LMFDB - Embedded newform 65.6.m.a.36.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,6,Mod(36,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("65.36");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	65.m (of order $6$, 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:	$10.4249482878$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			36.2
Character	$\chi$	$=$	65.36
Dual form			65.6.m.a.56.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.33226 + 4.81063i) q^{2} +(-13.0655 - 22.6301i) q^{3} +(30.2844 - 52.4542i) q^{4} +25.0000i q^{5} +(217.731 + 125.707i) q^{6} +(78.5374 + 45.3436i) q^{7} +274.868i q^{8} +(-219.915 + 380.904i) q^{9} +(-120.266 - 208.307i) q^{10} +(588.963 - 340.038i) q^{11} -1582.73 q^{12} +(-539.353 + 283.533i) q^{13} -872.526 q^{14} +(565.753 - 326.638i) q^{15} +(-353.191 - 611.744i) q^{16} +(489.974 - 848.660i) q^{17} -4231.73i q^{18} +(1747.20 + 1008.74i) q^{19} +(1311.35 + 757.110i) q^{20} -2369.75i q^{21} +(-3271.60 + 5666.57i) q^{22} +(-1848.24 - 3201.24i) q^{23} +(6220.31 - 3591.30i) q^{24} -625.000 q^{25} +(3130.06 - 4957.10i) q^{26} +5143.37 q^{27} +(4756.92 - 2746.41i) q^{28} +(-1488.84 - 2578.75i) q^{29} +(-3142.67 + 5443.26i) q^{30} -4154.25i q^{31} +(-1731.62 - 999.754i) q^{32} +(-15390.2 - 8885.54i) q^{33} +9428.35i q^{34} +(-1133.59 + 1963.44i) q^{35} +(13320.0 + 23070.9i) q^{36} +(-6213.06 + 3587.11i) q^{37} -19410.8 q^{38} +(13463.3 + 8501.14i) q^{39} -6871.71 q^{40} +(-7221.51 + 4169.34i) q^{41} +(11400.0 + 19745.4i) q^{42} +(199.223 - 345.064i) q^{43} -41191.4i q^{44} +(-9522.60 - 5497.88i) q^{45} +(30800.0 + 17782.4i) q^{46} -12247.0i q^{47} +(-9229.23 + 15985.5i) q^{48} +(-4291.42 - 7432.95i) q^{49} +(5207.67 - 3006.65i) q^{50} -25607.0 q^{51} +(-1461.53 + 36878.0i) q^{52} +33697.7 q^{53} +(-42856.0 + 24742.9i) q^{54} +(8500.95 + 14724.1i) q^{55} +(-12463.5 + 21587.5i) q^{56} -52719.0i q^{57} +(24810.9 + 14324.6i) q^{58} +(-7693.71 - 4441.96i) q^{59} -39568.1i q^{60} +(11282.1 - 19541.1i) q^{61} +(19984.6 + 34614.3i) q^{62} +(-34543.1 + 19943.5i) q^{63} +41842.0 q^{64} +(-7088.32 - 13483.8i) q^{65} +170980. q^{66} +(-28573.0 + 16496.7i) q^{67} +(-29677.2 - 51402.4i) q^{68} +(-48296.4 + 83651.7i) q^{69} -21813.1i q^{70} +(9690.68 + 5594.92i) q^{71} +(-104699. - 60447.7i) q^{72} -20827.1i q^{73} +(34512.5 - 59777.5i) q^{74} +(8165.94 + 14143.8i) q^{75} +(105826. - 61098.5i) q^{76} +61674.2 q^{77} +(-153076. - 6066.65i) q^{78} -75366.3 q^{79} +(15293.6 - 8829.76i) q^{80} +(-13761.4 - 23835.5i) q^{81} +(40114.4 - 69480.1i) q^{82} -80623.3i q^{83} +(-124303. - 71766.5i) q^{84} +(21216.5 + 12249.4i) q^{85} +3833.56i q^{86} +(-38905.0 + 67385.4i) q^{87} +(93465.7 + 161887. i) q^{88} +(40155.9 - 23184.0i) q^{89} +105793. q^{90} +(-55215.8 - 2188.30i) q^{91} -223891. q^{92} +(-94011.2 + 54277.4i) q^{93} +(58915.9 + 102045. i) q^{94} +(-25218.6 + 43679.9i) q^{95} +52249.2i q^{96} +(38502.2 + 22229.3i) q^{97} +(71514.4 + 41288.9i) q^{98} +299118. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 18 q^{3} + 416 q^{4} - 342 q^{6} + 546 q^{7} - 2216 q^{9} - 200 q^{10} + 504 q^{11} - 420 q^{12} + 1800 q^{13} - 1768 q^{14} + 1650 q^{15} - 7300 q^{16} - 4118 q^{17} - 3228 q^{19} - 5700 q^{20}+ \cdots + 251688 q^{98}+O(q^{100}) $ 48 * q + 18 * q^3 + 416 * q^4 - 342 * q^6 + 546 * q^7 - 2216 * q^9 - 200 * q^10 + 504 * q^11 - 420 * q^12 + 1800 * q^13 - 1768 * q^14 + 1650 * q^15 - 7300 * q^16 - 4118 * q^17 - 3228 * q^19 - 5700 * q^20 - 708 * q^22 - 4370 * q^23 + 1176 * q^24 - 30000 * q^25 - 1498 * q^26 - 26916 * q^27 + 57138 * q^28 + 2400 * q^29 - 9400 * q^30 - 68766 * q^32 - 41322 * q^33 + 11250 * q^35 + 104858 * q^36 - 3006 * q^37 + 19496 * q^38 + 84512 * q^39 - 19200 * q^40 + 7860 * q^41 + 13496 * q^42 - 65218 * q^43 + 39654 * q^46 + 136072 * q^48 + 87388 * q^49 + 28216 * q^51 + 192766 * q^52 - 61256 * q^53 + 203922 * q^54 + 40000 * q^55 - 111662 * q^56 - 121056 * q^58 - 60204 * q^59 - 36116 * q^61 + 59796 * q^62 - 331896 * q^63 - 230924 * q^64 + 53700 * q^65 - 493716 * q^66 + 11574 * q^67 + 107014 * q^68 - 113096 * q^69 - 71808 * q^71 + 199608 * q^72 + 131196 * q^74 - 11250 * q^75 + 508476 * q^76 + 324916 * q^77 - 76084 * q^78 + 279600 * q^79 - 207000 * q^80 - 237620 * q^81 + 46076 * q^82 - 148170 * q^84 + 26550 * q^85 + 113838 * q^87 + 264998 * q^88 - 557340 * q^89 + 375500 * q^90 - 344540 * q^91 - 1260284 * q^92 - 792600 * q^93 - 425238 * q^94 - 116400 * q^95 + 417390 * q^97 + 251688 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−8.33226	+	4.81063i	−1.47295	+	0.850408i	−0.999537	−	0.0304323i	$-0.990312\pi$
$2$	−8.33226	+	4.81063i	−1.47295	+	0.850408i	−0.473413	+	0.880840i	$0.656978\pi$
$3$	−13.0655	−	22.6301i	−0.838153	−	1.45172i	−0.891437	−	0.453144i	$-0.850302\pi$
$3$	−13.0655	−	22.6301i	−0.838153	−	1.45172i	0.0532845	−	0.998579i	$-0.483031\pi$
$4$	30.2844	−	52.4542i	0.946388	−	1.63919i
$5$			25.0000i			0.447214i
$5$			25.0000i			0.447214i
$6$	217.731	+	125.707i	2.46911	+	1.42554i
$7$	78.5374	+	45.3436i	0.605803	+	0.349761i	0.771321	−	0.636446i	$-0.219596\pi$
$7$	78.5374	+	45.3436i	0.605803	+	0.349761i	−0.165518	+	0.986207i	$0.552930\pi$
$8$			274.868i			1.51845i
$9$	−219.915	+	380.904i	−0.905000	+	1.56751i
$10$	−120.266	−	208.307i	−0.380314	−	0.658723i
$11$	588.963	−	340.038i	1.46760	−	0.847317i	0.468254	−	0.883594i	$-0.344883\pi$
$11$	588.963	−	340.038i	1.46760	−	0.847317i	0.999342	+	0.0362774i	$0.0115500\pi$
$12$	−1582.73			−3.17287
$13$	−539.353	+	283.533i	−0.885146	+	0.465313i
$13$	−539.353	+	283.533i	−0.885146	+	0.465313i
$14$	−872.526			−1.18976
$15$	565.753	−	326.638i	0.649230	−	0.374833i
$16$	−353.191	−	611.744i	−0.344913	−	0.597406i
$17$	489.974	−	848.660i	0.411198	−	0.712216i	−0.583823	−	0.811881i	$-0.698444\pi$
$17$	489.974	−	848.660i	0.411198	−	0.712216i	0.995021	+	0.0996653i	$0.0317772\pi$
$18$		−	4231.73i		−	3.07848i
$19$	1747.20	+	1008.74i	1.11034	+	0.641058i	0.938919	−	0.344139i	$-0.111829\pi$
$19$	1747.20	+	1008.74i	1.11034	+	0.641058i	0.171426	+	0.985197i	$0.445163\pi$
$20$	1311.35	+	757.110i	0.733069	+	0.423238i
$21$		−	2369.75i		−	1.17261i
$22$	−3271.60	+	5666.57i	−1.44113	+	2.49611i
$23$	−1848.24	−	3201.24i	−0.728515	−	1.26182i	−0.957511	−	0.288397i	$-0.906878\pi$
$23$	−1848.24	−	3201.24i	−0.728515	−	1.26182i	0.228996	−	0.973427i	$-0.426456\pi$
$24$	6220.31	−	3591.30i	2.20437	−	1.27269i
$25$	−625.000			−0.200000
$26$	3130.06	−	4957.10i	0.908071	−	1.43812i
$27$	5143.37			1.35781
$28$	4756.92	−	2746.41i	1.14665	−	0.662018i
$29$	−1488.84	−	2578.75i	−0.328741	−	0.569396i	0.653521	−	0.756908i	$-0.273291\pi$
$29$	−1488.84	−	2578.75i	−0.328741	−	0.569396i	−0.982262	+	0.187512i	$0.939958\pi$
$30$	−3142.67	+	5443.26i	−0.637523	+	1.10422i
$31$		−	4154.25i		−	0.776405i	−0.921574	−	0.388203i	$-0.873096\pi$
$31$		−	4154.25i		−	0.776405i	0.921574	−	0.388203i	$-0.126904\pi$
$32$	−1731.62	−	999.754i	−0.298936	−	0.172591i
$33$	−15390.2	−	8885.54i	−2.46014	−	1.42036i
$34$			9428.35i			1.39874i
$35$	−1133.59	+	1963.44i	−0.156418	+	0.270923i
$36$	13320.0	+	23070.9i	1.71296	+	2.96694i
$37$	−6213.06	+	3587.11i	−0.746107	+	0.430765i	−0.824285	−	0.566174i	$-0.808423\pi$
$37$	−6213.06	+	3587.11i	−0.746107	+	0.430765i	0.0781788	+	0.996939i	$0.475089\pi$
$38$	−19410.8			−2.18064
$39$	13463.3	+	8501.14i	1.41739	+	0.894984i
$40$	−6871.71			−0.679071
$41$	−7221.51	+	4169.34i	−0.670917	+	0.387354i	−0.796424	−	0.604739i	$-0.793278\pi$
$41$	−7221.51	+	4169.34i	−0.670917	+	0.387354i	0.125507	+	0.992093i	$0.459944\pi$
$42$	11400.0	+	19745.4i	0.997198	+	1.72720i
$43$	199.223	−	345.064i	0.0164312	−	0.0284596i	−0.857693	−	0.514162i	$-0.828103\pi$
$43$	199.223	−	345.064i	0.0164312	−	0.0284596i	0.874124	+	0.485703i	$0.161436\pi$
$44$		−	41191.4i		−	3.20756i
$45$	−9522.60	−	5497.88i	−0.701010	−	0.404729i
$46$	30800.0	+	17782.4i	2.14613	+	1.23907i
$47$		−	12247.0i		−	0.808696i	−0.914605	−	0.404348i	$-0.867498\pi$
$47$		−	12247.0i		−	0.808696i	0.914605	−	0.404348i	$-0.132502\pi$
$48$	−9229.23	+	15985.5i	−0.578179	+	1.00144i
$49$	−4291.42	−	7432.95i	−0.255335	−	0.442253i
$50$	5207.67	−	3006.65i	0.294590	−	0.170082i
$51$	−25607.0			−1.37859
$52$	−1461.53	+	36878.0i	−0.0749550	+	1.89129i
$53$	33697.7			1.64783			0.823913	−	0.566717i	$-0.191787\pi$
$53$	33697.7			1.64783			0.823913	+	0.566717i	$0.191787\pi$
$54$	−42856.0	+	24742.9i	−1.99999	+	1.15469i
$55$	8500.95	+	14724.1i	0.378932	+	0.656329i
$56$	−12463.5	+	21587.5i	−0.531093	+	0.919881i
$57$		−	52719.0i		−	2.14922i
$58$	24810.9	+	14324.6i	0.968438	+	0.559128i
$59$	−7693.71	−	4441.96i	−0.287744	−	0.166129i	0.349180	−	0.937056i	$-0.386460\pi$
$59$	−7693.71	−	4441.96i	−0.287744	−	0.166129i	−0.636924	+	0.770927i	$0.719793\pi$
$60$		−	39568.1i		−	1.41895i
$61$	11282.1	−	19541.1i	0.388208	−	0.672396i	−0.604001	−	0.796984i	$-0.706428\pi$
$61$	11282.1	−	19541.1i	0.388208	−	0.672396i	0.992209	+	0.124588i	$0.0397609\pi$
$62$	19984.6	+	34614.3i	0.660261	+	1.14361i
$63$	−34543.1	+	19943.5i	−1.09650	+	0.633067i
$64$	41842.0			1.27692
$65$	−7088.32	−	13483.8i	−0.208094	−	0.395849i
$66$	170980.			4.83155
$67$	−28573.0	+	16496.7i	−0.777624	+	0.448961i	−0.835588	−	0.549357i	$-0.814873\pi$
$67$	−28573.0	+	16496.7i	−0.777624	+	0.448961i	0.0579637	+	0.998319i	$0.481539\pi$
$68$	−29677.2	−	51402.4i	−0.778305	−	1.34806i
$69$	−48296.4	+	83651.7i	−1.22121	+	2.11520i
$70$		−	21813.1i		−	0.532076i
$71$	9690.68	+	5594.92i	0.228144	+	0.131719i	0.609715	−	0.792620i	$-0.291284\pi$
$71$	9690.68	+	5594.92i	0.228144	+	0.131719i	−0.381572	+	0.924339i	$0.624617\pi$
$72$	−104699.	−	60447.7i	−2.38018	−	1.37420i
$73$		−	20827.1i		−	0.457427i	−0.973494	−	0.228713i	$-0.926548\pi$
$73$		−	20827.1i		−	0.457427i	0.973494	−	0.228713i	$-0.0734518\pi$
$74$	34512.5	−	59777.5i	0.732652	−	1.26899i
$75$	8165.94	+	14143.8i	0.167631	+	0.290345i
$76$	105826.	−	61098.5i	2.10163	−	1.21338i
$77$	61674.2			1.18543
$78$	−153076.	−	6066.65i	−2.84885	−	0.112905i
$79$	−75366.3			−1.35866			−0.679328	−	0.733835i	$-0.737729\pi$
$79$	−75366.3			−1.35866			−0.679328	+	0.733835i	$0.737729\pi$
$80$	15293.6	−	8829.76i	0.267168	−	0.154250i
$81$	−13761.4	−	23835.5i	−0.233051	−	0.403657i
$82$	40114.4	−	69480.1i	0.658818	−	1.14111i
$83$		−	80623.3i		−	1.28459i	−0.766456	−	0.642296i	$-0.777982\pi$
$83$		−	80623.3i		−	1.28459i	0.766456	−	0.642296i	$-0.222018\pi$
$84$	−124303.	−	71766.5i	−1.92214	−	1.10975i
$85$	21216.5	+	12249.4i	0.318512	+	0.183893i
$86$			3833.56i			0.0558928i
$87$	−38905.0	+	67385.4i	−0.551070	+	0.954482i
$88$	93465.7	+	161887.i	1.28661	+	2.22847i
$89$	40155.9	−	23184.0i	0.537371	−	0.310251i	−0.206642	−	0.978417i	$-0.566254\pi$
$89$	40155.9	−	23184.0i	0.537371	−	0.310251i	0.744013	+	0.668165i	$0.232920\pi$
$90$	105793.			1.37674
$91$	−55215.8	−	2188.30i	−0.698972	−	0.0277014i
$92$	−223891.			−2.75783
$93$	−94011.2	+	54277.4i	−1.12713	+	0.650746i
$94$	58915.9	+	102045.i	0.687722	+	1.19117i
$95$	−25218.6	+	43679.9i	−0.286690	+	0.496561i
$96$			52249.2i			0.578631i
$97$	38502.2	+	22229.3i	0.415486	+	0.239881i	0.693144	−	0.720799i	$-0.256225\pi$
$97$	38502.2	+	22229.3i	0.415486	+	0.239881i	−0.277658	+	0.960680i	$0.589558\pi$
$98$	71514.4	+	41288.9i	0.752192	+	0.434278i
$99$			299118.i			3.06729i
$100$	−18927.8	+	32783.8i	−0.189278	+	0.327838i
$101$	−65184.8	−	112903.i	−0.635832	−	1.10129i	−0.986338	−	0.164734i	$-0.947324\pi$
$101$	−65184.8	−	112903.i	−0.635832	−	1.10129i	0.350506	−	0.936561i	$-0.386010\pi$
$102$	213365.	−	123186.i	2.03059	−	1.17236i
$103$	156988.			1.45806			0.729028	−	0.684483i	$-0.239972\pi$
$103$	156988.			1.45806			0.729028	+	0.684483i	$0.239972\pi$
$104$	−77934.2	−	148251.i	−0.706553	−	1.34405i
$105$	59243.7			0.524408
$106$	−280779.	+	162108.i	−2.42716	+	1.40132i
$107$	−80000.0	−	138564.i	−0.675508	−	1.17001i	−0.976320	−	0.216331i	$-0.930591\pi$
$107$	−80000.0	−	138564.i	−0.675508	−	1.17001i	0.300812	−	0.953683i	$-0.402742\pi$
$108$	155764.	−	269791.i	1.28501	−	2.22571i
$109$		−	236821.i		−	1.90921i	−0.297875	−	0.954605i	$-0.596278\pi$
$109$		−	236821.i		−	1.90921i	0.297875	−	0.954605i	$-0.403722\pi$
$110$	−141664.	−	81789.9i	−1.11629	−	0.644493i
$111$	162353.	+	93734.8i	1.25070	+	0.722094i
$112$		−	64059.7i		−	0.482547i
$113$	−47637.8	+	82511.1i	−0.350958	+	0.607877i	−0.986418	−	0.164257i	$-0.947477\pi$
$113$	−47637.8	+	82511.1i	−0.350958	+	0.607877i	0.635459	+	0.772134i	$0.280811\pi$
$114$	253612.	+	439269.i	1.82771	+	3.16569i
$115$	80031.1	−	46206.0i	0.564305	−	0.325802i
$116$	−180355.			−1.24447
$117$	10613.2	−	267795.i	0.0716771	−	1.80858i
$118$	85474.6			0.565109
$119$	76962.6	−	44434.4i	0.498210	−	0.287642i
$120$	89782.4	+	155508.i	0.569165	+	0.985823i
$121$	150726.	−	261065.i	0.935891	−	1.62101i
$122$			217096.i			1.32054i
$123$	188706.	+	108949.i	1.12466	+	0.649324i
$124$	−217908.	−	125809.i	−1.27268	−	0.734781i
$125$		−	15625.0i		−	0.0894427i
$126$	191882.	−	332349.i	1.07673	−	1.86495i
$127$	4340.90	+	7518.66i	0.0238820	+	0.0413648i	0.877719	−	0.479175i	$-0.159064\pi$
$127$	4340.90	+	7518.66i	0.0238820	+	0.0413648i	−0.853837	+	0.520540i	$0.825731\pi$
$128$	−293227.	+	169294.i	−1.58190	+	0.913309i
$129$	−10411.8			−0.0550873
$130$	123928.	+	78251.6i	0.643146	+	0.406102i
$131$	−138882.			−0.707076			−0.353538	−	0.935420i	$-0.615022\pi$
$131$	−138882.			−0.707076			−0.353538	+	0.935420i	$0.615022\pi$
$132$	−932167.	+	538187.i	−4.65649	+	2.68843i
$133$	91480.2	+	158448.i	0.448434	+	0.776710i
$134$	158719.	−	274909.i	0.763601	−	1.32260i
$135$			128584.i			0.607231i
$136$	233270.	+	134678.i	1.08146	+	0.624383i
$137$	191228.	+	110406.i	0.870464	+	0.502563i	0.867502	−	0.497433i	$-0.165724\pi$
$137$	191228.	+	110406.i	0.870464	+	0.502563i	0.00296165	+	0.999996i	$0.499057\pi$
$138$		−	929345.i		−	4.15412i
$139$	−38502.5	+	66688.2i	−0.169025	+	0.292760i	−0.938077	−	0.346426i	$-0.887395\pi$
$139$	−38502.5	+	66688.2i	−0.169025	+	0.292760i	0.769052	+	0.639186i	$0.220729\pi$
$140$	68660.2	+	118923.i	0.296064	+	0.512797i
$141$	−277151.	+	160013.i	−1.17400	+	0.677811i
$142$	−107660.			−0.448059
$143$	−221247.	+	350391.i	−0.904770	+	1.43289i
$144$	310688.			1.24858
$145$	64468.8	−	37221.1i	0.254642	−	0.147017i
$146$	100192.	+	173537.i	0.388999	+	0.673766i
$147$	−112139.	+	194231.i	−0.428020	+	0.741352i
$148$			434534.i			1.63068i
$149$	−378453.	−	218500.i	−1.39652	−	0.806280i	−0.402492	−	0.915424i	$-0.631856\pi$
$149$	−378453.	−	218500.i	−1.39652	−	0.806280i	−0.994026	+	0.109144i	$0.965189\pi$
$150$	−136082.	−	78566.8i	−0.493823	−	0.285109i
$151$		−	19270.2i		−	0.0687772i	−0.999409	−	0.0343886i	$-0.989052\pi$
$151$		−	19270.2i		−	0.0687772i	0.999409	−	0.0343886i	$-0.0109484\pi$
$152$	−277272.	+	480249.i	−0.973413	+	1.68600i
$153$	215505.	+	373266.i	0.744269	+	1.28911i
$154$	−513886.	+	296692.i	−1.74608	+	1.00810i
$155$	103856.			0.347219
$156$	853648.	−	448755.i	2.80846	−	1.47638i
$157$	−248330.			−0.804045			−0.402023	−	0.915630i	$-0.631693\pi$
$157$	−248330.			−0.804045			−0.402023	+	0.915630i	$0.631693\pi$
$158$	627972.	−	362560.i	2.00123	−	1.15541i
$159$	−440278.	−	762584.i	−1.38113	−	2.39219i
$160$	24993.8	−	43290.6i	0.0771850	−	0.133688i
$161$		−	335223.i		−	1.01922i
$162$	229328.	+	132403.i	0.686546	+	0.396377i
$163$	249389.	+	143985.i	0.735206	+	0.424471i	0.820324	−	0.571900i	$-0.193793\pi$
$163$	249389.	+	143985.i	0.735206	+	0.424471i	−0.0851178	+	0.996371i	$0.527127\pi$
$164$			505065.i			1.46635i
$165$	222138.	−	384755.i	0.635205	−	1.10021i
$166$	387849.	+	671775.i	1.09243	+	1.89214i
$167$	412298.	−	238041.i	1.14399	−	0.660480i	0.196571	−	0.980490i	$-0.437019\pi$
$167$	412298.	−	238041.i	1.14399	−	0.660480i	0.947414	+	0.320009i	$0.103686\pi$
$168$	651369.			1.78055
$169$	210511.	−	305849.i	0.566968	−	0.823740i
$170$	−235709.			−0.625537
$171$	−768470.	+	443676.i	−2.00972	+	1.16032i
$172$	−12066.7	−	20900.1i	−0.0311005	−	0.0538677i
$173$	−166461.	+	288319.i	−0.422860	+	0.732415i	−0.996218	−	0.0868898i	$-0.972307\pi$
$173$	−166461.	+	288319.i	−0.422860	+	0.732415i	0.573358	+	0.819305i	$0.305641\pi$
$174$		−	748631.i		−	1.87454i
$175$	−49085.9	−	28339.7i	−0.121161	−	0.0699521i
$176$	−416032.	−	240196.i	−1.01238	−	0.584500i
$177$			232146.i			0.556965i
$178$	−223060.	+	386350.i	−0.527680	+	0.913969i
$179$	−53445.9	−	92571.0i	−0.124676	−	0.215945i	0.796930	−	0.604071i	$-0.206456\pi$
$179$	−53445.9	−	92571.0i	−0.124676	−	0.215945i	−0.921606	+	0.388126i	$0.873122\pi$
$180$	−576773.	+	333000.i	−1.32686	+	0.766060i
$181$	−257132.			−0.583391			−0.291696	−	0.956511i	$-0.594219\pi$
$181$	−257132.			−0.583391			−0.291696	+	0.956511i	$0.594219\pi$
$182$	470600.	−	247390.i	1.05311	−	0.553609i
$183$	−589624.			−1.30151
$184$	879921.	−	508023.i	1.91602	−	1.10621i
$185$	−89677.7	−	155326.i	−0.192644	−	0.333669i
$186$	522218.	−	904508.i	1.10680	−	1.91703i
$187$		−	666439.i		−	1.39366i
$188$	−642407.	−	370894.i	−1.32561	−	0.765341i
$189$	403947.	+	233219.i	0.822565	+	0.474908i
$190$		−	485270.i		−	0.975213i
$191$	153668.	−	266160.i	0.304789	−	0.527910i	−0.672425	−	0.740165i	$-0.734747\pi$
$191$	153668.	−	266160.i	0.304789	−	0.527910i	0.977214	+	0.212255i	$0.0680808\pi$
$192$	−546687.	−	946890.i	−1.07025	−	1.85373i
$193$	−658542.	+	380209.i	−1.27260	+	0.734733i	−0.975476	−	0.220107i	$-0.929359\pi$
$193$	−658542.	+	380209.i	−1.27260	+	0.734733i	−0.297120	+	0.954840i	$0.596026\pi$
$194$	−427748.			−0.815987
$195$	−212528.	+	336583.i	−0.400249	+	0.633878i
$196$	−519852.			−0.966584
$197$	740781.	−	427690.i	1.35995	−	0.785170i	0.370337	−	0.928898i	$-0.379242\pi$
$197$	740781.	−	427690.i	1.35995	−	0.785170i	0.989617	+	0.143728i	$0.0459090\pi$
$198$	−1.43895e6	−	2.49233e6i	−2.60845	−	4.51796i
$199$	−388892.	+	673581.i	−0.696140	+	1.20575i	0.273655	+	0.961828i	$0.411767\pi$
$199$	−388892.	+	673581.i	−0.696140	+	1.20575i	−0.969795	+	0.243921i	$0.921566\pi$
$200$		−	171793.i		−	0.303690i
$201$	746643.	+	431074.i	1.30354	+	0.752596i
$202$	1.08627e6	+	627160.i	1.87310	+	1.08143i
$203$		−	270038.i		−	0.459923i
$204$	−775495.	+	1.34320e6i	−1.30468	+	2.25977i
$205$	−104234.	−	180538.i	−0.173230	−	0.300043i
$206$	−1.30807e6	+	755214.i	−2.14765	+	1.23994i
$207$	1.62582e6			2.63723
$208$	363944.	+	229805.i	0.583279	+	0.368300i
$209$	1.37205e6			2.17272
$210$	−493634.	+	285000.i	−0.772426	+	0.445961i
$211$	538486.	+	932686.i	0.832662	+	1.44221i	0.895920	+	0.444215i	$0.146517\pi$
$211$	538486.	+	932686.i	0.832662	+	1.44221i	−0.0632583	+	0.997997i	$0.520149\pi$
$212$	1.02052e6	−	1.76759e6i	1.55948	−	2.70110i
$213$		−	292402.i		−	0.441602i
$214$	1.33316e6	+	769702.i	1.98998	+	1.14892i
$215$	8626.61	+	4980.57i	0.0127275	+	0.00734824i
$216$			1.41375e6i			2.06176i
$217$	188369.	−	326264.i	0.271556	−	0.470349i
$218$	1.13926e6	+	1.97325e6i	1.62361	+	2.81217i
$219$	−471320.	+	272117.i	−0.664057	+	0.383393i
$220$	1.02979e6			1.43447
$221$	−23646.3	+	596651.i	−0.0325673	+	0.821751i
$222$	−1.80370e6			−2.45630
$223$	393575.	−	227230.i	0.529987	−	0.305988i	−0.211024	−	0.977481i	$-0.567680\pi$
$223$	393575.	−	227230.i	0.529987	−	0.305988i	0.741011	+	0.671493i	$0.234347\pi$
$224$	−90664.9	−	157036.i	−0.120731	−	0.209112i
$225$	137447.	−	238065.i	0.181000	−	0.313501i
$226$		−	916672.i		−	1.19383i
$227$	−402105.	−	232155.i	−0.517934	−	0.299030i	0.218155	−	0.975914i	$-0.429996\pi$
$227$	−402105.	−	232155.i	−0.517934	−	0.299030i	−0.736089	+	0.676885i	$0.763330\pi$
$228$	−2.76533e6	−	1.59657e6i	−3.52298	−	2.03399i
$229$			163066.i			0.205482i	0.994708	+	0.102741i	$0.0327613\pi$
$229$			163066.i			0.205482i	−0.994708	+	0.102741i	$0.967239\pi$
$230$	−444560.	+	770001.i	−0.554129	+	0.959779i
$231$	−805805.	−	1.39569e6i	−0.993573	−	1.72092i
$232$	708818.	−	409236.i	0.864599	−	0.499176i
$233$	879981.			1.06190			0.530950	−	0.847403i	$-0.321835\pi$
$233$	879981.			1.06190			0.530950	+	0.847403i	$0.321835\pi$
$234$	1.19983e6	+	2.28240e6i	1.43246	+	2.72490i
$235$	306175.			0.361660
$236$	−465999.	+	269045.i	−0.544634	+	0.314445i
$237$	984699.	+	1.70555e6i	1.13876	+	1.97239i
$238$	−427515.	+	740478.i	−0.489226	+	0.847363i
$239$			282603.i			0.320024i	0.987115	+	0.160012i	$0.0511533\pi$
$239$			282603.i			0.320024i	−0.987115	+	0.160012i	$0.948847\pi$
$240$	−399637.	−	230731.i	−0.447856	−	0.258570i
$241$	488757.	+	282184.i	0.542064	+	0.312961i	0.745915	−	0.666041i	$-0.232012\pi$
$241$	488757.	+	282184.i	0.542064	+	0.312961i	−0.203851	+	0.979002i	$0.565346\pi$
$242$			2.90035e6i			3.18356i
$243$	265320.	−	459547.i	0.288240	−	0.499245i
$244$	−683342.	−	1.18358e6i	−0.734791	−	1.27270i
$245$	185824.	−	107285.i	0.197782	−	0.114189i
$246$	−2.09646e6			−2.20876
$247$	−1.22837e6	−	48682.3i	−1.28111	−	0.0507725i
$248$	1.14187e6			1.17893
$249$	−1.82452e6	+	1.05338e6i	−1.86487	+	1.07668i
$250$	75166.2	+	130192.i	0.0760628	+	0.131745i
$251$	13980.9	−	24215.7i	0.0140072	−	0.0242612i	−0.858937	−	0.512082i	$-0.828875\pi$
$251$	13980.9	−	24215.7i	0.0140072	−	0.0242612i	0.872944	+	0.487820i	$0.162208\pi$
$252$			2.41591e6i			2.39651i
$253$	−2.17709e6	−	1.25694e6i	−2.13833	−	1.23457i
$254$	−72339.1	−	41765.0i	−0.0703540	−	0.0406189i
$255$		−	640176.i		−	0.616523i
$256$	959356.	−	1.66165e6i	0.914913	−	1.58468i
$257$	14568.8	+	25233.9i	0.0137591	+	0.0238315i	0.872823	−	0.488037i	$-0.162287\pi$
$257$	14568.8	+	25233.9i	0.0137591	+	0.0238315i	−0.859064	+	0.511868i	$0.828954\pi$
$258$	86753.8	−	50087.4i	0.0811408	−	0.0468467i
$259$	−650610.			−0.602658
$260$	−921949.	−	36538.4i	−0.845811	−	0.0335209i
$261$	1.30968e6			1.19004
$262$	1.15720e6	−	668108.i	1.04149	−	0.601303i
$263$	889158.	+	1.54007e6i	0.792665	+	1.37294i	0.924312	+	0.381639i	$0.124640\pi$
$263$	889158.	+	1.54007e6i	0.792665	+	1.37294i	−0.131647	+	0.991297i	$0.542027\pi$
$264$	2.44235e6	−	4.23028e6i	2.15675	−	3.73559i
$265$			842444.i			0.736930i
$266$	−1.52447e6	−	880156.i	−1.32104	−	0.762703i
$267$	−1.04931e6	−	605822.i	−0.900798	−	0.520076i
$268$			1.99837e6i			1.69957i
$269$	−51837.3	+	89784.9i	−0.0436779	+	0.0756523i	−0.887038	−	0.461697i	$-0.847241\pi$
$269$	−51837.3	+	89784.9i	−0.0436779	+	0.0756523i	0.843360	+	0.537349i	$0.180574\pi$
$270$	−618572.	−	1.07140e6i	−0.516394	−	0.894421i
$271$	318728.	−	184018.i	0.263631	−	0.152208i	−0.362359	−	0.932039i	$-0.618028\pi$
$271$	318728.	−	184018.i	0.263631	−	0.152208i	0.625990	+	0.779831i	$0.284695\pi$
$272$	−692217.			−0.567309
$273$	671901.	+	1.27813e6i	0.545631	+	1.03793i
$274$	−2.12449e6			−1.70953
$275$	−368102.	+	212524.i	−0.293519	+	0.169463i
$276$	2.92525e6	+	5.06669e6i	2.31148	+	4.00361i
$277$	575658.	−	997069.i	0.450781	−	0.780775i	−0.547654	−	0.836705i	$-0.684479\pi$
$277$	575658.	−	997069.i	0.450781	−	0.780775i	0.998435	+	0.0559300i	$0.0178124\pi$
$278$		−	740885.i		−	0.574962i
$279$	1.58237e6	+	913583.i	1.21702	+	0.702647i
$280$	−539686.	−	311588.i	−0.411383	−	0.237512i
$281$			412283.i			0.311479i	0.987798	+	0.155740i	$0.0497761\pi$
$281$			412283.i			0.311479i	−0.987798	+	0.155740i	$0.950224\pi$
$282$	1.53953e6	−	2.66655e6i	1.15283	−	1.99676i
$283$	−434358.	−	752329.i	−0.322390	−	0.558395i	0.658591	−	0.752501i	$-0.271153\pi$
$283$	−434358.	−	752329.i	−0.322390	−	0.558395i	−0.980981	+	0.194106i	$0.937819\pi$
$284$	586953.	−	338878.i	0.431825	−	0.249314i
$285$	1.31798e6			0.961159
$286$	157888.	−	3.98389e6i	0.114139	−	2.88000i
$287$	−756212.			−0.541925
$288$	761621.	−	439722.i	0.541075	−	0.312390i
$289$	229779.	+	397989.i	0.161833	+	0.280302i
$290$	−358114.	+	620272.i	−0.250050	+	0.433099i
$291$		−	1.16175e6i		−	0.804228i
$292$	−1.09247e6	−	630736.i	−0.749810	−	0.432903i
$293$	−1.22748e6	−	708684.i	−0.835304	−	0.482263i	0.0203615	−	0.999793i	$-0.493518\pi$
$293$	−1.22748e6	−	708684.i	−0.835304	−	0.482263i	−0.855665	+	0.517530i	$0.826852\pi$
$294$		−	2.15784e6i		−	1.45597i
$295$	111049.	−	192343.i	0.0742951	−	0.128683i
$296$	−985983.	−	1.70777e6i	−0.654094	−	1.13292i
$297$	3.02926e6	−	1.74894e6i	1.99271	−	1.15049i
$298$	4.20450e6			2.74267
$299$	1.90451e6	+	1.20257e6i	1.23199	+	0.777912i
$300$	989203.			0.634574
$301$	31292.9	−	18067.0i	0.0199081	−	0.0114939i
$302$	92702.1	+	160565.i	0.0584887	+	0.101305i
$303$	−1.70334e6	+	2.95028e6i	−1.06585	+	1.84611i
$304$		−	1.42512e6i		−	0.884436i
$305$	488528.	+	282052.i	0.300705	+	0.173612i
$306$	−3.59130e6	−	2.07344e6i	−2.19254	−	1.26586i
$307$			113476.i			0.0687158i	0.999410	+	0.0343579i	$0.0109386\pi$
$307$			113476.i			0.0687158i	−0.999410	+	0.0343579i	$0.989061\pi$
$308$	1.86777e6	−	3.23507e6i	1.12188	−	1.94315i
$309$	−2.05113e6	−	3.55267e6i	−1.22207	−	2.11670i
$310$	−865358.	+	499615.i	−0.511436	+	0.295278i
$311$	−1.13044e6			−0.662746			−0.331373	−	0.943500i	$-0.607512\pi$
$311$	−1.13044e6			−0.662746			−0.331373	+	0.943500i	$0.607512\pi$
$312$	−2.33669e6	+	3.70064e6i	−1.35899	+	2.15224i
$313$	−1.44445e6			−0.833379			−0.416690	−	0.909049i	$-0.636810\pi$
$313$	−1.44445e6			−0.833379			−0.416690	+	0.909049i	$0.636810\pi$
$314$	2.06915e6	−	1.19463e6i	1.18432	−	0.683766i
$315$	−498587.	−	863578.i	−0.283116	−	0.490372i
$316$	−2.28242e6	+	3.95328e6i	−1.28582	+	2.22710i
$317$			1.27897e6i			0.714847i	0.933942	+	0.357424i	$0.116345\pi$
$317$			1.27897e6i			0.714847i	−0.933942	+	0.357424i	$0.883655\pi$
$318$	7.33703e6	+	4.23604e6i	4.06867	+	2.34905i
$319$	−1.75375e6	−	1.01253e6i	−0.964918	−	0.557095i
$320$			1.04605e6i			0.571054i
$321$	−2.09048e6	+	3.62082e6i	−1.13236	+	1.96130i
$322$	1.61264e6	+	2.79317e6i	0.866756	+	1.50126i
$323$	1.71216e6	−	988517.i	0.913143	−	0.527203i
$324$	−1.66703e6			−0.882228
$325$	337096.	−	177208.i	0.177029	−	0.0930625i
$326$	−2.77064e6			−1.44390
$327$	−5.35929e6	+	3.09418e6i	−2.77164	+	1.60021i
$328$	−1.14602e6	−	1.98497e6i	−0.588177	−	1.01875i
$329$	555324.	−	961849.i	0.282850	−	0.489911i
$330$			4.27451e6i			2.16073i
$331$	1.68142e6	+	970767.i	0.843540	+	0.487018i	0.858466	−	0.512871i	$-0.171418\pi$
$331$	1.68142e6	+	970767.i	0.843540	+	0.487018i	−0.0149261	+	0.999889i	$0.504751\pi$
$332$	−4.22903e6	−	2.44163e6i	−2.10569	−	1.21572i
$333$		−	3.15544e6i		−	1.55937i
$334$	−2.29025e6	+	3.96683e6i	−1.12336	+	1.94571i
$335$	−412416.	−	714326.i	−0.200782	−	0.347764i
$336$	−1.44968e6	+	836973.i	−0.700525	+	0.404449i
$337$	3.07122e6			1.47311			0.736556	−	0.676376i	$-0.236451\pi$
$337$	3.07122e6			1.47311			0.736556	+	0.676376i	$0.236451\pi$
$338$	−282709.	+	3.56111e6i	−0.134601	+	1.69548i
$339$	2.48965e6			1.17663
$340$	1.28506e6	−	741929.i	0.602873	−	0.348069i
$341$	−1.41260e6	−	2.44670e6i	−0.657861	−	1.13945i
$342$	4.26873e6	−	7.39366e6i	1.97348	−	3.41817i
$343$		−	2.30253e6i		−	1.05675i
$344$	94847.3	+	54760.1i	0.0432144	+	0.0249499i
$345$	−2.09129e6	−	1.20741e6i	−0.945948	−	0.546143i
$346$		−	3.20313e6i		−	1.43842i
$347$	−441626.	+	764919.i	−0.196893	+	0.341029i	−0.947520	−	0.319698i	$-0.896419\pi$
$347$	−441626.	+	764919.i	−0.196893	+	0.341029i	0.750626	+	0.660727i	$0.229752\pi$
$348$	2.35643e6	+	4.08146e6i	1.04305	+	1.80662i
$349$	−222508.	+	128465.i	−0.0977874	+	0.0564576i	−0.548096	−	0.836415i	$-0.684647\pi$
$349$	−222508.	+	128465.i	−0.0977874	+	0.0564576i	0.450309	+	0.892873i	$0.351314\pi$
$350$	545329.			0.237951
$351$	−2.77410e6	+	1.45832e6i	−1.20186	+	0.631806i
$352$	−1.35982e6			−0.584957
$353$	2.52398e6	−	1.45722e6i	1.07808	−	0.622428i	0.147700	−	0.989032i	$-0.452813\pi$
$353$	2.52398e6	−	1.45722e6i	1.07808	−	0.622428i	0.930377	+	0.366604i	$0.119480\pi$
$354$	−1.11677e6	−	1.93430e6i	−0.473648	−	0.820382i
$355$	−139873.	+	242267.i	−0.0589064	+	0.102029i
$356$		−	2.80846e6i		−	1.17447i
$357$	−2.01111e6	−	1.16112e6i	−0.835152	−	0.482175i
$358$	890651.	+	514217.i	0.367282	+	0.212050i
$359$			484108.i			0.198247i	0.995075	+	0.0991234i	$0.0316039\pi$
$359$			484108.i			0.198247i	−0.995075	+	0.0991234i	$0.968396\pi$
$360$	1.51119e6	−	2.61746e6i	0.614559	−	1.06445i
$361$	797082.	+	1.38059e6i	0.321910	+	0.557565i
$362$	2.14249e6	−	1.23697e6i	0.859306	−	0.496121i
$363$	−7.87726e6			−3.13768
$364$	−1.78696e6	+	2.83003e6i	−0.706907	+	1.11953i
$365$	520677.			0.204567
$366$	4.91291e6	−	2.83647e6i	1.91706	−	1.10682i
$367$	−987085.	−	1.70968e6i	−0.382551	−	0.662598i	0.608875	−	0.793266i	$-0.291621\pi$
$367$	−987085.	−	1.70968e6i	−0.382551	−	0.662598i	−0.991426	+	0.130668i	$0.958288\pi$
$368$	−1.30556e6	+	2.26130e6i	−0.502548	+	0.870439i
$369$		−	3.66761e6i		−	1.40222i
$370$	1.49444e6	+	862814.i	0.567510	+	0.327652i
$371$	2.64653e6	+	1.52798e6i	0.998258	+	0.576344i
$372$			6.57504e6i			2.46343i
$373$	−1.04728e6	+	1.81394e6i	−0.389753	+	0.675072i	−0.992416	−	0.122924i	$-0.960773\pi$
$373$	−1.04728e6	+	1.81394e6i	−0.389753	+	0.675072i	0.602663	+	0.797996i	$0.294106\pi$
$374$	3.20600e6	+	5.55295e6i	1.18518	+	2.05279i
$375$	−353596.	+	204149.i	−0.129846	+	0.0749667i
$376$	3.36632e6			1.22796
$377$	1.53417e6	+	968723.i	0.555931	+	0.351032i
$378$	−4.48773e6			−1.61546
$379$	2.42215e6	−	1.39843e6i	0.866169	−	0.500083i	9.57450e−5	−	1.00000i	$-0.499970\pi$
$379$	2.42215e6	−	1.39843e6i	0.866169	−	0.500083i	0.866073	+	0.499917i	$0.166636\pi$
$380$	1.52746e6	+	2.64564e6i	0.542640	+	0.939879i
$381$	113432.	−	196470.i	0.0400335	−	0.0693401i
$382$			2.95696e6i			1.03678i
$383$	−1.46265e6	−	844463.i	−0.509500	−	0.294160i	0.223128	−	0.974789i	$-0.428373\pi$
$383$	−1.46265e6	−	844463.i	−0.509500	−	0.294160i	−0.732628	+	0.680629i	$0.761707\pi$
$384$	7.66231e6	+	4.42384e6i	2.65174	+	1.53099i
$385$			1.54185e6i			0.530141i
$386$	3.65810e6	−	6.33601e6i	1.24965	−	2.16445i
$387$	87624.3	+	151770.i	0.0297404	+	0.0515119i
$388$	2.33204e6	−	1.34640e6i	0.786422	−	0.454041i
$389$	−3.52645e6			−1.18158			−0.590791	−	0.806824i	$-0.701184\pi$
$389$	−3.52645e6			−1.18158			−0.590791	+	0.806824i	$0.701184\pi$
$390$	151666.	−	3.82689e6i	0.0504925	−	1.27405i
$391$	−3.62236e6			−1.19825
$392$	2.04308e6	−	1.17958e6i	0.671539	−	0.387713i
$393$	1.81456e6	+	3.14291e6i	0.592638	+	1.02648i
$394$	−4.11492e6	+	7.12725e6i	−1.33543	+	2.31303i
$395$		−	1.88416e6i		−	0.607609i
$396$	1.56900e7	+	9.05861e6i	5.02787	+	2.90284i
$397$	−2.06826e6	−	1.19411e6i	−0.658609	−	0.380248i	0.133138	−	0.991098i	$-0.457495\pi$
$397$	−2.06826e6	−	1.19411e6i	−0.658609	−	0.380248i	−0.791747	+	0.610849i	$0.790828\pi$
$398$		−	7.48327e6i		−	2.36801i
$399$	2.39047e6	−	4.14042e6i	0.751712	−	1.30200i
$400$	220744.	+	382340.i	0.0689825	+	0.119481i
$401$	1.55743e6	−	899182.i	0.483668	−	0.279246i	−0.238276	−	0.971198i	$-0.576582\pi$
$401$	1.55743e6	−	899182.i	0.483668	−	0.279246i	0.721944	+	0.691952i	$0.243249\pi$
$402$	−8.29497e6			−2.56006
$403$	1.17787e6	+	2.24061e6i	0.361271	+	0.687232i
$404$	−7.89633e6			−2.40698
$405$	595888.	−	344036.i	0.180521	−	0.104224i
$406$	1.29905e6	+	2.25003e6i	0.391122	+	0.677443i
$407$	−2.43951e6	+	4.22535e6i	−0.729988	+	1.26438i
$408$		−	7.03857e6i		−	2.09331i
$409$	−2.47847e6	−	1.43094e6i	−0.732614	−	0.422975i	0.0867639	−	0.996229i	$-0.472347\pi$
$409$	−2.47847e6	−	1.43094e6i	−0.732614	−	0.422975i	−0.819378	+	0.573254i	$0.805681\pi$
$410$	1.73700e6	+	1.00286e6i	0.510318	+	0.294632i
$411$		−	5.77003e6i		−	1.68490i
$412$	4.75430e6	−	8.23469e6i	1.37989	−	2.39004i
$413$	−402829.	−	697721.i	−0.116211	−	0.201283i
$414$	−1.35468e7	+	7.82124e6i	−3.88450	+	2.24272i
$415$	2.01558e6			0.574487
$416$	1.21742e6	+	48248.4i	0.344911	+	0.0136694i
$417$	2.01222e6			0.566676
$418$	−1.14322e7	+	6.60041e6i	−3.20030	+	1.84770i
$419$	−1.06475e6	−	1.84420e6i	−0.296286	−	0.513183i	0.678997	−	0.734141i	$-0.262415\pi$
$419$	−1.06475e6	−	1.84420e6i	−0.296286	−	0.513183i	−0.975283	+	0.220958i	$0.929082\pi$
$420$	1.79416e6	−	3.10758e6i	0.496293	−	0.859605i
$421$		−	192346.i		−	0.0528906i	−0.999650	−	0.0264453i	$-0.991581\pi$
$421$		−	192346.i		−	0.0528906i	0.999650	−	0.0264453i	$-0.00841879\pi$
$422$	−8.97362e6	−	5.18092e6i	−2.45294	−	1.41620i
$423$	4.66494e6	+	2.69330e6i	1.26764	+	0.731871i
$424$			9.26245e6i			2.50214i
$425$	−306234.	+	530413.i	−0.0822396	+	0.142443i
$426$	1.40664e6	+	2.43637e6i	0.375542	+	0.650458i
$427$	1.77213e6	−	1.02314e6i	0.470355	−	0.271560i
$428$	−9.69102e6			−2.55717
$429$	1.08201e7	+	428819.i	2.83850	+	0.112494i
$430$	−95838.9			−0.0249960
$431$	−3.43072e6	+	1.98073e6i	−0.889594	+	0.513607i	−0.873810	−	0.486268i	$-0.838358\pi$
$431$	−3.43072e6	+	1.98073e6i	−0.889594	+	0.513607i	−0.0157845	+	0.999875i	$0.505025\pi$
$432$	−1.81659e6	−	3.14643e6i	−0.468326	−	0.811164i
$433$	550534.	−	953552.i	0.141112	−	0.244413i	−0.786804	−	0.617203i	$-0.788266\pi$
$433$	550534.	−	953552.i	0.141112	−	0.244413i	0.927916	+	0.372790i	$0.121599\pi$
$434$			3.62469e6i			0.923734i
$435$	−1.68464e6	−	972625.i	−0.426857	−	0.246446i
$436$	−1.24222e7	−	7.17198e6i	−3.12956	−	1.80685i
$437$		−	7.45760e6i		−	1.86808i
$438$	2.61811e6	−	4.53469e6i	0.652082	−	1.12944i
$439$	−184232.	−	319099.i	−0.0456251	−	0.0790250i	0.842311	−	0.538992i	$-0.181195\pi$
$439$	−184232.	−	319099.i	−0.0456251	−	0.0790250i	−0.887936	+	0.459967i	$0.847861\pi$
$440$	−4.04718e6	+	2.33664e6i	−0.996601	+	0.575388i
$441$	3.77499e6			0.924313
$442$	−2.67325e6	−	5.08521e6i	−0.650853	−	1.23809i
$443$	4.49214e6			1.08754			0.543768	−	0.839235i	$-0.316997\pi$
$443$	4.49214e6			1.08754			0.543768	+	0.839235i	$0.316997\pi$
$444$	9.83356e6	−	5.67741e6i	2.36730	−	1.36676i
$445$	579600.	+	1.00390e6i	0.138749	+	0.240320i
$446$	−2.18624e6	+	3.78669e6i	−0.520429	+	0.901410i
$447$			1.14193e7i			2.70314i
$448$	3.28616e6	+	1.89727e6i	0.773560	+	0.446615i
$449$	949066.	+	547944.i	0.222168	+	0.128268i	0.606954	−	0.794737i	$-0.292391\pi$
$449$	949066.	+	547944.i	0.222168	+	0.128268i	−0.384786	+	0.923006i	$0.625725\pi$
$450$			2.64483e6i			0.615696i
$451$	−2.83547e6	+	4.91118e6i	−0.656423	+	1.13696i
$452$	2.88536e6	+	4.99760e6i	0.664285	+	1.15058i
$453$	−436088.	+	251775.i	−0.0998455	+	0.0576458i
$454$	4.46726e6			1.01719
$455$	54707.4	−	1.38040e6i	0.0123885	−	0.312590i
$456$	1.44908e7			3.26348
$457$	7.25172e6	−	4.18678e6i	1.62424	−	0.937756i	0.638473	−	0.769644i	$-0.279566\pi$
$457$	7.25172e6	−	4.18678e6i	1.62424	−	0.937756i	0.985768	−	0.168112i	$-0.0537671\pi$
$458$	−784449.	−	1.35871e6i	−0.174744	−	0.302665i
$459$	2.52012e6	−	4.36498e6i	0.558328	−	0.967053i
$460$		−	5.59728e6i		−	1.23334i
$461$	5.77891e6	+	3.33645e6i	1.26647	+	0.731194i	0.974317	−	0.225179i	$-0.0722967\pi$
$461$	5.77891e6	+	3.33645e6i	1.26647	+	0.731194i	0.292148	+	0.956373i	$0.405630\pi$
$462$	1.34284e7	+	7.75286e6i	2.92697	+	1.68989i
$463$			5.54392e6i			1.20189i	0.799291	+	0.600945i	$0.205209\pi$
$463$			5.54392e6i			1.20189i	−0.799291	+	0.600945i	$0.794791\pi$
$464$	−1.05169e6	+	1.82158e6i	−0.226774	+	0.392784i
$465$	−1.35694e6	−	2.35028e6i	−0.291023	−	0.504066i
$466$	−7.33223e6	+	4.23327e6i	−1.56412	+	0.903048i
$467$	−3.56549e6			−0.756531			−0.378265	−	0.925697i	$-0.623479\pi$
$467$	−3.56549e6			−0.756531			−0.378265	+	0.925697i	$0.623479\pi$
$468$	−1.37256e7	−	8.66672e6i	−2.89678	−	1.82911i
$469$	−2.99207e6			−0.628116
$470$	−2.55113e6	+	1.47290e6i	−0.532707	+	0.307559i
$471$	3.24456e6	+	5.61974e6i	0.673913	+	1.16725i
$472$	1.22096e6	−	2.11476e6i	0.252258	−	0.436924i
$473$		−	270973.i		−	0.0556896i
$474$	−1.64095e7	−	9.47406e6i	−3.35468	−	1.93682i
$475$	−1.09200e6	−	630465.i	−0.222069	−	0.128212i
$476$		−	5.38268e6i		−	1.08888i
$477$	−7.41064e6	+	1.28356e7i	−1.49128	+	2.58298i
$478$	−1.35950e6	−	2.35473e6i	−0.272151	−	0.471379i
$479$	6.74089e6	−	3.89185e6i	1.34239	−	0.775029i	0.355232	−	0.934778i	$-0.384402\pi$
$479$	6.74089e6	−	3.89185e6i	1.34239	−	0.775029i	0.987158	+	0.159750i	$0.0510687\pi$
$480$	−1.30623e6			−0.258771
$481$	2.33397e6	−	3.69632e6i	0.459973	−	0.728463i
$482$	−5.42994e6			−1.06458
$483$	−7.58614e6	+	4.37986e6i	−1.47963	+	0.854265i
$484$	−9.12931e6	−	1.58124e7i	−1.77143	−	3.06821i
$485$	−555732.	+	962556.i	−0.107278	+	0.185811i
$486$			5.10542e6i			0.980485i
$487$	6.18472e6	+	3.57075e6i	1.18167	+	0.682239i	0.956401	−	0.292057i	$-0.0943396\pi$
$487$	6.18472e6	+	3.57075e6i	1.18167	+	0.682239i	0.225272	+	0.974296i	$0.427673\pi$
$488$	5.37124e6	+	3.10109e6i	1.02100	+	0.589474i
$489$		−	7.52495e6i		−	1.42309i
$490$	−1.03222e6	+	1.78786e6i	−0.194215	+	0.336390i
$491$	4.21661e6	+	7.30338e6i	0.789331	+	1.36716i	0.926377	+	0.376597i	$0.122906\pi$
$491$	4.21661e6	+	7.30338e6i	0.789331	+	1.36716i	−0.137046	+	0.990565i	$0.543761\pi$
$492$	1.14297e7	−	6.59893e6i	2.12873	−	1.22902i
$493$	−2.91798e6			−0.540710
$494$	1.04693e7	−	5.50360e6i	1.93019	−	1.01468i
$495$	−7.47795e6			−1.37173
$496$	−2.54134e6	+	1.46724e6i	−0.463829	+	0.267792i
$497$	507387.	+	878820.i	0.0921401	+	0.159591i
$498$	1.01349e7	−	1.75542e7i	1.83124	−	3.17181i
$499$		−	1.36603e6i		−	0.245589i	−0.992432	−	0.122794i	$-0.960814\pi$
$499$		−	1.36603e6i		−	0.245589i	0.992432	−	0.122794i	$-0.0391856\pi$
$500$	−819596.	−	473194.i	−0.146614	−	0.0846475i
$501$	−1.07738e7	−	6.22024e6i	−1.91767	−	1.10717i
$502$			269029.i			0.0476474i
$503$	−725811.	+	1.25714e6i	−0.127910	+	0.221546i	−0.922867	−	0.385120i	$-0.874160\pi$
$503$	−725811.	+	1.25714e6i	−0.127910	+	0.221546i	0.794957	+	0.606666i	$0.207493\pi$
$504$	−5.48184e6	−	9.49482e6i	−0.961279	−	1.66498i
$505$	2.82258e6	−	1.62962e6i	0.492514	−	0.284353i
$506$	2.41868e7			4.19954
$507$	−9.67183e6	−	767828.i	−1.67105	−	0.132661i
$508$	525847.			0.0904065
$509$	−6.19342e6	+	3.57577e6i	−1.05959	+	0.611752i	−0.925318	−	0.379193i	$-0.876202\pi$
$509$	−6.19342e6	+	3.57577e6i	−1.05959	+	0.611752i	−0.134268	+	0.990945i	$0.542868\pi$
$510$	3.07965e6	+	5.33412e6i	0.524296	+	0.908107i
$511$	944375.	−	1.63571e6i	0.159990	−	0.277110i
$512$			7.62560e6i			1.28558i
$513$	8.98649e6	+	5.18835e6i	1.50764	+	0.870434i
$514$	−242782.	−	140170.i	−0.0405331	−	0.0234018i
$515$			3.92471e6i			0.652063i
$516$	−315315.	+	546142.i	−0.0521340	+	0.0902987i
$517$	−4.16445e6	−	7.21304e6i	−0.685222	−	1.18684i
$518$	5.42105e6	−	3.12985e6i	0.887686	−	0.512506i
$519$	8.69958e6			1.41769
$520$	3.70628e6	−	1.94836e6i	0.601077	−	0.315980i
$521$	1.00759e7			1.62627			0.813133	−	0.582078i	$-0.197760\pi$
$521$	1.00759e7			1.62627			0.813133	+	0.582078i	$0.197760\pi$
$522$	−1.09126e7	+	6.30037e6i	−1.75287	+	1.01202i
$523$	2.63475e6	+	4.56353e6i	0.421198	+	0.729536i	0.996057	−	0.0887166i	$-0.0282765\pi$
$523$	2.63475e6	+	4.56353e6i	0.421198	+	0.729536i	−0.574859	+	0.818252i	$0.694943\pi$
$524$	−4.20595e6	+	7.28491e6i	−0.669168	+	1.15903i
$525$			1.48109e6i			0.234522i
$526$	−1.48174e7	−	8.55483e6i	−2.33511	−	1.34818i
$527$	−3.52555e6	−	2.03548e6i	−0.552968	−	0.319256i
$528$			1.25532e7i			1.95960i
$529$	−3.61380e6	+	6.25928e6i	−0.561468	+	0.972491i
$530$	−4.05269e6	−	7.01946e6i	−0.626691	−	1.08546i
$531$	3.38392e6	−	1.95371e6i	0.520816	−	0.300693i
$532$	1.10817e7			1.69757
$533$	2.71280e6	−	4.29629e6i	0.413619	−	0.655051i
$534$	1.16575e7			1.76911
$535$	3.46410e6	−	2.00000e6i	0.523246	−	0.302096i
$536$	−4.53441e6	−	7.85383e6i	−0.681725	−	1.18078i
$537$	−1.39660e6	+	2.41898e6i	−0.208995	+	0.361989i
$538$		−	997482.i		−	0.148576i
$539$	−5.05497e6	−	2.91849e6i	−0.749457	−	0.432699i
$540$	6.74478e6	+	3.89410e6i	0.995368	+	0.574676i
$541$			774051.i			0.113704i	0.998383	+	0.0568521i	$0.0181063\pi$
$541$			774051.i			0.113704i	−0.998383	+	0.0568521i	$0.981894\pi$
$542$	−1.77048e6	+	3.06657e6i	−0.258877	+	0.448388i
$543$	3.35956e6	+	5.81893e6i	0.488971	+	0.846923i
$544$	−1.69690e6	+	979707.i	−0.245844	+	0.141938i
$545$	5.92052e6			0.853825
$546$	−1.17471e7	−	7.41746e6i	−1.68635	−	1.06481i
$547$	−4.24985e6			−0.607303			−0.303652	−	0.952783i	$-0.598206\pi$
$547$	−4.24985e6			−0.607303			−0.303652	+	0.952783i	$0.598206\pi$
$548$	1.15825e7	−	6.68715e6i	1.64759	−	0.951239i
$549$	4.96220e6	+	8.59478e6i	0.702657	+	1.21704i
$550$	2.04475e6	−	3.54161e6i	0.288226	−	0.499222i
$551$		−	6.00745e6i		−	0.842968i
$552$	−2.29932e7	−	1.32751e7i	−3.21183	−	1.85435i
$553$	−5.91907e6	−	3.41738e6i	−0.823078	−	0.475204i
$554$			1.10771e7i			1.53339i
$555$	−2.34337e6	+	4.05884e6i	−0.322930	+	0.559331i
$556$	2.33205e6	+	4.03923e6i	0.319927	+	0.554130i
$557$	−4.82582e6	+	2.78619e6i	−0.659073	+	0.380516i	−0.791924	−	0.610620i	$-0.790920\pi$
$557$	−4.82582e6	+	2.78619e6i	−0.659073	+	0.380516i	0.132851	+	0.991136i	$0.457587\pi$
$558$	−1.75797e7			−2.39015
$559$	−9614.56	+	242598.i	−0.00130137	+	0.0328365i
$560$	1.60149e6			0.215802
$561$	−1.50816e7	+	8.70737e6i	−2.02321	+	1.16810i
$562$	−1.98334e6	−	3.43525e6i	−0.264885	−	0.458794i
$563$	−4.11904e6	+	7.13438e6i	−0.547677	+	0.948605i	0.450756	+	0.892647i	$0.351155\pi$
$563$	−4.11904e6	+	7.13438e6i	−0.547677	+	0.948605i	−0.998433	+	0.0559579i	$0.982179\pi$
$564$			1.93837e7i			2.56589i
$565$	−2.06278e6	−	1.19094e6i	−0.271851	−	0.156953i
$566$	7.23836e6	+	4.17907e6i	0.949728	+	0.548326i
$567$		−	2.49597e6i		−	0.326049i
$568$	−1.53787e6	+	2.66366e6i	−0.200008	+	0.346424i
$569$	−3.97014e6	−	6.87649e6i	−0.514074	−	0.890402i	−0.999867	−	0.0163282i	$-0.994802\pi$
$569$	−3.97014e6	−	6.87649e6i	−0.514074	−	0.890402i	0.485793	−	0.874074i	$-0.338531\pi$
$570$	−1.09817e7	+	6.34030e6i	−1.41574	+	0.817378i
$571$	1.03513e7			1.32863			0.664316	−	0.747452i	$-0.268723\pi$
$571$	1.03513e7			1.32863			0.664316	+	0.747452i	$0.268723\pi$
$572$	1.16791e7	+	2.22167e7i	1.49252	+	2.83916i
$573$	−8.03099e6			−1.02184
$574$	6.30096e6	−	3.63786e6i	0.798228	−	0.460857i
$575$	1.15515e6	+	2.00078e6i	0.145703	+	0.252365i
$576$	−9.20169e6	+	1.59378e7i	−1.15561	+	2.00158i
$577$		−	8.63809e6i		−	1.08014i	−0.841622	−	0.540068i	$-0.818399\pi$
$577$		−	8.63809e6i		−	1.08014i	0.841622	−	0.540068i	$-0.181601\pi$
$578$	−3.82916e6	−	2.21077e6i	−0.476743	−	0.275248i
$579$	1.72084e7	+	9.93526e6i	2.13326	+	1.23164i
$580$		−	4.50887e6i		−	0.556542i
$581$	3.65575e6	−	6.33195e6i	0.449300	−	0.778210i
$582$	5.58874e6	+	9.67999e6i	0.683922	+	1.18459i
$583$	1.98467e7	−	1.14585e7i	2.41834	−	1.39623i
$584$	5.72471e6			0.694579
$585$	6.69488e6	+	265329.i	0.808822	+	0.0320550i
$586$	1.36369e7			1.64048
$587$	−5.99716e6	+	3.46246e6i	−0.718374	+	0.414754i	−0.814154	−	0.580649i	$-0.802799\pi$
$587$	−5.99716e6	+	3.46246e6i	−0.718374	+	0.414754i	0.0957798	+	0.995403i	$0.469466\pi$
$588$	6.79213e6	+	1.17643e7i	0.810145	+	1.40321i
$589$	4.19058e6	−	7.25829e6i	0.497721	−	0.862078i
$590$			2.13687e6i			0.252724i
$591$	−1.93574e7	−	1.11760e7i	−2.27970	−	1.31618i
$592$	4.38878e6	+	2.53387e6i	0.514683	+	0.297153i
$593$			1.09398e7i			1.27753i	0.769401	+	0.638766i	$0.220555\pi$
$593$			1.09398e7i			1.27753i	−0.769401	+	0.638766i	$0.779445\pi$
$594$	−1.68271e7	+	2.91453e7i	−1.95678	+	3.38924i
$595$	1.11086e6	+	1.92407e6i	0.128637	+	0.222806i
$596$	−2.29225e7	+	1.32343e7i	−2.64330	+	1.52611i
$597$	2.03243e7			2.33389
$598$	−2.16540e7	−	858184.i	−2.47620	−	0.0981358i
$599$	1.11997e7			1.27538			0.637690	−	0.770293i	$-0.279890\pi$
$599$	1.11997e7			1.27538			0.637690	+	0.770293i	$0.279890\pi$
$600$	−3.88769e6	+	2.24456e6i	−0.440873	+	0.254538i
$601$	−5.72157e6	−	9.91005e6i	−0.646144	−	1.11915i	−0.984036	−	0.177969i	$-0.943047\pi$
$601$	−5.72157e6	−	9.91005e6i	−0.646144	−	1.11915i	0.337893	−	0.941185i	$-0.390286\pi$
$602$	−173827.	+	301078.i	−0.0195491	+	0.0338600i
$603$		−	1.45115e7i		−	1.62524i
$604$	−1.01080e6	−	583588.i	−0.112739	−	0.0650899i
$605$	6.52664e6	+	3.76815e6i	0.724938	+	0.418543i
$606$		−	3.27767e7i		−	3.62563i
$607$	−2.88596e6	+	4.99863e6i	−0.317921	+	0.550655i	−0.980054	−	0.198731i	$-0.936318\pi$
$607$	−2.88596e6	+	4.99863e6i	−0.317921	+	0.550655i	0.662133	+	0.749386i	$0.269651\pi$
$608$	−2.01699e6	−	3.49353e6i	−0.221282	−	0.383271i
$609$	−6.11099e6	+	3.52818e6i	−0.667680	+	0.385485i
$610$	−5.42740e6			−0.590564
$611$	3.47243e6	+	6.60547e6i	0.376297	+	0.715815i
$612$	2.61058e7			2.81747
$613$	−7.08072e6	+	4.08806e6i	−0.761073	+	0.439406i	−0.829681	−	0.558238i	$-0.811478\pi$
$613$	−7.08072e6	+	4.08806e6i	−0.761073	+	0.439406i	0.0686077	+	0.997644i	$0.478144\pi$
$614$	−545889.	−	945508.i	−0.0584364	−	0.101215i
$615$	−2.72373e6	+	4.71764e6i	−0.290386	+	0.502964i
$616$			1.69523e7i			1.80002i
$617$	8.25899e6	+	4.76833e6i	0.873402	+	0.504259i	0.868477	−	0.495729i	$-0.165099\pi$
$617$	8.25899e6	+	4.76833e6i	0.873402	+	0.504259i	0.00492482	+	0.999988i	$0.498432\pi$
$618$	3.41812e7	+	1.97345e7i	3.60011	+	2.07852i
$619$		−	6.14078e6i		−	0.644165i	−0.946712	−	0.322082i	$-0.895617\pi$
$619$		−	6.14078e6i		−	0.644165i	0.946712	−	0.322082i	$-0.104383\pi$
$620$	3.14523e6	−	5.44769e6i	0.328604	−	0.569159i
$621$	−9.50618e6	−	1.64652e7i	−0.989184	−	1.71332i
$622$	9.41914e6	−	5.43814e6i	0.976192	−	0.563605i
$623$	4.20498e6			0.434054
$624$	445405.	−	1.12386e7i	0.0457925	−	1.15545i
$625$	390625.			0.0400000
$626$	1.20356e7	−	6.94874e6i	1.22753	−	0.708713i
$627$	−1.79265e7	−	3.10496e7i	−1.82107	−	3.15418i
$628$	−7.52053e6	+	1.30259e7i	−0.760939	+	1.31798i
$629$			7.03036e6i			0.708518i
$630$	8.30872e6	+	4.79704e6i	0.834032	+	0.481529i
$631$	3.02361e6	+	1.74568e6i	0.302310	+	0.174539i	0.643480	−	0.765463i	$-0.277490\pi$
$631$	3.02361e6	+	1.74568e6i	0.302310	+	0.174539i	−0.341170	+	0.940001i	$0.610823\pi$
$632$		−	2.07158e7i		−	2.06305i
$633$	1.40712e7	−	2.43720e7i	1.39580	−	2.41759i
$634$	−6.15267e6	−	1.06567e7i	−0.607912	−	1.05293i
$635$	−187967.	+	108523.i	−0.0184989	+	0.0106804i
$636$	−5.33343e7			−5.22834
$637$	4.42208e6	+	2.79223e6i	0.431795	+	0.272648i
$638$	1.94836e7			1.89503
$639$	−4.26225e6	+	2.46081e6i	−0.412940	+	0.238411i
$640$	−4.23236e6	−	7.33067e6i	−0.408444	−	0.707446i
$641$	−5.09967e6	+	8.83289e6i	−0.490227	+	0.849098i	−0.999937	−	0.0112486i	$-0.996419\pi$
$641$	−5.09967e6	+	8.83289e6i	−0.490227	+	0.849098i	0.509710	+	0.860346i	$0.329753\pi$
$642$		−	4.02262e7i		−	3.85187i
$643$	−1.40689e6	−	812269.i	−0.134194	−	0.0774769i	0.431400	−	0.902161i	$-0.358020\pi$
$643$	−1.40689e6	−	812269.i	−0.134194	−	0.0774769i	−0.565594	+	0.824684i	$0.691353\pi$
$644$	−1.75838e7	−	1.01520e7i	−1.67070	−	0.964581i
$645$		−	260295.i		−	0.0246358i
$646$	−9.51079e6	+	1.64732e7i	−0.896676	+	1.55309i
$647$	−1.59373e6	−	2.76043e6i	−0.149677	−	0.259248i	0.781431	−	0.623991i	$-0.214490\pi$
$647$	−1.59373e6	−	2.76043e6i	−0.149677	−	0.259248i	−0.931108	+	0.364743i	$0.881157\pi$
$648$	6.55163e6	−	3.78259e6i	0.612932	−	0.353876i
$649$	−6.04174e6			−0.563055
$650$	−1.95629e6	+	3.09819e6i	−0.181614	+	0.287624i
$651$	−9.84453e6			−0.910422
$652$	1.51052e7	−	8.72100e6i	1.39158	−	0.803429i
$653$	−679568.	−	1.17705e6i	−0.0623663	−	0.108022i	0.833156	−	0.553037i	$-0.186531\pi$
$653$	−679568.	−	1.17705e6i	−0.0623663	−	0.108022i	−0.895523	+	0.445016i	$0.853198\pi$
$654$	2.97700e7	−	5.15631e7i	2.72166	−	4.71406i
$655$		−	3.47204e6i		−	0.316214i
$656$	5.10114e6	+	2.94515e6i	0.462815	+	0.267207i
$657$	7.93312e6	+	4.58019e6i	0.717019	+	0.413971i
$658$			1.06858e7i			0.962152i
$659$	1.69305e6	−	2.93245e6i	0.151864	−	0.263037i	−0.780048	−	0.625719i	$-0.784806\pi$
$659$	1.69305e6	−	2.93245e6i	0.151864	−	0.263037i	0.931913	+	0.362682i	$0.118139\pi$
$660$	−1.34547e7	−	2.33042e7i	−1.20230	−	2.08245i
$661$	−3.65167e6	+	2.10829e6i	−0.325078	+	0.187684i	−0.653654	−	0.756794i	$-0.726765\pi$
$661$	−3.65167e6	+	2.10829e6i	−0.325078	+	0.187684i	0.328576	+	0.944478i	$0.393431\pi$
$662$	−1.86800e7			−1.65666
$663$	1.38112e7	−	7.26044e6i	1.22025	−	0.641474i
$664$	2.21608e7			1.95059
$665$	−3.96121e6	+	2.28701e6i	−0.347355	+	0.200546i
$666$	1.51797e7	+	2.62919e7i	1.32610	+	2.29687i
$667$	−5.50347e6	+	9.53230e6i	−0.478985	+	0.829627i
$668$		−	2.88357e7i		−	2.50028i
$669$	−1.02845e7	−	5.93776e6i	−0.888419	−	0.512929i
$670$	6.87273e6	+	3.96797e6i	0.591483	+	0.341493i
$671$		−	1.53453e7i		−	1.31574i
$672$	−2.36917e6	+	4.10352e6i	−0.202382	+	0.350536i
$673$	9.47389e6	+	1.64093e7i	0.806289	+	1.39653i	0.915417	+	0.402506i	$0.131861\pi$
$673$	9.47389e6	+	1.64093e7i	0.806289	+	1.39653i	−0.109128	+	0.994028i	$0.534806\pi$
$674$	−2.55902e7	+	1.47745e7i	−2.16982	+	1.25275i
$675$	−3.21461e6			−0.271562
$676$	−9.66782e6	−	2.03046e7i	−0.813696	−	1.70895i
$677$	−1.21964e7			−1.02272			−0.511362	−	0.859365i	$-0.670859\pi$
$677$	−1.21964e7			−1.02272			−0.511362	+	0.859365i	$0.670859\pi$
$678$	−2.07444e7	+	1.19768e7i	−1.73311	+	1.00061i
$679$	2.01591e6	+	3.49166e6i	0.167802	+	0.290641i
$680$	−3.36696e6	+	5.83175e6i	−0.279232	+	0.483645i
$681$			1.21329e7i			1.00253i
$682$	2.35404e7	+	1.35910e7i	1.93799	+	1.11890i
$683$	−2.91202e6	−	1.68126e6i	−0.238860	−	0.137906i	0.375793	−	0.926704i	$-0.377370\pi$
$683$	−2.91202e6	−	1.68126e6i	−0.238860	−	0.137906i	−0.614652	+	0.788798i	$0.710704\pi$
$684$			5.37459e7i			4.39243i
$685$	−2.76014e6	+	4.78071e6i	−0.224753	+	0.389283i
$686$	1.10766e7	+	1.91853e7i	0.898665	+	1.55653i
$687$	3.69020e6	−	2.13054e6i	0.298303	−	0.172225i
$688$	−281455.			−0.0226693
$689$	−1.81750e7	+	9.55442e6i	−1.45857	+	0.766754i
$690$	2.32336e7			1.85778
$691$	7.17590e6	−	4.14301e6i	0.571717	−	0.330081i	−0.186118	−	0.982527i	$-0.559591\pi$
$691$	7.17590e6	−	4.14301e6i	0.571717	−	0.330081i	0.757835	+	0.652446i	$0.226257\pi$
$692$	1.00823e7	+	1.74631e7i	0.800380	+	1.38630i
$693$	−1.35631e7	+	2.34920e7i	−1.07282	+	1.85817i
$694$		−	8.49801e6i		−	0.669759i
$695$	−1.66721e6	−	962561.i	−0.130926	−	0.0755904i
$696$	−1.85221e7	−	1.06938e7i	−1.44933	−	0.836772i
$697$			8.17148e6i			0.637117i
$698$	1.23600e6	−	2.14081e6i	0.0960240	−	0.166318i
$699$	−1.14974e7	−	1.99141e7i	−0.890034	−	1.54158i
$700$	−2.97307e6	+	1.71651e6i	−0.229330	+	0.132404i
$701$	−1.88313e7			−1.44739			−0.723694	−	0.690121i	$-0.757557\pi$
$701$	−1.88313e7			−1.44739			−0.723694	+	0.690121i	$0.757557\pi$
$702$	1.60991e7	−	2.54962e7i	1.23299	−	1.95269i
$703$	−1.44739e7			−1.10458
$704$	2.46434e7	−	1.42279e7i	1.87400	−	1.08195i
$705$	−4.00034e6	−	6.92879e6i	−0.303126	−	0.525030i
$706$	−1.40203e7	+	2.42839e7i	−1.05864	+	1.83361i
$707$		−	1.18228e7i		−	0.889557i
$708$	1.21770e7	+	7.03041e6i	0.912973	+	0.527105i
$709$	1.70914e7	+	9.86773e6i	1.27692	+	0.737228i	0.976280	−	0.216511i	$-0.0694678\pi$
$709$	1.70914e7	+	9.86773e6i	1.27692	+	0.737228i	0.300636	+	0.953739i	$0.402801\pi$
$710$		−	2.69151e6i		−	0.200378i
$711$	1.65742e7	−	2.87073e7i	1.22958	−	2.12970i
$712$	6.37255e6	+	1.10376e7i	0.471100	+	0.815970i
$713$	−1.32988e7	+	7.67805e6i	−0.979688	+	0.565623i
$714$	2.23428e7			1.64018
$715$	−8.75978e6	−	5.53118e6i	−0.640808	−	0.404625i
$716$	−6.47431e6			−0.471966
$717$	6.39535e6	−	3.69236e6i	0.464586	−	0.268229i
$718$	−2.32887e6	−	4.03372e6i	−0.168591	−	0.292008i
$719$	3.47720e6	−	6.02269e6i	0.250846	−	0.434479i	−0.712913	−	0.701253i	$-0.752624\pi$
$719$	3.47720e6	−	6.02269e6i	0.250846	−	0.434479i	0.963759	+	0.266774i	$0.0859577\pi$
$720$			7.76719e6i			0.558384i
$721$	1.23295e7	+	7.11842e6i	0.883295	+	0.509971i
$722$	−1.32830e7	−	7.66894e6i	−0.948315	−	0.547510i
$723$		−	1.47475e7i		−	1.04924i
$724$	−7.78710e6	+	1.34876e7i	−0.552114	+	0.956290i
$725$	930527.	+	1.61172e6i	0.0657482	+	0.113879i
$726$	6.56354e7	−	3.78946e7i	4.62164	−	2.66831i
$727$	1.05905e7			0.743160			0.371580	−	0.928401i	$-0.378816\pi$
$727$	1.05905e7			0.743160			0.371580	+	0.928401i	$0.378816\pi$
$728$	601493.	−	1.51771e7i	0.0420632	−	1.06135i
$729$	−2.05542e7			−1.43246
$730$	−4.33842e6	+	2.50479e6i	−0.301318	+	0.173966i
$731$	−195228.	−	338145.i	−0.0135129	−	0.0234051i
$732$	−1.78564e7	+	3.09282e7i	−1.23173	+	2.13343i
$733$			1.10988e7i			0.762986i	0.924372	+	0.381493i	$0.124590\pi$
$733$			1.10988e7i			0.762986i	−0.924372	+	0.381493i	$0.875410\pi$
$734$	1.64493e7	+	9.49701e6i	1.12696	+	0.650649i
$735$	−4.85577e6	−	2.80348e6i	−0.331543	−	0.191416i
$736$			7.39113e6i			0.502940i
$737$	−1.12190e7	+	1.94318e7i	−0.760825	+	1.31779i
$738$	1.76435e7	+	3.05595e7i	1.19246	+	2.06540i
$739$	2.46483e6	−	1.42307e6i	0.166026	−	0.0958550i	−0.414685	−	0.909965i	$-0.636108\pi$
$739$	2.46483e6	−	1.42307e6i	0.166026	−	0.0958550i	0.580710	+	0.814110i	$0.302775\pi$
$740$	−1.08634e7			−0.729264
$741$	1.49476e7	+	2.84342e7i	1.00006	+	1.90237i
$742$	−2.94022e7			−1.96051
$743$	−7.03719e6	+	4.06292e6i	−0.467657	+	0.270002i	−0.715258	−	0.698860i	$-0.753691\pi$
$743$	−7.03719e6	+	4.06292e6i	−0.467657	+	0.270002i	0.247602	+	0.968862i	$0.420358\pi$
$744$	−1.49192e7	−	2.58407e7i	−0.988125	−	1.71148i
$745$	5.46250e6	−	9.46133e6i	0.360579	−	0.624542i
$746$		−	2.01523e7i		−	1.32580i
$747$	3.07098e7	+	1.77303e7i	2.01361	+	1.16256i
$748$	−3.49575e7	−	2.01827e7i	−2.28448	−	1.31894i
$749$		−	1.45100e7i		−	0.945065i
$750$	1.96417e6	−	3.40204e6i	0.127505	−	0.220844i
$751$	9.75711e6	+	1.68998e7i	0.631279	+	1.09341i	0.987291	+	0.158925i	$0.0508029\pi$
$751$	9.75711e6	+	1.68998e7i	0.631279	+	1.09341i	−0.356012	+	0.934481i	$0.615864\pi$
$752$	−7.49204e6	+	4.32553e6i	−0.483120	+	0.278930i
$753$	−730672.			−0.0469607
$754$	−1.74433e7	−	691307.i	−1.11738	−	0.0442836i
$755$	481756.			0.0307581
$756$	2.44666e7	−	1.41258e7i	1.55693	−	0.898895i
$757$	−9.73213e6	−	1.68565e7i	−0.617260	−	1.06913i	−0.989983	−	0.141183i	$-0.954909\pi$
$757$	−9.73213e6	−	1.68565e7i	−0.617260	−	1.06913i	0.372723	−	0.927942i	$-0.378424\pi$
$758$	−1.34547e7	+	2.33041e7i	−0.850549	+	1.47319i
$759$			6.56904e7i			4.13902i
$760$	−1.20062e7	−	6.93180e6i	−0.754003	−	0.435324i
$761$	8.60886e6	+	4.97033e6i	0.538870	+	0.311117i	0.744621	−	0.667488i	$-0.232630\pi$
$761$	8.60886e6	+	4.97033e6i	0.538870	+	0.311117i	−0.205751	+	0.978604i	$0.565964\pi$
$762$			2.18272e6i			0.136179i
$763$	1.07383e7	−	1.85993e7i	0.667766	−	1.15661i
$764$	−9.30747e6	−	1.61210e7i	−0.576897	−	0.999215i
$765$	−9.33166e6	+	5.38764e6i	−0.576508	+	0.332847i
$766$	1.62496e7			1.00062
$767$	5.40907e6	+	214370.i	0.331997	+	0.0131576i
$768$	−5.01379e7			−3.06735
$769$	−8.53514e6	+	4.92776e6i	−0.520469	+	0.300493i	−0.737126	−	0.675755i	$-0.763818\pi$
$769$	−8.53514e6	+	4.92776e6i	−0.520469	+	0.300493i	0.216658	+	0.976248i	$0.430484\pi$
$770$	−7.41730e6	−	1.28471e7i	−0.450836	−	0.780872i
$771$	380698.	−	659388.i	0.0230645	−	0.0399489i
$772$			4.60577e7i			2.78137i
$773$	−1.43944e7	−	8.31061e6i	−0.866453	−	0.500247i	−0.000285013	−	1.00000i	$-0.500091\pi$
$773$	−1.43944e7	−	8.31061e6i	−0.866453	−	0.500247i	−0.866168	+	0.499753i	$0.833424\pi$
$774$	−1.46022e6	−	843057.i	−0.0876123	−	0.0505830i
$775$			2.59641e6i			0.155281i
$776$	−6.11013e6	+	1.05831e7i	−0.364247	+	0.630894i
$777$	8.50055e6	+	1.47234e7i	0.505120	+	0.874893i
$778$	2.93833e7	−	1.69645e7i	1.74041	−	1.00483i
$779$	−1.68232e7			−0.993265
$780$	1.12189e7	+	2.13412e7i	0.660256	+	1.25598i
$781$	7.60994e6			0.446430
$782$	3.01824e7	−	1.74258e7i	1.76497	−	1.01901i
$783$	−7.65768e6	−	1.32635e7i	−0.446368	−	0.773131i
$784$	−3.03138e6	+	5.25050e6i	−0.176137	+	0.305078i
$785$		−	6.20825e6i		−	0.359580i
$786$	−3.02388e7	−	1.74584e7i	−1.74585	−	1.00797i
$787$	7.03882e6	+	4.06387e6i	0.405101	+	0.233885i	0.688683	−	0.725063i	$-0.258189\pi$
$787$	7.03882e6	+	4.06387e6i	0.405101	+	0.233885i	−0.283582	+	0.958948i	$0.591523\pi$
$788$		−	5.18094e7i		−	2.97230i
$789$	2.32346e7	−	4.02435e7i	1.32875	−	2.30146i
$790$	9.06399e6	+	1.56993e7i	0.516716	+	0.894978i
$791$	−7.48270e6	+	4.32014e6i	−0.425223	+	0.245503i
$792$	−8.22181e7			−4.65752
$793$	−544476.	+	1.37384e7i	−0.0307465	+	0.775807i
$794$	2.29777e7			1.29347
$795$	1.90646e7	−	1.10070e7i	1.06982	−	0.617660i
$796$	2.35547e7	+	4.07980e7i	1.31764	+	2.28221i
$797$	7.29727e6	−	1.26392e7i	0.406925	−	0.704815i	−0.587618	−	0.809138i	$-0.699934\pi$
$797$	7.29727e6	−	1.26392e7i	0.406925	−	0.704815i	0.994543	+	0.104323i	$0.0332677\pi$
$798$			4.59987e7i			2.55705i
$799$	−1.03935e7	−	6.00072e6i	−0.575966	−	0.332534i
$800$	1.08227e6	+	624846.i	0.0597873	+	0.0345182i
$801$			2.03941e7i			1.12311i
$802$	−8.65128e6	+	1.49845e7i	−0.474946	+	0.822631i
$803$	−7.08200e6	−	1.22664e7i	−0.387585	−	0.671317i
$804$	4.52233e7	−	2.61097e7i	2.46730	−	1.42450i
$805$	8.38058e6			0.455810
$806$	−2.05931e7	−	1.30031e7i	−1.11656	−	0.705031i
$807$	2.70912e6			0.146435
$808$	3.10336e7	−	1.79172e7i	1.67226	−	0.965479i
$809$	−33743.2	−	58445.0i	−0.00181266	−	0.00313961i	0.865118	−	0.501569i	$-0.167244\pi$
$809$	−33743.2	−	58445.0i	−0.00181266	−	0.00313961i	−0.866930	+	0.498429i	$0.833910\pi$
$810$	−3.31006e6	+	5.73320e6i	−0.177265	+	0.307033i
$811$			4.48989e6i			0.239708i	0.992792	+	0.119854i	$0.0382427\pi$
$811$			4.48989e6i			0.239708i	−0.992792	+	0.119854i	$0.961757\pi$
$812$	−1.41646e7	−	8.17794e6i	−0.753902	−	0.435265i
$813$	−8.32868e6	−	4.80857e6i	−0.441926	−	0.255146i
$814$		−	4.69423e7i		−	2.48315i
$815$	−3.59963e6	+	6.23473e6i	−0.189829	+	0.328794i
$816$	9.04417e6	+	1.56650e7i	0.475492	+	0.823576i
$817$	696163.	−	401930.i	0.0364885	−	0.0210666i
$818$	2.75350e7			1.43880
$819$	1.29763e7	−	2.05507e7i	0.675993	−	1.07057i
$820$	−1.26266e7			−0.655771
$821$	−2.02140e7	+	1.16706e7i	−1.04663	+	0.604274i	−0.921705	−	0.387892i	$-0.873203\pi$
$821$	−2.02140e7	+	1.16706e7i	−1.04663	+	0.604274i	−0.124928	+	0.992166i	$0.539870\pi$
$822$	2.77575e7	+	4.80774e7i	1.43285	+	2.48177i
$823$	−1.08800e7	+	1.88447e7i	−0.559924	+	0.969817i	0.437578	+	0.899181i	$0.355836\pi$
$823$	−1.08800e7	+	1.88447e7i	−0.559924	+	0.969817i	−0.997502	+	0.0706367i	$0.977497\pi$
$824$			4.31512e7i			2.21398i
$825$	9.61888e6	+	5.55346e6i	0.492028	+	0.284072i
$826$	6.71296e6	+	3.87573e6i	0.342345	+	0.197653i
$827$		−	9.61954e6i		−	0.489092i	−0.969638	−	0.244546i	$-0.921361\pi$
$827$		−	9.61954e6i		−	0.489092i	0.969638	−	0.244546i	$-0.0786389\pi$
$828$	4.92371e7	−	8.52811e7i	2.49584	−	4.32292i
$829$	−6.17164e6	−	1.06896e7i	−0.311899	−	0.540225i	0.666874	−	0.745170i	$-0.267632\pi$
$829$	−6.17164e6	−	1.06896e7i	−0.311899	−	0.540225i	−0.978773	+	0.204945i	$0.934298\pi$
$830$	−1.67944e7	+	9.69623e6i	−0.846191	+	0.488549i
$831$	−3.00851e7			−1.51129
$832$	−2.25676e7	+	1.18636e7i	−1.13026	+	0.594165i
$833$	−8.41073e6			−0.419973
$834$	−1.67663e7	+	9.68004e6i	−0.834685	+	0.481906i
$835$	5.95101e6	+	1.03075e7i	0.295376	+	0.511606i
$836$	4.15516e7	−	7.19695e7i	2.05623	−	3.56150i
$837$		−	2.13669e7i		−	1.05421i
$838$	1.77435e7	+	1.02442e7i	0.872829	+	0.503928i
$839$	9.92914e6	+	5.73259e6i	0.486975	+	0.281155i	0.723319	−	0.690514i	$-0.242616\pi$
$839$	9.92914e6	+	5.73259e6i	0.486975	+	0.281155i	−0.236344	+	0.971670i	$0.575949\pi$
$840$			1.62842e7i			0.796286i
$841$	5.82227e6	−	1.00845e7i	0.283859	−	0.491658i
$842$	925308.	+	1.60268e6i	0.0449786	+	0.0779053i
$843$	9.33001e6	−	5.38668e6i	0.452182	−	0.261067i
$844$	6.52310e7			3.15208
$845$	7.64622e6	+	5.26278e6i	0.368388	+	0.253556i
$846$	−5.18260e7			−2.48955
$847$	2.36753e7	−	1.36689e7i	1.13393	−	0.654676i
$848$	−1.19017e7	−	2.06144e7i	−0.568356	−	0.984421i
$849$	−1.13502e7	+	1.96591e7i	−0.540424	+	0.936042i
$850$		−	5.89272e6i		−	0.279749i
$851$	2.29664e7	+	1.32597e7i	1.08710	+	0.627637i
$852$	−1.53377e7	−	8.85522e6i	−0.723870	−	0.417927i
$853$		−	8.75314e6i		−	0.411900i	−0.978563	−	0.205950i	$-0.933972\pi$
$853$		−	8.75314e6i		−	0.411900i	0.978563	−	0.205950i	$-0.0660284\pi$
$854$	−9.84391e6	+	1.70501e7i	−0.461873	+	0.799988i
$855$	−1.10919e7	−	1.92117e7i	−0.518909	−	0.898776i
$856$	3.80869e7	−	2.19895e7i	1.77661	−	1.02572i
$857$	−2.71428e7			−1.26242			−0.631208	−	0.775614i	$-0.717440\pi$
$857$	−2.71428e7			−1.26242			−0.631208	+	0.775614i	$0.717440\pi$
$858$	−9.22188e7	+	4.84785e7i	−4.27663	+	2.24818i
$859$	−8.02779e6			−0.371205			−0.185602	−	0.982625i	$-0.559424\pi$
$859$	−8.02779e6			−0.371205			−0.185602	+	0.982625i	$0.559424\pi$
$860$	522503.	−	301668.i	0.0240903	−	0.0139086i
$861$	9.88030e6	+	1.71132e7i	0.454216	+	0.786725i
$862$	1.90571e7	−	3.30079e7i	0.873552	−	1.51304i
$863$			1.62772e7i			0.743963i	0.928240	+	0.371982i	$0.121322\pi$
$863$			1.62772e7i			0.743963i	−0.928240	+	0.371982i	$0.878678\pi$
$864$	−8.90639e6	−	5.14211e6i	−0.405899	−	0.234346i
$865$	−7.20797e6	−	4.16152e6i	−0.327546	−	0.189109i
$866$			1.05937e7i			0.480011i
$867$	6.00437e6	−	1.03999e7i	0.271281	−	0.469872i
$868$	−1.14093e7	−	1.97614e7i	−0.513995	−	0.890265i
$869$	−4.43880e7	+	2.56274e7i	−1.99396	+	1.15121i
$870$	1.87158e7			0.838319
$871$	1.07336e7	−	1.69989e7i	0.479404	−	0.759235i
$872$	6.50946e7			2.89904
$873$	−1.69344e7	+	9.77711e6i	−0.752030	+	0.434185i
$874$	3.58758e7	+	6.21387e7i	1.58863	+	2.75159i
$875$	708494.	−	1.22715e6i	0.0312835	−	0.0541847i
$876$			3.29636e7i			1.45136i
$877$	2.97272e7	+	1.71630e7i	1.30514	+	0.753520i	0.981280	−	0.192587i	$-0.0616877\pi$
$877$	2.97272e7	+	1.71630e7i	1.30514	+	0.753520i	0.323855	+	0.946107i	$0.395021\pi$
$878$	3.07014e6	+	1.77255e6i	0.134407	+	0.0775999i
$879$			3.70373e7i			1.61684i
$880$	6.00491e6	−	1.04008e7i	0.261397	−	0.452752i
$881$	5.42879e6	+	9.40294e6i	0.235648	+	0.408154i	0.959461	−	0.281842i	$-0.0909455\pi$
$881$	5.42879e6	+	9.40294e6i	0.235648	+	0.408154i	−0.723813	+	0.689996i	$0.757612\pi$
$882$	−3.14542e7	+	1.81601e7i	−1.36147	+	0.786044i
$883$	2.61228e7			1.12750			0.563752	−	0.825944i	$-0.309357\pi$
$883$	2.61228e7			1.12750			0.563752	+	0.825944i	$0.309357\pi$
$884$	3.05807e7	+	1.93096e7i	1.31619	+	0.831079i
$885$	−5.80365e6			−0.249082
$886$	−3.74297e7	+	2.16100e7i	−1.60189	+	0.924850i
$887$	6.67531e6	+	1.15620e7i	0.284880	+	0.493427i	0.972580	−	0.232568i	$-0.0747128\pi$
$887$	6.67531e6	+	1.15620e7i	0.284880	+	0.493427i	−0.687700	+	0.725995i	$0.741380\pi$
$888$	−2.57647e7	+	4.46259e7i	−1.09646	+	1.89913i
$889$			787328.i			0.0334119i
$890$	−9.65876e6	−	5.57649e6i	−0.408739	−	0.235986i
$891$	−1.62100e7	−	9.35883e6i	−0.684050	−	0.394936i
$892$		−	2.75262e7i		−	1.15833i
$893$	1.23541e7	−	2.13979e7i	0.518421	−	0.897932i
$894$	−5.49339e7	−	9.51483e7i	−2.29877	−	3.98159i
$895$	2.31428e6	−	1.33615e6i	0.0965734	−	0.0557567i
$896$	−3.07057e7			−1.27776
$897$	2.33080e6	−	5.88115e7i	0.0967215	−	2.44051i
$898$	−1.05438e7			−0.436322
$899$	−1.07128e7	+	6.18503e6i	−0.442082	+	0.255236i
$900$	−8.32500e6	−	1.44193e7i	−0.342593	−	0.593388i
$901$	1.65110e7	−	2.85979e7i	0.677582	−	1.17361i
$902$		−	5.45617e7i		−	2.23291i
$903$	−817716.	−	472108.i	−0.0333721	−	0.0192674i
$904$	−2.26797e7	−	1.30941e7i	−0.923030	−	0.532912i
$905$		−	6.42830e6i		−	0.260900i
$906$	2.42240e6	−	4.19572e6i	0.0980450	−	0.169819i
$907$	−1.11331e7	−	1.92832e7i	−0.449365	−	0.778324i	0.548979	−	0.835836i	$-0.315017\pi$
$907$	−1.11331e7	−	1.92832e7i	−0.449365	−	0.778324i	−0.998345	+	0.0575121i	$0.981683\pi$
$908$	−2.43550e7	+	1.40614e7i	−0.980334	+	0.565996i
$909$	5.73405e7			2.30171
$910$	6.18474e6	+	1.17650e7i	0.247581	+	0.470965i
$911$	−2.21831e6			−0.0885575			−0.0442787	−	0.999019i	$-0.514099\pi$
$911$	−2.21831e6			−0.0885575			−0.0442787	+	0.999019i	$0.514099\pi$
$912$	−3.22506e7	+	1.86199e7i	−1.28396	+	0.741292i
$913$	−2.74150e7	−	4.74842e7i	−1.08846	−	1.88526i
$914$	−4.02822e7	+	6.97708e7i	−1.59495	+	2.76254i
$915$		−	1.47406e7i		−	0.582053i
$916$	8.55347e6	+	4.93835e6i	0.336824	+	0.194466i
$917$	−1.09074e7	−	6.29739e6i	−0.428349	−	0.247307i
$918$			4.84935e7i			1.89923i
$919$	−344365.	+	596458.i	−0.0134503	+	0.0232965i	−0.872672	−	0.488307i	$-0.837615\pi$
$919$	−344365.	+	596458.i	−0.0134503	+	0.0232965i	0.859222	+	0.511603i	$0.170948\pi$
$920$	1.27006e7	+	2.19980e7i	0.494713	+	0.856868i
$921$	2.56797e6	−	1.48262e6i	0.0997563	−	0.0575943i
$922$	−6.42018e7			−2.48725
$923$	−6.81304e6	−	270012.i	−0.263231	−	0.0104323i
$924$	−9.76133e7			−3.76122
$925$	3.88316e6	−	2.24194e6i	0.149221	−	0.0861530i
$926$	−2.66698e7	−	4.61934e7i	−1.02210	−	1.77032i
$927$	−3.45241e7	+	5.97975e7i	−1.31954	+	2.28551i
$928$			5.95391e6i			0.226951i
$929$	−2.98204e7	−	1.72168e7i	−1.13364	−	0.654506i	−0.188790	−	0.982017i	$-0.560457\pi$
$929$	−2.98204e7	−	1.72168e7i	−1.13364	−	0.654506i	−0.944847	+	0.327512i	$0.893790\pi$
$930$	2.26127e7	+	1.30554e7i	0.857324	+	0.494976i
$931$		−	1.73158e7i		−	0.654738i
$932$	2.66497e7	−	4.61586e7i	1.00497	−	1.74066i
$933$	1.47698e7	+	2.55820e7i	0.555483	+	0.962124i
$934$	2.97086e7	−	1.71523e7i	1.11433	−	0.643360i
$935$	1.66610e7			0.623263
$936$	7.36084e7	+	2.91723e6i	2.74624	+	0.108838i
$937$	−2.76511e7			−1.02888			−0.514438	−	0.857527i	$-0.672000\pi$
$937$	−2.76511e7			−1.02888			−0.514438	+	0.857527i	$0.672000\pi$
$938$	2.49307e7	−	1.43938e7i	0.925183	−	0.534155i
$939$	1.88725e7	+	3.26882e7i	0.698499	+	1.20984i
$940$	9.27234e6	−	1.60602e7i	0.342271	−	0.592830i
$941$		−	1.93316e7i		−	0.711693i	−0.934544	−	0.355846i	$-0.884193\pi$
$941$		−	1.93316e7i		−	0.711693i	0.934544	−	0.355846i	$-0.115807\pi$
$942$	−5.40691e7	−	3.12168e7i	−1.98528	−	1.14620i
$943$	2.66942e7	+	1.54119e7i	0.977546	+	0.564386i
$944$			6.27544e6i			0.229200i
$945$	−5.83048e6	+	1.00987e7i	−0.212385	+	0.367862i
$946$	1.30355e6	+	2.25782e6i	0.0473589	+	0.0820280i
$947$	2.72708e7	−	1.57448e7i	0.988150	−	0.570509i	0.0834294	−	0.996514i	$-0.473413\pi$
$947$	2.72708e7	−	1.57448e7i	0.988150	−	0.570509i	0.904721	+	0.426005i	$0.140079\pi$
$948$	1.19284e8			4.31084
$949$	5.90516e6	+	1.12332e7i	0.212846	+	0.404889i
$950$	1.21318e7			0.436129
$951$	2.89433e7	−	1.67104e7i	1.03776	−	0.599151i
$952$	1.22136e7	+	2.11546e7i	0.436769	+	0.756506i
$953$	1.77105e7	−	3.06755e7i	0.631683	−	1.09411i	−0.355525	−	0.934667i	$-0.615698\pi$
$953$	1.77105e7	−	3.06755e7i	0.631683	−	1.09411i	0.987208	−	0.159440i	$-0.0509688\pi$
$954$		−	1.42600e8i		−	5.07280i
$955$	6.65401e6	+	3.84169e6i	0.236088	+	0.136306i
$956$	1.48237e7	+	8.55848e6i	0.524581	+	0.302867i
$957$			5.29167e7i			1.86772i
$958$	−3.74446e7	+	6.48559e7i	−1.31818	+	2.28316i
$959$	1.00124e7	+	1.73420e7i	0.351553	+	0.608908i
$960$	2.36722e7	−	1.36672e7i	0.829013	−	0.478631i
$961$	1.13713e7			0.397195
$962$	−1.66559e6	+	4.20266e7i	−0.0580269	+	1.46415i
$963$	7.03728e7			2.44534
$964$	2.96035e7	−	1.70916e7i	1.02601	−	0.592365i
$965$	−9.50524e6	−	1.64636e7i	−0.328583	−	0.569122i
$966$	4.21398e7	−	7.29883e7i	1.45295	−	2.51658i
$967$			2.01194e7i			0.691907i	0.938252	+	0.345954i	$0.112445\pi$
$967$			2.01194e7i			0.691907i	−0.938252	+	0.345954i	$0.887555\pi$
$968$	7.17587e7	+	4.14299e7i	2.46142	+	1.42110i
$969$	−4.47406e7	−	2.58310e7i	−1.53071	−	0.883754i
$970$		−	1.06937e7i		−	0.364921i
$971$	−2.44715e7	+	4.23858e7i	−0.832936	+	1.44269i	0.0627633	+	0.998028i	$0.480009\pi$
$971$	−2.44715e7	+	4.23858e7i	−0.832936	+	1.44269i	−0.895700	+	0.444660i	$0.853325\pi$
$972$	−1.60701e7	−	2.78342e7i	−0.545573	−	0.944960i
$973$	−6.04777e6	+	3.49168e6i	−0.204792	+	0.118237i
$974$	−6.87103e7			−2.32073
$975$	−8.41457e6	−	5.31321e6i	−0.283479	−	0.178997i
$976$	−1.59389e7			−0.535591
$977$	3.93890e7	−	2.27412e7i	1.32020	−	0.762215i	0.336436	−	0.941706i	$-0.390779\pi$
$977$	3.93890e7	−	2.27412e7i	1.32020	−	0.762215i	0.983760	+	0.179491i	$0.0574452\pi$
$978$	3.61998e7	+	6.26999e7i	1.21020	+	2.09614i
$979$	1.57669e7	−	2.73090e7i	0.525762	−	0.910646i
$980$		−	1.29963e7i		−	0.432270i
$981$	9.02060e7	+	5.20805e7i	2.99270	+	1.72784i
$982$	−7.02678e7	−	4.05691e7i	−2.32529	−	1.34251i
$983$		−	3.48961e7i		−	1.15184i	−0.817505	−	0.575921i	$-0.804644\pi$
$983$		−	3.48961e7i		−	1.15184i	0.817505	−	0.575921i	$-0.195356\pi$
$984$	−2.99467e7	+	5.18692e7i	−0.985964	+	1.70774i
$985$	1.06922e7	+	1.85195e7i	0.351139	+	0.608190i
$986$	2.43134e7	−	1.40373e7i	0.796439	−	0.459825i
$987$	−2.90223e7			−0.948287
$988$	−3.97540e7	+	6.29587e7i	−1.29565	+	2.05193i
$989$	−1.47285e6			−0.0478814
$990$	6.23083e7	−	3.59737e7i	2.02049	−	1.16653i
$991$	−1.97875e7	−	3.42730e7i	−0.640040	−	1.10858i	−0.985423	−	0.170120i	$-0.945584\pi$
$991$	−1.97875e7	−	3.42730e7i	−0.640040	−	1.10858i	0.345383	−	0.938462i	$-0.387749\pi$
$992$	−4.15323e6	+	7.19360e6i	−0.134001	+	0.232096i
$993$		−	5.07343e7i		−	1.63278i
$994$	−8.45537e6	−	4.88171e6i	−0.271435	−	0.156713i
$995$	−1.68395e7	−	9.72230e6i	−0.539227	−	0.311323i
$996$			1.27605e8i			4.07585i
$997$	1.08892e7	−	1.88606e7i	0.346941	−	0.600920i	−0.638763	−	0.769403i	$-0.720554\pi$
$997$	1.08892e7	−	1.88606e7i	0.346941	−	0.600920i	0.985704	+	0.168483i	$0.0538869\pi$
$998$	6.57147e6	+	1.13821e7i	0.208851	+	0.361740i
$999$	−3.19561e7	+	1.84498e7i	−1.01307	+	0.584896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.6.m.a.36.2	✓	48
13.2	odd	12		845.6.a.o.1.3		24
13.4	even	6	inner	65.6.m.a.56.2	yes	48
13.11	odd	12		845.6.a.p.1.22		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.6.m.a.36.2	✓	48	1.1	even	1	trivial
65.6.m.a.56.2	yes	48	13.4	even	6	inner
845.6.a.o.1.3		24	13.2	odd	12
845.6.a.p.1.22		24	13.11	odd	12

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	65.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.33226 + 4.81063i) q^{2} +(-13.0655 - 22.6301i) q^{3} +(30.2844 - 52.4542i) q^{4} +25.0000i q^{5} +(217.731 + 125.707i) q^{6} +(78.5374 + 45.3436i) q^{7} +274.868i q^{8} +(-219.915 + 380.904i) q^{9} +(-120.266 - 208.307i) q^{10} +(588.963 - 340.038i) q^{11} -1582.73 q^{12} +(-539.353 + 283.533i) q^{13} -872.526 q^{14} +(565.753 - 326.638i) q^{15} +(-353.191 - 611.744i) q^{16} +(489.974 - 848.660i) q^{17} -4231.73i q^{18} +(1747.20 + 1008.74i) q^{19} +(1311.35 + 757.110i) q^{20} -2369.75i q^{21} +(-3271.60 + 5666.57i) q^{22} +(-1848.24 - 3201.24i) q^{23} +(6220.31 - 3591.30i) q^{24} -625.000 q^{25} +(3130.06 - 4957.10i) q^{26} +5143.37 q^{27} +(4756.92 - 2746.41i) q^{28} +(-1488.84 - 2578.75i) q^{29} +(-3142.67 + 5443.26i) q^{30} -4154.25i q^{31} +(-1731.62 - 999.754i) q^{32} +(-15390.2 - 8885.54i) q^{33} +9428.35i q^{34} +(-1133.59 + 1963.44i) q^{35} +(13320.0 + 23070.9i) q^{36} +(-6213.06 + 3587.11i) q^{37} -19410.8 q^{38} +(13463.3 + 8501.14i) q^{39} -6871.71 q^{40} +(-7221.51 + 4169.34i) q^{41} +(11400.0 + 19745.4i) q^{42} +(199.223 - 345.064i) q^{43} -41191.4i q^{44} +(-9522.60 - 5497.88i) q^{45} +(30800.0 + 17782.4i) q^{46} -12247.0i q^{47} +(-9229.23 + 15985.5i) q^{48} +(-4291.42 - 7432.95i) q^{49} +(5207.67 - 3006.65i) q^{50} -25607.0 q^{51} +(-1461.53 + 36878.0i) q^{52} +33697.7 q^{53} +(-42856.0 + 24742.9i) q^{54} +(8500.95 + 14724.1i) q^{55} +(-12463.5 + 21587.5i) q^{56} -52719.0i q^{57} +(24810.9 + 14324.6i) q^{58} +(-7693.71 - 4441.96i) q^{59} -39568.1i q^{60} +(11282.1 - 19541.1i) q^{61} +(19984.6 + 34614.3i) q^{62} +(-34543.1 + 19943.5i) q^{63} +41842.0 q^{64} +(-7088.32 - 13483.8i) q^{65} +170980. q^{66} +(-28573.0 + 16496.7i) q^{67} +(-29677.2 - 51402.4i) q^{68} +(-48296.4 + 83651.7i) q^{69} -21813.1i q^{70} +(9690.68 + 5594.92i) q^{71} +(-104699. - 60447.7i) q^{72} -20827.1i q^{73} +(34512.5 - 59777.5i) q^{74} +(8165.94 + 14143.8i) q^{75} +(105826. - 61098.5i) q^{76} +61674.2 q^{77} +(-153076. - 6066.65i) q^{78} -75366.3 q^{79} +(15293.6 - 8829.76i) q^{80} +(-13761.4 - 23835.5i) q^{81} +(40114.4 - 69480.1i) q^{82} -80623.3i q^{83} +(-124303. - 71766.5i) q^{84} +(21216.5 + 12249.4i) q^{85} +3833.56i q^{86} +(-38905.0 + 67385.4i) q^{87} +(93465.7 + 161887. i) q^{88} +(40155.9 - 23184.0i) q^{89} +105793. q^{90} +(-55215.8 - 2188.30i) q^{91} -223891. q^{92} +(-94011.2 + 54277.4i) q^{93} +(58915.9 + 102045. i) q^{94} +(-25218.6 + 43679.9i) q^{95} +52249.2i q^{96} +(38502.2 + 22229.3i) q^{97} +(71514.4 + 41288.9i) q^{98} +299118. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 18 q^{3} + 416 q^{4} - 342 q^{6} + 546 q^{7} - 2216 q^{9} - 200 q^{10} + 504 q^{11} - 420 q^{12} + 1800 q^{13} - 1768 q^{14} + 1650 q^{15} - 7300 q^{16} - 4118 q^{17} - 3228 q^{19} - 5700 q^{20}+ \cdots + 251688 q^{98}+O(q^{100}) \) 48 * q + 18 * q^3 + 416 * q^4 - 342 * q^6 + 546 * q^7 - 2216 * q^9 - 200 * q^10 + 504 * q^11 - 420 * q^12 + 1800 * q^13 - 1768 * q^14 + 1650 * q^15 - 7300 * q^16 - 4118 * q^17 - 3228 * q^19 - 5700 * q^20 - 708 * q^22 - 4370 * q^23 + 1176 * q^24 - 30000 * q^25 - 1498 * q^26 - 26916 * q^27 + 57138 * q^28 + 2400 * q^29 - 9400 * q^30 - 68766 * q^32 - 41322 * q^33 + 11250 * q^35 + 104858 * q^36 - 3006 * q^37 + 19496 * q^38 + 84512 * q^39 - 19200 * q^40 + 7860 * q^41 + 13496 * q^42 - 65218 * q^43 + 39654 * q^46 + 136072 * q^48 + 87388 * q^49 + 28216 * q^51 + 192766 * q^52 - 61256 * q^53 + 203922 * q^54 + 40000 * q^55 - 111662 * q^56 - 121056 * q^58 - 60204 * q^59 - 36116 * q^61 + 59796 * q^62 - 331896 * q^63 - 230924 * q^64 + 53700 * q^65 - 493716 * q^66 + 11574 * q^67 + 107014 * q^68 - 113096 * q^69 - 71808 * q^71 + 199608 * q^72 + 131196 * q^74 - 11250 * q^75 + 508476 * q^76 + 324916 * q^77 - 76084 * q^78 + 279600 * q^79 - 207000 * q^80 - 237620 * q^81 + 46076 * q^82 - 148170 * q^84 + 26550 * q^85 + 113838 * q^87 + 264998 * q^88 - 557340 * q^89 + 375500 * q^90 - 344540 * q^91 - 1260284 * q^92 - 792600 * q^93 - 425238 * q^94 - 116400 * q^95 + 417390 * q^97 + 251688 * q^98

Introduction

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