LMFDB - Embedded newform 304.4.i.c.273.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,4,Mod(49,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("304.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	304.i (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:	$17.9365806417$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{55})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 55x^{2} + 3025 $ x^4 + 55*x^2 + 3025
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			273.2
Root			$3.70810 + 6.42262i$ of defining polynomial
Character	$\chi$	$=$	304.273
Dual form			304.4.i.c.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.70810 + 6.42262i) q^{3} +(7.20810 + 12.4848i) q^{5} -0.416198 q^{7} +(-14.0000 + 24.2487i) q^{9} +O(q^{10})$	\(q+(3.70810 + 6.42262i) q^{3} +(7.20810 + 12.4848i) q^{5} -0.416198 q^{7} +(-14.0000 + 24.2487i) q^{9} -65.9134 q^{11} +(-22.6648 + 39.2566i) q^{13} +(-53.4567 + 92.5897i) q^{15} +(-1.66479 - 2.88351i) q^{17} +(82.3729 + 8.58525i) q^{19} +(-1.54331 - 2.67308i) q^{21} +(54.4567 - 94.3218i) q^{23} +(-41.4134 + 71.7301i) q^{25} -7.41620 q^{27} +(-29.5433 + 51.1705i) q^{29} -184.913 q^{31} +(-244.413 - 423.336i) q^{33} +(-3.00000 - 5.19615i) q^{35} +142.913 q^{37} -336.173 q^{39} +(87.5754 + 151.685i) q^{41} +(222.740 + 385.797i) q^{43} -403.654 q^{45} +(87.1215 - 150.899i) q^{47} -342.827 q^{49} +(12.3464 - 21.3847i) q^{51} +(117.173 - 202.950i) q^{53} +(-475.110 - 822.915i) q^{55} +(250.307 + 560.884i) q^{57} +(76.2053 + 131.991i) q^{59} +(-28.9651 + 50.1691i) q^{61} +(5.82678 - 10.0923i) q^{63} -653.480 q^{65} +(-418.610 + 725.054i) q^{67} +807.723 q^{69} +(263.740 + 456.811i) q^{71} +(-109.749 - 190.090i) q^{73} -614.260 q^{75} +27.4331 q^{77} +(-245.654 - 425.484i) q^{79} +(350.500 + 607.084i) q^{81} +692.433 q^{83} +(24.0000 - 41.5692i) q^{85} -438.198 q^{87} +(-413.642 + 716.450i) q^{89} +(9.43305 - 16.3385i) q^{91} +(-685.677 - 1187.63i) q^{93} +(486.567 + 1090.29i) q^{95} +(366.402 + 634.627i) q^{97} +(922.787 - 1598.31i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 14 q^{5} + 28 q^{7} - 56 q^{9}+O(q^{10}) $ 4 * q + 14 * q^5 + 28 * q^7 - 56 * q^9	$ 4 q + 14 q^{5} + 28 q^{7} - 56 q^{9} - 56 q^{11} + 28 q^{13} - 110 q^{15} + 112 q^{17} + 196 q^{19} - 110 q^{21} + 114 q^{23} + 42 q^{25} - 222 q^{29} - 532 q^{31} - 770 q^{33} - 12 q^{35} + 364 q^{37} - 1760 q^{39} - 154 q^{41} + 268 q^{43} - 784 q^{45} + 126 q^{47} - 956 q^{49} + 880 q^{51} + 884 q^{53} - 966 q^{55} - 660 q^{57} + 112 q^{59} - 546 q^{61} - 392 q^{63} - 1368 q^{65} - 740 q^{67} + 1540 q^{69} + 432 q^{71} - 350 q^{73} - 3080 q^{75} + 1148 q^{77} - 152 q^{79} + 1402 q^{81} + 3808 q^{83} + 96 q^{85} + 1540 q^{87} - 112 q^{89} + 1076 q^{91} - 770 q^{93} + 908 q^{95} + 546 q^{97} + 784 q^{99}+O(q^{100}) $ 4 * q + 14 * q^5 + 28 * q^7 - 56 * q^9 - 56 * q^11 + 28 * q^13 - 110 * q^15 + 112 * q^17 + 196 * q^19 - 110 * q^21 + 114 * q^23 + 42 * q^25 - 222 * q^29 - 532 * q^31 - 770 * q^33 - 12 * q^35 + 364 * q^37 - 1760 * q^39 - 154 * q^41 + 268 * q^43 - 784 * q^45 + 126 * q^47 - 956 * q^49 + 880 * q^51 + 884 * q^53 - 966 * q^55 - 660 * q^57 + 112 * q^59 - 546 * q^61 - 392 * q^63 - 1368 * q^65 - 740 * q^67 + 1540 * q^69 + 432 * q^71 - 350 * q^73 - 3080 * q^75 + 1148 * q^77 - 152 * q^79 + 1402 * q^81 + 3808 * q^83 + 96 * q^85 + 1540 * q^87 - 112 * q^89 + 1076 * q^91 - 770 * q^93 + 908 * q^95 + 546 * q^97 + 784 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	3.70810	+	6.42262i	0.713624	+	1.23603i	0.963488	+	0.267752i	$0.0862808\pi$
$3$	3.70810	+	6.42262i	0.713624	+	1.23603i	−0.249864	+	0.968281i	$0.580386\pi$
$4$		0			0
$5$	7.20810	+	12.4848i	0.644712	+	1.11667i	0.984368	+	0.176124i	$0.0563560\pi$
$5$	7.20810	+	12.4848i	0.644712	+	1.11667i	−0.339656	+	0.940550i	$0.610311\pi$
$6$		0			0
$7$	−0.416198			−0.0224726			−0.0112363	−	0.999937i	$-0.503577\pi$
$7$	−0.416198			−0.0224726			−0.0112363	+	0.999937i	$0.503577\pi$
$8$		0			0
$9$	−14.0000	+	24.2487i	−0.518519	+	0.898100i
$10$		0			0
$11$	−65.9134			−1.80669			−0.903347	−	0.428910i	$-0.858898\pi$
$11$	−65.9134			−1.80669			−0.903347	+	0.428910i	$0.858898\pi$
$12$		0			0
$13$	−22.6648	+	39.2566i	−0.483545	+	0.837524i	−0.999821	−	0.0188977i	$-0.993984\pi$
$13$	−22.6648	+	39.2566i	−0.483545	+	0.837524i	0.516277	+	0.856422i	$0.327318\pi$
$14$		0			0
$15$	−53.4567	+	92.5897i	−0.920164	+	1.59377i
$16$		0			0
$17$	−1.66479	−	2.88351i	−0.0237513	−	0.0411384i	0.853905	−	0.520428i	$-0.174228\pi$
$17$	−1.66479	−	2.88351i	−0.0237513	−	0.0411384i	−0.877657	+	0.479290i	$0.840894\pi$
$18$		0			0
$19$	82.3729	+	8.58525i	0.994613	+	0.103663i
$19$	82.3729	+	8.58525i	0.994613	+	0.103663i
$20$		0			0
$21$	−1.54331	−	2.67308i	−0.0160370	−	0.0277769i
$22$		0			0
$23$	54.4567	−	94.3218i	0.493696	−	0.855106i	−0.506278	−	0.862370i	$-0.668979\pi$
$23$	54.4567	−	94.3218i	0.493696	−	0.855106i	0.999974	+	0.00726411i	$0.00231226\pi$
$24$		0			0
$25$	−41.4134	+	71.7301i	−0.331307	+	0.573841i
$26$		0			0
$27$	−7.41620			−0.0528610
$28$		0			0
$29$	−29.5433	+	51.1705i	−0.189174	+	0.327659i	−0.944975	−	0.327142i	$-0.893914\pi$
$29$	−29.5433	+	51.1705i	−0.189174	+	0.327659i	0.755801	+	0.654801i	$0.227248\pi$
$30$		0			0
$31$	−184.913			−1.07134			−0.535668	−	0.844429i	$-0.679940\pi$
$31$	−184.913			−1.07134			−0.535668	+	0.844429i	$0.679940\pi$
$32$		0			0
$33$	−244.413	−	423.336i	−1.28930	−	2.23313i
$34$		0			0
$35$	−3.00000	−	5.19615i	−0.0144884	−	0.0250946i
$36$		0			0
$37$	142.913			0.634995			0.317498	−	0.948259i	$-0.397157\pi$
$37$	142.913			0.634995			0.317498	+	0.948259i	$0.397157\pi$
$38$		0			0
$39$	−336.173			−1.38028
$40$		0			0
$41$	87.5754	+	151.685i	0.333585	+	0.577786i	0.983212	−	0.182467i	$-0.0584083\pi$
$41$	87.5754	+	151.685i	0.333585	+	0.577786i	−0.649627	+	0.760253i	$0.725075\pi$
$42$		0			0
$43$	222.740	+	385.797i	0.789943	+	1.36822i	0.926001	+	0.377521i	$0.123223\pi$
$43$	222.740	+	385.797i	0.789943	+	1.36822i	−0.136058	+	0.990701i	$0.543443\pi$
$44$		0			0
$45$	−403.654			−1.33718
$46$		0			0
$47$	87.1215	−	150.899i	0.270382	−	0.468316i	−0.698577	−	0.715535i	$-0.746183\pi$
$47$	87.1215	−	150.899i	0.270382	−	0.468316i	0.968960	+	0.247218i	$0.0795165\pi$
$48$		0			0
$49$	−342.827			−0.999495
$50$		0			0
$51$	12.3464	−	21.3847i	0.0338990	−	0.0587147i
$52$		0			0
$53$	117.173	−	202.950i	0.303679	−	0.525987i	−0.673287	−	0.739381i	$-0.735118\pi$
$53$	117.173	−	202.950i	0.303679	−	0.525987i	0.976966	+	0.213394i	$0.0684517\pi$
$54$		0			0
$55$	−475.110	−	822.915i	−1.16480	−	2.01749i
$56$		0			0
$57$	250.307	+	560.884i	0.581649	+	1.30335i
$58$		0			0
$59$	76.2053	+	131.991i	0.168154	+	0.291251i	0.937771	−	0.347255i	$-0.112886\pi$
$59$	76.2053	+	131.991i	0.168154	+	0.291251i	−0.769617	+	0.638506i	$0.779553\pi$
$60$		0			0
$61$	−28.9651	+	50.1691i	−0.0607968	+	0.105303i	−0.894822	−	0.446424i	$-0.852697\pi$
$61$	−28.9651	+	50.1691i	−0.0607968	+	0.105303i	0.834025	+	0.551727i	$0.186031\pi$
$62$		0			0
$63$	5.82678	−	10.0923i	0.0116525	−	0.0201827i
$64$		0			0
$65$	−653.480			−1.24699
$66$		0			0
$67$	−418.610	+	725.054i	−0.763304	+	1.32208i	0.177834	+	0.984060i	$0.443091\pi$
$67$	−418.610	+	725.054i	−0.763304	+	1.32208i	−0.941138	+	0.338021i	$0.890242\pi$
$68$		0			0
$69$	807.723			1.40925
$70$		0			0
$71$	263.740	+	456.811i	0.440848	+	0.763571i	0.997753	−	0.0670055i	$-0.0213445\pi$
$71$	263.740	+	456.811i	0.440848	+	0.763571i	−0.556905	+	0.830576i	$0.688011\pi$
$72$		0			0
$73$	−109.749	−	190.090i	−0.175960	−	0.304772i	0.764533	−	0.644585i	$-0.222970\pi$
$73$	−109.749	−	190.090i	−0.175960	−	0.304772i	−0.940493	+	0.339813i	$0.889636\pi$
$74$		0			0
$75$	−614.260			−0.945715
$76$		0			0
$77$	27.4331			0.0406011
$78$		0			0
$79$	−245.654	−	425.484i	−0.349850	−	0.605959i	0.636372	−	0.771382i	$-0.280434\pi$
$79$	−245.654	−	425.484i	−0.349850	−	0.605959i	−0.986223	+	0.165423i	$0.947101\pi$
$80$		0			0
$81$	350.500	+	607.084i	0.480796	+	0.832762i
$82$		0			0
$83$	692.433			0.915716			0.457858	−	0.889025i	$-0.348617\pi$
$83$	692.433			0.915716			0.457858	+	0.889025i	$0.348617\pi$
$84$		0			0
$85$	24.0000	−	41.5692i	0.0306255	−	0.0530449i
$86$		0			0
$87$	−438.198			−0.539997
$88$		0			0
$89$	−413.642	+	716.450i	−0.492652	+	0.853298i	−0.999964	−	0.00846444i	$-0.997306\pi$
$89$	−413.642	+	716.450i	−0.492652	+	0.853298i	0.507313	+	0.861762i	$0.330639\pi$
$90$		0			0
$91$	9.43305	−	16.3385i	0.0108665	−	0.0188214i
$92$		0			0
$93$	−685.677	−	1187.63i	−0.764531	−	1.32421i
$94$		0			0
$95$	486.567	+	1090.29i	0.525481	+	1.17749i
$96$		0			0
$97$	366.402	+	634.627i	0.383531	+	0.664295i	0.991564	−	0.129616i	$-0.0413746\pi$
$97$	366.402	+	634.627i	0.383531	+	0.664295i	−0.608033	+	0.793912i	$0.708041\pi$
$98$		0			0
$99$	922.787	−	1598.31i	0.936804	−	1.62259i
$100$		0			0
$101$	−114.099	+	197.625i	−0.112409	+	0.194698i	−0.916741	−	0.399482i	$-0.869190\pi$
$101$	−114.099	+	197.625i	−0.112409	+	0.194698i	0.804332	+	0.594180i	$0.202523\pi$
$102$		0			0
$103$	−775.827			−0.742179			−0.371090	−	0.928597i	$-0.621016\pi$
$103$	−775.827			−0.742179			−0.371090	+	0.928597i	$0.621016\pi$
$104$		0			0
$105$	22.2486	−	38.5357i	0.0206785	−	0.0358162i
$106$		0			0
$107$	589.134			0.532278			0.266139	−	0.963935i	$-0.414252\pi$
$107$	589.134			0.532278			0.266139	+	0.963935i	$0.414252\pi$
$108$		0			0
$109$	−789.134	−	1366.82i	−0.693443	−	1.20108i	−0.970703	−	0.240284i	$-0.922759\pi$
$109$	−789.134	−	1366.82i	−0.693443	−	1.20108i	0.277259	−	0.960795i	$-0.410574\pi$
$110$		0			0
$111$	529.937	+	917.878i	0.453148	+	0.784875i
$112$		0			0
$113$	1129.27			0.940111			0.470056	−	0.882637i	$-0.344234\pi$
$113$	1129.27			0.940111			0.470056	+	0.882637i	$0.344234\pi$
$114$		0			0
$115$	1570.12			1.27317
$116$		0			0
$117$	−634.614	−	1099.18i	−0.501454	−	0.868544i
$118$		0			0
$119$	0.692885	+	1.20011i	0.000533753	+	0.000924488i
$120$		0			0
$121$	3013.57			2.26414
$122$		0			0
$123$	−649.476	+	1124.93i	−0.476108	+	0.824644i
$124$		0			0
$125$	607.978			0.435033
$126$		0			0
$127$	163.221	−	282.706i	0.114043	−	0.197528i	−0.803354	−	0.595502i	$-0.796953\pi$
$127$	163.221	−	282.706i	0.114043	−	0.197528i	0.917397	+	0.397974i	$0.130286\pi$
$128$		0			0
$129$	−1651.89	+	2861.15i	−1.12744	+	1.95279i
$130$		0			0
$131$	125.812	+	217.912i	0.0839100	+	0.145336i	0.904926	−	0.425568i	$-0.139926\pi$
$131$	125.812	+	217.912i	0.0839100	+	0.145336i	−0.821016	+	0.570905i	$0.806593\pi$
$132$		0			0
$133$	−34.2835	−	3.57317i	−0.0223515	−	0.00232957i
$134$		0			0
$135$	−53.4567	−	92.5897i	−0.0340801	−	0.0590285i
$136$		0			0
$137$	983.941	−	1704.24i	0.613604	−	1.06279i	−0.377024	−	0.926204i	$-0.623052\pi$
$137$	983.941	−	1704.24i	0.613604	−	1.06279i	0.990628	−	0.136590i	$-0.0436142\pi$
$138$		0			0
$139$	−466.236	+	807.544i	−0.284501	+	0.492770i	−0.972488	−	0.232953i	$-0.925161\pi$
$139$	−466.236	+	807.544i	−0.284501	+	0.492770i	0.687987	+	0.725723i	$0.258494\pi$
$140$		0			0
$141$	1292.22			0.771806
$142$		0			0
$143$	1493.91	−	2587.53i	0.873618	−	1.51315i
$144$		0			0
$145$	−851.804			−0.487852
$146$		0			0
$147$	−1271.24	−	2201.84i	−0.713264	−	1.23541i
$148$		0			0
$149$	232.370	+	402.477i	0.127762	+	0.221290i	0.922809	−	0.385258i	$-0.125887\pi$
$149$	232.370	+	402.477i	0.127762	+	0.221290i	−0.795047	+	0.606547i	$0.792554\pi$
$150$		0			0
$151$	1917.35			1.03333			0.516663	−	0.856189i	$-0.327174\pi$
$151$	1917.35			1.03333			0.516663	+	0.856189i	$0.327174\pi$
$152$		0			0
$153$	93.2285			0.0492619
$154$		0			0
$155$	−1332.87	−	2308.61i	−0.690703	−	1.19633i
$156$		0			0
$157$	−320.106	−	554.440i	−0.162721	−	0.281841i	0.773123	−	0.634257i	$-0.218694\pi$
$157$	−320.106	−	554.440i	−0.162721	−	0.281841i	−0.935844	+	0.352415i	$0.885360\pi$
$158$		0			0
$159$	1737.96			0.866850
$160$		0			0
$161$	−22.6648	+	39.2566i	−0.0110946	+	0.0192165i
$162$		0			0
$163$	708.969			0.340679			0.170340	−	0.985385i	$-0.445514\pi$
$163$	708.969			0.340679			0.170340	+	0.985385i	$0.445514\pi$
$164$		0			0
$165$	3523.51	−	6102.90i	1.66245	−	2.87946i
$166$		0			0
$167$	712.335	−	1233.80i	0.330073	−	0.571703i	−0.652453	−	0.757829i	$-0.726260\pi$
$167$	712.335	−	1233.80i	0.330073	−	0.571703i	0.982526	+	0.186126i	$0.0595934\pi$
$168$		0			0
$169$	71.1142	+	123.173i	0.0323688	+	0.0560644i
$170$		0			0
$171$	−1361.40	+	1877.24i	−0.608824	+	0.839511i
$172$		0			0
$173$	85.7041	+	148.444i	0.0376645	+	0.0652369i	0.884243	−	0.467027i	$-0.154675\pi$
$173$	85.7041	+	148.444i	0.0376645	+	0.0652369i	−0.846579	+	0.532264i	$0.821342\pi$
$174$		0			0
$175$	17.2362	−	29.8540i	0.00744533	−	0.0128957i
$176$		0			0
$177$	−565.154	+	978.875i	−0.239997	+	0.415688i
$178$		0			0
$179$	−440.433			−0.183908			−0.0919539	−	0.995763i	$-0.529311\pi$
$179$	−440.433			−0.183908			−0.0919539	+	0.995763i	$0.529311\pi$
$180$		0			0
$181$	225.004	−	389.719i	0.0924003	−	0.160042i	−0.816120	−	0.577882i	$-0.803879\pi$
$181$	225.004	−	389.719i	0.0924003	−	0.160042i	0.908521	+	0.417840i	$0.137213\pi$
$182$		0			0
$183$	−429.622			−0.173544
$184$		0			0
$185$	1030.13	+	1784.24i	0.409389	+	0.709082i
$186$		0			0
$187$	109.732	+	190.062i	0.0429113	+	0.0743246i
$188$		0			0
$189$	3.08661			0.00118793
$190$		0			0
$191$	2890.96			1.09520			0.547598	−	0.836741i	$-0.315542\pi$
$191$	2890.96			1.09520			0.547598	+	0.836741i	$0.315542\pi$
$192$		0			0
$193$	1785.48	+	3092.54i	0.665915	+	1.15340i	0.979036	+	0.203686i	$0.0652922\pi$
$193$	1785.48	+	3092.54i	0.665915	+	1.15340i	−0.313121	+	0.949713i	$0.601374\pi$
$194$		0			0
$195$	−2423.17	−	4197.05i	−0.889881	−	1.54132i
$196$		0			0
$197$	2644.14			0.956281			0.478140	−	0.878283i	$-0.341311\pi$
$197$	2644.14			0.956281			0.478140	+	0.878283i	$0.341311\pi$
$198$		0			0
$199$	−2181.50	+	3778.47i	−0.777097	+	1.34597i	0.156511	+	0.987676i	$0.449975\pi$
$199$	−2181.50	+	3778.47i	−0.777097	+	1.34597i	−0.933608	+	0.358296i	$0.883358\pi$
$200$		0			0
$201$	−6208.99			−2.17885
$202$		0			0
$203$	12.2959	−	21.2971i	0.00425124	−	0.00736336i
$204$		0			0
$205$	−1262.50	+	2186.72i	−0.430132	+	0.745011i
$206$		0			0
$207$	1524.79	+	2641.01i	0.511981	+	0.886777i
$208$		0			0
$209$	−5429.48	−	565.883i	−1.79696	−	0.187287i
$210$		0			0
$211$	1285.49	+	2226.53i	0.419415	+	0.726449i	0.995881	−	0.0906727i	$-0.0289017\pi$
$211$	1285.49	+	2226.53i	0.419415	+	0.726449i	−0.576465	+	0.817122i	$0.695568\pi$
$212$		0			0
$213$	−1955.95	+	3387.80i	−0.629199	+	1.08981i
$214$		0			0
$215$	−3211.07	+	5561.73i	−1.01857	+	1.76422i
$216$		0			0
$217$	76.9607			0.0240757
$218$		0			0
$219$	813.917	−	1409.75i	0.251139	−	0.434985i
$220$		0			0
$221$	150.929			0.0459392
$222$		0			0
$223$	503.831	+	872.661i	0.151296	+	0.262053i	0.931704	−	0.363218i	$-0.118322\pi$
$223$	503.831	+	872.661i	0.151296	+	0.262053i	−0.780408	+	0.625271i	$0.784989\pi$
$224$		0			0
$225$	−1159.57	−	2008.44i	−0.343578	−	0.595094i
$226$		0			0
$227$	−1268.86			−0.371000			−0.185500	−	0.982644i	$-0.559391\pi$
$227$	−1268.86			−0.371000			−0.185500	+	0.982644i	$0.559391\pi$
$228$		0			0
$229$	5310.46			1.53242			0.766212	−	0.642588i	$-0.222139\pi$
$229$	5310.46			1.53242			0.766212	+	0.642588i	$0.222139\pi$
$230$		0			0
$231$	101.724	+	176.192i	0.0289739	+	0.0501843i
$232$		0			0
$233$	−801.413	−	1388.09i	−0.225332	−	0.390286i	0.731087	−	0.682284i	$-0.239013\pi$
$233$	−801.413	−	1388.09i	−0.225332	−	0.390286i	−0.956419	+	0.291998i	$0.905680\pi$
$234$		0			0
$235$	2511.92			0.697275
$236$		0			0
$237$	1821.82	−	3155.48i	0.499323	−	0.864853i
$238$		0			0
$239$	−1301.76			−0.352318			−0.176159	−	0.984362i	$-0.556367\pi$
$239$	−1301.76			−0.352318			−0.176159	+	0.984362i	$0.556367\pi$
$240$		0			0
$241$	−3312.57	+	5737.53i	−0.885399	+	1.53356i	−0.0401434	+	0.999194i	$0.512781\pi$
$241$	−3312.57	+	5737.53i	−0.885399	+	1.53356i	−0.845256	+	0.534362i	$0.820552\pi$
$242$		0			0
$243$	−2699.50	+	4675.66i	−0.712645	+	1.23434i
$244$		0			0
$245$	−2471.13	−	4280.12i	−0.644386	−	1.11611i
$246$		0			0
$247$	−2203.99	+	3039.09i	−0.567760	+	0.782887i
$248$		0			0
$249$	2567.61	+	4447.23i	0.653477	+	1.13185i
$250$		0			0
$251$	1302.15	−	2255.39i	0.327454	−	0.567167i	−0.654552	−	0.756017i	$-0.727143\pi$
$251$	1302.15	−	2255.39i	0.327454	−	0.567167i	0.982006	+	0.188850i	$0.0604761\pi$
$252$		0			0
$253$	−3589.43	+	6217.07i	−0.891957	+	1.54492i
$254$		0			0
$255$	355.978			0.0874203
$256$		0			0
$257$	−468.905	+	812.167i	−0.113811	+	0.197127i	−0.917304	−	0.398188i	$-0.869639\pi$
$257$	−468.905	+	812.167i	−0.113811	+	0.197127i	0.803493	+	0.595315i	$0.202973\pi$
$258$		0			0
$259$	−59.4803			−0.0142700
$260$		0			0
$261$	−827.213	−	1432.77i	−0.196181	−	0.339795i
$262$		0			0
$263$	−3963.82	−	6865.54i	−0.929352	−	1.60968i	−0.784408	−	0.620245i	$-0.787033\pi$
$263$	−3963.82	−	6865.54i	−0.929352	−	1.60968i	−0.144944	−	0.989440i	$-0.546300\pi$
$264$		0			0
$265$	3378.38			0.783142
$266$		0			0
$267$	−6135.31			−1.40627
$268$		0			0
$269$	−4135.22	−	7162.41i	−0.937281	−	1.62342i	−0.770515	−	0.637422i	$-0.780001\pi$
$269$	−4135.22	−	7162.41i	−0.937281	−	1.62342i	−0.166767	−	0.985996i	$-0.553333\pi$
$270$		0			0
$271$	−941.761	−	1631.18i	−0.211099	−	0.365635i	0.740960	−	0.671550i	$-0.234371\pi$
$271$	−941.761	−	1631.18i	−0.211099	−	0.365635i	−0.952059	+	0.305915i	$0.901038\pi$
$272$		0			0
$273$	139.915			0.0310184
$274$		0			0
$275$	2729.70	−	4727.97i	0.598571	−	1.03675i
$276$		0			0
$277$	−4156.22			−0.901527			−0.450764	−	0.892643i	$-0.648848\pi$
$277$	−4156.22			−0.901527			−0.450764	+	0.892643i	$0.648848\pi$
$278$		0			0
$279$	2588.79	−	4483.91i	0.555508	−	0.962168i
$280$		0			0
$281$	2975.03	−	5152.90i	0.631585	−	1.09394i	−0.355643	−	0.934622i	$-0.615738\pi$
$281$	2975.03	−	5152.90i	0.631585	−	1.09394i	0.987228	−	0.159315i	$-0.0509285\pi$
$282$		0			0
$283$	−823.354	−	1426.09i	−0.172945	−	0.299549i	0.766504	−	0.642240i	$-0.221995\pi$
$283$	−823.354	−	1426.09i	−0.172945	−	0.299549i	−0.939448	+	0.342691i	$0.888661\pi$
$284$		0			0
$285$	−5198.29	+	7167.94i	−1.08042	+	1.48980i
$286$		0			0
$287$	−36.4487	−	63.1311i	−0.00749652	−	0.0129844i
$288$		0			0
$289$	2450.96	−	4245.18i	0.498872	−	0.864071i
$290$		0			0
$291$	−2717.31	+	4706.52i	−0.547394	+	0.948114i
$292$		0			0
$293$	7119.83			1.41961			0.709804	−	0.704400i	$-0.248784\pi$
$293$	7119.83			1.41961			0.709804	+	0.704400i	$0.248784\pi$
$294$		0			0
$295$	−1098.59	+	1902.81i	−0.216822	+	0.375546i
$296$		0			0
$297$	488.827			0.0955037
$298$		0			0
$299$	2468.50	+	4275.57i	0.477448	+	0.826965i
$300$		0			0
$301$	−92.7041	−	160.568i	−0.0177521	−	0.0307475i
$302$		0			0
$303$	−1692.36			−0.320870
$304$		0			0
$305$	−835.134			−0.156786
$306$		0			0
$307$	−2582.54	−	4473.10i	−0.480109	−	0.831573i	0.519631	−	0.854391i	$-0.326070\pi$
$307$	−2582.54	−	4473.10i	−0.480109	−	0.831573i	−0.999740	+	0.0228177i	$0.992736\pi$
$308$		0			0
$309$	−2876.84	−	4982.84i	−0.529637	−	0.917358i
$310$		0			0
$311$	828.756			0.151108			0.0755538	−	0.997142i	$-0.475928\pi$
$311$	828.756			0.151108			0.0755538	+	0.997142i	$0.475928\pi$
$312$		0			0
$313$	−1731.28	+	2998.67i	−0.312645	+	0.541517i	−0.978934	−	0.204176i	$-0.934548\pi$
$313$	−1731.28	+	2998.67i	−0.312645	+	0.541517i	0.666289	+	0.745694i	$0.267882\pi$
$314$		0			0
$315$	168.000			0.0300499
$316$		0			0
$317$	2253.11	−	3902.50i	0.399203	−	0.691440i	−0.594425	−	0.804151i	$-0.702620\pi$
$317$	2253.11	−	3902.50i	0.399203	−	0.691440i	0.993628	+	0.112712i	$0.0359536\pi$
$318$		0			0
$319$	1947.30	−	3372.82i	0.341780	−	0.591980i
$320$		0			0
$321$	2184.57	+	3783.78i	0.379846	+	0.657913i
$322$		0			0
$323$	−112.378	−	251.816i	−0.0193588	−	0.0433789i
$324$		0			0
$325$	−1877.25	−	3251.50i	−0.320404	−	0.554955i
$326$		0			0
$327$	5852.37	−	10136.6i	0.989716	−	1.71424i
$328$		0			0
$329$	−36.2598	+	62.8039i	−0.00607620	+	0.0105243i
$330$		0			0
$331$	5665.99			0.940879			0.470440	−	0.882432i	$-0.344095\pi$
$331$	5665.99			0.940879			0.470440	+	0.882432i	$0.344095\pi$
$332$		0			0
$333$	−2000.79	+	3465.47i	−0.329257	+	0.570289i
$334$		0			0
$335$	−12069.5			−1.96845
$336$		0			0
$337$	−3414.85	−	5914.70i	−0.551985	−	0.956066i	−0.998131	−	0.0611061i	$-0.980537\pi$
$337$	−3414.85	−	5914.70i	−0.551985	−	0.956066i	0.446146	−	0.894960i	$-0.352796\pi$
$338$		0			0
$339$	4187.44	+	7252.85i	0.670886	+	1.16201i
$340$		0			0
$341$	12188.3			1.93558
$342$		0			0
$343$	285.440			0.0449339
$344$		0			0
$345$	5822.15	+	10084.3i	0.908562	+	1.57368i
$346$		0			0
$347$	−2043.22	−	3538.95i	−0.316097	−	0.547496i	0.663573	−	0.748111i	$-0.269039\pi$
$347$	−2043.22	−	3538.95i	−0.316097	−	0.547496i	−0.979670	+	0.200616i	$0.935706\pi$
$348$		0			0
$349$	−10392.4			−1.59396			−0.796979	−	0.604007i	$-0.793570\pi$
$349$	−10392.4			−1.59396			−0.796979	+	0.604007i	$0.793570\pi$
$350$		0			0
$351$	168.087	−	291.135i	0.0255607	−	0.0442724i
$352$		0			0
$353$	−7054.66			−1.06369			−0.531843	−	0.846843i	$-0.678501\pi$
$353$	−7054.66			−1.06369			−0.531843	+	0.846843i	$0.678501\pi$
$354$		0			0
$355$	−3802.13	+	6585.48i	−0.568440	+	0.984567i
$356$		0			0
$357$	−5.13857	+	8.90027i	−0.000761798	+	0.00131947i
$358$		0			0
$359$	−5591.28	−	9684.37i	−0.821995	−	1.42374i	−0.904194	−	0.427121i	$-0.859528\pi$
$359$	−5591.28	−	9684.37i	−0.821995	−	1.42374i	0.0821991	−	0.996616i	$-0.473806\pi$
$360$		0			0
$361$	6711.59	+	1414.38i	0.978508	+	0.206208i
$362$		0			0
$363$	11174.6	+	19355.0i	1.61575	+	2.79856i
$364$		0			0
$365$	1582.16	−	2740.38i	0.226887	−	0.392981i
$366$		0			0
$367$	−3164.89	+	5481.74i	−0.450152	+	0.779686i	−0.998395	−	0.0566331i	$-0.981963\pi$
$367$	−3164.89	+	5481.74i	−0.450152	+	0.779686i	0.548243	+	0.836319i	$0.315297\pi$
$368$		0			0
$369$	−4904.22			−0.691880
$370$		0			0
$371$	−48.7673	+	84.4675i	−0.00682446	+	0.0118203i
$372$		0			0
$373$	−914.614			−0.126962			−0.0634811	−	0.997983i	$-0.520220\pi$
$373$	−914.614			−0.126962			−0.0634811	+	0.997983i	$0.520220\pi$
$374$		0			0
$375$	2254.44	+	3904.81i	0.310450	+	0.537716i
$376$		0			0
$377$	−1339.19	−	2319.54i	−0.182948	−	0.316876i
$378$		0			0
$379$	5052.39			0.684760			0.342380	−	0.939562i	$-0.388767\pi$
$379$	5052.39			0.684760			0.342380	+	0.939562i	$0.388767\pi$
$380$		0			0
$381$	2420.95			0.325536
$382$		0			0
$383$	7129.12	+	12348.0i	0.951126	+	1.64740i	0.742995	+	0.669297i	$0.233404\pi$
$383$	7129.12	+	12348.0i	0.951126	+	1.64740i	0.208130	+	0.978101i	$0.433262\pi$
$384$		0			0
$385$	197.740	+	342.496i	0.0261760	+	0.0453382i
$386$		0			0
$387$	−12473.4			−1.63840
$388$		0			0
$389$	−2888.08	+	5002.30i	−0.376430	+	0.651996i	−0.990540	−	0.137224i	$-0.956182\pi$
$389$	−2888.08	+	5002.30i	−0.376430	+	0.651996i	0.614110	+	0.789221i	$0.289515\pi$
$390$		0			0
$391$	−362.637			−0.0469036
$392$		0			0
$393$	−933.044	+	1616.08i	−0.119760	+	0.207431i
$394$		0			0
$395$	3541.39	−	6133.87i	0.451106	−	0.781338i
$396$		0			0
$397$	−306.917	−	531.596i	−0.0388003	−	0.0672041i	0.845973	−	0.533226i	$-0.179020\pi$
$397$	−306.917	−	531.596i	−0.0388003	−	0.0672041i	−0.884773	+	0.466021i	$0.845687\pi$
$398$		0			0
$399$	−104.177	−	233.439i	−0.0130712	−	0.0292897i
$400$		0			0
$401$	5005.59	+	8669.94i	0.623360	+	1.07969i	0.988856	+	0.148878i	$0.0475663\pi$
$401$	5005.59	+	8669.94i	0.623360	+	1.07969i	−0.365495	+	0.930813i	$0.619100\pi$
$402$		0			0
$403$	4191.02	−	7259.07i	0.518039	−	0.897270i
$404$		0			0
$405$	−5052.88	+	8751.84i	−0.619949	+	1.07378i
$406$		0			0
$407$	−9419.91			−1.14724
$408$		0			0
$409$	3740.85	−	6479.34i	0.452257	−	0.783332i	−0.546269	−	0.837610i	$-0.683952\pi$
$409$	3740.85	−	6479.34i	0.452257	−	0.783332i	0.998526	+	0.0542776i	$0.0172856\pi$
$410$		0			0
$411$	14594.2			1.75153
$412$		0			0
$413$	−31.7165	−	54.9346i	−0.00377886	−	0.00654517i
$414$		0			0
$415$	4991.13	+	8644.88i	0.590373	+	1.02256i
$416$		0			0
$417$	−6915.39			−0.812106
$418$		0			0
$419$	10791.7			1.25825			0.629125	−	0.777304i	$-0.283413\pi$
$419$	10791.7			1.25825			0.629125	+	0.777304i	$0.283413\pi$
$420$		0			0
$421$	2972.97	+	5149.33i	0.344165	+	0.596112i	0.985202	−	0.171399i	$-0.0548286\pi$
$421$	2972.97	+	5149.33i	0.344165	+	0.596112i	−0.641036	+	0.767510i	$0.721495\pi$
$422$		0			0
$423$	2439.40	+	4225.17i	0.280397	+	0.485661i
$424$		0			0
$425$	275.779			0.0314759
$426$		0			0
$427$	12.0552	−	20.8803i	0.00136626	−	0.00236644i
$428$		0			0
$429$	22158.3			2.49374
$430$		0			0
$431$	7741.76	−	13409.1i	0.865214	−	1.49859i	−0.00162037	−	0.999999i	$-0.500516\pi$
$431$	7741.76	−	13409.1i	0.865214	−	1.49859i	0.866834	−	0.498596i	$-0.166151\pi$
$432$		0			0
$433$	5495.74	−	9518.91i	0.609951	−	1.05647i	−0.381297	−	0.924452i	$-0.624523\pi$
$433$	5495.74	−	9518.91i	0.609951	−	1.05647i	0.991248	−	0.132013i	$-0.0421441\pi$
$434$		0			0
$435$	−3158.57	−	5470.81i	−0.348143	−	0.603001i
$436$		0			0
$437$	5295.53	−	7302.03i	0.579679	−	0.799322i
$438$		0			0
$439$	−7091.38	−	12282.6i	−0.770964	−	1.33535i	−0.937035	−	0.349235i	$-0.886441\pi$
$439$	−7091.38	−	12282.6i	−0.770964	−	1.33535i	0.166071	−	0.986114i	$-0.446892\pi$
$440$		0			0
$441$	4799.57	−	8313.11i	0.518257	−	0.897647i
$442$		0			0
$443$	4532.34	−	7850.25i	0.486091	−	0.841934i	−0.513782	−	0.857921i	$-0.671756\pi$
$443$	4532.34	−	7850.25i	0.486091	−	0.841934i	0.999872	+	0.0159875i	$0.00508919\pi$
$444$		0			0
$445$	−11926.3			−1.27047
$446$		0			0
$447$	−1723.30	+	2984.85i	−0.182348	+	0.315835i
$448$		0			0
$449$	7195.06			0.756249			0.378125	−	0.925755i	$-0.376569\pi$
$449$	7195.06			0.756249			0.378125	+	0.925755i	$0.376569\pi$
$450$		0			0
$451$	−5772.39	−	9998.07i	−0.602686	−	1.04388i
$452$		0			0
$453$	7109.74	+	12314.4i	0.737406	+	1.27722i
$454$		0			0
$455$	271.978			0.0280231
$456$		0			0
$457$	8519.82			0.872080			0.436040	−	0.899927i	$-0.356381\pi$
$457$	8519.82			0.872080			0.436040	+	0.899927i	$0.356381\pi$
$458$		0			0
$459$	12.3464	+	21.3847i	0.00125552	+	0.00217462i
$460$		0			0
$461$	−5518.91	−	9559.03i	−0.557573	−	0.965745i	−0.997698	−	0.0678087i	$-0.978399\pi$
$461$	−5518.91	−	9559.03i	−0.557573	−	0.965745i	0.440125	−	0.897936i	$-0.354934\pi$
$462$		0			0
$463$	−10524.2			−1.05637			−0.528187	−	0.849128i	$-0.677128\pi$
$463$	−10524.2			−1.05637			−0.528187	+	0.849128i	$0.677128\pi$
$464$		0			0
$465$	9884.86	−	17121.1i	0.985805	−	1.70746i
$466$		0			0
$467$	−8366.46			−0.829023			−0.414512	−	0.910044i	$-0.636048\pi$
$467$	−8366.46			−0.829023			−0.414512	+	0.910044i	$0.636048\pi$
$468$		0			0
$469$	174.225	−	301.766i	0.0171534	−	0.0297106i
$470$		0			0
$471$	2373.97	−	4111.83i	0.232243	−	0.402258i
$472$		0			0
$473$	−14681.6	−	25429.2i	−1.42719	−	2.47196i
$474$		0			0
$475$	−4027.16	+	5553.07i	−0.389008	+	0.536405i
$476$		0			0
$477$	3280.85	+	5682.60i	0.314926	+	0.545468i
$478$		0			0
$479$	−6313.55	+	10935.4i	−0.602241	+	1.04311i	0.390240	+	0.920713i	$0.372392\pi$
$479$	−6313.55	+	10935.4i	−0.602241	+	1.04311i	−0.992481	+	0.122399i	$0.960941\pi$
$480$		0			0
$481$	−3239.10	+	5610.29i	−0.307049	+	0.531824i
$482$		0			0
$483$	−336.173			−0.0316696
$484$		0			0
$485$	−5282.13	+	9148.91i	−0.494534	+	0.856558i
$486$		0			0
$487$	13305.1			1.23801			0.619006	−	0.785386i	$-0.287536\pi$
$487$	13305.1			1.23801			0.619006	+	0.785386i	$0.287536\pi$
$488$		0			0
$489$	2628.93	+	4553.43i	0.243117	+	0.421091i
$490$		0			0
$491$	2355.35	+	4079.59i	0.216488	+	0.374968i	0.953732	−	0.300658i	$-0.0972064\pi$
$491$	2355.35	+	4079.59i	0.216488	+	0.374968i	−0.737244	+	0.675627i	$0.763873\pi$
$492$		0			0
$493$	196.734			0.0179725
$494$		0			0
$495$	26606.2			2.41588
$496$		0			0
$497$	−109.768	−	190.124i	−0.00990700	−	0.0171594i
$498$		0			0
$499$	−8316.55	−	14404.7i	−0.746092	−	1.29227i	−0.949683	−	0.313213i	$-0.898595\pi$
$499$	−8316.55	−	14404.7i	−0.746092	−	1.29227i	0.203591	−	0.979056i	$-0.434739\pi$
$500$		0			0
$501$	10565.6			0.942191
$502$		0			0
$503$	10636.3	−	18422.6i	0.942841	−	1.63305i	0.182823	−	0.983146i	$-0.441476\pi$
$503$	10636.3	−	18422.6i	0.942841	−	1.63305i	0.760018	−	0.649903i	$-0.225190\pi$
$504$		0			0
$505$	−3289.75			−0.289885
$506$		0			0
$507$	−527.397	+	913.479i	−0.0461983	+	0.0800178i
$508$		0			0
$509$	−6197.37	+	10734.2i	−0.539673	+	0.934741i	0.459249	+	0.888308i	$0.348119\pi$
$509$	−6197.37	+	10734.2i	−0.539673	+	0.934741i	−0.998921	+	0.0464329i	$0.985215\pi$
$510$		0			0
$511$	45.6772	+	79.1152i	0.00395429	+	0.00684902i
$512$		0			0
$513$	−610.894	−	63.6699i	−0.0525763	−	0.00547972i
$514$		0			0
$515$	−5592.24	−	9686.04i	−0.478492	−	0.828772i
$516$		0			0
$517$	−5742.47	+	9946.25i	−0.488498	+	0.846104i
$518$		0			0
$519$	−635.599	+	1100.89i	−0.0537566	+	0.0931092i
$520$		0			0
$521$	1260.78			0.106019			0.0530094	−	0.998594i	$-0.483119\pi$
$521$	1260.78			0.106019			0.0530094	+	0.998594i	$0.483119\pi$
$522$		0			0
$523$	−11916.0	+	20639.1i	−0.996272	+	1.72559i	−0.423423	+	0.905932i	$0.639172\pi$
$523$	−11916.0	+	20639.1i	−0.996272	+	1.72559i	−0.572849	+	0.819661i	$0.694162\pi$
$524$		0			0
$525$	255.654			0.0212527
$526$		0			0
$527$	307.843	+	533.199i	0.0254456	+	0.0440731i
$528$		0			0
$529$	152.437	+	264.028i	0.0125287	+	0.0217004i
$530$		0			0
$531$	−4267.50			−0.348764
$532$		0			0
$533$	−7939.51			−0.645213
$534$		0			0
$535$	4246.54	+	7355.22i	0.343166	+	0.594381i
$536$		0			0
$537$	−1633.17	−	2828.73i	−0.131241	−	0.227316i
$538$		0			0
$539$	22596.9			1.80578
$540$		0			0
$541$	−2608.91	+	4518.77i	−0.207331	+	0.359107i	−0.950873	−	0.309582i	$-0.899811\pi$
$541$	−2608.91	+	4518.77i	−0.207331	+	0.359107i	0.743542	+	0.668689i	$0.233144\pi$
$542$		0			0
$543$	3337.36			0.263756
$544$		0			0
$545$	11376.3	−	19704.3i	0.894142	−	1.54870i
$546$		0			0
$547$	4890.58	−	8470.74i	0.382278	−	0.662125i	−0.609109	−	0.793086i	$-0.708473\pi$
$547$	4890.58	−	8470.74i	0.382278	−	0.662125i	0.991388	+	0.130961i	$0.0418062\pi$
$548$		0			0
$549$	−811.023	−	1404.73i	−0.0630485	−	0.109203i
$550$		0			0
$551$	−2872.88	+	3961.43i	−0.222121	+	0.306284i
$552$		0			0
$553$	102.241	+	177.086i	0.00786205	+	0.0136175i
$554$		0			0
$555$	−7639.68	+	13232.3i	−0.584300	+	1.01204i
$556$		0			0
$557$	9769.78	−	16921.8i	0.743194	−	1.28725i	−0.207840	−	0.978163i	$-0.566643\pi$
$557$	9769.78	−	16921.8i	0.743194	−	1.28725i	0.951034	−	0.309086i	$-0.100023\pi$
$558$		0			0
$559$	−20193.4			−1.52789
$560$		0			0
$561$	−813.796	+	1409.54i	−0.0612451	+	0.106080i
$562$		0			0
$563$	−6348.35			−0.475224			−0.237612	−	0.971360i	$-0.576365\pi$
$563$	−6348.35			−0.475224			−0.237612	+	0.971360i	$0.576365\pi$
$564$		0			0
$565$	8139.87	+	14098.7i	0.606101	+	1.04980i
$566$		0			0
$567$	−145.878	−	252.667i	−0.0108047	−	0.0187143i
$568$		0			0
$569$	−21005.9			−1.54765			−0.773824	−	0.633401i	$-0.781658\pi$
$569$	−21005.9			−1.54765			−0.773824	+	0.633401i	$0.781658\pi$
$570$		0			0
$571$	896.764			0.0657240			0.0328620	−	0.999460i	$-0.489538\pi$
$571$	896.764			0.0657240			0.0328620	+	0.999460i	$0.489538\pi$
$572$		0			0
$573$	10720.0	+	18567.5i	0.781559	+	1.35370i
$574$		0			0
$575$	4510.47	+	7812.37i	0.327130	+	0.566606i
$576$		0			0
$577$	−21971.7			−1.58526			−0.792630	−	0.609702i	$-0.791289\pi$
$577$	−21971.7			−1.58526			−0.792630	+	0.609702i	$0.791289\pi$
$578$		0			0
$579$	−13241.5	+	22934.9i	−0.950427	+	1.64619i
$580$		0			0
$581$	−288.190			−0.0205785
$582$		0			0
$583$	−7723.28	+	13377.1i	−0.548655	+	0.950298i
$584$		0			0
$585$	9148.72	−	15846.1i	0.646587	−	1.11992i
$586$		0			0
$587$	−1168.92	−	2024.63i	−0.0821915	−	0.142360i	0.822000	−	0.569488i	$-0.192859\pi$
$587$	−1168.92	−	2024.63i	−0.0821915	−	0.142360i	−0.904191	+	0.427128i	$0.859525\pi$
$588$		0			0
$589$	−15231.9	−	1587.53i	−1.06556	−	0.111058i
$590$		0			0
$591$	9804.74	+	16982.3i	0.682425	+	1.18199i
$592$		0			0
$593$	4055.21	−	7023.83i	0.280822	−	0.486398i	−0.690765	−	0.723079i	$-0.742726\pi$
$593$	4055.21	−	7023.83i	0.280822	−	0.486398i	0.971587	+	0.236681i	$0.0760595\pi$
$594$		0			0
$595$	−9.98876	+	17.3010i	−0.000688234	+	0.00119206i
$596$		0			0
$597$	−32356.9			−2.21822
$598$		0			0
$599$	9744.33	−	16877.7i	0.664679	−	1.15126i	−0.314694	−	0.949193i	$-0.601902\pi$
$599$	9744.33	−	16877.7i	0.664679	−	1.15126i	0.979372	−	0.202064i	$-0.0647649\pi$
$600$		0			0
$601$	−3084.73			−0.209366			−0.104683	−	0.994506i	$-0.533383\pi$
$601$	−3084.73			−0.209366			−0.104683	+	0.994506i	$0.533383\pi$
$602$		0			0
$603$	−11721.1	−	20301.5i	−0.791575	−	1.37105i
$604$		0			0
$605$	21722.1	+	37623.9i	1.45972	+	2.52831i
$606$		0			0
$607$	13705.6			0.916463			0.458231	−	0.888833i	$-0.348483\pi$
$607$	13705.6			0.916463			0.458231	+	0.888833i	$0.348483\pi$
$608$		0			0
$609$	182.377			0.0121351
$610$		0			0
$611$	3949.18	+	6840.18i	0.261484	+	0.452904i
$612$		0			0
$613$	−2932.32	−	5078.93i	−0.193206	−	0.334643i	0.753105	−	0.657901i	$-0.228555\pi$
$613$	−2932.32	−	5078.93i	−0.193206	−	0.334643i	−0.946311	+	0.323258i	$0.895222\pi$
$614$		0			0
$615$	−18726.0			−1.22781
$616$		0			0
$617$	−6835.55	+	11839.5i	−0.446011	+	0.772514i	−0.998122	−	0.0612569i	$-0.980489\pi$
$617$	−6835.55	+	11839.5i	−0.446011	+	0.772514i	0.552111	+	0.833771i	$0.313822\pi$
$618$		0			0
$619$	−1574.30			−0.102224			−0.0511118	−	0.998693i	$-0.516276\pi$
$619$	−1574.30			−0.102224			−0.0511118	+	0.998693i	$0.516276\pi$
$620$		0			0
$621$	−403.862	+	699.509i	−0.0260973	+	0.0452018i
$622$		0			0
$623$	172.157	−	298.185i	0.0110712	−	0.0191758i
$624$		0			0
$625$	9559.04	+	16556.7i	0.611778	+	1.05963i
$626$		0			0
$627$	−16498.6	−	36969.8i	−1.05086	−	2.35475i
$628$		0			0
$629$	−237.921	−	412.092i	−0.0150819	−	0.0261227i
$630$		0			0
$631$	−11752.8	+	20356.5i	−0.741479	+	1.28428i	0.210343	+	0.977628i	$0.432542\pi$
$631$	−11752.8	+	20356.5i	−0.741479	+	1.28428i	−0.951822	+	0.306652i	$0.900791\pi$
$632$		0			0
$633$	−9533.44	+	16512.4i	−0.598610	+	1.03682i
$634$		0			0
$635$	4706.04			0.294100
$636$		0			0
$637$	7770.10	−	13458.2i	0.483301	−	0.837101i
$638$		0			0
$639$	−14769.4			−0.914351
$640$		0			0
$641$	−4781.18	−	8281.26i	−0.294611	−	0.510281i	0.680284	−	0.732949i	$-0.261857\pi$
$641$	−4781.18	−	8281.26i	−0.294611	−	0.510281i	−0.974894	+	0.222668i	$0.928523\pi$
$642$		0			0
$643$	4145.36	+	7179.98i	0.254241	+	0.440359i	0.964689	−	0.263391i	$-0.0848410\pi$
$643$	4145.36	+	7179.98i	0.254241	+	0.440359i	−0.710448	+	0.703750i	$0.751508\pi$
$644$		0			0
$645$	−47627.8			−2.90751
$646$		0			0
$647$	−13673.8			−0.830870			−0.415435	−	0.909623i	$-0.636371\pi$
$647$	−13673.8			−0.830870			−0.415435	+	0.909623i	$0.636371\pi$
$648$		0			0
$649$	−5022.95	−	8700.00i	−0.303803	−	0.526202i
$650$		0			0
$651$	285.378	+	494.289i	0.0171810	+	0.0297584i
$652$		0			0
$653$	941.670			0.0564325			0.0282162	−	0.999602i	$-0.491017\pi$
$653$	941.670			0.0564325			0.0282162	+	0.999602i	$0.491017\pi$
$654$		0			0
$655$	−1813.72	+	3141.46i	−0.108196	+	0.187400i
$656$		0			0
$657$	6145.92			0.364955
$658$		0			0
$659$	8316.68	−	14404.9i	0.491611	−	0.851495i	−0.508342	−	0.861155i	$-0.669741\pi$
$659$	8316.68	−	14404.9i	0.491611	−	0.851495i	0.999953	+	0.00965969i	$0.00307482\pi$
$660$		0			0
$661$	9385.58	−	16256.3i	0.552279	−	0.956576i	−0.445830	−	0.895118i	$-0.647091\pi$
$661$	9385.58	−	16256.3i	0.552279	−	0.956576i	0.998110	−	0.0614585i	$-0.0195752\pi$
$662$		0			0
$663$	559.659	+	969.358i	0.0327833	+	0.0567824i
$664$		0			0
$665$	−202.508	−	453.778i	−0.0118089	−	0.0264613i
$666$		0			0
$667$	3217.66	+	5573.15i	0.186789	+	0.323528i
$668$		0			0
$669$	−3736.51	+	6471.83i	−0.215937	+	0.374014i
$670$		0			0
$671$	1909.19	−	3306.81i	0.109841	−	0.190251i
$672$		0			0
$673$	29366.8			1.68203			0.841017	−	0.541009i	$-0.181958\pi$
$673$	29366.8			1.68203			0.841017	+	0.541009i	$0.181958\pi$
$674$		0			0
$675$	307.130	−	531.965i	0.0175132	−	0.0303338i
$676$		0			0
$677$	−5330.95			−0.302636			−0.151318	−	0.988485i	$-0.548352\pi$
$677$	−5330.95			−0.302636			−0.151318	+	0.988485i	$0.548352\pi$
$678$		0			0
$679$	−152.496	−	264.131i	−0.00861894	−	0.0149284i
$680$		0			0
$681$	−4705.05	−	8149.39i	−0.264755	−	0.458569i
$682$		0			0
$683$	−27122.2			−1.51947			−0.759737	−	0.650230i	$-0.774672\pi$
$683$	−27122.2			−1.51947			−0.759737	+	0.650230i	$0.774672\pi$
$684$		0			0
$685$	28369.4			1.58239
$686$		0			0
$687$	19691.7	+	34107.0i	1.09357	+	1.89413i
$688$		0			0
$689$	5311.41	+	9199.64i	0.293685	+	0.508677i
$690$		0			0
$691$	−13894.6			−0.764945			−0.382473	−	0.923967i	$-0.624927\pi$
$691$	−13894.6			−0.764945			−0.382473	+	0.923967i	$0.624927\pi$
$692$		0			0
$693$	−384.063	+	665.216i	−0.0210524	+	0.0364639i
$694$		0			0
$695$	−13442.7			−0.733684
$696$		0			0
$697$	291.590	−	505.049i	0.0158461	−	0.0274463i
$698$		0			0
$699$	5943.44	−	10294.3i	0.321605	−	0.557035i
$700$		0			0
$701$	8057.12	+	13955.3i	0.434113	+	0.751906i	0.997223	−	0.0744764i	$-0.0237286\pi$
$701$	8057.12	+	13955.3i	0.434113	+	0.751906i	−0.563110	+	0.826382i	$0.690395\pi$
$702$		0			0
$703$	11772.2	+	1226.95i	0.631574	+	0.0658253i
$704$		0			0
$705$	9314.45	+	16133.1i	0.497592	+	0.861855i
$706$		0			0
$707$	47.4878	−	82.2513i	0.00252612	−	0.00437536i
$708$		0			0
$709$	−790.511	+	1369.21i	−0.0418735	+	0.0725270i	−0.886203	−	0.463298i	$-0.846666\pi$
$709$	−790.511	+	1369.21i	−0.0418735	+	0.0725270i	0.844329	+	0.535825i	$0.179999\pi$
$710$		0			0
$711$	13756.6			0.725616
$712$		0			0
$713$	−10069.8	+	17441.4i	−0.528914	+	0.916107i
$714$		0			0
$715$	43073.1			2.25293
$716$		0			0
$717$	−4827.07	−	8360.73i	−0.251423	−	0.435477i
$718$		0			0
$719$	8113.04	+	14052.2i	0.420814	+	0.728872i	0.996019	−	0.0891376i	$-0.0284111\pi$
$719$	8113.04	+	14052.2i	0.420814	+	0.728872i	−0.575205	+	0.818009i	$0.695078\pi$
$720$		0			0
$721$	322.898			0.0166787
$722$		0			0
$723$	−49133.3			−2.52737
$724$		0			0
$725$	−2446.98	−	4238.29i	−0.125350	−	0.217112i
$726$		0			0
$727$	−11537.6	−	19983.7i	−0.588590	−	1.01947i	−0.994417	−	0.105518i	$-0.966350\pi$
$727$	−11537.6	−	19983.7i	−0.588590	−	1.01947i	0.405827	−	0.913950i	$-0.366984\pi$
$728$		0			0
$729$	−21113.0			−1.07265
$730$		0			0
$731$	741.633	−	1284.55i	0.0375243	−	0.0649940i
$732$		0			0
$733$	−19437.2			−0.979439			−0.489719	−	0.871880i	$-0.662901\pi$
$733$	−19437.2			−0.979439			−0.489719	+	0.871880i	$0.662901\pi$
$734$		0			0
$735$	18326.4	−	31742.2i	0.919699	−	1.59297i
$736$		0			0
$737$	27592.0	−	47790.8i	1.37906	−	2.38860i
$738$		0			0
$739$	−3891.52	−	6740.30i	−0.193710	−	0.335516i	0.752767	−	0.658287i	$-0.228719\pi$
$739$	−3891.52	−	6740.30i	−0.193710	−	0.335516i	−0.946477	+	0.322772i	$0.895385\pi$
$740$		0			0
$741$	−27691.6	−	2886.13i	−1.37284	−	0.143083i
$742$		0			0
$743$	−2786.72	−	4826.75i	−0.137598	−	0.238326i	0.788989	−	0.614407i	$-0.210605\pi$
$743$	−2786.72	−	4826.75i	−0.137598	−	0.238326i	−0.926587	+	0.376081i	$0.877271\pi$
$744$		0			0
$745$	−3349.89	+	5802.19i	−0.164739	+	0.285336i
$746$		0			0
$747$	−9694.06	+	16790.6i	−0.474816	+	0.822405i
$748$		0			0
$749$	−245.197			−0.0119617
$750$		0			0
$751$	14862.4	−	25742.5i	0.722155	−	1.25081i	−0.237979	−	0.971270i	$-0.576485\pi$
$751$	14862.4	−	25742.5i	0.722155	−	1.25081i	0.960134	−	0.279539i	$-0.0901817\pi$
$752$		0			0
$753$	19314.0			0.934716
$754$		0			0
$755$	13820.5	+	23937.8i	0.666197	+	1.15389i
$756$		0			0
$757$	6077.39	+	10526.4i	0.291792	+	0.505399i	0.974234	−	0.225541i	$-0.0724151\pi$
$757$	6077.39	+	10526.4i	0.291792	+	0.505399i	−0.682441	+	0.730940i	$0.739082\pi$
$758$		0			0
$759$	−53239.8			−2.54609
$760$		0			0
$761$	−25318.1			−1.20602			−0.603010	−	0.797734i	$-0.706032\pi$
$761$	−25318.1			−1.20602			−0.603010	+	0.797734i	$0.706032\pi$
$762$		0			0
$763$	328.436	+	568.868i	0.0155835	+	0.0269914i
$764$		0			0
$765$	672.000	+	1163.94i	0.0317598	+	0.0550095i
$766$		0			0
$767$	−6908.71			−0.325240
$768$		0			0
$769$	−1024.54	+	1774.55i	−0.0480440	+	0.0832147i	−0.889047	−	0.457815i	$-0.848632\pi$
$769$	−1024.54	+	1774.55i	−0.0480440	+	0.0832147i	0.841003	+	0.541030i	$0.181965\pi$
$770$		0			0
$771$	−6954.98			−0.324874
$772$		0			0
$773$	−14837.6	+	25699.4i	−0.690389	+	1.19579i	0.281322	+	0.959614i	$0.409227\pi$
$773$	−14837.6	+	25699.4i	−0.690389	+	1.19579i	−0.971710	+	0.236175i	$0.924106\pi$
$774$		0			0
$775$	7657.89	−	13263.9i	0.354941	−	0.614776i
$776$		0			0
$777$	−220.559	−	382.019i	−0.0101834	−	0.0176382i
$778$		0			0
$779$	5911.58	+	13246.6i	0.271893	+	0.609253i
$780$		0			0
$781$	−17384.0	−	30110.0i	−0.796477	−	1.37954i
$782$		0			0
$783$	219.099	−	379.491i	0.00999995	−	0.0173204i
$784$		0			0
$785$	4614.71	−	7992.91i	0.209817	−	0.363413i
$786$		0			0
$787$	42499.6			1.92496			0.962482	−	0.271345i	$-0.0874683\pi$
$787$	42499.6			1.92496			0.962482	+	0.271345i	$0.0874683\pi$
$788$		0			0
$789$	29396.5	−	50916.2i	1.32642	−	2.29742i
$790$		0			0
$791$	−470.000			−0.0211268
$792$		0			0
$793$	−1312.98	−	2274.14i	−0.0587959	−	0.101838i
$794$		0			0
$795$	12527.4	+	21698.1i	0.558869	+	0.967989i
$796$		0			0
$797$	−10398.1			−0.462131			−0.231065	−	0.972938i	$-0.574221\pi$
$797$	−10398.1			−0.462131			−0.231065	+	0.972938i	$0.574221\pi$
$798$		0			0
$799$	−580.157			−0.0256877
$800$		0			0
$801$	−11582.0	−	20060.6i	−0.510898	−	0.884901i
$802$		0			0
$803$	7233.90	+	12529.5i	0.317906	+	0.550630i
$804$		0			0
$805$	−653.480			−0.0286114
$806$		0			0
$807$	30667.6	−	53117.8i	1.33773	−	2.31702i
$808$		0			0
$809$	−298.449			−0.0129702			−0.00648512	−	0.999979i	$-0.502064\pi$
$809$	−298.449			−0.0129702			−0.00648512	+	0.999979i	$0.502064\pi$
$810$		0			0
$811$	−3927.51	+	6802.64i	−0.170054	+	0.294541i	−0.938438	−	0.345447i	$-0.887727\pi$
$811$	−3927.51	+	6802.64i	−0.170054	+	0.294541i	0.768385	+	0.639988i	$0.221061\pi$
$812$		0			0
$813$	6984.28	−	12097.1i	0.301291	−	0.521851i
$814$		0			0
$815$	5110.32	+	8851.33i	0.219640	+	0.380428i
$816$		0			0
$817$	15035.6	+	33691.5i	0.643854	+	1.44274i
$818$		0			0
$819$	264.125	+	457.479i	0.0112690	+	0.0195184i
$820$		0			0
$821$	9327.00	−	16154.8i	0.396485	−	0.686733i	−0.596804	−	0.802387i	$-0.703563\pi$
$821$	9327.00	−	16154.8i	0.396485	−	0.686733i	0.993290	+	0.115654i	$0.0368964\pi$
$822$		0			0
$823$	−19245.0	+	33333.3i	−0.815113	+	1.41182i	0.0941338	+	0.995560i	$0.469992\pi$
$823$	−19245.0	+	33333.3i	−0.815113	+	1.41182i	−0.909247	+	0.416258i	$0.863341\pi$
$824$		0			0
$825$	40487.9			1.70862
$826$		0			0
$827$	7939.76	−	13752.1i	0.333848	−	0.578242i	−0.649415	−	0.760434i	$-0.724986\pi$
$827$	7939.76	−	13752.1i	0.333848	−	0.578242i	0.983263	+	0.182192i	$0.0583194\pi$
$828$		0			0
$829$	42150.6			1.76592			0.882961	−	0.469446i	$-0.155546\pi$
$829$	42150.6			1.76592			0.882961	+	0.469446i	$0.155546\pi$
$830$		0			0
$831$	−15411.7	−	26693.8i	−0.643352	−	1.11432i
$832$		0			0
$833$	570.736	+	988.544i	0.0237393	+	0.0411177i
$834$		0			0
$835$	20538.3			0.851208
$836$		0			0
$837$	1371.35			0.0566320
$838$		0			0
$839$	3371.43	+	5839.49i	0.138730	+	0.240288i	0.927016	−	0.375021i	$-0.122365\pi$
$839$	3371.43	+	5839.49i	0.138730	+	0.240288i	−0.788286	+	0.615309i	$0.789031\pi$
$840$		0			0
$841$	10448.9	+	18098.0i	0.428426	+	0.742056i
$842$		0			0
$843$	44126.8			1.80286
$844$		0			0
$845$	−1025.20	+	1775.69i	−0.0417371	+	0.0722908i
$846$		0			0
$847$	−1254.25			−0.0508812
$848$		0			0
$849$	6106.15	−	10576.2i	0.246835	−	0.427530i
$850$		0			0
$851$	7782.59	−	13479.8i	0.313494	−	0.542988i
$852$		0			0
$853$	14559.6	+	25218.0i	0.584422	+	1.01225i	0.994947	+	0.100400i	$0.0320121\pi$
$853$	14559.6	+	25218.0i	0.584422	+	1.01225i	−0.410525	+	0.911849i	$0.634655\pi$
$854$		0			0
$855$	−33250.1	−	3465.47i	−1.32998	−	0.138616i
$856$		0			0
$857$	788.496	+	1365.72i	0.0314288	+	0.0544364i	0.881312	−	0.472535i	$-0.156661\pi$
$857$	788.496	+	1365.72i	0.0314288	+	0.0544364i	−0.849883	+	0.526971i	$0.823328\pi$
$858$		0			0
$859$	−9000.91	+	15590.0i	−0.357517	+	0.619237i	−0.987545	−	0.157335i	$-0.949710\pi$
$859$	−9000.91	+	15590.0i	−0.357517	+	0.619237i	0.630028	+	0.776572i	$0.283043\pi$
$860$		0			0
$861$	270.311	−	468.193i	0.0106994	−	0.0185319i
$862$		0			0
$863$	23042.8			0.908906			0.454453	−	0.890771i	$-0.349835\pi$
$863$	23042.8			0.908906			0.454453	+	0.890771i	$0.349835\pi$
$864$		0			0
$865$	−1235.53	+	2140.00i	−0.0485655	+	0.0841180i
$866$		0			0
$867$	36353.6			1.42403
$868$		0			0
$869$	16191.9	+	28045.1i	0.632073	+	1.09478i
$870$		0			0
$871$	−18975.4	−	32866.4i	−0.738184	−	1.27857i
$872$		0			0
$873$	−20518.5			−0.795472
$874$		0			0
$875$	−253.039			−0.00977633
$876$		0			0
$877$	7637.95	+	13229.3i	0.294088	+	0.509376i	0.974772	−	0.223201i	$-0.0716507\pi$
$877$	7637.95	+	13229.3i	0.294088	+	0.509376i	−0.680684	+	0.732577i	$0.738317\pi$
$878$		0			0
$879$	26401.0	+	45727.9i	1.01307	+	1.75468i
$880$		0			0
$881$	−18730.1			−0.716270			−0.358135	−	0.933670i	$-0.616587\pi$
$881$	−18730.1			−0.716270			−0.358135	+	0.933670i	$0.616587\pi$
$882$		0			0
$883$	−6040.26	+	10462.0i	−0.230205	+	0.398726i	−0.957868	−	0.287208i	$-0.907273\pi$
$883$	−6040.26	+	10462.0i	−0.230205	+	0.398726i	0.727664	+	0.685934i	$0.240606\pi$
$884$		0			0
$885$	−16294.7			−0.618917
$886$		0			0
$887$	−9924.03	+	17188.9i	−0.375667	+	0.650674i	−0.990427	−	0.138041i	$-0.955920\pi$
$887$	−9924.03	+	17188.9i	−0.375667	+	0.650674i	0.614760	+	0.788714i	$0.289253\pi$
$888$		0			0
$889$	−67.9321	+	117.662i	−0.00256285	+	0.00443898i
$890$		0			0
$891$	−23102.6	−	40015.0i	−0.868651	−	1.50455i
$892$		0			0
$893$	8471.95	−	11682.0i	0.317473	−	0.437765i
$894$		0			0
$895$	−3174.69	−	5498.72i	−0.118568	−	0.205365i
$896$		0			0
$897$	−18306.9	+	31708.5i	−0.681437	+	1.18028i
$898$		0			0
$899$	5462.95	−	9462.11i	0.202669	−	0.351033i
$900$		0			0
$901$	−780.277			−0.0288511
$902$		0			0
$903$	687.512	−	1190.81i	0.0253366	−	0.0438843i
$904$		0			0
$905$	6487.42			0.238286
$906$		0			0
$907$	15976.8	+	27672.6i	0.584895	+	1.01307i	0.994888	+	0.100980i	$0.0321978\pi$
$907$	15976.8	+	27672.6i	0.584895	+	1.01307i	−0.409993	+	0.912089i	$0.634469\pi$
$908$		0			0
$909$	−3194.77	−	5533.51i	−0.116572	−	0.201909i
$910$		0			0
$911$	−37262.5			−1.35517			−0.677585	−	0.735444i	$-0.736974\pi$
$911$	−37262.5			−1.35517			−0.677585	+	0.735444i	$0.736974\pi$
$912$		0			0
$913$	−45640.6			−1.65442
$914$		0			0
$915$	−3096.76	−	5363.74i	−0.111886	−	0.193792i
$916$		0			0
$917$	−52.3626	−	90.6947i	−0.00188568	−	0.00326609i
$918$		0			0
$919$	−21349.4			−0.766325			−0.383163	−	0.923681i	$-0.625165\pi$
$919$	−21349.4			−0.766325			−0.383163	+	0.923681i	$0.625165\pi$
$920$		0			0
$921$	19152.7	−	33173.4i	0.685235	−	1.18686i
$922$		0			0
$923$	−23910.5			−0.852679
$924$		0			0
$925$	−5918.53	+	10251.2i	−0.210378	+	0.364386i
$926$		0			0
$927$	10861.6	−	18812.8i	0.384834	−	0.666552i
$928$		0			0
$929$	−6443.91	−	11161.2i	−0.227576	−	0.394173i	0.729513	−	0.683967i	$-0.239747\pi$
$929$	−6443.91	−	11161.2i	−0.227576	−	0.394173i	−0.957089	+	0.289794i	$0.906413\pi$
$930$		0			0
$931$	−28239.6	−	2943.25i	−0.994110	−	0.103610i
$932$		0			0
$933$	3073.11	+	5322.78i	0.107834	+	0.186774i
$934$		0			0
$935$	−1581.92	+	2739.97i	−0.0553309	+	0.0958359i
$936$		0			0
$937$	−3581.76	+	6203.78i	−0.124878	+	0.216295i	−0.921685	−	0.387938i	$-0.873187\pi$
$937$	−3581.76	+	6203.78i	−0.124878	+	0.216295i	0.796807	+	0.604234i	$0.206521\pi$
$938$		0			0
$939$	−25679.1			−0.892445
$940$		0			0
$941$	27824.9	−	48194.2i	0.963939	−	1.66959i	0.251501	−	0.967857i	$-0.419076\pi$
$941$	27824.9	−	48194.2i	0.963939	−	1.66959i	0.712438	−	0.701735i	$-0.247591\pi$
$942$		0			0
$943$	19076.3			0.658758
$944$		0			0
$945$	22.2486	+	38.5357i	0.000765870	+	0.00132653i
$946$		0			0
$947$	14281.7	+	24736.6i	0.490066	+	0.848819i	0.999935	−	0.0114331i	$-0.00363936\pi$
$947$	14281.7	+	24736.6i	0.490066	+	0.848819i	−0.509869	+	0.860252i	$0.670306\pi$
$948$		0			0
$949$	9949.72			0.340339
$950$		0			0
$951$	33419.0			1.13952
$952$		0			0
$953$	24971.8	+	43252.4i	0.848809	+	1.47018i	0.882272	+	0.470740i	$0.156013\pi$
$953$	24971.8	+	43252.4i	0.848809	+	1.47018i	−0.0334634	+	0.999440i	$0.510654\pi$
$954$		0			0
$955$	20838.3	+	36093.0i	0.706086	+	1.22298i
$956$		0			0
$957$	28883.1			0.975610
$958$		0			0
$959$	−409.515	+	709.300i	−0.0137893	+	0.0238837i
$960$		0			0
$961$	4401.96			0.147761
$962$		0			0
$963$	−8247.87	+	14285.7i	−0.275996	+	0.478039i
$964$		0			0
$965$	−25739.8	+	44582.7i	−0.858647	+	1.48722i
$966$		0			0
$967$	18013.0	+	31199.4i	0.599026	+	1.03754i	0.992965	+	0.118407i	$0.0377789\pi$
$967$	18013.0	+	31199.4i	0.599026	+	1.03754i	−0.393939	+	0.919137i	$0.628888\pi$
$968$		0			0
$969$	1200.60	−	1655.52i	0.0398029	−	0.0548844i
$970$		0			0
$971$	437.731	+	758.172i	0.0144670	+	0.0250576i	0.873168	−	0.487419i	$-0.162062\pi$
$971$	437.731	+	758.172i	0.0144670	+	0.0250576i	−0.858701	+	0.512476i	$0.828728\pi$
$972$		0			0
$973$	194.047	−	336.099i	0.00639347	−	0.0110738i
$974$		0			0
$975$	13922.1	−	24113.7i	0.457296	−	0.792059i
$976$		0			0
$977$	5586.26			0.182928			0.0914638	−	0.995808i	$-0.470845\pi$
$977$	5586.26			0.182928			0.0914638	+	0.995808i	$0.470845\pi$
$978$		0			0
$979$	27264.6	−	47223.6i	0.890071	−	1.54165i
$980$		0			0
$981$	44191.5			1.43825
$982$		0			0
$983$	2785.74	+	4825.05i	0.0903880	+	0.156557i	0.907674	−	0.419675i	$-0.137856\pi$
$983$	2785.74	+	4825.05i	0.0903880	+	0.156557i	−0.817286	+	0.576232i	$0.804523\pi$
$984$		0			0
$985$	19059.2	+	33011.6i	0.616526	+	1.06785i
$986$		0			0
$987$	−537.820			−0.0173445
$988$		0			0
$989$	48518.8			1.55997
$990$		0			0
$991$	−3647.50	−	6317.65i	−0.116919	−	0.202509i	0.801626	−	0.597825i	$-0.203968\pi$
$991$	−3647.50	−	6317.65i	−0.116919	−	0.202509i	−0.918545	+	0.395316i	$0.870635\pi$
$992$		0			0
$993$	21010.1	+	36390.5i	0.671434	+	1.16296i
$994$		0			0
$995$	−62897.9			−2.00402
$996$		0			0
$997$	4690.97	−	8124.99i	0.149011	−	0.258095i	−0.781851	−	0.623465i	$-0.785724\pi$
$997$	4690.97	−	8124.99i	0.149011	−	0.258095i	0.930862	+	0.365370i	$0.119058\pi$
$998$		0			0
$999$	−1059.87			−0.0335665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.4.i.c.273.2		4
4.3	odd	2		19.4.c.a.7.1	✓	4
12.11	even	2		171.4.f.e.64.1		4
19.11	even	3	inner	304.4.i.c.49.2		4
76.7	odd	6		361.4.a.g.1.2		2
76.11	odd	6		19.4.c.a.11.1	yes	4
76.31	even	6		361.4.a.d.1.1		2
228.11	even	6		171.4.f.e.163.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.4.c.a.7.1	✓	4	4.3	odd	2
19.4.c.a.11.1	yes	4	76.11	odd	6
171.4.f.e.64.1		4	12.11	even	2
171.4.f.e.163.1		4	228.11	even	6
304.4.i.c.49.2		4	19.11	even	3	inner
304.4.i.c.273.2		4	1.1	even	1	trivial
361.4.a.d.1.1		2	76.31	even	6
361.4.a.g.1.2		2	76.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	304.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.70810 + 6.42262i) q^{3} +(7.20810 + 12.4848i) q^{5} -0.416198 q^{7} +(-14.0000 + 24.2487i) q^{9} +O(q^{10})\)	\(q+(3.70810 + 6.42262i) q^{3} +(7.20810 + 12.4848i) q^{5} -0.416198 q^{7} +(-14.0000 + 24.2487i) q^{9} -65.9134 q^{11} +(-22.6648 + 39.2566i) q^{13} +(-53.4567 + 92.5897i) q^{15} +(-1.66479 - 2.88351i) q^{17} +(82.3729 + 8.58525i) q^{19} +(-1.54331 - 2.67308i) q^{21} +(54.4567 - 94.3218i) q^{23} +(-41.4134 + 71.7301i) q^{25} -7.41620 q^{27} +(-29.5433 + 51.1705i) q^{29} -184.913 q^{31} +(-244.413 - 423.336i) q^{33} +(-3.00000 - 5.19615i) q^{35} +142.913 q^{37} -336.173 q^{39} +(87.5754 + 151.685i) q^{41} +(222.740 + 385.797i) q^{43} -403.654 q^{45} +(87.1215 - 150.899i) q^{47} -342.827 q^{49} +(12.3464 - 21.3847i) q^{51} +(117.173 - 202.950i) q^{53} +(-475.110 - 822.915i) q^{55} +(250.307 + 560.884i) q^{57} +(76.2053 + 131.991i) q^{59} +(-28.9651 + 50.1691i) q^{61} +(5.82678 - 10.0923i) q^{63} -653.480 q^{65} +(-418.610 + 725.054i) q^{67} +807.723 q^{69} +(263.740 + 456.811i) q^{71} +(-109.749 - 190.090i) q^{73} -614.260 q^{75} +27.4331 q^{77} +(-245.654 - 425.484i) q^{79} +(350.500 + 607.084i) q^{81} +692.433 q^{83} +(24.0000 - 41.5692i) q^{85} -438.198 q^{87} +(-413.642 + 716.450i) q^{89} +(9.43305 - 16.3385i) q^{91} +(-685.677 - 1187.63i) q^{93} +(486.567 + 1090.29i) q^{95} +(366.402 + 634.627i) q^{97} +(922.787 - 1598.31i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 14 q^{5} + 28 q^{7} - 56 q^{9}+O(q^{10}) \) 4 * q + 14 * q^5 + 28 * q^7 - 56 * q^9	\( 4 q + 14 q^{5} + 28 q^{7} - 56 q^{9} - 56 q^{11} + 28 q^{13} - 110 q^{15} + 112 q^{17} + 196 q^{19} - 110 q^{21} + 114 q^{23} + 42 q^{25} - 222 q^{29} - 532 q^{31} - 770 q^{33} - 12 q^{35} + 364 q^{37} - 1760 q^{39} - 154 q^{41} + 268 q^{43} - 784 q^{45} + 126 q^{47} - 956 q^{49} + 880 q^{51} + 884 q^{53} - 966 q^{55} - 660 q^{57} + 112 q^{59} - 546 q^{61} - 392 q^{63} - 1368 q^{65} - 740 q^{67} + 1540 q^{69} + 432 q^{71} - 350 q^{73} - 3080 q^{75} + 1148 q^{77} - 152 q^{79} + 1402 q^{81} + 3808 q^{83} + 96 q^{85} + 1540 q^{87} - 112 q^{89} + 1076 q^{91} - 770 q^{93} + 908 q^{95} + 546 q^{97} + 784 q^{99}+O(q^{100}) \) 4 * q + 14 * q^5 + 28 * q^7 - 56 * q^9 - 56 * q^11 + 28 * q^13 - 110 * q^15 + 112 * q^17 + 196 * q^19 - 110 * q^21 + 114 * q^23 + 42 * q^25 - 222 * q^29 - 532 * q^31 - 770 * q^33 - 12 * q^35 + 364 * q^37 - 1760 * q^39 - 154 * q^41 + 268 * q^43 - 784 * q^45 + 126 * q^47 - 956 * q^49 + 880 * q^51 + 884 * q^53 - 966 * q^55 - 660 * q^57 + 112 * q^59 - 546 * q^61 - 392 * q^63 - 1368 * q^65 - 740 * q^67 + 1540 * q^69 + 432 * q^71 - 350 * q^73 - 3080 * q^75 + 1148 * q^77 - 152 * q^79 + 1402 * q^81 + 3808 * q^83 + 96 * q^85 + 1540 * q^87 - 112 * q^89 + 1076 * q^91 - 770 * q^93 + 908 * q^95 + 546 * q^97 + 784 * q^99

Introduction

L-functions

Modular forms

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Database

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