i	$0.853537\pi$
$198$	1.61268e7	0.147645
$199$	−1.44937e6	−0.0130375	−0.00651873	−	0.999979i	$-0.502075\pi$
$199$	−1.44937e6	−0.0130375	−0.00651873	+	0.999979i	$0.502075\pi$
$200$	−7.24944e7	−0.640766
$201$	−1.22754e8	−1.06623
$202$	−2.95882e7	−0.252574
$203$	−1.68808e7	−0.141630
$204$	−1.19744e8	−0.987524
$205$	−8.36590e6	−0.0678225
$206$	−1.61496e7	−0.128715
$207$	−1.54872e7	−0.121360
$208$	−6.55533e6	−0.0505095
$209$	1.93894e8	1.46910
$210$	1.77604e6	0.0132338
$211$	−2.14625e8	−1.57286	−0.786432	−	0.617676i	$-0.788074\pi$
$211$	−2.14625e8	−1.57286	−0.786432	+	0.617676i	$0.788074\pi$
$212$	1.56145e8	1.12552
$213$	9.90950e6	0.0702625
$214$	−4.31421e7	−0.300921
$215$	−440057.	−0.00301977
$216$	−1.84271e7	−0.124414
$217$	2.00013e8	1.32877
$218$	−3.19763e7	−0.209041
$219$	3.07285e7	0.197691
$220$	−1.68781e7	−0.106867
$221$	2.38165e7	0.148424
$222$	−3.46545e7	−0.212581
$223$	−2.05595e8	−1.24150	−0.620748	−	0.784011i	$-0.713171\pi$
$223$	−2.05595e8	−1.24150	−0.620748	+	0.784011i	$0.713171\pi$
$224$	1.04308e8	0.620082
$225$	−5.64503e7	−0.330390
$226$	7.26962e7	0.418921
$227$	1.87007e8	1.06113	0.530563	−	0.847646i	$-0.321981\pi$
$227$	1.87007e8	1.06113	0.530563	+	0.847646i	$0.321981\pi$
$228$	−1.03831e8	−0.580168
$229$	1.01441e8	0.558201	0.279100	−	0.960262i	$-0.409964\pi$
$229$	1.01441e8	0.558201	0.279100	+	0.960262i	$0.409964\pi$
$230$	−2.16839e6	−0.0117514
$231$	−9.90477e7	−0.528692
$232$	2.45223e7	0.128930
$233$	−1.98406e8	−1.02757	−0.513783	−	0.857920i	$-0.671756\pi$
$233$	−1.98406e8	−1.02757	−0.513783	+	0.857920i	$0.671756\pi$
$234$	1.71764e6	0.00876348
$235$	−2.00848e7	−0.100956
$236$	2.31866e7	0.114827
$237$	−8.23468e7	−0.401816
$238$	−9.83873e7	−0.473064
$239$	9.06262e7	0.429399	0.214700	−	0.976680i	$-0.431123\pi$
$239$	9.06262e7	0.429399	0.214700	+	0.976680i	$0.431123\pi$
$240$	7.66738e6	0.0358020
$241$	−2.22377e8	−1.02336	−0.511681	−	0.859175i	$-0.670977\pi$
$241$	−2.22377e8	−1.02336	−0.511681	+	0.859175i	$0.670977\pi$
$242$	−5.01900e7	−0.227648
$243$	−1.43489e7	−0.0641500
$244$	4.00030e7	0.176290
$245$	1.07213e7	0.0465763
$246$	3.34236e7	0.143146
$247$	2.06514e7	0.0871988
$248$	−2.90555e8	−1.20962
$249$	2.26718e8	0.930653
$250$	−1.58779e7	−0.0642690
$251$	4.71405e8	1.88164	0.940819	−	0.338909i	$-0.110058\pi$
$251$	4.71405e8	1.88164	0.940819	+	0.338909i	$0.110058\pi$
$252$	5.30402e7	0.208787
$253$	1.20929e8	0.469470
$254$	−5.43146e7	−0.207969
$255$	−2.78567e7	−0.105206
$256$	4.72267e6	0.0175933
$257$	−6.85596e6	−0.0251943	−0.0125972	−	0.999921i	$-0.504010\pi$
$257$	−6.85596e6	−0.0251943	−0.0125972	+	0.999921i	$0.504010\pi$
$258$	1.75812e6	0.00637354
$259$	2.12842e8	0.761216
$260$	−1.79767e6	−0.00634312
$261$	1.90952e7	0.0664786
$262$	−6.58363e7	−0.226158
$263$	−4.52181e8	−1.53273	−0.766367	−	0.642403i	$-0.777938\pi$
$263$	−4.52181e8	−1.53273	−0.766367	+	0.642403i	$0.777938\pi$
$264$	1.43885e8	0.481283
$265$	3.63250e7	0.119907
$266$	−8.53122e7	−0.277924
$267$	8.87384e7	0.285313
$268$	−5.13279e8	−1.62885
$269$	6.31747e7	0.197884	0.0989419	−	0.995093i	$-0.468454\pi$
$269$	6.31747e7	0.197884	0.0989419	+	0.995093i	$0.468454\pi$
$270$	−2.00902e6	−0.00621171
$271$	5.80213e8	1.77091	0.885453	−	0.464730i	$-0.153849\pi$
$271$	5.80213e8	1.77091	0.885453	+	0.464730i	$0.153849\pi$
$272$	−4.24749e8	−1.27980
$273$	−1.05494e7	−0.0313805
$274$	9.67226e7	0.284054
$275$	4.40781e8	1.27808
$276$	−6.47575e7	−0.185400
$277$	2.08756e8	0.590146	0.295073	−	0.955475i	$-0.404656\pi$
$277$	2.08756e8	0.590146	0.295073	+	0.955475i	$0.404656\pi$
$278$	2.29714e8	0.641253
$279$	−2.26251e8	−0.623700
$280$	1.58460e7	0.0431387
$281$	−6.75157e7	−0.181523	−0.0907617	−	0.995873i	$-0.528930\pi$
$281$	−6.75157e7	−0.181523	−0.0907617	+	0.995873i	$0.528930\pi$
$282$	8.02433e7	0.213077
$283$	5.48132e8	1.43758	0.718791	−	0.695226i	$-0.244696\pi$
$283$	5.48132e8	1.43758	0.718791	+	0.695226i	$0.244696\pi$
$284$	4.14352e7	0.107338
$285$	−2.41547e7	−0.0618081
$286$	−1.34119e7	−0.0339007
$287$	−2.05282e8	−0.512582
$288$	−1.17991e8	−0.291055
$289$	1.13284e9	2.76074
$290$	2.67356e6	0.00643719
$291$	−2.28435e8	−0.543421
$292$	1.28487e8	0.302008
$293$	2.36630e8	0.549582	0.274791	−	0.961504i	$-0.411391\pi$
$293$	2.36630e8	0.549582	0.274791	+	0.961504i	$0.411391\pi$
$294$	−4.28338e7	−0.0983040
$295$	5.39404e6	0.0122331
$296$	−3.09191e8	−0.692956
$297$	1.12041e8	0.248158
$298$	1.85456e8	0.405961
$299$	1.28800e7	0.0278654
$300$	−2.36039e8	−0.504730
$301$	−1.07981e7	−0.0228225
$302$	−6.68191e7	−0.139597
$303$	−2.05564e8	−0.424520
$304$	−3.68303e8	−0.751878
$305$	9.30614e6	0.0187811
$306$	1.11294e8	0.222047
$307$	−2.84146e7	−0.0560477	−0.0280238	−	0.999607i	$-0.508921\pi$
$307$	−2.84146e7	−0.0560477	−0.0280238	+	0.999607i	$0.508921\pi$
$308$	−4.14154e8	−0.807671
$309$	−1.12200e8	−0.216340
$310$	−3.16779e7	−0.0603936
$311$	3.86506e8	0.728609	0.364305	−	0.931280i	$-0.381307\pi$
$311$	3.86506e8	0.728609	0.364305	+	0.931280i	$0.381307\pi$
$312$	1.53250e7	0.0285666
$313$	7.79214e8	1.43632	0.718160	−	0.695878i	$-0.244984\pi$
$313$	7.79214e8	1.43632	0.718160	+	0.695878i	$0.244984\pi$
$314$	9.86264e7	0.179779
$315$	1.23391e7	0.0222431
$316$	−3.44322e8	−0.613847
$317$	−4.02260e8	−0.709251	−0.354625	−	0.935008i	$-0.615392\pi$
$317$	−4.02260e8	−0.709251	−0.354625	+	0.935008i	$0.615392\pi$
$318$	−1.45126e8	−0.253076
$319$	−1.49101e8	−0.257166
$320$	1.98289e7	0.0338278
$321$	−2.99730e8	−0.505781
$322$	−5.32079e7	−0.0888138
$323$	1.33810e9	2.20943
$324$	−5.99980e7	−0.0980007
$325$	4.69471e7	0.0758607
$326$	−2.46391e8	−0.393879
$327$	−2.22155e8	−0.351350
$328$	2.98209e8	0.466618
$329$	−4.92840e8	−0.762993
$330$	1.56871e7	0.0240294
$331$	−6.06425e8	−0.919135	−0.459568	−	0.888143i	$-0.651996\pi$
$331$	−6.06425e8	−0.919135	−0.459568	+	0.888143i	$0.651996\pi$
$332$	9.47989e8	1.42174
$333$	−2.40762e8	−0.357301
$334$	1.43091e8	0.210135
$335$	−1.19407e8	−0.173530
$336$	1.88141e8	0.270581
$337$	7.34722e8	1.04573	0.522864	−	0.852416i	$-0.324864\pi$
$337$	7.34722e8	1.04573	0.522864	+	0.852416i	$0.324864\pi$
$338$	2.42430e8	0.341490
$339$	5.05057e8	0.704112
$340$	−1.16479e8	−0.160721
$341$	1.76664e9	2.41272
$342$	9.65034e7	0.130452
$343$	7.93818e8	1.06216
$344$	1.56862e7	0.0207760
$345$	−1.50649e7	−0.0197515
$346$	2.44804e8	0.317726
$347$	−1.10182e9	−1.41566	−0.707830	−	0.706382i	$-0.750326\pi$
$347$	−1.10182e9	−1.41566	−0.707830	+	0.706382i	$0.750326\pi$
$348$	7.98438e7	0.101558
$349$	−1.38141e8	−0.173953	−0.0869766	−	0.996210i	$-0.527721\pi$
$349$	−1.38141e8	−0.173953	−0.0869766	+	0.996210i	$0.527721\pi$
$350$	−1.93941e8	−0.241786
$351$	1.19333e7	0.0147294
$352$	9.21310e8	1.12592
$353$	−2.28995e8	−0.277086	−0.138543	−	0.990356i	$-0.544242\pi$
$353$	−2.28995e8	−0.277086	−0.138543	+	0.990356i	$0.544242\pi$
$354$	−2.15504e7	−0.0258192
$355$	9.63932e6	0.0114353
$356$	3.71047e8	0.435867
$357$	−6.83546e8	−0.795113
$358$	6.55991e7	0.0755627
$359$	−1.59391e9	−1.81817	−0.909083	−	0.416615i	$-0.863216\pi$
$359$	−1.59391e9	−1.81817	−0.909083	+	0.416615i	$0.863216\pi$
$360$	−1.79247e7	−0.0202485
$361$	2.66402e8	0.298031
$362$	−2.10375e8	−0.233085
$363$	−3.48695e8	−0.382625
$364$	−4.41111e7	−0.0479394
$365$	2.98907e7	0.0321744
$366$	−3.71800e7	−0.0396393
$367$	−3.97853e8	−0.420137	−0.210069	−	0.977687i	$-0.567369\pi$
$367$	−3.97853e8	−0.420137	−0.210069	+	0.977687i	$0.567369\pi$
$368$	−2.29705e8	−0.240272
$369$	2.32210e8	0.240597
$370$	−3.37097e7	−0.0345978
$371$	8.91340e8	0.906222
$372$	−9.46038e8	−0.952814
$373$	1.35221e9	1.34916	0.674582	−	0.738200i	$-0.264324\pi$
$373$	1.35221e9	1.34916	0.674582	+	0.738200i	$0.264324\pi$
$374$	−8.69016e8	−0.858968
$375$	−1.10311e8	−0.108022
$376$	7.15939e8	0.694574
$377$	−1.58806e7	−0.0152641
$378$	−4.92972e7	−0.0469462
$379$	1.69493e9	1.59924	0.799621	−	0.600506i	$-0.205034\pi$
$379$	1.69493e9	1.59924	0.799621	+	0.600506i	$0.205034\pi$
$380$	−1.01000e8	−0.0944229
$381$	−3.77351e8	−0.349549
$382$	3.39970e8	0.312046
$383$	−1.90311e9	−1.73088	−0.865442	−	0.501010i	$-0.832962\pi$
$383$	−1.90311e9	−1.73088	−0.865442	+	0.501010i	$0.832962\pi$
$384$	−6.38585e8	−0.575519
$385$	−9.63472e7	−0.0860452
$386$	3.17906e8	0.281347
$387$	1.22146e7	0.0107125
$388$	−9.55169e8	−0.830174
$389$	−1.65443e9	−1.42503	−0.712516	−	0.701655i	$-0.752445\pi$
$389$	−1.65443e9	−1.42503	−0.712516	+	0.701655i	$0.752445\pi$
$390$	1.67081e6	0.00142627
$391$	8.34551e8	0.706048
$392$	−3.82168e8	−0.320445
$393$	−4.57398e8	−0.380120
$394$	7.47314e8	0.615554
$395$	−8.01017e7	−0.0653961
$396$	4.68483e8	0.379106
$397$	−1.76432e9	−1.41518	−0.707590	−	0.706623i	$-0.750218\pi$
$397$	−1.76432e9	−1.41518	−0.707590	+	0.706623i	$0.750218\pi$
$398$	5.63266e6	0.00447840
$399$	−5.92707e8	−0.467127
$400$	−8.37266e8	−0.654114
$401$	9.40134e8	0.728089	0.364045	−	0.931381i	$-0.381396\pi$
$401$	9.40134e8	0.728089	0.364045	+	0.931381i	$0.381396\pi$
$402$	4.77058e8	0.366252
$403$	1.88163e8	0.143207
$404$	−8.59538e8	−0.648530
$405$	−1.39577e7	−0.0104405
$406$	6.56035e7	0.0486503
$407$	1.87995e9	1.38218
$408$	9.92974e8	0.723814
$409$	−9.46509e8	−0.684059	−0.342029	−	0.939689i	$-0.611114\pi$
$409$	−9.46509e8	−0.684059	−0.342029	+	0.939689i	$0.611114\pi$
$410$	3.25123e7	0.0232972
$411$	6.71981e8	0.477431
$412$	−4.69148e8	−0.330498
$413$	1.32359e8	0.0924542
$414$	6.01877e7	0.0416875
$415$	2.20536e8	0.151465
$416$	9.81276e7	0.0668289
$417$	1.59594e9	1.07780
$418$	−7.53528e8	−0.504641
$419$	−7.99568e8	−0.531014	−0.265507	−	0.964109i	$-0.585539\pi$
$419$	−7.99568e8	−0.531014	−0.265507	+	0.964109i	$0.585539\pi$
$420$	5.15941e7	0.0339803
$421$	−1.69924e9	−1.10986	−0.554930	−	0.831897i	$-0.687255\pi$
$421$	−1.69924e9	−1.10986	−0.554930	+	0.831897i	$0.687255\pi$
$422$	8.34094e8	0.540283
$423$	5.57491e8	0.358135
$424$	−1.29483e9	−0.824960
$425$	3.04191e9	1.92214
$426$	−3.85112e7	−0.0241353
$427$	2.28353e8	0.141941
$428$	−1.25328e9	−0.772671
$429$	−9.31791e7	−0.0569794
$430$	1.71019e6	0.00103730
$431$	1.67268e9	1.00634	0.503168	−	0.864188i	$-0.332168\pi$
$431$	1.67268e9	1.00634	0.503168	+	0.864188i	$0.332168\pi$
$432$	−2.12822e8	−0.127006
$433$	1.83377e9	1.08552	0.542759	−	0.839889i	$-0.317380\pi$
$433$	1.83377e9	1.08552	0.542759	+	0.839889i	$0.317380\pi$
$434$	−7.77310e8	−0.456436
$435$	1.85745e7	0.0108195
$436$	−9.28912e8	−0.536750
$437$	7.23644e8	0.414801
$438$	−1.19420e8	−0.0679073
$439$	−8.26984e8	−0.466521	−0.233261	−	0.972414i	$-0.574940\pi$
$439$	−8.26984e8	−0.466521	−0.233261	+	0.972414i	$0.574940\pi$
$440$	1.39962e8	0.0783294
$441$	−2.97588e8	−0.165227
$442$	−9.25578e7	−0.0509841
$443$	4.49548e8	0.245676	0.122838	−	0.992427i	$-0.460800\pi$
$443$	4.49548e8	0.245676	0.122838	+	0.992427i	$0.460800\pi$
$444$	−1.00671e9	−0.545841
$445$	8.63190e7	0.0464351
$446$	7.99000e8	0.426457
$447$	1.28846e9	0.682328
$448$	4.86559e8	0.255660
$449$	−1.26664e9	−0.660377	−0.330188	−	0.943915i	$-0.607112\pi$
$449$	−1.26664e9	−0.660377	−0.330188	+	0.943915i	$0.607112\pi$
$450$	2.19382e8	0.113490
$451$	−1.81317e9	−0.930724
$452$	2.11183e9	1.07566
$453$	−4.64226e8	−0.234631
$454$	−7.26762e8	−0.364499
$455$	−1.02618e7	−0.00510722
$456$	8.61013e8	0.425239
$457$	−2.61328e8	−0.128079	−0.0640397	−	0.997947i	$-0.520398\pi$
$457$	−2.61328e8	−0.128079	−0.0640397	+	0.997947i	$0.520398\pi$
$458$	−3.94230e8	−0.191743
$459$	7.73213e8	0.373211
$460$	−6.29919e7	−0.0301740
$461$	−2.60747e9	−1.23956	−0.619779	−	0.784777i	$-0.712778\pi$
$461$	−2.60747e9	−1.23956	−0.619779	+	0.784777i	$0.712778\pi$
$462$	3.84928e8	0.181607
$463$	3.07005e9	1.43751	0.718757	−	0.695261i	$-0.244711\pi$
$463$	3.07005e9	1.43751	0.718757	+	0.695261i	$0.244711\pi$
$464$	2.83218e8	0.131616
$465$	−2.20082e8	−0.101508
$466$	7.71064e8	0.352971
$467$	−2.89908e9	−1.31720	−0.658599	−	0.752494i	$-0.728851\pi$
$467$	−2.89908e9	−1.31720	−0.658599	+	0.752494i	$0.728851\pi$
$468$	4.98975e7	0.0225019
$469$	−2.93000e9	−1.31149
$470$	7.80555e7	0.0346785
$471$	6.85207e8	0.302168
$472$	−1.92275e8	−0.0841637
$473$	−9.53752e7	−0.0414402
$474$	3.20023e8	0.138025
$475$	2.63766e9	1.12925
$476$	−2.85815e9	−1.21468
$477$	−1.00827e9	−0.425364
$478$	−3.52199e8	−0.147500
$479$	−2.72155e9	−1.13147	−0.565733	−	0.824588i	$-0.691407\pi$
$479$	−2.72155e9	−1.13147	−0.565733	+	0.824588i	$0.691407\pi$
$480$	−1.14774e8	−0.0473695
$481$	2.00231e8	0.0820395
$482$	8.64220e8	0.351528
$483$	−3.69662e8	−0.149276
$484$	−1.45802e9	−0.584528
$485$	−2.22207e8	−0.0884425
$486$	5.57640e7	0.0220357
$487$	−4.18049e9	−1.64012	−0.820060	−	0.572278i	$-0.806060\pi$
$487$	−4.18049e9	−1.64012	−0.820060	+	0.572278i	$0.806060\pi$
$488$	−3.31724e8	−0.129213
$489$	−1.71180e9	−0.662023
$490$	−4.16660e7	−0.0159991
$491$	1.16233e9	0.443144	0.221572	−	0.975144i	$-0.428881\pi$
$491$	1.16233e9	0.443144	0.221572	+	0.975144i	$0.428881\pi$
$492$	9.70956e8	0.367554
$493$	−1.02897e9	−0.386758
$494$	−8.02574e7	−0.0299530
$495$	1.08986e8	0.0403880
$496$	−3.35574e9	−1.23482
$497$	2.36529e8	0.0864245
$498$	−8.81090e8	−0.319682
$499$	−2.46041e9	−0.886453	−0.443227	−	0.896410i	$-0.646166\pi$
$499$	−2.46041e9	−0.886453	−0.443227	+	0.896410i	$0.646166\pi$
$500$	−4.61252e8	−0.165023
$501$	9.94124e8	0.353190
$502$	−1.83202e9	−0.646347
$503$	−3.44444e9	−1.20679	−0.603394	−	0.797443i	$-0.706185\pi$
$503$	−3.44444e9	−1.20679	−0.603394	+	0.797443i	$0.706185\pi$
$504$	−4.39835e8	−0.153032
$505$	−1.99960e8	−0.0690911
$506$	−4.69964e8	−0.161264
$507$	1.68429e9	0.573968
$508$	−1.57784e9	−0.533999
$509$	−1.85883e9	−0.624781	−0.312391	−	0.949954i	$-0.601130\pi$
$509$	−1.85883e9	−0.624781	−0.312391	+	0.949954i	$0.601130\pi$
$510$	1.08259e8	0.0361384
$511$	7.33455e8	0.243164
$512$	−3.04572e9	−1.00287
$513$	6.70458e8	0.219261
$514$	2.66442e7	0.00865431
$515$	−1.09141e8	−0.0352096
$516$	5.10735e7	0.0163652
$517$	−4.35306e9	−1.38541
$518$	−8.27164e8	−0.261480
$519$	1.70078e9	0.534025
$520$	1.49071e7	0.00464925
$521$	1.66724e9	0.516496	0.258248	−	0.966079i	$-0.416855\pi$
$521$	1.66724e9	0.516496	0.258248	+	0.966079i	$0.416855\pi$
$522$	−7.42093e7	−0.0228356
$523$	−5.43856e8	−0.166237	−0.0831186	−	0.996540i	$-0.526488\pi$
$523$	−5.43856e8	−0.166237	−0.0831186	+	0.996540i	$0.526488\pi$
$524$	−1.91255e9	−0.580701
$525$	−1.34741e9	−0.406388
$526$	1.75730e9	0.526498
$527$	1.21919e10	3.62856
$528$	1.66178e9	0.491309
$529$	−2.95350e9	−0.867445
$530$	−1.41169e8	−0.0411884
$531$	−1.49721e8	−0.0433963
$532$	−2.47832e9	−0.713620
$533$	−1.93119e8	−0.0552432
$534$	−3.44863e8	−0.0980059
$535$	−2.91558e8	−0.0823164
$536$	4.25636e9	1.19388
$537$	4.55750e8	0.127004
$538$	−2.45515e8	−0.0679736
$539$	2.32366e9	0.639164
$540$	−5.83621e7	−0.0159497
$541$	−2.30286e8	−0.0625283	−0.0312642	−	0.999511i	$-0.509953\pi$
$541$	−2.30286e8	−0.0625283	−0.0312642	+	0.999511i	$0.509953\pi$
$542$	−2.25488e9	−0.608310
$543$	−1.46158e9	−0.391763
$544$	6.35813e9	1.69330
$545$	−2.16098e8	−0.0571826
$546$	4.09982e7	0.0107793
$547$	4.00304e9	1.04576	0.522882	−	0.852405i	$-0.324857\pi$
$547$	4.00304e9	1.04576	0.522882	+	0.852405i	$0.324857\pi$
$548$	2.80979e9	0.729361
$549$	−2.58308e8	−0.0666247
$550$	−1.71300e9	−0.439024
$551$	−8.92229e8	−0.227219
$552$	5.37001e8	0.135890
$553$	−1.96553e9	−0.494244
$554$	−8.11285e8	−0.202717
$555$	−2.34198e8	−0.0581511
$556$	6.67318e9	1.64654
$557$	−3.49935e9	−0.858014	−0.429007	−	0.903301i	$-0.641136\pi$
$557$	−3.49935e9	−0.858014	−0.429007	+	0.903301i	$0.641136\pi$
$558$	8.79277e8	0.214243
$559$	−1.01583e7	−0.00245968
$560$	1.83012e8	0.0440373
$561$	−6.03749e9	−1.44373
$562$	2.62385e8	0.0623538
$563$	3.07572e9	0.726385	0.363193	−	0.931714i	$-0.381687\pi$
$563$	3.07572e9	0.726385	0.363193	+	0.931714i	$0.381687\pi$
$564$	2.33107e9	0.547115
$565$	4.91287e8	0.114595
$566$	−2.13020e9	−0.493813
$567$	−3.42492e8	−0.0789061
$568$	−3.43601e8	−0.0786747
$569$	−2.50567e9	−0.570206	−0.285103	−	0.958497i	$-0.592028\pi$
$569$	−2.50567e9	−0.570206	−0.285103	+	0.958497i	$0.592028\pi$
$570$	9.38722e7	0.0212312
$571$	−6.38840e9	−1.43604	−0.718019	−	0.696023i	$-0.754951\pi$
$571$	−6.38840e9	−1.43604	−0.718019	+	0.696023i	$0.754951\pi$
$572$	−3.89615e8	−0.0870462
$573$	2.36194e9	0.524479
$574$	7.97784e8	0.176073
$575$	1.64507e9	0.360866
$576$	−5.50386e8	−0.120002
$577$	−3.86927e9	−0.838520	−0.419260	−	0.907866i	$-0.637710\pi$
$577$	−3.86927e9	−0.838520	−0.419260	+	0.907866i	$0.637710\pi$
$578$	−4.40254e9	−0.948322
$579$	2.20865e9	0.472881
$580$	7.76669e7	0.0165287
$581$	5.41150e9	1.14473
$582$	8.87763e8	0.186667
$583$	7.87285e9	1.64548
$584$	−1.06547e9	−0.221360
$585$	1.16080e7	0.00239723
$586$	−9.19611e8	−0.188783
$587$	−3.35794e9	−0.685236	−0.342618	−	0.939475i	$-0.611314\pi$
$587$	−3.35794e9	−0.685236	−0.342618	+	0.939475i	$0.611314\pi$
$588$	−1.24432e9	−0.252414
$589$	1.05717e10	2.13177
$590$	−2.09628e7	−0.00420211
$591$	5.19197e9	1.03461
$592$	−3.57097e9	−0.707391
$593$	9.52200e9	1.87515	0.937576	−	0.347780i	$-0.113064\pi$
$593$	9.52200e9	1.87515	0.937576	+	0.347780i	$0.113064\pi$
$594$	−4.35422e8	−0.0852429
$595$	−6.64909e8	−0.129406
$596$	5.38750e9	1.04238
$597$	3.91329e7	0.00752718
$598$	−5.00553e7	−0.00957185
$599$	4.99052e8	0.0948750	0.0474375	−	0.998874i	$-0.484895\pi$
$599$	4.99052e8	0.0948750	0.0474375	+	0.998874i	$0.484895\pi$
$600$	1.95735e9	0.369946
$601$	−4.14166e9	−0.778241	−0.389120	−	0.921187i	$-0.627221\pi$
$601$	−4.14166e9	−0.778241	−0.389120	+	0.921187i	$0.627221\pi$
$602$	4.19645e7	0.00783960
$603$	3.31436e9	0.615587
$604$	−1.94110e9	−0.358441
$605$	−3.39188e8	−0.0622726
$606$	7.98881e8	0.145824
$607$	−4.83852e9	−0.878117	−0.439059	−	0.898458i	$-0.644688\pi$
$607$	−4.83852e9	−0.878117	−0.439059	+	0.898458i	$0.644688\pi$
$608$	5.51317e9	0.994807
$609$	4.55781e8	0.0817702
$610$	−3.61663e7	−0.00645134
$611$	−4.63639e8	−0.0822310
$612$	3.23308e9	0.570147
$613$	2.78195e9	0.487795	0.243898	−	0.969801i	$-0.421574\pi$
$613$	2.78195e9	0.487795	0.243898	+	0.969801i	$0.421574\pi$
$614$	1.10427e8	0.0192525
$615$	2.25879e8	0.0391574
$616$	3.43437e9	0.591990
$617$	6.18863e9	1.06071	0.530354	−	0.847776i	$-0.322059\pi$
$617$	6.18863e9	1.06071	0.530354	+	0.847776i	$0.322059\pi$
$618$	4.36040e8	0.0743134
$619$	3.57626e9	0.606055	0.303027	−	0.952982i	$-0.402003\pi$
$619$	3.57626e9	0.606055	0.303027	+	0.952982i	$0.402003\pi$
$620$	−9.20244e8	−0.155072
$621$	4.18154e8	0.0700674
$622$	−1.50207e9	−0.250279
$623$	2.11809e9	0.350942
$624$	1.76994e8	0.0291617
$625$	5.94232e9	0.973590
$626$	−3.02825e9	−0.493380
$627$	−5.23514e9	−0.848188
$628$	2.86510e9	0.461616
$629$	1.29739e10	2.07870
$630$	−4.79531e7	−0.00764055
$631$	1.06672e10	1.69024	0.845121	−	0.534574i	$-0.179528\pi$
$631$	1.06672e10	1.69024	0.845121	+	0.534574i	$0.179528\pi$
$632$	2.85528e9	0.449924
$633$	5.79487e9	0.908094
$634$	1.56330e9	0.243629
$635$	−3.67063e8	−0.0568895
$636$	−4.21592e9	−0.649820
$637$	2.47490e8	0.0379376
$638$	5.79449e8	0.0883371
$639$	−2.67557e8	−0.0405660
$640$	−6.21174e8	−0.0936664
$641$	−2.94407e9	−0.441515	−0.220757	−	0.975329i	$-0.570853\pi$
$641$	−2.94407e9	−0.441515	−0.220757	+	0.975329i	$0.570853\pi$
$642$	1.16484e9	0.173737
$643$	−1.24967e10	−1.85378	−0.926889	−	0.375335i	$-0.877528\pi$
$643$	−1.24967e10	−1.85378	−0.926889	+	0.375335i	$0.877528\pi$
$644$	−1.54569e9	−0.228046
$645$	1.18815e7	0.00174347
$646$	−5.20024e9	−0.758943
$647$	−1.89232e9	−0.274682	−0.137341	−	0.990524i	$-0.543856\pi$
$647$	−1.89232e9	−0.274682	−0.137341	+	0.990524i	$0.543856\pi$
$648$	4.97532e8	0.0718304
$649$	1.16907e9	0.167874
$650$	−1.82450e8	−0.0260583
$651$	−5.40036e9	−0.767166
$652$	−7.15767e9	−1.01136
$653$	−1.18782e9	−0.166937	−0.0834687	−	0.996510i	$-0.526600\pi$
$653$	−1.18782e9	−0.166937	−0.0834687	+	0.996510i	$0.526600\pi$
$654$	8.63360e8	0.120690
$655$	−4.44927e8	−0.0618649
$656$	3.44413e9	0.476338
$657$	−8.29669e8	−0.114137
$658$	1.91532e9	0.262090
$659$	−1.27625e10	−1.73715	−0.868574	−	0.495559i	$-0.834963\pi$
$659$	−1.27625e10	−1.73715	−0.868574	+	0.495559i	$0.834963\pi$
$660$	4.55710e8	0.0616999
$661$	5.94189e9	0.800239	0.400120	−	0.916463i	$-0.368969\pi$
$661$	5.94189e9	0.800239	0.400120	+	0.916463i	$0.368969\pi$
$662$	2.35674e9	0.315725
$663$	−6.43046e8	−0.0856928
$664$	−7.86118e9	−1.04208
$665$	−5.76547e8	−0.0760254
$666$	9.35671e8	0.122734
$667$	−5.56469e8	−0.0726107
$668$	4.15679e9	0.539561
$669$	5.55106e9	0.716778
$670$	4.64051e8	0.0596079
$671$	2.01695e9	0.257731
$672$	−2.81631e9	−0.358005
$673$	−4.95302e9	−0.626350	−0.313175	−	0.949695i	$-0.601393\pi$
$673$	−4.95302e9	−0.626350	−0.313175	+	0.949695i	$0.601393\pi$
$674$	−2.85534e9	−0.359210
$675$	1.52416e9	0.190751
$676$	7.04261e9	0.876839
$677$	1.35131e9	0.167377	0.0836886	−	0.996492i	$-0.473330\pi$
$677$	1.35131e9	0.167377	0.0836886	+	0.996492i	$0.473330\pi$
$678$	−1.96280e9	−0.241864
$679$	−5.45249e9	−0.668421
$680$	9.65900e8	0.117802
$681$	−5.04918e9	−0.612641
$682$	−6.86567e9	−0.828777
$683$	1.43057e10	1.71806	0.859029	−	0.511927i	$-0.171068\pi$
$683$	1.43057e10	1.71806	0.859029	+	0.511927i	$0.171068\pi$
$684$	2.80343e9	0.334960
$685$	6.53659e8	0.0777024
$686$	−3.08501e9	−0.364856
$687$	−2.73891e9	−0.322277
$688$	1.81166e8	0.0212088
$689$	8.38527e8	0.0976675
$690$	5.85467e7	0.00678470
$691$	−1.07877e10	−1.24382	−0.621909	−	0.783089i	$-0.713643\pi$
$691$	−1.07877e10	−1.24382	−0.621909	+	0.783089i	$0.713643\pi$
$692$	7.11157e9	0.815820
$693$	2.67429e9	0.305240
$694$	4.28201e9	0.486283
$695$	1.55242e9	0.175414
$696$	−6.62103e8	−0.0744378
$697$	−1.25130e10	−1.39974
$698$	5.36854e8	0.0597533
$699$	5.35697e9	0.593265
$700$	−5.63399e9	−0.620830
$701$	−3.29304e9	−0.361064	−0.180532	−	0.983569i	$-0.557782\pi$
$701$	−3.29304e9	−0.361064	−0.180532	+	0.983569i	$0.557782\pi$
$702$	−4.63763e7	−0.00505960
$703$	1.12497e10	1.22123
$704$	4.29759e9	0.464216
$705$	5.42291e8	0.0582868
$706$	8.89939e8	0.0951796
$707$	−4.90659e9	−0.522170
$708$	−6.26039e8	−0.0662956
$709$	4.66010e9	0.491059	0.245530	−	0.969389i	$-0.421038\pi$
$709$	4.66010e9	0.491059	0.245530	+	0.969389i	$0.421038\pi$
$710$	−3.74612e7	−0.00392805
$711$	2.22336e9	0.231989
$712$	−3.07690e9	−0.319473
$713$	6.59338e9	0.681232
$714$	2.65646e9	0.273123
$715$	−9.06386e7	−0.00927346
$716$	1.90566e9	0.194021
$717$	−2.44691e9	−0.247914
$718$	6.19440e9	0.624544
$719$	−2.36164e9	−0.236954	−0.118477	−	0.992957i	$-0.537801\pi$
$719$	−2.36164e9	−0.236954	−0.118477	+	0.992957i	$0.537801\pi$
$720$	−2.07019e8	−0.0206703
$721$	−2.67808e9	−0.266103
$722$	−1.03531e9	−0.102374
$723$	6.00417e9	0.590839
$724$	−6.11140e9	−0.598488
$725$	−2.02831e9	−0.197675
$726$	1.35513e9	0.131432
$727$	2.97525e9	0.287180	0.143590	−	0.989637i	$-0.454135\pi$
$727$	2.97525e9	0.287180	0.143590	+	0.989637i	$0.454135\pi$
$728$	3.65790e8	0.0351376
$729$	3.87420e8	0.0370370
$730$	−1.16164e8	−0.0110520
$731$	−6.58201e8	−0.0623229
$732$	−1.08008e9	−0.101781
$733$	−1.37632e10	−1.29079	−0.645397	−	0.763848i	$-0.723308\pi$
$733$	−1.37632e10	−1.29079	−0.645397	+	0.763848i	$0.723308\pi$
$734$	1.54617e9	0.144318
$735$	−2.89475e8	−0.0268909
$736$	3.43848e9	0.317903
$737$	−2.58796e10	−2.38134
$738$	−9.02436e8	−0.0826455
$739$	1.14115e10	1.04013	0.520064	−	0.854127i	$-0.325908\pi$
$739$	1.14115e10	1.04013	0.520064	+	0.854127i	$0.325908\pi$
$740$	−9.79266e8	−0.0888362
$741$	−5.57589e8	−0.0503443
$742$	−3.46400e9	−0.311290
$743$	5.94931e9	0.532115	0.266057	−	0.963957i	$-0.414279\pi$
$743$	5.94931e9	0.532115	0.266057	+	0.963957i	$0.414279\pi$
$744$	7.84500e9	0.698373
$745$	1.25333e9	0.111050
$746$	−5.25509e9	−0.463441
$747$	−6.12138e9	−0.537313
$748$	−2.52449e10	−2.20556
$749$	−7.15422e9	−0.622123
$750$	4.28702e8	0.0371057
$751$	−7.58856e9	−0.653762	−0.326881	−	0.945066i	$-0.605998\pi$
$751$	−7.58856e9	−0.653762	−0.326881	+	0.945066i	$0.605998\pi$
$752$	8.26865e9	0.709043
$753$	−1.27279e10	−1.08636
$754$	6.17164e7	0.00524326
$755$	−4.51569e8	−0.0381865
$756$	−1.43209e9	−0.120543
$757$	−1.43522e10	−1.20250	−0.601248	−	0.799063i	$-0.705329\pi$
$757$	−1.43522e10	−1.20250	−0.601248	+	0.799063i	$0.705329\pi$
$758$	−6.58698e9	−0.549343
$759$	−3.26508e9	−0.271049
$760$	8.37538e8	0.0692081
$761$	−5.32785e9	−0.438233	−0.219117	−	0.975699i	$-0.570318\pi$
$761$	−5.32785e9	−0.438233	−0.219117	+	0.975699i	$0.570318\pi$
$762$	1.46650e9	0.120071
$763$	−5.30260e9	−0.432169
$764$	9.87614e9	0.801236
$765$	7.52132e8	0.0607406
$766$	7.39602e9	0.594563
$767$	1.24516e8	0.00996419
$768$	−1.27512e8	−0.0101575
$769$	8.89088e9	0.705022	0.352511	−	0.935808i	$-0.385328\pi$
$769$	8.89088e9	0.705022	0.352511	+	0.935808i	$0.385328\pi$
$770$	3.74433e8	0.0295567
$771$	1.85111e8	0.0145459
$772$	9.23517e9	0.722411
$773$	−2.40093e10	−1.86961	−0.934807	−	0.355155i	$-0.884428\pi$
$773$	−2.40093e10	−1.86961	−0.934807	+	0.355155i	$0.884428\pi$
$774$	−4.74693e7	−0.00367976
$775$	2.40327e10	1.85458
$776$	7.92071e9	0.608483
$777$	−5.74673e9	−0.439488
$778$	6.42959e9	0.489502
$779$	−1.08501e10	−0.822343
$780$	4.85371e7	0.00366220
$781$	2.08917e9	0.156926
$782$	−3.24331e9	−0.242529
$783$	−5.15570e8	−0.0383814
$784$	−4.41380e9	−0.327120
$785$	6.66525e8	0.0491782
$786$	1.77758e9	0.130572
$787$	1.74554e10	1.27649	0.638246	−	0.769833i	$-0.279660\pi$
$787$	1.74554e10	1.27649	0.638246	+	0.769833i	$0.279660\pi$
$788$	2.17095e10	1.58055
$789$	1.22089e10	0.884925
$790$	3.11298e8	0.0224637
$791$	1.20552e10	0.866075
$792$	−3.88488e9	−0.277869
$793$	2.14823e8	0.0152976
$794$	6.85667e9	0.486118
$795$	−9.80775e8	−0.0692284
$796$	1.63629e8	0.0114991
$797$	−2.13622e10	−1.49466	−0.747329	−	0.664454i	$-0.768664\pi$
$797$	−2.13622e10	−1.49466	−0.747329	+	0.664454i	$0.768664\pi$
$798$	2.30343e9	0.160459
$799$	−3.00413e10	−2.08355
$800$	1.25331e10	0.865456
$801$	−2.39594e9	−0.164726
$802$	−3.65363e9	−0.250101
$803$	6.47831e9	0.441527
$804$	1.38585e10	0.940419
$805$	−3.59583e8	−0.0242948
$806$	−7.31254e8	−0.0491921
$807$	−1.70572e9	−0.114248
$808$	7.12770e9	0.475346
$809$	−8.12776e9	−0.539698	−0.269849	−	0.962903i	$-0.586974\pi$
$809$	−8.12776e9	−0.539698	−0.269849	+	0.962903i	$0.586974\pi$
$810$	5.42436e7	0.00358633
$811$	−4.71482e9	−0.310379	−0.155190	−	0.987885i	$-0.549599\pi$
$811$	−4.71482e9	−0.310379	−0.155190	+	0.987885i	$0.549599\pi$
$812$	1.90578e9	0.124919
$813$	−1.56658e10	−1.02243
$814$	−7.30601e9	−0.474783
$815$	−1.66513e9	−0.107745
$816$	1.14682e10	0.738892
$817$	−5.70730e8	−0.0366145
$818$	3.67841e9	0.234976
$819$	2.84835e8	0.0181176
$820$	9.44483e8	0.0598199
$821$	−1.97226e10	−1.24383	−0.621917	−	0.783083i	$-0.713646\pi$
$821$	−1.97226e10	−1.24383	−0.621917	+	0.783083i	$0.713646\pi$
$822$	−2.61151e9	−0.163999
$823$	1.20133e9	0.0751215	0.0375608	−	0.999294i	$-0.488041\pi$
$823$	1.20133e9	0.0751215	0.0375608	+	0.999294i	$0.488041\pi$
$824$	3.89040e9	0.242242
$825$	−1.19011e10	−0.737901
$826$	−5.14383e8	−0.0317583
$827$	8.23556e9	0.506319	0.253159	−	0.967425i	$-0.418530\pi$
$827$	8.23556e9	0.506319	0.253159	+	0.967425i	$0.418530\pi$
$828$	1.74845e9	0.107040
$829$	3.37482e9	0.205736	0.102868	−	0.994695i	$-0.467198\pi$
$829$	3.37482e9	0.205736	0.102868	+	0.994695i	$0.467198\pi$
$830$	−8.57067e8	−0.0520285
$831$	−5.63641e9	−0.340721
$832$	4.57731e8	0.0275536
$833$	1.60360e10	0.961255
$834$	−6.20226e9	−0.370228
$835$	9.67020e8	0.0574821
$836$	−2.18900e10	−1.29576
$837$	6.10878e9	0.360094
$838$	3.10735e9	0.182405
$839$	2.19151e10	1.28108	0.640540	−	0.767925i	$-0.278711\pi$
$839$	2.19151e10	1.28108	0.640540	+	0.767925i	$0.278711\pi$
$840$	−4.27843e8	−0.0249061
$841$	−1.65638e10	−0.960225
$842$	6.60375e9	0.381240
$843$	1.82292e9	0.104803
$844$	2.42305e10	1.38728
$845$	1.63836e9	0.0934140
$846$	−2.16657e9	−0.123020
$847$	−8.32297e9	−0.470637
$848$	−1.49545e10	−0.842145
$849$	−1.47996e10	−0.829988
$850$	−1.18217e10	−0.660260
$851$	7.01627e9	0.390259
$852$	−1.11875e9	−0.0619719
$853$	−2.68331e10	−1.48030	−0.740148	−	0.672444i	$-0.765245\pi$
$853$	−2.68331e10	−1.48030	−0.740148	+	0.672444i	$0.765245\pi$
$854$	−8.87446e8	−0.0487573
$855$	6.52178e8	0.0356849
$856$	1.03928e10	0.566336
$857$	−3.79081e9	−0.205731	−0.102865	−	0.994695i	$-0.532801\pi$
$857$	−3.79081e9	−0.205731	−0.102865	+	0.994695i	$0.532801\pi$
$858$	3.62121e8	0.0195726
$859$	−1.08182e10	−0.582342	−0.291171	−	0.956671i	$-0.594045\pi$
$859$	−1.08182e10	−0.582342	−0.291171	+	0.956671i	$0.594045\pi$
$860$	4.96810e7	0.00266346
$861$	5.54260e9	0.295939
$862$	−6.50053e9	−0.345679
$863$	−2.34587e10	−1.24241	−0.621206	−	0.783647i	$-0.713357\pi$
$863$	−2.34587e10	−1.24241	−0.621206	+	0.783647i	$0.713357\pi$
$864$	3.18576e9	0.168041
$865$	1.65441e9	0.0869133
$866$	−7.12655e9	−0.372878
$867$	−3.05867e10	−1.59392
$868$	−2.25809e10	−1.17198
$869$	−1.73607e10	−0.897426
$870$	−7.21860e7	−0.00371651
$871$	−2.75640e9	−0.141344
$872$	7.70299e9	0.393415
$873$	6.16774e9	0.313745
$874$	−2.81229e9	−0.142485
$875$	−2.63301e9	−0.132869
$876$	−3.46915e9	−0.174365
$877$	3.42071e10	1.71245	0.856224	−	0.516605i	$-0.172805\pi$
$877$	3.42071e10	1.71245	0.856224	+	0.516605i	$0.172805\pi$
$878$	3.21390e9	0.160251
$879$	−6.38900e9	−0.317302
$880$	1.61647e9	0.0799611
$881$	−5.54512e9	−0.273209	−0.136605	−	0.990626i	$-0.543619\pi$
$881$	−5.54512e9	−0.273209	−0.136605	+	0.990626i	$0.543619\pi$
$882$	1.15651e9	0.0567558
$883$	1.95899e10	0.957568	0.478784	−	0.877933i	$-0.341078\pi$
$883$	1.95899e10	0.957568	0.478784	+	0.877933i	$0.341078\pi$
$884$	−2.68881e9	−0.130911
$885$	−1.45639e8	−0.00706280
$886$	−1.74707e9	−0.0843904
$887$	2.41962e10	1.16416	0.582081	−	0.813131i	$-0.302238\pi$
$887$	2.41962e10	1.16416	0.582081	+	0.813131i	$0.302238\pi$
$888$	8.34816e9	0.400078
$889$	−9.00695e9	−0.429954
$890$	−3.35460e8	−0.0159506
$891$	−3.02510e9	−0.143274
$892$	2.32110e10	1.09501
$893$	−2.60489e10	−1.22408
$894$	−5.00731e9	−0.234382
$895$	4.43324e8	0.0206700
$896$	−1.52423e10	−0.707902
$897$	−3.47759e8	−0.0160881
$898$	4.92254e9	0.226841
$899$	−8.12941e9	−0.373164
$900$	6.37305e9	0.291406
$901$	5.43320e10	2.47468
$902$	7.04650e9	0.319706
$903$	2.91548e8	0.0131766
$904$	−1.75123e10	−0.788412
$905$	−1.42173e9	−0.0637599
$906$	1.80412e9	0.0805964
$907$	−1.77861e10	−0.791510	−0.395755	−	0.918356i	$-0.629517\pi$
$907$	−1.77861e10	−0.791510	−0.395755	+	0.918356i	$0.629517\pi$
$908$	−2.11125e10	−0.935919
$909$	5.55023e9	0.245097
$910$	3.98804e7	0.00175434
$911$	−3.79625e10	−1.66357	−0.831783	−	0.555101i	$-0.812680\pi$
$911$	−3.79625e10	−1.66357	−0.831783	+	0.555101i	$0.812680\pi$
$912$	9.94417e9	0.434097
$913$	4.77976e10	2.07854
$914$	1.01560e9	0.0439956
$915$	−2.51266e8	−0.0108432
$916$	−1.14524e10	−0.492337
$917$	−1.09176e10	−0.467556
$918$	−3.00493e9	−0.128199
$919$	−4.00064e10	−1.70030	−0.850149	−	0.526543i	$-0.823488\pi$
$919$	−4.00064e10	−1.70030	−0.850149	+	0.526543i	$0.823488\pi$
$920$	5.22359e8	0.0221163
$921$	7.67195e8	0.0323591
$922$	1.01334e10	0.425791
$923$	2.22514e8	0.00931434
$924$	1.11822e10	0.466309
$925$	2.55740e10	1.06244
$926$	−1.19311e10	−0.493790
$927$	3.02939e9	0.124904
$928$	−4.23953e9	−0.174140
$929$	−4.55114e10	−1.86237	−0.931183	−	0.364552i	$-0.881222\pi$
$929$	−4.55114e10	−1.86237	−0.931183	+	0.364552i	$0.881222\pi$
$930$	8.55304e8	0.0348682
$931$	1.39049e10	0.564735
$932$	2.23994e10	0.906319
$933$	−1.04357e10	−0.420663
$934$	1.12667e10	0.452461
$935$	−5.87288e9	−0.234969
$936$	−4.13774e8	−0.0164929
$937$	3.78655e9	0.150368	0.0751839	−	0.997170i	$-0.476046\pi$
$937$	3.78655e9	0.150368	0.0751839	+	0.997170i	$0.476046\pi$
$938$	1.13868e10	0.450498
$939$	−2.10388e10	−0.829260
$940$	2.26751e9	0.0890435
$941$	−9.78869e9	−0.382966	−0.191483	−	0.981496i	$-0.561330\pi$
$941$	−9.78869e9	−0.382966	−0.191483	+	0.981496i	$0.561330\pi$
$942$	−2.66291e9	−0.103796
$943$	−6.76705e9	−0.262790
$944$	−2.22065e9	−0.0859170
$945$	−3.33155e8	−0.0128421
$946$	3.70655e8	0.0142348
$947$	3.55199e10	1.35909	0.679543	−	0.733635i	$-0.262178\pi$
$947$	3.55199e10	1.35909	0.679543	+	0.733635i	$0.262178\pi$
$948$	9.29669e9	0.354405
$949$	6.89997e8	0.0262069
$950$	−1.02507e10	−0.387901
$951$	1.08610e10	0.409486
$952$	2.37012e10	0.890309
$953$	−1.87406e9	−0.0701389	−0.0350695	−	0.999385i	$-0.511165\pi$
$953$	−1.87406e9	−0.0701389	−0.0350695	+	0.999385i	$0.511165\pi$
$954$	3.91841e9	0.146114
$955$	2.29755e9	0.0853596
$956$	−1.02314e10	−0.378733
$957$	4.02573e9	0.148475
$958$	1.05767e10	0.388661
$959$	1.60394e10	0.587251
$960$	−5.35380e8	−0.0195305
$961$	6.88096e10	2.50102
$962$	−7.78154e8	−0.0281808
$963$	8.09271e9	0.292013
$964$	2.51056e10	0.902612
$965$	2.14843e9	0.0769620
$966$	1.43661e9	0.0512767
$967$	2.52830e10	0.899158	0.449579	−	0.893241i	$-0.351574\pi$
$967$	2.52830e10	0.899158	0.449579	+	0.893241i	$0.351574\pi$
$968$	1.20906e10	0.428434
$969$	−3.61287e10	−1.27561
$970$	8.63559e8	0.0303802
$971$	2.33470e10	0.818396	0.409198	−	0.912446i	$-0.365808\pi$
$971$	2.33470e10	0.818396	0.409198	+	0.912446i	$0.365808\pi$
$972$	1.61995e9	0.0565807
$973$	3.80932e10	1.32572
$974$	1.62466e10	0.563385
$975$	−1.26757e9	−0.0437982
$976$	−3.83121e9	−0.131905
$977$	−3.73874e9	−0.128261	−0.0641304	−	0.997942i	$-0.520427\pi$
$977$	−3.73874e9	−0.128261	−0.0641304	+	0.997942i	$0.520427\pi$
$978$	6.65256e9	0.227406
$979$	1.87082e10	0.637225
$980$	−1.21040e9	−0.0410806
$981$	5.99820e9	0.202852
$982$	−4.51716e9	−0.152221
$983$	−4.06366e10	−1.36452	−0.682261	−	0.731109i	$-0.739003\pi$
$983$	−4.06366e10	−1.36452	−0.682261	+	0.731109i	$0.739003\pi$
$984$	−8.05163e9	−0.269402
$985$	5.05041e9	0.168384
$986$	3.99889e9	0.132853
$987$	1.33067e10	0.440514
$988$	−2.33148e9	−0.0769099
$989$	−3.55956e8	−0.0117006
$990$	−4.23551e8	−0.0138734
$991$	2.46369e10	0.804134	0.402067	−	0.915610i	$-0.368292\pi$
$991$	2.46369e10	0.804134	0.402067	+	0.915610i	$0.368292\pi$
$992$	5.02325e10	1.63378
$993$	1.63735e10	0.530663
$994$	−9.19219e8	−0.0296870
$995$	3.80660e7	0.00122506
$996$	−2.55957e10	−0.820841
$997$	−1.08445e10	−0.346558	−0.173279	−	0.984873i	$-0.555436\pi$
$997$	−1.08445e10	−0.346558	−0.173279	+	0.984873i	$0.555436\pi$
$998$	9.56186e9	0.304499
$999$	6.50058e9	0.206288

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.c.1.8	✓	17
3.2	odd	2		531.8.a.c.1.10		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.8	✓	17	1.1	even	1	trivial
531.8.a.c.1.10		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)

\(f(q)\)	\(=\)	\(q-3.88629 q^{2} -27.0000 q^{3} -112.897 q^{4} -26.2639 q^{5} +104.930 q^{6} -644.460 q^{7} +936.194 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-3.88629 q^{2} -27.0000 q^{3} -112.897 q^{4} -26.2639 q^{5} +104.930 q^{6} -644.460 q^{7} +936.194 q^{8} +729.000 q^{9} +102.069 q^{10} -5692.26 q^{11} +3048.21 q^{12} -606.275 q^{13} +2504.56 q^{14} +709.124 q^{15} +10812.5 q^{16} -39283.3 q^{17} -2833.10 q^{18} -34062.8 q^{19} +2965.10 q^{20} +17400.4 q^{21} +22121.8 q^{22} -21244.4 q^{23} -25277.2 q^{24} -77435.2 q^{25} +2356.16 q^{26} -19683.0 q^{27} +72757.5 q^{28} +26193.7 q^{29} -2755.86 q^{30} -310358. q^{31} -161853. q^{32} +153691. q^{33} +152666. q^{34} +16926.0 q^{35} -82301.7 q^{36} -330264. q^{37} +132378. q^{38} +16369.4 q^{39} -24588.1 q^{40} +318533. q^{41} -67623.0 q^{42} +16755.2 q^{43} +642638. q^{44} -19146.3 q^{45} +82562.0 q^{46} +764733. q^{47} -291937. q^{48} -408214. q^{49} +300935. q^{50} +1.06065e6 q^{51} +68446.5 q^{52} -1.38308e6 q^{53} +76493.8 q^{54} +149501. q^{55} -603340. q^{56} +919695. q^{57} -101796. q^{58} -205379. q^{59} -80057.8 q^{60} -354332. q^{61} +1.20614e6 q^{62} -469811. q^{63} -754988. q^{64} +15923.1 q^{65} -597287. q^{66} +4.54645e6 q^{67} +4.43496e6 q^{68} +573600. q^{69} -65779.3 q^{70} -367019. q^{71} +682485. q^{72} -1.13809e6 q^{73} +1.28350e6 q^{74} +2.09075e6 q^{75} +3.84558e6 q^{76} +3.66843e6 q^{77} -63616.3 q^{78} +3.04988e6 q^{79} -283977. q^{80} +531441. q^{81} -1.23791e6 q^{82} -8.39695e6 q^{83} -1.96445e6 q^{84} +1.03173e6 q^{85} -65115.7 q^{86} -707229. q^{87} -5.32906e6 q^{88} -3.28661e6 q^{89} +74408.2 q^{90} +390720. q^{91} +2.39843e6 q^{92} +8.37967e6 q^{93} -2.97197e6 q^{94} +894620. q^{95} +4.37004e6 q^{96} +8.46055e6 q^{97} +1.58644e6 q^{98} -4.14966e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9}+O(q^{10}) \) 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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