LMFDB - Embedded newform 51.6.h.a.19.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,6,Mod(19,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.19"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	51.h (of order $8$, 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:	$8.17957481046$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	51.19
Dual form			51.6.h.a.43.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.44799 - 3.44799i) q^{2} +(8.31492 - 3.44415i) q^{3} -8.22272i q^{4} +(33.9684 + 82.0071i) q^{5} +(-40.5452 - 16.7944i) q^{6} +(-45.3741 + 109.543i) q^{7} +(-138.688 + 138.688i) q^{8} +(57.2756 - 57.2756i) q^{9} +(165.637 - 399.883i) q^{10} +(91.2207 + 37.7848i) q^{11} +(-28.3203 - 68.3712i) q^{12} +783.191i q^{13} +(534.152 - 221.253i) q^{14} +(564.890 + 564.890i) q^{15} +693.260 q^{16} +(1175.95 - 192.328i) q^{17} -394.972 q^{18} +(-466.593 - 466.593i) q^{19} +(674.321 - 279.313i) q^{20} +1067.11i q^{21} +(-184.246 - 444.810i) q^{22} +(3970.71 + 1644.72i) q^{23} +(-675.515 + 1630.84i) q^{24} +(-3361.60 + 3361.60i) q^{25} +(2700.43 - 2700.43i) q^{26} +(278.976 - 673.508i) q^{27} +(900.739 + 373.098i) q^{28} +(-2999.68 - 7241.87i) q^{29} -3895.47i q^{30} +(-4782.70 + 1981.06i) q^{31} +(2047.65 + 2047.65i) q^{32} +888.629 q^{33} +(-4717.82 - 3391.53i) q^{34} -10524.6 q^{35} +(-470.962 - 470.962i) q^{36} +(-7147.02 + 2960.39i) q^{37} +3217.62i q^{38} +(2697.43 + 6512.16i) q^{39} +(-16084.4 - 6662.36i) q^{40} +(-3572.56 + 8624.93i) q^{41} +(3679.40 - 3679.40i) q^{42} +(10379.9 - 10379.9i) q^{43} +(310.694 - 750.082i) q^{44} +(6642.57 + 2751.44i) q^{45} +(-8019.99 - 19362.0i) q^{46} +4979.13i q^{47} +(5764.40 - 2387.69i) q^{48} +(1943.54 + 1943.54i) q^{49} +23181.5 q^{50} +(9115.55 - 5649.35i) q^{51} +6439.96 q^{52} +(11149.4 + 11149.4i) q^{53} +(-3284.16 + 1360.34i) q^{54} +8764.23i q^{55} +(-8899.39 - 21485.0i) q^{56} +(-5486.70 - 2272.67i) q^{57} +(-14627.0 + 35312.8i) q^{58} +(8970.38 - 8970.38i) q^{59} +(4644.93 - 4644.93i) q^{60} +(-10981.2 + 26510.8i) q^{61} +(23321.4 + 9660.02i) q^{62} +(3675.30 + 8872.96i) q^{63} -36304.9i q^{64} +(-64227.2 + 26603.8i) q^{65} +(-3063.98 - 3063.98i) q^{66} +266.677 q^{67} +(-1581.46 - 9669.54i) q^{68} +38680.8 q^{69} +(36288.6 + 36288.6i) q^{70} +(41870.6 - 17343.4i) q^{71} +15886.8i q^{72} +(-27960.6 - 67502.8i) q^{73} +(34850.3 + 14435.5i) q^{74} +(-16373.6 + 39529.3i) q^{75} +(-3836.67 + 3836.67i) q^{76} +(-8278.11 + 8278.11i) q^{77} +(13153.2 - 31754.6i) q^{78} +(-6368.37 - 2637.87i) q^{79} +(23549.0 + 56852.2i) q^{80} -6561.00i q^{81} +(42056.9 - 17420.5i) q^{82} +(-43091.0 - 43091.0i) q^{83} +8774.58 q^{84} +(55717.6 + 89903.4i) q^{85} -71579.6 q^{86} +(-49884.2 - 49884.2i) q^{87} +(-17891.5 + 7410.88i) q^{88} +82549.9i q^{89} +(-13416.6 - 32390.5i) q^{90} +(-85792.9 - 35536.6i) q^{91} +(13524.1 - 32650.0i) q^{92} +(-32944.6 + 32944.6i) q^{93} +(17168.0 - 17168.0i) q^{94} +(22414.5 - 54113.4i) q^{95} +(24078.4 + 9973.61i) q^{96} +(-17439.5 - 42102.8i) q^{97} -13402.6i q^{98} +(7388.87 - 3060.57i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 88 q^{5} + 360 q^{6} + 1280 q^{10} - 632 q^{11} - 4256 q^{14} - 8192 q^{16} + 6248 q^{17} + 4152 q^{19} - 16384 q^{20} - 19592 q^{22} - 3608 q^{23} + 10440 q^{24} + 30384 q^{25} - 19936 q^{26} + 13624 q^{28}+ \cdots - 51192 q^{99}+O(q^{100}) $ 56 * q - 88 * q^5 + 360 * q^6 + 1280 * q^10 - 632 * q^11 - 4256 * q^14 - 8192 * q^16 + 6248 * q^17 + 4152 * q^19 - 16384 * q^20 - 19592 * q^22 - 3608 * q^23 + 10440 * q^24 + 30384 * q^25 - 19936 * q^26 + 13624 * q^28 - 23424 * q^29 + 2728 * q^31 + 67200 * q^32 + 20376 * q^33 + 11960 * q^34 + 26272 * q^35 + 3240 * q^36 + 32296 * q^37 - 22320 * q^39 - 100184 * q^40 + 6552 * q^41 - 21528 * q^42 - 38152 * q^43 - 26208 * q^44 + 31752 * q^45 + 106368 * q^46 + 9768 * q^49 + 96128 * q^50 - 62720 * q^52 + 65984 * q^53 + 29160 * q^54 - 268304 * q^56 - 28656 * q^57 - 139352 * q^58 - 67312 * q^59 - 109800 * q^60 - 307184 * q^61 + 150704 * q^62 - 696 * q^65 + 54720 * q^66 + 364272 * q^67 + 558960 * q^68 - 81864 * q^69 + 313960 * q^70 + 309808 * q^71 - 268752 * q^73 - 393712 * q^74 - 96624 * q^75 - 228552 * q^76 - 841536 * q^77 - 130824 * q^78 - 57216 * q^79 + 658528 * q^80 - 335992 * q^82 + 406240 * q^83 + 664848 * q^84 + 686840 * q^85 - 842560 * q^86 + 127224 * q^87 + 538248 * q^88 - 103680 * q^90 - 368592 * q^91 + 96752 * q^92 - 113472 * q^93 - 622576 * q^94 - 1143560 * q^95 - 375552 * q^96 - 40424 * q^97 - 51192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−3.44799	−	3.44799i	−0.609524	−	0.609524i	0.333297	−	0.942822i	$-0.391839\pi$
$2$	−3.44799	−	3.44799i	−0.609524	−	0.609524i	−0.942822	+	0.333297i	$0.891839\pi$
$3$	8.31492	−	3.44415i	0.533402	−	0.220942i
$3$	8.31492	−	3.44415i	0.533402	−	0.220942i
$4$		−	8.22272i		−	0.256960i
$5$	33.9684	+	82.0071i	0.607646	+	1.46699i	0.865553	+	0.500818i	$0.166967\pi$
$5$	33.9684	+	82.0071i	0.607646	+	1.46699i	−0.257907	+	0.966170i	$0.583033\pi$
$6$	−40.5452	−	16.7944i	−0.459791	−	0.190452i
$7$	−45.3741	+	109.543i	−0.349996	+	0.844965i	0.646624	+	0.762809i	$0.276180\pi$
$7$	−45.3741	+	109.543i	−0.349996	+	0.844965i	−0.996620	+	0.0821555i	$0.973820\pi$
$8$	−138.688	+	138.688i	−0.766148	+	0.766148i
$9$	57.2756	−	57.2756i	0.235702	−	0.235702i
$10$	165.637	−	399.883i	0.523790	−	1.26454i
$11$	91.2207	+	37.7848i	0.227306	+	0.0941534i	0.493430	−	0.869786i	$-0.335743\pi$
$11$	91.2207	+	37.7848i	0.227306	+	0.0941534i	−0.266124	+	0.963939i	$0.585743\pi$
$12$	−28.3203	−	68.3712i	−0.0567734	−	0.137063i
$13$			783.191i			1.28531i	0.766154	+	0.642657i	$0.222168\pi$
$13$			783.191i			1.28531i	−0.766154	+	0.642657i	$0.777832\pi$
$14$	534.152	−	221.253i	0.728358	−	0.301696i
$15$	564.890	+	564.890i	0.648239	+	0.648239i
$16$	693.260			0.677012
$17$	1175.95	−	192.328i	0.986888	−	0.161406i
$17$	1175.95	−	192.328i	0.986888	−	0.161406i
$18$	−394.972			−0.287333
$19$	−466.593	−	466.593i	−0.296520	−	0.296520i	0.543129	−	0.839649i	$-0.317239\pi$
$19$	−466.593	−	466.593i	−0.296520	−	0.296520i	−0.839649	+	0.543129i	$0.817239\pi$
$20$	674.321	−	279.313i	0.376957	−	0.156141i
$21$			1067.11i			0.528035i
$22$	−184.246	−	444.810i	−0.0811600	−	0.195938i
$23$	3970.71	+	1644.72i	1.56512	+	0.648295i	0.985970	−	0.166923i	$-0.0533832\pi$
$23$	3970.71	+	1644.72i	1.56512	+	0.648295i	0.579153	+	0.815219i	$0.303383\pi$
$24$	−675.515	+	1630.84i	−0.239390	+	0.577939i
$25$	−3361.60	+	3361.60i	−1.07571	+	1.07571i
$26$	2700.43	−	2700.43i	0.783430	−	0.783430i
$27$	278.976	−	673.508i	0.0736475	−	0.177801i
$28$	900.739	+	373.098i	0.217122	+	0.0899349i
$29$	−2999.68	−	7241.87i	−0.662338	−	1.59903i	−0.794130	−	0.607749i	$-0.792073\pi$
$29$	−2999.68	−	7241.87i	−0.662338	−	1.59903i	0.131791	−	0.991277i	$-0.457927\pi$
$30$		−	3895.47i		−	0.790235i
$31$	−4782.70	+	1981.06i	−0.893858	+	0.370248i	−0.781855	−	0.623460i	$-0.785726\pi$
$31$	−4782.70	+	1981.06i	−0.893858	+	0.370248i	−0.112003	+	0.993708i	$0.535726\pi$
$32$	2047.65	+	2047.65i	0.353493	+	0.353493i
$33$	888.629			0.142048
$34$	−4717.82	−	3391.53i	−0.699913	−	0.503151i
$35$	−10524.6			−1.45223
$36$	−470.962	−	470.962i	−0.0605661	−	0.0605661i
$37$	−7147.02	+	2960.39i	−0.858264	+	0.355505i	−0.768028	−	0.640416i	$-0.778762\pi$
$37$	−7147.02	+	2960.39i	−0.858264	+	0.355505i	−0.0902356	+	0.995920i	$0.528762\pi$
$38$			3217.62i			0.361473i
$39$	2697.43	+	6512.16i	0.283980	+	0.685589i
$40$	−16084.4	−	6662.36i	−1.58948	−	0.658382i
$41$	−3572.56	+	8624.93i	−0.331910	+	0.801302i	0.666531	+	0.745478i	$0.267779\pi$
$41$	−3572.56	+	8624.93i	−0.331910	+	0.801302i	−0.998441	+	0.0558241i	$0.982221\pi$
$42$	3679.40	−	3679.40i	0.321850	−	0.321850i
$43$	10379.9	−	10379.9i	0.856096	−	0.856096i	−0.134780	−	0.990876i	$-0.543033\pi$
$43$	10379.9	−	10379.9i	0.856096	−	0.856096i	0.990876	+	0.134780i	$0.0430328\pi$
$44$	310.694	−	750.082i	0.0241936	−	0.0584086i
$45$	6642.57	+	2751.44i	0.488996	+	0.202549i
$46$	−8019.99	−	19362.0i	−0.558829	−	1.34913i
$47$			4979.13i			0.328783i	0.986395	+	0.164391i	$0.0525660\pi$
$47$			4979.13i			0.328783i	−0.986395	+	0.164391i	$0.947434\pi$
$48$	5764.40	−	2387.69i	0.361119	−	0.149581i
$49$	1943.54	+	1943.54i	0.115639	+	0.115639i
$50$	23181.5			1.31134
$51$	9115.55	−	5649.35i	0.490747	−	0.304140i
$52$	6439.96			0.330274
$53$	11149.4	+	11149.4i	0.545206	+	0.545206i	0.925050	−	0.379844i	$-0.124022\pi$
$53$	11149.4	+	11149.4i	0.545206	+	0.545206i	−0.379844	+	0.925050i	$0.624022\pi$
$54$	−3284.16	+	1360.34i	−0.153264	+	0.0634839i
$55$			8764.23i			0.390667i
$56$	−8899.39	−	21485.0i	−0.379219	−	0.915516i
$57$	−5486.70	−	2272.67i	−0.223678	−	0.0926506i
$58$	−14627.0	+	35312.8i	−0.570934	+	1.37836i
$59$	8970.38	−	8970.38i	0.335491	−	0.335491i	−0.519176	−	0.854667i	$-0.673761\pi$
$59$	8970.38	−	8970.38i	0.335491	−	0.335491i	0.854667	+	0.519176i	$0.173761\pi$
$60$	4644.93	−	4644.93i	0.166572	−	0.166572i
$61$	−10981.2	+	26510.8i	−0.377853	+	0.912219i	0.614514	+	0.788906i	$0.289352\pi$
$61$	−10981.2	+	26510.8i	−0.377853	+	0.912219i	−0.992368	+	0.123313i	$0.960648\pi$
$62$	23321.4	+	9660.02i	0.770503	+	0.319153i
$63$	3675.30	+	8872.96i	0.116665	+	0.281655i
$64$		−	36304.9i		−	1.10794i
$65$	−64227.2	+	26603.8i	−1.88554	+	0.781016i
$66$	−3063.98	−	3063.98i	−0.0865818	−	0.0865818i
$67$	266.677			0.00725769			0.00362885	−	0.999993i	$-0.498845\pi$
$67$	266.677			0.00725769			0.00362885	+	0.999993i	$0.498845\pi$
$68$	−1581.46	−	9669.54i	−0.0414750	−	0.253591i
$69$	38680.8			0.978076
$70$	36288.6	+	36288.6i	0.885167	+	0.885167i
$71$	41870.6	−	17343.4i	0.985743	−	0.408308i	0.169193	−	0.985583i	$-0.445884\pi$
$71$	41870.6	−	17343.4i	0.985743	−	0.408308i	0.816550	+	0.577275i	$0.195884\pi$
$72$			15886.8i			0.361166i
$73$	−27960.6	−	67502.8i	−0.614100	−	1.48257i	−0.858458	−	0.512884i	$-0.828577\pi$
$73$	−27960.6	−	67502.8i	−0.614100	−	1.48257i	0.244358	−	0.969685i	$-0.421423\pi$
$74$	34850.3	+	14435.5i	0.739821	+	0.306444i
$75$	−16373.6	+	39529.3i	−0.336117	+	0.811457i
$76$	−3836.67	+	3836.67i	−0.0761939	+	0.0761939i
$77$	−8278.11	+	8278.11i	−0.159113	+	0.159113i
$78$	13153.2	−	31754.6i	0.244790	−	0.590976i
$79$	−6368.37	−	2637.87i	−0.114805	−	0.0475538i	0.324542	−	0.945871i	$-0.394790\pi$
$79$	−6368.37	−	2637.87i	−0.114805	−	0.0475538i	−0.439347	+	0.898318i	$0.644790\pi$
$80$	23549.0	+	56852.2i	0.411383	+	0.993167i
$81$		−	6561.00i		−	0.111111i
$82$	42056.9	−	17420.5i	0.690720	−	0.286106i
$83$	−43091.0	−	43091.0i	−0.686580	−	0.686580i	0.274895	−	0.961474i	$-0.411357\pi$
$83$	−43091.0	−	43091.0i	−0.686580	−	0.686580i	−0.961474	+	0.274895i	$0.911357\pi$
$84$	8774.58			0.135684
$85$	55717.6	+	89903.4i	0.836460	+	1.34967i
$86$	−71579.6			−1.04362
$87$	−49884.2	−	49884.2i	−0.706585	−	0.706585i
$88$	−17891.5	+	7410.88i	−0.246286	+	0.102015i
$89$			82549.9i			1.10469i	0.833615	+	0.552346i	$0.186267\pi$
$89$			82549.9i			1.10469i	−0.833615	+	0.552346i	$0.813733\pi$
$90$	−13416.6	−	32390.5i	−0.174597	−	0.421513i
$91$	−85792.9	−	35536.6i	−1.08604	−	0.449854i
$92$	13524.1	−	32650.0i	0.166586	−	0.402174i
$93$	−32944.6	+	32944.6i	−0.394982	+	0.394982i
$94$	17168.0	−	17168.0i	0.200401	−	0.200401i
$95$	22414.5	−	54113.4i	0.254812	−	0.615171i
$96$	24078.4	+	9973.61i	0.266655	+	0.110452i
$97$	−17439.5	−	42102.8i	−0.188194	−	0.454340i	0.801418	−	0.598105i	$-0.204079\pi$
$97$	−17439.5	−	42102.8i	−0.188194	−	0.454340i	−0.989612	+	0.143764i	$0.954079\pi$
$98$		−	13402.6i		−	0.140969i
$99$	7388.87	−	3060.57i	0.0757688	−	0.0313845i
$100$	27641.5	+	27641.5i	0.276415	+	0.276415i
$101$	138878.			1.35465			0.677327	−	0.735682i	$-0.263138\pi$
$101$	138878.			1.35465			0.677327	+	0.735682i	$0.263138\pi$
$102$	−50909.2	−	11951.4i	−0.484503	−	0.113741i
$103$	94745.1			0.879961			0.439981	−	0.898007i	$-0.354985\pi$
$103$	94745.1			0.879961			0.439981	+	0.898007i	$0.354985\pi$
$104$	−108619.	−	108619.i	−0.984740	−	0.984740i
$105$	−87510.9	+	36248.2i	−0.774620	+	0.320858i
$106$		−	76885.9i		−	0.664633i
$107$	−64467.9	−	155639.i	−0.544357	−	1.31419i	−0.921622	−	0.388089i	$-0.873135\pi$
$107$	−64467.9	−	155639.i	−0.544357	−	1.31419i	0.377265	−	0.926105i	$-0.376865\pi$
$108$	−5538.07	−	2293.94i	−0.0456877	−	0.0189245i
$109$	60101.7	−	145098.i	0.484530	−	1.16976i	−0.472906	−	0.881113i	$-0.656795\pi$
$109$	60101.7	−	145098.i	0.484530	−	1.16976i	0.957436	−	0.288646i	$-0.0932050\pi$
$110$	30219.0	−	30219.0i	0.238121	−	0.238121i
$111$	−49230.8	+	49230.8i	−0.379254	+	0.379254i
$112$	−31456.0	+	75941.6i	−0.236951	+	0.572051i
$113$	−110129.	−	45616.8i	−0.811342	−	0.336069i	−0.0618529	−	0.998085i	$-0.519701\pi$
$113$	−110129.	−	45616.8i	−0.811342	−	0.336069i	−0.749489	+	0.662016i	$0.769701\pi$
$114$	11082.0	+	26754.2i	0.0798646	+	0.192810i
$115$			381495.i			2.68995i
$116$	−59547.8	+	24665.5i	−0.410886	+	0.170194i
$117$	44857.8	+	44857.8i	0.302951	+	0.302951i
$118$	−61859.6			−0.408980
$119$	−32289.7	+	137544.i	−0.209024	+	0.890377i
$120$	−156686.			−0.993294
$121$	−106987.	−	106987.i	−0.664303	−	0.664303i
$122$	129272.	−	53546.2i	0.786330	−	0.325709i
$123$			84020.1i			0.500749i
$124$	16289.7	+	39326.8i	0.0951389	+	0.229686i
$125$	−133591.	−	55335.2i	−0.764720	−	0.316757i
$126$	17921.5	−	43266.3i	0.100565	−	0.242786i
$127$	113174.	−	113174.i	0.622638	−	0.622638i	−0.323567	−	0.946205i	$-0.604882\pi$
$127$	113174.	−	113174.i	0.622638	−	0.622638i	0.946205	+	0.323567i	$0.104882\pi$
$128$	−59654.1	+	59654.1i	−0.321822	+	0.321822i
$129$	50558.1	−	122058.i	0.267495	−	0.645791i
$130$	313184.	+	129725.i	1.62533	+	0.673234i
$131$	79471.5	+	191861.i	0.404607	+	0.976807i	0.986533	+	0.163565i	$0.0522994\pi$
$131$	79471.5	+	191861.i	0.404607	+	0.976807i	−0.581926	+	0.813242i	$0.697701\pi$
$132$		−	7306.94i		−	0.0365007i
$133$	72283.1	−	29940.7i	0.354330	−	0.146768i
$134$	−919.500	−	919.500i	−0.00442374	−	0.00442374i
$135$	64708.8			0.305583
$136$	−136417.	+	189764.i	−0.632441	+	0.879763i
$137$	225046.			1.02440			0.512200	−	0.858866i	$-0.328831\pi$
$137$	225046.			1.02440			0.512200	+	0.858866i	$0.328831\pi$
$138$	−133371.	−	133371.i	−0.596161	−	0.596161i
$139$	224253.	−	92888.8i	0.984469	−	0.407780i	0.168390	−	0.985720i	$-0.446143\pi$
$139$	224253.	−	92888.8i	0.984469	−	0.407780i	0.816079	+	0.577940i	$0.196143\pi$
$140$			86540.6i			0.373164i
$141$	17148.9	+	41401.1i	0.0726420	+	0.175373i
$142$	−204169.	−	84569.7i	−0.849708	−	0.351960i
$143$	−29592.7	+	71443.2i	−0.121017	+	0.292160i
$144$	39706.9	−	39706.9i	0.159573	−	0.159573i
$145$	491990.	−	491990.i	1.94328	−	1.94328i
$146$	−136341.	+	329157.i	−0.529353	+	1.27797i
$147$	22854.2	+	9466.52i	0.0872314	+	0.0361324i
$148$	24342.5	+	58768.0i	0.0913504	+	0.220539i
$149$			61901.5i			0.228421i	0.993457	+	0.114210i	$0.0364338\pi$
$149$			61901.5i			0.228421i	−0.993457	+	0.114210i	$0.963566\pi$
$150$	192752.	−	79840.7i	0.699474	−	0.289732i
$151$	123055.	+	123055.i	0.439193	+	0.439193i	0.891740	−	0.452547i	$-0.149485\pi$
$151$	123055.	+	123055.i	0.439193	+	0.439193i	−0.452547	+	0.891740i	$0.649485\pi$
$152$	129421.			0.454357
$153$	56337.8	−	78369.2i	0.194568	−	0.270656i
$154$	57085.7			0.193966
$155$	−324921.	−	324921.i	−1.08630	−	1.08630i
$156$	53547.7	−	22180.2i	0.176169	−	0.0729716i
$157$		−	205459.i		−	0.665235i	−0.943062	−	0.332618i	$-0.892068\pi$
$157$		−	205459.i		−	0.665235i	0.943062	−	0.332618i	$-0.107932\pi$
$158$	12862.7	+	31053.4i	0.0409912	+	0.0989616i
$159$	131106.	+	54306.0i	0.411273	+	0.170355i
$160$	−98366.3	+	237477.i	−0.303771	+	0.733368i
$161$	−360335.	+	360335.i	−1.09557	+	1.09557i
$162$	−22622.3	+	22622.3i	−0.0677249	+	0.0677249i
$163$	−170680.	+	412058.i	−0.503168	+	1.21476i	0.444581	+	0.895739i	$0.353353\pi$
$163$	−170680.	+	412058.i	−0.503168	+	1.21476i	−0.947749	+	0.319017i	$0.896647\pi$
$164$	70920.4	+	29376.2i	0.205903	+	0.0852876i
$165$	30185.3	+	72873.9i	0.0863150	+	0.208383i
$166$			297154.i			0.836974i
$167$	583456.	−	241676.i	1.61889	−	0.670566i	0.624968	−	0.780651i	$-0.285112\pi$
$167$	583456.	−	241676.i	1.61889	−	0.670566i	0.993922	+	0.110085i	$0.0351122\pi$
$168$	−147995.	−	147995.i	−0.404553	−	0.404553i
$169$	−242095.			−0.652031
$170$	117873.	−	502100.i	0.312817	−	1.33250i
$171$	−53448.9			−0.139781
$172$	−85351.1	−	85351.1i	−0.219982	−	0.219982i
$173$	−336851.	+	139528.i	−0.855702	+	0.354443i	−0.767025	−	0.641617i	$-0.778264\pi$
$173$	−336851.	+	139528.i	−0.855702	+	0.354443i	−0.0886767	+	0.996060i	$0.528264\pi$
$174$			344000.i			0.861362i
$175$	−215709.	−	520768.i	−0.532444	−	1.28543i
$176$	63239.6	+	26194.7i	0.153889	+	0.0637429i
$177$	43692.6	−	105483.i	0.104827	−	0.253076i
$178$	284631.	−	284631.i	0.673337	−	0.673337i
$179$	203082.	−	203082.i	0.473738	−	0.473738i	−0.429384	−	0.903122i	$-0.641269\pi$
$179$	203082.	−	203082.i	0.473738	−	0.473738i	0.903122	+	0.429384i	$0.141269\pi$
$180$	22624.4	−	54620.0i	0.0520469	−	0.125652i
$181$	−270471.	−	112033.i	−0.613656	−	0.254184i	0.0541350	−	0.998534i	$-0.482760\pi$
$181$	−270471.	−	112033.i	−0.613656	−	0.254184i	−0.667791	+	0.744349i	$0.732760\pi$
$182$	173283.	+	418343.i	0.387773	+	0.936168i
$183$			258256.i			0.570063i
$184$	−778791.	+	322586.i	−1.69581	+	0.702426i
$185$	−485547.	−	485547.i	−1.04304	−	1.04304i
$186$	227186.			0.481503
$187$	114538.	+	26888.9i	0.239523	+	0.0562301i
$188$	40942.0			0.0844840
$189$	61119.6	+	61119.6i	0.124459	+	0.124459i
$190$	−263868.	+	109297.i	−0.530276	+	0.219647i
$191$			22140.3i			0.0439136i	0.999759	+	0.0219568i	$0.00698963\pi$
$191$			22140.3i			0.0439136i	−0.999759	+	0.0219568i	$0.993010\pi$
$192$	−125039.	−	301872.i	−0.244790	−	0.590976i
$193$	−585230.	−	242410.i	−1.13092	−	0.468444i	−0.262829	−	0.964842i	$-0.584656\pi$
$193$	−585230.	−	242410.i	−1.13092	−	0.468444i	−0.868095	+	0.496398i	$0.834656\pi$
$194$	−85038.6	+	205301.i	−0.162223	+	0.391640i
$195$	−442416.	+	442416.i	−0.833191	+	0.833191i
$196$	15981.2	−	15981.2i	0.0297145	−	0.0297145i
$197$	−160302.	+	387004.i	−0.294289	+	0.710476i	0.705709	+	0.708502i	$0.250629\pi$
$197$	−160302.	+	387004.i	−0.294289	+	0.710476i	−0.999998	+	0.00197470i	$0.999371\pi$
$198$	−36029.6	−	14923.9i	−0.0653125	−	0.0270533i
$199$	4801.59	+	11592.1i	0.00859513	+	0.0207505i	0.928119	−	0.372284i	$-0.121425\pi$
$199$	4801.59	+	11592.1i	0.00859513	+	0.0207505i	−0.919524	+	0.393035i	$0.871425\pi$
$200$		−	932424.i		−	1.64831i
$201$	2217.40	−	918.476i	0.00387127	−	0.00160353i
$202$	−478849.	−	478849.i	−0.825695	−	0.825695i
$203$	929402.			1.58294
$204$	−46453.1	−	74954.6i	−0.0781518	−	0.126102i
$205$	−828660.			−1.37718
$206$	−326680.	−	326680.i	−0.536358	−	0.536358i
$207$	321628.	−	133222.i	0.521708	−	0.216098i
$208$			542955.i			0.870172i
$209$	−24932.8	−	60193.1i	−0.0394826	−	0.0953193i
$210$	426720.	+	176753.i	0.667721	+	0.276579i
$211$	379561.	−	916342.i	0.586916	−	1.41694i	−0.299521	−	0.954090i	$-0.596827\pi$
$211$	379561.	−	916342.i	0.586916	−	1.41694i	0.886436	−	0.462850i	$-0.153173\pi$
$212$	91678.2	−	91678.2i	0.140096	−	0.140096i
$213$	288417.	−	288417.i	0.435585	−	0.435585i
$214$	−314358.	+	758927.i	−0.469235	+	1.13283i
$215$	1.20382e6	+	498637.i	1.77608	+	0.735678i
$216$	54716.7	+	132098.i	0.0797968	+	0.192646i
$217$		−	613798.i		−	0.884864i
$218$	−707528.	+	293068.i	−1.00833	+	0.417664i
$219$	−464980.	−	464980.i	−0.655125	−	0.655125i
$220$	72065.8			0.100386
$221$	150630.	+	920996.i	0.207458	+	1.26846i
$222$	339495.			0.462329
$223$	490504.	+	490504.i	0.660512	+	0.660512i	0.955501	−	0.294989i	$-0.0953159\pi$
$223$	490504.	+	490504.i	0.660512	+	0.660512i	−0.294989	+	0.955501i	$0.595316\pi$
$224$	−317215.	+	131395.i	−0.422410	+	0.174968i
$225$			385075.i			0.507095i
$226$	222436.	+	537009.i	0.289691	+	0.699375i
$227$	907502.	+	375900.i	1.16892	+	0.484181i	0.880834	−	0.473425i	$-0.156983\pi$
$227$	907502.	+	375900.i	1.16892	+	0.484181i	0.288081	+	0.957606i	$0.406983\pi$
$228$	−18687.5	+	45115.6i	−0.0238075	+	0.0574764i
$229$	337945.	−	337945.i	0.425851	−	0.425851i	−0.461362	−	0.887212i	$-0.652639\pi$
$229$	337945.	−	337945.i	0.425851	−	0.425851i	0.887212	+	0.461362i	$0.152639\pi$
$230$	1.31539e6	−	1.31539e6i	1.63959	−	1.63959i
$231$	−40320.7	+	97342.8i	−0.0497162	+	0.120026i
$232$	1.42038e6	+	588339.i	1.73254	+	0.717641i
$233$	−358659.	−	865879.i	−0.432804	−	1.04488i	−0.978379	−	0.206820i	$-0.933689\pi$
$233$	−358659.	−	865879.i	−0.432804	−	1.04488i	0.545575	−	0.838062i	$-0.316311\pi$
$234$		−	309338.i		−	0.369312i
$235$	−408324.	+	169133.i	−0.482320	+	0.199783i
$236$	−73760.9	−	73760.9i	−0.0862077	−	0.0862077i
$237$	−62037.7			−0.0717439
$238$	585585.	−	362916.i	0.670112	−	0.415301i
$239$	−707183.			−0.800824			−0.400412	−	0.916335i	$-0.631133\pi$
$239$	−707183.			−0.800824			−0.400412	+	0.916335i	$0.631133\pi$
$240$	391615.	+	391615.i	0.438866	+	0.438866i
$241$	−1.61442e6	+	668715.i	−1.79050	+	0.741649i	−0.800720	+	0.599039i	$0.795549\pi$
$241$	−1.61442e6	+	668715.i	−1.79050	+	0.741649i	−0.989779	+	0.142610i	$0.954451\pi$
$242$			737779.i			0.809818i
$243$	−22597.1	−	54554.2i	−0.0245492	−	0.0592669i
$244$	217991.	+	90294.9i	0.234404	+	0.0970932i
$245$	−93364.9	+	225403.i	−0.0993730	+	0.239908i
$246$	289700.	−	289700.i	0.305219	−	0.305219i
$247$	365431.	−	365431.i	0.381122	−	0.381122i
$248$	388552.	−	938048.i	0.401163	−	0.968492i
$249$	−506709.	−	209886.i	−0.517918	−	0.214528i
$250$	269825.	+	651416.i	0.273044	+	0.659187i
$251$			1.43455e6i			1.43725i	0.695397	+	0.718626i	$0.255229\pi$
$251$			1.43455e6i			1.43725i	−0.695397	+	0.718626i	$0.744771\pi$
$252$	72959.9	−	30221.0i	0.0723740	−	0.0299783i
$253$	300065.	+	300065.i	0.294723	+	0.294723i
$254$	−780443.			−0.759027
$255$	772928.	+	555640.i	0.744370	+	0.535110i
$256$	−750382.			−0.715620
$257$	−13052.9	−	13052.9i	−0.0123274	−	0.0123274i	0.700916	−	0.713244i	$-0.252775\pi$
$257$	−13052.9	−	13052.9i	−0.0123274	−	0.0123274i	−0.713244	+	0.700916i	$0.752775\pi$
$258$	−595179.	+	246531.i	−0.556670	+	0.230580i
$259$		−	917230.i		−	0.849628i
$260$	218755.	+	528122.i	0.200690	+	0.484508i
$261$	−586591.	−	242974.i	−0.533009	−	0.220779i
$262$	387519.	−	935553.i	0.348770	−	0.842006i
$263$	−650598.	+	650598.i	−0.579994	+	0.579994i	−0.934901	−	0.354907i	$-0.884512\pi$
$263$	−650598.	+	650598.i	−0.579994	+	0.579994i	0.354907	+	0.934901i	$0.384512\pi$
$264$	−123242.	+	123242.i	−0.108830	+	0.108830i
$265$	−535601.	+	1.29305e6i	−0.468518	+	1.13110i
$266$	−352467.	−	145997.i	−0.305432	−	0.126514i
$267$	284314.	+	686395.i	0.244073	+	0.589245i
$268$		−	2192.81i		−	0.00186494i
$269$	1.86710e6	−	773380.i	1.57321	−	0.651647i	0.585894	−	0.810388i	$-0.300744\pi$
$269$	1.86710e6	−	773380.i	1.57321	−	0.651647i	0.987320	+	0.158741i	$0.0507435\pi$
$270$	−223115.	−	223115.i	−0.186260	−	0.186260i
$271$	−38431.2			−0.0317878			−0.0158939	−	0.999874i	$-0.505059\pi$
$271$	−38431.2			−0.0317878			−0.0158939	+	0.999874i	$0.505059\pi$
$272$	815241.	−	133333.i	0.668135	−	0.109274i
$273$	−835754.			−0.678690
$274$	−775956.	−	775956.i	−0.624397	−	0.624397i
$275$	−433665.	+	179630.i	−0.345798	+	0.143234i
$276$		−	318061.i		−	0.251326i
$277$	−155141.	−	374543.i	−0.121486	−	0.293293i	0.851424	−	0.524478i	$-0.175740\pi$
$277$	−155141.	−	374543.i	−0.121486	−	0.293293i	−0.972910	+	0.231185i	$0.925740\pi$
$278$	−1.09350e6	−	452944.i	−0.848610	−	0.351506i
$279$	−160466.	+	387398.i	−0.123416	+	0.297953i
$280$	1.45963e6	−	1.45963e6i	1.11262	−	1.11262i
$281$	112117.	−	112117.i	0.0847041	−	0.0847041i	−0.663485	−	0.748189i	$-0.730923\pi$
$281$	112117.	−	112117.i	0.0847041	−	0.0847041i	0.748189	+	0.663485i	$0.230923\pi$
$282$	83621.3	−	201880.i	0.0626173	−	0.151171i
$283$	874172.	+	362094.i	0.648830	+	0.268754i	0.682730	−	0.730671i	$-0.260793\pi$
$283$	874172.	+	362094.i	0.648830	+	0.268754i	−0.0338998	+	0.999425i	$0.510793\pi$
$284$	−142610.	−	344290.i	−0.104919	−	0.253296i
$285$		−	527147.i		−	0.384432i
$286$	348371.	−	144300.i	0.251841	−	0.104316i
$287$	−782697.	−	782697.i	−0.560905	−	0.560905i
$288$	234561.			0.166638
$289$	1.34588e6	−	452338.i	0.947896	−	0.318580i
$290$	−3.39275e6			−2.36896
$291$	−290017.	−	290017.i	−0.200766	−	0.200766i
$292$	−555057.	+	229912.i	−0.380961	+	0.157799i
$293$			721184.i			0.490769i	0.969426	+	0.245385i	$0.0789142\pi$
$293$			721184.i			0.490769i	−0.969426	+	0.245385i	$0.921086\pi$
$294$	−46160.6	−	111442.i	−0.0311461	−	0.0751932i
$295$	1.04034e6	+	430925.i	0.696021	+	0.288301i
$296$	580633.	−	1.40177e6i	0.385188	−	0.929926i
$297$	50896.8	−	50896.8i	0.0334811	−	0.0334811i
$298$	213436.	−	213436.i	0.139228	−	0.139228i
$299$	−1.28813e6	+	3.10982e6i	−0.833263	+	2.01167i
$300$	325038.	+	134635.i	0.208512	+	0.0863685i
$301$	666065.	+	1.60802e6i	0.423741	+	1.02300i
$302$		−	848582.i		−	0.535398i
$303$	1.15476e6	−	478315.i	0.722576	−	0.299301i
$304$	−323470.	−	323470.i	−0.200748	−	0.200748i
$305$	−2.54709e6			−1.56781
$306$	−464469.	+	75964.2i	−0.283565	+	0.0463773i
$307$	1.60726e6			0.973285			0.486643	−	0.873601i	$-0.338221\pi$
$307$	1.60726e6			0.973285			0.486643	+	0.873601i	$0.338221\pi$
$308$	68068.6	+	68068.6i	0.0408855	+	0.0408855i
$309$	787797.	−	326316.i	0.469373	−	0.194421i
$310$			2.24065e6i			1.32425i
$311$	234664.	+	566528.i	0.137577	+	0.332139i	0.977620	−	0.210381i	$-0.0674703\pi$
$311$	234664.	+	566528.i	0.137577	+	0.332139i	−0.840043	+	0.542520i	$0.817470\pi$
$312$	−1.27726e6	−	529057.i	−0.742833	−	0.307692i
$313$	−214555.	+	517982.i	−0.123788	+	0.298850i	−0.973610	−	0.228220i	$-0.926710\pi$
$313$	−214555.	+	517982.i	−0.123788	+	0.298850i	0.849822	+	0.527070i	$0.176710\pi$
$314$	−708419.	+	708419.i	−0.405477	+	0.405477i
$315$	−602802.	+	602802.i	−0.342293	+	0.342293i
$316$	−21690.4	+	52365.3i	−0.0122194	+	0.0295003i
$317$	−982053.	−	406780.i	−0.548892	−	0.227358i	0.0909631	−	0.995854i	$-0.471005\pi$
$317$	−982053.	−	406780.i	−0.548892	−	0.227358i	−0.639855	+	0.768496i	$0.721005\pi$
$318$	−264806.	−	639299.i	−0.146846	−	0.354517i
$319$		−	773950.i		−	0.425830i
$320$	2.97726e6	−	1.23322e6i	1.62533	−	0.673233i
$321$	−1.07209e6	−	1.07209e6i	−0.580722	−	0.580722i
$322$	2.48486e6			1.33556
$323$	−638431.	−	458953.i	−0.340493	−	0.244772i
$324$	−53949.3			−0.0285511
$325$	−2.63277e6	−	2.63277e6i	−1.38263	−	1.38263i
$326$	2.00927e6	−	832268.i	1.04712	−	0.433730i
$327$		−	1.41348e6i		−	0.731005i
$328$	−700701.	−	1.69164e6i	−0.359623	−	0.868208i
$329$	−545428.	−	225924.i	−0.277810	−	0.115073i
$330$	147190.	−	355347.i	0.0744033	−	0.179625i
$331$	−39994.7	+	39994.7i	−0.0200647	+	0.0200647i	−0.717068	−	0.697003i	$-0.754516\pi$
$331$	−39994.7	+	39994.7i	−0.0200647	+	0.0200647i	0.697003	+	0.717068i	$0.254516\pi$
$332$	−354325.	+	354325.i	−0.176424	+	0.176424i
$333$	−239792.	+	578909.i	−0.118502	+	0.286088i
$334$	−2.84505e6	−	1.17846e6i	−1.39548	−	0.578026i
$335$	9058.60	+	21869.4i	0.00441011	+	0.0106469i
$336$			739787.i			0.357486i
$337$	3.57543e6	−	1.48099e6i	1.71496	−	0.710358i	0.715019	−	0.699105i	$-0.246418\pi$
$337$	3.57543e6	−	1.48099e6i	1.71496	−	0.710358i	0.999937	−	0.0112535i	$-0.00358216\pi$
$338$	834740.	+	834740.i	0.397429	+	0.397429i
$339$	−1.07282e6			−0.507024
$340$	739251.	−	458150.i	0.346812	−	0.214937i
$341$	−511135.			−0.238040
$342$	184291.	+	184291.i	0.0851999	+	0.0851999i
$343$	−2.14217e6	+	887317.i	−0.983148	+	0.407233i
$344$			2.87913e6i			1.31179i
$345$	1.31393e6	+	3.17210e6i	0.594324	+	1.43483i
$346$	1.64255e6	+	680367.i	0.737613	+	0.305529i
$347$	488018.	−	1.17818e6i	0.217577	−	0.525276i	−0.776974	−	0.629533i	$-0.783246\pi$
$347$	488018.	−	1.17818e6i	0.217577	−	0.525276i	0.994550	+	0.104257i	$0.0332463\pi$
$348$	−410183.	+	410183.i	−0.181564	+	0.181564i
$349$	−2.48577e6	+	2.48577e6i	−1.09244	+	1.09244i	−0.0971739	+	0.995267i	$0.530980\pi$
$349$	−2.48577e6	+	2.48577e6i	−1.09244	+	1.09244i	−0.995267	+	0.0971739i	$0.969020\pi$
$350$	−1.05184e6	+	2.53937e6i	−0.458965	+	1.10804i
$351$	527485.	+	218492.i	0.228530	+	0.0946601i
$352$	109418.	+	264158.i	0.0470686	+	0.113634i
$353$		−	2.31834e6i		−	0.990240i	−0.868825	−	0.495120i	$-0.835124\pi$
$353$		−	2.31834e6i		−	0.990240i	0.868825	−	0.495120i	$-0.164876\pi$
$354$	−514357.	+	213054.i	−0.218151	+	0.0903610i
$355$	2.84456e6	+	2.84456e6i	1.19797	+	1.19797i
$356$	678785.			0.283862
$357$	205236.	+	1.25488e6i	0.0852281	+	0.521111i
$358$	−1.40045e6			−0.577510
$359$	−1.89939e6	−	1.89939e6i	−0.777819	−	0.777819i	0.201640	−	0.979460i	$-0.435373\pi$
$359$	−1.89939e6	−	1.89939e6i	−0.777819	−	0.777819i	−0.979460	+	0.201640i	$0.935373\pi$
$360$	−1.30283e6	+	539651.i	−0.529825	+	0.219461i
$361$		−	2.04068e6i		−	0.824151i
$362$	546294.	+	1.31887e6i	0.219106	+	0.528970i
$363$	−1.25806e6	−	521107.i	−0.501114	−	0.207568i
$364$	−292207.	+	705451.i	−0.115595	+	0.279070i
$365$	4.58593e6	−	4.58593e6i	1.80175	−	1.80175i
$366$	890465.	−	890465.i	0.347467	−	0.347467i
$367$	−911675.	+	2.20098e6i	−0.353325	+	0.853003i	0.642880	+	0.765967i	$0.277740\pi$
$367$	−911675.	+	2.20098e6i	−0.353325	+	0.853003i	−0.996205	+	0.0870360i	$0.972260\pi$
$368$	2.75273e6	+	1.14022e6i	1.05961	+	0.438903i
$369$	289378.	+	698620.i	0.110637	+	0.267101i
$370$			3.34832e6i			1.27152i
$371$	−1.72723e6	+	715440.i	−0.651500	+	0.269860i
$372$	270895.	+	270895.i	0.101495	+	0.101495i
$373$	−619300.			−0.230478			−0.115239	−	0.993338i	$-0.536763\pi$
$373$	−619300.			−0.230478			−0.115239	+	0.993338i	$0.536763\pi$
$374$	−302214.	−	487640.i	−0.111721	−	0.180269i
$375$	−1.30138e6			−0.477888
$376$	−690543.	−	690543.i	−0.251896	−	0.251896i
$377$	5.67176e6	−	2.34932e6i	2.05525	−	0.851312i
$378$		−	421480.i		−	0.151722i
$379$	506815.	+	1.22356e6i	0.181239	+	0.437550i	0.988222	−	0.153024i	$-0.0489013\pi$
$379$	506815.	+	1.22356e6i	0.181239	+	0.437550i	−0.806983	+	0.590574i	$0.798901\pi$
$380$	−444959.	−	184308.i	−0.158074	−	0.0654765i
$381$	551242.	−	1.33082e6i	0.194549	−	0.469684i
$382$	76339.4	−	76339.4i	0.0267664	−	0.0267664i
$383$	1.52949e6	−	1.52949e6i	0.532781	−	0.532781i	−0.388618	−	0.921399i	$-0.627047\pi$
$383$	1.52949e6	−	1.52949e6i	0.532781	−	0.532781i	0.921399	+	0.388618i	$0.127047\pi$
$384$	−290561.	+	701476.i	−0.100556	+	0.242764i
$385$	−960058.	−	397669.i	−0.330100	−	0.136732i
$386$	1.18204e6	+	2.85370e6i	0.403798	+	0.974854i
$387$		−	1.18903e6i		−	0.403567i
$388$	−346199.	+	143400.i	−0.116747	+	0.0483583i
$389$	−1.48812e6	−	1.48812e6i	−0.498613	−	0.498613i	0.412393	−	0.911006i	$-0.364693\pi$
$389$	−1.48812e6	−	1.48812e6i	−0.498613	−	0.498613i	−0.911006	+	0.412393i	$0.864693\pi$
$390$	3.05089e6			1.01570
$391$	4.98570e6	+	1.17044e6i	1.64924	+	0.387174i
$392$	−539089.			−0.177193
$393$	1.32160e6	+	1.32160e6i	0.431636	+	0.431636i
$394$	1.88711e6	−	781665.i	0.612429	−	0.253676i
$395$		−	611856.i		−	0.197313i
$396$	−25166.2	−	60756.6i	−0.00806455	−	0.0194695i
$397$	2.83684e6	+	1.17506e6i	0.903356	+	0.374182i	0.785510	−	0.618850i	$-0.212401\pi$
$397$	2.83684e6	+	1.17506e6i	0.903356	+	0.374182i	0.117846	+	0.993032i	$0.462401\pi$
$398$	23413.5	−	56525.1i	0.00740898	−	0.0178869i
$399$	497908.	−	497908.i	0.156573	−	0.156573i
$400$	−2.33046e6	+	2.33046e6i	−0.728269	+	0.728269i
$401$	−276091.	+	666544.i	−0.0857417	+	0.206999i	−0.960935	−	0.276775i	$-0.910734\pi$
$401$	−276091.	+	666544.i	−0.0857417	+	0.206999i	0.875193	+	0.483774i	$0.160734\pi$
$402$	−10812.5	−	4478.67i	−0.00333702	−	0.00138224i
$403$	−1.55155e6	−	3.74576e6i	−0.475885	−	1.14889i
$404$		−	1.14195e6i		−	0.348092i
$405$	538049.	−	222867.i	0.162999	−	0.0675162i
$406$	−3.20457e6	−	3.20457e6i	−0.964838	−	0.964838i
$407$	−763814.			−0.228561
$408$	−480718.	+	2.04771e6i	−0.142968	+	0.609001i
$409$	−3.62826e6			−1.07248			−0.536241	−	0.844065i	$-0.680156\pi$
$409$	−3.62826e6			−1.07248			−0.536241	+	0.844065i	$0.680156\pi$
$410$	2.85721e6	+	2.85721e6i	0.839427	+	0.839427i
$411$	1.87124e6	−	775092.i	0.546417	−	0.226333i
$412$		−	779062.i		−	0.226115i
$413$	575617.	+	1.38966e6i	0.166058	+	0.400898i
$414$	−1.56832e6	−	649619.i	−0.449711	−	0.186276i
$415$	2.07003e6	−	4.99750e6i	0.590006	−	1.42440i
$416$	−1.60370e6	+	1.60370e6i	−0.454349	+	0.454349i
$417$	1.54472e6	−	1.54472e6i	0.435022	−	0.435022i
$418$	−121577.	+	293513.i	−0.0340339	+	0.0821650i
$419$	4.10996e6	+	1.70240e6i	1.14368	+	0.473726i	0.872408	−	0.488778i	$-0.162557\pi$
$419$	4.10996e6	+	1.70240e6i	1.14368	+	0.473726i	0.271267	+	0.962504i	$0.412557\pi$
$420$	298059.	+	719578.i	0.0824477	+	0.199046i
$421$		−	2.44854e6i		−	0.673291i	−0.941632	−	0.336645i	$-0.890708\pi$
$421$		−	2.44854e6i		−	0.673291i	0.941632	−	0.336645i	$-0.109292\pi$
$422$	−4.46826e6	+	1.85082e6i	−1.22140	+	0.505920i
$423$	285183.	+	285183.i	0.0774948	+	0.0774948i
$424$	−3.09256e6			−0.835417
$425$	−3.30655e6	+	4.59961e6i	−0.887980	+	1.23523i
$426$	−1.98892e6			−0.530999
$427$	−2.40581e6	−	2.40581e6i	−0.638545	−	0.638545i
$428$	−1.27978e6	+	530101.i	−0.337695	+	0.139878i
$429$			695966.i			0.182576i
$430$	−2.43145e6	−	5.87004e6i	−0.634153	−	1.53098i
$431$	−1.87707e6	−	777508.i	−0.486729	−	0.201610i	0.125803	−	0.992055i	$-0.459849\pi$
$431$	−1.87707e6	−	777508.i	−0.486729	−	0.201610i	−0.612533	+	0.790445i	$0.709849\pi$
$432$	193403.	−	466916.i	0.0498602	−	0.120373i
$433$	−5.09966e6	+	5.09966e6i	−1.30714	+	1.30714i	−0.383664	+	0.923473i	$0.625338\pi$
$433$	−5.09966e6	+	5.09966e6i	−1.30714	+	1.30714i	−0.923473	+	0.383664i	$0.874662\pi$
$434$	−2.11637e6	+	2.11637e6i	−0.539346	+	0.539346i
$435$	2.39637e6	−	5.78534e6i	0.607198	−	1.46591i
$436$	−1.19310e6	−	494200.i	−0.300581	−	0.124505i
$437$	−1.08529e6	−	2.62012e6i	−0.271858	−	0.656324i
$438$			3.20649e6i			0.798629i
$439$	−3.37848e6	+	1.39941e6i	−0.836682	+	0.346565i	−0.759544	−	0.650455i	$-0.774578\pi$
$439$	−3.37848e6	+	1.39941e6i	−0.836682	+	0.346565i	−0.0771376	+	0.997020i	$0.524578\pi$
$440$	−1.21549e6	−	1.21549e6i	−0.299309	−	0.299309i
$441$	222635.			0.0545126
$442$	2.65622e6	−	3.69495e6i	0.646707	−	0.899608i
$443$	4.65092e6			1.12598			0.562989	−	0.826465i	$-0.309651\pi$
$443$	4.65092e6			1.12598			0.562989	+	0.826465i	$0.309651\pi$
$444$	404811.	+	404811.i	0.0974530	+	0.0974530i
$445$	−6.76968e6	+	2.80409e6i	−1.62057	+	0.671262i
$446$		−	3.38251e6i		−	0.805197i
$447$	213198.	+	514706.i	0.0504678	+	0.121840i
$448$	3.97693e6	+	1.64730e6i	0.936167	+	0.387773i
$449$	−1.84714e6	+	4.45940e6i	−0.432399	+	1.04390i	0.546112	+	0.837712i	$0.316107\pi$
$449$	−1.84714e6	+	4.45940e6i	−0.432399	+	1.04390i	−0.978512	+	0.206192i	$0.933893\pi$
$450$	1.32774e6	−	1.32774e6i	0.309087	−	0.309087i
$451$	−651783.	+	651783.i	−0.150891	+	0.150891i
$452$	−375094.	+	905557.i	−0.0863563	+	0.208483i
$453$	1.44701e6	+	599370.i	0.331303	+	0.137230i
$454$	−1.83296e6	−	4.42516e6i	−0.417363	−	1.00760i
$455$		−	8.24275e6i		−	1.86657i
$456$	1.07613e6	−	445747.i	0.242355	−	0.100387i
$457$	3.81638e6	+	3.81638e6i	0.854794	+	0.854794i	0.990719	−	0.135925i	$-0.0434006\pi$
$457$	3.81638e6	+	3.81638e6i	0.854794	+	0.854794i	−0.135925	+	0.990719i	$0.543401\pi$
$458$	−2.33046e6			−0.519133
$459$	198529.	−	845669.i	0.0439836	−	0.187357i
$460$	3.13693e6			0.691210
$461$	−396421.	−	396421.i	−0.0868770	−	0.0868770i	0.662333	−	0.749210i	$-0.269567\pi$
$461$	−396421.	−	396421.i	−0.0868770	−	0.0868770i	−0.749210	+	0.662333i	$0.769567\pi$
$462$	474663.	−	196612.i	0.103462	−	0.0428553i
$463$			4.64423e6i			1.00684i	0.864041	+	0.503421i	$0.167926\pi$
$463$			4.64423e6i			1.00684i	−0.864041	+	0.503421i	$0.832074\pi$
$464$	−2.07956e6	−	5.02050e6i	−0.448411	−	1.08256i
$465$	−3.82077e6	−	1.58262e6i	−0.819443	−	0.339425i
$466$	−1.74889e6	+	4.22220e6i	−0.373076	+	0.900686i
$467$	−2.37525e6	+	2.37525e6i	−0.503985	+	0.503985i	−0.912674	−	0.408689i	$-0.865986\pi$
$467$	−2.37525e6	+	2.37525e6i	−0.503985	+	0.503985i	0.408689	+	0.912674i	$0.365986\pi$
$468$	368853.	−	368853.i	0.0778464	−	0.0778464i
$469$	−12100.2	+	29212.5i	−0.00254016	+	0.00613249i
$470$	1.99107e6	+	824727.i	0.415759	+	0.172213i
$471$	−707630.	−	1.70837e6i	−0.146979	−	0.354838i
$472$			2.48816e6i			0.514071i
$473$	1.33906e6	−	554659.i	0.275200	−	0.113992i
$474$	213905.	+	213905.i	0.0437296	+	0.0437296i
$475$	3.13700e6			0.637941
$476$	1.13098e6	+	265509.i	0.228791	+	0.0537108i
$477$	1.27717e6			0.257013
$478$	2.43836e6	+	2.43836e6i	0.488122	+	0.488122i
$479$	−3.79126e6	+	1.57039e6i	−0.754996	+	0.312730i	−0.726778	−	0.686872i	$-0.758983\pi$
$479$	−3.79126e6	+	1.57039e6i	−0.754996	+	0.312730i	−0.0282179	+	0.999602i	$0.508983\pi$
$480$			2.31339e6i			0.458296i
$481$	−2.31855e6	−	5.59748e6i	−0.456935	−	1.10314i
$482$	7.87223e6	+	3.26078e6i	1.54341	+	0.639300i
$483$	−1.75511e6	+	4.23720e6i	−0.342323	+	0.826440i
$484$	−879722.	+	879722.i	−0.170699	+	0.170699i
$485$	2.86033e6	−	2.86033e6i	0.552156	−	0.552156i
$486$	−110188.	+	266017.i	−0.0211613	+	0.0510879i
$487$	2.66602e6	+	1.10430e6i	0.509378	+	0.210991i	0.622544	−	0.782585i	$-0.286099\pi$
$487$	2.66602e6	+	1.10430e6i	0.509378	+	0.210991i	−0.113166	+	0.993576i	$0.536099\pi$
$488$	−2.15378e6	−	5.19967e6i	−0.409403	−	0.988386i
$489$			4.01407e6i			0.759124i
$490$	1.09911e6	−	455266.i	0.206800	−	0.0856593i
$491$	−1.01380e6	−	1.01380e6i	−0.189779	−	0.189779i	0.605822	−	0.795600i	$-0.292844\pi$
$491$	−1.01380e6	−	1.01380e6i	−0.189779	−	0.189779i	−0.795600	+	0.605822i	$0.792844\pi$
$492$	690873.			0.128672
$493$	−4.92030e6	−	7.93918e6i	−0.911747	−	1.47115i
$494$	−2.52001e6			−0.464606
$495$	501977.	+	501977.i	0.0920812	+	0.0920812i
$496$	−3.31565e6	+	1.37339e6i	−0.605152	+	0.250662i
$497$			5.37356e6i			0.975824i
$498$	1.02344e6	+	2.47081e6i	0.184923	+	0.446444i
$499$	−6.69269e6	−	2.77220e6i	−1.20323	−	0.498395i	−0.311191	−	0.950348i	$-0.600728\pi$
$499$	−6.69269e6	−	2.77220e6i	−1.20323	−	0.498395i	−0.892042	+	0.451952i	$0.850728\pi$
$500$	−455006.	+	1.09848e6i	−0.0813940	+	0.196502i
$501$	4.01902e6	−	4.01902e6i	0.715363	−	0.715363i
$502$	4.94633e6	−	4.94633e6i	0.876040	−	0.876040i
$503$	2.27579e6	−	5.49424e6i	0.401063	−	0.968251i	−0.586346	−	0.810061i	$-0.699434\pi$
$503$	2.27579e6	−	5.49424e6i	0.401063	−	0.968251i	0.987409	−	0.158190i	$-0.0505659\pi$
$504$	−1.74029e6	−	720851.i	−0.305172	−	0.126406i
$505$	4.71746e6	+	1.13889e7i	0.823151	+	1.98726i
$506$		−	2.06924e6i		−	0.359282i
$507$	−2.01300e6	+	833811.i	−0.347795	+	0.144061i
$508$	−930595.	−	930595.i	−0.159993	−	0.159993i
$509$	5.10561e6			0.873481			0.436740	−	0.899588i	$-0.356133\pi$
$509$	5.10561e6			0.873481			0.436740	+	0.899588i	$0.356133\pi$
$510$	−749208.	−	4.58089e6i	−0.127549	−	0.779874i
$511$	8.66313e6			1.46765
$512$	4.49624e6	+	4.49624e6i	0.758010	+	0.758010i
$513$	−444423.	+	184086.i	−0.0745595	+	0.0308835i
$514$			90012.3i			0.0150278i
$515$	3.21834e6	+	7.76977e6i	0.534705	+	1.29089i
$516$	−1.00365e6	−	415725.i	−0.165942	−	0.0687356i
$517$	−188136.	+	454200.i	−0.0309560	+	0.0747344i
$518$	−3.16260e6	+	3.16260e6i	−0.517869	+	0.517869i
$519$	−2.32033e6	+	2.32033e6i	−0.378122	+	0.378122i
$520$	5.21790e6	−	1.25971e7i	0.846228	−	2.04298i
$521$	2.49402e6	+	1.03306e6i	0.402537	+	0.166736i	0.574760	−	0.818322i	$-0.305095\pi$
$521$	2.49402e6	+	1.03306e6i	0.402537	+	0.166736i	−0.172224	+	0.985058i	$0.555095\pi$
$522$	1.18479e6	+	2.86033e6i	0.190311	+	0.459452i
$523$			1.21306e7i			1.93922i	0.244661	+	0.969609i	$0.421323\pi$
$523$			1.21306e7i			1.93922i	−0.244661	+	0.969609i	$0.578677\pi$
$524$	1.57762e6	−	653472.i	0.251000	−	0.103968i
$525$	−3.58721e6	−	3.58721e6i	−0.568013	−	0.568013i
$526$	4.48651e6			0.707041
$527$	−5.24321e6	+	3.24948e6i	−0.822377	+	0.509668i
$528$	616051.			0.0961682
$529$	8.51025e6	+	8.51025e6i	1.32222	+	1.32222i
$530$	6.30519e6	−	2.61169e6i	0.975008	−	0.403862i
$531$		−	1.02757e6i		−	0.158152i
$532$	−246194.	−	594364.i	−0.0377136	−	0.0910486i
$533$	−6.75497e6	−	2.79800e6i	−1.02992	−	0.426609i
$534$	1.38637e6	−	3.34700e6i	0.210391	−	0.507928i
$535$	1.05736e7	−	1.05736e7i	1.59713	−	1.59713i
$536$	−36984.8	+	36984.8i	−0.00556047	+	0.00556047i
$537$	989164.	−	2.38805e6i	0.148024	−	0.357362i
$538$	−9.10436e6	−	3.77115e6i	−1.35611	−	0.561718i
$539$	103855.	+	250727.i	0.0153976	+	0.0371732i
$540$		−	532083.i		−	0.0785226i
$541$	−2.58620e6	+	1.07124e6i	−0.379899	+	0.157360i	−0.564458	−	0.825462i	$-0.690915\pi$
$541$	−2.58620e6	+	1.07124e6i	−0.379899	+	0.157360i	0.184558	+	0.982822i	$0.440915\pi$
$542$	132510.	+	132510.i	0.0193754	+	0.0193754i
$543$	−2.63480e6			−0.383485
$544$	2.80176e6	+	2.01412e6i	0.405914	+	0.291802i
$545$	1.39407e7			2.01044
$546$	2.88167e6	+	2.88167e6i	0.413678	+	0.413678i
$547$	−4.51357e6	+	1.86958e6i	−0.644988	+	0.267163i	−0.681106	−	0.732185i	$-0.738501\pi$
$547$	−4.51357e6	+	1.86958e6i	−0.644988	+	0.267163i	0.0361180	+	0.999348i	$0.488501\pi$
$548$		−	1.85049e6i		−	0.263230i
$549$	889473.	+	2.14738e6i	0.125951	+	0.304073i
$550$	2.11463e6	+	875910.i	0.298077	+	0.123468i
$551$	−1.97938e6	+	4.77864e6i	−0.277747	+	0.670540i
$552$	−5.36454e6	+	5.36454e6i	−0.749351	+	0.749351i
$553$	577918.	−	577918.i	0.0803625	−	0.0803625i
$554$	−756497.	+	1.82634e6i	−0.104721	+	0.252818i
$555$	−5.70957e6	−	2.36498e6i	−0.786812	−	0.325908i
$556$	−763798.	−	1.84397e6i	−0.104783	−	0.252969i
$557$		−	2.67518e6i		−	0.365355i	−0.983173	−	0.182678i	$-0.941524\pi$
$557$		−	2.67518e6i		−	0.365355i	0.983173	−	0.182678i	$-0.0584765\pi$
$558$	1.88903e6	−	782462.i	0.256834	−	0.106384i
$559$	8.12945e6	+	8.12945e6i	1.10035	+	1.10035i
$560$	−7.29626e6			−0.983174
$561$	1.04499e6	−	170908.i	0.140186	−	0.0229275i
$562$	−773155.			−0.103258
$563$	−9.61191e6	−	9.61191e6i	−1.27802	−	1.27802i	−0.941773	−	0.336250i	$-0.890841\pi$
$563$	−9.61191e6	−	9.61191e6i	−1.27802	−	1.27802i	−0.336250	−	0.941773i	$-0.609159\pi$
$564$	340429.	−	141010.i	0.0450639	−	0.0186661i
$565$		−	1.05809e7i		−	1.39444i
$566$	−1.76564e6	−	4.26263e6i	−0.231665	−	0.559290i
$567$	718710.	+	297699.i	0.0938850	+	0.0388884i
$568$	−3.40162e6	+	8.21224e6i	−0.442400	+	1.06805i
$569$	−8.19606e6	+	8.19606e6i	−1.06127	+	1.06127i	−0.0632700	+	0.997996i	$0.520153\pi$
$569$	−8.19606e6	+	8.19606e6i	−1.06127	+	1.06127i	−0.997996	+	0.0632700i	$0.979847\pi$
$570$	−1.81760e6	+	1.81760e6i	−0.234321	+	0.234321i
$571$	−3.03755e6	+	7.33329e6i	−0.389882	+	0.941258i	0.600082	+	0.799938i	$0.295135\pi$
$571$	−3.03755e6	+	7.33329e6i	−0.389882	+	0.941258i	−0.989964	+	0.141320i	$0.954865\pi$
$572$	587457.	+	243333.i	0.0750734	+	0.0310964i
$573$	76254.4	+	184094.i	0.00970238	+	0.0234236i
$574$			5.39746e6i			0.683770i
$575$	−1.88768e7	+	7.81904e6i	−2.38100	+	0.986243i
$576$	−2.07938e6	−	2.07938e6i	−0.261143	−	0.261143i
$577$	776797.			0.0971333			0.0485666	−	0.998820i	$-0.484535\pi$
$577$	776797.			0.0971333			0.0485666	+	0.998820i	$0.484535\pi$
$578$	−6.20023e6	−	3.08091e6i	−0.771948	−	0.383584i
$579$	−5.70104e6			−0.706736
$580$	−4.04550e6	−	4.04550e6i	−0.499346	−	0.499346i
$581$	6.67552e6	−	2.76509e6i	0.820436	−	0.339836i
$582$			1.99995e6i			0.244744i
$583$	595776.	+	1.43833e6i	0.0725958	+	0.175262i
$584$	1.32396e7	+	5.48402e6i	1.60636	+	0.665375i
$585$	−2.15491e6	+	5.20240e6i	−0.260339	+	0.628513i
$586$	2.48664e6	−	2.48664e6i	0.299136	−	0.299136i
$587$	5.09542e6	−	5.09542e6i	0.610358	−	0.610358i	−0.332681	−	0.943039i	$-0.607953\pi$
$587$	5.09542e6	−	5.09542e6i	0.610358	−	0.610358i	0.943039	+	0.332681i	$0.107953\pi$
$588$	77840.5	−	187924.i	0.00928458	−	0.0224150i
$589$	3.15592e6	+	1.30723e6i	0.374833	+	0.155261i
$590$	−2.10127e6	−	5.07292e6i	−0.248515	−	0.599968i
$591$			3.77001e6i			0.443991i
$592$	−4.95474e6	+	2.05232e6i	−0.581055	+	0.240681i
$593$	4.62959e6	+	4.62959e6i	0.540638	+	0.540638i	0.923716	−	0.383078i	$-0.125136\pi$
$593$	4.62959e6	+	4.62959e6i	0.540638	+	0.540638i	−0.383078	+	0.923716i	$0.625136\pi$
$594$	−350983.			−0.0408151
$595$	−1.23764e7	+	2.02417e6i	−1.43318	+	0.234398i
$596$	508999.			0.0586950
$597$	79849.6	+	79849.6i	0.00916932	+	0.00916932i
$598$	1.51641e7	−	6.28118e6i	1.73406	−	0.718271i
$599$		−	1.44144e7i		−	1.64145i	−0.571322	−	0.820726i	$-0.693569\pi$
$599$		−	1.44144e7i		−	1.64145i	0.571322	−	0.820726i	$-0.306431\pi$
$600$	−3.21141e6	−	7.75303e6i	−0.364181	−	0.879211i
$601$	−1.50682e7	−	6.24147e6i	−1.70167	−	0.704856i	−0.701702	−	0.712471i	$-0.747576\pi$
$601$	−1.50682e7	−	6.24147e6i	−1.70167	−	0.704856i	−0.999971	+	0.00761488i	$0.997576\pi$
$602$	3.24786e6	−	7.84103e6i	0.365263	−	0.881824i
$603$	15274.1	−	15274.1i	0.00171065	−	0.00171065i
$604$	1.01184e6	−	1.01184e6i	0.112855	−	0.112855i
$605$	5.13950e6	−	1.24078e7i	0.570863	−	1.37819i
$606$	−5.63081e6	−	2.33236e6i	−0.622859	−	0.257996i
$607$	269175.	+	649845.i	0.0296526	+	0.0715877i	0.938012	−	0.346602i	$-0.112665\pi$
$607$	269175.	+	649845.i	0.0296526	+	0.0715877i	−0.908360	+	0.418190i	$0.862665\pi$
$608$		−	1.91084e6i		−	0.209636i
$609$	7.72790e6	−	3.20100e6i	0.844341	−	0.349738i
$610$	8.78234e6	+	8.78234e6i	0.955621	+	0.955621i
$611$	−3.89961e6			−0.422589
$612$	−644408.	−	463250.i	−0.0695477	−	0.0499962i
$613$	5.70854e6			0.613583			0.306792	−	0.951777i	$-0.400745\pi$
$613$	5.70854e6			0.613583			0.306792	+	0.951777i	$0.400745\pi$
$614$	−5.54182e6	−	5.54182e6i	−0.593241	−	0.593241i
$615$	−6.89024e6	+	2.85403e6i	−0.734593	+	0.304278i
$616$		−	2.29614e6i		−	0.243807i
$617$	1.79768e6	+	4.33998e6i	0.190107	+	0.458960i	0.989980	−	0.141211i	$-0.0450995\pi$
$617$	1.79768e6	+	4.33998e6i	0.190107	+	0.458960i	−0.799872	+	0.600170i	$0.795099\pi$
$618$	−3.84145e6	−	1.59118e6i	−0.404599	−	0.167590i
$619$	6.39370e6	−	1.54357e7i	0.670695	−	1.61920i	−0.109736	−	0.993961i	$-0.535001\pi$
$619$	6.39370e6	−	1.54357e7i	0.670695	−	1.61920i	0.780432	−	0.625241i	$-0.214999\pi$
$620$	−2.67174e6	+	2.67174e6i	−0.279135	+	0.279135i
$621$	2.21547e6	−	2.21547e6i	0.230535	−	0.230535i
$622$	1.14427e6	−	2.76250e6i	0.118591	−	0.286303i
$623$	−9.04274e6	−	3.74563e6i	−0.933426	−	0.386638i
$624$	1.87002e6	+	4.51462e6i	0.192258	+	0.464152i
$625$			2.02124e6i			0.206975i
$626$	2.52578e6	−	1.04621e6i	0.257608	−	0.106705i
$627$	−414628.	−	414628.i	−0.0421202	−	0.0421202i
$628$	−1.68943e6			−0.170939
$629$	−7.83520e6	+	4.85586e6i	−0.789630	+	0.489372i
$630$	4.15691e6			0.417272
$631$	4.17046e6	+	4.17046e6i	0.416975	+	0.416975i	0.884160	−	0.467185i	$-0.154732\pi$
$631$	4.17046e6	+	4.17046e6i	0.416975	+	0.416975i	−0.467185	+	0.884160i	$0.654732\pi$
$632$	1.24905e6	−	517375.i	0.124391	−	0.0515244i
$633$		−	8.92657e6i		−	0.885473i
$634$	1.98354e6	+	4.78868e6i	0.195982	+	0.473143i
$635$	1.31254e7	+	5.43671e6i	1.29175	+	0.535059i
$636$	446543.	−	1.07805e6i	0.0437744	−	0.105681i
$637$	−1.52216e6	+	1.52216e6i	−0.148632	+	0.148632i
$638$	−2.66857e6	+	2.66857e6i	−0.259554	+	0.259554i
$639$	1.40481e6	−	3.39152e6i	0.136103	−	0.328581i
$640$	−6.91841e6	−	2.86570e6i	−0.667662	−	0.276555i
$641$	1.10097e6	+	2.65799e6i	0.105836	+	0.255510i	0.967922	−	0.251252i	$-0.0808423\pi$
$641$	1.10097e6	+	2.65799e6i	0.105836	+	0.255510i	−0.862086	+	0.506762i	$0.830842\pi$
$642$			7.39311e6i			0.707929i
$643$	−7.15082e6	+	2.96197e6i	−0.682069	+	0.282522i	−0.696692	−	0.717371i	$-0.745345\pi$
$643$	−7.15082e6	+	2.96197e6i	−0.682069	+	0.282522i	0.0146225	+	0.999893i	$0.495345\pi$
$644$	2.96293e6	+	2.96293e6i	0.281518	+	0.281518i
$645$	1.17270e7			1.10991
$646$	618838.	+	3.78377e6i	0.0583440	+	0.356733i
$647$	−3.92608e6			−0.368722			−0.184361	−	0.982859i	$-0.559021\pi$
$647$	−3.92608e6			−0.368722			−0.184361	+	0.982859i	$0.559021\pi$
$648$	909929.	+	909929.i	0.0851275	+	0.0851275i
$649$	1.15723e6	−	479340.i	0.107847	−	0.0446716i
$650$			1.81556e7i			1.68549i
$651$	−2.11401e6	−	5.10368e6i	−0.195504	−	0.471988i
$652$	3.38823e6	+	1.40345e6i	0.312144	+	0.129294i
$653$	−3.79529e6	+	9.16265e6i	−0.348307	+	0.840888i	0.648513	+	0.761204i	$0.275391\pi$
$653$	−3.79529e6	+	9.16265e6i	−0.348307	+	0.840888i	−0.996820	+	0.0796843i	$0.974609\pi$
$654$	−4.87367e6	+	4.87367e6i	−0.445565	+	0.445565i
$655$	−1.30345e7	+	1.30345e7i	−1.18711	+	1.18711i
$656$	−2.47672e6	+	5.97932e6i	−0.224707	+	0.542491i
$657$	−5.46773e6	−	2.26481e6i	−0.494190	−	0.204700i
$658$	1.10165e6	+	2.65961e6i	0.0991923	+	0.239471i
$659$			625321.i			0.0560905i	0.999607	+	0.0280453i	$0.00892825\pi$
$659$			625321.i			0.0560905i	−0.999607	+	0.0280453i	$0.991072\pi$
$660$	599221.	−	248206.i	0.0535460	−	0.0221795i
$661$	−8.18914e6	−	8.18914e6i	−0.729012	−	0.729012i	0.241411	−	0.970423i	$-0.422390\pi$
$661$	−8.18914e6	−	8.18914e6i	−0.729012	−	0.729012i	−0.970423	+	0.241411i	$0.922390\pi$
$662$	275803.			0.0244599
$663$	4.42452e6	+	7.13921e6i	0.390915	+	0.630763i
$664$	1.19524e7			1.05204
$665$	4.91069e6	+	4.91069e6i	0.430614	+	0.430614i
$666$	2.82287e6	−	1.16927e6i	0.246607	−	0.102148i
$667$		−	3.36890e7i		−	2.93206i
$668$	−1.98723e6	−	4.79760e6i	−0.172309	−	0.415990i
$669$	5.76787e6	+	2.38913e6i	0.498254	+	0.206383i
$670$	44171.5	−	106639.i	0.00380150	−	0.00917764i
$671$	−2.00342e6	+	2.00342e6i	−0.171777	+	0.171777i
$672$	−2.18507e6	+	2.18507e6i	−0.186656	+	0.186656i
$673$	6.88213e6	−	1.66149e7i	0.585714	−	1.41404i	−0.301851	−	0.953355i	$-0.597605\pi$
$673$	6.88213e6	−	1.66149e7i	0.585714	−	1.41404i	0.887565	−	0.460683i	$-0.152395\pi$
$674$	−1.74345e7	−	7.22160e6i	−1.47829	−	0.612327i
$675$	1.32626e6	+	3.20187e6i	0.112039	+	0.270486i
$676$			1.99068e6i			0.167546i
$677$	3.73894e6	−	1.54872e6i	0.313528	−	0.129868i	−0.220370	−	0.975416i	$-0.570726\pi$
$677$	3.73894e6	−	1.54872e6i	0.313528	−	0.129868i	0.533898	+	0.845549i	$0.320726\pi$
$678$	3.69908e6	+	3.69908e6i	0.309043	+	0.309043i
$679$	5.40336e6			0.449769
$680$	−2.01958e7	−	4.74115e6i	−1.67490	−	0.393198i
$681$	8.84046e6			0.730478
$682$	1.76239e6	+	1.76239e6i	0.145091	+	0.145091i
$683$	1.69704e7	−	7.02935e6i	1.39200	−	0.576585i	0.444337	−	0.895859i	$-0.353439\pi$
$683$	1.69704e7	−	7.02935e6i	1.39200	−	0.576585i	0.947662	+	0.319274i	$0.103439\pi$
$684$			439495.i			0.0359181i
$685$	7.64446e6	+	1.84553e7i	0.622472	+	1.50278i
$686$	1.04456e7	+	4.32673e6i	0.847471	+	0.351034i
$687$	1.64605e6	−	3.97392e6i	0.133061	−	0.321238i
$688$	7.19597e6	−	7.19597e6i	0.579587	−	0.579587i
$689$	−8.73208e6	+	8.73208e6i	−0.700761	+	0.700761i
$690$	6.40696e6	−	1.54678e7i	0.512306	−	1.23682i
$691$	−1.82758e6	−	757009.i	−0.145607	−	0.0603123i	0.308690	−	0.951163i	$-0.400109\pi$
$691$	−1.82758e6	−	757009.i	−0.145607	−	0.0603123i	−0.454297	+	0.890850i	$0.650109\pi$
$692$	1.14730e6	+	2.76983e6i	0.0910777	+	0.219881i
$693$			948268.i			0.0750064i
$694$	−5.74503e6	+	2.37967e6i	−0.452787	+	0.187550i
$695$	1.52351e7	+	1.52351e7i	1.19642	+	1.19642i
$696$	1.38366e7			1.08270
$697$	−2.54235e6	+	1.08296e7i	−0.198223	+	0.844368i
$698$	1.71419e7			1.33174
$699$	−5.96444e6	−	5.96444e6i	−0.461718	−	0.461718i
$700$	−4.28213e6	+	1.77372e6i	−0.330305	+	0.136817i
$701$			1.50720e7i			1.15845i	0.815169	+	0.579224i	$0.196644\pi$
$701$			1.50720e7i			1.15845i	−0.815169	+	0.579224i	$0.803356\pi$
$702$	−1.06541e6	−	2.57212e6i	−0.0815968	−	0.196992i
$703$	4.71605e6	+	1.95345e6i	0.359907	+	0.149078i
$704$	1.37177e6	−	3.31175e6i	0.104316	−	0.251841i
$705$	−2.81266e6	+	2.81266e6i	−0.213130	+	0.213130i
$706$	−7.99362e6	+	7.99362e6i	−0.603576	+	0.603576i
$707$	−6.30144e6	+	1.52130e7i	−0.474124	+	1.14464i
$708$	−867359.	−	359272.i	−0.0650303	−	0.0269364i
$709$	−3.89617e6	−	9.40617e6i	−0.291086	−	0.702744i	0.708910	−	0.705299i	$-0.249187\pi$
$709$	−3.89617e6	−	9.40617e6i	−0.291086	−	0.702744i	−0.999997	+	0.00255402i	$0.999187\pi$
$710$		−	1.96160e7i		−	1.46038i
$711$	−515838.	+	213667.i	−0.0382683	+	0.0158513i
$712$	−1.14486e7	−	1.14486e7i	−0.846358	−	0.846358i
$713$	−2.22490e7			−1.63903
$714$	3.61915e6	−	5.03445e6i	0.265681	−	0.369579i
$715$	−6.86407e6			−0.502130
$716$	−1.66989e6	−	1.66989e6i	−0.121732	−	0.121732i
$717$	−5.88017e6	+	2.43565e6i	−0.427161	+	0.176936i
$718$			1.30982e7i			0.948200i
$719$	−8.24177e6	−	1.98974e7i	−0.594563	−	1.43540i	−0.879053	−	0.476724i	$-0.841824\pi$
$719$	−8.24177e6	−	1.98974e7i	−0.594563	−	1.43540i	0.284490	−	0.958679i	$-0.408176\pi$
$720$	4.60503e6	+	1.90747e6i	0.331056	+	0.137128i
$721$	−4.29897e6	+	1.03786e7i	−0.307983	+	0.743536i
$722$	−7.03625e6	+	7.03625e6i	−0.502340	+	0.502340i
$723$	−1.11206e7	+	1.11206e7i	−0.791194	+	0.791194i
$724$	−921215.	+	2.22401e6i	−0.0653152	+	0.157685i
$725$	3.44280e7	+	1.42605e7i	2.43258	+	1.00761i
$726$	2.54102e6	+	6.13457e6i	0.178923	+	0.431959i
$727$		−	6.05970e6i		−	0.425221i	−0.977137	−	0.212611i	$-0.931803\pi$
$727$		−	6.05970e6i		−	0.425221i	0.977137	−	0.212611i	$-0.0681966\pi$
$728$	1.68269e7	−	6.96992e6i	1.17673	−	0.487416i
$729$	−375786.	−	375786.i	−0.0261891	−	0.0261891i
$730$	−3.16245e7			−2.19643
$731$	1.02099e7	−	1.42026e7i	0.706691	−	0.983050i
$732$	2.12357e6			0.146483
$733$	8.31696e6	+	8.31696e6i	0.571748	+	0.571748i	0.932617	−	0.360869i	$-0.117520\pi$
$733$	8.31696e6	+	8.31696e6i	0.571748	+	0.571748i	−0.360869	+	0.932617i	$0.617520\pi$
$734$	1.07324e7	−	4.44551e6i	0.735287	−	0.304566i
$735$			2.19577e6i			0.149923i
$736$	4.76281e6	+	1.14984e7i	0.324092	+	0.782427i
$737$	24326.5	+	10076.3i	0.00164972	+	0.000683336i
$738$	1.41106e6	−	3.40661e6i	0.0953686	−	0.230240i
$739$	1.36220e7	−	1.36220e7i	0.917550	−	0.917550i	−0.0793004	−	0.996851i	$-0.525269\pi$
$739$	1.36220e7	−	1.36220e7i	0.917550	−	0.917550i	0.996851	+	0.0793004i	$0.0252686\pi$
$740$	−3.99251e6	+	3.99251e6i	−0.268020	+	0.268020i
$741$	1.77993e6	−	4.29713e6i	0.119085	−	0.287497i
$742$	8.42229e6	+	3.48863e6i	0.561591	+	0.232619i
$743$	−1.04549e7	−	2.52403e7i	−0.694778	−	1.67734i	−0.734925	−	0.678148i	$-0.762783\pi$
$743$	−1.04549e7	−	2.52403e7i	−0.694778	−	1.67734i	0.0401471	−	0.999194i	$-0.487217\pi$
$744$		−	9.13803e6i		−	0.605229i
$745$	−5.07636e6	+	2.10270e6i	−0.335090	+	0.138799i
$746$	2.13534e6	+	2.13534e6i	0.140482	+	0.140482i
$747$	−4.93613e6			−0.323657
$748$	221100.	−	941817.i	0.0144489	−	0.0615478i
$749$	1.99743e7			1.30097
$750$	4.48715e6	+	4.48715e6i	0.291285	+	0.291285i
$751$	−2.12622e7	+	8.80709e6i	−1.37565	+	0.569813i	−0.943315	−	0.331899i	$-0.892311\pi$
$751$	−2.12622e7	+	8.80709e6i	−1.37565	+	0.569813i	−0.432336	+	0.901712i	$0.642311\pi$
$752$			3.45183e6i			0.222590i
$753$	4.94082e6	+	1.19282e7i	0.317550	+	0.766633i
$754$	−2.76566e7	−	1.14557e7i	−1.77162	−	0.733829i
$755$	−5.91137e6	+	1.42713e7i	−0.377417	+	0.911164i
$756$	502570.	−	502570.i	0.0319810	−	0.0319810i
$757$	1.69616e7	−	1.69616e7i	1.07579	−	1.07579i	0.0789087	−	0.996882i	$-0.474856\pi$
$757$	1.69616e7	−	1.69616e7i	1.07579	−	1.07579i	0.996882	−	0.0789087i	$-0.0251436\pi$
$758$	2.47133e6	−	5.96632e6i	0.156228	−	0.377167i
$759$	3.52849e6	+	1.46155e6i	0.222323	+	0.0920891i
$760$	4.39624e6	+	1.06135e7i	0.276088	+	0.666536i
$761$		−	7.31885e6i		−	0.458122i	−0.973412	−	0.229061i	$-0.926434\pi$
$761$		−	7.31885e6i		−	0.458122i	0.973412	−	0.229061i	$-0.0735656\pi$
$762$	−6.48932e6	+	2.68796e6i	−0.404866	+	0.167701i
$763$	1.31674e7	+	1.31674e7i	0.818821	+	0.818821i
$764$	182053.			0.0112840
$765$	8.34054e6	+	1.95802e6i	0.515277	+	0.120966i
$766$	−1.05473e7			−0.649486
$767$	7.02552e6	+	7.02552e6i	0.431211	+	0.431211i
$768$	−6.23936e6	+	2.58443e6i	−0.381713	+	0.158111i
$769$		−	6.38666e6i		−	0.389456i	−0.980857	−	0.194728i	$-0.937618\pi$
$769$		−	6.38666e6i		−	0.389456i	0.980857	−	0.194728i	$-0.0623824\pi$
$770$	1.93911e6	+	4.68143e6i	0.117863	+	0.284546i
$771$	−153490.	−	63577.4i	−0.00929914	−	0.00385183i
$772$	−1.99327e6	+	4.81218e6i	−0.120371	+	0.290602i
$773$	8.05244e6	−	8.05244e6i	0.484706	−	0.484706i	−0.421925	−	0.906631i	$-0.638645\pi$
$773$	8.05244e6	−	8.05244e6i	0.484706	−	0.484706i	0.906631	+	0.421925i	$0.138645\pi$
$774$	−4.09977e6	+	4.09977e6i	−0.245984	+	0.245984i
$775$	9.41798e6	−	2.27370e7i	0.563253	−	1.35981i
$776$	8.25778e6	+	3.42048e6i	0.492276	+	0.203908i
$777$	−3.15908e6	−	7.62669e6i	−0.187719	−	0.453193i
$778$			1.02620e7i			0.607833i
$779$	5.69127e6	−	2.35740e6i	0.336020	−	0.139184i
$780$	3.63787e6	+	3.63787e6i	0.214097	+	0.214097i
$781$	4.47478e6			0.262509
$782$	−1.31550e7	−	2.12263e7i	−0.769260	−	1.24124i
$783$	−5.71430e6			−0.333087
$784$	1.34738e6	+	1.34738e6i	0.0782887	+	0.0782887i
$785$	1.68491e7	−	6.97911e6i	0.975891	−	0.404227i
$786$		−	9.11371e6i		−	0.526186i
$787$	−2.10018e6	−	5.07028e6i	−0.120870	−	0.291807i	0.851851	−	0.523784i	$-0.175480\pi$
$787$	−2.10018e6	−	5.07028e6i	−0.120870	−	0.291807i	−0.972721	+	0.231978i	$0.925480\pi$
$788$	3.18222e6	+	1.31812e6i	0.182564	+	0.0756205i
$789$	−3.16891e6	+	7.65043e6i	−0.181225	+	0.437515i
$790$	−2.10967e6	+	2.10967e6i	−0.120267	+	0.120267i
$791$	9.99397e6	−	9.99397e6i	0.567933	−	0.567933i
$792$	−600282.	+	1.44921e6i	−0.0340049	+	0.0820952i
$793$	−2.07630e7	−	8.60033e6i	−1.17249	−	0.485660i
$794$	−5.72981e6	−	1.38330e7i	−0.322544	−	0.778691i
$795$			1.25963e7i			0.706848i
$796$	95318.3	−	39482.1i	0.00533204	−	0.00220860i
$797$	−9.76672e6	−	9.76672e6i	−0.544632	−	0.544632i	0.380251	−	0.924883i	$-0.375837\pi$
$797$	−9.76672e6	−	9.76672e6i	−0.544632	−	0.544632i	−0.924883	+	0.380251i	$0.875837\pi$
$798$	−3.43357e6			−0.190870
$799$	957627.	+	5.85523e6i	0.0530676	+	0.324472i
$800$	−1.37667e7			−0.760512
$801$	4.72810e6	+	4.72810e6i	0.260379	+	0.260379i
$802$	3.25020e6	−	1.34628e6i	0.178432	−	0.0739091i
$803$		−	7.21414e6i		−	0.394817i
$804$	−7552.37	−	18233.0i	−0.000412044	−	0.000994761i
$805$	−4.17900e7	−	1.73100e7i	−2.27291	−	0.941471i
$806$	−7.56564e6	+	1.82651e7i	−0.410212	+	0.990339i
$807$	1.28612e7	−	1.28612e7i	0.695179	−	0.695179i
$808$	−1.92606e7	+	1.92606e7i	−1.03787	+	1.03787i
$809$	−6.06353e6	+	1.46386e7i	−0.325727	+	0.786375i	0.673173	+	0.739485i	$0.264931\pi$
$809$	−6.06353e6	+	1.46386e7i	−0.325727	+	0.786375i	−0.998900	+	0.0468897i	$0.985069\pi$
$810$	−2.62363e6	−	1.08674e6i	−0.140504	−	0.0581988i
$811$	−1.01745e7	−	2.45633e7i	−0.543200	−	1.31140i	−0.922454	−	0.386108i	$-0.873819\pi$
$811$	−1.01745e7	−	2.45633e7i	−0.543200	−	1.31140i	0.379254	−	0.925293i	$-0.376181\pi$
$812$		−	7.64221e6i		−	0.406751i
$813$	−319552.	+	132363.i	−0.0169557	+	0.00702327i
$814$	2.63362e6	+	2.63362e6i	0.139313	+	0.139313i
$815$	−3.95894e7			−2.08778
$816$	6.31944e6	−	3.91647e6i	0.332241	−	0.205906i
$817$	−9.68639e6			−0.507699
$818$	1.25102e7	+	1.25102e7i	0.653704	+	0.653704i
$819$	−6.94922e6	+	2.87846e6i	−0.362015	+	0.149951i
$820$			6.81384e6i			0.353881i
$821$	2.81365e6	+	6.79275e6i	0.145684	+	0.351713i	0.979830	−	0.199831i	$-0.0640392\pi$
$821$	2.81365e6	+	6.79275e6i	0.145684	+	0.351713i	−0.834146	+	0.551543i	$0.814039\pi$
$822$	−9.12452e6	−	3.77950e6i	−0.471010	−	0.195099i
$823$	3.85486e6	−	9.30645e6i	0.198385	−	0.478944i	−0.793112	−	0.609076i	$-0.791540\pi$
$823$	3.85486e6	−	9.30645e6i	0.198385	−	0.478944i	0.991497	+	0.130133i	$0.0415403\pi$
$824$	−1.31400e7	+	1.31400e7i	−0.674180	+	0.674180i
$825$	−2.98721e6	+	2.98721e6i	−0.152803	+	0.152803i
$826$	2.80682e6	−	6.77627e6i	0.143141	−	0.345573i
$827$	−1.18406e7	−	4.90454e6i	−0.602018	−	0.249364i	0.0607932	−	0.998150i	$-0.480637\pi$
$827$	−1.18406e7	−	4.90454e6i	−0.602018	−	0.249364i	−0.662812	+	0.748786i	$0.730637\pi$
$828$	−1.09545e6	−	2.64465e6i	−0.0555287	−	0.134058i
$829$		−	5.12320e6i		−	0.258914i	−0.991585	−	0.129457i	$-0.958677\pi$
$829$		−	5.12320e6i		−	0.258914i	0.991585	−	0.129457i	$-0.0413234\pi$
$830$	−2.43688e7	+	1.00939e7i	−1.22783	+	0.508584i
$831$	−2.57996e6	−	2.57996e6i	−0.129602	−	0.129602i
$832$	2.84336e7			1.42405
$833$	2.65931e6	+	1.91171e6i	0.132787	+	0.0954576i
$834$	−1.06524e7			−0.530313
$835$	3.96382e7	+	3.96382e7i	1.96742	+	1.96742i
$836$	−494951.	+	205015.i	−0.0244932	+	0.0101454i
$837$			3.77385e6i			0.186196i
$838$	−8.30125e6	−	2.00410e7i	−0.408351	−	0.985846i
$839$	1.23645e7	+	5.12156e6i	0.606419	+	0.251187i	0.664696	−	0.747114i	$-0.268561\pi$
$839$	1.23645e7	+	5.12156e6i	0.606419	+	0.251187i	−0.0582777	+	0.998300i	$0.518561\pi$
$840$	7.10950e6	−	1.71639e7i	0.347649	−	0.839299i
$841$	−2.89430e7	+	2.89430e7i	−1.41109	+	1.41109i
$842$	−8.44256e6	+	8.44256e6i	−0.410387	+	0.410387i
$843$	546094.	−	1.31839e6i	0.0264666	−	0.0638961i
$844$	−7.53482e6	−	3.12103e6i	−0.364097	−	0.150814i
$845$	−8.22358e6	−	1.98535e7i	−0.396204	−	0.956522i
$846$		−	1.96662e6i		−	0.0944700i
$847$	1.65740e7	−	6.86520e6i	0.793816	−	0.328810i
$848$	7.72941e6	+	7.72941e6i	0.369111	+	0.369111i
$849$	8.51577e6			0.405466
$850$	2.72604e7	−	4.45846e6i	1.29415	−	0.211659i
$851$	−3.32478e7			−1.57376
$852$	−2.37158e6	−	2.37158e6i	−0.111928	−	0.111928i
$853$	1.77704e7	−	7.36075e6i	0.836228	−	0.346377i	0.0768631	−	0.997042i	$-0.475510\pi$
$853$	1.77704e7	−	7.36075e6i	0.836228	−	0.346377i	0.759365	+	0.650664i	$0.225510\pi$
$854$			1.65904e7i			0.778418i
$855$	−1.81557e6	−	4.38319e6i	−0.0849374	−	0.205057i
$856$	3.05261e7	+	1.26443e7i	1.42393	+	0.589809i
$857$	4.33554e6	−	1.04669e7i	0.201647	−	0.486819i	−0.790415	−	0.612572i	$-0.790135\pi$
$857$	4.33554e6	−	1.04669e7i	0.201647	−	0.486819i	0.992062	+	0.125754i	$0.0401349\pi$
$858$	2.39968e6	−	2.39968e6i	0.111285	−	0.111285i
$859$	1.73271e7	−	1.73271e7i	0.801204	−	0.801204i	−0.182079	−	0.983284i	$-0.558283\pi$
$859$	1.73271e7	−	1.73271e7i	0.801204	−	0.801204i	0.983284	+	0.182079i	$0.0582828\pi$
$860$	4.10015e6	−	9.89863e6i	0.189040	−	0.456383i
$861$	−9.20379e6	−	3.81233e6i	−0.423115	−	0.175260i
$862$	3.79128e6	+	9.15296e6i	0.173787	+	0.419560i
$863$		−	1.49919e7i		−	0.685219i	−0.939478	−	0.342610i	$-0.888689\pi$
$863$		−	1.49919e7i		−	0.685219i	0.939478	−	0.342610i	$-0.111311\pi$
$864$	1.95035e6	−	807863.i	0.0888851	−	0.0368174i
$865$	−2.28846e7	−	2.28846e7i	−1.03993	−	1.03993i
$866$	3.51671e7			1.59346
$867$	9.63293e6	−	8.39655e6i	0.435222	−	0.379362i
$868$	−5.04709e6			−0.227375
$869$	−481256.	−	481256.i	−0.0216185	−	0.0216185i
$870$	−2.82105e7	+	1.16852e7i	−1.26361	+	0.523403i
$871$			208859.i			0.00932841i
$872$	1.17880e7	+	2.84587e7i	0.524987	+	1.26743i
$873$	−3.41033e6	−	1.41260e6i	−0.151447	−	0.0627313i
$874$	−5.29209e6	+	1.27762e7i	−0.234341	+	0.565749i
$875$	1.21231e7	−	1.21231e7i	0.535297	−	0.535297i
$876$	−3.82340e6	+	3.82340e6i	−0.168341	+	0.168341i
$877$	−6.69027e6	+	1.61517e7i	−0.293727	+	0.709121i	0.706272	+	0.707941i	$0.250376\pi$
$877$	−6.69027e6	+	1.61517e7i	−0.293727	+	0.709121i	−0.999999	+	0.00118003i	$0.999624\pi$
$878$	1.64741e7	+	6.82381e6i	0.721218	+	0.298738i
$879$	2.48387e6	+	5.99659e6i	0.108432	+	0.261777i
$880$			6.07589e6i			0.264486i
$881$	−1.28054e7	+	5.30419e6i	−0.555846	+	0.230239i	−0.642881	−	0.765966i	$-0.722261\pi$
$881$	−1.28054e7	+	5.30419e6i	−0.555846	+	0.230239i	0.0870345	+	0.996205i	$0.472261\pi$
$882$	−767643.	−	767643.i	−0.0332267	−	0.0332267i
$883$	2.80065e7			1.20881			0.604404	−	0.796678i	$-0.293411\pi$
$883$	2.80065e7			1.20881			0.604404	+	0.796678i	$0.293411\pi$
$884$	7.57309e6	−	1.23858e6i	0.325944	−	0.0533083i
$885$	1.01345e7			0.434957
$886$	−1.60363e7	−	1.60363e7i	−0.686311	−	0.686311i
$887$	−3.71500e7	+	1.53880e7i	−1.58544	+	0.656710i	−0.989263	−	0.146144i	$-0.953314\pi$
$887$	−3.71500e7	+	1.53880e7i	−1.58544	+	0.656710i	−0.596176	+	0.802854i	$0.703314\pi$
$888$		−	1.36554e7i		−	0.581129i
$889$	7.26220e6	+	1.75325e7i	0.308187	+	0.744028i
$890$	3.30103e7	+	1.36733e7i	1.39693	+	0.578626i
$891$	247906.	−	598499.i	0.0104615	−	0.0252563i
$892$	4.03328e6	−	4.03328e6i	0.169725	−	0.169725i
$893$	2.32323e6	−	2.32323e6i	0.0974907	−	0.0974907i
$894$	1.03960e6	−	2.50981e6i	0.0435031	−	0.105026i
$895$	2.35525e7	+	9.75578e6i	0.982834	+	0.407103i
$896$	−3.82792e6	−	9.24142e6i	−0.159292	−	0.384564i
$897$			3.02944e7i			1.25713i
$898$	2.17449e7	−	9.00703e6i	0.899843	−	0.372727i
$899$	2.86931e7	+	2.86931e7i	1.18407	+	1.18407i
$900$	3.16637e6			0.130303
$901$	1.52555e7	+	1.09668e7i	0.626057	+	0.450058i
$902$	4.49469e6			0.183943
$903$	1.10765e7	+	1.10765e7i	0.452048	+	0.452048i
$904$	2.16000e7	−	8.94699e6i	0.879087	−	0.364130i
$905$		−	2.59861e7i		−	1.05468i
$906$	−2.92264e6	−	7.05589e6i	−0.118292	−	0.285582i
$907$	1.82907e7	+	7.57626e6i	0.738265	+	0.305800i	0.719944	−	0.694033i	$-0.244168\pi$
$907$	1.82907e7	+	7.57626e6i	0.738265	+	0.305800i	0.0183218	+	0.999832i	$0.494168\pi$
$908$	3.09092e6	−	7.46214e6i	0.124415	−	0.300365i
$909$	7.95430e6	−	7.95430e6i	0.319295	−	0.319295i
$910$	−2.84209e7	+	2.84209e7i	−1.13772	+	1.13772i
$911$	−1.46408e7	+	3.53461e7i	−0.584480	+	1.41106i	0.304234	+	0.952597i	$0.401599\pi$
$911$	−1.46408e7	+	3.53461e7i	−0.584480	+	1.41106i	−0.888714	+	0.458462i	$0.848401\pi$
$912$	−3.80371e6	−	1.57555e6i	−0.151433	−	0.0627256i
$913$	−2.30260e6	−	5.55897e6i	−0.0914201	−	0.220708i
$914$		−	2.63177e7i		−	1.04204i
$915$	−2.11788e7	+	8.77256e6i	−0.836275	+	0.346397i
$916$	−2.77883e6	−	2.77883e6i	−0.109427	−	0.109427i
$917$	−2.46229e7			−0.966978
$918$	−3.60038e6	+	2.23134e6i	−0.141007	+	0.0873893i
$919$	6.82747e6			0.266668			0.133334	−	0.991071i	$-0.457432\pi$
$919$	6.82747e6			0.266668			0.133334	+	0.991071i	$0.457432\pi$
$920$	−5.29086e7	−	5.29086e7i	−2.06090	−	2.06090i
$921$	1.33642e7	−	5.53565e6i	0.519152	−	0.215040i
$922$			2.73371e6i			0.105907i
$923$	1.35832e7	+	3.27927e7i	0.524804	+	1.26699i
$924$	800423.	+	331546.i	0.0308418	+	0.0127751i
$925$	1.40738e7	−	3.39771e7i	0.540824	−	1.30566i
$926$	1.60133e7	−	1.60133e7i	0.613695	−	0.613695i
$927$	5.42659e6	−	5.42659e6i	0.207409	−	0.207409i
$928$	8.68651e6	−	2.09711e7i	0.331112	−	0.799376i
$929$	6.99259e6	+	2.89642e6i	0.265827	+	0.110109i	0.511616	−	0.859214i	$-0.329047\pi$
$929$	6.99259e6	+	2.89642e6i	0.265827	+	0.110109i	−0.245789	+	0.969323i	$0.579047\pi$
$930$	7.71715e6	+	1.86308e7i	0.292583	+	0.706358i
$931$		−	1.81368e6i		−	0.0685784i
$932$	−7.11988e6	+	2.94915e6i	−0.268493	+	0.111213i
$933$	3.90241e6	+	3.90241e6i	0.146767	+	0.146767i
$934$	1.63797e7			0.614382
$935$	1.68561e6	+	1.03063e7i	0.0630562	+	0.385545i
$936$	−1.24424e7			−0.464211
$937$	2.18654e7	+	2.18654e7i	0.813597	+	0.813597i	0.985171	−	0.171574i	$-0.0548854\pi$
$937$	2.18654e7	+	2.18654e7i	0.813597	+	0.813597i	−0.171574	+	0.985171i	$0.554885\pi$
$938$	142446.	−	59003.1i	0.00528620	−	0.00218961i
$939$			5.04594e6i			0.186757i
$940$	1.39074e6	+	3.35753e6i	0.0513364	+	0.123937i
$941$	−898637.	−	372228.i	−0.0330834	−	0.0137036i	0.366080	−	0.930583i	$-0.380700\pi$
$941$	−898637.	−	372228.i	−0.0330834	−	0.0137036i	−0.399164	+	0.916880i	$0.630700\pi$
$942$	−3.45054e6	+	8.33035e6i	−0.126695	+	0.305869i
$943$	−2.83712e7	+	2.83712e7i	−1.03896	+	1.03896i
$944$	6.21880e6	−	6.21880e6i	0.227131	−	0.227131i
$945$	−2.93610e6	+	7.08838e6i	−0.106953	+	0.258207i
$946$	−6.52954e6	−	2.70462e6i	−0.237222	−	0.0982605i
$947$	−3.89832e6	−	9.41138e6i	−0.141255	−	0.341019i	0.837381	−	0.546619i	$-0.184085\pi$
$947$	−3.89832e6	−	9.41138e6i	−0.141255	−	0.341019i	−0.978636	+	0.205600i	$0.934085\pi$
$948$			510118.i			0.0184353i
$949$	5.28676e7	−	2.18985e7i	1.90557	−	0.789311i
$950$	−1.08163e7	−	1.08163e7i	−0.388840	−	0.388840i
$951$	−9.56669e6			−0.343013
$952$	−1.45975e7	−	2.35538e7i	−0.522017	−	0.842304i
$953$	−1.60340e7			−0.571887			−0.285943	−	0.958247i	$-0.592307\pi$
$953$	−1.60340e7			−0.571887			−0.285943	+	0.958247i	$0.592307\pi$
$954$	−4.40369e6	−	4.40369e6i	−0.156655	−	0.156655i
$955$	−1.81566e6	+	752070.i	−0.0644207	+	0.0266839i
$956$			5.81497e6i			0.205780i
$957$	−2.66560e6	−	6.43533e6i	−0.0940839	−	0.227139i
$958$	1.84869e7	+	7.65753e6i	0.650805	+	0.269572i
$959$	−1.02112e7	+	2.46521e7i	−0.358536	+	0.865582i
$960$	2.05082e7	−	2.05082e7i	0.718208	−	0.718208i
$961$	−1.29428e6	+	1.29428e6i	−0.0452084	+	0.0452084i
$962$	−1.13057e7	+	2.72944e7i	−0.393877	+	0.950903i
$963$	−1.26068e7	−	5.22190e6i	−0.438065	−	0.181452i
$964$	5.49865e6	+	1.32749e7i	0.190574	+	0.460087i
$965$		−	5.62273e7i		−	1.94370i
$966$	2.06614e7	−	8.55824e6i	0.712389	−	0.295081i
$967$	−2.68920e7	−	2.68920e7i	−0.924818	−	0.924818i	0.0725471	−	0.997365i	$-0.476887\pi$
$967$	−2.68920e7	−	2.68920e7i	−0.924818	−	0.924818i	−0.997365	+	0.0725471i	$0.976887\pi$
$968$	2.96755e7			1.01791
$969$	−6.88920e6	−	1.61730e6i	−0.235700	−	0.0553327i
$970$	−1.97248e7			−0.673106
$971$	−1.38813e7	−	1.38813e7i	−0.472480	−	0.472480i	0.430237	−	0.902716i	$-0.358430\pi$
$971$	−1.38813e7	−	1.38813e7i	−0.472480	−	0.472480i	−0.902716	+	0.430237i	$0.858430\pi$
$972$	−448584.	+	185809.i	−0.0152292	+	0.00630815i
$973$			2.87801e7i			0.974563i
$974$	−5.38479e6	−	1.30000e7i	−0.181874	−	0.439083i
$975$	−3.09590e7	−	1.28236e7i	−1.04298	−	0.432015i
$976$	−7.61279e6	+	1.83789e7i	−0.255811	+	0.617583i
$977$	−2.77036e7	+	2.77036e7i	−0.928539	+	0.928539i	−0.997612	−	0.0690728i	$-0.977996\pi$
$977$	−2.77036e7	+	2.77036e7i	−0.928539	+	0.928539i	0.0690728	+	0.997612i	$0.477996\pi$
$978$	1.38405e7	−	1.38405e7i	0.462705	−	0.462705i
$979$	−3.11913e6	+	7.53026e6i	−0.104011	+	0.251104i
$980$	1.85342e6	+	767714.i	0.0616467	+	0.0255349i
$981$	−4.86824e6	−	1.17530e7i	−0.161510	−	0.389920i
$982$			6.99112e6i			0.231349i
$983$	−4.37251e7	+	1.81115e7i	−1.44327	+	0.597821i	−0.960588	−	0.277977i	$-0.910336\pi$
$983$	−4.37251e7	+	1.81115e7i	−1.44327	+	0.597821i	−0.482679	+	0.875797i	$0.660336\pi$
$984$	−1.16525e7	−	1.16525e7i	−0.383648	−	0.383648i
$985$	−3.71823e7			−1.22108
$986$	−1.04091e7	+	4.43394e7i	−0.340973	+	1.45244i
$987$	−5.31330e6			−0.173609
$988$	−3.00484e6	−	3.00484e6i	−0.0979330	−	0.0979330i
$989$	5.82876e7	−	2.41435e7i	1.89490	−	0.784892i
$990$		−	3.46162e6i		−	0.112251i
$991$	7.71028e6	+	1.86143e7i	0.249394	+	0.602091i	0.998153	−	0.0607520i	$-0.0193499\pi$
$991$	7.71028e6	+	1.86143e7i	0.249394	+	0.602091i	−0.748759	+	0.662843i	$0.769350\pi$
$992$	−1.38498e7	−	5.73677e6i	−0.446852	−	0.185092i
$993$	−194805.	+	470301.i	−0.00626941	+	0.0151357i
$994$	1.85280e7	−	1.85280e7i	0.594788	−	0.594788i
$995$	−787529.	+	787529.i	−0.0252179	+	0.0252179i
$996$	−1.72583e6	+	4.16653e6i	−0.0551252	+	0.133084i
$997$	−4.77474e7	−	1.97776e7i	−1.52129	−	0.630138i	−0.543439	−	0.839449i	$-0.682878\pi$
$997$	−4.77474e7	−	1.97776e7i	−1.52129	−	0.630138i	−0.977849	+	0.209310i	$0.932878\pi$
$998$	1.35178e7	+	3.26349e7i	0.429616	+	1.03718i
$999$			5.63946e6i			0.178782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.6.h.a.19.5	✓	56
17.3	odd	16		867.6.a.u.1.9		28
17.9	even	8	inner	51.6.h.a.43.5	yes	56
17.14	odd	16		867.6.a.t.1.9		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.6.h.a.19.5	✓	56	1.1	even	1	trivial
51.6.h.a.43.5	yes	56	17.9	even	8	inner
867.6.a.t.1.9		28	17.14	odd	16
867.6.a.u.1.9		28	17.3	odd	16

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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	51.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.44799 - 3.44799i) q^{2} +(8.31492 - 3.44415i) q^{3} -8.22272i q^{4} +(33.9684 + 82.0071i) q^{5} +(-40.5452 - 16.7944i) q^{6} +(-45.3741 + 109.543i) q^{7} +(-138.688 + 138.688i) q^{8} +(57.2756 - 57.2756i) q^{9} +(165.637 - 399.883i) q^{10} +(91.2207 + 37.7848i) q^{11} +(-28.3203 - 68.3712i) q^{12} +783.191i q^{13} +(534.152 - 221.253i) q^{14} +(564.890 + 564.890i) q^{15} +693.260 q^{16} +(1175.95 - 192.328i) q^{17} -394.972 q^{18} +(-466.593 - 466.593i) q^{19} +(674.321 - 279.313i) q^{20} +1067.11i q^{21} +(-184.246 - 444.810i) q^{22} +(3970.71 + 1644.72i) q^{23} +(-675.515 + 1630.84i) q^{24} +(-3361.60 + 3361.60i) q^{25} +(2700.43 - 2700.43i) q^{26} +(278.976 - 673.508i) q^{27} +(900.739 + 373.098i) q^{28} +(-2999.68 - 7241.87i) q^{29} -3895.47i q^{30} +(-4782.70 + 1981.06i) q^{31} +(2047.65 + 2047.65i) q^{32} +888.629 q^{33} +(-4717.82 - 3391.53i) q^{34} -10524.6 q^{35} +(-470.962 - 470.962i) q^{36} +(-7147.02 + 2960.39i) q^{37} +3217.62i q^{38} +(2697.43 + 6512.16i) q^{39} +(-16084.4 - 6662.36i) q^{40} +(-3572.56 + 8624.93i) q^{41} +(3679.40 - 3679.40i) q^{42} +(10379.9 - 10379.9i) q^{43} +(310.694 - 750.082i) q^{44} +(6642.57 + 2751.44i) q^{45} +(-8019.99 - 19362.0i) q^{46} +4979.13i q^{47} +(5764.40 - 2387.69i) q^{48} +(1943.54 + 1943.54i) q^{49} +23181.5 q^{50} +(9115.55 - 5649.35i) q^{51} +6439.96 q^{52} +(11149.4 + 11149.4i) q^{53} +(-3284.16 + 1360.34i) q^{54} +8764.23i q^{55} +(-8899.39 - 21485.0i) q^{56} +(-5486.70 - 2272.67i) q^{57} +(-14627.0 + 35312.8i) q^{58} +(8970.38 - 8970.38i) q^{59} +(4644.93 - 4644.93i) q^{60} +(-10981.2 + 26510.8i) q^{61} +(23321.4 + 9660.02i) q^{62} +(3675.30 + 8872.96i) q^{63} -36304.9i q^{64} +(-64227.2 + 26603.8i) q^{65} +(-3063.98 - 3063.98i) q^{66} +266.677 q^{67} +(-1581.46 - 9669.54i) q^{68} +38680.8 q^{69} +(36288.6 + 36288.6i) q^{70} +(41870.6 - 17343.4i) q^{71} +15886.8i q^{72} +(-27960.6 - 67502.8i) q^{73} +(34850.3 + 14435.5i) q^{74} +(-16373.6 + 39529.3i) q^{75} +(-3836.67 + 3836.67i) q^{76} +(-8278.11 + 8278.11i) q^{77} +(13153.2 - 31754.6i) q^{78} +(-6368.37 - 2637.87i) q^{79} +(23549.0 + 56852.2i) q^{80} -6561.00i q^{81} +(42056.9 - 17420.5i) q^{82} +(-43091.0 - 43091.0i) q^{83} +8774.58 q^{84} +(55717.6 + 89903.4i) q^{85} -71579.6 q^{86} +(-49884.2 - 49884.2i) q^{87} +(-17891.5 + 7410.88i) q^{88} +82549.9i q^{89} +(-13416.6 - 32390.5i) q^{90} +(-85792.9 - 35536.6i) q^{91} +(13524.1 - 32650.0i) q^{92} +(-32944.6 + 32944.6i) q^{93} +(17168.0 - 17168.0i) q^{94} +(22414.5 - 54113.4i) q^{95} +(24078.4 + 9973.61i) q^{96} +(-17439.5 - 42102.8i) q^{97} -13402.6i q^{98} +(7388.87 - 3060.57i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 88 q^{5} + 360 q^{6} + 1280 q^{10} - 632 q^{11} - 4256 q^{14} - 8192 q^{16} + 6248 q^{17} + 4152 q^{19} - 16384 q^{20} - 19592 q^{22} - 3608 q^{23} + 10440 q^{24} + 30384 q^{25} - 19936 q^{26} + 13624 q^{28}+ \cdots - 51192 q^{99}+O(q^{100}) \) 56 * q - 88 * q^5 + 360 * q^6 + 1280 * q^10 - 632 * q^11 - 4256 * q^14 - 8192 * q^16 + 6248 * q^17 + 4152 * q^19 - 16384 * q^20 - 19592 * q^22 - 3608 * q^23 + 10440 * q^24 + 30384 * q^25 - 19936 * q^26 + 13624 * q^28 - 23424 * q^29 + 2728 * q^31 + 67200 * q^32 + 20376 * q^33 + 11960 * q^34 + 26272 * q^35 + 3240 * q^36 + 32296 * q^37 - 22320 * q^39 - 100184 * q^40 + 6552 * q^41 - 21528 * q^42 - 38152 * q^43 - 26208 * q^44 + 31752 * q^45 + 106368 * q^46 + 9768 * q^49 + 96128 * q^50 - 62720 * q^52 + 65984 * q^53 + 29160 * q^54 - 268304 * q^56 - 28656 * q^57 - 139352 * q^58 - 67312 * q^59 - 109800 * q^60 - 307184 * q^61 + 150704 * q^62 - 696 * q^65 + 54720 * q^66 + 364272 * q^67 + 558960 * q^68 - 81864 * q^69 + 313960 * q^70 + 309808 * q^71 - 268752 * q^73 - 393712 * q^74 - 96624 * q^75 - 228552 * q^76 - 841536 * q^77 - 130824 * q^78 - 57216 * q^79 + 658528 * q^80 - 335992 * q^82 + 406240 * q^83 + 664848 * q^84 + 686840 * q^85 - 842560 * q^86 + 127224 * q^87 + 538248 * q^88 - 103680 * q^90 - 368592 * q^91 + 96752 * q^92 - 113472 * q^93 - 622576 * q^94 - 1143560 * q^95 - 375552 * q^96 - 40424 * q^97 - 51192 * q^99

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