LMFDB - Embedded newform 180.7.c.b.91.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,7,Mod(91,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("180.91");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	180.c (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:	$41.4097350516$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.9
Character	$\chi$	$=$	180.91
Dual form			180.7.c.b.91.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.43879 - 7.22321i) q^{2} +(-40.3494 + 49.6782i) q^{4} -55.9017 q^{5} -472.024i q^{7} +(497.589 + 120.619i) q^{8} +O(q^{10})$	\(q+(-3.43879 - 7.22321i) q^{2} +(-40.3494 + 49.6782i) q^{4} -55.9017 q^{5} -472.024i q^{7} +(497.589 + 120.619i) q^{8} +(192.234 + 403.790i) q^{10} +939.392i q^{11} +22.5854 q^{13} +(-3409.52 + 1623.19i) q^{14} +(-839.847 - 4008.97i) q^{16} -6247.86 q^{17} -11163.0i q^{19} +(2255.60 - 2777.10i) q^{20} +(6785.42 - 3230.37i) q^{22} -1168.18i q^{23} +3125.00 q^{25} +(-77.6664 - 163.139i) q^{26} +(23449.3 + 19045.9i) q^{28} -25619.9 q^{29} -4304.29i q^{31} +(-26069.6 + 19852.4i) q^{32} +(21485.1 + 45129.6i) q^{34} +26386.9i q^{35} -50696.3 q^{37} +(-80632.6 + 38387.2i) q^{38} +(-27816.1 - 6742.82i) q^{40} +113093. q^{41} +113727. i q^{43} +(-46667.3 - 37903.9i) q^{44} +(-8438.03 + 4017.14i) q^{46} +184245. i q^{47} -105157. q^{49} +(-10746.2 - 22572.5i) q^{50} +(-911.307 + 1122.00i) q^{52} +133403. q^{53} -52513.6i q^{55} +(56935.1 - 234874. i) q^{56} +(88101.5 + 185058. i) q^{58} -55214.8i q^{59} +204814. q^{61} +(-31090.8 + 14801.5i) q^{62} +(233046. + 120038. i) q^{64} -1262.56 q^{65} +244236. i q^{67} +(252098. - 310383. i) q^{68} +(190598. - 90739.1i) q^{70} -14227.6i q^{71} -278492. q^{73} +(174334. + 366190. i) q^{74} +(554557. + 450420. i) q^{76} +443415. q^{77} +358976. i q^{79} +(46948.9 + 224108. i) q^{80} +(-388902. - 816892. i) q^{82} +820615. i q^{83} +349266. q^{85} +(821472. - 391083. i) q^{86} +(-113309. + 467431. i) q^{88} -1.00519e6 q^{89} -10660.8i q^{91} +(58033.3 + 47135.6i) q^{92} +(1.33084e6 - 633579. i) q^{94} +624030. i q^{95} +1.44195e6 q^{97} +(361614. + 759572. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8}+O(q^{10}) $ 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8	$ 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8} - 750 q^{10} + 5040 q^{13} + 2596 q^{14} + 4194 q^{16} - 7000 q^{20} + 45780 q^{22} + 75000 q^{25} - 75852 q^{26} + 54300 q^{28} - 132800 q^{29} + 10700 q^{32} - 173484 q^{34} - 69840 q^{37} - 215800 q^{38} - 14250 q^{40} + 70448 q^{41} + 395668 q^{44} - 158760 q^{46} - 642984 q^{49} - 62500 q^{50} - 210240 q^{52} + 644320 q^{53} + 917708 q^{56} - 1345020 q^{58} - 222864 q^{61} - 1948520 q^{62} + 935922 q^{64} - 266000 q^{65} - 572680 q^{68} + 220500 q^{70} + 771120 q^{73} + 589164 q^{74} - 191544 q^{76} - 1383840 q^{77} + 946000 q^{80} + 2672520 q^{82} - 372000 q^{85} - 1781528 q^{86} + 956940 q^{88} + 1566224 q^{89} + 3040560 q^{92} - 3788352 q^{94} - 1666800 q^{97} + 2709660 q^{98}+O(q^{100}) $ 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8 - 750 * q^10 + 5040 * q^13 + 2596 * q^14 + 4194 * q^16 - 7000 * q^20 + 45780 * q^22 + 75000 * q^25 - 75852 * q^26 + 54300 * q^28 - 132800 * q^29 + 10700 * q^32 - 173484 * q^34 - 69840 * q^37 - 215800 * q^38 - 14250 * q^40 + 70448 * q^41 + 395668 * q^44 - 158760 * q^46 - 642984 * q^49 - 62500 * q^50 - 210240 * q^52 + 644320 * q^53 + 917708 * q^56 - 1345020 * q^58 - 222864 * q^61 - 1948520 * q^62 + 935922 * q^64 - 266000 * q^65 - 572680 * q^68 + 220500 * q^70 + 771120 * q^73 + 589164 * q^74 - 191544 * q^76 - 1383840 * q^77 + 946000 * q^80 + 2672520 * q^82 - 372000 * q^85 - 1781528 * q^86 + 956940 * q^88 + 1566224 * q^89 + 3040560 * q^92 - 3788352 * q^94 - 1666800 * q^97 + 2709660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−3.43879	−	7.22321i	−0.429849	−	0.902901i
$2$	−3.43879	−	7.22321i	−0.429849	−	0.902901i
$3$		0			0
$3$		0			0
$4$	−40.3494	+	49.6782i	−0.630460	+	0.776222i
$5$	−55.9017			−0.447214
$5$	−55.9017			−0.447214
$6$		0			0
$7$		−	472.024i		−	1.37616i	−0.725634	−	0.688081i	$-0.758453\pi$
$7$		−	472.024i		−	1.37616i	0.725634	−	0.688081i	$-0.241547\pi$
$8$	497.589	+	120.619i	0.971854	+	0.235585i
$9$		0			0
$10$	192.234	+	403.790i	0.192234	+	0.403790i
$11$			939.392i			0.705779i	0.935665	+	0.352890i	$0.114801\pi$
$11$			939.392i			0.705779i	−0.935665	+	0.352890i	$0.885199\pi$
$12$		0			0
$13$	22.5854			0.0102801			0.00514005	−	0.999987i	$-0.498364\pi$
$13$	22.5854			0.0102801			0.00514005	+	0.999987i	$0.498364\pi$
$14$	−3409.52	+	1623.19i	−1.24254	+	0.591542i
$15$		0			0
$16$	−839.847	−	4008.97i	−0.205041	−	0.978753i
$17$	−6247.86			−1.27170			−0.635850	−	0.771813i	$-0.719350\pi$
$17$	−6247.86			−1.27170			−0.635850	+	0.771813i	$0.719350\pi$
$18$		0			0
$19$		−	11163.0i		−	1.62750i	−0.581219	−	0.813748i	$-0.697424\pi$
$19$		−	11163.0i		−	1.62750i	0.581219	−	0.813748i	$-0.302576\pi$
$20$	2255.60	−	2777.10i	0.281950	−	0.347137i
$21$		0			0
$22$	6785.42	−	3230.37i	0.637248	−	0.303378i
$23$		−	1168.18i		−	0.0960125i	−0.998847	−	0.0480062i	$-0.984713\pi$
$23$		−	1168.18i		−	0.0960125i	0.998847	−	0.0480062i	$-0.0152867\pi$
$24$		0			0
$25$	3125.00			0.200000
$26$	−77.6664	−	163.139i	−0.00441889	−	0.00928191i
$27$		0			0
$28$	23449.3	+	19045.9i	1.06821	+	0.867615i
$29$	−25619.9			−1.05047			−0.525235	−	0.850957i	$-0.676023\pi$
$29$	−25619.9			−1.05047			−0.525235	+	0.850957i	$0.676023\pi$
$30$		0			0
$31$		−	4304.29i		−	0.144483i	−0.997387	−	0.0722414i	$-0.976985\pi$
$31$		−	4304.29i		−	0.144483i	0.997387	−	0.0722414i	$-0.0230152\pi$
$32$	−26069.6	+	19852.4i	−0.795581	+	0.605848i
$33$		0			0
$34$	21485.1	+	45129.6i	0.546639	+	1.14822i
$35$			26386.9i			0.615438i
$36$		0			0
$37$	−50696.3			−1.00086			−0.500428	−	0.865778i	$-0.666824\pi$
$37$	−50696.3			−1.00086			−0.500428	+	0.865778i	$0.666824\pi$
$38$	−80632.6	+	38387.2i	−1.46947	+	0.699577i
$39$		0			0
$40$	−27816.1	−	6742.82i	−0.434626	−	0.105357i
$41$	113093.			1.64090			0.820452	−	0.571715i	$-0.193722\pi$
$41$	113093.			1.64090			0.820452	+	0.571715i	$0.193722\pi$
$42$		0			0
$43$			113727.i			1.43040i	0.698920	+	0.715200i	$0.253664\pi$
$43$			113727.i			1.43040i	−0.698920	+	0.715200i	$0.746336\pi$
$44$	−46667.3	−	37903.9i	−0.547841	−	0.444965i
$45$		0			0
$46$	−8438.03	+	4017.14i	−0.0866898	+	0.0412709i
$47$			184245.i			1.77460i	0.461190	+	0.887301i	$0.347422\pi$
$47$			184245.i			1.77460i	−0.461190	+	0.887301i	$0.652578\pi$
$48$		0			0
$49$	−105157.			−0.893822
$50$	−10746.2	−	22572.5i	−0.0859698	−	0.180580i
$51$		0			0
$52$	−911.307	+	1122.00i	−0.00648119	+	0.00797964i
$53$	133403.			0.896063			0.448032	−	0.894018i	$-0.352125\pi$
$53$	133403.			0.896063			0.448032	+	0.894018i	$0.352125\pi$
$54$		0			0
$55$		−	52513.6i		−	0.315634i
$56$	56935.1	−	234874.i	0.324202	−	1.33743i
$57$		0			0
$58$	88101.5	+	185058.i	0.451543	+	0.948470i
$59$		−	55214.8i		−	0.268844i	−0.990924	−	0.134422i	$-0.957082\pi$
$59$		−	55214.8i		−	0.268844i	0.990924	−	0.134422i	$-0.0429177\pi$
$60$		0			0
$61$	204814.			0.902341			0.451170	−	0.892438i	$-0.351007\pi$
$61$	204814.			0.902341			0.451170	+	0.892438i	$0.351007\pi$
$62$	−31090.8	+	14801.5i	−0.130454	+	0.0621058i
$63$		0			0
$64$	233046.	+	120038.i	0.889000	+	0.457907i
$65$	−1262.56			−0.00459740
$66$		0			0
$67$			244236.i			0.812056i	0.913861	+	0.406028i	$0.133086\pi$
$67$			244236.i			0.812056i	−0.913861	+	0.406028i	$0.866914\pi$
$68$	252098.	−	310383.i	0.801756	−	0.987121i
$69$		0			0
$70$	190598.	−	90739.1i	0.555680	−	0.264546i
$71$		−	14227.6i		−	0.0397518i	−0.999802	−	0.0198759i	$-0.993673\pi$
$71$		−	14227.6i		−	0.0397518i	0.999802	−	0.0198759i	$-0.00632711\pi$
$72$		0			0
$73$	−278492.			−0.715885			−0.357943	−	0.933744i	$-0.616522\pi$
$73$	−278492.			−0.715885			−0.357943	+	0.933744i	$0.616522\pi$
$74$	174334.	+	366190.i	0.430216	+	0.903673i
$75$		0			0
$76$	554557.	+	450420.i	1.26330	+	1.02607i
$77$	443415.			0.971266
$78$		0			0
$79$			358976.i			0.728088i	0.931382	+	0.364044i	$0.118604\pi$
$79$			358976.i			0.728088i	−0.931382	+	0.364044i	$0.881396\pi$
$80$	46948.9	+	224108.i	0.0916971	+	0.437712i
$81$		0			0
$82$	−388902.	−	816892.i	−0.705341	−	1.48157i
$83$			820615.i			1.43518i	0.696468	+	0.717588i	$0.254754\pi$
$83$			820615.i			1.43518i	−0.696468	+	0.717588i	$0.745246\pi$
$84$		0			0
$85$	349266.			0.568722
$86$	821472.	−	391083.i	1.29151	−	0.614856i
$87$		0			0
$88$	−113309.	+	467431.i	−0.166271	+	0.685914i
$89$	−1.00519e6			−1.42587			−0.712935	−	0.701230i	$-0.752635\pi$
$89$	−1.00519e6			−1.42587			−0.712935	+	0.701230i	$0.752635\pi$
$90$		0			0
$91$		−	10660.8i		−	0.0141471i
$92$	58033.3	+	47135.6i	0.0745270	+	0.0605320i
$93$		0			0
$94$	1.33084e6	−	633579.i	1.60229	−	0.762811i
$95$			624030.i			0.727838i
$96$		0			0
$97$	1.44195e6			1.57992			0.789962	−	0.613156i	$-0.210100\pi$
$97$	1.44195e6			1.57992			0.789962	+	0.613156i	$0.210100\pi$
$98$	361614.	+	759572.i	0.384208	+	0.807032i
$99$		0			0
$100$	−126092.	+	155244.i	−0.126092	+	0.155244i
$101$	−778264.			−0.755375			−0.377688	−	0.925933i	$-0.623281\pi$
$101$	−778264.			−0.755375			−0.377688	+	0.925933i	$0.623281\pi$
$102$		0			0
$103$			1.15772e6i			1.05948i	0.848161	+	0.529739i	$0.177710\pi$
$103$			1.15772e6i			1.05948i	−0.848161	+	0.529739i	$0.822290\pi$
$104$	11238.2	+	2724.23i	0.00999076	+	0.00242183i
$105$		0			0
$106$	−458746.	−	963599.i	−0.385172	−	0.809056i
$107$		−	1.02649e6i		−	0.837925i	−0.908004	−	0.418962i	$-0.862394\pi$
$107$		−	1.02649e6i		−	0.837925i	0.908004	−	0.418962i	$-0.137606\pi$
$108$		0			0
$109$	769438.			0.594147			0.297074	−	0.954855i	$-0.403989\pi$
$109$	769438.			0.594147			0.297074	+	0.954855i	$0.403989\pi$
$110$	−379317.	+	180583.i	−0.284986	+	0.135675i
$111$		0			0
$112$	−1.89233e6	+	396428.i	−1.34692	+	0.282169i
$113$	337398.			0.233834			0.116917	−	0.993142i	$-0.462699\pi$
$113$	337398.			0.233834			0.116917	+	0.993142i	$0.462699\pi$
$114$		0			0
$115$			65303.5i			0.0429381i
$116$	1.03375e6	−	1.27275e6i	0.662279	−	0.815398i
$117$		0			0
$118$	−398828.	+	189872.i	−0.242739	+	0.115562i
$119$			2.94914e6i			1.75007i
$120$		0			0
$121$	889104.			0.501876
$122$	−704313.	−	1.47942e6i	−0.387870	−	0.814724i
$123$		0			0
$124$	213829.	+	173676.i	0.112151	+	0.0910906i
$125$	−174693.			−0.0894427
$126$		0			0
$127$			3.10443e6i			1.51555i	0.652515	+	0.757776i	$0.273714\pi$
$127$			3.10443e6i			1.51555i	−0.652515	+	0.757776i	$0.726286\pi$
$128$	65660.6	−	2.09612e6i	0.0313094	−	0.999510i
$129$		0			0
$130$	4341.68	+	9119.74i	0.00197619	+	0.00415100i
$131$			70316.0i			0.0312781i	0.999878	+	0.0156390i	$0.00497826\pi$
$131$			70316.0i			0.0312781i	−0.999878	+	0.0156390i	$0.995022\pi$
$132$		0			0
$133$	−5.26919e6			−2.23970
$134$	1.76417e6	−	839878.i	0.733206	−	0.349061i
$135$		0			0
$136$	−3.10887e6	−	753613.i	−1.23591	−	0.299593i
$137$	−3.75318e6			−1.45961			−0.729807	−	0.683654i	$-0.760390\pi$
$137$	−3.75318e6			−1.45961			−0.729807	+	0.683654i	$0.760390\pi$
$138$		0			0
$139$		−	4.22525e6i		−	1.57329i	−0.617406	−	0.786645i	$-0.711816\pi$
$139$		−	4.22525e6i		−	1.57329i	0.617406	−	0.786645i	$-0.288184\pi$
$140$	−1.31085e6	−	1.06470e6i	−0.477717	−	0.388009i
$141$		0			0
$142$	−102769.	+	48925.7i	−0.0358919	+	0.0170873i
$143$			21216.5i			0.00725548i
$144$		0			0
$145$	1.43220e6			0.469784
$146$	957674.	+	2.01160e6i	0.307722	+	0.646373i
$147$		0			0
$148$	2.04557e6	−	2.51850e6i	0.630999	−	0.776886i
$149$	−3.77574e6			−1.14141			−0.570707	−	0.821154i	$-0.693331\pi$
$149$	−3.77574e6			−1.14141			−0.570707	+	0.821154i	$0.693331\pi$
$150$		0			0
$151$			3.33342e6i			0.968186i	0.875017	+	0.484093i	$0.160850\pi$
$151$			3.33342e6i			0.968186i	−0.875017	+	0.484093i	$0.839150\pi$
$152$	1.34647e6	−	5.55458e6i	0.383413	−	1.58169i
$153$		0			0
$154$	−1.52481e6	−	3.20288e6i	−0.417498	−	0.876957i
$155$			240617.i			0.0646147i
$156$		0			0
$157$	−7.25721e6			−1.87530			−0.937650	−	0.347580i	$-0.887003\pi$
$157$	−7.25721e6			−1.87530			−0.937650	+	0.347580i	$0.887003\pi$
$158$	2.59296e6	−	1.23444e6i	0.657392	−	0.312968i
$159$		0			0
$160$	1.45733e6	−	1.10978e6i	0.355794	−	0.270943i
$161$	−551410.			−0.132129
$162$		0			0
$163$		−	2.00685e6i		−	0.463396i	−0.972788	−	0.231698i	$-0.925572\pi$
$163$		−	2.00685e6i		−	0.463396i	0.972788	−	0.231698i	$-0.0744281\pi$
$164$	−4.56323e6	+	5.61824e6i	−1.03452	+	1.27371i
$165$		0			0
$166$	5.92747e6	−	2.82192e6i	1.29582	−	0.616909i
$167$			3.95037e6i			0.848182i	0.905620	+	0.424091i	$0.139406\pi$
$167$			3.95037e6i			0.848182i	−0.905620	+	0.424091i	$0.860594\pi$
$168$		0			0
$169$	−4.82630e6			−0.999894
$170$	−1.20105e6	−	2.52282e6i	−0.244464	−	0.513499i
$171$		0			0
$172$	−5.64974e6	−	4.58881e6i	−1.11031	−	0.901810i
$173$	4.23383e6			0.817703			0.408851	−	0.912601i	$-0.365929\pi$
$173$	4.23383e6			0.817703			0.408851	+	0.912601i	$0.365929\pi$
$174$		0			0
$175$		−	1.47507e6i		−	0.275232i
$176$	3.76600e6	−	788946.i	0.690784	−	0.144714i
$177$		0			0
$178$	3.45665e6	+	7.26072e6i	0.612909	+	1.28742i
$179$			5.09011e6i			0.887499i	0.896151	+	0.443750i	$0.146352\pi$
$179$			5.09011e6i			0.887499i	−0.896151	+	0.443750i	$0.853648\pi$
$180$		0			0
$181$	7.69100e6			1.29702			0.648510	−	0.761206i	$-0.275392\pi$
$181$	7.69100e6			1.29702			0.648510	+	0.761206i	$0.275392\pi$
$182$	−77005.4	+	36660.4i	−0.0127734	+	0.00608111i
$183$		0			0
$184$	140906.	−	581276.i	0.0226191	−	0.0933101i
$185$	2.83401e6			0.447596
$186$		0			0
$187$		−	5.86919e6i		−	0.897539i
$188$	−9.15294e6	−	7.43416e6i	−1.37749	−	1.11882i
$189$		0			0
$190$	4.50750e6	−	2.14591e6i	0.657165	−	0.312860i
$191$		−	472014.i		−	0.0677415i	−0.999426	−	0.0338708i	$-0.989217\pi$
$191$		−	472014.i		−	0.0677415i	0.999426	−	0.0338708i	$-0.0107835\pi$
$192$		0			0
$193$	−5.76885e6			−0.802449			−0.401225	−	0.915980i	$-0.631415\pi$
$193$	−5.76885e6			−0.802449			−0.401225	+	0.915980i	$0.631415\pi$
$194$	−4.95858e6	−	1.04155e7i	−0.679129	−	1.42651i
$195$		0			0
$196$	4.24303e6	−	5.22402e6i	0.563519	−	0.693804i
$197$	−1.01304e7			−1.32504			−0.662521	−	0.749043i	$-0.730514\pi$
$197$	−1.01304e7			−1.32504			−0.662521	+	0.749043i	$0.730514\pi$
$198$		0			0
$199$			8.69529e6i			1.10338i	0.834050	+	0.551690i	$0.186017\pi$
$199$			8.69529e6i			1.10338i	−0.834050	+	0.551690i	$0.813983\pi$
$200$	1.55497e6	+	376935.i	0.194371	+	0.0471169i
$201$		0			0
$202$	2.67629e6	+	5.62156e6i	0.324697	+	0.682029i
$203$			1.20932e7i			1.44562i
$204$		0			0
$205$	−6.32208e6			−0.733835
$206$	8.36246e6	−	3.98116e6i	0.956604	−	0.455416i
$207$		0			0
$208$	−18968.3	−	90544.2i	−0.00210784	−	0.0100617i
$209$	1.04864e7			1.14865
$210$		0			0
$211$		−	2.10959e6i		−	0.224570i	−0.993676	−	0.112285i	$-0.964183\pi$
$211$		−	2.10959e6i		−	0.224570i	0.993676	−	0.112285i	$-0.0358169\pi$
$212$	−5.38274e6	+	6.62723e6i	−0.564932	+	0.695544i
$213$		0			0
$214$	−7.41458e6	+	3.52990e6i	−0.756563	+	0.360181i
$215$		−	6.35752e6i		−	0.639694i
$216$		0			0
$217$	−2.03172e6			−0.198832
$218$	−2.64594e6	−	5.55781e6i	−0.255394	−	0.536456i
$219$		0			0
$220$	2.60878e6	+	2.11889e6i	0.245002	+	0.198995i
$221$	−141110.			−0.0130732
$222$		0			0
$223$		−	5.11069e6i		−	0.460855i	−0.973089	−	0.230428i	$-0.925987\pi$
$223$		−	5.11069e6i		−	0.460855i	0.973089	−	0.230428i	$-0.0740125\pi$
$224$	9.37081e6	+	1.23055e7i	0.833744	+	1.09485i
$225$		0			0
$226$	−1.16024e6	−	2.43709e6i	−0.100513	−	0.211129i
$227$		−	2.13819e6i		−	0.182797i	−0.995814	−	0.0913983i	$-0.970866\pi$
$227$		−	2.13819e6i		−	0.182797i	0.995814	−	0.0913983i	$-0.0291336\pi$
$228$		0			0
$229$	1.43797e7			1.19741			0.598706	−	0.800969i	$-0.295682\pi$
$229$	1.43797e7			1.19741			0.598706	+	0.800969i	$0.295682\pi$
$230$	471700.	−	224565.i	0.0387688	−	0.0184569i
$231$		0			0
$232$	−1.27482e7	−	3.09025e6i	−1.02090	−	0.247474i
$233$	2.16907e7			1.71477			0.857385	−	0.514676i	$-0.172088\pi$
$233$	2.16907e7			1.71477			0.857385	+	0.514676i	$0.172088\pi$
$234$		0			0
$235$		−	1.02996e7i		−	0.793626i
$236$	2.74297e6	+	2.22789e6i	0.208682	+	0.169495i
$237$		0			0
$238$	2.13022e7	−	1.01415e7i	1.58014	−	0.752264i
$239$		−	4.39731e6i		−	0.322102i	−0.986946	−	0.161051i	$-0.948512\pi$
$239$		−	4.39731e6i		−	0.322102i	0.986946	−	0.161051i	$-0.0514883\pi$
$240$		0			0
$241$	1.72165e7			1.22997			0.614985	−	0.788539i	$-0.289162\pi$
$241$	1.72165e7			1.22997			0.614985	+	0.788539i	$0.289162\pi$
$242$	−3.05744e6	−	6.42218e6i	−0.215731	−	0.453144i
$243$		0			0
$244$	−8.26414e6	+	1.01748e7i	−0.568890	+	0.700417i
$245$	5.87847e6			0.399729
$246$		0			0
$247$		−	252120.i		−	0.0167308i
$248$	519180.	−	2.14177e6i	0.0340379	−	0.140416i
$249$		0			0
$250$	600732.	+	1.26184e6i	0.0384469	+	0.0807579i
$251$		−	4.94767e6i		−	0.312881i	−0.987687	−	0.156441i	$-0.949998\pi$
$251$		−	4.94767e6i		−	0.312881i	0.987687	−	0.156441i	$-0.0500020\pi$
$252$		0			0
$253$	1.09738e6			0.0677636
$254$	2.24239e7	−	1.06755e7i	1.36839	−	0.651458i
$255$		0			0
$256$	−1.53665e7	+	6.73385e6i	−0.915916	+	0.401369i
$257$	−2.51861e7			−1.48375			−0.741876	−	0.670537i	$-0.766064\pi$
$257$	−2.51861e7			−1.48375			−0.741876	+	0.670537i	$0.766064\pi$
$258$		0			0
$259$			2.39299e7i			1.37734i
$260$	50943.6	−	62721.8i	0.00289848	−	0.00356860i
$261$		0			0
$262$	507907.	−	241802.i	0.0282410	−	0.0134448i
$263$		−	4.00969e6i		−	0.220416i	−0.993909	−	0.110208i	$-0.964848\pi$
$263$		−	4.00969e6i		−	0.220416i	0.993909	−	0.110208i	$-0.0351518\pi$
$264$		0			0
$265$	−7.45747e6			−0.400732
$266$	1.81197e7	+	3.80605e7i	0.962731	+	2.02222i
$267$		0			0
$268$	−1.21332e7	−	9.85480e6i	−0.630336	−	0.511969i
$269$	−777261.			−0.0399310			−0.0199655	−	0.999801i	$-0.506356\pi$
$269$	−777261.			−0.0399310			−0.0199655	+	0.999801i	$0.506356\pi$
$270$		0			0
$271$			3.29929e7i			1.65773i	0.559450	+	0.828864i	$0.311012\pi$
$271$			3.29929e7i			1.65773i	−0.559450	+	0.828864i	$0.688988\pi$
$272$	5.24725e6	+	2.50475e7i	0.260750	+	1.24468i
$273$		0			0
$274$	1.29064e7	+	2.71100e7i	0.627413	+	1.31789i
$275$			2.93560e6i			0.141156i
$276$		0			0
$277$	−2.00830e7			−0.944906			−0.472453	−	0.881356i	$-0.656631\pi$
$277$	−2.00830e7			−0.944906			−0.472453	+	0.881356i	$0.656631\pi$
$278$	−3.05199e7	+	1.45298e7i	−1.42052	+	0.676277i
$279$		0			0
$280$	−3.18277e6	+	1.31298e7i	−0.144988	+	0.598116i
$281$	−3.59969e7			−1.62235			−0.811177	−	0.584800i	$-0.801173\pi$
$281$	−3.59969e7			−1.62235			−0.811177	+	0.584800i	$0.801173\pi$
$282$		0			0
$283$			8.24433e6i			0.363744i	0.983322	+	0.181872i	$0.0582157\pi$
$283$			8.24433e6i			0.363744i	−0.983322	+	0.181872i	$0.941784\pi$
$284$	706801.	+	574075.i	0.0308562	+	0.0250619i
$285$		0			0
$286$	153251.	−	72959.2i	0.00655098	−	0.00311876i
$287$		−	5.33824e7i		−	2.25815i
$288$		0			0
$289$	1.48982e7			0.617221
$290$	−4.92502e6	−	1.03451e7i	−0.201936	−	0.424169i
$291$		0			0
$292$	1.12370e7	−	1.38350e7i	0.451337	−	0.555686i
$293$	−1.01669e7			−0.404191			−0.202096	−	0.979366i	$-0.564775\pi$
$293$	−1.01669e7			−0.404191			−0.202096	+	0.979366i	$0.564775\pi$
$294$		0			0
$295$			3.08660e6i			0.120230i
$296$	−2.52259e7	−	6.11495e6i	−0.972685	−	0.235786i
$297$		0			0
$298$	1.29840e7	+	2.72729e7i	0.490635	+	1.03058i
$299$		−	26383.9i		−	0.000987018i
$300$		0			0
$301$	5.36817e7			1.96846
$302$	2.40780e7	−	1.14629e7i	0.874176	−	0.416174i
$303$		0			0
$304$	−4.47521e7	+	9.37521e6i	−1.59292	+	0.333703i
$305$	−1.14495e7			−0.403539
$306$		0			0
$307$		−	1.30424e7i		−	0.450756i	−0.974271	−	0.225378i	$-0.927638\pi$
$307$		−	1.30424e7i		−	0.450756i	0.974271	−	0.225378i	$-0.0723617\pi$
$308$	−1.78915e7	+	2.20281e7i	−0.612344	+	0.753918i
$309$		0			0
$310$	1.73803e6	−	827432.i	0.0583406	−	0.0277745i
$311$			1.78289e7i			0.592712i	0.955077	+	0.296356i	$0.0957716\pi$
$311$			1.78289e7i			0.592712i	−0.955077	+	0.296356i	$0.904228\pi$
$312$		0			0
$313$	992789.			0.0323761			0.0161880	−	0.999869i	$-0.494847\pi$
$313$	992789.			0.0323761			0.0161880	+	0.999869i	$0.494847\pi$
$314$	2.49560e7	+	5.24203e7i	0.806096	+	1.69321i
$315$		0			0
$316$	−1.78333e7	−	1.44845e7i	−0.565158	−	0.459030i
$317$	4.91937e6			0.154430			0.0772150	−	0.997014i	$-0.475397\pi$
$317$	4.91937e6			0.154430			0.0772150	+	0.997014i	$0.475397\pi$
$318$		0			0
$319$		−	2.40671e7i		−	0.741400i
$320$	−1.30277e7	−	6.71031e6i	−0.397573	−	0.204782i
$321$		0			0
$322$	1.89619e6	+	3.98295e6i	0.0567954	+	0.119299i
$323$			6.97448e7i			2.06969i
$324$		0			0
$325$	70579.3			0.00205602
$326$	−1.44959e7	+	6.90114e6i	−0.418400	+	0.199190i
$327$		0			0
$328$	5.62737e7	+	1.36412e7i	1.59472	+	0.386572i
$329$	8.69678e7			2.44214
$330$		0			0
$331$		−	5.36048e7i		−	1.47815i	−0.673620	−	0.739077i	$-0.735262\pi$
$331$		−	5.36048e7i		−	1.47815i	0.673620	−	0.739077i	$-0.264738\pi$
$332$	−4.07667e7	−	3.31114e7i	−1.11402	−	0.904821i
$333$		0			0
$334$	2.85344e7	−	1.35845e7i	0.765824	−	0.364590i
$335$		−	1.36532e7i		−	0.363162i
$336$		0			0
$337$	6.45496e7			1.68657			0.843284	−	0.537468i	$-0.180619\pi$
$337$	6.45496e7			1.68657			0.843284	+	0.537468i	$0.180619\pi$
$338$	1.65966e7	+	3.48614e7i	0.429803	+	0.902805i
$339$		0			0
$340$	−1.40927e7	+	1.73509e7i	−0.358556	+	0.441454i
$341$	4.04341e6			0.101973
$342$		0			0
$343$		−	5.89641e6i		−	0.146119i
$344$	−1.37176e7	+	5.65892e7i	−0.336980	+	1.39014i
$345$		0			0
$346$	−1.45593e7	−	3.05819e7i	−0.351489	−	0.738305i
$347$		−	4.82937e7i		−	1.15585i	−0.816089	−	0.577926i	$-0.803862\pi$
$347$		−	4.82937e7i		−	1.15585i	0.816089	−	0.577926i	$-0.196138\pi$
$348$		0			0
$349$	−3.08221e7			−0.725081			−0.362541	−	0.931968i	$-0.618091\pi$
$349$	−3.08221e7			−0.725081			−0.362541	+	0.931968i	$0.618091\pi$
$350$	−1.06548e7	+	5.07247e6i	−0.248508	+	0.118308i
$351$		0			0
$352$	−1.86492e7	−	2.44896e7i	−0.427595	−	0.561504i
$353$	6.23969e7			1.41853			0.709266	−	0.704941i	$-0.249026\pi$
$353$	6.23969e7			1.41853			0.709266	+	0.704941i	$0.249026\pi$
$354$		0			0
$355$			795347.i			0.0177775i
$356$	4.05590e7	−	4.99362e7i	0.898954	−	1.10679i
$357$		0			0
$358$	3.67669e7	−	1.75038e7i	0.801324	−	0.381491i
$359$		−	5.26134e7i		−	1.13714i	−0.822636	−	0.568569i	$-0.807497\pi$
$359$		−	5.26134e7i		−	1.13714i	0.822636	−	0.568569i	$-0.192503\pi$
$360$		0			0
$361$	−7.75664e7			−1.64874
$362$	−2.64477e7	−	5.55537e7i	−0.557523	−	1.17108i
$363$		0			0
$364$	529611.	+	430158.i	0.0109813	+	0.00891917i
$365$	1.55681e7			0.320154
$366$		0			0
$367$			2.05775e7i			0.416288i	0.978098	+	0.208144i	$0.0667423\pi$
$367$			2.05775e7i			0.416288i	−0.978098	+	0.208144i	$0.933258\pi$
$368$	−4.68322e6	+	981096.i	−0.0939726	+	0.0196865i
$369$		0			0
$370$	−9.74557e6	−	2.04706e7i	−0.192399	−	0.404135i
$371$		−	6.29695e7i		−	1.23313i
$372$		0			0
$373$	−2.72046e7			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$373$	−2.72046e7			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$374$	−4.23944e7	+	2.01829e7i	−0.810389	+	0.385806i
$375$		0			0
$376$	−2.22234e7	+	9.16781e7i	−0.418069	+	1.72465i
$377$	−578635.			−0.0107989
$378$		0			0
$379$		−	7.15245e7i		−	1.31382i	−0.753967	−	0.656912i	$-0.771862\pi$
$379$		−	7.15245e7i		−	1.31382i	0.753967	−	0.656912i	$-0.228138\pi$
$380$	−3.10007e7	−	2.51793e7i	−0.564964	−	0.458873i
$381$		0			0
$382$	−3.40946e6	+	1.62316e6i	−0.0611639	+	0.0291186i
$383$		−	4.10963e7i		−	0.731486i	−0.930716	−	0.365743i	$-0.880815\pi$
$383$		−	4.10963e7i		−	0.731486i	0.930716	−	0.365743i	$-0.119185\pi$
$384$		0			0
$385$	−2.47877e7			−0.434363
$386$	1.98379e7	+	4.16696e7i	0.344932	+	0.724532i
$387$		0			0
$388$	−5.81820e7	+	7.16337e7i	−0.996078	+	1.22637i
$389$	1.73618e7			0.294948			0.147474	−	0.989066i	$-0.452886\pi$
$389$	1.73618e7			0.294948			0.147474	+	0.989066i	$0.452886\pi$
$390$		0			0
$391$			7.29865e6i			0.122099i
$392$	−5.23251e7	−	1.26840e7i	−0.868664	−	0.210571i
$393$		0			0
$394$	3.48365e7	+	7.31743e7i	0.569568	+	1.19638i
$395$		−	2.00674e7i		−	0.325611i
$396$		0			0
$397$	−1.59499e7			−0.254909			−0.127455	−	0.991844i	$-0.540681\pi$
$397$	−1.59499e7			−0.254909			−0.127455	+	0.991844i	$0.540681\pi$
$398$	6.28079e7	−	2.99013e7i	0.996242	−	0.474286i
$399$		0			0
$400$	−2.62452e6	−	1.25280e7i	−0.0410082	−	0.195751i
$401$	4.96019e7			0.769245			0.384623	−	0.923074i	$-0.374332\pi$
$401$	4.96019e7			0.769245			0.384623	+	0.923074i	$0.374332\pi$
$402$		0			0
$403$		−	97214.0i		−	0.00148530i
$404$	3.14025e7	−	3.86628e7i	0.476234	−	0.586339i
$405$		0			0
$406$	8.73517e7	−	4.15860e7i	1.30525	−	0.621397i
$407$		−	4.76237e7i		−	0.706383i
$408$		0			0
$409$	7.38246e7			1.07902			0.539512	−	0.841978i	$-0.318609\pi$
$409$	7.38246e7			1.07902			0.539512	+	0.841978i	$0.318609\pi$
$410$	2.17403e7	+	4.56657e7i	0.315438	+	0.662580i
$411$		0			0
$412$	−5.75135e7	−	4.67134e7i	−0.822390	−	0.667959i
$413$	−2.60627e7			−0.369972
$414$		0			0
$415$		−	4.58738e7i		−	0.641830i
$416$	−588792.	+	448374.i	−0.00817865	+	0.00622817i
$417$		0			0
$418$	−3.60606e7	−	7.57456e7i	−0.493747	−	1.03712i
$419$			1.31477e8i			1.78735i	0.448717	+	0.893674i	$0.351881\pi$
$419$			1.31477e8i			1.78735i	−0.448717	+	0.893674i	$0.648119\pi$
$420$		0			0
$421$	−1.33132e8			−1.78417			−0.892087	−	0.451863i	$-0.850760\pi$
$421$	−1.33132e8			−1.78417			−0.892087	+	0.451863i	$0.850760\pi$
$422$	−1.52380e7	+	7.25444e6i	−0.202764	+	0.0965310i
$423$		0			0
$424$	6.63800e7	+	1.60910e7i	0.870843	+	0.211099i
$425$	−1.95246e7			−0.254340
$426$		0			0
$427$		−	9.66771e7i		−	1.24177i
$428$	5.09944e7	+	4.14184e7i	0.650416	+	0.528278i
$429$		0			0
$430$	−4.59217e7	+	2.18622e7i	−0.577581	+	0.274972i
$431$		−	4.13997e7i		−	0.517089i	−0.965999	−	0.258544i	$-0.916757\pi$
$431$		−	4.13997e7i		−	0.517089i	0.965999	−	0.258544i	$-0.0832428\pi$
$432$		0			0
$433$	−1.14745e8			−1.41341			−0.706706	−	0.707507i	$-0.749820\pi$
$433$	−1.14745e8			−1.41341			−0.706706	+	0.707507i	$0.749820\pi$
$434$	6.98668e6	+	1.46756e7i	0.0854676	+	0.179525i
$435$		0			0
$436$	−3.10464e7	+	3.82243e7i	−0.374586	+	0.461190i
$437$	−1.30404e7			−0.156260
$438$		0			0
$439$		−	6.31007e7i		−	0.745832i	−0.927865	−	0.372916i	$-0.878358\pi$
$439$		−	6.31007e7i		−	0.745832i	0.927865	−	0.372916i	$-0.121642\pi$
$440$	6.33415e6	−	2.61302e7i	0.0743585	−	0.306750i
$441$		0			0
$442$	485249.	+	1.01927e6i	0.00561950	+	0.0118038i
$443$			3.81520e7i			0.438840i	0.975630	+	0.219420i	$0.0704165\pi$
$443$			3.81520e7i			0.438840i	−0.975630	+	0.219420i	$0.929584\pi$
$444$		0			0
$445$	5.61921e7			0.637668
$446$	−3.69156e7	+	1.75746e7i	−0.416107	+	0.198098i
$447$		0			0
$448$	5.66606e7	−	1.10003e8i	0.630155	−	1.22341i
$449$	−1.25616e8			−1.38773			−0.693867	−	0.720103i	$-0.744095\pi$
$449$	−1.25616e8			−1.38773			−0.693867	+	0.720103i	$0.744095\pi$
$450$		0			0
$451$			1.06238e8i			1.15812i
$452$	−1.36138e7	+	1.67613e7i	−0.147423	+	0.181507i
$453$		0			0
$454$	−1.54446e7	+	7.35278e6i	−0.165047	+	0.0785749i
$455$			595959.i			0.00632677i
$456$		0			0
$457$	5.74907e7			0.602350			0.301175	−	0.953569i	$-0.402621\pi$
$457$	5.74907e7			0.602350			0.301175	+	0.953569i	$0.402621\pi$
$458$	−4.94488e7	−	1.03868e8i	−0.514707	−	1.08114i
$459$		0			0
$460$	−3.24416e6	−	2.63496e6i	−0.0333295	−	0.0270707i
$461$	−2.77042e7			−0.282776			−0.141388	−	0.989954i	$-0.545156\pi$
$461$	−2.77042e7			−0.282776			−0.141388	+	0.989954i	$0.545156\pi$
$462$		0			0
$463$			1.76037e8i			1.77362i	0.462137	+	0.886809i	$0.347083\pi$
$463$			1.76037e8i			1.77362i	−0.462137	+	0.886809i	$0.652917\pi$
$464$	2.15168e7	+	1.02710e8i	0.215389	+	1.02815i
$465$		0			0
$466$	−7.45898e7	−	1.56676e8i	−0.737092	−	1.54827i
$467$			7.46722e7i			0.733176i	0.930383	+	0.366588i	$0.119474\pi$
$467$			7.46722e7i			0.733176i	−0.930383	+	0.366588i	$0.880526\pi$
$468$		0			0
$469$	1.15285e8			1.11752
$470$	−7.43960e7	+	3.54181e7i	−0.716566	+	0.341139i
$471$		0			0
$472$	6.65997e6	−	2.74743e7i	0.0633354	−	0.261277i
$473$	−1.06834e8			−1.00955
$474$		0			0
$475$		−	3.48843e7i		−	0.325499i
$476$	−1.46508e8	−	1.18996e8i	−1.35844	−	1.10335i
$477$		0			0
$478$	−3.17627e7	+	1.51214e7i	−0.290826	+	0.138455i
$479$			1.32477e7i			0.120541i	0.998182	+	0.0602705i	$0.0191963\pi$
$479$			1.32477e7i			0.120541i	−0.998182	+	0.0602705i	$0.980804\pi$
$480$		0			0
$481$	−1.14500e6			−0.0102889
$482$	−5.92040e7	−	1.24359e8i	−0.528701	−	1.11054i
$483$		0			0
$484$	−3.58748e7	+	4.41691e7i	−0.316413	+	0.389567i
$485$	−8.06077e7			−0.706563
$486$		0			0
$487$		−	4.04387e7i		−	0.350114i	−0.984558	−	0.175057i	$-0.943989\pi$
$487$		−	4.04387e7i		−	0.350114i	0.984558	−	0.175057i	$-0.0560110\pi$
$488$	1.01913e8	+	2.47045e7i	0.876943	+	0.212578i
$489$		0			0
$490$	−2.02148e7	−	4.24614e7i	−0.171823	−	0.360916i
$491$			2.04121e8i			1.72442i	0.506547	+	0.862212i	$0.330922\pi$
$491$			2.04121e8i			1.72442i	−0.506547	+	0.862212i	$0.669078\pi$
$492$		0			0
$493$	1.60070e8			1.33588
$494$	−1.82112e6	+	866989.i	−0.0151063	+	0.00719172i
$495$		0			0
$496$	−1.72558e7	+	3.61494e6i	−0.141413	+	0.0296249i
$497$	−6.71576e6			−0.0547049
$498$		0			0
$499$		−	6.92447e7i		−	0.557294i	−0.960394	−	0.278647i	$-0.910114\pi$
$499$		−	6.92447e7i		−	0.557294i	0.960394	−	0.278647i	$-0.0898860\pi$
$500$	7.04875e6	−	8.67842e6i	0.0563900	−	0.0694274i
$501$		0			0
$502$	−3.57381e7	+	1.70140e7i	−0.282501	+	0.134492i
$503$		−	1.44266e8i		−	1.13360i	−0.823856	−	0.566799i	$-0.808182\pi$
$503$		−	1.44266e8i		−	1.13360i	0.823856	−	0.566799i	$-0.191818\pi$
$504$		0			0
$505$	4.35063e7			0.337814
$506$	−3.77367e6	−	7.92662e6i	−0.0291281	−	0.0611838i
$507$		0			0
$508$	−1.54222e8	−	1.25262e8i	−1.17640	−	0.955494i
$509$	7.15475e7			0.542552			0.271276	−	0.962502i	$-0.412554\pi$
$509$	7.15475e7			0.542552			0.271276	+	0.962502i	$0.412554\pi$
$510$		0			0
$511$			1.31455e8i			0.985174i
$512$	1.01482e8	+	8.78393e7i	0.756102	+	0.654454i
$513$		0			0
$514$	8.66097e7	+	1.81924e8i	0.637789	+	1.33968i
$515$		−	6.47186e7i		−	0.473813i
$516$		0			0
$517$	−1.73078e8			−1.25248
$518$	1.72850e8	−	8.22898e7i	1.24360	−	0.592048i
$519$		0			0
$520$	−628237.	−	152289.i	−0.00446800	−	0.00108308i
$521$	−8.19625e7			−0.579565			−0.289783	−	0.957093i	$-0.593583\pi$
$521$	−8.19625e7			−0.579565			−0.289783	+	0.957093i	$0.593583\pi$
$522$		0			0
$523$			2.55778e8i			1.78796i	0.448107	+	0.893980i	$0.352098\pi$
$523$			2.55778e8i			1.78796i	−0.448107	+	0.893980i	$0.647902\pi$
$524$	−3.49317e6	−	2.83721e6i	−0.0242787	−	0.0197196i
$525$		0			0
$526$	−2.89628e7	+	1.37885e7i	−0.199014	+	0.0947457i
$527$			2.68926e7i			0.183739i
$528$		0			0
$529$	1.46671e8			0.990782
$530$	2.56447e7	+	5.38668e7i	0.172254	+	0.361821i
$531$		0			0
$532$	2.12609e8	−	2.61764e8i	1.41204	−	1.73850i
$533$	2.55424e6			0.0168687
$534$		0			0
$535$			5.73827e7i			0.374731i
$536$	−2.94596e7	+	1.21529e8i	−0.191308	+	0.789200i
$537$		0			0
$538$	2.67284e6	+	5.61432e6i	0.0171643	+	0.0360537i
$539$		−	9.87838e7i		−	0.630841i
$540$		0			0
$541$	−2.16239e8			−1.36566			−0.682831	−	0.730577i	$-0.739251\pi$
$541$	−2.16239e8			−1.36566			−0.682831	+	0.730577i	$0.739251\pi$
$542$	2.38315e8	−	1.13456e8i	1.49676	−	0.712573i
$543$		0			0
$544$	1.62879e8	−	1.24035e8i	1.01174	−	0.770456i
$545$	−4.30129e7			−0.265711
$546$		0			0
$547$		−	1.04526e6i		−	0.00638648i	−0.999995	−	0.00319324i	$-0.998984\pi$
$547$		−	1.04526e6i		−	0.00638648i	0.999995	−	0.00319324i	$-0.00101644\pi$
$548$	1.51439e8	−	1.86451e8i	0.920227	−	1.13298i
$549$		0			0
$550$	2.12044e7	−	1.00949e7i	0.127450	−	0.0606757i
$551$			2.85995e8i			1.70963i
$552$		0			0
$553$	1.69445e8			1.00197
$554$	6.90611e7	+	1.45063e8i	0.406167	+	0.853157i
$555$		0			0
$556$	2.09903e8	+	1.70487e8i	1.22122	+	0.991895i
$557$	−1.12606e8			−0.651624			−0.325812	−	0.945435i	$-0.605638\pi$
$557$	−1.12606e8			−0.651624			−0.325812	+	0.945435i	$0.605638\pi$
$558$		0			0
$559$			2.56856e6i			0.0147047i
$560$	1.05784e8	−	2.21610e7i	0.602362	−	0.126190i
$561$		0			0
$562$	1.23786e8	+	2.60013e8i	0.697367	+	1.46483i
$563$			1.29568e8i			0.726060i	0.931777	+	0.363030i	$0.118258\pi$
$563$			1.29568e8i			0.726060i	−0.931777	+	0.363030i	$0.881742\pi$
$564$		0			0
$565$	−1.88611e7			−0.104574
$566$	5.95505e7	−	2.83505e7i	0.328425	−	0.156355i
$567$		0			0
$568$	1.71612e6	−	7.07950e6i	0.00936490	−	0.0386329i
$569$	9.50189e7			0.515791			0.257895	−	0.966173i	$-0.416971\pi$
$569$	9.50189e7			0.515791			0.257895	+	0.966173i	$0.416971\pi$
$570$		0			0
$571$		−	2.03875e7i		−	0.109510i	−0.998500	−	0.0547552i	$-0.982562\pi$
$571$		−	2.03875e7i		−	0.109510i	0.998500	−	0.0547552i	$-0.0174378\pi$
$572$	−1.05400e6	−	856075.i	−0.00563186	−	0.00457429i
$573$		0			0
$574$	−3.85592e8	+	1.83571e8i	−2.03889	+	0.970663i
$575$		−	3.65058e6i		−	0.0192025i
$576$		0			0
$577$	−1.37188e8			−0.714149			−0.357074	−	0.934076i	$-0.616226\pi$
$577$	−1.37188e8			−0.714149			−0.357074	+	0.934076i	$0.616226\pi$
$578$	−5.12318e7	−	1.07613e8i	−0.265312	−	0.557289i
$579$		0			0
$580$	−5.77883e7	+	7.11489e7i	−0.296180	+	0.364657i
$581$	3.87350e8			1.97504
$582$		0			0
$583$			1.25318e8i			0.632423i
$584$	−1.38574e8	−	3.35914e7i	−0.695736	−	0.168651i
$585$		0			0
$586$	3.49619e7	+	7.34378e7i	0.173741	+	0.364945i
$587$			1.85031e8i			0.914808i	0.889259	+	0.457404i	$0.151221\pi$
$587$			1.85031e8i			0.914808i	−0.889259	+	0.457404i	$0.848779\pi$
$588$		0			0
$589$	−4.80487e7			−0.235145
$590$	2.22952e7	−	1.06142e7i	0.108556	−	0.0516809i
$591$		0			0
$592$	4.25772e7	+	2.03240e8i	0.205216	+	0.979590i
$593$	−1.40041e8			−0.671570			−0.335785	−	0.941939i	$-0.609002\pi$
$593$	−1.40041e8			−0.671570			−0.335785	+	0.941939i	$0.609002\pi$
$594$		0			0
$595$		−	1.64862e8i		−	0.782653i
$596$	1.52349e8	−	1.87572e8i	0.719616	−	0.885990i
$597$		0			0
$598$	−190576.	+	90728.7i	−0.000891179	+	0.000424269i
$599$			3.86610e6i			0.0179884i	0.999960	+	0.00899421i	$0.00286298\pi$
$599$			3.86610e6i			0.0179884i	−0.999960	+	0.00899421i	$0.997137\pi$
$600$		0			0
$601$	1.17489e8			0.541220			0.270610	−	0.962689i	$-0.412775\pi$
$601$	1.17489e8			0.541220			0.270610	+	0.962689i	$0.412775\pi$
$602$	−1.84600e8	−	3.87754e8i	−0.846141	−	1.77733i
$603$		0			0
$604$	−1.65598e8	−	1.34501e8i	−0.751527	−	0.610402i
$605$	−4.97024e7			−0.224446
$606$		0			0
$607$			3.82398e8i			1.70982i	0.518778	+	0.854909i	$0.326387\pi$
$607$			3.82398e8i			1.70982i	−0.518778	+	0.854909i	$0.673613\pi$
$608$	2.21612e8	+	2.91015e8i	0.986014	+	1.29480i
$609$		0			0
$610$	3.93723e7	+	8.27018e7i	0.173461	+	0.364356i
$611$			4.16123e6i			0.0182431i
$612$		0			0
$613$	−91040.9			−0.000395235			−0.000197617	−	1.00000i	$-0.500063\pi$
$613$	−91040.9			−0.000395235			−0.000197617		1.00000i	$0.500063\pi$
$614$	−9.42078e7	+	4.48500e7i	−0.406988	+	0.193757i
$615$		0			0
$616$	2.20639e8	+	5.34844e7i	0.943929	+	0.228815i
$617$	2.18687e8			0.931039			0.465519	−	0.885038i	$-0.345868\pi$
$617$	2.18687e8			0.931039			0.465519	+	0.885038i	$0.345868\pi$
$618$		0			0
$619$		−	1.09965e8i		−	0.463641i	−0.972759	−	0.231820i	$-0.925532\pi$
$619$		−	1.09965e8i		−	0.463641i	0.972759	−	0.231820i	$-0.0744682\pi$
$620$	−1.19534e7	−	9.70876e6i	−0.0501553	−	0.0407370i
$621$		0			0
$622$	1.28782e8	−	6.13100e7i	0.535161	−	0.254777i
$623$			4.74475e8i			1.96223i
$624$		0			0
$625$	9.76562e6			0.0400000
$626$	−3.41399e6	−	7.17112e6i	−0.0139168	−	0.0292324i
$627$		0			0
$628$	2.92824e8	−	3.60525e8i	1.18230	−	1.45565i
$629$	3.16744e8			1.27279
$630$		0			0
$631$			6.46615e6i			0.0257370i	0.999917	+	0.0128685i	$0.00409628\pi$
$631$			6.46615e6i			0.0257370i	−0.999917	+	0.0128685i	$0.995904\pi$
$632$	−4.32994e7	+	1.78623e8i	−0.171526	+	0.707596i
$633$		0			0
$634$	−1.69167e7	−	3.55336e7i	−0.0663815	−	0.139435i
$635$		−	1.73543e8i		−	0.677775i
$636$		0			0
$637$	−2.37502e6			−0.00918858
$638$	−1.73842e8	+	8.27619e7i	−0.669410	+	0.318690i
$639$		0			0
$640$	−3.67054e6	+	1.17177e8i	−0.0140020	+	0.446994i
$641$	−1.74561e7			−0.0662785			−0.0331393	−	0.999451i	$-0.510550\pi$
$641$	−1.74561e7			−0.0662785			−0.0331393	+	0.999451i	$0.510550\pi$
$642$		0			0
$643$			5.28201e7i			0.198685i	0.995053	+	0.0993427i	$0.0316740\pi$
$643$			5.28201e7i			0.198685i	−0.995053	+	0.0993427i	$0.968326\pi$
$644$	2.22491e7	−	2.73931e7i	0.0833019	−	0.102561i
$645$		0			0
$646$	5.03781e8	−	2.39838e8i	1.86872	−	0.889652i
$647$		−	2.46885e8i		−	0.911552i	−0.890094	−	0.455776i	$-0.849362\pi$
$647$		−	2.46885e8i		−	0.911552i	0.890094	−	0.455776i	$-0.150638\pi$
$648$		0			0
$649$	5.18683e7			0.189744
$650$	−242708.	−	509809.i	−0.000883778	−	0.00185638i
$651$		0			0
$652$	9.96967e7	+	8.09752e7i	0.359698	+	0.292152i
$653$	−4.03664e8			−1.44971			−0.724854	−	0.688903i	$-0.758093\pi$
$653$	−4.03664e8			−1.44971			−0.724854	+	0.688903i	$0.758093\pi$
$654$		0			0
$655$		−	3.93078e6i		−	0.0139880i
$656$	−9.49806e7	−	4.53386e8i	−0.336452	−	1.60604i
$657$		0			0
$658$	−2.99064e8	−	6.28186e8i	−1.04975	−	2.20501i
$659$			1.15030e8i			0.401935i	0.979598	+	0.200968i	$0.0644086\pi$
$659$			1.15030e8i			0.401935i	−0.979598	+	0.200968i	$0.935591\pi$
$660$		0			0
$661$	−1.28637e8			−0.445410			−0.222705	−	0.974886i	$-0.571489\pi$
$661$	−1.28637e8			−0.445410			−0.222705	+	0.974886i	$0.571489\pi$
$662$	−3.87199e8	+	1.84336e8i	−1.33463	+	0.635383i
$663$		0			0
$664$	−9.89820e7	+	4.08329e8i	−0.338105	+	1.39478i
$665$	2.94557e8			1.00162
$666$		0			0
$667$			2.99288e7i			0.100858i
$668$	−1.96248e8	−	1.59395e8i	−0.658377	−	0.534744i
$669$		0			0
$670$	−9.86201e7	+	4.69506e7i	−0.327900	+	0.156105i
$671$			1.92401e8i			0.636853i
$672$		0			0
$673$	−2.22256e7			−0.0729137			−0.0364568	−	0.999335i	$-0.511607\pi$
$673$	−2.22256e7			−0.0729137			−0.0364568	+	0.999335i	$0.511607\pi$
$674$	−2.21973e8	−	4.66255e8i	−0.724969	−	1.52280i
$675$		0			0
$676$	1.94738e8	−	2.39762e8i	0.630393	−	0.776140i
$677$	−1.43051e8			−0.461025			−0.230512	−	0.973069i	$-0.574040\pi$
$677$	−1.43051e8			−0.461025			−0.230512	+	0.973069i	$0.574040\pi$
$678$		0			0
$679$		−	6.80636e8i		−	2.17423i
$680$	1.73791e8	+	4.21282e7i	0.552714	+	0.133982i
$681$		0			0
$682$	−1.39045e7	−	2.92064e7i	−0.0438330	−	0.0920715i
$683$		−	1.47199e8i		−	0.461999i	−0.972954	−	0.231000i	$-0.925800\pi$
$683$		−	1.47199e8i		−	0.461999i	0.972954	−	0.231000i	$-0.0741996\pi$
$684$		0			0
$685$	2.09809e8			0.652759
$686$	−4.25910e7	+	2.02765e7i	−0.131931	+	0.0628089i
$687$		0			0
$688$	4.55928e8	−	9.55132e7i	1.40001	−	0.293290i
$689$	3.01296e6			0.00921162
$690$		0			0
$691$		−	4.86917e8i		−	1.47578i	−0.674922	−	0.737889i	$-0.735823\pi$
$691$		−	4.86917e8i		−	1.47578i	0.674922	−	0.737889i	$-0.264177\pi$
$692$	−1.70833e8	+	2.10329e8i	−0.515529	+	0.634719i
$693$		0			0
$694$	−3.48835e8	+	1.66072e8i	−1.04362	+	0.496842i
$695$			2.36199e8i			0.703596i
$696$		0			0
$697$	−7.06588e8			−2.08674
$698$	1.05991e8	+	2.22635e8i	0.311675	+	0.654676i
$699$		0			0
$700$	7.32790e7	+	5.95184e7i	0.213641	+	0.173523i
$701$	−3.70660e8			−1.07602			−0.538012	−	0.842937i	$-0.680824\pi$
$701$	−3.70660e8			−1.07602			−0.538012	+	0.842937i	$0.680824\pi$
$702$		0			0
$703$			5.65922e8i			1.62889i
$704$	−1.12762e8	+	2.18922e8i	−0.323182	+	0.627437i
$705$		0			0
$706$	−2.14570e8	−	4.50706e8i	−0.609754	−	1.28079i
$707$			3.67359e8i			1.03952i
$708$		0			0
$709$	−2.70875e8			−0.760028			−0.380014	−	0.924981i	$-0.624081\pi$
$709$	−2.70875e8			−0.760028			−0.380014	+	0.924981i	$0.624081\pi$
$710$	5.74495e6	−	2.73503e6i	0.0160513	−	0.00764165i
$711$		0			0
$712$	−5.00174e8	−	1.21246e8i	−1.38574	−	0.335913i
$713$	−5.02820e6			−0.0138722
$714$		0			0
$715$		−	1.18604e6i		−	0.00324475i
$716$	−2.52867e8	−	2.05383e8i	−0.688896	−	0.559532i
$717$		0			0
$718$	−3.80037e8	+	1.80926e8i	−1.02672	+	0.488797i
$719$		−	6.11851e8i		−	1.64611i	−0.567962	−	0.823055i	$-0.692268\pi$
$719$		−	6.11851e8i		−	1.64611i	0.567962	−	0.823055i	$-0.307732\pi$
$720$		0			0
$721$	5.46471e8			1.45801
$722$	2.66735e8	+	5.60278e8i	0.708709	+	1.48865i
$723$		0			0
$724$	−3.10327e8	+	3.82075e8i	−0.817719	+	1.00678i
$725$	−8.00622e7			−0.210094
$726$		0			0
$727$		−	4.50232e8i		−	1.17175i	−0.810403	−	0.585873i	$-0.800752\pi$
$727$		−	4.50232e8i		−	1.17175i	0.810403	−	0.585873i	$-0.199248\pi$
$728$	1.28590e6	−	5.30471e6i	0.00333283	−	0.0137489i
$729$		0			0
$730$	−5.35356e7	−	1.12452e8i	−0.137618	−	0.289067i
$731$		−	7.10550e8i		−	1.81904i
$732$		0			0
$733$	−6.51431e8			−1.65408			−0.827040	−	0.562143i	$-0.809977\pi$
$733$	−6.51431e8			−1.65408			−0.827040	+	0.562143i	$0.809977\pi$
$734$	1.48635e8	−	7.07617e7i	0.375867	−	0.178941i
$735$		0			0
$736$	2.31913e7	+	3.04541e7i	0.0581689	+	0.0763857i
$737$	−2.29434e8			−0.573132
$738$		0			0
$739$			4.11562e8i			1.01977i	0.860243	+	0.509885i	$0.170312\pi$
$739$			4.11562e8i			1.01977i	−0.860243	+	0.509885i	$0.829688\pi$
$740$	−1.14351e8	+	1.40789e8i	−0.282191	+	0.347434i
$741$		0			0
$742$	−4.54841e8	+	2.16539e8i	−1.11339	+	0.530059i
$743$			1.79409e8i			0.437400i	0.975792	+	0.218700i	$0.0701816\pi$
$743$			1.79409e8i			0.437400i	−0.975792	+	0.218700i	$0.929818\pi$
$744$		0			0
$745$	2.11070e8			0.510456
$746$	9.35508e7	+	1.96504e8i	0.225336	+	0.473320i
$747$		0			0
$748$	2.91571e8	+	2.36819e8i	0.696690	+	0.565862i
$749$	−4.84529e8			−1.15312
$750$		0			0
$751$			3.37918e8i			0.797796i	0.916995	+	0.398898i	$0.130607\pi$
$751$			3.37918e8i			0.797796i	−0.916995	+	0.398898i	$0.869393\pi$
$752$	7.38632e8	−	1.54737e8i	1.73690	−	0.363866i
$753$		0			0
$754$	1.98981e6	+	4.17960e6i	0.00464191	+	0.00975037i
$755$		−	1.86344e8i		−	0.432986i
$756$		0			0
$757$	4.17269e8			0.961896			0.480948	−	0.876749i	$-0.340293\pi$
$757$	4.17269e8			0.961896			0.480948	+	0.876749i	$0.340293\pi$
$758$	−5.16636e8	+	2.45958e8i	−1.18625	+	0.564746i
$759$		0			0
$760$	−7.52701e7	+	3.10511e8i	−0.171467	+	0.707352i
$761$	4.73073e8			1.07343			0.536715	−	0.843763i	$-0.319665\pi$
$761$	4.73073e8			1.07343			0.536715	+	0.843763i	$0.319665\pi$
$762$		0			0
$763$		−	3.63193e8i		−	0.817643i
$764$	2.34488e7	+	1.90455e7i	0.0525824	+	0.0427083i
$765$		0			0
$766$	−2.96847e8	+	1.41322e8i	−0.660460	+	0.314429i
$767$		−	1.24705e6i		−	0.00276374i
$768$		0			0
$769$	−1.35864e8			−0.298763			−0.149381	−	0.988780i	$-0.547728\pi$
$769$	−1.35864e8			−0.298763			−0.149381	+	0.988780i	$0.547728\pi$
$770$	8.52396e7	+	1.79046e8i	0.186711	+	0.392187i
$771$		0			0
$772$	2.32770e8	−	2.86586e8i	0.505912	−	0.622879i
$773$	−8.97765e8			−1.94368			−0.971839	−	0.235646i	$-0.924279\pi$
$773$	−8.97765e8			−1.94368			−0.971839	+	0.235646i	$0.924279\pi$
$774$		0			0
$775$		−	1.34509e7i		−	0.0288966i
$776$	7.17501e8	+	1.73927e8i	1.53545	+	0.372206i
$777$		0			0
$778$	−5.97035e7	−	1.25408e8i	−0.126783	−	0.266309i
$779$		−	1.26245e9i		−	2.67056i
$780$		0			0
$781$	1.33653e7			0.0280560
$782$	5.27197e7	−	2.50985e7i	0.110243	−	0.0524842i
$783$		0			0
$784$	8.83160e7	+	4.21573e8i	0.183270	+	0.874831i
$785$	4.05690e8			0.838660
$786$		0			0
$787$			5.14017e8i			1.05452i	0.849705	+	0.527258i	$0.176780\pi$
$787$			5.14017e8i			1.05452i	−0.849705	+	0.527258i	$0.823220\pi$
$788$	4.08758e8	−	5.03262e8i	0.835386	−	1.02853i
$789$		0			0
$790$	−1.44951e8	+	6.90075e7i	−0.293994	+	0.139964i
$791$		−	1.59260e8i		−	0.321793i
$792$		0			0
$793$	4.62581e6			0.00927615
$794$	5.48482e7	+	1.15209e8i	0.109572	+	0.230158i
$795$		0			0
$796$	−4.31966e8	−	3.50850e8i	−0.856467	−	0.695636i
$797$	7.71528e8			1.52397			0.761986	−	0.647594i	$-0.224225\pi$
$797$	7.71528e8			1.52397			0.761986	+	0.647594i	$0.224225\pi$
$798$		0			0
$799$		−	1.15113e9i		−	2.25676i
$800$	−8.14675e7	+	6.20388e7i	−0.159116	+	0.121170i
$801$		0			0
$802$	−1.70570e8	−	3.58284e8i	−0.330659	−	0.694552i
$803$		−	2.61613e8i		−	0.505257i
$804$		0			0
$805$	3.08248e7			0.0590898
$806$	−702197.	+	334299.i	−0.00134108	+	0.000638454i
$807$		0			0
$808$	−3.87256e8	−	9.38736e7i	−0.734114	−	0.177955i
$809$	1.84538e8			0.348529			0.174265	−	0.984699i	$-0.444245\pi$
$809$	1.84538e8			0.348529			0.174265	+	0.984699i	$0.444245\pi$
$810$		0			0
$811$			3.93099e8i			0.736952i	0.929637	+	0.368476i	$0.120120\pi$
$811$			3.93099e8i			0.736952i	−0.929637	+	0.368476i	$0.879880\pi$
$812$	−6.00768e8	−	4.87954e8i	−1.12212	−	0.911403i
$813$		0			0
$814$	−3.43996e8	+	1.63768e8i	−0.637793	+	0.303638i
$815$			1.12186e8i			0.207237i
$816$		0			0
$817$	1.26953e9			2.32797
$818$	−2.53867e8	−	5.33250e8i	−0.463817	−	0.974251i
$819$		0			0
$820$	2.55092e8	−	3.14069e8i	0.462653	−	0.569618i
$821$	−3.12484e8			−0.564674			−0.282337	−	0.959315i	$-0.591110\pi$
$821$	−3.12484e8			−0.564674			−0.282337	+	0.959315i	$0.591110\pi$
$822$		0			0
$823$		−	3.56442e8i		−	0.639424i	−0.947515	−	0.319712i	$-0.896414\pi$
$823$		−	3.56442e8i		−	0.639424i	0.947515	−	0.319712i	$-0.103586\pi$
$824$	−1.39643e8	+	5.76069e8i	−0.249597	+	1.02966i
$825$		0			0
$826$	8.96242e7	+	1.88256e8i	0.159032	+	0.334048i
$827$			3.14494e8i			0.556027i	0.960577	+	0.278014i	$0.0896760\pi$
$827$			3.14494e8i			0.556027i	−0.960577	+	0.278014i	$0.910324\pi$
$828$		0			0
$829$	−1.01121e8			−0.177491			−0.0887457	−	0.996054i	$-0.528286\pi$
$829$	−1.01121e8			−0.177491			−0.0887457	+	0.996054i	$0.528286\pi$
$830$	−3.31356e8	+	1.57750e8i	−0.579509	+	0.275890i
$831$		0			0
$832$	5.26343e6	+	2.71110e6i	0.00913901	+	0.00470733i
$833$	6.57008e8			1.13667
$834$		0			0
$835$		−	2.20833e8i		−	0.379318i
$836$	−4.23121e8	+	5.20947e8i	−0.724179	+	0.891609i
$837$		0			0
$838$	9.49688e8	−	4.52123e8i	1.61380	−	0.768289i
$839$		−	1.00055e9i		−	1.69416i	−0.531469	−	0.847078i	$-0.678360\pi$
$839$		−	1.00055e9i		−	1.69416i	0.531469	−	0.847078i	$-0.321640\pi$
$840$		0			0
$841$	6.15564e7			0.103487
$842$	4.57814e8	+	9.61643e8i	0.766926	+	1.61093i
$843$		0			0
$844$	1.04801e8	+	8.51208e7i	0.174316	+	0.141582i
$845$	2.69798e8			0.447166
$846$		0			0
$847$		−	4.19678e8i		−	0.690663i
$848$	−1.12038e8	−	5.34810e8i	−0.183730	−	0.877025i
$849$		0			0
$850$	6.71409e7	+	1.41030e8i	0.109328	+	0.229644i
$851$			5.92226e7i			0.0960946i
$852$		0			0
$853$	−2.13653e8			−0.344240			−0.172120	−	0.985076i	$-0.555062\pi$
$853$	−2.13653e8			−0.344240			−0.172120	+	0.985076i	$0.555062\pi$
$854$	−6.98319e8	+	3.32452e8i	−1.12119	+	0.533772i
$855$		0			0
$856$	1.23815e8	−	5.10772e8i	0.197402	−	0.814340i
$857$	4.72771e8			0.751118			0.375559	−	0.926799i	$-0.377451\pi$
$857$	4.72771e8			0.751118			0.375559	+	0.926799i	$0.377451\pi$
$858$		0			0
$859$		−	9.05036e8i		−	1.42786i	−0.700216	−	0.713931i	$-0.746913\pi$
$859$		−	9.05036e8i		−	1.42786i	0.700216	−	0.713931i	$-0.253087\pi$
$860$	3.15830e8	+	2.56522e8i	0.496545	+	0.403302i
$861$		0			0
$862$	−2.99038e8	+	1.42365e8i	−0.466880	+	0.222270i
$863$		−	2.48053e8i		−	0.385932i	−0.981205	−	0.192966i	$-0.938189\pi$
$863$		−	2.48053e8i		−	0.385932i	0.981205	−	0.192966i	$-0.0618108\pi$
$864$		0			0
$865$	−2.36679e8			−0.365688
$866$	3.94583e8	+	8.28824e8i	0.607554	+	1.27617i
$867$		0			0
$868$	8.19789e7	−	1.00932e8i	0.125355	−	0.154338i
$869$	−3.37219e8			−0.513870
$870$		0			0
$871$			5.51617e6i			0.00834802i
$872$	3.82864e8	+	9.28091e7i	0.577424	+	0.139972i
$873$		0			0
$874$	4.48433e7	+	9.41937e7i	0.0671681	+	0.141087i
$875$			8.24591e7i			0.123088i
$876$		0			0
$877$	3.09904e8			0.459439			0.229720	−	0.973257i	$-0.426219\pi$
$877$	3.09904e8			0.459439			0.229720	+	0.973257i	$0.426219\pi$
$878$	−4.55790e8	+	2.16990e8i	−0.673412	+	0.320595i
$879$		0			0
$880$	−2.10526e8	+	4.41034e7i	−0.308928	+	0.0647179i
$881$	−7.41617e8			−1.08456			−0.542278	−	0.840199i	$-0.682438\pi$
$881$	−7.41617e8			−1.08456			−0.542278	+	0.840199i	$0.682438\pi$
$882$		0			0
$883$			1.03000e9i			1.49608i	0.663656	+	0.748038i	$0.269004\pi$
$883$			1.03000e9i			1.49608i	−0.663656	+	0.748038i	$0.730996\pi$
$884$	5.69372e6	−	7.01011e6i	0.00824213	−	0.0101477i
$885$		0			0
$886$	2.75580e8	−	1.31197e8i	0.396229	−	0.188635i
$887$			1.01764e9i			1.45822i	0.684395	+	0.729112i	$0.260066\pi$
$887$			1.01764e9i			1.45822i	−0.684395	+	0.729112i	$0.739934\pi$
$888$		0			0
$889$	1.46536e9			2.08564
$890$	−1.93233e8	−	4.05887e8i	−0.274101	−	0.575751i
$891$		0			0
$892$	2.53890e8	+	2.06213e8i	0.357726	+	0.290551i
$893$	2.05672e9			2.88816
$894$		0			0
$895$		−	2.84546e8i		−	0.396902i
$896$	−9.89420e8	−	3.09934e7i	−1.37549	−	0.0430868i
$897$		0			0
$898$	4.31968e8	+	9.07352e8i	0.596516	+	1.25299i
$899$			1.10275e8i			0.151775i
$900$		0			0
$901$	−8.33485e8			−1.13952
$902$	7.67382e8	−	3.65332e8i	1.04566	−	0.497815i
$903$		0			0
$904$	1.67886e8	+	4.06967e7i	0.227252	+	0.0550876i
$905$	−4.29940e8			−0.580045
$906$		0			0
$907$			1.33458e9i			1.78864i	0.447430	+	0.894319i	$0.352339\pi$
$907$			1.33458e9i			1.78864i	−0.447430	+	0.894319i	$0.647661\pi$
$908$	1.06221e8	+	8.62746e7i	0.141891	+	0.115246i
$909$		0			0
$910$	4.30473e6	−	2.04938e6i	0.00571244	−	0.00271955i
$911$			2.62935e8i			0.347771i	0.984766	+	0.173886i	$0.0556323\pi$
$911$			2.62935e8i			0.347771i	−0.984766	+	0.173886i	$0.944368\pi$
$912$		0			0
$913$	−7.70879e8			−1.01292
$914$	−1.97698e8	−	4.15267e8i	−0.258919	−	0.543862i
$915$		0			0
$916$	−5.80213e8	+	7.14358e8i	−0.754921	+	0.929458i
$917$	3.31908e7			0.0430437
$918$		0			0
$919$		−	9.16411e8i		−	1.18071i	−0.807143	−	0.590356i	$-0.798987\pi$
$919$		−	9.16411e8i		−	1.18071i	0.807143	−	0.590356i	$-0.201013\pi$
$920$	−7.87686e6	+	3.24943e7i	−0.0101156	+	0.0417296i
$921$		0			0
$922$	9.52689e7	+	2.00113e8i	0.121551	+	0.255319i
$923$		−	321336.i		−	0.000408652i
$924$		0			0
$925$	−1.58426e8			−0.200171
$926$	1.27155e9	−	6.05353e8i	1.60140	−	0.762387i
$927$		0			0
$928$	6.67900e8	−	5.08617e8i	0.835733	−	0.636425i
$929$	−7.28953e8			−0.909185			−0.454592	−	0.890700i	$-0.650215\pi$
$929$	−7.28953e8			−0.909185			−0.454592	+	0.890700i	$0.650215\pi$
$930$		0			0
$931$			1.17387e9i			1.45469i
$932$	−8.75207e8	+	1.07755e9i	−1.08109	+	1.33104i
$933$		0			0
$934$	5.39373e8	−	2.56782e8i	0.661985	−	0.315155i
$935$			3.28098e8i			0.401392i
$936$		0			0
$937$	5.03858e8			0.612477			0.306238	−	0.951955i	$-0.400929\pi$
$937$	5.03858e8			0.612477			0.306238	+	0.951955i	$0.400929\pi$
$938$	−3.96442e8	−	8.32730e8i	−0.480365	−	1.00901i
$939$		0			0
$940$	5.11665e8	+	4.15582e8i	0.616030	+	0.500349i
$941$	−1.86452e8			−0.223768			−0.111884	−	0.993721i	$-0.535689\pi$
$941$	−1.86452e8			−0.223768			−0.111884	+	0.993721i	$0.535689\pi$
$942$		0			0
$943$		−	1.32113e8i		−	0.157547i
$944$	−2.21355e8	+	4.63720e7i	−0.263131	+	0.0551239i
$945$		0			0
$946$	3.67380e8	+	7.71685e8i	0.433953	+	0.911520i
$947$		−	5.29448e8i		−	0.623409i	−0.950179	−	0.311705i	$-0.899100\pi$
$947$		−	5.29448e8i		−	0.623409i	0.950179	−	0.311705i	$-0.100900\pi$
$948$		0			0
$949$	−6.28984e6			−0.00735937
$950$	−2.51977e8	+	1.19960e8i	−0.293893	+	0.139915i
$951$		0			0
$952$	−3.55723e8	+	1.46746e9i	−0.412288	+	1.70081i
$953$	6.70647e8			0.774846			0.387423	−	0.921902i	$-0.373365\pi$
$953$	6.70647e8			0.774846			0.387423	+	0.921902i	$0.373365\pi$
$954$		0			0
$955$			2.63864e7i			0.0302949i
$956$	2.18450e8	+	1.77429e8i	0.250023	+	0.203072i
$957$		0			0
$958$	9.56911e7	−	4.55562e7i	0.108837	−	0.0518145i
$959$			1.77159e9i			2.00866i
$960$		0			0
$961$	8.68977e8			0.979125
$962$	3.93740e6	+	8.27054e6i	0.00442267	+	0.00928985i
$963$		0			0
$964$	−6.94677e8	+	8.55286e8i	−0.775446	+	0.954729i
$965$	3.22489e8			0.358866
$966$		0			0
$967$			5.56891e8i			0.615872i	0.951407	+	0.307936i	$0.0996383\pi$
$967$			5.56891e8i			0.615872i	−0.951407	+	0.307936i	$0.900362\pi$
$968$	4.42408e8	+	1.07243e8i	0.487750	+	0.118234i
$969$		0			0
$970$	2.77193e8	+	5.82246e8i	0.303716	+	0.637957i
$971$		−	8.52936e8i		−	0.931663i	−0.884873	−	0.465832i	$-0.845755\pi$
$971$		−	8.52936e8i		−	0.931663i	0.884873	−	0.465832i	$-0.154245\pi$
$972$		0			0
$973$	−1.99442e9			−2.16510
$974$	−2.92097e8	+	1.39060e8i	−0.316119	+	0.150496i
$975$		0			0
$976$	−1.72013e8	−	8.21095e8i	−0.185017	−	0.883169i
$977$	4.87819e8			0.523089			0.261544	−	0.965191i	$-0.415768\pi$
$977$	4.87819e8			0.523089			0.261544	+	0.965191i	$0.415768\pi$
$978$		0			0
$979$		−	9.44271e8i		−	1.00635i
$980$	−2.37193e8	+	2.92032e8i	−0.252013	+	0.310279i
$981$		0			0
$982$	1.47441e9	−	7.01931e8i	1.55698	−	0.741242i
$983$			1.61387e8i			0.169906i	0.996385	+	0.0849528i	$0.0270739\pi$
$983$			1.61387e8i			0.169906i	−0.996385	+	0.0849528i	$0.972926\pi$
$984$		0			0
$985$	5.66309e8			0.592577
$986$	−5.50446e8	−	1.15622e9i	−0.574228	−	1.20617i
$987$		0			0
$988$	1.25249e7	+	1.01729e7i	0.0129868	+	0.0105481i
$989$	1.32854e8			0.137336
$990$		0			0
$991$			8.20569e8i			0.843129i	0.906798	+	0.421564i	$0.138519\pi$
$991$			8.20569e8i			0.843129i	−0.906798	+	0.421564i	$0.861481\pi$
$992$	8.54505e7	+	1.12211e8i	0.0875346	+	0.114948i
$993$		0			0
$994$	2.30941e7	+	4.85093e7i	0.0235148	+	0.0493931i
$995$		−	4.86081e8i		−	0.493446i
$996$		0			0
$997$	−1.48083e9			−1.49424			−0.747121	−	0.664689i	$-0.768564\pi$
$997$	−1.48083e9			−1.49424			−0.747121	+	0.664689i	$0.768564\pi$
$998$	−5.00169e8	+	2.38118e8i	−0.503182	+	0.239552i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.7.c.b.91.9		24
3.2	odd	2		60.7.c.a.31.16	yes	24
4.3	odd	2	inner	180.7.c.b.91.10		24
12.11	even	2		60.7.c.a.31.15	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.15	✓	24	12.11	even	2
60.7.c.a.31.16	yes	24	3.2	odd	2
180.7.c.b.91.9		24	1.1	even	1	trivial
180.7.c.b.91.10		24	4.3	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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.43879 - 7.22321i) q^{2} +(-40.3494 + 49.6782i) q^{4} -55.9017 q^{5} -472.024i q^{7} +(497.589 + 120.619i) q^{8} +O(q^{10})\)	\(q+(-3.43879 - 7.22321i) q^{2} +(-40.3494 + 49.6782i) q^{4} -55.9017 q^{5} -472.024i q^{7} +(497.589 + 120.619i) q^{8} +(192.234 + 403.790i) q^{10} +939.392i q^{11} +22.5854 q^{13} +(-3409.52 + 1623.19i) q^{14} +(-839.847 - 4008.97i) q^{16} -6247.86 q^{17} -11163.0i q^{19} +(2255.60 - 2777.10i) q^{20} +(6785.42 - 3230.37i) q^{22} -1168.18i q^{23} +3125.00 q^{25} +(-77.6664 - 163.139i) q^{26} +(23449.3 + 19045.9i) q^{28} -25619.9 q^{29} -4304.29i q^{31} +(-26069.6 + 19852.4i) q^{32} +(21485.1 + 45129.6i) q^{34} +26386.9i q^{35} -50696.3 q^{37} +(-80632.6 + 38387.2i) q^{38} +(-27816.1 - 6742.82i) q^{40} +113093. q^{41} +113727. i q^{43} +(-46667.3 - 37903.9i) q^{44} +(-8438.03 + 4017.14i) q^{46} +184245. i q^{47} -105157. q^{49} +(-10746.2 - 22572.5i) q^{50} +(-911.307 + 1122.00i) q^{52} +133403. q^{53} -52513.6i q^{55} +(56935.1 - 234874. i) q^{56} +(88101.5 + 185058. i) q^{58} -55214.8i q^{59} +204814. q^{61} +(-31090.8 + 14801.5i) q^{62} +(233046. + 120038. i) q^{64} -1262.56 q^{65} +244236. i q^{67} +(252098. - 310383. i) q^{68} +(190598. - 90739.1i) q^{70} -14227.6i q^{71} -278492. q^{73} +(174334. + 366190. i) q^{74} +(554557. + 450420. i) q^{76} +443415. q^{77} +358976. i q^{79} +(46948.9 + 224108. i) q^{80} +(-388902. - 816892. i) q^{82} +820615. i q^{83} +349266. q^{85} +(821472. - 391083. i) q^{86} +(-113309. + 467431. i) q^{88} -1.00519e6 q^{89} -10660.8i q^{91} +(58033.3 + 47135.6i) q^{92} +(1.33084e6 - 633579. i) q^{94} +624030. i q^{95} +1.44195e6 q^{97} +(361614. + 759572. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8}+O(q^{10}) \) 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8	\( 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8} - 750 q^{10} + 5040 q^{13} + 2596 q^{14} + 4194 q^{16} - 7000 q^{20} + 45780 q^{22} + 75000 q^{25} - 75852 q^{26} + 54300 q^{28} - 132800 q^{29} + 10700 q^{32} - 173484 q^{34} - 69840 q^{37} - 215800 q^{38} - 14250 q^{40} + 70448 q^{41} + 395668 q^{44} - 158760 q^{46} - 642984 q^{49} - 62500 q^{50} - 210240 q^{52} + 644320 q^{53} + 917708 q^{56} - 1345020 q^{58} - 222864 q^{61} - 1948520 q^{62} + 935922 q^{64} - 266000 q^{65} - 572680 q^{68} + 220500 q^{70} + 771120 q^{73} + 589164 q^{74} - 191544 q^{76} - 1383840 q^{77} + 946000 q^{80} + 2672520 q^{82} - 372000 q^{85} - 1781528 q^{86} + 956940 q^{88} + 1566224 q^{89} + 3040560 q^{92} - 3788352 q^{94} - 1666800 q^{97} + 2709660 q^{98}+O(q^{100}) \) 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8 - 750 * q^10 + 5040 * q^13 + 2596 * q^14 + 4194 * q^16 - 7000 * q^20 + 45780 * q^22 + 75000 * q^25 - 75852 * q^26 + 54300 * q^28 - 132800 * q^29 + 10700 * q^32 - 173484 * q^34 - 69840 * q^37 - 215800 * q^38 - 14250 * q^40 + 70448 * q^41 + 395668 * q^44 - 158760 * q^46 - 642984 * q^49 - 62500 * q^50 - 210240 * q^52 + 644320 * q^53 + 917708 * q^56 - 1345020 * q^58 - 222864 * q^61 - 1948520 * q^62 + 935922 * q^64 - 266000 * q^65 - 572680 * q^68 + 220500 * q^70 + 771120 * q^73 + 589164 * q^74 - 191544 * q^76 - 1383840 * q^77 + 946000 * q^80 + 2672520 * q^82 - 372000 * q^85 - 1781528 * q^86 + 956940 * q^88 + 1566224 * q^89 + 3040560 * q^92 - 3788352 * q^94 - 1666800 * q^97 + 2709660 * q^98

Introduction

L-functions

Modular forms

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Database

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