LMFDB - Embedded newform 177.8.a.d.1.13

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:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + \cdots + 51\!\cdots\!48 $ x^18 - 6x^17 - 1798x^16 + 11087x^15 + 1326765x^14 - 8403720x^13 - 518334228x^12 + 3375594921x^11 + 115310342333x^10 - 774932111214x^9 - 14600047830166x^8 + 102185027148481x^7 + 988557475638619x^6 - 7379206238519716x^5 - 30152342836849520x^4 + 260578770749067175x^3 + 182609347488069978x^2 - 3481290425710753600*x + 5164646074739714048
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$9.20800$ 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)

$f(q)$	$=$	$q+10.2080 q^{2} +27.0000 q^{3} -23.7967 q^{4} -397.678 q^{5} +275.616 q^{6} -505.577 q^{7} -1549.54 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+10.2080 q^{2} +27.0000 q^{3} -23.7967 q^{4} -397.678 q^{5} +275.616 q^{6} -505.577 q^{7} -1549.54 q^{8} +729.000 q^{9} -4059.50 q^{10} -5491.59 q^{11} -642.512 q^{12} +5262.48 q^{13} -5160.93 q^{14} -10737.3 q^{15} -12771.7 q^{16} +33639.9 q^{17} +7441.63 q^{18} +41812.3 q^{19} +9463.44 q^{20} -13650.6 q^{21} -56058.1 q^{22} -14742.3 q^{23} -41837.6 q^{24} +80022.8 q^{25} +53719.4 q^{26} +19683.0 q^{27} +12031.1 q^{28} +192269. q^{29} -109606. q^{30} -222873. q^{31} +67967.4 q^{32} -148273. q^{33} +343396. q^{34} +201057. q^{35} -17347.8 q^{36} +319803. q^{37} +426820. q^{38} +142087. q^{39} +616218. q^{40} -210002. q^{41} -139345. q^{42} -197848. q^{43} +130682. q^{44} -289907. q^{45} -150490. q^{46} +1.24221e6 q^{47} -344837. q^{48} -567935. q^{49} +816873. q^{50} +908276. q^{51} -125230. q^{52} -346356. q^{53} +200924. q^{54} +2.18388e6 q^{55} +783412. q^{56} +1.12893e6 q^{57} +1.96269e6 q^{58} +205379. q^{59} +255513. q^{60} -2.78811e6 q^{61} -2.27509e6 q^{62} -368566. q^{63} +2.32859e6 q^{64} -2.09277e6 q^{65} -1.51357e6 q^{66} -4.61431e6 q^{67} -800519. q^{68} -398043. q^{69} +2.05239e6 q^{70} +1.49916e6 q^{71} -1.12962e6 q^{72} -1.38946e6 q^{73} +3.26455e6 q^{74} +2.16062e6 q^{75} -994997. q^{76} +2.77642e6 q^{77} +1.45042e6 q^{78} +7.13579e6 q^{79} +5.07904e6 q^{80} +531441. q^{81} -2.14370e6 q^{82} +2.03328e6 q^{83} +324839. q^{84} -1.33778e7 q^{85} -2.01963e6 q^{86} +5.19128e6 q^{87} +8.50944e6 q^{88} +5.52152e6 q^{89} -2.95937e6 q^{90} -2.66059e6 q^{91} +350820. q^{92} -6.01757e6 q^{93} +1.26805e7 q^{94} -1.66278e7 q^{95} +1.83512e6 q^{96} +1.50671e7 q^{97} -5.79748e6 q^{98} -4.00337e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) $ 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9} + 3609 q^{10} + 15070 q^{11} + 36666 q^{12} + 13662 q^{13} + 20861 q^{14} + 18306 q^{15} + 60482 q^{16} + 71919 q^{17} + 17496 q^{18} + 56231 q^{19} + 143053 q^{20} + 83187 q^{21} + 274198 q^{22} + 150029 q^{23} + 110889 q^{24} + 399672 q^{25} + 182846 q^{26} + 354294 q^{27} + 434150 q^{28} + 591285 q^{29} + 97443 q^{30} + 426733 q^{31} + 1205630 q^{32} + 406890 q^{33} + 403548 q^{34} + 912879 q^{35} + 989982 q^{36} + 7703 q^{37} - 417859 q^{38} + 368874 q^{39} + 618020 q^{40} + 770959 q^{41} + 563247 q^{42} + 793050 q^{43} + 2591274 q^{44} + 494262 q^{45} - 4068019 q^{46} + 1410373 q^{47} + 1633014 q^{48} + 1637427 q^{49} + 1021549 q^{50} + 1941813 q^{51} - 3749190 q^{52} + 1037934 q^{53} + 472392 q^{54} + 331974 q^{55} - 391748 q^{56} + 1518237 q^{57} + 653724 q^{58} + 3696822 q^{59} + 3862431 q^{60} - 1374623 q^{61} + 5251718 q^{62} + 2246049 q^{63} + 5077197 q^{64} + 3257170 q^{65} + 7403346 q^{66} - 2436904 q^{67} + 14119909 q^{68} + 4050783 q^{69} + 5185580 q^{70} + 14289172 q^{71} + 2994003 q^{72} + 5482515 q^{73} + 14934154 q^{74} + 10791144 q^{75} + 3822912 q^{76} + 23157109 q^{77} + 4936842 q^{78} + 19786414 q^{79} + 31978143 q^{80} + 9565938 q^{81} + 9749509 q^{82} + 30227337 q^{83} + 11722050 q^{84} + 9946981 q^{85} + 44295864 q^{86} + 15964695 q^{87} + 39970897 q^{88} + 31061677 q^{89} + 2630961 q^{90} + 26377785 q^{91} + 4719698 q^{92} + 11521791 q^{93} + 44488296 q^{94} + 15534599 q^{95} + 32552010 q^{96} + 12084118 q^{97} + 42274744 q^{98} + 10986030 q^{99}+O(q^{100}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9 + 3609 * q^10 + 15070 * q^11 + 36666 * q^12 + 13662 * q^13 + 20861 * q^14 + 18306 * q^15 + 60482 * q^16 + 71919 * q^17 + 17496 * q^18 + 56231 * q^19 + 143053 * q^20 + 83187 * q^21 + 274198 * q^22 + 150029 * q^23 + 110889 * q^24 + 399672 * q^25 + 182846 * q^26 + 354294 * q^27 + 434150 * q^28 + 591285 * q^29 + 97443 * q^30 + 426733 * q^31 + 1205630 * q^32 + 406890 * q^33 + 403548 * q^34 + 912879 * q^35 + 989982 * q^36 + 7703 * q^37 - 417859 * q^38 + 368874 * q^39 + 618020 * q^40 + 770959 * q^41 + 563247 * q^42 + 793050 * q^43 + 2591274 * q^44 + 494262 * q^45 - 4068019 * q^46 + 1410373 * q^47 + 1633014 * q^48 + 1637427 * q^49 + 1021549 * q^50 + 1941813 * q^51 - 3749190 * q^52 + 1037934 * q^53 + 472392 * q^54 + 331974 * q^55 - 391748 * q^56 + 1518237 * q^57 + 653724 * q^58 + 3696822 * q^59 + 3862431 * q^60 - 1374623 * q^61 + 5251718 * q^62 + 2246049 * q^63 + 5077197 * q^64 + 3257170 * q^65 + 7403346 * q^66 - 2436904 * q^67 + 14119909 * q^68 + 4050783 * q^69 + 5185580 * q^70 + 14289172 * q^71 + 2994003 * q^72 + 5482515 * q^73 + 14934154 * q^74 + 10791144 * q^75 + 3822912 * q^76 + 23157109 * q^77 + 4936842 * q^78 + 19786414 * q^79 + 31978143 * q^80 + 9565938 * q^81 + 9749509 * q^82 + 30227337 * q^83 + 11722050 * q^84 + 9946981 * q^85 + 44295864 * q^86 + 15964695 * q^87 + 39970897 * q^88 + 31061677 * q^89 + 2630961 * q^90 + 26377785 * q^91 + 4719698 * q^92 + 11521791 * q^93 + 44488296 * q^94 + 15534599 * q^95 + 32552010 * q^96 + 12084118 * q^97 + 42274744 * q^98 + 10986030 * 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 $

$2$	10.2080	0.902268	0.451134	−	0.892456i	$-0.351020\pi$
$2$	10.2080	0.902268	0.451134	+	0.892456i	$0.351020\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	−23.7967	−0.185912
$5$	−397.678	−1.42278	−0.711388	−	0.702799i	$-0.751933\pi$
$5$	−397.678	−1.42278	−0.711388	+	0.702799i	$0.751933\pi$
$6$	275.616	0.520925
$7$	−505.577	−0.557114	−0.278557	−	0.960420i	$-0.589856\pi$
$7$	−505.577	−0.557114	−0.278557	+	0.960420i	$0.589856\pi$
$8$	−1549.54	−1.07001
$9$	729.000	0.333333
$10$	−4059.50	−1.28373
$11$	−5491.59	−1.24401	−0.622004	−	0.783014i	$-0.713681\pi$
$11$	−5491.59	−1.24401	−0.622004	+	0.783014i	$0.713681\pi$
$12$	−642.512	−0.107336
$13$	5262.48	0.664338	0.332169	−	0.943220i	$-0.392220\pi$
$13$	5262.48	0.664338	0.332169	+	0.943220i	$0.392220\pi$
$14$	−5160.93	−0.502666
$15$	−10737.3	−0.821440
$16$	−12771.7	−0.779525
$17$	33639.9	1.66067	0.830334	−	0.557265i	$-0.188149\pi$
$17$	33639.9	1.66067	0.830334	+	0.557265i	$0.188149\pi$
$18$	7441.63	0.300756
$19$	41812.3	1.39851	0.699257	−	0.714871i	$-0.253514\pi$
$19$	41812.3	1.39851	0.699257	+	0.714871i	$0.253514\pi$
$20$	9463.44	0.264511
$21$	−13650.6	−0.321650
$22$	−56058.1	−1.12243
$23$	−14742.3	−0.252650	−0.126325	−	0.991989i	$-0.540318\pi$
$23$	−14742.3	−0.252650	−0.126325	+	0.991989i	$0.540318\pi$
$24$	−41837.6	−0.617771
$25$	80022.8	1.02429
$26$	53719.4	0.599411
$27$	19683.0	0.192450
$28$	12031.1	0.103574
$29$	192269.	1.46392	0.731960	−	0.681348i	$-0.238606\pi$
$29$	192269.	1.46392	0.731960	+	0.681348i	$0.238606\pi$
$30$	−109606.	−0.741159
$31$	−222873.	−1.34367	−0.671833	−	0.740703i	$-0.734493\pi$
$31$	−222873.	−1.34367	−0.671833	+	0.740703i	$0.734493\pi$
$32$	67967.4	0.366670
$33$	−148273.	−0.718229
$34$	343396.	1.49837
$35$	201057.	0.792648
$36$	−17347.8	−0.0619707
$37$	319803.	1.03795	0.518975	−	0.854789i	$-0.326314\pi$
$37$	319803.	1.03795	0.518975	+	0.854789i	$0.326314\pi$
$38$	426820.	1.26183
$39$	142087.	0.383556
$40$	616218.	1.52239
$41$	−210002.	−0.475861	−0.237930	−	0.971282i	$-0.576469\pi$
$41$	−210002.	−0.475861	−0.237930	+	0.971282i	$0.576469\pi$
$42$	−139345.	−0.290214
$43$	−197848.	−0.379483	−0.189741	−	0.981834i	$-0.560765\pi$
$43$	−197848.	−0.379483	−0.189741	+	0.981834i	$0.560765\pi$
$44$	130682.	0.231276
$45$	−289907.	−0.474259
$46$	−150490.	−0.227958
$47$	1.24221e6	1.74523	0.872614	−	0.488410i	$-0.162423\pi$
$47$	1.24221e6	1.74523	0.872614	+	0.488410i	$0.162423\pi$
$48$	−344837.	−0.450059
$49$	−567935.	−0.689624
$50$	816873.	0.924186
$51$	908276.	0.958788
$52$	−125230.	−0.123508
$53$	−346356.	−0.319564	−0.159782	−	0.987152i	$-0.551079\pi$
$53$	−346356.	−0.319564	−0.159782	+	0.987152i	$0.551079\pi$
$54$	200924.	0.173642
$55$	2.18388e6	1.76995
$56$	783412.	0.596118
$57$	1.12893e6	0.807432
$58$	1.96269e6	1.32085
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	255513.	0.152716
$61$	−2.78811e6	−1.57274	−0.786368	−	0.617758i	$-0.788041\pi$
$61$	−2.78811e6	−1.57274	−0.786368	+	0.617758i	$0.788041\pi$
$62$	−2.27509e6	−1.21235
$63$	−368566.	−0.185705
$64$	2.32859e6	1.11036
$65$	−2.09277e6	−0.945204
$66$	−1.51357e6	−0.648035
$67$	−4.61431e6	−1.87432	−0.937162	−	0.348895i	$-0.886557\pi$
$67$	−4.61431e6	−1.87432	−0.937162	+	0.348895i	$0.886557\pi$
$68$	−800519.	−0.308738
$69$	−398043.	−0.145868
$70$	2.05239e6	0.715181
$71$	1.49916e6	0.497101	0.248550	−	0.968619i	$-0.420046\pi$
$71$	1.49916e6	0.497101	0.248550	+	0.968619i	$0.420046\pi$
$72$	−1.12962e6	−0.356670
$73$	−1.38946e6	−0.418039	−0.209019	−	0.977911i	$-0.567027\pi$
$73$	−1.38946e6	−0.418039	−0.209019	+	0.977911i	$0.567027\pi$
$74$	3.26455e6	0.936510
$75$	2.16062e6	0.591375
$76$	−994997.	−0.260000
$77$	2.77642e6	0.693055
$78$	1.45042e6	0.346070
$79$	7.13579e6	1.62835	0.814174	−	0.580621i	$-0.197190\pi$
$79$	7.13579e6	1.62835	0.814174	+	0.580621i	$0.197190\pi$
$80$	5.07904e6	1.10909
$81$	531441.	0.111111
$82$	−2.14370e6	−0.429354
$83$	2.03328e6	0.390322	0.195161	−	0.980771i	$-0.437477\pi$
$83$	2.03328e6	0.390322	0.195161	+	0.980771i	$0.437477\pi$
$84$	324839.	0.0597986
$85$	−1.33778e7	−2.36276
$86$	−2.01963e6	−0.342395
$87$	5.19128e6	0.845195
$88$	8.50944e6	1.33110
$89$	5.52152e6	0.830222	0.415111	−	0.909771i	$-0.363743\pi$
$89$	5.52152e6	0.830222	0.415111	+	0.909771i	$0.363743\pi$
$90$	−2.95937e6	−0.427909
$91$	−2.66059e6	−0.370112
$92$	350820.	0.0469707
$93$	−6.01757e6	−0.775766
$94$	1.26805e7	1.57466
$95$	−1.66278e7	−1.98977
$96$	1.83512e6	0.211697
$97$	1.50671e7	1.67621	0.838103	−	0.545512i	$-0.183665\pi$
$97$	1.50671e7	1.67621	0.838103	+	0.545512i	$0.183665\pi$
$98$	−5.79748e6	−0.622226
$99$	−4.00337e6	−0.414670
$100$	−1.90428e6	−0.190428
$101$	−7.10580e6	−0.686260	−0.343130	−	0.939288i	$-0.611487\pi$
$101$	−7.10580e6	−0.686260	−0.343130	+	0.939288i	$0.611487\pi$
$102$	9.27168e6	0.865084
$103$	5.41858e6	0.488602	0.244301	−	0.969699i	$-0.421442\pi$
$103$	5.41858e6	0.488602	0.244301	+	0.969699i	$0.421442\pi$
$104$	−8.15444e6	−0.710849
$105$	5.42853e6	0.457636
$106$	−3.53560e6	−0.288332
$107$	1.98181e7	1.56393	0.781967	−	0.623320i	$-0.214216\pi$
$107$	1.98181e7	1.56393	0.781967	+	0.623320i	$0.214216\pi$
$108$	−468391.	−0.0357788
$109$	9.80363e6	0.725094	0.362547	−	0.931966i	$-0.381907\pi$
$109$	9.80363e6	0.725094	0.362547	+	0.931966i	$0.381907\pi$
$110$	2.22931e7	1.59697
$111$	8.63468e6	0.599261
$112$	6.45709e6	0.434284
$113$	−1.24028e7	−0.808624	−0.404312	−	0.914621i	$-0.632489\pi$
$113$	−1.24028e7	−0.808624	−0.404312	+	0.914621i	$0.632489\pi$
$114$	1.15241e7	0.728520
$115$	5.86271e6	0.359464
$116$	−4.57539e6	−0.272160
$117$	3.83635e6	0.221446
$118$	2.09651e6	0.117465
$119$	−1.70075e7	−0.925182
$120$	1.66379e7	0.878950
$121$	1.06704e7	0.547558
$122$	−2.84611e7	−1.41903
$123$	−5.67005e6	−0.274738
$124$	5.30365e6	0.249804
$125$	−754706.	−0.0345615
$126$	−3.76232e6	−0.167555
$127$	9.12926e6	0.395478	0.197739	−	0.980255i	$-0.436640\pi$
$127$	9.12926e6	0.395478	0.197739	+	0.980255i	$0.436640\pi$
$128$	1.50705e7	0.635172
$129$	−5.34190e6	−0.219095
$130$	−2.13630e7	−0.852828
$131$	1.91545e7	0.744426	0.372213	−	0.928147i	$-0.378599\pi$
$131$	1.91545e7	0.744426	0.372213	+	0.928147i	$0.378599\pi$
$132$	3.52841e6	0.133527
$133$	−2.11393e7	−0.779131
$134$	−4.71028e7	−1.69114
$135$	−7.82750e6	−0.273813
$136$	−5.21264e7	−1.77693
$137$	−1.11699e7	−0.371132	−0.185566	−	0.982632i	$-0.559412\pi$
$137$	−1.11699e7	−0.371132	−0.185566	+	0.982632i	$0.559412\pi$
$138$	−4.06323e6	−0.131612
$139$	4.22972e7	1.33586	0.667928	−	0.744226i	$-0.267182\pi$
$139$	4.22972e7	1.33586	0.667928	+	0.744226i	$0.267182\pi$
$140$	−4.78449e6	−0.147363
$141$	3.35397e7	1.00761
$142$	1.53035e7	0.448518
$143$	−2.88994e7	−0.826442
$144$	−9.31059e6	−0.259842
$145$	−7.64613e7	−2.08283
$146$	−1.41836e7	−0.377183
$147$	−1.53342e7	−0.398155
$148$	−7.61027e6	−0.192967
$149$	5.92562e7	1.46751	0.733757	−	0.679412i	$-0.237765\pi$
$149$	5.92562e7	1.46751	0.733757	+	0.679412i	$0.237765\pi$
$150$	2.20556e7	0.533579
$151$	7.21512e7	1.70539	0.852697	−	0.522406i	$-0.174966\pi$
$151$	7.21512e7	1.70539	0.852697	+	0.522406i	$0.174966\pi$
$152$	−6.47899e7	−1.49642
$153$	2.45235e7	0.553556
$154$	2.83417e7	0.625321
$155$	8.86316e7	1.91174
$156$	−3.38121e6	−0.0713076
$157$	−5.11820e7	−1.05552	−0.527762	−	0.849392i	$-0.676969\pi$
$157$	−5.11820e7	−1.05552	−0.527762	+	0.849392i	$0.676969\pi$
$158$	7.28421e7	1.46921
$159$	−9.35161e6	−0.184500
$160$	−2.70291e7	−0.521690
$161$	7.45339e6	0.140755
$162$	5.42495e6	0.100252
$163$	3.02638e7	0.547352	0.273676	−	0.961822i	$-0.411760\pi$
$163$	3.02638e7	0.547352	0.273676	+	0.961822i	$0.411760\pi$
$164$	4.99736e6	0.0884682
$165$	5.89649e7	1.02188
$166$	2.07557e7	0.352175
$167$	5.48855e7	0.911906	0.455953	−	0.890004i	$-0.349298\pi$
$167$	5.48855e7	0.911906	0.455953	+	0.890004i	$0.349298\pi$
$168$	2.11521e7	0.344169
$169$	−3.50548e7	−0.558655
$170$	−1.36561e8	−2.13184
$171$	3.04812e7	0.466171
$172$	4.70814e6	0.0705504
$173$	−9.94511e7	−1.46032	−0.730161	−	0.683276i	$-0.760555\pi$
$173$	−9.94511e7	−1.46032	−0.730161	+	0.683276i	$0.760555\pi$
$174$	5.29925e7	0.762592
$175$	−4.04577e7	−0.570647
$176$	7.01371e7	0.969736
$177$	5.54523e6	0.0751646
$178$	5.63637e7	0.749083
$179$	1.27756e8	1.66493	0.832465	−	0.554078i	$-0.186929\pi$
$179$	1.27756e8	1.66493	0.832465	+	0.554078i	$0.186929\pi$
$180$	6.89885e6	0.0881704
$181$	5.65804e7	0.709237	0.354618	−	0.935011i	$-0.384611\pi$
$181$	5.65804e7	0.709237	0.354618	+	0.935011i	$0.384611\pi$
$182$	−2.71593e7	−0.333940
$183$	−7.52791e7	−0.908020
$184$	2.28439e7	0.270338
$185$	−1.27179e8	−1.47677
$186$	−6.14273e7	−0.699949
$187$	−1.84736e8	−2.06589
$188$	−2.95605e7	−0.324459
$189$	−9.95127e6	−0.107217
$190$	−1.69737e8	−1.79531
$191$	−1.10143e8	−1.14378	−0.571888	−	0.820331i	$-0.693789\pi$
$191$	−1.10143e8	−1.14378	−0.571888	+	0.820331i	$0.693789\pi$
$192$	6.28720e7	0.641066
$193$	8.48163e7	0.849236	0.424618	−	0.905373i	$-0.360408\pi$
$193$	8.48163e7	0.849236	0.424618	+	0.905373i	$0.360408\pi$
$194$	1.53804e8	1.51239
$195$	−5.65049e7	−0.545714
$196$	1.35150e7	0.128209
$197$	8.45072e7	0.787520	0.393760	−	0.919213i	$-0.371174\pi$
$197$	8.45072e7	0.787520	0.393760	+	0.919213i	$0.371174\pi$
$198$	−4.08664e7	−0.374143
$199$	−1.14880e8	−1.03337	−0.516686	−	0.856175i	$-0.672835\pi$
$199$	−1.14880e8	−1.03337	−0.516686	+	0.856175i	$0.672835\pi$
$200$	−1.23999e8	−1.09600
$201$	−1.24586e8	−1.08214
$202$	−7.25360e7	−0.619190
$203$	−9.72070e7	−0.815570
$204$	−2.16140e7	−0.178250
$205$	8.35132e7	0.677043
$206$	5.53129e7	0.440850
$207$	−1.07472e7	−0.0842167
$208$	−6.72110e7	−0.517868
$209$	−2.29616e8	−1.73976
$210$	5.54145e7	0.412910
$211$	−2.23391e8	−1.63711	−0.818555	−	0.574428i	$-0.805225\pi$
$211$	−2.23391e8	−1.63711	−0.818555	+	0.574428i	$0.805225\pi$
$212$	8.24214e6	0.0594107
$213$	4.04774e7	0.287001
$214$	2.02303e8	1.41109
$215$	7.86798e7	0.539919
$216$	−3.04996e7	−0.205924
$217$	1.12679e8	0.748575
$218$	1.00075e8	0.654229
$219$	−3.75155e7	−0.241355
$220$	−5.19693e7	−0.329054
$221$	1.77029e8	1.10325
$222$	8.81428e7	0.540694
$223$	−1.25281e8	−0.756519	−0.378259	−	0.925700i	$-0.623477\pi$
$223$	−1.25281e8	−0.756519	−0.378259	+	0.925700i	$0.623477\pi$
$224$	−3.43627e7	−0.204277
$225$	5.83366e7	0.341431
$226$	−1.26608e8	−0.729596
$227$	−1.69633e7	−0.0962540	−0.0481270	−	0.998841i	$-0.515325\pi$
$227$	−1.69633e7	−0.0962540	−0.0481270	+	0.998841i	$0.515325\pi$
$228$	−2.68649e7	−0.150111
$229$	−9.47495e7	−0.521378	−0.260689	−	0.965423i	$-0.583950\pi$
$229$	−9.47495e7	−0.521378	−0.260689	+	0.965423i	$0.583950\pi$
$230$	5.98465e7	0.324333
$231$	7.49633e7	0.400135
$232$	−2.97929e8	−1.56641
$233$	−1.23601e8	−0.640143	−0.320072	−	0.947393i	$-0.603707\pi$
$233$	−1.23601e8	−0.640143	−0.320072	+	0.947393i	$0.603707\pi$
$234$	3.91615e7	0.199804
$235$	−4.93999e8	−2.48307
$236$	−4.88735e6	−0.0242037
$237$	1.92666e8	0.940127
$238$	−1.73613e8	−0.834762
$239$	1.84669e8	0.874985	0.437493	−	0.899222i	$-0.355867\pi$
$239$	1.84669e8	0.874985	0.437493	+	0.899222i	$0.355867\pi$
$240$	1.37134e8	0.640333
$241$	−3.10641e8	−1.42955	−0.714775	−	0.699354i	$-0.753471\pi$
$241$	−3.10641e8	−1.42955	−0.714775	+	0.699354i	$0.753471\pi$
$242$	1.08923e8	0.494044
$243$	1.43489e7	0.0641500
$244$	6.63480e7	0.292391
$245$	2.25855e8	0.981181
$246$	−5.78799e7	−0.247888
$247$	2.20037e8	0.929086
$248$	3.45351e8	1.43774
$249$	5.48984e7	0.225352
$250$	−7.70404e6	−0.0311838
$251$	1.38239e8	0.551788	0.275894	−	0.961188i	$-0.411026\pi$
$251$	1.38239e8	0.551788	0.275894	+	0.961188i	$0.411026\pi$
$252$	8.77066e6	0.0345247
$253$	8.09589e7	0.314299
$254$	9.31915e7	0.356827
$255$	−3.61202e8	−1.36414
$256$	−1.44221e8	−0.537264
$257$	−1.25743e8	−0.462080	−0.231040	−	0.972944i	$-0.574213\pi$
$257$	−1.25743e8	−0.462080	−0.231040	+	0.972944i	$0.574213\pi$
$258$	−5.45301e7	−0.197682
$259$	−1.61685e8	−0.578257
$260$	4.98012e7	0.175725
$261$	1.40164e8	0.487973
$262$	1.95529e8	0.671672
$263$	−2.91293e8	−0.987380	−0.493690	−	0.869638i	$-0.664352\pi$
$263$	−2.91293e8	−0.987380	−0.493690	+	0.869638i	$0.664352\pi$
$264$	2.29755e8	0.768513
$265$	1.37738e8	0.454667
$266$	−2.15790e8	−0.702985
$267$	1.49081e8	0.479329
$268$	1.09805e8	0.348459
$269$	−7.18507e7	−0.225060	−0.112530	−	0.993648i	$-0.535895\pi$
$269$	−7.18507e7	−0.225060	−0.112530	+	0.993648i	$0.535895\pi$
$270$	−7.99031e7	−0.247053
$271$	2.99889e7	0.0915310	0.0457655	−	0.998952i	$-0.485427\pi$
$271$	2.99889e7	0.0915310	0.0457655	+	0.998952i	$0.485427\pi$
$272$	−4.29639e8	−1.29453
$273$	−7.18359e7	−0.213684
$274$	−1.14023e8	−0.334861
$275$	−4.39452e8	−1.27423
$276$	9.47213e6	0.0271185
$277$	3.52435e8	0.996322	0.498161	−	0.867085i	$-0.334009\pi$
$277$	3.52435e8	0.996322	0.498161	+	0.867085i	$0.334009\pi$
$278$	4.31769e8	1.20530
$279$	−1.62474e8	−0.447889
$280$	−3.11546e8	−0.848142
$281$	3.70901e8	0.997209	0.498605	−	0.866830i	$-0.333846\pi$
$281$	3.70901e8	0.997209	0.498605	+	0.866830i	$0.333846\pi$
$282$	3.42373e8	0.909133
$283$	1.18723e8	0.311373	0.155687	−	0.987807i	$-0.450241\pi$
$283$	1.18723e8	0.311373	0.155687	+	0.987807i	$0.450241\pi$
$284$	−3.56752e7	−0.0924170
$285$	−4.48952e8	−1.14880
$286$	−2.95005e8	−0.745673
$287$	1.06172e8	0.265109
$288$	4.95482e7	0.122223
$289$	7.21302e8	1.75782
$290$	−7.80517e8	−1.87927
$291$	4.06810e8	0.967758
$292$	3.30647e7	0.0777184
$293$	6.18045e8	1.43544	0.717718	−	0.696334i	$-0.245187\pi$
$293$	6.18045e8	1.43544	0.717718	+	0.696334i	$0.245187\pi$
$294$	−1.56532e8	−0.359242
$295$	−8.16747e7	−0.185230
$296$	−4.95548e8	−1.11062
$297$	−1.08091e8	−0.239410
$298$	6.04888e8	1.32409
$299$	−7.75814e7	−0.167845
$300$	−5.14156e7	−0.109944
$301$	1.00027e8	0.211415
$302$	7.36520e8	1.53872
$303$	−1.91857e8	−0.396212
$304$	−5.34016e8	−1.09018
$305$	1.10877e9	2.23765
$306$	2.50335e8	0.499456
$307$	−7.10474e8	−1.40141	−0.700703	−	0.713453i	$-0.747130\pi$
$307$	−7.10474e8	−1.40141	−0.700703	+	0.713453i	$0.747130\pi$
$308$	−6.60697e7	−0.128847
$309$	1.46302e8	0.282094
$310$	9.04752e8	1.72490
$311$	8.99410e8	1.69549	0.847747	−	0.530401i	$-0.177958\pi$
$311$	8.99410e8	1.69549	0.847747	+	0.530401i	$0.177958\pi$
$312$	−2.20170e8	−0.410409
$313$	−1.68969e8	−0.311459	−0.155729	−	0.987800i	$-0.549773\pi$
$313$	−1.68969e8	−0.311459	−0.155729	+	0.987800i	$0.549773\pi$
$314$	−5.22466e8	−0.952366
$315$	1.46570e8	0.264216
$316$	−1.69808e8	−0.302729
$317$	6.45496e8	1.13812	0.569058	−	0.822297i	$-0.307308\pi$
$317$	6.45496e8	1.13812	0.569058	+	0.822297i	$0.307308\pi$
$318$	−9.54613e7	−0.166469
$319$	−1.05586e9	−1.82113
$320$	−9.26030e8	−1.57979
$321$	5.35088e8	0.902938
$322$	7.60842e7	0.126999
$323$	1.40656e9	2.32247
$324$	−1.26466e7	−0.0206569
$325$	4.21119e8	0.680476
$326$	3.08933e8	0.493858
$327$	2.64698e8	0.418633
$328$	3.25407e8	0.509176
$329$	−6.28032e8	−0.972291
$330$	6.01913e8	0.922009
$331$	−1.03251e9	−1.56493	−0.782467	−	0.622692i	$-0.786039\pi$
$331$	−1.03251e9	−1.56493	−0.782467	+	0.622692i	$0.786039\pi$
$332$	−4.83853e7	−0.0725655
$333$	2.33136e8	0.345983
$334$	5.60272e8	0.822784
$335$	1.83501e9	2.66674
$336$	1.74341e8	0.250734
$337$	−2.83276e8	−0.403186	−0.201593	−	0.979469i	$-0.564612\pi$
$337$	−2.83276e8	−0.403186	−0.201593	+	0.979469i	$0.564612\pi$
$338$	−3.57839e8	−0.504057
$339$	−3.34877e8	−0.466859
$340$	3.18349e8	0.439265
$341$	1.22393e9	1.67153
$342$	3.11152e8	0.420611
$343$	7.03499e8	0.941313
$344$	3.06574e8	0.406051
$345$	1.58293e8	0.207537
$346$	−1.01520e9	−1.31760
$347$	3.08826e8	0.396790	0.198395	−	0.980122i	$-0.436427\pi$
$347$	3.08826e8	0.396790	0.198395	+	0.980122i	$0.436427\pi$
$348$	−1.23535e8	−0.157132
$349$	−9.76048e8	−1.22909	−0.614543	−	0.788884i	$-0.710659\pi$
$349$	−9.76048e8	−1.22909	−0.614543	+	0.788884i	$0.710659\pi$
$350$	−4.12992e8	−0.514877
$351$	1.03581e8	0.127852
$352$	−3.73249e8	−0.456141
$353$	−6.80666e8	−0.823612	−0.411806	−	0.911271i	$-0.635102\pi$
$353$	−6.80666e8	−0.823612	−0.411806	+	0.911271i	$0.635102\pi$
$354$	5.66057e7	0.0678186
$355$	−5.96184e8	−0.707263
$356$	−1.31394e8	−0.154348
$357$	−4.59203e8	−0.534154
$358$	1.30413e9	1.50221
$359$	8.85168e8	1.00971	0.504853	−	0.863205i	$-0.331547\pi$
$359$	8.85168e8	1.00971	0.504853	+	0.863205i	$0.331547\pi$
$360$	4.49223e8	0.507462
$361$	8.54398e8	0.955840
$362$	5.77573e8	0.639922
$363$	2.88100e8	0.316133
$364$	6.33134e7	0.0688083
$365$	5.52558e8	0.594776
$366$	−7.68449e8	−0.819277
$367$	1.33637e9	1.41122	0.705610	−	0.708601i	$-0.250673\pi$
$367$	1.33637e9	1.41122	0.705610	+	0.708601i	$0.250673\pi$
$368$	1.88285e8	0.196947
$369$	−1.53091e8	−0.158620
$370$	−1.29824e9	−1.33244
$371$	1.75110e8	0.178033
$372$	1.43198e8	0.144224
$373$	6.67780e8	0.666274	0.333137	−	0.942879i	$-0.391893\pi$
$373$	6.67780e8	0.666274	0.333137	+	0.942879i	$0.391893\pi$
$374$	−1.88579e9	−1.86398
$375$	−2.03771e7	−0.0199541
$376$	−1.92485e9	−1.86741
$377$	1.01182e9	0.972538
$378$	−1.01583e8	−0.0967382
$379$	1.22986e9	1.16043	0.580213	−	0.814465i	$-0.302969\pi$
$379$	1.22986e9	1.16043	0.580213	+	0.814465i	$0.302969\pi$
$380$	3.95688e8	0.369922
$381$	2.46490e8	0.228329
$382$	−1.12434e9	−1.03199
$383$	1.72139e9	1.56561	0.782805	−	0.622267i	$-0.213788\pi$
$383$	1.72139e9	1.56561	0.782805	+	0.622267i	$0.213788\pi$
$384$	4.06902e8	0.366717
$385$	−1.10412e9	−0.986062
$386$	8.65804e8	0.766239
$387$	−1.44231e8	−0.126494
$388$	−3.58547e8	−0.311627
$389$	−8.54144e8	−0.735712	−0.367856	−	0.929883i	$-0.619908\pi$
$389$	−8.54144e8	−0.735712	−0.367856	+	0.929883i	$0.619908\pi$
$390$	−5.76802e8	−0.492380
$391$	−4.95931e8	−0.419568
$392$	8.80039e8	0.737905
$393$	5.17172e8	0.429795
$394$	8.62649e8	0.710555
$395$	−2.83775e9	−2.31677
$396$	9.52671e7	0.0770921
$397$	4.64867e8	0.372874	0.186437	−	0.982467i	$-0.440306\pi$
$397$	4.64867e8	0.372874	0.186437	+	0.982467i	$0.440306\pi$
$398$	−1.17269e9	−0.932379
$399$	−5.70762e8	−0.449832
$400$	−1.02203e9	−0.798461
$401$	1.35635e9	1.05043	0.525216	−	0.850969i	$-0.323985\pi$
$401$	1.35635e9	1.05043	0.525216	+	0.850969i	$0.323985\pi$
$402$	−1.27178e9	−0.976382
$403$	−1.17287e9	−0.892648
$404$	1.69095e8	0.127584
$405$	−2.11342e8	−0.158086
$406$	−9.92289e8	−0.735863
$407$	−1.75623e9	−1.29122
$408$	−1.40741e9	−1.02591
$409$	−1.50649e9	−1.08876	−0.544382	−	0.838838i	$-0.683236\pi$
$409$	−1.50649e9	−1.08876	−0.544382	+	0.838838i	$0.683236\pi$
$410$	8.52502e8	0.610875
$411$	−3.01588e8	−0.214273
$412$	−1.28944e8	−0.0908370
$413$	−1.03835e8	−0.0725301
$414$	−1.09707e8	−0.0759860
$415$	−8.08589e8	−0.555341
$416$	3.57677e8	0.243593
$417$	1.14202e9	0.771256
$418$	−2.34392e9	−1.56973
$419$	−2.73741e9	−1.81799	−0.908995	−	0.416808i	$-0.863149\pi$
$419$	−2.73741e9	−1.81799	−0.908995	+	0.416808i	$0.863149\pi$
$420$	−1.29181e8	−0.0850800
$421$	−4.08418e8	−0.266758	−0.133379	−	0.991065i	$-0.542583\pi$
$421$	−4.08418e8	−0.266758	−0.133379	+	0.991065i	$0.542583\pi$
$422$	−2.28038e9	−1.47711
$423$	9.05571e8	0.581743
$424$	5.36693e8	0.341936
$425$	2.69196e9	1.70101
$426$	4.13193e8	0.258952
$427$	1.40961e9	0.876193
$428$	−4.71606e8	−0.290754
$429$	−7.80284e8	−0.477147
$430$	8.03164e8	0.487152
$431$	−7.95781e8	−0.478766	−0.239383	−	0.970925i	$-0.576945\pi$
$431$	−7.95781e8	−0.478766	−0.239383	+	0.970925i	$0.576945\pi$
$432$	−2.51386e8	−0.150020
$433$	−1.70983e9	−1.01215	−0.506076	−	0.862489i	$-0.668905\pi$
$433$	−1.70983e9	−1.01215	−0.506076	+	0.862489i	$0.668905\pi$
$434$	1.15023e9	0.675415
$435$	−2.06446e9	−1.20252
$436$	−2.33294e8	−0.134804
$437$	−6.16412e8	−0.353334
$438$	−3.82958e8	−0.217767
$439$	3.43402e9	1.93721	0.968606	−	0.248602i	$-0.0799712\pi$
$439$	3.43402e9	1.93721	0.968606	+	0.248602i	$0.0799712\pi$
$440$	−3.38402e9	−1.89386
$441$	−4.14025e8	−0.229875
$442$	1.80711e9	0.995423
$443$	−8.23020e7	−0.0449777	−0.0224888	−	0.999747i	$-0.507159\pi$
$443$	−8.23020e7	−0.0449777	−0.0224888	+	0.999747i	$0.507159\pi$
$444$	−2.05477e8	−0.111410
$445$	−2.19579e9	−1.18122
$446$	−1.27887e9	−0.682583
$447$	1.59992e9	0.847269
$448$	−1.17728e9	−0.618597
$449$	−1.42868e9	−0.744856	−0.372428	−	0.928061i	$-0.621475\pi$
$449$	−1.42868e9	−0.744856	−0.372428	+	0.928061i	$0.621475\pi$
$450$	5.95500e8	0.308062
$451$	1.15324e9	0.591975
$452$	2.95147e8	0.150333
$453$	1.94808e9	0.984609
$454$	−1.73161e8	−0.0868469
$455$	1.05806e9	0.526586
$456$	−1.74933e9	−0.863961
$457$	1.78047e9	0.872625	0.436312	−	0.899795i	$-0.356284\pi$
$457$	1.78047e9	0.872625	0.436312	+	0.899795i	$0.356284\pi$
$458$	−9.67203e8	−0.470423
$459$	6.62133e8	0.319596
$460$	−1.39513e8	−0.0668287
$461$	2.67034e9	1.26944	0.634722	−	0.772741i	$-0.281115\pi$
$461$	2.67034e9	1.26944	0.634722	+	0.772741i	$0.281115\pi$
$462$	7.65226e8	0.361029
$463$	9.93730e7	0.0465302	0.0232651	−	0.999729i	$-0.492594\pi$
$463$	9.93730e7	0.0465302	0.0232651	+	0.999729i	$0.492594\pi$
$464$	−2.45561e9	−1.14116
$465$	2.39305e9	1.10374
$466$	−1.26172e9	−0.577581
$467$	−2.09963e9	−0.953967	−0.476984	−	0.878912i	$-0.658270\pi$
$467$	−2.09963e9	−0.953967	−0.476984	+	0.878912i	$0.658270\pi$
$468$	−9.12926e7	−0.0411695
$469$	2.33289e9	1.04421
$470$	−5.04274e9	−2.24039
$471$	−1.38191e9	−0.609407
$472$	−3.18243e8	−0.139304
$473$	1.08650e9	0.472080
$474$	1.96674e9	0.848247
$475$	3.34594e9	1.43249
$476$	4.04724e8	0.172002
$477$	−2.52494e8	−0.106521
$478$	1.88510e9	0.789471
$479$	3.04269e8	0.126498	0.0632490	−	0.997998i	$-0.479854\pi$
$479$	3.04269e8	0.126498	0.0632490	+	0.997998i	$0.479854\pi$
$480$	−7.29787e8	−0.301198
$481$	1.68296e9	0.689550
$482$	−3.17103e9	−1.28984
$483$	2.01242e8	0.0812648
$484$	−2.53920e8	−0.101798
$485$	−5.99184e9	−2.38487
$486$	1.46474e8	0.0578805
$487$	−8.62328e8	−0.338315	−0.169157	−	0.985589i	$-0.554105\pi$
$487$	−8.62328e8	−0.338315	−0.169157	+	0.985589i	$0.554105\pi$
$488$	4.32030e9	1.68284
$489$	8.17122e8	0.316014
$490$	2.30553e9	0.885288
$491$	−1.09588e9	−0.417811	−0.208905	−	0.977936i	$-0.566990\pi$
$491$	−1.09588e9	−0.417811	−0.208905	+	0.977936i	$0.566990\pi$
$492$	1.34929e8	0.0510771
$493$	6.46792e9	2.43109
$494$	2.24613e9	0.838284
$495$	1.59205e9	0.589982
$496$	2.84647e9	1.04742
$497$	−7.57942e8	−0.276942
$498$	5.60403e8	0.203328
$499$	2.67449e9	0.963582	0.481791	−	0.876286i	$-0.339986\pi$
$499$	2.67449e9	0.963582	0.481791	+	0.876286i	$0.339986\pi$
$500$	1.79595e7	0.00642540
$501$	1.48191e9	0.526489
$502$	1.41114e9	0.497861
$503$	−4.00214e9	−1.40218	−0.701091	−	0.713072i	$-0.747303\pi$
$503$	−4.00214e9	−1.40218	−0.701091	+	0.713072i	$0.747303\pi$
$504$	5.71107e8	0.198706
$505$	2.82582e9	0.976394
$506$	8.26428e8	0.283582
$507$	−9.46479e8	−0.322540
$508$	−2.17247e8	−0.0735241
$509$	1.64260e9	0.552102	0.276051	−	0.961143i	$-0.410974\pi$
$509$	1.64260e9	0.552102	0.276051	+	0.961143i	$0.410974\pi$
$510$	−3.68715e9	−1.23082
$511$	7.02480e8	0.232895
$512$	−3.40122e9	−1.11993
$513$	8.22992e8	0.269144
$514$	−1.28358e9	−0.416920
$515$	−2.15485e9	−0.695171
$516$	1.27120e8	0.0407323
$517$	−6.82170e9	−2.17108
$518$	−1.65048e9	−0.521743
$519$	−2.68518e9	−0.843117
$520$	3.24284e9	1.01138
$521$	7.57722e8	0.234735	0.117368	−	0.993089i	$-0.462554\pi$
$521$	7.57722e8	0.234735	0.117368	+	0.993089i	$0.462554\pi$
$522$	1.43080e9	0.440283
$523$	7.00512e8	0.214121	0.107061	−	0.994252i	$-0.465856\pi$
$523$	7.00512e8	0.214121	0.107061	+	0.994252i	$0.465856\pi$
$524$	−4.55815e8	−0.138398
$525$	−1.09236e9	−0.329463
$526$	−2.97352e9	−0.890882
$527$	−7.49741e9	−2.23138
$528$	1.89370e9	0.559877
$529$	−3.18749e9	−0.936168
$530$	1.40603e9	0.410232
$531$	1.49721e8	0.0433963
$532$	5.03047e8	0.144850
$533$	−1.10513e9	−0.316132
$534$	1.52182e9	0.432483
$535$	−7.88122e9	−2.22513
$536$	7.15006e9	2.00555
$537$	3.44941e9	0.961248
$538$	−7.33452e8	−0.203064
$539$	3.11887e9	0.857899
$540$	1.86269e8	0.0509052
$541$	−1.39710e9	−0.379346	−0.189673	−	0.981847i	$-0.560743\pi$
$541$	−1.39710e9	−0.379346	−0.189673	+	0.981847i	$0.560743\pi$
$542$	3.06127e8	0.0825855
$543$	1.52767e9	0.409478
$544$	2.28641e9	0.608918
$545$	−3.89869e9	−1.03165
$546$	−7.33301e8	−0.192801
$547$	−1.96444e8	−0.0513197	−0.0256598	−	0.999671i	$-0.508169\pi$
$547$	−1.96444e8	−0.0513197	−0.0256598	+	0.999671i	$0.508169\pi$
$548$	2.65808e8	0.0689979
$549$	−2.03253e9	−0.524245
$550$	−4.48593e9	−1.14970
$551$	8.03923e9	2.04731
$552$	6.16785e8	0.156080
$553$	−3.60769e9	−0.907175
$554$	3.59766e9	0.898950
$555$	−3.43382e9	−0.852614
$556$	−1.00653e9	−0.248352
$557$	2.95103e9	0.723571	0.361785	−	0.932261i	$-0.382167\pi$
$557$	2.95103e9	0.723571	0.361785	+	0.932261i	$0.382167\pi$
$558$	−1.65854e9	−0.404116
$559$	−1.04117e9	−0.252105
$560$	−2.56784e9	−0.617889
$561$	−4.98788e9	−1.19274
$562$	3.78616e9	0.899750
$563$	−9.45756e7	−0.0223357	−0.0111679	−	0.999938i	$-0.503555\pi$
$563$	−9.45756e7	−0.0223357	−0.0111679	+	0.999938i	$0.503555\pi$
$564$	−7.98134e8	−0.187326
$565$	4.93234e9	1.15049
$566$	1.21192e9	0.280942
$567$	−2.68684e8	−0.0619015
$568$	−2.32301e9	−0.531903
$569$	6.34844e8	0.144469	0.0722344	−	0.997388i	$-0.476987\pi$
$569$	6.34844e8	0.144469	0.0722344	+	0.997388i	$0.476987\pi$
$570$	−4.58290e9	−1.03652
$571$	6.22435e9	1.39916	0.699580	−	0.714554i	$-0.253370\pi$
$571$	6.22435e9	1.39916	0.699580	+	0.714554i	$0.253370\pi$
$572$	6.87711e8	0.153646
$573$	−2.97387e9	−0.660360
$574$	1.08381e9	0.239199
$575$	−1.17972e9	−0.258787
$576$	1.69754e9	0.370120
$577$	5.59231e9	1.21193	0.605963	−	0.795493i	$-0.292788\pi$
$577$	5.59231e9	1.21193	0.605963	+	0.795493i	$0.292788\pi$
$578$	7.36305e9	1.58603
$579$	2.29004e9	0.490307
$580$	1.81953e9	0.387223
$581$	−1.02798e9	−0.217454
$582$	4.15272e9	0.873177
$583$	1.90204e9	0.397540
$584$	2.15303e9	0.447306
$585$	−1.52563e9	−0.315068
$586$	6.30901e9	1.29515
$587$	5.92527e9	1.20913	0.604567	−	0.796554i	$-0.293346\pi$
$587$	5.92527e9	1.20913	0.604567	+	0.796554i	$0.293346\pi$
$588$	3.64905e8	0.0740217
$589$	−9.31883e9	−1.87913
$590$	−8.33735e8	−0.167127
$591$	2.28169e9	0.454675
$592$	−4.08444e9	−0.809108
$593$	−4.66790e9	−0.919242	−0.459621	−	0.888115i	$-0.652015\pi$
$593$	−4.66790e9	−0.919242	−0.459621	+	0.888115i	$0.652015\pi$
$594$	−1.10339e9	−0.216012
$595$	6.76352e9	1.31633
$596$	−1.41011e9	−0.272828
$597$	−3.10175e9	−0.596618
$598$	−7.91951e8	−0.151441
$599$	2.89602e9	0.550563	0.275282	−	0.961364i	$-0.411229\pi$
$599$	2.89602e9	0.550563	0.275282	+	0.961364i	$0.411229\pi$
$600$	−3.34796e9	−0.632778
$601$	4.95609e9	0.931276	0.465638	−	0.884975i	$-0.345825\pi$
$601$	4.95609e9	0.931276	0.465638	+	0.884975i	$0.345825\pi$
$602$	1.02108e9	0.190753
$603$	−3.36383e9	−0.624774
$604$	−1.71696e9	−0.317053
$605$	−4.24337e9	−0.779053
$606$	−1.95847e9	−0.357490
$607$	−2.16921e9	−0.393678	−0.196839	−	0.980436i	$-0.563068\pi$
$607$	−2.16921e9	−0.393678	−0.196839	+	0.980436i	$0.563068\pi$
$608$	2.84187e9	0.512793
$609$	−2.62459e9	−0.470870
$610$	1.13183e10	2.01896
$611$	6.53711e9	1.15942
$612$	−5.83578e8	−0.102913
$613$	−2.26724e9	−0.397544	−0.198772	−	0.980046i	$-0.563695\pi$
$613$	−2.26724e9	−0.397544	−0.198772	+	0.980046i	$0.563695\pi$
$614$	−7.25252e9	−1.26444
$615$	2.25486e9	0.390891
$616$	−4.30218e9	−0.741576
$617$	3.64399e9	0.624567	0.312284	−	0.949989i	$-0.398906\pi$
$617$	3.64399e9	0.624567	0.312284	+	0.949989i	$0.398906\pi$
$618$	1.49345e9	0.254525
$619$	8.80200e9	1.49164	0.745820	−	0.666147i	$-0.232058\pi$
$619$	8.80200e9	1.49164	0.745820	+	0.666147i	$0.232058\pi$
$620$	−2.10914e9	−0.355415
$621$	−2.90174e8	−0.0486225
$622$	9.18118e9	1.52979
$623$	−2.79155e9	−0.462528
$624$	−1.81470e9	−0.298991
$625$	−5.95165e9	−0.975118
$626$	−1.72483e9	−0.281019
$627$	−6.19963e9	−1.00445
$628$	1.21796e9	0.196235
$629$	1.07581e10	1.72369
$630$	1.49619e9	0.238394
$631$	3.58813e9	0.568546	0.284273	−	0.958743i	$-0.408248\pi$
$631$	3.58813e9	0.568546	0.284273	+	0.958743i	$0.408248\pi$
$632$	−1.10572e10	−1.74235
$633$	−6.03157e9	−0.945186
$634$	6.58923e9	1.02689
$635$	−3.63051e9	−0.562677
$636$	2.22538e8	0.0343008
$637$	−2.98875e9	−0.458143
$638$	−1.07783e10	−1.64315
$639$	1.09289e9	0.165700
$640$	−5.99319e9	−0.903708
$641$	5.09433e9	0.763984	0.381992	−	0.924166i	$-0.375238\pi$
$641$	5.09433e9	0.763984	0.381992	+	0.924166i	$0.375238\pi$
$642$	5.46218e9	0.814692
$643$	−6.13203e9	−0.909633	−0.454816	−	0.890585i	$-0.650295\pi$
$643$	−6.13203e9	−0.909633	−0.454816	+	0.890585i	$0.650295\pi$
$644$	−1.77366e8	−0.0261680
$645$	2.12436e9	0.311723
$646$	1.43582e10	2.09549
$647$	−7.78100e9	−1.12946	−0.564729	−	0.825276i	$-0.691019\pi$
$647$	−7.78100e9	−1.12946	−0.564729	+	0.825276i	$0.691019\pi$
$648$	−8.23490e8	−0.118890
$649$	−1.12786e9	−0.161956
$650$	4.29878e9	0.613972
$651$	3.04234e9	0.432190
$652$	−7.20179e8	−0.101759
$653$	−6.82855e8	−0.0959693	−0.0479846	−	0.998848i	$-0.515280\pi$
$653$	−6.82855e8	−0.0959693	−0.0479846	+	0.998848i	$0.515280\pi$
$654$	2.70204e9	0.377719
$655$	−7.61733e9	−1.05915
$656$	2.68209e9	0.370945
$657$	−1.01292e9	−0.139346
$658$	−6.41095e9	−0.877267
$659$	6.06750e8	0.0825868	0.0412934	−	0.999147i	$-0.486852\pi$
$659$	6.06750e8	0.0825868	0.0412934	+	0.999147i	$0.486852\pi$
$660$	−1.40317e9	−0.189980
$661$	−1.22400e9	−0.164846	−0.0824228	−	0.996597i	$-0.526266\pi$
$661$	−1.22400e9	−0.164846	−0.0824228	+	0.996597i	$0.526266\pi$
$662$	−1.05399e10	−1.41199
$663$	4.77979e9	0.636959
$664$	−3.15064e9	−0.417649
$665$	8.40665e9	1.10853
$666$	2.37986e9	0.312170
$667$	−2.83450e9	−0.369859
$668$	−1.30610e9	−0.169534
$669$	−3.38260e9	−0.436776
$670$	1.87318e10	2.40612
$671$	1.53112e10	1.95650
$672$	−9.27794e8	−0.117939
$673$	−8.76801e9	−1.10879	−0.554394	−	0.832254i	$-0.687050\pi$
$673$	−8.76801e9	−1.10879	−0.554394	+	0.832254i	$0.687050\pi$
$674$	−2.89168e9	−0.363782
$675$	1.57509e9	0.197125
$676$	8.34189e8	0.103861
$677$	3.66670e9	0.454166	0.227083	−	0.973875i	$-0.427081\pi$
$677$	3.66670e9	0.454166	0.227083	+	0.973875i	$0.427081\pi$
$678$	−3.41842e9	−0.421232
$679$	−7.61755e9	−0.933837
$680$	2.07295e10	2.52818
$681$	−4.58008e8	−0.0555723
$682$	1.24938e10	1.50817
$683$	−2.41403e8	−0.0289915	−0.0144957	−	0.999895i	$-0.504614\pi$
$683$	−2.41403e8	−0.0289915	−0.0144957	+	0.999895i	$0.504614\pi$
$684$	−7.25353e8	−0.0866668
$685$	4.44203e9	0.528038
$686$	7.18132e9	0.849317
$687$	−2.55824e9	−0.301018
$688$	2.52686e9	0.295816
$689$	−1.82269e9	−0.212298
$690$	1.61586e9	0.187254
$691$	5.87544e9	0.677434	0.338717	−	0.940888i	$-0.390007\pi$
$691$	5.87544e9	0.677434	0.338717	+	0.940888i	$0.390007\pi$
$692$	2.36661e9	0.271491
$693$	2.02401e9	0.231018
$694$	3.15249e9	0.358011
$695$	−1.68206e10	−1.90062
$696$	−8.04409e9	−0.904367
$697$	−7.06444e9	−0.790247
$698$	−9.96349e9	−1.10896
$699$	−3.33723e9	−0.369587
$700$	9.62760e8	0.106090
$701$	−1.02557e10	−1.12449	−0.562243	−	0.826972i	$-0.690061\pi$
$701$	−1.02557e10	−1.12449	−0.562243	+	0.826972i	$0.690061\pi$
$702$	1.05736e9	0.115357
$703$	1.33717e10	1.45159
$704$	−1.27877e10	−1.38130
$705$	−1.33380e10	−1.43360
$706$	−6.94824e9	−0.743119
$707$	3.59253e9	0.382325
$708$	−1.31958e8	−0.0139740
$709$	−5.18318e9	−0.546178	−0.273089	−	0.961989i	$-0.588045\pi$
$709$	−5.18318e9	−0.546178	−0.273089	+	0.961989i	$0.588045\pi$
$710$	−6.08585e9	−0.638141
$711$	5.20199e9	0.542783
$712$	−8.55583e9	−0.888346
$713$	3.28567e9	0.339477
$714$	−4.68755e9	−0.481950
$715$	1.14927e10	1.17584
$716$	−3.04018e9	−0.309530
$717$	4.98606e9	0.505173
$718$	9.03579e9	0.911026
$719$	1.29607e10	1.30040	0.650202	−	0.759762i	$-0.274684\pi$
$719$	1.29607e10	1.30040	0.650202	+	0.759762i	$0.274684\pi$
$720$	3.70262e9	0.369696
$721$	−2.73951e9	−0.272207
$722$	8.72170e9	0.862424
$723$	−8.38731e9	−0.825351
$724$	−1.34643e9	−0.131856
$725$	1.53859e10	1.49948
$726$	2.94092e9	0.285237
$727$	4.17261e9	0.402752	0.201376	−	0.979514i	$-0.435459\pi$
$727$	4.17261e9	0.402752	0.201376	+	0.979514i	$0.435459\pi$
$728$	4.12269e9	0.396024
$729$	3.87420e8	0.0370370
$730$	5.64052e9	0.536647
$731$	−6.65558e9	−0.630195
$732$	1.79140e9	0.168812
$733$	−1.52037e10	−1.42589	−0.712944	−	0.701221i	$-0.752638\pi$
$733$	−1.52037e10	−1.42589	−0.712944	+	0.701221i	$0.752638\pi$
$734$	1.36416e10	1.27330
$735$	6.09809e9	0.566485
$736$	−1.00200e9	−0.0926392
$737$	2.53399e10	2.33168
$738$	−1.56276e9	−0.143118
$739$	−7.33278e9	−0.668364	−0.334182	−	0.942509i	$-0.608460\pi$
$739$	−7.33278e9	−0.668364	−0.334182	+	0.942509i	$0.608460\pi$
$740$	3.02644e9	0.274549
$741$	5.94099e9	0.536408
$742$	1.78752e9	0.160634
$743$	6.55520e9	0.586307	0.293154	−	0.956065i	$-0.405295\pi$
$743$	6.55520e9	0.586307	0.293154	+	0.956065i	$0.405295\pi$
$744$	9.32447e9	0.830078
$745$	−2.35649e10	−2.08794
$746$	6.81670e9	0.601158
$747$	1.48226e9	0.130107
$748$	4.39612e9	0.384073
$749$	−1.00196e10	−0.871290
$750$	−2.08009e8	−0.0180040
$751$	−7.42395e9	−0.639581	−0.319790	−	0.947488i	$-0.603612\pi$
$751$	−7.42395e9	−0.639581	−0.319790	+	0.947488i	$0.603612\pi$
$752$	−1.58652e10	−1.36045
$753$	3.73245e9	0.318575
$754$	1.03286e10	0.877490
$755$	−2.86930e10	−2.42639
$756$	2.36808e8	0.0199329
$757$	−1.49414e10	−1.25186	−0.625928	−	0.779880i	$-0.715280\pi$
$757$	−1.49414e10	−1.25186	−0.625928	+	0.779880i	$0.715280\pi$
$758$	1.25544e10	1.04701
$759$	2.18589e9	0.181461
$760$	2.57655e10	2.12908
$761$	−1.92886e10	−1.58655	−0.793276	−	0.608862i	$-0.791626\pi$
$761$	−1.92886e10	−1.58655	−0.793276	+	0.608862i	$0.791626\pi$
$762$	2.51617e9	0.206014
$763$	−4.95649e9	−0.403960
$764$	2.62105e9	0.212642
$765$	−9.75244e9	−0.787587
$766$	1.75720e10	1.41260
$767$	1.08080e9	0.0864894
$768$	−3.89396e9	−0.310190
$769$	1.59930e10	1.26820	0.634099	−	0.773252i	$-0.281371\pi$
$769$	1.59930e10	1.26820	0.634099	+	0.773252i	$0.281371\pi$
$770$	−1.12709e10	−0.889692
$771$	−3.39506e9	−0.266782
$772$	−2.01835e9	−0.157883
$773$	2.25204e10	1.75367	0.876833	−	0.480794i	$-0.159652\pi$
$773$	2.25204e10	1.75367	0.876833	+	0.480794i	$0.159652\pi$
$774$	−1.47231e9	−0.114132
$775$	−1.78349e10	−1.37631
$776$	−2.33470e10	−1.79356
$777$	−4.36550e9	−0.333857
$778$	−8.71910e9	−0.663809
$779$	−8.78067e9	−0.665498
$780$	1.34463e9	0.101455
$781$	−8.23278e9	−0.618398
$782$	−5.06246e9	−0.378563
$783$	3.78444e9	0.281732
$784$	7.25352e9	0.537579
$785$	2.03539e10	1.50178
$786$	5.27929e9	0.387790
$787$	−1.72331e10	−1.26024	−0.630119	−	0.776498i	$-0.716994\pi$
$787$	−1.72331e10	−1.26024	−0.630119	+	0.776498i	$0.716994\pi$
$788$	−2.01099e9	−0.146409
$789$	−7.86490e9	−0.570064
$790$	−2.89677e10	−2.09035
$791$	6.27059e9	0.450496
$792$	6.20338e9	0.443701
$793$	−1.46724e10	−1.04483
$794$	4.74537e9	0.336432
$795$	3.71893e9	0.262502
$796$	2.73376e9	0.192116
$797$	−1.26332e10	−0.883911	−0.441955	−	0.897037i	$-0.645715\pi$
$797$	−1.26332e10	−0.883911	−0.441955	+	0.897037i	$0.645715\pi$
$798$	−5.82634e9	−0.405869
$799$	4.17878e10	2.89825
$800$	5.43894e9	0.375577
$801$	4.02519e9	0.276741
$802$	1.38457e10	0.947771
$803$	7.63035e9	0.520044
$804$	2.96475e9	0.201183
$805$	−2.96405e9	−0.200263
$806$	−1.19726e10	−0.805408
$807$	−1.93997e9	−0.129938
$808$	1.10107e10	0.734305
$809$	9.80378e9	0.650989	0.325495	−	0.945544i	$-0.394469\pi$
$809$	9.80378e9	0.650989	0.325495	+	0.945544i	$0.394469\pi$
$810$	−2.15738e9	−0.142636
$811$	−1.10475e10	−0.727262	−0.363631	−	0.931543i	$-0.618463\pi$
$811$	−1.10475e10	−0.727262	−0.363631	+	0.931543i	$0.618463\pi$
$812$	2.31321e9	0.151624
$813$	8.09701e8	0.0528455
$814$	−1.79276e10	−1.16503
$815$	−1.20352e10	−0.778759
$816$	−1.16003e10	−0.747399
$817$	−8.27249e9	−0.530712
$818$	−1.53782e10	−0.982357
$819$	−1.93957e9	−0.123371
$820$	−1.98734e9	−0.125870
$821$	−1.50386e10	−0.948433	−0.474217	−	0.880408i	$-0.657269\pi$
$821$	−1.50386e10	−0.948433	−0.474217	+	0.880408i	$0.657269\pi$
$822$	−3.07861e9	−0.193332
$823$	−1.10764e10	−0.692625	−0.346313	−	0.938119i	$-0.612566\pi$
$823$	−1.10764e10	−0.692625	−0.346313	+	0.938119i	$0.612566\pi$
$824$	−8.39631e9	−0.522809
$825$	−1.18652e10	−0.735676
$826$	−1.05995e9	−0.0654416
$827$	3.12849e10	1.92338	0.961691	−	0.274137i	$-0.0883922\pi$
$827$	3.12849e10	1.92338	0.961691	+	0.274137i	$0.0883922\pi$
$828$	2.55748e8	0.0156569
$829$	1.84399e10	1.12413	0.562067	−	0.827092i	$-0.310006\pi$
$829$	1.84399e10	1.12413	0.562067	+	0.827092i	$0.310006\pi$
$830$	−8.25408e9	−0.501066
$831$	9.51574e9	0.575227
$832$	1.22542e10	0.737654
$833$	−1.91053e10	−1.14524
$834$	1.16578e10	0.695880
$835$	−2.18268e10	−1.29744
$836$	5.46411e9	0.323443
$837$	−4.38681e9	−0.258589
$838$	−2.79435e10	−1.64031
$839$	2.82373e10	1.65065	0.825327	−	0.564654i	$-0.190991\pi$
$839$	2.82373e10	1.65065	0.825327	+	0.564654i	$0.190991\pi$
$840$	−8.41173e9	−0.489675
$841$	1.97177e10	1.14306
$842$	−4.16913e9	−0.240687
$843$	1.00143e10	0.575739
$844$	5.31599e9	0.304358
$845$	1.39405e10	0.794841
$846$	9.24406e9	0.524888
$847$	−5.39469e9	−0.305052
$848$	4.42357e9	0.249108
$849$	3.20551e9	0.179771
$850$	2.74795e10	1.53477
$851$	−4.71465e9	−0.262238
$852$	−9.63230e8	−0.0533570
$853$	−1.66862e10	−0.920523	−0.460261	−	0.887783i	$-0.652244\pi$
$853$	−1.66862e10	−0.920523	−0.460261	+	0.887783i	$0.652244\pi$
$854$	1.43893e10	0.790561
$855$	−1.21217e10	−0.663257
$856$	−3.07089e10	−1.67343
$857$	−2.12716e10	−1.15443	−0.577215	−	0.816592i	$-0.695861\pi$
$857$	−2.12716e10	−1.15443	−0.577215	+	0.816592i	$0.695861\pi$
$858$	−7.96514e9	−0.430514
$859$	2.18013e10	1.17356	0.586781	−	0.809745i	$-0.300395\pi$
$859$	2.18013e10	1.17356	0.586781	+	0.809745i	$0.300395\pi$
$860$	−1.87232e9	−0.100377
$861$	2.86665e9	0.153061
$862$	−8.12333e9	−0.431975
$863$	−2.57691e10	−1.36478	−0.682388	−	0.730990i	$-0.739058\pi$
$863$	−2.57691e10	−1.36478	−0.682388	+	0.730990i	$0.739058\pi$
$864$	1.33780e9	0.0705657
$865$	3.95495e10	2.07771
$866$	−1.74540e10	−0.913233
$867$	1.94751e10	1.01488
$868$	−2.68140e9	−0.139169
$869$	−3.91868e10	−2.02568
$870$	−2.10740e10	−1.08500
$871$	−2.42827e10	−1.24518
$872$	−1.51911e10	−0.775858
$873$	1.09839e10	0.558735
$874$	−6.29233e9	−0.318802
$875$	3.81562e8	0.0192547
$876$	8.92746e8	0.0448708
$877$	−2.96656e10	−1.48510	−0.742549	−	0.669792i	$-0.766383\pi$
$877$	−2.96656e10	−1.48510	−0.742549	+	0.669792i	$0.766383\pi$
$878$	3.50545e10	1.74788
$879$	1.66872e10	0.828749
$880$	−2.78920e10	−1.37972
$881$	−2.10977e10	−1.03949	−0.519745	−	0.854322i	$-0.673973\pi$
$881$	−2.10977e10	−1.03949	−0.519745	+	0.854322i	$0.673973\pi$
$882$	−4.22636e9	−0.207409
$883$	2.21889e9	0.108461	0.0542304	−	0.998528i	$-0.482729\pi$
$883$	2.21889e9	0.108461	0.0542304	+	0.998528i	$0.482729\pi$
$884$	−4.21272e9	−0.205107
$885$	−2.20522e9	−0.106942
$886$	−8.40138e8	−0.0405819
$887$	−7.16266e9	−0.344621	−0.172311	−	0.985043i	$-0.555123\pi$
$887$	−7.16266e9	−0.344621	−0.172311	+	0.985043i	$0.555123\pi$
$888$	−1.33798e10	−0.641216
$889$	−4.61554e9	−0.220326
$890$	−2.24146e10	−1.06578
$891$	−2.91845e9	−0.138223
$892$	2.98129e9	0.140646
$893$	5.19397e10	2.44073
$894$	1.63320e10	0.764464
$895$	−5.08058e10	−2.36882
$896$	−7.61927e9	−0.353863
$897$	−2.09470e9	−0.0969053
$898$	−1.45840e10	−0.672060
$899$	−4.28516e10	−1.96702
$900$	−1.38822e9	−0.0634760
$901$	−1.16514e10	−0.530689
$902$	1.17723e10	0.534120
$903$	2.70074e9	0.122061
$904$	1.92187e10	0.865236
$905$	−2.25008e10	−1.00908
$906$	1.98860e10	0.888382
$907$	−8.53267e9	−0.379717	−0.189858	−	0.981811i	$-0.560803\pi$
$907$	−8.53267e9	−0.379717	−0.189858	+	0.981811i	$0.560803\pi$
$908$	4.03670e8	0.0178948
$909$	−5.18013e9	−0.228753
$910$	1.08007e10	0.475122
$911$	2.76004e9	0.120949	0.0604744	−	0.998170i	$-0.480739\pi$
$911$	2.76004e9	0.120949	0.0604744	+	0.998170i	$0.480739\pi$
$912$	−1.44184e10	−0.629413
$913$	−1.11659e10	−0.485564
$914$	1.81750e10	0.787342
$915$	2.99368e10	1.29191
$916$	2.25473e9	0.0969304
$917$	−9.68408e9	−0.414730
$918$	6.75906e9	0.288361
$919$	1.13500e10	0.482382	0.241191	−	0.970478i	$-0.422462\pi$
$919$	1.13500e10	0.482382	0.241191	+	0.970478i	$0.422462\pi$
$920$	−9.08451e9	−0.384631
$921$	−1.91828e10	−0.809102
$922$	2.72588e10	1.14538
$923$	7.88932e9	0.330243
$924$	−1.78388e9	−0.0743900
$925$	2.55915e10	1.06316
$926$	1.01440e9	0.0419827
$927$	3.95014e9	0.162867
$928$	1.30681e10	0.536776
$929$	4.41532e10	1.80679	0.903395	−	0.428810i	$-0.141067\pi$
$929$	4.41532e10	1.80679	0.903395	+	0.428810i	$0.141067\pi$
$930$	2.44283e10	0.995870
$931$	−2.37467e10	−0.964449
$932$	2.94131e9	0.119010
$933$	2.42841e10	0.978894
$934$	−2.14330e10	−0.860734
$935$	7.34655e10	2.93929
$936$	−5.94458e9	−0.236950
$937$	−3.84649e10	−1.52748	−0.763741	−	0.645522i	$-0.776640\pi$
$937$	−3.84649e10	−1.52748	−0.763741	+	0.645522i	$0.776640\pi$
$938$	2.38141e10	0.942159
$939$	−4.56215e9	−0.179821
$940$	1.17556e10	0.461632
$941$	2.95756e10	1.15710	0.578549	−	0.815648i	$-0.303619\pi$
$941$	2.95756e10	1.15710	0.578549	+	0.815648i	$0.303619\pi$
$942$	−1.41066e10	−0.549849
$943$	3.09592e9	0.120226
$944$	−2.62305e9	−0.101485
$945$	3.95740e9	0.152545
$946$	1.10910e10	0.425943
$947$	−4.30437e10	−1.64697	−0.823483	−	0.567341i	$-0.807972\pi$
$947$	−4.30437e10	−1.64697	−0.823483	+	0.567341i	$0.807972\pi$
$948$	−4.58483e9	−0.174781
$949$	−7.31202e9	−0.277719
$950$	3.41553e10	1.29249
$951$	1.74284e10	0.657091
$952$	2.63539e10	0.989954
$953$	2.33081e10	0.872333	0.436166	−	0.899866i	$-0.356336\pi$
$953$	2.33081e10	0.872333	0.436166	+	0.899866i	$0.356336\pi$
$954$	−2.57745e9	−0.0961107
$955$	4.38016e10	1.62734
$956$	−4.39451e9	−0.162670
$957$	−2.85083e10	−1.05143
$958$	3.10598e9	0.114135
$959$	5.64726e9	0.206763
$960$	−2.50028e10	−0.912094
$961$	2.21597e10	0.805438
$962$	1.71796e10	0.622159
$963$	1.44474e10	0.521311
$964$	7.39225e9	0.265771
$965$	−3.37296e10	−1.20827
$966$	2.05427e9	0.0733227
$967$	3.20553e9	0.114001	0.0570003	−	0.998374i	$-0.481846\pi$
$967$	3.20553e9	0.114001	0.0570003	+	0.998374i	$0.481846\pi$
$968$	−1.65342e10	−0.585893
$969$	3.79771e10	1.34088
$970$	−6.11647e10	−2.15179
$971$	−2.31196e10	−0.810424	−0.405212	−	0.914223i	$-0.632802\pi$
$971$	−2.31196e10	−0.810424	−0.405212	+	0.914223i	$0.632802\pi$
$972$	−3.41457e8	−0.0119263
$973$	−2.13845e10	−0.744224
$974$	−8.80265e9	−0.305251
$975$	1.13702e10	0.392873
$976$	3.56090e10	1.22599
$977$	9.17629e9	0.314801	0.157400	−	0.987535i	$-0.449689\pi$
$977$	9.17629e9	0.314801	0.157400	+	0.987535i	$0.449689\pi$
$978$	8.34119e9	0.285129
$979$	−3.03219e10	−1.03280
$980$	−5.37462e9	−0.182413
$981$	7.14684e9	0.241698
$982$	−1.11868e10	−0.376977
$983$	−2.25628e10	−0.757626	−0.378813	−	0.925473i	$-0.623668\pi$
$983$	−2.25628e10	−0.757626	−0.378813	+	0.925473i	$0.623668\pi$
$984$	8.78598e9	0.293973
$985$	−3.36066e10	−1.12046
$986$	6.60245e10	2.19349
$987$	−1.69569e10	−0.561353
$988$	−5.23615e9	−0.172728
$989$	2.91675e9	0.0958764
$990$	1.62517e10	0.532322
$991$	4.42802e10	1.44528	0.722640	−	0.691224i	$-0.242928\pi$
$991$	4.42802e10	1.44528	0.722640	+	0.691224i	$0.242928\pi$
$992$	−1.51481e10	−0.492682
$993$	−2.78778e10	−0.903515
$994$	−7.73707e9	−0.249876
$995$	4.56851e10	1.47026
$996$	−1.30640e9	−0.0418957
$997$	2.83830e10	0.907036	0.453518	−	0.891247i	$-0.350169\pi$
$997$	2.83830e10	0.907036	0.453518	+	0.891247i	$0.350169\pi$
$998$	2.73012e10	0.869409
$999$	6.29468e9	0.199754

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.d.1.13	✓	18
3.2	odd	2		531.8.a.e.1.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.d.1.13	✓	18	1.1	even	1	trivial
531.8.a.e.1.6		18	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)

\(f(q)\)	\(=\)	\(q+10.2080 q^{2} +27.0000 q^{3} -23.7967 q^{4} -397.678 q^{5} +275.616 q^{6} -505.577 q^{7} -1549.54 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+10.2080 q^{2} +27.0000 q^{3} -23.7967 q^{4} -397.678 q^{5} +275.616 q^{6} -505.577 q^{7} -1549.54 q^{8} +729.000 q^{9} -4059.50 q^{10} -5491.59 q^{11} -642.512 q^{12} +5262.48 q^{13} -5160.93 q^{14} -10737.3 q^{15} -12771.7 q^{16} +33639.9 q^{17} +7441.63 q^{18} +41812.3 q^{19} +9463.44 q^{20} -13650.6 q^{21} -56058.1 q^{22} -14742.3 q^{23} -41837.6 q^{24} +80022.8 q^{25} +53719.4 q^{26} +19683.0 q^{27} +12031.1 q^{28} +192269. q^{29} -109606. q^{30} -222873. q^{31} +67967.4 q^{32} -148273. q^{33} +343396. q^{34} +201057. q^{35} -17347.8 q^{36} +319803. q^{37} +426820. q^{38} +142087. q^{39} +616218. q^{40} -210002. q^{41} -139345. q^{42} -197848. q^{43} +130682. q^{44} -289907. q^{45} -150490. q^{46} +1.24221e6 q^{47} -344837. q^{48} -567935. q^{49} +816873. q^{50} +908276. q^{51} -125230. q^{52} -346356. q^{53} +200924. q^{54} +2.18388e6 q^{55} +783412. q^{56} +1.12893e6 q^{57} +1.96269e6 q^{58} +205379. q^{59} +255513. q^{60} -2.78811e6 q^{61} -2.27509e6 q^{62} -368566. q^{63} +2.32859e6 q^{64} -2.09277e6 q^{65} -1.51357e6 q^{66} -4.61431e6 q^{67} -800519. q^{68} -398043. q^{69} +2.05239e6 q^{70} +1.49916e6 q^{71} -1.12962e6 q^{72} -1.38946e6 q^{73} +3.26455e6 q^{74} +2.16062e6 q^{75} -994997. q^{76} +2.77642e6 q^{77} +1.45042e6 q^{78} +7.13579e6 q^{79} +5.07904e6 q^{80} +531441. q^{81} -2.14370e6 q^{82} +2.03328e6 q^{83} +324839. q^{84} -1.33778e7 q^{85} -2.01963e6 q^{86} +5.19128e6 q^{87} +8.50944e6 q^{88} +5.52152e6 q^{89} -2.95937e6 q^{90} -2.66059e6 q^{91} +350820. q^{92} -6.01757e6 q^{93} +1.26805e7 q^{94} -1.66278e7 q^{95} +1.83512e6 q^{96} +1.50671e7 q^{97} -5.79748e6 q^{98} -4.00337e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9} + 3609 q^{10} + 15070 q^{11} + 36666 q^{12} + 13662 q^{13} + 20861 q^{14} + 18306 q^{15} + 60482 q^{16} + 71919 q^{17} + 17496 q^{18} + 56231 q^{19} + 143053 q^{20} + 83187 q^{21} + 274198 q^{22} + 150029 q^{23} + 110889 q^{24} + 399672 q^{25} + 182846 q^{26} + 354294 q^{27} + 434150 q^{28} + 591285 q^{29} + 97443 q^{30} + 426733 q^{31} + 1205630 q^{32} + 406890 q^{33} + 403548 q^{34} + 912879 q^{35} + 989982 q^{36} + 7703 q^{37} - 417859 q^{38} + 368874 q^{39} + 618020 q^{40} + 770959 q^{41} + 563247 q^{42} + 793050 q^{43} + 2591274 q^{44} + 494262 q^{45} - 4068019 q^{46} + 1410373 q^{47} + 1633014 q^{48} + 1637427 q^{49} + 1021549 q^{50} + 1941813 q^{51} - 3749190 q^{52} + 1037934 q^{53} + 472392 q^{54} + 331974 q^{55} - 391748 q^{56} + 1518237 q^{57} + 653724 q^{58} + 3696822 q^{59} + 3862431 q^{60} - 1374623 q^{61} + 5251718 q^{62} + 2246049 q^{63} + 5077197 q^{64} + 3257170 q^{65} + 7403346 q^{66} - 2436904 q^{67} + 14119909 q^{68} + 4050783 q^{69} + 5185580 q^{70} + 14289172 q^{71} + 2994003 q^{72} + 5482515 q^{73} + 14934154 q^{74} + 10791144 q^{75} + 3822912 q^{76} + 23157109 q^{77} + 4936842 q^{78} + 19786414 q^{79} + 31978143 q^{80} + 9565938 q^{81} + 9749509 q^{82} + 30227337 q^{83} + 11722050 q^{84} + 9946981 q^{85} + 44295864 q^{86} + 15964695 q^{87} + 39970897 q^{88} + 31061677 q^{89} + 2630961 q^{90} + 26377785 q^{91} + 4719698 q^{92} + 11521791 q^{93} + 44488296 q^{94} + 15534599 q^{95} + 32552010 q^{96} + 12084118 q^{97} + 42274744 q^{98} + 10986030 q^{99}+O(q^{100}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9 + 3609 * q^10 + 15070 * q^11 + 36666 * q^12 + 13662 * q^13 + 20861 * q^14 + 18306 * q^15 + 60482 * q^16 + 71919 * q^17 + 17496 * q^18 + 56231 * q^19 + 143053 * q^20 + 83187 * q^21 + 274198 * q^22 + 150029 * q^23 + 110889 * q^24 + 399672 * q^25 + 182846 * q^26 + 354294 * q^27 + 434150 * q^28 + 591285 * q^29 + 97443 * q^30 + 426733 * q^31 + 1205630 * q^32 + 406890 * q^33 + 403548 * q^34 + 912879 * q^35 + 989982 * q^36 + 7703 * q^37 - 417859 * q^38 + 368874 * q^39 + 618020 * q^40 + 770959 * q^41 + 563247 * q^42 + 793050 * q^43 + 2591274 * q^44 + 494262 * q^45 - 4068019 * q^46 + 1410373 * q^47 + 1633014 * q^48 + 1637427 * q^49 + 1021549 * q^50 + 1941813 * q^51 - 3749190 * q^52 + 1037934 * q^53 + 472392 * q^54 + 331974 * q^55 - 391748 * q^56 + 1518237 * q^57 + 653724 * q^58 + 3696822 * q^59 + 3862431 * q^60 - 1374623 * q^61 + 5251718 * q^62 + 2246049 * q^63 + 5077197 * q^64 + 3257170 * q^65 + 7403346 * q^66 - 2436904 * q^67 + 14119909 * q^68 + 4050783 * q^69 + 5185580 * q^70 + 14289172 * q^71 + 2994003 * q^72 + 5482515 * q^73 + 14934154 * q^74 + 10791144 * q^75 + 3822912 * q^76 + 23157109 * q^77 + 4936842 * q^78 + 19786414 * q^79 + 31978143 * q^80 + 9565938 * q^81 + 9749509 * q^82 + 30227337 * q^83 + 11722050 * q^84 + 9946981 * q^85 + 44295864 * q^86 + 15964695 * q^87 + 39970897 * q^88 + 31061677 * q^89 + 2630961 * q^90 + 26377785 * q^91 + 4719698 * q^92 + 11521791 * q^93 + 44488296 * q^94 + 15534599 * q^95 + 32552010 * q^96 + 12084118 * q^97 + 42274744 * q^98 + 10986030 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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