LMFDB - Embedded newform 180.7.c.b.91.8

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			91.8
Character	$\chi$	$=$	180.91
Dual form			180.7.c.b.91.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.21792 + 6.06410i) q^{2} +(-9.54653 - 63.2840i) q^{4} -55.9017 q^{5} -234.050i q^{7} +(433.573 + 272.320i) q^{8} +O(q^{10})$	\(q+(-5.21792 + 6.06410i) q^{2} +(-9.54653 - 63.2840i) q^{4} -55.9017 q^{5} -234.050i q^{7} +(433.573 + 272.320i) q^{8} +(291.691 - 338.993i) q^{10} +611.126i q^{11} +446.025 q^{13} +(1419.30 + 1221.26i) q^{14} +(-3913.73 + 1208.29i) q^{16} +4753.29 q^{17} +4220.36i q^{19} +(533.667 + 3537.68i) q^{20} +(-3705.93 - 3188.81i) q^{22} +3897.71i q^{23} +3125.00 q^{25} +(-2327.33 + 2704.74i) q^{26} +(-14811.6 + 2234.37i) q^{28} -15226.1 q^{29} -25735.3i q^{31} +(13094.4 - 30038.0i) q^{32} +(-24802.3 + 28824.4i) q^{34} +13083.8i q^{35} -12963.9 q^{37} +(-25592.7 - 22021.5i) q^{38} +(-24237.5 - 15223.2i) q^{40} -71144.7 q^{41} -101623. i q^{43} +(38674.5 - 5834.13i) q^{44} +(-23636.1 - 20338.0i) q^{46} +132654. i q^{47} +62869.4 q^{49} +(-16306.0 + 18950.3i) q^{50} +(-4257.99 - 28226.3i) q^{52} -283151. q^{53} -34163.0i q^{55} +(63736.6 - 101478. i) q^{56} +(79448.8 - 92332.7i) q^{58} -176836. i q^{59} +219488. q^{61} +(156061. + 134285. i) q^{62} +(113828. + 236141. i) q^{64} -24933.6 q^{65} -420905. i q^{67} +(-45377.4 - 300807. i) q^{68} +(-79341.5 - 68270.4i) q^{70} -427721. i q^{71} +276028. q^{73} +(67644.4 - 78614.1i) q^{74} +(267081. - 40289.8i) q^{76} +143034. q^{77} -616843. i q^{79} +(218784. - 67545.2i) q^{80} +(371228. - 431429. i) q^{82} -632235. i q^{83} -265717. q^{85} +(616250. + 530260. i) q^{86} +(-166422. + 264968. i) q^{88} +1.04325e6 q^{89} -104392. i q^{91} +(246663. - 37209.6i) q^{92} +(-804429. - 692181. i) q^{94} -235925. i q^{95} -1.31029e6 q^{97} +(-328048. + 381246. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.21792	+	6.06410i	−0.652241	+	0.758012i
$2$	−5.21792	+	6.06410i	−0.652241	+	0.758012i
$3$		0			0
$3$		0			0
$4$	−9.54653	−	63.2840i	−0.149165	−	0.988812i
$5$	−55.9017			−0.447214
$5$	−55.9017			−0.447214
$6$		0			0
$7$		−	234.050i		−	0.682363i	−0.939997	−	0.341181i	$-0.889173\pi$
$7$		−	234.050i		−	0.682363i	0.939997	−	0.341181i	$-0.110827\pi$
$8$	433.573	+	272.320i	0.846823	+	0.531875i
$9$		0			0
$10$	291.691	−	338.993i	0.291691	−	0.338993i
$11$			611.126i			0.459148i	0.973291	+	0.229574i	$0.0737333\pi$
$11$			611.126i			0.459148i	−0.973291	+	0.229574i	$0.926267\pi$
$12$		0			0
$13$	446.025			0.203016			0.101508	−	0.994835i	$-0.467633\pi$
$13$	446.025			0.203016			0.101508	+	0.994835i	$0.467633\pi$
$14$	1419.30	+	1221.26i	0.517239	+	0.445065i
$15$		0			0
$16$	−3913.73	+	1208.29i	−0.955500	+	0.294991i
$17$	4753.29			0.967491			0.483746	−	0.875209i	$-0.339276\pi$
$17$	4753.29			0.967491			0.483746	+	0.875209i	$0.339276\pi$
$18$		0			0
$19$			4220.36i			0.615302i	0.951499	+	0.307651i	$0.0995430\pi$
$19$			4220.36i			0.615302i	−0.951499	+	0.307651i	$0.900457\pi$
$20$	533.667	+	3537.68i	0.0667084	+	0.442210i
$21$		0			0
$22$	−3705.93	−	3188.81i	−0.348040	−	0.299475i
$23$			3897.71i			0.320351i	0.987089	+	0.160176i	$0.0512061\pi$
$23$			3897.71i			0.320351i	−0.987089	+	0.160176i	$0.948794\pi$
$24$		0			0
$25$	3125.00			0.200000
$26$	−2327.33	+	2704.74i	−0.132415	+	0.153888i
$27$		0			0
$28$	−14811.6	+	2234.37i	−0.674729	+	0.101784i
$29$	−15226.1			−0.624303			−0.312152	−	0.950032i	$-0.601050\pi$
$29$	−15226.1			−0.624303			−0.312152	+	0.950032i	$0.601050\pi$
$30$		0			0
$31$		−	25735.3i		−	0.863862i	−0.901907	−	0.431931i	$-0.857832\pi$
$31$		−	25735.3i		−	0.863862i	0.901907	−	0.431931i	$-0.142168\pi$
$32$	13094.4	−	30038.0i	0.399609	−	0.916686i
$33$		0			0
$34$	−24802.3	+	28824.4i	−0.631037	+	0.733370i
$35$			13083.8i			0.305162i
$36$		0			0
$37$	−12963.9			−0.255935			−0.127967	−	0.991778i	$-0.540845\pi$
$37$	−12963.9			−0.255935			−0.127967	+	0.991778i	$0.540845\pi$
$38$	−25592.7	−	22021.5i	−0.466407	−	0.401325i
$39$		0			0
$40$	−24237.5	−	15223.2i	−0.378711	−	0.237862i
$41$	−71144.7			−1.03227			−0.516133	−	0.856509i	$-0.672629\pi$
$41$	−71144.7			−1.03227			−0.516133	+	0.856509i	$0.672629\pi$
$42$		0			0
$43$		−	101623.i		−	1.27816i	−0.769140	−	0.639080i	$-0.779315\pi$
$43$		−	101623.i		−	1.27816i	0.769140	−	0.639080i	$-0.220685\pi$
$44$	38674.5	−	5834.13i	0.454011	−	0.0684886i
$45$		0			0
$46$	−23636.1	−	20338.0i	−0.242830	−	0.208946i
$47$			132654.i			1.27770i	0.769332	+	0.638849i	$0.220589\pi$
$47$			132654.i			1.27770i	−0.769332	+	0.638849i	$0.779411\pi$
$48$		0			0
$49$	62869.4			0.534381
$50$	−16306.0	+	18950.3i	−0.130448	+	0.151602i
$51$		0			0
$52$	−4257.99	−	28226.3i	−0.0302827	−	0.200744i
$53$	−283151.			−1.90192			−0.950958	−	0.309321i	$-0.899898\pi$
$53$	−283151.			−1.90192			−0.950958	+	0.309321i	$0.899898\pi$
$54$		0			0
$55$		−	34163.0i		−	0.205337i
$56$	63736.6	−	101478.i	0.362932	−	0.577840i
$57$		0			0
$58$	79448.8	−	92332.7i	0.407196	−	0.473229i
$59$		−	176836.i		−	0.861022i	−0.902585	−	0.430511i	$-0.858333\pi$
$59$		−	176836.i		−	0.861022i	0.902585	−	0.430511i	$-0.141667\pi$
$60$		0			0
$61$	219488.			0.966986			0.483493	−	0.875348i	$-0.339368\pi$
$61$	219488.			0.966986			0.483493	+	0.875348i	$0.339368\pi$
$62$	156061.	+	134285.i	0.654817	+	0.563446i
$63$		0			0
$64$	113828.	+	236141.i	0.434218	+	0.900808i
$65$	−24933.6			−0.0907913
$66$		0			0
$67$		−	420905.i		−	1.39946i	−0.714408	−	0.699729i	$-0.753304\pi$
$67$		−	420905.i		−	1.39946i	0.714408	−	0.699729i	$-0.246696\pi$
$68$	−45377.4	−	300807.i	−0.144315	−	0.956668i
$69$		0			0
$70$	−79341.5	−	68270.4i	−0.231316	−	0.199039i
$71$		−	427721.i		−	1.19505i	−0.801851	−	0.597524i	$-0.796151\pi$
$71$		−	427721.i		−	1.19505i	0.801851	−	0.597524i	$-0.203849\pi$
$72$		0			0
$73$	276028.			0.709553			0.354777	−	0.934951i	$-0.384557\pi$
$73$	276028.			0.709553			0.354777	+	0.934951i	$0.384557\pi$
$74$	67644.4	−	78614.1i	0.166931	−	0.194002i
$75$		0			0
$76$	267081.	−	40289.8i	0.608419	−	0.0917813i
$77$	143034.			0.313305
$78$		0			0
$79$		−	616843.i		−	1.25110i	−0.780182	−	0.625552i	$-0.784874\pi$
$79$		−	616843.i		−	1.25110i	0.780182	−	0.625552i	$-0.215126\pi$
$80$	218784.	−	67545.2i	0.427313	−	0.131924i
$81$		0			0
$82$	371228.	−	431429.i	0.673285	−	0.782469i
$83$		−	632235.i		−	1.10572i	−0.833275	−	0.552859i	$-0.813537\pi$
$83$		−	632235.i		−	1.10572i	0.833275	−	0.552859i	$-0.186463\pi$
$84$		0			0
$85$	−265717.			−0.432675
$86$	616250.	+	530260.i	0.968861	+	0.833668i
$87$		0			0
$88$	−166422.	+	264968.i	−0.244209	+	0.388817i
$89$	1.04325e6			1.47985			0.739926	−	0.672689i	$-0.234861\pi$
$89$	1.04325e6			1.47985			0.739926	+	0.672689i	$0.234861\pi$
$90$		0			0
$91$		−	104392.i		−	0.138530i
$92$	246663.	−	37209.6i	0.316767	−	0.0477850i
$93$		0			0
$94$	−804429.	−	692181.i	−0.968510	−	0.833366i
$95$		−	235925.i		−	0.275172i
$96$		0			0
$97$	−1.31029e6			−1.43566			−0.717832	−	0.696216i	$-0.754866\pi$
$97$	−1.31029e6			−1.43566			−0.717832	+	0.696216i	$0.754866\pi$
$98$	−328048.	+	381246.i	−0.348545	+	0.405067i
$99$		0			0
$100$	−29832.9	−	197762.i	−0.0298329	−	0.197762i
$101$	591531.			0.574134			0.287067	−	0.957911i	$-0.407320\pi$
$101$	591531.			0.574134			0.287067	+	0.957911i	$0.407320\pi$
$102$		0			0
$103$		−	369642.i		−	0.338275i	−0.985592	−	0.169138i	$-0.945902\pi$
$103$		−	369642.i		−	0.338275i	0.985592	−	0.169138i	$-0.0540982\pi$
$104$	193385.	+	121462.i	0.171918	+	0.107979i
$105$		0			0
$106$	1.47746e6	−	1.71706e6i	1.24051	−	1.44167i
$107$		−	829937.i		−	0.677476i	−0.940881	−	0.338738i	$-0.890000\pi$
$107$		−	829937.i		−	0.677476i	0.940881	−	0.338738i	$-0.110000\pi$
$108$		0			0
$109$	−2.19532e6			−1.69519			−0.847594	−	0.530646i	$-0.821949\pi$
$109$	−2.19532e6			−1.69519			−0.847594	+	0.530646i	$0.821949\pi$
$110$	207168.	+	178260.i	0.155648	+	0.133929i
$111$		0			0
$112$	282800.	+	916010.i	0.201291	+	0.651998i
$113$	−2.57865e6			−1.78713			−0.893565	−	0.448933i	$-0.851804\pi$
$113$	−2.57865e6			−1.78713			−0.893565	+	0.448933i	$0.851804\pi$
$114$		0			0
$115$		−	217889.i		−	0.143265i
$116$	145357.	+	963571.i	0.0931239	+	0.617319i
$117$		0			0
$118$	1.07235e6	+	922716.i	0.652665	+	0.561593i
$119$		−	1.11251e6i		−	0.660180i
$120$		0			0
$121$	1.39809e6			0.789183
$122$	−1.14527e6	+	1.33099e6i	−0.630708	+	0.732987i
$123$		0			0
$124$	−1.62863e6	+	245683.i	−0.854197	+	0.128858i
$125$	−174693.			−0.0894427
$126$		0			0
$127$			3.88504e6i			1.89664i	0.317320	+	0.948319i	$0.397217\pi$
$127$			3.88504e6i			1.89664i	−0.317320	+	0.948319i	$0.602783\pi$
$128$	−2.02593e6	−	541906.i	−0.966038	−	0.258401i
$129$		0			0
$130$	130101.	−	151200.i	0.0592178	−	0.0688209i
$131$		−	2.17769e6i		−	0.968685i	−0.874878	−	0.484343i	$-0.839059\pi$
$131$		−	2.17769e6i		−	0.968685i	0.874878	−	0.484343i	$-0.160941\pi$
$132$		0			0
$133$	987777.			0.419859
$134$	2.55241e6	+	2.19625e6i	1.06081	+	0.912784i
$135$		0			0
$136$	2.06090e6	+	1.29441e6i	0.819294	+	0.514585i
$137$	−4.01481e6			−1.56136			−0.780681	−	0.624929i	$-0.785128\pi$
$137$	−4.01481e6			−1.56136			−0.780681	+	0.624929i	$0.785128\pi$
$138$		0			0
$139$		−	278268.i		−	0.103614i	−0.998657	−	0.0518070i	$-0.983502\pi$
$139$		−	278268.i		−	0.103614i	0.998657	−	0.0518070i	$-0.0164981\pi$
$140$	827996.	−	124905.i	0.301748	−	0.0455193i
$141$		0			0
$142$	2.59374e6	+	2.23181e6i	0.905861	+	0.779459i
$143$			272578.i			0.0932142i
$144$		0			0
$145$	851167.			0.279197
$146$	−1.44030e6	+	1.67386e6i	−0.462800	+	0.537850i
$147$		0			0
$148$	123760.	+	820405.i	0.0381764	+	0.253071i
$149$	−991141.			−0.299624			−0.149812	−	0.988715i	$-0.547867\pi$
$149$	−991141.			−0.299624			−0.149812	+	0.988715i	$0.547867\pi$
$150$		0			0
$151$		−	29572.7i		−	0.00858936i	−0.999991	−	0.00429468i	$-0.998633\pi$
$151$		−	29572.7i		−	0.00858936i	0.999991	−	0.00429468i	$-0.00136704\pi$
$152$	−1.14929e6	+	1.82984e6i	−0.327264	+	0.521052i
$153$		0			0
$154$	−746342.	+	867374.i	−0.204351	+	0.237489i
$155$			1.43865e6i			0.386331i
$156$		0			0
$157$	−2.86209e6			−0.739580			−0.369790	−	0.929115i	$-0.620570\pi$
$157$	−2.86209e6			−0.739580			−0.369790	+	0.929115i	$0.620570\pi$
$158$	3.74060e6	+	3.21864e6i	0.948352	+	0.816021i
$159$		0			0
$160$	−731998.	+	1.67917e6i	−0.178710	+	0.409954i
$161$	912262.			0.218596
$162$		0			0
$163$		−	5.86822e6i		−	1.35501i	−0.735517	−	0.677506i	$-0.763061\pi$
$163$		−	5.86822e6i		−	1.35501i	0.735517	−	0.677506i	$-0.236939\pi$
$164$	679185.	+	4.50232e6i	0.153977	+	1.02072i
$165$		0			0
$166$	3.83393e6	+	3.29895e6i	0.838147	+	0.721194i
$167$			635821.i			0.136517i	0.997668	+	0.0682583i	$0.0217442\pi$
$167$			635821.i			0.136517i	−0.997668	+	0.0682583i	$0.978256\pi$
$168$		0			0
$169$	−4.62787e6			−0.958785
$170$	1.38649e6	−	1.61133e6i	0.282208	−	0.327973i
$171$		0			0
$172$	−6.43109e6	+	970144.i	−1.26386	+	0.190656i
$173$	−7.53757e6			−1.45577			−0.727886	−	0.685698i	$-0.759497\pi$
$173$	−7.53757e6			−1.45577			−0.727886	+	0.685698i	$0.759497\pi$
$174$		0			0
$175$		−	731408.i		−	0.136473i
$176$	−738414.	−	2.39178e6i	−0.135445	−	0.438716i
$177$		0			0
$178$	−5.44360e6	+	6.32636e6i	−0.965219	+	1.12175i
$179$			878241.i			0.153128i	0.997065	+	0.0765640i	$0.0243949\pi$
$179$			878241.i			0.153128i	−0.997065	+	0.0765640i	$0.975605\pi$
$180$		0			0
$181$	−4.23487e6			−0.714174			−0.357087	−	0.934071i	$-0.616230\pi$
$181$	−4.23487e6			−0.714174			−0.357087	+	0.934071i	$0.616230\pi$
$182$	633046.	+	544712.i	0.105008	+	0.0903551i
$183$		0			0
$184$	−1.06143e6	+	1.68994e6i	−0.170387	+	0.271281i
$185$	724702.			0.114457
$186$		0			0
$187$			2.90486e6i			0.444222i
$188$	8.39490e6	−	1.26639e6i	1.26340	−	0.190587i
$189$		0			0
$190$	1.43067e6	+	1.23104e6i	0.208583	+	0.179478i
$191$		−	8.58674e6i		−	1.23233i	−0.787616	−	0.616167i	$-0.788685\pi$
$191$		−	8.58674e6i		−	1.23233i	0.787616	−	0.616167i	$-0.211315\pi$
$192$		0			0
$193$	9.47926e6			1.31857			0.659284	−	0.751894i	$-0.270859\pi$
$193$	9.47926e6			1.31857			0.659284	+	0.751894i	$0.270859\pi$
$194$	6.83701e6	−	7.94574e6i	0.936399	−	1.08825i
$195$		0			0
$196$	−600185.	−	3.97863e6i	−0.0797107	−	0.528403i
$197$	152893.			0.0199981			0.00999903	−	0.999950i	$-0.496817\pi$
$197$	152893.			0.0199981			0.00999903	+	0.999950i	$0.496817\pi$
$198$		0			0
$199$			4.24007e6i			0.538038i	0.963135	+	0.269019i	$0.0866995\pi$
$199$			4.24007e6i			0.538038i	−0.963135	+	0.269019i	$0.913300\pi$
$200$	1.35492e6	+	851000.i	0.169365	+	0.106375i
$201$		0			0
$202$	−3.08656e6	+	3.58710e6i	−0.374473	+	0.435200i
$203$			3.56368e6i			0.426001i
$204$		0			0
$205$	3.97711e6			0.461643
$206$	2.24155e6	+	1.92877e6i	0.256417	+	0.220637i
$207$		0			0
$208$	−1.74562e6	+	538926.i	−0.193981	+	0.0598879i
$209$	−2.57917e6			−0.282515
$210$		0			0
$211$		−	7.09394e6i		−	0.755162i	−0.925977	−	0.377581i	$-0.876756\pi$
$211$		−	7.09394e6i		−	0.755162i	0.925977	−	0.377581i	$-0.123244\pi$
$212$	2.70311e6	+	1.79190e7i	0.283698	+	1.88064i
$213$		0			0
$214$	5.03282e6	+	4.33055e6i	0.513535	+	0.441877i
$215$			5.68088e6i			0.571611i
$216$		0			0
$217$	−6.02336e6			−0.589467
$218$	1.14550e7	−	1.33126e7i	1.10567	−	1.28497i
$219$		0			0
$220$	−2.16197e6	+	326138.i	−0.203040	+	0.0306290i
$221$	2.12009e6			0.196416
$222$		0			0
$223$			1.19865e6i			0.108088i	0.998539	+	0.0540442i	$0.0172112\pi$
$223$			1.19865e6i			0.108088i	−0.998539	+	0.0540442i	$0.982789\pi$
$224$	−7.03040e6	−	3.06474e6i	−0.625512	−	0.272678i
$225$		0			0
$226$	1.34552e7	−	1.56372e7i	1.16564	−	1.35467i
$227$			5.84907e6i			0.500045i	0.968240	+	0.250023i	$0.0804380\pi$
$227$			5.84907e6i			0.500045i	−0.968240	+	0.250023i	$0.919562\pi$
$228$		0			0
$229$	1.27570e7			1.06228			0.531142	−	0.847283i	$-0.321763\pi$
$229$	1.27570e7			1.06228			0.531142	+	0.847283i	$0.321763\pi$
$230$	1.32130e6	+	1.13693e6i	0.108597	+	0.0934435i
$231$		0			0
$232$	−6.60164e6	−	4.14638e6i	−0.528674	−	0.332051i
$233$	6.04654e6			0.478012			0.239006	−	0.971018i	$-0.423178\pi$
$233$	6.04654e6			0.478012			0.239006	+	0.971018i	$0.423178\pi$
$234$		0			0
$235$		−	7.41561e6i		−	0.571404i
$236$	−1.11909e7	+	1.68817e6i	−0.851389	+	0.128434i
$237$		0			0
$238$	6.74636e6	+	5.80499e6i	0.500425	+	0.430596i
$239$		−	2.45629e7i		−	1.79923i	−0.436685	−	0.899614i	$-0.643848\pi$
$239$		−	2.45629e7i		−	1.79923i	0.436685	−	0.899614i	$-0.356152\pi$
$240$		0			0
$241$	−5.34775e6			−0.382050			−0.191025	−	0.981585i	$-0.561181\pi$
$241$	−5.34775e6			−0.382050			−0.191025	+	0.981585i	$0.561181\pi$
$242$	−7.29511e6	+	8.47813e6i	−0.514737	+	0.598210i
$243$		0			0
$244$	−2.09534e6	−	1.38900e7i	−0.144240	−	0.956168i
$245$	−3.51451e6			−0.238982
$246$		0			0
$247$			1.88239e6i			0.124916i
$248$	7.00824e6	−	1.11581e7i	0.459466	−	0.731538i
$249$		0			0
$250$	911534.	−	1.05935e6i	0.0583382	−	0.0677987i
$251$		−	1.62600e6i		−	0.102825i	−0.998677	−	0.0514126i	$-0.983628\pi$
$251$		−	1.62600e6i		−	0.102825i	0.998677	−	0.0514126i	$-0.0163724\pi$
$252$		0			0
$253$	−2.38199e6			−0.147089
$254$	−2.35593e7	−	2.02718e7i	−1.43767	−	1.23706i
$255$		0			0
$256$	1.38573e7	−	9.45780e6i	0.825960	−	0.563729i
$257$	5.96301e6			0.351290			0.175645	−	0.984454i	$-0.443799\pi$
$257$	5.96301e6			0.351290			0.175645	+	0.984454i	$0.443799\pi$
$258$		0			0
$259$			3.03420e6i			0.174640i
$260$	238029.	+	1.57790e6i	0.0135428	+	0.0897756i
$261$		0			0
$262$	1.32057e7	+	1.13630e7i	0.734275	+	0.631816i
$263$			5.56063e6i			0.305673i	0.988252	+	0.152836i	$0.0488407\pi$
$263$			5.56063e6i			0.305673i	−0.988252	+	0.152836i	$0.951159\pi$
$264$		0			0
$265$	1.58286e7			0.850562
$266$	−5.15415e6	+	5.98997e6i	−0.273849	+	0.318259i
$267$		0			0
$268$	−2.66366e7	+	4.01818e6i	−1.38380	+	0.208750i
$269$	−8.71314e6			−0.447629			−0.223814	−	0.974632i	$-0.571851\pi$
$269$	−8.71314e6			−0.447629			−0.223814	+	0.974632i	$0.571851\pi$
$270$		0			0
$271$			2.16067e7i			1.08563i	0.839853	+	0.542815i	$0.182641\pi$
$271$			2.16067e7i			1.08563i	−0.839853	+	0.542815i	$0.817359\pi$
$272$	−1.86031e7	+	5.74332e6i	−0.924438	+	0.285402i
$273$		0			0
$274$	2.09490e7	−	2.43462e7i	1.01838	−	1.18353i
$275$			1.90977e6i			0.0918296i
$276$		0			0
$277$	−1.96628e7			−0.925138			−0.462569	−	0.886583i	$-0.653072\pi$
$277$	−1.96628e7			−0.925138			−0.462569	+	0.886583i	$0.653072\pi$
$278$	1.68744e6	+	1.45198e6i	0.0785407	+	0.0675813i
$279$		0			0
$280$	−3.56299e6	+	5.67279e6i	−0.162308	+	0.258418i
$281$	4.23673e7			1.90946			0.954732	−	0.297467i	$-0.0961418\pi$
$281$	4.23673e7			1.90946			0.954732	+	0.297467i	$0.0961418\pi$
$282$		0			0
$283$		−	3.51305e7i		−	1.54998i	−0.631975	−	0.774989i	$-0.717755\pi$
$283$		−	3.51305e7i		−	1.54998i	0.631975	−	0.774989i	$-0.282245\pi$
$284$	−2.70679e7	+	4.08325e6i	−1.18168	+	0.178259i
$285$		0			0
$286$	−1.65294e6	−	1.42229e6i	−0.0706575	−	0.0607981i
$287$			1.66515e7i			0.704379i
$288$		0			0
$289$	−1.54385e6			−0.0639603
$290$	−4.44132e6	+	5.16156e6i	−0.182104	+	0.211635i
$291$		0			0
$292$	−2.63511e6	−	1.74682e7i	−0.105840	−	0.701615i
$293$	−1.11354e7			−0.442695			−0.221348	−	0.975195i	$-0.571046\pi$
$293$	−1.11354e7			−0.442695			−0.221348	+	0.975195i	$0.571046\pi$
$294$		0			0
$295$			9.88542e6i			0.385061i
$296$	−5.62078e6	−	3.53032e6i	−0.216731	−	0.136125i
$297$		0			0
$298$	5.17170e6	−	6.01037e6i	0.195427	−	0.227119i
$299$			1.73848e6i			0.0650363i
$300$		0			0
$301$	−2.37848e7			−0.872169
$302$	179332.	+	154308.i	0.00651084	+	0.00560233i
$303$		0			0
$304$	−5.09940e6	−	1.65173e7i	−0.181509	−	0.587921i
$305$	−1.22697e7			−0.432450
$306$		0			0
$307$			1.40533e7i			0.485695i	0.970064	+	0.242847i	$0.0780814\pi$
$307$			1.40533e7i			0.485695i	−0.970064	+	0.242847i	$0.921919\pi$
$308$	−1.36548e6	−	9.05178e6i	−0.0467341	−	0.309800i
$309$		0			0
$310$	−8.72409e6	−	7.50675e6i	−0.292843	−	0.251981i
$311$		−	4.02124e7i		−	1.33684i	−0.743785	−	0.668419i	$-0.766971\pi$
$311$		−	4.02124e7i		−	1.33684i	0.743785	−	0.668419i	$-0.233029\pi$
$312$		0			0
$313$	−2.19464e7			−0.715699			−0.357850	−	0.933779i	$-0.616490\pi$
$313$	−2.19464e7			−0.715699			−0.357850	+	0.933779i	$0.616490\pi$
$314$	1.49342e7	−	1.73560e7i	0.482384	−	0.560610i
$315$		0			0
$316$	−3.90363e7	+	5.88871e6i	−1.23711	+	0.186620i
$317$	2.87330e7			0.901992			0.450996	−	0.892526i	$-0.351069\pi$
$317$	2.87330e7			0.901992			0.450996	+	0.892526i	$0.351069\pi$
$318$		0			0
$319$		−	9.30508e6i		−	0.286648i
$320$	−6.36316e6	−	1.32007e7i	−0.194188	−	0.402854i
$321$		0			0
$322$	−4.76011e6	+	5.53204e6i	−0.142577	+	0.165698i
$323$			2.00606e7i			0.595300i
$324$		0			0
$325$	1.39383e6			0.0406031
$326$	3.55854e7	+	3.06199e7i	1.02712	+	0.883794i
$327$		0			0
$328$	−3.08465e7	−	1.93741e7i	−0.874146	−	0.549036i
$329$	3.10478e7			0.871853
$330$		0			0
$331$			6.61370e6i			0.182373i	0.995834	+	0.0911865i	$0.0290660\pi$
$331$			6.61370e6i			0.182373i	−0.995834	+	0.0911865i	$0.970934\pi$
$332$	−4.00104e7	+	6.03565e6i	−1.09335	+	0.164934i
$333$		0			0
$334$	−3.85568e6	−	3.31767e6i	−0.103481	−	0.0890417i
$335$			2.35293e7i			0.625857i
$336$		0			0
$337$	2.36992e7			0.619219			0.309610	−	0.950864i	$-0.399802\pi$
$337$	2.36992e7			0.619219			0.309610	+	0.950864i	$0.399802\pi$
$338$	2.41479e7	−	2.80639e7i	0.625358	−	0.726770i
$339$		0			0
$340$	2.53667e6	+	1.68156e7i	0.0645398	+	0.427835i
$341$	1.57275e7			0.396640
$342$		0			0
$343$		−	4.22504e7i		−	1.04700i
$344$	2.76739e7	−	4.40609e7i	0.679822	−	1.08238i
$345$		0			0
$346$	3.93305e7	−	4.57086e7i	0.949513	−	1.10349i
$347$			7.87037e7i			1.88368i	0.336065	+	0.941839i	$0.390904\pi$
$347$			7.87037e7i			1.88368i	−0.336065	+	0.941839i	$0.609096\pi$
$348$		0			0
$349$	5.84311e7			1.37457			0.687286	−	0.726387i	$-0.258802\pi$
$349$	5.84311e7			1.37457			0.687286	+	0.726387i	$0.258802\pi$
$350$	4.43533e6	+	3.81643e6i	0.103448	+	0.0890129i
$351$		0			0
$352$	1.83570e7	+	8.00231e6i	0.420894	+	0.183479i
$353$	−2.20704e6			−0.0501749			−0.0250875	−	0.999685i	$-0.507986\pi$
$353$	−2.20704e6			−0.0501749			−0.0250875	+	0.999685i	$0.507986\pi$
$354$		0			0
$355$			2.39103e7i			0.534442i
$356$	−9.95941e6	−	6.60210e7i	−0.220741	−	1.46330i
$357$		0			0
$358$	−5.32574e6	−	4.58259e6i	−0.116073	−	0.0998763i
$359$			1.20278e7i			0.259957i	0.991517	+	0.129979i	$0.0414909\pi$
$359$			1.20278e7i			0.259957i	−0.991517	+	0.129979i	$0.958509\pi$
$360$		0			0
$361$	2.92344e7			0.621403
$362$	2.20972e7	−	2.56806e7i	0.465813	−	0.541352i
$363$		0			0
$364$	−6.60637e6	+	996585.i	−0.136980	+	0.0206638i
$365$	−1.54305e7			−0.317322
$366$		0			0
$367$			7.63147e7i			1.54387i	0.635703	+	0.771934i	$0.280710\pi$
$367$			7.63147e7i			1.54387i	−0.635703	+	0.771934i	$0.719290\pi$
$368$	−4.70955e6	−	1.52546e7i	−0.0945009	−	0.306096i
$369$		0			0
$370$	−3.78144e6	+	4.39466e6i	−0.0746538	+	0.0867601i
$371$			6.62717e7i			1.29780i
$372$		0			0
$373$	5.43943e7			1.04816			0.524079	−	0.851669i	$-0.324410\pi$
$373$	5.43943e7			1.04816			0.524079	+	0.851669i	$0.324410\pi$
$374$	−1.76153e7	−	1.51573e7i	−0.336725	−	0.289739i
$375$		0			0
$376$	−3.61244e7	+	5.75154e7i	−0.679575	+	1.08198i
$377$	−6.79124e6			−0.126743
$378$		0			0
$379$		−	1.26362e7i		−	0.232113i	−0.993243	−	0.116057i	$-0.962975\pi$
$379$		−	1.26362e7i		−	0.232113i	0.993243	−	0.116057i	$-0.0370254\pi$
$380$	−1.49303e7	+	2.25227e6i	−0.272093	+	0.0410458i
$381$		0			0
$382$	5.20708e7	+	4.48050e7i	0.934124	+	0.803778i
$383$		−	6.10284e7i		−	1.08627i	−0.839647	−	0.543133i	$-0.817238\pi$
$383$		−	6.10284e7i		−	1.08627i	0.839647	−	0.543133i	$-0.182762\pi$
$384$		0			0
$385$	−7.99586e6			−0.140114
$386$	−4.94621e7	+	5.74832e7i	−0.860024	+	0.999491i
$387$		0			0
$388$	1.25087e7	+	8.29205e7i	0.214150	+	1.41960i
$389$	6.42261e7			1.09110			0.545548	−	0.838080i	$-0.316322\pi$
$389$	6.42261e7			1.09110			0.545548	+	0.838080i	$0.316322\pi$
$390$		0			0
$391$			1.85269e7i			0.309937i
$392$	2.72585e7	+	1.71206e7i	0.452526	+	0.284224i
$393$		0			0
$394$	−797782.	+	927156.i	−0.0130435	+	0.0151588i
$395$			3.44826e7i			0.559511i
$396$		0			0
$397$	5.76615e7			0.921540			0.460770	−	0.887520i	$-0.347573\pi$
$397$	5.76615e7			0.921540			0.460770	+	0.887520i	$0.347573\pi$
$398$	−2.57122e7	−	2.21243e7i	−0.407840	−	0.350931i
$399$		0			0
$400$	−1.22304e7	+	3.77589e6i	−0.191100	+	0.0589983i
$401$	−6.22427e7			−0.965285			−0.482643	−	0.875817i	$-0.660323\pi$
$401$	−6.22427e7			−0.965285			−0.482643	+	0.875817i	$0.660323\pi$
$402$		0			0
$403$		−	1.14786e7i		−	0.175377i
$404$	−5.64706e6	−	3.74344e7i	−0.0856404	−	0.567711i
$405$		0			0
$406$	−2.16105e7	−	1.85950e7i	−0.322914	−	0.277855i
$407$		−	7.92255e6i		−	0.117512i
$408$		0			0
$409$	6.41818e7			0.938084			0.469042	−	0.883176i	$-0.344599\pi$
$409$	6.41818e7			0.938084			0.469042	+	0.883176i	$0.344599\pi$
$410$	−2.07523e7	+	2.41176e7i	−0.301102	+	0.349931i
$411$		0			0
$412$	−2.33924e7	+	3.52880e6i	−0.334491	+	0.0504587i
$413$	−4.13885e7			−0.587529
$414$		0			0
$415$			3.53430e7i			0.494492i
$416$	5.84042e6	−	1.33977e7i	0.0811268	−	0.186102i
$417$		0			0
$418$	1.34579e7	−	1.56403e7i	0.184268	−	0.214150i
$419$		−	7.52734e6i		−	0.102329i	−0.998690	−	0.0511646i	$-0.983707\pi$
$419$		−	7.52734e6i		−	0.102329i	0.998690	−	0.0511646i	$-0.0162933\pi$
$420$		0			0
$421$	−9.54679e7			−1.27941			−0.639707	−	0.768619i	$-0.720944\pi$
$421$	−9.54679e7			−1.27941			−0.639707	+	0.768619i	$0.720944\pi$
$422$	4.30183e7	+	3.70156e7i	0.572422	+	0.492547i
$423$		0			0
$424$	−1.22767e8	−	7.71078e7i	−1.61059	−	1.01158i
$425$	1.48540e7			0.193498
$426$		0			0
$427$		−	5.13712e7i		−	0.659836i
$428$	−5.25217e7	+	7.92302e6i	−0.669897	+	0.101055i
$429$		0			0
$430$	−3.44494e7	−	2.96424e7i	−0.433288	−	0.372828i
$431$			6.05446e7i			0.756212i	0.925762	+	0.378106i	$0.123424\pi$
$431$			6.05446e7i			0.756212i	−0.925762	+	0.378106i	$0.876576\pi$
$432$		0			0
$433$	−4.68934e7			−0.577628			−0.288814	−	0.957385i	$-0.593261\pi$
$433$	−4.68934e7			−0.577628			−0.288814	+	0.957385i	$0.593261\pi$
$434$	3.14294e7	−	3.65262e7i	0.384474	−	0.446823i
$435$		0			0
$436$	2.09577e7	+	1.38928e8i	0.252862	+	1.67622i
$437$	−1.64498e7			−0.197113
$438$		0			0
$439$			7.62674e7i			0.901457i	0.892661	+	0.450729i	$0.148836\pi$
$439$			7.62674e7i			0.901457i	−0.892661	+	0.450729i	$0.851164\pi$
$440$	9.30326e6	−	1.48122e7i	0.109214	−	0.173884i
$441$		0			0
$442$	−1.10624e7	+	1.28564e7i	−0.128110	+	0.148886i
$443$		−	4.11703e7i		−	0.473558i	−0.971564	−	0.236779i	$-0.923908\pi$
$443$		−	4.11703e7i		−	0.473558i	0.971564	−	0.236779i	$-0.0760917\pi$
$444$		0			0
$445$	−5.83194e7			−0.661810
$446$	−7.26874e6	−	6.25448e6i	−0.0819322	−	0.0704996i
$447$		0			0
$448$	5.52690e7	−	2.66414e7i	0.614678	−	0.296294i
$449$	2.74161e7			0.302877			0.151439	−	0.988467i	$-0.451609\pi$
$449$	2.74161e7			0.302877			0.151439	+	0.988467i	$0.451609\pi$
$450$		0			0
$451$		−	4.34784e7i		−	0.473962i
$452$	2.46171e7	+	1.63187e8i	0.266577	+	1.76714i
$453$		0			0
$454$	−3.54693e7	−	3.05200e7i	−0.379040	−	0.326150i
$455$			5.83571e6i			0.0619526i
$456$		0			0
$457$	−3.51153e7			−0.367915			−0.183957	−	0.982934i	$-0.558891\pi$
$457$	−3.51153e7			−0.367915			−0.183957	+	0.982934i	$0.558891\pi$
$458$	−6.65649e7	+	7.73595e7i	−0.692865	+	0.805225i
$459$		0			0
$460$	−1.37889e7	+	2.08008e6i	−0.141663	+	0.0213701i
$461$	−7.39800e7			−0.755112			−0.377556	−	0.925987i	$-0.623235\pi$
$461$	−7.39800e7			−0.755112			−0.377556	+	0.925987i	$0.623235\pi$
$462$		0			0
$463$			1.00507e8i			1.01263i	0.862348	+	0.506316i	$0.168993\pi$
$463$			1.00507e8i			1.01263i	−0.862348	+	0.506316i	$0.831007\pi$
$464$	5.95909e7	−	1.83975e7i	0.596522	−	0.184164i
$465$		0			0
$466$	−3.15504e7	+	3.66668e7i	−0.311779	+	0.362339i
$467$			1.62350e8i			1.59405i	0.603945	+	0.797026i	$0.293595\pi$
$467$			1.62350e8i			1.59405i	−0.603945	+	0.797026i	$0.706405\pi$
$468$		0			0
$469$	−9.85131e7			−0.954938
$470$	4.49689e7	+	3.86941e7i	0.433131	+	0.372693i
$471$		0			0
$472$	4.81559e7	−	7.66713e7i	0.457956	−	0.729133i
$473$	6.21043e7			0.586865
$474$		0			0
$475$			1.31886e7i			0.123060i
$476$	−7.04040e7	+	1.06206e7i	−0.652794	+	0.0984755i
$477$		0			0
$478$	1.48952e8	+	1.28167e8i	1.36384	+	1.17353i
$479$		−	1.59054e8i		−	1.44723i	−0.690202	−	0.723617i	$-0.742478\pi$
$479$		−	1.59054e8i		−	1.44723i	0.690202	−	0.723617i	$-0.257522\pi$
$480$		0			0
$481$	−5.78221e6			−0.0519587
$482$	2.79042e7	−	3.24293e7i	0.249188	−	0.289598i
$483$		0			0
$484$	−1.33469e7	−	8.84765e7i	−0.117718	−	0.780354i
$485$	7.32476e7			0.642049
$486$		0			0
$487$			1.46667e7i			0.126983i	0.997982	+	0.0634914i	$0.0202236\pi$
$487$			1.46667e7i			0.126983i	−0.997982	+	0.0634914i	$0.979776\pi$
$488$	9.51639e7	+	5.97709e7i	0.818866	+	0.514316i
$489$		0			0
$490$	1.83384e7	−	2.13123e7i	0.155874	−	0.181152i
$491$		−	1.18752e8i		−	1.00322i	−0.865094	−	0.501610i	$-0.832741\pi$
$491$		−	1.18752e8i		−	1.00322i	0.865094	−	0.501610i	$-0.167259\pi$
$492$		0			0
$493$	−7.23742e7			−0.604008
$494$	−1.14150e7	−	9.82215e6i	−0.0946878	−	0.0814753i
$495$		0			0
$496$	3.10956e7	+	1.00721e8i	0.254832	+	0.825420i
$497$	−1.00108e8			−0.815456
$498$		0			0
$499$			2.10310e7i			0.169261i	0.996412	+	0.0846307i	$0.0269711\pi$
$499$			2.10310e7i			0.169261i	−0.996412	+	0.0846307i	$0.973029\pi$
$500$	1.66771e6	+	1.10553e7i	0.0133417	+	0.0884421i
$501$		0			0
$502$	9.86023e6	+	8.48435e6i	0.0779428	+	0.0670668i
$503$		−	1.30335e8i		−	1.02414i	−0.858944	−	0.512069i	$-0.828879\pi$
$503$		−	1.30335e8i		−	1.02414i	0.858944	−	0.512069i	$-0.171121\pi$
$504$		0			0
$505$	−3.30676e7			−0.256760
$506$	1.24291e7	−	1.44446e7i	0.0959372	−	0.111495i
$507$		0			0
$508$	2.45861e8	−	3.70886e7i	1.87542	−	0.282911i
$509$	9.12352e7			0.691846			0.345923	−	0.938263i	$-0.387566\pi$
$509$	9.12352e7			0.691846			0.345923	+	0.938263i	$0.387566\pi$
$510$		0			0
$511$		−	6.46046e7i		−	0.484173i
$512$	−1.49534e7	+	1.33382e8i	−0.111412	+	0.993774i
$513$		0			0
$514$	−3.11145e7	+	3.61603e7i	−0.229126	+	0.266282i
$515$			2.06636e7i			0.151281i
$516$		0			0
$517$	−8.10685e7			−0.586652
$518$	−1.83997e7	−	1.58322e7i	−0.132379	−	0.113907i
$519$		0			0
$520$	−1.08105e7	−	6.78991e6i	−0.0768842	−	0.0482896i
$521$	−1.57984e8			−1.11712			−0.558560	−	0.829464i	$-0.688646\pi$
$521$	−1.57984e8			−1.11712			−0.558560	+	0.829464i	$0.688646\pi$
$522$		0			0
$523$		−	1.17971e8i		−	0.824653i	−0.911036	−	0.412327i	$-0.864716\pi$
$523$		−	1.17971e8i		−	0.824653i	0.911036	−	0.412327i	$-0.135284\pi$
$524$	−1.37813e8	+	2.07894e7i	−0.957848	+	0.144494i
$525$		0			0
$526$	−3.37202e7	−	2.90149e7i	−0.231704	−	0.199372i
$527$		−	1.22327e8i		−	0.835779i
$528$		0			0
$529$	1.32844e8			0.897375
$530$	−8.25927e7	+	9.59864e7i	−0.554771	+	0.644736i
$531$		0			0
$532$	−9.42984e6	−	6.25105e7i	−0.0626281	−	0.415162i
$533$	−3.17324e7			−0.209566
$534$		0			0
$535$			4.63949e7i			0.302976i
$536$	1.14621e8	−	1.82493e8i	0.744337	−	1.18509i
$537$		0			0
$538$	4.54645e7	−	5.28373e7i	0.291962	−	0.339308i
$539$			3.84211e7i			0.245360i
$540$		0			0
$541$	−2.37184e7			−0.149794			−0.0748969	−	0.997191i	$-0.523863\pi$
$541$	−2.37184e7			−0.149794			−0.0748969	+	0.997191i	$0.523863\pi$
$542$	−1.31025e8	−	1.12742e8i	−0.822920	−	0.708091i
$543$		0			0
$544$	6.22413e7	−	1.42779e8i	0.386618	−	0.886886i
$545$	1.22722e8			0.758111
$546$		0			0
$547$		−	1.30769e8i		−	0.798992i	−0.916735	−	0.399496i	$-0.869185\pi$
$547$		−	1.30769e8i		−	0.798992i	0.916735	−	0.399496i	$-0.130815\pi$
$548$	3.83275e7	+	2.54073e8i	0.232900	+	1.54389i
$549$		0			0
$550$	−1.15810e7	−	9.96503e6i	−0.0696079	−	0.0598950i
$551$		−	6.42598e7i		−	0.384135i
$552$		0			0
$553$	−1.44372e8			−0.853707
$554$	1.02599e8	−	1.19237e8i	0.603412	−	0.701266i
$555$		0			0
$556$	−1.76099e7	+	2.65649e6i	−0.102455	+	0.0154555i
$557$	−8.04273e7			−0.465412			−0.232706	−	0.972547i	$-0.574758\pi$
$557$	−8.04273e7			−0.465412			−0.232706	+	0.972547i	$0.574758\pi$
$558$		0			0
$559$		−	4.53263e7i		−	0.259487i
$560$	−1.58090e7	−	5.12065e7i	−0.0900202	−	0.291582i
$561$		0			0
$562$	−2.21069e8	+	2.56919e8i	−1.24543	+	1.44740i
$563$		−	2.79719e8i		−	1.56746i	−0.621101	−	0.783730i	$-0.713314\pi$
$563$		−	2.79719e8i		−	1.56746i	0.621101	−	0.783730i	$-0.286686\pi$
$564$		0			0
$565$	1.44151e8			0.799229
$566$	2.13035e8	+	1.83308e8i	1.17490	+	1.01096i
$567$		0			0
$568$	1.16477e8	−	1.85448e8i	0.635616	−	1.01199i
$569$	−8.01186e7			−0.434907			−0.217454	−	0.976071i	$-0.569775\pi$
$569$	−8.01186e7			−0.434907			−0.217454	+	0.976071i	$0.569775\pi$
$570$		0			0
$571$		−	2.60254e8i		−	1.39794i	−0.715149	−	0.698972i	$-0.753641\pi$
$571$		−	2.60254e8i		−	1.39794i	0.715149	−	0.698972i	$-0.246359\pi$
$572$	1.72498e7	−	2.60217e6i	0.0921713	−	0.0139042i
$573$		0			0
$574$	−1.00976e8	−	8.68861e7i	−0.533928	−	0.459425i
$575$			1.21804e7i			0.0640703i
$576$		0			0
$577$	2.08528e8			1.08552			0.542760	−	0.839888i	$-0.317379\pi$
$577$	2.08528e8			1.08552			0.542760	+	0.839888i	$0.317379\pi$
$578$	8.05567e6	−	9.36203e6i	0.0417175	−	0.0484827i
$579$		0			0
$580$	−8.12569e6	−	5.38652e7i	−0.0416463	−	0.276073i
$581$	−1.47975e8			−0.754501
$582$		0			0
$583$		−	1.73041e8i		−	0.873260i
$584$	1.19679e8	+	7.51680e7i	0.600866	+	0.377394i
$585$		0			0
$586$	5.81039e7	−	6.75264e7i	0.288744	−	0.335568i
$587$		−	2.03436e8i		−	1.00580i	−0.864343	−	0.502902i	$-0.832266\pi$
$587$		−	2.03436e8i		−	1.00580i	0.864343	−	0.502902i	$-0.167734\pi$
$588$		0			0
$589$	1.08612e8			0.531536
$590$	−5.99461e7	−	5.15814e7i	−0.291881	−	0.251152i
$591$		0			0
$592$	5.07370e7	−	1.56640e7i	0.244546	−	0.0754985i
$593$	2.65879e7			0.127503			0.0637513	−	0.997966i	$-0.479694\pi$
$593$	2.65879e7			0.127503			0.0637513	+	0.997966i	$0.479694\pi$
$594$		0			0
$595$			6.21911e7i			0.295242i
$596$	9.46195e6	+	6.27233e7i	0.0446933	+	0.296272i
$597$		0			0
$598$	−1.05423e7	−	9.07125e6i	−0.0492983	−	0.0424193i
$599$			1.00479e8i			0.467516i	0.972295	+	0.233758i	$0.0751023\pi$
$599$			1.00479e8i			0.467516i	−0.972295	+	0.233758i	$0.924898\pi$
$600$		0			0
$601$	3.21498e8			1.48100			0.740500	−	0.672056i	$-0.234589\pi$
$601$	3.21498e8			1.48100			0.740500	+	0.672056i	$0.234589\pi$
$602$	1.24108e8	−	1.44234e8i	0.568864	−	0.661115i
$603$		0			0
$604$	−1.87148e6	+	282317.i	−0.00849327	+	0.00128123i
$605$	−7.81554e7			−0.352933
$606$		0			0
$607$		−	1.80290e8i		−	0.806130i	−0.915171	−	0.403065i	$-0.867945\pi$
$607$		−	1.80290e8i		−	0.806130i	0.915171	−	0.403065i	$-0.132055\pi$
$608$	1.26771e8	+	5.52630e7i	0.564039	+	0.245880i
$609$		0			0
$610$	6.40225e7	−	7.44048e7i	0.282061	−	0.327802i
$611$			5.91672e7i			0.259393i
$612$		0			0
$613$	−4.52010e8			−1.96230			−0.981152	−	0.193237i	$-0.938101\pi$
$613$	−4.52010e8			−1.96230			−0.981152	+	0.193237i	$0.938101\pi$
$614$	−8.52206e7	−	7.33291e7i	−0.368163	−	0.316790i
$615$		0			0
$616$	6.20158e7	+	3.89511e7i	0.265314	+	0.166639i
$617$	−5.84022e6			−0.0248641			−0.0124321	−	0.999923i	$-0.503957\pi$
$617$	−5.84022e6			−0.0248641			−0.0124321	+	0.999923i	$0.503957\pi$
$618$		0			0
$619$			2.69398e8i			1.13586i	0.823078	+	0.567928i	$0.192255\pi$
$619$			2.69398e8i			1.13586i	−0.823078	+	0.567928i	$0.807745\pi$
$620$	9.10433e7	−	1.37341e7i	0.382009	−	0.0576268i
$621$		0			0
$622$	2.43852e8	+	2.09825e8i	1.01334	+	0.871940i
$623$		−	2.44173e8i		−	1.00980i
$624$		0			0
$625$	9.76562e6			0.0400000
$626$	1.14515e8	−	1.33085e8i	0.466808	−	0.542509i
$627$		0			0
$628$	2.73231e7	+	1.81125e8i	0.110319	+	0.731306i
$629$	−6.16209e7			−0.247615
$630$		0			0
$631$		−	2.83825e8i		−	1.12970i	−0.825195	−	0.564848i	$-0.808935\pi$
$631$		−	2.83825e8i		−	1.12970i	0.825195	−	0.564848i	$-0.191065\pi$
$632$	1.67979e8	−	2.67447e8i	0.665431	−	1.05946i
$633$		0			0
$634$	−1.49926e8	+	1.74240e8i	−0.588316	+	0.683721i
$635$		−	2.17180e8i		−	0.848202i
$636$		0			0
$637$	2.80413e7			0.108488
$638$	5.64269e7	+	4.85532e7i	0.217282	+	0.186963i
$639$		0			0
$640$	1.13253e8	+	3.02935e7i	0.432025	+	0.115560i
$641$	−8.05312e7			−0.305767			−0.152883	−	0.988244i	$-0.548856\pi$
$641$	−8.05312e7			−0.305767			−0.152883	+	0.988244i	$0.548856\pi$
$642$		0			0
$643$		−	1.70629e8i		−	0.641829i	−0.947108	−	0.320915i	$-0.896010\pi$
$643$		−	1.70629e8i		−	0.641829i	0.947108	−	0.320915i	$-0.103990\pi$
$644$	−8.70893e6	−	5.77316e7i	−0.0326067	−	0.216150i
$645$		0			0
$646$	−1.21649e8	−	1.04675e8i	−0.451244	−	0.388279i
$647$			1.72635e8i			0.637404i	0.947855	+	0.318702i	$0.103247\pi$
$647$			1.72635e8i			0.637404i	−0.947855	+	0.318702i	$0.896753\pi$
$648$		0			0
$649$	1.08069e8			0.395336
$650$	−7.27289e6	+	8.45231e6i	−0.0264830	+	0.0307777i
$651$		0			0
$652$	−3.71364e8	+	5.60211e7i	−1.33985	+	0.202120i
$653$	9.10476e7			0.326986			0.163493	−	0.986545i	$-0.447724\pi$
$653$	9.10476e7			0.326986			0.163493	+	0.986545i	$0.447724\pi$
$654$		0			0
$655$			1.21737e8i			0.433209i
$656$	2.78441e8	−	8.59631e7i	0.986329	−	0.304509i
$657$		0			0
$658$	−1.62005e8	+	1.88277e8i	−0.568658	+	0.660875i
$659$			4.48502e8i			1.56714i	0.621302	+	0.783571i	$0.286604\pi$
$659$			4.48502e8i			1.56714i	−0.621302	+	0.783571i	$0.713396\pi$
$660$		0			0
$661$	−1.10377e8			−0.382186			−0.191093	−	0.981572i	$-0.561203\pi$
$661$	−1.10377e8			−0.382186			−0.191093	+	0.981572i	$0.561203\pi$
$662$	−4.01061e7	−	3.45098e7i	−0.138241	−	0.118951i
$663$		0			0
$664$	1.72170e8	−	2.74120e8i	0.588104	−	0.936347i
$665$	−5.52184e7			−0.187767
$666$		0			0
$667$		−	5.93471e7i		−	0.199996i
$668$	4.02373e7	−	6.06989e6i	0.134989	−	0.0203634i
$669$		0			0
$670$	−1.42684e8	−	1.22774e8i	−0.474407	−	0.408209i
$671$			1.34135e8i			0.443990i
$672$		0			0
$673$	−3.09349e8			−1.01485			−0.507427	−	0.861695i	$-0.669403\pi$
$673$	−3.09349e8			−1.01485			−0.507427	+	0.861695i	$0.669403\pi$
$674$	−1.23661e8	+	1.43714e8i	−0.403880	+	0.469376i
$675$		0			0
$676$	4.41801e7	+	2.92870e8i	0.143017	+	0.948058i
$677$	−1.46692e8			−0.472761			−0.236381	−	0.971661i	$-0.575961\pi$
$677$	−1.46692e8			−0.472761			−0.236381	+	0.971661i	$0.575961\pi$
$678$		0			0
$679$			3.06675e8i			0.979644i
$680$	−1.15208e8	−	7.23600e7i	−0.366399	−	0.230129i
$681$		0			0
$682$	−8.20649e7	+	9.53731e7i	−0.258705	+	0.300658i
$683$			4.83173e8i			1.51649i	0.651968	+	0.758247i	$0.273944\pi$
$683$			4.83173e8i			1.51649i	−0.651968	+	0.758247i	$0.726056\pi$
$684$		0			0
$685$	2.24435e8			0.698263
$686$	2.56211e8	+	2.20459e8i	0.793642	+	0.682899i
$687$		0			0
$688$	1.22789e8	+	3.97724e8i	0.377047	+	1.22128i
$689$	−1.26293e8			−0.386118
$690$		0			0
$691$		−	1.33819e8i		−	0.405586i	−0.979222	−	0.202793i	$-0.934998\pi$
$691$		−	1.33819e8i		−	0.405586i	0.979222	−	0.202793i	$-0.0650019\pi$
$692$	7.19577e7	+	4.77008e8i	0.217149	+	1.43948i
$693$		0			0
$694$	−4.77267e8	−	4.10670e8i	−1.42785	−	1.22861i
$695$			1.55556e7i			0.0463376i
$696$		0			0
$697$	−3.38171e8			−0.998708
$698$	−3.04889e8	+	3.54332e8i	−0.896552	+	1.04194i
$699$		0			0
$700$	−4.62864e7	+	6.98240e6i	−0.134946	+	0.0203569i
$701$	2.21186e8			0.642101			0.321050	−	0.947062i	$-0.395964\pi$
$701$	2.21186e8			0.642101			0.321050	+	0.947062i	$0.395964\pi$
$702$		0			0
$703$		−	5.47121e7i		−	0.157477i
$704$	−1.44312e8	+	6.95630e7i	−0.413604	+	0.199370i
$705$		0			0
$706$	1.15162e7	−	1.33837e7i	0.0327261	−	0.0380332i
$707$		−	1.38448e8i		−	0.391768i
$708$		0			0
$709$	4.32781e8			1.21431			0.607155	−	0.794583i	$-0.292311\pi$
$709$	4.32781e8			1.21431			0.607155	+	0.794583i	$0.292311\pi$
$710$	−1.44994e8	−	1.24762e8i	−0.405113	−	0.348584i
$711$		0			0
$712$	4.52325e8	+	2.84098e8i	1.25317	+	0.787096i
$713$	1.00309e8			0.276739
$714$		0			0
$715$		−	1.52375e7i		−	0.0416866i
$716$	5.55786e7	−	8.38415e6i	0.151415	−	0.0228413i
$717$		0			0
$718$	−7.29376e7	−	6.27601e7i	−0.197051	−	0.169555i
$719$			5.42829e8i			1.46042i	0.683225	+	0.730208i	$0.260577\pi$
$719$			5.42829e8i			1.46042i	−0.683225	+	0.730208i	$0.739423\pi$
$720$		0			0
$721$	−8.65150e7			−0.230826
$722$	−1.52543e8	+	1.77280e8i	−0.405304	+	0.471031i
$723$		0			0
$724$	4.04283e7	+	2.67999e8i	0.106529	+	0.706184i
$725$	−4.75817e7			−0.124861
$726$		0			0
$727$			1.71836e8i			0.447210i	0.974680	+	0.223605i	$0.0717826\pi$
$727$			1.71836e8i			0.447210i	−0.974680	+	0.223605i	$0.928217\pi$
$728$	2.84281e7	−	4.52618e7i	0.0736808	−	0.117311i
$729$		0			0
$730$	8.05149e7	−	9.35718e7i	0.206970	−	0.240534i
$731$		−	4.83042e8i		−	1.23661i
$732$		0			0
$733$	−3.55710e8			−0.903200			−0.451600	−	0.892221i	$-0.649147\pi$
$733$	−3.55710e8			−0.903200			−0.451600	+	0.892221i	$0.649147\pi$
$734$	−4.62780e8	−	3.98204e8i	−1.17027	−	1.00697i
$735$		0			0
$736$	1.17079e8	+	5.10381e7i	0.293661	+	0.128015i
$737$	2.57226e8			0.642558
$738$		0			0
$739$			6.71490e8i			1.66382i	0.554912	+	0.831909i	$0.312752\pi$
$739$			6.71490e8i			1.66382i	−0.554912	+	0.831909i	$0.687248\pi$
$740$	−6.91839e6	−	4.58620e7i	−0.0170730	−	0.113177i
$741$		0			0
$742$	−4.01878e8	−	3.45801e8i	−0.983745	−	0.846475i
$743$		−	2.37075e8i		−	0.577988i	−0.957331	−	0.288994i	$-0.906679\pi$
$743$		−	2.37075e8i		−	0.577988i	0.957331	−	0.288994i	$-0.0933208\pi$
$744$		0			0
$745$	5.54064e7			0.133996
$746$	−2.83825e8	+	3.29852e8i	−0.683652	+	0.794517i
$747$		0			0
$748$	1.83831e8	−	2.77313e7i	0.439252	−	0.0662621i
$749$	−1.94247e8			−0.462284
$750$		0			0
$751$			5.41645e8i			1.27878i	0.768884	+	0.639389i	$0.220813\pi$
$751$			5.41645e8i			1.27878i	−0.768884	+	0.639389i	$0.779187\pi$
$752$	−1.60284e8	−	5.19173e8i	−0.376910	−	1.22084i
$753$		0			0
$754$	3.54362e7	−	4.11827e7i	0.0826671	−	0.0960729i
$755$			1.65317e6i			0.00384128i
$756$		0			0
$757$	−5.37604e8			−1.23930			−0.619648	−	0.784880i	$-0.712725\pi$
$757$	−5.37604e8			−1.23930			−0.619648	+	0.784880i	$0.712725\pi$
$758$	7.66273e7	+	6.59349e7i	0.175945	+	0.151394i
$759$		0			0
$760$	6.42472e7	−	1.02291e8i	0.146357	−	0.233022i
$761$	4.02108e8			0.912407			0.456204	−	0.889875i	$-0.349209\pi$
$761$	4.02108e8			0.912407			0.456204	+	0.889875i	$0.349209\pi$
$762$		0			0
$763$			5.13815e8i			1.15673i
$764$	−5.43403e8	+	8.19736e7i	−1.21855	+	0.183820i
$765$		0			0
$766$	3.70082e8	+	3.18442e8i	0.823402	+	0.708506i
$767$		−	7.88732e7i		−	0.174801i
$768$		0			0
$769$	7.17215e8			1.57714			0.788570	−	0.614945i	$-0.210822\pi$
$769$	7.17215e8			1.57714			0.788570	+	0.614945i	$0.210822\pi$
$770$	4.17218e7	−	4.84877e7i	0.0913883	−	0.106208i
$771$		0			0
$772$	−9.04941e7	−	5.99886e8i	−0.196684	−	1.30382i
$773$	−7.16120e8			−1.55041			−0.775207	−	0.631708i	$-0.782354\pi$
$773$	−7.16120e8			−1.55041			−0.775207	+	0.631708i	$0.782354\pi$
$774$		0			0
$775$		−	8.04228e7i		−	0.172772i
$776$	−5.68108e8	−	3.56819e8i	−1.21575	−	0.763594i
$777$		0			0
$778$	−3.35127e8	+	3.89473e8i	−0.711657	+	0.827064i
$779$		−	3.00256e8i		−	0.635155i
$780$		0			0
$781$	2.61391e8			0.548704
$782$	−1.12349e8	−	9.66722e7i	−0.234936	−	0.202154i
$783$		0			0
$784$	−2.46054e8	+	7.59641e7i	−0.510601	+	0.157638i
$785$	1.59996e8			0.330750
$786$		0			0
$787$			4.14567e8i			0.850493i	0.905077	+	0.425247i	$0.139813\pi$
$787$			4.14567e8i			0.850493i	−0.905077	+	0.425247i	$0.860187\pi$
$788$	−1.45959e6	−	9.67566e6i	−0.00298300	−	0.0197743i
$789$		0			0
$790$	−2.09106e8	−	1.79928e8i	−0.424116	−	0.364936i
$791$			6.03533e8i			1.21947i
$792$		0			0
$793$	9.78970e7			0.196313
$794$	−3.00873e8	+	3.49665e8i	−0.601066	+	0.698538i
$795$		0			0
$796$	2.68328e8	−	4.04779e7i	0.532019	−	0.0802563i
$797$	8.17450e7			0.161468			0.0807339	−	0.996736i	$-0.474274\pi$
$797$	8.17450e7			0.161468			0.0807339	+	0.996736i	$0.474274\pi$
$798$		0			0
$799$			6.30544e8i			1.23616i
$800$	4.09199e7	−	9.38686e7i	0.0799217	−	0.183337i
$801$		0			0
$802$	3.24778e8	−	3.77446e8i	0.629598	−	0.731698i
$803$			1.68688e8i			0.325790i
$804$		0			0
$805$	−5.09970e7			−0.0977590
$806$	6.96073e7	+	5.98944e7i	0.132938	+	0.114388i
$807$		0			0
$808$	2.56472e8	+	1.61086e8i	0.486190	+	0.305367i
$809$	9.14566e8			1.72731			0.863653	−	0.504086i	$-0.168171\pi$
$809$	9.14566e8			1.72731			0.863653	+	0.504086i	$0.168171\pi$
$810$		0			0
$811$		−	2.18494e8i		−	0.409617i	−0.978802	−	0.204808i	$-0.934343\pi$
$811$		−	2.18494e8i		−	0.409617i	0.978802	−	0.204808i	$-0.0656572\pi$
$812$	2.25524e8	−	3.40208e7i	0.421235	−	0.0635443i
$813$		0			0
$814$	4.80431e7	+	4.13393e7i	0.0890754	+	0.0766460i
$815$			3.28043e8i			0.605980i
$816$		0			0
$817$	4.28884e8			0.786455
$818$	−3.34896e8	+	3.89204e8i	−0.611857	+	0.711079i
$819$		0			0
$820$	−3.79676e7	−	2.51688e8i	−0.0688608	−	0.456478i
$821$	8.45664e8			1.52816			0.764079	−	0.645123i	$-0.223194\pi$
$821$	8.45664e8			1.52816			0.764079	+	0.645123i	$0.223194\pi$
$822$		0			0
$823$		−	7.93523e8i		−	1.42351i	−0.702429	−	0.711754i	$-0.747901\pi$
$823$		−	7.93523e8i		−	1.42351i	0.702429	−	0.711754i	$-0.252099\pi$
$824$	1.00661e8	−	1.60267e8i	0.179920	−	0.286459i
$825$		0			0
$826$	2.15962e8	−	2.50984e8i	0.383210	−	0.445354i
$827$		−	2.55103e8i		−	0.451023i	−0.974240	−	0.225512i	$-0.927595\pi$
$827$		−	2.55103e8i		−	0.451023i	0.974240	−	0.225512i	$-0.0724053\pi$
$828$		0			0
$829$	−6.38970e8			−1.12155			−0.560773	−	0.827970i	$-0.689496\pi$
$829$	−6.38970e8			−1.12155			−0.560773	+	0.827970i	$0.689496\pi$
$830$	−2.14323e8	−	1.84417e8i	−0.374831	−	0.322528i
$831$		0			0
$832$	5.07700e7	+	1.05325e8i	0.0881530	+	0.182878i
$833$	2.98836e8			0.517009
$834$		0			0
$835$		−	3.55435e7i		−	0.0610521i
$836$	2.46221e7	+	1.63220e8i	0.0421412	+	0.279354i
$837$		0			0
$838$	4.56465e7	+	3.92771e7i	0.0775668	+	0.0667433i
$839$			8.37669e8i			1.41836i	0.705028	+	0.709180i	$0.250935\pi$
$839$			8.37669e8i			1.41836i	−0.705028	+	0.709180i	$0.749065\pi$
$840$		0			0
$841$	−3.62988e8			−0.610245
$842$	4.98144e8	−	5.78927e8i	0.834486	−	0.969812i
$843$		0			0
$844$	−4.48933e8	+	6.77225e7i	−0.746713	+	0.112643i
$845$	2.58706e8			0.428782
$846$		0			0
$847$		−	3.27223e8i		−	0.538509i
$848$	1.10818e9	−	3.42128e8i	1.81728	−	0.561049i
$849$		0			0
$850$	−7.75071e7	+	9.00762e7i	−0.126207	+	0.146674i
$851$		−	5.05294e7i		−	0.0819890i
$852$		0			0
$853$	6.48236e8			1.04445			0.522223	−	0.852809i	$-0.325103\pi$
$853$	6.48236e8			1.04445			0.522223	+	0.852809i	$0.325103\pi$
$854$	3.11520e8	+	2.68051e8i	0.500163	+	0.430372i
$855$		0			0
$856$	2.26009e8	−	3.59839e8i	0.360333	−	0.573702i
$857$	7.42707e8			1.17998			0.589991	−	0.807410i	$-0.299131\pi$
$857$	7.42707e8			1.17998			0.589991	+	0.807410i	$0.299131\pi$
$858$		0			0
$859$			1.14216e9i			1.80197i	0.433848	+	0.900986i	$0.357155\pi$
$859$			1.14216e9i			1.80197i	−0.433848	+	0.900986i	$0.642845\pi$
$860$	3.59509e8	−	5.42327e7i	0.565216	−	0.0852641i
$861$		0			0
$862$	−3.67148e8	−	3.15917e8i	−0.573218	−	0.493232i
$863$			7.21139e8i			1.12198i	0.827822	+	0.560992i	$0.189580\pi$
$863$			7.21139e8i			1.12198i	−0.827822	+	0.560992i	$0.810420\pi$
$864$		0			0
$865$	4.21363e8			0.651041
$866$	2.44686e8	−	2.84366e8i	0.376752	−	0.437849i
$867$		0			0
$868$	5.75022e7	+	3.81182e8i	0.0879276	+	0.582872i
$869$	3.76969e8			0.574442
$870$		0			0
$871$		−	1.87734e8i		−	0.284112i
$872$	−9.51831e8	−	5.97829e8i	−1.43552	−	0.901628i
$873$		0			0
$874$	8.58336e7	−	9.97529e7i	0.128565	−	0.149414i
$875$			4.08869e7i			0.0610324i
$876$		0			0
$877$	−6.88487e8			−1.02070			−0.510349	−	0.859967i	$-0.670484\pi$
$877$	−6.88487e8			−1.02070			−0.510349	+	0.859967i	$0.670484\pi$
$878$	−4.62493e8	−	3.97957e8i	−0.683315	−	0.587967i
$879$		0			0
$880$	4.12786e7	+	1.33705e8i	0.0605727	+	0.196200i
$881$	−4.33117e8			−0.633399			−0.316700	−	0.948526i	$-0.602575\pi$
$881$	−4.33117e8			−0.633399			−0.316700	+	0.948526i	$0.602575\pi$
$882$		0			0
$883$		−	1.05024e9i		−	1.52548i	−0.646705	−	0.762740i	$-0.723853\pi$
$883$		−	1.05024e9i		−	1.52548i	0.646705	−	0.762740i	$-0.276147\pi$
$884$	−2.02395e7	−	1.34167e8i	−0.0292983	−	0.194218i
$885$		0			0
$886$	2.49661e8	+	2.14824e8i	0.358963	+	0.308874i
$887$		−	7.88286e8i		−	1.12957i	−0.825238	−	0.564785i	$-0.808959\pi$
$887$		−	7.88286e8i		−	1.12957i	0.825238	−	0.564785i	$-0.191041\pi$
$888$		0			0
$889$	9.09295e8			1.29419
$890$	3.04306e8	−	3.53655e8i	0.431659	−	0.501660i
$891$		0			0
$892$	7.58555e7	−	1.14430e7i	0.106879	−	0.0161229i
$893$	−5.59849e8			−0.786170
$894$		0			0
$895$		−	4.90952e7i		−	0.0684809i
$896$	−1.26833e8	+	4.74169e8i	−0.176323	+	0.659188i
$897$		0			0
$898$	−1.43055e8	+	1.66254e8i	−0.197549	+	0.229584i
$899$			3.91849e8i			0.539312i
$900$		0			0
$901$	−1.34590e9			−1.84009
$902$	2.63657e8	+	2.26867e8i	0.359269	+	0.309137i
$903$		0			0
$904$	−1.11803e9	−	7.02217e8i	−1.51338	−	0.950530i
$905$	2.36736e8			0.319388
$906$		0			0
$907$			2.31644e7i			0.0310455i	0.999880	+	0.0155227i	$0.00494124\pi$
$907$			2.31644e7i			0.0310455i	−0.999880	+	0.0155227i	$0.995059\pi$
$908$	3.70152e8	−	5.58383e7i	0.494451	−	0.0745890i
$909$		0			0
$910$	−3.53883e7	−	3.04503e7i	−0.0469608	−	0.0404080i
$911$		−	5.38656e8i		−	0.712454i	−0.934399	−	0.356227i	$-0.884063\pi$
$911$		−	5.38656e8i		−	0.712454i	0.934399	−	0.356227i	$-0.115937\pi$
$912$		0			0
$913$	3.86375e8			0.507688
$914$	1.83229e8	−	2.12942e8i	0.239969	−	0.278884i
$915$		0			0
$916$	−1.21785e8	−	8.07312e8i	−0.158455	−	1.05040i
$917$	−5.09690e8			−0.660995
$918$		0			0
$919$		−	1.29910e9i		−	1.67377i	−0.547377	−	0.836886i	$-0.684374\pi$
$919$		−	1.29910e9i		−	1.67377i	0.547377	−	0.836886i	$-0.315626\pi$
$920$	5.93355e7	−	9.44708e7i	0.0761993	−	0.121320i
$921$		0			0
$922$	3.86022e8	−	4.48622e8i	0.492515	−	0.572384i
$923$		−	1.90774e8i		−	0.242613i
$924$		0			0
$925$	−4.05121e7			−0.0511869
$926$	−6.09482e8	−	5.24436e8i	−0.767588	−	0.660480i
$927$		0			0
$928$	−1.99377e8	+	4.57362e8i	−0.249477	+	0.572290i
$929$	4.24439e8			0.529381			0.264691	−	0.964333i	$-0.414730\pi$
$929$	4.24439e8			0.529381			0.264691	+	0.964333i	$0.414730\pi$
$930$		0			0
$931$			2.65331e8i			0.328806i
$932$	−5.77234e7	−	3.82649e8i	−0.0713024	−	0.472664i
$933$		0			0
$934$	−9.84508e8	−	8.47132e8i	−1.20831	−	1.03971i
$935$		−	1.62386e8i		−	0.198662i
$936$		0			0
$937$	1.45041e9			1.76308			0.881539	−	0.472111i	$-0.156508\pi$
$937$	1.45041e9			1.76308			0.881539	+	0.472111i	$0.156508\pi$
$938$	5.14034e8	−	5.97393e8i	0.622849	−	0.723855i
$939$		0			0
$940$	−4.69289e8	+	7.07933e7i	−0.565011	+	0.0852332i
$941$	−1.06912e9			−1.28309			−0.641544	−	0.767086i	$-0.721706\pi$
$941$	−1.06912e9			−1.28309			−0.641544	+	0.767086i	$0.721706\pi$
$942$		0			0
$943$		−	2.77302e8i		−	0.330687i
$944$	2.13668e8	+	6.92087e8i	0.253994	+	0.822706i
$945$		0			0
$946$	−3.24055e8	+	3.76606e8i	−0.382777	+	0.444851i
$947$		−	2.62002e8i		−	0.308499i	−0.988032	−	0.154250i	$-0.950704\pi$
$947$		−	2.62002e8i		−	0.308499i	0.988032	−	0.154250i	$-0.0492960\pi$
$948$		0			0
$949$	1.23116e8			0.144050
$950$	−7.99771e7	−	6.88172e7i	−0.0932813	−	0.0802650i
$951$		0			0
$952$	3.02958e8	−	4.82354e8i	0.351133	−	0.559056i
$953$	−9.09209e8			−1.05047			−0.525237	−	0.850956i	$-0.676023\pi$
$953$	−9.09209e8			−1.05047			−0.525237	+	0.850956i	$0.676023\pi$
$954$		0			0
$955$			4.80013e8i			0.551116i
$956$	−1.55444e9	+	2.34491e8i	−1.77910	+	0.268381i
$957$		0			0
$958$	9.64521e8	+	8.29933e8i	1.09702	+	0.943945i
$959$			9.39669e8i			1.06542i
$960$		0			0
$961$	2.25198e8			0.253743
$962$	3.01711e7	−	3.50639e7i	0.0338896	−	0.0393853i
$963$		0			0
$964$	5.10525e7	+	3.38427e8i	0.0569883	+	0.377776i
$965$	−5.29907e8			−0.589682
$966$		0			0
$967$		−	1.49745e9i		−	1.65605i	−0.560691	−	0.828025i	$-0.689464\pi$
$967$		−	1.49745e9i		−	1.65605i	0.560691	−	0.828025i	$-0.310536\pi$
$968$	6.06173e8	+	3.80727e8i	0.668298	+	0.419747i
$969$		0			0
$970$	−3.82200e8	+	4.44180e8i	−0.418770	+	0.486681i
$971$		−	4.91944e8i		−	0.537351i	−0.963231	−	0.268676i	$-0.913414\pi$
$971$		−	4.91944e8i		−	0.537351i	0.963231	−	0.268676i	$-0.0865860\pi$
$972$		0			0
$973$	−6.51287e7			−0.0707024
$974$	−8.89402e7	−	7.65297e7i	−0.0962546	−	0.0828234i
$975$		0			0
$976$	−8.59015e8	+	2.65204e8i	−0.923955	+	0.285253i
$977$	−7.44362e8			−0.798180			−0.399090	−	0.916912i	$-0.630674\pi$
$977$	−7.44362e8			−0.798180			−0.399090	+	0.916912i	$0.630674\pi$
$978$		0			0
$979$			6.37557e8i			0.679471i
$980$	3.35513e7	+	2.22412e8i	0.0356477	+	0.236309i
$981$		0			0
$982$	7.20124e8	+	6.19639e8i	0.760453	+	0.654341i
$983$			1.04089e9i			1.09584i	0.836532	+	0.547918i	$0.184580\pi$
$983$			1.04089e9i			1.09584i	−0.836532	+	0.547918i	$0.815420\pi$
$984$		0			0
$985$	−8.54696e6			−0.00894341
$986$	3.77643e8	−	4.38884e8i	0.393959	−	0.457845i
$987$		0			0
$988$	1.19125e8	−	1.79703e7i	0.123518	−	0.0186330i
$989$	3.96096e8			0.409460
$990$		0			0
$991$		−	3.31402e8i		−	0.340513i	−0.985400	−	0.170257i	$-0.945540\pi$
$991$		−	3.31402e8i		−	0.340513i	0.985400	−	0.170257i	$-0.0544597\pi$
$992$	−7.73036e8	−	3.36988e8i	−0.791890	−	0.345207i
$993$		0			0
$994$	5.22357e8	−	6.07066e8i	0.531874	−	0.618126i
$995$		−	2.37027e8i		−	0.240618i
$996$		0			0
$997$	−3.43230e7			−0.0346338			−0.0173169	−	0.999850i	$-0.505512\pi$
$997$	−3.43230e7			−0.0346338			−0.0173169	+	0.999850i	$0.505512\pi$
$998$	−1.27534e8	−	1.09738e8i	−0.128302	−	0.110399i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.7.c.b.91.8		24
3.2	odd	2		60.7.c.a.31.17	✓	24
4.3	odd	2	inner	180.7.c.b.91.7		24
12.11	even	2		60.7.c.a.31.18	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.17	✓	24	3.2	odd	2
60.7.c.a.31.18	yes	24	12.11	even	2
180.7.c.b.91.7		24	4.3	odd	2	inner
180.7.c.b.91.8		24	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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.21792 + 6.06410i) q^{2} +(-9.54653 - 63.2840i) q^{4} -55.9017 q^{5} -234.050i q^{7} +(433.573 + 272.320i) q^{8} +O(q^{10})\)	\(q+(-5.21792 + 6.06410i) q^{2} +(-9.54653 - 63.2840i) q^{4} -55.9017 q^{5} -234.050i q^{7} +(433.573 + 272.320i) q^{8} +(291.691 - 338.993i) q^{10} +611.126i q^{11} +446.025 q^{13} +(1419.30 + 1221.26i) q^{14} +(-3913.73 + 1208.29i) q^{16} +4753.29 q^{17} +4220.36i q^{19} +(533.667 + 3537.68i) q^{20} +(-3705.93 - 3188.81i) q^{22} +3897.71i q^{23} +3125.00 q^{25} +(-2327.33 + 2704.74i) q^{26} +(-14811.6 + 2234.37i) q^{28} -15226.1 q^{29} -25735.3i q^{31} +(13094.4 - 30038.0i) q^{32} +(-24802.3 + 28824.4i) q^{34} +13083.8i q^{35} -12963.9 q^{37} +(-25592.7 - 22021.5i) q^{38} +(-24237.5 - 15223.2i) q^{40} -71144.7 q^{41} -101623. i q^{43} +(38674.5 - 5834.13i) q^{44} +(-23636.1 - 20338.0i) q^{46} +132654. i q^{47} +62869.4 q^{49} +(-16306.0 + 18950.3i) q^{50} +(-4257.99 - 28226.3i) q^{52} -283151. q^{53} -34163.0i q^{55} +(63736.6 - 101478. i) q^{56} +(79448.8 - 92332.7i) q^{58} -176836. i q^{59} +219488. q^{61} +(156061. + 134285. i) q^{62} +(113828. + 236141. i) q^{64} -24933.6 q^{65} -420905. i q^{67} +(-45377.4 - 300807. i) q^{68} +(-79341.5 - 68270.4i) q^{70} -427721. i q^{71} +276028. q^{73} +(67644.4 - 78614.1i) q^{74} +(267081. - 40289.8i) q^{76} +143034. q^{77} -616843. i q^{79} +(218784. - 67545.2i) q^{80} +(371228. - 431429. i) q^{82} -632235. i q^{83} -265717. q^{85} +(616250. + 530260. i) q^{86} +(-166422. + 264968. i) q^{88} +1.04325e6 q^{89} -104392. i q^{91} +(246663. - 37209.6i) q^{92} +(-804429. - 692181. i) q^{94} -235925. i q^{95} -1.31029e6 q^{97} +(-328048. + 381246. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8}+O(q^{10}) \) 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

Varieties

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Groups

Database

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