LMFDB - Embedded newform 91.8.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(1,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3 x^{9} - 816 x^{8} + 2298 x^{7} + 213848 x^{6} - 507132 x^{5} - 19919976 x^{4} + \cdots - 7335224320 $ x^10 - 3x^9 - 816x^8 + 2298x^7 + 213848x^6 - 507132x^5 - 19919976x^4 + 24331248x^3 + 727257184x^2 - 56397312*x - 7335224320
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-19.0627$ of defining polynomial
Character	$\chi$	$=$	91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+19.0627 q^{2} -86.0671 q^{3} +235.388 q^{4} -217.435 q^{5} -1640.67 q^{6} -343.000 q^{7} +2047.10 q^{8} +5220.54 q^{9} +O(q^{10})$	\(q+19.0627 q^{2} -86.0671 q^{3} +235.388 q^{4} -217.435 q^{5} -1640.67 q^{6} -343.000 q^{7} +2047.10 q^{8} +5220.54 q^{9} -4144.91 q^{10} +1359.88 q^{11} -20259.1 q^{12} -2197.00 q^{13} -6538.52 q^{14} +18714.0 q^{15} +8893.70 q^{16} +18136.4 q^{17} +99517.8 q^{18} +37526.7 q^{19} -51181.5 q^{20} +29521.0 q^{21} +25923.0 q^{22} +106016. q^{23} -176188. q^{24} -30846.9 q^{25} -41880.8 q^{26} -261088. q^{27} -80737.9 q^{28} +95658.1 q^{29} +356740. q^{30} +134134. q^{31} -92490.6 q^{32} -117041. q^{33} +345728. q^{34} +74580.3 q^{35} +1.22885e6 q^{36} +305719. q^{37} +715362. q^{38} +189089. q^{39} -445112. q^{40} -428291. q^{41} +562751. q^{42} +314247. q^{43} +320099. q^{44} -1.13513e6 q^{45} +2.02096e6 q^{46} -1.21612e6 q^{47} -765455. q^{48} +117649. q^{49} -588027. q^{50} -1.56094e6 q^{51} -517146. q^{52} +767929. q^{53} -4.97705e6 q^{54} -295686. q^{55} -702155. q^{56} -3.22982e6 q^{57} +1.82350e6 q^{58} +186379. q^{59} +4.40505e6 q^{60} +1.76366e6 q^{61} +2.55696e6 q^{62} -1.79065e6 q^{63} -2.90152e6 q^{64} +477705. q^{65} -2.23112e6 q^{66} -410055. q^{67} +4.26907e6 q^{68} -9.12451e6 q^{69} +1.42170e6 q^{70} -641600. q^{71} +1.06870e7 q^{72} +4.66335e6 q^{73} +5.82784e6 q^{74} +2.65491e6 q^{75} +8.83333e6 q^{76} -466439. q^{77} +3.60456e6 q^{78} -6.39172e6 q^{79} -1.93380e6 q^{80} +1.10538e7 q^{81} -8.16440e6 q^{82} -1.65238e6 q^{83} +6.94888e6 q^{84} -3.94348e6 q^{85} +5.99041e6 q^{86} -8.23301e6 q^{87} +2.78381e6 q^{88} +1.16301e7 q^{89} -2.16387e7 q^{90} +753571. q^{91} +2.49549e7 q^{92} -1.15445e7 q^{93} -2.31825e7 q^{94} -8.15963e6 q^{95} +7.96040e6 q^{96} +5.73307e6 q^{97} +2.24271e6 q^{98} +7.09932e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 - 101 * q^3 + 361 * q^4 + 226 * q^5 + 1105 * q^6 - 3430 * q^7 + 291 * q^8 + 12247 * q^9	\( 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9} + 2548 q^{10} + 451 q^{11} - 16241 q^{12} - 21970 q^{13} + 1029 q^{14} + 27184 q^{15} + 11897 q^{16} - 8654 q^{17} + 159348 q^{18} + 10130 q^{19} - 82012 q^{20} + 34643 q^{21} - 57863 q^{22} - 52155 q^{23} - 49227 q^{24} + 47190 q^{25} + 6591 q^{26} - 155171 q^{27} - 123823 q^{28} + 520154 q^{29} + 1070236 q^{30} + 692605 q^{31} + 149835 q^{32} + 436053 q^{33} + 1059060 q^{34} - 77518 q^{35} + 2843742 q^{36} - 20511 q^{37} + 1905286 q^{38} + 221897 q^{39} + 636320 q^{40} + 355049 q^{41} - 379015 q^{42} + 1256772 q^{43} - 687913 q^{44} + 1259926 q^{45} + 4043075 q^{46} + 1260721 q^{47} + 1128551 q^{48} + 1176490 q^{49} + 609035 q^{50} + 1411976 q^{51} - 793117 q^{52} + 928854 q^{53} + 6642607 q^{54} + 3423196 q^{55} - 99813 q^{56} + 3014966 q^{57} + 1612588 q^{58} + 3144446 q^{59} + 7738848 q^{60} + 6322923 q^{61} + 6545331 q^{62} - 4200721 q^{63} - 6629943 q^{64} - 496522 q^{65} - 14343317 q^{66} + 3944507 q^{67} - 1787356 q^{68} - 148281 q^{69} - 873964 q^{70} + 6032248 q^{71} + 9760866 q^{72} + 1248533 q^{73} - 8263279 q^{74} + 1573413 q^{75} + 1788254 q^{76} - 154693 q^{77} - 2427685 q^{78} - 14947605 q^{79} - 9147616 q^{80} + 25716334 q^{81} - 6987095 q^{82} - 14177784 q^{83} + 5570663 q^{84} - 11788444 q^{85} + 8748840 q^{86} - 29484448 q^{87} - 15390723 q^{88} + 6734836 q^{89} + 5994972 q^{90} + 7535710 q^{91} - 24493215 q^{92} + 17307847 q^{93} - 22760149 q^{94} - 9329708 q^{95} - 36488483 q^{96} - 12365397 q^{97} - 352947 q^{98} - 43198042 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 101 * q^3 + 361 * q^4 + 226 * q^5 + 1105 * q^6 - 3430 * q^7 + 291 * q^8 + 12247 * q^9 + 2548 * q^10 + 451 * q^11 - 16241 * q^12 - 21970 * q^13 + 1029 * q^14 + 27184 * q^15 + 11897 * q^16 - 8654 * q^17 + 159348 * q^18 + 10130 * q^19 - 82012 * q^20 + 34643 * q^21 - 57863 * q^22 - 52155 * q^23 - 49227 * q^24 + 47190 * q^25 + 6591 * q^26 - 155171 * q^27 - 123823 * q^28 + 520154 * q^29 + 1070236 * q^30 + 692605 * q^31 + 149835 * q^32 + 436053 * q^33 + 1059060 * q^34 - 77518 * q^35 + 2843742 * q^36 - 20511 * q^37 + 1905286 * q^38 + 221897 * q^39 + 636320 * q^40 + 355049 * q^41 - 379015 * q^42 + 1256772 * q^43 - 687913 * q^44 + 1259926 * q^45 + 4043075 * q^46 + 1260721 * q^47 + 1128551 * q^48 + 1176490 * q^49 + 609035 * q^50 + 1411976 * q^51 - 793117 * q^52 + 928854 * q^53 + 6642607 * q^54 + 3423196 * q^55 - 99813 * q^56 + 3014966 * q^57 + 1612588 * q^58 + 3144446 * q^59 + 7738848 * q^60 + 6322923 * q^61 + 6545331 * q^62 - 4200721 * q^63 - 6629943 * q^64 - 496522 * q^65 - 14343317 * q^66 + 3944507 * q^67 - 1787356 * q^68 - 148281 * q^69 - 873964 * q^70 + 6032248 * q^71 + 9760866 * q^72 + 1248533 * q^73 - 8263279 * q^74 + 1573413 * q^75 + 1788254 * q^76 - 154693 * q^77 - 2427685 * q^78 - 14947605 * q^79 - 9147616 * q^80 + 25716334 * q^81 - 6987095 * q^82 - 14177784 * q^83 + 5570663 * q^84 - 11788444 * q^85 + 8748840 * q^86 - 29484448 * q^87 - 15390723 * q^88 + 6734836 * q^89 + 5994972 * q^90 + 7535710 * q^91 - 24493215 * q^92 + 17307847 * q^93 - 22760149 * q^94 - 9329708 * q^95 - 36488483 * q^96 - 12365397 * q^97 - 352947 * q^98 - 43198042 * 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 $

$2$	19.0627	1.68492	0.842461	−	0.538757i	$-0.181106\pi$
$2$	19.0627	1.68492	0.842461	+	0.538757i	$0.181106\pi$
$3$	−86.0671	−1.84040	−0.920201	−	0.391446i	$-0.871975\pi$
$3$	−86.0671	−1.84040	−0.920201	+	0.391446i	$0.871975\pi$
$4$	235.388	1.83897
$5$	−217.435	−0.777920	−0.388960	−	0.921255i	$-0.627166\pi$
$5$	−217.435	−0.777920	−0.388960	+	0.921255i	$0.627166\pi$
$6$	−1640.67	−3.10094
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	2047.10	1.41359
$9$	5220.54	2.38708
$10$	−4144.91	−1.31073
$11$	1359.88	0.308054	0.154027	−	0.988067i	$-0.450776\pi$
$11$	1359.88	0.308054	0.154027	+	0.988067i	$0.450776\pi$
$12$	−20259.1	−3.38444
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−6538.52	−0.636841
$15$	18714.0	1.43168
$16$	8893.70	0.542828
$17$	18136.4	0.895321	0.447661	−	0.894204i	$-0.352257\pi$
$17$	18136.4	0.895321	0.447661	+	0.894204i	$0.352257\pi$
$18$	99517.8	4.02204
$19$	37526.7	1.25517	0.627586	−	0.778547i	$-0.284043\pi$
$19$	37526.7	1.25517	0.627586	+	0.778547i	$0.284043\pi$
$20$	−51181.5	−1.43057
$21$	29521.0	0.695606
$22$	25923.0	0.519047
$23$	106016.	1.81687	0.908437	−	0.418021i	$-0.137276\pi$
$23$	106016.	1.81687	0.908437	+	0.418021i	$0.137276\pi$
$24$	−176188.	−2.60158
$25$	−30846.9	−0.394841
$26$	−41880.8	−0.467314
$27$	−261088.	−2.55278
$28$	−80737.9	−0.695064
$29$	95658.1	0.728331	0.364165	−	0.931334i	$-0.381354\pi$
$29$	95658.1	0.728331	0.364165	+	0.931334i	$0.381354\pi$
$30$	356740.	2.41228
$31$	134134.	0.808672	0.404336	−	0.914611i	$-0.367503\pi$
$31$	134134.	0.808672	0.404336	+	0.914611i	$0.367503\pi$
$32$	−92490.6	−0.498968
$33$	−117041.	−0.566943
$34$	345728.	1.50855
$35$	74580.3	0.294026
$36$	1.22885e6	4.38976
$37$	305719.	0.992239	0.496120	−	0.868254i	$-0.334758\pi$
$37$	305719.	0.992239	0.496120	+	0.868254i	$0.334758\pi$
$38$	715362.	2.11487
$39$	189089.	0.510436
$40$	−445112.	−1.09966
$41$	−428291.	−0.970500	−0.485250	−	0.874375i	$-0.661271\pi$
$41$	−428291.	−0.970500	−0.485250	+	0.874375i	$0.661271\pi$
$42$	562751.	1.17204
$43$	314247.	0.602743	0.301372	−	0.953507i	$-0.402556\pi$
$43$	314247.	0.602743	0.301372	+	0.953507i	$0.402556\pi$
$44$	320099.	0.566500
$45$	−1.13513e6	−1.85696
$46$	2.02096e6	3.06129
$47$	−1.21612e6	−1.70857	−0.854284	−	0.519806i	$-0.826004\pi$
$47$	−1.21612e6	−1.70857	−0.854284	+	0.519806i	$0.826004\pi$
$48$	−765455.	−0.999022
$49$	117649.	0.142857
$50$	−588027.	−0.665276
$51$	−1.56094e6	−1.64775
$52$	−517146.	−0.510037
$53$	767929.	0.708526	0.354263	−	0.935146i	$-0.384732\pi$
$53$	767929.	0.708526	0.354263	+	0.935146i	$0.384732\pi$
$54$	−4.97705e6	−4.30124
$55$	−295686.	−0.239641
$56$	−702155.	−0.534288
$57$	−3.22982e6	−2.31002
$58$	1.82350e6	1.22718
$59$	186379.	0.118145	0.0590724	−	0.998254i	$-0.481186\pi$
$59$	186379.	0.118145	0.0590724	+	0.998254i	$0.481186\pi$
$60$	4.40505e6	2.63282
$61$	1.76366e6	0.994856	0.497428	−	0.867505i	$-0.334278\pi$
$61$	1.76366e6	0.994856	0.497428	+	0.867505i	$0.334278\pi$
$62$	2.55696e6	1.36255
$63$	−1.79065e6	−0.902231
$64$	−2.90152e6	−1.38355
$65$	477705.	0.215756
$66$	−2.23112e6	−0.955255
$67$	−410055.	−0.166564	−0.0832819	−	0.996526i	$-0.526540\pi$
$67$	−410055.	−0.166564	−0.0832819	+	0.996526i	$0.526540\pi$
$68$	4.26907e6	1.64646
$69$	−9.12451e6	−3.34378
$70$	1.42170e6	0.495411
$71$	−641600.	−0.212745	−0.106373	−	0.994326i	$-0.533924\pi$
$71$	−641600.	−0.212745	−0.106373	+	0.994326i	$0.533924\pi$
$72$	1.06870e7	3.37436
$73$	4.66335e6	1.40303	0.701516	−	0.712654i	$-0.252507\pi$
$73$	4.66335e6	1.40303	0.701516	+	0.712654i	$0.252507\pi$
$74$	5.82784e6	1.67185
$75$	2.65491e6	0.726666
$76$	8.83333e6	2.30822
$77$	−466439.	−0.116433
$78$	3.60456e6	0.860045
$79$	−6.39172e6	−1.45856	−0.729278	−	0.684218i	$-0.760144\pi$
$79$	−6.39172e6	−1.45856	−0.729278	+	0.684218i	$0.760144\pi$
$80$	−1.93380e6	−0.422277
$81$	1.10538e7	2.31107
$82$	−8.16440e6	−1.63522
$83$	−1.65238e6	−0.317203	−0.158601	−	0.987343i	$-0.550699\pi$
$83$	−1.65238e6	−0.317203	−0.158601	+	0.987343i	$0.550699\pi$
$84$	6.94888e6	1.27920
$85$	−3.94348e6	−0.696488
$86$	5.99041e6	1.01558
$87$	−8.23301e6	−1.34042
$88$	2.78381e6	0.435462
$89$	1.16301e7	1.74871	0.874353	−	0.485290i	$-0.161286\pi$
$89$	1.16301e7	1.74871	0.874353	+	0.485290i	$0.161286\pi$
$90$	−2.16387e7	−3.12883
$91$	753571.	0.104828
$92$	2.49549e7	3.34117
$93$	−1.15445e7	−1.48828
$94$	−2.31825e7	−2.87881
$95$	−8.15963e6	−0.976423
$96$	7.96040e6	0.918302
$97$	5.73307e6	0.637803	0.318901	−	0.947788i	$-0.396686\pi$
$97$	5.73307e6	0.637803	0.318901	+	0.947788i	$0.396686\pi$
$98$	2.24271e6	0.240703
$99$	7.09932e6	0.735349
$100$	−7.26099e6	−0.726099
$101$	1.29076e7	1.24658	0.623291	−	0.781990i	$-0.285795\pi$
$101$	1.29076e7	1.24658	0.623291	+	0.781990i	$0.285795\pi$
$102$	−2.97558e7	−2.77633
$103$	−8.95372e6	−0.807371	−0.403686	−	0.914898i	$-0.632271\pi$
$103$	−8.95372e6	−0.807371	−0.403686	+	0.914898i	$0.632271\pi$
$104$	−4.49748e6	−0.392060
$105$	−6.41891e6	−0.541126
$106$	1.46388e7	1.19381
$107$	−7.43785e6	−0.586954	−0.293477	−	0.955966i	$-0.594812\pi$
$107$	−7.43785e6	−0.586954	−0.293477	+	0.955966i	$0.594812\pi$
$108$	−6.14569e7	−4.69448
$109$	2.67013e7	1.97488	0.987438	−	0.158007i	$-0.0505070\pi$
$109$	2.67013e7	1.97488	0.987438	+	0.158007i	$0.0505070\pi$
$110$	−5.63658e6	−0.403777
$111$	−2.63123e7	−1.82612
$112$	−3.05054e6	−0.205170
$113$	−6.91587e6	−0.450892	−0.225446	−	0.974256i	$-0.572384\pi$
$113$	−6.91587e6	−0.450892	−0.225446	+	0.974256i	$0.572384\pi$
$114$	−6.15691e7	−3.89221
$115$	−2.30517e7	−1.41338
$116$	2.25167e7	1.33937
$117$	−1.14695e7	−0.662057
$118$	3.55289e6	0.199065
$119$	−6.22077e6	−0.338400
$120$	3.83095e7	2.02382
$121$	−1.76379e7	−0.905103
$122$	3.36201e7	1.67626
$123$	3.68618e7	1.78611
$124$	3.15734e7	1.48712
$125$	2.36943e7	1.08507
$126$	−3.41346e7	−1.52019
$127$	2.32271e7	1.00619	0.503097	−	0.864230i	$-0.332194\pi$
$127$	2.32271e7	1.00619	0.503097	+	0.864230i	$0.332194\pi$
$128$	−4.34720e7	−1.83221
$129$	−2.70464e7	−1.10929
$130$	9.10636e6	0.363532
$131$	3.84927e7	1.49599	0.747996	−	0.663703i	$-0.231016\pi$
$131$	3.84927e7	1.49599	0.747996	+	0.663703i	$0.231016\pi$
$132$	−2.75500e7	−1.04259
$133$	−1.28717e7	−0.474410
$134$	−7.81677e6	−0.280647
$135$	5.67697e7	1.98586
$136$	3.71269e7	1.26562
$137$	−735092.	−0.0244242	−0.0122121	−	0.999925i	$-0.503887\pi$
$137$	−735092.	−0.0244242	−0.0122121	+	0.999925i	$0.503887\pi$
$138$	−1.73938e8	−5.63401
$139$	3.92490e7	1.23959	0.619794	−	0.784765i	$-0.287216\pi$
$139$	3.92490e7	1.23959	0.619794	+	0.784765i	$0.287216\pi$
$140$	1.75553e7	0.540704
$141$	1.04668e8	3.14445
$142$	−1.22306e7	−0.358460
$143$	−2.98766e6	−0.0854387
$144$	4.64299e7	1.29577
$145$	−2.07994e7	−0.566583
$146$	8.88961e7	2.36400
$147$	−1.01257e7	−0.262915
$148$	7.19624e7	1.82469
$149$	−1.81663e6	−0.0449899	−0.0224949	−	0.999747i	$-0.507161\pi$
$149$	−1.81663e6	−0.0449899	−0.0224949	+	0.999747i	$0.507161\pi$
$150$	5.06097e7	1.22438
$151$	−7.20574e7	−1.70317	−0.851587	−	0.524213i	$-0.824360\pi$
$151$	−7.20574e7	−1.70317	−0.851587	+	0.524213i	$0.824360\pi$
$152$	7.68210e7	1.77430
$153$	9.46816e7	2.13720
$154$	−8.89160e6	−0.196181
$155$	−2.91654e7	−0.629082
$156$	4.45093e7	0.938673
$157$	−3.93167e7	−0.810828	−0.405414	−	0.914133i	$-0.632873\pi$
$157$	−3.93167e7	−0.810828	−0.405414	+	0.914133i	$0.632873\pi$
$158$	−1.21844e8	−2.45755
$159$	−6.60934e7	−1.30397
$160$	2.01107e7	0.388157
$161$	−3.63636e7	−0.686714
$162$	2.10715e8	3.89397
$163$	−1.54892e6	−0.0280138	−0.0140069	−	0.999902i	$-0.504459\pi$
$163$	−1.54892e6	−0.0280138	−0.0140069	+	0.999902i	$0.504459\pi$
$164$	−1.00814e8	−1.78472
$165$	2.54488e7	0.441036
$166$	−3.14989e7	−0.534463
$167$	4.79827e7	0.797218	0.398609	−	0.917121i	$-0.369493\pi$
$167$	4.79827e7	0.797218	0.398609	+	0.917121i	$0.369493\pi$
$168$	6.04325e7	0.983304
$169$	4.82681e6	0.0769231
$170$	−7.51735e7	−1.17353
$171$	1.95910e8	2.99619
$172$	7.39700e7	1.10842
$173$	−9.90499e7	−1.45443	−0.727214	−	0.686410i	$-0.759185\pi$
$173$	−9.90499e7	−1.45443	−0.727214	+	0.686410i	$0.759185\pi$
$174$	−1.56944e8	−2.25851
$175$	1.05805e7	0.149236
$176$	1.20944e7	0.167220
$177$	−1.60411e7	−0.217434
$178$	2.21701e8	2.94644
$179$	−6.36964e7	−0.830098	−0.415049	−	0.909799i	$-0.636236\pi$
$179$	−6.36964e7	−0.830098	−0.415049	+	0.909799i	$0.636236\pi$
$180$	−2.67195e8	−3.41488
$181$	−2.18422e7	−0.273793	−0.136896	−	0.990585i	$-0.543713\pi$
$181$	−2.18422e7	−0.273793	−0.136896	+	0.990585i	$0.543713\pi$
$182$	1.43651e7	0.176628
$183$	−1.51793e8	−1.83093
$184$	2.17026e8	2.56832
$185$	−6.64741e7	−0.771882
$186$	−2.20070e8	−2.50764
$187$	2.46633e7	0.275807
$188$	−2.86259e8	−3.14200
$189$	8.95532e7	0.964861
$190$	−1.55545e8	−1.64520
$191$	1.15872e8	1.20326	0.601631	−	0.798774i	$-0.294518\pi$
$191$	1.15872e8	1.20326	0.601631	+	0.798774i	$0.294518\pi$
$192$	2.49725e8	2.54629
$193$	1.55286e8	1.55483	0.777414	−	0.628989i	$-0.216531\pi$
$193$	1.55286e8	1.55483	0.777414	+	0.628989i	$0.216531\pi$
$194$	1.09288e8	1.07465
$195$	−4.11147e7	−0.397078
$196$	2.76931e7	0.262709
$197$	1.08782e8	1.01374	0.506869	−	0.862023i	$-0.330803\pi$
$197$	1.08782e8	1.01374	0.506869	+	0.862023i	$0.330803\pi$
$198$	1.35332e8	1.23901
$199$	2.74085e7	0.246547	0.123273	−	0.992373i	$-0.460661\pi$
$199$	2.74085e7	0.246547	0.123273	+	0.992373i	$0.460661\pi$
$200$	−6.31468e7	−0.558144
$201$	3.52923e7	0.306544
$202$	2.46054e8	2.10039
$203$	−3.28107e7	−0.275283
$204$	−3.67427e8	−3.03016
$205$	9.31256e7	0.754971
$206$	−1.70682e8	−1.36036
$207$	5.53462e8	4.33702
$208$	−1.95395e7	−0.150554
$209$	5.10319e7	0.386660
$210$	−1.22362e8	−0.911756
$211$	9.93293e7	0.727929	0.363964	−	0.931413i	$-0.381423\pi$
$211$	9.93293e7	0.727929	0.363964	+	0.931413i	$0.381423\pi$
$212$	1.80761e8	1.30295
$213$	5.52206e7	0.391537
$214$	−1.41786e8	−0.988973
$215$	−6.83285e7	−0.468886
$216$	−5.34473e8	−3.60859
$217$	−4.60079e7	−0.305649
$218$	5.09000e8	3.32751
$219$	−4.01361e8	−2.58214
$220$	−6.96008e7	−0.440692
$221$	−3.98456e7	−0.248317
$222$	−5.01585e8	−3.07687
$223$	−5.87540e7	−0.354789	−0.177395	−	0.984140i	$-0.556767\pi$
$223$	−5.87540e7	−0.354789	−0.177395	+	0.984140i	$0.556767\pi$
$224$	3.17243e7	0.188592
$225$	−1.61038e8	−0.942516
$226$	−1.31835e8	−0.759718
$227$	1.29241e8	0.733345	0.366673	−	0.930350i	$-0.380497\pi$
$227$	1.29241e8	0.733345	0.366673	+	0.930350i	$0.380497\pi$
$228$	−7.60259e8	−4.24805
$229$	1.86669e8	1.02718	0.513592	−	0.858034i	$-0.328314\pi$
$229$	1.86669e8	1.02718	0.513592	+	0.858034i	$0.328314\pi$
$230$	−4.39427e8	−2.38144
$231$	4.01451e7	0.214284
$232$	1.95822e8	1.02956
$233$	−3.40765e8	−1.76486	−0.882428	−	0.470447i	$-0.844093\pi$
$233$	−3.40765e8	−1.76486	−0.882428	+	0.470447i	$0.844093\pi$
$234$	−2.18641e8	−1.11551
$235$	2.64426e8	1.32913
$236$	4.38713e7	0.217264
$237$	5.50117e8	2.68433
$238$	−1.18585e8	−0.570177
$239$	−2.68486e8	−1.27212	−0.636061	−	0.771638i	$-0.719438\pi$
$239$	−2.68486e8	−1.27212	−0.636061	+	0.771638i	$0.719438\pi$
$240$	1.66437e8	0.777159
$241$	−9.51070e7	−0.437676	−0.218838	−	0.975761i	$-0.570227\pi$
$241$	−9.51070e7	−0.437676	−0.218838	+	0.975761i	$0.570227\pi$
$242$	−3.36226e8	−1.52503
$243$	−3.80365e8	−1.70051
$244$	4.15143e8	1.82951
$245$	−2.55810e7	−0.111131
$246$	7.02686e8	3.00946
$247$	−8.24462e7	−0.348122
$248$	2.74585e8	1.14313
$249$	1.42216e8	0.583781
$250$	4.51679e8	1.82827
$251$	2.38071e8	0.950274	0.475137	−	0.879912i	$-0.342399\pi$
$251$	2.38071e8	0.950274	0.475137	+	0.879912i	$0.342399\pi$
$252$	−4.21496e8	−1.65917
$253$	1.44169e8	0.559695
$254$	4.42772e8	1.69536
$255$	3.39404e8	1.28182
$256$	−4.57301e8	−1.70358
$257$	−2.70376e8	−0.993580	−0.496790	−	0.867871i	$-0.665488\pi$
$257$	−2.70376e8	−0.993580	−0.496790	+	0.867871i	$0.665488\pi$
$258$	−5.15577e8	−1.86907
$259$	−1.04862e8	−0.375031
$260$	1.12446e8	0.396768
$261$	4.99387e8	1.73858
$262$	7.33777e8	2.52063
$263$	−4.80199e8	−1.62771	−0.813853	−	0.581070i	$-0.802634\pi$
$263$	−4.80199e8	−1.62771	−0.813853	+	0.581070i	$0.802634\pi$
$264$	−2.39595e8	−0.801426
$265$	−1.66975e8	−0.551176
$266$	−2.45369e8	−0.799345
$267$	−1.00097e9	−3.21832
$268$	−9.65219e7	−0.306305
$269$	5.58089e8	1.74812	0.874058	−	0.485822i	$-0.161480\pi$
$269$	5.58089e8	1.74812	0.874058	+	0.485822i	$0.161480\pi$
$270$	1.08219e9	3.34602
$271$	−3.34296e8	−1.02032	−0.510162	−	0.860078i	$-0.670415\pi$
$271$	−3.34296e8	−1.02032	−0.510162	+	0.860078i	$0.670415\pi$
$272$	1.61299e8	0.486006
$273$	−6.48577e7	−0.192927
$274$	−1.40129e7	−0.0411529
$275$	−4.19482e7	−0.121632
$276$	−2.14780e9	−6.14909
$277$	1.72977e7	0.0489000	0.0244500	−	0.999701i	$-0.492217\pi$
$277$	1.72977e7	0.0489000	0.0244500	+	0.999701i	$0.492217\pi$
$278$	7.48194e8	2.08861
$279$	7.00251e8	1.93036
$280$	1.52673e8	0.415633
$281$	6.56318e8	1.76458	0.882292	−	0.470703i	$-0.156000\pi$
$281$	6.56318e8	1.76458	0.882292	+	0.470703i	$0.156000\pi$
$282$	1.99525e9	5.29816
$283$	−4.00939e8	−1.05154	−0.525770	−	0.850627i	$-0.676223\pi$
$283$	−4.00939e8	−1.05154	−0.525770	+	0.850627i	$0.676223\pi$
$284$	−1.51025e8	−0.391231
$285$	7.02276e8	1.79701
$286$	−5.69529e7	−0.143958
$287$	1.46904e8	0.366815
$288$	−4.82851e8	−1.19108
$289$	−8.14111e7	−0.198400
$290$	−3.96494e8	−0.954648
$291$	−4.93429e8	−1.17381
$292$	1.09769e9	2.58013
$293$	−3.09442e8	−0.718692	−0.359346	−	0.933204i	$-0.617000\pi$
$293$	−3.09442e8	−0.718692	−0.359346	+	0.933204i	$0.617000\pi$
$294$	−1.93024e8	−0.442991
$295$	−4.05253e7	−0.0919072
$296$	6.25837e8	1.40262
$297$	−3.55049e8	−0.786394
$298$	−3.46299e7	−0.0758045
$299$	−2.32918e8	−0.503910
$300$	6.24932e8	1.33631
$301$	−1.07787e8	−0.227815
$302$	−1.37361e9	−2.86972
$303$	−1.11092e9	−2.29421
$304$	3.33751e8	0.681343
$305$	−3.83481e8	−0.773918
$306$	1.80489e9	3.60102
$307$	−8.07175e8	−1.59215	−0.796074	−	0.605200i	$-0.793093\pi$
$307$	−8.07175e8	−1.59215	−0.796074	+	0.605200i	$0.793093\pi$
$308$	−1.09794e8	−0.214117
$309$	7.70621e8	1.48589
$310$	−5.55972e8	−1.05995
$311$	−3.58067e8	−0.674998	−0.337499	−	0.941326i	$-0.609581\pi$
$311$	−3.58067e8	−0.674998	−0.337499	+	0.941326i	$0.609581\pi$
$312$	3.87085e8	0.721548
$313$	2.28625e8	0.421423	0.210712	−	0.977548i	$-0.432422\pi$
$313$	2.28625e8	0.421423	0.210712	+	0.977548i	$0.432422\pi$
$314$	−7.49484e8	−1.36618
$315$	3.89349e8	0.701863
$316$	−1.50453e9	−2.68223
$317$	−3.66493e8	−0.646187	−0.323094	−	0.946367i	$-0.604723\pi$
$317$	−3.66493e8	−0.646187	−0.323094	+	0.946367i	$0.604723\pi$
$318$	−1.25992e9	−2.19709
$319$	1.30084e8	0.224365
$320$	6.30892e8	1.07629
$321$	6.40154e8	1.08023
$322$	−6.93189e8	−1.15706
$323$	6.80598e8	1.12378
$324$	2.60192e9	4.24997
$325$	6.77707e7	0.109509
$326$	−2.95266e7	−0.0472011
$327$	−2.29810e9	−3.63457
$328$	−8.76755e8	−1.37189
$329$	4.17128e8	0.645778
$330$	4.85124e8	0.743112
$331$	−6.30923e7	−0.0956265	−0.0478132	−	0.998856i	$-0.515225\pi$
$331$	−6.30923e7	−0.0956265	−0.0478132	+	0.998856i	$0.515225\pi$
$332$	−3.88950e8	−0.583325
$333$	1.59602e9	2.36855
$334$	9.14681e8	1.34325
$335$	8.91605e7	0.129573
$336$	2.62551e8	0.377595
$337$	−6.80708e8	−0.968850	−0.484425	−	0.874833i	$-0.660971\pi$
$337$	−6.80708e8	−0.968850	−0.484425	+	0.874833i	$0.660971\pi$
$338$	9.20121e7	0.129609
$339$	5.95229e8	0.829822
$340$	−9.28247e8	−1.28082
$341$	1.82406e8	0.249114
$342$	3.73458e9	5.04836
$343$	−4.03536e7	−0.0539949
$344$	6.43296e8	0.852033
$345$	1.98399e9	2.60119
$346$	−1.88816e9	−2.45060
$347$	−1.01055e9	−1.29838	−0.649191	−	0.760625i	$-0.724892\pi$
$347$	−1.01055e9	−1.29838	−0.649191	+	0.760625i	$0.724892\pi$
$348$	−1.93795e9	−2.46499
$349$	−4.66558e8	−0.587512	−0.293756	−	0.955880i	$-0.594905\pi$
$349$	−4.66558e8	−0.587512	−0.293756	+	0.955880i	$0.594905\pi$
$350$	2.01693e8	0.251451
$351$	5.73610e8	0.708014
$352$	−1.25776e8	−0.153709
$353$	1.10221e9	1.33369	0.666843	−	0.745198i	$-0.267645\pi$
$353$	1.10221e9	1.33369	0.666843	+	0.745198i	$0.267645\pi$
$354$	−3.05787e8	−0.366360
$355$	1.39506e8	0.165499
$356$	2.73757e9	3.21581
$357$	5.35404e8	0.622791
$358$	−1.21423e9	−1.39865
$359$	1.43530e9	1.63723	0.818617	−	0.574339i	$-0.194741\pi$
$359$	1.43530e9	1.63723	0.818617	+	0.574339i	$0.194741\pi$
$360$	−2.32372e9	−2.62498
$361$	5.14384e8	0.575456
$362$	−4.16372e8	−0.461319
$363$	1.51804e9	1.66575
$364$	1.77381e8	0.192776
$365$	−1.01398e9	−1.09145
$366$	−2.89359e9	−3.08498
$367$	−2.60504e8	−0.275095	−0.137548	−	0.990495i	$-0.543922\pi$
$367$	−2.60504e8	−0.275095	−0.137548	+	0.990495i	$0.543922\pi$
$368$	9.42877e8	0.986251
$369$	−2.23591e9	−2.31666
$370$	−1.26718e9	−1.30056
$371$	−2.63400e8	−0.267798
$372$	−2.71743e9	−2.73690
$373$	5.70375e7	0.0569089	0.0284544	−	0.999595i	$-0.490941\pi$
$373$	5.70375e7	0.0569089	0.0284544	+	0.999595i	$0.490941\pi$
$374$	4.70150e8	0.464714
$375$	−2.03930e9	−1.99697
$376$	−2.48951e9	−2.41522
$377$	−2.10161e8	−0.202003
$378$	1.70713e9	1.62572
$379$	−1.33390e9	−1.25860	−0.629300	−	0.777163i	$-0.716658\pi$
$379$	−1.33390e9	−1.25860	−0.629300	+	0.777163i	$0.716658\pi$
$380$	−1.92068e9	−1.79561
$381$	−1.99909e9	−1.85180
$382$	2.20883e9	2.02740
$383$	−1.22400e9	−1.11323	−0.556614	−	0.830771i	$-0.687900\pi$
$383$	−1.22400e9	−1.11323	−0.556614	+	0.830771i	$0.687900\pi$
$384$	3.74151e9	3.37200
$385$	1.01420e8	0.0905758
$386$	2.96018e9	2.61977
$387$	1.64054e9	1.43880
$388$	1.34949e9	1.17290
$389$	1.55921e9	1.34301	0.671507	−	0.740998i	$-0.265647\pi$
$389$	1.55921e9	1.34301	0.671507	+	0.740998i	$0.265647\pi$
$390$	−7.83758e8	−0.669046
$391$	1.92275e9	1.62669
$392$	2.40839e8	0.201942
$393$	−3.31296e9	−2.75323
$394$	2.07368e9	1.70807
$395$	1.38978e9	1.13464
$396$	1.67109e9	1.35228
$397$	−4.39204e8	−0.352289	−0.176145	−	0.984364i	$-0.556363\pi$
$397$	−4.39204e8	−0.352289	−0.176145	+	0.984364i	$0.556363\pi$
$398$	5.22480e8	0.415412
$399$	1.10783e9	0.873106
$400$	−2.74343e8	−0.214331
$401$	−1.09759e9	−0.850034	−0.425017	−	0.905185i	$-0.639732\pi$
$401$	−1.09759e9	−0.850034	−0.425017	+	0.905185i	$0.639732\pi$
$402$	6.72767e8	0.516504
$403$	−2.94692e8	−0.224285
$404$	3.03829e9	2.29242
$405$	−2.40348e9	−1.79782
$406$	−6.25462e8	−0.463831
$407$	4.15741e8	0.305663
$408$	−3.19541e9	−2.32925
$409$	1.61412e8	0.116656	0.0583278	−	0.998297i	$-0.481423\pi$
$409$	1.61412e8	0.116656	0.0583278	+	0.998297i	$0.481423\pi$
$410$	1.77523e9	1.27207
$411$	6.32672e7	0.0449503
$412$	−2.10760e9	−1.48473
$413$	−6.39280e7	−0.0446546
$414$	1.05505e10	7.30755
$415$	3.59286e8	0.246758
$416$	2.03202e8	0.138389
$417$	−3.37805e9	−2.28134
$418$	9.72807e8	0.651493
$419$	−1.08282e9	−0.719127	−0.359563	−	0.933121i	$-0.617074\pi$
$419$	−1.08282e9	−0.719127	−0.359563	+	0.933121i	$0.617074\pi$
$420$	−1.51093e9	−0.995112
$421$	1.26221e9	0.824412	0.412206	−	0.911091i	$-0.364758\pi$
$421$	1.26221e9	0.824412	0.412206	+	0.911091i	$0.364758\pi$
$422$	1.89349e9	1.22650
$423$	−6.34878e9	−4.07849
$424$	1.57203e9	1.00157
$425$	−5.59451e8	−0.353509
$426$	1.05266e9	0.659710
$427$	−6.04935e8	−0.376020
$428$	−1.75078e9	−1.07939
$429$	2.57139e8	0.157242
$430$	−1.30253e9	−0.790036
$431$	1.81842e9	1.09402	0.547008	−	0.837127i	$-0.315767\pi$
$431$	1.81842e9	1.09402	0.547008	+	0.837127i	$0.315767\pi$
$432$	−2.32204e9	−1.38572
$433$	−1.15848e9	−0.685773	−0.342887	−	0.939377i	$-0.611405\pi$
$433$	−1.15848e9	−0.685773	−0.342887	+	0.939377i	$0.611405\pi$
$434$	−8.77036e8	−0.514996
$435$	1.79015e9	1.04274
$436$	6.28516e9	3.63173
$437$	3.97844e9	2.28049
$438$	−7.65103e9	−4.35071
$439$	−3.42765e9	−1.93362	−0.966809	−	0.255502i	$-0.917759\pi$
$439$	−3.42765e9	−1.93362	−0.966809	+	0.255502i	$0.917759\pi$
$440$	−6.05299e8	−0.338755
$441$	6.14191e8	0.341011
$442$	−7.59565e8	−0.418396
$443$	−4.61882e8	−0.252417	−0.126208	−	0.992004i	$-0.540281\pi$
$443$	−4.61882e8	−0.252417	−0.126208	+	0.992004i	$0.540281\pi$
$444$	−6.19360e9	−3.35817
$445$	−2.52878e9	−1.36035
$446$	−1.12001e9	−0.597792
$447$	1.56352e8	0.0827994
$448$	9.95220e8	0.522933
$449$	−1.29390e9	−0.674588	−0.337294	−	0.941399i	$-0.609512\pi$
$449$	−1.29390e9	−0.674588	−0.337294	+	0.941399i	$0.609512\pi$
$450$	−3.06982e9	−1.58807
$451$	−5.82425e8	−0.298966
$452$	−1.62791e9	−0.829174
$453$	6.20177e9	3.13453
$454$	2.46368e9	1.23563
$455$	−1.63853e8	−0.0815482
$456$	−6.61176e9	−3.26543
$457$	−1.28790e8	−0.0631210	−0.0315605	−	0.999502i	$-0.510048\pi$
$457$	−1.28790e8	−0.0631210	−0.0315605	+	0.999502i	$0.510048\pi$
$458$	3.55842e9	1.73073
$459$	−4.73519e9	−2.28556
$460$	−5.42607e9	−2.59916
$461$	−2.81077e9	−1.33620	−0.668101	−	0.744070i	$-0.732893\pi$
$461$	−2.81077e9	−1.33620	−0.668101	+	0.744070i	$0.732893\pi$
$462$	7.65274e8	0.361052
$463$	2.40896e8	0.112796	0.0563982	−	0.998408i	$-0.482038\pi$
$463$	2.40896e8	0.112796	0.0563982	+	0.998408i	$0.482038\pi$
$464$	8.50754e8	0.395359
$465$	2.51018e9	1.15776
$466$	−6.49591e9	−2.97365
$467$	−3.51134e8	−0.159538	−0.0797689	−	0.996813i	$-0.525418\pi$
$467$	−3.51134e8	−0.159538	−0.0797689	+	0.996813i	$0.525418\pi$
$468$	−2.69978e9	−1.21750
$469$	1.40649e8	0.0629552
$470$	5.04069e9	2.23948
$471$	3.38388e9	1.49225
$472$	3.81536e8	0.167009
$473$	4.27339e8	0.185677
$474$	1.04867e10	4.52289
$475$	−1.15758e9	−0.495593
$476$	−1.46429e9	−0.622305
$477$	4.00901e9	1.69131
$478$	−5.11808e9	−2.14343
$479$	1.52325e9	0.633281	0.316640	−	0.948546i	$-0.397445\pi$
$479$	1.52325e9	0.633281	0.316640	+	0.948546i	$0.397445\pi$
$480$	−1.73087e9	−0.714365
$481$	−6.71665e8	−0.275198
$482$	−1.81300e9	−0.737451
$483$	3.12971e9	1.26383
$484$	−4.15174e9	−1.66445
$485$	−1.24657e9	−0.496159
$486$	−7.25080e9	−2.86523
$487$	9.77957e8	0.383679	0.191840	−	0.981426i	$-0.438555\pi$
$487$	9.77957e8	0.383679	0.191840	+	0.981426i	$0.438555\pi$
$488$	3.61039e9	1.40632
$489$	1.33311e8	0.0515567
$490$	−4.87644e8	−0.187248
$491$	1.42118e9	0.541830	0.270915	−	0.962603i	$-0.412674\pi$
$491$	1.42118e9	0.541830	0.270915	+	0.962603i	$0.412674\pi$
$492$	8.67680e9	3.28460
$493$	1.73489e9	0.652090
$494$	−1.57165e9	−0.586559
$495$	−1.54364e9	−0.572042
$496$	1.19295e9	0.438970
$497$	2.20069e8	0.0804102
$498$	2.71102e9	0.983626
$499$	2.76996e9	0.997981	0.498990	−	0.866608i	$-0.333704\pi$
$499$	2.76996e9	0.997981	0.498990	+	0.866608i	$0.333704\pi$
$500$	5.57735e9	1.99541
$501$	−4.12973e9	−1.46720
$502$	4.53829e9	1.60114
$503$	4.40741e9	1.54417	0.772086	−	0.635517i	$-0.219213\pi$
$503$	4.40741e9	1.54417	0.772086	+	0.635517i	$0.219213\pi$
$504$	−3.66563e9	−1.27539
$505$	−2.80657e9	−0.969740
$506$	2.74826e9	0.943043
$507$	−4.15429e8	−0.141569
$508$	5.46737e9	1.85036
$509$	−2.30464e8	−0.0774624	−0.0387312	−	0.999250i	$-0.512332\pi$
$509$	−2.30464e8	−0.0774624	−0.0387312	+	0.999250i	$0.512332\pi$
$510$	6.46997e9	2.15976
$511$	−1.59953e9	−0.530296
$512$	−3.15299e9	−1.03819
$513$	−9.79778e9	−3.20418
$514$	−5.15411e9	−1.67411
$515$	1.94685e9	0.628070
$516$	−6.36638e9	−2.03994
$517$	−1.65377e9	−0.526331
$518$	−1.99895e9	−0.631899
$519$	8.52493e9	2.67673
$520$	9.77910e8	0.304991
$521$	2.00780e9	0.621997	0.310999	−	0.950410i	$-0.399337\pi$
$521$	2.00780e9	0.621997	0.310999	+	0.950410i	$0.399337\pi$
$522$	9.51968e9	2.92938
$523$	2.99708e9	0.916099	0.458050	−	0.888927i	$-0.348548\pi$
$523$	2.99708e9	0.916099	0.458050	+	0.888927i	$0.348548\pi$
$524$	9.06071e9	2.75108
$525$	−9.10633e8	−0.274654
$526$	−9.15390e9	−2.74256
$527$	2.43270e9	0.724021
$528$	−1.04093e9	−0.307753
$529$	7.83462e9	2.30103
$530$	−3.18300e9	−0.928690
$531$	9.72999e8	0.282021
$532$	−3.02983e9	−0.872424
$533$	9.40956e8	0.269168
$534$	−1.90811e10	−5.42263
$535$	1.61725e9	0.456603
$536$	−8.39424e8	−0.235453
$537$	5.48216e9	1.52771
$538$	1.06387e10	2.94544
$539$	1.59989e8	0.0440077
$540$	1.33629e10	3.65193
$541$	−3.87356e8	−0.105177	−0.0525884	−	0.998616i	$-0.516747\pi$
$541$	−3.87356e8	−0.105177	−0.0525884	+	0.998616i	$0.516747\pi$
$542$	−6.37259e9	−1.71917
$543$	1.87990e9	0.503888
$544$	−1.67744e9	−0.446737
$545$	−5.80580e9	−1.53629
$546$	−1.23636e9	−0.325066
$547$	−3.74739e9	−0.978978	−0.489489	−	0.872009i	$-0.662817\pi$
$547$	−3.74739e9	−0.978978	−0.489489	+	0.872009i	$0.662817\pi$
$548$	−1.73032e8	−0.0449152
$549$	9.20725e9	2.37480
$550$	−7.99646e8	−0.204941
$551$	3.58973e9	0.914180
$552$	−1.86788e10	−4.72674
$553$	2.19236e9	0.551282
$554$	3.29741e8	0.0823927
$555$	5.72123e9	1.42057
$556$	9.23874e9	2.27956
$557$	8.69904e8	0.213294	0.106647	−	0.994297i	$-0.465989\pi$
$557$	8.69904e8	0.213294	0.106647	+	0.994297i	$0.465989\pi$
$558$	1.33487e10	3.25251
$559$	−6.90402e8	−0.167171
$560$	6.63295e8	0.159606
$561$	−2.12270e9	−0.507596
$562$	1.25112e10	2.97319
$563$	3.77936e9	0.892563	0.446281	−	0.894893i	$-0.352748\pi$
$563$	3.77936e9	0.892563	0.446281	+	0.894893i	$0.352748\pi$
$564$	2.46374e10	5.78254
$565$	1.50375e9	0.350758
$566$	−7.64299e9	−1.77176
$567$	−3.79144e9	−0.873501
$568$	−1.31342e9	−0.300735
$569$	6.37372e9	1.45044	0.725220	−	0.688517i	$-0.241738\pi$
$569$	6.37372e9	1.45044	0.725220	+	0.688517i	$0.241738\pi$
$570$	1.33873e10	3.02782
$571$	1.03903e8	0.0233561	0.0116781	−	0.999932i	$-0.496283\pi$
$571$	1.03903e8	0.0233561	0.0116781	+	0.999932i	$0.496283\pi$
$572$	−7.03258e8	−0.157119
$573$	−9.97272e9	−2.21448
$574$	2.80039e9	0.618054
$575$	−3.27028e9	−0.717376
$576$	−1.51475e10	−3.30265
$577$	7.63241e8	0.165404	0.0827021	−	0.996574i	$-0.473645\pi$
$577$	7.63241e8	0.165404	0.0827021	+	0.996574i	$0.473645\pi$
$578$	−1.55192e9	−0.334289
$579$	−1.33650e10	−2.86151
$580$	−4.89593e9	−1.04193
$581$	5.66767e8	0.119891
$582$	−9.40610e9	−1.97778
$583$	1.04429e9	0.218264
$584$	9.54634e9	1.98332
$585$	2.49388e9	0.515027
$586$	−5.89881e9	−1.21094
$587$	−2.89106e9	−0.589961	−0.294981	−	0.955503i	$-0.595313\pi$
$587$	−2.89106e9	−0.589961	−0.294981	+	0.955503i	$0.595313\pi$
$588$	−2.38347e9	−0.483491
$589$	5.03360e9	1.01502
$590$	−7.72524e8	−0.154857
$591$	−9.36255e9	−1.86568
$592$	2.71897e9	0.538616
$593$	−6.37282e8	−0.125499	−0.0627495	−	0.998029i	$-0.519987\pi$
$593$	−6.37282e8	−0.125499	−0.0627495	+	0.998029i	$0.519987\pi$
$594$	−6.76820e9	−1.32501
$595$	1.35261e9	0.263248
$596$	−4.27612e8	−0.0827348
$597$	−2.35897e9	−0.453745
$598$	−4.44005e9	−0.849050
$599$	2.02809e9	0.385561	0.192781	−	0.981242i	$-0.438249\pi$
$599$	2.02809e9	0.385561	0.192781	+	0.981242i	$0.438249\pi$
$600$	5.43486e9	1.02721
$601$	−1.38106e9	−0.259509	−0.129755	−	0.991546i	$-0.541419\pi$
$601$	−1.38106e9	−0.259509	−0.129755	+	0.991546i	$0.541419\pi$
$602$	−2.05471e9	−0.383851
$603$	−2.14071e9	−0.397601
$604$	−1.69614e10	−3.13208
$605$	3.83510e9	0.704097
$606$	−2.11772e10	−3.86557
$607$	−5.28213e9	−0.958624	−0.479312	−	0.877644i	$-0.659114\pi$
$607$	−5.28213e9	−0.958624	−0.479312	+	0.877644i	$0.659114\pi$
$608$	−3.47087e9	−0.626291
$609$	2.82392e9	0.506632
$610$	−7.31020e9	−1.30399
$611$	2.67181e9	0.473872
$612$	2.22869e10	3.93024
$613$	−4.30516e9	−0.754879	−0.377440	−	0.926034i	$-0.623195\pi$
$613$	−4.30516e9	−0.754879	−0.377440	+	0.926034i	$0.623195\pi$
$614$	−1.53869e10	−2.68265
$615$	−8.01505e9	−1.38945
$616$	−9.54848e8	−0.164589
$617$	5.98875e9	1.02645	0.513226	−	0.858254i	$-0.328450\pi$
$617$	5.98875e9	1.02645	0.513226	+	0.858254i	$0.328450\pi$
$618$	1.46901e10	2.50361
$619$	5.70740e9	0.967211	0.483605	−	0.875286i	$-0.339327\pi$
$619$	5.70740e9	0.967211	0.483605	+	0.875286i	$0.339327\pi$
$620$	−6.86518e9	−1.15686
$621$	−2.76796e10	−4.63808
$622$	−6.82572e9	−1.13732
$623$	−3.98911e9	−0.660949
$624$	1.68170e9	0.277079
$625$	−2.74206e9	−0.449260
$626$	4.35821e9	0.710066
$627$	−4.39217e9	−0.711610
$628$	−9.25467e9	−1.49108
$629$	5.54463e9	0.888373
$630$	7.42206e9	1.18259
$631$	1.00384e10	1.59061	0.795305	−	0.606210i	$-0.207311\pi$
$631$	1.00384e10	1.59061	0.795305	+	0.606210i	$0.207311\pi$
$632$	−1.30845e10	−2.06180
$633$	−8.54898e9	−1.33968
$634$	−6.98636e9	−1.08878
$635$	−5.05039e9	−0.782738
$636$	−1.55576e10	−2.39796
$637$	−2.58475e8	−0.0396214
$638$	2.47975e9	0.378038
$639$	−3.34950e9	−0.507840
$640$	9.45235e9	1.42531
$641$	7.00300e9	1.05022	0.525111	−	0.851034i	$-0.324024\pi$
$641$	7.00300e9	1.05022	0.525111	+	0.851034i	$0.324024\pi$
$642$	1.22031e10	1.82011
$643$	−8.34621e9	−1.23809	−0.619043	−	0.785357i	$-0.712479\pi$
$643$	−8.34621e9	−1.23809	−0.619043	+	0.785357i	$0.712479\pi$
$644$	−8.55953e9	−1.26284
$645$	5.88083e9	0.862938
$646$	1.29741e10	1.89349
$647$	−3.70748e8	−0.0538162	−0.0269081	−	0.999638i	$-0.508566\pi$
$647$	−3.70748e8	−0.0538162	−0.0269081	+	0.999638i	$0.508566\pi$
$648$	2.26281e10	3.26691
$649$	2.53453e8	0.0363950
$650$	1.29189e9	0.184514
$651$	3.95977e9	0.562517
$652$	−3.64596e8	−0.0515164
$653$	−4.03555e8	−0.0567161	−0.0283581	−	0.999598i	$-0.509028\pi$
$653$	−4.03555e8	−0.0567161	−0.0283581	+	0.999598i	$0.509028\pi$
$654$	−4.38081e10	−6.12396
$655$	−8.36968e9	−1.16376
$656$	−3.80909e9	−0.526815
$657$	2.43452e10	3.34915
$658$	7.95159e9	1.08809
$659$	−3.72205e9	−0.506621	−0.253310	−	0.967385i	$-0.581519\pi$
$659$	−3.72205e9	−0.506621	−0.253310	+	0.967385i	$0.581519\pi$
$660$	5.99034e9	0.811050
$661$	−2.05999e9	−0.277435	−0.138717	−	0.990332i	$-0.544298\pi$
$661$	−2.05999e9	−0.277435	−0.138717	+	0.990332i	$0.544298\pi$
$662$	−1.20271e9	−0.161123
$663$	3.42939e9	0.457004
$664$	−3.38259e9	−0.448396
$665$	2.79875e9	0.369053
$666$	3.04245e10	3.99083
$667$	1.01413e10	1.32329
$668$	1.12945e10	1.46606
$669$	5.05678e9	0.652955
$670$	1.69964e9	0.218321
$671$	2.39837e9	0.306469
$672$	−2.73042e9	−0.347085
$673$	−1.09373e10	−1.38311	−0.691554	−	0.722325i	$-0.743074\pi$
$673$	−1.09373e10	−1.38311	−0.691554	+	0.722325i	$0.743074\pi$
$674$	−1.29762e10	−1.63244
$675$	8.05377e9	1.00794
$676$	1.13617e9	0.141459
$677$	1.43121e10	1.77273	0.886364	−	0.462989i	$-0.153223\pi$
$677$	1.43121e10	1.77273	0.886364	+	0.462989i	$0.153223\pi$
$678$	1.13467e10	1.39819
$679$	−1.96644e9	−0.241067
$680$	−8.07270e9	−0.984550
$681$	−1.11234e10	−1.34965
$682$	3.47716e9	0.419739
$683$	5.85021e9	0.702586	0.351293	−	0.936266i	$-0.385742\pi$
$683$	5.85021e9	0.702586	0.351293	+	0.936266i	$0.385742\pi$
$684$	4.61147e10	5.50990
$685$	1.59835e8	0.0190000
$686$	−7.69250e8	−0.0909773
$687$	−1.60661e10	−1.89043
$688$	2.79482e9	0.327186
$689$	−1.68714e9	−0.196510
$690$	3.78202e10	4.38281
$691$	−7.27490e9	−0.838791	−0.419396	−	0.907804i	$-0.637758\pi$
$691$	−7.27490e9	−0.838791	−0.419396	+	0.907804i	$0.637758\pi$
$692$	−2.33151e10	−2.67464
$693$	−2.43507e9	−0.277936
$694$	−1.92637e10	−2.18767
$695$	−8.53412e9	−0.964300
$696$	−1.68538e10	−1.89481
$697$	−7.76764e9	−0.868909
$698$	−8.89386e9	−0.989912
$699$	2.93286e10	3.24804
$700$	2.49052e9	0.274439
$701$	1.07123e10	1.17455	0.587273	−	0.809389i	$-0.300202\pi$
$701$	1.07123e10	1.17455	0.587273	+	0.809389i	$0.300202\pi$
$702$	1.09346e10	1.19295
$703$	1.14726e10	1.24543
$704$	−3.94572e9	−0.426208
$705$	−2.27584e10	−2.44613
$706$	2.10112e10	2.24716
$707$	−4.42731e9	−0.471164
$708$	−3.77587e9	−0.399854
$709$	−7.08677e9	−0.746770	−0.373385	−	0.927677i	$-0.621803\pi$
$709$	−7.08677e9	−0.746770	−0.373385	+	0.927677i	$0.621803\pi$
$710$	2.65937e9	0.278853
$711$	−3.33682e10	−3.48169
$712$	2.38079e10	2.47196
$713$	1.42204e10	1.46926
$714$	1.02063e10	1.04936
$715$	6.49622e8	0.0664645
$716$	−1.49933e10	−1.52652
$717$	2.31078e10	2.34122
$718$	2.73607e10	2.75861
$719$	−4.85731e9	−0.487354	−0.243677	−	0.969856i	$-0.578354\pi$
$719$	−4.85731e9	−0.487354	−0.243677	+	0.969856i	$0.578354\pi$
$720$	−1.00955e10	−1.00801
$721$	3.07113e9	0.305158
$722$	9.80556e9	0.969599
$723$	8.18558e9	0.805500
$724$	−5.14139e9	−0.503495
$725$	−2.95076e9	−0.287575
$726$	2.89380e10	2.80667
$727$	9.82914e9	0.948735	0.474368	−	0.880327i	$-0.342677\pi$
$727$	9.82914e9	0.948735	0.474368	+	0.880327i	$0.342677\pi$
$728$	1.54264e9	0.148185
$729$	8.56235e9	0.818552
$730$	−1.93291e10	−1.83900
$731$	5.69931e9	0.539649
$732$	−3.57302e10	−3.36703
$733$	1.21200e10	1.13668	0.568340	−	0.822793i	$-0.307586\pi$
$733$	1.21200e10	1.13668	0.568340	+	0.822793i	$0.307586\pi$
$734$	−4.96592e9	−0.463515
$735$	2.20168e9	0.204526
$736$	−9.80551e9	−0.906562
$737$	−5.57626e8	−0.0513106
$738$	−4.26226e10	−3.90339
$739$	−2.00332e10	−1.82598	−0.912988	−	0.407986i	$-0.866231\pi$
$739$	−2.00332e10	−1.82598	−0.912988	+	0.407986i	$0.866231\pi$
$740$	−1.56472e10	−1.41947
$741$	7.09591e9	0.640684
$742$	−5.02112e9	−0.451218
$743$	3.12428e9	0.279440	0.139720	−	0.990191i	$-0.455380\pi$
$743$	3.12428e9	0.279440	0.139720	+	0.990191i	$0.455380\pi$
$744$	−2.36328e10	−2.10382
$745$	3.94999e8	0.0349985
$746$	1.08729e9	0.0958870
$747$	−8.62633e9	−0.757188
$748$	5.80543e9	0.507200
$749$	2.55118e9	0.221848
$750$	−3.88747e10	−3.36475
$751$	1.48089e10	1.27580	0.637900	−	0.770120i	$-0.279803\pi$
$751$	1.48089e10	1.27580	0.637900	+	0.770120i	$0.279803\pi$
$752$	−1.08158e10	−0.927459
$753$	−2.04901e10	−1.74889
$754$	−4.00624e9	−0.340359
$755$	1.56678e10	1.32493
$756$	2.10797e10	1.77435
$757$	−5.89815e8	−0.0494174	−0.0247087	−	0.999695i	$-0.507866\pi$
$757$	−5.89815e8	−0.0494174	−0.0247087	+	0.999695i	$0.507866\pi$
$758$	−2.54279e10	−2.12064
$759$	−1.24082e10	−1.03006
$760$	−1.67036e10	−1.38026
$761$	−1.80400e10	−1.48385	−0.741924	−	0.670484i	$-0.766087\pi$
$761$	−1.80400e10	−1.48385	−0.741924	+	0.670484i	$0.766087\pi$
$762$	−3.81081e10	−3.12014
$763$	−9.15855e9	−0.746433
$764$	2.72747e10	2.21276
$765$	−2.05871e10	−1.66257
$766$	−2.33327e10	−1.87570
$767$	−4.09475e8	−0.0327675
$768$	3.93586e10	3.13527
$769$	1.52750e10	1.21126	0.605631	−	0.795746i	$-0.292921\pi$
$769$	1.52750e10	1.21126	0.605631	+	0.795746i	$0.292921\pi$
$770$	1.93335e9	0.152613
$771$	2.32705e10	1.82859
$772$	3.65525e10	2.85928
$773$	−1.06729e10	−0.831099	−0.415550	−	0.909570i	$-0.636411\pi$
$773$	−1.06729e10	−0.831099	−0.415550	+	0.909570i	$0.636411\pi$
$774$	3.12732e10	2.42426
$775$	−4.13762e9	−0.319297
$776$	1.17362e10	0.901593
$777$	9.02513e9	0.690208
$778$	2.97228e10	2.26288
$779$	−1.60724e10	−1.21814
$780$	−9.67788e9	−0.730213
$781$	−8.72500e8	−0.0655370
$782$	3.66528e10	2.74084
$783$	−2.49752e10	−1.85927
$784$	1.04633e9	0.0775469
$785$	8.54884e9	0.630759
$786$	−6.31540e10	−4.63897
$787$	2.31814e10	1.69522	0.847612	−	0.530616i	$-0.178039\pi$
$787$	2.31814e10	1.69522	0.847612	+	0.530616i	$0.178039\pi$
$788$	2.56059e10	1.86423
$789$	4.13293e10	2.99563
$790$	2.64931e10	1.91178
$791$	2.37214e9	0.170421
$792$	1.45330e10	1.03948
$793$	−3.87476e9	−0.275923
$794$	−8.37242e9	−0.593580
$795$	1.43710e10	1.01439
$796$	6.45161e9	0.453391
$797$	1.86371e10	1.30399	0.651996	−	0.758223i	$-0.273932\pi$
$797$	1.86371e10	1.30399	0.651996	+	0.758223i	$0.273932\pi$
$798$	2.11182e10	1.47112
$799$	−2.20559e10	−1.52972
$800$	2.85305e9	0.197013
$801$	6.07152e10	4.17430
$802$	−2.09231e10	−1.43224
$803$	6.34160e9	0.432209
$804$	8.30736e9	0.563724
$805$	7.90672e9	0.534208
$806$	−5.61763e9	−0.377903
$807$	−4.80331e10	−3.21724
$808$	2.64231e10	1.76216
$809$	1.53468e9	0.101905	0.0509527	−	0.998701i	$-0.483774\pi$
$809$	1.53468e9	0.101905	0.0509527	+	0.998701i	$0.483774\pi$
$810$	−4.58168e10	−3.02920
$811$	4.01760e9	0.264480	0.132240	−	0.991218i	$-0.457783\pi$
$811$	4.01760e9	0.264480	0.132240	+	0.991218i	$0.457783\pi$
$812$	−7.72324e9	−0.506236
$813$	2.87719e10	1.87781
$814$	7.92516e9	0.515019
$815$	3.36790e8	0.0217925
$816$	−1.38826e10	−0.894446
$817$	1.17927e10	0.756546
$818$	3.07696e9	0.196556
$819$	3.93405e9	0.250234
$820$	2.19206e10	1.38837
$821$	−2.04115e10	−1.28728	−0.643640	−	0.765329i	$-0.722577\pi$
$821$	−2.04115e10	−1.28728	−0.643640	+	0.765329i	$0.722577\pi$
$822$	1.20605e9	0.0757378
$823$	−5.94722e9	−0.371890	−0.185945	−	0.982560i	$-0.559535\pi$
$823$	−5.94722e9	−0.371890	−0.185945	+	0.982560i	$0.559535\pi$
$824$	−1.83292e10	−1.14129
$825$	3.61036e9	0.223852
$826$	−1.21864e9	−0.0752395
$827$	−9.84300e9	−0.605143	−0.302572	−	0.953127i	$-0.597845\pi$
$827$	−9.84300e9	−0.605143	−0.302572	+	0.953127i	$0.597845\pi$
$828$	1.30278e11	7.97563
$829$	−3.20244e10	−1.95227	−0.976135	−	0.217166i	$-0.930319\pi$
$829$	−3.20244e10	−1.95227	−0.976135	+	0.217166i	$0.930319\pi$
$830$	6.84897e9	0.415769
$831$	−1.48876e9	−0.0899956
$832$	6.37463e9	0.383728
$833$	2.13372e9	0.127903
$834$	−6.43949e10	−3.84388
$835$	−1.04331e10	−0.620171
$836$	1.20123e10	0.711055
$837$	−3.50207e10	−2.06436
$838$	−2.06414e10	−1.21167
$839$	−2.48443e10	−1.45231	−0.726157	−	0.687529i	$-0.758696\pi$
$839$	−2.48443e10	−1.45231	−0.726157	+	0.687529i	$0.758696\pi$
$840$	−1.31401e10	−0.764932
$841$	−8.09941e9	−0.469534
$842$	2.40612e10	1.38907
$843$	−5.64874e10	−3.24754
$844$	2.33809e10	1.33864
$845$	−1.04952e9	−0.0598400
$846$	−1.21025e11	−6.87194
$847$	6.04980e9	0.342097
$848$	6.82973e9	0.384608
$849$	3.45077e10	1.93526
$850$	−1.06647e10	−0.595636
$851$	3.24112e10	1.80277
$852$	1.29983e10	0.720023
$853$	−2.10601e9	−0.116182	−0.0580909	−	0.998311i	$-0.518501\pi$
$853$	−2.10601e9	−0.116182	−0.0580909	+	0.998311i	$0.518501\pi$
$854$	−1.15317e10	−0.633565
$855$	−4.25977e10	−2.33080
$856$	−1.52260e10	−0.829714
$857$	2.58468e10	1.40273	0.701366	−	0.712802i	$-0.252574\pi$
$857$	2.58468e10	1.40273	0.701366	+	0.712802i	$0.252574\pi$
$858$	4.90177e9	0.264940
$859$	5.54636e9	0.298560	0.149280	−	0.988795i	$-0.452304\pi$
$859$	5.54636e9	0.298560	0.149280	+	0.988795i	$0.452304\pi$
$860$	−1.60837e10	−0.862265
$861$	−1.26436e10	−0.675086
$862$	3.46640e10	1.84333
$863$	−2.34967e10	−1.24443	−0.622213	−	0.782848i	$-0.713766\pi$
$863$	−2.34967e10	−1.24443	−0.622213	+	0.782848i	$0.713766\pi$
$864$	2.41482e10	1.27376
$865$	2.15369e10	1.13143
$866$	−2.20838e10	−1.15548
$867$	7.00682e9	0.365136
$868$	−1.08297e10	−0.562078
$869$	−8.69198e9	−0.449313
$870$	3.41251e10	1.75694
$871$	9.00892e8	0.0461965
$872$	5.46602e10	2.79167
$873$	2.99297e10	1.52249
$874$	7.58400e10	3.84245
$875$	−8.12716e9	−0.410120
$876$	−9.44753e10	−4.74847
$877$	1.75591e10	0.879031	0.439516	−	0.898235i	$-0.355150\pi$
$877$	1.75591e10	0.879031	0.439516	+	0.898235i	$0.355150\pi$
$878$	−6.53403e10	−3.25800
$879$	2.66328e10	1.32268
$880$	−2.62974e9	−0.130084
$881$	−2.61430e10	−1.28807	−0.644036	−	0.764995i	$-0.722741\pi$
$881$	−2.61430e10	−1.28807	−0.644036	+	0.764995i	$0.722741\pi$
$882$	1.17082e10	0.574578
$883$	1.67966e10	0.821027	0.410514	−	0.911854i	$-0.365349\pi$
$883$	1.67966e10	0.821027	0.410514	+	0.911854i	$0.365349\pi$
$884$	−9.37915e9	−0.456647
$885$	3.48790e9	0.169146
$886$	−8.80473e9	−0.425303
$887$	−6.94232e9	−0.334019	−0.167010	−	0.985955i	$-0.553411\pi$
$887$	−6.94232e9	−0.334019	−0.167010	+	0.985955i	$0.553411\pi$
$888$	−5.38640e10	−2.58139
$889$	−7.96689e9	−0.380306
$890$	−4.82055e10	−2.29209
$891$	1.50318e10	0.711933
$892$	−1.38300e10	−0.652445
$893$	−4.56368e10	−2.14455
$894$	2.98050e9	0.139511
$895$	1.38498e10	0.645750
$896$	1.49109e10	0.692510
$897$	2.00465e10	0.927397
$898$	−2.46653e10	−1.13663
$899$	1.28310e10	0.588981
$900$	−3.79063e10	−1.73325
$901$	1.39274e10	0.634358
$902$	−1.11026e10	−0.503735
$903$	9.27690e9	0.419272
$904$	−1.41575e10	−0.637377
$905$	4.74927e9	0.212989
$906$	1.18223e11	5.28143
$907$	2.16539e10	0.963630	0.481815	−	0.876273i	$-0.339978\pi$
$907$	2.16539e10	0.963630	0.481815	+	0.876273i	$0.339978\pi$
$908$	3.04216e10	1.34860
$909$	6.73847e10	2.97569
$910$	−3.12348e9	−0.137402
$911$	2.77454e10	1.21584	0.607920	−	0.793999i	$-0.292004\pi$
$911$	2.77454e10	1.21584	0.607920	+	0.793999i	$0.292004\pi$
$912$	−2.87250e10	−1.25394
$913$	−2.24704e9	−0.0977156
$914$	−2.45508e9	−0.106354
$915$	3.30051e10	1.42432
$916$	4.39396e10	1.88896
$917$	−1.32030e10	−0.565432
$918$	−9.02656e10	−3.85099
$919$	−2.13902e10	−0.909098	−0.454549	−	0.890722i	$-0.650200\pi$
$919$	−2.13902e10	−0.909098	−0.454549	+	0.890722i	$0.650200\pi$
$920$	−4.71891e10	−1.99795
$921$	6.94712e10	2.93019
$922$	−5.35810e10	−2.25140
$923$	1.40960e9	0.0590050
$924$	9.44965e9	0.394061
$925$	−9.43049e9	−0.391776
$926$	4.59213e9	0.190053
$927$	−4.67433e10	−1.92726
$928$	−8.84747e9	−0.363414
$929$	2.10804e10	0.862628	0.431314	−	0.902202i	$-0.358050\pi$
$929$	2.10804e10	0.862628	0.431314	+	0.902202i	$0.358050\pi$
$930$	4.78509e10	1.95074
$931$	4.41498e9	0.179310
$932$	−8.02119e10	−3.24551
$933$	3.08177e10	1.24227
$934$	−6.69356e9	−0.268809
$935$	−5.36267e9	−0.214556
$936$	−2.34793e10	−0.935878
$937$	−3.81672e10	−1.51566	−0.757830	−	0.652452i	$-0.773740\pi$
$937$	−3.81672e10	−1.51566	−0.757830	+	0.652452i	$0.773740\pi$
$938$	2.68115e9	0.106075
$939$	−1.96771e10	−0.775588
$940$	6.22427e10	2.44422
$941$	2.33560e10	0.913764	0.456882	−	0.889527i	$-0.348966\pi$
$941$	2.33560e10	0.913764	0.456882	+	0.889527i	$0.348966\pi$
$942$	6.45059e10	2.51432
$943$	−4.54058e10	−1.76328
$944$	1.65760e9	0.0641324
$945$	−1.94720e10	−0.750584
$946$	8.14625e9	0.312852
$947$	−2.34273e10	−0.896392	−0.448196	−	0.893935i	$-0.647933\pi$
$947$	−2.34273e10	−0.896392	−0.448196	+	0.893935i	$0.647933\pi$
$948$	1.29491e11	4.93639
$949$	−1.02454e10	−0.389131
$950$	−2.20667e10	−0.835036
$951$	3.15430e10	1.18924
$952$	−1.27345e10	−0.478359
$953$	1.74489e10	0.653045	0.326523	−	0.945189i	$-0.394123\pi$
$953$	1.74489e10	0.653045	0.326523	+	0.945189i	$0.394123\pi$
$954$	7.64226e10	2.84972
$955$	−2.51945e10	−0.936041
$956$	−6.31983e10	−2.33939
$957$	−1.11959e10	−0.412922
$958$	2.90373e10	1.06703
$959$	2.52137e8	0.00923147
$960$	−5.42990e10	−1.98081
$961$	−9.52073e9	−0.346050
$962$	−1.28038e10	−0.463687
$963$	−3.88296e10	−1.40111
$964$	−2.23870e10	−0.804871
$965$	−3.37647e10	−1.20953
$966$	5.96607e10	2.12946
$967$	−7.58541e9	−0.269766	−0.134883	−	0.990862i	$-0.543066\pi$
$967$	−7.58541e9	−0.269766	−0.134883	+	0.990862i	$0.543066\pi$
$968$	−3.61065e10	−1.27945
$969$	−5.85771e10	−2.06821
$970$	−2.37631e10	−0.835990
$971$	−2.41799e10	−0.847592	−0.423796	−	0.905758i	$-0.639303\pi$
$971$	−2.41799e10	−0.847592	−0.423796	+	0.905758i	$0.639303\pi$
$972$	−8.95332e10	−3.12718
$973$	−1.34624e10	−0.468520
$974$	1.86425e10	0.646470
$975$	−5.83283e9	−0.201541
$976$	1.56855e10	0.540036
$977$	−6.35056e9	−0.217862	−0.108931	−	0.994049i	$-0.534743\pi$
$977$	−6.35056e9	−0.217862	−0.108931	+	0.994049i	$0.534743\pi$
$978$	2.54127e9	0.0868690
$979$	1.58155e10	0.538696
$980$	−6.02146e9	−0.204367
$981$	1.39395e11	4.71418
$982$	2.70915e10	0.912941
$983$	−9.54541e9	−0.320522	−0.160261	−	0.987075i	$-0.551234\pi$
$983$	−9.54541e9	−0.320522	−0.160261	+	0.987075i	$0.551234\pi$
$984$	7.54597e10	2.52483
$985$	−2.36530e10	−0.788606
$986$	3.30717e10	1.09872
$987$	−3.59010e10	−1.18849
$988$	−1.94068e10	−0.640184
$989$	3.33153e10	1.09511
$990$	−2.94260e10	−0.963847
$991$	−4.58841e10	−1.49763	−0.748815	−	0.662779i	$-0.769377\pi$
$991$	−4.58841e10	−1.49763	−0.748815	+	0.662779i	$0.769377\pi$
$992$	−1.24061e10	−0.403502
$993$	5.43017e9	0.175991
$994$	4.19511e9	0.135485
$995$	−5.95957e9	−0.191794
$996$	3.34758e10	1.07355
$997$	−6.08517e10	−1.94464	−0.972320	−	0.233652i	$-0.924932\pi$
$997$	−6.08517e10	−1.94464	−0.972320	+	0.233652i	$0.924932\pi$
$998$	5.28031e10	1.68152
$999$	−7.98196e10	−2.53297

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.d.1.10	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.d.1.10	✓	10	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q+19.0627 q^{2} -86.0671 q^{3} +235.388 q^{4} -217.435 q^{5} -1640.67 q^{6} -343.000 q^{7} +2047.10 q^{8} +5220.54 q^{9} +O(q^{10})\)	\(q+19.0627 q^{2} -86.0671 q^{3} +235.388 q^{4} -217.435 q^{5} -1640.67 q^{6} -343.000 q^{7} +2047.10 q^{8} +5220.54 q^{9} -4144.91 q^{10} +1359.88 q^{11} -20259.1 q^{12} -2197.00 q^{13} -6538.52 q^{14} +18714.0 q^{15} +8893.70 q^{16} +18136.4 q^{17} +99517.8 q^{18} +37526.7 q^{19} -51181.5 q^{20} +29521.0 q^{21} +25923.0 q^{22} +106016. q^{23} -176188. q^{24} -30846.9 q^{25} -41880.8 q^{26} -261088. q^{27} -80737.9 q^{28} +95658.1 q^{29} +356740. q^{30} +134134. q^{31} -92490.6 q^{32} -117041. q^{33} +345728. q^{34} +74580.3 q^{35} +1.22885e6 q^{36} +305719. q^{37} +715362. q^{38} +189089. q^{39} -445112. q^{40} -428291. q^{41} +562751. q^{42} +314247. q^{43} +320099. q^{44} -1.13513e6 q^{45} +2.02096e6 q^{46} -1.21612e6 q^{47} -765455. q^{48} +117649. q^{49} -588027. q^{50} -1.56094e6 q^{51} -517146. q^{52} +767929. q^{53} -4.97705e6 q^{54} -295686. q^{55} -702155. q^{56} -3.22982e6 q^{57} +1.82350e6 q^{58} +186379. q^{59} +4.40505e6 q^{60} +1.76366e6 q^{61} +2.55696e6 q^{62} -1.79065e6 q^{63} -2.90152e6 q^{64} +477705. q^{65} -2.23112e6 q^{66} -410055. q^{67} +4.26907e6 q^{68} -9.12451e6 q^{69} +1.42170e6 q^{70} -641600. q^{71} +1.06870e7 q^{72} +4.66335e6 q^{73} +5.82784e6 q^{74} +2.65491e6 q^{75} +8.83333e6 q^{76} -466439. q^{77} +3.60456e6 q^{78} -6.39172e6 q^{79} -1.93380e6 q^{80} +1.10538e7 q^{81} -8.16440e6 q^{82} -1.65238e6 q^{83} +6.94888e6 q^{84} -3.94348e6 q^{85} +5.99041e6 q^{86} -8.23301e6 q^{87} +2.78381e6 q^{88} +1.16301e7 q^{89} -2.16387e7 q^{90} +753571. q^{91} +2.49549e7 q^{92} -1.15445e7 q^{93} -2.31825e7 q^{94} -8.15963e6 q^{95} +7.96040e6 q^{96} +5.73307e6 q^{97} +2.24271e6 q^{98} +7.09932e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 - 101 * q^3 + 361 * q^4 + 226 * q^5 + 1105 * q^6 - 3430 * q^7 + 291 * q^8 + 12247 * q^9	\( 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9} + 2548 q^{10} + 451 q^{11} - 16241 q^{12} - 21970 q^{13} + 1029 q^{14} + 27184 q^{15} + 11897 q^{16} - 8654 q^{17} + 159348 q^{18} + 10130 q^{19} - 82012 q^{20} + 34643 q^{21} - 57863 q^{22} - 52155 q^{23} - 49227 q^{24} + 47190 q^{25} + 6591 q^{26} - 155171 q^{27} - 123823 q^{28} + 520154 q^{29} + 1070236 q^{30} + 692605 q^{31} + 149835 q^{32} + 436053 q^{33} + 1059060 q^{34} - 77518 q^{35} + 2843742 q^{36} - 20511 q^{37} + 1905286 q^{38} + 221897 q^{39} + 636320 q^{40} + 355049 q^{41} - 379015 q^{42} + 1256772 q^{43} - 687913 q^{44} + 1259926 q^{45} + 4043075 q^{46} + 1260721 q^{47} + 1128551 q^{48} + 1176490 q^{49} + 609035 q^{50} + 1411976 q^{51} - 793117 q^{52} + 928854 q^{53} + 6642607 q^{54} + 3423196 q^{55} - 99813 q^{56} + 3014966 q^{57} + 1612588 q^{58} + 3144446 q^{59} + 7738848 q^{60} + 6322923 q^{61} + 6545331 q^{62} - 4200721 q^{63} - 6629943 q^{64} - 496522 q^{65} - 14343317 q^{66} + 3944507 q^{67} - 1787356 q^{68} - 148281 q^{69} - 873964 q^{70} + 6032248 q^{71} + 9760866 q^{72} + 1248533 q^{73} - 8263279 q^{74} + 1573413 q^{75} + 1788254 q^{76} - 154693 q^{77} - 2427685 q^{78} - 14947605 q^{79} - 9147616 q^{80} + 25716334 q^{81} - 6987095 q^{82} - 14177784 q^{83} + 5570663 q^{84} - 11788444 q^{85} + 8748840 q^{86} - 29484448 q^{87} - 15390723 q^{88} + 6734836 q^{89} + 5994972 q^{90} + 7535710 q^{91} - 24493215 q^{92} + 17307847 q^{93} - 22760149 q^{94} - 9329708 q^{95} - 36488483 q^{96} - 12365397 q^{97} - 352947 q^{98} - 43198042 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 101 * q^3 + 361 * q^4 + 226 * q^5 + 1105 * q^6 - 3430 * q^7 + 291 * q^8 + 12247 * q^9 + 2548 * q^10 + 451 * q^11 - 16241 * q^12 - 21970 * q^13 + 1029 * q^14 + 27184 * q^15 + 11897 * q^16 - 8654 * q^17 + 159348 * q^18 + 10130 * q^19 - 82012 * q^20 + 34643 * q^21 - 57863 * q^22 - 52155 * q^23 - 49227 * q^24 + 47190 * q^25 + 6591 * q^26 - 155171 * q^27 - 123823 * q^28 + 520154 * q^29 + 1070236 * q^30 + 692605 * q^31 + 149835 * q^32 + 436053 * q^33 + 1059060 * q^34 - 77518 * q^35 + 2843742 * q^36 - 20511 * q^37 + 1905286 * q^38 + 221897 * q^39 + 636320 * q^40 + 355049 * q^41 - 379015 * q^42 + 1256772 * q^43 - 687913 * q^44 + 1259926 * q^45 + 4043075 * q^46 + 1260721 * q^47 + 1128551 * q^48 + 1176490 * q^49 + 609035 * q^50 + 1411976 * q^51 - 793117 * q^52 + 928854 * q^53 + 6642607 * q^54 + 3423196 * q^55 - 99813 * q^56 + 3014966 * q^57 + 1612588 * q^58 + 3144446 * q^59 + 7738848 * q^60 + 6322923 * q^61 + 6545331 * q^62 - 4200721 * q^63 - 6629943 * q^64 - 496522 * q^65 - 14343317 * q^66 + 3944507 * q^67 - 1787356 * q^68 - 148281 * q^69 - 873964 * q^70 + 6032248 * q^71 + 9760866 * q^72 + 1248533 * q^73 - 8263279 * q^74 + 1573413 * q^75 + 1788254 * q^76 - 154693 * q^77 - 2427685 * q^78 - 14947605 * q^79 - 9147616 * q^80 + 25716334 * q^81 - 6987095 * q^82 - 14177784 * q^83 + 5570663 * q^84 - 11788444 * q^85 + 8748840 * q^86 - 29484448 * q^87 - 15390723 * q^88 + 6734836 * q^89 + 5994972 * q^90 + 7535710 * q^91 - 24493215 * q^92 + 17307847 * q^93 - 22760149 * q^94 - 9329708 * q^95 - 36488483 * q^96 - 12365397 * q^97 - 352947 * q^98 - 43198042 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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