LMFDB - Embedded newform 336.7.bh.h.145.5

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			145.5
Character	$\chi$	$=$	336.145
Dual form			336.7.bh.h.241.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.5000 - 7.79423i) q^{3} +(-56.9387 - 32.8735i) q^{5} +(-298.061 + 169.732i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(13.5000 - 7.79423i) q^{3} +(-56.9387 - 32.8735i) q^{5} +(-298.061 + 169.732i) q^{7} +(121.500 - 210.444i) q^{9} +(-132.203 - 228.982i) q^{11} +3184.91i q^{13} -1024.90 q^{15} +(1907.27 - 1101.16i) q^{17} +(10100.6 + 5831.59i) q^{19} +(-2700.89 + 4614.53i) q^{21} +(8408.32 - 14563.6i) q^{23} +(-5651.16 - 9788.10i) q^{25} -3788.00i q^{27} +12226.4 q^{29} +(-49143.3 + 28372.9i) q^{31} +(-3569.48 - 2060.84i) q^{33} +(22550.9 + 134.029i) q^{35} +(15341.2 - 26571.7i) q^{37} +(24823.9 + 42996.3i) q^{39} -82153.5i q^{41} +20127.7 q^{43} +(-13836.1 + 7988.27i) q^{45} +(-171957. - 99279.3i) q^{47} +(60031.4 - 101181. i) q^{49} +(17165.4 - 29731.4i) q^{51} +(-72339.8 - 125296. i) q^{53} +17383.9i q^{55} +181811. q^{57} +(-197372. + 113953. i) q^{59} +(-239346. - 138186. i) q^{61} +(-495.368 + 83347.5i) q^{63} +(104699. - 181345. i) q^{65} +(-27469.7 - 47578.9i) q^{67} -262145. i q^{69} +191596. q^{71} +(127654. - 73701.0i) q^{73} +(-152581. - 88092.9i) q^{75} +(78270.0 + 45811.6i) q^{77} +(-482132. + 835078. i) q^{79} +(-29524.5 - 51137.9i) q^{81} +901135. i q^{83} -144796. q^{85} +(165057. - 95295.4i) q^{87} +(-598630. - 345619. i) q^{89} +(-540580. - 949297. i) q^{91} +(-442289. + 766068. i) q^{93} +(-383410. - 664085. i) q^{95} -681721. i q^{97} -64250.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−56.9387	−	32.8735i	−0.455509	−	0.262988i	0.254645	−	0.967035i	$-0.418041\pi$
$5$	−56.9387	−	32.8735i	−0.455509	−	0.262988i	−0.710154	+	0.704046i	$0.751375\pi$
$6$		0			0
$7$	−298.061	+	169.732i	−0.868982	+	0.494844i
$7$	−298.061	+	169.732i	−0.868982	+	0.494844i
$8$		0			0
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$		0			0
$11$	−132.203	−	228.982i	−0.0993260	−	0.172038i	0.812080	−	0.583546i	$-0.198335\pi$
$11$	−132.203	−	228.982i	−0.0993260	−	0.172038i	−0.911406	+	0.411509i	$0.865002\pi$
$12$		0			0
$13$			3184.91i			1.44966i	0.688926	+	0.724832i	$0.258083\pi$
$13$			3184.91i			1.44966i	−0.688926	+	0.724832i	$0.741917\pi$
$14$		0			0
$15$	−1024.90			−0.303673
$16$		0			0
$17$	1907.27	−	1101.16i	0.388208	−	0.224132i	−0.293175	−	0.956059i	$-0.594712\pi$
$17$	1907.27	−	1101.16i	0.388208	−	0.224132i	0.681384	+	0.731927i	$0.261379\pi$
$18$		0			0
$19$	10100.6	+	5831.59i	1.47261	+	0.850210i	0.999525	−	0.0308094i	$-0.00980848\pi$
$19$	10100.6	+	5831.59i	1.47261	+	0.850210i	0.473081	+	0.881019i	$0.343142\pi$
$20$		0			0
$21$	−2700.89	+	4614.53i	−0.291642	+	0.498275i
$22$		0			0
$23$	8408.32	−	14563.6i	0.691076	−	1.19698i	−0.280410	−	0.959880i	$-0.590470\pi$
$23$	8408.32	−	14563.6i	0.691076	−	1.19698i	0.971486	−	0.237098i	$-0.0761963\pi$
$24$		0			0
$25$	−5651.16	−	9788.10i	−0.361674	−	0.626438i
$26$		0			0
$27$		−	3788.00i		−	0.192450i
$28$		0			0
$29$	12226.4			0.501308			0.250654	−	0.968077i	$-0.419354\pi$
$29$	12226.4			0.501308			0.250654	+	0.968077i	$0.419354\pi$
$30$		0			0
$31$	−49143.3	+	28372.9i	−1.64960	+	0.952398i	−0.672371	+	0.740214i	$0.734724\pi$
$31$	−49143.3	+	28372.9i	−1.64960	+	0.952398i	−0.977230	+	0.212184i	$0.931943\pi$
$32$		0			0
$33$	−3569.48	−	2060.84i	−0.0993260	−	0.0573459i
$34$		0			0
$35$	22550.9	+	134.029i	0.525967	+	0.00312604i
$36$		0			0
$37$	15341.2	−	26571.7i	0.302868	−	0.524584i	−0.673916	−	0.738808i	$-0.735389\pi$
$37$	15341.2	−	26571.7i	0.302868	−	0.524584i	0.976784	+	0.214224i	$0.0687224\pi$
$38$		0			0
$39$	24823.9	+	42996.3i	0.418482	+	0.724832i
$40$		0			0
$41$		−	82153.5i		−	1.19200i	−0.802986	−	0.595998i	$-0.796757\pi$
$41$		−	82153.5i		−	1.19200i	0.802986	−	0.595998i	$-0.203243\pi$
$42$		0			0
$43$	20127.7			0.253157			0.126578	−	0.991957i	$-0.459600\pi$
$43$	20127.7			0.253157			0.126578	+	0.991957i	$0.459600\pi$
$44$		0			0
$45$	−13836.1	+	7988.27i	−0.151836	+	0.0876628i
$46$		0			0
$47$	−171957.	−	99279.3i	−1.65625	−	0.956236i	−0.974423	−	0.224723i	$-0.927852\pi$
$47$	−171957.	−	99279.3i	−1.65625	−	0.956236i	−0.681827	−	0.731513i	$-0.738814\pi$
$48$		0			0
$49$	60031.4	−	101181.i	0.510259	−	0.860021i
$50$		0			0
$51$	17165.4	−	29731.4i	0.129403	−	0.224132i
$52$		0			0
$53$	−72339.8	−	125296.i	−0.485903	−	0.841609i	0.513965	−	0.857811i	$-0.328176\pi$
$53$	−72339.8	−	125296.i	−0.485903	−	0.841609i	−0.999869	+	0.0162017i	$0.994843\pi$
$54$		0			0
$55$			17383.9i			0.104486i
$56$		0			0
$57$	181811.			0.981737
$58$		0			0
$59$	−197372.	+	113953.i	−0.961014	+	0.554842i	−0.896485	−	0.443074i	$-0.853888\pi$
$59$	−197372.	+	113953.i	−0.961014	+	0.554842i	−0.0645290	+	0.997916i	$0.520555\pi$
$60$		0			0
$61$	−239346.	−	138186.i	−1.05448	−	0.608802i	−0.130576	−	0.991438i	$-0.541683\pi$
$61$	−239346.	−	138186.i	−1.05448	−	0.608802i	−0.923899	+	0.382637i	$0.875016\pi$
$62$		0			0
$63$	−495.368	+	83347.5i	−0.00198110	+	0.333327i
$64$		0			0
$65$	104699.	−	181345.i	0.381245	−	0.660335i
$66$		0			0
$67$	−27469.7	−	47578.9i	−0.0913333	−	0.158194i	0.816739	−	0.577007i	$-0.195780\pi$
$67$	−27469.7	−	47578.9i	−0.0913333	−	0.158194i	−0.908072	+	0.418813i	$0.862446\pi$
$68$		0			0
$69$		−	262145.i		−	0.797986i
$70$		0			0
$71$	191596.			0.535318			0.267659	−	0.963514i	$-0.413750\pi$
$71$	191596.			0.535318			0.267659	+	0.963514i	$0.413750\pi$
$72$		0			0
$73$	127654.	−	73701.0i	0.328145	−	0.189454i	−0.326872	−	0.945068i	$-0.605995\pi$
$73$	127654.	−	73701.0i	0.328145	−	0.189454i	0.655017	+	0.755614i	$0.272661\pi$
$74$		0			0
$75$	−152581.	−	88092.9i	−0.361674	−	0.208813i
$76$		0			0
$77$	78270.0	+	45811.6i	0.171444	+	0.100347i
$78$		0			0
$79$	−482132.	+	835078.i	−0.977879	+	1.69374i	−0.307790	+	0.951454i	$0.599590\pi$
$79$	−482132.	+	835078.i	−0.977879	+	1.69374i	−0.670088	+	0.742281i	$0.733744\pi$
$80$		0			0
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			901135.i			1.57600i	0.615676	+	0.787999i	$0.288883\pi$
$83$			901135.i			1.57600i	−0.615676	+	0.787999i	$0.711117\pi$
$84$		0			0
$85$	−144796.			−0.235777
$86$		0			0
$87$	165057.	−	95295.4i	0.250654	−	0.144715i
$88$		0			0
$89$	−598630.	−	345619.i	−0.849158	−	0.490261i	0.0112088	−	0.999937i	$-0.496432\pi$
$89$	−598630.	−	345619.i	−0.849158	−	0.490261i	−0.860367	+	0.509676i	$0.829765\pi$
$90$		0			0
$91$	−540580.	−	949297.i	−0.717358	−	1.25973i
$92$		0			0
$93$	−442289.	+	766068.i	−0.549867	+	0.952398i
$94$		0			0
$95$	−383410.	−	664085.i	−0.447190	−	0.774557i
$96$		0			0
$97$		−	681721.i		−	0.746950i	−0.927640	−	0.373475i	$-0.878166\pi$
$97$		−	681721.i		−	0.746950i	0.927640	−	0.373475i	$-0.121834\pi$
$98$		0			0
$99$	−64250.6			−0.0662173
$100$		0			0
$101$	587877.	−	339411.i	0.570588	−	0.329429i	−0.186796	−	0.982399i	$-0.559810\pi$
$101$	587877.	−	339411.i	0.570588	−	0.329429i	0.757384	+	0.652970i	$0.226477\pi$
$102$		0			0
$103$	950419.	+	548725.i	0.869768	+	0.502161i	0.867271	−	0.497836i	$-0.165872\pi$
$103$	950419.	+	548725.i	0.869768	+	0.502161i	0.00249692	+	0.999997i	$0.499205\pi$
$104$		0			0
$105$	305481.	−	173957.i	0.263886	−	0.150271i
$106$		0			0
$107$	1.11057e6	−	1.92356e6i	0.906555	−	1.57020i	0.0877380	−	0.996144i	$-0.472036\pi$
$107$	1.11057e6	−	1.92356e6i	0.906555	−	1.57020i	0.818817	−	0.574055i	$-0.194631\pi$
$108$		0			0
$109$	−611475.	−	1.05911e6i	−0.472171	−	0.817824i	0.527322	−	0.849666i	$-0.323196\pi$
$109$	−611475.	−	1.05911e6i	−0.472171	−	0.817824i	−0.999493	+	0.0318414i	$0.989863\pi$
$110$		0			0
$111$		−	478291.i		−	0.349722i
$112$		0			0
$113$	−119510.			−0.0828264			−0.0414132	−	0.999142i	$-0.513186\pi$
$113$	−119510.			−0.0828264			−0.0414132	+	0.999142i	$0.513186\pi$
$114$		0			0
$115$	−957517.	+	552823.i	−0.629583	+	0.363490i
$116$		0			0
$117$	670246.	+	386967.i	0.418482	+	0.241611i
$118$		0			0
$119$	−381580.	+	651937.i	−0.226435	+	0.386869i
$120$		0			0
$121$	850825.	−	1.47367e6i	0.480269	−	0.831850i
$122$		0			0
$123$	−640323.	−	1.10907e6i	−0.344099	−	0.595998i
$124$		0			0
$125$			1.77039e6i			0.906441i
$126$		0			0
$127$	−778890.			−0.380246			−0.190123	−	0.981760i	$-0.560889\pi$
$127$	−778890.			−0.380246			−0.190123	+	0.981760i	$0.560889\pi$
$128$		0			0
$129$	271724.	−	156880.i	0.126578	−	0.0730800i
$130$		0			0
$131$	−2.73663e6	−	1.58000e6i	−1.21731	−	0.702816i	−0.252971	−	0.967474i	$-0.581408\pi$
$131$	−2.73663e6	−	1.58000e6i	−1.21731	−	0.702816i	−0.964342	+	0.264658i	$0.914741\pi$
$132$		0			0
$133$	−4.00040e6	−	23776.0i	−1.70039	−	0.0101061i
$134$		0			0
$135$	−124525.	+	215683.i	−0.0506121	+	0.0876628i
$136$		0			0
$137$	−611049.	−	1.05837e6i	−0.237637	−	0.411600i	0.722399	−	0.691477i	$-0.243040\pi$
$137$	−611049.	−	1.05837e6i	−0.237637	−	0.411600i	−0.960036	+	0.279877i	$0.909706\pi$
$138$		0			0
$139$			634161.i			0.236132i	0.993006	+	0.118066i	$0.0376695\pi$
$139$			634161.i			0.236132i	−0.993006	+	0.118066i	$0.962331\pi$
$140$		0			0
$141$	−3.09522e6			−1.10417
$142$		0			0
$143$	729288.	−	421055.i	0.249397	−	0.143989i
$144$		0			0
$145$	−696155.	−	401925.i	−0.228351	−	0.131838i
$146$		0			0
$147$	21799.2	−	1.83384e6i	0.00686261	−	0.577309i
$148$		0			0
$149$	−266123.	+	460938.i	−0.0804495	+	0.139343i	−0.903443	−	0.428708i	$-0.858969\pi$
$149$	−266123.	+	460938.i	−0.0804495	+	0.139343i	0.822994	+	0.568051i	$0.192302\pi$
$150$		0			0
$151$	−2.11694e6	−	3.66665e6i	−0.614863	−	1.06497i	−0.990409	−	0.138169i	$-0.955878\pi$
$151$	−2.11694e6	−	3.66665e6i	−0.614863	−	1.06497i	0.375546	−	0.926804i	$-0.377455\pi$
$152$		0			0
$153$		−	535165.i		−	0.149421i
$154$		0			0
$155$	3.73087e6			1.00188
$156$		0			0
$157$	1.49584e6	−	863623.i	0.386532	−	0.223164i	−0.294124	−	0.955767i	$-0.595028\pi$
$157$	1.49584e6	−	863623.i	0.386532	−	0.223164i	0.680657	+	0.732603i	$0.261695\pi$
$158$		0			0
$159$	−1.95318e6	−	1.12767e6i	−0.485903	−	0.280536i
$160$		0			0
$161$	−34281.6	+	5.76800e6i	−0.00821454	+	1.38213i
$162$		0			0
$163$	1.42938e6	−	2.47575e6i	0.330053	−	0.571669i	−0.652469	−	0.757816i	$-0.726267\pi$
$163$	1.42938e6	−	2.47575e6i	0.330053	−	0.571669i	0.982522	+	0.186147i	$0.0595999\pi$
$164$		0			0
$165$	135494.	+	234683.i	0.0301626	+	0.0522432i
$166$		0			0
$167$		−	8.62912e6i		−	1.85275i	−0.376601	−	0.926375i	$-0.622907\pi$
$167$		−	8.62912e6i		−	1.85275i	0.376601	−	0.926375i	$-0.377093\pi$
$168$		0			0
$169$	−5.31686e6			−1.10153
$170$		0			0
$171$	2.45445e6	−	1.41708e6i	0.490869	−	0.283403i
$172$		0			0
$173$	134105.	+	77425.3i	0.0259003	+	0.0149536i	0.512894	−	0.858452i	$-0.328573\pi$
$173$	134105.	+	77425.3i	0.0259003	+	0.0149536i	−0.486994	+	0.873405i	$0.661907\pi$
$174$		0			0
$175$	3.34574e6	+	1.95827e6i	0.624278	+	0.365391i
$176$		0			0
$177$	−1.77635e6	+	3.07673e6i	−0.320338	+	0.554842i
$178$		0			0
$179$	−2.52476e6	−	4.37301e6i	−0.440211	−	0.762468i	0.557494	−	0.830181i	$-0.311763\pi$
$179$	−2.52476e6	−	4.37301e6i	−0.440211	−	0.762468i	−0.997705	+	0.0677134i	$0.978430\pi$
$180$		0			0
$181$		−	1.12097e7i		−	1.89041i	−0.326471	−	0.945207i	$-0.605859\pi$
$181$		−	1.12097e7i		−	1.89041i	0.326471	−	0.945207i	$-0.394141\pi$
$182$		0			0
$183$	−4.30822e6			−0.702983
$184$		0			0
$185$	−1.74701e6	+	1.00864e6i	−0.275919	+	0.159302i
$186$		0			0
$187$	−504293.	−	291153.i	−0.0771184	−	0.0445243i
$188$		0			0
$189$	642942.	+	1.12905e6i	0.0952328	+	0.167236i
$190$		0			0
$191$	−612078.	+	1.06015e6i	−0.0878430	+	0.152148i	−0.906599	−	0.421993i	$-0.861331\pi$
$191$	−612078.	+	1.06015e6i	−0.0878430	+	0.152148i	0.818756	+	0.574141i	$0.194664\pi$
$192$		0			0
$193$	−594171.	−	1.02913e6i	−0.0826494	−	0.143153i	0.821738	−	0.569866i	$-0.193005\pi$
$193$	−594171.	−	1.02913e6i	−0.0826494	−	0.143153i	−0.904387	+	0.426713i	$0.859671\pi$
$194$		0			0
$195$		−	3.26420e6i		−	0.440224i
$196$		0			0
$197$	−1.13119e6			−0.147958			−0.0739788	−	0.997260i	$-0.523570\pi$
$197$	−1.13119e6			−0.147958			−0.0739788	+	0.997260i	$0.523570\pi$
$198$		0			0
$199$	1.38775e6	−	801217.i	0.176097	−	0.101670i	−0.409361	−	0.912373i	$-0.634248\pi$
$199$	1.38775e6	−	801217.i	0.176097	−	0.101670i	0.585458	+	0.810703i	$0.300915\pi$
$200$		0			0
$201$	−741681.	−	428210.i	−0.0913333	−	0.0527313i
$202$		0			0
$203$	−3.64421e6	+	2.07521e6i	−0.435628	+	0.248069i
$204$		0			0
$205$	−2.70068e6	+	4.67771e6i	−0.313481	+	0.542965i
$206$		0			0
$207$	−2.04322e6	−	3.53896e6i	−0.230359	−	0.398993i
$208$		0			0
$209$		−	3.08381e6i		−	0.337792i
$210$		0			0
$211$	555254.			0.0591077			0.0295539	−	0.999563i	$-0.490591\pi$
$211$	555254.			0.0591077			0.0295539	+	0.999563i	$0.490591\pi$
$212$		0			0
$213$	2.58655e6	−	1.49334e6i	0.267659	−	0.154533i
$214$		0			0
$215$	−1.14605e6	−	661670.i	−0.115315	−	0.0665772i
$216$		0			0
$217$	9.83191e6	−	1.67980e7i	0.962185	−	1.64391i
$218$		0			0
$219$	1.14888e6	−	1.98993e6i	0.109382	−	0.189454i
$220$		0			0
$221$	3.50710e6	+	6.07448e6i	0.324916	+	0.562772i
$222$		0			0
$223$			1.67118e7i			1.50698i	0.657457	+	0.753492i	$0.271632\pi$
$223$			1.67118e7i			1.50698i	−0.657457	+	0.753492i	$0.728368\pi$
$224$		0			0
$225$	−2.74646e6			−0.241116
$226$		0			0
$227$	−2.25696e6	+	1.30306e6i	−0.192950	+	0.111400i	−0.593363	−	0.804935i	$-0.702200\pi$
$227$	−2.25696e6	+	1.30306e6i	−0.192950	+	0.111400i	0.400413	+	0.916335i	$0.368867\pi$
$228$		0			0
$229$	−1.84553e6	−	1.06552e6i	−0.153679	−	0.0887266i	0.421189	−	0.906973i	$-0.361613\pi$
$229$	−1.84553e6	−	1.06552e6i	−0.153679	−	0.0887266i	−0.574868	+	0.818247i	$0.694946\pi$
$230$		0			0
$231$	1.41371e6	+	8402.25i	0.114690	+	0.000681648i
$232$		0			0
$233$	4.51536e6	−	7.82083e6i	0.356964	−	0.618279i	−0.630488	−	0.776199i	$-0.717145\pi$
$233$	4.51536e6	−	7.82083e6i	0.356964	−	0.618279i	0.987452	+	0.157919i	$0.0504786\pi$
$234$		0			0
$235$	6.52733e6	+	1.13057e7i	0.502958	+	0.871149i
$236$		0			0
$237$			1.50314e7i			1.12916i
$238$		0			0
$239$	2.12988e7			1.56013			0.780067	−	0.625697i	$-0.215185\pi$
$239$	2.12988e7			1.56013			0.780067	+	0.625697i	$0.215185\pi$
$240$		0			0
$241$	1.29033e7	−	7.44973e6i	0.921828	−	0.532218i	0.0376102	−	0.999292i	$-0.488025\pi$
$241$	1.29033e7	−	7.44973e6i	0.921828	−	0.532218i	0.884218	+	0.467075i	$0.154692\pi$
$242$		0			0
$243$	−797162.	−	460241.i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−6.74427e6	+	3.78764e6i	−0.458603	+	0.257555i
$246$		0			0
$247$	−1.85731e7	+	3.21695e7i	−1.23252	+	2.13478i
$248$		0			0
$249$	7.02366e6	+	1.21653e7i	0.454952	+	0.787999i
$250$		0			0
$251$			9.60625e6i			0.607481i	0.952755	+	0.303741i	$0.0982356\pi$
$251$			9.60625e6i			0.607481i	−0.952755	+	0.303741i	$0.901764\pi$
$252$		0			0
$253$	−4.44642e6			−0.274567
$254$		0			0
$255$	−1.95475e6	+	1.12858e6i	−0.117888	+	0.0680629i
$256$		0			0
$257$	1.18803e7	+	6.85911e6i	0.699889	+	0.404081i	0.807306	−	0.590133i	$-0.200925\pi$
$257$	1.18803e7	+	6.85911e6i	0.699889	+	0.404081i	−0.107417	+	0.994214i	$0.534258\pi$
$258$		0			0
$259$	−62547.7	+	1.05239e7i	−0.00360008	+	0.605726i
$260$		0			0
$261$	1.48551e6	−	2.57298e6i	0.0835514	−	0.144715i
$262$		0			0
$263$	−3.54193e6	−	6.13480e6i	−0.194703	−	0.337235i	0.752100	−	0.659049i	$-0.229041\pi$
$263$	−3.54193e6	−	6.13480e6i	−0.194703	−	0.337235i	−0.946803	+	0.321814i	$0.895708\pi$
$264$		0			0
$265$			9.51227e6i			0.511148i
$266$		0			0
$267$	−1.07753e7			−0.566105
$268$		0			0
$269$	2.73422e7	−	1.57860e7i	1.40468	−	0.810991i	0.409810	−	0.912171i	$-0.365595\pi$
$269$	2.73422e7	−	1.57860e7i	1.40468	−	0.810991i	0.994868	+	0.101180i	$0.0322618\pi$
$270$		0			0
$271$	−1.34007e7	−	7.73692e6i	−0.673319	−	0.388741i	0.124014	−	0.992280i	$-0.460423\pi$
$271$	−1.34007e7	−	7.73692e6i	−0.673319	−	0.388741i	−0.797333	+	0.603539i	$0.793757\pi$
$272$		0			0
$273$	−1.46969e7	−	8.60211e6i	−0.722332	−	0.422783i
$274$		0			0
$275$	−1.49420e6	+	2.58803e6i	−0.0718473	+	0.124443i
$276$		0			0
$277$	−1.10363e7	−	1.91155e7i	−0.519260	−	0.899385i	−0.999749	−	0.0223845i	$-0.992874\pi$
$277$	−1.10363e7	−	1.91155e7i	−0.519260	−	0.899385i	0.480489	−	0.877001i	$-0.340459\pi$
$278$		0			0
$279$			1.37892e7i			0.634932i
$280$		0			0
$281$	1.87044e7			0.842996			0.421498	−	0.906829i	$-0.361505\pi$
$281$	1.87044e7			0.842996			0.421498	+	0.906829i	$0.361505\pi$
$282$		0			0
$283$	−131675.	+	76022.7i	−0.00580958	+	0.00335416i	−0.502902	−	0.864343i	$-0.667734\pi$
$283$	−131675.	+	76022.7i	−0.00580958	+	0.00335416i	0.497092	+	0.867698i	$0.334401\pi$
$284$		0			0
$285$	−1.03521e7	−	5.97677e6i	−0.447190	−	0.258186i
$286$		0			0
$287$	1.39440e7	+	2.44867e7i	0.589852	+	1.03582i
$288$		0			0
$289$	−9.64367e6	+	1.67033e7i	−0.399530	+	0.692005i
$290$		0			0
$291$	−5.31349e6	−	9.20324e6i	−0.215626	−	0.373475i
$292$		0			0
$293$			3.90673e7i			1.55314i	0.630031	+	0.776570i	$0.283042\pi$
$293$			3.90673e7i			1.55314i	−0.630031	+	0.776570i	$0.716958\pi$
$294$		0			0
$295$	1.49841e7			0.583668
$296$		0			0
$297$	−867383.	+	500784.i	−0.0331087	+	0.0191153i
$298$		0			0
$299$	4.63839e7	+	2.67798e7i	1.73522	+	1.00183i
$300$		0			0
$301$	−5.99928e6	+	3.41631e6i	−0.219988	+	0.125273i
$302$		0			0
$303$	5.29090e6	−	9.16410e6i	0.190196	−	0.329429i
$304$		0			0
$305$	9.08535e6	+	1.57363e7i	0.320215	+	0.554629i
$306$		0			0
$307$		−	8.05114e6i		−	0.278255i	−0.990275	−	0.139127i	$-0.955570\pi$
$307$		−	8.05114e6i		−	0.278255i	0.990275	−	0.139127i	$-0.0444297\pi$
$308$		0			0
$309$	1.71075e7			0.579845
$310$		0			0
$311$	−1.86358e7	+	1.07594e7i	−0.619537	+	0.357690i	−0.776689	−	0.629885i	$-0.783102\pi$
$311$	−1.86358e7	+	1.07594e7i	−0.619537	+	0.357690i	0.157152	+	0.987574i	$0.449769\pi$
$312$		0			0
$313$	−3.74743e7	−	2.16358e7i	−1.22208	−	0.705569i	−0.256720	−	0.966486i	$-0.582642\pi$
$313$	−3.74743e7	−	2.16358e7i	−1.22208	−	0.705569i	−0.965361	+	0.260917i	$0.915975\pi$
$314$		0			0
$315$	2.76813e6	−	4.72941e6i	0.0885637	−	0.151313i
$316$		0			0
$317$	−1.35075e7	+	2.33957e7i	−0.424031	+	0.734444i	−0.996329	−	0.0856017i	$-0.972719\pi$
$317$	−1.35075e7	+	2.33957e7i	−0.424031	+	0.734444i	0.572298	+	0.820046i	$0.306052\pi$
$318$		0			0
$319$	−1.61637e6	−	2.79963e6i	−0.0497929	−	0.0862439i
$320$		0			0
$321$		−	3.46241e7i		−	1.04680i
$322$		0			0
$323$	2.56861e7			0.762237
$324$		0			0
$325$	3.11742e7	−	1.79984e7i	0.908125	−	0.524306i
$326$		0			0
$327$	−1.65098e7	−	9.53195e6i	−0.472171	−	0.272608i
$328$		0			0
$329$	6.81044e7	+	404772.i	1.91244	+	0.0113664i
$330$		0			0
$331$	2.14096e7	−	3.70825e7i	0.590370	−	1.02255i	−0.403813	−	0.914842i	$-0.632315\pi$
$331$	2.14096e7	−	3.70825e7i	0.590370	−	1.02255i	0.994182	−	0.107709i	$-0.0343514\pi$
$332$		0			0
$333$	−3.72791e6	−	6.45693e6i	−0.100956	−	0.174861i
$334$		0			0
$335$			3.61210e6i			0.0960784i
$336$		0			0
$337$	−5.69060e6			−0.148685			−0.0743427	−	0.997233i	$-0.523686\pi$
$337$	−5.69060e6			−0.148685			−0.0743427	+	0.997233i	$0.523686\pi$
$338$		0			0
$339$	−1.61338e6	+	931487.i	−0.0414132	+	0.0239099i
$340$		0			0
$341$	1.29938e7	+	7.50195e6i	0.327697	+	0.189196i
$342$		0			0
$343$	−719467.	+	4.03472e7i	−0.0178291	+	0.999841i
$344$		0			0
$345$	−8.61765e6	+	1.49262e7i	−0.209861	+	0.363490i
$346$		0			0
$347$	−6.96719e6	−	1.20675e7i	−0.166751	−	0.288822i	0.770525	−	0.637410i	$-0.219994\pi$
$347$	−6.96719e6	−	1.20675e7i	−0.166751	−	0.288822i	−0.937276	+	0.348589i	$0.886661\pi$
$348$		0			0
$349$			1.96958e7i			0.463337i	0.972795	+	0.231668i	$0.0744184\pi$
$349$			1.96958e7i			0.463337i	−0.972795	+	0.231668i	$0.925582\pi$
$350$		0			0
$351$	1.20644e7			0.278988
$352$		0			0
$353$	−8.50053e6	+	4.90778e6i	−0.193251	+	0.111574i	−0.593504	−	0.804831i	$-0.702256\pi$
$353$	−8.50053e6	+	4.90778e6i	−0.193251	+	0.111574i	0.400253	+	0.916405i	$0.368922\pi$
$354$		0			0
$355$	−1.09092e7	−	6.29844e6i	−0.243842	−	0.140782i
$356$		0			0
$357$	−69985.2	+	1.17753e7i	−0.00153816	+	0.258801i
$358$		0			0
$359$	8.24608e6	−	1.42826e7i	0.178223	−	0.308692i	−0.763049	−	0.646341i	$-0.776298\pi$
$359$	8.24608e6	−	1.42826e7i	0.178223	−	0.308692i	0.941272	+	0.337649i	$0.109632\pi$
$360$		0			0
$361$	4.44919e7	+	7.70622e7i	0.945713	+	1.63802i
$362$		0			0
$363$		−	2.65261e7i		−	0.554567i
$364$		0			0
$365$	−9.69125e6			−0.199297
$366$		0			0
$367$	−3.60767e7	+	2.08289e7i	−0.729842	+	0.421375i	−0.818364	−	0.574700i	$-0.805119\pi$
$367$	−3.60767e7	+	2.08289e7i	−0.729842	+	0.421375i	0.0885222	+	0.996074i	$0.471786\pi$
$368$		0			0
$369$	−1.72887e7	−	9.98165e6i	−0.344099	−	0.198666i
$370$		0			0
$371$	4.28284e7	+	2.50675e7i	0.838706	+	0.490897i
$372$		0			0
$373$	−7.69767e6	+	1.33328e7i	−0.148331	+	0.256917i	−0.930611	−	0.366010i	$-0.880724\pi$
$373$	−7.69767e6	+	1.33328e7i	−0.148331	+	0.256917i	0.782280	+	0.622927i	$0.214057\pi$
$374$		0			0
$375$	1.37988e7	+	2.39003e7i	0.261667	+	0.453221i
$376$		0			0
$377$			3.89400e7i			0.726729i
$378$		0			0
$379$	−7.50632e6			−0.137883			−0.0689413	−	0.997621i	$-0.521962\pi$
$379$	−7.50632e6			−0.137883			−0.0689413	+	0.997621i	$0.521962\pi$
$380$		0			0
$381$	−1.05150e7	+	6.07085e6i	−0.190123	+	0.109768i
$382$		0			0
$383$	7.01470e7	+	4.04994e7i	1.24857	+	0.720862i	0.970824	−	0.239792i	$-0.0770793\pi$
$383$	7.01470e7	+	4.04994e7i	1.24857	+	0.720862i	0.277746	+	0.960655i	$0.410413\pi$
$384$		0			0
$385$	−2.95060e6	−	5.18146e6i	−0.0517044	−	0.0907967i
$386$		0			0
$387$	2.44552e6	−	4.23576e6i	0.0421928	−	0.0730800i
$388$		0			0
$389$	3.36513e7	+	5.82857e7i	0.571680	+	0.990178i	0.996394	+	0.0848506i	$0.0270413\pi$
$389$	3.36513e7	+	5.82857e7i	0.571680	+	0.990178i	−0.424714	+	0.905328i	$0.639625\pi$
$390$		0			0
$391$		−	3.70357e7i		−	0.619569i
$392$		0			0
$393$	−4.92594e7			−0.811542
$394$		0			0
$395$	5.49039e7	−	3.16988e7i	0.890866	−	0.514341i
$396$		0			0
$397$	−1.65375e7	−	9.54792e6i	−0.264300	−	0.152594i	0.361994	−	0.932180i	$-0.382096\pi$
$397$	−1.65375e7	−	9.54792e6i	−0.264300	−	0.152594i	−0.626295	+	0.779586i	$0.715429\pi$
$398$		0			0
$399$	−5.41907e7	+	3.08590e7i	−0.853112	+	0.485807i
$400$		0			0
$401$	−7.96921e6	+	1.38031e7i	−0.123590	+	0.214064i	−0.921181	−	0.389135i	$-0.872774\pi$
$401$	−7.96921e6	+	1.38031e7i	−0.123590	+	0.214064i	0.797591	+	0.603198i	$0.206107\pi$
$402$		0			0
$403$	−9.03651e7	−	1.56517e8i	−1.38066	−	2.39137i
$404$		0			0
$405$			3.88230e6i			0.0584419i
$406$		0			0
$407$	−8.11260e6			−0.120331
$408$		0			0
$409$	−5.64334e7	+	3.25818e7i	−0.824833	+	0.476218i	−0.852080	−	0.523411i	$-0.824659\pi$
$409$	−5.64334e7	+	3.25818e7i	−0.824833	+	0.476218i	0.0272473	+	0.999629i	$0.491326\pi$
$410$		0			0
$411$	−1.64983e7	−	9.52532e6i	−0.237637	−	0.137200i
$412$		0			0
$413$	3.94875e7	−	6.74651e7i	0.560543	−	0.957699i
$414$		0			0
$415$	2.96235e7	−	5.13094e7i	0.414469	−	0.717882i
$416$		0			0
$417$	4.94280e6	+	8.56118e6i	0.0681655	+	0.118066i
$418$		0			0
$419$		−	7.07756e7i		−	0.962147i	−0.876680	−	0.481073i	$-0.840247\pi$
$419$		−	7.07756e7i		−	0.962147i	0.876680	−	0.481073i	$-0.159753\pi$
$420$		0			0
$421$	−7.01963e7			−0.940737			−0.470368	−	0.882470i	$-0.655879\pi$
$421$	−7.01963e7			−0.940737			−0.470368	+	0.882470i	$0.655879\pi$
$422$		0			0
$423$	−4.17855e7	+	2.41249e7i	−0.552083	+	0.318745i
$424$		0			0
$425$	−2.15565e7	−	1.24457e7i	−0.280810	−	0.162126i
$426$		0			0
$427$	9.47942e7	+	563400.i	1.21758	+	0.00723658i
$428$		0			0
$429$	6.56359e6	−	1.13685e7i	0.0831323	−	0.143989i
$430$		0			0
$431$	5.45773e7	+	9.45306e7i	0.681679	+	1.18070i	0.974468	+	0.224526i	$0.0720832\pi$
$431$	5.45773e7	+	9.45306e7i	0.681679	+	1.18070i	−0.292789	+	0.956177i	$0.594583\pi$
$432$		0			0
$433$			2.94027e7i			0.362180i	0.983467	+	0.181090i	$0.0579625\pi$
$433$			2.94027e7i			0.362180i	−0.983467	+	0.181090i	$0.942038\pi$
$434$		0			0
$435$	−1.25308e7			−0.152234
$436$		0			0
$437$	1.69858e8	−	9.80677e7i	2.03536	−	1.17512i
$438$		0			0
$439$	4.94252e7	+	2.85356e7i	0.584191	+	0.337283i	0.762797	−	0.646638i	$-0.223826\pi$
$439$	4.94252e7	+	2.85356e7i	0.584191	+	0.337283i	−0.178606	+	0.983921i	$0.557159\pi$
$440$		0			0
$441$	−1.39991e7	−	2.49267e7i	−0.163224	−	0.290636i
$442$		0			0
$443$	2.39980e7	−	4.15658e7i	0.276035	−	0.478107i	−0.694360	−	0.719627i	$-0.744313\pi$
$443$	2.39980e7	−	4.15658e7i	0.276035	−	0.478107i	0.970396	+	0.241520i	$0.0776460\pi$
$444$		0			0
$445$	2.27235e7	+	3.93582e7i	0.257866	+	0.446637i
$446$		0			0
$447$			8.29689e6i			0.0928951i
$448$		0			0
$449$	−1.65154e8			−1.82453			−0.912265	−	0.409601i	$-0.865668\pi$
$449$	−1.65154e8			−1.82453			−0.912265	+	0.409601i	$0.865668\pi$
$450$		0			0
$451$	−1.88117e7	+	1.08609e7i	−0.205068	+	0.118396i
$452$		0			0
$453$	−5.71574e7	−	3.29999e7i	−0.614863	−	0.354991i
$454$		0			0
$455$	−426870.	+	7.18225e7i	−0.00453171	+	0.762476i
$456$		0			0
$457$	−3.09976e7	+	5.36893e7i	−0.324772	+	0.562522i	−0.981466	−	0.191635i	$-0.938621\pi$
$457$	−3.09976e7	+	5.36893e7i	−0.324772	+	0.562522i	0.656694	+	0.754157i	$0.271954\pi$
$458$		0			0
$459$	−4.17119e6	−	7.22472e6i	−0.0431343	−	0.0747107i
$460$		0			0
$461$		−	7.61037e7i		−	0.776789i	−0.921493	−	0.388395i	$-0.873030\pi$
$461$		−	7.61037e7i		−	0.776789i	0.921493	−	0.388395i	$-0.126970\pi$
$462$		0			0
$463$	−1.37269e8			−1.38303			−0.691513	−	0.722364i	$-0.743055\pi$
$463$	−1.37269e8			−1.38303			−0.691513	+	0.722364i	$0.743055\pi$
$464$		0			0
$465$	5.03667e7	−	2.90792e7i	0.500939	−	0.289217i
$466$		0			0
$467$	−1.68460e8	−	9.72606e7i	−1.65404	−	0.954963i	−0.975385	−	0.220510i	$-0.929228\pi$
$467$	−1.68460e8	−	9.72606e7i	−1.65404	−	0.954963i	−0.678660	−	0.734453i	$-0.737439\pi$
$468$		0			0
$469$	1.62633e7	+	9.51892e6i	0.157648	+	0.0922719i
$470$		0			0
$471$	1.34625e7	−	2.33178e7i	0.128844	−	0.223164i
$472$		0			0
$473$	−2.66094e6	−	4.60889e6i	−0.0251450	−	0.0435525i
$474$		0			0
$475$		−	1.31821e8i		−	1.23000i
$476$		0			0
$477$	−3.51572e7			−0.323936
$478$		0			0
$479$	−1.33339e8	+	7.69832e7i	−1.21325	+	0.700470i	−0.963466	−	0.267832i	$-0.913693\pi$
$479$	−1.33339e8	+	7.69832e7i	−1.21325	+	0.700470i	−0.249783	+	0.968302i	$0.580359\pi$
$480$		0			0
$481$	8.46286e7	+	4.88604e7i	0.760470	+	0.439058i
$482$		0			0
$483$	4.44943e7	+	7.81353e7i	0.394878	+	0.693435i
$484$		0			0
$485$	−2.24106e7	+	3.88163e7i	−0.196439	+	0.340243i
$486$		0			0
$487$	−6.13308e7	−	1.06228e8i	−0.530997	−	0.919713i	−0.999346	−	0.0361697i	$-0.988484\pi$
$487$	−6.13308e7	−	1.06228e8i	−0.530997	−	0.919713i	0.468349	−	0.883544i	$-0.344849\pi$
$488$		0			0
$489$		−	4.45636e7i		−	0.381113i
$490$		0			0
$491$	2.22573e8			1.88031			0.940154	−	0.340750i	$-0.110681\pi$
$491$	2.22573e8			1.88031			0.940154	+	0.340750i	$0.110681\pi$
$492$		0			0
$493$	2.33190e7	−	1.34633e7i	0.194612	−	0.112359i
$494$		0			0
$495$	3.65834e6	+	2.11215e6i	0.0301626	+	0.0174144i
$496$		0			0
$497$	−5.71073e7	+	3.25199e7i	−0.465181	+	0.264899i
$498$		0			0
$499$	1.08978e6	−	1.88755e6i	0.00877076	−	0.0151914i	−0.861607	−	0.507576i	$-0.830541\pi$
$499$	1.08978e6	−	1.88755e6i	0.00877076	−	0.0151914i	0.870377	+	0.492385i	$0.163875\pi$
$500$		0			0
$501$	−6.72573e7	−	1.16493e8i	−0.534843	−	0.926375i
$502$		0			0
$503$			2.01731e8i			1.58515i	0.609776	+	0.792574i	$0.291259\pi$
$503$			2.01731e8i			1.58515i	−0.609776	+	0.792574i	$0.708741\pi$
$504$		0			0
$505$	−4.46306e7			−0.346544
$506$		0			0
$507$	−7.17776e7	+	4.14408e7i	−0.550763	+	0.317983i
$508$		0			0
$509$	−1.65894e8	−	9.57791e7i	−1.25799	−	0.726302i	−0.285308	−	0.958436i	$-0.592096\pi$
$509$	−1.65894e8	−	9.57791e7i	−1.25799	−	0.726302i	−0.972684	+	0.232134i	$0.925429\pi$
$510$		0			0
$511$	−2.55392e7	+	4.36342e7i	−0.191401	+	0.327013i
$512$		0			0
$513$	2.20900e7	−	3.82610e7i	0.163623	−	0.283403i
$514$		0			0
$515$	−3.60771e7	−	6.24873e7i	−0.264125	−	0.457478i
$516$		0			0
$517$			5.25001e7i			0.379916i
$518$		0			0
$519$	2.41388e6			0.0172669
$520$		0			0
$521$	1.72093e8	−	9.93581e7i	1.21689	−	0.702571i	0.252637	−	0.967561i	$-0.418702\pi$
$521$	1.72093e8	−	9.93581e7i	1.21689	−	0.702571i	0.964251	+	0.264991i	$0.0853688\pi$
$522$		0			0
$523$	−2.58988e7	−	1.49527e7i	−0.181040	−	0.104523i	0.406741	−	0.913543i	$-0.366665\pi$
$523$	−2.58988e7	−	1.49527e7i	−0.181040	−	0.104523i	−0.587781	+	0.809020i	$0.699998\pi$
$524$		0			0
$525$	6.04306e7	+	359164.i	0.417618	+	0.00248207i
$526$		0			0
$527$	−6.24862e7	+	1.08229e8i	−0.426926	+	0.739457i
$528$		0			0
$529$	−6.73817e7	−	1.16709e8i	−0.455171	−	0.788380i
$530$		0			0
$531$			5.53811e7i			0.369894i
$532$		0			0
$533$	2.61652e8			1.72799
$534$		0			0
$535$	−1.26469e8	+	7.30166e7i	−0.825888	+	0.476827i
$536$		0			0
$537$	−6.81685e7	−	3.93571e7i	−0.440211	−	0.254156i
$538$		0			0
$539$	−3.11049e7	−	369751.i	−0.198638	−	0.00236125i
$540$		0			0
$541$	9.78717e7	−	1.69519e8i	0.618109	−	1.07060i	−0.371721	−	0.928344i	$-0.621232\pi$
$541$	9.78717e7	−	1.69519e8i	0.618109	−	1.07060i	0.989830	−	0.142252i	$-0.0454344\pi$
$542$		0			0
$543$	−8.73707e7	−	1.51331e8i	−0.545716	−	0.945207i
$544$		0			0
$545$			8.04054e7i			0.496702i
$546$		0			0
$547$	1.16740e8			0.713277			0.356638	−	0.934242i	$-0.383923\pi$
$547$	1.16740e8			0.713277			0.356638	+	0.934242i	$0.383923\pi$
$548$		0			0
$549$	−5.81610e7	+	3.35793e7i	−0.351492	+	0.202934i
$550$		0			0
$551$	1.23494e8	+	7.12994e7i	0.738230	+	0.426217i
$552$		0			0
$553$	1.96570e6	−	3.30737e8i	0.0116237	−	1.95572i
$554$		0			0
$555$	−1.57231e7	+	2.72333e7i	−0.0919729	+	0.159302i
$556$		0			0
$557$	1.19297e8	+	2.06628e8i	0.690341	+	1.19571i	0.971726	+	0.236111i	$0.0758729\pi$
$557$	1.19297e8	+	2.06628e8i	0.690341	+	1.19571i	−0.281385	+	0.959595i	$0.590794\pi$
$558$		0			0
$559$			6.41050e7i			0.366992i
$560$		0			0
$561$	−9.07727e6			−0.0514122
$562$		0			0
$563$	1.20820e8	−	6.97557e7i	0.677041	−	0.390890i	−0.121698	−	0.992567i	$-0.538834\pi$
$563$	1.20820e8	−	6.97557e7i	0.677041	−	0.390890i	0.798739	+	0.601677i	$0.205501\pi$
$564$		0			0
$565$	6.80473e6	+	3.92871e6i	0.0377282	+	0.0217824i
$566$		0			0
$567$	1.74798e7	+	1.02310e7i	0.0958932	+	0.0561265i
$568$		0			0
$569$	1.64882e8	−	2.85584e8i	0.895027	−	1.55023i	0.0612558	−	0.998122i	$-0.480489\pi$
$569$	1.64882e8	−	2.85584e8i	0.895027	−	1.55023i	0.833771	−	0.552110i	$-0.186177\pi$
$570$		0			0
$571$	−1.50712e8	−	2.61041e8i	−0.809544	−	1.40217i	−0.913180	−	0.407556i	$-0.866381\pi$
$571$	−1.50712e8	−	2.61041e8i	−0.809544	−	1.40217i	0.103636	−	0.994615i	$-0.466952\pi$
$572$		0			0
$573$			1.90827e7i			0.101432i
$574$		0			0
$575$	−1.90067e8			−0.999777
$576$		0			0
$577$	6.30936e7	−	3.64271e7i	0.328442	−	0.189626i	−0.326707	−	0.945126i	$-0.605939\pi$
$577$	6.30936e7	−	3.64271e7i	0.328442	−	0.189626i	0.655149	+	0.755500i	$0.272606\pi$
$578$		0			0
$579$	−1.60426e7	−	9.26221e6i	−0.0826494	−	0.0477176i
$580$		0			0
$581$	−1.52951e8	−	2.68593e8i	−0.779874	−	1.36951i
$582$		0			0
$583$	−1.91271e7	+	3.31291e7i	−0.0965256	+	0.167187i
$584$		0			0
$585$	−2.54419e7	−	4.40667e7i	−0.127082	−	0.220112i
$586$		0			0
$587$			2.02140e8i			0.999398i	0.866199	+	0.499699i	$0.166556\pi$
$587$			2.02140e8i			0.999398i	−0.866199	+	0.499699i	$0.833444\pi$
$588$		0			0
$589$	−6.61836e8			−3.23895
$590$		0			0
$591$	−1.52711e7	+	8.81677e6i	−0.0739788	+	0.0427117i
$592$		0			0
$593$	1.25167e8	+	7.22651e7i	0.600240	+	0.346549i	0.769136	−	0.639085i	$-0.220687\pi$
$593$	1.25167e8	+	7.22651e7i	0.600240	+	0.346549i	−0.168896	+	0.985634i	$0.554020\pi$
$594$		0			0
$595$	4.31581e7	−	2.45765e7i	0.204886	−	0.116673i
$596$		0			0
$597$	1.24897e7	−	2.16329e7i	0.0586989	−	0.101670i
$598$		0			0
$599$	−7.09922e7	−	1.22962e8i	−0.330316	−	0.572125i	0.652257	−	0.757998i	$-0.273822\pi$
$599$	−7.09922e7	−	1.22962e8i	−0.330316	−	0.572125i	−0.982574	+	0.185873i	$0.940489\pi$
$600$		0			0
$601$			9.74425e7i			0.448875i	0.974489	+	0.224437i	$0.0720544\pi$
$601$			9.74425e7i			0.448875i	−0.974489	+	0.224437i	$0.927946\pi$
$602$		0			0
$603$	−1.33503e7			−0.0608889
$604$		0			0
$605$	−9.68897e7	+	5.59393e7i	−0.437534	+	0.252610i
$606$		0			0
$607$	−3.06007e8	−	1.76673e8i	−1.36825	−	0.789959i	−0.377545	−	0.925991i	$-0.623232\pi$
$607$	−3.06007e8	−	1.76673e8i	−1.36825	−	0.789959i	−0.990704	+	0.136032i	$0.956565\pi$
$608$		0			0
$609$	−3.30222e7	+	5.64191e7i	−0.146202	+	0.249790i
$610$		0			0
$611$	3.16196e8	−	5.47667e8i	1.38622	−	2.40101i
$612$		0			0
$613$	4.82450e7	+	8.35628e7i	0.209445	+	0.362770i	0.951540	−	0.307525i	$-0.0995008\pi$
$613$	4.82450e7	+	8.35628e7i	0.209445	+	0.362770i	−0.742095	+	0.670295i	$0.766167\pi$
$614$		0			0
$615$			8.41988e7i			0.361977i
$616$		0			0
$617$	−3.51295e8			−1.49560			−0.747802	−	0.663922i	$-0.768891\pi$
$617$	−3.51295e8			−1.49560			−0.747802	+	0.663922i	$0.768891\pi$
$618$		0			0
$619$	−1.67499e8	+	9.67058e7i	−0.706222	+	0.407738i	−0.809661	−	0.586898i	$-0.800349\pi$
$619$	−1.67499e8	+	9.67058e7i	−0.706222	+	0.407738i	0.103439	+	0.994636i	$0.467015\pi$
$620$		0			0
$621$	−5.51670e7	−	3.18507e7i	−0.230359	−	0.132998i
$622$		0			0
$623$	2.37091e8	+	1.40913e6i	0.980506	+	0.00582754i
$624$		0			0
$625$	−3.01003e7	+	5.21352e7i	−0.123291	+	0.213546i
$626$		0			0
$627$	−2.40359e7	−	4.16314e7i	−0.0975120	−	0.168896i
$628$		0			0
$629$		−	6.75725e7i		−	0.271530i
$630$		0			0
$631$	1.87540e8			0.746461			0.373230	−	0.927739i	$-0.378250\pi$
$631$	1.87540e8			0.746461			0.373230	+	0.927739i	$0.378250\pi$
$632$		0			0
$633$	7.49593e6	−	4.32777e6i	0.0295539	−	0.0170629i
$634$		0			0
$635$	4.43489e7	+	2.56049e7i	0.173206	+	0.100000i
$636$		0			0
$637$	3.22251e8	+	1.91195e8i	1.24674	+	0.739704i
$638$		0			0
$639$	2.32789e7	−	4.03203e7i	0.0892196	−	0.154533i
$640$		0			0
$641$	1.02183e8	+	1.76986e8i	0.387976	+	0.671995i	0.992177	−	0.124837i	$-0.0398409\pi$
$641$	1.02183e8	+	1.76986e8i	0.387976	+	0.671995i	−0.604201	+	0.796832i	$0.706508\pi$
$642$		0			0
$643$		−	4.84738e7i		−	0.182337i	−0.995835	−	0.0911683i	$-0.970940\pi$
$643$		−	4.84738e7i		−	0.182337i	0.995835	−	0.0911683i	$-0.0290601\pi$
$644$		0			0
$645$	−2.06288e7			−0.0768768
$646$		0			0
$647$	−1.17023e8	+	6.75630e7i	−0.432072	+	0.249457i	−0.700229	−	0.713918i	$-0.746919\pi$
$647$	−1.17023e8	+	6.75630e7i	−0.432072	+	0.249457i	0.268157	+	0.963375i	$0.413586\pi$
$648$		0			0
$649$	5.21863e7	+	3.01298e7i	0.190907	+	0.110220i
$650$		0			0
$651$	1.80326e6	−	3.03405e8i	0.00653605	−	1.09971i
$652$		0			0
$653$	−1.04003e8	+	1.80138e8i	−0.373512	+	0.646942i	−0.990103	−	0.140342i	$-0.955180\pi$
$653$	−1.04003e8	+	1.80138e8i	−0.373512	+	0.646942i	0.616591	+	0.787284i	$0.288513\pi$
$654$		0			0
$655$	1.03880e8	+	1.79926e8i	0.369665	+	0.640279i
$656$		0			0
$657$		−	3.58187e7i		−	0.126303i
$658$		0			0
$659$	−1.57325e8			−0.549721			−0.274861	−	0.961484i	$-0.588632\pi$
$659$	−1.57325e8			−0.549721			−0.274861	+	0.961484i	$0.588632\pi$
$660$		0			0
$661$	8.41490e6	−	4.85834e6i	0.0291370	−	0.0168222i	−0.485361	−	0.874314i	$-0.661312\pi$
$661$	8.41490e6	−	4.85834e6i	0.0291370	−	0.0168222i	0.514498	+	0.857492i	$0.327978\pi$
$662$		0			0
$663$	9.46918e7	+	5.46703e7i	0.324916	+	0.187591i
$664$		0			0
$665$	2.26996e8	+	1.32861e8i	0.771885	+	0.451786i
$666$		0			0
$667$	1.02804e8	−	1.78061e8i	0.346442	−	0.600055i
$668$		0			0
$669$	1.30256e8	+	2.25609e8i	0.435029	+	0.753492i
$670$		0			0
$671$			7.30745e7i			0.241879i
$672$		0			0
$673$	2.14510e7			0.0703723			0.0351862	−	0.999381i	$-0.488798\pi$
$673$	2.14510e7			0.0703723			0.0351862	+	0.999381i	$0.488798\pi$
$674$		0			0
$675$	−3.70773e7	+	2.14066e7i	−0.120558	+	0.0696042i
$676$		0			0
$677$	−1.84041e8	−	1.06256e8i	−0.593130	−	0.342444i	0.173204	−	0.984886i	$-0.444588\pi$
$677$	−1.84041e8	−	1.06256e8i	−0.593130	−	0.342444i	−0.766334	+	0.642442i	$0.777921\pi$
$678$		0			0
$679$	1.15710e8	+	2.03194e8i	0.369624	+	0.649086i
$680$		0			0
$681$	−2.03126e7	+	3.51825e7i	−0.0643168	+	0.111400i
$682$		0			0
$683$	3.53265e7	+	6.11873e7i	0.110876	+	0.192043i	0.916124	−	0.400896i	$-0.131301\pi$
$683$	3.53265e7	+	6.11873e7i	0.110876	+	0.192043i	−0.805248	+	0.592939i	$0.797968\pi$
$684$		0			0
$685$			8.03494e7i			0.249983i
$686$		0			0
$687$	−3.32195e7			−0.102453
$688$		0			0
$689$	3.99058e8	−	2.30396e8i	1.22005	−	0.704397i
$690$		0			0
$691$	1.46520e8	+	8.45936e7i	0.444083	+	0.256391i	0.705328	−	0.708881i	$-0.250800\pi$
$691$	1.46520e8	+	8.45936e7i	0.444083	+	0.256391i	−0.261245	+	0.965272i	$0.584133\pi$
$692$		0			0
$693$	1.91506e7	−	1.09054e7i	0.0575416	−	0.0327673i
$694$		0			0
$695$	2.08471e7	−	3.61083e7i	0.0621001	−	0.107560i
$696$		0			0
$697$	−9.04643e7	−	1.56689e8i	−0.267165	−	0.462743i
$698$		0			0
$699$		−	1.40775e8i		−	0.412186i
$700$		0			0
$701$	−3.16582e8			−0.919034			−0.459517	−	0.888169i	$-0.651978\pi$
$701$	−3.16582e8			−0.919034			−0.459517	+	0.888169i	$0.651978\pi$
$702$		0			0
$703$	3.09911e8	−	1.78927e8i	0.892012	−	0.515003i
$704$		0			0
$705$	1.76238e8	+	1.01751e8i	0.502958	+	0.290383i
$706$		0			0
$707$	−1.17614e8	+	2.00946e8i	−0.332814	+	0.568620i
$708$		0			0
$709$	−1.13615e8	+	1.96788e8i	−0.318785	+	0.552153i	−0.980235	−	0.197837i	$-0.936608\pi$
$709$	−1.13615e8	+	1.96788e8i	−0.318785	+	0.552153i	0.661449	+	0.749990i	$0.269942\pi$
$710$		0			0
$711$	1.17158e8	+	2.02924e8i	0.325960	+	0.564579i
$712$		0			0
$713$			9.54273e8i			2.63272i
$714$		0			0
$715$	−5.53662e7			−0.151470
$716$		0			0
$717$	2.87534e8	−	1.66008e8i	0.780067	−	0.450372i
$718$		0			0
$719$	7.41802e7	+	4.28279e7i	0.199573	+	0.115223i	0.596456	−	0.802646i	$-0.296575\pi$
$719$	7.41802e7	+	4.28279e7i	0.199573	+	0.115223i	−0.396883	+	0.917869i	$0.629908\pi$
$720$		0			0
$721$	−3.76418e8	−	2.23721e6i	−1.00430	−	0.00596899i
$722$		0			0
$723$	1.16130e8	−	2.01143e8i	0.307276	−	0.532218i
$724$		0			0
$725$	−6.90934e7	−	1.19673e8i	−0.181310	−	0.314039i
$726$		0			0
$727$			4.63487e8i			1.20624i	0.797650	+	0.603120i	$0.206076\pi$
$727$			4.63487e8i			1.20624i	−0.797650	+	0.603120i	$0.793924\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	3.83890e7	−	2.21639e7i	0.0982775	−	0.0567406i
$732$		0			0
$733$	3.32835e8	+	1.92162e8i	0.845117	+	0.487929i	0.859000	−	0.511975i	$-0.171086\pi$
$733$	3.32835e8	+	1.92162e8i	0.845117	+	0.487929i	−0.0138832	+	0.999904i	$0.504419\pi$
$734$		0			0
$735$	−6.15259e7	+	1.03700e8i	−0.154952	+	0.261165i
$736$		0			0
$737$	−7.26314e6	+	1.25801e7i	−0.0181435	+	0.0314255i
$738$		0			0
$739$	2.56716e7	+	4.44645e7i	0.0636091	+	0.110174i	0.896076	−	0.443900i	$-0.146406\pi$
$739$	2.56716e7	+	4.44645e7i	0.0636091	+	0.110174i	−0.832467	+	0.554075i	$0.813072\pi$
$740$		0			0
$741$			5.79052e8i			1.42319i
$742$		0			0
$743$	−1.71997e8			−0.419329			−0.209664	−	0.977773i	$-0.567237\pi$
$743$	−1.71997e8			−0.419329			−0.209664	+	0.977773i	$0.567237\pi$
$744$		0			0
$745$	3.03054e7	−	1.74968e7i	0.0732910	−	0.0423146i
$746$		0			0
$747$	1.89639e8	+	1.09488e8i	0.454952	+	0.262666i
$748$		0			0
$749$	−4.52790e6	+	7.61836e8i	−0.0107759	+	1.81308i
$750$		0			0
$751$	−2.73144e8	+	4.73100e8i	−0.644870	+	1.11695i	0.339462	+	0.940620i	$0.389755\pi$
$751$	−2.73144e8	+	4.73100e8i	−0.644870	+	1.11695i	−0.984332	+	0.176327i	$0.943578\pi$
$752$		0			0
$753$	7.48733e7	+	1.29684e8i	0.175365	+	0.303741i
$754$		0			0
$755$			2.78366e8i			0.646807i
$756$		0			0
$757$	4.59432e8			1.05909			0.529546	−	0.848281i	$-0.322362\pi$
$757$	4.59432e8			1.05909			0.529546	+	0.848281i	$0.322362\pi$
$758$		0			0
$759$	−6.00266e7	+	3.46564e7i	−0.137284	+	0.0792607i
$760$		0			0
$761$	1.81826e8	+	1.04977e8i	0.412575	+	0.238200i	0.691895	−	0.721998i	$-0.256776\pi$
$761$	1.81826e8	+	1.04977e8i	0.412575	+	0.238200i	−0.279321	+	0.960198i	$0.590109\pi$
$762$		0			0
$763$	3.62020e8	+	2.11891e8i	0.815004	+	0.477023i
$764$		0			0
$765$	−1.75928e7	+	3.04715e7i	−0.0392961	+	0.0680629i
$766$		0			0
$767$	−3.62930e8	−	6.28613e8i	−0.804334	−	1.39315i
$768$		0			0
$769$			4.90557e7i			0.107873i	0.998544	+	0.0539363i	$0.0171768\pi$
$769$			4.90557e7i			0.107873i	−0.998544	+	0.0539363i	$0.982823\pi$
$770$		0			0
$771$	2.13846e8			0.466592
$772$		0			0
$773$	−2.57313e8	+	1.48560e8i	−0.557088	+	0.321635i	−0.751976	−	0.659190i	$-0.770899\pi$
$773$	−2.57313e8	+	1.48560e8i	−0.557088	+	0.321635i	0.194888	+	0.980826i	$0.437566\pi$
$774$		0			0
$775$	5.55433e8	+	3.20679e8i	1.19324	+	0.688915i
$776$		0			0
$777$	8.11811e7	+	1.42560e8i	0.173058	+	0.303902i
$778$		0			0
$779$	4.79085e8	−	8.29800e8i	1.01345	−	1.75534i
$780$		0			0
$781$	−2.53296e7	−	4.38721e7i	−0.0531710	−	0.0920948i
$782$		0			0
$783$		−	4.63136e7i		−	0.0964768i
$784$		0			0
$785$	−1.13561e8			−0.234759
$786$		0			0
$787$	4.46095e8	−	2.57553e8i	0.915172	−	0.528375i	0.0330807	−	0.999453i	$-0.489468\pi$
$787$	4.46095e8	−	2.57553e8i	0.915172	−	0.528375i	0.882092	+	0.471078i	$0.156135\pi$
$788$		0			0
$789$	−9.56320e7	−	5.52132e7i	−0.194703	−	0.112412i
$790$		0			0
$791$	3.56212e7	−	2.02846e7i	0.0719746	−	0.0409861i
$792$		0			0
$793$	4.40111e8	−	7.62295e8i	0.882558	−	1.52863i
$794$		0			0
$795$	7.41408e7	+	1.28416e8i	0.147556	+	0.255574i
$796$		0			0
$797$		−	4.24228e8i		−	0.837962i	−0.907995	−	0.418981i	$-0.862387\pi$
$797$		−	4.24228e8i		−	0.837962i	0.907995	−	0.418981i	$-0.137613\pi$
$798$		0			0
$799$	−4.37290e8			−0.857293
$800$		0			0
$801$	−1.45467e8	+	8.39855e7i	−0.283053	+	0.163420i
$802$		0			0
$803$	−3.37524e7	−	1.94870e7i	−0.0651866	−	0.0376355i
$804$		0			0
$805$	1.91567e8	−	3.27295e8i	0.367225	−	0.627411i
$806$		0			0
$807$	2.46080e8	−	4.26223e8i	0.468226	−	0.810991i
$808$		0			0
$809$	−1.56671e8	−	2.71362e8i	−0.295899	−	0.512512i	0.679295	−	0.733866i	$-0.262286\pi$
$809$	−1.56671e8	−	2.71362e8i	−0.295899	−	0.512512i	−0.975194	+	0.221354i	$0.928952\pi$
$810$		0			0
$811$			5.64312e8i			1.05793i	0.848644	+	0.528965i	$0.177420\pi$
$811$			5.64312e8i			1.05793i	−0.848644	+	0.528965i	$0.822580\pi$
$812$		0			0
$813$	−2.41213e8			−0.448879
$814$		0			0
$815$	−1.62774e8	+	9.39774e7i	−0.300685	+	0.173600i
$816$		0			0
$817$	2.03302e8	+	1.17377e8i	0.372800	+	0.215236i
$818$		0			0
$819$	−2.65455e8	−	1.57770e6i	−0.483213	−	0.00287193i
$820$		0			0
$821$	1.96602e8	−	3.40524e8i	0.355270	−	0.615345i	−0.631894	−	0.775055i	$-0.717722\pi$
$821$	1.96602e8	−	3.40524e8i	0.355270	−	0.615345i	0.987164	+	0.159709i	$0.0510557\pi$
$822$		0			0
$823$	1.54690e8	+	2.67931e8i	0.277500	+	0.480644i	0.970763	−	0.240041i	$-0.0771608\pi$
$823$	1.54690e8	+	2.67931e8i	0.277500	+	0.480644i	−0.693263	+	0.720685i	$0.743827\pi$
$824$		0			0
$825$			4.65845e7i			0.0829621i
$826$		0			0
$827$	−4.65647e8			−0.823266			−0.411633	−	0.911350i	$-0.635041\pi$
$827$	−4.65647e8			−0.823266			−0.411633	+	0.911350i	$0.635041\pi$
$828$		0			0
$829$	1.14826e8	−	6.62946e7i	0.201546	−	0.116363i	−0.395830	−	0.918324i	$-0.629543\pi$
$829$	1.14826e8	−	6.62946e7i	0.201546	−	0.116363i	0.597377	+	0.801961i	$0.296210\pi$
$830$		0			0
$831$	−2.97981e8	−	1.72039e8i	−0.519260	−	0.299795i
$832$		0			0
$833$	3.07978e6	−	2.59083e8i	0.00532825	−	0.448233i
$834$		0			0
$835$	−2.83670e8	+	4.91330e8i	−0.487252	+	0.843945i
$836$		0			0
$837$	1.07476e8	+	1.86154e8i	0.183289	+	0.317466i
$838$		0			0
$839$			3.30763e8i			0.560055i	0.959992	+	0.280028i	$0.0903436\pi$
$839$			3.30763e8i			0.560055i	−0.959992	+	0.280028i	$0.909656\pi$
$840$		0			0
$841$	−4.45338e8			−0.748690
$842$		0			0
$843$	2.52510e8	−	1.45787e8i	0.421498	−	0.243352i
$844$		0			0
$845$	3.02735e8	+	1.74784e8i	0.501755	+	0.289689i
$846$		0			0
$847$	−3.46890e6	+	5.83656e8i	−0.00570876	+	0.960520i
$848$		0			0
$849$	−1.18508e6	+	2.05261e6i	−0.00193653	+	0.00335416i
$850$		0			0
$851$	−2.57987e8	−	4.46847e8i	−0.418610	−	0.725054i
$852$		0			0
$853$			4.69380e8i			0.756271i	0.925750	+	0.378135i	$0.123435\pi$
$853$			4.69380e8i			0.756271i	−0.925750	+	0.378135i	$0.876565\pi$
$854$		0			0
$855$	−1.86337e8			−0.298127
$856$		0			0
$857$	−6.76516e8	+	3.90587e8i	−1.07482	+	0.620547i	−0.929494	−	0.368836i	$-0.879756\pi$
$857$	−6.76516e8	+	3.90587e8i	−1.07482	+	0.620547i	−0.145325	+	0.989384i	$0.546423\pi$
$858$		0			0
$859$	5.62827e8	+	3.24948e8i	0.887964	+	0.512666i	0.873276	−	0.487226i	$-0.161991\pi$
$859$	5.62827e8	+	3.24948e8i	0.887964	+	0.512666i	0.0146882	+	0.999892i	$0.495324\pi$
$860$		0			0
$861$	3.79100e8	+	2.21888e8i	0.593942	+	0.347635i
$862$		0			0
$863$	−1.80414e8	+	3.12487e8i	−0.280697	+	0.486182i	−0.971557	−	0.236807i	$-0.923899\pi$
$863$	−1.80414e8	+	3.12487e8i	−0.280697	+	0.486182i	0.690859	+	0.722989i	$0.257232\pi$
$864$		0			0
$865$	−5.09049e6	−	8.81698e6i	−0.00786522	−	0.0136230i
$866$		0			0
$867$			3.00660e8i			0.461337i
$868$		0			0
$869$	2.54957e8			0.388515
$870$		0			0
$871$	1.51535e8	−	8.74885e7i	0.229328	−	0.132403i
$872$		0			0
$873$	−1.43464e8	−	8.28291e7i	−0.215626	−	0.124492i
$874$		0			0
$875$	−3.00492e8	−	5.27685e8i	−0.448547	−	0.787681i
$876$		0			0
$877$	5.64353e8	−	9.77488e8i	0.836665	−	1.44915i	−0.0560017	−	0.998431i	$-0.517835\pi$
$877$	5.64353e8	−	9.77488e8i	0.836665	−	1.44915i	0.892667	−	0.450716i	$-0.148831\pi$
$878$		0			0
$879$	3.04500e8	+	5.27409e8i	0.448353	+	0.776570i
$880$		0			0
$881$			1.78748e8i			0.261405i	0.991422	+	0.130702i	$0.0417232\pi$
$881$			1.78748e8i			0.261405i	−0.991422	+	0.130702i	$0.958277\pi$
$882$		0			0
$883$	−2.93480e8			−0.426281			−0.213141	−	0.977022i	$-0.568369\pi$
$883$	−2.93480e8			−0.426281			−0.213141	+	0.977022i	$0.568369\pi$
$884$		0			0
$885$	2.02286e8	−	1.16790e8i	0.291834	−	0.168490i
$886$		0			0
$887$	5.43501e8	+	3.13790e8i	0.778806	+	0.449644i	0.836007	−	0.548719i	$-0.184884\pi$
$887$	5.43501e8	+	3.13790e8i	0.778806	+	0.449644i	−0.0572010	+	0.998363i	$0.518218\pi$
$888$		0			0
$889$	2.32157e8	−	1.32202e8i	0.330427	−	0.188163i
$890$		0			0
$891$	−7.80645e6	+	1.35212e7i	−0.0110362	+	0.0191153i
$892$		0			0
$893$	−1.15791e9	−	2.00556e9i	−1.62600	−	2.81632i
$894$		0			0
$895$			3.31991e8i			0.463081i
$896$		0			0
$897$	8.34910e8			1.15681
$898$		0			0
$899$	−6.00846e8	+	3.46898e8i	−0.826959	+	0.477445i
$900$		0			0
$901$	−2.75943e8	−	1.59316e8i	−0.377263	−	0.217813i
$902$		0			0
$903$	−5.43628e7	+	9.28800e7i	−0.0738310	+	0.126142i
$904$		0			0
$905$	−3.68502e8	+	6.38263e8i	−0.497157	+	0.861101i
$906$		0			0
$907$	−4.23906e7	−	7.34227e7i	−0.0568130	−	0.0984030i	0.836220	−	0.548394i	$-0.184761\pi$
$907$	−4.23906e7	−	7.34227e7i	−0.0568130	−	0.0984030i	−0.893033	+	0.449991i	$0.851427\pi$
$908$		0			0
$909$		−	1.64954e8i		−	0.219619i
$910$		0			0
$911$	−7.48073e8			−0.989439			−0.494720	−	0.869053i	$-0.664729\pi$
$911$	−7.48073e8			−0.989439			−0.494720	+	0.869053i	$0.664729\pi$
$912$		0			0
$913$	2.06344e8	−	1.19133e8i	0.271131	−	0.156538i
$914$		0			0
$915$	2.45305e8	+	1.41627e8i	0.320215	+	0.184876i
$916$		0			0
$917$	1.08386e9	+	6.44180e6i	1.40561	+	0.00835410i
$918$		0			0
$919$	4.58229e8	−	7.93676e8i	0.590386	−	1.02258i	−0.403794	−	0.914850i	$-0.632309\pi$
$919$	4.58229e8	−	7.93676e8i	0.590386	−	1.02258i	0.994180	−	0.107729i	$-0.0343578\pi$
$920$		0			0
$921$	−6.27525e7	−	1.08690e8i	−0.0803252	−	0.139127i
$922$		0			0
$923$			6.10217e8i			0.776031i
$924$		0			0
$925$	−3.46782e8			−0.438159
$926$		0			0
$927$	2.30952e8	−	1.33340e8i	0.289923	−	0.167387i
$928$		0			0
$929$	−6.51398e8	−	3.76085e8i	−0.812455	−	0.469071i	0.0353530	−	0.999375i	$-0.488744\pi$
$929$	−6.51398e8	−	3.76085e8i	−0.812455	−	0.469071i	−0.847808	+	0.530304i	$0.822078\pi$
$930$		0			0
$931$	1.19640e9	−	6.71907e8i	1.48261	−	0.832646i
$932$		0			0
$933$	−1.67722e8	+	2.90504e8i	−0.206512	+	0.357690i
$934$		0			0
$935$	1.91425e7	+	3.31558e7i	0.0234187	+	0.0405625i
$936$		0			0
$937$			9.46314e8i			1.15031i	0.818043	+	0.575157i	$0.195059\pi$
$937$			9.46314e8i			1.15031i	−0.818043	+	0.575157i	$0.804941\pi$
$938$		0			0
$939$	−6.74537e8			−0.814721
$940$		0			0
$941$	−1.02724e8	+	5.93079e7i	−0.123283	+	0.0711777i	−0.560374	−	0.828240i	$-0.689342\pi$
$941$	−1.02724e8	+	5.93079e7i	−0.123283	+	0.0711777i	0.437090	+	0.899418i	$0.356009\pi$
$942$		0			0
$943$	−1.19645e9	−	6.90773e8i	−1.42679	−	0.823759i
$944$		0			0
$945$	507701.	−	8.54225e7i	0.000601606	−	0.101222i
$946$		0			0
$947$	−7.05600e8	+	1.22214e9i	−0.830824	+	1.43903i	0.0665621	+	0.997782i	$0.478797\pi$
$947$	−7.05600e8	+	1.22214e9i	−0.830824	+	1.43903i	−0.897386	+	0.441247i	$0.854536\pi$
$948$		0			0
$949$	2.34731e8	+	4.06566e8i	0.274645	+	0.475699i
$950$		0			0
$951$			4.21123e8i			0.489629i
$952$		0			0
$953$	4.73357e8			0.546903			0.273452	−	0.961886i	$-0.411835\pi$
$953$	4.73357e8			0.546903			0.273452	+	0.961886i	$0.411835\pi$
$954$		0			0
$955$	6.97018e7	−	4.02424e7i	0.0800266	−	0.0462034i
$956$		0			0
$957$	−4.36419e7	−	2.51967e7i	−0.0497929	−	0.0287480i
$958$		0			0
$959$	3.61768e8	+	2.11744e8i	0.410180	+	0.240079i
$960$		0			0
$961$	1.16629e9	−	2.02007e9i	1.31412	−	2.27613i
$962$		0			0
$963$	−2.69868e8	−	4.67425e8i	−0.302185	−	0.523400i
$964$		0			0
$965$			7.81301e7i			0.0869433i
$966$		0			0
$967$	−1.12682e9			−1.24617			−0.623084	−	0.782155i	$-0.714121\pi$
$967$	−1.12682e9			−1.24617			−0.623084	+	0.782155i	$0.714121\pi$
$968$		0			0
$969$	3.46762e8	−	2.00203e8i	0.381119	−	0.220039i
$970$		0			0
$971$	−1.33139e9	−	7.68681e8i	−1.45428	−	0.839631i	−0.455563	−	0.890203i	$-0.650562\pi$
$971$	−1.33139e9	−	7.68681e8i	−1.45428	−	0.839631i	−0.998720	+	0.0505722i	$0.983895\pi$
$972$		0			0
$973$	−1.07637e8	−	1.89019e8i	−0.116849	−	0.205195i
$974$		0			0
$975$	2.80568e8	−	4.85958e8i	0.302708	−	0.524306i
$976$		0			0
$977$	9.61091e6	+	1.66466e7i	0.0103058	+	0.0178501i	0.871132	−	0.491048i	$-0.163386\pi$
$977$	9.61091e6	+	1.66466e7i	0.0103058	+	0.0178501i	−0.860827	+	0.508899i	$0.830053\pi$
$978$		0			0
$979$			1.82767e8i			0.194783i
$980$		0			0
$981$	−2.97177e8			−0.314781
$982$		0			0
$983$	1.05413e9	−	6.08603e8i	1.10977	−	0.640727i	0.171002	−	0.985271i	$-0.445300\pi$
$983$	1.05413e9	−	6.08603e8i	1.10977	−	0.640727i	0.938770	+	0.344543i	$0.111966\pi$
$984$		0			0
$985$	6.44085e7	+	3.71863e7i	0.0673961	+	0.0389112i
$986$		0			0
$987$	9.22565e8	−	5.25357e8i	0.959501	−	0.546390i
$988$		0			0
$989$	1.69240e8	−	2.93133e8i	0.174950	−	0.303023i
$990$		0			0
$991$	6.93678e8	+	1.20149e9i	0.712750	+	1.23452i	0.963821	+	0.266550i	$0.0858837\pi$
$991$	6.93678e8	+	1.20149e9i	0.712750	+	1.23452i	−0.251072	+	0.967969i	$0.580783\pi$
$992$		0			0
$993$		−	6.67485e8i		−	0.681700i
$994$		0			0
$995$	−1.05355e8			−0.106952
$996$		0			0
$997$	−1.14500e9	+	6.61063e8i	−1.15536	+	0.667049i	−0.950188	−	0.311677i	$-0.899109\pi$
$997$	−1.14500e9	+	6.61063e8i	−1.15536	+	0.667049i	−0.205174	+	0.978726i	$0.565776\pi$
$998$		0			0
$999$	−1.00654e8	−	5.81124e7i	−0.100956	−	0.0582871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.h.145.5		24
4.3	odd	2		168.7.z.a.145.5	yes	24
7.3	odd	6	inner	336.7.bh.h.241.5		24
28.3	even	6		168.7.z.a.73.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.7.z.a.73.5	✓	24	28.3	even	6
168.7.z.a.145.5	yes	24	4.3	odd	2
336.7.bh.h.145.5		24	1.1	even	1	trivial
336.7.bh.h.241.5		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)

\(f(q)\)	\(=\)	\(q+(13.5000 - 7.79423i) q^{3} +(-56.9387 - 32.8735i) q^{5} +(-298.061 + 169.732i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(13.5000 - 7.79423i) q^{3} +(-56.9387 - 32.8735i) q^{5} +(-298.061 + 169.732i) q^{7} +(121.500 - 210.444i) q^{9} +(-132.203 - 228.982i) q^{11} +3184.91i q^{13} -1024.90 q^{15} +(1907.27 - 1101.16i) q^{17} +(10100.6 + 5831.59i) q^{19} +(-2700.89 + 4614.53i) q^{21} +(8408.32 - 14563.6i) q^{23} +(-5651.16 - 9788.10i) q^{25} -3788.00i q^{27} +12226.4 q^{29} +(-49143.3 + 28372.9i) q^{31} +(-3569.48 - 2060.84i) q^{33} +(22550.9 + 134.029i) q^{35} +(15341.2 - 26571.7i) q^{37} +(24823.9 + 42996.3i) q^{39} -82153.5i q^{41} +20127.7 q^{43} +(-13836.1 + 7988.27i) q^{45} +(-171957. - 99279.3i) q^{47} +(60031.4 - 101181. i) q^{49} +(17165.4 - 29731.4i) q^{51} +(-72339.8 - 125296. i) q^{53} +17383.9i q^{55} +181811. q^{57} +(-197372. + 113953. i) q^{59} +(-239346. - 138186. i) q^{61} +(-495.368 + 83347.5i) q^{63} +(104699. - 181345. i) q^{65} +(-27469.7 - 47578.9i) q^{67} -262145. i q^{69} +191596. q^{71} +(127654. - 73701.0i) q^{73} +(-152581. - 88092.9i) q^{75} +(78270.0 + 45811.6i) q^{77} +(-482132. + 835078. i) q^{79} +(-29524.5 - 51137.9i) q^{81} +901135. i q^{83} -144796. q^{85} +(165057. - 95295.4i) q^{87} +(-598630. - 345619. i) q^{89} +(-540580. - 949297. i) q^{91} +(-442289. + 766068. i) q^{93} +(-383410. - 664085. i) q^{95} -681721. i q^{97} -64250.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9}+O(q^{10}) \) 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

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