LMFDB - Embedded newform 59.7.b.c.58.16

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			58.16
Character	$\chi$	$=$	59.58
Dual form			59.7.b.c.58.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.70683i q^{2} -15.6097 q^{3} +41.8457 q^{4} -148.856 q^{5} -73.4721i q^{6} +233.894 q^{7} +498.198i q^{8} -485.338 q^{9} +O(q^{10})$	\(q+4.70683i q^{2} -15.6097 q^{3} +41.8457 q^{4} -148.856 q^{5} -73.4721i q^{6} +233.894 q^{7} +498.198i q^{8} -485.338 q^{9} -700.642i q^{10} -1373.15i q^{11} -653.197 q^{12} -2302.63i q^{13} +1100.90i q^{14} +2323.60 q^{15} +333.190 q^{16} -471.098 q^{17} -2284.41i q^{18} +10168.9 q^{19} -6229.00 q^{20} -3651.01 q^{21} +6463.18 q^{22} -23607.8i q^{23} -7776.71i q^{24} +6533.24 q^{25} +10838.1 q^{26} +18955.4 q^{27} +9787.46 q^{28} +6982.64 q^{29} +10936.8i q^{30} -36434.1i q^{31} +33453.0i q^{32} +21434.4i q^{33} -2217.38i q^{34} -34816.6 q^{35} -20309.3 q^{36} +2538.13i q^{37} +47863.2i q^{38} +35943.3i q^{39} -74160.0i q^{40} -77801.3 q^{41} -17184.7i q^{42} -78215.9i q^{43} -57460.3i q^{44} +72245.8 q^{45} +111118. q^{46} +97824.8i q^{47} -5200.98 q^{48} -62942.6 q^{49} +30750.9i q^{50} +7353.67 q^{51} -96355.1i q^{52} -248101. q^{53} +89220.0i q^{54} +204402. i q^{55} +116526. i q^{56} -158733. q^{57} +32866.1i q^{58} +(-124584. - 163277. i) q^{59} +97232.6 q^{60} +307369. i q^{61} +171489. q^{62} -113518. q^{63} -136133. q^{64} +342761. i q^{65} -100888. q^{66} +45137.6i q^{67} -19713.4 q^{68} +368510. i q^{69} -163876. i q^{70} +591363. q^{71} -241795. i q^{72} -480045. i q^{73} -11946.5 q^{74} -101982. q^{75} +425523. q^{76} -321171. i q^{77} -169179. q^{78} +255744. q^{79} -49597.4 q^{80} +57924.2 q^{81} -366198. i q^{82} -498342. i q^{83} -152779. q^{84} +70125.9 q^{85} +368149. q^{86} -108997. q^{87} +684100. q^{88} -156115. i q^{89} +340049. i q^{90} -538571. i q^{91} -987887. i q^{92} +568724. i q^{93} -460445. q^{94} -1.51370e6 q^{95} -522189. i q^{96} +1.15565e6i q^{97} -296260. i q^{98} +666441. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			4.70683i			0.588354i	0.955751	+	0.294177i	$0.0950456\pi$
$2$			4.70683i			0.588354i	−0.955751	+	0.294177i	$0.904954\pi$
$3$	−15.6097			−0.578136			−0.289068	−	0.957309i	$-0.593345\pi$
$3$	−15.6097			−0.578136			−0.289068	+	0.957309i	$0.593345\pi$
$4$	41.8457			0.653839
$5$	−148.856			−1.19085			−0.595426	−	0.803410i	$-0.703017\pi$
$5$	−148.856			−1.19085			−0.595426	+	0.803410i	$0.703017\pi$
$6$		−	73.4721i		−	0.340149i
$7$	233.894			0.681907			0.340953	−	0.940080i	$-0.389250\pi$
$7$	233.894			0.681907			0.340953	+	0.940080i	$0.389250\pi$
$8$			498.198i			0.973043i
$9$	−485.338			−0.665759
$10$		−	700.642i		−	0.700642i
$11$		−	1373.15i		−	1.03167i	−0.856689	−	0.515833i	$-0.827483\pi$
$11$		−	1373.15i		−	1.03167i	0.856689	−	0.515833i	$-0.172517\pi$
$12$	−653.197			−0.378008
$13$		−	2302.63i		−	1.04808i	−0.851694	−	0.524039i	$-0.824425\pi$
$13$		−	2302.63i		−	1.04808i	0.851694	−	0.524039i	$-0.175575\pi$
$14$			1100.90i			0.401203i
$15$	2323.60			0.688474
$16$	333.190			0.0813451
$17$	−471.098			−0.0958880			−0.0479440	−	0.998850i	$-0.515267\pi$
$17$	−471.098			−0.0958880			−0.0479440	+	0.998850i	$0.515267\pi$
$18$		−	2284.41i		−	0.391702i
$19$	10168.9			1.48256			0.741279	−	0.671197i	$-0.234220\pi$
$19$	10168.9			1.48256			0.741279	+	0.671197i	$0.234220\pi$
$20$	−6229.00			−0.778625
$21$	−3651.01			−0.394234
$22$	6463.18			0.606985
$23$		−	23607.8i		−	1.94032i	−0.242472	−	0.970158i	$-0.577958\pi$
$23$		−	23607.8i		−	1.94032i	0.242472	−	0.970158i	$-0.422042\pi$
$24$		−	7776.71i		−	0.562551i
$25$	6533.24			0.418127
$26$	10838.1			0.616641
$27$	18955.4			0.963035
$28$	9787.46			0.445857
$29$	6982.64			0.286303			0.143151	−	0.989701i	$-0.454276\pi$
$29$	6982.64			0.286303			0.143151	+	0.989701i	$0.454276\pi$
$30$			10936.8i			0.405066i
$31$		−	36434.1i		−	1.22299i	−0.791248	−	0.611496i	$-0.790568\pi$
$31$		−	36434.1i		−	1.22299i	0.791248	−	0.611496i	$-0.209432\pi$
$32$			33453.0i			1.02090i
$33$			21434.4i			0.596443i
$34$		−	2217.38i		−	0.0564161i
$35$	−34816.6			−0.812049
$36$	−20309.3			−0.435300
$37$			2538.13i			0.0501081i	0.999686	+	0.0250541i	$0.00797579\pi$
$37$			2538.13i			0.0501081i	−0.999686	+	0.0250541i	$0.992024\pi$
$38$			47863.2i			0.872269i
$39$			35943.3i			0.605932i
$40$		−	74160.0i		−	1.15875i
$41$	−77801.3			−1.12885			−0.564424	−	0.825485i	$-0.690902\pi$
$41$	−77801.3			−1.12885			−0.564424	+	0.825485i	$0.690902\pi$
$42$		−	17184.7i		−	0.231950i
$43$		−	78215.9i		−	0.983761i	−0.870663	−	0.491881i	$-0.836310\pi$
$43$		−	78215.9i		−	0.983761i	0.870663	−	0.491881i	$-0.163690\pi$
$44$		−	57460.3i		−	0.674544i
$45$	72245.8			0.792820
$46$	111118.			1.14159
$47$			97824.8i			0.942227i	0.882073	+	0.471113i	$0.156148\pi$
$47$			97824.8i			0.942227i	−0.882073	+	0.471113i	$0.843852\pi$
$48$	−5200.98			−0.0470285
$49$	−62942.6			−0.535003
$50$			30750.9i			0.246007i
$51$	7353.67			0.0554363
$52$		−	96355.1i		−	0.685275i
$53$	−248101.			−1.66648			−0.833242	−	0.552908i	$-0.813518\pi$
$53$	−248101.			−1.66648			−0.833242	+	0.552908i	$0.813518\pi$
$54$			89220.0i			0.566606i
$55$			204402.i			1.22856i
$56$			116526.i			0.663525i
$57$	−158733.			−0.857119
$58$			32866.1i			0.168447i
$59$	−124584.	−	163277.i	−0.606605	−	0.795004i
$59$	−124584.	−	163277.i	−0.606605	−	0.795004i
$60$	97232.6			0.450151
$61$			307369.i			1.35416i	0.735909	+	0.677081i	$0.236755\pi$
$61$			307369.i			1.35416i	−0.735909	+	0.677081i	$0.763245\pi$
$62$	171489.			0.719552
$63$	−113518.			−0.453986
$64$	−136133.			−0.519308
$65$			342761.i			1.24811i
$66$	−100888.			−0.350920
$67$			45137.6i			0.150077i	0.997181	+	0.0750385i	$0.0239080\pi$
$67$			45137.6i			0.150077i	−0.997181	+	0.0750385i	$0.976092\pi$
$68$	−19713.4			−0.0626953
$69$			368510.i			1.12177i
$70$		−	163876.i		−	0.477773i
$71$	591363.			1.65226			0.826131	−	0.563478i	$-0.190537\pi$
$71$	591363.			1.65226			0.826131	+	0.563478i	$0.190537\pi$
$72$		−	241795.i		−	0.647813i
$73$		−	480045.i		−	1.23400i	−0.786965	−	0.616998i	$-0.788349\pi$
$73$		−	480045.i		−	1.23400i	0.786965	−	0.616998i	$-0.211651\pi$
$74$	−11946.5			−0.0294813
$75$	−101982.			−0.241734
$76$	425523.			0.969355
$77$		−	321171.i		−	0.703500i
$78$	−169179.			−0.356502
$79$	255744.			0.518710			0.259355	−	0.965782i	$-0.416490\pi$
$79$	255744.			0.518710			0.259355	+	0.965782i	$0.416490\pi$
$80$	−49597.4			−0.0968700
$81$	57924.2			0.108995
$82$		−	366198.i		−	0.664162i
$83$		−	498342.i		−	0.871552i	−0.900055	−	0.435776i	$-0.856474\pi$
$83$		−	498342.i		−	0.871552i	0.900055	−	0.435776i	$-0.143526\pi$
$84$	−152779.			−0.257766
$85$	70125.9			0.114188
$86$	368149.			0.578800
$87$	−108997.			−0.165522
$88$	684100.			1.00386
$89$		−	156115.i		−	0.221449i	−0.993851	−	0.110725i	$-0.964683\pi$
$89$		−	156115.i		−	0.221449i	0.993851	−	0.110725i	$-0.0353172\pi$
$90$			340049.i			0.466459i
$91$		−	538571.i		−	0.714692i
$92$		−	987887.i		−	1.26866i
$93$			568724.i			0.707055i
$94$	−460445.			−0.554363
$95$	−1.51370e6			−1.76551
$96$		−	522189.i		−	0.590220i
$97$			1.15565e6i			1.26623i	0.774058	+	0.633115i	$0.218224\pi$
$97$			1.15565e6i			1.26623i	−0.774058	+	0.633115i	$0.781776\pi$
$98$		−	296260.i		−	0.314772i
$99$			666441.i			0.686841i
$100$	273388.			0.273388
$101$		−	85522.4i		−	0.0830072i	−0.999138	−	0.0415036i	$-0.986785\pi$
$101$		−	85522.4i		−	0.0830072i	0.999138	−	0.0415036i	$-0.0132148\pi$
$102$			34612.5i			0.0326162i
$103$			80369.0i			0.0735490i	0.999324	+	0.0367745i	$0.0117083\pi$
$103$			80369.0i			0.0735490i	−0.999324	+	0.0367745i	$0.988292\pi$
$104$	1.14717e6			1.01983
$105$	543476.			0.469475
$106$		−	1.16777e6i		−	0.980483i
$107$	−340748.			−0.278152			−0.139076	−	0.990282i	$-0.544413\pi$
$107$	−340748.			−0.278152			−0.139076	+	0.990282i	$0.544413\pi$
$108$	793203.			0.629670
$109$		−	479154.i		−	0.369995i	−0.982739	−	0.184997i	$-0.940772\pi$
$109$		−	479154.i		−	0.369995i	0.982739	−	0.184997i	$-0.0592277\pi$
$110$	−962085.			−0.722829
$111$		−	39619.3i		−	0.0289693i
$112$	77931.0			0.0554698
$113$		−	2.18698e6i		−	1.51569i	−0.652437	−	0.757843i	$-0.726253\pi$
$113$		−	2.18698e6i		−	1.51569i	0.652437	−	0.757843i	$-0.273747\pi$
$114$		−	747128.i		−	0.504290i
$115$			3.51418e6i			2.31063i
$116$	292193.			0.187196
$117$			1.11755e6i			0.697768i
$118$	768518.	−	586396.i	0.467744	−	0.356898i
$119$	−110187.			−0.0653866
$120$			1.15761e6i			0.669915i
$121$	−113973.			−0.0643345
$122$	−1.44673e6			−0.796727
$123$	1.21445e6			0.652627
$124$		−	1.52461e6i		−	0.799640i
$125$	1.35337e6			0.692924
$126$		−	534309.i		−	0.267104i
$127$	−843685.			−0.411879			−0.205939	−	0.978565i	$-0.566025\pi$
$127$	−843685.			−0.411879			−0.205939	+	0.978565i	$0.566025\pi$
$128$			1.50023e6i			0.715366i
$129$			1.22092e6i			0.568747i
$130$	−1.61332e6			−0.734328
$131$			3.95617e6i			1.75979i	0.475168	+	0.879895i	$0.342387\pi$
$131$			3.95617e6i			1.75979i	−0.475168	+	0.879895i	$0.657613\pi$
$132$			896936.i			0.389978i
$133$	2.37844e6			1.01097
$134$	−212455.			−0.0882984
$135$	−2.82164e6			−1.14683
$136$		−	234700.i		−	0.0933032i
$137$	−2.94919e6			−1.14694			−0.573471	−	0.819226i	$-0.694403\pi$
$137$	−2.94919e6			−1.14694			−0.573471	+	0.819226i	$0.694403\pi$
$138$	−1.73452e6			−0.659996
$139$	2.30160e6			0.857008			0.428504	−	0.903540i	$-0.359041\pi$
$139$	2.30160e6			0.857008			0.428504	+	0.903540i	$0.359041\pi$
$140$	−1.45693e6			−0.530950
$141$		−	1.52701e6i		−	0.544735i
$142$			2.78345e6i			0.972116i
$143$	−3.16185e6			−1.08127
$144$	−161710.			−0.0541563
$145$	−1.03941e6			−0.340944
$146$	2.25949e6			0.726026
$147$	982513.			0.309305
$148$			106210.i			0.0327627i
$149$		−	2.73708e6i		−	0.827426i	−0.910407	−	0.413713i	$-0.864232\pi$
$149$		−	2.73708e6i		−	0.827426i	0.910407	−	0.413713i	$-0.135768\pi$
$150$		−	480011.i		−	0.142225i
$151$		−	4.26973e6i		−	1.24014i	−0.784548	−	0.620068i	$-0.787105\pi$
$151$		−	4.26973e6i		−	1.24014i	0.784548	−	0.620068i	$-0.212895\pi$
$152$			5.06611e6i			1.44259i
$153$	228642.			0.0638383
$154$	1.51170e6			0.413907
$155$			5.42346e6i			1.45640i
$156$			1.50407e6i			0.396182i
$157$		−	881525.i		−	0.227791i	−0.993493	−	0.113895i	$-0.963667\pi$
$157$		−	881525.i		−	0.227791i	0.993493	−	0.113895i	$-0.0363328\pi$
$158$			1.20375e6i			0.305185i
$159$	3.87278e6			0.963454
$160$		−	4.97969e6i		−	1.21574i
$161$		−	5.52173e6i		−	1.32311i
$162$			272639.i			0.0641274i
$163$	−6.93212e6			−1.60068			−0.800338	−	0.599549i	$-0.795347\pi$
$163$	−6.93212e6			−1.60068			−0.800338	+	0.599549i	$0.795347\pi$
$164$	−3.25565e6			−0.738085
$165$		−	3.19064e6i		−	0.710275i
$166$	2.34561e6			0.512781
$167$	3.62470e6			0.778256			0.389128	−	0.921184i	$-0.372776\pi$
$167$	3.62470e6			0.778256			0.389128	+	0.921184i	$0.372776\pi$
$168$		−	1.81892e6i		−	0.383607i
$169$	−475289.			−0.0984686
$170$			330071.i			0.0671832i
$171$	−4.93534e6			−0.987027
$172$		−	3.27300e6i		−	0.643222i
$173$			3.10203e6i			0.599111i	0.954079	+	0.299555i	$0.0968383\pi$
$173$			3.10203e6i			0.599111i	−0.954079	+	0.299555i	$0.903162\pi$
$174$		−	513029.i		−	0.0973855i
$175$	1.52808e6			0.285124
$176$		−	457518.i		−	0.0839210i
$177$	1.94471e6	+	2.54870e6i	0.350700	+	0.459620i
$178$	734807.			0.130291
$179$			5.58080e6i			0.973055i	0.873665	+	0.486527i	$0.161737\pi$
$179$			5.58080e6i			0.973055i	−0.873665	+	0.486527i	$0.838263\pi$
$180$	3.02318e6			0.518377
$181$	−1.42891e6			−0.240973			−0.120487	−	0.992715i	$-0.538446\pi$
$181$	−1.42891e6			−0.240973			−0.120487	+	0.992715i	$0.538446\pi$
$182$	2.53496e6			0.420492
$183$		−	4.79793e6i		−	0.782889i
$184$	1.17614e7			1.88801
$185$		−	377817.i		−	0.0596713i
$186$	−2.67689e6			−0.415999
$187$			646886.i			0.0989244i
$188$			4.09355e6i			0.616065i
$189$	4.43356e6			0.656700
$190$		−	7.12474e6i		−	1.03874i
$191$		−	9.34395e6i		−	1.34101i	−0.741907	−	0.670503i	$-0.766079\pi$
$191$		−	9.34395e6i		−	1.34101i	0.741907	−	0.670503i	$-0.233921\pi$
$192$	2.12500e6			0.300230
$193$	1.30930e7			1.82124			0.910621	−	0.413243i	$-0.135604\pi$
$193$	1.30930e7			1.82124			0.910621	+	0.413243i	$0.135604\pi$
$194$	−5.43947e6			−0.744992
$195$		−	5.35038e6i		−	0.721574i
$196$	−2.63388e6			−0.349806
$197$	−1.50820e6			−0.197270			−0.0986349	−	0.995124i	$-0.531448\pi$
$197$	−1.50820e6			−0.197270			−0.0986349	+	0.995124i	$0.531448\pi$
$198$	−3.13683e6			−0.404106
$199$	−655081.			−0.0831257			−0.0415629	−	0.999136i	$-0.513234\pi$
$199$	−655081.			−0.0831257			−0.0415629	+	0.999136i	$0.513234\pi$
$200$			3.25485e6i			0.406856i
$201$		−	704583.i		−	0.0867648i
$202$	402540.			0.0488376
$203$	1.63320e6			0.195232
$204$	307720.			0.0362464
$205$	1.15812e7			1.34429
$206$	−378283.			−0.0432729
$207$			1.14578e7i			1.29178i
$208$		−	767212.i		−	0.0852561i
$209$		−	1.39633e7i		−	1.52950i
$210$			2.55805e6i			0.276217i
$211$		−	1.34310e7i		−	1.42975i	−0.699252	−	0.714875i	$-0.746483\pi$
$211$		−	1.34310e7i		−	1.42975i	0.699252	−	0.714875i	$-0.253517\pi$
$212$	−1.03820e7			−1.08961
$213$	−9.23098e6			−0.955232
$214$		−	1.60384e6i		−	0.163652i
$215$			1.16429e7i			1.17151i
$216$			9.44355e6i			0.937075i
$217$		−	8.52172e6i		−	0.833966i
$218$	2.25530e6			0.217688
$219$			7.49334e6i			0.713416i
$220$			8.55334e6i			0.803281i
$221$			1.08476e6i			0.100498i
$222$	186481.			0.0170442
$223$	−1.53029e7			−1.37994			−0.689970	−	0.723838i	$-0.742376\pi$
$223$	−1.53029e7			−1.37994			−0.689970	+	0.723838i	$0.742376\pi$
$224$			7.82444e6i			0.696161i
$225$	−3.17083e6			−0.278372
$226$	1.02937e7			0.891760
$227$			1.44798e7i			1.23790i	0.785431	+	0.618950i	$0.212442\pi$
$227$			1.44798e7i			1.23790i	−0.785431	+	0.618950i	$0.787558\pi$
$228$	−6.64228e6			−0.560418
$229$		−	5.12741e6i		−	0.426965i	−0.976947	−	0.213482i	$-0.931519\pi$
$229$		−	5.12741e6i		−	0.426965i	0.976947	−	0.213482i	$-0.0684806\pi$
$230$	−1.65407e7			−1.35947
$231$			5.01337e6i			0.406718i
$232$			3.47874e6i			0.278585i
$233$		−	984775.i		−	0.0778519i	−0.999242	−	0.0389260i	$-0.987606\pi$
$233$		−	984775.i		−	0.0778519i	0.999242	−	0.0389260i	$-0.0123937\pi$
$234$	−5.26014e6			−0.410535
$235$		−	1.45618e7i		−	1.12205i
$236$	−5.21330e6	−	6.83244e6i	−0.396622	−	0.519805i
$237$	−3.99208e6			−0.299885
$238$		−	518631.i		−	0.0384705i
$239$	1.59644e7			1.16939			0.584695	−	0.811253i	$-0.301214\pi$
$239$	1.59644e7			1.16939			0.584695	+	0.811253i	$0.301214\pi$
$240$	774199.			0.0560040
$241$	1.69765e7			1.21282			0.606410	−	0.795152i	$-0.292609\pi$
$241$	1.69765e7			1.21282			0.606410	+	0.795152i	$0.292609\pi$
$242$		−	536450.i		−	0.0378515i
$243$	−1.47227e7			−1.02605
$244$			1.28621e7i			0.885404i
$245$	9.36941e6			0.637110
$246$			5.71622e6i			0.383976i
$247$		−	2.34151e7i		−	1.55384i
$248$	1.81514e7			1.19002
$249$			7.77895e6i			0.503875i
$250$			6.37008e6i			0.407685i
$251$	6.21482e6			0.393013			0.196507	−	0.980503i	$-0.437040\pi$
$251$	6.21482e6			0.393013			0.196507	+	0.980503i	$0.437040\pi$
$252$	−4.75023e6			−0.296834
$253$	−3.24170e7			−2.00176
$254$		−	3.97109e6i		−	0.242330i
$255$	−1.09464e6			−0.0660163
$256$	−1.57739e7			−0.940196
$257$	−1.25694e7			−0.740481			−0.370241	−	0.928936i	$-0.620725\pi$
$257$	−1.25694e7			−0.740481			−0.370241	+	0.928936i	$0.620725\pi$
$258$	−5.74668e6			−0.334625
$259$			593653.i			0.0341691i
$260$			1.43431e7i			0.816061i
$261$	−3.38894e6			−0.190609
$262$	−1.86210e7			−1.03538
$263$	1.96139e7			1.07819			0.539096	−	0.842245i	$-0.318766\pi$
$263$	1.96139e7			1.07819			0.539096	+	0.842245i	$0.318766\pi$
$264$	−1.06786e7			−0.580365
$265$	3.69315e7			1.98454
$266$			1.11949e7i			0.594806i
$267$			2.43690e6i			0.128028i
$268$			1.88882e6i			0.0981262i
$269$			1.86852e7i			0.959931i	0.877287	+	0.479966i	$0.159351\pi$
$269$			1.86852e7i			0.959931i	−0.877287	+	0.479966i	$0.840649\pi$
$270$		−	1.32810e7i		−	0.674743i
$271$	8.28796e6			0.416428			0.208214	−	0.978083i	$-0.433235\pi$
$271$	8.28796e6			0.416428			0.208214	+	0.978083i	$0.433235\pi$
$272$	−156965.			−0.00780002
$273$			8.40691e6i			0.413189i
$274$		−	1.38814e7i		−	0.674808i
$275$		−	8.97110e6i		−	0.431368i
$276$			1.54206e7i			0.733455i
$277$	1.80384e6			0.0848707			0.0424354	−	0.999099i	$-0.486488\pi$
$277$	1.80384e6			0.0848707			0.0424354	+	0.999099i	$0.486488\pi$
$278$			1.08332e7i			0.504224i
$279$			1.76829e7i			0.814218i
$280$		−	1.73456e7i		−	0.790159i
$281$	2.16137e7			0.974114			0.487057	−	0.873370i	$-0.338070\pi$
$281$	2.16137e7			0.974114			0.487057	+	0.873370i	$0.338070\pi$
$282$	7.18739e6			0.320497
$283$			2.55194e7i			1.12593i	0.826481	+	0.562964i	$0.190339\pi$
$283$			2.55194e7i			1.12593i	−0.826481	+	0.562964i	$0.809661\pi$
$284$	2.47460e7			1.08031
$285$	2.36284e7			1.02070
$286$		−	1.48823e7i		−	0.636168i
$287$	−1.81973e7			−0.769768
$288$		−	1.62360e7i		−	0.679676i
$289$	−2.39156e7			−0.990805
$290$		−	4.89233e6i		−	0.200596i
$291$		−	1.80394e7i		−	0.732053i
$292$		−	2.00878e7i		−	0.806834i
$293$	−1.57283e7			−0.625286			−0.312643	−	0.949871i	$-0.601214\pi$
$293$	−1.57283e7			−0.625286			−0.312643	+	0.949871i	$0.601214\pi$
$294$			4.62453e6i			0.181981i
$295$	1.85451e7	+	2.43048e7i	0.722376	+	0.946731i
$296$	−1.26449e6			−0.0487574
$297$		−	2.60286e7i		−	0.993530i
$298$	1.28830e7			0.486819
$299$	−5.43601e7			−2.03360
$300$	−4.26749e6			−0.158055
$301$		−	1.82942e7i		−	0.670833i
$302$	2.00969e7			0.729639
$303$			1.33498e6i			0.0479894i
$304$	3.38816e6			0.120599
$305$		−	4.57539e7i		−	1.61261i
$306$			1.07618e6i			0.0375595i
$307$	4.99566e7			1.72654			0.863272	−	0.504739i	$-0.168411\pi$
$307$	4.99566e7			1.72654			0.863272	+	0.504739i	$0.168411\pi$
$308$		−	1.34396e7i		−	0.459976i
$309$		−	1.25453e6i		−	0.0425213i
$310$	−2.55273e7			−0.856880
$311$	1.64419e6			0.0546602			0.0273301	−	0.999626i	$-0.491299\pi$
$311$	1.64419e6			0.0546602			0.0273301	+	0.999626i	$0.491299\pi$
$312$	−1.79069e7			−0.589598
$313$			3.08929e7i			1.00746i	0.863862	+	0.503728i	$0.168039\pi$
$313$			3.08929e7i			1.00746i	−0.863862	+	0.503728i	$0.831961\pi$
$314$	4.14919e6			0.134022
$315$	1.68978e7			0.540629
$316$	1.07018e7			0.339153
$317$	−2.19714e7			−0.689730			−0.344865	−	0.938652i	$-0.612075\pi$
$317$	−2.19714e7			−0.689730			−0.344865	+	0.938652i	$0.612075\pi$
$318$			1.82285e7i			0.566852i
$319$		−	9.58819e6i		−	0.295369i
$320$	2.02643e7			0.618418
$321$	5.31896e6			0.160810
$322$	2.59899e7			0.778460
$323$	−4.79053e6			−0.142159
$324$	2.42388e6			0.0712649
$325$		−	1.50436e7i		−	0.438230i
$326$		−	3.26283e7i		−	0.941764i
$327$			7.47944e6i			0.213907i
$328$		−	3.87605e7i		−	1.09842i
$329$			2.28806e7i			0.642511i
$330$	1.50178e7			0.417893
$331$	−1.48661e6			−0.0409933			−0.0204966	−	0.999790i	$-0.506525\pi$
$331$	−1.48661e6			−0.0409933			−0.0204966	+	0.999790i	$0.506525\pi$
$332$		−	2.08535e7i		−	0.569855i
$333$		−	1.23185e6i		−	0.0333599i
$334$			1.70609e7i			0.457890i
$335$		−	6.71902e6i		−	0.178719i
$336$	−1.21648e6			−0.0320691
$337$		−	4.18544e7i		−	1.09358i	−0.837269	−	0.546791i	$-0.815849\pi$
$337$		−	4.18544e7i		−	1.09358i	0.837269	−	0.546791i	$-0.184151\pi$
$338$		−	2.23711e6i		−	0.0579344i
$339$			3.41380e7i			0.876272i
$340$	2.93447e6			0.0746608
$341$	−5.00294e7			−1.26172
$342$		−	2.32298e7i		−	0.580721i
$343$	−4.22393e7			−1.04673
$344$	3.89670e7			0.957242
$345$		−	5.48551e7i		−	1.33586i
$346$	−1.46007e7			−0.352489
$347$			3.48011e7i			0.832923i	0.909153	+	0.416461i	$0.136730\pi$
$347$			3.48011e7i			0.832923i	−0.909153	+	0.416461i	$0.863270\pi$
$348$	−4.56104e6			−0.108225
$349$			6.83832e7i			1.60869i	0.594161	+	0.804346i	$0.297484\pi$
$349$			6.83832e7i			1.60869i	−0.594161	+	0.804346i	$0.702516\pi$
$350$			7.19244e6i			0.167754i
$351$		−	4.36473e7i		−	1.00934i
$352$	4.59358e7			1.05323
$353$			4.21700e7i			0.958693i	0.877626	+	0.479347i	$0.159126\pi$
$353$			4.21700e7i			0.958693i	−0.877626	+	0.479347i	$0.840874\pi$
$354$	−1.19963e7	+	9.15344e6i	−0.270419	+	0.206336i
$355$	−8.80282e7			−1.96760
$356$		−	6.53274e6i		−	0.144792i
$357$	1.71998e6			0.0378023
$358$	−2.62679e7			−0.572501
$359$	5.22516e7			1.12932			0.564659	−	0.825324i	$-0.309008\pi$
$359$	5.22516e7			1.12932			0.564659	+	0.825324i	$0.309008\pi$
$360$			3.59927e7i			0.771449i
$361$	5.63599e7			1.19798
$362$		−	6.72564e6i		−	0.141778i
$363$	1.77907e6			0.0371941
$364$		−	2.25369e7i		−	0.467293i
$365$			7.14578e7i			1.46950i
$366$	2.25830e7			0.460616
$367$			4.11016e7i			0.831496i	0.909480	+	0.415748i	$0.136480\pi$
$367$			4.11016e7i			0.831496i	−0.909480	+	0.415748i	$0.863520\pi$
$368$		−	7.86589e6i		−	0.157835i
$369$	3.77600e7			0.751541
$370$	1.77832e6			0.0351079
$371$	−5.80294e7			−1.13639
$372$			2.37987e7i			0.462300i
$373$	1.63657e7			0.315360			0.157680	−	0.987490i	$-0.449598\pi$
$373$	1.63657e7			0.315360			0.157680	+	0.987490i	$0.449598\pi$
$374$	−3.04479e6			−0.0582026
$375$	−2.11256e7			−0.400604
$376$	−4.87361e7			−0.916827
$377$		−	1.60784e7i		−	0.300068i
$378$			2.08680e7i			0.386372i
$379$	7.61381e6			0.139857			0.0699285	−	0.997552i	$-0.477723\pi$
$379$	7.61381e6			0.139857			0.0699285	+	0.997552i	$0.477723\pi$
$380$	−6.33419e7			−1.15436
$381$	1.31696e7			0.238122
$382$	4.39804e7			0.788986
$383$	−6.00438e7			−1.06874			−0.534370	−	0.845251i	$-0.679451\pi$
$383$	−6.00438e7			−1.06874			−0.534370	+	0.845251i	$0.679451\pi$
$384$		−	2.34181e7i		−	0.413579i
$385$			4.78083e7i			0.837764i
$386$			6.16266e7i			1.07154i
$387$			3.79612e7i			0.654948i
$388$			4.83592e7i			0.827911i
$389$	3.81989e7			0.648936			0.324468	−	0.945897i	$-0.394815\pi$
$389$	3.81989e7			0.648936			0.324468	+	0.945897i	$0.394815\pi$
$390$	2.51834e7			0.424541
$391$			1.11216e7i			0.186053i
$392$		−	3.13579e7i		−	0.520581i
$393$		−	6.17544e7i		−	1.01740i
$394$		−	7.09885e6i		−	0.116064i
$395$	−3.80692e7			−0.617707
$396$			2.78877e7i			0.449084i
$397$			5.69576e7i			0.910291i	0.890417	+	0.455146i	$0.150413\pi$
$397$			5.69576e7i			0.910291i	−0.890417	+	0.455146i	$0.849587\pi$
$398$		−	3.08336e6i		−	0.0489074i
$399$	−3.71266e7			−0.584475
$400$	2.17681e6			0.0340126
$401$		−	4.25570e7i		−	0.659991i	−0.943982	−	0.329996i	$-0.892953\pi$
$401$		−	4.25570e7i		−	0.659991i	0.943982	−	0.329996i	$-0.107047\pi$
$402$	3.31635e6			0.0510485
$403$	−8.38943e7			−1.28179
$404$		−	3.57875e6i		−	0.0542734i
$405$	−8.62239e6			−0.129796
$406$			7.68719e6i			0.114865i
$407$	3.48522e6			0.0516948
$408$			3.66359e6i			0.0539419i
$409$		−	1.11089e8i		−	1.62369i	−0.583875	−	0.811843i	$-0.698464\pi$
$409$		−	1.11089e8i		−	1.62369i	0.583875	−	0.811843i	$-0.301536\pi$
$410$			5.45109e7i			0.790918i
$411$	4.60359e7			0.663088
$412$			3.36310e6i			0.0480892i
$413$	−2.91394e7	−	3.81895e7i	−0.413648	−	0.542118i
$414$	−5.39299e7			−0.760026
$415$			7.41814e7i			1.03789i
$416$	7.70297e7			1.06999
$417$	−3.59272e7			−0.495467
$418$	6.57232e7			0.899890
$419$			7.22123e7i			0.981678i	0.871250	+	0.490839i	$0.163310\pi$
$419$			7.22123e7i			0.981678i	−0.871250	+	0.490839i	$0.836690\pi$
$420$	2.27421e7			0.306961
$421$		−	8.66760e6i		−	0.116159i	−0.998312	−	0.0580795i	$-0.981502\pi$
$421$		−	8.66760e6i		−	0.116159i	0.998312	−	0.0580795i	$-0.0184977\pi$
$422$	6.32174e7			0.841200
$423$		−	4.74781e7i		−	0.627296i
$424$		−	1.23604e8i		−	1.62156i
$425$	−3.07779e6			−0.0400934
$426$		−	4.34487e7i		−	0.562015i
$427$			7.18918e7i			0.923412i
$428$	−1.42588e7			−0.181867
$429$	4.93554e7			0.625119
$430$	−5.48014e7			−0.689265
$431$		−	4.31647e7i		−	0.539134i	−0.962982	−	0.269567i	$-0.913119\pi$
$431$		−	4.31647e7i		−	0.539134i	0.962982	−	0.269567i	$-0.0868806\pi$
$432$	6.31575e6			0.0783382
$433$	−2.78962e6			−0.0343622			−0.0171811	−	0.999852i	$-0.505469\pi$
$433$	−2.78962e6			−0.0343622			−0.0171811	+	0.999852i	$0.505469\pi$
$434$	4.01103e7			0.490667
$435$	1.62248e7			0.197112
$436$		−	2.00506e7i		−	0.241917i
$437$		−	2.40065e8i		−	2.87663i
$438$	−3.52699e7			−0.419742
$439$	3.43354e7			0.405835			0.202917	−	0.979196i	$-0.434958\pi$
$439$	3.43354e7			0.405835			0.202917	+	0.979196i	$0.434958\pi$
$440$	−1.01833e8			−1.19544
$441$	3.05485e7			0.356183
$442$	−5.10580e6			−0.0591285
$443$			1.43492e7i			0.165051i	0.996589	+	0.0825254i	$0.0262985\pi$
$443$			1.43492e7i			0.165051i	−0.996589	+	0.0825254i	$0.973701\pi$
$444$		−	1.65790e6i		−	0.0189413i
$445$			2.32387e7i			0.263713i
$446$		−	7.20284e7i		−	0.811893i
$447$			4.27249e7i			0.478364i
$448$	−3.18408e7			−0.354119
$449$	8.20882e7			0.906863			0.453432	−	0.891291i	$-0.350200\pi$
$449$	8.20882e7			0.906863			0.453432	+	0.891291i	$0.350200\pi$
$450$		−	1.49246e7i		−	0.163781i
$451$			1.06833e8i			1.16459i
$452$		−	9.15157e7i		−	0.991015i
$453$			6.66490e7i			0.716966i
$454$	−6.81541e7			−0.728323
$455$			8.01697e7i			0.851092i
$456$		−	7.90803e7i		−	0.834014i
$457$		−	1.21706e8i		−	1.27515i	−0.770388	−	0.637576i	$-0.779937\pi$
$457$		−	1.21706e8i		−	1.27515i	0.770388	−	0.637576i	$-0.220063\pi$
$458$	2.41339e7			0.251206
$459$	−8.92985e6			−0.0923434
$460$			1.47053e8i			1.51078i
$461$	3.78252e7			0.386081			0.193040	−	0.981191i	$-0.438165\pi$
$461$	3.78252e7			0.386081			0.193040	+	0.981191i	$0.438165\pi$
$462$	−2.35971e7			−0.239294
$463$			1.51476e8i			1.52616i	0.646304	+	0.763080i	$0.276314\pi$
$463$			1.51476e8i			1.52616i	−0.646304	+	0.763080i	$0.723686\pi$
$464$	2.32654e6			0.0232893
$465$		−	8.46583e7i		−	0.841997i
$466$	4.63517e6			0.0458045
$467$		−	9.91328e7i		−	0.973344i	−0.873585	−	0.486672i	$-0.838211\pi$
$467$		−	9.91328e7i		−	0.973344i	0.873585	−	0.486672i	$-0.161789\pi$
$468$			4.67649e7i			0.456228i
$469$			1.05574e7i			0.102338i
$470$	6.85402e7			0.660164
$471$			1.37603e7i			0.131694i
$472$	8.13443e7	−	6.20675e7i	0.773573	−	0.590253i
$473$	−1.07402e8			−1.01491
$474$		−	1.87901e7i		−	0.176439i
$475$	6.64356e7			0.619898
$476$	−4.61085e6			−0.0427524
$477$	1.20413e8			1.10948
$478$			7.51418e7i			0.688015i
$479$	7.75512e7			0.705638			0.352819	−	0.935692i	$-0.385223\pi$
$479$	7.75512e7			0.705638			0.352819	+	0.935692i	$0.385223\pi$
$480$			7.77312e7i			0.702865i
$481$	5.84436e6			0.0525172
$482$			7.99055e7i			0.713568i
$483$			8.61923e7i			0.764940i
$484$	−4.76926e6			−0.0420644
$485$		−	1.72027e8i		−	1.50789i
$486$		−	6.92972e7i		−	0.603680i
$487$	−1.90488e8			−1.64923			−0.824616	−	0.565693i	$-0.808609\pi$
$487$	−1.90488e8			−1.64923			−0.824616	+	0.565693i	$0.808609\pi$
$488$	−1.53131e8			−1.31766
$489$	1.08208e8			0.925408
$490$			4.41003e7i			0.374846i
$491$	9.91577e6			0.0837687			0.0418844	−	0.999122i	$-0.486664\pi$
$491$	9.91577e6			0.0837687			0.0418844	+	0.999122i	$0.486664\pi$
$492$	5.08196e7			0.426713
$493$	−3.28950e6			−0.0274530
$494$	1.10211e8			0.914207
$495$		−	9.92041e7i		−	0.817926i
$496$		−	1.21395e7i		−	0.0994844i
$497$	1.38316e8			1.12669
$498$	−3.66142e7			−0.296457
$499$	−2.15355e7			−0.173322			−0.0866608	−	0.996238i	$-0.527620\pi$
$499$	−2.15355e7			−0.173322			−0.0866608	+	0.996238i	$0.527620\pi$
$500$	5.66326e7			0.453061
$501$	−5.65803e7			−0.449938
$502$			2.92521e7i			0.231231i
$503$		−	9.03968e7i		−	0.710312i	−0.934807	−	0.355156i	$-0.884428\pi$
$503$		−	9.03968e7i		−	0.710312i	0.934807	−	0.355156i	$-0.115572\pi$
$504$		−	5.65543e7i		−	0.441748i
$505$			1.27306e7i			0.0988493i
$506$		−	1.52582e8i		−	1.17774i
$507$	7.41910e6			0.0569282
$508$	−3.53046e7			−0.269302
$509$			2.49268e6i			0.0189022i	0.999955	+	0.00945111i	$0.00300843\pi$
$509$			2.49268e6i			0.0189022i	−0.999955	+	0.00945111i	$0.996992\pi$
$510$		−	5.15230e6i		−	0.0388410i
$511$		−	1.12280e8i		−	0.841469i
$512$			2.17698e7i			0.162198i
$513$	1.92755e8			1.42775
$514$		−	5.91619e7i		−	0.435665i
$515$		−	1.19634e7i		−	0.0875859i
$516$			5.10904e7i			0.371869i
$517$	1.34328e8			0.972063
$518$	−2.79422e6			−0.0201035
$519$		−	4.84216e7i		−	0.346367i
$520$	−1.70763e8			−1.21446
$521$	−4.22206e6			−0.0298546			−0.0149273	−	0.999889i	$-0.504752\pi$
$521$	−4.22206e6			−0.0298546			−0.0149273	+	0.999889i	$0.504752\pi$
$522$		−	1.59512e7i		−	0.112145i
$523$	8.42867e7			0.589188			0.294594	−	0.955622i	$-0.404816\pi$
$523$	8.42867e7			0.589188			0.294594	+	0.955622i	$0.404816\pi$
$524$			1.65549e8i			1.15062i
$525$	−2.38529e7			−0.164840
$526$			9.23192e7i			0.634358i
$527$			1.71640e7i			0.117270i
$528$			7.14171e6i			0.0485177i
$529$	−4.09294e8			−2.76483
$530$			1.73830e8i			1.16761i
$531$	6.04653e7	+	7.92446e7i	0.403853	+	0.529281i
$532$	9.95274e7			0.661009
$533$			1.79147e8i			1.18312i
$534$	−1.14701e7			−0.0753256
$535$	5.07225e7			0.331238
$536$	−2.24875e7			−0.146031
$537$		−	8.71144e7i		−	0.562558i
$538$	−8.79480e7			−0.564780
$539$			8.64295e7i			0.551945i
$540$	−1.18073e8			−0.749843
$541$			9.81644e7i			0.619958i	0.950743	+	0.309979i	$0.100322\pi$
$541$			9.81644e7i			0.619958i	−0.950743	+	0.309979i	$0.899678\pi$
$542$			3.90101e7i			0.245007i
$543$	2.23048e7			0.139315
$544$		−	1.57596e7i		−	0.0978923i
$545$			7.13252e7i			0.440609i
$546$	−3.95699e7			−0.243101
$547$	−3.07202e8			−1.87699			−0.938496	−	0.345291i	$-0.887780\pi$
$547$	−3.07202e8			−1.87699			−0.938496	+	0.345291i	$0.887780\pi$
$548$	−1.23411e8			−0.749916
$549$		−	1.49178e8i		−	0.901546i
$550$	4.22255e7			0.253797
$551$	7.10055e7			0.424460
$552$	−1.83591e8			−1.09153
$553$	5.98171e7			0.353712
$554$			8.49036e6i			0.0499341i
$555$			5.89759e6i			0.0344981i
$556$	9.63120e7			0.560346
$557$	−8.05711e7			−0.466245			−0.233122	−	0.972447i	$-0.574894\pi$
$557$	−8.05711e7			−0.466245			−0.233122	+	0.972447i	$0.574894\pi$
$558$	−8.32304e7			−0.479048
$559$	−1.80102e8			−1.03106
$560$	−1.16005e7			−0.0660563
$561$		−	1.00977e7i		−	0.0571917i
$562$			1.01732e8i			0.573124i
$563$		−	6.98753e7i		−	0.391560i	−0.980648	−	0.195780i	$-0.937276\pi$
$563$		−	6.98753e7i		−	0.391560i	0.980648	−	0.195780i	$-0.0627239\pi$
$564$		−	6.38989e7i		−	0.356169i
$565$			3.25546e8i			1.80496i
$566$	−1.20115e8			−0.662445
$567$	1.35481e7			0.0743241
$568$			2.94616e8i			1.60772i
$569$			1.10576e8i			0.600238i	0.953902	+	0.300119i	$0.0970264\pi$
$569$			1.10576e8i			0.600238i	−0.953902	+	0.300119i	$0.902974\pi$
$570$			1.11215e8i			0.600534i
$571$		−	2.10473e7i		−	0.113054i	−0.998401	−	0.0565272i	$-0.981997\pi$
$571$		−	2.10473e7i		−	0.113054i	0.998401	−	0.0565272i	$-0.0180028\pi$
$572$	−1.32310e8			−0.706975
$573$			1.45856e8i			0.775283i
$574$		−	8.56514e7i		−	0.452897i
$575$		−	1.54236e8i		−	0.811299i
$576$	6.60708e7			0.345734
$577$	2.99367e8			1.55839			0.779197	−	0.626779i	$-0.215627\pi$
$577$	2.99367e8			1.55839			0.779197	+	0.626779i	$0.215627\pi$
$578$		−	1.12567e8i		−	0.582945i
$579$	−2.04377e8			−1.05292
$580$	−4.34949e7			−0.222923
$581$		−	1.16559e8i		−	0.594317i
$582$	8.49083e7			0.430706
$583$			3.40679e8i			1.71926i
$584$	2.39158e8			1.20073
$585$		−	1.66355e8i		−	0.830938i
$586$		−	7.40305e7i		−	0.367890i
$587$		−	3.39071e8i		−	1.67640i	−0.545366	−	0.838198i	$-0.683609\pi$
$587$		−	3.39071e8i		−	1.67640i	0.545366	−	0.838198i	$-0.316391\pi$
$588$	4.11140e7			0.202235
$589$		−	3.70494e8i		−	1.81316i
$590$	−1.14399e8	+	8.72888e7i	−0.557013	+	0.425013i
$591$	2.35425e7			0.114049
$592$			845678.i			0.00407605i
$593$	1.60443e8			0.769408			0.384704	−	0.923040i	$-0.374303\pi$
$593$	1.60443e8			0.769408			0.384704	+	0.923040i	$0.374303\pi$
$594$	1.22512e8			0.584548
$595$	1.64020e7			0.0778658
$596$		−	1.14535e8i		−	0.541003i
$597$	1.02256e7			0.0480579
$598$		−	2.55864e8i		−	1.19648i
$599$	1.49626e8			0.696189			0.348095	−	0.937459i	$-0.386829\pi$
$599$	1.49626e8			0.696189			0.348095	+	0.937459i	$0.386829\pi$
$600$		−	5.08071e7i		−	0.235218i
$601$			1.68119e7i			0.0774451i	0.999250	+	0.0387226i	$0.0123289\pi$
$601$			1.68119e7i			0.0774451i	−0.999250	+	0.0387226i	$0.987671\pi$
$602$	8.61079e7			0.394688
$603$		−	2.19070e7i		−	0.0999151i
$604$		−	1.78670e8i		−	0.810849i
$605$	1.69655e7			0.0766129
$606$	−6.28351e6			−0.0282348
$607$	2.95183e7			0.131985			0.0659925	−	0.997820i	$-0.478979\pi$
$607$	2.95183e7			0.131985			0.0659925	+	0.997820i	$0.478979\pi$
$608$			3.40179e8i			1.51355i
$609$	−2.54936e7			−0.112870
$610$	2.15356e8			0.948783
$611$	2.25254e8			0.987527
$612$	9.56768e6			0.0417400
$613$			6.71286e7i			0.291425i	0.989327	+	0.145712i	$0.0465474\pi$
$613$			6.71286e7i			0.291425i	−0.989327	+	0.145712i	$0.953453\pi$
$614$			2.35137e8i			1.01582i
$615$	−1.80779e8			−0.777182
$616$	1.60007e8			0.684536
$617$	−3.12412e8			−1.33006			−0.665031	−	0.746815i	$-0.731582\pi$
$617$	−3.12412e8			−1.33006			−0.665031	+	0.746815i	$0.731582\pi$
$618$	5.90487e6			0.0250176
$619$	2.42354e8			1.02183			0.510914	−	0.859632i	$-0.329307\pi$
$619$	2.42354e8			1.02183			0.510914	+	0.859632i	$0.329307\pi$
$620$			2.26948e8i			0.952252i
$621$		−	4.47496e8i		−	1.86859i
$622$			7.73894e6i			0.0321596i
$623$		−	3.65143e7i		−	0.151008i
$624$			1.19759e7i			0.0492896i
$625$	−3.03539e8			−1.24330
$626$	−1.45408e8			−0.592741
$627$			2.17963e8i			0.884261i
$628$		−	3.68881e7i		−	0.148938i
$629$		−	1.19571e6i		−	0.00480477i
$630$			7.95354e7i			0.318082i
$631$	2.28665e8			0.910147			0.455074	−	0.890454i	$-0.349613\pi$
$631$	2.28665e8			0.910147			0.455074	+	0.890454i	$0.349613\pi$
$632$			1.27411e8i			0.504728i
$633$			2.09653e8i			0.826590i
$634$		−	1.03416e8i		−	0.405805i
$635$	1.25588e8			0.490486
$636$	1.62059e8			0.629944
$637$			1.44933e8i			0.560726i
$638$	4.51300e7			0.173781
$639$	−2.87011e8			−1.10001
$640$		−	2.23319e8i		−	0.851895i
$641$	4.59906e8			1.74620			0.873101	−	0.487539i	$-0.162105\pi$
$641$	4.59906e8			1.74620			0.873101	+	0.487539i	$0.162105\pi$
$642$			2.50355e7i			0.0946130i
$643$	2.19308e6			0.00824938			0.00412469	−	0.999991i	$-0.498687\pi$
$643$	2.19308e6			0.00824938			0.00412469	+	0.999991i	$0.498687\pi$
$644$		−	2.31061e8i		−	0.865105i
$645$		−	1.81742e8i		−	0.677294i
$646$		−	2.25482e7i		−	0.0836401i
$647$	5.12664e7			0.189286			0.0946432	−	0.995511i	$-0.469829\pi$
$647$	5.12664e7			0.189286			0.0946432	+	0.995511i	$0.469829\pi$
$648$			2.88577e7i			0.106056i
$649$	−2.24203e8	+	1.71072e8i	−0.820178	+	0.625813i
$650$	7.08078e7			0.257835
$651$			1.33021e8i			0.482145i
$652$	−2.90080e8			−1.04658
$653$	−4.33474e7			−0.155676			−0.0778382	−	0.996966i	$-0.524802\pi$
$653$	−4.33474e7			−0.155676			−0.0778382	+	0.996966i	$0.524802\pi$
$654$	−3.52045e7			−0.125853
$655$		−	5.88901e8i		−	2.09565i
$656$	−2.59226e7			−0.0918262
$657$			2.32984e8i			0.821544i
$658$	−1.07695e8			−0.378024
$659$		−	4.84504e8i		−	1.69294i	−0.532439	−	0.846469i	$-0.678724\pi$
$659$		−	4.84504e8i		−	1.69294i	0.532439	−	0.846469i	$-0.321276\pi$
$660$		−	1.33515e8i		−	0.464406i
$661$	−4.64218e8			−1.60738			−0.803689	−	0.595050i	$-0.797132\pi$
$661$	−4.64218e8			−1.60738			−0.803689	+	0.595050i	$0.797132\pi$
$662$		−	6.99722e6i		−	0.0241186i
$663$		−	1.69328e7i		−	0.0581015i
$664$	2.48273e8			0.848058
$665$	−3.54045e8			−1.20391
$666$	5.79812e6			0.0196275
$667$		−	1.64845e8i		−	0.555518i
$668$	1.51678e8			0.508854
$669$	2.38874e8			0.797792
$670$	3.16253e7			0.105150
$671$	4.22063e8			1.39704
$672$		−	1.22137e8i		−	0.402475i
$673$		−	5.59966e7i		−	0.183703i	−0.995773	−	0.0918516i	$-0.970721\pi$
$673$		−	5.59966e7i		−	0.183703i	0.995773	−	0.0918516i	$-0.0292785\pi$
$674$	1.97002e8			0.643413
$675$	1.23840e8			0.402671
$676$	−1.98888e7			−0.0643826
$677$	3.37470e8			1.08760			0.543800	−	0.839215i	$-0.316985\pi$
$677$	3.37470e8			1.08760			0.543800	+	0.839215i	$0.316985\pi$
$678$	−1.60682e8			−0.515558
$679$			2.70301e8i			0.863451i
$680$			3.49366e7i			0.111110i
$681$		−	2.26025e8i		−	0.715674i
$682$		−	2.35480e8i		−	0.742337i
$683$			7.44655e7i			0.233719i	0.993148	+	0.116859i	$0.0372826\pi$
$683$			7.44655e7i			0.233719i	−0.993148	+	0.116859i	$0.962717\pi$
$684$	−2.06523e8			−0.645357
$685$	4.39006e8			1.36584
$686$		−	1.98813e8i		−	0.615847i
$687$			8.00372e7i			0.246843i
$688$		−	2.60607e7i		−	0.0800242i
$689$			5.71285e8i			1.74661i
$690$	2.58194e8			0.785957
$691$		−	5.91098e7i		−	0.179153i	−0.995980	−	0.0895767i	$-0.971449\pi$
$691$		−	5.91098e7i		−	0.179153i	0.995980	−	0.0895767i	$-0.0285514\pi$
$692$			1.29806e8i			0.391722i
$693$			1.55877e8i			0.468361i
$694$	−1.63803e8			−0.490054
$695$	−3.42608e8			−1.02057
$696$		−	5.43019e7i		−	0.161060i
$697$	3.66520e7			0.108243
$698$	−3.21868e8			−0.946481
$699$			1.53720e7i			0.0450090i
$700$	6.39438e7			0.186425
$701$		−	3.82178e8i		−	1.10946i	−0.832030	−	0.554730i	$-0.812821\pi$
$701$		−	3.82178e8i		−	1.10946i	0.832030	−	0.554730i	$-0.187179\pi$
$702$	2.05440e8			0.593847
$703$			2.58099e7i			0.0742882i
$704$			1.86931e8i			0.535752i
$705$			2.27306e8i			0.648698i
$706$	−1.98487e8			−0.564051
$707$		−	2.00032e7i		−	0.0566032i
$708$	8.13779e7	+	1.06652e8i	0.229301	+	0.300518i
$709$	−5.09362e8			−1.42918			−0.714592	−	0.699542i	$-0.753387\pi$
$709$	−5.09362e8			−1.42918			−0.714592	+	0.699542i	$0.753387\pi$
$710$		−	4.14334e8i		−	1.15765i
$711$	−1.24123e8			−0.345336
$712$	7.77761e7			0.215480
$713$	−8.60131e8			−2.37299
$714$			8.09566e6i			0.0222412i
$715$	4.70661e8			1.28763
$716$			2.33533e8i			0.636222i
$717$	−2.49199e8			−0.676066
$718$			2.45940e8i			0.664439i
$719$		−	5.36209e8i		−	1.44260i	−0.692621	−	0.721302i	$-0.743544\pi$
$719$		−	5.36209e8i		−	1.44260i	0.692621	−	0.721302i	$-0.256456\pi$
$720$	2.40715e7			0.0644921
$721$			1.87978e7i			0.0501535i
$722$			2.65277e8i			0.704835i
$723$	−2.64997e8			−0.701175
$724$	−5.97938e7			−0.157558
$725$	4.56192e7			0.119711
$726$			8.37380e6i			0.0218833i
$727$	6.53736e7			0.170137			0.0850685	−	0.996375i	$-0.472889\pi$
$727$	6.53736e7			0.170137			0.0850685	+	0.996375i	$0.472889\pi$
$728$	2.68315e8			0.695426
$729$	1.87589e8			0.484201
$730$	−3.36340e8			−0.864589
$731$			3.68473e7i			0.0943309i
$732$		−	2.00773e8i		−	0.511884i
$733$	−3.16817e8			−0.804445			−0.402222	−	0.915542i	$-0.631762\pi$
$733$	−3.16817e8			−0.804445			−0.402222	+	0.915542i	$0.631762\pi$
$734$	−1.93458e8			−0.489214
$735$	−1.46253e8			−0.368336
$736$	7.89752e8			1.98088
$737$	6.19806e7			0.154829
$738$			1.77730e8i			0.442172i
$739$			4.57789e8i			1.13431i	0.823611	+	0.567155i	$0.191956\pi$
$739$			4.57789e8i			1.13431i	−0.823611	+	0.567155i	$0.808044\pi$
$740$		−	1.58100e7i		−	0.0390155i
$741$			3.65502e8i			0.898329i
$742$		−	2.73135e8i		−	0.668598i
$743$	1.64603e8			0.401301			0.200651	−	0.979663i	$-0.435694\pi$
$743$	1.64603e8			0.401301			0.200651	+	0.979663i	$0.435694\pi$
$744$	−2.83338e8			−0.687995
$745$			4.07432e8i			0.985341i
$746$			7.70305e7i			0.185544i
$747$			2.41865e8i			0.580244i
$748$			2.70694e7i			0.0646806i
$749$	−7.96989e7			−0.189674
$750$		−	9.94347e7i		−	0.235697i
$751$			6.85819e8i			1.61916i	0.587010	+	0.809579i	$0.300305\pi$
$751$			6.85819e8i			1.61916i	−0.587010	+	0.809579i	$0.699695\pi$
$752$			3.25942e7i			0.0766455i
$753$	−9.70112e7			−0.227215
$754$	7.56785e7			0.176546
$755$			6.35576e8i			1.47682i
$756$	1.85525e8			0.429376
$757$	−1.39036e7			−0.0320508			−0.0160254	−	0.999872i	$-0.505101\pi$
$757$	−1.39036e7			−0.0320508			−0.0160254	+	0.999872i	$0.505101\pi$
$758$			3.58369e7i			0.0822855i
$759$	5.06019e8			1.15729
$760$		−	7.54123e8i		−	1.71791i
$761$	2.69986e8			0.612614			0.306307	−	0.951933i	$-0.400907\pi$
$761$	2.69986e8			0.612614			0.306307	+	0.951933i	$0.400907\pi$
$762$			6.19873e7i			0.140100i
$763$		−	1.12071e8i		−	0.252302i
$764$		−	3.91004e8i		−	0.876802i
$765$	−3.40348e7			−0.0760219
$766$		−	2.82616e8i		−	0.628798i
$767$	−3.75966e8	+	2.86870e8i	−0.833226	+	0.635769i
$768$	2.46225e8			0.543561
$769$			7.62063e8i			1.67576i	0.545855	+	0.837880i	$0.316205\pi$
$769$			7.62063e8i			1.67576i	−0.545855	+	0.837880i	$0.683795\pi$
$770$	−2.25026e8			−0.492902
$771$	1.96204e8			0.428099
$772$	5.47886e8			1.19080
$773$			8.45218e8i			1.82991i	0.403553	+	0.914956i	$0.367775\pi$
$773$			8.45218e8i			1.82991i	−0.403553	+	0.914956i	$0.632225\pi$
$774$	−1.78677e8			−0.385341
$775$		−	2.38033e8i		−	0.511366i
$776$	−5.75745e8			−1.23210
$777$		−	9.26672e6i		−	0.0197544i
$778$			1.79796e8i			0.381804i
$779$	−7.91151e8			−1.67358
$780$		−	2.23891e8i		−	0.471794i
$781$		−	8.12028e8i		−	1.70458i
$782$	−5.23475e7			−0.109465
$783$	1.32359e8			0.275719
$784$	−2.09718e7			−0.0435199
$785$			1.31221e8i			0.271265i
$786$	2.90668e8			0.598590
$787$	2.72490e8			0.559019			0.279509	−	0.960143i	$-0.409828\pi$
$787$	2.72490e8			0.559019			0.279509	+	0.960143i	$0.409828\pi$
$788$	−6.31117e7			−0.128983
$789$	−3.06166e8			−0.623341
$790$		−	1.79185e8i		−	0.363430i
$791$		−	5.11521e8i		−	1.03356i
$792$	−3.32020e8			−0.668326
$793$	7.07757e8			1.41927
$794$	−2.68090e8			−0.535574
$795$	−5.76488e8			−1.14733
$796$	−2.74123e7			−0.0543509
$797$			2.10539e8i			0.415869i	0.978143	+	0.207935i	$0.0666741\pi$
$797$			2.10539e8i			0.415869i	−0.978143	+	0.207935i	$0.933326\pi$
$798$		−	1.74749e8i		−	0.343879i
$799$		−	4.60850e7i		−	0.0903482i
$800$			2.18556e8i			0.426867i
$801$			7.57685e7i			0.147432i
$802$	2.00309e8			0.388309
$803$	−6.59173e8			−1.27307
$804$		−	2.94838e7i		−	0.0567303i
$805$			8.21945e8i			1.57563i
$806$		−	3.94876e8i		−	0.754147i
$807$		−	2.91669e8i		−	0.554970i
$808$	4.26071e7			0.0807696
$809$			1.14677e6i			0.00216586i	0.999999	+	0.00108293i	$0.000344707\pi$
$809$			1.14677e6i			0.00216586i	−0.999999	+	0.00108293i	$0.999655\pi$
$810$		−	4.05841e7i		−	0.0763662i
$811$		−	7.03143e8i		−	1.31820i	−0.752056	−	0.659099i	$-0.770938\pi$
$811$		−	7.03143e8i		−	1.31820i	0.752056	−	0.659099i	$-0.229062\pi$
$812$	6.83423e7			0.127650
$813$	−1.29372e8			−0.240752
$814$			1.64044e7i			0.0304149i
$815$	1.03189e9			1.90617
$816$	2.45017e6			0.00450947
$817$		−	7.95367e8i		−	1.45848i
$818$	5.22879e8			0.955303
$819$			2.61389e8i			0.475813i
$820$	4.84625e8			0.878949
$821$			1.09496e9i			1.97865i	0.145736	+	0.989324i	$0.453445\pi$
$821$			1.09496e9i			1.97865i	−0.145736	+	0.989324i	$0.546555\pi$
$822$			2.16683e8i			0.390131i
$823$		−	2.87604e8i		−	0.515935i	−0.966154	−	0.257968i	$-0.916947\pi$
$823$		−	2.87604e8i		−	0.515935i	0.966154	−	0.257968i	$-0.0830528\pi$
$824$	−4.00397e7			−0.0715663
$825$			1.40036e8i			0.249389i
$826$	1.79752e8	−	1.37154e8i	0.318958	−	0.243371i
$827$	−3.39238e7			−0.0599775			−0.0299887	−	0.999550i	$-0.509547\pi$
$827$	−3.39238e7			−0.0599775			−0.0299887	+	0.999550i	$0.509547\pi$
$828$			4.79459e8i			0.844619i
$829$	4.19909e8			0.737040			0.368520	−	0.929620i	$-0.379865\pi$
$829$	4.19909e8			0.737040			0.368520	+	0.929620i	$0.379865\pi$
$830$	−3.49160e8			−0.610646
$831$	−2.81573e7			−0.0490668
$832$			3.13465e8i			0.544275i
$833$	2.96521e7			0.0513004
$834$		−	1.69103e8i		−	0.291510i
$835$	−5.39560e8			−0.926787
$836$		−	5.84306e8i		−	1.00005i
$837$		−	6.90624e8i		−	1.17778i
$838$	−3.39891e8			−0.577574
$839$		−	2.11633e8i		−	0.358342i	−0.983818	−	0.179171i	$-0.942658\pi$
$839$		−	2.11633e8i		−	0.358342i	0.983818	−	0.179171i	$-0.0573416\pi$
$840$			2.70759e8i			0.456819i
$841$	−5.46066e8			−0.918031
$842$	4.07970e7			0.0683426
$843$	−3.37382e8			−0.563170
$844$		−	5.62029e8i		−	0.934827i
$845$	7.07498e7			0.117261
$846$	2.23472e8			0.369072
$847$	−2.66575e7			−0.0438701
$848$	−8.26647e7			−0.135560
$849$		−	3.98349e8i		−	0.650939i
$850$		−	1.44867e7i		−	0.0235891i
$851$	5.99197e7			0.0972256
$852$	−3.86277e8			−0.624568
$853$	−8.32254e7			−0.134094			−0.0670469	−	0.997750i	$-0.521358\pi$
$853$	−8.32254e7			−0.134094			−0.0670469	+	0.997750i	$0.521358\pi$
$854$	−3.38383e8			−0.543293
$855$	7.34657e8			1.17540
$856$		−	1.69760e8i		−	0.270654i
$857$		−	6.14368e8i		−	0.976082i	−0.872821	−	0.488041i	$-0.837712\pi$
$857$		−	6.14368e8i		−	0.976082i	0.872821	−	0.488041i	$-0.162288\pi$
$858$			2.32308e8i			0.367791i
$859$		−	7.31226e8i		−	1.15364i	−0.816870	−	0.576822i	$-0.804292\pi$
$859$		−	7.31226e8i		−	1.15364i	0.816870	−	0.576822i	$-0.195708\pi$
$860$			4.87207e8i			0.765981i
$861$	2.84053e8			0.445031
$862$	2.03169e8			0.317202
$863$		−	2.35373e8i		−	0.366204i	−0.983094	−	0.183102i	$-0.941386\pi$
$863$		−	2.35373e8i		−	0.366204i	0.983094	−	0.183102i	$-0.0586139\pi$
$864$			6.34115e8i			0.983165i
$865$		−	4.61756e8i		−	0.713452i
$866$		−	1.31303e7i		−	0.0202171i
$867$	3.73315e8			0.572820
$868$		−	3.56598e8i		−	0.545280i
$869$		−	3.51175e8i		−	0.535136i
$870$			7.63677e7i			0.115972i
$871$	1.03935e8			0.157292
$872$	2.38714e8			0.360021
$873$		−	5.60884e8i		−	0.843005i
$874$	1.12995e9			1.69248
$875$	3.16544e8			0.472509
$876$			3.13564e8i			0.466460i
$877$	3.87783e8			0.574897			0.287449	−	0.957796i	$-0.407193\pi$
$877$	3.87783e8			0.574897			0.287449	+	0.957796i	$0.407193\pi$
$878$			1.61611e8i			0.238774i
$879$	2.45513e8			0.361500
$880$			6.81046e7i			0.0999374i
$881$		−	7.92872e8i		−	1.15951i	−0.814790	−	0.579756i	$-0.803148\pi$
$881$		−	7.92872e8i		−	1.15951i	0.814790	−	0.579756i	$-0.196852\pi$
$882$			1.43787e8i			0.209562i
$883$	−1.40778e8			−0.204480			−0.102240	−	0.994760i	$-0.532601\pi$
$883$	−1.40778e8			−0.204480			−0.102240	+	0.994760i	$0.532601\pi$
$884$			4.53927e7i			0.0657096i
$885$	−2.89483e8	−	3.79390e8i	−0.417631	−	0.547339i
$886$	−6.75394e7			−0.0971083
$887$		−	4.26577e8i		−	0.611261i	−0.952150	−	0.305630i	$-0.901133\pi$
$887$		−	4.26577e8i		−	0.611261i	0.952150	−	0.305630i	$-0.0988672\pi$
$888$	1.97383e7			0.0281884
$889$	−1.97333e8			−0.280863
$890$	−1.09381e8			−0.155157
$891$		−	7.95384e7i		−	0.112446i
$892$	−6.40362e8			−0.902259
$893$			9.94767e8i			1.39691i
$894$	−2.01099e8			−0.281448
$895$		−	8.30738e8i		−	1.15876i
$896$			3.50895e8i			0.487813i
$897$	8.48542e8			1.17570
$898$			3.86376e8i			0.533557i
$899$		−	2.54406e8i		−	0.350146i
$900$	−1.32686e8			−0.182011
$901$	1.16880e8			0.159796
$902$	−5.02843e8			−0.685193
$903$			2.85567e8i			0.387833i
$904$	1.08955e9			1.47483
$905$	2.12702e8			0.286964
$906$	−3.13706e8			−0.421830
$907$	7.80639e8			1.04623			0.523116	−	0.852261i	$-0.324769\pi$
$907$	7.80639e8			1.04623			0.523116	+	0.852261i	$0.324769\pi$
$908$			6.05918e8i			0.809387i
$909$			4.15073e7i			0.0552628i
$910$	−3.77346e8			−0.500743
$911$	1.45132e9			1.91959			0.959797	−	0.280694i	$-0.0905647\pi$
$911$	1.45132e9			1.91959			0.959797	+	0.280694i	$0.0905647\pi$
$912$	−5.28880e7			−0.0697225
$913$	−6.84297e8			−0.899150
$914$	5.72848e8			0.750241
$915$			7.14202e8i			0.932305i
$916$		−	2.14560e8i		−	0.279166i
$917$			9.25324e8i			1.20001i
$918$		−	4.20313e7i		−	0.0543307i
$919$			4.01208e8i			0.516919i	0.966022	+	0.258460i	$0.0832149\pi$
$919$			4.01208e8i			0.516919i	−0.966022	+	0.258460i	$0.916785\pi$
$920$	−1.75076e9			−2.24834
$921$	−7.79805e8			−0.998176
$922$			1.78037e8i			0.227152i
$923$		−	1.36169e9i		−	1.73170i
$924$			2.09788e8i			0.265928i
$925$			1.65822e7i			0.0209516i
$926$	−7.12971e8			−0.897923
$927$		−	3.90061e7i		−	0.0489659i
$928$			2.33590e8i			0.292287i
$929$			1.30069e9i			1.62228i	0.584853	+	0.811139i	$0.301152\pi$
$929$			1.30069e9i			1.62228i	−0.584853	+	0.811139i	$0.698848\pi$
$930$	3.98473e8			0.495393
$931$	−6.40055e8			−0.793173
$932$		−	4.12086e7i		−	0.0509027i
$933$	−2.56653e7			−0.0316010
$934$	4.66601e8			0.572671
$935$		−	9.62932e7i		−	0.117804i
$936$	−5.56763e8			−0.678958
$937$			2.66532e8i			0.323989i	0.986792	+	0.161995i	$0.0517927\pi$
$937$			2.66532e8i			0.323989i	−0.986792	+	0.161995i	$0.948207\pi$
$938$	−4.96920e7			−0.0602113
$939$		−	4.82228e8i		−	0.582446i
$940$		−	6.09351e8i		−	0.733642i
$941$		−	6.35587e7i		−	0.0762792i	−0.999272	−	0.0381396i	$-0.987857\pi$
$941$		−	6.35587e7i		−	0.0762792i	0.999272	−	0.0381396i	$-0.0121431\pi$
$942$	−6.47675e7			−0.0774826
$943$			1.83672e9i			2.19032i
$944$	−4.15101e7	−	5.44022e7i	−0.0493443	−	0.0646697i
$945$	−6.59963e8			−0.782032
$946$		−	5.05523e8i		−	0.597128i
$947$	5.96832e8			0.702753			0.351376	−	0.936234i	$-0.385714\pi$
$947$	5.96832e8			0.702753			0.351376	+	0.936234i	$0.385714\pi$
$948$	−1.67052e8			−0.196077
$949$	−1.10537e9			−1.29332
$950$			3.12701e8i			0.364719i
$951$	3.42965e8			0.398757
$952$		−	5.48949e7i		−	0.0636240i
$953$	1.52348e9			1.76018			0.880092	−	0.474803i	$-0.157481\pi$
$953$	1.52348e9			1.76018			0.880092	+	0.474803i	$0.157481\pi$
$954$			5.66764e8i			0.652766i
$955$			1.39091e9i			1.59694i
$956$	6.68042e8			0.764593
$957$			1.49668e8i			0.170763i
$958$			3.65020e8i			0.415165i
$959$	−6.89798e8			−0.782107
$960$	−3.16319e8			−0.357530
$961$	−4.39942e8			−0.495708
$962$			2.75084e7i			0.0308987i
$963$	1.65378e8			0.185182
$964$	7.10393e8			0.792990
$965$	−1.94898e9			−2.16883
$966$	−4.05693e8			−0.450056
$967$		−	9.93727e8i		−	1.09897i	−0.835502	−	0.549487i	$-0.814823\pi$
$967$		−	9.93727e8i		−	1.09897i	0.835502	−	0.549487i	$-0.185177\pi$
$968$		−	5.67809e7i		−	0.0626003i
$969$	7.47785e7			0.0821874
$970$	8.09701e8			0.887175
$971$	3.75429e8			0.410082			0.205041	−	0.978753i	$-0.434267\pi$
$971$	3.75429e8			0.410082			0.205041	+	0.978753i	$0.434267\pi$
$972$	−6.16081e8			−0.670871
$973$	5.38330e8			0.584399
$974$		−	8.96597e8i		−	0.970332i
$975$			2.34826e8i			0.253356i
$976$			1.02412e8i			0.110154i
$977$		−	7.48178e8i		−	0.802271i	−0.916019	−	0.401136i	$-0.868616\pi$
$977$		−	7.48178e8i		−	0.802271i	0.916019	−	0.401136i	$-0.131384\pi$
$978$			5.09317e8i			0.544468i
$979$	−2.14369e8			−0.228462
$980$	3.92070e8			0.416567
$981$			2.32552e8i			0.246328i
$982$			4.66719e7i			0.0492857i
$983$		−	1.49945e9i		−	1.57860i	−0.614008	−	0.789300i	$-0.710444\pi$
$983$		−	1.49945e9i		−	1.57860i	0.614008	−	0.789300i	$-0.289556\pi$
$984$			6.05038e8i			0.635034i
$985$	2.24505e8			0.234919
$986$		−	1.54831e7i		−	0.0161521i
$987$		−	3.57159e8i		−	0.371458i
$988$		−	9.79822e8i		−	1.01596i
$989$	−1.84651e9			−1.90881
$990$	4.66937e8			0.481230
$991$			5.59497e8i			0.574879i	0.957799	+	0.287440i	$0.0928041\pi$
$991$			5.59497e8i			0.574879i	−0.957799	+	0.287440i	$0.907196\pi$
$992$	1.21883e9			1.24856
$993$	2.32054e7			0.0236997
$994$			6.51031e8i			0.662892i
$995$	9.75129e7			0.0989904
$996$			3.25516e8i			0.329453i
$997$	2.75289e8			0.277782			0.138891	−	0.990308i	$-0.455646\pi$
$997$	2.75289e8			0.277782			0.138891	+	0.990308i	$0.455646\pi$
$998$		−	1.01364e8i		−	0.101975i
$999$			4.81112e7i			0.0482559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	59.7.b.c.58.16	yes	26
59.58	odd	2	inner	59.7.b.c.58.11	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.7.b.c.58.11	✓	26	59.58	odd	2	inner
59.7.b.c.58.16	yes	26	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	59.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.70683i q^{2} -15.6097 q^{3} +41.8457 q^{4} -148.856 q^{5} -73.4721i q^{6} +233.894 q^{7} +498.198i q^{8} -485.338 q^{9} +O(q^{10})\)	\(q+4.70683i q^{2} -15.6097 q^{3} +41.8457 q^{4} -148.856 q^{5} -73.4721i q^{6} +233.894 q^{7} +498.198i q^{8} -485.338 q^{9} -700.642i q^{10} -1373.15i q^{11} -653.197 q^{12} -2302.63i q^{13} +1100.90i q^{14} +2323.60 q^{15} +333.190 q^{16} -471.098 q^{17} -2284.41i q^{18} +10168.9 q^{19} -6229.00 q^{20} -3651.01 q^{21} +6463.18 q^{22} -23607.8i q^{23} -7776.71i q^{24} +6533.24 q^{25} +10838.1 q^{26} +18955.4 q^{27} +9787.46 q^{28} +6982.64 q^{29} +10936.8i q^{30} -36434.1i q^{31} +33453.0i q^{32} +21434.4i q^{33} -2217.38i q^{34} -34816.6 q^{35} -20309.3 q^{36} +2538.13i q^{37} +47863.2i q^{38} +35943.3i q^{39} -74160.0i q^{40} -77801.3 q^{41} -17184.7i q^{42} -78215.9i q^{43} -57460.3i q^{44} +72245.8 q^{45} +111118. q^{46} +97824.8i q^{47} -5200.98 q^{48} -62942.6 q^{49} +30750.9i q^{50} +7353.67 q^{51} -96355.1i q^{52} -248101. q^{53} +89220.0i q^{54} +204402. i q^{55} +116526. i q^{56} -158733. q^{57} +32866.1i q^{58} +(-124584. - 163277. i) q^{59} +97232.6 q^{60} +307369. i q^{61} +171489. q^{62} -113518. q^{63} -136133. q^{64} +342761. i q^{65} -100888. q^{66} +45137.6i q^{67} -19713.4 q^{68} +368510. i q^{69} -163876. i q^{70} +591363. q^{71} -241795. i q^{72} -480045. i q^{73} -11946.5 q^{74} -101982. q^{75} +425523. q^{76} -321171. i q^{77} -169179. q^{78} +255744. q^{79} -49597.4 q^{80} +57924.2 q^{81} -366198. i q^{82} -498342. i q^{83} -152779. q^{84} +70125.9 q^{85} +368149. q^{86} -108997. q^{87} +684100. q^{88} -156115. i q^{89} +340049. i q^{90} -538571. i q^{91} -987887. i q^{92} +568724. i q^{93} -460445. q^{94} -1.51370e6 q^{95} -522189. i q^{96} +1.15565e6i q^{97} -296260. i q^{98} +666441. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 10 q^{3} - 1090 q^{4} + 142 q^{5} + 406 q^{7} + 5432 q^{9}+O(q^{10}) \) 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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