LMFDB - Embedded newform 336.7.bh.d.145.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$77.2981720963$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 $ x^8 - x^7 + 212x^6 + 473x^5 + 39800x^4 + 36821x^3 + 985651x^2 - 601290x + 21068100
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3\cdot 7 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.4
Root			$-2.75320 - 4.76869i$ of defining polynomial
Character	$\chi$	$=$	336.145
Dual form			336.7.bh.d.241.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.5000 - 7.79423i) q^{3} +(53.9244 + 31.1333i) q^{5} +(-218.833 - 264.124i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(13.5000 - 7.79423i) q^{3} +(53.9244 + 31.1333i) q^{5} +(-218.833 - 264.124i) q^{7} +(121.500 - 210.444i) q^{9} +(9.71675 + 16.8299i) q^{11} +1642.65i q^{13} +970.639 q^{15} +(-186.054 + 107.418i) q^{17} +(8237.53 + 4755.94i) q^{19} +(-5012.88 - 1860.04i) q^{21} +(-7223.90 + 12512.2i) q^{23} +(-5873.94 - 10174.0i) q^{25} -3788.00i q^{27} +43016.4 q^{29} +(7799.62 - 4503.11i) q^{31} +(262.352 + 151.469i) q^{33} +(-3577.38 - 21055.7i) q^{35} +(16564.6 - 28690.7i) q^{37} +(12803.2 + 22175.8i) q^{39} -73712.4i q^{41} -4761.19 q^{43} +(13103.6 - 7565.38i) q^{45} +(63760.5 + 36812.2i) q^{47} +(-21873.6 + 115598. i) q^{49} +(-1674.48 + 2900.29i) q^{51} +(-119317. - 206663. i) q^{53} +1210.06i q^{55} +148275. q^{57} +(282811. - 163281. i) q^{59} +(350517. + 202371. i) q^{61} +(-82171.4 + 13961.0i) q^{63} +(-51141.0 + 88578.8i) q^{65} +(109982. + 190494. i) q^{67} +225219. i q^{69} -350228. q^{71} +(-174606. + 100809. i) q^{73} +(-158596. - 91565.7i) q^{75} +(2318.83 - 6249.36i) q^{77} +(197745. - 342505. i) q^{79} +(-29524.5 - 51137.9i) q^{81} -13229.0i q^{83} -13377.1 q^{85} +(580722. - 335280. i) q^{87} +(-199460. - 115158. i) q^{89} +(433862. - 359465. i) q^{91} +(70196.6 - 121584. i) q^{93} +(296136. + 512922. i) q^{95} -662517. i q^{97} +4722.34 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 108 q^{3} - 294 q^{5} + 656 q^{7} + 972 q^{9}+O(q^{10}) $ 8 * q + 108 * q^3 - 294 * q^5 + 656 * q^7 + 972 * q^9	$ 8 q + 108 q^{3} - 294 q^{5} + 656 q^{7} + 972 q^{9} + 314 q^{11} - 5292 q^{15} - 5532 q^{17} + 18234 q^{19} + 9342 q^{21} - 3928 q^{23} - 17038 q^{25} - 8300 q^{29} + 89508 q^{31} + 8478 q^{33} + 25860 q^{35} + 64706 q^{37} - 29106 q^{39} - 45740 q^{43} - 71442 q^{45} - 483276 q^{47} - 310684 q^{49} - 49788 q^{51} - 540974 q^{53} + 328212 q^{57} + 181770 q^{59} + 418224 q^{61} + 92826 q^{63} - 414204 q^{65} + 1158902 q^{67} - 1442344 q^{71} - 378666 q^{73} - 460026 q^{75} + 1065994 q^{77} - 611452 q^{79} - 236196 q^{81} - 275112 q^{85} - 112050 q^{87} - 989196 q^{89} - 304446 q^{91} + 805572 q^{93} + 591792 q^{95} + 152604 q^{99}+O(q^{100}) $ 8 * q + 108 * q^3 - 294 * q^5 + 656 * q^7 + 972 * q^9 + 314 * q^11 - 5292 * q^15 - 5532 * q^17 + 18234 * q^19 + 9342 * q^21 - 3928 * q^23 - 17038 * q^25 - 8300 * q^29 + 89508 * q^31 + 8478 * q^33 + 25860 * q^35 + 64706 * q^37 - 29106 * q^39 - 45740 * q^43 - 71442 * q^45 - 483276 * q^47 - 310684 * q^49 - 49788 * q^51 - 540974 * q^53 + 328212 * q^57 + 181770 * q^59 + 418224 * q^61 + 92826 * q^63 - 414204 * q^65 + 1158902 * q^67 - 1442344 * q^71 - 378666 * q^73 - 460026 * q^75 + 1065994 * q^77 - 611452 * q^79 - 236196 * q^81 - 275112 * q^85 - 112050 * q^87 - 989196 * q^89 - 304446 * q^91 + 805572 * q^93 + 591792 * q^95 + 152604 * 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
$5$	53.9244	+	31.1333i	0.431395	+	0.249066i	0.699941	−	0.714201i	$-0.253210\pi$
$5$	53.9244	+	31.1333i	0.431395	+	0.249066i	−0.268546	+	0.963267i	$0.586543\pi$
$6$		0			0
$7$	−218.833	−	264.124i	−0.637996	−	0.770040i
$7$	−218.833	−	264.124i	−0.637996	−	0.770040i
$8$		0			0
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$		0			0
$11$	9.71675	+	16.8299i	0.00730034	+	0.0126446i	0.869652	−	0.493664i	$-0.164343\pi$
$11$	9.71675	+	16.8299i	0.00730034	+	0.0126446i	−0.862352	+	0.506309i	$0.831010\pi$
$12$		0			0
$13$			1642.65i			0.747678i	0.927494	+	0.373839i	$0.121959\pi$
$13$			1642.65i			0.747678i	−0.927494	+	0.373839i	$0.878041\pi$
$14$		0			0
$15$	970.639			0.287597
$16$		0			0
$17$	−186.054	+	107.418i	−0.0378697	+	0.0218641i	−0.518815	−	0.854886i	$-0.673627\pi$
$17$	−186.054	+	107.418i	−0.0378697	+	0.0218641i	0.480946	+	0.876750i	$0.340293\pi$
$18$		0			0
$19$	8237.53	+	4755.94i	1.20098	+	0.693387i	0.960773	−	0.277335i	$-0.0894512\pi$
$19$	8237.53	+	4755.94i	1.20098	+	0.693387i	0.240208	+	0.970722i	$0.422785\pi$
$20$		0			0
$21$	−5012.88	−	1860.04i	−0.541289	−	0.200846i
$22$		0			0
$23$	−7223.90	+	12512.2i	−0.593729	+	1.02837i	0.399996	+	0.916517i	$0.369012\pi$
$23$	−7223.90	+	12512.2i	−0.593729	+	1.02837i	−0.993725	+	0.111852i	$0.964322\pi$
$24$		0			0
$25$	−5873.94	−	10174.0i	−0.375932	−	0.651134i
$26$		0			0
$27$		−	3788.00i		−	0.192450i
$28$		0			0
$29$	43016.4			1.76376			0.881882	−	0.471471i	$-0.156277\pi$
$29$	43016.4			1.76376			0.881882	+	0.471471i	$0.156277\pi$
$30$		0			0
$31$	7799.62	−	4503.11i	0.261811	−	0.151157i	−0.363349	−	0.931653i	$-0.618367\pi$
$31$	7799.62	−	4503.11i	0.261811	−	0.151157i	0.625161	+	0.780496i	$0.285033\pi$
$32$		0			0
$33$	262.352	+	151.469i	0.00730034	+	0.00421485i
$34$		0			0
$35$	−3577.38	−	21055.7i	−0.0834375	−	0.491094i
$36$		0			0
$37$	16564.6	−	28690.7i	0.327020	−	0.566416i	−0.654899	−	0.755717i	$-0.727289\pi$
$37$	16564.6	−	28690.7i	0.327020	−	0.566416i	0.981919	+	0.189301i	$0.0606221\pi$
$38$		0			0
$39$	12803.2	+	22175.8i	0.215836	+	0.373839i
$40$		0			0
$41$		−	73712.4i		−	1.06952i	−0.845004	−	0.534760i	$-0.820402\pi$
$41$		−	73712.4i		−	1.06952i	0.845004	−	0.534760i	$-0.179598\pi$
$42$		0			0
$43$	−4761.19			−0.0598839			−0.0299420	−	0.999552i	$-0.509532\pi$
$43$	−4761.19			−0.0598839			−0.0299420	+	0.999552i	$0.509532\pi$
$44$		0			0
$45$	13103.6	−	7565.38i	0.143798	−	0.0830220i
$46$		0			0
$47$	63760.5	+	36812.2i	0.614127	+	0.354567i	0.774579	−	0.632477i	$-0.217962\pi$
$47$	63760.5	+	36812.2i	0.614127	+	0.354567i	−0.160452	+	0.987044i	$0.551295\pi$
$48$		0			0
$49$	−21873.6	+	115598.i	−0.185922	+	0.982564i
$50$		0			0
$51$	−1674.48	+	2900.29i	−0.0126232	+	0.0218641i
$52$		0			0
$53$	−119317.	−	206663.i	−0.801447	−	1.38815i	−0.918664	−	0.395041i	$-0.870730\pi$
$53$	−119317.	−	206663.i	−0.801447	−	1.38815i	0.117216	−	0.993106i	$-0.462603\pi$
$54$		0			0
$55$			1210.06i			0.00727307i
$56$		0			0
$57$	148275.			0.800654
$58$		0			0
$59$	282811.	−	163281.i	1.37702	−	0.795023i	0.385221	−	0.922824i	$-0.374125\pi$
$59$	282811.	−	163281.i	1.37702	−	0.795023i	0.991800	+	0.127801i	$0.0407919\pi$
$60$		0			0
$61$	350517.	+	202371.i	1.54426	+	0.891578i	0.998563	+	0.0535954i	$0.0170681\pi$
$61$	350517.	+	202371.i	1.54426	+	0.891578i	0.545696	+	0.837983i	$0.316265\pi$
$62$		0			0
$63$	−82171.4	+	13961.0i	−0.328624	+	0.0558336i
$64$		0			0
$65$	−51141.0	+	88578.8i	−0.186221	+	0.322545i
$66$		0			0
$67$	109982.	+	190494.i	0.365676	+	0.633369i	0.988884	−	0.148687i	$-0.0475046\pi$
$67$	109982.	+	190494.i	0.365676	+	0.633369i	−0.623209	+	0.782056i	$0.714171\pi$
$68$		0			0
$69$			225219.i			0.685579i
$70$		0			0
$71$	−350228.			−0.978535			−0.489267	−	0.872134i	$-0.662736\pi$
$71$	−350228.			−0.978535			−0.489267	+	0.872134i	$0.662736\pi$
$72$		0			0
$73$	−174606.	+	100809.i	−0.448838	+	0.259137i	−0.707339	−	0.706874i	$-0.750105\pi$
$73$	−174606.	+	100809.i	−0.448838	+	0.259137i	0.258501	+	0.966011i	$0.416771\pi$
$74$		0			0
$75$	−158596.	−	91565.7i	−0.375932	−	0.217045i
$76$		0			0
$77$	2318.83	−	6249.36i	0.00507923	−	0.0136887i
$78$		0			0
$79$	197745.	−	342505.i	0.401074	−	0.694681i	−0.592782	−	0.805363i	$-0.701970\pi$
$79$	197745.	−	342505.i	0.401074	−	0.694681i	0.993856	+	0.110682i	$0.0353036\pi$
$80$		0			0
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	13229.0i		−	0.0231362i	−0.999933	−	0.0115681i	$-0.996318\pi$
$83$		−	13229.0i		−	0.0231362i	0.999933	−	0.0115681i	$-0.00368232\pi$
$84$		0			0
$85$	−13377.1			−0.0217824
$86$		0			0
$87$	580722.	−	335280.i	0.881882	−	0.509155i
$88$		0			0
$89$	−199460.	−	115158.i	−0.282934	−	0.163352i	0.351817	−	0.936069i	$-0.385564\pi$
$89$	−199460.	−	115158.i	−0.282934	−	0.163352i	−0.634751	+	0.772717i	$0.718897\pi$
$90$		0			0
$91$	433862.	−	359465.i	0.575742	−	0.477015i
$92$		0			0
$93$	70196.6	−	121584.i	0.0872705	−	0.151157i
$94$		0			0
$95$	296136.	+	512922.i	0.345398	+	0.598247i
$96$		0			0
$97$		−	662517.i		−	0.725909i	−0.931807	−	0.362954i	$-0.881768\pi$
$97$		−	662517.i		−	0.725909i	0.931807	−	0.362954i	$-0.118232\pi$
$98$		0			0
$99$	4722.34			0.00486689
$100$		0			0
$101$	1.62606e6	−	938803.i	1.57823	−	0.911193i	0.583127	−	0.812381i	$-0.301829\pi$
$101$	1.62606e6	−	938803.i	1.57823	−	0.911193i	0.995106	−	0.0988126i	$-0.0315044\pi$
$102$		0			0
$103$	−782887.	−	452000.i	−0.716452	−	0.413644i	0.0969931	−	0.995285i	$-0.469078\pi$
$103$	−782887.	−	452000.i	−0.716452	−	0.413644i	−0.813446	+	0.581641i	$0.802411\pi$
$104$		0			0
$105$	−212407.	−	256369.i	−0.183485	−	0.221461i
$106$		0			0
$107$	423106.	−	732842.i	0.345381	−	0.598217i	−0.640042	−	0.768340i	$-0.721083\pi$
$107$	423106.	−	732842.i	0.345381	−	0.598217i	0.985423	+	0.170123i	$0.0544164\pi$
$108$		0			0
$109$	847674.	+	1.46821e6i	0.654560	+	1.13373i	0.982004	+	0.188861i	$0.0604794\pi$
$109$	847674.	+	1.46821e6i	0.654560	+	1.13373i	−0.327444	+	0.944871i	$0.606187\pi$
$110$		0			0
$111$		−	516432.i		−	0.377611i
$112$		0			0
$113$	−152753.			−0.105866			−0.0529328	−	0.998598i	$-0.516857\pi$
$113$	−152753.			−0.105866			−0.0529328	+	0.998598i	$0.516857\pi$
$114$		0			0
$115$	−779089.	+	449807.i	−0.512264	+	0.295756i
$116$		0			0
$117$	345686.	+	199582.i	0.215836	+	0.124613i
$118$		0			0
$119$	69086.3	+	25634.6i	0.0409969	+	0.0152120i
$120$		0			0
$121$	885592.	−	1.53389e6i	0.499893	−	0.865841i
$122$		0			0
$123$	−574531.	−	995117.i	−0.308744	−	0.534760i
$124$		0			0
$125$		−	1.70441e6i		−	0.872660i
$126$		0			0
$127$	2.82114e6			1.37725			0.688627	−	0.725116i	$-0.258214\pi$
$127$	2.82114e6			1.37725			0.688627	+	0.725116i	$0.258214\pi$
$128$		0			0
$129$	−64276.1	+	37109.8i	−0.0299420	+	0.0172870i
$130$		0			0
$131$	3.86131e6	+	2.22933e6i	1.71759	+	0.991654i	0.923262	+	0.384171i	$0.125513\pi$
$131$	3.86131e6	+	2.22933e6i	1.71759	+	0.991654i	0.794333	+	0.607482i	$0.207820\pi$
$132$		0			0
$133$	−546484.	−	3.21648e6i	−0.232286	−	1.36718i
$134$		0			0
$135$	117933.	−	204265.i	0.0479328	−	0.0830220i
$136$		0			0
$137$	−649623.	−	1.12518e6i	−0.252639	−	0.437583i	0.711613	−	0.702572i	$-0.247965\pi$
$137$	−649623.	−	1.12518e6i	−0.252639	−	0.437583i	−0.964252	+	0.264989i	$0.914632\pi$
$138$		0			0
$139$			119566.i			0.0445207i	0.999752	+	0.0222603i	$0.00708627\pi$
$139$			119566.i			0.0445207i	−0.999752	+	0.0222603i	$0.992914\pi$
$140$		0			0
$141$	1.14769e6			0.409418
$142$		0			0
$143$	−27645.6	+	15961.2i	−0.00945406	+	0.00545830i
$144$		0			0
$145$	2.31963e6	+	1.33924e6i	0.760879	+	0.439293i
$146$		0			0
$147$	605702.	+	1.73106e6i	0.190681	+	0.544953i
$148$		0			0
$149$	−3.12914e6	+	5.41983e6i	−0.945946	+	1.63843i	−0.192101	+	0.981375i	$0.561530\pi$
$149$	−3.12914e6	+	5.41983e6i	−0.945946	+	1.63843i	−0.753845	+	0.657052i	$0.771803\pi$
$150$		0			0
$151$	−753969.	−	1.30591e6i	−0.218989	−	0.379300i	0.735510	−	0.677514i	$-0.236943\pi$
$151$	−753969.	−	1.30591e6i	−0.218989	−	0.379300i	−0.954499	+	0.298213i	$0.903609\pi$
$152$		0			0
$153$			52205.3i			0.0145761i
$154$		0			0
$155$	560786.			0.150592
$156$		0			0
$157$	2.14761e6	−	1.23992e6i	0.554954	−	0.320403i	−0.196164	−	0.980571i	$-0.562848\pi$
$157$	2.14761e6	−	1.23992e6i	0.554954	−	0.320403i	0.751118	+	0.660169i	$0.229515\pi$
$158$		0			0
$159$	−3.22156e6	−	1.85997e6i	−0.801447	−	0.462716i
$160$		0			0
$161$	4.88558e6	−	830066.i	1.17068	−	0.198900i
$162$		0			0
$163$	3.29510e6	−	5.70727e6i	0.760861	−	1.31785i	−0.181546	−	0.983382i	$-0.558110\pi$
$163$	3.29510e6	−	5.70727e6i	0.760861	−	1.31785i	0.942407	−	0.334468i	$-0.108556\pi$
$164$		0			0
$165$	9431.46	+	16335.8i	0.00209955	+	0.00363653i
$166$		0			0
$167$			5.45006e6i			1.17018i	0.810969	+	0.585089i	$0.198941\pi$
$167$			5.45006e6i			1.17018i	−0.810969	+	0.585089i	$0.801059\pi$
$168$		0			0
$169$	2.12851e6			0.440978
$170$		0			0
$171$	2.00172e6	−	1.15569e6i	0.400327	−	0.231129i
$172$		0			0
$173$	2.39148e6	+	1.38072e6i	0.461879	+	0.266666i	0.712834	−	0.701333i	$-0.247411\pi$
$173$	2.39148e6	+	1.38072e6i	0.461879	+	0.266666i	−0.250955	+	0.967999i	$0.580745\pi$
$174$		0			0
$175$	−1.40177e6	+	3.77784e6i	−0.261556	+	0.704903i
$176$		0			0
$177$	2.54530e6	−	4.40859e6i	0.459007	−	0.795023i
$178$		0			0
$179$	−743863.	−	1.28841e6i	−0.129698	−	0.224644i	0.793861	−	0.608099i	$-0.208068\pi$
$179$	−743863.	−	1.28841e6i	−0.129698	−	0.224644i	−0.923560	+	0.383455i	$0.874734\pi$
$180$		0			0
$181$			6.01679e6i			1.01468i	0.861746	+	0.507340i	$0.169371\pi$
$181$			6.01679e6i			1.01468i	−0.861746	+	0.507340i	$0.830629\pi$
$182$		0			0
$183$	6.30931e6			1.02951
$184$		0			0
$185$	1.78647e6	−	1.03142e6i	0.282150	−	0.162899i
$186$		0			0
$187$	−3615.68	−	2087.51i	−0.000552923	−	0.000319230i
$188$		0			0
$189$	−1.00050e6	+	828937.i	−0.148194	+	0.122782i
$190$		0			0
$191$	3.20172e6	−	5.54554e6i	0.459498	−	0.795874i	−0.539437	−	0.842026i	$-0.681363\pi$
$191$	3.20172e6	−	5.54554e6i	0.459498	−	0.795874i	0.998934	+	0.0461527i	$0.0146961\pi$
$192$		0			0
$193$	−4.92592e6	−	8.53194e6i	−0.685197	−	1.18680i	−0.973375	−	0.229219i	$-0.926383\pi$
$193$	−4.92592e6	−	8.53194e6i	−0.685197	−	1.18680i	0.288178	−	0.957577i	$-0.406951\pi$
$194$		0			0
$195$			1.59442e6i			0.215030i
$196$		0			0
$197$	2.38883e6			0.312454			0.156227	−	0.987721i	$-0.450067\pi$
$197$	2.38883e6			0.312454			0.156227	+	0.987721i	$0.450067\pi$
$198$		0			0
$199$	1.36103e7	−	7.85789e6i	1.72706	−	0.997118i	0.825594	−	0.564264i	$-0.190840\pi$
$199$	1.36103e7	−	7.85789e6i	1.72706	−	0.997118i	0.901464	−	0.432854i	$-0.142493\pi$
$200$		0			0
$201$	2.96951e6	+	1.71445e6i	0.365676	+	0.211123i
$202$		0			0
$203$	−9.41339e6	−	1.13617e7i	−1.12527	−	1.35817i
$204$		0			0
$205$	2.29491e6	−	3.97490e6i	0.266381	−	0.461386i
$206$		0			0
$207$	1.75541e6	+	3.04046e6i	0.197910	+	0.342790i
$208$		0			0
$209$			184849.i			0.0202478i
$210$		0			0
$211$	−1.46740e6			−0.156207			−0.0781034	−	0.996945i	$-0.524886\pi$
$211$	−1.46740e6			−0.156207			−0.0781034	+	0.996945i	$0.524886\pi$
$212$		0			0
$213$	−4.72808e6	+	2.72976e6i	−0.489267	+	0.282479i
$214$		0			0
$215$	−256744.	−	148231.i	−0.0258336	−	0.0149151i
$216$		0			0
$217$	−2.89619e6	−	1.07464e6i	−0.283431	−	0.105168i
$218$		0			0
$219$	−1.57145e6	+	2.72183e6i	−0.149613	+	0.259137i
$220$		0			0
$221$	−176450.	−	305621.i	−0.0163473	−	0.0283143i
$222$		0			0
$223$		−	3.63341e6i		−	0.327642i	−0.986490	−	0.163821i	$-0.947618\pi$
$223$		−	3.63341e6i		−	0.327642i	0.986490	−	0.163821i	$-0.0523820\pi$
$224$		0			0
$225$	−2.85474e6			−0.250621
$226$		0			0
$227$	−5.14121e6	+	2.96828e6i	−0.439529	+	0.253762i	−0.703398	−	0.710796i	$-0.748335\pi$
$227$	−5.14121e6	+	2.96828e6i	−0.439529	+	0.253762i	0.263869	+	0.964559i	$0.415001\pi$
$228$		0			0
$229$	1.05964e7	+	6.11784e6i	0.882373	+	0.509438i	0.871440	−	0.490502i	$-0.163187\pi$
$229$	1.05964e7	+	6.11784e6i	0.882373	+	0.509438i	0.0109329	+	0.999940i	$0.496520\pi$
$230$		0			0
$231$	−17404.6	−	102440.i	−0.00141198	−	0.00831061i
$232$		0			0
$233$	−6.06046e6	+	1.04970e7i	−0.479113	+	0.829848i	−0.999713	−	0.0239524i	$-0.992375\pi$
$233$	−6.06046e6	+	1.04970e7i	−0.479113	+	0.829848i	0.520600	+	0.853801i	$0.325708\pi$
$234$		0			0
$235$	2.29216e6	+	3.97015e6i	0.176621	+	0.305917i
$236$		0			0
$237$		−	6.16509e6i		−	0.463121i
$238$		0			0
$239$	−1.19016e7			−0.871790			−0.435895	−	0.899998i	$-0.643568\pi$
$239$	−1.19016e7			−0.871790			−0.435895	+	0.899998i	$0.643568\pi$
$240$		0			0
$241$	−8.62117e6	+	4.97743e6i	−0.615907	+	0.355594i	−0.775274	−	0.631625i	$-0.782388\pi$
$241$	−8.62117e6	+	4.97743e6i	−0.615907	+	0.355594i	0.159367	+	0.987219i	$0.449055\pi$
$242$		0			0
$243$	−797162.	−	460241.i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−4.77845e6	+	5.55254e6i	−0.324929	+	0.377566i
$246$		0			0
$247$	−7.81234e6	+	1.35314e7i	−0.518430	+	0.897947i
$248$		0			0
$249$	−103109.	−	178591.i	−0.00667883	−	0.0115681i
$250$		0			0
$251$			4.57737e6i			0.289464i	0.989471	+	0.144732i	$0.0462320\pi$
$251$			4.57737e6i			0.289464i	−0.989471	+	0.144732i	$0.953768\pi$
$252$		0			0
$253$	−280772.			−0.0173377
$254$		0			0
$255$	−180591.	+	104264.i	−0.0108912	+	0.00628804i
$256$		0			0
$257$	−3.50429e6	−	2.02320e6i	−0.206443	−	0.119190i	0.393214	−	0.919447i	$-0.371363\pi$
$257$	−3.50429e6	−	2.02320e6i	−0.206443	−	0.119190i	−0.599657	+	0.800257i	$0.704696\pi$
$258$		0			0
$259$	−1.12028e7	+	1.90336e6i	−0.644801	+	0.109552i
$260$		0			0
$261$	5.22650e6	−	9.05256e6i	0.293961	−	0.509155i
$262$		0			0
$263$	1.48379e7	+	2.56999e7i	0.815651	+	1.41275i	0.908860	+	0.417102i	$0.136954\pi$
$263$	1.48379e7	+	2.56999e7i	0.815651	+	1.41275i	−0.0932094	+	0.995647i	$0.529713\pi$
$264$		0			0
$265$		−	1.48589e7i		−	0.798453i
$266$		0			0
$267$	−3.59027e6			−0.188623
$268$		0			0
$269$	−1.77285e7	+	1.02355e7i	−0.910783	+	0.525841i	−0.880683	−	0.473706i	$-0.842916\pi$
$269$	−1.77285e7	+	1.02355e7i	−0.910783	+	0.525841i	−0.0300997	+	0.999547i	$0.509582\pi$
$270$		0			0
$271$	−2.19287e6	−	1.26606e6i	−0.110181	−	0.0636128i	0.443897	−	0.896078i	$-0.353596\pi$
$271$	−2.19287e6	−	1.26606e6i	−0.110181	−	0.0636128i	−0.554078	+	0.832465i	$0.686929\pi$
$272$		0			0
$273$	3.05539e6	−	8.23440e6i	0.150168	−	0.404710i
$274$		0			0
$275$	114151.	−	197716.i	0.00548887	−	0.00950700i
$276$		0			0
$277$	−1.52864e7	−	2.64769e7i	−0.719229	−	1.24574i	−0.961306	−	0.275484i	$-0.911162\pi$
$277$	−1.52864e7	−	2.64769e7i	−0.719229	−	1.24574i	0.242077	−	0.970257i	$-0.422171\pi$
$278$		0			0
$279$		−	2.18851e6i		−	0.100771i
$280$		0			0
$281$	−2.27089e7			−1.02348			−0.511738	−	0.859142i	$-0.670998\pi$
$281$	−2.27089e7			−1.02348			−0.511738	+	0.859142i	$0.670998\pi$
$282$		0			0
$283$	−3.54922e7	+	2.04914e7i	−1.56593	+	0.904092i	−0.569297	+	0.822132i	$0.692784\pi$
$283$	−3.54922e7	+	2.04914e7i	−1.56593	+	0.904092i	−0.996636	+	0.0819595i	$0.973882\pi$
$284$		0			0
$285$	7.99566e6	+	4.61630e6i	0.345398	+	0.199416i
$286$		0			0
$287$	−1.94692e7	+	1.61307e7i	−0.823573	+	0.682349i
$288$		0			0
$289$	−1.20457e7	+	2.08638e7i	−0.499044	+	0.864369i
$290$		0			0
$291$	−5.16381e6	−	8.94398e6i	−0.209552	−	0.362954i
$292$		0			0
$293$			2.94333e7i			1.17014i	0.810984	+	0.585069i	$0.198932\pi$
$293$			2.94333e7i			1.17014i	−0.810984	+	0.585069i	$0.801068\pi$
$294$		0			0
$295$	2.03339e7			0.792053
$296$		0			0
$297$	63751.6	−	36807.0i	0.00243345	−	0.00140495i
$298$		0			0
$299$	−2.05531e7	−	1.18663e7i	−0.768889	−	0.443918i
$300$		0			0
$301$	1.04190e6	+	1.25754e6i	0.0382057	+	0.0461130i
$302$		0			0
$303$	1.46345e7	−	2.53477e7i	0.526078	−	0.911193i
$304$		0			0
$305$	1.26010e7	+	2.18255e7i	0.444124	+	0.769245i
$306$		0			0
$307$		−	4.67295e6i		−	0.161501i	−0.996734	−	0.0807506i	$-0.974268\pi$
$307$		−	4.67295e6i		−	0.161501i	0.996734	−	0.0807506i	$-0.0257317\pi$
$308$		0			0
$309$	−1.40920e7			−0.477635
$310$		0			0
$311$	−2.77399e7	+	1.60156e7i	−0.922196	+	0.532430i	−0.884335	−	0.466853i	$-0.845388\pi$
$311$	−2.77399e7	+	1.60156e7i	−0.922196	+	0.532430i	−0.0378610	+	0.999283i	$0.512054\pi$
$312$		0			0
$313$	1.88804e7	+	1.09006e7i	0.615714	+	0.355483i	0.775199	−	0.631718i	$-0.217650\pi$
$313$	1.88804e7	+	1.09006e7i	0.615714	+	0.355483i	−0.159484	+	0.987200i	$0.550983\pi$
$314$		0			0
$315$	−4.86570e6	−	1.80542e6i	−0.155673	−	0.0577627i
$316$		0			0
$317$	−5.26241e6	+	9.11476e6i	−0.165199	+	0.286133i	−0.936726	−	0.350064i	$-0.886160\pi$
$317$	−5.26241e6	+	9.11476e6i	−0.165199	+	0.286133i	0.771527	+	0.636196i	$0.219493\pi$
$318$		0			0
$319$	417980.	+	723962.i	0.0128761	+	0.0223020i
$320$		0			0
$321$		−	1.31911e7i		−	0.398811i
$322$		0			0
$323$	−2.04350e6			−0.0606410
$324$		0			0
$325$	1.67122e7	−	9.64882e6i	0.486838	−	0.281076i
$326$		0			0
$327$	2.28872e7	+	1.32139e7i	0.654560	+	0.377910i
$328$		0			0
$329$	−4.22992e6	−	2.48964e7i	−0.118780	−	0.699114i
$330$		0			0
$331$	2.03472e7	−	3.52425e7i	0.561076	−	0.971812i	−0.436327	−	0.899788i	$-0.643721\pi$
$331$	2.03472e7	−	3.52425e7i	0.561076	−	0.971812i	0.997403	−	0.0720239i	$-0.0229458\pi$
$332$		0			0
$333$	−4.02519e6	−	6.97183e6i	−0.109007	−	0.188805i
$334$		0			0
$335$			1.36964e7i			0.364310i
$336$		0			0
$337$	−4.05258e7			−1.05887			−0.529434	−	0.848351i	$-0.677596\pi$
$337$	−4.05258e7			−1.05887			−0.529434	+	0.848351i	$0.677596\pi$
$338$		0			0
$339$	−2.06217e6	+	1.19059e6i	−0.0529328	+	0.0305607i
$340$		0			0
$341$	151574.	+	87511.3i	0.00382262	+	0.00220699i
$342$		0			0
$343$	3.53187e7	−	1.95192e7i	0.875231	−	0.483704i
$344$		0			0
$345$	−7.01180e6	+	1.21448e7i	−0.170755	+	0.295756i
$346$		0			0
$347$	−8.26775e6	−	1.43202e7i	−0.197879	−	0.342736i	0.749962	−	0.661481i	$-0.230072\pi$
$347$	−8.26775e6	−	1.43202e7i	−0.197879	−	0.342736i	−0.947840	+	0.318745i	$0.896738\pi$
$348$		0			0
$349$			5.07209e6i			0.119319i	0.998219	+	0.0596597i	$0.0190015\pi$
$349$			5.07209e6i			0.119319i	−0.998219	+	0.0596597i	$0.980998\pi$
$350$		0			0
$351$	6.22234e6			0.143891
$352$		0			0
$353$	−3.94332e7	+	2.27668e7i	−0.896475	+	0.517580i	−0.876055	−	0.482211i	$-0.839834\pi$
$353$	−3.94332e7	+	2.27668e7i	−0.896475	+	0.517580i	−0.0204200	+	0.999791i	$0.506500\pi$
$354$		0			0
$355$	−1.88858e7	−	1.09037e7i	−0.422135	−	0.243720i
$356$		0			0
$357$	1.13247e6	−	192408.i	0.0248898	−	0.00422880i
$358$		0			0
$359$	−2.00085e7	+	3.46558e7i	−0.432446	+	0.749018i	−0.997083	−	0.0763210i	$-0.975683\pi$
$359$	−2.00085e7	+	3.46558e7i	−0.432446	+	0.749018i	0.564638	+	0.825339i	$0.309016\pi$
$360$		0			0
$361$	2.17150e7	+	3.76114e7i	0.461570	+	0.799463i
$362$		0			0
$363$		−	2.76100e7i		−	0.577227i
$364$		0			0
$365$	−1.25540e7			−0.258169
$366$		0			0
$367$	−1.53736e7	+	8.87597e6i	−0.311013	+	0.179563i	−0.647380	−	0.762168i	$-0.724135\pi$
$367$	−1.53736e7	+	8.87597e6i	−0.311013	+	0.179563i	0.336367	+	0.941731i	$0.390802\pi$
$368$		0			0
$369$	−1.55123e7	−	8.95606e6i	−0.308744	−	0.178253i
$370$		0			0
$371$	−2.84742e7	+	7.67391e7i	−0.557609	+	1.50278i
$372$		0			0
$373$	2.69790e6	−	4.67291e6i	0.0519876	−	0.0900452i	−0.838860	−	0.544346i	$-0.816778\pi$
$373$	2.69790e6	−	4.67291e6i	0.0519876	−	0.0900452i	0.890848	+	0.454301i	$0.150111\pi$
$374$		0			0
$375$	−1.32846e7	−	2.30096e7i	−0.251915	−	0.436330i
$376$		0			0
$377$			7.06609e7i			1.31873i
$378$		0			0
$379$	−3.47845e7			−0.638951			−0.319475	−	0.947595i	$-0.603507\pi$
$379$	−3.47845e7			−0.638951			−0.319475	+	0.947595i	$0.603507\pi$
$380$		0			0
$381$	3.80854e7	−	2.19886e7i	0.688627	−	0.397579i
$382$		0			0
$383$	4.90000e7	+	2.82902e7i	0.872168	+	0.503546i	0.868068	−	0.496445i	$-0.165362\pi$
$383$	4.90000e7	+	2.82902e7i	0.872168	+	0.503546i	0.00409994	+	0.999992i	$0.498695\pi$
$384$		0			0
$385$	319605.	−	264800.i	0.00560055	−	0.00464019i
$386$		0			0
$387$	−578485.	+	1.00196e6i	−0.00998065	+	0.0172870i
$388$		0			0
$389$	1.30039e7	+	2.25234e7i	0.220915	+	0.382636i	0.955086	−	0.296329i	$-0.0957624\pi$
$389$	1.30039e7	+	2.25234e7i	0.220915	+	0.382636i	−0.734171	+	0.678964i	$0.762429\pi$
$390$		0			0
$391$		−	3.10392e6i		−	0.0519254i
$392$		0			0
$393$	6.95036e7			1.14506
$394$		0			0
$395$	2.13266e7	−	1.23129e7i	0.346043	−	0.199788i
$396$		0			0
$397$	−1.18039e7	−	6.81496e6i	−0.188648	−	0.108916i	0.402701	−	0.915331i	$-0.368071\pi$
$397$	−1.18039e7	−	6.81496e6i	−0.188648	−	0.108916i	−0.591350	+	0.806415i	$0.701405\pi$
$398$		0			0
$399$	−3.24475e7	−	3.91631e7i	−0.510814	−	0.616535i
$400$		0			0
$401$	2.00929e7	−	3.48019e7i	0.311609	−	0.539722i	−0.667102	−	0.744966i	$-0.732465\pi$
$401$	2.00929e7	−	3.48019e7i	0.311609	−	0.539722i	0.978711	+	0.205244i	$0.0657988\pi$
$402$		0			0
$403$	7.39703e6	+	1.28120e7i	0.113017	+	0.195751i
$404$		0			0
$405$		−	3.67677e6i		−	0.0553480i
$406$		0			0
$407$	643815.			0.00954944
$408$		0			0
$409$	6.55577e6	−	3.78497e6i	0.0958194	−	0.0553214i	−0.451325	−	0.892360i	$-0.649048\pi$
$409$	6.55577e6	−	3.78497e6i	0.0958194	−	0.0553214i	0.547144	+	0.837038i	$0.315715\pi$
$410$		0			0
$411$	−1.75398e7	−	1.01266e7i	−0.252639	−	0.145861i
$412$		0			0
$413$	−1.05015e8	−	3.89659e7i	−1.49073	−	0.553139i
$414$		0			0
$415$	411860.	−	713363.i	0.00576243	−	0.00998082i
$416$		0			0
$417$	931921.	+	1.61413e6i	0.0128520	+	0.0222603i
$418$		0			0
$419$			3.12413e7i			0.424705i	0.977193	+	0.212353i	$0.0681125\pi$
$419$			3.12413e7i			0.424705i	−0.977193	+	0.212353i	$0.931887\pi$
$420$		0			0
$421$	5.98978e7			0.802721			0.401361	−	0.915920i	$-0.368537\pi$
$421$	5.98978e7			0.802721			0.401361	+	0.915920i	$0.368537\pi$
$422$		0			0
$423$	1.54938e7	−	8.94536e6i	0.204709	−	0.118189i
$424$		0			0
$425$	2.18574e6	+	1.26194e6i	0.0284729	+	0.0164388i
$426$		0			0
$427$	−2.32536e7	−	1.36865e8i	−0.298680	−	1.75796i
$428$		0			0
$429$	−248811.	+	430953.i	−0.00315135	+	0.00545830i
$430$		0			0
$431$	4.81510e7	+	8.33999e7i	0.601414	+	1.04168i	0.992607	+	0.121371i	$0.0387290\pi$
$431$	4.81510e7	+	8.33999e7i	0.601414	+	1.04168i	−0.391194	+	0.920308i	$0.627938\pi$
$432$		0			0
$433$		−	1.11186e8i		−	1.36958i	−0.728741	−	0.684790i	$-0.759894\pi$
$433$		−	1.11186e8i		−	1.36958i	0.728741	−	0.684790i	$-0.240106\pi$
$434$		0			0
$435$	4.17534e7			0.507252
$436$		0			0
$437$	−1.19014e8	+	6.87129e7i	−1.42611	+	0.823368i
$438$		0			0
$439$	7.90517e7	+	4.56405e7i	0.934367	+	0.539457i	0.888190	−	0.459476i	$-0.151963\pi$
$439$	7.90517e7	+	4.56405e7i	0.934367	+	0.539457i	0.0461770	+	0.998933i	$0.485296\pi$
$440$		0			0
$441$	2.16692e7	+	1.86483e7i	0.252655	+	0.217432i
$442$		0			0
$443$	−5.31635e7	+	9.20820e7i	−0.611509	+	1.05916i	0.379477	+	0.925201i	$0.376104\pi$
$443$	−5.31635e7	+	9.20820e7i	−0.611509	+	1.05916i	−0.990986	+	0.133963i	$0.957230\pi$
$444$		0			0
$445$	−7.17049e6	−	1.24197e7i	−0.0813709	−	0.140939i
$446$		0			0
$447$			9.75570e7i			1.09228i
$448$		0			0
$449$	7.74221e7			0.855315			0.427657	−	0.903941i	$-0.359339\pi$
$449$	7.74221e7			0.855315			0.427657	+	0.903941i	$0.359339\pi$
$450$		0			0
$451$	1.24057e6	−	716245.i	0.0135236	−	0.00780786i
$452$		0			0
$453$	−2.03572e7	−	1.17532e7i	−0.218989	−	0.126433i
$454$		0			0
$455$	3.45871e7	−	5.87638e6i	0.367180	−	0.0623844i
$456$		0			0
$457$	−9.50468e6	+	1.64626e7i	−0.0995838	+	0.172484i	−0.911512	−	0.411272i	$-0.865084\pi$
$457$	−9.50468e6	+	1.64626e7i	−0.0995838	+	0.172484i	0.811929	+	0.583757i	$0.198418\pi$
$458$		0			0
$459$	406900.	+	704771.i	0.00420774	+	0.00728803i
$460$		0			0
$461$		−	1.05709e8i		−	1.07897i	−0.841996	−	0.539483i	$-0.818620\pi$
$461$		−	1.05709e8i		−	1.07897i	0.841996	−	0.539483i	$-0.181380\pi$
$462$		0			0
$463$	2.82212e7			0.284336			0.142168	−	0.989843i	$-0.454593\pi$
$463$	2.82212e7			0.284336			0.142168	+	0.989843i	$0.454593\pi$
$464$		0			0
$465$	7.57062e6	−	4.37090e6i	0.0752961	−	0.0434722i
$466$		0			0
$467$	−1.49701e8	−	8.64297e7i	−1.46985	−	0.848619i	−0.470423	−	0.882441i	$-0.655899\pi$
$467$	−1.49701e8	−	8.64297e7i	−1.46985	−	0.848619i	−0.999428	+	0.0338227i	$0.989232\pi$
$468$		0			0
$469$	2.62464e7	−	7.07351e7i	0.254420	−	0.685672i
$470$		0			0
$471$	1.93285e7	−	3.34779e7i	0.184985	−	0.320403i
$472$		0			0
$473$	−46263.3	−	80130.4i	−0.000437173	−	0.000757206i
$474$		0			0
$475$		−	1.11744e8i		−	1.04267i
$476$		0			0
$477$	−5.79881e7			−0.534298
$478$		0			0
$479$	2.41808e7	−	1.39608e7i	0.220021	−	0.127029i	−0.385939	−	0.922524i	$-0.626122\pi$
$479$	2.41808e7	−	1.39608e7i	0.220021	−	0.127029i	0.605960	+	0.795495i	$0.292789\pi$
$480$		0			0
$481$	4.71287e7	+	2.72098e7i	0.423497	+	0.244506i
$482$		0			0
$483$	5.94857e7	−	4.92853e7i	0.527923	−	0.437397i
$484$		0			0
$485$	2.06263e7	−	3.57258e7i	0.180799	−	0.313153i
$486$		0			0
$487$	2.68794e7	+	4.65566e7i	0.232720	+	0.403082i	0.958608	−	0.284731i	$-0.0919042\pi$
$487$	2.68794e7	+	4.65566e7i	0.232720	+	0.403082i	−0.725888	+	0.687813i	$0.758571\pi$
$488$		0			0
$489$		−	1.02731e8i		−	0.878567i
$490$		0			0
$491$	−9.34867e7			−0.789779			−0.394889	−	0.918729i	$-0.629217\pi$
$491$	−9.34867e7			−0.789779			−0.394889	+	0.918729i	$0.629217\pi$
$492$		0			0
$493$	−8.00337e6	+	4.62075e6i	−0.0667932	+	0.0385631i
$494$		0			0
$495$	254649.	+	147022.i	0.00209955	+	0.00121218i
$496$		0			0
$497$	7.66414e7	+	9.25036e7i	0.624301	+	0.753511i
$498$		0			0
$499$	2.51376e6	−	4.35396e6i	0.0202312	−	0.0350415i	−0.855733	−	0.517418i	$-0.826893\pi$
$499$	2.51376e6	−	4.35396e6i	0.0202312	−	0.0350415i	0.875964	+	0.482377i	$0.160226\pi$
$500$		0			0
$501$	4.24790e7	+	7.35759e7i	0.337802	+	0.585089i
$502$		0			0
$503$		−	1.45016e8i		−	1.13949i	−0.821820	−	0.569747i	$-0.807041\pi$
$503$		−	1.45016e8i		−	1.13949i	0.821820	−	0.569747i	$-0.192959\pi$
$504$		0			0
$505$	1.16912e8			0.907789
$506$		0			0
$507$	2.87349e7	−	1.65901e7i	0.220489	−	0.127299i
$508$		0			0
$509$	1.14421e7	+	6.60609e6i	0.0867665	+	0.0500946i	0.542755	−	0.839891i	$-0.317381\pi$
$509$	1.14421e7	+	6.60609e6i	0.0867665	+	0.0500946i	−0.455989	+	0.889985i	$0.650714\pi$
$510$		0			0
$511$	6.48353e7	+	2.40573e7i	0.485903	+	0.180295i
$512$		0			0
$513$	1.80155e7	−	3.12037e7i	0.133442	−	0.231129i
$514$		0			0
$515$	−2.81445e7	−	4.87476e7i	−0.206049	−	0.356888i
$516$		0			0
$517$			1.43078e6i			0.0103538i
$518$		0			0
$519$	4.30466e7			0.307919
$520$		0			0
$521$	−6.70170e7	+	3.86923e7i	−0.473884	+	0.273597i	−0.717864	−	0.696183i	$-0.754880\pi$
$521$	−6.70170e7	+	3.86923e7i	−0.473884	+	0.273597i	0.243980	+	0.969780i	$0.421547\pi$
$522$		0			0
$523$	1.16424e8	+	6.72177e7i	0.813840	+	0.469871i	0.848288	−	0.529536i	$-0.177634\pi$
$523$	1.16424e8	+	6.72177e7i	0.813840	+	0.469871i	−0.0344475	+	0.999407i	$0.510967\pi$
$524$		0			0
$525$	1.05214e7	+	6.19266e7i	0.0727103	+	0.427956i
$526$		0			0
$527$	−967433.	+	1.67564e6i	−0.00660981	+	0.0114485i
$528$		0			0
$529$	−3.03516e7	−	5.25705e7i	−0.205029	−	0.355120i
$530$		0			0
$531$		−	7.93546e7i		−	0.530016i
$532$		0			0
$533$	1.21084e8			0.799657
$534$		0			0
$535$	4.56315e7	−	2.63453e7i	0.297991	−	0.172045i
$536$		0			0
$537$	−2.00843e7	−	1.15957e7i	−0.129698	−	0.0748813i
$538$		0			0
$539$	−2.15804e6	+	755104.i	−0.0137814	+	0.00482215i
$540$		0			0
$541$	7.51469e7	−	1.30158e8i	0.474590	−	0.822015i	−0.524986	−	0.851111i	$-0.675930\pi$
$541$	7.51469e7	−	1.30158e8i	0.474590	−	0.822015i	0.999577	+	0.0290960i	$0.00926284\pi$
$542$		0			0
$543$	4.68962e7	+	8.12266e7i	0.292913	+	0.507340i
$544$		0			0
$545$			1.05563e8i			0.652115i
$546$		0			0
$547$	6.65431e7			0.406576			0.203288	−	0.979119i	$-0.434837\pi$
$547$	6.65431e7			0.406576			0.203288	+	0.979119i	$0.434837\pi$
$548$		0			0
$549$	8.51757e7	−	4.91762e7i	0.514753	−	0.297193i
$550$		0			0
$551$	3.54349e8	+	2.04583e8i	2.11825	+	1.22297i
$552$		0			0
$553$	−1.33737e8	+	2.27220e7i	−0.790816	+	0.134360i
$554$		0			0
$555$	1.60782e7	−	2.78483e7i	0.0940500	−	0.162899i
$556$		0			0
$557$	1.26843e8	+	2.19698e8i	0.734007	+	1.27134i	0.955158	+	0.296097i	$0.0956852\pi$
$557$	1.26843e8	+	2.19698e8i	0.734007	+	1.27134i	−0.221151	+	0.975240i	$0.570981\pi$
$558$		0			0
$559$		−	7.82096e6i		−	0.0447739i
$560$		0			0
$561$	−65082.2			−0.000368616
$562$		0			0
$563$	−1.43519e8	+	8.28606e7i	−0.804236	+	0.464326i	−0.844950	−	0.534845i	$-0.820370\pi$
$563$	−1.43519e8	+	8.28606e7i	−0.804236	+	0.464326i	0.0407139	+	0.999171i	$0.487037\pi$
$564$		0			0
$565$	−8.23711e6	−	4.75570e6i	−0.0456699	−	0.0263675i
$566$		0			0
$567$	−7.04581e6	+	1.89888e7i	−0.0386529	+	0.104171i
$568$		0			0
$569$	−8.19891e7	+	1.42009e8i	−0.445061	+	0.770868i	−0.998056	−	0.0623160i	$-0.980151\pi$
$569$	−8.19891e7	+	1.42009e8i	−0.445061	+	0.770868i	0.552996	+	0.833184i	$0.313485\pi$
$570$		0			0
$571$	−1.70285e8	−	2.94942e8i	−0.914677	−	1.58427i	−0.807373	−	0.590042i	$-0.799111\pi$
$571$	−1.70285e8	−	2.94942e8i	−0.914677	−	1.58427i	−0.107305	−	0.994226i	$-0.534222\pi$
$572$		0			0
$573$		−	9.98198e7i		−	0.530582i
$574$		0			0
$575$	1.69731e8			0.892808
$576$		0			0
$577$	2.37115e8	−	1.36899e8i	1.23433	−	0.712642i	0.266402	−	0.963862i	$-0.414165\pi$
$577$	2.37115e8	−	1.36899e8i	1.23433	−	0.712642i	0.967930	+	0.251220i	$0.0808317\pi$
$578$		0			0
$579$	−1.33000e8	−	7.67875e7i	−0.685197	−	0.395599i
$580$		0			0
$581$	−3.49408e6	+	2.89493e6i	−0.0178158	+	0.0147608i
$582$		0			0
$583$	2.31875e6	−	4.01619e6i	0.0117017	−	0.0202679i
$584$		0			0
$585$	1.24273e7	+	2.15246e7i	0.0620737	+	0.107515i
$586$		0			0
$587$		−	2.96429e8i		−	1.46557i	−0.680460	−	0.732785i	$-0.738220\pi$
$587$		−	2.96429e8i		−	1.46557i	0.680460	−	0.732785i	$-0.261780\pi$
$588$		0			0
$589$	8.56661e7			0.419241
$590$		0			0
$591$	3.22492e7	−	1.86191e7i	0.156227	−	0.0901978i
$592$		0			0
$593$	−1.12529e8	−	6.49684e7i	−0.539633	−	0.311557i	0.205297	−	0.978700i	$-0.434184\pi$
$593$	−1.12529e8	−	6.49684e7i	−0.539633	−	0.311557i	−0.744930	+	0.667142i	$0.767517\pi$
$594$		0			0
$595$	2.92735e6	+	3.53321e6i	0.0138971	+	0.0167733i
$596$		0			0
$597$	1.22492e8	−	2.12163e8i	0.575686	−	0.997118i
$598$		0			0
$599$	−3.82426e7	−	6.62382e7i	−0.177937	−	0.308197i	0.763237	−	0.646119i	$-0.223609\pi$
$599$	−3.82426e7	−	6.62382e7i	−0.177937	−	0.308197i	−0.941174	+	0.337923i	$0.890276\pi$
$600$		0			0
$601$		−	1.12466e8i		−	0.518080i	−0.965867	−	0.259040i	$-0.916594\pi$
$601$		−	1.12466e8i		−	0.518080i	0.965867	−	0.259040i	$-0.0834061\pi$
$602$		0			0
$603$	5.34511e7			0.243784
$604$		0			0
$605$	9.55100e7	−	5.51427e7i	0.431303	−	0.249013i
$606$		0			0
$607$	4.03159e6	+	2.32764e6i	0.0180264	+	0.0104076i	0.508986	−	0.860775i	$-0.330020\pi$
$607$	4.03159e6	+	2.32764e6i	0.0180264	+	0.0104076i	−0.490960	+	0.871182i	$0.663354\pi$
$608$		0			0
$609$	−2.15636e8	−	8.00122e7i	−0.954706	−	0.354245i
$610$		0			0
$611$	−6.04695e7	+	1.04736e8i	−0.265102	+	0.459170i
$612$		0			0
$613$	1.02768e8	+	1.78000e8i	0.446147	+	0.772749i	0.998131	−	0.0611054i	$-0.0194626\pi$
$613$	1.02768e8	+	1.78000e8i	0.446147	+	0.772749i	−0.551984	+	0.833854i	$0.686129\pi$
$614$		0			0
$615$		−	7.15481e7i		−	0.307590i
$616$		0			0
$617$	1.85696e8			0.790583			0.395292	−	0.918556i	$-0.370644\pi$
$617$	1.85696e8			0.790583			0.395292	+	0.918556i	$0.370644\pi$
$618$		0			0
$619$	−7.59648e7	+	4.38583e7i	−0.320288	+	0.184918i	−0.651521	−	0.758631i	$-0.725869\pi$
$619$	−7.59648e7	+	4.38583e7i	−0.320288	+	0.184918i	0.331233	+	0.943549i	$0.392535\pi$
$620$		0			0
$621$	4.73960e7	+	2.73641e7i	0.197910	+	0.114263i
$622$		0			0
$623$	1.32323e7	+	7.78824e7i	0.0547232	+	0.322088i
$624$		0			0
$625$	−3.87164e7	+	6.70588e7i	−0.158582	+	0.274673i
$626$		0			0
$627$	1.44076e6	+	2.49546e6i	0.00584505	+	0.0101239i
$628$		0			0
$629$			7.11735e6i			0.0286000i
$630$		0			0
$631$	4.15732e8			1.65472			0.827362	−	0.561670i	$-0.189841\pi$
$631$	4.15732e8			1.65472			0.827362	+	0.561670i	$0.189841\pi$
$632$		0			0
$633$	−1.98099e7	+	1.14372e7i	−0.0781034	+	0.0450930i
$634$		0			0
$635$	1.52128e8	+	8.78313e7i	0.594140	+	0.343027i
$636$		0			0
$637$	−1.89886e8	−	3.59306e7i	−0.734642	−	0.139010i
$638$		0			0
$639$	−4.25527e7	+	7.37035e7i	−0.163089	+	0.282479i
$640$		0			0
$641$	−8.98600e7	−	1.55642e8i	−0.341187	−	0.590953i	0.643466	−	0.765474i	$-0.277496\pi$
$641$	−8.98600e7	−	1.55642e8i	−0.341187	−	0.590953i	−0.984653	+	0.174521i	$0.944162\pi$
$642$		0			0
$643$		−	8.10561e7i		−	0.304897i	−0.988311	−	0.152448i	$-0.951284\pi$
$643$		−	8.10561e7i		−	0.304897i	0.988311	−	0.152448i	$-0.0487158\pi$
$644$		0			0
$645$	−4.62140e6			−0.0172224
$646$		0			0
$647$	−9.06246e7	+	5.23221e7i	−0.334606	+	0.193185i	−0.657884	−	0.753119i	$-0.728548\pi$
$647$	−9.06246e7	+	5.23221e7i	−0.334606	+	0.193185i	0.323278	+	0.946304i	$0.395215\pi$
$648$		0			0
$649$	5.49601e6	+	3.17312e6i	0.0201054	+	0.0116079i
$650$		0			0
$651$	−4.74745e7	+	8.06598e6i	−0.172075	+	0.0292357i
$652$		0			0
$653$	−2.36179e8	+	4.09074e8i	−0.848206	+	1.46914i	0.0346020	+	0.999401i	$0.488984\pi$
$653$	−2.36179e8	+	4.09074e8i	−0.848206	+	1.46914i	−0.882808	+	0.469734i	$0.844350\pi$
$654$		0			0
$655$	1.38812e8	+	2.40430e8i	0.493975	+	0.855589i
$656$		0			0
$657$			4.89930e7i			0.172758i
$658$		0			0
$659$	−1.73758e8			−0.607141			−0.303570	−	0.952809i	$-0.598179\pi$
$659$	−1.73758e8			−0.607141			−0.303570	+	0.952809i	$0.598179\pi$
$660$		0			0
$661$	−1.91974e7	+	1.10836e7i	−0.0664720	+	0.0383776i	−0.532868	−	0.846199i	$-0.678886\pi$
$661$	−1.91974e7	+	1.10836e7i	−0.0664720	+	0.0383776i	0.466396	+	0.884576i	$0.345552\pi$
$662$		0			0
$663$	−4.76416e6	−	2.75059e6i	−0.0163473	−	0.00943811i
$664$		0			0
$665$	7.06707e7	−	1.90460e8i	0.240311	−	0.647649i
$666$		0			0
$667$	−3.10746e8	+	5.38229e8i	−1.04720	+	1.81380i
$668$		0			0
$669$	−2.83196e7	−	4.90510e7i	−0.0945821	−	0.163821i
$670$		0			0
$671$			7.86557e6i			0.0260353i
$672$		0			0
$673$	−4.00045e8			−1.31239			−0.656195	−	0.754591i	$-0.727835\pi$
$673$	−4.00045e8			−1.31239			−0.656195	+	0.754591i	$0.727835\pi$
$674$		0			0
$675$	−3.85389e7	+	2.22505e7i	−0.125311	+	0.0723482i
$676$		0			0
$677$	−2.51224e8	−	1.45044e8i	−0.809646	−	0.467449i	0.0371872	−	0.999308i	$-0.488160\pi$
$677$	−2.51224e8	−	1.45044e8i	−0.809646	−	0.467449i	−0.846833	+	0.531859i	$0.821494\pi$
$678$		0			0
$679$	−1.74987e8	+	1.44980e8i	−0.558979	+	0.463127i
$680$		0			0
$681$	−4.62709e7	+	8.01435e7i	−0.146510	+	0.253762i
$682$		0			0
$683$	5.77014e7	+	9.99417e7i	0.181102	+	0.313678i	0.942256	−	0.334893i	$-0.108700\pi$
$683$	5.77014e7	+	9.99417e7i	0.181102	+	0.313678i	−0.761154	+	0.648571i	$0.775367\pi$
$684$		0			0
$685$		−	8.08996e7i		−	0.251695i
$686$		0			0
$687$	1.90735e8			0.588249
$688$		0			0
$689$	3.39475e8	−	1.95996e8i	1.03789	−	0.599224i
$690$		0			0
$691$	−3.59314e8	−	2.07450e8i	−1.08903	−	0.628752i	−0.155712	−	0.987802i	$-0.549767\pi$
$691$	−3.59314e8	−	2.07450e8i	−1.08903	−	0.628752i	−0.933318	+	0.359051i	$0.883101\pi$
$692$		0			0
$693$	−1.03340e6	−	1.24728e6i	−0.00310506	−	0.00374770i
$694$		0			0
$695$	−3.72246e6	+	6.44750e6i	−0.0110886	+	0.0192060i
$696$		0			0
$697$	7.91806e6	+	1.37145e7i	0.0233841	+	0.0405024i
$698$		0			0
$699$			1.88947e8i			0.553232i
$700$		0			0
$701$	5.13427e8			1.49047			0.745237	−	0.666800i	$-0.232336\pi$
$701$	5.13427e8			1.49047			0.745237	+	0.666800i	$0.232336\pi$
$702$		0			0
$703$	2.72902e8	−	1.57560e8i	0.785491	−	0.453503i
$704$		0			0
$705$	6.18885e7	+	3.57313e7i	0.176621	+	0.101972i
$706$		0			0
$707$	−6.03794e8	−	2.24039e8i	−1.70856	−	0.633965i
$708$		0			0
$709$	−1.64200e8	+	2.84402e8i	−0.460716	+	0.797984i	−0.998997	−	0.0447818i	$-0.985741\pi$
$709$	−1.64200e8	+	2.84402e8i	−0.460716	+	0.797984i	0.538281	+	0.842766i	$0.319074\pi$
$710$		0			0
$711$	−4.80521e7	−	8.32287e7i	−0.133691	−	0.231560i
$712$		0			0
$713$			1.30120e8i			0.358985i
$714$		0			0
$715$	−1.98770e6			−0.00543791
$716$		0			0
$717$	−1.60672e8	+	9.27638e7i	−0.435895	+	0.251664i
$718$		0			0
$719$	−9.79686e7	−	5.65622e7i	−0.263573	−	0.152174i	0.362391	−	0.932026i	$-0.381961\pi$
$719$	−9.79686e7	−	5.65622e7i	−0.263573	−	0.152174i	−0.625963	+	0.779853i	$0.715294\pi$
$720$		0			0
$721$	5.19373e7	+	3.05691e8i	0.138571	+	0.815600i
$722$		0			0
$723$	−7.75905e7	+	1.34391e8i	−0.205302	+	0.355594i
$724$		0			0
$725$	−2.52676e8	−	4.37648e8i	−0.663055	−	1.14845i
$726$		0			0
$727$		−	9.97740e7i		−	0.259666i	−0.991536	−	0.129833i	$-0.958556\pi$
$727$		−	9.97740e7i		−	0.259666i	0.991536	−	0.129833i	$-0.0414440\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	885838.	−	511439.i	0.00226779	−	0.00130931i
$732$		0			0
$733$	3.13962e8	+	1.81266e8i	0.797197	+	0.460262i	0.842490	−	0.538712i	$-0.181089\pi$
$733$	3.13962e8	+	1.81266e8i	0.797197	+	0.460262i	−0.0452931	+	0.998974i	$0.514422\pi$
$734$		0			0
$735$	−2.12314e7	+	1.12204e8i	−0.0534707	+	0.282582i
$736$		0			0
$737$	−2.13733e6	+	3.70197e6i	−0.00533912	+	0.00924762i
$738$		0			0
$739$	−1.02140e8	−	1.76912e8i	−0.253083	−	0.438352i	0.711290	−	0.702899i	$-0.248111\pi$
$739$	−1.02140e8	−	1.76912e8i	−0.253083	−	0.438352i	−0.964373	+	0.264546i	$0.914778\pi$
$740$		0			0
$741$			2.43565e8i			0.598631i
$742$		0			0
$743$	−2.63900e8			−0.643389			−0.321695	−	0.946844i	$-0.604252\pi$
$743$	−2.63900e8			−0.643389			−0.321695	+	0.946844i	$0.604252\pi$
$744$		0			0
$745$	−3.37474e8	+	1.94841e8i	−0.816153	+	0.471206i
$746$		0			0
$747$	−2.78396e6	−	1.60732e6i	−0.00667883	−	0.00385603i
$748$		0			0
$749$	−2.86150e8	+	4.86172e7i	−0.681002	+	0.115703i
$750$		0			0
$751$	−3.68938e8	+	6.39019e8i	−0.871031	+	1.50867i	−0.0100992	+	0.999949i	$0.503215\pi$
$751$	−3.68938e8	+	6.39019e8i	−0.871031	+	1.50867i	−0.860932	+	0.508721i	$0.830119\pi$
$752$		0			0
$753$	3.56770e7	+	6.17945e7i	0.0835611	+	0.144732i
$754$		0			0
$755$		−	9.38940e7i		−	0.218171i
$756$		0			0
$757$	−1.43307e8			−0.330355			−0.165177	−	0.986264i	$-0.552820\pi$
$757$	−1.43307e8			−0.330355			−0.165177	+	0.986264i	$0.552820\pi$
$758$		0			0
$759$	−3.79042e6	+	2.18840e6i	−0.00866885	+	0.00500496i
$760$		0			0
$761$	−6.67428e8	−	3.85340e8i	−1.51444	−	0.874360i	−0.999857	−	0.0169164i	$-0.994615\pi$
$761$	−6.67428e8	−	3.85340e8i	−1.51444	−	0.874360i	−0.514578	−	0.857443i	$-0.672052\pi$
$762$		0			0
$763$	2.02291e8	−	5.45184e8i	0.455411	−	1.22735i
$764$		0			0
$765$	−1.62532e6	+	2.81514e6i	−0.00363040	+	0.00628804i
$766$		0			0
$767$	2.68213e8	+	4.64559e8i	0.594421	+	1.02957i
$768$		0			0
$769$		−	6.97335e8i		−	1.53343i	−0.641990	−	0.766713i	$-0.721891\pi$
$769$		−	6.97335e8i		−	1.53343i	0.641990	−	0.766713i	$-0.278109\pi$
$770$		0			0
$771$	−6.30772e7			−0.137629
$772$		0			0
$773$	−7.04415e8	+	4.06694e8i	−1.52507	+	0.880500i	−0.525513	+	0.850786i	$0.676126\pi$
$773$	−7.04415e8	+	4.06694e8i	−1.52507	+	0.880500i	−0.999558	+	0.0297144i	$0.990540\pi$
$774$		0			0
$775$	−9.16290e7	−	5.29021e7i	−0.196847	−	0.113649i
$776$		0			0
$777$	−1.36402e8	+	1.13012e8i	−0.290775	+	0.240914i
$778$		0			0
$779$	3.50572e8	−	6.07208e8i	0.741591	−	1.28447i
$780$		0			0
$781$	−3.40308e6	−	5.89431e6i	−0.00714364	−	0.0123731i
$782$		0			0
$783$		−	1.62946e8i		−	0.339436i
$784$		0			0
$785$	1.54411e8			0.319206
$786$		0			0
$787$	−3.22928e8	+	1.86443e8i	−0.662494	+	0.382491i	−0.793227	−	0.608927i	$-0.791600\pi$
$787$	−3.22928e8	+	1.86443e8i	−0.662494	+	0.382491i	0.130733	+	0.991418i	$0.458267\pi$
$788$		0			0
$789$	4.00622e8	+	2.31299e8i	0.815651	+	0.470916i
$790$		0			0
$791$	3.34273e7	+	4.03457e7i	0.0675418	+	0.0815207i
$792$		0			0
$793$	−3.32425e8	+	5.75777e8i	−0.666614	+	1.15461i
$794$		0			0
$795$	−1.15814e8	−	2.00595e8i	−0.230494	−	0.399227i
$796$		0			0
$797$		−	4.15047e8i		−	0.819827i	−0.912124	−	0.409913i	$-0.865559\pi$
$797$		−	4.15047e8i		−	0.819827i	0.912124	−	0.409913i	$-0.134441\pi$
$798$		0			0
$799$	−1.58172e7			−0.0310091
$800$		0			0
$801$	−4.84687e7	+	2.79834e7i	−0.0943113	+	0.0544507i
$802$		0			0
$803$	−3.39320e6	−	1.95906e6i	−0.00655334	−	0.00378357i
$804$		0			0
$805$	2.89295e8	+	1.07343e8i	0.554566	+	0.205773i
$806$		0			0
$807$	−1.59556e8	+	2.76360e8i	−0.303594	+	0.525841i
$808$		0			0
$809$	1.17384e8	+	2.03314e8i	0.221698	+	0.383992i	0.955324	−	0.295562i	$-0.0955068\pi$
$809$	1.17384e8	+	2.03314e8i	0.221698	+	0.383992i	−0.733626	+	0.679554i	$0.762173\pi$
$810$		0			0
$811$			8.08164e7i			0.151508i	0.997127	+	0.0757542i	$0.0241364\pi$
$811$			8.08164e7i			0.151508i	−0.997127	+	0.0757542i	$0.975864\pi$
$812$		0			0
$813$	−3.94717e7			−0.0734538
$814$		0			0
$815$	3.55372e8	−	2.05174e8i	0.656463	−	0.379009i
$816$		0			0
$817$	−3.92204e7	−	2.26439e7i	−0.0719194	−	0.0415227i
$818$		0			0
$819$	−2.29331e7	−	1.34979e8i	−0.0417455	−	0.245705i
$820$		0			0
$821$	3.22564e7	−	5.58697e7i	0.0582890	−	0.100959i	−0.835408	−	0.549630i	$-0.814769\pi$
$821$	3.22564e7	−	5.58697e7i	0.0582890	−	0.100959i	0.893697	+	0.448670i	$0.148102\pi$
$822$		0			0
$823$	−7.83609e7	−	1.35725e8i	−0.140572	−	0.243478i	0.787140	−	0.616774i	$-0.211561\pi$
$823$	−7.83609e7	−	1.35725e8i	−0.140572	−	0.243478i	−0.927712	+	0.373296i	$0.878228\pi$
$824$		0			0
$825$		−	3.55888e6i		−	0.00633800i
$826$		0			0
$827$	6.46564e8			1.14313			0.571565	−	0.820557i	$-0.306337\pi$
$827$	6.46564e8			1.14313			0.571565	+	0.820557i	$0.306337\pi$
$828$		0			0
$829$	−8.11604e8	+	4.68580e8i	−1.42456	+	0.822470i	−0.996684	−	0.0813680i	$-0.974071\pi$
$829$	−8.11604e8	+	4.68580e8i	−1.42456	+	0.822470i	−0.427875	+	0.903838i	$0.640738\pi$
$830$		0			0
$831$	−4.12734e8	−	2.38292e8i	−0.719229	−	0.415247i
$832$		0			0
$833$	−8.34764e6	−	2.38570e7i	−0.0144420	−	0.0412744i
$834$		0			0
$835$	−1.69678e8	+	2.93891e8i	−0.291452	+	0.504809i
$836$		0			0
$837$	−1.70578e7	−	2.95449e7i	−0.0290902	−	0.0503856i
$838$		0			0
$839$		−	7.25284e8i		−	1.22807i	−0.789280	−	0.614034i	$-0.789546\pi$
$839$		−	7.25284e8i		−	1.22807i	0.789280	−	0.614034i	$-0.210454\pi$
$840$		0			0
$841$	1.25559e9			2.11086
$842$		0			0
$843$	−3.06570e8	+	1.76998e8i	−0.511738	+	0.295452i
$844$		0			0
$845$	1.14779e8	+	6.62676e7i	0.190236	+	0.109833i
$846$		0			0
$847$	−5.98933e8	+	1.01759e8i	−0.985662	+	0.167465i
$848$		0			0
$849$	−3.19429e8	+	5.53268e8i	−0.521978	+	0.904092i
$850$		0			0
$851$	2.39322e8	+	4.14517e8i	0.388323	+	0.672595i
$852$		0			0
$853$		−	1.38063e8i		−	0.222449i	−0.993795	−	0.111224i	$-0.964523\pi$
$853$		−	1.38063e8i		−	0.222449i	0.993795	−	0.111224i	$-0.0354772\pi$
$854$		0			0
$855$	1.43922e8			0.230265
$856$		0			0
$857$	6.12238e8	−	3.53476e8i	0.972698	−	0.561588i	0.0726405	−	0.997358i	$-0.476857\pi$
$857$	6.12238e8	−	3.53476e8i	0.972698	−	0.561588i	0.900058	+	0.435771i	$0.143524\pi$
$858$		0			0
$859$	−2.85515e8	−	1.64842e8i	−0.450453	−	0.260069i	0.257569	−	0.966260i	$-0.417079\pi$
$859$	−2.85515e8	−	1.64842e8i	−0.450453	−	0.260069i	−0.708021	+	0.706191i	$0.750412\pi$
$860$		0			0
$861$	−1.37108e8	+	3.69511e8i	−0.214809	+	0.578920i
$862$		0			0
$863$	−4.84152e8	+	8.38576e8i	−0.753268	+	1.30470i	0.192962	+	0.981206i	$0.438190\pi$
$863$	−4.84152e8	+	8.38576e8i	−0.753268	+	1.30470i	−0.946231	+	0.323493i	$0.895143\pi$
$864$		0			0
$865$	8.59726e7	+	1.48909e8i	0.132835	+	0.230077i
$866$		0			0
$867$			3.75548e8i			0.576246i
$868$		0			0
$869$	7.68577e6			0.0117119
$870$		0			0
$871$	−3.12915e8	+	1.80661e8i	−0.473556	+	0.273408i
$872$		0			0
$873$	−1.39423e8	−	8.04959e7i	−0.209552	−	0.120985i
$874$		0			0
$875$	−4.50176e8	+	3.72981e8i	−0.671983	+	0.556753i
$876$		0			0
$877$	−1.33382e8	+	2.31025e8i	−0.197742	+	0.342500i	−0.947796	−	0.318877i	$-0.896694\pi$
$877$	−1.33382e8	+	2.31025e8i	−0.197742	+	0.342500i	0.750054	+	0.661377i	$0.230028\pi$
$878$		0			0
$879$	2.29410e8	+	3.97350e8i	0.337790	+	0.585069i
$880$		0			0
$881$		−	6.08909e8i		−	0.890481i	−0.895411	−	0.445241i	$-0.853118\pi$
$881$		−	6.08909e8i		−	0.890481i	0.895411	−	0.445241i	$-0.146882\pi$
$882$		0			0
$883$	6.56488e8			0.953553			0.476777	−	0.879025i	$-0.341805\pi$
$883$	6.56488e8			0.953553			0.476777	+	0.879025i	$0.341805\pi$
$884$		0			0
$885$	2.74507e8	−	1.58487e8i	0.396027	−	0.228646i
$886$		0			0
$887$	6.04195e7	+	3.48832e7i	0.0865778	+	0.0499857i	0.542664	−	0.839950i	$-0.317416\pi$
$887$	6.04195e7	+	3.48832e7i	0.0865778	+	0.0499857i	−0.456086	+	0.889936i	$0.650749\pi$
$888$		0			0
$889$	−6.17358e8	−	7.45130e8i	−0.878682	−	1.06054i
$890$		0			0
$891$	573765.	−	993789.i	0.000811149	−	0.00140495i
$892$		0			0
$893$	3.50153e8	+	6.06482e8i	0.491703	+	0.851655i
$894$		0			0
$895$		−	9.26355e7i		−	0.129214i
$896$		0			0
$897$	−3.69956e8			−0.512593
$898$		0			0
$899$	3.35512e8	−	1.93708e8i	0.461773	−	0.266605i
$900$		0			0
$901$	4.43988e7	+	2.56337e7i	0.0607011	+	0.0350458i
$902$		0			0
$903$	2.38673e7	+	8.85600e6i	0.0324145	+	0.0120275i
$904$		0			0
$905$	−1.87322e8	+	3.24451e8i	−0.252722	+	0.437728i
$906$		0			0
$907$	4.31361e8	+	7.47140e8i	0.578122	+	1.00134i	0.995695	+	0.0926927i	$0.0295474\pi$
$907$	4.31361e8	+	7.47140e8i	0.578122	+	1.00134i	−0.417573	+	0.908643i	$0.637119\pi$
$908$		0			0
$909$		−	4.56258e8i		−	0.607462i
$910$		0			0
$911$	1.41296e8			0.186885			0.0934425	−	0.995625i	$-0.470213\pi$
$911$	1.41296e8			0.186885			0.0934425	+	0.995625i	$0.470213\pi$
$912$		0			0
$913$	222642.	−	128542.i	0.000292547	−	0.000168902i
$914$		0			0
$915$	3.40226e8	+	1.96429e8i	0.444124	+	0.256415i
$916$		0			0
$917$	−2.56162e8	−	1.50771e9i	−0.332206	−	1.95529i
$918$		0			0
$919$	5.59845e8	−	9.69681e8i	0.721309	−	1.24934i	−0.239166	−	0.970979i	$-0.576874\pi$
$919$	5.59845e8	−	9.69681e8i	0.721309	−	1.24934i	0.960475	−	0.278366i	$-0.0897927\pi$
$920$		0			0
$921$	−3.64220e7	−	6.30848e7i	−0.0466214	−	0.0807506i
$922$		0			0
$923$		−	5.75302e8i		−	0.731629i
$924$		0			0
$925$	−3.89197e8			−0.491750
$926$		0			0
$927$	−1.90242e8	+	1.09836e8i	−0.238817	+	0.137881i
$928$		0			0
$929$	1.14228e9	+	6.59494e8i	1.42470	+	0.822553i	0.996696	−	0.0812225i	$-0.0258824\pi$
$929$	1.14228e9	+	6.59494e8i	1.42470	+	0.822553i	0.428007	+	0.903775i	$0.359216\pi$
$930$		0			0
$931$	−7.29960e8	+	8.48210e8i	−0.904586	+	1.05112i
$932$		0			0
$933$	−2.49659e8	+	4.32422e8i	−0.307399	+	0.532430i
$934$		0			0
$935$	−129982.	−	225136.i	−0.000159019	−	0.000275429i
$936$		0			0
$937$			1.04041e6i			0.00126469i	1.00000		0.000632345i	$0.000201282\pi$
$937$			1.04041e6i			0.00126469i	−1.00000		0.000632345i	$0.999799\pi$
$938$		0			0
$939$	3.39848e8			0.410476
$940$		0			0
$941$	5.93842e8	−	3.42855e8i	0.712692	−	0.411473i	−0.0993650	−	0.995051i	$-0.531681\pi$
$941$	5.93842e8	−	3.42855e8i	0.712692	−	0.411473i	0.812057	+	0.583578i	$0.198348\pi$
$942$		0			0
$943$	9.22302e8	+	5.32491e8i	1.09986	+	0.635005i
$944$		0			0
$945$	−7.97588e7	+	1.35511e7i	−0.0945112	+	0.0160576i
$946$		0			0
$947$	2.67038e8	−	4.62523e8i	0.314429	−	0.544608i	−0.664887	−	0.746944i	$-0.731520\pi$
$947$	2.67038e8	−	4.62523e8i	0.314429	−	0.544608i	0.979316	+	0.202337i	$0.0648535\pi$
$948$		0			0
$949$	−1.65593e8	−	2.86816e8i	−0.193751	−	0.335586i
$950$		0			0
$951$			1.64066e8i			0.190755i
$952$		0			0
$953$	8.66817e8			1.00150			0.500748	−	0.865593i	$-0.333058\pi$
$953$	8.66817e8			1.00150			0.500748	+	0.865593i	$0.333058\pi$
$954$		0			0
$955$	3.45302e8	−	1.99360e8i	0.396450	−	0.228891i
$956$		0			0
$957$	1.12855e7	+	6.51566e6i	0.0128761	+	0.00743400i
$958$		0			0
$959$	−1.55028e8	+	4.17807e8i	−0.175774	+	0.473718i
$960$		0			0
$961$	−4.03196e8	+	6.98356e8i	−0.454303	+	0.786876i
$962$		0			0
$963$	−1.02815e8	−	1.78080e8i	−0.115127	−	0.199406i
$964$		0			0
$965$		−	6.13440e8i		−	0.682637i
$966$		0			0
$967$	−1.71422e8			−0.189577			−0.0947886	−	0.995497i	$-0.530218\pi$
$967$	−1.71422e8			−0.189577			−0.0947886	+	0.995497i	$0.530218\pi$
$968$		0			0
$969$	−2.75872e7	+	1.59275e7i	−0.0303205	+	0.0175056i
$970$		0			0
$971$	−9.77273e8	−	5.64229e8i	−1.06748	−	0.616308i	−0.139985	−	0.990154i	$-0.544706\pi$
$971$	−9.77273e8	−	5.64229e8i	−1.06748	−	0.616308i	−0.927491	+	0.373846i	$0.878039\pi$
$972$		0			0
$973$	3.15801e7	−	2.61648e7i	0.0342827	−	0.0284040i
$974$		0			0
$975$	1.50410e8	−	2.60518e8i	0.162279	−	0.281076i
$976$		0			0
$977$	2.09709e8	+	3.63227e8i	0.224871	+	0.389488i	0.956281	−	0.292450i	$-0.0944706\pi$
$977$	2.09709e8	+	3.63227e8i	0.224871	+	0.389488i	−0.731410	+	0.681938i	$0.761137\pi$
$978$		0			0
$979$		−	4.47585e6i		−	0.00477010i
$980$		0			0
$981$	4.11970e8			0.436373
$982$		0			0
$983$	5.99335e8	−	3.46026e8i	0.630971	−	0.364291i	−0.150157	−	0.988662i	$-0.547978\pi$
$983$	5.99335e8	−	3.46026e8i	0.630971	−	0.364291i	0.781128	+	0.624371i	$0.214645\pi$
$984$		0			0
$985$	1.28816e8	+	7.43720e7i	0.134791	+	0.0778217i
$986$		0			0
$987$	−2.51152e8	−	3.03132e8i	−0.261207	−	0.315268i
$988$		0			0
$989$	3.43944e7	−	5.95728e7i	0.0355548	−	0.0615828i
$990$		0			0
$991$	−4.13436e8	−	7.16091e8i	−0.424802	−	0.735779i	0.571600	−	0.820533i	$-0.306323\pi$
$991$	−4.13436e8	−	7.16091e8i	−0.424802	−	0.735779i	−0.996402	+	0.0847535i	$0.972990\pi$
$992$		0			0
$993$		−	6.34364e8i		−	0.647875i
$994$		0			0
$995$	9.78566e8			0.993393
$996$		0			0
$997$	1.48696e9	−	8.58496e8i	1.50042	−	0.866269i	0.500421	−	0.865782i	$-0.333178\pi$
$997$	1.48696e9	−	8.58496e8i	1.50042	−	0.866269i	1.00000		0.000486585i	$-0.000154885\pi$
$998$		0			0
$999$	−1.08680e8	−	6.27465e7i	−0.109007	−	0.0629351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.d.145.4		8
4.3	odd	2		21.7.f.a.19.3	yes	8
7.3	odd	6	inner	336.7.bh.d.241.4		8
12.11	even	2		63.7.m.d.19.2		8
28.3	even	6		21.7.f.a.10.3	✓	8
28.11	odd	6		147.7.f.d.31.3		8
28.19	even	6		147.7.d.b.97.4		8
28.23	odd	6		147.7.d.b.97.3		8
28.27	even	2		147.7.f.d.19.3		8
84.23	even	6		441.7.d.c.244.6		8
84.47	odd	6		441.7.d.c.244.5		8
84.59	odd	6		63.7.m.d.10.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.a.10.3	✓	8	28.3	even	6
21.7.f.a.19.3	yes	8	4.3	odd	2
63.7.m.d.10.2		8	84.59	odd	6
63.7.m.d.19.2		8	12.11	even	2
147.7.d.b.97.3		8	28.23	odd	6
147.7.d.b.97.4		8	28.19	even	6
147.7.f.d.19.3		8	28.27	even	2
147.7.f.d.31.3		8	28.11	odd	6
336.7.bh.d.145.4		8	1.1	even	1	trivial
336.7.bh.d.241.4		8	7.3	odd	6	inner
441.7.d.c.244.5		8	84.47	odd	6
441.7.d.c.244.6		8	84.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(13.5000 - 7.79423i) q^{3} +(53.9244 + 31.1333i) q^{5} +(-218.833 - 264.124i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(13.5000 - 7.79423i) q^{3} +(53.9244 + 31.1333i) q^{5} +(-218.833 - 264.124i) q^{7} +(121.500 - 210.444i) q^{9} +(9.71675 + 16.8299i) q^{11} +1642.65i q^{13} +970.639 q^{15} +(-186.054 + 107.418i) q^{17} +(8237.53 + 4755.94i) q^{19} +(-5012.88 - 1860.04i) q^{21} +(-7223.90 + 12512.2i) q^{23} +(-5873.94 - 10174.0i) q^{25} -3788.00i q^{27} +43016.4 q^{29} +(7799.62 - 4503.11i) q^{31} +(262.352 + 151.469i) q^{33} +(-3577.38 - 21055.7i) q^{35} +(16564.6 - 28690.7i) q^{37} +(12803.2 + 22175.8i) q^{39} -73712.4i q^{41} -4761.19 q^{43} +(13103.6 - 7565.38i) q^{45} +(63760.5 + 36812.2i) q^{47} +(-21873.6 + 115598. i) q^{49} +(-1674.48 + 2900.29i) q^{51} +(-119317. - 206663. i) q^{53} +1210.06i q^{55} +148275. q^{57} +(282811. - 163281. i) q^{59} +(350517. + 202371. i) q^{61} +(-82171.4 + 13961.0i) q^{63} +(-51141.0 + 88578.8i) q^{65} +(109982. + 190494. i) q^{67} +225219. i q^{69} -350228. q^{71} +(-174606. + 100809. i) q^{73} +(-158596. - 91565.7i) q^{75} +(2318.83 - 6249.36i) q^{77} +(197745. - 342505. i) q^{79} +(-29524.5 - 51137.9i) q^{81} -13229.0i q^{83} -13377.1 q^{85} +(580722. - 335280. i) q^{87} +(-199460. - 115158. i) q^{89} +(433862. - 359465. i) q^{91} +(70196.6 - 121584. i) q^{93} +(296136. + 512922. i) q^{95} -662517. i q^{97} +4722.34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 108 q^{3} - 294 q^{5} + 656 q^{7} + 972 q^{9}+O(q^{10}) \) 8 * q + 108 * q^3 - 294 * q^5 + 656 * q^7 + 972 * q^9	\( 8 q + 108 q^{3} - 294 q^{5} + 656 q^{7} + 972 q^{9} + 314 q^{11} - 5292 q^{15} - 5532 q^{17} + 18234 q^{19} + 9342 q^{21} - 3928 q^{23} - 17038 q^{25} - 8300 q^{29} + 89508 q^{31} + 8478 q^{33} + 25860 q^{35} + 64706 q^{37} - 29106 q^{39} - 45740 q^{43} - 71442 q^{45} - 483276 q^{47} - 310684 q^{49} - 49788 q^{51} - 540974 q^{53} + 328212 q^{57} + 181770 q^{59} + 418224 q^{61} + 92826 q^{63} - 414204 q^{65} + 1158902 q^{67} - 1442344 q^{71} - 378666 q^{73} - 460026 q^{75} + 1065994 q^{77} - 611452 q^{79} - 236196 q^{81} - 275112 q^{85} - 112050 q^{87} - 989196 q^{89} - 304446 q^{91} + 805572 q^{93} + 591792 q^{95} + 152604 q^{99}+O(q^{100}) \) 8 * q + 108 * q^3 - 294 * q^5 + 656 * q^7 + 972 * q^9 + 314 * q^11 - 5292 * q^15 - 5532 * q^17 + 18234 * q^19 + 9342 * q^21 - 3928 * q^23 - 17038 * q^25 - 8300 * q^29 + 89508 * q^31 + 8478 * q^33 + 25860 * q^35 + 64706 * q^37 - 29106 * q^39 - 45740 * q^43 - 71442 * q^45 - 483276 * q^47 - 310684 * q^49 - 49788 * q^51 - 540974 * q^53 + 328212 * q^57 + 181770 * q^59 + 418224 * q^61 + 92826 * q^63 - 414204 * q^65 + 1158902 * q^67 - 1442344 * q^71 - 378666 * q^73 - 460026 * q^75 + 1065994 * q^77 - 611452 * q^79 - 236196 * q^81 - 275112 * q^85 - 112050 * q^87 - 989196 * q^89 - 304446 * q^91 + 805572 * q^93 + 591792 * q^95 + 152604 * q^99

Introduction

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