LMFDB - Embedded newform 91.8.a.d.1.7

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			1.7
Root			$-6.50047$ 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)

$f(q)$	$=$	$q+6.50047 q^{2} -52.7234 q^{3} -85.7438 q^{4} +295.835 q^{5} -342.727 q^{6} -343.000 q^{7} -1389.44 q^{8} +592.761 q^{9} +O(q^{10})$	\(q+6.50047 q^{2} -52.7234 q^{3} -85.7438 q^{4} +295.835 q^{5} -342.727 q^{6} -343.000 q^{7} -1389.44 q^{8} +592.761 q^{9} +1923.06 q^{10} -4167.20 q^{11} +4520.71 q^{12} -2197.00 q^{13} -2229.66 q^{14} -15597.4 q^{15} +1943.22 q^{16} +31905.1 q^{17} +3853.23 q^{18} -16829.1 q^{19} -25366.0 q^{20} +18084.1 q^{21} -27088.8 q^{22} -41368.2 q^{23} +73255.9 q^{24} +9393.08 q^{25} -14281.5 q^{26} +84053.8 q^{27} +29410.1 q^{28} +192426. q^{29} -101391. q^{30} +305729. q^{31} +190480. q^{32} +219709. q^{33} +207399. q^{34} -101471. q^{35} -50825.6 q^{36} +50734.5 q^{37} -109397. q^{38} +115833. q^{39} -411043. q^{40} +654222. q^{41} +117555. q^{42} -226236. q^{43} +357312. q^{44} +175359. q^{45} -268913. q^{46} -466460. q^{47} -102453. q^{48} +117649. q^{49} +61059.5 q^{50} -1.68215e6 q^{51} +188379. q^{52} +444270. q^{53} +546389. q^{54} -1.23280e6 q^{55} +476577. q^{56} +887288. q^{57} +1.25086e6 q^{58} -652349. q^{59} +1.33738e6 q^{60} -434908. q^{61} +1.98738e6 q^{62} -203317. q^{63} +989476. q^{64} -649949. q^{65} +1.42821e6 q^{66} +3.08414e6 q^{67} -2.73567e6 q^{68} +2.18108e6 q^{69} -659611. q^{70} -3.79278e6 q^{71} -823604. q^{72} -168997. q^{73} +329799. q^{74} -495236. q^{75} +1.44299e6 q^{76} +1.42935e6 q^{77} +752972. q^{78} +1.62128e6 q^{79} +574871. q^{80} -5.72797e6 q^{81} +4.25275e6 q^{82} +5.01049e6 q^{83} -1.55060e6 q^{84} +9.43864e6 q^{85} -1.47064e6 q^{86} -1.01454e7 q^{87} +5.79006e6 q^{88} -1.21431e7 q^{89} +1.13992e6 q^{90} +753571. q^{91} +3.54707e6 q^{92} -1.61191e7 q^{93} -3.03221e6 q^{94} -4.97863e6 q^{95} -1.00427e7 q^{96} +9.64770e6 q^{97} +764774. q^{98} -2.47015e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	6.50047	0.574566	0.287283	−	0.957846i	$-0.407248\pi$
$2$	6.50047	0.574566	0.287283	+	0.957846i	$0.407248\pi$
$3$	−52.7234	−1.12740	−0.563702	−	0.825978i	$-0.690623\pi$
$3$	−52.7234	−1.12740	−0.563702	+	0.825978i	$0.690623\pi$
$4$	−85.7438	−0.669874
$5$	295.835	1.05841	0.529205	−	0.848494i	$-0.322490\pi$
$5$	295.835	1.05841	0.529205	+	0.848494i	$0.322490\pi$
$6$	−342.727	−0.647768
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	−1389.44	−0.959453
$9$	592.761	0.271039
$10$	1923.06	0.608127
$11$	−4167.20	−0.943996	−0.471998	−	0.881600i	$-0.656467\pi$
$11$	−4167.20	−0.943996	−0.471998	+	0.881600i	$0.656467\pi$
$12$	4520.71	0.755218
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−2229.66	−0.217166
$15$	−15597.4	−1.19325
$16$	1943.22	0.118605
$17$	31905.1	1.57503	0.787516	−	0.616294i	$-0.211367\pi$
$17$	31905.1	1.57503	0.787516	+	0.616294i	$0.211367\pi$
$18$	3853.23	0.155730
$19$	−16829.1	−0.562889	−0.281445	−	0.959577i	$-0.590814\pi$
$19$	−16829.1	−0.562889	−0.281445	+	0.959577i	$0.590814\pi$
$20$	−25366.0	−0.709001
$21$	18084.1	0.426118
$22$	−27088.8	−0.542388
$23$	−41368.2	−0.708957	−0.354478	−	0.935064i	$-0.615342\pi$
$23$	−41368.2	−0.708957	−0.354478	+	0.935064i	$0.615342\pi$
$24$	73255.9	1.08169
$25$	9393.08	0.120231
$26$	−14281.5	−0.159356
$27$	84053.8	0.821834
$28$	29410.1	0.253188
$29$	192426.	1.46511	0.732555	−	0.680708i	$-0.238328\pi$
$29$	192426.	1.46511	0.732555	+	0.680708i	$0.238328\pi$
$30$	−101391.	−0.685604
$31$	305729.	1.84319	0.921595	−	0.388153i	$-0.126887\pi$
$31$	305729.	1.84319	0.921595	+	0.388153i	$0.126887\pi$
$32$	190480.	1.02760
$33$	219709.	1.06426
$34$	207399.	0.904960
$35$	−101471.	−0.400041
$36$	−50825.6	−0.181562
$37$	50734.5	0.164664	0.0823318	−	0.996605i	$-0.473763\pi$
$37$	50734.5	0.164664	0.0823318	+	0.996605i	$0.473763\pi$
$38$	−109397.	−0.323417
$39$	115833.	0.312685
$40$	−411043.	−1.01549
$41$	654222.	1.48245	0.741227	−	0.671254i	$-0.234244\pi$
$41$	654222.	1.48245	0.741227	+	0.671254i	$0.234244\pi$
$42$	117555.	0.244833
$43$	−226236.	−0.433932	−0.216966	−	0.976179i	$-0.569616\pi$
$43$	−226236.	−0.433932	−0.216966	+	0.976179i	$0.569616\pi$
$44$	357312.	0.632358
$45$	175359.	0.286870
$46$	−268913.	−0.407343
$47$	−466460.	−0.655348	−0.327674	−	0.944791i	$-0.606265\pi$
$47$	−466460.	−0.655348	−0.327674	+	0.944791i	$0.606265\pi$
$48$	−102453.	−0.133715
$49$	117649.	0.142857
$50$	61059.5	0.0690809
$51$	−1.68215e6	−1.77570
$52$	188379.	0.185790
$53$	444270.	0.409904	0.204952	−	0.978772i	$-0.434296\pi$
$53$	444270.	0.409904	0.204952	+	0.978772i	$0.434296\pi$
$54$	546389.	0.472198
$55$	−1.23280e6	−0.999134
$56$	476577.	0.362639
$57$	887288.	0.634604
$58$	1.25086e6	0.841803
$59$	−652349.	−0.413521	−0.206761	−	0.978392i	$-0.566292\pi$
$59$	−652349.	−0.413521	−0.206761	+	0.978392i	$0.566292\pi$
$60$	1.33738e6	0.799330
$61$	−434908.	−0.245326	−0.122663	−	0.992448i	$-0.539143\pi$
$61$	−434908.	−0.245326	−0.122663	+	0.992448i	$0.539143\pi$
$62$	1.98738e6	1.05903
$63$	−203317.	−0.102443
$64$	989476.	0.471819
$65$	−649949.	−0.293550
$66$	1.42821e6	0.611490
$67$	3.08414e6	1.25277	0.626386	−	0.779513i	$-0.284533\pi$
$67$	3.08414e6	1.25277	0.626386	+	0.779513i	$0.284533\pi$
$68$	−2.73567e6	−1.05507
$69$	2.18108e6	0.799280
$70$	−659611.	−0.229850
$71$	−3.79278e6	−1.25763	−0.628816	−	0.777554i	$-0.716460\pi$
$71$	−3.79278e6	−1.25763	−0.628816	+	0.777554i	$0.716460\pi$
$72$	−823604.	−0.260049
$73$	−168997.	−0.0508450	−0.0254225	−	0.999677i	$-0.508093\pi$
$73$	−168997.	−0.0508450	−0.0254225	+	0.999677i	$0.508093\pi$
$74$	329799.	0.0946101
$75$	−495236.	−0.135549
$76$	1.44299e6	0.377065
$77$	1.42935e6	0.356797
$78$	752972.	0.179658
$79$	1.62128e6	0.369966	0.184983	−	0.982742i	$-0.440777\pi$
$79$	1.62128e6	0.369966	0.184983	+	0.982742i	$0.440777\pi$
$80$	574871.	0.125532
$81$	−5.72797e6	−1.19758
$82$	4.25275e6	0.851768
$83$	5.01049e6	0.961848	0.480924	−	0.876762i	$-0.340301\pi$
$83$	5.01049e6	0.961848	0.480924	+	0.876762i	$0.340301\pi$
$84$	−1.55060e6	−0.285446
$85$	9.43864e6	1.66703
$86$	−1.47064e6	−0.249323
$87$	−1.01454e7	−1.65177
$88$	5.79006e6	0.905719
$89$	−1.21431e7	−1.82584	−0.912922	−	0.408134i	$-0.866180\pi$
$89$	−1.21431e7	−1.82584	−0.912922	+	0.408134i	$0.866180\pi$
$90$	1.13992e6	0.164826
$91$	753571.	0.104828
$92$	3.54707e6	0.474911
$93$	−1.61191e7	−2.07802
$94$	−3.03221e6	−0.376541
$95$	−4.97863e6	−0.595768
$96$	−1.00427e7	−1.15852
$97$	9.64770e6	1.07330	0.536652	−	0.843804i	$-0.319689\pi$
$97$	9.64770e6	1.07330	0.536652	+	0.843804i	$0.319689\pi$
$98$	764774.	0.0820809
$99$	−2.47015e6	−0.255859
$100$	−805399.	−0.0805399
$101$	−2.37966e6	−0.229821	−0.114911	−	0.993376i	$-0.536658\pi$
$101$	−2.37966e6	−0.229821	−0.114911	+	0.993376i	$0.536658\pi$
$102$	−1.09348e7	−1.02026
$103$	2.27003e6	0.204692	0.102346	−	0.994749i	$-0.467365\pi$
$103$	2.27003e6	0.204692	0.102346	+	0.994749i	$0.467365\pi$
$104$	3.05259e6	0.266104
$105$	5.34991e6	0.451008
$106$	2.88797e6	0.235517
$107$	706516.	0.0557544	0.0278772	−	0.999611i	$-0.491125\pi$
$107$	706516.	0.0557544	0.0278772	+	0.999611i	$0.491125\pi$
$108$	−7.20709e6	−0.550525
$109$	1.99236e7	1.47359	0.736794	−	0.676117i	$-0.236339\pi$
$109$	1.99236e7	1.47359	0.736794	+	0.676117i	$0.236339\pi$
$110$	−8.01380e6	−0.574069
$111$	−2.67490e6	−0.185642
$112$	−666523.	−0.0448283
$113$	−3.31200e6	−0.215931	−0.107966	−	0.994155i	$-0.534434\pi$
$113$	−3.31200e6	−0.215931	−0.107966	+	0.994155i	$0.534434\pi$
$114$	5.76779e6	0.364622
$115$	−1.22382e7	−0.750367
$116$	−1.64993e7	−0.981439
$117$	−1.30230e6	−0.0751726
$118$	−4.24058e6	−0.237595
$119$	−1.09435e7	−0.595306
$120$	2.16716e7	1.14487
$121$	−2.12161e6	−0.108872
$122$	−2.82711e6	−0.140956
$123$	−3.44928e7	−1.67132
$124$	−2.62143e7	−1.23470
$125$	−2.03333e7	−0.931156
$126$	−1.32166e6	−0.0588602
$127$	2.01961e7	0.874892	0.437446	−	0.899245i	$-0.355883\pi$
$127$	2.01961e7	0.874892	0.437446	+	0.899245i	$0.355883\pi$
$128$	−1.79493e7	−0.756508
$129$	1.19279e7	0.489216
$130$	−4.22497e6	−0.168664
$131$	1.87268e7	0.727804	0.363902	−	0.931437i	$-0.381444\pi$
$131$	1.87268e7	0.727804	0.363902	+	0.931437i	$0.381444\pi$
$132$	−1.88387e7	−0.712922
$133$	5.77238e6	0.212752
$134$	2.00484e7	0.719800
$135$	2.48660e7	0.869837
$136$	−4.43302e7	−1.51117
$137$	3.78003e7	1.25595	0.627977	−	0.778232i	$-0.283883\pi$
$137$	3.78003e7	1.25595	0.627977	+	0.778232i	$0.283883\pi$
$138$	1.41780e7	0.459239
$139$	−3.65756e7	−1.15515	−0.577577	−	0.816336i	$-0.696002\pi$
$139$	−3.65756e7	−1.15515	−0.577577	+	0.816336i	$0.696002\pi$
$140$	8.70053e6	0.267977
$141$	2.45934e7	0.738842
$142$	−2.46549e7	−0.722593
$143$	9.15534e6	0.261817
$144$	1.15186e6	0.0321464
$145$	5.69262e7	1.55069
$146$	−1.09856e6	−0.0292138
$147$	−6.20286e6	−0.161058
$148$	−4.35017e6	−0.110304
$149$	3.97274e7	0.983871	0.491935	−	0.870632i	$-0.336290\pi$
$149$	3.97274e7	0.983871	0.491935	+	0.870632i	$0.336290\pi$
$150$	−3.21927e6	−0.0778821
$151$	6.19695e7	1.46473	0.732367	−	0.680910i	$-0.238416\pi$
$151$	6.19695e7	1.46473	0.732367	+	0.680910i	$0.238416\pi$
$152$	2.33830e7	0.540066
$153$	1.89121e7	0.426894
$154$	9.29145e6	0.205003
$155$	9.04451e7	1.95085
$156$	−9.93200e6	−0.209460
$157$	9.21530e7	1.90047	0.950234	−	0.311536i	$-0.100843\pi$
$157$	9.21530e7	1.90047	0.950234	+	0.311536i	$0.100843\pi$
$158$	1.05391e7	0.212570
$159$	−2.34235e7	−0.462127
$160$	5.63505e7	1.08762
$161$	1.41893e7	0.267960
$162$	−3.72345e7	−0.688087
$163$	−6.01364e7	−1.08763	−0.543814	−	0.839206i	$-0.683020\pi$
$163$	−6.01364e7	−1.08763	−0.543814	+	0.839206i	$0.683020\pi$
$164$	−5.60955e7	−0.993057
$165$	6.49976e7	1.12643
$166$	3.25705e7	0.552645
$167$	−8.63275e7	−1.43431	−0.717153	−	0.696916i	$-0.754555\pi$
$167$	−8.63275e7	−1.43431	−0.717153	+	0.696916i	$0.754555\pi$
$168$	−2.51268e7	−0.408841
$169$	4.82681e6	0.0769231
$170$	6.13556e7	0.957819
$171$	−9.97563e6	−0.152565
$172$	1.93983e7	0.290680
$173$	−1.09221e8	−1.60378	−0.801891	−	0.597470i	$-0.796173\pi$
$173$	−1.09221e8	−1.60378	−0.801891	+	0.597470i	$0.796173\pi$
$174$	−6.59496e7	−0.949052
$175$	−3.22183e6	−0.0454432
$176$	−8.09777e6	−0.111962
$177$	3.43941e7	0.466205
$178$	−7.89358e7	−1.04907
$179$	8.79839e7	1.14661	0.573307	−	0.819340i	$-0.305660\pi$
$179$	8.79839e7	1.14661	0.573307	+	0.819340i	$0.305660\pi$
$180$	−1.50360e7	−0.192167
$181$	9.60304e7	1.20374	0.601871	−	0.798593i	$-0.294422\pi$
$181$	9.60304e7	1.20374	0.601871	+	0.798593i	$0.294422\pi$
$182$	4.89857e6	0.0602309
$183$	2.29299e7	0.276581
$184$	5.74785e7	0.680211
$185$	1.50090e7	0.174282
$186$	−1.04782e8	−1.19396
$187$	−1.32955e8	−1.48682
$188$	3.99961e7	0.439001
$189$	−2.88304e7	−0.310624
$190$	−3.23634e7	−0.342308
$191$	1.28873e8	1.33828	0.669139	−	0.743138i	$-0.266663\pi$
$191$	1.28873e8	1.33828	0.669139	+	0.743138i	$0.266663\pi$
$192$	−5.21686e7	−0.531931
$193$	−8.87057e7	−0.888180	−0.444090	−	0.895982i	$-0.646473\pi$
$193$	−8.87057e7	−0.888180	−0.444090	+	0.895982i	$0.646473\pi$
$194$	6.27146e7	0.616684
$195$	3.42675e7	0.330949
$196$	−1.00877e7	−0.0956962
$197$	2.17845e6	0.0203009	0.0101505	−	0.999948i	$-0.496769\pi$
$197$	2.17845e6	0.0203009	0.0101505	+	0.999948i	$0.496769\pi$
$198$	−1.60572e7	−0.147008
$199$	−5.39231e7	−0.485052	−0.242526	−	0.970145i	$-0.577976\pi$
$199$	−5.39231e7	−0.485052	−0.242526	+	0.970145i	$0.577976\pi$
$200$	−1.30511e7	−0.115356
$201$	−1.62606e8	−1.41238
$202$	−1.54689e7	−0.132047
$203$	−6.60021e7	−0.553760
$204$	1.44234e8	1.18949
$205$	1.93541e8	1.56904
$206$	1.47563e7	0.117609
$207$	−2.45215e7	−0.192155
$208$	−4.26925e6	−0.0328950
$209$	7.01302e7	0.531365
$210$	3.47770e7	0.259134
$211$	−1.74383e8	−1.27795	−0.638977	−	0.769226i	$-0.720642\pi$
$211$	−1.74383e8	−1.27795	−0.638977	+	0.769226i	$0.720642\pi$
$212$	−3.80934e7	−0.274584
$213$	1.99968e8	1.41786
$214$	4.59269e6	0.0320346
$215$	−6.69283e7	−0.459278
$216$	−1.16787e8	−0.788511
$217$	−1.04865e8	−0.696660
$218$	1.29513e8	0.846674
$219$	8.91009e6	0.0573229
$220$	1.05705e8	0.669294
$221$	−7.00956e7	−0.436835
$222$	−1.73881e7	−0.106664
$223$	2.20113e8	1.32917	0.664583	−	0.747215i	$-0.268609\pi$
$223$	2.20113e8	1.32917	0.664583	+	0.747215i	$0.268609\pi$
$224$	−6.53345e7	−0.388396
$225$	5.56786e6	0.0325874
$226$	−2.15296e7	−0.124067
$227$	2.09224e8	1.18719	0.593597	−	0.804762i	$-0.297707\pi$
$227$	2.09224e8	1.18719	0.593597	+	0.804762i	$0.297707\pi$
$228$	−7.60795e7	−0.425104
$229$	−7.00169e6	−0.0385282	−0.0192641	−	0.999814i	$-0.506132\pi$
$229$	−7.00169e6	−0.0385282	−0.0192641	+	0.999814i	$0.506132\pi$
$230$	−7.95538e7	−0.431135
$231$	−7.53602e7	−0.402254
$232$	−2.67363e8	−1.40570
$233$	9.83820e7	0.509530	0.254765	−	0.967003i	$-0.418002\pi$
$233$	9.83820e7	0.509530	0.254765	+	0.967003i	$0.418002\pi$
$234$	−8.46554e6	−0.0431916
$235$	−1.37995e8	−0.693627
$236$	5.59349e7	0.277007
$237$	−8.54792e7	−0.417101
$238$	−7.11377e7	−0.342043
$239$	−3.50782e8	−1.66205	−0.831026	−	0.556233i	$-0.812246\pi$
$239$	−3.50782e8	−1.66205	−0.831026	+	0.556233i	$0.812246\pi$
$240$	−3.03092e7	−0.141525
$241$	2.81267e8	1.29437	0.647186	−	0.762332i	$-0.275946\pi$
$241$	2.81267e8	1.29437	0.647186	+	0.762332i	$0.275946\pi$
$242$	−1.37915e7	−0.0625542
$243$	1.18173e8	0.528318
$244$	3.72907e7	0.164337
$245$	3.48046e7	0.151201
$246$	−2.24220e8	−0.960286
$247$	3.69735e7	0.156117
$248$	−4.24790e8	−1.76845
$249$	−2.64170e8	−1.08439
$250$	−1.32176e8	−0.535011
$251$	−1.90101e8	−0.758798	−0.379399	−	0.925233i	$-0.623869\pi$
$251$	−1.90101e8	−0.758798	−0.379399	+	0.925233i	$0.623869\pi$
$252$	1.74332e7	0.0686238
$253$	1.72390e8	0.669252
$254$	1.31284e8	0.502684
$255$	−4.97638e8	−1.87941
$256$	−2.43332e8	−0.906483
$257$	−5.05144e7	−0.185631	−0.0928153	−	0.995683i	$-0.529587\pi$
$257$	−5.05144e7	−0.185631	−0.0928153	+	0.995683i	$0.529587\pi$
$258$	7.75372e7	0.281087
$259$	−1.74019e7	−0.0622370
$260$	5.57291e7	0.196641
$261$	1.14063e8	0.397101
$262$	1.21733e8	0.418171
$263$	4.21930e8	1.43020	0.715098	−	0.699024i	$-0.246382\pi$
$263$	4.21930e8	1.43020	0.715098	+	0.699024i	$0.246382\pi$
$264$	−3.05272e8	−1.02111
$265$	1.31430e8	0.433846
$266$	3.75232e7	0.122240
$267$	6.40225e8	2.05846
$268$	−2.64446e8	−0.839199
$269$	2.50710e8	0.785304	0.392652	−	0.919687i	$-0.371558\pi$
$269$	2.50710e8	0.785304	0.392652	+	0.919687i	$0.371558\pi$
$270$	1.61641e8	0.499779
$271$	−4.90223e7	−0.149624	−0.0748121	−	0.997198i	$-0.523836\pi$
$271$	−4.90223e7	−0.149624	−0.0748121	+	0.997198i	$0.523836\pi$
$272$	6.19986e7	0.186806
$273$	−3.97309e7	−0.118184
$274$	2.45720e8	0.721628
$275$	−3.91429e7	−0.113498
$276$	−1.87014e8	−0.535417
$277$	−4.88373e8	−1.38061	−0.690307	−	0.723517i	$-0.742524\pi$
$277$	−4.88373e8	−1.38061	−0.690307	+	0.723517i	$0.742524\pi$
$278$	−2.37759e8	−0.663713
$279$	1.81224e8	0.499576
$280$	1.40988e8	0.383821
$281$	−2.94543e8	−0.791911	−0.395956	−	0.918270i	$-0.629587\pi$
$281$	−2.94543e8	−0.791911	−0.395956	+	0.918270i	$0.629587\pi$
$282$	1.59869e8	0.424514
$283$	−3.25069e8	−0.852557	−0.426279	−	0.904592i	$-0.640176\pi$
$283$	−3.25069e8	−0.852557	−0.426279	+	0.904592i	$0.640176\pi$
$284$	3.25208e8	0.842455
$285$	2.62490e8	0.671671
$286$	5.95140e7	0.150431
$287$	−2.24398e8	−0.560315
$288$	1.12909e8	0.278519
$289$	6.07599e8	1.48073
$290$	3.70047e8	0.890973
$291$	−5.08660e8	−1.21005
$292$	1.44904e7	0.0340598
$293$	2.16739e8	0.503385	0.251693	−	0.967807i	$-0.419013\pi$
$293$	2.16739e8	0.503385	0.251693	+	0.967807i	$0.419013\pi$
$294$	−4.03215e7	−0.0925383
$295$	−1.92987e8	−0.437675
$296$	−7.04924e7	−0.157987
$297$	−3.50269e8	−0.775807
$298$	2.58247e8	0.565299
$299$	9.08860e7	0.196629
$300$	4.24634e7	0.0908010
$301$	7.75988e7	0.164011
$302$	4.02831e8	0.841586
$303$	1.25464e8	0.259101
$304$	−3.27026e7	−0.0667612
$305$	−1.28661e8	−0.259655
$306$	1.22938e8	0.245279
$307$	5.01134e8	0.988483	0.494242	−	0.869325i	$-0.335446\pi$
$307$	5.01134e8	0.988483	0.494242	+	0.869325i	$0.335446\pi$
$308$	−1.22558e8	−0.239009
$309$	−1.19684e8	−0.230771
$310$	5.87936e8	1.12089
$311$	3.33730e8	0.629120	0.314560	−	0.949238i	$-0.398143\pi$
$311$	3.33730e8	0.629120	0.314560	+	0.949238i	$0.398143\pi$
$312$	−1.60943e8	−0.300007
$313$	1.00705e9	1.85628	0.928142	−	0.372226i	$-0.121405\pi$
$313$	1.00705e9	1.85628	0.928142	+	0.372226i	$0.121405\pi$
$314$	5.99038e8	1.09195
$315$	−6.01482e7	−0.108427
$316$	−1.39014e8	−0.247831
$317$	5.51513e8	0.972408	0.486204	−	0.873845i	$-0.338381\pi$
$317$	5.51513e8	0.972408	0.486204	+	0.873845i	$0.338381\pi$
$318$	−1.52264e8	−0.265522
$319$	−8.01877e8	−1.38306
$320$	2.92721e8	0.499378
$321$	−3.72500e7	−0.0628576
$322$	9.22372e7	0.153961
$323$	−5.36935e8	−0.886569
$324$	4.91138e8	0.802225
$325$	−2.06366e7	−0.0333462
$326$	−3.90915e8	−0.624914
$327$	−1.05044e9	−1.66133
$328$	−9.08999e8	−1.42235
$329$	1.59996e8	0.247698
$330$	4.22515e8	0.647207
$331$	9.73421e8	1.47538	0.737688	−	0.675141i	$-0.235917\pi$
$331$	9.73421e8	1.47538	0.737688	+	0.675141i	$0.235917\pi$
$332$	−4.29618e8	−0.644317
$333$	3.00735e7	0.0446302
$334$	−5.61170e8	−0.824103
$335$	9.12395e8	1.32595
$336$	3.51414e7	0.0505396
$337$	2.52523e8	0.359415	0.179708	−	0.983720i	$-0.442485\pi$
$337$	2.52523e8	0.359415	0.179708	+	0.983720i	$0.442485\pi$
$338$	3.13765e7	0.0441974
$339$	1.74620e8	0.243442
$340$	−8.09305e8	−1.11670
$341$	−1.27403e9	−1.73996
$342$	−6.48464e7	−0.0876585
$343$	−4.03536e7	−0.0539949
$344$	3.14340e8	0.416337
$345$	6.45238e8	0.845966
$346$	−7.09989e8	−0.921479
$347$	6.79989e8	0.873673	0.436837	−	0.899541i	$-0.356099\pi$
$347$	6.79989e8	0.873673	0.436837	+	0.899541i	$0.356099\pi$
$348$	8.69901e8	1.10648
$349$	1.02039e7	0.0128492	0.00642460	−	0.999979i	$-0.497955\pi$
$349$	1.02039e7	0.0128492	0.00642460	+	0.999979i	$0.497955\pi$
$350$	−2.09434e7	−0.0261101
$351$	−1.84666e8	−0.227936
$352$	−7.93767e8	−0.970049
$353$	−1.11308e9	−1.34684	−0.673420	−	0.739260i	$-0.735175\pi$
$353$	−1.11308e9	−1.34684	−0.673420	+	0.739260i	$0.735175\pi$
$354$	2.23578e8	0.267866
$355$	−1.12204e9	−1.33109
$356$	1.04119e9	1.22308
$357$	5.76977e8	0.671150
$358$	5.71937e8	0.658806
$359$	2.08301e8	0.237608	0.118804	−	0.992918i	$-0.462094\pi$
$359$	2.08301e8	0.237608	0.118804	+	0.992918i	$0.462094\pi$
$360$	−2.43650e8	−0.275238
$361$	−6.10653e8	−0.683155
$362$	6.24243e8	0.691630
$363$	1.11859e8	0.122743
$364$	−6.46141e7	−0.0702218
$365$	−4.99951e7	−0.0538149
$366$	1.49055e8	0.158914
$367$	−9.63868e8	−1.01786	−0.508928	−	0.860809i	$-0.669958\pi$
$367$	−9.63868e8	−1.01786	−0.508928	+	0.860809i	$0.669958\pi$
$368$	−8.03875e7	−0.0840855
$369$	3.87797e8	0.401802
$370$	9.75658e7	0.100136
$371$	−1.52385e8	−0.154929
$372$	1.38211e9	1.39201
$373$	3.60216e8	0.359403	0.179701	−	0.983721i	$-0.442487\pi$
$373$	3.60216e8	0.359403	0.179701	+	0.983721i	$0.442487\pi$
$374$	−8.64271e8	−0.854278
$375$	1.07204e9	1.04979
$376$	6.48117e8	0.628776
$377$	−4.22760e8	−0.406349
$378$	−1.87412e8	−0.178474
$379$	3.66248e8	0.345572	0.172786	−	0.984959i	$-0.444723\pi$
$379$	3.66248e8	0.345572	0.172786	+	0.984959i	$0.444723\pi$
$380$	4.26887e8	0.399089
$381$	−1.06481e9	−0.986357
$382$	8.37737e8	0.768929
$383$	−7.49814e8	−0.681958	−0.340979	−	0.940071i	$-0.610759\pi$
$383$	−7.49814e8	−0.681958	−0.340979	+	0.940071i	$0.610759\pi$
$384$	9.46351e8	0.852889
$385$	4.22851e8	0.377637
$386$	−5.76629e8	−0.510318
$387$	−1.34104e8	−0.117612
$388$	−8.27231e8	−0.718978
$389$	−2.72592e8	−0.234795	−0.117398	−	0.993085i	$-0.537455\pi$
$389$	−2.72592e8	−0.234795	−0.117398	+	0.993085i	$0.537455\pi$
$390$	2.22755e8	0.190152
$391$	−1.31986e9	−1.11663
$392$	−1.63466e8	−0.137065
$393$	−9.87342e8	−0.820528
$394$	1.41610e7	0.0116642
$395$	4.79629e8	0.391576
$396$	2.11801e8	0.171393
$397$	−1.80915e9	−1.45113	−0.725567	−	0.688152i	$-0.758422\pi$
$397$	−1.80915e9	−1.45113	−0.725567	+	0.688152i	$0.758422\pi$
$398$	−3.50525e8	−0.278695
$399$	−3.04340e8	−0.239858
$400$	1.82528e7	0.0142600
$401$	2.25412e9	1.74571	0.872855	−	0.487980i	$-0.162266\pi$
$401$	2.25412e9	1.74571	0.872855	+	0.487980i	$0.162266\pi$
$402$	−1.05702e9	−0.811505
$403$	−6.71686e8	−0.511209
$404$	2.04041e8	0.153951
$405$	−1.69453e9	−1.26753
$406$	−4.29045e8	−0.318172
$407$	−2.11421e8	−0.155442
$408$	2.33724e9	1.70370
$409$	−1.99782e8	−0.144386	−0.0721930	−	0.997391i	$-0.523000\pi$
$409$	−1.99782e8	−0.144386	−0.0721930	+	0.997391i	$0.523000\pi$
$410$	1.25811e9	0.901520
$411$	−1.99296e9	−1.41597
$412$	−1.94641e8	−0.137118
$413$	2.23756e8	0.156296
$414$	−1.59401e8	−0.110406
$415$	1.48227e9	1.01803
$416$	−4.18484e8	−0.285005
$417$	1.92839e9	1.30233
$418$	4.55880e8	0.305304
$419$	2.88959e9	1.91905	0.959526	−	0.281619i	$-0.0908713\pi$
$419$	2.88959e9	1.91905	0.959526	+	0.281619i	$0.0908713\pi$
$420$	−4.58722e8	−0.302118
$421$	−6.08313e8	−0.397319	−0.198660	−	0.980069i	$-0.563659\pi$
$421$	−6.08313e8	−0.397319	−0.198660	+	0.980069i	$0.563659\pi$
$422$	−1.13357e9	−0.734270
$423$	−2.76500e8	−0.177625
$424$	−6.17285e8	−0.393283
$425$	2.99688e8	0.189368
$426$	1.29989e9	0.814654
$427$	1.49174e8	0.0927245
$428$	−6.05794e7	−0.0373484
$429$	−4.82701e8	−0.295174
$430$	−4.35066e8	−0.263885
$431$	7.49585e7	0.0450973	0.0225486	−	0.999746i	$-0.492822\pi$
$431$	7.49585e7	0.0450973	0.0225486	+	0.999746i	$0.492822\pi$
$432$	1.63335e8	0.0974732
$433$	1.67605e9	0.992153	0.496077	−	0.868279i	$-0.334774\pi$
$433$	1.67605e9	0.992153	0.496077	+	0.868279i	$0.334774\pi$
$434$	−6.81672e8	−0.400278
$435$	−3.00135e9	−1.74825
$436$	−1.70833e9	−0.987118
$437$	6.96190e8	0.399064
$438$	5.79198e7	0.0329358
$439$	1.92663e8	0.108686	0.0543429	−	0.998522i	$-0.482694\pi$
$439$	1.92663e8	0.108686	0.0543429	+	0.998522i	$0.482694\pi$
$440$	1.71290e9	0.958622
$441$	6.97378e7	0.0387198
$442$	−4.55655e8	−0.250991
$443$	−1.47972e9	−0.808662	−0.404331	−	0.914613i	$-0.632496\pi$
$443$	−1.47972e9	−0.808662	−0.404331	+	0.914613i	$0.632496\pi$
$444$	2.29356e8	0.124357
$445$	−3.59234e9	−1.93249
$446$	1.43084e9	0.763694
$447$	−2.09456e9	−1.10922
$448$	−3.39390e8	−0.178331
$449$	2.90185e9	1.51291	0.756454	−	0.654046i	$-0.226930\pi$
$449$	2.90185e9	1.51291	0.756454	+	0.654046i	$0.226930\pi$
$450$	3.61937e7	0.0187236
$451$	−2.72627e9	−1.39943
$452$	2.83984e8	0.144647
$453$	−3.26724e9	−1.65135
$454$	1.36006e9	0.682122
$455$	2.22932e8	0.110952
$456$	−1.23283e9	−0.608872
$457$	−2.23509e9	−1.09544	−0.547720	−	0.836661i	$-0.684504\pi$
$457$	−2.23509e9	−1.09544	−0.547720	+	0.836661i	$0.684504\pi$
$458$	−4.55143e7	−0.0221370
$459$	2.68175e9	1.29441
$460$	1.04935e9	0.502651
$461$	−2.50252e9	−1.18967	−0.594833	−	0.803849i	$-0.702782\pi$
$461$	−2.50252e9	−1.18967	−0.594833	+	0.803849i	$0.702782\pi$
$462$	−4.89877e8	−0.231122
$463$	1.61344e9	0.755475	0.377737	−	0.925913i	$-0.376702\pi$
$463$	1.61344e9	0.755475	0.377737	+	0.925913i	$0.376702\pi$
$464$	3.73925e8	0.173769
$465$	−4.76858e9	−2.19940
$466$	6.39529e8	0.292759
$467$	5.43251e7	0.0246826	0.0123413	−	0.999924i	$-0.496072\pi$
$467$	5.43251e7	0.0246826	0.0123413	+	0.999924i	$0.496072\pi$
$468$	1.11664e8	0.0503561
$469$	−1.05786e9	−0.473503
$470$	−8.97034e8	−0.398535
$471$	−4.85862e9	−2.14260
$472$	9.06397e8	0.396754
$473$	9.42769e8	0.409630
$474$	−5.55656e8	−0.239652
$475$	−1.58077e8	−0.0676770
$476$	9.38334e8	0.398780
$477$	2.63346e8	0.111100
$478$	−2.28025e9	−0.954959
$479$	3.25378e9	1.35274	0.676370	−	0.736562i	$-0.263552\pi$
$479$	3.25378e9	1.35274	0.676370	+	0.736562i	$0.263552\pi$
$480$	−2.97099e9	−1.22619
$481$	−1.11464e8	−0.0456695
$482$	1.82837e9	0.743702
$483$	−7.48109e8	−0.302100
$484$	1.81915e8	0.0729306
$485$	2.85412e9	1.13600
$486$	7.68179e8	0.303554
$487$	−1.98132e9	−0.777327	−0.388663	−	0.921380i	$-0.627063\pi$
$487$	−1.98132e9	−0.777327	−0.388663	+	0.921380i	$0.627063\pi$
$488$	6.04278e8	0.235379
$489$	3.17060e9	1.22620
$490$	2.26247e8	0.0868752
$491$	4.58463e8	0.174791	0.0873954	−	0.996174i	$-0.472146\pi$
$491$	4.58463e8	0.174791	0.0873954	+	0.996174i	$0.472146\pi$
$492$	2.95755e9	1.11958
$493$	6.13937e9	2.30760
$494$	2.40345e8	0.0896998
$495$	−7.30757e8	−0.270804
$496$	5.94097e8	0.218611
$497$	1.30092e9	0.475340
$498$	−1.71723e9	−0.623054
$499$	−2.67502e9	−0.963773	−0.481887	−	0.876234i	$-0.660048\pi$
$499$	−2.67502e9	−0.963773	−0.481887	+	0.876234i	$0.660048\pi$
$500$	1.74345e9	0.623757
$501$	4.55148e9	1.61704
$502$	−1.23575e9	−0.435980
$503$	−3.20863e9	−1.12417	−0.562084	−	0.827080i	$-0.690000\pi$
$503$	−3.20863e9	−1.12417	−0.562084	+	0.827080i	$0.690000\pi$
$504$	2.82496e8	0.0982892
$505$	−7.03985e8	−0.243245
$506$	1.12062e9	0.384530
$507$	−2.54486e8	−0.0867233
$508$	−1.73169e9	−0.586067
$509$	5.69298e9	1.91349	0.956747	−	0.290921i	$-0.0939616\pi$
$509$	5.69298e9	1.91349	0.956747	+	0.290921i	$0.0939616\pi$
$510$	−3.23488e9	−1.07985
$511$	5.79659e7	0.0192176
$512$	7.15740e8	0.235673
$513$	−1.41455e9	−0.462602
$514$	−3.28368e8	−0.106657
$515$	6.71553e8	0.216648
$516$	−1.02275e9	−0.327713
$517$	1.94383e9	0.618646
$518$	−1.13121e8	−0.0357593
$519$	5.75852e9	1.80811
$520$	9.03062e8	0.281647
$521$	4.01360e9	1.24338	0.621688	−	0.783265i	$-0.286447\pi$
$521$	4.01360e9	1.24338	0.621688	+	0.783265i	$0.286447\pi$
$522$	7.41461e8	0.228161
$523$	3.14718e9	0.961980	0.480990	−	0.876726i	$-0.340277\pi$
$523$	3.14718e9	0.961980	0.480990	+	0.876726i	$0.340277\pi$
$524$	−1.60571e9	−0.487536
$525$	1.69866e8	0.0512328
$526$	2.74275e9	0.821743
$527$	9.75431e9	2.90308
$528$	4.26943e8	0.126227
$529$	−1.69349e9	−0.497380
$530$	8.54361e8	0.249273
$531$	−3.86687e8	−0.112080
$532$	−4.94946e8	−0.142517
$533$	−1.43732e9	−0.411159
$534$	4.16176e9	1.18272
$535$	2.09012e8	0.0590110
$536$	−4.28521e9	−1.20198
$537$	−4.63881e9	−1.29270
$538$	1.62973e9	0.451209
$539$	−4.90267e8	−0.134857
$540$	−2.13211e9	−0.582681
$541$	1.40011e9	0.380165	0.190082	−	0.981768i	$-0.439124\pi$
$541$	1.40011e9	0.380165	0.190082	+	0.981768i	$0.439124\pi$
$542$	−3.18669e8	−0.0859690
$543$	−5.06305e9	−1.35710
$544$	6.07728e9	1.61850
$545$	5.89410e9	1.55966
$546$	−2.58269e8	−0.0679045
$547$	6.13945e8	0.160389	0.0801944	−	0.996779i	$-0.474446\pi$
$547$	6.13945e8	0.160389	0.0801944	+	0.996779i	$0.474446\pi$
$548$	−3.24114e9	−0.841330
$549$	−2.57797e8	−0.0664928
$550$	−2.54447e8	−0.0652121
$551$	−3.23835e9	−0.824695
$552$	−3.03047e9	−0.766872
$553$	−5.56098e8	−0.139834
$554$	−3.17465e9	−0.793254
$555$	−7.91328e8	−0.196486
$556$	3.13614e9	0.773808
$557$	2.17564e9	0.533451	0.266725	−	0.963773i	$-0.414058\pi$
$557$	2.17564e9	0.533451	0.266725	+	0.963773i	$0.414058\pi$
$558$	1.17804e9	0.287039
$559$	4.97040e8	0.120351
$560$	−1.97181e8	−0.0474467
$561$	7.00985e9	1.67625
$562$	−1.91467e9	−0.455006
$563$	2.66923e9	0.630385	0.315193	−	0.949028i	$-0.397931\pi$
$563$	2.66923e9	0.630385	0.315193	+	0.949028i	$0.397931\pi$
$564$	−2.10873e9	−0.494931
$565$	−9.79804e8	−0.228544
$566$	−2.11311e9	−0.489851
$567$	1.96469e9	0.452641
$568$	5.26983e9	1.20664
$569$	3.22353e9	0.733565	0.366782	−	0.930307i	$-0.380459\pi$
$569$	3.22353e9	0.733565	0.366782	+	0.930307i	$0.380459\pi$
$570$	1.70631e9	0.385919
$571$	−2.77463e9	−0.623704	−0.311852	−	0.950131i	$-0.600949\pi$
$571$	−2.77463e9	−0.623704	−0.311852	+	0.950131i	$0.600949\pi$
$572$	−7.85014e8	−0.175385
$573$	−6.79464e9	−1.50878
$574$	−1.45869e9	−0.321938
$575$	−3.88575e8	−0.0852389
$576$	5.86523e8	0.127881
$577$	1.90843e9	0.413581	0.206791	−	0.978385i	$-0.433698\pi$
$577$	1.90843e9	0.413581	0.206791	+	0.978385i	$0.433698\pi$
$578$	3.94968e9	0.850775
$579$	4.67687e9	1.00134
$580$	−4.88107e9	−1.03876
$581$	−1.71860e9	−0.363544
$582$	−3.30653e9	−0.695252
$583$	−1.85136e9	−0.386947
$584$	2.34810e8	0.0487834
$585$	−3.85264e8	−0.0795634
$586$	1.40891e9	0.289228
$587$	−3.28107e9	−0.669549	−0.334774	−	0.942298i	$-0.608660\pi$
$587$	−3.28107e9	−0.669549	−0.334774	+	0.942298i	$0.608660\pi$
$588$	5.31857e8	0.107888
$589$	−5.14514e9	−1.03751
$590$	−1.25451e9	−0.251473
$591$	−1.14856e8	−0.0228874
$592$	9.85882e7	0.0195299
$593$	−6.58808e9	−1.29738	−0.648690	−	0.761053i	$-0.724683\pi$
$593$	−6.58808e9	−1.29738	−0.648690	+	0.761053i	$0.724683\pi$
$594$	−2.27691e9	−0.445753
$595$	−3.23745e9	−0.630078
$596$	−3.40638e9	−0.659069
$597$	2.84301e9	0.546850
$598$	5.90802e8	0.112976
$599$	3.71767e9	0.706769	0.353384	−	0.935478i	$-0.385031\pi$
$599$	3.71767e9	0.706769	0.353384	+	0.935478i	$0.385031\pi$
$600$	6.88098e8	0.130053
$601$	2.62109e9	0.492518	0.246259	−	0.969204i	$-0.420799\pi$
$601$	2.62109e9	0.492518	0.246259	+	0.969204i	$0.420799\pi$
$602$	5.04429e8	0.0942351
$603$	1.82816e9	0.339549
$604$	−5.31350e9	−0.981186
$605$	−6.27646e8	−0.115231
$606$	8.15574e8	0.148871
$607$	−1.04965e10	−1.90494	−0.952472	−	0.304627i	$-0.901468\pi$
$607$	−1.04965e10	−1.90494	−0.952472	+	0.304627i	$0.901468\pi$
$608$	−3.20560e9	−0.578425
$609$	3.47986e9	0.624311
$610$	−8.36357e8	−0.149189
$611$	1.02481e9	0.181761
$612$	−1.62160e9	−0.285965
$613$	2.60944e9	0.457547	0.228774	−	0.973480i	$-0.426528\pi$
$613$	2.60944e9	0.457547	0.228774	+	0.973480i	$0.426528\pi$
$614$	3.25761e9	0.567949
$615$	−1.02042e10	−1.76895
$616$	−1.98599e9	−0.342330
$617$	−6.60062e9	−1.13132	−0.565662	−	0.824637i	$-0.691379\pi$
$617$	−6.60062e9	−1.13132	−0.565662	+	0.824637i	$0.691379\pi$
$618$	−7.78001e8	−0.132593
$619$	7.56093e9	1.28132	0.640661	−	0.767824i	$-0.278661\pi$
$619$	7.56093e9	1.28132	0.640661	+	0.767824i	$0.278661\pi$
$620$	−7.75511e9	−1.30682
$621$	−3.47716e9	−0.582644
$622$	2.16940e9	0.361471
$623$	4.16508e9	0.690104
$624$	2.25089e8	0.0370859
$625$	−6.74912e9	−1.10578
$626$	6.54628e9	1.06656
$627$	−3.69751e9	−0.599063
$628$	−7.90155e9	−1.27307
$629$	1.61869e9	0.259350
$630$	−3.90992e8	−0.0622983
$631$	3.56014e9	0.564111	0.282056	−	0.959398i	$-0.408984\pi$
$631$	3.56014e9	0.564111	0.282056	+	0.959398i	$0.408984\pi$
$632$	−2.25266e9	−0.354965
$633$	9.19407e9	1.44077
$634$	3.58510e9	0.558712
$635$	5.97471e9	0.925995
$636$	2.00842e9	0.309567
$637$	−2.58475e8	−0.0396214
$638$	−5.21258e9	−0.794658
$639$	−2.24821e9	−0.340867
$640$	−5.31003e9	−0.800695
$641$	−3.70708e9	−0.555941	−0.277971	−	0.960590i	$-0.589662\pi$
$641$	−3.70708e9	−0.555941	−0.277971	+	0.960590i	$0.589662\pi$
$642$	−2.42142e8	−0.0361159
$643$	−4.37448e9	−0.648915	−0.324458	−	0.945900i	$-0.605182\pi$
$643$	−4.37448e9	−0.648915	−0.324458	+	0.945900i	$0.605182\pi$
$644$	−1.21665e9	−0.179500
$645$	3.52869e9	0.517791
$646$	−3.49033e9	−0.509393
$647$	−8.40749e9	−1.22040	−0.610199	−	0.792248i	$-0.708911\pi$
$647$	−8.40749e9	−1.22040	−0.610199	+	0.792248i	$0.708911\pi$
$648$	7.95865e9	1.14902
$649$	2.71847e9	0.390362
$650$	−1.34148e8	−0.0191596
$651$	5.52884e9	0.785417
$652$	5.15632e9	0.728574
$653$	−4.62631e9	−0.650188	−0.325094	−	0.945682i	$-0.605396\pi$
$653$	−4.62631e9	−0.650188	−0.325094	+	0.945682i	$0.605396\pi$
$654$	−6.82838e9	−0.954543
$655$	5.54004e9	0.770315
$656$	1.27129e9	0.175826
$657$	−1.00175e8	−0.0137810
$658$	1.04005e9	0.142319
$659$	8.59881e9	1.17041	0.585207	−	0.810884i	$-0.301013\pi$
$659$	8.59881e9	1.17041	0.585207	+	0.810884i	$0.301013\pi$
$660$	−5.57314e9	−0.754564
$661$	−3.09178e9	−0.416393	−0.208197	−	0.978087i	$-0.566759\pi$
$661$	−3.09178e9	−0.416393	−0.208197	+	0.978087i	$0.566759\pi$
$662$	6.32770e9	0.847702
$663$	3.69568e9	0.492490
$664$	−6.96175e9	−0.922848
$665$	1.70767e9	0.225179
$666$	1.95492e8	0.0256430
$667$	−7.96032e9	−1.03870
$668$	7.40205e9	0.960804
$669$	−1.16051e10	−1.49851
$670$	5.93100e9	0.761844
$671$	1.81235e9	0.231587
$672$	3.44466e9	0.437879
$673$	3.53335e9	0.446821	0.223411	−	0.974724i	$-0.428281\pi$
$673$	3.53335e9	0.446821	0.223411	+	0.974724i	$0.428281\pi$
$674$	1.64152e9	0.206508
$675$	7.89524e8	0.0988103
$676$	−4.13869e8	−0.0515287
$677$	7.28572e9	0.902427	0.451213	−	0.892416i	$-0.350991\pi$
$677$	7.28572e9	0.902427	0.451213	+	0.892416i	$0.350991\pi$
$678$	1.13511e9	0.139873
$679$	−3.30916e9	−0.405671
$680$	−1.31144e10	−1.59944
$681$	−1.10310e10	−1.33845
$682$	−8.28182e9	−0.999724
$683$	4.58761e9	0.550952	0.275476	−	0.961308i	$-0.411165\pi$
$683$	4.58761e9	0.550952	0.275476	+	0.961308i	$0.411165\pi$
$684$	8.55349e8	0.102199
$685$	1.11826e10	1.32931
$686$	−2.62318e8	−0.0310237
$687$	3.69153e8	0.0434368
$688$	−4.39625e8	−0.0514663
$689$	−9.76062e8	−0.113687
$690$	4.19435e9	0.486063
$691$	−4.79400e9	−0.552745	−0.276373	−	0.961051i	$-0.589132\pi$
$691$	−4.79400e9	−0.552745	−0.276373	+	0.961051i	$0.589132\pi$
$692$	9.36504e9	1.07433
$693$	8.47263e8	0.0967057
$694$	4.42025e9	0.501983
$695$	−1.08203e10	−1.22263
$696$	1.40963e10	1.58480
$697$	2.08730e10	2.33491
$698$	6.63301e7	0.00738272
$699$	−5.18704e9	−0.574446
$700$	2.76252e8	0.0304412
$701$	−1.30910e10	−1.43535	−0.717676	−	0.696377i	$-0.754794\pi$
$701$	−1.30910e10	−1.43535	−0.717676	+	0.696377i	$0.754794\pi$
$702$	−1.20042e9	−0.130964
$703$	−8.53816e8	−0.0926874
$704$	−4.12335e9	−0.445395
$705$	7.27558e9	0.781998
$706$	−7.23556e9	−0.773848
$707$	8.16223e8	0.0868642
$708$	−2.94908e9	−0.312299
$709$	−3.90402e7	−0.00411386	−0.00205693	−	0.999998i	$-0.500655\pi$
$709$	−3.90402e7	−0.00411386	−0.00205693	+	0.999998i	$0.500655\pi$
$710$	−7.29376e9	−0.764799
$711$	9.61029e8	0.100275
$712$	1.68720e10	1.75181
$713$	−1.26475e10	−1.30674
$714$	3.75062e9	0.385620
$715$	2.70847e9	0.277110
$716$	−7.54408e9	−0.768087
$717$	1.84944e10	1.87380
$718$	1.35406e9	0.136521
$719$	−1.42934e10	−1.43412	−0.717059	−	0.697013i	$-0.754512\pi$
$719$	−1.42934e10	−1.43412	−0.717059	+	0.697013i	$0.754512\pi$
$720$	3.40761e8	0.0340241
$721$	−7.78620e8	−0.0773663
$722$	−3.96954e9	−0.392518
$723$	−1.48294e10	−1.45928
$724$	−8.23401e9	−0.806355
$725$	1.80747e9	0.176152
$726$	7.27134e8	0.0705239
$727$	7.90232e9	0.762753	0.381377	−	0.924420i	$-0.375450\pi$
$727$	7.90232e9	0.762753	0.381377	+	0.924420i	$0.375450\pi$
$728$	−1.04704e9	−0.100578
$729$	6.29660e9	0.601949
$730$	−3.24992e8	−0.0309202
$731$	−7.21808e9	−0.683457
$732$	−1.96610e9	−0.185275
$733$	8.00899e9	0.751128	0.375564	−	0.926797i	$-0.377449\pi$
$733$	8.00899e9	0.751128	0.375564	+	0.926797i	$0.377449\pi$
$734$	−6.26560e9	−0.584825
$735$	−1.83502e9	−0.170465
$736$	−7.87981e9	−0.728523
$737$	−1.28522e10	−1.18261
$738$	2.52087e9	0.230862
$739$	−7.30652e9	−0.665971	−0.332985	−	0.942932i	$-0.608056\pi$
$739$	−7.30652e9	−0.665971	−0.332985	+	0.942932i	$0.608056\pi$
$740$	−1.28693e9	−0.116747
$741$	−1.94937e9	−0.176007
$742$	−9.90573e8	−0.0890170
$743$	7.68027e9	0.686935	0.343468	−	0.939165i	$-0.388398\pi$
$743$	7.68027e9	0.686935	0.343468	+	0.939165i	$0.388398\pi$
$744$	2.23964e10	1.99376
$745$	1.17527e10	1.04134
$746$	2.34157e9	0.206501
$747$	2.97002e9	0.260698
$748$	1.14001e10	0.995984
$749$	−2.42335e8	−0.0210732
$750$	6.96877e9	0.603173
$751$	1.28085e10	1.10347	0.551734	−	0.834020i	$-0.313966\pi$
$751$	1.28085e10	1.10347	0.551734	+	0.834020i	$0.313966\pi$
$752$	−9.06434e8	−0.0777273
$753$	1.00228e10	0.855472
$754$	−2.74814e9	−0.233474
$755$	1.83327e10	1.55029
$756$	2.47203e9	0.208079
$757$	−1.53569e10	−1.28667	−0.643336	−	0.765584i	$-0.722450\pi$
$757$	−1.53569e10	−1.28667	−0.643336	+	0.765584i	$0.722450\pi$
$758$	2.38079e9	0.198554
$759$	−9.08898e9	−0.754517
$760$	6.91749e9	0.571611
$761$	1.70998e10	1.40651	0.703257	−	0.710935i	$-0.251728\pi$
$761$	1.70998e10	1.40651	0.703257	+	0.710935i	$0.251728\pi$
$762$	−6.92176e9	−0.566727
$763$	−6.83381e9	−0.556964
$764$	−1.10501e10	−0.896477
$765$	5.59486e9	0.451829
$766$	−4.87415e9	−0.391830
$767$	1.43321e9	0.114690
$768$	1.28293e10	1.02197
$769$	−2.35139e9	−0.186459	−0.0932294	−	0.995645i	$-0.529719\pi$
$769$	−2.35139e9	−0.186459	−0.0932294	+	0.995645i	$0.529719\pi$
$770$	2.74873e9	0.216978
$771$	2.66329e9	0.209281
$772$	7.60597e9	0.594968
$773$	−2.34257e9	−0.182417	−0.0912083	−	0.995832i	$-0.529073\pi$
$773$	−2.34257e9	−0.182417	−0.0912083	+	0.995832i	$0.529073\pi$
$774$	−8.71738e8	−0.0675760
$775$	2.87173e9	0.221609
$776$	−1.34049e10	−1.02978
$777$	9.17490e8	0.0701662
$778$	−1.77198e9	−0.134906
$779$	−1.10100e10	−0.834458
$780$	−2.93823e9	−0.221694
$781$	1.58053e10	1.18720
$782$	−8.57971e9	−0.641578
$783$	1.61741e10	1.20408
$784$	2.28618e8	0.0169435
$785$	2.72620e10	2.01148
$786$	−6.41819e9	−0.471448
$787$	7.91498e9	0.578813	0.289406	−	0.957206i	$-0.406542\pi$
$787$	7.91498e9	0.578813	0.289406	+	0.957206i	$0.406542\pi$
$788$	−1.86789e8	−0.0135991
$789$	−2.22456e10	−1.61241
$790$	3.11782e9	0.224986
$791$	1.13602e9	0.0816144
$792$	3.43212e9	0.245485
$793$	9.55494e8	0.0680412
$794$	−1.17603e10	−0.833772
$795$	−6.92947e9	−0.489119
$796$	4.62357e9	0.324924
$797$	1.19781e10	0.838075	0.419038	−	0.907969i	$-0.362368\pi$
$797$	1.19781e10	0.838075	0.419038	+	0.907969i	$0.362368\pi$
$798$	−1.97835e9	−0.137814
$799$	−1.48825e10	−1.03219
$800$	1.78919e9	0.123550
$801$	−7.19794e9	−0.494874
$802$	1.46529e10	1.00303
$803$	7.04244e8	0.0479975
$804$	1.39425e10	0.946116
$805$	4.19769e9	0.283612
$806$	−4.36628e9	−0.293723
$807$	−1.32183e10	−0.885355
$808$	3.30638e9	0.220503
$809$	1.85053e10	1.22879	0.614394	−	0.789000i	$-0.289401\pi$
$809$	1.85053e10	1.22879	0.614394	+	0.789000i	$0.289401\pi$
$810$	−1.10153e10	−0.728278
$811$	−8.34631e9	−0.549442	−0.274721	−	0.961524i	$-0.588585\pi$
$811$	−8.34631e9	−0.549442	−0.274721	+	0.961524i	$0.588585\pi$
$812$	5.65927e9	0.370949
$813$	2.58463e9	0.168687
$814$	−1.37434e9	−0.0893116
$815$	−1.77904e10	−1.15116
$816$	−3.26878e9	−0.210606
$817$	3.80734e9	0.244256
$818$	−1.29868e9	−0.0829593
$819$	4.46688e8	0.0284126
$820$	−1.65950e10	−1.05106
$821$	−1.52462e10	−0.961525	−0.480762	−	0.876851i	$-0.659640\pi$
$821$	−1.52462e10	−0.961525	−0.480762	+	0.876851i	$0.659640\pi$
$822$	−1.29552e10	−0.813566
$823$	−2.79970e10	−1.75070	−0.875352	−	0.483486i	$-0.839370\pi$
$823$	−2.79970e10	−1.75070	−0.875352	+	0.483486i	$0.839370\pi$
$824$	−3.15406e9	−0.196392
$825$	2.06375e9	0.127958
$826$	1.45452e9	0.0898026
$827$	−1.18156e10	−0.726418	−0.363209	−	0.931708i	$-0.618319\pi$
$827$	−1.18156e10	−0.726418	−0.363209	+	0.931708i	$0.618319\pi$
$828$	2.10257e9	0.128719
$829$	1.38969e10	0.847185	0.423592	−	0.905853i	$-0.360769\pi$
$829$	1.38969e10	0.847185	0.423592	+	0.905853i	$0.360769\pi$
$830$	9.63549e9	0.584925
$831$	2.57487e10	1.55651
$832$	−2.17388e9	−0.130859
$833$	3.75361e9	0.225005
$834$	1.25355e10	0.748272
$835$	−2.55387e10	−1.51808
$836$	−6.01323e9	−0.355948
$837$	2.56976e10	1.51480
$838$	1.87837e10	1.10262
$839$	−2.03877e9	−0.119180	−0.0595898	−	0.998223i	$-0.518979\pi$
$839$	−2.03877e9	−0.119180	−0.0595898	+	0.998223i	$0.518979\pi$
$840$	−7.43336e9	−0.432721
$841$	1.97778e10	1.14655
$842$	−3.95432e9	−0.228286
$843$	1.55293e10	0.892804
$844$	1.49523e10	0.856068
$845$	1.42794e9	0.0814161
$846$	−1.79738e9	−0.102057
$847$	7.27712e8	0.0411498
$848$	8.63313e8	0.0486164
$849$	1.71388e10	0.961176
$850$	1.94811e9	0.108805
$851$	−2.09880e9	−0.116739
$852$	−1.71461e10	−0.949786
$853$	−2.35848e10	−1.30110	−0.650550	−	0.759464i	$-0.725461\pi$
$853$	−2.35848e10	−1.30110	−0.650550	+	0.759464i	$0.725461\pi$
$854$	9.69699e8	0.0532763
$855$	−2.95114e9	−0.161476
$856$	−9.81659e8	−0.0534937
$857$	−5.84270e9	−0.317089	−0.158544	−	0.987352i	$-0.550680\pi$
$857$	−5.84270e9	−0.317089	−0.158544	+	0.987352i	$0.550680\pi$
$858$	−3.13779e9	−0.169597
$859$	1.89371e10	1.01938	0.509691	−	0.860358i	$-0.329760\pi$
$859$	1.89371e10	1.01938	0.509691	+	0.860358i	$0.329760\pi$
$860$	5.73869e9	0.307658
$861$	1.18310e10	0.631701
$862$	4.87266e8	0.0259114
$863$	−1.94559e9	−0.103042	−0.0515208	−	0.998672i	$-0.516407\pi$
$863$	−1.94559e9	−0.103042	−0.0515208	+	0.998672i	$0.516407\pi$
$864$	1.60105e10	0.844516
$865$	−3.23114e10	−1.69746
$866$	1.08951e10	0.570058
$867$	−3.20347e10	−1.66938
$868$	8.99152e9	0.466675
$869$	−6.75618e9	−0.349247
$870$	−1.95102e10	−1.00449
$871$	−6.77585e9	−0.347456
$872$	−2.76826e10	−1.41384
$873$	5.71878e9	0.290907
$874$	4.52557e9	0.229289
$875$	6.97431e9	0.351944
$876$	−7.63986e8	−0.0383991
$877$	−2.89874e9	−0.145115	−0.0725574	−	0.997364i	$-0.523116\pi$
$877$	−2.89874e9	−0.145115	−0.0725574	+	0.997364i	$0.523116\pi$
$878$	1.25240e9	0.0624472
$879$	−1.14272e10	−0.567518
$880$	−2.39560e9	−0.118502
$881$	1.73032e10	0.852534	0.426267	−	0.904598i	$-0.359828\pi$
$881$	1.73032e10	0.852534	0.426267	+	0.904598i	$0.359828\pi$
$882$	4.53329e8	0.0222471
$883$	2.28544e10	1.11714	0.558570	−	0.829457i	$-0.311350\pi$
$883$	2.28544e10	1.11714	0.558570	+	0.829457i	$0.311350\pi$
$884$	6.01026e9	0.292624
$885$	1.01750e10	0.493436
$886$	−9.61890e9	−0.464630
$887$	−1.52330e10	−0.732913	−0.366457	−	0.930435i	$-0.619429\pi$
$887$	−1.52330e10	−0.732913	−0.366457	+	0.930435i	$0.619429\pi$
$888$	3.71660e9	0.178115
$889$	−6.92726e9	−0.330678
$890$	−2.33519e10	−1.11034
$891$	2.38696e10	1.13051
$892$	−1.88734e10	−0.890373
$893$	7.85011e9	0.368889
$894$	−1.36157e10	−0.637320
$895$	2.60287e10	1.21359
$896$	6.15662e9	0.285933
$897$	−4.79182e9	−0.221680
$898$	1.88634e10	0.869266
$899$	5.88301e10	2.70048
$900$	−4.77409e8	−0.0218294
$901$	1.41745e10	0.645611
$902$	−1.77221e10	−0.804065
$903$	−4.09128e9	−0.184906
$904$	4.60181e9	0.207176
$905$	2.84091e10	1.27405
$906$	−2.12386e10	−0.948807
$907$	−2.39482e10	−1.06573	−0.532865	−	0.846200i	$-0.678885\pi$
$907$	−2.39482e10	−1.06573	−0.532865	+	0.846200i	$0.678885\pi$
$908$	−1.79397e10	−0.795271
$909$	−1.41057e9	−0.0622904
$910$	1.44917e9	0.0637490
$911$	−2.95933e10	−1.29682	−0.648409	−	0.761292i	$-0.724565\pi$
$911$	−2.95933e10	−1.29682	−0.648409	+	0.761292i	$0.724565\pi$
$912$	1.72419e9	0.0752669
$913$	−2.08797e10	−0.907981
$914$	−1.45292e10	−0.629403
$915$	6.78345e9	0.292736
$916$	6.00351e8	0.0258090
$917$	−6.42329e9	−0.275084
$918$	1.74326e10	0.743727
$919$	−1.40021e10	−0.595097	−0.297548	−	0.954707i	$-0.596169\pi$
$919$	−1.40021e10	−0.595097	−0.297548	+	0.954707i	$0.596169\pi$
$920$	1.70041e10	0.719942
$921$	−2.64215e10	−1.11442
$922$	−1.62676e10	−0.683542
$923$	8.33274e9	0.348804
$924$	6.46168e9	0.269459
$925$	4.76554e8	0.0197977
$926$	1.04881e10	0.434070
$927$	1.34558e9	0.0554794
$928$	3.66532e10	1.50555
$929$	−4.47459e10	−1.83104	−0.915520	−	0.402272i	$-0.868221\pi$
$929$	−4.47459e10	−1.83104	−0.915520	+	0.402272i	$0.868221\pi$
$930$	−3.09980e10	−1.26370
$931$	−1.97993e9	−0.0804128
$932$	−8.43565e9	−0.341321
$933$	−1.75954e10	−0.709272
$934$	3.53139e8	0.0141818
$935$	−3.93327e10	−1.57367
$936$	1.80946e9	0.0721245
$937$	−3.99242e10	−1.58543	−0.792716	−	0.609591i	$-0.791334\pi$
$937$	−3.99242e10	−1.58543	−0.792716	+	0.609591i	$0.791334\pi$
$938$	−6.87659e9	−0.272059
$939$	−5.30950e10	−2.09278
$940$	1.18322e10	0.464643
$941$	−7.73309e9	−0.302544	−0.151272	−	0.988492i	$-0.548337\pi$
$941$	−7.73309e9	−0.302544	−0.151272	+	0.988492i	$0.548337\pi$
$942$	−3.15834e10	−1.23106
$943$	−2.70640e10	−1.05100
$944$	−1.26766e9	−0.0490455
$945$	−8.52904e9	−0.328767
$946$	6.12845e9	0.235359
$947$	−2.90345e10	−1.11094	−0.555468	−	0.831538i	$-0.687461\pi$
$947$	−2.90345e10	−1.11094	−0.555468	+	0.831538i	$0.687461\pi$
$948$	7.32932e9	0.279405
$949$	3.71286e8	0.0141019
$950$	−1.02758e9	−0.0388849
$951$	−2.90777e10	−1.09630
$952$	1.52052e10	0.571168
$953$	3.39685e10	1.27131	0.635655	−	0.771973i	$-0.280730\pi$
$953$	3.39685e10	1.27131	0.635655	+	0.771973i	$0.280730\pi$
$954$	1.71188e9	0.0638341
$955$	3.81252e10	1.41645
$956$	3.00774e10	1.11337
$957$	4.22777e10	1.55926
$958$	2.11511e10	0.777239
$959$	−1.29655e10	−0.474706
$960$	−1.54333e10	−0.563001
$961$	6.59574e10	2.39735
$962$	−7.24567e8	−0.0262401
$963$	4.18795e8	0.0151116
$964$	−2.41169e10	−0.867065
$965$	−2.62422e10	−0.940059
$966$	−4.86306e9	−0.173576
$967$	−2.42149e10	−0.861173	−0.430587	−	0.902549i	$-0.641693\pi$
$967$	−2.42149e10	−0.861173	−0.430587	+	0.902549i	$0.641693\pi$
$968$	2.94784e9	0.104458
$969$	2.83090e10	0.999521
$970$	1.85532e10	0.652705
$971$	4.08684e9	0.143259	0.0716293	−	0.997431i	$-0.477180\pi$
$971$	4.08684e9	0.143259	0.0716293	+	0.997431i	$0.477180\pi$
$972$	−1.01326e10	−0.353907
$973$	1.25454e10	0.436608
$974$	−1.28795e10	−0.446626
$975$	1.08803e9	0.0375946
$976$	−8.45121e8	−0.0290968
$977$	−2.94781e10	−1.01127	−0.505636	−	0.862747i	$-0.668742\pi$
$977$	−2.94781e10	−1.01127	−0.505636	+	0.862747i	$0.668742\pi$
$978$	2.06104e10	0.704531
$979$	5.06026e10	1.72359
$980$	−2.98428e9	−0.101286
$981$	1.18100e10	0.399399
$982$	2.98022e9	0.100429
$983$	−2.06234e10	−0.692504	−0.346252	−	0.938142i	$-0.612546\pi$
$983$	−2.06234e10	−0.692504	−0.346252	+	0.938142i	$0.612546\pi$
$984$	4.79256e10	1.60356
$985$	6.44462e8	0.0214867
$986$	3.99088e10	1.32587
$987$	−8.43554e9	−0.279256
$988$	−3.17025e9	−0.104579
$989$	9.35897e9	0.307639
$990$	−4.75027e9	−0.155595
$991$	−4.08599e10	−1.33364	−0.666821	−	0.745218i	$-0.732345\pi$
$991$	−4.08599e10	−1.33364	−0.666821	+	0.745218i	$0.732345\pi$
$992$	5.82351e10	1.89406
$993$	−5.13221e10	−1.66334
$994$	8.45662e9	0.273114
$995$	−1.59523e10	−0.513384
$996$	2.26510e10	0.726405
$997$	−6.62022e7	−0.00211563	−0.00105781	−	0.999999i	$-0.500337\pi$
$997$	−6.62022e7	−0.00211563	−0.00105781	+	0.999999i	$0.500337\pi$
$998$	−1.73889e10	−0.553751
$999$	4.26443e9	0.135326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.d.1.7	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.d.1.7	✓	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)

\(f(q)\)	\(=\)	\(q+6.50047 q^{2} -52.7234 q^{3} -85.7438 q^{4} +295.835 q^{5} -342.727 q^{6} -343.000 q^{7} -1389.44 q^{8} +592.761 q^{9} +O(q^{10})\)	\(q+6.50047 q^{2} -52.7234 q^{3} -85.7438 q^{4} +295.835 q^{5} -342.727 q^{6} -343.000 q^{7} -1389.44 q^{8} +592.761 q^{9} +1923.06 q^{10} -4167.20 q^{11} +4520.71 q^{12} -2197.00 q^{13} -2229.66 q^{14} -15597.4 q^{15} +1943.22 q^{16} +31905.1 q^{17} +3853.23 q^{18} -16829.1 q^{19} -25366.0 q^{20} +18084.1 q^{21} -27088.8 q^{22} -41368.2 q^{23} +73255.9 q^{24} +9393.08 q^{25} -14281.5 q^{26} +84053.8 q^{27} +29410.1 q^{28} +192426. q^{29} -101391. q^{30} +305729. q^{31} +190480. q^{32} +219709. q^{33} +207399. q^{34} -101471. q^{35} -50825.6 q^{36} +50734.5 q^{37} -109397. q^{38} +115833. q^{39} -411043. q^{40} +654222. q^{41} +117555. q^{42} -226236. q^{43} +357312. q^{44} +175359. q^{45} -268913. q^{46} -466460. q^{47} -102453. q^{48} +117649. q^{49} +61059.5 q^{50} -1.68215e6 q^{51} +188379. q^{52} +444270. q^{53} +546389. q^{54} -1.23280e6 q^{55} +476577. q^{56} +887288. q^{57} +1.25086e6 q^{58} -652349. q^{59} +1.33738e6 q^{60} -434908. q^{61} +1.98738e6 q^{62} -203317. q^{63} +989476. q^{64} -649949. q^{65} +1.42821e6 q^{66} +3.08414e6 q^{67} -2.73567e6 q^{68} +2.18108e6 q^{69} -659611. q^{70} -3.79278e6 q^{71} -823604. q^{72} -168997. q^{73} +329799. q^{74} -495236. q^{75} +1.44299e6 q^{76} +1.42935e6 q^{77} +752972. q^{78} +1.62128e6 q^{79} +574871. q^{80} -5.72797e6 q^{81} +4.25275e6 q^{82} +5.01049e6 q^{83} -1.55060e6 q^{84} +9.43864e6 q^{85} -1.47064e6 q^{86} -1.01454e7 q^{87} +5.79006e6 q^{88} -1.21431e7 q^{89} +1.13992e6 q^{90} +753571. q^{91} +3.54707e6 q^{92} -1.61191e7 q^{93} -3.03221e6 q^{94} -4.97863e6 q^{95} -1.00427e7 q^{96} +9.64770e6 q^{97} +764774. q^{98} -2.47015e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9}+O(q^{10}) \) 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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