LMFDB - Embedded newform 43.8.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,8,Mod(1,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("43.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	43.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:	$13.4325560958$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 1279 x^{11} + 3765 x^{10} + 598742 x^{9} - 1518614 x^{8} - 124677082 x^{7} + \cdots + 1551032970660 $ x^13 - 3x^12 - 1279x^11 + 3765x^10 + 598742x^9 - 1518614x^8 - 124677082x^7 + 193428526x^6 + 11160446785x^5 + 1754605765x^4 - 349352939351x^3 - 481872751923x^2 + 2098464001560x + 1551032970660
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.684341$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.315659 q^{2} +82.9732 q^{3} -127.900 q^{4} +531.642 q^{5} +26.1913 q^{6} -349.841 q^{7} -80.7773 q^{8} +4697.55 q^{9} +O(q^{10})$	\(q+0.315659 q^{2} +82.9732 q^{3} -127.900 q^{4} +531.642 q^{5} +26.1913 q^{6} -349.841 q^{7} -80.7773 q^{8} +4697.55 q^{9} +167.818 q^{10} +3331.87 q^{11} -10612.3 q^{12} -8584.81 q^{13} -110.430 q^{14} +44112.0 q^{15} +16345.7 q^{16} -25786.3 q^{17} +1482.83 q^{18} +16993.6 q^{19} -67997.2 q^{20} -29027.4 q^{21} +1051.73 q^{22} +80723.2 q^{23} -6702.35 q^{24} +204518. q^{25} -2709.87 q^{26} +208308. q^{27} +44744.7 q^{28} -67762.5 q^{29} +13924.4 q^{30} +18887.5 q^{31} +15499.2 q^{32} +276455. q^{33} -8139.67 q^{34} -185990. q^{35} -600818. q^{36} -179478. q^{37} +5364.19 q^{38} -712309. q^{39} -42944.6 q^{40} -611192. q^{41} -9162.77 q^{42} -79507.0 q^{43} -426147. q^{44} +2.49741e6 q^{45} +25481.0 q^{46} -1.18047e6 q^{47} +1.35626e6 q^{48} -701155. q^{49} +64557.9 q^{50} -2.13957e6 q^{51} +1.09800e6 q^{52} +538854. q^{53} +65754.5 q^{54} +1.77136e6 q^{55} +28259.2 q^{56} +1.41001e6 q^{57} -21389.9 q^{58} -1.96283e6 q^{59} -5.64194e6 q^{60} +2.10797e6 q^{61} +5962.00 q^{62} -1.64339e6 q^{63} -2.08736e6 q^{64} -4.56404e6 q^{65} +87265.7 q^{66} -813166. q^{67} +3.29807e6 q^{68} +6.69786e6 q^{69} -58709.4 q^{70} +1.76280e6 q^{71} -379456. q^{72} -3.47624e6 q^{73} -56653.7 q^{74} +1.69695e7 q^{75} -2.17349e6 q^{76} -1.16562e6 q^{77} -224847. q^{78} -3.68544e6 q^{79} +8.69008e6 q^{80} +7.01047e6 q^{81} -192928. q^{82} +3.77929e6 q^{83} +3.71261e6 q^{84} -1.37091e7 q^{85} -25097.1 q^{86} -5.62247e6 q^{87} -269139. q^{88} -2.83826e6 q^{89} +788332. q^{90} +3.00331e6 q^{91} -1.03245e7 q^{92} +1.56715e6 q^{93} -372627. q^{94} +9.03452e6 q^{95} +1.28602e6 q^{96} +4.40344e6 q^{97} -221326. q^{98} +1.56516e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9}+O(q^{10}) $ 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9} + 4667 q^{10} + 1620 q^{11} - 19681 q^{12} + 13550 q^{13} + 44160 q^{14} + 31412 q^{15} + 114026 q^{16} + 110880 q^{17} + 159267 q^{18} + 105058 q^{19} + 167251 q^{20} + 129840 q^{21} + 201504 q^{22} + 160184 q^{23} + 161289 q^{24} + 270149 q^{25} + 272104 q^{26} + 252544 q^{27} + 208172 q^{28} + 285546 q^{29} + 107580 q^{30} - 99616 q^{31} + 200126 q^{32} + 531468 q^{33} - 80941 q^{34} - 187104 q^{35} - 608975 q^{36} + 176038 q^{37} + 652165 q^{38} - 794680 q^{39} - 895387 q^{40} - 410260 q^{41} - 3413218 q^{42} - 1033591 q^{43} - 2177076 q^{44} - 1051178 q^{45} - 3975765 q^{46} - 424556 q^{47} - 2360477 q^{48} - 1561359 q^{49} - 4063801 q^{50} - 2375738 q^{51} - 4172312 q^{52} + 3992458 q^{53} - 10438626 q^{54} + 406960 q^{55} + 1559556 q^{56} - 3116152 q^{57} - 4052005 q^{58} + 2248836 q^{59} - 2911436 q^{60} + 6210394 q^{61} + 885317 q^{62} + 11622368 q^{63} - 3096318 q^{64} + 5600420 q^{65} - 2174604 q^{66} - 1993648 q^{67} + 9327135 q^{68} + 13366240 q^{69} - 1105098 q^{70} + 4978064 q^{71} + 11370663 q^{72} + 8224814 q^{73} - 3613563 q^{74} + 27115592 q^{75} + 10687121 q^{76} + 17261892 q^{77} - 15226630 q^{78} + 6945708 q^{79} + 15822799 q^{80} + 35113185 q^{81} - 508449 q^{82} + 22937328 q^{83} - 14010106 q^{84} - 575532 q^{85} - 1272112 q^{86} + 9081380 q^{87} + 11202656 q^{88} + 9291302 q^{89} + 2841402 q^{90} + 25581108 q^{91} - 14388137 q^{92} + 25930480 q^{93} - 24645805 q^{94} + 30750464 q^{95} - 22461255 q^{96} + 10001852 q^{97} - 32304856 q^{98} + 5055452 q^{99}+O(q^{100}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9 + 4667 * q^10 + 1620 * q^11 - 19681 * q^12 + 13550 * q^13 + 44160 * q^14 + 31412 * q^15 + 114026 * q^16 + 110880 * q^17 + 159267 * q^18 + 105058 * q^19 + 167251 * q^20 + 129840 * q^21 + 201504 * q^22 + 160184 * q^23 + 161289 * q^24 + 270149 * q^25 + 272104 * q^26 + 252544 * q^27 + 208172 * q^28 + 285546 * q^29 + 107580 * q^30 - 99616 * q^31 + 200126 * q^32 + 531468 * q^33 - 80941 * q^34 - 187104 * q^35 - 608975 * q^36 + 176038 * q^37 + 652165 * q^38 - 794680 * q^39 - 895387 * q^40 - 410260 * q^41 - 3413218 * q^42 - 1033591 * q^43 - 2177076 * q^44 - 1051178 * q^45 - 3975765 * q^46 - 424556 * q^47 - 2360477 * q^48 - 1561359 * q^49 - 4063801 * q^50 - 2375738 * q^51 - 4172312 * q^52 + 3992458 * q^53 - 10438626 * q^54 + 406960 * q^55 + 1559556 * q^56 - 3116152 * q^57 - 4052005 * q^58 + 2248836 * q^59 - 2911436 * q^60 + 6210394 * q^61 + 885317 * q^62 + 11622368 * q^63 - 3096318 * q^64 + 5600420 * q^65 - 2174604 * q^66 - 1993648 * q^67 + 9327135 * q^68 + 13366240 * q^69 - 1105098 * q^70 + 4978064 * q^71 + 11370663 * q^72 + 8224814 * q^73 - 3613563 * q^74 + 27115592 * q^75 + 10687121 * q^76 + 17261892 * q^77 - 15226630 * q^78 + 6945708 * q^79 + 15822799 * q^80 + 35113185 * q^81 - 508449 * q^82 + 22937328 * q^83 - 14010106 * q^84 - 575532 * q^85 - 1272112 * q^86 + 9081380 * q^87 + 11202656 * q^88 + 9291302 * q^89 + 2841402 * q^90 + 25581108 * q^91 - 14388137 * q^92 + 25930480 * q^93 - 24645805 * q^94 + 30750464 * q^95 - 22461255 * q^96 + 10001852 * q^97 - 32304856 * q^98 + 5055452 * 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 $

$2$	0.315659	0.0279006	0.0139503	−	0.999903i	$-0.495559\pi$
$2$	0.315659	0.0279006	0.0139503	+	0.999903i	$0.495559\pi$
$3$	82.9732	1.77424	0.887122	−	0.461535i	$-0.152701\pi$
$3$	82.9732	1.77424	0.887122	+	0.461535i	$0.152701\pi$
$4$	−127.900	−0.999222
$5$	531.642	1.90206	0.951029	−	0.309100i	$-0.100028\pi$
$5$	531.642	1.90206	0.951029	+	0.309100i	$0.100028\pi$
$6$	26.1913	0.0495025
$7$	−349.841	−0.385502	−0.192751	−	0.981248i	$-0.561741\pi$
$7$	−349.841	−0.385502	−0.192751	+	0.981248i	$0.561741\pi$
$8$	−80.7773	−0.0557795
$9$	4697.55	2.14794
$10$	167.818	0.0530686
$11$	3331.87	0.754767	0.377384	−	0.926057i	$-0.376824\pi$
$11$	3331.87	0.754767	0.377384	+	0.926057i	$0.376824\pi$
$12$	−10612.3	−1.77286
$13$	−8584.81	−1.08375	−0.541875	−	0.840459i	$-0.682285\pi$
$13$	−8584.81	−1.08375	−0.541875	+	0.840459i	$0.682285\pi$
$14$	−110.430	−0.0107557
$15$	44112.0	3.37472
$16$	16345.7	0.997665
$17$	−25786.3	−1.27297	−0.636484	−	0.771290i	$-0.719612\pi$
$17$	−25786.3	−1.27297	−0.636484	+	0.771290i	$0.719612\pi$
$18$	1482.83	0.0599289
$19$	16993.6	0.568392	0.284196	−	0.958766i	$-0.408273\pi$
$19$	16993.6	0.568392	0.284196	+	0.958766i	$0.408273\pi$
$20$	−67997.2	−1.90058
$21$	−29027.4	−0.683975
$22$	1051.73	0.0210585
$23$	80723.2	1.38341	0.691705	−	0.722180i	$-0.256860\pi$
$23$	80723.2	1.38341	0.691705	+	0.722180i	$0.256860\pi$
$24$	−6702.35	−0.0989664
$25$	204518.	2.61783
$26$	−2709.87	−0.0302373
$27$	208308.	2.03673
$28$	44744.7	0.385202
$29$	−67762.5	−0.515937	−0.257968	−	0.966153i	$-0.583053\pi$
$29$	−67762.5	−0.515937	−0.257968	+	0.966153i	$0.583053\pi$
$30$	13924.4	0.0941566
$31$	18887.5	0.113870	0.0569348	−	0.998378i	$-0.481867\pi$
$31$	18887.5	0.113870	0.0569348	+	0.998378i	$0.481867\pi$
$32$	15499.2	0.0836150
$33$	276455.	1.33914
$34$	−8139.67	−0.0355166
$35$	−185990.	−0.733248
$36$	−600818.	−2.14627
$37$	−179478.	−0.582511	−0.291255	−	0.956645i	$-0.594073\pi$
$37$	−179478.	−0.582511	−0.291255	+	0.956645i	$0.594073\pi$
$38$	5364.19	0.0158585
$39$	−712309.	−1.92284
$40$	−42944.6	−0.106096
$41$	−611192.	−1.38495	−0.692475	−	0.721442i	$-0.743480\pi$
$41$	−611192.	−1.38495	−0.692475	+	0.721442i	$0.743480\pi$
$42$	−9162.77	−0.0190833
$43$	−79507.0	−0.152499
$43$	−79507.0	−0.152499
$44$	−426147.	−0.754180
$45$	2.49741e6	4.08551
$46$	25481.0	0.0385980
$47$	−1.18047e6	−1.65849	−0.829245	−	0.558885i	$-0.811229\pi$
$47$	−1.18047e6	−1.65849	−0.829245	+	0.558885i	$0.811229\pi$
$48$	1.35626e6	1.77010
$49$	−701155.	−0.851388
$50$	64557.9	0.0730390
$51$	−2.13957e6	−2.25855
$52$	1.09800e6	1.08291
$53$	538854.	0.497170	0.248585	−	0.968610i	$-0.420034\pi$
$53$	538854.	0.497170	0.248585	+	0.968610i	$0.420034\pi$
$54$	65754.5	0.0568260
$55$	1.77136e6	1.43561
$56$	28259.2	0.0215031
$57$	1.41001e6	1.00847
$58$	−21389.9	−0.0143949
$59$	−1.96283e6	−1.24423	−0.622113	−	0.782927i	$-0.713726\pi$
$59$	−1.96283e6	−1.24423	−0.622113	+	0.782927i	$0.713726\pi$
$60$	−5.64194e6	−3.37209
$61$	2.10797e6	1.18907	0.594537	−	0.804068i	$-0.297335\pi$
$61$	2.10797e6	1.18907	0.594537	+	0.804068i	$0.297335\pi$
$62$	5962.00	0.00317703
$63$	−1.64339e6	−0.828037
$64$	−2.08736e6	−0.995332
$65$	−4.56404e6	−2.06136
$66$	87265.7	0.0373629
$67$	−813166.	−0.330307	−0.165153	−	0.986268i	$-0.552812\pi$
$67$	−813166.	−0.330307	−0.165153	+	0.986268i	$0.552812\pi$
$68$	3.29807e6	1.27198
$69$	6.69786e6	2.45451
$70$	−58709.4	−0.0204581
$71$	1.76280e6	0.584521	0.292260	−	0.956339i	$-0.405593\pi$
$71$	1.76280e6	0.584521	0.292260	+	0.956339i	$0.405593\pi$
$72$	−379456.	−0.119811
$73$	−3.47624e6	−1.04588	−0.522938	−	0.852371i	$-0.675164\pi$
$73$	−3.47624e6	−1.04588	−0.522938	+	0.852371i	$0.675164\pi$
$74$	−56653.7	−0.0162524
$75$	1.69695e7	4.64467
$76$	−2.17349e6	−0.567950
$77$	−1.16562e6	−0.290965
$78$	−224847.	−0.0536483
$79$	−3.68544e6	−0.840997	−0.420498	−	0.907293i	$-0.638145\pi$
$79$	−3.68544e6	−0.840997	−0.420498	+	0.907293i	$0.638145\pi$
$80$	8.69008e6	1.89762
$81$	7.01047e6	1.46571
$82$	−192928.	−0.0386409
$83$	3.77929e6	0.725500	0.362750	−	0.931887i	$-0.381838\pi$
$83$	3.77929e6	0.725500	0.362750	+	0.931887i	$0.381838\pi$
$84$	3.71261e6	0.683443
$85$	−1.37091e7	−2.42126
$86$	−25097.1	−0.00425480
$87$	−5.62247e6	−0.915398
$88$	−269139.	−0.0421005
$89$	−2.83826e6	−0.426764	−0.213382	−	0.976969i	$-0.568448\pi$
$89$	−2.83826e6	−0.426764	−0.213382	+	0.976969i	$0.568448\pi$
$90$	788332.	0.113988
$91$	3.00331e6	0.417788
$92$	−1.03245e7	−1.38233
$93$	1.56715e6	0.202032
$94$	−372627.	−0.0462729
$95$	9.03452e6	1.08112
$96$	1.28602e6	0.148353
$97$	4.40344e6	0.489882	0.244941	−	0.969538i	$-0.421231\pi$
$97$	4.40344e6	0.489882	0.244941	+	0.969538i	$0.421231\pi$
$98$	−221326.	−0.0237542
$99$	1.56516e7	1.62120
$100$	−2.61579e7	−2.61579
$101$	−5.88409e6	−0.568269	−0.284135	−	0.958784i	$-0.591706\pi$
$101$	−5.88409e6	−0.568269	−0.284135	+	0.958784i	$0.591706\pi$
$102$	−675375.	−0.0630150
$103$	698841.	0.0630156	0.0315078	−	0.999504i	$-0.489969\pi$
$103$	698841.	0.0630156	0.0315078	+	0.999504i	$0.489969\pi$
$104$	693458.	0.0604510
$105$	−1.54322e7	−1.30096
$106$	170094.	0.0138714
$107$	−2.58664e6	−0.204123	−0.102062	−	0.994778i	$-0.532544\pi$
$107$	−2.58664e6	−0.204123	−0.102062	+	0.994778i	$0.532544\pi$
$108$	−2.66427e7	−2.03515
$109$	1.24939e7	0.924070	0.462035	−	0.886862i	$-0.347119\pi$
$109$	1.24939e7	0.924070	0.462035	+	0.886862i	$0.347119\pi$
$110$	559146.	0.0400544
$111$	−1.48918e7	−1.03352
$112$	−5.71841e6	−0.384602
$113$	1.92969e7	1.25810	0.629048	−	0.777367i	$-0.283445\pi$
$113$	1.92969e7	1.25810	0.629048	+	0.777367i	$0.283445\pi$
$114$	445084.	0.0281368
$115$	4.29158e7	2.63133
$116$	8.66685e6	0.515535
$117$	−4.03276e7	−2.32783
$118$	−619584.	−0.0347147
$119$	9.02108e6	0.490732
$120$	−3.56325e6	−0.188240
$121$	−8.38585e6	−0.430326
$122$	665399.	0.0331759
$123$	−5.07125e7	−2.45724
$124$	−2.41571e6	−0.113781
$125$	6.71957e7	3.07720
$126$	−518753.	−0.0231027
$127$	−5.00899e6	−0.216989	−0.108494	−	0.994097i	$-0.534603\pi$
$127$	−5.00899e6	−0.216989	−0.108494	+	0.994097i	$0.534603\pi$
$128$	−2.64279e6	−0.111385
$129$	−6.59695e6	−0.270570
$130$	−1.44068e6	−0.0575131
$131$	−4.18902e7	−1.62803	−0.814016	−	0.580843i	$-0.802723\pi$
$131$	−4.18902e7	−1.62803	−0.814016	+	0.580843i	$0.802723\pi$
$132$	−3.53588e7	−1.33810
$133$	−5.94506e6	−0.219117
$134$	−256683.	−0.00921575
$135$	1.10745e8	3.87398
$136$	2.08295e6	0.0710055
$137$	3.89920e7	1.29555	0.647774	−	0.761833i	$-0.275700\pi$
$137$	3.89920e7	1.29555	0.647774	+	0.761833i	$0.275700\pi$
$138$	2.11424e6	0.0684823
$139$	6.03467e7	1.90591	0.952954	−	0.303115i	$-0.0980267\pi$
$139$	6.03467e7	1.90591	0.952954	+	0.303115i	$0.0980267\pi$
$140$	2.37882e7	0.732677
$141$	−9.79475e7	−2.94257
$142$	556446.	0.0163085
$143$	−2.86034e7	−0.817978
$144$	7.67850e7	2.14293
$145$	−3.60254e7	−0.981342
$146$	−1.09731e6	−0.0291806
$147$	−5.81770e7	−1.51057
$148$	2.29552e7	0.582057
$149$	−1.86557e7	−0.462018	−0.231009	−	0.972952i	$-0.574203\pi$
$149$	−1.86557e7	−0.462018	−0.231009	+	0.972952i	$0.574203\pi$
$150$	5.35658e6	0.129589
$151$	−1.15952e7	−0.274070	−0.137035	−	0.990566i	$-0.543757\pi$
$151$	−1.15952e7	−0.274070	−0.137035	+	0.990566i	$0.543757\pi$
$152$	−1.37270e6	−0.0317046
$153$	−1.21132e8	−2.73426
$154$	−367939.	−0.00811809
$155$	1.00414e7	0.216587
$156$	9.11046e7	1.92134
$157$	2.89477e7	0.596988	0.298494	−	0.954412i	$-0.403516\pi$
$157$	2.89477e7	0.596988	0.298494	+	0.954412i	$0.403516\pi$
$158$	−1.16334e6	−0.0234643
$159$	4.47104e7	0.882102
$160$	8.24001e6	0.159041
$161$	−2.82403e7	−0.533308
$162$	2.21292e6	0.0408943
$163$	779647.	0.0141007	0.00705036	−	0.999975i	$-0.497756\pi$
$163$	779647.	0.0141007	0.00705036	+	0.999975i	$0.497756\pi$
$164$	7.81716e7	1.38387
$165$	1.46975e8	2.54713
$166$	1.19297e6	0.0202419
$167$	−4.18156e7	−0.694754	−0.347377	−	0.937726i	$-0.612928\pi$
$167$	−4.18156e7	−0.694754	−0.347377	+	0.937726i	$0.612928\pi$
$168$	2.34476e6	0.0381518
$169$	1.09504e7	0.174513
$170$	−4.32739e6	−0.0675546
$171$	7.98284e7	1.22087
$172$	1.01690e7	0.152380
$173$	9.94492e7	1.46029	0.730147	−	0.683291i	$-0.239452\pi$
$173$	9.94492e7	1.46029	0.730147	+	0.683291i	$0.239452\pi$
$174$	−1.77478e6	−0.0255401
$175$	−7.15486e7	−1.00918
$176$	5.44618e7	0.753005
$177$	−1.62862e8	−2.20756
$178$	−895924.	−0.0119070
$179$	7.81297e7	1.01819	0.509097	−	0.860709i	$-0.329979\pi$
$179$	7.81297e7	1.01819	0.509097	+	0.860709i	$0.329979\pi$
$180$	−3.19420e8	−4.08233
$181$	1.22327e7	0.153337	0.0766684	−	0.997057i	$-0.475572\pi$
$181$	1.22327e7	0.153337	0.0766684	+	0.997057i	$0.475572\pi$
$182$	948024.	0.0116565
$183$	1.74905e8	2.10971
$184$	−6.52061e6	−0.0771659
$185$	−9.54177e7	−1.10797
$186$	494686.	0.00563682
$187$	−8.59164e7	−0.960794
$188$	1.50983e8	1.65720
$189$	−7.28747e7	−0.785164
$190$	2.85183e6	0.0301638
$191$	−9.63352e7	−1.00039	−0.500194	−	0.865914i	$-0.666738\pi$
$191$	−9.63352e7	−1.00039	−0.500194	+	0.865914i	$0.666738\pi$
$192$	−1.73195e8	−1.76596
$193$	2.89017e7	0.289383	0.144692	−	0.989477i	$-0.453781\pi$
$193$	2.89017e7	0.289383	0.144692	+	0.989477i	$0.453781\pi$
$194$	1.38999e6	0.0136680
$195$	−3.78693e8	−3.65735
$196$	8.96779e7	0.850725
$197$	4.17794e7	0.389342	0.194671	−	0.980869i	$-0.437636\pi$
$197$	4.17794e7	0.389342	0.194671	+	0.980869i	$0.437636\pi$
$198$	4.94057e6	0.0452324
$199$	5.54068e7	0.498399	0.249199	−	0.968452i	$-0.419833\pi$
$199$	5.54068e7	0.498399	0.249199	+	0.968452i	$0.419833\pi$
$200$	−1.65204e7	−0.146021
$201$	−6.74710e7	−0.586045
$202$	−1.85737e6	−0.0158551
$203$	2.37061e7	0.198895
$204$	2.73652e8	2.25680
$205$	−3.24935e8	−2.63426
$206$	220596.	0.00175817
$207$	3.79201e8	2.97149
$208$	−1.40325e8	−1.08122
$209$	5.66205e7	0.429004
$210$	−4.87131e6	−0.0362976
$211$	−9.44194e7	−0.691947	−0.345973	−	0.938244i	$-0.612451\pi$
$211$	−9.44194e7	−0.691947	−0.345973	+	0.938244i	$0.612451\pi$
$212$	−6.89196e7	−0.496783
$213$	1.46265e8	1.03708
$214$	−816497.	−0.00569517
$215$	−4.22692e7	−0.290061
$216$	−1.68266e7	−0.113608
$217$	−6.60760e6	−0.0438970
$218$	3.94381e6	0.0257821
$219$	−2.88435e8	−1.85564
$220$	−2.26557e8	−1.43449
$221$	2.21370e8	1.37958
$222$	−4.70074e6	−0.0288357
$223$	1.04942e7	0.0633697	0.0316848	−	0.999498i	$-0.489913\pi$
$223$	1.04942e7	0.0633697	0.0316848	+	0.999498i	$0.489913\pi$
$224$	−5.42224e6	−0.0322338
$225$	9.60733e8	5.62294
$226$	6.09126e6	0.0351016
$227$	2.42554e7	0.137632	0.0688158	−	0.997629i	$-0.478078\pi$
$227$	2.42554e7	0.137632	0.0688158	+	0.997629i	$0.478078\pi$
$228$	−1.80341e8	−1.00768
$229$	7.20589e7	0.396519	0.198259	−	0.980150i	$-0.436471\pi$
$229$	7.20589e7	0.396519	0.198259	+	0.980150i	$0.436471\pi$
$230$	1.35468e7	0.0734157
$231$	−9.67153e7	−0.516242
$232$	5.47367e6	0.0287787
$233$	6.20516e7	0.321372	0.160686	−	0.987006i	$-0.448629\pi$
$233$	6.20516e7	0.321372	0.160686	+	0.987006i	$0.448629\pi$
$234$	−1.27298e7	−0.0649479
$235$	−6.27588e8	−3.15455
$236$	2.51046e8	1.24326
$237$	−3.05792e8	−1.49213
$238$	2.84759e6	0.0136917
$239$	1.05074e8	0.497853	0.248926	−	0.968522i	$-0.419922\pi$
$239$	1.05074e8	0.497853	0.248926	+	0.968522i	$0.419922\pi$
$240$	7.21044e8	3.36684
$241$	3.02273e8	1.39104	0.695520	−	0.718507i	$-0.255174\pi$
$241$	3.02273e8	1.39104	0.695520	+	0.718507i	$0.255174\pi$
$242$	−2.64707e6	−0.0120064
$243$	1.26111e8	0.563806
$244$	−2.69610e8	−1.18815
$245$	−3.72763e8	−1.61939
$246$	−1.60079e7	−0.0685584
$247$	−1.45887e8	−0.615995
$248$	−1.52568e6	−0.00635158
$249$	3.13580e8	1.28721
$250$	2.12109e7	0.0858558
$251$	−1.60365e8	−0.640105	−0.320052	−	0.947400i	$-0.603701\pi$
$251$	−1.60365e8	−0.640105	−0.320052	+	0.947400i	$0.603701\pi$
$252$	2.10191e8	0.827392
$253$	2.68959e8	1.04415
$254$	−1.58114e6	−0.00605412
$255$	−1.13748e9	−4.29590
$256$	2.66348e8	0.992225
$257$	9.94729e7	0.365543	0.182772	−	0.983155i	$-0.441493\pi$
$257$	9.94729e7	0.365543	0.182772	+	0.983155i	$0.441493\pi$
$258$	−2.08239e6	−0.00754906
$259$	6.27885e7	0.224559
$260$	5.83743e8	2.05975
$261$	−3.18318e8	−1.10820
$262$	−1.32230e7	−0.0454231
$263$	1.41037e7	0.0478066	0.0239033	−	0.999714i	$-0.492391\pi$
$263$	1.41037e7	0.0478066	0.0239033	+	0.999714i	$0.492391\pi$
$264$	−2.23313e7	−0.0746966
$265$	2.86477e8	0.945647
$266$	−1.87661e6	−0.00611349
$267$	−2.35500e8	−0.757183
$268$	1.04004e8	0.330049
$269$	9.31759e7	0.291857	0.145929	−	0.989295i	$-0.453383\pi$
$269$	9.31759e7	0.291857	0.145929	+	0.989295i	$0.453383\pi$
$270$	3.49578e7	0.108086
$271$	4.68939e8	1.43128	0.715639	−	0.698470i	$-0.246135\pi$
$271$	4.68939e8	1.43128	0.715639	+	0.698470i	$0.246135\pi$
$272$	−4.21496e8	−1.27000
$273$	2.49195e8	0.741258
$274$	1.23082e7	0.0361466
$275$	6.81426e8	1.97585
$276$	−8.56659e8	−2.45260
$277$	−6.06565e7	−0.171474	−0.0857370	−	0.996318i	$-0.527324\pi$
$277$	−6.06565e7	−0.171474	−0.0857370	+	0.996318i	$0.527324\pi$
$278$	1.90490e7	0.0531760
$279$	8.87248e7	0.244585
$280$	1.50238e7	0.0409002
$281$	−6.12917e8	−1.64789	−0.823947	−	0.566667i	$-0.808233\pi$
$281$	−6.12917e8	−1.64789	−0.823947	+	0.566667i	$0.808233\pi$
$282$	−3.09180e7	−0.0820994
$283$	−6.99501e8	−1.83458	−0.917288	−	0.398224i	$-0.869627\pi$
$283$	−6.99501e8	−1.83458	−0.917288	+	0.398224i	$0.869627\pi$
$284$	−2.25463e8	−0.584066
$285$	7.49623e8	1.91816
$286$	−9.02894e6	−0.0228221
$287$	2.13820e8	0.533901
$288$	7.28082e7	0.179600
$289$	2.54593e8	0.620446
$290$	−1.13717e7	−0.0273800
$291$	3.65368e8	0.869170
$292$	4.44613e8	1.04506
$293$	7.00364e8	1.62662	0.813312	−	0.581828i	$-0.197662\pi$
$293$	7.00364e8	1.62662	0.813312	+	0.581828i	$0.197662\pi$
$294$	−1.83641e7	−0.0421458
$295$	−1.04352e9	−2.36659
$296$	1.44977e7	0.0324922
$297$	6.94055e8	1.53726
$298$	−5.88884e6	−0.0128906
$299$	−6.92994e8	−1.49927
$300$	−2.17040e9	−4.64105
$301$	2.78148e7	0.0587886
$302$	−3.66015e6	−0.00764671
$303$	−4.88221e8	−1.00825
$304$	2.77773e8	0.567065
$305$	1.12068e9	2.26169
$306$	−3.82365e7	−0.0762875
$307$	5.88458e8	1.16073	0.580365	−	0.814357i	$-0.302910\pi$
$307$	5.88458e8	1.16073	0.580365	+	0.814357i	$0.302910\pi$
$308$	1.49083e8	0.290738
$309$	5.79850e7	0.111805
$310$	3.16965e6	0.00604290
$311$	7.48619e7	0.141123	0.0705617	−	0.997507i	$-0.477521\pi$
$311$	7.48619e7	0.141123	0.0705617	+	0.997507i	$0.477521\pi$
$312$	5.75384e7	0.107255
$313$	2.61454e8	0.481937	0.240969	−	0.970533i	$-0.422535\pi$
$313$	2.61454e8	0.481937	0.240969	+	0.970533i	$0.422535\pi$
$314$	9.13762e6	0.0166563
$315$	−8.73697e8	−1.57498
$316$	4.71369e8	0.840342
$317$	−1.08258e9	−1.90877	−0.954384	−	0.298582i	$-0.903486\pi$
$317$	−1.08258e9	−1.90877	−0.954384	+	0.298582i	$0.903486\pi$
$318$	1.41133e7	0.0246112
$319$	−2.25775e8	−0.389412
$320$	−1.10973e9	−1.89318
$321$	−2.14622e8	−0.362165
$322$	−8.91430e6	−0.0148796
$323$	−4.38202e8	−0.723545
$324$	−8.96641e8	−1.46457
$325$	−1.75575e9	−2.83707
$326$	246103.	0.000393419 0
$327$	1.03666e9	1.63953
$328$	4.93704e7	0.0772518
$329$	4.12977e8	0.639352
$330$	4.63941e7	0.0710663
$331$	−4.20559e8	−0.637425	−0.318713	−	0.947851i	$-0.603250\pi$
$331$	−4.20559e8	−0.637425	−0.318713	+	0.947851i	$0.603250\pi$
$332$	−4.83373e8	−0.724935
$333$	−8.43105e8	−1.25120
$334$	−1.31995e7	−0.0193841
$335$	−4.32313e8	−0.628263
$336$	−4.74474e8	−0.682378
$337$	1.18120e9	1.68119	0.840597	−	0.541662i	$-0.182205\pi$
$337$	1.18120e9	1.68119	0.840597	+	0.541662i	$0.182205\pi$
$338$	3.45660e6	0.00486901
$339$	1.60113e9	2.23217
$340$	1.75339e9	2.41937
$341$	6.29305e7	0.0859450
$342$	2.51986e7	0.0340631
$343$	5.33401e8	0.713714
$344$	6.42236e6	0.00850629
$345$	3.56086e9	4.66862
$346$	3.13921e7	0.0407431
$347$	1.04092e9	1.33741	0.668707	−	0.743526i	$-0.266848\pi$
$347$	1.04092e9	1.33741	0.668707	+	0.743526i	$0.266848\pi$
$348$	7.19116e8	0.914685
$349$	−6.58581e8	−0.829316	−0.414658	−	0.909977i	$-0.636099\pi$
$349$	−6.58581e8	−0.829316	−0.414658	+	0.909977i	$0.636099\pi$
$350$	−2.25850e7	−0.0281567
$351$	−1.78829e9	−2.20731
$352$	5.16412e7	0.0631098
$353$	3.03399e8	0.367115	0.183557	−	0.983009i	$-0.441239\pi$
$353$	3.03399e8	0.367115	0.183557	+	0.983009i	$0.441239\pi$
$354$	−5.14089e7	−0.0615923
$355$	9.37180e8	1.11179
$356$	3.63015e8	0.426431
$357$	7.48508e8	0.870678
$358$	2.46624e7	0.0284082
$359$	1.42234e9	1.62245	0.811226	−	0.584733i	$-0.198801\pi$
$359$	1.42234e9	1.62245	0.811226	+	0.584733i	$0.198801\pi$
$360$	−2.01734e8	−0.227888
$361$	−6.05089e8	−0.676930
$362$	3.86136e6	0.00427819
$363$	−6.95800e8	−0.763504
$364$	−3.84125e8	−0.417463
$365$	−1.84812e9	−1.98932
$366$	5.52103e7	0.0588621
$367$	5.93187e8	0.626413	0.313206	−	0.949685i	$-0.398597\pi$
$367$	5.93187e8	0.626413	0.313206	+	0.949685i	$0.398597\pi$
$368$	1.31948e9	1.38018
$369$	−2.87110e9	−2.97479
$370$	−3.01195e7	−0.0309130
$371$	−1.88513e8	−0.191660
$372$	−2.00439e8	−0.201875
$373$	−3.41490e8	−0.340719	−0.170360	−	0.985382i	$-0.554493\pi$
$373$	−3.41490e8	−0.340719	−0.170360	+	0.985382i	$0.554493\pi$
$374$	−2.71203e7	−0.0268067
$375$	5.57544e9	5.45971
$376$	9.53553e7	0.0925098
$377$	5.81728e8	0.559146
$378$	−2.30036e7	−0.0219066
$379$	−1.21788e9	−1.14912	−0.574561	−	0.818462i	$-0.694827\pi$
$379$	−1.21788e9	−1.14912	−0.574561	+	0.818462i	$0.694827\pi$
$380$	−1.15552e9	−1.08027
$381$	−4.15612e8	−0.384991
$382$	−3.04091e7	−0.0279114
$383$	1.21649e9	1.10640	0.553200	−	0.833048i	$-0.313406\pi$
$383$	1.21649e9	1.10640	0.553200	+	0.833048i	$0.313406\pi$
$384$	−2.19281e8	−0.197625
$385$	−6.19693e8	−0.553432
$386$	9.12310e6	0.00807397
$387$	−3.73488e8	−0.327558
$388$	−5.63202e8	−0.489500
$389$	−2.23009e7	−0.0192087	−0.00960436	−	0.999954i	$-0.503057\pi$
$389$	−2.23009e7	−0.0192087	−0.00960436	+	0.999954i	$0.503057\pi$
$390$	−1.19538e8	−0.102042
$391$	−2.08155e9	−1.76104
$392$	5.66374e7	0.0474900
$393$	−3.47576e9	−2.88853
$394$	1.31881e7	0.0108629
$395$	−1.95933e9	−1.59962
$396$	−2.00185e9	−1.61993
$397$	−8.33419e8	−0.668493	−0.334246	−	0.942486i	$-0.608482\pi$
$397$	−8.33419e8	−0.668493	−0.334246	+	0.942486i	$0.608482\pi$
$398$	1.74897e7	0.0139056
$399$	−4.93280e8	−0.388766
$400$	3.34300e9	2.61172
$401$	−1.28321e9	−0.993786	−0.496893	−	0.867812i	$-0.665526\pi$
$401$	−1.28321e9	−0.993786	−0.496893	+	0.867812i	$0.665526\pi$
$402$	−2.12978e7	−0.0163510
$403$	−1.62145e8	−0.123406
$404$	7.52577e8	0.567827
$405$	3.72706e9	2.78788
$406$	7.48304e6	0.00554928
$407$	−5.97995e8	−0.439660
$408$	1.72829e8	0.125981
$409$	3.97834e8	0.287522	0.143761	−	0.989612i	$-0.454080\pi$
$409$	3.97834e8	0.287522	0.143761	+	0.989612i	$0.454080\pi$
$410$	−1.02569e8	−0.0734973
$411$	3.23529e9	2.29862
$412$	−8.93820e7	−0.0629665
$413$	6.86676e8	0.479652
$414$	1.19698e8	0.0829063
$415$	2.00923e9	1.37994
$416$	−1.33058e8	−0.0906177
$417$	5.00716e9	3.38155
$418$	1.78728e7	0.0119695
$419$	−1.83847e9	−1.22097	−0.610487	−	0.792026i	$-0.709026\pi$
$419$	−1.83847e9	−1.22097	−0.610487	+	0.792026i	$0.709026\pi$
$420$	1.97378e9	1.29995
$421$	2.99208e9	1.95428	0.977139	−	0.212604i	$-0.0681943\pi$
$421$	2.99208e9	1.95428	0.977139	+	0.212604i	$0.0681943\pi$
$422$	−2.98044e7	−0.0193057
$423$	−5.54532e9	−3.56234
$424$	−4.35272e7	−0.0277319
$425$	−5.27375e9	−3.33241
$426$	4.61701e7	0.0289352
$427$	−7.37452e8	−0.458391
$428$	3.30832e8	0.203965
$429$	−2.37332e9	−1.45129
$430$	−1.33427e7	−0.00809288
$431$	7.52649e7	0.0452816	0.0226408	−	0.999744i	$-0.492793\pi$
$431$	7.52649e7	0.0452816	0.0226408	+	0.999744i	$0.492793\pi$
$432$	3.40496e9	2.03198
$433$	2.36792e9	1.40172	0.700858	−	0.713301i	$-0.252801\pi$
$433$	2.36792e9	1.40172	0.700858	+	0.713301i	$0.252801\pi$
$434$	−2.08575e6	−0.00122475
$435$	−2.98914e9	−1.74114
$436$	−1.59797e9	−0.923351
$437$	1.37178e9	0.786320
$438$	−9.10472e7	−0.0517735
$439$	1.98503e9	1.11980	0.559901	−	0.828559i	$-0.310839\pi$
$439$	1.98503e9	1.11980	0.559901	+	0.828559i	$0.310839\pi$
$440$	−1.43086e8	−0.0800777
$441$	−3.29371e9	−1.82873
$442$	6.98775e7	0.0384910
$443$	−2.46053e9	−1.34467	−0.672335	−	0.740247i	$-0.734709\pi$
$443$	−2.46053e9	−1.34467	−0.672335	+	0.740247i	$0.734709\pi$
$444$	1.90467e9	1.03271
$445$	−1.50894e9	−0.811730
$446$	3.31259e6	0.00176805
$447$	−1.54792e9	−0.819734
$448$	7.30244e8	0.383703
$449$	−1.53414e9	−0.799839	−0.399920	−	0.916550i	$-0.630962\pi$
$449$	−1.53414e9	−0.799839	−0.399920	+	0.916550i	$0.630962\pi$
$450$	3.03264e8	0.156884
$451$	−2.03641e9	−1.04531
$452$	−2.46808e9	−1.25712
$453$	−9.62095e8	−0.486266
$454$	7.65645e6	0.00384000
$455$	1.59669e9	0.794657
$456$	−1.13897e8	−0.0562518
$457$	1.63707e9	0.802345	0.401173	−	0.916002i	$-0.368603\pi$
$457$	1.63707e9	0.802345	0.401173	+	0.916002i	$0.368603\pi$
$458$	2.27461e7	0.0110631
$459$	−5.37150e9	−2.59269
$460$	−5.48895e9	−2.62928
$461$	3.59530e9	1.70916	0.854579	−	0.519321i	$-0.173815\pi$
$461$	3.59530e9	1.70916	0.854579	+	0.519321i	$0.173815\pi$
$462$	−3.05291e7	−0.0144035
$463$	−3.31932e9	−1.55423	−0.777115	−	0.629359i	$-0.783318\pi$
$463$	−3.31932e9	−1.55423	−0.777115	+	0.629359i	$0.783318\pi$
$464$	−1.10763e9	−0.514732
$465$	8.33163e8	0.384277
$466$	1.95872e7	0.00896646
$467$	2.20717e9	1.00283	0.501415	−	0.865207i	$-0.332813\pi$
$467$	2.20717e9	1.00283	0.501415	+	0.865207i	$0.332813\pi$
$468$	5.15791e9	2.32602
$469$	2.84478e8	0.127334
$470$	−1.98104e8	−0.0880138
$471$	2.40188e9	1.05920
$472$	1.58552e8	0.0694023
$473$	−2.64907e8	−0.115101
$474$	−9.65262e7	−0.0416314
$475$	3.47550e9	1.48795
$476$	−1.15380e9	−0.490350
$477$	2.53129e9	1.06789
$478$	3.31675e7	0.0138904
$479$	1.10499e9	0.459394	0.229697	−	0.973262i	$-0.426226\pi$
$479$	1.10499e9	0.459394	0.229697	+	0.973262i	$0.426226\pi$
$480$	6.83700e8	0.282177
$481$	1.54078e9	0.631296
$482$	9.54152e7	0.0388108
$483$	−2.34318e9	−0.946219
$484$	1.07255e9	0.429991
$485$	2.34105e9	0.931784
$486$	3.98080e7	0.0157305
$487$	1.39608e9	0.547719	0.273859	−	0.961770i	$-0.411700\pi$
$487$	1.39608e9	0.547719	0.273859	+	0.961770i	$0.411700\pi$
$488$	−1.70276e8	−0.0663260
$489$	6.46898e7	0.0250181
$490$	−1.17666e8	−0.0451820
$491$	−4.32305e9	−1.64818	−0.824091	−	0.566458i	$-0.808313\pi$
$491$	−4.32305e9	−1.64818	−0.824091	+	0.566458i	$0.808313\pi$
$492$	6.48615e9	2.45533
$493$	1.74734e9	0.656770
$494$	−4.60506e7	−0.0171866
$495$	8.32104e9	3.08361
$496$	3.08730e8	0.113604
$497$	−6.16700e8	−0.225334
$498$	9.89844e7	0.0359140
$499$	5.09888e8	0.183706	0.0918528	−	0.995773i	$-0.470721\pi$
$499$	5.09888e8	0.183706	0.0918528	+	0.995773i	$0.470721\pi$
$500$	−8.59435e9	−3.07481
$501$	−3.46958e9	−1.23266
$502$	−5.06207e7	−0.0178593
$503$	−3.07862e9	−1.07862	−0.539310	−	0.842108i	$-0.681315\pi$
$503$	−3.07862e9	−1.07862	−0.539310	+	0.842108i	$0.681315\pi$
$504$	1.32749e8	0.0461875
$505$	−3.12823e9	−1.08088
$506$	8.48994e7	0.0291325
$507$	9.08591e8	0.309628
$508$	6.40652e8	0.216820
$509$	3.54159e9	1.19038	0.595191	−	0.803584i	$-0.297076\pi$
$509$	3.54159e9	1.19038	0.595191	+	0.803584i	$0.297076\pi$
$510$	−3.59057e8	−0.119858
$511$	1.21613e9	0.403188
$512$	4.22353e8	0.139069
$513$	3.53991e9	1.15766
$514$	3.13996e7	0.0101989
$515$	3.71533e8	0.119859
$516$	8.43752e8	0.270359
$517$	−3.93317e9	−1.25177
$518$	1.98198e7	0.00626534
$519$	8.25162e9	2.59092
$520$	3.68671e8	0.114981
$521$	−2.36861e9	−0.733773	−0.366886	−	0.930266i	$-0.619576\pi$
$521$	−2.36861e9	−0.733773	−0.366886	+	0.930266i	$0.619576\pi$
$522$	−1.00480e8	−0.0309195
$523$	2.62233e9	0.801551	0.400776	−	0.916176i	$-0.368741\pi$
$523$	2.62233e9	0.801551	0.400776	+	0.916176i	$0.368741\pi$
$524$	5.35777e9	1.62676
$525$	−5.93662e9	−1.79053
$526$	4.45196e6	0.00133383
$527$	−4.87037e8	−0.144952
$528$	4.51887e9	1.33601
$529$	3.11142e9	0.913825
$530$	9.04291e7	0.0263841
$531$	−9.22047e9	−2.67253
$532$	7.60375e8	0.218946
$533$	5.24696e9	1.50094
$534$	−7.43376e7	−0.0211259
$535$	−1.37517e9	−0.388255
$536$	6.56854e7	0.0184243
$537$	6.48267e9	1.80653
$538$	2.94118e7	0.00814300
$539$	−2.33615e9	−0.642600
$540$	−1.41644e10	−3.87097
$541$	−3.96326e9	−1.07612	−0.538062	−	0.842905i	$-0.680843\pi$
$541$	−3.96326e9	−1.07612	−0.538062	+	0.842905i	$0.680843\pi$
$542$	1.48025e8	0.0399335
$543$	1.01498e9	0.272057
$544$	−3.99666e8	−0.106439
$545$	6.64227e9	1.75764
$546$	7.86606e7	0.0206815
$547$	−5.89175e9	−1.53918	−0.769588	−	0.638540i	$-0.779538\pi$
$547$	−5.89175e9	−1.53918	−0.769588	+	0.638540i	$0.779538\pi$
$548$	−4.98709e9	−1.29454
$549$	9.90227e9	2.55406
$550$	2.15098e8	0.0551274
$551$	−1.15153e9	−0.293254
$552$	−5.41036e8	−0.136911
$553$	1.28932e9	0.324206
$554$	−1.91468e7	−0.00478423
$555$	−7.91711e9	−1.96581
$556$	−7.71837e9	−1.90442
$557$	9.78407e8	0.239898	0.119949	−	0.992780i	$-0.461727\pi$
$557$	9.78407e8	0.239898	0.119949	+	0.992780i	$0.461727\pi$
$558$	2.80068e7	0.00682407
$559$	6.82552e8	0.165270
$560$	−3.04014e9	−0.731536
$561$	−7.12875e9	−1.70468
$562$	−1.93473e8	−0.0459772
$563$	2.19945e9	0.519439	0.259719	−	0.965684i	$-0.416370\pi$
$563$	2.19945e9	0.519439	0.259719	+	0.965684i	$0.416370\pi$
$564$	1.25275e10	2.94028
$565$	1.02591e10	2.39297
$566$	−2.20804e8	−0.0511858
$567$	−2.45255e9	−0.565037
$568$	−1.42395e8	−0.0326043
$569$	−5.53125e9	−1.25872	−0.629362	−	0.777112i	$-0.716684\pi$
$569$	−5.53125e9	−1.25872	−0.629362	+	0.777112i	$0.716684\pi$
$570$	2.36625e8	0.0535179
$571$	−2.15374e9	−0.484135	−0.242067	−	0.970259i	$-0.577825\pi$
$571$	−2.15374e9	−0.484135	−0.242067	+	0.970259i	$0.577825\pi$
$572$	3.65839e9	0.817342
$573$	−7.99324e9	−1.77493
$574$	6.74942e7	0.0148962
$575$	1.65093e10	3.62153
$576$	−9.80549e9	−2.13792
$577$	−8.51167e9	−1.84459	−0.922294	−	0.386490i	$-0.873688\pi$
$577$	−8.51167e9	−1.84459	−0.922294	+	0.386490i	$0.873688\pi$
$578$	8.03646e7	0.0173108
$579$	2.39807e9	0.513437
$580$	4.60766e9	0.980578
$581$	−1.32215e9	−0.279682
$582$	1.15332e8	0.0242504
$583$	1.79539e9	0.375248
$584$	2.80802e8	0.0583384
$585$	−2.14398e10	−4.42767
$586$	2.21076e8	0.0453838
$587$	−6.09853e9	−1.24449	−0.622246	−	0.782822i	$-0.713779\pi$
$587$	−6.09853e9	−1.24449	−0.622246	+	0.782822i	$0.713779\pi$
$588$	7.44086e9	1.50939
$589$	3.20966e8	0.0647226
$590$	−3.29397e8	−0.0660294
$591$	3.46657e9	0.690787
$592$	−2.93369e9	−0.581151
$593$	−6.67019e9	−1.31355	−0.656775	−	0.754087i	$-0.728080\pi$
$593$	−6.67019e9	−1.31355	−0.656775	+	0.754087i	$0.728080\pi$
$594$	2.19085e8	0.0428904
$595$	4.79598e9	0.933401
$596$	2.38607e9	0.461659
$597$	4.59728e9	0.884281
$598$	−2.18750e8	−0.0418306
$599$	2.30726e8	0.0438635	0.0219318	−	0.999759i	$-0.493018\pi$
$599$	2.30726e8	0.0438635	0.0219318	+	0.999759i	$0.493018\pi$
$600$	−1.37075e9	−0.259077
$601$	6.63912e9	1.24753	0.623763	−	0.781613i	$-0.285603\pi$
$601$	6.63912e9	1.24753	0.623763	+	0.781613i	$0.285603\pi$
$602$	8.77999e6	0.00164024
$603$	−3.81989e9	−0.709480
$604$	1.48304e9	0.273856
$605$	−4.45826e9	−0.818506
$606$	−1.54112e8	−0.0281307
$607$	−4.67413e9	−0.848282	−0.424141	−	0.905596i	$-0.639424\pi$
$607$	−4.67413e9	−0.848282	−0.424141	+	0.905596i	$0.639424\pi$
$608$	2.63387e8	0.0475261
$609$	1.96697e9	0.352888
$610$	3.53754e8	0.0631025
$611$	1.01341e10	1.79739
$612$	1.54929e10	2.73213
$613$	−1.56186e9	−0.273861	−0.136931	−	0.990581i	$-0.543724\pi$
$613$	−1.56186e9	−0.273861	−0.136931	+	0.990581i	$0.543724\pi$
$614$	1.85752e8	0.0323850
$615$	−2.69609e10	−4.67381
$616$	9.41558e7	0.0162299
$617$	3.07047e9	0.526268	0.263134	−	0.964759i	$-0.415244\pi$
$617$	3.07047e9	0.526268	0.263134	+	0.964759i	$0.415244\pi$
$618$	1.83035e7	0.00311943
$619$	−1.00411e9	−0.170162	−0.0850811	−	0.996374i	$-0.527115\pi$
$619$	−1.00411e9	−0.170162	−0.0850811	+	0.996374i	$0.527115\pi$
$620$	−1.28429e9	−0.216418
$621$	1.68153e10	2.81764
$622$	2.36308e7	0.00393743
$623$	9.92939e8	0.164518
$624$	−1.16432e10	−1.91835
$625$	1.97461e10	3.23519
$626$	8.25305e7	0.0134463
$627$	4.69798e9	0.761158
$628$	−3.70242e9	−0.596523
$629$	4.62805e9	0.741517
$630$	−2.75790e8	−0.0439428
$631$	−1.07127e9	−0.169745	−0.0848725	−	0.996392i	$-0.527048\pi$
$631$	−1.07127e9	−0.169745	−0.0848725	+	0.996392i	$0.527048\pi$
$632$	2.97700e8	0.0469104
$633$	−7.83428e9	−1.22768
$634$	−3.41727e8	−0.0532558
$635$	−2.66299e9	−0.412726
$636$	−5.71848e9	−0.881415
$637$	6.01928e9	0.922691
$638$	−7.12681e7	−0.0108648
$639$	8.28086e9	1.25552
$640$	−1.40502e9	−0.211861
$641$	3.42898e9	0.514236	0.257118	−	0.966380i	$-0.417227\pi$
$641$	3.42898e9	0.514236	0.257118	+	0.966380i	$0.417227\pi$
$642$	−6.77474e7	−0.0101046
$643$	4.41718e9	0.655249	0.327624	−	0.944808i	$-0.393752\pi$
$643$	4.41718e9	0.655249	0.327624	+	0.944808i	$0.393752\pi$
$644$	3.61194e9	0.532893
$645$	−3.50721e9	−0.514640
$646$	−1.38323e8	−0.0201873
$647$	−6.14010e9	−0.891272	−0.445636	−	0.895214i	$-0.647022\pi$
$647$	−6.14010e9	−0.891272	−0.445636	+	0.895214i	$0.647022\pi$
$648$	−5.66287e8	−0.0817568
$649$	−6.53987e9	−0.939102
$650$	−5.54218e8	−0.0791559
$651$	−5.48254e8	−0.0778840
$652$	−9.97171e7	−0.0140897
$653$	7.83011e9	1.10045	0.550227	−	0.835015i	$-0.314541\pi$
$653$	7.83011e9	1.10045	0.550227	+	0.835015i	$0.314541\pi$
$654$	3.27231e8	0.0457438
$655$	−2.22706e10	−3.09661
$656$	−9.99039e9	−1.38172
$657$	−1.63298e10	−2.24648
$658$	1.30360e8	0.0178383
$659$	9.87256e9	1.34379	0.671894	−	0.740647i	$-0.265481\pi$
$659$	9.87256e9	1.34379	0.671894	+	0.740647i	$0.265481\pi$
$660$	−1.87982e10	−2.54514
$661$	1.73018e9	0.233017	0.116508	−	0.993190i	$-0.462830\pi$
$661$	1.73018e9	0.233017	0.116508	+	0.993190i	$0.462830\pi$
$662$	−1.32753e8	−0.0177845
$663$	1.83678e10	2.44771
$664$	−3.05281e8	−0.0404680
$665$	−3.16064e9	−0.416773
$666$	−2.66134e8	−0.0349092
$667$	−5.47001e9	−0.713752
$668$	5.34823e9	0.694213
$669$	8.70736e8	0.112433
$670$	−1.36464e8	−0.0175289
$671$	7.02346e9	0.897474
$672$	−4.49901e8	−0.0571906
$673$	1.06458e10	1.34625	0.673127	−	0.739527i	$-0.264951\pi$
$673$	1.06458e10	1.34625	0.673127	+	0.739527i	$0.264951\pi$
$674$	3.72856e8	0.0469063
$675$	4.26028e10	5.33181
$676$	−1.40056e9	−0.174377
$677$	8.45984e9	1.04786	0.523928	−	0.851763i	$-0.324466\pi$
$677$	8.45984e9	1.04786	0.523928	+	0.851763i	$0.324466\pi$
$678$	5.05411e8	0.0622789
$679$	−1.54050e9	−0.188851
$680$	1.10738e9	0.135057
$681$	2.01255e9	0.244192
$682$	1.98646e7	0.00239792
$683$	−7.82807e9	−0.940117	−0.470059	−	0.882635i	$-0.655767\pi$
$683$	−7.82807e9	−0.940117	−0.470059	+	0.882635i	$0.655767\pi$
$684$	−1.02101e10	−1.21992
$685$	2.07298e10	2.46421
$686$	1.68373e8	0.0199131
$687$	5.97896e9	0.703521
$688$	−1.29960e9	−0.152143
$689$	−4.62595e9	−0.538808
$690$	1.12402e9	0.130257
$691$	−8.92999e9	−1.02962	−0.514811	−	0.857304i	$-0.672138\pi$
$691$	−8.92999e9	−1.02962	−0.514811	+	0.857304i	$0.672138\pi$
$692$	−1.27196e10	−1.45916
$693$	−5.47557e9	−0.624975
$694$	3.28577e8	0.0373147
$695$	3.20828e10	3.62515
$696$	4.54168e8	0.0510604
$697$	1.57604e10	1.76300
$698$	−2.07887e8	−0.0231384
$699$	5.14862e9	0.570192
$700$	9.15110e9	1.00839
$701$	1.21758e10	1.33501	0.667504	−	0.744606i	$-0.267363\pi$
$701$	1.21758e10	1.33501	0.667504	+	0.744606i	$0.267363\pi$
$702$	−5.64490e8	−0.0615852
$703$	−3.04997e9	−0.331095
$704$	−6.95481e9	−0.751244
$705$	−5.20730e10	−5.59694
$706$	9.57706e7	0.0102427
$707$	2.05849e9	0.219069
$708$	2.08301e10	2.20584
$709$	−1.53335e10	−1.61577	−0.807885	−	0.589340i	$-0.799388\pi$
$709$	−1.53335e10	−1.61577	−0.807885	+	0.589340i	$0.799388\pi$
$710$	2.95830e8	0.0310197
$711$	−1.73125e10	−1.80641
$712$	2.29267e8	0.0238047
$713$	1.52466e9	0.157528
$714$	2.36274e8	0.0242924
$715$	−1.52068e10	−1.55584
$716$	−9.99282e9	−1.01740
$717$	8.71829e9	0.883312
$718$	4.48974e8	0.0452674
$719$	3.82428e8	0.0383706	0.0191853	−	0.999816i	$-0.493893\pi$
$719$	3.82428e8	0.0383706	0.0191853	+	0.999816i	$0.493893\pi$
$720$	4.08221e10	4.07597
$721$	−2.44483e8	−0.0242926
$722$	−1.91002e8	−0.0188868
$723$	2.50805e10	2.46804
$724$	−1.56456e9	−0.153217
$725$	−1.38586e10	−1.35063
$726$	−2.19636e8	−0.0213022
$727$	−3.79482e9	−0.366286	−0.183143	−	0.983086i	$-0.558627\pi$
$727$	−3.79482e9	−0.366286	−0.183143	+	0.983086i	$0.558627\pi$
$728$	−2.42600e8	−0.0233040
$729$	−4.86810e9	−0.465386
$730$	−5.83375e8	−0.0555032
$731$	2.05019e9	0.194126
$732$	−2.23704e10	−2.10807
$733$	−1.11789e10	−1.04842	−0.524211	−	0.851588i	$-0.675640\pi$
$733$	−1.11789e10	−1.04842	−0.524211	+	0.851588i	$0.675640\pi$
$734$	1.87245e8	0.0174773
$735$	−3.09293e10	−2.87319
$736$	1.25114e9	0.115674
$737$	−2.70936e9	−0.249305
$738$	−9.06291e8	−0.0829985
$739$	−1.77973e10	−1.62218	−0.811091	−	0.584921i	$-0.801126\pi$
$739$	−1.77973e10	−1.62218	−0.811091	+	0.584921i	$0.801126\pi$
$740$	1.22040e10	1.10711
$741$	−1.21047e10	−1.09293
$742$	−5.95058e7	−0.00534744
$743$	2.77646e7	0.00248331	0.00124165	−	0.999999i	$-0.499605\pi$
$743$	2.77646e7	0.00248331	0.00124165	+	0.999999i	$0.499605\pi$
$744$	−1.26590e8	−0.0112693
$745$	−9.91814e9	−0.878786
$746$	−1.07794e8	−0.00950627
$747$	1.77534e10	1.55833
$748$	1.09887e10	0.960046
$749$	9.04912e8	0.0786901
$750$	1.75994e9	0.152329
$751$	−1.10248e10	−0.949798	−0.474899	−	0.880040i	$-0.657515\pi$
$751$	−1.10248e10	−0.949798	−0.474899	+	0.880040i	$0.657515\pi$
$752$	−1.92957e10	−1.65462
$753$	−1.33060e10	−1.13570
$754$	1.83628e8	0.0156005
$755$	−6.16452e9	−0.521296
$756$	9.32070e9	0.784553
$757$	−2.07834e10	−1.74133	−0.870664	−	0.491879i	$-0.836310\pi$
$757$	−2.07834e10	−1.74133	−0.870664	+	0.491879i	$0.836310\pi$
$758$	−3.84434e8	−0.0320612
$759$	2.23164e10	1.85258
$760$	−7.29784e8	−0.0603041
$761$	8.64340e9	0.710949	0.355474	−	0.934686i	$-0.384319\pi$
$761$	8.64340e9	0.710949	0.355474	+	0.934686i	$0.384319\pi$
$762$	−1.31192e8	−0.0107415
$763$	−4.37087e9	−0.356231
$764$	1.23213e10	0.999609
$765$	−6.43990e10	−5.20072
$766$	3.83996e8	0.0308692
$767$	1.68505e10	1.34843
$768$	2.20998e10	1.76045
$769$	2.17566e9	0.172523	0.0862617	−	0.996273i	$-0.472508\pi$
$769$	2.17566e9	0.172523	0.0862617	+	0.996273i	$0.472508\pi$
$770$	−1.95612e8	−0.0154411
$771$	8.25359e9	0.648563
$772$	−3.69654e9	−0.289158
$773$	5.58417e9	0.434841	0.217421	−	0.976078i	$-0.430236\pi$
$773$	5.58417e9	0.434841	0.217421	+	0.976078i	$0.430236\pi$
$774$	−1.17895e8	−0.00913907
$775$	3.86282e9	0.298091
$776$	−3.55698e8	−0.0273253
$777$	5.20976e9	0.398423
$778$	−7.03948e6	−0.000535935 0
$779$	−1.03864e10	−0.787195
$780$	4.84350e10	3.65450
$781$	5.87343e9	0.441177
$782$	−6.57061e8	−0.0491340
$783$	−1.41155e10	−1.05082
$784$	−1.14609e10	−0.849400
$785$	1.53898e10	1.13551
$786$	−1.09716e9	−0.0805916
$787$	−7.26404e9	−0.531211	−0.265605	−	0.964082i	$-0.585572\pi$
$787$	−7.26404e9	−0.531211	−0.265605	+	0.964082i	$0.585572\pi$
$788$	−5.34360e9	−0.389038
$789$	1.17023e9	0.0848206
$790$	−6.18481e8	−0.0446305
$791$	−6.75085e9	−0.484999
$792$	−1.26429e9	−0.0904295
$793$	−1.80965e10	−1.28866
$794$	−2.63076e8	−0.0186514
$795$	2.37699e10	1.67781
$796$	−7.08654e9	−0.498011
$797$	1.81556e10	1.27030	0.635150	−	0.772389i	$-0.280938\pi$
$797$	1.81556e10	1.27030	0.635150	+	0.772389i	$0.280938\pi$
$798$	−1.55709e8	−0.0108468
$799$	3.04400e10	2.11120
$800$	3.16986e9	0.218890
$801$	−1.33329e10	−0.916664
$802$	−4.05058e8	−0.0277272
$803$	−1.15824e10	−0.789393
$804$	8.62956e9	0.585588
$805$	−1.50137e10	−1.01438
$806$	−5.11826e7	−0.00344310
$807$	7.73110e9	0.517826
$808$	4.75301e8	0.0316978
$809$	−2.32465e10	−1.54361	−0.771806	−	0.635858i	$-0.780647\pi$
$809$	−2.32465e10	−1.54361	−0.771806	+	0.635858i	$0.780647\pi$
$810$	1.17648e9	0.0777834
$811$	−1.13477e10	−0.747024	−0.373512	−	0.927625i	$-0.621847\pi$
$811$	−1.13477e10	−0.747024	−0.373512	+	0.927625i	$0.621847\pi$
$812$	−3.03201e9	−0.198740
$813$	3.89094e10	2.53944
$814$	−1.88763e8	−0.0122668
$815$	4.14493e8	0.0268204
$816$	−3.49729e10	−2.25328
$817$	−1.35111e9	−0.0866790
$818$	1.25580e8	0.00802202
$819$	1.41082e10	0.897385
$820$	4.15593e10	2.63221
$821$	−6.60382e9	−0.416480	−0.208240	−	0.978078i	$-0.566774\pi$
$821$	−6.60382e9	−0.416480	−0.208240	+	0.978078i	$0.566774\pi$
$822$	1.02125e9	0.0641328
$823$	−3.82454e9	−0.239155	−0.119577	−	0.992825i	$-0.538154\pi$
$823$	−3.82454e9	−0.239155	−0.119577	+	0.992825i	$0.538154\pi$
$824$	−5.64505e7	−0.00351498
$825$	5.65401e10	3.50564
$826$	2.16756e8	0.0133826
$827$	1.37532e10	0.845541	0.422770	−	0.906237i	$-0.361058\pi$
$827$	1.37532e10	0.845541	0.422770	+	0.906237i	$0.361058\pi$
$828$	−4.85000e10	−2.96917
$829$	1.83250e10	1.11713	0.558563	−	0.829462i	$-0.311353\pi$
$829$	1.83250e10	1.11713	0.558563	+	0.829462i	$0.311353\pi$
$830$	6.34232e8	0.0385012
$831$	−5.03286e9	−0.304237
$832$	1.79196e10	1.07869
$833$	1.80802e10	1.08379
$834$	1.58056e9	0.0943472
$835$	−2.22309e10	−1.32146
$836$	−7.24178e9	−0.428670
$837$	3.93442e9	0.231922
$838$	−5.80329e8	−0.0340659
$839$	1.70662e10	0.997630	0.498815	−	0.866708i	$-0.333769\pi$
$839$	1.70662e10	0.997630	0.498815	+	0.866708i	$0.333769\pi$
$840$	1.24657e9	0.0725670
$841$	−1.26581e10	−0.733809
$842$	9.44478e8	0.0545255
$843$	−5.08556e10	−2.92377
$844$	1.20763e10	0.691408
$845$	5.82169e9	0.331933
$846$	−1.75043e9	−0.0993915
$847$	2.93371e9	0.165892
$848$	8.80796e9	0.496010
$849$	−5.80398e10	−3.25499
$850$	−1.66471e9	−0.0929762
$851$	−1.44880e10	−0.805852
$852$	−1.87074e10	−1.03628
$853$	−6.70515e9	−0.369902	−0.184951	−	0.982748i	$-0.559213\pi$
$853$	−6.70515e9	−0.369902	−0.184951	+	0.982748i	$0.559213\pi$
$854$	−2.32784e8	−0.0127894
$855$	4.24401e10	2.32217
$856$	2.08942e8	0.0113859
$857$	2.45826e9	0.133412	0.0667061	−	0.997773i	$-0.478751\pi$
$857$	2.45826e9	0.133412	0.0667061	+	0.997773i	$0.478751\pi$
$858$	−7.49160e8	−0.0404920
$859$	−2.04474e10	−1.10068	−0.550340	−	0.834941i	$-0.685502\pi$
$859$	−2.04474e10	−1.10068	−0.550340	+	0.834941i	$0.685502\pi$
$860$	5.40625e9	0.289835
$861$	1.77413e10	0.947271
$862$	2.37581e7	0.00126338
$863$	−2.86480e10	−1.51725	−0.758624	−	0.651529i	$-0.774128\pi$
$863$	−2.86480e10	−1.51725	−0.758624	+	0.651529i	$0.774128\pi$
$864$	3.22861e9	0.170301
$865$	5.28713e10	2.77756
$866$	7.47457e8	0.0391087
$867$	2.11244e10	1.10082
$868$	8.45114e8	0.0438628
$869$	−1.22794e10	−0.634757
$870$	−9.43549e8	−0.0485789
$871$	6.98087e9	0.357970
$872$	−1.00922e9	−0.0515442
$873$	2.06854e10	1.05224
$874$	4.33015e8	0.0219388
$875$	−2.35078e10	−1.18627
$876$	3.68910e10	1.85420
$877$	2.41157e10	1.20726	0.603631	−	0.797264i	$-0.293720\pi$
$877$	2.41157e10	1.20726	0.603631	+	0.797264i	$0.293720\pi$
$878$	6.26593e8	0.0312432
$879$	5.81114e10	2.88603
$880$	2.89542e10	1.43226
$881$	8.73417e9	0.430334	0.215167	−	0.976577i	$-0.430970\pi$
$881$	8.73417e9	0.430334	0.215167	+	0.976577i	$0.430970\pi$
$882$	−1.03969e9	−0.0510227
$883$	−1.22297e10	−0.597795	−0.298898	−	0.954285i	$-0.596619\pi$
$883$	−1.22297e10	−0.597795	−0.298898	+	0.954285i	$0.596619\pi$
$884$	−2.83133e10	−1.37850
$885$	−8.65841e10	−4.19891
$886$	−7.76690e8	−0.0375171
$887$	−3.43901e9	−0.165463	−0.0827315	−	0.996572i	$-0.526364\pi$
$887$	−3.43901e9	−0.165463	−0.0827315	+	0.996572i	$0.526364\pi$
$888$	1.20292e9	0.0576490
$889$	1.75235e9	0.0836497
$890$	−4.76310e8	−0.0226477
$891$	2.33579e10	1.10627
$892$	−1.34221e9	−0.0633204
$893$	−2.00605e10	−0.942674
$894$	−4.88616e8	−0.0228711
$895$	4.15370e10	1.93667
$896$	9.24556e8	0.0429393
$897$	−5.74999e10	−2.66007
$898$	−4.84266e8	−0.0223160
$899$	−1.27986e9	−0.0587495
$900$	−1.22878e11	−5.61857
$901$	−1.38950e10	−0.632882
$902$	−6.42811e8	−0.0291649
$903$	2.30788e9	0.104305
$904$	−1.55875e9	−0.0701759
$905$	6.50340e9	0.291655
$906$	−3.03694e8	−0.0135671
$907$	2.11330e10	0.940451	0.470226	−	0.882546i	$-0.344173\pi$
$907$	2.11330e10	0.940451	0.470226	+	0.882546i	$0.344173\pi$
$908$	−3.10228e9	−0.137524
$909$	−2.76408e10	−1.22061
$910$	5.04009e8	0.0221714
$911$	3.25882e10	1.42806	0.714029	−	0.700116i	$-0.246869\pi$
$911$	3.25882e10	1.42806	0.714029	+	0.700116i	$0.246869\pi$
$912$	2.30477e10	1.00611
$913$	1.25921e10	0.547583
$914$	5.16757e8	0.0223859
$915$	9.29866e10	4.01279
$916$	−9.21636e9	−0.396210
$917$	1.46549e10	0.627610
$918$	−1.69556e9	−0.0723377
$919$	2.90516e10	1.23471	0.617356	−	0.786684i	$-0.288204\pi$
$919$	2.90516e10	1.23471	0.617356	+	0.786684i	$0.288204\pi$
$920$	−3.46663e9	−0.146774
$921$	4.88262e10	2.05942
$922$	1.13489e9	0.0476865
$923$	−1.51333e10	−0.633474
$924$	1.23699e10	0.515840
$925$	−3.67063e10	−1.52491
$926$	−1.04777e9	−0.0433639
$927$	3.28284e9	0.135354
$928$	−1.05026e9	−0.0431400
$929$	5.17888e9	0.211924	0.105962	−	0.994370i	$-0.466208\pi$
$929$	5.17888e9	0.211924	0.105962	+	0.994370i	$0.466208\pi$
$930$	2.62996e8	0.0107216
$931$	−1.19152e10	−0.483922
$932$	−7.93642e9	−0.321121
$933$	6.21153e9	0.250388
$934$	6.96715e8	0.0279796
$935$	−4.56767e10	−1.82749
$936$	3.25755e9	0.129845
$937$	5.65702e9	0.224646	0.112323	−	0.993672i	$-0.464171\pi$
$937$	5.65702e9	0.224646	0.112323	+	0.993672i	$0.464171\pi$
$938$	8.97982e7	0.00355269
$939$	2.16937e10	0.855075
$940$	8.02687e10	3.15209
$941$	1.93533e10	0.757168	0.378584	−	0.925567i	$-0.376411\pi$
$941$	1.93533e10	0.757168	0.378584	+	0.925567i	$0.376411\pi$
$942$	7.58177e8	0.0295524
$943$	−4.93374e10	−1.91595
$944$	−3.20838e10	−1.24132
$945$	−3.87432e10	−1.49343
$946$	−8.36202e7	−0.00321139
$947$	2.30104e10	0.880438	0.440219	−	0.897890i	$-0.354901\pi$
$947$	2.30104e10	0.880438	0.440219	+	0.897890i	$0.354901\pi$
$948$	3.91110e10	1.49097
$949$	2.98429e10	1.13347
$950$	1.09707e9	0.0415148
$951$	−8.98252e10	−3.38662
$952$	−7.28699e8	−0.0273728
$953$	−1.01231e10	−0.378867	−0.189434	−	0.981894i	$-0.560665\pi$
$953$	−1.01231e10	−0.378867	−0.189434	+	0.981894i	$0.560665\pi$
$954$	7.99026e8	0.0297949
$955$	−5.12158e10	−1.90280
$956$	−1.34390e10	−0.497465
$957$	−1.87333e10	−0.690912
$958$	3.48801e8	0.0128174
$959$	−1.36410e10	−0.499437
$960$	−9.20778e10	−3.35897
$961$	−2.71559e10	−0.987034
$962$	4.86362e8	0.0176135
$963$	−1.21509e10	−0.438446
$964$	−3.86608e10	−1.38996
$965$	1.53654e10	0.550424
$966$	−7.39648e8	−0.0264001
$967$	6.28463e8	0.0223505	0.0111752	−	0.999938i	$-0.496443\pi$
$967$	6.28463e8	0.0223505	0.0111752	+	0.999938i	$0.496443\pi$
$968$	6.77386e8	0.0240034
$969$	−3.63590e10	−1.28375
$970$	7.38975e8	0.0259973
$971$	2.05584e10	0.720645	0.360322	−	0.932828i	$-0.382667\pi$
$971$	2.05584e10	0.720645	0.360322	+	0.932828i	$0.382667\pi$
$972$	−1.61296e10	−0.563367
$973$	−2.11117e10	−0.734732
$974$	4.40684e8	0.0152817
$975$	−1.45680e11	−5.03365
$976$	3.44563e10	1.18630
$977$	4.09891e10	1.40617	0.703084	−	0.711107i	$-0.251806\pi$
$977$	4.09891e10	1.40617	0.703084	+	0.711107i	$0.251806\pi$
$978$	2.04199e7	0.000698021 0
$979$	−9.45670e9	−0.322107
$980$	4.76765e10	1.61813
$981$	5.86907e10	1.98485
$982$	−1.36461e9	−0.0459853
$983$	3.77468e10	1.26748	0.633742	−	0.773544i	$-0.281518\pi$
$983$	3.77468e10	1.26748	0.633742	+	0.773544i	$0.281518\pi$
$984$	4.09642e9	0.137064
$985$	2.22117e10	0.740551
$986$	5.51565e8	0.0183243
$987$	3.42660e10	1.13437
$988$	1.86590e10	0.615515
$989$	−6.41806e9	−0.210968
$990$	2.62662e9	0.0860346
$991$	−1.40838e10	−0.459688	−0.229844	−	0.973227i	$-0.573822\pi$
$991$	−1.40838e10	−0.459688	−0.229844	+	0.973227i	$0.573822\pi$
$992$	2.92740e8	0.00952119
$993$	−3.48951e10	−1.13095
$994$	−1.94667e8	−0.00628696
$995$	2.94565e10	0.947984
$996$	−4.01070e10	−1.28621
$997$	8.84518e9	0.282666	0.141333	−	0.989962i	$-0.454861\pi$
$997$	8.84518e9	0.282666	0.141333	+	0.989962i	$0.454861\pi$
$998$	1.60951e8	0.00512550
$999$	−3.73867e10	−1.18642

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.b.1.7	✓	13
3.2	odd	2		387.8.a.d.1.7		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.b.1.7	✓	13	1.1	even	1	trivial
387.8.a.d.1.7		13	3.2	odd	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q+0.315659 q^{2} +82.9732 q^{3} -127.900 q^{4} +531.642 q^{5} +26.1913 q^{6} -349.841 q^{7} -80.7773 q^{8} +4697.55 q^{9} +O(q^{10})\)	\(q+0.315659 q^{2} +82.9732 q^{3} -127.900 q^{4} +531.642 q^{5} +26.1913 q^{6} -349.841 q^{7} -80.7773 q^{8} +4697.55 q^{9} +167.818 q^{10} +3331.87 q^{11} -10612.3 q^{12} -8584.81 q^{13} -110.430 q^{14} +44112.0 q^{15} +16345.7 q^{16} -25786.3 q^{17} +1482.83 q^{18} +16993.6 q^{19} -67997.2 q^{20} -29027.4 q^{21} +1051.73 q^{22} +80723.2 q^{23} -6702.35 q^{24} +204518. q^{25} -2709.87 q^{26} +208308. q^{27} +44744.7 q^{28} -67762.5 q^{29} +13924.4 q^{30} +18887.5 q^{31} +15499.2 q^{32} +276455. q^{33} -8139.67 q^{34} -185990. q^{35} -600818. q^{36} -179478. q^{37} +5364.19 q^{38} -712309. q^{39} -42944.6 q^{40} -611192. q^{41} -9162.77 q^{42} -79507.0 q^{43} -426147. q^{44} +2.49741e6 q^{45} +25481.0 q^{46} -1.18047e6 q^{47} +1.35626e6 q^{48} -701155. q^{49} +64557.9 q^{50} -2.13957e6 q^{51} +1.09800e6 q^{52} +538854. q^{53} +65754.5 q^{54} +1.77136e6 q^{55} +28259.2 q^{56} +1.41001e6 q^{57} -21389.9 q^{58} -1.96283e6 q^{59} -5.64194e6 q^{60} +2.10797e6 q^{61} +5962.00 q^{62} -1.64339e6 q^{63} -2.08736e6 q^{64} -4.56404e6 q^{65} +87265.7 q^{66} -813166. q^{67} +3.29807e6 q^{68} +6.69786e6 q^{69} -58709.4 q^{70} +1.76280e6 q^{71} -379456. q^{72} -3.47624e6 q^{73} -56653.7 q^{74} +1.69695e7 q^{75} -2.17349e6 q^{76} -1.16562e6 q^{77} -224847. q^{78} -3.68544e6 q^{79} +8.69008e6 q^{80} +7.01047e6 q^{81} -192928. q^{82} +3.77929e6 q^{83} +3.71261e6 q^{84} -1.37091e7 q^{85} -25097.1 q^{86} -5.62247e6 q^{87} -269139. q^{88} -2.83826e6 q^{89} +788332. q^{90} +3.00331e6 q^{91} -1.03245e7 q^{92} +1.56715e6 q^{93} -372627. q^{94} +9.03452e6 q^{95} +1.28602e6 q^{96} +4.40344e6 q^{97} -221326. q^{98} +1.56516e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9}+O(q^{10}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9} + 4667 q^{10} + 1620 q^{11} - 19681 q^{12} + 13550 q^{13} + 44160 q^{14} + 31412 q^{15} + 114026 q^{16} + 110880 q^{17} + 159267 q^{18} + 105058 q^{19} + 167251 q^{20} + 129840 q^{21} + 201504 q^{22} + 160184 q^{23} + 161289 q^{24} + 270149 q^{25} + 272104 q^{26} + 252544 q^{27} + 208172 q^{28} + 285546 q^{29} + 107580 q^{30} - 99616 q^{31} + 200126 q^{32} + 531468 q^{33} - 80941 q^{34} - 187104 q^{35} - 608975 q^{36} + 176038 q^{37} + 652165 q^{38} - 794680 q^{39} - 895387 q^{40} - 410260 q^{41} - 3413218 q^{42} - 1033591 q^{43} - 2177076 q^{44} - 1051178 q^{45} - 3975765 q^{46} - 424556 q^{47} - 2360477 q^{48} - 1561359 q^{49} - 4063801 q^{50} - 2375738 q^{51} - 4172312 q^{52} + 3992458 q^{53} - 10438626 q^{54} + 406960 q^{55} + 1559556 q^{56} - 3116152 q^{57} - 4052005 q^{58} + 2248836 q^{59} - 2911436 q^{60} + 6210394 q^{61} + 885317 q^{62} + 11622368 q^{63} - 3096318 q^{64} + 5600420 q^{65} - 2174604 q^{66} - 1993648 q^{67} + 9327135 q^{68} + 13366240 q^{69} - 1105098 q^{70} + 4978064 q^{71} + 11370663 q^{72} + 8224814 q^{73} - 3613563 q^{74} + 27115592 q^{75} + 10687121 q^{76} + 17261892 q^{77} - 15226630 q^{78} + 6945708 q^{79} + 15822799 q^{80} + 35113185 q^{81} - 508449 q^{82} + 22937328 q^{83} - 14010106 q^{84} - 575532 q^{85} - 1272112 q^{86} + 9081380 q^{87} + 11202656 q^{88} + 9291302 q^{89} + 2841402 q^{90} + 25581108 q^{91} - 14388137 q^{92} + 25930480 q^{93} - 24645805 q^{94} + 30750464 q^{95} - 22461255 q^{96} + 10001852 q^{97} - 32304856 q^{98} + 5055452 q^{99}+O(q^{100}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9 + 4667 * q^10 + 1620 * q^11 - 19681 * q^12 + 13550 * q^13 + 44160 * q^14 + 31412 * q^15 + 114026 * q^16 + 110880 * q^17 + 159267 * q^18 + 105058 * q^19 + 167251 * q^20 + 129840 * q^21 + 201504 * q^22 + 160184 * q^23 + 161289 * q^24 + 270149 * q^25 + 272104 * q^26 + 252544 * q^27 + 208172 * q^28 + 285546 * q^29 + 107580 * q^30 - 99616 * q^31 + 200126 * q^32 + 531468 * q^33 - 80941 * q^34 - 187104 * q^35 - 608975 * q^36 + 176038 * q^37 + 652165 * q^38 - 794680 * q^39 - 895387 * q^40 - 410260 * q^41 - 3413218 * q^42 - 1033591 * q^43 - 2177076 * q^44 - 1051178 * q^45 - 3975765 * q^46 - 424556 * q^47 - 2360477 * q^48 - 1561359 * q^49 - 4063801 * q^50 - 2375738 * q^51 - 4172312 * q^52 + 3992458 * q^53 - 10438626 * q^54 + 406960 * q^55 + 1559556 * q^56 - 3116152 * q^57 - 4052005 * q^58 + 2248836 * q^59 - 2911436 * q^60 + 6210394 * q^61 + 885317 * q^62 + 11622368 * q^63 - 3096318 * q^64 + 5600420 * q^65 - 2174604 * q^66 - 1993648 * q^67 + 9327135 * q^68 + 13366240 * q^69 - 1105098 * q^70 + 4978064 * q^71 + 11370663 * q^72 + 8224814 * q^73 - 3613563 * q^74 + 27115592 * q^75 + 10687121 * q^76 + 17261892 * q^77 - 15226630 * q^78 + 6945708 * q^79 + 15822799 * q^80 + 35113185 * q^81 - 508449 * q^82 + 22937328 * q^83 - 14010106 * q^84 - 575532 * q^85 - 1272112 * q^86 + 9081380 * q^87 + 11202656 * q^88 + 9291302 * q^89 + 2841402 * q^90 + 25581108 * q^91 - 14388137 * q^92 + 25930480 * q^93 - 24645805 * q^94 + 30750464 * q^95 - 22461255 * q^96 + 10001852 * q^97 - 32304856 * q^98 + 5055452 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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