LMFDB - Embedded newform 336.7.bh.h.145.6

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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.6
Character	$\chi$	$=$	336.145
Dual form			336.7.bh.h.241.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.5000 - 7.79423i) q^{3} +(-51.6596 - 29.8257i) q^{5} +(-161.216 - 302.751i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(13.5000 - 7.79423i) q^{3} +(-51.6596 - 29.8257i) q^{5} +(-161.216 - 302.751i) q^{7} +(121.500 - 210.444i) q^{9} +(476.131 + 824.684i) q^{11} -2023.12i q^{13} -929.874 q^{15} +(-2966.27 + 1712.58i) q^{17} +(-1122.70 - 648.191i) q^{19} +(-4536.13 - 2830.59i) q^{21} +(6669.65 - 11552.2i) q^{23} +(-6033.35 - 10450.1i) q^{25} -3788.00i q^{27} +20978.8 q^{29} +(-25495.7 + 14719.9i) q^{31} +(12855.5 + 7422.15i) q^{33} +(-701.396 + 20448.4i) q^{35} +(15206.3 - 26338.1i) q^{37} +(-15768.7 - 27312.1i) q^{39} +60095.0i q^{41} -120913. q^{43} +(-12553.3 + 7247.65i) q^{45} +(-14594.7 - 8426.27i) q^{47} +(-65667.6 + 97616.8i) q^{49} +(-26696.4 + 46239.6i) q^{51} +(65541.3 + 113521. i) q^{53} -56803.8i q^{55} -20208.6 q^{57} +(-150782. + 87054.1i) q^{59} +(303679. + 175329. i) q^{61} +(-83300.0 - 2857.25i) q^{63} +(-60341.0 + 104514. i) q^{65} +(-170366. - 295083. i) q^{67} -207939. i q^{69} -376407. q^{71} +(-65701.4 + 37932.7i) q^{73} +(-162901. - 94050.7i) q^{75} +(172914. - 277102. i) q^{77} +(-349906. + 606056. i) q^{79} +(-29524.5 - 51137.9i) q^{81} -298037. i q^{83} +204315. q^{85} +(283213. - 163513. i) q^{87} +(191152. + 110362. i) q^{89} +(-612503. + 326160. i) q^{91} +(-229461. + 397438. i) q^{93} +(38665.5 + 66970.6i) q^{95} +859530. i q^{97} +231400. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9}+O(q^{10}) $ 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9	$ 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9} + 1190 q^{11} - 2268 q^{15} - 1500 q^{17} + 13446 q^{19} - 2106 q^{21} - 21504 q^{23} + 22542 q^{25} - 85484 q^{29} - 6264 q^{31} + 32130 q^{33} - 32268 q^{35} - 46938 q^{37} + 17010 q^{39} + 19548 q^{43} - 30618 q^{45} + 167004 q^{47} + 250644 q^{49} - 13500 q^{51} - 258982 q^{53} + 242028 q^{57} - 744834 q^{59} - 390096 q^{61} - 59778 q^{63} - 19388 q^{65} - 62742 q^{67} + 1102984 q^{71} - 663534 q^{73} + 608634 q^{75} + 404298 q^{77} + 271032 q^{79} - 708588 q^{81} + 2540040 q^{85} - 1154034 q^{87} - 433740 q^{89} + 2142270 q^{91} - 56376 q^{93} - 2205360 q^{95} + 578340 q^{99}+O(q^{100}) $ 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9 + 1190 * q^11 - 2268 * q^15 - 1500 * q^17 + 13446 * q^19 - 2106 * q^21 - 21504 * q^23 + 22542 * q^25 - 85484 * q^29 - 6264 * q^31 + 32130 * q^33 - 32268 * q^35 - 46938 * q^37 + 17010 * q^39 + 19548 * q^43 - 30618 * q^45 + 167004 * q^47 + 250644 * q^49 - 13500 * q^51 - 258982 * q^53 + 242028 * q^57 - 744834 * q^59 - 390096 * q^61 - 59778 * q^63 - 19388 * q^65 - 62742 * q^67 + 1102984 * q^71 - 663534 * q^73 + 608634 * q^75 + 404298 * q^77 + 271032 * q^79 - 708588 * q^81 + 2540040 * q^85 - 1154034 * q^87 - 433740 * q^89 + 2142270 * q^91 - 56376 * q^93 - 2205360 * q^95 + 578340 * 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
$5$	−51.6596	−	29.8257i	−0.413277	−	0.238606i	0.278920	−	0.960314i	$-0.410024\pi$
$5$	−51.6596	−	29.8257i	−0.413277	−	0.238606i	−0.692197	+	0.721709i	$0.743357\pi$
$6$		0			0
$7$	−161.216	−	302.751i	−0.470018	−	0.882657i
$7$	−161.216	−	302.751i	−0.470018	−	0.882657i
$8$		0			0
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$		0			0
$11$	476.131	+	824.684i	0.357725	+	0.619597i	0.987580	−	0.157115i	$-0.0502193\pi$
$11$	476.131	+	824.684i	0.357725	+	0.619597i	−0.629856	+	0.776712i	$0.716886\pi$
$12$		0			0
$13$		−	2023.12i		−	0.920857i	−0.887697	−	0.460428i	$-0.847696\pi$
$13$		−	2023.12i		−	0.920857i	0.887697	−	0.460428i	$-0.152304\pi$
$14$		0			0
$15$	−929.874			−0.275518
$16$		0			0
$17$	−2966.27	+	1712.58i	−0.603760	+	0.348581i	−0.770519	−	0.637417i	$-0.780003\pi$
$17$	−2966.27	+	1712.58i	−0.603760	+	0.348581i	0.166759	+	0.985998i	$0.446670\pi$
$18$		0			0
$19$	−1122.70	−	648.191i	−0.163683	−	0.0945023i	0.415921	−	0.909401i	$-0.363459\pi$
$19$	−1122.70	−	648.191i	−0.163683	−	0.0945023i	−0.579604	+	0.814898i	$0.696793\pi$
$20$		0			0
$21$	−4536.13	−	2830.59i	−0.489810	−	0.305646i
$22$		0			0
$23$	6669.65	−	11552.2i	0.548176	−	0.949468i	−0.450224	−	0.892916i	$-0.648656\pi$
$23$	6669.65	−	11552.2i	0.548176	−	0.949468i	0.998400	−	0.0565523i	$-0.0180108\pi$
$24$		0			0
$25$	−6033.35	−	10450.1i	−0.386135	−	0.668805i
$26$		0			0
$27$		−	3788.00i		−	0.192450i
$28$		0			0
$29$	20978.8			0.860173			0.430086	−	0.902788i	$-0.358483\pi$
$29$	20978.8			0.860173			0.430086	+	0.902788i	$0.358483\pi$
$30$		0			0
$31$	−25495.7	+	14719.9i	−0.855817	+	0.494106i	−0.862609	−	0.505870i	$-0.831171\pi$
$31$	−25495.7	+	14719.9i	−0.855817	+	0.494106i	0.00679196	+	0.999977i	$0.497838\pi$
$32$		0			0
$33$	12855.5	+	7422.15i	0.357725	+	0.206532i
$34$		0			0
$35$	−701.396	+	20448.4i	−0.0163591	+	0.476931i
$36$		0			0
$37$	15206.3	−	26338.1i	0.300205	−	0.519971i	−0.675977	−	0.736923i	$-0.736278\pi$
$37$	15206.3	−	26338.1i	0.300205	−	0.519971i	0.976182	+	0.216952i	$0.0696115\pi$
$38$		0			0
$39$	−15768.7	−	27312.1i	−0.265828	−	0.460428i
$40$		0			0
$41$			60095.0i			0.871940i	0.899961	+	0.435970i	$0.143595\pi$
$41$			60095.0i			0.871940i	−0.899961	+	0.435970i	$0.856405\pi$
$42$		0			0
$43$	−120913.			−1.52078			−0.760391	−	0.649465i	$-0.774993\pi$
$43$	−120913.			−1.52078			−0.760391	+	0.649465i	$0.774993\pi$
$44$		0			0
$45$	−12553.3	+	7247.65i	−0.137759	+	0.0795352i
$46$		0			0
$47$	−14594.7	−	8426.27i	−0.140573	−	0.0811600i	0.428064	−	0.903748i	$-0.359196\pi$
$47$	−14594.7	−	8426.27i	−0.140573	−	0.0811600i	−0.568637	+	0.822588i	$0.692529\pi$
$48$		0			0
$49$	−65667.6	+	97616.8i	−0.558166	+	0.829730i
$50$		0			0
$51$	−26696.4	+	46239.6i	−0.201253	+	0.348581i
$52$		0			0
$53$	65541.3	+	113521.i	0.440238	+	0.762514i	0.997707	−	0.0676835i	$-0.0215608\pi$
$53$	65541.3	+	113521.i	0.440238	+	0.762514i	−0.557469	+	0.830198i	$0.688227\pi$
$54$		0			0
$55$		−	56803.8i		−	0.341420i
$56$		0			0
$57$	−20208.6			−0.109122
$58$		0			0
$59$	−150782.	+	87054.1i	−0.734165	+	0.423871i	−0.819944	−	0.572444i	$-0.805996\pi$
$59$	−150782.	+	87054.1i	−0.734165	+	0.423871i	0.0857787	+	0.996314i	$0.472662\pi$
$60$		0			0
$61$	303679.	+	175329.i	1.33790	+	0.772439i	0.986496	−	0.163783i	$-0.0523697\pi$
$61$	303679.	+	175329.i	1.33790	+	0.772439i	0.351408	+	0.936222i	$0.385703\pi$
$62$		0			0
$63$	−83300.0	−	2857.25i	−0.333137	−	0.0114269i
$64$		0			0
$65$	−60341.0	+	104514.i	−0.219722	+	0.380569i
$66$		0			0
$67$	−170366.	−	295083.i	−0.566447	−	0.981115i	−0.996913	−	0.0785086i	$-0.974984\pi$
$67$	−170366.	−	295083.i	−0.566447	−	0.981115i	0.430466	−	0.902607i	$-0.358349\pi$
$68$		0			0
$69$		−	207939.i		−	0.632979i
$70$		0			0
$71$	−376407.			−1.05168			−0.525838	−	0.850585i	$-0.676248\pi$
$71$	−376407.			−1.05168			−0.525838	+	0.850585i	$0.676248\pi$
$72$		0			0
$73$	−65701.4	+	37932.7i	−0.168891	+	0.0975091i	−0.582063	−	0.813144i	$-0.697754\pi$
$73$	−65701.4	+	37932.7i	−0.168891	+	0.0975091i	0.413172	+	0.910653i	$0.364421\pi$
$74$		0			0
$75$	−162901.	−	94050.7i	−0.386135	−	0.222935i
$76$		0			0
$77$	172914.	−	277102.i	0.378754	−	0.606970i
$78$		0			0
$79$	−349906.	+	606056.i	−0.709693	+	1.22922i	0.255278	+	0.966868i	$0.417833\pi$
$79$	−349906.	+	606056.i	−0.709693	+	1.22922i	−0.964971	+	0.262357i	$0.915500\pi$
$80$		0			0
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	298037.i		−	0.521239i	−0.965442	−	0.260619i	$-0.916073\pi$
$83$		−	298037.i		−	0.521239i	0.965442	−	0.260619i	$-0.0839267\pi$
$84$		0			0
$85$	204315.			0.332693
$86$		0			0
$87$	283213.	−	163513.i	0.430086	−	0.248310i
$88$		0			0
$89$	191152.	+	110362.i	0.271150	+	0.156548i	0.629410	−	0.777073i	$-0.283297\pi$
$89$	191152.	+	110362.i	0.271150	+	0.156548i	−0.358260	+	0.933622i	$0.616630\pi$
$90$		0			0
$91$	−612503.	+	326160.i	−0.812800	+	0.432819i
$92$		0			0
$93$	−229461.	+	397438.i	−0.285272	+	0.494106i
$94$		0			0
$95$	38665.5	+	66970.6i	0.0450976	+	0.0781113i
$96$		0			0
$97$			859530.i			0.941772i	0.882194	+	0.470886i	$0.156066\pi$
$97$			859530.i			0.941772i	−0.882194	+	0.470886i	$0.843934\pi$
$98$		0			0
$99$	231400.			0.238483
$100$		0			0
$101$	−319286.	+	184340.i	−0.309896	+	0.178918i	−0.646880	−	0.762592i	$-0.723926\pi$
$101$	−319286.	+	184340.i	−0.309896	+	0.178918i	0.336984	+	0.941510i	$0.390593\pi$
$102$		0			0
$103$	754381.	+	435542.i	0.690366	+	0.398583i	0.803749	−	0.594969i	$-0.202835\pi$
$103$	754381.	+	435542.i	0.690366	+	0.398583i	−0.113383	+	0.993551i	$0.536169\pi$
$104$		0			0
$105$	149911.	+	281520.i	0.129499	+	0.243188i
$106$		0			0
$107$	−299572.	+	518874.i	−0.244540	+	0.423556i	−0.962002	−	0.273042i	$-0.911970\pi$
$107$	−299572.	+	518874.i	−0.244540	+	0.423556i	0.717462	+	0.696598i	$0.245304\pi$
$108$		0			0
$109$	175515.	+	304000.i	0.135530	+	0.234744i	0.925800	−	0.378015i	$-0.123393\pi$
$109$	175515.	+	304000.i	0.135530	+	0.234744i	−0.790270	+	0.612759i	$0.790060\pi$
$110$		0			0
$111$		−	474086.i		−	0.346647i
$112$		0			0
$113$	−907461.			−0.628916			−0.314458	−	0.949271i	$-0.601823\pi$
$113$	−907461.			−0.628916			−0.314458	+	0.949271i	$0.601823\pi$
$114$		0			0
$115$	−689104.	+	397854.i	−0.453097	+	0.261596i
$116$		0			0
$117$	−425754.	−	245809.i	−0.265828	−	0.153476i
$118$		0			0
$119$	996696.	+	621947.i	0.591455	+	0.369073i
$120$		0			0
$121$	432378.	−	748901.i	0.244066	−	0.422735i
$122$		0			0
$123$	468394.	+	811282.i	0.251707	+	0.435970i
$124$		0			0
$125$			1.65185e6i			0.845747i
$126$		0			0
$127$	−3.02400e6			−1.47628			−0.738142	−	0.674645i	$-0.764297\pi$
$127$	−3.02400e6			−1.47628			−0.738142	+	0.674645i	$0.764297\pi$
$128$		0			0
$129$	−1.63232e6	+	942423.i	−0.760391	+	0.439012i
$130$		0			0
$131$	−1.63682e6	−	945016.i	−0.728092	−	0.420364i	0.0896320	−	0.995975i	$-0.471431\pi$
$131$	−1.63682e6	−	945016.i	−0.728092	−	0.420364i	−0.817724	+	0.575611i	$0.804764\pi$
$132$		0			0
$133$	−15243.2	+	444398.i	−0.00647919	+	0.188893i
$134$		0			0
$135$	−112980.	+	195686.i	−0.0459197	+	0.0795352i
$136$		0			0
$137$	−2.17364e6	−	3.76485e6i	−0.845327	−	1.46415i	−0.885337	−	0.464951i	$-0.846072\pi$
$137$	−2.17364e6	−	3.76485e6i	−0.845327	−	1.46415i	0.0400092	−	0.999199i	$-0.487261\pi$
$138$		0			0
$139$			1.94798e6i			0.725336i	0.931918	+	0.362668i	$0.118134\pi$
$139$			1.94798e6i			0.725336i	−0.931918	+	0.362668i	$0.881866\pi$
$140$		0			0
$141$	−262705.			−0.0937155
$142$		0			0
$143$	1.66844e6	−	963272.i	0.570560	−	0.329413i
$144$		0			0
$145$	−1.08375e6	−	625706.i	−0.355490	−	0.205242i
$146$		0			0
$147$	−125665.	+	1.82966e6i	−0.0395605	+	0.575993i
$148$		0			0
$149$	−2.79882e6	+	4.84770e6i	−0.846089	+	1.46547i	0.0385829	+	0.999255i	$0.487716\pi$
$149$	−2.79882e6	+	4.84770e6i	−0.846089	+	1.46547i	−0.884672	+	0.466214i	$0.845618\pi$
$150$		0			0
$151$	−285092.	−	493794.i	−0.0828046	−	0.143422i	0.821649	−	0.569994i	$-0.193054\pi$
$151$	−285092.	−	493794.i	−0.0828046	−	0.143422i	−0.904454	+	0.426572i	$0.859721\pi$
$152$		0			0
$153$			832313.i			0.232387i
$154$		0			0
$155$	1.75613e6			0.471586
$156$		0			0
$157$	−2.00743e6	+	1.15899e6i	−0.518729	+	0.299489i	−0.736415	−	0.676530i	$-0.763483\pi$
$157$	−2.00743e6	+	1.15899e6i	−0.518729	+	0.299489i	0.217685	+	0.976019i	$0.430149\pi$
$158$		0			0
$159$	1.76961e6	+	1.02169e6i	0.440238	+	0.254171i
$160$		0			0
$161$	−4.57269e6	−	156847.i	−1.09571	−	0.0375836i
$162$		0			0
$163$	−1.26275e6	+	2.18715e6i	−0.291579	+	0.505029i	−0.974183	−	0.225759i	$-0.927514\pi$
$163$	−1.26275e6	+	2.18715e6i	−0.291579	+	0.505029i	0.682604	+	0.730788i	$0.260847\pi$
$164$		0			0
$165$	−442742.	−	766852.i	−0.0985596	−	0.170710i
$166$		0			0
$167$			3.22357e6i			0.692130i	0.938211	+	0.346065i	$0.112482\pi$
$167$			3.22357e6i			0.692130i	−0.938211	+	0.346065i	$0.887518\pi$
$168$		0			0
$169$	733786.			0.152023
$170$		0			0
$171$	−272816.	+	157510.i	−0.0545609	+	0.0315008i
$172$		0			0
$173$	−8.17865e6	−	4.72195e6i	−1.57959	−	0.911975i	−0.994916	−	0.100704i	$-0.967890\pi$
$173$	−8.17865e6	−	4.72195e6i	−1.57959	−	0.911975i	−0.584671	−	0.811271i	$-0.698776\pi$
$174$		0			0
$175$	−2.19110e6	+	3.51133e6i	−0.408835	+	0.655175i
$176$		0			0
$177$	−1.35704e6	+	2.35046e6i	−0.244722	+	0.423871i
$178$		0			0
$179$	1.90836e6	+	3.30538e6i	0.332738	+	0.576318i	0.983048	−	0.183351i	$-0.0586944\pi$
$179$	1.90836e6	+	3.30538e6i	0.332738	+	0.576318i	−0.650310	+	0.759669i	$0.725361\pi$
$180$		0			0
$181$			2.76928e6i			0.467015i	0.972355	+	0.233508i	$0.0750204\pi$
$181$			2.76928e6i			0.467015i	−0.972355	+	0.233508i	$0.924980\pi$
$182$		0			0
$183$	5.46622e6			0.891936
$184$		0			0
$185$	−1.57110e6	+	907077.i	−0.248136	+	0.143261i
$186$		0			0
$187$	−2.82467e6	−	1.63082e6i	−0.431959	−	0.249392i
$188$		0			0
$189$	−1.14682e6	+	610686.i	−0.169867	+	0.0904551i
$190$		0			0
$191$	−352332.	+	610256.i	−0.0505652	+	0.0875815i	−0.890200	−	0.455570i	$-0.849436\pi$
$191$	−352332.	+	610256.i	−0.0505652	+	0.0875815i	0.839635	+	0.543151i	$0.182769\pi$
$192$		0			0
$193$	−1.84667e6	−	3.19852e6i	−0.256872	−	0.444915i	0.708531	−	0.705680i	$-0.249358\pi$
$193$	−1.84667e6	−	3.19852e6i	−0.256872	−	0.444915i	−0.965402	+	0.260765i	$0.916025\pi$
$194$		0			0
$195$			1.88125e6i			0.253713i
$196$		0			0
$197$	7.76425e6			1.01555			0.507775	−	0.861490i	$-0.330468\pi$
$197$	7.76425e6			1.01555			0.507775	+	0.861490i	$0.330468\pi$
$198$		0			0
$199$	−2.91422e6	+	1.68252e6i	−0.369796	+	0.213502i	−0.673369	−	0.739306i	$-0.735154\pi$
$199$	−2.91422e6	+	1.68252e6i	−0.369796	+	0.213502i	0.303573	+	0.952808i	$0.401820\pi$
$200$		0			0
$201$	−4.59989e6	−	2.65575e6i	−0.566447	−	0.327038i
$202$		0			0
$203$	−3.38212e6	−	6.35134e6i	−0.404297	−	0.759237i
$204$		0			0
$205$	1.79238e6	−	3.10449e6i	0.208050	−	0.360353i
$206$		0			0
$207$	−1.62073e6	−	2.80718e6i	−0.182725	−	0.316489i
$208$		0			0
$209$		−	1.23450e6i		−	0.135223i
$210$		0			0
$211$	−1.52878e7			−1.62741			−0.813705	−	0.581279i	$-0.802553\pi$
$211$	−1.52878e7			−1.62741			−0.813705	+	0.581279i	$0.802553\pi$
$212$		0			0
$213$	−5.08149e6	+	2.93380e6i	−0.525838	+	0.303593i
$214$		0			0
$215$	6.24632e6	+	3.60631e6i	0.628505	+	0.362867i
$216$		0			0
$217$	8.56679e6	+	5.34575e6i	0.838376	+	0.523154i
$218$		0			0
$219$	−591312.	+	1.02418e6i	−0.0562969	+	0.0975091i
$220$		0			0
$221$	3.46475e6	+	6.00113e6i	0.320993	+	0.555976i
$222$		0			0
$223$		−	1.25080e6i		−	0.112791i	−0.998409	−	0.0563953i	$-0.982039\pi$
$223$		−	1.25080e6i		−	0.112791i	0.998409	−	0.0563953i	$-0.0179607\pi$
$224$		0			0
$225$	−2.93221e6			−0.257423
$226$		0			0
$227$	1.93735e7	−	1.11853e7i	1.65626	−	0.956244i	0.681847	−	0.731495i	$-0.261177\pi$
$227$	1.93735e7	−	1.11853e7i	1.65626	−	0.956244i	0.974416	−	0.224750i	$-0.0721565\pi$
$228$		0			0
$229$	9.34279e6	+	5.39406e6i	0.777983	+	0.449169i	0.835715	−	0.549163i	$-0.185054\pi$
$229$	9.34279e6	+	5.39406e6i	0.777983	+	0.449169i	−0.0577319	+	0.998332i	$0.518387\pi$
$230$		0			0
$231$	174543.	−	5.08861e6i	0.0141601	−	0.412822i
$232$		0			0
$233$	1.79232e6	−	3.10439e6i	0.141693	−	0.245419i	−0.786441	−	0.617665i	$-0.788079\pi$
$233$	1.79232e6	−	3.10439e6i	0.141693	−	0.245419i	0.928134	+	0.372246i	$0.121412\pi$
$234$		0			0
$235$	502639.	+	870596.i	0.0387305	+	0.0670831i
$236$		0			0
$237$			1.09090e7i			0.819483i
$238$		0			0
$239$	−1.26123e7			−0.923845			−0.461923	−	0.886920i	$-0.652840\pi$
$239$	−1.26123e7			−0.923845			−0.461923	+	0.886920i	$0.652840\pi$
$240$		0			0
$241$	2.03365e7	−	1.17413e7i	1.45287	−	0.838813i	0.454224	−	0.890887i	$-0.349916\pi$
$241$	2.03365e7	−	1.17413e7i	1.45287	−	0.838813i	0.998643	+	0.0520739i	$0.0165831\pi$
$242$		0			0
$243$	−797162.	−	460241.i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	6.30386e6	−	3.08427e6i	0.428655	−	0.209727i
$246$		0			0
$247$	−1.31137e6	+	2.27136e6i	−0.0870231	+	0.150728i
$248$		0			0
$249$	−2.32297e6	−	4.02351e6i	−0.150469	−	0.260619i
$250$		0			0
$251$		−	1.49696e7i		−	0.946648i	−0.880888	−	0.473324i	$-0.843054\pi$
$251$		−	1.49696e7i		−	0.946648i	0.880888	−	0.473324i	$-0.156946\pi$
$252$		0			0
$253$	1.27025e7			0.784383
$254$		0			0
$255$	2.75826e6	−	1.59248e6i	0.166347	−	0.0960403i
$256$		0			0
$257$	1.08423e7	+	6.25978e6i	0.638735	+	0.368774i	0.784127	−	0.620600i	$-0.213111\pi$
$257$	1.08423e7	+	6.25978e6i	0.638735	+	0.368774i	−0.145392	+	0.989374i	$0.546444\pi$
$258$		0			0
$259$	−1.04254e7	−	357599.i	−0.600058	−	0.0205824i
$260$		0			0
$261$	2.54892e6	−	4.41486e6i	0.143362	−	0.248310i
$262$		0			0
$263$	2.38358e6	+	4.12847e6i	0.131027	+	0.226946i	0.924073	−	0.382216i	$-0.124839\pi$
$263$	2.38358e6	+	4.12847e6i	0.131027	+	0.226946i	−0.793046	+	0.609162i	$0.791506\pi$
$264$		0			0
$265$		−	7.81926e6i		−	0.420173i
$266$		0			0
$267$	3.44074e6			0.180766
$268$		0			0
$269$	1.35946e7	−	7.84885e6i	0.698409	−	0.403227i	−0.108345	−	0.994113i	$-0.534555\pi$
$269$	1.35946e7	−	7.84885e6i	0.698409	−	0.403227i	0.806755	+	0.590886i	$0.201222\pi$
$270$		0			0
$271$	−1.73973e7	−	1.00443e7i	−0.874125	−	0.504676i	−0.00540833	−	0.999985i	$-0.501722\pi$
$271$	−1.73973e7	−	1.00443e7i	−0.874125	−	0.504676i	−0.868717	+	0.495309i	$0.835055\pi$
$272$		0			0
$273$	−5.72662e6	+	9.17715e6i	−0.281456	+	0.451045i
$274$		0			0
$275$	5.74534e6	−	9.95122e6i	0.276260	−	0.478496i
$276$		0			0
$277$	−4.25382e6	−	7.36783e6i	−0.200143	−	0.346657i	0.748432	−	0.663212i	$-0.230807\pi$
$277$	−4.25382e6	−	7.36783e6i	−0.200143	−	0.346657i	−0.948574	+	0.316555i	$0.897474\pi$
$278$		0			0
$279$			7.15388e6i			0.329404i
$280$		0			0
$281$	6.90476e6			0.311193			0.155596	−	0.987821i	$-0.450270\pi$
$281$	6.90476e6			0.311193			0.155596	+	0.987821i	$0.450270\pi$
$282$		0			0
$283$	2.29451e6	−	1.32473e6i	0.101235	−	0.0584480i	−0.448528	−	0.893769i	$-0.648051\pi$
$283$	2.29451e6	−	1.32473e6i	0.101235	−	0.0584480i	0.549763	+	0.835321i	$0.314718\pi$
$284$		0			0
$285$	1.04397e6	+	602736.i	0.0450976	+	0.0260371i
$286$		0			0
$287$	1.81938e7	−	9.68829e6i	0.769624	−	0.409828i
$288$		0			0
$289$	−6.20294e6	+	1.07438e7i	−0.256983	+	0.445107i
$290$		0			0
$291$	6.69937e6	+	1.16037e7i	0.271866	+	0.470886i
$292$		0			0
$293$		−	3.72796e7i		−	1.48207i	−0.671466	−	0.741035i	$-0.734335\pi$
$293$		−	3.72796e7i		−	1.48207i	0.671466	−	0.741035i	$-0.265665\pi$
$294$		0			0
$295$	1.03858e7			0.404552
$296$		0			0
$297$	3.12390e6	−	1.80358e6i	0.119242	−	0.0688441i
$298$		0			0
$299$	−2.33715e7	−	1.34935e7i	−0.874324	−	0.504791i
$300$		0			0
$301$	1.94931e7	+	3.66065e7i	0.714796	+	1.34233i
$302$		0			0
$303$	−2.87357e6	+	4.97717e6i	−0.103299	+	0.178918i
$304$		0			0
$305$	−1.04586e7	−	1.81149e7i	−0.368617	−	0.638463i
$306$		0			0
$307$		−	1.58997e7i		−	0.549507i	−0.961515	−	0.274753i	$-0.911404\pi$
$307$		−	1.58997e7i		−	0.549507i	0.961515	−	0.274753i	$-0.0885962\pi$
$308$		0			0
$309$	1.35789e7			0.460244
$310$		0			0
$311$	4.25580e7	−	2.45709e7i	1.41482	−	0.816844i	0.418978	−	0.907996i	$-0.362388\pi$
$311$	4.25580e7	−	2.45709e7i	1.41482	−	0.816844i	0.995837	+	0.0911521i	$0.0290550\pi$
$312$		0			0
$313$	2.09774e7	+	1.21113e7i	0.684099	+	0.394965i	0.801398	−	0.598132i	$-0.204090\pi$
$313$	2.09774e7	+	1.21113e7i	0.684099	+	0.394965i	−0.117299	+	0.993097i	$0.537423\pi$
$314$		0			0
$315$	4.21803e6	+	2.63209e6i	0.134952	+	0.0842109i
$316$		0			0
$317$	1.89432e7	−	3.28105e7i	0.594668	−	1.03000i	−0.398926	−	0.916983i	$-0.630617\pi$
$317$	1.89432e7	−	3.28105e7i	0.594668	−	1.03000i	0.993594	−	0.113012i	$-0.0360498\pi$
$318$		0			0
$319$	9.98864e6	+	1.73008e7i	0.307705	+	0.532961i
$320$		0			0
$321$			9.33974e6i			0.282371i
$322$		0			0
$323$	4.44031e6			0.131767
$324$		0			0
$325$	−2.11418e7	+	1.22062e7i	−0.615873	+	0.355575i
$326$		0			0
$327$	4.73890e6	+	2.73600e6i	0.135530	+	0.0782480i
$328$		0			0
$329$	−198156.	+	5.77702e6i	−0.00556442	+	0.162225i
$330$		0			0
$331$	−2.86231e7	+	4.95767e7i	−0.789283	+	1.36708i	0.137123	+	0.990554i	$0.456214\pi$
$331$	−2.86231e7	+	4.95767e7i	−0.789283	+	1.36708i	−0.926406	+	0.376525i	$0.877119\pi$
$332$		0			0
$333$	−3.69513e6	−	6.40015e6i	−0.100068	−	0.173324i
$334$		0			0
$335$			2.03252e7i			0.540630i
$336$		0			0
$337$	1.51633e7			0.396190			0.198095	−	0.980183i	$-0.436525\pi$
$337$	1.51633e7			0.396190			0.198095	+	0.980183i	$0.436525\pi$
$338$		0			0
$339$	−1.22507e7	+	7.07296e6i	−0.314458	+	0.181553i
$340$		0			0
$341$	−2.42786e7	−	1.40172e7i	−0.612294	−	0.353508i
$342$		0			0
$343$	4.01403e7	+	4.14353e6i	0.994714	+	0.102681i
$344$		0			0
$345$	−6.20193e6	+	1.07421e7i	−0.151032	+	0.261596i
$346$		0			0
$347$	−3.17694e7	−	5.50262e7i	−0.760363	−	1.31699i	−0.942664	−	0.333744i	$-0.891688\pi$
$347$	−3.17694e7	−	5.50262e7i	−0.760363	−	1.31699i	0.182301	−	0.983243i	$-0.441645\pi$
$348$		0			0
$349$		−	3.14652e7i		−	0.740210i	−0.928990	−	0.370105i	$-0.879322\pi$
$349$		−	3.14652e7i		−	0.740210i	0.928990	−	0.370105i	$-0.120678\pi$
$350$		0			0
$351$	−7.66358e6			−0.177219
$352$		0			0
$353$	−4.79170e6	+	2.76649e6i	−0.108935	+	0.0628934i	−0.553477	−	0.832864i	$-0.686699\pi$
$353$	−4.79170e6	+	2.76649e6i	−0.108935	+	0.0628934i	0.444543	+	0.895758i	$0.353366\pi$
$354$		0			0
$355$	1.94450e7	+	1.12266e7i	0.434634	+	0.250936i
$356$		0			0
$357$	1.83030e7	+	627807.i	0.402270	+	0.0137982i
$358$		0			0
$359$	2.84972e7	−	4.93586e7i	0.615912	−	1.06679i	−0.374312	−	0.927303i	$-0.622121\pi$
$359$	2.84972e7	−	4.93586e7i	0.615912	−	1.06679i	0.990224	−	0.139488i	$-0.0445457\pi$
$360$		0			0
$361$	−2.26826e7	−	3.92875e7i	−0.482139	−	0.835089i
$362$		0			0
$363$		−	1.34802e7i		−	0.281823i
$364$		0			0
$365$	4.52548e6			0.0930649
$366$		0			0
$367$	8.33088e7	−	4.80984e7i	1.68536	−	0.973043i	0.727368	−	0.686248i	$-0.240743\pi$
$367$	8.33088e7	−	4.80984e7i	1.68536	−	0.973043i	0.957992	−	0.286795i	$-0.0925899\pi$
$368$		0			0
$369$	1.26466e7	+	7.30154e6i	0.251707	+	0.145323i
$370$		0			0
$371$	2.38023e7	−	3.81441e7i	0.466118	−	0.746974i
$372$		0			0
$373$	−4.63224e6	+	8.02328e6i	−0.0892616	+	0.154606i	−0.907199	−	0.420701i	$-0.861784\pi$
$373$	−4.63224e6	+	8.02328e6i	−0.0892616	+	0.154606i	0.817938	+	0.575307i	$0.195117\pi$
$374$		0			0
$375$	1.28749e7	+	2.23000e7i	0.244146	+	0.422873i
$376$		0			0
$377$		−	4.24426e7i		−	0.792096i
$378$		0			0
$379$	−2.76771e7			−0.508396			−0.254198	−	0.967152i	$-0.581812\pi$
$379$	−2.76771e7			−0.508396			−0.254198	+	0.967152i	$0.581812\pi$
$380$		0			0
$381$	−4.08239e7	+	2.35697e7i	−0.738142	+	0.426167i
$382$		0			0
$383$	−3.28931e7	−	1.89908e7i	−0.585475	−	0.338024i	0.177831	−	0.984061i	$-0.443092\pi$
$383$	−3.28931e7	−	1.89908e7i	−0.585475	−	0.338024i	−0.763306	+	0.646037i	$0.776425\pi$
$384$		0			0
$385$	−1.71974e7	+	9.15770e6i	−0.301357	+	0.160474i
$386$		0			0
$387$	−1.46909e7	+	2.54454e7i	−0.253464	+	0.439012i
$388$		0			0
$389$	−3.68009e7	−	6.37410e7i	−0.625187	−	1.08286i	−0.988505	−	0.151190i	$-0.951689\pi$
$389$	−3.68009e7	−	6.37410e7i	−0.625187	−	1.08286i	0.363318	−	0.931665i	$-0.381644\pi$
$390$		0			0
$391$			4.56892e7i			0.764334i
$392$		0			0
$393$	−2.94627e7			−0.485394
$394$		0			0
$395$	3.61521e7	−	2.08724e7i	0.586600	−	0.338674i
$396$		0			0
$397$	−3.44400e7	−	1.98839e7i	−0.550416	−	0.317783i	0.198873	−	0.980025i	$-0.436272\pi$
$397$	−3.44400e7	−	1.98839e7i	−0.550416	−	0.317783i	−0.749290	+	0.662242i	$0.769605\pi$
$398$		0			0
$399$	3.25795e6	+	6.11818e6i	0.0512893	+	0.0963171i
$400$		0			0
$401$	3.88807e7	−	6.73434e7i	0.602977	−	1.04439i	−0.389390	−	0.921073i	$-0.627314\pi$
$401$	3.88807e7	−	6.73434e7i	0.602977	−	1.04439i	0.992368	−	0.123315i	$-0.0393524\pi$
$402$		0			0
$403$	2.97802e7	+	5.15808e7i	0.455001	+	0.788085i
$404$		0			0
$405$			3.52236e6i			0.0530235i
$406$		0			0
$407$	2.89608e7			0.429563
$408$		0			0
$409$	−8.43664e7	+	4.87089e7i	−1.23310	+	0.711932i	−0.967676	−	0.252198i	$-0.918846\pi$
$409$	−8.43664e7	+	4.87089e7i	−1.23310	+	0.711932i	−0.265428	+	0.964131i	$0.585513\pi$
$410$		0			0
$411$	−5.86881e7	−	3.38836e7i	−0.845327	−	0.488050i
$412$		0			0
$413$	5.06643e7	+	3.16149e7i	0.719203	+	0.448789i
$414$		0			0
$415$	−8.88918e6	+	1.53965e7i	−0.124370	+	0.215416i
$416$		0			0
$417$	1.51830e7	+	2.62977e7i	0.209386	+	0.362668i
$418$		0			0
$419$			3.94345e7i			0.536085i	0.963407	+	0.268043i	$0.0863768\pi$
$419$			3.94345e7i			0.536085i	−0.963407	+	0.268043i	$0.913623\pi$
$420$		0			0
$421$	−1.00001e8			−1.34017			−0.670084	−	0.742285i	$-0.733742\pi$
$421$	−1.00001e8			−1.34017			−0.670084	+	0.742285i	$0.733742\pi$
$422$		0			0
$423$	−3.54652e6	+	2.04758e6i	−0.0468577	+	0.0270533i
$424$		0			0
$425$	3.57931e7	+	2.06652e7i	0.466265	+	0.269198i
$426$		0			0
$427$	4.12312e6	−	1.20205e8i	0.0529594	−	1.54397i
$428$		0			0
$429$	1.50159e7	−	2.60083e7i	0.190187	−	0.329413i
$430$		0			0
$431$	6.94696e7	+	1.20325e8i	0.867686	+	1.50288i	0.864355	+	0.502882i	$0.167727\pi$
$431$	6.94696e7	+	1.20325e8i	0.867686	+	1.50288i	0.00333146	+	0.999994i	$0.498940\pi$
$432$		0			0
$433$			7.72315e7i			0.951329i	0.879627	+	0.475664i	$0.157792\pi$
$433$			7.72315e7i			0.951329i	−0.879627	+	0.475664i	$0.842208\pi$
$434$		0			0
$435$	−1.95076e7			−0.236993
$436$		0			0
$437$	−1.49760e7	+	8.64642e6i	−0.179454	+	0.103608i
$438$		0			0
$439$	8.58013e7	+	4.95374e7i	1.01415	+	0.585518i	0.912403	−	0.409293i	$-0.134225\pi$
$439$	8.58013e7	+	4.95374e7i	1.01415	+	0.585518i	0.101743	+	0.994811i	$0.467558\pi$
$440$		0			0
$441$	1.25643e7	+	2.56798e7i	0.146495	+	0.299417i
$442$		0			0
$443$	−3.94690e7	+	6.83622e7i	−0.453988	+	0.786330i	−0.998629	−	0.0523386i	$-0.983332\pi$
$443$	−3.94690e7	+	6.83622e7i	−0.453988	+	0.786330i	0.544641	+	0.838669i	$0.316666\pi$
$444$		0			0
$445$	−6.58323e6	−	1.14025e7i	−0.0747066	−	0.129396i
$446$		0			0
$447$			8.72586e7i			0.976980i
$448$		0			0
$449$	1.39364e8			1.53962			0.769809	−	0.638275i	$-0.220352\pi$
$449$	1.39364e8			1.53962			0.769809	+	0.638275i	$0.220352\pi$
$450$		0			0
$451$	−4.95594e7	+	2.86131e7i	−0.540252	+	0.311914i
$452$		0			0
$453$	−7.69748e6	−	4.44414e6i	−0.0828046	−	0.0478072i
$454$		0			0
$455$	4.13696e7	+	1.41901e6i	0.439185	+	0.0150644i
$456$		0			0
$457$	−1.00446e6	+	1.73978e6i	−0.0105241	+	0.0182283i	−0.871240	−	0.490858i	$-0.836683\pi$
$457$	−1.00446e6	+	1.73978e6i	−0.0105241	+	0.0182283i	0.860715	+	0.509086i	$0.170017\pi$
$458$		0			0
$459$	6.48724e6	+	1.12362e7i	0.0670844	+	0.116194i
$460$		0			0
$461$			4.19744e7i			0.428431i	0.976786	+	0.214216i	$0.0687196\pi$
$461$			4.19744e7i			0.428431i	−0.976786	+	0.214216i	$0.931280\pi$
$462$		0			0
$463$	4.15795e6			0.0418925			0.0209463	−	0.999781i	$-0.493332\pi$
$463$	4.15795e6			0.0418925			0.0209463	+	0.999781i	$0.493332\pi$
$464$		0			0
$465$	2.37077e7	−	1.36877e7i	0.235793	−	0.136135i
$466$		0			0
$467$	−1.23857e8	−	7.15087e7i	−1.21610	−	0.702115i	−0.252018	−	0.967723i	$-0.581094\pi$
$467$	−1.23857e8	−	7.15087e7i	−1.21610	−	0.702115i	−0.964081	+	0.265608i	$0.914427\pi$
$468$		0			0
$469$	−6.18710e7	+	9.91508e7i	−0.599747	+	0.961120i
$470$		0			0
$471$	−1.80668e7	+	3.12927e7i	−0.172910	+	0.299489i
$472$		0			0
$473$	−5.75704e7	−	9.97149e7i	−0.544021	−	0.942273i
$474$		0			0
$475$			1.56431e7i			0.145962i
$476$		0			0
$477$	3.18531e7			0.293492
$478$		0			0
$479$	5.32093e7	−	3.07204e7i	0.484151	−	0.279525i	−0.237994	−	0.971267i	$-0.576490\pi$
$479$	5.32093e7	−	3.07204e7i	0.484151	−	0.279525i	0.722145	+	0.691742i	$0.243156\pi$
$480$		0			0
$481$	−5.32852e7	−	3.07642e7i	−0.478819	−	0.276446i
$482$		0			0
$483$	−6.29538e7	+	3.35232e7i	−0.558703	+	0.297511i
$484$		0			0
$485$	2.56361e7	−	4.44030e7i	0.224712	−	0.389213i
$486$		0			0
$487$	2.49050e7	+	4.31367e7i	0.215625	+	0.373474i	0.953466	−	0.301501i	$-0.0974877\pi$
$487$	2.49050e7	+	4.31367e7i	0.215625	+	0.373474i	−0.737841	+	0.674975i	$0.764154\pi$
$488$		0			0
$489$			3.93688e7i			0.336686i
$490$		0			0
$491$	−1.93555e8			−1.63516			−0.817578	−	0.575818i	$-0.804684\pi$
$491$	−1.93555e8			−1.63516			−0.817578	+	0.575818i	$0.804684\pi$
$492$		0			0
$493$	−6.22287e7	+	3.59277e7i	−0.519338	+	0.299840i
$494$		0			0
$495$	−1.19540e7	−	6.90166e6i	−0.0985596	−	0.0569034i
$496$		0			0
$497$	6.06829e7	+	1.13958e8i	0.494307	+	0.928269i
$498$		0			0
$499$	4.89086e7	−	8.47121e7i	0.393626	−	0.681780i	−0.599299	−	0.800525i	$-0.704554\pi$
$499$	4.89086e7	−	8.47121e7i	0.393626	−	0.681780i	0.992925	+	0.118746i	$0.0378873\pi$
$500$		0			0
$501$	2.51252e7	+	4.35182e7i	0.199801	+	0.346065i
$502$		0			0
$503$		−	1.48399e8i		−	1.16608i	−0.812445	−	0.583038i	$-0.801864\pi$
$503$		−	1.48399e8i		−	1.16608i	0.812445	−	0.583038i	$-0.198136\pi$
$504$		0			0
$505$	2.19923e7			0.170764
$506$		0			0
$507$	9.90611e6	−	5.71930e6i	0.0760115	−	0.0438853i
$508$		0			0
$509$	−1.07313e7	−	6.19571e6i	−0.0813764	−	0.0469827i	0.458760	−	0.888560i	$-0.348294\pi$
$509$	−1.07313e7	−	6.19571e6i	−0.0813764	−	0.0469827i	−0.540136	+	0.841578i	$0.681627\pi$
$510$		0			0
$511$	2.20763e7	+	1.37758e7i	0.165449	+	0.103241i
$512$		0			0
$513$	−2.45534e6	+	4.25278e6i	−0.0181870	+	0.0315008i
$514$		0			0
$515$	−2.59807e7	−	4.49999e7i	−0.190208	−	0.329450i
$516$		0			0
$517$		−	1.60481e7i		−	0.116132i
$518$		0			0
$519$	−1.47216e8			−1.05306
$520$		0			0
$521$	−7.59336e7	+	4.38403e7i	−0.536934	+	0.309999i	−0.743835	−	0.668363i	$-0.766995\pi$
$521$	−7.59336e7	+	4.38403e7i	−0.536934	+	0.309999i	0.206902	+	0.978362i	$0.433662\pi$
$522$		0			0
$523$	−1.55132e8	−	8.95655e7i	−1.08442	−	0.626089i	−0.152333	−	0.988329i	$-0.548679\pi$
$523$	−1.55132e8	−	8.95655e7i	−1.08442	−	0.626089i	−0.932085	+	0.362240i	$0.882012\pi$
$524$		0			0
$525$	−2.21174e6	+	6.44809e7i	−0.0152847	+	0.445608i
$526$		0			0
$527$	5.04180e7	−	8.73266e7i	0.344472	−	0.596643i
$528$		0			0
$529$	−1.49506e7	−	2.58951e7i	−0.100993	−	0.174925i
$530$		0			0
$531$			4.23083e7i			0.282580i
$532$		0			0
$533$	1.21579e8			0.802932
$534$		0			0
$535$	3.09516e7	−	1.78699e7i	0.202126	−	0.116697i
$536$		0			0
$537$	5.15258e7	+	2.97484e7i	0.332738	+	0.192106i
$538$		0			0
$539$	−1.11769e8	−	7.67658e6i	−0.713768	−	0.0490232i
$540$		0			0
$541$	−5.99024e7	+	1.03754e8i	−0.378314	+	0.655259i	−0.990817	−	0.135209i	$-0.956829\pi$
$541$	−5.99024e7	+	1.03754e8i	−0.378314	+	0.655259i	0.612503	+	0.790468i	$0.290163\pi$
$542$		0			0
$543$	2.15844e7	+	3.73853e7i	0.134816	+	0.233508i
$544$		0			0
$545$		−	2.09394e7i		−	0.129352i
$546$		0			0
$547$	−3.04795e8			−1.86228			−0.931141	−	0.364660i	$-0.881185\pi$
$547$	−3.04795e8			−1.86228			−0.931141	+	0.364660i	$0.881185\pi$
$548$		0			0
$549$	7.37940e7	−	4.26050e7i	0.445968	−	0.257480i
$550$		0			0
$551$	−2.35528e7	−	1.35982e7i	−0.140795	−	0.0812883i
$552$		0			0
$553$	2.39895e8	+	8.22857e6i	1.41855	+	0.0486574i
$554$		0			0
$555$	−1.41399e7	+	2.44911e7i	−0.0827120	+	0.143261i
$556$		0			0
$557$	−2.29772e7	−	3.97977e7i	−0.132963	−	0.230299i	0.791854	−	0.610710i	$-0.209116\pi$
$557$	−2.29772e7	−	3.97977e7i	−0.132963	−	0.230299i	−0.924818	+	0.380411i	$0.875783\pi$
$558$		0			0
$559$			2.44622e8i			1.40042i
$560$		0			0
$561$	−5.08441e7			−0.287973
$562$		0			0
$563$	−1.18383e8	+	6.83486e7i	−0.663384	+	0.383005i	−0.793565	−	0.608485i	$-0.791778\pi$
$563$	−1.18383e8	+	6.83486e7i	−0.663384	+	0.383005i	0.130181	+	0.991490i	$0.458444\pi$
$564$		0			0
$565$	4.68791e7	+	2.70657e7i	0.259917	+	0.150063i
$566$		0			0
$567$	−1.07222e7	+	1.71828e7i	−0.0588216	+	0.0942640i
$568$		0			0
$569$	8.16814e7	−	1.41476e8i	0.443391	−	0.767975i	−0.554548	−	0.832152i	$-0.687109\pi$
$569$	8.16814e7	−	1.41476e8i	0.443391	−	0.767975i	0.997939	+	0.0641767i	$0.0204421\pi$
$570$		0			0
$571$	4.06619e7	+	7.04285e7i	0.218413	+	0.378303i	0.954323	−	0.298777i	$-0.0965785\pi$
$571$	4.06619e7	+	7.04285e7i	0.218413	+	0.378303i	−0.735910	+	0.677080i	$0.763245\pi$
$572$		0			0
$573$			1.09846e7i			0.0583877i
$574$		0			0
$575$	−1.60961e8			−0.846678
$576$		0			0
$577$	−3.20448e8	+	1.85011e8i	−1.66813	+	0.963096i	−0.699486	+	0.714646i	$0.746588\pi$
$577$	−3.20448e8	+	1.85011e8i	−1.66813	+	0.963096i	−0.968645	+	0.248450i	$0.920079\pi$
$578$		0			0
$579$	−4.98600e7	−	2.87867e7i	−0.256872	−	0.148305i
$580$		0			0
$581$	−9.02312e7	+	4.80485e7i	−0.460075	+	0.244992i
$582$		0			0
$583$	−6.24125e7	+	1.08102e8i	−0.314968	+	0.545540i
$584$		0			0
$585$	1.46629e7	+	2.53968e7i	0.0732405	+	0.126856i
$586$		0			0
$587$		−	2.78706e7i		−	0.137794i	−0.997624	−	0.0688972i	$-0.978052\pi$
$587$		−	2.78706e7i		−	0.137794i	0.997624	−	0.0688972i	$-0.0219480\pi$
$588$		0			0
$589$	3.81653e7			0.186777
$590$		0			0
$591$	1.04817e8	−	6.05164e7i	0.507775	−	0.293164i
$592$		0			0
$593$	6.32941e7	+	3.65429e7i	0.303528	+	0.175242i	0.644027	−	0.765003i	$-0.277262\pi$
$593$	6.32941e7	+	3.65429e7i	0.303528	+	0.175242i	−0.340499	+	0.940245i	$0.610596\pi$
$594$		0			0
$595$	−3.29390e7	−	6.18567e7i	−0.156372	−	0.293654i
$596$		0			0
$597$	−2.62279e7	+	4.54281e7i	−0.123265	+	0.213502i
$598$		0			0
$599$	4.30143e7	+	7.45030e7i	0.200139	+	0.346651i	0.948573	−	0.316558i	$-0.102527\pi$
$599$	4.30143e7	+	7.45030e7i	0.200139	+	0.346651i	−0.748434	+	0.663209i	$0.769194\pi$
$600$		0			0
$601$			2.16837e8i			0.998874i	0.866350	+	0.499437i	$0.166460\pi$
$601$			2.16837e8i			0.998874i	−0.866350	+	0.499437i	$0.833540\pi$
$602$		0			0
$603$	−8.27980e7			−0.377631
$604$		0			0
$605$	−4.46730e7	+	2.57920e7i	−0.201734	+	0.116471i
$606$		0			0
$607$	2.82213e8	+	1.62936e8i	1.26186	+	0.728534i	0.973434	−	0.228969i	$-0.0735354\pi$
$607$	2.82213e8	+	1.62936e8i	1.26186	+	0.728534i	0.288424	+	0.957503i	$0.406869\pi$
$608$		0			0
$609$	−9.51624e7	−	5.93822e7i	−0.421321	−	0.262908i
$610$		0			0
$611$	−1.70474e7	+	2.95269e7i	−0.0747367	+	0.129448i
$612$		0			0
$613$	−1.45053e8	−	2.51240e8i	−0.629718	−	1.09070i	−0.987608	−	0.156940i	$-0.949837\pi$
$613$	−1.45053e8	−	2.51240e8i	−0.629718	−	1.09070i	0.357890	−	0.933764i	$-0.383496\pi$
$614$		0			0
$615$		−	5.58807e7i		−	0.240235i
$616$		0			0
$617$	−3.10620e8			−1.32243			−0.661217	−	0.750195i	$-0.729960\pi$
$617$	−3.10620e8			−1.32243			−0.661217	+	0.750195i	$0.729960\pi$
$618$		0			0
$619$	1.78106e8	−	1.02829e8i	0.750941	−	0.433556i	−0.0750926	−	0.997177i	$-0.523925\pi$
$619$	1.78106e8	−	1.02829e8i	0.750941	−	0.433556i	0.826034	+	0.563620i	$0.190592\pi$
$620$		0			0
$621$	−4.37596e7	−	2.52646e7i	−0.182725	−	0.105496i
$622$		0			0
$623$	2.59532e6	−	7.56636e7i	0.0107331	−	0.312912i
$624$		0			0
$625$	−4.50036e7	+	7.79485e7i	−0.184335	+	0.319277i
$626$		0			0
$627$	−9.62195e6	−	1.66657e7i	−0.0390356	−	0.0676116i
$628$		0			0
$629$			1.04168e8i			0.418583i
$630$		0			0
$631$	−2.51762e8			−1.00208			−0.501039	−	0.865425i	$-0.667049\pi$
$631$	−2.51762e8			−1.00208			−0.501039	+	0.865425i	$0.667049\pi$
$632$		0			0
$633$	−2.06385e8	+	1.19156e8i	−0.813705	+	0.469793i
$634$		0			0
$635$	1.56219e8	+	9.01928e7i	0.610115	+	0.352250i
$636$		0			0
$637$	1.97491e8	+	1.32854e8i	0.764062	+	0.513991i
$638$		0			0
$639$	−4.57334e7	+	7.92126e7i	−0.175279	+	0.303593i
$640$		0			0
$641$	−8.61512e7	−	1.49218e8i	−0.327105	−	0.566562i	0.654831	−	0.755775i	$-0.272740\pi$
$641$	−8.61512e7	−	1.49218e8i	−0.327105	−	0.566562i	−0.981936	+	0.189213i	$0.939406\pi$
$642$		0			0
$643$			2.98599e8i			1.12319i	0.827411	+	0.561597i	$0.189813\pi$
$643$			2.98599e8i			1.12319i	−0.827411	+	0.561597i	$0.810187\pi$
$644$		0			0
$645$	1.12434e8			0.419003
$646$		0			0
$647$	3.71972e8	−	2.14758e8i	1.37340	−	0.792933i	0.382046	−	0.924143i	$-0.375220\pi$
$647$	3.71972e8	−	2.14758e8i	1.37340	−	0.792933i	0.991355	+	0.131210i	$0.0418864\pi$
$648$		0			0
$649$	−1.43584e8	−	8.28984e7i	−0.525258	−	0.303258i
$650$		0			0
$651$	1.57318e8	+	5.39611e6i	0.570210	+	0.0195586i
$652$		0			0
$653$	1.40453e8	−	2.43271e8i	0.504418	−	0.873678i	−0.495568	−	0.868569i	$-0.665040\pi$
$653$	1.40453e8	−	2.43271e8i	0.504418	−	0.873678i	0.999987	−	0.00510957i	$-0.00162643\pi$
$654$		0			0
$655$	5.63716e7	+	9.76384e7i	0.200602	+	0.347454i
$656$		0			0
$657$			1.84353e7i			0.0650061i
$658$		0			0
$659$	−1.21155e8			−0.423337			−0.211668	−	0.977342i	$-0.567890\pi$
$659$	−1.21155e8			−0.423337			−0.211668	+	0.977342i	$0.567890\pi$
$660$		0			0
$661$	3.52336e8	−	2.03421e8i	1.21998	−	0.704355i	0.255065	−	0.966924i	$-0.417903\pi$
$661$	3.52336e8	−	2.03421e8i	1.21998	−	0.704355i	0.964913	+	0.262569i	$0.0845697\pi$
$662$		0			0
$663$	9.35484e7	+	5.40102e7i	0.320993	+	0.185325i
$664$		0			0
$665$	1.40419e7	−	2.25028e7i	0.0477488	−	0.0765194i
$666$		0			0
$667$	1.39921e8	−	2.42350e8i	0.471526	−	0.816706i
$668$		0			0
$669$	−9.74900e6	−	1.68858e7i	−0.0325598	−	0.0563953i
$670$		0			0
$671$			3.33919e8i			1.10528i
$672$		0			0
$673$	−1.33935e8			−0.439389			−0.219694	−	0.975569i	$-0.570506\pi$
$673$	−1.33935e8			−0.439389			−0.219694	+	0.975569i	$0.570506\pi$
$674$		0			0
$675$	−3.95848e7	+	2.28543e7i	−0.128712	+	0.0743117i
$676$		0			0
$677$	−1.80599e6	−	1.04269e6i	−0.00582037	−	0.00336039i	0.497087	−	0.867701i	$-0.334403\pi$
$677$	−1.80599e6	−	1.04269e6i	−0.00582037	−	0.00336039i	−0.502907	+	0.864340i	$0.667736\pi$
$678$		0			0
$679$	2.60224e8	−	1.38570e8i	0.831262	−	0.442650i
$680$		0			0
$681$	1.74361e8	−	3.02002e8i	0.552088	−	0.956244i
$682$		0			0
$683$	−1.09208e8	−	1.89154e8i	−0.342761	−	0.593680i	0.642183	−	0.766551i	$-0.278029\pi$
$683$	−1.09208e8	−	1.89154e8i	−0.342761	−	0.593680i	−0.984944	+	0.172871i	$0.944696\pi$
$684$		0			0
$685$			2.59321e8i			0.806800i
$686$		0			0
$687$	1.68170e8			0.518655
$688$		0			0
$689$	2.29667e8	−	1.32598e8i	0.702166	−	0.405396i
$690$		0			0
$691$	−2.42471e8	−	1.39990e8i	−0.734894	−	0.424291i	0.0853156	−	0.996354i	$-0.472810\pi$
$691$	−2.42471e8	−	1.39990e8i	−0.734894	−	0.424291i	−0.820210	+	0.572062i	$0.806143\pi$
$692$		0			0
$693$	−3.73054e7	−	7.00566e7i	−0.112091	−	0.210499i
$694$		0			0
$695$	5.80997e7	−	1.00632e8i	0.173069	−	0.299765i
$696$		0			0
$697$	−1.02917e8	−	1.78258e8i	−0.303942	−	0.526442i
$698$		0			0
$699$		−	5.58791e7i		−	0.163613i
$700$		0			0
$701$	−4.39447e8			−1.27571			−0.637856	−	0.770155i	$-0.720179\pi$
$701$	−4.39447e8			−1.27571			−0.637856	+	0.770155i	$0.720179\pi$
$702$		0			0
$703$	−3.41442e7	+	1.97132e7i	−0.0982769	+	0.0567402i
$704$		0			0
$705$	1.35713e7	+	7.83537e6i	0.0387305	+	0.0223610i
$706$		0			0
$707$	1.07283e8	+	6.69456e7i	0.303580	+	0.189437i
$708$		0			0
$709$	9.66919e7	−	1.67475e8i	0.271301	−	0.469907i	−0.697894	−	0.716201i	$-0.745879\pi$
$709$	9.66919e7	−	1.67475e8i	0.271301	−	0.469907i	0.969195	+	0.246294i	$0.0792128\pi$
$710$		0			0
$711$	8.50273e7	+	1.47272e8i	0.236564	+	0.409742i
$712$		0			0
$713$			3.92707e8i			1.08343i
$714$		0			0
$715$	−1.14921e8			−0.314399
$716$		0			0
$717$	−1.70265e8	+	9.83028e7i	−0.461923	+	0.266691i
$718$		0			0
$719$	2.89846e8	+	1.67343e8i	0.779796	+	0.450215i	0.836358	−	0.548184i	$-0.184680\pi$
$719$	2.89846e8	+	1.67343e8i	0.779796	+	0.450215i	−0.0565619	+	0.998399i	$0.518014\pi$
$720$		0			0
$721$	1.02424e7	−	2.98606e8i	0.0273273	−	0.796697i
$722$		0			0
$723$	1.83029e8	−	3.17015e8i	0.484289	−	0.838813i
$724$		0			0
$725$	−1.26572e8	−	2.19230e8i	−0.332143	−	0.575288i
$726$		0			0
$727$		−	2.53706e8i		−	0.660278i	−0.943932	−	0.330139i	$-0.892904\pi$
$727$		−	2.53706e8i		−	0.660278i	0.943932	−	0.330139i	$-0.107096\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	3.58660e8	−	2.07073e8i	0.918187	−	0.530116i
$732$		0			0
$733$	2.31716e8	+	1.33781e8i	0.588362	+	0.339691i	0.764450	−	0.644684i	$-0.223011\pi$
$733$	2.31716e8	+	1.33781e8i	0.588362	+	0.339691i	−0.176088	+	0.984374i	$0.556344\pi$
$734$		0			0
$735$	6.10626e7	−	9.07713e7i	0.153785	−	0.228605i
$736$		0			0
$737$	1.62234e8	−	2.80997e8i	0.405264	−	0.701938i
$738$		0			0
$739$	−1.31477e8	−	2.27725e8i	−0.325774	−	0.564258i	0.655894	−	0.754853i	$-0.272292\pi$
$739$	−1.31477e8	−	2.27725e8i	−0.325774	−	0.564258i	−0.981669	+	0.190595i	$0.938958\pi$
$740$		0			0
$741$			4.08845e7i			0.100486i
$742$		0			0
$743$	3.98060e8			0.970471			0.485235	−	0.874384i	$-0.338734\pi$
$743$	3.98060e8			0.970471			0.485235	+	0.874384i	$0.338734\pi$
$744$		0			0
$745$	2.89172e8	−	1.66954e8i	0.699339	−	0.403763i
$746$		0			0
$747$	−6.27203e7	−	3.62116e7i	−0.150469	−	0.0868731i
$748$		0			0
$749$	2.05386e8	+	7.04489e6i	0.488793	+	0.0167660i
$750$		0			0
$751$	1.69338e8	−	2.93301e8i	0.399791	−	0.692459i	−0.593909	−	0.804533i	$-0.702416\pi$
$751$	1.69338e8	−	2.93301e8i	0.399791	−	0.692459i	0.993700	+	0.112074i	$0.0357493\pi$
$752$		0			0
$753$	−1.16676e8	−	2.02089e8i	−0.273274	−	0.473324i
$754$		0			0
$755$			3.40123e7i			0.0790305i
$756$		0			0
$757$	5.64318e8			1.30088			0.650439	−	0.759558i	$-0.274585\pi$
$757$	5.64318e8			1.30088			0.650439	+	0.759558i	$0.274585\pi$
$758$		0			0
$759$	1.71484e8	−	9.90064e7i	0.392192	−	0.226432i
$760$		0			0
$761$	1.33173e8	+	7.68874e7i	0.302177	+	0.174462i	0.643421	−	0.765513i	$-0.277515\pi$
$761$	1.33173e8	+	7.68874e7i	0.302177	+	0.174462i	−0.341243	+	0.939975i	$0.610848\pi$
$762$		0			0
$763$	6.37407e7	−	1.02147e8i	0.143497	−	0.229960i
$764$		0			0
$765$	2.48243e7	−	4.29970e7i	0.0554489	−	0.0960403i
$766$		0			0
$767$	1.76121e8	+	3.05051e8i	0.390324	+	0.676061i
$768$		0			0
$769$		−	4.55265e8i		−	1.00112i	−0.865702	−	0.500559i	$-0.833128\pi$
$769$		−	4.55265e8i		−	1.00112i	0.865702	−	0.500559i	$-0.166872\pi$
$770$		0			0
$771$	1.95161e8			0.425823
$772$		0			0
$773$	−6.77780e8	+	3.91316e8i	−1.46741	+	0.847207i	−0.999334	−	0.0364834i	$-0.988384\pi$
$773$	−6.77780e8	+	3.91316e8i	−1.46741	+	0.847207i	−0.468072	+	0.883691i	$0.655051\pi$
$774$		0			0
$775$	3.07649e8	+	1.77621e8i	0.660922	+	0.381583i
$776$		0			0
$777$	−1.43530e8	+	7.64303e7i	−0.305971	+	0.162931i
$778$		0			0
$779$	3.89530e7	−	6.74686e7i	0.0824003	−	0.142722i
$780$		0			0
$781$	−1.79219e8	−	3.10416e8i	−0.376211	−	0.651616i
$782$		0			0
$783$		−	7.94674e7i		−	0.165540i
$784$		0			0
$785$	1.38271e8			0.285839
$786$		0			0
$787$	−3.54827e8	+	2.04859e8i	−0.727934	+	0.420273i	−0.817666	−	0.575693i	$-0.804732\pi$
$787$	−3.54827e8	+	2.04859e8i	−0.727934	+	0.420273i	0.0897316	+	0.995966i	$0.471399\pi$
$788$		0			0
$789$	6.43565e7	+	3.71563e7i	0.131027	+	0.0756486i
$790$		0			0
$791$	1.46298e8	+	2.74735e8i	0.295602	+	0.555117i
$792$		0			0
$793$	3.54712e8	−	6.14379e8i	0.711306	−	1.23202i
$794$		0			0
$795$	−6.09451e7	−	1.05560e8i	−0.121293	−	0.210086i
$796$		0			0
$797$			7.29987e8i			1.44192i	0.692979	+	0.720958i	$0.256298\pi$
$797$			7.29987e8i			1.44192i	−0.692979	+	0.720958i	$0.743702\pi$
$798$		0			0
$799$	5.77226e7			0.113163
$800$		0			0
$801$	4.64499e7	−	2.68179e7i	0.0903832	−	0.0521828i
$802$		0			0
$803$	−6.25650e7	−	3.61219e7i	−0.120833	−	0.0697628i
$804$		0			0
$805$	2.31546e8	+	1.44486e8i	0.443863	+	0.276974i
$806$		0			0
$807$	1.22352e8	−	2.11919e8i	0.232803	−	0.403227i
$808$		0			0
$809$	3.45501e8	+	5.98426e8i	0.652535	+	1.13022i	0.982506	+	0.186233i	$0.0596280\pi$
$809$	3.45501e8	+	5.98426e8i	0.652535	+	1.13022i	−0.329970	+	0.943991i	$0.607039\pi$
$810$		0			0
$811$			7.51873e8i			1.40955i	0.709429	+	0.704777i	$0.248953\pi$
$811$			7.51873e8i			1.40955i	−0.709429	+	0.704777i	$0.751047\pi$
$812$		0			0
$813$	−3.13151e8			−0.582750
$814$		0			0
$815$	1.30467e8	−	7.53250e7i	0.241006	−	0.139145i
$816$		0			0
$817$	1.35749e8	+	7.83747e7i	0.248926	+	0.143717i
$818$		0			0
$819$	−5.78057e6	+	1.68526e8i	−0.0105225	+	0.306772i
$820$		0			0
$821$	1.48378e6	−	2.56999e6i	0.00268128	−	0.00464411i	−0.864682	−	0.502320i	$-0.832480\pi$
$821$	1.48378e6	−	2.56999e6i	0.00268128	−	0.00464411i	0.867363	+	0.497676i	$0.165813\pi$
$822$		0			0
$823$	−4.34709e8	−	7.52938e8i	−0.779828	−	1.35070i	−0.932041	−	0.362354i	$-0.881973\pi$
$823$	−4.34709e8	−	7.52938e8i	−0.779828	−	1.35070i	0.152212	−	0.988348i	$-0.451360\pi$
$824$		0			0
$825$		−	1.79122e8i		−	0.318997i
$826$		0			0
$827$	−1.69939e8			−0.300452			−0.150226	−	0.988652i	$-0.548000\pi$
$827$	−1.69939e8			−0.300452			−0.150226	+	0.988652i	$0.548000\pi$
$828$		0			0
$829$	8.47570e8	−	4.89345e8i	1.48769	−	0.858917i	0.487787	−	0.872963i	$-0.337804\pi$
$829$	8.47570e8	−	4.89345e8i	1.48769	−	0.858917i	0.999901	+	0.0140454i	$0.00447093\pi$
$830$		0			0
$831$	−1.14853e8	−	6.63105e7i	−0.200143	−	0.115552i
$832$		0			0
$833$	2.76116e7	−	4.02019e8i	0.0477701	−	0.695523i
$834$		0			0
$835$	9.61452e7	−	1.66528e8i	0.165146	−	0.286041i
$836$		0			0
$837$	5.57590e7	+	9.65774e7i	0.0950908	+	0.164702i
$838$		0			0
$839$			8.21112e8i			1.39032i	0.718853	+	0.695162i	$0.244668\pi$
$839$			8.21112e8i			1.39032i	−0.718853	+	0.695162i	$0.755332\pi$
$840$		0			0
$841$	−1.54715e8			−0.260103
$842$		0			0
$843$	9.32143e7	−	5.38173e7i	0.155596	−	0.0898337i
$844$		0			0
$845$	−3.79071e7	−	2.18857e7i	−0.0628276	−	0.0362736i
$846$		0			0
$847$	−2.96437e8	−	1.01680e7i	−0.487846	−	0.0167335i
$848$		0			0
$849$	2.06506e7	−	3.57678e7i	0.0337450	−	0.0584480i
$850$		0			0
$851$	−2.02841e8	−	3.51332e8i	−0.329130	−	0.570071i
$852$		0			0
$853$		−	8.68534e7i		−	0.139939i	−0.997549	−	0.0699696i	$-0.977710\pi$
$853$		−	8.68534e7i		−	0.139939i	0.997549	−	0.0699696i	$-0.0222902\pi$
$854$		0			0
$855$	1.87914e7			0.0300650
$856$		0			0
$857$	7.72814e7	−	4.46184e7i	0.122781	−	0.0708879i	−0.437351	−	0.899291i	$-0.644083\pi$
$857$	7.72814e7	−	4.46184e7i	0.122781	−	0.0708879i	0.560133	+	0.828403i	$0.310750\pi$
$858$		0			0
$859$	−1.27107e8	−	7.33852e7i	−0.200535	−	0.115779i	0.396370	−	0.918091i	$-0.370270\pi$
$859$	−1.27107e8	−	7.33852e7i	−0.200535	−	0.115779i	−0.596905	+	0.802312i	$0.703603\pi$
$860$		0			0
$861$	1.70104e8	−	2.72599e8i	0.266505	−	0.427085i
$862$		0			0
$863$	9.79242e7	−	1.69610e8i	0.152355	−	0.263887i	−0.779738	−	0.626107i	$-0.784647\pi$
$863$	9.79242e7	−	1.69610e8i	0.152355	−	0.263887i	0.932093	+	0.362219i	$0.117981\pi$
$864$		0			0
$865$	2.81671e8	+	4.87868e8i	0.435205	+	0.753797i
$866$		0			0
$867$			1.93389e8i			0.296738i
$868$		0			0
$869$	−6.66406e8			−1.01550
$870$		0			0
$871$	−5.96989e8	+	3.44672e8i	−0.903467	+	0.521617i
$872$		0			0
$873$	1.80883e8	+	1.04433e8i	0.271866	+	0.156962i
$874$		0			0
$875$	5.00100e8	−	2.66305e8i	0.746504	−	0.397517i
$876$		0			0
$877$	−4.25970e7	+	7.37801e7i	−0.0631509	+	0.109381i	−0.895872	−	0.444312i	$-0.853448\pi$
$877$	−4.25970e7	+	7.37801e7i	−0.0631509	+	0.109381i	0.832721	+	0.553692i	$0.186782\pi$
$878$		0			0
$879$	−2.90566e8	−	5.03275e8i	−0.427837	−	0.741035i
$880$		0			0
$881$			3.32013e8i			0.485543i	0.970084	+	0.242771i	$0.0780565\pi$
$881$			3.32013e8i			0.485543i	−0.970084	+	0.242771i	$0.921943\pi$
$882$		0			0
$883$	−8.83118e8			−1.28273			−0.641367	−	0.767234i	$-0.721633\pi$
$883$	−8.83118e8			−1.28273			−0.641367	+	0.767234i	$0.721633\pi$
$884$		0			0
$885$	1.40208e8	−	8.09493e7i	0.202276	−	0.116784i
$886$		0			0
$887$	−1.10590e9	−	6.38492e8i	−1.58469	−	0.914923i	−0.994161	−	0.107910i	$-0.965584\pi$
$887$	−1.10590e9	−	6.38492e8i	−1.58469	−	0.914923i	−0.590533	−	0.807014i	$-0.701082\pi$
$888$		0			0
$889$	4.87517e8	+	9.15519e8i	0.693881	+	1.30305i
$890$		0			0
$891$	2.81151e7	−	4.86968e7i	0.0397472	−	0.0688441i
$892$		0			0
$893$	1.09237e7	+	1.89203e7i	0.0153396	+	0.0265690i
$894$		0			0
$895$		−	2.27673e8i		−	0.317572i
$896$		0			0
$897$	−4.20686e8			−0.582883
$898$		0			0
$899$	−5.34867e8	+	3.08806e8i	−0.736151	+	0.425017i
$900$		0			0
$901$	−3.88826e8	−	2.24489e8i	−0.531596	−	0.306917i
$902$		0			0
$903$	5.48477e8	+	3.42254e8i	0.744895	+	0.464821i
$904$		0			0
$905$	8.25957e7	−	1.43060e8i	0.111432	−	0.193007i
$906$		0			0
$907$	−4.00853e8	−	6.94298e8i	−0.537234	−	0.930517i	−0.999052	−	0.0435417i	$-0.986136\pi$
$907$	−4.00853e8	−	6.94298e8i	−0.537234	−	0.930517i	0.461818	−	0.886975i	$-0.347197\pi$
$908$		0			0
$909$			8.95891e7i			0.119279i
$910$		0			0
$911$	−6.91508e8			−0.914623			−0.457311	−	0.889307i	$-0.651187\pi$
$911$	−6.91508e8			−0.914623			−0.457311	+	0.889307i	$0.651187\pi$
$912$		0			0
$913$	2.45787e8	−	1.41905e8i	0.322958	−	0.186460i
$914$		0			0
$915$	−2.82383e8	−	1.63034e8i	−0.368617	−	0.212821i
$916$		0			0
$917$	−2.22235e7	+	6.47900e8i	−0.0288206	+	0.840234i
$918$		0			0
$919$	7.60702e8	−	1.31757e9i	0.980095	−	1.69757i	0.318114	−	0.948052i	$-0.396950\pi$
$919$	7.60702e8	−	1.31757e9i	0.980095	−	1.69757i	0.661980	−	0.749521i	$-0.269716\pi$
$920$		0			0
$921$	−1.23926e8	−	2.14646e8i	−0.158629	−	0.274753i
$922$		0			0
$923$			7.61517e8i			0.968444i
$924$		0			0
$925$	−3.66980e8			−0.463679
$926$		0			0
$927$	1.83315e8	−	1.05837e8i	0.230122	−	0.132861i
$928$		0			0
$929$	3.90635e8	+	2.25533e8i	0.487219	+	0.281296i	0.723420	−	0.690408i	$-0.242569\pi$
$929$	3.90635e8	+	2.25533e8i	0.487219	+	0.281296i	−0.236201	+	0.971704i	$0.575902\pi$
$930$		0			0
$931$	1.36999e8	−	6.70293e7i	0.169773	−	0.0830645i
$932$		0			0
$933$	3.83022e8	−	6.63413e8i	0.471605	−	0.816844i
$934$		0			0
$935$	9.72810e7	+	1.68496e8i	0.119013	+	0.206136i
$936$		0			0
$937$			2.21823e8i			0.269643i	0.990870	+	0.134821i	$0.0430460\pi$
$937$			2.21823e8i			0.269643i	−0.990870	+	0.134821i	$0.956954\pi$
$938$		0			0
$939$	3.77594e8			0.456066
$940$		0			0
$941$	1.07470e9	−	6.20479e8i	1.28979	−	0.744660i	0.311172	−	0.950353i	$-0.399278\pi$
$941$	1.07470e9	−	6.20479e8i	1.28979	−	0.744660i	0.978616	+	0.205693i	$0.0659450\pi$
$942$		0			0
$943$	6.94228e8	+	4.00813e8i	0.827879	+	0.477976i
$944$		0			0
$945$	7.74585e7	+	2.65688e6i	0.0917854	+	0.00314831i
$946$		0			0
$947$	−1.27754e8	+	2.21276e8i	−0.150426	+	0.260546i	−0.931384	−	0.364038i	$-0.881398\pi$
$947$	−1.27754e8	+	2.21276e8i	−0.150426	+	0.260546i	0.780958	+	0.624584i	$0.214731\pi$
$948$		0			0
$949$	7.67425e7	+	1.32922e8i	0.0897919	+	0.155524i
$950$		0			0
$951$		−	5.90589e8i		−	0.686663i
$952$		0			0
$953$	−1.06492e9			−1.23038			−0.615190	−	0.788379i	$-0.710921\pi$
$953$	−1.06492e9			−1.23038			−0.615190	+	0.788379i	$0.710921\pi$
$954$		0			0
$955$	3.64027e7	−	2.10171e7i	0.0417949	−	0.0241303i
$956$		0			0
$957$	2.69693e8	+	1.55708e8i	0.307705	+	0.177654i
$958$		0			0
$959$	−7.89387e8	+	1.26503e9i	−0.895022	+	1.43431i
$960$		0			0
$961$	−1.03994e7	+	1.80123e7i	−0.0117176	+	0.0202955i
$962$		0			0
$963$	7.27961e7	+	1.26086e8i	0.0815134	+	0.141185i
$964$		0			0
$965$			2.20312e8i			0.245164i
$966$		0			0
$967$	−4.41062e8			−0.487776			−0.243888	−	0.969803i	$-0.578423\pi$
$967$	−4.41062e8			−0.487776			−0.243888	+	0.969803i	$0.578423\pi$
$968$		0			0
$969$	5.99442e7	−	3.46088e7i	0.0658834	−	0.0380378i
$970$		0			0
$971$	−3.69510e8	−	2.13336e8i	−0.403616	−	0.233028i	0.284427	−	0.958698i	$-0.408197\pi$
$971$	−3.69510e8	−	2.13336e8i	−0.403616	−	0.233028i	−0.688043	+	0.725670i	$0.741530\pi$
$972$		0			0
$973$	5.89752e8	−	3.14045e8i	0.640222	−	0.340921i
$974$		0			0
$975$	−1.90276e8	+	3.29568e8i	−0.205291	+	0.355575i
$976$		0			0
$977$	2.72315e8	+	4.71663e8i	0.292003	+	0.505764i	0.974283	−	0.225327i	$-0.0723449\pi$
$977$	2.72315e8	+	4.71663e8i	0.292003	+	0.505764i	−0.682280	+	0.731091i	$0.739012\pi$
$978$		0			0
$979$			2.10187e8i			0.224005i
$980$		0			0
$981$	8.53001e7			0.0903530
$982$		0			0
$983$	−4.79345e8	+	2.76750e8i	−0.504647	+	0.291358i	−0.730631	−	0.682773i	$-0.760774\pi$
$983$	−4.79345e8	+	2.76750e8i	−0.504647	+	0.291358i	0.225983	+	0.974131i	$0.427441\pi$
$984$		0			0
$985$	−4.01099e8	−	2.31574e8i	−0.419703	−	0.242316i
$986$		0			0
$987$	4.23523e7	+	7.95343e7i	0.0440480	+	0.0827186i
$988$		0			0
$989$	−8.06447e8	+	1.39681e9i	−0.833656	+	1.44393i
$990$		0			0
$991$	2.81840e8	+	4.88162e8i	0.289589	+	0.501583i	0.973712	−	0.227784i	$-0.0731480\pi$
$991$	2.81840e8	+	4.88162e8i	0.289589	+	0.501583i	−0.684123	+	0.729367i	$0.739815\pi$
$992$		0			0
$993$			8.92381e8i			0.911386i
$994$		0			0
$995$	2.00730e8			0.203771
$996$		0			0
$997$	7.18953e8	−	4.15088e8i	0.725463	−	0.418846i	−0.0912973	−	0.995824i	$-0.529101\pi$
$997$	7.18953e8	−	4.15088e8i	0.725463	−	0.418846i	0.816760	+	0.576978i	$0.195768\pi$
$998$		0			0
$999$	−9.97685e7	−	5.76014e7i	−0.100068	−	0.0577745i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.h.145.6		24
4.3	odd	2		168.7.z.a.145.6	yes	24
7.3	odd	6	inner	336.7.bh.h.241.6		24
28.3	even	6		168.7.z.a.73.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.7.z.a.73.6	✓	24	28.3	even	6
168.7.z.a.145.6	yes	24	4.3	odd	2
336.7.bh.h.145.6		24	1.1	even	1	trivial
336.7.bh.h.241.6		24	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(13.5000 - 7.79423i) q^{3} +(-51.6596 - 29.8257i) q^{5} +(-161.216 - 302.751i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(13.5000 - 7.79423i) q^{3} +(-51.6596 - 29.8257i) q^{5} +(-161.216 - 302.751i) q^{7} +(121.500 - 210.444i) q^{9} +(476.131 + 824.684i) q^{11} -2023.12i q^{13} -929.874 q^{15} +(-2966.27 + 1712.58i) q^{17} +(-1122.70 - 648.191i) q^{19} +(-4536.13 - 2830.59i) q^{21} +(6669.65 - 11552.2i) q^{23} +(-6033.35 - 10450.1i) q^{25} -3788.00i q^{27} +20978.8 q^{29} +(-25495.7 + 14719.9i) q^{31} +(12855.5 + 7422.15i) q^{33} +(-701.396 + 20448.4i) q^{35} +(15206.3 - 26338.1i) q^{37} +(-15768.7 - 27312.1i) q^{39} +60095.0i q^{41} -120913. q^{43} +(-12553.3 + 7247.65i) q^{45} +(-14594.7 - 8426.27i) q^{47} +(-65667.6 + 97616.8i) q^{49} +(-26696.4 + 46239.6i) q^{51} +(65541.3 + 113521. i) q^{53} -56803.8i q^{55} -20208.6 q^{57} +(-150782. + 87054.1i) q^{59} +(303679. + 175329. i) q^{61} +(-83300.0 - 2857.25i) q^{63} +(-60341.0 + 104514. i) q^{65} +(-170366. - 295083. i) q^{67} -207939. i q^{69} -376407. q^{71} +(-65701.4 + 37932.7i) q^{73} +(-162901. - 94050.7i) q^{75} +(172914. - 277102. i) q^{77} +(-349906. + 606056. i) q^{79} +(-29524.5 - 51137.9i) q^{81} -298037. i q^{83} +204315. q^{85} +(283213. - 163513. i) q^{87} +(191152. + 110362. i) q^{89} +(-612503. + 326160. i) q^{91} +(-229461. + 397438. i) q^{93} +(38665.5 + 66970.6i) q^{95} +859530. i q^{97} +231400. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9}+O(q^{10}) \) 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9	\( 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9} + 1190 q^{11} - 2268 q^{15} - 1500 q^{17} + 13446 q^{19} - 2106 q^{21} - 21504 q^{23} + 22542 q^{25} - 85484 q^{29} - 6264 q^{31} + 32130 q^{33} - 32268 q^{35} - 46938 q^{37} + 17010 q^{39} + 19548 q^{43} - 30618 q^{45} + 167004 q^{47} + 250644 q^{49} - 13500 q^{51} - 258982 q^{53} + 242028 q^{57} - 744834 q^{59} - 390096 q^{61} - 59778 q^{63} - 19388 q^{65} - 62742 q^{67} + 1102984 q^{71} - 663534 q^{73} + 608634 q^{75} + 404298 q^{77} + 271032 q^{79} - 708588 q^{81} + 2540040 q^{85} - 1154034 q^{87} - 433740 q^{89} + 2142270 q^{91} - 56376 q^{93} - 2205360 q^{95} + 578340 q^{99}+O(q^{100}) \) 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9 + 1190 * q^11 - 2268 * q^15 - 1500 * q^17 + 13446 * q^19 - 2106 * q^21 - 21504 * q^23 + 22542 * q^25 - 85484 * q^29 - 6264 * q^31 + 32130 * q^33 - 32268 * q^35 - 46938 * q^37 + 17010 * q^39 + 19548 * q^43 - 30618 * q^45 + 167004 * q^47 + 250644 * q^49 - 13500 * q^51 - 258982 * q^53 + 242028 * q^57 - 744834 * q^59 - 390096 * q^61 - 59778 * q^63 - 19388 * q^65 - 62742 * q^67 + 1102984 * q^71 - 663534 * q^73 + 608634 * q^75 + 404298 * q^77 + 271032 * q^79 - 708588 * q^81 + 2540040 * q^85 - 1154034 * q^87 - 433740 * q^89 + 2142270 * q^91 - 56376 * q^93 - 2205360 * q^95 + 578340 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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