LMFDB - Embedded newform 304.5.r.c.145.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,5,Mod(65,304)]

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, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("304.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	304.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$31.4244687775$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 1024 x^{14} - 7028 x^{13} + 404698 x^{12} - 2337188 x^{11} + 77836288 x^{10} + \cdots + 23840536514409 $ x^16 - 8x^15 + 1024x^14 - 7028x^13 + 404698x^12 - 2337188x^11 + 77836288x^10 - 367923764x^9 + 7565874847x^8 - 28081380444x^7 + 352870494000x^6 - 961846520868x^5 + 6856327325898x^4 - 12141615583188x^3 + 32749209391860x^2 - 26834137576128*x + 23840536514409
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.5
Root			$0.500000 - 2.12625i$ of defining polynomial
Character	$\chi$	$=$	304.145
Dual form			304.5.r.c.65.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36664 - 0.789030i) q^{3} +(11.3097 + 19.5890i) q^{5} +73.1169 q^{7} +(-39.2549 + 67.9914i) q^{9} +O(q^{10})$	\(q+(1.36664 - 0.789030i) q^{3} +(11.3097 + 19.5890i) q^{5} +73.1169 q^{7} +(-39.2549 + 67.9914i) q^{9} +110.621 q^{11} +(-23.5523 - 13.5979i) q^{13} +(30.9126 + 17.8474i) q^{15} +(156.828 + 271.635i) q^{17} +(-56.4250 - 356.563i) q^{19} +(99.9244 - 57.6914i) q^{21} +(-439.502 + 761.239i) q^{23} +(56.6806 - 98.1737i) q^{25} +251.716i q^{27} +(-377.728 - 218.081i) q^{29} -1478.96i q^{31} +(151.179 - 87.2831i) q^{33} +(826.931 + 1432.29i) q^{35} +1501.33i q^{37} -42.9167 q^{39} +(-191.992 + 110.847i) q^{41} +(645.877 + 1118.69i) q^{43} -1775.85 q^{45} +(-870.891 + 1508.43i) q^{47} +2945.08 q^{49} +(428.656 + 247.484i) q^{51} +(3592.31 + 2074.02i) q^{53} +(1251.09 + 2166.95i) q^{55} +(-358.451 - 442.772i) q^{57} +(2018.50 - 1165.38i) q^{59} +(-842.159 + 1458.66i) q^{61} +(-2870.19 + 4971.32i) q^{63} -615.155i q^{65} +(-405.677 - 234.218i) q^{67} +1387.12i q^{69} +(-1065.87 + 615.378i) q^{71} +(2173.25 + 3764.18i) q^{73} -178.891i q^{75} +8088.25 q^{77} +(9607.24 - 5546.74i) q^{79} +(-2981.03 - 5163.30i) q^{81} +2902.91 q^{83} +(-3547.37 + 6144.22i) q^{85} -688.290 q^{87} +(415.977 + 240.164i) q^{89} +(-1722.07 - 994.239i) q^{91} +(-1166.94 - 2021.20i) q^{93} +(6346.56 - 5137.94i) q^{95} +(-15206.7 + 8779.57i) q^{97} +(-4342.40 + 7521.26i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9}+O(q^{10}) $ 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9	$ 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9} + 84 q^{11} + 450 q^{13} + 390 q^{15} + 606 q^{17} + 306 q^{19} - 2160 q^{21} + 54 q^{23} - 434 q^{25} - 4914 q^{29} + 7890 q^{33} - 2328 q^{35} - 7620 q^{39} - 1692 q^{41} + 7402 q^{43} - 16720 q^{45} - 3198 q^{47} + 24816 q^{49} - 10710 q^{51} + 3870 q^{53} + 13588 q^{55} + 3702 q^{57} + 18288 q^{59} - 6522 q^{61} + 15676 q^{63} + 30168 q^{67} - 35874 q^{71} - 8080 q^{73} + 34560 q^{77} + 30738 q^{79} - 30920 q^{81} + 1476 q^{83} + 33626 q^{85} - 113100 q^{87} + 19782 q^{89} + 34260 q^{91} - 4272 q^{93} + 23706 q^{95} - 9936 q^{97} - 3848 q^{99}+O(q^{100}) $ 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9 + 84 * q^11 + 450 * q^13 + 390 * q^15 + 606 * q^17 + 306 * q^19 - 2160 * q^21 + 54 * q^23 - 434 * q^25 - 4914 * q^29 + 7890 * q^33 - 2328 * q^35 - 7620 * q^39 - 1692 * q^41 + 7402 * q^43 - 16720 * q^45 - 3198 * q^47 + 24816 * q^49 - 10710 * q^51 + 3870 * q^53 + 13588 * q^55 + 3702 * q^57 + 18288 * q^59 - 6522 * q^61 + 15676 * q^63 + 30168 * q^67 - 35874 * q^71 - 8080 * q^73 + 34560 * q^77 + 30738 * q^79 - 30920 * q^81 + 1476 * q^83 + 33626 * q^85 - 113100 * q^87 + 19782 * q^89 + 34260 * q^91 - 4272 * q^93 + 23706 * q^95 - 9936 * q^97 - 3848 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	1.36664	−	0.789030i	0.151849	−	0.0876700i	−0.422150	−	0.906526i	$-0.638725\pi$
$3$	1.36664	−	0.789030i	0.151849	−	0.0876700i	0.573999	+	0.818856i	$0.305391\pi$
$4$		0			0
$5$	11.3097	+	19.5890i	0.452389	+	0.783560i	0.998534	−	0.0541304i	$-0.0172387\pi$
$5$	11.3097	+	19.5890i	0.452389	+	0.783560i	−0.546145	+	0.837691i	$0.683905\pi$
$6$		0			0
$7$	73.1169			1.49218			0.746091	−	0.665844i	$-0.231929\pi$
$7$	73.1169			1.49218			0.746091	+	0.665844i	$0.231929\pi$
$8$		0			0
$9$	−39.2549	+	67.9914i	−0.484628	+	0.839400i
$10$		0			0
$11$	110.621			0.914221			0.457111	−	0.889410i	$-0.348884\pi$
$11$	110.621			0.914221			0.457111	+	0.889410i	$0.348884\pi$
$12$		0			0
$13$	−23.5523	−	13.5979i	−0.139363	−	0.0804612i	0.428697	−	0.903448i	$-0.358973\pi$
$13$	−23.5523	−	13.5979i	−0.139363	−	0.0804612i	−0.568060	+	0.822987i	$0.692306\pi$
$14$		0			0
$15$	30.9126	+	17.8474i	0.137389	+	0.0793218i
$16$		0			0
$17$	156.828	+	271.635i	0.542659	+	0.939912i	0.998750	+	0.0499796i	$0.0159156\pi$
$17$	156.828	+	271.635i	0.542659	+	0.939912i	−0.456092	+	0.889933i	$0.650751\pi$
$18$		0			0
$19$	−56.4250	−	356.563i	−0.156302	−	0.987709i
$19$	−56.4250	−	356.563i	−0.156302	−	0.987709i
$20$		0			0
$21$	99.9244	−	57.6914i	0.226586	−	0.130819i
$22$		0			0
$23$	−439.502	+	761.239i	−0.830816	+	1.43902i	0.0665762	+	0.997781i	$0.478792\pi$
$23$	−439.502	+	761.239i	−0.830816	+	1.43902i	−0.897392	+	0.441234i	$0.854541\pi$
$24$		0			0
$25$	56.6806	−	98.1737i	0.0906890	−	0.157078i
$26$		0			0
$27$			251.716i			0.345289i
$28$		0			0
$29$	−377.728	−	218.081i	−0.449141	−	0.259312i	0.258326	−	0.966058i	$-0.416829\pi$
$29$	−377.728	−	218.081i	−0.449141	−	0.259312i	−0.707467	+	0.706746i	$0.750162\pi$
$30$		0			0
$31$		−	1478.96i		−	1.53898i	−0.638661	−	0.769488i	$-0.720512\pi$
$31$		−	1478.96i		−	1.53898i	0.638661	−	0.769488i	$-0.279488\pi$
$32$		0			0
$33$	151.179	−	87.2831i	0.138823	−	0.0801497i
$34$		0			0
$35$	826.931	+	1432.29i	0.675046	+	1.16921i
$36$		0			0
$37$			1501.33i			1.09666i	0.836262	+	0.548330i	$0.184736\pi$
$37$			1501.33i			1.09666i	−0.836262	+	0.548330i	$0.815264\pi$
$38$		0			0
$39$	−42.9167			−0.0282161
$40$		0			0
$41$	−191.992	+	110.847i	−0.114213	+	0.0659410i	−0.556018	−	0.831170i	$-0.687672\pi$
$41$	−191.992	+	110.847i	−0.114213	+	0.0659410i	0.441805	+	0.897111i	$0.354338\pi$
$42$		0			0
$43$	645.877	+	1118.69i	0.349312	+	0.605026i	0.986127	−	0.165991i	$-0.0530821\pi$
$43$	645.877	+	1118.69i	0.349312	+	0.605026i	−0.636816	+	0.771016i	$0.719749\pi$
$44$		0			0
$45$	−1775.85			−0.876961
$46$		0			0
$47$	−870.891	+	1508.43i	−0.394247	+	0.682855i	−0.993005	−	0.118075i	$-0.962328\pi$
$47$	−870.891	+	1508.43i	−0.394247	+	0.682855i	0.598758	+	0.800930i	$0.295661\pi$
$48$		0			0
$49$	2945.08			1.22660
$50$		0			0
$51$	428.656	+	247.484i	0.164804	+	0.0951497i
$52$		0			0
$53$	3592.31	+	2074.02i	1.27886	+	0.738349i	0.976638	−	0.214890i	$-0.0689392\pi$
$53$	3592.31	+	2074.02i	1.27886	+	0.738349i	0.302219	+	0.953238i	$0.402273\pi$
$54$		0			0
$55$	1251.09	+	2166.95i	0.413583	+	0.716347i
$56$		0			0
$57$	−358.451	−	442.772i	−0.110327	−	0.136280i
$58$		0			0
$59$	2018.50	−	1165.38i	0.579863	−	0.334784i	−0.181216	−	0.983443i	$-0.558003\pi$
$59$	2018.50	−	1165.38i	0.579863	−	0.334784i	0.761079	+	0.648659i	$0.224670\pi$
$60$		0			0
$61$	−842.159	+	1458.66i	−0.226326	+	0.392008i	−0.956716	−	0.291022i	$-0.906005\pi$
$61$	−842.159	+	1458.66i	−0.226326	+	0.392008i	0.730390	+	0.683030i	$0.239338\pi$
$62$		0			0
$63$	−2870.19	+	4971.32i	−0.723153	+	1.25254i
$64$		0			0
$65$		−	615.155i		−	0.145599i
$66$		0			0
$67$	−405.677	−	234.218i	−0.0903714	−	0.0521759i	0.454133	−	0.890934i	$-0.349949\pi$
$67$	−405.677	−	234.218i	−0.0903714	−	0.0521759i	−0.544505	+	0.838758i	$0.683282\pi$
$68$		0			0
$69$			1387.12i			0.291350i
$70$		0			0
$71$	−1065.87	+	615.378i	−0.211439	+	0.122075i	−0.601980	−	0.798511i	$-0.705621\pi$
$71$	−1065.87	+	615.378i	−0.211439	+	0.122075i	0.390541	+	0.920586i	$0.372288\pi$
$72$		0			0
$73$	2173.25	+	3764.18i	0.407816	+	0.706358i	0.994645	−	0.103353i	$-0.0329572\pi$
$73$	2173.25	+	3764.18i	0.407816	+	0.706358i	−0.586829	+	0.809711i	$0.699624\pi$
$74$		0			0
$75$		−	178.891i		−	0.0318028i
$76$		0			0
$77$	8088.25			1.36418
$78$		0			0
$79$	9607.24	−	5546.74i	1.53938	−	0.888759i	0.540500	−	0.841344i	$-0.318235\pi$
$79$	9607.24	−	5546.74i	1.53938	−	0.888759i	0.998875	−	0.0474147i	$-0.0150982\pi$
$80$		0			0
$81$	−2981.03	−	5163.30i	−0.454356	−	0.786968i
$82$		0			0
$83$	2902.91			0.421384			0.210692	−	0.977553i	$-0.432428\pi$
$83$	2902.91			0.421384			0.210692	+	0.977553i	$0.432428\pi$
$84$		0			0
$85$	−3547.37	+	6144.22i	−0.490985	+	0.850411i
$86$		0			0
$87$	−688.290			−0.0909354
$88$		0			0
$89$	415.977	+	240.164i	0.0525157	+	0.0303200i	0.526028	−	0.850467i	$-0.323681\pi$
$89$	415.977	+	240.164i	0.0525157	+	0.0303200i	−0.473512	+	0.880787i	$0.657014\pi$
$90$		0			0
$91$	−1722.07	−	994.239i	−0.207955	−	0.120063i
$92$		0			0
$93$	−1166.94	−	2021.20i	−0.134922	−	0.233692i
$94$		0			0
$95$	6346.56	−	5137.94i	0.703220	−	0.569300i
$96$		0			0
$97$	−15206.7	+	8779.57i	−1.61618	+	0.933104i	−0.628288	+	0.777981i	$0.716244\pi$
$97$	−15206.7	+	8779.57i	−1.61618	+	0.933104i	−0.987895	+	0.155123i	$0.950423\pi$
$98$		0			0
$99$	−4342.40	+	7521.26i	−0.443057	+	0.767398i
$100$		0			0
$101$	−8164.07	+	14140.6i	−0.800320	+	1.38620i	0.119085	+	0.992884i	$0.462004\pi$
$101$	−8164.07	+	14140.6i	−0.800320	+	1.38620i	−0.919405	+	0.393311i	$0.871329\pi$
$102$		0			0
$103$			2634.39i			0.248317i	0.992262	+	0.124158i	$0.0396231\pi$
$103$			2634.39i			0.248317i	−0.992262	+	0.124158i	$0.960377\pi$
$104$		0			0
$105$	2260.23	+	1304.95i	0.205010	+	0.118362i
$106$		0			0
$107$			9717.42i			0.848757i	0.905485	+	0.424379i	$0.139507\pi$
$107$			9717.42i			0.848757i	−0.905485	+	0.424379i	$0.860493\pi$
$108$		0			0
$109$	18379.5	−	10611.4i	1.54697	−	0.893142i	0.548596	−	0.836088i	$-0.315163\pi$
$109$	18379.5	−	10611.4i	1.54697	−	0.893142i	0.998371	−	0.0570541i	$-0.0181707\pi$
$110$		0			0
$111$	1184.59	+	2051.78i	0.0961442	+	0.166527i
$112$		0			0
$113$			2618.95i			0.205102i	0.994728	+	0.102551i	$0.0327005\pi$
$113$			2618.95i			0.205102i	−0.994728	+	0.102551i	$0.967300\pi$
$114$		0			0
$115$	−19882.6			−1.50341
$116$		0			0
$117$	1849.09	−	1067.57i	0.135078	−	0.0779875i
$118$		0			0
$119$	11466.8	+	19861.1i	0.809745	+	1.40252i
$120$		0			0
$121$	−2404.04			−0.164199
$122$		0			0
$123$	−174.923	+	302.975i	−0.0115621	+	0.0200261i
$124$		0			0
$125$	16701.3			1.06888
$126$		0			0
$127$	−639.877	−	369.433i	−0.0396724	−	0.0229049i	0.480033	−	0.877251i	$-0.340625\pi$
$127$	−639.877	−	369.433i	−0.0396724	−	0.0229049i	−0.519705	+	0.854346i	$0.673958\pi$
$128$		0			0
$129$	1765.36	+	1019.23i	0.106085	+	0.0612483i
$130$		0			0
$131$	−15992.5	−	27699.9i	−0.931911	−	1.61412i	−0.780052	−	0.625715i	$-0.784807\pi$
$131$	−15992.5	−	27699.9i	−0.931911	−	1.61412i	−0.151859	−	0.988402i	$-0.548526\pi$
$132$		0			0
$133$	−4125.62	−	26070.8i	−0.233231	−	1.47384i
$134$		0			0
$135$	−4930.86	+	2846.83i	−0.270555	+	0.156205i
$136$		0			0
$137$	11363.7	−	19682.5i	0.605451	−	1.04867i	−0.386529	−	0.922277i	$-0.626326\pi$
$137$	11363.7	−	19682.5i	0.605451	−	1.04867i	0.991980	−	0.126394i	$-0.0403405\pi$
$138$		0			0
$139$	−2923.30	+	5063.31i	−0.151302	+	0.262063i	−0.931706	−	0.363212i	$-0.881680\pi$
$139$	−2923.30	+	5063.31i	−0.151302	+	0.262063i	0.780404	+	0.625275i	$0.215013\pi$
$140$		0			0
$141$			2748.63i			0.138254i
$142$		0			0
$143$	−2605.38	−	1504.21i	−0.127408	−	0.0735593i
$144$		0			0
$145$		−	9865.75i		−	0.469239i
$146$		0			0
$147$	4024.86	−	2323.75i	0.186258	−	0.107536i
$148$		0			0
$149$	−1425.65	−	2469.30i	−0.0642156	−	0.111225i	0.832130	−	0.554580i	$-0.187121\pi$
$149$	−1425.65	−	2469.30i	−0.0642156	−	0.111225i	−0.896346	+	0.443356i	$0.853788\pi$
$150$		0			0
$151$		−	32911.8i		−	1.44344i	−0.692186	−	0.721719i	$-0.743352\pi$
$151$		−	32911.8i		−	1.44344i	0.692186	−	0.721719i	$-0.256648\pi$
$152$		0			0
$153$	−24625.1			−1.05195
$154$		0			0
$155$	28971.3	−	16726.6i	1.20588	−	0.696215i
$156$		0			0
$157$	−18066.0	−	31291.1i	−0.732928	−	1.26947i	−0.955626	−	0.294582i	$-0.904820\pi$
$157$	−18066.0	−	31291.1i	−0.732928	−	1.26947i	0.222698	−	0.974887i	$-0.428514\pi$
$158$		0			0
$159$	6545.86			0.258924
$160$		0			0
$161$	−32135.0	+	55659.4i	−1.23973	+	2.14727i
$162$		0			0
$163$	2482.60			0.0934396			0.0467198	−	0.998908i	$-0.485123\pi$
$163$	2482.60			0.0934396			0.0467198	+	0.998908i	$0.485123\pi$
$164$		0			0
$165$	3419.58	+	1974.29i	0.125604	+	0.0725177i
$166$		0			0
$167$	−31474.9	−	18172.0i	−1.12858	−	0.651584i	−0.185001	−	0.982738i	$-0.559229\pi$
$167$	−31474.9	−	18172.0i	−1.12858	−	0.651584i	−0.943577	+	0.331154i	$0.892562\pi$
$168$		0			0
$169$	−13910.7	−	24094.0i	−0.487052	−	0.843599i
$170$		0			0
$171$	26458.2	+	10160.4i	0.904832	+	0.347472i
$172$		0			0
$173$	47488.4	−	27417.5i	1.58670	−	0.916083i	0.592857	−	0.805307i	$-0.298000\pi$
$173$	47488.4	−	27417.5i	1.58670	−	0.916083i	0.993845	−	0.110776i	$-0.0353335\pi$
$174$		0			0
$175$	4144.31	−	7178.16i	0.135324	−	0.234389i
$176$		0			0
$177$	1839.04	−	3185.32i	0.0587010	−	0.101673i
$178$		0			0
$179$		−	18328.9i		−	0.572046i	−0.958223	−	0.286023i	$-0.907667\pi$
$179$		−	18328.9i		−	0.572046i	0.958223	−	0.286023i	$-0.0923333\pi$
$180$		0			0
$181$	36497.0	+	21071.6i	1.11404	+	0.643191i	0.939873	−	0.341525i	$-0.110943\pi$
$181$	36497.0	+	21071.6i	1.11404	+	0.643191i	0.174167	+	0.984716i	$0.444277\pi$
$182$		0			0
$183$			2657.95i			0.0793680i
$184$		0			0
$185$	−29409.5	+	16979.6i	−0.859300	+	0.496117i
$186$		0			0
$187$	17348.5	+	30048.4i	0.496110	+	0.859288i
$188$		0			0
$189$			18404.7i			0.515234i
$190$		0			0
$191$	−56894.2			−1.55956			−0.779778	−	0.626056i	$-0.784668\pi$
$191$	−56894.2			−1.55956			−0.779778	+	0.626056i	$0.784668\pi$
$192$		0			0
$193$	−29436.7	+	16995.3i	−0.790270	+	0.456262i	−0.840057	−	0.542497i	$-0.817479\pi$
$193$	−29436.7	+	16995.3i	−0.790270	+	0.456262i	0.0497879	+	0.998760i	$0.484145\pi$
$194$		0			0
$195$	−485.376	−	840.695i	−0.0127646	−	0.0221090i
$196$		0			0
$197$	−31473.2			−0.810978			−0.405489	−	0.914100i	$-0.632899\pi$
$197$	−31473.2			−0.810978			−0.405489	+	0.914100i	$0.632899\pi$
$198$		0			0
$199$	−10860.1	+	18810.3i	−0.274239	+	0.474996i	−0.969943	−	0.243333i	$-0.921759\pi$
$199$	−10860.1	+	18810.3i	−0.274239	+	0.474996i	0.695704	+	0.718329i	$0.255093\pi$
$200$		0			0
$201$	−739.219			−0.0182970
$202$		0			0
$203$	−27618.3	−	15945.4i	−0.670200	−	0.386940i
$204$		0			0
$205$	−4342.76	−	2507.29i	−0.103337	−	0.0596619i
$206$		0			0
$207$	−34505.2	−	59764.7i	−0.805273	−	1.39477i
$208$		0			0
$209$	−6241.78	−	39443.3i	−0.142895	−	0.902985i
$210$		0			0
$211$	25900.4	−	14953.6i	0.581758	−	0.335878i	−0.180074	−	0.983653i	$-0.557634\pi$
$211$	25900.4	−	14953.6i	0.581758	−	0.335878i	0.761832	+	0.647775i	$0.224300\pi$
$212$		0			0
$213$	−971.103	+	1682.00i	−0.0214045	+	0.0370738i
$214$		0			0
$215$	−14609.4	+	25304.2i	−0.316049	+	0.547413i
$216$		0			0
$217$		−	108137.i		−	2.29643i
$218$		0			0
$219$	5940.10	+	3429.52i	0.123853	+	0.0715064i
$220$		0			0
$221$		−	8530.17i		−	0.174652i
$222$		0			0
$223$	8360.67	−	4827.04i	0.168125	−	0.0970668i	−0.413577	−	0.910469i	$-0.635721\pi$
$223$	8360.67	−	4827.04i	0.168125	−	0.0970668i	0.581701	+	0.813403i	$0.302387\pi$
$224$		0			0
$225$	4449.98	+	7707.59i	0.0879009	+	0.152249i
$226$		0			0
$227$		−	38749.0i		−	0.751985i	−0.926623	−	0.375992i	$-0.877302\pi$
$227$		−	38749.0i		−	0.751985i	0.926623	−	0.375992i	$-0.122698\pi$
$228$		0			0
$229$	79418.4			1.51443			0.757217	−	0.653164i	$-0.226559\pi$
$229$	79418.4			1.51443			0.757217	+	0.653164i	$0.226559\pi$
$230$		0			0
$231$	11053.7	−	6381.87i	0.207150	−	0.119598i
$232$		0			0
$233$	−7082.83	−	12267.8i	−0.130465	−	0.225973i	0.793391	−	0.608713i	$-0.208314\pi$
$233$	−7082.83	−	12267.8i	−0.130465	−	0.225973i	−0.923856	+	0.382740i	$0.874980\pi$
$234$		0			0
$235$	−39398.1			−0.713411
$236$		0			0
$237$	8753.09	−	15160.8i	0.155835	−	0.269914i
$238$		0			0
$239$	79792.6			1.39691			0.698453	−	0.715656i	$-0.253872\pi$
$239$	79792.6			1.39691			0.698453	+	0.715656i	$0.253872\pi$
$240$		0			0
$241$	−70993.6	−	40988.2i	−1.22232	−	0.705707i	−0.256908	−	0.966436i	$-0.582704\pi$
$241$	−70993.6	−	40988.2i	−1.22232	−	0.705707i	−0.965412	+	0.260729i	$0.916037\pi$
$242$		0			0
$243$	−25805.4	−	14898.7i	−0.437016	−	0.252311i
$244$		0			0
$245$	33308.0	+	57691.1i	0.554902	+	0.961119i
$246$		0			0
$247$	−3519.58	+	9165.15i	−0.0576896	+	0.150226i
$248$		0			0
$249$	3967.23	−	2290.48i	0.0639866	−	0.0369427i
$250$		0			0
$251$	2914.20	−	5047.54i	0.0462563	−	0.0801183i	−0.841970	−	0.539524i	$-0.818604\pi$
$251$	2914.20	−	5047.54i	0.0462563	−	0.0801183i	0.888227	+	0.459406i	$0.151938\pi$
$252$		0			0
$253$	−48618.0	+	84208.9i	−0.759550	+	1.31558i
$254$		0			0
$255$			11195.9i			0.172179i
$256$		0			0
$257$	−16843.2	−	9724.45i	−0.255011	−	0.147231i	0.367045	−	0.930203i	$-0.380369\pi$
$257$	−16843.2	−	9724.45i	−0.255011	−	0.147231i	−0.622057	+	0.782972i	$0.713703\pi$
$258$		0			0
$259$			109772.i			1.63642i
$260$		0			0
$261$	29655.3	−	17121.5i	0.435333	−	0.251339i
$262$		0			0
$263$	15106.9	+	26165.9i	0.218406	+	0.378290i	0.954321	−	0.298784i	$-0.0965810\pi$
$263$	15106.9	+	26165.9i	0.218406	+	0.378290i	−0.735915	+	0.677074i	$0.763248\pi$
$264$		0			0
$265$			93826.4i			1.33608i
$266$		0			0
$267$	757.987			0.0106326
$268$		0			0
$269$	22912.1	−	13228.3i	0.316636	−	0.182810i	−0.333256	−	0.942836i	$-0.608147\pi$
$269$	22912.1	−	13228.3i	0.316636	−	0.182810i	0.649892	+	0.760027i	$0.274814\pi$
$270$		0			0
$271$	−16754.7	−	29019.9i	−0.228138	−	0.395146i	0.729119	−	0.684387i	$-0.239930\pi$
$271$	−16754.7	−	29019.9i	−0.228138	−	0.395146i	−0.957256	+	0.289242i	$0.906597\pi$
$272$		0			0
$273$	−3137.93			−0.0421035
$274$		0			0
$275$	6270.05	−	10860.1i	0.0829098	−	0.143604i
$276$		0			0
$277$	57229.6			0.745866			0.372933	−	0.927858i	$-0.378352\pi$
$277$	57229.6			0.745866			0.372933	+	0.927858i	$0.378352\pi$
$278$		0			0
$279$	100556.	+	58056.2i	1.29182	+	0.745831i
$280$		0			0
$281$	18804.7	+	10856.9i	0.238151	+	0.137497i	0.614327	−	0.789052i	$-0.289428\pi$
$281$	18804.7	+	10856.9i	0.238151	+	0.137497i	−0.376175	+	0.926548i	$0.622761\pi$
$282$		0			0
$283$	23029.3	+	39887.9i	0.287546	+	0.498044i	0.973223	−	0.229861i	$-0.0738272\pi$
$283$	23029.3	+	39887.9i	0.287546	+	0.498044i	−0.685677	+	0.727906i	$0.740494\pi$
$284$		0			0
$285$	4619.48	−	12029.3i	0.0568726	−	0.148099i
$286$		0			0
$287$	−14037.9	+	8104.77i	−0.170427	+	0.0983959i
$288$		0			0
$289$	−7429.77	+	12868.7i	−0.0889569	+	0.154078i
$290$		0			0
$291$	−13854.7	+	23997.0i	−0.163610	+	0.283381i
$292$		0			0
$293$		−	20842.9i		−	0.242785i	−0.992605	−	0.121393i	$-0.961264\pi$
$293$		−	20842.9i		−	0.242785i	0.992605	−	0.121393i	$-0.0387360\pi$
$294$		0			0
$295$	45657.4	+	26360.3i	0.524647	+	0.302905i
$296$		0			0
$297$			27845.0i			0.315671i
$298$		0			0
$299$	20702.6	−	11952.6i	0.231570	−	0.133697i
$300$		0			0
$301$	47224.5	+	81795.3i	0.521236	+	0.902808i
$302$		0			0
$303$			25766.8i			0.280656i
$304$		0			0
$305$	−38098.3			−0.409549
$306$		0			0
$307$	−84702.8	+	48903.2i	−0.898713	+	0.518872i	−0.876782	−	0.480888i	$-0.840315\pi$
$307$	−84702.8	+	48903.2i	−0.898713	+	0.518872i	−0.0219303	+	0.999760i	$0.506981\pi$
$308$		0			0
$309$	2078.61	+	3600.26i	0.0217699	+	0.0377066i
$310$		0			0
$311$	−3668.66			−0.0379303			−0.0189652	−	0.999820i	$-0.506037\pi$
$311$	−3668.66			−0.0379303			−0.0189652	+	0.999820i	$0.506037\pi$
$312$		0			0
$313$	47390.1	−	82082.1i	0.483726	−	0.837838i	−0.516099	−	0.856529i	$-0.672616\pi$
$313$	47390.1	−	82082.1i	0.483726	−	0.837838i	0.999825	+	0.0186908i	$0.00594981\pi$
$314$		0			0
$315$	−129844.			−1.30858
$316$		0			0
$317$	161263.	+	93105.1i	1.60478	+	0.926520i	0.990513	+	0.137422i	$0.0438818\pi$
$317$	161263.	+	93105.1i	1.60478	+	0.926520i	0.614268	+	0.789098i	$0.289452\pi$
$318$		0			0
$319$	−41784.5	−	24124.3i	−0.410614	−	0.237068i
$320$		0			0
$321$	7667.33	+	13280.2i	0.0744105	+	0.128883i
$322$		0			0
$323$	88005.9	−	71246.2i	0.843542	−	0.682899i
$324$		0			0
$325$	−2669.92	+	1541.48i	−0.0252773	+	0.0145939i
$326$		0			0
$327$	16745.4	−	29004.0i	0.156603	−	0.271245i
$328$		0			0
$329$	−63676.8	+	110291.i	−0.588287	+	1.01894i
$330$		0			0
$331$		−	75616.7i		−	0.690179i	−0.938570	−	0.345089i	$-0.887849\pi$
$331$		−	75616.7i		−	0.690179i	0.938570	−	0.345089i	$-0.112151\pi$
$332$		0			0
$333$	−102077.	−	58934.5i	−0.920538	−	0.531473i
$334$		0			0
$335$		−	10595.7i		−	0.0944152i
$336$		0			0
$337$	−134676.	+	77755.2i	−1.18585	+	0.684651i	−0.957361	−	0.288895i	$-0.906712\pi$
$337$	−134676.	+	77755.2i	−1.18585	+	0.684651i	−0.228490	+	0.973546i	$0.573379\pi$
$338$		0			0
$339$	2066.43	+	3579.15i	0.0179813	+	0.0311445i
$340$		0			0
$341$		−	163603.i		−	1.40696i
$342$		0			0
$343$	39781.3			0.338135
$344$		0			0
$345$	−27172.3	+	15687.9i	−0.228291	+	0.131804i
$346$		0			0
$347$	41732.7	+	72283.1i	0.346591	+	0.600313i	0.985641	−	0.168852i	$-0.0540058\pi$
$347$	41732.7	+	72283.1i	0.346591	+	0.600313i	−0.639050	+	0.769165i	$0.720673\pi$
$348$		0			0
$349$	30334.2			0.249047			0.124524	−	0.992217i	$-0.460260\pi$
$349$	30334.2			0.249047			0.124524	+	0.992217i	$0.460260\pi$
$350$		0			0
$351$	3422.82	−	5928.49i	0.0277824	−	0.0481205i
$352$		0			0
$353$	18838.1			0.151177			0.0755887	−	0.997139i	$-0.475916\pi$
$353$	18838.1			0.151177			0.0755887	+	0.997139i	$0.475916\pi$
$354$		0			0
$355$	−24109.3	−	13919.5i	−0.191305	−	0.110450i
$356$		0			0
$357$	31342.0	+	18095.3i	0.245918	+	0.141981i
$358$		0			0
$359$	91651.5	+	158745.i	0.711133	+	1.23172i	0.964432	+	0.264330i	$0.0851509\pi$
$359$	91651.5	+	158745.i	0.711133	+	1.23172i	−0.253299	+	0.967388i	$0.581516\pi$
$360$		0			0
$361$	−123953.	+	40238.1i	−0.951139	+	0.308762i
$362$		0			0
$363$	−3285.46	+	1896.86i	−0.0249335	+	0.0143954i
$364$		0			0
$365$	−49157.7	+	85143.6i	−0.368983	+	0.639097i
$366$		0			0
$367$	91616.3	−	158684.i	0.680206	−	1.17815i	−0.294712	−	0.955586i	$-0.595224\pi$
$367$	91616.3	−	158684.i	0.680206	−	1.17815i	0.974918	−	0.222565i	$-0.0714431\pi$
$368$		0			0
$369$		−	17405.1i		−	0.127827i
$370$		0			0
$371$	262659.	+	151646.i	1.90829	+	1.10175i
$372$		0			0
$373$			204178.i			1.46754i	0.679395	+	0.733772i	$0.262242\pi$
$373$			204178.i			1.46754i	−0.679395	+	0.733772i	$0.737758\pi$
$374$		0			0
$375$	22824.7	−	13177.8i	0.162309	−	0.0937090i
$376$		0			0
$377$	5930.91	+	10272.6i	0.0417290	+	0.0722768i
$378$		0			0
$379$		−	115338.i		−	0.802959i	−0.915868	−	0.401479i	$-0.868496\pi$
$379$		−	115338.i		−	0.802959i	0.915868	−	0.401479i	$-0.131504\pi$
$380$		0			0
$381$	−1165.97			−0.00803228
$382$		0			0
$383$	−182138.	+	105158.i	−1.24166	+	0.716875i	−0.969433	−	0.245357i	$-0.921095\pi$
$383$	−182138.	+	105158.i	−1.24166	+	0.716875i	−0.272231	+	0.962232i	$0.587761\pi$
$384$		0			0
$385$	91475.8	+	158441.i	0.617141	+	1.06892i
$386$		0			0
$387$	−101415.			−0.677145
$388$		0			0
$389$	110736.	−	191800.i	0.731795	−	1.26751i	−0.224320	−	0.974515i	$-0.572016\pi$
$389$	110736.	−	191800.i	0.731795	−	1.26751i	0.956115	−	0.292991i	$-0.0946505\pi$
$390$		0			0
$391$	−275705.			−1.80340
$392$		0			0
$393$	−43712.0	−	25237.1i	−0.283019	−	0.163401i
$394$		0			0
$395$	217310.	+	125464.i	1.39279	+	0.804129i
$396$		0			0
$397$	52380.5	+	90725.7i	0.332345	+	0.575638i	0.982971	−	0.183760i	$-0.0588270\pi$
$397$	52380.5	+	90725.7i	0.332345	+	0.575638i	−0.650627	+	0.759398i	$0.725494\pi$
$398$		0			0
$399$	−26208.9	−	32374.1i	−0.164627	−	0.203354i
$400$		0			0
$401$	238145.	−	137493.i	1.48099	−	0.855052i	0.481226	−	0.876597i	$-0.340192\pi$
$401$	238145.	−	137493.i	1.48099	−	0.855052i	0.999768	+	0.0215447i	$0.00685841\pi$
$402$		0			0
$403$	−20110.7	+	34832.8i	−0.123828	+	0.214476i
$404$		0			0
$405$	67429.3	−	116791.i	0.411091	−	0.712031i
$406$		0			0
$407$			166078.i			1.00259i
$408$		0			0
$409$	−61205.7	−	35337.1i	−0.365886	−	0.211244i	0.305774	−	0.952104i	$-0.401085\pi$
$409$	−61205.7	−	35337.1i	−0.365886	−	0.211244i	−0.671660	+	0.740860i	$0.734418\pi$
$410$		0			0
$411$		−	35865.2i		−	0.212319i
$412$		0			0
$413$	147587.	−	85209.2i	0.865261	−	0.499559i
$414$		0			0
$415$	32831.1	+	56865.1i	0.190629	+	0.330179i
$416$		0			0
$417$			9226.30i			0.0530585i
$418$		0			0
$419$	−85946.2			−0.489552			−0.244776	−	0.969580i	$-0.578714\pi$
$419$	−85946.2			−0.489552			−0.244776	+	0.969580i	$0.578714\pi$
$420$		0			0
$421$	9110.60	−	5260.01i	0.0514023	−	0.0296771i	−0.474079	−	0.880483i	$-0.657219\pi$
$421$	9110.60	−	5260.01i	0.0514023	−	0.0296771i	0.525481	+	0.850805i	$0.323885\pi$
$422$		0			0
$423$	−68373.4	−	118426.i	−0.382126	−	0.661861i
$424$		0			0
$425$	35556.5			0.196853
$426$		0			0
$427$	−61576.1	+	106653.i	−0.337720	+	0.584947i
$428$		0			0
$429$	−4747.48			−0.0257958
$430$		0			0
$431$	115177.	+	66497.7i	0.620030	+	0.357975i	0.776881	−	0.629648i	$-0.216801\pi$
$431$	115177.	+	66497.7i	0.620030	+	0.357975i	−0.156851	+	0.987622i	$0.550134\pi$
$432$		0			0
$433$	−275126.	−	158844.i	−1.46743	−	0.847219i	−0.468092	−	0.883680i	$-0.655058\pi$
$433$	−275126.	−	158844.i	−1.46743	−	0.847219i	−0.999335	+	0.0364607i	$0.988392\pi$
$434$		0			0
$435$	−7784.36	−	13482.9i	−0.0411381	−	0.0712534i
$436$		0			0
$437$	296229.	+	113757.i	1.55119	+	0.595684i
$438$		0			0
$439$	−74815.5	+	43194.8i	−0.388207	+	0.224131i	−0.681383	−	0.731927i	$-0.738621\pi$
$439$	−74815.5	+	43194.8i	−0.388207	+	0.224131i	0.293176	+	0.956058i	$0.405288\pi$
$440$		0			0
$441$	−115609.	+	200240.i	−0.594447	+	1.02961i
$442$		0			0
$443$	130084.	−	225313.i	0.662853	−	1.14810i	−0.317009	−	0.948422i	$-0.602679\pi$
$443$	130084.	−	225313.i	0.662853	−	1.14810i	0.979863	−	0.199673i	$-0.0639881\pi$
$444$		0			0
$445$			10864.8i			0.0548656i
$446$		0			0
$447$	−3896.70	−	2249.76i	−0.0195021	−	0.0112596i
$448$		0			0
$449$		−	196506.i		−	0.974729i	−0.873199	−	0.487365i	$-0.837958\pi$
$449$		−	196506.i		−	0.974729i	0.873199	−	0.487365i	$-0.162042\pi$
$450$		0			0
$451$	−21238.3	+	12262.0i	−0.104416	+	0.0602846i
$452$		0			0
$453$	−25968.4	−	44978.6i	−0.126546	−	0.219184i
$454$		0			0
$455$		−	44978.2i		−	0.217260i
$456$		0			0
$457$	−68849.9			−0.329664			−0.164832	−	0.986322i	$-0.552708\pi$
$457$	−68849.9			−0.329664			−0.164832	+	0.986322i	$0.552708\pi$
$458$		0			0
$459$	−68374.7	+	39476.2i	−0.324542	+	0.187374i
$460$		0			0
$461$	−65996.6	−	114310.i	−0.310542	−	0.537874i	0.667938	−	0.744217i	$-0.267177\pi$
$461$	−65996.6	−	114310.i	−0.310542	−	0.537874i	−0.978480	+	0.206343i	$0.933844\pi$
$462$		0			0
$463$	35802.9			0.167015			0.0835077	−	0.996507i	$-0.473388\pi$
$463$	35802.9			0.167015			0.0835077	+	0.996507i	$0.473388\pi$
$464$		0			0
$465$	26395.5	−	45718.4i	0.122074	−	0.211439i
$466$		0			0
$467$	100470.			0.460684			0.230342	−	0.973110i	$-0.426016\pi$
$467$	100470.			0.460684			0.230342	+	0.973110i	$0.426016\pi$
$468$		0			0
$469$	−29661.8	−	17125.3i	−0.134850	−	0.0778559i
$470$		0			0
$471$	−49379.3	−	28509.1i	−0.222589	−	0.128512i
$472$		0			0
$473$	71447.4	+	123751.i	0.319348	+	0.553127i
$474$		0			0
$475$	−38203.3	−	14670.8i	−0.169322	−	0.0650228i
$476$		0			0
$477$	−282031.	+	162831.i	−1.23954	+	0.715649i
$478$		0			0
$479$	140851.	−	243960.i	0.613886	−	1.06328i	−0.376693	−	0.926338i	$-0.622939\pi$
$479$	140851.	−	243960.i	0.613886	−	1.06328i	0.990579	−	0.136943i	$-0.0437277\pi$
$480$		0			0
$481$	20415.0	−	35359.8i	0.0882386	−	0.152834i
$482$		0			0
$483$			101422.i			0.434748i
$484$		0			0
$485$	−343966.	−	198589.i	−1.46229	−	0.844251i
$486$		0			0
$487$		−	407655.i		−	1.71884i	−0.511272	−	0.859419i	$-0.670825\pi$
$487$		−	407655.i		−	1.71884i	0.511272	−	0.859419i	$-0.329175\pi$
$488$		0			0
$489$	3392.82	−	1958.84i	0.0141887	−	0.00819185i
$490$		0			0
$491$	−196558.	−	340449.i	−0.815321	−	1.41218i	−0.909097	−	0.416584i	$-0.863227\pi$
$491$	−196558.	−	340449.i	−0.815321	−	1.41218i	0.0937762	−	0.995593i	$-0.470106\pi$
$492$		0			0
$493$		−	136805.i		−	0.562871i
$494$		0			0
$495$	−196445.			−0.801736
$496$		0			0
$497$	−77932.8	+	44994.5i	−0.315506	+	0.182157i
$498$		0			0
$499$	−180801.	−	313157.i	−0.726107	−	1.25765i	−0.958517	−	0.285036i	$-0.907995\pi$
$499$	−180801.	−	313157.i	−0.726107	−	1.25765i	0.232410	−	0.972618i	$-0.425339\pi$
$500$		0			0
$501$	−57353.1			−0.228498
$502$		0			0
$503$	−57534.5	+	99652.7i	−0.227401	+	0.393870i	−0.957037	−	0.289965i	$-0.906356\pi$
$503$	−57534.5	+	99652.7i	−0.227401	+	0.393870i	0.729636	+	0.683836i	$0.239690\pi$
$504$		0			0
$505$	−369333.			−1.44822
$506$		0			0
$507$	−38021.8	−	21951.9i	−0.147917	−	0.0853997i
$508$		0			0
$509$	−5754.73	−	3322.50i	−0.0222121	−	0.0128242i	0.488853	−	0.872366i	$-0.337416\pi$
$509$	−5754.73	−	3322.50i	−0.0222121	−	0.0128242i	−0.511065	+	0.859542i	$0.670749\pi$
$510$		0			0
$511$	158901.	+	275225.i	0.608535	+	1.05401i
$512$		0			0
$513$	89752.6	−	14203.1i	0.341045	−	0.0539694i
$514$		0			0
$515$	−51605.1	+	29794.2i	−0.194571	+	0.112336i
$516$		0			0
$517$	−96338.6	+	166863.i	−0.360429	+	0.624281i
$518$		0			0
$519$	43266.4	−	74939.6i	0.160626	−	0.278212i
$520$		0			0
$521$			116139.i			0.427860i	0.976849	+	0.213930i	$0.0686264\pi$
$521$			116139.i			0.427860i	−0.976849	+	0.213930i	$0.931374\pi$
$522$		0			0
$523$	−162046.	−	93557.1i	−0.592426	−	0.342037i	0.173630	−	0.984811i	$-0.444450\pi$
$523$	−162046.	−	93557.1i	−0.592426	−	0.342037i	−0.766056	+	0.642774i	$0.777784\pi$
$524$		0			0
$525$		−	13079.9i		−	0.0474555i
$526$		0			0
$527$	401736.	−	231942.i	1.44650	−	0.835139i
$528$		0			0
$529$	−246403.	−	426782.i	−0.880510	−	1.52509i
$530$		0			0
$531$			182988.i			0.648983i
$532$		0			0
$533$	6029.15			0.0212227
$534$		0			0
$535$	−190355.	+	109901.i	−0.665052	+	0.383968i
$536$		0			0
$537$	−14462.1	−	25049.0i	−0.0501512	−	0.0868645i
$538$		0			0
$539$	325787.			1.12139
$540$		0			0
$541$	96918.4	−	167868.i	0.331140	−	0.573551i	−0.651596	−	0.758566i	$-0.725900\pi$
$541$	96918.4	−	167868.i	0.331140	−	0.573551i	0.982736	+	0.185015i	$0.0592334\pi$
$542$		0			0
$543$	66504.4			0.225554
$544$		0			0
$545$	415734.	+	240024.i	1.39966	+	0.808094i
$546$		0			0
$547$	−370085.	−	213668.i	−1.23688	−	0.714111i	−0.268422	−	0.963301i	$-0.586502\pi$
$547$	−370085.	−	213668.i	−1.23688	−	0.714111i	−0.968454	+	0.249191i	$0.919835\pi$
$548$		0			0
$549$	−66117.7	−	114519.i	−0.219368	−	0.379956i
$550$		0			0
$551$	−56446.4	+	146989.i	−0.185923	+	0.484152i
$552$		0			0
$553$	702451.	−	405561.i	2.29703	−	1.32619i
$554$		0			0
$555$	−26794.8	+	46410.0i	−0.0869891	+	0.150670i
$556$		0			0
$557$	−40691.7	+	70480.2i	−0.131158	+	0.227173i	−0.924123	−	0.382094i	$-0.875203\pi$
$557$	−40691.7	+	70480.2i	−0.131158	+	0.227173i	0.792965	+	0.609267i	$0.208536\pi$
$558$		0			0
$559$		−	35130.4i		−	0.112424i
$560$		0			0
$561$	47418.2	+	27376.9i	0.150667	+	0.0869879i
$562$		0			0
$563$			345286.i			1.08934i	0.838651	+	0.544669i	$0.183345\pi$
$563$			345286.i			1.08934i	−0.838651	+	0.544669i	$0.816655\pi$
$564$		0			0
$565$	−51302.5	+	29619.5i	−0.160710	+	0.0927857i
$566$		0			0
$567$	−217964.	−	377524.i	−0.677982	−	1.17430i
$568$		0			0
$569$			145648.i			0.449864i	0.974374	+	0.224932i	$0.0722160\pi$
$569$			145648.i			0.449864i	−0.974374	+	0.224932i	$0.927784\pi$
$570$		0			0
$571$	497452.			1.52573			0.762867	−	0.646555i	$-0.223791\pi$
$571$	497452.			1.52573			0.762867	+	0.646555i	$0.223791\pi$
$572$		0			0
$573$	−77753.8	+	44891.2i	−0.236817	+	0.136726i
$574$		0			0
$575$	49822.5	+	86295.0i	0.150692	+	0.261006i
$576$		0			0
$577$	610231.			1.83292			0.916458	−	0.400131i	$-0.131035\pi$
$577$	610231.			1.83292			0.916458	+	0.400131i	$0.131035\pi$
$578$		0			0
$579$	−26819.6	+	46452.9i	−0.0800010	+	0.138566i
$580$		0			0
$581$	212252.			0.628781
$582$		0			0
$583$	397384.	+	229430.i	1.16916	+	0.675014i
$584$		0			0
$585$	41825.3	+	24147.8i	0.122216	+	0.0705613i
$586$		0			0
$587$	−245509.	−	425234.i	−0.712511	−	1.23410i	−0.963912	−	0.266222i	$-0.914225\pi$
$587$	−245509.	−	425234.i	−0.712511	−	1.23410i	0.251401	−	0.967883i	$-0.419109\pi$
$588$		0			0
$589$	−527341.	+	83450.1i	−1.52006	+	0.240545i
$590$		0			0
$591$	−43012.6	+	24833.3i	−0.123146	+	0.0710984i
$592$		0			0
$593$	73953.0	−	128090.i	0.210303	−	0.364256i	−0.741506	−	0.670946i	$-0.765888\pi$
$593$	73953.0	−	128090.i	0.210303	−	0.364256i	0.951809	+	0.306690i	$0.0992215\pi$
$594$		0			0
$595$	−259373.	+	449246.i	−0.732639	+	1.26897i
$596$		0			0
$597$			34275.9i			0.0961700i
$598$		0			0
$599$	−360776.	−	208294.i	−1.00550	−	0.580528i	−0.0956318	−	0.995417i	$-0.530487\pi$
$599$	−360776.	−	208294.i	−1.00550	−	0.580528i	−0.909872	+	0.414889i	$0.863820\pi$
$600$		0			0
$601$		−	550321.i		−	1.52359i	−0.647821	−	0.761793i	$-0.724319\pi$
$601$		−	550321.i		−	1.52359i	0.647821	−	0.761793i	$-0.275681\pi$
$602$		0			0
$603$	31849.6	−	18388.4i	0.0875930	−	0.0505718i
$604$		0			0
$605$	−27189.1	−	47092.8i	−0.0742820	−	0.128660i
$606$		0			0
$607$			120758.i			0.327747i	0.986481	+	0.163873i	$0.0523988\pi$
$607$			120758.i			0.327747i	−0.986481	+	0.163873i	$0.947601\pi$
$608$		0			0
$609$	−50325.6			−0.135692
$610$		0			0
$611$	41023.0	−	23684.6i	0.109887	−	0.0634431i
$612$		0			0
$613$	−126804.	−	219631.i	−0.337451	−	0.584483i	0.646501	−	0.762913i	$-0.276232\pi$
$613$	−126804.	−	219631.i	−0.337451	−	0.584483i	−0.983953	+	0.178430i	$0.942898\pi$
$614$		0			0
$615$	−7913.31			−0.0209222
$616$		0			0
$617$	−194985.	+	337724.i	−0.512190	+	0.887139i	0.487710	+	0.873006i	$0.337832\pi$
$617$	−194985.	+	337724.i	−0.512190	+	0.887139i	−0.999900	+	0.0141336i	$0.995501\pi$
$618$		0			0
$619$	44794.9			0.116909			0.0584544	−	0.998290i	$-0.481383\pi$
$619$	44794.9			0.116909			0.0584544	+	0.998290i	$0.481383\pi$
$620$		0			0
$621$	−191616.	−	110629.i	−0.496876	−	0.286872i
$622$		0			0
$623$	30414.9	+	17560.1i	0.0783629	+	0.0452429i
$624$		0			0
$625$	153462.	+	265803.i	0.392862	+	0.680457i
$626$		0			0
$627$	−39652.2	−	48979.8i	−0.100863	−	0.124590i
$628$		0			0
$629$	−407813.	+	235451.i	−1.03077	+	0.595113i
$630$		0			0
$631$	−202872.	+	351384.i	−0.509521	+	0.882517i	0.490418	+	0.871487i	$0.336844\pi$
$631$	−202872.	+	351384.i	−0.509521	+	0.882517i	−0.999939	+	0.0110295i	$0.996489\pi$
$632$		0			0
$633$	23597.7	−	40872.4i	0.0588928	−	0.102005i
$634$		0			0
$635$		−	16712.7i		−	0.0414477i
$636$		0			0
$637$	−69363.4	−	40047.0i	−0.170943	−	0.0986940i
$638$		0			0
$639$		−	96626.3i		−	0.236643i
$640$		0			0
$641$	−193963.	+	111985.i	−0.472066	+	0.272547i	−0.717104	−	0.696966i	$-0.754533\pi$
$641$	−193963.	+	111985.i	−0.472066	+	0.272547i	0.245038	+	0.969513i	$0.421199\pi$
$642$		0			0
$643$	109275.	+	189270.i	0.264301	+	0.457782i	0.967380	−	0.253329i	$-0.0815255\pi$
$643$	109275.	+	189270.i	0.264301	+	0.457782i	−0.703079	+	0.711111i	$0.748192\pi$
$644$		0			0
$645$			46108.9i			0.110832i
$646$		0			0
$647$	453681.			1.08378			0.541891	−	0.840448i	$-0.317708\pi$
$647$	453681.			1.08378			0.541891	+	0.840448i	$0.317708\pi$
$648$		0			0
$649$	223288.	−	128916.i	0.530123	−	0.306067i
$650$		0			0
$651$	−85323.0	−	147784.i	−0.201328	−	0.348710i
$652$		0			0
$653$	−16725.0			−0.0392230			−0.0196115	−	0.999808i	$-0.506243\pi$
$653$	−16725.0			−0.0392230			−0.0196115	+	0.999808i	$0.506243\pi$
$654$		0			0
$655$	361742.	−	626555.i	0.843172	−	1.46042i
$656$		0			0
$657$	−341243.			−0.790556
$658$		0			0
$659$	16767.9	+	9680.94i	0.0386107	+	0.0222919i	0.519181	−	0.854664i	$-0.326237\pi$
$659$	16767.9	+	9680.94i	0.0386107	+	0.0222919i	−0.480570	+	0.876956i	$0.659570\pi$
$660$		0			0
$661$	−172732.	−	99726.9i	−0.395339	−	0.228249i	0.289132	−	0.957289i	$-0.406633\pi$
$661$	−172732.	−	99726.9i	−0.395339	−	0.228249i	−0.684471	+	0.729040i	$0.739967\pi$
$662$		0			0
$663$	−6730.55	−	11657.7i	−0.0153117	−	0.0265207i
$664$		0			0
$665$	464041.	−	375670.i	1.04933	−	0.849499i
$666$		0			0
$667$	332024.	−	191694.i	0.746307	−	0.430881i
$668$		0			0
$669$	7617.35	−	13193.6i	0.0170197	−	0.0294790i
$670$		0			0
$671$	−93160.3	+	161358.i	−0.206912	+	0.358382i
$672$		0			0
$673$			614825.i			1.35744i	0.734396	+	0.678721i	$0.237465\pi$
$673$			614825.i			1.35744i	−0.734396	+	0.678721i	$0.762535\pi$
$674$		0			0
$675$	24711.9	+	14267.4i	0.0542373	+	0.0313139i
$676$		0			0
$677$			183890.i			0.401219i	0.979671	+	0.200610i	$0.0642923\pi$
$677$			183890.i			0.401219i	−0.979671	+	0.200610i	$0.935708\pi$
$678$		0			0
$679$	−1.11186e6	+	641935.i	−2.41164	+	1.39236i
$680$		0			0
$681$	−30574.1	−	52955.9i	−0.0659265	−	0.114188i
$682$		0			0
$683$		−	314895.i		−	0.675033i	−0.941320	−	0.337516i	$-0.890413\pi$
$683$		−	314895.i		−	0.675033i	0.941320	−	0.337516i	$-0.109587\pi$
$684$		0			0
$685$	514081.			1.09560
$686$		0			0
$687$	108536.	−	62663.5i	0.229965	−	0.132770i
$688$		0			0
$689$	−56404.8	−	97696.0i	−0.118817	−	0.205797i
$690$		0			0
$691$	350514.			0.734091			0.367045	−	0.930203i	$-0.380369\pi$
$691$	350514.			0.734091			0.367045	+	0.930203i	$0.380369\pi$
$692$		0			0
$693$	−317503.	+	549931.i	−0.661122	+	1.14510i
$694$		0			0
$695$	−132247.			−0.273789
$696$		0			0
$697$	−60219.7	−	34767.8i	−0.123957	−	0.0715669i
$698$		0			0
$699$	−19359.4	−	11177.1i	−0.0396220	−	0.0228758i
$700$		0			0
$701$	−80954.3	−	140217.i	−0.164742	−	0.285341i	0.771822	−	0.635839i	$-0.219346\pi$
$701$	−80954.3	−	140217.i	−0.164742	−	0.285341i	−0.936564	+	0.350498i	$0.886012\pi$
$702$		0			0
$703$	535318.	−	84712.5i	1.08318	−	0.171410i
$704$		0			0
$705$	−53843.0	+	31086.3i	−0.108331	+	0.0625447i
$706$		0			0
$707$	−596931.	+	1.03392e6i	−1.19422	+	2.06845i
$708$		0			0
$709$	−161036.	+	278922.i	−0.320354	+	0.554869i	−0.980561	−	0.196214i	$-0.937135\pi$
$709$	−161036.	+	278922.i	−0.320354	+	0.554869i	0.660207	+	0.751084i	$0.270469\pi$
$710$		0			0
$711$			870947.i			1.72287i
$712$		0			0
$713$	1.12584e6	+	650003.i	2.21461	+	1.27861i
$714$		0			0
$715$		−	68048.9i		−	0.133110i
$716$		0			0
$717$	109048.	−	62958.7i	0.212118	−	0.122467i
$718$		0			0
$719$	18235.7	+	31585.1i	0.0352748	+	0.0610977i	0.883124	−	0.469140i	$-0.155436\pi$
$719$	18235.7	+	31585.1i	0.0352748	+	0.0610977i	−0.847849	+	0.530238i	$0.822103\pi$
$720$		0			0
$721$			192618.i			0.370533i
$722$		0			0
$723$	−129363.			−0.247477
$724$		0			0
$725$	−42819.7	+	24722.0i	−0.0814643	+	0.0470334i
$726$		0			0
$727$	−230222.	−	398756.i	−0.435590	−	0.754463i	0.561754	−	0.827304i	$-0.310127\pi$
$727$	−230222.	−	398756.i	−0.435590	−	0.754463i	−0.997344	+	0.0728410i	$0.976793\pi$
$728$		0			0
$729$	435905.			0.820232
$730$		0			0
$731$	−202584.	+	350885.i	−0.379114	+	0.656645i
$732$		0			0
$733$	66626.7			0.124005			0.0620027	−	0.998076i	$-0.480251\pi$
$733$	66626.7			0.124005			0.0620027	+	0.998076i	$0.480251\pi$
$734$		0			0
$735$	91040.0	+	52562.0i	0.168522	+	0.0972965i
$736$		0			0
$737$	−44876.3	−	25909.4i	−0.0826194	−	0.0477003i
$738$		0			0
$739$	392332.	+	679539.i	0.718398	+	1.24430i	0.961634	+	0.274335i	$0.0884576\pi$
$739$	392332.	+	679539.i	0.718398	+	1.24430i	−0.243236	+	0.969967i	$0.578209\pi$
$740$		0			0
$741$	2421.57	+	15302.5i	0.00441023	+	0.0278693i
$742$		0			0
$743$	841688.	−	485949.i	1.52466	−	0.880263i	0.525088	−	0.851048i	$-0.324032\pi$
$743$	841688.	−	485949.i	1.52466	−	0.880263i	0.999573	−	0.0292155i	$-0.00930091\pi$
$744$		0			0
$745$	32247.4	−	55854.2i	0.0581009	−	0.100634i
$746$		0			0
$747$	−113953.	+	197373.i	−0.204214	+	0.353709i
$748$		0			0
$749$			710508.i			1.26650i
$750$		0			0
$751$	−285644.	−	164917.i	−0.506460	−	0.292405i	0.224917	−	0.974378i	$-0.427789\pi$
$751$	−285644.	−	164917.i	−0.506460	−	0.292405i	−0.731377	+	0.681973i	$0.761122\pi$
$752$		0			0
$753$		−	9197.55i		−	0.0162212i
$754$		0			0
$755$	644710.	−	372223.i	1.13102	−	0.652995i
$756$		0			0
$757$	−16928.1	−	29320.4i	−0.0295404	−	0.0511656i	0.850877	−	0.525365i	$-0.176071\pi$
$757$	−16928.1	−	29320.4i	−0.0295404	−	0.0511656i	−0.880418	+	0.474199i	$0.842738\pi$
$758$		0			0
$759$			153444.i			0.266359i
$760$		0			0
$761$	247695.			0.427708			0.213854	−	0.976866i	$-0.431398\pi$
$761$	247695.			0.427708			0.213854	+	0.976866i	$0.431398\pi$
$762$		0			0
$763$	1.34385e6	−	775874.i	2.30835	−	1.33273i
$764$		0			0
$765$	−278503.	−	482381.i	−0.475890	−	0.824266i
$766$		0			0
$767$	−63387.3			−0.107749
$768$		0			0
$769$	−519701.	+	900148.i	−0.878821	+	1.52216i	−0.0261858	+	0.999657i	$0.508336\pi$
$769$	−519701.	+	900148.i	−0.878821	+	1.52216i	−0.852636	+	0.522506i	$0.824997\pi$
$770$		0			0
$771$	−30691.5			−0.0516309
$772$		0			0
$773$	429217.	+	247809.i	0.718321	+	0.414723i	0.814134	−	0.580677i	$-0.197212\pi$
$773$	429217.	+	247809.i	0.718321	+	0.414723i	−0.0958136	+	0.995399i	$0.530545\pi$
$774$		0			0
$775$	−145195.	−	83828.1i	−0.241739	−	0.139568i
$776$		0			0
$777$	86613.7	+	150019.i	0.143465	+	0.248488i
$778$		0			0
$779$	50357.0	+	62202.8i	0.0829822	+	0.102503i
$780$		0			0
$781$	−117907.	+	68073.6i	−0.193302	+	0.111603i
$782$		0			0
$783$	54894.5	−	95080.0i	0.0895375	−	0.155084i
$784$		0			0
$785$	408642.	−	707788.i	0.663137	−	1.14859i
$786$		0			0
$787$			510008.i			0.823431i	0.911312	+	0.411716i	$0.135070\pi$
$787$			510008.i			0.823431i	−0.911312	+	0.411716i	$0.864930\pi$
$788$		0			0
$789$	41291.4	+	23839.6i	0.0663293	+	0.0382952i
$790$		0			0
$791$			191489.i			0.306049i
$792$		0			0
$793$	39669.6	−	22903.3i	0.0630829	−	0.0364209i
$794$		0			0
$795$	74031.8	+	128227.i	0.117134	+	0.202883i
$796$		0			0
$797$		−	309557.i		−	0.487331i	−0.969859	−	0.243665i	$-0.921650\pi$
$797$		−	309557.i		−	0.487331i	0.969859	−	0.243665i	$-0.0783499\pi$
$798$		0			0
$799$	−546321.			−0.855765
$800$		0			0
$801$	−32658.2	+	18855.2i	−0.0509011	+	0.0293878i
$802$		0			0
$803$	240407.	+	416397.i	0.372834	+	0.645767i
$804$		0			0
$805$	−1.45375e6			−2.24336
$806$		0			0
$807$	20875.0	−	36156.6i	0.0320538	−	0.0555189i
$808$		0			0
$809$	−250646.			−0.382968			−0.191484	−	0.981496i	$-0.561330\pi$
$809$	−250646.			−0.382968			−0.191484	+	0.981496i	$0.561330\pi$
$810$		0			0
$811$	−750672.	−	433401.i	−1.14132	−	0.658943i	−0.194565	−	0.980890i	$-0.562330\pi$
$811$	−750672.	−	433401.i	−1.14132	−	0.658943i	−0.946758	+	0.321947i	$0.895663\pi$
$812$		0			0
$813$	−45795.1	−	26439.8i	−0.0692848	−	0.0400016i
$814$		0			0
$815$	28077.5	+	48631.6i	0.0422710	+	0.0732156i
$816$		0			0
$817$	362441.	−	293418.i	0.542991	−	0.439585i
$818$		0			0
$819$	135199.	−	78057.4i	0.201561	−	0.116371i
$820$		0			0
$821$	1105.17	−	1914.21i	0.00163961	−	0.00283990i	−0.865204	−	0.501419i	$-0.832811\pi$
$821$	1105.17	−	1914.21i	0.00163961	−	0.00283990i	0.866844	+	0.498579i	$0.166145\pi$
$822$		0			0
$823$	−442414.	+	766283.i	−0.653174	+	1.13133i	0.329174	+	0.944269i	$0.393230\pi$
$823$	−442414.	+	766283.i	−0.653174	+	1.13133i	−0.982348	+	0.187062i	$0.940104\pi$
$824$		0			0
$825$		−	19789.0i		−	0.0290748i
$826$		0			0
$827$	302972.	+	174921.i	0.442987	+	0.255759i	0.704864	−	0.709343i	$-0.251008\pi$
$827$	302972.	+	174921.i	0.442987	+	0.255759i	−0.261877	+	0.965101i	$0.584341\pi$
$828$		0			0
$829$			202618.i			0.294829i	0.989075	+	0.147414i	$0.0470951\pi$
$829$			202618.i			0.294829i	−0.989075	+	0.147414i	$0.952905\pi$
$830$		0			0
$831$	78212.2	−	45155.8i	0.113259	−	0.0653901i
$832$		0			0
$833$	461872.	+	799985.i	0.665628	+	1.15290i
$834$		0			0
$835$		−	822082.i		−	1.17908i
$836$		0			0
$837$	372277.			0.531392
$838$		0			0
$839$	160638.	−	92744.3i	0.228204	−	0.131754i	−0.381539	−	0.924353i	$-0.624606\pi$
$839$	160638.	−	92744.3i	0.228204	−	0.131754i	0.609743	+	0.792599i	$0.291272\pi$
$840$		0			0
$841$	−258522.	−	447773.i	−0.365515	−	0.633090i
$842$		0			0
$843$	34265.6			0.0482173
$844$		0			0
$845$	314652.	−	544993.i	0.440674	−	0.763269i
$846$		0			0
$847$	−175776.			−0.245015
$848$		0			0
$849$	62945.4	+	36341.6i	0.0873271	+	0.0504183i
$850$		0			0
$851$	−1.14287e6	−	659836.i	−1.57811	−	0.911123i
$852$		0			0
$853$	−458496.	−	794138.i	−0.630140	−	1.09143i	−0.987523	−	0.157477i	$-0.949664\pi$
$853$	−458496.	−	794138.i	−0.630140	−	1.09143i	0.357382	−	0.933958i	$-0.383669\pi$
$854$		0			0
$855$	100202.	+	633201.i	0.137071	+	0.866182i
$856$		0			0
$857$	−170476.	+	98424.4i	−0.232114	+	0.134011i	−0.611547	−	0.791208i	$-0.709452\pi$
$857$	−170476.	+	98424.4i	−0.232114	+	0.134011i	0.379433	+	0.925219i	$0.376119\pi$
$858$		0			0
$859$	−122445.	+	212081.i	−0.165942	+	0.287420i	−0.936989	−	0.349358i	$-0.886400\pi$
$859$	−122445.	+	212081.i	−0.165942	+	0.287420i	0.771048	+	0.636778i	$0.219733\pi$
$860$		0			0
$861$	−12789.8	+	22152.6i	−0.0172527	+	0.0298826i
$862$		0			0
$863$		−	598666.i		−	0.803828i	−0.915677	−	0.401914i	$-0.868345\pi$
$863$		−	598666.i		−	0.803828i	0.915677	−	0.401914i	$-0.131655\pi$
$864$		0			0
$865$	1.07416e6	+	620167.i	1.43561	+	0.828851i
$866$		0			0
$867$			23449.2i			0.0311954i
$868$		0			0
$869$	1.06276e6	−	613585.i	1.40733	−	0.812522i
$870$		0			0
$871$	6369.76	+	11032.7i	0.00839627	+	0.0145428i
$872$		0			0
$873$		−	1.37856e6i		−	1.80883i
$874$		0			0
$875$	1.22115e6			1.59497
$876$		0			0
$877$	−600243.	+	346551.i	−0.780419	+	0.450575i	−0.836579	−	0.547846i	$-0.815448\pi$
$877$	−600243.	+	346551.i	−0.780419	+	0.450575i	0.0561595	+	0.998422i	$0.482114\pi$
$878$		0			0
$879$	−16445.6	−	28484.7i	−0.0212850	−	0.0368666i
$880$		0			0
$881$	−526857.			−0.678798			−0.339399	−	0.940642i	$-0.610224\pi$
$881$	−526857.			−0.678798			−0.339399	+	0.940642i	$0.610224\pi$
$882$		0			0
$883$	−518325.	+	897765.i	−0.664784	+	1.15144i	0.314560	+	0.949238i	$0.398143\pi$
$883$	−518325.	+	897765.i	−0.664784	+	1.15144i	−0.979344	+	0.202202i	$0.935190\pi$
$884$		0			0
$885$	83196.3			0.106223
$886$		0			0
$887$	380002.	+	219394.i	0.482991	+	0.278855i	0.721662	−	0.692246i	$-0.243379\pi$
$887$	380002.	+	219394.i	0.482991	+	0.278855i	−0.238671	+	0.971100i	$0.576712\pi$
$888$		0			0
$889$	−46785.8	−	27011.8i	−0.0591985	−	0.0341783i
$890$		0			0
$891$	−329764.	−	571168.i	−0.415382	−	0.719463i
$892$		0			0
$893$	586989.	+	225414.i	0.736084	+	0.282669i
$894$		0			0
$895$	359045.	−	207295.i	0.448232	−	0.258787i
$896$		0			0
$897$	18862.0	−	32669.9i	0.0234424	−	0.0406034i
$898$		0			0
$899$	−322532.	+	558642.i	−0.399074	+	0.691217i
$900$		0			0
$901$			1.30106e6i			1.60269i
$902$		0			0
$903$	129078.	+	74523.1i	0.158298	+	0.0913935i
$904$		0			0
$905$			953254.i			1.16389i
$906$		0			0
$907$	−1.38857e6	+	801689.i	−1.68792	+	0.974522i	−0.731814	+	0.681504i	$0.761326\pi$
$907$	−1.38857e6	+	801689.i	−1.68792	+	0.974522i	−0.956107	+	0.293017i	$0.905341\pi$
$908$		0			0
$909$	−640959.	−	1.11017e6i	−0.775715	−	1.34358i
$910$		0			0
$911$		−	90745.7i		−	0.109343i	−0.998504	−	0.0546713i	$-0.982589\pi$
$911$		−	90745.7i		−	0.109343i	0.998504	−	0.0546713i	$-0.0174111\pi$
$912$		0			0
$913$	321122.			0.385238
$914$		0			0
$915$	−52066.7	+	30060.7i	−0.0621896	+	0.0359052i
$916$		0			0
$917$	−1.16932e6	−	2.02533e6i	−1.39058	−	2.40855i
$918$		0			0
$919$	−126721.			−0.150043			−0.0750216	−	0.997182i	$-0.523903\pi$
$919$	−126721.			−0.150043			−0.0750216	+	0.997182i	$0.523903\pi$
$920$		0			0
$921$	−77172.1	+	133666.i	−0.0909790	+	0.157580i
$922$		0			0
$923$	33471.5			0.0392890
$924$		0			0
$925$	147391.	+	85096.3i	0.172261	+	0.0994551i
$926$		0			0
$927$	−179116.	−	103413.i	−0.208437	−	0.120341i
$928$		0			0
$929$	413421.	+	716067.i	0.479029	+	0.829702i	0.999711	−	0.0240486i	$-0.00765564\pi$
$929$	413421.	+	716067.i	0.479029	+	0.829702i	−0.520682	+	0.853751i	$0.674322\pi$
$930$		0			0
$931$	−166176.	−	1.05011e6i	−0.191721	−	1.21153i
$932$		0			0
$933$	−5013.73	+	2894.68i	−0.00575967	+	0.00332535i
$934$		0			0
$935$	−392413.	+	679679.i	−0.448869	+	0.777464i
$936$		0			0
$937$	−500310.	+	866563.i	−0.569850	+	0.987009i	0.426730	+	0.904379i	$0.359665\pi$
$937$	−500310.	+	866563.i	−0.569850	+	0.987009i	−0.996580	+	0.0826300i	$0.973668\pi$
$938$		0			0
$939$		−	149569.i		−	0.169633i
$940$		0			0
$941$	667083.	+	385140.i	0.753356	+	0.434950i	0.826905	−	0.562341i	$-0.190099\pi$
$941$	667083.	+	385140.i	0.753356	+	0.434950i	−0.0735490	+	0.997292i	$0.523433\pi$
$942$		0			0
$943$		−	194869.i		−	0.219139i
$944$		0			0
$945$	−360529.	+	208152.i	−0.403717	+	0.233086i
$946$		0			0
$947$	241127.	+	417644.i	0.268872	+	0.465700i	0.968571	−	0.248738i	$-0.0800158\pi$
$947$	241127.	+	417644.i	0.268872	+	0.465700i	−0.699699	+	0.714438i	$0.746682\pi$
$948$		0			0
$949$		−	118207.i		−	0.131253i
$950$		0			0
$951$	293851.			0.324912
$952$		0			0
$953$	475964.	−	274798.i	0.524068	−	0.302571i	−0.214529	−	0.976718i	$-0.568822\pi$
$953$	475964.	−	274798.i	0.524068	−	0.302571i	0.738598	+	0.674147i	$0.235488\pi$
$954$		0			0
$955$	−643457.	−	1.11450e6i	−0.705525	−	1.22201i
$956$		0			0
$957$	−76139.2			−0.0831351
$958$		0			0
$959$	830879.	−	1.43912e6i	0.903442	−	1.56481i
$960$		0			0
$961$	−1.26379e6			−1.36845
$962$		0			0
$963$	−660701.	−	381456.i	−0.712447	−	0.411332i
$964$		0			0
$965$	−665843.	−	384424.i	−0.715018	−	0.412816i
$966$		0			0
$967$	154396.	+	267422.i	0.165114	+	0.285986i	0.936696	−	0.350144i	$-0.113868\pi$
$967$	154396.	+	267422.i	0.165114	+	0.285986i	−0.771582	+	0.636130i	$0.780534\pi$
$968$		0			0
$969$	64056.9	−	166807.i	0.0682211	−	0.177651i
$970$		0			0
$971$	1.31701e6	−	760378.i	1.39686	−	0.806476i	0.402795	−	0.915290i	$-0.368039\pi$
$971$	1.31701e6	−	760378.i	1.39686	−	0.806476i	0.994062	+	0.108814i	$0.0347054\pi$
$972$		0			0
$973$	−213743.	+	370214.i	−0.225770	+	0.391045i
$974$		0			0
$975$	−2432.55	+	4213.29i	−0.00255889	+	0.00443213i
$976$		0			0
$977$		−	1.48203e6i		−	1.55263i	−0.630344	−	0.776316i	$-0.717086\pi$
$977$		−	1.48203e6i		−	1.55263i	0.630344	−	0.776316i	$-0.282914\pi$
$978$		0			0
$979$	46015.7	+	26567.2i	0.0480110	+	0.0277191i
$980$		0			0
$981$			1.66620e6i			1.73137i
$982$		0			0
$983$	260045.	−	150137.i	0.269118	−	0.155375i	−0.359369	−	0.933196i	$-0.617008\pi$
$983$	260045.	−	150137.i	0.269118	−	0.155375i	0.628487	+	0.777820i	$0.283675\pi$
$984$		0			0
$985$	−355953.	−	616529.i	−0.366877	−	0.635450i
$986$		0			0
$987$			200972.i			0.206301i
$988$		0			0
$989$	−1.13546e6			−1.16085
$990$		0			0
$991$	228856.	−	132130.i	0.233032	−	0.134541i	−0.378938	−	0.925422i	$-0.623711\pi$
$991$	228856.	−	132130.i	0.233032	−	0.134541i	0.611970	+	0.790881i	$0.290377\pi$
$992$		0			0
$993$	−59663.8	−	103341.i	−0.0605080	−	0.104803i
$994$		0			0
$995$	−491300.			−0.496250
$996$		0			0
$997$	252125.	−	436693.i	0.253645	−	0.439325i	−0.710882	−	0.703311i	$-0.751704\pi$
$997$	252125.	−	436693.i	0.253645	−	0.439325i	0.964526	+	0.263986i	$0.0850373\pi$
$998$		0			0
$999$	−377908.			−0.378665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.c.145.5		16
4.3	odd	2		38.5.d.a.31.2	yes	16
12.11	even	2		342.5.m.c.145.5		16
19.8	odd	6	inner	304.5.r.c.65.5		16
76.27	even	6		38.5.d.a.27.2	✓	16
228.179	odd	6		342.5.m.c.217.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.d.a.27.2	✓	16	76.27	even	6
38.5.d.a.31.2	yes	16	4.3	odd	2
304.5.r.c.65.5		16	19.8	odd	6	inner
304.5.r.c.145.5		16	1.1	even	1	trivial
342.5.m.c.145.5		16	12.11	even	2
342.5.m.c.217.5		16	228.179	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	304.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36664 - 0.789030i) q^{3} +(11.3097 + 19.5890i) q^{5} +73.1169 q^{7} +(-39.2549 + 67.9914i) q^{9} +O(q^{10})\)	\(q+(1.36664 - 0.789030i) q^{3} +(11.3097 + 19.5890i) q^{5} +73.1169 q^{7} +(-39.2549 + 67.9914i) q^{9} +110.621 q^{11} +(-23.5523 - 13.5979i) q^{13} +(30.9126 + 17.8474i) q^{15} +(156.828 + 271.635i) q^{17} +(-56.4250 - 356.563i) q^{19} +(99.9244 - 57.6914i) q^{21} +(-439.502 + 761.239i) q^{23} +(56.6806 - 98.1737i) q^{25} +251.716i q^{27} +(-377.728 - 218.081i) q^{29} -1478.96i q^{31} +(151.179 - 87.2831i) q^{33} +(826.931 + 1432.29i) q^{35} +1501.33i q^{37} -42.9167 q^{39} +(-191.992 + 110.847i) q^{41} +(645.877 + 1118.69i) q^{43} -1775.85 q^{45} +(-870.891 + 1508.43i) q^{47} +2945.08 q^{49} +(428.656 + 247.484i) q^{51} +(3592.31 + 2074.02i) q^{53} +(1251.09 + 2166.95i) q^{55} +(-358.451 - 442.772i) q^{57} +(2018.50 - 1165.38i) q^{59} +(-842.159 + 1458.66i) q^{61} +(-2870.19 + 4971.32i) q^{63} -615.155i q^{65} +(-405.677 - 234.218i) q^{67} +1387.12i q^{69} +(-1065.87 + 615.378i) q^{71} +(2173.25 + 3764.18i) q^{73} -178.891i q^{75} +8088.25 q^{77} +(9607.24 - 5546.74i) q^{79} +(-2981.03 - 5163.30i) q^{81} +2902.91 q^{83} +(-3547.37 + 6144.22i) q^{85} -688.290 q^{87} +(415.977 + 240.164i) q^{89} +(-1722.07 - 994.239i) q^{91} +(-1166.94 - 2021.20i) q^{93} +(6346.56 - 5137.94i) q^{95} +(-15206.7 + 8779.57i) q^{97} +(-4342.40 + 7521.26i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9}+O(q^{10}) \) 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9	\( 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9} + 84 q^{11} + 450 q^{13} + 390 q^{15} + 606 q^{17} + 306 q^{19} - 2160 q^{21} + 54 q^{23} - 434 q^{25} - 4914 q^{29} + 7890 q^{33} - 2328 q^{35} - 7620 q^{39} - 1692 q^{41} + 7402 q^{43} - 16720 q^{45} - 3198 q^{47} + 24816 q^{49} - 10710 q^{51} + 3870 q^{53} + 13588 q^{55} + 3702 q^{57} + 18288 q^{59} - 6522 q^{61} + 15676 q^{63} + 30168 q^{67} - 35874 q^{71} - 8080 q^{73} + 34560 q^{77} + 30738 q^{79} - 30920 q^{81} + 1476 q^{83} + 33626 q^{85} - 113100 q^{87} + 19782 q^{89} + 34260 q^{91} - 4272 q^{93} + 23706 q^{95} - 9936 q^{97} - 3848 q^{99}+O(q^{100}) \) 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9 + 84 * q^11 + 450 * q^13 + 390 * q^15 + 606 * q^17 + 306 * q^19 - 2160 * q^21 + 54 * q^23 - 434 * q^25 - 4914 * q^29 + 7890 * q^33 - 2328 * q^35 - 7620 * q^39 - 1692 * q^41 + 7402 * q^43 - 16720 * q^45 - 3198 * q^47 + 24816 * q^49 - 10710 * q^51 + 3870 * q^53 + 13588 * q^55 + 3702 * q^57 + 18288 * q^59 - 6522 * q^61 + 15676 * q^63 + 30168 * q^67 - 35874 * q^71 - 8080 * q^73 + 34560 * q^77 + 30738 * q^79 - 30920 * q^81 + 1476 * q^83 + 33626 * q^85 - 113100 * q^87 + 19782 * q^89 + 34260 * q^91 - 4272 * q^93 + 23706 * q^95 - 9936 * q^97 - 3848 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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