LMFDB - Embedded newform 91.8.a.d.1.6

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			1.6
Root			$-4.83483$ 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)

$f(q)$	$=$	$q+4.83483 q^{2} +62.4820 q^{3} -104.624 q^{4} +314.530 q^{5} +302.090 q^{6} -343.000 q^{7} -1124.70 q^{8} +1717.00 q^{9} +O(q^{10})$	\(q+4.83483 q^{2} +62.4820 q^{3} -104.624 q^{4} +314.530 q^{5} +302.090 q^{6} -343.000 q^{7} -1124.70 q^{8} +1717.00 q^{9} +1520.70 q^{10} +8467.65 q^{11} -6537.15 q^{12} -2197.00 q^{13} -1658.35 q^{14} +19652.4 q^{15} +7954.20 q^{16} +11951.4 q^{17} +8301.41 q^{18} +6886.88 q^{19} -32907.5 q^{20} -21431.3 q^{21} +40939.6 q^{22} +103273. q^{23} -70273.5 q^{24} +20803.8 q^{25} -10622.1 q^{26} -29366.4 q^{27} +35886.2 q^{28} -101393. q^{29} +95016.1 q^{30} +240887. q^{31} +182419. q^{32} +529076. q^{33} +57783.1 q^{34} -107884. q^{35} -179640. q^{36} -494398. q^{37} +33296.9 q^{38} -137273. q^{39} -353751. q^{40} -517724. q^{41} -103617. q^{42} +670384. q^{43} -885923. q^{44} +540048. q^{45} +499309. q^{46} +390703. q^{47} +496995. q^{48} +117649. q^{49} +100583. q^{50} +746750. q^{51} +229860. q^{52} +316966. q^{53} -141982. q^{54} +2.66333e6 q^{55} +385772. q^{56} +430306. q^{57} -490216. q^{58} +2.76489e6 q^{59} -2.05613e6 q^{60} +50060.8 q^{61} +1.16465e6 q^{62} -588932. q^{63} -136175. q^{64} -691021. q^{65} +2.55799e6 q^{66} -710978. q^{67} -1.25041e6 q^{68} +6.45272e6 q^{69} -521599. q^{70} -4.81274e6 q^{71} -1.93111e6 q^{72} +319628. q^{73} -2.39033e6 q^{74} +1.29987e6 q^{75} -720536. q^{76} -2.90440e6 q^{77} -663691. q^{78} +395221. q^{79} +2.50183e6 q^{80} -5.58996e6 q^{81} -2.50311e6 q^{82} -5.55444e6 q^{83} +2.24224e6 q^{84} +3.75908e6 q^{85} +3.24119e6 q^{86} -6.33521e6 q^{87} -9.52355e6 q^{88} -1.22040e7 q^{89} +2.61104e6 q^{90} +753571. q^{91} -1.08049e7 q^{92} +1.50511e7 q^{93} +1.88898e6 q^{94} +2.16613e6 q^{95} +1.13979e7 q^{96} -5.15456e6 q^{97} +568813. q^{98} +1.45390e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.83483	0.427342	0.213671	−	0.976906i	$-0.431458\pi$
$2$	4.83483	0.427342	0.213671	+	0.976906i	$0.431458\pi$
$3$	62.4820	1.33607	0.668037	−	0.744128i	$-0.267135\pi$
$3$	62.4820	1.33607	0.668037	+	0.744128i	$0.267135\pi$
$4$	−104.624	−0.817378
$5$	314.530	1.12530	0.562648	−	0.826697i	$-0.309783\pi$
$5$	314.530	1.12530	0.562648	+	0.826697i	$0.309783\pi$
$6$	302.090	0.570961
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	−1124.70	−0.776643
$9$	1717.00	0.785094
$10$	1520.70	0.480886
$11$	8467.65	1.91818	0.959088	−	0.283109i	$-0.0913658\pi$
$11$	8467.65	1.91818	0.959088	+	0.283109i	$0.0913658\pi$
$12$	−6537.15	−1.09208
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−1658.35	−0.161520
$15$	19652.4	1.50348
$16$	7954.20	0.485486
$17$	11951.4	0.589996	0.294998	−	0.955498i	$-0.404681\pi$
$17$	11951.4	0.589996	0.294998	+	0.955498i	$0.404681\pi$
$18$	8301.41	0.335504
$19$	6886.88	0.230348	0.115174	−	0.993345i	$-0.463257\pi$
$19$	6886.88	0.230348	0.115174	+	0.993345i	$0.463257\pi$
$20$	−32907.5	−0.919792
$21$	−21431.3	−0.504989
$22$	40939.6	0.819718
$23$	103273.	1.76987	0.884934	−	0.465717i	$-0.154204\pi$
$23$	103273.	1.76987	0.884934	+	0.465717i	$0.154204\pi$
$24$	−70273.5	−1.03765
$25$	20803.8	0.266289
$26$	−10622.1	−0.118523
$27$	−29366.4	−0.287130
$28$	35886.2	0.308940
$29$	−101393.	−0.771993	−0.385996	−	0.922500i	$-0.626142\pi$
$29$	−101393.	−0.771993	−0.385996	+	0.922500i	$0.626142\pi$
$30$	95016.1	0.642500
$31$	240887.	1.45227	0.726137	−	0.687551i	$-0.241314\pi$
$31$	240887.	1.45227	0.726137	+	0.687551i	$0.241314\pi$
$32$	182419.	0.984112
$33$	529076.	2.56282
$34$	57783.1	0.252130
$35$	−107884.	−0.425322
$36$	−179640.	−0.641719
$37$	−494398.	−1.60461	−0.802307	−	0.596912i	$-0.796394\pi$
$37$	−494398.	−1.60461	−0.802307	+	0.596912i	$0.796394\pi$
$38$	33296.9	0.0984376
$39$	−137273.	−0.370560
$40$	−353751.	−0.873952
$41$	−517724.	−1.17315	−0.586577	−	0.809893i	$-0.699525\pi$
$41$	−517724.	−1.17315	−0.586577	+	0.809893i	$0.699525\pi$
$42$	−103617.	−0.215803
$43$	670384.	1.28583	0.642916	−	0.765937i	$-0.277724\pi$
$43$	670384.	1.28583	0.642916	+	0.765937i	$0.277724\pi$
$44$	−885923.	−1.56788
$45$	540048.	0.883463
$46$	499309.	0.756339
$47$	390703.	0.548914	0.274457	−	0.961599i	$-0.411502\pi$
$47$	390703.	0.548914	0.274457	+	0.961599i	$0.411502\pi$
$48$	496995.	0.648645
$49$	117649.	0.142857
$50$	100583.	0.113797
$51$	746750.	0.788278
$52$	229860.	0.226700
$53$	316966.	0.292447	0.146224	−	0.989252i	$-0.453288\pi$
$53$	316966.	0.292447	0.146224	+	0.989252i	$0.453288\pi$
$54$	−141982.	−0.122703
$55$	2.66333e6	2.15851
$56$	385772.	0.293543
$57$	430306.	0.307762
$58$	−490216.	−0.329905
$59$	2.76489e6	1.75265	0.876326	−	0.481719i	$-0.159987\pi$
$59$	2.76489e6	1.75265	0.876326	+	0.481719i	$0.159987\pi$
$60$	−2.05613e6	−1.22891
$61$	50060.8	0.0282386	0.0141193	−	0.999900i	$-0.495506\pi$
$61$	50060.8	0.0282386	0.0141193	+	0.999900i	$0.495506\pi$
$62$	1.16465e6	0.620618
$63$	−588932.	−0.296738
$64$	−136175.	−0.0649334
$65$	−691021.	−0.312101
$66$	2.55799e6	1.09520
$67$	−710978.	−0.288798	−0.144399	−	0.989520i	$-0.546125\pi$
$67$	−710978.	−0.288798	−0.144399	+	0.989520i	$0.546125\pi$
$68$	−1.25041e6	−0.482250
$69$	6.45272e6	2.36467
$70$	−521599.	−0.181758
$71$	−4.81274e6	−1.59584	−0.797918	−	0.602766i	$-0.794065\pi$
$71$	−4.81274e6	−1.59584	−0.797918	+	0.602766i	$0.794065\pi$
$72$	−1.93111e6	−0.609738
$73$	319628.	0.0961645	0.0480822	−	0.998843i	$-0.484689\pi$
$73$	319628.	0.0961645	0.0480822	+	0.998843i	$0.484689\pi$
$74$	−2.39033e6	−0.685720
$75$	1.29987e6	0.355782
$76$	−720536.	−0.188282
$77$	−2.90440e6	−0.725002
$78$	−663691.	−0.158356
$79$	395221.	0.0901872	0.0450936	−	0.998983i	$-0.485641\pi$
$79$	395221.	0.0901872	0.0450936	+	0.998983i	$0.485641\pi$
$80$	2.50183e6	0.546315
$81$	−5.58996e6	−1.16872
$82$	−2.50311e6	−0.501339
$83$	−5.55444e6	−1.06627	−0.533135	−	0.846030i	$-0.678986\pi$
$83$	−5.55444e6	−1.06627	−0.533135	+	0.846030i	$0.678986\pi$
$84$	2.24224e6	0.412767
$85$	3.75908e6	0.663919
$86$	3.24119e6	0.549490
$87$	−6.33521e6	−1.03144
$88$	−9.52355e6	−1.48974
$89$	−1.22040e7	−1.83500	−0.917500	−	0.397735i	$-0.869796\pi$
$89$	−1.22040e7	−1.83500	−0.917500	+	0.397735i	$0.869796\pi$
$90$	2.61104e6	0.377541
$91$	753571.	0.104828
$92$	−1.08049e7	−1.44665
$93$	1.50511e7	1.94034
$94$	1.88898e6	0.234574
$95$	2.16613e6	0.259210
$96$	1.13979e7	1.31485
$97$	−5.15456e6	−0.573443	−0.286721	−	0.958014i	$-0.592565\pi$
$97$	−5.15456e6	−0.573443	−0.286721	+	0.958014i	$0.592565\pi$
$98$	568813.	0.0610489
$99$	1.45390e7	1.50595
$100$	−2.17659e6	−0.217659
$101$	5.66908e6	0.547504	0.273752	−	0.961800i	$-0.411735\pi$
$101$	5.66908e6	0.547504	0.273752	+	0.961800i	$0.411735\pi$
$102$	3.61041e6	0.336865
$103$	−8.15115e6	−0.735003	−0.367501	−	0.930023i	$-0.619787\pi$
$103$	−8.15115e6	−0.735003	−0.367501	+	0.930023i	$0.619787\pi$
$104$	2.47096e6	0.215402
$105$	−6.74079e6	−0.568261
$106$	1.53248e6	0.124975
$107$	−1.74326e7	−1.37568	−0.687841	−	0.725861i	$-0.741441\pi$
$107$	−1.74326e7	−1.37568	−0.687841	+	0.725861i	$0.741441\pi$
$108$	3.07245e6	0.234694
$109$	3.93590e6	0.291106	0.145553	−	0.989350i	$-0.453504\pi$
$109$	3.93590e6	0.291106	0.145553	+	0.989350i	$0.453504\pi$
$110$	1.28767e7	0.922424
$111$	−3.08910e7	−2.14388
$112$	−2.72829e6	−0.183496
$113$	−2.61919e7	−1.70762	−0.853812	−	0.520581i	$-0.825715\pi$
$113$	−2.61919e7	−1.70762	−0.853812	+	0.520581i	$0.825715\pi$
$114$	2.08046e6	0.131520
$115$	3.24825e7	1.99162
$116$	1.06081e7	0.631010
$117$	−3.77225e6	−0.217746
$118$	1.33678e7	0.748982
$119$	−4.09934e6	−0.222997
$120$	−2.21031e7	−1.16767
$121$	5.22139e7	2.67940
$122$	242036.	0.0120676
$123$	−3.23485e7	−1.56742
$124$	−2.52027e7	−1.18706
$125$	−1.80292e7	−0.825641
$126$	−2.84738e6	−0.126809
$127$	5.87479e6	0.254495	0.127247	−	0.991871i	$-0.459386\pi$
$127$	5.87479e6	0.254495	0.127247	+	0.991871i	$0.459386\pi$
$128$	−2.40080e7	−1.01186
$129$	4.18870e7	1.71797
$130$	−3.34097e6	−0.133374
$131$	−1.07603e6	−0.0418190	−0.0209095	−	0.999781i	$-0.506656\pi$
$131$	−1.07603e6	−0.0418190	−0.0209095	+	0.999781i	$0.506656\pi$
$132$	−5.53542e7	−2.09480
$133$	−2.36220e6	−0.0870634
$134$	−3.43746e6	−0.123416
$135$	−9.23662e6	−0.323106
$136$	−1.34418e7	−0.458216
$137$	−3.97143e7	−1.31955	−0.659773	−	0.751465i	$-0.729348\pi$
$137$	−3.97143e7	−1.31955	−0.659773	+	0.751465i	$0.729348\pi$
$138$	3.11978e7	1.01053
$139$	2.73886e6	0.0865003	0.0432501	−	0.999064i	$-0.486229\pi$
$139$	2.73886e6	0.0865003	0.0432501	+	0.999064i	$0.486229\pi$
$140$	1.12873e7	0.347649
$141$	2.44119e7	0.733389
$142$	−2.32688e7	−0.681968
$143$	−1.86034e7	−0.532006
$144$	1.36574e7	0.381152
$145$	−3.18910e7	−0.868720
$146$	1.54535e6	0.0410952
$147$	7.35095e6	0.190868
$148$	5.17261e7	1.31158
$149$	5.33444e7	1.32110	0.660552	−	0.750781i	$-0.270322\pi$
$149$	5.33444e7	1.32110	0.660552	+	0.750781i	$0.270322\pi$
$150$	6.28462e6	0.152041
$151$	−3.23075e7	−0.763632	−0.381816	−	0.924238i	$-0.624701\pi$
$151$	−3.23075e7	−0.763632	−0.381816	+	0.924238i	$0.624701\pi$
$152$	−7.74567e6	−0.178898
$153$	2.05206e7	0.463202
$154$	−1.40423e7	−0.309824
$155$	7.57662e7	1.63424
$156$	1.43621e7	0.302888
$157$	9.76430e6	0.201369	0.100684	−	0.994918i	$-0.467897\pi$
$157$	9.76430e6	0.201369	0.100684	+	0.994918i	$0.467897\pi$
$158$	1.91082e6	0.0385408
$159$	1.98047e7	0.390731
$160$	5.73761e7	1.10742
$161$	−3.54227e7	−0.668947
$162$	−2.70265e7	−0.499444
$163$	1.91293e7	0.345972	0.172986	−	0.984924i	$-0.444658\pi$
$163$	1.91293e7	0.345972	0.172986	+	0.984924i	$0.444658\pi$
$164$	5.41666e7	0.958911
$165$	1.66410e8	2.88393
$166$	−2.68548e7	−0.455662
$167$	6.64443e7	1.10395	0.551976	−	0.833860i	$-0.313874\pi$
$167$	6.64443e7	1.10395	0.551976	+	0.833860i	$0.313874\pi$
$168$	2.41038e7	0.392196
$169$	4.82681e6	0.0769231
$170$	1.81745e7	0.283721
$171$	1.18248e7	0.180845
$172$	−7.01386e7	−1.05101
$173$	8.10105e7	1.18954	0.594771	−	0.803895i	$-0.297243\pi$
$173$	8.10105e7	1.18954	0.594771	+	0.803895i	$0.297243\pi$
$174$	−3.06297e7	−0.440778
$175$	−7.13571e6	−0.100648
$176$	6.73534e7	0.931247
$177$	1.72756e8	2.34167
$178$	−5.90041e7	−0.784174
$179$	−6.95288e7	−0.906106	−0.453053	−	0.891484i	$-0.649665\pi$
$179$	−6.95288e7	−0.906106	−0.453053	+	0.891484i	$0.649665\pi$
$180$	−5.65022e7	−0.722124
$181$	−1.08438e8	−1.35927	−0.679637	−	0.733548i	$-0.737863\pi$
$181$	−1.08438e8	−1.35927	−0.679637	+	0.733548i	$0.737863\pi$
$182$	3.64339e6	0.0447977
$183$	3.12790e6	0.0377289
$184$	−1.16151e8	−1.37455
$185$	−1.55503e8	−1.80566
$186$	7.27696e7	0.829192
$187$	1.01201e8	1.13172
$188$	−4.08771e7	−0.448670
$189$	1.00727e7	0.108525
$190$	1.04728e7	0.110771
$191$	6.71166e7	0.696968	0.348484	−	0.937315i	$-0.386697\pi$
$191$	6.71166e7	0.696968	0.348484	+	0.937315i	$0.386697\pi$
$192$	−8.50850e6	−0.0867558
$193$	8.36893e7	0.837953	0.418976	−	0.907997i	$-0.362389\pi$
$193$	8.36893e7	0.837953	0.418976	+	0.907997i	$0.362389\pi$
$194$	−2.49214e7	−0.245056
$195$	−4.31764e7	−0.416990
$196$	−1.23090e7	−0.116768
$197$	−9.70987e7	−0.904860	−0.452430	−	0.891800i	$-0.649443\pi$
$197$	−9.70987e7	−0.904860	−0.452430	+	0.891800i	$0.649443\pi$
$198$	7.02934e7	0.643556
$199$	2.29633e7	0.206561	0.103280	−	0.994652i	$-0.467066\pi$
$199$	2.29633e7	0.206561	0.103280	+	0.994652i	$0.467066\pi$
$200$	−2.33980e7	−0.206811
$201$	−4.44233e7	−0.385856
$202$	2.74090e7	0.233972
$203$	3.47777e7	0.291786
$204$	−7.81283e7	−0.644322
$205$	−1.62840e8	−1.32014
$206$	−3.94094e7	−0.314098
$207$	1.77320e8	1.38951
$208$	−1.74754e7	−0.134650
$209$	5.83157e7	0.441848
$210$	−3.25905e7	−0.242842
$211$	7.86028e6	0.0576036	0.0288018	−	0.999585i	$-0.490831\pi$
$211$	7.86028e6	0.0576036	0.0288018	+	0.999585i	$0.490831\pi$
$212$	−3.31624e7	−0.239040
$213$	−3.00710e8	−2.13215
$214$	−8.42835e7	−0.587887
$215$	2.10856e8	1.44694
$216$	3.30284e7	0.222997
$217$	−8.26244e7	−0.548908
$218$	1.90294e7	0.124402
$219$	1.99710e7	0.128483
$220$	−2.78649e8	−1.76432
$221$	−2.62573e7	−0.163635
$222$	−1.49353e8	−0.916172
$223$	1.68887e8	1.01983	0.509916	−	0.860224i	$-0.329676\pi$
$223$	1.68887e8	1.01983	0.509916	+	0.860224i	$0.329676\pi$
$224$	−6.25696e7	−0.371959
$225$	3.57202e7	0.209062
$226$	−1.26633e8	−0.729740
$227$	−4.61537e6	−0.0261888	−0.0130944	−	0.999914i	$-0.504168\pi$
$227$	−4.61537e6	−0.0261888	−0.0130944	+	0.999914i	$0.504168\pi$
$228$	−4.50205e7	−0.251558
$229$	−3.10653e8	−1.70943	−0.854716	−	0.519096i	$-0.826269\pi$
$229$	−3.10653e8	−1.70943	−0.854716	+	0.519096i	$0.826269\pi$
$230$	1.57047e8	0.851105
$231$	−1.81473e8	−0.968657
$232$	1.14036e8	0.599563
$233$	9.25305e7	0.479225	0.239612	−	0.970869i	$-0.422980\pi$
$233$	9.25305e7	0.479225	0.239612	+	0.970869i	$0.422980\pi$
$234$	−1.82382e7	−0.0930521
$235$	1.22888e8	0.617690
$236$	−2.89275e8	−1.43258
$237$	2.46942e7	0.120497
$238$	−1.98196e7	−0.0952963
$239$	2.39451e8	1.13455	0.567275	−	0.823528i	$-0.307998\pi$
$239$	2.39451e8	1.13455	0.567275	+	0.823528i	$0.307998\pi$
$240$	1.56319e8	0.729917
$241$	1.76231e8	0.811005	0.405502	−	0.914094i	$-0.367097\pi$
$241$	1.76231e8	0.811005	0.405502	+	0.914094i	$0.367097\pi$
$242$	2.52445e8	1.14502
$243$	−2.85047e8	−1.27437
$244$	−5.23759e6	−0.0230817
$245$	3.70041e7	0.160756
$246$	−1.56399e8	−0.669826
$247$	−1.51305e7	−0.0638871
$248$	−2.70926e8	−1.12790
$249$	−3.47053e8	−1.42462
$250$	−8.71681e7	−0.352832
$251$	2.42360e8	0.967393	0.483696	−	0.875236i	$-0.339294\pi$
$251$	2.42360e8	0.967393	0.483696	+	0.875236i	$0.339294\pi$
$252$	6.16166e7	0.242547
$253$	8.74482e8	3.39492
$254$	2.84036e7	0.108756
$255$	2.34875e8	0.887046
$256$	−9.86440e7	−0.367477
$257$	−1.66761e8	−0.612816	−0.306408	−	0.951900i	$-0.599127\pi$
$257$	−1.66761e8	−0.612816	−0.306408	+	0.951900i	$0.599127\pi$
$258$	2.02516e8	0.734160
$259$	1.69578e8	0.606487
$260$	7.22977e7	0.255104
$261$	−1.74091e8	−0.606087
$262$	−5.20240e6	−0.0178710
$263$	−3.88876e8	−1.31815	−0.659077	−	0.752076i	$-0.729053\pi$
$263$	−3.88876e8	−1.31815	−0.659077	+	0.752076i	$0.729053\pi$
$264$	−5.95051e8	−1.99040
$265$	9.96952e7	0.329089
$266$	−1.14208e7	−0.0372059
$267$	−7.62529e8	−2.45170
$268$	7.43857e7	0.236057
$269$	−7.59623e7	−0.237939	−0.118969	−	0.992898i	$-0.537959\pi$
$269$	−7.59623e7	−0.237939	−0.118969	+	0.992898i	$0.537959\pi$
$270$	−4.46574e7	−0.138077
$271$	4.51789e8	1.37893	0.689466	−	0.724318i	$-0.257845\pi$
$271$	4.51789e8	1.37893	0.689466	+	0.724318i	$0.257845\pi$
$272$	9.50642e7	0.286435
$273$	4.70846e7	0.140059
$274$	−1.92012e8	−0.563898
$275$	1.76160e8	0.510789
$276$	−6.75113e8	−1.93283
$277$	−1.85269e8	−0.523750	−0.261875	−	0.965102i	$-0.584341\pi$
$277$	−1.85269e8	−0.523750	−0.261875	+	0.965102i	$0.584341\pi$
$278$	1.32419e7	0.0369652
$279$	4.13604e8	1.14017
$280$	1.21337e8	0.330323
$281$	−1.75327e8	−0.471385	−0.235693	−	0.971828i	$-0.575736\pi$
$281$	−1.75327e8	−0.471385	−0.235693	+	0.971828i	$0.575736\pi$
$282$	1.18027e8	0.313408
$283$	5.10613e8	1.33918	0.669591	−	0.742730i	$-0.266469\pi$
$283$	5.10613e8	1.33918	0.669591	+	0.742730i	$0.266469\pi$
$284$	5.03530e8	1.30440
$285$	1.35344e8	0.346323
$286$	−8.99443e7	−0.227349
$287$	1.77579e8	0.443411
$288$	3.13213e8	0.772621
$289$	−2.67502e8	−0.651905
$290$	−1.54187e8	−0.371241
$291$	−3.22067e8	−0.766162
$292$	−3.34409e7	−0.0786028
$293$	6.87785e8	1.59741	0.798704	−	0.601724i	$-0.205519\pi$
$293$	6.87785e8	1.59741	0.798704	+	0.601724i	$0.205519\pi$
$294$	3.55406e7	0.0815659
$295$	8.69639e8	1.97225
$296$	5.56049e8	1.24621
$297$	−2.48665e8	−0.550765
$298$	2.57911e8	0.564563
$299$	−2.26891e8	−0.490873
$300$	−1.35998e8	−0.290809
$301$	−2.29942e8	−0.485999
$302$	−1.56201e8	−0.326332
$303$	3.54215e8	0.731506
$304$	5.47796e7	0.111831
$305$	1.57456e7	0.0317768
$306$	9.92137e7	0.197946
$307$	−8.22599e8	−1.62257	−0.811286	−	0.584650i	$-0.801232\pi$
$307$	−8.22599e8	−1.62257	−0.811286	+	0.584650i	$0.801232\pi$
$308$	3.03872e8	0.592601
$309$	−5.09301e8	−0.982018
$310$	3.66317e8	0.698378
$311$	−3.26737e8	−0.615939	−0.307969	−	0.951396i	$-0.599649\pi$
$311$	−3.26737e8	−0.615939	−0.307969	+	0.951396i	$0.599649\pi$
$312$	1.54391e8	0.287793
$313$	−3.79034e8	−0.698672	−0.349336	−	0.936998i	$-0.613593\pi$
$313$	−3.79034e8	−0.698672	−0.349336	+	0.936998i	$0.613593\pi$
$314$	4.72087e7	0.0860534
$315$	−1.85236e8	−0.333918
$316$	−4.13498e7	−0.0737171
$317$	−1.32838e8	−0.234214	−0.117107	−	0.993119i	$-0.537362\pi$
$317$	−1.32838e8	−0.234214	−0.117107	+	0.993119i	$0.537362\pi$
$318$	9.57522e7	0.166976
$319$	−8.58557e8	−1.48082
$320$	−4.28311e7	−0.0730692
$321$	−1.08922e9	−1.83801
$322$	−1.71263e8	−0.285869
$323$	8.23081e7	0.135904
$324$	5.84846e8	0.955288
$325$	−4.57060e7	−0.0738553
$326$	9.24866e7	0.147849
$327$	2.45923e8	0.388939
$328$	5.82284e8	0.911122
$329$	−1.34011e8	−0.207470
$330$	8.04563e8	1.23243
$331$	2.57230e8	0.389873	0.194937	−	0.980816i	$-0.437550\pi$
$331$	2.57230e8	0.389873	0.194937	+	0.980816i	$0.437550\pi$
$332$	5.81131e8	0.871546
$333$	−8.48882e8	−1.25977
$334$	3.21247e8	0.471765
$335$	−2.23624e8	−0.324983
$336$	−1.70469e8	−0.245165
$337$	3.24693e8	0.462135	0.231067	−	0.972938i	$-0.425778\pi$
$337$	3.24693e8	0.462135	0.231067	+	0.972938i	$0.425778\pi$
$338$	2.33368e7	0.0328725
$339$	−1.63652e9	−2.28151
$340$	−3.93292e8	−0.542673
$341$	2.03975e9	2.78571
$342$	5.71708e7	0.0772828
$343$	−4.03536e7	−0.0539949
$344$	−7.53980e8	−0.998632
$345$	2.02957e9	2.66096
$346$	3.91672e8	0.508342
$347$	−3.43601e8	−0.441470	−0.220735	−	0.975334i	$-0.570846\pi$
$347$	−3.43601e8	−0.441470	−0.220735	+	0.975334i	$0.570846\pi$
$348$	6.62818e8	0.843076
$349$	−1.00954e9	−1.27127	−0.635633	−	0.771991i	$-0.719261\pi$
$349$	−1.00954e9	−1.27127	−0.635633	+	0.771991i	$0.719261\pi$
$350$	−3.44999e7	−0.0430111
$351$	6.45181e7	0.0796355
$352$	1.54466e9	1.88770
$353$	9.78169e7	0.118359	0.0591796	−	0.998247i	$-0.481152\pi$
$353$	9.78169e7	0.118359	0.0591796	+	0.998247i	$0.481152\pi$
$354$	8.35244e8	1.00070
$355$	−1.51375e9	−1.79579
$356$	1.27683e9	1.49989
$357$	−2.56135e8	−0.297941
$358$	−3.36160e8	−0.387218
$359$	1.47626e9	1.68396	0.841978	−	0.539511i	$-0.181391\pi$
$359$	1.47626e9	1.68396	0.841978	+	0.539511i	$0.181391\pi$
$360$	−6.07391e8	−0.686135
$361$	−8.46443e8	−0.946940
$362$	−5.24280e8	−0.580876
$363$	3.26243e9	3.57987
$364$	−7.88419e7	−0.0856845
$365$	1.00532e8	0.108213
$366$	1.51229e7	0.0161232
$367$	−1.45180e8	−0.153312	−0.0766559	−	0.997058i	$-0.524424\pi$
$367$	−1.45180e8	−0.153312	−0.0766559	+	0.997058i	$0.524424\pi$
$368$	8.21457e8	0.859246
$369$	−8.88934e8	−0.921037
$370$	−7.51829e8	−0.771637
$371$	−1.08719e8	−0.110535
$372$	−1.57472e9	−1.58600
$373$	−1.71209e7	−0.0170823	−0.00854114	−	0.999964i	$-0.502719\pi$
$373$	−1.71209e7	−0.0170823	−0.00854114	+	0.999964i	$0.502719\pi$
$374$	4.89287e8	0.483630
$375$	−1.12650e9	−1.10312
$376$	−4.39423e8	−0.426310
$377$	2.22759e8	0.214112
$378$	4.86997e7	0.0463773
$379$	3.62265e8	0.341814	0.170907	−	0.985287i	$-0.445330\pi$
$379$	3.62265e8	0.341814	0.170907	+	0.985287i	$0.445330\pi$
$380$	−2.26630e8	−0.211872
$381$	3.67069e8	0.340024
$382$	3.24497e8	0.297844
$383$	3.36403e8	0.305960	0.152980	−	0.988229i	$-0.451113\pi$
$383$	3.36403e8	0.305960	0.152980	+	0.988229i	$0.451113\pi$
$384$	−1.50007e9	−1.35192
$385$	−9.13521e8	−0.815841
$386$	4.04623e8	0.358093
$387$	1.15105e9	1.00950
$388$	5.39293e8	0.468720
$389$	−7.45679e7	−0.0642286	−0.0321143	−	0.999484i	$-0.510224\pi$
$389$	−7.45679e7	−0.0642286	−0.0321143	+	0.999484i	$0.510224\pi$
$390$	−2.08750e8	−0.178197
$391$	1.23426e9	1.04421
$392$	−1.32320e8	−0.110949
$393$	−6.72323e7	−0.0558733
$394$	−4.69455e8	−0.386685
$395$	1.24309e8	0.101487
$396$	−1.52113e9	−1.23093
$397$	1.66485e9	1.33539	0.667696	−	0.744434i	$-0.267281\pi$
$397$	1.66485e9	1.33539	0.667696	+	0.744434i	$0.267281\pi$
$398$	1.11023e8	0.0882722
$399$	−1.47595e8	−0.116323
$400$	1.65478e8	0.129280
$401$	9.52020e8	0.737294	0.368647	−	0.929569i	$-0.379821\pi$
$401$	9.52020e8	0.737294	0.368647	+	0.929569i	$0.379821\pi$
$402$	−2.14779e8	−0.164893
$403$	−5.29230e8	−0.402788
$404$	−5.93124e8	−0.447518
$405$	−1.75821e9	−1.31516
$406$	1.68144e8	0.124692
$407$	−4.18639e9	−3.07793
$408$	−8.39869e8	−0.612211
$409$	−1.66648e9	−1.20439	−0.602197	−	0.798348i	$-0.705708\pi$
$409$	−1.66648e9	−1.20439	−0.602197	+	0.798348i	$0.705708\pi$
$410$	−7.87301e8	−0.564154
$411$	−2.48143e9	−1.76301
$412$	8.52810e8	0.600775
$413$	−9.48357e8	−0.662440
$414$	8.57314e8	0.593798
$415$	−1.74704e9	−1.19987
$416$	−4.00774e8	−0.272943
$417$	1.71129e8	0.115571
$418$	2.81946e8	0.188821
$419$	7.54096e8	0.500815	0.250408	−	0.968141i	$-0.419435\pi$
$419$	7.54096e8	0.500815	0.250408	+	0.968141i	$0.419435\pi$
$420$	7.05251e8	0.464484
$421$	9.66522e8	0.631284	0.315642	−	0.948878i	$-0.397780\pi$
$421$	9.66522e8	0.631284	0.315642	+	0.948878i	$0.397780\pi$
$422$	3.80031e7	0.0246165
$423$	6.70837e8	0.430949
$424$	−3.56492e8	−0.227127
$425$	2.48636e8	0.157109
$426$	−1.45388e9	−0.911160
$427$	−1.71709e7	−0.0106732
$428$	1.82387e9	1.12445
$429$	−1.16238e9	−0.710800
$430$	1.01945e9	0.618339
$431$	1.15524e9	0.695025	0.347512	−	0.937675i	$-0.387026\pi$
$431$	1.15524e9	0.695025	0.347512	+	0.937675i	$0.387026\pi$
$432$	−2.33587e8	−0.139398
$433$	−1.01905e9	−0.603237	−0.301619	−	0.953429i	$-0.597527\pi$
$433$	−1.01905e9	−0.603237	−0.301619	+	0.953429i	$0.597527\pi$
$434$	−3.99475e8	−0.234572
$435$	−1.99261e9	−1.16067
$436$	−4.11791e8	−0.237944
$437$	7.11231e8	0.407686
$438$	9.65563e7	0.0549062
$439$	2.05507e9	1.15931	0.579655	−	0.814862i	$-0.303187\pi$
$439$	2.05507e9	1.15931	0.579655	+	0.814862i	$0.303187\pi$
$440$	−2.99544e9	−1.67639
$441$	2.02004e8	0.112156
$442$	−1.26950e8	−0.0699283
$443$	1.38350e9	0.756079	0.378040	−	0.925789i	$-0.376598\pi$
$443$	1.38350e9	0.756079	0.378040	+	0.925789i	$0.376598\pi$
$444$	3.23195e9	1.75236
$445$	−3.83851e9	−2.06492
$446$	8.16539e8	0.435818
$447$	3.33306e9	1.76509
$448$	4.67081e7	0.0245425
$449$	1.79991e9	0.938404	0.469202	−	0.883091i	$-0.344542\pi$
$449$	1.79991e9	0.938404	0.469202	+	0.883091i	$0.344542\pi$
$450$	1.72701e8	0.0893411
$451$	−4.38391e9	−2.25032
$452$	2.74031e9	1.39578
$453$	−2.01864e9	−1.02027
$454$	−2.23145e7	−0.0111916
$455$	2.37020e8	0.117963
$456$	−4.83965e8	−0.239021
$457$	1.35945e9	0.666279	0.333139	−	0.942878i	$-0.391892\pi$
$457$	1.35945e9	0.666279	0.333139	+	0.942878i	$0.391892\pi$
$458$	−1.50196e9	−0.730513
$459$	−3.50971e8	−0.169405
$460$	−3.39846e9	−1.62791
$461$	9.44068e8	0.448797	0.224399	−	0.974497i	$-0.427958\pi$
$461$	9.44068e8	0.448797	0.224399	+	0.974497i	$0.427958\pi$
$462$	−8.77390e8	−0.413948
$463$	−2.11591e8	−0.0990751	−0.0495375	−	0.998772i	$-0.515775\pi$
$463$	−2.11591e8	−0.0990751	−0.0495375	+	0.998772i	$0.515775\pi$
$464$	−8.06497e8	−0.374792
$465$	4.73403e9	2.18346
$466$	4.47369e8	0.204793
$467$	−1.11706e9	−0.507535	−0.253768	−	0.967265i	$-0.581670\pi$
$467$	−1.11706e9	−0.507535	−0.253768	+	0.967265i	$0.581670\pi$
$468$	3.94670e8	0.177981
$469$	2.43866e8	0.109155
$470$	5.94140e8	0.263965
$471$	6.10093e8	0.269044
$472$	−3.10967e9	−1.36118
$473$	5.67658e9	2.46645
$474$	1.19392e8	0.0514934
$475$	1.43273e8	0.0613392
$476$	4.28891e8	0.182273
$477$	5.44231e8	0.229599
$478$	1.15770e9	0.484842
$479$	−2.45192e9	−1.01937	−0.509684	−	0.860361i	$-0.670238\pi$
$479$	−2.45192e9	−1.01937	−0.509684	+	0.860361i	$0.670238\pi$
$480$	3.58497e9	1.47959
$481$	1.08619e9	0.445040
$482$	8.52048e8	0.346577
$483$	−2.21328e9	−0.893763
$484$	−5.46285e9	−2.19008
$485$	−1.62126e9	−0.645292
$486$	−1.37815e9	−0.544592
$487$	−3.55244e9	−1.39372	−0.696860	−	0.717207i	$-0.745420\pi$
$487$	−3.55244e9	−1.39372	−0.696860	+	0.717207i	$0.745420\pi$
$488$	−5.63034e7	−0.0219313
$489$	1.19523e9	0.462245
$490$	1.78908e8	0.0686980
$491$	−8.10999e8	−0.309197	−0.154598	−	0.987977i	$-0.549408\pi$
$491$	−8.10999e8	−0.309197	−0.154598	+	0.987977i	$0.549408\pi$
$492$	3.38444e9	1.28118
$493$	−1.21179e9	−0.455472
$494$	−7.31532e7	−0.0273017
$495$	4.57293e9	1.69464
$496$	1.91607e9	0.705058
$497$	1.65077e9	0.603169
$498$	−1.67794e9	−0.608799
$499$	−3.77182e9	−1.35894	−0.679468	−	0.733705i	$-0.737789\pi$
$499$	−3.77182e9	−1.35894	−0.679468	+	0.733705i	$0.737789\pi$
$500$	1.88630e9	0.674861
$501$	4.15157e9	1.47496
$502$	1.17177e9	0.413408
$503$	−4.69213e9	−1.64393	−0.821963	−	0.569541i	$-0.807121\pi$
$503$	−4.69213e9	−1.64393	−0.821963	+	0.569541i	$0.807121\pi$
$504$	6.62371e8	0.230459
$505$	1.78309e9	0.616104
$506$	4.22797e9	1.45079
$507$	3.01589e8	0.102775
$508$	−6.14646e8	−0.208019
$509$	2.19417e9	0.737494	0.368747	−	0.929530i	$-0.379787\pi$
$509$	2.19417e9	0.737494	0.368747	+	0.929530i	$0.379787\pi$
$510$	1.13558e9	0.379072
$511$	−1.09632e8	−0.0363468
$512$	2.59609e9	0.854822
$513$	−2.02243e8	−0.0661398
$514$	−8.06263e8	−0.261882
$515$	−2.56378e9	−0.827095
$516$	−4.38240e9	−1.40423
$517$	3.30833e9	1.05291
$518$	8.19883e8	0.259178
$519$	5.06170e9	1.58932
$520$	7.77191e8	0.242391
$521$	−2.61146e9	−0.809005	−0.404503	−	0.914537i	$-0.632555\pi$
$521$	−2.61146e9	−0.809005	−0.404503	+	0.914537i	$0.632555\pi$
$522$	−8.41701e8	−0.259007
$523$	−2.69127e9	−0.822625	−0.411312	−	0.911495i	$-0.634929\pi$
$523$	−2.69127e9	−0.822625	−0.411312	+	0.911495i	$0.634929\pi$
$524$	1.12579e8	0.0341819
$525$	−4.45854e8	−0.134473
$526$	−1.88015e9	−0.563303
$527$	2.87895e9	0.856835
$528$	4.20837e9	1.24422
$529$	7.26055e9	2.13243
$530$	4.82009e8	0.140634
$531$	4.74732e9	1.37600
$532$	2.47144e8	0.0711638
$533$	1.13744e9	0.325374
$534$	−3.68670e9	−1.04771
$535$	−5.48306e9	−1.54805
$536$	7.99637e8	0.224293
$537$	−4.34430e9	−1.21063
$538$	−3.67265e8	−0.101681
$539$	9.96210e8	0.274025
$540$	9.66376e8	0.264100
$541$	−4.26647e9	−1.15845	−0.579227	−	0.815166i	$-0.696645\pi$
$541$	−4.26647e9	−1.15845	−0.579227	+	0.815166i	$0.696645\pi$
$542$	2.18432e9	0.589276
$543$	−6.77544e9	−1.81609
$544$	2.18017e9	0.580622
$545$	1.23796e9	0.327580
$546$	2.27646e8	0.0598530
$547$	5.32779e9	1.39185	0.695923	−	0.718116i	$-0.254995\pi$
$547$	5.32779e9	1.39185	0.695923	+	0.718116i	$0.254995\pi$
$548$	4.15508e9	1.07857
$549$	8.59545e7	0.0221700
$550$	8.51701e8	0.218282
$551$	−6.98278e8	−0.177827
$552$	−7.25737e9	−1.83651
$553$	−1.35561e8	−0.0340876
$554$	−8.95744e8	−0.223820
$555$	−9.71612e9	−2.41250
$556$	−2.86551e8	−0.0707035
$557$	3.19673e9	0.783812	0.391906	−	0.920005i	$-0.371816\pi$
$557$	3.19673e9	0.783812	0.391906	+	0.920005i	$0.371816\pi$
$558$	1.99970e9	0.487244
$559$	−1.47283e9	−0.356626
$560$	−8.58128e8	−0.206488
$561$	6.32321e9	1.51206
$562$	−8.47674e8	−0.201443
$563$	2.46611e9	0.582417	0.291208	−	0.956660i	$-0.405943\pi$
$563$	2.46611e9	0.582417	0.291208	+	0.956660i	$0.405943\pi$
$564$	−2.55408e9	−0.599457
$565$	−8.23813e9	−1.92158
$566$	2.46873e9	0.572289
$567$	1.91736e9	0.441735
$568$	5.41288e9	1.23939
$569$	−7.64209e9	−1.73908	−0.869539	−	0.493864i	$-0.835584\pi$
$569$	−7.64209e9	−1.73908	−0.869539	+	0.493864i	$0.835584\pi$
$570$	6.54365e8	0.147999
$571$	−2.39383e9	−0.538104	−0.269052	−	0.963126i	$-0.586710\pi$
$571$	−2.39383e9	−0.538104	−0.269052	+	0.963126i	$0.586710\pi$
$572$	1.94637e9	0.434850
$573$	4.19358e9	0.931201
$574$	8.58566e8	0.189488
$575$	2.14848e9	0.471296
$576$	−2.33813e8	−0.0509788
$577$	4.29479e9	0.930736	0.465368	−	0.885117i	$-0.345922\pi$
$577$	4.29479e9	0.930736	0.465368	+	0.885117i	$0.345922\pi$
$578$	−1.29333e9	−0.278587
$579$	5.22908e9	1.11957
$580$	3.33657e9	0.710073
$581$	1.90517e9	0.403012
$582$	−1.55714e9	−0.327414
$583$	2.68396e9	0.560965
$584$	−3.59485e8	−0.0746854
$585$	−1.18648e9	−0.245029
$586$	3.32532e9	0.682640
$587$	−4.21222e9	−0.859563	−0.429782	−	0.902933i	$-0.641409\pi$
$587$	−4.21222e9	−0.859563	−0.429782	+	0.902933i	$0.641409\pi$
$588$	−7.69089e8	−0.156011
$589$	1.65896e9	0.334529
$590$	4.20455e9	0.842826
$591$	−6.06692e9	−1.20896
$592$	−3.93254e9	−0.779018
$593$	−1.53014e9	−0.301328	−0.150664	−	0.988585i	$-0.548141\pi$
$593$	−1.53014e9	−0.301328	−0.150664	+	0.988585i	$0.548141\pi$
$594$	−1.20225e9	−0.235365
$595$	−1.28936e9	−0.250938
$596$	−5.58113e9	−1.07984
$597$	1.43479e9	0.275981
$598$	−1.09698e9	−0.209771
$599$	−5.16267e9	−0.981478	−0.490739	−	0.871307i	$-0.663273\pi$
$599$	−5.16267e9	−0.981478	−0.490739	+	0.871307i	$0.663273\pi$
$600$	−1.46196e9	−0.276316
$601$	−1.95738e9	−0.367803	−0.183901	−	0.982945i	$-0.558873\pi$
$601$	−1.95738e9	−0.367803	−0.183901	+	0.982945i	$0.558873\pi$
$602$	−1.11173e9	−0.207688
$603$	−1.22075e9	−0.226734
$604$	3.38016e9	0.624176
$605$	1.64228e10	3.01511
$606$	1.71257e9	0.312604
$607$	4.00519e9	0.726880	0.363440	−	0.931618i	$-0.381602\pi$
$607$	4.00519e9	0.726880	0.363440	+	0.931618i	$0.381602\pi$
$608$	1.25630e9	0.226688
$609$	2.17298e9	0.389847
$610$	7.61273e7	0.0135796
$611$	−8.58374e8	−0.152241
$612$	−2.14696e9	−0.378612
$613$	2.44078e9	0.427974	0.213987	−	0.976837i	$-0.431355\pi$
$613$	2.44078e9	0.427974	0.213987	+	0.976837i	$0.431355\pi$
$614$	−3.97712e9	−0.693394
$615$	−1.01745e10	−1.76381
$616$	3.26658e9	0.563068
$617$	7.35176e9	1.26007	0.630033	−	0.776569i	$-0.283042\pi$
$617$	7.35176e9	1.26007	0.630033	+	0.776569i	$0.283042\pi$
$618$	−2.46238e9	−0.419658
$619$	−4.08633e9	−0.692495	−0.346248	−	0.938143i	$-0.612544\pi$
$619$	−4.08633e9	−0.692495	−0.346248	+	0.938143i	$0.612544\pi$
$620$	−7.92700e9	−1.33579
$621$	−3.03277e9	−0.508182
$622$	−1.57972e9	−0.263217
$623$	4.18596e9	0.693565
$624$	−1.09190e9	−0.179902
$625$	−7.29602e9	−1.19538
$626$	−1.83257e9	−0.298572
$627$	3.64368e9	0.590342
$628$	−1.02158e9	−0.164595
$629$	−5.90876e9	−0.946715
$630$	−8.95586e8	−0.142697
$631$	2.99656e9	0.474811	0.237406	−	0.971411i	$-0.423703\pi$
$631$	2.99656e9	0.474811	0.237406	+	0.971411i	$0.423703\pi$
$632$	−4.44504e8	−0.0700432
$633$	4.91126e8	0.0769627
$634$	−6.42247e8	−0.100090
$635$	1.84779e9	0.286382
$636$	−2.07205e9	−0.319375
$637$	−2.58475e8	−0.0396214
$638$	−4.15097e9	−0.632816
$639$	−8.26348e9	−1.25288
$640$	−7.55122e9	−1.13864
$641$	3.86937e9	0.580279	0.290140	−	0.956984i	$-0.406298\pi$
$641$	3.86937e9	0.580279	0.290140	+	0.956984i	$0.406298\pi$
$642$	−5.26620e9	−0.785461
$643$	−6.05858e9	−0.898736	−0.449368	−	0.893347i	$-0.648351\pi$
$643$	−6.05858e9	−0.898736	−0.449368	+	0.893347i	$0.648351\pi$
$644$	3.70609e9	0.546783
$645$	1.31747e10	1.93322
$646$	3.97945e8	0.0580777
$647$	−1.17641e10	−1.70763	−0.853817	−	0.520573i	$-0.825718\pi$
$647$	−1.17641e10	−1.70763	−0.853817	+	0.520573i	$0.825718\pi$
$648$	6.28702e9	0.907679
$649$	2.34121e10	3.36189
$650$	−2.20981e8	−0.0315615
$651$	−5.16254e9	−0.733381
$652$	−2.00139e9	−0.282790
$653$	−1.25932e9	−0.176987	−0.0884934	−	0.996077i	$-0.528205\pi$
$653$	−1.25932e9	−0.176987	−0.0884934	+	0.996077i	$0.528205\pi$
$654$	1.18899e9	0.166210
$655$	−3.38442e8	−0.0470587
$656$	−4.11808e9	−0.569550
$657$	5.48802e8	0.0754982
$658$	−6.47920e8	−0.0886607
$659$	9.16362e9	1.24729	0.623646	−	0.781707i	$-0.285651\pi$
$659$	9.16362e9	1.24729	0.623646	+	0.781707i	$0.285651\pi$
$660$	−1.74105e10	−2.35727
$661$	1.30199e10	1.75348	0.876742	−	0.480961i	$-0.159712\pi$
$661$	1.30199e10	1.75348	0.876742	+	0.480961i	$0.159712\pi$
$662$	1.24366e9	0.166609
$663$	−1.64061e9	−0.218629
$664$	6.24708e9	0.828111
$665$	−7.42982e8	−0.0979721
$666$	−4.10420e9	−0.538355
$667$	−1.04711e10	−1.36632
$668$	−6.95170e9	−0.902346
$669$	1.05524e10	1.36257
$670$	−1.08118e9	−0.138879
$671$	4.23898e8	0.0541667
$672$	−3.90947e9	−0.496965
$673$	−1.04391e10	−1.32011	−0.660053	−	0.751219i	$-0.729466\pi$
$673$	−1.04391e10	−1.32011	−0.660053	+	0.751219i	$0.729466\pi$
$674$	1.56984e9	0.197490
$675$	−6.10935e8	−0.0764595
$676$	−5.05002e8	−0.0628753
$677$	−8.55686e9	−1.05987	−0.529937	−	0.848037i	$-0.677784\pi$
$677$	−8.55686e9	−1.05987	−0.529937	+	0.848037i	$0.677784\pi$
$678$	−7.91230e9	−0.974987
$679$	1.76801e9	0.216741
$680$	−4.22783e9	−0.515628
$681$	−2.88378e8	−0.0349902
$682$	9.86184e9	1.19045
$683$	1.80307e9	0.216540	0.108270	−	0.994122i	$-0.465469\pi$
$683$	1.80307e9	0.216540	0.108270	+	0.994122i	$0.465469\pi$
$684$	−1.23716e9	−0.147819
$685$	−1.24913e10	−1.48488
$686$	−1.95103e8	−0.0230743
$687$	−1.94102e10	−2.28393
$688$	5.33237e9	0.624253
$689$	−6.96375e8	−0.0811102
$690$	9.81263e9	1.13714
$691$	1.68072e9	0.193786	0.0968928	−	0.995295i	$-0.469110\pi$
$691$	1.68072e9	0.193786	0.0968928	+	0.995295i	$0.469110\pi$
$692$	−8.47568e9	−0.972306
$693$	−4.98686e9	−0.569195
$694$	−1.66125e9	−0.188659
$695$	8.61451e8	0.0973384
$696$	7.12521e9	0.801060
$697$	−6.18755e9	−0.692156
$698$	−4.88097e9	−0.543266
$699$	5.78149e9	0.640280
$700$	7.46570e8	0.0822673
$701$	−1.60557e10	−1.76041	−0.880207	−	0.474590i	$-0.842596\pi$
$701$	−1.60557e10	−1.76041	−0.880207	+	0.474590i	$0.842596\pi$
$702$	3.11934e8	0.0340316
$703$	−3.40486e9	−0.369620
$704$	−1.15308e9	−0.124554
$705$	7.67826e9	0.825279
$706$	4.72928e8	0.0505799
$707$	−1.94449e9	−0.206937
$708$	−1.80745e10	−1.91403
$709$	−7.44466e9	−0.784482	−0.392241	−	0.919862i	$-0.628300\pi$
$709$	−7.44466e9	−0.784482	−0.392241	+	0.919862i	$0.628300\pi$
$710$	−7.31871e9	−0.767416
$711$	6.78595e8	0.0708055
$712$	1.37258e10	1.42514
$713$	2.48772e10	2.57033
$714$	−1.23837e9	−0.127323
$715$	−5.85133e9	−0.598664
$716$	7.27441e9	0.740632
$717$	1.49614e10	1.51584
$718$	7.13744e9	0.719626
$719$	1.47292e10	1.47784	0.738922	−	0.673791i	$-0.235335\pi$
$719$	1.47292e10	1.47784	0.738922	+	0.673791i	$0.235335\pi$
$720$	4.29565e9	0.428909
$721$	2.79585e9	0.277805
$722$	−4.09240e9	−0.404667
$723$	1.10113e10	1.08356
$724$	1.13453e10	1.11104
$725$	−2.10935e9	−0.205573
$726$	1.57733e10	1.52983
$727$	−2.84326e9	−0.274439	−0.137219	−	0.990541i	$-0.543817\pi$
$727$	−2.84326e9	−0.274439	−0.137219	+	0.990541i	$0.543817\pi$
$728$	−8.47541e8	−0.0814143
$729$	−5.58509e9	−0.533930
$730$	4.86057e8	0.0462442
$731$	8.01205e9	0.758635
$732$	−3.27255e8	−0.0308388
$733$	5.86487e9	0.550041	0.275020	−	0.961438i	$-0.411315\pi$
$733$	5.86487e9	0.550041	0.275020	+	0.961438i	$0.411315\pi$
$734$	−7.01920e8	−0.0655166
$735$	2.31209e9	0.214783
$736$	1.88390e10	1.74175
$737$	−6.02031e9	−0.553966
$738$	−4.29784e9	−0.393598
$739$	1.71343e10	1.56175	0.780873	−	0.624690i	$-0.214775\pi$
$739$	1.71343e10	1.56175	0.780873	+	0.624690i	$0.214775\pi$
$740$	1.62694e10	1.47591
$741$	−9.45382e8	−0.0853579
$742$	−5.25640e8	−0.0472361
$743$	8.14736e9	0.728712	0.364356	−	0.931260i	$-0.381289\pi$
$743$	8.14736e9	0.728712	0.364356	+	0.931260i	$0.381289\pi$
$744$	−1.69280e10	−1.50695
$745$	1.67784e10	1.48663
$746$	−8.27766e7	−0.00729998
$747$	−9.53699e9	−0.837123
$748$	−1.05881e10	−0.925040
$749$	5.97937e9	0.519959
$750$	−5.44644e9	−0.471409
$751$	1.07000e10	0.921815	0.460907	−	0.887448i	$-0.347524\pi$
$751$	1.07000e10	0.921815	0.460907	+	0.887448i	$0.347524\pi$
$752$	3.10773e9	0.266490
$753$	1.51431e10	1.29251
$754$	1.07700e9	0.0914992
$755$	−1.01617e10	−0.859311
$756$	−1.05385e9	−0.0887059
$757$	−6.06443e9	−0.508106	−0.254053	−	0.967190i	$-0.581764\pi$
$757$	−6.06443e9	−0.508106	−0.254053	+	0.967190i	$0.581764\pi$
$758$	1.75149e9	0.146071
$759$	5.46394e10	4.53586
$760$	−2.43624e9	−0.201313
$761$	−1.38928e10	−1.14273	−0.571364	−	0.820697i	$-0.693586\pi$
$761$	−1.38928e10	−1.14273	−0.571364	+	0.820697i	$0.693586\pi$
$762$	1.77471e9	0.145307
$763$	−1.35001e9	−0.110028
$764$	−7.02203e9	−0.569687
$765$	6.45435e9	0.521239
$766$	1.62645e9	0.130749
$767$	−6.07446e9	−0.486098
$768$	−6.16347e9	−0.490977
$769$	5.83542e9	0.462733	0.231366	−	0.972867i	$-0.425680\pi$
$769$	5.83542e9	0.462733	0.231366	+	0.972867i	$0.425680\pi$
$770$	−4.41671e9	−0.348644
$771$	−1.04196e10	−0.818767
$772$	−8.75595e9	−0.684924
$773$	−1.21327e10	−0.944778	−0.472389	−	0.881390i	$-0.656608\pi$
$773$	−1.21327e10	−0.944778	−0.472389	+	0.881390i	$0.656608\pi$
$774$	5.56513e9	0.431402
$775$	5.01138e9	0.386724
$776$	5.79732e9	0.445360
$777$	1.05956e10	0.810312
$778$	−3.60523e8	−0.0274476
$779$	−3.56551e9	−0.270234
$780$	4.51731e9	0.340838
$781$	−4.07526e10	−3.06109
$782$	5.96746e9	0.446237
$783$	2.97754e9	0.221662
$784$	9.35804e8	0.0693551
$785$	3.07116e9	0.226599
$786$	−3.25057e8	−0.0238770
$787$	6.77656e9	0.495562	0.247781	−	0.968816i	$-0.420299\pi$
$787$	6.77656e9	0.495562	0.247781	+	0.968816i	$0.420299\pi$
$788$	1.01589e10	0.739613
$789$	−2.42978e10	−1.76115
$790$	6.01011e8	0.0433698
$791$	8.98382e9	0.645421
$792$	−1.63520e10	−1.16958
$793$	−1.09984e8	−0.00783199
$794$	8.04927e9	0.570670
$795$	6.22916e9	0.439688
$796$	−2.40252e9	−0.168838
$797$	−1.31908e10	−0.922925	−0.461462	−	0.887160i	$-0.652675\pi$
$797$	−1.31908e10	−0.922925	−0.461462	+	0.887160i	$0.652675\pi$
$798$	−7.13596e8	−0.0497098
$799$	4.66946e9	0.323857
$800$	3.79501e9	0.262058
$801$	−2.09542e10	−1.44065
$802$	4.60285e9	0.315077
$803$	2.70650e9	0.184460
$804$	4.64777e9	0.315390
$805$	−1.11415e10	−0.752763
$806$	−2.55873e9	−0.172128
$807$	−4.74628e9	−0.317904
$808$	−6.37601e9	−0.425215
$809$	3.68694e8	0.0244820	0.0122410	−	0.999925i	$-0.496103\pi$
$809$	3.68694e8	0.0244820	0.0122410	+	0.999925i	$0.496103\pi$
$810$	−8.50063e9	−0.562022
$811$	9.58211e9	0.630795	0.315397	−	0.948960i	$-0.397862\pi$
$811$	9.58211e9	0.630795	0.315397	+	0.948960i	$0.397862\pi$
$812$	−3.63859e9	−0.238499
$813$	2.82287e10	1.84236
$814$	−2.02405e10	−1.31533
$815$	6.01672e9	0.389321
$816$	5.93980e9	0.382698
$817$	4.61685e9	0.296189
$818$	−8.05714e9	−0.514688
$819$	1.29388e9	0.0823003
$820$	1.70370e10	1.07906
$821$	−2.19021e9	−0.138129	−0.0690646	−	0.997612i	$-0.522001\pi$
$821$	−2.19021e9	−0.138129	−0.0690646	+	0.997612i	$0.522001\pi$
$822$	−1.19973e10	−0.753409
$823$	−1.01062e10	−0.631957	−0.315978	−	0.948766i	$-0.602333\pi$
$823$	−1.01062e10	−0.631957	−0.315978	+	0.948766i	$0.602333\pi$
$824$	9.16760e9	0.570835
$825$	1.10068e10	0.682452
$826$	−4.58514e9	−0.283089
$827$	−1.63226e10	−1.00351	−0.501753	−	0.865011i	$-0.667312\pi$
$827$	−1.63226e10	−1.00351	−0.501753	+	0.865011i	$0.667312\pi$
$828$	−1.85521e10	−1.13576
$829$	−2.02220e10	−1.23277	−0.616387	−	0.787444i	$-0.711404\pi$
$829$	−2.02220e10	−1.23277	−0.616387	+	0.787444i	$0.711404\pi$
$830$	−8.44662e9	−0.512755
$831$	−1.15760e10	−0.699768
$832$	2.99177e8	0.0180093
$833$	1.40607e9	0.0842851
$834$	8.27381e8	0.0493883
$835$	2.08987e10	1.24227
$836$	−6.10124e9	−0.361157
$837$	−7.07401e9	−0.416991
$838$	3.64592e9	0.214020
$839$	−9.25923e9	−0.541263	−0.270631	−	0.962683i	$-0.587232\pi$
$839$	−9.25923e9	−0.541263	−0.270631	+	0.962683i	$0.587232\pi$
$840$	7.58136e9	0.441336
$841$	−6.96942e9	−0.404027
$842$	4.67297e9	0.269774
$843$	−1.09548e10	−0.629806
$844$	−8.22377e8	−0.0470839
$845$	1.51817e9	0.0865612
$846$	3.24338e9	0.184163
$847$	−1.79094e10	−1.01272
$848$	2.52121e9	0.141979
$849$	3.19041e10	1.78925
$850$	1.20211e9	0.0671395
$851$	−5.10581e10	−2.83995
$852$	3.14616e10	1.74278
$853$	−1.03242e10	−0.569552	−0.284776	−	0.958594i	$-0.591919\pi$
$853$	−1.03242e10	−0.569552	−0.284776	+	0.958594i	$0.591919\pi$
$854$	−8.30182e7	−0.00456111
$855$	3.71924e9	0.203504
$856$	1.96064e10	1.06841
$857$	1.34846e10	0.731824	0.365912	−	0.930649i	$-0.380757\pi$
$857$	1.34846e10	0.731824	0.365912	+	0.930649i	$0.380757\pi$
$858$	−5.61990e9	−0.303755
$859$	−7.04555e9	−0.379262	−0.189631	−	0.981855i	$-0.560729\pi$
$859$	−7.04555e9	−0.379262	−0.189631	+	0.981855i	$0.560729\pi$
$860$	−2.20607e10	−1.18270
$861$	1.10955e10	0.592430
$862$	5.58537e9	0.297014
$863$	5.76366e9	0.305254	0.152627	−	0.988284i	$-0.451227\pi$
$863$	5.76366e9	0.305254	0.152627	+	0.988284i	$0.451227\pi$
$864$	−5.35699e9	−0.282568
$865$	2.54802e10	1.33859
$866$	−4.92693e9	−0.257789
$867$	−1.67141e10	−0.870993
$868$	8.64453e9	0.448665
$869$	3.34659e9	0.172995
$870$	−9.63393e9	−0.496005
$871$	1.56202e9	0.0800982
$872$	−4.42670e9	−0.226085
$873$	−8.85038e9	−0.450207
$874$	3.43868e9	0.174221
$875$	6.18402e9	0.312063
$876$	−2.08945e9	−0.105019
$877$	2.42411e10	1.21354	0.606771	−	0.794877i	$-0.292465\pi$
$877$	2.42411e10	1.21354	0.606771	+	0.794877i	$0.292465\pi$
$878$	9.93588e9	0.495423
$879$	4.29742e10	2.13426
$880$	2.11846e10	1.04793
$881$	−1.64052e10	−0.808285	−0.404143	−	0.914696i	$-0.632430\pi$
$881$	−1.64052e10	−0.808285	−0.404143	+	0.914696i	$0.632430\pi$
$882$	9.76652e8	0.0479292
$883$	2.40299e10	1.17460	0.587299	−	0.809370i	$-0.300191\pi$
$883$	2.40299e10	1.17460	0.587299	+	0.809370i	$0.300191\pi$
$884$	2.74716e9	0.133752
$885$	5.43368e10	2.63507
$886$	6.68900e9	0.323105
$887$	2.04477e10	0.983813	0.491906	−	0.870648i	$-0.336300\pi$
$887$	2.04477e10	0.983813	0.491906	+	0.870648i	$0.336300\pi$
$888$	3.47430e10	1.66503
$889$	−2.01505e9	−0.0961901
$890$	−1.85585e10	−0.882427
$891$	−4.73338e10	−2.24181
$892$	−1.76697e10	−0.833589
$893$	2.69072e9	0.126441
$894$	1.61148e10	0.754299
$895$	−2.18689e10	−1.01964
$896$	8.23474e9	0.382447
$897$	−1.41766e10	−0.655843
$898$	8.70228e9	0.401020
$899$	−2.44242e10	−1.12114
$900$	−3.73721e9	−0.170883
$901$	3.78820e9	0.172543
$902$	−2.11954e10	−0.961655
$903$	−1.43672e10	−0.649330
$904$	2.94580e10	1.32621
$905$	−3.41070e10	−1.52959
$906$	−9.75977e9	−0.436004
$907$	1.70630e10	0.759329	0.379664	−	0.925124i	$-0.376040\pi$
$907$	1.70630e10	0.759329	0.379664	+	0.925124i	$0.376040\pi$
$908$	4.82880e8	0.0214062
$909$	9.73381e9	0.429843
$910$	1.14595e9	0.0504106
$911$	−5.54686e9	−0.243071	−0.121536	−	0.992587i	$-0.538782\pi$
$911$	−5.54686e9	−0.243071	−0.121536	+	0.992587i	$0.538782\pi$
$912$	3.42274e9	0.149414
$913$	−4.70331e10	−2.04529
$914$	6.57270e9	0.284729
$915$	9.83818e8	0.0424562
$916$	3.25019e10	1.39725
$917$	3.69077e8	0.0158061
$918$	−1.69689e9	−0.0723941
$919$	−1.28731e10	−0.547115	−0.273557	−	0.961856i	$-0.588200\pi$
$919$	−1.28731e10	−0.547115	−0.273557	+	0.961856i	$0.588200\pi$
$920$	−3.65330e10	−1.54678
$921$	−5.13976e10	−2.16788
$922$	4.56441e9	0.191790
$923$	1.05736e10	0.442605
$924$	1.89865e10	0.791759
$925$	−1.02854e10	−0.427291
$926$	−1.02301e9	−0.0423390
$927$	−1.39955e10	−0.577046
$928$	−1.84959e10	−0.759727
$929$	3.77350e10	1.54415	0.772075	−	0.635531i	$-0.219219\pi$
$929$	3.77350e10	1.54415	0.772075	+	0.635531i	$0.219219\pi$
$930$	2.28882e10	0.933085
$931$	8.10234e8	0.0329069
$932$	−9.68096e9	−0.391708
$933$	−2.04152e10	−0.822940
$934$	−5.40078e9	−0.216891
$935$	3.18306e10	1.27351
$936$	4.24265e9	0.169111
$937$	−1.35680e10	−0.538801	−0.269401	−	0.963028i	$-0.586826\pi$
$937$	−1.35680e10	−0.538801	−0.269401	+	0.963028i	$0.586826\pi$
$938$	1.17905e9	0.0466468
$939$	−2.36828e10	−0.933478
$940$	−1.28570e10	−0.504886
$941$	1.66279e10	0.650541	0.325270	−	0.945621i	$-0.394545\pi$
$941$	1.66279e10	0.650541	0.325270	+	0.945621i	$0.394545\pi$
$942$	2.94969e9	0.114974
$943$	−5.34671e10	−2.07633
$944$	2.19925e10	0.850888
$945$	3.16816e9	0.122122
$946$	2.74453e10	1.05402
$947$	−3.94921e10	−1.51107	−0.755536	−	0.655107i	$-0.772624\pi$
$947$	−3.94921e10	−1.51107	−0.755536	+	0.655107i	$0.772624\pi$
$948$	−2.58362e9	−0.0984915
$949$	−7.02222e8	−0.0266712
$950$	6.92703e8	0.0262128
$951$	−8.29996e9	−0.312928
$952$	4.61053e9	0.173189
$953$	−5.06925e10	−1.89723	−0.948613	−	0.316439i	$-0.897513\pi$
$953$	−5.06925e10	−1.89723	−0.948613	+	0.316439i	$0.897513\pi$
$954$	2.63126e9	0.0981172
$955$	2.11101e10	0.784295
$956$	−2.50524e10	−0.927357
$957$	−5.36443e10	−1.97848
$958$	−1.18546e10	−0.435619
$959$	1.36220e10	0.498741
$960$	−2.67617e9	−0.0976259
$961$	3.05142e10	1.10910
$962$	5.25155e9	0.190184
$963$	−2.99317e10	−1.08004
$964$	−1.84381e10	−0.662898
$965$	2.63228e10	0.942944
$966$	−1.07008e10	−0.381943
$967$	4.34587e10	1.54555	0.772776	−	0.634679i	$-0.218868\pi$
$967$	4.34587e10	1.54555	0.772776	+	0.634679i	$0.218868\pi$
$968$	−5.87249e10	−2.08093
$969$	5.14278e9	0.181578
$970$	−7.83851e9	−0.275761
$971$	−2.42378e10	−0.849623	−0.424812	−	0.905282i	$-0.639660\pi$
$971$	−2.42378e10	−0.849623	−0.424812	+	0.905282i	$0.639660\pi$
$972$	2.98229e10	1.04164
$973$	−9.39428e8	−0.0326940
$974$	−1.71754e10	−0.595596
$975$	−2.85580e9	−0.0986762
$976$	3.98194e8	0.0137095
$977$	5.82477e10	1.99824	0.999120	−	0.0419334i	$-0.0133517\pi$
$977$	5.82477e10	1.99824	0.999120	+	0.0419334i	$0.0133517\pi$
$978$	5.77875e9	0.197537
$979$	−1.03339e11	−3.51985
$980$	−3.87153e9	−0.131399
$981$	6.75794e9	0.228546
$982$	−3.92104e9	−0.132133
$983$	−3.52029e10	−1.18207	−0.591033	−	0.806648i	$-0.701280\pi$
$983$	−3.52029e10	−1.18207	−0.591033	+	0.806648i	$0.701280\pi$
$984$	3.63823e10	1.21733
$985$	−3.05404e10	−1.01823
$986$	−5.85878e9	−0.194643
$987$	−8.37328e9	−0.277195
$988$	1.58302e9	0.0522199
$989$	6.92328e10	2.27575
$990$	2.21093e10	0.724190
$991$	2.65405e10	0.866266	0.433133	−	0.901330i	$-0.357408\pi$
$991$	2.65405e10	0.866266	0.433133	+	0.901330i	$0.357408\pi$
$992$	4.39424e10	1.42920
$993$	1.60722e10	0.520900
$994$	7.98119e9	0.257760
$995$	7.22263e9	0.232442
$996$	3.63102e10	1.16445
$997$	−3.04787e9	−0.0974009	−0.0487004	−	0.998813i	$-0.515508\pi$
$997$	−3.04787e9	−0.0974009	−0.0487004	+	0.998813i	$0.515508\pi$
$998$	−1.82361e10	−0.580731
$999$	1.45187e10	0.460732

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.d.1.6	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.d.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+4.83483 q^{2} +62.4820 q^{3} -104.624 q^{4} +314.530 q^{5} +302.090 q^{6} -343.000 q^{7} -1124.70 q^{8} +1717.00 q^{9} +O(q^{10})\)	\(q+4.83483 q^{2} +62.4820 q^{3} -104.624 q^{4} +314.530 q^{5} +302.090 q^{6} -343.000 q^{7} -1124.70 q^{8} +1717.00 q^{9} +1520.70 q^{10} +8467.65 q^{11} -6537.15 q^{12} -2197.00 q^{13} -1658.35 q^{14} +19652.4 q^{15} +7954.20 q^{16} +11951.4 q^{17} +8301.41 q^{18} +6886.88 q^{19} -32907.5 q^{20} -21431.3 q^{21} +40939.6 q^{22} +103273. q^{23} -70273.5 q^{24} +20803.8 q^{25} -10622.1 q^{26} -29366.4 q^{27} +35886.2 q^{28} -101393. q^{29} +95016.1 q^{30} +240887. q^{31} +182419. q^{32} +529076. q^{33} +57783.1 q^{34} -107884. q^{35} -179640. q^{36} -494398. q^{37} +33296.9 q^{38} -137273. q^{39} -353751. q^{40} -517724. q^{41} -103617. q^{42} +670384. q^{43} -885923. q^{44} +540048. q^{45} +499309. q^{46} +390703. q^{47} +496995. q^{48} +117649. q^{49} +100583. q^{50} +746750. q^{51} +229860. q^{52} +316966. q^{53} -141982. q^{54} +2.66333e6 q^{55} +385772. q^{56} +430306. q^{57} -490216. q^{58} +2.76489e6 q^{59} -2.05613e6 q^{60} +50060.8 q^{61} +1.16465e6 q^{62} -588932. q^{63} -136175. q^{64} -691021. q^{65} +2.55799e6 q^{66} -710978. q^{67} -1.25041e6 q^{68} +6.45272e6 q^{69} -521599. q^{70} -4.81274e6 q^{71} -1.93111e6 q^{72} +319628. q^{73} -2.39033e6 q^{74} +1.29987e6 q^{75} -720536. q^{76} -2.90440e6 q^{77} -663691. q^{78} +395221. q^{79} +2.50183e6 q^{80} -5.58996e6 q^{81} -2.50311e6 q^{82} -5.55444e6 q^{83} +2.24224e6 q^{84} +3.75908e6 q^{85} +3.24119e6 q^{86} -6.33521e6 q^{87} -9.52355e6 q^{88} -1.22040e7 q^{89} +2.61104e6 q^{90} +753571. q^{91} -1.08049e7 q^{92} +1.50511e7 q^{93} +1.88898e6 q^{94} +2.16613e6 q^{95} +1.13979e7 q^{96} -5.15456e6 q^{97} +568813. q^{98} +1.45390e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more