LMFDB - Embedded newform 11.5.d.a.6.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [11,5,Mod(2,11)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("11.2"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(11, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	11.d (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.13706959392$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 115x^{10} + 5030x^{8} + 102975x^{6} + 953170x^{4} + 2910655x^{2} + 73205 $ x^12 + 115x^10 + 5030x^8 + 102975x^6 + 953170x^4 + 2910655*x^2 + 73205
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			6.3
Root			$5.04186i$ of defining polynomial
Character	$\chi$	$=$	11.6
Dual form			11.5.d.a.2.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.67706 - 1.19475i) q^{2} +(-1.64569 - 1.19566i) q^{3} +(-0.850950 + 0.618251i) q^{4} +(-1.76709 + 5.43854i) q^{5} +(-7.47979 - 2.43033i) q^{6} +(-2.52826 - 3.47985i) q^{7} +(-38.7511 + 53.3363i) q^{8} +(-23.7517 - 73.1002i) q^{9} +22.1090i q^{10} +(120.958 - 3.19753i) q^{11} +2.13961 q^{12} +(189.406 - 61.5418i) q^{13} +(-13.4541 - 9.77497i) q^{14} +(9.41072 - 6.83729i) q^{15} +(-73.5659 + 226.413i) q^{16} +(-269.440 - 87.5465i) q^{17} +(-174.673 - 240.416i) q^{18} +(-237.059 + 326.284i) q^{19} +(-1.85868 - 5.72043i) q^{20} +8.74968i q^{21} +(440.948 - 156.272i) q^{22} -189.240 q^{23} +(127.544 - 41.4416i) q^{24} +(479.181 + 348.145i) q^{25} +(622.930 - 452.585i) q^{26} +(-99.2315 + 305.403i) q^{27} +(4.30284 + 1.39808i) q^{28} +(-797.600 - 1097.80i) q^{29} +(26.4349 - 36.3845i) q^{30} +(421.011 + 1295.74i) q^{31} -134.411i q^{32} +(-202.882 - 139.362i) q^{33} -1095.34 q^{34} +(23.3929 - 7.60083i) q^{35} +(65.4058 + 47.5201i) q^{36} +(690.326 - 501.551i) q^{37} +(-481.853 + 1482.99i) q^{38} +(-385.286 - 125.187i) q^{39} +(-221.595 - 304.999i) q^{40} +(218.820 - 301.180i) q^{41} +(10.4537 + 32.1731i) q^{42} -854.475i q^{43} +(-100.952 + 77.5032i) q^{44} +439.530 q^{45} +(-695.846 + 226.094i) q^{46} +(1283.36 + 932.413i) q^{47} +(391.779 - 284.644i) q^{48} +(736.233 - 2265.89i) q^{49} +(2177.92 + 707.649i) q^{50} +(338.738 + 466.233i) q^{51} +(-123.127 + 169.469i) q^{52} +(-274.987 - 846.322i) q^{53} +1241.54i q^{54} +(-196.353 + 663.484i) q^{55} +283.575 q^{56} +(780.250 - 253.519i) q^{57} +(-4244.42 - 3083.75i) q^{58} +(-4679.23 + 3399.66i) q^{59} +(-3.78089 + 11.6364i) q^{60} +(-3716.82 - 1207.67i) q^{61} +(3096.16 + 4261.50i) q^{62} +(-194.327 + 267.468i) q^{63} +(-1337.64 - 4116.84i) q^{64} +1138.84i q^{65} +(-912.510 - 270.051i) q^{66} +6198.68 q^{67} +(283.406 - 92.0841i) q^{68} +(311.430 + 226.267i) q^{69} +(76.9361 - 55.8974i) q^{70} +(1651.10 - 5081.57i) q^{71} +(4819.30 + 1565.88i) q^{72} +(3573.88 + 4919.03i) q^{73} +(1939.14 - 2669.00i) q^{74} +(-372.317 - 1145.87i) q^{75} -424.213i q^{76} +(-316.939 - 412.830i) q^{77} -1566.29 q^{78} +(-4601.08 + 1494.98i) q^{79} +(-1101.36 - 800.182i) q^{80} +(-4508.34 + 3275.50i) q^{81} +(444.780 - 1368.89i) q^{82} +(-2421.43 - 786.770i) q^{83} +(-5.40950 - 7.44553i) q^{84} +(952.250 - 1310.66i) q^{85} +(-1020.88 - 3141.95i) q^{86} +2760.30i q^{87} +(-4516.70 + 6575.34i) q^{88} -1607.22 q^{89} +(1616.18 - 525.127i) q^{90} +(-693.023 - 503.511i) q^{91} +(161.034 - 116.998i) q^{92} +(856.411 - 2635.76i) q^{93} +(5832.97 + 1895.25i) q^{94} +(-1355.60 - 1865.83i) q^{95} +(-160.710 + 221.199i) q^{96} +(4666.32 + 14361.5i) q^{97} -9211.42i q^{98} +(-3106.69 - 8766.09i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9} - 43 q^{11} + 594 q^{12} + 250 q^{13} + 610 q^{14} + 1134 q^{15} - 633 q^{16} - 1250 q^{17} - 3150 q^{18} - 1025 q^{19}+ \cdots - 3269 q^{99}+O(q^{100}) $ 12 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 - 18 * q^5 + 75 * q^6 - 80 * q^7 - 245 * q^8 + q^9 - 43 * q^11 + 594 * q^12 + 250 * q^13 + 610 * q^14 + 1134 * q^15 - 633 * q^16 - 1250 * q^17 - 3150 * q^18 - 1025 * q^19 + 752 * q^20 - 35 * q^22 + 1684 * q^23 + 5345 * q^24 + 197 * q^25 + 3490 * q^26 - 687 * q^27 - 3580 * q^28 - 2690 * q^29 - 6740 * q^30 - 1136 * q^31 + 5939 * q^33 + 2370 * q^34 + 3610 * q^35 - 514 * q^36 - 336 * q^37 + 1900 * q^38 - 6880 * q^39 - 2340 * q^40 - 4550 * q^41 + 1310 * q^42 - 6268 * q^44 + 5136 * q^45 + 4150 * q^46 + 24 * q^47 + 344 * q^48 + 827 * q^49 + 8895 * q^50 + 13155 * q^51 + 14070 * q^52 + 414 * q^53 - 2738 * q^55 - 21340 * q^56 - 26925 * q^57 + 2980 * q^58 - 10011 * q^59 - 6856 * q^60 + 9460 * q^61 - 6200 * q^62 + 9150 * q^63 - 2633 * q^64 - 3210 * q^66 + 12154 * q^67 - 9400 * q^68 - 9022 * q^69 - 9380 * q^70 + 17574 * q^71 + 43045 * q^72 + 27950 * q^73 + 43270 * q^74 - 1761 * q^75 + 4090 * q^77 - 42920 * q^78 - 41540 * q^79 - 2308 * q^80 - 21080 * q^81 - 28175 * q^82 - 18665 * q^83 + 26250 * q^84 - 4230 * q^85 - 10125 * q^86 - 15125 * q^88 + 5554 * q^89 + 18400 * q^90 + 7390 * q^91 + 3904 * q^92 + 36898 * q^93 + 18920 * q^94 + 14110 * q^95 - 21140 * q^96 + 20769 * q^97 - 3269 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.67706	−	1.19475i	0.919264	−	0.298687i	0.189099	−	0.981958i	$-0.439443\pi$
$2$	3.67706	−	1.19475i	0.919264	−	0.298687i	0.730165	+	0.683271i	$0.239443\pi$
$3$	−1.64569	−	1.19566i	−0.182854	−	0.132851i	0.492593	−	0.870260i	$-0.336049\pi$
$3$	−1.64569	−	1.19566i	−0.182854	−	0.132851i	−0.675447	+	0.737409i	$0.736049\pi$
$4$	−0.850950	+	0.618251i	−0.0531844	+	0.0386407i
$5$	−1.76709	+	5.43854i	−0.0706835	+	0.217542i	−0.980158	−	0.198219i	$-0.936484\pi$
$5$	−1.76709	+	5.43854i	−0.0706835	+	0.217542i	0.909474	+	0.415760i	$0.136484\pi$
$6$	−7.47979	−	2.43033i	−0.207772	−	0.0675092i
$7$	−2.52826	−	3.47985i	−0.0515971	−	0.0710173i	0.782439	−	0.622727i	$-0.213975\pi$
$7$	−2.52826	−	3.47985i	−0.0515971	−	0.0710173i	−0.834036	+	0.551710i	$0.813975\pi$
$8$	−38.7511	+	53.3363i	−0.605485	+	0.833379i
$9$	−23.7517	−	73.1002i	−0.293231	−	0.902472i
$10$			22.1090i			0.221090i
$11$	120.958	−	3.19753i	0.999651	−	0.0264259i
$11$	120.958	−	3.19753i	0.999651	−	0.0264259i
$12$	2.13961			0.0148584
$13$	189.406	−	61.5418i	1.12075	−	0.364152i	0.310694	−	0.950510i	$-0.399439\pi$
$13$	189.406	−	61.5418i	1.12075	−	0.364152i	0.810052	+	0.586358i	$0.199439\pi$
$14$	−13.4541	−	9.77497i	−0.0686433	−	0.0498723i
$15$	9.41072	−	6.83729i	0.0418254	−	0.0303880i
$16$	−73.5659	+	226.413i	−0.287367	+	0.884424i
$17$	−269.440	−	87.5465i	−0.932319	−	0.302929i	−0.196809	−	0.980442i	$-0.563058\pi$
$17$	−269.440	−	87.5465i	−0.932319	−	0.302929i	−0.735511	+	0.677513i	$0.763058\pi$
$18$	−174.673	−	240.416i	−0.539113	−	0.742026i
$19$	−237.059	+	326.284i	−0.656674	+	0.903834i	−0.999366	−	0.0356142i	$-0.988661\pi$
$19$	−237.059	+	326.284i	−0.656674	+	0.903834i	0.342692	+	0.939448i	$0.388661\pi$
$20$	−1.85868	−	5.72043i	−0.00464670	−	0.0143011i
$21$			8.74968i			0.0198405i
$22$	440.948	−	156.272i	0.911050	−	0.322875i
$23$	−189.240			−0.357731			−0.178866	−	0.983873i	$-0.557243\pi$
$23$	−189.240			−0.357731			−0.178866	+	0.983873i	$0.557243\pi$
$24$	127.544	−	41.4416i	0.221431	−	0.0719473i
$25$	479.181	+	348.145i	0.766689	+	0.557032i
$26$	622.930	−	452.585i	0.921494	−	0.669505i
$27$	−99.2315	+	305.403i	−0.136120	+	0.418934i
$28$	4.30284	+	1.39808i	0.00548832	+	0.00178326i
$29$	−797.600	−	1097.80i	−0.948394	−	1.30535i	−0.952237	−	0.305360i	$-0.901223\pi$
$29$	−797.600	−	1097.80i	−0.948394	−	1.30535i	0.00384249	−	0.999993i	$-0.498777\pi$
$30$	26.4349	−	36.3845i	0.0293721	−	0.0404273i
$31$	421.011	+	1295.74i	0.438096	+	1.34832i	0.889880	+	0.456195i	$0.150788\pi$
$31$	421.011	+	1295.74i	0.438096	+	1.34832i	−0.451784	+	0.892128i	$0.649212\pi$
$32$		−	134.411i		−	0.131261i
$33$	−202.882	−	139.362i	−0.186301	−	0.127973i
$34$	−1095.34			−0.947529
$35$	23.3929	−	7.60083i	0.0190963	−	0.00620476i
$36$	65.4058	+	47.5201i	0.0504674	+	0.0366667i
$37$	690.326	−	501.551i	0.504255	−	0.366363i	−0.306385	−	0.951908i	$-0.599119\pi$
$37$	690.326	−	501.551i	0.504255	−	0.366363i	0.810640	+	0.585545i	$0.199119\pi$
$38$	−481.853	+	1482.99i	−0.333693	+	1.02700i
$39$	−385.286	−	125.187i	−0.253311	−	0.0823057i
$40$	−221.595	−	304.999i	−0.138497	−	0.190624i
$41$	218.820	−	301.180i	0.130173	−	0.179167i	−0.738956	−	0.673754i	$-0.764681\pi$
$41$	218.820	−	301.180i	0.130173	−	0.179167i	0.869128	+	0.494587i	$0.164681\pi$
$42$	10.4537	+	32.1731i	0.00592611	+	0.0182387i
$43$		−	854.475i		−	0.462128i	−0.972939	−	0.231064i	$-0.925779\pi$
$43$		−	854.475i		−	0.462128i	0.972939	−	0.231064i	$-0.0742207\pi$
$44$	−100.952	+	77.5032i	−0.0521447	+	0.0400326i
$45$	439.530			0.217052
$46$	−695.846	+	226.094i	−0.328850	+	0.106850i
$47$	1283.36	+	932.413i	0.580967	+	0.422097i	0.839073	−	0.544020i	$-0.183098\pi$
$47$	1283.36	+	932.413i	0.580967	+	0.422097i	−0.258106	+	0.966117i	$0.583098\pi$
$48$	391.779	−	284.644i	0.170043	−	0.123544i
$49$	736.233	−	2265.89i	0.306636	−	0.943728i
$50$	2177.92	+	707.649i	0.871168	+	0.283060i
$51$	338.738	+	466.233i	0.130234	+	0.179252i
$52$	−123.127	+	169.469i	−0.0455350	+	0.0626736i
$53$	−274.987	−	846.322i	−0.0978949	−	0.301289i	0.890102	−	0.455761i	$-0.150633\pi$
$53$	−274.987	−	846.322i	−0.0978949	−	0.301289i	−0.987997	+	0.154471i	$0.950633\pi$
$54$			1241.54i			0.425769i
$55$	−196.353	+	663.484i	−0.0649101	+	0.219333i
$56$	283.575			0.0904256
$57$	780.250	−	253.519i	0.240151	−	0.0780297i
$58$	−4244.42	−	3083.75i	−1.26172	−	0.916691i
$59$	−4679.23	+	3399.66i	−1.34422	+	0.976632i	−0.344941	+	0.938624i	$0.612101\pi$
$59$	−4679.23	+	3399.66i	−1.34422	+	0.976632i	−0.999277	+	0.0380079i	$0.987899\pi$
$60$	−3.78089	+	11.6364i	−0.00105025	+	0.00323233i
$61$	−3716.82	−	1207.67i	−0.998877	−	0.324555i	−0.236460	−	0.971641i	$-0.575987\pi$
$61$	−3716.82	−	1207.67i	−0.998877	−	0.324555i	−0.762417	+	0.647086i	$0.775987\pi$
$62$	3096.16	+	4261.50i	0.805453	+	1.10861i
$63$	−194.327	+	267.468i	−0.0489613	+	0.0673894i
$64$	−1337.64	−	4116.84i	−0.326573	−	1.00509i
$65$			1138.84i			0.269548i
$66$	−912.510	−	270.051i	−0.209484	−	0.0619951i
$67$	6198.68			1.38086			0.690430	−	0.723399i	$-0.257421\pi$
$67$	6198.68			1.38086			0.690430	+	0.723399i	$0.257421\pi$
$68$	283.406	−	92.0841i	0.0612902	−	0.0199144i
$69$	311.430	+	226.267i	0.0654126	+	0.0475251i
$70$	76.9361	−	55.8974i	0.0157012	−	0.0114076i
$71$	1651.10	−	5081.57i	0.327535	−	1.00805i	−0.642749	−	0.766077i	$-0.722206\pi$
$71$	1651.10	−	5081.57i	0.327535	−	1.00805i	0.970283	−	0.241971i	$-0.0777940\pi$
$72$	4819.30	+	1565.88i	0.929648	+	0.302061i
$73$	3573.88	+	4919.03i	0.670648	+	0.923068i	0.999775	−	0.0212178i	$-0.00675434\pi$
$73$	3573.88	+	4919.03i	0.670648	+	0.923068i	−0.329127	+	0.944286i	$0.606754\pi$
$74$	1939.14	−	2669.00i	0.354116	−	0.487399i
$75$	−372.317	−	1145.87i	−0.0661897	−	0.203711i
$76$		−	424.213i		−	0.0734441i
$77$	−316.939	−	412.830i	−0.0534558	−	0.0696290i
$78$	−1566.29			−0.257443
$79$	−4601.08	+	1494.98i	−0.737235	+	0.239542i	−0.653480	−	0.756944i	$-0.726691\pi$
$79$	−4601.08	+	1494.98i	−0.737235	+	0.239542i	−0.0837555	+	0.996486i	$0.526691\pi$
$80$	−1101.36	−	800.182i	−0.172087	−	0.125029i
$81$	−4508.34	+	3275.50i	−0.687142	+	0.499238i
$82$	444.780	−	1368.89i	0.0661481	−	0.203583i
$83$	−2421.43	−	786.770i	−0.351492	−	0.114207i	0.127949	−	0.991781i	$-0.459161\pi$
$83$	−2421.43	−	786.770i	−0.351492	−	0.114207i	−0.479441	+	0.877574i	$0.659161\pi$
$84$	−5.40950	−	7.44553i	−0.000766652	−	0.00105521i
$85$	952.250	−	1310.66i	0.131799	−	0.181406i
$86$	−1020.88	−	3141.95i	−0.138032	−	0.424818i
$87$			2760.30i			0.364684i
$88$	−4516.70	+	6575.34i	−0.583251	+	0.849089i
$89$	−1607.22			−0.202906			−0.101453	−	0.994840i	$-0.532349\pi$
$89$	−1607.22			−0.202906			−0.101453	+	0.994840i	$0.532349\pi$
$90$	1616.18	−	525.127i	0.199528	−	0.0648305i
$91$	−693.023	−	503.511i	−0.0836884	−	0.0608031i
$92$	161.034	−	116.998i	0.0190257	−	0.0138230i
$93$	856.411	−	2635.76i	0.0990185	−	0.304748i
$94$	5832.97	+	1895.25i	0.660137	+	0.214492i
$95$	−1355.60	−	1865.83i	−0.150205	−	0.206740i
$96$	−160.710	+	221.199i	−0.0174382	+	0.0240016i
$97$	4666.32	+	14361.5i	0.495943	+	1.52635i	0.815483	+	0.578781i	$0.196472\pi$
$97$	4666.32	+	14361.5i	0.495943	+	1.52635i	−0.319540	+	0.947573i	$0.603528\pi$
$98$		−	9211.42i		−	0.959123i
$99$	−3106.69	−	8766.09i	−0.316977	−	0.894408i
$100$	−623.000			−0.0623000
$101$	−4217.78	+	1370.44i	−0.413467	+	0.134344i	−0.508362	−	0.861144i	$-0.669749\pi$
$101$	−4217.78	+	1370.44i	−0.413467	+	0.134344i	0.0948944	+	0.995487i	$0.469749\pi$
$102$	1802.59	+	1309.66i	0.173259	+	0.125880i
$103$	12242.8	−	8894.90i	1.15400	−	0.838430i	0.164992	−	0.986295i	$-0.447240\pi$
$103$	12242.8	−	8894.90i	1.15400	−	0.838430i	0.989008	+	0.147865i	$0.0472402\pi$
$104$	−4057.28	+	12487.0i	−0.375118	+	1.15450i
$105$	−47.5855	−	15.4615i	−0.00431614	−	0.00140240i
$106$	−2022.28	−	2783.43i	−0.179982	−	0.247725i
$107$	7188.59	−	9894.25i	0.627880	−	0.864202i	−0.370017	−	0.929025i	$-0.620648\pi$
$107$	7188.59	−	9894.25i	0.627880	−	0.864202i	0.997897	+	0.0648227i	$0.0206482\pi$
$108$	−104.375	−	321.233i	−0.00894846	−	0.0275405i
$109$			2157.06i			0.181555i	0.995871	+	0.0907777i	$0.0289353\pi$
$109$			2157.06i			0.181555i	−0.995871	+	0.0907777i	$0.971065\pi$
$110$	70.6944	+	2674.26i	0.00584251	+	0.221013i
$111$	−1735.74			−0.140877
$112$	973.875	−	316.431i	0.0776367	−	0.0252257i
$113$	8413.03	+	6112.42i	0.658863	+	0.478692i	0.866279	−	0.499561i	$-0.166505\pi$
$113$	8413.03	+	6112.42i	0.658863	+	0.478692i	−0.207416	+	0.978253i	$0.566505\pi$
$114$	2566.13	−	1864.40i	0.197456	−	0.143460i
$115$	334.404	−	1029.19i	0.0252857	−	0.0778215i
$116$	1357.43	+	441.057i	0.100879	+	0.0327777i
$117$	−8997.43	−	12383.9i	−0.657275	−	0.904661i
$118$	−13144.0	+	18091.2i	−0.943985	+	1.29928i
$119$	376.566	+	1158.95i	0.0265918	+	0.0818411i
$120$			766.885i			0.0532559i
$121$	14620.6	−	773.533i	0.998603	−	0.0528333i
$122$	−15109.8			−1.01517
$123$	−720.218	+	234.013i	−0.0476052	+	0.0154679i
$124$	−1159.35	−	842.317i	−0.0754000	−	0.0547813i
$125$	−5631.59	+	4091.59i	−0.360422	+	0.261862i
$126$	−394.995	+	1215.67i	−0.0248800	+	0.0765727i
$127$	−18504.7	−	6012.53i	−1.14729	−	0.372778i	−0.327169	−	0.944966i	$-0.606095\pi$
$127$	−18504.7	−	6012.53i	−1.14729	−	0.372778i	−0.820122	+	0.572188i	$0.806095\pi$
$128$	−8573.09	−	11799.9i	−0.523260	−	0.720206i
$129$	−1021.66	+	1406.20i	−0.0613943	+	0.0845020i
$130$	1360.63	+	4187.59i	0.0805106	+	0.247786i
$131$			10666.5i			0.621556i	0.950483	+	0.310778i	$0.100589\pi$
$131$			10666.5i			0.621556i	−0.950483	+	0.310778i	$0.899411\pi$
$132$	258.803	−	6.84149i	0.0148532	−	0.000392648i
$133$	1734.76			0.0980703
$134$	22792.9	−	7405.86i	1.26938	−	0.412445i
$135$	−1485.60	−	1079.35i	−0.0815142	−	0.0592235i
$136$	15110.5	−	10978.4i	0.816961	−	0.593557i
$137$	−5728.06	+	17629.1i	−0.305187	+	0.939269i	0.674420	+	0.738348i	$0.264394\pi$
$137$	−5728.06	+	17629.1i	−0.305187	+	0.939269i	−0.979607	+	0.200922i	$0.935606\pi$
$138$	1415.48	+	459.916i	0.0743266	+	0.0241502i
$139$	3900.98	+	5369.23i	0.201903	+	0.277896i	0.897947	−	0.440103i	$-0.145058\pi$
$139$	3900.98	+	5369.23i	0.201903	+	0.277896i	−0.696044	+	0.717999i	$0.745058\pi$
$140$	−15.2070	+	20.9306i	−0.000775867	+	0.00106789i
$141$	−997.152	−	3068.92i	−0.0501560	−	0.154364i
$142$		−	20657.9i		−	1.02449i
$143$	22713.3	−	8049.58i	1.11073	−	0.393642i
$144$	18298.1			0.882433
$145$	7379.87	−	2397.86i	0.351004	−	0.114048i
$146$	19018.4	+	13817.7i	0.892211	+	0.648229i
$147$	−3920.84	+	2848.66i	−0.181445	+	0.131827i
$148$	−277.348	+	853.589i	−0.0126620	+	0.0389696i
$149$	−16560.8	−	5380.94i	−0.745950	−	0.242374i	−0.0887125	−	0.996057i	$-0.528275\pi$
$149$	−16560.8	−	5380.94i	−0.745950	−	0.242374i	−0.657238	+	0.753683i	$0.728275\pi$
$150$	−2738.06	−	3768.62i	−0.121692	−	0.167494i
$151$	−15126.5	+	20819.8i	−0.663413	+	0.913110i	−0.999588	−	0.0286898i	$-0.990867\pi$
$151$	−15126.5	+	20819.8i	−0.663413	+	0.913110i	0.336175	+	0.941799i	$0.390867\pi$
$152$	−8216.47	−	25287.7i	−0.355630	−	1.09452i
$153$			21775.5i			0.930220i
$154$	−1658.63	−	1139.34i	−0.0699372	−	0.0480409i
$155$	−7790.88			−0.324282
$156$	405.256	−	131.676i	0.0166525	−	0.00541074i
$157$	−28801.8	−	20925.8i	−1.16848	−	0.848950i	−0.177653	−	0.984093i	$-0.556851\pi$
$157$	−28801.8	−	20925.8i	−1.16848	−	0.848950i	−0.990826	+	0.135143i	$0.956851\pi$
$158$	−15132.3	+	10994.3i	−0.606166	+	0.440405i
$159$	−559.372	+	1721.57i	−0.0221262	+	0.0680974i
$160$	731.001	+	237.517i	0.0285547	+	0.00927799i
$161$	478.447	+	658.526i	0.0184579	+	0.0254051i
$162$	−12664.0	+	17430.5i	−0.482549	+	0.664172i
$163$	1002.80	+	3086.30i	0.0377432	+	0.116162i	0.968153	−	0.250359i	$-0.0805488\pi$
$163$	1002.80	+	3086.30i	0.0377432	+	0.116162i	−0.930410	+	0.366521i	$0.880549\pi$
$164$			391.575i			0.0145589i
$165$	1116.44	−	857.114i	0.0410078	−	0.0314826i
$166$	−9843.73			−0.357226
$167$	−9806.86	+	3186.44i	−0.351639	+	0.114254i	−0.479510	−	0.877536i	$-0.659186\pi$
$167$	−9806.86	+	3186.44i	−0.351639	+	0.114254i	0.127871	+	0.991791i	$0.459186\pi$
$168$	−466.675	−	339.059i	−0.0165347	−	0.0120132i
$169$	8980.94	−	6525.03i	0.314448	−	0.228460i
$170$	1935.57	−	5957.07i	0.0669747	−	0.206127i
$171$	29482.0	+	9579.28i	1.00824	+	0.327597i
$172$	528.280	+	727.115i	0.0178570	+	0.0245780i
$173$	28966.7	−	39869.2i	0.967846	−	1.33213i	0.0247192	−	0.999694i	$-0.492131\pi$
$173$	28966.7	−	39869.2i	0.967846	−	1.33213i	0.943127	−	0.332432i	$-0.107869\pi$
$174$	3297.86	+	10149.8i	0.108926	+	0.335241i
$175$		−	2547.68i		−	0.0831894i
$176$	−8174.41	+	27621.6i	−0.263895	+	0.891709i
$177$	11765.4			0.375543
$178$	−5909.83	+	1920.22i	−0.186524	+	0.0606053i
$179$	15035.7	+	10924.1i	0.469264	+	0.340940i	0.797154	−	0.603776i	$-0.206338\pi$
$179$	15035.7	+	10924.1i	0.469264	+	0.340940i	−0.327891	+	0.944716i	$0.606338\pi$
$180$	−374.018	+	271.740i	−0.0115438	+	0.00838703i
$181$	10097.8	−	31077.9i	0.308227	−	0.948626i	−0.670226	−	0.742157i	$-0.733803\pi$
$181$	10097.8	−	31077.9i	0.308227	−	0.948626i	0.978453	−	0.206469i	$-0.0661972\pi$
$182$	−3149.85	−	1023.45i	−0.0950928	−	0.0308975i
$183$	4672.76	+	6431.50i	0.139531	+	0.192048i
$184$	7333.25	−	10093.4i	0.216601	−	0.298126i
$185$	1507.84	+	4640.65i	0.0440566	+	0.135592i
$186$		−	10715.0i		−	0.309719i
$187$	−32870.8	−	9727.88i	−0.939999	−	0.278186i
$188$	−1668.54			−0.0472085
$189$	1313.64	−	426.827i	0.0367750	−	0.0119489i
$190$	−7213.83	−	5241.15i	−0.199829	−	0.145184i
$191$	−6005.73	+	4363.41i	−0.164626	+	0.119608i	−0.667048	−	0.745015i	$-0.732442\pi$
$191$	−6005.73	+	4363.41i	−0.164626	+	0.119608i	0.502422	+	0.864623i	$0.332442\pi$
$192$	−2721.01	+	8374.39i	−0.0738120	+	0.227170i
$193$	16807.7	+	5461.14i	0.451225	+	0.146612i	0.525809	−	0.850603i	$-0.323763\pi$
$193$	16807.7	+	5461.14i	0.451225	+	0.146612i	−0.0745837	+	0.997215i	$0.523763\pi$
$194$	34316.7	+	47232.8i	0.911804	+	1.25499i
$195$	1361.67	−	1874.18i	0.0358098	−	0.0492880i
$196$	774.393	+	2383.34i	0.0201581	+	0.0620402i
$197$		−	32273.4i		−	0.831596i	−0.909457	−	0.415798i	$-0.863502\pi$
$197$		−	32273.4i		−	0.831596i	0.909457	−	0.415798i	$-0.136498\pi$
$198$	−21896.8	−	28521.7i	−0.558534	−	0.727520i
$199$	18945.7			0.478414			0.239207	−	0.970969i	$-0.423113\pi$
$199$	18945.7			0.478414			0.239207	+	0.970969i	$0.423113\pi$
$200$	−37137.5	+	12066.7i	−0.928438	+	0.301668i
$201$	−10201.1	−	7411.52i	−0.252496	−	0.183449i
$202$	−13871.7	+	10078.4i	−0.339959	+	0.246995i
$203$	−1803.65	+	5551.05i	−0.0437682	+	0.134705i
$204$	−576.499	−	187.316i	−0.0138528	−	0.00450105i
$205$	1251.31	+	1722.27i	0.0297753	+	0.0409821i
$206$	34390.2	−	47334.1i	0.810402	−	1.11542i
$207$	4494.77	+	13833.5i	0.104898	+	0.322843i
$208$			47411.3i			1.09586i
$209$	−27630.8	+	40224.6i	−0.632560	+	0.920871i
$210$	−193.447			−0.00438655
$211$	−44193.5	+	14359.3i	−0.992644	+	0.322530i	−0.759923	−	0.650014i	$-0.774763\pi$
$211$	−44193.5	+	14359.3i	−0.992644	+	0.322530i	−0.232722	+	0.972543i	$0.574763\pi$
$212$	757.239	+	550.167i	0.0168485	+	0.0122412i
$213$	−8793.03	+	6388.51i	−0.193811	+	0.140812i
$214$	14611.7	−	44970.3i	0.319061	−	0.981970i
$215$	4647.10	+	1509.93i	0.100532	+	0.0326649i
$216$	−12443.7	−	17127.3i	−0.266713	−	0.367098i
$217$	3444.55	−	4741.01i	0.0731497	−	0.100682i
$218$	2577.14	+	7931.63i	0.0542282	+	0.166897i
$219$		−	12368.3i		−	0.257883i
$220$	−243.113	−	685.987i	−0.00502300	−	0.0141733i
$221$	−56421.4			−1.15521
$222$	−6382.43	+	2073.78i	−0.129503	+	0.0420781i
$223$	11958.4	+	8688.31i	0.240472	+	0.174713i	0.701494	−	0.712676i	$-0.252517\pi$
$223$	11958.4	+	8688.31i	0.240472	+	0.174713i	−0.461022	+	0.887389i	$0.652517\pi$
$224$	−467.731	+	339.826i	−0.00932180	+	0.00677269i
$225$	14068.1	−	43297.2i	0.277889	−	0.855254i
$226$	38238.0	+	12424.3i	0.748649	+	0.243251i
$227$	27805.3	+	38270.7i	0.539605	+	0.742703i	0.988556	−	0.150853i	$-0.0482021\pi$
$227$	27805.3	+	38270.7i	0.539605	+	0.742703i	−0.448951	+	0.893556i	$0.648202\pi$
$228$	−507.215	+	698.122i	−0.00975714	+	0.0134296i
$229$	−3741.55	−	11515.3i	−0.0713479	−	0.219586i	0.909024	−	0.416744i	$-0.136829\pi$
$229$	−3741.55	−	11515.3i	−0.0713479	−	0.219586i	−0.980372	+	0.197158i	$0.936829\pi$
$230$		−	4183.91i		−	0.0790910i
$231$	27.9774	+	1058.34i	0.000524304	+	0.0198336i
$232$	89460.5			1.66209
$233$	56685.5	−	18418.2i	1.04414	−	0.339263i	0.263776	−	0.964584i	$-0.415032\pi$
$233$	56685.5	−	18418.2i	1.04414	−	0.339263i	0.780368	+	0.625321i	$0.215032\pi$
$234$	−47879.7	−	34786.6i	−0.874419	−	0.635303i
$235$	−7338.77	+	5331.93i	−0.132888	+	0.0965491i
$236$	1879.94	−	5785.87i	0.0337537	−	0.103883i
$237$	9359.43	+	3041.06i	0.166630	+	0.0541413i
$238$	2769.31	+	3811.63i	0.0488897	+	0.0672909i
$239$	−8291.68	+	11412.5i	−0.145160	+	0.199795i	−0.875406	−	0.483389i	$-0.839406\pi$
$239$	−8291.68	+	11412.5i	−0.145160	+	0.199795i	0.730246	+	0.683185i	$0.239406\pi$
$240$	855.740	+	2633.70i	0.0148566	+	0.0457239i
$241$			30792.3i			0.530161i	0.964226	+	0.265080i	$0.0853985\pi$
$241$			30792.3i			0.530161i	−0.964226	+	0.265080i	$0.914602\pi$
$242$	52836.4	−	20312.2i	0.902200	−	0.346838i
$243$	37346.4			0.632465
$244$	3909.47	−	1270.26i	0.0656656	−	0.0213361i
$245$	11022.1	+	8008.06i	0.183626	+	0.133412i
$246$	−2368.70	+	1720.96i	−0.0391417	+	0.0284381i
$247$	−24820.4	+	76389.2i	−0.406831	+	1.25210i
$248$	−85424.4	−	27756.1i	−1.38892	−	0.451289i
$249$	3044.20	+	4189.99i	0.0490993	+	0.0675793i
$250$	−15819.3	+	21773.3i	−0.253108	+	0.348373i
$251$	−34770.1	−	107011.i	−0.551898	−	1.69857i	−0.703998	−	0.710202i	$-0.748604\pi$
$251$	−34770.1	−	107011.i	−0.551898	−	1.69857i	0.152100	−	0.988365i	$-0.451396\pi$
$252$		−	347.745i		−	0.00547596i
$253$	−22890.0	+	605.101i	−0.357607	+	0.00945338i
$254$	−75226.2			−1.16601
$255$	−3134.21	+	1018.37i	−0.0482001	+	0.0156611i
$256$	10410.3	+	7563.52i	0.158848	+	0.115410i
$257$	−28119.5	+	20430.0i	−0.425737	+	0.309316i	−0.779942	−	0.625852i	$-0.784751\pi$
$257$	−28119.5	+	20430.0i	−0.425737	+	0.309316i	0.354205	+	0.935168i	$0.384751\pi$
$258$	−2076.66	+	6391.30i	−0.0311979	+	0.0960173i
$259$	−3490.64	−	1134.18i	−0.0520362	−	0.0169076i
$260$	−704.090	−	969.097i	−0.0104155	−	0.0143358i
$261$	−61305.2	+	84379.4i	−0.899946	+	1.23867i
$262$	12743.8	+	39221.4i	0.185651	+	0.571374i
$263$		−	78599.0i		−	1.13633i	−0.822913	−	0.568167i	$-0.807653\pi$
$263$		−	78599.0i		−	1.13633i	0.822913	−	0.568167i	$-0.192347\pi$
$264$	15294.9	−	5420.51i	0.219452	−	0.0777736i
$265$	5088.68			0.0724625
$266$	6378.83	−	2072.61i	0.0901525	−	0.0292923i
$267$	2644.97	+	1921.69i	0.0371021	+	0.0269563i
$268$	−5274.77	+	3832.34i	−0.0734401	+	0.0533574i
$269$	−9888.51	+	30433.7i	−0.136655	+	0.420582i	−0.995844	−	0.0910775i	$-0.970969\pi$
$269$	−9888.51	+	30433.7i	−0.136655	+	0.420582i	0.859189	+	0.511659i	$0.170969\pi$
$270$	−6752.17	−	2193.91i	−0.0926224	−	0.0300948i
$271$	−44758.1	−	61604.2i	−0.609442	−	0.838825i	0.387089	−	0.922042i	$-0.373481\pi$
$271$	−44758.1	−	61604.2i	−0.609442	−	0.838825i	−0.996531	+	0.0832170i	$0.973481\pi$
$272$	39643.3	−	54564.3i	0.535836	−	0.737514i
$273$	538.470	+	1657.24i	0.00722498	+	0.0222362i
$274$			71666.9i			0.954592i
$275$	59073.8	+	40578.6i	0.781141	+	0.536577i
$276$	−404.901			−0.00531533
$277$	124457.	−	40438.5i	1.62203	−	0.527031i	0.649613	−	0.760265i	$-0.274931\pi$
$277$	124457.	−	40438.5i	1.62203	−	0.527031i	0.972421	+	0.233234i	$0.0749308\pi$
$278$	20759.0	+	15082.3i	0.268607	+	0.195154i
$279$	84719.0	−	61551.9i	1.08836	−	0.790739i
$280$	−501.102	+	1542.23i	−0.00639160	+	0.0196713i
$281$	9194.42	+	2987.45i	0.116443	+	0.0378345i	0.366659	−	0.930356i	$-0.380502\pi$
$281$	9194.42	+	2987.45i	0.116443	+	0.0378345i	−0.250216	+	0.968190i	$0.580502\pi$
$282$	−7333.17	−	10093.2i	−0.0922132	−	0.126921i
$283$	−47234.2	+	65012.3i	−0.589771	+	0.811751i	−0.994724	−	0.102587i	$-0.967288\pi$
$283$	−47234.2	+	65012.3i	−0.589771	+	0.811751i	0.404953	+	0.914338i	$0.367288\pi$
$284$	1736.68	+	5344.96i	0.0215320	+	0.0662686i
$285$			4691.41i			0.0577582i
$286$	73901.0	−	56735.5i	0.903480	−	0.693622i
$287$	−1601.29			−0.0194405
$288$	−9825.49	+	3192.50i	−0.118459	+	0.0384898i
$289$	−2636.20	−	1915.31i	−0.0315634	−	0.0229321i
$290$	24271.3	−	17634.2i	0.288601	−	0.209681i
$291$	9492.14	−	29213.8i	0.112093	−	0.344987i
$292$	−6082.39	−	1976.29i	−0.0713360	−	0.0231785i
$293$	−38585.5	−	53108.3i	−0.449457	−	0.618625i	0.522823	−	0.852441i	$-0.324879\pi$
$293$	−38585.5	−	53108.3i	−0.449457	−	0.618625i	−0.972281	+	0.233816i	$0.924879\pi$
$294$	−11013.7	+	15159.1i	−0.127421	+	0.175380i
$295$	−10220.6	−	31455.6i	−0.117444	−	0.361455i
$296$			56255.0i			0.642063i
$297$	−11026.3	+	37258.2i	−0.125002	+	0.422385i
$298$	−67324.0			−0.758119
$299$	−35843.2	+	11646.2i	−0.400926	+	0.130269i
$300$	1025.26	+	744.896i	0.0113918	+	0.00827662i
$301$	−2973.44	+	2160.33i	−0.0328191	+	0.0238445i
$302$	−30746.5	+	94628.0i	−0.337118	+	1.03754i
$303$	8579.72	+	2787.72i	0.0934518	+	0.0303643i
$304$	−56435.3	−	77676.6i	−0.610666	−	0.840510i
$305$	13135.9	−	18080.0i	0.141208	−	0.194357i
$306$	26016.3	+	80069.8i	0.277845	+	0.855118i
$307$		−	120881.i		−	1.28257i	−0.767303	−	0.641284i	$-0.778402\pi$
$307$		−	120881.i		−	1.28257i	0.767303	−	0.641284i	$-0.221598\pi$
$308$	524.932	+	155.350i	0.00553352	+	0.00163761i
$309$	−30783.1			−0.322400
$310$	−28647.5	+	9308.14i	−0.298101	+	0.0968589i
$311$	92238.4	+	67015.1i	0.953654	+	0.692870i	0.951668	−	0.307128i	$-0.0993679\pi$
$311$	92238.4	+	67015.1i	0.953654	+	0.692870i	0.00198576	+	0.999998i	$0.499368\pi$
$312$	21607.3	−	15698.6i	0.221968	−	0.161269i
$313$	−22788.6	+	70136.1i	−0.232610	+	0.715901i	0.764819	+	0.644245i	$0.222828\pi$
$313$	−22788.6	+	70136.1i	−0.232610	+	0.715901i	−0.997429	+	0.0716561i	$0.977172\pi$
$314$	−130907.	−	42534.3i	−1.32771	−	0.431400i
$315$	−1111.24	−	1529.50i	−0.0111992	−	0.0154144i
$316$	2991.02	−	4116.78i	0.0299533	−	0.0412272i
$317$	46335.7	+	142607.i	0.461102	+	1.41913i	0.863819	+	0.503801i	$0.168066\pi$
$317$	46335.7	+	142607.i	0.461102	+	1.41913i	−0.402718	+	0.915324i	$0.631934\pi$
$318$			6998.62i			0.0692083i
$319$	−99986.1	−	130237.i	−0.982558	−	1.27983i
$320$	24753.3			0.241732
$321$	−23660.3	+	7687.71i	−0.229621	+	0.0746083i
$322$	2546.05	+	1849.81i	0.0245559	+	0.0178409i
$323$	92438.3	−	67160.4i	0.886027	−	0.643736i
$324$	1811.29	−	5574.57i	0.0172543	−	0.0531033i
$325$	112185.	+	36451.2i	1.06211	+	0.345100i
$326$	7374.69	+	10150.4i	0.0693919	+	0.0955097i
$327$	2579.11	−	3549.84i	0.0241198	−	0.0331981i
$328$	7584.31	+	23342.1i	0.0704966	+	0.216966i
$329$		−	6823.26i		−	0.0630377i
$330$	3081.17	−	4485.52i	0.0282935	−	0.0411893i
$331$	−78994.5			−0.721009			−0.360505	−	0.932757i	$-0.617395\pi$
$331$	−78994.5			−0.721009			−0.360505	+	0.932757i	$0.617395\pi$
$332$	2546.94	−	827.550i	0.0231069	−	0.00750789i
$333$	−53059.9	−	38550.3i	−0.478495	−	0.347647i
$334$	−32253.4	+	23433.5i	−0.289123	+	0.210060i
$335$	−10953.6	+	33711.8i	−0.0976041	+	0.300394i
$336$	−1981.04	−	643.678i	−0.0175475	−	0.00570151i
$337$	−54120.2	−	74490.1i	−0.476540	−	0.655902i	0.501295	−	0.865276i	$-0.332857\pi$
$337$	−54120.2	−	74490.1i	−0.476540	−	0.655902i	−0.977835	+	0.209375i	$0.932857\pi$
$338$	25227.6	−	34722.9i	0.220822	−	0.303936i
$339$	−6536.82	−	20118.3i	−0.0568810	−	0.175062i
$340$			1704.03i			0.0147408i
$341$	55067.7	+	155383.i	0.473574	+	1.33627i
$342$	119852.			1.02469
$343$	−19568.4	+	6358.15i	−0.166328	+	0.0540434i
$344$	45574.5	+	33111.8i	0.385128	+	0.279812i
$345$	−1780.88	+	1293.89i	−0.0149623	+	0.0108707i
$346$	58878.4	−	181209.i	0.491818	−	1.51366i
$347$	6762.59	+	2197.30i	0.0561635	+	0.0182486i	0.336964	−	0.941518i	$-0.390600\pi$
$347$	6762.59	+	2197.30i	0.0561635	+	0.0182486i	−0.280801	+	0.959766i	$0.590600\pi$
$348$	−1706.56	−	2348.87i	−0.0140917	−	0.0193955i
$349$	58471.7	−	80479.3i	0.480059	−	0.660744i	−0.498457	−	0.866914i	$-0.666100\pi$
$349$	58471.7	−	80479.3i	0.480059	−	0.660744i	0.978516	+	0.206170i	$0.0660999\pi$
$350$	−3043.83	−	9367.95i	−0.0248476	−	0.0764730i
$351$			63952.1i			0.519088i
$352$	−429.785	−	16258.1i	−0.00346869	−	0.131215i
$353$	−84674.3			−0.679520			−0.339760	−	0.940512i	$-0.610346\pi$
$353$	−84674.3			−0.679520			−0.339760	+	0.940512i	$0.610346\pi$
$354$	43261.9	−	14056.7i	0.345223	−	0.112170i
$355$	24718.7	+	17959.2i	0.196141	+	0.142505i
$356$	1367.66	−	993.664i	0.0107914	−	0.00784042i
$357$	766.003	−	2357.52i	0.00601027	−	0.0184977i
$358$	68338.5	+	22204.5i	0.533212	+	0.173251i
$359$	107040.	+	147328.i	0.830534	+	1.14313i	0.987823	+	0.155580i	$0.0497246\pi$
$359$	107040.	+	147328.i	0.830534	+	1.14313i	−0.157289	+	0.987553i	$0.550275\pi$
$360$	−17032.2	+	23442.9i	−0.131422	+	0.180886i
$361$	−9992.76	−	30754.6i	−0.0766780	−	0.235991i
$362$		−	126340.i		−	0.964101i
$363$	−24985.7	−	16208.2i	−0.189618	−	0.123005i
$364$	901.024			0.00680039
$365$	−33067.7	+	10744.3i	−0.248209	+	0.0806481i
$366$	24866.0	+	18066.2i	0.185628	+	0.134867i
$367$	−116948.	+	84967.6i	−0.868281	+	0.630843i	−0.930125	−	0.367243i	$-0.880302\pi$
$367$	−116948.	+	84967.6i	−0.868281	+	0.630843i	0.0618443	+	0.998086i	$0.480302\pi$
$368$	13921.6	−	42846.3i	0.102800	−	0.316386i
$369$	−27213.7	−	8842.26i	−0.199864	−	0.0649397i
$370$	11088.8	+	15262.4i	0.0809993	+	0.111486i
$371$	−2249.83	+	3096.63i	−0.0163457	+	0.0224979i
$372$	900.801	+	2772.38i	0.00650943	+	0.0200340i
$373$			106987.i			0.768979i	0.923129	+	0.384489i	$0.125622\pi$
$373$			106987.i			0.768979i	−0.923129	+	0.384489i	$0.874378\pi$
$374$	−132490.	+	3502.40i	−0.947198	+	0.0250393i
$375$	14160.0			0.100693
$376$	−99462.8	+	32317.4i	−0.703534	+	0.228592i
$377$	−218631.	−	158845.i	−1.53826	−	1.11761i
$378$	4320.38	−	3138.94i	0.0302369	−	0.0219684i
$379$	−37945.5	+	116784.i	−0.264169	+	0.813028i	0.727715	+	0.685880i	$0.240582\pi$
$379$	−37945.5	+	116784.i	−0.264169	+	0.813028i	−0.991884	+	0.127148i	$0.959418\pi$
$380$	2307.10	+	749.622i	0.0159772	+	0.00519129i
$381$	23263.9	+	32020.0i	0.160263	+	0.220583i
$382$	−16870.2	+	23219.9i	−0.115610	+	0.159123i
$383$	−57765.5	−	177784.i	−0.393796	−	1.21198i	−0.929896	−	0.367824i	$-0.880103\pi$
$383$	−57765.5	−	177784.i	−0.393796	−	1.21198i	0.536100	−	0.844154i	$-0.319897\pi$
$384$			29669.4i			0.201208i
$385$	2805.25	−	994.179i	0.0189256	−	0.00670723i
$386$	68327.5			0.458586
$387$	−62462.3	+	20295.2i	−0.417058	+	0.135510i
$388$	−12849.8	−	9335.93i	−0.0853558	−	0.0620146i
$389$	−60422.4	+	43899.4i	−0.399299	+	0.290108i	−0.769256	−	0.638941i	$-0.779373\pi$
$389$	−60422.4	+	43899.4i	−0.399299	+	0.290108i	0.369956	+	0.929049i	$0.379373\pi$
$390$	2767.77	−	8518.31i	0.0181970	−	0.0560046i
$391$	50988.9	+	16567.3i	0.333520	+	0.108367i
$392$	92324.4	+	127074.i	0.600820	+	0.826957i
$393$	12753.5	−	17553.7i	0.0825744	−	0.113654i
$394$	−38558.6	−	118671.i	−0.248387	−	0.764457i
$395$		−	27664.9i		−	0.177311i
$396$	8063.28	+	5538.79i	0.0514188	+	0.0353203i
$397$	245289.			1.55631			0.778157	−	0.628070i	$-0.216155\pi$
$397$	245289.			1.55631			0.778157	+	0.628070i	$0.216155\pi$
$398$	69664.3	−	22635.3i	0.439789	−	0.142896i
$399$	−2854.88	−	2074.19i	−0.0179325	−	0.0130288i
$400$	−114076.	+	82880.9i	−0.712974	+	0.518006i
$401$	81207.9	−	249932.i	0.505021	−	1.55429i	−0.295715	−	0.955276i	$-0.595558\pi$
$401$	81207.9	−	249932.i	0.505021	−	1.55429i	0.800735	−	0.599018i	$-0.204442\pi$
$402$	−46364.9	−	15064.9i	−0.286904	−	0.0932208i
$403$	159484.	+	219511.i	0.981990	+	1.35159i
$404$	2741.84	−	3773.82i	0.0167989	−	0.0231216i
$405$	−9847.31	−	30306.9i	−0.0600354	−	0.184770i
$406$			22566.4i			0.136902i
$407$	81896.5	−	62873.8i	0.494398	−	0.379560i
$408$	−37993.6			−0.228239
$409$	293990.	−	95523.0i	1.75746	−	0.571033i	0.760528	−	0.649305i	$-0.224940\pi$
$409$	293990.	−	95523.0i	1.75746	−	0.571033i	0.996932	+	0.0782718i	$0.0249402\pi$
$410$	6658.80	+	4837.90i	0.0396122	+	0.0287799i
$411$	30505.1	−	22163.2i	0.180588	−	0.131205i
$412$	−4918.71	+	15138.2i	−0.0289772	+	0.0891827i
$413$	23660.6	+	7687.79i	0.138716	+	0.0450714i
$414$	33055.1	+	45496.4i	0.192858	+	0.265446i
$415$	8557.76	−	11778.8i	0.0496894	−	0.0683916i
$416$	−8271.91	−	25458.3i	−0.0477990	−	0.147110i
$417$		−	13500.3i		−	0.0776376i
$418$	−53541.9	+	180920.i	−0.306437	+	1.03546i
$419$	48418.4			0.275793			0.137896	−	0.990447i	$-0.455966\pi$
$419$	48418.4			0.275793			0.137896	+	0.990447i	$0.455966\pi$
$420$	50.0519	−	16.2628i	0.000283741	−	9.21930e-5i
$421$	−88758.3	−	64486.7i	−0.500778	−	0.363836i	0.308536	−	0.951213i	$-0.400161\pi$
$421$	−88758.3	−	64486.7i	−0.500778	−	0.363836i	−0.809314	+	0.587376i	$0.800161\pi$
$422$	−145346.	+	105600.i	−0.816167	+	0.592980i
$423$	37677.7	−	115960.i	0.210573	−	0.648078i
$424$	55795.7	+	18129.1i	0.310362	+	0.100843i
$425$	−98631.7	−	135755.i	−0.546058	−	0.751584i
$426$	−24699.8	+	33996.4i	−0.136105	+	0.187333i
$427$	5194.58	+	15987.3i	0.0284901	+	0.0876836i
$428$			12863.9i			0.0702237i
$429$	−47003.6	−	13910.4i	−0.255398	−	0.0755830i
$430$	18891.6			0.102172
$431$	−297973.	+	96817.2i	−1.60406	+	0.521192i	−0.968108	−	0.250533i	$-0.919394\pi$
$431$	−297973.	+	96817.2i	−1.60406	+	0.521192i	−0.635957	+	0.771725i	$0.719394\pi$
$432$	−61847.1	−	44934.5i	−0.331399	−	0.240776i
$433$	21555.5	−	15661.0i	0.114969	−	0.0835301i	−0.528815	−	0.848737i	$-0.677363\pi$
$433$	21555.5	−	15661.0i	0.114969	−	0.0835301i	0.643784	+	0.765207i	$0.277363\pi$
$434$	7001.48	−	21548.3i	0.0371715	−	0.114402i
$435$	−15012.0	−	4877.69i	−0.0793340	−	0.0257772i
$436$	−1333.60	−	1835.55i	−0.00701543	−	0.00965590i
$437$	44861.1	−	61746.0i	0.234913	−	0.323330i
$438$	−14777.0	−	45479.1i	−0.0770263	−	0.237063i
$439$			191516.i			0.993745i	0.867824	+	0.496872i	$0.165518\pi$
$439$			191516.i			0.993745i	−0.867824	+	0.496872i	$0.834482\pi$
$440$	−27778.9	−	36183.5i	−0.143486	−	0.186898i
$441$	−183124.			−0.941603
$442$	−207465.	+	67409.4i	−1.06194	+	0.345045i
$443$	66184.9	+	48086.2i	0.337250	+	0.245026i	0.743501	−	0.668735i	$-0.233164\pi$
$443$	66184.9	+	48086.2i	0.337250	+	0.245026i	−0.406251	+	0.913762i	$0.633164\pi$
$444$	1477.03	−	1073.13i	0.00749245	−	0.00544358i
$445$	2840.09	−	8740.91i	0.0143421	−	0.0441404i
$446$	54352.2	+	17660.1i	0.273242	+	0.0887816i
$447$	20820.2	+	28656.5i	0.104200	+	0.143419i
$448$	−10944.1	+	15063.2i	−0.0545284	+	0.0750519i
$449$	43036.9	+	132454.i	0.213476	+	0.657011i	0.999258	+	0.0385080i	$0.0122605\pi$
$449$	43036.9	+	132454.i	0.213476	+	0.657011i	−0.785783	+	0.618503i	$0.787740\pi$
$450$		−	176014.i		−	0.869206i
$451$	25505.0	−	37129.7i	0.125392	−	0.182545i
$452$	−10938.1			−0.0535382
$453$	49786.9	−	16176.7i	0.242615	−	0.0788305i
$454$	147966.	+	107503.i	0.717876	+	0.521567i
$455$	3963.00	−	2879.29i	0.0191426	−	0.0139079i
$456$	−16713.8	+	51439.7i	−0.0803795	+	0.247383i
$457$	−154413.	−	50171.8i	−0.739352	−	0.240230i	−0.0849588	−	0.996384i	$-0.527076\pi$
$457$	−154413.	−	50171.8i	−0.739352	−	0.240230i	−0.654393	+	0.756154i	$0.727076\pi$
$458$	−27515.8	−	37872.3i	−0.131175	−	0.180547i
$459$	53473.9	−	73600.6i	0.253815	−	0.349346i
$460$	351.736	+	1082.53i	0.00166227	+	0.00511594i
$461$			112857.i			0.531039i	0.964106	+	0.265519i	$0.0855435\pi$
$461$			112857.i			0.531039i	−0.964106	+	0.265519i	$0.914457\pi$
$462$	1367.33	+	3858.15i	0.00640601	+	0.0180757i
$463$	87643.3			0.408843			0.204422	−	0.978883i	$-0.434469\pi$
$463$	87643.3			0.408843			0.204422	+	0.978883i	$0.434469\pi$
$464$	307232.	−	99825.8i	1.42702	−	0.463668i
$465$	12821.3	+	9315.25i	0.0592963	+	0.0430813i
$466$	186431.	−	135450.i	0.858510	−	0.623744i
$467$	−79391.5	+	244342.i	−0.364033	+	1.12038i	0.586552	+	0.809911i	$0.300485\pi$
$467$	−79391.5	+	244342.i	−0.364033	+	1.12038i	−0.950585	+	0.310465i	$0.899515\pi$
$468$	15312.7	+	4975.41i	0.0699135	+	0.0227163i
$469$	−15671.9	−	21570.5i	−0.0712484	−	0.0980649i
$470$	−20614.8	+	28373.8i	−0.0933217	+	0.128446i
$471$	22378.7	+	68874.5i	0.100877	+	0.310468i
$472$		−	381313.i		−	1.71158i
$473$	−2732.21	−	103355.i	−0.0122122	−	0.461967i
$474$	38048.5			0.169348
$475$	−227188.	+	73817.9i	−1.00693	+	0.327171i
$476$	−1036.96	−	753.397i	−0.00457666	−	0.00332514i
$477$	−55334.9	+	40203.2i	−0.243199	+	0.176695i
$478$	−16853.9	+	51870.9i	−0.0737640	+	0.227022i
$479$	−1835.97	−	596.544i	−0.00800194	−	0.00259999i	0.305013	−	0.952348i	$-0.401339\pi$
$479$	−1835.97	−	596.544i	−0.00800194	−	0.00259999i	−0.313015	+	0.949748i	$0.601339\pi$
$480$	−919.009	−	1264.91i	−0.00398875	−	0.00549005i
$481$	99885.5	−	137481.i	0.431730	−	0.594226i
$482$	36789.0	+	113225.i	0.158352	+	0.487358i
$483$		−	1655.79i		−	0.00709758i
$484$	−11963.1	+	9697.41i	−0.0510686	+	0.0413966i
$485$	−86351.2			−0.367100
$486$	137325.	−	44619.6i	0.581402	−	0.188909i
$487$	40263.5	+	29253.1i	0.169767	+	0.123343i	0.669424	−	0.742880i	$-0.266541\pi$
$487$	40263.5	+	29253.1i	0.169767	+	0.123343i	−0.499657	+	0.866223i	$0.666541\pi$
$488$	208443.	−	151443.i	0.875283	−	0.635930i
$489$	2039.87	−	6278.08i	0.00853071	−	0.0262548i
$490$	50096.7	+	16277.4i	0.208649	+	0.0677942i
$491$	−153461.	−	211221.i	−0.636552	−	0.876139i	0.361873	−	0.932227i	$-0.382137\pi$
$491$	−153461.	−	211221.i	−0.636552	−	0.876139i	−0.998426	+	0.0560880i	$0.982137\pi$
$492$	468.191	−	644.409i	0.00193416	−	0.00266214i
$493$	118797.	+	365619.i	0.488777	+	1.50430i
$494$			310541.i			1.27252i
$495$	53164.5	−	1405.41i	0.216976	−	0.00573579i
$496$	−324343.			−1.31838
$497$	−21857.5	+	7101.94i	−0.0884887	+	0.0287517i
$498$	16199.7	+	11769.8i	0.0653203	+	0.0474579i
$499$	244238.	−	177450.i	0.980873	−	0.712646i	0.0229696	−	0.999736i	$-0.492688\pi$
$499$	244238.	−	177450.i	0.980873	−	0.712646i	0.957904	+	0.287090i	$0.0926879\pi$
$500$	2262.57	−	6963.48i	0.00905028	−	0.0278539i
$501$	19948.9	+	6481.80i	0.0794774	+	0.0258238i
$502$	−255703.	−	351945.i	−1.01468	−	1.39659i
$503$	−117828.	+	162177.i	−0.465708	+	0.640992i	−0.975680	−	0.219199i	$-0.929656\pi$
$503$	−117828.	+	162177.i	−0.465708	+	0.640992i	0.509972	+	0.860191i	$0.329656\pi$
$504$	−6735.38	−	20729.4i	−0.0265156	−	0.0816066i
$505$		−	25360.2i		−	0.0994422i
$506$	−83445.0	+	29572.8i	−0.325911	+	0.115503i
$507$	−22581.5			−0.0878491
$508$	19463.8	−	6324.17i	0.0754224	−	0.0245062i
$509$	95901.4	+	69676.5i	0.370160	+	0.268937i	0.757277	−	0.653094i	$-0.226529\pi$
$509$	95901.4	+	69676.5i	0.370160	+	0.268937i	−0.387117	+	0.922030i	$0.626529\pi$
$510$	−10308.0	+	7489.18i	−0.0396308	+	0.0287935i
$511$	8081.77	−	24873.1i	0.0309503	−	0.0952552i
$512$	269261.	+	87488.1i	1.02715	+	0.333741i
$513$	−76124.4	−	104776.i	−0.289261	−	0.398133i
$514$	−78988.2	+	108718.i	−0.298976	+	0.411505i
$515$	26741.2	+	82300.9i	0.100825	+	0.310306i
$516$		−	1828.25i		−	0.00686650i
$517$	158213.	+	108679.i	0.591918	+	0.406597i
$518$	−14190.3			−0.0528851
$519$	−95340.1	+	30977.9i	−0.353949	+	0.115005i
$520$	−60741.6	−	44131.4i	−0.224636	−	0.163208i
$521$	−110386.	+	80200.2i	−0.406667	+	0.295461i	−0.772251	−	0.635318i	$-0.780869\pi$
$521$	−110386.	+	80200.2i	−0.406667	+	0.295461i	0.365584	+	0.930778i	$0.380869\pi$
$522$	−124611.	+	383512.i	−0.457313	+	1.40747i
$523$	−494141.	−	160556.i	−1.80654	−	0.586980i	−0.806548	−	0.591169i	$-0.798667\pi$
$523$	−494141.	−	160556.i	−1.80654	−	0.586980i	−0.999991	+	0.00418925i	$0.998667\pi$
$524$	−6594.58	−	9076.67i	−0.0240173	−	0.0330570i
$525$	−3046.16	+	4192.67i	−0.0110518	+	0.0152115i
$526$	−93906.1	−	289013.i	−0.339408	−	1.04459i
$527$		−	385982.i		−	1.38978i
$528$	46478.6	−	35682.7i	0.166719	−	0.127994i
$529$	−244029.			−0.872028
$530$	18711.4	−	6079.69i	0.0666122	−	0.0216436i
$531$	359655.	+	261305.i	1.27555	+	0.926741i
$532$	−1476.20	+	1072.52i	−0.00521580	+	0.00378950i
$533$	22910.7	−	70511.9i	0.0806462	−	0.248204i
$534$	12021.7	+	3906.07i	0.0421582	+	0.0136980i
$535$	41107.4	+	56579.5i	0.143619	+	0.197675i
$536$	−240206.	+	330615.i	−0.836091	+	1.15078i
$537$	−11682.5	−	35955.1i	−0.0405124	−	0.124684i
$538$			123721.i			0.427443i
$539$	81807.8	−	276431.i	0.281590	−	0.951501i
$540$	1931.48			0.00662372
$541$	365219.	−	118667.i	1.24784	−	0.405447i	0.390693	−	0.920521i	$-0.372236\pi$
$541$	365219.	−	118667.i	1.24784	−	0.405447i	0.857146	+	0.515074i	$0.172236\pi$
$542$	−238179.	−	173047.i	−0.810785	−	0.589070i
$543$	−53776.5	+	39070.9i	−0.182387	+	0.132512i
$544$	−11767.2	+	36215.8i	−0.0397628	+	0.122377i
$545$	−11731.3	−	3811.71i	−0.0394958	−	0.0128330i
$546$	3959.97	+	5450.43i	0.0132833	+	0.0182829i
$547$	−30441.8	+	41899.6i	−0.101741	+	0.140035i	−0.856852	−	0.515563i	$-0.827583\pi$
$547$	−30441.8	+	41899.6i	−0.101741	+	0.140035i	0.755111	+	0.655597i	$0.227583\pi$
$548$	−6024.95	−	18542.9i	−0.0200628	−	0.0617471i
$549$			300385.i			0.996628i
$550$	265699.	+	78631.6i	0.878344	+	0.259939i
$551$	547273.			1.80261
$552$	−24136.5	+	7842.41i	−0.0792128	+	0.0257378i
$553$	16835.0	+	12231.4i	0.0550508	+	0.0399968i
$554$	409322.	−	297390.i	1.33366	−	0.968961i
$555$	3067.21	−	9439.91i	0.00995768	−	0.0306466i
$556$	−6639.07	−	2157.16i	−0.0214762	−	0.00697804i
$557$	−107037.	−	147324.i	−0.345005	−	0.474859i	0.600890	−	0.799332i	$-0.294813\pi$
$557$	−107037.	−	147324.i	−0.345005	−	0.474859i	−0.945895	+	0.324473i	$0.894813\pi$
$558$	237977.	−	327548.i	0.764306	−	1.05198i
$559$	−52585.9	−	161843.i	−0.168285	−	0.517928i
$560$			5855.62i			0.0186723i
$561$	42463.8	+	55311.4i	0.134925	+	0.175747i
$562$	37377.6			0.118342
$563$	183696.	−	59686.4i	0.579539	−	0.188304i	−0.00455489	−	0.999990i	$-0.501450\pi$
$563$	183696.	−	59686.4i	0.579539	−	0.188304i	0.584094	+	0.811686i	$0.301450\pi$
$564$	2745.89	+	1995.00i	0.00863226	+	0.00627170i
$565$	−48109.2	+	34953.4i	−0.150706	+	0.109494i
$566$	−96009.5	+	295487.i	−0.299696	+	0.922371i
$567$	22796.5	+	7407.03i	0.0709091	+	0.0230398i
$568$	207050.	+	284980.i	0.641769	+	0.883319i
$569$	−154526.	+	212687.i	−0.477285	+	0.656926i	−0.977980	−	0.208697i	$-0.933078\pi$
$569$	−154526.	+	212687.i	−0.477285	+	0.656926i	0.500695	+	0.865624i	$0.333078\pi$
$570$	5605.05	+	17250.6i	0.0172516	+	0.0530950i
$571$		−	235361.i		−	0.721876i	−0.932590	−	0.360938i	$-0.882457\pi$
$571$		−	235361.i		−	0.721876i	0.932590	−	0.360938i	$-0.117543\pi$
$572$	−14351.3	+	20892.3i	−0.0438629	+	0.0638550i
$573$	15100.7			0.0459926
$574$	−5888.05	+	1913.14i	−0.0178710	+	0.00580662i
$575$	−90680.1	−	65882.9i	−0.274269	−	0.199268i
$576$	−269171.	+	195564.i	−0.811302	+	0.589446i
$577$	47468.2	−	146092.i	0.142578	−	0.438809i	−0.854114	−	0.520086i	$-0.825900\pi$
$577$	47468.2	−	146092.i	0.142578	−	0.438809i	0.996692	+	0.0812772i	$0.0258999\pi$
$578$	−11981.8	−	3893.12i	−0.0358646	−	0.0116531i
$579$	−21130.5	−	29083.6i	−0.0630307	−	0.0867543i
$580$	−4797.41	+	6603.07i	−0.0142610	+	0.0196286i
$581$	3384.16	+	10415.4i	0.0100253	+	0.0308548i
$582$		−	118762.i		−	0.350614i
$583$	−35967.9	−	101490.i	−0.105823	−	0.298597i
$584$	−400855.			−1.17533
$585$	83249.6	−	27049.4i	0.243260	−	0.0790399i
$586$	−205332.	−	149182.i	−0.597945	−	0.434433i
$587$	−362051.	+	263045.i	−1.05073	+	0.763404i	−0.972352	−	0.233520i	$-0.924976\pi$
$587$	−362051.	+	263045.i	−1.05073	+	0.763404i	−0.0783829	+	0.996923i	$0.524976\pi$
$588$	1575.25	−	4848.13i	0.00455613	−	0.0140223i
$589$	−522583.	−	169797.i	−1.50635	−	0.489441i
$590$	−75163.2	−	103453.i	−0.215924	−	0.297194i
$591$	−38588.1	+	53111.9i	−0.110479	+	0.152061i
$592$	62773.0	+	193196.i	0.179114	+	0.551256i
$593$			505323.i			1.43701i	0.695522	+	0.718505i	$0.255173\pi$
$593$			505323.i			1.43701i	−0.695522	+	0.718505i	$0.744827\pi$
$594$	3969.87	+	150174.i	0.0112513	+	0.425620i
$595$	−6968.43			−0.0196834
$596$	17419.2	−	5659.85i	0.0490384	−	0.0159335i
$597$	−31178.6	−	22652.6i	−0.0874799	−	0.0635578i
$598$	−117883.	+	85647.2i	−0.329647	+	0.239503i
$599$	137321.	−	422632.i	0.382723	−	1.17790i	−0.555396	−	0.831586i	$-0.687433\pi$
$599$	137321.	−	422632.i	0.382723	−	1.17790i	0.938119	−	0.346314i	$-0.112567\pi$
$600$	75544.4	+	24545.9i	0.209846	+	0.0681829i
$601$	239758.	+	329999.i	0.663780	+	0.913615i	0.999599	−	0.0283113i	$-0.00901296\pi$
$601$	239758.	+	329999.i	0.663780	+	0.913615i	−0.335819	+	0.941927i	$0.609013\pi$
$602$	−8352.47	+	11496.2i	−0.0230474	+	0.0317220i
$603$	−147229.	−	453125.i	−0.404911	−	1.24619i
$604$		−	27068.6i		−	0.0741979i
$605$	−21628.9	+	80881.3i	−0.0590914	+	0.220972i
$606$	34878.7			0.0949764
$607$	−295657.	+	96064.8i	−0.802437	+	0.260728i	−0.681391	−	0.731919i	$-0.738625\pi$
$607$	−295657.	+	96064.8i	−0.802437	+	0.260728i	−0.121046	+	0.992647i	$0.538625\pi$
$608$	43856.2	+	31863.4i	0.118638	+	0.0861956i
$609$	9605.41	−	6978.74i	0.0258989	−	0.0188167i
$610$	26700.4	−	82175.3i	0.0717559	−	0.220842i
$611$	300458.	+	97624.6i	0.804824	+	0.261503i
$612$	−13462.7	−	18529.9i	−0.0359444	−	0.0494732i
$613$	14556.6	−	20035.5i	0.0387382	−	0.0533186i	−0.789209	−	0.614125i	$-0.789509\pi$
$613$	14556.6	−	20035.5i	0.0387382	−	0.0533186i	0.827947	+	0.560807i	$0.189509\pi$
$614$	−144422.	−	444486.i	−0.383087	−	1.17902i
$615$		−	4330.46i		−	0.0114494i
$616$	34300.6	−	906.740i	0.0903941	−	0.00238958i
$617$	697011.			1.83092			0.915460	−	0.402408i	$-0.131827\pi$
$617$	697011.			1.83092			0.915460	+	0.402408i	$0.131827\pi$
$618$	−113191.	+	36778.0i	−0.296371	+	0.0962966i
$619$	74677.2	+	54256.1i	0.194898	+	0.141601i	0.680954	−	0.732326i	$-0.261565\pi$
$619$	74677.2	+	54256.1i	0.194898	+	0.141601i	−0.486057	+	0.873927i	$0.661565\pi$
$620$	6629.65	−	4816.72i	0.0172467	−	0.0125305i
$621$	18778.6	−	57794.5i	0.0486944	−	0.149866i
$622$	419232.	+	136217.i	1.08361	+	0.352087i
$623$	4063.46	+	5592.87i	0.0104693	+	0.0144098i
$624$	56687.8	−	78024.1i	0.145586	−	0.200382i
$625$	102093.	+	314211.i	0.261359	+	0.804381i
$626$			285121.i			0.727580i
$627$	93566.6	−	33159.9i	0.238005	−	0.0843487i
$628$	37446.3			0.0949488
$629$	−229911.	+	74702.5i	−0.581109	+	0.188814i
$630$	−5913.47	−	4296.39i	−0.0148991	−	0.0108249i
$631$	275611.	−	200243.i	0.692210	−	0.502920i	−0.185176	−	0.982705i	$-0.559286\pi$
$631$	275611.	−	200243.i	0.692210	−	0.502920i	0.877386	+	0.479785i	$0.159286\pi$
$632$	98560.1	−	303337.i	0.246756	−	0.759436i
$633$	89897.6	+	29209.5i	0.224357	+	0.0728982i
$634$	340758.	+	469013.i	0.847749	+	1.16683i
$635$	65398.8	−	90013.7i	0.162189	−	0.223234i
$636$	−588.366	−	1810.80i	−0.00145456	−	0.00447669i
$637$		−	474483.i		−	1.16934i
$638$	−523255.	−	359432.i	−1.28550	−	0.883029i
$639$	−410680.			−1.00578
$640$	79323.4	−	25773.7i	0.193661	−	0.0629241i
$641$	−90020.7	−	65403.8i	−0.219092	−	0.159180i	0.472826	−	0.881156i	$-0.343234\pi$
$641$	−90020.7	−	65403.8i	−0.219092	−	0.159180i	−0.691918	+	0.721976i	$0.743234\pi$
$642$	−77815.5	+	56536.3i	−0.188797	+	0.137169i
$643$	−19816.2	+	60988.0i	−0.0479290	+	0.147510i	−0.972157	−	0.234331i	$-0.924710\pi$
$643$	−19816.2	+	60988.0i	−0.0479290	+	0.147510i	0.924228	+	0.381841i	$0.124710\pi$
$644$	−814.269	−	264.572i	−0.00196334	−	0.000637929i
$645$	−5842.29	−	8041.23i	−0.0140431	−	0.0193287i
$646$	259661.	−	357393.i	0.622217	−	0.856408i
$647$	178305.	+	548767.i	0.425947	+	1.31093i	0.902084	+	0.431560i	$0.142037\pi$
$647$	178305.	+	548767.i	0.425947	+	1.31093i	−0.476137	+	0.879371i	$0.657963\pi$
$648$		−	367387.i		−	0.874932i
$649$	−555118.	+	426177.i	−1.31794	+	1.01181i
$650$	456061.			1.07943
$651$	−11337.3	+	3683.71i	−0.0267514	+	0.00869207i
$652$	−2761.44	−	2006.30i	−0.00649591	−	0.00471955i
$653$	−266908.	+	193920.i	−0.625943	+	0.454774i	−0.854992	−	0.518641i	$-0.826438\pi$
$653$	−266908.	+	193920.i	−0.625943	+	0.454774i	0.229050	+	0.973415i	$0.426438\pi$
$654$	5242.37	−	16134.4i	0.0122567	−	0.0377221i
$655$	−58010.3	−	18848.7i	−0.135214	−	0.0439337i
$656$	52093.3	+	71700.2i	0.121053	+	0.166615i
$657$	274696.	−	378087.i	0.636388	−	0.875913i
$658$	−8152.08	−	25089.5i	−0.0188285	−	0.0579483i
$659$			148224.i			0.341310i	0.985331	+	0.170655i	$0.0545883\pi$
$659$			148224.i			0.341310i	−0.985331	+	0.170655i	$0.945412\pi$
$660$	−420.120	+	1419.60i	−0.000964463	+	0.00325895i
$661$	−275401.			−0.630321			−0.315161	−	0.949038i	$-0.602058\pi$
$661$	−275401.			−0.630321			−0.315161	+	0.949038i	$0.602058\pi$
$662$	−290467.	+	94378.5i	−0.662798	+	0.215356i
$663$	92851.9	+	67460.9i	0.211234	+	0.153470i
$664$	135796.	−	98661.9i	0.308001	−	0.223776i
$665$	−3065.48	+	9434.59i	−0.00693195	+	0.0213344i
$666$	−241162.	−	78358.3i	−0.543701	−	0.176659i
$667$	150938.	+	207748.i	0.339271	+	0.466966i
$668$	6375.12	−	8774.60i	0.0142868	−	0.0196641i
$669$	−9291.55	−	28596.5i	−0.0207604	−	0.0638940i
$670$			137047.i			0.305295i
$671$	−453440.	−	134192.i	−1.00710	−	0.298045i
$672$	1176.06			0.00260429
$673$	−139591.	+	45355.8i	−0.308196	+	0.100139i	−0.459031	−	0.888420i	$-0.651803\pi$
$673$	−139591.	+	45355.8i	−0.308196	+	0.100139i	0.150836	+	0.988559i	$0.451803\pi$
$674$	−288000.	−	209244.i	−0.633976	−	0.460610i
$675$	−153874.	+	111796.i	−0.337722	+	0.245369i
$676$	−3608.22	+	11104.9i	−0.00789585	+	0.0243009i
$677$	613923.	+	199476.i	1.33948	+	0.435224i	0.889141	−	0.457634i	$-0.151303\pi$
$677$	613923.	+	199476.i	1.33948	+	0.435224i	0.450340	+	0.892857i	$0.351303\pi$
$678$	−48072.5	−	66166.1i	−0.104577	−	0.143938i
$679$	38178.0	−	52547.6i	0.0828084	−	0.113976i
$680$	33005.0	+	101579.i	0.0713776	+	0.219678i
$681$		−	96227.4i		−	0.207493i
$682$	388131.	+	505561.i	0.834467	+	1.08694i
$683$	−298959.			−0.640871			−0.320435	−	0.947270i	$-0.603829\pi$
$683$	−298959.			−0.640871			−0.320435	+	0.947270i	$0.603829\pi$
$684$	−31010.1	+	10075.8i	−0.0662813	+	0.0215361i
$685$	−85754.8	−	62304.5i	−0.182758	−	0.132782i
$686$	−64357.6	+	46758.5i	−0.136758	+	0.0993603i
$687$	−7610.99	+	23424.2i	−0.0161260	+	0.0496309i
$688$	193464.	+	62860.3i	0.408718	+	0.132800i
$689$	−104168.	−	143375.i	−0.219431	−	0.302020i
$690$	−5002.54	+	6885.41i	−0.0105073	+	0.0144621i
$691$	−58239.2	−	179242.i	−0.121972	−	0.375391i	0.871365	−	0.490635i	$-0.163235\pi$
$691$	−58239.2	−	179242.i	−0.121972	−	0.375391i	−0.993337	+	0.115244i	$0.963235\pi$
$692$			51835.4i			0.108247i
$693$	−22650.1	+	32973.7i	−0.0471633	+	0.0686597i
$694$	27491.6			0.0570797
$695$	−36094.2	+	11727.7i	−0.0747253	+	0.0242797i
$696$	−147224.	−	106964.i	−0.303920	−	0.220811i
$697$	−85326.2	+	61993.1i	−0.175637	+	0.127608i
$698$	118851.	−	365786.i	0.243945	−	0.750786i
$699$	−115309.	−	37466.0i	−0.235997	−	0.0766802i
$700$	1575.10	+	2167.94i	0.00321450	+	0.00442437i
$701$	71959.7	−	99044.0i	0.146438	−	0.201554i	−0.729497	−	0.683984i	$-0.760246\pi$
$701$	71959.7	−	99044.0i	0.146438	−	0.201554i	0.875935	+	0.482430i	$0.160246\pi$
$702$	76406.7	+	235155.i	0.155045	+	0.477179i
$703$			344139.i			0.696344i
$704$	−174962.	−	493687.i	−0.353019	−	0.996107i
$705$	18452.5			0.0371259
$706$	−311352.	+	101165.i	−0.624659	+	0.202964i
$707$	15432.5	+	11212.4i	0.0308744	+	0.0224316i
$708$	−10011.7	+	7273.96i	−0.0199730	+	0.0145112i
$709$	56691.8	−	174479.i	0.112779	−	0.347098i	−0.878698	−	0.477377i	$-0.841587\pi$
$709$	56691.8	−	174479.i	0.112779	−	0.347098i	0.991477	+	0.130280i	$0.0415875\pi$
$710$	112349.	+	36504.3i	0.222870	+	0.0724148i
$711$	218567.	+	300832.i	0.432360	+	0.595093i
$712$	62281.4	−	85723.0i	0.122857	−	0.169097i
$713$	−79672.0	−	245205.i	−0.156721	−	0.482337i
$714$		−	9583.90i		−	0.0187995i
$715$	3641.49	+	137752.i	0.00712306	+	0.269454i
$716$	−19548.4			−0.0381316
$717$	27291.0	−	8867.38i	0.0530861	−	0.0172487i
$718$	569613.	+	413848.i	1.10492	+	0.802771i
$719$	511463.	−	371599.i	0.989364	−	0.718815i	0.0295825	−	0.999562i	$-0.490582\pi$
$719$	511463.	−	371599.i	0.989364	−	0.718815i	0.959782	+	0.280747i	$0.0905822\pi$
$720$	−32334.4	+	99515.1i	−0.0623735	+	0.191966i
$721$	−61905.8	−	20114.4i	−0.119086	−	0.0386934i
$722$	−73487.9	−	101147.i	−0.140975	−	0.194035i
$723$	36817.1	−	50674.4i	0.0704325	−	0.0969420i
$724$	10621.2	+	32688.8i	0.0202627	+	0.0623622i
$725$		−	803726.i		−	1.52909i
$726$	−111239.	−	29746.9i	−0.211049	−	0.0564377i
$727$	358284.			0.677889			0.338945	−	0.940806i	$-0.389930\pi$
$727$	358284.			0.677889			0.338945	+	0.940806i	$0.389930\pi$
$728$	53710.8	−	17451.7i	0.101344	−	0.0329287i
$729$	303715.	+	220662.i	0.571494	+	0.415214i
$730$	−108755.	+	79015.2i	−0.204081	+	0.148274i
$731$	−74806.3	+	230230.i	−0.139992	+	0.430851i
$732$	−7952.56	−	2583.94i	−0.0148417	−	0.00482238i
$733$	−158935.	−	218755.i	−0.295809	−	0.407147i	0.635081	−	0.772446i	$-0.280967\pi$
$733$	−158935.	−	218755.i	−0.295809	−	0.407147i	−0.930890	+	0.365299i	$0.880967\pi$
$734$	−328509.	+	452154.i	−0.609755	+	0.839256i
$735$	−8564.07	−	26357.5i	−0.0158528	−	0.0487899i
$736$			25436.0i			0.0469562i
$737$	749778.	−	19820.5i	1.38038	−	0.0364905i
$738$	−110631.			−0.203124
$739$	395453.	−	128491.i	0.724113	−	0.235278i	0.0763074	−	0.997084i	$-0.475687\pi$
$739$	395453.	−	128491.i	0.724113	−	0.235278i	0.647805	+	0.761806i	$0.275687\pi$
$740$	−4152.18	−	3016.74i	−0.00758251	−	0.00550901i
$741$	132182.	−	96035.9i	0.240733	−	0.174903i
$742$	−4573.07	+	14074.5i	−0.00830616	+	0.0255637i
$743$	220573.	+	71668.6i	0.399554	+	0.129823i	0.501899	−	0.864926i	$-0.332635\pi$
$743$	220573.	+	71668.6i	0.399554	+	0.129823i	−0.102345	+	0.994749i	$0.532635\pi$
$744$	107395.	+	147816.i	0.194016	+	0.267040i
$745$	58528.9	−	80558.2i	0.105453	−	0.145143i
$746$	127823.	+	393398.i	0.229684	+	0.706895i
$747$			195694.i			0.350701i
$748$	33985.7	−	12044.5i	0.0607425	−	0.0215271i
$749$	−52605.1			−0.0937701
$750$	52067.1	−	16917.6i	0.0925637	−	0.0300758i
$751$	−533061.	−	387292.i	−0.945143	−	0.686686i	0.00451049	−	0.999990i	$-0.498564\pi$
$751$	−533061.	−	387292.i	−0.945143	−	0.686686i	−0.949653	+	0.313304i	$0.898564\pi$
$752$	−305521.	+	221974.i	−0.540264	+	0.392525i
$753$	−70728.7	+	217680.i	−0.124740	+	0.383910i
$754$	−993697.	−	322872.i	−1.74788	−	0.567920i
$755$	−86499.5	−	119056.i	−0.151747	−	0.208862i
$756$	−853.955	+	1175.37i	−0.00149414	+	0.00205651i
$757$	−239422.	−	736865.i	−0.417803	−	1.28587i	−0.909719	−	0.415224i	$-0.863703\pi$
$757$	−239422.	−	736865.i	−0.417803	−	1.28587i	0.491916	−	0.870643i	$-0.336297\pi$
$758$			474757.i			0.826291i
$759$	38393.3	+	26372.9i	0.0666457	+	0.0457799i
$760$	152047.			0.263240
$761$	377991.	−	122817.i	0.652698	−	0.212074i	0.0360944	−	0.999348i	$-0.488508\pi$
$761$	377991.	−	122817.i	0.652698	−	0.212074i	0.616603	+	0.787274i	$0.288508\pi$
$762$	123799.	+	89945.0i	0.213209	+	0.154906i
$763$	7506.24	−	5453.60i	0.0128936	−	0.00936773i
$764$	2412.88	−	7426.09i	0.00413380	−	0.0127225i
$765$	−118427.	−	38479.3i	−0.202362	−	0.0657513i
$766$	−424814.	−	584706.i	−0.724004	−	0.996506i
$767$	−677053.	+	931883.i	−1.15088	+	1.58406i
$768$	−8088.67	−	24894.4i	−0.0137137	−	0.0422064i
$769$			467800.i			0.791056i	0.918454	+	0.395528i	$0.129438\pi$
$769$			467800.i			0.791056i	−0.918454	+	0.395528i	$0.870562\pi$
$770$	9127.28	−	7007.22i	0.0153943	−	0.0118186i
$771$	70703.2			0.118941
$772$	−17678.8	+	5744.21i	−0.0296633	+	0.00963819i
$773$	−815285.	−	592339.i	−1.36443	−	0.991314i	−0.998149	−	0.0608086i	$-0.980632\pi$
$773$	−815285.	−	592339.i	−1.36443	−	0.991314i	−0.366278	−	0.930506i	$-0.619368\pi$
$774$	−205430.	+	149253.i	−0.342911	+	0.249139i
$775$	−249364.	+	767465.i	−0.415175	+	1.27778i
$776$	−946812.	−	307638.i	−1.57232	−	0.510877i
$777$	4388.41	+	6040.12i	0.00726884	+	0.0100047i
$778$	−169728.	+	233610.i	−0.280410	+	0.385951i
$779$	46396.9	+	142795.i	0.0764564	+	0.235309i
$780$			2436.68i			0.00400507i
$781$	183465.	−	619935.i	0.300782	−	1.01635i
$782$	207283.			0.338961
$783$	414419.	−	134653.i	0.675953	−	0.219630i
$784$	458865.	+	333385.i	0.746539	+	0.542392i
$785$	164701.	−	119662.i	0.267274	−	0.194186i
$786$	25923.2	−	79783.3i	0.0419607	−	0.129142i
$787$	464002.	+	150763.i	0.749153	+	0.243415i	0.658617	−	0.752478i	$-0.271142\pi$
$787$	464002.	+	150763.i	0.749153	+	0.243415i	0.0905365	+	0.995893i	$0.471142\pi$
$788$	19953.1	+	27463.1i	0.0321335	+	0.0442279i
$789$	−93977.8	+	129349.i	−0.150963	+	0.207783i
$790$	−33052.6	−	101726.i	−0.0529605	−	0.162996i
$791$		−	44729.8i		−	0.0714898i
$792$	587938.	+	173996.i	0.937306	+	0.277389i
$793$	−778310.			−1.23767
$794$	901942.	−	293059.i	1.43066	−	0.464851i
$795$	−8374.37	−	6084.34i	−0.0132501	−	0.00962673i
$796$	−16121.8	+	11713.2i	−0.0254441	+	0.0184862i
$797$	−40264.9	+	123923.i	−0.0633884	+	0.195089i	−0.977735	−	0.209843i	$-0.932705\pi$
$797$	−40264.9	+	123923.i	−0.0633884	+	0.195089i	0.914347	+	0.404932i	$0.132705\pi$
$798$	−12975.7	−	4216.06i	−0.0203763	−	0.00662065i
$799$	−264158.	−	363583.i	−0.413781	−	0.569521i
$800$	46794.6	−	64407.3i	0.0731166	−	0.100636i
$801$	38174.1	+	117488.i	0.0594982	+	0.183117i
$802$		−	1.01604e6i		−	1.57965i
$803$	448018.	+	583567.i	0.694807	+	0.905023i
$804$	13262.8			0.0205174
$805$	−4426.88	+	1438.38i	−0.00683134	+	0.00221964i
$806$	848692.	+	616611.i	1.30641	+	0.949163i
$807$	52661.8	−	38261.0i	0.0808627	−	0.0587502i
$808$	90349.3	−	278067.i	0.138389	−	0.425918i
$809$	561871.	+	182563.i	0.858498	+	0.278943i	0.705001	−	0.709206i	$-0.250947\pi$
$809$	561871.	+	182563.i	0.858498	+	0.278943i	0.153497	+	0.988149i	$0.450947\pi$
$810$	−72418.2	−	99675.1i	−0.110377	−	0.151921i
$811$	147448.	−	202945.i	0.224180	−	0.308558i	−0.682080	−	0.731277i	$-0.738924\pi$
$811$	147448.	−	202945.i	0.224180	−	0.308558i	0.906261	+	0.422720i	$0.138924\pi$
$812$	−1897.13	−	5838.77i	−0.00287730	−	0.00885542i
$813$			154897.i			0.234348i
$814$	226020.	−	329036.i	0.341112	−	0.496587i
$815$	−18557.0			−0.0279378
$816$	−130481.	+	42395.8i	−0.195959	+	0.0636711i
$817$	278802.	+	202561.i	0.417687	+	0.303467i
$818$	966891.	−	702487.i	1.44501	−	1.04986i
$819$	−20346.3	+	62619.4i	−0.0303331	+	0.0933557i
$820$	−2129.60	−	691.947i	−0.00316716	−	0.00102907i
$821$	80188.7	+	110370.i	0.118967	+	0.163744i	0.864347	−	0.502896i	$-0.167732\pi$
$821$	80188.7	+	110370.i	0.118967	+	0.163744i	−0.745380	+	0.666640i	$0.767732\pi$
$822$	85689.4	−	117941.i	0.126819	−	0.174551i
$823$	−107933.	−	332183.i	−0.159351	−	0.490431i	0.839225	−	0.543784i	$-0.183009\pi$
$823$	−107933.	−	332183.i	−0.159351	−	0.490431i	−0.998576	+	0.0533534i	$0.983009\pi$
$824$			997671.i			1.46938i
$825$	−48698.6	−	137412.i	−0.0715499	−	0.201891i
$826$	96186.2			0.140978
$827$	−1.10535e6	+	359149.i	−1.61617	+	0.525126i	−0.971034	−	0.238941i	$-0.923200\pi$
$827$	−1.10535e6	+	359149.i	−1.61617	+	0.525126i	−0.645137	+	0.764067i	$0.723200\pi$
$828$	−12377.4	−	8992.70i	−0.0180538	−	0.0131168i
$829$	217448.	−	157985.i	0.316407	−	0.229883i	−0.418234	−	0.908339i	$-0.637351\pi$
$829$	217448.	−	157985.i	0.316407	−	0.229883i	0.734641	+	0.678456i	$0.237351\pi$
$830$	17394.7	−	53535.5i	0.0252500	−	0.0777116i
$831$	−253168.	−	82259.3i	−0.366612	−	0.119119i
$832$	−506715.	−	697434.i	−0.732010	−	1.00753i
$833$	−396741.	+	546068.i	−0.571765	+	0.786967i
$834$	−16129.5	−	49641.4i	−0.0231893	−	0.0713694i
$835$		−	58965.7i		−	0.0845720i
$836$	−1356.44	−	51311.9i	−0.00194083	−	0.0734185i
$837$	−437500.			−0.624492
$838$	178037.	−	57847.9i	0.253526	−	0.0823757i
$839$	−59621.4	−	43317.5i	−0.0846990	−	0.0615374i	0.544630	−	0.838677i	$-0.316670\pi$
$839$	−59621.4	−	43317.5i	−0.0846990	−	0.0615374i	−0.629329	+	0.777139i	$0.716670\pi$
$840$	2668.64	−	1938.88i	0.00378209	−	0.00274785i
$841$	−350442.	+	1.07855e6i	−0.495477	+	1.52492i
$842$	−403415.	−	131077.i	−0.569020	−	0.184886i
$843$	−11559.2	−	15909.8i	−0.0162656	−	0.0223877i
$844$	28728.8	−	39541.8i	0.0403304	−	0.0555100i
$845$	19616.5	+	60373.5i	0.0274732	+	0.0845537i
$846$		−	471407.i		−	0.658651i
$847$	−39656.3	−	48921.6i	−0.0552771	−	0.0681921i
$848$	211848.			0.294599
$849$	155465.	−	50513.8i	0.215684	−	0.0700800i
$850$	−524867.	−	381338.i	−0.726460	−	0.527804i
$851$	−130637.	+	94913.5i	−0.180388	+	0.131060i
$852$	3532.72	−	10872.6i	0.00486665	−	0.0149780i
$853$	124657.	+	40503.6i	0.171325	+	0.0556668i	0.393423	−	0.919357i	$-0.371291\pi$
$853$	124657.	+	40503.6i	0.171325	+	0.0556668i	−0.222099	+	0.975024i	$0.571291\pi$
$854$	38201.5	+	52579.9i	0.0523799	+	0.0720948i
$855$	−104195.	+	143411.i	−0.142532	+	0.196179i
$856$	249157.	+	766826.i	0.340036	+	1.04652i
$857$		−	685022.i		−	0.932702i	−0.884600	−	0.466351i	$-0.845568\pi$
$857$		−	685022.i		−	0.932702i	0.884600	−	0.466351i	$-0.154432\pi$
$858$	−189454.	+	5008.25i	−0.257353	+	0.00680317i
$859$	−603707.			−0.818164			−0.409082	−	0.912498i	$-0.634151\pi$
$859$	−603707.			−0.818164			−0.409082	+	0.912498i	$0.634151\pi$
$860$	−4887.96	+	1588.20i	−0.00660893	+	0.00214737i
$861$	2635.23	+	1914.61i	0.00355477	+	0.00258269i
$862$	−979990.	+	712005.i	−1.31889	+	0.958227i
$863$	−40130.6	+	123509.i	−0.0538832	+	0.165836i	−0.974377	−	0.224923i	$-0.927787\pi$
$863$	−40130.6	+	123509.i	−0.0538832	+	0.165836i	0.920493	+	0.390758i	$0.127787\pi$
$864$	41049.6	+	13337.8i	0.0549898	+	0.0178673i
$865$	165644.	+	227989.i	0.221382	+	0.304706i
$866$	60549.8	−	83339.7i	0.0807378	−	0.111126i
$867$	2048.30	+	6304.01i	0.00272493	+	0.00838646i
$868$			6163.96i			0.00818126i
$869$	−551757.	+	195542.i	−0.730648	+	0.258941i
$870$	−61027.5			−0.0806282
$871$	1.17407e6	−	381478.i	1.54759	−	0.502844i
$872$	−115049.	−	83588.4i	−0.151304	−	0.109929i
$873$	938993.	−	682218.i	1.23207	−	0.895148i
$874$	91185.8	−	280641.i	0.119373	−	0.367391i
$875$	28476.2	+	9252.49i	0.0371934	+	0.0120849i
$876$	7646.73	+	10524.8i	0.00996478	+	0.0137153i
$877$	120617.	−	166015.i	0.156823	−	0.215848i	−0.723375	−	0.690456i	$-0.757410\pi$
$877$	120617.	−	166015.i	0.156823	−	0.215848i	0.880197	+	0.474608i	$0.157410\pi$
$878$	228813.	+	704213.i	0.296819	+	0.913514i
$879$			133535.i			0.172829i
$880$	−135776.	−	93266.6i	−0.175331	−	0.120437i
$881$	506687.			0.652811			0.326406	−	0.945230i	$-0.394162\pi$
$881$	506687.			0.652811			0.326406	+	0.945230i	$0.394162\pi$
$882$	−673357.	+	218787.i	−0.865582	+	0.281245i
$883$	545222.	+	396127.i	0.699282	+	0.508058i	0.879698	−	0.475532i	$-0.157745\pi$
$883$	545222.	+	396127.i	0.699282	+	0.508058i	−0.180416	+	0.983590i	$0.557745\pi$
$884$	48011.8	−	34882.6i	0.0614389	−	0.0446379i
$885$	−20790.5	+	63986.4i	−0.0265447	+	0.0816961i
$886$	300817.	+	97741.3i	0.383208	+	0.124512i
$887$	−672807.	−	926039.i	−0.855152	−	1.17702i	−0.982704	−	0.185184i	$-0.940712\pi$
$887$	−672807.	−	926039.i	−0.855152	−	1.17702i	0.127552	−	0.991832i	$-0.459288\pi$
$888$	67261.9	−	92578.1i	0.0852989	−	0.117404i
$889$	25861.9	+	79594.7i	0.0327232	+	0.100712i
$890$		−	35534.0i		−	0.0448605i
$891$	−534845.	+	410613.i	−0.673710	+	0.517222i
$892$	−15547.6			−0.0195404
$893$	−608463.	+	197701.i	−0.763011	+	0.247917i
$894$	110794.	+	80496.7i	0.138625	+	0.100717i
$895$	−85980.3	+	62468.3i	−0.107338	+	0.0779855i
$896$	−19386.7	+	59666.1i	−0.0241484	+	0.0743210i
$897$	72911.5	+	23690.4i	0.0906173	+	0.0294434i
$898$	316498.	+	435623.i	0.392481	+	0.540204i
$899$	1.08667e6	−	1.49567e6i	1.34455	−	1.85061i
$900$	14797.3	+	45541.4i	0.0182683	+	0.0562240i
$901$			252107.i			0.310553i
$902$	49422.5	−	167000.i	0.0607451	−	0.205260i
$903$	7476.38			0.00916887
$904$	−652027.	+	211857.i	−0.797864	+	0.259242i
$905$	151175.	+	109835.i	0.184579	+	0.134105i
$906$	163742.	−	118966.i	0.199482	−	0.144932i
$907$	301408.	−	927639.i	0.366387	−	1.12762i	−0.582721	−	0.812673i	$-0.698012\pi$
$907$	301408.	−	927639.i	0.366387	−	1.12762i	0.949108	−	0.314951i	$-0.101988\pi$
$908$	−47321.9	−	15375.8i	−0.0573971	−	0.0186495i
$909$	200359.	+	275770.i	0.242483	+	0.333749i
$910$	11132.1	−	15322.1i	0.0134430	−	0.0185027i
$911$	46581.2	+	143362.i	0.0561273	+	0.172742i	0.975190	−	0.221369i	$-0.0710525\pi$
$911$	46581.2	+	143362.i	0.0561273	+	0.172742i	−0.919063	+	0.394111i	$0.871053\pi$
$912$			195309.i			0.234818i
$913$	−295406.	−	87423.4i	−0.354388	−	0.104878i
$914$	−627728.			−0.751413
$915$	−43235.1	+	14047.9i	−0.0516410	+	0.0167792i
$916$	10303.2	+	7485.74i	0.0122796	+	0.00892162i
$917$	37117.8	−	26967.7i	0.0441412	−	0.0320705i
$918$	108693.	−	334521.i	0.128978	−	0.396952i
$919$	1.53858e6	+	499916.i	1.82176	+	0.591924i	0.999748	+	0.0224486i	$0.00714620\pi$
$919$	1.53858e6	+	499916.i	1.82176	+	0.591924i	0.822008	+	0.569476i	$0.192854\pi$
$920$	41934.6	+	57718.0i	0.0495447	+	0.0681924i
$921$	−144533.	+	198932.i	−0.170391	+	0.234523i
$922$	134836.	+	414981.i	0.158614	+	0.488165i
$923$		−	1.06409e6i		−	1.24904i
$924$	−678.128	−	883.298i	−0.000794269	−	0.00103458i
$925$	505403.			0.590683
$926$	322269.	−	104712.i	0.375835	−	0.122116i
$927$	−941006.	−	683681.i	−1.09505	−	0.795598i
$928$	−147557.	+	107206.i	−0.171342	+	0.124487i
$929$	82655.6	−	254388.i	0.0957725	−	0.294757i	−0.891682	−	0.452663i	$-0.850474\pi$
$929$	82655.6	−	254388.i	0.0957725	−	0.294757i	0.987454	+	0.157905i	$0.0504741\pi$
$930$	58274.2	+	18934.4i	0.0673768	+	0.0218921i
$931$	564793.	+	777371.i	0.651613	+	0.896869i
$932$	−36849.4	+	50718.9i	−0.0424228	+	0.0583899i
$933$	−71668.1	−	220572.i	−0.0823308	−	0.253388i
$934$			993312.i			1.13865i
$935$	110991.	−	161579.i	0.126959	−	0.184826i
$936$	1.00917e6			1.15190
$937$	−1.10220e6	+	358125.i	−1.25539	+	0.407902i	−0.859850	−	0.510546i	$-0.829443\pi$
$937$	−1.10220e6	+	358125.i	−1.25539	+	0.407902i	−0.395542	+	0.918448i	$0.629443\pi$
$938$	−83397.6	−	60591.9i	−0.0947868	−	0.0688666i
$939$	121362.	−	88174.6i	0.137642	−	0.100003i
$940$	2948.45	−	9074.40i	0.00333686	−	0.0102698i
$941$	−576099.	−	187186.i	−0.650605	−	0.211395i	−0.0349244	−	0.999390i	$-0.511119\pi$
$941$	−576099.	−	187186.i	−0.650605	−	0.211395i	−0.615681	+	0.787995i	$0.711119\pi$
$942$	164575.	+	226519.i	0.185465	+	0.255271i
$943$	−41409.5	+	56995.3i	−0.0465668	+	0.0640937i
$944$	−425494.	−	1.30953e6i	−0.477473	−	1.46951i
$945$			7898.52i			0.00884468i
$946$	−133530.	−	376779.i	−0.149210	−	0.421022i
$947$	−359430.			−0.400788			−0.200394	−	0.979715i	$-0.564222\pi$
$947$	−359430.			−0.400788			−0.200394	+	0.979715i	$0.564222\pi$
$948$	−9844.55	+	3198.69i	−0.0109542	+	0.00355922i
$949$	979641.	+	711751.i	1.08776	+	0.790307i
$950$	−747190.	+	542865.i	−0.827912	+	0.601513i
$951$	94255.1	−	290087.i	0.104218	−	0.320751i
$952$	−76406.5	−	24826.0i	−0.0843056	−	0.0273925i
$953$	651891.	+	897251.i	0.717777	+	0.987935i	0.999595	+	0.0284668i	$0.00906249\pi$
$953$	651891.	+	897251.i	0.717777	+	0.987935i	−0.281818	+	0.959468i	$0.590938\pi$
$954$	−155437.	+	213941.i	−0.170788	+	0.235070i
$955$	−13118.0	−	40372.9i	−0.0143833	−	0.0442673i
$956$		−	14837.8i		−	0.0162351i
$957$	8826.14	+	333879.i	0.00963711	+	0.364557i
$958$	−7463.70			−0.00813248
$959$	75828.7	−	24638.3i	0.0824511	−	0.0267900i
$960$	−40736.2	−	29596.6i	−0.0442016	−	0.0321144i
$961$	−754542.	+	548207.i	−0.817027	+	0.593605i
$962$	203030.	−	624862.i	0.219387	−	0.675203i
$963$	−894013.	−	290482.i	−0.964032	−	0.313233i
$964$	−19037.3	−	26202.7i	−0.0204858	−	0.0281963i
$965$	−59401.3	+	81758.9i	−0.0637883	+	0.0877971i
$966$	−1978.25	−	6088.43i	−0.00211996	−	0.00652455i
$967$			355560.i			0.380242i	0.981761	+	0.190121i	$0.0608881\pi$
$967$			355560.i			0.380242i	−0.981761	+	0.190121i	$0.939112\pi$
$968$	−525305.	+	809781.i	−0.560610	+	0.864205i
$969$	−232425.			−0.247535
$970$	−317518.	+	103168.i	−0.337462	+	0.109648i
$971$	−1.13033e6	−	821235.i	−1.19886	−	0.871021i	−0.204686	−	0.978828i	$-0.565617\pi$
$971$	−1.13033e6	−	821235.i	−1.19886	−	0.871021i	−0.994172	+	0.107806i	$0.965617\pi$
$972$	−31779.9	+	23089.5i	−0.0336372	+	0.0244389i
$973$	8821.44	−	27149.6i	0.00931781	−	0.0286773i
$974$	183001.	+	59460.7i	0.192902	+	0.0626775i
$975$	−141038.	−	194123.i	−0.148364	−	0.204205i
$976$	546863.	−	752692.i	0.574088	−	0.790165i
$977$	−206153.	−	634473.i	−0.215973	−	0.664697i	−0.999083	−	0.0428140i	$-0.986368\pi$
$977$	−206153.	−	634473.i	−0.215973	−	0.664697i	0.783110	−	0.621884i	$-0.213632\pi$
$978$		−	25522.0i		−	0.0266831i
$979$	−194405.	+	5139.13i	−0.202835	+	0.00536197i
$980$	−14330.3			−0.0149212
$981$	157681.	−	51233.8i	0.163849	−	0.0532376i
$982$	−816639.	−	593323.i	−0.846851	−	0.615273i
$983$	−991387.	+	720285.i	−1.02597	+	0.745413i	−0.967499	−	0.252876i	$-0.918624\pi$
$983$	−991387.	+	720285.i	−1.02597	+	0.745413i	−0.0584744	+	0.998289i	$0.518624\pi$
$984$	15427.8	−	47482.0i	0.0159336	−	0.0490387i
$985$	175520.	+	57030.0i	0.180907	+	0.0587802i
$986$	873645.	+	1.20247e6i	0.898631	+	1.23686i
$987$	−8158.31	+	11228.9i	−0.00837463	+	0.0115267i
$988$	−26106.8	−	80348.6i	−0.0267449	−	0.0823122i
$989$			161701.i			0.165318i
$990$	193810.	−	68686.0i	0.197745	−	0.0700806i
$991$	884970.			0.901117			0.450558	−	0.892747i	$-0.351225\pi$
$991$	884970.			0.901117			0.450558	+	0.892747i	$0.351225\pi$
$992$	174162.	−	56588.6i	0.176982	−	0.0575050i
$993$	130000.	+	94450.6i	0.131839	+	0.0957869i
$994$	−71886.3	+	52228.4i	−0.0727567	+	0.0528609i
$995$	−33478.7	+	103037.i	−0.0338160	+	0.104075i
$996$	−5180.93	−	1683.39i	−0.00522263	−	0.00169693i
$997$	−138865.	−	191132.i	−0.139702	−	0.192284i	0.733433	−	0.679762i	$-0.237917\pi$
$997$	−138865.	−	191132.i	−0.139702	−	0.192284i	−0.873135	+	0.487478i	$0.837917\pi$
$998$	686071.	−	944296.i	0.688823	−	0.948084i
$999$	84673.2	+	260597.i	0.0848428	+	0.261119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.5.d.a.6.3	yes	12
3.2	odd	2		99.5.k.a.28.1		12
4.3	odd	2		176.5.n.a.17.2		12
11.2	odd	10	inner	11.5.d.a.2.3	✓	12
11.3	even	5		121.5.b.b.120.4		12
11.4	even	5		121.5.d.c.118.3		12
11.5	even	5		121.5.d.e.40.1		12
11.6	odd	10		121.5.d.c.40.3		12
11.7	odd	10		121.5.d.e.118.1		12
11.8	odd	10		121.5.b.b.120.9		12
11.9	even	5		121.5.d.d.112.1		12
11.10	odd	2		121.5.d.d.94.1		12
33.2	even	10		99.5.k.a.46.1		12
44.35	even	10		176.5.n.a.145.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.5.d.a.2.3	✓	12	11.2	odd	10	inner
11.5.d.a.6.3	yes	12	1.1	even	1	trivial
99.5.k.a.28.1		12	3.2	odd	2
99.5.k.a.46.1		12	33.2	even	10
121.5.b.b.120.4		12	11.3	even	5
121.5.b.b.120.9		12	11.8	odd	10
121.5.d.c.40.3		12	11.6	odd	10
121.5.d.c.118.3		12	11.4	even	5
121.5.d.d.94.1		12	11.10	odd	2
121.5.d.d.112.1		12	11.9	even	5
121.5.d.e.40.1		12	11.5	even	5
121.5.d.e.118.1		12	11.7	odd	10
176.5.n.a.17.2		12	4.3	odd	2
176.5.n.a.145.2		12	44.35	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	11.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.67706 - 1.19475i) q^{2} +(-1.64569 - 1.19566i) q^{3} +(-0.850950 + 0.618251i) q^{4} +(-1.76709 + 5.43854i) q^{5} +(-7.47979 - 2.43033i) q^{6} +(-2.52826 - 3.47985i) q^{7} +(-38.7511 + 53.3363i) q^{8} +(-23.7517 - 73.1002i) q^{9} +22.1090i q^{10} +(120.958 - 3.19753i) q^{11} +2.13961 q^{12} +(189.406 - 61.5418i) q^{13} +(-13.4541 - 9.77497i) q^{14} +(9.41072 - 6.83729i) q^{15} +(-73.5659 + 226.413i) q^{16} +(-269.440 - 87.5465i) q^{17} +(-174.673 - 240.416i) q^{18} +(-237.059 + 326.284i) q^{19} +(-1.85868 - 5.72043i) q^{20} +8.74968i q^{21} +(440.948 - 156.272i) q^{22} -189.240 q^{23} +(127.544 - 41.4416i) q^{24} +(479.181 + 348.145i) q^{25} +(622.930 - 452.585i) q^{26} +(-99.2315 + 305.403i) q^{27} +(4.30284 + 1.39808i) q^{28} +(-797.600 - 1097.80i) q^{29} +(26.4349 - 36.3845i) q^{30} +(421.011 + 1295.74i) q^{31} -134.411i q^{32} +(-202.882 - 139.362i) q^{33} -1095.34 q^{34} +(23.3929 - 7.60083i) q^{35} +(65.4058 + 47.5201i) q^{36} +(690.326 - 501.551i) q^{37} +(-481.853 + 1482.99i) q^{38} +(-385.286 - 125.187i) q^{39} +(-221.595 - 304.999i) q^{40} +(218.820 - 301.180i) q^{41} +(10.4537 + 32.1731i) q^{42} -854.475i q^{43} +(-100.952 + 77.5032i) q^{44} +439.530 q^{45} +(-695.846 + 226.094i) q^{46} +(1283.36 + 932.413i) q^{47} +(391.779 - 284.644i) q^{48} +(736.233 - 2265.89i) q^{49} +(2177.92 + 707.649i) q^{50} +(338.738 + 466.233i) q^{51} +(-123.127 + 169.469i) q^{52} +(-274.987 - 846.322i) q^{53} +1241.54i q^{54} +(-196.353 + 663.484i) q^{55} +283.575 q^{56} +(780.250 - 253.519i) q^{57} +(-4244.42 - 3083.75i) q^{58} +(-4679.23 + 3399.66i) q^{59} +(-3.78089 + 11.6364i) q^{60} +(-3716.82 - 1207.67i) q^{61} +(3096.16 + 4261.50i) q^{62} +(-194.327 + 267.468i) q^{63} +(-1337.64 - 4116.84i) q^{64} +1138.84i q^{65} +(-912.510 - 270.051i) q^{66} +6198.68 q^{67} +(283.406 - 92.0841i) q^{68} +(311.430 + 226.267i) q^{69} +(76.9361 - 55.8974i) q^{70} +(1651.10 - 5081.57i) q^{71} +(4819.30 + 1565.88i) q^{72} +(3573.88 + 4919.03i) q^{73} +(1939.14 - 2669.00i) q^{74} +(-372.317 - 1145.87i) q^{75} -424.213i q^{76} +(-316.939 - 412.830i) q^{77} -1566.29 q^{78} +(-4601.08 + 1494.98i) q^{79} +(-1101.36 - 800.182i) q^{80} +(-4508.34 + 3275.50i) q^{81} +(444.780 - 1368.89i) q^{82} +(-2421.43 - 786.770i) q^{83} +(-5.40950 - 7.44553i) q^{84} +(952.250 - 1310.66i) q^{85} +(-1020.88 - 3141.95i) q^{86} +2760.30i q^{87} +(-4516.70 + 6575.34i) q^{88} -1607.22 q^{89} +(1616.18 - 525.127i) q^{90} +(-693.023 - 503.511i) q^{91} +(161.034 - 116.998i) q^{92} +(856.411 - 2635.76i) q^{93} +(5832.97 + 1895.25i) q^{94} +(-1355.60 - 1865.83i) q^{95} +(-160.710 + 221.199i) q^{96} +(4666.32 + 14361.5i) q^{97} -9211.42i q^{98} +(-3106.69 - 8766.09i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9} - 43 q^{11} + 594 q^{12} + 250 q^{13} + 610 q^{14} + 1134 q^{15} - 633 q^{16} - 1250 q^{17} - 3150 q^{18} - 1025 q^{19}+ \cdots - 3269 q^{99}+O(q^{100}) \) 12 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 - 18 * q^5 + 75 * q^6 - 80 * q^7 - 245 * q^8 + q^9 - 43 * q^11 + 594 * q^12 + 250 * q^13 + 610 * q^14 + 1134 * q^15 - 633 * q^16 - 1250 * q^17 - 3150 * q^18 - 1025 * q^19 + 752 * q^20 - 35 * q^22 + 1684 * q^23 + 5345 * q^24 + 197 * q^25 + 3490 * q^26 - 687 * q^27 - 3580 * q^28 - 2690 * q^29 - 6740 * q^30 - 1136 * q^31 + 5939 * q^33 + 2370 * q^34 + 3610 * q^35 - 514 * q^36 - 336 * q^37 + 1900 * q^38 - 6880 * q^39 - 2340 * q^40 - 4550 * q^41 + 1310 * q^42 - 6268 * q^44 + 5136 * q^45 + 4150 * q^46 + 24 * q^47 + 344 * q^48 + 827 * q^49 + 8895 * q^50 + 13155 * q^51 + 14070 * q^52 + 414 * q^53 - 2738 * q^55 - 21340 * q^56 - 26925 * q^57 + 2980 * q^58 - 10011 * q^59 - 6856 * q^60 + 9460 * q^61 - 6200 * q^62 + 9150 * q^63 - 2633 * q^64 - 3210 * q^66 + 12154 * q^67 - 9400 * q^68 - 9022 * q^69 - 9380 * q^70 + 17574 * q^71 + 43045 * q^72 + 27950 * q^73 + 43270 * q^74 - 1761 * q^75 + 4090 * q^77 - 42920 * q^78 - 41540 * q^79 - 2308 * q^80 - 21080 * q^81 - 28175 * q^82 - 18665 * q^83 + 26250 * q^84 - 4230 * q^85 - 10125 * q^86 - 15125 * q^88 + 5554 * q^89 + 18400 * q^90 + 7390 * q^91 + 3904 * q^92 + 36898 * q^93 + 18920 * q^94 + 14110 * q^95 - 21140 * q^96 + 20769 * q^97 - 3269 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more