LMFDB - Embedded newform 336.7.bh.b.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,7,Mod(145,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	336.bh (of order $6$, degree $2$, not 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:	$77.2981720963$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} - 787x^{5} + 38792x^{4} - 92833x^{3} + 1563109x^{2} + 3107772x + 38787984 $ x^8 - x^7 + 212x^6 - 787x^5 + 38792x^4 - 92833x^3 + 1563109x^2 + 3107772x + 38787984
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$-7.08935 + 12.2791i$ of defining polynomial
Character	$\chi$	$=$	336.145
Dual form			336.7.bh.b.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.5000 + 7.79423i) q^{3} +(-68.9069 - 39.7834i) q^{5} +(-284.244 - 191.975i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(-13.5000 + 7.79423i) q^{3} +(-68.9069 - 39.7834i) q^{5} +(-284.244 - 191.975i) q^{7} +(121.500 - 210.444i) q^{9} +(411.119 + 712.080i) q^{11} +2429.15i q^{13} +1240.32 q^{15} +(6751.11 - 3897.76i) q^{17} +(-5786.98 - 3341.12i) q^{19} +(5333.59 + 376.196i) q^{21} +(9416.30 - 16309.5i) q^{23} +(-4647.06 - 8048.94i) q^{25} +3788.00i q^{27} +13888.2 q^{29} +(24131.1 - 13932.1i) q^{31} +(-11100.2 - 6408.72i) q^{33} +(11949.0 + 24536.6i) q^{35} +(-39837.6 + 69000.8i) q^{37} +(-18933.3 - 32793.5i) q^{39} +59196.1i q^{41} +91825.9 q^{43} +(-16744.4 + 9667.37i) q^{45} +(4347.44 + 2509.99i) q^{47} +(43940.4 + 109135. i) q^{49} +(-60760.0 + 105239. i) q^{51} +(-93194.8 - 161418. i) q^{53} -65422.9i q^{55} +104166. q^{57} +(-195032. + 112602. i) q^{59} +(-125018. - 72179.1i) q^{61} +(-74935.6 + 36492.6i) q^{63} +(96639.7 - 167385. i) q^{65} +(-117740. - 203932. i) q^{67} +293571. i q^{69} -96269.3 q^{71} +(238634. - 137775. i) q^{73} +(125471. + 72440.5i) q^{75} +(19843.1 - 281329. i) q^{77} +(-340667. + 590052. i) q^{79} +(-29524.5 - 51137.9i) q^{81} +128019. i q^{83} -620264. q^{85} +(-187491. + 108248. i) q^{87} +(-322756. - 186343. i) q^{89} +(466335. - 690470. i) q^{91} +(-217180. + 376167. i) q^{93} +(265842. + 460452. i) q^{95} +620049. i q^{97} +199804. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9}+O(q^{10}) $ 8 * q - 108 * q^3 - 42 * q^5 - 748 * q^7 + 972 * q^9	$ 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9} + 1070 q^{11} + 756 q^{15} + 7212 q^{17} + 24606 q^{19} + 8154 q^{21} + 15224 q^{23} + 22274 q^{25} + 32524 q^{29} - 40200 q^{31} - 28890 q^{33} + 242436 q^{35} - 45670 q^{37} - 93366 q^{39} + 445660 q^{43} - 10206 q^{45} - 82884 q^{47} + 24116 q^{49} - 64908 q^{51} - 13034 q^{53} - 442908 q^{57} - 1810362 q^{59} - 392856 q^{61} - 38394 q^{63} - 389004 q^{65} - 384094 q^{67} - 225688 q^{71} + 903078 q^{73} - 601398 q^{75} - 327674 q^{77} + 559592 q^{79} - 236196 q^{81} + 1953576 q^{85} - 439074 q^{87} - 1770036 q^{89} + 2960718 q^{91} + 361800 q^{93} - 1160112 q^{95} + 520020 q^{99}+O(q^{100}) $ 8 * q - 108 * q^3 - 42 * q^5 - 748 * q^7 + 972 * q^9 + 1070 * q^11 + 756 * q^15 + 7212 * q^17 + 24606 * q^19 + 8154 * q^21 + 15224 * q^23 + 22274 * q^25 + 32524 * q^29 - 40200 * q^31 - 28890 * q^33 + 242436 * q^35 - 45670 * q^37 - 93366 * q^39 + 445660 * q^43 - 10206 * q^45 - 82884 * q^47 + 24116 * q^49 - 64908 * q^51 - 13034 * q^53 - 442908 * q^57 - 1810362 * q^59 - 392856 * q^61 - 38394 * q^63 - 389004 * q^65 - 384094 * q^67 - 225688 * q^71 + 903078 * q^73 - 601398 * q^75 - 327674 * q^77 + 559592 * q^79 - 236196 * q^81 + 1953576 * q^85 - 439074 * q^87 - 1770036 * q^89 + 2960718 * q^91 + 361800 * q^93 - 1160112 * q^95 + 520020 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−13.5000	+	7.79423i	−0.500000	+	0.288675i
$3$	−13.5000	+	7.79423i	−0.500000	+	0.288675i
$4$		0			0
$5$	−68.9069	−	39.7834i	−0.551255	−	0.318267i	0.198373	−	0.980127i	$-0.436434\pi$
$5$	−68.9069	−	39.7834i	−0.551255	−	0.318267i	−0.749628	+	0.661859i	$0.769768\pi$
$6$		0			0
$7$	−284.244	−	191.975i	−0.828700	−	0.559693i
$7$	−284.244	−	191.975i	−0.828700	−	0.559693i
$8$		0			0
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$		0			0
$11$	411.119	+	712.080i	0.308880	+	0.534996i	0.978118	−	0.208052i	$-0.0667125\pi$
$11$	411.119	+	712.080i	0.308880	+	0.534996i	−0.669238	+	0.743049i	$0.733379\pi$
$12$		0			0
$13$			2429.15i			1.10567i	0.833292	+	0.552833i	$0.186453\pi$
$13$			2429.15i			1.10567i	−0.833292	+	0.552833i	$0.813547\pi$
$14$		0			0
$15$	1240.32			0.367503
$16$		0			0
$17$	6751.11	−	3897.76i	1.37413	−	0.793355i	0.382687	−	0.923878i	$-0.374999\pi$
$17$	6751.11	−	3897.76i	1.37413	−	0.793355i	0.991445	+	0.130523i	$0.0416656\pi$
$18$		0			0
$19$	−5786.98	−	3341.12i	−0.843706	−	0.487114i	0.0148160	−	0.999890i	$-0.495284\pi$
$19$	−5786.98	−	3341.12i	−0.843706	−	0.487114i	−0.858522	+	0.512776i	$0.828617\pi$
$20$		0			0
$21$	5333.59	+	376.196i	0.575919	+	0.0406215i
$22$		0			0
$23$	9416.30	−	16309.5i	0.773921	−	1.34047i	−0.161478	−	0.986876i	$-0.551626\pi$
$23$	9416.30	−	16309.5i	0.773921	−	1.34047i	0.935399	−	0.353594i	$-0.115041\pi$
$24$		0			0
$25$	−4647.06	−	8048.94i	−0.297412	−	0.515132i
$26$		0			0
$27$			3788.00i			0.192450i
$28$		0			0
$29$	13888.2			0.569446			0.284723	−	0.958610i	$-0.408098\pi$
$29$	13888.2			0.569446			0.284723	+	0.958610i	$0.408098\pi$
$30$		0			0
$31$	24131.1	−	13932.1i	0.810014	−	0.467662i	−0.0369467	−	0.999317i	$-0.511763\pi$
$31$	24131.1	−	13932.1i	0.810014	−	0.467662i	0.846961	+	0.531655i	$0.178430\pi$
$32$		0			0
$33$	−11100.2	−	6408.72i	−0.308880	−	0.178332i
$34$		0			0
$35$	11949.0	+	24536.6i	0.278693	+	0.572282i
$36$		0			0
$37$	−39837.6	+	69000.8i	−0.786481	+	1.36223i	0.141629	+	0.989920i	$0.454766\pi$
$37$	−39837.6	+	69000.8i	−0.786481	+	1.36223i	−0.928110	+	0.372305i	$0.878567\pi$
$38$		0			0
$39$	−18933.3	−	32793.5i	−0.319178	−	0.552833i
$40$		0			0
$41$			59196.1i			0.858898i	0.903091	+	0.429449i	$0.141292\pi$
$41$			59196.1i			0.858898i	−0.903091	+	0.429449i	$0.858708\pi$
$42$		0			0
$43$	91825.9			1.15494			0.577471	−	0.816411i	$-0.304040\pi$
$43$	91825.9			1.15494			0.577471	+	0.816411i	$0.304040\pi$
$44$		0			0
$45$	−16744.4	+	9667.37i	−0.183752	+	0.106089i
$46$		0			0
$47$	4347.44	+	2509.99i	0.0418735	+	0.0241757i	0.520791	−	0.853684i	$-0.325637\pi$
$47$	4347.44	+	2509.99i	0.0418735	+	0.0241757i	−0.478917	+	0.877860i	$0.658971\pi$
$48$		0			0
$49$	43940.4	+	109135.i	0.373487	+	0.927635i
$50$		0			0
$51$	−60760.0	+	105239.i	−0.458044	+	0.793355i
$52$		0			0
$53$	−93194.8	−	161418.i	−0.625985	−	1.08424i	−0.988350	−	0.152201i	$-0.951364\pi$
$53$	−93194.8	−	161418.i	−0.625985	−	1.08424i	0.362365	−	0.932036i	$-0.381970\pi$
$54$		0			0
$55$		−	65422.9i		−	0.393226i
$56$		0			0
$57$	104166.			0.562471
$58$		0			0
$59$	−195032.	+	112602.i	−0.949618	+	0.548262i	−0.892962	−	0.450132i	$-0.851377\pi$
$59$	−195032.	+	112602.i	−0.949618	+	0.548262i	−0.0566558	+	0.998394i	$0.518044\pi$
$60$		0			0
$61$	−125018.	−	72179.1i	−0.550786	−	0.317996i	0.198653	−	0.980070i	$-0.436343\pi$
$61$	−125018.	−	72179.1i	−0.550786	−	0.317996i	−0.749439	+	0.662074i	$0.769677\pi$
$62$		0			0
$63$	−74935.6	+	36492.6i	−0.299686	+	0.145943i
$64$		0			0
$65$	96639.7	−	167385.i	0.351897	−	0.609504i
$66$		0			0
$67$	−117740.	−	203932.i	−0.391471	−	0.678048i	0.601173	−	0.799119i	$-0.294700\pi$
$67$	−117740.	−	203932.i	−0.391471	−	0.678048i	−0.992644	+	0.121071i	$0.961367\pi$
$68$		0			0
$69$			293571.i			0.893647i
$70$		0			0
$71$	−96269.3			−0.268975			−0.134488	−	0.990915i	$-0.542939\pi$
$71$	−96269.3			−0.268975			−0.134488	+	0.990915i	$0.542939\pi$
$72$		0			0
$73$	238634.	−	137775.i	0.613428	−	0.354163i	−0.160878	−	0.986974i	$-0.551433\pi$
$73$	238634.	−	137775.i	0.613428	−	0.354163i	0.774306	+	0.632812i	$0.218099\pi$
$74$		0			0
$75$	125471.	+	72440.5i	0.297412	+	0.171711i
$76$		0			0
$77$	19843.1	−	281329.i	0.0434647	−	0.616229i
$78$		0			0
$79$	−340667.	+	590052.i	−0.690953	+	1.19677i	0.280573	+	0.959833i	$0.409476\pi$
$79$	−340667.	+	590052.i	−0.690953	+	1.19677i	−0.971526	+	0.236933i	$0.923858\pi$
$80$		0			0
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			128019.i			0.223893i	0.993714	+	0.111946i	$0.0357085\pi$
$83$			128019.i			0.223893i	−0.993714	+	0.111946i	$0.964291\pi$
$84$		0			0
$85$	−620264.			−1.01000
$86$		0			0
$87$	−187491.	+	108248.i	−0.284723	+	0.164385i
$88$		0			0
$89$	−322756.	−	186343.i	−0.457829	−	0.264328i	0.253302	−	0.967387i	$-0.418483\pi$
$89$	−322756.	−	186343.i	−0.457829	−	0.264328i	−0.711131	+	0.703059i	$0.751817\pi$
$90$		0			0
$91$	466335.	−	690470.i	0.618833	−	0.916265i
$92$		0			0
$93$	−217180.	+	376167.i	−0.270005	+	0.467662i
$94$		0			0
$95$	265842.	+	460452.i	0.310065	+	0.537048i
$96$		0			0
$97$			620049.i			0.679377i	0.940538	+	0.339688i	$0.110322\pi$
$97$			620049.i			0.679377i	−0.940538	+	0.339688i	$0.889678\pi$
$98$		0			0
$99$	199804.			0.205920
$100$		0			0
$101$	−578698.	+	334111.i	−0.561678	+	0.324285i	−0.753819	−	0.657082i	$-0.771790\pi$
$101$	−578698.	+	334111.i	−0.561678	+	0.324285i	0.192141	+	0.981367i	$0.438457\pi$
$102$		0			0
$103$	−1.34180e6	−	774691.i	−1.22794	−	0.708952i	−0.261342	−	0.965246i	$-0.584165\pi$
$103$	−1.34180e6	−	774691.i	−1.22794	−	0.708952i	−0.966599	+	0.256294i	$0.917498\pi$
$104$		0			0
$105$	−352555.	−	238111.i	−0.304550	−	0.205689i
$106$		0			0
$107$	−477948.	+	827829.i	−0.390148	+	0.675755i	−0.992469	−	0.122498i	$-0.960909\pi$
$107$	−477948.	+	827829.i	−0.390148	+	0.675755i	0.602321	+	0.798254i	$0.294243\pi$
$108$		0			0
$109$	−785863.	−	1.36115e6i	−0.606830	−	1.05106i	−0.991759	−	0.128115i	$-0.959107\pi$
$109$	−785863.	−	1.36115e6i	−0.606830	−	1.05106i	0.384929	−	0.922946i	$-0.374226\pi$
$110$		0			0
$111$		−	1.24201e6i		−	0.908150i
$112$		0			0
$113$	−2.47576e6			−1.71582			−0.857912	−	0.513797i	$-0.828238\pi$
$113$	−2.47576e6			−1.71582			−0.857912	+	0.513797i	$0.828238\pi$
$114$		0			0
$115$	−1.29770e6	+	749225.i	−0.853256	+	0.492628i
$116$		0			0
$117$	511200.	+	295141.i	0.319178	+	0.184278i
$118$		0			0
$119$	−2.66723e6	−	188129.i	−1.58278	−	0.111639i
$120$		0			0
$121$	547742.	−	948717.i	0.309186	−	0.535526i
$122$		0			0
$123$	−461388.	−	799148.i	−0.247943	−	0.429449i
$124$		0			0
$125$			1.98274e6i			1.01516i
$126$		0			0
$127$	−292592.			−0.142840			−0.0714202	−	0.997446i	$-0.522753\pi$
$127$	−292592.			−0.142840			−0.0714202	+	0.997446i	$0.522753\pi$
$128$		0			0
$129$	−1.23965e6	+	715712.i	−0.577471	+	0.333403i
$130$		0			0
$131$	2.36324e6	+	1.36442e6i	1.05122	+	0.606924i	0.922991	−	0.384820i	$-0.125737\pi$
$131$	2.36324e6	+	1.36442e6i	1.05122	+	0.606924i	0.128231	+	0.991744i	$0.459070\pi$
$132$		0			0
$133$	1.00351e6	+	2.06065e6i	0.426545	+	0.875888i
$134$		0			0
$135$	150699.	−	261019.i	0.0612506	−	0.106089i
$136$		0			0
$137$	453922.	+	786216.i	0.176530	+	0.305760i	0.940690	−	0.339268i	$-0.110179\pi$
$137$	453922.	+	786216.i	0.176530	+	0.305760i	−0.764159	+	0.645027i	$0.776846\pi$
$138$		0			0
$139$			4640.07i			0.00172775i	1.00000		0.000863874i	$0.000274980\pi$
$139$			4640.07i			0.00172775i	−1.00000		0.000863874i	$0.999725\pi$
$140$		0			0
$141$	−78253.8			−0.0279157
$142$		0			0
$143$	−1.72975e6	+	998669.i	−0.591526	+	0.341518i
$144$		0			0
$145$	−956994.	−	552521.i	−0.313910	−	0.181236i
$146$		0			0
$147$	−1.44382e6	−	1.13085e6i	−0.454529	−	0.356001i
$148$		0			0
$149$	823601.	−	1.42652e6i	0.248976	−	0.431240i	−0.714266	−	0.699875i	$-0.753239\pi$
$149$	823601.	−	1.42652e6i	0.248976	−	0.431240i	0.963242	+	0.268635i	$0.0865725\pi$
$150$		0			0
$151$	−1.22295e6	−	2.11820e6i	−0.355203	−	0.615229i	0.631950	−	0.775009i	$-0.282255\pi$
$151$	−1.22295e6	−	2.11820e6i	−0.355203	−	0.615229i	−0.987153	+	0.159780i	$0.948921\pi$
$152$		0			0
$153$		−	1.89431e6i		−	0.528904i
$154$		0			0
$155$	−2.21707e6			−0.595366
$156$		0			0
$157$	−2.43822e6	+	1.40771e6i	−0.630049	+	0.363759i	−0.780771	−	0.624817i	$-0.785174\pi$
$157$	−2.43822e6	+	1.40771e6i	−0.630049	+	0.363759i	0.150722	+	0.988576i	$0.451840\pi$
$158$		0			0
$159$	2.51626e6	+	1.45276e6i	0.625985	+	0.361413i
$160$		0			0
$161$	−5.80754e6	+	2.82819e6i	−1.39160	+	0.677690i
$162$		0			0
$163$	−781407.	+	1.35344e6i	−0.180432	+	0.312518i	−0.942028	−	0.335535i	$-0.891083\pi$
$163$	−781407.	+	1.35344e6i	−0.180432	+	0.312518i	0.761596	+	0.648053i	$0.224416\pi$
$164$		0			0
$165$	509921.	+	883210.i	0.113515	+	0.196613i
$166$		0			0
$167$		−	1.15538e6i		−	0.248070i	−0.992278	−	0.124035i	$-0.960416\pi$
$167$		−	1.15538e6i		−	0.248070i	0.992278	−	0.124035i	$-0.0395835\pi$
$168$		0			0
$169$	−1.07394e6			−0.222495
$170$		0			0
$171$	−1.40624e6	+	811891.i	−0.281235	+	0.162371i
$172$		0			0
$173$	−4.98920e6	−	2.88052e6i	−0.963591	−	0.556330i	−0.0663149	−	0.997799i	$-0.521124\pi$
$173$	−4.98920e6	−	2.88052e6i	−0.963591	−	0.556330i	−0.897277	+	0.441469i	$0.854458\pi$
$174$		0			0
$175$	−224295.	+	3.17998e6i	−0.0418509	+	0.593350i
$176$		0			0
$177$	1.75528e6	−	3.04024e6i	0.316539	−	0.548262i
$178$		0			0
$179$	−597801.	−	1.03542e6i	−0.104231	−	0.180534i	0.809193	−	0.587543i	$-0.199905\pi$
$179$	−597801.	−	1.03542e6i	−0.104231	−	0.180534i	−0.913424	+	0.407010i	$0.866571\pi$
$180$		0			0
$181$			1.00030e7i			1.68692i	0.537191	+	0.843461i	$0.319486\pi$
$181$			1.00030e7i			1.68692i	−0.537191	+	0.843461i	$0.680514\pi$
$182$		0			0
$183$	2.25032e6			0.367190
$184$		0			0
$185$	5.49017e6	−	3.16975e6i	0.867104	−	0.500622i
$186$		0			0
$187$	5.55102e6	+	3.20489e6i	0.848884	+	0.490103i
$188$		0			0
$189$	727199.	−	1.07672e6i	0.107713	−	0.159483i
$190$		0			0
$191$	−3.79135e6	+	6.56682e6i	−0.544120	+	0.942443i	0.454542	+	0.890725i	$0.349803\pi$
$191$	−3.79135e6	+	6.56682e6i	−0.544120	+	0.942443i	−0.998662	+	0.0517175i	$0.983530\pi$
$192$		0			0
$193$	−3.54806e6	−	6.14542e6i	−0.493537	−	0.854830i	0.506436	−	0.862278i	$-0.330963\pi$
$193$	−3.54806e6	−	6.14542e6i	−0.493537	−	0.854830i	−0.999972	+	0.00744730i	$0.997629\pi$
$194$		0			0
$195$			3.01293e6i			0.406336i
$196$		0			0
$197$	2.00096e6			0.261722			0.130861	−	0.991401i	$-0.458226\pi$
$197$	2.00096e6			0.261722			0.130861	+	0.991401i	$0.458226\pi$
$198$		0			0
$199$	3.76381e6	−	2.17304e6i	0.477605	−	0.275745i	−0.241813	−	0.970323i	$-0.577742\pi$
$199$	3.76381e6	−	2.17304e6i	0.477605	−	0.275745i	0.719418	+	0.694578i	$0.244409\pi$
$200$		0			0
$201$	3.17898e6	+	1.83539e6i	0.391471	+	0.226016i
$202$		0			0
$203$	−3.94764e6	−	2.66619e6i	−0.471900	−	0.318715i
$204$		0			0
$205$	2.35502e6	−	4.07902e6i	0.273359	−	0.473472i
$206$		0			0
$207$	−2.28816e6	−	3.96321e6i	−0.257974	−	0.446824i
$208$		0			0
$209$		−	5.49439e6i		−	0.601839i
$210$		0			0
$211$	−1.03642e7			−1.10328			−0.551641	−	0.834082i	$-0.685998\pi$
$211$	−1.03642e7			−1.10328			−0.551641	+	0.834082i	$0.685998\pi$
$212$		0			0
$213$	1.29964e6	−	750345.i	0.134488	−	0.0776465i
$214$		0			0
$215$	−6.32744e6	−	3.65315e6i	−0.636667	−	0.367580i
$216$		0			0
$217$	−9.53375e6	−	672446.i	−0.933006	−	0.0658079i
$218$		0			0
$219$	−2.14770e6	+	3.71993e6i	−0.204476	+	0.354163i
$220$		0			0
$221$	9.46822e6	+	1.63994e7i	0.877185	+	1.51933i
$222$		0			0
$223$			4.84791e6i			0.437159i	0.975819	+	0.218580i	$0.0701424\pi$
$223$			4.84791e6i			0.437159i	−0.975819	+	0.218580i	$0.929858\pi$
$224$		0			0
$225$	−2.25847e6			−0.198275
$226$		0			0
$227$	1.30838e7	−	7.55396e6i	1.11856	−	0.645798i	0.177524	−	0.984117i	$-0.443191\pi$
$227$	1.30838e7	−	7.55396e6i	1.11856	−	0.645798i	0.941032	+	0.338318i	$0.109858\pi$
$228$		0			0
$229$	−3.68382e6	−	2.12685e6i	−0.306755	−	0.177105i	0.338718	−	0.940888i	$-0.390007\pi$
$229$	−3.68382e6	−	2.12685e6i	−0.306755	−	0.177105i	−0.645474	+	0.763783i	$0.723340\pi$
$230$		0			0
$231$	1.92486e6	+	3.95260e6i	0.156158	+	0.320662i
$232$		0			0
$233$	−6.29087e6	+	1.08961e7i	−0.497328	+	0.861397i	−0.999995	−	0.00308269i	$-0.999019\pi$
$233$	−6.29087e6	+	1.08961e7i	−0.497328	+	0.861397i	0.502667	+	0.864480i	$0.332352\pi$
$234$		0			0
$235$	−199712.	−	345912.i	−0.0153887	−	0.0266540i
$236$		0			0
$237$		−	1.06209e7i		−	0.797844i
$238$		0			0
$239$	−7.54342e6			−0.552554			−0.276277	−	0.961078i	$-0.589101\pi$
$239$	−7.54342e6			−0.552554			−0.276277	+	0.961078i	$0.589101\pi$
$240$		0			0
$241$	1.69553e7	−	9.78914e6i	1.21131	−	0.699348i	0.248262	−	0.968693i	$-0.420140\pi$
$241$	1.69553e7	−	9.78914e6i	1.21131	−	0.699348i	0.963044	+	0.269345i	$0.0868071\pi$
$242$		0			0
$243$	797162.	+	460241.i	0.0555556	+	0.0320750i
$244$		0			0
$245$	1.31398e6	−	9.26828e6i	0.0893492	−	0.630233i
$246$		0			0
$247$	8.11606e6	−	1.40574e7i	0.538585	−	0.932857i
$248$		0			0
$249$	−997810.	−	1.72826e6i	−0.0646323	−	0.111946i
$250$		0			0
$251$			1.39590e7i			0.882743i	0.897324	+	0.441372i	$0.145508\pi$
$251$			1.39590e7i			0.882743i	−0.897324	+	0.441372i	$0.854492\pi$
$252$		0			0
$253$	1.54849e7			0.956195
$254$		0			0
$255$	8.37356e6	−	4.83448e6i	0.504998	−	0.291561i
$256$		0			0
$257$	−567649.	−	327732.i	−0.0334411	−	0.0193072i	0.483186	−	0.875518i	$-0.339479\pi$
$257$	−567649.	−	327732.i	−0.0334411	−	0.0193072i	−0.516627	+	0.856210i	$0.672813\pi$
$258$		0			0
$259$	2.45700e7	−	1.19652e7i	1.41418	−	0.688688i
$260$		0			0
$261$	1.68742e6	−	2.92269e6i	0.0949076	−	0.164385i
$262$		0			0
$263$	−7.46998e6	−	1.29384e7i	−0.410632	−	0.711235i	0.584327	−	0.811518i	$-0.301358\pi$
$263$	−7.46998e6	−	1.29384e7i	−0.410632	−	0.711235i	−0.994959	+	0.100283i	$0.968025\pi$
$264$		0			0
$265$			1.48304e7i			0.796922i
$266$		0			0
$267$	5.80960e6			0.305220
$268$		0			0
$269$	−2.72017e7	+	1.57049e7i	−1.39746	+	0.806825i	−0.994126	−	0.108227i	$-0.965483\pi$
$269$	−2.72017e7	+	1.57049e7i	−1.39746	+	0.806825i	−0.403335	+	0.915052i	$0.632149\pi$
$270$		0			0
$271$	1.29500e6	+	747670.i	0.0650673	+	0.0375666i	0.532181	−	0.846631i	$-0.321373\pi$
$271$	1.29500e6	+	747670.i	0.0650673	+	0.0375666i	−0.467113	+	0.884197i	$0.654706\pi$
$272$		0			0
$273$	−913834.	+	1.29561e7i	−0.0449138	+	0.636774i
$274$		0			0
$275$	3.82099e6	−	6.61815e6i	0.183729	−	0.318228i
$276$		0			0
$277$	991747.	+	1.71776e6i	0.0466618	+	0.0808207i	0.888413	−	0.459045i	$-0.151808\pi$
$277$	991747.	+	1.71776e6i	0.0466618	+	0.0808207i	−0.841751	+	0.539866i	$0.818475\pi$
$278$		0			0
$279$		−	6.77101e6i		−	0.311775i
$280$		0			0
$281$	−3.50353e6			−0.157902			−0.0789508	−	0.996879i	$-0.525157\pi$
$281$	−3.50353e6			−0.157902			−0.0789508	+	0.996879i	$0.525157\pi$
$282$		0			0
$283$	−2.82715e7	+	1.63226e7i	−1.24736	+	0.720161i	−0.970581	−	0.240774i	$-0.922599\pi$
$283$	−2.82715e7	+	1.63226e7i	−1.24736	+	0.720161i	−0.276774	+	0.960935i	$0.589265\pi$
$284$		0			0
$285$	−7.17773e6	−	4.14407e6i	−0.310065	−	0.179016i
$286$		0			0
$287$	1.13642e7	−	1.68261e7i	0.480719	−	0.711769i
$288$		0			0
$289$	1.83162e7	−	3.17246e7i	0.758826	−	1.31432i
$290$		0			0
$291$	−4.83280e6	−	8.37066e6i	−0.196119	−	0.339688i
$292$		0			0
$293$			2.57653e7i			1.02431i	0.858892	+	0.512156i	$0.171153\pi$
$293$			2.57653e7i			1.02431i	−0.858892	+	0.512156i	$0.828847\pi$
$294$		0			0
$295$	1.79187e7			0.697976
$296$		0			0
$297$	−2.69735e6	+	1.55732e6i	−0.102960	+	0.0594440i
$298$		0			0
$299$	3.96182e7	+	2.28736e7i	1.48211	+	0.855698i
$300$		0			0
$301$	−2.61010e7	−	1.76283e7i	−0.957100	−	0.646413i
$302$		0			0
$303$	5.20828e6	−	9.02100e6i	0.187226	−	0.324285i
$304$		0			0
$305$	5.74306e6	+	9.94727e6i	0.202416	+	0.350594i
$306$		0			0
$307$			1.89894e7i			0.656289i	0.944628	+	0.328145i	$0.106423\pi$
$307$			1.89894e7i			0.656289i	−0.944628	+	0.328145i	$0.893577\pi$
$308$		0			0
$309$	2.41525e7			0.818627
$310$		0			0
$311$	−2.80365e7	+	1.61869e7i	−0.932057	+	0.538124i	−0.887462	−	0.460881i	$-0.847533\pi$
$311$	−2.80365e7	+	1.61869e7i	−0.932057	+	0.538124i	−0.0445958	+	0.999005i	$0.514200\pi$
$312$		0			0
$313$	2.81397e7	+	1.62465e7i	0.917671	+	0.529818i	0.882891	−	0.469577i	$-0.155594\pi$
$313$	2.81397e7	+	1.62465e7i	0.917671	+	0.529818i	0.0347798	+	0.999395i	$0.488927\pi$
$314$		0			0
$315$	6.61538e6	+	466604.i	0.211652	+	0.0149285i
$316$		0			0
$317$	8.17142e6	−	1.41533e7i	0.256519	−	0.444304i	−0.708788	−	0.705422i	$-0.750758\pi$
$317$	8.17142e6	−	1.41533e7i	0.256519	−	0.444304i	0.965307	+	0.261118i	$0.0840910\pi$
$318$		0			0
$319$	5.70972e6	+	9.88952e6i	0.175891	+	0.304651i
$320$		0			0
$321$		−	1.49009e7i		−	0.450504i
$322$		0			0
$323$	−5.20914e7			−1.54582
$324$		0			0
$325$	1.95521e7	−	1.12884e7i	0.569564	−	0.328838i
$326$		0			0
$327$	2.12183e7	+	1.22504e7i	0.606830	+	0.350354i
$328$		0			0
$329$	−753878.	−	1.54805e6i	−0.0211696	−	0.0434707i
$330$		0			0
$331$	2.58785e7	−	4.48229e7i	0.713601	−	1.23599i	−0.249896	−	0.968273i	$-0.580396\pi$
$331$	2.58785e7	−	4.48229e7i	0.713601	−	1.23599i	0.963497	−	0.267720i	$-0.0862702\pi$
$332$		0			0
$333$	9.68054e6	+	1.67672e7i	0.262160	+	0.454075i
$334$		0			0
$335$			1.87364e7i			0.498370i
$336$		0			0
$337$	6.13986e7			1.60424			0.802119	−	0.597164i	$-0.203706\pi$
$337$	6.13986e7			1.60424			0.802119	+	0.597164i	$0.203706\pi$
$338$		0			0
$339$	3.34227e7	−	1.92966e7i	0.857912	−	0.495316i
$340$		0			0
$341$	1.98416e7	+	1.14555e7i	0.500395	+	0.288903i
$342$		0			0
$343$	8.46143e6	−	3.94565e7i	0.209682	−	0.977770i
$344$		0			0
$345$	1.16793e7	−	2.02291e7i	0.284419	−	0.492628i
$346$		0			0
$347$	1.77833e7	+	3.08017e7i	0.425623	+	0.737200i	0.996478	−	0.0838501i	$-0.0267217\pi$
$347$	1.77833e7	+	3.08017e7i	0.425623	+	0.737200i	−0.570855	+	0.821051i	$0.693388\pi$
$348$		0			0
$349$		−	5.17156e7i		−	1.21659i	−0.793710	−	0.608297i	$-0.791853\pi$
$349$		−	5.17156e7i		−	1.21659i	0.793710	−	0.608297i	$-0.208147\pi$
$350$		0			0
$351$	−9.20159e6			−0.212785
$352$		0			0
$353$	−669058.	+	386281.i	−0.0152104	+	0.00878171i	−0.507586	−	0.861601i	$-0.669462\pi$
$353$	−669058.	+	386281.i	−0.0152104	+	0.00878171i	0.492376	+	0.870383i	$0.336129\pi$
$354$		0			0
$355$	6.63362e6	+	3.82992e6i	0.148274	+	0.0856061i
$356$		0			0
$357$	3.74740e7	−	1.82493e7i	0.823617	−	0.401090i
$358$		0			0
$359$	−2.08340e7	+	3.60856e7i	−0.450287	+	0.779920i	−0.998404	−	0.0564819i	$-0.982012\pi$
$359$	−2.08340e7	+	3.60856e7i	−0.450287	+	0.779920i	0.548117	+	0.836402i	$0.315345\pi$
$360$		0			0
$361$	−1.19684e6	−	2.07298e6i	−0.0254398	−	0.0440630i
$362$		0			0
$363$			1.70769e7i			0.357017i
$364$		0			0
$365$	−2.19247e7			−0.450874
$366$		0			0
$367$	−5.71734e6	+	3.30091e6i	−0.115663	+	0.0667783i	−0.556716	−	0.830703i	$-0.687939\pi$
$367$	−5.71734e6	+	3.30091e6i	−0.115663	+	0.0667783i	0.441052	+	0.897481i	$0.354605\pi$
$368$		0			0
$369$	1.24575e7	+	7.19233e6i	0.247943	+	0.143150i
$370$		0			0
$371$	−4.49813e6	+	6.37732e7i	−0.0880867	+	1.24887i
$372$		0			0
$373$	2.47581e6	−	4.28823e6i	0.0477080	−	0.0826326i	−0.841185	−	0.540747i	$-0.818142\pi$
$373$	2.47581e6	−	4.28823e6i	0.0477080	−	0.0826326i	0.888893	+	0.458114i	$0.151475\pi$
$374$		0			0
$375$	−1.54539e7	−	2.67669e7i	−0.293052	−	0.507580i
$376$		0			0
$377$			3.37365e7i			0.629616i
$378$		0			0
$379$	1.05876e8			1.94482			0.972409	−	0.233282i	$-0.0749466\pi$
$379$	1.05876e8			1.94482			0.972409	+	0.233282i	$0.0749466\pi$
$380$		0			0
$381$	3.94999e6	−	2.28053e6i	0.0714202	−	0.0412345i
$382$		0			0
$383$	4.26092e7	+	2.46004e7i	0.758414	+	0.437871i	0.828726	−	0.559654i	$-0.189066\pi$
$383$	4.26092e7	+	2.46004e7i	0.758414	+	0.437871i	−0.0703117	+	0.997525i	$0.522399\pi$
$384$		0			0
$385$	−1.25596e7	+	1.85961e7i	−0.220086	+	0.325866i
$386$		0			0
$387$	1.11568e7	−	1.93242e7i	0.192490	−	0.333403i
$388$		0			0
$389$	−3.33099e7	−	5.76945e7i	−0.565880	−	0.980134i	−0.996967	−	0.0778231i	$-0.975203\pi$
$389$	−3.33099e7	−	5.76945e7i	−0.565880	−	0.980134i	0.431087	−	0.902310i	$-0.358130\pi$
$390$		0			0
$391$		−	1.46810e8i		−	2.45598i
$392$		0			0
$393$	−4.25384e7			−0.700815
$394$		0			0
$395$	4.69486e7	−	2.71058e7i	0.761783	−	0.439816i
$396$		0			0
$397$	4.16040e7	+	2.40201e7i	0.664911	+	0.383887i	0.794146	−	0.607727i	$-0.207919\pi$
$397$	4.16040e7	+	2.40201e7i	0.664911	+	0.383887i	−0.129234	+	0.991614i	$0.541252\pi$
$398$		0			0
$399$	−2.96085e7	−	1.99972e7i	−0.466120	−	0.314811i
$400$		0			0
$401$	−6.97156e6	+	1.20751e7i	−0.108118	+	0.187265i	−0.915008	−	0.403436i	$-0.867816\pi$
$401$	−6.97156e6	+	1.20751e7i	−0.108118	+	0.187265i	0.806890	+	0.590702i	$0.201149\pi$
$402$		0			0
$403$	3.38431e7	+	5.86180e7i	0.517077	+	0.895604i
$404$		0			0
$405$			4.69834e6i			0.0707261i
$406$		0			0
$407$	−6.55121e7			−0.971713
$408$		0			0
$409$	1.93849e7	−	1.11919e7i	0.283331	−	0.163581i	−0.351599	−	0.936151i	$-0.614362\pi$
$409$	1.93849e7	−	1.11919e7i	0.283331	−	0.163581i	0.634931	+	0.772569i	$0.281029\pi$
$410$		0			0
$411$	−1.22559e7	−	7.07594e6i	−0.176530	−	0.101920i
$412$		0			0
$413$	7.70532e7	+	5.43482e6i	1.09381	+	0.0771498i
$414$		0			0
$415$	5.09304e6	−	8.82140e6i	0.0712578	−	0.123422i
$416$		0			0
$417$	−36165.8	−	62641.0i	−0.000498758	−	0.000863874i
$418$		0			0
$419$			5.41233e7i			0.735770i	0.929871	+	0.367885i	$0.119918\pi$
$419$			5.41233e7i			0.735770i	−0.929871	+	0.367885i	$0.880082\pi$
$420$		0			0
$421$	−1.30034e8			−1.74265			−0.871323	−	0.490709i	$-0.836738\pi$
$421$	−1.30034e8			−1.74265			−0.871323	+	0.490709i	$0.836738\pi$
$422$		0			0
$423$	1.05643e6	−	609928.i	0.0139578	−	0.00805856i
$424$		0			0
$425$	−6.27456e7	−	3.62262e7i	−0.817366	−	0.471907i
$426$		0			0
$427$	2.16790e7	+	4.45167e7i	0.278456	+	0.571794i
$428$		0			0
$429$	1.55677e7	−	2.69641e7i	0.197175	−	0.341518i
$430$		0			0
$431$	−5.99710e7	−	1.03873e8i	−0.749047	−	1.29739i	−0.948280	−	0.317436i	$-0.897178\pi$
$431$	−5.99710e7	−	1.03873e8i	−0.749047	−	1.29739i	0.199233	−	0.979952i	$-0.436155\pi$
$432$		0			0
$433$			1.11549e8i			1.37404i	0.726636	+	0.687022i	$0.241083\pi$
$433$			1.11549e8i			1.37404i	−0.726636	+	0.687022i	$0.758917\pi$
$434$		0			0
$435$	1.72259e7			0.209273
$436$		0			0
$437$	−1.08984e8	+	6.29219e7i	−1.30592	+	0.753976i
$438$		0			0
$439$	−1.06743e8	−	6.16284e7i	−1.26168	−	0.728429i	−0.288277	−	0.957547i	$-0.593082\pi$
$439$	−1.06743e8	−	6.16284e7i	−1.26168	−	0.728429i	−0.973399	+	0.229118i	$0.926416\pi$
$440$		0			0
$441$	2.83057e7	+	4.01295e6i	0.330033	+	0.0467894i
$442$		0			0
$443$	−3.55708e7	+	6.16104e7i	−0.409150	+	0.708669i	−0.994795	−	0.101899i	$-0.967508\pi$
$443$	−3.55708e7	+	6.16104e7i	−0.409150	+	0.708669i	0.585645	+	0.810568i	$0.300841\pi$
$444$		0			0
$445$	1.48267e7	+	2.56806e7i	0.168254	+	0.291424i
$446$		0			0
$447$			2.56773e7i			0.287493i
$448$		0			0
$449$	−1.07566e8			−1.18833			−0.594165	−	0.804343i	$-0.702517\pi$
$449$	−1.07566e8			−1.18833			−0.594165	+	0.804343i	$0.702517\pi$
$450$		0			0
$451$	−4.21524e7	+	2.43367e7i	−0.459507	+	0.265297i
$452$		0			0
$453$	3.30195e7	+	1.90638e7i	0.355203	+	0.205076i
$454$		0			0
$455$	−5.96030e7	+	2.90258e7i	−0.632752	+	0.308141i
$456$		0			0
$457$	−6.43381e6	+	1.11437e7i	−0.0674093	+	0.116756i	−0.897760	−	0.440485i	$-0.854807\pi$
$457$	−6.43381e6	+	1.11437e7i	−0.0674093	+	0.116756i	0.830351	+	0.557241i	$0.188140\pi$
$458$		0			0
$459$	1.47647e7	+	2.55732e7i	0.152681	+	0.264452i
$460$		0			0
$461$		−	7.08717e6i		−	0.0723386i	−0.999346	−	0.0361693i	$-0.988484\pi$
$461$		−	7.08717e6i		−	0.0723386i	0.999346	−	0.0361693i	$-0.0115156\pi$
$462$		0			0
$463$	−1.44698e8			−1.45788			−0.728938	−	0.684580i	$-0.759986\pi$
$463$	−1.44698e8			−1.45788			−0.728938	+	0.684580i	$0.759986\pi$
$464$		0			0
$465$	2.99304e7	−	1.72803e7i	0.297683	−	0.171867i
$466$		0			0
$467$	−7.34759e7	−	4.24214e7i	−0.721431	−	0.416518i	0.0938485	−	0.995586i	$-0.470083\pi$
$467$	−7.34759e7	−	4.24214e7i	−0.721431	−	0.416518i	−0.815279	+	0.579068i	$0.803416\pi$
$468$		0			0
$469$	−5.68283e6	+	8.05695e7i	−0.0550866	+	0.781002i
$470$		0			0
$471$	2.19440e7	−	3.80082e7i	0.210016	−	0.363759i
$472$		0			0
$473$	3.77514e7	+	6.53874e7i	0.356738	+	0.617889i
$474$		0			0
$475$			6.21054e7i			0.579494i
$476$		0			0
$477$	−4.52927e7			−0.417323
$478$		0			0
$479$	−1.38250e8	+	7.98185e7i	−1.25793	+	0.726268i	−0.972672	−	0.232182i	$-0.925414\pi$
$479$	−1.38250e8	+	7.98185e7i	−1.25793	+	0.726268i	−0.285261	+	0.958450i	$0.592080\pi$
$480$		0			0
$481$	−1.67613e8	−	9.67714e7i	−1.50616	−	0.869585i
$482$		0			0
$483$	5.63582e7	−	8.34459e7i	0.500168	−	0.740565i
$484$		0			0
$485$	2.46677e7	−	4.27256e7i	0.216223	−	0.374510i
$486$		0			0
$487$	6.90017e7	+	1.19515e8i	0.597411	+	1.03475i	0.993202	+	0.116405i	$0.0371372\pi$
$487$	6.90017e7	+	1.19515e8i	0.597411	+	1.03475i	−0.395791	+	0.918341i	$0.629529\pi$
$488$		0			0
$489$		−	2.43619e7i		−	0.208345i
$490$		0			0
$491$	3.91824e7			0.331014			0.165507	−	0.986209i	$-0.447074\pi$
$491$	3.91824e7			0.331014			0.165507	+	0.986209i	$0.447074\pi$
$492$		0			0
$493$	9.37609e7	−	5.41329e7i	0.782494	−	0.451773i
$494$		0			0
$495$	−1.37679e7	−	7.94889e6i	−0.113515	−	0.0655376i
$496$		0			0
$497$	2.73640e7	+	1.84813e7i	0.222900	+	0.150544i
$498$		0			0
$499$	1.14482e7	−	1.98288e7i	0.0921370	−	0.159586i	−0.816273	−	0.577666i	$-0.803964\pi$
$499$	1.14482e7	−	1.98288e7i	0.0921370	−	0.159586i	0.908410	+	0.418080i	$0.137297\pi$
$500$		0			0
$501$	9.00527e6	+	1.55976e7i	0.0716116	+	0.124035i
$502$		0			0
$503$		−	1.38751e8i		−	1.09027i	−0.838349	−	0.545133i	$-0.816479\pi$
$503$		−	1.38751e8i		−	1.09027i	0.838349	−	0.545133i	$-0.183521\pi$
$504$		0			0
$505$	5.31683e7			0.412837
$506$		0			0
$507$	1.44982e7	−	8.37055e6i	0.111248	−	0.0642289i
$508$		0			0
$509$	−5.07588e7	−	2.93056e7i	−0.384909	−	0.222227i	0.295043	−	0.955484i	$-0.404666\pi$
$509$	−5.07588e7	−	2.93056e7i	−0.384909	−	0.222227i	−0.679952	+	0.733257i	$0.737999\pi$
$510$		0			0
$511$	−9.42796e7	−	6.64985e6i	−0.706570	−	0.0498367i
$512$		0			0
$513$	1.26561e7	−	2.19211e7i	0.0937451	−	0.162371i
$514$		0			0
$515$	6.16397e7	+	1.06763e8i	0.451272	+	0.781627i
$516$		0			0
$517$			4.12763e6i			0.0298696i
$518$		0			0
$519$	8.98057e7			0.642394
$520$		0			0
$521$	−1.88084e8	+	1.08590e8i	−1.32996	+	0.767853i	−0.985293	−	0.170872i	$-0.945342\pi$
$521$	−1.88084e8	+	1.08590e8i	−1.32996	+	0.767853i	−0.344668	+	0.938725i	$0.612008\pi$
$522$		0			0
$523$	−1.64929e7	−	9.52217e6i	−0.115290	−	0.0665627i	0.441246	−	0.897386i	$-0.354537\pi$
$523$	−1.64929e7	−	9.52217e6i	−0.115290	−	0.0665627i	−0.556536	+	0.830823i	$0.687870\pi$
$524$		0			0
$525$	−2.17575e7	−	4.46780e7i	−0.150360	−	0.308756i
$526$		0			0
$527$	1.08608e8	−	1.88114e8i	0.742044	−	1.28526i
$528$		0			0
$529$	−1.03315e8	−	1.78948e8i	−0.697908	−	1.20881i
$530$		0			0
$531$			5.47244e7i			0.365508i
$532$		0			0
$533$	−1.43796e8			−0.949654
$534$		0			0
$535$	6.58678e7	−	3.80288e7i	0.430142	−	0.248342i
$536$		0			0
$537$	1.61406e7	+	9.31879e6i	0.104231	+	0.0601778i
$538$		0			0
$539$	−5.96483e7	+	7.61567e7i	−0.380918	+	0.486342i
$540$		0			0
$541$	5.05360e7	−	8.75310e7i	0.319161	−	0.552803i	−0.661152	−	0.750252i	$-0.729932\pi$
$541$	5.05360e7	−	8.75310e7i	0.319161	−	0.552803i	0.980313	+	0.197449i	$0.0632657\pi$
$542$		0			0
$543$	−7.79657e7	−	1.35041e8i	−0.486972	−	0.843461i
$544$		0			0
$545$			1.25057e8i			0.772537i
$546$		0			0
$547$	2.29198e7			0.140039			0.0700196	−	0.997546i	$-0.477694\pi$
$547$	2.29198e7			0.140039			0.0700196	+	0.997546i	$0.477694\pi$
$548$		0			0
$549$	−3.03793e7	+	1.75395e7i	−0.183595	+	0.105999i
$550$		0			0
$551$	−8.03708e7	−	4.64021e7i	−0.480445	−	0.277385i
$552$		0			0
$553$	2.10108e8	−	1.02319e8i	1.24241	−	0.605038i
$554$		0			0
$555$	−4.94116e7	+	8.55834e7i	−0.289035	+	0.500622i
$556$		0			0
$557$	−6.91655e7	−	1.19798e8i	−0.400243	−	0.693242i	0.593512	−	0.804825i	$-0.297741\pi$
$557$	−6.91655e7	−	1.19798e8i	−0.400243	−	0.693242i	−0.993755	+	0.111584i	$0.964408\pi$
$558$		0			0
$559$			2.23059e8i			1.27698i
$560$		0			0
$561$	−9.99184e7			−0.565923
$562$		0			0
$563$	−1.95097e8	+	1.12639e8i	−1.09326	+	0.631195i	−0.934443	−	0.356112i	$-0.884102\pi$
$563$	−1.95097e8	+	1.12639e8i	−1.09326	+	0.631195i	−0.158819	+	0.987308i	$0.550769\pi$
$564$		0			0
$565$	1.70597e8	+	9.84941e7i	0.945857	+	0.546091i
$566$		0			0
$567$	−1.42503e6	+	2.02036e7i	−0.00781761	+	0.110836i
$568$		0			0
$569$	−1.10276e8	+	1.91003e8i	−0.598609	+	1.03682i	0.394417	+	0.918931i	$0.370946\pi$
$569$	−1.10276e8	+	1.91003e8i	−0.598609	+	1.03682i	−0.993027	+	0.117890i	$0.962387\pi$
$570$		0			0
$571$	−3.36594e7	−	5.82999e7i	−0.180800	−	0.313155i	0.761353	−	0.648337i	$-0.224535\pi$
$571$	−3.36594e7	−	5.82999e7i	−0.180800	−	0.313155i	−0.942153	+	0.335182i	$0.891202\pi$
$572$		0			0
$573$		−	1.18203e8i		−	0.628295i
$574$		0			0
$575$	−1.75032e8			−0.920693
$576$		0			0
$577$	−9.29650e6	+	5.36734e6i	−0.0483941	+	0.0279403i	−0.524002	−	0.851717i	$-0.675562\pi$
$577$	−9.29650e6	+	5.36734e6i	−0.0483941	+	0.0279403i	0.475608	+	0.879657i	$0.342228\pi$
$578$		0			0
$579$	9.57977e7	+	5.53088e7i	0.493537	+	0.284943i
$580$		0			0
$581$	2.45764e7	−	3.63887e7i	0.125311	−	0.185540i
$582$		0			0
$583$	7.66284e7	−	1.32724e8i	0.386709	−	0.669799i
$584$		0			0
$585$	−2.34835e7	−	4.06745e7i	−0.117299	−	0.203168i
$586$		0			0
$587$			2.34143e8i			1.15762i	0.815461	+	0.578812i	$0.196484\pi$
$587$			2.34143e8i			1.15762i	−0.815461	+	0.578812i	$0.803516\pi$
$588$		0			0
$589$	−1.86195e8			−0.911219
$590$		0			0
$591$	−2.70130e7	+	1.55960e7i	−0.130861	+	0.0755527i
$592$		0			0
$593$	1.45328e8	+	8.39054e7i	0.696926	+	0.402370i	0.806202	−	0.591641i	$-0.201520\pi$
$593$	1.45328e8	+	8.39054e7i	0.696926	+	0.402370i	−0.109275	+	0.994012i	$0.534853\pi$
$594$		0			0
$595$	1.76306e8	+	1.19075e8i	0.836984	+	0.565288i
$596$		0			0
$597$	−3.38743e7	+	5.86720e7i	−0.159202	+	0.275745i
$598$		0			0
$599$	2.72137e7	+	4.71356e7i	0.126622	+	0.219315i	0.922366	−	0.386318i	$-0.126253\pi$
$599$	2.72137e7	+	4.71356e7i	0.126622	+	0.219315i	−0.795744	+	0.605633i	$0.792920\pi$
$600$		0			0
$601$		−	1.02729e7i		−	0.0473226i	−0.999720	−	0.0236613i	$-0.992468\pi$
$601$		−	1.02729e7i		−	0.0473226i	0.999720	−	0.0236613i	$-0.00753233\pi$
$602$		0			0
$603$	−5.72217e7			−0.260981
$604$		0			0
$605$	−7.54864e7	+	4.35821e7i	−0.340881	+	0.196808i
$606$		0			0
$607$	−3.20092e8	−	1.84805e8i	−1.43123	−	0.826319i	−0.434012	−	0.900907i	$-0.642902\pi$
$607$	−3.20092e8	−	1.84805e8i	−1.43123	−	0.826319i	−0.997214	+	0.0745880i	$0.976236\pi$
$608$		0			0
$609$	7.40740e7	+	5.22468e6i	0.327955	+	0.0231317i
$610$		0			0
$611$	−6.09714e6	+	1.05606e7i	−0.0267302	+	0.0462981i
$612$		0			0
$613$	−2.33412e7	−	4.04282e7i	−0.101331	−	0.175510i	0.810902	−	0.585182i	$-0.198977\pi$
$613$	−2.33412e7	−	4.04282e7i	−0.101331	−	0.175510i	−0.912233	+	0.409671i	$0.865643\pi$
$614$		0			0
$615$			7.34224e7i			0.315648i
$616$		0			0
$617$	4.39158e8			1.86967			0.934836	−	0.355080i	$-0.115546\pi$
$617$	4.39158e8			1.86967			0.934836	+	0.355080i	$0.115546\pi$
$618$		0			0
$619$	1.84752e8	−	1.06666e8i	0.778962	−	0.449734i	−0.0571005	−	0.998368i	$-0.518186\pi$
$619$	1.84752e8	−	1.06666e8i	0.778962	−	0.449734i	0.836062	+	0.548635i	$0.184852\pi$
$620$		0			0
$621$	6.17803e7	+	3.56689e7i	0.257974	+	0.148941i
$622$		0			0
$623$	5.59682e7	+	1.14928e8i	0.231461	+	0.475292i
$624$		0			0
$625$	6.26968e6	−	1.08594e7i	0.0256806	−	0.0444801i
$626$		0			0
$627$	4.28245e7	+	7.41743e7i	0.173736	+	0.300920i
$628$		0			0
$629$			6.21109e8i			2.49584i
$630$		0			0
$631$	−2.58817e8			−1.03016			−0.515080	−	0.857142i	$-0.672238\pi$
$631$	−2.58817e8			−1.03016			−0.515080	+	0.857142i	$0.672238\pi$
$632$		0			0
$633$	1.39916e8	−	8.07806e7i	0.551641	−	0.318490i
$634$		0			0
$635$	2.01616e7	+	1.16403e7i	0.0787415	+	0.0454614i
$636$		0			0
$637$	−2.65106e8	+	1.06738e8i	−1.02565	+	0.412952i
$638$		0			0
$639$	−1.16967e7	+	2.02593e7i	−0.0448292	+	0.0776465i
$640$		0			0
$641$	−6.64356e7	−	1.15070e8i	−0.252247	−	0.436905i	0.711897	−	0.702284i	$-0.247836\pi$
$641$	−6.64356e7	−	1.15070e8i	−0.252247	−	0.436905i	−0.964144	+	0.265379i	$0.914503\pi$
$642$		0			0
$643$			1.84168e8i			0.692757i	0.938095	+	0.346378i	$0.112589\pi$
$643$			1.84168e8i			0.692757i	−0.938095	+	0.346378i	$0.887411\pi$
$644$		0			0
$645$	1.13894e8			0.424445
$646$		0			0
$647$	2.88189e8	−	1.66386e8i	1.06405	−	0.614332i	0.137504	−	0.990501i	$-0.456092\pi$
$647$	2.88189e8	−	1.66386e8i	1.06405	−	0.614332i	0.926551	+	0.376169i	$0.122759\pi$
$648$		0			0
$649$	−1.60363e8	−	9.25854e7i	−0.586636	−	0.338695i
$650$		0			0
$651$	1.33947e8	−	6.52302e7i	0.485500	−	0.236432i
$652$		0			0
$653$	−1.28291e8	+	2.22206e8i	−0.460741	+	0.798026i	−0.998998	−	0.0447544i	$-0.985749\pi$
$653$	−1.28291e8	+	2.22206e8i	−0.460741	+	0.798026i	0.538257	+	0.842780i	$0.319083\pi$
$654$		0			0
$655$	−1.08563e8	−	1.88036e8i	−0.386328	−	0.669140i
$656$		0			0
$657$		−	6.69588e7i		−	0.236108i
$658$		0			0
$659$	−1.84717e8			−0.645431			−0.322715	−	0.946496i	$-0.604596\pi$
$659$	−1.84717e8			−0.645431			−0.322715	+	0.946496i	$0.604596\pi$
$660$		0			0
$661$	1.74480e8	−	1.00736e8i	0.604144	−	0.348803i	−0.166526	−	0.986037i	$-0.553255\pi$
$661$	1.74480e8	−	1.00736e8i	0.604144	−	0.348803i	0.770670	+	0.637234i	$0.219922\pi$
$662$		0			0
$663$	−2.55642e8	−	1.47595e8i	−0.877185	−	0.506443i
$664$		0			0
$665$	1.28311e7	−	1.81916e8i	0.0436314	−	0.618593i
$666$		0			0
$667$	1.30776e8	−	2.26510e8i	0.440706	−	0.763326i
$668$		0			0
$669$	−3.77857e7	−	6.54468e7i	−0.126197	−	0.218580i
$670$		0			0
$671$		−	1.18697e8i		−	0.392891i
$672$		0			0
$673$	−4.93893e8			−1.62027			−0.810135	−	0.586243i	$-0.800606\pi$
$673$	−4.93893e8			−1.62027			−0.810135	+	0.586243i	$0.800606\pi$
$674$		0			0
$675$	3.04894e7	−	1.76030e7i	0.0991373	−	0.0572369i
$676$		0			0
$677$	−2.71512e8	−	1.56758e8i	−0.875030	−	0.505199i	−0.00601364	−	0.999982i	$-0.501914\pi$
$677$	−2.71512e8	−	1.56758e8i	−0.875030	−	0.505199i	−0.869017	+	0.494783i	$0.835248\pi$
$678$		0			0
$679$	1.19034e8	−	1.76245e8i	0.380243	−	0.563000i
$680$		0			0
$681$	−1.17755e8	+	2.03957e8i	−0.372852	+	0.645798i
$682$		0			0
$683$	−7.42502e7	−	1.28605e8i	−0.233043	−	0.403642i	0.725659	−	0.688054i	$-0.241535\pi$
$683$	−7.42502e7	−	1.28605e8i	−0.233043	−	0.403642i	−0.958702	+	0.284412i	$0.908202\pi$
$684$		0			0
$685$		−	7.22343e7i		−	0.224735i
$686$		0			0
$687$	6.63087e7			0.204503
$688$		0			0
$689$	3.92108e8	−	2.26384e8i	1.19880	−	0.692130i
$690$		0			0
$691$	3.35862e8	+	1.93910e8i	1.01795	+	0.587714i	0.913510	−	0.406817i	$-0.133361\pi$
$691$	3.35862e8	+	1.93910e8i	1.01795	+	0.587714i	0.104441	+	0.994531i	$0.466695\pi$
$692$		0			0
$693$	−5.67931e7	−	3.83573e7i	−0.170646	−	0.115252i
$694$		0			0
$695$	184598.	−	319733.i	0.000549886	−	0.000952430i
$696$		0			0
$697$	2.30732e8	+	3.99640e8i	0.681412	+	1.18024i
$698$		0			0
$699$		−	1.96130e8i		−	0.574265i
$700$		0			0
$701$	4.86782e7			0.141312			0.0706562	−	0.997501i	$-0.477491\pi$
$701$	4.86782e7			0.141312			0.0706562	+	0.997501i	$0.477491\pi$
$702$		0			0
$703$	4.61079e8	−	2.66204e8i	1.32712	−	0.766212i
$704$		0			0
$705$	5.39223e6	+	3.11320e6i	0.0153887	+	0.00888465i
$706$		0			0
$707$	2.28632e8	+	1.61262e7i	0.646963	+	0.0456324i
$708$		0			0
$709$	1.58977e8	−	2.75357e8i	0.446064	−	0.772605i	−0.552062	−	0.833803i	$-0.686159\pi$
$709$	1.58977e8	−	2.75357e8i	0.446064	−	0.772605i	0.998126	+	0.0611981i	$0.0194921\pi$
$710$		0			0
$711$	8.27820e7	+	1.43383e8i	0.230318	+	0.398922i
$712$		0			0
$713$		−	5.24756e8i		−	1.44773i
$714$		0			0
$715$	1.58922e8			0.434776
$716$		0			0
$717$	1.01836e8	−	5.87951e7i	0.276277	−	0.159509i
$718$		0			0
$719$	1.50536e8	+	8.69119e7i	0.404998	+	0.233826i	0.688638	−	0.725105i	$-0.258209\pi$
$719$	1.50536e8	+	8.69119e7i	0.404998	+	0.233826i	−0.283640	+	0.958931i	$0.591542\pi$
$720$		0			0
$721$	2.32679e8	+	4.77794e8i	0.620799	+	1.27478i
$722$		0			0
$723$	−1.52598e8	+	2.64307e8i	−0.403769	+	0.699348i
$724$		0			0
$725$	−6.45394e7	−	1.11785e8i	−0.169360	−	0.293340i
$726$		0			0
$727$			4.58803e8i			1.19405i	0.802222	+	0.597026i	$0.203651\pi$
$727$			4.58803e8i			1.19405i	−0.802222	+	0.597026i	$0.796349\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	6.19927e8	−	3.57915e8i	1.58704	−	0.916279i
$732$		0			0
$733$	5.55746e8	+	3.20860e8i	1.41112	+	0.814711i	0.995494	−	0.0948235i	$-0.0302287\pi$
$733$	5.55746e8	+	3.20860e8i	1.41112	+	0.814711i	0.415627	+	0.909535i	$0.363562\pi$
$734$		0			0
$735$	5.45003e7	+	1.35363e8i	0.137258	+	0.340909i
$736$		0			0
$737$	9.68105e7	−	1.67681e8i	0.241835	−	0.418871i
$738$		0			0
$739$	−1.70001e8	−	2.94450e8i	−0.421229	−	0.729590i	0.574831	−	0.818272i	$-0.305068\pi$
$739$	−1.70001e8	−	2.94450e8i	−0.421229	−	0.729590i	−0.996060	+	0.0886823i	$0.971734\pi$
$740$		0			0
$741$			2.53034e8i			0.621904i
$742$		0			0
$743$	−6.08554e8			−1.48365			−0.741827	−	0.670591i	$-0.766040\pi$
$743$	−6.08554e8			−1.48365			−0.741827	+	0.670591i	$0.766040\pi$
$744$		0			0
$745$	−1.13504e8	+	6.55313e7i	−0.274499	+	0.158482i
$746$		0			0
$747$	2.69409e7	+	1.55543e7i	0.0646323	+	0.0373155i
$748$		0			0
$749$	2.94776e8	−	1.43552e8i	0.701531	−	0.341636i
$750$		0			0
$751$	8.06132e7	−	1.39626e8i	0.190321	−	0.329645i	−0.755036	−	0.655684i	$-0.772381\pi$
$751$	8.06132e7	−	1.39626e8i	0.190321	−	0.329645i	0.945357	+	0.326038i	$0.105714\pi$
$752$		0			0
$753$	−1.08800e8	−	1.88447e8i	−0.254826	−	0.441372i
$754$		0			0
$755$			1.94612e8i			0.452198i
$756$		0			0
$757$	1.60953e8			0.371031			0.185516	−	0.982641i	$-0.440604\pi$
$757$	1.60953e8			0.371031			0.185516	+	0.982641i	$0.440604\pi$
$758$		0			0
$759$	−2.09046e8	+	1.20693e8i	−0.478098	+	0.276030i
$760$		0			0
$761$	−3.75605e8	−	2.16856e8i	−0.852271	−	0.492059i	0.00914540	−	0.999958i	$-0.497089\pi$
$761$	−3.75605e8	−	2.16856e8i	−0.852271	−	0.492059i	−0.861416	+	0.507899i	$0.830422\pi$
$762$		0			0
$763$	−3.79304e7	+	5.37766e8i	−0.0853913	+	1.21065i
$764$		0			0
$765$	−7.53621e7	+	1.30531e8i	−0.168333	+	0.291561i
$766$		0			0
$767$	−2.73526e8	−	4.73760e8i	−0.606194	−	1.04996i
$768$		0			0
$769$		−	3.73405e8i		−	0.821110i	−0.911836	−	0.410555i	$-0.865335\pi$
$769$		−	3.73405e8i		−	0.821110i	0.911836	−	0.410555i	$-0.134665\pi$
$770$		0			0
$771$	1.02177e7			0.0222941
$772$		0			0
$773$	5.92885e8	−	3.42302e8i	1.28361	−	0.741090i	0.306100	−	0.951999i	$-0.400976\pi$
$773$	5.92885e8	−	3.42302e8i	1.28361	−	0.741090i	0.977506	+	0.210909i	$0.0676423\pi$
$774$		0			0
$775$	−2.24278e8	−	1.29487e8i	−0.481816	−	0.278176i
$776$		0			0
$777$	−2.38435e8	+	3.53035e8i	−0.508285	+	0.752584i
$778$		0			0
$779$	1.97781e8	−	3.42567e8i	0.418381	−	0.724658i
$780$		0			0
$781$	−3.95782e7	−	6.85514e7i	−0.0830812	−	0.143901i
$782$		0			0
$783$			5.26085e7i			0.109590i
$784$		0			0
$785$	2.24014e8			0.463091
$786$		0			0
$787$	−6.27494e8	+	3.62284e8i	−1.28732	+	0.743233i	−0.978175	−	0.207783i	$-0.933375\pi$
$787$	−6.27494e8	+	3.62284e8i	−1.28732	+	0.743233i	−0.309142	+	0.951016i	$0.600042\pi$
$788$		0			0
$789$	2.01690e8	+	1.16446e8i	0.410632	+	0.237078i
$790$		0			0
$791$	7.03719e8	+	4.75283e8i	1.42190	+	0.960335i
$792$		0			0
$793$	1.75334e8	−	3.03687e8i	0.351597	−	0.608984i
$794$		0			0
$795$	−1.15592e8	−	2.00211e8i	−0.230052	−	0.398461i
$796$		0			0
$797$			5.85510e7i			0.115654i	0.998327	+	0.0578268i	$0.0184171\pi$
$797$			5.85510e7i			0.115654i	−0.998327	+	0.0578268i	$0.981583\pi$
$798$		0			0
$799$	3.91334e7			0.0767197
$800$		0			0
$801$	−7.84296e7	+	4.52813e7i	−0.152610	+	0.0881093i
$802$		0			0
$803$	1.96214e8	+	1.13284e8i	0.378951	+	0.218788i
$804$		0			0
$805$	5.12695e8	+	3.61620e7i	0.982814	+	0.0693211i
$806$		0			0
$807$	2.44816e8	−	4.24033e8i	0.465821	−	0.806825i
$808$		0			0
$809$	−2.55763e8	−	4.42994e8i	−0.483049	−	0.836666i	0.516761	−	0.856129i	$-0.327137\pi$
$809$	−2.55763e8	−	4.42994e8i	−0.483049	−	0.836666i	−0.999811	+	0.0194637i	$0.993804\pi$
$810$		0			0
$811$			7.81509e8i			1.46511i	0.680706	+	0.732557i	$0.261673\pi$
$811$			7.81509e8i			1.46511i	−0.680706	+	0.732557i	$0.738327\pi$
$812$		0			0
$813$	−2.33101e7			−0.0433782
$814$		0			0
$815$	1.07689e8	−	6.21741e7i	0.198929	−	0.114851i
$816$		0			0
$817$	−5.31395e8	−	3.06801e8i	−0.974431	−	0.562588i
$818$		0			0
$819$	−8.86458e7	−	1.82030e8i	−0.161364	−	0.331353i
$820$		0			0
$821$	2.75815e8	−	4.77726e8i	0.498412	−	0.863275i	−0.501586	−	0.865108i	$-0.667250\pi$
$821$	2.75815e8	−	4.77726e8i	0.498412	−	0.863275i	0.999998	+	0.00183255i	$0.000583318\pi$
$822$		0			0
$823$	−1.78646e8	−	3.09423e8i	−0.320474	−	0.555077i	0.660112	−	0.751167i	$-0.270509\pi$
$823$	−1.78646e8	−	3.09423e8i	−0.320474	−	0.555077i	−0.980586	+	0.196090i	$0.937175\pi$
$824$		0			0
$825$			1.19127e8i			0.212152i
$826$		0			0
$827$	4.42420e8			0.782201			0.391101	−	0.920348i	$-0.372094\pi$
$827$	4.42420e8			0.782201			0.391101	+	0.920348i	$0.372094\pi$
$828$		0			0
$829$	−1.02602e8	+	5.92376e7i	−0.180092	+	0.103976i	−0.587336	−	0.809343i	$-0.699823\pi$
$829$	−1.02602e8	+	5.92376e7i	−0.180092	+	0.103976i	0.407244	+	0.913319i	$0.366490\pi$
$830$		0			0
$831$	−2.67772e7	−	1.54598e7i	−0.0466618	−	0.0269402i
$832$		0			0
$833$	7.22029e8	+	5.65516e8i	1.24917	+	0.978385i
$834$		0			0
$835$	−4.59648e7	+	7.96134e7i	−0.0789526	+	0.136750i
$836$		0			0
$837$	5.27748e7	+	9.14086e7i	0.0900016	+	0.155887i
$838$		0			0
$839$		−	1.02452e9i		−	1.73474i	−0.497660	−	0.867372i	$-0.665807\pi$
$839$		−	1.02452e9i		−	1.73474i	0.497660	−	0.867372i	$-0.334193\pi$
$840$		0			0
$841$	−4.01941e8			−0.675731
$842$		0			0
$843$	4.72976e7	−	2.73073e7i	0.0789508	−	0.0455823i
$844$		0			0
$845$	7.40021e7	+	4.27251e7i	0.122652	+	0.0708130i
$846$		0			0
$847$	−3.37822e8	+	1.64515e8i	−0.555953	+	0.270741i
$848$		0			0
$849$	2.54444e8	−	4.40710e8i	0.415785	−	0.720161i
$850$		0			0
$851$	7.50246e8	+	1.29946e9i	1.21735	+	2.10851i
$852$		0			0
$853$			1.03709e9i			1.67097i	0.549517	+	0.835483i	$0.314812\pi$
$853$			1.03709e9i			1.67097i	−0.549517	+	0.835483i	$0.685188\pi$
$854$		0			0
$855$	1.29199e8			0.206710
$856$		0			0
$857$	4.76107e8	−	2.74881e8i	0.756419	−	0.436719i	−0.0715895	−	0.997434i	$-0.522807\pi$
$857$	4.76107e8	−	2.74881e8i	0.756419	−	0.436719i	0.828009	+	0.560715i	$0.189474\pi$
$858$		0			0
$859$	−1.23390e8	−	7.12392e7i	−0.194671	−	0.112393i	0.399497	−	0.916735i	$-0.369185\pi$
$859$	−1.23390e8	−	7.12392e7i	−0.194671	−	0.112393i	−0.594167	+	0.804342i	$0.702518\pi$
$860$		0			0
$861$	−2.22693e7	+	3.15728e8i	−0.0348897	+	0.494656i
$862$		0			0
$863$	−2.00417e8	+	3.47132e8i	−0.311818	+	0.540085i	−0.978756	−	0.205028i	$-0.934271\pi$
$863$	−2.00417e8	+	3.47132e8i	−0.311818	+	0.540085i	0.666938	+	0.745113i	$0.267605\pi$
$864$		0			0
$865$	2.29194e8	+	3.96975e8i	0.354123	+	0.613359i
$866$		0			0
$867$			5.71043e8i			0.876216i
$868$		0			0
$869$	−5.60219e8			−0.853687
$870$		0			0
$871$	4.95380e8	−	2.86008e8i	0.749694	−	0.432836i
$872$		0			0
$873$	1.30486e8	+	7.53359e7i	0.196119	+	0.113229i
$874$		0			0
$875$	3.80635e8	−	5.63581e8i	0.568178	−	0.841263i
$876$		0			0
$877$	1.80269e8	−	3.12235e8i	0.267252	−	0.462895i	−0.700899	−	0.713261i	$-0.747218\pi$
$877$	1.80269e8	−	3.12235e8i	0.267252	−	0.462895i	0.968151	+	0.250366i	$0.0805509\pi$
$878$		0			0
$879$	−2.00821e8	−	3.47832e8i	−0.295694	−	0.512156i
$880$		0			0
$881$			1.27541e9i			1.86519i	0.360924	+	0.932595i	$0.382461\pi$
$881$			1.27541e9i			1.86519i	−0.360924	+	0.932595i	$0.617539\pi$
$882$		0			0
$883$	2.92638e8			0.425058			0.212529	−	0.977155i	$-0.431830\pi$
$883$	2.92638e8			0.425058			0.212529	+	0.977155i	$0.431830\pi$
$884$		0			0
$885$	−2.41902e8	+	1.39662e8i	−0.348988	+	0.201488i
$886$		0			0
$887$	7.14682e8	+	4.12622e8i	1.02410	+	0.591264i	0.915289	−	0.402798i	$-0.131962\pi$
$887$	7.14682e8	+	4.12622e8i	1.02410	+	0.591264i	0.108811	+	0.994062i	$0.465296\pi$
$888$		0			0
$889$	8.31675e7	+	5.61703e7i	0.118372	+	0.0799468i
$890$		0			0
$891$	2.42762e7	−	4.20476e7i	0.0343200	−	0.0594440i
$892$		0			0
$893$	−1.67724e7	−	2.90506e7i	−0.0235526	−	0.0407944i
$894$		0			0
$895$			9.51302e7i			0.132693i
$896$		0			0
$897$	−7.13127e8			−0.988075
$898$		0			0
$899$	3.35138e8	−	1.93492e8i	0.461259	−	0.266308i
$900$		0			0
$901$	−1.25834e9	−	7.26501e8i	−1.72037	−	0.993257i
$902$		0			0
$903$	4.89762e8	+	3.45445e7i	0.665153	+	0.0469154i
$904$		0			0
$905$	3.97954e8	−	6.89276e8i	0.536892	−	0.929924i
$906$		0			0
$907$	−4.80348e8	−	8.31987e8i	−0.643775	−	1.11505i	−0.984583	−	0.174918i	$-0.944034\pi$
$907$	−4.80348e8	−	8.31987e8i	−0.643775	−	1.11505i	0.340808	−	0.940133i	$-0.389300\pi$
$908$		0			0
$909$			1.62378e8i			0.216190i
$910$		0			0
$911$	−1.01677e9			−1.34483			−0.672413	−	0.740176i	$-0.734742\pi$
$911$	−1.01677e9			−1.34483			−0.672413	+	0.740176i	$0.734742\pi$
$912$		0			0
$913$	−9.11598e7	+	5.26311e7i	−0.119782	+	0.0691561i
$914$		0			0
$915$	−1.55063e8	−	8.95255e7i	−0.202416	−	0.116865i
$916$		0			0
$917$	−4.09804e8	−	8.41512e8i	−0.531457	−	1.09132i
$918$		0			0
$919$	−2.43093e8	+	4.21050e8i	−0.313203	+	0.542484i	−0.979054	−	0.203601i	$-0.934735\pi$
$919$	−2.43093e8	+	4.21050e8i	−0.313203	+	0.542484i	0.665851	+	0.746085i	$0.268069\pi$
$920$		0			0
$921$	−1.48007e8	−	2.56356e8i	−0.189454	−	0.328145i
$922$		0			0
$923$		−	2.33852e8i		−	0.297397i
$924$		0			0
$925$	7.40511e8			0.935635
$926$		0			0
$927$	−3.26058e8	+	1.88250e8i	−0.409314	+	0.236317i
$928$		0			0
$929$	7.80354e8	+	4.50538e8i	0.973295	+	0.561932i	0.900239	−	0.435395i	$-0.143391\pi$
$929$	7.80354e8	+	4.50538e8i	0.973295	+	0.561932i	0.0730561	+	0.997328i	$0.476725\pi$
$930$		0			0
$931$	1.10352e8	−	7.78374e8i	0.136751	−	0.964583i
$932$		0			0
$933$	2.52329e8	−	4.37046e8i	0.310686	−	0.538124i
$934$		0			0
$935$	−2.55003e8	−	4.41677e8i	−0.311968	−	0.540344i
$936$		0			0
$937$			6.19442e8i			0.752977i	0.926421	+	0.376489i	$0.122869\pi$
$937$			6.19442e8i			0.752977i	−0.926421	+	0.376489i	$0.877131\pi$
$938$		0			0
$939$	−5.06515e8			−0.611781
$940$		0			0
$941$	−4.29312e8	+	2.47863e8i	−0.515234	+	0.297470i	−0.734982	−	0.678086i	$-0.762810\pi$
$941$	−4.29312e8	+	2.47863e8i	−0.515234	+	0.297470i	0.219749	+	0.975557i	$0.429476\pi$
$942$		0			0
$943$	9.65460e8	+	5.57408e8i	1.15133	+	0.664720i
$944$		0			0
$945$	−9.29445e7	+	4.52626e7i	−0.110136	+	0.0536345i
$946$		0			0
$947$	5.84700e8	−	1.01273e9i	0.688467	−	1.19246i	−0.283866	−	0.958864i	$-0.591617\pi$
$947$	5.84700e8	−	1.01273e9i	0.688467	−	1.19246i	0.972334	−	0.233597i	$-0.0750495\pi$
$948$		0			0
$949$	3.34676e8	+	5.79677e8i	0.391585	+	0.678246i
$950$		0			0
$951$			2.54760e8i			0.296203i
$952$		0			0
$953$	−2.23017e8			−0.257667			−0.128834	−	0.991666i	$-0.541123\pi$
$953$	−2.23017e8			−0.257667			−0.128834	+	0.991666i	$0.541123\pi$
$954$		0			0
$955$	5.22501e8	−	3.01666e8i	0.599897	−	0.346351i
$956$		0			0
$957$	−1.54162e8	−	8.90057e7i	−0.175891	−	0.101550i
$958$		0			0
$959$	2.19089e7	−	3.10619e8i	0.0248408	−	0.352186i
$960$		0			0
$961$	−5.55442e7	+	9.62054e7i	−0.0625847	+	0.108400i
$962$		0			0
$963$	1.16141e8	+	2.01163e8i	0.130049	+	0.225252i
$964$		0			0
$965$			5.64616e8i			0.628306i
$966$		0			0
$967$	−4.77842e8			−0.528451			−0.264226	−	0.964461i	$-0.585116\pi$
$967$	−4.77842e8			−0.528451			−0.264226	+	0.964461i	$0.585116\pi$
$968$		0			0
$969$	7.03234e8	−	4.06012e8i	0.772909	−	0.446239i
$970$		0			0
$971$	−8.66630e8	−	5.00349e8i	−0.946621	−	0.546532i	−0.0545914	−	0.998509i	$-0.517386\pi$
$971$	−8.66630e8	−	5.00349e8i	−0.946621	−	0.546532i	−0.892030	+	0.451977i	$0.850719\pi$
$972$		0			0
$973$	890777.	−	1.31891e6i	0.000967009	−	0.00143178i
$974$		0			0
$975$	−1.75969e8	+	3.04786e8i	−0.189855	+	0.328838i
$976$		0			0
$977$	2.65667e8	+	4.60149e8i	0.284875	+	0.493417i	0.972579	−	0.232574i	$-0.0747147\pi$
$977$	2.65667e8	+	4.60149e8i	0.284875	+	0.493417i	−0.687704	+	0.725991i	$0.741381\pi$
$978$		0			0
$979$		−	3.06437e8i		−	0.326583i
$980$		0			0
$981$	−3.81929e8			−0.404554
$982$		0			0
$983$	−6.03725e8	+	3.48561e8i	−0.635592	+	0.366959i	−0.782915	−	0.622129i	$-0.786268\pi$
$983$	−6.03725e8	+	3.48561e8i	−0.635592	+	0.366959i	0.147322	+	0.989089i	$0.452935\pi$
$984$		0			0
$985$	−1.37880e8	−	7.96052e7i	−0.144276	−	0.0832976i
$986$		0			0
$987$	2.22432e7	+	1.50228e7i	0.0231337	+	0.0156242i
$988$		0			0
$989$	8.64660e8	−	1.49764e9i	0.893833	−	1.54816i
$990$		0			0
$991$	3.67589e8	+	6.36684e8i	0.377696	+	0.654188i	0.990727	−	0.135871i	$-0.0433832\pi$
$991$	3.67589e8	+	6.36684e8i	0.377696	+	0.654188i	−0.613031	+	0.790059i	$0.710050\pi$
$992$		0			0
$993$			8.06812e8i			0.823995i
$994$		0			0
$995$	−3.45803e8			−0.351043
$996$		0			0
$997$	−4.85470e8	+	2.80286e8i	−0.489866	+	0.282824i	−0.724519	−	0.689255i	$-0.757938\pi$
$997$	−4.85470e8	+	2.80286e8i	−0.489866	+	0.282824i	0.234653	+	0.972079i	$0.424605\pi$
$998$		0			0
$999$	−2.61375e8	−	1.50905e8i	−0.262160	−	0.151358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.b.145.2		8
4.3	odd	2		21.7.f.b.19.4	yes	8
7.3	odd	6	inner	336.7.bh.b.241.2		8
12.11	even	2		63.7.m.c.19.1		8
28.3	even	6		21.7.f.b.10.4	✓	8
28.11	odd	6		147.7.f.a.31.4		8
28.19	even	6		147.7.d.a.97.1		8
28.23	odd	6		147.7.d.a.97.2		8
28.27	even	2		147.7.f.a.19.4		8
84.23	even	6		441.7.d.d.244.7		8
84.47	odd	6		441.7.d.d.244.8		8
84.59	odd	6		63.7.m.c.10.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.4	✓	8	28.3	even	6
21.7.f.b.19.4	yes	8	4.3	odd	2
63.7.m.c.10.1		8	84.59	odd	6
63.7.m.c.19.1		8	12.11	even	2
147.7.d.a.97.1		8	28.19	even	6
147.7.d.a.97.2		8	28.23	odd	6
147.7.f.a.19.4		8	28.27	even	2
147.7.f.a.31.4		8	28.11	odd	6
336.7.bh.b.145.2		8	1.1	even	1	trivial
336.7.bh.b.241.2		8	7.3	odd	6	inner
441.7.d.d.244.7		8	84.23	even	6
441.7.d.d.244.8		8	84.47	odd	6

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-13.5000 + 7.79423i) q^{3} +(-68.9069 - 39.7834i) q^{5} +(-284.244 - 191.975i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(-13.5000 + 7.79423i) q^{3} +(-68.9069 - 39.7834i) q^{5} +(-284.244 - 191.975i) q^{7} +(121.500 - 210.444i) q^{9} +(411.119 + 712.080i) q^{11} +2429.15i q^{13} +1240.32 q^{15} +(6751.11 - 3897.76i) q^{17} +(-5786.98 - 3341.12i) q^{19} +(5333.59 + 376.196i) q^{21} +(9416.30 - 16309.5i) q^{23} +(-4647.06 - 8048.94i) q^{25} +3788.00i q^{27} +13888.2 q^{29} +(24131.1 - 13932.1i) q^{31} +(-11100.2 - 6408.72i) q^{33} +(11949.0 + 24536.6i) q^{35} +(-39837.6 + 69000.8i) q^{37} +(-18933.3 - 32793.5i) q^{39} +59196.1i q^{41} +91825.9 q^{43} +(-16744.4 + 9667.37i) q^{45} +(4347.44 + 2509.99i) q^{47} +(43940.4 + 109135. i) q^{49} +(-60760.0 + 105239. i) q^{51} +(-93194.8 - 161418. i) q^{53} -65422.9i q^{55} +104166. q^{57} +(-195032. + 112602. i) q^{59} +(-125018. - 72179.1i) q^{61} +(-74935.6 + 36492.6i) q^{63} +(96639.7 - 167385. i) q^{65} +(-117740. - 203932. i) q^{67} +293571. i q^{69} -96269.3 q^{71} +(238634. - 137775. i) q^{73} +(125471. + 72440.5i) q^{75} +(19843.1 - 281329. i) q^{77} +(-340667. + 590052. i) q^{79} +(-29524.5 - 51137.9i) q^{81} +128019. i q^{83} -620264. q^{85} +(-187491. + 108248. i) q^{87} +(-322756. - 186343. i) q^{89} +(466335. - 690470. i) q^{91} +(-217180. + 376167. i) q^{93} +(265842. + 460452. i) q^{95} +620049. i q^{97} +199804. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9}+O(q^{10}) \) 8 * q - 108 * q^3 - 42 * q^5 - 748 * q^7 + 972 * q^9	\( 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9} + 1070 q^{11} + 756 q^{15} + 7212 q^{17} + 24606 q^{19} + 8154 q^{21} + 15224 q^{23} + 22274 q^{25} + 32524 q^{29} - 40200 q^{31} - 28890 q^{33} + 242436 q^{35} - 45670 q^{37} - 93366 q^{39} + 445660 q^{43} - 10206 q^{45} - 82884 q^{47} + 24116 q^{49} - 64908 q^{51} - 13034 q^{53} - 442908 q^{57} - 1810362 q^{59} - 392856 q^{61} - 38394 q^{63} - 389004 q^{65} - 384094 q^{67} - 225688 q^{71} + 903078 q^{73} - 601398 q^{75} - 327674 q^{77} + 559592 q^{79} - 236196 q^{81} + 1953576 q^{85} - 439074 q^{87} - 1770036 q^{89} + 2960718 q^{91} + 361800 q^{93} - 1160112 q^{95} + 520020 q^{99}+O(q^{100}) \) 8 * q - 108 * q^3 - 42 * q^5 - 748 * q^7 + 972 * q^9 + 1070 * q^11 + 756 * q^15 + 7212 * q^17 + 24606 * q^19 + 8154 * q^21 + 15224 * q^23 + 22274 * q^25 + 32524 * q^29 - 40200 * q^31 - 28890 * q^33 + 242436 * q^35 - 45670 * q^37 - 93366 * q^39 + 445660 * q^43 - 10206 * q^45 - 82884 * q^47 + 24116 * q^49 - 64908 * q^51 - 13034 * q^53 - 442908 * q^57 - 1810362 * q^59 - 392856 * q^61 - 38394 * q^63 - 389004 * q^65 - 384094 * q^67 - 225688 * q^71 + 903078 * q^73 - 601398 * q^75 - 327674 * q^77 + 559592 * q^79 - 236196 * q^81 + 1953576 * q^85 - 439074 * q^87 - 1770036 * q^89 + 2960718 * q^91 + 361800 * q^93 - 1160112 * q^95 + 520020 * q^99

Introduction

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