LMFDB - Embedded newform 91.8.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 1243 x^{10} + 5598 x^{9} + 567554 x^{8} - 1739560 x^{7} - 117081910 x^{6} + \cdots + 59402280000 $ x^12 - 6x^11 - 1243x^10 + 5598x^9 + 567554x^8 - 1739560x^7 - 117081910x^6 + 186018392x^5 + 10752389517x^4 + 491049966x^3 - 344602049215x^2 - 835334324470*x + 59402280000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-13.1706$ 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)

$f(q)$	$=$	$q+14.1706 q^{2} -35.5734 q^{3} +72.8048 q^{4} -268.857 q^{5} -504.095 q^{6} +343.000 q^{7} -782.147 q^{8} -921.532 q^{9} +O(q^{10})$	\(q+14.1706 q^{2} -35.5734 q^{3} +72.8048 q^{4} -268.857 q^{5} -504.095 q^{6} +343.000 q^{7} -782.147 q^{8} -921.532 q^{9} -3809.85 q^{10} +8281.37 q^{11} -2589.92 q^{12} +2197.00 q^{13} +4860.50 q^{14} +9564.16 q^{15} -20402.5 q^{16} +35908.0 q^{17} -13058.6 q^{18} +21219.5 q^{19} -19574.1 q^{20} -12201.7 q^{21} +117352. q^{22} -20961.4 q^{23} +27823.6 q^{24} -5840.92 q^{25} +31132.7 q^{26} +110581. q^{27} +24972.1 q^{28} -79144.2 q^{29} +135530. q^{30} +236751. q^{31} -189000. q^{32} -294597. q^{33} +508837. q^{34} -92217.9 q^{35} -67091.9 q^{36} +185863. q^{37} +300692. q^{38} -78154.8 q^{39} +210286. q^{40} +90803.1 q^{41} -172905. q^{42} +161814. q^{43} +602924. q^{44} +247760. q^{45} -297035. q^{46} +635227. q^{47} +725786. q^{48} +117649. q^{49} -82769.1 q^{50} -1.27737e6 q^{51} +159952. q^{52} -1.27974e6 q^{53} +1.56700e6 q^{54} -2.22650e6 q^{55} -268276. q^{56} -754850. q^{57} -1.12152e6 q^{58} -513817. q^{59} +696317. q^{60} -1.64041e6 q^{61} +3.35490e6 q^{62} -316085. q^{63} -66716.0 q^{64} -590679. q^{65} -4.17460e6 q^{66} +3.79675e6 q^{67} +2.61428e6 q^{68} +745668. q^{69} -1.30678e6 q^{70} +3.37217e6 q^{71} +720773. q^{72} +248442. q^{73} +2.63378e6 q^{74} +207781. q^{75} +1.54488e6 q^{76} +2.84051e6 q^{77} -1.10750e6 q^{78} +1.45545e6 q^{79} +5.48535e6 q^{80} -1.91836e6 q^{81} +1.28673e6 q^{82} +6.46725e6 q^{83} -888341. q^{84} -9.65412e6 q^{85} +2.29300e6 q^{86} +2.81543e6 q^{87} -6.47725e6 q^{88} -6.96379e6 q^{89} +3.51090e6 q^{90} +753571. q^{91} -1.52609e6 q^{92} -8.42206e6 q^{93} +9.00153e6 q^{94} -5.70501e6 q^{95} +6.72337e6 q^{96} -6.83330e6 q^{97} +1.66715e6 q^{98} -7.63155e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9} + 6668 q^{10} + 12168 q^{11} - 183 q^{12} + 26364 q^{13} + 2058 q^{14} - 28790 q^{15} + 85914 q^{16} + 82710 q^{17} - 44965 q^{18} - 10302 q^{19} + 141318 q^{20} + 28126 q^{21} - 97457 q^{22} + 98376 q^{23} - 519981 q^{24} + 272736 q^{25} + 13182 q^{26} + 306652 q^{27} + 338198 q^{28} + 350592 q^{29} + 231528 q^{30} + 55092 q^{31} + 114420 q^{32} + 609912 q^{33} + 812002 q^{34} + 351918 q^{35} + 1472143 q^{36} + 376310 q^{37} + 2825424 q^{38} + 180154 q^{39} + 2169290 q^{40} + 1387272 q^{41} + 105987 q^{42} + 568708 q^{43} + 3392031 q^{44} + 3556226 q^{45} - 1736829 q^{46} + 1359444 q^{47} + 4151249 q^{48} + 1411788 q^{49} + 3983712 q^{50} + 2709260 q^{51} + 2166242 q^{52} + 2061780 q^{53} + 2196651 q^{54} - 2112846 q^{55} + 78204 q^{56} + 2359902 q^{57} + 670268 q^{58} + 395964 q^{59} - 1052376 q^{60} + 444006 q^{61} + 2854353 q^{62} + 3739386 q^{63} + 12026858 q^{64} + 2254122 q^{65} - 4605681 q^{66} - 3094010 q^{67} + 4668954 q^{68} + 3839892 q^{69} + 2287124 q^{70} + 5694366 q^{71} - 9780585 q^{72} + 7052346 q^{73} - 4436259 q^{74} - 16288696 q^{75} - 3051830 q^{76} + 4173624 q^{77} + 678873 q^{78} + 4304160 q^{79} + 3807018 q^{80} - 6689556 q^{81} - 4733665 q^{82} + 2704554 q^{83} - 62769 q^{84} + 9301878 q^{85} + 1510998 q^{86} + 16231802 q^{87} - 70453923 q^{88} - 10986042 q^{89} - 12851300 q^{90} + 9042852 q^{91} - 16505451 q^{92} - 47230934 q^{93} - 24306151 q^{94} - 21839424 q^{95} - 86512741 q^{96} - 24462382 q^{97} + 705894 q^{98} + 11555078 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9 + 6668 * q^10 + 12168 * q^11 - 183 * q^12 + 26364 * q^13 + 2058 * q^14 - 28790 * q^15 + 85914 * q^16 + 82710 * q^17 - 44965 * q^18 - 10302 * q^19 + 141318 * q^20 + 28126 * q^21 - 97457 * q^22 + 98376 * q^23 - 519981 * q^24 + 272736 * q^25 + 13182 * q^26 + 306652 * q^27 + 338198 * q^28 + 350592 * q^29 + 231528 * q^30 + 55092 * q^31 + 114420 * q^32 + 609912 * q^33 + 812002 * q^34 + 351918 * q^35 + 1472143 * q^36 + 376310 * q^37 + 2825424 * q^38 + 180154 * q^39 + 2169290 * q^40 + 1387272 * q^41 + 105987 * q^42 + 568708 * q^43 + 3392031 * q^44 + 3556226 * q^45 - 1736829 * q^46 + 1359444 * q^47 + 4151249 * q^48 + 1411788 * q^49 + 3983712 * q^50 + 2709260 * q^51 + 2166242 * q^52 + 2061780 * q^53 + 2196651 * q^54 - 2112846 * q^55 + 78204 * q^56 + 2359902 * q^57 + 670268 * q^58 + 395964 * q^59 - 1052376 * q^60 + 444006 * q^61 + 2854353 * q^62 + 3739386 * q^63 + 12026858 * q^64 + 2254122 * q^65 - 4605681 * q^66 - 3094010 * q^67 + 4668954 * q^68 + 3839892 * q^69 + 2287124 * q^70 + 5694366 * q^71 - 9780585 * q^72 + 7052346 * q^73 - 4436259 * q^74 - 16288696 * q^75 - 3051830 * q^76 + 4173624 * q^77 + 678873 * q^78 + 4304160 * q^79 + 3807018 * q^80 - 6689556 * q^81 - 4733665 * q^82 + 2704554 * q^83 - 62769 * q^84 + 9301878 * q^85 + 1510998 * q^86 + 16231802 * q^87 - 70453923 * q^88 - 10986042 * q^89 - 12851300 * q^90 + 9042852 * q^91 - 16505451 * q^92 - 47230934 * q^93 - 24306151 * q^94 - 21839424 * q^95 - 86512741 * q^96 - 24462382 * q^97 + 705894 * q^98 + 11555078 * 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 $

$2$	14.1706	1.25251	0.626256	−	0.779617i	$-0.284586\pi$
$2$	14.1706	1.25251	0.626256	+	0.779617i	$0.284586\pi$
$3$	−35.5734	−0.760679	−0.380339	−	0.924847i	$-0.624193\pi$
$3$	−35.5734	−0.760679	−0.380339	+	0.924847i	$0.624193\pi$
$4$	72.8048	0.568788
$5$	−268.857	−0.961892	−0.480946	−	0.876750i	$-0.659707\pi$
$5$	−268.857	−0.961892	−0.480946	+	0.876750i	$0.659707\pi$
$6$	−504.095	−0.952760
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−782.147	−0.540099
$9$	−921.532	−0.421368
$10$	−3809.85	−1.20478
$11$	8281.37	1.87598	0.937989	−	0.346664i	$-0.112686\pi$
$11$	8281.37	1.87598	0.937989	+	0.346664i	$0.112686\pi$
$12$	−2589.92	−0.432665
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	4860.50	0.473405
$15$	9564.16	0.731691
$16$	−20402.5	−1.24527
$17$	35908.0	1.77264	0.886319	−	0.463076i	$-0.153254\pi$
$17$	35908.0	1.77264	0.886319	+	0.463076i	$0.153254\pi$
$18$	−13058.6	−0.527769
$19$	21219.5	0.709737	0.354868	−	0.934916i	$-0.384526\pi$
$19$	21219.5	0.709737	0.354868	+	0.934916i	$0.384526\pi$
$20$	−19574.1	−0.547112
$21$	−12201.7	−0.287510
$22$	117352.	2.34969
$23$	−20961.4	−0.359230	−0.179615	−	0.983737i	$-0.557485\pi$
$23$	−20961.4	−0.359230	−0.179615	+	0.983737i	$0.557485\pi$
$24$	27823.6	0.410842
$25$	−5840.92	−0.0747637
$26$	31132.7	0.347384
$27$	110581.	1.08120
$28$	24972.1	0.214982
$29$	−79144.2	−0.602596	−0.301298	−	0.953530i	$-0.597420\pi$
$29$	−79144.2	−0.602596	−0.301298	+	0.953530i	$0.597420\pi$
$30$	135530.	0.916452
$31$	236751.	1.42734	0.713669	−	0.700483i	$-0.247032\pi$
$31$	236751.	1.42734	0.713669	+	0.700483i	$0.247032\pi$
$32$	−189000.	−1.01962
$33$	−294597.	−1.42702
$34$	508837.	2.22025
$35$	−92217.9	−0.363561
$36$	−67091.9	−0.239669
$37$	185863.	0.603236	0.301618	−	0.953429i	$-0.402473\pi$
$37$	185863.	0.603236	0.301618	+	0.953429i	$0.402473\pi$
$38$	300692.	0.888954
$39$	−78154.8	−0.210974
$40$	210286.	0.519517
$41$	90803.1	0.205758	0.102879	−	0.994694i	$-0.467195\pi$
$41$	90803.1	0.205758	0.102879	+	0.994694i	$0.467195\pi$
$42$	−172905.	−0.360109
$43$	161814.	0.310368	0.155184	−	0.987886i	$-0.450403\pi$
$43$	161814.	0.310368	0.155184	+	0.987886i	$0.450403\pi$
$44$	602924.	1.06703
$45$	247760.	0.405310
$46$	−297035.	−0.449940
$47$	635227.	0.892456	0.446228	−	0.894919i	$-0.352767\pi$
$47$	635227.	0.892456	0.446228	+	0.894919i	$0.352767\pi$
$48$	725786.	0.947249
$49$	117649.	0.142857
$50$	−82769.1	−0.0936425
$51$	−1.27737e6	−1.34841
$52$	159952.	0.157753
$53$	−1.27974e6	−1.18075	−0.590373	−	0.807130i	$-0.701019\pi$
$53$	−1.27974e6	−1.18075	−0.590373	+	0.807130i	$0.701019\pi$
$54$	1.56700e6	1.35422
$55$	−2.22650e6	−1.80449
$56$	−268276.	−0.204138
$57$	−754850.	−0.539882
$58$	−1.12152e6	−0.754758
$59$	−513817.	−0.325706	−0.162853	−	0.986650i	$-0.552070\pi$
$59$	−513817.	−0.325706	−0.162853	+	0.986650i	$0.552070\pi$
$60$	696317.	0.416177
$61$	−1.64041e6	−0.925335	−0.462667	−	0.886532i	$-0.653108\pi$
$61$	−1.64041e6	−0.925335	−0.462667	+	0.886532i	$0.653108\pi$
$62$	3.35490e6	1.78776
$63$	−316085.	−0.159262
$64$	−66716.0	−0.0318127
$65$	−590679.	−0.266781
$66$	−4.17460e6	−1.78736
$67$	3.79675e6	1.54224	0.771118	−	0.636693i	$-0.219698\pi$
$67$	3.79675e6	1.54224	0.771118	+	0.636693i	$0.219698\pi$
$68$	2.61428e6	1.00825
$69$	745668.	0.273259
$70$	−1.30678e6	−0.455365
$71$	3.37217e6	1.11816	0.559082	−	0.829112i	$-0.311154\pi$
$71$	3.37217e6	1.11816	0.559082	+	0.829112i	$0.311154\pi$
$72$	720773.	0.227580
$73$	248442.	0.0747472	0.0373736	−	0.999301i	$-0.488101\pi$
$73$	248442.	0.0747472	0.0373736	+	0.999301i	$0.488101\pi$
$74$	2.63378e6	0.755560
$75$	207781.	0.0568712
$76$	1.54488e6	0.403689
$77$	2.84051e6	0.709053
$78$	−1.10750e6	−0.264248
$79$	1.45545e6	0.332125	0.166062	−	0.986115i	$-0.446895\pi$
$79$	1.45545e6	0.332125	0.166062	+	0.986115i	$0.446895\pi$
$80$	5.48535e6	1.19781
$81$	−1.91836e6	−0.401081
$82$	1.28673e6	0.257715
$83$	6.46725e6	1.24150	0.620749	−	0.784009i	$-0.286828\pi$
$83$	6.46725e6	1.24150	0.620749	+	0.784009i	$0.286828\pi$
$84$	−888341.	−0.163532
$85$	−9.65412e6	−1.70509
$86$	2.29300e6	0.388740
$87$	2.81543e6	0.458382
$88$	−6.47725e6	−1.01321
$89$	−6.96379e6	−1.04708	−0.523541	−	0.852000i	$-0.675389\pi$
$89$	−6.96379e6	−1.04708	−0.523541	+	0.852000i	$0.675389\pi$
$90$	3.51090e6	0.507656
$91$	753571.	0.104828
$92$	−1.52609e6	−0.204326
$93$	−8.42206e6	−1.08575
$94$	9.00153e6	1.11781
$95$	−5.70501e6	−0.682690
$96$	6.72337e6	0.775600
$97$	−6.83330e6	−0.760203	−0.380101	−	0.924945i	$-0.624111\pi$
$97$	−6.83330e6	−0.760203	−0.380101	+	0.924945i	$0.624111\pi$
$98$	1.66715e6	0.178930
$99$	−7.63155e6	−0.790477
$100$	−425247.	−0.0425247
$101$	7.32356e6	0.707290	0.353645	−	0.935380i	$-0.384942\pi$
$101$	7.32356e6	0.707290	0.353645	+	0.935380i	$0.384942\pi$
$102$	−1.81011e7	−1.68890
$103$	1.12875e7	1.01781	0.508907	−	0.860822i	$-0.330050\pi$
$103$	1.12875e7	1.01781	0.508907	+	0.860822i	$0.330050\pi$
$104$	−1.71838e6	−0.149796
$105$	3.28051e6	0.276553
$106$	−1.81347e7	−1.47890
$107$	−5.26433e6	−0.415432	−0.207716	−	0.978189i	$-0.566603\pi$
$107$	−5.26433e6	−0.415432	−0.207716	+	0.978189i	$0.566603\pi$
$108$	8.05084e6	0.614976
$109$	−1.13029e7	−0.835985	−0.417992	−	0.908451i	$-0.637266\pi$
$109$	−1.13029e7	−0.835985	−0.417992	+	0.908451i	$0.637266\pi$
$110$	−3.15508e7	−2.26014
$111$	−6.61179e6	−0.458869
$112$	−6.99805e6	−0.470667
$113$	−2.76479e7	−1.80255	−0.901275	−	0.433247i	$-0.857368\pi$
$113$	−2.76479e7	−1.80255	−0.901275	+	0.433247i	$0.857368\pi$
$114$	−1.06966e7	−0.676208
$115$	5.63561e6	0.345540
$116$	−5.76208e6	−0.342749
$117$	−2.02461e6	−0.116866
$118$	−7.28107e6	−0.407951
$119$	1.23164e7	0.669994
$120$	−7.48058e6	−0.395185
$121$	4.90939e7	2.51930
$122$	−2.32456e7	−1.15899
$123$	−3.23018e6	−0.156516
$124$	1.72366e7	0.811852
$125$	2.25748e7	1.03381
$126$	−4.47911e6	−0.199478
$127$	−1.55458e7	−0.673443	−0.336722	−	0.941604i	$-0.609318\pi$
$127$	−1.55458e7	−0.673443	−0.336722	+	0.941604i	$0.609318\pi$
$128$	2.32466e7	0.979770
$129$	−5.75628e6	−0.236090
$130$	−8.37025e6	−0.334146
$131$	2.17523e7	0.845387	0.422693	−	0.906273i	$-0.361085\pi$
$131$	2.17523e7	0.845387	0.422693	+	0.906273i	$0.361085\pi$
$132$	−2.14481e7	−0.811670
$133$	7.27828e6	0.268255
$134$	5.38021e7	1.93167
$135$	−2.97305e7	−1.04000
$136$	−2.80853e7	−0.957400
$137$	−8.09380e6	−0.268924	−0.134462	−	0.990919i	$-0.542931\pi$
$137$	−8.09380e6	−0.268924	−0.134462	+	0.990919i	$0.542931\pi$
$138$	1.05665e7	0.342260
$139$	−3.40398e7	−1.07507	−0.537533	−	0.843243i	$-0.680644\pi$
$139$	−3.40398e7	−1.07507	−0.537533	+	0.843243i	$0.680644\pi$
$140$	−6.71391e6	−0.206789
$141$	−2.25972e7	−0.678872
$142$	4.77856e7	1.40052
$143$	1.81942e7	0.520303
$144$	1.88015e7	0.524716
$145$	2.12785e7	0.579632
$146$	3.52056e6	0.0936218
$147$	−4.18518e6	−0.108668
$148$	1.35317e7	0.343113
$149$	4.47952e7	1.10938	0.554689	−	0.832058i	$-0.312837\pi$
$149$	4.47952e7	1.10938	0.554689	+	0.832058i	$0.312837\pi$
$150$	2.94438e6	0.0712319
$151$	7.00158e7	1.65492	0.827460	−	0.561525i	$-0.189785\pi$
$151$	7.00158e7	1.65492	0.827460	+	0.561525i	$0.189785\pi$
$152$	−1.65967e7	−0.383328
$153$	−3.30904e7	−0.746933
$154$	4.02516e7	0.888098
$155$	−6.36523e7	−1.37294
$156$	−5.69005e6	−0.120000
$157$	3.62431e7	0.747440	0.373720	−	0.927542i	$-0.378082\pi$
$157$	3.62431e7	0.747440	0.373720	+	0.927542i	$0.378082\pi$
$158$	2.06245e7	0.415990
$159$	4.55248e7	0.898169
$160$	5.08139e7	0.980760
$161$	−7.18975e6	−0.135776
$162$	−2.71842e7	−0.502359
$163$	1.31797e7	0.238368	0.119184	−	0.992872i	$-0.461972\pi$
$163$	1.31797e7	0.238368	0.119184	+	0.992872i	$0.461972\pi$
$164$	6.61090e6	0.117033
$165$	7.92044e7	1.37264
$166$	9.16446e7	1.55499
$167$	3.50778e7	0.582806	0.291403	−	0.956600i	$-0.405878\pi$
$167$	3.50778e7	0.582806	0.291403	+	0.956600i	$0.405878\pi$
$168$	9.54351e6	0.155284
$169$	4.82681e6	0.0769231
$170$	−1.36804e8	−2.13564
$171$	−1.95544e7	−0.299060
$172$	1.17808e7	0.176533
$173$	9.32329e7	1.36901	0.684507	−	0.729007i	$-0.260018\pi$
$173$	9.32329e7	1.36901	0.684507	+	0.729007i	$0.260018\pi$
$174$	3.98962e7	0.574129
$175$	−2.00343e6	−0.0282580
$176$	−1.68960e8	−2.33610
$177$	1.82782e7	0.247758
$178$	−9.86809e7	−1.31148
$179$	−1.17490e8	−1.53114	−0.765571	−	0.643351i	$-0.777543\pi$
$179$	−1.17490e8	−1.53114	−0.765571	+	0.643351i	$0.777543\pi$
$180$	1.80381e7	0.230536
$181$	−3.61485e7	−0.453123	−0.226561	−	0.973997i	$-0.572748\pi$
$181$	−3.61485e7	−0.453123	−0.226561	+	0.973997i	$0.572748\pi$
$182$	1.06785e7	0.131299
$183$	5.83551e7	0.703882
$184$	1.63949e7	0.194020
$185$	−4.99706e7	−0.580248
$186$	−1.19345e8	−1.35991
$187$	2.97367e8	3.32543
$188$	4.62476e7	0.507618
$189$	3.79293e7	0.408657
$190$	−8.08432e7	−0.855078
$191$	1.37913e8	1.43215	0.716074	−	0.698025i	$-0.245937\pi$
$191$	1.37913e8	1.43215	0.716074	+	0.698025i	$0.245937\pi$
$192$	2.37332e6	0.0241992
$193$	5.50663e7	0.551360	0.275680	−	0.961249i	$-0.411097\pi$
$193$	5.50663e7	0.551360	0.275680	+	0.961249i	$0.411097\pi$
$194$	−9.68317e7	−0.952164
$195$	2.10125e7	0.202935
$196$	8.56541e6	0.0812554
$197$	1.49349e8	1.39178	0.695888	−	0.718151i	$-0.255011\pi$
$197$	1.49349e8	1.39178	0.695888	+	0.718151i	$0.255011\pi$
$198$	−1.08143e8	−0.990083
$199$	−4.40038e7	−0.395826	−0.197913	−	0.980220i	$-0.563416\pi$
$199$	−4.40038e7	−0.395826	−0.197913	+	0.980220i	$0.563416\pi$
$200$	4.56845e6	0.0403798
$201$	−1.35064e8	−1.17315
$202$	1.03779e8	0.885890
$203$	−2.71464e7	−0.227760
$204$	−9.29987e7	−0.766958
$205$	−2.44130e7	−0.197917
$206$	1.59951e8	1.27482
$207$	1.93166e7	0.151368
$208$	−4.48242e7	−0.345375
$209$	1.75726e8	1.33145
$210$	4.64866e7	0.346386
$211$	−1.44931e8	−1.06212	−0.531059	−	0.847335i	$-0.678206\pi$
$211$	−1.44931e8	−1.06212	−0.531059	+	0.847335i	$0.678206\pi$
$212$	−9.31714e7	−0.671594
$213$	−1.19960e8	−0.850564
$214$	−7.45985e7	−0.520334
$215$	−4.35049e7	−0.298540
$216$	−8.64906e7	−0.583957
$217$	8.12057e7	0.539483
$218$	−1.60169e8	−1.04708
$219$	−8.83793e6	−0.0568586
$220$	−1.62100e8	−1.02637
$221$	7.88899e7	0.491641
$222$	−9.36927e7	−0.574739
$223$	−2.20856e8	−1.33365	−0.666826	−	0.745214i	$-0.732347\pi$
$223$	−2.20856e8	−1.33365	−0.666826	+	0.745214i	$0.732347\pi$
$224$	−6.48269e7	−0.385378
$225$	5.38259e6	0.0315030
$226$	−3.91786e8	−2.25772
$227$	9.41476e7	0.534218	0.267109	−	0.963666i	$-0.413932\pi$
$227$	9.41476e7	0.534218	0.267109	+	0.963666i	$0.413932\pi$
$228$	−5.49567e7	−0.307078
$229$	2.86530e8	1.57669	0.788344	−	0.615234i	$-0.210939\pi$
$229$	2.86530e8	1.57669	0.788344	+	0.615234i	$0.210939\pi$
$230$	7.98598e7	0.432794
$231$	−1.01047e8	−0.539362
$232$	6.19023e7	0.325461
$233$	−3.69368e8	−1.91299	−0.956497	−	0.291742i	$-0.905765\pi$
$233$	−3.69368e8	−1.91299	−0.956497	+	0.291742i	$0.905765\pi$
$234$	−2.86898e7	−0.146377
$235$	−1.70785e8	−0.858446
$236$	−3.74083e7	−0.185258
$237$	−5.17752e7	−0.252640
$238$	1.74531e8	0.839176
$239$	4.21189e7	0.199565	0.0997825	−	0.995009i	$-0.468185\pi$
$239$	4.21189e7	0.199565	0.0997825	+	0.995009i	$0.468185\pi$
$240$	−1.95133e8	−0.911151
$241$	3.00883e8	1.38464	0.692322	−	0.721589i	$-0.256588\pi$
$241$	3.00883e8	1.38464	0.692322	+	0.721589i	$0.256588\pi$
$242$	6.95689e8	3.15545
$243$	−1.73598e8	−0.776110
$244$	−1.19430e8	−0.526319
$245$	−3.16308e7	−0.137413
$246$	−4.57734e7	−0.196038
$247$	4.66192e7	0.196846
$248$	−1.85174e8	−0.770903
$249$	−2.30062e8	−0.944382
$250$	3.19898e8	1.29486
$251$	7.74919e7	0.309313	0.154657	−	0.987968i	$-0.450573\pi$
$251$	7.74919e7	0.309313	0.154657	+	0.987968i	$0.450573\pi$
$252$	−2.30125e7	−0.0905863
$253$	−1.73589e8	−0.673908
$254$	−2.20293e8	−0.843496
$255$	3.43430e8	1.29702
$256$	3.37957e8	1.25899
$257$	−1.10787e8	−0.407119	−0.203559	−	0.979063i	$-0.565251\pi$
$257$	−1.10787e8	−0.407119	−0.203559	+	0.979063i	$0.565251\pi$
$258$	−8.15698e7	−0.295706
$259$	6.37510e7	0.228002
$260$	−4.30043e7	−0.151742
$261$	7.29339e7	0.253914
$262$	3.08242e8	1.05886
$263$	2.04966e8	0.694764	0.347382	−	0.937724i	$-0.387071\pi$
$263$	2.04966e8	0.694764	0.347382	+	0.937724i	$0.387071\pi$
$264$	2.30418e8	0.770730
$265$	3.44067e8	1.13575
$266$	1.03137e8	0.335993
$267$	2.47726e8	0.796493
$268$	2.76422e8	0.877204
$269$	−3.26675e8	−1.02325	−0.511626	−	0.859208i	$-0.670957\pi$
$269$	−3.26675e8	−1.02325	−0.511626	+	0.859208i	$0.670957\pi$
$270$	−4.21298e8	−1.30262
$271$	−2.38383e7	−0.0727584	−0.0363792	−	0.999338i	$-0.511582\pi$
$271$	−2.38383e7	−0.0727584	−0.0363792	+	0.999338i	$0.511582\pi$
$272$	−7.32612e8	−2.20741
$273$	−2.68071e7	−0.0797408
$274$	−1.14694e8	−0.336831
$275$	−4.83708e7	−0.140255
$276$	5.42882e7	0.155426
$277$	−1.71114e8	−0.483734	−0.241867	−	0.970309i	$-0.577760\pi$
$277$	−1.71114e8	−0.483734	−0.241867	+	0.970309i	$0.577760\pi$
$278$	−4.82363e8	−1.34653
$279$	−2.18174e8	−0.601434
$280$	7.21280e7	0.196359
$281$	−4.20183e8	−1.12971	−0.564854	−	0.825191i	$-0.691068\pi$
$281$	−4.20183e8	−1.12971	−0.564854	+	0.825191i	$0.691068\pi$
$282$	−3.20215e8	−0.850296
$283$	−4.55946e8	−1.19581	−0.597903	−	0.801568i	$-0.703999\pi$
$283$	−4.55946e8	−1.19581	−0.597903	+	0.801568i	$0.703999\pi$
$284$	2.45510e8	0.635998
$285$	2.02947e8	0.519308
$286$	2.57822e8	0.651686
$287$	3.11455e7	0.0777693
$288$	1.74169e8	0.429633
$289$	8.79046e8	2.14224
$290$	3.01528e8	0.725996
$291$	2.43084e8	0.578270
$292$	1.80878e7	0.0425153
$293$	3.64875e8	0.847437	0.423719	−	0.905794i	$-0.360725\pi$
$293$	3.64875e8	0.847437	0.423719	+	0.905794i	$0.360725\pi$
$294$	−5.93063e7	−0.136109
$295$	1.38143e8	0.313294
$296$	−1.45372e8	−0.325807
$297$	9.15763e8	2.02832
$298$	6.34773e8	1.38951
$299$	−4.60522e7	−0.0996324
$300$	1.51275e7	0.0323476
$301$	5.55022e7	0.117308
$302$	9.92163e8	2.07281
$303$	−2.60524e8	−0.538021
$304$	−4.32930e8	−0.883813
$305$	4.41037e8	0.890072
$306$	−4.68909e8	−0.935542
$307$	−9.30201e8	−1.83482	−0.917408	−	0.397947i	$-0.869723\pi$
$307$	−9.30201e8	−1.83482	−0.917408	+	0.397947i	$0.869723\pi$
$308$	2.06803e8	0.403301
$309$	−4.01536e8	−0.774229
$310$	−9.01988e8	−1.71963
$311$	−7.79249e8	−1.46898	−0.734489	−	0.678621i	$-0.762578\pi$
$311$	−7.79249e8	−1.46898	−0.734489	+	0.678621i	$0.762578\pi$
$312$	6.11285e7	0.113947
$313$	−6.32169e8	−1.16527	−0.582637	−	0.812732i	$-0.697979\pi$
$313$	−6.32169e8	−1.16527	−0.582637	+	0.812732i	$0.697979\pi$
$314$	5.13585e8	0.936178
$315$	8.49818e7	0.153193
$316$	1.05963e8	0.188908
$317$	−5.01978e8	−0.885069	−0.442535	−	0.896751i	$-0.645921\pi$
$317$	−5.01978e8	−0.885069	−0.442535	+	0.896751i	$0.645921\pi$
$318$	6.45112e8	1.12497
$319$	−6.55422e8	−1.13046
$320$	1.79371e7	0.0306004
$321$	1.87270e8	0.316010
$322$	−1.01883e8	−0.170061
$323$	7.61949e8	1.25811
$324$	−1.39666e8	−0.228130
$325$	−1.28325e7	−0.0207357
$326$	1.86763e8	0.298559
$327$	4.02084e8	0.635916
$328$	−7.10213e7	−0.111130
$329$	2.17883e8	0.337317
$330$	1.12237e9	1.71924
$331$	−1.02587e9	−1.55487	−0.777433	−	0.628966i	$-0.783479\pi$
$331$	−1.02587e9	−1.55487	−0.777433	+	0.628966i	$0.783479\pi$
$332$	4.70847e8	0.706149
$333$	−1.71279e8	−0.254184
$334$	4.97072e8	0.729972
$335$	−1.02078e9	−1.48346
$336$	2.48945e8	0.358026
$337$	5.29598e8	0.753775	0.376887	−	0.926259i	$-0.376994\pi$
$337$	5.29598e8	0.753775	0.376887	+	0.926259i	$0.376994\pi$
$338$	6.83986e7	0.0963471
$339$	9.83530e8	1.37116
$340$	−7.02866e8	−0.969832
$341$	1.96063e9	2.67765
$342$	−2.77097e8	−0.374577
$343$	4.03536e7	0.0539949
$344$	−1.26562e8	−0.167629
$345$	−2.00478e8	−0.262845
$346$	1.32116e9	1.71471
$347$	−6.79063e8	−0.872483	−0.436241	−	0.899830i	$-0.643691\pi$
$347$	−6.79063e8	−0.872483	−0.436241	+	0.899830i	$0.643691\pi$
$348$	2.04977e8	0.260722
$349$	2.70597e7	0.0340749	0.0170374	−	0.999855i	$-0.494577\pi$
$349$	2.70597e7	0.0340749	0.0170374	+	0.999855i	$0.494577\pi$
$350$	−2.83898e7	−0.0353935
$351$	2.42947e8	0.299872
$352$	−1.56518e9	−1.91278
$353$	1.25096e9	1.51367	0.756836	−	0.653604i	$-0.226744\pi$
$353$	1.25096e9	1.51367	0.756836	+	0.653604i	$0.226744\pi$
$354$	2.59013e8	0.310320
$355$	−9.06632e8	−1.07555
$356$	−5.06998e8	−0.595568
$357$	−4.38138e8	−0.509650
$358$	−1.66490e9	−1.91777
$359$	4.89627e8	0.558515	0.279257	−	0.960216i	$-0.409912\pi$
$359$	4.89627e8	0.558515	0.279257	+	0.960216i	$0.409912\pi$
$360$	−1.93785e8	−0.218908
$361$	−4.43605e8	−0.496274
$362$	−5.12245e8	−0.567542
$363$	−1.74644e9	−1.91637
$364$	5.48636e7	0.0596252
$365$	−6.67953e7	−0.0718987
$366$	8.26925e8	0.881622
$367$	−2.47681e8	−0.261554	−0.130777	−	0.991412i	$-0.541747\pi$
$367$	−2.47681e8	−0.261554	−0.130777	+	0.991412i	$0.541747\pi$
$368$	4.27664e8	0.447338
$369$	−8.36779e7	−0.0866999
$370$	−7.08111e8	−0.726768
$371$	−4.38951e8	−0.446280
$372$	−6.13166e8	−0.617558
$373$	−1.60366e9	−1.60005	−0.800023	−	0.599969i	$-0.795179\pi$
$373$	−1.60366e9	−1.60005	−0.800023	+	0.599969i	$0.795179\pi$
$374$	4.21386e9	4.16514
$375$	−8.03064e8	−0.786395
$376$	−4.96841e8	−0.482014
$377$	−1.73880e8	−0.167130
$378$	5.37480e8	0.511848
$379$	1.02451e9	0.966668	0.483334	−	0.875436i	$-0.339426\pi$
$379$	1.02451e9	0.966668	0.483334	+	0.875436i	$0.339426\pi$
$380$	−4.15352e8	−0.388306
$381$	5.53019e8	0.512274
$382$	1.95430e9	1.79378
$383$	1.90530e9	1.73287	0.866436	−	0.499288i	$-0.166405\pi$
$383$	1.90530e9	1.73287	0.866436	+	0.499288i	$0.166405\pi$
$384$	−8.26960e8	−0.745290
$385$	−7.63691e8	−0.682033
$386$	7.80320e8	0.690585
$387$	−1.49117e8	−0.130779
$388$	−4.97497e8	−0.432394
$389$	4.30629e8	0.370919	0.185460	−	0.982652i	$-0.440623\pi$
$389$	4.30629e8	0.370919	0.185460	+	0.982652i	$0.440623\pi$
$390$	2.97758e8	0.254178
$391$	−7.52681e8	−0.636784
$392$	−9.20188e7	−0.0771570
$393$	−7.73804e8	−0.643068
$394$	2.11635e9	1.74322
$395$	−3.91307e8	−0.319468
$396$	−5.55613e8	−0.449614
$397$	1.25572e9	1.00723	0.503614	−	0.863929i	$-0.332003\pi$
$397$	1.25572e9	1.00723	0.503614	+	0.863929i	$0.332003\pi$
$398$	−6.23559e8	−0.495777
$399$	−2.58913e8	−0.204056
$400$	1.19169e8	0.0931009
$401$	−1.82084e8	−0.141015	−0.0705076	−	0.997511i	$-0.522462\pi$
$401$	−1.82084e8	−0.141015	−0.0705076	+	0.997511i	$0.522462\pi$
$402$	−1.91393e9	−1.46938
$403$	5.20143e8	0.395872
$404$	5.33191e8	0.402298
$405$	5.15764e8	0.385797
$406$	−3.84680e8	−0.285272
$407$	1.53920e9	1.13166
$408$	9.99091e8	0.728273
$409$	−1.08547e9	−0.784487	−0.392243	−	0.919861i	$-0.628301\pi$
$409$	−1.08547e9	−0.784487	−0.392243	+	0.919861i	$0.628301\pi$
$410$	−3.45947e8	−0.247894
$411$	2.87924e8	0.204565
$412$	8.21786e8	0.578920
$413$	−1.76239e8	−0.123105
$414$	2.73727e8	0.189590
$415$	−1.73877e9	−1.19419
$416$	−4.15232e8	−0.282790
$417$	1.21091e9	0.817779
$418$	2.49014e9	1.66766
$419$	2.11501e8	0.140464	0.0702319	−	0.997531i	$-0.477626\pi$
$419$	2.11501e8	0.140464	0.0702319	+	0.997531i	$0.477626\pi$
$420$	2.38837e8	0.157300
$421$	−2.57859e9	−1.68421	−0.842104	−	0.539316i	$-0.818683\pi$
$421$	−2.57859e9	−1.68421	−0.842104	+	0.539316i	$0.818683\pi$
$422$	−2.05376e9	−1.33032
$423$	−5.85382e8	−0.376052
$424$	1.00095e9	0.637720
$425$	−2.09736e8	−0.132529
$426$	−1.69990e9	−1.06534
$427$	−5.62662e8	−0.349744
$428$	−3.83269e8	−0.236293
$429$	−6.47229e8	−0.395783
$430$	−6.16488e8	−0.373926
$431$	1.99982e9	1.20315	0.601576	−	0.798816i	$-0.294540\pi$
$431$	1.99982e9	1.20315	0.601576	+	0.798816i	$0.294540\pi$
$432$	−2.25613e9	−1.34639
$433$	−1.05800e9	−0.626292	−0.313146	−	0.949705i	$-0.601383\pi$
$433$	−1.05800e9	−0.626292	−0.313146	+	0.949705i	$0.601383\pi$
$434$	1.15073e9	0.675709
$435$	−7.56948e8	−0.440914
$436$	−8.22908e8	−0.475498
$437$	−4.44790e8	−0.254959
$438$	−1.25238e8	−0.0712161
$439$	−2.07900e9	−1.17281	−0.586406	−	0.810017i	$-0.699458\pi$
$439$	−2.07900e9	−1.17281	−0.586406	+	0.810017i	$0.699458\pi$
$440$	1.74145e9	0.974602
$441$	−1.08417e8	−0.0601954
$442$	1.11791e9	0.615787
$443$	−2.20392e9	−1.20444	−0.602218	−	0.798332i	$-0.705716\pi$
$443$	−2.20392e9	−1.20444	−0.602218	+	0.798332i	$0.705716\pi$
$444$	−4.81370e8	−0.260999
$445$	1.87226e9	1.00718
$446$	−3.12965e9	−1.67041
$447$	−1.59352e9	−0.843880
$448$	−2.28836e7	−0.0120241
$449$	−1.43396e9	−0.747608	−0.373804	−	0.927508i	$-0.621947\pi$
$449$	−1.43396e9	−0.747608	−0.373804	+	0.927508i	$0.621947\pi$
$450$	7.62743e7	0.0394579
$451$	7.51974e8	0.385998
$452$	−2.01290e9	−1.02527
$453$	−2.49070e9	−1.25886
$454$	1.33412e9	0.669115
$455$	−2.02603e8	−0.100834
$456$	5.90403e8	0.291589
$457$	−3.28039e9	−1.60775	−0.803876	−	0.594797i	$-0.797232\pi$
$457$	−3.28039e9	−1.60775	−0.803876	+	0.594797i	$0.797232\pi$
$458$	4.06029e9	1.97482
$459$	3.97075e9	1.91658
$460$	4.10300e8	0.196539
$461$	2.16381e8	0.102865	0.0514323	−	0.998676i	$-0.483621\pi$
$461$	2.16381e8	0.102865	0.0514323	+	0.998676i	$0.483621\pi$
$462$	−1.43189e9	−0.675557
$463$	−1.77434e9	−0.830814	−0.415407	−	0.909636i	$-0.636361\pi$
$463$	−1.77434e9	−0.830814	−0.415407	+	0.909636i	$0.636361\pi$
$464$	1.61474e9	0.750393
$465$	2.26433e9	1.04437
$466$	−5.23415e9	−2.39605
$467$	−1.26204e9	−0.573409	−0.286705	−	0.958019i	$-0.592560\pi$
$467$	−1.26204e9	−0.573409	−0.286705	+	0.958019i	$0.592560\pi$
$468$	−1.47401e8	−0.0664722
$469$	1.30229e9	0.582910
$470$	−2.42012e9	−1.07521
$471$	−1.28929e9	−0.568561
$472$	4.01880e8	0.175914
$473$	1.34004e9	0.582244
$474$	−7.33683e8	−0.316435
$475$	−1.23941e8	−0.0530626
$476$	8.96696e8	0.381084
$477$	1.17932e9	0.497529
$478$	5.96849e8	0.249958
$479$	−1.64302e9	−0.683075	−0.341537	−	0.939868i	$-0.610948\pi$
$479$	−1.64302e9	−0.683075	−0.341537	+	0.939868i	$0.610948\pi$
$480$	−1.80762e9	−0.746043
$481$	4.08341e8	0.167308
$482$	4.26368e9	1.73428
$483$	2.55764e8	0.103282
$484$	3.57428e9	1.43294
$485$	1.83718e9	0.731233
$486$	−2.45999e9	−0.972088
$487$	2.24768e9	0.881827	0.440913	−	0.897550i	$-0.354655\pi$
$487$	2.24768e9	0.881827	0.440913	+	0.897550i	$0.354655\pi$
$488$	1.28304e9	0.499772
$489$	−4.68845e8	−0.181321
$490$	−4.48226e8	−0.172112
$491$	1.09323e9	0.416800	0.208400	−	0.978044i	$-0.433174\pi$
$491$	1.09323e9	0.416800	0.208400	+	0.978044i	$0.433174\pi$
$492$	−2.35172e8	−0.0890243
$493$	−2.84191e9	−1.06818
$494$	6.60620e8	0.246551
$495$	2.05179e9	0.760354
$496$	−4.83031e9	−1.77742
$497$	1.15666e9	0.422626
$498$	−3.26011e9	−1.18285
$499$	1.15533e9	0.416249	0.208124	−	0.978102i	$-0.433264\pi$
$499$	1.15533e9	0.416249	0.208124	+	0.978102i	$0.433264\pi$
$500$	1.64356e9	0.588016
$501$	−1.24784e9	−0.443328
$502$	1.09810e9	0.387419
$503$	3.27151e9	1.14620	0.573100	−	0.819485i	$-0.305741\pi$
$503$	3.27151e9	1.14620	0.573100	+	0.819485i	$0.305741\pi$
$504$	2.47225e8	0.0860173
$505$	−1.96899e9	−0.680337
$506$	−2.45985e9	−0.844078
$507$	−1.71706e8	−0.0585137
$508$	−1.13181e9	−0.383046
$509$	1.97392e9	0.663463	0.331732	−	0.943374i	$-0.392367\pi$
$509$	1.97392e9	0.663463	0.331732	+	0.943374i	$0.392367\pi$
$510$	4.86660e9	1.62454
$511$	8.52156e7	0.0282518
$512$	1.81347e9	0.597127
$513$	2.34647e9	0.767370
$514$	−1.56991e9	−0.509922
$515$	−3.03473e9	−0.979027
$516$	−4.19085e8	−0.134285
$517$	5.26055e9	1.67423
$518$	9.03388e8	0.285575
$519$	−3.31661e9	−1.04138
$520$	4.61997e8	0.144088
$521$	−3.14520e8	−0.0974354	−0.0487177	−	0.998813i	$-0.515513\pi$
$521$	−3.14520e8	−0.0974354	−0.0487177	+	0.998813i	$0.515513\pi$
$522$	1.03351e9	0.318031
$523$	2.14743e9	0.656391	0.328196	−	0.944610i	$-0.393559\pi$
$523$	2.14743e9	0.656391	0.328196	+	0.944610i	$0.393559\pi$
$524$	1.58367e9	0.480846
$525$	7.12690e7	0.0214953
$526$	2.90449e9	0.870201
$527$	8.50127e9	2.53015
$528$	6.01050e9	1.77702
$529$	−2.96545e9	−0.870954
$530$	4.87563e9	1.42254
$531$	4.73498e8	0.137242
$532$	5.29894e8	0.152580
$533$	1.99494e8	0.0570671
$534$	3.51042e9	0.997618
$535$	1.41535e9	0.399601
$536$	−2.96962e9	−0.832959
$537$	4.17952e9	1.16471
$538$	−4.62917e9	−1.28164
$539$	9.74295e8	0.267997
$540$	−2.16452e9	−0.591540
$541$	2.27447e9	0.617576	0.308788	−	0.951131i	$-0.400077\pi$
$541$	2.27447e9	0.617576	0.308788	+	0.951131i	$0.400077\pi$
$542$	−3.37802e8	−0.0911308
$543$	1.28593e9	0.344681
$544$	−6.78660e9	−1.80741
$545$	3.03887e9	0.804127
$546$	−3.79872e8	−0.0998763
$547$	6.55877e9	1.71343	0.856716	−	0.515789i	$-0.172501\pi$
$547$	6.55877e9	1.71343	0.856716	+	0.515789i	$0.172501\pi$
$548$	−5.89267e8	−0.152961
$549$	1.51169e9	0.389906
$550$	−6.85441e8	−0.175671
$551$	−1.67940e9	−0.427684
$552$	−5.83222e8	−0.147587
$553$	4.99218e8	0.125531
$554$	−2.42478e9	−0.605883
$555$	1.77763e9	0.441382
$556$	−2.47826e9	−0.611484
$557$	4.69479e9	1.15113	0.575563	−	0.817757i	$-0.304783\pi$
$557$	4.69479e9	1.15113	0.575563	+	0.817757i	$0.304783\pi$
$558$	−3.09165e9	−0.753304
$559$	3.55506e8	0.0860806
$560$	1.88147e9	0.452731
$561$	−1.05784e10	−2.52958
$562$	−5.95423e9	−1.41497
$563$	−4.45968e9	−1.05323	−0.526616	−	0.850103i	$-0.676539\pi$
$563$	−4.45968e9	−1.05323	−0.526616	+	0.850103i	$0.676539\pi$
$564$	−1.64519e9	−0.386134
$565$	7.43333e9	1.73386
$566$	−6.46101e9	−1.49776
$567$	−6.57997e8	−0.151594
$568$	−2.63753e9	−0.603919
$569$	6.72103e9	1.52948	0.764738	−	0.644341i	$-0.222868\pi$
$569$	6.72103e9	1.52948	0.764738	+	0.644341i	$0.222868\pi$
$570$	2.87587e9	0.650439
$571$	5.11494e9	1.14978	0.574889	−	0.818231i	$-0.305045\pi$
$571$	5.11494e9	1.14978	0.574889	+	0.818231i	$0.305045\pi$
$572$	1.32462e9	0.295942
$573$	−4.90603e9	−1.08940
$574$	4.41349e8	0.0974070
$575$	1.22434e8	0.0268574
$576$	6.14809e7	0.0134048
$577$	−8.53489e9	−1.84962	−0.924811	−	0.380428i	$-0.875777\pi$
$577$	−8.53489e9	−1.84962	−0.924811	+	0.380428i	$0.875777\pi$
$578$	1.24566e10	2.68319
$579$	−1.95890e9	−0.419408
$580$	1.54917e9	0.329687
$581$	2.21827e9	0.469242
$582$	3.44464e9	0.724291
$583$	−1.05980e10	−2.21506
$584$	−1.94318e8	−0.0403709
$585$	5.44329e8	0.112413
$586$	5.17048e9	1.06143
$587$	6.46689e9	1.31966	0.659830	−	0.751415i	$-0.270628\pi$
$587$	6.46689e9	1.31966	0.659830	+	0.751415i	$0.270628\pi$
$588$	−3.04701e8	−0.0618092
$589$	5.02374e9	1.01303
$590$	1.95757e9	0.392405
$591$	−5.31284e9	−1.05869
$592$	−3.79207e9	−0.751190
$593$	2.56974e9	0.506055	0.253027	−	0.967459i	$-0.418574\pi$
$593$	2.56974e9	0.506055	0.253027	+	0.967459i	$0.418574\pi$
$594$	1.29769e10	2.54049
$595$	−3.31136e9	−0.644462
$596$	3.26131e9	0.631001
$597$	1.56537e9	0.301097
$598$	−6.52585e8	−0.124791
$599$	−7.86893e9	−1.49597	−0.747983	−	0.663718i	$-0.768977\pi$
$599$	−7.86893e9	−1.49597	−0.747983	+	0.663718i	$0.768977\pi$
$600$	−1.62515e8	−0.0307161
$601$	−5.50910e9	−1.03519	−0.517595	−	0.855626i	$-0.673172\pi$
$601$	−5.50910e9	−1.03519	−0.517595	+	0.855626i	$0.673172\pi$
$602$	7.86498e8	0.146930
$603$	−3.49883e9	−0.649848
$604$	5.09749e9	0.941298
$605$	−1.31993e10	−2.42329
$606$	−3.69177e9	−0.673877
$607$	8.05733e8	0.146228	0.0731141	−	0.997324i	$-0.476706\pi$
$607$	8.05733e8	0.146228	0.0731141	+	0.997324i	$0.476706\pi$
$608$	−4.01048e9	−0.723658
$609$	9.65692e8	0.173252
$610$	6.24974e9	1.11483
$611$	1.39559e9	0.247523
$612$	−2.40914e9	−0.424846
$613$	−6.04548e9	−1.06003	−0.530016	−	0.847987i	$-0.677814\pi$
$613$	−6.04548e9	−1.06003	−0.530016	+	0.847987i	$0.677814\pi$
$614$	−1.31815e10	−2.29813
$615$	8.68456e8	0.150551
$616$	−2.22170e9	−0.382959
$617$	−6.51610e9	−1.11684	−0.558419	−	0.829559i	$-0.688592\pi$
$617$	−6.51610e9	−1.11684	−0.558419	+	0.829559i	$0.688592\pi$
$618$	−5.68999e9	−0.969732
$619$	−6.79414e8	−0.115138	−0.0575688	−	0.998342i	$-0.518335\pi$
$619$	−6.79414e8	−0.115138	−0.0575688	+	0.998342i	$0.518335\pi$
$620$	−4.63419e9	−0.780914
$621$	−2.31793e9	−0.388401
$622$	−1.10424e10	−1.83991
$623$	−2.38858e9	−0.395760
$624$	1.59455e9	0.262720
$625$	−5.61308e9	−0.919647
$626$	−8.95819e9	−1.45952
$627$	−6.25119e9	−1.01281
$628$	2.63867e9	0.425134
$629$	6.67397e9	1.06932
$630$	1.20424e9	0.191876
$631$	3.12547e9	0.495236	0.247618	−	0.968858i	$-0.420352\pi$
$631$	3.12547e9	0.495236	0.247618	+	0.968858i	$0.420352\pi$
$632$	−1.13837e9	−0.179380
$633$	5.15570e9	0.807931
$634$	−7.11331e9	−1.10856
$635$	4.17961e9	0.647780
$636$	3.31442e9	0.510867
$637$	2.58475e8	0.0396214
$638$	−9.28770e9	−1.41591
$639$	−3.10756e9	−0.471159
$640$	−6.25000e9	−0.942432
$641$	4.87353e8	0.0730871	0.0365436	−	0.999332i	$-0.488365\pi$
$641$	4.87353e8	0.0730871	0.0365436	+	0.999332i	$0.488365\pi$
$642$	2.65372e9	0.395807
$643$	1.17932e10	1.74942	0.874712	−	0.484643i	$-0.161051\pi$
$643$	1.17932e10	1.74942	0.874712	+	0.484643i	$0.161051\pi$
$644$	−5.23449e8	−0.0772278
$645$	1.54762e9	0.227093
$646$	1.07972e10	1.57579
$647$	−1.33088e10	−1.93185	−0.965926	−	0.258820i	$-0.916667\pi$
$647$	−1.33088e10	−1.93185	−0.965926	+	0.258820i	$0.916667\pi$
$648$	1.50044e9	0.216623
$649$	−4.25511e9	−0.611018
$650$	−1.81844e8	−0.0259718
$651$	−2.88877e9	−0.410373
$652$	9.59542e8	0.135581
$653$	1.37102e10	1.92685	0.963424	−	0.267981i	$-0.0863565\pi$
$653$	1.37102e10	1.92685	0.963424	+	0.267981i	$0.0863565\pi$
$654$	5.69776e9	0.796493
$655$	−5.84826e9	−0.813171
$656$	−1.85261e9	−0.256224
$657$	−2.28947e8	−0.0314961
$658$	3.08752e9	0.422493
$659$	−1.59299e9	−0.216827	−0.108414	−	0.994106i	$-0.534577\pi$
$659$	−1.59299e9	−0.216827	−0.108414	+	0.994106i	$0.534577\pi$
$660$	5.76646e9	0.780739
$661$	2.76568e9	0.372475	0.186238	−	0.982505i	$-0.440371\pi$
$661$	2.76568e9	0.372475	0.186238	+	0.982505i	$0.440371\pi$
$662$	−1.45371e10	−1.94749
$663$	−2.80638e9	−0.373981
$664$	−5.05834e9	−0.670532
$665$	−1.95682e9	−0.258033
$666$	−2.42712e9	−0.318369
$667$	1.65897e9	0.216470
$668$	2.55383e9	0.331493
$669$	7.85660e9	1.01448
$670$	−1.44651e10	−1.85806
$671$	−1.35849e10	−1.73591
$672$	2.30612e9	0.293149
$673$	9.77771e9	1.23647	0.618236	−	0.785992i	$-0.287847\pi$
$673$	9.77771e9	1.23647	0.618236	+	0.785992i	$0.287847\pi$
$674$	7.50470e9	0.944112
$675$	−6.45895e8	−0.0808349
$676$	3.51415e8	0.0437529
$677$	9.51919e9	1.17907	0.589535	−	0.807743i	$-0.299311\pi$
$677$	9.51919e9	1.17907	0.589535	+	0.807743i	$0.299311\pi$
$678$	1.39372e10	1.71740
$679$	−2.34382e9	−0.287330
$680$	7.55093e9	0.920915
$681$	−3.34915e9	−0.406369
$682$	2.77832e10	3.35380
$683$	1.31983e10	1.58506	0.792530	−	0.609833i	$-0.208763\pi$
$683$	1.31983e10	1.58506	0.792530	+	0.609833i	$0.208763\pi$
$684$	−1.42366e9	−0.170102
$685$	2.17607e9	0.258676
$686$	5.71833e8	0.0676293
$687$	−1.01929e10	−1.19935
$688$	−3.30141e9	−0.386491
$689$	−2.81159e9	−0.327480
$690$	−2.84089e9	−0.329217
$691$	−1.21113e9	−0.139643	−0.0698214	−	0.997560i	$-0.522243\pi$
$691$	−1.21113e9	−0.139643	−0.0698214	+	0.997560i	$0.522243\pi$
$692$	6.78780e9	0.778678
$693$	−2.61762e9	−0.298772
$694$	−9.62270e9	−1.09280
$695$	9.15183e9	1.03410
$696$	−2.20208e9	−0.247571
$697$	3.26056e9	0.364735
$698$	3.83451e8	0.0426792
$699$	1.31397e10	1.45517
$700$	−1.45860e8	−0.0160728
$701$	−2.60762e8	−0.0285912	−0.0142956	−	0.999898i	$-0.504551\pi$
$701$	−2.60762e8	−0.0285912	−0.0142956	+	0.999898i	$0.504551\pi$
$702$	3.44269e9	0.375594
$703$	3.94392e9	0.428139
$704$	−5.52500e8	−0.0596799
$705$	6.07542e9	0.653002
$706$	1.77268e10	1.89589
$707$	2.51198e9	0.267331
$708$	1.33074e9	0.140922
$709$	2.17497e9	0.229188	0.114594	−	0.993412i	$-0.463443\pi$
$709$	2.17497e9	0.229188	0.114594	+	0.993412i	$0.463443\pi$
$710$	−1.28475e10	−1.34714
$711$	−1.34124e9	−0.139947
$712$	5.44671e9	0.565528
$713$	−4.96264e9	−0.512742
$714$	−6.20866e9	−0.638343
$715$	−4.89163e9	−0.500475
$716$	−8.55384e9	−0.870895
$717$	−1.49831e9	−0.151805
$718$	6.93829e9	0.699547
$719$	1.68337e9	0.168899	0.0844495	−	0.996428i	$-0.473087\pi$
$719$	1.68337e9	0.168899	0.0844495	+	0.996428i	$0.473087\pi$
$720$	−5.05492e9	−0.504720
$721$	3.87162e9	0.384697
$722$	−6.28614e9	−0.621589
$723$	−1.07034e10	−1.05327
$724$	−2.63179e9	−0.257731
$725$	4.62274e8	0.0450523
$726$	−2.47480e10	−2.40028
$727$	−1.75058e10	−1.68970	−0.844852	−	0.535001i	$-0.820311\pi$
$727$	−1.75058e10	−1.68970	−0.844852	+	0.535001i	$0.820311\pi$
$728$	−5.89403e8	−0.0566177
$729$	1.03709e10	0.991452
$730$	−9.46527e8	−0.0900540
$731$	5.81042e9	0.550170
$732$	4.24853e9	0.400360
$733$	1.37262e10	1.28732	0.643660	−	0.765311i	$-0.277415\pi$
$733$	1.37262e10	1.28732	0.643660	+	0.765311i	$0.277415\pi$
$734$	−3.50978e9	−0.327600
$735$	1.12521e9	0.104527
$736$	3.96170e9	0.366276
$737$	3.14423e10	2.89320
$738$	−1.18576e9	−0.108593
$739$	1.13260e10	1.03234	0.516168	−	0.856487i	$-0.327358\pi$
$739$	1.13260e10	1.03234	0.516168	+	0.856487i	$0.327358\pi$
$740$	−3.63810e9	−0.330038
$741$	−1.65840e9	−0.149736
$742$	−6.22019e9	−0.558972
$743$	−5.70850e9	−0.510577	−0.255289	−	0.966865i	$-0.582170\pi$
$743$	−5.70850e9	−0.510577	−0.255289	+	0.966865i	$0.582170\pi$
$744$	6.58728e9	0.586410
$745$	−1.20435e10	−1.06710
$746$	−2.27248e10	−2.00408
$747$	−5.95978e9	−0.523128
$748$	2.16498e10	1.89146
$749$	−1.80567e9	−0.157019
$750$	−1.13799e10	−0.984969
$751$	1.07519e9	0.0926283	0.0463142	−	0.998927i	$-0.485252\pi$
$751$	1.07519e9	0.0926283	0.0463142	+	0.998927i	$0.485252\pi$
$752$	−1.29602e10	−1.11135
$753$	−2.75665e9	−0.235288
$754$	−2.46397e9	−0.209332
$755$	−1.88242e10	−1.59185
$756$	2.76144e9	0.232439
$757$	4.56624e9	0.382581	0.191290	−	0.981534i	$-0.438733\pi$
$757$	4.56624e9	0.382581	0.191290	+	0.981534i	$0.438733\pi$
$758$	1.45178e10	1.21076
$759$	6.17515e9	0.512627
$760$	4.46215e9	0.368720
$761$	−9.12007e9	−0.750157	−0.375078	−	0.926993i	$-0.622384\pi$
$761$	−9.12007e9	−0.750157	−0.375078	+	0.926993i	$0.622384\pi$
$762$	7.83658e9	0.641630
$763$	−3.87691e9	−0.315973
$764$	1.00407e10	0.814588
$765$	8.89657e9	0.718469
$766$	2.69991e10	2.17044
$767$	−1.12885e9	−0.0903346
$768$	−1.20223e10	−0.957684
$769$	−9.06393e9	−0.718744	−0.359372	−	0.933194i	$-0.617009\pi$
$769$	−9.06393e9	−0.718744	−0.359372	+	0.933194i	$0.617009\pi$
$770$	−1.08219e10	−0.854254
$771$	3.94106e9	0.309687
$772$	4.00909e9	0.313607
$773$	1.23553e10	0.962114	0.481057	−	0.876689i	$-0.340253\pi$
$773$	1.23553e10	0.962114	0.481057	+	0.876689i	$0.340253\pi$
$774$	−2.11307e9	−0.163802
$775$	−1.38284e9	−0.106713
$776$	5.34464e9	0.410585
$777$	−2.26784e9	−0.173436
$778$	6.10225e9	0.464581
$779$	1.92679e9	0.146034
$780$	1.52981e9	0.115427
$781$	2.79262e10	2.09765
$782$	−1.06659e10	−0.797580
$783$	−8.75185e9	−0.651529
$784$	−2.40033e9	−0.177895
$785$	−9.74420e9	−0.718956
$786$	−1.09652e10	−0.805451
$787$	−1.47967e10	−1.08206	−0.541032	−	0.841002i	$-0.681966\pi$
$787$	−1.47967e10	−1.08206	−0.541032	+	0.841002i	$0.681966\pi$
$788$	1.08733e10	0.791625
$789$	−7.29136e9	−0.528492
$790$	−5.54504e9	−0.400138
$791$	−9.48323e9	−0.681300
$792$	5.96899e9	0.426936
$793$	−3.60399e9	−0.256642
$794$	1.77943e10	1.26157
$795$	−1.22397e10	−0.863942
$796$	−3.20369e9	−0.225141
$797$	8.97144e9	0.627708	0.313854	−	0.949471i	$-0.398380\pi$
$797$	8.97144e9	0.627708	0.313854	+	0.949471i	$0.398380\pi$
$798$	−3.66895e9	−0.255583
$799$	2.28097e10	1.58200
$800$	1.10393e9	0.0762302
$801$	6.41736e9	0.441207
$802$	−2.58023e9	−0.176623
$803$	2.05744e9	0.140224
$804$	−9.83328e9	−0.667271
$805$	1.93302e9	0.130602
$806$	7.37072e9	0.495835
$807$	1.16209e10	0.778367
$808$	−5.72810e9	−0.382007
$809$	1.17374e10	0.779384	0.389692	−	0.920945i	$-0.372581\pi$
$809$	1.17374e10	0.779384	0.389692	+	0.920945i	$0.372581\pi$
$810$	7.30867e9	0.483215
$811$	1.34450e10	0.885091	0.442546	−	0.896746i	$-0.354076\pi$
$811$	1.34450e10	0.885091	0.442546	+	0.896746i	$0.354076\pi$
$812$	−1.97639e9	−0.129547
$813$	8.48010e8	0.0553457
$814$	2.18113e10	1.41742
$815$	−3.54344e9	−0.229284
$816$	2.60615e10	1.67913
$817$	3.43361e9	0.220279
$818$	−1.53817e10	−0.982580
$819$	−6.94440e8	−0.0441714
$820$	−1.77739e9	−0.112573
$821$	−2.64873e10	−1.67046	−0.835231	−	0.549900i	$-0.814666\pi$
$821$	−2.64873e10	−1.67046	−0.835231	+	0.549900i	$0.814666\pi$
$822$	4.08005e9	0.256220
$823$	−1.08450e10	−0.678156	−0.339078	−	0.940758i	$-0.610115\pi$
$823$	−1.08450e10	−0.678156	−0.339078	+	0.940758i	$0.610115\pi$
$824$	−8.82850e9	−0.549720
$825$	1.72071e9	0.106689
$826$	−2.49741e9	−0.154191
$827$	−1.64684e10	−1.01247	−0.506235	−	0.862395i	$-0.668963\pi$
$827$	−1.64684e10	−1.01247	−0.506235	+	0.862395i	$0.668963\pi$
$828$	1.40634e9	0.0860962
$829$	−3.51141e9	−0.214063	−0.107031	−	0.994256i	$-0.534134\pi$
$829$	−3.51141e9	−0.214063	−0.107031	+	0.994256i	$0.534134\pi$
$830$	−2.46393e10	−1.49574
$831$	6.08712e9	0.367966
$832$	−1.46575e8	−0.00882325
$833$	4.22454e9	0.253234
$834$	1.71593e10	1.02428
$835$	−9.43091e9	−0.560597
$836$	1.27937e10	0.757313
$837$	2.61802e10	1.54324
$838$	2.99709e9	0.175933
$839$	−1.02661e10	−0.600120	−0.300060	−	0.953920i	$-0.597007\pi$
$839$	−1.02661e10	−0.600120	−0.300060	+	0.953920i	$0.597007\pi$
$840$	−2.56584e9	−0.149366
$841$	−1.09861e10	−0.636879
$842$	−3.65401e10	−2.10949
$843$	1.49473e10	0.859345
$844$	−1.05517e10	−0.604120
$845$	−1.29772e9	−0.0739917
$846$	−8.29519e9	−0.471010
$847$	1.68392e10	0.952204
$848$	2.61099e10	1.47035
$849$	1.62196e10	0.909625
$850$	−2.97207e9	−0.165994
$851$	−3.89595e9	−0.216700
$852$	−8.73365e9	−0.483790
$853$	−4.23136e9	−0.233431	−0.116716	−	0.993165i	$-0.537237\pi$
$853$	−4.23136e9	−0.233431	−0.116716	+	0.993165i	$0.537237\pi$
$854$	−7.97323e9	−0.438058
$855$	5.25734e9	0.287664
$856$	4.11748e9	0.224374
$857$	1.57920e10	0.857046	0.428523	−	0.903531i	$-0.359034\pi$
$857$	1.57920e10	0.857046	0.428523	+	0.903531i	$0.359034\pi$
$858$	−9.17160e9	−0.495724
$859$	1.38033e10	0.743029	0.371514	−	0.928427i	$-0.378839\pi$
$859$	1.38033e10	0.743029	0.371514	+	0.928427i	$0.378839\pi$
$860$	−3.16736e9	−0.169806
$861$	−1.10795e9	−0.0591574
$862$	2.83386e10	1.50696
$863$	1.59707e10	0.845835	0.422917	−	0.906168i	$-0.361006\pi$
$863$	1.59707e10	0.845835	0.422917	+	0.906168i	$0.361006\pi$
$864$	−2.08998e10	−1.10241
$865$	−2.50663e10	−1.31684
$866$	−1.49924e10	−0.784438
$867$	−3.12707e10	−1.62956
$868$	5.91217e9	0.306851
$869$	1.20531e10	0.623059
$870$	−1.07264e10	−0.552250
$871$	8.34147e9	0.427739
$872$	8.84055e9	0.451514
$873$	6.29710e9	0.320325
$874$	−6.30292e9	−0.319339
$875$	7.74316e9	0.390742
$876$	−6.43444e8	−0.0323405
$877$	−3.01803e10	−1.51086	−0.755431	−	0.655228i	$-0.772572\pi$
$877$	−3.01803e10	−1.51086	−0.755431	+	0.655228i	$0.772572\pi$
$878$	−2.94606e10	−1.46896
$879$	−1.29799e10	−0.644627
$880$	4.54262e10	2.24707
$881$	1.14852e10	0.565876	0.282938	−	0.959138i	$-0.408691\pi$
$881$	1.14852e10	0.565876	0.282938	+	0.959138i	$0.408691\pi$
$882$	−1.53633e9	−0.0753955
$883$	−2.94392e10	−1.43901	−0.719503	−	0.694489i	$-0.755631\pi$
$883$	−2.94392e10	−1.43901	−0.719503	+	0.694489i	$0.755631\pi$
$884$	5.74356e9	0.279639
$885$	−4.91423e9	−0.238316
$886$	−3.12308e10	−1.50857
$887$	−1.71201e10	−0.823710	−0.411855	−	0.911249i	$-0.635119\pi$
$887$	−1.71201e10	−0.823710	−0.411855	+	0.911249i	$0.635119\pi$
$888$	5.17139e9	0.247834
$889$	−5.33222e9	−0.254538
$890$	2.65310e10	1.26151
$891$	−1.58866e10	−0.752420
$892$	−1.60794e10	−0.758564
$893$	1.34792e10	0.633409
$894$	−2.25811e10	−1.05697
$895$	3.15880e10	1.47279
$896$	7.97357e9	0.370318
$897$	1.63823e9	0.0757883
$898$	−2.03200e10	−0.936389
$899$	−1.87375e10	−0.860107
$900$	3.91878e8	0.0179185
$901$	−4.59530e10	−2.09304
$902$	1.06559e10	0.483467
$903$	−1.97440e9	−0.0892337
$904$	2.16247e10	0.973556
$905$	9.71879e9	0.435855
$906$	−3.52946e10	−1.57674
$907$	1.47140e10	0.654795	0.327397	−	0.944887i	$-0.393828\pi$
$907$	1.47140e10	0.654795	0.327397	+	0.944887i	$0.393828\pi$
$908$	6.85440e9	0.303857
$909$	−6.74889e9	−0.298029
$910$	−2.87100e9	−0.126295
$911$	−1.42171e10	−0.623014	−0.311507	−	0.950244i	$-0.600834\pi$
$911$	−1.42171e10	−0.623014	−0.311507	+	0.950244i	$0.600834\pi$
$912$	1.54008e10	0.672297
$913$	5.35577e10	2.32903
$914$	−4.64850e10	−2.01373
$915$	−1.56892e10	−0.677059
$916$	2.08608e10	0.896801
$917$	7.46104e9	0.319526
$918$	5.62677e10	2.40054
$919$	3.34757e10	1.42274	0.711369	−	0.702819i	$-0.248076\pi$
$919$	3.34757e10	1.42274	0.711369	+	0.702819i	$0.248076\pi$
$920$	−4.40788e9	−0.186626
$921$	3.30904e10	1.39571
$922$	3.06624e9	0.128839
$923$	7.40867e9	0.310123
$924$	−7.35669e9	−0.306782
$925$	−1.08561e9	−0.0451002
$926$	−2.51434e10	−1.04061
$927$	−1.04018e10	−0.428874
$928$	1.49582e10	0.614416
$929$	−8.97152e9	−0.367123	−0.183561	−	0.983008i	$-0.558763\pi$
$929$	−8.97152e9	−0.367123	−0.183561	+	0.983008i	$0.558763\pi$
$930$	3.20868e10	1.30809
$931$	2.49645e9	0.101391
$932$	−2.68918e10	−1.08809
$933$	2.77206e10	1.11742
$934$	−1.78838e10	−0.718202
$935$	−7.99493e10	−3.19870
$936$	1.58354e9	0.0631194
$937$	−1.98008e10	−0.786310	−0.393155	−	0.919472i	$-0.628616\pi$
$937$	−1.98008e10	−0.786310	−0.393155	+	0.919472i	$0.628616\pi$
$938$	1.84541e10	0.730102
$939$	2.24884e10	0.886399
$940$	−1.24340e10	−0.488274
$941$	2.21665e10	0.867230	0.433615	−	0.901098i	$-0.357238\pi$
$941$	2.21665e10	0.867230	0.433615	+	0.901098i	$0.357238\pi$
$942$	−1.82700e10	−0.712130
$943$	−1.90336e9	−0.0739145
$944$	1.04831e10	0.405592
$945$	−1.01976e10	−0.393084
$946$	1.89892e10	0.729267
$947$	−2.98304e10	−1.14139	−0.570695	−	0.821162i	$-0.693326\pi$
$947$	−2.98304e10	−1.14139	−0.570695	+	0.821162i	$0.693326\pi$
$948$	−3.76948e9	−0.143699
$949$	5.45827e8	0.0207311
$950$	−1.75632e9	−0.0664615
$951$	1.78571e10	0.673253
$952$	−9.63326e9	−0.361863
$953$	−2.16222e8	−0.00809236	−0.00404618	−	0.999992i	$-0.501288\pi$
$953$	−2.16222e8	−0.00809236	−0.00404618	+	0.999992i	$0.501288\pi$
$954$	1.67117e10	0.623161
$955$	−3.70788e10	−1.37757
$956$	3.06646e9	0.113510
$957$	2.33156e10	0.859914
$958$	−2.32825e10	−0.855559
$959$	−2.77617e9	−0.101644
$960$	−6.38083e8	−0.0232770
$961$	2.85386e10	1.03729
$962$	5.78642e9	0.209555
$963$	4.85125e9	0.175050
$964$	2.19057e10	0.787568
$965$	−1.48050e10	−0.530349
$966$	3.62432e9	0.129362
$967$	−5.01717e10	−1.78429	−0.892147	−	0.451745i	$-0.850802\pi$
$967$	−5.01717e10	−1.78429	−0.892147	+	0.451745i	$0.850802\pi$
$968$	−3.83987e10	−1.36067
$969$	−2.71051e10	−0.957014
$970$	2.60339e10	0.915879
$971$	3.75887e10	1.31762	0.658809	−	0.752310i	$-0.271060\pi$
$971$	3.75887e10	1.31762	0.658809	+	0.752310i	$0.271060\pi$
$972$	−1.26388e10	−0.441442
$973$	−1.16756e10	−0.406336
$974$	3.18509e10	1.10450
$975$	4.56496e8	0.0157732
$976$	3.34685e10	1.15229
$977$	4.34777e10	1.49154	0.745771	−	0.666202i	$-0.232081\pi$
$977$	4.34777e10	1.49154	0.745771	+	0.666202i	$0.232081\pi$
$978$	−6.64380e9	−0.227107
$979$	−5.76698e10	−1.96430
$980$	−2.30287e9	−0.0781589
$981$	1.04160e10	0.352257
$982$	1.54917e10	0.522047
$983$	−1.55800e10	−0.523156	−0.261578	−	0.965182i	$-0.584243\pi$
$983$	−1.55800e10	−0.523156	−0.261578	+	0.965182i	$0.584243\pi$
$984$	2.52647e9	0.0845340
$985$	−4.01534e10	−1.33874
$986$	−4.02714e10	−1.33791
$987$	−7.75084e9	−0.256590
$988$	3.39410e9	0.111963
$989$	−3.39185e9	−0.111493
$990$	2.90751e10	0.952353
$991$	−2.93115e10	−0.956709	−0.478354	−	0.878167i	$-0.658767\pi$
$991$	−2.93115e10	−0.956709	−0.478354	+	0.878167i	$0.658767\pi$
$992$	−4.47460e10	−1.45533
$993$	3.64936e10	1.18275
$994$	1.63905e10	0.529345
$995$	1.18307e10	0.380742
$996$	−1.67496e10	−0.537153
$997$	3.13985e10	1.00340	0.501701	−	0.865041i	$-0.332708\pi$
$997$	3.13985e10	1.00340	0.501701	+	0.865041i	$0.332708\pi$
$998$	1.63716e10	0.521357
$999$	2.05529e10	0.652221

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.e.1.10	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.e.1.10	✓	12	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)

\(f(q)\)	\(=\)	\(q+14.1706 q^{2} -35.5734 q^{3} +72.8048 q^{4} -268.857 q^{5} -504.095 q^{6} +343.000 q^{7} -782.147 q^{8} -921.532 q^{9} +O(q^{10})\)	\(q+14.1706 q^{2} -35.5734 q^{3} +72.8048 q^{4} -268.857 q^{5} -504.095 q^{6} +343.000 q^{7} -782.147 q^{8} -921.532 q^{9} -3809.85 q^{10} +8281.37 q^{11} -2589.92 q^{12} +2197.00 q^{13} +4860.50 q^{14} +9564.16 q^{15} -20402.5 q^{16} +35908.0 q^{17} -13058.6 q^{18} +21219.5 q^{19} -19574.1 q^{20} -12201.7 q^{21} +117352. q^{22} -20961.4 q^{23} +27823.6 q^{24} -5840.92 q^{25} +31132.7 q^{26} +110581. q^{27} +24972.1 q^{28} -79144.2 q^{29} +135530. q^{30} +236751. q^{31} -189000. q^{32} -294597. q^{33} +508837. q^{34} -92217.9 q^{35} -67091.9 q^{36} +185863. q^{37} +300692. q^{38} -78154.8 q^{39} +210286. q^{40} +90803.1 q^{41} -172905. q^{42} +161814. q^{43} +602924. q^{44} +247760. q^{45} -297035. q^{46} +635227. q^{47} +725786. q^{48} +117649. q^{49} -82769.1 q^{50} -1.27737e6 q^{51} +159952. q^{52} -1.27974e6 q^{53} +1.56700e6 q^{54} -2.22650e6 q^{55} -268276. q^{56} -754850. q^{57} -1.12152e6 q^{58} -513817. q^{59} +696317. q^{60} -1.64041e6 q^{61} +3.35490e6 q^{62} -316085. q^{63} -66716.0 q^{64} -590679. q^{65} -4.17460e6 q^{66} +3.79675e6 q^{67} +2.61428e6 q^{68} +745668. q^{69} -1.30678e6 q^{70} +3.37217e6 q^{71} +720773. q^{72} +248442. q^{73} +2.63378e6 q^{74} +207781. q^{75} +1.54488e6 q^{76} +2.84051e6 q^{77} -1.10750e6 q^{78} +1.45545e6 q^{79} +5.48535e6 q^{80} -1.91836e6 q^{81} +1.28673e6 q^{82} +6.46725e6 q^{83} -888341. q^{84} -9.65412e6 q^{85} +2.29300e6 q^{86} +2.81543e6 q^{87} -6.47725e6 q^{88} -6.96379e6 q^{89} +3.51090e6 q^{90} +753571. q^{91} -1.52609e6 q^{92} -8.42206e6 q^{93} +9.00153e6 q^{94} -5.70501e6 q^{95} +6.72337e6 q^{96} -6.83330e6 q^{97} +1.66715e6 q^{98} -7.63155e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9} + 6668 q^{10} + 12168 q^{11} - 183 q^{12} + 26364 q^{13} + 2058 q^{14} - 28790 q^{15} + 85914 q^{16} + 82710 q^{17} - 44965 q^{18} - 10302 q^{19} + 141318 q^{20} + 28126 q^{21} - 97457 q^{22} + 98376 q^{23} - 519981 q^{24} + 272736 q^{25} + 13182 q^{26} + 306652 q^{27} + 338198 q^{28} + 350592 q^{29} + 231528 q^{30} + 55092 q^{31} + 114420 q^{32} + 609912 q^{33} + 812002 q^{34} + 351918 q^{35} + 1472143 q^{36} + 376310 q^{37} + 2825424 q^{38} + 180154 q^{39} + 2169290 q^{40} + 1387272 q^{41} + 105987 q^{42} + 568708 q^{43} + 3392031 q^{44} + 3556226 q^{45} - 1736829 q^{46} + 1359444 q^{47} + 4151249 q^{48} + 1411788 q^{49} + 3983712 q^{50} + 2709260 q^{51} + 2166242 q^{52} + 2061780 q^{53} + 2196651 q^{54} - 2112846 q^{55} + 78204 q^{56} + 2359902 q^{57} + 670268 q^{58} + 395964 q^{59} - 1052376 q^{60} + 444006 q^{61} + 2854353 q^{62} + 3739386 q^{63} + 12026858 q^{64} + 2254122 q^{65} - 4605681 q^{66} - 3094010 q^{67} + 4668954 q^{68} + 3839892 q^{69} + 2287124 q^{70} + 5694366 q^{71} - 9780585 q^{72} + 7052346 q^{73} - 4436259 q^{74} - 16288696 q^{75} - 3051830 q^{76} + 4173624 q^{77} + 678873 q^{78} + 4304160 q^{79} + 3807018 q^{80} - 6689556 q^{81} - 4733665 q^{82} + 2704554 q^{83} - 62769 q^{84} + 9301878 q^{85} + 1510998 q^{86} + 16231802 q^{87} - 70453923 q^{88} - 10986042 q^{89} - 12851300 q^{90} + 9042852 q^{91} - 16505451 q^{92} - 47230934 q^{93} - 24306151 q^{94} - 21839424 q^{95} - 86512741 q^{96} - 24462382 q^{97} + 705894 q^{98} + 11555078 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9 + 6668 * q^10 + 12168 * q^11 - 183 * q^12 + 26364 * q^13 + 2058 * q^14 - 28790 * q^15 + 85914 * q^16 + 82710 * q^17 - 44965 * q^18 - 10302 * q^19 + 141318 * q^20 + 28126 * q^21 - 97457 * q^22 + 98376 * q^23 - 519981 * q^24 + 272736 * q^25 + 13182 * q^26 + 306652 * q^27 + 338198 * q^28 + 350592 * q^29 + 231528 * q^30 + 55092 * q^31 + 114420 * q^32 + 609912 * q^33 + 812002 * q^34 + 351918 * q^35 + 1472143 * q^36 + 376310 * q^37 + 2825424 * q^38 + 180154 * q^39 + 2169290 * q^40 + 1387272 * q^41 + 105987 * q^42 + 568708 * q^43 + 3392031 * q^44 + 3556226 * q^45 - 1736829 * q^46 + 1359444 * q^47 + 4151249 * q^48 + 1411788 * q^49 + 3983712 * q^50 + 2709260 * q^51 + 2166242 * q^52 + 2061780 * q^53 + 2196651 * q^54 - 2112846 * q^55 + 78204 * q^56 + 2359902 * q^57 + 670268 * q^58 + 395964 * q^59 - 1052376 * q^60 + 444006 * q^61 + 2854353 * q^62 + 3739386 * q^63 + 12026858 * q^64 + 2254122 * q^65 - 4605681 * q^66 - 3094010 * q^67 + 4668954 * q^68 + 3839892 * q^69 + 2287124 * q^70 + 5694366 * q^71 - 9780585 * q^72 + 7052346 * q^73 - 4436259 * q^74 - 16288696 * q^75 - 3051830 * q^76 + 4173624 * q^77 + 678873 * q^78 + 4304160 * q^79 + 3807018 * q^80 - 6689556 * q^81 - 4733665 * q^82 + 2704554 * q^83 - 62769 * q^84 + 9301878 * q^85 + 1510998 * q^86 + 16231802 * q^87 - 70453923 * q^88 - 10986042 * q^89 - 12851300 * q^90 + 9042852 * q^91 - 16505451 * q^92 - 47230934 * q^93 - 24306151 * q^94 - 21839424 * q^95 - 86512741 * q^96 - 24462382 * q^97 + 705894 * q^98 + 11555078 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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