LMFDB - Embedded newform 59.7.b.c.58.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [59,7,Mod(58,59)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(59, 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("59.58");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 59 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	59.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:	$13.5731909336$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.9
Character	$\chi$	$=$	59.58
Dual form			59.7.b.c.58.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-7.19418i q^{2} +44.5169 q^{3} +12.2438 q^{4} +52.8479 q^{5} -320.263i q^{6} -372.902 q^{7} -548.511i q^{8} +1252.76 q^{9} -380.197i q^{10} -2143.87i q^{11} +545.055 q^{12} +2575.41i q^{13} +2682.72i q^{14} +2352.63 q^{15} -3162.49 q^{16} +6451.40 q^{17} -9012.55i q^{18} +8212.43 q^{19} +647.058 q^{20} -16600.4 q^{21} -15423.4 q^{22} -282.064i q^{23} -24418.0i q^{24} -12832.1 q^{25} +18528.0 q^{26} +23316.0 q^{27} -4565.72 q^{28} -20472.9 q^{29} -16925.2i q^{30} +26070.3i q^{31} -12353.2i q^{32} -95438.4i q^{33} -46412.6i q^{34} -19707.1 q^{35} +15338.5 q^{36} +39772.6i q^{37} -59081.7i q^{38} +114649. i q^{39} -28987.7i q^{40} +35582.4 q^{41} +119426. i q^{42} +125517. i q^{43} -26249.0i q^{44} +66205.5 q^{45} -2029.22 q^{46} +125680. i q^{47} -140784. q^{48} +21406.6 q^{49} +92316.4i q^{50} +287197. q^{51} +31532.8i q^{52} -263897. q^{53} -167740. i q^{54} -113299. i q^{55} +204541. i q^{56} +365592. q^{57} +147285. i q^{58} +(-16121.5 - 204745. i) q^{59} +28805.0 q^{60} -2078.21i q^{61} +187554. q^{62} -467155. q^{63} -291271. q^{64} +136105. i q^{65} -686601. q^{66} +86383.7i q^{67} +78989.5 q^{68} -12556.6i q^{69} +141776. i q^{70} +313286. q^{71} -687151. i q^{72} -322759. i q^{73} +286131. q^{74} -571246. q^{75} +100551. q^{76} +799452. i q^{77} +824808. q^{78} +295321. q^{79} -167131. q^{80} +124698. q^{81} -255986. i q^{82} +892234. i q^{83} -203252. q^{84} +340943. q^{85} +902993. q^{86} -911389. q^{87} -1.17594e6 q^{88} -953067. i q^{89} -476295. i q^{90} -960375. i q^{91} -3453.52i q^{92} +1.16057e6i q^{93} +904168. q^{94} +434010. q^{95} -549927. i q^{96} +562716. i q^{97} -154003. i q^{98} -2.68574e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 10 q^{3} - 1090 q^{4} + 142 q^{5} + 406 q^{7} + 5432 q^{9} - 1124 q^{12} + 14982 q^{15} + 12734 q^{16} - 9108 q^{17} + 3850 q^{19} - 46896 q^{20} - 49034 q^{21} + 11238 q^{22} + 18792 q^{25} - 64590 q^{26}+ \cdots - 2396490 q^{95}+O(q^{100}) $ 26 * q + 10 * q^3 - 1090 * q^4 + 142 * q^5 + 406 * q^7 + 5432 * q^9 - 1124 * q^12 + 14982 * q^15 + 12734 * q^16 - 9108 * q^17 + 3850 * q^19 - 46896 * q^20 - 49034 * q^21 + 11238 * q^22 + 18792 * q^25 - 64590 * q^26 + 3550 * q^27 - 45542 * q^28 - 31730 * q^29 + 163558 * q^35 - 325266 * q^36 + 91914 * q^41 + 736396 * q^45 + 287148 * q^46 + 479572 * q^48 - 462900 * q^49 + 329932 * q^51 + 8238 * q^53 - 187506 * q^57 + 326182 * q^59 - 970064 * q^60 + 630140 * q^62 + 630508 * q^63 - 1800262 * q^64 - 869200 * q^66 - 319586 * q^68 + 1763840 * q^71 - 2294090 * q^74 + 354736 * q^75 + 247144 * q^76 - 375064 * q^78 + 4702 * q^79 + 1920984 * q^80 - 2435946 * q^81 - 1007672 * q^84 + 864044 * q^85 + 5031110 * q^86 - 1519202 * q^87 + 725994 * q^88 + 2835768 * q^94 - 2396490 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/59\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	7.19418i		−	0.899272i	−0.893212	−	0.449636i	$-0.851554\pi$
$2$		−	7.19418i		−	0.899272i	0.893212	−	0.449636i	$-0.148446\pi$
$3$	44.5169			1.64877			0.824387	−	0.566026i	$-0.191520\pi$
$3$	44.5169			1.64877			0.824387	+	0.566026i	$0.191520\pi$
$4$	12.2438			0.191309
$5$	52.8479			0.422783			0.211392	−	0.977401i	$-0.432200\pi$
$5$	52.8479			0.422783			0.211392	+	0.977401i	$0.432200\pi$
$6$		−	320.263i		−	1.48270i
$7$	−372.902			−1.08718			−0.543588	−	0.839352i	$-0.682935\pi$
$7$	−372.902			−1.08718			−0.543588	+	0.839352i	$0.682935\pi$
$8$		−	548.511i		−	1.07131i
$9$	1252.76			1.71846
$10$		−	380.197i		−	0.380197i
$11$		−	2143.87i		−	1.61072i	−0.592786	−	0.805360i	$-0.701972\pi$
$11$		−	2143.87i		−	1.61072i	0.592786	−	0.805360i	$-0.298028\pi$
$12$	545.055			0.315425
$13$			2575.41i			1.17224i	0.810224	+	0.586120i	$0.199345\pi$
$13$			2575.41i			1.17224i	−0.810224	+	0.586120i	$0.800655\pi$
$14$			2682.72i			0.977668i
$15$	2352.63			0.697074
$16$	−3162.49			−0.772092
$17$	6451.40			1.31313			0.656565	−	0.754270i	$-0.272009\pi$
$17$	6451.40			1.31313			0.656565	+	0.754270i	$0.272009\pi$
$18$		−	9012.55i		−	1.54536i
$19$	8212.43			1.19732			0.598661	−	0.801003i	$-0.295700\pi$
$19$	8212.43			1.19732			0.598661	+	0.801003i	$0.295700\pi$
$20$	647.058			0.0808822
$21$	−16600.4			−1.79251
$22$	−15423.4			−1.44848
$23$		−	282.064i		−	0.0231827i	−0.999933	−	0.0115913i	$-0.996310\pi$
$23$		−	282.064i		−	0.0231827i	0.999933	−	0.0115913i	$-0.00368972\pi$
$24$		−	24418.0i		−	1.76635i
$25$	−12832.1			−0.821254
$26$	18528.0			1.05416
$27$	23316.0			1.18458
$28$	−4565.72			−0.207987
$29$	−20472.9			−0.839430			−0.419715	−	0.907656i	$-0.637870\pi$
$29$	−20472.9			−0.839430			−0.419715	+	0.907656i	$0.637870\pi$
$30$		−	16925.2i		−	0.626860i
$31$			26070.3i			0.875106i	0.899193	+	0.437553i	$0.144155\pi$
$31$			26070.3i			0.875106i	−0.899193	+	0.437553i	$0.855845\pi$
$32$		−	12353.2i		−	0.376990i
$33$		−	95438.4i		−	2.65571i
$34$		−	46412.6i		−	1.18086i
$35$	−19707.1			−0.459640
$36$	15338.5			0.328757
$37$			39772.6i			0.785198i	0.919710	+	0.392599i	$0.128424\pi$
$37$			39772.6i			0.785198i	−0.919710	+	0.392599i	$0.871576\pi$
$38$		−	59081.7i		−	1.07672i
$39$			114649.i			1.93276i
$40$		−	28987.7i		−	0.452932i
$41$	35582.4			0.516278			0.258139	−	0.966108i	$-0.416891\pi$
$41$	35582.4			0.516278			0.258139	+	0.966108i	$0.416891\pi$
$42$			119426.i			1.61195i
$43$			125517.i			1.57869i	0.613948	+	0.789347i	$0.289581\pi$
$43$			125517.i			1.57869i	−0.613948	+	0.789347i	$0.710419\pi$
$44$		−	26249.0i		−	0.308145i
$45$	66205.5			0.726535
$46$	−2029.22			−0.0208475
$47$			125680.i			1.21053i	0.796025	+	0.605263i	$0.206932\pi$
$47$			125680.i			1.21053i	−0.796025	+	0.605263i	$0.793068\pi$
$48$	−140784.			−1.27301
$49$	21406.6			0.181953
$50$			92316.4i			0.738531i
$51$	287197.			2.16505
$52$			31532.8i			0.224260i
$53$	−263897.			−1.77258			−0.886292	−	0.463126i	$-0.846728\pi$
$53$	−263897.			−1.77258			−0.886292	+	0.463126i	$0.846728\pi$
$54$		−	167740.i		−	1.06526i
$55$		−	113299.i		−	0.680985i
$56$			204541.i			1.16470i
$57$	365592.			1.97411
$58$			147285.i			0.754876i
$59$	−16121.5	−	204745.i	−0.0784966	−	0.996914i
$59$	−16121.5	−	204745.i	−0.0784966	−	0.996914i
$60$	28805.0			0.133357
$61$		−	2078.21i		−	0.00915587i	−0.999990	−	0.00457794i	$-0.998543\pi$
$61$		−	2078.21i		−	0.00915587i	0.999990	−	0.00457794i	$-0.00145721\pi$
$62$	187554.			0.786958
$63$	−467155.			−1.86827
$64$	−291271.			−1.11111
$65$			136105.i			0.495603i
$66$	−686601.			−2.38821
$67$			86383.7i			0.287215i	0.989635	+	0.143608i	$0.0458703\pi$
$67$			86383.7i			0.287215i	−0.989635	+	0.143608i	$0.954130\pi$
$68$	78989.5			0.251213
$69$		−	12556.6i		−	0.0382230i
$70$			141776.i			0.413342i
$71$	313286.			0.875319			0.437660	−	0.899141i	$-0.355808\pi$
$71$	313286.			0.875319			0.437660	+	0.899141i	$0.355808\pi$
$72$		−	687151.i		−	1.84100i
$73$		−	322759.i		−	0.829678i	−0.909895	−	0.414839i	$-0.863838\pi$
$73$		−	322759.i		−	0.829678i	0.909895	−	0.414839i	$-0.136162\pi$
$74$	286131.			0.706107
$75$	−571246.			−1.35406
$76$	100551.			0.229058
$77$			799452.i			1.75114i
$78$	824808.			1.73808
$79$	295321.			0.598981			0.299490	−	0.954099i	$-0.403183\pi$
$79$	295321.			0.598981			0.299490	+	0.954099i	$0.403183\pi$
$80$	−167131.			−0.326427
$81$	124698.			0.234641
$82$		−	255986.i		−	0.464275i
$83$			892234.i			1.56043i	0.625511	+	0.780215i	$0.284890\pi$
$83$			892234.i			1.56043i	−0.625511	+	0.780215i	$0.715110\pi$
$84$	−203252.			−0.342923
$85$	340943.			0.555169
$86$	902993.			1.41968
$87$	−911389.			−1.38403
$88$	−1.17594e6			−1.72558
$89$		−	953067.i		−	1.35193i	−0.736935	−	0.675964i	$-0.763727\pi$
$89$		−	953067.i		−	1.35193i	0.736935	−	0.675964i	$-0.236273\pi$
$90$		−	476295.i		−	0.653353i
$91$		−	960375.i		−	1.27443i
$92$		−	3453.52i		−	0.00443505i
$93$			1.16057e6i			1.44285i
$94$	904168.			1.08859
$95$	434010.			0.506208
$96$		−	549927.i		−	0.621572i
$97$			562716.i			0.616558i	0.951296	+	0.308279i	$0.0997530\pi$
$97$			562716.i			0.616558i	−0.951296	+	0.308279i	$0.900247\pi$
$98$		−	154003.i		−	0.163625i
$99$		−	2.68574e6i		−	2.76796i
$100$	−157113.			−0.157113
$101$			839770.i			0.815073i	0.913189	+	0.407536i	$0.133612\pi$
$101$			839770.i			0.815073i	−0.913189	+	0.407536i	$0.866388\pi$
$102$		−	2.06614e6i		−	1.94697i
$103$		−	1.16383e6i		−	1.06507i	−0.846407	−	0.532536i	$-0.821239\pi$
$103$		−	1.16383e6i		−	1.06507i	0.846407	−	0.532536i	$-0.178761\pi$
$104$	1.41264e6			1.25583
$105$	−877298.			−0.757843
$106$			1.89852e6i			1.59404i
$107$	1.21993e6			0.995825			0.497912	−	0.867227i	$-0.334100\pi$
$107$	1.21993e6			0.995825			0.497912	+	0.867227i	$0.334100\pi$
$108$	285476.			0.226620
$109$			598890.i			0.462453i	0.972900	+	0.231226i	$0.0742738\pi$
$109$			598890.i			0.462453i	−0.972900	+	0.231226i	$0.925726\pi$
$110$	−815093.			−0.612391
$111$			1.77055e6i			1.29461i
$112$	1.17930e6			0.839400
$113$		−	1.13583e6i		−	0.787184i	−0.919285	−	0.393592i	$-0.871232\pi$
$113$		−	1.13583e6i		−	0.787184i	0.919285	−	0.393592i	$-0.128768\pi$
$114$		−	2.63014e6i		−	1.77527i
$115$		−	14906.5i		−	0.00980124i
$116$	−250665.			−0.160590
$117$			3.22636e6i			2.01445i
$118$	−1.47297e6	+	115981.i	−0.896498	+	0.0705898i
$119$	−2.40574e6			−1.42760
$120$		−	1.29044e6i		−	0.746784i
$121$	−2.82461e6			−1.59442
$122$	−14951.0			−0.00823362
$123$	1.58402e6			0.851227
$124$			319199.i			0.167416i
$125$	−1.50390e6			−0.769996
$126$			3.36080e6i			1.68008i
$127$	−772958.			−0.377350			−0.188675	−	0.982040i	$-0.560419\pi$
$127$	−772958.			−0.377350			−0.188675	+	0.982040i	$0.560419\pi$
$128$			1.30485e6i			0.622199i
$129$			5.58764e6i			2.60291i
$130$	979164.			0.445682
$131$			1.86313e6i			0.828759i	0.910104	+	0.414380i	$0.136001\pi$
$131$			1.86313e6i			0.828759i	−0.910104	+	0.414380i	$0.863999\pi$
$132$		−	1.16853e6i		−	0.508062i
$133$	−3.06243e6			−1.30170
$134$	621460.			0.258285
$135$	1.23220e6			0.500819
$136$		−	3.53867e6i		−	1.40677i
$137$	3.13776e6			1.22027			0.610137	−	0.792296i	$-0.291114\pi$
$137$	3.13776e6			1.22027			0.610137	+	0.792296i	$0.291114\pi$
$138$	−90334.4			−0.0343729
$139$	1.49256e6			0.555761			0.277881	−	0.960616i	$-0.410368\pi$
$139$	1.49256e6			0.555761			0.277881	+	0.960616i	$0.410368\pi$
$140$	−241289.			−0.0879333
$141$			5.59491e6i			1.99589i
$142$		−	2.25384e6i		−	0.787150i
$143$	5.52134e6			1.88815
$144$	−3.96183e6			−1.32681
$145$	−1.08195e6			−0.354897
$146$	−2.32199e6			−0.746107
$147$	952954.			0.299999
$148$			486967.i			0.150215i
$149$			2.30008e6i			0.695320i	0.937621	+	0.347660i	$0.113024\pi$
$149$			2.30008e6i			0.695320i	−0.937621	+	0.347660i	$0.886976\pi$
$150$			4.10964e6i			1.21767i
$151$		−	5.58036e6i		−	1.62081i	−0.585872	−	0.810403i	$-0.699248\pi$
$151$		−	5.58036e6i		−	1.62081i	0.585872	−	0.810403i	$-0.300752\pi$
$152$		−	4.50461e6i		−	1.28270i
$153$	8.08204e6			2.25656
$154$	5.75140e6			1.57475
$155$			1.37776e6i			0.369980i
$156$			1.40374e6i			0.369754i
$157$		−	5.27078e6i		−	1.36200i	−0.732285	−	0.680998i	$-0.761546\pi$
$157$		−	5.27078e6i		−	1.36200i	0.732285	−	0.680998i	$-0.238454\pi$
$158$		−	2.12459e6i		−	0.538647i
$159$	−1.17479e7			−2.92259
$160$		−	652842.i		−	0.159385i
$161$			105182.i			0.0252037i
$162$		−	897100.i		−	0.211007i
$163$	−6.98284e6			−1.61239			−0.806194	−	0.591651i	$-0.798476\pi$
$163$	−6.98284e6			−1.61239			−0.806194	+	0.591651i	$0.798476\pi$
$164$	435663.			0.0987687
$165$		−	5.04372e6i		−	1.12279i
$166$	6.41889e6			1.40325
$167$	−2.76029e6			−0.592660			−0.296330	−	0.955086i	$-0.595763\pi$
$167$	−2.76029e6			−0.592660			−0.296330	+	0.955086i	$0.595763\pi$
$168$			9.10552e6i			1.92034i
$169$	−1.80593e6			−0.374146
$170$		−	2.45281e6i		−	0.499248i
$171$	1.02882e7			2.05755
$172$			1.53680e6i			0.302018i
$173$		−	8.49343e6i		−	1.64038i	−0.572090	−	0.820191i	$-0.693867\pi$
$173$		−	8.49343e6i		−	1.64038i	0.572090	−	0.820191i	$-0.306133\pi$
$174$			6.55669e6i			1.24462i
$175$	4.78511e6			0.892848
$176$			6.77996e6i			1.24362i
$177$	−717682.	−	9.11463e6i	−0.129423	−	1.64369i
$178$	−6.85654e6			−1.21575
$179$		−	1.47515e6i		−	0.257204i	−0.991696	−	0.128602i	$-0.958951\pi$
$179$		−	1.47515e6i		−	0.257204i	0.991696	−	0.128602i	$-0.0410490\pi$
$180$	810606.			0.138993
$181$	4.19936e6			0.708187			0.354093	−	0.935210i	$-0.384790\pi$
$181$	4.19936e6			0.708187			0.354093	+	0.935210i	$0.384790\pi$
$182$	−6.90911e6			−1.14606
$183$		−	92515.5i		−	0.0150960i
$184$	−154715.			−0.0248359
$185$			2.10190e6i			0.331968i
$186$	8.34934e6			1.29752
$187$		−	1.38310e7i		−	2.11508i
$188$			1.53880e6i			0.231585i
$189$	−8.69458e6			−1.28784
$190$		−	3.12234e6i		−	0.455219i
$191$			6.17029e6i			0.885535i	0.896637	+	0.442767i	$0.146003\pi$
$191$			6.17029e6i			0.885535i	−0.896637	+	0.442767i	$0.853997\pi$
$192$	−1.29665e7			−1.83197
$193$	1.11963e7			1.55741			0.778707	−	0.627388i	$-0.215876\pi$
$193$	1.11963e7			1.55741			0.778707	+	0.627388i	$0.215876\pi$
$194$	4.04828e6			0.554454
$195$			6.05898e6i			0.817138i
$196$	262097.			0.0348092
$197$	−1.18163e6			−0.154555			−0.0772774	−	0.997010i	$-0.524623\pi$
$197$	−1.18163e6			−0.154555			−0.0772774	+	0.997010i	$0.524623\pi$
$198$	−1.93217e7			−2.48915
$199$	−9.77688e6			−1.24063			−0.620313	−	0.784354i	$-0.712995\pi$
$199$	−9.77688e6			−1.24063			−0.620313	+	0.784354i	$0.712995\pi$
$200$			7.03855e6i			0.879819i
$201$			3.84553e6i			0.473553i
$202$	6.04146e6			0.732972
$203$	7.63436e6			0.912609
$204$	3.51637e6			0.414194
$205$	1.88046e6			0.218274
$206$	−8.37283e6			−0.957791
$207$		−	353357.i		−	0.0398385i
$208$		−	8.14471e6i		−	0.905077i
$209$		−	1.76064e7i		−	1.92855i
$210$			6.31144e6i			0.681507i
$211$		−	7.34804e6i		−	0.782212i	−0.920346	−	0.391106i	$-0.872093\pi$
$211$		−	7.34804e6i		−	0.782212i	0.920346	−	0.391106i	$-0.127907\pi$
$212$	−3.23110e6			−0.339111
$213$	1.39465e7			1.44320
$214$		−	8.77638e6i		−	0.895518i
$215$			6.63332e6i			0.667445i
$216$		−	1.27891e7i		−	1.26905i
$217$		−	9.72164e6i		−	0.951394i
$218$	4.30852e6			0.415871
$219$		−	1.43682e7i		−	1.36795i
$220$		−	1.38721e6i		−	0.130279i
$221$			1.66150e7i			1.53930i
$222$	1.27377e7			1.16421
$223$	1.18507e7			1.06864			0.534318	−	0.845284i	$-0.320569\pi$
$223$	1.18507e7			1.06864			0.534318	+	0.845284i	$0.320569\pi$
$224$			4.60654e6i			0.409855i
$225$	−1.60755e7			−1.41129
$226$	−8.17134e6			−0.707893
$227$			750175.i			0.0641335i	0.999486	+	0.0320668i	$0.0102089\pi$
$227$			750175.i			0.0641335i	−0.999486	+	0.0320668i	$0.989791\pi$
$228$	4.47623e6			0.377666
$229$		−	1.38502e7i		−	1.15332i	−0.816984	−	0.576660i	$-0.804356\pi$
$229$		−	1.38502e7i		−	1.15332i	0.816984	−	0.576660i	$-0.195644\pi$
$230$	−107240.			−0.00881399
$231$			3.55891e7i			2.88723i
$232$			1.12296e7i			0.899291i
$233$		−	5.27802e6i		−	0.417257i	−0.977995	−	0.208628i	$-0.933100\pi$
$233$		−	5.27802e6i		−	0.417257i	0.977995	−	0.208628i	$-0.0668999\pi$
$234$	2.32110e7			1.81154
$235$			6.64195e6i			0.511790i
$236$	−197389.	−	2.50686e6i	−0.0150171	−	0.190719i
$237$	1.31468e7			0.987584
$238$			1.73073e7i			1.28380i
$239$	−7.29198e6			−0.534136			−0.267068	−	0.963678i	$-0.586055\pi$
$239$	−7.29198e6			−0.534136			−0.267068	+	0.963678i	$0.586055\pi$
$240$	−7.44015e6			−0.538205
$241$	−8.13367e6			−0.581080			−0.290540	−	0.956863i	$-0.593835\pi$
$241$	−8.13367e6			−0.581080			−0.290540	+	0.956863i	$0.593835\pi$
$242$			2.03207e7i			1.43382i
$243$	−1.14462e7			−0.797706
$244$		−	25445.1i		−	0.00175160i
$245$	1.13129e6			0.0769266
$246$		−	1.13957e7i		−	0.765485i
$247$			2.11504e7i			1.40355i
$248$	1.42998e7			0.937511
$249$			3.97195e7i			2.57280i
$250$			1.08193e7i			0.692436i
$251$	−1.58703e7			−1.00361			−0.501804	−	0.864981i	$-0.667330\pi$
$251$	−1.58703e7			−1.00361			−0.501804	+	0.864981i	$0.667330\pi$
$252$	−5.71974e6			−0.357416
$253$	−604707.			−0.0373408
$254$			5.56080e6i			0.339341i
$255$	1.51777e7			0.915349
$256$	−9.25401e6			−0.551582
$257$	−2.92740e6			−0.172458			−0.0862289	−	0.996275i	$-0.527482\pi$
$257$	−2.92740e6			−0.172458			−0.0862289	+	0.996275i	$0.527482\pi$
$258$	4.01985e7			2.34073
$259$		−	1.48313e7i		−	0.853648i
$260$			1.66644e6i			0.0948134i
$261$	−2.56475e7			−1.44253
$262$	1.34037e7			0.745281
$263$	−2.71004e6			−0.148973			−0.0744866	−	0.997222i	$-0.523732\pi$
$263$	−2.71004e6			−0.148973			−0.0744866	+	0.997222i	$0.523732\pi$
$264$	−5.23491e7			−2.84510
$265$	−1.39464e7			−0.749419
$266$			2.20317e7i			1.17058i
$267$		−	4.24276e7i		−	2.22903i
$268$			1.05766e6i			0.0549468i
$269$		−	2.40580e7i		−	1.23596i	−0.786196	−	0.617978i	$-0.787952\pi$
$269$		−	2.40580e7i		−	1.23596i	0.786196	−	0.617978i	$-0.212048\pi$
$270$		−	8.86469e6i		−	0.450373i
$271$	2.69790e7			1.35556			0.677778	−	0.735266i	$-0.262943\pi$
$271$	2.69790e7			1.35556			0.677778	+	0.735266i	$0.262943\pi$
$272$	−2.04025e7			−1.01386
$273$		−	4.27529e7i		−	2.10125i
$274$		−	2.25736e7i		−	1.09736i
$275$			2.75103e7i			1.32281i
$276$		−	153740.i		−	0.00731240i
$277$	5.77138e6			0.271544			0.135772	−	0.990740i	$-0.456648\pi$
$277$	5.77138e6			0.271544			0.135772	+	0.990740i	$0.456648\pi$
$278$		−	1.07378e7i		−	0.499781i
$279$			3.26597e7i			1.50383i
$280$			1.08096e7i			0.492418i
$281$	−4.19786e7			−1.89195			−0.945974	−	0.324242i	$-0.894891\pi$
$281$	−4.19786e7			−1.89195			−0.945974	+	0.324242i	$0.894891\pi$
$282$	4.02508e7			1.79485
$283$			3.17844e7i			1.40234i	0.712992	+	0.701172i	$0.247339\pi$
$283$			3.17844e7i			1.40234i	−0.712992	+	0.701172i	$0.752661\pi$
$284$	3.83581e6			0.167456
$285$	1.93208e7			0.834622
$286$		−	3.97215e7i		−	1.69796i
$287$	−1.32687e7			−0.561286
$288$		−	1.54756e7i		−	0.647842i
$289$	1.74830e7			0.724308
$290$			7.78373e6i			0.319149i
$291$			2.50504e7i			1.01657i
$292$		−	3.95179e6i		−	0.158725i
$293$	−984166.			−0.0391260			−0.0195630	−	0.999809i	$-0.506227\pi$
$293$	−984166.			−0.0391260			−0.0195630	+	0.999809i	$0.506227\pi$
$294$		−	6.85572e6i		−	0.269781i
$295$	−851990.	−	1.08204e7i	−0.0331870	−	0.421479i
$296$	2.18157e7			0.841191
$297$		−	4.99865e7i		−	1.90802i
$298$	1.65472e7			0.625282
$299$	726430.			0.0271756
$300$	−6.99420e6			−0.259045
$301$		−	4.68055e7i		−	1.71632i
$302$	−4.01461e7			−1.45755
$303$			3.73840e7i			1.34387i
$304$	−2.59717e7			−0.924442
$305$		−	109829.i		−	0.00387095i
$306$		−	5.81436e7i		−	2.02926i
$307$	−1.83381e7			−0.633780			−0.316890	−	0.948462i	$-0.602639\pi$
$307$	−1.83381e7			−0.633780			−0.316890	+	0.948462i	$0.602639\pi$
$308$			9.78831e6i			0.335008i
$309$		−	5.18103e7i		−	1.75607i
$310$	9.91185e6			0.332713
$311$	−2.87727e7			−0.956531			−0.478265	−	0.878215i	$-0.658734\pi$
$311$	−2.87727e7			−0.956531			−0.478265	+	0.878215i	$0.658734\pi$
$312$	6.28865e7			2.07059
$313$		−	8.75157e6i		−	0.285399i	−0.989766	−	0.142700i	$-0.954422\pi$
$313$		−	8.75157e6i		−	0.285399i	0.989766	−	0.142700i	$-0.0455783\pi$
$314$	−3.79190e7			−1.22481
$315$	−2.46881e7			−0.789872
$316$	3.61584e6			0.114590
$317$	4.02075e7			1.26220			0.631102	−	0.775700i	$-0.282603\pi$
$317$	4.02075e7			1.26220			0.631102	+	0.775700i	$0.282603\pi$
$318$			8.45164e7i			2.62821i
$319$			4.38911e7i			1.35209i
$320$	−1.53930e7			−0.469758
$321$	5.43075e7			1.64189
$322$	756698.			0.0226649
$323$	5.29817e7			1.57224
$324$	1.52677e6			0.0448890
$325$		−	3.30479e7i		−	0.962707i
$326$			5.02358e7i			1.44998i
$327$			2.66607e7i			0.762481i
$328$		−	1.95174e7i		−	0.553095i
$329$		−	4.68664e7i		−	1.31606i
$330$	−3.62854e7			−1.00970
$331$	−2.54741e7			−0.702449			−0.351224	−	0.936291i	$-0.614235\pi$
$331$	−2.54741e7			−0.702449			−0.351224	+	0.936291i	$0.614235\pi$
$332$			1.09243e7i			0.298524i
$333$			4.98254e7i			1.34933i
$334$			1.98580e7i			0.532963i
$335$			4.56520e6i			0.121430i
$336$	5.24987e7			1.38398
$337$			1.95808e7i			0.511612i	0.966728	+	0.255806i	$0.0823408\pi$
$337$			1.95808e7i			0.511612i	−0.966728	+	0.255806i	$0.917659\pi$
$338$			1.29922e7i			0.336460i
$339$		−	5.05635e7i		−	1.29789i
$340$	4.17443e6			0.106209
$341$	5.58912e7			1.40955
$342$		−	7.40150e7i		−	1.85030i
$343$	3.58890e7			0.889362
$344$	6.88476e7			1.69127
$345$		−	663590.i		−	0.0161600i
$346$	−6.11033e7			−1.47515
$347$		−	1.45453e7i		−	0.348124i	−0.984735	−	0.174062i	$-0.944311\pi$
$347$		−	1.45453e7i		−	0.348124i	0.984735	−	0.174062i	$-0.0556893\pi$
$348$	−1.11588e7			−0.264778
$349$			2.05319e7i			0.483006i	0.970400	+	0.241503i	$0.0776404\pi$
$349$			2.05319e7i			0.483006i	−0.970400	+	0.241503i	$0.922360\pi$
$350$		−	3.44249e7i		−	0.802914i
$351$			6.00483e7i			1.38861i
$352$	−2.64837e7			−0.607226
$353$			2.23794e6i			0.0508772i	0.999676	+	0.0254386i	$0.00809824\pi$
$353$			2.23794e6i			0.0508772i	−0.999676	+	0.0254386i	$0.991902\pi$
$354$	−6.55723e7	+	5.16313e6i	−1.47812	+	0.116387i
$355$	1.65565e7			0.370070
$356$		−	1.16691e7i		−	0.258636i
$357$	−1.07096e8			−2.35380
$358$	−1.06125e7			−0.231296
$359$	2.98632e7			0.645437			0.322718	−	0.946495i	$-0.395403\pi$
$359$	2.98632e7			0.645437			0.322718	+	0.946495i	$0.395403\pi$
$360$		−	3.63145e7i		−	0.778346i
$361$	2.03981e7			0.433579
$362$		−	3.02110e7i		−	0.636853i
$363$	−1.25743e8			−2.62884
$364$		−	1.17586e7i		−	0.243810i
$365$		−	1.70571e7i		−	0.350774i
$366$	−665573.			−0.0135754
$367$			3.63988e7i			0.736359i	0.929755	+	0.368179i	$0.120019\pi$
$367$			3.63988e7i			0.736359i	−0.929755	+	0.368179i	$0.879981\pi$
$368$			892023.i			0.0178991i
$369$	4.45761e7			0.887203
$370$	1.51214e7			0.298530
$371$	9.84076e7			1.92711
$372$			1.42097e7i			0.276031i
$373$	−4.10541e7			−0.791098			−0.395549	−	0.918445i	$-0.629446\pi$
$373$	−4.10541e7			−0.791098			−0.395549	+	0.918445i	$0.629446\pi$
$374$	−9.95024e7			−1.90204
$375$	−6.69489e7			−1.26955
$376$	6.89372e7			1.29685
$377$		−	5.27260e7i		−	0.984013i
$378$			6.25504e7i			1.15812i
$379$	−4.32229e7			−0.793956			−0.396978	−	0.917828i	$-0.629941\pi$
$379$	−4.32229e7			−0.793956			−0.396978	+	0.917828i	$0.629941\pi$
$380$	5.31392e6			0.0968421
$381$	−3.44097e7			−0.622166
$382$	4.43902e7			0.796337
$383$	9.83708e7			1.75093			0.875467	−	0.483278i	$-0.160554\pi$
$383$	9.83708e7			1.75093			0.875467	+	0.483278i	$0.160554\pi$
$384$			5.80878e7i			1.02587i
$385$			4.22493e7i			0.740351i
$386$		−	8.05485e7i		−	1.40054i
$387$			1.57242e8i			2.71292i
$388$			6.88977e6i			0.117953i
$389$	−4.97440e7			−0.845069			−0.422534	−	0.906347i	$-0.638859\pi$
$389$	−4.97440e7			−0.845069			−0.422534	+	0.906347i	$0.638859\pi$
$390$	4.35894e7			0.734830
$391$		−	1.81971e6i		−	0.0304418i
$392$		−	1.17417e7i		−	0.194928i
$393$			8.29407e7i			1.36644i
$394$			8.50085e6i			0.138987i
$395$	1.56071e7			0.253239
$396$		−	3.28836e7i		−	0.529535i
$397$		−	4.07638e7i		−	0.651483i	−0.945459	−	0.325742i	$-0.894386\pi$
$397$		−	4.07638e7i		−	0.651483i	0.945459	−	0.325742i	$-0.105614\pi$
$398$			7.03366e7i			1.11566i
$399$	−1.36330e8			−2.14621
$400$	4.05814e7			0.634084
$401$			7.92566e7i			1.22914i	0.788862	+	0.614571i	$0.210671\pi$
$401$			7.92566e7i			1.22914i	−0.788862	+	0.614571i	$0.789329\pi$
$402$	2.76655e7			0.425853
$403$	−6.71417e7			−1.02583
$404$			1.02820e7i			0.155931i
$405$	6.59003e6			0.0992024
$406$		−	5.49230e7i		−	0.820684i
$407$	8.52672e7			1.26473
$408$		−	1.57531e8i		−	2.31945i
$409$			4.53606e7i			0.662993i	0.943456	+	0.331497i	$0.107554\pi$
$409$			4.53606e7i			0.662993i	−0.943456	+	0.331497i	$0.892446\pi$
$410$		−	1.35283e7i		−	0.196288i
$411$	1.39683e8			2.01196
$412$		−	1.42497e7i		−	0.203758i
$413$	6.01175e6	+	7.63498e7i	0.0853396	+	1.08382i
$414$	−2.54211e6			−0.0358256
$415$			4.71527e7i			0.659724i
$416$	3.18146e7			0.441923
$417$	6.64443e7			0.916325
$418$	−1.26663e8			−1.73429
$419$			5.00796e7i			0.680799i	0.940281	+	0.340399i	$0.110562\pi$
$419$			5.00796e7i			0.680799i	−0.940281	+	0.340399i	$0.889438\pi$
$420$	−1.07414e7			−0.144982
$421$		−	1.17905e8i		−	1.58010i	−0.613043	−	0.790049i	$-0.710055\pi$
$421$		−	1.17905e8i		−	1.58010i	0.613043	−	0.790049i	$-0.289945\pi$
$422$	−5.28632e7			−0.703422
$423$			1.57447e8i			2.08024i
$424$			1.44751e8i			1.89899i
$425$	−8.27850e7			−1.07841
$426$		−	1.00334e8i		−	1.29783i
$427$			774967.i			0.00995405i
$428$	1.49365e7			0.190510
$429$	2.45793e8			3.11313
$430$	4.77213e7			0.600215
$431$		−	1.12512e8i		−	1.40529i	−0.711541	−	0.702645i	$-0.752002\pi$
$431$		−	1.12512e8i		−	1.40529i	0.711541	−	0.702645i	$-0.247998\pi$
$432$	−7.37366e7			−0.914602
$433$	−5.56087e7			−0.684982			−0.342491	−	0.939521i	$-0.611271\pi$
$433$	−5.56087e7			−0.684982			−0.342491	+	0.939521i	$0.611271\pi$
$434$	−6.99393e7			−0.855563
$435$	−4.81650e7			−0.585145
$436$			7.33267e6i			0.0884714i
$437$		−	2.31643e6i		−	0.0277571i
$438$	−1.03368e8			−1.23016
$439$	3.84071e7			0.453960			0.226980	−	0.973899i	$-0.427115\pi$
$439$	3.84071e7			0.453960			0.226980	+	0.973899i	$0.427115\pi$
$440$	−6.21458e7			−0.729547
$441$	2.68172e7			0.312678
$442$	1.19531e8			1.38425
$443$		−	1.36815e8i		−	1.57371i	−0.617140	−	0.786853i	$-0.711709\pi$
$443$		−	1.36815e8i		−	1.57371i	0.617140	−	0.786853i	$-0.288291\pi$
$444$			2.16783e7i			0.247671i
$445$		−	5.03676e7i		−	0.571573i
$446$		−	8.52561e7i		−	0.960995i
$447$			1.02393e8i			1.14643i
$448$	1.08615e8			1.20797
$449$	−7.83838e7			−0.865939			−0.432969	−	0.901409i	$-0.642534\pi$
$449$	−7.83838e7			−0.865939			−0.432969	+	0.901409i	$0.642534\pi$
$450$			1.15650e8i			1.26914i
$451$		−	7.62840e7i		−	0.831579i
$452$		−	1.39068e7i		−	0.150595i
$453$		−	2.48420e8i		−	2.67235i
$454$	5.39690e6			0.0576735
$455$		−	5.07538e7i		−	0.538808i
$456$		−	2.00531e8i		−	2.11489i
$457$			3.20033e7i			0.335309i	0.985846	+	0.167655i	$0.0536194\pi$
$457$			3.20033e7i			0.335309i	−0.985846	+	0.167655i	$0.946381\pi$
$458$	−9.96410e7			−1.03715
$459$	1.50421e8			1.55550
$460$		−	182511.i		−	0.00187507i
$461$	7.84507e7			0.800745			0.400373	−	0.916352i	$-0.368881\pi$
$461$	7.84507e7			0.800745			0.400373	+	0.916352i	$0.368881\pi$
$462$	2.56035e8			2.59641
$463$			1.77167e8i			1.78500i	0.451045	+	0.892501i	$0.351051\pi$
$463$			1.77167e8i			1.78500i	−0.451045	+	0.892501i	$0.648949\pi$
$464$	6.47452e7			0.648117
$465$			6.13336e7i			0.610014i
$466$	−3.79710e7			−0.375227
$467$		−	1.65563e8i		−	1.62560i	−0.582543	−	0.812800i	$-0.697942\pi$
$467$		−	1.65563e8i		−	1.62560i	0.582543	−	0.812800i	$-0.302058\pi$
$468$			3.95029e7i			0.385382i
$469$		−	3.22126e7i		−	0.312253i
$470$	4.77834e7			0.460239
$471$		−	2.34639e8i		−	2.24563i
$472$	−1.12305e8	+	8.84285e6i	−1.06801	+	0.0840943i
$473$	2.69092e8			2.54283
$474$		−	9.45803e7i		−	0.888108i
$475$	−1.05383e8			−0.983306
$476$	−2.94553e7			−0.273113
$477$	−3.30599e8			−3.04611
$478$			5.24598e7i			0.480334i
$479$	−3.25732e7			−0.296384			−0.148192	−	0.988959i	$-0.547345\pi$
$479$	−3.25732e7			−0.296384			−0.148192	+	0.988959i	$0.547345\pi$
$480$		−	2.90625e7i		−	0.262790i
$481$	−1.02431e8			−0.920440
$482$			5.85151e7i			0.522549i
$483$			4.68238e6i			0.0415551i
$484$	−3.45839e7			−0.305026
$485$			2.97383e7i			0.260670i
$486$			8.23461e7i			0.717355i
$487$	−1.98742e8			−1.72069			−0.860344	−	0.509714i	$-0.829751\pi$
$487$	−1.98742e8			−1.72069			−0.860344	+	0.509714i	$0.829751\pi$
$488$	−1.13992e6			−0.00980879
$489$	−3.10855e8			−2.65846
$490$		−	8.13872e6i		−	0.0691779i
$491$	−8.63955e7			−0.729872			−0.364936	−	0.931033i	$-0.618909\pi$
$491$	−8.63955e7			−0.729872			−0.364936	+	0.931033i	$0.618909\pi$
$492$	1.93944e7			0.162847
$493$	−1.32079e8			−1.10228
$494$	1.52160e8			1.26217
$495$		−	1.41936e8i		−	1.17025i
$496$		−	8.24469e7i		−	0.675662i
$497$	−1.16825e8			−0.951626
$498$	2.85749e8			2.31365
$499$	2.26160e8			1.82018			0.910089	−	0.414413i	$-0.136013\pi$
$499$	2.26160e8			1.82018			0.910089	+	0.414413i	$0.136013\pi$
$500$	−1.84134e7			−0.147307
$501$	−1.22880e8			−0.977163
$502$			1.14174e8i			0.902517i
$503$			6.92678e7i			0.544287i	0.962257	+	0.272143i	$0.0877325\pi$
$503$			6.92678e7i			0.544287i	−0.962257	+	0.272143i	$0.912268\pi$
$504$			2.56240e8i			2.00150i
$505$			4.43801e7i			0.344599i
$506$			4.35037e6i			0.0335795i
$507$	−8.03946e7			−0.616883
$508$	−9.46392e6			−0.0721905
$509$			9.84616e7i			0.746644i	0.927702	+	0.373322i	$0.121781\pi$
$509$			9.84616e7i			0.746644i	−0.927702	+	0.373322i	$0.878219\pi$
$510$		−	1.09191e8i		−	0.823148i
$511$			1.20357e8i			0.902007i
$512$			1.50085e8i			1.11822i
$513$	1.91481e8			1.41832
$514$			2.10602e7i			0.155087i
$515$		−	6.15062e7i		−	0.450295i
$516$			6.84138e7i			0.497960i
$517$	2.69442e8			1.94982
$518$	−1.06699e8			−0.767663
$519$		−	3.78101e8i		−	2.70462i
$520$	7.46552e7			0.530946
$521$	9.36915e7			0.662502			0.331251	−	0.943543i	$-0.392529\pi$
$521$	9.36915e7			0.662502			0.331251	+	0.943543i	$0.392529\pi$
$522$			1.84513e8i			1.29722i
$523$	−1.55315e8			−1.08569			−0.542846	−	0.839832i	$-0.682653\pi$
$523$	−1.55315e8			−1.08569			−0.542846	+	0.839832i	$0.682653\pi$
$524$			2.28117e7i			0.158549i
$525$	2.13018e8			1.47211
$526$			1.94965e7i			0.133967i
$527$			1.68190e8i			1.14913i
$528$			3.01823e8i			2.05046i
$529$	1.47956e8			0.999463
$530$			1.00333e8i			0.673932i
$531$	−2.01964e7	−	2.56496e8i	−0.134893	−	1.71316i
$532$	−3.74957e7			−0.249027
$533$			9.16393e7i			0.605202i
$534$	−3.05232e8			−2.00450
$535$	6.44707e7			0.421018
$536$	4.73824e7			0.307697
$537$		−	6.56692e7i		−	0.424072i
$538$	−1.73078e8			−1.11146
$539$		−	4.58928e7i		−	0.293075i
$540$	1.50868e7			0.0958112
$541$			2.63293e8i			1.66283i	0.555651	+	0.831416i	$0.312469\pi$
$541$			2.63293e8i			1.66283i	−0.555651	+	0.831416i	$0.687531\pi$
$542$		−	1.94092e8i		−	1.21902i
$543$	1.86943e8			1.16764
$544$		−	7.96956e7i		−	0.495037i
$545$			3.16501e7i			0.195517i
$546$	−3.07572e8			−1.88960
$547$	2.27028e8			1.38713			0.693567	−	0.720392i	$-0.256038\pi$
$547$	2.27028e8			1.38713			0.693567	+	0.720392i	$0.256038\pi$
$548$	3.84180e7			0.233450
$549$		−	2.60349e6i		−	0.0157340i
$550$	1.97914e8			1.18957
$551$	−1.68132e8			−1.00507
$552$	−6.88744e6			−0.0409487
$553$	−1.10126e8			−0.651198
$554$		−	4.15204e7i		−	0.244192i
$555$			9.35701e7i			0.547341i
$556$	1.82746e7			0.106322
$557$	4.30150e6			0.0248917			0.0124459	−	0.999923i	$-0.496038\pi$
$557$	4.30150e6			0.0248917			0.0124459	+	0.999923i	$0.496038\pi$
$558$	2.34960e8			1.35236
$559$	−3.23258e8			−1.85061
$560$	6.23234e7			0.354884
$561$		−	6.15712e8i		−	3.48730i
$562$			3.02002e8i			1.70138i
$563$			1.61271e7i			0.0903714i	0.998979	+	0.0451857i	$0.0143880\pi$
$563$			1.61271e7i			0.0903714i	−0.998979	+	0.0451857i	$0.985612\pi$
$564$			6.85028e7i			0.381831i
$565$		−	6.00260e7i		−	0.332808i
$566$	2.28663e8			1.26109
$567$	−4.65001e7			−0.255097
$568$		−	1.71841e8i		−	0.937739i
$569$		−	2.91576e8i		−	1.58276i	−0.611325	−	0.791379i	$-0.709363\pi$
$569$		−	2.91576e8i		−	1.58276i	0.611325	−	0.791379i	$-0.290637\pi$
$570$		−	1.38997e8i		−	0.750553i
$571$			2.35358e8i			1.26421i	0.774881	+	0.632107i	$0.217810\pi$
$571$			2.35358e8i			1.26421i	−0.774881	+	0.632107i	$0.782190\pi$
$572$	6.76021e7			0.361220
$573$			2.74682e8i			1.46005i
$574$			9.54577e7i			0.504749i
$575$			3.61947e6i			0.0190389i
$576$	−3.64891e8			−1.90939
$577$	2.06502e8			1.07497			0.537486	−	0.843273i	$-0.319374\pi$
$577$	2.06502e8			1.07497			0.537486	+	0.843273i	$0.319374\pi$
$578$		−	1.25776e8i		−	0.651350i
$579$	4.98427e8			2.56783
$580$	−1.32471e7			−0.0678950
$581$		−	3.32715e8i		−	1.69646i
$582$	1.80217e8			0.914169
$583$			5.65760e8i			2.85514i
$584$	−1.77037e8			−0.888844
$585$			1.70506e8i			0.851674i
$586$			7.08027e6i			0.0351849i
$587$			1.27556e7i			0.0630649i	0.999503	+	0.0315324i	$0.0100387\pi$
$587$			1.27556e7i			0.0630649i	−0.999503	+	0.0315324i	$0.989961\pi$
$588$	1.16678e7			0.0573925
$589$			2.14100e8i			1.04778i
$590$	−7.78436e7	+	6.12937e6i	−0.379024	+	0.0298442i
$591$	−5.26025e7			−0.254826
$592$		−	1.25780e8i		−	0.606245i
$593$	1.44245e8			0.691729			0.345864	−	0.938285i	$-0.387586\pi$
$593$	1.44245e8			0.691729			0.345864	+	0.938285i	$0.387586\pi$
$594$	−3.59612e8			−1.71583
$595$	−1.27138e8			−0.603567
$596$			2.81617e7i			0.133021i
$597$	−4.35237e8			−2.04551
$598$		−	5.22606e6i		−	0.0244383i
$599$	4.87986e7			0.227053			0.113526	−	0.993535i	$-0.463785\pi$
$599$	4.87986e7			0.227053			0.113526	+	0.993535i	$0.463785\pi$
$600$			3.13335e8i			1.45062i
$601$			5.77810e7i			0.266172i	0.991105	+	0.133086i	$0.0424886\pi$
$601$			5.77810e7i			0.266172i	−0.991105	+	0.133086i	$0.957511\pi$
$602$	−3.36728e8			−1.54344
$603$			1.08218e8i			0.493567i
$604$		−	6.83247e7i		−	0.310075i
$605$	−1.49275e8			−0.674093
$606$	2.68947e8			1.20851
$607$	1.45131e8			0.648924			0.324462	−	0.945899i	$-0.394817\pi$
$607$	1.45131e8			0.648924			0.324462	+	0.945899i	$0.394817\pi$
$608$		−	1.01450e8i		−	0.451379i
$609$	3.39858e8			1.50469
$610$	−790129.			−0.00348104
$611$	−3.23679e8			−1.41903
$612$	9.89546e7			0.431700
$613$		−	1.86591e8i		−	0.810046i	−0.914306	−	0.405023i	$-0.867264\pi$
$613$		−	1.86591e8i		−	0.810046i	0.914306	−	0.405023i	$-0.132736\pi$
$614$			1.31927e8i			0.569941i
$615$	8.37121e7			0.359884
$616$	4.38508e8			1.87601
$617$	−2.66448e8			−1.13438			−0.567188	−	0.823589i	$-0.691969\pi$
$617$	−2.66448e8			−1.13438			−0.567188	+	0.823589i	$0.691969\pi$
$618$	−3.72733e8			−1.57918
$619$	3.38540e8			1.42738			0.713688	−	0.700464i	$-0.247023\pi$
$619$	3.38540e8			1.42738			0.713688	+	0.700464i	$0.247023\pi$
$620$			1.68690e7i			0.0707805i
$621$		−	6.57660e6i		−	0.0274616i
$622$			2.06996e8i			0.860182i
$623$			3.55400e8i			1.46978i
$624$		−	3.62577e8i		−	1.49227i
$625$	1.21024e8			0.495713
$626$	−6.29603e7			−0.256652
$627$		−	7.83781e8i		−	3.17974i
$628$		−	6.45343e7i		−	0.260562i
$629$			2.56589e8i			1.03107i
$630$			1.77611e8i			0.710310i
$631$	−4.83502e8			−1.92447			−0.962233	−	0.272226i	$-0.912240\pi$
$631$	−4.83502e8			−1.92447			−0.962233	+	0.272226i	$0.912240\pi$
$632$		−	1.61987e8i		−	0.641695i
$633$		−	3.27112e8i		−	1.28969i
$634$		−	2.89260e8i		−	1.13507i
$635$	−4.08492e7			−0.159537
$636$	−1.43838e8			−0.559118
$637$			5.51307e7i			0.213292i
$638$	3.15760e8			1.21589
$639$	3.92471e8			1.50420
$640$			6.89584e7i			0.263055i
$641$	−2.27407e8			−0.863436			−0.431718	−	0.902009i	$-0.642092\pi$
$641$	−2.27407e8			−0.863436			−0.431718	+	0.902009i	$0.642092\pi$
$642$		−	3.90698e8i		−	1.47651i
$643$	−4.67470e7			−0.175841			−0.0879206	−	0.996127i	$-0.528022\pi$
$643$	−4.67470e7			−0.175841			−0.0879206	+	0.996127i	$0.528022\pi$
$644$			1.28782e6i			0.00482168i
$645$			2.95295e8i			1.10047i
$646$		−	3.81160e8i		−	1.41387i
$647$	8.05596e7			0.297444			0.148722	−	0.988879i	$-0.452484\pi$
$647$	8.05596e7			0.297444			0.148722	+	0.988879i	$0.452484\pi$
$648$		−	6.83983e7i		−	0.251374i
$649$	−4.38947e8	+	3.45625e7i	−1.60575	+	0.126436i
$650$	−2.37753e8			−0.865736
$651$		−	4.32778e8i		−	1.56863i
$652$	−8.54964e7			−0.308464
$653$	−1.27620e7			−0.0458331			−0.0229165	−	0.999737i	$-0.507295\pi$
$653$	−1.27620e7			−0.0458331			−0.0229165	+	0.999737i	$0.507295\pi$
$654$	1.91802e8			0.685678
$655$			9.84623e7i			0.350386i
$656$	−1.12529e8			−0.398614
$657$		−	4.04338e8i		−	1.42577i
$658$	−3.37166e8			−1.18349
$659$		−	1.06999e7i		−	0.0373872i	−0.999825	−	0.0186936i	$-0.994049\pi$
$659$		−	1.06999e7i		−	0.0373872i	0.999825	−	0.0186936i	$-0.00595071\pi$
$660$		−	6.17542e7i		−	0.214800i
$661$	2.52333e8			0.873713			0.436857	−	0.899531i	$-0.356092\pi$
$661$	2.52333e8			0.873713			0.436857	+	0.899531i	$0.356092\pi$
$662$			1.83265e8i			0.631693i
$663$			7.39649e8i			2.53796i
$664$	4.89400e8			1.67171
$665$	−1.61843e8			−0.550337
$666$	3.58453e8			1.21342
$667$			5.77465e6i			0.0194602i
$668$	−3.37964e7			−0.113381
$669$	5.27557e8			1.76194
$670$	3.28428e7			0.109198
$671$	−4.45541e6			−0.0147475
$672$			2.05069e8i			0.675759i
$673$		−	2.13094e8i		−	0.699080i	−0.936921	−	0.349540i	$-0.886338\pi$
$673$		−	2.13094e8i		−	0.699080i	0.936921	−	0.349540i	$-0.113662\pi$
$674$	1.40868e8			0.460078
$675$	−2.99193e8			−0.972839
$676$	−2.21114e7			−0.0715776
$677$	5.03604e8			1.62302			0.811509	−	0.584341i	$-0.198647\pi$
$677$	5.03604e8			1.62302			0.811509	+	0.584341i	$0.198647\pi$
$678$	−3.63763e8			−1.16716
$679$		−	2.09838e8i		−	0.670307i
$680$		−	1.87011e8i		−	0.594759i
$681$			3.33955e7i			0.105742i
$682$		−	4.02091e8i		−	1.26757i
$683$			5.88779e8i			1.84795i	0.382453	+	0.923975i	$0.375079\pi$
$683$			5.88779e8i			1.84795i	−0.382453	+	0.923975i	$0.624921\pi$
$684$	1.25966e8			0.393627
$685$	1.65824e8			0.515912
$686$		−	2.58192e8i		−	0.799779i
$687$		−	6.16569e8i		−	1.90157i
$688$		−	3.96947e8i		−	1.21890i
$689$		−	6.79643e8i		−	2.07789i
$690$	−4.77399e6			−0.0145323
$691$		−	5.06413e8i		−	1.53487i	−0.641128	−	0.767434i	$-0.721533\pi$
$691$		−	5.06413e8i		−	1.53487i	0.641128	−	0.767434i	$-0.278467\pi$
$692$		−	1.03992e8i		−	0.313820i
$693$			1.00152e9i			3.00926i
$694$	−1.04641e8			−0.313058
$695$	7.88788e7			0.234967
$696$			4.99907e8i			1.48273i
$697$	2.29556e8			0.677940
$698$	1.47710e8			0.434354
$699$		−	2.34961e8i		−	0.687962i
$700$	5.85878e7			0.170810
$701$		−	1.28590e8i		−	0.373296i	−0.982427	−	0.186648i	$-0.940238\pi$
$701$		−	1.28590e8i		−	0.373296i	0.982427	−	0.186648i	$-0.0597624\pi$
$702$	4.31999e8			1.24874
$703$			3.26630e8i			0.940134i
$704$			6.24446e8i			1.78969i
$705$			2.95679e8i			0.843827i
$706$	1.61001e7			0.0457525
$707$		−	3.13152e8i		−	0.886128i
$708$	−8.78713e6	−	1.11597e8i	−0.0247598	−	0.314452i
$709$	−4.30633e8			−1.20828			−0.604142	−	0.796877i	$-0.706484\pi$
$709$	−4.30633e8			−1.20828			−0.604142	+	0.796877i	$0.706484\pi$
$710$		−	1.19111e8i		−	0.332794i
$711$	3.69965e8			1.02932
$712$	−5.22768e8			−1.44834
$713$	7.35347e6			0.0202873
$714$			7.70468e8i			2.11670i
$715$	2.91791e8			0.798278
$716$		−	1.80614e7i		−	0.0492054i
$717$	−3.24616e8			−0.880670
$718$		−	2.14842e8i		−	0.580423i
$719$			1.53429e8i			0.412781i	0.978470	+	0.206390i	$0.0661717\pi$
$719$			1.53429e8i			0.412781i	−0.978470	+	0.206390i	$0.933828\pi$
$720$	−2.09374e8			−0.560952
$721$			4.33995e8i			1.15792i
$722$		−	1.46748e8i		−	0.389906i
$723$	−3.62086e8			−0.958070
$724$	5.14161e7			0.135482
$725$	2.62710e8			0.689386
$726$			9.04617e8i			2.36404i
$727$	2.46836e8			0.642399			0.321199	−	0.947012i	$-0.395914\pi$
$727$	2.46836e8			0.642399			0.321199	+	0.947012i	$0.395914\pi$
$728$	−5.26777e8			−1.36531
$729$	−6.00455e8			−1.54988
$730$	−1.22712e8			−0.315441
$731$			8.09762e8i			2.07303i
$732$		−	1.13274e6i		−	0.00288799i
$733$	5.18307e7			0.131606			0.0658029	−	0.997833i	$-0.479039\pi$
$733$	5.18307e7			0.131606			0.0658029	+	0.997833i	$0.479039\pi$
$734$	2.61860e8			0.662187
$735$	5.03616e7			0.126835
$736$	−3.48439e6			−0.00873964
$737$	1.85195e8			0.462623
$738$		−	3.20688e8i		−	0.797837i
$739$		−	2.77948e8i		−	0.688700i	−0.938841	−	0.344350i	$-0.888099\pi$
$739$		−	2.77948e8i		−	0.688700i	0.938841	−	0.344350i	$-0.111901\pi$
$740$			2.57352e7i			0.0635085i
$741$			9.41550e8i			2.31414i
$742$		−	7.07962e8i		−	1.73300i
$743$	−6.69603e8			−1.63249			−0.816246	−	0.577704i	$-0.803949\pi$
$743$	−6.69603e8			−1.63249			−0.816246	+	0.577704i	$0.803949\pi$
$744$	6.36585e8			1.54574
$745$			1.21555e8i			0.293970i
$746$			2.95351e8i			0.711413i
$747$			1.11775e9i			2.68154i
$748$		−	1.69343e8i		−	0.404634i
$749$	−4.54913e8			−1.08264
$750$			4.81643e8i			1.14167i
$751$			5.70436e8i			1.34675i	0.739301	+	0.673375i	$0.235156\pi$
$751$			5.70436e8i			1.34675i	−0.739301	+	0.673375i	$0.764844\pi$
$752$		−	3.97463e8i		−	0.934638i
$753$	−7.06497e8			−1.65472
$754$	−3.79321e8			−0.884896
$755$		−	2.94910e8i		−	0.685250i
$756$	−1.06454e8			−0.246376
$757$	−7.71740e8			−1.77903			−0.889515	−	0.456907i	$-0.848957\pi$
$757$	−7.71740e8			−1.77903			−0.889515	+	0.456907i	$0.848957\pi$
$758$			3.10953e8i			0.713983i
$759$	−2.69197e7			−0.0615665
$760$		−	2.38059e8i		−	0.542306i
$761$	8.58889e8			1.94887			0.974435	−	0.224668i	$-0.0721298\pi$
$761$	8.58889e8			1.94887			0.974435	+	0.224668i	$0.0721298\pi$
$762$			2.47550e8i			0.559496i
$763$		−	2.23327e8i		−	0.502768i
$764$			7.55477e7i			0.169411i
$765$	4.27119e8			0.954035
$766$		−	7.07697e8i		−	1.57457i
$767$	5.27303e8	−	4.15196e7i	1.16862	−	0.0920168i
$768$	−4.11960e8			−0.909435
$769$		−	4.22927e8i		−	0.930007i	−0.885309	−	0.465003i	$-0.846053\pi$
$769$		−	4.22927e8i		−	0.930007i	0.885309	−	0.465003i	$-0.153947\pi$
$770$	3.03949e8			0.665777
$771$	−1.30319e8			−0.284344
$772$	1.37085e8			0.297947
$773$		−	6.35429e8i		−	1.37572i	−0.725845	−	0.687858i	$-0.758551\pi$
$773$		−	6.35429e8i		−	1.37572i	0.725845	−	0.687858i	$-0.241449\pi$
$774$	1.13123e9			2.43965
$775$		−	3.34536e8i		−	0.718684i
$776$	3.08656e8			0.660526
$777$		−	6.60243e8i		−	1.40747i
$778$			3.57867e8i			0.759947i
$779$	2.92218e8			0.618151
$780$			7.41848e7i			0.156326i
$781$		−	6.71645e8i		−	1.40989i
$782$	−1.30913e7			−0.0273755
$783$	−4.77346e8			−0.994369
$784$	−6.76980e7			−0.140484
$785$		−	2.78550e8i		−	0.575829i
$786$	5.96690e8			1.22880
$787$	1.49996e7			0.0307720			0.0153860	−	0.999882i	$-0.495102\pi$
$787$	1.49996e7			0.0307720			0.0153860	+	0.999882i	$0.495102\pi$
$788$	−1.44676e7			−0.0295677
$789$	−1.20643e8			−0.245623
$790$		−	1.12280e8i		−	0.227731i
$791$			4.23551e8i			0.855808i
$792$	−1.47316e9			−2.96534
$793$	5.35224e6			0.0107329
$794$	−2.93262e8			−0.585861
$795$	−6.20851e8			−1.23562
$796$	−1.19706e8			−0.237343
$797$			7.55224e8i			1.49177i	0.666077	+	0.745883i	$0.267972\pi$
$797$			7.55224e8i			1.49177i	−0.666077	+	0.745883i	$0.732028\pi$
$798$			9.80781e8i			1.93003i
$799$			8.10816e8i			1.58958i
$800$			1.58518e8i			0.309605i
$801$		−	1.19396e9i		−	2.32323i
$802$	5.70186e8			1.10533
$803$	−6.91952e8			−1.33638
$804$			4.70839e7i			0.0905949i
$805$			5.55864e6i			0.0106557i
$806$			4.83029e8i			0.922504i
$807$		−	1.07099e9i		−	2.03781i
$808$	4.60624e8			0.873197
$809$		−	3.52224e8i		−	0.665233i	−0.943062	−	0.332616i	$-0.892069\pi$
$809$		−	3.52224e8i		−	0.665233i	0.943062	−	0.332616i	$-0.107931\pi$
$810$		−	4.74099e7i		−	0.0892100i
$811$			1.85193e8i			0.347186i	0.984817	+	0.173593i	$0.0555377\pi$
$811$			1.85193e8i			0.347186i	−0.984817	+	0.173593i	$0.944462\pi$
$812$	9.34734e7			0.174590
$813$	1.20102e9			2.23501
$814$		−	6.13428e8i		−	1.13734i
$815$	−3.69029e8			−0.681691
$816$	−9.08256e8			−1.67162
$817$			1.03080e9i			1.89020i
$818$	3.26332e8			0.596211
$819$		−	1.20312e9i		−	2.19006i
$820$	2.30239e7			0.0417577
$821$		−	4.19768e8i		−	0.758542i	−0.925286	−	0.379271i	$-0.876175\pi$
$821$		−	4.19768e8i		−	0.758542i	0.925286	−	0.379271i	$-0.123825\pi$
$822$		−	1.00491e9i		−	1.80930i
$823$			6.55987e8i			1.17678i	0.808577	+	0.588391i	$0.200238\pi$
$823$			6.55987e8i			1.17678i	−0.808577	+	0.588391i	$0.799762\pi$
$824$	−6.38376e8			−1.14102
$825$			1.22468e9i			2.18102i
$826$	5.49274e8	−	4.32496e7i	0.974651	−	0.0767436i
$827$	1.01039e9			1.78637			0.893183	−	0.449694i	$-0.148467\pi$
$827$	1.01039e9			1.78637			0.893183	+	0.449694i	$0.148467\pi$
$828$		−	4.32642e6i		−	0.00762145i
$829$	2.10445e8			0.369382			0.184691	−	0.982797i	$-0.440872\pi$
$829$	2.10445e8			0.369382			0.184691	+	0.982797i	$0.440872\pi$
$830$	3.39225e8			0.593271
$831$	2.56924e8			0.447715
$832$		−	7.50141e8i		−	1.30249i
$833$	1.38102e8			0.238927
$834$		−	4.78012e8i		−	0.824026i
$835$	−1.45876e8			−0.250567
$836$		−	2.15568e8i		−	0.368949i
$837$			6.07855e8i			1.03663i
$838$	3.60282e8			0.612223
$839$		−	2.95771e8i		−	0.500807i	−0.968142	−	0.250404i	$-0.919437\pi$
$839$		−	2.95771e8i		−	0.500807i	0.968142	−	0.250404i	$-0.0805633\pi$
$840$			4.81208e8i			0.811886i
$841$	−1.75685e8			−0.295357
$842$	−8.48226e8			−1.42094
$843$	−1.86876e9			−3.11940
$844$		−	8.99678e7i		−	0.149644i
$845$	−9.54398e7			−0.158183
$846$	1.13270e9			1.87070
$847$	1.05330e9			1.73341
$848$	8.34571e8			1.36860
$849$			1.41494e9i			2.31215i
$850$			5.95571e8i			0.969787i
$851$	1.12184e7			0.0182030
$852$	1.70758e8			0.276098
$853$	−1.92543e8			−0.310228			−0.155114	−	0.987897i	$-0.549574\pi$
$853$	−1.92543e8			−0.310228			−0.155114	+	0.987897i	$0.549574\pi$
$854$	5.57525e6			0.00895140
$855$	5.43708e8			0.869897
$856$		−	6.69145e8i		−	1.06684i
$857$			5.93331e8i			0.942659i	0.881957	+	0.471329i	$0.156226\pi$
$857$			5.93331e8i			0.942659i	−0.881957	+	0.471329i	$0.843774\pi$
$858$		−	1.76828e9i		−	2.79956i
$859$		−	1.32685e8i		−	0.209335i	−0.994507	−	0.104667i	$-0.966622\pi$
$859$		−	1.32685e8i		−	0.209335i	0.994507	−	0.104667i	$-0.0333778\pi$
$860$			8.12169e7i			0.127688i
$861$	−5.90683e8			−0.925433
$862$	−8.09429e8			−1.26374
$863$		−	3.00677e8i		−	0.467809i	−0.972260	−	0.233904i	$-0.924850\pi$
$863$		−	3.00677e8i		−	0.467809i	0.972260	−	0.233904i	$-0.0751503\pi$
$864$		−	2.88028e8i		−	0.446574i
$865$		−	4.48860e8i		−	0.693526i
$866$			4.00059e8i			0.615985i
$867$	7.78291e8			1.19422
$868$		−	1.19030e8i		−	0.182010i
$869$		−	6.33129e8i		−	0.964790i
$870$			3.46507e8i			0.526205i
$871$	−2.22473e8			−0.336685
$872$	3.28498e8			0.495431
$873$			7.04946e8i			1.05953i
$874$	−1.66648e7			−0.0249612
$875$	5.60806e8			0.837121
$876$		−	1.75921e8i		−	0.261702i
$877$	1.10676e8			0.164080			0.0820399	−	0.996629i	$-0.473857\pi$
$877$	1.10676e8			0.164080			0.0820399	+	0.996629i	$0.473857\pi$
$878$		−	2.76308e8i		−	0.408234i
$879$	−4.38121e7			−0.0645100
$880$			3.58307e8i			0.525783i
$881$			4.54991e8i			0.665388i	0.943035	+	0.332694i	$0.107958\pi$
$881$			4.54991e8i			0.665388i	−0.943035	+	0.332694i	$0.892042\pi$
$882$		−	1.92928e8i		−	0.281183i
$883$	1.74482e8			0.253436			0.126718	−	0.991939i	$-0.459556\pi$
$883$	1.74482e8			0.253436			0.126718	+	0.991939i	$0.459556\pi$
$884$			2.03431e8i			0.294482i
$885$	−3.79280e7	−	4.81689e8i	−0.0547179	−	0.694923i
$886$	−9.84274e8			−1.41519
$887$			5.35324e8i			0.767089i	0.923522	+	0.383545i	$0.125297\pi$
$887$			5.35324e8i			0.767089i	−0.923522	+	0.383545i	$0.874703\pi$
$888$	9.71169e8			1.38693
$889$	2.88237e8			0.410246
$890$	−3.62354e8			−0.513999
$891$		−	2.67336e8i		−	0.377941i
$892$	1.45097e8			0.204440
$893$			1.03214e9i			1.44939i
$894$	7.36631e8			1.03095
$895$		−	7.79587e7i		−	0.108742i
$896$		−	4.86579e8i		−	0.676441i
$897$	3.23384e7			0.0448065
$898$			5.63907e8i			0.778715i
$899$		−	5.33733e8i		−	0.734590i
$900$	−1.96825e8			−0.269993
$901$	−1.70251e9			−2.32763
$902$	−5.48801e8			−0.747817
$903$		−	2.08364e9i		−	2.82982i
$904$	−6.23013e8			−0.843320
$905$	2.21928e8			0.299409
$906$	−1.78718e9			−2.40317
$907$	−1.83370e8			−0.245757			−0.122878	−	0.992422i	$-0.539213\pi$
$907$	−1.83370e8			−0.245757			−0.122878	+	0.992422i	$0.539213\pi$
$908$			9.18498e6i			0.0122693i
$909$			1.05203e9i			1.40067i
$910$	−3.65132e8			−0.484536
$911$	−6.63478e8			−0.877549			−0.438774	−	0.898597i	$-0.644587\pi$
$911$	−6.63478e8			−0.877549			−0.438774	+	0.898597i	$0.644587\pi$
$912$	−1.15618e9			−1.52420
$913$	1.91283e9			2.51342
$914$	2.30237e8			0.301535
$915$		−	4.88925e6i		−	0.00638232i
$916$		−	1.69579e8i		−	0.220641i
$917$		−	6.94763e8i		−	0.901008i
$918$		−	1.08216e9i		−	1.39882i
$919$		−	9.75020e8i		−	1.25622i	−0.778123	−	0.628112i	$-0.783828\pi$
$919$		−	9.75020e8i		−	1.25622i	0.778123	−	0.628112i	$-0.216172\pi$
$920$	−8.17637e6			−0.0105002
$921$	−8.16354e8			−1.04496
$922$		−	5.64389e8i		−	0.720088i
$923$			8.06841e8i			1.02608i
$924$			4.35745e8i			0.552353i
$925$		−	5.10366e8i		−	0.644847i
$926$	1.27457e9			1.60520
$927$		−	1.45800e9i		−	1.83028i
$928$			2.52906e8i			0.316457i
$929$		−	1.98118e8i		−	0.247102i	−0.992338	−	0.123551i	$-0.960572\pi$
$929$		−	1.98118e8i		−	0.247102i	0.992338	−	0.123551i	$-0.0394283\pi$
$930$	4.41245e8			0.548568
$931$	1.75800e8			0.217856
$932$		−	6.46229e7i		−	0.0798250i
$933$	−1.28087e9			−1.57710
$934$	−1.19109e9			−1.46186
$935$		−	7.30937e8i		−	0.894222i
$936$	1.76970e9			2.15810
$937$			7.24622e8i			0.880831i	0.897794	+	0.440415i	$0.145169\pi$
$937$			7.24622e8i			0.880831i	−0.897794	+	0.440415i	$0.854831\pi$
$938$	−2.31743e8			−0.280801
$939$		−	3.89593e8i		−	0.470559i
$940$			8.13225e7i			0.0979101i
$941$			7.46437e8i			0.895827i	0.894077	+	0.447913i	$0.147833\pi$
$941$			7.46437e8i			0.895827i	−0.894077	+	0.447913i	$0.852167\pi$
$942$	−1.68804e9			−2.01943
$943$		−	1.00365e7i		−	0.0119687i
$944$	5.09842e7	+	6.47505e8i	0.0606066	+	0.769710i
$945$	−4.59490e8			−0.544479
$946$		−	1.93590e9i		−	2.28670i
$947$	1.36406e9			1.60614			0.803068	−	0.595887i	$-0.203200\pi$
$947$	1.36406e9			1.60614			0.803068	+	0.595887i	$0.203200\pi$
$948$	1.60966e8			0.188934
$949$	8.31237e8			0.972582
$950$			7.58142e8i			0.884260i
$951$	1.78992e9			2.08109
$952$			1.31957e9i			1.52941i
$953$	5.55368e8			0.641656			0.320828	−	0.947137i	$-0.396039\pi$
$953$	5.55368e8			0.641656			0.320828	+	0.947137i	$0.396039\pi$
$954$			2.37839e9i			2.73929i
$955$			3.26087e8i			0.374389i
$956$	−8.92813e7			−0.102185
$957$			1.95390e9i			2.22929i
$958$			2.34338e8i			0.266530i
$959$	−1.17007e9			−1.32665
$960$	−6.85251e8			−0.774526
$961$	2.07845e8			0.234190
$962$			7.36906e8i			0.827726i
$963$	1.52827e9			1.71128
$964$	−9.95869e7			−0.111166
$965$	5.91703e8			0.658449
$966$	3.36858e7			0.0373694
$967$		−	5.81264e8i		−	0.642826i	−0.946939	−	0.321413i	$-0.895842\pi$
$967$		−	5.81264e8i		−	0.642826i	0.946939	−	0.321413i	$-0.104158\pi$
$968$			1.54933e9i			1.70812i
$969$	2.35858e9			2.59227
$970$	2.13943e8			0.234414
$971$	−1.01856e7			−0.0111257			−0.00556287	−	0.999985i	$-0.501771\pi$
$971$	−1.01856e7			−0.0111257			−0.00556287	+	0.999985i	$0.501771\pi$
$972$	−1.40145e8			−0.152608
$973$	−5.56579e8			−0.604211
$974$			1.42978e9i			1.54737i
$975$		−	1.47119e9i		−	1.58729i
$976$			6.57231e6i			0.00706917i
$977$		−	2.07791e8i		−	0.222814i	−0.993775	−	0.111407i	$-0.964464\pi$
$977$		−	2.07791e8i		−	0.222814i	0.993775	−	0.111407i	$-0.0355358\pi$
$978$			2.23634e9i			2.39068i
$979$	−2.04325e9			−2.17758
$980$	1.38513e7			0.0147167
$981$			7.50263e8i			0.794706i
$982$			6.21545e8i			0.656354i
$983$		−	5.64843e8i		−	0.594658i	−0.954775	−	0.297329i	$-0.903904\pi$
$983$		−	5.64843e8i		−	0.594658i	0.954775	−	0.297329i	$-0.0960958\pi$
$984$		−	8.68853e8i		−	0.911929i
$985$	−6.24466e7			−0.0653432
$986$			9.50198e8i			0.991250i
$987$		−	2.08635e9i		−	2.16988i
$988$			2.58961e8i			0.268511i
$989$	3.54038e7			0.0365983
$990$	−1.02111e9			−1.05237
$991$			6.24542e8i			0.641713i	0.947128	+	0.320856i	$0.103971\pi$
$991$			6.24542e8i			0.641713i	−0.947128	+	0.320856i	$0.896029\pi$
$992$	3.22052e8			0.329906
$993$	−1.13403e9			−1.15818
$994$			8.40460e8i			0.855771i
$995$	−5.16688e8			−0.524516
$996$			4.86317e8i			0.492199i
$997$	2.74791e8			0.277279			0.138640	−	0.990343i	$-0.455727\pi$
$997$	2.74791e8			0.277279			0.138640	+	0.990343i	$0.455727\pi$
$998$		−	1.62703e9i		−	1.63684i
$999$			9.27339e8i			0.930127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	59.7.b.c.58.9	✓	26
59.58	odd	2	inner	59.7.b.c.58.18	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.7.b.c.58.9	✓	26	1.1	even	1	trivial
59.7.b.c.58.18	yes	26	59.58	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:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	59.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-7.19418i q^{2} +44.5169 q^{3} +12.2438 q^{4} +52.8479 q^{5} -320.263i q^{6} -372.902 q^{7} -548.511i q^{8} +1252.76 q^{9} -380.197i q^{10} -2143.87i q^{11} +545.055 q^{12} +2575.41i q^{13} +2682.72i q^{14} +2352.63 q^{15} -3162.49 q^{16} +6451.40 q^{17} -9012.55i q^{18} +8212.43 q^{19} +647.058 q^{20} -16600.4 q^{21} -15423.4 q^{22} -282.064i q^{23} -24418.0i q^{24} -12832.1 q^{25} +18528.0 q^{26} +23316.0 q^{27} -4565.72 q^{28} -20472.9 q^{29} -16925.2i q^{30} +26070.3i q^{31} -12353.2i q^{32} -95438.4i q^{33} -46412.6i q^{34} -19707.1 q^{35} +15338.5 q^{36} +39772.6i q^{37} -59081.7i q^{38} +114649. i q^{39} -28987.7i q^{40} +35582.4 q^{41} +119426. i q^{42} +125517. i q^{43} -26249.0i q^{44} +66205.5 q^{45} -2029.22 q^{46} +125680. i q^{47} -140784. q^{48} +21406.6 q^{49} +92316.4i q^{50} +287197. q^{51} +31532.8i q^{52} -263897. q^{53} -167740. i q^{54} -113299. i q^{55} +204541. i q^{56} +365592. q^{57} +147285. i q^{58} +(-16121.5 - 204745. i) q^{59} +28805.0 q^{60} -2078.21i q^{61} +187554. q^{62} -467155. q^{63} -291271. q^{64} +136105. i q^{65} -686601. q^{66} +86383.7i q^{67} +78989.5 q^{68} -12556.6i q^{69} +141776. i q^{70} +313286. q^{71} -687151. i q^{72} -322759. i q^{73} +286131. q^{74} -571246. q^{75} +100551. q^{76} +799452. i q^{77} +824808. q^{78} +295321. q^{79} -167131. q^{80} +124698. q^{81} -255986. i q^{82} +892234. i q^{83} -203252. q^{84} +340943. q^{85} +902993. q^{86} -911389. q^{87} -1.17594e6 q^{88} -953067. i q^{89} -476295. i q^{90} -960375. i q^{91} -3453.52i q^{92} +1.16057e6i q^{93} +904168. q^{94} +434010. q^{95} -549927. i q^{96} +562716. i q^{97} -154003. i q^{98} -2.68574e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 10 q^{3} - 1090 q^{4} + 142 q^{5} + 406 q^{7} + 5432 q^{9} - 1124 q^{12} + 14982 q^{15} + 12734 q^{16} - 9108 q^{17} + 3850 q^{19} - 46896 q^{20} - 49034 q^{21} + 11238 q^{22} + 18792 q^{25} - 64590 q^{26}+ \cdots - 2396490 q^{95}+O(q^{100}) \) 26 * q + 10 * q^3 - 1090 * q^4 + 142 * q^5 + 406 * q^7 + 5432 * q^9 - 1124 * q^12 + 14982 * q^15 + 12734 * q^16 - 9108 * q^17 + 3850 * q^19 - 46896 * q^20 - 49034 * q^21 + 11238 * q^22 + 18792 * q^25 - 64590 * q^26 + 3550 * q^27 - 45542 * q^28 - 31730 * q^29 + 163558 * q^35 - 325266 * q^36 + 91914 * q^41 + 736396 * q^45 + 287148 * q^46 + 479572 * q^48 - 462900 * q^49 + 329932 * q^51 + 8238 * q^53 - 187506 * q^57 + 326182 * q^59 - 970064 * q^60 + 630140 * q^62 + 630508 * q^63 - 1800262 * q^64 - 869200 * q^66 - 319586 * q^68 + 1763840 * q^71 - 2294090 * q^74 + 354736 * q^75 + 247144 * q^76 - 375064 * q^78 + 4702 * q^79 + 1920984 * q^80 - 2435946 * q^81 - 1007672 * q^84 + 864044 * q^85 + 5031110 * q^86 - 1519202 * q^87 + 725994 * q^88 + 2835768 * q^94 - 2396490 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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