LMFDB - Embedded newform 336.6.q.l.289.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,6,Mod(193,336)]

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, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	336.q (of order $3$, 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:	$53.8889634572$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 564x^{8} + 117814x^{6} + 11067780x^{4} + 427918225x^{2} + 3489248448 $ x^10 + 564x^8 + 117814x^6 + 11067780x^4 + 427918225x^2 + 3489248448
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.4
Root			$14.3017i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.6.q.l.193.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.50000 - 7.79423i) q^{3} +(13.3782 - 23.1717i) q^{5} +(66.5893 + 111.233i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-4.50000 - 7.79423i) q^{3} +(13.3782 - 23.1717i) q^{5} +(66.5893 + 111.233i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-81.6815 - 141.477i) q^{11} -595.608 q^{13} -240.807 q^{15} +(301.837 + 522.796i) q^{17} +(1240.58 - 2148.75i) q^{19} +(567.327 - 1019.56i) q^{21} +(784.296 - 1358.44i) q^{23} +(1204.55 + 2086.34i) q^{25} +729.000 q^{27} -2060.19 q^{29} +(2997.58 + 5191.96i) q^{31} +(-735.134 + 1273.29i) q^{33} +(3468.31 - 54.8858i) q^{35} +(295.197 - 511.297i) q^{37} +(2680.24 + 4642.30i) q^{39} -2920.62 q^{41} +9413.21 q^{43} +(1083.63 + 1876.91i) q^{45} +(13540.4 - 23452.7i) q^{47} +(-7938.73 + 14813.9i) q^{49} +(2716.53 - 4705.17i) q^{51} +(-16037.7 - 27778.1i) q^{53} -4371.00 q^{55} -22330.4 q^{57} +(-5177.78 - 8968.18i) q^{59} +(5202.80 - 9011.52i) q^{61} +(-10499.7 + 166.157i) q^{63} +(-7968.15 + 13801.2i) q^{65} +(-23318.2 - 40388.3i) q^{67} -14117.3 q^{69} +42000.8 q^{71} +(-9583.83 - 16599.7i) q^{73} +(10840.9 - 18777.1i) q^{75} +(10297.8 - 18506.5i) q^{77} +(35576.9 - 61621.0i) q^{79} +(-3280.50 - 5681.99i) q^{81} +7301.98 q^{83} +16152.1 q^{85} +(9270.85 + 16057.6i) q^{87} +(12177.2 - 21091.5i) q^{89} +(-39661.1 - 66251.5i) q^{91} +(26978.2 - 46727.6i) q^{93} +(-33193.4 - 57492.6i) q^{95} +92726.4 q^{97} +13232.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9}+O(q^{10}) $ 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9	$ 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9} - 424 q^{11} + 374 q^{13} + 108 q^{15} - 952 q^{17} - 139 q^{19} - 1044 q^{21} - 4288 q^{23} - 5605 q^{25} + 7290 q^{27} - 4216 q^{29} - 8131 q^{31} - 3816 q^{33} - 20106 q^{35} - 5425 q^{37} - 1683 q^{39} + 29364 q^{41} + 46862 q^{43} - 486 q^{45} + 17190 q^{47} + 23255 q^{49} - 8568 q^{51} + 15064 q^{53} + 1176 q^{55} + 2502 q^{57} + 83242 q^{59} + 14954 q^{61} + 1539 q^{63} - 23250 q^{65} - 39501 q^{67} + 77184 q^{69} + 56020 q^{71} - 90395 q^{73} - 50445 q^{75} + 63448 q^{77} + 43067 q^{79} - 32805 q^{81} + 75672 q^{83} - 75272 q^{85} + 18972 q^{87} - 72608 q^{89} - 288287 q^{91} - 73179 q^{93} - 190138 q^{95} + 183000 q^{97} + 68688 q^{99}+O(q^{100}) $ 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9 - 424 * q^11 + 374 * q^13 + 108 * q^15 - 952 * q^17 - 139 * q^19 - 1044 * q^21 - 4288 * q^23 - 5605 * q^25 + 7290 * q^27 - 4216 * q^29 - 8131 * q^31 - 3816 * q^33 - 20106 * q^35 - 5425 * q^37 - 1683 * q^39 + 29364 * q^41 + 46862 * q^43 - 486 * q^45 + 17190 * q^47 + 23255 * q^49 - 8568 * q^51 + 15064 * q^53 + 1176 * q^55 + 2502 * q^57 + 83242 * q^59 + 14954 * q^61 + 1539 * q^63 - 23250 * q^65 - 39501 * q^67 + 77184 * q^69 + 56020 * q^71 - 90395 * q^73 - 50445 * q^75 + 63448 * q^77 + 43067 * q^79 - 32805 * q^81 + 75672 * q^83 - 75272 * q^85 + 18972 * q^87 - 72608 * q^89 - 288287 * q^91 - 73179 * q^93 - 190138 * q^95 + 183000 * q^97 + 68688 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$4$		0			0
$5$	13.3782	−	23.1717i	0.239316	−	0.414508i	−0.721202	−	0.692725i	$-0.756410\pi$
$5$	13.3782	−	23.1717i	0.239316	−	0.414508i	0.960518	+	0.278217i	$0.0897435\pi$
$6$		0			0
$7$	66.5893	+	111.233i	0.513640	+	0.858006i
$7$	66.5893	+	111.233i	0.513640	+	0.858006i
$8$		0			0
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$		0			0
$11$	−81.6815	−	141.477i	−0.203536	−	0.352535i	0.746129	−	0.665801i	$-0.231910\pi$
$11$	−81.6815	−	141.477i	−0.203536	−	0.352535i	−0.949665	+	0.313266i	$0.898577\pi$
$12$		0			0
$13$	−595.608			−0.977467			−0.488733	−	0.872433i	$-0.662541\pi$
$13$	−595.608			−0.977467			−0.488733	+	0.872433i	$0.662541\pi$
$14$		0			0
$15$	−240.807			−0.276338
$16$		0			0
$17$	301.837	+	522.796i	0.253308	+	0.438743i	0.964435	−	0.264321i	$-0.0851479\pi$
$17$	301.837	+	522.796i	0.253308	+	0.438743i	−0.711126	+	0.703064i	$0.751815\pi$
$18$		0			0
$19$	1240.58	−	2148.75i	0.788389	−	1.36553i	−0.138565	−	0.990353i	$-0.544249\pi$
$19$	1240.58	−	2148.75i	0.788389	−	1.36553i	0.926954	−	0.375176i	$-0.122418\pi$
$20$		0			0
$21$	567.327	−	1019.56i	0.280728	−	0.504505i
$22$		0			0
$23$	784.296	−	1358.44i	0.309144	−	0.535452i	−0.669032	−	0.743234i	$-0.733291\pi$
$23$	784.296	−	1358.44i	0.309144	−	0.535452i	0.978175	+	0.207781i	$0.0666243\pi$
$24$		0			0
$25$	1204.55	+	2086.34i	0.385456	+	0.667629i
$26$		0			0
$27$	729.000			0.192450
$28$		0			0
$29$	−2060.19			−0.454896			−0.227448	−	0.973790i	$-0.573038\pi$
$29$	−2060.19			−0.454896			−0.227448	+	0.973790i	$0.573038\pi$
$30$		0			0
$31$	2997.58	+	5191.96i	0.560230	+	0.970347i	0.997476	+	0.0710050i	$0.0226206\pi$
$31$	2997.58	+	5191.96i	0.560230	+	0.970347i	−0.437246	+	0.899342i	$0.644046\pi$
$32$		0			0
$33$	−735.134	+	1273.29i	−0.117512	+	0.203536i
$34$		0			0
$35$	3468.31	−	54.8858i	0.478572	−	0.00757338i
$36$		0			0
$37$	295.197	−	511.297i	0.0354493	−	0.0614000i	−0.847756	−	0.530386i	$-0.822047\pi$
$37$	295.197	−	511.297i	0.0354493	−	0.0614000i	0.883206	+	0.468986i	$0.155380\pi$
$38$		0			0
$39$	2680.24	+	4642.30i	0.282170	+	0.488733i
$40$		0			0
$41$	−2920.62			−0.271341			−0.135670	−	0.990754i	$-0.543319\pi$
$41$	−2920.62			−0.271341			−0.135670	+	0.990754i	$0.543319\pi$
$42$		0			0
$43$	9413.21			0.776366			0.388183	−	0.921582i	$-0.373103\pi$
$43$	9413.21			0.776366			0.388183	+	0.921582i	$0.373103\pi$
$44$		0			0
$45$	1083.63	+	1876.91i	0.0797720	+	0.138169i
$46$		0			0
$47$	13540.4	−	23452.7i	0.894101	−	1.54863i	0.0591882	−	0.998247i	$-0.481149\pi$
$47$	13540.4	−	23452.7i	0.894101	−	1.54863i	0.834913	−	0.550382i	$-0.185518\pi$
$48$		0			0
$49$	−7938.73	+	14813.9i	−0.472347	+	0.881413i
$50$		0			0
$51$	2716.53	−	4705.17i	0.146248	−	0.253308i
$52$		0			0
$53$	−16037.7	−	27778.1i	−0.784247	−	1.35836i	−0.929448	−	0.368953i	$-0.879716\pi$
$53$	−16037.7	−	27778.1i	−0.784247	−	1.35836i	0.145201	−	0.989402i	$-0.453617\pi$
$54$		0			0
$55$	−4371.00			−0.194838
$56$		0			0
$57$	−22330.4			−0.910353
$58$		0			0
$59$	−5177.78	−	8968.18i	−0.193648	−	0.335409i	0.752808	−	0.658240i	$-0.228699\pi$
$59$	−5177.78	−	8968.18i	−0.193648	−	0.335409i	−0.946457	+	0.322831i	$0.895365\pi$
$60$		0			0
$61$	5202.80	−	9011.52i	0.179025	−	0.310080i	−0.762522	−	0.646962i	$-0.776039\pi$
$61$	5202.80	−	9011.52i	0.179025	−	0.310080i	0.941547	+	0.336882i	$0.109372\pi$
$62$		0			0
$63$	−10499.7	+	166.157i	−0.333292	+	0.00527432i
$64$		0			0
$65$	−7968.15	+	13801.2i	−0.233924	+	0.405167i
$66$		0			0
$67$	−23318.2	−	40388.3i	−0.634611	−	1.09918i	−0.986597	−	0.163174i	$-0.947827\pi$
$67$	−23318.2	−	40388.3i	−0.634611	−	1.09918i	0.351986	−	0.936005i	$-0.385506\pi$
$68$		0			0
$69$	−14117.3			−0.356968
$70$		0			0
$71$	42000.8			0.988807			0.494404	−	0.869232i	$-0.335386\pi$
$71$	42000.8			0.988807			0.494404	+	0.869232i	$0.335386\pi$
$72$		0			0
$73$	−9583.83	−	16599.7i	−0.210490	−	0.364580i	0.741378	−	0.671088i	$-0.234173\pi$
$73$	−9583.83	−	16599.7i	−0.210490	−	0.364580i	−0.951868	+	0.306508i	$0.900839\pi$
$74$		0			0
$75$	10840.9	−	18777.1i	0.222543	−	0.385456i
$76$		0			0
$77$	10297.8	−	18506.5i	0.197933	−	0.355712i
$78$		0			0
$79$	35576.9	−	61621.0i	0.641358	−	1.11086i	−0.343772	−	0.939053i	$-0.611705\pi$
$79$	35576.9	−	61621.0i	0.641358	−	1.11086i	0.985130	−	0.171811i	$-0.0549618\pi$
$80$		0			0
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	7301.98			0.116344			0.0581722	−	0.998307i	$-0.481473\pi$
$83$	7301.98			0.116344			0.0581722	+	0.998307i	$0.481473\pi$
$84$		0			0
$85$	16152.1			0.242483
$86$		0			0
$87$	9270.85	+	16057.6i	0.131317	+	0.227448i
$88$		0			0
$89$	12177.2	−	21091.5i	0.162956	−	0.282249i	−0.772971	−	0.634441i	$-0.781230\pi$
$89$	12177.2	−	21091.5i	0.162956	−	0.282249i	0.935928	+	0.352192i	$0.114564\pi$
$90$		0			0
$91$	−39661.1	−	66251.5i	−0.502067	−	0.838672i
$92$		0			0
$93$	26978.2	−	46727.6i	0.323449	−	0.560230i
$94$		0			0
$95$	−33193.4	−	57492.6i	−0.377348	−	0.653586i
$96$		0			0
$97$	92726.4			1.00063			0.500316	−	0.865843i	$-0.333217\pi$
$97$	92726.4			1.00063			0.500316	+	0.865843i	$0.333217\pi$
$98$		0			0
$99$	13232.4			0.135691
$100$		0			0
$101$	−88097.2	−	152589.i	−0.859327	−	1.48840i	−0.872572	−	0.488486i	$-0.837549\pi$
$101$	−88097.2	−	152589.i	−0.859327	−	1.48840i	0.0132450	−	0.999912i	$-0.495784\pi$
$102$		0			0
$103$	−15806.4	+	27377.4i	−0.146804	+	0.254272i	−0.930045	−	0.367447i	$-0.880232\pi$
$103$	−15806.4	+	27377.4i	−0.146804	+	0.254272i	0.783240	+	0.621719i	$0.213565\pi$
$104$		0			0
$105$	−16035.2	−	26785.8i	−0.141939	−	0.237100i
$106$		0			0
$107$	−39570.7	+	68538.5i	−0.334129	+	0.578729i	−0.983317	−	0.181899i	$-0.941776\pi$
$107$	−39570.7	+	68538.5i	−0.334129	+	0.578729i	0.649188	+	0.760628i	$0.275109\pi$
$108$		0			0
$109$	−19841.6	−	34366.6i	−0.159959	−	0.277058i	0.774894	−	0.632091i	$-0.217803\pi$
$109$	−19841.6	−	34366.6i	−0.159959	−	0.277058i	−0.934854	+	0.355033i	$0.884470\pi$
$110$		0			0
$111$	−5313.55			−0.0409334
$112$		0			0
$113$	76185.5			0.561276			0.280638	−	0.959814i	$-0.409454\pi$
$113$	76185.5			0.561276			0.280638	+	0.959814i	$0.409454\pi$
$114$		0			0
$115$	−20984.9	−	36346.9i	−0.147966	−	0.256285i
$116$		0			0
$117$	24122.1	−	41780.7i	0.162911	−	0.282170i
$118$		0			0
$119$	−38053.3	+	68387.0i	−0.246335	+	0.442696i
$120$		0			0
$121$	67181.8	−	116362.i	0.417146	−	0.722518i
$122$		0			0
$123$	13142.8	+	22763.9i	0.0783293	+	0.135670i
$124$		0			0
$125$	148072.			0.847615
$126$		0			0
$127$	−330407.			−1.81777			−0.908887	−	0.417042i	$-0.863067\pi$
$127$	−330407.			−1.81777			−0.908887	+	0.417042i	$0.863067\pi$
$128$		0			0
$129$	−42359.4	−	73368.7i	−0.224118	−	0.388183i
$130$		0			0
$131$	116335.	−	201498.i	0.592287	−	1.02587i	−0.401636	−	0.915799i	$-0.631558\pi$
$131$	116335.	−	201498.i	0.592287	−	1.02587i	0.993924	−	0.110072i	$-0.0351082\pi$
$132$		0			0
$133$	321622.	−	5089.64i	1.57658	−	0.0249493i
$134$		0			0
$135$	9752.69	−	16892.2i	0.0460564	−	0.0797720i
$136$		0			0
$137$	−48363.9	−	83768.8i	−0.220151	−	0.381312i	0.734703	−	0.678389i	$-0.237322\pi$
$137$	−48363.9	−	83768.8i	−0.220151	−	0.381312i	−0.954854	+	0.297077i	$0.903988\pi$
$138$		0			0
$139$	−177589.			−0.779613			−0.389806	−	0.920897i	$-0.627458\pi$
$139$	−177589.			−0.779613			−0.389806	+	0.920897i	$0.627458\pi$
$140$		0			0
$141$	−243727.			−1.03242
$142$		0			0
$143$	48650.1	+	84264.5i	0.198950	+	0.344592i
$144$		0			0
$145$	−27561.6	+	47738.1i	−0.108864	+	0.188558i
$146$		0			0
$147$	151187.	−	4786.26i	0.577061	−	0.0182685i
$148$		0			0
$149$	23813.2	−	41245.7i	0.0878723	−	0.152199i	−0.818739	−	0.574166i	$-0.805327\pi$
$149$	23813.2	−	41245.7i	0.0878723	−	0.152199i	0.906612	+	0.421966i	$0.138660\pi$
$150$		0			0
$151$	−252349.	−	437081.i	−0.900657	−	1.55998i	−0.826644	−	0.562726i	$-0.809753\pi$
$151$	−252349.	−	437081.i	−0.900657	−	1.55998i	−0.0740127	−	0.997257i	$-0.523581\pi$
$152$		0			0
$153$	−48897.5			−0.168872
$154$		0			0
$155$	160409.			0.536288
$156$		0			0
$157$	128179.	+	222012.i	0.415017	+	0.718831i	0.995430	−	0.0954911i	$-0.0304421\pi$
$157$	128179.	+	222012.i	0.415017	+	0.718831i	−0.580413	+	0.814322i	$0.697109\pi$
$158$		0			0
$159$	−144339.	+	250003.i	−0.452785	+	0.784247i
$160$		0			0
$161$	203330.	−	3217.68i	0.618210	−	0.00978314i
$162$		0			0
$163$	−14351.4	+	24857.3i	−0.0423083	+	0.0732800i	−0.886404	−	0.462912i	$-0.846804\pi$
$163$	−14351.4	+	24857.3i	−0.0423083	+	0.0732800i	0.844096	+	0.536192i	$0.180138\pi$
$164$		0			0
$165$	19669.5	+	34068.6i	0.0562449	+	0.0974190i
$166$		0			0
$167$	671712.			1.86377			0.931884	−	0.362757i	$-0.118164\pi$
$167$	671712.			1.86377			0.931884	+	0.362757i	$0.118164\pi$
$168$		0			0
$169$	−16544.3			−0.0445585
$170$		0			0
$171$	100487.	+	174048.i	0.262796	+	0.455176i
$172$		0			0
$173$	174668.	−	302534.i	0.443709	−	0.768526i	−0.554253	−	0.832348i	$-0.686996\pi$
$173$	174668.	−	302534.i	0.443709	−	0.768526i	0.997961	+	0.0638227i	$0.0203292\pi$
$174$		0			0
$175$	−151861.	+	272914.i	−0.374844	+	0.673644i
$176$		0			0
$177$	−46600.0	+	80713.6i	−0.111803	+	0.193648i
$178$		0			0
$179$	−9320.90	−	16144.3i	−0.0217433	−	0.0376605i	0.854949	−	0.518712i	$-0.173588\pi$
$179$	−9320.90	−	16144.3i	−0.0217433	−	0.0376605i	−0.876692	+	0.481052i	$0.840255\pi$
$180$		0			0
$181$	−317959.			−0.721397			−0.360699	−	0.932682i	$-0.617462\pi$
$181$	−317959.			−0.721397			−0.360699	+	0.932682i	$0.617462\pi$
$182$		0			0
$183$	−93650.5			−0.206720
$184$		0			0
$185$	−7898.40	−	13680.4i	−0.0169672	−	0.0293880i
$186$		0			0
$187$	49308.9	−	85405.6i	0.103115	−	0.178600i
$188$		0			0
$189$	48543.6	+	81089.1i	0.0988502	+	0.165123i
$190$		0			0
$191$	4388.68	−	7601.42i	0.00870464	−	0.0150769i	−0.861640	−	0.507519i	$-0.830563\pi$
$191$	4388.68	−	7601.42i	0.00870464	−	0.0150769i	0.870345	+	0.492443i	$0.163896\pi$
$192$		0			0
$193$	292255.	+	506200.i	0.564766	+	0.978203i	0.997071	+	0.0764758i	$0.0243668\pi$
$193$	292255.	+	506200.i	0.564766	+	0.978203i	−0.432306	+	0.901727i	$0.642300\pi$
$194$		0			0
$195$	143427.			0.270112
$196$		0			0
$197$	−310165.			−0.569412			−0.284706	−	0.958615i	$-0.591896\pi$
$197$	−310165.			−0.569412			−0.284706	+	0.958615i	$0.591896\pi$
$198$		0			0
$199$	−40846.9	−	70749.0i	−0.0731184	−	0.126645i	0.827148	−	0.561984i	$-0.189962\pi$
$199$	−40846.9	−	70749.0i	−0.0731184	−	0.126645i	−0.900267	+	0.435339i	$0.856628\pi$
$200$		0			0
$201$	−209864.	+	363494.i	−0.366393	+	0.634611i
$202$		0			0
$203$	−137187.	−	229162.i	−0.233653	−	0.390303i
$204$		0			0
$205$	−39072.5	+	67675.6i	−0.0649362	+	0.112473i
$206$		0			0
$207$	63528.0	+	110034.i	0.103048	+	0.178484i
$208$		0			0
$209$	−405329.			−0.641863
$210$		0			0
$211$	700566.			1.08328			0.541642	−	0.840609i	$-0.317803\pi$
$211$	700566.			1.08328			0.541642	+	0.840609i	$0.317803\pi$
$212$		0			0
$213$	−189004.	−	327364.i	−0.285444	−	0.494404i
$214$		0			0
$215$	125932.	−	218120.i	0.185797	−	0.321810i
$216$		0			0
$217$	−377913.	+	679160.i	−0.544806	+	0.979090i
$218$		0			0
$219$	−86254.4	+	149397.i	−0.121527	+	0.210490i
$220$		0			0
$221$	−179776.	−	311382.i	−0.247601	−	0.428857i
$222$		0			0
$223$	−292308.			−0.393621			−0.196810	−	0.980442i	$-0.563058\pi$
$223$	−292308.			−0.393621			−0.196810	+	0.980442i	$0.563058\pi$
$224$		0			0
$225$	−195137.			−0.256970
$226$		0			0
$227$	414937.	+	718692.i	0.534463	+	0.925717i	0.999189	+	0.0402625i	$0.0128194\pi$
$227$	414937.	+	718692.i	0.534463	+	0.925717i	−0.464726	+	0.885454i	$0.653847\pi$
$228$		0			0
$229$	−438454.	+	759424.i	−0.552503	+	0.956964i	0.445590	+	0.895237i	$0.352994\pi$
$229$	−438454.	+	759424.i	−0.552503	+	0.956964i	−0.998093	+	0.0617267i	$0.980339\pi$
$230$		0			0
$231$	−190584.	+	3015.98i	−0.234994	+	0.00371877i
$232$		0			0
$233$	427589.	−	740606.i	0.515984	−	0.893711i	−0.483843	−	0.875155i	$-0.660760\pi$
$233$	427589.	−	740606.i	0.515984	−	0.893711i	0.999828	−	0.0185566i	$-0.00590710\pi$
$234$		0			0
$235$	−362292.	−	627507.i	−0.427946	−	0.741224i
$236$		0			0
$237$	−640384.			−0.740576
$238$		0			0
$239$	−61088.9			−0.0691779			−0.0345889	−	0.999402i	$-0.511012\pi$
$239$	−61088.9			−0.0691779			−0.0345889	+	0.999402i	$0.511012\pi$
$240$		0			0
$241$	−85910.9	−	148802.i	−0.0952808	−	0.165031i	0.814445	−	0.580241i	$-0.197042\pi$
$241$	−85910.9	−	148802.i	−0.0952808	−	0.165031i	−0.909726	+	0.415210i	$0.863708\pi$
$242$		0			0
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	237057.	+	382137.i	0.252312	+	0.406728i
$246$		0			0
$247$	−738899.	+	1.27981e6i	−0.770624	+	1.33476i
$248$		0			0
$249$	−32858.9	−	56913.3i	−0.0335857	−	0.0581722i
$250$		0			0
$251$	1.87213e6			1.87565			0.937826	−	0.347104i	$-0.112835\pi$
$251$	1.87213e6			1.87565			0.937826	+	0.347104i	$0.112835\pi$
$252$		0			0
$253$	−256250.			−0.251688
$254$		0			0
$255$	−72684.4	−	125893.i	−0.0699989	−	0.121242i
$256$		0			0
$257$	−1.03511e6	+	1.79287e6i	−0.977588	+	1.69323i	−0.306470	+	0.951880i	$0.599148\pi$
$257$	−1.03511e6	+	1.79287e6i	−0.977588	+	1.69323i	−0.671118	+	0.741351i	$0.734185\pi$
$258$		0			0
$259$	76530.2	−	1211.09i	0.0708898	−	0.00112183i
$260$		0			0
$261$	83437.7	−	144518.i	0.0758160	−	0.131317i
$262$		0			0
$263$	−43069.8	−	74599.1i	−0.0383958	−	0.0665034i	0.846189	−	0.532883i	$-0.178891\pi$
$263$	−43069.8	−	74599.1i	−0.0383958	−	0.0665034i	−0.884585	+	0.466380i	$0.845558\pi$
$264$		0			0
$265$	−858221.			−0.750732
$266$		0			0
$267$	−219189.			−0.188166
$268$		0			0
$269$	760410.	+	1.31707e6i	0.640718	+	1.10976i	0.985273	+	0.170990i	$0.0546966\pi$
$269$	760410.	+	1.31707e6i	0.640718	+	1.10976i	−0.344555	+	0.938766i	$0.611970\pi$
$270$		0			0
$271$	−797683.	+	1.38163e6i	−0.659792	+	1.14279i	0.320877	+	0.947121i	$0.396022\pi$
$271$	−797683.	+	1.38163e6i	−0.659792	+	1.14279i	−0.980669	+	0.195672i	$0.937311\pi$
$272$		0			0
$273$	−337904.	+	607259.i	−0.274402	+	0.493137i
$274$		0			0
$275$	196779.	−	340831.i	0.156908	−	0.271773i
$276$		0			0
$277$	435077.	+	753575.i	0.340695	+	0.590102i	0.984562	−	0.175036i	$-0.0560042\pi$
$277$	435077.	+	753575.i	0.340695	+	0.590102i	−0.643867	+	0.765138i	$0.722671\pi$
$278$		0			0
$279$	−485608.			−0.373487
$280$		0			0
$281$	1.63359e6			1.23417			0.617087	−	0.786895i	$-0.288313\pi$
$281$	1.63359e6			1.23417			0.617087	+	0.786895i	$0.288313\pi$
$282$		0			0
$283$	280329.	+	485543.i	0.208066	+	0.360381i	0.951105	−	0.308867i	$-0.0999498\pi$
$283$	280329.	+	485543.i	0.208066	+	0.360381i	−0.743039	+	0.669248i	$0.766616\pi$
$284$		0			0
$285$	−298740.	+	517433.i	−0.217862	+	0.377348i
$286$		0			0
$287$	−194482.	−	324870.i	−0.139372	−	0.232812i
$288$		0			0
$289$	527718.	−	914034.i	0.371670	−	0.643751i
$290$		0			0
$291$	−417269.	−	722731.i	−0.288857	−	0.500316i
$292$		0			0
$293$	1.01211e6			0.688747			0.344374	−	0.938833i	$-0.388091\pi$
$293$	1.01211e6			0.688747			0.344374	+	0.938833i	$0.388091\pi$
$294$		0			0
$295$	−277077.			−0.185373
$296$		0			0
$297$	−59545.8	−	103136.i	−0.0391706	−	0.0678455i
$298$		0			0
$299$	−467133.	+	809098.i	−0.302178	+	0.523387i
$300$		0			0
$301$	626819.	+	1.04706e6i	0.398773	+	0.666126i
$302$		0			0
$303$	−792874.	+	1.37330e6i	−0.496133	+	0.859327i
$304$		0			0
$305$	−139208.	−	241115.i	−0.0856869	−	0.148414i
$306$		0			0
$307$	2.74706e6			1.66350			0.831749	−	0.555153i	$-0.187340\pi$
$307$	2.74706e6			1.66350			0.831749	+	0.555153i	$0.187340\pi$
$308$		0			0
$309$	284514.			0.169515
$310$		0			0
$311$	156619.	+	271272.i	0.0918213	+	0.159039i	0.908278	−	0.418368i	$-0.137398\pi$
$311$	156619.	+	271272.i	0.0918213	+	0.159039i	−0.816456	+	0.577407i	$0.804064\pi$
$312$		0			0
$313$	61781.7	−	107009.i	0.0356450	−	0.0617390i	−0.847653	−	0.530552i	$-0.821985\pi$
$313$	61781.7	−	107009.i	0.0356450	−	0.0617390i	0.883298	+	0.468813i	$0.155318\pi$
$314$		0			0
$315$	−136616.	+	245518.i	−0.0775758	+	0.139414i
$316$		0			0
$317$	1.24968e6	−	2.16450e6i	0.698472	−	1.20979i	−0.270524	−	0.962713i	$-0.587197\pi$
$317$	1.24968e6	−	2.16450e6i	0.698472	−	1.20979i	0.968996	−	0.247076i	$-0.0794698\pi$
$318$		0			0
$319$	168279.	+	291468.i	0.0925879	+	0.160367i
$320$		0			0
$321$	712273.			0.385819
$322$		0			0
$323$	1.49781e6			0.798822
$324$		0			0
$325$	−717439.	−	1.24264e6i	−0.376770	−	0.652585i
$326$		0			0
$327$	−178574.	+	309299.i	−0.0923526	+	0.159959i
$328$		0			0
$329$	3.51036e6	−	55551.3i	1.78798	−	0.0282947i
$330$		0			0
$331$	−1.38949e6	+	2.40666e6i	−0.697083	+	1.20738i	0.272390	+	0.962187i	$0.412186\pi$
$331$	−1.38949e6	+	2.40666e6i	−0.697083	+	1.20738i	−0.969473	+	0.245197i	$0.921147\pi$
$332$		0			0
$333$	23911.0	+	41415.0i	0.0118164	+	0.0204667i
$334$		0			0
$335$	−1.24782e6			−0.607491
$336$		0			0
$337$	737417.			0.353703			0.176851	−	0.984238i	$-0.443409\pi$
$337$	737417.			0.353703			0.176851	+	0.984238i	$0.443409\pi$
$338$		0			0
$339$	−342835.	−	593807.i	−0.162026	−	0.280638i
$340$		0			0
$341$	489694.	−	848174.i	0.228054	−	0.395002i
$342$		0			0
$343$	−2.17644e6	+	103395.i	−0.998873	+	0.0474530i
$344$		0			0
$345$	−188864.	+	327122.i	−0.0854283	+	0.147966i
$346$		0			0
$347$	−1.04336e6	−	1.80716e6i	−0.465169	−	0.805697i	0.534040	−	0.845459i	$-0.320673\pi$
$347$	−1.04336e6	−	1.80716e6i	−0.465169	−	0.805697i	−0.999209	+	0.0397624i	$0.987340\pi$
$348$		0			0
$349$	−3.35404e6			−1.47403			−0.737013	−	0.675879i	$-0.763764\pi$
$349$	−3.35404e6			−1.47403			−0.737013	+	0.675879i	$0.763764\pi$
$350$		0			0
$351$	−434198.			−0.188114
$352$		0			0
$353$	−496079.	−	859234.i	−0.211892	−	0.367007i	0.740415	−	0.672150i	$-0.234629\pi$
$353$	−496079.	−	859234.i	−0.211892	−	0.367007i	−0.952307	+	0.305143i	$0.901296\pi$
$354$		0			0
$355$	561894.	−	973229.i	0.236637	−	0.409868i
$356$		0			0
$357$	704264.	−	11144.9i	0.292459	−	0.00462814i
$358$		0			0
$359$	−2.22630e6	+	3.85606e6i	−0.911689	+	1.57909i	−0.100012	+	0.994986i	$0.531888\pi$
$359$	−2.22630e6	+	3.85606e6i	−0.911689	+	1.57909i	−0.811677	+	0.584106i	$0.801445\pi$
$360$		0			0
$361$	−1.84002e6	−	3.18701e6i	−0.743113	−	1.28711i
$362$		0			0
$363$	−1.20927e6			−0.481679
$364$		0			0
$365$	−512856.			−0.201495
$366$		0			0
$367$	445316.	+	771309.i	0.172585	+	0.298926i	0.939323	−	0.343034i	$-0.111455\pi$
$367$	445316.	+	771309.i	0.172585	+	0.298926i	−0.766738	+	0.641960i	$0.778121\pi$
$368$		0			0
$369$	118285.	−	204876.i	0.0452234	−	0.0783293i
$370$		0			0
$371$	2.02192e6	−	3.63366e6i	0.762655	−	1.37059i
$372$		0			0
$373$	146486.	−	253721.i	0.0545160	−	0.0944245i	−0.837480	−	0.546469i	$-0.815972\pi$
$373$	146486.	−	253721.i	0.0545160	−	0.0944245i	0.891996	+	0.452044i	$0.149305\pi$
$374$		0			0
$375$	−666325.	−	1.15411e6i	−0.244685	−	0.423808i
$376$		0			0
$377$	1.22707e6			0.444646
$378$		0			0
$379$	1.24947e6			0.446814			0.223407	−	0.974725i	$-0.428282\pi$
$379$	1.24947e6			0.446814			0.223407	+	0.974725i	$0.428282\pi$
$380$		0			0
$381$	1.48683e6	+	2.57527e6i	0.524746	+	0.908887i
$382$		0			0
$383$	1.05565e6	−	1.82843e6i	0.367723	−	0.636915i	−0.621486	−	0.783425i	$-0.713471\pi$
$383$	1.05565e6	−	1.82843e6i	0.367723	−	0.636915i	0.989209	+	0.146510i	$0.0468041\pi$
$384$		0			0
$385$	−291062.	−	486201.i	−0.100077	−	0.167172i
$386$		0			0
$387$	−381235.	+	660318.i	−0.129394	+	0.224118i
$388$		0			0
$389$	1.73067e6	+	2.99761e6i	0.579883	+	1.00439i	0.995492	+	0.0948435i	$0.0302351\pi$
$389$	1.73067e6	+	2.99761e6i	0.579883	+	1.00439i	−0.415609	+	0.909543i	$0.636432\pi$
$390$		0			0
$391$	946917.			0.313235
$392$		0			0
$393$	−2.09403e6			−0.683914
$394$		0			0
$395$	−951908.	−	1.64875e6i	−0.306974	−	0.531695i
$396$		0			0
$397$	−1.22234e6	+	2.11716e6i	−0.389239	+	0.674181i	−0.992347	−	0.123478i	$-0.960595\pi$
$397$	−1.22234e6	+	2.11716e6i	−0.389239	+	0.674181i	0.603109	+	0.797659i	$0.293929\pi$
$398$		0			0
$399$	−1.48697e6	−	2.48389e6i	−0.467594	−	0.781088i
$400$		0			0
$401$	2.66753e6	−	4.62030e6i	0.828416	−	1.43486i	−0.0708651	−	0.997486i	$-0.522576\pi$
$401$	2.66753e6	−	4.62030e6i	0.828416	−	1.43486i	0.899281	−	0.437372i	$-0.144091\pi$
$402$		0			0
$403$	−1.78538e6	−	3.09237e6i	−0.547606	−	0.948482i
$404$		0			0
$405$	−175548.			−0.0531814
$406$		0			0
$407$	−96448.6			−0.0288609
$408$		0			0
$409$	−2.09530e6	−	3.62916e6i	−0.619352	−	1.07275i	−0.989604	−	0.143818i	$-0.954062\pi$
$409$	−2.09530e6	−	3.62916e6i	−0.619352	−	1.07275i	0.370252	−	0.928931i	$-0.379271\pi$
$410$		0			0
$411$	−435275.	+	753919.i	−0.127104	+	0.220151i
$412$		0			0
$413$	652776.	−	1.17313e6i	0.188317	−	0.338431i
$414$		0			0
$415$	97687.2	−	169199.i	0.0278431	−	0.0482256i
$416$		0			0
$417$	799150.	+	1.38417e6i	0.225055	+	0.389806i
$418$		0			0
$419$	5.21033e6			1.44987			0.724937	−	0.688815i	$-0.241869\pi$
$419$	5.21033e6			1.44987			0.724937	+	0.688815i	$0.241869\pi$
$420$		0			0
$421$	1.05706e6			0.290665			0.145333	−	0.989383i	$-0.453575\pi$
$421$	1.05706e6			0.290665			0.145333	+	0.989383i	$0.453575\pi$
$422$		0			0
$423$	1.09677e6	+	1.89966e6i	0.298034	+	0.516210i
$424$		0			0
$425$	−727154.	+	1.25947e6i	−0.195278	+	0.338232i
$426$		0			0
$427$	1.34883e6	−	21345.2i	0.358004	−	0.00566540i
$428$		0			0
$429$	437851.	−	758381.i	0.114864	−	0.198950i
$430$		0			0
$431$	−2.48147e6	−	4.29803e6i	−0.643451	−	1.11449i	−0.984657	−	0.174501i	$-0.944169\pi$
$431$	−2.48147e6	−	4.29803e6i	−0.643451	−	1.11449i	0.341206	−	0.939988i	$-0.389165\pi$
$432$		0			0
$433$	−4.95367e6			−1.26972			−0.634859	−	0.772628i	$-0.718942\pi$
$433$	−4.95367e6			−1.26972			−0.634859	+	0.772628i	$0.718942\pi$
$434$		0			0
$435$	496108.			0.125705
$436$		0			0
$437$	−1.94596e6	−	3.37050e6i	−0.487451	−	0.844289i
$438$		0			0
$439$	−1.77419e6	+	3.07298e6i	−0.439378	+	0.761025i	−0.997642	−	0.0686387i	$-0.978134\pi$
$439$	−1.77419e6	+	3.07298e6i	−0.439378	+	0.761025i	0.558264	+	0.829664i	$0.311468\pi$
$440$		0			0
$441$	−717648.	−	1.15685e6i	−0.175717	−	0.283257i
$442$		0			0
$443$	3.68493e6	−	6.38249e6i	0.892114	−	1.54519i	0.0547773	−	0.998499i	$-0.482555\pi$
$443$	3.68493e6	−	6.38249e6i	0.892114	−	1.54519i	0.837337	−	0.546688i	$-0.184112\pi$
$444$		0			0
$445$	−325817.	−	564331.i	−0.0779962	−	0.135093i
$446$		0			0
$447$	−428638.			−0.101466
$448$		0			0
$449$	2.53641e6			0.593750			0.296875	−	0.954916i	$-0.404056\pi$
$449$	2.53641e6			0.593750			0.296875	+	0.954916i	$0.404056\pi$
$450$		0			0
$451$	238560.	+	413199.i	0.0552277	+	0.0956571i
$452$		0			0
$453$	−2.27114e6	+	3.93373e6i	−0.519994	+	0.900657i
$454$		0			0
$455$	−2.06575e6	+	32690.4i	−0.467789	+	0.00740273i
$456$		0			0
$457$	−1.05909e6	+	1.83440e6i	−0.237215	+	0.410869i	−0.959914	−	0.280294i	$-0.909568\pi$
$457$	−1.05909e6	+	1.83440e6i	−0.237215	+	0.410869i	0.722699	+	0.691163i	$0.242901\pi$
$458$		0			0
$459$	220039.	+	381119.i	0.0487492	+	0.0844362i
$460$		0			0
$461$	−7.00292e6			−1.53471			−0.767356	−	0.641221i	$-0.778428\pi$
$461$	−7.00292e6			−1.53471			−0.767356	+	0.641221i	$0.778428\pi$
$462$		0			0
$463$	3.94469e6			0.855185			0.427593	−	0.903971i	$-0.359362\pi$
$463$	3.94469e6			0.855185			0.427593	+	0.903971i	$0.359362\pi$
$464$		0			0
$465$	−721839.	−	1.25026e6i	−0.154813	−	0.268144i
$466$		0			0
$467$	2.15442e6	−	3.73156e6i	0.457128	−	0.791769i	−0.541680	−	0.840585i	$-0.682212\pi$
$467$	2.15442e6	−	3.73156e6i	0.457128	−	0.791769i	0.998808	+	0.0488161i	$0.0155448\pi$
$468$		0			0
$469$	2.93978e6	−	5.28319e6i	0.617139	−	1.10908i
$470$		0			0
$471$	1.15361e6	−	1.99811e6i	0.239610	−	0.415017i
$472$		0			0
$473$	−768885.	−	1.33175e6i	−0.158019	−	0.273696i
$474$		0			0
$475$	5.97735e6			1.21556
$476$		0			0
$477$	2.59811e6			0.522831
$478$		0			0
$479$	1.82969e6	+	3.16912e6i	0.364368	+	0.631103i	0.988674	−	0.150076i	$-0.0479518\pi$
$479$	1.82969e6	+	3.16912e6i	0.364368	+	0.631103i	−0.624307	+	0.781179i	$0.714619\pi$
$480$		0			0
$481$	−175822.	+	304532.i	−0.0346505	+	0.0600165i
$482$		0			0
$483$	−940062.	−	1.57032e6i	−0.183353	−	0.306281i
$484$		0			0
$485$	1.24051e6	−	2.14863e6i	0.239467	−	0.414769i
$486$		0			0
$487$	−3.66804e6	−	6.35324e6i	−0.700829	−	1.21387i	−0.968176	−	0.250271i	$-0.919480\pi$
$487$	−3.66804e6	−	6.35324e6i	−0.700829	−	1.21387i	0.267347	−	0.963600i	$-0.413853\pi$
$488$		0			0
$489$	258325.			0.0488534
$490$		0			0
$491$	6.95510e6			1.30197			0.650983	−	0.759092i	$-0.274357\pi$
$491$	6.95510e6			1.30197			0.650983	+	0.759092i	$0.274357\pi$
$492$		0			0
$493$	−621841.	−	1.07706e6i	−0.115229	−	0.199583i
$494$		0			0
$495$	177025.	−	306617.i	0.0324730	−	0.0562449i
$496$		0			0
$497$	2.79680e6	+	4.67189e6i	0.507891	+	0.848402i
$498$		0			0
$499$	139655.	−	241889.i	0.0251075	−	0.0434875i	−0.853199	−	0.521586i	$-0.825341\pi$
$499$	139655.	−	241889.i	0.0251075	−	0.0434875i	0.878306	+	0.478099i	$0.158674\pi$
$500$		0			0
$501$	−3.02270e6	−	5.23548e6i	−0.538023	−	0.931884i
$502$		0			0
$503$	−9.11670e6			−1.60664			−0.803318	−	0.595550i	$-0.796934\pi$
$503$	−9.11670e6			−1.60664			−0.803318	+	0.595550i	$0.796934\pi$
$504$		0			0
$505$	−4.71432e6			−0.822603
$506$		0			0
$507$	74449.2	+	128950.i	0.0128629	+	0.0222793i
$508$		0			0
$509$	−211761.	+	366780.i	−0.0362285	+	0.0627497i	−0.883571	−	0.468297i	$-0.844868\pi$
$509$	−211761.	+	366780.i	−0.0362285	+	0.0627497i	0.847343	+	0.531047i	$0.178201\pi$
$510$		0			0
$511$	1.20826e6	−	2.17140e6i	0.204695	−	0.367865i
$512$		0			0
$513$	904382.	−	1.56644e6i	0.151725	−	0.262796i
$514$		0			0
$515$	422920.	+	732520.i	0.0702652	+	0.121703i
$516$		0			0
$517$	−4.42400e6			−0.727928
$518$		0			0
$519$	−3.14402e6			−0.512350
$520$		0			0
$521$	1.66620e6	+	2.88594e6i	0.268926	+	0.465793i	0.968585	−	0.248684i	$-0.0799980\pi$
$521$	1.66620e6	+	2.88594e6i	0.268926	+	0.465793i	−0.699659	+	0.714477i	$0.746665\pi$
$522$		0			0
$523$	563848.	−	976613.i	0.0901380	−	0.156124i	−0.817431	−	0.576026i	$-0.804603\pi$
$523$	563848.	−	976613.i	0.0901380	−	0.156124i	0.907569	+	0.419903i	$0.137936\pi$
$524$		0			0
$525$	2.81053e6	−	44476.4i	0.445030	−	0.00704258i
$526$		0			0
$527$	−1.80956e6	+	3.13425e6i	−0.283822	+	0.491594i
$528$		0			0
$529$	1.98793e6	+	3.44320e6i	0.308860	+	0.534962i
$530$		0			0
$531$	838800.			0.129099
$532$		0			0
$533$	1.73954e6			0.265226
$534$		0			0
$535$	1.05877e6	+	1.83384e6i	0.159925	+	0.276998i
$536$		0			0
$537$	−83888.1	+	145298.i	−0.0125535	+	0.0217433i
$538$		0			0
$539$	2.74427e6	−	86877.5i	0.406869	−	0.0128806i
$540$		0			0
$541$	632670.	−	1.09582e6i	0.0929360	−	0.160970i	−0.815809	−	0.578321i	$-0.803708\pi$
$541$	632670.	−	1.09582e6i	0.0929360	−	0.160970i	0.908745	+	0.417351i	$0.137041\pi$
$542$		0			0
$543$	1.43081e6	+	2.47824e6i	0.208249	+	0.360699i
$544$		0			0
$545$	−1.06178e6			−0.153123
$546$		0			0
$547$	6.48152e6			0.926208			0.463104	−	0.886304i	$-0.346736\pi$
$547$	6.48152e6			0.926208			0.463104	+	0.886304i	$0.346736\pi$
$548$		0			0
$549$	421427.	+	729933.i	0.0596749	+	0.103360i
$550$		0			0
$551$	−2.55583e6	+	4.42682e6i	−0.358635	+	0.621174i
$552$		0			0
$553$	9.22335e6	−	145959.i	1.28255	−	0.0202964i
$554$		0			0
$555$	−71085.6	+	123124.i	−0.00979601	+	0.0169672i
$556$		0			0
$557$	−1.73942e6	−	3.01277e6i	−0.237557	−	0.411460i	0.722456	−	0.691417i	$-0.243013\pi$
$557$	−1.73942e6	−	3.01277e6i	−0.237557	−	0.411460i	−0.960013	+	0.279957i	$0.909680\pi$
$558$		0			0
$559$	−5.60658e6			−0.758872
$560$		0			0
$561$	−887561.			−0.119067
$562$		0			0
$563$	4.94660e6	+	8.56777e6i	0.657713	+	1.13919i	0.981206	+	0.192961i	$0.0618092\pi$
$563$	4.94660e6	+	8.56777e6i	0.657713	+	1.13919i	−0.323494	+	0.946230i	$0.604857\pi$
$564$		0			0
$565$	1.01922e6	−	1.76535e6i	0.134322	−	0.232653i
$566$		0			0
$567$	413581.	−	743261.i	0.0540260	−	0.0970921i
$568$		0			0
$569$	−5.94944e6	+	1.03047e7i	−0.770363	+	1.33431i	0.167001	+	0.985957i	$0.446592\pi$
$569$	−5.94944e6	+	1.03047e7i	−0.770363	+	1.33431i	−0.937364	+	0.348351i	$0.886742\pi$
$570$		0			0
$571$	−2.85004e6	−	4.93642e6i	−0.365815	−	0.633610i	0.623092	−	0.782149i	$-0.285876\pi$
$571$	−2.85004e6	−	4.93642e6i	−0.365815	−	0.633610i	−0.988907	+	0.148539i	$0.952543\pi$
$572$		0			0
$573$	−78996.3			−0.0100513
$574$		0			0
$575$	3.77889e6			0.476645
$576$		0			0
$577$	6.40787e6	+	1.10988e7i	0.801262	+	1.38783i	0.918786	+	0.394756i	$0.129171\pi$
$577$	6.40787e6	+	1.10988e7i	0.801262	+	1.38783i	−0.117524	+	0.993070i	$0.537496\pi$
$578$		0			0
$579$	2.63029e6	−	4.55580e6i	0.326068	−	0.564766i
$580$		0			0
$581$	486234.	+	812224.i	0.0597592	+	0.0998241i
$582$		0			0
$583$	−2.61997e6	+	4.53792e6i	−0.319245	+	0.552949i
$584$		0			0
$585$	−645420.	−	1.11790e6i	−0.0779745	−	0.135056i
$586$		0			0
$587$	−1.06067e7			−1.27053			−0.635267	−	0.772293i	$-0.719110\pi$
$587$	−1.06067e7			−1.27053			−0.635267	+	0.772293i	$0.719110\pi$
$588$		0			0
$589$	1.48749e7			1.76672
$590$		0			0
$591$	1.39574e6	+	2.41749e6i	0.164375	+	0.284706i
$592$		0			0
$593$	−1.03390e6	+	1.79076e6i	−0.120737	+	0.209123i	−0.920059	−	0.391781i	$-0.871859\pi$
$593$	−1.03390e6	+	1.79076e6i	−0.120737	+	0.209123i	0.799322	+	0.600904i	$0.205192\pi$
$594$		0			0
$595$	1.07556e6	+	1.79665e6i	0.124549	+	0.208052i
$596$		0			0
$597$	−367623.	+	636741.i	−0.0422150	+	0.0731184i
$598$		0			0
$599$	−3.35372e6	−	5.80881e6i	−0.381909	−	0.661485i	0.609426	−	0.792843i	$-0.291400\pi$
$599$	−3.35372e6	−	5.80881e6i	−0.381909	−	0.661485i	−0.991335	+	0.131357i	$0.958066\pi$
$600$		0			0
$601$	−762575.			−0.0861185			−0.0430592	−	0.999073i	$-0.513710\pi$
$601$	−762575.			−0.0861185			−0.0430592	+	0.999073i	$0.513710\pi$
$602$		0			0
$603$	3.77755e6			0.423074
$604$		0			0
$605$	−1.79754e6	−	3.11343e6i	−0.199659	−	0.345820i
$606$		0			0
$607$	−3.35168e6	+	5.80529e6i	−0.369225	+	0.639517i	−0.989445	−	0.144912i	$-0.953710\pi$
$607$	−3.35168e6	+	5.80529e6i	−0.369225	+	0.639517i	0.620219	+	0.784428i	$0.287044\pi$
$608$		0			0
$609$	−1.16880e6	+	2.10049e6i	−0.127702	+	0.229497i
$610$		0			0
$611$	−8.06477e6	+	1.39686e7i	−0.873954	+	1.51373i
$612$		0			0
$613$	3.64607e6	+	6.31518e6i	0.391899	+	0.678788i	0.992700	−	0.120610i	$-0.0384851\pi$
$613$	3.64607e6	+	6.31518e6i	0.391899	+	0.678788i	−0.600801	+	0.799398i	$0.705152\pi$
$614$		0			0
$615$	703305.			0.0749818
$616$		0			0
$617$	−3.70607e6			−0.391923			−0.195962	−	0.980612i	$-0.562783\pi$
$617$	−3.70607e6			−0.391923			−0.195962	+	0.980612i	$0.562783\pi$
$618$		0			0
$619$	−2.46700e6	−	4.27296e6i	−0.258787	−	0.448232i	0.707131	−	0.707083i	$-0.249989\pi$
$619$	−2.46700e6	−	4.27296e6i	−0.258787	−	0.448232i	−0.965917	+	0.258851i	$0.916656\pi$
$620$		0			0
$621$	571752.	−	990303.i	0.0594947	−	0.103048i
$622$		0			0
$623$	3.15695e6	−	49958.5i	0.325872	−	0.00515691i
$624$		0			0
$625$	−1.78328e6	+	3.08873e6i	−0.182608	+	0.316286i
$626$		0			0
$627$	1.82398e6	+	3.15923e6i	0.185290	+	0.320932i
$628$		0			0
$629$	356405.			0.0359185
$630$		0			0
$631$	−1.30887e7			−1.30865			−0.654326	−	0.756213i	$-0.727047\pi$
$631$	−1.30887e7			−1.30865			−0.654326	+	0.756213i	$0.727047\pi$
$632$		0			0
$633$	−3.15255e6	−	5.46037e6i	−0.312717	−	0.541642i
$634$		0			0
$635$	−4.42024e6	+	7.65609e6i	−0.435023	+	0.753482i
$636$		0			0
$637$	4.72837e6	−	8.82328e6i	0.461703	−	0.861552i
$638$		0			0
$639$	−1.70103e6	+	2.94627e6i	−0.164801	+	0.285444i
$640$		0			0
$641$	−9.27660e6	−	1.60675e7i	−0.891751	−	1.54456i	−0.837775	−	0.546016i	$-0.816144\pi$
$641$	−9.27660e6	−	1.60675e7i	−0.891751	−	1.54456i	−0.0539767	−	0.998542i	$-0.517190\pi$
$642$		0			0
$643$	−1.07346e7			−1.02390			−0.511949	−	0.859016i	$-0.671076\pi$
$643$	−1.07346e7			−1.02390			−0.511949	+	0.859016i	$0.671076\pi$
$644$		0			0
$645$	−2.26677e6			−0.214540
$646$		0			0
$647$	1.63282e6	+	2.82812e6i	0.153348	+	0.265606i	0.932456	−	0.361283i	$-0.117661\pi$
$647$	1.63282e6	+	2.82812e6i	0.153348	+	0.265606i	−0.779109	+	0.626889i	$0.784328\pi$
$648$		0			0
$649$	−845858.	+	1.46507e6i	−0.0788289	+	0.136536i
$650$		0			0
$651$	6.99413e6	−	110682.i	0.646817	−	0.0102358i
$652$		0			0
$653$	−1.41947e6	+	2.45859e6i	−0.130270	+	0.225633i	−0.923780	−	0.382923i	$-0.874918\pi$
$653$	−1.41947e6	+	2.45859e6i	−0.130270	+	0.225633i	0.793511	+	0.608556i	$0.208251\pi$
$654$		0			0
$655$	−3.11270e6	−	5.39136e6i	−0.283488	−	0.491015i
$656$		0			0
$657$	1.55258e6			0.140327
$658$		0			0
$659$	−1.20588e7			−1.08166			−0.540828	−	0.841133i	$-0.681889\pi$
$659$	−1.20588e7			−1.08166			−0.540828	+	0.841133i	$0.681889\pi$
$660$		0			0
$661$	2.99879e6	+	5.19405e6i	0.266957	+	0.462384i	0.968075	−	0.250662i	$-0.0806484\pi$
$661$	2.99879e6	+	5.19405e6i	0.266957	+	0.462384i	−0.701117	+	0.713046i	$0.747315\pi$
$662$		0			0
$663$	−1.61799e6	+	2.80244e6i	−0.142952	+	0.247601i
$664$		0			0
$665$	4.18477e6	−	7.52060e6i	0.366959	−	0.659475i
$666$		0			0
$667$	−1.61580e6	+	2.79864e6i	−0.140628	+	0.243575i
$668$		0			0
$669$	1.31538e6	+	2.27831e6i	0.113628	+	0.196810i
$670$		0			0
$671$	−1.69989e6			−0.145752
$672$		0			0
$673$	1.89426e7			1.61214			0.806069	−	0.591822i	$-0.201591\pi$
$673$	1.89426e7			1.61214			0.806069	+	0.591822i	$0.201591\pi$
$674$		0			0
$675$	878116.	+	1.52094e6i	0.0741810	+	0.128485i
$676$		0			0
$677$	−2.22818e6	+	3.85931e6i	−0.186843	+	0.323622i	−0.944196	−	0.329384i	$-0.893159\pi$
$677$	−2.22818e6	+	3.85931e6i	−0.186843	+	0.323622i	0.757353	+	0.653006i	$0.226492\pi$
$678$		0			0
$679$	6.17459e6	+	1.03143e7i	0.513965	+	0.858547i
$680$		0			0
$681$	3.73443e6	−	6.46823e6i	0.308572	−	0.534463i
$682$		0			0
$683$	2.21187e6	+	3.83106e6i	0.181429	+	0.314245i	0.942367	−	0.334580i	$-0.108594\pi$
$683$	2.21187e6	+	3.83106e6i	0.181429	+	0.314245i	−0.760938	+	0.648824i	$0.775261\pi$
$684$		0			0
$685$	−2.58808e6			−0.210742
$686$		0			0
$687$	7.89217e6			0.637976
$688$		0			0
$689$	9.55219e6	+	1.65449e7i	0.766575	+	1.32775i
$690$		0			0
$691$	−2.37228e6	+	4.10890e6i	−0.189004	+	0.327364i	−0.944918	−	0.327306i	$-0.893859\pi$
$691$	−2.37228e6	+	4.10890e6i	−0.189004	+	0.327364i	0.755915	+	0.654670i	$0.227192\pi$
$692$		0			0
$693$	881136.	+	1.47189e6i	0.0696963	+	0.116424i
$694$		0			0
$695$	−2.37582e6	+	4.11503e6i	−0.186574	+	0.323155i
$696$		0			0
$697$	−881549.	−	1.52689e6i	−0.0687329	−	0.119049i
$698$		0			0
$699$	−7.69660e6			−0.595807
$700$		0			0
$701$	−2.02431e7			−1.55590			−0.777952	−	0.628324i	$-0.783741\pi$
$701$	−2.02431e7			−1.55590			−0.777952	+	0.628324i	$0.783741\pi$
$702$		0			0
$703$	−732431.	−	1.26861e6i	−0.0558957	−	0.0968142i
$704$		0			0
$705$	−3.26062e6	+	5.64757e6i	−0.247075	+	0.427946i
$706$		0			0
$707$	1.11066e7	−	1.99601e7i	0.835668	−	1.50181i
$708$		0			0
$709$	−1.08834e7	+	1.88507e7i	−0.813112	+	1.40835i	0.0975645	+	0.995229i	$0.468895\pi$
$709$	−1.08834e7	+	1.88507e7i	−0.813112	+	1.40835i	−0.910676	+	0.413121i	$0.864439\pi$
$710$		0			0
$711$	2.88173e6	+	4.99130e6i	0.213786	+	0.370288i
$712$		0			0
$713$	9.40395e6			0.692766
$714$		0			0
$715$	2.60340e6			0.190448
$716$		0			0
$717$	274900.	+	476141.i	0.0199699	+	0.0345889i
$718$		0			0
$719$	−5.70313e6	+	9.87812e6i	−0.411426	+	0.712610i	−0.995046	−	0.0994167i	$-0.968302\pi$
$719$	−5.70313e6	+	9.87812e6i	−0.411426	+	0.712610i	0.583620	+	0.812027i	$0.301636\pi$
$720$		0			0
$721$	−4.09782e6	+	64847.7i	−0.293572	+	0.00464576i
$722$		0			0
$723$	−773198.	+	1.33922e6i	−0.0550104	+	0.0952808i
$724$		0			0
$725$	−2.48160e6	−	4.29826e6i	−0.175342	−	0.303702i
$726$		0			0
$727$	−635734.			−0.0446107			−0.0223054	−	0.999751i	$-0.507101\pi$
$727$	−635734.			−0.0446107			−0.0223054	+	0.999751i	$0.507101\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	2.84125e6	+	4.92119e6i	0.196660	+	0.340625i
$732$		0			0
$733$	−4.20000e6	+	7.27462e6i	−0.288729	+	0.500093i	−0.973507	−	0.228659i	$-0.926566\pi$
$733$	−4.20000e6	+	7.27462e6i	−0.288729	+	0.500093i	0.684778	+	0.728752i	$0.259899\pi$
$734$		0			0
$735$	1.91170e6	−	3.56729e6i	0.130528	−	0.243568i
$736$		0			0
$737$	−3.80933e6	+	6.59795e6i	−0.258333	+	0.447446i
$738$		0			0
$739$	2.90264e6	+	5.02752e6i	0.195516	+	0.338644i	0.947070	−	0.321028i	$-0.104029\pi$
$739$	2.90264e6	+	5.02752e6i	0.195516	+	0.338644i	−0.751554	+	0.659672i	$0.770695\pi$
$740$		0			0
$741$	1.33002e7			0.889840
$742$		0			0
$743$	1.80938e7			1.20242			0.601212	−	0.799090i	$-0.294685\pi$
$743$	1.80938e7			1.20242			0.601212	+	0.799090i	$0.294685\pi$
$744$		0			0
$745$	−637154.	−	1.10358e6i	−0.0420585	−	0.0728475i
$746$		0			0
$747$	−295730.	+	512220.i	−0.0193907	+	0.0335857i
$748$		0			0
$749$	−1.02588e7	+	162344.i	−0.668175	+	0.0105738i
$750$		0			0
$751$	1.45350e7	−	2.51753e7i	0.940404	−	1.62883i	0.175701	−	0.984444i	$-0.443781\pi$
$751$	1.45350e7	−	2.51753e7i	0.940404	−	1.62883i	0.764703	−	0.644383i	$-0.222886\pi$
$752$		0			0
$753$	−8.42460e6	−	1.45918e7i	−0.541454	−	0.937826i
$754$		0			0
$755$	−1.35039e7			−0.862166
$756$		0			0
$757$	2.75384e7			1.74662			0.873311	−	0.487163i	$-0.161968\pi$
$757$	2.75384e7			1.74662			0.873311	+	0.487163i	$0.161968\pi$
$758$		0			0
$759$	1.15312e6	+	1.99727e6i	0.0726560	+	0.125844i
$760$		0			0
$761$	−1.27683e7	+	2.21153e7i	−0.799229	+	1.38430i	0.120890	+	0.992666i	$0.461425\pi$
$761$	−1.27683e7	+	2.21153e7i	−0.799229	+	1.38430i	−0.920119	+	0.391639i	$0.871908\pi$
$762$		0			0
$763$	2.50148e6	−	4.49549e6i	0.155555	−	0.279554i
$764$		0			0
$765$	−654160.	+	1.13304e6i	−0.0404139	+	0.0699989i
$766$		0			0
$767$	3.08393e6	+	5.34152e6i	0.189285	+	0.327851i
$768$		0			0
$769$	−1.51037e7			−0.921015			−0.460507	−	0.887656i	$-0.652332\pi$
$769$	−1.51037e7			−0.921015			−0.460507	+	0.887656i	$0.652332\pi$
$770$		0			0
$771$	1.86321e7			1.12882
$772$		0			0
$773$	4.50268e6	+	7.79887e6i	0.271033	+	0.469443i	0.969127	−	0.246564i	$-0.0793014\pi$
$773$	4.50268e6	+	7.79887e6i	0.271033	+	0.469443i	−0.698094	+	0.716006i	$0.745968\pi$
$774$		0			0
$775$	−7.22146e6	+	1.25079e7i	−0.431888	+	0.748051i
$776$		0			0
$777$	−353826.	−	591044.i	−0.0210250	−	0.0351211i
$778$		0			0
$779$	−3.62325e6	+	6.27566e6i	−0.213922	+	0.370524i
$780$		0			0
$781$	−3.43069e6	−	5.94213e6i	−0.201258	−	0.348589i
$782$		0			0
$783$	−1.50188e6			−0.0875448
$784$		0			0
$785$	6.85918e6			0.397281
$786$		0			0
$787$	−1.17443e7	−	2.03417e7i	−0.675912	−	1.17071i	−0.976201	−	0.216866i	$-0.930417\pi$
$787$	−1.17443e7	−	2.03417e7i	−0.675912	−	1.17071i	0.300289	−	0.953848i	$-0.402917\pi$
$788$		0			0
$789$	−387628.	+	671392.i	−0.0221678	+	0.0383958i
$790$		0			0
$791$	5.07314e6	+	8.47437e6i	0.288294	+	0.481578i
$792$		0			0
$793$	−3.09883e6	+	5.36733e6i	−0.174991	+	0.303093i
$794$		0			0
$795$	3.86200e6	+	6.68917e6i	0.216718	+	0.375366i
$796$		0			0
$797$	−2.81831e7			−1.57160			−0.785802	−	0.618478i	$-0.787750\pi$
$797$	−2.81831e7			−1.57160			−0.785802	+	0.618478i	$0.787750\pi$
$798$		0			0
$799$	1.63480e7			0.905934
$800$		0			0
$801$	986351.	+	1.70841e6i	0.0543188	+	0.0940829i
$802$		0			0
$803$	−1.56564e6	+	2.71177e6i	−0.0856848	+	0.148410i
$804$		0			0
$805$	2.64562e6	−	4.75453e6i	0.143892	−	0.258594i
$806$		0			0
$807$	6.84369e6	−	1.18536e7i	0.369919	−	0.640718i
$808$		0			0
$809$	−6.66312e6	−	1.15409e7i	−0.357937	−	0.619965i	0.629679	−	0.776855i	$-0.283186\pi$
$809$	−6.66312e6	−	1.15409e7i	−0.357937	−	0.619965i	−0.987616	+	0.156890i	$0.949853\pi$
$810$		0			0
$811$	3.58038e7			1.91151			0.955757	−	0.294158i	$-0.0950391\pi$
$811$	3.58038e7			1.91151			0.955757	+	0.294158i	$0.0950391\pi$
$812$		0			0
$813$	1.43583e7			0.761862
$814$		0			0
$815$	383991.	+	665092.i	0.0202501	+	0.0350742i
$816$		0			0
$817$	1.16778e7	−	2.02266e7i	0.612078	−	1.06015i
$818$		0			0
$819$	6.25369e6	−	98964.3i	0.325781	−	0.00515547i
$820$		0			0
$821$	−1.26845e7	+	2.19702e7i	−0.656772	+	1.13756i	0.324674	+	0.945826i	$0.394745\pi$
$821$	−1.26845e7	+	2.19702e7i	−0.656772	+	1.13756i	−0.981446	+	0.191737i	$0.938588\pi$
$822$		0			0
$823$	−1.33837e7	−	2.31813e7i	−0.688774	−	1.19299i	−0.972235	−	0.234008i	$-0.924816\pi$
$823$	−1.33837e7	−	2.31813e7i	−0.688774	−	1.19299i	0.283461	−	0.958984i	$-0.408517\pi$
$824$		0			0
$825$	−3.54202e6			−0.181182
$826$		0			0
$827$	−3.81253e7			−1.93843			−0.969213	−	0.246224i	$-0.920810\pi$
$827$	−3.81253e7			−1.93843			−0.969213	+	0.246224i	$0.920810\pi$
$828$		0			0
$829$	1.06070e7	+	1.83719e7i	0.536051	+	0.928468i	0.999112	+	0.0421411i	$0.0134179\pi$
$829$	1.06070e7	+	1.83719e7i	0.536051	+	0.928468i	−0.463061	+	0.886327i	$0.653249\pi$
$830$		0			0
$831$	3.91569e6	−	6.78217e6i	0.196701	−	0.340695i
$832$		0			0
$833$	−1.01409e7	+	321037.i	−0.506363	+	0.0160304i
$834$		0			0
$835$	8.98628e6	−	1.55647e7i	0.446030	−	0.772546i
$836$		0			0
$837$	2.18524e6	+	3.78494e6i	0.107816	+	0.186743i
$838$		0			0
$839$	−6.95969e6			−0.341338			−0.170669	−	0.985328i	$-0.554593\pi$
$839$	−6.95969e6			−0.341338			−0.170669	+	0.985328i	$0.554593\pi$
$840$		0			0
$841$	−1.62668e7			−0.793070
$842$		0			0
$843$	−7.35114e6	−	1.27325e7i	−0.356275	−	0.617087i
$844$		0			0
$845$	−221332.	+	383358.i	−0.0106636	+	0.0184698i
$846$		0			0
$847$	1.74170e7	−	275622.i	0.834187	−	0.0132010i
$848$		0			0
$849$	2.52296e6	−	4.36989e6i	0.120127	−	0.208066i
$850$		0			0
$851$	−463044.	−	802016.i	−0.0219179	−	0.0379629i
$852$		0			0
$853$	−6.50813e6			−0.306255			−0.153128	−	0.988206i	$-0.548935\pi$
$853$	−6.50813e6			−0.306255			−0.153128	+	0.988206i	$0.548935\pi$
$854$		0			0
$855$	5.37732e6			0.251565
$856$		0			0
$857$	8.67971e6	+	1.50337e7i	0.403695	+	0.699220i	0.994169	−	0.107837i	$-0.0343924\pi$
$857$	8.67971e6	+	1.50337e7i	0.403695	+	0.699220i	−0.590474	+	0.807057i	$0.701059\pi$
$858$		0			0
$859$	−2.06441e7	+	3.57566e7i	−0.954580	+	1.65338i	−0.219255	+	0.975668i	$0.570363\pi$
$859$	−2.06441e7	+	3.57566e7i	−0.954580	+	1.65338i	−0.735325	+	0.677714i	$0.762971\pi$
$860$		0			0
$861$	−1.65694e6	+	2.97775e6i	−0.0761728	+	0.136893i
$862$		0			0
$863$	6.34758e6	−	1.09943e7i	0.290123	−	0.502507i	−0.683716	−	0.729748i	$-0.739637\pi$
$863$	6.34758e6	−	1.09943e7i	0.290123	−	0.502507i	0.973838	+	0.227241i	$0.0729706\pi$
$864$		0			0
$865$	−4.67347e6	−	8.09470e6i	−0.212373	−	0.367841i
$866$		0			0
$867$	−9.49892e6			−0.429167
$868$		0			0
$869$	−1.16239e7			−0.522158
$870$		0			0
$871$	1.38885e7	+	2.40556e7i	0.620311	+	1.07441i
$872$		0			0
$873$	−3.75542e6	+	6.50458e6i	−0.166772	+	0.288857i
$874$		0			0
$875$	9.86003e6	+	1.64706e7i	0.435369	+	0.727258i
$876$		0			0
$877$	9.51380e6	−	1.64784e7i	0.417691	−	0.723462i	−0.578016	−	0.816026i	$-0.696173\pi$
$877$	9.51380e6	−	1.64784e7i	0.417691	−	0.723462i	0.995707	+	0.0925634i	$0.0295061\pi$
$878$		0			0
$879$	−4.55451e6	−	7.88864e6i	−0.198824	−	0.344374i
$880$		0			0
$881$	3.60494e7			1.56480			0.782399	−	0.622778i	$-0.213996\pi$
$881$	3.60494e7			1.56480			0.782399	+	0.622778i	$0.213996\pi$
$882$		0			0
$883$	−1.13710e7			−0.490790			−0.245395	−	0.969423i	$-0.578918\pi$
$883$	−1.13710e7			−0.490790			−0.245395	+	0.969423i	$0.578918\pi$
$884$		0			0
$885$	1.24685e6	+	2.15960e6i	0.0535124	+	0.0926863i
$886$		0			0
$887$	1.56953e7	−	2.71850e7i	0.669823	−	1.16017i	−0.308131	−	0.951344i	$-0.599703\pi$
$887$	1.56953e7	−	2.71850e7i	0.669823	−	1.16017i	0.977953	−	0.208823i	$-0.0669633\pi$
$888$		0			0
$889$	−2.20016e7	−	3.67523e7i	−0.933683	−	1.55966i
$890$		0			0
$891$	−535912.	+	928227.i	−0.0226152	+	0.0391706i
$892$		0			0
$893$	−3.35959e7	−	5.81897e7i	−1.40980	−	2.44184i
$894$		0			0
$895$	−498787.			−0.0208141
$896$		0			0
$897$	8.40839e6			0.348925
$898$		0			0
$899$	−6.17558e6	−	1.06964e7i	−0.254846	−	0.441407i
$900$		0			0
$901$	9.68154e6	−	1.67689e7i	0.397313	−	0.688166i
$902$		0			0
$903$	5.34036e6	−	9.59735e6i	0.217947	−	0.391681i
$904$		0			0
$905$	−4.25371e6	+	7.36764e6i	−0.172642	+	0.299025i
$906$		0			0
$907$	−1.94598e7	−	3.37054e7i	−0.785454	−	1.36045i	−0.928727	−	0.370763i	$-0.879096\pi$
$907$	−1.94598e7	−	3.37054e7i	−0.785454	−	1.36045i	0.143273	−	0.989683i	$-0.454237\pi$
$908$		0			0
$909$	1.42717e7			0.572885
$910$		0			0
$911$	1.37630e7			0.549437			0.274719	−	0.961525i	$-0.411415\pi$
$911$	1.37630e7			0.549437			0.274719	+	0.961525i	$0.411415\pi$
$912$		0			0
$913$	−596437.	−	1.03306e6i	−0.0236803	−	0.0410155i
$914$		0			0
$915$	−1.25287e6	+	2.17004e6i	−0.0494714	+	0.0856869i
$916$		0			0
$917$	3.01600e7	−	477280.i	1.18443	−	0.0187435i
$918$		0			0
$919$	2.06989e7	−	3.58515e7i	0.808460	−	1.40029i	−0.105470	−	0.994422i	$-0.533635\pi$
$919$	2.06989e7	−	3.58515e7i	0.808460	−	1.40029i	0.913930	−	0.405871i	$-0.133032\pi$
$920$		0			0
$921$	−1.23618e7	−	2.14112e7i	−0.480210	−	0.831749i
$922$		0			0
$923$	−2.50160e7			−0.966526
$924$		0			0
$925$	1.42232e6			0.0546566
$926$		0			0
$927$	−1.28031e6	−	2.21757e6i	−0.0489348	−	0.0847575i
$928$		0			0
$929$	−1.29015e6	+	2.23460e6i	−0.0490456	+	0.0849494i	−0.889506	−	0.456924i	$-0.848951\pi$
$929$	−1.29015e6	+	2.23460e6i	−0.0490456	+	0.0849494i	0.840460	+	0.541873i	$0.182285\pi$
$930$		0			0
$931$	2.19827e7	+	3.54361e7i	0.831202	+	1.33990i
$932$		0			0
$933$	1.40957e6	−	2.44145e6i	0.0530131	−	0.0918213i
$934$		0			0
$935$	−1.31933e6	−	2.28514e6i	−0.0493541	−	0.0854839i
$936$		0			0
$937$	1.18054e7			0.439269			0.219634	−	0.975582i	$-0.429514\pi$
$937$	1.18054e7			0.439269			0.219634	+	0.975582i	$0.429514\pi$
$938$		0			0
$939$	−1.11207e6			−0.0411593
$940$		0			0
$941$	−1.61777e7	−	2.80206e7i	−0.595583	−	1.03158i	−0.993464	−	0.114143i	$-0.963588\pi$
$941$	−1.61777e7	−	2.80206e7i	−0.595583	−	1.03158i	0.397881	−	0.917437i	$-0.369746\pi$
$942$		0			0
$943$	−2.29063e6	+	3.96748e6i	−0.0838832	+	0.145290i
$944$		0			0
$945$	2.52840e6	−	40011.7i	0.0921013	−	0.00145750i
$946$		0			0
$947$	−415142.	+	719047.i	−0.0150426	+	0.0260545i	−0.873449	−	0.486916i	$-0.838122\pi$
$947$	−415142.	+	719047.i	−0.0150426	+	0.0260545i	0.858406	+	0.512971i	$0.171455\pi$
$948$		0			0
$949$	5.70820e6	+	9.88690e6i	0.205747	+	0.356365i
$950$		0			0
$951$	−2.24942e7			−0.806526
$952$		0			0
$953$	5.26012e7			1.87613			0.938066	−	0.346457i	$-0.112615\pi$
$953$	5.26012e7			1.87613			0.938066	+	0.346457i	$0.112615\pi$
$954$		0			0
$955$	−117425.	−	203386.i	−0.00416632	−	0.00721628i
$956$		0			0
$957$	1.51451e6	−	2.62322e6i	0.0534556	−	0.0925879i
$958$		0			0
$959$	6.09737e6	−	1.09578e7i	0.214090	−	0.384748i
$960$		0			0
$961$	−3.65639e6	+	6.33305e6i	−0.127715	+	0.221210i
$962$		0			0
$963$	−3.20523e6	−	5.55162e6i	−0.111376	−	0.192910i
$964$		0			0
$965$	1.56393e7			0.540630
$966$		0			0
$967$	2.79449e7			0.961029			0.480514	−	0.876987i	$-0.340450\pi$
$967$	2.79449e7			0.961029			0.480514	+	0.876987i	$0.340450\pi$
$968$		0			0
$969$	−6.74014e6	−	1.16743e7i	−0.230600	−	0.399411i
$970$		0			0
$971$	−1.66081e7	+	2.87661e7i	−0.565291	+	0.979113i	0.431731	+	0.902002i	$0.357903\pi$
$971$	−1.66081e7	+	2.87661e7i	−0.565291	+	0.979113i	−0.997023	+	0.0771108i	$0.975430\pi$
$972$		0			0
$973$	−1.18255e7	−	1.97538e7i	−0.400441	−	0.668912i
$974$		0			0
$975$	−6.45695e6	+	1.11838e7i	−0.217528	+	0.376770i
$976$		0			0
$977$	1.04933e7	+	1.81750e7i	0.351704	+	0.609169i	0.986548	−	0.163471i	$-0.0522691\pi$
$977$	1.04933e7	+	1.81750e7i	0.351704	+	0.609169i	−0.634844	+	0.772640i	$0.718936\pi$
$978$		0			0
$979$	−3.97860e6			−0.132670
$980$		0			0
$981$	3.21433e6			0.106640
$982$		0			0
$983$	−1.70372e7	−	2.95092e7i	−0.562359	−	0.974034i	−0.997290	−	0.0735703i	$-0.976561\pi$
$983$	−1.70372e7	−	2.95092e7i	−0.562359	−	0.974034i	0.434931	−	0.900464i	$-0.356773\pi$
$984$		0			0
$985$	−4.14944e6	+	7.18704e6i	−0.136269	+	0.236026i
$986$		0			0
$987$	−1.62296e7	−	2.71106e7i	−0.530292	−	0.885821i
$988$		0			0
$989$	7.38274e6	−	1.27873e7i	0.240009	−	0.415707i
$990$		0			0
$991$	5.42227e6	+	9.39165e6i	0.175387	+	0.303779i	0.940295	−	0.340360i	$-0.110549\pi$
$991$	5.42227e6	+	9.39165e6i	0.175387	+	0.303779i	−0.764908	+	0.644139i	$0.777216\pi$
$992$		0			0
$993$	2.50108e7			0.804922
$994$		0			0
$995$	−2.18583e6			−0.0699937
$996$		0			0
$997$	6.78414e6	+	1.17505e7i	0.216151	+	0.374384i	0.953628	−	0.300988i	$-0.0973163\pi$
$997$	6.78414e6	+	1.17505e7i	0.216151	+	0.374384i	−0.737477	+	0.675372i	$0.763983\pi$
$998$		0			0
$999$	215199.	−	372735.i	0.00682223	−	0.0118164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.6.q.l.289.4		10
4.3	odd	2		168.6.q.c.121.4	yes	10
7.4	even	3	inner	336.6.q.l.193.4		10
12.11	even	2		504.6.s.c.289.2		10
28.11	odd	6		168.6.q.c.25.4	✓	10
84.11	even	6		504.6.s.c.361.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.6.q.c.25.4	✓	10	28.11	odd	6
168.6.q.c.121.4	yes	10	4.3	odd	2
336.6.q.l.193.4		10	7.4	even	3	inner
336.6.q.l.289.4		10	1.1	even	1	trivial
504.6.s.c.289.2		10	12.11	even	2
504.6.s.c.361.2		10	84.11	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	336.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.50000 - 7.79423i) q^{3} +(13.3782 - 23.1717i) q^{5} +(66.5893 + 111.233i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-4.50000 - 7.79423i) q^{3} +(13.3782 - 23.1717i) q^{5} +(66.5893 + 111.233i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-81.6815 - 141.477i) q^{11} -595.608 q^{13} -240.807 q^{15} +(301.837 + 522.796i) q^{17} +(1240.58 - 2148.75i) q^{19} +(567.327 - 1019.56i) q^{21} +(784.296 - 1358.44i) q^{23} +(1204.55 + 2086.34i) q^{25} +729.000 q^{27} -2060.19 q^{29} +(2997.58 + 5191.96i) q^{31} +(-735.134 + 1273.29i) q^{33} +(3468.31 - 54.8858i) q^{35} +(295.197 - 511.297i) q^{37} +(2680.24 + 4642.30i) q^{39} -2920.62 q^{41} +9413.21 q^{43} +(1083.63 + 1876.91i) q^{45} +(13540.4 - 23452.7i) q^{47} +(-7938.73 + 14813.9i) q^{49} +(2716.53 - 4705.17i) q^{51} +(-16037.7 - 27778.1i) q^{53} -4371.00 q^{55} -22330.4 q^{57} +(-5177.78 - 8968.18i) q^{59} +(5202.80 - 9011.52i) q^{61} +(-10499.7 + 166.157i) q^{63} +(-7968.15 + 13801.2i) q^{65} +(-23318.2 - 40388.3i) q^{67} -14117.3 q^{69} +42000.8 q^{71} +(-9583.83 - 16599.7i) q^{73} +(10840.9 - 18777.1i) q^{75} +(10297.8 - 18506.5i) q^{77} +(35576.9 - 61621.0i) q^{79} +(-3280.50 - 5681.99i) q^{81} +7301.98 q^{83} +16152.1 q^{85} +(9270.85 + 16057.6i) q^{87} +(12177.2 - 21091.5i) q^{89} +(-39661.1 - 66251.5i) q^{91} +(26978.2 - 46727.6i) q^{93} +(-33193.4 - 57492.6i) q^{95} +92726.4 q^{97} +13232.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9}+O(q^{10}) \) 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9	\( 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9} - 424 q^{11} + 374 q^{13} + 108 q^{15} - 952 q^{17} - 139 q^{19} - 1044 q^{21} - 4288 q^{23} - 5605 q^{25} + 7290 q^{27} - 4216 q^{29} - 8131 q^{31} - 3816 q^{33} - 20106 q^{35} - 5425 q^{37} - 1683 q^{39} + 29364 q^{41} + 46862 q^{43} - 486 q^{45} + 17190 q^{47} + 23255 q^{49} - 8568 q^{51} + 15064 q^{53} + 1176 q^{55} + 2502 q^{57} + 83242 q^{59} + 14954 q^{61} + 1539 q^{63} - 23250 q^{65} - 39501 q^{67} + 77184 q^{69} + 56020 q^{71} - 90395 q^{73} - 50445 q^{75} + 63448 q^{77} + 43067 q^{79} - 32805 q^{81} + 75672 q^{83} - 75272 q^{85} + 18972 q^{87} - 72608 q^{89} - 288287 q^{91} - 73179 q^{93} - 190138 q^{95} + 183000 q^{97} + 68688 q^{99}+O(q^{100}) \) 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9 - 424 * q^11 + 374 * q^13 + 108 * q^15 - 952 * q^17 - 139 * q^19 - 1044 * q^21 - 4288 * q^23 - 5605 * q^25 + 7290 * q^27 - 4216 * q^29 - 8131 * q^31 - 3816 * q^33 - 20106 * q^35 - 5425 * q^37 - 1683 * q^39 + 29364 * q^41 + 46862 * q^43 - 486 * q^45 + 17190 * q^47 + 23255 * q^49 - 8568 * q^51 + 15064 * q^53 + 1176 * q^55 + 2502 * q^57 + 83242 * q^59 + 14954 * q^61 + 1539 * q^63 - 23250 * q^65 - 39501 * q^67 + 77184 * q^69 + 56020 * q^71 - 90395 * q^73 - 50445 * q^75 + 63448 * q^77 + 43067 * q^79 - 32805 * q^81 + 75672 * q^83 - 75272 * q^85 + 18972 * q^87 - 72608 * q^89 - 288287 * q^91 - 73179 * q^93 - 190138 * q^95 + 183000 * q^97 + 68688 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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