LMFDB - Embedded newform 289.10.a.h.1.32

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:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.32
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)

$f(q)$	$=$	$q+37.7187 q^{2} +226.248 q^{3} +910.699 q^{4} +2062.07 q^{5} +8533.76 q^{6} +6871.89 q^{7} +15038.4 q^{8} +31505.0 q^{9} +O(q^{10})$	\(q+37.7187 q^{2} +226.248 q^{3} +910.699 q^{4} +2062.07 q^{5} +8533.76 q^{6} +6871.89 q^{7} +15038.4 q^{8} +31505.0 q^{9} +77778.4 q^{10} -61445.8 q^{11} +206044. q^{12} +145225. q^{13} +259199. q^{14} +466538. q^{15} +100951. q^{16} +1.18833e6 q^{18} -668803. q^{19} +1.87792e6 q^{20} +1.55475e6 q^{21} -2.31765e6 q^{22} +470052. q^{23} +3.40240e6 q^{24} +2.29899e6 q^{25} +5.47769e6 q^{26} +2.67470e6 q^{27} +6.25823e6 q^{28} -5.12697e6 q^{29} +1.75972e7 q^{30} -4.67583e6 q^{31} -3.89193e6 q^{32} -1.39020e7 q^{33} +1.41703e7 q^{35} +2.86916e7 q^{36} -6.72308e6 q^{37} -2.52264e7 q^{38} +3.28568e7 q^{39} +3.10102e7 q^{40} -1.09604e7 q^{41} +5.86431e7 q^{42} -7.03708e6 q^{43} -5.59586e7 q^{44} +6.49654e7 q^{45} +1.77297e7 q^{46} +4.68861e7 q^{47} +2.28399e7 q^{48} +6.86929e6 q^{49} +8.67150e7 q^{50} +1.32256e8 q^{52} +2.76023e7 q^{53} +1.00886e8 q^{54} -1.26705e8 q^{55} +1.03342e8 q^{56} -1.51315e8 q^{57} -1.93382e8 q^{58} -7.22761e7 q^{59} +4.24876e8 q^{60} +8.21760e7 q^{61} -1.76366e8 q^{62} +2.16499e8 q^{63} -1.98485e8 q^{64} +2.99463e8 q^{65} -5.24364e8 q^{66} -1.82418e8 q^{67} +1.06348e8 q^{69} +5.34485e8 q^{70} -2.28223e7 q^{71} +4.73785e8 q^{72} +3.41963e8 q^{73} -2.53586e8 q^{74} +5.20142e8 q^{75} -6.09078e8 q^{76} -4.22249e8 q^{77} +1.23931e9 q^{78} +1.65497e8 q^{79} +2.08168e8 q^{80} -1.49683e7 q^{81} -4.13411e8 q^{82} -8.05614e8 q^{83} +1.41591e9 q^{84} -2.65430e8 q^{86} -1.15996e9 q^{87} -9.24047e8 q^{88} -5.38809e8 q^{89} +2.45041e9 q^{90} +9.97970e8 q^{91} +4.28076e8 q^{92} -1.05789e9 q^{93} +1.76848e9 q^{94} -1.37912e9 q^{95} -8.80539e8 q^{96} +3.81943e8 q^{97} +2.59100e8 q^{98} -1.93585e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	37.7187	1.66695	0.833473	−	0.552560i	$-0.186349\pi$
$2$	37.7187	1.66695	0.833473	+	0.552560i	$0.186349\pi$
$3$	226.248	1.61264	0.806322	−	0.591477i	$-0.201455\pi$
$3$	226.248	1.61264	0.806322	+	0.591477i	$0.201455\pi$
$4$	910.699	1.77871
$5$	2062.07	1.47549	0.737747	−	0.675077i	$-0.235890\pi$
$5$	2062.07	1.47549	0.737747	+	0.675077i	$0.235890\pi$
$6$	8533.76	2.68819
$7$	6871.89	1.08177	0.540885	−	0.841096i	$-0.318089\pi$
$7$	6871.89	1.08177	0.540885	+	0.841096i	$0.318089\pi$
$8$	15038.4	1.29807
$9$	31505.0	1.60062
$10$	77778.4	2.45957
$11$	−61445.8	−1.26539	−0.632696	−	0.774400i	$-0.718052\pi$
$11$	−61445.8	−1.26539	−0.632696	+	0.774400i	$0.718052\pi$
$12$	206044.	2.86842
$13$	145225.	1.41025	0.705125	−	0.709083i	$-0.250891\pi$
$13$	145225.	1.41025	0.705125	+	0.709083i	$0.250891\pi$
$14$	259199.	1.80325
$15$	466538.	2.37945
$16$	100951.	0.385098
$17$	0	0
$17$	0	0
$18$	1.18833e6	2.66815
$19$	−668803.	−1.17735	−0.588677	−	0.808369i	$-0.700351\pi$
$19$	−668803.	−1.17735	−0.588677	+	0.808369i	$0.700351\pi$
$20$	1.87792e6	2.62448
$21$	1.55475e6	1.74451
$22$	−2.31765e6	−2.10934
$23$	470052.	0.350244	0.175122	−	0.984547i	$-0.443968\pi$
$23$	470052.	0.350244	0.175122	+	0.984547i	$0.443968\pi$
$24$	3.40240e6	2.09332
$25$	2.29899e6	1.17708
$26$	5.47769e6	2.35081
$27$	2.67470e6	0.968586
$28$	6.25823e6	1.92416
$29$	−5.12697e6	−1.34608	−0.673038	−	0.739608i	$-0.735011\pi$
$29$	−5.12697e6	−1.34608	−0.673038	+	0.739608i	$0.735011\pi$
$30$	1.75972e7	3.96641
$31$	−4.67583e6	−0.909349	−0.454675	−	0.890658i	$-0.650244\pi$
$31$	−4.67583e6	−0.909349	−0.454675	+	0.890658i	$0.650244\pi$
$32$	−3.89193e6	−0.656130
$33$	−1.39020e7	−2.04063
$34$	0	0
$35$	1.41703e7	1.59615
$36$	2.86916e7	2.84704
$37$	−6.72308e6	−0.589740	−0.294870	−	0.955537i	$-0.595276\pi$
$37$	−6.72308e6	−0.589740	−0.294870	+	0.955537i	$0.595276\pi$
$38$	−2.52264e7	−1.96258
$39$	3.28568e7	2.27423
$40$	3.10102e7	1.91529
$41$	−1.09604e7	−0.605757	−0.302878	−	0.953029i	$-0.597948\pi$
$41$	−1.09604e7	−0.605757	−0.302878	+	0.953029i	$0.597948\pi$
$42$	5.86431e7	2.90800
$43$	−7.03708e6	−0.313895	−0.156948	−	0.987607i	$-0.550165\pi$
$43$	−7.03708e6	−0.313895	−0.156948	+	0.987607i	$0.550165\pi$
$44$	−5.59586e7	−2.25076
$45$	6.49654e7	2.36171
$46$	1.77297e7	0.583837
$47$	4.68861e7	1.40153	0.700767	−	0.713390i	$-0.252841\pi$
$47$	4.68861e7	1.40153	0.700767	+	0.713390i	$0.252841\pi$
$48$	2.28399e7	0.621025
$49$	6.86929e6	0.170227
$50$	8.67150e7	1.96214
$51$	0	0
$52$	1.32256e8	2.50842
$53$	2.76023e7	0.480511	0.240255	−	0.970710i	$-0.422769\pi$
$53$	2.76023e7	0.480511	0.240255	+	0.970710i	$0.422769\pi$
$54$	1.00886e8	1.61458
$55$	−1.26705e8	−1.86708
$56$	1.03342e8	1.40421
$57$	−1.51315e8	−1.89865
$58$	−1.93382e8	−2.24384
$59$	−7.22761e7	−0.776534	−0.388267	−	0.921547i	$-0.626926\pi$
$59$	−7.22761e7	−0.776534	−0.388267	+	0.921547i	$0.626926\pi$
$60$	4.24876e8	4.23235
$61$	8.21760e7	0.759907	0.379954	−	0.925006i	$-0.375940\pi$
$61$	8.21760e7	0.759907	0.379954	+	0.925006i	$0.375940\pi$
$62$	−1.76366e8	−1.51584
$63$	2.16499e8	1.73150
$64$	−1.98485e8	−1.47883
$65$	2.99463e8	2.08082
$66$	−5.24364e8	−3.40161
$67$	−1.82418e8	−1.10594	−0.552970	−	0.833201i	$-0.686506\pi$
$67$	−1.82418e8	−1.10594	−0.552970	+	0.833201i	$0.686506\pi$
$68$	0	0
$69$	1.06348e8	0.564818
$70$	5.34485e8	2.66069
$71$	−2.28223e7	−0.106585	−0.0532927	−	0.998579i	$-0.516972\pi$
$71$	−2.28223e7	−0.106585	−0.0532927	+	0.998579i	$0.516972\pi$
$72$	4.73785e8	2.07771
$73$	3.41963e8	1.40938	0.704688	−	0.709517i	$-0.251087\pi$
$73$	3.41963e8	1.40938	0.704688	+	0.709517i	$0.251087\pi$
$74$	−2.53586e8	−0.983065
$75$	5.20142e8	1.89822
$76$	−6.09078e8	−2.09417
$77$	−4.22249e8	−1.36886
$78$	1.23931e9	3.79102
$79$	1.65497e8	0.478043	0.239022	−	0.971014i	$-0.423173\pi$
$79$	1.65497e8	0.478043	0.239022	+	0.971014i	$0.423173\pi$
$80$	2.08168e8	0.568209
$81$	−1.49683e7	−0.0386357
$82$	−4.13411e8	−1.00976
$83$	−8.05614e8	−1.86327	−0.931634	−	0.363397i	$-0.881617\pi$
$83$	−8.05614e8	−1.86327	−0.931634	+	0.363397i	$0.881617\pi$
$84$	1.41591e9	3.10298
$85$	0	0
$86$	−2.65430e8	−0.523246
$87$	−1.15996e9	−2.17074
$88$	−9.24047e8	−1.64256
$89$	−5.38809e8	−0.910290	−0.455145	−	0.890417i	$-0.650413\pi$
$89$	−5.38809e8	−0.910290	−0.455145	+	0.890417i	$0.650413\pi$
$90$	2.45041e9	3.93684
$91$	9.97970e8	1.52557
$92$	4.28076e8	0.622982
$93$	−1.05789e9	−1.46646
$94$	1.76848e9	2.33628
$95$	−1.37912e9	−1.73718
$96$	−8.80539e8	−1.05810
$97$	3.81943e8	0.438053	0.219026	−	0.975719i	$-0.429712\pi$
$97$	3.81943e8	0.438053	0.219026	+	0.975719i	$0.429712\pi$
$98$	2.59100e8	0.283760
$99$	−1.93585e9	−2.02541
$100$	2.09369e9	2.09369
$101$	1.16934e9	1.11813	0.559067	−	0.829122i	$-0.311159\pi$
$101$	1.16934e9	1.11813	0.559067	+	0.829122i	$0.311159\pi$
$102$	0	0
$103$	1.63086e9	1.42774	0.713869	−	0.700279i	$-0.246941\pi$
$103$	1.63086e9	1.42774	0.713869	+	0.700279i	$0.246941\pi$
$104$	2.18395e9	1.83060
$105$	3.20600e9	2.57402
$106$	1.04112e9	0.800986
$107$	6.06398e8	0.447230	0.223615	−	0.974678i	$-0.428214\pi$
$107$	6.06398e8	0.447230	0.223615	+	0.974678i	$0.428214\pi$
$108$	2.43585e9	1.72283
$109$	−9.84892e8	−0.668297	−0.334148	−	0.942521i	$-0.608449\pi$
$109$	−9.84892e8	−0.668297	−0.334148	+	0.942521i	$0.608449\pi$
$110$	−4.77916e9	−3.11232
$111$	−1.52108e9	−0.951041
$112$	6.93724e8	0.416587
$113$	−4.51348e8	−0.260411	−0.130205	−	0.991487i	$-0.541564\pi$
$113$	−4.51348e8	−0.260411	−0.130205	+	0.991487i	$0.541564\pi$
$114$	−5.70740e9	−3.16495
$115$	9.69278e8	0.516783
$116$	−4.66912e9	−2.39428
$117$	4.57531e9	2.25727
$118$	−2.72616e9	−1.29444
$119$	0	0
$120$	7.01598e9	3.08868
$121$	1.41764e9	0.601216
$122$	3.09957e9	1.26672
$123$	−2.47976e9	−0.976870
$124$	−4.25827e9	−1.61747
$125$	7.13204e8	0.261287
$126$	8.16606e9	2.88632
$127$	5.99440e8	0.204470	0.102235	−	0.994760i	$-0.467401\pi$
$127$	5.99440e8	0.204470	0.102235	+	0.994760i	$0.467401\pi$
$128$	−5.49394e9	−1.80900
$129$	−1.59212e9	−0.506201
$130$	1.12954e10	3.46861
$131$	5.14850e9	1.52742	0.763712	−	0.645557i	$-0.223375\pi$
$131$	5.14850e9	1.52742	0.763712	+	0.645557i	$0.223375\pi$
$132$	−1.26605e10	−3.62968
$133$	−4.59594e9	−1.27363
$134$	−6.88057e9	−1.84354
$135$	5.51541e9	1.42914
$136$	0	0
$137$	3.80438e9	0.922658	0.461329	−	0.887229i	$-0.347373\pi$
$137$	3.80438e9	0.922658	0.461329	+	0.887229i	$0.347373\pi$
$138$	4.01131e9	0.941521
$139$	6.10572e8	0.138730	0.0693650	−	0.997591i	$-0.477903\pi$
$139$	6.10572e8	0.138730	0.0693650	+	0.997591i	$0.477903\pi$
$140$	1.29049e10	2.83908
$141$	1.06079e10	2.26018
$142$	−8.60828e8	−0.177672
$143$	−8.92345e9	−1.78452
$144$	3.18046e9	0.616395
$145$	−1.05721e10	−1.98613
$146$	1.28984e10	2.34935
$147$	1.55416e9	0.274516
$148$	−6.12271e9	−1.04898
$149$	6.80463e9	1.13101	0.565505	−	0.824745i	$-0.308681\pi$
$149$	6.80463e9	1.13101	0.565505	+	0.824745i	$0.308681\pi$
$150$	1.96191e10	3.16423
$151$	−2.13868e9	−0.334772	−0.167386	−	0.985891i	$-0.553533\pi$
$151$	−2.13868e9	−0.334772	−0.167386	+	0.985891i	$0.553533\pi$
$152$	−1.00577e10	−1.52828
$153$	0	0
$154$	−1.59267e10	−2.28182
$155$	−9.64187e9	−1.34174
$156$	2.99226e10	4.04519
$157$	−1.46008e9	−0.191791	−0.0958954	−	0.995391i	$-0.530571\pi$
$157$	−1.46008e9	−0.191791	−0.0958954	+	0.995391i	$0.530571\pi$
$158$	6.24231e9	0.796872
$159$	6.24495e9	0.774893
$160$	−8.02541e9	−0.968116
$161$	3.23014e9	0.378883
$162$	−5.64583e8	−0.0644036
$163$	−6.99736e8	−0.0776408	−0.0388204	−	0.999246i	$-0.512360\pi$
$163$	−6.99736e8	−0.0776408	−0.0388204	+	0.999246i	$0.512360\pi$
$164$	−9.98161e9	−1.07747
$165$	−2.86668e10	−3.01093
$166$	−3.03867e10	−3.10597
$167$	1.55966e10	1.55169	0.775844	−	0.630924i	$-0.217324\pi$
$167$	1.55966e10	1.55169	0.775844	+	0.630924i	$0.217324\pi$
$168$	2.33810e10	2.26449
$169$	1.04858e10	0.988803
$170$	0	0
$171$	−2.10706e10	−1.88450
$172$	−6.40867e9	−0.558328
$173$	−1.04649e10	−0.888236	−0.444118	−	0.895968i	$-0.646483\pi$
$173$	−1.04649e10	−0.888236	−0.444118	+	0.895968i	$0.646483\pi$
$174$	−4.37523e10	−3.61851
$175$	1.57984e10	1.27334
$176$	−6.20301e9	−0.487299
$177$	−1.63523e10	−1.25227
$178$	−2.03232e10	−1.51741
$179$	1.01165e10	0.736535	0.368268	−	0.929720i	$-0.379951\pi$
$179$	1.01165e10	0.736535	0.368268	+	0.929720i	$0.379951\pi$
$180$	5.91639e10	4.20079
$181$	2.29901e10	1.59216	0.796082	−	0.605189i	$-0.206903\pi$
$181$	2.29901e10	1.59216	0.796082	+	0.605189i	$0.206903\pi$
$182$	3.76421e10	2.54304
$183$	1.85921e10	1.22546
$184$	7.06883e9	0.454639
$185$	−1.38634e10	−0.870159
$186$	−3.99024e10	−2.44450
$187$	0	0
$188$	4.26992e10	2.49292
$189$	1.83803e10	1.04779
$190$	−5.20184e10	−2.89578
$191$	4.71633e9	0.256421	0.128211	−	0.991747i	$-0.459077\pi$
$191$	4.71633e9	0.256421	0.128211	+	0.991747i	$0.459077\pi$
$192$	−4.49068e10	−2.38483
$193$	−2.33113e10	−1.20937	−0.604683	−	0.796466i	$-0.706700\pi$
$193$	−2.33113e10	−1.20937	−0.604683	+	0.796466i	$0.706700\pi$
$194$	1.44064e10	0.730210
$195$	6.77529e10	3.35561
$196$	6.25585e9	0.302785
$197$	−2.50414e10	−1.18457	−0.592286	−	0.805728i	$-0.701774\pi$
$197$	−2.50414e10	−1.18457	−0.592286	+	0.805728i	$0.701774\pi$
$198$	−7.30177e10	−3.37625
$199$	3.47133e10	1.56913	0.784563	−	0.620049i	$-0.212887\pi$
$199$	3.47133e10	1.56913	0.784563	+	0.620049i	$0.212887\pi$
$200$	3.45732e10	1.52793
$201$	−4.12717e10	−1.78349
$202$	4.41059e10	1.86387
$203$	−3.52320e10	−1.45614
$204$	0	0
$205$	−2.26010e10	−0.893791
$206$	6.15138e10	2.37996
$207$	1.48090e10	0.560607
$208$	1.46606e10	0.543084
$209$	4.10951e10	1.48981
$210$	1.20926e11	4.29075
$211$	2.08217e10	0.723178	0.361589	−	0.932338i	$-0.382234\pi$
$211$	2.08217e10	0.723178	0.361589	+	0.932338i	$0.382234\pi$
$212$	2.51374e10	0.854689
$213$	−5.16350e9	−0.171884
$214$	2.28725e10	0.745508
$215$	−1.45109e10	−0.463151
$216$	4.02232e10	1.25729
$217$	−3.21318e10	−0.983707
$218$	−3.71488e10	−1.11401
$219$	7.73684e10	2.27282
$220$	−1.15390e11	−3.32099
$221$	0	0
$222$	−5.73732e10	−1.58533
$223$	1.44771e10	0.392020	0.196010	−	0.980602i	$-0.437201\pi$
$223$	1.44771e10	0.392020	0.196010	+	0.980602i	$0.437201\pi$
$224$	−2.67449e10	−0.709782
$225$	7.24298e10	1.88407
$226$	−1.70243e10	−0.434091
$227$	7.67388e9	0.191822	0.0959111	−	0.995390i	$-0.469424\pi$
$227$	7.67388e9	0.191822	0.0959111	+	0.995390i	$0.469424\pi$
$228$	−1.37802e11	−3.37715
$229$	−4.87034e10	−1.17031	−0.585153	−	0.810923i	$-0.698966\pi$
$229$	−4.87034e10	−1.17031	−0.585153	+	0.810923i	$0.698966\pi$
$230$	3.65599e10	0.861449
$231$	−9.55328e10	−2.20749
$232$	−7.71014e10	−1.74730
$233$	2.45298e10	0.545246	0.272623	−	0.962121i	$-0.412109\pi$
$233$	2.45298e10	0.545246	0.272623	+	0.962121i	$0.412109\pi$
$234$	1.72575e11	3.76275
$235$	9.66823e10	2.06796
$236$	−6.58218e10	−1.38123
$237$	3.74432e10	0.770913
$238$	0	0
$239$	3.93815e10	0.780731	0.390365	−	0.920660i	$-0.372349\pi$
$239$	3.93815e10	0.780731	0.390365	+	0.920660i	$0.372349\pi$
$240$	4.70975e10	0.916319
$241$	3.84246e10	0.733723	0.366862	−	0.930275i	$-0.380432\pi$
$241$	3.84246e10	0.733723	0.366862	+	0.930275i	$0.380432\pi$
$242$	5.34713e10	1.00219
$243$	−5.60327e10	−1.03089
$244$	7.48376e10	1.35165
$245$	1.41649e10	0.251169
$246$	−9.35333e10	−1.62839
$247$	−9.71268e10	−1.66036
$248$	−7.03170e10	−1.18040
$249$	−1.82268e11	−3.00479
$250$	2.69011e10	0.435552
$251$	3.41651e10	0.543314	0.271657	−	0.962394i	$-0.412428\pi$
$251$	3.41651e10	0.543314	0.271657	+	0.962394i	$0.412428\pi$
$252$	1.97165e11	3.07984
$253$	−2.88827e10	−0.443195
$254$	2.26101e10	0.340840
$255$	0	0
$256$	−1.05600e11	−1.53668
$257$	1.22632e10	0.175350	0.0876748	−	0.996149i	$-0.472056\pi$
$257$	1.22632e10	0.175350	0.0876748	+	0.996149i	$0.472056\pi$
$258$	−6.00528e10	−0.843810
$259$	−4.62003e10	−0.637964
$260$	2.72721e11	3.70117
$261$	−1.61525e11	−2.15456
$262$	1.94195e11	2.54613
$263$	1.18519e11	1.52752	0.763759	−	0.645501i	$-0.223351\pi$
$263$	1.18519e11	1.52752	0.763759	+	0.645501i	$0.223351\pi$
$264$	−2.09063e11	−2.64887
$265$	5.69177e10	0.708991
$266$	−1.73353e11	−2.12307
$267$	−1.21904e11	−1.46797
$268$	−1.66128e11	−1.96715
$269$	7.97732e10	0.928906	0.464453	−	0.885598i	$-0.346251\pi$
$269$	7.97732e10	0.928906	0.464453	+	0.885598i	$0.346251\pi$
$270$	2.08034e11	2.38231
$271$	−1.13078e11	−1.27355	−0.636773	−	0.771051i	$-0.719731\pi$
$271$	−1.13078e11	−1.27355	−0.636773	+	0.771051i	$0.719731\pi$
$272$	0	0
$273$	2.25788e11	2.46019
$274$	1.43496e11	1.53802
$275$	−1.41263e11	−1.48947
$276$	9.68511e10	1.00465
$277$	−1.68740e11	−1.72210	−0.861049	−	0.508522i	$-0.830192\pi$
$277$	−1.68740e11	−1.72210	−0.861049	+	0.508522i	$0.830192\pi$
$278$	2.30300e10	0.231255
$279$	−1.47312e11	−1.45552
$280$	2.13099e11	2.07190
$281$	−4.50946e10	−0.431465	−0.215733	−	0.976452i	$-0.569214\pi$
$281$	−4.50946e10	−0.431465	−0.215733	+	0.976452i	$0.569214\pi$
$282$	4.00115e11	3.76759
$283$	3.11841e10	0.288998	0.144499	−	0.989505i	$-0.453843\pi$
$283$	3.11841e10	0.288998	0.144499	+	0.989505i	$0.453843\pi$
$284$	−2.07843e10	−0.189584
$285$	−3.12022e11	−2.80145
$286$	−3.36581e11	−2.97469
$287$	−7.53186e10	−0.655290
$288$	−1.22615e11	−1.05021
$289$	0	0
$290$	−3.98767e11	−3.31077
$291$	8.64138e10	0.706423
$292$	3.11426e11	2.50687
$293$	−5.20574e9	−0.0412647	−0.0206323	−	0.999787i	$-0.506568\pi$
$293$	−5.20574e9	−0.0412647	−0.0206323	+	0.999787i	$0.506568\pi$
$294$	5.86209e10	0.457603
$295$	−1.49038e11	−1.14577
$296$	−1.01104e11	−0.765522
$297$	−1.64349e11	−1.22564
$298$	2.56662e11	1.88533
$299$	6.82632e10	0.493931
$300$	4.73693e11	3.37638
$301$	−4.83581e10	−0.339563
$302$	−8.06682e10	−0.558048
$303$	2.64560e11	1.80315
$304$	−6.75163e10	−0.453396
$305$	1.69452e11	1.12124
$306$	0	0
$307$	2.84128e11	1.82554	0.912769	−	0.408476i	$-0.133940\pi$
$307$	2.84128e11	1.82554	0.912769	+	0.408476i	$0.133940\pi$
$308$	−3.84542e11	−2.43481
$309$	3.68978e11	2.30243
$310$	−3.63679e11	−2.23661
$311$	6.75686e10	0.409565	0.204783	−	0.978807i	$-0.434351\pi$
$311$	6.75686e10	0.409565	0.204783	+	0.978807i	$0.434351\pi$
$312$	4.94114e11	2.95210
$313$	3.27571e11	1.92911	0.964553	−	0.263890i	$-0.0850056\pi$
$313$	3.27571e11	1.92911	0.964553	+	0.263890i	$0.0850056\pi$
$314$	−5.50722e10	−0.319705
$315$	4.46435e11	2.55482
$316$	1.50718e11	0.850300
$317$	2.31963e11	1.29019	0.645093	−	0.764104i	$-0.276819\pi$
$317$	2.31963e11	1.29019	0.645093	+	0.764104i	$0.276819\pi$
$318$	2.35551e11	1.29170
$319$	3.15030e11	1.70331
$320$	−4.09290e11	−2.18201
$321$	1.37196e11	0.721222
$322$	1.21837e11	0.631578
$323$	0	0
$324$	−1.36316e10	−0.0687217
$325$	3.33871e11	1.65998
$326$	−2.63931e10	−0.129423
$327$	−2.22829e11	−1.07772
$328$	−1.64827e11	−0.786313
$329$	3.22196e11	1.51614
$330$	−1.08127e12	−5.01906
$331$	7.65440e10	0.350497	0.175249	−	0.984524i	$-0.443927\pi$
$331$	7.65440e10	0.350497	0.175249	+	0.984524i	$0.443927\pi$
$332$	−7.33672e11	−3.31421
$333$	−2.11811e11	−0.943950
$334$	5.88282e11	2.58658
$335$	−3.76158e11	−1.63181
$336$	1.56954e11	0.671807
$337$	4.13927e10	0.174819	0.0874096	−	0.996172i	$-0.472141\pi$
$337$	4.13927e10	0.174819	0.0874096	+	0.996172i	$0.472141\pi$
$338$	3.95509e11	1.64828
$339$	−1.02116e11	−0.419950
$340$	0	0
$341$	2.87310e11	1.15068
$342$	−7.94756e11	−3.14135
$343$	−2.30101e11	−0.897624
$344$	−1.05827e11	−0.407457
$345$	2.19297e11	0.833386
$346$	−3.94723e11	−1.48064
$347$	4.59267e11	1.70052	0.850261	−	0.526361i	$-0.176444\pi$
$347$	4.59267e11	1.70052	0.850261	+	0.526361i	$0.176444\pi$
$348$	−1.05638e12	−3.86112
$349$	−3.00390e11	−1.08385	−0.541927	−	0.840425i	$-0.682305\pi$
$349$	−3.00390e11	−1.08385	−0.541927	+	0.840425i	$0.682305\pi$
$350$	5.95896e11	2.12258
$351$	3.88433e11	1.36595
$352$	2.39142e11	0.830261
$353$	−4.73281e11	−1.62231	−0.811153	−	0.584834i	$-0.801160\pi$
$353$	−4.73281e11	−1.62231	−0.811153	+	0.584834i	$0.801160\pi$
$354$	−6.16787e11	−2.08747
$355$	−4.70612e10	−0.157266
$356$	−4.90693e11	−1.61914
$357$	0	0
$358$	3.81583e11	1.22776
$359$	−3.04623e11	−0.967915	−0.483957	−	0.875092i	$-0.660801\pi$
$359$	−3.04623e11	−0.967915	−0.483957	+	0.875092i	$0.660801\pi$
$360$	9.76976e11	3.06565
$361$	1.24609e11	0.386161
$362$	8.67157e11	2.65405
$363$	3.20737e11	0.969547
$364$	9.08850e11	2.71354
$365$	7.05151e11	2.07953
$366$	7.01270e11	2.04277
$367$	−2.93387e11	−0.844196	−0.422098	−	0.906550i	$-0.638706\pi$
$367$	−2.93387e11	−0.844196	−0.422098	+	0.906550i	$0.638706\pi$
$368$	4.74522e10	0.134878
$369$	−3.45307e11	−0.969586
$370$	−5.22911e11	−1.45051
$371$	1.89680e11	0.519802
$372$	−9.63424e11	−2.60840
$373$	3.20364e10	0.0856948	0.0428474	−	0.999082i	$-0.486357\pi$
$373$	3.20364e10	0.0856948	0.0428474	+	0.999082i	$0.486357\pi$
$374$	0	0
$375$	1.61361e11	0.421364
$376$	7.05093e11	1.81929
$377$	−7.44563e11	−1.89830
$378$	6.93279e11	1.74661
$379$	4.39592e11	1.09439	0.547197	−	0.837004i	$-0.315695\pi$
$379$	4.39592e11	1.09439	0.547197	+	0.837004i	$0.315695\pi$
$380$	−1.25596e12	−3.08994
$381$	1.35622e11	0.329737
$382$	1.77894e11	0.427440
$383$	−6.55441e10	−0.155646	−0.0778232	−	0.996967i	$-0.524797\pi$
$383$	−6.55441e10	−0.155646	−0.0778232	+	0.996967i	$0.524797\pi$
$384$	−1.24299e12	−2.91727
$385$	−8.70705e11	−2.01975
$386$	−8.79270e11	−2.01595
$387$	−2.21703e11	−0.502427
$388$	3.47836e11	0.779168
$389$	1.12931e11	0.250057	0.125028	−	0.992153i	$-0.460098\pi$
$389$	1.12931e11	0.250057	0.125028	+	0.992153i	$0.460098\pi$
$390$	2.55555e12	5.59363
$391$	0	0
$392$	1.03303e11	0.220966
$393$	1.16484e12	2.46319
$394$	−9.44530e11	−1.97462
$395$	3.41265e11	0.705350
$396$	−1.76298e12	−3.60262
$397$	−3.44606e11	−0.696250	−0.348125	−	0.937448i	$-0.613182\pi$
$397$	−3.44606e11	−0.696250	−0.348125	+	0.937448i	$0.613182\pi$
$398$	1.30934e12	2.61565
$399$	−1.03982e12	−2.05390
$400$	2.32086e11	0.453292
$401$	−5.59517e11	−1.08060	−0.540298	−	0.841474i	$-0.681689\pi$
$401$	−5.59517e11	−1.08060	−0.540298	+	0.841474i	$0.681689\pi$
$402$	−1.55671e12	−2.97298
$403$	−6.79046e11	−1.28241
$404$	1.06492e12	1.98884
$405$	−3.08656e10	−0.0570068
$406$	−1.32890e12	−2.42731
$407$	4.13105e11	0.746252
$408$	0	0
$409$	−5.66357e11	−1.00077	−0.500386	−	0.865802i	$-0.666809\pi$
$409$	−5.66357e11	−1.00077	−0.500386	+	0.865802i	$0.666809\pi$
$410$	−8.52481e11	−1.48990
$411$	8.60731e11	1.48792
$412$	1.48522e12	2.53953
$413$	−4.96673e11	−0.840032
$414$	5.58575e11	0.934502
$415$	−1.66123e12	−2.74924
$416$	−5.65204e11	−0.925306
$417$	1.38140e11	0.223722
$418$	1.55005e12	2.48344
$419$	5.54739e11	0.879277	0.439639	−	0.898175i	$-0.355107\pi$
$419$	5.54739e11	0.879277	0.439639	+	0.898175i	$0.355107\pi$
$420$	2.91970e12	4.57843
$421$	−1.02889e12	−1.59624	−0.798121	−	0.602497i	$-0.794172\pi$
$421$	−1.02889e12	−1.59624	−0.798121	+	0.602497i	$0.794172\pi$
$422$	7.85367e11	1.20550
$423$	1.47715e12	2.24332
$424$	4.15094e11	0.623735
$425$	0	0
$426$	−1.94760e11	−0.286522
$427$	5.64704e11	0.822045
$428$	5.52246e11	0.795491
$429$	−2.01891e12	−2.87779
$430$	−5.47333e11	−0.772047
$431$	6.22150e11	0.868455	0.434227	−	0.900803i	$-0.357021\pi$
$431$	6.22150e11	0.868455	0.434227	+	0.900803i	$0.357021\pi$
$432$	2.70014e11	0.373000
$433$	5.64074e10	0.0771152	0.0385576	−	0.999256i	$-0.487724\pi$
$433$	5.64074e10	0.0771152	0.0385576	+	0.999256i	$0.487724\pi$
$434$	−1.21197e12	−1.63979
$435$	−2.39192e12	−3.20292
$436$	−8.96940e11	−1.18871
$437$	−3.14372e11	−0.412360
$438$	2.91824e12	3.78867
$439$	−5.00594e11	−0.643273	−0.321637	−	0.946863i	$-0.604233\pi$
$439$	−5.00594e11	−0.643273	−0.321637	+	0.946863i	$0.604233\pi$
$440$	−1.90545e12	−2.42359
$441$	2.16417e11	0.272469
$442$	0	0
$443$	−1.13303e12	−1.39774	−0.698869	−	0.715249i	$-0.746313\pi$
$443$	−1.13303e12	−1.39774	−0.698869	+	0.715249i	$0.746313\pi$
$444$	−1.38525e12	−1.69163
$445$	−1.11106e12	−1.34313
$446$	5.46056e11	0.653477
$447$	1.53953e12	1.82392
$448$	−1.36397e12	−1.59975
$449$	−7.52134e11	−0.873347	−0.436673	−	0.899620i	$-0.643843\pi$
$449$	−7.52134e11	−0.873347	−0.436673	+	0.899620i	$0.643843\pi$
$450$	2.73196e12	3.14064
$451$	6.73469e11	0.766520
$452$	−4.11042e11	−0.463195
$453$	−4.83872e11	−0.539869
$454$	2.89449e11	0.319757
$455$	2.05788e12	2.25096
$456$	−2.27554e12	−2.46458
$457$	−1.04067e12	−1.11606	−0.558031	−	0.829820i	$-0.688443\pi$
$457$	−1.04067e12	−1.11606	−0.558031	+	0.829820i	$0.688443\pi$
$458$	−1.83703e12	−1.95084
$459$	0	0
$460$	8.82720e11	0.919206
$461$	−1.52960e12	−1.57733	−0.788667	−	0.614820i	$-0.789229\pi$
$461$	−1.52960e12	−1.57733	−0.788667	+	0.614820i	$0.789229\pi$
$462$	−3.60337e12	−3.67976
$463$	−8.60918e11	−0.870658	−0.435329	−	0.900271i	$-0.643368\pi$
$463$	−8.60918e11	−0.870658	−0.435329	+	0.900271i	$0.643368\pi$
$464$	−5.17572e11	−0.518370
$465$	−2.18145e12	−2.16375
$466$	9.25231e11	0.908895
$467$	−1.07959e12	−1.05034	−0.525172	−	0.850996i	$-0.675999\pi$
$467$	−1.07959e12	−1.05034	−0.525172	+	0.850996i	$0.675999\pi$
$468$	4.16673e12	4.01503
$469$	−1.25356e12	−1.19637
$470$	3.64673e12	3.44717
$471$	−3.30339e11	−0.309290
$472$	−1.08692e12	−1.00799
$473$	4.32399e11	0.397200
$474$	1.41231e12	1.28507
$475$	−1.53757e12	−1.38584
$476$	0	0
$477$	8.69609e11	0.769115
$478$	1.48542e12	1.30144
$479$	−3.69744e11	−0.320916	−0.160458	−	0.987043i	$-0.551297\pi$
$479$	−3.69744e11	−0.320916	−0.160458	+	0.987043i	$0.551297\pi$
$480$	−1.81573e12	−1.56123
$481$	−9.76359e11	−0.831681
$482$	1.44932e12	1.22308
$483$	7.30812e11	0.611004
$484$	1.29104e12	1.06939
$485$	7.87593e11	0.646344
$486$	−2.11348e12	−1.71844
$487$	−9.18766e11	−0.740158	−0.370079	−	0.929000i	$-0.620669\pi$
$487$	−9.18766e11	−0.740158	−0.370079	+	0.929000i	$0.620669\pi$
$488$	1.23580e12	0.986410
$489$	−1.58314e11	−0.125207
$490$	5.34282e11	0.418686
$491$	3.08095e11	0.239232	0.119616	−	0.992820i	$-0.461834\pi$
$491$	3.08095e11	0.239232	0.119616	+	0.992820i	$0.461834\pi$
$492$	−2.25832e12	−1.73757
$493$	0	0
$494$	−3.66349e12	−2.76773
$495$	−3.99185e12	−2.98848
$496$	−4.72029e11	−0.350188
$497$	−1.56833e11	−0.115301
$498$	−6.87492e12	−5.00882
$499$	1.77593e12	1.28225	0.641126	−	0.767436i	$-0.278468\pi$
$499$	1.77593e12	1.28225	0.641126	+	0.767436i	$0.278468\pi$
$500$	6.49514e11	0.464754
$501$	3.52868e12	2.50232
$502$	1.28866e12	0.905674
$503$	1.78568e12	1.24379	0.621895	−	0.783101i	$-0.286363\pi$
$503$	1.78568e12	1.24379	0.621895	+	0.783101i	$0.286363\pi$
$504$	3.25580e12	2.24761
$505$	2.41125e12	1.64980
$506$	−1.08942e12	−0.738783
$507$	2.37238e12	1.59459
$508$	5.45909e11	0.363692
$509$	−1.65522e12	−1.09301	−0.546506	−	0.837455i	$-0.684042\pi$
$509$	−1.65522e12	−1.09301	−0.546506	+	0.837455i	$0.684042\pi$
$510$	0	0
$511$	2.34994e12	1.52462
$512$	−1.17018e12	−0.752556
$513$	−1.78885e12	−1.14037
$514$	4.62552e11	0.292298
$515$	3.36294e12	2.10662
$516$	−1.44995e12	−0.900385
$517$	−2.88095e12	−1.77349
$518$	−1.74261e12	−1.06345
$519$	−2.36766e12	−1.43241
$520$	4.50345e12	2.70104
$521$	−1.34161e12	−0.797733	−0.398867	−	0.917009i	$-0.630596\pi$
$521$	−1.34161e12	−0.797733	−0.398867	+	0.917009i	$0.630596\pi$
$522$	−6.09251e12	−3.59153
$523$	−3.25410e12	−1.90184	−0.950919	−	0.309439i	$-0.899859\pi$
$523$	−3.25410e12	−1.90184	−0.950919	+	0.309439i	$0.899859\pi$
$524$	4.68873e12	2.71684
$525$	3.57436e12	2.05344
$526$	4.47038e12	2.54629
$527$	0	0
$528$	−1.40342e12	−0.785840
$529$	−1.58020e12	−0.877329
$530$	2.14686e12	1.18185
$531$	−2.27706e12	−1.24294
$532$	−4.18552e12	−2.26541
$533$	−1.59172e12	−0.854268
$534$	−4.59807e12	−2.44703
$535$	1.25043e12	0.659885
$536$	−2.74328e12	−1.43558
$537$	2.28884e12	1.18777
$538$	3.00894e12	1.54844
$539$	−4.22089e11	−0.215404
$540$	5.02288e12	2.54203
$541$	−7.92197e11	−0.397599	−0.198800	−	0.980040i	$-0.563704\pi$
$541$	−7.92197e11	−0.397599	−0.198800	+	0.980040i	$0.563704\pi$
$542$	−4.26514e12	−2.12293
$543$	5.20146e12	2.56759
$544$	0	0
$545$	−2.03091e12	−0.986068
$546$	8.51644e12	4.10101
$547$	2.31300e12	1.10467	0.552336	−	0.833622i	$-0.313737\pi$
$547$	2.31300e12	1.10467	0.552336	+	0.833622i	$0.313737\pi$
$548$	3.46464e12	1.64114
$549$	2.58895e12	1.21632
$550$	−5.32827e12	−2.48287
$551$	3.42893e12	1.58481
$552$	1.59931e12	0.733172
$553$	1.13727e12	0.517133
$554$	−6.36463e12	−2.87064
$555$	−3.13657e12	−1.40326
$556$	5.56047e11	0.246760
$557$	−1.60536e12	−0.706683	−0.353341	−	0.935494i	$-0.614955\pi$
$557$	−1.60536e12	−0.706683	−0.353341	+	0.935494i	$0.614955\pi$
$558$	−5.55641e12	−2.42628
$559$	−1.02196e12	−0.442670
$560$	1.43051e12	0.614672
$561$	0	0
$562$	−1.70091e12	−0.719230
$563$	−3.25808e12	−1.36670	−0.683352	−	0.730089i	$-0.739479\pi$
$563$	−3.25808e12	−1.36670	−0.683352	+	0.730089i	$0.739479\pi$
$564$	9.66058e12	4.02020
$565$	−9.30710e11	−0.384235
$566$	1.17622e12	0.481743
$567$	−1.02860e11	−0.0417950
$568$	−3.43212e11	−0.138355
$569$	−1.46203e12	−0.584726	−0.292363	−	0.956307i	$-0.594441\pi$
$569$	−1.46203e12	−0.584726	−0.292363	+	0.956307i	$0.594441\pi$
$570$	−1.17690e13	−4.66987
$571$	−2.80071e12	−1.10257	−0.551284	−	0.834318i	$-0.685862\pi$
$571$	−2.80071e12	−1.10257	−0.551284	+	0.834318i	$0.685862\pi$
$572$	−8.12658e12	−3.17414
$573$	1.06706e12	0.413516
$574$	−2.84092e12	−1.09233
$575$	1.08065e12	0.412266
$576$	−6.25328e12	−2.36705
$577$	−3.34815e12	−1.25752	−0.628759	−	0.777600i	$-0.716437\pi$
$577$	−3.34815e12	−1.25752	−0.628759	+	0.777600i	$0.716437\pi$
$578$	0	0
$579$	−5.27412e12	−1.95028
$580$	−9.62804e12	−3.53274
$581$	−5.53609e12	−2.01563
$582$	3.25941e12	1.17757
$583$	−1.69604e12	−0.608034
$584$	5.14259e12	1.82946
$585$	9.43459e12	3.33059
$586$	−1.96354e11	−0.0687860
$587$	1.79944e12	0.625557	0.312779	−	0.949826i	$-0.398740\pi$
$587$	1.79944e12	0.625557	0.312779	+	0.949826i	$0.398740\pi$
$588$	1.41537e12	0.488284
$589$	3.12721e12	1.07063
$590$	−5.62152e12	−1.90994
$591$	−5.66557e12	−1.91029
$592$	−6.78702e11	−0.227108
$593$	2.73634e12	0.908708	0.454354	−	0.890821i	$-0.349870\pi$
$593$	2.73634e12	0.908708	0.454354	+	0.890821i	$0.349870\pi$
$594$	−6.19903e12	−2.04308
$595$	0	0
$596$	6.19697e12	2.01174
$597$	7.85381e12	2.53044
$598$	2.57480e12	0.823356
$599$	3.10716e12	0.986149	0.493074	−	0.869987i	$-0.335873\pi$
$599$	3.10716e12	0.986149	0.493074	+	0.869987i	$0.335873\pi$
$600$	7.82211e12	2.46401
$601$	−7.98642e11	−0.249699	−0.124850	−	0.992176i	$-0.539845\pi$
$601$	−7.98642e11	−0.249699	−0.124850	+	0.992176i	$0.539845\pi$
$602$	−1.82400e12	−0.566032
$603$	−5.74708e12	−1.77019
$604$	−1.94769e12	−0.595463
$605$	2.92326e12	0.887091
$606$	9.97886e12	3.00576
$607$	−2.81159e12	−0.840625	−0.420312	−	0.907379i	$-0.638080\pi$
$607$	−2.81159e12	−0.840625	−0.420312	+	0.907379i	$0.638080\pi$
$608$	2.60293e12	0.772496
$609$	−7.97115e12	−2.34824
$610$	6.39152e12	1.86904
$611$	6.80903e12	1.97651
$612$	0	0
$613$	6.03464e12	1.72615	0.863077	−	0.505072i	$-0.168534\pi$
$613$	6.03464e12	1.72615	0.863077	+	0.505072i	$0.168534\pi$
$614$	1.07169e13	3.04307
$615$	−5.11343e12	−1.44137
$616$	−6.34995e12	−1.77688
$617$	8.19820e11	0.227738	0.113869	−	0.993496i	$-0.463676\pi$
$617$	8.19820e11	0.227738	0.113869	+	0.993496i	$0.463676\pi$
$618$	1.39174e13	3.83803
$619$	−3.66059e12	−1.00217	−0.501087	−	0.865397i	$-0.667066\pi$
$619$	−3.66059e12	−1.00217	−0.501087	+	0.865397i	$0.667066\pi$
$620$	−8.78084e12	−2.38657
$621$	1.25725e12	0.339241
$622$	2.54860e12	0.682723
$623$	−3.70264e12	−0.984725
$624$	3.31693e12	0.875800
$625$	−3.01955e12	−0.791556
$626$	1.23555e13	3.21572
$627$	9.29767e12	2.40254
$628$	−1.32969e12	−0.341140
$629$	0	0
$630$	1.68390e13	4.25875
$631$	1.58487e12	0.397980	0.198990	−	0.980001i	$-0.436234\pi$
$631$	1.58487e12	0.397980	0.198990	+	0.980001i	$0.436234\pi$
$632$	2.48880e12	0.620532
$633$	4.71086e12	1.16623
$634$	8.74934e12	2.15067
$635$	1.23608e12	0.301694
$636$	5.68727e12	1.37831
$637$	9.97591e11	0.240063
$638$	1.18825e13	2.83933
$639$	−7.19018e11	−0.170603
$640$	−1.13289e13	−2.66917
$641$	6.77677e11	0.158548	0.0792742	−	0.996853i	$-0.474740\pi$
$641$	6.77677e11	0.158548	0.0792742	+	0.996853i	$0.474740\pi$
$642$	5.17485e12	1.20224
$643$	8.52112e11	0.196584	0.0982918	−	0.995158i	$-0.468662\pi$
$643$	8.52112e11	0.196584	0.0982918	+	0.995158i	$0.468662\pi$
$644$	2.94169e12	0.673923
$645$	−3.28306e12	−0.746897
$646$	0	0
$647$	7.35479e12	1.65006	0.825032	−	0.565086i	$-0.191157\pi$
$647$	7.35479e12	1.65006	0.825032	+	0.565086i	$0.191157\pi$
$648$	−2.25099e11	−0.0501517
$649$	4.44106e12	0.982620
$650$	1.25932e13	2.76710
$651$	−7.26974e12	−1.58637
$652$	−6.37249e11	−0.138100
$653$	2.12014e12	0.456304	0.228152	−	0.973626i	$-0.426732\pi$
$653$	2.12014e12	0.456304	0.228152	+	0.973626i	$0.426732\pi$
$654$	−8.40483e12	−1.79651
$655$	1.06165e13	2.25371
$656$	−1.10646e12	−0.233275
$657$	1.07736e13	2.25588
$658$	1.21528e13	2.52732
$659$	4.22525e12	0.872707	0.436353	−	0.899775i	$-0.356270\pi$
$659$	4.22525e12	0.872707	0.436353	+	0.899775i	$0.356270\pi$
$660$	−2.61068e13	−5.35557
$661$	−4.60044e12	−0.937330	−0.468665	−	0.883376i	$-0.655265\pi$
$661$	−4.60044e12	−0.937330	−0.468665	+	0.883376i	$0.655265\pi$
$662$	2.88714e12	0.584260
$663$	0	0
$664$	−1.21151e13	−2.41865
$665$	−9.47713e12	−1.87923
$666$	−7.98922e12	−1.57351
$667$	−2.40994e12	−0.471454
$668$	1.42038e13	2.76000
$669$	3.27540e12	0.632189
$670$	−1.41882e13	−2.72014
$671$	−5.04937e12	−0.961580
$672$	−6.05097e12	−1.14462
$673$	9.41555e12	1.76920	0.884602	−	0.466346i	$-0.154430\pi$
$673$	9.41555e12	1.76920	0.884602	+	0.466346i	$0.154430\pi$
$674$	1.56128e12	0.291414
$675$	6.14912e12	1.14011
$676$	9.54938e12	1.75879
$677$	−7.17338e12	−1.31243	−0.656213	−	0.754576i	$-0.727843\pi$
$677$	−7.17338e12	−1.31243	−0.656213	+	0.754576i	$0.727843\pi$
$678$	−3.85170e12	−0.700033
$679$	2.62467e12	0.473872
$680$	0	0
$681$	1.73620e12	0.309341
$682$	1.08369e13	1.91813
$683$	1.03920e12	0.182729	0.0913643	−	0.995818i	$-0.470877\pi$
$683$	1.03920e12	0.182729	0.0913643	+	0.995818i	$0.470877\pi$
$684$	−1.91890e13	−3.35197
$685$	7.84488e12	1.36138
$686$	−8.67909e12	−1.49629
$687$	−1.10190e13	−1.88729
$688$	−7.10401e11	−0.120880
$689$	4.00853e12	0.677640
$690$	8.27159e12	1.38921
$691$	1.02636e12	0.171257	0.0856283	−	0.996327i	$-0.472710\pi$
$691$	1.02636e12	0.171257	0.0856283	+	0.996327i	$0.472710\pi$
$692$	−9.53040e12	−1.57991
$693$	−1.33029e13	−2.19103
$694$	1.73229e13	2.83468
$695$	1.25904e12	0.204695
$696$	−1.74440e13	−2.81777
$697$	0	0
$698$	−1.13303e13	−1.80673
$699$	5.54981e12	0.879287
$700$	1.43876e13	2.26489
$701$	−3.78304e12	−0.591711	−0.295856	−	0.955233i	$-0.595605\pi$
$701$	−3.78304e12	−0.591711	−0.295856	+	0.955233i	$0.595605\pi$
$702$	1.46512e13	2.27696
$703$	4.49642e12	0.694333
$704$	1.21961e13	1.87130
$705$	2.18741e13	3.33488
$706$	−1.78515e13	−2.70430
$707$	8.03557e12	1.20956
$708$	−1.48920e13	−2.22743
$709$	−1.32474e11	−0.0196889	−0.00984447	−	0.999952i	$-0.503134\pi$
$709$	−1.32474e11	−0.0196889	−0.00984447	+	0.999952i	$0.503134\pi$
$710$	−1.77509e12	−0.262154
$711$	5.21397e12	0.765165
$712$	−8.10283e12	−1.18162
$713$	−2.19788e12	−0.318494
$714$	0	0
$715$	−1.84008e13	−2.63305
$716$	9.21313e12	1.31008
$717$	8.90996e12	1.25904
$718$	−1.14900e13	−1.61346
$719$	−9.94954e12	−1.38843	−0.694213	−	0.719769i	$-0.744248\pi$
$719$	−9.94954e12	−1.38843	−0.694213	+	0.719769i	$0.744248\pi$
$720$	6.55832e12	0.909487
$721$	1.12071e13	1.54449
$722$	4.70010e12	0.643709
$723$	8.69347e12	1.18323
$724$	2.09371e13	2.83200
$725$	−1.17869e13	−1.58444
$726$	1.20978e13	1.61618
$727$	−3.01257e12	−0.399974	−0.199987	−	0.979799i	$-0.564090\pi$
$727$	−3.01257e12	−0.399974	−0.199987	+	0.979799i	$0.564090\pi$
$728$	1.50079e13	1.98029
$729$	−1.23826e13	−1.62383
$730$	2.65974e13	3.46646
$731$	0	0
$732$	1.69318e13	2.17974
$733$	−1.72087e12	−0.220181	−0.110091	−	0.993922i	$-0.535114\pi$
$733$	−1.72087e12	−0.220181	−0.110091	+	0.993922i	$0.535114\pi$
$734$	−1.10662e13	−1.40723
$735$	3.20478e12	0.405047
$736$	−1.82941e12	−0.229805
$737$	1.12088e13	1.39945
$738$	−1.30245e13	−1.61625
$739$	−3.69061e12	−0.455196	−0.227598	−	0.973755i	$-0.573087\pi$
$739$	−3.69061e12	−0.455196	−0.227598	+	0.973755i	$0.573087\pi$
$740$	−1.26254e13	−1.54776
$741$	−2.19747e13	−2.67757
$742$	7.15447e12	0.866483
$743$	6.97750e12	0.839944	0.419972	−	0.907537i	$-0.362040\pi$
$743$	6.97750e12	0.839944	0.419972	+	0.907537i	$0.362040\pi$
$744$	−1.59091e13	−1.90356
$745$	1.40316e13	1.66880
$746$	1.20837e12	0.142849
$747$	−2.53809e13	−2.98238
$748$	0	0
$749$	4.16710e12	0.483800
$750$	6.08631e12	0.702390
$751$	1.20976e13	1.38778	0.693890	−	0.720081i	$-0.255895\pi$
$751$	1.20976e13	1.38778	0.693890	+	0.720081i	$0.255895\pi$
$752$	4.73320e12	0.539728
$753$	7.72977e12	0.876171
$754$	−2.80839e13	−3.16437
$755$	−4.41010e12	−0.493955
$756$	1.67389e13	1.86371
$757$	3.55686e12	0.393673	0.196836	−	0.980436i	$-0.436933\pi$
$757$	3.55686e12	0.393673	0.196836	+	0.980436i	$0.436933\pi$
$758$	1.65808e13	1.82430
$759$	−6.53464e12	−0.714716
$760$	−2.07397e13	−2.25497
$761$	9.85116e12	1.06477	0.532386	−	0.846502i	$-0.321296\pi$
$761$	9.85116e12	1.06477	0.532386	+	0.846502i	$0.321296\pi$
$762$	5.11548e12	0.549653
$763$	−6.76807e12	−0.722943
$764$	4.29515e12	0.456098
$765$	0	0
$766$	−2.47224e12	−0.259454
$767$	−1.04963e13	−1.09511
$768$	−2.38917e13	−2.47811
$769$	1.63183e13	1.68269	0.841347	−	0.540495i	$-0.181763\pi$
$769$	1.63183e13	1.68269	0.841347	+	0.540495i	$0.181763\pi$
$770$	−3.28418e13	−3.36681
$771$	2.77452e12	0.282777
$772$	−2.12295e13	−2.15111
$773$	−1.74713e13	−1.76002	−0.880008	−	0.474959i	$-0.842463\pi$
$773$	−1.74713e13	−1.76002	−0.880008	+	0.474959i	$0.842463\pi$
$774$	−8.36236e12	−0.837519
$775$	−1.07497e13	−1.07038
$776$	5.74382e12	0.568621
$777$	−1.04527e13	−1.02881
$778$	4.25960e12	0.416831
$779$	7.33033e12	0.713190
$780$	6.17025e13	5.96866
$781$	1.40234e12	0.134872
$782$	0	0
$783$	−1.37131e13	−1.30379
$784$	6.93461e11	0.0655541
$785$	−3.01078e12	−0.282986
$786$	4.39361e13	4.10601
$787$	−3.80029e12	−0.353127	−0.176563	−	0.984289i	$-0.556498\pi$
$787$	−3.80029e12	−0.353127	−0.176563	+	0.984289i	$0.556498\pi$
$788$	−2.28052e13	−2.10701
$789$	2.68146e13	2.46334
$790$	1.28721e13	1.17578
$791$	−3.10162e12	−0.281705
$792$	−2.91121e13	−2.62912
$793$	1.19340e13	1.07166
$794$	−1.29981e13	−1.16061
$795$	1.28775e13	1.14335
$796$	3.16134e13	2.79102
$797$	1.19614e13	1.05008	0.525039	−	0.851078i	$-0.324051\pi$
$797$	1.19614e13	1.05008	0.525039	+	0.851078i	$0.324051\pi$
$798$	−3.92207e13	−3.42375
$799$	0	0
$800$	−8.94751e12	−0.772320
$801$	−1.69752e13	−1.45703
$802$	−2.11042e13	−1.80130
$803$	−2.10122e13	−1.78341
$804$	−3.75861e13	−3.17230
$805$	6.66077e12	0.559040
$806$	−2.56127e13	−2.13771
$807$	1.80485e13	1.49800
$808$	1.75850e13	1.45141
$809$	3.93121e12	0.322669	0.161335	−	0.986900i	$-0.448420\pi$
$809$	3.93121e12	0.322669	0.161335	+	0.986900i	$0.448420\pi$
$810$	−1.16421e12	−0.0950272
$811$	−5.71939e12	−0.464254	−0.232127	−	0.972685i	$-0.574568\pi$
$811$	−5.71939e12	−0.464254	−0.232127	+	0.972685i	$0.574568\pi$
$812$	−3.20857e13	−2.59006
$813$	−2.55835e13	−2.05378
$814$	1.55818e13	1.24396
$815$	−1.44290e12	−0.114559
$816$	0	0
$817$	4.70642e12	0.369565
$818$	−2.13622e13	−1.66823
$819$	3.14410e13	2.44185
$820$	−2.05827e13	−1.58979
$821$	1.27812e13	0.981811	0.490905	−	0.871213i	$-0.336666\pi$
$821$	1.27812e13	0.981811	0.490905	+	0.871213i	$0.336666\pi$
$822$	3.24657e13	2.48028
$823$	−7.03006e12	−0.534146	−0.267073	−	0.963676i	$-0.586056\pi$
$823$	−7.03006e12	−0.534146	−0.267073	+	0.963676i	$0.586056\pi$
$824$	2.45255e13	1.85330
$825$	−3.19605e13	−2.40199
$826$	−1.87339e13	−1.40029
$827$	−1.64458e13	−1.22259	−0.611294	−	0.791403i	$-0.709351\pi$
$827$	−1.64458e13	−1.22259	−0.611294	+	0.791403i	$0.709351\pi$
$828$	1.34865e13	0.997157
$829$	1.84055e13	1.35348	0.676742	−	0.736221i	$-0.263391\pi$
$829$	1.84055e13	1.35348	0.676742	+	0.736221i	$0.263391\pi$
$830$	−6.26594e13	−4.58284
$831$	−3.81769e13	−2.77713
$832$	−2.88250e13	−2.08552
$833$	0	0
$834$	5.21047e12	0.372932
$835$	3.21611e13	2.28951
$836$	3.74253e13	2.64994
$837$	−1.25064e13	−0.880783
$838$	2.09240e13	1.46571
$839$	2.38752e13	1.66348	0.831742	−	0.555163i	$-0.187344\pi$
$839$	2.38752e13	1.66348	0.831742	+	0.555163i	$0.187344\pi$
$840$	4.82131e13	3.34124
$841$	1.17786e13	0.811919
$842$	−3.88083e13	−2.66085
$843$	−1.02025e13	−0.695800
$844$	1.89623e13	1.28632
$845$	2.16223e13	1.45897
$846$	5.57161e13	3.73950
$847$	9.74183e12	0.650377
$848$	2.78648e12	0.185044
$849$	7.05533e12	0.466050
$850$	0	0
$851$	−3.16020e12	−0.206553
$852$	−4.70239e12	−0.305732
$853$	−2.97739e13	−1.92560	−0.962798	−	0.270221i	$-0.912903\pi$
$853$	−2.97739e13	−1.92560	−0.962798	+	0.270221i	$0.912903\pi$
$854$	2.12999e13	1.37030
$855$	−4.34490e13	−2.78056
$856$	9.11926e12	0.580534
$857$	2.21936e12	0.140544	0.0702722	−	0.997528i	$-0.477613\pi$
$857$	2.21936e12	0.140544	0.0702722	+	0.997528i	$0.477613\pi$
$858$	−7.61507e13	−4.79712
$859$	−1.13481e13	−0.711136	−0.355568	−	0.934650i	$-0.615713\pi$
$859$	−1.13481e13	−0.711136	−0.355568	+	0.934650i	$0.615713\pi$
$860$	−1.32151e13	−0.823810
$861$	−1.70406e13	−1.05675
$862$	2.34667e13	1.44767
$863$	−1.52449e13	−0.935571	−0.467785	−	0.883842i	$-0.654948\pi$
$863$	−1.52449e13	−0.935571	−0.467785	+	0.883842i	$0.654948\pi$
$864$	−1.04097e13	−0.635518
$865$	−2.15794e13	−1.31059
$866$	2.12761e12	0.128547
$867$	0	0
$868$	−2.92624e13	−1.74973
$869$	−1.01691e13	−0.604912
$870$	−9.02202e13	−5.33909
$871$	−2.64917e13	−1.55965
$872$	−1.48112e13	−0.867493
$873$	1.20331e13	0.701156
$874$	−1.18577e13	−0.687383
$875$	4.90106e12	0.282653
$876$	7.04594e13	4.04269
$877$	−2.67455e13	−1.52669	−0.763347	−	0.645988i	$-0.776446\pi$
$877$	−2.67455e13	−1.52669	−0.763347	+	0.645988i	$0.776446\pi$
$878$	−1.88818e13	−1.07230
$879$	−1.17779e12	−0.0665452
$880$	−1.27910e13	−0.719007
$881$	−1.09607e13	−0.612982	−0.306491	−	0.951874i	$-0.599155\pi$
$881$	−1.09607e13	−0.612982	−0.306491	+	0.951874i	$0.599155\pi$
$882$	8.16296e12	0.454191
$883$	3.23917e13	1.79313	0.896563	−	0.442916i	$-0.146056\pi$
$883$	3.23917e13	1.79313	0.896563	+	0.442916i	$0.146056\pi$
$884$	0	0
$885$	−3.37195e13	−1.84772
$886$	−4.27365e13	−2.32996
$887$	3.42855e13	1.85975	0.929875	−	0.367876i	$-0.119915\pi$
$887$	3.42855e13	1.85975	0.929875	+	0.367876i	$0.119915\pi$
$888$	−2.28747e13	−1.23451
$889$	4.11929e12	0.221189
$890$	−4.19077e13	−2.23892
$891$	9.19736e11	0.0488893
$892$	1.31843e13	0.697290
$893$	−3.13576e13	−1.65010
$894$	5.80691e13	3.04037
$895$	2.08610e13	1.08675
$896$	−3.77537e13	−1.95692
$897$	1.54444e13	0.796535
$898$	−2.83695e13	−1.45582
$899$	2.39728e13	1.22405
$900$	6.59618e13	3.35120
$901$	0	0
$902$	2.54024e13	1.27775
$903$	−1.09409e13	−0.547593
$904$	−6.78756e12	−0.338030
$905$	4.74072e13	2.34923
$906$	−1.82510e13	−0.899932
$907$	−5.03141e12	−0.246863	−0.123432	−	0.992353i	$-0.539390\pi$
$907$	−5.03141e12	−0.246863	−0.123432	+	0.992353i	$0.539390\pi$
$908$	6.98860e12	0.341196
$909$	3.68400e13	1.78971
$910$	7.76205e13	3.75224
$911$	−6.78962e11	−0.0326598	−0.0163299	−	0.999867i	$-0.505198\pi$
$911$	−6.78962e11	−0.0326598	−0.0163299	+	0.999867i	$0.505198\pi$
$912$	−1.52754e13	−0.731166
$913$	4.95016e13	2.35776
$914$	−3.92526e13	−1.86042
$915$	3.83382e13	1.80816
$916$	−4.43541e13	−2.08163
$917$	3.53799e13	1.65232
$918$	0	0
$919$	7.57807e12	0.350460	0.175230	−	0.984527i	$-0.443933\pi$
$919$	7.57807e12	0.350460	0.175230	+	0.984527i	$0.443933\pi$
$920$	1.45764e13	0.670818
$921$	6.42832e13	2.94394
$922$	−5.76945e13	−2.62933
$923$	−3.31437e12	−0.150312
$924$	−8.70016e13	−3.92648
$925$	−1.54563e13	−0.694174
$926$	−3.24727e13	−1.45134
$927$	5.13802e13	2.28527
$928$	1.99538e13	0.883200
$929$	8.54936e12	0.376585	0.188292	−	0.982113i	$-0.439705\pi$
$929$	8.54936e12	0.376585	0.188292	+	0.982113i	$0.439705\pi$
$930$	−8.22814e13	−3.60685
$931$	−4.59420e12	−0.200418
$932$	2.23393e13	0.969833
$933$	1.52872e13	0.660483
$934$	−4.07206e13	−1.75087
$935$	0	0
$936$	6.88054e13	2.93009
$937$	3.10939e13	1.31779	0.658897	−	0.752233i	$-0.271023\pi$
$937$	3.10939e13	1.31779	0.658897	+	0.752233i	$0.271023\pi$
$938$	−4.72826e13	−1.99429
$939$	7.41122e13	3.11096
$940$	8.80485e13	3.67830
$941$	−4.33473e13	−1.80222	−0.901111	−	0.433588i	$-0.857247\pi$
$941$	−4.33473e13	−1.80222	−0.901111	+	0.433588i	$0.857247\pi$
$942$	−1.24600e13	−0.515570
$943$	−5.15194e12	−0.212162
$944$	−7.29634e12	−0.299041
$945$	3.79013e13	1.54601
$946$	1.63095e13	0.662111
$947$	2.72531e13	1.10114	0.550568	−	0.834790i	$-0.314411\pi$
$947$	2.72531e13	1.10114	0.550568	+	0.834790i	$0.314411\pi$
$948$	3.40995e13	1.37123
$949$	4.96616e13	1.98757
$950$	−5.79952e13	−2.31013
$951$	5.24811e13	2.08061
$952$	0	0
$953$	−4.59885e13	−1.80605	−0.903027	−	0.429583i	$-0.858661\pi$
$953$	−4.59885e13	−1.80605	−0.903027	+	0.429583i	$0.858661\pi$
$954$	3.28005e13	1.28207
$955$	9.72538e12	0.378348
$956$	3.58647e13	1.38869
$957$	7.12749e13	2.74684
$958$	−1.39463e13	−0.534950
$959$	2.61433e13	0.998105
$960$	−9.26009e13	−3.51880
$961$	−4.57626e12	−0.173084
$962$	−3.68270e13	−1.38637
$963$	1.91046e13	0.715845
$964$	3.49932e13	1.30508
$965$	−4.80694e13	−1.78441
$966$	2.75653e13	1.01851
$967$	−4.69401e13	−1.72633	−0.863167	−	0.504919i	$-0.831523\pi$
$967$	−4.69401e13	−1.72633	−0.863167	+	0.504919i	$0.831523\pi$
$968$	2.13190e13	0.780418
$969$	0	0
$970$	2.97070e13	1.07742
$971$	3.50267e13	1.26448	0.632242	−	0.774771i	$-0.282135\pi$
$971$	3.50267e13	1.26448	0.632242	+	0.774771i	$0.282135\pi$
$972$	−5.10289e13	−1.83366
$973$	4.19578e12	0.150074
$974$	−3.46546e13	−1.23380
$975$	7.55375e13	2.67696
$976$	8.29575e12	0.292638
$977$	3.53570e13	1.24151	0.620754	−	0.784005i	$-0.286827\pi$
$977$	3.53570e13	1.24151	0.620754	+	0.784005i	$0.286827\pi$
$978$	−5.97138e12	−0.208713
$979$	3.31075e13	1.15187
$980$	1.29000e13	0.446757
$981$	−3.10290e13	−1.06969
$982$	1.16210e13	0.398786
$983$	−5.14055e13	−1.75598	−0.877988	−	0.478683i	$-0.841114\pi$
$983$	−5.14055e13	−1.75598	−0.877988	+	0.478683i	$0.841114\pi$
$984$	−3.72917e13	−1.26804
$985$	−5.16371e13	−1.74783
$986$	0	0
$987$	7.28962e13	2.44499
$988$	−8.84533e13	−2.95330
$989$	−3.30779e12	−0.109940
$990$	−1.50567e14	−4.98164
$991$	4.22728e13	1.39229	0.696146	−	0.717901i	$-0.254897\pi$
$991$	4.22728e13	1.39229	0.696146	+	0.717901i	$0.254897\pi$
$992$	1.81980e13	0.596651
$993$	1.73179e13	0.565228
$994$	−5.91552e12	−0.192200
$995$	7.15812e13	2.31524
$996$	−1.65992e14	−5.34464
$997$	2.68976e11	0.00862155	0.00431077	−	0.999991i	$-0.498628\pi$
$997$	2.68976e11	0.00862155	0.00431077	+	0.999991i	$0.498628\pi$
$998$	6.69857e13	2.13744
$999$	−1.79822e13	−0.571214

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.32	yes	36
17.16	even	2		289.10.a.g.1.32	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.32	✓	36	17.16	even	2
289.10.a.h.1.32	yes	36	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+37.7187 q^{2} +226.248 q^{3} +910.699 q^{4} +2062.07 q^{5} +8533.76 q^{6} +6871.89 q^{7} +15038.4 q^{8} +31505.0 q^{9} +O(q^{10})\)	\(q+37.7187 q^{2} +226.248 q^{3} +910.699 q^{4} +2062.07 q^{5} +8533.76 q^{6} +6871.89 q^{7} +15038.4 q^{8} +31505.0 q^{9} +77778.4 q^{10} -61445.8 q^{11} +206044. q^{12} +145225. q^{13} +259199. q^{14} +466538. q^{15} +100951. q^{16} +1.18833e6 q^{18} -668803. q^{19} +1.87792e6 q^{20} +1.55475e6 q^{21} -2.31765e6 q^{22} +470052. q^{23} +3.40240e6 q^{24} +2.29899e6 q^{25} +5.47769e6 q^{26} +2.67470e6 q^{27} +6.25823e6 q^{28} -5.12697e6 q^{29} +1.75972e7 q^{30} -4.67583e6 q^{31} -3.89193e6 q^{32} -1.39020e7 q^{33} +1.41703e7 q^{35} +2.86916e7 q^{36} -6.72308e6 q^{37} -2.52264e7 q^{38} +3.28568e7 q^{39} +3.10102e7 q^{40} -1.09604e7 q^{41} +5.86431e7 q^{42} -7.03708e6 q^{43} -5.59586e7 q^{44} +6.49654e7 q^{45} +1.77297e7 q^{46} +4.68861e7 q^{47} +2.28399e7 q^{48} +6.86929e6 q^{49} +8.67150e7 q^{50} +1.32256e8 q^{52} +2.76023e7 q^{53} +1.00886e8 q^{54} -1.26705e8 q^{55} +1.03342e8 q^{56} -1.51315e8 q^{57} -1.93382e8 q^{58} -7.22761e7 q^{59} +4.24876e8 q^{60} +8.21760e7 q^{61} -1.76366e8 q^{62} +2.16499e8 q^{63} -1.98485e8 q^{64} +2.99463e8 q^{65} -5.24364e8 q^{66} -1.82418e8 q^{67} +1.06348e8 q^{69} +5.34485e8 q^{70} -2.28223e7 q^{71} +4.73785e8 q^{72} +3.41963e8 q^{73} -2.53586e8 q^{74} +5.20142e8 q^{75} -6.09078e8 q^{76} -4.22249e8 q^{77} +1.23931e9 q^{78} +1.65497e8 q^{79} +2.08168e8 q^{80} -1.49683e7 q^{81} -4.13411e8 q^{82} -8.05614e8 q^{83} +1.41591e9 q^{84} -2.65430e8 q^{86} -1.15996e9 q^{87} -9.24047e8 q^{88} -5.38809e8 q^{89} +2.45041e9 q^{90} +9.97970e8 q^{91} +4.28076e8 q^{92} -1.05789e9 q^{93} +1.76848e9 q^{94} -1.37912e9 q^{95} -8.80539e8 q^{96} +3.81943e8 q^{97} +2.59100e8 q^{98} -1.93585e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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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