LMFDB - Embedded newform 91.8.a.d.1.5

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			1.5
Root			$3.66228$ 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)

$f(q)$	$=$	$q-3.66228 q^{2} +42.3449 q^{3} -114.588 q^{4} -251.753 q^{5} -155.079 q^{6} -343.000 q^{7} +888.424 q^{8} -393.907 q^{9} +O(q^{10})$	\(q-3.66228 q^{2} +42.3449 q^{3} -114.588 q^{4} -251.753 q^{5} -155.079 q^{6} -343.000 q^{7} +888.424 q^{8} -393.907 q^{9} +921.992 q^{10} -2926.60 q^{11} -4852.21 q^{12} -2197.00 q^{13} +1256.16 q^{14} -10660.5 q^{15} +11413.6 q^{16} +27794.8 q^{17} +1442.60 q^{18} +34316.1 q^{19} +28847.8 q^{20} -14524.3 q^{21} +10718.0 q^{22} -21674.2 q^{23} +37620.3 q^{24} -14745.2 q^{25} +8046.03 q^{26} -109288. q^{27} +39303.6 q^{28} +115035. q^{29} +39041.7 q^{30} +13017.1 q^{31} -155518. q^{32} -123927. q^{33} -101793. q^{34} +86351.4 q^{35} +45136.9 q^{36} +481169. q^{37} -125675. q^{38} -93031.8 q^{39} -223664. q^{40} +316118. q^{41} +53192.1 q^{42} +75163.9 q^{43} +335353. q^{44} +99167.4 q^{45} +79377.0 q^{46} +500395. q^{47} +483307. q^{48} +117649. q^{49} +54001.2 q^{50} +1.17697e6 q^{51} +251749. q^{52} -466960. q^{53} +400245. q^{54} +736782. q^{55} -304730. q^{56} +1.45311e6 q^{57} -421289. q^{58} +1.34767e6 q^{59} +1.22156e6 q^{60} +2.22618e6 q^{61} -47672.2 q^{62} +135110. q^{63} -891386. q^{64} +553102. q^{65} +453855. q^{66} -2.36745e6 q^{67} -3.18495e6 q^{68} -917792. q^{69} -316243. q^{70} +619229. q^{71} -349957. q^{72} +4.50615e6 q^{73} -1.76217e6 q^{74} -624386. q^{75} -3.93221e6 q^{76} +1.00383e6 q^{77} +340709. q^{78} -188250. q^{79} -2.87340e6 q^{80} -3.76633e6 q^{81} -1.15771e6 q^{82} -5.10902e6 q^{83} +1.66431e6 q^{84} -6.99745e6 q^{85} -275271. q^{86} +4.87114e6 q^{87} -2.60007e6 q^{88} +1.60970e6 q^{89} -363179. q^{90} +753571. q^{91} +2.48360e6 q^{92} +551207. q^{93} -1.83259e6 q^{94} -8.63921e6 q^{95} -6.58540e6 q^{96} -811101. q^{97} -430864. q^{98} +1.15281e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.66228	−0.323703	−0.161851	−	0.986815i	$-0.551747\pi$
$2$	−3.66228	−0.323703	−0.161851	+	0.986815i	$0.551747\pi$
$3$	42.3449	0.905476	0.452738	−	0.891644i	$-0.350447\pi$
$3$	42.3449	0.905476	0.452738	+	0.891644i	$0.350447\pi$
$4$	−114.588	−0.895216
$5$	−251.753	−0.900700	−0.450350	−	0.892852i	$-0.648701\pi$
$5$	−251.753	−0.900700	−0.450350	+	0.892852i	$0.648701\pi$
$6$	−155.079	−0.293105
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	888.424	0.613487
$9$	−393.907	−0.180113
$10$	921.992	0.291559
$11$	−2926.60	−0.662963	−0.331482	−	0.943462i	$-0.607549\pi$
$11$	−2926.60	−0.662963	−0.331482	+	0.943462i	$0.607549\pi$
$12$	−4852.21	−0.810597
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	1256.16	0.122348
$15$	−10660.5	−0.815563
$16$	11413.6	0.696629
$17$	27794.8	1.37212	0.686061	−	0.727544i	$-0.259338\pi$
$17$	27794.8	1.37212	0.686061	+	0.727544i	$0.259338\pi$
$18$	1442.60	0.0583031
$19$	34316.1	1.14779	0.573893	−	0.818930i	$-0.305433\pi$
$19$	34316.1	1.14779	0.573893	+	0.818930i	$0.305433\pi$
$20$	28847.8	0.806322
$21$	−14524.3	−0.342238
$22$	10718.0	0.214603
$23$	−21674.2	−0.371446	−0.185723	−	0.982602i	$-0.559463\pi$
$23$	−21674.2	−0.371446	−0.185723	+	0.982602i	$0.559463\pi$
$24$	37620.3	0.555498
$25$	−14745.2	−0.188739
$26$	8046.03	0.0897790
$27$	−109288.	−1.06856
$28$	39303.6	0.338360
$29$	115035.	0.875862	0.437931	−	0.899009i	$-0.355711\pi$
$29$	115035.	0.875862	0.437931	+	0.899009i	$0.355711\pi$
$30$	39041.7	0.264000
$31$	13017.1	0.0784779	0.0392390	−	0.999230i	$-0.487507\pi$
$31$	13017.1	0.0784779	0.0392390	+	0.999230i	$0.487507\pi$
$32$	−155518.	−0.838988
$33$	−123927.	−0.600298
$34$	−101793.	−0.444160
$35$	86351.4	0.340433
$36$	45136.9	0.161240
$37$	481169.	1.56168	0.780839	−	0.624733i	$-0.214792\pi$
$37$	481169.	1.56168	0.780839	+	0.624733i	$0.214792\pi$
$38$	−125675.	−0.371542
$39$	−93031.8	−0.251134
$40$	−223664.	−0.552568
$41$	316118.	0.716317	0.358158	−	0.933661i	$-0.383405\pi$
$41$	316118.	0.716317	0.358158	+	0.933661i	$0.383405\pi$
$42$	53192.1	0.110783
$43$	75163.9	0.144168	0.0720841	−	0.997399i	$-0.477035\pi$
$43$	75163.9	0.144168	0.0720841	+	0.997399i	$0.477035\pi$
$44$	335353.	0.593496
$45$	99167.4	0.162228
$46$	79377.0	0.120238
$47$	500395.	0.703025	0.351512	−	0.936183i	$-0.385668\pi$
$47$	500395.	0.703025	0.351512	+	0.936183i	$0.385668\pi$
$48$	483307.	0.630781
$49$	117649.	0.142857
$50$	54001.2	0.0610954
$51$	1.17697e6	1.24242
$52$	251749.	0.248288
$53$	−466960.	−0.430838	−0.215419	−	0.976522i	$-0.569112\pi$
$53$	−466960.	−0.430838	−0.215419	+	0.976522i	$0.569112\pi$
$54$	400245.	0.345897
$55$	736782.	0.597131
$56$	−304730.	−0.231876
$57$	1.45311e6	1.03929
$58$	−421289.	−0.283519
$59$	1.34767e6	0.854280	0.427140	−	0.904186i	$-0.359521\pi$
$59$	1.34767e6	0.854280	0.427140	+	0.904186i	$0.359521\pi$
$60$	1.22156e6	0.730105
$61$	2.22618e6	1.25576	0.627879	−	0.778311i	$-0.283923\pi$
$61$	2.22618e6	1.25576	0.627879	+	0.778311i	$0.283923\pi$
$62$	−47672.2	−0.0254035
$63$	135110.	0.0680763
$64$	−891386.	−0.425046
$65$	553102.	0.249809
$66$	453855.	0.194318
$67$	−2.36745e6	−0.961654	−0.480827	−	0.876816i	$-0.659663\pi$
$67$	−2.36745e6	−0.961654	−0.480827	+	0.876816i	$0.659663\pi$
$68$	−3.18495e6	−1.22835
$69$	−917792.	−0.336335
$70$	−316243.	−0.110199
$71$	619229.	0.205327	0.102664	−	0.994716i	$-0.467263\pi$
$71$	619229.	0.205327	0.102664	+	0.994716i	$0.467263\pi$
$72$	−349957.	−0.110497
$73$	4.50615e6	1.35574	0.677868	−	0.735183i	$-0.262904\pi$
$73$	4.50615e6	1.35574	0.677868	+	0.735183i	$0.262904\pi$
$74$	−1.76217e6	−0.505520
$75$	−624386.	−0.170899
$76$	−3.93221e6	−1.02752
$77$	1.00383e6	0.250577
$78$	340709.	0.0812928
$79$	−188250.	−0.0429577	−0.0214789	−	0.999769i	$-0.506837\pi$
$79$	−188250.	−0.0429577	−0.0214789	+	0.999769i	$0.506837\pi$
$80$	−2.87340e6	−0.627454
$81$	−3.76633e6	−0.787446
$82$	−1.15771e6	−0.231874
$83$	−5.10902e6	−0.980763	−0.490381	−	0.871508i	$-0.663143\pi$
$83$	−5.10902e6	−0.980763	−0.490381	+	0.871508i	$0.663143\pi$
$84$	1.66431e6	0.306377
$85$	−6.99745e6	−1.23587
$86$	−275271.	−0.0466677
$87$	4.87114e6	0.793072
$88$	−2.60007e6	−0.406720
$89$	1.60970e6	0.242036	0.121018	−	0.992650i	$-0.461384\pi$
$89$	1.60970e6	0.242036	0.121018	+	0.992650i	$0.461384\pi$
$90$	−363179.	−0.0525136
$91$	753571.	0.104828
$92$	2.48360e6	0.332524
$93$	551207.	0.0710599
$94$	−1.83259e6	−0.227571
$95$	−8.63921e6	−1.03381
$96$	−6.58540e6	−0.759684
$97$	−811101.	−0.0902348	−0.0451174	−	0.998982i	$-0.514366\pi$
$97$	−811101.	−0.0902348	−0.0451174	+	0.998982i	$0.514366\pi$
$98$	−430864.	−0.0462433
$99$	1.15281e6	0.119408
$100$	1.68962e6	0.168962
$101$	−2.55347e6	−0.246608	−0.123304	−	0.992369i	$-0.539349\pi$
$101$	−2.55347e6	−0.246608	−0.123304	+	0.992369i	$0.539349\pi$
$102$	−4.31040e6	−0.402176
$103$	1.20270e7	1.08449	0.542245	−	0.840220i	$-0.317574\pi$
$103$	1.20270e7	1.08449	0.542245	+	0.840220i	$0.317574\pi$
$104$	−1.95187e6	−0.170151
$105$	3.65654e6	0.308254
$106$	1.71014e6	0.139464
$107$	4.99152e6	0.393904	0.196952	−	0.980413i	$-0.436896\pi$
$107$	4.99152e6	0.393904	0.196952	+	0.980413i	$0.436896\pi$
$108$	1.25231e7	0.956596
$109$	−1.63927e7	−1.21243	−0.606217	−	0.795299i	$-0.707314\pi$
$109$	−1.63927e7	−1.21243	−0.606217	+	0.795299i	$0.707314\pi$
$110$	−2.69830e6	−0.193293
$111$	2.03751e7	1.41406
$112$	−3.91485e6	−0.263301
$113$	−6.66918e6	−0.434808	−0.217404	−	0.976082i	$-0.569759\pi$
$113$	−6.66918e6	−0.434808	−0.217404	+	0.976082i	$0.569759\pi$
$114$	−5.32171e6	−0.336422
$115$	5.45655e6	0.334561
$116$	−1.31816e7	−0.784086
$117$	865414.	0.0499544
$118$	−4.93553e6	−0.276533
$119$	−9.53363e6	−0.518614
$120$	−9.47103e6	−0.500337
$121$	−1.09222e7	−0.560480
$122$	−8.15290e6	−0.406493
$123$	1.33860e7	0.648608
$124$	−1.49160e6	−0.0702547
$125$	2.33804e7	1.07070
$126$	−494811.	−0.0220365
$127$	−4.30152e7	−1.86341	−0.931707	−	0.363212i	$-0.881680\pi$
$127$	−4.30152e7	−1.86341	−0.931707	+	0.363212i	$0.881680\pi$
$128$	2.31708e7	0.976577
$129$	3.18281e6	0.130541
$130$	−2.02562e6	−0.0808640
$131$	−647043.	−0.0251469	−0.0125734	−	0.999921i	$-0.504002\pi$
$131$	−647043.	−0.0251469	−0.0125734	+	0.999921i	$0.504002\pi$
$132$	1.42005e7	0.537396
$133$	−1.17704e7	−0.433822
$134$	8.67026e6	0.311290
$135$	2.75137e7	0.962456
$136$	2.46936e7	0.841780
$137$	−1.45963e7	−0.484976	−0.242488	−	0.970154i	$-0.577963\pi$
$137$	−1.45963e7	−0.484976	−0.242488	+	0.970154i	$0.577963\pi$
$138$	3.36121e6	0.108873
$139$	−1.58494e7	−0.500567	−0.250284	−	0.968173i	$-0.580524\pi$
$139$	−1.58494e7	−0.500567	−0.250284	+	0.968173i	$0.580524\pi$
$140$	−9.89481e6	−0.304761
$141$	2.11892e7	0.636572
$142$	−2.26779e6	−0.0664651
$143$	6.42975e6	0.183873
$144$	−4.49589e6	−0.125472
$145$	−2.89604e7	−0.788889
$146$	−1.65028e7	−0.438856
$147$	4.98184e6	0.129354
$148$	−5.51360e7	−1.39804
$149$	−4.00703e7	−0.992363	−0.496182	−	0.868219i	$-0.665265\pi$
$149$	−4.00703e7	−0.992363	−0.496182	+	0.868219i	$0.665265\pi$
$150$	2.28668e6	0.0553204
$151$	7.97551e7	1.88512	0.942561	−	0.334035i	$-0.108410\pi$
$151$	7.97551e7	1.88512	0.942561	+	0.334035i	$0.108410\pi$
$152$	3.04873e7	0.704152
$153$	−1.09486e7	−0.247137
$154$	−3.67629e6	−0.0811124
$155$	−3.27709e6	−0.0706851
$156$	1.06603e7	0.224819
$157$	−1.82222e7	−0.375796	−0.187898	−	0.982189i	$-0.560167\pi$
$157$	−1.82222e7	−0.375796	−0.187898	+	0.982189i	$0.560167\pi$
$158$	689426.	0.0139055
$159$	−1.97734e7	−0.390114
$160$	3.91522e7	0.755677
$161$	7.43425e6	0.140393
$162$	1.37934e7	0.254899
$163$	9.13519e7	1.65219	0.826097	−	0.563528i	$-0.190556\pi$
$163$	9.13519e7	1.65219	0.826097	+	0.563528i	$0.190556\pi$
$164$	−3.62232e7	−0.641258
$165$	3.11990e7	0.540688
$166$	1.87107e7	0.317476
$167$	6.09136e7	1.01206	0.506030	−	0.862516i	$-0.331112\pi$
$167$	6.09136e7	1.01206	0.506030	+	0.862516i	$0.331112\pi$
$168$	−1.29037e7	−0.209958
$169$	4.82681e6	0.0769231
$170$	2.56266e7	0.400055
$171$	−1.35174e7	−0.206731
$172$	−8.61286e6	−0.129062
$173$	1.26181e8	1.85282	0.926408	−	0.376520i	$-0.122880\pi$
$173$	1.26181e8	1.85282	0.926408	+	0.376520i	$0.122880\pi$
$174$	−1.78395e7	−0.256720
$175$	5.05762e6	0.0713367
$176$	−3.34030e7	−0.461839
$177$	5.70668e7	0.773530
$178$	−5.89517e6	−0.0783478
$179$	2.72460e7	0.355073	0.177536	−	0.984114i	$-0.443187\pi$
$179$	2.72460e7	0.355073	0.177536	+	0.984114i	$0.443187\pi$
$180$	−1.13634e7	−0.145229
$181$	8.01601e7	1.00481	0.502404	−	0.864633i	$-0.332449\pi$
$181$	8.01601e7	1.00481	0.502404	+	0.864633i	$0.332449\pi$
$182$	−2.75979e6	−0.0339333
$183$	9.42674e7	1.13706
$184$	−1.92559e7	−0.227877
$185$	−1.21136e8	−1.40660
$186$	−2.01868e6	−0.0230023
$187$	−8.13445e7	−0.909667
$188$	−5.73391e7	−0.629359
$189$	3.74859e7	0.403879
$190$	3.16392e7	0.334648
$191$	6.94392e7	0.721088	0.360544	−	0.932742i	$-0.382591\pi$
$191$	6.94392e7	0.721088	0.360544	+	0.932742i	$0.382591\pi$
$192$	−3.77457e7	−0.384869
$193$	4.35489e7	0.436040	0.218020	−	0.975944i	$-0.430040\pi$
$193$	4.35489e7	0.436040	0.218020	+	0.975944i	$0.430040\pi$
$194$	2.97048e6	0.0292093
$195$	2.34211e7	0.226196
$196$	−1.34811e7	−0.127888
$197$	8.12640e7	0.757298	0.378649	−	0.925540i	$-0.376389\pi$
$197$	8.12640e7	0.757298	0.378649	+	0.925540i	$0.376389\pi$
$198$	−4.22191e6	−0.0386528
$199$	−3.16714e6	−0.0284893	−0.0142446	−	0.999899i	$-0.504534\pi$
$199$	−3.16714e6	−0.0284893	−0.0142446	+	0.999899i	$0.504534\pi$
$200$	−1.31000e7	−0.115789
$201$	−1.00249e8	−0.870755
$202$	9.35154e6	0.0798276
$203$	−3.94569e7	−0.331045
$204$	−1.34866e8	−1.11224
$205$	−7.95837e7	−0.645187
$206$	−4.40461e7	−0.351053
$207$	8.53762e6	0.0669022
$208$	−2.50756e7	−0.193210
$209$	−1.00430e8	−0.760940
$210$	−1.33913e7	−0.0997826
$211$	−1.68103e8	−1.23193	−0.615966	−	0.787772i	$-0.711234\pi$
$211$	−1.68103e8	−1.23193	−0.615966	+	0.787772i	$0.711234\pi$
$212$	5.35079e7	0.385694
$213$	2.62212e7	0.185919
$214$	−1.82804e7	−0.127508
$215$	−1.89228e7	−0.129852
$216$	−9.70944e7	−0.655550
$217$	−4.46486e6	−0.0296619
$218$	6.00347e7	0.392469
$219$	1.90812e8	1.22759
$220$	−8.44262e7	−0.534562
$221$	−6.10653e7	−0.380558
$222$	−7.46192e7	−0.457736
$223$	7.63326e7	0.460938	0.230469	−	0.973080i	$-0.425974\pi$
$223$	7.63326e7	0.460938	0.230469	+	0.973080i	$0.425974\pi$
$224$	5.33427e7	0.317108
$225$	5.80826e6	0.0339944
$226$	2.44244e7	0.140749
$227$	4.57199e7	0.259427	0.129714	−	0.991552i	$-0.458594\pi$
$227$	4.57199e7	0.259427	0.129714	+	0.991552i	$0.458594\pi$
$228$	−1.66509e8	−0.930392
$229$	1.99587e8	1.09827	0.549133	−	0.835735i	$-0.314958\pi$
$229$	1.99587e8	1.09827	0.549133	+	0.835735i	$0.314958\pi$
$230$	−1.99834e7	−0.108298
$231$	4.25069e7	0.226891
$232$	1.02200e8	0.537330
$233$	6.01329e7	0.311434	0.155717	−	0.987802i	$-0.450231\pi$
$233$	6.01329e7	0.311434	0.155717	+	0.987802i	$0.450231\pi$
$234$	−3.16939e6	−0.0161704
$235$	−1.25976e8	−0.633215
$236$	−1.54426e8	−0.764765
$237$	−7.97145e6	−0.0388972
$238$	3.49148e7	0.167877
$239$	2.93560e8	1.39093	0.695464	−	0.718561i	$-0.255199\pi$
$239$	2.93560e8	1.39093	0.695464	+	0.718561i	$0.255199\pi$
$240$	−1.21674e8	−0.568144
$241$	−4.20654e8	−1.93582	−0.967910	−	0.251297i	$-0.919143\pi$
$241$	−4.20654e8	−1.93582	−0.967910	+	0.251297i	$0.919143\pi$
$242$	4.00000e7	0.181429
$243$	7.95285e7	0.355550
$244$	−2.55093e8	−1.12418
$245$	−2.96185e7	−0.128671
$246$	−4.90232e7	−0.209956
$247$	−7.53926e7	−0.318339
$248$	1.15647e7	0.0481452
$249$	−2.16341e8	−0.888057
$250$	−8.56256e7	−0.346588
$251$	4.62621e8	1.84658	0.923289	−	0.384106i	$-0.125490\pi$
$251$	4.62621e8	1.84658	0.923289	+	0.384106i	$0.125490\pi$
$252$	−1.54820e7	−0.0609430
$253$	6.34318e7	0.246255
$254$	1.57534e8	0.603192
$255$	−2.96306e8	−1.11905
$256$	2.92394e7	0.108925
$257$	−2.21165e8	−0.812738	−0.406369	−	0.913709i	$-0.633205\pi$
$257$	−2.21165e8	−0.812738	−0.406369	+	0.913709i	$0.633205\pi$
$258$	−1.16563e7	−0.0422565
$259$	−1.65041e8	−0.590259
$260$	−6.33787e7	−0.223633
$261$	−4.53130e7	−0.157754
$262$	2.36965e6	0.00814011
$263$	5.16193e8	1.74971	0.874857	−	0.484381i	$-0.160955\pi$
$263$	5.16193e8	1.74971	0.874857	+	0.484381i	$0.160955\pi$
$264$	−1.10100e8	−0.368275
$265$	1.17559e8	0.388056
$266$	4.31067e7	0.140430
$267$	6.81626e7	0.219158
$268$	2.71280e8	0.860888
$269$	−5.39449e8	−1.68973	−0.844865	−	0.534979i	$-0.820320\pi$
$269$	−5.39449e8	−1.68973	−0.844865	+	0.534979i	$0.820320\pi$
$270$	−1.00763e8	−0.311550
$271$	−1.64435e8	−0.501882	−0.250941	−	0.968002i	$-0.580740\pi$
$271$	−1.64435e8	−0.501882	−0.250941	+	0.968002i	$0.580740\pi$
$272$	3.17238e8	0.955860
$273$	3.19099e7	0.0949197
$274$	5.34557e7	0.156988
$275$	4.31535e7	0.125127
$276$	1.05168e8	0.301093
$277$	−4.88376e8	−1.38062	−0.690312	−	0.723512i	$-0.742527\pi$
$277$	−4.88376e8	−1.38062	−0.690312	+	0.723512i	$0.742527\pi$
$278$	5.80451e7	0.162035
$279$	−5.12752e6	−0.0141349
$280$	7.67167e7	0.208851
$281$	5.32145e8	1.43073	0.715365	−	0.698751i	$-0.246261\pi$
$281$	5.32145e8	1.43073	0.715365	+	0.698751i	$0.246261\pi$
$282$	−7.76008e7	−0.206060
$283$	−6.50933e8	−1.70720	−0.853599	−	0.520930i	$-0.825585\pi$
$283$	−6.50933e8	−1.70720	−0.853599	+	0.520930i	$0.825585\pi$
$284$	−7.09560e7	−0.183813
$285$	−3.65827e8	−0.936091
$286$	−2.35475e7	−0.0595202
$287$	−1.08428e8	−0.270742
$288$	6.12596e7	0.151113
$289$	3.62215e8	0.882721
$290$	1.06061e8	0.255366
$291$	−3.43460e7	−0.0817054
$292$	−5.16349e8	−1.21368
$293$	6.98043e8	1.62123	0.810616	−	0.585578i	$-0.199132\pi$
$293$	6.98043e8	1.62123	0.810616	+	0.585578i	$0.199132\pi$
$294$	−1.82449e7	−0.0418722
$295$	−3.39279e8	−0.769450
$296$	4.27482e8	0.958069
$297$	3.19844e8	0.708419
$298$	1.46749e8	0.321231
$299$	4.76182e7	0.103021
$300$	7.15470e7	0.152991
$301$	−2.57812e7	−0.0544905
$302$	−2.92086e8	−0.610219
$303$	−1.08127e8	−0.223297
$304$	3.91670e8	0.799581
$305$	−5.60448e8	−1.13106
$306$	4.00968e7	0.0799990
$307$	2.24284e6	0.00442398	0.00221199	−	0.999998i	$-0.499296\pi$
$307$	2.24284e6	0.00442398	0.00221199	+	0.999998i	$0.499296\pi$
$308$	−1.15026e8	−0.224320
$309$	5.09281e8	0.981981
$310$	1.20016e7	0.0228810
$311$	1.35544e8	0.255517	0.127758	−	0.991805i	$-0.459222\pi$
$311$	1.35544e8	0.255517	0.127758	+	0.991805i	$0.459222\pi$
$312$	−8.26517e7	−0.154067
$313$	4.00803e8	0.738798	0.369399	−	0.929271i	$-0.379564\pi$
$313$	4.00803e8	0.738798	0.369399	+	0.929271i	$0.379564\pi$
$314$	6.67347e7	0.121646
$315$	−3.40144e7	−0.0613164
$316$	2.15712e7	0.0384564
$317$	9.32010e8	1.64329	0.821643	−	0.570002i	$-0.193058\pi$
$317$	9.32010e8	1.64329	0.821643	+	0.570002i	$0.193058\pi$
$318$	7.24157e7	0.126281
$319$	−3.36661e8	−0.580665
$320$	2.24409e8	0.382839
$321$	2.11366e8	0.356670
$322$	−2.72263e7	−0.0454457
$323$	9.53812e8	1.57490
$324$	4.31575e8	0.704935
$325$	3.23953e7	0.0523468
$326$	−3.34556e8	−0.534820
$327$	−6.94149e8	−1.09783
$328$	2.80846e8	0.439451
$329$	−1.71636e8	−0.265718
$330$	−1.14259e8	−0.175022
$331$	4.77925e8	0.724372	0.362186	−	0.932106i	$-0.382031\pi$
$331$	4.77925e8	0.724372	0.362186	+	0.932106i	$0.382031\pi$
$332$	5.85430e8	0.877995
$333$	−1.89536e8	−0.281278
$334$	−2.23083e8	−0.327607
$335$	5.96013e8	0.866162
$336$	−1.65774e8	−0.238413
$337$	3.00880e8	0.428242	0.214121	−	0.976807i	$-0.431311\pi$
$337$	3.00880e8	0.428242	0.214121	+	0.976807i	$0.431311\pi$
$338$	−1.76771e7	−0.0249002
$339$	−2.82406e8	−0.393709
$340$	8.01821e8	1.10637
$341$	−3.80958e7	−0.0520280
$342$	4.95044e7	0.0669195
$343$	−4.03536e7	−0.0539949
$344$	6.67774e7	0.0884454
$345$	2.31057e8	0.302937
$346$	−4.62110e8	−0.599762
$347$	1.04913e8	0.134796	0.0673980	−	0.997726i	$-0.478530\pi$
$347$	1.04913e8	0.134796	0.0673980	+	0.997726i	$0.478530\pi$
$348$	−5.58172e8	−0.709971
$349$	−1.54627e8	−0.194713	−0.0973567	−	0.995250i	$-0.531039\pi$
$349$	−1.54627e8	−0.194713	−0.0973567	+	0.995250i	$0.531039\pi$
$350$	−1.85224e7	−0.0230919
$351$	2.40106e8	0.296366
$352$	4.55140e8	0.556218
$353$	1.29968e9	1.57262	0.786312	−	0.617830i	$-0.211988\pi$
$353$	1.29968e9	1.57262	0.786312	+	0.617830i	$0.211988\pi$
$354$	−2.08995e8	−0.250394
$355$	−1.55893e8	−0.184939
$356$	−1.84452e8	−0.216675
$357$	−4.03701e8	−0.469592
$358$	−9.97825e7	−0.114938
$359$	−1.35313e9	−1.54351	−0.771755	−	0.635920i	$-0.780621\pi$
$359$	−1.35313e9	−1.54351	−0.771755	+	0.635920i	$0.780621\pi$
$360$	8.81028e7	0.0995247
$361$	2.83726e8	0.317413
$362$	−2.93569e8	−0.325259
$363$	−4.62498e8	−0.507501
$364$	−8.63500e7	−0.0938442
$365$	−1.13444e9	−1.22111
$366$	−3.45234e8	−0.368069
$367$	−1.45759e8	−0.153923	−0.0769617	−	0.997034i	$-0.524522\pi$
$367$	−1.45759e8	−0.153923	−0.0769617	+	0.997034i	$0.524522\pi$
$368$	−2.47380e8	−0.258760
$369$	−1.24521e8	−0.129018
$370$	4.43633e8	0.455322
$371$	1.60167e8	0.162842
$372$	−6.31616e7	−0.0636140
$373$	8.21893e8	0.820039	0.410019	−	0.912077i	$-0.365522\pi$
$373$	8.21893e8	0.820039	0.410019	+	0.912077i	$0.365522\pi$
$374$	2.97906e8	0.294462
$375$	9.90041e8	0.969491
$376$	4.44563e8	0.431297
$377$	−2.52731e8	−0.242920
$378$	−1.37284e8	−0.130737
$379$	−3.42342e8	−0.323015	−0.161508	−	0.986871i	$-0.551636\pi$
$379$	−3.42342e8	−0.323015	−0.161508	+	0.986871i	$0.551636\pi$
$380$	9.89947e8	0.925485
$381$	−1.82148e9	−1.68728
$382$	−2.54306e8	−0.233418
$383$	−3.24840e8	−0.295443	−0.147722	−	0.989029i	$-0.547194\pi$
$383$	−3.24840e8	−0.295443	−0.147722	+	0.989029i	$0.547194\pi$
$384$	9.81166e8	0.884267
$385$	−2.52716e8	−0.225694
$386$	−1.59488e8	−0.141147
$387$	−2.96076e7	−0.0259666
$388$	9.29422e7	0.0807796
$389$	−7.62926e8	−0.657141	−0.328571	−	0.944479i	$-0.606567\pi$
$389$	−7.62926e8	−0.657141	−0.328571	+	0.944479i	$0.606567\pi$
$390$	−8.57745e7	−0.0732204
$391$	−6.02431e8	−0.509669
$392$	1.04522e8	0.0876410
$393$	−2.73990e7	−0.0227699
$394$	−2.97612e8	−0.245139
$395$	4.73927e7	0.0386920
$396$	−1.32098e8	−0.106896
$397$	3.17876e8	0.254971	0.127486	−	0.991840i	$-0.459309\pi$
$397$	3.17876e8	0.254971	0.127486	+	0.991840i	$0.459309\pi$
$398$	1.15990e7	0.00922207
$399$	−4.98418e8	−0.392816
$400$	−1.68296e8	−0.131481
$401$	−1.32306e8	−0.102464	−0.0512322	−	0.998687i	$-0.516315\pi$
$401$	−1.32306e8	−0.102464	−0.0512322	+	0.998687i	$0.516315\pi$
$402$	3.67142e8	0.281866
$403$	−2.85985e7	−0.0217659
$404$	2.92597e8	0.220767
$405$	9.48187e8	0.709253
$406$	1.44502e8	0.107160
$407$	−1.40819e9	−1.03533
$408$	1.04565e9	0.762211
$409$	−1.26662e9	−0.915405	−0.457702	−	0.889105i	$-0.651328\pi$
$409$	−1.26662e9	−0.915405	−0.457702	+	0.889105i	$0.651328\pi$
$410$	2.91458e8	0.208849
$411$	−6.18078e8	−0.439134
$412$	−1.37814e9	−0.970854
$413$	−4.62249e8	−0.322887
$414$	−3.12672e7	−0.0216564
$415$	1.28621e9	0.883373
$416$	3.41673e8	0.232693
$417$	−6.71144e8	−0.453252
$418$	3.67802e8	0.246319
$419$	−8.44907e8	−0.561125	−0.280563	−	0.959836i	$-0.590521\pi$
$419$	−8.44907e8	−0.561125	−0.280563	+	0.959836i	$0.590521\pi$
$420$	−4.18995e8	−0.275954
$421$	9.22607e8	0.602601	0.301300	−	0.953529i	$-0.402579\pi$
$421$	9.22607e8	0.602601	0.301300	+	0.953529i	$0.402579\pi$
$422$	6.15641e8	0.398780
$423$	−1.97109e8	−0.126624
$424$	−4.14859e8	−0.264314
$425$	−4.09842e8	−0.258973
$426$	−9.60294e7	−0.0601826
$427$	−7.63580e8	−0.474632
$428$	−5.71967e8	−0.352629
$429$	2.72267e8	0.166493
$430$	6.93005e7	0.0420336
$431$	6.54823e8	0.393961	0.196981	−	0.980407i	$-0.436886\pi$
$431$	6.54823e8	0.393961	0.196981	+	0.980407i	$0.436886\pi$
$432$	−1.24737e9	−0.744393
$433$	−3.21139e9	−1.90101	−0.950507	−	0.310702i	$-0.899436\pi$
$433$	−3.21139e9	−1.90101	−0.950507	+	0.310702i	$0.899436\pi$
$434$	1.63516e7	0.00960163
$435$	−1.22632e9	−0.714320
$436$	1.87840e9	1.08539
$437$	−7.43775e8	−0.426340
$438$	−6.98809e8	−0.397374
$439$	−2.88389e9	−1.62687	−0.813434	−	0.581658i	$-0.802404\pi$
$439$	−2.88389e9	−1.62687	−0.813434	+	0.581658i	$0.802404\pi$
$440$	6.54575e8	0.366332
$441$	−4.63428e7	−0.0257304
$442$	2.23638e8	0.123188
$443$	1.64951e9	0.901452	0.450726	−	0.892662i	$-0.351165\pi$
$443$	1.64951e9	0.901452	0.450726	+	0.892662i	$0.351165\pi$
$444$	−2.33473e9	−1.26589
$445$	−4.05247e8	−0.218002
$446$	−2.79551e8	−0.149207
$447$	−1.69677e9	−0.898561
$448$	3.05745e8	0.160652
$449$	8.94046e8	0.466120	0.233060	−	0.972462i	$-0.425126\pi$
$449$	8.94046e8	0.466120	0.233060	+	0.972462i	$0.425126\pi$
$450$	−2.12715e7	−0.0110041
$451$	−9.25151e8	−0.474892
$452$	7.64206e8	0.389248
$453$	3.37722e9	1.70693
$454$	−1.67439e8	−0.0839773
$455$	−1.89714e8	−0.0944190
$456$	1.29098e9	0.637593
$457$	2.84806e9	1.39586	0.697930	−	0.716166i	$-0.254105\pi$
$457$	2.84806e9	1.39586	0.697930	+	0.716166i	$0.254105\pi$
$458$	−7.30943e8	−0.355512
$459$	−3.03765e9	−1.46620
$460$	−6.25254e8	−0.299505
$461$	−8.96558e8	−0.426212	−0.213106	−	0.977029i	$-0.568358\pi$
$461$	−8.96558e8	−0.426212	−0.213106	+	0.977029i	$0.568358\pi$
$462$	−1.55672e8	−0.0734453
$463$	7.62965e8	0.357249	0.178625	−	0.983917i	$-0.442835\pi$
$463$	7.62965e8	0.357249	0.178625	+	0.983917i	$0.442835\pi$
$464$	1.31296e9	0.610151
$465$	−1.38768e8	−0.0640037
$466$	−2.20223e8	−0.100812
$467$	2.52211e9	1.14592	0.572960	−	0.819583i	$-0.305795\pi$
$467$	2.52211e9	1.14592	0.572960	+	0.819583i	$0.305795\pi$
$468$	−9.91658e7	−0.0447200
$469$	8.12035e8	0.363471
$470$	4.61360e8	0.204973
$471$	−7.71617e8	−0.340274
$472$	1.19730e9	0.524090
$473$	−2.19975e8	−0.0955783
$474$	2.91937e7	0.0125911
$475$	−5.06000e8	−0.216632
$476$	1.09244e9	0.464271
$477$	1.83939e8	0.0775996
$478$	−1.07510e9	−0.450247
$479$	7.30274e7	0.0303607	0.0151803	−	0.999885i	$-0.495168\pi$
$479$	7.30274e7	0.0303607	0.0151803	+	0.999885i	$0.495168\pi$
$480$	1.65790e9	0.684247
$481$	−1.05713e9	−0.433131
$482$	1.54055e9	0.626631
$483$	3.14803e8	0.127123
$484$	1.25155e9	0.501750
$485$	2.04197e8	0.0812745
$486$	−2.91256e8	−0.115093
$487$	−1.94137e9	−0.761653	−0.380826	−	0.924647i	$-0.624360\pi$
$487$	−1.94137e9	−0.761653	−0.380826	+	0.924647i	$0.624360\pi$
$488$	1.97779e9	0.770391
$489$	3.86829e9	1.49602
$490$	1.08471e8	0.0416513
$491$	4.02561e9	1.53478	0.767391	−	0.641180i	$-0.221555\pi$
$491$	4.02561e9	1.53478	0.767391	+	0.641180i	$0.221555\pi$
$492$	−1.53387e9	−0.580644
$493$	3.19737e9	1.20179
$494$	2.76109e8	0.103047
$495$	−2.90224e8	−0.107551
$496$	1.48571e8	0.0546700
$497$	−2.12396e8	−0.0776065
$498$	7.92301e8	0.287467
$499$	−2.79089e9	−1.00552	−0.502761	−	0.864426i	$-0.667682\pi$
$499$	−2.79089e9	−1.00552	−0.502761	+	0.864426i	$0.667682\pi$
$500$	−2.67911e9	−0.958506
$501$	2.57938e9	0.916397
$502$	−1.69425e9	−0.597743
$503$	4.23835e9	1.48494	0.742470	−	0.669879i	$-0.233654\pi$
$503$	4.23835e9	1.48494	0.742470	+	0.669879i	$0.233654\pi$
$504$	1.20035e8	0.0417639
$505$	6.42846e8	0.222120
$506$	−2.32305e8	−0.0797135
$507$	2.04391e8	0.0696520
$508$	4.92902e9	1.66816
$509$	3.80443e9	1.27873	0.639363	−	0.768905i	$-0.279198\pi$
$509$	3.80443e9	1.27873	0.639363	+	0.768905i	$0.279198\pi$
$510$	1.08516e9	0.362240
$511$	−1.54561e9	−0.512420
$512$	−3.07295e9	−1.01184
$513$	−3.75035e9	−1.22648
$514$	8.09968e8	0.263086
$515$	−3.02783e9	−0.976801
$516$	−3.64711e8	−0.116862
$517$	−1.46446e9	−0.466080
$518$	6.04426e8	0.191068
$519$	5.34312e9	1.67768
$520$	4.91389e8	0.153255
$521$	7.33979e8	0.227380	0.113690	−	0.993516i	$-0.463733\pi$
$521$	7.33979e8	0.227380	0.113690	+	0.993516i	$0.463733\pi$
$522$	1.65949e8	0.0510655
$523$	−3.33450e9	−1.01924	−0.509619	−	0.860400i	$-0.670213\pi$
$523$	−3.33450e9	−1.01924	−0.509619	+	0.860400i	$0.670213\pi$
$524$	7.41432e7	0.0225119
$525$	2.14164e8	0.0645936
$526$	−1.89044e9	−0.566388
$527$	3.61808e8	0.107681
$528$	−1.41445e9	−0.418185
$529$	−2.93505e9	−0.862028
$530$	−4.30533e8	−0.125615
$531$	−5.30855e8	−0.153867
$532$	1.34875e9	0.388365
$533$	−6.94510e8	−0.198671
$534$	−2.49631e8	−0.0709420
$535$	−1.25663e9	−0.354789
$536$	−2.10330e9	−0.589962
$537$	1.15373e9	0.321510
$538$	1.97561e9	0.546971
$539$	−3.44312e8	−0.0947091
$540$	−3.15273e9	−0.861606
$541$	−7.29442e8	−0.198062	−0.0990308	−	0.995084i	$-0.531574\pi$
$541$	−7.29442e8	−0.198062	−0.0990308	+	0.995084i	$0.531574\pi$
$542$	6.02207e8	0.162461
$543$	3.39437e9	0.909830
$544$	−4.32260e9	−1.15119
$545$	4.12692e9	1.09204
$546$	−1.16863e8	−0.0307258
$547$	−7.28347e9	−1.90275	−0.951377	−	0.308028i	$-0.900331\pi$
$547$	−7.28347e9	−1.90275	−0.951377	+	0.308028i	$0.900331\pi$
$548$	1.67255e9	0.434158
$549$	−8.76908e8	−0.226178
$550$	−1.58040e8	−0.0405040
$551$	3.94755e9	1.00530
$552$	−8.15389e8	−0.206337
$553$	6.45699e7	0.0162365
$554$	1.78857e9	0.446912
$555$	−5.12949e9	−1.27365
$556$	1.81615e9	0.448116
$557$	1.25258e9	0.307124	0.153562	−	0.988139i	$-0.450926\pi$
$557$	1.25258e9	0.307124	0.153562	+	0.988139i	$0.450926\pi$
$558$	1.87784e7	0.00457551
$559$	−1.65135e8	−0.0399851
$560$	9.85578e8	0.237155
$561$	−3.44453e9	−0.823682
$562$	−1.94886e9	−0.463131
$563$	−6.94124e9	−1.63930	−0.819649	−	0.572866i	$-0.805832\pi$
$563$	−6.94124e9	−1.63930	−0.819649	+	0.572866i	$0.805832\pi$
$564$	−2.42802e9	−0.569870
$565$	1.67899e9	0.391632
$566$	2.38390e9	0.552625
$567$	1.29185e9	0.297627
$568$	5.50138e8	0.125966
$569$	2.86322e9	0.651570	0.325785	−	0.945444i	$-0.394371\pi$
$569$	2.86322e9	0.651570	0.325785	+	0.945444i	$0.394371\pi$
$570$	1.33976e9	0.303016
$571$	5.45875e9	1.22706	0.613532	−	0.789670i	$-0.289748\pi$
$571$	5.45875e9	1.22706	0.613532	+	0.789670i	$0.289748\pi$
$572$	−7.36770e8	−0.164606
$573$	2.94040e9	0.652928
$574$	3.97095e8	0.0876401
$575$	3.19591e8	0.0701063
$576$	3.51123e8	0.0765563
$577$	4.92177e9	1.06661	0.533306	−	0.845923i	$-0.320950\pi$
$577$	4.92177e9	1.06661	0.533306	+	0.845923i	$0.320950\pi$
$578$	−1.32653e9	−0.285739
$579$	1.84407e9	0.394824
$580$	3.31850e9	0.706227
$581$	1.75239e9	0.370693
$582$	1.25785e8	0.0264483
$583$	1.36661e9	0.285630
$584$	4.00337e9	0.831727
$585$	−2.17871e8	−0.0449939
$586$	−2.55643e9	−0.524798
$587$	−6.14056e9	−1.25307	−0.626534	−	0.779394i	$-0.715527\pi$
$587$	−6.14056e9	−1.25307	−0.626534	+	0.779394i	$0.715527\pi$
$588$	−5.70857e8	−0.115800
$589$	4.46696e8	0.0900759
$590$	1.24254e9	0.249073
$591$	3.44112e9	0.685715
$592$	5.49185e9	1.08791
$593$	9.20031e7	0.0181180	0.00905901	−	0.999959i	$-0.497116\pi$
$593$	9.20031e7	0.0181180	0.00905901	+	0.999959i	$0.497116\pi$
$594$	−1.17136e9	−0.229317
$595$	2.40012e9	0.467115
$596$	4.59156e9	0.888380
$597$	−1.34112e8	−0.0257964
$598$	−1.74391e8	−0.0333481
$599$	−1.30152e9	−0.247432	−0.123716	−	0.992318i	$-0.539481\pi$
$599$	−1.30152e9	−0.247432	−0.123716	+	0.992318i	$0.539481\pi$
$600$	−5.54720e8	−0.104844
$601$	−9.25912e8	−0.173984	−0.0869920	−	0.996209i	$-0.527725\pi$
$601$	−9.25912e8	−0.173984	−0.0869920	+	0.996209i	$0.527725\pi$
$602$	9.44181e7	0.0176387
$603$	9.32555e8	0.173206
$604$	−9.13896e9	−1.68759
$605$	2.74969e9	0.504824
$606$	3.95990e8	0.0722820
$607$	−4.23987e9	−0.769471	−0.384736	−	0.923027i	$-0.625707\pi$
$607$	−4.23987e9	−0.769471	−0.384736	+	0.923027i	$0.625707\pi$
$608$	−5.33678e9	−0.962979
$609$	−1.67080e9	−0.299753
$610$	2.05252e9	0.366128
$611$	−1.09937e9	−0.194984
$612$	1.25457e9	0.221241
$613$	7.05872e8	0.123770	0.0618848	−	0.998083i	$-0.480289\pi$
$613$	7.05872e8	0.123770	0.0618848	+	0.998083i	$0.480289\pi$
$614$	−8.21389e6	−0.00143206
$615$	−3.36996e9	−0.584201
$616$	8.91823e8	0.153726
$617$	−2.81933e9	−0.483223	−0.241611	−	0.970373i	$-0.577676\pi$
$617$	−2.81933e9	−0.483223	−0.241611	+	0.970373i	$0.577676\pi$
$618$	−1.86513e9	−0.317870
$619$	7.25478e8	0.122944	0.0614719	−	0.998109i	$-0.480421\pi$
$619$	7.25478e8	0.122944	0.0614719	+	0.998109i	$0.480421\pi$
$620$	3.75515e8	0.0632785
$621$	2.36874e9	0.396914
$622$	−4.96401e8	−0.0827116
$623$	−5.52127e8	−0.0914810
$624$	−1.06182e9	−0.174947
$625$	−4.73412e9	−0.775638
$626$	−1.46785e9	−0.239151
$627$	−4.25269e9	−0.689013
$628$	2.08804e9	0.336418
$629$	1.33740e10	2.14281
$630$	1.24570e8	0.0198483
$631$	6.24005e9	0.988748	0.494374	−	0.869249i	$-0.335397\pi$
$631$	6.24005e9	0.988748	0.494374	+	0.869249i	$0.335397\pi$
$632$	−1.67246e8	−0.0263540
$633$	−7.11831e9	−1.11549
$634$	−3.41328e9	−0.531937
$635$	1.08292e10	1.67838
$636$	2.26579e9	0.349236
$637$	−2.58475e8	−0.0396214
$638$	1.23295e9	0.187963
$639$	−2.43919e8	−0.0369822
$640$	−5.83333e9	−0.879603
$641$	6.88175e9	1.03204	0.516019	−	0.856577i	$-0.327413\pi$
$641$	6.88175e9	1.03204	0.516019	+	0.856577i	$0.327413\pi$
$642$	−7.74081e8	−0.115455
$643$	−6.87511e9	−1.01986	−0.509931	−	0.860215i	$-0.670329\pi$
$643$	−6.87511e9	−1.01986	−0.509931	+	0.860215i	$0.670329\pi$
$644$	−8.51873e8	−0.125682
$645$	−8.01283e8	−0.117578
$646$	−3.49313e9	−0.509801
$647$	−1.33004e9	−0.193064	−0.0965318	−	0.995330i	$-0.530775\pi$
$647$	−1.33004e9	−0.193064	−0.0965318	+	0.995330i	$0.530775\pi$
$648$	−3.34610e9	−0.483088
$649$	−3.94408e9	−0.566356
$650$	−1.18641e8	−0.0169448
$651$	−1.89064e8	−0.0268581
$652$	−1.04678e10	−1.47907
$653$	−1.24447e10	−1.74899	−0.874497	−	0.485031i	$-0.838808\pi$
$653$	−1.24447e10	−1.74899	−0.874497	+	0.485031i	$0.838808\pi$
$654$	2.54217e9	0.355371
$655$	1.62895e8	0.0226498
$656$	3.60803e9	0.499007
$657$	−1.77500e9	−0.244186
$658$	6.28578e8	0.0860138
$659$	−1.28083e10	−1.74338	−0.871691	−	0.490057i	$-0.836976\pi$
$659$	−1.28083e10	−1.74338	−0.871691	+	0.490057i	$0.836976\pi$
$660$	−3.57502e9	−0.484033
$661$	3.13568e9	0.422306	0.211153	−	0.977453i	$-0.432278\pi$
$661$	3.13568e9	0.422306	0.211153	+	0.977453i	$0.432278\pi$
$662$	−1.75029e9	−0.234481
$663$	−2.58580e9	−0.344587
$664$	−4.53897e9	−0.601685
$665$	2.96325e9	0.390744
$666$	6.94133e8	0.0910506
$667$	−2.49328e9	−0.325335
$668$	−6.97995e9	−0.906013
$669$	3.23230e9	0.417369
$670$	−2.18277e9	−0.280379
$671$	−6.51515e9	−0.832522
$672$	2.25879e9	0.287133
$673$	−6.36507e9	−0.804916	−0.402458	−	0.915438i	$-0.631844\pi$
$673$	−6.36507e9	−0.804916	−0.402458	+	0.915438i	$0.631844\pi$
$674$	−1.10191e9	−0.138623
$675$	1.61148e9	0.201680
$676$	−5.53093e8	−0.0688628
$677$	−3.81955e9	−0.473098	−0.236549	−	0.971620i	$-0.576016\pi$
$677$	−3.81955e9	−0.473098	−0.236549	+	0.971620i	$0.576016\pi$
$678$	1.03425e9	0.127445
$679$	2.78208e8	0.0341055
$680$	−6.21670e9	−0.758191
$681$	1.93601e9	0.234905
$682$	1.39518e8	0.0168416
$683$	−6.09849e9	−0.732403	−0.366202	−	0.930536i	$-0.619342\pi$
$683$	−6.09849e9	−0.732403	−0.366202	+	0.930536i	$0.619342\pi$
$684$	1.54892e9	0.185069
$685$	3.67466e9	0.436818
$686$	1.47786e8	0.0174783
$687$	8.45149e9	0.994454
$688$	8.57888e8	0.100432
$689$	1.02591e9	0.119493
$690$	−8.46196e8	−0.0980617
$691$	3.92762e9	0.452852	0.226426	−	0.974028i	$-0.427296\pi$
$691$	3.92762e9	0.452852	0.226426	+	0.974028i	$0.427296\pi$
$692$	−1.44588e10	−1.65867
$693$	−3.95414e8	−0.0451321
$694$	−3.84221e8	−0.0436338
$695$	3.99015e9	0.450861
$696$	4.32763e9	0.486540
$697$	8.78644e9	0.982874
$698$	5.66287e8	0.0630293
$699$	2.54632e9	0.281996
$700$	−5.79541e8	−0.0638618
$701$	8.10924e9	0.889134	0.444567	−	0.895746i	$-0.353358\pi$
$701$	8.10924e9	0.889134	0.444567	+	0.895746i	$0.353358\pi$
$702$	−8.79337e8	−0.0959347
$703$	1.65119e10	1.79247
$704$	2.60873e9	0.281790
$705$	−5.33445e9	−0.573361
$706$	−4.75979e9	−0.509063
$707$	8.75842e8	0.0932089
$708$	−6.53915e9	−0.692477
$709$	1.39644e10	1.47150	0.735751	−	0.677253i	$-0.236830\pi$
$709$	1.39644e10	1.47150	0.735751	+	0.677253i	$0.236830\pi$
$710$	5.70924e8	0.0598651
$711$	7.41532e7	0.00773724
$712$	1.43010e9	0.148486
$713$	−2.82135e8	−0.0291503
$714$	1.47847e9	0.152008
$715$	−1.61871e9	−0.165614
$716$	−3.12206e9	−0.317867
$717$	1.24308e10	1.25945
$718$	4.95555e9	0.499639
$719$	4.82788e9	0.484401	0.242201	−	0.970226i	$-0.422131\pi$
$719$	4.82788e9	0.484401	0.242201	+	0.970226i	$0.422131\pi$
$720$	1.13185e9	0.113013
$721$	−4.12525e9	−0.409899
$722$	−1.03909e9	−0.102747
$723$	−1.78125e10	−1.75284
$724$	−9.18536e9	−0.899521
$725$	−1.69621e9	−0.165309
$726$	1.69380e9	0.164280
$727$	−1.24688e10	−1.20352	−0.601761	−	0.798677i	$-0.705534\pi$
$727$	−1.24688e10	−1.20352	−0.601761	+	0.798677i	$0.705534\pi$
$728$	6.69491e8	0.0643109
$729$	1.16046e10	1.10939
$730$	4.15463e9	0.395278
$731$	2.08917e9	0.197817
$732$	−1.08019e10	−1.01791
$733$	1.65314e10	1.55041	0.775205	−	0.631710i	$-0.217647\pi$
$733$	1.65314e10	1.55041	0.775205	+	0.631710i	$0.217647\pi$
$734$	5.33811e8	0.0498255
$735$	−1.25419e9	−0.116509
$736$	3.37073e9	0.311639
$737$	6.92858e9	0.637541
$738$	4.56031e8	0.0417635
$739$	1.33868e10	1.22017	0.610084	−	0.792337i	$-0.291136\pi$
$739$	1.33868e10	1.22017	0.610084	+	0.792337i	$0.291136\pi$
$740$	1.38807e10	1.25921
$741$	−3.19249e9	−0.288248
$742$	−5.86578e8	−0.0527123
$743$	−2.04467e10	−1.82878	−0.914392	−	0.404830i	$-0.867331\pi$
$743$	−2.04467e10	−1.82878	−0.914392	+	0.404830i	$0.867331\pi$
$744$	4.89706e8	0.0435943
$745$	1.00878e10	0.893822
$746$	−3.01000e9	−0.265449
$747$	2.01248e9	0.176648
$748$	9.32108e9	0.814349
$749$	−1.71209e9	−0.148882
$750$	−3.62581e9	−0.313827
$751$	4.82638e8	0.0415797	0.0207899	−	0.999784i	$-0.493382\pi$
$751$	4.82638e8	0.0415797	0.0207899	+	0.999784i	$0.493382\pi$
$752$	5.71129e9	0.489747
$753$	1.95897e10	1.67203
$754$	9.25573e8	0.0786341
$755$	−2.00786e10	−1.69793
$756$	−4.29542e9	−0.361559
$757$	2.12332e10	1.77902	0.889509	−	0.456917i	$-0.151046\pi$
$757$	2.12332e10	1.77902	0.889509	+	0.456917i	$0.151046\pi$
$758$	1.25375e9	0.104561
$759$	2.68601e9	0.222978
$760$	−7.67528e9	−0.634230
$761$	1.25867e10	1.03530	0.517651	−	0.855592i	$-0.326807\pi$
$761$	1.25867e10	1.03530	0.517651	+	0.855592i	$0.326807\pi$
$762$	6.67076e9	0.546176
$763$	5.62270e9	0.458257
$764$	−7.95688e9	−0.645529
$765$	2.75634e9	0.222596
$766$	1.18966e9	0.0956359
$767$	−2.96082e9	−0.236935
$768$	1.23814e9	0.0986292
$769$	−1.20255e10	−0.953592	−0.476796	−	0.879014i	$-0.658202\pi$
$769$	−1.20255e10	−0.953592	−0.476796	+	0.879014i	$0.658202\pi$
$770$	9.25518e8	0.0730579
$771$	−9.36522e9	−0.735915
$772$	−4.99016e9	−0.390350
$773$	1.38597e10	1.07926	0.539628	−	0.841904i	$-0.318565\pi$
$773$	1.38597e10	1.07926	0.539628	+	0.841904i	$0.318565\pi$
$774$	1.08431e8	0.00840546
$775$	−1.91940e8	−0.0148119
$776$	−7.20602e8	−0.0553579
$777$	−6.98864e9	−0.534465
$778$	2.79405e9	0.212718
$779$	1.08479e10	0.822178
$780$	−2.68377e9	−0.202495
$781$	−1.81224e9	−0.136125
$782$	2.20627e9	0.164981
$783$	−1.25719e10	−0.935915
$784$	1.34279e9	0.0995184
$785$	4.58750e9	0.338479
$786$	1.00343e8	0.00737068
$787$	2.07864e10	1.52008	0.760042	−	0.649874i	$-0.225178\pi$
$787$	2.07864e10	1.52008	0.760042	+	0.649874i	$0.225178\pi$
$788$	−9.31186e9	−0.677945
$789$	2.18582e10	1.58432
$790$	−1.73565e8	−0.0125247
$791$	2.28753e9	0.164342
$792$	1.02418e9	0.0732555
$793$	−4.89092e9	−0.348285
$794$	−1.16415e9	−0.0825349
$795$	4.97802e9	0.351376
$796$	3.62915e8	0.0255041
$797$	−1.53592e10	−1.07465	−0.537323	−	0.843377i	$-0.680564\pi$
$797$	−1.53592e10	−1.07465	−0.537323	+	0.843377i	$0.680564\pi$
$798$	1.82535e9	0.127156
$799$	1.39084e10	0.964636
$800$	2.29315e9	0.158350
$801$	−6.34072e8	−0.0435938
$802$	4.84541e8	0.0331681
$803$	−1.31877e10	−0.898804
$804$	1.14874e10	0.779514
$805$	−1.87160e9	−0.126452
$806$	1.04736e8	0.00704567
$807$	−2.28429e10	−1.53001
$808$	−2.26857e9	−0.151291
$809$	2.72236e10	1.80770	0.903850	−	0.427850i	$-0.140729\pi$
$809$	2.72236e10	1.80770	0.903850	+	0.427850i	$0.140729\pi$
$810$	−3.47253e9	−0.229587
$811$	−8.41383e9	−0.553886	−0.276943	−	0.960886i	$-0.589321\pi$
$811$	−8.41383e9	−0.553886	−0.276943	+	0.960886i	$0.589321\pi$
$812$	4.52128e9	0.296357
$813$	−6.96299e9	−0.454442
$814$	5.15719e9	0.335141
$815$	−2.29982e10	−1.48813
$816$	1.34334e10	0.865509
$817$	2.57934e9	0.165474
$818$	4.63870e9	0.296319
$819$	−2.96837e8	−0.0188810
$820$	9.11931e9	0.577582
$821$	−1.89305e10	−1.19388	−0.596939	−	0.802287i	$-0.703617\pi$
$821$	−1.89305e10	−1.19388	−0.596939	+	0.802287i	$0.703617\pi$
$822$	2.26358e9	0.142149
$823$	−4.76908e9	−0.298219	−0.149109	−	0.988821i	$-0.547641\pi$
$823$	−4.76908e9	−0.298219	−0.149109	+	0.988821i	$0.547641\pi$
$824$	1.06850e10	0.665321
$825$	1.82733e9	0.113300
$826$	1.69289e9	0.104520
$827$	−1.27860e10	−0.786079	−0.393039	−	0.919522i	$-0.628576\pi$
$827$	−1.27860e10	−0.786079	−0.393039	+	0.919522i	$0.628576\pi$
$828$	−9.78306e8	−0.0598920
$829$	4.84354e9	0.295272	0.147636	−	0.989042i	$-0.452834\pi$
$829$	4.84354e9	0.295272	0.147636	+	0.989042i	$0.452834\pi$
$830$	−4.71047e9	−0.285951
$831$	−2.06803e10	−1.25012
$832$	1.95838e9	0.117887
$833$	3.27004e9	0.196018
$834$	2.45792e9	0.146719
$835$	−1.53352e10	−0.911563
$836$	1.15080e10	0.681206
$837$	−1.42261e9	−0.0838587
$838$	3.09429e9	0.181638
$839$	9.01419e9	0.526938	0.263469	−	0.964668i	$-0.415133\pi$
$839$	9.01419e9	0.526938	0.263469	+	0.964668i	$0.415133\pi$
$840$	3.24856e9	0.189110
$841$	−4.01690e9	−0.232865
$842$	−3.37885e9	−0.195064
$843$	2.25336e10	1.29549
$844$	1.92625e10	1.10285
$845$	−1.21517e9	−0.0692846
$846$	7.21869e8	0.0409885
$847$	3.74630e9	0.211841
$848$	−5.32968e9	−0.300134
$849$	−2.75637e10	−1.54583
$850$	1.50096e9	0.0838304
$851$	−1.04289e10	−0.580079
$852$	−3.00463e9	−0.166438
$853$	−1.27370e10	−0.702663	−0.351331	−	0.936251i	$-0.614271\pi$
$853$	−1.27370e10	−0.702663	−0.351331	+	0.936251i	$0.614271\pi$
$854$	2.79644e9	0.153640
$855$	3.40304e9	0.186203
$856$	4.43459e9	0.241655
$857$	−3.24724e10	−1.76231	−0.881154	−	0.472830i	$-0.843232\pi$
$857$	−3.24724e10	−1.76231	−0.881154	+	0.472830i	$0.843232\pi$
$858$	−9.97119e8	−0.0538941
$859$	−1.83427e10	−0.987385	−0.493692	−	0.869637i	$-0.664353\pi$
$859$	−1.83427e10	−0.987385	−0.493692	+	0.869637i	$0.664353\pi$
$860$	2.16832e9	0.116246
$861$	−4.59139e9	−0.245151
$862$	−2.39815e9	−0.127526
$863$	1.03550e10	0.548418	0.274209	−	0.961670i	$-0.411584\pi$
$863$	1.03550e10	0.548418	0.274209	+	0.961670i	$0.411584\pi$
$864$	1.69963e10	0.896512
$865$	−3.17665e10	−1.66883
$866$	1.17610e10	0.615364
$867$	1.53379e10	0.799283
$868$	5.11618e8	0.0265538
$869$	5.50934e8	0.0284794
$870$	4.49115e9	0.231228
$871$	5.20128e9	0.266715
$872$	−1.45637e10	−0.743813
$873$	3.19499e8	0.0162525
$874$	2.72391e9	0.138008
$875$	−8.01948e9	−0.404686
$876$	−2.18648e10	−1.09896
$877$	−1.19121e10	−0.596336	−0.298168	−	0.954513i	$-0.596376\pi$
$877$	−1.19121e10	−0.596336	−0.298168	+	0.954513i	$0.596376\pi$
$878$	1.05616e10	0.526622
$879$	2.95586e10	1.46799
$880$	8.40932e9	0.415979
$881$	1.16583e10	0.574406	0.287203	−	0.957870i	$-0.407275\pi$
$881$	1.16583e10	0.574406	0.287203	+	0.957870i	$0.407275\pi$
$882$	1.69720e8	0.00832902
$883$	1.60409e10	0.784092	0.392046	−	0.919946i	$-0.371767\pi$
$883$	1.60409e10	0.784092	0.392046	+	0.919946i	$0.371767\pi$
$884$	6.99733e9	0.340682
$885$	−1.43668e10	−0.696719
$886$	−6.04098e9	−0.291803
$887$	−1.93804e10	−0.932461	−0.466231	−	0.884663i	$-0.654388\pi$
$887$	−1.93804e10	−0.932461	−0.466231	+	0.884663i	$0.654388\pi$
$888$	1.81017e10	0.867509
$889$	1.47542e10	0.704304
$890$	1.48413e9	0.0705678
$891$	1.10226e10	0.522048
$892$	−8.74677e9	−0.412640
$893$	1.71716e10	0.806922
$894$	6.21406e9	0.290867
$895$	−6.85927e9	−0.319814
$896$	−7.94759e9	−0.369111
$897$	2.01639e9	0.0932826
$898$	−3.27425e9	−0.150884
$899$	1.49742e9	0.0687359
$900$	−6.65555e8	−0.0304323
$901$	−1.29791e10	−0.591163
$902$	3.38816e9	0.153724
$903$	−1.09170e9	−0.0493398
$904$	−5.92506e9	−0.266749
$905$	−2.01806e10	−0.905031
$906$	−1.23683e10	−0.552539
$907$	−4.28945e10	−1.90887	−0.954436	−	0.298417i	$-0.903541\pi$
$907$	−4.28945e10	−1.90887	−0.954436	+	0.298417i	$0.903541\pi$
$908$	−5.23894e9	−0.232243
$909$	1.00583e9	0.0444173
$910$	6.94786e8	0.0305637
$911$	1.77908e10	0.779619	0.389809	−	0.920896i	$-0.372541\pi$
$911$	1.77908e10	0.779619	0.389809	+	0.920896i	$0.372541\pi$
$912$	1.65852e10	0.724001
$913$	1.49521e10	0.650210
$914$	−1.04304e10	−0.451844
$915$	−2.37321e10	−1.02415
$916$	−2.28702e10	−0.983186
$917$	2.21936e8	0.00950462
$918$	1.11247e10	0.474614
$919$	2.58002e9	0.109652	0.0548262	−	0.998496i	$-0.482540\pi$
$919$	2.58002e9	0.109652	0.0548262	+	0.998496i	$0.482540\pi$
$920$	4.84773e9	0.205249
$921$	9.49727e7	0.00400581
$922$	3.28345e9	0.137966
$923$	−1.36045e9	−0.0569476
$924$	−4.87077e9	−0.203117
$925$	−7.09495e9	−0.294750
$926$	−2.79419e9	−0.115643
$927$	−4.73751e9	−0.195331
$928$	−1.78900e10	−0.734838
$929$	−4.51111e10	−1.84598	−0.922992	−	0.384819i	$-0.874264\pi$
$929$	−4.51111e10	−1.84598	−0.922992	+	0.384819i	$0.874264\pi$
$930$	5.08208e8	0.0207182
$931$	4.03726e9	0.163969
$932$	−6.89049e9	−0.278801
$933$	5.73961e9	0.231364
$934$	−9.23666e9	−0.370938
$935$	2.04788e10	0.819337
$936$	7.68855e8	0.0306464
$937$	3.60079e10	1.42991	0.714957	−	0.699169i	$-0.246446\pi$
$937$	3.60079e10	1.42991	0.714957	+	0.699169i	$0.246446\pi$
$938$	−2.97390e9	−0.117657
$939$	1.69720e10	0.668964
$940$	1.44353e10	0.566864
$941$	−2.33906e10	−0.915117	−0.457559	−	0.889179i	$-0.651276\pi$
$941$	−2.33906e10	−0.915117	−0.457559	+	0.889179i	$0.651276\pi$
$942$	2.82588e9	0.110148
$943$	−6.85159e9	−0.266073
$944$	1.53817e10	0.595116
$945$	−9.43720e9	−0.363774
$946$	8.05610e8	0.0309390
$947$	−1.85649e10	−0.710342	−0.355171	−	0.934801i	$-0.615577\pi$
$947$	−1.85649e10	−0.710342	−0.355171	+	0.934801i	$0.615577\pi$
$948$	9.13430e8	0.0348214
$949$	−9.90000e9	−0.376014
$950$	1.85311e9	0.0701244
$951$	3.94659e10	1.48796
$952$	−8.46991e9	−0.318163
$953$	−1.84417e10	−0.690200	−0.345100	−	0.938566i	$-0.612155\pi$
$953$	−1.84417e10	−0.690200	−0.345100	+	0.938566i	$0.612155\pi$
$954$	−6.73636e8	−0.0251192
$955$	−1.74816e10	−0.649484
$956$	−3.36384e10	−1.24518
$957$	−1.42559e10	−0.525778
$958$	−2.67447e8	−0.00982784
$959$	5.00652e9	0.183304
$960$	9.50260e9	0.346652
$961$	−2.73432e10	−0.993841
$962$	3.87150e9	0.140206
$963$	−1.96620e9	−0.0709472
$964$	4.82017e10	1.73298
$965$	−1.09636e10	−0.392741
$966$	−1.15290e9	−0.0411500
$967$	−8.38242e9	−0.298110	−0.149055	−	0.988829i	$-0.547623\pi$
$967$	−8.38242e9	−0.298110	−0.149055	+	0.988829i	$0.547623\pi$
$968$	−9.70351e9	−0.343847
$969$	4.03891e10	1.42604
$970$	−7.47828e8	−0.0263088
$971$	−2.38373e10	−0.835583	−0.417791	−	0.908543i	$-0.637196\pi$
$971$	−2.38373e10	−0.835583	−0.417791	+	0.908543i	$0.637196\pi$
$972$	−9.11299e9	−0.318294
$973$	5.43636e9	0.189197
$974$	7.10984e9	0.246549
$975$	1.37178e9	0.0473988
$976$	2.54087e10	0.874797
$977$	8.95023e8	0.0307046	0.0153523	−	0.999882i	$-0.495113\pi$
$977$	8.95023e8	0.0307046	0.0153523	+	0.999882i	$0.495113\pi$
$978$	−1.41668e10	−0.484267
$979$	−4.71095e9	−0.160461
$980$	3.39392e9	0.115189
$981$	6.45721e9	0.218375
$982$	−1.47429e10	−0.496813
$983$	−5.06403e10	−1.70043	−0.850215	−	0.526435i	$-0.823528\pi$
$983$	−5.06403e10	−1.70043	−0.850215	+	0.526435i	$0.823528\pi$
$984$	1.18924e10	0.397912
$985$	−2.04585e10	−0.682098
$986$	−1.17097e10	−0.389023
$987$	−7.26789e9	−0.240602
$988$	8.63906e9	0.284982
$989$	−1.62912e9	−0.0535507
$990$	1.06288e9	0.0348146
$991$	4.44477e10	1.45075	0.725374	−	0.688355i	$-0.241667\pi$
$991$	4.44477e10	1.45075	0.725374	+	0.688355i	$0.241667\pi$
$992$	−2.02439e9	−0.0658420
$993$	2.02377e10	0.655901
$994$	7.77852e8	0.0251215
$995$	7.97338e8	0.0256603
$996$	2.47900e10	0.795003
$997$	−3.96617e10	−1.26747	−0.633736	−	0.773550i	$-0.718479\pi$
$997$	−3.96617e10	−1.26747	−0.633736	+	0.773550i	$0.718479\pi$
$998$	1.02210e10	0.325490
$999$	−5.25861e10	−1.66875

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.d.1.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.d.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-3.66228 q^{2} +42.3449 q^{3} -114.588 q^{4} -251.753 q^{5} -155.079 q^{6} -343.000 q^{7} +888.424 q^{8} -393.907 q^{9} +O(q^{10})\)	\(q-3.66228 q^{2} +42.3449 q^{3} -114.588 q^{4} -251.753 q^{5} -155.079 q^{6} -343.000 q^{7} +888.424 q^{8} -393.907 q^{9} +921.992 q^{10} -2926.60 q^{11} -4852.21 q^{12} -2197.00 q^{13} +1256.16 q^{14} -10660.5 q^{15} +11413.6 q^{16} +27794.8 q^{17} +1442.60 q^{18} +34316.1 q^{19} +28847.8 q^{20} -14524.3 q^{21} +10718.0 q^{22} -21674.2 q^{23} +37620.3 q^{24} -14745.2 q^{25} +8046.03 q^{26} -109288. q^{27} +39303.6 q^{28} +115035. q^{29} +39041.7 q^{30} +13017.1 q^{31} -155518. q^{32} -123927. q^{33} -101793. q^{34} +86351.4 q^{35} +45136.9 q^{36} +481169. q^{37} -125675. q^{38} -93031.8 q^{39} -223664. q^{40} +316118. q^{41} +53192.1 q^{42} +75163.9 q^{43} +335353. q^{44} +99167.4 q^{45} +79377.0 q^{46} +500395. q^{47} +483307. q^{48} +117649. q^{49} +54001.2 q^{50} +1.17697e6 q^{51} +251749. q^{52} -466960. q^{53} +400245. q^{54} +736782. q^{55} -304730. q^{56} +1.45311e6 q^{57} -421289. q^{58} +1.34767e6 q^{59} +1.22156e6 q^{60} +2.22618e6 q^{61} -47672.2 q^{62} +135110. q^{63} -891386. q^{64} +553102. q^{65} +453855. q^{66} -2.36745e6 q^{67} -3.18495e6 q^{68} -917792. q^{69} -316243. q^{70} +619229. q^{71} -349957. q^{72} +4.50615e6 q^{73} -1.76217e6 q^{74} -624386. q^{75} -3.93221e6 q^{76} +1.00383e6 q^{77} +340709. q^{78} -188250. q^{79} -2.87340e6 q^{80} -3.76633e6 q^{81} -1.15771e6 q^{82} -5.10902e6 q^{83} +1.66431e6 q^{84} -6.99745e6 q^{85} -275271. q^{86} +4.87114e6 q^{87} -2.60007e6 q^{88} +1.60970e6 q^{89} -363179. q^{90} +753571. q^{91} +2.48360e6 q^{92} +551207. q^{93} -1.83259e6 q^{94} -8.63921e6 q^{95} -6.58540e6 q^{96} -811101. q^{97} -430864. q^{98} +1.15281e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9}+O(q^{10}) \) 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

Representations

Groups

Database

Properties

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