LMFDB - Embedded newform 546.8.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,8,Mod(1,546)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("546.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	546.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:	$170.562223914$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 33506x + 97248 $ x^3 - x^2 - 33506*x + 97248
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$182.082$ of defining polynomial
Character	$\chi$	$=$	546.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +64.4978 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +64.4978 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +515.983 q^{10} -5872.75 q^{11} +1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} +1741.44 q^{15} +4096.00 q^{16} -15651.6 q^{17} +5832.00 q^{18} +30126.6 q^{19} +4127.86 q^{20} -9261.00 q^{21} -46982.0 q^{22} +33071.2 q^{23} +13824.0 q^{24} -73965.0 q^{25} +17576.0 q^{26} +19683.0 q^{27} -21952.0 q^{28} -9791.55 q^{29} +13931.5 q^{30} +139192. q^{31} +32768.0 q^{32} -158564. q^{33} -125213. q^{34} -22122.8 q^{35} +46656.0 q^{36} -314150. q^{37} +241013. q^{38} +59319.0 q^{39} +33022.9 q^{40} +22504.1 q^{41} -74088.0 q^{42} +70031.9 q^{43} -375856. q^{44} +47018.9 q^{45} +264569. q^{46} -843159. q^{47} +110592. q^{48} +117649. q^{49} -591720. q^{50} -422595. q^{51} +140608. q^{52} -1.32192e6 q^{53} +157464. q^{54} -378780. q^{55} -175616. q^{56} +813419. q^{57} -78332.4 q^{58} -2.13368e6 q^{59} +111452. q^{60} +783179. q^{61} +1.11353e6 q^{62} -250047. q^{63} +262144. q^{64} +141702. q^{65} -1.26851e6 q^{66} -2.87302e6 q^{67} -1.00171e6 q^{68} +892921. q^{69} -176982. q^{70} -3.88885e6 q^{71} +373248. q^{72} +3.47390e6 q^{73} -2.51320e6 q^{74} -1.99706e6 q^{75} +1.92810e6 q^{76} +2.01435e6 q^{77} +474552. q^{78} -41311.4 q^{79} +264183. q^{80} +531441. q^{81} +180033. q^{82} -9.55513e6 q^{83} -592704. q^{84} -1.00950e6 q^{85} +560255. q^{86} -264372. q^{87} -3.00685e6 q^{88} +9.05791e6 q^{89} +376151. q^{90} -753571. q^{91} +2.11655e6 q^{92} +3.75818e6 q^{93} -6.74527e6 q^{94} +1.94310e6 q^{95} +884736. q^{96} -6.52408e6 q^{97} +941192. q^{98} -4.28123e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 24 q^{2} + 81 q^{3} + 192 q^{4} - 378 q^{5} + 648 q^{6} - 1029 q^{7} + 1536 q^{8} + 2187 q^{9}+O(q^{10}) $ 3 * q + 24 * q^2 + 81 * q^3 + 192 * q^4 - 378 * q^5 + 648 * q^6 - 1029 * q^7 + 1536 * q^8 + 2187 * q^9	\( 3 q + 24 q^{2} + 81 q^{3} + 192 q^{4} - 378 q^{5} + 648 q^{6} - 1029 q^{7} + 1536 q^{8} + 2187 q^{9} - 3024 q^{10} - 6069 q^{11} + 5184 q^{12} + 6591 q^{13} - 8232 q^{14} - 10206 q^{15} + 12288 q^{16} - 12231 q^{17} + 17496 q^{18} - 4836 q^{19} - 24192 q^{20} - 27783 q^{21} - 48552 q^{22} + 111606 q^{23} + 41472 q^{24} + 41919 q^{25} + 52728 q^{26} + 59049 q^{27} - 65856 q^{28} + 105414 q^{29} - 81648 q^{30} - 263061 q^{31} + 98304 q^{32} - 163863 q^{33} - 97848 q^{34} + 129654 q^{35} + 139968 q^{36} - 585969 q^{37} - 38688 q^{38} + 177957 q^{39} - 193536 q^{40} - 649608 q^{41} - 222264 q^{42} - 76182 q^{43} - 388416 q^{44} - 275562 q^{45} + 892848 q^{46} - 1269219 q^{47} + 331776 q^{48} + 352947 q^{49} + 335352 q^{50} - 330237 q^{51} + 421824 q^{52} + 326511 q^{53} + 472392 q^{54} + 475311 q^{55} - 526848 q^{56} - 130572 q^{57} + 843312 q^{58} - 3434316 q^{59} - 653184 q^{60} - 1450497 q^{61} - 2104488 q^{62} - 750141 q^{63} + 786432 q^{64} - 830466 q^{65} - 1310904 q^{66} - 1302372 q^{67} - 782784 q^{68} + 3013362 q^{69} + 1037232 q^{70} - 5186076 q^{71} + 1119744 q^{72} - 3662940 q^{73} - 4687752 q^{74} + 1131813 q^{75} - 309504 q^{76} + 2081667 q^{77} + 1423656 q^{78} - 2950251 q^{79} - 1548288 q^{80} + 1594323 q^{81} - 5196864 q^{82} - 13650225 q^{83} - 1778112 q^{84} - 9353769 q^{85} - 609456 q^{86} + 2846178 q^{87} - 3107328 q^{88} + 6379533 q^{89} - 2204496 q^{90} - 2260713 q^{91} + 7142784 q^{92} - 7102647 q^{93} - 10153752 q^{94} - 10607646 q^{95} + 2654208 q^{96} - 18032235 q^{97} + 2823576 q^{98} - 4424301 q^{99}+O(q^{100}) \) 3 * q + 24 * q^2 + 81 * q^3 + 192 * q^4 - 378 * q^5 + 648 * q^6 - 1029 * q^7 + 1536 * q^8 + 2187 * q^9 - 3024 * q^10 - 6069 * q^11 + 5184 * q^12 + 6591 * q^13 - 8232 * q^14 - 10206 * q^15 + 12288 * q^16 - 12231 * q^17 + 17496 * q^18 - 4836 * q^19 - 24192 * q^20 - 27783 * q^21 - 48552 * q^22 + 111606 * q^23 + 41472 * q^24 + 41919 * q^25 + 52728 * q^26 + 59049 * q^27 - 65856 * q^28 + 105414 * q^29 - 81648 * q^30 - 263061 * q^31 + 98304 * q^32 - 163863 * q^33 - 97848 * q^34 + 129654 * q^35 + 139968 * q^36 - 585969 * q^37 - 38688 * q^38 + 177957 * q^39 - 193536 * q^40 - 649608 * q^41 - 222264 * q^42 - 76182 * q^43 - 388416 * q^44 - 275562 * q^45 + 892848 * q^46 - 1269219 * q^47 + 331776 * q^48 + 352947 * q^49 + 335352 * q^50 - 330237 * q^51 + 421824 * q^52 + 326511 * q^53 + 472392 * q^54 + 475311 * q^55 - 526848 * q^56 - 130572 * q^57 + 843312 * q^58 - 3434316 * q^59 - 653184 * q^60 - 1450497 * q^61 - 2104488 * q^62 - 750141 * q^63 + 786432 * q^64 - 830466 * q^65 - 1310904 * q^66 - 1302372 * q^67 - 782784 * q^68 + 3013362 * q^69 + 1037232 * q^70 - 5186076 * q^71 + 1119744 * q^72 - 3662940 * q^73 - 4687752 * q^74 + 1131813 * q^75 - 309504 * q^76 + 2081667 * q^77 + 1423656 * q^78 - 2950251 * q^79 - 1548288 * q^80 + 1594323 * q^81 - 5196864 * q^82 - 13650225 * q^83 - 1778112 * q^84 - 9353769 * q^85 - 609456 * q^86 + 2846178 * q^87 - 3107328 * q^88 + 6379533 * q^89 - 2204496 * q^90 - 2260713 * q^91 + 7142784 * q^92 - 7102647 * q^93 - 10153752 * q^94 - 10607646 * q^95 + 2654208 * q^96 - 18032235 * q^97 + 2823576 * q^98 - 4424301 * 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 $

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	64.0000	0.500000
$5$	64.4978	0.230754	0.115377	−	0.993322i	$-0.463192\pi$
$5$	64.4978	0.230754	0.115377	+	0.993322i	$0.463192\pi$
$6$	216.000	0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	515.983	0.163168
$11$	−5872.75	−1.33035	−0.665177	−	0.746686i	$-0.731644\pi$
$11$	−5872.75	−1.33035	−0.665177	+	0.746686i	$0.731644\pi$
$12$	1728.00	0.288675
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−2744.00	−0.267261
$15$	1741.44	0.133226
$16$	4096.00	0.250000
$17$	−15651.6	−0.772661	−0.386330	−	0.922360i	$-0.626258\pi$
$17$	−15651.6	−0.772661	−0.386330	+	0.922360i	$0.626258\pi$
$18$	5832.00	0.235702
$19$	30126.6	1.00766	0.503829	−	0.863803i	$-0.331924\pi$
$19$	30126.6	1.00766	0.503829	+	0.863803i	$0.331924\pi$
$20$	4127.86	0.115377
$21$	−9261.00	−0.218218
$22$	−46982.0	−0.940702
$23$	33071.2	0.566764	0.283382	−	0.959007i	$-0.408544\pi$
$23$	33071.2	0.566764	0.283382	+	0.959007i	$0.408544\pi$
$24$	13824.0	0.204124
$25$	−73965.0	−0.946752
$26$	17576.0	0.196116
$27$	19683.0	0.192450
$28$	−21952.0	−0.188982
$29$	−9791.55	−0.0745519	−0.0372759	−	0.999305i	$-0.511868\pi$
$29$	−9791.55	−0.0745519	−0.0372759	+	0.999305i	$0.511868\pi$
$30$	13931.5	0.0942051
$31$	139192.	0.839165	0.419583	−	0.907717i	$-0.362176\pi$
$31$	139192.	0.839165	0.419583	+	0.907717i	$0.362176\pi$
$32$	32768.0	0.176777
$33$	−158564.	−0.768080
$34$	−125213.	−0.546354
$35$	−22122.8	−0.0872170
$36$	46656.0	0.166667
$37$	−314150.	−1.01960	−0.509802	−	0.860292i	$-0.670281\pi$
$37$	−314150.	−1.01960	−0.509802	+	0.860292i	$0.670281\pi$
$38$	241013.	0.712522
$39$	59319.0	0.160128
$40$	33022.9	0.0815840
$41$	22504.1	0.0509938	0.0254969	−	0.999675i	$-0.491883\pi$
$41$	22504.1	0.0509938	0.0254969	+	0.999675i	$0.491883\pi$
$42$	−74088.0	−0.154303
$43$	70031.9	0.134325	0.0671624	−	0.997742i	$-0.478605\pi$
$43$	70031.9	0.134325	0.0671624	+	0.997742i	$0.478605\pi$
$44$	−375856.	−0.665177
$45$	47018.9	0.0769181
$46$	264569.	0.400762
$47$	−843159.	−1.18459	−0.592293	−	0.805722i	$-0.701777\pi$
$47$	−843159.	−1.18459	−0.592293	+	0.805722i	$0.701777\pi$
$48$	110592.	0.144338
$49$	117649.	0.142857
$50$	−591720.	−0.669455
$51$	−422595.	−0.446096
$52$	140608.	0.138675
$53$	−1.32192e6	−1.21966	−0.609831	−	0.792531i	$-0.708763\pi$
$53$	−1.32192e6	−1.21966	−0.609831	+	0.792531i	$0.708763\pi$
$54$	157464.	0.136083
$55$	−378780.	−0.306985
$56$	−175616.	−0.133631
$57$	813419.	0.581771
$58$	−78332.4	−0.0527161
$59$	−2.13368e6	−1.35253	−0.676267	−	0.736657i	$-0.736403\pi$
$59$	−2.13368e6	−1.35253	−0.676267	+	0.736657i	$0.736403\pi$
$60$	111452.	0.0666131
$61$	783179.	0.441780	0.220890	−	0.975299i	$-0.429104\pi$
$61$	783179.	0.441780	0.220890	+	0.975299i	$0.429104\pi$
$62$	1.11353e6	0.593379
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	141702.	0.0639998
$66$	−1.26851e6	−0.543115
$67$	−2.87302e6	−1.16702	−0.583509	−	0.812107i	$-0.698321\pi$
$67$	−2.87302e6	−1.16702	−0.583509	+	0.812107i	$0.698321\pi$
$68$	−1.00171e6	−0.386330
$69$	892921.	0.327221
$70$	−176982.	−0.0616717
$71$	−3.88885e6	−1.28949	−0.644744	−	0.764399i	$-0.723036\pi$
$71$	−3.88885e6	−1.28949	−0.644744	+	0.764399i	$0.723036\pi$
$72$	373248.	0.117851
$73$	3.47390e6	1.04517	0.522585	−	0.852587i	$-0.324968\pi$
$73$	3.47390e6	1.04517	0.522585	+	0.852587i	$0.324968\pi$
$74$	−2.51320e6	−0.720969
$75$	−1.99706e6	−0.546608
$76$	1.92810e6	0.503829
$77$	2.01435e6	0.502826
$78$	474552.	0.113228
$79$	−41311.4	−0.00942704	−0.00471352	−	0.999989i	$-0.501500\pi$
$79$	−41311.4	−0.00942704	−0.00471352	+	0.999989i	$0.501500\pi$
$80$	264183.	0.0576886
$81$	531441.	0.111111
$82$	180033.	0.0360581
$83$	−9.55513e6	−1.83427	−0.917135	−	0.398576i	$-0.869504\pi$
$83$	−9.55513e6	−1.83427	−0.917135	+	0.398576i	$0.869504\pi$
$84$	−592704.	−0.109109
$85$	−1.00950e6	−0.178295
$86$	560255.	0.0949820
$87$	−264372.	−0.0430426
$88$	−3.00685e6	−0.470351
$89$	9.05791e6	1.36196	0.680978	−	0.732304i	$-0.261555\pi$
$89$	9.05791e6	1.36196	0.680978	+	0.732304i	$0.261555\pi$
$90$	376151.	0.0543893
$91$	−753571.	−0.104828
$92$	2.11655e6	0.283382
$93$	3.75818e6	0.484492
$94$	−6.74527e6	−0.837629
$95$	1.94310e6	0.232521
$96$	884736.	0.102062
$97$	−6.52408e6	−0.725803	−0.362901	−	0.931828i	$-0.618214\pi$
$97$	−6.52408e6	−0.725803	−0.362901	+	0.931828i	$0.618214\pi$
$98$	941192.	0.101015
$99$	−4.28123e6	−0.443451
$100$	−4.73376e6	−0.473376
$101$	−4.35536e6	−0.420629	−0.210314	−	0.977634i	$-0.567449\pi$
$101$	−4.35536e6	−0.420629	−0.210314	+	0.977634i	$0.567449\pi$
$102$	−3.38076e6	−0.315437
$103$	1.32372e7	1.19362	0.596809	−	0.802383i	$-0.296435\pi$
$103$	1.32372e7	1.19362	0.596809	+	0.802383i	$0.296435\pi$
$104$	1.12486e6	0.0980581
$105$	−597314.	−0.0503547
$106$	−1.05754e7	−0.862432
$107$	−6.19012e6	−0.488490	−0.244245	−	0.969714i	$-0.578540\pi$
$107$	−6.19012e6	−0.488490	−0.244245	+	0.969714i	$0.578540\pi$
$108$	1.25971e6	0.0962250
$109$	−1.74717e7	−1.29224	−0.646118	−	0.763238i	$-0.723609\pi$
$109$	−1.74717e7	−1.29224	−0.646118	+	0.763238i	$0.723609\pi$
$110$	−3.03024e6	−0.217071
$111$	−8.48206e6	−0.588669
$112$	−1.40493e6	−0.0944911
$113$	−1.86535e7	−1.21615	−0.608075	−	0.793880i	$-0.708058\pi$
$113$	−1.86535e7	−1.21615	−0.608075	+	0.793880i	$0.708058\pi$
$114$	6.50735e6	0.411375
$115$	2.13302e6	0.130783
$116$	−626659.	−0.0372759
$117$	1.60161e6	0.0924500
$118$	−1.70695e7	−0.956386
$119$	5.36852e6	0.292038
$120$	891618.	0.0471026
$121$	1.50020e7	0.769841
$122$	6.26543e6	0.312386
$123$	607610.	0.0294413
$124$	8.90827e6	0.419583
$125$	−9.80948e6	−0.449222
$126$	−2.00038e6	−0.0890871
$127$	−6.14354e6	−0.266137	−0.133069	−	0.991107i	$-0.542483\pi$
$127$	−6.14354e6	−0.266137	−0.133069	+	0.991107i	$0.542483\pi$
$128$	2.09715e6	0.0883883
$129$	1.89086e6	0.0775524
$130$	1.13361e6	0.0452547
$131$	1.10211e7	0.428329	0.214164	−	0.976798i	$-0.431297\pi$
$131$	1.10211e7	0.428329	0.214164	+	0.976798i	$0.431297\pi$
$132$	−1.01481e7	−0.384040
$133$	−1.03334e7	−0.380859
$134$	−2.29842e7	−0.825206
$135$	1.26951e6	0.0444087
$136$	−8.01364e6	−0.273177
$137$	4.75548e7	1.58006	0.790028	−	0.613070i	$-0.210066\pi$
$137$	4.75548e7	1.58006	0.790028	+	0.613070i	$0.210066\pi$
$138$	7.14337e6	0.231380
$139$	−2.16895e7	−0.685012	−0.342506	−	0.939516i	$-0.611276\pi$
$139$	−2.16895e7	−0.685012	−0.342506	+	0.939516i	$0.611276\pi$
$140$	−1.41586e6	−0.0436085
$141$	−2.27653e7	−0.683922
$142$	−3.11108e7	−0.911806
$143$	−1.29024e7	−0.368974
$144$	2.98598e6	0.0833333
$145$	−631534.	−0.0172032
$146$	2.77912e7	0.739047
$147$	3.17652e6	0.0824786
$148$	−2.01056e7	−0.509802
$149$	796330.	0.0197216	0.00986078	−	0.999951i	$-0.496861\pi$
$149$	796330.	0.0197216	0.00986078	+	0.999951i	$0.496861\pi$
$150$	−1.59764e7	−0.386510
$151$	−3.13894e7	−0.741932	−0.370966	−	0.928647i	$-0.620973\pi$
$151$	−3.13894e7	−0.741932	−0.370966	+	0.928647i	$0.620973\pi$
$152$	1.54248e7	0.356261
$153$	−1.14101e7	−0.257554
$154$	1.61148e7	0.355552
$155$	8.97756e6	0.193641
$156$	3.79642e6	0.0800641
$157$	−1.86295e7	−0.384196	−0.192098	−	0.981376i	$-0.561529\pi$
$157$	−1.86295e7	−0.384196	−0.192098	+	0.981376i	$0.561529\pi$
$158$	−330491.	−0.00666592
$159$	−3.56919e7	−0.704173
$160$	2.11346e6	0.0407920
$161$	−1.13434e7	−0.214217
$162$	4.25153e6	0.0785674
$163$	4.37118e7	0.790573	0.395287	−	0.918558i	$-0.370645\pi$
$163$	4.37118e7	0.790573	0.395287	+	0.918558i	$0.370645\pi$
$164$	1.44026e6	0.0254969
$165$	−1.02270e7	−0.177238
$166$	−7.64411e7	−1.29703
$167$	5.10033e7	0.847405	0.423703	−	0.905801i	$-0.360730\pi$
$167$	5.10033e7	0.847405	0.423703	+	0.905801i	$0.360730\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	−8.07598e6	−0.126074
$171$	2.19623e7	0.335886
$172$	4.48204e6	0.0671624
$173$	−7.83016e7	−1.14976	−0.574882	−	0.818236i	$-0.694952\pi$
$173$	−7.83016e7	−1.14976	−0.574882	+	0.818236i	$0.694952\pi$
$174$	−2.11498e6	−0.0304357
$175$	2.53700e7	0.357839
$176$	−2.40548e7	−0.332588
$177$	−5.76095e7	−0.780886
$178$	7.24633e7	0.963049
$179$	−5.04710e7	−0.657744	−0.328872	−	0.944375i	$-0.606668\pi$
$179$	−5.04710e7	−0.657744	−0.328872	+	0.944375i	$0.606668\pi$
$180$	3.00921e6	0.0384591
$181$	2.94210e6	0.0368793	0.0184396	−	0.999830i	$-0.494130\pi$
$181$	2.94210e6	0.0368793	0.0184396	+	0.999830i	$0.494130\pi$
$182$	−6.02857e6	−0.0741249
$183$	2.11458e7	0.255062
$184$	1.69324e7	0.200381
$185$	−2.02620e7	−0.235278
$186$	3.00654e7	0.342588
$187$	9.19182e7	1.02791
$188$	−5.39622e7	−0.592293
$189$	−6.75127e6	−0.0727393
$190$	1.55448e7	0.164418
$191$	−1.83485e7	−0.190538	−0.0952692	−	0.995452i	$-0.530371\pi$
$191$	−1.83485e7	−0.190538	−0.0952692	+	0.995452i	$0.530371\pi$
$192$	7.07789e6	0.0721688
$193$	−6.70755e7	−0.671605	−0.335802	−	0.941932i	$-0.609007\pi$
$193$	−6.70755e7	−0.671605	−0.335802	+	0.941932i	$0.609007\pi$
$194$	−5.21927e7	−0.513220
$195$	3.82595e6	0.0369503
$196$	7.52954e6	0.0714286
$197$	1.32392e8	1.23376	0.616878	−	0.787059i	$-0.288397\pi$
$197$	1.32392e8	1.23376	0.616878	+	0.787059i	$0.288397\pi$
$198$	−3.42499e7	−0.313567
$199$	1.79590e8	1.61546	0.807730	−	0.589552i	$-0.200696\pi$
$199$	1.79590e8	1.61546	0.807730	+	0.589552i	$0.200696\pi$
$200$	−3.78701e7	−0.334728
$201$	−7.75716e7	−0.673778
$202$	−3.48429e7	−0.297429
$203$	3.35850e6	0.0281780
$204$	−2.70460e7	−0.223048
$205$	1.45146e6	0.0117671
$206$	1.05897e8	0.844015
$207$	2.41089e7	0.188921
$208$	8.99891e6	0.0693375
$209$	−1.76926e8	−1.34054
$210$	−4.77851e6	−0.0356062
$211$	−2.29188e8	−1.67959	−0.839796	−	0.542903i	$-0.817325\pi$
$211$	−2.29188e8	−1.67959	−0.839796	+	0.542903i	$0.817325\pi$
$212$	−8.46029e7	−0.609831
$213$	−1.04999e8	−0.744486
$214$	−4.95209e7	−0.345415
$215$	4.51690e6	0.0309960
$216$	1.00777e7	0.0680414
$217$	−4.77428e7	−0.317175
$218$	−1.39773e8	−0.913749
$219$	9.37953e7	0.603430
$220$	−2.42419e7	−0.153493
$221$	−3.43867e7	−0.214298
$222$	−6.78565e7	−0.416252
$223$	−3.63717e6	−0.0219632	−0.0109816	−	0.999940i	$-0.503496\pi$
$223$	−3.63717e6	−0.0219632	−0.0109816	+	0.999940i	$0.503496\pi$
$224$	−1.12394e7	−0.0668153
$225$	−5.39205e7	−0.315584
$226$	−1.49228e8	−0.859947
$227$	8.56917e6	0.0486238	0.0243119	−	0.999704i	$-0.492261\pi$
$227$	8.56917e6	0.0486238	0.0243119	+	0.999704i	$0.492261\pi$
$228$	5.20588e7	0.290886
$229$	1.73439e7	0.0954384	0.0477192	−	0.998861i	$-0.484805\pi$
$229$	1.73439e7	0.0954384	0.0477192	+	0.998861i	$0.484805\pi$
$230$	1.70641e7	0.0924777
$231$	5.43875e7	0.290307
$232$	−5.01328e6	−0.0263581
$233$	2.08479e8	1.07973	0.539866	−	0.841751i	$-0.318475\pi$
$233$	2.08479e8	1.07973	0.539866	+	0.841751i	$0.318475\pi$
$234$	1.28129e7	0.0653720
$235$	−5.43819e7	−0.273349
$236$	−1.36556e8	−0.676267
$237$	−1.11541e6	−0.00544270
$238$	4.29481e7	0.206502
$239$	−4.46958e7	−0.211774	−0.105887	−	0.994378i	$-0.533768\pi$
$239$	−4.46958e7	−0.211774	−0.105887	+	0.994378i	$0.533768\pi$
$240$	7.13294e6	0.0333065
$241$	−2.14819e8	−0.988583	−0.494291	−	0.869296i	$-0.664572\pi$
$241$	−2.14819e8	−0.988583	−0.494291	+	0.869296i	$0.664572\pi$
$242$	1.20016e8	0.544360
$243$	1.43489e7	0.0641500
$244$	5.01234e7	0.220890
$245$	7.58810e6	0.0329649
$246$	4.86088e6	0.0208181
$247$	6.61882e7	0.279474
$248$	7.12662e7	0.296690
$249$	−2.57989e8	−1.05902
$250$	−7.84758e7	−0.317648
$251$	−3.23074e8	−1.28957	−0.644784	−	0.764365i	$-0.723053\pi$
$251$	−3.23074e8	−1.28957	−0.644784	+	0.764365i	$0.723053\pi$
$252$	−1.60030e7	−0.0629941
$253$	−1.94219e8	−0.753996
$254$	−4.91483e7	−0.188187
$255$	−2.72564e7	−0.102939
$256$	1.67772e7	0.0625000
$257$	8.55956e7	0.314547	0.157273	−	0.987555i	$-0.449730\pi$
$257$	8.55956e7	0.314547	0.157273	+	0.987555i	$0.449730\pi$
$258$	1.51269e7	0.0548379
$259$	1.07754e8	0.385374
$260$	9.06891e6	0.0319999
$261$	−7.13804e6	−0.0248506
$262$	8.81692e7	0.302874
$263$	−1.74097e8	−0.590126	−0.295063	−	0.955478i	$-0.595341\pi$
$263$	−1.74097e8	−0.590126	−0.295063	+	0.955478i	$0.595341\pi$
$264$	−8.11849e7	−0.271557
$265$	−8.52610e7	−0.281443
$266$	−8.26675e7	−0.269308
$267$	2.44564e8	0.786326
$268$	−1.83873e8	−0.583509
$269$	8.68329e7	0.271989	0.135995	−	0.990710i	$-0.456577\pi$
$269$	8.68329e7	0.271989	0.135995	+	0.990710i	$0.456577\pi$
$270$	1.01561e7	0.0314017
$271$	1.87782e7	0.0573140	0.0286570	−	0.999589i	$-0.490877\pi$
$271$	1.87782e7	0.0573140	0.0286570	+	0.999589i	$0.490877\pi$
$272$	−6.41092e7	−0.193165
$273$	−2.03464e7	−0.0605228
$274$	3.80439e8	1.11727
$275$	4.34378e8	1.25952
$276$	5.71470e7	0.163611
$277$	−2.91740e8	−0.824740	−0.412370	−	0.911016i	$-0.635299\pi$
$277$	−2.91740e8	−0.824740	−0.412370	+	0.911016i	$0.635299\pi$
$278$	−1.73516e8	−0.484377
$279$	1.01471e8	0.279722
$280$	−1.13269e7	−0.0308359
$281$	2.05821e8	0.553371	0.276686	−	0.960961i	$-0.410764\pi$
$281$	2.05821e8	0.553371	0.276686	+	0.960961i	$0.410764\pi$
$282$	−1.82122e8	−0.483606
$283$	4.20543e8	1.10296	0.551478	−	0.834190i	$-0.314064\pi$
$283$	4.20543e8	1.10296	0.551478	+	0.834190i	$0.314064\pi$
$284$	−2.48887e8	−0.644744
$285$	5.24638e7	0.134246
$286$	−1.03219e8	−0.260904
$287$	−7.71890e6	−0.0192739
$288$	2.38879e7	0.0589256
$289$	−1.65365e8	−0.402995
$290$	−5.05227e6	−0.0121645
$291$	−1.76150e8	−0.419042
$292$	2.22330e8	0.522585
$293$	5.56877e6	0.0129337	0.00646685	−	0.999979i	$-0.497942\pi$
$293$	5.56877e6	0.0129337	0.00646685	+	0.999979i	$0.497942\pi$
$294$	2.54122e7	0.0583212
$295$	−1.37618e8	−0.312103
$296$	−1.60845e8	−0.360485
$297$	−1.15593e8	−0.256027
$298$	6.37064e6	0.0139453
$299$	7.26573e7	0.157192
$300$	−1.27812e8	−0.273304
$301$	−2.40209e7	−0.0507700
$302$	−2.51115e8	−0.524625
$303$	−1.17595e8	−0.242850
$304$	1.23399e8	0.251914
$305$	5.05133e7	0.101943
$306$	−9.12804e7	−0.182118
$307$	7.75228e8	1.52913	0.764566	−	0.644546i	$-0.222953\pi$
$307$	7.75228e8	1.52913	0.764566	+	0.644546i	$0.222953\pi$
$308$	1.28919e8	0.251413
$309$	3.57404e8	0.689136
$310$	7.18205e7	0.136925
$311$	9.89100e7	0.186457	0.0932285	−	0.995645i	$-0.470281\pi$
$311$	9.89100e7	0.186457	0.0932285	+	0.995645i	$0.470281\pi$
$312$	3.03713e7	0.0566139
$313$	8.87990e8	1.63683	0.818414	−	0.574629i	$-0.194854\pi$
$313$	8.87990e8	1.63683	0.818414	+	0.574629i	$0.194854\pi$
$314$	−1.49036e8	−0.271668
$315$	−1.61275e7	−0.0290723
$316$	−2.64393e6	−0.00471352
$317$	−9.12749e8	−1.60933	−0.804663	−	0.593732i	$-0.797654\pi$
$317$	−9.12749e8	−1.60933	−0.804663	+	0.593732i	$0.797654\pi$
$318$	−2.85535e8	−0.497925
$319$	5.75033e7	0.0991804
$320$	1.69077e7	0.0288443
$321$	−1.67133e8	−0.282030
$322$	−9.07473e7	−0.151474
$323$	−4.71532e8	−0.778578
$324$	3.40122e7	0.0555556
$325$	−1.62501e8	−0.262582
$326$	3.49694e8	0.559020
$327$	−4.71735e8	−0.746073
$328$	1.15221e7	0.0180290
$329$	2.89203e8	0.447732
$330$	−8.18164e7	−0.125326
$331$	−6.64240e8	−1.00676	−0.503381	−	0.864064i	$-0.667911\pi$
$331$	−6.64240e8	−1.00676	−0.503381	+	0.864064i	$0.667911\pi$
$332$	−6.11528e8	−0.917135
$333$	−2.29016e8	−0.339868
$334$	4.08027e8	0.599206
$335$	−1.85304e8	−0.269294
$336$	−3.79331e7	−0.0545545
$337$	−4.22017e8	−0.600656	−0.300328	−	0.953836i	$-0.597096\pi$
$337$	−4.22017e8	−0.600656	−0.300328	+	0.953836i	$0.597096\pi$
$338$	3.86145e7	0.0543928
$339$	−5.03646e8	−0.702144
$340$	−6.46078e7	−0.0891474
$341$	−8.17438e8	−1.11639
$342$	1.75699e8	0.237507
$343$	−4.03536e7	−0.0539949
$344$	3.58563e7	0.0474910
$345$	5.75915e7	0.0755077
$346$	−6.26412e8	−0.813006
$347$	1.01379e9	1.30256	0.651278	−	0.758839i	$-0.274233\pi$
$347$	1.01379e9	1.30256	0.651278	+	0.758839i	$0.274233\pi$
$348$	−1.69198e7	−0.0215213
$349$	−1.10515e9	−1.39165	−0.695827	−	0.718209i	$-0.744962\pi$
$349$	−1.10515e9	−1.39165	−0.695827	+	0.718209i	$0.744962\pi$
$350$	2.02960e8	0.253030
$351$	4.32436e7	0.0533761
$352$	−1.92438e8	−0.235176
$353$	−9.31318e8	−1.12690	−0.563451	−	0.826149i	$-0.690527\pi$
$353$	−9.31318e8	−1.12690	−0.563451	+	0.826149i	$0.690527\pi$
$354$	−4.60876e8	−0.552170
$355$	−2.50823e8	−0.297555
$356$	5.79707e8	0.680978
$357$	1.44950e8	0.168608
$358$	−4.03768e8	−0.465095
$359$	−4.79644e8	−0.547128	−0.273564	−	0.961854i	$-0.588203\pi$
$359$	−4.79644e8	−0.547128	−0.273564	+	0.961854i	$0.588203\pi$
$360$	2.40737e7	0.0271947
$361$	1.37425e7	0.0153741
$362$	2.35368e7	0.0260776
$363$	4.05055e8	0.444468
$364$	−4.82285e7	−0.0524142
$365$	2.24059e8	0.241178
$366$	1.69167e8	0.180356
$367$	−1.56315e9	−1.65070	−0.825351	−	0.564620i	$-0.809023\pi$
$367$	−1.56315e9	−1.65070	−0.825351	+	0.564620i	$0.809023\pi$
$368$	1.35459e8	0.141691
$369$	1.64055e7	0.0169979
$370$	−1.62096e8	−0.166367
$371$	4.53419e8	0.460989
$372$	2.40523e8	0.242246
$373$	1.17308e9	1.17043	0.585214	−	0.810879i	$-0.301010\pi$
$373$	1.17308e9	1.17043	0.585214	+	0.810879i	$0.301010\pi$
$374$	7.35346e8	0.726844
$375$	−2.64856e8	−0.259358
$376$	−4.31697e8	−0.418815
$377$	−2.15120e7	−0.0206770
$378$	−5.40102e7	−0.0514344
$379$	−5.48626e8	−0.517654	−0.258827	−	0.965924i	$-0.583336\pi$
$379$	−5.48626e8	−0.517654	−0.258827	+	0.965924i	$0.583336\pi$
$380$	1.24359e8	0.116261
$381$	−1.65876e8	−0.153654
$382$	−1.46788e8	−0.134731
$383$	−2.66068e8	−0.241990	−0.120995	−	0.992653i	$-0.538608\pi$
$383$	−2.66068e8	−0.241990	−0.120995	+	0.992653i	$0.538608\pi$
$384$	5.66231e7	0.0510310
$385$	1.29921e8	0.116029
$386$	−5.36604e8	−0.474896
$387$	5.10532e7	0.0447749
$388$	−4.17541e8	−0.362901
$389$	2.18997e9	1.88632	0.943160	−	0.332339i	$-0.107838\pi$
$389$	2.18997e9	1.88632	0.943160	+	0.332339i	$0.107838\pi$
$390$	3.06076e7	0.0261278
$391$	−5.17618e8	−0.437916
$392$	6.02363e7	0.0505076
$393$	2.97571e8	0.247296
$394$	1.05913e9	0.872397
$395$	−2.66450e6	−0.00217533
$396$	−2.73999e8	−0.221726
$397$	−9.13823e8	−0.732986	−0.366493	−	0.930421i	$-0.619442\pi$
$397$	−9.13823e8	−0.732986	−0.366493	+	0.930421i	$0.619442\pi$
$398$	1.43672e9	1.14230
$399$	−2.79003e8	−0.219889
$400$	−3.02961e8	−0.236688
$401$	−1.14284e8	−0.0885075	−0.0442538	−	0.999020i	$-0.514091\pi$
$401$	−1.14284e8	−0.0885075	−0.0442538	+	0.999020i	$0.514091\pi$
$402$	−6.20573e8	−0.476433
$403$	3.05804e8	0.232743
$404$	−2.78743e8	−0.210314
$405$	3.42768e7	0.0256394
$406$	2.68680e7	0.0199248
$407$	1.84493e9	1.35643
$408$	−2.16368e8	−0.157719
$409$	−3.88721e8	−0.280936	−0.140468	−	0.990085i	$-0.544861\pi$
$409$	−3.88721e8	−0.280936	−0.140468	+	0.990085i	$0.544861\pi$
$410$	1.16117e7	0.00832056
$411$	1.28398e9	0.912246
$412$	8.47180e8	0.596809
$413$	7.31854e8	0.511210
$414$	1.92871e8	0.133587
$415$	−6.16285e8	−0.423266
$416$	7.19913e7	0.0490290
$417$	−5.85617e8	−0.395492
$418$	−1.41541e9	−0.947906
$419$	4.72674e7	0.0313916	0.0156958	−	0.999877i	$-0.495004\pi$
$419$	4.72674e7	0.0313916	0.0156958	+	0.999877i	$0.495004\pi$
$420$	−3.82281e7	−0.0251774
$421$	4.32503e8	0.282489	0.141245	−	0.989975i	$-0.454890\pi$
$421$	4.32503e8	0.282489	0.141245	+	0.989975i	$0.454890\pi$
$422$	−1.83351e9	−1.18765
$423$	−6.14663e8	−0.394862
$424$	−6.76823e8	−0.431216
$425$	1.15767e9	0.731518
$426$	−8.39992e8	−0.526431
$427$	−2.68630e8	−0.166977
$428$	−3.96167e8	−0.244245
$429$	−3.48366e8	−0.213027
$430$	3.61352e7	0.0219175
$431$	8.45750e7	0.0508829	0.0254414	−	0.999676i	$-0.491901\pi$
$431$	8.45750e7	0.0508829	0.0254414	+	0.999676i	$0.491901\pi$
$432$	8.06216e7	0.0481125
$433$	2.51807e9	1.49060	0.745299	−	0.666730i	$-0.232307\pi$
$433$	2.51807e9	1.49060	0.745299	+	0.666730i	$0.232307\pi$
$434$	−3.81942e8	−0.224276
$435$	−1.70514e7	−0.00993226
$436$	−1.11819e9	−0.646118
$437$	9.96323e8	0.571104
$438$	7.50362e8	0.426689
$439$	−3.66101e8	−0.206526	−0.103263	−	0.994654i	$-0.532928\pi$
$439$	−3.66101e8	−0.206526	−0.103263	+	0.994654i	$0.532928\pi$
$440$	−1.93935e8	−0.108536
$441$	8.57661e7	0.0476190
$442$	−2.75093e8	−0.151531
$443$	−1.07649e9	−0.588300	−0.294150	−	0.955759i	$-0.595037\pi$
$443$	−1.07649e9	−0.588300	−0.294150	+	0.955759i	$0.595037\pi$
$444$	−5.42852e8	−0.294334
$445$	5.84216e8	0.314277
$446$	−2.90973e7	−0.0155304
$447$	2.15009e7	0.0113862
$448$	−8.99154e7	−0.0472456
$449$	3.34803e9	1.74553	0.872764	−	0.488143i	$-0.162325\pi$
$449$	3.34803e9	1.74553	0.872764	+	0.488143i	$0.162325\pi$
$450$	−4.31364e8	−0.223152
$451$	−1.32161e8	−0.0678398
$452$	−1.19383e9	−0.608075
$453$	−8.47514e8	−0.428354
$454$	6.85534e7	0.0343822
$455$	−4.86037e7	−0.0241896
$456$	4.16471e8	0.205687
$457$	1.10267e9	0.540430	0.270215	−	0.962800i	$-0.412905\pi$
$457$	1.10267e9	0.540430	0.270215	+	0.962800i	$0.412905\pi$
$458$	1.38751e8	0.0674851
$459$	−3.08071e8	−0.148699
$460$	1.36513e8	0.0653916
$461$	−1.47377e9	−0.700609	−0.350304	−	0.936636i	$-0.613922\pi$
$461$	−1.47377e9	−0.700609	−0.350304	+	0.936636i	$0.613922\pi$
$462$	4.35100e8	0.205278
$463$	2.01070e9	0.941487	0.470743	−	0.882270i	$-0.343986\pi$
$463$	2.01070e9	0.941487	0.470743	+	0.882270i	$0.343986\pi$
$464$	−4.01062e7	−0.0186380
$465$	2.42394e8	0.111799
$466$	1.66783e9	0.763486
$467$	5.56877e7	0.0253017	0.0126509	−	0.999920i	$-0.495973\pi$
$467$	5.56877e7	0.0253017	0.0126509	+	0.999920i	$0.495973\pi$
$468$	1.02503e8	0.0462250
$469$	9.85447e8	0.441091
$470$	−4.35055e8	−0.193287
$471$	−5.02997e8	−0.221816
$472$	−1.09245e9	−0.478193
$473$	−4.11280e8	−0.178699
$474$	−8.92326e6	−0.00384857
$475$	−2.22832e9	−0.954002
$476$	3.43585e8	0.146019
$477$	−9.63680e8	−0.406554
$478$	−3.57566e8	−0.149747
$479$	2.29894e9	0.955769	0.477885	−	0.878423i	$-0.341404\pi$
$479$	2.29894e9	0.955769	0.477885	+	0.878423i	$0.341404\pi$
$480$	5.70635e7	0.0235513
$481$	−6.90189e8	−0.282787
$482$	−1.71855e9	−0.699034
$483$	−3.06272e8	−0.123678
$484$	9.60129e8	0.384920
$485$	−4.20789e8	−0.167482
$486$	1.14791e8	0.0453609
$487$	−1.19801e9	−0.470014	−0.235007	−	0.971994i	$-0.575511\pi$
$487$	−1.19801e9	−0.470014	−0.235007	+	0.971994i	$0.575511\pi$
$488$	4.00988e8	0.156193
$489$	1.18022e9	0.456438
$490$	6.07048e7	0.0233097
$491$	−1.37101e8	−0.0522704	−0.0261352	−	0.999658i	$-0.508320\pi$
$491$	−1.37101e8	−0.0522704	−0.0261352	+	0.999658i	$0.508320\pi$
$492$	3.88870e7	0.0147207
$493$	1.53254e8	0.0576033
$494$	5.29506e8	0.197618
$495$	−2.76130e8	−0.102328
$496$	5.70129e8	0.209791
$497$	1.33388e9	0.487381
$498$	−2.06391e9	−0.748838
$499$	3.88029e9	1.39802	0.699008	−	0.715114i	$-0.253625\pi$
$499$	3.88029e9	1.39802	0.699008	+	0.715114i	$0.253625\pi$
$500$	−6.27806e8	−0.224611
$501$	1.37709e9	0.489250
$502$	−2.58459e9	−0.911863
$503$	−2.99805e9	−1.05039	−0.525195	−	0.850982i	$-0.676008\pi$
$503$	−2.99805e9	−1.05039	−0.525195	+	0.850982i	$0.676008\pi$
$504$	−1.28024e8	−0.0445435
$505$	−2.80911e8	−0.0970619
$506$	−1.55375e9	−0.533156
$507$	1.30324e8	0.0444116
$508$	−3.93187e8	−0.133069
$509$	4.12358e9	1.38600	0.692999	−	0.720939i	$-0.256289\pi$
$509$	4.12358e9	1.38600	0.692999	+	0.720939i	$0.256289\pi$
$510$	−2.18051e8	−0.0727886
$511$	−1.19155e9	−0.395037
$512$	1.34218e8	0.0441942
$513$	5.92983e8	0.193924
$514$	6.84765e8	0.222418
$515$	8.53770e8	0.275433
$516$	1.21015e8	0.0387762
$517$	4.95166e9	1.57592
$518$	8.62029e8	0.272501
$519$	−2.11414e9	−0.663817
$520$	7.25513e7	0.0226273
$521$	−1.97614e9	−0.612189	−0.306094	−	0.952001i	$-0.599022\pi$
$521$	−1.97614e9	−0.612189	−0.306094	+	0.952001i	$0.599022\pi$
$522$	−5.71043e7	−0.0175720
$523$	2.57751e9	0.787852	0.393926	−	0.919142i	$-0.371117\pi$
$523$	2.57751e9	0.787852	0.393926	+	0.919142i	$0.371117\pi$
$524$	7.05353e8	0.214164
$525$	6.84990e8	0.206598
$526$	−1.39277e9	−0.417282
$527$	−2.17858e9	−0.648390
$528$	−6.49479e8	−0.192020
$529$	−2.31112e9	−0.678779
$530$	−6.82088e8	−0.199010
$531$	−1.55546e9	−0.450845
$532$	−6.61340e8	−0.190429
$533$	4.94415e7	0.0141431
$534$	1.95651e9	0.556016
$535$	−3.99249e8	−0.112721
$536$	−1.47099e9	−0.412603
$537$	−1.36272e9	−0.379749
$538$	6.94664e8	0.192325
$539$	−6.90923e8	−0.190051
$540$	8.12487e7	0.0222044
$541$	−4.78834e9	−1.30015	−0.650076	−	0.759869i	$-0.725263\pi$
$541$	−4.78834e9	−1.30015	−0.650076	+	0.759869i	$0.725263\pi$
$542$	1.50225e8	0.0405271
$543$	7.94366e7	0.0212922
$544$	−5.12873e8	−0.136588
$545$	−1.12689e9	−0.298189
$546$	−1.62771e8	−0.0427960
$547$	5.41849e9	1.41554	0.707771	−	0.706442i	$-0.249701\pi$
$547$	5.41849e9	1.41554	0.707771	+	0.706442i	$0.249701\pi$
$548$	3.04351e9	0.790028
$549$	5.70937e8	0.147260
$550$	3.47503e9	0.890612
$551$	−2.94987e8	−0.0751228
$552$	4.57176e8	0.115690
$553$	1.41698e7	0.00356308
$554$	−2.33392e9	−0.583179
$555$	−5.47075e8	−0.135838
$556$	−1.38813e9	−0.342506
$557$	−7.53467e9	−1.84744	−0.923721	−	0.383065i	$-0.874869\pi$
$557$	−7.53467e9	−1.84744	−0.923721	+	0.383065i	$0.874869\pi$
$558$	8.11766e8	0.197793
$559$	1.53860e8	0.0372550
$560$	−9.06148e7	−0.0218042
$561$	2.48179e9	0.593465
$562$	1.64656e9	0.391292
$563$	2.14390e9	0.506320	0.253160	−	0.967424i	$-0.418530\pi$
$563$	2.14390e9	0.506320	0.253160	+	0.967424i	$0.418530\pi$
$564$	−1.45698e9	−0.341961
$565$	−1.20311e9	−0.280632
$566$	3.36434e9	0.779907
$567$	−1.82284e8	−0.0419961
$568$	−1.99109e9	−0.455903
$569$	−2.07542e9	−0.472295	−0.236148	−	0.971717i	$-0.575885\pi$
$569$	−2.07542e9	−0.472295	−0.236148	+	0.971717i	$0.575885\pi$
$570$	4.19710e8	0.0949265
$571$	1.87810e9	0.422175	0.211088	−	0.977467i	$-0.432299\pi$
$571$	1.87810e9	0.422175	0.211088	+	0.977467i	$0.432299\pi$
$572$	−8.25756e8	−0.184487
$573$	−4.95408e8	−0.110007
$574$	−6.17512e7	−0.0136287
$575$	−2.44611e9	−0.536585
$576$	1.91103e8	0.0416667
$577$	5.47499e9	1.18650	0.593251	−	0.805018i	$-0.297844\pi$
$577$	5.47499e9	1.18650	0.593251	+	0.805018i	$0.297844\pi$
$578$	−1.32292e9	−0.284961
$579$	−1.81104e9	−0.387751
$580$	−4.04182e7	−0.00860159
$581$	3.27741e9	0.693289
$582$	−1.40920e9	−0.296308
$583$	7.76331e9	1.62258
$584$	1.77864e9	0.369524
$585$	1.03301e8	0.0213333
$586$	4.45502e7	0.00914551
$587$	2.41330e9	0.492468	0.246234	−	0.969210i	$-0.420807\pi$
$587$	2.41330e9	0.492468	0.246234	+	0.969210i	$0.420807\pi$
$588$	2.03297e8	0.0412393
$589$	4.19338e9	0.845591
$590$	−1.10094e9	−0.220690
$591$	3.57458e9	0.712309
$592$	−1.28676e9	−0.254901
$593$	2.77785e9	0.547037	0.273518	−	0.961867i	$-0.411813\pi$
$593$	2.77785e9	0.547037	0.273518	+	0.961867i	$0.411813\pi$
$594$	−9.24747e8	−0.181038
$595$	3.46258e8	0.0673891
$596$	5.09651e7	0.00986078
$597$	4.84893e9	0.932687
$598$	5.81259e8	0.111152
$599$	4.21728e9	0.801750	0.400875	−	0.916133i	$-0.368706\pi$
$599$	4.21728e9	0.801750	0.400875	+	0.916133i	$0.368706\pi$
$600$	−1.02249e9	−0.193255
$601$	−7.01385e8	−0.131794	−0.0658970	−	0.997826i	$-0.520991\pi$
$601$	−7.01385e8	−0.131794	−0.0658970	+	0.997826i	$0.520991\pi$
$602$	−1.92167e8	−0.0358998
$603$	−2.09443e9	−0.389006
$604$	−2.00892e9	−0.370966
$605$	9.67598e8	0.177644
$606$	−9.40757e8	−0.171721
$607$	4.40540e9	0.799512	0.399756	−	0.916622i	$-0.369095\pi$
$607$	4.40540e9	0.799512	0.399756	+	0.916622i	$0.369095\pi$
$608$	9.87190e8	0.178130
$609$	9.06796e7	0.0162686
$610$	4.04107e8	0.0720844
$611$	−1.85242e9	−0.328545
$612$	−7.30243e8	−0.128777
$613$	−7.06089e9	−1.23808	−0.619039	−	0.785360i	$-0.712478\pi$
$613$	−7.06089e9	−1.23808	−0.619039	+	0.785360i	$0.712478\pi$
$614$	6.20182e9	1.08126
$615$	3.91895e7	0.00679371
$616$	1.03135e9	0.177776
$617$	1.98525e9	0.340265	0.170132	−	0.985421i	$-0.445580\pi$
$617$	1.98525e9	0.340265	0.170132	+	0.985421i	$0.445580\pi$
$618$	2.85923e9	0.487293
$619$	4.32660e8	0.0733212	0.0366606	−	0.999328i	$-0.488328\pi$
$619$	4.32660e8	0.0733212	0.0366606	+	0.999328i	$0.488328\pi$
$620$	5.74564e8	0.0968205
$621$	6.50940e8	0.109074
$622$	7.91280e8	0.131845
$623$	−3.10686e9	−0.514771
$624$	2.42971e8	0.0400320
$625$	5.14583e9	0.843092
$626$	7.10392e9	1.15741
$627$	−4.77701e9	−0.773962
$628$	−1.19229e9	−0.192098
$629$	4.91697e9	0.787808
$630$	−1.29020e8	−0.0205572
$631$	1.01114e10	1.60217	0.801086	−	0.598549i	$-0.204256\pi$
$631$	1.01114e10	1.60217	0.801086	+	0.598549i	$0.204256\pi$
$632$	−2.11514e7	−0.00333296
$633$	−6.18808e9	−0.969712
$634$	−7.30199e9	−1.13797
$635$	−3.96245e8	−0.0614123
$636$	−2.28428e9	−0.352086
$637$	2.58475e8	0.0396214
$638$	4.60027e8	0.0701311
$639$	−2.83497e9	−0.429829
$640$	1.35262e8	0.0203960
$641$	−1.23899e9	−0.185809	−0.0929044	−	0.995675i	$-0.529615\pi$
$641$	−1.23899e9	−0.185809	−0.0929044	+	0.995675i	$0.529615\pi$
$642$	−1.33707e9	−0.199425
$643$	1.10373e10	1.63728	0.818641	−	0.574306i	$-0.194728\pi$
$643$	1.10373e10	1.63728	0.818641	+	0.574306i	$0.194728\pi$
$644$	−7.25978e8	−0.107108
$645$	1.21956e8	0.0178956
$646$	−3.77225e9	−0.550538
$647$	7.21143e9	1.04678	0.523391	−	0.852093i	$-0.324667\pi$
$647$	7.21143e9	1.04678	0.523391	+	0.852093i	$0.324667\pi$
$648$	2.72098e8	0.0392837
$649$	1.25306e10	1.79935
$650$	−1.30001e9	−0.185673
$651$	−1.28905e9	−0.183121
$652$	2.79756e9	0.395287
$653$	1.01510e10	1.42663	0.713315	−	0.700844i	$-0.247193\pi$
$653$	1.01510e10	1.42663	0.713315	+	0.700844i	$0.247193\pi$
$654$	−3.77388e9	−0.527553
$655$	7.10840e8	0.0988388
$656$	9.21767e7	0.0127485
$657$	2.53247e9	0.348390
$658$	2.31363e9	0.316594
$659$	8.68982e9	1.18280	0.591401	−	0.806378i	$-0.298575\pi$
$659$	8.68982e9	1.18280	0.591401	+	0.806378i	$0.298575\pi$
$660$	−6.54531e8	−0.0886189
$661$	1.15618e10	1.55712	0.778558	−	0.627573i	$-0.215952\pi$
$661$	1.15618e10	1.55712	0.778558	+	0.627573i	$0.215952\pi$
$662$	−5.31392e9	−0.711889
$663$	−9.28440e8	−0.123725
$664$	−4.89223e9	−0.648513
$665$	−6.66484e8	−0.0878849
$666$	−1.83213e9	−0.240323
$667$	−3.23818e8	−0.0422533
$668$	3.26421e9	0.423703
$669$	−9.82035e7	−0.0126805
$670$	−1.48243e9	−0.190420
$671$	−4.59941e9	−0.587724
$672$	−3.03464e8	−0.0385758
$673$	3.92321e9	0.496122	0.248061	−	0.968744i	$-0.420207\pi$
$673$	3.92321e9	0.496122	0.248061	+	0.968744i	$0.420207\pi$
$674$	−3.37614e9	−0.424728
$675$	−1.45585e9	−0.182203
$676$	3.08916e8	0.0384615
$677$	−1.19781e10	−1.48364	−0.741821	−	0.670597i	$-0.766038\pi$
$677$	−1.19781e10	−1.48364	−0.741821	+	0.670597i	$0.766038\pi$
$678$	−4.02917e9	−0.496491
$679$	2.23776e9	0.274328
$680$	−5.16863e8	−0.0630368
$681$	2.31368e8	0.0280729
$682$	−6.53950e9	−0.789404
$683$	2.59108e9	0.311177	0.155589	−	0.987822i	$-0.450273\pi$
$683$	2.59108e9	0.311177	0.155589	+	0.987822i	$0.450273\pi$
$684$	1.40559e9	0.167943
$685$	3.06718e9	0.364605
$686$	−3.22829e8	−0.0381802
$687$	4.68286e8	0.0551014
$688$	2.86851e8	0.0335812
$689$	−2.90426e9	−0.338274
$690$	4.60732e8	0.0533920
$691$	−4.21958e9	−0.486515	−0.243258	−	0.969962i	$-0.578216\pi$
$691$	−4.21958e9	−0.486515	−0.243258	+	0.969962i	$0.578216\pi$
$692$	−5.01130e9	−0.574882
$693$	1.46846e9	0.167609
$694$	8.11035e9	0.921046
$695$	−1.39893e9	−0.158070
$696$	−1.35358e8	−0.0152178
$697$	−3.52226e8	−0.0394009
$698$	−8.84118e9	−0.984048
$699$	5.62892e9	0.623383
$700$	1.62368e9	0.178919
$701$	−1.47437e9	−0.161656	−0.0808281	−	0.996728i	$-0.525756\pi$
$701$	−1.47437e9	−0.161656	−0.0808281	+	0.996728i	$0.525756\pi$
$702$	3.45948e8	0.0377426
$703$	−9.46430e9	−1.02741
$704$	−1.53951e9	−0.166294
$705$	−1.46831e9	−0.157818
$706$	−7.45054e9	−0.796840
$707$	1.49389e9	0.158983
$708$	−3.68701e9	−0.390443
$709$	1.10955e10	1.16919	0.584597	−	0.811324i	$-0.301253\pi$
$709$	1.10955e10	1.16919	0.584597	+	0.811324i	$0.301253\pi$
$710$	−2.00658e9	−0.210403
$711$	−3.01160e7	−0.00314235
$712$	4.63765e9	0.481524
$713$	4.60323e9	0.475608
$714$	1.15960e9	0.119224
$715$	−8.32179e8	−0.0851423
$716$	−3.23015e9	−0.328872
$717$	−1.20679e9	−0.122268
$718$	−3.83716e9	−0.386878
$719$	1.58120e10	1.58648	0.793240	−	0.608910i	$-0.208393\pi$
$719$	1.58120e10	1.58648	0.793240	+	0.608910i	$0.208393\pi$
$720$	1.92589e8	0.0192295
$721$	−4.54035e9	−0.451145
$722$	1.09940e8	0.0108712
$723$	−5.80011e9	−0.570759
$724$	1.88294e8	0.0184396
$725$	7.24233e8	0.0705822
$726$	3.24044e9	0.314286
$727$	9.87137e9	0.952812	0.476406	−	0.879225i	$-0.341939\pi$
$727$	9.87137e9	0.952812	0.476406	+	0.879225i	$0.341939\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	1.79247e9	0.170538
$731$	−1.09611e9	−0.103787
$732$	1.35333e9	0.127531
$733$	−6.81775e9	−0.639407	−0.319703	−	0.947518i	$-0.603583\pi$
$733$	−6.81775e9	−0.639407	−0.319703	+	0.947518i	$0.603583\pi$
$734$	−1.25052e10	−1.16722
$735$	2.04879e8	0.0190323
$736$	1.08368e9	0.100191
$737$	1.68725e10	1.55255
$738$	1.31244e8	0.0120194
$739$	1.56723e10	1.42849	0.714247	−	0.699894i	$-0.246769\pi$
$739$	1.56723e10	1.42849	0.714247	+	0.699894i	$0.246769\pi$
$740$	−1.29677e9	−0.117639
$741$	1.78708e9	0.161354
$742$	3.62735e9	0.325969
$743$	−1.71945e8	−0.0153791	−0.00768953	−	0.999970i	$-0.502448\pi$
$743$	−1.71945e8	−0.0153791	−0.00768953	+	0.999970i	$0.502448\pi$
$744$	1.92419e9	0.171294
$745$	5.13616e7	0.00455084
$746$	9.38460e9	0.827618
$747$	−6.96569e9	−0.611424
$748$	5.88277e9	0.513956
$749$	2.12321e9	0.184632
$750$	−2.11885e9	−0.183394
$751$	2.02723e10	1.74648	0.873241	−	0.487288i	$-0.162014\pi$
$751$	2.02723e10	1.74648	0.873241	+	0.487288i	$0.162014\pi$
$752$	−3.45358e9	−0.296147
$753$	−8.72301e9	−0.744533
$754$	−1.72096e8	−0.0146208
$755$	−2.02455e9	−0.171204
$756$	−4.32081e8	−0.0363696
$757$	−3.84532e9	−0.322179	−0.161089	−	0.986940i	$-0.551501\pi$
$757$	−3.84532e9	−0.322179	−0.161089	+	0.986940i	$0.551501\pi$
$758$	−4.38901e9	−0.366036
$759$	−5.24390e9	−0.435320
$760$	9.94869e8	0.0822088
$761$	6.02175e9	0.495309	0.247655	−	0.968848i	$-0.420340\pi$
$761$	6.02175e9	0.495309	0.247655	+	0.968848i	$0.420340\pi$
$762$	−1.32700e9	−0.108650
$763$	5.99278e9	0.488419
$764$	−1.17430e9	−0.0952692
$765$	−7.35924e8	−0.0594316
$766$	−2.12855e9	−0.171113
$767$	−4.68770e9	−0.375125
$768$	4.52985e8	0.0360844
$769$	5.07521e9	0.402450	0.201225	−	0.979545i	$-0.435508\pi$
$769$	5.07521e9	0.402450	0.201225	+	0.979545i	$0.435508\pi$
$770$	1.03937e9	0.0820452
$771$	2.31108e9	0.181604
$772$	−4.29283e9	−0.335802
$773$	1.49026e10	1.16047	0.580234	−	0.814450i	$-0.302961\pi$
$773$	1.49026e10	1.16047	0.580234	+	0.814450i	$0.302961\pi$
$774$	4.08426e8	0.0316607
$775$	−1.02953e10	−0.794482
$776$	−3.34033e9	−0.256610
$777$	2.90935e9	0.222496
$778$	1.75198e10	1.33383
$779$	6.77972e8	0.0513843
$780$	2.44861e8	0.0184751
$781$	2.28383e10	1.71547
$782$	−4.14095e9	−0.309653
$783$	−1.92727e8	−0.0143475
$784$	4.81890e8	0.0357143
$785$	−1.20156e9	−0.0886550
$786$	2.38057e9	0.174864
$787$	6.23622e9	0.456047	0.228023	−	0.973656i	$-0.426774\pi$
$787$	6.23622e9	0.456047	0.228023	+	0.973656i	$0.426774\pi$
$788$	8.47307e9	0.616878
$789$	−4.70061e9	−0.340710
$790$	−2.13160e7	−0.00153819
$791$	6.39817e9	0.459661
$792$	−2.19199e9	−0.156784
$793$	1.72064e9	0.122528
$794$	−7.31059e9	−0.518299
$795$	−2.30205e9	−0.162491
$796$	1.14938e10	0.807730
$797$	−1.61581e10	−1.13054	−0.565271	−	0.824906i	$-0.691228\pi$
$797$	−1.61581e10	−1.13054	−0.565271	+	0.824906i	$0.691228\pi$
$798$	−2.23202e9	−0.155485
$799$	1.31968e10	0.915284
$800$	−2.42369e9	−0.167364
$801$	6.60322e9	0.453985
$802$	−9.14272e8	−0.0625843
$803$	−2.04013e10	−1.39045
$804$	−4.96458e9	−0.336889
$805$	−7.31625e8	−0.0494314
$806$	2.44643e9	0.164574
$807$	2.34449e9	0.157033
$808$	−2.22994e9	−0.148715
$809$	−2.33422e10	−1.54996	−0.774982	−	0.631983i	$-0.782241\pi$
$809$	−2.33422e10	−1.54996	−0.774982	+	0.631983i	$0.782241\pi$
$810$	2.74214e8	0.0181298
$811$	3.95487e9	0.260351	0.130175	−	0.991491i	$-0.458446\pi$
$811$	3.95487e9	0.260351	0.130175	+	0.991491i	$0.458446\pi$
$812$	2.14944e8	0.0140890
$813$	5.07010e8	0.0330902
$814$	1.47594e10	0.959144
$815$	2.81932e9	0.182428
$816$	−1.73095e9	−0.111524
$817$	2.10982e9	0.135353
$818$	−3.10977e9	−0.198651
$819$	−5.49353e8	−0.0349428
$820$	9.28937e7	0.00588353
$821$	−1.48747e10	−0.938096	−0.469048	−	0.883173i	$-0.655403\pi$
$821$	−1.48747e10	−0.938096	−0.469048	+	0.883173i	$0.655403\pi$
$822$	1.02718e10	0.645055
$823$	3.23768e9	0.202458	0.101229	−	0.994863i	$-0.467723\pi$
$823$	3.23768e9	0.202458	0.101229	+	0.994863i	$0.467723\pi$
$824$	6.77744e9	0.422008
$825$	1.17282e10	0.727182
$826$	5.85483e9	0.361480
$827$	−1.34297e10	−0.825649	−0.412825	−	0.910811i	$-0.635458\pi$
$827$	−1.34297e10	−0.825649	−0.412825	+	0.910811i	$0.635458\pi$
$828$	1.54297e9	0.0944606
$829$	−1.67063e10	−1.01845	−0.509226	−	0.860633i	$-0.670068\pi$
$829$	−1.67063e10	−1.01845	−0.509226	+	0.860633i	$0.670068\pi$
$830$	−4.93028e9	−0.299294
$831$	−7.87699e9	−0.476164
$832$	5.75930e8	0.0346688
$833$	−1.84140e9	−0.110380
$834$	−4.68494e9	−0.279655
$835$	3.28961e9	0.195542
$836$	−1.13233e10	−0.670271
$837$	2.73971e9	0.161497
$838$	3.78139e8	0.0221972
$839$	−3.16216e10	−1.84849	−0.924244	−	0.381802i	$-0.875304\pi$
$839$	−3.16216e10	−1.84849	−0.924244	+	0.381802i	$0.875304\pi$
$840$	−3.05825e8	−0.0178031
$841$	−1.71540e10	−0.994442
$842$	3.46003e9	0.199750
$843$	5.55715e9	0.319489
$844$	−1.46680e10	−0.839796
$845$	3.11319e8	0.0177503
$846$	−4.91730e9	−0.279210
$847$	−5.14569e9	−0.290972
$848$	−5.41459e9	−0.304916
$849$	1.13547e10	0.636792
$850$	9.26140e9	0.517262
$851$	−1.03893e10	−0.577875
$852$	−6.71994e9	−0.372243
$853$	−1.44652e10	−0.798001	−0.399000	−	0.916951i	$-0.630643\pi$
$853$	−1.44652e10	−0.798001	−0.399000	+	0.916951i	$0.630643\pi$
$854$	−2.14904e9	−0.118071
$855$	1.41652e9	0.0775072
$856$	−3.16934e9	−0.172707
$857$	−4.93647e9	−0.267907	−0.133953	−	0.990988i	$-0.542767\pi$
$857$	−4.93647e9	−0.267907	−0.133953	+	0.990988i	$0.542767\pi$
$858$	−2.78693e9	−0.150633
$859$	−9.91361e9	−0.533649	−0.266824	−	0.963745i	$-0.585974\pi$
$859$	−9.91361e9	−0.533649	−0.266824	+	0.963745i	$0.585974\pi$
$860$	2.89082e8	0.0154980
$861$	−2.08410e8	−0.0111278
$862$	6.76600e8	0.0359796
$863$	−3.92623e9	−0.207940	−0.103970	−	0.994580i	$-0.533155\pi$
$863$	−3.92623e9	−0.207940	−0.103970	+	0.994580i	$0.533155\pi$
$864$	6.44973e8	0.0340207
$865$	−5.05028e9	−0.265313
$866$	2.01446e10	1.05401
$867$	−4.46484e9	−0.232669
$868$	−3.05554e9	−0.158587
$869$	2.42612e8	0.0125413
$870$	−1.36411e8	−0.00702317
$871$	−6.31203e9	−0.323672
$872$	−8.94550e9	−0.456874
$873$	−4.75606e9	−0.241934
$874$	7.97058e9	0.403831
$875$	3.36465e9	0.169790
$876$	6.00290e9	0.301715
$877$	−4.17893e9	−0.209202	−0.104601	−	0.994514i	$-0.533357\pi$
$877$	−4.17893e9	−0.209202	−0.104601	+	0.994514i	$0.533357\pi$
$878$	−2.92881e9	−0.146036
$879$	1.50357e8	0.00746727
$880$	−1.55148e9	−0.0767463
$881$	3.77440e9	0.185965	0.0929826	−	0.995668i	$-0.470360\pi$
$881$	3.77440e9	0.185965	0.0929826	+	0.995668i	$0.470360\pi$
$882$	6.86129e8	0.0336718
$883$	−1.77730e10	−0.868757	−0.434379	−	0.900730i	$-0.643032\pi$
$883$	−1.77730e10	−0.868757	−0.434379	+	0.900730i	$0.643032\pi$
$884$	−2.20075e9	−0.107149
$885$	−3.71569e9	−0.180193
$886$	−8.61196e9	−0.415991
$887$	−2.82373e10	−1.35860	−0.679299	−	0.733861i	$-0.737716\pi$
$887$	−2.82373e10	−1.35860	−0.679299	+	0.733861i	$0.737716\pi$
$888$	−4.34282e9	−0.208126
$889$	2.10723e9	0.100590
$890$	4.67373e9	0.222228
$891$	−3.12102e9	−0.147817
$892$	−2.32779e8	−0.0109816
$893$	−2.54015e10	−1.19366
$894$	1.72007e8	0.00805129
$895$	−3.25527e9	−0.151777
$896$	−7.19323e8	−0.0334077
$897$	1.96175e9	0.0907548
$898$	2.67842e10	1.23427
$899$	−1.36290e9	−0.0625613
$900$	−3.45091e9	−0.157792
$901$	2.06902e10	0.942386
$902$	−1.05729e9	−0.0479700
$903$	−6.48565e8	−0.0293121
$904$	−9.55061e9	−0.429974
$905$	1.89759e8	0.00851005
$906$	−6.78011e9	−0.302892
$907$	2.77847e10	1.23646	0.618229	−	0.785998i	$-0.287850\pi$
$907$	2.77847e10	1.23646	0.618229	+	0.785998i	$0.287850\pi$
$908$	5.48427e8	0.0243119
$909$	−3.17505e9	−0.140210
$910$	−3.88830e8	−0.0171047
$911$	3.03754e10	1.33109	0.665545	−	0.746358i	$-0.268199\pi$
$911$	3.03754e10	1.33109	0.665545	+	0.746358i	$0.268199\pi$
$912$	3.33177e9	0.145443
$913$	5.61149e10	2.44023
$914$	8.82138e9	0.382142
$915$	1.36386e9	0.0588567
$916$	1.11001e9	0.0477192
$917$	−3.78025e9	−0.161893
$918$	−2.46457e9	−0.105146
$919$	−4.64931e9	−0.197599	−0.0987994	−	0.995107i	$-0.531500\pi$
$919$	−4.64931e9	−0.197599	−0.0987994	+	0.995107i	$0.531500\pi$
$920$	1.09211e9	0.0462389
$921$	2.09311e10	0.882845
$922$	−1.17901e10	−0.495405
$923$	−8.54381e9	−0.357640
$924$	3.48080e9	0.145153
$925$	2.32361e10	0.965313
$926$	1.60856e10	0.665732
$927$	9.64991e9	0.397873
$928$	−3.20850e8	−0.0131790
$929$	−4.29001e10	−1.75551	−0.877756	−	0.479109i	$-0.840960\pi$
$929$	−4.29001e10	−1.75551	−0.877756	+	0.479109i	$0.840960\pi$
$930$	1.93915e9	0.0790536
$931$	3.54437e9	0.143951
$932$	1.33426e10	0.539866
$933$	2.67057e9	0.107651
$934$	4.45502e8	0.0178910
$935$	5.92853e9	0.237195
$936$	8.20026e8	0.0326860
$937$	−1.23329e10	−0.489754	−0.244877	−	0.969554i	$-0.578748\pi$
$937$	−1.23329e10	−0.489754	−0.244877	+	0.969554i	$0.578748\pi$
$938$	7.88358e9	0.311899
$939$	2.39757e10	0.945023
$940$	−3.48044e9	−0.136674
$941$	−3.04804e10	−1.19249	−0.596247	−	0.802801i	$-0.703342\pi$
$941$	−3.04804e10	−1.19249	−0.596247	+	0.802801i	$0.703342\pi$
$942$	−4.02398e9	−0.156847
$943$	7.44236e8	0.0289015
$944$	−8.73957e9	−0.338133
$945$	−4.35442e8	−0.0167849
$946$	−3.29024e9	−0.126360
$947$	−3.65100e10	−1.39697	−0.698484	−	0.715625i	$-0.746142\pi$
$947$	−3.65100e10	−1.39697	−0.698484	+	0.715625i	$0.746142\pi$
$948$	−7.13861e7	−0.00272135
$949$	7.63216e9	0.289878
$950$	−1.78265e10	−0.674582
$951$	−2.46442e10	−0.929145
$952$	2.74868e9	0.103251
$953$	−1.11257e10	−0.416390	−0.208195	−	0.978087i	$-0.566759\pi$
$953$	−1.11257e10	−0.416390	−0.208195	+	0.978087i	$0.566759\pi$
$954$	−7.70944e9	−0.287477
$955$	−1.18344e9	−0.0439676
$956$	−2.86053e9	−0.105887
$957$	1.55259e9	0.0572618
$958$	1.83915e10	0.675831
$959$	−1.63113e10	−0.597205
$960$	4.56508e8	0.0166533
$961$	−8.13828e9	−0.295802
$962$	−5.52151e9	−0.199961
$963$	−4.51259e9	−0.162830
$964$	−1.37484e10	−0.494291
$965$	−4.32623e9	−0.154976
$966$	−2.45018e9	−0.0874535
$967$	3.46167e10	1.23110	0.615550	−	0.788098i	$-0.288934\pi$
$967$	3.46167e10	1.23110	0.615550	+	0.788098i	$0.288934\pi$
$968$	7.68103e9	0.272180
$969$	−1.27314e10	−0.449512
$970$	−3.36631e9	−0.118428
$971$	−8.94170e9	−0.313439	−0.156719	−	0.987643i	$-0.550092\pi$
$971$	−8.94170e9	−0.313439	−0.156719	+	0.987643i	$0.550092\pi$
$972$	9.18330e8	0.0320750
$973$	7.43951e9	0.258910
$974$	−9.58411e9	−0.332350
$975$	−4.38753e9	−0.151602
$976$	3.20790e9	0.110445
$977$	2.82017e10	0.967487	0.483743	−	0.875210i	$-0.339277\pi$
$977$	2.82017e10	0.967487	0.483743	+	0.875210i	$0.339277\pi$
$978$	9.44175e9	0.322750
$979$	−5.31949e10	−1.81188
$980$	4.85639e8	0.0164825
$981$	−1.27369e10	−0.430745
$982$	−1.09681e9	−0.0369607
$983$	−4.45399e10	−1.49559	−0.747794	−	0.663930i	$-0.768887\pi$
$983$	−4.45399e10	−1.49559	−0.747794	+	0.663930i	$0.768887\pi$
$984$	3.11096e8	0.0104091
$985$	8.53898e9	0.284695
$986$	1.22603e9	0.0407317
$987$	7.80849e9	0.258498
$988$	4.23605e9	0.139737
$989$	2.31604e9	0.0761304
$990$	−2.20904e9	−0.0723571
$991$	−3.74106e10	−1.22106	−0.610530	−	0.791993i	$-0.709043\pi$
$991$	−3.74106e10	−1.22106	−0.610530	+	0.791993i	$0.709043\pi$
$992$	4.56103e9	0.148345
$993$	−1.79345e10	−0.581255
$994$	1.06710e10	0.344630
$995$	1.15832e10	0.372775
$996$	−1.65113e10	−0.529508
$997$	−1.78609e10	−0.570781	−0.285391	−	0.958411i	$-0.592123\pi$
$997$	−1.78609e10	−0.570781	−0.285391	+	0.958411i	$0.592123\pi$
$998$	3.10423e10	0.988547
$999$	−6.18342e9	−0.196223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.e.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.e.1.2	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	546.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +64.4978 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +64.4978 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +515.983 q^{10} -5872.75 q^{11} +1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} +1741.44 q^{15} +4096.00 q^{16} -15651.6 q^{17} +5832.00 q^{18} +30126.6 q^{19} +4127.86 q^{20} -9261.00 q^{21} -46982.0 q^{22} +33071.2 q^{23} +13824.0 q^{24} -73965.0 q^{25} +17576.0 q^{26} +19683.0 q^{27} -21952.0 q^{28} -9791.55 q^{29} +13931.5 q^{30} +139192. q^{31} +32768.0 q^{32} -158564. q^{33} -125213. q^{34} -22122.8 q^{35} +46656.0 q^{36} -314150. q^{37} +241013. q^{38} +59319.0 q^{39} +33022.9 q^{40} +22504.1 q^{41} -74088.0 q^{42} +70031.9 q^{43} -375856. q^{44} +47018.9 q^{45} +264569. q^{46} -843159. q^{47} +110592. q^{48} +117649. q^{49} -591720. q^{50} -422595. q^{51} +140608. q^{52} -1.32192e6 q^{53} +157464. q^{54} -378780. q^{55} -175616. q^{56} +813419. q^{57} -78332.4 q^{58} -2.13368e6 q^{59} +111452. q^{60} +783179. q^{61} +1.11353e6 q^{62} -250047. q^{63} +262144. q^{64} +141702. q^{65} -1.26851e6 q^{66} -2.87302e6 q^{67} -1.00171e6 q^{68} +892921. q^{69} -176982. q^{70} -3.88885e6 q^{71} +373248. q^{72} +3.47390e6 q^{73} -2.51320e6 q^{74} -1.99706e6 q^{75} +1.92810e6 q^{76} +2.01435e6 q^{77} +474552. q^{78} -41311.4 q^{79} +264183. q^{80} +531441. q^{81} +180033. q^{82} -9.55513e6 q^{83} -592704. q^{84} -1.00950e6 q^{85} +560255. q^{86} -264372. q^{87} -3.00685e6 q^{88} +9.05791e6 q^{89} +376151. q^{90} -753571. q^{91} +2.11655e6 q^{92} +3.75818e6 q^{93} -6.74527e6 q^{94} +1.94310e6 q^{95} +884736. q^{96} -6.52408e6 q^{97} +941192. q^{98} -4.28123e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 24 q^{2} + 81 q^{3} + 192 q^{4} - 378 q^{5} + 648 q^{6} - 1029 q^{7} + 1536 q^{8} + 2187 q^{9}+O(q^{10}) \) 3 * q + 24 * q^2 + 81 * q^3 + 192 * q^4 - 378 * q^5 + 648 * q^6 - 1029 * q^7 + 1536 * q^8 + 2187 * q^9	\( 3 q + 24 q^{2} + 81 q^{3} + 192 q^{4} - 378 q^{5} + 648 q^{6} - 1029 q^{7} + 1536 q^{8} + 2187 q^{9} - 3024 q^{10} - 6069 q^{11} + 5184 q^{12} + 6591 q^{13} - 8232 q^{14} - 10206 q^{15} + 12288 q^{16} - 12231 q^{17} + 17496 q^{18} - 4836 q^{19} - 24192 q^{20} - 27783 q^{21} - 48552 q^{22} + 111606 q^{23} + 41472 q^{24} + 41919 q^{25} + 52728 q^{26} + 59049 q^{27} - 65856 q^{28} + 105414 q^{29} - 81648 q^{30} - 263061 q^{31} + 98304 q^{32} - 163863 q^{33} - 97848 q^{34} + 129654 q^{35} + 139968 q^{36} - 585969 q^{37} - 38688 q^{38} + 177957 q^{39} - 193536 q^{40} - 649608 q^{41} - 222264 q^{42} - 76182 q^{43} - 388416 q^{44} - 275562 q^{45} + 892848 q^{46} - 1269219 q^{47} + 331776 q^{48} + 352947 q^{49} + 335352 q^{50} - 330237 q^{51} + 421824 q^{52} + 326511 q^{53} + 472392 q^{54} + 475311 q^{55} - 526848 q^{56} - 130572 q^{57} + 843312 q^{58} - 3434316 q^{59} - 653184 q^{60} - 1450497 q^{61} - 2104488 q^{62} - 750141 q^{63} + 786432 q^{64} - 830466 q^{65} - 1310904 q^{66} - 1302372 q^{67} - 782784 q^{68} + 3013362 q^{69} + 1037232 q^{70} - 5186076 q^{71} + 1119744 q^{72} - 3662940 q^{73} - 4687752 q^{74} + 1131813 q^{75} - 309504 q^{76} + 2081667 q^{77} + 1423656 q^{78} - 2950251 q^{79} - 1548288 q^{80} + 1594323 q^{81} - 5196864 q^{82} - 13650225 q^{83} - 1778112 q^{84} - 9353769 q^{85} - 609456 q^{86} + 2846178 q^{87} - 3107328 q^{88} + 6379533 q^{89} - 2204496 q^{90} - 2260713 q^{91} + 7142784 q^{92} - 7102647 q^{93} - 10153752 q^{94} - 10607646 q^{95} + 2654208 q^{96} - 18032235 q^{97} + 2823576 q^{98} - 4424301 q^{99}+O(q^{100}) \) 3 * q + 24 * q^2 + 81 * q^3 + 192 * q^4 - 378 * q^5 + 648 * q^6 - 1029 * q^7 + 1536 * q^8 + 2187 * q^9 - 3024 * q^10 - 6069 * q^11 + 5184 * q^12 + 6591 * q^13 - 8232 * q^14 - 10206 * q^15 + 12288 * q^16 - 12231 * q^17 + 17496 * q^18 - 4836 * q^19 - 24192 * q^20 - 27783 * q^21 - 48552 * q^22 + 111606 * q^23 + 41472 * q^24 + 41919 * q^25 + 52728 * q^26 + 59049 * q^27 - 65856 * q^28 + 105414 * q^29 - 81648 * q^30 - 263061 * q^31 + 98304 * q^32 - 163863 * q^33 - 97848 * q^34 + 129654 * q^35 + 139968 * q^36 - 585969 * q^37 - 38688 * q^38 + 177957 * q^39 - 193536 * q^40 - 649608 * q^41 - 222264 * q^42 - 76182 * q^43 - 388416 * q^44 - 275562 * q^45 + 892848 * q^46 - 1269219 * q^47 + 331776 * q^48 + 352947 * q^49 + 335352 * q^50 - 330237 * q^51 + 421824 * q^52 + 326511 * q^53 + 472392 * q^54 + 475311 * q^55 - 526848 * q^56 - 130572 * q^57 + 843312 * q^58 - 3434316 * q^59 - 653184 * q^60 - 1450497 * q^61 - 2104488 * q^62 - 750141 * q^63 + 786432 * q^64 - 830466 * q^65 - 1310904 * q^66 - 1302372 * q^67 - 782784 * q^68 + 3013362 * q^69 + 1037232 * q^70 - 5186076 * q^71 + 1119744 * q^72 - 3662940 * q^73 - 4687752 * q^74 + 1131813 * q^75 - 309504 * q^76 + 2081667 * q^77 + 1423656 * q^78 - 2950251 * q^79 - 1548288 * q^80 + 1594323 * q^81 - 5196864 * q^82 - 13650225 * q^83 - 1778112 * q^84 - 9353769 * q^85 - 609456 * q^86 + 2846178 * q^87 - 3107328 * q^88 + 6379533 * q^89 - 2204496 * q^90 - 2260713 * q^91 + 7142784 * q^92 - 7102647 * q^93 - 10153752 * q^94 - 10607646 * q^95 + 2654208 * q^96 - 18032235 * q^97 + 2823576 * q^98 - 4424301 * q^99

Introduction

L-functions

Modular forms

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