LMFDB - Embedded newform 289.10.a.g.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.9493 q^{2} -87.8502 q^{3} -369.213 q^{4} -13.1947 q^{5} -1049.75 q^{6} +9375.81 q^{7} -10529.9 q^{8} -11965.3 q^{9} +O(q^{10})$	\(q+11.9493 q^{2} -87.8502 q^{3} -369.213 q^{4} -13.1947 q^{5} -1049.75 q^{6} +9375.81 q^{7} -10529.9 q^{8} -11965.3 q^{9} -157.668 q^{10} +23234.7 q^{11} +32435.5 q^{12} -19001.0 q^{13} +112035. q^{14} +1159.16 q^{15} +63211.4 q^{16} -142978. q^{18} -494664. q^{19} +4871.67 q^{20} -823668. q^{21} +277639. q^{22} -1.11440e6 q^{23} +925056. q^{24} -1.95295e6 q^{25} -227049. q^{26} +2.78031e6 q^{27} -3.46167e6 q^{28} +5.04385e6 q^{29} +13851.2 q^{30} +9.14986e6 q^{31} +6.14665e6 q^{32} -2.04117e6 q^{33} -123711. q^{35} +4.41776e6 q^{36} -7.97118e6 q^{37} -5.91092e6 q^{38} +1.66924e6 q^{39} +138939. q^{40} +1.11923e7 q^{41} -9.84229e6 q^{42} -4.06201e6 q^{43} -8.57855e6 q^{44} +157879. q^{45} -1.33163e7 q^{46} +1.71037e6 q^{47} -5.55314e6 q^{48} +4.75523e7 q^{49} -2.33365e7 q^{50} +7.01541e6 q^{52} +4.70576e6 q^{53} +3.32229e7 q^{54} -306575. q^{55} -9.87266e7 q^{56} +4.34564e7 q^{57} +6.02707e7 q^{58} +1.62484e8 q^{59} -427977. q^{60} -8.09997e7 q^{61} +1.09335e8 q^{62} -1.12185e8 q^{63} +4.10843e7 q^{64} +250713. q^{65} -2.43907e7 q^{66} -1.08385e8 q^{67} +9.79000e7 q^{69} -1.47827e6 q^{70} +2.89201e8 q^{71} +1.25994e8 q^{72} +8.83100e7 q^{73} -9.52505e7 q^{74} +1.71567e8 q^{75} +1.82637e8 q^{76} +2.17844e8 q^{77} +1.99463e7 q^{78} -5.77142e8 q^{79} -834057. q^{80} -8.73759e6 q^{81} +1.33741e8 q^{82} +4.14681e8 q^{83} +3.04109e8 q^{84} -4.85384e7 q^{86} -4.43103e8 q^{87} -2.44659e8 q^{88} -7.23081e8 q^{89} +1.88655e6 q^{90} -1.78150e8 q^{91} +4.11450e8 q^{92} -8.03817e8 q^{93} +2.04378e7 q^{94} +6.52696e6 q^{95} -5.39985e8 q^{96} -3.43128e8 q^{97} +5.68219e8 q^{98} -2.78011e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) $ 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9} - 60000 q^{10} - 76902 q^{11} - 373248 q^{12} + 54216 q^{13} - 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} - 6439479 q^{20} - 138102 q^{21} - 267324 q^{22} - 4041462 q^{23} - 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} - 13281612 q^{27} - 18614784 q^{28} - 4005936 q^{29} + 22471686 q^{30} - 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} - 22076682 q^{37} - 27401376 q^{38} - 62736162 q^{39} + 12231630 q^{40} - 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} + 49578936 q^{44} - 129308238 q^{45} - 140524827 q^{46} - 118557912 q^{47} - 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} - 209848575 q^{54} - 365439924 q^{55} - 203095059 q^{56} + 4614108 q^{57} + 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} - 175597116 q^{61} - 720602571 q^{62} - 587415936 q^{63} + 853082511 q^{64} - 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} - 1308709542 q^{71} - 275337849 q^{72} - 494841342 q^{73} - 1545361890 q^{74} - 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} - 2270624538 q^{78} - 1980107868 q^{79} - 2897000199 q^{80} + 1598298840 q^{81} - 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} + 2705904618 q^{88} + 148394658 q^{89} - 117916215 q^{90} - 636340896 q^{91} + 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} - 4878626298 q^{95} + 8390096634 q^{96} + 891786822 q^{97} + 4285627647 q^{98} + 1476187998 q^{99}+O(q^{100}) \) 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9 - 60000 * q^10 - 76902 * q^11 - 373248 * q^12 + 54216 * q^13 - 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 - 6439479 * q^20 - 138102 * q^21 - 267324 * q^22 - 4041462 * q^23 - 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 - 13281612 * q^27 - 18614784 * q^28 - 4005936 * q^29 + 22471686 * q^30 - 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 - 22076682 * q^37 - 27401376 * q^38 - 62736162 * q^39 + 12231630 * q^40 - 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 + 49578936 * q^44 - 129308238 * q^45 - 140524827 * q^46 - 118557912 * q^47 - 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 - 209848575 * q^54 - 365439924 * q^55 - 203095059 * q^56 + 4614108 * q^57 + 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 - 175597116 * q^61 - 720602571 * q^62 - 587415936 * q^63 + 853082511 * q^64 - 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 - 1308709542 * q^71 - 275337849 * q^72 - 494841342 * q^73 - 1545361890 * q^74 - 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 - 2270624538 * q^78 - 1980107868 * q^79 - 2897000199 * q^80 + 1598298840 * q^81 - 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 + 2705904618 * q^88 + 148394658 * q^89 - 117916215 * q^90 - 636340896 * q^91 + 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 - 4878626298 * q^95 + 8390096634 * q^96 + 891786822 * q^97 + 4285627647 * q^98 + 1476187998 * 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 $

$2$	11.9493	0.528092	0.264046	−	0.964510i	$-0.414943\pi$
$2$	11.9493	0.528092	0.264046	+	0.964510i	$0.414943\pi$
$3$	−87.8502	−0.626177	−0.313089	−	0.949724i	$-0.601364\pi$
$3$	−87.8502	−0.626177	−0.313089	+	0.949724i	$0.601364\pi$
$4$	−369.213	−0.721119
$5$	−13.1947	−0.00944138	−0.00472069	−	0.999989i	$-0.501503\pi$
$5$	−13.1947	−0.00944138	−0.00472069	+	0.999989i	$0.501503\pi$
$6$	−1049.75	−0.330679
$7$	9375.81	1.47594	0.737968	−	0.674835i	$-0.235785\pi$
$7$	9375.81	1.47594	0.737968	+	0.674835i	$0.235785\pi$
$8$	−10529.9	−0.908909
$9$	−11965.3	−0.607902
$10$	−157.668	−0.00498591
$11$	23234.7	0.478486	0.239243	−	0.970960i	$-0.423101\pi$
$11$	23234.7	0.478486	0.239243	+	0.970960i	$0.423101\pi$
$12$	32435.5	0.451549
$13$	−19001.0	−0.184515	−0.0922573	−	0.995735i	$-0.529408\pi$
$13$	−19001.0	−0.184515	−0.0922573	+	0.995735i	$0.529408\pi$
$14$	112035.	0.779430
$15$	1159.16	0.00591198
$16$	63211.4	0.241132
$17$	0	0
$17$	0	0
$18$	−142978.	−0.321028
$19$	−494664.	−0.870802	−0.435401	−	0.900237i	$-0.643393\pi$
$19$	−494664.	−0.870802	−0.435401	+	0.900237i	$0.643393\pi$
$20$	4871.67	0.00680836
$21$	−823668.	−0.924198
$22$	277639.	0.252685
$23$	−1.11440e6	−0.830356	−0.415178	−	0.909740i	$-0.636281\pi$
$23$	−1.11440e6	−0.830356	−0.415178	+	0.909740i	$0.636281\pi$
$24$	925056.	0.569138
$25$	−1.95295e6	−0.999911
$26$	−227049.	−0.0974406
$27$	2.78031e6	1.00683
$28$	−3.46167e6	−1.06433
$29$	5.04385e6	1.32425	0.662126	−	0.749392i	$-0.269654\pi$
$29$	5.04385e6	1.32425	0.662126	+	0.749392i	$0.269654\pi$
$30$	13851.2	0.00312207
$31$	9.14986e6	1.77945	0.889727	−	0.456493i	$-0.150895\pi$
$31$	9.14986e6	1.77945	0.889727	+	0.456493i	$0.150895\pi$
$32$	6.14665e6	1.03625
$33$	−2.04117e6	−0.299617
$34$	0	0
$35$	−123711.	−0.0139349
$36$	4.41776e6	0.438370
$37$	−7.97118e6	−0.699222	−0.349611	−	0.936895i	$-0.613686\pi$
$37$	−7.97118e6	−0.699222	−0.349611	+	0.936895i	$0.613686\pi$
$38$	−5.91092e6	−0.459863
$39$	1.66924e6	0.115539
$40$	138939.	0.00858135
$41$	1.11923e7	0.618576	0.309288	−	0.950968i	$-0.399909\pi$
$41$	1.11923e7	0.618576	0.309288	+	0.950968i	$0.399909\pi$
$42$	−9.84229e6	−0.488061
$43$	−4.06201e6	−0.181190	−0.0905948	−	0.995888i	$-0.528877\pi$
$43$	−4.06201e6	−0.181190	−0.0905948	+	0.995888i	$0.528877\pi$
$44$	−8.57855e6	−0.345046
$45$	157879.	0.00573943
$46$	−1.33163e7	−0.438504
$47$	1.71037e6	0.0511270	0.0255635	−	0.999673i	$-0.491862\pi$
$47$	1.71037e6	0.0511270	0.0255635	+	0.999673i	$0.491862\pi$
$48$	−5.55314e6	−0.150992
$49$	4.75523e7	1.17839
$50$	−2.33365e7	−0.528044
$51$	0	0
$52$	7.01541e6	0.133057
$53$	4.70576e6	0.0819197	0.0409599	−	0.999161i	$-0.486958\pi$
$53$	4.70576e6	0.0819197	0.0409599	+	0.999161i	$0.486958\pi$
$54$	3.32229e7	0.531699
$55$	−306575.	−0.00451757
$56$	−9.87266e7	−1.34149
$57$	4.34564e7	0.545277
$58$	6.02707e7	0.699327
$59$	1.62484e8	1.74573	0.872864	−	0.487964i	$-0.162260\pi$
$59$	1.62484e8	1.74573	0.872864	+	0.487964i	$0.162260\pi$
$60$	−427977.	−0.00426324
$61$	−8.09997e7	−0.749030	−0.374515	−	0.927221i	$-0.622191\pi$
$61$	−8.09997e7	−0.749030	−0.374515	+	0.927221i	$0.622191\pi$
$62$	1.09335e8	0.939715
$63$	−1.12185e8	−0.897225
$64$	4.10843e7	0.306102
$65$	250713.	0.00174207
$66$	−2.43907e7	−0.158225
$67$	−1.08385e8	−0.657100	−0.328550	−	0.944487i	$-0.606560\pi$
$67$	−1.08385e8	−0.657100	−0.328550	+	0.944487i	$0.606560\pi$
$68$	0	0
$69$	9.79000e7	0.519950
$70$	−1.47827e6	−0.00735889
$71$	2.89201e8	1.35063	0.675317	−	0.737527i	$-0.264007\pi$
$71$	2.89201e8	1.35063	0.675317	+	0.737527i	$0.264007\pi$
$72$	1.25994e8	0.552527
$73$	8.83100e7	0.363963	0.181981	−	0.983302i	$-0.441749\pi$
$73$	8.83100e7	0.363963	0.181981	+	0.983302i	$0.441749\pi$
$74$	−9.52505e7	−0.369253
$75$	1.71567e8	0.626122
$76$	1.82637e8	0.627952
$77$	2.17844e8	0.706216
$78$	1.99463e7	0.0610151
$79$	−5.77142e8	−1.66710	−0.833549	−	0.552446i	$-0.813695\pi$
$79$	−5.77142e8	−1.66710	−0.833549	+	0.552446i	$0.813695\pi$
$80$	−834057.	−0.00227662
$81$	−8.73759e6	−0.0225533
$82$	1.33741e8	0.326665
$83$	4.14681e8	0.959097	0.479549	−	0.877515i	$-0.340800\pi$
$83$	4.14681e8	0.959097	0.479549	+	0.877515i	$0.340800\pi$
$84$	3.04109e8	0.666457
$85$	0	0
$86$	−4.85384e7	−0.0956847
$87$	−4.43103e8	−0.829217
$88$	−2.44659e8	−0.434900
$89$	−7.23081e8	−1.22161	−0.610804	−	0.791782i	$-0.709154\pi$
$89$	−7.23081e8	−1.22161	−0.610804	+	0.791782i	$0.709154\pi$
$90$	1.88655e6	0.00303095
$91$	−1.78150e8	−0.272332
$92$	4.11450e8	0.598786
$93$	−8.03817e8	−1.11425
$94$	2.04378e7	0.0269997
$95$	6.52696e6	0.00822157
$96$	−5.39985e8	−0.648875
$97$	−3.43128e8	−0.393534	−0.196767	−	0.980450i	$-0.563044\pi$
$97$	−3.43128e8	−0.393534	−0.196767	+	0.980450i	$0.563044\pi$
$98$	5.68219e8	0.622298
$99$	−2.78011e8	−0.290873
$100$	7.21055e8	0.721055
$101$	−7.19762e8	−0.688244	−0.344122	−	0.938925i	$-0.611823\pi$
$101$	−7.19762e8	−0.688244	−0.344122	+	0.938925i	$0.611823\pi$
$102$	0	0
$103$	−1.08162e9	−0.946906	−0.473453	−	0.880819i	$-0.656993\pi$
$103$	−1.08162e9	−0.946906	−0.473453	+	0.880819i	$0.656993\pi$
$104$	2.00079e8	0.167707
$105$	1.08681e7	0.00872570
$106$	5.62308e7	0.0432611
$107$	−3.57334e7	−0.0263540	−0.0131770	−	0.999913i	$-0.504194\pi$
$107$	−3.57334e7	−0.0263540	−0.0131770	+	0.999913i	$0.504194\pi$
$108$	−1.02653e9	−0.726046
$109$	−2.26706e9	−1.53831	−0.769154	−	0.639064i	$-0.779322\pi$
$109$	−2.26706e9	−1.53831	−0.769154	+	0.639064i	$0.779322\pi$
$110$	−3.66337e6	−0.00238569
$111$	7.00271e8	0.437837
$112$	5.92658e8	0.355896
$113$	−1.60055e9	−0.923458	−0.461729	−	0.887021i	$-0.652771\pi$
$113$	−1.60055e9	−0.923458	−0.461729	+	0.887021i	$0.652771\pi$
$114$	5.19276e8	0.287956
$115$	1.47042e7	0.00783971
$116$	−1.86225e9	−0.954944
$117$	2.27353e8	0.112167
$118$	1.94158e9	0.921904
$119$	0	0
$120$	−1.22059e7	−0.00537345
$121$	−1.81810e9	−0.771051
$122$	−9.67894e8	−0.395557
$123$	−9.83248e8	−0.387338
$124$	−3.37825e9	−1.28320
$125$	5.15396e7	0.0188819
$126$	−1.34053e9	−0.473817
$127$	2.56067e9	0.873448	0.436724	−	0.899596i	$-0.356139\pi$
$127$	2.56067e9	0.873448	0.436724	+	0.899596i	$0.356139\pi$
$128$	−2.65616e9	−0.874599
$129$	3.56849e8	0.113457
$130$	2.99585e6	0.000919973 0
$131$	−4.64130e9	−1.37695	−0.688476	−	0.725259i	$-0.741720\pi$
$131$	−4.64130e9	−1.37695	−0.688476	+	0.725259i	$0.741720\pi$
$132$	7.53627e8	0.216060
$133$	−4.63788e9	−1.28525
$134$	−1.29513e9	−0.347009
$135$	−3.66855e7	−0.00950588
$136$	0	0
$137$	7.68686e9	1.86426	0.932130	−	0.362124i	$-0.117948\pi$
$137$	7.68686e9	1.86426	0.932130	+	0.362124i	$0.117948\pi$
$138$	1.16984e9	0.274581
$139$	6.96747e9	1.58310	0.791550	−	0.611105i	$-0.209274\pi$
$139$	6.96747e9	1.58310	0.791550	+	0.611105i	$0.209274\pi$
$140$	4.56758e7	0.0100487
$141$	−1.50257e8	−0.0320146
$142$	3.45577e9	0.713259
$143$	−4.41481e8	−0.0882877
$144$	−7.56345e8	−0.146585
$145$	−6.65522e7	−0.0125028
$146$	1.05525e9	0.192206
$147$	−4.17748e9	−0.737881
$148$	2.94307e9	0.504222
$149$	−2.32799e9	−0.386939	−0.193470	−	0.981106i	$-0.561974\pi$
$149$	−2.32799e9	−0.386939	−0.193470	+	0.981106i	$0.561974\pi$
$150$	2.05012e9	0.330649
$151$	−8.99613e9	−1.40818	−0.704092	−	0.710108i	$-0.748646\pi$
$151$	−8.99613e9	−1.40818	−0.704092	+	0.710108i	$0.748646\pi$
$152$	5.20878e9	0.791479
$153$	0	0
$154$	2.60309e9	0.372946
$155$	−1.20730e8	−0.0168005
$156$	−6.16305e8	−0.0833173
$157$	−1.03091e10	−1.35416	−0.677082	−	0.735907i	$-0.736756\pi$
$157$	−1.03091e10	−1.35416	−0.677082	+	0.735907i	$0.736756\pi$
$158$	−6.89648e9	−0.880380
$159$	−4.13402e8	−0.0512963
$160$	−8.11034e7	−0.00978361
$161$	−1.04484e10	−1.22555
$162$	−1.04409e8	−0.0119102
$163$	3.32689e8	0.0369143	0.0184571	−	0.999830i	$-0.494125\pi$
$163$	3.32689e8	0.0369143	0.0184571	+	0.999830i	$0.494125\pi$
$164$	−4.13235e9	−0.446067
$165$	2.69327e7	0.00282880
$166$	4.95517e9	0.506491
$167$	6.88418e9	0.684902	0.342451	−	0.939536i	$-0.388743\pi$
$167$	6.88418e9	0.684902	0.342451	+	0.939536i	$0.388743\pi$
$168$	8.67315e9	0.840012
$169$	−1.02435e10	−0.965954
$170$	0	0
$171$	5.91883e9	0.529362
$172$	1.49975e9	0.130659
$173$	6.01333e9	0.510396	0.255198	−	0.966889i	$-0.417859\pi$
$173$	6.01333e9	0.510396	0.255198	+	0.966889i	$0.417859\pi$
$174$	−5.29479e9	−0.437903
$175$	−1.83105e10	−1.47581
$176$	1.46870e9	0.115379
$177$	−1.42743e10	−1.09314
$178$	−8.64034e9	−0.645121
$179$	−1.19820e10	−0.872352	−0.436176	−	0.899861i	$-0.643668\pi$
$179$	−1.19820e10	−0.872352	−0.436176	+	0.899861i	$0.643668\pi$
$180$	−5.82911e7	−0.00413882
$181$	−1.48274e10	−1.02686	−0.513431	−	0.858131i	$-0.671626\pi$
$181$	−1.48274e10	−1.02686	−0.513431	+	0.858131i	$0.671626\pi$
$182$	−2.12877e9	−0.143816
$183$	7.11585e9	0.469026
$184$	1.17345e10	0.754718
$185$	1.05178e8	0.00660162
$186$	−9.60509e9	−0.588428
$187$	0	0
$188$	−6.31492e8	−0.0368687
$189$	2.60677e10	1.48602
$190$	7.79929e7	0.00434174
$191$	−3.31620e10	−1.80298	−0.901490	−	0.432799i	$-0.857526\pi$
$191$	−3.31620e10	−1.80298	−0.901490	+	0.432799i	$0.857526\pi$
$192$	−3.60926e9	−0.191674
$193$	4.14885e9	0.215238	0.107619	−	0.994192i	$-0.465677\pi$
$193$	4.14885e9	0.215238	0.107619	+	0.994192i	$0.465677\pi$
$194$	−4.10015e9	−0.207822
$195$	−2.20252e7	−0.00109085
$196$	−1.75569e10	−0.849760
$197$	−3.95264e10	−1.86978	−0.934888	−	0.354943i	$-0.884500\pi$
$197$	−3.95264e10	−1.86978	−0.934888	+	0.354943i	$0.884500\pi$
$198$	−3.32205e9	−0.153607
$199$	7.29277e9	0.329650	0.164825	−	0.986323i	$-0.447294\pi$
$199$	7.29277e9	0.329650	0.164825	+	0.986323i	$0.447294\pi$
$200$	2.05644e10	0.908828
$201$	9.52163e9	0.411461
$202$	−8.60068e9	−0.363456
$203$	4.72902e10	1.95451
$204$	0	0
$205$	−1.47680e8	−0.00584021
$206$	−1.29246e10	−0.500053
$207$	1.33341e10	0.504775
$208$	−1.20108e9	−0.0444924
$209$	−1.14934e10	−0.416667
$210$	1.29866e8	0.00460797
$211$	−1.01627e10	−0.352971	−0.176486	−	0.984303i	$-0.556473\pi$
$211$	−1.01627e10	−0.352971	−0.176486	+	0.984303i	$0.556473\pi$
$212$	−1.73743e9	−0.0590739
$213$	−2.54064e10	−0.845737
$214$	−4.26991e8	−0.0139173
$215$	5.35972e7	0.00171068
$216$	−2.92765e10	−0.915118
$217$	8.57874e10	2.62636
$218$	−2.70898e10	−0.812367
$219$	−7.75805e9	−0.227905
$220$	1.13192e8	0.00325771
$221$	0	0
$222$	8.36778e9	0.231218
$223$	4.85121e10	1.31364	0.656822	−	0.754045i	$-0.271900\pi$
$223$	4.85121e10	1.31364	0.656822	+	0.754045i	$0.271900\pi$
$224$	5.76299e10	1.52944
$225$	2.33677e10	0.607848
$226$	−1.91256e10	−0.487670
$227$	−3.09601e10	−0.773901	−0.386951	−	0.922100i	$-0.626472\pi$
$227$	−3.09601e10	−0.773901	−0.386951	+	0.922100i	$0.626472\pi$
$228$	−1.60447e10	−0.393209
$229$	1.33918e10	0.321795	0.160898	−	0.986971i	$-0.448561\pi$
$229$	1.33918e10	0.321795	0.160898	+	0.986971i	$0.448561\pi$
$230$	1.75705e8	0.00414008
$231$	−1.91376e10	−0.442216
$232$	−5.31113e10	−1.20362
$233$	4.68751e9	0.104193	0.0520967	−	0.998642i	$-0.483410\pi$
$233$	4.68751e9	0.104193	0.0520967	+	0.998642i	$0.483410\pi$
$234$	2.71672e9	0.0592343
$235$	−2.25679e7	−0.000482709 0
$236$	−5.99912e10	−1.25888
$237$	5.07021e10	1.04390
$238$	0	0
$239$	3.26030e10	0.646350	0.323175	−	0.946339i	$-0.395250\pi$
$239$	3.26030e10	0.646350	0.323175	+	0.946339i	$0.395250\pi$
$240$	7.32721e7	0.00142557
$241$	7.77778e10	1.48518	0.742590	−	0.669746i	$-0.233597\pi$
$241$	7.77778e10	1.48518	0.742590	+	0.669746i	$0.233597\pi$
$242$	−2.17251e10	−0.407185
$243$	−5.39573e10	−0.992709
$244$	2.99062e10	0.540140
$245$	−6.27439e8	−0.0111256
$246$	−1.17492e10	−0.204550
$247$	9.39910e9	0.160676
$248$	−9.63473e10	−1.61736
$249$	−3.64298e10	−0.600565
$250$	6.15865e8	0.00997138
$251$	8.26646e10	1.31458	0.657291	−	0.753637i	$-0.271702\pi$
$251$	8.26646e10	1.31458	0.657291	+	0.753637i	$0.271702\pi$
$252$	4.14201e10	0.647006
$253$	−2.58926e10	−0.397314
$254$	3.05983e10	0.461260
$255$	0	0
$256$	−5.27745e10	−0.767970
$257$	−3.45108e10	−0.493465	−0.246732	−	0.969084i	$-0.579357\pi$
$257$	−3.45108e10	−0.493465	−0.246732	+	0.969084i	$0.579357\pi$
$258$	4.26411e9	0.0599156
$259$	−7.47363e10	−1.03201
$260$	−9.25664e7	−0.00125624
$261$	−6.03513e10	−0.805016
$262$	−5.54605e10	−0.727157
$263$	−1.33213e11	−1.71690	−0.858452	−	0.512893i	$-0.828574\pi$
$263$	−1.33213e11	−1.71690	−0.858452	+	0.512893i	$0.828574\pi$
$264$	2.14934e10	0.272325
$265$	−6.20912e7	−0.000773435 0
$266$	−5.54197e10	−0.678729
$267$	6.35228e10	0.764943
$268$	4.00171e10	0.473848
$269$	5.04947e9	0.0587977	0.0293989	−	0.999568i	$-0.490641\pi$
$269$	5.04947e9	0.0587977	0.0293989	+	0.999568i	$0.490641\pi$
$270$	−4.38368e8	−0.00501997
$271$	2.17449e9	0.0244903	0.0122452	−	0.999925i	$-0.496102\pi$
$271$	2.17449e9	0.0244903	0.0122452	+	0.999925i	$0.496102\pi$
$272$	0	0
$273$	1.56505e10	0.170528
$274$	9.18530e10	0.984500
$275$	−4.53762e10	−0.478444
$276$	−3.61460e10	−0.374946
$277$	−2.79184e10	−0.284926	−0.142463	−	0.989800i	$-0.545502\pi$
$277$	−2.79184e10	−0.284926	−0.142463	+	0.989800i	$0.545502\pi$
$278$	8.32567e10	0.836022
$279$	−1.09481e11	−1.08173
$280$	1.30267e9	0.0126655
$281$	−1.56867e11	−1.50090	−0.750450	−	0.660927i	$-0.770163\pi$
$281$	−1.56867e11	−1.50090	−0.750450	+	0.660927i	$0.770163\pi$
$282$	−1.79547e9	−0.0169066
$283$	−5.01719e10	−0.464966	−0.232483	−	0.972600i	$-0.574685\pi$
$283$	−5.01719e10	−0.464966	−0.232483	+	0.972600i	$0.574685\pi$
$284$	−1.06777e11	−0.973968
$285$	−5.73395e8	−0.00514816
$286$	−5.27541e9	−0.0466240
$287$	1.04937e11	0.912979
$288$	−7.35468e10	−0.629938
$289$	0	0
$290$	−7.95255e8	−0.00660261
$291$	3.01438e10	0.246422
$292$	−3.26052e10	−0.262460
$293$	−2.31612e11	−1.83593	−0.917966	−	0.396658i	$-0.870170\pi$
$293$	−2.31612e11	−1.83593	−0.917966	+	0.396658i	$0.870170\pi$
$294$	−4.99181e10	−0.389669
$295$	−2.14393e9	−0.0164821
$296$	8.39359e10	0.635529
$297$	6.45997e10	0.481755
$298$	−2.78179e10	−0.204339
$299$	2.11746e10	0.153213
$300$	−6.33449e10	−0.451508
$301$	−3.80847e10	−0.267425
$302$	−1.07498e11	−0.743651
$303$	6.32312e10	0.430963
$304$	−3.12684e10	−0.209979
$305$	1.06877e9	0.00707188
$306$	0	0
$307$	2.57747e11	1.65604	0.828019	−	0.560699i	$-0.189468\pi$
$307$	2.57747e11	1.65604	0.828019	+	0.560699i	$0.189468\pi$
$308$	−8.04308e10	−0.509266
$309$	9.50205e10	0.592931
$310$	−1.44264e9	−0.00887220
$311$	−1.32742e11	−0.804611	−0.402305	−	0.915506i	$-0.631791\pi$
$311$	−1.32742e11	−0.804611	−0.402305	+	0.915506i	$0.631791\pi$
$312$	−1.75770e10	−0.105014
$313$	−1.55181e11	−0.913879	−0.456939	−	0.889498i	$-0.651054\pi$
$313$	−1.55181e11	−0.913879	−0.456939	+	0.889498i	$0.651054\pi$
$314$	−1.23187e11	−0.715123
$315$	1.48025e9	0.00847104
$316$	2.13089e11	1.20218
$317$	7.27830e10	0.404821	0.202411	−	0.979301i	$-0.435122\pi$
$317$	7.27830e10	0.404821	0.202411	+	0.979301i	$0.435122\pi$
$318$	−4.93989e9	−0.0270891
$319$	1.17192e11	0.633637
$320$	−5.42096e8	−0.00289002
$321$	3.13919e9	0.0165023
$322$	−1.24851e11	−0.647204
$323$	0	0
$324$	3.22603e9	0.0162636
$325$	3.71080e10	0.184498
$326$	3.97542e9	0.0194941
$327$	1.99161e11	0.963253
$328$	−1.17854e11	−0.562229
$329$	1.60361e10	0.0754602
$330$	3.21828e8	0.00149387
$331$	1.77845e11	0.814357	0.407179	−	0.913349i	$-0.366513\pi$
$331$	1.77845e11	0.814357	0.407179	+	0.913349i	$0.366513\pi$
$332$	−1.53106e11	−0.691623
$333$	9.53779e10	0.425058
$334$	8.22615e10	0.361691
$335$	1.43011e9	0.00620393
$336$	−5.20652e10	−0.222854
$337$	−2.89678e11	−1.22344	−0.611718	−	0.791076i	$-0.709521\pi$
$337$	−2.89678e11	−1.22344	−0.611718	+	0.791076i	$0.709521\pi$
$338$	−1.22403e11	−0.510112
$339$	1.40609e11	0.578248
$340$	0	0
$341$	2.12594e11	0.851444
$342$	7.07261e10	0.279552
$343$	6.74934e10	0.263292
$344$	4.27727e10	0.164685
$345$	−1.29176e9	−0.00490905
$346$	7.18554e10	0.269536
$347$	3.59514e11	1.33117	0.665585	−	0.746322i	$-0.268182\pi$
$347$	3.59514e11	1.33117	0.665585	+	0.746322i	$0.268182\pi$
$348$	1.63600e11	0.597965
$349$	3.06108e11	1.10448	0.552242	−	0.833684i	$-0.313772\pi$
$349$	3.06108e11	1.10448	0.552242	+	0.833684i	$0.313772\pi$
$350$	−2.18799e11	−0.779360
$351$	−5.28287e10	−0.185775
$352$	1.42816e11	0.495831
$353$	−5.40179e11	−1.85162	−0.925809	−	0.377992i	$-0.876615\pi$
$353$	−5.40179e11	−1.85162	−0.925809	+	0.377992i	$0.876615\pi$
$354$	−1.70568e11	−0.577276
$355$	−3.81593e9	−0.0127518
$356$	2.66971e11	0.880925
$357$	0	0
$358$	−1.43177e11	−0.460682
$359$	−5.90971e11	−1.87777	−0.938883	−	0.344237i	$-0.888138\pi$
$359$	−5.90971e11	−1.87777	−0.938883	+	0.344237i	$0.888138\pi$
$360$	−1.66246e9	−0.00521662
$361$	−7.79948e10	−0.241704
$362$	−1.77178e11	−0.542278
$363$	1.59720e11	0.482815
$364$	6.57751e10	0.196384
$365$	−1.16523e9	−0.00343631
$366$	8.50297e10	0.247689
$367$	1.30010e11	0.374092	0.187046	−	0.982351i	$-0.440109\pi$
$367$	1.30010e11	0.374092	0.187046	+	0.982351i	$0.440109\pi$
$368$	−7.04425e10	−0.200226
$369$	−1.33920e11	−0.376033
$370$	1.25680e9	0.00348626
$371$	4.41203e10	0.120908
$372$	2.96780e11	0.803510
$373$	−4.27210e11	−1.14275	−0.571375	−	0.820689i	$-0.693590\pi$
$373$	−4.27210e11	−1.14275	−0.571375	+	0.820689i	$0.693590\pi$
$374$	0	0
$375$	−4.52777e9	−0.0118234
$376$	−1.80101e10	−0.0464698
$377$	−9.58380e10	−0.244344
$378$	3.11492e11	0.784755
$379$	6.30202e11	1.56893	0.784465	−	0.620173i	$-0.212938\pi$
$379$	6.30202e11	1.56893	0.784465	+	0.620173i	$0.212938\pi$
$380$	−2.40984e9	−0.00592873
$381$	−2.24955e11	−0.546933
$382$	−3.96265e11	−0.952139
$383$	6.08533e11	1.44507	0.722537	−	0.691333i	$-0.242976\pi$
$383$	6.08533e11	1.44507	0.722537	+	0.691333i	$0.242976\pi$
$384$	2.33344e11	0.547654
$385$	−2.87439e9	−0.00666765
$386$	4.95760e10	0.113665
$387$	4.86034e10	0.110146
$388$	1.26687e11	0.283785
$389$	−2.18499e10	−0.0483811	−0.0241906	−	0.999707i	$-0.507701\pi$
$389$	−2.18499e10	−0.0483811	−0.0241906	+	0.999707i	$0.507701\pi$
$390$	−2.63186e8	−0.000576066 0
$391$	0	0
$392$	−5.00722e11	−1.07105
$393$	4.07739e11	0.862216
$394$	−4.72315e11	−0.987413
$395$	7.61524e9	0.0157397
$396$	1.02645e11	0.209754
$397$	−8.30935e11	−1.67884	−0.839421	−	0.543482i	$-0.817106\pi$
$397$	−8.30935e11	−1.67884	−0.839421	+	0.543482i	$0.817106\pi$
$398$	8.71438e10	0.174086
$399$	4.07439e11	0.804794
$400$	−1.23449e11	−0.241111
$401$	6.07641e10	0.117354	0.0586769	−	0.998277i	$-0.481312\pi$
$401$	6.07641e10	0.117354	0.0586769	+	0.998277i	$0.481312\pi$
$402$	1.13777e11	0.217289
$403$	−1.73856e11	−0.328335
$404$	2.65745e11	0.496306
$405$	1.15290e8	0.000212934 0
$406$	5.65087e11	1.03216
$407$	−1.85208e11	−0.334568
$408$	0	0
$409$	−8.81188e11	−1.55709	−0.778545	−	0.627588i	$-0.784042\pi$
$409$	−8.81188e11	−1.55709	−0.778545	+	0.627588i	$0.784042\pi$
$410$	−1.76468e9	−0.00308416
$411$	−6.75293e11	−1.16736
$412$	3.99348e11	0.682832
$413$	1.52342e12	2.57658
$414$	1.59334e11	0.266567
$415$	−5.47160e9	−0.00905520
$416$	−1.16792e11	−0.191203
$417$	−6.12094e11	−0.991301
$418$	−1.37338e11	−0.220038
$419$	3.41942e11	0.541988	0.270994	−	0.962581i	$-0.412648\pi$
$419$	3.41942e11	0.541988	0.270994	+	0.962581i	$0.412648\pi$
$420$	−4.01263e9	−0.00629227
$421$	−4.41263e11	−0.684585	−0.342293	−	0.939593i	$-0.611203\pi$
$421$	−4.41263e11	−0.684585	−0.342293	+	0.939593i	$0.611203\pi$
$422$	−1.21438e11	−0.186401
$423$	−2.04652e10	−0.0310802
$424$	−4.95513e10	−0.0744575
$425$	0	0
$426$	−3.03590e11	−0.446626
$427$	−7.59438e11	−1.10552
$428$	1.31932e10	0.0190044
$429$	3.87842e10	0.0552837
$430$	6.40451e8	0.000903396 0
$431$	−3.01082e11	−0.420278	−0.210139	−	0.977672i	$-0.567392\pi$
$431$	−3.01082e11	−0.420278	−0.210139	+	0.977672i	$0.567392\pi$
$432$	1.75748e11	0.242780
$433$	7.35571e11	1.00561	0.502805	−	0.864400i	$-0.332302\pi$
$433$	7.35571e11	1.00561	0.502805	+	0.864400i	$0.332302\pi$
$434$	1.02510e12	1.38696
$435$	5.84663e9	0.00782895
$436$	8.37027e11	1.10930
$437$	5.51252e11	0.723076
$438$	−9.27037e10	−0.120355
$439$	8.85875e11	1.13837	0.569183	−	0.822211i	$-0.307259\pi$
$439$	8.85875e11	1.13837	0.569183	+	0.822211i	$0.307259\pi$
$440$	3.22821e9	0.00410606
$441$	−5.68979e11	−0.716345
$442$	0	0
$443$	1.28950e11	0.159076	0.0795382	−	0.996832i	$-0.474655\pi$
$443$	1.28950e11	0.159076	0.0795382	+	0.996832i	$0.474655\pi$
$444$	−2.58549e11	−0.315733
$445$	9.54085e9	0.0115337
$446$	5.79688e11	0.693725
$447$	2.04514e11	0.242293
$448$	3.85199e11	0.451787
$449$	1.55749e12	1.80850	0.904249	−	0.427006i	$-0.140432\pi$
$449$	1.55749e12	1.80850	0.904249	+	0.427006i	$0.140432\pi$
$450$	2.79229e11	0.320999
$451$	2.60050e11	0.295980
$452$	5.90945e11	0.665923
$453$	7.90313e11	0.881773
$454$	−3.69953e11	−0.408691
$455$	2.35063e9	0.00257119
$456$	−4.57592e11	−0.495607
$457$	−2.73319e11	−0.293121	−0.146560	−	0.989202i	$-0.546820\pi$
$457$	−2.73319e11	−0.293121	−0.146560	+	0.989202i	$0.546820\pi$
$458$	1.60023e11	0.169937
$459$	0	0
$460$	−5.42897e9	−0.00565336
$461$	5.89272e11	0.607662	0.303831	−	0.952726i	$-0.401734\pi$
$461$	5.89272e11	0.607662	0.303831	+	0.952726i	$0.401734\pi$
$462$	−2.28682e11	−0.233531
$463$	1.34363e12	1.35883	0.679413	−	0.733756i	$-0.262235\pi$
$463$	1.34363e12	1.35883	0.679413	+	0.733756i	$0.262235\pi$
$464$	3.18829e11	0.319320
$465$	1.06062e10	0.0105201
$466$	5.60127e10	0.0550237
$467$	6.38082e10	0.0620798	0.0310399	−	0.999518i	$-0.490118\pi$
$467$	6.38082e10	0.0620798	0.0310399	+	0.999518i	$0.490118\pi$
$468$	−8.39417e10	−0.0808856
$469$	−1.01620e12	−0.969839
$470$	−2.69672e8	−0.000254915 0
$471$	9.05655e11	0.847947
$472$	−1.71094e12	−1.58671
$473$	−9.43796e10	−0.0866968
$474$	6.05857e11	0.551274
$475$	9.66055e11	0.870724
$476$	0	0
$477$	−5.63060e10	−0.0497992
$478$	3.89585e11	0.341332
$479$	−1.15346e11	−0.100114	−0.0500568	−	0.998746i	$-0.515940\pi$
$479$	−1.15346e11	−0.100114	−0.0500568	+	0.998746i	$0.515940\pi$
$480$	7.12496e9	0.00612628
$481$	1.51460e11	0.129017
$482$	9.29394e11	0.784311
$483$	9.17892e11	0.767414
$484$	6.71265e11	0.556020
$485$	4.52747e9	0.00371551
$486$	−6.44755e11	−0.524241
$487$	1.92135e12	1.54784	0.773921	−	0.633283i	$-0.218293\pi$
$487$	1.92135e12	1.54784	0.773921	+	0.633283i	$0.218293\pi$
$488$	8.52921e11	0.680800
$489$	−2.92268e10	−0.0231149
$490$	−7.49749e9	−0.00587535
$491$	−1.25106e12	−0.971430	−0.485715	−	0.874117i	$-0.661441\pi$
$491$	−1.25106e12	−0.971430	−0.485715	+	0.874117i	$0.661441\pi$
$492$	3.63028e11	0.279317
$493$	0	0
$494$	1.12313e11	0.0848515
$495$	3.66827e9	0.00274624
$496$	5.78375e11	0.429084
$497$	2.71150e12	1.99345
$498$	−4.35313e11	−0.317153
$499$	6.12106e11	0.441951	0.220975	−	0.975279i	$-0.429076\pi$
$499$	6.12106e11	0.441951	0.220975	+	0.975279i	$0.429076\pi$
$500$	−1.90291e10	−0.0136161
$501$	−6.04777e11	−0.428870
$502$	9.87788e11	0.694220
$503$	2.15448e12	1.50067	0.750337	−	0.661056i	$-0.229891\pi$
$503$	2.15448e12	1.50067	0.750337	+	0.661056i	$0.229891\pi$
$504$	1.18130e12	0.815495
$505$	9.49706e9	0.00649797
$506$	−3.09400e11	−0.209818
$507$	8.99891e11	0.604859
$508$	−9.45433e11	−0.629860
$509$	−2.44832e12	−1.61673	−0.808367	−	0.588679i	$-0.799648\pi$
$509$	−2.44832e12	−1.61673	−0.808367	+	0.588679i	$0.799648\pi$
$510$	0	0
$511$	8.27978e11	0.537186
$512$	7.29331e11	0.469040
$513$	−1.37532e12	−0.876751
$514$	−4.12382e11	−0.260594
$515$	1.42717e10	0.00894010
$516$	−1.31753e11	−0.0818159
$517$	3.97399e10	0.0244636
$518$	−8.93051e11	−0.544994
$519$	−5.28273e11	−0.319599
$520$	−2.63998e9	−0.00158338
$521$	−4.93030e11	−0.293159	−0.146580	−	0.989199i	$-0.546826\pi$
$521$	−4.93030e11	−0.293159	−0.146580	+	0.989199i	$0.546826\pi$
$522$	−7.21159e11	−0.425122
$523$	−7.48265e11	−0.437318	−0.218659	−	0.975801i	$-0.570168\pi$
$523$	−7.48265e11	−0.437318	−0.218659	+	0.975801i	$0.570168\pi$
$524$	1.71363e12	0.992947
$525$	1.60858e12	0.924116
$526$	−1.59181e12	−0.906683
$527$	0	0
$528$	−1.29025e11	−0.0722474
$529$	−5.59274e11	−0.310509
$530$	−7.41950e8	−0.000408445 0
$531$	−1.94418e12	−1.06123
$532$	1.71237e12	0.926818
$533$	−2.12665e11	−0.114136
$534$	7.59056e11	0.403960
$535$	4.71492e8	0.000248819 0
$536$	1.14128e12	0.597244
$537$	1.05262e12	0.546247
$538$	6.03379e10	0.0310506
$539$	1.10486e12	0.563843
$540$	1.35448e10	0.00685487
$541$	−1.55217e12	−0.779026	−0.389513	−	0.921021i	$-0.627357\pi$
$541$	−1.55217e12	−0.779026	−0.389513	+	0.921021i	$0.627357\pi$
$542$	2.59837e10	0.0129331
$543$	1.30259e12	0.642998
$544$	0	0
$545$	2.99132e10	0.0145237
$546$	1.87013e11	0.0900544
$547$	−3.78215e12	−1.80632	−0.903162	−	0.429300i	$-0.858760\pi$
$547$	−3.78215e12	−1.80632	−0.903162	+	0.429300i	$0.858760\pi$
$548$	−2.83809e12	−1.34435
$549$	9.69189e11	0.455337
$550$	−5.42216e11	−0.252662
$551$	−2.49501e12	−1.15316
$552$	−1.03088e12	−0.472587
$553$	−5.41118e12	−2.46053
$554$	−3.33607e11	−0.150467
$555$	−9.23988e9	−0.00413378
$556$	−2.57248e12	−1.14160
$557$	−1.59132e12	−0.700501	−0.350251	−	0.936656i	$-0.613904\pi$
$557$	−1.59132e12	−0.700501	−0.350251	+	0.936656i	$0.613904\pi$
$558$	−1.30823e12	−0.571254
$559$	7.71822e10	0.0334321
$560$	−7.81996e9	−0.00336015
$561$	0	0
$562$	−1.87445e12	−0.792613
$563$	−1.57665e12	−0.661374	−0.330687	−	0.943741i	$-0.607280\pi$
$563$	−1.57665e12	−0.661374	−0.330687	+	0.943741i	$0.607280\pi$
$564$	5.54767e10	0.0230863
$565$	2.11189e10	0.00871872
$566$	−5.99521e11	−0.245545
$567$	−8.19220e10	−0.0332872
$568$	−3.04527e12	−1.22760
$569$	2.23114e12	0.892321	0.446160	−	0.894953i	$-0.352791\pi$
$569$	2.23114e12	0.892321	0.446160	+	0.894953i	$0.352791\pi$
$570$	−6.85170e9	−0.00271870
$571$	−9.16846e11	−0.360939	−0.180470	−	0.983581i	$-0.557762\pi$
$571$	−9.16846e11	−0.360939	−0.180470	+	0.983581i	$0.557762\pi$
$572$	1.63001e11	0.0636659
$573$	2.91329e12	1.12899
$574$	1.25393e12	0.482136
$575$	2.17636e12	0.830282
$576$	−4.91587e11	−0.186080
$577$	1.39411e12	0.523609	0.261804	−	0.965121i	$-0.415682\pi$
$577$	1.39411e12	0.523609	0.261804	+	0.965121i	$0.415682\pi$
$578$	0	0
$579$	−3.64477e11	−0.134777
$580$	2.45719e10	0.00901599
$581$	3.88797e12	1.41557
$582$	3.60199e11	0.130134
$583$	1.09337e11	0.0391975
$584$	−9.29897e11	−0.330809
$585$	−2.99986e9	−0.00105901
$586$	−2.76761e12	−0.969541
$587$	3.69526e12	1.28462	0.642309	−	0.766446i	$-0.277977\pi$
$587$	3.69526e12	1.28462	0.642309	+	0.766446i	$0.277977\pi$
$588$	1.54238e12	0.532100
$589$	−4.52611e12	−1.54955
$590$	−2.56186e10	−0.00870405
$591$	3.47241e12	1.17081
$592$	−5.03870e11	−0.168605
$593$	−1.83960e12	−0.610911	−0.305456	−	0.952206i	$-0.598809\pi$
$593$	−1.83960e12	−0.610911	−0.305456	+	0.952206i	$0.598809\pi$
$594$	7.71924e11	0.254411
$595$	0	0
$596$	8.59524e11	0.279029
$597$	−6.40672e11	−0.206420
$598$	2.53023e11	0.0809104
$599$	1.96213e12	0.622741	0.311370	−	0.950289i	$-0.399212\pi$
$599$	1.96213e12	0.622741	0.311370	+	0.950289i	$0.399212\pi$
$600$	−1.80659e12	−0.569087
$601$	−4.32477e11	−0.135216	−0.0676080	−	0.997712i	$-0.521537\pi$
$601$	−4.32477e11	−0.135216	−0.0676080	+	0.997712i	$0.521537\pi$
$602$	−4.55087e11	−0.141225
$603$	1.29686e12	0.399453
$604$	3.32149e12	1.01547
$605$	2.39893e10	0.00727978
$606$	7.55572e11	0.227588
$607$	−4.28237e12	−1.28037	−0.640185	−	0.768221i	$-0.721142\pi$
$607$	−4.28237e12	−1.28037	−0.640185	+	0.768221i	$0.721142\pi$
$608$	−3.04053e12	−0.902367
$609$	−4.15445e12	−1.22387
$610$	1.27711e10	0.00373460
$611$	−3.24987e10	−0.00943367
$612$	0	0
$613$	2.51089e12	0.718217	0.359108	−	0.933296i	$-0.383081\pi$
$613$	2.51089e12	0.718217	0.359108	+	0.933296i	$0.383081\pi$
$614$	3.07991e12	0.874540
$615$	1.29737e10	0.00365701
$616$	−2.29388e12	−0.641885
$617$	−4.14534e12	−1.15153	−0.575767	−	0.817614i	$-0.695296\pi$
$617$	−4.14534e12	−1.15153	−0.575767	+	0.817614i	$0.695296\pi$
$618$	1.13543e12	0.313122
$619$	2.30355e12	0.630651	0.315325	−	0.948984i	$-0.397886\pi$
$619$	2.30355e12	0.630651	0.315325	+	0.948984i	$0.397886\pi$
$620$	4.45751e10	0.0121152
$621$	−3.09837e12	−0.836029
$622$	−1.58618e12	−0.424908
$623$	−6.77947e12	−1.80302
$624$	1.05515e11	0.0278601
$625$	3.81368e12	0.999733
$626$	−1.85431e12	−0.482612
$627$	1.00970e12	0.260907
$628$	3.80625e12	0.976514
$629$	0	0
$630$	1.76880e10	0.00447348
$631$	−3.70828e12	−0.931195	−0.465598	−	0.884997i	$-0.654161\pi$
$631$	−3.70828e12	−0.931195	−0.465598	+	0.884997i	$0.654161\pi$
$632$	6.07726e12	1.51524
$633$	8.92798e11	0.221023
$634$	8.69709e11	0.213783
$635$	−3.37873e10	−0.00824655
$636$	1.52634e11	0.0369907
$637$	−9.03539e11	−0.217430
$638$	1.40037e12	0.334618
$639$	−3.46039e12	−0.821053
$640$	3.50473e10	0.00825742
$641$	4.07381e11	0.0953102	0.0476551	−	0.998864i	$-0.484825\pi$
$641$	4.07381e11	0.0953102	0.0476551	+	0.998864i	$0.484825\pi$
$642$	3.75112e10	0.00871473
$643$	−4.35895e12	−1.00562	−0.502808	−	0.864398i	$-0.667700\pi$
$643$	−4.35895e12	−1.00562	−0.502808	+	0.864398i	$0.667700\pi$
$644$	3.85768e12	0.883770
$645$	−4.70853e9	−0.00107119
$646$	0	0
$647$	4.35019e12	0.975975	0.487987	−	0.872851i	$-0.337731\pi$
$647$	4.35019e12	0.975975	0.487987	+	0.872851i	$0.337731\pi$
$648$	9.20062e10	0.0204988
$649$	3.77526e12	0.835307
$650$	4.43416e11	0.0974319
$651$	−7.53644e12	−1.64457
$652$	−1.22833e11	−0.0266196
$653$	−9.70029e11	−0.208773	−0.104387	−	0.994537i	$-0.533288\pi$
$653$	−9.70029e11	−0.208773	−0.104387	+	0.994537i	$0.533288\pi$
$654$	2.37985e12	0.508686
$655$	6.12407e10	0.0130003
$656$	7.07482e11	0.149159
$657$	−1.05666e12	−0.221254
$658$	1.91621e11	0.0398499
$659$	8.95610e12	1.84984	0.924921	−	0.380160i	$-0.124131\pi$
$659$	8.95610e12	1.84984	0.924921	+	0.380160i	$0.124131\pi$
$660$	−9.94391e9	−0.00203990
$661$	−3.58110e12	−0.729643	−0.364822	−	0.931077i	$-0.618870\pi$
$661$	−3.58110e12	−0.729643	−0.364822	+	0.931077i	$0.618870\pi$
$662$	2.12513e12	0.430055
$663$	0	0
$664$	−4.36656e12	−0.871732
$665$	6.11956e10	0.0121345
$666$	1.13970e12	0.224470
$667$	−5.62084e12	−1.09960
$668$	−2.54173e12	−0.493896
$669$	−4.26180e12	−0.822575
$670$	1.70889e10	0.00327624
$671$	−1.88200e12	−0.358401
$672$	−5.06280e12	−0.957699
$673$	−2.42644e12	−0.455933	−0.227967	−	0.973669i	$-0.573208\pi$
$673$	−2.42644e12	−0.455933	−0.227967	+	0.973669i	$0.573208\pi$
$674$	−3.46147e12	−0.646087
$675$	−5.42982e12	−1.00674
$676$	3.78202e12	0.696568
$677$	5.57708e12	1.02037	0.510186	−	0.860064i	$-0.329577\pi$
$677$	5.57708e12	1.02037	0.510186	+	0.860064i	$0.329577\pi$
$678$	1.68019e12	0.305368
$679$	−3.21710e12	−0.580832
$680$	0	0
$681$	2.71985e12	0.484600
$682$	2.54036e12	0.449641
$683$	−3.41770e12	−0.600953	−0.300476	−	0.953789i	$-0.597146\pi$
$683$	−3.41770e12	−0.600953	−0.300476	+	0.953789i	$0.597146\pi$
$684$	−2.18531e12	−0.381733
$685$	−1.01426e11	−0.0176012
$686$	8.06502e11	0.139042
$687$	−1.17647e12	−0.201501
$688$	−2.56766e11	−0.0436907
$689$	−8.94140e10	−0.0151154
$690$	−1.54357e10	−0.00259243
$691$	−6.82270e12	−1.13843	−0.569213	−	0.822190i	$-0.692752\pi$
$691$	−6.82270e12	−1.13843	−0.569213	+	0.822190i	$0.692752\pi$
$692$	−2.22020e12	−0.368057
$693$	−2.60658e12	−0.429310
$694$	4.29596e12	0.702980
$695$	−9.19338e10	−0.0149466
$696$	4.66584e12	0.753683
$697$	0	0
$698$	3.65779e12	0.583269
$699$	−4.11799e11	−0.0652436
$700$	6.76048e12	1.06423
$701$	−1.09353e13	−1.71041	−0.855205	−	0.518291i	$-0.826569\pi$
$701$	−1.09353e13	−1.71041	−0.855205	+	0.518291i	$0.826569\pi$
$702$	−6.31268e11	−0.0981063
$703$	3.94306e12	0.608884
$704$	9.54580e11	0.146466
$705$	1.98259e9	0.000302262 0
$706$	−6.45478e12	−0.977824
$707$	−6.74835e12	−1.01580
$708$	5.27024e12	0.788281
$709$	2.51896e12	0.374380	0.187190	−	0.982324i	$-0.440062\pi$
$709$	2.51896e12	0.374380	0.187190	+	0.982324i	$0.440062\pi$
$710$	−4.55979e10	−0.00673414
$711$	6.90570e12	1.01343
$712$	7.61398e12	1.11033
$713$	−1.01966e13	−1.47758
$714$	0	0
$715$	5.82522e9	0.000833557 0
$716$	4.42392e12	0.629070
$717$	−2.86419e12	−0.404730
$718$	−7.06172e12	−0.991632
$719$	1.02273e12	0.142719	0.0713595	−	0.997451i	$-0.477266\pi$
$719$	1.02273e12	0.142719	0.0713595	+	0.997451i	$0.477266\pi$
$720$	9.97977e9	0.00138396
$721$	−1.01411e13	−1.39757
$722$	−9.31987e11	−0.127642
$723$	−6.83280e12	−0.929986
$724$	5.47448e12	0.740491
$725$	−9.85039e12	−1.32413
$726$	1.90855e12	0.254970
$727$	−2.78462e11	−0.0369710	−0.0184855	−	0.999829i	$-0.505884\pi$
$727$	−2.78462e11	−0.0369710	−0.0184855	+	0.999829i	$0.505884\pi$
$728$	1.87590e12	0.247525
$729$	4.91215e12	0.644165
$730$	−1.39237e10	−0.00181469
$731$	0	0
$732$	−2.62726e12	−0.338224
$733$	5.30668e12	0.678977	0.339488	−	0.940610i	$-0.389746\pi$
$733$	5.30668e12	0.678977	0.339488	+	0.940610i	$0.389746\pi$
$734$	1.55353e12	0.197555
$735$	5.51207e10	0.00696661
$736$	−6.84981e12	−0.860455
$737$	−2.51828e12	−0.314413
$738$	−1.60026e12	−0.198580
$739$	3.78591e12	0.466950	0.233475	−	0.972363i	$-0.424990\pi$
$739$	3.78591e12	0.466950	0.233475	+	0.972363i	$0.424990\pi$
$740$	−3.88329e10	−0.00476056
$741$	−8.25713e11	−0.100611
$742$	5.27209e11	0.0638507
$743$	−1.97364e12	−0.237584	−0.118792	−	0.992919i	$-0.537902\pi$
$743$	−1.97364e12	−0.237584	−0.118792	+	0.992919i	$0.537902\pi$
$744$	8.46413e12	1.01275
$745$	3.07172e10	0.00365324
$746$	−5.10488e12	−0.603477
$747$	−4.96179e12	−0.583037
$748$	0	0
$749$	−3.35030e11	−0.0388969
$750$	−5.41039e10	−0.00624385
$751$	3.16072e11	0.0362583	0.0181291	−	0.999836i	$-0.494229\pi$
$751$	3.16072e11	0.0362583	0.0181291	+	0.999836i	$0.494229\pi$
$752$	1.08115e11	0.0123284
$753$	−7.26210e12	−0.823161
$754$	−1.14520e12	−0.129036
$755$	1.18702e11	0.0132952
$756$	−9.62454e12	−1.07160
$757$	1.03321e13	1.14355	0.571775	−	0.820411i	$-0.306255\pi$
$757$	1.03321e13	1.14355	0.571775	+	0.820411i	$0.306255\pi$
$758$	7.53051e12	0.828539
$759$	2.27467e12	0.248789
$760$	−6.87284e10	−0.00747266
$761$	1.77902e12	0.192287	0.0961435	−	0.995367i	$-0.469349\pi$
$761$	1.77902e12	0.192287	0.0961435	+	0.995367i	$0.469349\pi$
$762$	−2.68807e12	−0.288831
$763$	−2.12555e13	−2.27044
$764$	1.22439e13	1.30016
$765$	0	0
$766$	7.27158e12	0.763131
$767$	−3.08735e12	−0.322112
$768$	4.63625e12	0.480885
$769$	4.28074e12	0.441418	0.220709	−	0.975340i	$-0.429163\pi$
$769$	4.28074e12	0.441418	0.220709	+	0.975340i	$0.429163\pi$
$770$	−3.43471e10	−0.00352113
$771$	3.03178e12	0.308996
$772$	−1.53181e12	−0.155212
$773$	−1.39043e13	−1.40069	−0.700343	−	0.713807i	$-0.746970\pi$
$773$	−1.39043e13	−1.40069	−0.700343	+	0.713807i	$0.746970\pi$
$774$	5.80779e11	0.0581669
$775$	−1.78692e13	−1.77930
$776$	3.61311e12	0.357687
$777$	6.56561e12	0.646220
$778$	−2.61092e11	−0.0255497
$779$	−5.53644e12	−0.538657
$780$	8.13198e9	0.000786630 0
$781$	6.71950e12	0.646260
$782$	0	0
$783$	1.40235e13	1.33330
$784$	3.00585e12	0.284148
$785$	1.36025e11	0.0127852
$786$	4.87222e12	0.455329
$787$	1.03400e13	0.960806	0.480403	−	0.877048i	$-0.340490\pi$
$787$	1.03400e13	0.960806	0.480403	+	0.877048i	$0.340490\pi$
$788$	1.45937e13	1.34833
$789$	1.17028e13	1.07509
$790$	9.09971e10	0.00831200
$791$	−1.50065e13	−1.36297
$792$	2.92743e12	0.264377
$793$	1.53907e12	0.138207
$794$	−9.92913e12	−0.886582
$795$	5.45473e9	0.000484307 0
$796$	−2.69259e12	−0.237717
$797$	−1.22177e13	−1.07257	−0.536286	−	0.844036i	$-0.680173\pi$
$797$	−1.22177e13	−1.07257	−0.536286	+	0.844036i	$0.680173\pi$
$798$	4.86863e12	0.425005
$799$	0	0
$800$	−1.20041e13	−1.03616
$801$	8.65190e12	0.742617
$802$	7.26091e11	0.0619736
$803$	2.05185e12	0.174151
$804$	−3.51551e12	−0.296713
$805$	1.37863e11	0.0115709
$806$	−2.07747e12	−0.173391
$807$	−4.43597e11	−0.0368178
$808$	7.57903e12	0.625551
$809$	−1.36574e13	−1.12098	−0.560490	−	0.828161i	$-0.689387\pi$
$809$	−1.36574e13	−1.12098	−0.560490	+	0.828161i	$0.689387\pi$
$810$	1.37764e9	0.000112449 0
$811$	2.08036e13	1.68867	0.844334	−	0.535817i	$-0.179996\pi$
$811$	2.08036e13	1.68867	0.844334	+	0.535817i	$0.179996\pi$
$812$	−1.74602e13	−1.40944
$813$	−1.91029e11	−0.0153353
$814$	−2.21311e12	−0.176683
$815$	−4.38974e9	−0.000348522 0
$816$	0	0
$817$	2.00933e12	0.157780
$818$	−1.05296e13	−0.822286
$819$	2.13162e12	0.165551
$820$	5.45253e10	0.00421149
$821$	−3.70041e12	−0.284254	−0.142127	−	0.989848i	$-0.545394\pi$
$821$	−3.70041e12	−0.284254	−0.142127	+	0.989848i	$0.545394\pi$
$822$	−8.06931e12	−0.616472
$823$	−1.80532e13	−1.37168	−0.685842	−	0.727751i	$-0.740566\pi$
$823$	−1.80532e13	−1.37168	−0.685842	+	0.727751i	$0.740566\pi$
$824$	1.13894e13	0.860651
$825$	3.98631e12	0.299591
$826$	1.82039e13	1.36067
$827$	1.73862e13	1.29250	0.646249	−	0.763127i	$-0.276337\pi$
$827$	1.73862e13	1.29250	0.646249	+	0.763127i	$0.276337\pi$
$828$	−4.92313e12	−0.364003
$829$	1.39706e13	1.02735	0.513676	−	0.857984i	$-0.328283\pi$
$829$	1.39706e13	1.02735	0.513676	+	0.857984i	$0.328283\pi$
$830$	−6.53821e10	−0.00478197
$831$	2.45264e12	0.178414
$832$	−7.80641e11	−0.0564802
$833$	0	0
$834$	−7.31412e12	−0.523498
$835$	−9.08349e10	−0.00646642
$836$	4.24350e12	0.300467
$837$	2.54395e13	1.79161
$838$	4.08599e12	0.286219
$839$	−9.86320e12	−0.687209	−0.343605	−	0.939114i	$-0.611648\pi$
$839$	−9.86320e12	−0.687209	−0.343605	+	0.939114i	$0.611648\pi$
$840$	−1.14440e11	−0.00793087
$841$	1.09333e13	0.753646
$842$	−5.27280e12	−0.361524
$843$	1.37808e13	0.939830
$844$	3.75221e12	0.254534
$845$	1.35160e11	0.00911994
$846$	−2.44545e11	−0.0164132
$847$	−1.70461e13	−1.13802
$848$	2.97458e11	0.0197535
$849$	4.40761e12	0.291151
$850$	0	0
$851$	8.88306e12	0.580603
$852$	9.38038e12	0.609877
$853$	−2.33943e13	−1.51300	−0.756500	−	0.653994i	$-0.773092\pi$
$853$	−2.33943e13	−1.51300	−0.756500	+	0.653994i	$0.773092\pi$
$854$	−9.07479e12	−0.583817
$855$	−7.80973e10	−0.00499791
$856$	3.76270e11	0.0239534
$857$	−2.44699e12	−0.154960	−0.0774799	−	0.996994i	$-0.524687\pi$
$857$	−2.44699e12	−0.154960	−0.0774799	+	0.996994i	$0.524687\pi$
$858$	4.63446e11	0.0291949
$859$	−1.61824e11	−0.0101409	−0.00507043	−	0.999987i	$-0.501614\pi$
$859$	−1.61824e11	−0.0101409	−0.00507043	+	0.999987i	$0.501614\pi$
$860$	−1.97888e10	−0.00123360
$861$	−9.21875e12	−0.571687
$862$	−3.59773e12	−0.221945
$863$	−9.09905e12	−0.558402	−0.279201	−	0.960233i	$-0.590070\pi$
$863$	−9.09905e12	−0.558402	−0.279201	+	0.960233i	$0.590070\pi$
$864$	1.70896e13	1.04333
$865$	−7.93443e10	−0.00481885
$866$	8.78960e12	0.531054
$867$	0	0
$868$	−3.16738e13	−1.89392
$869$	−1.34097e13	−0.797683
$870$	6.98634e10	0.00413440
$871$	2.05942e12	0.121245
$872$	2.38719e13	1.39818
$873$	4.10564e12	0.239230
$874$	6.58710e12	0.381850
$875$	4.83226e11	0.0278685
$876$	2.86437e12	0.164347
$877$	−2.44380e12	−0.139498	−0.0697489	−	0.997565i	$-0.522220\pi$
$877$	−2.44380e12	−0.139498	−0.0697489	+	0.997565i	$0.522220\pi$
$878$	1.05856e13	0.601162
$879$	2.03472e13	1.14962
$880$	−1.93790e10	−0.00108933
$881$	−5.73549e11	−0.0320759	−0.0160379	−	0.999871i	$-0.505105\pi$
$881$	−5.73549e11	−0.0320759	−0.0160379	+	0.999871i	$0.505105\pi$
$882$	−6.79893e12	−0.378296
$883$	−1.23459e13	−0.683441	−0.341721	−	0.939802i	$-0.611010\pi$
$883$	−1.23459e13	−0.683441	−0.341721	+	0.939802i	$0.611010\pi$
$884$	0	0
$885$	1.88345e11	0.0103207
$886$	1.54087e12	0.0840069
$887$	−2.65385e13	−1.43953	−0.719765	−	0.694218i	$-0.755750\pi$
$887$	−2.65385e13	−1.43953	−0.719765	+	0.694218i	$0.755750\pi$
$888$	−7.37379e12	−0.397954
$889$	2.40084e13	1.28915
$890$	1.14007e11	0.00609083
$891$	−2.03015e11	−0.0107914
$892$	−1.79113e13	−0.947295
$893$	−8.46060e11	−0.0445215
$894$	2.44381e12	0.127953
$895$	1.58100e11	0.00823621
$896$	−2.49036e13	−1.29085
$897$	−1.86019e12	−0.0959384
$898$	1.86110e13	0.955053
$899$	4.61505e13	2.35645
$900$	−8.62766e12	−0.438331
$901$	0	0
$902$	3.10743e12	0.156305
$903$	3.34575e12	0.167455
$904$	1.68537e13	0.839339
$905$	1.95644e11	0.00969500
$906$	9.44372e12	0.465657
$907$	−1.38313e13	−0.678626	−0.339313	−	0.940674i	$-0.610194\pi$
$907$	−1.38313e13	−0.678626	−0.339313	+	0.940674i	$0.610194\pi$
$908$	1.14309e13	0.558075
$909$	8.61219e12	0.418385
$910$	2.80885e10	0.00135782
$911$	−2.14644e13	−1.03249	−0.516244	−	0.856441i	$-0.672670\pi$
$911$	−2.14644e13	−1.03249	−0.516244	+	0.856441i	$0.672670\pi$
$912$	2.74694e12	0.131484
$913$	9.63497e12	0.458915
$914$	−3.26598e12	−0.154794
$915$	−9.38917e10	−0.00442825
$916$	−4.94443e12	−0.232053
$917$	−4.35160e13	−2.03229
$918$	0	0
$919$	−2.64775e13	−1.22450	−0.612248	−	0.790666i	$-0.709734\pi$
$919$	−2.64775e13	−1.22450	−0.612248	+	0.790666i	$0.709734\pi$
$920$	−1.54834e11	−0.00712558
$921$	−2.26431e13	−1.03697
$922$	7.04142e12	0.320901
$923$	−5.49510e12	−0.249212
$924$	7.06587e12	0.318891
$925$	1.55673e13	0.699160
$926$	1.60555e13	0.717585
$927$	1.29419e13	0.575626
$928$	3.10028e13	1.37226
$929$	2.21866e13	0.977281	0.488640	−	0.872485i	$-0.337493\pi$
$929$	2.21866e13	0.977281	0.488640	+	0.872485i	$0.337493\pi$
$930$	1.26737e11	0.00555557
$931$	−2.35224e13	−1.02614
$932$	−1.73069e12	−0.0751359
$933$	1.16614e13	0.503829
$934$	7.62466e11	0.0327838
$935$	0	0
$936$	−2.39401e12	−0.101949
$937$	−2.22025e13	−0.940966	−0.470483	−	0.882409i	$-0.655920\pi$
$937$	−2.22025e13	−0.940966	−0.470483	+	0.882409i	$0.655920\pi$
$938$	−1.21429e13	−0.512164
$939$	1.36327e13	0.572250
$940$	8.33236e9	0.000348091 0
$941$	−1.31832e12	−0.0548108	−0.0274054	−	0.999624i	$-0.508725\pi$
$941$	−1.31832e12	−0.0548108	−0.0274054	+	0.999624i	$0.508725\pi$
$942$	1.08220e13	0.447794
$943$	−1.24727e13	−0.513638
$944$	1.02708e13	0.420951
$945$	−3.43956e11	−0.0140301
$946$	−1.12777e12	−0.0457838
$947$	−6.19592e11	−0.0250341	−0.0125170	−	0.999922i	$-0.503984\pi$
$947$	−6.19592e11	−0.0250341	−0.0125170	+	0.999922i	$0.503984\pi$
$948$	−1.87199e13	−0.752776
$949$	−1.67797e12	−0.0671564
$950$	1.15437e13	0.459822
$951$	−6.39400e12	−0.253490
$952$	0	0
$953$	3.01822e13	1.18531	0.592657	−	0.805455i	$-0.298079\pi$
$953$	3.01822e13	1.18531	0.592657	+	0.805455i	$0.298079\pi$
$954$	−6.72820e11	−0.0262985
$955$	4.37564e11	0.0170226
$956$	−1.20375e13	−0.466095
$957$	−1.02954e13	−0.396769
$958$	−1.37831e12	−0.0528692
$959$	7.20706e13	2.75153
$960$	4.76233e10	0.00180967
$961$	5.72803e13	2.16646
$962$	1.80985e12	0.0681326
$963$	4.27562e11	0.0160207
$964$	−2.87166e13	−1.07099
$965$	−5.47429e10	−0.00203215
$966$	1.09682e13	0.405265
$967$	1.16727e13	0.429291	0.214646	−	0.976692i	$-0.431140\pi$
$967$	1.16727e13	0.429291	0.214646	+	0.976692i	$0.431140\pi$
$968$	1.91444e13	0.700815
$969$	0	0
$970$	5.41004e10	0.00196213
$971$	−1.98303e13	−0.715885	−0.357943	−	0.933744i	$-0.616522\pi$
$971$	−1.98303e13	−0.715885	−0.357943	+	0.933744i	$0.616522\pi$
$972$	1.99217e13	0.715862
$973$	6.53257e13	2.33656
$974$	2.29589e13	0.817402
$975$	−3.25994e12	−0.115529
$976$	−5.12011e12	−0.180615
$977$	3.14683e13	1.10496	0.552482	−	0.833525i	$-0.313681\pi$
$977$	3.14683e13	1.10496	0.552482	+	0.833525i	$0.313681\pi$
$978$	−3.49241e11	−0.0122068
$979$	−1.68005e13	−0.584522
$980$	2.31659e11	0.00802290
$981$	2.71261e13	0.935140
$982$	−1.49494e13	−0.513004
$983$	−4.11496e13	−1.40564	−0.702821	−	0.711367i	$-0.748076\pi$
$983$	−4.11496e13	−1.40564	−0.702821	+	0.711367i	$0.748076\pi$
$984$	1.03535e13	0.352055
$985$	5.21540e11	0.0176533
$986$	0	0
$987$	−1.40878e12	−0.0472515
$988$	−3.47027e12	−0.115866
$989$	4.52669e12	0.150452
$990$	4.38335e10	0.00145027
$991$	1.78109e13	0.586615	0.293308	−	0.956018i	$-0.405244\pi$
$991$	1.78109e13	0.586615	0.293308	+	0.956018i	$0.405244\pi$
$992$	5.62410e13	1.84396
$993$	−1.56237e13	−0.509932
$994$	3.24006e13	1.05272
$995$	−9.62261e10	−0.00311235
$996$	1.34504e13	0.433079
$997$	−5.88070e12	−0.188495	−0.0942476	−	0.995549i	$-0.530045\pi$
$997$	−5.88070e12	−0.188495	−0.0942476	+	0.995549i	$0.530045\pi$
$998$	7.31427e12	0.233391
$999$	−2.21624e13	−0.703999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.g.1.23	✓	36
17.16	even	2		289.10.a.h.1.23	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.23	✓	36	1.1	even	1	trivial
289.10.a.h.1.23	yes	36	17.16	even	2

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+11.9493 q^{2} -87.8502 q^{3} -369.213 q^{4} -13.1947 q^{5} -1049.75 q^{6} +9375.81 q^{7} -10529.9 q^{8} -11965.3 q^{9} +O(q^{10})\)	\(q+11.9493 q^{2} -87.8502 q^{3} -369.213 q^{4} -13.1947 q^{5} -1049.75 q^{6} +9375.81 q^{7} -10529.9 q^{8} -11965.3 q^{9} -157.668 q^{10} +23234.7 q^{11} +32435.5 q^{12} -19001.0 q^{13} +112035. q^{14} +1159.16 q^{15} +63211.4 q^{16} -142978. q^{18} -494664. q^{19} +4871.67 q^{20} -823668. q^{21} +277639. q^{22} -1.11440e6 q^{23} +925056. q^{24} -1.95295e6 q^{25} -227049. q^{26} +2.78031e6 q^{27} -3.46167e6 q^{28} +5.04385e6 q^{29} +13851.2 q^{30} +9.14986e6 q^{31} +6.14665e6 q^{32} -2.04117e6 q^{33} -123711. q^{35} +4.41776e6 q^{36} -7.97118e6 q^{37} -5.91092e6 q^{38} +1.66924e6 q^{39} +138939. q^{40} +1.11923e7 q^{41} -9.84229e6 q^{42} -4.06201e6 q^{43} -8.57855e6 q^{44} +157879. q^{45} -1.33163e7 q^{46} +1.71037e6 q^{47} -5.55314e6 q^{48} +4.75523e7 q^{49} -2.33365e7 q^{50} +7.01541e6 q^{52} +4.70576e6 q^{53} +3.32229e7 q^{54} -306575. q^{55} -9.87266e7 q^{56} +4.34564e7 q^{57} +6.02707e7 q^{58} +1.62484e8 q^{59} -427977. q^{60} -8.09997e7 q^{61} +1.09335e8 q^{62} -1.12185e8 q^{63} +4.10843e7 q^{64} +250713. q^{65} -2.43907e7 q^{66} -1.08385e8 q^{67} +9.79000e7 q^{69} -1.47827e6 q^{70} +2.89201e8 q^{71} +1.25994e8 q^{72} +8.83100e7 q^{73} -9.52505e7 q^{74} +1.71567e8 q^{75} +1.82637e8 q^{76} +2.17844e8 q^{77} +1.99463e7 q^{78} -5.77142e8 q^{79} -834057. q^{80} -8.73759e6 q^{81} +1.33741e8 q^{82} +4.14681e8 q^{83} +3.04109e8 q^{84} -4.85384e7 q^{86} -4.43103e8 q^{87} -2.44659e8 q^{88} -7.23081e8 q^{89} +1.88655e6 q^{90} -1.78150e8 q^{91} +4.11450e8 q^{92} -8.03817e8 q^{93} +2.04378e7 q^{94} +6.52696e6 q^{95} -5.39985e8 q^{96} -3.43128e8 q^{97} +5.68219e8 q^{98} -2.78011e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9} - 60000 q^{10} - 76902 q^{11} - 373248 q^{12} + 54216 q^{13} - 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} - 6439479 q^{20} - 138102 q^{21} - 267324 q^{22} - 4041462 q^{23} - 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} - 13281612 q^{27} - 18614784 q^{28} - 4005936 q^{29} + 22471686 q^{30} - 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} - 22076682 q^{37} - 27401376 q^{38} - 62736162 q^{39} + 12231630 q^{40} - 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} + 49578936 q^{44} - 129308238 q^{45} - 140524827 q^{46} - 118557912 q^{47} - 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} - 209848575 q^{54} - 365439924 q^{55} - 203095059 q^{56} + 4614108 q^{57} + 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} - 175597116 q^{61} - 720602571 q^{62} - 587415936 q^{63} + 853082511 q^{64} - 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} - 1308709542 q^{71} - 275337849 q^{72} - 494841342 q^{73} - 1545361890 q^{74} - 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} - 2270624538 q^{78} - 1980107868 q^{79} - 2897000199 q^{80} + 1598298840 q^{81} - 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} + 2705904618 q^{88} + 148394658 q^{89} - 117916215 q^{90} - 636340896 q^{91} + 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} - 4878626298 q^{95} + 8390096634 q^{96} + 891786822 q^{97} + 4285627647 q^{98} + 1476187998 q^{99}+O(q^{100}) \) 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9 - 60000 * q^10 - 76902 * q^11 - 373248 * q^12 + 54216 * q^13 - 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 - 6439479 * q^20 - 138102 * q^21 - 267324 * q^22 - 4041462 * q^23 - 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 - 13281612 * q^27 - 18614784 * q^28 - 4005936 * q^29 + 22471686 * q^30 - 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 - 22076682 * q^37 - 27401376 * q^38 - 62736162 * q^39 + 12231630 * q^40 - 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 + 49578936 * q^44 - 129308238 * q^45 - 140524827 * q^46 - 118557912 * q^47 - 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 - 209848575 * q^54 - 365439924 * q^55 - 203095059 * q^56 + 4614108 * q^57 + 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 - 175597116 * q^61 - 720602571 * q^62 - 587415936 * q^63 + 853082511 * q^64 - 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 - 1308709542 * q^71 - 275337849 * q^72 - 494841342 * q^73 - 1545361890 * q^74 - 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 - 2270624538 * q^78 - 1980107868 * q^79 - 2897000199 * q^80 + 1598298840 * q^81 - 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 + 2705904618 * q^88 + 148394658 * q^89 - 117916215 * q^90 - 636340896 * q^91 + 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 - 4878626298 * q^95 + 8390096634 * q^96 + 891786822 * q^97 + 4285627647 * q^98 + 1476187998 * q^99

Introduction

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