LMFDB - Embedded newform 546.8.a.m.1.1

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:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 197669x^{3} - 12910499x^{2} + 9274302080x + 1050512243200 $ x^5 - x^4 - 197669x^3 - 12910499x^2 + 9274302080*x + 1050512243200
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$390.906$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -330.906 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -330.906 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -2647.25 q^{10} +4519.30 q^{11} +1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} -8934.47 q^{15} +4096.00 q^{16} +13929.8 q^{17} +5832.00 q^{18} -17964.9 q^{19} -21178.0 q^{20} -9261.00 q^{21} +36154.4 q^{22} -13223.1 q^{23} +13824.0 q^{24} +31374.0 q^{25} -17576.0 q^{26} +19683.0 q^{27} -21952.0 q^{28} -6179.34 q^{29} -71475.8 q^{30} +47237.9 q^{31} +32768.0 q^{32} +122021. q^{33} +111438. q^{34} +113501. q^{35} +46656.0 q^{36} -448372. q^{37} -143719. q^{38} -59319.0 q^{39} -169424. q^{40} -32173.1 q^{41} -74088.0 q^{42} +824429. q^{43} +289235. q^{44} -241231. q^{45} -105785. q^{46} +400844. q^{47} +110592. q^{48} +117649. q^{49} +250992. q^{50} +376104. q^{51} -140608. q^{52} -1.68286e6 q^{53} +157464. q^{54} -1.49546e6 q^{55} -175616. q^{56} -485051. q^{57} -49434.7 q^{58} -1.00121e6 q^{59} -571806. q^{60} +2.11553e6 q^{61} +377903. q^{62} -250047. q^{63} +262144. q^{64} +727001. q^{65} +976168. q^{66} +3.03100e6 q^{67} +891505. q^{68} -357024. q^{69} +908007. q^{70} -1.41071e6 q^{71} +373248. q^{72} +3.58877e6 q^{73} -3.58698e6 q^{74} +847097. q^{75} -1.14975e6 q^{76} -1.55012e6 q^{77} -474552. q^{78} +3.09169e6 q^{79} -1.35539e6 q^{80} +531441. q^{81} -257385. q^{82} +732145. q^{83} -592704. q^{84} -4.60945e6 q^{85} +6.59543e6 q^{86} -166842. q^{87} +2.31388e6 q^{88} -439716. q^{89} -1.92985e6 q^{90} +753571. q^{91} -846279. q^{92} +1.27542e6 q^{93} +3.20675e6 q^{94} +5.94469e6 q^{95} +884736. q^{96} +1.26283e7 q^{97} +941192. q^{98} +3.29457e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 40 q^{2} + 135 q^{3} + 320 q^{4} + 299 q^{5} + 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9}+O(q^{10}) $ 5 * q + 40 * q^2 + 135 * q^3 + 320 * q^4 + 299 * q^5 + 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9	\( 5 q + 40 q^{2} + 135 q^{3} + 320 q^{4} + 299 q^{5} + 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9} + 2392 q^{10} + 1838 q^{11} + 8640 q^{12} - 10985 q^{13} - 13720 q^{14} + 8073 q^{15} + 20480 q^{16} + 56444 q^{17} + 29160 q^{18} - 20639 q^{19} + 19136 q^{20} - 46305 q^{21} + 14704 q^{22} + 74395 q^{23} + 69120 q^{24} + 22594 q^{25} - 87880 q^{26} + 98415 q^{27} - 109760 q^{28} + 130059 q^{29} + 64584 q^{30} + 330083 q^{31} + 163840 q^{32} + 49626 q^{33} + 451552 q^{34} - 102557 q^{35} + 233280 q^{36} + 410632 q^{37} - 165112 q^{38} - 296595 q^{39} + 153088 q^{40} + 172558 q^{41} - 370440 q^{42} + 886497 q^{43} + 117632 q^{44} + 217971 q^{45} + 595160 q^{46} + 763969 q^{47} + 552960 q^{48} + 588245 q^{49} + 180752 q^{50} + 1523988 q^{51} - 703040 q^{52} + 1714575 q^{53} + 787320 q^{54} + 2699318 q^{55} - 878080 q^{56} - 557253 q^{57} + 1040472 q^{58} + 603580 q^{59} + 516672 q^{60} + 6172268 q^{61} + 2640664 q^{62} - 1250235 q^{63} + 1310720 q^{64} - 656903 q^{65} + 397008 q^{66} + 5490834 q^{67} + 3612416 q^{68} + 2008665 q^{69} - 820456 q^{70} - 1581200 q^{71} + 1866240 q^{72} + 2100143 q^{73} + 3285056 q^{74} + 610038 q^{75} - 1320896 q^{76} - 630434 q^{77} - 2372760 q^{78} + 6357137 q^{79} + 1224704 q^{80} + 2657205 q^{81} + 1380464 q^{82} + 5292133 q^{83} - 2963520 q^{84} - 836908 q^{85} + 7091976 q^{86} + 3511593 q^{87} + 941056 q^{88} + 13229719 q^{89} + 1743768 q^{90} + 3767855 q^{91} + 4761280 q^{92} + 8912241 q^{93} + 6111752 q^{94} + 25806433 q^{95} + 4423680 q^{96} + 22321383 q^{97} + 4705960 q^{98} + 1339902 q^{99}+O(q^{100}) \) 5 * q + 40 * q^2 + 135 * q^3 + 320 * q^4 + 299 * q^5 + 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9 + 2392 * q^10 + 1838 * q^11 + 8640 * q^12 - 10985 * q^13 - 13720 * q^14 + 8073 * q^15 + 20480 * q^16 + 56444 * q^17 + 29160 * q^18 - 20639 * q^19 + 19136 * q^20 - 46305 * q^21 + 14704 * q^22 + 74395 * q^23 + 69120 * q^24 + 22594 * q^25 - 87880 * q^26 + 98415 * q^27 - 109760 * q^28 + 130059 * q^29 + 64584 * q^30 + 330083 * q^31 + 163840 * q^32 + 49626 * q^33 + 451552 * q^34 - 102557 * q^35 + 233280 * q^36 + 410632 * q^37 - 165112 * q^38 - 296595 * q^39 + 153088 * q^40 + 172558 * q^41 - 370440 * q^42 + 886497 * q^43 + 117632 * q^44 + 217971 * q^45 + 595160 * q^46 + 763969 * q^47 + 552960 * q^48 + 588245 * q^49 + 180752 * q^50 + 1523988 * q^51 - 703040 * q^52 + 1714575 * q^53 + 787320 * q^54 + 2699318 * q^55 - 878080 * q^56 - 557253 * q^57 + 1040472 * q^58 + 603580 * q^59 + 516672 * q^60 + 6172268 * q^61 + 2640664 * q^62 - 1250235 * q^63 + 1310720 * q^64 - 656903 * q^65 + 397008 * q^66 + 5490834 * q^67 + 3612416 * q^68 + 2008665 * q^69 - 820456 * q^70 - 1581200 * q^71 + 1866240 * q^72 + 2100143 * q^73 + 3285056 * q^74 + 610038 * q^75 - 1320896 * q^76 - 630434 * q^77 - 2372760 * q^78 + 6357137 * q^79 + 1224704 * q^80 + 2657205 * q^81 + 1380464 * q^82 + 5292133 * q^83 - 2963520 * q^84 - 836908 * q^85 + 7091976 * q^86 + 3511593 * q^87 + 941056 * q^88 + 13229719 * q^89 + 1743768 * q^90 + 3767855 * q^91 + 4761280 * q^92 + 8912241 * q^93 + 6111752 * q^94 + 25806433 * q^95 + 4423680 * q^96 + 22321383 * q^97 + 4705960 * q^98 + 1339902 * 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
$5$	−330.906	−1.18389	−0.591943	−	0.805980i	$-0.701639\pi$
$5$	−330.906	−1.18389	−0.591943	+	0.805980i	$0.701639\pi$
$6$	216.000	0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	−2647.25	−0.837134
$11$	4519.30	1.02376	0.511878	−	0.859058i	$-0.328950\pi$
$11$	4519.30	1.02376	0.511878	+	0.859058i	$0.328950\pi$
$12$	1728.00	0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−2744.00	−0.267261
$15$	−8934.47	−0.683517
$16$	4096.00	0.250000
$17$	13929.8	0.687658	0.343829	−	0.939032i	$-0.388276\pi$
$17$	13929.8	0.687658	0.343829	+	0.939032i	$0.388276\pi$
$18$	5832.00	0.235702
$19$	−17964.9	−0.600878	−0.300439	−	0.953801i	$-0.597133\pi$
$19$	−17964.9	−0.600878	−0.300439	+	0.953801i	$0.597133\pi$
$20$	−21178.0	−0.591943
$21$	−9261.00	−0.218218
$22$	36154.4	0.723905
$23$	−13223.1	−0.226614	−0.113307	−	0.993560i	$-0.536144\pi$
$23$	−13223.1	−0.226614	−0.113307	+	0.993560i	$0.536144\pi$
$24$	13824.0	0.204124
$25$	31374.0	0.401587
$26$	−17576.0	−0.196116
$27$	19683.0	0.192450
$28$	−21952.0	−0.188982
$29$	−6179.34	−0.0470489	−0.0235244	−	0.999723i	$-0.507489\pi$
$29$	−6179.34	−0.0470489	−0.0235244	+	0.999723i	$0.507489\pi$
$30$	−71475.8	−0.483320
$31$	47237.9	0.284790	0.142395	−	0.989810i	$-0.454520\pi$
$31$	47237.9	0.284790	0.142395	+	0.989810i	$0.454520\pi$
$32$	32768.0	0.176777
$33$	122021.	0.591066
$34$	111438.	0.486248
$35$	113501.	0.447467
$36$	46656.0	0.166667
$37$	−448372.	−1.45523	−0.727616	−	0.685984i	$-0.759372\pi$
$37$	−448372.	−1.45523	−0.727616	+	0.685984i	$0.759372\pi$
$38$	−143719.	−0.424885
$39$	−59319.0	−0.160128
$40$	−169424.	−0.418567
$41$	−32173.1	−0.0729037	−0.0364519	−	0.999335i	$-0.511606\pi$
$41$	−32173.1	−0.0729037	−0.0364519	+	0.999335i	$0.511606\pi$
$42$	−74088.0	−0.154303
$43$	824429.	1.58130	0.790649	−	0.612270i	$-0.209743\pi$
$43$	824429.	1.58130	0.790649	+	0.612270i	$0.209743\pi$
$44$	289235.	0.511878
$45$	−241231.	−0.394629
$46$	−105785.	−0.160240
$47$	400844.	0.563162	0.281581	−	0.959538i	$-0.409141\pi$
$47$	400844.	0.563162	0.281581	+	0.959538i	$0.409141\pi$
$48$	110592.	0.144338
$49$	117649.	0.142857
$50$	250992.	0.283965
$51$	376104.	0.397020
$52$	−140608.	−0.138675
$53$	−1.68286e6	−1.55268	−0.776340	−	0.630315i	$-0.782926\pi$
$53$	−1.68286e6	−1.55268	−0.776340	+	0.630315i	$0.782926\pi$
$54$	157464.	0.136083
$55$	−1.49546e6	−1.21201
$56$	−175616.	−0.133631
$57$	−485051.	−0.346917
$58$	−49434.7	−0.0332686
$59$	−1.00121e6	−0.634664	−0.317332	−	0.948314i	$-0.602787\pi$
$59$	−1.00121e6	−0.634664	−0.317332	+	0.948314i	$0.602787\pi$
$60$	−571806.	−0.341759
$61$	2.11553e6	1.19334	0.596671	−	0.802486i	$-0.296490\pi$
$61$	2.11553e6	1.19334	0.596671	+	0.802486i	$0.296490\pi$
$62$	377903.	0.201377
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	727001.	0.328351
$66$	976168.	0.417946
$67$	3.03100e6	1.23119	0.615594	−	0.788064i	$-0.288916\pi$
$67$	3.03100e6	1.23119	0.615594	+	0.788064i	$0.288916\pi$
$68$	891505.	0.343829
$69$	−357024.	−0.130835
$70$	908007.	0.316407
$71$	−1.41071e6	−0.467771	−0.233886	−	0.972264i	$-0.575144\pi$
$71$	−1.41071e6	−0.467771	−0.233886	+	0.972264i	$0.575144\pi$
$72$	373248.	0.117851
$73$	3.58877e6	1.07973	0.539866	−	0.841751i	$-0.318475\pi$
$73$	3.58877e6	1.07973	0.539866	+	0.841751i	$0.318475\pi$
$74$	−3.58698e6	−1.02901
$75$	847097.	0.231856
$76$	−1.14975e6	−0.300439
$77$	−1.55012e6	−0.386943
$78$	−474552.	−0.113228
$79$	3.09169e6	0.705506	0.352753	−	0.935716i	$-0.385246\pi$
$79$	3.09169e6	0.705506	0.352753	+	0.935716i	$0.385246\pi$
$80$	−1.35539e6	−0.295972
$81$	531441.	0.111111
$82$	−257385.	−0.0515507
$83$	732145.	0.140548	0.0702738	−	0.997528i	$-0.477613\pi$
$83$	732145.	0.140548	0.0702738	+	0.997528i	$0.477613\pi$
$84$	−592704.	−0.109109
$85$	−4.60945e6	−0.814109
$86$	6.59543e6	1.11815
$87$	−166842.	−0.0271637
$88$	2.31388e6	0.361952
$89$	−439716.	−0.0661161	−0.0330581	−	0.999453i	$-0.510525\pi$
$89$	−439716.	−0.0661161	−0.0330581	+	0.999453i	$0.510525\pi$
$90$	−1.92985e6	−0.279045
$91$	753571.	0.104828
$92$	−846279.	−0.113307
$93$	1.27542e6	0.164423
$94$	3.20675e6	0.398215
$95$	5.94469e6	0.711371
$96$	884736.	0.102062
$97$	1.26283e7	1.40490	0.702449	−	0.711734i	$-0.252090\pi$
$97$	1.26283e7	1.40490	0.702449	+	0.711734i	$0.252090\pi$
$98$	941192.	0.101015
$99$	3.29457e6	0.341252
$100$	2.00793e6	0.200793
$101$	1.15917e7	1.11950	0.559749	−	0.828662i	$-0.310897\pi$
$101$	1.15917e7	1.11950	0.559749	+	0.828662i	$0.310897\pi$
$102$	3.00883e6	0.280735
$103$	1.70401e7	1.53653	0.768265	−	0.640132i	$-0.221120\pi$
$103$	1.70401e7	1.53653	0.768265	+	0.640132i	$0.221120\pi$
$104$	−1.12486e6	−0.0980581
$105$	3.06452e6	0.258345
$106$	−1.34629e7	−1.09791
$107$	−4.52612e6	−0.357177	−0.178588	−	0.983924i	$-0.557153\pi$
$107$	−4.52612e6	−0.357177	−0.178588	+	0.983924i	$0.557153\pi$
$108$	1.25971e6	0.0962250
$109$	1.86275e7	1.37773	0.688863	−	0.724892i	$-0.258110\pi$
$109$	1.86275e7	1.37773	0.688863	+	0.724892i	$0.258110\pi$
$110$	−1.19637e7	−0.857021
$111$	−1.21060e7	−0.840179
$112$	−1.40493e6	−0.0944911
$113$	2.27125e7	1.48078	0.740388	−	0.672180i	$-0.234642\pi$
$113$	2.27125e7	1.48078	0.740388	+	0.672180i	$0.234642\pi$
$114$	−3.88041e6	−0.245307
$115$	4.37561e6	0.268285
$116$	−395478.	−0.0235244
$117$	−1.60161e6	−0.0924500
$118$	−8.00970e6	−0.448775
$119$	−4.77791e6	−0.259910
$120$	−4.57445e6	−0.241660
$121$	936857.	0.0480756
$122$	1.69243e7	0.843821
$123$	−868674.	−0.0420910
$124$	3.02322e6	0.142395
$125$	1.54702e7	0.708453
$126$	−2.00038e6	−0.0890871
$127$	−3.08569e7	−1.33671	−0.668357	−	0.743840i	$-0.733002\pi$
$127$	−3.08569e7	−1.33671	−0.668357	+	0.743840i	$0.733002\pi$
$128$	2.09715e6	0.0883883
$129$	2.22596e7	0.912962
$130$	5.81601e6	0.232179
$131$	3.92850e7	1.52678	0.763391	−	0.645936i	$-0.223533\pi$
$131$	3.92850e7	1.52678	0.763391	+	0.645936i	$0.223533\pi$
$132$	7.80934e6	0.295533
$133$	6.16195e6	0.227111
$134$	2.42480e7	0.870581
$135$	−6.51323e6	−0.227839
$136$	7.13204e6	0.243124
$137$	−2.23775e6	−0.0743513	−0.0371757	−	0.999309i	$-0.511836\pi$
$137$	−2.23775e6	−0.0743513	−0.0371757	+	0.999309i	$0.511836\pi$
$138$	−2.85619e6	−0.0925146
$139$	3.68858e7	1.16495	0.582474	−	0.812849i	$-0.302085\pi$
$139$	3.68858e7	1.16495	0.582474	+	0.812849i	$0.302085\pi$
$140$	7.26405e6	0.223733
$141$	1.08228e7	0.325141
$142$	−1.12857e7	−0.330764
$143$	−9.92889e6	−0.283939
$144$	2.98598e6	0.0833333
$145$	2.04478e6	0.0557005
$146$	2.87102e7	0.763486
$147$	3.17652e6	0.0824786
$148$	−2.86958e7	−0.727616
$149$	3.78524e6	0.0937435	0.0468718	−	0.998901i	$-0.485075\pi$
$149$	3.78524e6	0.0937435	0.0468718	+	0.998901i	$0.485075\pi$
$150$	6.77678e6	0.163947
$151$	−3.95980e7	−0.935953	−0.467977	−	0.883741i	$-0.655017\pi$
$151$	−3.95980e7	−0.935953	−0.467977	+	0.883741i	$0.655017\pi$
$152$	−9.19801e6	−0.212442
$153$	1.01548e7	0.229219
$154$	−1.24009e7	−0.273610
$155$	−1.56313e7	−0.337159
$156$	−3.79642e6	−0.0800641
$157$	2.13204e7	0.439690	0.219845	−	0.975535i	$-0.429445\pi$
$157$	2.13204e7	0.439690	0.219845	+	0.975535i	$0.429445\pi$
$158$	2.47335e7	0.498868
$159$	−4.54371e7	−0.896440
$160$	−1.08431e7	−0.209284
$161$	4.53552e6	0.0856519
$162$	4.25153e6	0.0785674
$163$	5.83320e7	1.05500	0.527498	−	0.849557i	$-0.323130\pi$
$163$	5.83320e7	1.05500	0.527498	+	0.849557i	$0.323130\pi$
$164$	−2.05908e6	−0.0364519
$165$	−4.03775e7	−0.699754
$166$	5.85716e6	0.0993822
$167$	6.88509e7	1.14394	0.571968	−	0.820276i	$-0.306180\pi$
$167$	6.88509e7	1.14394	0.571968	+	0.820276i	$0.306180\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	−3.68756e7	−0.575662
$171$	−1.30964e7	−0.200293
$172$	5.27634e7	0.790649
$173$	−9.09314e6	−0.133522	−0.0667609	−	0.997769i	$-0.521266\pi$
$173$	−9.09314e6	−0.133522	−0.0667609	+	0.997769i	$0.521266\pi$
$174$	−1.33474e6	−0.0192076
$175$	−1.07613e7	−0.151786
$176$	1.85110e7	0.255939
$177$	−2.70327e7	−0.366424
$178$	−3.51773e6	−0.0467512
$179$	6.43990e6	0.0839254	0.0419627	−	0.999119i	$-0.486639\pi$
$179$	6.43990e6	0.0839254	0.0419627	+	0.999119i	$0.486639\pi$
$180$	−1.54388e7	−0.197314
$181$	−1.07115e8	−1.34269	−0.671347	−	0.741144i	$-0.734284\pi$
$181$	−1.07115e8	−1.34269	−0.671347	+	0.741144i	$0.734284\pi$
$182$	6.02857e6	0.0741249
$183$	5.71194e7	0.688977
$184$	−6.77023e6	−0.0801200
$185$	1.48369e8	1.72283
$186$	1.02034e7	0.116265
$187$	6.29528e7	0.703994
$188$	2.56540e7	0.281581
$189$	−6.75127e6	−0.0727393
$190$	4.75575e7	0.503015
$191$	1.74081e8	1.80774	0.903869	−	0.427810i	$-0.140715\pi$
$191$	1.74081e8	1.80774	0.903869	+	0.427810i	$0.140715\pi$
$192$	7.07789e6	0.0721688
$193$	−1.94018e8	−1.94263	−0.971316	−	0.237792i	$-0.923576\pi$
$193$	−1.94018e8	−1.94263	−0.971316	+	0.237792i	$0.923576\pi$
$194$	1.01027e8	0.993412
$195$	1.96290e7	0.189574
$196$	7.52954e6	0.0714286
$197$	−2.01869e8	−1.88121	−0.940605	−	0.339504i	$-0.889741\pi$
$197$	−2.01869e8	−1.88121	−0.940605	+	0.339504i	$0.889741\pi$
$198$	2.63565e7	0.241302
$199$	−4.68750e7	−0.421654	−0.210827	−	0.977523i	$-0.567616\pi$
$199$	−4.68750e7	−0.421654	−0.210827	+	0.977523i	$0.567616\pi$
$200$	1.60635e7	0.141982
$201$	8.18370e7	0.710826
$202$	9.27339e7	0.791605
$203$	2.11951e6	0.0177828
$204$	2.40706e7	0.198510
$205$	1.06463e7	0.0863097
$206$	1.36321e8	1.08649
$207$	−9.63964e6	−0.0755379
$208$	−8.99891e6	−0.0693375
$209$	−8.11885e7	−0.615152
$210$	2.45162e7	0.182678
$211$	−7.85890e7	−0.575935	−0.287967	−	0.957640i	$-0.592979\pi$
$211$	−7.85890e7	−0.575935	−0.287967	+	0.957640i	$0.592979\pi$
$212$	−1.07703e8	−0.776340
$213$	−3.80892e7	−0.270068
$214$	−3.62090e7	−0.252562
$215$	−2.72809e8	−1.87208
$216$	1.00777e7	0.0680414
$217$	−1.62026e7	−0.107640
$218$	1.49020e8	0.974199
$219$	9.68969e7	0.623384
$220$	−9.57096e7	−0.606005
$221$	−3.06037e7	−0.190722
$222$	−9.68484e7	−0.594096
$223$	−2.47465e8	−1.49433	−0.747165	−	0.664639i	$-0.768585\pi$
$223$	−2.47465e8	−1.49433	−0.747165	+	0.664639i	$0.768585\pi$
$224$	−1.12394e7	−0.0668153
$225$	2.28716e7	0.133862
$226$	1.81700e8	1.04707
$227$	1.43862e8	0.816313	0.408157	−	0.912912i	$-0.366172\pi$
$227$	1.43862e8	0.816313	0.408157	+	0.912912i	$0.366172\pi$
$228$	−3.10433e7	−0.173459
$229$	−1.14575e8	−0.630472	−0.315236	−	0.949013i	$-0.602084\pi$
$229$	−1.14575e8	−0.630472	−0.315236	+	0.949013i	$0.602084\pi$
$230$	3.50049e7	0.189706
$231$	−4.18532e7	−0.223402
$232$	−3.16382e6	−0.0166343
$233$	7.78376e7	0.403129	0.201564	−	0.979475i	$-0.435397\pi$
$233$	7.78376e7	0.403129	0.201564	+	0.979475i	$0.435397\pi$
$234$	−1.28129e7	−0.0653720
$235$	−1.32642e8	−0.666719
$236$	−6.40776e7	−0.317332
$237$	8.34755e7	0.407324
$238$	−3.82233e7	−0.183784
$239$	2.19725e8	1.04109	0.520543	−	0.853835i	$-0.325730\pi$
$239$	2.19725e8	1.04109	0.520543	+	0.853835i	$0.325730\pi$
$240$	−3.65956e7	−0.170879
$241$	9.81475e7	0.451668	0.225834	−	0.974166i	$-0.427489\pi$
$241$	9.81475e7	0.451668	0.225834	+	0.974166i	$0.427489\pi$
$242$	7.49485e6	0.0339946
$243$	1.43489e7	0.0641500
$244$	1.35394e8	0.596671
$245$	−3.89308e7	−0.169127
$246$	−6.94939e6	−0.0297628
$247$	3.94688e7	0.166654
$248$	2.41858e7	0.100688
$249$	1.97679e7	0.0811452
$250$	1.23762e8	0.500952
$251$	2.18390e8	0.871716	0.435858	−	0.900015i	$-0.356445\pi$
$251$	2.18390e8	0.871716	0.435858	+	0.900015i	$0.356445\pi$
$252$	−1.60030e7	−0.0629941
$253$	−5.97591e7	−0.231997
$254$	−2.46855e8	−0.945200
$255$	−1.24455e8	−0.470026
$256$	1.67772e7	0.0625000
$257$	4.13664e8	1.52013	0.760066	−	0.649846i	$-0.225167\pi$
$257$	4.13664e8	1.52013	0.760066	+	0.649846i	$0.225167\pi$
$258$	1.78077e8	0.645562
$259$	1.53792e8	0.550026
$260$	4.65281e7	0.164175
$261$	−4.50474e6	−0.0156830
$262$	3.14280e8	1.07960
$263$	3.49550e8	1.18485	0.592426	−	0.805625i	$-0.298170\pi$
$263$	3.49550e8	1.18485	0.592426	+	0.805625i	$0.298170\pi$
$264$	6.24747e7	0.208973
$265$	5.56868e8	1.83820
$266$	4.92956e7	0.160591
$267$	−1.18723e7	−0.0381722
$268$	1.93984e8	0.615594
$269$	−1.57531e8	−0.493439	−0.246720	−	0.969087i	$-0.579353\pi$
$269$	−1.57531e8	−0.493439	−0.246720	+	0.969087i	$0.579353\pi$
$270$	−5.21058e7	−0.161107
$271$	6.09914e6	0.0186155	0.00930777	−	0.999957i	$-0.497037\pi$
$271$	6.09914e6	0.0186155	0.00930777	+	0.999957i	$0.497037\pi$
$272$	5.70563e7	0.171915
$273$	2.03464e7	0.0605228
$274$	−1.79020e7	−0.0525743
$275$	1.41788e8	0.411127
$276$	−2.28495e7	−0.0654177
$277$	−2.02409e8	−0.572203	−0.286101	−	0.958199i	$-0.592359\pi$
$277$	−2.02409e8	−0.572203	−0.286101	+	0.958199i	$0.592359\pi$
$278$	2.95086e8	0.823743
$279$	3.44364e7	0.0949299
$280$	5.81124e7	0.158203
$281$	−5.70114e8	−1.53281	−0.766407	−	0.642355i	$-0.777958\pi$
$281$	−5.70114e8	−1.53281	−0.766407	+	0.642355i	$0.777958\pi$
$282$	8.65823e7	0.229910
$283$	1.15868e8	0.303886	0.151943	−	0.988389i	$-0.451447\pi$
$283$	1.15868e8	0.303886	0.151943	+	0.988389i	$0.451447\pi$
$284$	−9.02854e7	−0.233886
$285$	1.60507e8	0.410710
$286$	−7.94311e7	−0.200775
$287$	1.10354e7	0.0275550
$288$	2.38879e7	0.0589256
$289$	−2.16300e8	−0.527126
$290$	1.63583e7	0.0393862
$291$	3.40965e8	0.811118
$292$	2.29681e8	0.539866
$293$	3.76473e8	0.874373	0.437186	−	0.899371i	$-0.355975\pi$
$293$	3.76473e8	0.874373	0.437186	+	0.899371i	$0.355975\pi$
$294$	2.54122e7	0.0583212
$295$	3.31307e8	0.751370
$296$	−2.29566e8	−0.514503
$297$	8.89533e7	0.197022
$298$	3.02819e7	0.0662867
$299$	2.90512e7	0.0628513
$300$	5.42142e7	0.115928
$301$	−2.82779e8	−0.597674
$302$	−3.16784e8	−0.661819
$303$	3.12977e8	0.646343
$304$	−7.35841e7	−0.150220
$305$	−7.00043e8	−1.41278
$306$	8.12384e7	0.162083
$307$	5.15240e8	1.01631	0.508154	−	0.861266i	$-0.330328\pi$
$307$	5.15240e8	1.01631	0.508154	+	0.861266i	$0.330328\pi$
$308$	−9.92076e7	−0.193472
$309$	4.60082e8	0.887116
$310$	−1.25050e8	−0.238407
$311$	−7.17912e8	−1.35335	−0.676675	−	0.736282i	$-0.736580\pi$
$311$	−7.17912e8	−1.35335	−0.676675	+	0.736282i	$0.736580\pi$
$312$	−3.03713e7	−0.0566139
$313$	7.17851e8	1.32321	0.661606	−	0.749852i	$-0.269875\pi$
$313$	7.17851e8	1.32321	0.661606	+	0.749852i	$0.269875\pi$
$314$	1.70563e8	0.310908
$315$	8.27421e7	0.149156
$316$	1.97868e8	0.352753
$317$	6.41149e8	1.13045	0.565225	−	0.824937i	$-0.308789\pi$
$317$	6.41149e8	1.13045	0.565225	+	0.824937i	$0.308789\pi$
$318$	−3.63497e8	−0.633879
$319$	−2.79263e7	−0.0481666
$320$	−8.67451e7	−0.147986
$321$	−1.22205e8	−0.206216
$322$	3.62842e7	0.0605650
$323$	−2.50246e8	−0.413199
$324$	3.40122e7	0.0555556
$325$	−6.89286e7	−0.111380
$326$	4.66656e8	0.745994
$327$	5.02944e8	0.795430
$328$	−1.64726e7	−0.0257754
$329$	−1.37490e8	−0.212855
$330$	−3.23020e8	−0.494801
$331$	−1.20407e8	−0.182496	−0.0912481	−	0.995828i	$-0.529086\pi$
$331$	−1.20407e8	−0.182496	−0.0912481	+	0.995828i	$0.529086\pi$
$332$	4.68572e7	0.0702738
$333$	−3.26863e8	−0.485078
$334$	5.50807e8	0.808885
$335$	−1.00298e9	−1.45759
$336$	−3.79331e7	−0.0545545
$337$	−1.17938e9	−1.67861	−0.839304	−	0.543662i	$-0.817037\pi$
$337$	−1.17938e9	−1.67861	−0.839304	+	0.543662i	$0.817037\pi$
$338$	3.86145e7	0.0543928
$339$	6.13236e8	0.854927
$340$	−2.95005e8	−0.407055
$341$	2.13482e8	0.291555
$342$	−1.04771e8	−0.141628
$343$	−4.03536e7	−0.0539949
$344$	4.22108e8	0.559073
$345$	1.18141e8	0.154894
$346$	−7.27451e7	−0.0944142
$347$	−1.90113e8	−0.244264	−0.122132	−	0.992514i	$-0.538973\pi$
$347$	−1.90113e8	−0.244264	−0.122132	+	0.992514i	$0.538973\pi$
$348$	−1.06779e7	−0.0135818
$349$	7.20103e8	0.906788	0.453394	−	0.891310i	$-0.350213\pi$
$349$	7.20103e8	0.906788	0.453394	+	0.891310i	$0.350213\pi$
$350$	−8.60902e7	−0.107329
$351$	−4.32436e7	−0.0533761
$352$	1.48088e8	0.180976
$353$	−6.62358e8	−0.801459	−0.400730	−	0.916196i	$-0.631243\pi$
$353$	−6.62358e8	−0.801459	−0.400730	+	0.916196i	$0.631243\pi$
$354$	−2.16262e8	−0.259101
$355$	4.66813e8	0.553788
$356$	−2.81418e7	−0.0330581
$357$	−1.29004e8	−0.150059
$358$	5.15192e7	0.0593442
$359$	4.40830e8	0.502852	0.251426	−	0.967877i	$-0.419100\pi$
$359$	4.40830e8	0.502852	0.251426	+	0.967877i	$0.419100\pi$
$360$	−1.23510e8	−0.139522
$361$	−5.71135e8	−0.638946
$362$	−8.56923e8	−0.949427
$363$	2.52951e7	0.0277564
$364$	4.82285e7	0.0524142
$365$	−1.18755e9	−1.27828
$366$	4.56955e8	0.487180
$367$	−6.67989e8	−0.705405	−0.352702	−	0.935736i	$-0.614737\pi$
$367$	−6.67989e8	−0.705405	−0.352702	+	0.935736i	$0.614737\pi$
$368$	−5.41618e7	−0.0566534
$369$	−2.34542e7	−0.0243012
$370$	1.18695e9	1.21822
$371$	5.77220e8	0.586858
$372$	8.16270e7	0.0822117
$373$	6.76194e8	0.674669	0.337334	−	0.941385i	$-0.390475\pi$
$373$	6.76194e8	0.674669	0.337334	+	0.941385i	$0.390475\pi$
$374$	5.03622e8	0.497799
$375$	4.17696e8	0.409026
$376$	2.05232e8	0.199108
$377$	1.35760e7	0.0130490
$378$	−5.40102e7	−0.0514344
$379$	1.07748e9	1.01665	0.508325	−	0.861165i	$-0.330265\pi$
$379$	1.07748e9	1.01665	0.508325	+	0.861165i	$0.330265\pi$
$380$	3.80460e8	0.355686
$381$	−8.33135e8	−0.771753
$382$	1.39265e9	1.27826
$383$	5.23778e8	0.476378	0.238189	−	0.971219i	$-0.423446\pi$
$383$	5.23778e8	0.476378	0.238189	+	0.971219i	$0.423446\pi$
$384$	5.66231e7	0.0510310
$385$	5.12944e8	0.458097
$386$	−1.55214e9	−1.37365
$387$	6.01009e8	0.527099
$388$	8.08213e8	0.702449
$389$	1.87338e9	1.61362	0.806811	−	0.590810i	$-0.201192\pi$
$389$	1.87338e9	1.61362	0.806811	+	0.590810i	$0.201192\pi$
$390$	1.57032e8	0.134049
$391$	−1.84195e8	−0.155833
$392$	6.02363e7	0.0505076
$393$	1.06070e9	0.881489
$394$	−1.61495e9	−1.33022
$395$	−1.02306e9	−0.835239
$396$	2.10852e8	0.170626
$397$	1.09789e8	0.0880627	0.0440314	−	0.999030i	$-0.485980\pi$
$397$	1.09789e8	0.0880627	0.0440314	+	0.999030i	$0.485980\pi$
$398$	−3.75000e8	−0.298154
$399$	1.66373e8	0.131122
$400$	1.28508e8	0.100397
$401$	1.06006e8	0.0820969	0.0410484	−	0.999157i	$-0.486930\pi$
$401$	1.06006e8	0.0820969	0.0410484	+	0.999157i	$0.486930\pi$
$402$	6.54696e8	0.502630
$403$	−1.03782e8	−0.0789864
$404$	7.41871e8	0.559749
$405$	−1.75857e8	−0.131543
$406$	1.69561e7	0.0125743
$407$	−2.02633e9	−1.48980
$408$	1.92565e8	0.140368
$409$	−1.27099e9	−0.918564	−0.459282	−	0.888290i	$-0.651893\pi$
$409$	−1.27099e9	−0.918564	−0.459282	+	0.888290i	$0.651893\pi$
$410$	8.51703e7	0.0610302
$411$	−6.04191e7	−0.0429268
$412$	1.09056e9	0.768265
$413$	3.43416e8	0.239881
$414$	−7.71171e7	−0.0534133
$415$	−2.42271e8	−0.166392
$416$	−7.19913e7	−0.0490290
$417$	9.95915e8	0.672584
$418$	−6.49508e8	−0.434978
$419$	−1.96264e8	−0.130344	−0.0651719	−	0.997874i	$-0.520760\pi$
$419$	−1.96264e8	−0.130344	−0.0651719	+	0.997874i	$0.520760\pi$
$420$	1.96129e8	0.129173
$421$	−1.85401e9	−1.21095	−0.605473	−	0.795866i	$-0.707016\pi$
$421$	−1.85401e9	−1.21095	−0.605473	+	0.795866i	$0.707016\pi$
$422$	−6.28712e8	−0.407247
$423$	2.92215e8	0.187721
$424$	−8.61623e8	−0.548955
$425$	4.37032e8	0.276155
$426$	−3.04713e8	−0.190967
$427$	−7.25628e8	−0.451041
$428$	−2.89672e8	−0.178588
$429$	−2.68080e8	−0.163932
$430$	−2.18247e9	−1.32376
$431$	−4.47219e8	−0.269060	−0.134530	−	0.990909i	$-0.542953\pi$
$431$	−4.47219e8	−0.269060	−0.134530	+	0.990909i	$0.542953\pi$
$432$	8.06216e7	0.0481125
$433$	−1.92198e9	−1.13774	−0.568868	−	0.822429i	$-0.692618\pi$
$433$	−1.92198e9	−1.13774	−0.568868	+	0.822429i	$0.692618\pi$
$434$	−1.29621e8	−0.0761132
$435$	5.52091e7	0.0321587
$436$	1.19216e9	0.688863
$437$	2.37551e8	0.136167
$438$	7.75175e8	0.440799
$439$	3.28291e8	0.185197	0.0925985	−	0.995704i	$-0.470483\pi$
$439$	3.28291e8	0.185197	0.0925985	+	0.995704i	$0.470483\pi$
$440$	−7.65677e8	−0.428510
$441$	8.57661e7	0.0476190
$442$	−2.44830e8	−0.134861
$443$	1.79341e9	0.980094	0.490047	−	0.871696i	$-0.336980\pi$
$443$	1.79341e9	0.980094	0.490047	+	0.871696i	$0.336980\pi$
$444$	−7.74787e8	−0.420090
$445$	1.45505e8	0.0782740
$446$	−1.97972e9	−1.05665
$447$	1.02201e8	0.0541228
$448$	−8.99154e7	−0.0472456
$449$	1.31145e9	0.683737	0.341869	−	0.939748i	$-0.388940\pi$
$449$	1.31145e9	0.683737	0.341869	+	0.939748i	$0.388940\pi$
$450$	1.82973e8	0.0946549
$451$	−1.45400e8	−0.0746356
$452$	1.45360e9	0.740388
$453$	−1.06915e9	−0.540373
$454$	1.15090e9	0.577221
$455$	−2.49361e8	−0.124105
$456$	−2.48346e8	−0.122654
$457$	2.86023e9	1.40183	0.700913	−	0.713246i	$-0.252776\pi$
$457$	2.86023e9	1.40183	0.700913	+	0.713246i	$0.252776\pi$
$458$	−9.16600e8	−0.445811
$459$	2.74180e8	0.132340
$460$	2.80039e8	0.134142
$461$	−1.27819e9	−0.607633	−0.303816	−	0.952731i	$-0.598261\pi$
$461$	−1.27819e9	−0.607633	−0.303816	+	0.952731i	$0.598261\pi$
$462$	−3.34826e8	−0.157969
$463$	−1.36657e9	−0.639880	−0.319940	−	0.947438i	$-0.603663\pi$
$463$	−1.36657e9	−0.639880	−0.319940	+	0.947438i	$0.603663\pi$
$464$	−2.53106e7	−0.0117622
$465$	−4.22045e8	−0.194659
$466$	6.22701e8	0.285055
$467$	−1.56209e9	−0.709734	−0.354867	−	0.934917i	$-0.615474\pi$
$467$	−1.56209e9	−0.709734	−0.354867	+	0.934917i	$0.615474\pi$
$468$	−1.02503e8	−0.0462250
$469$	−1.03963e9	−0.465345
$470$	−1.06113e9	−0.471442
$471$	5.75651e8	0.253855
$472$	−5.12621e8	−0.224388
$473$	3.72584e9	1.61886
$474$	6.67804e8	0.288022
$475$	−5.63629e8	−0.241305
$476$	−3.05786e8	−0.129955
$477$	−1.22680e9	−0.517560
$478$	1.75780e9	0.736159
$479$	2.36731e9	0.984194	0.492097	−	0.870540i	$-0.336231\pi$
$479$	2.36731e9	0.984194	0.492097	+	0.870540i	$0.336231\pi$
$480$	−2.92765e8	−0.120830
$481$	9.85073e8	0.403609
$482$	7.85180e8	0.319378
$483$	1.22459e8	0.0494511
$484$	5.99588e7	0.0240378
$485$	−4.17879e9	−1.66324
$486$	1.14791e8	0.0453609
$487$	1.84374e9	0.723349	0.361674	−	0.932304i	$-0.382205\pi$
$487$	1.84374e9	0.723349	0.361674	+	0.932304i	$0.382205\pi$
$488$	1.08315e9	0.421910
$489$	1.57496e9	0.609102
$490$	−3.11446e8	−0.119591
$491$	−2.74421e9	−1.04624	−0.523121	−	0.852258i	$-0.675233\pi$
$491$	−2.74421e9	−1.04624	−0.523121	+	0.852258i	$0.675233\pi$
$492$	−5.55952e7	−0.0210455
$493$	−8.60768e7	−0.0323536
$494$	3.15750e8	0.117842
$495$	−1.09019e9	−0.404003
$496$	1.93486e8	0.0711974
$497$	4.83873e8	0.176801
$498$	1.58143e8	0.0573783
$499$	3.17258e9	1.14304	0.571518	−	0.820589i	$-0.306355\pi$
$499$	3.17258e9	1.14304	0.571518	+	0.820589i	$0.306355\pi$
$500$	9.90093e8	0.354227
$501$	1.85897e9	0.660452
$502$	1.74712e9	0.616396
$503$	2.82366e9	0.989292	0.494646	−	0.869095i	$-0.335298\pi$
$503$	2.82366e9	0.989292	0.494646	+	0.869095i	$0.335298\pi$
$504$	−1.28024e8	−0.0445435
$505$	−3.83578e9	−1.32536
$506$	−4.78073e8	−0.164047
$507$	1.30324e8	0.0444116
$508$	−1.97484e9	−0.668357
$509$	−1.05411e9	−0.354302	−0.177151	−	0.984184i	$-0.556688\pi$
$509$	−1.05411e9	−0.354302	−0.177151	+	0.984184i	$0.556688\pi$
$510$	−9.95641e8	−0.332359
$511$	−1.23095e9	−0.408100
$512$	1.34218e8	0.0441942
$513$	−3.53602e8	−0.115639
$514$	3.30931e9	1.07490
$515$	−5.63867e9	−1.81908
$516$	1.42461e9	0.456481
$517$	1.81153e9	0.576540
$518$	1.23033e9	0.388927
$519$	−2.45515e8	−0.0770889
$520$	3.72225e8	0.116090
$521$	−1.10300e9	−0.341698	−0.170849	−	0.985297i	$-0.554651\pi$
$521$	−1.10300e9	−0.341698	−0.170849	+	0.985297i	$0.554651\pi$
$522$	−3.60379e7	−0.0110895
$523$	3.34803e9	1.02337	0.511686	−	0.859172i	$-0.329021\pi$
$523$	3.34803e9	1.02337	0.511686	+	0.859172i	$0.329021\pi$
$524$	2.51424e9	0.763391
$525$	−2.90554e8	−0.0876334
$526$	2.79640e9	0.837817
$527$	6.58013e8	0.195838
$528$	4.99798e8	0.147766
$529$	−3.22998e9	−0.948646
$530$	4.45494e9	1.29980
$531$	−7.29884e8	−0.211555
$532$	3.94365e8	0.113555
$533$	7.06844e7	0.0202199
$534$	−9.49787e7	−0.0269918
$535$	1.49772e9	0.422856
$536$	1.55187e9	0.435290
$537$	1.73877e8	0.0484543
$538$	−1.26025e9	−0.348914
$539$	5.31691e8	0.146251
$540$	−4.16847e8	−0.113920
$541$	9.02397e8	0.245023	0.122512	−	0.992467i	$-0.460905\pi$
$541$	9.02397e8	0.245023	0.122512	+	0.992467i	$0.460905\pi$
$542$	4.87931e7	0.0131632
$543$	−2.89211e9	−0.775204
$544$	4.56451e8	0.121562
$545$	−6.16397e9	−1.63107
$546$	1.62771e8	0.0427960
$547$	−1.50151e9	−0.392258	−0.196129	−	0.980578i	$-0.562837\pi$
$547$	−1.50151e9	−0.392258	−0.196129	+	0.980578i	$0.562837\pi$
$548$	−1.43216e8	−0.0371757
$549$	1.54222e9	0.397781
$550$	1.13431e9	0.290711
$551$	1.11011e8	0.0282706
$552$	−1.82796e8	−0.0462573
$553$	−1.06045e9	−0.266656
$554$	−1.61927e9	−0.404608
$555$	4.00597e9	0.994677
$556$	2.36069e9	0.582474
$557$	−3.63103e9	−0.890301	−0.445151	−	0.895456i	$-0.646850\pi$
$557$	−3.63103e9	−0.890301	−0.445151	+	0.895456i	$0.646850\pi$
$558$	2.75491e8	0.0671256
$559$	−1.81127e9	−0.438573
$560$	4.64900e8	0.111867
$561$	1.69972e9	0.406451
$562$	−4.56091e9	−1.08386
$563$	2.78815e9	0.658470	0.329235	−	0.944248i	$-0.393209\pi$
$563$	2.78815e9	0.658470	0.329235	+	0.944248i	$0.393209\pi$
$564$	6.92659e8	0.162571
$565$	−7.51569e9	−1.75307
$566$	9.26945e8	0.214880
$567$	−1.82284e8	−0.0419961
$568$	−7.22283e8	−0.165382
$569$	7.31288e8	0.166416	0.0832081	−	0.996532i	$-0.473483\pi$
$569$	7.31288e8	0.166416	0.0832081	+	0.996532i	$0.473483\pi$
$570$	1.28405e9	0.290416
$571$	6.57397e9	1.47775	0.738876	−	0.673842i	$-0.235357\pi$
$571$	6.57397e9	1.47775	0.738876	+	0.673842i	$0.235357\pi$
$572$	−6.35449e8	−0.141969
$573$	4.70020e9	1.04370
$574$	8.82831e7	0.0194843
$575$	−4.14861e8	−0.0910050
$576$	1.91103e8	0.0416667
$577$	−6.74147e9	−1.46096	−0.730482	−	0.682932i	$-0.760704\pi$
$577$	−6.74147e9	−1.46096	−0.730482	+	0.682932i	$0.760704\pi$
$578$	−1.73040e9	−0.372734
$579$	−5.23848e9	−1.12158
$580$	1.30866e8	0.0278503
$581$	−2.51126e8	−0.0531220
$582$	2.72772e9	0.573547
$583$	−7.60533e9	−1.58956
$584$	1.83745e9	0.381743
$585$	5.29984e8	0.109450
$586$	3.01178e9	0.618275
$587$	−4.20332e9	−0.857746	−0.428873	−	0.903365i	$-0.641089\pi$
$587$	−4.20332e9	−0.857746	−0.428873	+	0.903365i	$0.641089\pi$
$588$	2.03297e8	0.0412393
$589$	−8.48622e8	−0.171124
$590$	2.65046e9	0.531299
$591$	−5.45045e9	−1.08612
$592$	−1.83653e9	−0.363808
$593$	1.17304e9	0.231005	0.115502	−	0.993307i	$-0.463152\pi$
$593$	1.17304e9	0.231005	0.115502	+	0.993307i	$0.463152\pi$
$594$	7.11626e8	0.139315
$595$	1.58104e9	0.307704
$596$	2.42255e8	0.0468718
$597$	−1.26563e9	−0.243442
$598$	2.32409e8	0.0444426
$599$	6.38901e9	1.21462	0.607309	−	0.794465i	$-0.292249\pi$
$599$	6.38901e9	1.21462	0.607309	+	0.794465i	$0.292249\pi$
$600$	4.33714e8	0.0819736
$601$	1.77640e9	0.333796	0.166898	−	0.985974i	$-0.446625\pi$
$601$	1.77640e9	0.333796	0.166898	+	0.985974i	$0.446625\pi$
$602$	−2.26223e9	−0.422619
$603$	2.20960e9	0.410396
$604$	−2.53427e9	−0.467977
$605$	−3.10012e8	−0.0569160
$606$	2.50381e9	0.457034
$607$	−3.62433e9	−0.657760	−0.328880	−	0.944372i	$-0.606671\pi$
$607$	−3.62433e9	−0.657760	−0.328880	+	0.944372i	$0.606671\pi$
$608$	−5.88673e8	−0.106221
$609$	5.72269e7	0.0102669
$610$	−5.60034e9	−0.998988
$611$	−8.80655e8	−0.156193
$612$	6.49907e8	0.114610
$613$	−7.13353e9	−1.25081	−0.625407	−	0.780298i	$-0.715067\pi$
$613$	−7.13353e9	−1.25081	−0.625407	+	0.780298i	$0.715067\pi$
$614$	4.12192e9	0.718638
$615$	2.87450e8	0.0498309
$616$	−7.93661e8	−0.136805
$617$	−7.56361e9	−1.29638	−0.648188	−	0.761480i	$-0.724473\pi$
$617$	−7.56361e9	−1.29638	−0.648188	+	0.761480i	$0.724473\pi$
$618$	3.68066e9	0.627286
$619$	−7.24065e9	−1.22705	−0.613523	−	0.789677i	$-0.710248\pi$
$619$	−7.24065e9	−1.22705	−0.613523	+	0.789677i	$0.710248\pi$
$620$	−1.00040e9	−0.168579
$621$	−2.60270e8	−0.0436118
$622$	−5.74330e9	−0.956963
$623$	1.50823e8	0.0249896
$624$	−2.42971e8	−0.0400320
$625$	−7.57028e9	−1.24031
$626$	5.74281e9	0.935652
$627$	−2.19209e9	−0.355158
$628$	1.36451e9	0.219845
$629$	−6.24572e9	−1.00070
$630$	6.61937e8	0.105469
$631$	3.97503e9	0.629851	0.314925	−	0.949116i	$-0.398020\pi$
$631$	3.97503e9	0.629851	0.314925	+	0.949116i	$0.398020\pi$
$632$	1.58294e9	0.249434
$633$	−2.12190e9	−0.332516
$634$	5.12919e9	0.799349
$635$	1.02107e10	1.58252
$636$	−2.90798e9	−0.448220
$637$	−2.58475e8	−0.0396214
$638$	−2.23410e8	−0.0340589
$639$	−1.02841e9	−0.155924
$640$	−6.93961e8	−0.104642
$641$	−7.14852e9	−1.07204	−0.536022	−	0.844204i	$-0.680074\pi$
$641$	−7.14852e9	−1.07204	−0.536022	+	0.844204i	$0.680074\pi$
$642$	−9.77642e8	−0.145817
$643$	−1.26537e10	−1.87706	−0.938528	−	0.345202i	$-0.887810\pi$
$643$	−1.26537e10	−1.87706	−0.938528	+	0.345202i	$0.887810\pi$
$644$	2.90274e8	0.0428259
$645$	−7.36583e9	−1.08084
$646$	−2.00197e9	−0.292176
$647$	7.31608e9	1.06197	0.530986	−	0.847380i	$-0.321822\pi$
$647$	7.31608e9	1.06197	0.530986	+	0.847380i	$0.321822\pi$
$648$	2.72098e8	0.0392837
$649$	−4.52477e9	−0.649741
$650$	−5.51429e8	−0.0787577
$651$	−4.37470e8	−0.0621462
$652$	3.73325e9	0.527498
$653$	−9.46134e8	−0.132971	−0.0664854	−	0.997787i	$-0.521179\pi$
$653$	−9.46134e8	−0.132971	−0.0664854	+	0.997787i	$0.521179\pi$
$654$	4.02355e9	0.562454
$655$	−1.29997e10	−1.80754
$656$	−1.31781e8	−0.0182259
$657$	2.61622e9	0.359911
$658$	−1.09992e9	−0.150511
$659$	−7.73539e9	−1.05289	−0.526445	−	0.850209i	$-0.676476\pi$
$659$	−7.73539e9	−1.05289	−0.526445	+	0.850209i	$0.676476\pi$
$660$	−2.58416e9	−0.349877
$661$	−1.43614e10	−1.93416	−0.967081	−	0.254471i	$-0.918099\pi$
$661$	−1.43614e10	−1.93416	−0.967081	+	0.254471i	$0.918099\pi$
$662$	−9.63256e8	−0.129044
$663$	−8.26300e8	−0.110113
$664$	3.74858e8	0.0496911
$665$	−2.03903e9	−0.268873
$666$	−2.61491e9	−0.343002
$667$	8.17101e7	0.0106619
$668$	4.40646e9	0.571968
$669$	−6.68155e9	−0.862752
$670$	−8.02382e9	−1.03067
$671$	9.56071e9	1.22169
$672$	−3.03464e8	−0.0385758
$673$	1.09570e9	0.138560	0.0692802	−	0.997597i	$-0.477930\pi$
$673$	1.09570e9	0.138560	0.0692802	+	0.997597i	$0.477930\pi$
$674$	−9.43504e9	−1.18696
$675$	6.17534e8	0.0772854
$676$	3.08916e8	0.0384615
$677$	−5.66982e9	−0.702277	−0.351139	−	0.936323i	$-0.614205\pi$
$677$	−5.66982e9	−0.702277	−0.351139	+	0.936323i	$0.614205\pi$
$678$	4.90589e9	0.604524
$679$	−4.33151e9	−0.531001
$680$	−2.36004e9	−0.287831
$681$	3.88428e9	0.471299
$682$	1.70785e9	0.206161
$683$	−5.43549e8	−0.0652780	−0.0326390	−	0.999467i	$-0.510391\pi$
$683$	−5.43549e8	−0.0652780	−0.0326390	+	0.999467i	$0.510391\pi$
$684$	−8.38169e8	−0.100146
$685$	7.40484e8	0.0880235
$686$	−3.22829e8	−0.0381802
$687$	−3.09353e9	−0.364003
$688$	3.37686e9	0.395324
$689$	3.69724e9	0.430636
$690$	9.45131e8	0.109527
$691$	3.43362e9	0.395895	0.197947	−	0.980213i	$-0.436573\pi$
$691$	3.43362e9	0.395895	0.197947	+	0.980213i	$0.436573\pi$
$692$	−5.81961e8	−0.0667609
$693$	−1.13004e9	−0.128981
$694$	−1.52091e9	−0.172721
$695$	−1.22057e10	−1.37917
$696$	−8.54232e7	−0.00960381
$697$	−4.48164e8	−0.0501329
$698$	5.76083e9	0.641196
$699$	2.10162e9	0.232747
$700$	−6.88721e8	−0.0758928
$701$	6.53943e9	0.717013	0.358507	−	0.933527i	$-0.383286\pi$
$701$	6.53943e9	0.717013	0.358507	+	0.933527i	$0.383286\pi$
$702$	−3.45948e8	−0.0377426
$703$	8.05494e9	0.874418
$704$	1.18471e9	0.127969
$705$	−3.58133e9	−0.384931
$706$	−5.29887e9	−0.566717
$707$	−3.97597e9	−0.423131
$708$	−1.73009e9	−0.183212
$709$	−1.19763e10	−1.26201	−0.631003	−	0.775781i	$-0.717356\pi$
$709$	−1.19763e10	−1.26201	−0.631003	+	0.775781i	$0.717356\pi$
$710$	3.73450e9	0.391587
$711$	2.25384e9	0.235169
$712$	−2.25135e8	−0.0233756
$713$	−6.24631e8	−0.0645372
$714$	−1.03203e9	−0.106108
$715$	3.28553e9	0.336151
$716$	4.12153e8	0.0419627
$717$	5.93257e9	0.601071
$718$	3.52664e9	0.355570
$719$	−5.04786e9	−0.506473	−0.253236	−	0.967404i	$-0.581495\pi$
$719$	−5.04786e9	−0.506473	−0.253236	+	0.967404i	$0.581495\pi$
$720$	−9.88081e8	−0.0986572
$721$	−5.84475e9	−0.580754
$722$	−4.56908e9	−0.451803
$723$	2.64998e9	0.260771
$724$	−6.85538e9	−0.671347
$725$	−1.93870e8	−0.0188942
$726$	2.02361e8	0.0196268
$727$	1.58429e9	0.152920	0.0764601	−	0.997073i	$-0.475638\pi$
$727$	1.58429e9	0.152920	0.0764601	+	0.997073i	$0.475638\pi$
$728$	3.85828e8	0.0370625
$729$	3.87420e8	0.0370370
$730$	−9.50038e9	−0.903880
$731$	1.14841e10	1.08739
$732$	3.65564e9	0.344488
$733$	−5.17513e9	−0.485353	−0.242676	−	0.970107i	$-0.578025\pi$
$733$	−5.17513e9	−0.485353	−0.242676	+	0.970107i	$0.578025\pi$
$734$	−5.34391e9	−0.498796
$735$	−1.05113e9	−0.0976453
$736$	−4.33295e8	−0.0400600
$737$	1.36980e10	1.26043
$738$	−1.87634e8	−0.0171836
$739$	8.80228e9	0.802305	0.401153	−	0.916011i	$-0.368610\pi$
$739$	8.80228e9	0.802305	0.401153	+	0.916011i	$0.368610\pi$
$740$	9.49562e9	0.861415
$741$	1.06566e9	0.0962175
$742$	4.61776e9	0.414971
$743$	2.36879e9	0.211869	0.105934	−	0.994373i	$-0.466217\pi$
$743$	2.36879e9	0.211869	0.105934	+	0.994373i	$0.466217\pi$
$744$	6.53016e8	0.0581325
$745$	−1.25256e9	−0.110982
$746$	5.40955e9	0.477063
$747$	5.33733e8	0.0468492
$748$	4.02898e9	0.351997
$749$	1.55246e9	0.135000
$750$	3.34157e9	0.289225
$751$	−5.13067e9	−0.442013	−0.221006	−	0.975272i	$-0.570934\pi$
$751$	−5.13067e9	−0.442013	−0.221006	+	0.975272i	$0.570934\pi$
$752$	1.64186e9	0.140790
$753$	5.89654e9	0.503286
$754$	1.08608e8	0.00922704
$755$	1.31032e10	1.10806
$756$	−4.32081e8	−0.0363696
$757$	−1.48284e10	−1.24239	−0.621195	−	0.783656i	$-0.713353\pi$
$757$	−1.48284e10	−1.24239	−0.621195	+	0.783656i	$0.713353\pi$
$758$	8.61984e9	0.718881
$759$	−1.61350e9	−0.133943
$760$	3.04368e9	0.251508
$761$	1.00301e9	0.0825010	0.0412505	−	0.999149i	$-0.486866\pi$
$761$	1.00301e9	0.0825010	0.0412505	+	0.999149i	$0.486866\pi$
$762$	−6.66508e9	−0.545712
$763$	−6.38925e9	−0.520731
$764$	1.11412e10	0.903869
$765$	−3.36029e9	−0.271370
$766$	4.19022e9	0.336850
$767$	2.19966e9	0.176024
$768$	4.52985e8	0.0360844
$769$	1.80067e10	1.42788	0.713941	−	0.700206i	$-0.246909\pi$
$769$	1.80067e10	1.42788	0.713941	+	0.700206i	$0.246909\pi$
$770$	4.10355e9	0.323923
$771$	1.11689e10	0.877649
$772$	−1.24171e10	−0.971316
$773$	−1.27604e10	−0.993656	−0.496828	−	0.867849i	$-0.665502\pi$
$773$	−1.27604e10	−0.993656	−0.496828	+	0.867849i	$0.665502\pi$
$774$	4.80807e9	0.372715
$775$	1.48204e9	0.114368
$776$	6.46570e9	0.496706
$777$	4.15237e9	0.317558
$778$	1.49870e10	1.14100
$779$	5.77986e8	0.0438062
$780$	1.25626e9	0.0947868
$781$	−6.37541e9	−0.478883
$782$	−1.47356e9	−0.110190
$783$	−1.21628e8	−0.00905456
$784$	4.81890e8	0.0357143
$785$	−7.05505e9	−0.520543
$786$	8.48556e9	0.623307
$787$	−4.43605e9	−0.324403	−0.162202	−	0.986758i	$-0.551859\pi$
$787$	−4.43605e9	−0.324403	−0.162202	+	0.986758i	$0.551859\pi$
$788$	−1.29196e10	−0.940605
$789$	9.43785e9	0.684075
$790$	−8.18447e9	−0.590603
$791$	−7.79037e9	−0.559681
$792$	1.68682e9	0.120651
$793$	−4.64782e9	−0.330974
$794$	8.78312e8	0.0622697
$795$	1.50354e10	1.06128
$796$	−3.00000e9	−0.210827
$797$	−8.86132e8	−0.0620004	−0.0310002	−	0.999519i	$-0.509869\pi$
$797$	−8.86132e8	−0.0620004	−0.0310002	+	0.999519i	$0.509869\pi$
$798$	1.33098e9	0.0927175
$799$	5.58367e9	0.387263
$800$	1.02806e9	0.0709912
$801$	−3.20553e8	−0.0220387
$802$	8.48051e8	0.0580512
$803$	1.62187e10	1.10538
$804$	5.23757e9	0.355413
$805$	−1.50083e9	−0.101402
$806$	−8.30253e8	−0.0558519
$807$	−4.25334e9	−0.284887
$808$	5.93497e9	0.395803
$809$	1.97819e10	1.31355	0.656776	−	0.754085i	$-0.271920\pi$
$809$	1.97819e10	1.31355	0.656776	+	0.754085i	$0.271920\pi$
$810$	−1.40686e9	−0.0930149
$811$	2.45131e10	1.61371	0.806854	−	0.590751i	$-0.201168\pi$
$811$	2.45131e10	1.61371	0.806854	+	0.590751i	$0.201168\pi$
$812$	1.35649e8	0.00889140
$813$	1.64677e8	0.0107477
$814$	−1.62106e10	−1.05345
$815$	−1.93024e10	−1.24899
$816$	1.54052e9	0.0992549
$817$	−1.48108e10	−0.950167
$818$	−1.01679e10	−0.649523
$819$	5.49353e8	0.0349428
$820$	6.81362e8	0.0431549
$821$	2.19434e10	1.38389	0.691947	−	0.721948i	$-0.256753\pi$
$821$	2.19434e10	1.38389	0.691947	+	0.721948i	$0.256753\pi$
$822$	−4.83353e8	−0.0303538
$823$	5.07122e9	0.317112	0.158556	−	0.987350i	$-0.449316\pi$
$823$	5.07122e9	0.317112	0.158556	+	0.987350i	$0.449316\pi$
$824$	8.72452e9	0.543246
$825$	3.82828e9	0.237364
$826$	2.74733e9	0.169621
$827$	−2.34646e10	−1.44260	−0.721298	−	0.692625i	$-0.756454\pi$
$827$	−2.34646e10	−1.44260	−0.721298	+	0.692625i	$0.756454\pi$
$828$	−6.16937e8	−0.0377689
$829$	7.86354e8	0.0479377	0.0239689	−	0.999713i	$-0.492370\pi$
$829$	7.86354e8	0.0479377	0.0239689	+	0.999713i	$0.492370\pi$
$830$	−1.93817e9	−0.117657
$831$	−5.46503e9	−0.330361
$832$	−5.75930e8	−0.0346688
$833$	1.63882e9	0.0982369
$834$	7.96732e9	0.475588
$835$	−2.27832e10	−1.35429
$836$	−5.19607e9	−0.307576
$837$	9.29783e8	0.0548078
$838$	−1.57011e9	−0.0921670
$839$	4.99447e9	0.291960	0.145980	−	0.989288i	$-0.453367\pi$
$839$	4.99447e9	0.291960	0.145980	+	0.989288i	$0.453367\pi$
$840$	1.56904e9	0.0913388
$841$	−1.72117e10	−0.997786
$842$	−1.48321e10	−0.856269
$843$	−1.53931e10	−0.884971
$844$	−5.02970e9	−0.287967
$845$	−1.59722e9	−0.0910682
$846$	2.33772e9	0.132738
$847$	−3.21342e8	−0.0181709
$848$	−6.89298e9	−0.388170
$849$	3.12844e9	0.175449
$850$	3.49626e9	0.195271
$851$	5.92887e9	0.329776
$852$	−2.43771e9	−0.135034
$853$	−2.19778e10	−1.21245	−0.606223	−	0.795295i	$-0.707316\pi$
$853$	−2.19778e10	−1.21245	−0.606223	+	0.795295i	$0.707316\pi$
$854$	−5.80502e9	−0.318934
$855$	4.33368e9	0.237124
$856$	−2.31737e9	−0.126281
$857$	1.96280e10	1.06523	0.532616	−	0.846357i	$-0.321209\pi$
$857$	1.96280e10	1.06523	0.532616	+	0.846357i	$0.321209\pi$
$858$	−2.14464e9	−0.115917
$859$	2.32980e10	1.25413	0.627065	−	0.778967i	$-0.284256\pi$
$859$	2.32980e10	1.25413	0.627065	+	0.778967i	$0.284256\pi$
$860$	−1.74598e10	−0.936038
$861$	2.97955e8	0.0159089
$862$	−3.57775e9	−0.190254
$863$	−3.11421e10	−1.64934	−0.824670	−	0.565614i	$-0.808639\pi$
$863$	−3.11421e10	−1.64934	−0.824670	+	0.565614i	$0.808639\pi$
$864$	6.44973e8	0.0340207
$865$	3.00898e9	0.158075
$866$	−1.53758e10	−0.804501
$867$	−5.84010e9	−0.304336
$868$	−1.03697e9	−0.0538202
$869$	1.39722e10	0.722266
$870$	4.41673e8	0.0227396
$871$	−6.65911e9	−0.341470
$872$	9.53730e9	0.487100
$873$	9.20605e9	0.468299
$874$	1.90041e9	0.0962847
$875$	−5.30628e9	−0.267770
$876$	6.20140e9	0.311692
$877$	2.06458e10	1.03356	0.516778	−	0.856120i	$-0.327131\pi$
$877$	2.06458e10	1.03356	0.516778	+	0.856120i	$0.327131\pi$
$878$	2.62633e9	0.130954
$879$	1.01648e10	0.504819
$880$	−6.12542e9	−0.303003
$881$	2.12045e10	1.04475	0.522376	−	0.852715i	$-0.325046\pi$
$881$	2.12045e10	1.04475	0.522376	+	0.852715i	$0.325046\pi$
$882$	6.86129e8	0.0336718
$883$	−7.16963e9	−0.350457	−0.175228	−	0.984528i	$-0.556066\pi$
$883$	−7.16963e9	−0.350457	−0.175228	+	0.984528i	$0.556066\pi$
$884$	−1.95864e9	−0.0953611
$885$	8.94530e9	0.433804
$886$	1.43473e10	0.693031
$887$	−1.68403e10	−0.810247	−0.405124	−	0.914262i	$-0.632772\pi$
$887$	−1.68403e10	−0.810247	−0.405124	+	0.914262i	$0.632772\pi$
$888$	−6.19830e9	−0.297048
$889$	1.05839e10	0.505231
$890$	1.16404e9	0.0553481
$891$	2.40174e9	0.113751
$892$	−1.58377e10	−0.747165
$893$	−7.20111e9	−0.338391
$894$	8.17611e8	0.0382706
$895$	−2.13100e9	−0.0993581
$896$	−7.19323e8	−0.0334077
$897$	7.84381e8	0.0362872
$898$	1.04916e10	0.483475
$899$	−2.91899e8	−0.0133990
$900$	1.46378e9	0.0669311
$901$	−2.34418e10	−1.06771
$902$	−1.16320e9	−0.0527753
$903$	−7.63503e9	−0.345067
$904$	1.16288e10	0.523533
$905$	3.54451e10	1.58960
$906$	−8.55317e9	−0.382101
$907$	1.21805e10	0.542052	0.271026	−	0.962572i	$-0.412637\pi$
$907$	1.21805e10	0.542052	0.271026	+	0.962572i	$0.412637\pi$
$908$	9.20719e9	0.408157
$909$	8.45038e9	0.373166
$910$	−1.99489e9	−0.0877555
$911$	1.50255e10	0.658439	0.329220	−	0.944253i	$-0.393214\pi$
$911$	1.50255e10	0.658439	0.329220	+	0.944253i	$0.393214\pi$
$912$	−1.98677e9	−0.0867293
$913$	3.30878e9	0.143886
$914$	2.28818e10	0.991241
$915$	−1.89012e10	−0.815670
$916$	−7.33280e9	−0.315236
$917$	−1.34748e10	−0.577070
$918$	2.19344e9	0.0935785
$919$	3.72817e9	0.158450	0.0792248	−	0.996857i	$-0.474755\pi$
$919$	3.72817e9	0.158450	0.0792248	+	0.996857i	$0.474755\pi$
$920$	2.24031e9	0.0948530
$921$	1.39115e10	0.586766
$922$	−1.02255e10	−0.429661
$923$	3.09933e9	0.129736
$924$	−2.67860e9	−0.111701
$925$	−1.40672e10	−0.584402
$926$	−1.09326e10	−0.452464
$927$	1.24222e10	0.512177
$928$	−2.02485e8	−0.00831714
$929$	−2.90129e10	−1.18723	−0.593616	−	0.804748i	$-0.702300\pi$
$929$	−2.90129e10	−1.18723	−0.593616	+	0.804748i	$0.702300\pi$
$930$	−3.37636e9	−0.137644
$931$	−2.11355e9	−0.0858397
$932$	4.98161e9	0.201564
$933$	−1.93836e10	−0.781357
$934$	−1.24967e10	−0.501858
$935$	−2.08315e10	−0.833449
$936$	−8.20026e8	−0.0326860
$937$	−4.73439e9	−0.188008	−0.0940038	−	0.995572i	$-0.529967\pi$
$937$	−4.73439e9	−0.188008	−0.0940038	+	0.995572i	$0.529967\pi$
$938$	−8.31706e9	−0.329049
$939$	1.93820e10	0.763956
$940$	−8.48908e9	−0.333360
$941$	2.78995e10	1.09152	0.545762	−	0.837940i	$-0.316240\pi$
$941$	2.78995e10	1.09152	0.545762	+	0.837940i	$0.316240\pi$
$942$	4.60521e9	0.179503
$943$	4.25429e8	0.0165210
$944$	−4.10097e9	−0.158666
$945$	2.23404e9	0.0861151
$946$	2.98067e10	1.14471
$947$	3.54127e10	1.35498	0.677492	−	0.735531i	$-0.263067\pi$
$947$	3.54127e10	1.35498	0.677492	+	0.735531i	$0.263067\pi$
$948$	5.34243e9	0.203662
$949$	−7.88453e9	−0.299464
$950$	−4.50903e9	−0.170628
$951$	1.73110e10	0.652666
$952$	−2.44629e9	−0.0918922
$953$	4.95999e10	1.85633	0.928166	−	0.372167i	$-0.121385\pi$
$953$	4.95999e10	1.85633	0.928166	+	0.372167i	$0.121385\pi$
$954$	−9.81442e9	−0.365970
$955$	−5.76046e10	−2.14016
$956$	1.40624e10	0.520543
$957$	−7.54009e8	−0.0278090
$958$	1.89385e10	0.695930
$959$	7.67547e8	0.0281022
$960$	−2.34212e9	−0.0854396
$961$	−2.52812e10	−0.918895
$962$	7.88059e9	0.285395
$963$	−3.29954e9	−0.119059
$964$	6.28144e9	0.225834
$965$	6.42016e10	2.29986
$966$	9.79673e8	0.0349672
$967$	6.53751e9	0.232498	0.116249	−	0.993220i	$-0.462913\pi$
$967$	6.53751e9	0.232498	0.116249	+	0.993220i	$0.462913\pi$
$968$	4.79671e8	0.0169973
$969$	−6.75665e9	−0.238560
$970$	−3.34303e10	−1.17609
$971$	2.80625e9	0.0983692	0.0491846	−	0.998790i	$-0.484338\pi$
$971$	2.80625e9	0.0983692	0.0491846	+	0.998790i	$0.484338\pi$
$972$	9.18330e8	0.0320750
$973$	−1.26518e10	−0.440309
$974$	1.47499e10	0.511485
$975$	−1.86107e9	−0.0643054
$976$	8.66522e9	0.298336
$977$	1.76070e10	0.604024	0.302012	−	0.953304i	$-0.402342\pi$
$977$	1.76070e10	0.604024	0.302012	+	0.953304i	$0.402342\pi$
$978$	1.25997e10	0.430700
$979$	−1.98721e9	−0.0676868
$980$	−2.49157e9	−0.0845633
$981$	1.35795e10	0.459242
$982$	−2.19537e10	−0.739805
$983$	−1.09487e10	−0.367643	−0.183822	−	0.982960i	$-0.558847\pi$
$983$	−1.09487e10	−0.367643	−0.183822	+	0.982960i	$0.558847\pi$
$984$	−4.44761e8	−0.0148814
$985$	6.67996e10	2.22714
$986$	−6.88615e8	−0.0228774
$987$	−3.71222e9	−0.122892
$988$	2.52600e9	0.0833268
$989$	−1.09015e10	−0.358343
$990$	−8.72154e9	−0.285674
$991$	5.64966e10	1.84401	0.922007	−	0.387173i	$-0.126548\pi$
$991$	5.64966e10	1.84401	0.922007	+	0.387173i	$0.126548\pi$
$992$	1.54789e9	0.0503442
$993$	−3.25099e9	−0.105364
$994$	3.87099e9	0.125017
$995$	1.55112e10	0.499190
$996$	1.26515e9	0.0405726
$997$	3.48642e10	1.11416	0.557079	−	0.830460i	$-0.311922\pi$
$997$	3.48642e10	1.11416	0.557079	+	0.830460i	$0.311922\pi$
$998$	2.53806e10	0.808249
$999$	−8.82531e9	−0.280060

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.m.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.m.1.1	✓	5	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)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -330.906 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -330.906 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -2647.25 q^{10} +4519.30 q^{11} +1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} -8934.47 q^{15} +4096.00 q^{16} +13929.8 q^{17} +5832.00 q^{18} -17964.9 q^{19} -21178.0 q^{20} -9261.00 q^{21} +36154.4 q^{22} -13223.1 q^{23} +13824.0 q^{24} +31374.0 q^{25} -17576.0 q^{26} +19683.0 q^{27} -21952.0 q^{28} -6179.34 q^{29} -71475.8 q^{30} +47237.9 q^{31} +32768.0 q^{32} +122021. q^{33} +111438. q^{34} +113501. q^{35} +46656.0 q^{36} -448372. q^{37} -143719. q^{38} -59319.0 q^{39} -169424. q^{40} -32173.1 q^{41} -74088.0 q^{42} +824429. q^{43} +289235. q^{44} -241231. q^{45} -105785. q^{46} +400844. q^{47} +110592. q^{48} +117649. q^{49} +250992. q^{50} +376104. q^{51} -140608. q^{52} -1.68286e6 q^{53} +157464. q^{54} -1.49546e6 q^{55} -175616. q^{56} -485051. q^{57} -49434.7 q^{58} -1.00121e6 q^{59} -571806. q^{60} +2.11553e6 q^{61} +377903. q^{62} -250047. q^{63} +262144. q^{64} +727001. q^{65} +976168. q^{66} +3.03100e6 q^{67} +891505. q^{68} -357024. q^{69} +908007. q^{70} -1.41071e6 q^{71} +373248. q^{72} +3.58877e6 q^{73} -3.58698e6 q^{74} +847097. q^{75} -1.14975e6 q^{76} -1.55012e6 q^{77} -474552. q^{78} +3.09169e6 q^{79} -1.35539e6 q^{80} +531441. q^{81} -257385. q^{82} +732145. q^{83} -592704. q^{84} -4.60945e6 q^{85} +6.59543e6 q^{86} -166842. q^{87} +2.31388e6 q^{88} -439716. q^{89} -1.92985e6 q^{90} +753571. q^{91} -846279. q^{92} +1.27542e6 q^{93} +3.20675e6 q^{94} +5.94469e6 q^{95} +884736. q^{96} +1.26283e7 q^{97} +941192. q^{98} +3.29457e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 40 q^{2} + 135 q^{3} + 320 q^{4} + 299 q^{5} + 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9}+O(q^{10}) \) 5 * q + 40 * q^2 + 135 * q^3 + 320 * q^4 + 299 * q^5 + 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9	\( 5 q + 40 q^{2} + 135 q^{3} + 320 q^{4} + 299 q^{5} + 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9} + 2392 q^{10} + 1838 q^{11} + 8640 q^{12} - 10985 q^{13} - 13720 q^{14} + 8073 q^{15} + 20480 q^{16} + 56444 q^{17} + 29160 q^{18} - 20639 q^{19} + 19136 q^{20} - 46305 q^{21} + 14704 q^{22} + 74395 q^{23} + 69120 q^{24} + 22594 q^{25} - 87880 q^{26} + 98415 q^{27} - 109760 q^{28} + 130059 q^{29} + 64584 q^{30} + 330083 q^{31} + 163840 q^{32} + 49626 q^{33} + 451552 q^{34} - 102557 q^{35} + 233280 q^{36} + 410632 q^{37} - 165112 q^{38} - 296595 q^{39} + 153088 q^{40} + 172558 q^{41} - 370440 q^{42} + 886497 q^{43} + 117632 q^{44} + 217971 q^{45} + 595160 q^{46} + 763969 q^{47} + 552960 q^{48} + 588245 q^{49} + 180752 q^{50} + 1523988 q^{51} - 703040 q^{52} + 1714575 q^{53} + 787320 q^{54} + 2699318 q^{55} - 878080 q^{56} - 557253 q^{57} + 1040472 q^{58} + 603580 q^{59} + 516672 q^{60} + 6172268 q^{61} + 2640664 q^{62} - 1250235 q^{63} + 1310720 q^{64} - 656903 q^{65} + 397008 q^{66} + 5490834 q^{67} + 3612416 q^{68} + 2008665 q^{69} - 820456 q^{70} - 1581200 q^{71} + 1866240 q^{72} + 2100143 q^{73} + 3285056 q^{74} + 610038 q^{75} - 1320896 q^{76} - 630434 q^{77} - 2372760 q^{78} + 6357137 q^{79} + 1224704 q^{80} + 2657205 q^{81} + 1380464 q^{82} + 5292133 q^{83} - 2963520 q^{84} - 836908 q^{85} + 7091976 q^{86} + 3511593 q^{87} + 941056 q^{88} + 13229719 q^{89} + 1743768 q^{90} + 3767855 q^{91} + 4761280 q^{92} + 8912241 q^{93} + 6111752 q^{94} + 25806433 q^{95} + 4423680 q^{96} + 22321383 q^{97} + 4705960 q^{98} + 1339902 q^{99}+O(q^{100}) \) 5 * q + 40 * q^2 + 135 * q^3 + 320 * q^4 + 299 * q^5 + 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9 + 2392 * q^10 + 1838 * q^11 + 8640 * q^12 - 10985 * q^13 - 13720 * q^14 + 8073 * q^15 + 20480 * q^16 + 56444 * q^17 + 29160 * q^18 - 20639 * q^19 + 19136 * q^20 - 46305 * q^21 + 14704 * q^22 + 74395 * q^23 + 69120 * q^24 + 22594 * q^25 - 87880 * q^26 + 98415 * q^27 - 109760 * q^28 + 130059 * q^29 + 64584 * q^30 + 330083 * q^31 + 163840 * q^32 + 49626 * q^33 + 451552 * q^34 - 102557 * q^35 + 233280 * q^36 + 410632 * q^37 - 165112 * q^38 - 296595 * q^39 + 153088 * q^40 + 172558 * q^41 - 370440 * q^42 + 886497 * q^43 + 117632 * q^44 + 217971 * q^45 + 595160 * q^46 + 763969 * q^47 + 552960 * q^48 + 588245 * q^49 + 180752 * q^50 + 1523988 * q^51 - 703040 * q^52 + 1714575 * q^53 + 787320 * q^54 + 2699318 * q^55 - 878080 * q^56 - 557253 * q^57 + 1040472 * q^58 + 603580 * q^59 + 516672 * q^60 + 6172268 * q^61 + 2640664 * q^62 - 1250235 * q^63 + 1310720 * q^64 - 656903 * q^65 + 397008 * q^66 + 5490834 * q^67 + 3612416 * q^68 + 2008665 * q^69 - 820456 * q^70 - 1581200 * q^71 + 1866240 * q^72 + 2100143 * q^73 + 3285056 * q^74 + 610038 * q^75 - 1320896 * q^76 - 630434 * q^77 - 2372760 * q^78 + 6357137 * q^79 + 1224704 * q^80 + 2657205 * q^81 + 1380464 * q^82 + 5292133 * q^83 - 2963520 * q^84 - 836908 * q^85 + 7091976 * q^86 + 3511593 * q^87 + 941056 * q^88 + 13229719 * q^89 + 1743768 * q^90 + 3767855 * q^91 + 4761280 * q^92 + 8912241 * q^93 + 6111752 * q^94 + 25806433 * q^95 + 4423680 * q^96 + 22321383 * q^97 + 4705960 * q^98 + 1339902 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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