LMFDB - Embedded newform 51.6.e.a.4.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [51,6,Mod(4,51)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(51, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("51.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	51.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.17957481046$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			4.13
Character	$\chi$	$=$	51.4
Dual form			51.6.e.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.37886i q^{2} +(6.36396 - 6.36396i) q^{3} -38.2052 q^{4} +(50.4918 - 50.4918i) q^{5} +(53.3227 + 53.3227i) q^{6} +(101.302 + 101.302i) q^{7} -51.9926i q^{8} -81.0000i q^{9} +O(q^{10})$	\(q+8.37886i q^{2} +(6.36396 - 6.36396i) q^{3} -38.2052 q^{4} +(50.4918 - 50.4918i) q^{5} +(53.3227 + 53.3227i) q^{6} +(101.302 + 101.302i) q^{7} -51.9926i q^{8} -81.0000i q^{9} +(423.064 + 423.064i) q^{10} +(201.114 + 201.114i) q^{11} +(-243.137 + 243.137i) q^{12} +544.563 q^{13} +(-848.794 + 848.794i) q^{14} -642.656i q^{15} -786.928 q^{16} +(-1189.12 + 76.5042i) q^{17} +678.687 q^{18} -1265.13i q^{19} +(-1929.05 + 1929.05i) q^{20} +1289.36 q^{21} +(-1685.10 + 1685.10i) q^{22} +(2877.50 + 2877.50i) q^{23} +(-330.879 - 330.879i) q^{24} -1973.85i q^{25} +4562.81i q^{26} +(-515.481 - 515.481i) q^{27} +(-3870.26 - 3870.26i) q^{28} +(-3146.71 + 3146.71i) q^{29} +5384.72 q^{30} +(3006.87 - 3006.87i) q^{31} -8257.32i q^{32} +2559.76 q^{33} +(-641.018 - 9963.46i) q^{34} +10229.8 q^{35} +3094.62i q^{36} +(3428.09 - 3428.09i) q^{37} +10600.3 q^{38} +(3465.58 - 3465.58i) q^{39} +(-2625.20 - 2625.20i) q^{40} +(-12253.2 - 12253.2i) q^{41} +10803.4i q^{42} -7679.15i q^{43} +(-7683.60 - 7683.60i) q^{44} +(-4089.84 - 4089.84i) q^{45} +(-24110.2 + 24110.2i) q^{46} -5048.30 q^{47} +(-5007.98 + 5007.98i) q^{48} +3717.16i q^{49} +16538.6 q^{50} +(-7080.64 + 8054.38i) q^{51} -20805.1 q^{52} +29278.4i q^{53} +(4319.14 - 4319.14i) q^{54} +20309.2 q^{55} +(5266.95 - 5266.95i) q^{56} +(-8051.24 - 8051.24i) q^{57} +(-26365.8 - 26365.8i) q^{58} -25359.7i q^{59} +24552.8i q^{60} +(-12341.3 - 12341.3i) q^{61} +(25194.1 + 25194.1i) q^{62} +(8205.46 - 8205.46i) q^{63} +44005.2 q^{64} +(27496.0 - 27496.0i) q^{65} +21447.9i q^{66} -47211.9 q^{67} +(45430.6 - 2922.86i) q^{68} +36624.6 q^{69} +85714.4i q^{70} +(-33586.8 + 33586.8i) q^{71} -4211.40 q^{72} +(14810.6 - 14810.6i) q^{73} +(28723.5 + 28723.5i) q^{74} +(-12561.5 - 12561.5i) q^{75} +48334.6i q^{76} +40746.4i q^{77} +(29037.6 + 29037.6i) q^{78} +(-64296.4 - 64296.4i) q^{79} +(-39733.5 + 39733.5i) q^{80} -6561.00 q^{81} +(102668. - 102668. i) q^{82} -70007.4i q^{83} -49260.4 q^{84} +(-56178.0 + 63903.6i) q^{85} +64342.5 q^{86} +40051.0i q^{87} +(10456.4 - 10456.4i) q^{88} -92608.7 q^{89} +(34268.2 - 34268.2i) q^{90} +(55165.3 + 55165.3i) q^{91} +(-109936. - 109936. i) q^{92} -38271.2i q^{93} -42299.0i q^{94} +(-63878.8 - 63878.8i) q^{95} +(-52549.3 - 52549.3i) q^{96} +(78477.8 - 78477.8i) q^{97} -31145.6 q^{98} +(16290.2 - 16290.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 576 q^{4} + 76 q^{5} - 180 q^{6} + 236 q^{7}+O(q^{10}) $ 32 * q - 576 * q^4 + 76 * q^5 - 180 * q^6 + 236 * q^7	\( 32 q - 576 q^{4} + 76 q^{5} - 180 q^{6} + 236 q^{7} + 724 q^{10} - 672 q^{11} - 2684 q^{13} + 2832 q^{14} + 8824 q^{16} - 4868 q^{17} + 1296 q^{18} + 4464 q^{20} - 3528 q^{21} - 1628 q^{22} + 5584 q^{23} + 10872 q^{24} - 36792 q^{28} + 4820 q^{29} - 1728 q^{30} + 13880 q^{31} + 7236 q^{33} + 5068 q^{34} - 12152 q^{35} - 33328 q^{37} - 29256 q^{38} - 11160 q^{39} - 43288 q^{40} - 50932 q^{41} + 116000 q^{44} - 6156 q^{45} + 47596 q^{46} - 16552 q^{47} + 27360 q^{48} + 139080 q^{50} + 12924 q^{51} + 186888 q^{52} - 14580 q^{54} - 129428 q^{55} - 117024 q^{56} + 19440 q^{57} - 212912 q^{58} + 118952 q^{61} - 219736 q^{62} + 19116 q^{63} - 143848 q^{64} + 220976 q^{65} + 98632 q^{67} + 367680 q^{68} + 156060 q^{69} - 205512 q^{71} - 62208 q^{72} - 40924 q^{73} - 178760 q^{74} - 58896 q^{75} + 87012 q^{78} - 309916 q^{79} - 664992 q^{80} - 209952 q^{81} + 350116 q^{82} + 6264 q^{84} + 335336 q^{85} + 1139576 q^{86} - 307696 q^{88} - 62680 q^{89} + 58644 q^{90} + 174460 q^{91} - 94256 q^{92} + 367240 q^{95} - 508824 q^{96} - 299020 q^{97} - 1191536 q^{98} - 54432 q^{99}+O(q^{100}) \) 32 * q - 576 * q^4 + 76 * q^5 - 180 * q^6 + 236 * q^7 + 724 * q^10 - 672 * q^11 - 2684 * q^13 + 2832 * q^14 + 8824 * q^16 - 4868 * q^17 + 1296 * q^18 + 4464 * q^20 - 3528 * q^21 - 1628 * q^22 + 5584 * q^23 + 10872 * q^24 - 36792 * q^28 + 4820 * q^29 - 1728 * q^30 + 13880 * q^31 + 7236 * q^33 + 5068 * q^34 - 12152 * q^35 - 33328 * q^37 - 29256 * q^38 - 11160 * q^39 - 43288 * q^40 - 50932 * q^41 + 116000 * q^44 - 6156 * q^45 + 47596 * q^46 - 16552 * q^47 + 27360 * q^48 + 139080 * q^50 + 12924 * q^51 + 186888 * q^52 - 14580 * q^54 - 129428 * q^55 - 117024 * q^56 + 19440 * q^57 - 212912 * q^58 + 118952 * q^61 - 219736 * q^62 + 19116 * q^63 - 143848 * q^64 + 220976 * q^65 + 98632 * q^67 + 367680 * q^68 + 156060 * q^69 - 205512 * q^71 - 62208 * q^72 - 40924 * q^73 - 178760 * q^74 - 58896 * q^75 + 87012 * q^78 - 309916 * q^79 - 664992 * q^80 - 209952 * q^81 + 350116 * q^82 + 6264 * q^84 + 335336 * q^85 + 1139576 * q^86 - 307696 * q^88 - 62680 * q^89 + 58644 * q^90 + 174460 * q^91 - 94256 * q^92 + 367240 * q^95 - 508824 * q^96 - 299020 * q^97 - 1191536 * q^98 - 54432 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$			8.37886i			1.48119i	0.671954	+	0.740593i	$0.265455\pi$
$2$			8.37886i			1.48119i	−0.671954	+	0.740593i	$0.734545\pi$
$3$	6.36396	−	6.36396i	0.408248	−	0.408248i
$3$	6.36396	−	6.36396i	0.408248	−	0.408248i
$4$	−38.2052			−1.19391
$5$	50.4918	−	50.4918i	0.903225	−	0.903225i	−0.0924883	−	0.995714i	$-0.529482\pi$
$5$	50.4918	−	50.4918i	0.903225	−	0.903225i	0.995714	+	0.0924883i	$0.0294821\pi$
$6$	53.3227	+	53.3227i	0.604692	+	0.604692i
$7$	101.302	+	101.302i	0.781399	+	0.781399i	0.980067	−	0.198668i	$-0.0636616\pi$
$7$	101.302	+	101.302i	0.781399	+	0.781399i	−0.198668	+	0.980067i	$0.563662\pi$
$8$		−	51.9926i		−	0.287221i
$9$		−	81.0000i		−	0.333333i
$10$	423.064	+	423.064i	1.33785	+	1.33785i
$11$	201.114	+	201.114i	0.501141	+	0.501141i	0.911792	−	0.410651i	$-0.134699\pi$
$11$	201.114	+	201.114i	0.501141	+	0.501141i	−0.410651	+	0.911792i	$0.634699\pi$
$12$	−243.137	+	243.137i	−0.487413	+	0.487413i
$13$	544.563			0.893696			0.446848	−	0.894610i	$-0.352547\pi$
$13$	544.563			0.893696			0.446848	+	0.894610i	$0.352547\pi$
$14$	−848.794	+	848.794i	−1.15740	+	1.15740i
$15$		−	642.656i		−	0.737481i
$16$	−786.928			−0.768485
$17$	−1189.12	+	76.5042i	−0.997937	+	0.0642042i
$17$	−1189.12	+	76.5042i	−0.997937	+	0.0642042i
$18$	678.687			0.493729
$19$		−	1265.13i		−	0.803991i	−0.915642	−	0.401996i	$-0.868317\pi$
$19$		−	1265.13i		−	0.803991i	0.915642	−	0.401996i	$-0.131683\pi$
$20$	−1929.05	+	1929.05i	−1.07837	+	1.07837i
$21$	1289.36			0.638009
$22$	−1685.10	+	1685.10i	−0.742283	+	0.742283i
$23$	2877.50	+	2877.50i	1.13422	+	1.13422i	0.989468	+	0.144748i	$0.0462373\pi$
$23$	2877.50	+	2877.50i	1.13422	+	1.13422i	0.144748	+	0.989468i	$0.453763\pi$
$24$	−330.879	−	330.879i	−0.117258	−	0.117258i
$25$		−	1973.85i		−	0.631633i
$26$			4562.81i			1.32373i
$27$	−515.481	−	515.481i	−0.136083	−	0.136083i
$28$	−3870.26	−	3870.26i	−0.932922	−	0.932922i
$29$	−3146.71	+	3146.71i	−0.694802	+	0.694802i	−0.963285	−	0.268482i	$-0.913478\pi$
$29$	−3146.71	+	3146.71i	−0.694802	+	0.694802i	0.268482	+	0.963285i	$0.413478\pi$
$30$	5384.72			1.09235
$31$	3006.87	−	3006.87i	0.561967	−	0.561967i	−0.367899	−	0.929866i	$-0.619923\pi$
$31$	3006.87	−	3006.87i	0.561967	−	0.561967i	0.929866	+	0.367899i	$0.119923\pi$
$32$		−	8257.32i		−	1.42549i
$33$	2559.76			0.409180
$34$	−641.018	−	9963.46i	−0.0950983	−	1.47813i
$35$	10229.8			1.41156
$36$			3094.62i			0.397971i
$37$	3428.09	−	3428.09i	0.411669	−	0.411669i	−0.470650	−	0.882320i	$-0.655981\pi$
$37$	3428.09	−	3428.09i	0.411669	−	0.411669i	0.882320	+	0.470650i	$0.155981\pi$
$38$	10600.3			1.19086
$39$	3465.58	−	3465.58i	0.364850	−	0.364850i
$40$	−2625.20	−	2625.20i	−0.259426	−	0.259426i
$41$	−12253.2	−	12253.2i	−1.13839	−	1.13839i	−0.988739	−	0.149648i	$-0.952186\pi$
$41$	−12253.2	−	12253.2i	−1.13839	−	1.13839i	−0.149648	−	0.988739i	$-0.547814\pi$
$42$			10803.4i			0.945011i
$43$		−	7679.15i		−	0.633348i	−0.948534	−	0.316674i	$-0.897434\pi$
$43$		−	7679.15i		−	0.633348i	0.948534	−	0.316674i	$-0.102566\pi$
$44$	−7683.60	−	7683.60i	−0.598319	−	0.598319i
$45$	−4089.84	−	4089.84i	−0.301075	−	0.301075i
$46$	−24110.2	+	24110.2i	−1.67999	+	1.67999i
$47$	−5048.30			−0.333350			−0.166675	−	0.986012i	$-0.553303\pi$
$47$	−5048.30			−0.333350			−0.166675	+	0.986012i	$0.553303\pi$
$48$	−5007.98	+	5007.98i	−0.313733	+	0.313733i
$49$			3717.16i			0.221167i
$50$	16538.6			0.935566
$51$	−7080.64	+	8054.38i	−0.381195	+	0.433617i
$52$	−20805.1			−1.06700
$53$			29278.4i			1.43172i	0.698245	+	0.715859i	$0.253965\pi$
$53$			29278.4i			1.43172i	−0.698245	+	0.715859i	$0.746035\pi$
$54$	4319.14	−	4319.14i	0.201564	−	0.201564i
$55$	20309.2			0.905287
$56$	5266.95	−	5266.95i	0.224434	−	0.224434i
$57$	−8051.24	−	8051.24i	−0.328228	−	0.328228i
$58$	−26365.8	−	26365.8i	−1.02913	−	1.02913i
$59$		−	25359.7i		−	0.948449i	−0.880404	−	0.474224i	$-0.842729\pi$
$59$		−	25359.7i		−	0.948449i	0.880404	−	0.474224i	$-0.157271\pi$
$60$			24552.8i			0.880488i
$61$	−12341.3	−	12341.3i	−0.424657	−	0.424657i	0.462147	−	0.886803i	$-0.347079\pi$
$61$	−12341.3	−	12341.3i	−0.424657	−	0.424657i	−0.886803	+	0.462147i	$0.847079\pi$
$62$	25194.1	+	25194.1i	0.832377	+	0.832377i
$63$	8205.46	−	8205.46i	0.260466	−	0.260466i
$64$	44005.2			1.34293
$65$	27496.0	−	27496.0i	0.807209	−	0.807209i
$66$			21447.9i			0.606072i
$67$	−47211.9			−1.28488			−0.642442	−	0.766334i	$-0.722079\pi$
$67$	−47211.9			−1.28488			−0.642442	+	0.766334i	$0.722079\pi$
$68$	45430.6	−	2922.86i	1.19145	−	0.0766542i
$69$	36624.6			0.926084
$70$			85714.4i			2.09078i
$71$	−33586.8	+	33586.8i	−0.790720	+	0.790720i	−0.981611	−	0.190891i	$-0.938862\pi$
$71$	−33586.8	+	33586.8i	−0.790720	+	0.790720i	0.190891	+	0.981611i	$0.438862\pi$
$72$	−4211.40			−0.0957405
$73$	14810.6	−	14810.6i	0.325287	−	0.325287i	−0.525504	−	0.850791i	$-0.676123\pi$
$73$	14810.6	−	14810.6i	0.325287	−	0.325287i	0.850791	+	0.525504i	$0.176123\pi$
$74$	28723.5	+	28723.5i	0.609759	+	0.609759i
$75$	−12561.5	−	12561.5i	−0.257863	−	0.257863i
$76$			48334.6i			0.959895i
$77$			40746.4i			0.783182i
$78$	29037.6	+	29037.6i	0.540411	+	0.540411i
$79$	−64296.4	−	64296.4i	−1.15909	−	1.15909i	−0.984671	−	0.174424i	$-0.944194\pi$
$79$	−64296.4	−	64296.4i	−1.15909	−	1.15909i	−0.174424	−	0.984671i	$-0.555806\pi$
$80$	−39733.5	+	39733.5i	−0.694115	+	0.694115i
$81$	−6561.00			−0.111111
$82$	102668.	−	102668.i	1.68616	−	1.68616i
$83$		−	70007.4i		−	1.11545i	−0.830027	−	0.557723i	$-0.811675\pi$
$83$		−	70007.4i		−	1.11545i	0.830027	−	0.557723i	$-0.188325\pi$
$84$	−49260.4			−0.761728
$85$	−56178.0	+	63903.6i	−0.843371	+	0.959353i
$86$	64342.5			0.938106
$87$			40051.0i			0.567304i
$88$	10456.4	−	10456.4i	0.143938	−	0.143938i
$89$	−92608.7			−1.23930			−0.619650	−	0.784878i	$-0.712726\pi$
$89$	−92608.7			−1.23930			−0.619650	+	0.784878i	$0.712726\pi$
$90$	34268.2	−	34268.2i	0.445948	−	0.445948i
$91$	55165.3	+	55165.3i	0.698333	+	0.698333i
$92$	−109936.	−	109936.i	−1.35416	−	1.35416i
$93$		−	38271.2i		−	0.458844i
$94$		−	42299.0i		−	0.493753i
$95$	−63878.8	−	63878.8i	−0.726185	−	0.726185i
$96$	−52549.3	−	52549.3i	−0.581954	−	0.581954i
$97$	78477.8	−	78477.8i	0.846872	−	0.846872i	−0.142870	−	0.989741i	$-0.545633\pi$
$97$	78477.8	−	78477.8i	0.846872	−	0.846872i	0.989741	+	0.142870i	$0.0456330\pi$
$98$	−31145.6			−0.327590
$99$	16290.2	−	16290.2i	0.167047	−	0.167047i
$100$			75411.4i			0.754114i
$101$	−30339.6			−0.295942			−0.147971	−	0.988992i	$-0.547274\pi$
$101$	−30339.6			−0.295942			−0.147971	+	0.988992i	$0.547274\pi$
$102$	−67486.5	−	59327.6i	−0.642268	−	0.564620i
$103$	136247.			1.26541			0.632707	−	0.774391i	$-0.281944\pi$
$103$	136247.			1.26541			0.632707	+	0.774391i	$0.281944\pi$
$104$		−	28313.3i		−	0.256689i
$105$	65102.3	−	65102.3i	0.576266	−	0.576266i
$106$	−245319.			−2.12064
$107$	−135966.	+	135966.i	−1.14807	+	1.14807i	−0.161141	+	0.986931i	$0.551518\pi$
$107$	−135966.	+	135966.i	−1.14807	+	1.14807i	−0.986931	+	0.161141i	$0.948482\pi$
$108$	19694.1	+	19694.1i	0.162471	+	0.162471i
$109$	63580.9	+	63580.9i	0.512579	+	0.512579i	0.915316	−	0.402737i	$-0.131941\pi$
$109$	63580.9	+	63580.9i	0.512579	+	0.512579i	−0.402737	+	0.915316i	$0.631941\pi$
$110$			170168.i			1.34090i
$111$		−	43632.5i		−	0.336127i
$112$	−79717.4	−	79717.4i	−0.600493	−	0.600493i
$113$	111425.	+	111425.i	0.820890	+	0.820890i	0.986236	−	0.165346i	$-0.0528740\pi$
$113$	111425.	+	111425.i	0.820890	+	0.820890i	−0.165346	+	0.986236i	$0.552874\pi$
$114$	67460.2	−	67460.2i	0.486167	−	0.486167i
$115$	290581.			2.04891
$116$	120221.	−	120221.i	0.829534	−	0.829534i
$117$		−	44109.6i		−	0.297899i
$118$	212485.			1.40483
$119$	−128210.	−	112710.i	−0.829955	−	0.729617i
$120$	−33413.4			−0.211820
$121$		−	80157.5i		−	0.497715i
$122$	103406.	−	103406.i	0.628995	−	0.628995i
$123$	−155958.			−0.929490
$124$	−114878.	+	114878.i	−0.670939	+	0.670939i
$125$	58123.6	+	58123.6i	0.332719	+	0.332719i
$126$	68752.3	+	68752.3i	0.385799	+	0.385799i
$127$			133291.i			0.733316i	0.930356	+	0.366658i	$0.119498\pi$
$127$			133291.i			0.733316i	−0.930356	+	0.366658i	$0.880502\pi$
$128$			104479.i			0.563643i
$129$	−48869.8	−	48869.8i	−0.258563	−	0.258563i
$130$	230385.	+	230385.i	1.19563	+	1.19563i
$131$	−73468.0	+	73468.0i	−0.374042	+	0.374042i	−0.868947	−	0.494905i	$-0.835203\pi$
$131$	−73468.0	+	73468.0i	−0.374042	+	0.374042i	0.494905	+	0.868947i	$0.335203\pi$
$132$	−97796.2			−0.488525
$133$	128160.	−	128160.i	0.628237	−	0.628237i
$134$		−	395581.i		−	1.90315i
$135$	−52055.2			−0.245827
$136$	3977.66	+	61825.4i	0.0184408	+	0.286629i
$137$	152466.			0.694021			0.347011	−	0.937861i	$-0.387197\pi$
$137$	152466.			0.694021			0.347011	+	0.937861i	$0.387197\pi$
$138$			306872.i			1.37170i
$139$	−47649.9	+	47649.9i	−0.209182	+	0.209182i	−0.803920	−	0.594738i	$-0.797256\pi$
$139$	−47649.9	+	47649.9i	−0.209182	+	0.209182i	0.594738	+	0.803920i	$0.297256\pi$
$140$	−390833.			−1.68528
$141$	−32127.2	+	32127.2i	−0.136090	+	0.136090i
$142$	−281419.	−	281419.i	−1.17120	−	1.17120i
$143$	109519.	+	109519.i	0.447868	+	0.447868i
$144$			63741.2i			0.256162i
$145$			317766.i			1.25513i
$146$	124096.	+	124096.i	0.481810	+	0.481810i
$147$	23655.9	+	23655.9i	0.0902912	+	0.0902912i
$148$	−130971.	+	130971.i	−0.491497	+	0.491497i
$149$	−18297.2			−0.0675179			−0.0337589	−	0.999430i	$-0.510748\pi$
$149$	−18297.2			−0.0675179			−0.0337589	+	0.999430i	$0.510748\pi$
$150$	105251.	−	105251.i	0.381943	−	0.381943i
$151$			509942.i			1.82003i	0.414576	+	0.910015i	$0.363930\pi$
$151$			509942.i			1.82003i	−0.414576	+	0.910015i	$0.636070\pi$
$152$	−65777.4			−0.230923
$153$	6196.84	+	96318.6i	0.0214014	+	0.332646i
$154$	−341408.			−1.16004
$155$		−	303645.i		−	1.01516i
$156$	−132403.	+	132403.i	−0.435599	+	0.435599i
$157$	−364650.			−1.18067			−0.590334	−	0.807159i	$-0.701004\pi$
$157$	−364650.			−1.18067			−0.590334	+	0.807159i	$0.701004\pi$
$158$	538730.	−	538730.i	1.71684	−	1.71684i
$159$	186327.	+	186327.i	0.584497	+	0.584497i
$160$	−416927.	−	416927.i	−1.28754	−	1.28754i
$161$			582993.i			1.77255i
$162$		−	54973.7i		−	0.164576i
$163$	−182034.	−	182034.i	−0.536640	−	0.536640i	0.385901	−	0.922540i	$-0.373891\pi$
$163$	−182034.	−	182034.i	−0.536640	−	0.536640i	−0.922540	+	0.385901i	$0.873891\pi$
$164$	468136.	+	468136.i	1.35914	+	1.35914i
$165$	129247.	−	129247.i	0.369582	−	0.369582i
$166$	586582.			1.65218
$167$	481265.	−	481265.i	1.33534	−	1.33534i	0.434834	−	0.900511i	$-0.356807\pi$
$167$	481265.	−	481265.i	1.33534	−	1.33534i	0.900511	−	0.434834i	$-0.143193\pi$
$168$		−	67037.4i		−	0.183250i
$169$	−74744.2			−0.201308
$170$	−535439.	−	470707.i	−1.42098	−	1.24919i
$171$	−102476.			−0.267997
$172$			293384.i			0.756162i
$173$	−448785.	+	448785.i	−1.14005	+	1.14005i	−0.151608	+	0.988441i	$0.548445\pi$
$173$	−448785.	+	448785.i	−1.14005	+	1.14005i	−0.988441	+	0.151608i	$0.951555\pi$
$174$	−335582.			−0.840282
$175$	199955.	−	199955.i	0.493557	−	0.493557i
$176$	−158262.	−	158262.i	−0.385119	−	0.385119i
$177$	−161388.	−	161388.i	−0.387203	−	0.387203i
$178$		−	775955.i		−	1.83563i
$179$		−	308332.i		−	0.719259i	−0.933095	−	0.359630i	$-0.882903\pi$
$179$		−	308332.i		−	0.719259i	0.933095	−	0.359630i	$-0.117097\pi$
$180$	156253.	+	156253.i	0.359458	+	0.359458i
$181$	577773.	+	577773.i	1.31087	+	1.31087i	0.920772	+	0.390102i	$0.127560\pi$
$181$	577773.	+	577773.i	1.31087	+	1.31087i	0.390102	+	0.920772i	$0.372440\pi$
$182$	−462222.	+	462222.i	−1.03436	+	1.03436i
$183$	−157080.			−0.346731
$184$	149609.	−	149609.i	0.325771	−	0.325771i
$185$		−	346182.i		−	0.743660i
$186$	320669.			0.679633
$187$	−254534.	−	223762.i	−0.532283	−	0.467932i
$188$	192871.			0.397991
$189$		−	104438.i		−	0.212670i
$190$	535231.	−	535231.i	1.07562	−	1.07562i
$191$	302954.			0.600889			0.300444	−	0.953799i	$-0.402865\pi$
$191$	302954.			0.600889			0.300444	+	0.953799i	$0.402865\pi$
$192$	280047.	−	280047.i	0.548250	−	0.548250i
$193$	171151.	+	171151.i	0.330740	+	0.330740i	0.852867	−	0.522127i	$-0.174861\pi$
$193$	171151.	+	171151.i	0.330740	+	0.330740i	−0.522127	+	0.852867i	$0.674861\pi$
$194$	657554.	+	657554.i	1.25437	+	1.25437i
$195$		−	349967.i		−	0.659083i
$196$		−	142015.i		−	0.264055i
$197$	264268.	+	264268.i	0.485153	+	0.485153i	0.906773	−	0.421620i	$-0.138538\pi$
$197$	264268.	+	264268.i	0.485153	+	0.485153i	−0.421620	+	0.906773i	$0.638538\pi$
$198$	136493.	+	136493.i	0.247428	+	0.247428i
$199$	391556.	−	391556.i	0.700909	−	0.700909i	−0.263697	−	0.964606i	$-0.584942\pi$
$199$	391556.	−	391556.i	0.700909	−	0.700909i	0.964606	+	0.263697i	$0.0849418\pi$
$200$	−102626.			−0.181418
$201$	−300454.	+	300454.i	−0.524552	+	0.524552i
$202$		−	254211.i		−	0.438346i
$203$	−637535.			−1.08584
$204$	270517.	−	307719.i	0.455113	−	0.517701i
$205$	−1.23737e6			−2.05644
$206$			1.14159e6i			1.87431i
$207$	233078.	−	233078.i	0.378072	−	0.378072i
$208$	−428532.			−0.686792
$209$	254435.	−	254435.i	0.402913	−	0.402913i
$210$	545483.	+	545483.i	0.853558	+	0.853558i
$211$	−151006.	−	151006.i	−0.233500	−	0.233500i	0.580652	−	0.814152i	$-0.302798\pi$
$211$	−151006.	−	151006.i	−0.233500	−	0.233500i	−0.814152	+	0.580652i	$0.802798\pi$
$212$		−	1.11859e6i		−	1.70935i
$213$			427490.i			0.645620i
$214$	−1.13924e6	−	1.13924e6i	−1.70051	−	1.70051i
$215$	−387735.	−	387735.i	−0.572056	−	0.572056i
$216$	−26801.2	+	26801.2i	−0.0390859	+	0.0390859i
$217$	609203.			0.878240
$218$	−532735.	+	532735.i	−0.759225	+	0.759225i
$219$		−	188508.i		−	0.265595i
$220$	−775918.			−1.08083
$221$	−647550.	+	41661.4i	−0.891852	+	0.0573790i
$222$	365591.			0.497866
$223$		−	228931.i		−	0.308277i	−0.988049	−	0.154139i	$-0.950740\pi$
$223$		−	228931.i		−	0.308277i	0.988049	−	0.154139i	$-0.0492602\pi$
$224$	836483.	−	836483.i	1.11388	−	1.11388i
$225$	−159882.			−0.210544
$226$	−933611.	+	933611.i	−1.21589	+	1.21589i
$227$	−683152.	−	683152.i	−0.879939	−	0.879939i	0.113589	−	0.993528i	$-0.463765\pi$
$227$	−683152.	−	683152.i	−0.879939	−	0.879939i	−0.993528	+	0.113589i	$0.963765\pi$
$228$	307599.	+	307599.i	0.391876	+	0.391876i
$229$			1.27235e6i			1.60331i	0.597789	+	0.801653i	$0.296046\pi$
$229$			1.27235e6i			1.60331i	−0.597789	+	0.801653i	$0.703954\pi$
$230$			2.43473e6i			3.03481i
$231$	259309.	+	259309.i	0.319733	+	0.319733i
$232$	163606.	+	163606.i	0.199562	+	0.199562i
$233$	−698325.	+	698325.i	−0.842690	+	0.842690i	−0.989208	−	0.146518i	$-0.953193\pi$
$233$	−698325.	+	698325.i	−0.842690	+	0.842690i	0.146518	+	0.989208i	$0.453193\pi$
$234$	369588.			0.441243
$235$	−254898.	+	254898.i	−0.301090	+	0.301090i
$236$			968872.i			1.13237i
$237$	−818360.			−0.946397
$238$	944381.	−	1.07425e6i	1.08070	−	1.22932i
$239$	500443.			0.566708			0.283354	−	0.959015i	$-0.408553\pi$
$239$	500443.			0.566708			0.283354	+	0.959015i	$0.408553\pi$
$240$			505724.i			0.566742i
$241$	809621.	−	809621.i	0.897923	−	0.897923i	−0.0973289	−	0.995252i	$-0.531030\pi$
$241$	809621.	−	809621.i	0.897923	−	0.897923i	0.995252	+	0.0973289i	$0.0310299\pi$
$242$	671628.			0.737209
$243$	−41753.9	+	41753.9i	−0.0453609	+	0.0453609i
$244$	471504.	+	471504.i	0.507003	+	0.507003i
$245$	187686.	+	187686.i	0.199764	+	0.199764i
$246$		−	1.30675e6i		−	1.37675i
$247$		−	688943.i		−	0.718523i
$248$	−156335.	−	156335.i	−0.161409	−	0.161409i
$249$	−445524.	−	445524.i	−0.455379	−	0.455379i
$250$	−487009.	+	487009.i	−0.492819	+	0.492819i
$251$	1.57721e6			1.58018			0.790089	−	0.612992i	$-0.210034\pi$
$251$	1.57721e6			1.58018			0.790089	+	0.612992i	$0.210034\pi$
$252$	−313491.	+	313491.i	−0.310974	+	0.310974i
$253$			1.15741e6i			1.13681i
$254$	−1.11682e6			−1.08618
$255$	49165.9	+	764195.i	0.0473493	+	0.735959i
$256$	532753.			0.508073
$257$		−	463610.i		−	0.437845i	−0.975742	−	0.218922i	$-0.929746\pi$
$257$		−	463610.i		−	0.437845i	0.975742	−	0.218922i	$-0.0702542\pi$
$258$	409473.	−	409473.i	0.382980	−	0.382980i
$259$	694545.			0.643356
$260$	−1.05049e6	+	1.05049e6i	−0.963737	+	0.963737i
$261$	254883.	+	254883.i	0.231601	+	0.231601i
$262$	−615578.	−	615578.i	−0.554025	−	0.554025i
$263$		−	2.01847e6i		−	1.79942i	−0.436491	−	0.899709i	$-0.643779\pi$
$263$		−	2.01847e6i		−	1.79942i	0.436491	−	0.899709i	$-0.356221\pi$
$264$		−	133089.i		−	0.117525i
$265$	1.47832e6	+	1.47832e6i	1.29316	+	1.29316i
$266$	1.07384e6	+	1.07384e6i	0.930537	+	0.930537i
$267$	−589358.	+	589358.i	−0.505942	+	0.505942i
$268$	1.80374e6			1.53404
$269$	1.16901e6	−	1.16901e6i	0.985003	−	0.985003i	−0.0148860	−	0.999889i	$-0.504739\pi$
$269$	1.16901e6	−	1.16901e6i	0.985003	−	0.985003i	0.999889	+	0.0148860i	$0.00473855\pi$
$270$		−	436163.i		−	0.364115i
$271$	−694838.			−0.574725			−0.287363	−	0.957822i	$-0.592778\pi$
$271$	−694838.			−0.574725			−0.287363	+	0.957822i	$0.592778\pi$
$272$	935751.	−	60203.3i	0.766899	−	0.0493399i
$273$	702139.			0.570186
$274$			1.27749e6i			1.02797i
$275$	396969.	−	396969.i	0.316537	−	0.316537i
$276$	−1.39925e6			−1.10566
$277$	−849305.	+	849305.i	−0.665065	+	0.665065i	−0.956570	−	0.291504i	$-0.905844\pi$
$277$	−849305.	+	849305.i	−0.665065	+	0.665065i	0.291504	+	0.956570i	$0.405844\pi$
$278$	−399251.	−	399251.i	−0.309838	−	0.309838i
$279$	−243556.	−	243556.i	−0.187322	−	0.187322i
$280$		−	531876.i		−	0.405430i
$281$		−	173736.i		−	0.131258i	−0.997844	−	0.0656288i	$-0.979095\pi$
$281$		−	173736.i		−	0.131258i	0.997844	−	0.0656288i	$-0.0209053\pi$
$282$	−269189.	−	269189.i	−0.201574	−	0.201574i
$283$	−522855.	−	522855.i	−0.388075	−	0.388075i	0.485926	−	0.874000i	$-0.338483\pi$
$283$	−522855.	−	522855.i	−0.388075	−	0.388075i	−0.874000	+	0.485926i	$0.838483\pi$
$284$	1.28319e6	−	1.28319e6i	0.944051	−	0.944051i
$285$	−813044.			−0.592928
$286$	−917645.	+	917645.i	−0.663376	+	0.663376i
$287$		−	2.48255e6i		−	1.77907i
$288$	−668843.			−0.475163
$289$	1.40815e6	−	181945.i	0.991756	−	0.128143i
$290$	−2.66252e6			−1.85908
$291$		−	998860.i		−	0.691468i
$292$	−565843.	+	565843.i	−0.388364	+	0.388364i
$293$	318263.			0.216579			0.108290	−	0.994119i	$-0.465463\pi$
$293$	318263.			0.216579			0.108290	+	0.994119i	$0.465463\pi$
$294$	−198209.	+	198209.i	−0.133738	+	0.133738i
$295$	−1.28046e6	−	1.28046e6i	−0.856663	−	0.856663i
$296$	−178236.	−	178236.i	−0.118240	−	0.118240i
$297$		−	207341.i		−	0.136393i
$298$		−	153310.i		−	0.100007i
$299$	1.56698e6	+	1.56698e6i	1.01364	+	1.01364i
$300$	479915.	+	479915.i	0.307866	+	0.307866i
$301$	777913.	−	777913.i	0.494897	−	0.494897i
$302$	−4.27273e6			−2.69580
$303$	−193080.	+	193080.i	−0.120818	+	0.120818i
$304$			995567.i			0.617855i
$305$	−1.24627e6			−0.767121
$306$	−807040.	+	51922.5i	−0.492710	+	0.0316994i
$307$	−478029.			−0.289473			−0.144737	−	0.989470i	$-0.546234\pi$
$307$	−478029.			−0.289473			−0.144737	+	0.989470i	$0.546234\pi$
$308$		−	1.55673e6i		−	0.935051i
$309$	867068.	−	867068.i	0.516603	−	0.516603i
$310$	2.54420e6			1.50365
$311$	−96128.3	+	96128.3i	−0.0563573	+	0.0563573i	−0.734724	−	0.678366i	$-0.762688\pi$
$311$	−96128.3	+	96128.3i	−0.0563573	+	0.0563573i	0.678366	+	0.734724i	$0.262688\pi$
$312$	−180184.	−	180184.i	−0.104793	−	0.104793i
$313$	−60986.3	−	60986.3i	−0.0351861	−	0.0351861i	0.689295	−	0.724481i	$-0.257920\pi$
$313$	−60986.3	−	60986.3i	−0.0351861	−	0.0351861i	−0.724481	+	0.689295i	$0.757920\pi$
$314$		−	3.05535e6i		−	1.74879i
$315$		−	828617.i		−	0.470519i
$316$	2.45646e6	+	2.45646e6i	1.38386	+	1.38386i
$317$	59704.6	+	59704.6i	0.0333703	+	0.0333703i	0.723595	−	0.690225i	$-0.242488\pi$
$317$	59704.6	+	59704.6i	0.0333703	+	0.0333703i	−0.690225	+	0.723595i	$0.742488\pi$
$318$	−1.56120e6	+	1.56120e6i	−0.865748	+	0.865748i
$319$	−1.26569e6			−0.696388
$320$	2.22190e6	−	2.22190e6i	1.21297	−	1.21297i
$321$			1.73056e6i			0.937397i
$322$	−4.88482e6			−2.62548
$323$	96787.8	+	1.50439e6i	0.0516196	+	0.802332i
$324$	250664.			0.132657
$325$		−	1.07489e6i		−	0.564487i
$326$	1.52523e6	−	1.52523e6i	0.794863	−	0.794863i
$327$	809253.			0.418519
$328$	−637076.	+	637076.i	−0.326969	+	0.326969i
$329$	−511402.	−	511402.i	−0.260479	−	0.260479i
$330$	1.08294e6	+	1.08294e6i	0.547420	+	0.547420i
$331$		−	1.67812e6i		−	0.841885i	−0.907087	−	0.420942i	$-0.861699\pi$
$331$		−	1.67812e6i		−	0.841885i	0.907087	−	0.420942i	$-0.138301\pi$
$332$			2.67465e6i			1.33175i
$333$	−277676.	−	277676.i	−0.137223	−	0.137223i
$334$	4.03245e6	+	4.03245e6i	1.97789	+	1.97789i
$335$	−2.38381e6	+	2.38381e6i	−1.16054	+	1.16054i
$336$	−1.01464e6			−0.490300
$337$	−358523.	+	358523.i	−0.171966	+	0.171966i	−0.787843	−	0.615877i	$-0.788802\pi$
$337$	−358523.	+	358523.i	−0.171966	+	0.171966i	0.615877	+	0.787843i	$0.288802\pi$
$338$		−	626271.i		−	0.298174i
$339$	1.41820e6			0.670254
$340$	2.14629e6	−	2.44145e6i	1.00691	−	1.14538i
$341$	1.20945e6			0.563249
$342$		−	858628.i		−	0.396954i
$343$	1.32603e6	−	1.32603e6i	0.608579	−	0.608579i
$344$	−399259.			−0.181911
$345$	1.84924e6	−	1.84924e6i	0.836463	−	0.836463i
$346$	−3.76031e6	−	3.76031e6i	−1.68863	−	1.68863i
$347$	2.00209e6	+	2.00209e6i	0.892606	+	0.892606i	0.994768	−	0.102162i	$-0.0325759\pi$
$347$	2.00209e6	+	2.00209e6i	0.892606	+	0.892606i	−0.102162	+	0.994768i	$0.532576\pi$
$348$		−	1.53016e6i		−	0.677311i
$349$		−	617490.i		−	0.271373i	−0.990752	−	0.135686i	$-0.956676\pi$
$349$		−	617490.i		−	0.271373i	0.990752	−	0.135686i	$-0.0433240\pi$
$350$	1.67539e6	+	1.67539e6i	0.731050	+	0.731050i
$351$	−280712.	−	280712.i	−0.121617	−	0.121617i
$352$	1.66066e6	−	1.66066e6i	0.714372	−	0.714372i
$353$	−1.74483e6			−0.745273			−0.372636	−	0.927977i	$-0.621546\pi$
$353$	−1.74483e6			−0.745273			−0.372636	+	0.927977i	$0.621546\pi$
$354$	1.35225e6	−	1.35225e6i	0.573519	−	0.573519i
$355$			3.39172e6i			1.42840i
$356$	3.53813e6			1.47962
$357$	−1.53321e6	+	98641.7i	−0.636693	+	0.0409628i
$358$	2.58347e6			1.06536
$359$			2.73400e6i			1.11960i	0.828628	+	0.559799i	$0.189122\pi$
$359$			2.73400e6i			1.11960i	−0.828628	+	0.559799i	$0.810878\pi$
$360$	−212641.	+	212641.i	−0.0864752	+	0.0864752i
$361$	875545.			0.353598
$362$	−4.84108e6	+	4.84108e6i	−1.94165	+	1.94165i
$363$	−510119.	−	510119.i	−0.203191	−	0.203191i
$364$	−2.10760e6	−	2.10760e6i	−0.833748	−	0.833748i
$365$		−	1.49563e6i		−	0.587614i
$366$		−	1.31615e6i		−	0.513573i
$367$	2.25964e6	+	2.25964e6i	0.875739	+	0.875739i	0.993090	−	0.117351i	$-0.0374403\pi$
$367$	2.25964e6	+	2.25964e6i	0.875739	+	0.875739i	−0.117351	+	0.993090i	$0.537440\pi$
$368$	−2.26439e6	−	2.26439e6i	−0.871628	−	0.871628i
$369$	−992510.	+	992510.i	−0.379463	+	0.379463i
$370$	2.90061e6			1.10150
$371$	−2.96596e6	+	2.96596e6i	−1.11874	+	1.11874i
$372$			1.46216e6i			0.547820i
$373$	333884.			0.124258			0.0621288	−	0.998068i	$-0.480211\pi$
$373$	333884.			0.124258			0.0621288	+	0.998068i	$0.480211\pi$
$374$	1.87487e6	−	2.13271e6i	0.693094	−	0.788410i
$375$	739793.			0.271664
$376$			262474.i			0.0957452i
$377$	−1.71358e6	+	1.71358e6i	−0.620942	+	0.620942i
$378$	875074.			0.315004
$379$	−1.29185e6	+	1.29185e6i	−0.461969	+	0.461969i	−0.899300	−	0.437332i	$-0.855924\pi$
$379$	−1.29185e6	+	1.29185e6i	−0.461969	+	0.461969i	0.437332	+	0.899300i	$0.355924\pi$
$380$	2.44050e6	+	2.44050e6i	0.867002	+	0.867002i
$381$	848258.	+	848258.i	0.299375	+	0.299375i
$382$			2.53841e6i			0.890028i
$383$		−	1.27434e6i		−	0.443904i	−0.975058	−	0.221952i	$-0.928757\pi$
$383$		−	1.27434e6i		−	0.443904i	0.975058	−	0.221952i	$-0.0712429\pi$
$384$	664900.	+	664900.i	0.230106	+	0.230106i
$385$	2.05736e6	+	2.05736e6i	0.707390	+	0.707390i
$386$	−1.43405e6	+	1.43405e6i	−0.489888	+	0.489888i
$387$	−622012.			−0.211116
$388$	−2.99826e6	+	2.99826e6i	−1.01109	+	1.01109i
$389$			5.72819e6i			1.91930i	0.281191	+	0.959652i	$0.409271\pi$
$389$			5.72819e6i			1.91930i	−0.281191	+	0.959652i	$0.590729\pi$
$390$	2.93232e6			0.976225
$391$	−3.64183e6	−	3.20155e6i	−1.20470	−	1.05906i
$392$	193265.			0.0635240
$393$			935095.i			0.305404i
$394$	−2.21426e6	+	2.21426e6i	−0.718602	+	0.718602i
$395$	−6.49289e6			−2.09385
$396$	−622371.	+	622371.i	−0.199440	+	0.199440i
$397$	−3.18374e6	−	3.18374e6i	−1.01382	−	1.01382i	−0.999903	−	0.0139177i	$-0.995570\pi$
$397$	−3.18374e6	−	3.18374e6i	−1.01382	−	1.01382i	−0.0139177	−	0.999903i	$-0.504430\pi$
$398$	3.28080e6	+	3.28080e6i	1.03818	+	1.03818i
$399$		−	1.63121e6i		−	0.512954i
$400$			1.55328e6i			0.485400i
$401$	−2.33203e6	−	2.33203e6i	−0.724226	−	0.724226i	0.245237	−	0.969463i	$-0.421134\pi$
$401$	−2.33203e6	−	2.33203e6i	−0.724226	−	0.724226i	−0.969463	+	0.245237i	$0.921134\pi$
$402$	−2.51746e6	−	2.51746e6i	−0.776959	−	0.776959i
$403$	1.63743e6	−	1.63743e6i	0.502227	−	0.502227i
$404$	1.15913e6			0.353329
$405$	−331277.	+	331277.i	−0.100358	+	0.100358i
$406$		−	5.34181e6i		−	1.60832i
$407$	1.37887e6			0.412609
$408$	418768.	+	368141.i	0.124544	+	0.109487i
$409$	−2.76328e6			−0.816802			−0.408401	−	0.912803i	$-0.633913\pi$
$409$	−2.76328e6			−0.816802			−0.408401	+	0.912803i	$0.633913\pi$
$410$		−	1.03678e7i		−	3.04597i
$411$	970290.	−	970290.i	0.283333	−	0.283333i
$412$	−5.20533e6			−1.51079
$413$	2.56899e6	−	2.56899e6i	0.741116	−	0.741116i
$414$	1.95292e6	+	1.95292e6i	0.559996	+	0.559996i
$415$	−3.53480e6	−	3.53480e6i	−1.00750	−	1.00750i
$416$		−	4.49663e6i		−	1.27395i
$417$			606484.i			0.170797i
$418$	2.13187e6	+	2.13187e6i	0.596789	+	0.596789i
$419$	−165048.	−	165048.i	−0.0459277	−	0.0459277i	0.683770	−	0.729698i	$-0.260339\pi$
$419$	−165048.	−	165048.i	−0.0459277	−	0.0459277i	−0.729698	+	0.683770i	$0.760339\pi$
$420$	−2.48725e6	+	2.48725e6i	−0.688012	+	0.688012i
$421$	3.32930e6			0.915479			0.457739	−	0.889086i	$-0.348659\pi$
$421$	3.32930e6			0.915479			0.457739	+	0.889086i	$0.348659\pi$
$422$	1.26525e6	−	1.26525e6i	0.345857	−	0.345857i
$423$			408912.i			0.111117i
$424$	1.52226e6			0.411220
$425$	151008.	+	2.34714e6i	0.0405534	+	0.630329i
$426$	−3.58188e6			−0.956284
$427$		−	2.50040e6i		−	0.663652i
$428$	5.19459e6	−	5.19459e6i	1.37070	−	1.37070i
$429$	1.39395e6			0.365683
$430$	3.24877e6	−	3.24877e6i	0.847321	−	0.847321i
$431$	869048.	+	869048.i	0.225346	+	0.225346i	0.810745	−	0.585399i	$-0.199062\pi$
$431$	869048.	+	869048.i	0.225346	+	0.225346i	−0.585399	+	0.810745i	$0.699062\pi$
$432$	405646.	+	405646.i	0.104578	+	0.104578i
$433$			4.43874e6i			1.13773i	0.822431	+	0.568865i	$0.192617\pi$
$433$			4.43874e6i			1.13773i	−0.822431	+	0.568865i	$0.807383\pi$
$434$			5.10443e6i			1.30084i
$435$	2.02225e6	+	2.02225e6i	0.512403	+	0.512403i
$436$	−2.42912e6	−	2.42912e6i	−0.611975	−	0.611975i
$437$	3.64042e6	−	3.64042e6i	0.911900	−	0.911900i
$438$	1.57948e6			0.393396
$439$	191279.	−	191279.i	0.0473703	−	0.0473703i	−0.683025	−	0.730395i	$-0.739336\pi$
$439$	191279.	−	191279.i	0.0473703	−	0.0473703i	0.730395	+	0.683025i	$0.239336\pi$
$440$		−	1.05593e6i		−	0.260018i
$441$	301090.			0.0737225
$442$	−349075.	−	5.42573e6i	−0.0849890	−	1.32100i
$443$	2.24620e6			0.543799			0.271900	−	0.962326i	$-0.412348\pi$
$443$	2.24620e6			0.543799			0.271900	+	0.962326i	$0.412348\pi$
$444$			1.66699e6i			0.401306i
$445$	−4.67598e6	+	4.67598e6i	−1.11937	+	1.11937i
$446$	1.91818e6			0.456616
$447$	−116443.	+	116443.i	−0.0275641	+	0.0275641i
$448$	4.45781e6	+	4.45781e6i	1.04937	+	1.04937i
$449$	3.80610e6	+	3.80610e6i	0.890972	+	0.890972i	0.994615	−	0.103643i	$-0.0330498\pi$
$449$	3.80610e6	+	3.80610e6i	0.890972	+	0.890972i	−0.103643	+	0.994615i	$0.533050\pi$
$450$		−	1.33963e6i		−	0.311855i
$451$		−	4.92858e6i		−	1.14099i
$452$	−4.25700e6	−	4.25700e6i	−0.980071	−	0.980071i
$453$	3.24525e6	+	3.24525e6i	0.743024	+	0.743024i
$454$	5.72403e6	−	5.72403e6i	1.30335	−	1.30335i
$455$	5.57079e6			1.26150
$456$	−418605.	+	418605.i	−0.0942741	+	0.0942741i
$457$			6.93950e6i			1.55431i	0.629309	+	0.777155i	$0.283338\pi$
$457$			6.93950e6i			1.55431i	−0.629309	+	0.777155i	$0.716662\pi$
$458$	−1.06608e7			−2.37480
$459$	652405.	+	573532.i	0.144539	+	0.127065i
$460$	−1.11017e7			−2.44622
$461$			1.94291e6i			0.425795i	0.977075	+	0.212898i	$0.0682901\pi$
$461$			1.94291e6i			0.425795i	−0.977075	+	0.212898i	$0.931710\pi$
$462$	−2.17271e6	+	2.17271e6i	−0.473584	+	0.473584i
$463$	7.52001e6			1.63029			0.815147	−	0.579254i	$-0.196656\pi$
$463$	7.52001e6			1.63029			0.815147	+	0.579254i	$0.196656\pi$
$464$	2.47623e6	−	2.47623e6i	0.533945	−	0.533945i
$465$	−1.93238e6	−	1.93238e6i	−0.414439	−	0.414439i
$466$	−5.85117e6	−	5.85117e6i	−1.24818	−	1.24818i
$467$			5.44570e6i			1.15548i	0.816222	+	0.577738i	$0.196065\pi$
$467$			5.44570e6i			1.15548i	−0.816222	+	0.577738i	$0.803935\pi$
$468$			1.68522e6i			0.355665i
$469$	−4.78265e6	−	4.78265e6i	−1.00401	−	1.00401i
$470$	−2.13575e6	−	2.13575e6i	−0.445971	−	0.445971i
$471$	−2.32062e6	+	2.32062e6i	−0.482006	+	0.482006i
$472$	−1.31852e6			−0.272415
$473$	1.54438e6	−	1.54438e6i	0.317397	−	0.317397i
$474$		−	6.85692e6i		−	1.40179i
$475$	−2.49718e6			−0.507827
$476$	4.89829e6	+	4.30611e6i	0.990895	+	0.871100i
$477$	2.37155e6			0.477240
$478$			4.19314e6i			0.839400i
$479$	3.64642e6	−	3.64642e6i	0.726152	−	0.726152i	−0.243699	−	0.969851i	$-0.578361\pi$
$479$	3.64642e6	−	3.64642e6i	0.726152	−	0.726152i	0.969851	+	0.243699i	$0.0783608\pi$
$480$	−5.30662e6			−1.05127
$481$	1.86681e6	−	1.86681e6i	0.367907	−	0.367907i
$482$	6.78370e6	+	6.78370e6i	1.32999	+	1.32999i
$483$	3.71015e6	+	3.71015e6i	0.723641	+	0.723641i
$484$			3.06243e6i			0.594228i
$485$		−	7.92498e6i		−	1.52983i
$486$	−349850.	−	349850.i	−0.0671880	−	0.0671880i
$487$	−2.83300e6	−	2.83300e6i	−0.541282	−	0.541282i	0.382623	−	0.923905i	$-0.375021\pi$
$487$	−2.83300e6	−	2.83300e6i	−0.541282	−	0.541282i	−0.923905	+	0.382623i	$0.875021\pi$
$488$	−641659.	+	641659.i	−0.121970	+	0.121970i
$489$	−2.31691e6			−0.438164
$490$	−1.57260e6	+	1.57260e6i	−0.295888	+	0.295888i
$491$			5.75109e6i			1.07658i	0.842759	+	0.538290i	$0.180930\pi$
$491$			5.75109e6i			1.07658i	−0.842759	+	0.538290i	$0.819070\pi$
$492$	5.95840e6			1.10973
$493$	3.50107e6	−	3.98254e6i	0.648760	−	0.737978i
$494$	5.77255e6			1.06427
$495$		−	1.64505e6i		−	0.301762i
$496$	−2.36619e6	+	2.36619e6i	−0.431863	+	0.431863i
$497$	−6.80481e6			−1.23573
$498$	3.73298e6	−	3.73298e6i	0.674501	−	0.674501i
$499$	392210.	+	392210.i	0.0705127	+	0.0705127i	0.741484	−	0.670971i	$-0.234122\pi$
$499$	392210.	+	392210.i	0.0705127	+	0.0705127i	−0.670971	+	0.741484i	$0.734122\pi$
$500$	−2.22062e6	−	2.22062e6i	−0.397237	−	0.397237i
$501$		−	6.12551e6i		−	1.09030i
$502$			1.32152e7i			2.34054i
$503$	−4.52403e6	−	4.52403e6i	−0.797270	−	0.797270i	0.185394	−	0.982664i	$-0.440644\pi$
$503$	−4.52403e6	−	4.52403e6i	−0.797270	−	0.797270i	−0.982664	+	0.185394i	$0.940644\pi$
$504$	−426623.	−	426623.i	−0.0748115	−	0.0748115i
$505$	−1.53190e6	+	1.53190e6i	−0.267303	+	0.267303i
$506$	−9.69778e6			−1.68382
$507$	−475669.	+	475669.i	−0.0821836	+	0.0821836i
$508$		−	5.09241e6i		−	0.875515i
$509$	−5.07250e6			−0.867816			−0.433908	−	0.900957i	$-0.642866\pi$
$509$	−5.07250e6			−0.867816			−0.433908	+	0.900957i	$0.642866\pi$
$510$	−6.40308e6	+	411954.i	−1.09009	+	0.0701332i
$511$	3.00069e6			0.508357
$512$			7.80718e6i			1.31619i
$513$	−652150.	+	652150.i	−0.109409	+	0.109409i
$514$	3.88452e6			0.648530
$515$	6.87934e6	−	6.87934e6i	1.14295	−	1.14295i
$516$	1.86708e6	+	1.86708e6i	0.308702	+	0.308702i
$517$	−1.01528e6	−	1.01528e6i	−0.167055	−	0.167055i
$518$			5.81949e6i			0.952929i
$519$			5.71211e6i			0.930846i
$520$	−1.42959e6	−	1.42959e6i	−0.231848	−	0.231848i
$521$	616106.	+	616106.i	0.0994401	+	0.0994401i	0.755077	−	0.655637i	$-0.227600\pi$
$521$	616106.	+	616106.i	0.0994401	+	0.0994401i	−0.655637	+	0.755077i	$0.727600\pi$
$522$	−2.13563e6	+	2.13563e6i	−0.343044	+	0.343044i
$523$	−6.45768e6			−1.03234			−0.516170	−	0.856486i	$-0.672643\pi$
$523$	−6.45768e6			−1.03234			−0.516170	+	0.856486i	$0.672643\pi$
$524$	2.80686e6	−	2.80686e6i	0.446573	−	0.446573i
$525$		−	2.54501e6i		−	0.402987i
$526$	1.69124e7			2.66527
$527$	−3.34549e6	+	3.80556e6i	−0.524726	+	0.596888i
$528$	−2.01435e6			−0.314449
$529$			1.01237e7i			1.57290i
$530$	−1.23866e7	+	1.23866e7i	−1.91542	+	1.91542i
$531$	−2.05413e6			−0.316150
$532$	−4.89639e6	+	4.89639e6i	−0.750061	+	0.750061i
$533$	−6.67264e6	−	6.67264e6i	−1.01737	−	1.01737i
$534$	−4.93814e6	−	4.93814e6i	−0.749395	−	0.749395i
$535$			1.37303e7i			2.07394i
$536$			2.45467e6i			0.369046i
$537$	−1.96221e6	−	1.96221e6i	−0.293636	−	0.293636i
$538$	9.79497e6	+	9.79497e6i	1.45897	+	1.45897i
$539$	−747572.	+	747572.i	−0.110836	+	0.110836i
$540$	1.98878e6			0.293496
$541$	6.64944e6	−	6.64944e6i	0.976769	−	0.976769i	−0.0229668	−	0.999736i	$-0.507311\pi$
$541$	6.64944e6	−	6.64944e6i	0.976769	−	0.976769i	0.999736	+	0.0229668i	$0.00731119\pi$
$542$		−	5.82194e6i		−	0.851275i
$543$	7.35385e6			1.07032
$544$	631720.	+	9.81894e6i	0.0915224	+	1.42255i
$545$	6.42064e6			0.925949
$546$			5.88312e6i			0.844552i
$547$	7.19044e6	−	7.19044e6i	1.02751	−	1.02751i	0.0279023	−	0.999611i	$-0.491117\pi$
$547$	7.19044e6	−	7.19044e6i	1.02751	−	1.02751i	0.999611	−	0.0279023i	$-0.00888272\pi$
$548$	−5.82501e6			−0.828601
$549$	−999649.	+	999649.i	−0.141552	+	0.141552i
$550$	3.32614e6	+	3.32614e6i	0.468850	+	0.468850i
$551$	3.98099e6	+	3.98099e6i	0.558615	+	0.558615i
$552$		−	1.90421e6i		−	0.265991i
$553$		−	1.30267e7i		−	1.81143i
$554$	−7.11620e6	−	7.11620e6i	−0.985085	−	0.985085i
$555$	−2.20309e6	−	2.20309e6i	−0.303598	−	0.303598i
$556$	1.82047e6	−	1.82047e6i	0.249745	−	0.249745i
$557$	652353.			0.0890932			0.0445466	−	0.999007i	$-0.485816\pi$
$557$	652353.			0.0890932			0.0445466	+	0.999007i	$0.485816\pi$
$558$	2.04072e6	−	2.04072e6i	0.277459	−	0.277459i
$559$		−	4.18178e6i		−	0.566020i
$560$	−8.05015e6			−1.08476
$561$	−3.04386e6	+	195833.i	−0.408336	+	0.0262711i
$562$	1.45571e6			0.194417
$563$			3.19751e6i			0.425149i	0.977145	+	0.212575i	$0.0681848\pi$
$563$			3.19751e6i			0.425149i	−0.977145	+	0.212575i	$0.931815\pi$
$564$	1.22743e6	−	1.22743e6i	0.162479	−	0.162479i
$565$	1.12521e7			1.48290
$566$	4.38093e6	−	4.38093e6i	0.574811	−	0.574811i
$567$	−664642.	−	664642.i	−0.0868221	−	0.0868221i
$568$	1.74627e6	+	1.74627e6i	0.227112	+	0.227112i
$569$			1.40126e7i			1.81442i	0.420673	+	0.907212i	$0.361794\pi$
$569$			1.40126e7i			1.81442i	−0.420673	+	0.907212i	$0.638206\pi$
$570$		−	6.81238e6i		−	0.878236i
$571$	−5.60912e6	−	5.60912e6i	−0.719954	−	0.719954i	0.248642	−	0.968596i	$-0.420016\pi$
$571$	−5.60912e6	−	5.60912e6i	−0.719954	−	0.719954i	−0.968596	+	0.248642i	$0.920016\pi$
$572$	−4.18420e6	−	4.18420e6i	−0.534715	−	0.534715i
$573$	1.92799e6	−	1.92799e6i	0.245312	−	0.245312i
$574$	2.08009e7			2.63513
$575$	5.67976e6	−	5.67976e6i	0.716408	−	0.716408i
$576$		−	3.56442e6i		−	0.447644i
$577$	−5.22670e6			−0.653563			−0.326782	−	0.945100i	$-0.605964\pi$
$577$	−5.22670e6			−0.653563			−0.326782	+	0.945100i	$0.605964\pi$
$578$	1.52449e6	+	1.17987e7i	0.189804	+	1.46897i
$579$	2.17840e6			0.270048
$580$		−	1.21403e7i		−	1.49851i
$581$	7.09189e6	−	7.09189e6i	0.871608	−	0.871608i
$582$	8.36930e6			1.02419
$583$	−5.88829e6	+	5.88829e6i	−0.717493	+	0.717493i
$584$	−770043.	−	770043.i	−0.0934292	−	0.0934292i
$585$	−2.22717e6	−	2.22717e6i	−0.269070	−	0.269070i
$586$			2.66668e6i			0.320795i
$587$			7.44515e6i			0.891822i	0.895077	+	0.445911i	$0.147120\pi$
$587$			7.44515e6i			0.891822i	−0.895077	+	0.445911i	$0.852880\pi$
$588$	−903778.	−	903778.i	−0.107800	−	0.107800i
$589$	−3.80408e6	−	3.80408e6i	−0.451816	−	0.451816i
$590$	1.07288e7	−	1.07288e7i	1.26888	−	1.26888i
$591$	3.36358e6			0.396126
$592$	−2.69766e6	+	2.69766e6i	−0.316361	+	0.316361i
$593$		−	1.04176e7i		−	1.21655i	−0.793726	−	0.608276i	$-0.791861\pi$
$593$		−	1.04176e7i		−	1.21655i	0.793726	−	0.608276i	$-0.208139\pi$
$594$	1.73728e6			0.202024
$595$	−1.21645e7	+	782626.i	−1.40865	+	0.0906279i
$596$	699048.			0.0806105
$597$		−	4.98370e6i		−	0.572290i
$598$	−1.31295e7	+	1.31295e7i	−1.50140	+	1.50140i
$599$	2.04795e6			0.233213			0.116606	−	0.993178i	$-0.462798\pi$
$599$	2.04795e6			0.233213			0.116606	+	0.993178i	$0.462798\pi$
$600$	−653106.	+	653106.i	−0.0740637	+	0.0740637i
$601$	−9.86483e6	−	9.86483e6i	−1.11405	−	1.11405i	−0.992598	−	0.121449i	$-0.961246\pi$
$601$	−9.86483e6	−	9.86483e6i	−1.11405	−	1.11405i	−0.121449	−	0.992598i	$-0.538754\pi$
$602$	6.51802e6	+	6.51802e6i	0.733035	+	0.733035i
$603$			3.82416e6i			0.428295i
$604$		−	1.94824e7i		−	2.17296i
$605$	−4.04730e6	−	4.04730e6i	−0.449549	−	0.449549i
$606$	−1.61779e6	−	1.61779e6i	−0.178954	−	0.178954i
$607$	−9.09590e6	+	9.09590e6i	−1.00201	+	1.00201i	−0.00201588	+	0.999998i	$0.500642\pi$
$607$	−9.09590e6	+	9.09590e6i	−1.00201	+	1.00201i	−0.999998	+	0.00201588i	$0.999358\pi$
$608$	−1.04466e7			−1.14608
$609$	−4.05725e6	+	4.05725e6i	−0.443290	+	0.443290i
$610$		−	1.04424e7i		−	1.13625i
$611$	−2.74912e6			−0.297913
$612$	−236752.	−	3.67987e6i	−0.0255514	−	0.397150i
$613$	−187106.			−0.0201112			−0.0100556	−	0.999949i	$-0.503201\pi$
$613$	−187106.			−0.0201112			−0.0100556	+	0.999949i	$0.503201\pi$
$614$		−	4.00534e6i		−	0.428764i
$615$	−7.87460e6	+	7.87460e6i	−0.839539	+	0.839539i
$616$	2.11851e6			0.224947
$617$	−5.74408e6	+	5.74408e6i	−0.607446	+	0.607446i	−0.942278	−	0.334832i	$-0.891321\pi$
$617$	−5.74408e6	+	5.74408e6i	−0.607446	+	0.607446i	0.334832	+	0.942278i	$0.391321\pi$
$618$	7.26504e6	+	7.26504e6i	0.765185	+	0.765185i
$619$	−1.02197e6	−	1.02197e6i	−0.107204	−	0.107204i	0.651470	−	0.758674i	$-0.274153\pi$
$619$	−1.02197e6	−	1.02197e6i	−0.107204	−	0.107204i	−0.758674	+	0.651470i	$0.774153\pi$
$620$			1.16008e7i			1.21202i
$621$		−	2.96659e6i		−	0.308695i
$622$	−805445.	−	805445.i	−0.0834757	−	0.0834757i
$623$	−9.38144e6	−	9.38144e6i	−0.968388	−	0.968388i
$624$	−2.72716e6	+	2.72716e6i	−0.280381	+	0.280381i
$625$	1.20378e7			1.23267
$626$	510995.	−	510995.i	0.0521172	−	0.0521172i
$627$		−	3.23843e6i		−	0.328977i
$628$	1.39316e7			1.40961
$629$	−3.81415e6	+	4.33868e6i	−0.384389	+	0.437251i
$630$	6.94286e6			0.696927
$631$			9.06720e6i			0.906567i	0.891366	+	0.453283i	$0.149747\pi$
$631$			9.06720e6i			0.906567i	−0.891366	+	0.453283i	$0.850253\pi$
$632$	−3.34294e6	+	3.34294e6i	−0.332917	+	0.332917i
$633$	−1.92199e6			−0.190652
$634$	−500256.	+	500256.i	−0.0494276	+	0.0494276i
$635$	6.73010e6	+	6.73010e6i	0.662350	+	0.662350i
$636$	−7.11865e6	−	7.11865e6i	−0.697838	−	0.697838i
$637$			2.02423e6i			0.197656i
$638$		−	1.06051e7i		−	1.03148i
$639$	2.72053e6	+	2.72053e6i	0.263573	+	0.263573i
$640$	5.27533e6	+	5.27533e6i	0.509096	+	0.509096i
$641$	2.72778e6	−	2.72778e6i	0.262219	−	0.262219i	−0.563736	−	0.825955i	$-0.690637\pi$
$641$	2.72778e6	−	2.72778e6i	0.262219	−	0.262219i	0.825955	+	0.563736i	$0.190637\pi$
$642$	−1.45001e7			−1.38846
$643$	2.28037e6	−	2.28037e6i	0.217509	−	0.217509i	−0.589939	−	0.807448i	$-0.700848\pi$
$643$	2.28037e6	−	2.28037e6i	0.217509	−	0.217509i	0.807448	+	0.589939i	$0.200848\pi$
$644$		−	2.22734e7i		−	2.11627i
$645$	−4.93506e6			−0.467082
$646$	−1.26051e7	+	810971.i	−1.18840	+	0.0764582i
$647$	1.73048e6			0.162519			0.0812596	−	0.996693i	$-0.474106\pi$
$647$	1.73048e6			0.162519			0.0812596	+	0.996693i	$0.474106\pi$
$648$			341124.i			0.0319135i
$649$	5.10018e6	−	5.10018e6i	0.475307	−	0.475307i
$650$	9.00632e6			0.836111
$651$	3.87695e6	−	3.87695e6i	0.358540	−	0.358540i
$652$	6.95464e6	+	6.95464e6i	0.640701	+	0.640701i
$653$	−1.50985e7	−	1.50985e7i	−1.38564	−	1.38564i	−0.834240	−	0.551401i	$-0.814093\pi$
$653$	−1.50985e7	−	1.50985e7i	−1.38564	−	1.38564i	−0.551401	−	0.834240i	$-0.685907\pi$
$654$			6.78062e6i			0.619904i
$655$			7.41907e6i			0.675688i
$656$	9.64240e6	+	9.64240e6i	0.874833	+	0.874833i
$657$	−1.19966e6	−	1.19966e6i	−0.108429	−	0.108429i
$658$	4.28497e6	−	4.28497e6i	0.385818	−	0.385818i
$659$	2.01821e6			0.181031			0.0905157	−	0.995895i	$-0.471148\pi$
$659$	2.01821e6			0.181031			0.0905157	+	0.995895i	$0.471148\pi$
$660$	−4.93791e6	+	4.93791e6i	−0.441249	+	0.441249i
$661$			1.58836e7i			1.41399i	0.707219	+	0.706995i	$0.249949\pi$
$661$			1.58836e7i			1.41399i	−0.707219	+	0.706995i	$0.750051\pi$
$662$	1.40607e7			1.24699
$663$	−3.85585e6	+	4.38612e6i	−0.340672	+	0.387522i
$664$	−3.63987e6			−0.320380
$665$		−	1.29421e7i		−	1.13488i
$666$	2.32660e6	−	2.32660e6i	0.203253	−	0.203253i
$667$	−1.81093e7			−1.57611
$668$	−1.83868e7	+	1.83868e7i	−1.59429	+	1.59429i
$669$	−1.45690e6	−	1.45690e6i	−0.125854	−	0.125854i
$670$	−1.99736e7	−	1.99736e7i	−1.71898	−	1.71898i
$671$		−	4.96403e6i		−	0.425626i
$672$		−	1.06467e7i		−	0.909476i
$673$	8.90430e6	+	8.90430e6i	0.757813	+	0.757813i	0.975924	−	0.218111i	$-0.0699894\pi$
$673$	8.90430e6	+	8.90430e6i	0.757813	+	0.757813i	−0.218111	+	0.975924i	$0.569989\pi$
$674$	−3.00401e6	−	3.00401e6i	−0.254713	−	0.254713i
$675$	−1.01748e6	+	1.01748e6i	−0.0859543	+	0.0859543i
$676$	2.85562e6			0.240344
$677$	1.06568e7	−	1.06568e7i	0.893622	−	0.893622i	−0.101240	−	0.994862i	$-0.532281\pi$
$677$	1.06568e7	−	1.06568e7i	0.893622	−	0.893622i	0.994862	+	0.101240i	$0.0322811\pi$
$678$			1.18829e7i			0.992771i
$679$	1.58999e7			1.32349
$680$	3.32252e6	+	2.92084e6i	0.275547	+	0.242234i
$681$	−8.69510e6			−0.718467
$682$			1.01338e7i			0.834277i
$683$	9.33995e6	−	9.33995e6i	0.766113	−	0.766113i	−0.211307	−	0.977420i	$-0.567772\pi$
$683$	9.33995e6	−	9.33995e6i	0.766113	−	0.766113i	0.977420	+	0.211307i	$0.0677719\pi$
$684$	3.91510e6			0.319965
$685$	7.69831e6	−	7.69831e6i	0.626857	−	0.626857i
$686$	1.11106e7	+	1.11106e7i	0.901418	+	0.901418i
$687$	8.09716e6	+	8.09716e6i	0.654547	+	0.654547i
$688$			6.04294e6i			0.486718i
$689$			1.59439e7i			1.27952i
$690$	1.54946e7	+	1.54946e7i	1.23896	+	1.23896i
$691$	−6.26061e6	−	6.26061e6i	−0.498794	−	0.498794i	0.412268	−	0.911063i	$-0.364737\pi$
$691$	−6.26061e6	−	6.26061e6i	−0.498794	−	0.498794i	−0.911063	+	0.412268i	$0.864737\pi$
$692$	1.71459e7	−	1.71459e7i	1.36112	−	1.36112i
$693$	3.30046e6			0.261061
$694$	−1.67752e7	+	1.67752e7i	−1.32212	+	1.32212i
$695$			4.81186e6i			0.377877i
$696$	2.08236e6			0.162942
$697$	1.55079e7	+	1.36331e7i	1.20913	+	1.06295i
$698$	5.17386e6			0.401954
$699$			8.88823e6i			0.688054i
$700$	−7.63932e6	+	7.63932e6i	−0.589264	+	0.589264i
$701$	8.37641e6			0.643818			0.321909	−	0.946771i	$-0.395676\pi$
$701$	8.37641e6			0.643818			0.321909	+	0.946771i	$0.395676\pi$
$702$	2.35204e6	−	2.35204e6i	0.180137	−	0.180137i
$703$	−4.33699e6	−	4.33699e6i	−0.330978	−	0.330978i
$704$	8.85005e6	+	8.85005e6i	0.672999	+	0.672999i
$705$			3.24432e6i			0.245839i
$706$		−	1.46196e7i		−	1.10389i
$707$	−3.07346e6	−	3.07346e6i	−0.231249	−	0.231249i
$708$	6.16587e6	+	6.16587e6i	0.462286	+	0.462286i
$709$	−9.89781e6	+	9.89781e6i	−0.739475	+	0.739475i	−0.972476	−	0.233001i	$-0.925145\pi$
$709$	−9.89781e6	+	9.89781e6i	−0.739475	+	0.739475i	0.233001	+	0.972476i	$0.425145\pi$
$710$	−2.84187e7			−2.11572
$711$	−5.20801e6	+	5.20801e6i	−0.386365	+	0.386365i
$712$			4.81497e6i			0.355954i
$713$	1.73046e7			1.27478
$714$	−826505.	−	1.28465e7i	−0.0606736	−	0.943061i
$715$	1.10596e7			0.809051
$716$			1.17799e7i			0.858733i
$717$	3.18480e6	−	3.18480e6i	0.231358	−	0.231358i
$718$	−2.29078e7			−1.65833
$719$	6.49134e6	−	6.49134e6i	0.468287	−	0.468287i	−0.433072	−	0.901359i	$-0.642571\pi$
$719$	6.49134e6	−	6.49134e6i	0.468287	−	0.468287i	0.901359	+	0.433072i	$0.142571\pi$
$720$	3.21841e6	+	3.21841e6i	0.231372	+	0.231372i
$721$	1.38020e7	+	1.38020e7i	0.988792	+	0.988792i
$722$			7.33606e6i			0.523745i
$723$		−	1.03048e7i		−	0.733151i
$724$	−2.20739e7	−	2.20739e7i	−1.56507	−	1.56507i
$725$	6.21113e6	+	6.21113e6i	0.438860	+	0.438860i
$726$	4.27422e6	−	4.27422e6i	0.300964	−	0.300964i
$727$	−2.11166e6			−0.148180			−0.0740899	−	0.997252i	$-0.523605\pi$
$727$	−2.11166e6			−0.148180			−0.0740899	+	0.997252i	$0.523605\pi$
$728$	2.86819e6	−	2.86819e6i	0.200576	−	0.200576i
$729$			531441.i			0.0370370i
$730$	1.25317e7			0.870366
$731$	587488.	+	9.13143e6i	0.0406636	+	0.632041i
$732$	6.00126e6			0.413966
$733$		−	1.73478e7i		−	1.19257i	−0.802771	−	0.596287i	$-0.796642\pi$
$733$		−	1.73478e7i		−	1.19257i	0.802771	−	0.596287i	$-0.203358\pi$
$734$	−1.89332e7	+	1.89332e7i	−1.29713	+	1.29713i
$735$	2.38886e6			0.163107
$736$	2.37605e7	−	2.37605e7i	1.61682	−	1.61682i
$737$	−9.49496e6	−	9.49496e6i	−0.643909	−	0.643909i
$738$	−8.31610e6	−	8.31610e6i	−0.562055	−	0.562055i
$739$		−	3.04726e6i		−	0.205257i	−0.994720	−	0.102629i	$-0.967275\pi$
$739$		−	3.04726e6i		−	0.205257i	0.994720	−	0.102629i	$-0.0327253\pi$
$740$			1.32259e7i			0.887866i
$741$	−4.38441e6	−	4.38441e6i	−0.293336	−	0.293336i
$742$	−2.48513e7	−	2.48513e7i	−1.65707	−	1.65707i
$743$	−3.32370e6	+	3.32370e6i	−0.220877	+	0.220877i	−0.808868	−	0.587991i	$-0.799919\pi$
$743$	−3.32370e6	+	3.32370e6i	−0.220877	+	0.220877i	0.587991	+	0.808868i	$0.299919\pi$
$744$	−1.98982e6			−0.131790
$745$	−923859.	+	923859.i	−0.0609839	+	0.0609839i
$746$			2.79756e6i			0.184049i
$747$	−5.67060e6			−0.371816
$748$	9.72454e6	+	8.54888e6i	0.635499	+	0.558670i
$749$	−2.75471e7			−1.79420
$750$			6.19861e6i			0.402385i
$751$	−7.41156e6	+	7.41156e6i	−0.479524	+	0.479524i	−0.904979	−	0.425456i	$-0.860114\pi$
$751$	−7.41156e6	+	7.41156e6i	−0.479524	+	0.479524i	0.425456	+	0.904979i	$0.360114\pi$
$752$	3.97265e6			0.256174
$753$	1.00373e7	−	1.00373e7i	0.645105	−	0.645105i
$754$	−1.43578e7	−	1.43578e7i	−0.919731	−	0.919731i
$755$	2.57479e7	+	2.57479e7i	1.64390	+	1.64390i
$756$			3.99009e6i			0.253909i
$757$		−	1.99911e7i		−	1.26793i	−0.773360	−	0.633967i	$-0.781426\pi$
$757$		−	1.99911e7i		−	1.26793i	0.773360	−	0.633967i	$-0.218574\pi$
$758$	−1.08242e7	−	1.08242e7i	−0.684262	−	0.684262i
$759$	7.36572e6	+	7.36572e6i	0.464099	+	0.464099i
$760$	−3.32122e6	+	3.32122e6i	−0.208576	+	0.208576i
$761$	−2.66316e6			−0.166700			−0.0833501	−	0.996520i	$-0.526562\pi$
$761$	−2.66316e6			−0.166700			−0.0833501	+	0.996520i	$0.526562\pi$
$762$	−7.10743e6	+	7.10743e6i	−0.443430	+	0.443430i
$763$			1.28817e7i			0.801057i
$764$	−1.15744e7			−0.717409
$765$	5.17620e6	+	4.55042e6i	0.319784	+	0.281124i
$766$	1.06775e7			0.657505
$767$		−	1.38099e7i		−	0.847625i
$768$	3.39042e6	−	3.39042e6i	0.207420	−	0.207420i
$769$	1.87027e7			1.14048			0.570241	−	0.821478i	$-0.306850\pi$
$769$	1.87027e7			1.14048			0.570241	+	0.821478i	$0.306850\pi$
$770$	−1.72383e7	+	1.72383e7i	−1.04778	+	1.04778i
$771$	−2.95040e6	−	2.95040e6i	−0.178749	−	0.178749i
$772$	−6.53887e6	−	6.53887e6i	−0.394875	−	0.394875i
$773$			6.05068e6i			0.364213i	0.983279	+	0.182106i	$0.0582916\pi$
$773$			6.05068e6i			0.364213i	−0.983279	+	0.182106i	$0.941708\pi$
$774$		−	5.21174e6i		−	0.312702i
$775$	−5.93512e6	−	5.93512e6i	−0.354956	−	0.354956i
$776$	−4.08027e6	−	4.08027e6i	−0.243240	−	0.243240i
$777$	4.42006e6	−	4.42006e6i	0.262649	−	0.262649i
$778$	−4.79957e7			−2.84285
$779$	−1.55019e7	+	1.55019e7i	−0.915253	+	0.915253i
$780$			1.33706e7i			0.786888i
$781$	−1.35095e7			−0.792525
$782$	2.68253e7	−	3.05144e7i	1.56866	−	1.78438i
$783$	3.24413e6			0.189101
$784$		−	2.92514e6i		−	0.169964i
$785$	−1.84119e7	+	1.84119e7i	−1.06641	+	1.06641i
$786$	−7.83503e6			−0.452360
$787$	2.87678e6	−	2.87678e6i	0.165565	−	0.165565i	−0.619462	−	0.785027i	$-0.712649\pi$
$787$	2.87678e6	−	2.87678e6i	0.165565	−	0.165565i	0.785027	+	0.619462i	$0.212649\pi$
$788$	−1.00964e7	−	1.00964e7i	−0.579230	−	0.579230i
$789$	−1.28454e7	−	1.28454e7i	−0.734609	−	0.734609i
$790$		−	5.44030e7i		−	3.10138i
$791$			2.25751e7i			1.28288i
$792$	−846971.	−	846971.i	−0.0479795	−	0.0479795i
$793$	−6.72064e6	−	6.72064e6i	−0.379514	−	0.379514i
$794$	2.66761e7	−	2.66761e7i	1.50166	−	1.50166i
$795$	1.88159e7			1.05586
$796$	−1.49595e7	+	1.49595e7i	−0.836825	+	0.836825i
$797$			3.77817e6i			0.210686i	0.994436	+	0.105343i	$0.0335941\pi$
$797$			3.77817e6i			0.210686i	−0.994436	+	0.105343i	$0.966406\pi$
$798$	1.36677e7			0.759780
$799$	6.00303e6	−	386216.i	0.332662	−	0.0214024i
$800$	−1.62987e7			−0.900386
$801$			7.50130e6i			0.413100i
$802$	1.95398e7	−	1.95398e7i	1.07271	−	1.07271i
$803$	5.95724e6			0.326029
$804$	1.14789e7	−	1.14789e7i	0.626269	−	0.626269i
$805$	2.94364e7	+	2.94364e7i	1.60101	+	1.60101i
$806$	1.37198e7	+	1.37198e7i	0.743892	+	0.743892i
$807$		−	1.48791e7i		−	0.804252i
$808$			1.57744e6i			0.0850009i
$809$	321622.	+	321622.i	0.0172773	+	0.0172773i	0.715693	−	0.698415i	$-0.246111\pi$
$809$	321622.	+	321622.i	0.0172773	+	0.0172773i	−0.698415	+	0.715693i	$0.746111\pi$
$810$	−2.77572e6	−	2.77572e6i	−0.148649	−	0.148649i
$811$	−1.48771e7	+	1.48771e7i	−0.794265	+	0.794265i	−0.982185	−	0.187919i	$-0.939826\pi$
$811$	−1.48771e7	+	1.48771e7i	−0.794265	+	0.794265i	0.187919	+	0.982185i	$0.439826\pi$
$812$	2.43572e7			1.29639
$813$	−4.42192e6	+	4.42192e6i	−0.234631	+	0.234631i
$814$			1.15534e7i			0.611151i
$815$	−1.83824e7			−0.969413
$816$	5.57195e6	−	6.33822e6i	0.292942	−	0.333228i
$817$	−9.71513e6			−0.509206
$818$		−	2.31531e7i		−	1.20984i
$819$	4.46839e6	−	4.46839e6i	0.232778	−	0.232778i
$820$	4.72741e7			2.45521
$821$	−3.79231e6	+	3.79231e6i	−0.196357	+	0.196357i	−0.798436	−	0.602079i	$-0.794339\pi$
$821$	−3.79231e6	+	3.79231e6i	−0.196357	+	0.196357i	0.602079	+	0.798436i	$0.294339\pi$
$822$	8.12992e6	+	8.12992e6i	0.419669	+	0.419669i
$823$	1.83509e7	+	1.83509e7i	0.944404	+	0.944404i	0.998534	−	0.0541296i	$-0.0172384\pi$
$823$	1.83509e7	+	1.83509e7i	0.944404	+	0.944404i	−0.0541296	+	0.998534i	$0.517238\pi$
$824$		−	7.08382e6i		−	0.363454i
$825$		−	5.05259e6i		−	0.258451i
$826$	2.15252e7	+	2.15252e7i	1.09773	+	1.09773i
$827$	−1.57791e7	−	1.57791e7i	−0.802267	−	0.802267i	0.181183	−	0.983449i	$-0.442007\pi$
$827$	−1.57791e7	−	1.57791e7i	−0.802267	−	0.802267i	−0.983449	+	0.181183i	$0.942007\pi$
$828$	−8.90478e6	+	8.90478e6i	−0.451385	+	0.451385i
$829$	4.31396e6			0.218017			0.109008	−	0.994041i	$-0.465232\pi$
$829$	4.31396e6			0.218017			0.109008	+	0.994041i	$0.465232\pi$
$830$	2.96176e7	−	2.96176e7i	1.49229	−	1.49229i
$831$			1.08099e7i			0.543023i
$832$	2.39636e7			1.20017
$833$	−284379.	−	4.42015e6i	−0.0141999	−	0.220711i
$834$	−5.08164e6			−0.252982
$835$		−	4.85999e7i		−	2.41223i
$836$	−9.72075e6	+	9.72075e6i	−0.481043	+	0.481043i
$837$	−3.09997e6			−0.152948
$838$	1.38291e6	−	1.38291e6i	0.0680274	−	0.0680274i
$839$	−1.21119e7	−	1.21119e7i	−0.594029	−	0.594029i	0.344688	−	0.938717i	$-0.387985\pi$
$839$	−1.21119e7	−	1.21119e7i	−0.594029	−	0.594029i	−0.938717	+	0.344688i	$0.887985\pi$
$840$	−3.38484e6	−	3.38484e6i	−0.165516	−	0.165516i
$841$			707627.i			0.0344996i
$842$			2.78958e7i			1.35599i
$843$	−1.10565e6	−	1.10565e6i	−0.0535857	−	0.0535857i
$844$	5.76920e6	+	5.76920e6i	0.278779	+	0.278779i
$845$	−3.77397e6	+	3.77397e6i	−0.181826	+	0.181826i
$846$	−3.42622e6			−0.164584
$847$	8.12011e6	−	8.12011e6i	0.388914	−	0.388914i
$848$		−	2.30400e7i		−	1.10025i
$849$	−6.65486e6			−0.316862
$850$	−1.96664e7	+	1.26527e6i	−0.933635	+	0.0600672i
$851$	1.97287e7			0.933844
$852$		−	1.63324e7i		−	0.770814i
$853$	−1.23482e6	+	1.23482e6i	−0.0581073	+	0.0581073i	−0.735563	−	0.677456i	$-0.763082\pi$
$853$	−1.23482e6	+	1.23482e6i	−0.0581073	+	0.0581073i	0.677456	+	0.735563i	$0.263082\pi$
$854$	2.09505e7			0.982992
$855$	−5.17418e6	+	5.17418e6i	−0.242062	+	0.242062i
$856$	7.06921e6	+	7.06921e6i	0.329751	+	0.329751i
$857$	−2.10651e7	−	2.10651e7i	−0.979743	−	0.979743i	0.0200555	−	0.999799i	$-0.493616\pi$
$857$	−2.10651e7	−	2.10651e7i	−0.979743	−	0.979743i	−0.999799	+	0.0200555i	$0.993616\pi$
$858$			1.16797e7i			0.541644i
$859$		−	2.09665e6i		−	0.0969488i	−0.998824	−	0.0484744i	$-0.984564\pi$
$859$		−	2.09665e6i		−	0.0969488i	0.998824	−	0.0484744i	$-0.0154359\pi$
$860$	1.48135e7	+	1.48135e7i	0.682985	+	0.682985i
$861$	−1.57988e7	−	1.57988e7i	−0.726302	−	0.726302i
$862$	−7.28163e6	+	7.28163e6i	−0.333780	+	0.333780i
$863$	7.53447e6			0.344370			0.172185	−	0.985065i	$-0.444917\pi$
$863$	7.53447e6			0.344370			0.172185	+	0.985065i	$0.444917\pi$
$864$	−4.25649e6	+	4.25649e6i	−0.193985	+	0.193985i
$865$			4.53200e7i			2.05944i
$866$	−3.71915e7			−1.68519
$867$	7.80353e6	−	1.01193e7i	0.352568	−	0.457197i
$868$	−2.32748e7			−1.04854
$869$		−	2.58618e7i		−	1.16174i
$870$	−1.69441e7	+	1.69441e7i	−0.758965	+	0.758965i
$871$	−2.57098e7			−1.14830
$872$	3.30574e6	−	3.30574e6i	0.147224	−	0.147224i
$873$	−6.35670e6	−	6.35670e6i	−0.282291	−	0.282291i
$874$	3.05025e7	+	3.05025e7i	1.35069	+	1.35069i
$875$			1.17761e7i			0.519972i
$876$			7.20201e6i			0.317098i
$877$	2.13511e7	+	2.13511e7i	0.937394	+	0.937394i	0.998152	−	0.0607587i	$-0.0193520\pi$
$877$	2.13511e7	+	2.13511e7i	0.937394	+	0.937394i	−0.0607587	+	0.998152i	$0.519352\pi$
$878$	1.60270e6	+	1.60270e6i	0.0701643	+	0.0701643i
$879$	2.02541e6	−	2.02541e6i	0.0884182	−	0.0884182i
$880$	−1.59819e7			−0.695699
$881$	−1.68537e7	+	1.68537e7i	−0.731568	+	0.731568i	−0.970930	−	0.239362i	$-0.923062\pi$
$881$	−1.68537e7	+	1.68537e7i	−0.731568	+	0.731568i	0.239362	+	0.970930i	$0.423062\pi$
$882$			2.52279e6i			0.109197i
$883$	1.96805e7			0.849445			0.424722	−	0.905324i	$-0.360372\pi$
$883$	1.96805e7			0.849445			0.424722	+	0.905324i	$0.360372\pi$
$884$	2.47398e7	−	1.59168e6i	1.06479	−	0.0685055i
$885$	−1.62976e7			−0.699462
$886$			1.88206e7i			0.805468i
$887$	−7.00117e6	+	7.00117e6i	−0.298787	+	0.298787i	−0.840539	−	0.541752i	$-0.817761\pi$
$887$	−7.00117e6	+	7.00117e6i	−0.298787	+	0.298787i	0.541752	+	0.840539i	$0.317761\pi$
$888$	−2.26857e6			−0.0965427
$889$	−1.35026e7	+	1.35026e7i	−0.573012	+	0.573012i
$890$	−3.91794e7	−	3.91794e7i	−1.65799	−	1.65799i
$891$	−1.31951e6	−	1.31951e6i	−0.0556824	−	0.0556824i
$892$			8.74634e6i			0.368056i
$893$			6.38675e6i			0.268010i
$894$	−975656.	−	975656.i	−0.0408275	−	0.0408275i
$895$	−1.55682e7	−	1.55682e7i	−0.649653	−	0.649653i
$896$	−1.05839e7	+	1.05839e7i	−0.440430	+	0.440430i
$897$	1.99444e7			0.827638
$898$	−3.18907e7	+	3.18907e7i	−1.31970	+	1.31970i
$899$			1.89235e7i			0.780911i
$900$	6.10833e6			0.251371
$901$	−2.23992e6	−	3.48155e7i	−0.0919223	−	1.42876i
$902$	4.12958e7			1.69001
$903$		−	9.90122e6i		−	0.404082i
$904$	5.79326e6	−	5.79326e6i	0.235777	−	0.235777i
$905$	5.83457e7			2.36803
$906$	−2.71915e7	+	2.71915e7i	−1.10056	+	1.10056i
$907$	2.60026e7	+	2.60026e7i	1.04954	+	1.04954i	0.998707	+	0.0508303i	$0.0161868\pi$
$907$	2.60026e7	+	2.60026e7i	1.04954	+	1.04954i	0.0508303	+	0.998707i	$0.483813\pi$
$908$	2.61000e7	+	2.61000e7i	1.05057	+	1.05057i
$909$			2.45751e6i			0.0986474i
$910$			4.66769e7i			1.86852i
$911$	−1.33751e7	−	1.33751e7i	−0.533949	−	0.533949i	0.387796	−	0.921745i	$-0.373236\pi$
$911$	−1.33751e7	−	1.33751e7i	−0.533949	−	0.533949i	−0.921745	+	0.387796i	$0.873236\pi$
$912$	6.33575e6	+	6.33575e6i	0.252238	+	0.252238i
$913$	1.40795e7	−	1.40795e7i	0.558996	−	0.558996i
$914$	−5.81450e7			−2.30222
$915$	−7.93124e6	+	7.93124e6i	−0.313176	+	0.313176i
$916$		−	4.86103e7i		−	1.91421i
$917$	−1.48849e7			−0.584551
$918$	−4.80554e6	+	5.46640e6i	−0.188207	+	0.214089i
$919$	−1.98246e7			−0.774311			−0.387156	−	0.922014i	$-0.626542\pi$
$919$	−1.98246e7			−0.774311			−0.387156	+	0.922014i	$0.626542\pi$
$920$		−	1.51081e7i		−	0.588490i
$921$	−3.04216e6	+	3.04216e6i	−0.118177	+	0.118177i
$922$	−1.62794e7			−0.630682
$923$	−1.82901e7	+	1.82901e7i	−0.706663	+	0.706663i
$924$	−9.90694e6	−	9.90694e6i	−0.381733	−	0.381733i
$925$	−6.76655e6	−	6.76655e6i	−0.260024	−	0.260024i
$926$			6.30091e7i			2.41477i
$927$		−	1.10360e7i		−	0.421805i
$928$	2.59834e7	+	2.59834e7i	0.990434	+	0.990434i
$929$	1.77614e7	+	1.77614e7i	0.675208	+	0.675208i	0.958912	−	0.283704i	$-0.0915634\pi$
$929$	1.77614e7	+	1.77614e7i	0.675208	+	0.675208i	−0.283704	+	0.958912i	$0.591563\pi$
$930$	1.61912e7	−	1.61912e7i	0.613862	−	0.613862i
$931$	4.70269e6			0.177817
$932$	2.66797e7	−	2.66797e7i	1.00610	−	1.00610i
$933$			1.22351e6i			0.0460156i
$934$	−4.56287e7			−1.71148
$935$	−2.41501e7	+	1.55374e6i	−0.903419	+	0.0581232i
$936$	−2.29337e6			−0.0855628
$937$			3.38340e7i			1.25894i	0.777026	+	0.629468i	$0.216727\pi$
$937$			3.38340e7i			1.25894i	−0.777026	+	0.629468i	$0.783273\pi$
$938$	4.00732e7	−	4.00732e7i	1.48712	−	1.48712i
$939$	−776229.			−0.0287293
$940$	9.73843e6	−	9.73843e6i	0.359475	−	0.359475i
$941$	−3.29364e7	−	3.29364e7i	−1.21256	−	1.21256i	−0.970184	−	0.242372i	$-0.922075\pi$
$941$	−3.29364e7	−	3.29364e7i	−1.21256	−	1.21256i	−0.242372	−	0.970184i	$-0.577925\pi$
$942$	−1.94442e7	−	1.94442e7i	−0.713940	−	0.713940i
$943$		−	7.05173e7i		−	2.58236i
$944$			1.99563e7i			0.728868i
$945$	−5.27329e6	−	5.27329e6i	−0.192089	−	0.192089i
$946$	1.29402e7	+	1.29402e7i	0.470124	+	0.470124i
$947$	204706.	−	204706.i	0.00741745	−	0.00741745i	−0.703388	−	0.710806i	$-0.748330\pi$
$947$	204706.	−	204706.i	0.00741745	−	0.00741745i	0.710806	+	0.703388i	$0.248330\pi$
$948$	3.12656e7			1.12992
$949$	8.06532e6	−	8.06532e6i	0.290707	−	0.290707i
$950$		−	2.09235e7i		−	0.752186i
$951$	759916.			0.0272467
$952$	−5.86009e6	+	6.66598e6i	−0.209562	+	0.238381i
$953$	−3.68475e6			−0.131424			−0.0657122	−	0.997839i	$-0.520932\pi$
$953$	−3.68475e6			−0.131424			−0.0657122	+	0.997839i	$0.520932\pi$
$954$			1.98709e7i			0.706881i
$955$	1.52967e7	−	1.52967e7i	0.542738	−	0.542738i
$956$	−1.91195e7			−0.676600
$957$	−8.05481e6	+	8.05481e6i	−0.284299	+	0.284299i
$958$	3.05528e7	+	3.05528e7i	1.07557	+	1.07557i
$959$	1.54451e7	+	1.54451e7i	0.542307	+	0.542307i
$960$		−	2.82802e7i		−	0.990386i
$961$			1.05466e7i			0.368387i
$962$	1.56418e7	+	1.56418e7i	0.544939	+	0.544939i
$963$	1.10132e7	+	1.10132e7i	0.382691	+	0.382691i
$964$	−3.09318e7	+	3.09318e7i	−1.07204	+	1.07204i
$965$	1.72835e7			0.597466
$966$	−3.10868e7	+	3.10868e7i	−1.07185	+	1.07185i
$967$		−	3.24074e7i		−	1.11449i	−0.830347	−	0.557247i	$-0.811858\pi$
$967$		−	3.24074e7i		−	1.11449i	0.830347	−	0.557247i	$-0.188142\pi$
$968$	−4.16760e6			−0.142954
$969$	1.01898e7	+	8.95793e6i	0.348624	+	0.306477i
$970$	6.64022e7			2.26597
$971$		−	2.67527e7i		−	0.910582i	−0.890343	−	0.455291i	$-0.849535\pi$
$971$		−	2.67527e7i		−	0.910582i	0.890343	−	0.455291i	$-0.150465\pi$
$972$	1.59522e6	−	1.59522e6i	0.0541570	−	0.0541570i
$973$	−9.65405e6			−0.326909
$974$	2.37373e7	−	2.37373e7i	0.801740	−	0.801740i
$975$	−6.84054e6	−	6.84054e6i	−0.230451	−	0.230451i
$976$	9.71175e6	+	9.71175e6i	0.326342	+	0.326342i
$977$		−	4.21874e7i		−	1.41399i	−0.707219	−	0.706994i	$-0.750051\pi$
$977$		−	4.21874e7i		−	1.41399i	0.707219	−	0.706994i	$-0.249949\pi$
$978$		−	1.94131e7i		−	0.649003i
$979$	−1.86249e7	−	1.86249e7i	−0.621064	−	0.621064i
$980$	−7.17060e6	−	7.17060e6i	−0.238501	−	0.238501i
$981$	5.15006e6	−	5.15006e6i	0.170860	−	0.170860i
$982$	−4.81876e7			−1.59462
$983$	−3.28951e6	+	3.28951e6i	−0.108579	+	0.108579i	−0.759309	−	0.650730i	$-0.774463\pi$
$983$	−3.28951e6	+	3.28951e6i	−0.108579	+	0.108579i	0.650730	+	0.759309i	$0.274463\pi$
$984$			8.10866e6i			0.266969i
$985$	2.66867e7			0.876405
$986$	3.33692e7	+	2.93350e7i	1.09308	+	0.960934i
$987$	−6.50909e6			−0.212680
$988$			2.63212e7i			0.857854i
$989$	2.20968e7	−	2.20968e7i	0.718354	−	0.718354i
$990$	1.37836e7			0.446966
$991$	4.36870e6	−	4.36870e6i	0.141308	−	0.141308i	−0.632914	−	0.774222i	$-0.718141\pi$
$991$	4.36870e6	−	4.36870e6i	0.141308	−	0.141308i	0.774222	+	0.632914i	$0.218141\pi$
$992$	−2.48287e7	−	2.48287e7i	−0.801078	−	0.801078i
$993$	−1.06795e7	−	1.06795e7i	−0.343698	−	0.343698i
$994$		−	5.70166e7i		−	1.83035i
$995$		−	3.95408e7i		−	1.26616i
$996$	1.70214e7	+	1.70214e7i	0.543683	+	0.543683i
$997$	1.56559e7	+	1.56559e7i	0.498815	+	0.498815i	0.911069	−	0.412254i	$-0.135258\pi$
$997$	1.56559e7	+	1.56559e7i	0.498815	+	0.498815i	−0.412254	+	0.911069i	$0.635258\pi$
$998$	−3.28627e6	+	3.28627e6i	−0.104442	+	0.104442i
$999$	−3.53423e6			−0.112042

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.6.e.a.4.13	✓	32
3.2	odd	2		153.6.f.c.55.4		32
17.8	even	8		867.6.a.n.1.13		16
17.9	even	8		867.6.a.o.1.13		16
17.13	even	4	inner	51.6.e.a.13.4	yes	32
51.47	odd	4		153.6.f.c.64.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.6.e.a.4.13	✓	32	1.1	even	1	trivial
51.6.e.a.13.4	yes	32	17.13	even	4	inner
153.6.f.c.55.4		32	3.2	odd	2
153.6.f.c.64.13		32	51.47	odd	4
867.6.a.n.1.13		16	17.8	even	8
867.6.a.o.1.13		16	17.9	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	51.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+8.37886i q^{2} +(6.36396 - 6.36396i) q^{3} -38.2052 q^{4} +(50.4918 - 50.4918i) q^{5} +(53.3227 + 53.3227i) q^{6} +(101.302 + 101.302i) q^{7} -51.9926i q^{8} -81.0000i q^{9} +O(q^{10})\)	\(q+8.37886i q^{2} +(6.36396 - 6.36396i) q^{3} -38.2052 q^{4} +(50.4918 - 50.4918i) q^{5} +(53.3227 + 53.3227i) q^{6} +(101.302 + 101.302i) q^{7} -51.9926i q^{8} -81.0000i q^{9} +(423.064 + 423.064i) q^{10} +(201.114 + 201.114i) q^{11} +(-243.137 + 243.137i) q^{12} +544.563 q^{13} +(-848.794 + 848.794i) q^{14} -642.656i q^{15} -786.928 q^{16} +(-1189.12 + 76.5042i) q^{17} +678.687 q^{18} -1265.13i q^{19} +(-1929.05 + 1929.05i) q^{20} +1289.36 q^{21} +(-1685.10 + 1685.10i) q^{22} +(2877.50 + 2877.50i) q^{23} +(-330.879 - 330.879i) q^{24} -1973.85i q^{25} +4562.81i q^{26} +(-515.481 - 515.481i) q^{27} +(-3870.26 - 3870.26i) q^{28} +(-3146.71 + 3146.71i) q^{29} +5384.72 q^{30} +(3006.87 - 3006.87i) q^{31} -8257.32i q^{32} +2559.76 q^{33} +(-641.018 - 9963.46i) q^{34} +10229.8 q^{35} +3094.62i q^{36} +(3428.09 - 3428.09i) q^{37} +10600.3 q^{38} +(3465.58 - 3465.58i) q^{39} +(-2625.20 - 2625.20i) q^{40} +(-12253.2 - 12253.2i) q^{41} +10803.4i q^{42} -7679.15i q^{43} +(-7683.60 - 7683.60i) q^{44} +(-4089.84 - 4089.84i) q^{45} +(-24110.2 + 24110.2i) q^{46} -5048.30 q^{47} +(-5007.98 + 5007.98i) q^{48} +3717.16i q^{49} +16538.6 q^{50} +(-7080.64 + 8054.38i) q^{51} -20805.1 q^{52} +29278.4i q^{53} +(4319.14 - 4319.14i) q^{54} +20309.2 q^{55} +(5266.95 - 5266.95i) q^{56} +(-8051.24 - 8051.24i) q^{57} +(-26365.8 - 26365.8i) q^{58} -25359.7i q^{59} +24552.8i q^{60} +(-12341.3 - 12341.3i) q^{61} +(25194.1 + 25194.1i) q^{62} +(8205.46 - 8205.46i) q^{63} +44005.2 q^{64} +(27496.0 - 27496.0i) q^{65} +21447.9i q^{66} -47211.9 q^{67} +(45430.6 - 2922.86i) q^{68} +36624.6 q^{69} +85714.4i q^{70} +(-33586.8 + 33586.8i) q^{71} -4211.40 q^{72} +(14810.6 - 14810.6i) q^{73} +(28723.5 + 28723.5i) q^{74} +(-12561.5 - 12561.5i) q^{75} +48334.6i q^{76} +40746.4i q^{77} +(29037.6 + 29037.6i) q^{78} +(-64296.4 - 64296.4i) q^{79} +(-39733.5 + 39733.5i) q^{80} -6561.00 q^{81} +(102668. - 102668. i) q^{82} -70007.4i q^{83} -49260.4 q^{84} +(-56178.0 + 63903.6i) q^{85} +64342.5 q^{86} +40051.0i q^{87} +(10456.4 - 10456.4i) q^{88} -92608.7 q^{89} +(34268.2 - 34268.2i) q^{90} +(55165.3 + 55165.3i) q^{91} +(-109936. - 109936. i) q^{92} -38271.2i q^{93} -42299.0i q^{94} +(-63878.8 - 63878.8i) q^{95} +(-52549.3 - 52549.3i) q^{96} +(78477.8 - 78477.8i) q^{97} -31145.6 q^{98} +(16290.2 - 16290.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 576 q^{4} + 76 q^{5} - 180 q^{6} + 236 q^{7}+O(q^{10}) \) 32 * q - 576 * q^4 + 76 * q^5 - 180 * q^6 + 236 * q^7	\( 32 q - 576 q^{4} + 76 q^{5} - 180 q^{6} + 236 q^{7} + 724 q^{10} - 672 q^{11} - 2684 q^{13} + 2832 q^{14} + 8824 q^{16} - 4868 q^{17} + 1296 q^{18} + 4464 q^{20} - 3528 q^{21} - 1628 q^{22} + 5584 q^{23} + 10872 q^{24} - 36792 q^{28} + 4820 q^{29} - 1728 q^{30} + 13880 q^{31} + 7236 q^{33} + 5068 q^{34} - 12152 q^{35} - 33328 q^{37} - 29256 q^{38} - 11160 q^{39} - 43288 q^{40} - 50932 q^{41} + 116000 q^{44} - 6156 q^{45} + 47596 q^{46} - 16552 q^{47} + 27360 q^{48} + 139080 q^{50} + 12924 q^{51} + 186888 q^{52} - 14580 q^{54} - 129428 q^{55} - 117024 q^{56} + 19440 q^{57} - 212912 q^{58} + 118952 q^{61} - 219736 q^{62} + 19116 q^{63} - 143848 q^{64} + 220976 q^{65} + 98632 q^{67} + 367680 q^{68} + 156060 q^{69} - 205512 q^{71} - 62208 q^{72} - 40924 q^{73} - 178760 q^{74} - 58896 q^{75} + 87012 q^{78} - 309916 q^{79} - 664992 q^{80} - 209952 q^{81} + 350116 q^{82} + 6264 q^{84} + 335336 q^{85} + 1139576 q^{86} - 307696 q^{88} - 62680 q^{89} + 58644 q^{90} + 174460 q^{91} - 94256 q^{92} + 367240 q^{95} - 508824 q^{96} - 299020 q^{97} - 1191536 q^{98} - 54432 q^{99}+O(q^{100}) \) 32 * q - 576 * q^4 + 76 * q^5 - 180 * q^6 + 236 * q^7 + 724 * q^10 - 672 * q^11 - 2684 * q^13 + 2832 * q^14 + 8824 * q^16 - 4868 * q^17 + 1296 * q^18 + 4464 * q^20 - 3528 * q^21 - 1628 * q^22 + 5584 * q^23 + 10872 * q^24 - 36792 * q^28 + 4820 * q^29 - 1728 * q^30 + 13880 * q^31 + 7236 * q^33 + 5068 * q^34 - 12152 * q^35 - 33328 * q^37 - 29256 * q^38 - 11160 * q^39 - 43288 * q^40 - 50932 * q^41 + 116000 * q^44 - 6156 * q^45 + 47596 * q^46 - 16552 * q^47 + 27360 * q^48 + 139080 * q^50 + 12924 * q^51 + 186888 * q^52 - 14580 * q^54 - 129428 * q^55 - 117024 * q^56 + 19440 * q^57 - 212912 * q^58 + 118952 * q^61 - 219736 * q^62 + 19116 * q^63 - 143848 * q^64 + 220976 * q^65 + 98632 * q^67 + 367680 * q^68 + 156060 * q^69 - 205512 * q^71 - 62208 * q^72 - 40924 * q^73 - 178760 * q^74 - 58896 * q^75 + 87012 * q^78 - 309916 * q^79 - 664992 * q^80 - 209952 * q^81 + 350116 * q^82 + 6264 * q^84 + 335336 * q^85 + 1139576 * q^86 - 307696 * q^88 - 62680 * q^89 + 58644 * q^90 + 174460 * q^91 - 94256 * q^92 + 367240 * q^95 - 508824 * q^96 - 299020 * q^97 - 1191536 * q^98 - 54432 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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