LMFDB - Embedded newform 43.7.b.b.42.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(42,43)]

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([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 1038 x^{18} + 455829 x^{16} + 110435384 x^{14} + 16133606976 x^{12} + 1458210485616 x^{10} + \cdots + 64\!\cdots\!40 $ x^20 + 1038x^18 + 455829x^16 + 110435384x^14 + 16133606976x^12 + 1458210485616x^10 + 80362197690736x^8 + 2545997652841536x^6 + 40210452531479040x^4 + 212033222410436608*x^2 + 64236717122519040
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.7
Root			$-7.14115i$ of defining polynomial
Character	$\chi$	$=$	43.42
Dual form			43.7.b.b.42.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.14115i q^{2} -19.7617i q^{3} +13.0039 q^{4} -151.678i q^{5} -141.122 q^{6} +62.8896i q^{7} -549.897i q^{8} +338.474 q^{9} +O(q^{10})$	\(q-7.14115i q^{2} -19.7617i q^{3} +13.0039 q^{4} -151.678i q^{5} -141.122 q^{6} +62.8896i q^{7} -549.897i q^{8} +338.474 q^{9} -1083.16 q^{10} -497.851 q^{11} -256.980i q^{12} +850.633 q^{13} +449.105 q^{14} -2997.43 q^{15} -3094.65 q^{16} -8046.00 q^{17} -2417.10i q^{18} +11446.3i q^{19} -1972.42i q^{20} +1242.81 q^{21} +3555.23i q^{22} +6206.07 q^{23} -10866.9 q^{24} -7381.34 q^{25} -6074.50i q^{26} -21095.1i q^{27} +817.813i q^{28} -23809.8i q^{29} +21405.1i q^{30} +26939.3 q^{31} -13094.1i q^{32} +9838.40i q^{33} +57457.7i q^{34} +9539.00 q^{35} +4401.49 q^{36} -23588.9i q^{37} +81740.0 q^{38} -16810.0i q^{39} -83407.5 q^{40} +87352.8 q^{41} -8875.08i q^{42} +(79070.1 - 8323.35i) q^{43} -6474.02 q^{44} -51339.2i q^{45} -44318.5i q^{46} -39004.6 q^{47} +61155.6i q^{48} +113694. q^{49} +52711.3i q^{50} +159003. i q^{51} +11061.6 q^{52} -178171. q^{53} -150644. q^{54} +75513.3i q^{55} +34582.8 q^{56} +226199. q^{57} -170030. q^{58} +19938.3 q^{59} -38978.3 q^{60} +34949.8i q^{61} -192377. i q^{62} +21286.5i q^{63} -291564. q^{64} -129023. i q^{65} +70257.5 q^{66} -299904. q^{67} -104630. q^{68} -122643. i q^{69} -68119.5i q^{70} -362351. i q^{71} -186126. i q^{72} -89951.1i q^{73} -168452. q^{74} +145868. i q^{75} +148847. i q^{76} -31309.7i q^{77} -120043. q^{78} +434327. q^{79} +469391. i q^{80} -170129. q^{81} -623800. i q^{82} +662276. q^{83} +16161.4 q^{84} +1.22041e6i q^{85} +(-59438.3 - 564652. i) q^{86} -470523. q^{87} +273767. i q^{88} +1.26108e6i q^{89} -366621. q^{90} +53496.0i q^{91} +80703.2 q^{92} -532366. i q^{93} +278538. i q^{94} +1.73616e6 q^{95} -258761. q^{96} +83771.3 q^{97} -811906. i q^{98} -168510. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 796 q^{4} - 258 q^{6} - 2736 q^{9}+O(q^{10}) $ 20 * q - 796 * q^4 - 258 * q^6 - 2736 * q^9	$ 20 q - 796 q^{4} - 258 q^{6} - 2736 q^{9} - 1962 q^{10} + 2616 q^{11} - 5612 q^{13} - 3876 q^{14} + 4048 q^{15} + 14900 q^{16} + 3328 q^{17} + 10544 q^{21} - 836 q^{23} + 26966 q^{24} - 57904 q^{25} + 17116 q^{31} - 150472 q^{35} - 132110 q^{36} + 2266 q^{38} + 401286 q^{40} - 141936 q^{41} + 58160 q^{43} + 88544 q^{44} + 48452 q^{47} - 20644 q^{49} + 12292 q^{52} + 425212 q^{53} + 173740 q^{54} + 447864 q^{56} - 92904 q^{57} + 86502 q^{58} - 918856 q^{59} + 429848 q^{60} - 156892 q^{64} - 1246176 q^{66} + 1098496 q^{67} - 2589854 q^{68} - 1224106 q^{74} + 855716 q^{78} - 401492 q^{79} + 470644 q^{81} + 1354360 q^{83} - 637268 q^{84} + 3046356 q^{86} + 2116740 q^{87} - 683716 q^{90} - 485998 q^{92} - 2711660 q^{95} - 2480062 q^{96} + 7814560 q^{97} + 3744560 q^{99}+O(q^{100}) $ 20 * q - 796 * q^4 - 258 * q^6 - 2736 * q^9 - 1962 * q^10 + 2616 * q^11 - 5612 * q^13 - 3876 * q^14 + 4048 * q^15 + 14900 * q^16 + 3328 * q^17 + 10544 * q^21 - 836 * q^23 + 26966 * q^24 - 57904 * q^25 + 17116 * q^31 - 150472 * q^35 - 132110 * q^36 + 2266 * q^38 + 401286 * q^40 - 141936 * q^41 + 58160 * q^43 + 88544 * q^44 + 48452 * q^47 - 20644 * q^49 + 12292 * q^52 + 425212 * q^53 + 173740 * q^54 + 447864 * q^56 - 92904 * q^57 + 86502 * q^58 - 918856 * q^59 + 429848 * q^60 - 156892 * q^64 - 1246176 * q^66 + 1098496 * q^67 - 2589854 * q^68 - 1224106 * q^74 + 855716 * q^78 - 401492 * q^79 + 470644 * q^81 + 1354360 * q^83 - 637268 * q^84 + 3046356 * q^86 + 2116740 * q^87 - 683716 * q^90 - 485998 * q^92 - 2711660 * q^95 - 2480062 * q^96 + 7814560 * q^97 + 3744560 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$		−	7.14115i		−	0.892644i	−0.894872	−	0.446322i	$-0.852734\pi$
$2$		−	7.14115i		−	0.892644i	0.894872	−	0.446322i	$-0.147266\pi$
$3$		−	19.7617i		−	0.731916i	−0.930631	−	0.365958i	$-0.880741\pi$
$3$		−	19.7617i		−	0.731916i	0.930631	−	0.365958i	$-0.119259\pi$
$4$	13.0039			0.203186
$5$		−	151.678i		−	1.21343i	−0.794920	−	0.606714i	$-0.792487\pi$
$5$		−	151.678i		−	1.21343i	0.794920	−	0.606714i	$-0.207513\pi$
$6$	−141.122			−0.653340
$7$			62.8896i			0.183352i	0.995789	+	0.0916759i	$0.0292224\pi$
$7$			62.8896i			0.183352i	−0.995789	+	0.0916759i	$0.970778\pi$
$8$		−	549.897i		−	1.07402i
$9$	338.474			0.464299
$10$	−1083.16			−1.08316
$11$	−497.851			−0.374043			−0.187021	−	0.982356i	$-0.559883\pi$
$11$	−497.851			−0.374043			−0.187021	+	0.982356i	$0.559883\pi$
$12$		−	256.980i		−	0.148715i
$13$	850.633			0.387179			0.193590	−	0.981083i	$-0.437987\pi$
$13$	850.633			0.387179			0.193590	+	0.981083i	$0.437987\pi$
$14$	449.105			0.163668
$15$	−2997.43			−0.888127
$16$	−3094.65			−0.755529
$17$	−8046.00			−1.63770			−0.818848	−	0.574010i	$-0.805387\pi$
$17$	−8046.00			−1.63770			−0.818848	+	0.574010i	$0.805387\pi$
$18$		−	2417.10i		−	0.414454i
$19$			11446.3i			1.66880i	0.551156	+	0.834402i	$0.314187\pi$
$19$			11446.3i			1.66880i	−0.551156	+	0.834402i	$0.685813\pi$
$20$		−	1972.42i		−	0.246552i
$21$	1242.81			0.134198
$22$			3555.23i			0.333887i
$23$	6206.07			0.510074			0.255037	−	0.966931i	$-0.417912\pi$
$23$	6206.07			0.510074			0.255037	+	0.966931i	$0.417912\pi$
$24$	−10866.9			−0.786090
$25$	−7381.34			−0.472406
$26$		−	6074.50i		−	0.345613i
$27$		−	21095.1i		−	1.07174i
$28$			817.813i			0.0372546i
$29$		−	23809.8i		−	0.976253i	−0.872773	−	0.488126i	$-0.837680\pi$
$29$		−	23809.8i		−	0.976253i	0.872773	−	0.488126i	$-0.162320\pi$
$30$			21405.1i			0.792781i
$31$	26939.3			0.904275			0.452138	−	0.891948i	$-0.350662\pi$
$31$	26939.3			0.904275			0.452138	+	0.891948i	$0.350662\pi$
$32$		−	13094.1i		−	0.399599i
$33$			9838.40i			0.273768i
$34$			57457.7i			1.46188i
$35$	9539.00			0.222484
$36$	4401.49			0.0943393
$37$		−	23588.9i		−	0.465696i	−0.972513	−	0.232848i	$-0.925196\pi$
$37$		−	23588.9i		−	0.465696i	0.972513	−	0.232848i	$-0.0748044\pi$
$38$	81740.0			1.48965
$39$		−	16810.0i		−	0.283383i
$40$	−83407.5			−1.30324
$41$	87352.8			1.26743			0.633717	−	0.773565i	$-0.281528\pi$
$41$	87352.8			1.26743			0.633717	+	0.773565i	$0.281528\pi$
$42$		−	8875.08i		−	0.119791i
$43$	79070.1	−	8323.35i	0.994505	−	0.104687i
$43$	79070.1	−	8323.35i	0.994505	−	0.104687i
$44$	−6474.02			−0.0760004
$45$		−	51339.2i		−	0.563393i
$46$		−	44318.5i		−	0.455314i
$47$	−39004.6			−0.375684			−0.187842	−	0.982199i	$-0.560149\pi$
$47$	−39004.6			−0.375684			−0.187842	+	0.982199i	$0.560149\pi$
$48$			61155.6i			0.552984i
$49$	113694.			0.966382
$50$			52711.3i			0.421690i
$51$			159003.i			1.19866i
$52$	11061.6			0.0786696
$53$	−178171.			−1.19676			−0.598382	−	0.801211i	$-0.704190\pi$
$53$	−178171.			−1.19676			−0.598382	+	0.801211i	$0.704190\pi$
$54$	−150644.			−0.956686
$55$			75513.3i			0.453874i
$56$	34582.8			0.196923
$57$	226199.			1.22142
$58$	−170030.			−0.871446
$59$	19938.3			0.0970806			0.0485403	−	0.998821i	$-0.484543\pi$
$59$	19938.3			0.0970806			0.0485403	+	0.998821i	$0.484543\pi$
$60$	−38978.3			−0.180455
$61$			34949.8i			0.153977i	0.997032	+	0.0769885i	$0.0245305\pi$
$61$			34949.8i			0.153977i	−0.997032	+	0.0769885i	$0.975470\pi$
$62$		−	192377.i		−	0.807196i
$63$			21286.5i			0.0851301i
$64$	−291564.			−1.11223
$65$		−	129023.i		−	0.469814i
$66$	70257.5			0.244377
$67$	−299904.			−0.997143			−0.498572	−	0.866849i	$-0.666142\pi$
$67$	−299904.			−0.997143			−0.498572	+	0.866849i	$0.666142\pi$
$68$	−104630.			−0.332758
$69$		−	122643.i		−	0.373331i
$70$		−	68119.5i		−	0.198599i
$71$		−	362351.i		−	1.01241i	−0.862414	−	0.506203i	$-0.831049\pi$
$71$		−	362351.i		−	1.01241i	0.862414	−	0.506203i	$-0.168951\pi$
$72$		−	186126.i		−	0.498665i
$73$		−	89951.1i		−	0.231227i	−0.993294	−	0.115613i	$-0.963117\pi$
$73$		−	89951.1i		−	0.231227i	0.993294	−	0.115613i	$-0.0368833\pi$
$74$	−168452.			−0.415701
$75$			145868.i			0.345761i
$76$			148847.i			0.339078i
$77$		−	31309.7i		−	0.0685814i
$78$	−120043.			−0.252960
$79$	434327.			0.880917			0.440459	−	0.897773i	$-0.354816\pi$
$79$	434327.			0.880917			0.440459	+	0.897773i	$0.354816\pi$
$80$			469391.i			0.916779i
$81$	−170129.			−0.320127
$82$		−	623800.i		−	1.13137i
$83$	662276.			1.15826			0.579128	−	0.815236i	$-0.303393\pi$
$83$	662276.			1.15826			0.579128	+	0.815236i	$0.303393\pi$
$84$	16161.4			0.0272672
$85$			1.22041e6i			1.98723i
$86$	−59438.3	−	564652.i	−0.0934483	−	0.887739i
$87$	−470523.			−0.714535
$88$			273767.i			0.401729i
$89$			1.26108e6i			1.78884i	0.447223	+	0.894422i	$0.352413\pi$
$89$			1.26108e6i			1.78884i	−0.447223	+	0.894422i	$0.647587\pi$
$90$	−366621.			−0.502910
$91$			53496.0i			0.0709900i
$92$	80703.2			0.103640
$93$		−	532366.i		−	0.661853i
$94$			278538.i			0.335352i
$95$	1.73616e6			2.02497
$96$	−258761.			−0.292473
$97$	83771.3			0.0917868			0.0458934	−	0.998946i	$-0.485387\pi$
$97$	83771.3			0.0917868			0.0458934	+	0.998946i	$0.485387\pi$
$98$		−	811906.i		−	0.862635i
$99$	−168510.			−0.173668
$100$	−95986.5			−0.0959865
$101$	1.19842e6			1.16318			0.581588	−	0.813483i	$-0.302432\pi$
$101$	1.19842e6			1.16318			0.581588	+	0.813483i	$0.302432\pi$
$102$	1.13546e6			1.06997
$103$	737144.			0.674592			0.337296	−	0.941399i	$-0.390488\pi$
$103$	737144.			0.674592			0.337296	+	0.941399i	$0.390488\pi$
$104$		−	467760.i		−	0.415837i
$105$		−	188507.i		−	0.162840i
$106$			1.27234e6i			1.06829i
$107$	−604874.			−0.493758			−0.246879	−	0.969046i	$-0.579405\pi$
$107$	−604874.			−0.493758			−0.246879	+	0.969046i	$0.579405\pi$
$108$		−	274320.i		−	0.217764i
$109$	−1.09966e6			−0.849137			−0.424569	−	0.905396i	$-0.639574\pi$
$109$	−1.09966e6			−0.849137			−0.424569	+	0.905396i	$0.639574\pi$
$110$	539252.			0.405148
$111$	−466157.			−0.340850
$112$		−	194621.i		−	0.138528i
$113$			543549.i			0.376707i	0.982101	+	0.188354i	$0.0603151\pi$
$113$			543549.i			0.376707i	−0.982101	+	0.188354i	$0.939685\pi$
$114$		−	1.61532e6i		−	1.09030i
$115$		−	941326.i		−	0.618937i
$116$		−	309621.i		−	0.198361i
$117$	287917.			0.179767
$118$		−	142383.i		−	0.0866585i
$119$		−	506010.i		−	0.300275i
$120$			1.64828e6i			0.953864i
$121$	−1.52371e6			−0.860092
$122$	249582.			0.137447
$123$		−	1.72624e6i		−	0.927655i
$124$	350316.			0.183736
$125$		−	1.25038e6i		−	0.640197i
$126$	152010.			0.0759908
$127$	−1.48723e6			−0.726050			−0.363025	−	0.931779i	$-0.618256\pi$
$127$	−1.48723e6			−0.726050			−0.363025	+	0.931779i	$0.618256\pi$
$128$			1.24408e6i			0.593225i
$129$	−164484.	−	1.56256e6i	−0.0766221	−	0.727894i
$130$	−921370.			−0.419377
$131$		−	1.22120e6i		−	0.543216i	−0.962408	−	0.271608i	$-0.912445\pi$
$131$		−	1.22120e6i		−	0.543216i	0.962408	−	0.271608i	$-0.0875554\pi$
$132$			127938.i			0.0556259i
$133$	−719856.			−0.305978
$134$			2.14166e6i			0.890094i
$135$	−3.19968e6			−1.30048
$136$			4.42447e6i			1.75891i
$137$			4.63396e6i			1.80215i	0.433663	+	0.901075i	$0.357221\pi$
$137$			4.63396e6i			1.80215i	−0.433663	+	0.901075i	$0.642779\pi$
$138$	−875809.			−0.333252
$139$	4.40785e6			1.64128			0.820640	−	0.571445i	$-0.193617\pi$
$139$	4.40785e6			1.64128			0.820640	+	0.571445i	$0.193617\pi$
$140$	124045.			0.0452057
$141$			770799.i			0.274969i
$142$	−2.58761e6			−0.903718
$143$	−423488.			−0.144822
$144$	−1.04746e6			−0.350791
$145$	−3.61144e6			−1.18461
$146$	−642355.			−0.206403
$147$		−	2.24679e6i		−	0.707310i
$148$		−	306748.i		−	0.0946231i
$149$			285992.i			0.0864560i	0.999065	+	0.0432280i	$0.0137642\pi$
$149$			285992.i			0.0864560i	−0.999065	+	0.0432280i	$0.986236\pi$
$150$	1.04167e6			0.308642
$151$			663208.i			0.192628i	0.995351	+	0.0963139i	$0.0307053\pi$
$151$			663208.i			0.192628i	−0.995351	+	0.0963139i	$0.969295\pi$
$152$	6.29430e6			1.79233
$153$	−2.72336e6			−0.760381
$154$	−223587.			−0.0612188
$155$		−	4.08610e6i		−	1.09727i
$156$		−	218596.i		−	0.0575795i
$157$		−	5.29376e6i		−	1.36793i	−0.729513	−	0.683967i	$-0.760253\pi$
$157$		−	5.29376e6i		−	1.36793i	0.729513	−	0.683967i	$-0.239747\pi$
$158$		−	3.10159e6i		−	0.786346i
$159$			3.52096e6i			0.875931i
$160$	−1.98609e6			−0.484884
$161$			390297.i			0.0935229i
$162$			1.21492e6i			0.285760i
$163$		−	3.06833e6i		−	0.708499i	−0.935151	−	0.354250i	$-0.884736\pi$
$163$		−	3.06833e6i		−	0.708499i	0.935151	−	0.354250i	$-0.115264\pi$
$164$	1.13593e6			0.257525
$165$	1.49227e6			0.332198
$166$		−	4.72942e6i		−	1.03391i
$167$	3.30726e6			0.710100			0.355050	−	0.934847i	$-0.384464\pi$
$167$	3.30726e6			0.710100			0.355050	+	0.934847i	$0.384464\pi$
$168$		−	683416.i		−	0.144131i
$169$	−4.10323e6			−0.850092
$170$	8.71510e6			1.77389
$171$			3.87429e6i			0.774825i
$172$	1.02822e6	−	108236.i	0.202070	−	0.0212710i
$173$	4.04583e6			0.781393			0.390696	−	0.920520i	$-0.372234\pi$
$173$	4.04583e6			0.781393			0.390696	+	0.920520i	$0.372234\pi$
$174$			3.36008e6i			0.637825i
$175$		−	464210.i		−	0.0866165i
$176$	1.54067e6			0.282600
$177$		−	394016.i		−	0.0710549i
$178$	9.00557e6			1.59680
$179$			1.00806e7i			1.75763i	0.477160	+	0.878816i	$0.341666\pi$
$179$			1.00806e7i			1.75763i	−0.477160	+	0.878816i	$0.658334\pi$
$180$		−	667612.i		−	0.114474i
$181$	−7.62117e6			−1.28524			−0.642622	−	0.766183i	$-0.722154\pi$
$181$	−7.62117e6			−1.28524			−0.642622	+	0.766183i	$0.722154\pi$
$182$	382023.			0.0633688
$183$	690669.			0.112698
$184$		−	3.41270e6i		−	0.547828i
$185$	−3.57793e6			−0.565088
$186$	−3.80171e6			−0.590800
$187$	4.00571e6			0.612569
$188$	−507213.			−0.0763339
$189$	1.32667e6			0.196506
$190$		−	1.23982e7i		−	1.80758i
$191$			9.84078e6i			1.41231i	0.708058	+	0.706154i	$0.249571\pi$
$191$			9.84078e6i			1.41231i	−0.708058	+	0.706154i	$0.750429\pi$
$192$			5.76181e6i			0.814058i
$193$	2.29302e6			0.318960			0.159480	−	0.987201i	$-0.449018\pi$
$193$	2.29302e6			0.318960			0.159480	+	0.987201i	$0.449018\pi$
$194$		−	598224.i		−	0.0819329i
$195$	−2.54971e6			−0.343864
$196$	1.47847e6			0.196356
$197$	3.50465e6			0.458401			0.229201	−	0.973379i	$-0.426389\pi$
$197$	3.50465e6			0.458401			0.229201	+	0.973379i	$0.426389\pi$
$198$			1.20335e6i			0.155024i
$199$			7.63511e6i			0.968849i	0.874833	+	0.484425i	$0.160971\pi$
$199$			7.63511e6i			0.968849i	−0.874833	+	0.484425i	$0.839029\pi$
$200$			4.05898e6i			0.507372i
$201$			5.92662e6i			0.729825i
$202$		−	8.55811e6i		−	1.03830i
$203$	1.49739e6			0.178998
$204$			2.06766e6i			0.243551i
$205$		−	1.32495e7i		−	1.53794i
$206$		−	5.26406e6i		−	0.602170i
$207$	2.10059e6			0.236827
$208$	−2.63241e6			−0.292525
$209$		−	5.69857e6i		−	0.624205i
$210$	−1.34616e6			−0.145358
$211$			1.06028e7i			1.12869i	0.825540	+	0.564344i	$0.190871\pi$
$211$			1.06028e7i			1.12869i	−0.825540	+	0.564344i	$0.809129\pi$
$212$	−2.31692e6			−0.243166
$213$	−7.16069e6			−0.740996
$214$			4.31950e6i			0.440750i
$215$	−1.26247e6	−	1.19932e7i	−0.127030	−	1.20676i
$216$	−1.16001e7			−1.15107
$217$			1.69420e6i			0.165800i
$218$			7.85282e6i			0.757978i
$219$	−1.77759e6			−0.169238
$220$			981969.i			0.0922210i
$221$	−6.84419e6			−0.634082
$222$			3.32890e6i			0.304258i
$223$		−	6.78272e6i		−	0.611631i	−0.952091	−	0.305815i	$-0.901071\pi$
$223$		−	6.78272e6i		−	0.611631i	0.952091	−	0.305815i	$-0.0989290\pi$
$224$	823481.			0.0732671
$225$	−2.49839e6			−0.219338
$226$	3.88157e6			0.336265
$227$		−	2.30718e6i		−	0.197244i	−0.995125	−	0.0986220i	$-0.968557\pi$
$227$		−	2.30718e6i		−	0.197244i	0.995125	−	0.0986220i	$-0.0314435\pi$
$228$	2.94148e6			0.248177
$229$	−3.28542e6			−0.273580			−0.136790	−	0.990600i	$-0.543679\pi$
$229$	−3.28542e6			−0.273580			−0.136790	+	0.990600i	$0.543679\pi$
$230$	−6.72215e6			−0.552491
$231$	−618733.			−0.0501958
$232$	−1.30930e7			−1.04851
$233$		−	1.01559e6i		−	0.0802878i	−0.999194	−	0.0401439i	$-0.987218\pi$
$233$		−	1.01559e6i		−	0.0802878i	0.999194	−	0.0401439i	$-0.0127816\pi$
$234$		−	2.05606e6i		−	0.160468i
$235$			5.91616e6i			0.455865i
$236$	259277.			0.0197255
$237$		−	8.58304e6i		−	0.644757i
$238$	−3.61350e6			−0.268038
$239$	1.27984e7			0.937479			0.468740	−	0.883336i	$-0.344708\pi$
$239$	1.27984e7			0.937479			0.468740	+	0.883336i	$0.344708\pi$
$240$	9.27598e6			0.671005
$241$			7.77825e6i			0.555688i	0.960626	+	0.277844i	$0.0896198\pi$
$241$			7.77825e6i			0.555688i	−0.960626	+	0.277844i	$0.910380\pi$
$242$			1.08810e7i			0.767756i
$243$		−	1.20163e7i		−	0.837438i
$244$			454485.i			0.0312860i
$245$		−	1.72449e7i		−	1.17263i
$246$	−1.23274e7			−0.828066
$247$			9.73662e6i			0.646127i
$248$		−	1.48138e7i		−	0.971207i
$249$		−	1.30877e7i		−	0.847746i
$250$	−8.92919e6			−0.571468
$251$	1.19067e7			0.752956			0.376478	−	0.926425i	$-0.377135\pi$
$251$	1.19067e7			0.752956			0.376478	+	0.926425i	$0.377135\pi$
$252$			276808.i			0.0172973i
$253$	−3.08970e6			−0.190789
$254$			1.06205e7i			0.648104i
$255$	2.41173e7			1.45448
$256$	−9.77590e6			−0.582689
$257$		−	6.20650e6i		−	0.365635i	−0.983147	−	0.182817i	$-0.941478\pi$
$257$		−	6.20650e6i		−	0.365635i	0.983147	−	0.182817i	$-0.0585217\pi$
$258$	−1.11585e7	+	1.17460e6i	−0.649750	+	0.0683963i
$259$	1.48350e6			0.0853861
$260$		−	1.67780e6i		−	0.0954598i
$261$		−	8.05901e6i		−	0.453273i
$262$	−8.72076e6			−0.484898
$263$			1.56294e7i			0.859162i	0.903028	+	0.429581i	$0.141339\pi$
$263$			1.56294e7i			0.859162i	−0.903028	+	0.429581i	$0.858661\pi$
$264$	5.41010e6			0.294032
$265$			2.70247e7i			1.45219i
$266$			5.14060e6i			0.273130i
$267$	2.49211e7			1.30928
$268$	−3.89993e6			−0.202606
$269$	−2.69821e7			−1.38618			−0.693090	−	0.720851i	$-0.743751\pi$
$269$	−2.69821e7			−1.38618			−0.693090	+	0.720851i	$0.743751\pi$
$270$			2.28494e7i			1.16087i
$271$	2.23391e7			1.12243			0.561213	−	0.827672i	$-0.310335\pi$
$271$	2.23391e7			1.12243			0.561213	+	0.827672i	$0.310335\pi$
$272$	2.48995e7			1.23733
$273$	1.05717e6			0.0519587
$274$	3.30919e7			1.60868
$275$	3.67481e6			0.176700
$276$		−	1.59484e6i		−	0.0758558i
$277$			3.66692e7i			1.72529i	0.505812	+	0.862644i	$0.331193\pi$
$277$			3.66692e7i			1.72529i	−0.505812	+	0.862644i	$0.668807\pi$
$278$		−	3.14772e7i		−	1.46508i
$279$	9.11824e6			0.419854
$280$		−	5.24547e6i		−	0.238952i
$281$	−3.37401e7			−1.52065			−0.760323	−	0.649546i	$-0.774959\pi$
$281$	−3.37401e7			−1.52065			−0.760323	+	0.649546i	$0.774959\pi$
$282$	5.50439e6			0.245449
$283$	−1.38133e7			−0.609448			−0.304724	−	0.952441i	$-0.598564\pi$
$283$	−1.38133e7			−0.609448			−0.304724	+	0.952441i	$0.598564\pi$
$284$		−	4.71199e6i		−	0.205707i
$285$		−	3.43096e7i		−	1.48211i
$286$			3.02420e6i			0.129274i
$287$			5.49359e6i			0.232386i
$288$		−	4.43200e6i		−	0.185533i
$289$	4.06006e7			1.68205
$290$			2.57898e7i			1.05744i
$291$		−	1.65547e6i		−	0.0671802i
$292$		−	1.16972e6i		−	0.0469821i
$293$	3.07684e7			1.22321			0.611605	−	0.791163i	$-0.290524\pi$
$293$	3.07684e7			1.22321			0.611605	+	0.791163i	$0.290524\pi$
$294$	−1.60447e7			−0.631377
$295$		−	3.02421e6i		−	0.117800i
$296$	−1.29715e7			−0.500165
$297$			1.05022e7i			0.400878i
$298$	2.04231e6			0.0771744
$299$	5.27908e6			0.197490
$300$			1.89686e6i			0.0702540i
$301$	523453.	+	4.97269e6i	0.0191946	+	0.182344i
$302$	4.73607e6			0.171948
$303$		−	2.36829e7i		−	0.851347i
$304$		−	3.54223e7i		−	1.26083i
$305$	5.30114e6			0.186840
$306$			1.94480e7i			0.678750i
$307$	1.70554e7			0.589450			0.294725	−	0.955582i	$-0.404772\pi$
$307$	1.70554e7			0.589450			0.294725	+	0.955582i	$0.404772\pi$
$308$		−	407149.i		−	0.0139348i
$309$		−	1.45672e7i		−	0.493744i
$310$	−2.91795e7			−0.979474
$311$	−1.62947e7			−0.541709			−0.270855	−	0.962620i	$-0.587306\pi$
$311$	−1.62947e7			−0.541709			−0.270855	+	0.962620i	$0.587306\pi$
$312$	−9.24375e6			−0.304358
$313$			3.82726e7i			1.24811i	0.781379	+	0.624057i	$0.214517\pi$
$313$			3.82726e7i			1.24811i	−0.781379	+	0.624057i	$0.785483\pi$
$314$	−3.78035e7			−1.22108
$315$	3.22870e6			0.103299
$316$	5.64795e6			0.178990
$317$	−3.73589e7			−1.17278			−0.586390	−	0.810029i	$-0.699452\pi$
$317$	−3.73589e7			−1.17278			−0.586390	+	0.810029i	$0.699452\pi$
$318$	2.51437e7			0.781895
$319$			1.18538e7i			0.365160i
$320$			4.42240e7i			1.34961i
$321$			1.19534e7i			0.361389i
$322$	2.78717e6			0.0834826
$323$		−	9.20972e7i		−	2.73300i
$324$	−2.21234e6			−0.0650455
$325$	−6.27881e6			−0.182906
$326$	−2.19114e7			−0.632438
$327$			2.17311e7i			0.621497i
$328$		−	4.80350e7i		−	1.36125i
$329$		−	2.45299e6i		−	0.0688823i
$330$		−	1.06565e7i		−	0.296534i
$331$		−	5.23966e7i		−	1.44484i	−0.691455	−	0.722419i	$-0.743030\pi$
$331$		−	5.23966e7i		−	1.44484i	0.691455	−	0.722419i	$-0.256970\pi$
$332$	8.61219e6			0.235342
$333$		−	7.98423e6i		−	0.216222i
$334$		−	2.36177e7i		−	0.633866i
$335$			4.54889e7i			1.20996i
$336$	−3.84605e6			−0.101390
$337$	−1.79657e7			−0.469413			−0.234706	−	0.972066i	$-0.575413\pi$
$337$	−1.79657e7			−0.469413			−0.234706	+	0.972066i	$0.575413\pi$
$338$			2.93018e7i			0.758830i
$339$	1.07415e7			0.275718
$340$			1.58701e7i			0.403777i
$341$	−1.34117e7			−0.338238
$342$	2.76669e7			0.691643
$343$			1.45491e7i			0.360540i
$344$	−4.57699e6	−	4.34804e7i	−0.112436	−	1.06812i
$345$	−1.86022e7			−0.453010
$346$		−	2.88919e7i		−	0.697506i
$347$			1.42201e7i			0.340342i	0.985415	+	0.170171i	$0.0544319\pi$
$347$			1.42201e7i			0.340342i	−0.985415	+	0.170171i	$0.945568\pi$
$348$	−6.11865e6			−0.145184
$349$			5.94543e7i			1.39864i	0.714807	+	0.699322i	$0.246515\pi$
$349$			5.94543e7i			1.39864i	−0.714807	+	0.699322i	$0.753485\pi$
$350$	−3.31500e6			−0.0773177
$351$		−	1.79442e7i		−	0.414957i
$352$			6.51889e6i			0.149467i
$353$	−4.22812e7			−0.961222			−0.480611	−	0.876934i	$-0.659585\pi$
$353$	−4.22812e7			−0.961222			−0.480611	+	0.876934i	$0.659585\pi$
$354$	−2.81373e6			−0.0634267
$355$	−5.49609e7			−1.22848
$356$			1.63990e7i			0.363469i
$357$	−9.99964e6			−0.219776
$358$	7.19873e7			1.56894
$359$	−4.65626e6			−0.100636			−0.0503181	−	0.998733i	$-0.516024\pi$
$359$	−4.65626e6			−0.100636			−0.0503181	+	0.998733i	$0.516024\pi$
$360$	−2.82313e7			−0.605094
$361$	−8.39726e7			−1.78491
$362$			5.44239e7i			1.14727i
$363$			3.01110e7i			0.629515i
$364$			695658.i			0.0144242i
$365$	−1.36436e7			−0.280577
$366$		−	4.93218e6i		−	0.100599i
$367$	8.70497e7			1.76104			0.880519	−	0.474010i	$-0.157194\pi$
$367$	8.70497e7			1.76104			0.880519	+	0.474010i	$0.157194\pi$
$368$	−1.92056e7			−0.385375
$369$	2.95667e7			0.588469
$370$			2.55505e7i			0.504423i
$371$		−	1.12051e7i		−	0.219429i
$372$		−	6.92285e6i		−	0.134480i
$373$			7.31787e7i			1.41013i	0.709144	+	0.705064i	$0.249082\pi$
$373$			7.31787e7i			1.41013i	−0.709144	+	0.705064i	$0.750918\pi$
$374$		−	2.86054e7i		−	0.546806i
$375$	−2.47098e7			−0.468570
$376$			2.14485e7i			0.403491i
$377$		−	2.02534e7i		−	0.377985i
$378$		−	9.47392e6i		−	0.175410i
$379$	6.34098e7			1.16477			0.582383	−	0.812914i	$-0.302120\pi$
$379$	6.34098e7			1.16477			0.582383	+	0.812914i	$0.302120\pi$
$380$	2.25769e7			0.411447
$381$			2.93902e7i			0.531407i
$382$	7.02745e7			1.26069
$383$			3.12303e7i			0.555878i	0.960599	+	0.277939i	$0.0896514\pi$
$383$			3.12303e7i			0.555878i	−0.960599	+	0.277939i	$0.910349\pi$
$384$	2.45852e7			0.434191
$385$	−4.74900e6			−0.0832186
$386$		−	1.63748e7i		−	0.284718i
$387$	2.67632e7	−	2.81724e6i	0.461748	−	0.0486061i
$388$	1.08936e6			0.0186498
$389$		−	8.33816e7i		−	1.41652i	−0.705954	−	0.708258i	$-0.749481\pi$
$389$		−	8.33816e7i		−	1.41652i	0.705954	−	0.708258i	$-0.250519\pi$
$390$			1.82079e7i			0.306948i
$391$	−4.99340e7			−0.835346
$392$		−	6.25199e7i		−	1.03791i
$393$	−2.41330e7			−0.397588
$394$		−	2.50272e7i		−	0.409189i
$395$		−	6.58780e7i		−	1.06893i
$396$	−2.19129e6			−0.0352869
$397$	5.18629e7			0.828868			0.414434	−	0.910079i	$-0.363980\pi$
$397$	5.18629e7			0.828868			0.414434	+	0.910079i	$0.363980\pi$
$398$	5.45235e7			0.864838
$399$			1.42256e7i			0.223950i
$400$	2.28426e7			0.356916
$401$	−7.16633e7			−1.11138			−0.555692	−	0.831389i	$-0.687546\pi$
$401$	−7.16633e7			−1.11138			−0.555692	+	0.831389i	$0.687546\pi$
$402$	4.23229e7			0.651474
$403$	2.29154e7			0.350117
$404$	1.55842e7			0.236342
$405$			2.58049e7i			0.388451i
$406$		−	1.06931e7i		−	0.159781i
$407$			1.17438e7i			0.174190i
$408$	8.74352e7			1.28738
$409$		−	7.67014e7i		−	1.12107i	−0.828130	−	0.560536i	$-0.810595\pi$
$409$		−	7.67014e7i		−	1.12107i	0.828130	−	0.560536i	$-0.189405\pi$
$410$	−9.46170e7			−1.37283
$411$	9.15751e7			1.31902
$412$	9.58577e6			0.137068
$413$			1.25391e6i			0.0177999i
$414$		−	1.50007e7i		−	0.211402i
$415$		−	1.00453e8i		−	1.40546i
$416$		−	1.11382e7i		−	0.154716i
$417$		−	8.71068e7i		−	1.20128i
$418$	−4.06944e7			−0.557193
$419$			1.21037e8i			1.64542i	0.568463	+	0.822709i	$0.307538\pi$
$419$			1.21037e8i			1.64542i	−0.568463	+	0.822709i	$0.692462\pi$
$420$		−	2.45133e6i		−	0.0330868i
$421$		−	9.79470e7i		−	1.31264i	−0.754484	−	0.656319i	$-0.772113\pi$
$421$		−	9.79470e7i		−	1.31264i	0.754484	−	0.656319i	$-0.227887\pi$
$422$	7.57163e7			1.00752
$423$	−1.32021e7			−0.174430
$424$			9.79755e7i			1.28535i
$425$	5.93903e7			0.773658
$426$			5.11356e7i			0.661446i
$427$	−2.19798e6			−0.0282319
$428$	−7.86574e6			−0.100325
$429$			8.36886e6i			0.105997i
$430$	−8.56455e7	+	9.01551e6i	−1.07721	+	0.113393i
$431$	−1.07153e8			−1.33836			−0.669180	−	0.743100i	$-0.733355\pi$
$431$	−1.07153e8			−1.33836			−0.669180	+	0.743100i	$0.733355\pi$
$432$			6.52820e7i			0.809733i
$433$			6.76798e7i			0.833672i	0.908982	+	0.416836i	$0.136861\pi$
$433$			6.76798e7i			0.833672i	−0.908982	+	0.416836i	$0.863139\pi$
$434$	1.20985e7			0.148001
$435$			7.13683e7i			0.867036i
$436$	−1.42999e7			−0.172533
$437$			7.10367e7i			0.851213i
$438$			1.26940e7i			0.151070i
$439$	−4.94825e7			−0.584868			−0.292434	−	0.956286i	$-0.594465\pi$
$439$	−4.94825e7			−0.584868			−0.292434	+	0.956286i	$0.594465\pi$
$440$	4.15245e7			0.487468
$441$	3.84824e7			0.448690
$442$			4.88754e7i			0.566010i
$443$	−1.18835e8			−1.36689			−0.683446	−	0.730001i	$-0.739520\pi$
$443$	−1.18835e8			−1.36689			−0.683446	+	0.730001i	$0.739520\pi$
$444$	−6.06188e6			−0.0692561
$445$	1.91279e8			2.17063
$446$	−4.84365e7			−0.545969
$447$	5.65170e6			0.0632785
$448$		−	1.83364e7i		−	0.203929i
$449$			4.56263e7i			0.504054i	0.967720	+	0.252027i	$0.0810971\pi$
$449$			4.56263e7i			0.504054i	−0.967720	+	0.252027i	$0.918903\pi$
$450$			1.78414e7i			0.195791i
$451$	−4.34887e7			−0.474075
$452$			7.06828e6i			0.0765418i
$453$	1.31061e7			0.140987
$454$	−1.64759e7			−0.176069
$455$	8.11419e6			0.0861412
$456$		−	1.24386e8i		−	1.31183i
$457$		−	1.21404e8i		−	1.27199i	−0.771693	−	0.635996i	$-0.780590\pi$
$457$		−	1.21404e8i		−	1.27199i	0.771693	−	0.635996i	$-0.219410\pi$
$458$			2.34617e7i			0.244209i
$459$			1.69732e8i			1.75519i
$460$		−	1.22409e7i		−	0.125760i
$461$	−1.90871e8			−1.94821			−0.974106	−	0.226093i	$-0.927405\pi$
$461$	−1.90871e8			−1.94821			−0.974106	+	0.226093i	$0.927405\pi$
$462$			4.41847e6i			0.0448070i
$463$		−	8.17525e6i		−	0.0823680i	−0.999152	−	0.0411840i	$-0.986887\pi$
$463$		−	8.17525e6i		−	0.0823680i	0.999152	−	0.0411840i	$-0.0131130\pi$
$464$			7.36830e7i			0.737587i
$465$	−8.07485e7			−0.803111
$466$	−7.25247e6			−0.0716684
$467$		−	1.86571e8i		−	1.83186i	−0.401334	−	0.915932i	$-0.631453\pi$
$467$		−	1.86571e8i		−	1.83186i	0.401334	−	0.915932i	$-0.368547\pi$
$468$	3.74405e6			0.0365262
$469$		−	1.88608e7i		−	0.182828i
$470$	4.22482e7			0.406925
$471$	−1.04614e8			−1.00121
$472$		−	1.09640e7i		−	0.104266i
$473$	−3.93652e7	+	4.14379e6i	−0.371988	+	0.0391574i
$474$	−6.12928e7			−0.575539
$475$		−	8.44893e7i		−	0.788353i
$476$		−	6.58012e6i		−	0.0610117i
$477$	−6.03062e7			−0.555657
$478$		−	9.13952e7i		−	0.836835i
$479$	1.51306e8			1.37673			0.688365	−	0.725364i	$-0.258329\pi$
$479$	1.51306e8			1.37673			0.688365	+	0.725364i	$0.258329\pi$
$480$			3.92485e7i			0.354894i
$481$		−	2.00655e7i		−	0.180308i
$482$	5.55457e7			0.496031
$483$	7.71295e6			0.0684509
$484$	−1.98142e7			−0.174759
$485$		−	1.27063e7i		−	0.111377i
$486$	−8.58103e7			−0.747534
$487$	1.17577e8			1.01797			0.508984	−	0.860776i	$-0.330021\pi$
$487$	1.17577e8			1.01797			0.508984	+	0.860776i	$0.330021\pi$
$488$	1.92188e7			0.165374
$489$	−6.06355e7			−0.518562
$490$	−1.23149e8			−1.04675
$491$			1.63911e7i			0.138472i	0.997600	+	0.0692362i	$0.0220562\pi$
$491$			1.63911e7i			0.138472i	−0.997600	+	0.0692362i	$0.977944\pi$
$492$		−	2.24479e7i		−	0.188487i
$493$			1.91574e8i			1.59881i
$494$	6.95307e7			0.576761
$495$			2.55593e7i			0.210733i
$496$	−8.33675e7			−0.683206
$497$	2.27881e7			0.185626
$498$	−9.34614e7			−0.756736
$499$		−	1.32763e8i		−	1.06850i	−0.845325	−	0.534252i	$-0.820593\pi$
$499$		−	1.32763e8i		−	1.06850i	0.845325	−	0.534252i	$-0.179407\pi$
$500$		−	1.62599e7i		−	0.130079i
$501$		−	6.53572e7i		−	0.519733i
$502$		−	8.50275e7i		−	0.672122i
$503$			2.13319e8i			1.67620i	0.545518	+	0.838099i	$0.316333\pi$
$503$			2.13319e8i			1.67620i	−0.545518	+	0.838099i	$0.683667\pi$
$504$	1.17054e7			0.0914312
$505$		−	1.81775e8i		−	1.41143i
$506$			2.20640e7i			0.170307i
$507$			8.10870e7i			0.622196i
$508$	−1.93398e7			−0.147523
$509$	2.22706e8			1.68880			0.844400	−	0.535713i	$-0.179957\pi$
$509$	2.22706e8			1.68880			0.844400	+	0.535713i	$0.179957\pi$
$510$		−	1.72225e8i		−	1.29834i
$511$	5.65699e6			0.0423958
$512$			1.49433e8i			1.11336i
$513$	2.41462e8			1.78853
$514$	−4.43216e7			−0.326382
$515$		−	1.11809e8i		−	0.818568i
$516$	−2.13894e6	−	2.03195e7i	−0.0155686	−	0.147898i
$517$	1.94185e7			0.140522
$518$		−	1.05939e7i		−	0.0762194i
$519$		−	7.99526e7i		−	0.571914i
$520$	−7.09491e7			−0.504588
$521$		−	8.01608e7i		−	0.566825i	−0.958998	−	0.283412i	$-0.908533\pi$
$521$		−	8.01608e7i		−	0.566825i	0.958998	−	0.283412i	$-0.0914665\pi$
$522$	−5.75506e7			−0.404612
$523$			1.76645e8i			1.23480i	0.786650	+	0.617400i	$0.211814\pi$
$523$			1.76645e8i			1.23480i	−0.786650	+	0.617400i	$0.788186\pi$
$524$		−	1.58804e7i		−	0.110374i
$525$	−9.17359e6			−0.0633960
$526$	1.11612e8			0.766926
$527$	−2.16753e8			−1.48093
$528$		−	3.04464e7i		−	0.206840i
$529$	−1.09521e8			−0.739825
$530$	1.92987e8			1.29629
$531$	6.74861e6			0.0450745
$532$	−9.36095e6			−0.0621706
$533$	7.43052e7			0.490724
$534$		−	1.77966e8i		−	1.16872i
$535$			9.17464e7i			0.599139i
$536$			1.64916e8i			1.07095i
$537$	1.99210e8			1.28644
$538$			1.92684e8i			1.23736i
$539$	−5.66026e7			−0.361468
$540$	−4.16084e7			−0.264241
$541$	−6.68009e7			−0.421882			−0.210941	−	0.977499i	$-0.567653\pi$
$541$	−6.68009e7			−0.421882			−0.210941	+	0.977499i	$0.567653\pi$
$542$		−	1.59527e8i		−	1.00193i
$543$			1.50607e8i			0.940691i
$544$			1.05355e8i			0.654422i
$545$			1.66794e8i			1.03037i
$546$		−	7.54944e6i		−	0.0463806i
$547$	1.50528e8			0.919718			0.459859	−	0.887992i	$-0.347900\pi$
$547$	1.50528e8			0.919718			0.459859	+	0.887992i	$0.347900\pi$
$548$			6.02598e7i			0.366172i
$549$			1.18296e7i			0.0714914i
$550$		−	2.62424e7i		−	0.157730i
$551$	2.72535e8			1.62918
$552$	−6.74408e7			−0.400964
$553$			2.73146e7i			0.161518i
$554$	2.61860e8			1.54007
$555$			7.07060e7i			0.413597i
$556$	5.73194e7			0.333486
$557$	2.12922e8			1.23213			0.616063	−	0.787697i	$-0.288727\pi$
$557$	2.12922e8			1.23213			0.616063	+	0.787697i	$0.288727\pi$
$558$		−	6.51148e7i		−	0.374780i
$559$	6.72596e7	−	7.08012e6i	0.385052	−	0.0405326i
$560$	−2.95198e7			−0.168093
$561$		−	7.91598e7i		−	0.448349i
$562$			2.40943e8i			1.35739i
$563$	−2.20517e8			−1.23571			−0.617854	−	0.786293i	$-0.711998\pi$
$563$	−2.20517e8			−1.23571			−0.617854	+	0.786293i	$0.711998\pi$
$564$			1.00234e7i			0.0558700i
$565$	8.24447e7			0.457107
$566$			9.86426e7i			0.544021i
$567$		−	1.06993e7i		−	0.0586959i
$568$	−1.99256e8			−1.08734
$569$	−7.04114e7			−0.382214			−0.191107	−	0.981569i	$-0.561208\pi$
$569$	−7.04114e7			−0.382214			−0.191107	+	0.981569i	$0.561208\pi$
$570$	−2.45010e8			−1.32300
$571$		−	1.62010e8i		−	0.870230i	−0.900375	−	0.435115i	$-0.856708\pi$
$571$		−	1.62010e8i		−	0.870230i	0.900375	−	0.435115i	$-0.143292\pi$
$572$	−5.50701e6			−0.0294258
$573$	1.94471e8			1.03369
$574$	3.92306e7			0.207438
$575$	−4.58091e7			−0.240962
$576$	−9.86869e7			−0.516407
$577$			1.10893e8i			0.577267i	0.957440	+	0.288633i	$0.0932009\pi$
$577$			1.10893e8i			0.577267i	−0.957440	+	0.288633i	$0.906799\pi$
$578$		−	2.89935e8i		−	1.50147i
$579$		−	4.53140e7i		−	0.233452i
$580$	−4.69629e7			−0.240697
$581$			4.16503e7i			0.212368i
$582$	−1.18219e7			−0.0599680
$583$	8.87025e7			0.447641
$584$	−4.94638e7			−0.248341
$585$		−	4.36708e7i		−	0.218134i
$586$		−	2.19722e8i		−	1.09189i
$587$		−	3.50946e8i		−	1.73510i	−0.497346	−	0.867552i	$-0.665692\pi$
$587$		−	3.50946e8i		−	1.73510i	0.497346	−	0.867552i	$-0.334308\pi$
$588$		−	2.92171e7i		−	0.143716i
$589$			3.08356e8i			1.50906i
$590$	−2.15964e7			−0.105154
$591$		−	6.92579e7i		−	0.335511i
$592$			7.29993e7i			0.351847i
$593$		−	2.22461e8i		−	1.06682i	−0.845857	−	0.533409i	$-0.820911\pi$
$593$		−	2.22461e8i		−	1.06682i	0.845857	−	0.533409i	$-0.179089\pi$
$594$	7.49981e7			0.357842
$595$	−7.67508e7			−0.364361
$596$			3.71902e6i			0.0175667i
$597$	1.50883e8			0.709116
$598$		−	3.76987e7i		−	0.176288i
$599$	−1.33213e8			−0.619818			−0.309909	−	0.950766i	$-0.600299\pi$
$599$	−1.33213e8			−0.619818			−0.309909	+	0.950766i	$0.600299\pi$
$600$	8.02124e7			0.371354
$601$			2.01869e8i			0.929923i	0.885331	+	0.464961i	$0.153932\pi$
$601$			2.01869e8i			0.929923i	−0.885331	+	0.464961i	$0.846068\pi$
$602$	3.55108e7	−	3.73806e6i	0.162769	−	0.0171339i
$603$	−1.01510e8			−0.462973
$604$			8.62432e6i			0.0391394i
$605$			2.31113e8i			1.04366i
$606$	−1.69123e8			−0.759950
$607$		−	2.22303e8i		−	0.993984i	−0.867755	−	0.496992i	$-0.834438\pi$
$607$		−	2.22303e8i		−	0.993984i	0.867755	−	0.496992i	$-0.165562\pi$
$608$	1.49879e8			0.666853
$609$		−	2.95911e7i		−	0.131011i
$610$		−	3.78562e7i		−	0.166782i
$611$	−3.31786e7			−0.145457
$612$	−3.54144e7			−0.154499
$613$	−1.59462e8			−0.692272			−0.346136	−	0.938184i	$-0.612506\pi$
$613$	−1.59462e8			−0.692272			−0.346136	+	0.938184i	$0.612506\pi$
$614$		−	1.21795e8i		−	0.526169i
$615$	−2.61834e8			−1.12564
$616$	−1.72171e7			−0.0736576
$617$	2.02638e8			0.862710			0.431355	−	0.902182i	$-0.358036\pi$
$617$	2.02638e8			0.862710			0.431355	+	0.902182i	$0.358036\pi$
$618$	−1.04027e8			−0.440738
$619$	−3.11733e8			−1.31435			−0.657176	−	0.753737i	$-0.728249\pi$
$619$	−3.11733e8			−1.31435			−0.657176	+	0.753737i	$0.728249\pi$
$620$		−	5.31354e7i		−	0.222951i
$621$		−	1.30918e8i		−	0.546668i
$622$			1.16363e8i			0.483554i
$623$	−7.93089e7			−0.327988
$624$			5.20209e7i			0.214104i
$625$	−3.04990e8			−1.24924
$626$	2.73310e8			1.11412
$627$	−1.12614e8			−0.456865
$628$		−	6.88397e7i		−	0.277946i
$629$			1.89796e8i			0.762668i
$630$		−	2.30567e7i		−	0.0922094i
$631$			5.37251e7i			0.213840i	0.994268	+	0.106920i	$0.0340989\pi$
$631$			5.37251e7i			0.213840i	−0.994268	+	0.106920i	$0.965901\pi$
$632$		−	2.38835e8i		−	0.946120i
$633$	2.09530e8			0.826105
$634$			2.66786e8i			1.04688i
$635$			2.25580e8i			0.881008i
$636$			4.57863e7i			0.177977i
$637$	9.67117e7			0.374163
$638$	8.46495e7			0.325958
$639$		−	1.22647e8i		−	0.470059i
$640$	1.88701e8			0.719836
$641$		−	2.85462e8i		−	1.08386i	−0.840423	−	0.541932i	$-0.817693\pi$
$641$		−	2.85462e8i		−	1.08386i	0.840423	−	0.541932i	$-0.182307\pi$
$642$	8.53608e7			0.322592
$643$	1.02329e7			0.0384917			0.0192458	−	0.999815i	$-0.493873\pi$
$643$	1.02329e7			0.0384917			0.0192458	+	0.999815i	$0.493873\pi$
$644$			5.07540e6i			0.0190026i
$645$	−2.37007e8	+	2.49486e7i	−0.883247	+	0.0929754i
$646$	−6.57680e8			−2.43959
$647$			3.72540e8i			1.37550i	0.725948	+	0.687750i	$0.241401\pi$
$647$			3.72540e8i			1.37550i	−0.725948	+	0.687750i	$0.758599\pi$
$648$			9.35532e7i			0.343822i
$649$	−9.92632e6			−0.0363123
$650$			4.48380e7i			0.163270i
$651$	3.34803e7			0.121352
$652$		−	3.99004e7i		−	0.143957i
$653$			4.26942e7i			0.153331i	0.997057	+	0.0766653i	$0.0244273\pi$
$653$			4.26942e7i			0.153331i	−0.997057	+	0.0766653i	$0.975573\pi$
$654$	1.55185e8			0.554776
$655$	−1.85229e8			−0.659153
$656$	−2.70326e8			−0.957583
$657$		−	3.04461e7i		−	0.107358i
$658$	−1.75172e7			−0.0614874
$659$	5.08637e8			1.77726			0.888632	−	0.458621i	$-0.151656\pi$
$659$	5.08637e8			1.77726			0.888632	+	0.458621i	$0.151656\pi$
$660$	1.94054e7			0.0674980
$661$	−2.03116e7			−0.0703299			−0.0351650	−	0.999382i	$-0.511196\pi$
$661$	−2.03116e7			−0.0703299			−0.0351650	+	0.999382i	$0.511196\pi$
$662$	−3.74172e8			−1.28973
$663$			1.35253e8i			0.464095i
$664$		−	3.64184e8i		−	1.24399i
$665$			1.09187e8i			0.371282i
$666$	−5.70166e7			−0.193009
$667$		−	1.47765e8i		−	0.497961i
$668$	4.30074e7			0.144283
$669$	−1.34038e8			−0.447662
$670$	3.24843e8			1.08006
$671$		−	1.73998e7i		−	0.0575940i
$672$		−	1.62734e7i		−	0.0536254i
$673$			1.75373e8i			0.575329i	0.957731	+	0.287665i	$0.0928789\pi$
$673$			1.75373e8i			0.575329i	−0.957731	+	0.287665i	$0.907121\pi$
$674$			1.28296e8i			0.419018i
$675$			1.55710e8i			0.506298i
$676$	−5.33582e7			−0.172727
$677$		−	5.93350e8i		−	1.91225i	−0.292956	−	0.956126i	$-0.594639\pi$
$677$		−	5.93350e8i		−	1.91225i	0.292956	−	0.956126i	$-0.405361\pi$
$678$		−	7.67065e7i		−	0.246118i
$679$			5.26835e6i			0.0168293i
$680$	6.71097e8			2.13432
$681$	−4.55939e7			−0.144366
$682$			9.57753e7i			0.301926i
$683$	−3.53734e8			−1.11024			−0.555118	−	0.831772i	$-0.687327\pi$
$683$	−3.53734e8			−1.11024			−0.555118	+	0.831772i	$0.687327\pi$
$684$			5.03810e7i			0.157434i
$685$	7.02872e8			2.18678
$686$	1.03897e8			0.321834
$687$			6.49255e7i			0.200237i
$688$	−2.44694e8	+	2.57578e7i	−0.751377	+	0.0790941i
$689$	−1.51558e8			−0.463362
$690$			1.32841e8i			0.404377i
$691$			8.65200e7i			0.262230i	0.991367	+	0.131115i	$0.0418557\pi$
$691$			8.65200e7i			0.262230i	−0.991367	+	0.131115i	$0.958144\pi$
$692$	5.26117e7			0.158768
$693$		−	1.05975e7i		−	0.0318423i
$694$	1.01548e8			0.303804
$695$		−	6.68576e8i		−	1.99158i
$696$			2.58739e8i			0.767423i
$697$	−7.02841e8			−2.07567
$698$	4.24573e8			1.24849
$699$	−2.00698e7			−0.0587639
$700$		−	6.03656e6i		−	0.0175993i
$701$	1.50201e8			0.436032			0.218016	−	0.975945i	$-0.430042\pi$
$701$	1.50201e8			0.436032			0.218016	+	0.975945i	$0.430042\pi$
$702$	−1.28142e8			−0.370409
$703$	2.70006e8			0.777155
$704$	1.45155e8			0.416021
$705$	1.16914e8			0.333655
$706$			3.01937e8i			0.858029i
$707$			7.53683e7i			0.213270i
$708$		−	5.12375e6i		−	0.0144374i
$709$	7.03450e8			1.97376			0.986880	−	0.161454i	$-0.0516184\pi$
$709$	7.03450e8			1.97376			0.986880	+	0.161454i	$0.0516184\pi$
$710$			3.92484e8i			1.09660i
$711$	1.47008e8			0.409009
$712$	6.93464e8			1.92125
$713$	1.67187e8			0.461247
$714$			7.14090e7i			0.196181i
$715$			6.42341e7i			0.175731i
$716$			1.31088e8i			0.357127i
$717$		−	2.52918e8i		−	0.686156i
$718$			3.32511e7i			0.0898323i
$719$	−6.87823e8			−1.85050			−0.925252	−	0.379354i	$-0.876146\pi$
$719$	−6.87823e8			−1.85050			−0.925252	+	0.379354i	$0.876146\pi$
$720$			1.58877e8i			0.425660i
$721$			4.63587e7i			0.123688i
$722$			5.99661e8i			1.59329i
$723$	1.53712e8			0.406717
$724$	−9.91052e7			−0.261144
$725$			1.75749e8i			0.461188i
$726$	2.15028e8			0.561933
$727$		−	4.47696e8i		−	1.16514i	−0.812779	−	0.582572i	$-0.802046\pi$
$727$		−	4.47696e8i		−	1.16514i	0.812779	−	0.582572i	$-0.197954\pi$
$728$	2.94173e7			0.0762445
$729$	−3.61487e8			−0.933061
$730$			9.74313e7i			0.250455i
$731$	−6.36199e8	+	6.69697e7i	−1.62870	+	0.171446i
$732$	8.98142e6			0.0228987
$733$		−	5.04366e8i		−	1.28066i	−0.768100	−	0.640330i	$-0.778798\pi$
$733$		−	5.04366e8i		−	1.28066i	0.768100	−	0.640330i	$-0.221202\pi$
$734$		−	6.21635e8i		−	1.57198i
$735$	−3.40789e8			−0.858270
$736$		−	8.12626e7i		−	0.203825i
$737$	1.49307e8			0.372974
$738$		−	2.11140e8i		−	0.525293i
$739$		−	2.26091e8i		−	0.560209i	−0.959970	−	0.280104i	$-0.909631\pi$
$739$		−	2.26091e8i		−	0.560209i	0.959970	−	0.280104i	$-0.0903691\pi$
$740$	−4.65271e7			−0.114818
$741$	1.92413e8			0.472910
$742$	−8.00173e7			−0.195872
$743$			2.00268e8i			0.488252i	0.969743	+	0.244126i	$0.0785011\pi$
$743$			2.00268e8i			0.488252i	−0.969743	+	0.244126i	$0.921499\pi$
$744$	−2.92747e8			−0.710842
$745$	4.33788e7			0.104908
$746$	5.22580e8			1.25874
$747$	2.24163e8			0.537778
$748$	5.20900e7			0.124466
$749$		−	3.80403e7i		−	0.0905313i
$750$			1.76456e8i			0.418267i
$751$		−	7.41639e8i		−	1.75095i	−0.483267	−	0.875473i	$-0.660550\pi$
$751$		−	7.41639e8i		−	1.75095i	0.483267	−	0.875473i	$-0.339450\pi$
$752$	1.20706e8			0.283840
$753$		−	2.35297e8i		−	0.551101i
$754$	−1.44633e8			−0.337406
$755$	1.00594e8			0.233740
$756$	1.72519e7			0.0399274
$757$			4.49947e8i			1.03723i	0.855009	+	0.518614i	$0.173552\pi$
$757$			4.49947e8i			1.03723i	−0.855009	+	0.518614i	$0.826448\pi$
$758$		−	4.52819e8i		−	1.03972i
$759$			6.10577e7i			0.139642i
$760$		−	9.54710e8i		−	2.17486i
$761$			3.06930e8i			0.696442i	0.937412	+	0.348221i	$0.113214\pi$
$761$			3.06930e8i			0.696442i	−0.937412	+	0.348221i	$0.886786\pi$
$762$	2.09880e8			0.474358
$763$		−	6.91571e7i		−	0.155691i
$764$			1.27969e8i			0.286962i
$765$			4.13076e8i			0.922667i
$766$	2.23020e8			0.496201
$767$	1.69602e7			0.0375876
$768$			1.93189e8i			0.426480i
$769$	5.68563e8			1.25026			0.625129	−	0.780522i	$-0.285046\pi$
$769$	5.68563e8			1.25026			0.625129	+	0.780522i	$0.285046\pi$
$770$			3.39134e7i			0.0742846i
$771$	−1.22651e8			−0.267614
$772$	2.98183e7			0.0648083
$773$		−	1.80822e8i		−	0.391483i	−0.980656	−	0.195741i	$-0.937289\pi$
$773$		−	1.80822e8i		−	0.391483i	0.980656	−	0.195741i	$-0.0627113\pi$
$774$	−2.01183e7	−	1.91120e8i	−0.0433880	−	0.412177i
$775$	−1.98848e8			−0.427185
$776$		−	4.60656e7i		−	0.0985806i
$777$		−	2.93165e7i		−	0.0624955i
$778$	−5.95441e8			−1.26444
$779$			9.99870e8i			2.11510i
$780$	−3.31563e7			−0.0698685
$781$			1.80397e8i			0.378683i
$782$			3.56587e8i			0.745667i
$783$	−5.02272e8			−1.04629
$784$	−3.51842e8			−0.730130
$785$	−8.02949e8			−1.65989
$786$			1.72337e8i			0.354905i
$787$	−7.97430e8			−1.63594			−0.817972	−	0.575258i	$-0.804902\pi$
$787$	−7.97430e8			−1.63594			−0.817972	+	0.575258i	$0.804902\pi$
$788$	4.55742e7			0.0931409
$789$	3.08864e8			0.628834
$790$	−4.70445e8			−0.954173
$791$	−3.41836e7			−0.0690699
$792$			9.26630e7i			0.186522i
$793$			2.97295e7i			0.0596167i
$794$		−	3.70361e8i		−	0.739884i
$795$	5.34054e8			1.06288
$796$			9.92865e7i			0.196857i
$797$	−6.23204e8			−1.23099			−0.615496	−	0.788140i	$-0.711044\pi$
$797$	−6.23204e8			−1.23099			−0.615496	+	0.788140i	$0.711044\pi$
$798$	1.01587e8			0.199908
$799$	3.13831e8			0.615256
$800$			9.66517e7i			0.188773i
$801$			4.26843e8i			0.830559i
$802$			5.11759e8i			0.992070i
$803$			4.47823e7i			0.0864887i
$804$			7.70693e7i			0.148290i
$805$	5.91997e7			0.113483
$806$		−	1.63643e8i		−	0.312529i
$807$			5.33214e8i			1.01457i
$808$		−	6.59008e8i		−	1.24927i
$809$	−7.50640e7			−0.141771			−0.0708853	−	0.997484i	$-0.522582\pi$
$809$	−7.50640e7			−0.141771			−0.0708853	+	0.997484i	$0.522582\pi$
$810$	1.84276e8			0.346749
$811$			7.34418e8i			1.37683i	0.725317	+	0.688415i	$0.241693\pi$
$811$			7.34418e8i			1.37683i	−0.725317	+	0.688415i	$0.758307\pi$
$812$	1.94720e7			0.0363699
$813$		−	4.41459e8i		−	0.821521i
$814$	8.38640e7			0.155490
$815$	−4.65400e8			−0.859712
$816$		−	4.92058e8i		−	0.905619i
$817$	9.52719e7	+	9.05063e8i	0.174702	+	1.65964i
$818$	−5.47736e8			−1.00072
$819$			1.81070e7i			0.0329606i
$820$		−	1.72296e8i		−	0.312488i
$821$	2.55907e8			0.462436			0.231218	−	0.972902i	$-0.425729\pi$
$821$	2.55907e8			0.462436			0.231218	+	0.972902i	$0.425729\pi$
$822$		−	6.53952e8i		−	1.17742i
$823$	2.70463e7			0.0485186			0.0242593	−	0.999706i	$-0.492277\pi$
$823$	2.70463e7			0.0485186			0.0242593	+	0.999706i	$0.492277\pi$
$824$		−	4.05353e8i		−	0.724523i
$825$		−	7.26206e7i		−	0.129330i
$826$	8.95439e6			0.0158890
$827$	7.15059e8			1.26423			0.632114	−	0.774876i	$-0.282188\pi$
$827$	7.15059e8			1.26423			0.632114	+	0.774876i	$0.282188\pi$
$828$	2.73160e7			0.0481200
$829$		−	4.42063e8i		−	0.775927i	−0.921675	−	0.387964i	$-0.873179\pi$
$829$		−	4.42063e8i		−	0.775927i	0.921675	−	0.387964i	$-0.126821\pi$
$830$	−7.17350e8			−1.25458
$831$	7.24646e8			1.26277
$832$	−2.48014e8			−0.430632
$833$	−9.14782e8			−1.58264
$834$	−6.22043e8			−1.07232
$835$		−	5.01641e8i		−	0.861655i
$836$		−	7.41038e7i		−	0.126830i
$837$		−	5.68287e8i		−	0.969151i
$838$	8.64344e8			1.46877
$839$			9.68041e7i			0.163911i	0.996636	+	0.0819555i	$0.0261165\pi$
$839$			9.68041e7i			0.163911i	−0.996636	+	0.0819555i	$0.973883\pi$
$840$	−1.03660e8			−0.174893
$841$	2.79153e7			0.0469303
$842$	−6.99455e8			−1.17172
$843$			6.66763e8i			1.11298i
$844$			1.37878e8i			0.229334i
$845$			6.22372e8i			1.03153i
$846$			9.42779e7i			0.155704i
$847$		−	9.58253e7i		−	0.157699i
$848$	5.51375e8			0.904190
$849$			2.72974e8i			0.446065i
$850$		−	4.24115e8i		−	0.690601i
$851$		−	1.46394e8i		−	0.237539i
$852$	−9.31171e7			−0.150560
$853$	2.63624e8			0.424754			0.212377	−	0.977188i	$-0.431879\pi$
$853$	2.63624e8			0.424754			0.212377	+	0.977188i	$0.431879\pi$
$854$			1.56961e7i			0.0252011i
$855$	5.87646e8			0.940193
$856$			3.32618e8i			0.530304i
$857$	3.79690e8			0.603235			0.301617	−	0.953429i	$-0.402474\pi$
$857$	3.79690e8			0.603235			0.301617	+	0.953429i	$0.402474\pi$
$858$	5.97633e7			0.0946178
$859$			5.37277e7i			0.0847654i	0.999101	+	0.0423827i	$0.0134949\pi$
$859$			5.37277e7i			0.0847654i	−0.999101	+	0.0423827i	$0.986505\pi$
$860$	−1.64171e7	−	1.55959e8i	−0.0258108	−	0.245197i
$861$	1.08563e8			0.170087
$862$			7.65197e8i			1.19468i
$863$		−	1.15271e9i		−	1.79345i	−0.442593	−	0.896723i	$-0.645941\pi$
$863$		−	1.15271e9i		−	1.79345i	0.442593	−	0.896723i	$-0.354059\pi$
$864$	−2.76221e8			−0.428268
$865$		−	6.13665e8i		−	0.948163i
$866$	4.83312e8			0.744172
$867$		−	8.02338e8i		−	1.23112i
$868$			2.20313e7i			0.0336884i
$869$	−2.16230e8			−0.329501
$870$	5.09652e8			0.773955
$871$	−2.55108e8			−0.386073
$872$			6.04698e8i			0.911988i
$873$	2.83544e7			0.0426165
$874$	5.07284e8			0.759830
$875$	7.86362e7			0.117381
$876$	−2.31156e7			−0.0343870
$877$	−6.96046e8			−1.03190			−0.515952	−	0.856617i	$-0.672562\pi$
$877$	−6.96046e8			−1.03190			−0.515952	+	0.856617i	$0.672562\pi$
$878$			3.53362e8i			0.522079i
$879$		−	6.08036e8i		−	0.895287i
$880$		−	2.33687e8i		−	0.342915i
$881$	−8.69205e7			−0.127114			−0.0635572	−	0.997978i	$-0.520245\pi$
$881$	−8.69205e7			−0.127114			−0.0635572	+	0.997978i	$0.520245\pi$
$882$		−	2.74809e8i		−	0.400521i
$883$	3.48995e8			0.506918			0.253459	−	0.967346i	$-0.418432\pi$
$883$	3.48995e8			0.506918			0.253459	+	0.967346i	$0.418432\pi$
$884$	−8.90014e7			−0.128837
$885$	−5.97637e7			−0.0862199
$886$			8.48621e8i			1.22015i
$887$			1.18586e9i			1.69927i	0.527374	+	0.849633i	$0.323177\pi$
$887$			1.18586e9i			1.69927i	−0.527374	+	0.849633i	$0.676823\pi$
$888$			2.56338e8i			0.366079i
$889$		−	9.35312e7i		−	0.133122i
$890$		−	1.36595e9i		−	1.93760i
$891$	8.46988e7			0.119741
$892$		−	8.82020e7i		−	0.124275i
$893$		−	4.46460e8i		−	0.626943i
$894$		−	4.03596e7i		−	0.0564852i
$895$	1.52901e9			2.13276
$896$	−7.82400e7			−0.108769
$897$		−	1.04324e8i		−	0.144546i
$898$	3.25825e8			0.449940
$899$		−	6.41419e8i		−	0.882801i
$900$	−3.24889e7			−0.0445664
$901$	1.43356e9			1.95994
$902$			3.10560e8i			0.423180i
$903$	9.82690e7	−	1.03443e7i	0.133461	−	0.0140488i
$904$	2.98896e8			0.404590
$905$			1.15597e9i			1.55955i
$906$		−	9.35930e7i		−	0.125852i
$907$	−3.44670e8			−0.461936			−0.230968	−	0.972961i	$-0.574189\pi$
$907$	−3.44670e8			−0.461936			−0.230968	+	0.972961i	$0.574189\pi$
$908$		−	3.00024e7i		−	0.0400773i
$909$	4.05635e8			0.540062
$910$		−	5.79447e7i		−	0.0768934i
$911$		−	2.34712e8i		−	0.310441i	−0.987880	−	0.155221i	$-0.950391\pi$
$911$		−	2.34712e8i		−	0.310441i	0.987880	−	0.155221i	$-0.0496088\pi$
$912$	−7.00007e8			−0.922822
$913$	−3.29715e8			−0.433238
$914$	−8.66964e8			−1.13544
$915$		−	1.04760e8i		−	0.136751i
$916$	−4.27233e7			−0.0555877
$917$	7.68007e7			0.0995995
$918$	1.21208e9			1.56676
$919$	2.29468e8			0.295648			0.147824	−	0.989014i	$-0.452773\pi$
$919$	2.29468e8			0.295648			0.147824	+	0.989014i	$0.452773\pi$
$920$	−5.17632e8			−0.664749
$921$		−	3.37045e8i		−	0.431428i
$922$			1.36304e9i			1.73906i
$923$		−	3.08228e8i		−	0.391983i
$924$	−8.04597e6			−0.0101991
$925$			1.74118e8i			0.219997i
$926$	−5.83807e7			−0.0735253
$927$	2.49504e8			0.313212
$928$	−3.11767e8			−0.390110
$929$			7.55756e8i			0.942615i	0.881969	+	0.471308i	$0.156218\pi$
$929$			7.55756e8i			0.942615i	−0.881969	+	0.471308i	$0.843782\pi$
$930$			5.76637e8i			0.716892i
$931$			1.30138e9i			1.61270i
$932$		−	1.32066e7i		−	0.0163134i
$933$			3.22012e8i			0.396486i
$934$	−1.33233e9			−1.63520
$935$		−	6.07580e8i		−	0.743308i
$936$		−	1.58325e8i		−	0.193073i
$937$		−	7.08819e8i		−	0.861622i	−0.902442	−	0.430811i	$-0.858228\pi$
$937$		−	7.08819e8i		−	0.861622i	0.902442	−	0.430811i	$-0.141772\pi$
$938$	−1.34688e8			−0.163200
$939$	7.56332e8			0.913515
$940$			7.69333e7i			0.0926256i
$941$	1.27658e9			1.53207			0.766034	−	0.642800i	$-0.222227\pi$
$941$	1.27658e9			1.53207			0.766034	+	0.642800i	$0.222227\pi$
$942$			7.47063e8i			0.893727i
$943$	5.42117e8			0.646485
$944$	−6.17021e7			−0.0733472
$945$		−	2.01227e8i		−	0.238446i
$946$	2.95914e7	+	2.81113e8i	0.0349537	+	0.332053i
$947$	−1.28977e9			−1.51866			−0.759332	−	0.650703i	$-0.774474\pi$
$947$	−1.28977e9			−1.51866			−0.759332	+	0.650703i	$0.774474\pi$
$948$		−	1.11613e8i		−	0.131006i
$949$		−	7.65153e7i		−	0.0895261i
$950$	−6.03351e8			−0.703719
$951$			7.38277e8i			0.858377i
$952$	−2.78253e8			−0.322500
$953$		−	1.85601e8i		−	0.214438i	−0.994235	−	0.107219i	$-0.965805\pi$
$953$		−	1.85601e8i		−	0.214438i	0.994235	−	0.107219i	$-0.0341946\pi$
$954$			4.30656e8i			0.496004i
$955$	1.49263e9			1.71373
$956$	1.66429e8			0.190483
$957$	2.34251e8			0.267267
$958$		−	1.08050e9i		−	1.22893i
$959$	−2.91428e8			−0.330427
$960$	8.73942e8			0.987800
$961$	−1.61780e8			−0.182286
$962$	−1.43291e8			−0.160951
$963$	−2.04734e8			−0.229251
$964$			1.01148e8i			0.112908i
$965$		−	3.47802e8i		−	0.387035i
$966$		−	5.50793e7i		−	0.0611023i
$967$	−1.18105e9			−1.30614			−0.653069	−	0.757299i	$-0.726519\pi$
$967$	−1.18105e9			−1.30614			−0.653069	+	0.757299i	$0.726519\pi$
$968$			8.37881e8i			0.923754i
$969$	−1.82000e9			−2.00032
$970$	−9.07377e7			−0.0994197
$971$	−6.52107e8			−0.712297			−0.356149	−	0.934429i	$-0.615910\pi$
$971$	−6.52107e8			−0.712297			−0.356149	+	0.934429i	$0.615910\pi$
$972$		−	1.56259e8i		−	0.170156i
$973$			2.77208e8i			0.300932i
$974$		−	8.39632e8i		−	0.908682i
$975$			1.24080e8i			0.133872i
$976$		−	1.08157e8i		−	0.116334i
$977$	−9.78836e8			−1.04961			−0.524803	−	0.851224i	$-0.675861\pi$
$977$	−9.78836e8			−1.04961			−0.524803	+	0.851224i	$0.675861\pi$
$978$			4.33008e8i			0.462891i
$979$		−	6.27830e8i		−	0.669105i
$980$		−	2.24252e8i		−	0.238263i
$981$	−3.72206e8			−0.394254
$982$	1.17051e8			0.123607
$983$			2.69098e8i			0.283303i	0.989917	+	0.141651i	$0.0452412\pi$
$983$			2.69098e8i			0.283303i	−0.989917	+	0.141651i	$0.954759\pi$
$984$	−9.49256e8			−0.996318
$985$		−	5.31580e8i		−	0.556237i
$986$	1.36806e9			1.42716
$987$	−4.84753e7			−0.0504160
$988$			1.26614e8i			0.131284i
$989$	4.90714e8	−	5.16553e7i	0.507271	−	0.0533981i
$990$	1.82523e8			0.188110
$991$		−	8.36450e6i		−	0.00859447i	−0.999991	−	0.00429723i	$-0.998632\pi$
$991$		−	8.36450e6i		−	0.00859447i	0.999991	−	0.00429723i	$-0.00136786\pi$
$992$		−	3.52744e8i		−	0.361347i
$993$	−1.03545e9			−1.05750
$994$		−	1.62734e8i		−	0.165698i
$995$	1.15808e9			1.17563
$996$		−	1.70192e8i		−	0.172251i
$997$		−	1.20623e9i		−	1.21715i	−0.793497	−	0.608574i	$-0.791742\pi$
$997$		−	1.20623e9i		−	1.21715i	0.793497	−	0.608574i	$-0.208258\pi$
$998$	−9.48082e8			−0.953794
$999$	−4.97611e8			−0.499107

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.b.b.42.7	✓	20
43.42	odd	2	inner	43.7.b.b.42.14	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.b.b.42.7	✓	20	1.1	even	1	trivial
43.7.b.b.42.14	yes	20	43.42	odd	2	inner

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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-7.14115i q^{2} -19.7617i q^{3} +13.0039 q^{4} -151.678i q^{5} -141.122 q^{6} +62.8896i q^{7} -549.897i q^{8} +338.474 q^{9} +O(q^{10})\)	\(q-7.14115i q^{2} -19.7617i q^{3} +13.0039 q^{4} -151.678i q^{5} -141.122 q^{6} +62.8896i q^{7} -549.897i q^{8} +338.474 q^{9} -1083.16 q^{10} -497.851 q^{11} -256.980i q^{12} +850.633 q^{13} +449.105 q^{14} -2997.43 q^{15} -3094.65 q^{16} -8046.00 q^{17} -2417.10i q^{18} +11446.3i q^{19} -1972.42i q^{20} +1242.81 q^{21} +3555.23i q^{22} +6206.07 q^{23} -10866.9 q^{24} -7381.34 q^{25} -6074.50i q^{26} -21095.1i q^{27} +817.813i q^{28} -23809.8i q^{29} +21405.1i q^{30} +26939.3 q^{31} -13094.1i q^{32} +9838.40i q^{33} +57457.7i q^{34} +9539.00 q^{35} +4401.49 q^{36} -23588.9i q^{37} +81740.0 q^{38} -16810.0i q^{39} -83407.5 q^{40} +87352.8 q^{41} -8875.08i q^{42} +(79070.1 - 8323.35i) q^{43} -6474.02 q^{44} -51339.2i q^{45} -44318.5i q^{46} -39004.6 q^{47} +61155.6i q^{48} +113694. q^{49} +52711.3i q^{50} +159003. i q^{51} +11061.6 q^{52} -178171. q^{53} -150644. q^{54} +75513.3i q^{55} +34582.8 q^{56} +226199. q^{57} -170030. q^{58} +19938.3 q^{59} -38978.3 q^{60} +34949.8i q^{61} -192377. i q^{62} +21286.5i q^{63} -291564. q^{64} -129023. i q^{65} +70257.5 q^{66} -299904. q^{67} -104630. q^{68} -122643. i q^{69} -68119.5i q^{70} -362351. i q^{71} -186126. i q^{72} -89951.1i q^{73} -168452. q^{74} +145868. i q^{75} +148847. i q^{76} -31309.7i q^{77} -120043. q^{78} +434327. q^{79} +469391. i q^{80} -170129. q^{81} -623800. i q^{82} +662276. q^{83} +16161.4 q^{84} +1.22041e6i q^{85} +(-59438.3 - 564652. i) q^{86} -470523. q^{87} +273767. i q^{88} +1.26108e6i q^{89} -366621. q^{90} +53496.0i q^{91} +80703.2 q^{92} -532366. i q^{93} +278538. i q^{94} +1.73616e6 q^{95} -258761. q^{96} +83771.3 q^{97} -811906. i q^{98} -168510. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 796 q^{4} - 258 q^{6} - 2736 q^{9}+O(q^{10}) \) 20 * q - 796 * q^4 - 258 * q^6 - 2736 * q^9	\( 20 q - 796 q^{4} - 258 q^{6} - 2736 q^{9} - 1962 q^{10} + 2616 q^{11} - 5612 q^{13} - 3876 q^{14} + 4048 q^{15} + 14900 q^{16} + 3328 q^{17} + 10544 q^{21} - 836 q^{23} + 26966 q^{24} - 57904 q^{25} + 17116 q^{31} - 150472 q^{35} - 132110 q^{36} + 2266 q^{38} + 401286 q^{40} - 141936 q^{41} + 58160 q^{43} + 88544 q^{44} + 48452 q^{47} - 20644 q^{49} + 12292 q^{52} + 425212 q^{53} + 173740 q^{54} + 447864 q^{56} - 92904 q^{57} + 86502 q^{58} - 918856 q^{59} + 429848 q^{60} - 156892 q^{64} - 1246176 q^{66} + 1098496 q^{67} - 2589854 q^{68} - 1224106 q^{74} + 855716 q^{78} - 401492 q^{79} + 470644 q^{81} + 1354360 q^{83} - 637268 q^{84} + 3046356 q^{86} + 2116740 q^{87} - 683716 q^{90} - 485998 q^{92} - 2711660 q^{95} - 2480062 q^{96} + 7814560 q^{97} + 3744560 q^{99}+O(q^{100}) \) 20 * q - 796 * q^4 - 258 * q^6 - 2736 * q^9 - 1962 * q^10 + 2616 * q^11 - 5612 * q^13 - 3876 * q^14 + 4048 * q^15 + 14900 * q^16 + 3328 * q^17 + 10544 * q^21 - 836 * q^23 + 26966 * q^24 - 57904 * q^25 + 17116 * q^31 - 150472 * q^35 - 132110 * q^36 + 2266 * q^38 + 401286 * q^40 - 141936 * q^41 + 58160 * q^43 + 88544 * q^44 + 48452 * q^47 - 20644 * q^49 + 12292 * q^52 + 425212 * q^53 + 173740 * q^54 + 447864 * q^56 - 92904 * q^57 + 86502 * q^58 - 918856 * q^59 + 429848 * q^60 - 156892 * q^64 - 1246176 * q^66 + 1098496 * q^67 - 2589854 * q^68 - 1224106 * q^74 + 855716 * q^78 - 401492 * q^79 + 470644 * q^81 + 1354360 * q^83 - 637268 * q^84 + 3046356 * q^86 + 2116740 * q^87 - 683716 * q^90 - 485998 * q^92 - 2711660 * q^95 - 2480062 * q^96 + 7814560 * q^97 + 3744560 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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