LMFDB - Embedded newform 76.8.d.a.75.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,8,Mod(75,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("76.75");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	76.d (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:	$23.7412619368$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.3
Character	$\chi$	$=$	76.75
Dual form			76.8.d.a.75.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.1927 - 1.65015i) q^{2} -65.7104 q^{3} +(122.554 + 36.9394i) q^{4} -95.9690 q^{5} +(735.478 + 108.432i) q^{6} +851.669i q^{7} +(-1310.76 - 615.686i) q^{8} +2130.86 q^{9} +O(q^{10})$	\(q+(-11.1927 - 1.65015i) q^{2} -65.7104 q^{3} +(122.554 + 36.9394i) q^{4} -95.9690 q^{5} +(735.478 + 108.432i) q^{6} +851.669i q^{7} +(-1310.76 - 615.686i) q^{8} +2130.86 q^{9} +(1074.15 + 158.364i) q^{10} -2279.40i q^{11} +(-8053.07 - 2427.30i) q^{12} -12626.0i q^{13} +(1405.38 - 9532.49i) q^{14} +6306.16 q^{15} +(13655.0 + 9054.15i) q^{16} +23515.2 q^{17} +(-23850.1 - 3516.24i) q^{18} +(-15823.4 - 25367.2i) q^{19} +(-11761.4 - 3545.04i) q^{20} -55963.5i q^{21} +(-3761.36 + 25512.7i) q^{22} -37267.2i q^{23} +(86130.4 + 40457.0i) q^{24} -68915.0 q^{25} +(-20834.9 + 141319. i) q^{26} +3689.15 q^{27} +(-31460.2 + 104375. i) q^{28} +262235. i q^{29} +(-70583.1 - 10406.1i) q^{30} +67159.0 q^{31} +(-137895. - 123873. i) q^{32} +149780. i q^{33} +(-263199. - 38803.7i) q^{34} -81733.8i q^{35} +(261145. + 78712.7i) q^{36} -295883. i q^{37} +(135247. + 310039. i) q^{38} +829660. i q^{39} +(125792. + 59086.7i) q^{40} +438259. i q^{41} +(-92348.4 + 626384. i) q^{42} -230063. i q^{43} +(84199.8 - 279350. i) q^{44} -204496. q^{45} +(-61496.6 + 417121. i) q^{46} +712136. i q^{47} +(-897273. - 594952. i) q^{48} +98203.2 q^{49} +(771346. + 113720. i) q^{50} -1.54519e6 q^{51} +(466397. - 1.54737e6i) q^{52} +154721. i q^{53} +(-41291.7 - 6087.67i) q^{54} +218752. i q^{55} +(524360. - 1.11633e6i) q^{56} +(1.03976e6 + 1.66689e6i) q^{57} +(432728. - 2.93512e6i) q^{58} +707384. q^{59} +(772845. + 232946. i) q^{60} -3.10918e6 q^{61} +(-751692. - 110823. i) q^{62} +1.81478e6i q^{63} +(1.33901e6 + 1.61403e6i) q^{64} +1.21170e6i q^{65} +(247161. - 1.67645e6i) q^{66} -155450. q^{67} +(2.88188e6 + 868638. i) q^{68} +2.44884e6i q^{69} +(-134873. + 914823. i) q^{70} -3.51389e6 q^{71} +(-2.79304e6 - 1.31194e6i) q^{72} -933723. q^{73} +(-488253. + 3.31174e6i) q^{74} +4.52843e6 q^{75} +(-1.00217e6 - 3.69335e6i) q^{76} +1.94130e6 q^{77} +(1.36907e6 - 9.28615e6i) q^{78} +4.27796e6 q^{79} +(-1.31045e6 - 868917. i) q^{80} -4.90260e6 q^{81} +(723194. - 4.90531e6i) q^{82} -3.72571e6i q^{83} +(2.06726e6 - 6.85855e6i) q^{84} -2.25673e6 q^{85} +(-379639. + 2.57503e6i) q^{86} -1.72315e7i q^{87} +(-1.40340e6 + 2.98774e6i) q^{88} +3.99893e6i q^{89} +(2.28887e6 + 337450. i) q^{90} +1.07532e7 q^{91} +(1.37663e6 - 4.56724e6i) q^{92} -4.41304e6 q^{93} +(1.17513e6 - 7.97074e6i) q^{94} +(1.51855e6 + 2.43446e6i) q^{95} +(9.06116e6 + 8.13977e6i) q^{96} +5.49101e6i q^{97} +(-1.09916e6 - 162050. i) q^{98} -4.85708e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9}+O(q^{10}) $ 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9	$ 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9} + 13050 q^{16} + 23968 q^{17} - 79660 q^{20} - 232154 q^{24} + 937496 q^{25} - 391242 q^{26} - 37666 q^{28} - 468496 q^{30} - 1128652 q^{36} - 530466 q^{38} + 651806 q^{42} + 1433776 q^{44} - 321252 q^{45} - 4014380 q^{49} + 1697586 q^{54} + 137420 q^{57} + 2227894 q^{58} - 3042164 q^{61} + 2261524 q^{62} + 9825150 q^{64} - 749476 q^{66} - 11176962 q^{68} + 598424 q^{73} - 6195964 q^{74} - 1714536 q^{76} - 2556764 q^{77} + 16623216 q^{80} + 43726748 q^{81} - 20460388 q^{82} + 27222844 q^{85} - 61733582 q^{92} + 17778200 q^{93} - 36370886 q^{96}+O(q^{100}) $ 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9 + 13050 * q^16 + 23968 * q^17 - 79660 * q^20 - 232154 * q^24 + 937496 * q^25 - 391242 * q^26 - 37666 * q^28 - 468496 * q^30 - 1128652 * q^36 - 530466 * q^38 + 651806 * q^42 + 1433776 * q^44 - 321252 * q^45 - 4014380 * q^49 + 1697586 * q^54 + 137420 * q^57 + 2227894 * q^58 - 3042164 * q^61 + 2261524 * q^62 + 9825150 * q^64 - 749476 * q^66 - 11176962 * q^68 + 598424 * q^73 - 6195964 * q^74 - 1714536 * q^76 - 2556764 * q^77 + 16623216 * q^80 + 43726748 * q^81 - 20460388 * q^82 + 27222844 * q^85 - 61733582 * q^92 + 17778200 * q^93 - 36370886 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−11.1927	−	1.65015i	−0.989306	−	0.145854i
$2$	−11.1927	−	1.65015i	−0.989306	−	0.145854i
$3$	−65.7104			−1.40511			−0.702554	−	0.711630i	$-0.747957\pi$
$3$	−65.7104			−1.40511			−0.702554	+	0.711630i	$0.747957\pi$
$4$	122.554	+	36.9394i	0.957453	+	0.288589i
$5$	−95.9690			−0.343349			−0.171675	−	0.985154i	$-0.554918\pi$
$5$	−95.9690			−0.343349			−0.171675	+	0.985154i	$0.554918\pi$
$6$	735.478	+	108.432i	1.39008	+	0.204941i
$7$			851.669i			0.938486i	0.883069	+	0.469243i	$0.155473\pi$
$7$			851.669i			0.938486i	−0.883069	+	0.469243i	$0.844527\pi$
$8$	−1310.76	−	615.686i	−0.905122	−	0.425152i
$9$	2130.86			0.974329
$10$	1074.15	+	158.364i	0.339677	+	0.0500790i
$11$		−	2279.40i		−	0.516353i	−0.966098	−	0.258176i	$-0.916878\pi$
$11$		−	2279.40i		−	0.516353i	0.966098	−	0.258176i	$-0.0831216\pi$
$12$	−8053.07	−	2427.30i	−1.34533	−	0.405499i
$13$		−	12626.0i		−	1.59391i	−0.604038	−	0.796956i	$-0.706442\pi$
$13$		−	12626.0i		−	1.59391i	0.604038	−	0.796956i	$-0.293558\pi$
$14$	1405.38	−	9532.49i	0.136882	−	0.928450i
$15$	6306.16			0.482443
$16$	13655.0	+	9054.15i	0.833432	+	0.552621i
$17$	23515.2			1.16085			0.580427	−	0.814312i	$-0.302886\pi$
$17$	23515.2			1.16085			0.580427	+	0.814312i	$0.302886\pi$
$18$	−23850.1	−	3516.24i	−0.963910	−	0.142110i
$19$	−15823.4	−	25367.2i	−0.529251	−	0.848466i
$19$	−15823.4	−	25367.2i	−0.529251	−	0.848466i
$20$	−11761.4	−	3545.04i	−0.328741	−	0.0990869i
$21$		−	55963.5i		−	1.31867i
$22$	−3761.36	+	25512.7i	−0.0753123	+	0.510831i
$23$		−	37267.2i		−	0.638673i	−0.947641	−	0.319337i	$-0.896540\pi$
$23$		−	37267.2i		−	0.638673i	0.947641	−	0.319337i	$-0.103460\pi$
$24$	86130.4	+	40457.0i	1.27179	+	0.597384i
$25$	−68915.0			−0.882111
$26$	−20834.9	+	141319.i	−0.232479	+	1.57687i
$27$	3689.15			0.0360706
$28$	−31460.2	+	104375.i	−0.270837	+	0.898556i
$29$			262235.i			1.99663i	0.0580455	+	0.998314i	$0.481513\pi$
$29$			262235.i			1.99663i	−0.0580455	+	0.998314i	$0.518487\pi$
$30$	−70583.1	−	10406.1i	−0.477283	−	0.0703664i
$31$	67159.0			0.404891			0.202445	−	0.979294i	$-0.435111\pi$
$31$	67159.0			0.404891			0.202445	+	0.979294i	$0.435111\pi$
$32$	−137895.	−	123873.i	−0.743918	−	0.668271i
$33$			149780.i			0.725532i
$34$	−263199.	−	38803.7i	−1.14844	−	0.169316i
$35$		−	81733.8i		−	0.322228i
$36$	261145.	+	78712.7i	0.932874	+	0.281181i
$37$		−	295883.i		−	0.960317i	−0.877182	−	0.480159i	$-0.840579\pi$
$37$		−	295883.i		−	0.960317i	0.877182	−	0.480159i	$-0.159421\pi$
$38$	135247.	+	310039.i	0.399838	+	0.916586i
$39$			829660.i			2.23962i
$40$	125792.	+	59086.7i	0.310773	+	0.145975i
$41$			438259.i			0.993086i	0.868012	+	0.496543i	$0.165398\pi$
$41$			438259.i			0.993086i	−0.868012	+	0.496543i	$0.834602\pi$
$42$	−92348.4	+	626384.i	−0.192334	+	1.30457i
$43$		−	230063.i		−	0.441272i	−0.975356	−	0.220636i	$-0.929187\pi$
$43$		−	230063.i		−	0.441272i	0.975356	−	0.220636i	$-0.0708133\pi$
$44$	84199.8	−	279350.i	0.149014	−	0.494384i
$45$	−204496.			−0.334535
$46$	−61496.6	+	417121.i	−0.0931533	+	0.631844i
$47$			712136.i			1.00051i	0.865879	+	0.500254i	$0.166760\pi$
$47$			712136.i			1.00051i	−0.865879	+	0.500254i	$0.833240\pi$
$48$	−897273.	−	594952.i	−1.17106	−	0.776493i
$49$	98203.2			0.119245
$50$	771346.	+	113720.i	0.872678	+	0.128660i
$51$	−1.54519e6			−1.63113
$52$	466397.	−	1.54737e6i	0.459986	−	1.52610i
$53$			154721.i			0.142753i	0.997449	+	0.0713763i	$0.0227391\pi$
$53$			154721.i			0.142753i	−0.997449	+	0.0713763i	$0.977261\pi$
$54$	−41291.7	−	6087.67i	−0.0356849	−	0.00526106i
$55$			218752.i			0.177289i
$56$	524360.	−	1.11633e6i	0.398999	−	0.849444i
$57$	1.03976e6	+	1.66689e6i	0.743654	+	1.19219i
$58$	432728.	−	2.93512e6i	0.291217	−	1.97528i
$59$	707384.			0.448408			0.224204	−	0.974542i	$-0.428022\pi$
$59$	707384.			0.448408			0.224204	+	0.974542i	$0.428022\pi$
$60$	772845.	+	232946.i	0.461916	+	0.139228i
$61$	−3.10918e6			−1.75385			−0.876923	−	0.480630i	$-0.840408\pi$
$61$	−3.10918e6			−1.75385			−0.876923	+	0.480630i	$0.840408\pi$
$62$	−751692.	−	110823.i	−0.400561	−	0.0590551i
$63$			1.81478e6i			0.914394i
$64$	1.33901e6	+	1.61403e6i	0.638492	+	0.769629i
$65$			1.21170e6i			0.547268i
$66$	247161.	−	1.67645e6i	0.105822	−	0.717773i
$67$	−155450.			−0.0631436			−0.0315718	−	0.999501i	$-0.510051\pi$
$67$	−155450.			−0.0631436			−0.0315718	+	0.999501i	$0.510051\pi$
$68$	2.88188e6	+	868638.i	1.11146	+	0.335010i
$69$			2.44884e6i			0.897405i
$70$	−134873.	+	914823.i	−0.0469984	+	0.318782i
$71$	−3.51389e6			−1.16516			−0.582578	−	0.812775i	$-0.697956\pi$
$71$	−3.51389e6			−1.16516			−0.582578	+	0.812775i	$0.697956\pi$
$72$	−2.79304e6	−	1.31194e6i	−0.881887	−	0.414238i
$73$	−933723.			−0.280924			−0.140462	−	0.990086i	$-0.544859\pi$
$73$	−933723.			−0.280924			−0.140462	+	0.990086i	$0.544859\pi$
$74$	−488253.	+	3.31174e6i	−0.140066	+	0.950048i
$75$	4.52843e6			1.23946
$76$	−1.00217e6	−	3.69335e6i	−0.261874	−	0.965102i
$77$	1.94130e6			0.484590
$78$	1.36907e6	−	9.28615e6i	0.326658	−	2.21567i
$79$	4.27796e6			0.976207			0.488103	−	0.872786i	$-0.337689\pi$
$79$	4.27796e6			0.976207			0.488103	+	0.872786i	$0.337689\pi$
$80$	−1.31045e6	−	868917.i	−0.286158	−	0.189742i
$81$	−4.90260e6			−1.02501
$82$	723194.	−	4.90531e6i	0.144846	−	0.982466i
$83$		−	3.72571e6i		−	0.715214i	−0.933872	−	0.357607i	$-0.883593\pi$
$83$		−	3.72571e6i		−	0.715214i	0.933872	−	0.357607i	$-0.116407\pi$
$84$	2.06726e6	−	6.85855e6i	0.380555	−	1.26257i
$85$	−2.25673e6			−0.398578
$86$	−379639.	+	2.57503e6i	−0.0643615	+	0.436553i
$87$		−	1.72315e7i		−	2.80548i
$88$	−1.40340e6	+	2.98774e6i	−0.219528	+	0.467362i
$89$			3.99893e6i			0.601282i	0.953737	+	0.300641i	$0.0972006\pi$
$89$			3.99893e6i			0.601282i	−0.953737	+	0.300641i	$0.902799\pi$
$90$	2.28887e6	+	337450.i	0.330957	+	0.0487934i
$91$	1.07532e7			1.49586
$92$	1.37663e6	−	4.56724e6i	0.184314	−	0.611500i
$93$	−4.41304e6			−0.568916
$94$	1.17513e6	−	7.97074e6i	0.145928	−	0.989808i
$95$	1.51855e6	+	2.43446e6i	0.181718	+	0.291320i
$96$	9.06116e6	+	8.13977e6i	1.04528	+	0.938994i
$97$			5.49101e6i			0.610873i	0.952212	+	0.305437i	$0.0988024\pi$
$97$			5.49101e6i			0.610873i	−0.952212	+	0.305437i	$0.901198\pi$
$98$	−1.09916e6	−	162050.i	−0.117970	−	0.0173924i
$99$		−	4.85708e6i		−	0.503097i
$100$	−8.44580e6	−	2.54568e6i	−0.844580	−	0.254568i
$101$	−1.16288e7			−1.12308			−0.561539	−	0.827450i	$-0.689791\pi$
$101$	−1.16288e7			−1.12308			−0.561539	+	0.827450i	$0.689791\pi$
$102$	1.72949e7	+	2.54981e6i	1.61368	+	0.237907i
$103$	1.03356e6			0.0931977			0.0465989	−	0.998914i	$-0.485162\pi$
$103$	1.03356e6			0.0931977			0.0465989	+	0.998914i	$0.485162\pi$
$104$	−7.77365e6	+	1.65496e7i	−0.677654	+	1.44268i
$105$			5.37076e6i			0.452765i
$106$	255314.	−	1.73175e6i	0.0208211	−	0.141226i
$107$	−9.71657e6			−0.766779			−0.383389	−	0.923587i	$-0.625243\pi$
$107$	−9.71657e6			−0.766779			−0.383389	+	0.923587i	$0.625243\pi$
$108$	452120.	+	136275.i	0.0345359	+	0.0104096i
$109$			1.69381e7i			1.25277i	0.779513	+	0.626386i	$0.215466\pi$
$109$			1.69381e7i			1.25277i	−0.779513	+	0.626386i	$0.784534\pi$
$110$	360974.	−	2.44843e6i	0.0258584	−	0.175393i
$111$			1.94426e7i			1.34935i
$112$	−7.71114e6	+	1.16295e7i	−0.518627	+	0.782164i
$113$			1.04311e7i			0.680071i	0.940413	+	0.340035i	$0.110439\pi$
$113$			1.04311e7i			0.680071i	−0.940413	+	0.340035i	$0.889561\pi$
$114$	−8.88712e6	−	2.03728e7i	−0.561816	−	1.28790i
$115$			3.57649e6i			0.219288i
$116$	−9.68680e6	+	3.21379e7i	−0.576205	+	1.91168i
$117$		−	2.69042e7i		−	1.55299i
$118$	−7.91755e6	−	1.16729e6i	−0.443612	−	0.0654022i
$119$			2.00272e7i			1.08944i
$120$	−8.26584e6	−	3.88261e6i	−0.436669	−	0.205111i
$121$	1.42915e7			0.733380
$122$	3.48002e7	+	5.13063e6i	1.73509	+	0.255806i
$123$		−	2.87982e7i		−	1.39539i
$124$	8.23060e6	+	2.48081e6i	0.387664	+	0.116847i
$125$	1.41113e7			0.646221
$126$	2.99467e6	−	2.03124e7i	0.133368	−	0.904615i
$127$	−1.49746e7			−0.648699			−0.324349	−	0.945937i	$-0.605145\pi$
$127$	−1.49746e7			−0.648699			−0.324349	+	0.945937i	$0.605145\pi$
$128$	−1.23238e7	−	2.02749e7i	−0.519410	−	0.854525i
$129$			1.51175e7i			0.620035i
$130$	1.99950e6	−	1.35623e7i	0.0798214	−	0.541416i
$131$			4.01857e7i			1.56179i	0.624664	+	0.780893i	$0.285236\pi$
$131$			4.01857e7i			1.56179i	−0.624664	+	0.780893i	$0.714764\pi$
$132$	−5.53280e6	+	1.83562e7i	−0.209381	+	0.694662i
$133$	2.16044e7	−	1.34763e7i	0.796273	−	0.496694i
$134$	1.73991e6	+	256517.i	0.0624683	+	0.00920977i
$135$	−354044.			−0.0123848
$136$	−3.08227e7	−	1.44780e7i	−1.05071	−	0.493539i
$137$	−4.32227e7			−1.43612			−0.718059	−	0.695982i	$-0.754969\pi$
$137$	−4.32227e7			−1.43612			−0.718059	+	0.695982i	$0.754969\pi$
$138$	4.04096e6	−	2.74092e7i	0.130891	−	0.887809i
$139$			3.49442e7i			1.10363i	0.833967	+	0.551815i	$0.186064\pi$
$139$			3.49442e7i			1.10363i	−0.833967	+	0.551815i	$0.813936\pi$
$140$	3.01920e6	−	1.00168e7i	0.0929916	−	0.308518i
$141$		−	4.67947e7i		−	1.40582i
$142$	3.93300e7	+	5.79846e6i	1.15270	+	0.169943i
$143$	−2.87797e7			−0.823021
$144$	2.90968e7	+	1.92931e7i	0.812037	+	0.538435i
$145$		−	2.51664e7i		−	0.685540i
$146$	1.04509e7	+	1.54079e6i	0.277919	+	0.0409739i
$147$	−6.45297e6			−0.167552
$148$	1.09298e7	−	3.62617e7i	0.277137	−	0.919459i
$149$	3.06096e7			0.758063			0.379032	−	0.925384i	$-0.376257\pi$
$149$	3.06096e7			0.758063			0.379032	+	0.925384i	$0.376257\pi$
$150$	−5.06854e7	−	7.47261e6i	−1.22621	−	0.180781i
$151$	−6.53382e7			−1.54436			−0.772178	−	0.635406i	$-0.780833\pi$
$151$	−6.53382e7			−1.54436			−0.772178	+	0.635406i	$0.780833\pi$
$152$	5.12239e6	+	4.29924e7i	0.118310	+	0.992977i
$153$	5.01075e7			1.13105
$154$	−2.17284e7	−	3.20344e6i	−0.479408	−	0.0706795i
$155$	−6.44518e6			−0.139019
$156$	−3.06472e7	+	1.01678e8i	−0.646330	+	2.14433i
$157$	5.69477e7			1.17443			0.587216	−	0.809431i	$-0.300224\pi$
$157$	5.69477e7			1.17443			0.587216	+	0.809431i	$0.300224\pi$
$158$	−4.78820e7	−	7.05929e6i	−0.965767	−	0.142384i
$159$		−	1.01668e7i		−	0.200583i
$160$	1.32337e7	+	1.18880e7i	0.255423	+	0.229450i
$161$	3.17393e7			0.599386
$162$	5.48734e7	+	8.09005e6i	1.01405	+	0.149503i
$163$			3.31661e6i			0.0599843i	0.999550	+	0.0299921i	$0.00954822\pi$
$163$			3.31661e6i			0.0599843i	−0.999550	+	0.0299921i	$0.990452\pi$
$164$	−1.61890e7	+	5.37103e7i	−0.286594	+	0.950833i
$165$		−	1.43743e7i		−	0.249111i
$166$	−6.14800e6	+	4.17009e7i	−0.104317	+	0.707566i
$167$	1.02027e8			1.69515			0.847574	−	0.530677i	$-0.178062\pi$
$167$	1.02027e8			1.69515			0.847574	+	0.530677i	$0.178062\pi$
$168$	−3.44559e7	+	7.33545e7i	−0.560637	+	1.19356i
$169$	−9.66675e7			−1.54055
$170$	2.52589e7	+	3.72395e6i	0.394316	+	0.0581344i
$171$	−3.37173e7	−	5.40538e7i	−0.515664	−	0.826685i
$172$	8.49839e6	−	2.81951e7i	0.127346	−	0.422498i
$173$			4.55355e6i			0.0668634i	0.999441	+	0.0334317i	$0.0106436\pi$
$173$			4.55355e6i			0.0668634i	−0.999441	+	0.0334317i	$0.989356\pi$
$174$	−2.84347e7	+	1.92868e8i	−0.409191	+	2.77548i
$175$		−	5.86927e7i		−	0.827849i
$176$	2.06380e7	−	3.11251e7i	0.285348	−	0.430345i
$177$	−4.64825e7			−0.630061
$178$	6.59884e6	−	4.47589e7i	0.0876997	−	0.594852i
$179$	3.41444e7			0.444974			0.222487	−	0.974936i	$-0.428583\pi$
$179$	3.41444e7			0.444974			0.222487	+	0.974936i	$0.428583\pi$
$180$	−2.50618e7	−	7.55397e6i	−0.320301	−	0.0965432i
$181$		−	1.15782e8i		−	1.45133i	−0.688047	−	0.725666i	$-0.741532\pi$
$181$		−	1.15782e8i		−	1.45133i	0.688047	−	0.725666i	$-0.258468\pi$
$182$	−1.20357e8	−	1.77444e7i	−1.47987	−	0.218178i
$183$	2.04306e8			2.46434
$184$	−2.29449e7	+	4.88482e7i	−0.271533	+	0.578077i
$185$			2.83956e7i			0.329724i
$186$	4.93940e7	+	7.28220e6i	0.562832	+	0.0829789i
$187$		−	5.36006e7i		−	0.599410i
$188$	−2.63059e7	+	8.72751e7i	−0.288736	+	0.957939i
$189$			3.14194e6i			0.0338518i
$190$	−1.29795e7	−	2.97541e7i	−0.137284	−	0.314709i
$191$		−	7.47997e7i		−	0.776754i	−0.921501	−	0.388377i	$-0.873036\pi$
$191$		−	7.47997e7i		−	0.776754i	0.921501	−	0.388377i	$-0.126964\pi$
$192$	−8.79872e7	−	1.06058e8i	−0.897150	−	1.08141i
$193$		−	3.87375e7i		−	0.387865i	−0.981015	−	0.193933i	$-0.937876\pi$
$193$		−	3.87375e7i		−	0.387865i	0.981015	−	0.193933i	$-0.0621243\pi$
$194$	9.06101e6	−	6.14593e7i	0.0890985	−	0.604340i
$195$		−	7.96216e7i		−	0.768971i
$196$	1.20352e7	+	3.62757e6i	0.114171	+	0.0344128i
$197$	4.01567e7			0.374219			0.187110	−	0.982339i	$-0.440088\pi$
$197$	4.01567e7			0.374219			0.187110	+	0.982339i	$0.440088\pi$
$198$	−8.01493e6	+	5.43639e7i	−0.0733790	+	0.497717i
$199$			1.08568e8i			0.976596i	0.872677	+	0.488298i	$0.162382\pi$
$199$			1.08568e8i			0.976596i	−0.872677	+	0.488298i	$0.837618\pi$
$200$	9.03307e7	+	4.24300e7i	0.798419	+	0.375031i
$201$	1.02147e7			0.0887235
$202$	1.30158e8	+	1.91893e7i	1.11107	+	0.163806i
$203$	−2.23337e8			−1.87381
$204$	−1.89370e8	−	5.70786e7i	−1.56173	−	0.470725i
$205$		−	4.20592e7i		−	0.340975i
$206$	−1.15683e7	−	1.70553e6i	−0.0922011	−	0.0135933i
$207$		−	7.94110e7i		−	0.622278i
$208$	1.14318e8	−	1.72408e8i	0.880830	−	1.32842i
$209$	−5.78220e7	+	3.60678e7i	−0.438108	+	0.273280i
$210$	8.86258e6	−	6.01134e7i	0.0660378	−	0.447924i
$211$	1.61640e8			1.18457			0.592283	−	0.805730i	$-0.298227\pi$
$211$	1.61640e8			1.18457			0.592283	+	0.805730i	$0.298227\pi$
$212$	−5.71531e6	+	1.89617e7i	−0.0411969	+	0.136679i
$213$	2.30899e8			1.63717
$214$	1.08755e8	+	1.60338e7i	0.758579	+	0.111838i
$215$			2.20789e7i			0.151510i
$216$	−4.83558e6	−	2.27136e6i	−0.0326483	−	0.0153355i
$217$			5.71972e7i			0.379984i
$218$	2.79505e7	−	1.89583e8i	0.182722	−	1.23937i
$219$	6.13553e7			0.394728
$220$	−8.08057e6	+	2.68089e7i	−0.0511638	+	0.169746i
$221$		−	2.96903e8i		−	1.85030i
$222$	3.20833e7	−	2.17616e8i	0.196809	−	1.33492i
$223$	−3.08329e8			−1.86186			−0.930931	−	0.365196i	$-0.881002\pi$
$223$	−3.08329e8			−1.86186			−0.930931	+	0.365196i	$0.881002\pi$
$224$	1.05499e8	−	1.17441e8i	0.627163	−	0.698156i
$225$	−1.46848e8			−0.859467
$226$	1.72129e7	−	1.16752e8i	0.0991913	−	0.672798i
$227$	−3.74342e7			−0.212412			−0.106206	−	0.994344i	$-0.533870\pi$
$227$	−3.74342e7			−0.212412			−0.106206	+	0.994344i	$0.533870\pi$
$228$	6.58529e7	+	2.42692e8i	0.367962	+	1.35607i
$229$	1.46709e8			0.807294			0.403647	−	0.914915i	$-0.367742\pi$
$229$	1.46709e8			0.807294			0.403647	+	0.914915i	$0.367742\pi$
$230$	5.90176e6	−	4.00307e7i	0.0319841	−	0.216943i
$231$	−1.27563e8			−0.680901
$232$	1.61454e8	−	3.43726e8i	0.848870	−	1.80719i
$233$	8.76843e7			0.454126			0.227063	−	0.973880i	$-0.427088\pi$
$233$	8.76843e7			0.454126			0.227063	+	0.973880i	$0.427088\pi$
$234$	−4.43961e7	+	3.01131e8i	−0.226511	+	1.53639i
$235$		−	6.83429e7i		−	0.343523i
$236$	8.66927e7	+	2.61304e7i	0.429329	+	0.129406i
$237$	−2.81106e8			−1.37168
$238$	3.30479e7	−	2.24158e8i	0.158900	−	1.07779i
$239$			2.63970e8i			1.25072i	0.780334	+	0.625362i	$0.215049\pi$
$239$			2.63970e8i			1.25072i	−0.780334	+	0.625362i	$0.784951\pi$
$240$	8.61103e7	+	5.70969e7i	0.402083	+	0.266608i
$241$			1.44649e8i			0.665667i	0.942986	+	0.332834i	$0.108005\pi$
$241$			1.44649e8i			0.665667i	−0.942986	+	0.332834i	$0.891995\pi$
$242$	−1.59961e8	−	2.35832e7i	−0.725537	−	0.106967i
$243$	3.14084e8			1.40418
$244$	−3.81043e8	−	1.14851e8i	−1.67923	−	0.506141i
$245$	−9.42446e6			−0.0409426
$246$	−4.75214e7	+	3.22330e8i	−0.203524	+	1.38047i
$247$	−3.20286e8	+	1.99786e8i	−1.35238	+	0.843579i
$248$	−8.80291e7	−	4.13488e7i	−0.366476	−	0.172140i
$249$			2.44818e8i			1.00495i
$250$	−1.57944e8	−	2.32858e7i	−0.639310	−	0.0942542i
$251$			4.87124e8i			1.94438i	0.234193	+	0.972190i	$0.424755\pi$
$251$			4.87124e8i			1.94438i	−0.234193	+	0.972190i	$0.575245\pi$
$252$	−6.70371e7	+	2.22409e8i	−0.263884	+	0.875489i
$253$	−8.49468e7			−0.329781
$254$	1.67607e8	+	2.47104e7i	0.641762	+	0.0946156i
$255$	1.48291e8			0.560045
$256$	1.04480e8	+	2.47268e8i	0.389219	+	0.921145i
$257$			4.07775e8i			1.49849i	0.662291	+	0.749247i	$0.269584\pi$
$257$			4.07775e8i			1.49849i	−0.662291	+	0.749247i	$0.730416\pi$
$258$	2.49462e7	−	1.69206e8i	0.0904349	−	0.613405i
$259$	2.51995e8			0.901244
$260$	−4.47597e7	+	1.48499e8i	−0.157936	+	0.523983i
$261$			5.58785e8i			1.94537i
$262$	6.63126e7	−	4.49787e8i	0.227794	−	1.54509i
$263$			1.84282e8i			0.624650i	0.949975	+	0.312325i	$0.101108\pi$
$263$			1.84282e8i			0.624650i	−0.949975	+	0.312325i	$0.898892\pi$
$264$	9.22177e7	−	1.96326e8i	0.308461	−	0.656695i
$265$		−	1.48484e7i		−	0.0490139i
$266$	−2.64050e8	+	1.15186e8i	−0.860202	+	0.375243i
$267$		−	2.62771e8i		−	0.844867i
$268$	−1.90510e7	−	5.74224e6i	−0.0604570	−	0.0182226i
$269$			1.19232e7i			0.0373474i	0.999826	+	0.0186737i	$0.00594436\pi$
$269$			1.19232e7i			0.0373474i	−0.999826	+	0.0186737i	$0.994056\pi$
$270$	3.96272e6	+	584228.i	0.0122524	+	0.00180638i
$271$		−	4.62328e8i		−	1.41110i	−0.708661	−	0.705549i	$-0.750700\pi$
$271$		−	4.62328e8i		−	1.41110i	0.708661	−	0.705549i	$-0.249300\pi$
$272$	3.21099e8	+	2.12910e8i	0.967493	+	0.641513i
$273$	−7.06596e8			−2.10185
$274$	4.83780e8	+	7.13242e7i	1.42076	+	0.209464i
$275$			1.57085e8i			0.455481i
$276$	−9.04588e7	+	3.00115e8i	−0.258982	+	0.859223i
$277$	1.26408e8			0.357350			0.178675	−	0.983908i	$-0.442819\pi$
$277$	1.26408e8			0.357350			0.178675	+	0.983908i	$0.442819\pi$
$278$	5.76633e7	−	3.91121e8i	0.160969	−	1.09183i
$279$	1.43106e8			0.394497
$280$	−5.03223e7	+	1.07133e8i	−0.136996	+	0.291656i
$281$			3.46415e8i			0.931374i	0.884950	+	0.465687i	$0.154193\pi$
$281$			3.46415e8i			0.931374i	−0.884950	+	0.465687i	$0.845807\pi$
$282$	−7.72185e7	+	5.23760e8i	−0.205045	+	1.39079i
$283$			4.43927e7i			0.116428i	0.998304	+	0.0582142i	$0.0185406\pi$
$283$			4.43927e7i			0.116428i	−0.998304	+	0.0582142i	$0.981459\pi$
$284$	−4.30642e8	−	1.29801e8i	−1.11558	−	0.336252i
$285$	−9.97847e7	−	1.59969e8i	−0.255333	−	0.409336i
$286$	3.22124e8	+	4.74910e7i	0.814219	+	0.120041i
$287$	−3.73251e8			−0.931997
$288$	−2.93835e8	−	2.63956e8i	−0.724820	−	0.651116i
$289$	1.42626e8			0.347581
$290$	−4.15284e7	+	2.81680e8i	−0.0999891	+	0.678209i
$291$		−	3.60816e8i		−	0.858343i
$292$	−1.14432e8	−	3.44912e7i	−0.268971	−	0.0810715i
$293$		−	5.69115e8i		−	1.32179i	−0.750477	−	0.660897i	$-0.770176\pi$
$293$		−	5.69115e8i		−	1.32179i	0.750477	−	0.660897i	$-0.229824\pi$
$294$	7.22263e7	+	1.06484e7i	0.165760	+	0.0244382i
$295$	−6.78869e7			−0.153960
$296$	−1.82171e8	+	3.87831e8i	−0.408281	+	0.869204i
$297$		−	8.40906e6i		−	0.0186252i
$298$	−3.42604e8	−	5.05105e7i	−0.749956	−	0.110567i
$299$	−4.70535e8			−1.01799
$300$	5.54977e8	+	1.67278e8i	1.18673	+	0.357695i
$301$	1.95937e8			0.414128
$302$	7.31312e8	+	1.07818e8i	1.52784	+	0.225251i
$303$	7.64133e8			1.57805
$304$	1.36106e7	−	4.89655e8i	0.0277856	−	0.999614i
$305$	2.98385e8			0.602182
$306$	−5.60840e8	−	8.26852e7i	−1.11896	−	0.164969i
$307$	−1.55277e8			−0.306283			−0.153141	−	0.988204i	$-0.548939\pi$
$307$	−1.55277e8			−0.306283			−0.153141	+	0.988204i	$0.548939\pi$
$308$	2.37914e8	+	7.17104e7i	0.463972	+	0.139847i
$309$	−6.79156e7			−0.130953
$310$	7.21391e7	+	1.06355e7i	0.137532	+	0.0202765i
$311$			7.16865e8i			1.35138i	0.737188	+	0.675688i	$0.236153\pi$
$311$			7.16865e8i			1.35138i	−0.737188	+	0.675688i	$0.763847\pi$
$312$	5.10810e8	−	1.08748e9i	0.952178	−	2.02713i
$313$	−4.06883e8			−0.750006			−0.375003	−	0.927024i	$-0.622358\pi$
$313$	−4.06883e8			−0.750006			−0.375003	+	0.927024i	$0.622358\pi$
$314$	−6.37400e8	−	9.39725e7i	−1.16187	−	0.171296i
$315$		−	1.74163e8i		−	0.313956i
$316$	5.24281e8	+	1.58025e8i	0.934672	+	0.281723i
$317$			5.67181e8i			1.00003i	0.866016	+	0.500017i	$0.166673\pi$
$317$			5.67181e8i			1.00003i	−0.866016	+	0.500017i	$0.833327\pi$
$318$	−1.67768e7	+	1.13794e8i	−0.0292559	+	0.198438i
$319$	5.97738e8			1.03096
$320$	−1.28504e8	−	1.54897e8i	−0.219226	−	0.264251i
$321$	6.38480e8			1.07741
$322$	−3.55249e8	−	5.23747e7i	−0.592976	−	0.0874231i
$323$	−3.72090e8	−	5.96514e8i	−0.614383	−	0.984944i
$324$	−6.00833e8	−	1.81099e8i	−0.981401	−	0.295808i
$325$			8.70121e8i			1.40601i
$326$	5.47291e6	−	3.71219e7i	0.00874897	−	0.0593428i
$327$		−	1.11301e9i		−	1.76028i
$328$	2.69830e8	−	5.74450e8i	0.422212	−	0.898864i
$329$	−6.06504e8			−0.938962
$330$	−2.37198e7	+	1.60887e8i	−0.0363339	+	0.246447i
$331$	4.02076e8			0.609410			0.304705	−	0.952447i	$-0.401442\pi$
$331$	4.02076e8			0.609410			0.304705	+	0.952447i	$0.401442\pi$
$332$	1.37626e8	−	4.56601e8i	0.206403	−	0.684784i
$333$		−	6.30485e8i		−	0.935665i
$334$	−1.14196e9	−	1.68360e8i	−1.67702	−	0.247245i
$335$	1.49184e7			0.0216803
$336$	5.06702e8	−	7.64179e8i	0.728727	−	1.09903i
$337$		−	8.59668e8i		−	1.22356i	−0.791027	−	0.611781i	$-0.790453\pi$
$337$		−	8.59668e8i		−	1.22356i	0.791027	−	0.611781i	$-0.209547\pi$
$338$	1.08197e9	+	1.59516e8i	1.52408	+	0.224697i
$339$		−	6.85430e8i		−	0.955573i
$340$	−2.76571e8	−	8.33623e7i	−0.381620	−	0.115025i
$341$		−	1.53082e8i		−	0.209067i
$342$	2.88192e8	+	6.60648e8i	0.389574	+	0.893056i
$343$			7.85023e8i			1.05040i
$344$	−1.41646e8	+	3.01556e8i	−0.187608	+	0.399405i
$345$		−	2.35013e8i		−	0.308123i
$346$	7.51406e6	−	5.09666e7i	0.00975233	−	0.0661484i
$347$			1.28212e9i			1.64731i	0.567088	+	0.823657i	$0.308070\pi$
$347$			1.28212e9i			1.64731i	−0.567088	+	0.823657i	$0.691930\pi$
$348$	6.36524e8	−	2.11179e9i	0.809631	−	2.68611i
$349$	−1.14608e9			−1.44320			−0.721598	−	0.692312i	$-0.756592\pi$
$349$	−1.14608e9			−1.44320			−0.721598	+	0.692312i	$0.756592\pi$
$350$	−9.68520e7	+	6.56931e8i	−0.120745	+	0.818996i
$351$		−	4.65793e7i		−	0.0574934i
$352$	−2.82357e8	+	3.14319e8i	−0.345064	+	0.384124i
$353$	5.84728e8			0.707526			0.353763	−	0.935335i	$-0.384902\pi$
$353$	5.84728e8			0.707526			0.353763	+	0.935335i	$0.384902\pi$
$354$	5.20265e8	+	7.67033e7i	0.623323	+	0.0918972i
$355$	3.37225e8			0.400055
$356$	−1.47718e8	+	4.90084e8i	−0.173524	+	0.575699i
$357$		−	1.31599e9i		−	1.53079i
$358$	−3.82169e8	−	5.63436e7i	−0.440215	−	0.0649014i
$359$		−	2.14308e8i		−	0.244460i	−0.992502	−	0.122230i	$-0.960995\pi$
$359$		−	2.14308e8i		−	0.244460i	0.992502	−	0.122230i	$-0.0390045\pi$
$360$	2.68045e8	+	1.25905e8i	0.302795	+	0.142228i
$361$	−3.93114e8	+	8.02788e8i	−0.439788	+	0.898102i
$362$	−1.91058e8	+	1.29592e9i	−0.211683	+	1.43581i
$363$	−9.39100e8			−1.03048
$364$	1.31784e9	+	3.97216e8i	1.43222	+	0.431690i
$365$	8.96085e7			0.0964548
$366$	−2.28673e9	−	3.37136e8i	−2.43799	−	0.359435i
$367$			7.04524e8i			0.743985i	0.928236	+	0.371993i	$0.121325\pi$
$367$			7.04524e8i			0.743985i	−0.928236	+	0.371993i	$0.878675\pi$
$368$	3.37422e8	−	5.08881e8i	0.352945	−	0.532291i
$369$			9.33867e8i			0.967593i
$370$	4.68572e7	−	3.17824e8i	0.0480917	−	0.326198i
$371$	−1.31771e8			−0.133971
$372$	−5.40836e8	−	1.63015e8i	−0.544710	−	0.164183i
$373$		−	2.79872e7i		−	0.0279241i	−0.999903	−	0.0139620i	$-0.995556\pi$
$373$		−	2.79872e7i		−	0.0279241i	0.999903	−	0.0139620i	$-0.00444440\pi$
$374$	−8.84493e7	+	5.99937e8i	−0.0874266	+	0.593000i
$375$	−9.27257e8			−0.908011
$376$	4.38452e8	−	9.33437e8i	0.425368	−	0.905581i
$377$	3.31098e9			3.18245
$378$	5.18468e6	−	3.51668e7i	0.00493743	−	0.0334897i
$379$	1.12336e9			1.05994			0.529972	−	0.848015i	$-0.322202\pi$
$379$	1.12336e9			1.05994			0.529972	+	0.848015i	$0.322202\pi$
$380$	9.61771e7	+	3.54447e8i	0.0899143	+	0.331367i
$381$	9.83989e8			0.911492
$382$	−1.23431e8	+	8.37213e8i	−0.113293	+	0.768447i
$383$	−1.05996e8			−0.0964039			−0.0482020	−	0.998838i	$-0.515349\pi$
$383$	−1.05996e8			−0.0964039			−0.0482020	+	0.998838i	$0.515349\pi$
$384$	8.09803e8	+	1.33227e9i	0.729827	+	1.20070i
$385$	−1.86304e8			−0.166383
$386$	−6.39228e7	+	4.33578e8i	−0.0565718	+	0.383717i
$387$		−	4.90231e8i		−	0.429944i
$388$	−2.02835e8	+	6.72945e8i	−0.176291	+	0.584882i
$389$	−1.49288e8			−0.128588			−0.0642939	−	0.997931i	$-0.520480\pi$
$389$	−1.49288e8			−0.128588			−0.0642939	+	0.997931i	$0.520480\pi$
$390$	−1.31388e8	+	8.91182e8i	−0.112158	+	0.760747i
$391$		−	8.76345e8i		−	0.741407i
$392$	−1.28720e8	−	6.04623e7i	−0.107931	−	0.0506971i
$393$		−	2.64062e9i		−	2.19448i
$394$	−4.49463e8	−	6.62648e7i	−0.370218	−	0.0545816i
$395$	−4.10551e8			−0.335180
$396$	1.79418e8	−	5.95255e8i	0.145189	−	0.481692i
$397$	−1.94958e9			−1.56378			−0.781889	−	0.623417i	$-0.785744\pi$
$397$	−1.94958e9			−1.56378			−0.781889	+	0.623417i	$0.785744\pi$
$398$	1.79153e8	−	1.21517e9i	0.142441	−	0.966152i
$399$	−1.41964e9	+	8.85531e8i	−1.11885	+	0.697909i
$400$	−9.41031e8	−	6.23966e8i	−0.735180	−	0.487474i
$401$		−	2.46897e9i		−	1.91210i	−0.293201	−	0.956051i	$-0.594720\pi$
$401$		−	2.46897e9i		−	1.91210i	0.293201	−	0.956051i	$-0.405280\pi$
$402$	−1.14330e8	−	1.68558e7i	−0.0877747	−	0.0129407i
$403$		−	8.47950e8i		−	0.645360i
$404$	−1.42516e9	−	4.29561e8i	−1.07529	−	0.324108i
$405$	4.70498e8			0.351937
$406$	2.49975e9	+	3.68541e8i	1.85377	+	0.273303i
$407$	−6.74437e8			−0.495862
$408$	2.02537e9	+	9.51354e8i	1.47637	+	0.693476i
$409$			1.79791e9i			1.29938i	0.760199	+	0.649690i	$0.225101\pi$
$409$			1.79791e9i			1.29938i	−0.760199	+	0.649690i	$0.774899\pi$
$410$	−6.94042e7	+	4.70757e8i	−0.0497327	+	0.337329i
$411$	2.84018e9			2.01790
$412$	1.26667e8	+	3.81791e7i	0.0892325	+	0.0268959i
$413$			6.02457e8i			0.420824i
$414$	−1.31040e8	+	8.88825e8i	−0.0907620	+	0.615623i
$415$			3.57553e8i			0.245568i
$416$	−1.56403e9	+	1.74107e9i	−1.06517	+	1.18574i
$417$		−	2.29620e9i		−	1.55072i
$418$	7.06702e8	−	3.08282e8i	0.473282	−	0.206458i
$419$		−	6.78355e8i		−	0.450514i	−0.974299	−	0.225257i	$-0.927678\pi$
$419$		−	6.78355e8i		−	0.450514i	0.974299	−	0.225257i	$-0.0723221\pi$
$420$	−1.98393e8	+	6.58208e8i	−0.130663	+	0.433502i
$421$			2.06412e9i			1.34818i	0.738651	+	0.674088i	$0.235463\pi$
$421$			2.06412e9i			1.34818i	−0.738651	+	0.674088i	$0.764537\pi$
$422$	−1.80919e9	−	2.66730e8i	−1.17190	−	0.172774i
$423$			1.51746e9i			0.974823i
$424$	9.52595e7	−	2.02802e8i	0.0606915	−	0.129208i
$425$	−1.62055e9			−1.02400
$426$	−2.58439e9	−	3.81019e8i	−1.61966	−	0.238789i
$427$		−	2.64799e9i		−	1.64596i
$428$	−1.19080e9	−	3.58925e8i	−0.734154	−	0.221284i
$429$	1.89113e9			1.15643
$430$	3.64336e7	−	2.47123e8i	0.0220985	−	0.149890i
$431$	1.09723e9			0.660128			0.330064	−	0.943959i	$-0.392930\pi$
$431$	1.09723e9			0.660128			0.330064	+	0.943959i	$0.392930\pi$
$432$	5.03752e7	+	3.34021e7i	0.0300624	+	0.0199334i
$433$		−	6.96119e8i		−	0.412074i	−0.978544	−	0.206037i	$-0.933943\pi$
$433$		−	6.96119e8i		−	0.412074i	0.978544	−	0.206037i	$-0.0660568\pi$
$434$	9.43842e7	−	6.40192e8i	0.0554224	−	0.375921i
$435$			1.65369e9i			0.963258i
$436$	−6.25683e8	+	2.07583e9i	−0.361536	+	1.19947i
$437$	−9.45362e8	+	5.89692e8i	−0.541892	+	0.338018i
$438$	−6.86733e8	−	1.01246e8i	−0.390507	−	0.0575728i
$439$	3.36456e8			0.189803			0.0949014	−	0.995487i	$-0.469746\pi$
$439$	3.36456e8			0.189803			0.0949014	+	0.995487i	$0.469746\pi$
$440$	1.34682e8	−	2.86730e8i	0.0753748	−	0.160468i
$441$	2.09257e8			0.116184
$442$	−4.89936e8	+	3.32315e9i	−0.269874	+	1.83051i
$443$			2.21727e8i			0.121173i	0.998163	+	0.0605863i	$0.0192970\pi$
$443$			2.21727e8i			0.121173i	−0.998163	+	0.0605863i	$0.980703\pi$
$444$	−7.18199e8	+	2.38277e9i	−0.389408	+	1.29194i
$445$		−	3.83773e8i		−	0.206450i
$446$	3.45104e9	+	5.08790e8i	1.84195	+	0.271561i
$447$	−2.01137e9			−1.06516
$448$	−1.37462e9	+	1.14040e9i	−0.722285	+	0.599215i
$449$		−	1.22306e9i		−	0.637656i	−0.947813	−	0.318828i	$-0.896711\pi$
$449$		−	1.22306e9i		−	0.637656i	0.947813	−	0.318828i	$-0.103289\pi$
$450$	1.64363e9	+	2.42322e8i	0.850276	+	0.125357i
$451$	9.98968e8			0.512783
$452$	−3.85318e8	+	1.27837e9i	−0.196261	+	0.651136i
$453$	4.29340e9			2.16999
$454$	4.18991e8	+	6.17723e7i	0.210140	+	0.0309812i
$455$	−1.03197e9			−0.513603
$456$	−3.36594e8	−	2.82505e9i	−0.166238	−	1.39524i
$457$	2.73191e9			1.33894			0.669469	−	0.742840i	$-0.266522\pi$
$457$	2.73191e9			1.33894			0.669469	+	0.742840i	$0.266522\pi$
$458$	−1.64207e9	−	2.42092e8i	−0.798661	−	0.117747i
$459$	8.67512e7			0.0418727
$460$	−1.32114e8	+	4.38313e8i	−0.0632841	+	0.209958i
$461$	−1.69276e9			−0.804715			−0.402357	−	0.915483i	$-0.631809\pi$
$461$	−1.69276e9			−0.804715			−0.402357	+	0.915483i	$0.631809\pi$
$462$	1.42778e9	+	2.10499e8i	0.673619	+	0.0993124i
$463$			1.38820e9i			0.650007i	0.945713	+	0.325003i	$0.105365\pi$
$463$			1.38820e9i			0.650007i	−0.945713	+	0.325003i	$0.894635\pi$
$464$	−2.37431e9	+	3.58080e9i	−1.10338	+	1.66405i
$465$	4.23515e8			0.195337
$466$	−9.81426e8	−	1.44693e8i	−0.449269	−	0.0662363i
$467$		−	2.94927e9i		−	1.34000i	−0.742360	−	0.670001i	$-0.766294\pi$
$467$		−	2.94927e9i		−	1.34000i	0.742360	−	0.670001i	$-0.233706\pi$
$468$	9.93826e8	−	3.29722e9i	0.448177	−	1.48692i
$469$		−	1.32392e8i		−	0.0592593i
$470$	−1.12776e8	+	7.64943e8i	−0.0501044	+	0.339850i
$471$	−3.74206e9			−1.65020
$472$	−9.27208e8	−	4.35526e8i	−0.405864	−	0.190641i
$473$	−5.24406e8			−0.227852
$474$	3.14635e9	+	4.63869e8i	1.35701	+	0.200065i
$475$	1.09047e9	+	1.74818e9i	0.466858	+	0.748441i
$476$	−7.39792e8	+	2.45441e9i	−0.314402	+	1.04309i
$477$			3.29688e8i			0.139088i
$478$	4.35591e8	−	2.95454e9i	0.182424	−	1.23735i
$479$			3.36401e9i			1.39857i	0.714845	+	0.699283i	$0.246497\pi$
$479$			3.36401e9i			1.39857i	−0.714845	+	0.699283i	$0.753503\pi$
$480$	−8.69590e8	−	7.81165e8i	−0.358897	−	0.322403i
$481$	−3.73583e9			−1.53066
$482$	2.38694e8	−	1.61902e9i	0.0970905	−	0.658549i
$483$	−2.08560e9			−0.842202
$484$	1.75148e9	+	5.27920e8i	0.702177	+	0.211646i
$485$		−	5.26966e8i		−	0.209743i
$486$	−3.51545e9	−	5.18287e8i	−1.38917	−	0.204806i
$487$	4.06977e8			0.159668			0.0798341	−	0.996808i	$-0.474561\pi$
$487$	4.06977e8			0.159668			0.0798341	+	0.996808i	$0.474561\pi$
$488$	4.07538e9	+	1.91428e9i	1.58745	+	0.745651i
$489$		−	2.17936e8i		−	0.0842844i
$490$	1.05485e8	+	1.55518e7i	0.0405047	+	0.00597165i
$491$		−	1.83223e9i		−	0.698547i	−0.937021	−	0.349274i	$-0.886428\pi$
$491$		−	1.83223e9i		−	0.698547i	0.937021	−	0.349274i	$-0.113572\pi$
$492$	1.06379e9	−	3.52933e9i	0.402696	−	1.33602i
$493$			6.16650e9i			2.31779i
$494$	3.91455e9	−	1.70763e9i	1.46096	−	0.637307i
$495$			4.66129e8i			0.172738i
$496$	9.17053e8	+	6.08067e8i	0.337449	+	0.223751i
$497$		−	2.99267e9i		−	1.09348i
$498$	4.03988e8	−	2.74018e9i	0.146577	−	0.994207i
$499$		−	3.10292e9i		−	1.11794i	−0.829188	−	0.558969i	$-0.811197\pi$
$499$		−	3.10292e9i		−	1.11794i	0.829188	−	0.558969i	$-0.188803\pi$
$500$	1.72939e9	+	5.21262e8i	0.618726	+	0.186492i
$501$	−6.70424e9			−2.38187
$502$	8.03829e8	−	5.45224e9i	0.283596	−	1.92359i
$503$			3.92897e9i			1.37654i	0.725452	+	0.688272i	$0.241631\pi$
$503$			3.92897e9i			1.37654i	−0.725452	+	0.688272i	$0.758369\pi$
$504$	1.11734e9	−	2.37874e9i	0.388756	−	0.827638i
$505$	1.11600e9			0.385608
$506$	9.50786e8	+	1.40175e8i	0.326254	+	0.0481000i
$507$	6.35206e9			2.16465
$508$	−1.83520e9	−	5.53154e8i	−0.621099	−	0.187208i
$509$			1.02125e8i			0.0343256i	0.999853	+	0.0171628i	$0.00546336\pi$
$509$			1.02125e8i			0.0343256i	−0.999853	+	0.0171628i	$0.994537\pi$
$510$	−1.65978e9	−	2.44702e8i	−0.554056	−	0.0816851i
$511$		−	7.95223e8i		−	0.263643i
$512$	−7.61388e8	−	2.94001e9i	−0.250704	−	0.968064i
$513$	−5.83748e7	−	9.35833e7i	−0.0190904	−	0.0306047i
$514$	6.72892e8	−	4.56412e9i	0.218562	−	1.48247i
$515$	−9.91897e7			−0.0319994
$516$	−5.58432e8	+	1.85271e9i	−0.178936	+	0.593655i
$517$	1.62324e9			0.516615
$518$	−2.82051e9	−	4.15830e8i	−0.891606	−	0.131450i
$519$		−	2.99216e8i		−	0.0939504i
$520$	7.46029e8	−	1.58825e9i	0.232672	−	0.495344i
$521$			6.06005e9i			1.87735i	0.344810	+	0.938673i	$0.387943\pi$
$521$			6.06005e9i			1.87735i	−0.344810	+	0.938673i	$0.612057\pi$
$522$	9.22081e8	−	6.25432e9i	0.283741	−	1.92457i
$523$	−6.20968e9			−1.89807			−0.949037	−	0.315164i	$-0.897941\pi$
$523$	−6.20968e9			−1.89807			−0.949037	+	0.315164i	$0.897941\pi$
$524$	−1.48444e9	+	4.92492e9i	−0.450715	+	1.49534i
$525$			3.85672e9i			1.16322i
$526$	3.04093e8	−	2.06261e9i	0.0911080	−	0.617970i
$527$	1.57926e9			0.470019
$528$	−1.35613e9	+	2.04525e9i	−0.400944	+	0.604682i
$529$	2.01598e9			0.592096
$530$	−2.45022e7	+	1.66194e8i	−0.00714890	+	0.0484898i
$531$	1.50733e9			0.436897
$532$	3.14551e9	−	8.53516e8i	0.905734	−	0.245765i
$533$	5.53346e9			1.58289
$534$	−4.33613e8	+	2.94112e9i	−0.123227	+	0.835832i
$535$	9.32490e8			0.263273
$536$	2.03757e8	+	9.57084e7i	0.0571526	+	0.0268456i
$537$	−2.24365e9			−0.625236
$538$	1.96751e7	−	1.33453e8i	0.00544728	−	0.0369480i
$539$		−	2.23845e8i		−	0.0615724i
$540$	−4.33895e7	−	1.30782e7i	−0.0118579	−	0.00357412i
$541$	−7.04766e9			−1.91362			−0.956808	−	0.290722i	$-0.906105\pi$
$541$	−7.04766e9			−1.91362			−0.956808	+	0.290722i	$0.906105\pi$
$542$	−7.62912e8	+	5.17470e9i	−0.205815	+	1.39601i
$543$			7.60809e9i			2.03928i
$544$	−3.24264e9	−	2.91291e9i	−0.863579	−	0.775765i
$545$		−	1.62553e9i		−	0.430138i
$546$	7.90873e9	+	1.16599e9i	2.07937	+	0.306564i
$547$	5.59729e9			1.46225			0.731126	−	0.682243i	$-0.238995\pi$
$547$	5.59729e9			1.46225			0.731126	+	0.682243i	$0.238995\pi$
$548$	−5.29712e9	−	1.59662e9i	−1.37502	−	0.414448i
$549$	−6.62522e9			−1.70882
$550$	2.59214e8	−	1.75821e9i	0.0664339	−	0.450610i
$551$	6.65215e9	−	4.14944e9i	1.69407	−	1.05672i
$552$	1.50772e9	−	3.20983e9i	0.381534	−	0.812261i
$553$			3.64341e9i			0.916156i
$554$	−1.41484e9	−	2.08592e8i	−0.353529	−	0.0521211i
$555$		−	1.86589e9i		−	0.463298i
$556$	−1.29082e9	+	4.28255e9i	−0.318496	+	1.05667i
$557$	1.32642e9			0.325228			0.162614	−	0.986690i	$-0.448007\pi$
$557$	1.32642e9			0.325228			0.162614	+	0.986690i	$0.448007\pi$
$558$	−1.60175e9	−	2.36147e8i	−0.390278	−	0.0575391i
$559$	−2.90477e9			−0.703349
$560$	7.40030e8	−	1.11607e9i	0.178070	−	0.268555i
$561$			3.52212e9i			0.842236i
$562$	5.71637e8	−	3.87732e9i	0.135845	−	0.921414i
$563$	−4.44310e9			−1.04932			−0.524659	−	0.851313i	$-0.675807\pi$
$563$	−4.44310e9			−1.04932			−0.524659	+	0.851313i	$0.675807\pi$
$564$	1.72857e9	−	5.73488e9i	0.405705	−	1.34601i
$565$		−	1.00106e9i		−	0.233502i
$566$	7.32547e7	−	4.96875e8i	0.0169816	−	0.115183i
$567$		−	4.17539e9i		−	0.961959i
$568$	4.60586e9	+	2.16345e9i	1.05461	+	0.495368i
$569$		−	5.62317e9i		−	1.27964i	−0.768525	−	0.639820i	$-0.779009\pi$
$569$		−	5.62317e9i		−	1.27964i	0.768525	−	0.639820i	$-0.220991\pi$
$570$	8.52888e8	+	1.95515e9i	0.192899	+	0.442200i
$571$		−	7.89864e9i		−	1.77552i	−0.460305	−	0.887761i	$-0.652260\pi$
$571$		−	7.89864e9i		−	1.77552i	0.460305	−	0.887761i	$-0.347740\pi$
$572$	−3.52707e9	−	1.06311e9i	−0.788004	−	0.237515i
$573$			4.91512e9i			1.09142i
$574$	4.17770e9	+	6.15922e8i	0.922030	+	0.135936i
$575$			2.56826e9i			0.563381i
$576$	2.85325e9	+	3.43926e9i	0.622101	+	0.749871i
$577$	−8.57711e9			−1.85877			−0.929385	−	0.369112i	$-0.879662\pi$
$577$	−8.57711e9			−1.85877			−0.929385	+	0.369112i	$0.879662\pi$
$578$	−1.59637e9	−	2.35355e8i	−0.343864	−	0.0506963i
$579$			2.54546e9i			0.544993i
$580$	9.29632e8	−	3.08424e9i	0.197840	−	0.656373i
$581$	3.17308e9			0.671218
$582$	−5.95403e8	+	4.03852e9i	−0.125193	+	0.849164i
$583$	3.52671e8			0.0737107
$584$	1.22388e9	+	5.74880e8i	0.254270	+	0.119435i
$585$			2.58197e9i			0.533219i
$586$	−9.39128e8	+	6.36995e9i	−0.192789	+	1.30766i
$587$		−	6.85625e9i		−	1.39912i	−0.714576	−	0.699558i	$-0.753380\pi$
$587$		−	6.85625e9i		−	1.39912i	0.714576	−	0.699558i	$-0.246620\pi$
$588$	−7.90837e8	−	2.38369e8i	−0.160423	−	0.0483536i
$589$	−1.06268e9	−	1.70363e9i	−0.214289	−	0.343536i
$590$	7.59839e8	+	1.12024e8i	0.152314	+	0.0224558i
$591$	−2.63871e9			−0.525819
$592$	2.67897e9	−	4.04028e9i	0.530692	−	0.800359i
$593$	4.59277e9			0.904448			0.452224	−	0.891904i	$-0.350631\pi$
$593$	4.59277e9			0.904448			0.452224	+	0.891904i	$0.350631\pi$
$594$	−1.38763e7	+	9.41203e7i	−0.00271656	+	0.0184260i
$595$		−	1.92199e9i		−	0.374060i
$596$	3.75133e9	+	1.13070e9i	0.725810	+	0.218769i
$597$		−	7.13403e9i		−	1.37222i
$598$	5.26657e9	+	7.76456e8i	1.00710	+	0.148478i
$599$	−2.63520e9			−0.500980			−0.250490	−	0.968119i	$-0.580592\pi$
$599$	−2.63520e9			−0.500980			−0.250490	+	0.968119i	$0.580592\pi$
$600$	−5.93567e9	−	2.78809e9i	−1.12186	−	0.526960i
$601$			8.74575e7i			0.0164337i	0.999966	+	0.00821687i	$0.00261554\pi$
$601$			8.74575e7i			0.0164337i	−0.999966	+	0.00821687i	$0.997384\pi$
$602$	−2.19307e9	−	3.23327e8i	−0.409699	−	0.0604024i
$603$	−3.31242e8			−0.0615226
$604$	−8.00745e9	−	2.41355e9i	−1.47865	−	0.445685i
$605$	−1.37154e9			−0.251805
$606$	−8.55273e9	−	1.26094e9i	−1.56117	−	0.230165i
$607$	−1.28108e9			−0.232496			−0.116248	−	0.993220i	$-0.537087\pi$
$607$	−1.28108e9			−0.232496			−0.116248	+	0.993220i	$0.537087\pi$
$608$	−9.60345e8	+	5.45811e9i	−0.173287	+	0.984871i
$609$	1.46756e10			2.63290
$610$	−3.33974e9	−	4.92381e8i	−0.595742	−	0.0878308i
$611$	8.99143e9			1.59472
$612$	6.14088e9	+	1.85094e9i	1.08293	+	0.326410i
$613$	2.05372e9			0.360105			0.180053	−	0.983657i	$-0.442373\pi$
$613$	2.05372e9			0.360105			0.180053	+	0.983657i	$0.442373\pi$
$614$	1.73797e9	+	2.56231e8i	0.303008	+	0.0446727i
$615$			2.76373e9i			0.479107i
$616$	−2.54457e9	−	1.19523e9i	−0.438613	−	0.206024i
$617$	2.58182e8			0.0442514			0.0221257	−	0.999755i	$-0.492957\pi$
$617$	2.58182e8			0.0442514			0.0221257	+	0.999755i	$0.492957\pi$
$618$	7.60161e8	+	1.12071e8i	0.129553	+	0.0191001i
$619$			5.13102e9i			0.869533i	0.900543	+	0.434766i	$0.143169\pi$
$619$			5.13102e9i			0.869533i	−0.900543	+	0.434766i	$0.856831\pi$
$620$	−7.89882e8	−	2.38081e8i	−0.133104	−	0.0401194i
$621$		−	1.37484e8i		−	0.0230373i
$622$	1.18294e9	−	8.02367e9i	0.197104	−	1.33692i
$623$	−3.40576e9			−0.564295
$624$	−7.51186e9	+	1.13290e10i	−1.23766	+	1.86657i
$625$	4.02974e9			0.660232
$626$	4.55413e9	+	6.71420e8i	0.741985	+	0.109392i
$627$	3.79950e9	−	2.37003e9i	0.615589	−	0.383988i
$628$	6.97917e9	+	2.10362e9i	1.12446	+	0.338928i
$629$		−	6.95776e9i		−	1.11479i
$630$	−2.87396e8	+	1.94936e9i	−0.0457919	+	0.310599i
$631$		−	1.83720e9i		−	0.291108i	−0.989350	−	0.145554i	$-0.953504\pi$
$631$		−	1.83720e9i		−	0.291108i	0.989350	−	0.145554i	$-0.0464965\pi$
$632$	−5.60736e9	−	2.63388e9i	−0.883586	−	0.415036i
$633$	−1.06214e10			−1.66444
$634$	9.35937e8	−	6.34830e9i	0.145859	−	0.989339i
$635$	1.43710e9			0.222730
$636$	3.75555e8	−	1.24598e9i	0.0578860	−	0.192049i
$637$		−	1.23991e9i		−	0.190066i
$638$	−6.69032e9	−	9.86360e8i	−1.01994	−	0.150371i
$639$	−7.48760e9			−1.13525
$640$	1.18270e9	+	1.94577e9i	0.178339	+	0.293400i
$641$			1.97789e9i			0.296619i	0.988941	+	0.148309i	$0.0473832\pi$
$641$			1.97789e9i			0.296619i	−0.988941	+	0.148309i	$0.952617\pi$
$642$	−7.14633e9	−	1.05359e9i	−1.06589	−	0.157145i
$643$			9.86193e9i			1.46293i	0.681879	+	0.731465i	$0.261163\pi$
$643$			9.86193e9i			1.46293i	−0.681879	+	0.731465i	$0.738837\pi$
$644$	3.88978e9	+	1.17243e9i	0.573884	+	0.172976i
$645$		−	1.45081e9i		−	0.212889i
$646$	3.18036e9	+	7.29062e9i	0.464154	+	1.06402i
$647$			9.10174e8i			0.132117i	0.997816	+	0.0660586i	$0.0210424\pi$
$647$			9.10174e8i			0.132117i	−0.997816	+	0.0660586i	$0.978958\pi$
$648$	6.42612e9	+	3.01846e9i	0.927761	+	0.435786i
$649$		−	1.61241e9i		−	0.231537i
$650$	1.43583e9	−	9.73902e9i	0.205072	−	1.39097i
$651$		−	3.75845e9i		−	0.533919i
$652$	−1.22514e8	+	4.06463e8i	−0.0173108	+	0.0574321i
$653$	−9.48723e9			−1.33335			−0.666674	−	0.745350i	$-0.732282\pi$
$653$	−9.48723e9			−1.33335			−0.666674	+	0.745350i	$0.732282\pi$
$654$	−1.83664e9	+	1.24576e10i	−0.256744	+	1.74145i
$655$		−	3.85658e9i		−	0.536238i
$656$	−3.96806e9	+	5.98440e9i	−0.548801	+	0.827670i
$657$	−1.98963e9			−0.273712
$658$	6.78843e9	+	1.00082e9i	0.928920	+	0.136952i
$659$	−7.74112e9			−1.05367			−0.526836	−	0.849967i	$-0.676622\pi$
$659$	−7.74112e9			−1.05367			−0.526836	+	0.849967i	$0.676622\pi$
$660$	5.30977e8	−	1.76162e9i	0.0718906	−	0.238512i
$661$		−	1.37129e9i		−	0.184682i	−0.995727	−	0.0923411i	$-0.970565\pi$
$661$		−	1.37129e9i		−	0.184682i	0.995727	−	0.0923411i	$-0.0294350\pi$
$662$	−4.50032e9	−	6.63487e8i	−0.602893	−	0.0888852i
$663$			1.95096e10i			2.59987i
$664$	−2.29387e9	+	4.88351e9i	−0.304075	+	0.647356i
$665$	−2.07335e9	+	1.29330e9i	−0.273399	+	0.170539i
$666$	−1.04040e9	+	7.05685e9i	−0.136471	+	0.925659i
$667$	9.77274e9			1.27519
$668$	1.25038e10	+	3.76882e9i	1.62302	+	0.489202i
$669$	2.02604e10			2.61612
$670$	−1.66977e8	−	2.46176e7i	−0.0214484	−	0.00316216i
$671$			7.08707e9i			0.905604i
$672$	−6.93239e9	+	7.71711e9i	−0.881232	+	0.980985i
$673$			1.80224e9i			0.227908i	0.993486	+	0.113954i	$0.0363517\pi$
$673$			1.80224e9i			0.227908i	−0.993486	+	0.113954i	$0.963648\pi$
$674$	−1.41858e9	+	9.62202e9i	−0.178462	+	1.21048i
$675$	−2.54238e8			−0.0318183
$676$	−1.18470e10	−	3.57084e9i	−1.47501	−	0.444587i
$677$			4.95318e9i			0.613513i	0.951788	+	0.306756i	$0.0992437\pi$
$677$			4.95318e9i			0.613513i	−0.951788	+	0.306756i	$0.900756\pi$
$678$	−1.13106e9	+	7.67182e9i	−0.139375	+	0.945354i
$679$	−4.67652e9			−0.573296
$680$	2.95802e9	+	1.38944e9i	0.360762	+	0.169456i
$681$	2.45982e9			0.298461
$682$	−2.52609e8	+	1.71341e9i	−0.0304933	+	0.206831i
$683$	−2.87179e9			−0.344890			−0.172445	−	0.985019i	$-0.555167\pi$
$683$	−2.87179e9			−0.344890			−0.172445	+	0.985019i	$0.555167\pi$
$684$	−2.13548e9	−	7.87001e9i	−0.255152	−	0.940327i
$685$	4.14804e9			0.493090
$686$	1.29541e9	−	8.78654e9i	0.153205	−	1.03916i
$687$	−9.64029e9			−1.13434
$688$	2.08302e9	−	3.14150e9i	0.243857	−	0.367771i
$689$	1.95351e9			0.227535
$690$	−3.87807e8	+	2.63043e9i	−0.0449411	+	0.304828i
$691$			1.28787e10i			1.48490i	0.669901	+	0.742451i	$0.266337\pi$
$691$			1.28787e10i			1.48490i	−0.669901	+	0.742451i	$0.733663\pi$
$692$	−1.68206e8	+	5.58056e8i	−0.0192961	+	0.0640186i
$693$	4.13662e9			0.472150
$694$	2.11570e9	−	1.43504e10i	0.240268	−	1.62970i
$695$		−	3.35356e9i		−	0.378930i
$696$	−1.06092e10	+	2.25864e10i	−1.19275	+	2.53930i
$697$			1.03057e10i			1.15283i
$698$	1.28277e10	+	1.89121e9i	1.42776	+	0.210497i
$699$	−5.76177e9			−0.638096
$700$	2.16808e9	−	7.19303e9i	0.238908	−	0.792626i
$701$	−1.05229e9			−0.115378			−0.0576891	−	0.998335i	$-0.518373\pi$
$701$	−1.05229e9			−0.115378			−0.0576891	+	0.998335i	$0.518373\pi$
$702$	−7.68630e7	+	5.21349e8i	−0.00838566	+	0.0568785i
$703$	−7.50572e9	+	4.68187e9i	−0.814796	+	0.508248i
$704$	3.67902e9	−	3.05215e9i	0.397400	−	0.329687i
$705$			4.49084e9i			0.482687i
$706$	−6.54470e9	−	9.64892e8i	−0.699960	−	0.103196i
$707$		−	9.90389e9i		−	1.05399i
$708$	−5.69661e9	−	1.71704e9i	−0.603254	−	0.181829i
$709$	−3.13967e9			−0.330844			−0.165422	−	0.986223i	$-0.552899\pi$
$709$	−3.13967e9			−0.330844			−0.165422	+	0.986223i	$0.552899\pi$
$710$	−3.77446e9	−	5.56473e8i	−0.395777	−	0.0583498i
$711$	9.11572e9			0.951147
$712$	2.46208e9	−	5.24162e9i	0.255636	−	0.544234i
$713$		−	2.50282e9i		−	0.258593i
$714$	−2.17159e9	+	1.47295e10i	−0.223272	+	1.51442i
$715$	2.76196e9			0.282583
$716$	4.18454e9	+	1.26128e9i	0.426041	+	0.128415i
$717$		−	1.73456e10i		−	1.75740i
$718$	−3.53641e8	+	2.39869e9i	−0.0356555	+	0.241845i
$719$		−	4.36867e9i		−	0.438327i	−0.975688	−	0.219163i	$-0.929667\pi$
$719$		−	4.36867e9i		−	0.438327i	0.975688	−	0.219163i	$-0.0703328\pi$
$720$	−2.79239e9	−	1.85154e9i	−0.278812	−	0.184871i
$721$			8.80251e8i			0.0874647i
$722$	5.72474e9	−	8.33668e9i	0.566077	−	0.824353i
$723$		−	9.50498e9i		−	0.935335i
$724$	4.27693e9	−	1.41896e10i	0.418839	−	1.38958i
$725$		−	1.80719e10i		−	1.76125i
$726$	1.05111e10	+	1.54966e9i	1.01946	+	0.150300i
$727$			3.06737e9i			0.296071i	0.988982	+	0.148035i	$0.0472949\pi$
$727$			3.06737e9i			0.296071i	−0.988982	+	0.148035i	$0.952705\pi$
$728$	−1.40948e10	−	6.62058e9i	−1.35394	−	0.635969i
$729$	−9.91658e9			−0.948016
$730$	−1.00296e9	−	1.47868e8i	−0.0954234	−	0.0140684i
$731$		−	5.40997e9i		−	0.512253i
$732$	2.50385e10	+	7.54693e9i	2.35949	+	0.711183i
$733$	−1.22662e10			−1.15039			−0.575196	−	0.818015i	$-0.695074\pi$
$733$	−1.22662e10			−1.15039			−0.575196	+	0.818015i	$0.695074\pi$
$734$	1.16257e9	−	7.88554e9i	0.108514	−	0.736029i
$735$	6.19285e8			0.0575287
$736$	−4.61641e9	+	5.13897e9i	−0.426807	+	0.475120i
$737$			3.54333e8i			0.0326044i
$738$	1.54102e9	−	1.04525e10i	0.141128	−	0.957245i
$739$		−	8.36331e9i		−	0.762294i	−0.924514	−	0.381147i	$-0.875529\pi$
$739$		−	8.36331e9i		−	0.762294i	0.924514	−	0.381147i	$-0.124471\pi$
$740$	−1.04892e9	+	3.48000e9i	−0.0951548	+	0.315695i
$741$	2.10461e10	−	1.31280e10i	1.90024	−	1.18532i
$742$	1.47488e9	+	2.17443e8i	0.132539	+	0.0195403i
$743$	8.14455e9			0.728461			0.364230	−	0.931309i	$-0.381332\pi$
$743$	8.14455e9			0.728461			0.364230	+	0.931309i	$0.381332\pi$
$744$	5.78443e9	+	2.71705e9i	0.514938	+	0.241876i
$745$	−2.93757e9			−0.260280
$746$	−4.61833e7	+	3.13253e8i	−0.00407285	+	0.0276255i
$747$		−	7.93897e9i		−	0.696854i
$748$	1.97998e9	−	6.56897e9i	0.172983	−	0.573907i
$749$		−	8.27530e9i		−	0.719611i
$750$	1.03785e10	+	1.53012e9i	0.898300	+	0.132437i
$751$	5.78813e9			0.498653			0.249327	−	0.968419i	$-0.419791\pi$
$751$	5.78813e9			0.498653			0.249327	+	0.968419i	$0.419791\pi$
$752$	−6.44778e9	+	9.72418e9i	−0.552902	+	0.833855i
$753$		−	3.20091e10i		−	2.73206i
$754$	−3.70588e10	−	5.46362e9i	−3.14842	−	0.464174i
$755$	6.27044e9			0.530253
$756$	−1.16061e8	+	3.85057e8i	−0.00976925	+	0.0324115i
$757$	1.85609e10			1.55512			0.777558	−	0.628812i	$-0.216458\pi$
$757$	1.85609e10			1.55512			0.777558	+	0.628812i	$0.216458\pi$
$758$	−1.25735e10	−	1.85372e9i	−1.04861	−	0.154598i
$759$	5.58189e9			0.463378
$760$	−4.91591e8	−	4.12594e9i	−0.0406215	−	0.340938i
$761$	1.40157e10			1.15284			0.576420	−	0.817154i	$-0.304449\pi$
$761$	1.40157e10			1.15284			0.576420	+	0.817154i	$0.304449\pi$
$762$	−1.10135e10	−	1.62373e9i	−0.901745	−	0.132945i
$763$	−1.44256e10			−1.17571
$764$	2.76306e9	−	9.16701e9i	0.224163	−	0.743705i
$765$	−4.80877e9			−0.388346
$766$	1.18639e9	+	1.74910e8i	0.0953730	+	0.0140609i
$767$		−	8.93143e9i		−	0.714722i
$768$	−6.86544e9	−	1.62481e10i	−0.546895	−	1.29431i
$769$	9.93943e9			0.788169			0.394084	−	0.919074i	$-0.371062\pi$
$769$	9.93943e9			0.788169			0.394084	+	0.919074i	$0.371062\pi$
$770$	2.08525e9	+	3.07431e8i	0.164604	+	0.0242677i
$771$		−	2.67951e10i		−	2.10555i
$772$	1.43094e9	−	4.74743e9i	0.111934	−	0.371363i
$773$			3.46341e9i			0.269697i	0.990866	+	0.134848i	$0.0430548\pi$
$773$			3.46341e9i			0.269697i	−0.990866	+	0.134848i	$0.956945\pi$
$774$	−8.08957e8	+	5.48702e9i	−0.0627093	+	0.425347i
$775$	−4.62826e9			−0.357159
$776$	3.38073e9	−	7.19738e9i	0.259714	−	0.552915i
$777$	−1.65587e10			−1.26635
$778$	1.67093e9	+	2.46347e8i	0.127213	+	0.0187551i
$779$	1.11174e10	−	6.93473e9i	0.842599	−	0.525591i
$780$	2.94118e9	−	9.75795e9i	0.221917	−	0.736253i
$781$			8.00957e9i			0.601632i
$782$	−1.44610e9	+	9.80868e9i	−0.108137	+	0.733478i
$783$			9.67424e8i			0.0720196i
$784$	1.34096e9	+	8.89146e8i	0.0993824	+	0.0658972i
$785$	−5.46521e9			−0.403240
$786$	−4.35743e9	+	2.95557e10i	−0.320075	+	2.17101i
$787$	2.30979e10			1.68912			0.844562	−	0.535457i	$-0.179861\pi$
$787$	2.30979e10			1.68912			0.844562	+	0.535457i	$0.179861\pi$
$788$	4.92137e9	+	1.48337e9i	0.358298	+	0.107996i
$789$		−	1.21092e10i		−	0.877701i
$790$	4.59519e9	+	6.77473e8i	0.331595	+	0.0488874i
$791$	−8.88381e9			−0.638237
$792$	−2.99043e9	+	6.36645e9i	−0.213893	+	0.455365i
$793$			3.92565e10i			2.79548i
$794$	2.18212e10	+	3.21712e9i	1.54706	+	0.228084i
$795$			9.75696e8i			0.0688699i
$796$	−4.01043e9	+	1.33054e10i	−0.281835	+	0.935044i
$797$			2.97700e9i			0.208293i	0.994562	+	0.104146i	$0.0332111\pi$
$797$			2.97700e9i			0.208293i	−0.994562	+	0.104146i	$0.966789\pi$
$798$	1.73508e10	−	7.56889e9i	1.20868	−	0.527256i
$799$			1.67460e10i			1.16144i
$800$	9.50305e9	+	8.53673e9i	0.656218	+	0.589490i
$801$			8.52114e9i			0.585847i
$802$	−4.07419e9	+	2.76345e10i	−0.278888	+	1.89165i
$803$			2.12833e9i			0.145056i
$804$	1.25185e9	+	3.77325e8i	0.0849486	+	0.0256047i
$805$	−3.04599e9			−0.205799
$806$	−1.39925e9	+	9.49086e9i	−0.0941287	+	0.638459i
$807$		−	7.83479e8i		−	0.0524771i
$808$	1.52425e10	+	7.15968e9i	1.01652	+	0.477479i
$809$	−1.83177e10			−1.21633			−0.608165	−	0.793811i	$-0.708094\pi$
$809$	−1.83177e10			−1.21633			−0.608165	+	0.793811i	$0.708094\pi$
$810$	−5.26615e9	−	7.76394e8i	−0.348173	−	0.0513315i
$811$	−4.72596e9			−0.311112			−0.155556	−	0.987827i	$-0.549717\pi$
$811$	−4.72596e9			−0.311112			−0.155556	+	0.987827i	$0.549717\pi$
$812$	−2.73709e10	−	8.24995e9i	−1.79408	−	0.540761i
$813$			3.03797e10i			1.98275i
$814$	7.54879e9	+	1.11293e9i	0.490560	+	0.0723237i
$815$		−	3.18291e8i		−	0.0205955i
$816$	−2.10996e10	−	1.39904e10i	−1.35943	−	0.901395i
$817$	−5.83604e9	+	3.64037e9i	−0.374404	+	0.233544i
$818$	2.96683e9	−	2.01235e10i	0.189520	−	1.28548i
$819$	2.29135e10			1.45746
$820$	1.55364e9	−	5.15453e9i	0.0984018	−	0.326468i
$821$	−8.26532e9			−0.521265			−0.260633	−	0.965438i	$-0.583931\pi$
$821$	−8.26532e9			−0.521265			−0.260633	+	0.965438i	$0.583931\pi$
$822$	−3.17894e10	−	4.68674e9i	−1.99632	−	0.294320i
$823$			1.64112e10i			1.02622i	0.858322	+	0.513111i	$0.171507\pi$
$823$			1.64112e10i			1.02622i	−0.858322	+	0.513111i	$0.828493\pi$
$824$	−1.35475e9	−	6.36348e8i	−0.0843553	−	0.0396232i
$825$		−	1.03221e10i		−	0.640000i
$826$	9.94147e8	−	6.74313e9i	0.0613791	−	0.416324i
$827$	2.37954e10			1.46293			0.731464	−	0.681880i	$-0.238837\pi$
$827$	2.37954e10			1.46293			0.731464	+	0.681880i	$0.238837\pi$
$828$	2.93340e9	−	9.73214e9i	0.179583	−	0.595802i
$829$			2.69057e10i			1.64023i	0.572202	+	0.820113i	$0.306089\pi$
$829$			2.69057e10i			1.64023i	−0.572202	+	0.820113i	$0.693911\pi$
$830$	5.90018e8	−	4.00199e9i	0.0358172	−	0.242942i
$831$	−8.30629e9			−0.502116
$832$	2.03787e10	−	1.69064e10i	1.22672	−	1.01770i
$833$	2.30927e9			0.138426
$834$	−3.78908e9	+	2.57007e10i	−0.226179	+	1.53414i
$835$	−9.79143e9			−0.582027
$836$	−8.41864e9	+	2.28434e9i	−0.498333	+	0.135220i
$837$	2.47760e8			0.0146047
$838$	−1.11939e9	+	7.59264e9i	−0.0657094	+	0.445696i
$839$	−3.18793e10			−1.86356			−0.931778	−	0.363028i	$-0.881743\pi$
$839$	−3.18793e10			−1.86356			−0.931778	+	0.363028i	$0.881743\pi$
$840$	3.30670e9	−	7.03976e9i	0.192494	−	0.409808i
$841$	−5.15172e10			−2.98652
$842$	3.40611e9	−	2.31031e10i	0.196637	−	1.33376i
$843$		−	2.27630e10i		−	1.30868i
$844$	1.98096e10	+	5.97087e9i	1.13417	+	0.341853i
$845$	9.27708e9			0.528948
$846$	2.50404e9	−	1.69845e10i	0.142182	−	0.964398i
$847$			1.21716e10i			0.688266i
$848$	−1.40087e9	+	2.11271e9i	−0.0788881	+	0.118975i
$849$		−	2.91706e9i		−	0.163594i
$850$	1.81384e10	+	2.67416e9i	1.01305	+	0.149355i
$851$	−1.10267e10			−0.613329
$852$	2.82976e10	+	8.52929e9i	1.56751	+	0.472470i
$853$	−1.80521e10			−0.995878			−0.497939	−	0.867212i	$-0.665910\pi$
$853$	−1.80521e10			−0.995878			−0.497939	+	0.867212i	$0.665910\pi$
$854$	−4.36960e9	+	2.96382e10i	−0.240070	+	1.62836i
$855$	3.23582e9	+	5.18749e9i	0.177053	+	0.283841i
$856$	1.27361e10	+	5.98236e9i	0.694028	+	0.325997i
$857$			4.39427e9i			0.238481i	0.992865	+	0.119240i	$0.0380459\pi$
$857$			4.39427e9i			0.238481i	−0.992865	+	0.119240i	$0.961954\pi$
$858$	−2.11669e10	−	3.12065e9i	−1.14407	−	0.168671i
$859$		−	1.06603e10i		−	0.573841i	−0.957954	−	0.286920i	$-0.907368\pi$
$859$		−	1.06603e10i		−	0.573841i	0.957954	−	0.286920i	$-0.0926315\pi$
$860$	−8.15581e8	+	2.70586e9i	−0.0437243	+	0.145064i
$861$	2.45265e10			1.30956
$862$	−1.22810e10	−	1.81060e9i	−0.653069	−	0.0962826i
$863$	2.19935e10			1.16481			0.582407	−	0.812898i	$-0.302111\pi$
$863$	2.19935e10			1.16481			0.582407	+	0.812898i	$0.302111\pi$
$864$	−5.08717e8	−	4.56988e8i	−0.0268336	−	0.0241050i
$865$		−	4.36999e8i		−	0.0229575i
$866$	−1.14870e9	+	7.79146e9i	−0.0601029	+	0.407668i
$867$	−9.37202e9			−0.488389
$868$	−2.11283e9	+	7.00975e9i	−0.109659	+	0.363817i
$869$		−	9.75119e9i		−	0.504067i
$870$	2.72885e9	−	1.85093e10i	0.140495	−	0.952957i
$871$			1.96271e9i			0.100645i
$872$	1.04285e10	−	2.22017e10i	0.532618	−	1.13391i
$873$			1.17006e10i			0.595191i
$874$	1.15543e10	−	5.04027e9i	0.585399	−	0.255366i
$875$			1.20181e10i			0.606469i
$876$	7.51934e9	+	2.26643e9i	0.377934	+	0.113914i
$877$			2.98444e10i			1.49405i	0.664797	+	0.747024i	$0.268518\pi$
$877$			2.98444e10i			1.49405i	−0.664797	+	0.747024i	$0.731482\pi$
$878$	−3.76586e9	−	5.55205e8i	−0.187773	−	0.0276836i
$879$			3.73968e10i			1.85726i
$880$	−1.98061e9	+	2.98705e9i	−0.0979738	+	0.147759i
$881$	2.62000e10			1.29088			0.645440	−	0.763811i	$-0.276674\pi$
$881$	2.62000e10			1.29088			0.645440	+	0.763811i	$0.276674\pi$
$882$	−2.34215e9	−	3.45306e8i	−0.114941	−	0.0169459i
$883$			5.98290e9i			0.292448i	0.989251	+	0.146224i	$0.0467121\pi$
$883$			5.98290e9i			0.292448i	−0.989251	+	0.146224i	$0.953288\pi$
$884$	1.09674e10	−	3.63867e10i	0.533976	−	1.77157i
$885$	4.46088e9			0.216331
$886$	3.65883e8	−	2.48172e9i	0.0176736	−	0.119877i
$887$	−1.61623e10			−0.777626			−0.388813	−	0.921317i	$-0.627115\pi$
$887$	−1.61623e10			−0.777626			−0.388813	+	0.921317i	$0.627115\pi$
$888$	1.19705e10	−	2.54845e10i	0.573678	−	1.22133i
$889$		−	1.27534e10i		−	0.608794i
$890$	−6.33284e8	+	4.29546e9i	−0.0301116	+	0.204242i
$891$			1.11750e10i			0.529268i
$892$	−3.77870e10	−	1.13895e10i	−1.78265	−	0.537313i
$893$	1.80649e10	−	1.12684e10i	0.848896	−	0.529519i
$894$	2.25127e10	+	3.31907e9i	1.05377	+	0.155358i
$895$	−3.27681e9			−0.152781
$896$	1.72675e10	−	1.04958e10i	0.801960	−	0.487459i
$897$	3.09191e10			1.43038
$898$	−2.01824e9	+	1.36894e10i	−0.0930049	+	0.630837i
$899$			1.76114e10i			0.808417i
$900$	−1.79968e10	−	5.42448e9i	−0.822899	−	0.248033i
$901$			3.63830e9i			0.165715i
$902$	−1.11812e10	−	1.64845e9i	−0.507299	−	0.0747916i
$903$	−1.28751e10			−0.581894
$904$	6.42226e9	−	1.36726e10i	0.289133	−	0.615547i
$905$			1.11115e10i			0.498313i
$906$	−4.80548e10	−	7.08477e9i	−2.14678	−	0.316502i
$907$	−3.91266e10			−1.74119			−0.870597	−	0.491997i	$-0.836267\pi$
$907$	−3.91266e10			−1.74119			−0.870597	+	0.491997i	$0.836267\pi$
$908$	−4.58771e9	−	1.38280e9i	−0.203374	−	0.0612997i
$909$	−2.47793e10			−1.09425
$910$	1.15506e10	+	1.70291e9i	0.508111	+	0.0749113i
$911$	1.27769e10			0.559900			0.279950	−	0.960015i	$-0.409682\pi$
$911$	1.27769e10			0.559900			0.279950	+	0.960015i	$0.409682\pi$
$912$	−8.94357e8	+	3.21754e10i	−0.0390417	+	1.40457i
$913$	−8.49240e9			−0.369303
$914$	−3.05776e10	−	4.50808e9i	−1.32462	−	0.195290i
$915$	−1.96070e10			−0.846130
$916$	1.79797e10	+	5.41934e9i	0.772946	+	0.232977i
$917$	−3.42249e10			−1.46571
$918$	−9.70982e8	−	1.43153e8i	−0.0414249	−	0.00610732i
$919$			3.67168e10i			1.56049i	0.625476	+	0.780243i	$0.284905\pi$
$919$			3.67168e10i			1.56049i	−0.625476	+	0.780243i	$0.715095\pi$
$920$	2.20199e9	−	4.68791e9i	0.0932307	−	0.198482i
$921$	1.02033e10			0.430361
$922$	1.89466e10	+	2.79331e9i	0.796109	+	0.117371i
$923$			4.43664e10i			1.85716i
$924$	−1.56334e10	−	4.71212e9i	−0.651931	−	0.196501i
$925$			2.03908e10i			0.847107i
$926$	2.29074e9	−	1.55377e10i	0.0948064	−	0.643056i
$927$	2.20237e9			0.0908053
$928$	3.24839e10	−	3.61610e10i	1.33429	−	1.48533i
$929$	2.94042e10			1.20324			0.601622	−	0.798781i	$-0.294521\pi$
$929$	2.94042e10			1.20324			0.601622	+	0.798781i	$0.294521\pi$
$930$	−4.74029e9	−	6.98865e8i	−0.193248	−	0.0284907i
$931$	−1.55390e9	−	2.49114e9i	−0.0631103	−	0.101175i
$932$	1.07461e10	+	3.23901e9i	0.434804	+	0.131056i
$933$		−	4.71055e10i		−	1.89883i
$934$	−4.86675e9	+	3.30104e10i	−0.195445	+	1.32567i
$935$			5.14399e9i			0.205807i
$936$	−1.65645e10	+	3.52649e10i	−0.660258	+	1.40565i
$937$	3.19605e9			0.126918			0.0634592	−	0.997984i	$-0.479787\pi$
$937$	3.19605e9			0.126918			0.0634592	+	0.997984i	$0.479787\pi$
$938$	−2.18467e8	+	1.48183e9i	−0.00864323	+	0.0586256i
$939$	2.67365e10			1.05384
$940$	2.52455e9	−	8.37570e9i	0.0991371	−	0.328907i
$941$		−	1.08078e10i		−	0.422836i	−0.977396	−	0.211418i	$-0.932192\pi$
$941$		−	1.08078e10i		−	0.422836i	0.977396	−	0.211418i	$-0.0678082\pi$
$942$	4.18838e10	+	6.17497e9i	1.63256	+	0.240689i
$943$	1.63327e10			0.634258
$944$	9.65930e9	+	6.40476e9i	0.373718	+	0.247800i
$945$		−	3.01528e8i		−	0.0116230i
$946$	5.86952e9	+	8.65350e8i	0.225416	+	0.0332332i
$947$		−	3.36631e10i		−	1.28804i	−0.765009	−	0.644020i	$-0.777265\pi$
$947$		−	3.36631e10i		−	1.28804i	0.765009	−	0.644020i	$-0.222735\pi$
$948$	−3.44507e10	−	1.03839e10i	−1.31332	−	0.395851i
$949$			1.17892e10i			0.447767i
$950$	−9.32053e9	−	2.13663e10i	−0.352702	−	0.808531i
$951$		−	3.72697e10i		−	1.40516i
$952$	1.23304e10	−	2.62507e10i	0.463179	−	0.986080i
$953$			4.55999e9i			0.170663i	0.996353	+	0.0853313i	$0.0271949\pi$
$953$			4.55999e9i			0.170663i	−0.996353	+	0.0853313i	$0.972805\pi$
$954$	5.44037e8	−	3.69011e9i	0.0202866	−	0.137601i
$955$			7.17845e9i			0.266698i
$956$	−9.75090e9	+	3.23506e10i	−0.360946	+	1.19751i
$957$	−3.92776e10			−1.44862
$958$	5.55113e9	−	3.76524e10i	0.203987	−	1.38361i
$959$		−	3.68114e10i		−	1.34778i
$960$	8.44404e9	+	1.01783e10i	0.308036	+	0.371302i
$961$	−2.30023e10			−0.836063
$962$	4.18141e10	+	6.16469e9i	1.51429	+	0.223254i
$963$	−2.07046e10			−0.747094
$964$	−5.34327e9	+	1.77274e10i	−0.192104	+	0.637345i
$965$			3.71760e9i			0.133173i
$966$	2.33435e10	+	3.44156e9i	0.833196	+	0.122839i
$967$		−	3.80903e10i		−	1.35463i	−0.735691	−	0.677317i	$-0.763143\pi$
$967$		−	3.80903e10i		−	1.35463i	0.735691	−	0.677317i	$-0.236857\pi$
$968$	−1.87327e10	−	8.79907e9i	−0.663798	−	0.311798i
$969$	2.44502e10	+	3.91972e10i	0.863274	+	1.38395i
$970$	−8.69576e8	+	5.89819e9i	−0.0305919	+	0.207500i
$971$	3.45775e10			1.21207			0.606033	−	0.795440i	$-0.292760\pi$
$971$	3.45775e10			1.21207			0.606033	+	0.795440i	$0.292760\pi$
$972$	3.84922e10	+	1.16021e10i	1.34444	+	0.405232i
$973$	−2.97609e10			−1.03574
$974$	−4.55518e9	−	6.71575e8i	−0.157961	−	0.0232883i
$975$		−	5.71760e10i		−	1.97559i
$976$	−4.24557e10	−	2.81510e10i	−1.46171	−	0.969213i
$977$		−	1.31226e10i		−	0.450182i	−0.974338	−	0.225091i	$-0.927732\pi$
$977$		−	1.31226e10i		−	0.450182i	0.974338	−	0.225091i	$-0.0722680\pi$
$978$	−3.59627e8	+	2.43929e9i	−0.0122932	+	0.0833831i
$979$	9.11516e9			0.310474
$980$	−1.15500e9	−	3.48134e8i	−0.0392006	−	0.0118156i
$981$			3.60927e10i			1.22061i
$982$	−3.02347e9	+	2.05077e10i	−0.101886	+	0.691077i
$983$	−3.08571e10			−1.03614			−0.518069	−	0.855339i	$-0.673349\pi$
$983$	−3.08571e10			−1.03614			−0.518069	+	0.855339i	$0.673349\pi$
$984$	−1.77306e10	+	3.77474e10i	−0.593254	+	1.26300i
$985$	−3.85380e9			−0.128488
$986$	1.01757e10	−	6.90199e10i	0.338060	−	2.29301i
$987$	3.98536e10			1.31934
$988$	−4.66323e10	+	1.26534e10i	−1.53829	+	0.417405i
$989$	−8.57379e9			−0.281829
$990$	7.69185e8	−	5.21725e9i	0.0251946	−	0.170891i
$991$	1.42619e10			0.465500			0.232750	−	0.972537i	$-0.425228\pi$
$991$	1.42619e10			0.465500			0.232750	+	0.972537i	$0.425228\pi$
$992$	−9.26091e9	−	8.31921e9i	−0.301206	−	0.270577i
$993$	−2.64206e10			−0.856288
$994$	−4.93837e9	+	3.34961e10i	−0.159489	+	1.08179i
$995$		−	1.04191e10i		−	0.335313i
$996$	−9.04345e9	+	3.00034e10i	−0.290019	+	0.962196i
$997$	4.57776e10			1.46292			0.731460	−	0.681885i	$-0.238839\pi$
$997$	4.57776e10			1.46292			0.731460	+	0.681885i	$0.238839\pi$
$998$	−5.12029e9	+	3.47301e10i	−0.163056	+	1.10598i
$999$		−	1.09156e9i		−	0.0346392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.d.a.75.3	✓	68
4.3	odd	2	inner	76.8.d.a.75.65	yes	68
19.18	odd	2	inner	76.8.d.a.75.66	yes	68
76.75	even	2	inner	76.8.d.a.75.4	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.d.a.75.3	✓	68	1.1	even	1	trivial
76.8.d.a.75.4	yes	68	76.75	even	2	inner
76.8.d.a.75.65	yes	68	4.3	odd	2	inner
76.8.d.a.75.66	yes	68	19.18	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.1927 - 1.65015i) q^{2} -65.7104 q^{3} +(122.554 + 36.9394i) q^{4} -95.9690 q^{5} +(735.478 + 108.432i) q^{6} +851.669i q^{7} +(-1310.76 - 615.686i) q^{8} +2130.86 q^{9} +O(q^{10})\)	\(q+(-11.1927 - 1.65015i) q^{2} -65.7104 q^{3} +(122.554 + 36.9394i) q^{4} -95.9690 q^{5} +(735.478 + 108.432i) q^{6} +851.669i q^{7} +(-1310.76 - 615.686i) q^{8} +2130.86 q^{9} +(1074.15 + 158.364i) q^{10} -2279.40i q^{11} +(-8053.07 - 2427.30i) q^{12} -12626.0i q^{13} +(1405.38 - 9532.49i) q^{14} +6306.16 q^{15} +(13655.0 + 9054.15i) q^{16} +23515.2 q^{17} +(-23850.1 - 3516.24i) q^{18} +(-15823.4 - 25367.2i) q^{19} +(-11761.4 - 3545.04i) q^{20} -55963.5i q^{21} +(-3761.36 + 25512.7i) q^{22} -37267.2i q^{23} +(86130.4 + 40457.0i) q^{24} -68915.0 q^{25} +(-20834.9 + 141319. i) q^{26} +3689.15 q^{27} +(-31460.2 + 104375. i) q^{28} +262235. i q^{29} +(-70583.1 - 10406.1i) q^{30} +67159.0 q^{31} +(-137895. - 123873. i) q^{32} +149780. i q^{33} +(-263199. - 38803.7i) q^{34} -81733.8i q^{35} +(261145. + 78712.7i) q^{36} -295883. i q^{37} +(135247. + 310039. i) q^{38} +829660. i q^{39} +(125792. + 59086.7i) q^{40} +438259. i q^{41} +(-92348.4 + 626384. i) q^{42} -230063. i q^{43} +(84199.8 - 279350. i) q^{44} -204496. q^{45} +(-61496.6 + 417121. i) q^{46} +712136. i q^{47} +(-897273. - 594952. i) q^{48} +98203.2 q^{49} +(771346. + 113720. i) q^{50} -1.54519e6 q^{51} +(466397. - 1.54737e6i) q^{52} +154721. i q^{53} +(-41291.7 - 6087.67i) q^{54} +218752. i q^{55} +(524360. - 1.11633e6i) q^{56} +(1.03976e6 + 1.66689e6i) q^{57} +(432728. - 2.93512e6i) q^{58} +707384. q^{59} +(772845. + 232946. i) q^{60} -3.10918e6 q^{61} +(-751692. - 110823. i) q^{62} +1.81478e6i q^{63} +(1.33901e6 + 1.61403e6i) q^{64} +1.21170e6i q^{65} +(247161. - 1.67645e6i) q^{66} -155450. q^{67} +(2.88188e6 + 868638. i) q^{68} +2.44884e6i q^{69} +(-134873. + 914823. i) q^{70} -3.51389e6 q^{71} +(-2.79304e6 - 1.31194e6i) q^{72} -933723. q^{73} +(-488253. + 3.31174e6i) q^{74} +4.52843e6 q^{75} +(-1.00217e6 - 3.69335e6i) q^{76} +1.94130e6 q^{77} +(1.36907e6 - 9.28615e6i) q^{78} +4.27796e6 q^{79} +(-1.31045e6 - 868917. i) q^{80} -4.90260e6 q^{81} +(723194. - 4.90531e6i) q^{82} -3.72571e6i q^{83} +(2.06726e6 - 6.85855e6i) q^{84} -2.25673e6 q^{85} +(-379639. + 2.57503e6i) q^{86} -1.72315e7i q^{87} +(-1.40340e6 + 2.98774e6i) q^{88} +3.99893e6i q^{89} +(2.28887e6 + 337450. i) q^{90} +1.07532e7 q^{91} +(1.37663e6 - 4.56724e6i) q^{92} -4.41304e6 q^{93} +(1.17513e6 - 7.97074e6i) q^{94} +(1.51855e6 + 2.43446e6i) q^{95} +(9.06116e6 + 8.13977e6i) q^{96} +5.49101e6i q^{97} +(-1.09916e6 - 162050. i) q^{98} -4.85708e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9}+O(q^{10}) \) 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9	\( 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9} + 13050 q^{16} + 23968 q^{17} - 79660 q^{20} - 232154 q^{24} + 937496 q^{25} - 391242 q^{26} - 37666 q^{28} - 468496 q^{30} - 1128652 q^{36} - 530466 q^{38} + 651806 q^{42} + 1433776 q^{44} - 321252 q^{45} - 4014380 q^{49} + 1697586 q^{54} + 137420 q^{57} + 2227894 q^{58} - 3042164 q^{61} + 2261524 q^{62} + 9825150 q^{64} - 749476 q^{66} - 11176962 q^{68} + 598424 q^{73} - 6195964 q^{74} - 1714536 q^{76} - 2556764 q^{77} + 16623216 q^{80} + 43726748 q^{81} - 20460388 q^{82} + 27222844 q^{85} - 61733582 q^{92} + 17778200 q^{93} - 36370886 q^{96}+O(q^{100}) \) 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9 + 13050 * q^16 + 23968 * q^17 - 79660 * q^20 - 232154 * q^24 + 937496 * q^25 - 391242 * q^26 - 37666 * q^28 - 468496 * q^30 - 1128652 * q^36 - 530466 * q^38 + 651806 * q^42 + 1433776 * q^44 - 321252 * q^45 - 4014380 * q^49 + 1697586 * q^54 + 137420 * q^57 + 2227894 * q^58 - 3042164 * q^61 + 2261524 * q^62 + 9825150 * q^64 - 749476 * q^66 - 11176962 * q^68 + 598424 * q^73 - 6195964 * q^74 - 1714536 * q^76 - 2556764 * q^77 + 16623216 * q^80 + 43726748 * q^81 - 20460388 * q^82 + 27222844 * q^85 - 61733582 * q^92 + 17778200 * q^93 - 36370886 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more