LMFDB - Embedded newform 546.8.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$170.562223914$
Analytic rank:	$1$
Dimension:	$5$
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} - 2x^{4} - 122890x^{3} - 6160660x^{2} + 3465881625x + 278845474950 $ x^5 - 2x^4 - 122890x^3 - 6160660x^2 + 3465881625x + 278845474950
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$315.005$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -17.2693 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -17.2693 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -138.154 q^{10} -6366.67 q^{11} -1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +466.270 q^{15} +4096.00 q^{16} +31491.6 q^{17} +5832.00 q^{18} +46684.6 q^{19} -1105.23 q^{20} +9261.00 q^{21} -50933.4 q^{22} -36298.3 q^{23} -13824.0 q^{24} -77826.8 q^{25} -17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +42877.1 q^{29} +3730.16 q^{30} +96053.5 q^{31} +32768.0 q^{32} +171900. q^{33} +251933. q^{34} +5923.35 q^{35} +46656.0 q^{36} +246253. q^{37} +373477. q^{38} +59319.0 q^{39} -8841.86 q^{40} +29230.7 q^{41} +74088.0 q^{42} -290329. q^{43} -407467. q^{44} -12589.3 q^{45} -290386. q^{46} +985829. q^{47} -110592. q^{48} +117649. q^{49} -622614. q^{50} -850273. q^{51} -140608. q^{52} -1.38599e6 q^{53} -157464. q^{54} +109948. q^{55} -175616. q^{56} -1.26048e6 q^{57} +343017. q^{58} -1.70085e6 q^{59} +29841.3 q^{60} -2.60810e6 q^{61} +768428. q^{62} -250047. q^{63} +262144. q^{64} +37940.6 q^{65} +1.37520e6 q^{66} -3.89646e6 q^{67} +2.01546e6 q^{68} +980054. q^{69} +47386.8 q^{70} +1.70688e6 q^{71} +373248. q^{72} +2.08824e6 q^{73} +1.97003e6 q^{74} +2.10132e6 q^{75} +2.98782e6 q^{76} +2.18377e6 q^{77} +474552. q^{78} +4.85807e6 q^{79} -70734.9 q^{80} +531441. q^{81} +233845. q^{82} +1.90272e6 q^{83} +592704. q^{84} -543836. q^{85} -2.32263e6 q^{86} -1.15768e6 q^{87} -3.25973e6 q^{88} -1.67512e6 q^{89} -100714. q^{90} +753571. q^{91} -2.32309e6 q^{92} -2.59344e6 q^{93} +7.88663e6 q^{94} -806208. q^{95} -884736. q^{96} -4.89220e6 q^{97} +941192. q^{98} -4.64130e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 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 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9	\( 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9} - 2000 q^{10} + 659 q^{11} - 8640 q^{12} - 10985 q^{13} - 13720 q^{14} + 6750 q^{15} + 20480 q^{16} + 24575 q^{17} + 29160 q^{18} - 6446 q^{19} - 16000 q^{20} + 46305 q^{21} + 5272 q^{22} + 30268 q^{23} - 69120 q^{24} + 38965 q^{25} - 87880 q^{26} - 98415 q^{27} - 109760 q^{28} + 130950 q^{29} + 54000 q^{30} + 262979 q^{31} + 163840 q^{32} - 17793 q^{33} + 196600 q^{34} + 85750 q^{35} + 233280 q^{36} - 101549 q^{37} - 51568 q^{38} + 296595 q^{39} - 128000 q^{40} - 247328 q^{41} + 370440 q^{42} - 19092 q^{43} + 42176 q^{44} - 182250 q^{45} + 242144 q^{46} - 126419 q^{47} - 552960 q^{48} + 588245 q^{49} + 311720 q^{50} - 663525 q^{51} - 703040 q^{52} - 302793 q^{53} - 787320 q^{54} + 943985 q^{55} - 878080 q^{56} + 174042 q^{57} + 1047600 q^{58} - 2798636 q^{59} + 432000 q^{60} - 2493751 q^{61} + 2103832 q^{62} - 1250235 q^{63} + 1310720 q^{64} + 549250 q^{65} - 142344 q^{66} + 160188 q^{67} + 1572800 q^{68} - 817236 q^{69} + 686000 q^{70} + 3846088 q^{71} + 1866240 q^{72} + 5655872 q^{73} - 812392 q^{74} - 1052055 q^{75} - 412544 q^{76} - 226037 q^{77} + 2372760 q^{78} + 5647991 q^{79} - 1024000 q^{80} + 2657205 q^{81} - 1978624 q^{82} - 4607669 q^{83} + 2963520 q^{84} + 3873935 q^{85} - 152736 q^{86} - 3535650 q^{87} + 337408 q^{88} - 17424029 q^{89} - 1458000 q^{90} + 3767855 q^{91} + 1937152 q^{92} - 7100433 q^{93} - 1011352 q^{94} - 24593720 q^{95} - 4423680 q^{96} - 18380577 q^{97} + 4705960 q^{98} + 480411 q^{99}+O(q^{100}) \) 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9 - 2000 * q^10 + 659 * q^11 - 8640 * q^12 - 10985 * q^13 - 13720 * q^14 + 6750 * q^15 + 20480 * q^16 + 24575 * q^17 + 29160 * q^18 - 6446 * q^19 - 16000 * q^20 + 46305 * q^21 + 5272 * q^22 + 30268 * q^23 - 69120 * q^24 + 38965 * q^25 - 87880 * q^26 - 98415 * q^27 - 109760 * q^28 + 130950 * q^29 + 54000 * q^30 + 262979 * q^31 + 163840 * q^32 - 17793 * q^33 + 196600 * q^34 + 85750 * q^35 + 233280 * q^36 - 101549 * q^37 - 51568 * q^38 + 296595 * q^39 - 128000 * q^40 - 247328 * q^41 + 370440 * q^42 - 19092 * q^43 + 42176 * q^44 - 182250 * q^45 + 242144 * q^46 - 126419 * q^47 - 552960 * q^48 + 588245 * q^49 + 311720 * q^50 - 663525 * q^51 - 703040 * q^52 - 302793 * q^53 - 787320 * q^54 + 943985 * q^55 - 878080 * q^56 + 174042 * q^57 + 1047600 * q^58 - 2798636 * q^59 + 432000 * q^60 - 2493751 * q^61 + 2103832 * q^62 - 1250235 * q^63 + 1310720 * q^64 + 549250 * q^65 - 142344 * q^66 + 160188 * q^67 + 1572800 * q^68 - 817236 * q^69 + 686000 * q^70 + 3846088 * q^71 + 1866240 * q^72 + 5655872 * q^73 - 812392 * q^74 - 1052055 * q^75 - 412544 * q^76 - 226037 * q^77 + 2372760 * q^78 + 5647991 * q^79 - 1024000 * q^80 + 2657205 * q^81 - 1978624 * q^82 - 4607669 * q^83 + 2963520 * q^84 + 3873935 * q^85 - 152736 * q^86 - 3535650 * q^87 + 337408 * q^88 - 17424029 * q^89 - 1458000 * q^90 + 3767855 * q^91 + 1937152 * q^92 - 7100433 * q^93 - 1011352 * q^94 - 24593720 * q^95 - 4423680 * q^96 - 18380577 * q^97 + 4705960 * q^98 + 480411 * 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
$5$	−17.2693	−0.0617844	−0.0308922	−	0.999523i	$-0.509835\pi$
$5$	−17.2693	−0.0617844	−0.0308922	+	0.999523i	$0.509835\pi$
$6$	−216.000	−0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	−138.154	−0.0436881
$11$	−6366.67	−1.44224	−0.721121	−	0.692810i	$-0.756373\pi$
$11$	−6366.67	−1.44224	−0.721121	+	0.692810i	$0.756373\pi$
$12$	−1728.00	−0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−2744.00	−0.267261
$15$	466.270	0.0356712
$16$	4096.00	0.250000
$17$	31491.6	1.55462	0.777308	−	0.629120i	$-0.216585\pi$
$17$	31491.6	1.55462	0.777308	+	0.629120i	$0.216585\pi$
$18$	5832.00	0.235702
$19$	46684.6	1.56148	0.780740	−	0.624857i	$-0.214843\pi$
$19$	46684.6	1.56148	0.780740	+	0.624857i	$0.214843\pi$
$20$	−1105.23	−0.0308922
$21$	9261.00	0.218218
$22$	−50933.4	−1.01982
$23$	−36298.3	−0.622069	−0.311035	−	0.950399i	$-0.600676\pi$
$23$	−36298.3	−0.622069	−0.311035	+	0.950399i	$0.600676\pi$
$24$	−13824.0	−0.204124
$25$	−77826.8	−0.996183
$26$	−17576.0	−0.196116
$27$	−19683.0	−0.192450
$28$	−21952.0	−0.188982
$29$	42877.1	0.326462	0.163231	−	0.986588i	$-0.447808\pi$
$29$	42877.1	0.326462	0.163231	+	0.986588i	$0.447808\pi$
$30$	3730.16	0.0252234
$31$	96053.5	0.579091	0.289546	−	0.957164i	$-0.406496\pi$
$31$	96053.5	0.579091	0.289546	+	0.957164i	$0.406496\pi$
$32$	32768.0	0.176777
$33$	171900.	0.832678
$34$	251933.	1.09928
$35$	5923.35	0.0233523
$36$	46656.0	0.166667
$37$	246253.	0.799238	0.399619	−	0.916681i	$-0.369143\pi$
$37$	246253.	0.799238	0.399619	+	0.916681i	$0.369143\pi$
$38$	373477.	1.10413
$39$	59319.0	0.160128
$40$	−8841.86	−0.0218441
$41$	29230.7	0.0662362	0.0331181	−	0.999451i	$-0.489456\pi$
$41$	29230.7	0.0662362	0.0331181	+	0.999451i	$0.489456\pi$
$42$	74088.0	0.154303
$43$	−290329.	−0.556866	−0.278433	−	0.960456i	$-0.589815\pi$
$43$	−290329.	−0.556866	−0.278433	+	0.960456i	$0.589815\pi$
$44$	−407467.	−0.721121
$45$	−12589.3	−0.0205948
$46$	−290386.	−0.439869
$47$	985829.	1.38503	0.692515	−	0.721404i	$-0.256503\pi$
$47$	985829.	1.38503	0.692515	+	0.721404i	$0.256503\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	−622614.	−0.704408
$51$	−850273.	−0.897558
$52$	−140608.	−0.138675
$53$	−1.38599e6	−1.27877	−0.639387	−	0.768885i	$-0.720812\pi$
$53$	−1.38599e6	−1.27877	−0.639387	+	0.768885i	$0.720812\pi$
$54$	−157464.	−0.136083
$55$	109948.	0.0891080
$56$	−175616.	−0.133631
$57$	−1.26048e6	−0.901520
$58$	343017.	0.230843
$59$	−1.70085e6	−1.07816	−0.539080	−	0.842254i	$-0.681228\pi$
$59$	−1.70085e6	−1.07816	−0.539080	+	0.842254i	$0.681228\pi$
$60$	29841.3	0.0178356
$61$	−2.60810e6	−1.47119	−0.735596	−	0.677421i	$-0.763098\pi$
$61$	−2.60810e6	−1.47119	−0.735596	+	0.677421i	$0.763098\pi$
$62$	768428.	0.409479
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	37940.6	0.0171359
$66$	1.37520e6	0.588792
$67$	−3.89646e6	−1.58274	−0.791368	−	0.611340i	$-0.790631\pi$
$67$	−3.89646e6	−1.58274	−0.791368	+	0.611340i	$0.790631\pi$
$68$	2.01546e6	0.777308
$69$	980054.	0.359152
$70$	47386.8	0.0165126
$71$	1.70688e6	0.565978	0.282989	−	0.959123i	$-0.408674\pi$
$71$	1.70688e6	0.565978	0.282989	+	0.959123i	$0.408674\pi$
$72$	373248.	0.117851
$73$	2.08824e6	0.628275	0.314138	−	0.949377i	$-0.398285\pi$
$73$	2.08824e6	0.628275	0.314138	+	0.949377i	$0.398285\pi$
$74$	1.97003e6	0.565146
$75$	2.10132e6	0.575146
$76$	2.98782e6	0.780740
$77$	2.18377e6	0.545116
$78$	474552.	0.113228
$79$	4.85807e6	1.10859	0.554293	−	0.832322i	$-0.312989\pi$
$79$	4.85807e6	1.10859	0.554293	+	0.832322i	$0.312989\pi$
$80$	−70734.9	−0.0154461
$81$	531441.	0.111111
$82$	233845.	0.0468360
$83$	1.90272e6	0.365259	0.182630	−	0.983182i	$-0.441539\pi$
$83$	1.90272e6	0.365259	0.182630	+	0.983182i	$0.441539\pi$
$84$	592704.	0.109109
$85$	−543836.	−0.0960510
$86$	−2.32263e6	−0.393764
$87$	−1.15768e6	−0.188483
$88$	−3.25973e6	−0.509909
$89$	−1.67512e6	−0.251873	−0.125936	−	0.992038i	$-0.540193\pi$
$89$	−1.67512e6	−0.251873	−0.125936	+	0.992038i	$0.540193\pi$
$90$	−100714.	−0.0145627
$91$	753571.	0.104828
$92$	−2.32309e6	−0.311035
$93$	−2.59344e6	−0.334339
$94$	7.88663e6	0.979364
$95$	−806208.	−0.0964750
$96$	−884736.	−0.102062
$97$	−4.89220e6	−0.544255	−0.272128	−	0.962261i	$-0.587727\pi$
$97$	−4.89220e6	−0.544255	−0.272128	+	0.962261i	$0.587727\pi$
$98$	941192.	0.101015
$99$	−4.64130e6	−0.480747
$100$	−4.98091e6	−0.498091
$101$	−2.64383e6	−0.255334	−0.127667	−	0.991817i	$-0.540749\pi$
$101$	−2.64383e6	−0.255334	−0.127667	+	0.991817i	$0.540749\pi$
$102$	−6.80218e6	−0.634669
$103$	−2.56466e6	−0.231260	−0.115630	−	0.993292i	$-0.536889\pi$
$103$	−2.56466e6	−0.231260	−0.115630	+	0.993292i	$0.536889\pi$
$104$	−1.12486e6	−0.0980581
$105$	−159931.	−0.0134825
$106$	−1.10879e7	−0.904229
$107$	7.33860e6	0.579122	0.289561	−	0.957160i	$-0.406491\pi$
$107$	7.33860e6	0.579122	0.289561	+	0.957160i	$0.406491\pi$
$108$	−1.25971e6	−0.0962250
$109$	−2.02890e7	−1.50061	−0.750306	−	0.661091i	$-0.770094\pi$
$109$	−2.02890e7	−1.50061	−0.750306	+	0.661091i	$0.770094\pi$
$110$	879581.	0.0630088
$111$	−6.64884e6	−0.461440
$112$	−1.40493e6	−0.0944911
$113$	1.91208e6	0.124662	0.0623308	−	0.998056i	$-0.480147\pi$
$113$	1.91208e6	0.124662	0.0623308	+	0.998056i	$0.480147\pi$
$114$	−1.00839e7	−0.637471
$115$	626845.	0.0384342
$116$	2.74413e6	0.163231
$117$	−1.60161e6	−0.0924500
$118$	−1.36068e7	−0.762375
$119$	−1.08016e7	−0.587590
$120$	238730.	0.0126117
$121$	2.10473e7	1.08006
$122$	−2.08648e7	−1.04029
$123$	−789228.	−0.0382415
$124$	6.14742e6	0.289546
$125$	2.69317e6	0.123333
$126$	−2.00038e6	−0.0890871
$127$	1.90374e7	0.824699	0.412349	−	0.911026i	$-0.364708\pi$
$127$	1.90374e7	0.824699	0.412349	+	0.911026i	$0.364708\pi$
$128$	2.09715e6	0.0883883
$129$	7.83888e6	0.321507
$130$	303524.	0.0121169
$131$	−2.24107e7	−0.870974	−0.435487	−	0.900195i	$-0.643424\pi$
$131$	−2.24107e7	−0.870974	−0.435487	+	0.900195i	$0.643424\pi$
$132$	1.10016e7	0.416339
$133$	−1.60128e7	−0.590184
$134$	−3.11717e7	−1.11916
$135$	339911.	0.0118904
$136$	1.61237e7	0.549640
$137$	−2.33530e7	−0.775926	−0.387963	−	0.921675i	$-0.626821\pi$
$137$	−2.33530e7	−0.775926	−0.387963	+	0.921675i	$0.626821\pi$
$138$	7.84043e6	0.253959
$139$	3.49584e7	1.10408	0.552039	−	0.833819i	$-0.313850\pi$
$139$	3.49584e7	1.10408	0.552039	+	0.833819i	$0.313850\pi$
$140$	379095.	0.0116761
$141$	−2.66174e7	−0.799647
$142$	1.36551e7	0.400207
$143$	1.39876e7	0.400006
$144$	2.98598e6	0.0833333
$145$	−740455.	−0.0201702
$146$	1.67059e7	0.444258
$147$	−3.17652e6	−0.0824786
$148$	1.57602e7	0.399619
$149$	−2.53533e6	−0.0627888	−0.0313944	−	0.999507i	$-0.509995\pi$
$149$	−2.53533e6	−0.0627888	−0.0313944	+	0.999507i	$0.509995\pi$
$150$	1.68106e7	0.406690
$151$	−7.46151e7	−1.76363	−0.881815	−	0.471595i	$-0.843678\pi$
$151$	−7.46151e7	−1.76363	−0.881815	+	0.471595i	$0.843678\pi$
$152$	2.39025e7	0.552066
$153$	2.29574e7	0.518205
$154$	1.74701e7	0.385455
$155$	−1.65877e6	−0.0357788
$156$	3.79642e6	0.0800641
$157$	−5.00343e7	−1.03186	−0.515928	−	0.856632i	$-0.672553\pi$
$157$	−5.00343e7	−1.03186	−0.515928	+	0.856632i	$0.672553\pi$
$158$	3.88646e7	0.783888
$159$	3.74216e7	0.738300
$160$	−565879.	−0.0109220
$161$	1.24503e7	0.235120
$162$	4.25153e6	0.0785674
$163$	−4.72558e7	−0.854671	−0.427335	−	0.904093i	$-0.640548\pi$
$163$	−4.72558e7	−0.854671	−0.427335	+	0.904093i	$0.640548\pi$
$164$	1.87076e6	0.0331181
$165$	−2.96859e6	−0.0514465
$166$	1.52217e7	0.258277
$167$	−1.04290e8	−1.73275	−0.866375	−	0.499394i	$-0.833556\pi$
$167$	−1.04290e8	−1.73275	−0.866375	+	0.499394i	$0.833556\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	−4.35069e6	−0.0679183
$171$	3.40331e7	0.520493
$172$	−1.85811e7	−0.278433
$173$	−1.17020e8	−1.71830	−0.859148	−	0.511728i	$-0.829006\pi$
$173$	−1.17020e8	−1.71830	−0.859148	+	0.511728i	$0.829006\pi$
$174$	−9.26145e6	−0.133277
$175$	2.66946e7	0.376522
$176$	−2.60779e7	−0.360560
$177$	4.59229e7	0.622476
$178$	−1.34010e7	−0.178101
$179$	−2.74389e7	−0.357586	−0.178793	−	0.983887i	$-0.557219\pi$
$179$	−2.74389e7	−0.357586	−0.178793	+	0.983887i	$0.557219\pi$
$180$	−805714.	−0.0102974
$181$	−1.24054e8	−1.55502	−0.777509	−	0.628872i	$-0.783517\pi$
$181$	−1.24054e8	−1.55502	−0.777509	+	0.628872i	$0.783517\pi$
$182$	6.02857e6	0.0741249
$183$	7.04186e7	0.849393
$184$	−1.85847e7	−0.219935
$185$	−4.25261e6	−0.0493804
$186$	−2.07475e7	−0.236413
$187$	−2.00496e8	−2.24213
$188$	6.30931e7	0.692515
$189$	6.75127e6	0.0727393
$190$	−6.44967e6	−0.0682181
$191$	1.77095e8	1.83903	0.919517	−	0.393050i	$-0.128580\pi$
$191$	1.77095e8	1.83903	0.919517	+	0.393050i	$0.128580\pi$
$192$	−7.07789e6	−0.0721688
$193$	2.29976e7	0.230267	0.115134	−	0.993350i	$-0.463270\pi$
$193$	2.29976e7	0.230267	0.115134	+	0.993350i	$0.463270\pi$
$194$	−3.91376e7	−0.384847
$195$	−1.02439e6	−0.00989342
$196$	7.52954e6	0.0714286
$197$	−1.11687e8	−1.04081	−0.520405	−	0.853919i	$-0.674219\pi$
$197$	−1.11687e8	−1.04081	−0.520405	+	0.853919i	$0.674219\pi$
$198$	−3.71304e7	−0.339940
$199$	4.87890e7	0.438870	0.219435	−	0.975627i	$-0.429579\pi$
$199$	4.87890e7	0.438870	0.219435	+	0.975627i	$0.429579\pi$
$200$	−3.98473e7	−0.352204
$201$	1.05204e8	0.913793
$202$	−2.11506e7	−0.180548
$203$	−1.47068e7	−0.123391
$204$	−5.44174e7	−0.448779
$205$	−504792.	−0.00409236
$206$	−2.05173e7	−0.163525
$207$	−2.64615e7	−0.207356
$208$	−8.99891e6	−0.0693375
$209$	−2.97225e8	−2.25203
$210$	−1.27944e6	−0.00953353
$211$	1.78179e8	1.30577	0.652885	−	0.757457i	$-0.273558\pi$
$211$	1.78179e8	1.30577	0.652885	+	0.757457i	$0.273558\pi$
$212$	−8.87031e7	−0.639387
$213$	−4.60858e7	−0.326767
$214$	5.87088e7	0.409501
$215$	5.01376e6	0.0344056
$216$	−1.00777e7	−0.0680414
$217$	−3.29463e7	−0.218876
$218$	−1.62312e8	−1.06109
$219$	−5.63824e7	−0.362735
$220$	7.03665e6	0.0445540
$221$	−6.91870e7	−0.431173
$222$	−5.31907e7	−0.326287
$223$	−1.42968e8	−0.863317	−0.431659	−	0.902037i	$-0.642071\pi$
$223$	−1.42968e8	−0.863317	−0.431659	+	0.902037i	$0.642071\pi$
$224$	−1.12394e7	−0.0668153
$225$	−5.67357e7	−0.332061
$226$	1.52967e7	0.0881490
$227$	3.04658e8	1.72871	0.864354	−	0.502884i	$-0.167728\pi$
$227$	3.04658e8	1.72871	0.864354	+	0.502884i	$0.167728\pi$
$228$	−8.06710e7	−0.450760
$229$	−2.13410e8	−1.17433	−0.587165	−	0.809467i	$-0.699756\pi$
$229$	−2.13410e8	−1.17433	−0.587165	+	0.809467i	$0.699756\pi$
$230$	5.01476e6	0.0271771
$231$	−5.89617e7	−0.314723
$232$	2.19531e7	0.115422
$233$	−6.43656e7	−0.333356	−0.166678	−	0.986011i	$-0.553304\pi$
$233$	−6.43656e7	−0.333356	−0.166678	+	0.986011i	$0.553304\pi$
$234$	−1.28129e7	−0.0653720
$235$	−1.70245e7	−0.0855732
$236$	−1.08854e8	−0.539080
$237$	−1.31168e8	−0.640042
$238$	−8.64129e7	−0.415489
$239$	−6.62558e7	−0.313929	−0.156964	−	0.987604i	$-0.550171\pi$
$239$	−6.62558e7	−0.313929	−0.156964	+	0.987604i	$0.550171\pi$
$240$	1.90984e6	0.00891781
$241$	−2.98304e8	−1.37278	−0.686389	−	0.727235i	$-0.740805\pi$
$241$	−2.98304e8	−1.37278	−0.686389	+	0.727235i	$0.740805\pi$
$242$	1.68378e8	0.763717
$243$	−1.43489e7	−0.0641500
$244$	−1.66918e8	−0.735596
$245$	−2.03171e6	−0.00882634
$246$	−6.31382e6	−0.0270408
$247$	−1.02566e8	−0.433076
$248$	4.91794e7	0.204740
$249$	−5.13734e7	−0.210883
$250$	2.15454e7	0.0872095
$251$	−3.10746e8	−1.24036	−0.620180	−	0.784460i	$-0.712940\pi$
$251$	−3.10746e8	−1.24036	−0.620180	+	0.784460i	$0.712940\pi$
$252$	−1.60030e7	−0.0629941
$253$	2.31099e8	0.897174
$254$	1.52299e8	0.583150
$255$	1.46836e7	0.0554551
$256$	1.67772e7	0.0625000
$257$	5.93193e6	0.0217987	0.0108993	−	0.999941i	$-0.496531\pi$
$257$	5.93193e6	0.0217987	0.0108993	+	0.999941i	$0.496531\pi$
$258$	6.27110e7	0.227340
$259$	−8.44649e7	−0.302083
$260$	2.42820e6	0.00856795
$261$	3.12574e7	0.108821
$262$	−1.79285e8	−0.615872
$263$	3.35505e8	1.13724	0.568622	−	0.822599i	$-0.307477\pi$
$263$	3.35505e8	1.13724	0.568622	+	0.822599i	$0.307477\pi$
$264$	8.80128e7	0.294396
$265$	2.39350e7	0.0790082
$266$	−1.28103e8	−0.417323
$267$	4.52282e7	0.145419
$268$	−2.49374e8	−0.791368
$269$	−2.67432e7	−0.0837684	−0.0418842	−	0.999122i	$-0.513336\pi$
$269$	−2.67432e7	−0.0837684	−0.0418842	+	0.999122i	$0.513336\pi$
$270$	2.71929e6	0.00840779
$271$	−2.99466e8	−0.914018	−0.457009	−	0.889462i	$-0.651079\pi$
$271$	−2.99466e8	−0.914018	−0.457009	+	0.889462i	$0.651079\pi$
$272$	1.28989e8	0.388654
$273$	−2.03464e7	−0.0605228
$274$	−1.86824e8	−0.548663
$275$	4.95497e8	1.43674
$276$	6.27235e7	0.179576
$277$	2.92186e7	0.0826001	0.0413000	−	0.999147i	$-0.486850\pi$
$277$	2.92186e7	0.0826001	0.0413000	+	0.999147i	$0.486850\pi$
$278$	2.79667e8	0.780701
$279$	7.00230e7	0.193030
$280$	3.03276e6	0.00825628
$281$	−7.21369e8	−1.93948	−0.969740	−	0.244138i	$-0.921495\pi$
$281$	−7.21369e8	−1.93948	−0.969740	+	0.244138i	$0.921495\pi$
$282$	−2.12939e8	−0.565436
$283$	−6.21761e8	−1.63069	−0.815344	−	0.578977i	$-0.803452\pi$
$283$	−6.21761e8	−1.63069	−0.815344	+	0.578977i	$0.803452\pi$
$284$	1.09240e8	0.282989
$285$	2.17676e7	0.0556999
$286$	1.11901e8	0.282847
$287$	−1.00261e7	−0.0250349
$288$	2.38879e7	0.0589256
$289$	5.81381e8	1.41683
$290$	−5.92364e6	−0.0142625
$291$	1.32089e8	0.314226
$292$	1.33647e8	0.314138
$293$	4.75845e8	1.10517	0.552585	−	0.833456i	$-0.313641\pi$
$293$	4.75845e8	1.10517	0.552585	+	0.833456i	$0.313641\pi$
$294$	−2.54122e7	−0.0583212
$295$	2.93724e7	0.0666135
$296$	1.26082e8	0.282573
$297$	1.25315e8	0.277559
$298$	−2.02826e7	−0.0443984
$299$	7.97474e7	0.172531
$300$	1.34485e8	0.287573
$301$	9.95828e7	0.210476
$302$	−5.96921e8	−1.24708
$303$	7.13833e7	0.147417
$304$	1.91220e8	0.390370
$305$	4.50399e7	0.0908966
$306$	1.83659e8	0.366427
$307$	2.16226e8	0.426505	0.213253	−	0.976997i	$-0.431594\pi$
$307$	2.16226e8	0.426505	0.213253	+	0.976997i	$0.431594\pi$
$308$	1.39761e8	0.272558
$309$	6.92459e7	0.133518
$310$	−1.32702e7	−0.0252994
$311$	−3.92463e8	−0.739839	−0.369919	−	0.929064i	$-0.620615\pi$
$311$	−3.92463e8	−0.739839	−0.369919	+	0.929064i	$0.620615\pi$
$312$	3.03713e7	0.0566139
$313$	4.30979e8	0.794422	0.397211	−	0.917727i	$-0.369978\pi$
$313$	4.30979e8	0.794422	0.397211	+	0.917727i	$0.369978\pi$
$314$	−4.00275e8	−0.729633
$315$	4.31813e6	0.00778410
$316$	3.10917e8	0.554293
$317$	−2.52760e8	−0.445657	−0.222829	−	0.974858i	$-0.571529\pi$
$317$	−2.52760e8	−0.445657	−0.222829	+	0.974858i	$0.571529\pi$
$318$	2.99373e8	0.522057
$319$	−2.72984e8	−0.470837
$320$	−4.52703e6	−0.00772305
$321$	−1.98142e8	−0.334356
$322$	9.96025e7	0.166255
$323$	1.47017e9	2.42750
$324$	3.40122e7	0.0555556
$325$	1.70985e8	0.276291
$326$	−3.78047e8	−0.604344
$327$	5.47804e8	0.866379
$328$	1.49661e7	0.0234180
$329$	−3.38139e8	−0.523492
$330$	−2.37487e7	−0.0363782
$331$	−1.03391e9	−1.56705	−0.783526	−	0.621359i	$-0.786581\pi$
$331$	−1.03391e9	−1.56705	−0.783526	+	0.621359i	$0.786581\pi$
$332$	1.21774e8	0.182630
$333$	1.79519e8	0.266413
$334$	−8.34322e8	−1.22524
$335$	6.72890e7	0.0977884
$336$	3.79331e7	0.0545545
$337$	−3.98599e8	−0.567325	−0.283662	−	0.958924i	$-0.591549\pi$
$337$	−3.98599e8	−0.567325	−0.283662	+	0.958924i	$0.591549\pi$
$338$	3.86145e7	0.0543928
$339$	−5.16263e7	−0.0719734
$340$	−3.48055e7	−0.0480255
$341$	−6.11541e8	−0.835189
$342$	2.72265e8	0.368044
$343$	−4.03536e7	−0.0539949
$344$	−1.48648e8	−0.196882
$345$	−1.69248e7	−0.0221900
$346$	−9.36158e8	−1.21502
$347$	−9.63106e8	−1.23743	−0.618715	−	0.785615i	$-0.712347\pi$
$347$	−9.63106e8	−1.23743	−0.618715	+	0.785615i	$0.712347\pi$
$348$	−7.40916e7	−0.0942414
$349$	1.32415e9	1.66743	0.833717	−	0.552191i	$-0.186208\pi$
$349$	1.32415e9	1.66743	0.833717	+	0.552191i	$0.186208\pi$
$350$	2.13557e8	0.266241
$351$	4.32436e7	0.0533761
$352$	−2.08623e8	−0.254955
$353$	−1.32391e9	−1.60194	−0.800969	−	0.598706i	$-0.795682\pi$
$353$	−1.32391e9	−1.60194	−0.800969	+	0.598706i	$0.795682\pi$
$354$	3.67383e8	0.440157
$355$	−2.94766e7	−0.0349686
$356$	−1.07208e8	−0.125936
$357$	2.91643e8	0.339245
$358$	−2.19511e8	−0.252852
$359$	4.14851e8	0.473218	0.236609	−	0.971605i	$-0.423964\pi$
$359$	4.14851e8	0.473218	0.236609	+	0.971605i	$0.423964\pi$
$360$	−6.44571e6	−0.00728136
$361$	1.28558e9	1.43822
$362$	−9.92431e8	−1.09956
$363$	−5.68277e8	−0.623573
$364$	4.82285e7	0.0524142
$365$	−3.60623e7	−0.0388176
$366$	5.63349e8	0.600611
$367$	2.03316e8	0.214704	0.107352	−	0.994221i	$-0.465763\pi$
$367$	2.03316e8	0.214704	0.107352	+	0.994221i	$0.465763\pi$
$368$	−1.48678e8	−0.155517
$369$	2.13092e7	0.0220787
$370$	−3.40209e7	−0.0349172
$371$	4.75393e8	0.483331
$372$	−1.65980e8	−0.167169
$373$	−2.01932e8	−0.201477	−0.100738	−	0.994913i	$-0.532120\pi$
$373$	−2.01932e8	−0.201477	−0.100738	+	0.994913i	$0.532120\pi$
$374$	−1.60397e9	−1.58543
$375$	−7.27156e7	−0.0712063
$376$	5.04745e8	0.489682
$377$	−9.42010e7	−0.0905442
$378$	5.40102e7	0.0514344
$379$	1.81680e9	1.71423	0.857115	−	0.515125i	$-0.172254\pi$
$379$	1.81680e9	1.71423	0.857115	+	0.515125i	$0.172254\pi$
$380$	−5.15973e7	−0.0482375
$381$	−5.14011e8	−0.476140
$382$	1.41676e9	1.30039
$383$	4.97022e7	0.0452043	0.0226021	−	0.999745i	$-0.492805\pi$
$383$	4.97022e7	0.0452043	0.0226021	+	0.999745i	$0.492805\pi$
$384$	−5.66231e7	−0.0510310
$385$	−3.77120e7	−0.0336796
$386$	1.83981e8	0.162824
$387$	−2.11650e8	−0.185622
$388$	−3.13101e8	−0.272128
$389$	−7.80289e8	−0.672097	−0.336048	−	0.941845i	$-0.609091\pi$
$389$	−7.80289e8	−0.672097	−0.336048	+	0.941845i	$0.609091\pi$
$390$	−8.19516e6	−0.00699570
$391$	−1.14309e9	−0.967079
$392$	6.02363e7	0.0505076
$393$	6.05088e8	0.502857
$394$	−8.93498e8	−0.735964
$395$	−8.38953e7	−0.0684932
$396$	−2.97043e8	−0.240374
$397$	2.22245e9	1.78265	0.891324	−	0.453367i	$-0.149777\pi$
$397$	2.22245e9	1.78265	0.891324	+	0.453367i	$0.149777\pi$
$398$	3.90312e8	0.310328
$399$	4.32346e8	0.340743
$400$	−3.18778e8	−0.249046
$401$	−8.88297e8	−0.687944	−0.343972	−	0.938980i	$-0.611773\pi$
$401$	−8.88297e8	−0.687944	−0.343972	+	0.938980i	$0.611773\pi$
$402$	8.41636e8	0.646149
$403$	−2.11029e8	−0.160611
$404$	−1.69205e8	−0.127667
$405$	−9.17759e6	−0.00686493
$406$	−1.17655e8	−0.0872506
$407$	−1.56781e9	−1.15269
$408$	−4.35340e8	−0.317335
$409$	−1.53205e9	−1.10724	−0.553620	−	0.832769i	$-0.686754\pi$
$409$	−1.53205e9	−1.10724	−0.553620	+	0.832769i	$0.686754\pi$
$410$	−4.03833e6	−0.00289374
$411$	6.30531e8	0.447981
$412$	−1.64138e8	−0.115630
$413$	5.83391e8	0.407506
$414$	−2.11692e8	−0.146623
$415$	−3.28585e7	−0.0225673
$416$	−7.19913e7	−0.0490290
$417$	−9.43876e8	−0.637439
$418$	−2.37780e9	−1.59243
$419$	−5.56107e8	−0.369325	−0.184663	−	0.982802i	$-0.559119\pi$
$419$	−5.56107e8	−0.369325	−0.184663	+	0.982802i	$0.559119\pi$
$420$	−1.02356e7	−0.00674123
$421$	1.74619e9	1.14053	0.570263	−	0.821462i	$-0.306841\pi$
$421$	1.74619e9	1.14053	0.570263	+	0.821462i	$0.306841\pi$
$422$	1.42543e9	0.923319
$423$	7.18669e8	0.461677
$424$	−7.09625e8	−0.452115
$425$	−2.45089e9	−1.54868
$426$	−3.68687e8	−0.231059
$427$	8.94577e8	0.556058
$428$	4.69671e8	0.289561
$429$	−3.77664e8	−0.230943
$430$	4.01101e7	0.0243284
$431$	1.55597e9	0.936118	0.468059	−	0.883697i	$-0.344953\pi$
$431$	1.55597e9	0.936118	0.468059	+	0.883697i	$0.344953\pi$
$432$	−8.06216e7	−0.0481125
$433$	2.68061e9	1.58681	0.793407	−	0.608692i	$-0.208305\pi$
$433$	2.68061e9	1.58681	0.793407	+	0.608692i	$0.208305\pi$
$434$	−2.63571e8	−0.154769
$435$	1.99923e7	0.0116453
$436$	−1.29850e9	−0.750306
$437$	−1.69457e9	−0.971348
$438$	−4.51059e8	−0.256492
$439$	2.20605e9	1.24448	0.622242	−	0.782825i	$-0.286222\pi$
$439$	2.20605e9	1.24448	0.622242	+	0.782825i	$0.286222\pi$
$440$	5.62932e7	0.0315044
$441$	8.57661e7	0.0476190
$442$	−5.53496e8	−0.304885
$443$	3.03233e9	1.65716	0.828578	−	0.559874i	$-0.189151\pi$
$443$	3.03233e9	1.65716	0.828578	+	0.559874i	$0.189151\pi$
$444$	−4.25526e8	−0.230720
$445$	2.89281e7	0.0155618
$446$	−1.14374e9	−0.610457
$447$	6.84538e7	0.0362511
$448$	−8.99154e7	−0.0472456
$449$	1.13559e9	0.592051	0.296025	−	0.955180i	$-0.404339\pi$
$449$	1.13559e9	0.592051	0.296025	+	0.955180i	$0.404339\pi$
$450$	−4.53886e8	−0.234803
$451$	−1.86102e8	−0.0955285
$452$	1.22373e8	0.0623308
$453$	2.01461e9	1.01823
$454$	2.43726e9	1.22238
$455$	−1.30136e7	−0.00647676
$456$	−6.45368e8	−0.318736
$457$	−1.90034e9	−0.931377	−0.465688	−	0.884949i	$-0.654193\pi$
$457$	−1.90034e9	−0.931377	−0.465688	+	0.884949i	$0.654193\pi$
$458$	−1.70728e9	−0.830377
$459$	−6.19849e8	−0.299186
$460$	4.01181e7	0.0192171
$461$	1.65878e9	0.788562	0.394281	−	0.918990i	$-0.370994\pi$
$461$	1.65878e9	0.788562	0.394281	+	0.918990i	$0.370994\pi$
$462$	−4.71694e8	−0.222543
$463$	−3.84728e9	−1.80144	−0.900721	−	0.434397i	$-0.856961\pi$
$463$	−3.84728e9	−1.80144	−0.900721	+	0.434397i	$0.856961\pi$
$464$	1.75625e8	0.0816154
$465$	4.47868e7	0.0206569
$466$	−5.14924e8	−0.235718
$467$	−2.44108e9	−1.10911	−0.554553	−	0.832149i	$-0.687111\pi$
$467$	−2.44108e9	−1.10911	−0.554553	+	0.832149i	$0.687111\pi$
$468$	−1.02503e8	−0.0462250
$469$	1.33649e9	0.598218
$470$	−1.36196e8	−0.0605094
$471$	1.35093e9	0.595743
$472$	−8.70834e8	−0.381187
$473$	1.84843e9	0.803135
$474$	−1.04934e9	−0.452578
$475$	−3.63331e9	−1.55552
$476$	−6.91303e8	−0.293795
$477$	−1.01038e9	−0.426258
$478$	−5.30046e8	−0.221981
$479$	−6.79391e8	−0.282452	−0.141226	−	0.989977i	$-0.545104\pi$
$479$	−6.79391e8	−0.282452	−0.141226	+	0.989977i	$0.545104\pi$
$480$	1.52787e7	0.00630584
$481$	−5.41018e8	−0.221669
$482$	−2.38644e9	−0.970700
$483$	−3.36159e8	−0.135747
$484$	1.34703e9	0.540030
$485$	8.44846e7	0.0336265
$486$	−1.14791e8	−0.0453609
$487$	−1.52178e8	−0.0597036	−0.0298518	−	0.999554i	$-0.509504\pi$
$487$	−1.52178e8	−0.0597036	−0.0298518	+	0.999554i	$0.509504\pi$
$488$	−1.33535e9	−0.520145
$489$	1.27591e9	0.493444
$490$	−1.62537e7	−0.00624116
$491$	1.26029e9	0.480489	0.240245	−	0.970712i	$-0.422772\pi$
$491$	1.26029e9	0.480489	0.240245	+	0.970712i	$0.422772\pi$
$492$	−5.05106e7	−0.0191207
$493$	1.35027e9	0.507523
$494$	−8.20529e8	−0.306231
$495$	8.01518e7	0.0297027
$496$	3.93435e8	0.144773
$497$	−5.85461e8	−0.213919
$498$	−4.10987e8	−0.149116
$499$	−1.27347e9	−0.458814	−0.229407	−	0.973331i	$-0.573679\pi$
$499$	−1.27347e9	−0.458814	−0.229407	+	0.973331i	$0.573679\pi$
$500$	1.72363e8	0.0616664
$501$	2.81584e9	1.00040
$502$	−2.48597e9	−0.877067
$503$	9.56647e8	0.335169	0.167584	−	0.985858i	$-0.446403\pi$
$503$	9.56647e8	0.335169	0.167584	+	0.985858i	$0.446403\pi$
$504$	−1.28024e8	−0.0445435
$505$	4.56569e7	0.0157756
$506$	1.84879e9	0.634398
$507$	−1.30324e8	−0.0444116
$508$	1.21840e9	0.412349
$509$	−2.17508e9	−0.731075	−0.365538	−	0.930797i	$-0.619115\pi$
$509$	−2.17508e9	−0.731075	−0.365538	+	0.930797i	$0.619115\pi$
$510$	1.17469e8	0.0392126
$511$	−7.16265e8	−0.237466
$512$	1.34218e8	0.0441942
$513$	−9.18893e8	−0.300507
$514$	4.74554e7	0.0154140
$515$	4.42898e7	0.0142882
$516$	5.01688e8	0.160753
$517$	−6.27645e9	−1.99755
$518$	−6.75719e8	−0.213605
$519$	3.15953e9	0.992058
$520$	1.94256e7	0.00605846
$521$	2.31046e9	0.715758	0.357879	−	0.933768i	$-0.383500\pi$
$521$	2.31046e9	0.715758	0.357879	+	0.933768i	$0.383500\pi$
$522$	2.50059e8	0.0769478
$523$	1.91977e9	0.586804	0.293402	−	0.955989i	$-0.405212\pi$
$523$	1.91977e9	0.586804	0.293402	+	0.955989i	$0.405212\pi$
$524$	−1.43428e9	−0.435487
$525$	−7.20754e8	−0.217385
$526$	2.68404e9	0.804153
$527$	3.02488e9	0.900265
$528$	7.04103e8	0.208170
$529$	−2.08726e9	−0.613030
$530$	1.91480e8	0.0558672
$531$	−1.23992e9	−0.359387
$532$	−1.02482e9	−0.295092
$533$	−6.42198e7	−0.0183706
$534$	3.61826e8	0.102827
$535$	−1.26732e8	−0.0357807
$536$	−1.99499e9	−0.559582
$537$	7.40850e8	0.206453
$538$	−2.13945e8	−0.0592332
$539$	−7.49032e8	−0.206034
$540$	2.17543e7	0.00594520
$541$	−2.09153e8	−0.0567904	−0.0283952	−	0.999597i	$-0.509040\pi$
$541$	−2.09153e8	−0.0567904	−0.0283952	+	0.999597i	$0.509040\pi$
$542$	−2.39573e9	−0.646308
$543$	3.34946e9	0.897790
$544$	1.03192e9	0.274820
$545$	3.50376e8	0.0927144
$546$	−1.62771e8	−0.0427960
$547$	−1.08327e9	−0.282996	−0.141498	−	0.989939i	$-0.545192\pi$
$547$	−1.08327e9	−0.282996	−0.141498	+	0.989939i	$0.545192\pi$
$548$	−1.49459e9	−0.387963
$549$	−1.90130e9	−0.490397
$550$	3.96398e9	1.01593
$551$	2.00170e9	0.509763
$552$	5.01788e8	0.126979
$553$	−1.66632e9	−0.419006
$554$	2.33749e8	0.0584071
$555$	1.14820e8	0.0285098
$556$	2.23734e9	0.552039
$557$	4.70813e9	1.15440	0.577199	−	0.816604i	$-0.304146\pi$
$557$	4.70813e9	1.15440	0.577199	+	0.816604i	$0.304146\pi$
$558$	5.60184e8	0.136493
$559$	6.37853e8	0.154447
$560$	2.42621e7	0.00583807
$561$	5.41340e9	1.29450
$562$	−5.77095e9	−1.37142
$563$	−7.11679e7	−0.0168076	−0.00840378	−	0.999965i	$-0.502675\pi$
$563$	−7.11679e7	−0.0168076	−0.00840378	+	0.999965i	$0.502675\pi$
$564$	−1.70351e9	−0.399824
$565$	−3.30203e7	−0.00770213
$566$	−4.97409e9	−1.15307
$567$	−1.82284e8	−0.0419961
$568$	8.73924e8	0.200103
$569$	3.37971e9	0.769107	0.384553	−	0.923103i	$-0.374355\pi$
$569$	3.37971e9	0.769107	0.384553	+	0.923103i	$0.374355\pi$
$570$	1.74141e8	0.0393858
$571$	−2.83549e9	−0.637385	−0.318693	−	0.947858i	$-0.603244\pi$
$571$	−2.83549e9	−0.637385	−0.318693	+	0.947858i	$0.603244\pi$
$572$	8.95205e8	0.200003
$573$	−4.78157e9	−1.06177
$574$	−8.02089e7	−0.0177024
$575$	2.82498e9	0.619695
$576$	1.91103e8	0.0416667
$577$	−1.62806e9	−0.352822	−0.176411	−	0.984317i	$-0.556449\pi$
$577$	−1.62806e9	−0.352822	−0.176411	+	0.984317i	$0.556449\pi$
$578$	4.65105e9	1.00185
$579$	−6.20936e8	−0.132945
$580$	−4.73891e7	−0.0100851
$581$	−6.52632e8	−0.138055
$582$	1.05671e9	0.222191
$583$	8.82412e9	1.84430
$584$	1.06918e9	0.222129
$585$	2.76587e7	0.00571197
$586$	3.80676e9	0.781473
$587$	7.21774e8	0.147288	0.0736441	−	0.997285i	$-0.476537\pi$
$587$	7.21774e8	0.147288	0.0736441	+	0.997285i	$0.476537\pi$
$588$	−2.03297e8	−0.0412393
$589$	4.48422e9	0.904239
$590$	2.34979e8	0.0471028
$591$	3.01556e9	0.600912
$592$	1.00865e9	0.199809
$593$	9.08076e9	1.78826	0.894130	−	0.447807i	$-0.147795\pi$
$593$	9.08076e9	1.78826	0.894130	+	0.447807i	$0.147795\pi$
$594$	1.00252e9	0.196264
$595$	1.86536e8	0.0363039
$596$	−1.62261e8	−0.0313944
$597$	−1.31730e9	−0.253382
$598$	6.37979e8	0.121998
$599$	2.15705e9	0.410078	0.205039	−	0.978754i	$-0.434268\pi$
$599$	2.15705e9	0.410078	0.205039	+	0.978754i	$0.434268\pi$
$600$	1.07588e9	0.203345
$601$	−3.45569e9	−0.649343	−0.324671	−	0.945827i	$-0.605254\pi$
$601$	−3.45569e9	−0.649343	−0.324671	+	0.945827i	$0.605254\pi$
$602$	7.96663e8	0.148829
$603$	−2.84052e9	−0.527579
$604$	−4.77537e9	−0.881815
$605$	−3.63471e8	−0.0667308
$606$	5.71066e8	0.104240
$607$	3.11495e9	0.565316	0.282658	−	0.959221i	$-0.408784\pi$
$607$	3.11495e9	0.565316	0.282658	+	0.959221i	$0.408784\pi$
$608$	1.52976e9	0.276033
$609$	3.97085e8	0.0712398
$610$	3.60319e8	0.0642736
$611$	−2.16587e9	−0.384138
$612$	1.46927e9	0.259103
$613$	3.69814e9	0.648443	0.324221	−	0.945981i	$-0.394898\pi$
$613$	3.69814e9	0.648443	0.324221	+	0.945981i	$0.394898\pi$
$614$	1.72981e9	0.301585
$615$	1.36294e7	0.00236272
$616$	1.11809e9	0.192728
$617$	−6.49779e8	−0.111370	−0.0556849	−	0.998448i	$-0.517734\pi$
$617$	−6.49779e8	−0.111370	−0.0556849	+	0.998448i	$0.517734\pi$
$618$	5.53967e8	0.0944114
$619$	3.98935e9	0.676060	0.338030	−	0.941135i	$-0.390240\pi$
$619$	3.98935e9	0.676060	0.338030	+	0.941135i	$0.390240\pi$
$620$	−1.06161e8	−0.0178894
$621$	7.14459e8	0.119717
$622$	−3.13970e9	−0.523145
$623$	5.74566e8	0.0951989
$624$	2.42971e8	0.0400320
$625$	6.03371e9	0.988563
$626$	3.44784e9	0.561741
$627$	8.02509e9	1.30021
$628$	−3.20220e9	−0.515928
$629$	7.75490e9	1.24251
$630$	3.45450e7	0.00550419
$631$	−8.73103e9	−1.38345	−0.691724	−	0.722162i	$-0.743148\pi$
$631$	−8.73103e9	−1.38345	−0.691724	+	0.722162i	$0.743148\pi$
$632$	2.48733e9	0.391944
$633$	−4.81082e9	−0.753887
$634$	−2.02208e9	−0.315127
$635$	−3.28762e8	−0.0509535
$636$	2.39499e9	0.369150
$637$	−2.58475e8	−0.0396214
$638$	−2.18387e9	−0.332932
$639$	1.24432e9	0.188659
$640$	−3.62163e7	−0.00546102
$641$	−3.80807e9	−0.571087	−0.285543	−	0.958366i	$-0.592174\pi$
$641$	−3.80807e9	−0.571087	−0.285543	+	0.958366i	$0.592174\pi$
$642$	−1.58514e9	−0.236426
$643$	−6.90209e9	−1.02386	−0.511932	−	0.859026i	$-0.671070\pi$
$643$	−6.90209e9	−1.02386	−0.511932	+	0.859026i	$0.671070\pi$
$644$	7.96820e8	0.117560
$645$	−1.35372e8	−0.0198641
$646$	1.17614e10	1.71650
$647$	−1.48243e9	−0.215184	−0.107592	−	0.994195i	$-0.534314\pi$
$647$	−1.48243e9	−0.215184	−0.107592	+	0.994195i	$0.534314\pi$
$648$	2.72098e8	0.0392837
$649$	1.08287e10	1.55497
$650$	1.36788e9	0.195367
$651$	8.89551e8	0.126368
$652$	−3.02437e9	−0.427335
$653$	5.44881e9	0.765783	0.382892	−	0.923793i	$-0.374928\pi$
$653$	5.44881e9	0.765783	0.382892	+	0.923793i	$0.374928\pi$
$654$	4.38243e9	0.612622
$655$	3.87015e8	0.0538126
$656$	1.19729e8	0.0165590
$657$	1.52233e9	0.209425
$658$	−2.70512e9	−0.370165
$659$	5.31741e9	0.723771	0.361885	−	0.932223i	$-0.382133\pi$
$659$	5.31741e9	0.723771	0.361885	+	0.932223i	$0.382133\pi$
$660$	−1.89990e8	−0.0257233
$661$	6.77864e9	0.912930	0.456465	−	0.889741i	$-0.349115\pi$
$661$	6.77864e9	0.912930	0.456465	+	0.889741i	$0.349115\pi$
$662$	−8.27125e9	−1.10807
$663$	1.86805e9	0.248938
$664$	9.74192e8	0.129139
$665$	2.76530e8	0.0364641
$666$	1.43615e9	0.188382
$667$	−1.55637e9	−0.203082
$668$	−6.67457e9	−0.866375
$669$	3.86012e9	0.498436
$670$	5.38312e8	0.0691468
$671$	1.66049e10	2.12181
$672$	3.03464e8	0.0385758
$673$	−1.46642e10	−1.85441	−0.927204	−	0.374556i	$-0.877795\pi$
$673$	−1.46642e10	−1.85441	−0.927204	+	0.374556i	$0.877795\pi$
$674$	−3.18879e9	−0.401159
$675$	1.53186e9	0.191715
$676$	3.08916e8	0.0384615
$677$	6.31710e9	0.782452	0.391226	−	0.920295i	$-0.372051\pi$
$677$	6.31710e9	0.782452	0.391226	+	0.920295i	$0.372051\pi$
$678$	−4.13010e8	−0.0508928
$679$	1.67802e9	0.205709
$680$	−2.78444e8	−0.0339591
$681$	−8.22576e9	−0.998070
$682$	−4.89233e9	−0.590568
$683$	2.83532e9	0.340510	0.170255	−	0.985400i	$-0.445541\pi$
$683$	2.83532e9	0.340510	0.170255	+	0.985400i	$0.445541\pi$
$684$	2.17812e9	0.260247
$685$	4.03289e8	0.0479401
$686$	−3.22829e8	−0.0381802
$687$	5.76206e9	0.678000
$688$	−1.18919e9	−0.139217
$689$	3.04501e9	0.354668
$690$	−1.35398e8	−0.0156907
$691$	6.93920e9	0.800085	0.400042	−	0.916497i	$-0.368995\pi$
$691$	6.93920e9	0.800085	0.400042	+	0.916497i	$0.368995\pi$
$692$	−7.48926e9	−0.859148
$693$	1.59197e9	0.181705
$694$	−7.70485e9	−0.874996
$695$	−6.03705e8	−0.0682147
$696$	−5.92733e8	−0.0666387
$697$	9.20520e8	0.102972
$698$	1.05932e10	1.17905
$699$	1.73787e9	0.192463
$700$	1.70845e9	0.188261
$701$	−4.76326e9	−0.522265	−0.261133	−	0.965303i	$-0.584096\pi$
$701$	−4.76326e9	−0.522265	−0.261133	+	0.965303i	$0.584096\pi$
$702$	3.45948e8	0.0377426
$703$	1.14962e10	1.24799
$704$	−1.66898e9	−0.180280
$705$	4.59662e8	0.0494057
$706$	−1.05912e10	−1.13274
$707$	9.06832e8	0.0965071
$708$	2.93907e9	0.311238
$709$	1.20409e9	0.126881	0.0634406	−	0.997986i	$-0.479793\pi$
$709$	1.20409e9	0.126881	0.0634406	+	0.997986i	$0.479793\pi$
$710$	−2.35813e8	−0.0247265
$711$	3.54153e9	0.369528
$712$	−8.57662e8	−0.0890504
$713$	−3.48658e9	−0.360235
$714$	2.33315e9	0.239882
$715$	−2.41555e8	−0.0247141
$716$	−1.75609e9	−0.178793
$717$	1.78891e9	0.181247
$718$	3.31881e9	0.334616
$719$	3.42723e9	0.343868	0.171934	−	0.985108i	$-0.444998\pi$
$719$	3.42723e9	0.343868	0.171934	+	0.985108i	$0.444998\pi$
$720$	−5.15657e7	−0.00514870
$721$	8.79679e8	0.0874080
$722$	1.02847e10	1.01697
$723$	8.05422e9	0.792573
$724$	−7.93945e9	−0.777509
$725$	−3.33699e9	−0.325216
$726$	−4.54622e9	−0.440932
$727$	−3.19742e9	−0.308624	−0.154312	−	0.988022i	$-0.549316\pi$
$727$	−3.19742e9	−0.308624	−0.154312	+	0.988022i	$0.549316\pi$
$728$	3.85828e8	0.0370625
$729$	3.87420e8	0.0370370
$730$	−2.88498e8	−0.0274482
$731$	−9.14292e9	−0.865713
$732$	4.50679e9	0.424696
$733$	−1.19932e10	−1.12479	−0.562395	−	0.826869i	$-0.690120\pi$
$733$	−1.19932e10	−1.12479	−0.562395	+	0.826869i	$0.690120\pi$
$734$	1.62653e9	0.151819
$735$	5.48562e7	0.00509589
$736$	−1.18942e9	−0.109967
$737$	2.48075e10	2.28269
$738$	1.70473e8	0.0156120
$739$	1.84002e10	1.67713	0.838567	−	0.544798i	$-0.183394\pi$
$739$	1.84002e10	1.67713	0.838567	+	0.544798i	$0.183394\pi$
$740$	−2.72167e8	−0.0246902
$741$	2.76928e9	0.250037
$742$	3.80315e9	0.341767
$743$	1.37821e10	1.23269	0.616346	−	0.787476i	$-0.288612\pi$
$743$	1.37821e10	1.23269	0.616346	+	0.787476i	$0.288612\pi$
$744$	−1.32784e9	−0.118207
$745$	4.37832e7	0.00387936
$746$	−1.61546e9	−0.142466
$747$	1.38708e9	0.121753
$748$	−1.28318e10	−1.12107
$749$	−2.51714e9	−0.218888
$750$	−5.81725e8	−0.0503504
$751$	−1.49296e10	−1.28620	−0.643100	−	0.765782i	$-0.722352\pi$
$751$	−1.49296e10	−1.28620	−0.643100	+	0.765782i	$0.722352\pi$
$752$	4.03796e9	0.346257
$753$	8.39014e9	0.716122
$754$	−7.53608e8	−0.0640244
$755$	1.28855e9	0.108965
$756$	4.32081e8	0.0363696
$757$	−1.44421e10	−1.21002	−0.605012	−	0.796216i	$-0.706832\pi$
$757$	−1.44421e10	−1.21002	−0.605012	+	0.796216i	$0.706832\pi$
$758$	1.45344e10	1.21214
$759$	−6.23968e9	−0.517984
$760$	−4.12779e8	−0.0341091
$761$	1.79186e10	1.47387	0.736933	−	0.675966i	$-0.236273\pi$
$761$	1.79186e10	1.47387	0.736933	+	0.675966i	$0.236273\pi$
$762$	−4.11209e9	−0.336682
$763$	6.95914e9	0.567178
$764$	1.13341e10	0.919517
$765$	−3.96456e8	−0.0320170
$766$	3.97617e8	0.0319643
$767$	3.73676e9	0.299028
$768$	−4.52985e8	−0.0360844
$769$	5.34345e9	0.423721	0.211860	−	0.977300i	$-0.432048\pi$
$769$	5.34345e9	0.423721	0.211860	+	0.977300i	$0.432048\pi$
$770$	−3.01696e8	−0.0238151
$771$	−1.60162e8	−0.0125855
$772$	1.47185e9	0.115134
$773$	−1.81113e10	−1.41033	−0.705166	−	0.709042i	$-0.749128\pi$
$773$	−1.81113e10	−1.41033	−0.705166	+	0.709042i	$0.749128\pi$
$774$	−1.69320e9	−0.131255
$775$	−7.47553e9	−0.576881
$776$	−2.50480e9	−0.192423
$777$	2.28055e9	0.174408
$778$	−6.24231e9	−0.475244
$779$	1.36462e9	0.103426
$780$	−6.55613e7	−0.00494671
$781$	−1.08672e10	−0.816276
$782$	−9.14472e9	−0.683828
$783$	−8.43950e8	−0.0628276
$784$	4.81890e8	0.0357143
$785$	8.64056e8	0.0637526
$786$	4.84070e9	0.355574
$787$	−1.34001e10	−0.979930	−0.489965	−	0.871742i	$-0.662990\pi$
$787$	−1.34001e10	−0.979930	−0.489965	+	0.871742i	$0.662990\pi$
$788$	−7.14798e9	−0.520405
$789$	−9.05863e9	−0.656588
$790$	−6.71162e8	−0.0484320
$791$	−6.55845e8	−0.0471176
$792$	−2.37635e9	−0.169970
$793$	5.72999e9	0.408035
$794$	1.77796e10	1.26052
$795$	−6.46244e8	−0.0456154
$796$	3.12250e9	0.219435
$797$	−7.54941e9	−0.528213	−0.264106	−	0.964494i	$-0.585077\pi$
$797$	−7.54941e9	−0.528213	−0.264106	+	0.964494i	$0.585077\pi$
$798$	3.45877e9	0.240941
$799$	3.10453e10	2.15319
$800$	−2.55023e9	−0.176102
$801$	−1.22116e9	−0.0839575
$802$	−7.10638e9	−0.486450
$803$	−1.32951e10	−0.906124
$804$	6.73308e9	0.456897
$805$	−2.15008e8	−0.0145267
$806$	−1.68824e9	−0.113569
$807$	7.22066e8	0.0483637
$808$	−1.35364e9	−0.0902741
$809$	8.18752e9	0.543667	0.271833	−	0.962344i	$-0.412370\pi$
$809$	8.18752e9	0.543667	0.271833	+	0.962344i	$0.412370\pi$
$810$	−7.34207e7	−0.00485424
$811$	−1.11910e10	−0.736706	−0.368353	−	0.929686i	$-0.620078\pi$
$811$	−1.11910e10	−0.736706	−0.368353	+	0.929686i	$0.620078\pi$
$812$	−9.41238e8	−0.0616955
$813$	8.08558e9	0.527709
$814$	−1.25425e10	−0.815077
$815$	8.16073e8	0.0528053
$816$	−3.48272e9	−0.224390
$817$	−1.35539e10	−0.869535
$818$	−1.22564e10	−0.782937
$819$	5.49353e8	0.0349428
$820$	−3.23067e7	−0.00204618
$821$	−2.92344e10	−1.84371	−0.921855	−	0.387535i	$-0.873327\pi$
$821$	−2.92344e10	−1.84371	−0.921855	+	0.387535i	$0.873327\pi$
$822$	5.04425e9	0.316771
$823$	−2.95262e10	−1.84633	−0.923163	−	0.384410i	$-0.874405\pi$
$823$	−2.95262e10	−1.84633	−0.923163	+	0.384410i	$0.874405\pi$
$824$	−1.31311e9	−0.0817627
$825$	−1.33784e10	−0.829500
$826$	4.66713e9	0.288151
$827$	2.37879e9	0.146247	0.0731235	−	0.997323i	$-0.476703\pi$
$827$	2.37879e9	0.146247	0.0731235	+	0.997323i	$0.476703\pi$
$828$	−1.69353e9	−0.103678
$829$	1.59710e10	0.973626	0.486813	−	0.873506i	$-0.338159\pi$
$829$	1.59710e10	0.973626	0.486813	+	0.873506i	$0.338159\pi$
$830$	−2.62868e8	−0.0159575
$831$	−7.88903e8	−0.0476892
$832$	−5.75930e8	−0.0346688
$833$	3.70495e9	0.222088
$834$	−7.55101e9	−0.450738
$835$	1.80101e9	0.107057
$836$	−1.90224e10	−1.12601
$837$	−1.89062e9	−0.111446
$838$	−4.44885e9	−0.261152
$839$	2.27440e10	1.32953	0.664767	−	0.747051i	$-0.268531\pi$
$839$	2.27440e10	1.32953	0.664767	+	0.747051i	$0.268531\pi$
$840$	−8.18845e7	−0.00476677
$841$	−1.54114e10	−0.893423
$842$	1.39695e10	0.806473
$843$	1.94770e10	1.11976
$844$	1.14034e10	0.652885
$845$	−8.33554e7	−0.00475264
$846$	5.74936e9	0.326455
$847$	−7.21923e9	−0.408224
$848$	−5.67700e9	−0.319693
$849$	1.67875e10	0.941478
$850$	−1.96071e10	−1.09508
$851$	−8.93857e9	−0.497181
$852$	−2.94949e9	−0.163384
$853$	−2.26033e10	−1.24696	−0.623478	−	0.781841i	$-0.714281\pi$
$853$	−2.26033e10	−1.24696	−0.623478	+	0.781841i	$0.714281\pi$
$854$	7.15662e9	0.393192
$855$	−5.87726e8	−0.0321583
$856$	3.75737e9	0.204751
$857$	−7.53555e8	−0.0408961	−0.0204481	−	0.999791i	$-0.506509\pi$
$857$	−7.53555e8	−0.0408961	−0.0204481	+	0.999791i	$0.506509\pi$
$858$	−3.02132e9	−0.163302
$859$	−2.24138e10	−1.20653	−0.603266	−	0.797540i	$-0.706134\pi$
$859$	−2.24138e10	−1.20653	−0.603266	+	0.797540i	$0.706134\pi$
$860$	3.20881e8	0.0172028
$861$	2.70705e8	0.0144539
$862$	1.24478e10	0.661935
$863$	9.57096e9	0.506895	0.253447	−	0.967349i	$-0.418436\pi$
$863$	9.57096e9	0.506895	0.253447	+	0.967349i	$0.418436\pi$
$864$	−6.44973e8	−0.0340207
$865$	2.02084e9	0.106164
$866$	2.14449e10	1.12205
$867$	−1.56973e10	−0.818008
$868$	−2.10857e9	−0.109438
$869$	−3.09297e10	−1.59885
$870$	1.59938e8	0.00823446
$871$	8.56053e9	0.438972
$872$	−1.03880e10	−0.530547
$873$	−3.56641e9	−0.181418
$874$	−1.35566e10	−0.686847
$875$	−9.23758e8	−0.0466154
$876$	−3.60847e9	−0.181367
$877$	1.32581e10	0.663715	0.331857	−	0.943330i	$-0.392325\pi$
$877$	1.32581e10	0.663715	0.331857	+	0.943330i	$0.392325\pi$
$878$	1.76484e10	0.879983
$879$	−1.28478e10	−0.638070
$880$	4.50346e8	0.0222770
$881$	−2.53389e10	−1.24845	−0.624226	−	0.781244i	$-0.714586\pi$
$881$	−2.53389e10	−1.24845	−0.624226	+	0.781244i	$0.714586\pi$
$882$	6.86129e8	0.0336718
$883$	5.43794e9	0.265810	0.132905	−	0.991129i	$-0.457569\pi$
$883$	5.43794e9	0.265810	0.132905	+	0.991129i	$0.457569\pi$
$884$	−4.42797e9	−0.215586
$885$	−7.93054e8	−0.0384593
$886$	2.42586e10	1.17179
$887$	−8.74030e9	−0.420527	−0.210263	−	0.977645i	$-0.567432\pi$
$887$	−8.74030e9	−0.420527	−0.210263	+	0.977645i	$0.567432\pi$
$888$	−3.40420e9	−0.163144
$889$	−6.52984e9	−0.311707
$890$	2.31425e8	0.0110038
$891$	−3.38351e9	−0.160249
$892$	−9.14992e9	−0.431659
$893$	4.60231e10	2.16270
$894$	5.47631e8	0.0256334
$895$	4.73849e8	0.0220932
$896$	−7.19323e8	−0.0334077
$897$	−2.15318e9	−0.0996108
$898$	9.08471e9	0.418643
$899$	4.11849e9	0.189051
$900$	−3.63109e9	−0.166030
$901$	−4.36469e10	−1.98800
$902$	−1.48882e9	−0.0675489
$903$	−2.68874e9	−0.121518
$904$	9.78987e8	0.0440745
$905$	2.14232e9	0.0960758
$906$	1.61169e10	0.719999
$907$	−3.97846e10	−1.77047	−0.885236	−	0.465141i	$-0.846004\pi$
$907$	−3.97846e10	−1.77047	−0.885236	+	0.465141i	$0.846004\pi$
$908$	1.94981e10	0.864354
$909$	−1.92735e9	−0.0851112
$910$	−1.04109e8	−0.00457976
$911$	1.92105e10	0.841829	0.420914	−	0.907100i	$-0.361709\pi$
$911$	1.92105e10	0.841829	0.420914	+	0.907100i	$0.361709\pi$
$912$	−5.16294e9	−0.225380
$913$	−1.21140e10	−0.526792
$914$	−1.52027e10	−0.658583
$915$	−1.21608e9	−0.0524792
$916$	−1.36582e10	−0.587165
$917$	7.68686e9	0.329197
$918$	−4.95879e9	−0.211556
$919$	−1.42698e10	−0.606476	−0.303238	−	0.952915i	$-0.598068\pi$
$919$	−1.42698e10	−0.606476	−0.303238	+	0.952915i	$0.598068\pi$
$920$	3.20944e8	0.0135885
$921$	−5.83811e9	−0.246243
$922$	1.32703e10	0.557598
$923$	−3.75002e9	−0.156974
$924$	−3.77355e9	−0.157361
$925$	−1.91651e10	−0.796187
$926$	−3.07783e10	−1.27381
$927$	−1.86964e9	−0.0770866
$928$	1.40500e9	0.0577108
$929$	1.79166e10	0.733162	0.366581	−	0.930386i	$-0.380528\pi$
$929$	1.79166e10	0.733162	0.366581	+	0.930386i	$0.380528\pi$
$930$	3.58295e8	0.0146066
$931$	5.49240e9	0.223068
$932$	−4.11940e9	−0.166678
$933$	1.05965e10	0.427146
$934$	−1.95286e10	−0.784256
$935$	3.46242e9	0.138529
$936$	−8.20026e8	−0.0326860
$937$	−3.89744e10	−1.54771	−0.773857	−	0.633361i	$-0.781675\pi$
$937$	−3.89744e10	−1.54771	−0.773857	+	0.633361i	$0.781675\pi$
$938$	1.06919e10	0.423004
$939$	−1.16364e10	−0.458660
$940$	−1.08957e9	−0.0427866
$941$	−7.73440e8	−0.0302596	−0.0151298	−	0.999886i	$-0.504816\pi$
$941$	−7.73440e8	−0.0302596	−0.0151298	+	0.999886i	$0.504816\pi$
$942$	1.08074e10	0.421254
$943$	−1.06102e9	−0.0412035
$944$	−6.96667e9	−0.269540
$945$	−1.16589e8	−0.00449415
$946$	1.47874e10	0.567902
$947$	3.31534e10	1.26854	0.634269	−	0.773113i	$-0.281301\pi$
$947$	3.31534e10	1.26854	0.634269	+	0.773113i	$0.281301\pi$
$948$	−8.39475e9	−0.320021
$949$	−4.58786e9	−0.174252
$950$	−2.90665e10	−1.09992
$951$	6.82452e9	0.257300
$952$	−5.53042e9	−0.207744
$953$	2.09417e10	0.783766	0.391883	−	0.920015i	$-0.371824\pi$
$953$	2.09417e10	0.783766	0.391883	+	0.920015i	$0.371824\pi$
$954$	−8.08307e9	−0.301410
$955$	−3.05830e9	−0.113624
$956$	−4.24037e9	−0.156964
$957$	7.37057e9	0.271838
$958$	−5.43512e9	−0.199724
$959$	8.01007e9	0.293273
$960$	1.22230e8	0.00445890
$961$	−1.82863e10	−0.664653
$962$	−4.32815e9	−0.156743
$963$	5.34984e9	0.193041
$964$	−1.90915e10	−0.686389
$965$	−3.97152e8	−0.0142269
$966$	−2.68927e9	−0.0959874
$967$	1.60900e10	0.572220	0.286110	−	0.958197i	$-0.407638\pi$
$967$	1.60900e10	0.572220	0.286110	+	0.958197i	$0.407638\pi$
$968$	1.07762e10	0.381859
$969$	−3.96946e10	−1.40152
$970$	6.75877e8	0.0237775
$971$	2.11517e10	0.741443	0.370722	−	0.928744i	$-0.379110\pi$
$971$	2.11517e10	0.741443	0.370722	+	0.928744i	$0.379110\pi$
$972$	−9.18330e8	−0.0320750
$973$	−1.19907e10	−0.417302
$974$	−1.21742e9	−0.0422168
$975$	−4.61661e9	−0.159517
$976$	−1.06828e10	−0.367798
$977$	5.08868e10	1.74572	0.872859	−	0.487973i	$-0.162264\pi$
$977$	5.08868e10	1.74572	0.872859	+	0.487973i	$0.162264\pi$
$978$	1.02073e10	0.348918
$979$	1.06649e10	0.363261
$980$	−1.30029e8	−0.00441317
$981$	−1.47907e10	−0.500204
$982$	1.00823e10	0.339757
$983$	4.91736e9	0.165118	0.0825590	−	0.996586i	$-0.473691\pi$
$983$	4.91736e9	0.165118	0.0825590	+	0.996586i	$0.473691\pi$
$984$	−4.04085e8	−0.0135204
$985$	1.92876e9	0.0643058
$986$	1.08021e10	0.358873
$987$	9.12976e9	0.302238
$988$	−6.56423e9	−0.216538
$989$	1.05384e10	0.346409
$990$	6.41215e8	0.0210029
$991$	2.30540e10	0.752469	0.376234	−	0.926525i	$-0.377219\pi$
$991$	2.30540e10	0.752469	0.376234	+	0.926525i	$0.377219\pi$
$992$	3.14748e9	0.102370
$993$	2.79155e10	0.904738
$994$	−4.68368e9	−0.151264
$995$	−8.42550e8	−0.0271153
$996$	−3.28790e9	−0.105441
$997$	−2.53208e10	−0.809178	−0.404589	−	0.914499i	$-0.632585\pi$
$997$	−2.53208e10	−0.809178	−0.404589	+	0.914499i	$0.632585\pi$
$998$	−1.01878e10	−0.324431
$999$	−4.84700e9	−0.153813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.l.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.l.1.3	✓	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)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -17.2693 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -17.2693 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -138.154 q^{10} -6366.67 q^{11} -1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +466.270 q^{15} +4096.00 q^{16} +31491.6 q^{17} +5832.00 q^{18} +46684.6 q^{19} -1105.23 q^{20} +9261.00 q^{21} -50933.4 q^{22} -36298.3 q^{23} -13824.0 q^{24} -77826.8 q^{25} -17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +42877.1 q^{29} +3730.16 q^{30} +96053.5 q^{31} +32768.0 q^{32} +171900. q^{33} +251933. q^{34} +5923.35 q^{35} +46656.0 q^{36} +246253. q^{37} +373477. q^{38} +59319.0 q^{39} -8841.86 q^{40} +29230.7 q^{41} +74088.0 q^{42} -290329. q^{43} -407467. q^{44} -12589.3 q^{45} -290386. q^{46} +985829. q^{47} -110592. q^{48} +117649. q^{49} -622614. q^{50} -850273. q^{51} -140608. q^{52} -1.38599e6 q^{53} -157464. q^{54} +109948. q^{55} -175616. q^{56} -1.26048e6 q^{57} +343017. q^{58} -1.70085e6 q^{59} +29841.3 q^{60} -2.60810e6 q^{61} +768428. q^{62} -250047. q^{63} +262144. q^{64} +37940.6 q^{65} +1.37520e6 q^{66} -3.89646e6 q^{67} +2.01546e6 q^{68} +980054. q^{69} +47386.8 q^{70} +1.70688e6 q^{71} +373248. q^{72} +2.08824e6 q^{73} +1.97003e6 q^{74} +2.10132e6 q^{75} +2.98782e6 q^{76} +2.18377e6 q^{77} +474552. q^{78} +4.85807e6 q^{79} -70734.9 q^{80} +531441. q^{81} +233845. q^{82} +1.90272e6 q^{83} +592704. q^{84} -543836. q^{85} -2.32263e6 q^{86} -1.15768e6 q^{87} -3.25973e6 q^{88} -1.67512e6 q^{89} -100714. q^{90} +753571. q^{91} -2.32309e6 q^{92} -2.59344e6 q^{93} +7.88663e6 q^{94} -806208. q^{95} -884736. q^{96} -4.89220e6 q^{97} +941192. q^{98} -4.64130e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9}+O(q^{10}) \) 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9	\( 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9} - 2000 q^{10} + 659 q^{11} - 8640 q^{12} - 10985 q^{13} - 13720 q^{14} + 6750 q^{15} + 20480 q^{16} + 24575 q^{17} + 29160 q^{18} - 6446 q^{19} - 16000 q^{20} + 46305 q^{21} + 5272 q^{22} + 30268 q^{23} - 69120 q^{24} + 38965 q^{25} - 87880 q^{26} - 98415 q^{27} - 109760 q^{28} + 130950 q^{29} + 54000 q^{30} + 262979 q^{31} + 163840 q^{32} - 17793 q^{33} + 196600 q^{34} + 85750 q^{35} + 233280 q^{36} - 101549 q^{37} - 51568 q^{38} + 296595 q^{39} - 128000 q^{40} - 247328 q^{41} + 370440 q^{42} - 19092 q^{43} + 42176 q^{44} - 182250 q^{45} + 242144 q^{46} - 126419 q^{47} - 552960 q^{48} + 588245 q^{49} + 311720 q^{50} - 663525 q^{51} - 703040 q^{52} - 302793 q^{53} - 787320 q^{54} + 943985 q^{55} - 878080 q^{56} + 174042 q^{57} + 1047600 q^{58} - 2798636 q^{59} + 432000 q^{60} - 2493751 q^{61} + 2103832 q^{62} - 1250235 q^{63} + 1310720 q^{64} + 549250 q^{65} - 142344 q^{66} + 160188 q^{67} + 1572800 q^{68} - 817236 q^{69} + 686000 q^{70} + 3846088 q^{71} + 1866240 q^{72} + 5655872 q^{73} - 812392 q^{74} - 1052055 q^{75} - 412544 q^{76} - 226037 q^{77} + 2372760 q^{78} + 5647991 q^{79} - 1024000 q^{80} + 2657205 q^{81} - 1978624 q^{82} - 4607669 q^{83} + 2963520 q^{84} + 3873935 q^{85} - 152736 q^{86} - 3535650 q^{87} + 337408 q^{88} - 17424029 q^{89} - 1458000 q^{90} + 3767855 q^{91} + 1937152 q^{92} - 7100433 q^{93} - 1011352 q^{94} - 24593720 q^{95} - 4423680 q^{96} - 18380577 q^{97} + 4705960 q^{98} + 480411 q^{99}+O(q^{100}) \) 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9 - 2000 * q^10 + 659 * q^11 - 8640 * q^12 - 10985 * q^13 - 13720 * q^14 + 6750 * q^15 + 20480 * q^16 + 24575 * q^17 + 29160 * q^18 - 6446 * q^19 - 16000 * q^20 + 46305 * q^21 + 5272 * q^22 + 30268 * q^23 - 69120 * q^24 + 38965 * q^25 - 87880 * q^26 - 98415 * q^27 - 109760 * q^28 + 130950 * q^29 + 54000 * q^30 + 262979 * q^31 + 163840 * q^32 - 17793 * q^33 + 196600 * q^34 + 85750 * q^35 + 233280 * q^36 - 101549 * q^37 - 51568 * q^38 + 296595 * q^39 - 128000 * q^40 - 247328 * q^41 + 370440 * q^42 - 19092 * q^43 + 42176 * q^44 - 182250 * q^45 + 242144 * q^46 - 126419 * q^47 - 552960 * q^48 + 588245 * q^49 + 311720 * q^50 - 663525 * q^51 - 703040 * q^52 - 302793 * q^53 - 787320 * q^54 + 943985 * q^55 - 878080 * q^56 + 174042 * q^57 + 1047600 * q^58 - 2798636 * q^59 + 432000 * q^60 - 2493751 * q^61 + 2103832 * q^62 - 1250235 * q^63 + 1310720 * q^64 + 549250 * q^65 - 142344 * q^66 + 160188 * q^67 + 1572800 * q^68 - 817236 * q^69 + 686000 * q^70 + 3846088 * q^71 + 1866240 * q^72 + 5655872 * q^73 - 812392 * q^74 - 1052055 * q^75 - 412544 * q^76 - 226037 * q^77 + 2372760 * q^78 + 5647991 * q^79 - 1024000 * q^80 + 2657205 * q^81 - 1978624 * q^82 - 4607669 * q^83 + 2963520 * q^84 + 3873935 * q^85 - 152736 * q^86 - 3535650 * q^87 + 337408 * q^88 - 17424029 * q^89 - 1458000 * q^90 + 3767855 * q^91 + 1937152 * q^92 - 7100433 * q^93 - 1011352 * q^94 - 24593720 * q^95 - 4423680 * q^96 - 18380577 * q^97 + 4705960 * q^98 + 480411 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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