LMFDB - Embedded newform 59.7.b.c.58.7

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			58.7
Character	$\chi$	$=$	59.58
Dual form			59.7.b.c.58.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.3981i q^{2} +12.0734 q^{3} -44.1211 q^{4} -27.1374 q^{5} -125.541i q^{6} +631.586 q^{7} -206.703i q^{8} -583.232 q^{9} +O(q^{10})$	\(q-10.3981i q^{2} +12.0734 q^{3} -44.1211 q^{4} -27.1374 q^{5} -125.541i q^{6} +631.586 q^{7} -206.703i q^{8} -583.232 q^{9} +282.178i q^{10} -1420.06i q^{11} -532.694 q^{12} -1316.49i q^{13} -6567.31i q^{14} -327.642 q^{15} -4973.08 q^{16} +3331.61 q^{17} +6064.52i q^{18} +1228.40 q^{19} +1197.33 q^{20} +7625.41 q^{21} -14766.0 q^{22} +141.218i q^{23} -2495.62i q^{24} -14888.6 q^{25} -13689.1 q^{26} -15843.2 q^{27} -27866.3 q^{28} +798.729 q^{29} +3406.86i q^{30} -24058.2i q^{31} +38481.7i q^{32} -17145.0i q^{33} -34642.5i q^{34} -17139.6 q^{35} +25732.9 q^{36} +76640.4i q^{37} -12773.1i q^{38} -15894.6i q^{39} +5609.38i q^{40} +68465.1 q^{41} -79290.1i q^{42} -40649.8i q^{43} +62654.8i q^{44} +15827.4 q^{45} +1468.40 q^{46} -148584. i q^{47} -60042.2 q^{48} +281251. q^{49} +154813. i q^{50} +40224.0 q^{51} +58085.2i q^{52} +158295. q^{53} +164739. i q^{54} +38536.8i q^{55} -130551. i q^{56} +14831.1 q^{57} -8305.29i q^{58} +(173326. - 110176. i) q^{59} +14455.9 q^{60} +178055. i q^{61} -250160. q^{62} -368361. q^{63} +81861.0 q^{64} +35726.2i q^{65} -178276. q^{66} +192925. i q^{67} -146994. q^{68} +1704.98i q^{69} +178220. i q^{70} -164490. q^{71} +120556. i q^{72} +668672. i q^{73} +796917. q^{74} -179756. q^{75} -54198.6 q^{76} -896891. i q^{77} -165274. q^{78} +350521. q^{79} +134956. q^{80} +233894. q^{81} -711909. i q^{82} +62493.2i q^{83} -336442. q^{84} -90411.1 q^{85} -422682. q^{86} +9643.41 q^{87} -293531. q^{88} +703247. i q^{89} -164575. i q^{90} -831478. i q^{91} -6230.68i q^{92} -290465. i q^{93} -1.54499e6 q^{94} -33335.7 q^{95} +464607. i q^{96} -1.11923e6i q^{97} -2.92449e6i q^{98} +828226. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 10 q^{3} - 1090 q^{4} + 142 q^{5} + 406 q^{7} + 5432 q^{9}+O(q^{10}) $ 26 * q + 10 * q^3 - 1090 * q^4 + 142 * q^5 + 406 * q^7 + 5432 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$		−	10.3981i		−	1.29977i	−0.760034	−	0.649883i	$-0.774818\pi$
$2$		−	10.3981i		−	1.29977i	0.760034	−	0.649883i	$-0.225182\pi$
$3$	12.0734			0.447165			0.223582	−	0.974685i	$-0.428225\pi$
$3$	12.0734			0.447165			0.223582	+	0.974685i	$0.428225\pi$
$4$	−44.1211			−0.689393
$5$	−27.1374			−0.217099			−0.108550	−	0.994091i	$-0.534621\pi$
$5$	−27.1374			−0.217099			−0.108550	+	0.994091i	$0.534621\pi$
$6$		−	125.541i		−	0.581210i
$7$	631.586			1.84136			0.920679	−	0.390322i	$-0.127636\pi$
$7$	631.586			1.84136			0.920679	+	0.390322i	$0.127636\pi$
$8$		−	206.703i		−	0.403717i
$9$	−583.232			−0.800044
$10$			282.178i			0.282178i
$11$		−	1420.06i		−	1.06691i	−0.845827	−	0.533457i	$-0.820893\pi$
$11$		−	1420.06i		−	1.06691i	0.845827	−	0.533457i	$-0.179107\pi$
$12$	−532.694			−0.308272
$13$		−	1316.49i		−	0.599223i	−0.954061	−	0.299611i	$-0.903143\pi$
$13$		−	1316.49i		−	0.599223i	0.954061	−	0.299611i	$-0.0968570\pi$
$14$		−	6567.31i		−	2.39333i
$15$	−327.642			−0.0970791
$16$	−4973.08			−1.21413
$17$	3331.61			0.678120			0.339060	−	0.940765i	$-0.389891\pi$
$17$	3331.61			0.678120			0.339060	+	0.940765i	$0.389891\pi$
$18$			6064.52i			1.03987i
$19$	1228.40			0.179094			0.0895469	−	0.995983i	$-0.471458\pi$
$19$	1228.40			0.179094			0.0895469	+	0.995983i	$0.471458\pi$
$20$	1197.33			0.149667
$21$	7625.41			0.823390
$22$	−14766.0			−1.38674
$23$			141.218i			0.0116066i	0.999983	+	0.00580331i	$0.00184726\pi$
$23$			141.218i			0.0116066i	−0.999983	+	0.00580331i	$0.998153\pi$
$24$		−	2495.62i		−	0.180528i
$25$	−14888.6			−0.952868
$26$	−13689.1			−0.778850
$27$	−15843.2			−0.804916
$28$	−27866.3			−1.26942
$29$	798.729			0.0327496			0.0163748	−	0.999866i	$-0.494788\pi$
$29$	798.729			0.0327496			0.0163748	+	0.999866i	$0.494788\pi$
$30$			3406.86i			0.126180i
$31$		−	24058.2i		−	0.807565i	−0.914855	−	0.403782i	$-0.867695\pi$
$31$		−	24058.2i		−	0.807565i	0.914855	−	0.403782i	$-0.132305\pi$
$32$			38481.7i			1.17437i
$33$		−	17145.0i		−	0.477086i
$34$		−	34642.5i		−	0.881398i
$35$	−17139.6			−0.399757
$36$	25732.9			0.551544
$37$			76640.4i			1.51305i	0.653966	+	0.756524i	$0.273104\pi$
$37$			76640.4i			1.51305i	−0.653966	+	0.756524i	$0.726896\pi$
$38$		−	12773.1i		−	0.232780i
$39$		−	15894.6i		−	0.267951i
$40$			5609.38i			0.0876466i
$41$	68465.1			0.993385			0.496692	−	0.867927i	$-0.334548\pi$
$41$	68465.1			0.993385			0.496692	+	0.867927i	$0.334548\pi$
$42$		−	79290.1i		−	1.07021i
$43$		−	40649.8i		−	0.511273i	−0.966773	−	0.255637i	$-0.917715\pi$
$43$		−	40649.8i		−	0.511273i	0.966773	−	0.255637i	$-0.0822851\pi$
$44$			62654.8i			0.735523i
$45$	15827.4			0.173689
$46$	1468.40			0.0150859
$47$		−	148584.i		−	1.43113i	−0.698548	−	0.715563i	$-0.746170\pi$
$47$		−	148584.i		−	1.43113i	0.698548	−	0.715563i	$-0.253830\pi$
$48$	−60042.2			−0.542916
$49$	281251.			2.39060
$50$			154813.i			1.23851i
$51$	40224.0			0.303231
$52$			58085.2i			0.413100i
$53$	158295.			1.06326			0.531631	−	0.846976i	$-0.321579\pi$
$53$	158295.			1.06326			0.531631	+	0.846976i	$0.321579\pi$
$54$			164739.i			1.04620i
$55$			38536.8i			0.231626i
$56$		−	130551.i		−	0.743387i
$57$	14831.1			0.0800844
$58$		−	8305.29i		−	0.0425668i
$59$	173326.	−	110176.i	0.843931	−	0.536451i
$59$	173326.	−	110176.i	0.843931	−	0.536451i
$60$	14455.9			0.0669256
$61$			178055.i			0.784448i	0.919870	+	0.392224i	$0.128294\pi$
$61$			178055.i			0.784448i	−0.919870	+	0.392224i	$0.871706\pi$
$62$	−250160.			−1.04965
$63$	−368361.			−1.47317
$64$	81861.0			0.312275
$65$			35726.2i			0.130091i
$66$	−178276.			−0.620101
$67$			192925.i			0.641453i	0.947172	+	0.320727i	$0.103927\pi$
$67$			192925.i			0.641453i	−0.947172	+	0.320727i	$0.896073\pi$
$68$	−146994.			−0.467491
$69$			1704.98i			0.00519007i
$70$			178220.i			0.519591i
$71$	−164490.			−0.459583			−0.229791	−	0.973240i	$-0.573804\pi$
$71$	−164490.			−0.459583			−0.229791	+	0.973240i	$0.573804\pi$
$72$			120556.i			0.322991i
$73$			668672.i			1.71888i	0.511241	+	0.859438i	$0.329186\pi$
$73$			668672.i			1.71888i	−0.511241	+	0.859438i	$0.670814\pi$
$74$	796917.			1.96661
$75$	−179756.			−0.426089
$76$	−54198.6			−0.123466
$77$		−	896891.i		−	1.96457i
$78$	−165274.			−0.348274
$79$	350521.			0.710941			0.355470	−	0.934688i	$-0.384321\pi$
$79$	350521.			0.710941			0.355470	+	0.934688i	$0.384321\pi$
$80$	134956.			0.263587
$81$	233894.			0.440114
$82$		−	711909.i		−	1.29117i
$83$			62493.2i			0.109294i	0.998506	+	0.0546472i	$0.0174034\pi$
$83$			62493.2i			0.109294i	−0.998506	+	0.0546472i	$0.982597\pi$
$84$	−336442.			−0.567639
$85$	−90411.1			−0.147219
$86$	−422682.			−0.664536
$87$	9643.41			0.0146444
$88$	−293531.			−0.430731
$89$			703247.i			0.997558i	0.866729	+	0.498779i	$0.166218\pi$
$89$			703247.i			0.997558i	−0.866729	+	0.498779i	$0.833782\pi$
$90$		−	164575.i		−	0.225755i
$91$		−	831478.i		−	1.10338i
$92$		−	6230.68i		−	0.00800151i
$93$		−	290465.i		−	0.361114i
$94$	−1.54499e6			−1.86013
$95$	−33335.7			−0.0388811
$96$			464607.i			0.525136i
$97$		−	1.11923e6i		−	1.22632i	−0.789958	−	0.613161i	$-0.789898\pi$
$97$		−	1.11923e6i		−	1.22632i	0.789958	−	0.613161i	$-0.210102\pi$
$98$		−	2.92449e6i		−	3.10722i
$99$			828226.i			0.853578i
$100$	656900.			0.656900
$101$		−	795468.i		−	0.772074i	−0.922483	−	0.386037i	$-0.873844\pi$
$101$		−	795468.i		−	0.772074i	0.922483	−	0.386037i	$-0.126156\pi$
$102$		−	418254.i		−	0.394130i
$103$			2.01092e6i			1.84027i	0.391599	+	0.920136i	$0.371922\pi$
$103$			2.01092e6i			1.84027i	−0.391599	+	0.920136i	$0.628078\pi$
$104$	−272123.			−0.241916
$105$	−206934.			−0.178757
$106$		−	1.64597e6i		−	1.38199i
$107$	1.26015e6			1.02865			0.514327	−	0.857594i	$-0.328042\pi$
$107$	1.26015e6			1.02865			0.514327	+	0.857594i	$0.328042\pi$
$108$	699018.			0.554903
$109$			2.36014e6i			1.82246i	0.411899	+	0.911230i	$0.364866\pi$
$109$			2.36014e6i			1.82246i	−0.411899	+	0.911230i	$0.635134\pi$
$110$	400711.			0.301060
$111$			925314.i			0.676581i
$112$	−3.14092e6			−2.23565
$113$			1.44309e6i			1.00013i	0.865987	+	0.500067i	$0.166691\pi$
$113$			1.44309e6i			1.00013i	−0.865987	+	0.500067i	$0.833309\pi$
$114$		−	154215.i		−	0.104091i
$115$		−	3832.28i		−	0.00251979i
$116$	−35240.8			−0.0225773
$117$			767821.i			0.479405i
$118$	−1.14562e6	−	1.80226e6i	−0.697262	−	1.09691i
$119$	2.10419e6			1.24866
$120$			67724.6i			0.0391925i
$121$	−245016.			−0.138305
$122$	1.85144e6			1.01960
$123$	826609.			0.444207
$124$			1.06147e6i			0.556729i
$125$	828059.			0.423966
$126$			3.83026e6i			1.91477i
$127$	−2.88560e6			−1.40872			−0.704361	−	0.709842i	$-0.748766\pi$
$127$	−2.88560e6			−1.40872			−0.704361	+	0.709842i	$0.748766\pi$
$128$			1.61163e6i			0.768484i
$129$		−	490783.i		−	0.228623i
$130$	371486.			0.169088
$131$			585324.i			0.260365i	0.991490	+	0.130182i	$0.0415563\pi$
$131$			585324.i			0.260365i	−0.991490	+	0.130182i	$0.958444\pi$
$132$			756459.i			0.328900i
$133$	775842.			0.329776
$134$	2.00606e6			0.833739
$135$	429942.			0.174747
$136$		−	688653.i		−	0.273769i
$137$	−2.48917e6			−0.968039			−0.484019	−	0.875057i	$-0.660824\pi$
$137$	−2.48917e6			−0.968039			−0.484019	+	0.875057i	$0.660824\pi$
$138$	17728.6			0.00674587
$139$	1.53149e6			0.570255			0.285127	−	0.958490i	$-0.407964\pi$
$139$	1.53149e6			0.570255			0.285127	+	0.958490i	$0.407964\pi$
$140$	756218.			0.275590
$141$		−	1.79392e6i		−	0.639949i
$142$			1.71039e6i			0.597350i
$143$	−1.86950e6			−0.639319
$144$	2.90046e6			0.971357
$145$	−21675.4			−0.00710990
$146$	6.95294e6			2.23414
$147$	3.39567e6			1.06899
$148$		−	3.38146e6i		−	1.04308i
$149$		−	1.89995e6i		−	0.574358i	−0.957877	−	0.287179i	$-0.907283\pi$
$149$		−	1.89995e6i		−	0.574358i	0.957877	−	0.287179i	$-0.0927175\pi$
$150$			1.86913e6i			0.553816i
$151$		−	4.19828e6i		−	1.21938i	−0.792639	−	0.609691i	$-0.791293\pi$
$151$		−	4.19828e6i		−	1.21938i	0.792639	−	0.609691i	$-0.208707\pi$
$152$		−	253915.i		−	0.0723032i
$153$	−1.94310e6			−0.542526
$154$	−9.32599e6			−2.55348
$155$			652876.i			0.175322i
$156$			701288.i			0.184724i
$157$			3.51025e6i			0.907067i	0.891239	+	0.453534i	$0.149837\pi$
$157$			3.51025e6i			0.907067i	−0.891239	+	0.453534i	$0.850163\pi$
$158$		−	3.64477e6i		−	0.924057i
$159$	1.91117e6			0.475453
$160$		−	1.04429e6i		−	0.254955i
$161$			89191.0i			0.0213719i
$162$		−	2.43207e6i		−	0.572045i
$163$	3.15911e6			0.729462			0.364731	−	0.931113i	$-0.381161\pi$
$163$	3.15911e6			0.729462			0.364731	+	0.931113i	$0.381161\pi$
$164$	−3.02076e6			−0.684832
$165$			465272.i			0.103575i
$166$	649812.			0.142057
$167$	352928.			0.0757770			0.0378885	−	0.999282i	$-0.487937\pi$
$167$	352928.			0.0757770			0.0378885	+	0.999282i	$0.487937\pi$
$168$		−	1.57620e6i		−	0.332416i
$169$	3.09366e6			0.640932
$170$			940107.i			0.191351i
$171$	−716444.			−0.143283
$172$			1.79352e6i			0.352468i
$173$		−	4.67157e6i		−	0.902246i	−0.892462	−	0.451123i	$-0.851024\pi$
$173$		−	4.67157e6i		−	0.902246i	0.892462	−	0.451123i	$-0.148976\pi$
$174$		−	100273.i		−	0.0190344i
$175$	−9.40340e6			−1.75457
$176$			7.06208e6i			1.29537i
$177$	2.09264e6	−	1.33020e6i	0.377376	−	0.239882i
$178$	7.31246e6			1.29659
$179$			235405.i			0.0410446i	0.999789	+	0.0205223i	$0.00653291\pi$
$179$			235405.i			0.0410446i	−0.999789	+	0.0205223i	$0.993467\pi$
$180$	−698323.			−0.119740
$181$	2.07735e6			0.350327			0.175164	−	0.984539i	$-0.443955\pi$
$181$	2.07735e6			0.350327			0.175164	+	0.984539i	$0.443955\pi$
$182$	−8.64581e6			−1.43414
$183$			2.14974e6i			0.350778i
$184$	29190.1			0.00468579
$185$		−	2.07982e6i		−	0.328481i
$186$	−3.02029e6			−0.469364
$187$		−	4.73109e6i		−	0.723496i
$188$			6.55569e6i			0.986608i
$189$	−1.00063e7			−1.48214
$190$			346629.i			0.0505364i
$191$		−	6.40816e6i		−	0.919672i	−0.888004	−	0.459836i	$-0.847908\pi$
$191$		−	6.40816e6i		−	0.919672i	0.888004	−	0.459836i	$-0.152092\pi$
$192$	988345.			0.139638
$193$	6.55952e6			0.912431			0.456216	−	0.889869i	$-0.349205\pi$
$193$	6.55952e6			0.912431			0.456216	+	0.889869i	$0.349205\pi$
$194$	−1.16379e7			−1.59393
$195$			431338.i			0.0581720i
$196$	−1.24091e7			−1.64806
$197$	−4.24542e6			−0.555293			−0.277647	−	0.960683i	$-0.589554\pi$
$197$	−4.24542e6			−0.555293			−0.277647	+	0.960683i	$0.589554\pi$
$198$	8.61200e6			1.10945
$199$	−9.08561e6			−1.15291			−0.576454	−	0.817129i	$-0.695564\pi$
$199$	−9.08561e6			−1.15291			−0.576454	+	0.817129i	$0.695564\pi$
$200$			3.07751e6i			0.384689i
$201$			2.32927e6i			0.286835i
$202$	−8.27138e6			−1.00352
$203$	504466.			0.0603036
$204$	−1.77473e6			−0.209046
$205$	−1.85796e6			−0.215663
$206$	2.09098e7			2.39192
$207$		−	82362.6i		−	0.00928580i
$208$			6.54702e6i			0.727535i
$209$		−	1.74441e6i		−	0.191078i
$210$			2.15173e6i			0.232343i
$211$			3.62124e6i			0.385488i	0.981249	+	0.192744i	$0.0617386\pi$
$211$			3.62124e6i			0.385488i	−0.981249	+	0.192744i	$0.938261\pi$
$212$	−6.98416e6			−0.733005
$213$	−1.98596e6			−0.205509
$214$		−	1.31032e7i		−	1.33701i
$215$			1.10313e6i			0.110997i
$216$			3.27483e6i			0.324958i
$217$		−	1.51948e7i		−	1.48702i
$218$	2.45410e7			2.36877
$219$			8.07317e6i			0.768620i
$220$		−	1.70029e6i		−	0.159681i
$221$		−	4.38603e6i		−	0.406345i
$222$	9.62153e6			0.879398
$223$	−1.00929e6			−0.0910126			−0.0455063	−	0.998964i	$-0.514490\pi$
$223$	−1.00929e6			−0.0910126			−0.0455063	+	0.998964i	$0.514490\pi$
$224$			2.43045e7i			2.16243i
$225$	8.68348e6			0.762336
$226$	1.50054e7			1.29994
$227$		−	1.09403e7i		−	0.935304i	−0.883913	−	0.467652i	$-0.845100\pi$
$227$		−	1.09403e7i		−	0.935304i	0.883913	−	0.467652i	$-0.154900\pi$
$228$	−654364.			−0.0552096
$229$		−	1.69996e7i		−	1.41557i	−0.706427	−	0.707786i	$-0.749694\pi$
$229$		−	1.69996e7i		−	1.41557i	0.706427	−	0.707786i	$-0.250306\pi$
$230$	−39848.5			−0.00327513
$231$		−	1.08286e7i		−	0.878486i
$232$		−	165100.i		−	0.0132216i
$233$			2.32761e7i			1.84011i	0.391795	+	0.920053i	$0.371854\pi$
$233$			2.32761e7i			1.84011i	−0.391795	+	0.920053i	$0.628146\pi$
$234$	7.98390e6			0.623114
$235$			4.03218e6i			0.310696i
$236$	−7.64733e6	+	4.86108e6i	−0.581800	+	0.369826i
$237$	4.23200e6			0.317907
$238$		−	2.18797e7i		−	1.62297i
$239$	−1.39812e7			−1.02412			−0.512062	−	0.858949i	$-0.671118\pi$
$239$	−1.39812e7			−1.02412			−0.512062	+	0.858949i	$0.671118\pi$
$240$	1.62939e6			0.117867
$241$	−2.32724e7			−1.66261			−0.831304	−	0.555818i	$-0.812405\pi$
$241$	−2.32724e7			−1.66261			−0.831304	+	0.555818i	$0.812405\pi$
$242$			2.54771e6i			0.179765i
$243$	1.43736e7			1.00172
$244$		−	7.85598e6i		−	0.540793i
$245$	−7.63243e6			−0.518997
$246$		−	8.59519e6i		−	0.577365i
$247$		−	1.61718e6i		−	0.107317i
$248$	−4.97290e6			−0.326028
$249$			754508.i			0.0488726i
$250$		−	8.61026e6i		−	0.551057i
$251$	2.68275e7			1.69652			0.848261	−	0.529578i	$-0.177650\pi$
$251$	2.68275e7			1.69652			0.848261	+	0.529578i	$0.177650\pi$
$252$	1.62525e7			1.01559
$253$	200538.			0.0123833
$254$			3.00049e7i			1.83101i
$255$	−1.09157e6			−0.0658313
$256$	2.19970e7			1.31113
$257$	3.54446e6			0.208810			0.104405	−	0.994535i	$-0.466706\pi$
$257$	3.54446e6			0.208810			0.104405	+	0.994535i	$0.466706\pi$
$258$	−5.10323e6			−0.297157
$259$			4.84050e7i			2.78606i
$260$		−	1.57628e6i		−	0.0896837i
$261$	−465844.			−0.0262011
$262$	6.08628e6			0.338414
$263$	2.09087e7			1.14937			0.574684	−	0.818375i	$-0.305125\pi$
$263$	2.09087e7			1.14937			0.574684	+	0.818375i	$0.305125\pi$
$264$	−3.54393e6			−0.192608
$265$	−4.29572e6			−0.230833
$266$		−	8.06731e6i		−	0.428631i
$267$			8.49062e6i			0.446073i
$268$		−	8.51209e6i		−	0.442213i
$269$			1.85345e7i			0.952190i	0.879394	+	0.476095i	$0.157948\pi$
$269$			1.85345e7i			0.952190i	−0.879394	+	0.476095i	$0.842052\pi$
$270$		−	4.47060e6i		−	0.227130i
$271$	−1.50471e7			−0.756039			−0.378020	−	0.925798i	$-0.623395\pi$
$271$	−1.50471e7			−0.756039			−0.378020	+	0.925798i	$0.623395\pi$
$272$	−1.65683e7			−0.823327
$273$		−	1.00388e7i		−	0.493394i
$274$			2.58827e7i			1.25822i
$275$			2.11427e7i			1.01663i
$276$		−	75225.8i		−	0.00357799i
$277$	−1.66463e7			−0.783210			−0.391605	−	0.920133i	$-0.628080\pi$
$277$	−1.66463e7			−0.783210			−0.391605	+	0.920133i	$0.628080\pi$
$278$		−	1.59246e7i		−	0.741198i
$279$			1.40315e7i			0.646087i
$280$			3.54281e6i			0.161389i
$281$	−3.98924e7			−1.79792			−0.898961	−	0.438028i	$-0.855677\pi$
$281$	−3.98924e7			−1.79792			−0.898961	+	0.438028i	$0.855677\pi$
$282$	−1.86534e7			−0.831784
$283$		−	2.97490e7i		−	1.31254i	−0.754525	−	0.656271i	$-0.772133\pi$
$283$		−	2.97490e7i		−	1.31254i	0.754525	−	0.656271i	$-0.227867\pi$
$284$	7.25747e6			0.316833
$285$	−402477.			−0.0173863
$286$			1.94393e7i			0.830966i
$287$	4.32416e7			1.82918
$288$		−	2.24438e7i		−	0.939547i
$289$	−1.30380e7			−0.540153
$290$			225384.i			0.00924121i
$291$		−	1.35130e7i		−	0.548368i
$292$		−	2.95026e7i		−	1.18498i
$293$	−3.35403e7			−1.33341			−0.666706	−	0.745321i	$-0.732296\pi$
$293$	−3.35403e7			−1.33341			−0.666706	+	0.745321i	$0.732296\pi$
$294$		−	3.53086e7i		−	1.38944i
$295$	−4.70361e6	+	2.98989e6i	−0.183217	+	0.116463i
$296$	1.58418e7			0.610843
$297$			2.24983e7i			0.858776i
$298$	−1.97559e7			−0.746532
$299$	185912.			0.00695495
$300$	7.93105e6			0.293743
$301$		−	2.56738e7i		−	0.941437i
$302$	−4.36542e7			−1.58491
$303$		−	9.60404e6i		−	0.345244i
$304$	−6.10895e6			−0.217443
$305$		−	4.83195e6i		−	0.170303i
$306$			2.02046e7i			0.705157i
$307$	−1.05640e7			−0.365103			−0.182551	−	0.983196i	$-0.558436\pi$
$307$	−1.05640e7			−0.365103			−0.182551	+	0.983196i	$0.558436\pi$
$308$			3.95718e7i			1.35436i
$309$			2.42787e7i			0.822905i
$310$	6.78869e6			0.227877
$311$	2.24060e6			0.0744873			0.0372437	−	0.999306i	$-0.488142\pi$
$311$	2.24060e6			0.0744873			0.0372437	+	0.999306i	$0.488142\pi$
$312$	−3.28546e6			−0.108176
$313$		−	4.77524e7i		−	1.55726i	−0.627482	−	0.778631i	$-0.715914\pi$
$313$		−	4.77524e7i		−	1.55726i	0.627482	−	0.778631i	$-0.284086\pi$
$314$	3.65001e7			1.17898
$315$	9.99636e6			0.319823
$316$	−1.54654e7			−0.490117
$317$	8.13139e6			0.255262			0.127631	−	0.991822i	$-0.459263\pi$
$317$	8.13139e6			0.255262			0.127631	+	0.991822i	$0.459263\pi$
$318$		−	1.98726e7i		−	0.617978i
$319$		−	1.13425e6i		−	0.0349410i
$320$	−2.22150e6			−0.0677947
$321$	1.52143e7			0.459978
$322$	927420.			0.0277785
$323$	4.09256e6			0.121447
$324$	−1.03197e7			−0.303411
$325$			1.96007e7i			0.570980i
$326$		−	3.28489e7i		−	0.948130i
$327$			2.84950e7i			0.814939i
$328$		−	1.41519e7i		−	0.401046i
$329$		−	9.38434e7i		−	2.63521i
$330$	4.83796e6			0.134623
$331$	1.27673e7			0.352058			0.176029	−	0.984385i	$-0.443675\pi$
$331$	1.27673e7			0.352058			0.176029	+	0.984385i	$0.443675\pi$
$332$		−	2.75727e6i		−	0.0753468i
$333$		−	4.46991e7i		−	1.21050i
$334$		−	3.66980e6i		−	0.0984924i
$335$		−	5.23549e6i		−	0.139259i
$336$	−3.79218e7			−0.999703
$337$		−	1.54490e7i		−	0.403656i	−0.979421	−	0.201828i	$-0.935312\pi$
$337$		−	1.54490e7i		−	0.403656i	0.979421	−	0.201828i	$-0.0646882\pi$
$338$		−	3.21682e7i		−	0.833062i
$339$			1.74231e7i			0.447225i
$340$	3.98904e6			0.101492
$341$	−3.41641e7			−0.861602
$342$			7.44968e6i			0.186234i
$343$	1.03329e8			2.56058
$344$	−8.40244e6			−0.206410
$345$		−	46268.8i		−	0.00112676i
$346$	−4.85756e7			−1.17271
$347$			4.14163e7i			0.991250i	0.868537	+	0.495625i	$0.165061\pi$
$347$			4.14163e7i			0.991250i	−0.868537	+	0.495625i	$0.834939\pi$
$348$	−425478.			−0.0100958
$349$			6.21714e7i			1.46256i	0.682076	+	0.731281i	$0.261077\pi$
$349$			6.21714e7i			1.46256i	−0.682076	+	0.731281i	$0.738923\pi$
$350$			9.77778e7i			2.28053i
$351$			2.08574e7i			0.482324i
$352$	5.46464e7			1.25295
$353$			3.82256e7i			0.869021i	0.900667	+	0.434510i	$0.143079\pi$
$353$			3.82256e7i			0.869021i	−0.900667	+	0.434510i	$0.856921\pi$
$354$	−1.38316e7	−	2.17595e7i	−0.311791	−	0.490501i
$355$	4.46382e6			0.0997751
$356$		−	3.10281e7i		−	0.687709i
$357$	2.54049e7			0.558358
$358$	2.44777e6			0.0533484
$359$	−4.55313e6			−0.0984071			−0.0492035	−	0.998789i	$-0.515668\pi$
$359$	−4.55313e6			−0.0984071			−0.0492035	+	0.998789i	$0.515668\pi$
$360$		−	3.27157e6i		−	0.0701211i
$361$	−4.55369e7			−0.967925
$362$		−	2.16005e7i		−	0.455343i
$363$	−2.95819e6			−0.0618452
$364$			3.66857e7i			0.760664i
$365$		−	1.81460e7i		−	0.373166i
$366$	2.23532e7			0.455929
$367$			1.30645e7i			0.264298i	0.991230	+	0.132149i	$0.0421877\pi$
$367$			1.30645e7i			0.264298i	−0.991230	+	0.132149i	$0.957812\pi$
$368$		−	702286.i		−	0.0140919i
$369$	−3.99310e7			−0.794751
$370$	−2.16263e7			−0.426949
$371$	9.99769e7			1.95784
$372$			1.28156e7i			0.248950i
$373$	8.61924e7			1.66090			0.830448	−	0.557096i	$-0.188084\pi$
$373$	8.61924e7			1.66090			0.830448	+	0.557096i	$0.188084\pi$
$374$	−4.91945e7			−0.940376
$375$	9.99752e6			0.189583
$376$	−3.07127e7			−0.577770
$377$		−	1.05152e6i		−	0.0196243i
$378$			1.04047e8i			1.92643i
$379$	−5.47329e7			−1.00538			−0.502690	−	0.864467i	$-0.667656\pi$
$379$	−5.47329e7			−1.00538			−0.502690	+	0.864467i	$0.667656\pi$
$380$	1.47081e6			0.0268044
$381$	−3.48391e7			−0.629930
$382$	−6.66329e7			−1.19536
$383$	−7.65908e6			−0.136326			−0.0681632	−	0.997674i	$-0.521714\pi$
$383$	−7.65908e6			−0.136326			−0.0681632	+	0.997674i	$0.521714\pi$
$384$			1.94579e7i			0.343639i
$385$			2.43393e7i			0.426507i
$386$		−	6.82068e7i		−	1.18595i
$387$			2.37083e7i			0.409041i
$388$			4.93817e7i			0.845417i
$389$	7.74406e7			1.31559			0.657794	−	0.753198i	$-0.271490\pi$
$389$	7.74406e7			1.31559			0.657794	+	0.753198i	$0.271490\pi$
$390$	4.48511e6			0.0756100
$391$			470481.i			0.00787068i
$392$		−	5.81355e7i		−	0.965124i
$393$			7.06688e6i			0.116426i
$394$			4.41445e7i			0.721752i
$395$	−9.51224e6			−0.154345
$396$		−	3.65423e7i		−	0.588450i
$397$		−	3.16272e7i		−	0.505463i	−0.967537	−	0.252731i	$-0.918671\pi$
$397$		−	3.16272e7i		−	0.505463i	0.967537	−	0.252731i	$-0.0813289\pi$
$398$			9.44734e7i			1.49851i
$399$	9.36709e6			0.147464
$400$	7.40420e7			1.15691
$401$		−	1.10078e8i		−	1.70714i	−0.520979	−	0.853570i	$-0.674433\pi$
$401$		−	1.10078e8i		−	1.70714i	0.520979	−	0.853570i	$-0.325567\pi$
$402$	2.42201e7			0.372819
$403$	−3.16724e7			−0.483911
$404$			3.50970e7i			0.532262i
$405$	−6.34729e6			−0.0955483
$406$		−	5.24550e6i		−	0.0783807i
$407$	1.08834e8			1.61429
$408$		−	8.31442e6i		−	0.122420i
$409$			8.02932e7i			1.17357i	0.809743	+	0.586785i	$0.199607\pi$
$409$			8.02932e7i			1.17357i	−0.809743	+	0.586785i	$0.800393\pi$
$410$			1.93194e7i			0.280312i
$411$	−3.00529e7			−0.432873
$412$		−	8.87239e7i		−	1.26867i
$413$	1.09470e8	−	6.95855e7i	1.55398	−	0.987799i
$414$	−856417.			−0.0120694
$415$		−	1.69590e6i		−	0.0237277i
$416$	5.06609e7			0.703709
$417$	1.84903e7			0.254998
$418$	−1.81386e7			−0.248356
$419$		−	4.57634e7i		−	0.622123i	−0.950390	−	0.311061i	$-0.899316\pi$
$419$		−	4.57634e7i		−	0.622123i	0.950390	−	0.311061i	$-0.100684\pi$
$420$	9.13016e6			0.123234
$421$			7.01556e7i			0.940191i	0.882616	+	0.470095i	$0.155780\pi$
$421$			7.01556e7i			0.940191i	−0.882616	+	0.470095i	$0.844220\pi$
$422$	3.76542e7			0.501044
$423$			8.66588e7i			1.14496i
$424$		−	3.27201e7i		−	0.429257i
$425$	−4.96028e7			−0.646159
$426$			2.06503e7i			0.267114i
$427$			1.12457e8i			1.44445i
$428$	−5.55991e7			−0.709147
$429$	−2.25713e7			−0.285881
$430$	1.14705e7			0.144270
$431$		−	1.09471e8i		−	1.36731i	−0.729804	−	0.683656i	$-0.760389\pi$
$431$		−	1.09471e8i		−	1.36731i	0.729804	−	0.683656i	$-0.239611\pi$
$432$	7.87893e7			0.977273
$433$	6.27330e7			0.772738			0.386369	−	0.922344i	$-0.373729\pi$
$433$	6.27330e7			0.772738			0.386369	+	0.922344i	$0.373729\pi$
$434$	−1.57997e8			−1.93277
$435$	−261697.			−0.00317930
$436$		−	1.04132e8i		−	1.25639i
$437$			173472.i			0.00207867i
$438$	8.39459e7			0.999027
$439$	7.37570e7			0.871786			0.435893	−	0.899999i	$-0.356433\pi$
$439$	7.37570e7			0.871786			0.435893	+	0.899999i	$0.356433\pi$
$440$	7.96567e6			0.0935114
$441$	−1.64035e8			−1.91258
$442$	−4.56066e7			−0.528154
$443$		−	1.02968e8i		−	1.18438i	−0.805797	−	0.592192i	$-0.798263\pi$
$443$		−	1.02968e8i		−	1.18438i	0.805797	−	0.592192i	$-0.201737\pi$
$444$		−	4.08259e7i		−	0.466430i
$445$		−	1.90843e7i		−	0.216569i
$446$			1.04947e7i			0.118295i
$447$		−	2.29389e7i		−	0.256833i
$448$	5.17022e7			0.575010
$449$	−6.80743e7			−0.752046			−0.376023	−	0.926610i	$-0.622709\pi$
$449$	−6.80743e7			−0.752046			−0.376023	+	0.926610i	$0.622709\pi$
$450$		−	9.02920e7i		−	0.990859i
$451$		−	9.72247e7i		−	1.05986i
$452$		−	6.36708e7i		−	0.689485i
$453$		−	5.06877e7i		−	0.545265i
$454$	−1.13759e8			−1.21568
$455$			2.25641e7i			0.239544i
$456$		−	3.06563e6i		−	0.0323314i
$457$			2.29133e7i			0.240070i	0.992770	+	0.120035i	$0.0383008\pi$
$457$			2.29133e7i			0.240070i	−0.992770	+	0.120035i	$0.961699\pi$
$458$	−1.76764e8			−1.83991
$459$	−5.27832e7			−0.545830
$460$			169085.i			0.00173712i
$461$	−1.11350e8			−1.13655			−0.568274	−	0.822839i	$-0.692389\pi$
$461$	−1.11350e8			−1.13655			−0.568274	+	0.822839i	$0.692389\pi$
$462$	−1.12597e8			−1.14183
$463$			6.73553e7i			0.678623i	0.940674	+	0.339312i	$0.110194\pi$
$463$			6.73553e7i			0.678623i	−0.940674	+	0.339312i	$0.889806\pi$
$464$	−3.97214e6			−0.0397622
$465$			7.88246e6i			0.0783977i
$466$	2.42028e8			2.39171
$467$		−	5.79276e7i		−	0.568768i	−0.958710	−	0.284384i	$-0.908211\pi$
$467$		−	5.79276e7i		−	0.568768i	0.958710	−	0.284384i	$-0.0917890\pi$
$468$		−	3.38771e7i		−	0.330498i
$469$			1.21849e8i			1.18114i
$470$	4.19271e7			0.403833
$471$			4.23809e7i			0.405608i
$472$	−2.27737e7	−	3.58270e7i	−0.216575	−	0.340709i
$473$	−5.77252e7			−0.545484
$474$		−	4.40049e7i		−	0.413205i
$475$	−1.82892e7			−0.170653
$476$	−9.28394e7			−0.860818
$477$	−9.23228e7			−0.850656
$478$			1.45379e8i			1.33112i
$479$	5.07990e7			0.462220			0.231110	−	0.972928i	$-0.425764\pi$
$479$	5.07990e7			0.462220			0.231110	+	0.972928i	$0.425764\pi$
$480$		−	1.26082e7i		−	0.114007i
$481$	1.00897e8			0.906653
$482$			2.41989e8i			2.16100i
$483$			1.07684e6i			0.00955677i
$484$	1.08104e7			0.0953467
$485$			3.03730e7i			0.266233i
$486$		−	1.49458e8i		−	1.30200i
$487$	2.00213e7			0.173342			0.0866712	−	0.996237i	$-0.472377\pi$
$487$	2.00213e7			0.173342			0.0866712	+	0.996237i	$0.472377\pi$
$488$	3.68045e7			0.316695
$489$	3.81414e7			0.326190
$490$			7.93630e7i			0.674574i
$491$	−1.29504e8			−1.09406			−0.547028	−	0.837114i	$-0.684241\pi$
$491$	−1.29504e8			−1.09406			−0.547028	+	0.837114i	$0.684241\pi$
$492$	−3.64709e7			−0.306233
$493$	2.66105e6			0.0222081
$494$	−1.68157e7			−0.139487
$495$		−	2.24759e7i		−	0.185311i
$496$			1.19643e8i			0.980489i
$497$	−1.03889e8			−0.846256
$498$	7.84547e6			0.0635230
$499$	5.14206e7			0.413843			0.206922	−	0.978358i	$-0.433656\pi$
$499$	5.14206e7			0.413843			0.206922	+	0.978358i	$0.433656\pi$
$500$	−3.65349e7			−0.292279
$501$	4.26106e6			0.0338848
$502$		−	2.78956e8i		−	2.20508i
$503$			2.13623e8i			1.67859i	0.543678	+	0.839294i	$0.317031\pi$
$503$			2.13623e8i			1.67859i	−0.543678	+	0.839294i	$0.682969\pi$
$504$			7.61413e7i			0.594742i
$505$			2.15869e7i			0.167617i
$506$		−	2.08522e6i		−	0.0160953i
$507$	3.73511e7			0.286602
$508$	1.27316e8			0.971162
$509$		−	8.36346e7i		−	0.634209i	−0.948391	−	0.317105i	$-0.897289\pi$
$509$		−	8.36346e7i		−	0.634209i	0.948391	−	0.317105i	$-0.102711\pi$
$510$			1.13503e7i			0.0855653i
$511$			4.22323e8i			3.16506i
$512$		−	1.25584e8i		−	0.935672i
$513$	−1.94618e7			−0.144155
$514$		−	3.68557e7i		−	0.271404i
$515$		−	5.45710e7i		−	0.399522i
$516$			2.16539e7i			0.157611i
$517$	−2.10998e8			−1.52689
$518$	5.03321e8			3.62123
$519$		−	5.64020e7i		−	0.403452i
$520$	7.38471e6			0.0525199
$521$	−8.93995e7			−0.632153			−0.316076	−	0.948734i	$-0.602366\pi$
$521$	−8.93995e7			−0.632153			−0.316076	+	0.948734i	$0.602366\pi$
$522$			4.84391e6i			0.0340553i
$523$	1.61511e6			0.0112901			0.00564503	−	0.999984i	$-0.498203\pi$
$523$	1.61511e6			0.0112901			0.00564503	+	0.999984i	$0.498203\pi$
$524$		−	2.58252e7i		−	0.179494i
$525$	−1.13531e8			−0.784582
$526$		−	2.17411e8i		−	1.49391i
$527$		−	8.01523e7i		−	0.547626i
$528$			8.52637e7i			0.579245i
$529$	1.48016e8			0.999865
$530$			4.46674e7i			0.300029i
$531$	−1.01089e8	+	6.42581e7i	−0.675182	+	0.429185i
$532$	−3.42310e7			−0.227345
$533$		−	9.01338e7i		−	0.595259i
$534$	8.82866e7			0.579790
$535$	−3.41971e7			−0.223320
$536$	3.98783e7			0.258966
$537$			2.84215e6i			0.0183537i
$538$	1.92724e8			1.23762
$539$		−	3.99394e8i		−	2.55056i
$540$	−1.89695e7			−0.120469
$541$		−	4.12560e7i		−	0.260553i	−0.991478	−	0.130276i	$-0.958414\pi$
$541$		−	4.12560e7i		−	0.260553i	0.991478	−	0.130276i	$-0.0415864\pi$
$542$			1.56462e8i			0.982675i
$543$	2.50808e7			0.156654
$544$			1.28206e8i			0.796364i
$545$		−	6.40480e7i		−	0.395654i
$546$	−1.04385e8			−0.641297
$547$	−8.94238e7			−0.546375			−0.273188	−	0.961961i	$-0.588078\pi$
$547$	−8.94238e7			−0.546375			−0.273188	+	0.961961i	$0.588078\pi$
$548$	1.09825e8			0.667359
$549$		−	1.03847e8i		−	0.627593i
$550$	2.19844e8			1.32138
$551$	981162.			0.00586524
$552$	352425.			0.00209532
$553$	2.21384e8			1.30910
$554$			1.73090e8i			1.01799i
$555$		−	2.51106e7i		−	0.146885i
$556$	−6.75710e7			−0.393130
$557$	1.85645e8			1.07428			0.537140	−	0.843493i	$-0.319505\pi$
$557$	1.85645e8			1.07428			0.537140	+	0.843493i	$0.319505\pi$
$558$	1.45901e8			0.839762
$559$	−5.35152e7			−0.306367
$560$	8.52365e7			0.485357
$561$		−	5.71205e7i		−	0.323522i
$562$			4.14806e8i			2.33688i
$563$			3.18120e8i			1.78265i	0.453365	+	0.891325i	$0.350223\pi$
$563$			3.18120e8i			1.78265i	−0.453365	+	0.891325i	$0.649777\pi$
$564$			7.91497e7i			0.441176i
$565$		−	3.91617e7i		−	0.217128i
$566$	−3.09334e8			−1.70600
$567$	1.47724e8			0.810407
$568$			3.40005e7i			0.185541i
$569$		−	1.24522e8i		−	0.675944i	−0.941156	−	0.337972i	$-0.890259\pi$
$569$		−	1.24522e8i		−	0.675944i	0.941156	−	0.337972i	$-0.109741\pi$
$570$			4.18501e6i			0.0225981i
$571$		−	3.21884e8i		−	1.72898i	−0.502648	−	0.864491i	$-0.667641\pi$
$571$		−	3.21884e8i		−	1.72898i	0.502648	−	0.864491i	$-0.332359\pi$
$572$	8.24845e7			0.440742
$573$		−	7.73685e7i		−	0.411245i
$574$		−	4.49631e8i		−	2.37750i
$575$		−	2.10253e6i		−	0.0110596i
$576$	−4.77440e7			−0.249834
$577$	−1.50027e8			−0.780982			−0.390491	−	0.920607i	$-0.627695\pi$
$577$	−1.50027e8			−0.780982			−0.390491	+	0.920607i	$0.627695\pi$
$578$			1.35571e8i			0.702072i
$579$	7.91960e7			0.408007
$580$	956345.			0.00490152
$581$			3.94698e7i			0.201250i
$582$	−1.40510e8			−0.712750
$583$		−	2.24789e8i		−	1.13441i
$584$	1.38216e8			0.693939
$585$		−	2.08367e7i		−	0.104078i
$586$			3.48757e8i			1.73312i
$587$			2.82523e8i			1.39681i	0.715700	+	0.698407i	$0.246108\pi$
$587$			2.82523e8i			1.39681i	−0.715700	+	0.698407i	$0.753892\pi$
$588$	−1.49821e8			−0.736954
$589$		−	2.95531e7i		−	0.144630i
$590$	3.10892e7	+	4.89088e7i	0.151375	+	0.238139i
$591$	−5.12569e7			−0.248308
$592$		−	3.81139e8i		−	1.83704i
$593$	1.05175e8			0.504367			0.252184	−	0.967679i	$-0.418851\pi$
$593$	1.05175e8			0.504367			0.252184	+	0.967679i	$0.418851\pi$
$594$	2.33940e8			1.11621
$595$	−5.71024e7			−0.271084
$596$			8.38279e7i			0.395958i
$597$	−1.09695e8			−0.515540
$598$		−	1.93314e6i		−	0.00903981i
$599$	1.22960e8			0.572115			0.286058	−	0.958212i	$-0.407655\pi$
$599$	1.22960e8			0.572115			0.286058	+	0.958212i	$0.407655\pi$
$600$			3.71562e7i			0.172019i
$601$			1.21439e8i			0.559415i	0.960085	+	0.279708i	$0.0902375\pi$
$601$			1.21439e8i			0.559415i	−0.960085	+	0.279708i	$0.909762\pi$
$602$	−2.66960e8			−1.22365
$603$		−	1.12520e8i		−	0.513191i
$604$			1.85233e8i			0.840634i
$605$	6.64911e6			0.0300260
$606$	−9.98641e7			−0.448737
$607$	1.75009e8			0.782517			0.391259	−	0.920281i	$-0.372040\pi$
$607$	1.75009e8			0.782517			0.391259	+	0.920281i	$0.372040\pi$
$608$			4.72711e7i			0.210322i
$609$	6.09064e6			0.0269657
$610$	−5.02432e7			−0.221354
$611$	−1.95609e8			−0.857563
$612$	8.57317e7			0.374013
$613$			2.35371e8i			1.02181i	0.859637	+	0.510906i	$0.170690\pi$
$613$			2.35371e8i			1.02181i	−0.859637	+	0.510906i	$0.829310\pi$
$614$			1.09846e8i			0.474548i
$615$	−2.24320e7			−0.0964369
$616$	−1.85390e8			−0.793130
$617$	−4.60953e8			−1.96246			−0.981231	−	0.192834i	$-0.938232\pi$
$617$	−4.60953e8			−1.96246			−0.981231	+	0.192834i	$0.938232\pi$
$618$	2.52453e8			1.06958
$619$	−1.29564e7			−0.0546276			−0.0273138	−	0.999627i	$-0.508695\pi$
$619$	−1.29564e7			−0.0546276			−0.0273138	+	0.999627i	$0.508695\pi$
$620$		−	2.88056e7i		−	0.120865i
$621$		−	2.23733e6i		−	0.00934235i
$622$		−	2.32980e7i		−	0.0968161i
$623$			4.44161e8i			1.83686i
$624$			7.90451e7i			0.325328i
$625$	2.10162e8			0.860825
$626$	−4.96535e8			−2.02408
$627$		−	2.10610e7i		−	0.0854432i
$628$		−	1.54876e8i		−	0.625326i
$629$			2.55336e8i			1.02603i
$630$		−	1.03943e8i		−	0.415696i
$631$	3.52161e8			1.40170			0.700848	−	0.713311i	$-0.252805\pi$
$631$	3.52161e8			1.40170			0.700848	+	0.713311i	$0.252805\pi$
$632$		−	7.24538e7i		−	0.287019i
$633$			4.37209e7i			0.172376i
$634$		−	8.45512e7i		−	0.331781i
$635$	7.83077e7			0.305832
$636$	−8.43229e7			−0.327774
$637$		−	3.70265e8i		−	1.43250i
$638$	−1.17940e7			−0.0454151
$639$	9.59357e7			0.367686
$640$		−	4.37354e7i		−	0.166837i
$641$	1.22889e8			0.466595			0.233297	−	0.972405i	$-0.425048\pi$
$641$	1.22889e8			0.466595			0.233297	+	0.972405i	$0.425048\pi$
$642$		−	1.58200e8i		−	0.597864i
$643$	−1.84011e8			−0.692166			−0.346083	−	0.938204i	$-0.612489\pi$
$643$	−1.84011e8			−0.692166			−0.346083	+	0.938204i	$0.612489\pi$
$644$		−	3.93521e6i		−	0.0147336i
$645$			1.33186e7i			0.0496339i
$646$		−	4.25550e7i		−	0.157853i
$647$	−3.00507e8			−1.10954			−0.554769	−	0.832005i	$-0.687193\pi$
$647$	−3.00507e8			−1.10954			−0.554769	+	0.832005i	$0.687193\pi$
$648$		−	4.83467e7i		−	0.177681i
$649$	−1.56457e8	−	2.46133e8i	−0.572347	−	0.900402i
$650$	2.03810e8			0.742141
$651$		−	1.83453e8i		−	0.664941i
$652$	−1.39384e8			−0.502886
$653$	−4.77086e8			−1.71339			−0.856697	−	0.515821i	$-0.827487\pi$
$653$	−4.77086e8			−1.71339			−0.856697	+	0.515821i	$0.827487\pi$
$654$	2.96295e8			1.05923
$655$		−	1.58842e7i		−	0.0565250i
$656$	−3.40482e8			−1.20610
$657$		−	3.89991e8i		−	1.37518i
$658$	−9.75796e8			−3.42516
$659$			2.82503e8i			0.987112i	0.869714	+	0.493556i	$0.164303\pi$
$659$			2.82503e8i			0.987112i	−0.869714	+	0.493556i	$0.835697\pi$
$660$		−	2.05283e7i		−	0.0714039i
$661$	4.75098e8			1.64505			0.822524	−	0.568730i	$-0.192565\pi$
$661$	4.75098e8			1.64505			0.822524	+	0.568730i	$0.192565\pi$
$662$		−	1.32756e8i		−	0.457593i
$663$		−	5.29546e7i		−	0.181703i
$664$	1.29175e7			0.0441240
$665$	−2.10543e7			−0.0715940
$666$	−4.64787e8			−1.57337
$667$			112795.i			0.000380111i
$668$	−1.55716e7			−0.0522401
$669$	−1.21856e7			−0.0406976
$670$	−5.44394e7			−0.181004
$671$	2.52849e8			0.836939
$672$			2.93439e8i			0.966964i
$673$			3.21642e8i			1.05518i	0.849499	+	0.527591i	$0.176905\pi$
$673$			3.21642e8i			1.05518i	−0.849499	+	0.527591i	$0.823095\pi$
$674$	−1.60641e8			−0.524659
$675$	2.35882e8			0.766979
$676$	−1.36496e8			−0.441854
$677$	5.26941e8			1.69823			0.849114	−	0.528209i	$-0.177136\pi$
$677$	5.26941e8			1.69823			0.849114	+	0.528209i	$0.177136\pi$
$678$	1.81167e8			0.581287
$679$		−	7.06890e8i		−	2.25810i
$680$			1.86883e7i			0.0594350i
$681$		−	1.32088e8i		−	0.418235i
$682$			3.55243e8i			1.11988i
$683$		−	3.88061e8i		−	1.21798i	−0.793180	−	0.608988i	$-0.791576\pi$
$683$		−	3.88061e8i		−	1.21798i	0.793180	−	0.608988i	$-0.208424\pi$
$684$	3.16103e7			0.0987781
$685$	6.75496e7			0.210160
$686$		−	1.07443e9i		−	3.32816i
$687$		−	2.05244e8i		−	0.632994i
$688$			2.02155e8i			0.620752i
$689$		−	2.08394e8i		−	0.637130i
$690$	−481109.			−0.00146452
$691$			8.11341e7i			0.245906i	0.992412	+	0.122953i	$0.0392365\pi$
$691$			8.11341e7i			0.245906i	−0.992412	+	0.122953i	$0.960764\pi$
$692$			2.06115e8i			0.622002i
$693$			5.23095e8i			1.57174i
$694$	4.30653e8			1.28839
$695$	−4.15606e7			−0.123802
$696$		−	1.99332e6i		−	0.00591221i
$697$	2.28099e8			0.673635
$698$	6.46467e8			1.90099
$699$			2.81023e8i			0.822830i
$700$	4.14889e8			1.20959
$701$			1.74092e8i			0.505388i	0.967546	+	0.252694i	$0.0813166\pi$
$701$			1.74092e8i			0.505388i	−0.967546	+	0.252694i	$0.918683\pi$
$702$	2.16878e8			0.626909
$703$			9.41454e7i			0.270977i
$704$		−	1.16248e8i		−	0.333171i
$705$			4.86823e7i			0.138932i
$706$	3.97475e8			1.12952
$707$		−	5.02406e8i		−	1.42166i
$708$	−9.23296e7	+	5.86900e7i	−0.260160	+	0.165373i
$709$	−1.63860e8			−0.459764			−0.229882	−	0.973219i	$-0.573834\pi$
$709$	−1.63860e8			−0.459764			−0.229882	+	0.973219i	$0.573834\pi$
$710$		−	4.64154e7i		−	0.129684i
$711$	−2.04435e8			−0.568784
$712$	1.45363e8			0.402731
$713$	3.39744e6			0.00937309
$714$		−	2.64163e8i		−	0.725734i
$715$	5.07334e7			0.138796
$716$		−	1.03863e7i		−	0.0282958i
$717$	−1.68802e8			−0.457952
$718$			4.73440e7i			0.127906i
$719$			3.01034e8i			0.809894i	0.914340	+	0.404947i	$0.132710\pi$
$719$			3.01034e8i			0.809894i	−0.914340	+	0.404947i	$0.867290\pi$
$720$	−7.87109e7			−0.210881
$721$			1.27006e9i			3.38860i
$722$			4.73499e8i			1.25808i
$723$	−2.80978e8			−0.743459
$724$	−9.16550e7			−0.241513
$725$	−1.18919e7			−0.0312060
$726$			3.07597e7i			0.0803844i
$727$	−5.20478e8			−1.35456			−0.677282	−	0.735724i	$-0.736842\pi$
$727$	−5.20478e8			−1.35456			−0.677282	+	0.735724i	$0.736842\pi$
$728$	−1.71869e8			−0.445455
$729$	3.02953e6			0.00781974
$730$	−1.88685e8			−0.485029
$731$		−	1.35429e8i		−	0.346705i
$732$		−	9.48488e7i		−	0.241824i
$733$	−4.33546e7			−0.110084			−0.0550419	−	0.998484i	$-0.517529\pi$
$733$	−4.33546e7			−0.110084			−0.0550419	+	0.998484i	$0.517529\pi$
$734$	1.35846e8			0.343525
$735$	−9.21497e7			−0.232077
$736$	−5.43430e6			−0.0136304
$737$	2.73966e8			0.684375
$738$			4.15208e8i			1.03299i
$739$			4.70381e7i			0.116551i	0.998301	+	0.0582756i	$0.0185602\pi$
$739$			4.70381e7i			0.116551i	−0.998301	+	0.0582756i	$0.981440\pi$
$740$			9.17641e7i			0.226453i
$741$		−	1.95250e7i		−	0.0479884i
$742$		−	1.03957e9i		−	2.54474i
$743$	−3.83331e8			−0.934562			−0.467281	−	0.884109i	$-0.654766\pi$
$743$	−3.83331e8			−0.934562			−0.467281	+	0.884109i	$0.654766\pi$
$744$	−6.00400e7			−0.145788
$745$			5.15596e7i			0.124693i
$746$		−	8.96240e8i		−	2.15878i
$747$		−	3.64480e7i		−	0.0874404i
$748$			2.08741e8i			0.498773i
$749$	7.95890e8			1.89412
$750$		−	1.03956e8i		−	0.246413i
$751$		−	4.20163e8i		−	0.991969i	−0.868331	−	0.495985i	$-0.834807\pi$
$751$		−	4.20163e8i		−	0.991969i	0.868331	−	0.495985i	$-0.165193\pi$
$752$			7.38919e8i			1.73757i
$753$	3.23901e8			0.758625
$754$	−1.09339e7			−0.0255070
$755$			1.13930e8i			0.264727i
$756$	4.41490e8			1.02178
$757$	3.41463e8			0.787146			0.393573	−	0.919293i	$-0.371239\pi$
$757$	3.41463e8			0.787146			0.393573	+	0.919293i	$0.371239\pi$
$758$			5.69120e8i			1.30676i
$759$	2.42118e6			0.00553735
$760$			6.89059e6i			0.0156970i
$761$	−4.95852e8			−1.12512			−0.562559	−	0.826757i	$-0.690183\pi$
$761$	−4.95852e8			−1.12512			−0.562559	+	0.826757i	$0.690183\pi$
$762$			3.62262e8i			0.818762i
$763$			1.49063e9i			3.35580i
$764$			2.82735e8i			0.634015i
$765$	5.27306e7			0.117782
$766$			7.96401e7i			0.177193i
$767$	−1.45046e8	−	2.28182e8i	−0.321454	−	0.505703i
$768$	2.65580e8			0.586289
$769$		−	3.44369e8i		−	0.757260i	−0.925548	−	0.378630i	$-0.876395\pi$
$769$		−	3.44369e8i		−	0.757260i	0.925548	−	0.378630i	$-0.123605\pi$
$770$	2.53083e8			0.554359
$771$	4.27938e7			0.0933722
$772$	−2.89414e8			−0.629024
$773$			6.82495e7i			0.147761i	0.997267	+	0.0738807i	$0.0235384\pi$
$773$			6.82495e7i			0.147761i	−0.997267	+	0.0738807i	$0.976462\pi$
$774$	2.46522e8			0.531658
$775$			3.58191e8i			0.769503i
$776$	−2.31348e8			−0.495087
$777$			5.84415e8i			1.24583i
$778$		−	8.05238e8i		−	1.70996i
$779$	8.41028e7			0.177909
$780$		−	1.90311e7i		−	0.0401034i
$781$			2.33586e8i			0.490335i
$782$	4.89213e6			0.0102300
$783$	−1.26544e7			−0.0263606
$784$	−1.39868e9			−2.90250
$785$		−	9.52592e7i		−	0.196924i
$786$	7.34823e7			0.151327
$787$	6.31772e8			1.29609			0.648047	−	0.761601i	$-0.275586\pi$
$787$	6.31772e8			1.29609			0.648047	+	0.761601i	$0.275586\pi$
$788$	1.87313e8			0.382815
$789$	2.52440e8			0.513957
$790$			9.89095e7i			0.200612i
$791$			9.11435e8i			1.84160i
$792$	1.71197e8			0.344604
$793$	2.34408e8			0.470059
$794$	−3.28864e8			−0.656983
$795$	−5.18641e7			−0.103220
$796$	4.00867e8			0.794807
$797$		−	3.61765e8i		−	0.714581i	−0.933993	−	0.357291i	$-0.883701\pi$
$797$		−	3.61765e8i		−	0.714581i	0.933993	−	0.357291i	$-0.116299\pi$
$798$		−	9.74002e7i		−	0.191669i
$799$		−	4.95023e8i		−	0.970476i
$800$		−	5.72938e8i		−	1.11902i
$801$		−	4.10156e8i		−	0.798090i
$802$	−1.14461e9			−2.21888
$803$	9.49556e8			1.83389
$804$		−	1.02770e8i		−	0.197742i
$805$		−	2.42041e6i		−	0.00463983i
$806$			3.29334e8i			0.628972i
$807$			2.23775e8i			0.425786i
$808$	−1.64426e8			−0.311699
$809$		−	8.36258e8i		−	1.57941i	−0.613488	−	0.789704i	$-0.710234\pi$
$809$		−	8.36258e8i		−	1.57941i	0.613488	−	0.789704i	$-0.289766\pi$
$810$			6.59999e7i			0.124191i
$811$		−	1.51088e8i		−	0.283248i	−0.989921	−	0.141624i	$-0.954768\pi$
$811$		−	1.51088e8i		−	0.283248i	0.989921	−	0.141624i	$-0.0452324\pi$
$812$	−2.22576e7			−0.0415729
$813$	−1.81670e8			−0.338074
$814$		−	1.13167e9i		−	2.09820i
$815$	−8.57302e7			−0.158366
$816$	−2.00037e8			−0.368163
$817$		−	4.99344e7i		−	0.0915658i
$818$	8.34900e8			1.52537
$819$			4.84944e8i			0.882755i
$820$	8.19755e7			0.148677
$821$			8.18613e8i			1.47928i	0.673005	+	0.739638i	$0.265003\pi$
$821$			8.18613e8i			1.47928i	−0.673005	+	0.739638i	$0.734997\pi$
$822$			3.12494e8i			0.562634i
$823$		−	7.83273e8i		−	1.40512i	−0.711624	−	0.702560i	$-0.752040\pi$
$823$		−	7.83273e8i		−	1.40512i	0.711624	−	0.702560i	$-0.247960\pi$
$824$	4.15662e8			0.742949
$825$			2.55265e8i			0.454600i
$826$	−7.23559e8	−	1.13828e9i	−1.28391	−	2.01981i
$827$	−1.02693e9			−1.81563			−0.907813	−	0.419376i	$-0.862249\pi$
$827$	−1.02693e9			−1.81563			−0.907813	+	0.419376i	$0.862249\pi$
$828$			3.63393e6i			0.00640156i
$829$	−8.74100e8			−1.53425			−0.767127	−	0.641495i	$-0.778315\pi$
$829$	−8.74100e8			−1.53425			−0.767127	+	0.641495i	$0.778315\pi$
$830$	−1.76342e7			−0.0308405
$831$	−2.00978e8			−0.350224
$832$		−	1.07769e8i		−	0.187122i
$833$	9.37018e8			1.62111
$834$		−	1.92265e8i		−	0.331438i
$835$	−9.57756e6			−0.0164511
$836$			7.69654e7i			0.131728i
$837$			3.81157e8i			0.650022i
$838$	−4.75854e8			−0.808614
$839$		−	1.71015e7i		−	0.0289567i	−0.999895	−	0.0144783i	$-0.995391\pi$
$839$		−	1.71015e7i		−	0.0289567i	0.999895	−	0.0144783i	$-0.00460876\pi$
$840$			4.27739e7i			0.0721673i
$841$	−5.94185e8			−0.998927
$842$	7.29487e8			1.22203
$843$	−4.81639e8			−0.803968
$844$		−	1.59773e8i		−	0.265752i
$845$	−8.39538e7			−0.139146
$846$	9.01090e8			1.48818
$847$	−1.54749e8			−0.254669
$848$	−7.87214e8			−1.29094
$849$		−	3.59173e8i		−	0.586923i
$850$			5.15777e8i			0.839856i
$851$	−1.08230e7			−0.0175614
$852$	8.76227e7			0.141677
$853$	8.71387e8			1.40399			0.701995	−	0.712182i	$-0.252293\pi$
$853$	8.71387e8			1.40399			0.701995	+	0.712182i	$0.252293\pi$
$854$	1.16934e9			1.87745
$855$	1.94424e7			0.0311066
$856$		−	2.60476e8i		−	0.415285i
$857$		−	6.38810e8i		−	1.01491i	−0.861677	−	0.507457i	$-0.830586\pi$
$857$		−	6.38810e8i		−	1.01491i	0.861677	−	0.507457i	$-0.169414\pi$
$858$			2.34700e8i			0.371578i
$859$		−	1.18416e7i		−	0.0186823i	−0.999956	−	0.00934117i	$-0.997027\pi$
$859$		−	1.18416e7i		−	0.0186823i	0.999956	−	0.00934117i	$-0.00297343\pi$
$860$		−	4.86713e7i		−	0.0765205i
$861$	5.22075e8			0.817943
$862$	−1.13830e9			−1.77719
$863$		−	1.08456e9i		−	1.68741i	−0.536806	−	0.843705i	$-0.680369\pi$
$863$		−	1.08456e9i		−	1.68741i	0.536806	−	0.843705i	$-0.319631\pi$
$864$		−	6.09672e8i		−	0.945268i
$865$			1.26774e8i			0.195877i
$866$		−	6.52306e8i		−	1.00438i
$867$	−1.57413e8			−0.241537
$868$			6.70411e8i			1.02514i
$869$		−	4.97762e8i		−	0.758512i
$870$			2.72116e6i			0.00413234i
$871$	2.53985e8			0.384373
$872$	4.87848e8			0.735758
$873$			6.52771e8i			0.981111i
$874$	1.80379e6			0.00270179
$875$	5.22990e8			0.780673
$876$		−	3.56197e8i		−	0.529881i
$877$	7.51130e7			0.111357			0.0556784	−	0.998449i	$-0.482268\pi$
$877$	7.51130e7			0.111357			0.0556784	+	0.998449i	$0.482268\pi$
$878$		−	7.66935e8i		−	1.13312i
$879$	−4.04947e8			−0.596255
$880$		−	1.91647e8i		−	0.281224i
$881$			1.85155e8i			0.270774i	0.990793	+	0.135387i	$0.0432277\pi$
$881$			1.85155e8i			0.270774i	−0.990793	+	0.135387i	$0.956772\pi$
$882$			1.70565e9i			2.48591i
$883$	−8.23156e8			−1.19564			−0.597820	−	0.801631i	$-0.703966\pi$
$883$	−8.23156e8			−1.19564			−0.597820	+	0.801631i	$0.703966\pi$
$884$			1.93517e8i			0.280131i
$885$	−5.67888e7	+	3.60982e7i	−0.0819281	+	0.0520782i
$886$	−1.07068e9			−1.53942
$887$		−	7.99364e8i		−	1.14544i	−0.819750	−	0.572722i	$-0.805888\pi$
$887$		−	7.99364e8i		−	1.14544i	0.819750	−	0.572722i	$-0.194112\pi$
$888$	1.91265e8			0.273147
$889$	−1.82250e9			−2.59396
$890$	−1.98441e8			−0.281489
$891$		−	3.32145e8i		−	0.469563i
$892$	4.45310e7			0.0627434
$893$		−	1.82521e8i		−	0.256306i
$894$	−2.38522e8			−0.333823
$895$		−	6.38827e6i		−	0.00891075i
$896$			1.01788e9i			1.41505i
$897$	2.24460e6			0.00311001
$898$			7.07846e8i			0.977484i
$899$		−	1.92160e7i		−	0.0264474i
$900$	−3.83125e8			−0.525549
$901$	5.27377e8			0.721019
$902$	−1.01096e9			−1.37757
$903$		−	3.09972e8i		−	0.420977i
$904$	2.98291e8			0.403771
$905$	−5.63738e7			−0.0760557
$906$	−5.27057e8			−0.708717
$907$	9.06113e8			1.21440			0.607198	−	0.794551i	$-0.292293\pi$
$907$	9.06113e8			1.21440			0.607198	+	0.794551i	$0.292293\pi$
$908$			4.82700e8i			0.644792i
$909$			4.63943e8i			0.617693i
$910$	2.34625e8			0.311351
$911$	−6.08785e8			−0.805209			−0.402605	−	0.915374i	$-0.631895\pi$
$911$	−6.08785e8			−0.805209			−0.402605	+	0.915374i	$0.631895\pi$
$912$	−7.37561e7			−0.0972329
$913$	8.87442e7			0.116608
$914$	2.38255e8			0.312036
$915$		−	5.83382e7i		−	0.0761535i
$916$			7.50041e8i			0.975885i
$917$			3.69682e8i			0.479425i
$918$			5.48846e8i			0.709451i
$919$			6.44347e8i			0.830182i	0.909780	+	0.415091i	$0.136250\pi$
$919$			6.44347e8i			0.830182i	−0.909780	+	0.415091i	$0.863750\pi$
$920$	−792144.			−0.00101728
$921$	−1.27544e8			−0.163261
$922$			1.15783e9i			1.47725i
$923$			2.16550e8i			0.275393i
$924$			4.77769e8i			0.605622i
$925$		−	1.14107e9i		−	1.44173i
$926$	7.00369e8			0.882051
$927$		−	1.17283e9i		−	1.47230i
$928$			3.07365e7i			0.0384601i
$929$			6.14742e8i			0.766736i	0.923596	+	0.383368i	$0.125236\pi$
$929$			6.14742e8i			0.766736i	−0.923596	+	0.383368i	$0.874764\pi$
$930$	8.19629e7			0.101899
$931$	3.45490e8			0.428141
$932$		−	1.02697e9i		−	1.26856i
$933$	2.70517e7			0.0333081
$934$	−6.02339e8			−0.739265
$935$			1.28389e8i			0.157070i
$936$	1.58711e8			0.193544
$937$		−	9.42363e8i		−	1.14551i	−0.819726	−	0.572756i	$-0.805874\pi$
$937$		−	9.42363e8i		−	1.14551i	0.819726	−	0.572756i	$-0.194126\pi$
$938$	1.26700e9			1.53521
$939$		−	5.76536e8i		−	0.696353i
$940$		−	1.77904e8i		−	0.214192i
$941$			1.22623e9i			1.47165i	0.677174	+	0.735823i	$0.263205\pi$
$941$			1.22623e9i			1.47165i	−0.677174	+	0.735823i	$0.736795\pi$
$942$	4.40682e8			0.527196
$943$			9.66848e6i			0.0115298i
$944$	−8.61962e8	+	5.47913e8i	−1.02464	+	0.651322i
$945$	2.71545e8			0.321771
$946$			6.00235e8i			0.709002i
$947$	9.99627e8			1.17703			0.588516	−	0.808486i	$-0.299713\pi$
$947$	9.99627e8			1.17703			0.588516	+	0.808486i	$0.299713\pi$
$948$	−1.86721e8			−0.219163
$949$	8.80301e8			1.02999
$950$			1.90173e8i			0.221809i
$951$	9.81739e7			0.114144
$952$		−	4.34943e8i		−	0.504106i
$953$	5.15456e8			0.595543			0.297771	−	0.954637i	$-0.403757\pi$
$953$	5.15456e8			0.595543			0.297771	+	0.954637i	$0.403757\pi$
$954$			9.59984e8i			1.10565i
$955$			1.73901e8i			0.199660i
$956$	6.16869e8			0.706023
$957$		−	1.36942e7i		−	0.0156244i
$958$		−	5.28214e8i		−	0.600778i
$959$	−1.57212e9			−1.78251
$960$	−2.68211e7			−0.0303154
$961$	3.08708e8			0.347839
$962$		−	1.04914e9i		−	1.17844i
$963$	−7.34958e8			−0.822969
$964$	1.02680e9			1.14619
$965$	−1.78008e8			−0.198088
$966$	1.11972e7			0.0124216
$967$			6.08925e8i			0.673418i	0.941609	+	0.336709i	$0.109314\pi$
$967$			6.08925e8i			0.673418i	−0.941609	+	0.336709i	$0.890686\pi$
$968$			5.06456e7i			0.0558362i
$969$	4.94113e7			0.0543069
$970$	3.15822e8			0.346041
$971$	−1.48724e9			−1.62452			−0.812259	−	0.583297i	$-0.801763\pi$
$971$	−1.48724e9			−1.62452			−0.812259	+	0.583297i	$0.801763\pi$
$972$	−6.34179e8			−0.690578
$973$	9.67265e8			1.05004
$974$		−	2.08184e8i		−	0.225305i
$975$			2.36648e8i			0.255322i
$976$		−	8.85481e8i		−	0.952423i
$977$			1.33819e9i			1.43495i	0.696586	+	0.717473i	$0.254701\pi$
$977$			1.33819e9i			1.43495i	−0.696586	+	0.717473i	$0.745299\pi$
$978$		−	3.96599e8i		−	0.423970i
$979$	9.98655e8			1.06431
$980$	3.36751e8			0.357792
$981$		−	1.37651e9i		−	1.45805i
$982$			1.34660e9i			1.42202i
$983$			1.03785e8i			0.109263i	0.998507	+	0.0546315i	$0.0173984\pi$
$983$			1.03785e8i			0.109263i	−0.998507	+	0.0546315i	$0.982602\pi$
$984$		−	1.70863e8i		−	0.179334i
$985$	1.15210e8			0.120554
$986$		−	2.76700e7i		−	0.0288654i
$987$		−	1.13301e9i		−	1.17837i
$988$			7.13520e7i			0.0739836i
$989$	5.74047e6			0.00593415
$990$	−2.33707e8			−0.240861
$991$			2.28391e8i			0.234671i	0.993092	+	0.117335i	$0.0374352\pi$
$991$			2.28391e8i			0.234671i	−0.993092	+	0.117335i	$0.962565\pi$
$992$	9.25800e8			0.948379
$993$	1.54145e8			0.157428
$994$			1.08025e9i			1.09994i
$995$	2.46560e8			0.250296
$996$		−	3.32897e7i		−	0.0336924i
$997$	4.50823e8			0.454905			0.227453	−	0.973789i	$-0.426960\pi$
$997$	4.50823e8			0.454905			0.227453	+	0.973789i	$0.426960\pi$
$998$		−	5.34678e8i		−	0.537899i
$999$		−	1.21423e9i		−	1.21788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	59.7.b.c.58.7	✓	26
59.58	odd	2	inner	59.7.b.c.58.20	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.7.b.c.58.7	✓	26	1.1	even	1	trivial
59.7.b.c.58.20	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)

\(f(q)\)	\(=\)	\(q-10.3981i q^{2} +12.0734 q^{3} -44.1211 q^{4} -27.1374 q^{5} -125.541i q^{6} +631.586 q^{7} -206.703i q^{8} -583.232 q^{9} +O(q^{10})\)	\(q-10.3981i q^{2} +12.0734 q^{3} -44.1211 q^{4} -27.1374 q^{5} -125.541i q^{6} +631.586 q^{7} -206.703i q^{8} -583.232 q^{9} +282.178i q^{10} -1420.06i q^{11} -532.694 q^{12} -1316.49i q^{13} -6567.31i q^{14} -327.642 q^{15} -4973.08 q^{16} +3331.61 q^{17} +6064.52i q^{18} +1228.40 q^{19} +1197.33 q^{20} +7625.41 q^{21} -14766.0 q^{22} +141.218i q^{23} -2495.62i q^{24} -14888.6 q^{25} -13689.1 q^{26} -15843.2 q^{27} -27866.3 q^{28} +798.729 q^{29} +3406.86i q^{30} -24058.2i q^{31} +38481.7i q^{32} -17145.0i q^{33} -34642.5i q^{34} -17139.6 q^{35} +25732.9 q^{36} +76640.4i q^{37} -12773.1i q^{38} -15894.6i q^{39} +5609.38i q^{40} +68465.1 q^{41} -79290.1i q^{42} -40649.8i q^{43} +62654.8i q^{44} +15827.4 q^{45} +1468.40 q^{46} -148584. i q^{47} -60042.2 q^{48} +281251. q^{49} +154813. i q^{50} +40224.0 q^{51} +58085.2i q^{52} +158295. q^{53} +164739. i q^{54} +38536.8i q^{55} -130551. i q^{56} +14831.1 q^{57} -8305.29i q^{58} +(173326. - 110176. i) q^{59} +14455.9 q^{60} +178055. i q^{61} -250160. q^{62} -368361. q^{63} +81861.0 q^{64} +35726.2i q^{65} -178276. q^{66} +192925. i q^{67} -146994. q^{68} +1704.98i q^{69} +178220. i q^{70} -164490. q^{71} +120556. i q^{72} +668672. i q^{73} +796917. q^{74} -179756. q^{75} -54198.6 q^{76} -896891. i q^{77} -165274. q^{78} +350521. q^{79} +134956. q^{80} +233894. q^{81} -711909. i q^{82} +62493.2i q^{83} -336442. q^{84} -90411.1 q^{85} -422682. q^{86} +9643.41 q^{87} -293531. q^{88} +703247. i q^{89} -164575. i q^{90} -831478. i q^{91} -6230.68i q^{92} -290465. i q^{93} -1.54499e6 q^{94} -33335.7 q^{95} +464607. i q^{96} -1.11923e6i q^{97} -2.92449e6i q^{98} +828226. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 10 q^{3} - 1090 q^{4} + 142 q^{5} + 406 q^{7} + 5432 q^{9}+O(q^{10}) \) 26 * q + 10 * q^3 - 1090 * q^4 + 142 * q^5 + 406 * q^7 + 5432 * q^9	\( 26 q + 10 q^{3} - 1090 q^{4} + 142 q^{5} + 406 q^{7} + 5432 q^{9} - 1124 q^{12} + 14982 q^{15} + 12734 q^{16} - 9108 q^{17} + 3850 q^{19} - 46896 q^{20} - 49034 q^{21} + 11238 q^{22} + 18792 q^{25} - 64590 q^{26} + 3550 q^{27} - 45542 q^{28} - 31730 q^{29} + 163558 q^{35} - 325266 q^{36} + 91914 q^{41} + 736396 q^{45} + 287148 q^{46} + 479572 q^{48} - 462900 q^{49} + 329932 q^{51} + 8238 q^{53} - 187506 q^{57} + 326182 q^{59} - 970064 q^{60} + 630140 q^{62} + 630508 q^{63} - 1800262 q^{64} - 869200 q^{66} - 319586 q^{68} + 1763840 q^{71} - 2294090 q^{74} + 354736 q^{75} + 247144 q^{76} - 375064 q^{78} + 4702 q^{79} + 1920984 q^{80} - 2435946 q^{81} - 1007672 q^{84} + 864044 q^{85} + 5031110 q^{86} - 1519202 q^{87} + 725994 q^{88} + 2835768 q^{94} - 2396490 q^{95}+O(q^{100}) \) 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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