LMFDB - Embedded newform 51.7.f.a.38.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,7,Mod(38,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.38"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	51.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$11.7327582646$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			38.10
Character	$\chi$	$=$	51.38
Dual form			51.7.f.a.47.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-7.21375 q^{2} +(-16.6299 + 21.2708i) q^{3} -11.9618 q^{4} +(-104.798 - 104.798i) q^{5} +(119.964 - 153.442i) q^{6} +(-266.693 - 266.693i) q^{7} +547.970 q^{8} +(-175.895 - 707.462i) q^{9} +(755.989 + 755.989i) q^{10} +(-623.310 + 623.310i) q^{11} +(198.923 - 254.438i) q^{12} -3523.10 q^{13} +(1923.86 + 1923.86i) q^{14} +(3971.93 - 486.363i) q^{15} -3187.36 q^{16} +(3316.34 + 3624.84i) q^{17} +(1268.86 + 5103.45i) q^{18} +5004.35i q^{19} +(1253.58 + 1253.58i) q^{20} +(10107.9 - 1237.71i) q^{21} +(4496.40 - 4496.40i) q^{22} +(6087.39 - 6087.39i) q^{23} +(-9112.66 + 11655.8i) q^{24} +6340.40i q^{25} +25414.8 q^{26} +(17973.4 + 8023.57i) q^{27} +(3190.14 + 3190.14i) q^{28} +(-895.240 - 895.240i) q^{29} +(-28652.5 + 3508.50i) q^{30} +(7448.69 - 7448.69i) q^{31} -12077.2 q^{32} +(-2892.74 - 23623.9i) q^{33} +(-23923.3 - 26148.7i) q^{34} +55898.1i q^{35} +(2104.02 + 8462.53i) q^{36} +(-31902.6 + 31902.6i) q^{37} -36100.1i q^{38} +(58588.7 - 74939.2i) q^{39} +(-57426.3 - 57426.3i) q^{40} +(-1211.93 + 1211.93i) q^{41} +(-72915.6 + 8928.52i) q^{42} +28919.4i q^{43} +(7455.92 - 7455.92i) q^{44} +(-55707.3 + 92574.3i) q^{45} +(-43912.9 + 43912.9i) q^{46} -159472. i q^{47} +(53005.4 - 67797.7i) q^{48} +24601.7i q^{49} -45738.0i q^{50} +(-132254. + 10260.7i) q^{51} +42142.7 q^{52} +264611. q^{53} +(-129656. - 57880.0i) q^{54} +130644. q^{55} +(-146140. - 146140. i) q^{56} +(-106447. - 83221.7i) q^{57} +(6458.04 + 6458.04i) q^{58} -158768. q^{59} +(-47511.5 + 5817.79i) q^{60} +(-2820.82 - 2820.82i) q^{61} +(-53733.0 + 53733.0i) q^{62} +(-141765. + 235585. i) q^{63} +291113. q^{64} +(369215. + 369215. i) q^{65} +(20867.5 + 170417. i) q^{66} +472006. q^{67} +(-39669.5 - 43359.6i) q^{68} +(28251.2 + 230716. i) q^{69} -403235. i q^{70} +(347538. + 347538. i) q^{71} +(-96385.0 - 387667. i) q^{72} +(-514670. + 514670. i) q^{73} +(230138. - 230138. i) q^{74} +(-134865. - 105440. i) q^{75} -59861.1i q^{76} +332465. q^{77} +(-422644. + 540593. i) q^{78} +(-521127. - 521127. i) q^{79} +(334030. + 334030. i) q^{80} +(-469563. + 248878. i) q^{81} +(8742.57 - 8742.57i) q^{82} +314933. q^{83} +(-120908. + 14805.2i) q^{84} +(32329.9 - 727424. i) q^{85} -208617. i q^{86} +(33930.2 - 4154.76i) q^{87} +(-341555. + 341555. i) q^{88} -772524. i q^{89} +(401859. - 667808. i) q^{90} +(939588. + 939588. i) q^{91} +(-72816.2 + 72816.2i) q^{92} +(34568.9 + 282311. i) q^{93} +1.15039e6i q^{94} +(524448. - 524448. i) q^{95} +(200843. - 256893. i) q^{96} +(667648. - 667648. i) q^{97} -177471. i q^{98} +(550605. + 331331. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 18 q^{3} + 2040 q^{4} - 290 q^{6} - 4 q^{7} - 4256 q^{10} + 4182 q^{12} - 1832 q^{13} + 54976 q^{16} + 10940 q^{18} - 1604 q^{21} + 19576 q^{22} + 15110 q^{24} + 37314 q^{27} - 63120 q^{28} + 51360 q^{30}+ \cdots + 203004 q^{99}+O(q^{100}) $ 68 * q + 18 * q^3 + 2040 * q^4 - 290 * q^6 - 4 * q^7 - 4256 * q^10 + 4182 * q^12 - 1832 * q^13 + 54976 * q^16 + 10940 * q^18 - 1604 * q^21 + 19576 * q^22 + 15110 * q^24 + 37314 * q^27 - 63120 * q^28 + 51360 * q^30 - 88660 * q^31 - 128604 * q^33 + 80200 * q^34 + 335180 * q^37 + 31460 * q^39 - 286828 * q^40 + 45484 * q^45 - 85244 * q^46 + 111922 * q^48 - 590566 * q^51 - 904320 * q^52 - 1215638 * q^54 - 731624 * q^55 + 753144 * q^57 - 328292 * q^58 + 751532 * q^61 + 88664 * q^63 + 870368 * q^64 + 174232 * q^67 + 1420428 * q^69 + 1158660 * q^72 + 2397332 * q^73 + 1415042 * q^75 - 1868044 * q^78 - 1438708 * q^79 - 2973932 * q^81 - 617036 * q^82 + 4901976 * q^84 + 2375468 * q^85 + 521156 * q^88 - 3185088 * q^90 + 1741672 * q^91 + 4082570 * q^96 + 2753300 * q^97 + 203004 * q^99

Character values

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

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

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 $

$2$	−7.21375			−0.901719			−0.450859	−	0.892595i	$-0.648882\pi$
$2$	−7.21375			−0.901719			−0.450859	+	0.892595i	$0.648882\pi$
$3$	−16.6299	+	21.2708i	−0.615921	+	0.787808i
$3$	−16.6299	+	21.2708i	−0.615921	+	0.787808i
$4$	−11.9618			−0.186903
$5$	−104.798	−	104.798i	−0.838387	−	0.838387i	0.150260	−	0.988647i	$-0.451989\pi$
$5$	−104.798	−	104.798i	−0.838387	−	0.838387i	−0.988647	+	0.150260i	$0.951989\pi$
$6$	119.964	−	153.442i	0.555388	−	0.710381i
$7$	−266.693	−	266.693i	−0.777532	−	0.777532i	0.201879	−	0.979411i	$-0.435295\pi$
$7$	−266.693	−	266.693i	−0.777532	−	0.777532i	−0.979411	+	0.201879i	$0.935295\pi$
$8$	547.970			1.07025
$9$	−175.895	−	707.462i	−0.241282	−	0.970455i
$10$	755.989	+	755.989i	0.755989	+	0.755989i
$11$	−623.310	+	623.310i	−0.468302	+	0.468302i	−0.901364	−	0.433062i	$-0.857433\pi$
$11$	−623.310	+	623.310i	−0.468302	+	0.468302i	0.433062	+	0.901364i	$0.357433\pi$
$12$	198.923	−	254.438i	0.115118	−	0.147244i
$13$	−3523.10			−1.60360			−0.801798	−	0.597595i	$-0.796123\pi$
$13$	−3523.10			−1.60360			−0.801798	+	0.597595i	$0.796123\pi$
$14$	1923.86	+	1923.86i	0.701115	+	0.701115i
$15$	3971.93	−	486.363i	1.17687	−	0.144108i
$16$	−3187.36			−0.778164
$17$	3316.34	+	3624.84i	0.675014	+	0.737805i
$17$	3316.34	+	3624.84i	0.675014	+	0.737805i
$18$	1268.86	+	5103.45i	0.217569	+	0.875077i
$19$			5004.35i			0.729604i	0.931085	+	0.364802i	$0.118863\pi$
$19$			5004.35i			0.729604i	−0.931085	+	0.364802i	$0.881137\pi$
$20$	1253.58	+	1253.58i	0.156697	+	0.156697i
$21$	10107.9	−	1237.71i	1.09144	−	0.133647i
$22$	4496.40	−	4496.40i	0.422276	−	0.422276i
$23$	6087.39	−	6087.39i	0.500320	−	0.500320i	−0.411218	−	0.911537i	$-0.634896\pi$
$23$	6087.39	−	6087.39i	0.500320	−	0.500320i	0.911537	+	0.411218i	$0.134896\pi$
$24$	−9112.66	+	11655.8i	−0.659191	+	0.843154i
$25$			6340.40i			0.405785i
$26$	25414.8			1.44599
$27$	17973.4	+	8023.57i	0.913143	+	0.407640i
$28$	3190.14	+	3190.14i	0.145323	+	0.145323i
$29$	−895.240	−	895.240i	−0.0367067	−	0.0367067i	0.688515	−	0.725222i	$-0.258263\pi$
$29$	−895.240	−	895.240i	−0.0367067	−	0.0367067i	−0.725222	+	0.688515i	$0.758263\pi$
$30$	−28652.5	+	3508.50i	−1.06120	+	0.129945i
$31$	7448.69	−	7448.69i	0.250032	−	0.250032i	−0.570952	−	0.820984i	$-0.693426\pi$
$31$	7448.69	−	7448.69i	0.250032	−	0.250032i	0.820984	+	0.570952i	$0.193426\pi$
$32$	−12077.2			−0.368568
$33$	−2892.74	−	23623.9i	−0.0804949	−	0.657369i
$34$	−23923.3	−	26148.7i	−0.608672	−	0.665293i
$35$			55898.1i			1.30374i
$36$	2104.02	+	8462.53i	0.0450965	+	0.181381i
$37$	−31902.6	+	31902.6i	−0.629827	+	0.629827i	−0.948024	−	0.318197i	$-0.896923\pi$
$37$	−31902.6	+	31902.6i	−0.629827	+	0.629827i	0.318197	+	0.948024i	$0.396923\pi$
$38$		−	36100.1i		−	0.657897i
$39$	58588.7	−	74939.2i	0.987689	−	1.26333i
$40$	−57426.3	−	57426.3i	−0.897286	−	0.897286i
$41$	−1211.93	+	1211.93i	−0.0175844	+	0.0175844i	−0.715844	−	0.698260i	$-0.753958\pi$
$41$	−1211.93	+	1211.93i	−0.0175844	+	0.0175844i	0.698260	+	0.715844i	$0.253958\pi$
$42$	−72915.6	+	8928.52i	−0.984175	+	0.120512i
$43$			28919.4i			0.363734i	0.983323	+	0.181867i	$0.0582140\pi$
$43$			28919.4i			0.363734i	−0.983323	+	0.181867i	$0.941786\pi$
$44$	7455.92	−	7455.92i	0.0875272	−	0.0875272i
$45$	−55707.3	+	92574.3i	−0.611329	+	1.01590i
$46$	−43912.9	+	43912.9i	−0.451148	+	0.451148i
$47$		−	159472.i		−	1.53599i	−0.640453	−	0.767997i	$-0.721253\pi$
$47$		−	159472.i		−	1.53599i	0.640453	−	0.767997i	$-0.278747\pi$
$48$	53005.4	−	67797.7i	0.479287	−	0.613043i
$49$			24601.7i			0.209111i
$50$		−	45738.0i		−	0.365904i
$51$	−132254.	+	10260.7i	−0.997004	+	0.0773511i
$52$	42142.7			0.299718
$53$	264611.			1.77738			0.888691	−	0.458506i	$-0.151615\pi$
$53$	264611.			1.77738			0.888691	+	0.458506i	$0.151615\pi$
$54$	−129656.	−	57880.0i	−0.823398	−	0.367576i
$55$	130644.			0.785236
$56$	−146140.	−	146140.i	−0.832156	−	0.832156i
$57$	−106447.	−	83221.7i	−0.574788	−	0.449378i
$58$	6458.04	+	6458.04i	0.0330991	+	0.0330991i
$59$	−158768.			−0.773048			−0.386524	−	0.922279i	$-0.626324\pi$
$59$	−158768.			−0.773048			−0.386524	+	0.922279i	$0.626324\pi$
$60$	−47511.5	+	5817.79i	−0.219961	+	0.0269342i
$61$	−2820.82	−	2820.82i	−0.0124276	−	0.0124276i	0.700866	−	0.713293i	$-0.252797\pi$
$61$	−2820.82	−	2820.82i	−0.0124276	−	0.0124276i	−0.713293	+	0.700866i	$0.752797\pi$
$62$	−53733.0	+	53733.0i	−0.225458	+	0.225458i
$63$	−141765.	+	235585.i	−0.566955	+	0.942164i
$64$	291113.			1.11051
$65$	369215.	+	369215.i	1.34443	+	1.34443i
$66$	20867.5	+	170417.i	0.0725837	+	0.592762i
$67$	472006.			1.56936			0.784681	−	0.619900i	$-0.212827\pi$
$67$	472006.			1.56936			0.784681	+	0.619900i	$0.212827\pi$
$68$	−39669.5	−	43359.6i	−0.126162	−	0.137898i
$69$	28251.2	+	230716.i	0.0859983	+	0.702313i
$70$		−	403235.i		−	1.17561i
$71$	347538.	+	347538.i	0.971019	+	0.971019i	0.999592	−	0.0285730i	$-0.00909630\pi$
$71$	347538.	+	347538.i	0.971019	+	0.971019i	−0.0285730	+	0.999592i	$0.509096\pi$
$72$	−96385.0	−	387667.i	−0.258233	−	1.03863i
$73$	−514670.	+	514670.i	−1.32300	+	1.32300i	−0.411665	+	0.911335i	$0.635053\pi$
$73$	−514670.	+	514670.i	−1.32300	+	1.32300i	−0.911335	+	0.411665i	$0.864947\pi$
$74$	230138.	−	230138.i	0.567927	−	0.567927i
$75$	−134865.	−	105440.i	−0.319681	−	0.249932i
$76$		−	59861.1i		−	0.136365i
$77$	332465.			0.728239
$78$	−422644.	+	540593.i	−0.890618	+	1.13916i
$79$	−521127.	−	521127.i	−1.05697	−	1.05697i	−0.998276	−	0.0586941i	$-0.981306\pi$
$79$	−521127.	−	521127.i	−1.05697	−	1.05697i	−0.0586941	−	0.998276i	$-0.518694\pi$
$80$	334030.	+	334030.i	0.652402	+	0.652402i
$81$	−469563.	+	248878.i	−0.883566	+	0.468307i
$82$	8742.57	−	8742.57i	0.0158561	−	0.0158561i
$83$	314933.			0.550788			0.275394	−	0.961331i	$-0.411192\pi$
$83$	314933.			0.550788			0.275394	+	0.961331i	$0.411192\pi$
$84$	−120908.	+	14805.2i	−0.203995	+	0.0249791i
$85$	32329.9	−	727424.i	0.0526438	−	1.18449i
$86$		−	208617.i		−	0.327986i
$87$	33930.2	−	4154.76i	0.0515263	−	0.00630940i
$88$	−341555.	+	341555.i	−0.501201	+	0.501201i
$89$		−	772524.i		−	1.09583i	−0.836535	−	0.547914i	$-0.815422\pi$
$89$		−	772524.i		−	1.09583i	0.836535	−	0.547914i	$-0.184578\pi$
$90$	401859.	−	667808.i	0.551247	−	0.916060i
$91$	939588.	+	939588.i	1.24685	+	1.24685i
$92$	−72816.2	+	72816.2i	−0.0935114	+	0.0935114i
$93$	34568.9	+	282311.i	0.0429771	+	0.350977i
$94$			1.15039e6i			1.38503i
$95$	524448.	−	524448.i	0.611690	−	0.611690i
$96$	200843.	−	256893.i	0.227009	−	0.290361i
$97$	667648.	−	667648.i	0.731530	−	0.731530i	−0.239393	−	0.970923i	$-0.576948\pi$
$97$	667648.	−	667648.i	0.731530	−	0.731530i	0.970923	+	0.239393i	$0.0769483\pi$
$98$		−	177471.i		−	0.188560i
$99$	550605.	+	331331.i	0.567459	+	0.341473i
$100$		−	75842.6i		−	0.0758426i
$101$			1.91648e6i			1.86012i	0.367408	+	0.930060i	$0.380245\pi$
$101$			1.91648e6i			1.86012i	−0.367408	+	0.930060i	$0.619755\pi$
$102$	954044.	−	74018.1i	0.899017	−	0.0697489i
$103$	464408.			0.424999			0.212500	−	0.977161i	$-0.431840\pi$
$103$	464408.			0.424999			0.212500	+	0.977161i	$0.431840\pi$
$104$	−1.93055e6			−1.71625
$105$	−1.18900e6	−	929578.i	−1.02710	−	0.803004i
$106$	−1.90884e6			−1.60270
$107$	−301793.	−	301793.i	−0.246353	−	0.246353i	0.573119	−	0.819472i	$-0.305733\pi$
$107$	−301793.	−	301793.i	−0.246353	−	0.246353i	−0.819472	+	0.573119i	$0.805733\pi$
$108$	−214994.	−	95976.5i	−0.170669	−	0.0761892i
$109$	−779394.	−	779394.i	−0.601835	−	0.601835i	0.338964	−	0.940799i	$-0.389923\pi$
$109$	−779394.	−	779394.i	−0.601835	−	0.601835i	−0.940799	+	0.338964i	$0.889923\pi$
$110$	−942431.			−0.708062
$111$	−148058.	−	1.20913e6i	−0.108259	−	0.884107i
$112$	850048.	+	850048.i	0.605047	+	0.605047i
$113$	22607.8	−	22607.8i	0.0156683	−	0.0156683i	−0.699229	−	0.714898i	$-0.746473\pi$
$113$	22607.8	−	22607.8i	0.0156683	−	0.0156683i	0.714898	+	0.699229i	$0.246473\pi$
$114$	767879.	+	600341.i	0.518297	+	0.405213i
$115$	−1.27590e6			−0.838923
$116$	10708.7	+	10708.7i	0.00686061	+	0.00686061i
$117$	619695.	+	2.49246e6i	0.386920	+	1.55622i
$118$	1.14531e6			0.697072
$119$	82273.9	−	1.85117e6i	0.0488226	−	1.09851i
$120$	2.17650e6	−	266512.i	1.25955	−	0.154232i
$121$			994531.i			0.561387i
$122$	20348.7	+	20348.7i	0.0112062	+	0.0112062i
$123$	−5624.50	−	45933.0i	−0.00302252	−	0.0246837i
$124$	−89099.9	+	89099.9i	−0.0467318	+	0.0467318i
$125$	−973011.	+	973011.i	−0.498182	+	0.498182i
$126$	1.02266e6	−	1.69945e6i	0.511234	−	0.849567i
$127$		−	1.42355e6i		−	0.694964i	−0.937687	−	0.347482i	$-0.887037\pi$
$127$		−	1.42355e6i		−	0.694964i	0.937687	−	0.347482i	$-0.112963\pi$
$128$	−1.32707e6			−0.632798
$129$	−615139.	−	480926.i	−0.286553	−	0.224031i
$130$	−2.66343e6	−	2.66343e6i	−1.21230	−	1.21230i
$131$	−2.14338e6	−	2.14338e6i	−0.953424	−	0.953424i	0.0455383	−	0.998963i	$-0.485500\pi$
$131$	−2.14338e6	−	2.14338e6i	−0.953424	−	0.953424i	−0.998963	+	0.0455383i	$0.985500\pi$
$132$	34602.5	+	282584.i	0.0150448	+	0.122864i
$133$	1.33463e6	−	1.33463e6i	0.567290	−	0.567290i
$134$	−3.40493e6			−1.41512
$135$	−1.04273e6	−	2.72444e6i	−0.423807	−	1.10733i
$136$	1.81725e6	+	1.98630e6i	0.722435	+	0.789638i
$137$			2.35427e6i			0.915575i	0.889062	+	0.457787i	$0.151358\pi$
$137$			2.35427e6i			0.915575i	−0.889062	+	0.457787i	$0.848642\pi$
$138$	−203797.	−	1.66433e6i	−0.0775463	−	0.633289i
$139$	−956491.	+	956491.i	−0.356153	+	0.356153i	−0.862393	−	0.506240i	$-0.831035\pi$
$139$	−956491.	+	956491.i	−0.356153	+	0.356153i	0.506240	+	0.862393i	$0.331035\pi$
$140$		−	668642.i		−	0.243674i
$141$	3.39209e6	+	2.65199e6i	1.21007	+	0.946051i
$142$	−2.50705e6	−	2.50705e6i	−0.875586	−	0.875586i
$143$	2.19598e6	−	2.19598e6i	0.750967	−	0.750967i
$144$	560640.	+	2.25493e6i	0.187757	+	0.755173i
$145$			187639.i			0.0615489i
$146$	3.71270e6	−	3.71270e6i	1.19297	−	1.19297i
$147$	−523299.	−	409124.i	−0.164740	−	0.128796i
$148$	381613.	−	381613.i	0.117717	−	0.117717i
$149$			5.32800e6i			1.61067i	0.592822	+	0.805333i	$0.298014\pi$
$149$			5.32800e6i			1.61067i	−0.592822	+	0.805333i	$0.701986\pi$
$150$	972885.	+	760617.i	0.288262	+	0.225368i
$151$			5.11410e6i			1.48538i	0.669634	+	0.742692i	$0.266451\pi$
$151$			5.11410e6i			1.48538i	−0.669634	+	0.742692i	$0.733549\pi$
$152$			2.74223e6i			0.780861i
$153$	1.98111e6	−	2.98377e6i	0.553138	−	0.833090i
$154$	−2.39832e6			−0.656667
$155$	−1.56122e6			−0.419247
$156$	−700828.	+	896409.i	−0.184602	+	0.236120i
$157$	4.65865e6			1.20382			0.601910	−	0.798564i	$-0.294407\pi$
$157$	4.65865e6			1.20382			0.601910	+	0.798564i	$0.294407\pi$
$158$	3.75928e6	+	3.75928e6i	0.953090	+	0.953090i
$159$	−4.40045e6	+	5.62850e6i	−1.09473	+	1.40024i
$160$	1.26568e6	+	1.26568e6i	0.309003	+	0.309003i
$161$	−3.24693e6			−0.778029
$162$	3.38731e6	−	1.79534e6i	0.796728	−	0.422281i
$163$	138474.	+	138474.i	0.0319745	+	0.0319745i	0.722913	−	0.690939i	$-0.242803\pi$
$163$	138474.	+	138474.i	0.0319745	+	0.0319745i	−0.690939	+	0.722913i	$0.742803\pi$
$164$	14496.9	−	14496.9i	0.00328658	−	0.00328658i
$165$	−2.17259e6	+	2.77890e6i	−0.483644	+	0.618615i
$166$	−2.27185e6			−0.496656
$167$	2.54670e6	+	2.54670e6i	0.546799	+	0.546799i	0.925514	−	0.378714i	$-0.123634\pi$
$167$	2.54670e6	+	2.54670e6i	0.546799	+	0.546799i	−0.378714	+	0.925514i	$0.623634\pi$
$168$	5.53880e6	−	678227.i	1.16812	−	0.143037i
$169$	7.58544e6			1.57152
$170$	−233220.	+	5.24746e6i	−0.0474699	+	1.06808i
$171$	3.54039e6	−	880240.i	0.708048	−	0.176041i
$172$		−	345929.i		−	0.0679831i
$173$	−1.33969e6	−	1.33969e6i	−0.258742	−	0.258742i	0.565800	−	0.824542i	$-0.308567\pi$
$173$	−1.33969e6	−	1.33969e6i	−0.258742	−	0.258742i	−0.824542	+	0.565800i	$0.808567\pi$
$174$	−244764.	+	29971.4i	−0.0464622	+	0.00568930i
$175$	1.69094e6	−	1.69094e6i	0.315511	−	0.315511i
$176$	1.98671e6	−	1.98671e6i	0.364415	−	0.364415i
$177$	2.64029e6	−	3.37712e6i	0.476136	−	0.609013i
$178$			5.57280e6i			0.988128i
$179$	−4.23491e6			−0.738389			−0.369195	−	0.929352i	$-0.620366\pi$
$179$	−4.23491e6			−0.738389			−0.369195	+	0.929352i	$0.620366\pi$
$180$	666361.	−	1.10736e6i	0.114259	−	0.189876i
$181$	−1.41519e6	−	1.41519e6i	−0.238660	−	0.238660i	0.577635	−	0.816295i	$-0.303976\pi$
$181$	−1.41519e6	−	1.41519e6i	−0.238660	−	0.238660i	−0.816295	+	0.577635i	$0.803976\pi$
$182$	−6.77795e6	−	6.77795e6i	−1.12431	−	1.12431i
$183$	106911.	−	13091.3i	0.0174449	−	0.00213613i
$184$	3.33570e6	−	3.33570e6i	0.535469	−	0.535469i
$185$	6.68669e6			1.05608
$186$	−249372.	−	2.03652e6i	−0.0387533	−	0.316482i
$187$	−4.32650e6	−	192289.i	−0.661626	−	0.0294055i
$188$			1.90757e6i			0.287083i
$189$	−2.65355e6	−	6.93322e6i	−0.393045	−	1.02695i
$190$	−3.78324e6	+	3.78324e6i	−0.551573	+	0.551573i
$191$		−	6.27409e6i		−	0.900431i	−0.892920	−	0.450216i	$-0.851347\pi$
$191$		−	6.27409e6i		−	0.900431i	0.892920	−	0.450216i	$-0.148653\pi$
$192$	−4.84117e6	+	6.19221e6i	−0.683986	+	0.874867i
$193$	−2.27808e6	−	2.27808e6i	−0.316882	−	0.316882i	0.530686	−	0.847568i	$-0.321934\pi$
$193$	−2.27808e6	−	2.27808e6i	−0.316882	−	0.316882i	−0.847568	+	0.530686i	$0.821934\pi$
$194$	−4.81624e6	+	4.81624e6i	−0.659634	+	0.659634i
$195$	−1.39935e7	+	1.71351e6i	−1.88722	+	0.231090i
$196$		−	294281.i		−	0.0390836i
$197$	9.72267e6	−	9.72267e6i	1.27171	−	1.27171i	0.326515	−	0.945192i	$-0.394126\pi$
$197$	9.72267e6	−	9.72267e6i	1.27171	−	1.27171i	0.945192	−	0.326515i	$-0.105874\pi$
$198$	−3.97192e6	−	2.39014e6i	−0.511688	−	0.307912i
$199$	2.45821e6	−	2.45821e6i	0.311932	−	0.311932i	−0.533726	−	0.845658i	$-0.679209\pi$
$199$	2.45821e6	−	2.45821e6i	0.311932	−	0.311932i	0.845658	+	0.533726i	$0.179209\pi$
$200$			3.47434e6i			0.434293i
$201$	−7.84940e6	+	1.00399e7i	−0.966603	+	1.23636i
$202$		−	1.38250e7i		−	1.67730i
$203$			477509.i			0.0570813i
$204$	1.58199e6	−	122737.i	0.186343	−	0.0144572i
$205$	254017.			0.0294850
$206$	−3.35013e6			−0.383230
$207$	−5.37733e6	−	3.23585e6i	−0.606256	−	0.364819i
$208$	1.12294e7			1.24786
$209$	−3.11926e6	−	3.11926e6i	−0.341675	−	0.341675i
$210$	8.57713e6	+	6.70574e6i	0.926156	+	0.724084i
$211$	−3.15520e6	−	3.15520e6i	−0.335877	−	0.335877i	0.518936	−	0.854813i	$-0.326328\pi$
$211$	−3.15520e6	−	3.15520e6i	−0.335877	−	0.335877i	−0.854813	+	0.518936i	$0.826328\pi$
$212$	−3.16523e6			−0.332199
$213$	−1.31719e7	+	1.61290e6i	−1.36305	+	0.166905i
$214$	2.17706e6	+	2.17706e6i	0.222141	+	0.222141i
$215$	3.03071e6	−	3.03071e6i	0.304950	−	0.304950i
$216$	9.84887e6	+	4.39667e6i	0.977294	+	0.436277i
$217$	−3.97303e6			−0.388815
$218$	5.62235e6	+	5.62235e6i	0.542686	+	0.542686i
$219$	−2.38855e6	−	1.95063e7i	−0.227406	−	1.85713i
$220$	−1.56274e6			−0.146763
$221$	−1.16838e7	−	1.27707e7i	−1.08245	−	1.18314i
$222$	1.06806e6	+	8.72237e6i	0.0976191	+	0.797215i
$223$			5.04825e6i			0.455225i	0.973752	+	0.227613i	$0.0730920\pi$
$223$			5.04825e6i			0.455225i	−0.973752	+	0.227613i	$0.926908\pi$
$224$	3.22092e6	+	3.22092e6i	0.286573	+	0.286573i
$225$	4.48559e6	−	1.11524e6i	0.393796	−	0.0979088i
$226$	−163087.	+	163087.i	−0.0141284	+	0.0141284i
$227$	−3.52945e6	+	3.52945e6i	−0.301738	+	0.301738i	−0.841694	−	0.539956i	$-0.818441\pi$
$227$	−3.52945e6	+	3.52945e6i	−0.301738	+	0.301738i	0.539956	+	0.841694i	$0.318441\pi$
$228$	1.27330e6	+	995483.i	0.107430	+	0.0839903i
$229$			2.74019e6i			0.228178i	0.993471	+	0.114089i	$0.0363950\pi$
$229$			2.74019e6i			0.228178i	−0.993471	+	0.114089i	$0.963605\pi$
$230$	9.20400e6			0.756472
$231$	−5.52885e6	+	7.07180e6i	−0.448538	+	0.573712i
$232$	−490564.	−	490564.i	−0.0392855	−	0.0392855i
$233$	1.06219e7	+	1.06219e7i	0.839723	+	0.839723i	0.988822	−	0.149099i	$-0.0476374\pi$
$233$	1.06219e7	+	1.06219e7i	0.839723	+	0.839723i	−0.149099	+	0.988822i	$0.547637\pi$
$234$	−4.47033e6	−	1.79800e7i	−0.348893	−	1.40327i
$235$	−1.67124e7	+	1.67124e7i	−1.28776	+	1.28776i
$236$	1.89915e6			0.144485
$237$	1.97511e7	−	2.41852e6i	1.48370	−	0.181679i
$238$	−593503.	+	1.33539e7i	−0.0440243	+	0.990548i
$239$		−	1.32990e7i		−	0.974146i	−0.873361	−	0.487073i	$-0.838065\pi$
$239$		−	1.32990e7i		−	0.974146i	0.873361	−	0.487073i	$-0.161935\pi$
$240$	−1.26600e7	+	1.55021e6i	−0.915796	+	0.112139i
$241$	−8.76355e6	+	8.76355e6i	−0.626079	+	0.626079i	−0.947079	−	0.321000i	$-0.895981\pi$
$241$	−8.76355e6	+	8.76355e6i	−0.626079	+	0.626079i	0.321000	+	0.947079i	$0.395981\pi$
$242$		−	7.17430e6i		−	0.506213i
$243$	2.51494e6	−	1.41268e7i	0.175271	−	0.984520i
$244$	33742.1	+	33742.1i	0.00232275	+	0.00232275i
$245$	2.57822e6	−	2.57822e6i	0.175316	−	0.175316i
$246$	40573.8	+	331349.i	0.00272546	+	0.0222577i
$247$		−	1.76308e7i		−	1.16999i
$248$	4.08166e6	−	4.08166e6i	0.267597	−	0.267597i
$249$	−5.23730e6	+	6.69889e6i	−0.339242	+	0.433915i
$250$	7.01906e6	−	7.01906e6i	0.449220	−	0.449220i
$251$			1.46572e7i			0.926891i	0.886125	+	0.463445i	$0.153387\pi$
$251$			1.46572e7i			0.926891i	−0.886125	+	0.463445i	$0.846613\pi$
$252$	1.69577e6	−	2.81803e6i	0.105966	−	0.176094i
$253$			7.58866e6i			0.468601i
$254$			1.02691e7i			0.626662i
$255$	1.49353e7	+	1.27847e7i	0.900725	+	0.771025i
$256$	−9.05806e6			−0.539903
$257$	1.99841e7			1.17730			0.588648	−	0.808390i	$-0.299661\pi$
$257$	1.99841e7			1.17730			0.588648	+	0.808390i	$0.299661\pi$
$258$	4.43746e6	+	3.46928e6i	0.258390	+	0.202013i
$259$	1.70164e7			0.979421
$260$	−4.41649e6	−	4.41649e6i	−0.251279	−	0.251279i
$261$	−475880.	+	790816.i	−0.0267655	+	0.0444789i
$262$	1.54618e7	+	1.54618e7i	0.859720	+	0.859720i
$263$	2.10868e7			1.15916			0.579581	−	0.814915i	$-0.303216\pi$
$263$	2.10868e7			1.15916			0.579581	+	0.814915i	$0.303216\pi$
$264$	−1.58514e6	−	1.29452e7i	−0.0861499	−	0.703551i
$265$	−2.77308e7	−	2.77308e7i	−1.49013	−	1.49013i
$266$	−9.62767e6	+	9.62767e6i	−0.511536	+	0.511536i
$267$	1.64322e7	+	1.28470e7i	0.863301	+	0.674943i
$268$	−5.64605e6			−0.293319
$269$	2.56767e7	+	2.56767e7i	1.31911	+	1.31911i	0.914478	+	0.404635i	$0.132601\pi$
$269$	2.56767e7	+	2.56767e7i	1.31911	+	1.31911i	0.404635	+	0.914478i	$0.367399\pi$
$270$	7.52196e6	+	1.96534e7i	0.382155	+	0.998497i
$271$	81469.8			0.00409344			0.00204672	−	0.999998i	$-0.499349\pi$
$271$	81469.8			0.00409344			0.00204672	+	0.999998i	$0.499349\pi$
$272$	−1.05704e7	−	1.15537e7i	−0.525271	−	0.574133i
$273$	−3.56110e7	+	4.36057e6i	−1.75024	+	0.214317i
$274$		−	1.69831e7i		−	0.825591i
$275$	−3.95203e6	−	3.95203e6i	−0.190030	−	0.190030i
$276$	−337936.	−	2.75978e6i	−0.0160734	−	0.131265i
$277$	1.86794e7	−	1.86794e7i	0.878866	−	0.878866i	−0.114551	−	0.993417i	$-0.536543\pi$
$277$	1.86794e7	−	1.86794e7i	0.878866	−	0.878866i	0.993417	+	0.114551i	$0.0365430\pi$
$278$	6.89989e6	−	6.89989e6i	0.321150	−	0.321150i
$279$	−6.57985e6	−	3.95948e6i	−0.302973	−	0.182316i
$280$			3.06304e7i			1.39534i
$281$	2.77249e7			1.24954			0.624771	−	0.780808i	$-0.285192\pi$
$281$	2.77249e7			1.24954			0.624771	+	0.780808i	$0.285192\pi$
$282$	−2.44697e7	−	1.91308e7i	−1.09114	−	0.853072i
$283$	−1.94918e7	−	1.94918e7i	−0.859987	−	0.859987i	0.131349	−	0.991336i	$-0.458069\pi$
$283$	−1.94918e7	−	1.94918e7i	−0.859987	−	0.859987i	−0.991336	+	0.131349i	$0.958069\pi$
$284$	−4.15719e6	−	4.15719e6i	−0.181487	−	0.181487i
$285$	2.43393e6	+	1.98769e7i	0.105141	+	0.858647i
$286$	−1.58413e7	+	1.58413e7i	−0.677161	+	0.677161i
$287$	646428.			0.0273448
$288$	2.12432e6	+	8.54419e6i	0.0889290	+	0.357679i
$289$	−2.14133e6	+	2.40424e7i	−0.0887134	+	0.996057i
$290$		−	1.35358e6i		−	0.0554998i
$291$	3.09851e6	+	2.53043e7i	0.125740	+	1.02687i
$292$	6.15638e6	−	6.15638e6i	0.247273	−	0.247273i
$293$			3.22499e6i			0.128211i	0.997943	+	0.0641056i	$0.0204195\pi$
$293$			3.22499e6i			0.128211i	−0.997943	+	0.0641056i	$0.979581\pi$
$294$	3.77495e6	+	2.95132e6i	0.148549	+	0.116138i
$295$	1.66386e7	+	1.66386e7i	0.648113	+	0.648113i
$296$	−1.74817e7	+	1.74817e7i	−0.674074	+	0.674074i
$297$	−1.62042e7	+	6.20182e6i	−0.618525	+	0.236728i
$298$		−	3.84349e7i		−	1.45237i
$299$	−2.14465e7	+	2.14465e7i	−0.802311	+	0.802311i
$300$	1.61323e6	+	1.26125e6i	0.0597494	+	0.0467131i
$301$	7.71261e6	−	7.71261e6i	0.282815	−	0.282815i
$302$		−	3.68918e7i		−	1.33940i
$303$	−4.07652e7	−	3.18709e7i	−1.46542	−	1.14569i
$304$		−	1.59507e7i		−	0.567751i
$305$			591234.i			0.0208382i
$306$	−1.42912e7	+	2.15242e7i	−0.498775	+	0.751213i
$307$	2.50073e7			0.864275			0.432137	−	0.901808i	$-0.357760\pi$
$307$	2.50073e7			0.864275			0.432137	+	0.901808i	$0.357760\pi$
$308$	−3.97689e6			−0.136110
$309$	−7.72305e6	+	9.87834e6i	−0.261766	+	0.334818i
$310$	1.12623e7			0.378042
$311$	5.59278e6	+	5.59278e6i	0.185929	+	0.185929i	0.793933	−	0.608005i	$-0.208030\pi$
$311$	5.59278e6	+	5.59278e6i	0.185929	+	0.185929i	−0.608005	+	0.793933i	$0.708030\pi$
$312$	3.21048e7	−	4.10644e7i	1.05708	−	1.35208i
$313$	1.17169e7	+	1.17169e7i	0.382102	+	0.382102i	0.871859	−	0.489757i	$-0.162915\pi$
$313$	1.17169e7	+	1.17169e7i	0.382102	+	0.382102i	−0.489757	+	0.871859i	$0.662915\pi$
$314$	−3.36064e7			−1.08551
$315$	3.95457e7	−	9.83218e6i	1.26523	−	0.314571i
$316$	6.23363e6	+	6.23363e6i	0.197551	+	0.197551i
$317$	2.55349e7	−	2.55349e7i	0.801597	−	0.801597i	−0.181748	−	0.983345i	$-0.558176\pi$
$317$	2.55349e7	−	2.55349e7i	0.801597	−	0.801597i	0.983345	+	0.181748i	$0.0581755\pi$
$318$	3.17438e7	−	4.06026e7i	0.987136	−	1.26262i
$319$	1.11602e6			0.0343796
$320$	−3.05082e7	−	3.05082e7i	−0.931036	−	0.931036i
$321$	1.14382e7	−	1.40060e6i	0.345813	−	0.0423448i
$322$	2.34226e7			0.701563
$323$	−1.81400e7	+	1.65961e7i	−0.538306	+	0.492492i
$324$	5.61683e6	−	2.97703e6i	0.165141	−	0.0875282i
$325$		−	2.23379e7i		−	0.650716i
$326$	−998913.	−	998913.i	−0.0288320	−	0.0288320i
$327$	2.95395e7	−	3.61712e6i	0.844813	−	0.103447i
$328$	−664102.	+	664102.i	−0.0188197	+	0.0188197i
$329$	−4.25300e7	+	4.25300e7i	−1.19428	+	1.19428i
$330$	1.56725e7	−	2.00463e7i	0.436110	−	0.557817i
$331$			6.36159e7i			1.75421i	0.480298	+	0.877105i	$0.340528\pi$
$331$			6.36159e7i			1.75421i	−0.480298	+	0.877105i	$0.659472\pi$
$332$	−3.76718e6			−0.102944
$333$	2.81814e7	+	1.69584e7i	0.763185	+	0.459253i
$334$	−1.83712e7	−	1.83712e7i	−0.493059	−	0.493059i
$335$	−4.94654e7	−	4.94654e7i	−1.31573	−	1.31573i
$336$	−3.22174e7	+	3.94502e6i	−0.849322	+	0.104000i
$337$	−1.62434e7	+	1.62434e7i	−0.424412	+	0.424412i	−0.886720	−	0.462307i	$-0.847022\pi$
$337$	−1.62434e7	+	1.62434e7i	−0.424412	+	0.424412i	0.462307	+	0.886720i	$0.347022\pi$
$338$	−5.47195e7			−1.41707
$339$	104922.	+	856851.i	0.00269318	+	0.0219941i
$340$	−386724.	+	8.70132e6i	−0.00983931	+	0.221385i
$341$			9.28568e6i			0.234181i
$342$	−2.55395e7	+	6.34983e6i	−0.638460	+	0.158739i
$343$	−2.48151e7	+	2.48151e7i	−0.614941	+	0.614941i
$344$			1.58470e7i			0.389287i
$345$	2.12180e7	−	2.71394e7i	0.516710	−	0.660910i
$346$	9.66421e6	+	9.66421e6i	0.233313	+	0.233313i
$347$	1.17160e7	−	1.17160e7i	0.280408	−	0.280408i	−0.552864	−	0.833272i	$-0.686465\pi$
$347$	1.17160e7	−	1.17160e7i	0.280408	−	0.280408i	0.833272	+	0.552864i	$0.186465\pi$
$348$	−405867.	+	49698.4i	−0.00963044	+	0.00117925i
$349$			3.00886e7i			0.707825i	0.935279	+	0.353912i	$0.115149\pi$
$349$			3.00886e7i			0.707825i	−0.935279	+	0.353912i	$0.884851\pi$
$350$	−1.21980e7	+	1.21980e7i	−0.284502	+	0.284502i
$351$	−6.33221e7	−	2.82679e7i	−1.46431	−	0.653689i
$352$	7.52786e6	−	7.52786e6i	0.172601	−	0.172601i
$353$		−	1.68746e7i		−	0.383628i	−0.981431	−	0.191814i	$-0.938563\pi$
$353$		−	1.68746e7i		−	0.383628i	0.981431	−	0.191814i	$-0.0614370\pi$
$354$	−1.90464e7	+	2.43617e7i	−0.429341	+	0.549158i
$355$		−	7.28429e7i		−	1.62818i
$356$			9.24079e6i			0.204814i
$357$	3.80076e7	+	3.25347e7i	0.835345	+	0.715059i
$358$	3.05496e7			0.665819
$359$	5.09899e7			1.10205			0.551024	−	0.834489i	$-0.314237\pi$
$359$	5.09899e7			1.10205			0.551024	+	0.834489i	$0.314237\pi$
$360$	−3.05259e7	+	5.07279e7i	−0.654276	+	1.08728i
$361$	2.20023e7			0.467678
$362$	1.02089e7	+	1.02089e7i	0.215204	+	0.215204i
$363$	−2.11545e7	−	1.65389e7i	−0.442265	−	0.345770i
$364$	−1.12392e7	−	1.12392e7i	−0.233040	−	0.233040i
$365$	1.07873e8			2.21837
$366$	−771229.	+	94437.0i	−0.0157304	+	0.00192619i
$367$	−3.86515e7	−	3.86515e7i	−0.781931	−	0.781931i	0.198225	−	0.980157i	$-0.436482\pi$
$367$	−3.86515e7	−	3.86515e7i	−0.781931	−	0.781931i	−0.980157	+	0.198225i	$0.936482\pi$
$368$	−1.94027e7	+	1.94027e7i	−0.389331	+	0.389331i
$369$	1.07057e6	+	644223.i	0.0213076	+	0.0128220i
$370$	−4.82361e7			−0.952285
$371$	−7.05701e7	−	7.05701e7i	−1.38197	−	1.38197i
$372$	−413507.	−	3.37695e6i	−0.00803257	−	0.0655987i
$373$	5.31174e7			1.02355			0.511776	−	0.859119i	$-0.328988\pi$
$373$	5.31174e7			1.02355			0.511776	+	0.859119i	$0.328988\pi$
$374$	3.12103e7	+	1.38712e6i	0.596600	+	0.0265155i
$375$	−4.51569e6	−	3.68778e7i	−0.0856308	−	0.699312i
$376$		−	8.73855e7i		−	1.64390i
$377$	3.15402e6	+	3.15402e6i	0.0588628	+	0.0588628i
$378$	1.91421e7	+	5.00145e7i	0.354416	+	0.926020i
$379$	−2.08154e7	+	2.08154e7i	−0.382355	+	0.382355i	−0.871950	−	0.489595i	$-0.837145\pi$
$379$	−2.08154e7	+	2.08154e7i	−0.382355	+	0.382355i	0.489595	+	0.871950i	$0.337145\pi$
$380$	−6.27335e6	+	6.27335e6i	−0.114327	+	0.114327i
$381$	3.02801e7	+	2.36735e7i	0.547498	+	0.428043i
$382$			4.52597e7i			0.811936i
$383$	−9.90886e7			−1.76371			−0.881855	−	0.471520i	$-0.843705\pi$
$383$	−9.90886e7			−1.76371			−0.881855	+	0.471520i	$0.843705\pi$
$384$	2.20691e7	−	2.82279e7i	0.389754	−	0.498523i
$385$	−3.48418e7	−	3.48418e7i	−0.610546	−	0.610546i
$386$	1.64335e7	+	1.64335e7i	0.285738	+	0.285738i
$387$	2.04594e7	−	5.08677e6i	0.352988	−	0.0877626i
$388$	−7.98628e6	+	7.98628e6i	−0.136725	+	0.136725i
$389$	3.43181e7			0.583008			0.291504	−	0.956570i	$-0.405844\pi$
$389$	3.43181e7			0.583008			0.291504	+	0.956570i	$0.405844\pi$
$390$	1.00946e8	−	1.23608e7i	1.70174	−	0.208379i
$391$	4.22537e7	+	1.87794e6i	0.706861	+	0.0314160i
$392$			1.34810e7i			0.223802i
$393$	8.12357e7	−	9.94732e6i	1.33835	−	0.163881i
$394$	−7.01369e7	+	7.01369e7i	−1.14672	+	1.14672i
$395$			1.09227e8i			1.77230i
$396$	−6.58623e6	−	3.96332e6i	−0.106060	−	0.0638224i
$397$	2.64253e7	+	2.64253e7i	0.422326	+	0.422326i	0.886004	−	0.463678i	$-0.153470\pi$
$397$	2.64253e7	+	2.64253e7i	0.422326	+	0.422326i	−0.463678	+	0.886004i	$0.653470\pi$
$398$	−1.77329e7	+	1.77329e7i	−0.281275	+	0.281275i
$399$	6.19393e6	+	5.05833e7i	0.0975096	+	0.796322i
$400$		−	2.02091e7i		−	0.315767i
$401$	−1.65716e7	+	1.65716e7i	−0.256999	+	0.256999i	−0.823832	−	0.566834i	$-0.808168\pi$
$401$	−1.65716e7	+	1.65716e7i	−0.256999	+	0.256999i	0.566834	+	0.823832i	$0.308168\pi$
$402$	5.66236e7	−	7.24257e7i	0.871604	−	1.11484i
$403$	−2.62425e7	+	2.62425e7i	−0.400950	+	0.400950i
$404$		−	2.29246e7i		−	0.347663i
$405$	7.52914e7	+	2.31275e7i	1.13339	+	0.348147i
$406$		−	3.44463e6i		−	0.0514713i
$407$		−	3.97704e7i		−	0.589898i
$408$	−7.24709e7	+	5.62255e6i	−1.06705	+	0.0827852i
$409$	−4.54975e7			−0.664993			−0.332497	−	0.943104i	$-0.607891\pi$
$409$	−4.54975e7			−0.664993			−0.332497	+	0.943104i	$0.607891\pi$
$410$	−1.83241e6			−0.0265872
$411$	−5.00771e7	−	3.91511e7i	−0.721297	−	0.563922i
$412$	−5.55517e6			−0.0794338
$413$	4.23423e7	+	4.23423e7i	0.601069	+	0.601069i
$414$	3.87907e7	+	2.33426e7i	0.546672	+	0.328964i
$415$	−3.30045e7	−	3.30045e7i	−0.461774	−	0.461774i
$416$	4.25494e7			0.591035
$417$	−4.43902e6	−	3.62517e7i	−0.0612180	−	0.499942i
$418$	2.25016e7	+	2.25016e7i	0.308094	+	0.308094i
$419$	5.61517e7	−	5.61517e7i	0.763345	−	0.763345i	−0.213581	−	0.976925i	$-0.568513\pi$
$419$	5.61517e7	−	5.61517e7i	0.763345	−	0.763345i	0.976925	+	0.213581i	$0.0685126\pi$
$420$	1.42226e7	+	1.11194e7i	0.191969	+	0.150084i
$421$	−7.91699e7			−1.06100			−0.530498	−	0.847686i	$-0.677995\pi$
$421$	−7.91699e7			−1.06100			−0.530498	+	0.847686i	$0.677995\pi$
$422$	2.27608e7	+	2.27608e7i	0.302866	+	0.302866i
$423$	−1.12820e8	+	2.80502e7i	−1.49061	+	0.370608i
$424$	1.44999e8			1.90225
$425$	−2.29829e7	+	2.10269e7i	−0.299391	+	0.273911i
$426$	9.50191e7	−	1.16351e7i	1.22909	−	0.150502i
$427$			1.50459e6i			0.0193256i
$428$	3.60999e6	+	3.60999e6i	0.0460442	+	0.0460442i
$429$	1.01914e7	+	8.32293e7i	0.129081	+	1.05415i
$430$	−2.18628e7	+	2.18628e7i	−0.274979	+	0.274979i
$431$	1.37404e7	−	1.37404e7i	0.171620	−	0.171620i	−0.616071	−	0.787691i	$-0.711276\pi$
$431$	1.37404e7	−	1.37404e7i	0.171620	−	0.171620i	0.787691	+	0.616071i	$0.211276\pi$
$432$	−5.72876e7	−	2.55740e7i	−0.710575	−	0.317210i
$433$			3.68121e7i			0.453447i	0.973959	+	0.226724i	$0.0728014\pi$
$433$			3.68121e7i			0.453447i	−0.973959	+	0.226724i	$0.927199\pi$
$434$	2.86605e7			0.350602
$435$	−3.99124e6	−	3.12042e6i	−0.0484887	−	0.0379092i
$436$	9.32296e6	+	9.32296e6i	0.112485	+	0.112485i
$437$	3.04634e7	+	3.04634e7i	0.365035	+	0.365035i
$438$	1.72304e7	+	1.40714e8i	0.205056	+	1.67461i
$439$	1.11231e8	−	1.11231e8i	1.31472	−	1.31472i	0.396831	−	0.917892i	$-0.370110\pi$
$439$	1.11231e8	−	1.11231e8i	1.31472	−	1.31472i	0.917892	−	0.396831i	$-0.129890\pi$
$440$	7.15887e7			0.840401
$441$	1.74048e7	−	4.32732e6i	0.202933	−	0.0504549i
$442$	8.42841e7	+	9.21244e7i	0.976065	+	1.06686i
$443$			1.11843e7i			0.128647i	0.997929	+	0.0643233i	$0.0204889\pi$
$443$			1.11843e7i			0.128647i	−0.997929	+	0.0643233i	$0.979511\pi$
$444$	1.77105e6	+	1.44634e7i	0.0202340	+	0.165243i
$445$	−8.09593e7	+	8.09593e7i	−0.918727	+	0.918727i
$446$		−	3.64168e7i		−	0.410485i
$447$	−1.13331e8	−	8.86040e7i	−1.26890	−	0.992043i
$448$	−7.76380e7	−	7.76380e7i	−0.863456	−	0.863456i
$449$	−1.16323e8	+	1.16323e8i	−1.28507	+	1.28507i	−0.347322	+	0.937746i	$0.612909\pi$
$449$	−1.16323e8	+	1.16323e8i	−1.28507	+	1.28507i	−0.937746	+	0.347322i	$0.887091\pi$
$450$	−3.23579e7	+	8.04508e6i	−0.355094	+	0.0882862i
$451$		−	1.51082e6i		−	0.0164696i
$452$	−270430.	+	270430.i	−0.00292847	+	0.00292847i
$453$	−1.08781e8	−	8.50468e7i	−1.17020	−	0.914879i
$454$	2.54606e7	−	2.54606e7i	0.272083	−	0.272083i
$455$		−	1.96935e8i		−	2.09068i
$456$	−5.83295e7	−	4.56030e7i	−0.615168	−	0.480949i
$457$			1.55090e8i			1.62493i	0.583008	+	0.812466i	$0.301875\pi$
$457$			1.55090e8i			1.62493i	−0.583008	+	0.812466i	$0.698125\pi$
$458$		−	1.97671e7i		−	0.205753i
$459$	3.05218e7	+	9.17595e7i	0.315625	+	0.948884i
$460$	1.52620e7			0.156798
$461$	−1.30365e8			−1.33063			−0.665315	−	0.746563i	$-0.731703\pi$
$461$	−1.30365e8			−1.33063			−0.665315	+	0.746563i	$0.731703\pi$
$462$	3.98838e7	−	5.10142e7i	0.404455	−	0.517327i
$463$	1.25009e8			1.25950			0.629752	−	0.776796i	$-0.283156\pi$
$463$	1.25009e8			1.25950			0.629752	+	0.776796i	$0.283156\pi$
$464$	2.85345e6	+	2.85345e6i	0.0285638	+	0.0285638i
$465$	2.59629e7	−	3.32085e7i	0.258223	−	0.330286i
$466$	−7.66240e7	−	7.66240e7i	−0.757194	−	0.757194i
$467$	8.94598e7			0.878370			0.439185	−	0.898397i	$-0.355267\pi$
$467$	8.94598e7			0.878370			0.439185	+	0.898397i	$0.355267\pi$
$468$	−7.41268e6	−	2.98143e7i	−0.0723166	−	0.290862i
$469$	−1.25881e8	−	1.25881e8i	−1.22023	−	1.22023i
$470$	1.20559e8	−	1.20559e8i	1.16120	−	1.16120i
$471$	−7.74728e7	+	9.90934e7i	−0.741458	+	0.948379i
$472$	−8.69999e7			−0.827357
$473$	−1.80257e7	−	1.80257e7i	−0.170337	−	0.170337i
$474$	−1.42479e8	+	1.74466e7i	−1.33788	+	0.163823i
$475$	−3.17296e7			−0.296062
$476$	−984145.	+	2.21433e7i	−0.00912511	+	0.205316i
$477$	−4.65438e7	−	1.87202e8i	−0.428851	−	1.72487i
$478$			9.59354e7i			0.878406i
$479$	−3.67816e7	−	3.67816e7i	−0.334676	−	0.334676i	0.519683	−	0.854359i	$-0.326050\pi$
$479$	−3.67816e7	−	3.67816e7i	−0.334676	−	0.334676i	−0.854359	+	0.519683i	$0.826050\pi$
$480$	−4.79700e7	+	5.87392e6i	−0.433756	+	0.0531135i
$481$	1.12396e8	−	1.12396e8i	1.00999	−	1.00999i
$482$	6.32181e7	−	6.32181e7i	0.564547	−	0.564547i
$483$	5.39961e7	−	6.90649e7i	0.479204	−	0.612937i
$484$		−	1.18964e7i		−	0.104925i
$485$	−1.39937e8			−1.22661
$486$	−1.81422e7	+	1.01907e8i	−0.158045	+	0.887760i
$487$	−8.59571e7	−	8.59571e7i	−0.744209	−	0.744209i	0.229176	−	0.973385i	$-0.426397\pi$
$487$	−8.59571e7	−	8.59571e7i	−0.744209	−	0.744209i	−0.973385	+	0.229176i	$0.926397\pi$
$488$	−1.54572e6	−	1.54572e6i	−0.0133006	−	0.0133006i
$489$	−5.24824e6	+	642647.i	−0.0448835	+	0.00549599i
$490$	−1.85986e7	+	1.85986e7i	−0.158086	+	0.158086i
$491$	9.25313e7			0.781707			0.390854	−	0.920453i	$-0.372180\pi$
$491$	9.25313e7			0.781707			0.390854	+	0.920453i	$0.372180\pi$
$492$	67279.3	+	549442.i	0.000564919	+	0.00461346i
$493$	276178.	−	6.21402e6i	0.00230488	−	0.0518599i
$494$			1.27184e8i			1.05500i
$495$	−2.29795e7	−	9.24254e7i	−0.189464	−	0.762036i
$496$	−2.37417e7	+	2.37417e7i	−0.194566	+	0.194566i
$497$		−	1.85372e8i		−	1.51000i
$498$	3.77806e7	−	4.83241e7i	0.305901	−	0.391269i
$499$	7.30043e7	+	7.30043e7i	0.587553	+	0.587553i	0.936968	−	0.349415i	$-0.113620\pi$
$499$	7.30043e7	+	7.30043e7i	0.587553	+	0.587553i	−0.349415	+	0.936968i	$0.613620\pi$
$500$	1.16390e7	−	1.16390e7i	0.0931119	−	0.0931119i
$501$	−9.65216e7	+	1.18191e7i	−0.767558	+	0.0939875i
$502$		−	1.05733e8i		−	0.835795i
$503$	−5.29290e7	+	5.29290e7i	−0.415901	+	0.415901i	−0.883788	−	0.467887i	$-0.845015\pi$
$503$	−5.29290e7	+	5.29290e7i	−0.415901	+	0.415901i	0.467887	+	0.883788i	$0.345015\pi$
$504$	−7.76831e7	+	1.29094e8i	−0.606785	+	1.00835i
$505$	2.00844e8	−	2.00844e8i	1.55950	−	1.55950i
$506$		−	5.47427e7i		−	0.422546i
$507$	−1.26145e8	+	1.61348e8i	−0.967934	+	1.23806i
$508$			1.70283e7i			0.129891i
$509$			1.32715e8i			1.00639i	0.864172	+	0.503196i	$0.167843\pi$
$509$			1.32715e8i			1.00639i	−0.864172	+	0.503196i	$0.832157\pi$
$510$	−1.07739e8	−	9.22253e7i	−0.812201	−	0.695248i
$511$	2.74518e8			2.05735
$512$	1.50275e8			1.11964
$513$	−4.01528e7	+	8.99452e7i	−0.297415	+	0.666232i
$514$	−1.44160e8			−1.06159
$515$	−4.86692e7	−	4.86692e7i	−0.356314	−	0.356314i
$516$	7.35818e6	+	5.75275e6i	0.0535576	+	0.0418722i
$517$	9.94002e7	+	9.94002e7i	0.719309	+	0.719309i
$518$	−1.22752e8			−0.883162
$519$	5.07753e7	−	6.21744e6i	0.363204	−	0.0444743i
$520$	2.02319e8	+	2.02319e8i	1.43889	+	1.43889i
$521$	−3.72188e7	+	3.72188e7i	−0.263178	+	0.263178i	−0.826344	−	0.563166i	$-0.809583\pi$
$521$	−3.72188e7	+	3.72188e7i	−0.263178	+	0.263178i	0.563166	+	0.826344i	$0.309583\pi$
$522$	3.43288e6	−	5.70475e6i	0.0241350	−	0.0401075i
$523$	4.99050e7			0.348850			0.174425	−	0.984670i	$-0.444193\pi$
$523$	4.99050e7			0.348850			0.174425	+	0.984670i	$0.444193\pi$
$524$	2.56388e7	+	2.56388e7i	0.178198	+	0.178198i
$525$	7.84756e6	+	6.40878e7i	0.0542321	+	0.442892i
$526$	−1.52115e8			−1.04524
$527$	5.17027e7	+	2.29789e6i	0.353249	+	0.0156999i
$528$	9.22021e6	+	7.52977e7i	0.0626382	+	0.511541i
$529$			7.39233e7i			0.499361i
$530$	2.00043e8	+	2.00043e8i	1.34368	+	1.34368i
$531$	2.79264e7	+	1.12322e8i	0.186523	+	0.750208i
$532$	−1.59646e7	+	1.59646e7i	−0.106028	+	0.106028i
$533$	4.26976e6	−	4.26976e6i	0.0281982	−	0.0281982i
$534$	−1.18538e8	−	9.26749e7i	−0.778455	−	0.608609i
$535$			6.32549e7i			0.413078i
$536$	2.58645e8			1.67961
$537$	7.04261e7	−	9.00800e7i	0.454790	−	0.581709i
$538$	−1.85225e8	−	1.85225e8i	−1.18947	−	1.18947i
$539$	−1.53345e7	−	1.53345e7i	−0.0979272	−	0.0979272i
$540$	1.24729e7	+	3.25892e7i	0.0792110	+	0.206963i
$541$	−3.27118e7	+	3.27118e7i	−0.206592	+	0.206592i	−0.802817	−	0.596225i	$-0.796666\pi$
$541$	−3.27118e7	+	3.27118e7i	−0.206592	+	0.206592i	0.596225	+	0.802817i	$0.296666\pi$
$542$	−587703.			−0.00369113
$543$	5.36368e7	−	6.56783e6i	0.335014	−	0.0410225i
$544$	−4.00523e7	−	4.37780e7i	−0.248789	−	0.271932i
$545$			1.63358e8i			1.00914i
$546$	2.56889e8	−	3.14561e7i	1.57822	−	0.193253i
$547$	1.03237e8	−	1.03237e8i	0.630770	−	0.630770i	−0.317491	−	0.948261i	$-0.602840\pi$
$547$	1.03237e8	−	1.03237e8i	0.630770	−	0.630770i	0.948261	+	0.317491i	$0.102840\pi$
$548$		−	2.81613e7i		−	0.171124i
$549$	−1.49945e6	+	2.49179e6i	−0.00906183	+	0.0150589i
$550$	2.85090e7	+	2.85090e7i	0.171354	+	0.171354i
$551$	4.48010e6	−	4.48010e6i	0.0267814	−	0.0267814i
$552$	1.54808e7	+	1.26425e8i	0.0920399	+	0.751653i
$553$			2.77963e8i			1.64366i
$554$	−1.34748e8	+	1.34748e8i	−0.792490	+	0.792490i
$555$	−1.11199e8	+	1.42231e8i	−0.650461	+	0.831986i
$556$	1.14414e7	−	1.14414e7i	0.0665662	−	0.0665662i
$557$		−	1.45852e8i		−	0.844008i	−0.906594	−	0.422004i	$-0.861327\pi$
$557$		−	1.45852e8i		−	0.844008i	0.906594	−	0.422004i	$-0.138673\pi$
$558$	4.74654e7	+	2.85627e7i	0.273196	+	0.164398i
$559$		−	1.01886e8i		−	0.583283i
$560$		−	1.78167e8i		−	1.01453i
$561$	7.60393e7	−	8.88305e7i	0.430675	−	0.503122i
$562$	−2.00001e8			−1.12674
$563$	−1.02418e8			−0.573919			−0.286960	−	0.957943i	$-0.592645\pi$
$563$	−1.02418e8			−0.573919			−0.286960	+	0.957943i	$0.592645\pi$
$564$	−4.05755e7	−	3.17226e7i	−0.226166	−	0.176820i
$565$	−4.73852e6			−0.0262723
$566$	1.40609e8	+	1.40609e8i	0.775467	+	0.775467i
$567$	1.91603e8	+	5.88553e7i	1.05112	+	0.322877i
$568$	1.90440e8	+	1.90440e8i	1.03924	+	1.03924i
$569$	6.38457e7			0.346573			0.173286	−	0.984871i	$-0.444561\pi$
$569$	6.38457e7			0.346573			0.173286	+	0.984871i	$0.444561\pi$
$570$	−1.75578e7	−	1.43387e8i	−0.0948080	−	0.774258i
$571$	−1.93481e8	−	1.93481e8i	−1.03927	−	1.03927i	−0.999197	−	0.0400758i	$-0.987240\pi$
$571$	−1.93481e8	−	1.93481e8i	−1.03927	−	1.03927i	−0.0400758	−	0.999197i	$-0.512760\pi$
$572$	−2.62680e7	+	2.62680e7i	−0.140358	+	0.140358i
$573$	1.33455e8	+	1.04337e8i	0.709367	+	0.554594i
$574$	−4.66317e6			−0.0246573
$575$	3.85964e7	+	3.85964e7i	0.203022	+	0.203022i
$576$	−5.12053e7	−	2.05951e8i	−0.267946	−	1.07770i
$577$	−9.76879e7			−0.508526			−0.254263	−	0.967135i	$-0.581833\pi$
$577$	−9.76879e7			−0.508526			−0.254263	+	0.967135i	$0.581833\pi$
$578$	1.54470e7	−	1.73436e8i	0.0799946	−	0.898163i
$579$	8.63409e7	−	1.05724e7i	0.444816	−	0.0544678i
$580$		−	2.24451e6i		−	0.0115037i
$581$	−8.39907e7	−	8.39907e7i	−0.428255	−	0.428255i
$582$	−2.23519e7	−	1.82539e8i	−0.113382	−	0.925948i
$583$	−1.64935e8	+	1.64935e8i	−0.832352	+	0.832352i
$584$	−2.82023e8	+	2.82023e8i	−1.41594	+	1.41594i
$585$	1.96263e8	−	3.26149e8i	0.980325	−	1.62910i
$586$		−	2.32643e7i		−	0.115610i
$587$	2.24980e8			1.11232			0.556159	−	0.831076i	$-0.312274\pi$
$587$	2.24980e8			1.11232			0.556159	+	0.831076i	$0.312274\pi$
$588$	6.25961e6	+	4.89386e6i	0.0307904	+	0.0240724i
$589$	3.72759e7	+	3.72759e7i	0.182424	+	0.182424i
$590$	−1.20027e8	−	1.20027e8i	−0.584416	−	0.584416i
$591$	4.51224e7	+	3.68496e8i	0.218590	+	1.78513i
$592$	1.01685e8	−	1.01685e8i	0.490109	−	0.490109i
$593$	1.31842e8			0.632253			0.316126	−	0.948717i	$-0.397618\pi$
$593$	1.31842e8			0.632253			0.316126	+	0.948717i	$0.397618\pi$
$594$	1.16893e8	−	4.47384e7i	0.557735	−	0.213462i
$595$	−2.02621e8	+	1.85377e8i	−0.961910	+	0.880045i
$596$		−	6.37326e7i		−	0.301039i
$597$	1.14084e7	+	9.31679e7i	0.0536170	+	0.437868i
$598$	1.54710e8	−	1.54710e8i	0.723459	−	0.723459i
$599$		−	2.27191e8i		−	1.05709i	−0.848906	−	0.528544i	$-0.822738\pi$
$599$		−	2.27191e8i		−	1.05709i	0.848906	−	0.528544i	$-0.177262\pi$
$600$	−7.39021e7	−	5.77779e7i	−0.342139	−	0.267490i
$601$	−1.90876e8	−	1.90876e8i	−0.879282	−	0.879282i	0.114178	−	0.993460i	$-0.463576\pi$
$601$	−1.90876e8	−	1.90876e8i	−0.879282	−	0.879282i	−0.993460	+	0.114178i	$0.963576\pi$
$602$	−5.56369e7	+	5.56369e7i	−0.255019	+	0.255019i
$603$	−8.30234e7	−	3.33926e8i	−0.378659	−	1.52299i
$604$		−	6.11739e7i		−	0.277623i
$605$	1.04225e8	−	1.04225e8i	0.470659	−	0.470659i
$606$	2.94070e8	+	2.29908e8i	1.32139	+	1.03309i
$607$	−1.97674e8	+	1.97674e8i	−0.883860	+	0.883860i	−0.993924	−	0.110065i	$-0.964894\pi$
$607$	−1.97674e8	+	1.97674e8i	−0.883860	+	0.883860i	0.110065	+	0.993924i	$0.464894\pi$
$608$		−	6.04388e7i		−	0.268909i
$609$	−1.01570e7	−	7.94092e6i	−0.0449691	−	0.0351576i
$610$		−	4.26502e6i		−	0.0187902i
$611$			5.61835e8i			2.46312i
$612$	−2.36976e7	+	3.56914e7i	−0.103383	+	0.155707i
$613$	−3.25001e8			−1.41092			−0.705462	−	0.708748i	$-0.749260\pi$
$613$	−3.25001e8			−1.41092			−0.705462	+	0.708748i	$0.749260\pi$
$614$	−1.80396e8			−0.779333
$615$	−4.22427e6	+	5.40315e6i	−0.0181604	+	0.0232285i
$616$	1.82181e8			0.779400
$617$	−2.38151e7	−	2.38151e7i	−0.101390	−	0.101390i	0.654592	−	0.755982i	$-0.272840\pi$
$617$	−2.38151e7	−	2.38151e7i	−0.101390	−	0.101390i	−0.755982	+	0.654592i	$0.772840\pi$
$618$	5.57121e7	−	7.12599e7i	0.236039	−	0.301911i
$619$	1.62122e7	+	1.62122e7i	0.0683548	+	0.0683548i	0.740458	−	0.672103i	$-0.234609\pi$
$619$	1.62122e7	+	1.62122e7i	0.0683548	+	0.0683548i	−0.672103	+	0.740458i	$0.734609\pi$
$620$	1.86750e7			0.0783586
$621$	1.58254e8	−	6.05684e7i	0.660813	−	0.252913i
$622$	−4.03449e7	−	4.03449e7i	−0.167655	−	0.167655i
$623$	−2.06027e8	+	2.06027e8i	−0.852040	+	0.852040i
$624$	−1.86743e8	+	2.38858e8i	−0.768584	+	0.983075i
$625$	3.03009e8			1.24112
$626$	−8.45226e7	−	8.45226e7i	−0.344548	−	0.344548i
$627$	1.18222e8	−	1.44763e7i	0.479619	−	0.0587293i
$628$	−5.57260e7			−0.224998
$629$	−2.21442e8	−	9.84184e6i	−0.889832	−	0.0395480i
$630$	−2.85273e8	+	7.09269e7i	−1.14088	+	0.283654i
$631$		−	3.39145e8i		−	1.34989i	−0.737869	−	0.674944i	$-0.764168\pi$
$631$		−	3.39145e8i		−	1.34989i	0.737869	−	0.674944i	$-0.235832\pi$
$632$	−2.85562e8	−	2.85562e8i	−1.13123	−	1.13123i
$633$	1.19584e8	−	1.46431e7i	0.471480	−	0.0577328i
$634$	−1.84202e8	+	1.84202e8i	−0.722815	+	0.722815i
$635$	−1.49186e8	+	1.49186e8i	−0.582648	+	0.582648i
$636$	5.26374e7	−	6.73271e7i	0.204608	−	0.261709i
$637$		−	8.66744e7i		−	0.335330i
$638$	−8.05071e6			−0.0310008
$639$	1.84740e8	−	3.07000e8i	0.708040	−	1.17662i
$640$	1.39075e8	+	1.39075e8i	0.530530	+	0.530530i
$641$	−2.16734e8	−	2.16734e8i	−0.822910	−	0.822910i	0.163614	−	0.986524i	$-0.447685\pi$
$641$	−2.16734e8	−	2.16734e8i	−0.822910	−	0.822910i	−0.986524	+	0.163614i	$0.947685\pi$
$642$	−8.25121e7	+	1.01036e7i	−0.311826	+	0.0381831i
$643$	4.91841e6	−	4.91841e6i	0.0185008	−	0.0185008i	−0.697796	−	0.716297i	$-0.745836\pi$
$643$	4.91841e6	−	4.91841e6i	0.0185008	−	0.0185008i	0.716297	+	0.697796i	$0.245836\pi$
$644$	3.88392e7			0.145416
$645$	1.40653e7	+	1.14866e8i	0.0524168	+	0.428067i
$646$	1.30857e8	−	1.19720e8i	0.485400	−	0.444090i
$647$		−	5.00184e7i		−	0.184679i	−0.995728	−	0.0923395i	$-0.970566\pi$
$647$		−	5.00184e7i		−	0.184679i	0.995728	−	0.0923395i	$-0.0294345\pi$
$648$	−2.57306e8	+	1.36377e8i	−0.945639	+	0.501207i
$649$	9.89615e7	−	9.89615e7i	0.362020	−	0.362020i
$650$			1.61140e8i			0.586763i
$651$	6.60710e7	−	8.45097e7i	0.239479	−	0.306312i
$652$	−1.65639e6	−	1.65639e6i	−0.00597614	−	0.00597614i
$653$	−9.72404e7	+	9.72404e7i	−0.349226	+	0.349226i	−0.859821	−	0.510595i	$-0.829425\pi$
$653$	−9.72404e7	+	9.72404e7i	−0.349226	+	0.349226i	0.510595	+	0.859821i	$0.329425\pi$
$654$	−2.13091e8	+	2.60930e7i	−0.761784	+	0.0932805i
$655$			4.49246e8i			1.59868i
$656$	3.86286e6	−	3.86286e6i	0.0136835	−	0.0136835i
$657$	4.54637e8	+	2.73581e8i	1.60313	+	0.964696i
$658$	3.06801e8	−	3.06801e8i	1.07691	−	1.07691i
$659$			2.32939e8i			0.813929i	0.913444	+	0.406964i	$0.133413\pi$
$659$			2.32939e8i			0.813929i	−0.913444	+	0.406964i	$0.866587\pi$
$660$	2.59881e7	−	3.32407e7i	0.0903946	−	0.115621i
$661$		−	1.75647e8i		−	0.608187i	−0.952642	−	0.304094i	$-0.901646\pi$
$661$		−	1.75647e8i		−	0.608187i	0.952642	−	0.304094i	$-0.0983536\pi$
$662$		−	4.58909e8i		−	1.58180i
$663$	4.65943e8	−	3.61495e7i	1.59879	−	0.124040i
$664$	1.72574e8			0.589483
$665$	−2.79734e8			−0.951217
$666$	−2.03294e8	−	1.22334e8i	−0.688178	−	0.414117i
$667$	−1.08993e7			−0.0367302
$668$	−3.04631e7	−	3.04631e7i	−0.102199	−	0.102199i
$669$	−1.07380e8	−	8.39517e7i	−0.358630	−	0.280383i
$670$	3.56831e8	+	3.56831e8i	1.18642	+	1.18642i
$671$	3.51649e6			0.0116397
$672$	−1.22075e8	+	1.49481e7i	−0.402271	+	0.0492582i
$673$	1.46586e8	+	1.46586e8i	0.480892	+	0.480892i	0.905416	−	0.424525i	$-0.139559\pi$
$673$	1.46586e8	+	1.46586e8i	0.480892	+	0.480892i	−0.424525	+	0.905416i	$0.639559\pi$
$674$	1.17176e8	−	1.17176e8i	0.382701	−	0.382701i
$675$	−5.08726e7	+	1.13958e8i	−0.165414	+	0.370540i
$676$	−9.07356e7			−0.293723
$677$	1.64381e8	+	1.64381e8i	0.529767	+	0.529767i	0.920503	−	0.390736i	$-0.127779\pi$
$677$	1.64381e8	+	1.64381e8i	0.529767	+	0.529767i	−0.390736	+	0.920503i	$0.627779\pi$
$678$	−756878.	−	6.18111e6i	−0.00242849	−	0.0198325i
$679$	−3.56114e8			−1.13758
$680$	1.77158e7	−	3.98606e8i	0.0563422	−	1.26770i
$681$	−1.63800e7	−	1.33769e8i	−0.0518648	−	0.423558i
$682$		−	6.69846e7i		−	0.211165i
$683$	2.93999e8	+	2.93999e8i	0.922749	+	0.922749i	0.997223	−	0.0744744i	$-0.0237279\pi$
$683$	2.93999e8	+	2.93999e8i	0.922749	+	0.922749i	−0.0744744	+	0.997223i	$0.523728\pi$
$684$	−4.23495e7	+	1.05293e7i	−0.132336	+	0.0329026i
$685$	2.46723e8	−	2.46723e8i	0.767606	−	0.767606i
$686$	1.79010e8	−	1.79010e8i	0.554504	−	0.554504i
$687$	−5.82861e7	−	4.55690e7i	−0.179761	−	0.140540i
$688$		−	9.21765e7i		−	0.283045i
$689$	−9.32253e8			−2.85021
$690$	−1.53061e8	+	1.95777e8i	−0.465927	+	0.595955i
$691$	2.37798e8	+	2.37798e8i	0.720731	+	0.720731i	0.968754	−	0.248023i	$-0.0797808\pi$
$691$	2.37798e8	+	2.37798e8i	0.720731	+	0.720731i	−0.248023	+	0.968754i	$0.579781\pi$
$692$	1.60252e7	+	1.60252e7i	0.0483598	+	0.0483598i
$693$	−5.84789e7	−	2.35206e8i	−0.175711	−	0.706723i
$694$	−8.45161e7	+	8.45161e7i	−0.252849	+	0.252849i
$695$	2.00477e8			0.597188
$696$	1.85927e7	−	2.27668e6i	0.0551462	−	0.00675265i
$697$	−8.41223e6	−	373876.i	−0.0248435	−	0.00110415i
$698$		−	2.17052e8i		−	0.638259i
$699$	−4.02579e8	+	4.92958e7i	−1.17874	+	0.144337i
$700$	−2.02267e7	+	2.02267e7i	−0.0589701	+	0.0589701i
$701$		−	3.58910e8i		−	1.04191i	−0.853583	−	0.520957i	$-0.825575\pi$
$701$		−	3.58910e8i		−	1.04191i	0.853583	−	0.520957i	$-0.174425\pi$
$702$	4.56790e8	+	2.03917e8i	1.32040	+	0.589444i
$703$	−1.59652e8	−	1.59652e8i	−0.459524	−	0.459524i
$704$	−1.81454e8	+	1.81454e8i	−0.520053	+	0.520053i
$705$	−7.75611e7	−	6.33410e8i	−0.221348	−	1.80766i
$706$			1.21729e8i			0.345924i
$707$	5.11113e8	−	5.11113e8i	1.44630	−	1.44630i
$708$	−3.15826e7	+	4.03965e7i	−0.0889915	+	0.113827i
$709$	−1.38220e8	+	1.38220e8i	−0.387821	+	0.387821i	−0.873910	−	0.486088i	$-0.838423\pi$
$709$	−1.38220e8	+	1.38220e8i	−0.387821	+	0.387821i	0.486088	+	0.873910i	$0.338423\pi$
$710$			5.25470e8i			1.46816i
$711$	−2.77014e8	+	4.60341e8i	−0.770714	+	1.28077i
$712$		−	4.23320e8i		−	1.17281i
$713$		−	9.06862e7i		−	0.250191i
$714$	−2.74177e8	−	2.34697e8i	−0.753246	−	0.644782i
$715$	−4.60271e8			−1.25920
$716$	5.06573e7			0.138007
$717$	2.82880e8	+	2.21160e8i	0.767440	+	0.599997i
$718$	−3.67828e8			−0.993737
$719$	3.48629e8	+	3.48629e8i	0.937944	+	0.937944i	0.998184	−	0.0602402i	$-0.0191867\pi$
$719$	3.48629e8	+	3.48629e8i	0.937944	+	0.937944i	−0.0602402	+	0.998184i	$0.519187\pi$
$720$	1.77559e8	−	2.95068e8i	0.475714	−	0.790540i
$721$	−1.23855e8	−	1.23855e8i	−0.330451	−	0.330451i
$722$	−1.58719e8			−0.421714
$723$	−4.06711e7	−	3.32145e8i	−0.107615	−	0.878845i
$724$	1.69283e7	+	1.69283e7i	0.0446064	+	0.0446064i
$725$	5.67618e6	−	5.67618e6i	0.0148950	−	0.0148950i
$726$	1.52603e8	+	1.19308e8i	0.398799	+	0.311787i
$727$	1.83334e8			0.477133			0.238566	−	0.971126i	$-0.423323\pi$
$727$	1.83334e8			0.477133			0.238566	+	0.971126i	$0.423323\pi$
$728$	5.14866e8	+	5.14866e8i	1.33444	+	1.33444i
$729$	2.58665e8	+	2.88422e8i	0.667660	+	0.744466i
$730$	−7.78169e8			−2.00035
$731$	−1.04828e8	+	9.59066e7i	−0.268365	+	0.245525i
$732$	−1.27885e6	+	156595.i	−0.00326051	+	0.000399250i
$733$			5.12019e8i			1.30009i	0.759895	+	0.650046i	$0.225250\pi$
$733$			5.12019e8i			1.30009i	−0.759895	+	0.650046i	$0.774750\pi$
$734$	2.78823e8	+	2.78823e8i	0.705082	+	0.705082i
$735$	1.19654e7	+	9.77164e7i	0.0301345	+	0.246096i
$736$	−7.35189e7	+	7.35189e7i	−0.184402	+	0.184402i
$737$	−2.94206e8	+	2.94206e8i	−0.734935	+	0.734935i
$738$	−7.72281e6	−	4.64726e6i	−0.0192135	−	0.0115619i
$739$			3.27699e8i			0.811973i	0.913879	+	0.405987i	$0.133072\pi$
$739$			3.27699e8i			0.811973i	−0.913879	+	0.405987i	$0.866928\pi$
$740$	−7.99849e7			−0.197384
$741$	3.75022e8	+	2.93199e8i	0.921727	+	0.720622i
$742$	5.09075e8	+	5.09075e8i	1.24615	+	1.24615i
$743$	2.65704e8	+	2.65704e8i	0.647786	+	0.647786i	0.952458	−	0.304671i	$-0.0985466\pi$
$743$	2.65704e8	+	2.65704e8i	0.647786	+	0.647786i	−0.304671	+	0.952458i	$0.598547\pi$
$744$	1.89427e7	+	1.54698e8i	0.0459964	+	0.375634i
$745$	5.58366e8	−	5.58366e8i	1.35036	−	1.35036i
$746$	−3.83175e8			−0.922956
$747$	−5.53952e7	−	2.22803e8i	−0.132895	−	0.534515i
$748$	5.17528e7	+	2.30012e6i	0.123660	+	0.00549599i
$749$			1.60972e8i			0.383095i
$750$	3.25751e7	+	2.66027e8i	0.0772149	+	0.630583i
$751$	5.52972e8	−	5.52972e8i	1.30552	−	1.30552i	0.380905	−	0.924614i	$-0.375613\pi$
$751$	5.52972e8	−	5.52972e8i	1.30552	−	1.30552i	0.924614	−	0.380905i	$-0.124387\pi$
$752$			5.08293e8i			1.19526i
$753$	−3.11770e8	−	2.43747e8i	−0.730212	−	0.570892i
$754$	−2.27523e7	−	2.27523e7i	−0.0530777	−	0.0530777i
$755$	5.35949e8	−	5.35949e8i	1.24533	−	1.24533i
$756$	3.17413e7	+	8.29339e7i	0.0734614	+	0.191940i
$757$		−	3.19789e8i		−	0.737184i	−0.929591	−	0.368592i	$-0.879840\pi$
$757$		−	3.19789e8i		−	0.737184i	0.929591	−	0.368592i	$-0.120160\pi$
$758$	1.50157e8	−	1.50157e8i	0.344777	−	0.344777i
$759$	−1.61417e8	−	1.26198e8i	−0.369168	−	0.288621i
$760$	2.87381e8	−	2.87381e8i	0.654663	−	0.654663i
$761$		−	1.54050e8i		−	0.349549i	−0.984608	−	0.174775i	$-0.944080\pi$
$761$		−	1.54050e8i		−	0.349549i	0.984608	−	0.174775i	$-0.0559197\pi$
$762$	−2.18433e8	−	1.70775e8i	−0.493689	−	0.385974i
$763$			4.15718e8i			0.935891i
$764$			7.50495e7i			0.168294i
$765$	−5.20311e8	+	1.05078e8i	−1.16220	+	0.234708i
$766$	7.14800e8			1.59037
$767$	5.59355e8			1.23966
$768$	1.50634e8	−	1.92672e8i	0.332537	−	0.425340i
$769$	−3.24593e8			−0.713773			−0.356887	−	0.934148i	$-0.616162\pi$
$769$	−3.24593e8			−0.713773			−0.356887	+	0.934148i	$0.616162\pi$
$770$	2.51340e8	+	2.51340e8i	0.550541	+	0.550541i
$771$	−3.32333e8	+	4.25078e8i	−0.725121	+	0.927483i
$772$	2.72500e7	+	2.72500e7i	0.0592263	+	0.0592263i
$773$	4.14201e8			0.896753			0.448377	−	0.893845i	$-0.352002\pi$
$773$	4.14201e8			0.896753			0.448377	+	0.893845i	$0.352002\pi$
$774$	−1.47589e8	+	3.66947e7i	−0.318295	+	0.0791372i
$775$	4.72277e7	+	4.72277e7i	0.101459	+	0.101459i
$776$	3.65851e8	−	3.65851e8i	0.782922	−	0.782922i
$777$	−2.82981e8	+	3.61954e8i	−0.603246	+	0.771596i
$778$	−2.47562e8			−0.525709
$779$	−6.06493e6	−	6.06493e6i	−0.0128296	−	0.0128296i
$780$	1.67388e8	−	2.04967e7i	0.352728	−	0.0431916i
$781$	−4.33248e8			−0.909460
$782$	−3.04807e8	−	1.35470e7i	−0.637390	−	0.0283284i
$783$	−8.90748e6	−	2.32735e7i	−0.0185554	−	0.0484816i
$784$		−	7.84146e7i		−	0.162723i
$785$	−4.88219e8	−	4.88219e8i	−1.00927	−	1.00927i
$786$	−5.86014e8	+	7.17575e7i	−1.20681	+	0.147775i
$787$	−3.26000e8	+	3.26000e8i	−0.668795	+	0.668795i	−0.957437	−	0.288642i	$-0.906796\pi$
$787$	−3.26000e8	+	3.26000e8i	−0.668795	+	0.668795i	0.288642	+	0.957437i	$0.406796\pi$
$788$	−1.16301e8	+	1.16301e8i	−0.237686	+	0.237686i
$789$	−3.50671e8	+	4.48534e8i	−0.713952	+	0.913196i
$790$		−	7.87933e8i		−	1.59812i
$791$	−1.20587e7			−0.0243653
$792$	3.01715e8	+	1.81559e8i	0.607324	+	0.365462i
$793$	9.93803e6	+	9.93803e6i	0.0199288	+	0.0199288i
$794$	−1.90625e8	−	1.90625e8i	−0.380819	−	0.380819i
$795$	1.05102e9	−	1.28697e8i	2.09175	−	0.256134i
$796$	−2.94047e7	+	2.94047e7i	−0.0583011	+	0.0583011i
$797$	2.35997e8			0.466157			0.233079	−	0.972458i	$-0.425120\pi$
$797$	2.35997e8			0.466157			0.233079	+	0.972458i	$0.425120\pi$
$798$	−4.46815e7	−	3.64895e8i	−0.0879263	−	0.718058i
$799$	5.78058e8	−	5.28862e8i	1.13326	−	1.03682i
$800$		−	7.65745e7i		−	0.149560i
$801$	−5.46531e8	+	1.35883e8i	−1.06345	+	0.264404i
$802$	1.19543e8	−	1.19543e8i	0.231741	−	0.231741i
$803$		−	6.41597e8i		−	1.23913i
$804$	9.38930e7	−	1.20096e8i	0.180661	−	0.231079i
$805$	3.40273e8	+	3.40273e8i	0.652289	+	0.652289i
$806$	1.89307e8	−	1.89307e8i	0.361544	−	0.361544i
$807$	−9.73164e8	+	1.19164e8i	−1.85168	+	0.226738i
$808$			1.05017e9i			1.99080i
$809$	−8.65577e7	+	8.65577e7i	−0.163478	+	0.163478i	−0.784106	−	0.620627i	$-0.786878\pi$
$809$	−8.65577e7	+	8.65577e7i	−0.163478	+	0.163478i	0.620627	+	0.784106i	$0.286878\pi$
$810$	−5.43133e8	−	1.66836e8i	−1.02200	−	0.313931i
$811$	−3.56923e8	+	3.56923e8i	−0.669133	+	0.669133i	−0.957515	−	0.288382i	$-0.906883\pi$
$811$	−3.56923e8	+	3.56923e8i	−0.669133	+	0.669133i	0.288382	+	0.957515i	$0.406883\pi$
$812$		−	5.71188e6i		−	0.0106687i
$813$	−1.35483e6	+	1.73293e6i	−0.00252124	+	0.00322485i
$814$			2.86894e8i			0.531922i
$815$		−	2.90236e7i		−	0.0536140i
$816$	4.21540e8	−	3.27045e7i	0.775832	−	0.0601918i
$817$	−1.44723e8			−0.265382
$818$	3.28207e8			0.599637
$819$	4.99454e8	−	8.29991e8i	0.909167	−	1.51085i
$820$	−3.03850e6			−0.00551084
$821$	−2.43461e8	−	2.43461e8i	−0.439947	−	0.439947i	0.452047	−	0.891994i	$-0.350694\pi$
$821$	−2.43461e8	−	2.43461e8i	−0.439947	−	0.439947i	−0.891994	+	0.452047i	$0.850694\pi$
$822$	3.61244e8	+	2.82426e8i	0.650407	+	0.508499i
$823$	3.62631e8	+	3.62631e8i	0.650527	+	0.650527i	0.953120	−	0.302593i	$-0.0978523\pi$
$823$	3.62631e8	+	3.62631e8i	0.650527	+	0.650527i	−0.302593	+	0.953120i	$0.597852\pi$
$824$	2.54482e8			0.454857
$825$	1.49785e8	−	1.83411e7i	0.266751	−	0.0326636i
$826$	−3.05447e8	−	3.05447e8i	−0.541995	−	0.541995i
$827$	−7.08393e7	+	7.08393e7i	−0.125244	+	0.125244i	−0.766951	−	0.641706i	$-0.778227\pi$
$827$	−7.08393e7	+	7.08393e7i	−0.125244	+	0.125244i	0.641706	+	0.766951i	$0.278227\pi$
$828$	6.43227e7	+	3.87067e7i	0.113311	+	0.0681860i
$829$	7.69982e6			0.0135150			0.00675751	−	0.999977i	$-0.497849\pi$
$829$	7.69982e6			0.0135150			0.00675751	+	0.999977i	$0.497849\pi$
$830$	2.38086e8	+	2.38086e8i	0.416390	+	0.416390i
$831$	8.66898e7	+	7.07960e8i	0.151065	+	1.23369i
$832$	−1.02562e9			−1.78081
$833$	−8.91773e7	+	8.15878e7i	−0.154283	+	0.141153i
$834$	3.20220e7	+	2.61510e8i	0.0552014	+	0.450807i
$835$		−	5.33779e8i		−	0.916859i
$836$	3.73120e7	+	3.73120e7i	0.0638602	+	0.0638602i
$837$	1.93643e8	−	7.41132e7i	0.330237	−	0.126392i
$838$	−4.05064e8	+	4.05064e8i	−0.688322	+	0.688322i
$839$	4.19680e8	−	4.19680e8i	0.710611	−	0.710611i	−0.256052	−	0.966663i	$-0.582422\pi$
$839$	4.19680e8	−	4.19680e8i	0.710611	−	0.710611i	0.966663	+	0.256052i	$0.0824217\pi$
$840$	−6.51534e8	−	5.09380e8i	−1.09926	−	0.859417i
$841$		−	5.93220e8i		−	0.997305i
$842$	5.71112e8			0.956720
$843$	−4.61062e8	+	5.89731e8i	−0.769620	+	0.984400i
$844$	3.77420e7	+	3.77420e7i	0.0627765	+	0.0627765i
$845$	−7.94942e8	−	7.94942e8i	−1.31754	−	1.31754i
$846$	8.13855e8	−	2.02347e8i	1.34411	−	0.334184i
$847$	2.65235e8	−	2.65235e8i	0.436496	−	0.436496i
$848$	−8.43412e8			−1.38309
$849$	7.38752e8	−	9.04602e7i	1.20719	−	0.147820i
$850$	1.65793e8	−	1.51683e8i	0.269966	−	0.246990i
$851$			3.88407e8i			0.630230i
$852$	1.57560e8	−	1.92933e7i	0.254758	−	0.0311952i
$853$	−7.74360e7	+	7.74360e7i	−0.124766	+	0.124766i	−0.766733	−	0.641967i	$-0.778119\pi$
$853$	−7.74360e7	+	7.74360e7i	−0.124766	+	0.124766i	0.641967	+	0.766733i	$0.278119\pi$
$854$		−	1.08537e7i		−	0.0174263i
$855$	−4.63274e8	−	2.78779e8i	−0.741208	−	0.446028i
$856$	−1.65373e8	−	1.65373e8i	−0.263660	−	0.263660i
$857$	−6.77754e8	+	6.77754e8i	−1.07679	+	1.07679i	−0.0799902	+	0.996796i	$0.525489\pi$
$857$	−6.77754e8	+	6.77754e8i	−1.07679	+	1.07679i	−0.996796	+	0.0799902i	$0.974511\pi$
$858$	−7.35184e7	−	6.00395e8i	−0.116395	−	0.950551i
$859$		−	1.39683e8i		−	0.220376i	−0.993911	−	0.110188i	$-0.964855\pi$
$859$		−	1.39683e8i		−	0.220376i	0.993911	−	0.110188i	$-0.0351452\pi$
$860$	−3.62528e7	+	3.62528e7i	−0.0569962	+	0.0569962i
$861$	−1.07500e7	+	1.37501e7i	−0.0168422	+	0.0215424i
$862$	−9.91199e7	+	9.91199e7i	−0.154753	+	0.154753i
$863$			6.84792e8i			1.06543i	0.846294	+	0.532717i	$0.178829\pi$
$863$			6.84792e8i			1.06543i	−0.846294	+	0.532717i	$0.821171\pi$
$864$	−2.17069e8	−	9.69026e7i	−0.336555	−	0.150243i
$865$			2.80795e8i			0.433852i
$866$		−	2.65553e8i		−	0.408882i
$867$	−4.75791e8	−	4.45370e8i	−0.730061	−	0.683382i
$868$	4.75247e7			0.0726709
$869$	6.49648e8			0.989962
$870$	2.87918e7	+	2.25099e7i	0.0437231	+	0.0341835i
$871$	−1.66292e9			−2.51662
$872$	−4.27084e8	−	4.27084e8i	−0.644116	−	0.644116i
$873$	−5.89771e8	−	3.54899e8i	−0.886422	−	0.533412i
$874$	−2.19756e8	−	2.19756e8i	−0.329159	−	0.329159i
$875$	5.18991e8			0.774704
$876$	2.85714e7	+	2.33331e8i	0.0425030	+	0.347105i
$877$	−3.40280e8	−	3.40280e8i	−0.504472	−	0.504472i	0.408352	−	0.912824i	$-0.366104\pi$
$877$	−3.40280e8	−	3.40280e8i	−0.504472	−	0.504472i	−0.912824	+	0.408352i	$0.866104\pi$
$878$	−8.02396e8	+	8.02396e8i	−1.18551	+	1.18551i
$879$	−6.85983e7	−	5.36312e7i	−0.101006	−	0.0789680i
$880$	−4.16408e8			−0.611042
$881$	−6.77374e8	−	6.77374e8i	−0.990605	−	0.990605i	0.00935101	−	0.999956i	$-0.497023\pi$
$881$	−6.77374e8	−	6.77374e8i	−0.990605	−	0.990605i	−0.999956	+	0.00935101i	$0.997023\pi$
$882$	−1.25554e8	+	3.12162e7i	−0.182989	+	0.0454961i
$883$	8.11285e8			1.17840			0.589198	−	0.807989i	$-0.299444\pi$
$883$	8.11285e8			1.17840			0.589198	+	0.807989i	$0.299444\pi$
$884$	1.39760e8	+	1.52760e8i	0.202313	+	0.221133i
$885$	−6.30614e8	+	7.72188e7i	−0.909775	+	0.111402i
$886$		−	8.06809e7i		−	0.116003i
$887$	1.89425e7	+	1.89425e7i	0.0271436	+	0.0271436i	0.720548	−	0.693405i	$-0.243890\pi$
$887$	1.89425e7	+	1.89425e7i	0.0271436	+	0.0271436i	−0.693405	+	0.720548i	$0.743890\pi$
$888$	−8.11314e7	−	6.62567e8i	−0.115864	−	0.946218i
$889$	−3.79652e8	+	3.79652e8i	−0.540356	+	0.540356i
$890$	5.84020e8	−	5.84020e8i	0.828433	−	0.828433i
$891$	1.37555e8	−	4.47811e8i	0.194466	−	0.633085i
$892$		−	6.03862e7i		−	0.0850831i
$893$	7.98052e8			1.12067
$894$	8.17541e8	+	6.39167e8i	1.14419	+	0.894544i
$895$	4.43812e8	+	4.43812e8i	0.619056	+	0.619056i
$896$	3.53922e8	+	3.53922e8i	0.492021	+	0.492021i
$897$	−9.95319e7	−	8.12837e8i	−0.137907	−	1.12623i
$898$	8.39124e8	−	8.39124e8i	1.15877	−	1.15877i
$899$	−1.33367e7			−0.0183557
$900$	−5.36558e7	+	1.33403e7i	−0.0736019	+	0.0182995i
$901$	8.77542e8	+	9.59174e8i	1.19976	+	1.31136i
$902$			1.08987e7i			0.0148509i
$903$	3.57938e7	+	2.92313e8i	0.0486121	+	0.396995i
$904$	1.23884e7	−	1.23884e7i	0.0167691	−	0.0167691i
$905$			2.96620e8i			0.400179i
$906$	7.84720e8	+	6.13507e8i	1.05519	+	0.824963i
$907$	−4.26053e8	−	4.26053e8i	−0.571008	−	0.571008i	0.361402	−	0.932410i	$-0.382298\pi$
$907$	−4.26053e8	−	4.26053e8i	−0.571008	−	0.571008i	−0.932410	+	0.361402i	$0.882298\pi$
$908$	4.22187e7	−	4.22187e7i	0.0563959	−	0.0563959i
$909$	1.35584e9	−	3.37100e8i	1.80516	−	0.448814i
$910$			1.42064e9i			1.88521i
$911$	−1.51230e8	+	1.51230e8i	−0.200024	+	0.200024i	−0.800010	−	0.599986i	$-0.795173\pi$
$911$	−1.51230e8	+	1.51230e8i	−0.200024	+	0.200024i	0.599986	+	0.800010i	$0.295173\pi$
$912$	3.39284e8	+	2.65257e8i	0.447279	+	0.349690i
$913$	−1.96301e8	+	1.96301e8i	−0.257935	+	0.257935i
$914$		−	1.11878e9i		−	1.46523i
$915$	−1.25760e7	−	9.83215e6i	−0.0164165	−	0.0128347i
$916$		−	3.27777e7i		−	0.0426473i
$917$			1.14325e9i			1.48264i
$918$	−2.20176e8	−	6.61930e8i	−0.284605	−	0.855626i
$919$	8.46401e8			1.09051			0.545255	−	0.838270i	$-0.316433\pi$
$919$	8.46401e8			1.09051			0.545255	+	0.838270i	$0.316433\pi$
$920$	−6.99153e8			−0.897860
$921$	−4.15868e8	+	5.31926e8i	−0.532325	+	0.680883i
$922$	9.40418e8			1.19985
$923$	−1.22441e9	−	1.22441e9i	−1.55712	−	1.55712i
$924$	6.61351e7	−	8.45916e7i	0.0838332	−	0.107229i
$925$	−2.02275e8	−	2.02275e8i	−0.255575	−	0.255575i
$926$	−9.01787e8			−1.13572
$927$	−8.16870e7	−	3.28551e8i	−0.102545	−	0.412443i
$928$	1.08120e7	+	1.08120e7i	0.0135289	+	0.0135289i
$929$	2.01166e8	−	2.01166e8i	0.250904	−	0.250904i	−0.570437	−	0.821341i	$-0.693226\pi$
$929$	2.01166e8	−	2.01166e8i	0.250904	−	0.250904i	0.821341	+	0.570437i	$0.193226\pi$
$930$	−1.87290e8	+	2.39557e8i	−0.232844	+	0.297825i
$931$	−1.23116e8			−0.152568
$932$	−1.27058e8	−	1.27058e8i	−0.156947	−	0.156947i
$933$	−2.11970e8	+	2.59557e7i	−0.260993	+	0.0319587i
$934$	−6.45341e8			−0.792042
$935$	4.33259e8	+	4.73562e8i	0.530045	+	0.579351i
$936$	3.39574e8	+	1.36579e9i	0.414102	+	1.66555i
$937$		−	8.59089e7i		−	0.104429i	−0.998636	−	0.0522143i	$-0.983372\pi$
$937$		−	8.59089e7i		−	0.104429i	0.998636	−	0.0522143i	$-0.0166279\pi$
$938$	9.08073e8	+	9.08073e8i	1.10030	+	1.10030i
$939$	−4.44078e8	+	5.43773e7i	−0.536367	+	0.0656782i
$940$	1.99910e8	−	1.99910e8i	0.240686	−	0.240686i
$941$	−1.96694e8	+	1.96694e8i	−0.236059	+	0.236059i	−0.815216	−	0.579157i	$-0.803382\pi$
$941$	−1.96694e8	+	1.96694e8i	−0.236059	+	0.236059i	0.579157	+	0.815216i	$0.303382\pi$
$942$	5.58870e8	−	7.14835e8i	0.668587	−	0.855171i
$943$			1.47550e7i			0.0175956i
$944$	5.06050e8			0.601558
$945$	−4.48502e8	+	1.00468e9i	−0.531458	+	1.19051i
$946$	1.30033e8	+	1.30033e8i	0.153596	+	0.153596i
$947$	7.33019e8	+	7.33019e8i	0.863109	+	0.863109i	0.991698	−	0.128589i	$-0.0410448\pi$
$947$	7.33019e8	+	7.33019e8i	0.863109	+	0.863109i	−0.128589	+	0.991698i	$0.541045\pi$
$948$	−2.36259e8	+	2.89299e7i	−0.277308	+	0.0339564i
$949$	1.81323e9	−	1.81323e9i	2.12156	−	2.12156i
$950$	2.28889e8			0.266965
$951$	1.18506e8	+	9.67790e8i	0.137784	+	1.12523i
$952$	4.50836e7	−	1.01438e9i	0.0522526	−	1.17569i
$953$		−	1.25429e9i		−	1.44917i	−0.689187	−	0.724584i	$-0.742032\pi$
$953$		−	1.25429e9i		−	1.44917i	0.689187	−	0.724584i	$-0.257968\pi$
$954$	3.35755e8	+	1.35043e9i	0.386703	+	1.55535i
$955$	−6.57514e8	+	6.57514e8i	−0.754910	+	0.754910i
$956$			1.59080e8i			0.182071i
$957$	−1.85593e7	+	2.37387e7i	−0.0211751	+	0.0270845i
$958$	2.65334e8	+	2.65334e8i	0.301784	+	0.301784i
$959$	6.27867e8	−	6.27867e8i	0.711888	−	0.711888i
$960$	1.15628e9	−	1.41587e8i	1.30692	−	0.160033i
$961$			7.76538e8i			0.874968i
$962$	−8.10798e8	+	8.10798e8i	−0.910726	+	0.910726i
$963$	−1.60423e8	+	2.66591e8i	−0.179634	+	0.298515i
$964$	1.04828e8	−	1.04828e8i	0.117016	−	0.117016i
$965$			4.77479e8i			0.531339i
$966$	−3.89514e8	+	4.98217e8i	−0.432108	+	0.552697i
$967$		−	8.80473e8i		−	0.973726i	−0.873478	−	0.486863i	$-0.838141\pi$
$967$		−	8.80473e8i		−	0.973726i	0.873478	−	0.486863i	$-0.161859\pi$
$968$			5.44973e8i			0.600826i
$969$	−5.13481e7	−	6.61843e8i	−0.0564356	−	0.727418i
$970$	1.00947e9			1.10606
$971$	7.48114e8			0.817165			0.408583	−	0.912721i	$-0.366023\pi$
$971$	7.48114e8			0.817165			0.408583	+	0.912721i	$0.366023\pi$
$972$	−3.00833e7	+	1.68982e8i	−0.0327587	+	0.184010i
$973$	5.10180e8			0.553840
$974$	6.20073e8	+	6.20073e8i	0.671067	+	0.671067i
$975$	4.75144e8	+	3.71476e8i	0.512639	+	0.400790i
$976$	8.99096e6	+	8.99096e6i	0.00967067	+	0.00967067i
$977$	7.88868e8			0.845904			0.422952	−	0.906152i	$-0.360994\pi$
$977$	7.88868e8			0.845904			0.422952	+	0.906152i	$0.360994\pi$
$978$	3.78595e7	−	4.63590e6i	0.0404723	−	0.00495584i
$979$	4.81522e8	+	4.81522e8i	0.513178	+	0.513178i
$980$	−3.08402e7	+	3.08402e7i	−0.0327672	+	0.0327672i
$981$	−4.14300e8	+	6.88482e8i	−0.438841	+	0.729266i
$982$	−6.67498e8			−0.704880
$983$	−1.43138e8	−	1.43138e8i	−0.150693	−	0.150693i	0.627734	−	0.778428i	$-0.283982\pi$
$983$	−1.43138e8	−	1.43138e8i	−0.150693	−	0.150693i	−0.778428	+	0.627734i	$0.783982\pi$
$984$	−3.08206e6	−	2.51699e7i	−0.00323486	−	0.0264178i
$985$	−2.03784e9			−2.13237
$986$	−1.99228e6	+	4.48264e7i	−0.00207835	+	0.0467631i
$987$	−1.97379e8	−	1.61192e9i	−0.205282	−	1.67645i
$988$			2.10897e8i			0.218675i
$989$	1.76044e8	+	1.76044e8i	0.181983	+	0.181983i
$990$	1.65769e8	+	6.66734e8i	0.170843	+	0.687142i
$991$	−2.66733e8	+	2.66733e8i	−0.274067	+	0.274067i	−0.830735	−	0.556668i	$-0.812079\pi$
$991$	−2.66733e8	+	2.66733e8i	−0.274067	+	0.274067i	0.556668	+	0.830735i	$0.312079\pi$
$992$	−8.99597e7	+	8.99597e7i	−0.0921537	+	0.0921537i
$993$	−1.35316e9	−	1.05792e9i	−1.38198	−	1.08046i
$994$			1.33723e9i			1.36159i
$995$	−5.15233e8			−0.523039
$996$	6.26477e7	−	8.01309e7i	0.0634055	−	0.0811002i
$997$	1.37365e8	+	1.37365e8i	0.138609	+	0.138609i	0.773007	−	0.634398i	$-0.218752\pi$
$997$	1.37365e8	+	1.37365e8i	0.138609	+	0.138609i	−0.634398	+	0.773007i	$0.718752\pi$
$998$	−5.26635e8	−	5.26635e8i	−0.529807	−	0.529807i
$999$	−8.29372e8	+	3.17426e8i	−0.831865	+	0.318380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.7.f.a.38.10	✓	68
3.2	odd	2	inner	51.7.f.a.38.25	yes	68
17.13	even	4	inner	51.7.f.a.47.25	yes	68
51.47	odd	4	inner	51.7.f.a.47.10	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.7.f.a.38.10	✓	68	1.1	even	1	trivial
51.7.f.a.38.25	yes	68	3.2	odd	2	inner
51.7.f.a.47.10	yes	68	51.47	odd	4	inner
51.7.f.a.47.25	yes	68	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	51.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-7.21375 q^{2} +(-16.6299 + 21.2708i) q^{3} -11.9618 q^{4} +(-104.798 - 104.798i) q^{5} +(119.964 - 153.442i) q^{6} +(-266.693 - 266.693i) q^{7} +547.970 q^{8} +(-175.895 - 707.462i) q^{9} +(755.989 + 755.989i) q^{10} +(-623.310 + 623.310i) q^{11} +(198.923 - 254.438i) q^{12} -3523.10 q^{13} +(1923.86 + 1923.86i) q^{14} +(3971.93 - 486.363i) q^{15} -3187.36 q^{16} +(3316.34 + 3624.84i) q^{17} +(1268.86 + 5103.45i) q^{18} +5004.35i q^{19} +(1253.58 + 1253.58i) q^{20} +(10107.9 - 1237.71i) q^{21} +(4496.40 - 4496.40i) q^{22} +(6087.39 - 6087.39i) q^{23} +(-9112.66 + 11655.8i) q^{24} +6340.40i q^{25} +25414.8 q^{26} +(17973.4 + 8023.57i) q^{27} +(3190.14 + 3190.14i) q^{28} +(-895.240 - 895.240i) q^{29} +(-28652.5 + 3508.50i) q^{30} +(7448.69 - 7448.69i) q^{31} -12077.2 q^{32} +(-2892.74 - 23623.9i) q^{33} +(-23923.3 - 26148.7i) q^{34} +55898.1i q^{35} +(2104.02 + 8462.53i) q^{36} +(-31902.6 + 31902.6i) q^{37} -36100.1i q^{38} +(58588.7 - 74939.2i) q^{39} +(-57426.3 - 57426.3i) q^{40} +(-1211.93 + 1211.93i) q^{41} +(-72915.6 + 8928.52i) q^{42} +28919.4i q^{43} +(7455.92 - 7455.92i) q^{44} +(-55707.3 + 92574.3i) q^{45} +(-43912.9 + 43912.9i) q^{46} -159472. i q^{47} +(53005.4 - 67797.7i) q^{48} +24601.7i q^{49} -45738.0i q^{50} +(-132254. + 10260.7i) q^{51} +42142.7 q^{52} +264611. q^{53} +(-129656. - 57880.0i) q^{54} +130644. q^{55} +(-146140. - 146140. i) q^{56} +(-106447. - 83221.7i) q^{57} +(6458.04 + 6458.04i) q^{58} -158768. q^{59} +(-47511.5 + 5817.79i) q^{60} +(-2820.82 - 2820.82i) q^{61} +(-53733.0 + 53733.0i) q^{62} +(-141765. + 235585. i) q^{63} +291113. q^{64} +(369215. + 369215. i) q^{65} +(20867.5 + 170417. i) q^{66} +472006. q^{67} +(-39669.5 - 43359.6i) q^{68} +(28251.2 + 230716. i) q^{69} -403235. i q^{70} +(347538. + 347538. i) q^{71} +(-96385.0 - 387667. i) q^{72} +(-514670. + 514670. i) q^{73} +(230138. - 230138. i) q^{74} +(-134865. - 105440. i) q^{75} -59861.1i q^{76} +332465. q^{77} +(-422644. + 540593. i) q^{78} +(-521127. - 521127. i) q^{79} +(334030. + 334030. i) q^{80} +(-469563. + 248878. i) q^{81} +(8742.57 - 8742.57i) q^{82} +314933. q^{83} +(-120908. + 14805.2i) q^{84} +(32329.9 - 727424. i) q^{85} -208617. i q^{86} +(33930.2 - 4154.76i) q^{87} +(-341555. + 341555. i) q^{88} -772524. i q^{89} +(401859. - 667808. i) q^{90} +(939588. + 939588. i) q^{91} +(-72816.2 + 72816.2i) q^{92} +(34568.9 + 282311. i) q^{93} +1.15039e6i q^{94} +(524448. - 524448. i) q^{95} +(200843. - 256893. i) q^{96} +(667648. - 667648. i) q^{97} -177471. i q^{98} +(550605. + 331331. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 18 q^{3} + 2040 q^{4} - 290 q^{6} - 4 q^{7} - 4256 q^{10} + 4182 q^{12} - 1832 q^{13} + 54976 q^{16} + 10940 q^{18} - 1604 q^{21} + 19576 q^{22} + 15110 q^{24} + 37314 q^{27} - 63120 q^{28} + 51360 q^{30}+ \cdots + 203004 q^{99}+O(q^{100}) \) 68 * q + 18 * q^3 + 2040 * q^4 - 290 * q^6 - 4 * q^7 - 4256 * q^10 + 4182 * q^12 - 1832 * q^13 + 54976 * q^16 + 10940 * q^18 - 1604 * q^21 + 19576 * q^22 + 15110 * q^24 + 37314 * q^27 - 63120 * q^28 + 51360 * q^30 - 88660 * q^31 - 128604 * q^33 + 80200 * q^34 + 335180 * q^37 + 31460 * q^39 - 286828 * q^40 + 45484 * q^45 - 85244 * q^46 + 111922 * q^48 - 590566 * q^51 - 904320 * q^52 - 1215638 * q^54 - 731624 * q^55 + 753144 * q^57 - 328292 * q^58 + 751532 * q^61 + 88664 * q^63 + 870368 * q^64 + 174232 * q^67 + 1420428 * q^69 + 1158660 * q^72 + 2397332 * q^73 + 1415042 * q^75 - 1868044 * q^78 - 1438708 * q^79 - 2973932 * q^81 - 617036 * q^82 + 4901976 * q^84 + 2375468 * q^85 + 521156 * q^88 - 3185088 * q^90 + 1741672 * q^91 + 4082570 * q^96 + 2753300 * q^97 + 203004 * q^99

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