LMFDB - Embedded newform 68.7.c.a.35.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [68,7,Mod(35,68)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(68, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("68.35");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 68 = 2^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	68.c (of order $2$, degree $1$, 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:	$15.6436776861$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			35.11
Character	$\chi$	$=$	68.35
Dual form			68.7.c.a.35.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.51785 - 4.63871i) q^{2} +15.6750i q^{3} +(20.9647 + 60.4688i) q^{4} +40.3553 q^{5} +(72.7119 - 102.167i) q^{6} +429.939i q^{7} +(143.853 - 491.376i) q^{8} +483.294 q^{9} +O(q^{10})$	\(q+(-6.51785 - 4.63871i) q^{2} +15.6750i q^{3} +(20.9647 + 60.4688i) q^{4} +40.3553 q^{5} +(72.7119 - 102.167i) q^{6} +429.939i q^{7} +(143.853 - 491.376i) q^{8} +483.294 q^{9} +(-263.030 - 187.196i) q^{10} -392.915i q^{11} +(-947.850 + 328.622i) q^{12} -1144.69 q^{13} +(1994.36 - 2802.28i) q^{14} +632.570i q^{15} +(-3216.96 + 2535.42i) q^{16} -1191.58 q^{17} +(-3150.04 - 2241.86i) q^{18} -4514.09i q^{19} +(846.036 + 2440.24i) q^{20} -6739.30 q^{21} +(-1822.62 + 2560.96i) q^{22} +23112.9i q^{23} +(7702.33 + 2254.90i) q^{24} -13996.5 q^{25} +(7460.91 + 5309.88i) q^{26} +19002.7i q^{27} +(-25997.9 + 9013.54i) q^{28} +36449.8 q^{29} +(2934.31 - 4122.99i) q^{30} +44021.2i q^{31} +(32728.8 - 1602.93i) q^{32} +6158.95 q^{33} +(7766.52 + 5527.39i) q^{34} +17350.3i q^{35} +(10132.1 + 29224.2i) q^{36} -75944.5 q^{37} +(-20939.6 + 29422.2i) q^{38} -17943.0i q^{39} +(5805.22 - 19829.6i) q^{40} -132006. q^{41} +(43925.8 + 31261.7i) q^{42} -8206.47i q^{43} +(23759.1 - 8237.34i) q^{44} +19503.4 q^{45} +(107214. - 150646. i) q^{46} +4888.02i q^{47} +(-39742.8 - 50426.0i) q^{48} -67198.7 q^{49} +(91226.8 + 64925.5i) q^{50} -18678.0i q^{51} +(-23998.1 - 69218.0i) q^{52} -103615. q^{53} +(88148.2 - 123857. i) q^{54} -15856.2i q^{55} +(211262. + 61848.0i) q^{56} +70758.5 q^{57} +(-237574. - 169080. i) q^{58} -177119. i q^{59} +(-38250.8 + 13261.6i) q^{60} +76596.8 q^{61} +(204201. - 286923. i) q^{62} +207787. i q^{63} +(-220757. - 141372. i) q^{64} -46194.2 q^{65} +(-40143.1 - 28569.6i) q^{66} +110199. i q^{67} +(-24981.1 - 72053.3i) q^{68} -362295. q^{69} +(80483.1 - 113087. i) q^{70} +168287. i q^{71} +(69523.2 - 237479. i) q^{72} +220591. q^{73} +(494995. + 352285. i) q^{74} -219395. i q^{75} +(272962. - 94636.6i) q^{76} +168929. q^{77} +(-83232.5 + 116950. i) q^{78} -39949.2i q^{79} +(-129821. + 102318. i) q^{80} +54453.0 q^{81} +(860397. + 612339. i) q^{82} +593883. i q^{83} +(-141287. - 407518. i) q^{84} -48086.4 q^{85} +(-38067.5 + 53488.5i) q^{86} +571352. i q^{87} +(-193069. - 56521.9i) q^{88} -715182. q^{89} +(-127121. - 90470.9i) q^{90} -492147. i q^{91} +(-1.39761e6 + 484555. i) q^{92} -690032. q^{93} +(22674.1 - 31859.4i) q^{94} -182167. i q^{95} +(25125.9 + 513024. i) q^{96} +458639. q^{97} +(437991. + 311715. i) q^{98} -189893. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 10 q^{2} + 90 q^{4} - 510 q^{6} + 1406 q^{8} - 11664 q^{9}+O(q^{10}) $ 48 * q - 10 * q^2 + 90 * q^4 - 510 * q^6 + 1406 * q^8 - 11664 * q^9	\( 48 q - 10 q^{2} + 90 q^{4} - 510 q^{6} + 1406 q^{8} - 11664 q^{9} - 1710 q^{10} - 6234 q^{12} - 5040 q^{13} + 9040 q^{14} - 1230 q^{16} - 6974 q^{18} + 1046 q^{20} - 35488 q^{21} - 13254 q^{22} + 22838 q^{24} + 173856 q^{25} + 44744 q^{26} + 42864 q^{28} - 83536 q^{29} - 95104 q^{30} - 53050 q^{32} + 9072 q^{33} + 24174 q^{36} + 62640 q^{37} + 399840 q^{38} - 58218 q^{40} + 70448 q^{41} - 90520 q^{42} - 356746 q^{44} - 103808 q^{45} - 177084 q^{46} + 808886 q^{48} - 758880 q^{49} - 560506 q^{50} - 85800 q^{52} + 744784 q^{53} - 263596 q^{54} - 701896 q^{56} - 125008 q^{57} - 351534 q^{58} - 64960 q^{60} + 196560 q^{61} + 1428016 q^{62} - 60246 q^{64} - 708656 q^{65} + 1089052 q^{66} + 428496 q^{69} - 1132824 q^{70} - 1043230 q^{72} - 454272 q^{73} - 1135082 q^{74} + 850224 q^{76} - 549200 q^{77} + 703076 q^{78} + 1608910 q^{80} + 3871872 q^{81} - 328536 q^{82} + 2825208 q^{84} + 3243644 q^{86} + 691398 q^{88} - 1729776 q^{89} + 214114 q^{90} + 1469284 q^{92} - 6618704 q^{93} - 551136 q^{94} - 5148618 q^{96} + 4548720 q^{97} - 2942042 q^{98}+O(q^{100}) \) 48 * q - 10 * q^2 + 90 * q^4 - 510 * q^6 + 1406 * q^8 - 11664 * q^9 - 1710 * q^10 - 6234 * q^12 - 5040 * q^13 + 9040 * q^14 - 1230 * q^16 - 6974 * q^18 + 1046 * q^20 - 35488 * q^21 - 13254 * q^22 + 22838 * q^24 + 173856 * q^25 + 44744 * q^26 + 42864 * q^28 - 83536 * q^29 - 95104 * q^30 - 53050 * q^32 + 9072 * q^33 + 24174 * q^36 + 62640 * q^37 + 399840 * q^38 - 58218 * q^40 + 70448 * q^41 - 90520 * q^42 - 356746 * q^44 - 103808 * q^45 - 177084 * q^46 + 808886 * q^48 - 758880 * q^49 - 560506 * q^50 - 85800 * q^52 + 744784 * q^53 - 263596 * q^54 - 701896 * q^56 - 125008 * q^57 - 351534 * q^58 - 64960 * q^60 + 196560 * q^61 + 1428016 * q^62 - 60246 * q^64 - 708656 * q^65 + 1089052 * q^66 + 428496 * q^69 - 1132824 * q^70 - 1043230 * q^72 - 454272 * q^73 - 1135082 * q^74 + 850224 * q^76 - 549200 * q^77 + 703076 * q^78 + 1608910 * q^80 + 3871872 * q^81 - 328536 * q^82 + 2825208 * q^84 + 3243644 * q^86 + 691398 * q^88 - 1729776 * q^89 + 214114 * q^90 + 1469284 * q^92 - 6618704 * q^93 - 551136 * q^94 - 5148618 * q^96 + 4548720 * q^97 - 2942042 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/68\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$1$

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 $

$2$	−6.51785	−	4.63871i	−0.814731	−	0.579839i
$2$	−6.51785	−	4.63871i	−0.814731	−	0.579839i
$3$			15.6750i			0.580556i	0.956942	+	0.290278i	$0.0937478\pi$
$3$			15.6750i			0.580556i	−0.956942	+	0.290278i	$0.906252\pi$
$4$	20.9647	+	60.4688i	0.327573	+	0.944826i
$5$	40.3553			0.322842			0.161421	−	0.986886i	$-0.448392\pi$
$5$	40.3553			0.322842			0.161421	+	0.986886i	$0.448392\pi$
$6$	72.7119	−	102.167i	0.336629	−	0.472997i
$7$			429.939i			1.25347i	0.779234	+	0.626733i	$0.215609\pi$
$7$			429.939i			1.25347i	−0.779234	+	0.626733i	$0.784391\pi$
$8$	143.853	−	491.376i	0.280963	−	0.959719i
$9$	483.294			0.662954
$10$	−263.030	−	187.196i	−0.263030	−	0.187196i
$11$		−	392.915i		−	0.295203i	−0.989047	−	0.147601i	$-0.952845\pi$
$11$		−	392.915i		−	0.295203i	0.989047	−	0.147601i	$-0.0471553\pi$
$12$	−947.850	+	328.622i	−0.548525	+	0.190175i
$13$	−1144.69			−0.521024			−0.260512	−	0.965471i	$-0.583891\pi$
$13$	−1144.69			−0.521024			−0.260512	+	0.965471i	$0.583891\pi$
$14$	1994.36	−	2802.28i	0.726809	−	1.02124i
$15$			632.570i			0.187428i
$16$	−3216.96	+	2535.42i	−0.785391	+	0.618999i
$17$	−1191.58			−0.242536
$17$	−1191.58			−0.242536
$18$	−3150.04	−	2241.86i	−0.540129	−	0.384407i
$19$		−	4514.09i		−	0.658127i	−0.944308	−	0.329063i	$-0.893267\pi$
$19$		−	4514.09i		−	0.658127i	0.944308	−	0.329063i	$-0.106733\pi$
$20$	846.036	+	2440.24i	0.105754	+	0.305030i
$21$	−6739.30			−0.727708
$22$	−1822.62	+	2560.96i	−0.171170	+	0.240511i
$23$			23112.9i			1.89964i	0.312800	+	0.949819i	$0.398733\pi$
$23$			23112.9i			1.89964i	−0.312800	+	0.949819i	$0.601267\pi$
$24$	7702.33	+	2254.90i	0.557171	+	0.163115i
$25$	−13996.5			−0.895773
$26$	7460.91	+	5309.88i	0.424494	+	0.302110i
$27$			19002.7i			0.965439i
$28$	−25997.9	+	9013.54i	−1.18431	+	0.410602i
$29$	36449.8			1.49452			0.747259	−	0.664533i	$-0.231369\pi$
$29$	36449.8			1.49452			0.747259	+	0.664533i	$0.231369\pi$
$30$	2934.31	−	4122.99i	0.108678	−	0.152703i
$31$			44021.2i			1.47767i	0.673888	+	0.738833i	$0.264623\pi$
$31$			44021.2i			1.47767i	−0.673888	+	0.738833i	$0.735377\pi$
$32$	32728.8	−	1602.93i	0.998803	−	0.0489175i
$33$	6158.95			0.171382
$34$	7766.52	+	5527.39i	0.197601	+	0.140632i
$35$			17350.3i			0.404672i
$36$	10132.1	+	29224.2i	0.217166	+	0.626376i
$37$	−75944.5			−1.49931			−0.749654	−	0.661829i	$-0.769780\pi$
$37$	−75944.5			−1.49931			−0.749654	+	0.661829i	$0.769780\pi$
$38$	−20939.6	+	29422.2i	−0.381608	+	0.536196i
$39$		−	17943.0i		−	0.302484i
$40$	5805.22	−	19829.6i	0.0907066	−	0.309838i
$41$	−132006.			−1.91533			−0.957663	−	0.287891i	$-0.907046\pi$
$41$	−132006.			−1.91533			−0.957663	+	0.287891i	$0.907046\pi$
$42$	43925.8	+	31261.7i	0.592886	+	0.421954i
$43$		−	8206.47i		−	0.103217i	−0.998667	−	0.0516085i	$-0.983565\pi$
$43$		−	8206.47i		−	0.103217i	0.998667	−	0.0516085i	$-0.0164348\pi$
$44$	23759.1	−	8237.34i	0.278915	−	0.0967005i
$45$	19503.4			0.214030
$46$	107214.	−	150646.i	1.10148	−	1.54769i
$47$			4888.02i			0.0470803i	0.999723	+	0.0235402i	$0.00749376\pi$
$47$			4888.02i			0.0470803i	−0.999723	+	0.0235402i	$0.992506\pi$
$48$	−39742.8	−	50426.0i	−0.359364	−	0.455964i
$49$	−67198.7			−0.571179
$50$	91226.8	+	64925.5i	0.729814	+	0.519404i
$51$		−	18678.0i		−	0.140806i
$52$	−23998.1	−	69218.0i	−0.170673	−	0.492277i
$53$	−103615.			−0.695979			−0.347989	−	0.937498i	$-0.613135\pi$
$53$	−103615.			−0.695979			−0.347989	+	0.937498i	$0.613135\pi$
$54$	88148.2	−	123857.i	0.559799	−	0.786573i
$55$		−	15856.2i		−	0.0953039i
$56$	211262.	+	61848.0i	1.20298	+	0.352177i
$57$	70758.5			0.382080
$58$	−237574.	−	169080.i	−1.21763	−	0.866580i
$59$		−	177119.i		−	0.862400i	−0.902256	−	0.431200i	$-0.858090\pi$
$59$		−	177119.i		−	0.862400i	0.902256	−	0.431200i	$-0.141910\pi$
$60$	−38250.8	+	13261.6i	−0.177087	+	0.0613964i
$61$	76596.8			0.337459			0.168729	−	0.985662i	$-0.446034\pi$
$61$	76596.8			0.337459			0.168729	+	0.985662i	$0.446034\pi$
$62$	204201.	−	286923.i	0.856809	−	1.20390i
$63$			207787.i			0.830991i
$64$	−220757.	−	141372.i	−0.842120	−	0.539290i
$65$	−46194.2			−0.168208
$66$	−40143.1	−	28569.6i	−0.139630	−	0.0993739i
$67$			110199.i			0.366397i	0.983076	+	0.183198i	$0.0586450\pi$
$67$			110199.i			0.366397i	−0.983076	+	0.183198i	$0.941355\pi$
$68$	−24981.1	−	72053.3i	−0.0794482	−	0.229154i
$69$	−362295.			−1.10285
$70$	80483.1	−	113087.i	0.234645	−	0.329699i
$71$			168287.i			0.470193i	0.971972	+	0.235096i	$0.0755406\pi$
$71$			168287.i			0.470193i	−0.971972	+	0.235096i	$0.924459\pi$
$72$	69523.2	−	237479.i	0.186265	−	0.636250i
$73$	220591.			0.567048			0.283524	−	0.958965i	$-0.408497\pi$
$73$	220591.			0.567048			0.283524	+	0.958965i	$0.408497\pi$
$74$	494995.	+	352285.i	1.22153	+	0.869358i
$75$		−	219395.i		−	0.520047i
$76$	272962.	−	94636.6i	0.621815	−	0.215585i
$77$	168929.			0.370027
$78$	−83232.5	+	116950.i	−0.175392	+	0.246443i
$79$		−	39949.2i		−	0.0810264i	−0.999179	−	0.0405132i	$-0.987101\pi$
$79$		−	39949.2i		−	0.0810264i	0.999179	−	0.0405132i	$-0.0128993\pi$
$80$	−129821.	+	102318.i	−0.253557	+	0.199839i
$81$	54453.0			0.102463
$82$	860397.	+	612339.i	1.56048	+	1.11058i
$83$			593883.i			1.03864i	0.854579	+	0.519322i	$0.173815\pi$
$83$			593883.i			1.03864i	−0.854579	+	0.519322i	$0.826185\pi$
$84$	−141287.	−	407518.i	−0.238378	−	0.687557i
$85$	−48086.4			−0.0783007
$86$	−38067.5	+	53488.5i	−0.0598492	+	0.0840941i
$87$			571352.i			0.867652i
$88$	−193069.	−	56521.9i	−0.283312	−	0.0829409i
$89$	−715182.			−1.01449			−0.507244	−	0.861803i	$-0.669336\pi$
$89$	−715182.			−1.01449			−0.507244	+	0.861803i	$0.669336\pi$
$90$	−127121.	−	90470.9i	−0.174377	−	0.124103i
$91$		−	492147.i		−	0.653086i
$92$	−1.39761e6	+	484555.i	−1.79483	+	0.622271i
$93$	−690032.			−0.857868
$94$	22674.1	−	31859.4i	0.0272990	−	0.0383578i
$95$		−	182167.i		−	0.212471i
$96$	25125.9	+	513024.i	0.0283994	+	0.579861i
$97$	458639.			0.502522			0.251261	−	0.967919i	$-0.419155\pi$
$97$	458639.			0.502522			0.251261	+	0.967919i	$0.419155\pi$
$98$	437991.	+	311715.i	0.465357	+	0.331192i
$99$		−	189893.i		−	0.195706i
$100$	−293431.	−	846349.i	−0.293431	−	0.846349i
$101$	1.50439e6			1.46014			0.730071	−	0.683371i	$-0.239487\pi$
$101$	1.50439e6			1.46014			0.730071	+	0.683371i	$0.239487\pi$
$102$	−86641.9	+	121740.i	−0.0816446	+	0.114719i
$103$		−	668245.i		−	0.611539i	−0.952106	−	0.305769i	$-0.901086\pi$
$103$		−	668245.i		−	0.611539i	0.952106	−	0.305769i	$-0.0989136\pi$
$104$	−164667.	+	562473.i	−0.146388	+	0.500036i
$105$	−271966.			−0.234935
$106$	675348.	+	480641.i	0.567036	+	0.403556i
$107$			1.09502e6i			0.893861i	0.894569	+	0.446931i	$0.147483\pi$
$107$			1.09502e6i			0.893861i	−0.894569	+	0.446931i	$0.852517\pi$
$108$	−1.14907e6	+	398386.i	−0.912171	+	0.316252i
$109$	−571011.			−0.440925			−0.220463	−	0.975395i	$-0.570757\pi$
$109$	−571011.			−0.440925			−0.220463	+	0.975395i	$0.570757\pi$
$110$	−73552.3	+	103348.i	−0.0552609	+	0.0776470i
$111$		−	1.19043e6i		−	0.870433i
$112$	−1.09008e6	−	1.38310e6i	−0.775895	−	0.984462i
$113$	1.00186e6			0.694339			0.347170	−	0.937802i	$-0.387143\pi$
$113$	1.00186e6			0.694339			0.347170	+	0.937802i	$0.387143\pi$
$114$	−461193.	−	328228.i	−0.311292	−	0.221545i
$115$			932727.i			0.613283i
$116$	764159.	+	2.20408e6i	0.489565	+	1.41206i
$117$	−553221.			−0.345415
$118$	−821604.	+	1.15443e6i	−0.500053	+	0.702624i
$119$		−	512306.i		−	0.304010i
$120$	310830.	+	90997.0i	0.179878	+	0.0526603i
$121$	1.61718e6			0.912855
$122$	−499246.	−	355310.i	−0.274938	−	0.195672i
$123$		−	2.06920e6i		−	1.11195i
$124$	−2.66191e6	+	922890.i	−1.39614	+	0.484044i
$125$	−1.19538e6			−0.612035
$126$	963864.	−	1.35432e6i	0.481841	−	0.677034i
$127$		−	2.74305e6i		−	1.33913i	−0.742754	−	0.669564i	$-0.766481\pi$
$127$		−	2.74305e6i		−	1.33913i	0.742754	−	0.669564i	$-0.233519\pi$
$128$	783076.	+	1.94547e6i	0.373400	+	0.927671i
$129$	128637.			0.0599233
$130$	301087.	+	214282.i	0.137045	+	0.0975338i
$131$			2.36766e6i			1.05319i	0.850117	+	0.526594i	$0.176531\pi$
$131$			2.36766e6i			1.05319i	−0.850117	+	0.526594i	$0.823469\pi$
$132$	129120.	+	372424.i	0.0561401	+	0.161926i
$133$	1.94079e6			0.824940
$134$	511179.	−	718257.i	0.212451	−	0.298515i
$135$			766860.i			0.311684i
$136$	−171412.	+	585513.i	−0.0681435	+	0.232766i
$137$	2.70856e6			1.05336			0.526680	−	0.850063i	$-0.323437\pi$
$137$	2.70856e6			1.05336			0.526680	+	0.850063i	$0.323437\pi$
$138$	2.36138e6	+	1.68058e6i	0.898524	+	0.639474i
$139$			2.38113e6i			0.886623i	0.896368	+	0.443311i	$0.146196\pi$
$139$			2.38113e6i			0.886623i	−0.896368	+	0.443311i	$0.853804\pi$
$140$	−1.04915e6	+	363744.i	−0.382344	+	0.132560i
$141$	−76619.8			−0.0273328
$142$	780636.	−	1.09687e6i	0.272636	−	0.383081i
$143$			449765.i			0.153808i
$144$	−1.55474e6	+	1.22535e6i	−0.520679	+	0.410368i
$145$	1.47094e6			0.482494
$146$	−1.43778e6	−	1.02326e6i	−0.461991	−	0.328796i
$147$		−	1.05334e6i		−	0.331602i
$148$	−1.59215e6	−	4.59228e6i	−0.491134	−	1.41659i
$149$	6.16145e6			1.86262			0.931310	−	0.364227i	$-0.118667\pi$
$149$	6.16145e6			1.86262			0.931310	+	0.364227i	$0.118667\pi$
$150$	−1.01771e6	+	1.42998e6i	−0.301543	+	0.423698i
$151$		−	4.89413e6i		−	1.42149i	−0.703449	−	0.710746i	$-0.748358\pi$
$151$		−	4.89413e6i		−	1.42149i	0.703449	−	0.710746i	$-0.251642\pi$
$152$	−2.21812e6	−	649365.i	−0.631617	−	0.184909i
$153$	−575882.			−0.160790
$154$	−1.10106e6	−	783615.i	−0.301472	−	0.214556i
$155$			1.77649e6i			0.477053i
$156$	1.08499e6	−	376170.i	0.285794	−	0.0990856i
$157$	−352719.			−0.0911443			−0.0455721	−	0.998961i	$-0.514511\pi$
$157$	−352719.			−0.0911443			−0.0455721	+	0.998961i	$0.514511\pi$
$158$	−185313.	+	260383.i	−0.0469823	+	0.0660147i
$159$		−	1.62417e6i		−	0.404055i
$160$	1.32078e6	−	64686.6i	0.322456	−	0.0157926i
$161$	−9.93714e6			−2.38113
$162$	−354916.	−	252592.i	−0.0834797	−	0.0594120i
$163$		−	2.88579e6i		−	0.666349i	−0.942865	−	0.333174i	$-0.891880\pi$
$163$		−	2.88579e6i		−	0.666349i	0.942865	−	0.333174i	$-0.108120\pi$
$164$	−2.76747e6	−	7.98226e6i	−0.627410	−	1.80965i
$165$	248546.			0.0553293
$166$	2.75485e6	−	3.87084e6i	0.602246	−	0.846215i
$167$			3.96327e6i			0.850951i	0.904970	+	0.425475i	$0.139893\pi$
$167$			3.96327e6i			0.850951i	−0.904970	+	0.425475i	$0.860107\pi$
$168$	−969469.	+	3.31153e6i	−0.204459	+	0.698395i
$169$	−3.51650e6			−0.728534
$170$	313420.	+	223059.i	0.0637940	+	0.0454018i
$171$		−	2.18163e6i		−	0.436308i
$172$	496236.	−	172046.i	0.0975221	−	0.0338111i
$173$	7.44430e6			1.43776			0.718879	−	0.695135i	$-0.244656\pi$
$173$	7.44430e6			1.43776			0.718879	+	0.695135i	$0.244656\pi$
$174$	2.65034e6	−	3.72398e6i	0.503099	−	0.706903i
$175$		−	6.01762e6i		−	1.12282i
$176$	996205.	+	1.26399e6i	0.182730	+	0.231850i
$177$	2.77634e6			0.500672
$178$	4.66145e6	+	3.31752e6i	0.826534	+	0.588239i
$179$		−	893984.i		−	0.155873i	−0.996958	−	0.0779365i	$-0.975167\pi$
$179$		−	893984.i		−	0.155873i	0.996958	−	0.0779365i	$-0.0248331\pi$
$180$	408884.	+	1.17935e6i	0.0701104	+	0.202221i
$181$	556410.			0.0938337			0.0469169	−	0.998899i	$-0.485060\pi$
$181$	556410.			0.0938337			0.0469169	+	0.998899i	$0.485060\pi$
$182$	−2.28293e6	+	3.20774e6i	−0.378685	+	0.532089i
$183$			1.20066e6i			0.195914i
$184$	1.13571e7	+	3.32486e6i	1.82312	+	0.533727i
$185$	−3.06476e6			−0.484040
$186$	4.49753e6	+	3.20086e6i	0.698932	+	0.497426i
$187$			468188.i			0.0715972i
$188$	−295573.	+	102476.i	−0.0444827	+	0.0154223i
$189$	−8.17002e6			−1.21015
$190$	−845022.	+	1.18734e6i	−0.123199	+	0.173107i
$191$		−	5.18166e6i		−	0.743650i	−0.928303	−	0.371825i	$-0.878732\pi$
$191$		−	5.18166e6i		−	0.743650i	0.928303	−	0.371825i	$-0.121268\pi$
$192$	2.21600e6	−	3.46037e6i	0.313088	−	0.488898i
$193$	4.26012e6			0.592583			0.296292	−	0.955098i	$-0.404250\pi$
$193$	4.26012e6			0.592583			0.296292	+	0.955098i	$0.404250\pi$
$194$	−2.98934e6	−	2.12749e6i	−0.409421	−	0.291382i
$195$		−	724096.i		−	0.0976544i
$196$	−1.40880e6	−	4.06343e6i	−0.187103	−	0.539665i
$197$	−8.26126e6			−1.08056			−0.540279	−	0.841486i	$-0.681681\pi$
$197$	−8.26126e6			−1.08056			−0.540279	+	0.841486i	$0.681681\pi$
$198$	−880860.	+	1.23770e6i	−0.113478	+	0.159448i
$199$			4.68070e6i			0.593953i	0.954885	+	0.296976i	$0.0959783\pi$
$199$			4.68070e6i			0.593953i	−0.954885	+	0.296976i	$0.904022\pi$
$200$	−2.01343e6	+	6.87752e6i	−0.251679	+	0.859690i
$201$	−1.72736e6			−0.212714
$202$	−9.80536e6	−	6.97842e6i	−1.18962	−	0.846648i
$203$			1.56712e7i			1.87333i
$204$	1.12944e6	−	391579.i	0.133037	−	0.0461242i
$205$	−5.32715e6			−0.618348
$206$	−3.09979e6	+	4.35552e6i	−0.354594	+	0.498239i
$207$			1.11703e7i			1.25937i
$208$	3.68242e6	−	2.90227e6i	0.409208	−	0.322513i
$209$	−1.77365e6			−0.194281
$210$	1.77264e6	+	1.26157e6i	0.191409	+	0.136224i
$211$			5.80817e6i			0.618290i	0.951015	+	0.309145i	$0.100043\pi$
$211$			5.80817e6i			0.618290i	−0.951015	+	0.309145i	$0.899957\pi$
$212$	−2.17226e6	−	6.26549e6i	−0.227984	−	0.657579i
$213$	−2.63790e6			−0.272973
$214$	5.07948e6	−	7.13716e6i	0.518296	−	0.728256i
$215$		−	331174.i		−	0.0333228i
$216$	9.33748e6	+	2.73360e6i	0.926550	+	0.271252i
$217$	−1.89264e7			−1.85221
$218$	3.72176e6	+	2.64876e6i	0.359235	+	0.255666i
$219$			3.45777e6i			0.329203i
$220$	958805.	−	332420.i	0.0900456	−	0.0312190i
$221$	1.36399e6			0.126367
$222$	−5.52207e6	+	7.75905e6i	−0.504711	+	0.709169i
$223$			1.33658e7i			1.20526i	0.798022	+	0.602628i	$0.205880\pi$
$223$			1.33658e7i			1.20526i	−0.798022	+	0.602628i	$0.794120\pi$
$224$	689162.	+	1.40714e7i	0.0613165	+	1.25197i
$225$	−6.76440e6			−0.593857
$226$	−6.52997e6	−	4.64734e6i	−0.565700	−	0.402605i
$227$			5.87946e6i			0.502643i	0.967904	+	0.251322i	$0.0808652\pi$
$227$			5.87946e6i			0.502643i	−0.967904	+	0.251322i	$0.919135\pi$
$228$	1.48343e6	+	4.27869e6i	0.125159	+	0.360999i
$229$	1.73076e7			1.44122			0.720611	−	0.693340i	$-0.243862\pi$
$229$	1.73076e7			1.44122			0.720611	+	0.693340i	$0.243862\pi$
$230$	4.32665e6	−	6.07937e6i	0.355606	−	0.499661i
$231$			2.64797e6i			0.214821i
$232$	5.24341e6	−	1.79106e7i	0.419904	−	1.43432i
$233$	1.45717e7			1.15197			0.575986	−	0.817460i	$-0.304618\pi$
$233$	1.45717e7			1.15197			0.575986	+	0.817460i	$0.304618\pi$
$234$	3.60581e6	+	2.56623e6i	0.281420	+	0.200285i
$235$			197257.i			0.0151995i
$236$	1.07102e7	−	3.71324e6i	0.814818	−	0.282499i
$237$	626204.			0.0470404
$238$	−2.37644e6	+	3.33913e6i	−0.176277	+	0.247687i
$239$		−	6.72769e6i		−	0.492802i	−0.969168	−	0.246401i	$-0.920752\pi$
$239$		−	6.72769e6i		−	0.492802i	0.969168	−	0.246401i	$-0.0792480\pi$
$240$	−1.60383e6	−	2.03495e6i	−0.116018	−	0.147204i
$241$	−1.58223e7			−1.13037			−0.565184	−	0.824965i	$-0.691195\pi$
$241$	−1.58223e7			−1.13037			−0.565184	+	0.824965i	$0.691195\pi$
$242$	−1.05405e7	−	7.50163e6i	−0.743732	−	0.529309i
$243$			1.47065e7i			1.02492i
$244$	1.60583e6	+	4.63172e6i	0.110543	+	0.318840i
$245$	−2.71182e6			−0.184401
$246$	−9.59842e6	+	1.34867e7i	−0.644755	+	0.905944i
$247$			5.16723e6i			0.342900i
$248$	2.16309e7	+	6.33257e6i	1.41814	+	0.415169i
$249$	−9.30913e6			−0.602991
$250$	7.79132e6	+	5.54503e6i	0.498644	+	0.354882i
$251$		−	3.13554e7i		−	1.98286i	−0.130643	−	0.991430i	$-0.541704\pi$
$251$		−	3.13554e7i		−	1.98286i	0.130643	−	0.991430i	$-0.458296\pi$
$252$	−1.25646e7	+	4.35619e6i	−0.785142	+	0.272211i
$253$	9.08140e6			0.560778
$254$	−1.27242e7	+	1.78788e7i	−0.776479	+	1.09103i
$255$		−	753756.i		−	0.0454580i
$256$	3.92049e6	−	1.63127e7i	0.233679	−	0.972314i
$257$	6.79344e6			0.400212			0.200106	−	0.979774i	$-0.435871\pi$
$257$	6.79344e6			0.400212			0.200106	+	0.979774i	$0.435871\pi$
$258$	−838434.	−	596708.i	−0.0488213	−	0.0347459i
$259$		−	3.26515e7i		−	1.87933i
$260$	−968448.	−	2.79331e6i	−0.0551006	−	0.158928i
$261$	1.76160e7			0.990798
$262$	1.09829e7	−	1.54321e7i	0.610679	−	0.858064i
$263$			2.96877e7i			1.63196i	0.578082	+	0.815979i	$0.303801\pi$
$263$			2.96877e7i			1.63196i	−0.578082	+	0.815979i	$0.696199\pi$
$264$	885982.	−	3.02636e6i	0.0481519	−	0.164478i
$265$	−4.18142e6			−0.224691
$266$	−1.26497e7	−	9.00274e6i	−0.672105	−	0.478333i
$267$		−	1.12105e7i		−	0.588967i
$268$	−6.66358e6	+	2.31028e6i	−0.346181	+	0.120022i
$269$	4.70915e6			0.241928			0.120964	−	0.992657i	$-0.461401\pi$
$269$	4.70915e6			0.241928			0.120964	+	0.992657i	$0.461401\pi$
$270$	3.55724e6	−	4.99828e6i	0.180727	−	0.253939i
$271$		−	1.81010e7i		−	0.909483i	−0.890624	−	0.454741i	$-0.849732\pi$
$271$		−	1.81010e7i		−	0.909483i	0.890624	−	0.454741i	$-0.150268\pi$
$272$	3.83326e6	−	3.02115e6i	0.190485	−	0.150129i
$273$	7.71441e6			0.379153
$274$	−1.76540e7	−	1.25642e7i	−0.858206	−	0.610780i
$275$			5.49941e6i			0.264435i
$276$	−7.59541e6	−	2.19076e7i	−0.361263	−	1.04200i
$277$	921050.			0.0433355			0.0216677	−	0.999765i	$-0.493102\pi$
$277$	921050.			0.0433355			0.0216677	+	0.999765i	$0.493102\pi$
$278$	1.10454e7	−	1.55198e7i	0.514098	−	0.722359i
$279$			2.12751e7i			0.979625i
$280$	8.52552e6	+	2.49589e6i	0.388371	+	0.113698i
$281$	−1.30007e7			−0.585935			−0.292967	−	0.956122i	$-0.594643\pi$
$281$	−1.30007e7			−0.585935			−0.292967	+	0.956122i	$0.594643\pi$
$282$	499396.	+	355417.i	0.0222689	+	0.0158486i
$283$		−	3.84140e7i		−	1.69485i	−0.530917	−	0.847424i	$-0.678152\pi$
$283$		−	3.84140e7i		−	1.69485i	0.530917	−	0.847424i	$-0.321848\pi$
$284$	−1.01761e7	+	3.52809e6i	−0.444250	+	0.154023i
$285$	2.85548e6			0.123351
$286$	2.08633e6	−	2.93150e6i	0.0891837	−	0.125312i
$287$		−	5.67546e7i		−	2.40080i
$288$	1.58176e7	−	774685.i	0.662161	−	0.0324301i
$289$	1.41986e6			0.0588235
$290$	−9.58738e6	−	6.82328e6i	−0.393103	−	0.279769i
$291$			7.18917e6i			0.291743i
$292$	4.62463e6	+	1.33389e7i	0.185750	+	0.535761i
$293$	−8.40507e6			−0.334148			−0.167074	−	0.985944i	$-0.553432\pi$
$293$	−8.40507e6			−0.334148			−0.167074	+	0.985944i	$0.553432\pi$
$294$	−4.88614e6	+	6.86551e6i	−0.192276	+	0.270166i
$295$		−	7.14768e6i		−	0.278419i
$296$	−1.09248e7	+	3.73173e7i	−0.421250	+	1.43891i
$297$	7.46645e6			0.285000
$298$	−4.01594e7	−	2.85812e7i	−1.51753	−	1.08002i
$299$		−	2.64571e7i		−	0.989756i
$300$	1.32665e7	−	4.59954e6i	0.491353	−	0.170353i
$301$	3.52828e6			0.129379
$302$	−2.27024e7	+	3.18992e7i	−0.824237	+	1.15813i
$303$			2.35813e7i			0.847695i
$304$	1.14451e7	+	1.45217e7i	0.407380	+	0.516887i
$305$	3.09108e6			0.108946
$306$	3.75351e6	+	2.67135e6i	0.131001	+	0.0932323i
$307$			4.42683e7i			1.52995i	0.644058	+	0.764977i	$0.277250\pi$
$307$			4.42683e7i			1.52995i	−0.644058	+	0.764977i	$0.722750\pi$
$308$	3.54155e6	+	1.02150e7i	0.121211	+	0.349611i
$309$	1.04747e7			0.355033
$310$	8.24060e6	−	1.15789e7i	0.276614	−	0.388670i
$311$		−	2.63900e7i		−	0.877322i	−0.898653	−	0.438661i	$-0.855453\pi$
$311$		−	2.63900e7i		−	0.877322i	0.898653	−	0.438661i	$-0.144547\pi$
$312$	−8.81677e6	−	2.58116e6i	−0.290299	−	0.0849866i
$313$	3.35199e7			1.09312			0.546562	−	0.837419i	$-0.315936\pi$
$313$	3.35199e7			1.09312			0.546562	+	0.837419i	$0.315936\pi$
$314$	2.29897e6	+	1.63616e6i	0.0742581	+	0.0528490i
$315$			8.38530e6i			0.268279i
$316$	2.41568e6	−	837522.i	0.0765558	−	0.0265421i
$317$	5.45401e7			1.71214			0.856068	−	0.516864i	$-0.172901\pi$
$317$	5.45401e7			1.71214			0.856068	+	0.516864i	$0.172901\pi$
$318$	−7.53406e6	+	1.05861e7i	−0.234287	+	0.329196i
$319$		−	1.43217e7i		−	0.441186i
$320$	−8.90870e6	−	5.70509e6i	−0.271872	−	0.174106i
$321$	−1.71644e7			−0.518937
$322$	6.47688e7	+	4.60955e7i	1.93998	+	1.38067i
$323$			5.37889e6i			0.159619i
$324$	1.14159e6	+	3.29271e6i	0.0335641	+	0.0968095i
$325$	1.60216e7			0.466719
$326$	−1.33863e7	+	1.88091e7i	−0.386375	+	0.542895i
$327$		−	8.95061e6i		−	0.255982i
$328$	−1.89895e7	+	6.48647e7i	−0.538135	+	1.83817i
$329$	−2.10155e6			−0.0590136
$330$	−1.61999e6	−	1.15293e6i	−0.0450785	−	0.0320821i
$331$			1.98223e7i			0.546599i	0.961929	+	0.273300i	$0.0881151\pi$
$331$			1.98223e7i			0.546599i	−0.961929	+	0.273300i	$0.911885\pi$
$332$	−3.59114e7	+	1.24506e7i	−0.981337	+	0.340232i
$333$	−3.67035e7			−0.993973
$334$	1.83845e7	−	2.58320e7i	0.493414	−	0.693296i
$335$			4.44709e6i			0.118288i
$336$	2.16801e7	−	1.70870e7i	0.571536	−	0.450451i
$337$	3.69467e6			0.0965354			0.0482677	−	0.998834i	$-0.484630\pi$
$337$	3.69467e6			0.0965354			0.0482677	+	0.998834i	$0.484630\pi$
$338$	2.29200e7	+	1.63120e7i	0.593560	+	0.422433i
$339$			1.57042e7i			0.403103i
$340$	−1.00812e6	−	2.90773e6i	−0.0256492	−	0.0739805i
$341$	1.72966e7			0.436211
$342$	−1.01200e7	+	1.42196e7i	−0.252989	+	0.355474i
$343$			2.16906e7i			0.537513i
$344$	−4.03246e6	−	1.18052e6i	−0.0990593	−	0.0290001i
$345$	−1.46205e7			−0.356045
$346$	−4.85208e7	−	3.45320e7i	−1.17139	−	0.833668i
$347$		−	3.89821e7i		−	0.932990i	−0.884524	−	0.466495i	$-0.845516\pi$
$347$		−	3.89821e7i		−	0.932990i	0.884524	−	0.466495i	$-0.154484\pi$
$348$	−3.45490e7	+	1.19782e7i	−0.819780	+	0.284220i
$349$	4.40260e7			1.03570			0.517849	−	0.855472i	$-0.326733\pi$
$349$	4.40260e7			1.03570			0.517849	+	0.855472i	$0.326733\pi$
$350$	−2.79140e7	+	3.92220e7i	−0.651056	+	0.914798i
$351$		−	2.17522e7i		−	0.503016i
$352$	−629814.	−	1.28596e7i	−0.0144406	−	0.294849i
$353$	−2.76880e7			−0.629460			−0.314730	−	0.949181i	$-0.601914\pi$
$353$	−2.76880e7			−0.629460			−0.314730	+	0.949181i	$0.601914\pi$
$354$	−1.80958e7	−	1.28787e7i	−0.407913	−	0.290309i
$355$			6.79127e6i			0.151798i
$356$	−1.49936e7	−	4.32462e7i	−0.332319	−	0.958514i
$357$	8.03040e6			0.176495
$358$	−4.14694e6	+	5.82685e6i	−0.0903812	+	0.126995i
$359$			9.07358e7i			1.96108i	0.196317	+	0.980541i	$0.437102\pi$
$359$			9.07358e7i			1.96108i	−0.196317	+	0.980541i	$0.562898\pi$
$360$	2.80563e6	−	9.58353e6i	0.0601343	−	0.205408i
$361$	2.66688e7			0.566869
$362$	−3.62659e6	−	2.58102e6i	−0.0764493	−	0.0544085i
$363$			2.53493e7i			0.529964i
$364$	2.97595e7	−	1.03177e7i	0.617052	−	0.213934i
$365$	8.90201e6			0.183067
$366$	5.56950e6	−	7.82569e6i	0.113599	−	0.159617i
$367$		−	8.01784e6i		−	0.162203i	−0.996706	−	0.0811016i	$-0.974156\pi$
$367$		−	8.01784e6i		−	0.162203i	0.996706	−	0.0811016i	$-0.0258438\pi$
$368$	−5.86009e7	−	7.43533e7i	−1.17587	−	1.49196i
$369$	−6.37978e7			−1.26977
$370$	1.99756e7	+	1.42165e7i	0.394362	+	0.280665i
$371$		−	4.45482e7i		−	0.872386i
$372$	−1.44663e7	−	4.17255e7i	−0.281015	−	0.810536i
$373$	−4.84836e7			−0.934261			−0.467130	−	0.884188i	$-0.654712\pi$
$373$	−4.84836e7			−0.934261			−0.467130	+	0.884188i	$0.654712\pi$
$374$	2.17179e6	−	3.05158e6i	0.0415148	−	0.0583324i
$375$		−	1.87376e7i		−	0.355321i
$376$	2.40186e6	+	703156.i	0.0451839	+	0.0132278i
$377$	−4.17237e7			−0.778680
$378$	5.32509e7	+	3.78984e7i	0.985943	+	0.701690i
$379$			5.37404e7i			0.987151i	0.869703	+	0.493575i	$0.164310\pi$
$379$			5.37404e7i			0.987151i	−0.869703	+	0.493575i	$0.835690\pi$
$380$	1.10155e7	−	3.81908e6i	0.200748	−	0.0695999i
$381$	4.29973e7			0.777440
$382$	−2.40362e7	+	3.37733e7i	−0.431197	+	0.605875i
$383$			2.06446e7i			0.367460i	0.982977	+	0.183730i	$0.0588172\pi$
$383$			2.06446e7i			0.367460i	−0.982977	+	0.183730i	$0.941183\pi$
$384$	−3.04952e7	+	1.22747e7i	−0.538565	+	0.216780i
$385$	6.81719e6			0.119460
$386$	−2.77668e7	−	1.97615e7i	−0.482796	−	0.343603i
$387$		−	3.96614e6i		−	0.0684281i
$388$	9.61522e6	+	2.77334e7i	0.164613	+	0.474796i
$389$	5.53084e7			0.939598			0.469799	−	0.882773i	$-0.344326\pi$
$389$	5.53084e7			0.939598			0.469799	+	0.882773i	$0.344326\pi$
$390$	−3.35887e6	+	4.71954e6i	−0.0566239	+	0.0795621i
$391$		−	2.75408e7i		−	0.460730i
$392$	−9.66672e6	+	3.30198e7i	−0.160480	+	0.548171i
$393$	−3.71131e7			−0.611435
$394$	5.38457e7	+	3.83216e7i	0.880364	+	0.626549i
$395$		−	1.61216e6i		−	0.0261587i
$396$	1.14826e7	−	3.98105e6i	0.184908	−	0.0641081i
$397$	−8.01222e7			−1.28051			−0.640253	−	0.768164i	$-0.721170\pi$
$397$	−8.01222e7			−1.28051			−0.640253	+	0.768164i	$0.721170\pi$
$398$	2.17124e7	−	3.05081e7i	0.344397	−	0.483912i
$399$			3.04218e7i			0.478924i
$400$	4.50261e7	−	3.54869e7i	0.703532	−	0.554483i
$401$	1.31504e7			0.203942			0.101971	−	0.994787i	$-0.467485\pi$
$401$	1.31504e7			0.203942			0.101971	+	0.994787i	$0.467485\pi$
$402$	1.12587e7	+	8.01275e6i	0.173305	+	0.123340i
$403$		−	5.03905e7i		−	0.769899i
$404$	3.15390e7	+	9.09685e7i	0.478304	+	1.37958i
$405$	2.19746e6			0.0330793
$406$	7.26942e7	−	1.02143e8i	1.08623	−	1.52626i
$407$			2.98397e7i			0.442600i
$408$	−9.17792e6	−	2.68688e6i	−0.135134	−	0.0395611i
$409$	−1.16615e8			−1.70445			−0.852227	−	0.523172i	$-0.824748\pi$
$409$	−1.16615e8			−1.70445			−0.852227	+	0.523172i	$0.824748\pi$
$410$	3.47215e7	+	2.47111e7i	0.503787	+	0.358542i
$411$			4.24568e7i			0.611535i
$412$	4.04080e7	−	1.40095e7i	0.577797	−	0.200324i
$413$	7.61504e7			1.08099
$414$	5.18159e7	−	7.28064e7i	0.730234	−	1.02605i
$415$			2.39663e7i			0.335318i
$416$	−3.74643e7	+	1.83485e6i	−0.520400	+	0.0254872i
$417$	−3.73243e7			−0.514734
$418$	1.15604e7	+	8.22747e6i	0.158287	+	0.112652i
$419$		−	7.23253e7i		−	0.983214i	−0.870817	−	0.491607i	$-0.836410\pi$
$419$		−	7.23253e7i		−	0.983214i	0.870817	−	0.491607i	$-0.163590\pi$
$420$	−5.70169e6	−	1.64455e7i	−0.0769584	−	0.221972i
$421$	4.64379e6			0.0622338			0.0311169	−	0.999516i	$-0.490094\pi$
$421$	4.64379e6			0.0622338			0.0311169	+	0.999516i	$0.490094\pi$
$422$	2.69424e7	−	3.78568e7i	0.358508	−	0.503740i
$423$			2.36235e6i			0.0312121i
$424$	−1.49054e7	+	5.09140e7i	−0.195544	+	0.667944i
$425$	1.66779e7			0.217257
$426$	1.71935e7	+	1.22365e7i	0.222400	+	0.158281i
$427$			3.29319e7i			0.422994i
$428$	−6.62145e7	+	2.29567e7i	−0.844543	+	0.292805i
$429$	−7.05008e6			−0.0892940
$430$	−1.53622e6	+	2.15854e6i	−0.0193219	+	0.0271491i
$431$		−	6.93358e7i		−	0.866016i	−0.901390	−	0.433008i	$-0.857452\pi$
$431$		−	6.93358e7i		−	0.866016i	0.901390	−	0.433008i	$-0.142548\pi$
$432$	−4.81799e7	−	6.11311e7i	−0.597606	−	0.758247i
$433$	−1.08955e8			−1.34209			−0.671046	−	0.741416i	$-0.734155\pi$
$433$	−1.08955e8			−1.34209			−0.671046	+	0.741416i	$0.734155\pi$
$434$	1.23360e8	+	8.77942e7i	1.50905	+	1.07398i
$435$			2.30570e7i			0.280115i
$436$	−1.19711e7	−	3.45284e7i	−0.144435	−	0.416597i
$437$	1.04334e8			1.25020
$438$	1.60396e7	−	2.25372e7i	0.190885	−	0.268212i
$439$		−	1.63490e8i		−	1.93240i	−0.257793	−	0.966200i	$-0.582995\pi$
$439$		−	1.63490e8i		−	1.93240i	0.257793	−	0.966200i	$-0.417005\pi$
$440$	−7.79135e6	−	2.28096e6i	−0.0914649	−	0.0267768i
$441$	−3.24767e7			−0.378666
$442$	−8.89025e6	−	6.32714e6i	−0.102955	−	0.0732724i
$443$			1.07969e8i			1.24191i	0.783847	+	0.620954i	$0.213255\pi$
$443$			1.07969e8i			1.24191i	−0.783847	+	0.620954i	$0.786745\pi$
$444$	7.19840e7	−	2.49570e7i	0.822408	−	0.285131i
$445$	−2.88614e7			−0.327519
$446$	6.20000e7	−	8.71161e7i	0.698855	−	0.981960i
$447$			9.65809e7i			1.08136i
$448$	6.07812e7	−	9.49119e7i	0.675982	−	1.05557i
$449$	−6.68929e7			−0.738994			−0.369497	−	0.929232i	$-0.620470\pi$
$449$	−6.68929e7			−0.738994			−0.369497	+	0.929232i	$0.620470\pi$
$450$	4.40893e7	+	3.13781e7i	0.483833	+	0.344341i
$451$			5.18672e7i			0.565410i
$452$	2.10037e7	+	6.05813e7i	0.227447	+	0.656030i
$453$	7.67155e7			0.825256
$454$	2.72731e7	−	3.83214e7i	0.291452	−	0.409519i
$455$		−	1.98607e7i		−	0.210844i
$456$	1.01788e7	−	3.47690e7i	0.107350	−	0.366689i
$457$	−5.26009e7			−0.551118			−0.275559	−	0.961284i	$-0.588863\pi$
$457$	−5.26009e7			−0.551118			−0.275559	+	0.961284i	$0.588863\pi$
$458$	−1.12808e8	−	8.02850e7i	−1.17421	−	0.835676i
$459$		−	2.26432e7i		−	0.234153i
$460$	−5.64009e7	+	1.95543e7i	−0.579446	+	0.200895i
$461$	1.22174e8			1.24703			0.623515	−	0.781812i	$-0.285704\pi$
$461$	1.22174e8			1.24703			0.623515	+	0.781812i	$0.285704\pi$
$462$	1.22832e7	−	1.72591e7i	0.124562	−	0.175022i
$463$			5.28282e7i			0.532259i	0.963937	+	0.266130i	$0.0857449\pi$
$463$			5.28282e7i			0.532259i	−0.963937	+	0.266130i	$0.914255\pi$
$464$	−1.17258e8	+	9.24157e7i	−1.17378	+	0.925106i
$465$	−2.78464e7			−0.276956
$466$	−9.49760e7	−	6.75938e7i	−0.938547	−	0.667958i
$467$		−	355244.i		−	0.00348800i	−0.999998	−	0.00174400i	$-0.999445\pi$
$467$		−	355244.i		−	0.00348800i	0.999998	−	0.00174400i	$-0.000555133\pi$
$468$	−1.15981e7	−	3.34526e7i	−0.113149	−	0.326357i
$469$	−4.73787e7			−0.459266
$470$	915020.	−	1.28569e6i	0.00881327	−	0.0123835i
$471$		−	5.52887e6i		−	0.0529144i
$472$	−8.70320e7	−	2.54791e7i	−0.827662	−	0.242302i
$473$	−3.22444e6			−0.0304699
$474$	−4.08150e6	−	2.90478e6i	−0.0383253	−	0.0272759i
$475$			6.31813e7i			0.589532i
$476$	3.09785e7	−	1.07403e7i	0.287237	−	0.0995857i
$477$	−5.00766e7			−0.461402
$478$	−3.12078e7	+	4.38501e7i	−0.285746	+	0.401501i
$479$			3.25388e7i			0.296070i	0.988982	+	0.148035i	$0.0472949\pi$
$479$			3.25388e7i			0.296070i	−0.988982	+	0.148035i	$0.952705\pi$
$480$	1.01396e6	+	2.07032e7i	0.00916851	+	0.187204i
$481$	8.69328e7			0.781175
$482$	1.03128e8	+	7.33953e7i	0.920945	+	0.655431i
$483$		−	1.55765e8i		−	1.38238i
$484$	3.39037e7	+	9.77889e7i	0.299027	+	0.862489i
$485$	1.85085e7			0.162235
$486$	6.82194e7	−	9.58550e7i	0.594291	−	0.835037i
$487$		−	2.97160e7i		−	0.257278i	−0.991691	−	0.128639i	$-0.958939\pi$
$487$		−	2.97160e7i		−	0.257278i	0.991691	−	0.128639i	$-0.0410609\pi$
$488$	1.10187e7	−	3.76378e7i	0.0948134	−	0.323866i
$489$	4.52348e7			0.386853
$490$	1.76752e7	+	1.25794e7i	0.150237	+	0.106923i
$491$		−	1.52774e8i		−	1.29064i	−0.763913	−	0.645319i	$-0.776724\pi$
$491$		−	1.52774e8i		−	1.29064i	0.763913	−	0.645319i	$-0.223276\pi$
$492$	1.25122e8	−	4.33802e7i	1.05060	−	0.364247i
$493$	−4.34328e7			−0.362474
$494$	2.39693e7	−	3.36792e7i	0.198827	−	0.279371i
$495$		−	7.66319e6i		−	0.0631821i
$496$	−1.11612e8	−	1.41614e8i	−0.914675	−	1.16055i
$497$	−7.23532e7			−0.589371
$498$	6.06755e7	+	4.31824e7i	0.491276	+	0.349638i
$499$		−	1.09429e8i		−	0.880704i	−0.897825	−	0.440352i	$-0.854854\pi$
$499$		−	1.09429e8i		−	0.880704i	0.897825	−	0.440352i	$-0.145146\pi$
$500$	−2.50608e7	−	7.22833e7i	−0.200486	−	0.578267i
$501$	−6.21244e7			−0.494025
$502$	−1.45449e8	+	2.04370e8i	−1.14974	+	1.61550i
$503$			1.54840e8i			1.21669i	0.793672	+	0.608346i	$0.208167\pi$
$503$			1.54840e8i			1.21669i	−0.793672	+	0.608346i	$0.791833\pi$
$504$	1.02101e8	+	2.98907e7i	0.797518	+	0.233478i
$505$	6.07099e7			0.471396
$506$	−5.91912e7	−	4.21260e7i	−0.456884	−	0.325161i
$507$		−	5.51211e7i		−	0.422955i
$508$	1.65869e8	−	5.75072e7i	1.26524	−	0.438663i
$509$	−6.39832e7			−0.485191			−0.242595	−	0.970128i	$-0.577999\pi$
$509$	−6.39832e7			−0.485191			−0.242595	+	0.970128i	$0.577999\pi$
$510$	−3.49646e6	+	4.91287e6i	−0.0263583	+	0.0370360i
$511$			9.48408e7i			0.710775i
$512$	−1.01223e8	+	8.81378e7i	−0.754171	+	0.656678i
$513$	8.57801e7			0.635381
$514$	−4.42786e7	−	3.15128e7i	−0.326066	−	0.232059i
$515$		−	2.69672e7i		−	0.197430i
$516$	2.69683e6	+	7.77851e6i	0.0196293	+	0.0566170i
$517$	1.92058e6			0.0138982
$518$	−1.51461e8	+	2.12818e8i	−1.08971	+	1.53115i
$519$			1.16690e8i			0.834699i
$520$	−6.64517e6	+	2.26987e7i	−0.0472603	+	0.161433i
$521$	7.97491e7			0.563914			0.281957	−	0.959427i	$-0.409016\pi$
$521$	7.97491e7			0.563914			0.281957	+	0.959427i	$0.409016\pi$
$522$	−1.14818e8	−	8.17154e7i	−0.807234	−	0.574503i
$523$			2.11434e8i			1.47798i	0.673716	+	0.738991i	$0.264697\pi$
$523$			2.11434e8i			1.47798i	−0.673716	+	0.738991i	$0.735303\pi$
$524$	−1.43170e8	+	4.96373e7i	−0.995079	+	0.344996i
$525$	9.43264e7			0.651861
$526$	1.37713e8	−	1.93500e8i	0.946272	−	1.32961i
$527$		−	5.24546e7i		−	0.358387i
$528$	−1.98131e7	+	1.56155e7i	−0.134602	+	0.106085i
$529$	−3.86170e8			−2.60862
$530$	2.72539e7	+	1.93964e7i	0.183063	+	0.130285i
$531$		−	8.56005e7i		−	0.571732i
$532$	4.06880e7	+	1.17357e8i	0.270228	+	0.779425i
$533$	1.51106e8			0.997930
$534$	−5.20023e7	+	7.30683e7i	−0.341506	+	0.479850i
$535$			4.41898e7i			0.288576i
$536$	5.41489e7	+	1.58524e7i	0.351638	+	0.102944i
$537$	1.40132e7			0.0904930
$538$	−3.06935e7	−	2.18444e7i	−0.197106	−	0.140279i
$539$			2.64034e7i			0.168614i
$540$	−4.63712e7	+	1.60770e7i	−0.294487	+	0.102099i
$541$	1.70224e8			1.07505			0.537525	−	0.843248i	$-0.319359\pi$
$541$	1.70224e8			1.07505			0.537525	+	0.843248i	$0.319359\pi$
$542$	−8.39653e7	+	1.17979e8i	−0.527353	+	0.740984i
$543$			8.72173e6i			0.0544758i
$544$	−3.89989e7	+	1.91001e6i	−0.242245	+	0.0118642i
$545$	−2.30433e7			−0.142349
$546$	−5.02813e7	−	3.57849e7i	−0.308908	−	0.219848i
$547$			1.86466e8i			1.13930i	0.821888	+	0.569649i	$0.192921\pi$
$547$			1.86466e8i			1.13930i	−0.821888	+	0.569649i	$0.807079\pi$
$548$	5.67842e7	+	1.63784e8i	0.345053	+	0.995242i
$549$	3.70187e7			0.223720
$550$	2.55102e7	−	3.58443e7i	0.153330	−	0.215443i
$551$		−	1.64538e8i		−	0.983583i
$552$	−5.21172e7	+	1.78023e8i	−0.309859	+	1.05842i
$553$	1.71757e7			0.101564
$554$	−6.00326e6	−	4.27249e6i	−0.0353068	−	0.0251276i
$555$		−	4.80402e7i		−	0.281013i
$556$	−1.43984e8	+	4.99197e7i	−0.837704	+	0.290434i
$557$	2.84114e8			1.64410			0.822048	−	0.569418i	$-0.192831\pi$
$557$	2.84114e8			1.64410			0.822048	+	0.569418i	$0.192831\pi$
$558$	9.86893e7	−	1.38668e8i	0.568025	−	0.798131i
$559$			9.39386e6i			0.0537785i
$560$	−4.39904e7	−	5.58153e7i	−0.250492	−	0.317826i
$561$	−7.33886e6			−0.0415662
$562$	8.47369e7	+	6.03067e7i	0.477379	+	0.339748i
$563$		−	9.60127e7i		−	0.538026i	−0.963137	−	0.269013i	$-0.913302\pi$
$563$		−	9.60127e7i		−	0.538026i	0.963137	−	0.269013i	$-0.0866975\pi$
$564$	−1.60631e6	−	4.63311e6i	−0.00895349	−	0.0258247i
$565$	4.04303e7			0.224162
$566$	−1.78192e8	+	2.50377e8i	−0.982739	+	1.38084i
$567$			2.34115e7i			0.128434i
$568$	8.26922e7	+	2.42086e7i	0.451253	+	0.132107i
$569$	2.57804e8			1.39944			0.699718	−	0.714419i	$-0.253309\pi$
$569$	2.57804e8			1.39944			0.699718	+	0.714419i	$0.253309\pi$
$570$	−1.86116e7	−	1.32457e7i	−0.100498	−	0.0715240i
$571$			2.81559e8i			1.51238i	0.654351	+	0.756191i	$0.272942\pi$
$571$			2.81559e8i			1.51238i	−0.654351	+	0.756191i	$0.727058\pi$
$572$	−2.71968e7	+	9.42919e6i	−0.145321	+	0.0503833i
$573$	8.12226e7			0.431731
$574$	−2.63268e8	+	3.69918e8i	−1.39208	+	1.95601i
$575$		−	3.23499e8i		−	1.70164i
$576$	−1.06690e8	−	6.83241e7i	−0.558287	−	0.357525i
$577$	−9.01192e7			−0.469126			−0.234563	−	0.972101i	$-0.575366\pi$
$577$	−9.01192e7			−0.469126			−0.234563	+	0.972101i	$0.575366\pi$
$578$	−9.25441e6	−	6.58631e6i	−0.0479254	−	0.0341082i
$579$			6.67774e7i			0.344028i
$580$	3.08379e7	+	8.89462e7i	0.158052	+	0.455872i
$581$	−2.55333e8			−1.30191
$582$	3.33485e7	−	4.68579e7i	0.169164	−	0.237692i
$583$			4.07120e7i			0.205455i
$584$	3.17327e7	−	1.08393e8i	0.159319	−	0.544206i
$585$	−2.23254e7			−0.111514
$586$	5.47830e7	+	3.89887e7i	0.272240	+	0.193752i
$587$		−	6.86900e7i		−	0.339609i	−0.985478	−	0.169804i	$-0.945686\pi$
$587$		−	6.86900e7i		−	0.339609i	0.985478	−	0.169804i	$-0.0543136\pi$
$588$	6.36943e7	−	2.20830e7i	0.313306	−	0.108624i
$589$	1.98716e8			0.972492
$590$	−3.31560e7	+	4.65875e7i	−0.161438	+	0.226837i
$591$		−	1.29495e8i		−	0.627324i
$592$	2.44311e8	−	1.92551e8i	1.17754	−	0.928071i
$593$	3.00305e7			0.144012			0.0720060	−	0.997404i	$-0.477060\pi$
$593$	3.00305e7			0.144012			0.0720060	+	0.997404i	$0.477060\pi$
$594$	−4.86652e7	−	3.46347e7i	−0.232198	−	0.165254i
$595$		−	2.06742e7i		−	0.0981474i
$596$	1.29173e8	+	3.72576e8i	0.610145	+	1.75985i
$597$	−7.33701e7			−0.344823
$598$	−1.22727e8	+	1.72443e8i	−0.573899	+	0.806385i
$599$		−	1.80810e8i		−	0.841282i	−0.907227	−	0.420641i	$-0.861805\pi$
$599$		−	1.80810e8i		−	0.841282i	0.907227	−	0.420641i	$-0.138195\pi$
$600$	−1.07805e8	−	3.15606e7i	−0.499098	−	0.146114i
$601$	−1.98760e8			−0.915598			−0.457799	−	0.889056i	$-0.651362\pi$
$601$	−1.98760e8			−0.915598			−0.457799	+	0.889056i	$0.651362\pi$
$602$	−2.29968e7	−	1.63667e7i	−0.105409	−	0.0750190i
$603$			5.32583e7i			0.242904i
$604$	2.95942e8	−	1.02604e8i	1.34306	−	0.465643i
$605$	6.52617e7			0.294708
$606$	1.09387e8	−	1.53699e8i	0.491527	−	0.690644i
$607$		−	2.63782e8i		−	1.17945i	−0.807605	−	0.589724i	$-0.799236\pi$
$607$		−	2.63782e8i		−	1.17945i	0.807605	−	0.589724i	$-0.200764\pi$
$608$	−7.23577e6	−	1.47741e8i	−0.0321939	−	0.657339i
$609$	−2.45646e8			−1.08757
$610$	−2.01472e7	−	1.43386e7i	−0.0887616	−	0.0631711i
$611$		−	5.59526e6i		−	0.0245300i
$612$	−1.20732e7	−	3.48229e7i	−0.0526705	−	0.151919i
$613$	3.58088e8			1.55456			0.777282	−	0.629152i	$-0.216598\pi$
$613$	3.58088e8			1.55456			0.777282	+	0.629152i	$0.216598\pi$
$614$	2.05348e8	−	2.88534e8i	0.887127	−	1.24650i
$615$		−	8.35031e7i		−	0.358986i
$616$	2.43010e7	−	8.30079e7i	0.103964	−	0.355122i
$617$	−7.69196e7			−0.327478			−0.163739	−	0.986504i	$-0.552355\pi$
$617$	−7.69196e7			−0.327478			−0.163739	+	0.986504i	$0.552355\pi$
$618$	−6.82728e7	−	4.85894e7i	−0.289256	−	0.205862i
$619$		−	3.95026e6i		−	0.0166553i	−0.999965	−	0.00832766i	$-0.997349\pi$
$619$		−	3.95026e6i		−	0.0166553i	0.999965	−	0.00832766i	$-0.00265081\pi$
$620$	−1.07422e8	+	3.72435e7i	−0.450732	+	0.156270i
$621$	−4.39208e8			−1.83398
$622$	−1.22416e8	+	1.72006e8i	−0.508705	+	0.714781i
$623$		−	3.07485e8i		−	1.27163i
$624$	4.54931e7	+	5.77220e7i	0.187237	+	0.237568i
$625$	1.70455e8			0.698182
$626$	−2.18477e8	−	1.55489e8i	−0.890602	−	0.633836i
$627$		−	2.78021e7i		−	0.112791i
$628$	−7.39464e6	−	2.13285e7i	−0.0298564	−	0.0861155i
$629$	9.04937e7			0.363636
$630$	3.88970e7	−	5.46541e7i	0.155559	−	0.218575i
$631$			6.05340e7i			0.240941i	0.992717	+	0.120471i	$0.0384404\pi$
$631$			6.05340e7i			0.240941i	−0.992717	+	0.120471i	$0.961560\pi$
$632$	−1.96301e7	−	5.74680e6i	−0.0777625	−	0.0227654i
$633$	−9.10432e7			−0.358952
$634$	−3.55484e8	−	2.52996e8i	−1.39493	−	0.992763i
$635$		−	1.10696e8i		−	0.432327i
$636$	9.82118e7	−	3.40502e7i	0.381761	−	0.132358i
$637$	7.69216e7			0.297598
$638$	−6.64341e7	+	9.33465e7i	−0.255817	+	0.359448i
$639$			8.13321e7i			0.311716i
$640$	3.16012e7	+	7.85098e7i	0.120549	+	0.299491i
$641$	4.33234e8			1.64493			0.822467	−	0.568813i	$-0.192597\pi$
$641$	4.33234e8			1.64493			0.822467	+	0.568813i	$0.192597\pi$
$642$	1.11875e8	+	7.96209e7i	0.422794	+	0.300900i
$643$			5.93659e7i			0.223308i	0.993747	+	0.111654i	$0.0356148\pi$
$643$			5.93659e7i			0.223308i	−0.993747	+	0.111654i	$0.964385\pi$
$644$	−2.08329e8	−	6.00887e8i	−0.779996	−	2.24976i
$645$	5.19117e6			0.0193458
$646$	2.49511e7	−	3.50588e7i	0.0925535	−	0.130047i
$647$			6.22424e7i			0.229812i	0.993376	+	0.114906i	$0.0366567\pi$
$647$			6.22424e7i			0.229812i	−0.993376	+	0.114906i	$0.963343\pi$
$648$	7.83321e6	−	2.67569e7i	0.0287882	−	0.0983355i
$649$	−6.95927e7			−0.254583
$650$	−1.04426e8	−	7.43195e7i	−0.380250	−	0.270622i
$651$		−	2.96672e8i		−	1.07531i
$652$	1.74500e8	−	6.04996e7i	0.629583	−	0.218278i
$653$	1.57459e8			0.565493			0.282747	−	0.959195i	$-0.408754\pi$
$653$	1.57459e8			0.565493			0.282747	+	0.959195i	$0.408754\pi$
$654$	−4.15193e7	+	5.83387e7i	−0.148428	+	0.208556i
$655$			9.55476e7i			0.340013i
$656$	4.24659e8	−	3.34691e8i	1.50428	−	1.18559i
$657$	1.06610e8			0.375927
$658$	1.36976e7	+	9.74849e6i	0.0480802	+	0.0342184i
$659$		−	6.26318e7i		−	0.218846i	−0.993995	−	0.109423i	$-0.965100\pi$
$659$		−	6.26318e7i		−	0.218846i	0.993995	−	0.109423i	$-0.0349003\pi$
$660$	5.21069e6	+	1.50293e7i	0.0181244	+	0.0522765i
$661$	−1.47605e8			−0.511090			−0.255545	−	0.966797i	$-0.582255\pi$
$661$	−1.47605e8			−0.511090			−0.255545	+	0.966797i	$0.582255\pi$
$662$	9.19497e7	−	1.29198e8i	0.316940	−	0.445331i
$663$			2.13805e7i			0.0733630i
$664$	2.91820e8	+	8.54318e7i	0.996806	+	0.291820i
$665$	7.83209e7			0.266326
$666$	2.39228e8	+	1.70257e8i	0.809821	+	0.576345i
$667$			8.42461e8i			2.83904i
$668$	−2.39654e8	+	8.30888e7i	−0.804000	+	0.278749i
$669$	−2.09509e8			−0.699719
$670$	2.06288e7	−	2.89855e7i	0.0685882	−	0.0963731i
$671$		−	3.00960e7i		−	0.0996188i
$672$	−2.20569e8	+	1.08026e7i	−0.726837	+	0.0355977i
$673$	−5.28771e8			−1.73469			−0.867346	−	0.497705i	$-0.834176\pi$
$673$	−5.28771e8			−1.73469			−0.867346	+	0.497705i	$0.834176\pi$
$674$	−2.40813e7	−	1.71385e7i	−0.0786504	−	0.0559750i
$675$		−	2.65971e8i		−	0.864814i
$676$	−7.37223e7	−	2.12638e8i	−0.238648	−	0.688338i
$677$	3.02186e8			0.973887			0.486944	−	0.873433i	$-0.338112\pi$
$677$	3.02186e8			0.973887			0.486944	+	0.873433i	$0.338112\pi$
$678$	7.28472e7	−	1.02357e8i	0.233735	−	0.328421i
$679$			1.97187e8i			0.629895i
$680$	−6.91737e6	+	2.36285e7i	−0.0219996	+	0.0751467i
$681$	−9.21606e7			−0.291813
$682$	−1.12736e8	−	8.02338e7i	−0.355395	−	0.252932i
$683$		−	5.42293e7i		−	0.170205i	−0.996372	−	0.0851024i	$-0.972878\pi$
$683$		−	5.42293e7i		−	0.170205i	0.996372	−	0.0851024i	$-0.0271217\pi$
$684$	1.31921e8	−	4.57373e7i	0.412235	−	0.142923i
$685$	1.09305e8			0.340069
$686$	1.00616e8	−	1.41376e8i	0.311671	−	0.437928i
$687$			2.71297e8i			0.836710i
$688$	2.08069e7	+	2.63999e7i	0.0638913	+	0.0810657i
$689$	1.18607e8			0.362621
$690$	9.52943e7	+	6.78204e7i	0.290081	+	0.206449i
$691$		−	3.58326e8i		−	1.08604i	−0.839721	−	0.543018i	$-0.817281\pi$
$691$		−	3.58326e8i		−	1.08604i	0.839721	−	0.543018i	$-0.182719\pi$
$692$	1.56068e8	+	4.50148e8i	0.470971	+	1.35843i
$693$	8.16426e7			0.245311
$694$	−1.80827e8	+	2.54080e8i	−0.540984	+	0.760136i
$695$			9.60912e7i			0.286239i
$696$	2.80748e8	+	8.21906e7i	0.832702	+	0.243778i
$697$	1.57296e8			0.464535
$698$	−2.86955e8	−	2.04224e8i	−0.843815	−	0.600538i
$699$			2.28411e8i			0.668784i
$700$	3.63879e8	−	1.26158e8i	1.06087	−	0.367806i
$701$	1.32776e8			0.385447			0.192724	−	0.981253i	$-0.438268\pi$
$701$	1.32776e8			0.385447			0.192724	+	0.981253i	$0.438268\pi$
$702$	−1.00902e8	+	1.41778e8i	−0.291669	+	0.409823i
$703$			3.42820e8i			0.986736i
$704$	−5.55470e7	+	8.67386e7i	−0.159200	+	0.248596i
$705$	−3.09201e6			−0.00882417
$706$	1.80466e8	+	1.28437e8i	0.512840	+	0.364985i
$707$			6.46795e8i			1.83024i
$708$	5.82052e7	+	1.67882e8i	0.164007	+	0.473048i
$709$	−6.42637e8			−1.80313			−0.901565	−	0.432644i	$-0.857581\pi$
$709$	−6.42637e8			−1.80313			−0.901565	+	0.432644i	$0.857581\pi$
$710$	3.15028e7	−	4.42645e7i	0.0880184	−	0.123675i
$711$		−	1.93072e7i		−	0.0537168i
$712$	−1.02881e8	+	3.51423e8i	−0.285033	+	0.973622i
$713$	−1.01746e9			−2.80703
$714$	−5.23410e7	−	3.72507e7i	−0.143796	−	0.102339i
$715$			1.81504e7i			0.0496556i
$716$	5.40582e7	−	1.87421e7i	0.147273	−	0.0510598i
$717$	1.05457e8			0.286099
$718$	4.20898e8	−	5.91403e8i	1.13711	−	1.59775i
$719$		−	1.61019e8i		−	0.433201i	−0.976260	−	0.216601i	$-0.930503\pi$
$719$		−	1.61019e8i		−	0.433201i	0.976260	−	0.216601i	$-0.0694970\pi$
$720$	−6.27419e7	+	4.94495e7i	−0.168097	+	0.132484i
$721$	2.87305e8			0.766543
$722$	−1.73823e8	−	1.23709e8i	−0.461846	−	0.328693i
$723$		−	2.48016e8i		−	0.656242i
$724$	1.16650e7	+	3.36455e7i	0.0307374	+	0.0886565i
$725$	−5.10168e8			−1.33875
$726$	1.17588e8	−	1.65223e8i	0.307294	−	0.431778i
$727$		−	1.95529e8i		−	0.508872i	−0.967090	−	0.254436i	$-0.918110\pi$
$727$		−	1.95529e8i		−	0.508872i	0.967090	−	0.254436i	$-0.0818898\pi$
$728$	−2.41829e8	−	7.07967e7i	−0.626779	−	0.183493i
$729$	−1.90829e8			−0.492563
$730$	−5.80220e7	−	4.12939e7i	−0.149150	−	0.106149i
$731$			9.77865e6i			0.0250338i
$732$	−7.26023e7	+	2.51714e7i	−0.185104	+	0.0641762i
$733$	−5.55527e8			−1.41057			−0.705283	−	0.708926i	$-0.749180\pi$
$733$	−5.55527e8			−1.41057			−0.705283	+	0.708926i	$0.749180\pi$
$734$	−3.71925e7	+	5.22591e7i	−0.0940518	+	0.132152i
$735$		−	4.25078e7i		−	0.107055i
$736$	3.70483e7	+	7.56457e8i	0.0929255	+	1.89736i
$737$	4.32986e7			0.108161
$738$	4.15824e8	+	2.95940e8i	1.03452	+	0.736265i
$739$			4.21776e8i			1.04508i	0.852616	+	0.522539i	$0.175015\pi$
$739$			4.21776e8i			1.04508i	−0.852616	+	0.522539i	$0.824985\pi$
$740$	−6.42518e7	−	1.85323e8i	−0.158559	−	0.457334i
$741$	−8.09965e7			−0.199073
$742$	−2.06647e8	+	2.90359e8i	−0.505844	+	0.710760i
$743$			1.07343e8i			0.261703i	0.991402	+	0.130852i	$0.0417712\pi$
$743$			1.07343e8i			0.261703i	−0.991402	+	0.130852i	$0.958229\pi$
$744$	−9.92632e7	+	3.39065e8i	−0.241029	+	0.823312i
$745$	2.48647e8			0.601332
$746$	3.16009e8	+	2.24901e8i	0.761171	+	0.541721i
$747$			2.87020e8i			0.688573i
$748$	−2.83108e7	+	9.81543e6i	−0.0676469	+	0.0234533i
$749$	−4.70791e8			−1.12043
$750$	−8.69185e7	+	1.22129e8i	−0.206029	+	0.289491i
$751$			1.75778e8i			0.414997i	0.978235	+	0.207499i	$0.0665323\pi$
$751$			1.75778e8i			0.414997i	−0.978235	+	0.207499i	$0.933468\pi$
$752$	−1.23932e7	−	1.57246e7i	−0.0291427	−	0.0369765i
$753$	4.91497e8			1.15116
$754$	2.71949e8	+	1.93544e8i	0.634414	+	0.451509i
$755$		−	1.97504e8i		−	0.458917i
$756$	−1.71282e8	−	4.94032e8i	−0.396411	−	1.14338i
$757$	3.32883e8			0.767367			0.383684	−	0.923465i	$-0.374655\pi$
$757$	3.32883e8			0.767367			0.383684	+	0.923465i	$0.374655\pi$
$758$	2.49286e8	−	3.50272e8i	0.572389	−	0.804262i
$759$			1.42351e8i			0.325563i
$760$	−8.95127e7	−	2.62053e7i	−0.203913	−	0.0596965i
$761$	1.16687e8			0.264771			0.132385	−	0.991198i	$-0.457736\pi$
$761$	1.16687e8			0.264771			0.132385	+	0.991198i	$0.457736\pi$
$762$	−2.80250e8	−	1.99452e8i	−0.633404	−	0.450790i
$763$		−	2.45500e8i		−	0.552685i
$764$	3.13329e8	−	1.08632e8i	0.702620	−	0.243600i
$765$	−2.32399e7			−0.0519098
$766$	9.57644e7	−	1.34558e8i	0.213068	−	0.299381i
$767$			2.02746e8i			0.449331i
$768$	2.55702e8	+	6.14537e7i	0.564483	+	0.135664i
$769$	−2.61619e8			−0.575295			−0.287647	−	0.957736i	$-0.592873\pi$
$769$	−2.61619e8			−0.575295			−0.287647	+	0.957736i	$0.592873\pi$
$770$	−4.44334e7	−	3.16230e7i	−0.0973280	−	0.0692677i
$771$			1.06487e8i			0.232346i
$772$	8.93120e7	+	2.57604e8i	0.194115	+	0.559888i
$773$	1.95442e8			0.423136			0.211568	−	0.977363i	$-0.432143\pi$
$773$	1.95442e8			0.423136			0.211568	+	0.977363i	$0.432143\pi$
$774$	−1.83978e7	+	2.58507e7i	−0.0396773	+	0.0557505i
$775$		−	6.16140e8i		−	1.32365i
$776$	6.59765e7	−	2.25364e8i	0.141190	−	0.482280i
$777$	5.11813e8			1.09106
$778$	−3.60492e8	−	2.56560e8i	−0.765520	−	0.544816i
$779$			5.95888e8i			1.26053i
$780$	4.37852e7	−	1.51804e7i	0.0922664	−	0.0319890i
$781$	6.61225e7			0.138802
$782$	−1.27754e8	+	1.79507e8i	−0.267149	+	0.375371i
$783$			6.92646e8i			1.44287i
$784$	2.16176e8	−	1.70377e8i	0.448599	−	0.353560i
$785$	−1.42341e7			−0.0294252
$786$	2.41898e8	+	1.72157e8i	0.498155	+	0.354534i
$787$		−	8.73483e8i		−	1.79197i	−0.444087	−	0.895984i	$-0.646472\pi$
$787$		−	8.73483e8i		−	1.79197i	0.444087	−	0.895984i	$-0.353528\pi$
$788$	−1.73195e8	−	4.99549e8i	−0.353962	−	1.02094i
$789$	−4.65355e8			−0.947443
$790$	−7.47834e6	+	1.05078e7i	−0.0151679	+	0.0213123i
$791$			4.30739e8i			0.870331i
$792$	−9.33090e7	−	2.73167e7i	−0.187823	−	0.0549861i
$793$	−8.76795e7			−0.175824
$794$	5.22225e8	+	3.71664e8i	1.04327	+	0.742487i
$795$		−	6.55439e7i		−	0.130446i
$796$	−2.83037e8	+	9.81295e7i	−0.561182	+	0.194563i
$797$	−1.00527e8			−0.198567			−0.0992837	−	0.995059i	$-0.531655\pi$
$797$	−1.00527e8			−0.198567			−0.0992837	+	0.995059i	$0.531655\pi$
$798$	1.41118e8	−	1.98285e8i	0.277699	−	0.390195i
$799$		−	5.82446e6i		−	0.0114187i
$800$	−4.58087e8	+	2.24353e7i	−0.894701	+	0.0438190i
$801$	−3.45643e8			−0.672559
$802$	−8.57123e7	−	6.10009e7i	−0.166157	−	0.118253i
$803$		−	8.66735e7i		−	0.167394i
$804$	−3.62137e7	−	1.04452e8i	−0.0696794	−	0.200978i
$805$	−4.01016e8			−0.768730
$806$	−2.33747e8	+	3.28438e8i	−0.446418	+	0.627261i
$807$			7.38160e7i			0.140453i
$808$	2.16410e8	−	7.39219e8i	0.410246	−	1.40133i
$809$	2.52614e8			0.477103			0.238552	−	0.971130i	$-0.423327\pi$
$809$	2.52614e8			0.477103			0.238552	+	0.971130i	$0.423327\pi$
$810$	−1.43227e7	−	1.01934e7i	−0.0269507	−	0.0191807i
$811$		−	3.65940e8i		−	0.686036i	−0.939329	−	0.343018i	$-0.888551\pi$
$811$		−	3.65940e8i		−	0.686036i	0.939329	−	0.343018i	$-0.111449\pi$
$812$	−9.47620e8	+	3.28542e8i	−1.76997	+	0.613653i
$813$	2.83733e8			0.528006
$814$	1.38418e8	−	1.94491e8i	0.256637	−	0.360600i
$815$		−	1.16457e8i		−	0.215125i
$816$	4.73566e7	+	6.00864e7i	0.0871586	+	0.110587i
$817$	−3.70448e7			−0.0679299
$818$	7.60080e8	+	5.40944e8i	1.38867	+	0.988309i
$819$		−	2.37851e8i		−	0.432966i
$820$	−1.11682e8	−	3.22126e8i	−0.202554	−	0.584231i
$821$	8.71802e8			1.57539			0.787695	−	0.616065i	$-0.211274\pi$
$821$	8.71802e8			1.57539			0.787695	+	0.616065i	$0.211274\pi$
$822$	1.96945e8	−	2.76727e8i	0.354592	−	0.498237i
$823$		−	5.93480e8i		−	1.06465i	−0.846541	−	0.532324i	$-0.821319\pi$
$823$		−	5.93480e8i		−	1.06465i	0.846541	−	0.532324i	$-0.178681\pi$
$824$	−3.28359e8	−	9.61289e7i	−0.586905	−	0.171820i
$825$	−8.62034e7			−0.153519
$826$	−4.96337e8	−	3.53240e8i	−0.880716	−	0.626800i
$827$		−	6.00875e8i		−	1.06235i	−0.847262	−	0.531175i	$-0.821751\pi$
$827$		−	6.00875e8i		−	1.06235i	0.847262	−	0.531175i	$-0.178249\pi$
$828$	−6.75456e8	+	2.34182e8i	−1.18989	+	0.412537i
$829$	5.03115e8			0.883087			0.441543	−	0.897240i	$-0.354431\pi$
$829$	5.03115e8			0.883087			0.441543	+	0.897240i	$0.354431\pi$
$830$	1.11173e8	−	1.56209e8i	0.194430	−	0.273194i
$831$			1.44375e7i			0.0251587i
$832$	2.52698e8	+	1.61827e8i	0.438764	+	0.280983i
$833$	8.00724e7			0.138531
$834$	2.43274e8	+	1.73137e8i	0.419370	+	0.298463i
$835$			1.59939e8i			0.274723i
$836$	−3.71841e7	−	1.07251e8i	−0.0636412	−	0.183562i
$837$	−8.36522e8			−1.42660
$838$	−3.35496e8	+	4.71405e8i	−0.570106	+	0.801055i
$839$			1.06305e9i			1.79999i	0.435902	+	0.899994i	$0.356429\pi$
$839$			1.06305e9i			1.79999i	−0.435902	+	0.899994i	$0.643571\pi$
$840$	−3.91232e7	+	1.33638e8i	−0.0660079	+	0.225471i
$841$	7.33766e8			1.23359
$842$	−3.02675e7	−	2.15412e7i	−0.0507038	−	0.0360856i
$843$		−	2.03787e8i		−	0.340168i
$844$	−3.51213e8	+	1.21767e8i	−0.584176	+	0.202535i
$845$	−1.41909e8			−0.235202
$846$	1.09583e7	−	1.53974e7i	0.0180980	−	0.0254295i
$847$			6.95289e8i			1.14423i
$848$	3.33326e8	−	2.62708e8i	0.546616	−	0.430811i
$849$	6.02141e8			0.983954
$850$	−1.08704e8	−	7.73638e7i	−0.177006	−	0.125974i
$851$		−	1.75530e9i		−	2.84814i
$852$	−5.53029e7	−	1.59511e8i	−0.0894188	−	0.257912i
$853$	−4.66246e8			−0.751221			−0.375611	−	0.926778i	$-0.622567\pi$
$853$	−4.66246e8			−0.751221			−0.375611	+	0.926778i	$0.622567\pi$
$854$	1.52762e8	−	2.14645e8i	0.245268	−	0.344626i
$855$		−	8.80404e7i		−	0.140859i
$856$	5.38066e8	+	1.57522e8i	0.857855	+	0.251142i
$857$	−5.53460e7			−0.0879314			−0.0439657	−	0.999033i	$-0.513999\pi$
$857$	−5.53460e7			−0.0879314			−0.0439657	+	0.999033i	$0.513999\pi$
$858$	4.59514e7	+	3.27033e7i	0.0727506	+	0.0517761i
$859$		−	7.86285e8i		−	1.24051i	−0.784400	−	0.620255i	$-0.787029\pi$
$859$		−	7.86285e8i		−	1.24051i	0.784400	−	0.620255i	$-0.212971\pi$
$860$	2.00257e7	−	6.94297e6i	0.0314842	−	0.0109157i
$861$	8.89630e8			1.39380
$862$	−3.21629e8	+	4.51921e8i	−0.502150	+	0.705570i
$863$		−	7.76987e8i		−	1.20887i	−0.796653	−	0.604437i	$-0.793398\pi$
$863$		−	7.76987e8i		−	1.20887i	0.796653	−	0.604437i	$-0.206602\pi$
$864$	3.04600e7	+	6.21936e8i	0.0472268	+	0.964283i
$865$	3.00417e8			0.464169
$866$	7.10150e8	+	5.05409e8i	1.09344	+	0.778197i
$867$			2.22563e7i			0.0341504i
$868$	−3.96787e8	−	1.14446e9i	−0.606733	−	1.75001i
$869$	−1.56966e7			−0.0239192
$870$	1.06955e8	−	1.50282e8i	0.162421	−	0.228218i
$871$		−	1.26143e8i		−	0.190901i
$872$	−8.21416e7	+	2.80581e8i	−0.123884	+	0.423164i
$873$	2.21657e8			0.333149
$874$	−6.80032e8	−	4.83974e8i	−1.01858	−	0.724917i
$875$		−	5.13941e8i		−	0.767166i
$876$	−2.09087e8	+	7.24911e7i	−0.311040	+	0.107838i
$877$	−6.09441e8			−0.903509			−0.451755	−	0.892142i	$-0.649202\pi$
$877$	−6.09441e8			−0.903509			−0.451755	+	0.892142i	$0.649202\pi$
$878$	−7.58382e8	+	1.06560e9i	−1.12048	+	1.57439i
$879$		−	1.31750e8i		−	0.193992i
$880$	4.02021e7	+	5.10088e7i	0.0589931	+	0.0748508i
$881$	2.95320e8			0.431882			0.215941	−	0.976406i	$-0.430718\pi$
$881$	2.95320e8			0.431882			0.215941	+	0.976406i	$0.430718\pi$
$882$	2.11678e8	+	1.50650e8i	0.308511	+	0.219565i
$883$			1.10139e9i			1.59978i	0.600146	+	0.799891i	$0.295109\pi$
$883$			1.10139e9i			1.59978i	−0.600146	+	0.799891i	$0.704891\pi$
$884$	2.85955e7	+	8.24786e7i	0.0413944	+	0.119395i
$885$	1.12040e8			0.161638
$886$	5.00839e8	−	7.03728e8i	0.720107	−	1.01182i
$887$			4.88680e8i			0.700251i	0.936703	+	0.350125i	$0.113861\pi$
$887$			4.88680e8i			0.700251i	−0.936703	+	0.350125i	$0.886139\pi$
$888$	−5.84949e8	−	1.71247e8i	−0.835371	−	0.244559i
$889$	1.17934e9			1.67855
$890$	1.88114e8	+	1.33880e8i	0.266840	+	0.189908i
$891$		−	2.13954e7i		−	0.0302473i
$892$	−8.08213e8	+	2.80209e8i	−1.13876	+	0.394810i
$893$	2.20650e7			0.0309848
$894$	4.48011e8	−	6.29500e8i	0.627013	−	0.881014i
$895$		−	3.60770e7i		−	0.0503224i
$896$	−8.36432e8	+	3.36675e8i	−1.16280	+	0.468044i
$897$	4.14715e8			0.574609
$898$	4.35998e8	+	3.10297e8i	0.602082	+	0.428498i
$899$			1.60456e9i			2.20840i
$900$	−1.41814e8	−	4.09035e8i	−0.194532	−	0.561091i
$901$	1.23466e8			0.168800
$902$	2.40597e8	−	3.38063e8i	0.327847	−	0.460657i
$903$			5.53059e7i			0.0751118i
$904$	1.44120e8	−	4.92290e8i	0.195083	−	0.666370i
$905$	2.24541e7			0.0302935
$906$	−5.00020e8	−	3.55861e8i	−0.672362	−	0.478516i
$907$		−	6.54255e8i		−	0.876850i	−0.898768	−	0.438425i	$-0.855537\pi$
$907$		−	6.54255e8i		−	0.876850i	0.898768	−	0.438425i	$-0.144463\pi$
$908$	−3.55524e8	+	1.23261e8i	−0.474910	+	0.164653i
$909$	7.27061e8			0.968008
$910$	−9.21281e7	+	1.29449e8i	−0.122255	+	0.171781i
$911$		−	2.02216e8i		−	0.267460i	−0.991018	−	0.133730i	$-0.957304\pi$
$911$		−	2.02216e8i		−	0.267460i	0.991018	−	0.133730i	$-0.0426956\pi$
$912$	−2.27627e8	+	1.79403e8i	−0.300082	+	0.236507i
$913$	2.33345e8			0.306610
$914$	3.42845e8	+	2.44000e8i	0.449013	+	0.319560i
$915$			4.84528e7i			0.0632493i
$916$	3.62849e8	+	1.04657e9i	0.472106	+	1.36170i
$917$	−1.01795e9			−1.32014
$918$	−1.05035e8	+	1.47585e8i	−0.135771	+	0.190772i
$919$		−	2.25225e8i		−	0.290181i	−0.989418	−	0.145091i	$-0.953653\pi$
$919$		−	2.25225e8i		−	0.290181i	0.989418	−	0.145091i	$-0.0463474\pi$
$920$	4.58320e8	+	1.34175e8i	0.588579	+	0.172310i
$921$	−6.93907e8			−0.888224
$922$	−7.96313e8	−	5.66731e8i	−1.01599	−	0.723076i
$923$		−	1.92636e8i		−	0.244981i
$924$	−1.60120e8	+	5.55139e7i	−0.202969	+	0.0703698i
$925$	1.06295e9			1.34304
$926$	2.45055e8	−	3.44327e8i	0.308625	−	0.433648i
$927$		−	3.22958e8i		−	0.405422i
$928$	1.19296e9	−	5.84265e7i	1.49273	−	0.0731081i
$929$	−2.93160e8			−0.365643			−0.182821	−	0.983146i	$-0.558523\pi$
$929$	−2.93160e8			−0.365643			−0.182821	+	0.983146i	$0.558523\pi$
$930$	1.81499e8	+	1.29172e8i	0.225645	+	0.160590i
$931$			3.03341e8i			0.375908i
$932$	3.05491e8	+	8.81133e8i	0.377355	+	1.08841i
$933$	4.13664e8			0.509335
$934$	−1.64788e6	+	2.31543e6i	−0.00202248	+	0.00284178i
$935$			1.88939e7i			0.0231146i
$936$	−7.95824e7	+	2.71840e8i	−0.0970487	+	0.331501i
$937$	1.45308e9			1.76633			0.883165	−	0.469062i	$-0.155408\pi$
$937$	1.45308e9			1.76633			0.883165	+	0.469062i	$0.155408\pi$
$938$	3.08807e8	+	2.19776e8i	0.374178	+	0.266300i
$939$			5.25425e8i			0.634620i
$940$	−1.19279e7	+	4.13544e6i	−0.0143609	+	0.00497896i
$941$	−9.82624e8			−1.17928			−0.589642	−	0.807665i	$-0.700731\pi$
$941$	−9.82624e8			−1.17928			−0.589642	+	0.807665i	$0.700731\pi$
$942$	−2.56468e7	+	3.60363e7i	−0.0306818	+	0.0431110i
$943$		−	3.05105e9i		−	3.63843i
$944$	4.49071e8	+	5.69785e8i	0.533825	+	0.677322i
$945$	−3.29703e8			−0.390686
$946$	2.10164e7	+	1.49573e7i	0.0248248	+	0.0176677i
$947$		−	3.44398e8i		−	0.405518i	−0.979229	−	0.202759i	$-0.935009\pi$
$947$		−	3.44398e8i		−	0.405518i	0.979229	−	0.202759i	$-0.0649908\pi$
$948$	1.31282e7	+	3.78658e7i	0.0154092	+	0.0444450i
$949$	−2.52508e8			−0.295445
$950$	2.93080e8	−	4.11806e8i	0.341834	−	0.480310i
$951$			8.54917e8i			0.993991i
$952$	−2.51735e8	−	7.36967e7i	−0.291764	−	0.0854156i
$953$	−8.23673e8			−0.951647			−0.475824	−	0.879541i	$-0.657850\pi$
$953$	−8.23673e8			−0.951647			−0.475824	+	0.879541i	$0.657850\pi$
$954$	3.26392e8	+	2.32291e8i	0.375919	+	0.267539i
$955$		−	2.09107e8i		−	0.240082i
$956$	4.06816e8	−	1.41044e8i	0.465612	−	0.161429i
$957$	2.24493e8			0.256133
$958$	1.50938e8	−	2.12083e8i	0.171673	−	0.241218i
$959$			1.16452e9i			1.32035i
$960$	8.94274e7	−	1.39644e8i	0.101078	−	0.157837i
$961$	−1.05036e9			−1.18350
$962$	−5.66615e8	−	4.03256e8i	−0.636448	−	0.452956i
$963$			5.29216e8i			0.592589i
$964$	−3.31711e8	−	9.56759e8i	−0.370278	−	1.06800i
$965$	1.71918e8			0.191311
$966$	−7.22548e8	+	1.01525e9i	−0.801559	+	1.12627i
$967$			2.46456e8i			0.272558i	0.990670	+	0.136279i	$0.0435144\pi$
$967$			2.46456e8i			0.272558i	−0.990670	+	0.136279i	$0.956486\pi$
$968$	2.32636e8	−	7.94643e8i	0.256478	−	0.876084i
$969$	−8.43142e7			−0.0926680
$970$	−1.20636e8	−	8.58555e7i	−0.132178	−	0.0940704i
$971$		−	1.22112e8i		−	0.133383i	−0.997774	−	0.0666916i	$-0.978756\pi$
$971$		−	1.22112e8i		−	0.133383i	0.997774	−	0.0666916i	$-0.0212444\pi$
$972$	−8.89288e8	+	3.08318e8i	−0.968375	+	0.335738i
$973$	−1.02374e9			−1.11135
$974$	−1.37844e8	+	1.93684e8i	−0.149180	+	0.209613i
$975$			2.51139e8i			0.270957i
$976$	−2.46409e8	+	1.94205e8i	−0.265037	+	0.208887i
$977$	−4.70331e8			−0.504336			−0.252168	−	0.967683i	$-0.581144\pi$
$977$	−4.70331e8			−0.504336			−0.252168	+	0.967683i	$0.581144\pi$
$978$	−2.94833e8	−	2.09831e8i	−0.315181	−	0.224312i
$979$			2.81006e8i			0.299479i
$980$	−5.68525e7	−	1.63981e8i	−0.0604048	−	0.174227i
$981$	−2.75966e8			−0.292313
$982$	−7.08674e8	+	9.95756e8i	−0.748362	+	1.05152i
$983$		−	2.93341e8i		−	0.308825i	−0.988007	−	0.154412i	$-0.950652\pi$
$983$		−	2.93341e8i		−	0.308825i	0.988007	−	0.154412i	$-0.0493484\pi$
$984$	−1.01676e9	−	2.97660e8i	−1.06716	−	0.312418i
$985$	−3.33386e8			−0.348849
$986$	2.83088e8	+	2.01472e8i	0.295319	+	0.210177i
$987$		−	3.29419e7i		−	0.0342607i
$988$	−3.12457e8	+	1.08329e8i	−0.323981	+	0.112325i
$989$	1.89675e8			0.196075
$990$	−3.55474e7	+	4.99475e7i	−0.0366355	+	0.0514764i
$991$		−	1.85185e9i		−	1.90277i	−0.308010	−	0.951383i	$-0.599663\pi$
$991$		−	1.85185e9i		−	1.90277i	0.308010	−	0.951383i	$-0.400337\pi$
$992$	7.05628e7	+	1.44076e9i	0.0722837	+	1.47590i
$993$	−3.10714e8			−0.317332
$994$	4.71587e8	+	3.35626e8i	0.480179	+	0.341740i
$995$			1.88891e8i			0.191753i
$996$	−1.95163e8	−	5.62912e8i	−0.197524	−	0.569721i
$997$	6.20164e8			0.625779			0.312889	−	0.949790i	$-0.398703\pi$
$997$	6.20164e8			0.625779			0.312889	+	0.949790i	$0.398703\pi$
$998$	−5.07609e8	+	7.13241e8i	−0.510667	+	0.717537i
$999$		−	1.44315e9i		−	1.44749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	68.7.c.a.35.11	✓	48
4.3	odd	2	inner	68.7.c.a.35.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.7.c.a.35.11	✓	48	1.1	even	1	trivial
68.7.c.a.35.12	yes	48	4.3	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 68 = 2^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	68.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.51785 - 4.63871i) q^{2} +15.6750i q^{3} +(20.9647 + 60.4688i) q^{4} +40.3553 q^{5} +(72.7119 - 102.167i) q^{6} +429.939i q^{7} +(143.853 - 491.376i) q^{8} +483.294 q^{9} +O(q^{10})\)	\(q+(-6.51785 - 4.63871i) q^{2} +15.6750i q^{3} +(20.9647 + 60.4688i) q^{4} +40.3553 q^{5} +(72.7119 - 102.167i) q^{6} +429.939i q^{7} +(143.853 - 491.376i) q^{8} +483.294 q^{9} +(-263.030 - 187.196i) q^{10} -392.915i q^{11} +(-947.850 + 328.622i) q^{12} -1144.69 q^{13} +(1994.36 - 2802.28i) q^{14} +632.570i q^{15} +(-3216.96 + 2535.42i) q^{16} -1191.58 q^{17} +(-3150.04 - 2241.86i) q^{18} -4514.09i q^{19} +(846.036 + 2440.24i) q^{20} -6739.30 q^{21} +(-1822.62 + 2560.96i) q^{22} +23112.9i q^{23} +(7702.33 + 2254.90i) q^{24} -13996.5 q^{25} +(7460.91 + 5309.88i) q^{26} +19002.7i q^{27} +(-25997.9 + 9013.54i) q^{28} +36449.8 q^{29} +(2934.31 - 4122.99i) q^{30} +44021.2i q^{31} +(32728.8 - 1602.93i) q^{32} +6158.95 q^{33} +(7766.52 + 5527.39i) q^{34} +17350.3i q^{35} +(10132.1 + 29224.2i) q^{36} -75944.5 q^{37} +(-20939.6 + 29422.2i) q^{38} -17943.0i q^{39} +(5805.22 - 19829.6i) q^{40} -132006. q^{41} +(43925.8 + 31261.7i) q^{42} -8206.47i q^{43} +(23759.1 - 8237.34i) q^{44} +19503.4 q^{45} +(107214. - 150646. i) q^{46} +4888.02i q^{47} +(-39742.8 - 50426.0i) q^{48} -67198.7 q^{49} +(91226.8 + 64925.5i) q^{50} -18678.0i q^{51} +(-23998.1 - 69218.0i) q^{52} -103615. q^{53} +(88148.2 - 123857. i) q^{54} -15856.2i q^{55} +(211262. + 61848.0i) q^{56} +70758.5 q^{57} +(-237574. - 169080. i) q^{58} -177119. i q^{59} +(-38250.8 + 13261.6i) q^{60} +76596.8 q^{61} +(204201. - 286923. i) q^{62} +207787. i q^{63} +(-220757. - 141372. i) q^{64} -46194.2 q^{65} +(-40143.1 - 28569.6i) q^{66} +110199. i q^{67} +(-24981.1 - 72053.3i) q^{68} -362295. q^{69} +(80483.1 - 113087. i) q^{70} +168287. i q^{71} +(69523.2 - 237479. i) q^{72} +220591. q^{73} +(494995. + 352285. i) q^{74} -219395. i q^{75} +(272962. - 94636.6i) q^{76} +168929. q^{77} +(-83232.5 + 116950. i) q^{78} -39949.2i q^{79} +(-129821. + 102318. i) q^{80} +54453.0 q^{81} +(860397. + 612339. i) q^{82} +593883. i q^{83} +(-141287. - 407518. i) q^{84} -48086.4 q^{85} +(-38067.5 + 53488.5i) q^{86} +571352. i q^{87} +(-193069. - 56521.9i) q^{88} -715182. q^{89} +(-127121. - 90470.9i) q^{90} -492147. i q^{91} +(-1.39761e6 + 484555. i) q^{92} -690032. q^{93} +(22674.1 - 31859.4i) q^{94} -182167. i q^{95} +(25125.9 + 513024. i) q^{96} +458639. q^{97} +(437991. + 311715. i) q^{98} -189893. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 10 q^{2} + 90 q^{4} - 510 q^{6} + 1406 q^{8} - 11664 q^{9}+O(q^{10}) \) 48 * q - 10 * q^2 + 90 * q^4 - 510 * q^6 + 1406 * q^8 - 11664 * q^9	\( 48 q - 10 q^{2} + 90 q^{4} - 510 q^{6} + 1406 q^{8} - 11664 q^{9} - 1710 q^{10} - 6234 q^{12} - 5040 q^{13} + 9040 q^{14} - 1230 q^{16} - 6974 q^{18} + 1046 q^{20} - 35488 q^{21} - 13254 q^{22} + 22838 q^{24} + 173856 q^{25} + 44744 q^{26} + 42864 q^{28} - 83536 q^{29} - 95104 q^{30} - 53050 q^{32} + 9072 q^{33} + 24174 q^{36} + 62640 q^{37} + 399840 q^{38} - 58218 q^{40} + 70448 q^{41} - 90520 q^{42} - 356746 q^{44} - 103808 q^{45} - 177084 q^{46} + 808886 q^{48} - 758880 q^{49} - 560506 q^{50} - 85800 q^{52} + 744784 q^{53} - 263596 q^{54} - 701896 q^{56} - 125008 q^{57} - 351534 q^{58} - 64960 q^{60} + 196560 q^{61} + 1428016 q^{62} - 60246 q^{64} - 708656 q^{65} + 1089052 q^{66} + 428496 q^{69} - 1132824 q^{70} - 1043230 q^{72} - 454272 q^{73} - 1135082 q^{74} + 850224 q^{76} - 549200 q^{77} + 703076 q^{78} + 1608910 q^{80} + 3871872 q^{81} - 328536 q^{82} + 2825208 q^{84} + 3243644 q^{86} + 691398 q^{88} - 1729776 q^{89} + 214114 q^{90} + 1469284 q^{92} - 6618704 q^{93} - 551136 q^{94} - 5148618 q^{96} + 4548720 q^{97} - 2942042 q^{98}+O(q^{100}) \) 48 * q - 10 * q^2 + 90 * q^4 - 510 * q^6 + 1406 * q^8 - 11664 * q^9 - 1710 * q^10 - 6234 * q^12 - 5040 * q^13 + 9040 * q^14 - 1230 * q^16 - 6974 * q^18 + 1046 * q^20 - 35488 * q^21 - 13254 * q^22 + 22838 * q^24 + 173856 * q^25 + 44744 * q^26 + 42864 * q^28 - 83536 * q^29 - 95104 * q^30 - 53050 * q^32 + 9072 * q^33 + 24174 * q^36 + 62640 * q^37 + 399840 * q^38 - 58218 * q^40 + 70448 * q^41 - 90520 * q^42 - 356746 * q^44 - 103808 * q^45 - 177084 * q^46 + 808886 * q^48 - 758880 * q^49 - 560506 * q^50 - 85800 * q^52 + 744784 * q^53 - 263596 * q^54 - 701896 * q^56 - 125008 * q^57 - 351534 * q^58 - 64960 * q^60 + 196560 * q^61 + 1428016 * q^62 - 60246 * q^64 - 708656 * q^65 + 1089052 * q^66 + 428496 * q^69 - 1132824 * q^70 - 1043230 * q^72 - 454272 * q^73 - 1135082 * q^74 + 850224 * q^76 - 549200 * q^77 + 703076 * q^78 + 1608910 * q^80 + 3871872 * q^81 - 328536 * q^82 + 2825208 * q^84 + 3243644 * q^86 + 691398 * q^88 - 1729776 * q^89 + 214114 * q^90 + 1469284 * q^92 - 6618704 * q^93 - 551136 * q^94 - 5148618 * q^96 + 4548720 * q^97 - 2942042 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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