LMFDB - Embedded newform 546.8.a.q.1.5

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:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 367021x^{4} - 17702143x^{3} + 34815194576x^{2} + 1422988371620x - 933871993059968 $ x^6 - x^5 - 367021x^4 - 17702143x^3 + 34815194576x^2 + 1422988371620x - 933871993059968
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$285.402$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +287.402 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +287.402 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +2299.22 q^{10} -3517.26 q^{11} -1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -7759.86 q^{15} +4096.00 q^{16} +10914.5 q^{17} +5832.00 q^{18} -25836.8 q^{19} +18393.7 q^{20} -9261.00 q^{21} -28138.1 q^{22} +64084.6 q^{23} -13824.0 q^{24} +4475.01 q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} +216819. q^{29} -62078.9 q^{30} -190075. q^{31} +32768.0 q^{32} +94966.1 q^{33} +87316.4 q^{34} +98578.9 q^{35} +46656.0 q^{36} +107669. q^{37} -206695. q^{38} +59319.0 q^{39} +147150. q^{40} +561658. q^{41} -74088.0 q^{42} -277509. q^{43} -225105. q^{44} +209516. q^{45} +512677. q^{46} +511134. q^{47} -110592. q^{48} +117649. q^{49} +35800.1 q^{50} -294693. q^{51} -140608. q^{52} +1.28966e6 q^{53} -157464. q^{54} -1.01087e6 q^{55} +175616. q^{56} +697594. q^{57} +1.73455e6 q^{58} +611752. q^{59} -496631. q^{60} -620011. q^{61} -1.52060e6 q^{62} +250047. q^{63} +262144. q^{64} -631423. q^{65} +759729. q^{66} +1.99589e6 q^{67} +698531. q^{68} -1.73028e6 q^{69} +788632. q^{70} -3.28215e6 q^{71} +373248. q^{72} +2.89327e6 q^{73} +861355. q^{74} -120825. q^{75} -1.65356e6 q^{76} -1.20642e6 q^{77} +474552. q^{78} -2.70379e6 q^{79} +1.17720e6 q^{80} +531441. q^{81} +4.49327e6 q^{82} -3.10630e6 q^{83} -592704. q^{84} +3.13686e6 q^{85} -2.22007e6 q^{86} -5.85410e6 q^{87} -1.80084e6 q^{88} -30105.8 q^{89} +1.67613e6 q^{90} -753571. q^{91} +4.10141e6 q^{92} +5.13202e6 q^{93} +4.08907e6 q^{94} -7.42556e6 q^{95} -884736. q^{96} +9.04415e6 q^{97} +941192. q^{98} -2.56408e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 q^{5} - 1296 q^{6} + 2058 q^{7} + 3072 q^{8} + 4374 q^{9}+O(q^{10}) $ 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 13 * q^5 - 1296 * q^6 + 2058 * q^7 + 3072 * q^8 + 4374 * q^9	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 q^{5} - 1296 q^{6} + 2058 q^{7} + 3072 q^{8} + 4374 q^{9} + 104 q^{10} + 10054 q^{11} - 10368 q^{12} - 13182 q^{13} + 16464 q^{14} - 351 q^{15} + 24576 q^{16} + 21222 q^{17} + 34992 q^{18} + 9527 q^{19} + 832 q^{20} - 55566 q^{21} + 80432 q^{22} + 33229 q^{23} - 82944 q^{24} + 265321 q^{25} - 105456 q^{26} - 118098 q^{27} + 131712 q^{28} + 174185 q^{29} - 2808 q^{30} + 119045 q^{31} + 196608 q^{32} - 271458 q^{33} + 169776 q^{34} + 4459 q^{35} + 279936 q^{36} + 56562 q^{37} + 76216 q^{38} + 355914 q^{39} + 6656 q^{40} + 101632 q^{41} - 444528 q^{42} + 441323 q^{43} + 643456 q^{44} + 9477 q^{45} + 265832 q^{46} - 892849 q^{47} - 663552 q^{48} + 705894 q^{49} + 2122568 q^{50} - 572994 q^{51} - 843648 q^{52} + 2093965 q^{53} - 944784 q^{54} - 331222 q^{55} + 1053696 q^{56} - 257229 q^{57} + 1393480 q^{58} - 136204 q^{59} - 22464 q^{60} - 3989946 q^{61} + 952360 q^{62} + 1500282 q^{63} + 1572864 q^{64} - 28561 q^{65} - 2171664 q^{66} - 2218250 q^{67} + 1358208 q^{68} - 897183 q^{69} + 35672 q^{70} + 2045928 q^{71} + 2239488 q^{72} - 8557479 q^{73} + 452496 q^{74} - 7163667 q^{75} + 609728 q^{76} + 3448522 q^{77} + 2847312 q^{78} - 8559709 q^{79} + 53248 q^{80} + 3188646 q^{81} + 813056 q^{82} + 2496351 q^{83} - 3556224 q^{84} + 5335304 q^{85} + 3530584 q^{86} - 4702995 q^{87} + 5147648 q^{88} - 2446683 q^{89} + 75816 q^{90} - 4521426 q^{91} + 2126656 q^{92} - 3214215 q^{93} - 7142792 q^{94} + 16410211 q^{95} - 5308416 q^{96} + 5786889 q^{97} + 5647152 q^{98} + 7329366 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 13 * q^5 - 1296 * q^6 + 2058 * q^7 + 3072 * q^8 + 4374 * q^9 + 104 * q^10 + 10054 * q^11 - 10368 * q^12 - 13182 * q^13 + 16464 * q^14 - 351 * q^15 + 24576 * q^16 + 21222 * q^17 + 34992 * q^18 + 9527 * q^19 + 832 * q^20 - 55566 * q^21 + 80432 * q^22 + 33229 * q^23 - 82944 * q^24 + 265321 * q^25 - 105456 * q^26 - 118098 * q^27 + 131712 * q^28 + 174185 * q^29 - 2808 * q^30 + 119045 * q^31 + 196608 * q^32 - 271458 * q^33 + 169776 * q^34 + 4459 * q^35 + 279936 * q^36 + 56562 * q^37 + 76216 * q^38 + 355914 * q^39 + 6656 * q^40 + 101632 * q^41 - 444528 * q^42 + 441323 * q^43 + 643456 * q^44 + 9477 * q^45 + 265832 * q^46 - 892849 * q^47 - 663552 * q^48 + 705894 * q^49 + 2122568 * q^50 - 572994 * q^51 - 843648 * q^52 + 2093965 * q^53 - 944784 * q^54 - 331222 * q^55 + 1053696 * q^56 - 257229 * q^57 + 1393480 * q^58 - 136204 * q^59 - 22464 * q^60 - 3989946 * q^61 + 952360 * q^62 + 1500282 * q^63 + 1572864 * q^64 - 28561 * q^65 - 2171664 * q^66 - 2218250 * q^67 + 1358208 * q^68 - 897183 * q^69 + 35672 * q^70 + 2045928 * q^71 + 2239488 * q^72 - 8557479 * q^73 + 452496 * q^74 - 7163667 * q^75 + 609728 * q^76 + 3448522 * q^77 + 2847312 * q^78 - 8559709 * q^79 + 53248 * q^80 + 3188646 * q^81 + 813056 * q^82 + 2496351 * q^83 - 3556224 * q^84 + 5335304 * q^85 + 3530584 * q^86 - 4702995 * q^87 + 5147648 * q^88 - 2446683 * q^89 + 75816 * q^90 - 4521426 * q^91 + 2126656 * q^92 - 3214215 * q^93 - 7142792 * q^94 + 16410211 * q^95 - 5308416 * q^96 + 5786889 * q^97 + 5647152 * q^98 + 7329366 * 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
$5$	287.402	1.02824	0.514121	−	0.857718i	$-0.328118\pi$
$5$	287.402	1.02824	0.514121	+	0.857718i	$0.328118\pi$
$6$	−216.000	−0.408248
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	2299.22	0.727076
$11$	−3517.26	−0.796765	−0.398383	−	0.917219i	$-0.630428\pi$
$11$	−3517.26	−0.796765	−0.398383	+	0.917219i	$0.630428\pi$
$12$	−1728.00	−0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	2744.00	0.267261
$15$	−7759.86	−0.593655
$16$	4096.00	0.250000
$17$	10914.5	0.538808	0.269404	−	0.963027i	$-0.413173\pi$
$17$	10914.5	0.538808	0.269404	+	0.963027i	$0.413173\pi$
$18$	5832.00	0.235702
$19$	−25836.8	−0.864175	−0.432087	−	0.901832i	$-0.642223\pi$
$19$	−25836.8	−0.864175	−0.432087	+	0.901832i	$0.642223\pi$
$20$	18393.7	0.514121
$21$	−9261.00	−0.218218
$22$	−28138.1	−0.563398
$23$	64084.6	1.09826	0.549131	−	0.835736i	$-0.314959\pi$
$23$	64084.6	1.09826	0.549131	+	0.835736i	$0.314959\pi$
$24$	−13824.0	−0.204124
$25$	4475.01	0.0572801
$26$	−17576.0	−0.196116
$27$	−19683.0	−0.192450
$28$	21952.0	0.188982
$29$	216819.	1.65083	0.825417	−	0.564523i	$-0.190940\pi$
$29$	216819.	1.65083	0.825417	+	0.564523i	$0.190940\pi$
$30$	−62078.9	−0.419778
$31$	−190075.	−1.14593	−0.572966	−	0.819579i	$-0.694207\pi$
$31$	−190075.	−1.14593	−0.572966	+	0.819579i	$0.694207\pi$
$32$	32768.0	0.176777
$33$	94966.1	0.460013
$34$	87316.4	0.380995
$35$	98578.9	0.388639
$36$	46656.0	0.166667
$37$	107669.	0.349451	0.174725	−	0.984617i	$-0.444096\pi$
$37$	107669.	0.349451	0.174725	+	0.984617i	$0.444096\pi$
$38$	−206695.	−0.611064
$39$	59319.0	0.160128
$40$	147150.	0.363538
$41$	561658.	1.27271	0.636354	−	0.771397i	$-0.280442\pi$
$41$	561658.	1.27271	0.636354	+	0.771397i	$0.280442\pi$
$42$	−74088.0	−0.154303
$43$	−277509.	−0.532277	−0.266138	−	0.963935i	$-0.585748\pi$
$43$	−277509.	−0.532277	−0.266138	+	0.963935i	$0.585748\pi$
$44$	−225105.	−0.398383
$45$	209516.	0.342747
$46$	512677.	0.776589
$47$	511134.	0.718112	0.359056	−	0.933316i	$-0.383099\pi$
$47$	511134.	0.718112	0.359056	+	0.933316i	$0.383099\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	35800.1	0.0405032
$51$	−294693.	−0.311081
$52$	−140608.	−0.138675
$53$	1.28966e6	1.18990	0.594951	−	0.803762i	$-0.297172\pi$
$53$	1.28966e6	1.18990	0.594951	+	0.803762i	$0.297172\pi$
$54$	−157464.	−0.136083
$55$	−1.01087e6	−0.819267
$56$	175616.	0.133631
$57$	697594.	0.498932
$58$	1.73455e6	1.16732
$59$	611752.	0.387787	0.193894	−	0.981023i	$-0.437888\pi$
$59$	611752.	0.387787	0.193894	+	0.981023i	$0.437888\pi$
$60$	−496631.	−0.296828
$61$	−620011.	−0.349740	−0.174870	−	0.984592i	$-0.555950\pi$
$61$	−620011.	−0.349740	−0.174870	+	0.984592i	$0.555950\pi$
$62$	−1.52060e6	−0.810296
$63$	250047.	0.125988
$64$	262144.	0.125000
$65$	−631423.	−0.285183
$66$	759729.	0.325278
$67$	1.99589e6	0.810728	0.405364	−	0.914155i	$-0.367145\pi$
$67$	1.99589e6	0.810728	0.405364	+	0.914155i	$0.367145\pi$
$68$	698531.	0.269404
$69$	−1.73028e6	−0.634082
$70$	788632.	0.274809
$71$	−3.28215e6	−1.08831	−0.544157	−	0.838983i	$-0.683150\pi$
$71$	−3.28215e6	−1.08831	−0.544157	+	0.838983i	$0.683150\pi$
$72$	373248.	0.117851
$73$	2.89327e6	0.870480	0.435240	−	0.900314i	$-0.356664\pi$
$73$	2.89327e6	0.870480	0.435240	+	0.900314i	$0.356664\pi$
$74$	861355.	0.247099
$75$	−120825.	−0.0330707
$76$	−1.65356e6	−0.432087
$77$	−1.20642e6	−0.301149
$78$	474552.	0.113228
$79$	−2.70379e6	−0.616989	−0.308495	−	0.951226i	$-0.599825\pi$
$79$	−2.70379e6	−0.616989	−0.308495	+	0.951226i	$0.599825\pi$
$80$	1.17720e6	0.257060
$81$	531441.	0.111111
$82$	4.49327e6	0.899940
$83$	−3.10630e6	−0.596308	−0.298154	−	0.954518i	$-0.596371\pi$
$83$	−3.10630e6	−0.596308	−0.298154	+	0.954518i	$0.596371\pi$
$84$	−592704.	−0.109109
$85$	3.13686e6	0.554025
$86$	−2.22007e6	−0.376377
$87$	−5.85410e6	−0.953110
$88$	−1.80084e6	−0.281699
$89$	−30105.8	−0.00452674	−0.00226337	−	0.999997i	$-0.500720\pi$
$89$	−30105.8	−0.00452674	−0.00226337	+	0.999997i	$0.500720\pi$
$90$	1.67613e6	0.242359
$91$	−753571.	−0.104828
$92$	4.10141e6	0.549131
$93$	5.13202e6	0.661604
$94$	4.08907e6	0.507782
$95$	−7.42556e6	−0.888580
$96$	−884736.	−0.102062
$97$	9.04415e6	1.00616	0.503080	−	0.864240i	$-0.332200\pi$
$97$	9.04415e6	1.00616	0.503080	+	0.864240i	$0.332200\pi$
$98$	941192.	0.101015
$99$	−2.56408e6	−0.265588
$100$	286401.	0.0286401
$101$	−2.61539e6	−0.252587	−0.126294	−	0.991993i	$-0.540308\pi$
$101$	−2.61539e6	−0.252587	−0.126294	+	0.991993i	$0.540308\pi$
$102$	−2.35754e6	−0.219968
$103$	−7.41803e6	−0.668895	−0.334448	−	0.942414i	$-0.608550\pi$
$103$	−7.41803e6	−0.668895	−0.334448	+	0.942414i	$0.608550\pi$
$104$	−1.12486e6	−0.0980581
$105$	−2.66163e6	−0.224381
$106$	1.03173e7	0.841387
$107$	1.42614e7	1.12543	0.562715	−	0.826651i	$-0.309757\pi$
$107$	1.42614e7	1.12543	0.562715	+	0.826651i	$0.309757\pi$
$108$	−1.25971e6	−0.0962250
$109$	−1.82390e7	−1.34899	−0.674493	−	0.738281i	$-0.735638\pi$
$109$	−1.82390e7	−1.34899	−0.674493	+	0.738281i	$0.735638\pi$
$110$	−8.08695e6	−0.579309
$111$	−2.90707e6	−0.201755
$112$	1.40493e6	0.0944911
$113$	2.88688e7	1.88215	0.941075	−	0.338198i	$-0.109817\pi$
$113$	2.88688e7	1.88215	0.941075	+	0.338198i	$0.109817\pi$
$114$	5.58076e6	0.352798
$115$	1.84180e7	1.12928
$116$	1.38764e7	0.825417
$117$	−1.60161e6	−0.0924500
$118$	4.89402e6	0.274207
$119$	3.74369e6	0.203650
$120$	−3.97305e6	−0.209889
$121$	−7.11603e6	−0.365165
$122$	−4.96009e6	−0.247303
$123$	−1.51648e7	−0.734798
$124$	−1.21648e7	−0.572966
$125$	−2.11672e7	−0.969343
$126$	2.00038e6	0.0890871
$127$	3.03113e7	1.31308	0.656541	−	0.754291i	$-0.272019\pi$
$127$	3.03113e7	1.31308	0.656541	+	0.754291i	$0.272019\pi$
$128$	2.09715e6	0.0883883
$129$	7.49275e6	0.307310
$130$	−5.05138e6	−0.201655
$131$	3.34282e7	1.29916	0.649581	−	0.760292i	$-0.274944\pi$
$131$	3.34282e7	1.29916	0.649581	+	0.760292i	$0.274944\pi$
$132$	6.07783e6	0.230006
$133$	−8.86203e6	−0.326627
$134$	1.59671e7	0.573271
$135$	−5.65694e6	−0.197885
$136$	5.58825e6	0.190498
$137$	−2.80128e7	−0.930754	−0.465377	−	0.885113i	$-0.654081\pi$
$137$	−2.80128e7	−0.930754	−0.465377	+	0.885113i	$0.654081\pi$
$138$	−1.38423e7	−0.448364
$139$	−1.21769e7	−0.384578	−0.192289	−	0.981338i	$-0.561591\pi$
$139$	−1.21769e7	−0.384578	−0.192289	+	0.981338i	$0.561591\pi$
$140$	6.30905e6	0.194319
$141$	−1.38006e7	−0.414602
$142$	−2.62572e7	−0.769554
$143$	7.72743e6	0.220983
$144$	2.98598e6	0.0833333
$145$	6.23141e7	1.69746
$146$	2.31462e7	0.615522
$147$	−3.17652e6	−0.0824786
$148$	6.89084e6	0.174725
$149$	7.04276e6	0.174418	0.0872089	−	0.996190i	$-0.472205\pi$
$149$	7.04276e6	0.174418	0.0872089	+	0.996190i	$0.472205\pi$
$150$	−966602.	−0.0233845
$151$	−1.85979e7	−0.439586	−0.219793	−	0.975547i	$-0.570538\pi$
$151$	−1.85979e7	−0.439586	−0.219793	+	0.975547i	$0.570538\pi$
$152$	−1.32285e7	−0.305532
$153$	7.95670e6	0.179603
$154$	−9.65137e6	−0.212945
$155$	−5.46279e7	−1.17829
$156$	3.79642e6	0.0800641
$157$	1.49954e6	0.0309250	0.0154625	−	0.999880i	$-0.495078\pi$
$157$	1.49954e6	0.0309250	0.0154625	+	0.999880i	$0.495078\pi$
$158$	−2.16303e7	−0.436277
$159$	−3.48209e7	−0.686990
$160$	9.41759e6	0.181769
$161$	2.19810e7	0.415104
$162$	4.25153e6	0.0785674
$163$	−3.53009e7	−0.638453	−0.319227	−	0.947678i	$-0.603423\pi$
$163$	−3.53009e7	−0.638453	−0.319227	+	0.947678i	$0.603423\pi$
$164$	3.59461e7	0.636354
$165$	2.72935e7	0.473004
$166$	−2.48504e7	−0.421653
$167$	9.19470e7	1.52767	0.763836	−	0.645411i	$-0.223314\pi$
$167$	9.19470e7	1.52767	0.763836	+	0.645411i	$0.223314\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	2.50949e7	0.391755
$171$	−1.88350e7	−0.288058
$172$	−1.77606e7	−0.266138
$173$	1.32661e8	1.94796	0.973981	−	0.226629i	$-0.0727704\pi$
$173$	1.32661e8	1.94796	0.973981	+	0.226629i	$0.0727704\pi$
$174$	−4.68328e7	−0.673950
$175$	1.53493e6	0.0216499
$176$	−1.44067e7	−0.199191
$177$	−1.65173e7	−0.223889
$178$	−240847.	−0.00320089
$179$	−1.16724e7	−0.152116	−0.0760582	−	0.997103i	$-0.524233\pi$
$179$	−1.16724e7	−0.152116	−0.0760582	+	0.997103i	$0.524233\pi$
$180$	1.34090e7	0.171374
$181$	9.37365e7	1.17499	0.587494	−	0.809228i	$-0.300114\pi$
$181$	9.37365e7	1.17499	0.587494	+	0.809228i	$0.300114\pi$
$182$	−6.02857e6	−0.0741249
$183$	1.67403e7	0.201922
$184$	3.28113e7	0.388294
$185$	3.09444e7	0.359320
$186$	4.10562e7	0.467825
$187$	−3.83893e7	−0.429304
$188$	3.27126e7	0.359056
$189$	−6.75127e6	−0.0727393
$190$	−5.94045e7	−0.628321
$191$	1.11753e8	1.16049	0.580245	−	0.814442i	$-0.302957\pi$
$191$	1.11753e8	1.16049	0.580245	+	0.814442i	$0.302957\pi$
$192$	−7.07789e6	−0.0721688
$193$	−2.11019e7	−0.211287	−0.105643	−	0.994404i	$-0.533690\pi$
$193$	−2.11019e7	−0.211287	−0.105643	+	0.994404i	$0.533690\pi$
$194$	7.23532e7	0.711462
$195$	1.70484e7	0.164650
$196$	7.52954e6	0.0714286
$197$	7.67918e7	0.715621	0.357810	−	0.933794i	$-0.383523\pi$
$197$	7.67918e7	0.715621	0.357810	+	0.933794i	$0.383523\pi$
$198$	−2.05127e7	−0.187799
$199$	1.99509e8	1.79464	0.897321	−	0.441380i	$-0.145511\pi$
$199$	1.99509e8	1.79464	0.897321	+	0.441380i	$0.145511\pi$
$200$	2.29121e6	0.0202516
$201$	−5.38891e7	−0.468074
$202$	−2.09231e7	−0.178606
$203$	7.43688e7	0.623957
$204$	−1.88603e7	−0.155541
$205$	1.61422e8	1.30865
$206$	−5.93442e7	−0.472980
$207$	4.67177e7	0.366087
$208$	−8.99891e6	−0.0693375
$209$	9.08749e7	0.688545
$210$	−2.12931e7	−0.158661
$211$	1.74866e8	1.28149	0.640747	−	0.767752i	$-0.278625\pi$
$211$	1.74866e8	1.28149	0.640747	+	0.767752i	$0.278625\pi$
$212$	8.25385e7	0.594951
$213$	8.86181e7	0.628339
$214$	1.14091e8	0.795799
$215$	−7.97567e7	−0.547309
$216$	−1.00777e7	−0.0680414
$217$	−6.51957e7	−0.433122
$218$	−1.45912e8	−0.953877
$219$	−7.81183e7	−0.502572
$220$	−6.46956e7	−0.409634
$221$	−2.39793e7	−0.149439
$222$	−2.32566e7	−0.142663
$223$	−2.34627e8	−1.41681	−0.708404	−	0.705808i	$-0.750584\pi$
$223$	−2.34627e8	−1.41681	−0.708404	+	0.705808i	$0.750584\pi$
$224$	1.12394e7	0.0668153
$225$	3.26228e6	0.0190934
$226$	2.30950e8	1.33088
$227$	2.48898e8	1.41231	0.706157	−	0.708056i	$-0.250427\pi$
$227$	2.48898e8	1.41231	0.706157	+	0.708056i	$0.250427\pi$
$228$	4.46460e7	0.249466
$229$	2.28854e8	1.25932	0.629659	−	0.776872i	$-0.283195\pi$
$229$	2.28854e8	1.25932	0.629659	+	0.776872i	$0.283195\pi$
$230$	1.47344e8	0.798521
$231$	3.25734e7	0.173868
$232$	1.11011e8	0.583658
$233$	3.63509e8	1.88265	0.941325	−	0.337501i	$-0.109582\pi$
$233$	3.63509e8	1.88265	0.941325	+	0.337501i	$0.109582\pi$
$234$	−1.28129e7	−0.0653720
$235$	1.46901e8	0.738392
$236$	3.91522e7	0.193894
$237$	7.30023e7	0.356219
$238$	2.99495e7	0.144003
$239$	−1.96099e8	−0.929142	−0.464571	−	0.885536i	$-0.653791\pi$
$239$	−1.96099e8	−0.929142	−0.464571	+	0.885536i	$0.653791\pi$
$240$	−3.17844e7	−0.148414
$241$	−9.03845e7	−0.415943	−0.207972	−	0.978135i	$-0.566686\pi$
$241$	−9.03845e7	−0.415943	−0.207972	+	0.978135i	$0.566686\pi$
$242$	−5.69282e7	−0.258211
$243$	−1.43489e7	−0.0641500
$244$	−3.96807e7	−0.174870
$245$	3.38126e7	0.146892
$246$	−1.21318e8	−0.519581
$247$	5.67635e7	0.239679
$248$	−9.73184e7	−0.405148
$249$	8.38702e7	0.344279
$250$	−1.69337e8	−0.685429
$251$	−3.02094e7	−0.120582	−0.0602911	−	0.998181i	$-0.519203\pi$
$251$	−3.02094e7	−0.120582	−0.0602911	+	0.998181i	$0.519203\pi$
$252$	1.60030e7	0.0629941
$253$	−2.25402e8	−0.875058
$254$	2.42490e8	0.928489
$255$	−8.46953e7	−0.319867
$256$	1.67772e7	0.0625000
$257$	−3.72951e8	−1.37052	−0.685261	−	0.728298i	$-0.740312\pi$
$257$	−3.72951e8	−1.37052	−0.685261	+	0.728298i	$0.740312\pi$
$258$	5.99420e7	0.217301
$259$	3.69306e7	0.132080
$260$	−4.04110e7	−0.142591
$261$	1.58061e8	0.550278
$262$	2.67426e8	0.918646
$263$	1.64651e8	0.558110	0.279055	−	0.960275i	$-0.409979\pi$
$263$	1.64651e8	0.558110	0.279055	+	0.960275i	$0.409979\pi$
$264$	4.86226e7	0.162639
$265$	3.70652e8	1.22351
$266$	−7.08963e7	−0.230960
$267$	812857.	0.00261351
$268$	1.27737e8	0.405364
$269$	−4.31852e8	−1.35270	−0.676351	−	0.736579i	$-0.736440\pi$
$269$	−4.31852e8	−1.35270	−0.676351	+	0.736579i	$0.736440\pi$
$270$	−4.52555e7	−0.139926
$271$	−5.71179e7	−0.174333	−0.0871665	−	0.996194i	$-0.527781\pi$
$271$	−5.71179e7	−0.174333	−0.0871665	+	0.996194i	$0.527781\pi$
$272$	4.47060e7	0.134702
$273$	2.03464e7	0.0605228
$274$	−2.24103e8	−0.658142
$275$	−1.57398e7	−0.0456388
$276$	−1.10738e8	−0.317041
$277$	2.63212e8	0.744091	0.372045	−	0.928215i	$-0.378657\pi$
$277$	2.63212e8	0.744091	0.372045	+	0.928215i	$0.378657\pi$
$278$	−9.74150e7	−0.271938
$279$	−1.38565e8	−0.381977
$280$	5.04724e7	0.137405
$281$	4.49585e8	1.20876	0.604380	−	0.796696i	$-0.293421\pi$
$281$	4.49585e8	1.20876	0.604380	+	0.796696i	$0.293421\pi$
$282$	−1.10405e8	−0.293168
$283$	−4.77230e8	−1.25163	−0.625814	−	0.779972i	$-0.715233\pi$
$283$	−4.77230e8	−1.25163	−0.625814	+	0.779972i	$0.715233\pi$
$284$	−2.10058e8	−0.544157
$285$	2.00490e8	0.513022
$286$	6.18194e7	0.156259
$287$	1.92649e8	0.481038
$288$	2.38879e7	0.0589256
$289$	−2.91211e8	−0.709685
$290$	4.98513e8	1.20028
$291$	−2.44192e8	−0.580906
$292$	1.85169e8	0.435240
$293$	5.25029e6	0.0121940	0.00609701	−	0.999981i	$-0.498059\pi$
$293$	5.25029e6	0.0121940	0.00609701	+	0.999981i	$0.498059\pi$
$294$	−2.54122e7	−0.0583212
$295$	1.75819e8	0.398739
$296$	5.51267e7	0.123549
$297$	6.92303e7	0.153338
$298$	5.63421e7	0.123332
$299$	−1.40794e8	−0.304603
$300$	−7.73282e6	−0.0165354
$301$	−9.51856e7	−0.201182
$302$	−1.48783e8	−0.310834
$303$	7.06155e7	0.145831
$304$	−1.05828e8	−0.216044
$305$	−1.78193e8	−0.359617
$306$	6.36536e7	0.126998
$307$	1.91174e7	0.0377090	0.0188545	−	0.999822i	$-0.493998\pi$
$307$	1.91174e7	0.0377090	0.0188545	+	0.999822i	$0.493998\pi$
$308$	−7.72110e7	−0.150575
$309$	2.00287e8	0.386187
$310$	−4.37024e8	−0.833180
$311$	−3.00942e8	−0.567312	−0.283656	−	0.958926i	$-0.591547\pi$
$311$	−3.00942e8	−0.567312	−0.283656	+	0.958926i	$0.591547\pi$
$312$	3.03713e7	0.0566139
$313$	2.75131e8	0.507147	0.253574	−	0.967316i	$-0.418394\pi$
$313$	2.75131e8	0.507147	0.253574	+	0.967316i	$0.418394\pi$
$314$	1.19963e7	0.0218673
$315$	7.18641e7	0.129546
$316$	−1.73042e8	−0.308495
$317$	−3.48501e8	−0.614464	−0.307232	−	0.951635i	$-0.599403\pi$
$317$	−3.48501e8	−0.614464	−0.307232	+	0.951635i	$0.599403\pi$
$318$	−2.78567e8	−0.485775
$319$	−7.62608e8	−1.31533
$320$	7.53408e7	0.128530
$321$	−3.85057e8	−0.649767
$322$	1.75848e8	0.293523
$323$	−2.81997e8	−0.465625
$324$	3.40122e7	0.0555556
$325$	−9.83160e6	−0.0158867
$326$	−2.82407e8	−0.451455
$327$	4.92452e8	0.778837
$328$	2.87569e8	0.449970
$329$	1.75319e8	0.271421
$330$	2.18348e8	0.334464
$331$	4.63729e8	0.702855	0.351428	−	0.936215i	$-0.385696\pi$
$331$	4.63729e8	0.702855	0.351428	+	0.936215i	$0.385696\pi$
$332$	−1.98803e8	−0.298154
$333$	7.84909e7	0.116484
$334$	7.35576e8	1.08023
$335$	5.73624e8	0.833624
$336$	−3.79331e7	−0.0545545
$337$	−4.28582e8	−0.610000	−0.305000	−	0.952352i	$-0.598656\pi$
$337$	−4.28582e8	−0.610000	−0.305000	+	0.952352i	$0.598656\pi$
$338$	3.86145e7	0.0543928
$339$	−7.79458e8	−1.08666
$340$	2.00759e8	0.277013
$341$	6.68544e8	0.913039
$342$	−1.50680e8	−0.203688
$343$	4.03536e7	0.0539949
$344$	−1.42085e8	−0.188188
$345$	−4.97287e8	−0.651989
$346$	1.06128e9	1.37742
$347$	8.76369e8	1.12599	0.562994	−	0.826461i	$-0.309649\pi$
$347$	8.76369e8	1.12599	0.562994	+	0.826461i	$0.309649\pi$
$348$	−3.74663e8	−0.476555
$349$	−1.20567e9	−1.51824	−0.759121	−	0.650950i	$-0.774371\pi$
$349$	−1.20567e9	−1.51824	−0.759121	+	0.650950i	$0.774371\pi$
$350$	1.22794e7	0.0153088
$351$	4.32436e7	0.0533761
$352$	−1.15254e8	−0.140850
$353$	−8.95397e8	−1.08344	−0.541719	−	0.840560i	$-0.682226\pi$
$353$	−8.95397e8	−1.08344	−0.541719	+	0.840560i	$0.682226\pi$
$354$	−1.32139e8	−0.158314
$355$	−9.43297e8	−1.11905
$356$	−1.92677e6	−0.00226337
$357$	−1.01080e8	−0.117578
$358$	−9.33795e7	−0.107563
$359$	−4.94478e8	−0.564048	−0.282024	−	0.959407i	$-0.591006\pi$
$359$	−4.94478e8	−0.564048	−0.282024	+	0.959407i	$0.591006\pi$
$360$	1.07272e8	0.121179
$361$	−2.26330e8	−0.253202
$362$	7.49892e8	0.830842
$363$	1.92133e8	0.210828
$364$	−4.82285e7	−0.0524142
$365$	8.31532e8	0.895063
$366$	1.33922e8	0.142781
$367$	4.93677e8	0.521329	0.260664	−	0.965429i	$-0.416058\pi$
$367$	4.93677e8	0.521329	0.260664	+	0.965429i	$0.416058\pi$
$368$	2.62490e8	0.274566
$369$	4.09449e8	0.424236
$370$	2.47555e8	0.254077
$371$	4.42355e8	0.449741
$372$	3.28449e8	0.330802
$373$	1.72228e9	1.71840	0.859198	−	0.511643i	$-0.170963\pi$
$373$	1.72228e9	1.71840	0.859198	+	0.511643i	$0.170963\pi$
$374$	−3.07115e8	−0.303564
$375$	5.71514e8	0.559651
$376$	2.61701e8	0.253891
$377$	−4.76351e8	−0.457859
$378$	−5.40102e7	−0.0514344
$379$	6.09310e8	0.574912	0.287456	−	0.957794i	$-0.407191\pi$
$379$	6.09310e8	0.574912	0.287456	+	0.957794i	$0.407191\pi$
$380$	−4.75236e8	−0.444290
$381$	−8.18405e8	−0.758108
$382$	8.94021e8	0.820590
$383$	−6.40183e8	−0.582248	−0.291124	−	0.956685i	$-0.594029\pi$
$383$	−6.40183e8	−0.582248	−0.291124	+	0.956685i	$0.594029\pi$
$384$	−5.66231e7	−0.0510310
$385$	−3.46728e8	−0.309654
$386$	−1.68816e8	−0.149402
$387$	−2.02304e8	−0.177426
$388$	5.78826e8	0.503080
$389$	−8.23729e7	−0.0709514	−0.0354757	−	0.999371i	$-0.511295\pi$
$389$	−8.23729e7	−0.0709514	−0.0354757	+	0.999371i	$0.511295\pi$
$390$	1.36387e8	0.116425
$391$	6.99454e8	0.591753
$392$	6.02363e7	0.0505076
$393$	−9.02561e8	−0.750072
$394$	6.14334e8	0.506020
$395$	−7.77074e8	−0.634414
$396$	−1.64101e8	−0.132794
$397$	2.61533e7	0.0209778	0.0104889	−	0.999945i	$-0.496661\pi$
$397$	2.61533e7	0.0209778	0.0104889	+	0.999945i	$0.496661\pi$
$398$	1.59608e9	1.26900
$399$	2.39275e8	0.188578
$400$	1.83296e7	0.0143200
$401$	1.57626e9	1.22074	0.610368	−	0.792118i	$-0.291022\pi$
$401$	1.57626e9	1.22074	0.610368	+	0.792118i	$0.291022\pi$
$402$	−4.31113e8	−0.330978
$403$	4.17595e8	0.317824
$404$	−1.67385e8	−0.126294
$405$	1.52737e8	0.114249
$406$	5.94950e8	0.441204
$407$	−3.78701e8	−0.278430
$408$	−1.50883e8	−0.109984
$409$	−1.97505e9	−1.42740	−0.713701	−	0.700450i	$-0.752983\pi$
$409$	−1.97505e9	−1.42740	−0.713701	+	0.700450i	$0.752983\pi$
$410$	1.29137e9	0.925356
$411$	7.56346e8	0.537371
$412$	−4.74754e8	−0.334448
$413$	2.09831e8	0.146570
$414$	3.73741e8	0.258863
$415$	−8.92759e8	−0.613149
$416$	−7.19913e7	−0.0490290
$417$	3.28776e8	0.222036
$418$	7.26999e8	0.486875
$419$	−1.58753e9	−1.05432	−0.527162	−	0.849765i	$-0.676744\pi$
$419$	−1.58753e9	−1.05432	−0.527162	+	0.849765i	$0.676744\pi$
$420$	−1.70344e8	−0.112190
$421$	−2.14716e9	−1.40242	−0.701210	−	0.712955i	$-0.747356\pi$
$421$	−2.14716e9	−1.40242	−0.701210	+	0.712955i	$0.747356\pi$
$422$	1.39893e9	0.906153
$423$	3.72617e8	0.239371
$424$	6.60308e8	0.420694
$425$	4.88427e7	0.0308630
$426$	7.08945e8	0.444302
$427$	−2.12664e8	−0.132189
$428$	9.12729e8	0.562715
$429$	−2.08641e8	−0.127585
$430$	−6.38054e8	−0.387006
$431$	−5.97101e7	−0.0359234	−0.0179617	−	0.999839i	$-0.505718\pi$
$431$	−5.97101e7	−0.0359234	−0.0179617	+	0.999839i	$0.505718\pi$
$432$	−8.06216e7	−0.0481125
$433$	2.72594e9	1.61365	0.806823	−	0.590794i	$-0.201185\pi$
$433$	2.72594e9	1.61365	0.806823	+	0.590794i	$0.201185\pi$
$434$	−5.21566e8	−0.306263
$435$	−1.68248e9	−0.980027
$436$	−1.16729e9	−0.674493
$437$	−1.65574e9	−0.949091
$438$	−6.24946e8	−0.355372
$439$	−1.53065e9	−0.863474	−0.431737	−	0.902000i	$-0.642099\pi$
$439$	−1.53065e9	−0.863474	−0.431737	+	0.902000i	$0.642099\pi$
$440$	−5.17565e8	−0.289655
$441$	8.57661e7	0.0476190
$442$	−1.91834e8	−0.105669
$443$	1.54984e9	0.846981	0.423490	−	0.905901i	$-0.360805\pi$
$443$	1.54984e9	0.846981	0.423490	+	0.905901i	$0.360805\pi$
$444$	−1.86053e8	−0.100878
$445$	−8.65248e6	−0.00465458
$446$	−1.87702e9	−1.00183
$447$	−1.90154e8	−0.100700
$448$	8.99154e7	0.0472456
$449$	2.25662e9	1.17651	0.588257	−	0.808674i	$-0.299814\pi$
$449$	2.25662e9	1.17651	0.588257	+	0.808674i	$0.299814\pi$
$450$	2.60983e7	0.0135011
$451$	−1.97550e9	−1.01405
$452$	1.84760e9	0.941075
$453$	5.02142e8	0.253795
$454$	1.99118e9	0.998656
$455$	−2.16578e8	−0.107789
$456$	3.57168e8	0.176399
$457$	−9.22071e8	−0.451916	−0.225958	−	0.974137i	$-0.572551\pi$
$457$	−9.22071e8	−0.451916	−0.225958	+	0.974137i	$0.572551\pi$
$458$	1.83084e9	0.890472
$459$	−2.14831e8	−0.103694
$460$	1.17876e9	0.564639
$461$	3.40218e9	1.61735	0.808676	−	0.588255i	$-0.200185\pi$
$461$	3.40218e9	1.61735	0.808676	+	0.588255i	$0.200185\pi$
$462$	2.60587e8	0.122944
$463$	−1.27583e9	−0.597394	−0.298697	−	0.954348i	$-0.596552\pi$
$463$	−1.27583e9	−0.597394	−0.298697	+	0.954348i	$0.596552\pi$
$464$	8.88089e8	0.412709
$465$	1.47495e9	0.680289
$466$	2.90807e9	1.33123
$467$	4.23326e9	1.92338	0.961692	−	0.274132i	$-0.0883904\pi$
$467$	4.23326e9	1.92338	0.961692	+	0.274132i	$0.0883904\pi$
$468$	−1.02503e8	−0.0462250
$469$	6.84591e8	0.306426
$470$	1.17521e9	0.522122
$471$	−4.04876e7	−0.0178546
$472$	3.13217e8	0.137104
$473$	9.76073e8	0.424100
$474$	5.84018e8	0.251885
$475$	−1.15620e8	−0.0495001
$476$	2.39596e8	0.101825
$477$	9.40165e8	0.396634
$478$	−1.56879e9	−0.657003
$479$	−3.66335e9	−1.52301	−0.761507	−	0.648156i	$-0.775540\pi$
$479$	−3.66335e9	−1.52301	−0.761507	+	0.648156i	$0.775540\pi$
$480$	−2.54275e8	−0.104944
$481$	−2.36550e8	−0.0969202
$482$	−7.23076e8	−0.294116
$483$	−5.93487e8	−0.239661
$484$	−4.55426e8	−0.182582
$485$	2.59931e9	1.03457
$486$	−1.14791e8	−0.0453609
$487$	−6.70678e8	−0.263125	−0.131563	−	0.991308i	$-0.541999\pi$
$487$	−6.70678e8	−0.263125	−0.131563	+	0.991308i	$0.541999\pi$
$488$	−3.17446e8	−0.123652
$489$	9.53124e8	0.368611
$490$	2.70501e8	0.103868
$491$	−2.84339e9	−1.08406	−0.542028	−	0.840360i	$-0.682343\pi$
$491$	−2.84339e9	−1.08406	−0.542028	+	0.840360i	$0.682343\pi$
$492$	−9.70546e8	−0.367399
$493$	2.36648e9	0.889484
$494$	4.54108e8	0.169479
$495$	−7.36924e8	−0.273089
$496$	−7.78547e8	−0.286483
$497$	−1.12578e9	−0.411344
$498$	6.70962e8	0.243442
$499$	3.14281e9	1.13231	0.566156	−	0.824298i	$-0.308430\pi$
$499$	3.14281e9	1.13231	0.566156	+	0.824298i	$0.308430\pi$
$500$	−1.35470e9	−0.484672
$501$	−2.48257e9	−0.882002
$502$	−2.41675e8	−0.0852645
$503$	6.79858e8	0.238194	0.119097	−	0.992883i	$-0.462000\pi$
$503$	6.79858e8	0.238194	0.119097	+	0.992883i	$0.462000\pi$
$504$	1.28024e8	0.0445435
$505$	−7.51669e8	−0.259721
$506$	−1.80322e9	−0.618759
$507$	−1.30324e8	−0.0444116
$508$	1.93992e9	0.656541
$509$	1.56897e9	0.527355	0.263678	−	0.964611i	$-0.415064\pi$
$509$	1.56897e9	0.527355	0.263678	+	0.964611i	$0.415064\pi$
$510$	−6.77563e8	−0.226180
$511$	9.92391e8	0.329011
$512$	1.34218e8	0.0441942
$513$	5.08546e8	0.166311
$514$	−2.98361e9	−0.969105
$515$	−2.13196e9	−0.687786
$516$	4.79536e8	0.153655
$517$	−1.79779e9	−0.572167
$518$	2.95445e8	0.0933946
$519$	−3.58184e9	−1.12466
$520$	−3.23288e8	−0.100827
$521$	−5.47294e9	−1.69547	−0.847733	−	0.530424i	$-0.822033\pi$
$521$	−5.47294e9	−1.69547	−0.847733	+	0.530424i	$0.822033\pi$
$522$	1.26449e9	0.389105
$523$	−3.72307e9	−1.13801	−0.569004	−	0.822335i	$-0.692671\pi$
$523$	−3.72307e9	−1.13801	−0.569004	+	0.822335i	$0.692671\pi$
$524$	2.13940e9	0.649581
$525$	−4.14431e7	−0.0124996
$526$	1.31721e9	0.394643
$527$	−2.07458e9	−0.617438
$528$	3.88981e8	0.115003
$529$	7.02009e8	0.206181
$530$	2.96522e9	0.865149
$531$	4.45967e8	0.129262
$532$	−5.67170e8	−0.163314
$533$	−1.23396e9	−0.352986
$534$	6.50286e6	0.00184803
$535$	4.09875e9	1.15721
$536$	1.02190e9	0.286636
$537$	3.15156e8	0.0878244
$538$	−3.45482e9	−0.956505
$539$	−4.13803e8	−0.113824
$540$	−3.62044e8	−0.0989426
$541$	4.22328e9	1.14673	0.573363	−	0.819301i	$-0.305638\pi$
$541$	4.22328e9	1.14673	0.573363	+	0.819301i	$0.305638\pi$
$542$	−4.56943e8	−0.123272
$543$	−2.53089e9	−0.678380
$544$	3.57648e8	0.0952488
$545$	−5.24192e9	−1.38708
$546$	1.62771e8	0.0427960
$547$	−3.72289e9	−0.972579	−0.486290	−	0.873798i	$-0.661650\pi$
$547$	−3.72289e9	−0.972579	−0.486290	+	0.873798i	$0.661650\pi$
$548$	−1.79282e9	−0.465377
$549$	−4.51988e8	−0.116580
$550$	−1.25918e8	−0.0322715
$551$	−5.60191e9	−1.42661
$552$	−8.85905e8	−0.224182
$553$	−9.27399e8	−0.233200
$554$	2.10569e9	0.526152
$555$	−8.35499e8	−0.207453
$556$	−7.79320e8	−0.192289
$557$	−1.51634e9	−0.371794	−0.185897	−	0.982569i	$-0.559519\pi$
$557$	−1.51634e9	−0.371794	−0.185897	+	0.982569i	$0.559519\pi$
$558$	−1.10852e9	−0.270099
$559$	6.09687e8	0.147627
$560$	4.03779e8	0.0971597
$561$	1.03651e9	0.247859
$562$	3.59668e9	0.854722
$563$	−1.12443e9	−0.265553	−0.132777	−	0.991146i	$-0.542389\pi$
$563$	−1.12443e9	−0.265553	−0.132777	+	0.991146i	$0.542389\pi$
$564$	−8.83239e8	−0.207301
$565$	8.29696e9	1.93530
$566$	−3.81784e9	−0.885035
$567$	1.82284e8	0.0419961
$568$	−1.68046e9	−0.384777
$569$	4.73165e9	1.07676	0.538381	−	0.842701i	$-0.319036\pi$
$569$	4.73165e9	1.07676	0.538381	+	0.842701i	$0.319036\pi$
$570$	1.60392e9	0.362761
$571$	−3.52395e8	−0.0792142	−0.0396071	−	0.999215i	$-0.512611\pi$
$571$	−3.52395e8	−0.0792142	−0.0396071	+	0.999215i	$0.512611\pi$
$572$	4.94555e8	0.110491
$573$	−3.01732e9	−0.670009
$574$	1.54119e9	0.340145
$575$	2.86779e8	0.0629086
$576$	1.91103e8	0.0416667
$577$	−3.04877e9	−0.660707	−0.330354	−	0.943857i	$-0.607168\pi$
$577$	−3.04877e9	−0.660707	−0.330354	+	0.943857i	$0.607168\pi$
$578$	−2.32969e9	−0.501823
$579$	5.69753e8	0.121986
$580$	3.98811e9	0.848728
$581$	−1.06546e9	−0.225383
$582$	−1.95354e9	−0.410763
$583$	−4.53609e9	−0.948072
$584$	1.48135e9	0.307761
$585$	−4.60307e8	−0.0950609
$586$	4.20023e7	0.00862247
$587$	−2.10059e9	−0.428655	−0.214327	−	0.976762i	$-0.568756\pi$
$587$	−2.10059e9	−0.428655	−0.214327	+	0.976762i	$0.568756\pi$
$588$	−2.03297e8	−0.0412393
$589$	4.91093e9	0.990286
$590$	1.40655e9	0.281951
$591$	−2.07338e9	−0.413164
$592$	4.41014e8	0.0873627
$593$	2.27623e9	0.448255	0.224128	−	0.974560i	$-0.428047\pi$
$593$	2.27623e9	0.448255	0.224128	+	0.974560i	$0.428047\pi$
$594$	5.53842e8	0.108426
$595$	1.07594e9	0.209402
$596$	4.50736e8	0.0872089
$597$	−5.38675e9	−1.03614
$598$	−1.12635e9	−0.215387
$599$	−1.02748e7	−0.00195334	−0.000976672	−	1.00000i	$-0.500311\pi$
$599$	−1.02748e7	−0.00195334	−0.000976672		1.00000i	$0.500311\pi$
$600$	−6.18625e7	−0.0116923
$601$	−1.02256e10	−1.92144	−0.960722	−	0.277513i	$-0.910490\pi$
$601$	−1.02256e10	−1.92144	−0.960722	+	0.277513i	$0.910490\pi$
$602$	−7.61485e8	−0.142257
$603$	1.45501e9	0.270243
$604$	−1.19026e9	−0.219793
$605$	−2.04516e9	−0.375478
$606$	5.64924e8	0.103118
$607$	−9.02774e7	−0.0163840	−0.00819198	−	0.999966i	$-0.502608\pi$
$607$	−9.02774e7	−0.0163840	−0.00819198	+	0.999966i	$0.502608\pi$
$608$	−8.46621e8	−0.152766
$609$	−2.00796e9	−0.360242
$610$	−1.42554e9	−0.254287
$611$	−1.12296e9	−0.199168
$612$	5.09229e8	0.0898014
$613$	−6.23451e9	−1.09318	−0.546588	−	0.837401i	$-0.684074\pi$
$613$	−6.23451e9	−1.09318	−0.546588	+	0.837401i	$0.684074\pi$
$614$	1.52940e8	0.0266643
$615$	−4.35839e9	−0.755550
$616$	−6.17688e8	−0.106472
$617$	6.17858e9	1.05899	0.529494	−	0.848314i	$-0.322382\pi$
$617$	6.17858e9	1.05899	0.529494	+	0.848314i	$0.322382\pi$
$618$	1.60229e9	0.273075
$619$	−2.29126e9	−0.388291	−0.194145	−	0.980973i	$-0.562193\pi$
$619$	−2.29126e9	−0.388291	−0.194145	+	0.980973i	$0.562193\pi$
$620$	−3.49619e9	−0.589147
$621$	−1.26138e9	−0.211361
$622$	−2.40754e9	−0.401150
$623$	−1.03263e7	−0.00171095
$624$	2.42971e8	0.0400320
$625$	−6.43310e9	−1.05400
$626$	2.20105e9	0.358607
$627$	−2.45362e9	−0.397531
$628$	9.59707e7	0.0154625
$629$	1.17516e9	0.188287
$630$	5.74912e8	0.0916030
$631$	3.63119e9	0.575368	0.287684	−	0.957725i	$-0.407115\pi$
$631$	3.63119e9	0.575368	0.287684	+	0.957725i	$0.407115\pi$
$632$	−1.38434e9	−0.218139
$633$	−4.72138e9	−0.739871
$634$	−2.78801e9	−0.434492
$635$	8.71153e9	1.35016
$636$	−2.22854e9	−0.343495
$637$	−2.58475e8	−0.0396214
$638$	−6.10087e9	−0.930077
$639$	−2.39269e9	−0.362771
$640$	6.02726e8	0.0908845
$641$	7.55654e9	1.13323	0.566617	−	0.823981i	$-0.308252\pi$
$641$	7.55654e9	1.13323	0.566617	+	0.823981i	$0.308252\pi$
$642$	−3.08046e9	−0.459455
$643$	6.07377e9	0.900990	0.450495	−	0.892779i	$-0.351248\pi$
$643$	6.07377e9	0.900990	0.450495	+	0.892779i	$0.351248\pi$
$644$	1.40678e9	0.207552
$645$	2.15343e9	0.315989
$646$	−2.25598e9	−0.329246
$647$	−9.06304e9	−1.31555	−0.657777	−	0.753213i	$-0.728503\pi$
$647$	−9.06304e9	−1.31555	−0.657777	+	0.753213i	$0.728503\pi$
$648$	2.72098e8	0.0392837
$649$	−2.15169e9	−0.308976
$650$	−7.86528e7	−0.0112336
$651$	1.76028e9	0.250063
$652$	−2.25926e9	−0.319227
$653$	5.11882e9	0.719405	0.359703	−	0.933067i	$-0.382878\pi$
$653$	5.11882e9	0.719405	0.359703	+	0.933067i	$0.382878\pi$
$654$	3.93962e9	0.550721
$655$	9.60733e9	1.33585
$656$	2.30055e9	0.318177
$657$	2.10919e9	0.290160
$658$	1.40255e9	0.191924
$659$	−7.01319e9	−0.954589	−0.477295	−	0.878743i	$-0.658383\pi$
$659$	−7.01319e9	−0.954589	−0.477295	+	0.878743i	$0.658383\pi$
$660$	1.74678e9	0.236502
$661$	2.47324e9	0.333089	0.166545	−	0.986034i	$-0.446739\pi$
$661$	2.47324e9	0.333089	0.166545	+	0.986034i	$0.446739\pi$
$662$	3.70983e9	0.496994
$663$	6.47440e8	0.0862784
$664$	−1.59043e9	−0.210827
$665$	−2.54697e9	−0.335852
$666$	6.27927e8	0.0823663
$667$	1.38947e10	1.81305
$668$	5.88461e9	0.763836
$669$	6.33493e9	0.817994
$670$	4.58899e9	0.589461
$671$	2.18074e9	0.278661
$672$	−3.03464e8	−0.0385758
$673$	8.63601e8	0.109209	0.0546047	−	0.998508i	$-0.482610\pi$
$673$	8.63601e8	0.109209	0.0546047	+	0.998508i	$0.482610\pi$
$674$	−3.42866e9	−0.431335
$675$	−8.80816e7	−0.0110236
$676$	3.08916e8	0.0384615
$677$	3.19919e8	0.0396259	0.0198130	−	0.999804i	$-0.493693\pi$
$677$	3.19919e8	0.0396259	0.0198130	+	0.999804i	$0.493693\pi$
$678$	−6.23566e9	−0.768384
$679$	3.10214e9	0.380292
$680$	1.60607e9	0.195877
$681$	−6.72025e9	−0.815399
$682$	5.34835e9	0.645616
$683$	−1.10213e10	−1.32361	−0.661804	−	0.749677i	$-0.730209\pi$
$683$	−1.10213e10	−1.32361	−0.661804	+	0.749677i	$0.730209\pi$
$684$	−1.20544e9	−0.144029
$685$	−8.05094e9	−0.957039
$686$	3.22829e8	0.0381802
$687$	−6.17907e9	−0.727067
$688$	−1.13668e9	−0.133069
$689$	−2.83339e9	−0.330019
$690$	−3.97830e9	−0.461026
$691$	−1.56486e10	−1.80428	−0.902138	−	0.431448i	$-0.858003\pi$
$691$	−1.56486e10	−1.80428	−0.902138	+	0.431448i	$0.858003\pi$
$692$	8.49028e9	0.973981
$693$	−8.79481e8	−0.100383
$694$	7.01095e9	0.796194
$695$	−3.49966e9	−0.395439
$696$	−2.99730e9	−0.336975
$697$	6.13024e9	0.685746
$698$	−9.64539e9	−1.07356
$699$	−9.81475e9	−1.08695
$700$	9.82354e7	0.0108249
$701$	−7.67098e9	−0.841081	−0.420540	−	0.907274i	$-0.638160\pi$
$701$	−7.67098e9	−0.841081	−0.420540	+	0.907274i	$0.638160\pi$
$702$	3.45948e8	0.0377426
$703$	−2.78183e9	−0.301987
$704$	−9.22029e8	−0.0995957
$705$	−3.96633e9	−0.426311
$706$	−7.16317e9	−0.766106
$707$	−8.97079e8	−0.0954691
$708$	−1.05711e9	−0.111945
$709$	−1.15081e10	−1.21266	−0.606332	−	0.795212i	$-0.707360\pi$
$709$	−1.15081e10	−1.21266	−0.606332	+	0.795212i	$0.707360\pi$
$710$	−7.54638e9	−0.791288
$711$	−1.97106e9	−0.205663
$712$	−1.54142e7	−0.00160044
$713$	−1.21809e10	−1.25853
$714$	−8.08637e8	−0.0831399
$715$	2.22088e9	0.227224
$716$	−7.47036e8	−0.0760582
$717$	5.29466e9	0.536440
$718$	−3.95582e9	−0.398842
$719$	−1.49179e10	−1.49678	−0.748389	−	0.663260i	$-0.769172\pi$
$719$	−1.49179e10	−1.49678	−0.748389	+	0.663260i	$0.769172\pi$
$720$	8.58178e8	0.0856868
$721$	−2.54438e9	−0.252819
$722$	−1.81064e9	−0.179041
$723$	2.44038e9	0.240145
$724$	5.99914e9	0.587494
$725$	9.70266e8	0.0945600
$726$	1.53706e9	0.149078
$727$	−2.24015e9	−0.216226	−0.108113	−	0.994139i	$-0.534481\pi$
$727$	−2.24015e9	−0.216226	−0.108113	+	0.994139i	$0.534481\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	6.65225e9	0.632905
$731$	−3.02889e9	−0.286795
$732$	1.07138e9	0.100961
$733$	7.57707e9	0.710620	0.355310	−	0.934748i	$-0.384375\pi$
$733$	7.57707e9	0.710620	0.355310	+	0.934748i	$0.384375\pi$
$734$	3.94942e9	0.368635
$735$	−9.12940e8	−0.0848079
$736$	2.09992e9	0.194147
$737$	−7.02008e9	−0.645960
$738$	3.27559e9	0.299980
$739$	−4.16117e9	−0.379280	−0.189640	−	0.981854i	$-0.560732\pi$
$739$	−4.16117e9	−0.379280	−0.189640	+	0.981854i	$0.560732\pi$
$740$	1.98044e9	0.179660
$741$	−1.53261e9	−0.138379
$742$	3.53884e9	0.318015
$743$	−1.87849e10	−1.68015	−0.840077	−	0.542467i	$-0.817490\pi$
$743$	−1.87849e10	−1.68015	−0.840077	+	0.542467i	$0.817490\pi$
$744$	2.62760e9	0.233912
$745$	2.02410e9	0.179344
$746$	1.37783e10	1.21509
$747$	−2.26450e9	−0.198769
$748$	−2.45692e9	−0.214652
$749$	4.89165e9	0.425373
$750$	4.57211e9	0.395733
$751$	−3.05552e9	−0.263236	−0.131618	−	0.991301i	$-0.542017\pi$
$751$	−3.05552e9	−0.263236	−0.131618	+	0.991301i	$0.542017\pi$
$752$	2.09360e9	0.179528
$753$	8.15653e8	0.0696182
$754$	−3.81080e9	−0.323755
$755$	−5.34506e9	−0.452000
$756$	−4.32081e8	−0.0363696
$757$	−2.34720e9	−0.196659	−0.0983295	−	0.995154i	$-0.531350\pi$
$757$	−2.34720e9	−0.196659	−0.0983295	+	0.995154i	$0.531350\pi$
$758$	4.87448e9	0.406524
$759$	6.08586e9	0.505215
$760$	−3.80189e9	−0.314161
$761$	−1.64745e10	−1.35509	−0.677544	−	0.735483i	$-0.736955\pi$
$761$	−1.64745e10	−1.35509	−0.677544	+	0.735483i	$0.736955\pi$
$762$	−6.54724e9	−0.536063
$763$	−6.25597e9	−0.509869
$764$	7.15217e9	0.580245
$765$	2.28677e9	0.184675
$766$	−5.12146e9	−0.411712
$767$	−1.34402e9	−0.107553
$768$	−4.52985e8	−0.0360844
$769$	−1.04854e10	−0.831465	−0.415732	−	0.909487i	$-0.636475\pi$
$769$	−1.04854e10	−0.831465	−0.415732	+	0.909487i	$0.636475\pi$
$770$	−2.77382e9	−0.218958
$771$	1.00697e10	0.791271
$772$	−1.35052e9	−0.105643
$773$	−7.53799e9	−0.586985	−0.293493	−	0.955961i	$-0.594818\pi$
$773$	−7.53799e9	−0.586985	−0.293493	+	0.955961i	$0.594818\pi$
$774$	−1.61843e9	−0.125459
$775$	−8.50587e8	−0.0656392
$776$	4.63060e9	0.355731
$777$	−9.97126e8	−0.0762564
$778$	−6.58983e8	−0.0501702
$779$	−1.45115e10	−1.09984
$780$	1.09110e9	0.0823252
$781$	1.15442e10	0.867131
$782$	5.59563e9	0.418433
$783$	−4.26764e9	−0.317703
$784$	4.81890e8	0.0357143
$785$	4.30972e8	0.0317984
$786$	−7.22049e9	−0.530381
$787$	2.27545e10	1.66401	0.832005	−	0.554768i	$-0.187193\pi$
$787$	2.27545e10	1.66401	0.832005	+	0.554768i	$0.187193\pi$
$788$	4.91467e9	0.357810
$789$	−4.44558e9	−0.322225
$790$	−6.21659e9	−0.448598
$791$	9.90200e9	0.711386
$792$	−1.31281e9	−0.0938997
$793$	1.36216e9	0.0970003
$794$	2.09226e8	0.0148335
$795$	−1.00076e10	−0.706391
$796$	1.27686e10	0.897321
$797$	5.92842e8	0.0414796	0.0207398	−	0.999785i	$-0.493398\pi$
$797$	5.92842e8	0.0414796	0.0207398	+	0.999785i	$0.493398\pi$
$798$	1.91420e9	0.133345
$799$	5.57879e9	0.386925
$800$	1.46637e8	0.0101258
$801$	−2.19472e7	−0.00150891
$802$	1.26101e10	0.863191
$803$	−1.01764e10	−0.693568
$804$	−3.44890e9	−0.234037
$805$	6.31739e9	0.426827
$806$	3.34076e9	0.224736
$807$	1.16600e10	0.780983
$808$	−1.33908e9	−0.0893031
$809$	−2.10016e10	−1.39454	−0.697272	−	0.716806i	$-0.745603\pi$
$809$	−2.10016e10	−1.39454	−0.697272	+	0.716806i	$0.745603\pi$
$810$	1.22190e9	0.0807863
$811$	2.26623e10	1.49187	0.745936	−	0.666017i	$-0.232002\pi$
$811$	2.26623e10	1.49187	0.745936	+	0.666017i	$0.232002\pi$
$812$	4.75960e9	0.311978
$813$	1.54218e9	0.100651
$814$	−3.02961e9	−0.196880
$815$	−1.01456e10	−0.656484
$816$	−1.20706e9	−0.0777703
$817$	7.16996e9	0.459980
$818$	−1.58004e10	−1.00933
$819$	−5.49353e8	−0.0349428
$820$	1.03310e10	0.654325
$821$	6.69701e9	0.422357	0.211179	−	0.977447i	$-0.432270\pi$
$821$	6.69701e9	0.422357	0.211179	+	0.977447i	$0.432270\pi$
$822$	6.05077e9	0.379979
$823$	6.85362e9	0.428569	0.214285	−	0.976771i	$-0.431258\pi$
$823$	6.85362e9	0.428569	0.214285	+	0.976771i	$0.431258\pi$
$824$	−3.79803e9	−0.236490
$825$	4.24974e8	0.0263496
$826$	1.67865e9	0.103641
$827$	8.71864e9	0.536018	0.268009	−	0.963416i	$-0.413634\pi$
$827$	8.71864e9	0.536018	0.268009	+	0.963416i	$0.413634\pi$
$828$	2.98993e9	0.183044
$829$	1.73628e10	1.05847	0.529235	−	0.848475i	$-0.322479\pi$
$829$	1.73628e10	1.05847	0.529235	+	0.848475i	$0.322479\pi$
$830$	−7.14207e9	−0.433561
$831$	−7.10671e9	−0.429601
$832$	−5.75930e8	−0.0346688
$833$	1.28409e9	0.0769726
$834$	2.63021e9	0.157003
$835$	2.64258e10	1.57081
$836$	5.81600e9	0.344272
$837$	3.74124e9	0.220535
$838$	−1.27003e10	−0.745520
$839$	−2.28163e10	−1.33376	−0.666882	−	0.745164i	$-0.732371\pi$
$839$	−2.28163e10	−1.33376	−0.666882	+	0.745164i	$0.732371\pi$
$840$	−1.36276e9	−0.0793305
$841$	2.97604e10	1.72526
$842$	−1.71773e10	−0.991660
$843$	−1.21388e10	−0.697878
$844$	1.11914e10	0.640747
$845$	1.38724e9	0.0790955
$846$	2.98093e9	0.169261
$847$	−2.44080e9	−0.138019
$848$	5.28246e9	0.297475
$849$	1.28852e10	0.722628
$850$	3.90742e8	0.0218235
$851$	6.89994e9	0.383789
$852$	5.67156e9	0.314169
$853$	−1.38482e10	−0.763962	−0.381981	−	0.924170i	$-0.624758\pi$
$853$	−1.38482e10	−0.763962	−0.381981	+	0.924170i	$0.624758\pi$
$854$	−1.70131e9	−0.0934719
$855$	−5.41323e9	−0.296193
$856$	7.30183e9	0.397900
$857$	1.62737e10	0.883188	0.441594	−	0.897215i	$-0.354413\pi$
$857$	1.62737e10	0.883188	0.441594	+	0.897215i	$0.354413\pi$
$858$	−1.66912e9	−0.0902159
$859$	−1.05712e10	−0.569047	−0.284524	−	0.958669i	$-0.591835\pi$
$859$	−1.05712e10	−0.569047	−0.284524	+	0.958669i	$0.591835\pi$
$860$	−5.10443e9	−0.273655
$861$	−5.20152e9	−0.277728
$862$	−4.77681e8	−0.0254017
$863$	−1.49720e8	−0.00792941	−0.00396470	−	0.999992i	$-0.501262\pi$
$863$	−1.49720e8	−0.00792941	−0.00396470	+	0.999992i	$0.501262\pi$
$864$	−6.44973e8	−0.0340207
$865$	3.81269e10	2.00298
$866$	2.18075e10	1.14102
$867$	7.86271e9	0.409737
$868$	−4.17252e9	−0.216561
$869$	9.50993e9	0.491596
$870$	−1.34599e10	−0.692984
$871$	−4.38497e9	−0.224856
$872$	−9.33835e9	−0.476939
$873$	6.59318e9	0.335386
$874$	−1.32459e10	−0.671109
$875$	−7.26034e9	−0.366377
$876$	−4.99957e9	−0.251286
$877$	2.82110e10	1.41228	0.706138	−	0.708074i	$-0.250436\pi$
$877$	2.82110e10	1.41228	0.706138	+	0.708074i	$0.250436\pi$
$878$	−1.22452e10	−0.610568
$879$	−1.41758e8	−0.00704022
$880$	−4.14052e9	−0.204817
$881$	1.13329e10	0.558373	0.279187	−	0.960237i	$-0.409935\pi$
$881$	1.13329e10	0.558373	0.279187	+	0.960237i	$0.409935\pi$
$882$	6.86129e8	0.0336718
$883$	−5.55367e9	−0.271467	−0.135734	−	0.990745i	$-0.543339\pi$
$883$	−5.55367e9	−0.271467	−0.135734	+	0.990745i	$0.543339\pi$
$884$	−1.53467e9	−0.0747193
$885$	−4.74711e9	−0.230212
$886$	1.23987e10	0.598906
$887$	−4.16027e9	−0.200165	−0.100083	−	0.994979i	$-0.531911\pi$
$887$	−4.16027e9	−0.200165	−0.100083	+	0.994979i	$0.531911\pi$
$888$	−1.48842e9	−0.0713313
$889$	1.03968e10	0.496298
$890$	−6.92199e7	−0.00329129
$891$	−1.86922e9	−0.0885295
$892$	−1.50161e10	−0.708404
$893$	−1.32061e10	−0.620574
$894$	−1.52124e9	−0.0712058
$895$	−3.35468e9	−0.156412
$896$	7.19323e8	0.0334077
$897$	3.80143e9	0.175863
$898$	1.80530e10	0.831921
$899$	−4.12118e10	−1.89174
$900$	2.08786e8	0.00954669
$901$	1.40761e10	0.641129
$902$	−1.58040e10	−0.717041
$903$	2.57001e9	0.116152
$904$	1.47808e10	0.665440
$905$	2.69401e10	1.20817
$906$	4.01714e9	0.179460
$907$	2.52488e10	1.12361	0.561804	−	0.827271i	$-0.310108\pi$
$907$	2.52488e10	1.12361	0.561804	+	0.827271i	$0.310108\pi$
$908$	1.59295e10	0.706157
$909$	−1.90662e9	−0.0841958
$910$	−1.73262e9	−0.0762183
$911$	−4.60044e9	−0.201597	−0.100799	−	0.994907i	$-0.532140\pi$
$911$	−4.60044e9	−0.201597	−0.100799	+	0.994907i	$0.532140\pi$
$912$	2.85735e9	0.124733
$913$	1.09257e10	0.475118
$914$	−7.37657e9	−0.319553
$915$	4.81120e9	0.207625
$916$	1.46467e10	0.629659
$917$	1.14659e10	0.491037
$918$	−1.71865e9	−0.0733225
$919$	1.41325e10	0.600640	0.300320	−	0.953839i	$-0.402907\pi$
$919$	1.41325e10	0.600640	0.300320	+	0.953839i	$0.402907\pi$
$920$	9.43004e9	0.399260
$921$	−5.16171e8	−0.0217713
$922$	2.72175e10	1.14364
$923$	7.21089e9	0.301844
$924$	2.08470e9	0.0869342
$925$	4.81821e8	0.0200166
$926$	−1.02067e10	−0.422421
$927$	−5.40774e9	−0.222965
$928$	7.10471e9	0.291829
$929$	−4.45261e9	−0.182205	−0.0911024	−	0.995842i	$-0.529039\pi$
$929$	−4.45261e9	−0.182205	−0.0911024	+	0.995842i	$0.529039\pi$
$930$	1.17996e10	0.481037
$931$	−3.03968e9	−0.123454
$932$	2.32646e10	0.941325
$933$	8.12544e9	0.327538
$934$	3.38661e10	1.36004
$935$	−1.10332e10	−0.441428
$936$	−8.20026e8	−0.0326860
$937$	1.52816e10	0.606849	0.303425	−	0.952855i	$-0.401870\pi$
$937$	1.52816e10	0.606849	0.303425	+	0.952855i	$0.401870\pi$
$938$	5.47673e9	0.216676
$939$	−7.42853e9	−0.292802
$940$	9.40166e9	0.369196
$941$	−1.62754e10	−0.636747	−0.318374	−	0.947965i	$-0.603137\pi$
$941$	−1.62754e10	−0.636747	−0.318374	+	0.947965i	$0.603137\pi$
$942$	−3.23901e8	−0.0126251
$943$	3.59936e10	1.39777
$944$	2.50574e9	0.0969468
$945$	−1.94033e9	−0.0747935
$946$	7.80858e9	0.299884
$947$	1.76582e10	0.675648	0.337824	−	0.941209i	$-0.390309\pi$
$947$	1.76582e10	0.675648	0.337824	+	0.941209i	$0.390309\pi$
$948$	4.67214e9	0.178109
$949$	−6.35651e9	−0.241428
$950$	−9.24961e8	−0.0350018
$951$	9.40952e9	0.354761
$952$	1.91677e9	0.0720013
$953$	2.02839e10	0.759147	0.379574	−	0.925162i	$-0.376071\pi$
$953$	2.02839e10	0.759147	0.379574	+	0.925162i	$0.376071\pi$
$954$	7.52132e9	0.280462
$955$	3.21180e10	1.19326
$956$	−1.25503e10	−0.464571
$957$	2.05904e10	0.759405
$958$	−2.93068e10	−1.07693
$959$	−9.60840e9	−0.351792
$960$	−2.03420e9	−0.0742069
$961$	8.61586e9	0.313160
$962$	−1.89240e9	−0.0685329
$963$	1.03965e10	0.375143
$964$	−5.78461e9	−0.207972
$965$	−6.06475e9	−0.217254
$966$	−4.74790e9	−0.169466
$967$	1.37829e10	0.490171	0.245086	−	0.969501i	$-0.421184\pi$
$967$	1.37829e10	0.490171	0.245086	+	0.969501i	$0.421184\pi$
$968$	−3.64341e9	−0.129105
$969$	7.61392e9	0.268829
$970$	2.07945e10	0.731554
$971$	−4.58501e10	−1.60721	−0.803606	−	0.595161i	$-0.797088\pi$
$971$	−4.58501e10	−1.60721	−0.803606	+	0.595161i	$0.797088\pi$
$972$	−9.18330e8	−0.0320750
$973$	−4.17667e9	−0.145357
$974$	−5.36543e9	−0.186058
$975$	2.65453e8	0.00917216
$976$	−2.53957e9	−0.0874349
$977$	−1.35238e10	−0.463945	−0.231973	−	0.972722i	$-0.574518\pi$
$977$	−1.35238e10	−0.463945	−0.231973	+	0.972722i	$0.574518\pi$
$978$	7.62499e9	0.260647
$979$	1.05890e8	0.00360675
$980$	2.16401e9	0.0734458
$981$	−1.32962e10	−0.449662
$982$	−2.27471e10	−0.766543
$983$	−2.37303e10	−0.796831	−0.398415	−	0.917205i	$-0.630440\pi$
$983$	−2.37303e10	−0.796831	−0.398415	+	0.917205i	$0.630440\pi$
$984$	−7.76436e9	−0.259790
$985$	2.20701e10	0.735831
$986$	1.89318e10	0.628960
$987$	−4.73361e9	−0.156705
$988$	3.63286e9	0.119839
$989$	−1.77841e10	−0.584580
$990$	−5.89539e9	−0.193103
$991$	5.70744e9	0.186288	0.0931438	−	0.995653i	$-0.470308\pi$
$991$	5.70744e9	0.186288	0.0931438	+	0.995653i	$0.470308\pi$
$992$	−6.22838e9	−0.202574
$993$	−1.25207e10	−0.405794
$994$	−9.00622e9	−0.290864
$995$	5.73394e10	1.84532
$996$	5.36769e9	0.172139
$997$	−1.53823e9	−0.0491572	−0.0245786	−	0.999698i	$-0.507824\pi$
$997$	−1.53823e9	−0.0491572	−0.0245786	+	0.999698i	$0.507824\pi$
$998$	2.51425e10	0.800666
$999$	−2.11926e9	−0.0672518

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.q.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.q.1.5	✓	6	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)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +287.402 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +287.402 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +2299.22 q^{10} -3517.26 q^{11} -1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -7759.86 q^{15} +4096.00 q^{16} +10914.5 q^{17} +5832.00 q^{18} -25836.8 q^{19} +18393.7 q^{20} -9261.00 q^{21} -28138.1 q^{22} +64084.6 q^{23} -13824.0 q^{24} +4475.01 q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} +216819. q^{29} -62078.9 q^{30} -190075. q^{31} +32768.0 q^{32} +94966.1 q^{33} +87316.4 q^{34} +98578.9 q^{35} +46656.0 q^{36} +107669. q^{37} -206695. q^{38} +59319.0 q^{39} +147150. q^{40} +561658. q^{41} -74088.0 q^{42} -277509. q^{43} -225105. q^{44} +209516. q^{45} +512677. q^{46} +511134. q^{47} -110592. q^{48} +117649. q^{49} +35800.1 q^{50} -294693. q^{51} -140608. q^{52} +1.28966e6 q^{53} -157464. q^{54} -1.01087e6 q^{55} +175616. q^{56} +697594. q^{57} +1.73455e6 q^{58} +611752. q^{59} -496631. q^{60} -620011. q^{61} -1.52060e6 q^{62} +250047. q^{63} +262144. q^{64} -631423. q^{65} +759729. q^{66} +1.99589e6 q^{67} +698531. q^{68} -1.73028e6 q^{69} +788632. q^{70} -3.28215e6 q^{71} +373248. q^{72} +2.89327e6 q^{73} +861355. q^{74} -120825. q^{75} -1.65356e6 q^{76} -1.20642e6 q^{77} +474552. q^{78} -2.70379e6 q^{79} +1.17720e6 q^{80} +531441. q^{81} +4.49327e6 q^{82} -3.10630e6 q^{83} -592704. q^{84} +3.13686e6 q^{85} -2.22007e6 q^{86} -5.85410e6 q^{87} -1.80084e6 q^{88} -30105.8 q^{89} +1.67613e6 q^{90} -753571. q^{91} +4.10141e6 q^{92} +5.13202e6 q^{93} +4.08907e6 q^{94} -7.42556e6 q^{95} -884736. q^{96} +9.04415e6 q^{97} +941192. q^{98} -2.56408e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 q^{5} - 1296 q^{6} + 2058 q^{7} + 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 13 * q^5 - 1296 * q^6 + 2058 * q^7 + 3072 * q^8 + 4374 * q^9	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 q^{5} - 1296 q^{6} + 2058 q^{7} + 3072 q^{8} + 4374 q^{9} + 104 q^{10} + 10054 q^{11} - 10368 q^{12} - 13182 q^{13} + 16464 q^{14} - 351 q^{15} + 24576 q^{16} + 21222 q^{17} + 34992 q^{18} + 9527 q^{19} + 832 q^{20} - 55566 q^{21} + 80432 q^{22} + 33229 q^{23} - 82944 q^{24} + 265321 q^{25} - 105456 q^{26} - 118098 q^{27} + 131712 q^{28} + 174185 q^{29} - 2808 q^{30} + 119045 q^{31} + 196608 q^{32} - 271458 q^{33} + 169776 q^{34} + 4459 q^{35} + 279936 q^{36} + 56562 q^{37} + 76216 q^{38} + 355914 q^{39} + 6656 q^{40} + 101632 q^{41} - 444528 q^{42} + 441323 q^{43} + 643456 q^{44} + 9477 q^{45} + 265832 q^{46} - 892849 q^{47} - 663552 q^{48} + 705894 q^{49} + 2122568 q^{50} - 572994 q^{51} - 843648 q^{52} + 2093965 q^{53} - 944784 q^{54} - 331222 q^{55} + 1053696 q^{56} - 257229 q^{57} + 1393480 q^{58} - 136204 q^{59} - 22464 q^{60} - 3989946 q^{61} + 952360 q^{62} + 1500282 q^{63} + 1572864 q^{64} - 28561 q^{65} - 2171664 q^{66} - 2218250 q^{67} + 1358208 q^{68} - 897183 q^{69} + 35672 q^{70} + 2045928 q^{71} + 2239488 q^{72} - 8557479 q^{73} + 452496 q^{74} - 7163667 q^{75} + 609728 q^{76} + 3448522 q^{77} + 2847312 q^{78} - 8559709 q^{79} + 53248 q^{80} + 3188646 q^{81} + 813056 q^{82} + 2496351 q^{83} - 3556224 q^{84} + 5335304 q^{85} + 3530584 q^{86} - 4702995 q^{87} + 5147648 q^{88} - 2446683 q^{89} + 75816 q^{90} - 4521426 q^{91} + 2126656 q^{92} - 3214215 q^{93} - 7142792 q^{94} + 16410211 q^{95} - 5308416 q^{96} + 5786889 q^{97} + 5647152 q^{98} + 7329366 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 13 * q^5 - 1296 * q^6 + 2058 * q^7 + 3072 * q^8 + 4374 * q^9 + 104 * q^10 + 10054 * q^11 - 10368 * q^12 - 13182 * q^13 + 16464 * q^14 - 351 * q^15 + 24576 * q^16 + 21222 * q^17 + 34992 * q^18 + 9527 * q^19 + 832 * q^20 - 55566 * q^21 + 80432 * q^22 + 33229 * q^23 - 82944 * q^24 + 265321 * q^25 - 105456 * q^26 - 118098 * q^27 + 131712 * q^28 + 174185 * q^29 - 2808 * q^30 + 119045 * q^31 + 196608 * q^32 - 271458 * q^33 + 169776 * q^34 + 4459 * q^35 + 279936 * q^36 + 56562 * q^37 + 76216 * q^38 + 355914 * q^39 + 6656 * q^40 + 101632 * q^41 - 444528 * q^42 + 441323 * q^43 + 643456 * q^44 + 9477 * q^45 + 265832 * q^46 - 892849 * q^47 - 663552 * q^48 + 705894 * q^49 + 2122568 * q^50 - 572994 * q^51 - 843648 * q^52 + 2093965 * q^53 - 944784 * q^54 - 331222 * q^55 + 1053696 * q^56 - 257229 * q^57 + 1393480 * q^58 - 136204 * q^59 - 22464 * q^60 - 3989946 * q^61 + 952360 * q^62 + 1500282 * q^63 + 1572864 * q^64 - 28561 * q^65 - 2171664 * q^66 - 2218250 * q^67 + 1358208 * q^68 - 897183 * q^69 + 35672 * q^70 + 2045928 * q^71 + 2239488 * q^72 - 8557479 * q^73 + 452496 * q^74 - 7163667 * q^75 + 609728 * q^76 + 3448522 * q^77 + 2847312 * q^78 - 8559709 * q^79 + 53248 * q^80 + 3188646 * q^81 + 813056 * q^82 + 2496351 * q^83 - 3556224 * q^84 + 5335304 * q^85 + 3530584 * q^86 - 4702995 * q^87 + 5147648 * q^88 - 2446683 * q^89 + 75816 * q^90 - 4521426 * q^91 + 2126656 * q^92 - 3214215 * q^93 - 7142792 * q^94 + 16410211 * q^95 - 5308416 * q^96 + 5786889 * q^97 + 5647152 * q^98 + 7329366 * q^99

Introduction

L-functions

Modular forms

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