LMFDB - Embedded newform 84.6.e.a.71.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,6,Mod(71,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("84.71");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	84.e (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:	$13.4722408643$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.36
Character	$\chi$	$=$	84.71
Dual form			84.6.e.a.71.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.70277 + 5.39449i) q^{2} +(-12.7602 - 8.95421i) q^{3} +(-26.2011 + 18.3712i) q^{4} +95.2519i q^{5} +(26.5758 - 84.0817i) q^{6} -49.0000i q^{7} +(-143.718 - 110.060i) q^{8} +(82.6442 + 228.515i) q^{9} +(-513.836 + 162.192i) q^{10} -125.966 q^{11} +(498.831 + 0.191203i) q^{12} -253.495 q^{13} +(264.330 - 83.4357i) q^{14} +(852.905 - 1215.43i) q^{15} +(349.000 - 962.691i) q^{16} -1112.95i q^{17} +(-1092.00 + 834.932i) q^{18} -1557.48i q^{19} +(-1749.89 - 2495.71i) q^{20} +(-438.756 + 625.249i) q^{21} +(-214.491 - 679.523i) q^{22} -237.367 q^{23} +(848.362 + 2691.26i) q^{24} -5947.92 q^{25} +(-431.643 - 1367.48i) q^{26} +(991.613 - 3655.90i) q^{27} +(900.187 + 1283.86i) q^{28} -7326.00i q^{29} +(8008.94 + 2531.39i) q^{30} +7619.67i q^{31} +(5787.50 + 243.437i) q^{32} +(1607.35 + 1127.93i) q^{33} +(6003.79 - 1895.09i) q^{34} +4667.34 q^{35} +(-6363.45 - 4469.07i) q^{36} -2788.72 q^{37} +(8401.79 - 2652.02i) q^{38} +(3234.64 + 2269.85i) q^{39} +(10483.4 - 13689.4i) q^{40} +18108.6i q^{41} +(-4120.00 - 1302.21i) q^{42} -6773.38i q^{43} +(3300.45 - 2314.14i) q^{44} +(-21766.4 + 7872.02i) q^{45} +(-404.182 - 1280.48i) q^{46} -19971.7 q^{47} +(-13073.4 + 9159.09i) q^{48} -2401.00 q^{49} +(-10127.9 - 32086.0i) q^{50} +(-9965.56 + 14201.4i) q^{51} +(6641.85 - 4657.00i) q^{52} +18968.3i q^{53} +(21410.2 - 875.907i) q^{54} -11998.5i q^{55} +(-5392.94 + 7042.17i) q^{56} +(-13946.0 + 19873.7i) q^{57} +(39520.0 - 12474.5i) q^{58} -43286.1 q^{59} +(-18.2124 + 47514.6i) q^{60} +12386.7 q^{61} +(-41104.3 + 12974.6i) q^{62} +(11197.2 - 4049.57i) q^{63} +(8541.56 + 31635.2i) q^{64} -24145.9i q^{65} +(-3347.64 + 10591.4i) q^{66} -49209.6i q^{67} +(20446.1 + 29160.5i) q^{68} +(3028.85 + 2125.43i) q^{69} +(7947.41 + 25178.0i) q^{70} +31069.0 q^{71} +(13272.9 - 41937.4i) q^{72} -45958.4 q^{73} +(-4748.55 - 15043.7i) q^{74} +(75896.5 + 53259.0i) q^{75} +(28612.6 + 40807.6i) q^{76} +6172.33i q^{77} +(-6736.82 + 21314.3i) q^{78} -81796.8i q^{79} +(91698.2 + 33242.9i) q^{80} +(-45388.9 + 37770.8i) q^{81} +(-97686.5 + 30834.7i) q^{82} -57577.8 q^{83} +(9.36893 - 24442.7i) q^{84} +106010. q^{85} +(36539.0 - 11533.5i) q^{86} +(-65598.5 + 93481.0i) q^{87} +(18103.5 + 13863.8i) q^{88} +120380. i q^{89} +(-79528.8 - 104015. i) q^{90} +12421.2i q^{91} +(6219.29 - 4360.71i) q^{92} +(68228.2 - 97228.4i) q^{93} +(-34007.2 - 107737. i) q^{94} +148352. q^{95} +(-71669.8 - 54928.8i) q^{96} +25284.0 q^{97} +(-4088.35 - 12952.2i) q^{98} +(-10410.4 - 28785.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 20 q^{4} - 114 q^{6} + 44 q^{9} + 668 q^{10} + 786 q^{12} - 3004 q^{16} - 3320 q^{18} + 7120 q^{22} + 16466 q^{24} - 37500 q^{25} - 7448 q^{28} - 35236 q^{30} - 9424 q^{33} + 43360 q^{34} + 50524 q^{36}+ \cdots + 232584 q^{97}+O(q^{100}) $ 60 * q - 20 * q^4 - 114 * q^6 + 44 * q^9 + 668 * q^10 + 786 * q^12 - 3004 * q^16 - 3320 * q^18 + 7120 * q^22 + 16466 * q^24 - 37500 * q^25 - 7448 * q^28 - 35236 * q^30 - 9424 * q^33 + 43360 * q^34 + 50524 * q^36 - 15056 * q^37 - 35468 * q^40 - 20090 * q^42 + 36024 * q^45 + 124416 * q^46 + 88654 * q^48 - 144060 * q^49 - 140108 * q^52 + 19486 * q^54 - 65072 * q^57 + 115616 * q^58 + 164908 * q^60 - 169424 * q^61 + 20116 * q^64 - 98484 * q^66 + 142536 * q^69 + 35868 * q^70 + 121312 * q^72 + 107256 * q^73 + 214836 * q^76 + 263708 * q^78 - 114932 * q^81 - 479624 * q^82 + 40474 * q^84 - 383992 * q^85 - 107320 * q^88 + 423760 * q^90 + 545208 * q^93 - 448512 * q^94 - 751618 * q^96 + 232584 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.70277	+	5.39449i	0.301010	+	0.953621i
$2$	1.70277	+	5.39449i	0.301010	+	0.953621i
$3$	−12.7602	−	8.95421i	−0.818566	−	0.574413i
$3$	−12.7602	−	8.95421i	−0.818566	−	0.574413i
$4$	−26.2011	+	18.3712i	−0.818786	+	0.574099i
$5$			95.2519i			1.70392i	0.523609	+	0.851959i	$0.324585\pi$
$5$			95.2519i			1.70392i	−0.523609	+	0.851959i	$0.675415\pi$
$6$	26.5758	−	84.0817i	0.301376	−	0.953506i
$7$		−	49.0000i		−	0.377964i
$7$		−	49.0000i		−	0.377964i
$8$	−143.718	−	110.060i	−0.793936	−	0.608002i
$9$	82.6442	+	228.515i	0.340100	+	0.940389i
$10$	−513.836	+	162.192i	−1.62489	+	0.512896i
$11$	−125.966			−0.313886			−0.156943	−	0.987608i	$-0.550164\pi$
$11$	−125.966			−0.313886			−0.156943	+	0.987608i	$0.550164\pi$
$12$	498.831	+	0.191203i	1.00000	+	0.000383302i
$13$	−253.495			−0.416017			−0.208008	−	0.978127i	$-0.566698\pi$
$13$	−253.495			−0.416017			−0.208008	+	0.978127i	$0.566698\pi$
$14$	264.330	−	83.4357i	0.360435	−	0.113771i
$15$	852.905	−	1215.43i	0.978752	−	1.39477i
$16$	349.000	−	962.691i	0.340820	−	0.940128i
$17$		−	1112.95i		−	0.934011i	−0.884254	−	0.467006i	$-0.845333\pi$
$17$		−	1112.95i		−	0.934011i	0.884254	−	0.467006i	$-0.154667\pi$
$18$	−1092.00	+	834.932i	−0.794402	+	0.607393i
$19$		−	1557.48i		−	0.989777i	−0.868957	−	0.494888i	$-0.835209\pi$
$19$		−	1557.48i		−	0.989777i	0.868957	−	0.494888i	$-0.164791\pi$
$20$	−1749.89	−	2495.71i	−0.978218	−	1.39514i
$21$	−438.756	+	625.249i	−0.217108	+	0.309389i
$22$	−214.491	−	679.523i	−0.0944827	−	0.299328i
$23$	−237.367			−0.0935623			−0.0467811	−	0.998905i	$-0.514896\pi$
$23$	−237.367			−0.0935623			−0.0467811	+	0.998905i	$0.514896\pi$
$24$	848.362	+	2691.26i	0.300645	+	0.953736i
$25$	−5947.92			−1.90334
$26$	−431.643	−	1367.48i	−0.125225	−	0.396722i
$27$	991.613	−	3655.90i	0.261778	−	0.965128i
$28$	900.187	+	1283.86i	0.216989	+	0.309472i
$29$		−	7326.00i		−	1.61760i	−0.588082	−	0.808801i	$-0.700117\pi$
$29$		−	7326.00i		−	1.61760i	0.588082	−	0.808801i	$-0.299883\pi$
$30$	8008.94	+	2531.39i	1.62469	+	0.513519i
$31$			7619.67i			1.42407i	0.702143	+	0.712036i	$0.252227\pi$
$31$			7619.67i			1.42407i	−0.702143	+	0.712036i	$0.747773\pi$
$32$	5787.50	+	243.437i	0.999117	+	0.0420254i
$33$	1607.35	+	1127.93i	0.256936	+	0.180300i
$34$	6003.79	−	1895.09i	0.890693	−	0.281147i
$35$	4667.34			0.644020
$36$	−6363.45	−	4469.07i	−0.818345	−	0.574727i
$37$	−2788.72			−0.334889			−0.167444	−	0.985882i	$-0.553551\pi$
$37$	−2788.72			−0.334889			−0.167444	+	0.985882i	$0.553551\pi$
$38$	8401.79	−	2652.02i	0.943872	−	0.297933i
$39$	3234.64	+	2269.85i	0.340537	+	0.238965i
$40$	10483.4	−	13689.4i	1.03598	−	1.35280i
$41$			18108.6i			1.68238i	0.540740	+	0.841190i	$0.318144\pi$
$41$			18108.6i			1.68238i	−0.540740	+	0.841190i	$0.681856\pi$
$42$	−4120.00	−	1302.21i	−0.360391	−	0.113909i
$43$		−	6773.38i		−	0.558643i	−0.960198	−	0.279321i	$-0.909891\pi$
$43$		−	6773.38i		−	0.558643i	0.960198	−	0.279321i	$-0.0901095\pi$
$44$	3300.45	−	2314.14i	0.257005	−	0.180201i
$45$	−21766.4	+	7872.02i	−1.60235	+	0.579502i
$46$	−404.182	−	1280.48i	−0.0281632	−	0.0892230i
$47$	−19971.7			−1.31877			−0.659386	−	0.751804i	$-0.729184\pi$
$47$	−19971.7			−1.31877			−0.659386	+	0.751804i	$0.729184\pi$
$48$	−13073.4	+	9159.09i	−0.819006	+	0.573785i
$49$	−2401.00			−0.142857
$50$	−10127.9	−	32086.0i	−0.572923	−	1.81506i
$51$	−9965.56	+	14201.4i	−0.536508	+	0.764550i
$52$	6641.85	−	4657.00i	0.340628	−	0.238835i
$53$			18968.3i			0.927555i	0.885952	+	0.463777i	$0.153506\pi$
$53$			18968.3i			0.927555i	−0.885952	+	0.463777i	$0.846494\pi$
$54$	21410.2	−	875.907i	0.999164	−	0.0408765i
$55$		−	11998.5i		−	0.534835i
$56$	−5392.94	+	7042.17i	−0.229803	+	0.300079i
$57$	−13946.0	+	19873.7i	−0.568540	+	0.810197i
$58$	39520.0	−	12474.5i	1.54258	−	0.486915i
$59$	−43286.1			−1.61889			−0.809447	−	0.587192i	$-0.800233\pi$
$59$	−43286.1			−1.61889			−0.809447	+	0.587192i	$0.800233\pi$
$60$	−18.2124	+	47514.6i	−0.000653115	+	1.70392i
$61$	12386.7			0.426218			0.213109	−	0.977028i	$-0.431641\pi$
$61$	12386.7			0.426218			0.213109	+	0.977028i	$0.431641\pi$
$62$	−41104.3	+	12974.6i	−1.35803	+	0.428660i
$63$	11197.2	−	4049.57i	0.355434	−	0.128546i
$64$	8541.56	+	31635.2i	0.260668	+	0.965429i
$65$		−	24145.9i		−	0.708858i
$66$	−3347.64	+	10591.4i	−0.0945975	+	0.299292i
$67$		−	49209.6i		−	1.33925i	−0.742697	−	0.669627i	$-0.766454\pi$
$67$		−	49209.6i		−	1.33925i	0.742697	−	0.669627i	$-0.233546\pi$
$68$	20446.1	+	29160.5i	0.536215	+	0.764755i
$69$	3028.85	+	2125.43i	0.0765869	+	0.0537434i
$70$	7947.41	+	25178.0i	0.193857	+	0.614151i
$71$	31069.0			0.731445			0.365723	−	0.930724i	$-0.380822\pi$
$71$	31069.0			0.731445			0.365723	+	0.930724i	$0.380822\pi$
$72$	13272.9	−	41937.4i	0.301741	−	0.953390i
$73$	−45958.4			−1.00939			−0.504693	−	0.863299i	$-0.668394\pi$
$73$	−45958.4			−1.00939			−0.504693	+	0.863299i	$0.668394\pi$
$74$	−4748.55	−	15043.7i	−0.100805	−	0.319357i
$75$	75896.5	+	53259.0i	1.55801	+	1.09330i
$76$	28612.6	+	40807.6i	0.568230	+	0.810415i
$77$			6172.33i			0.118638i
$78$	−6736.82	+	21314.3i	−0.125377	+	0.396674i
$79$		−	81796.8i		−	1.47458i	−0.675576	−	0.737290i	$-0.736105\pi$
$79$		−	81796.8i		−	1.47458i	0.675576	−	0.737290i	$-0.263895\pi$
$80$	91698.2	+	33242.9i	1.60190	+	0.580730i
$81$	−45388.9	+	37770.8i	−0.768664	+	0.639652i
$82$	−97686.5	+	30834.7i	−1.60435	+	0.506413i
$83$	−57577.8			−0.917402			−0.458701	−	0.888591i	$-0.651685\pi$
$83$	−57577.8			−0.917402			−0.458701	+	0.888591i	$0.651685\pi$
$84$	9.36893	−	24442.7i	0.000144874	−	0.377964i
$85$	106010.			1.59148
$86$	36539.0	−	11533.5i	0.532733	−	0.168157i
$87$	−65598.5	+	93481.0i	−0.929171	+	1.32411i
$88$	18103.5	+	13863.8i	0.249205	+	0.190843i
$89$			120380.i			1.61094i	0.592633	+	0.805472i	$0.298088\pi$
$89$			120380.i			1.61094i	−0.592633	+	0.805472i	$0.701912\pi$
$90$	−79528.8	−	104015.i	−1.03495	−	1.35359i
$91$			12421.2i			0.157239i
$92$	6219.29	−	4360.71i	0.0766075	−	0.0537140i
$93$	68228.2	−	97228.4i	0.818006	−	1.16570i
$94$	−34007.2	−	107737.i	−0.396964	−	1.25761i
$95$	148352.			1.68650
$96$	−71669.8	−	54928.8i	−0.793703	−	0.608306i
$97$	25284.0			0.272846			0.136423	−	0.990651i	$-0.456439\pi$
$97$	25284.0			0.272846			0.136423	+	0.990651i	$0.456439\pi$
$98$	−4088.35	−	12952.2i	−0.0430014	−	0.136232i
$99$	−10410.4	−	28785.1i	−0.106752	−	0.295175i
$100$	155842.	−	109270.i	1.55842	−	1.09270i
$101$		−	127952.i		−	1.24809i	−0.781390	−	0.624043i	$-0.785489\pi$
$101$		−	127952.i		−	1.24809i	0.781390	−	0.624043i	$-0.214511\pi$
$102$	−93578.4	−	29577.4i	−0.890585	−	0.281488i
$103$			82379.9i			0.765118i	0.923931	+	0.382559i	$0.124957\pi$
$103$			82379.9i			0.765118i	−0.923931	+	0.382559i	$0.875043\pi$
$104$	36431.7	+	27899.6i	0.330290	+	0.252939i
$105$	−59556.1	−	41792.4i	−0.527173	−	0.369934i
$106$	−102325.	+	32298.7i	−0.884535	+	0.279203i
$107$	−154742.			−1.30662			−0.653309	−	0.757091i	$-0.726620\pi$
$107$	−154742.			−1.30662			−0.653309	+	0.757091i	$0.726620\pi$
$108$	41181.8	+	114006.i	0.339739	+	0.940520i
$109$	52980.6			0.427121			0.213560	−	0.976930i	$-0.431494\pi$
$109$	52980.6			0.427121			0.213560	+	0.976930i	$0.431494\pi$
$110$	64725.8	−	20430.7i	0.510030	−	0.160991i
$111$	35584.6	+	24970.8i	0.274129	+	0.192364i
$112$	−47171.9	−	17101.0i	−0.355335	−	0.128818i
$113$		−	112019.i		−	0.825270i	−0.910896	−	0.412635i	$-0.864609\pi$
$113$		−	112019.i		−	0.825270i	0.910896	−	0.412635i	$-0.135391\pi$
$114$	−130955.	−	41391.1i	−0.943757	−	0.298295i
$115$		−	22609.7i		−	0.159422i
$116$	134587.	+	191949.i	0.928664	+	1.32447i
$117$	−20949.9	−	57927.3i	−0.141487	−	0.391218i
$118$	−73706.3	−	233507.i	−0.487304	−	1.54381i
$119$	−54534.4			−0.353023
$120$	−256348.	+	80808.1i	−1.62509	+	0.512274i
$121$	−145184.			−0.901476
$122$	21091.7	+	66820.1i	0.128296	+	0.406450i
$123$	162148.	−	231068.i	0.966381	−	1.37714i
$124$	−139982.	−	199644.i	−0.817559	−	1.16601i
$125$		−	268889.i		−	1.53921i
$126$	40911.7	+	53507.8i	0.229573	+	0.300256i
$127$		−	15421.2i		−	0.0848418i	−0.999100	−	0.0424209i	$-0.986493\pi$
$127$		−	15421.2i		−	0.0848418i	0.999100	−	0.0424209i	$-0.0135071\pi$
$128$	−156111.	+	99944.8i	−0.842189	+	0.539182i
$129$	−60650.3	+	86429.5i	−0.320892	+	0.457286i
$130$	130255.	−	41114.8i	0.675982	−	0.213373i
$131$	−21670.4			−0.110329			−0.0551643	−	0.998477i	$-0.517568\pi$
$131$	−21670.4			−0.110329			−0.0551643	+	0.998477i	$0.517568\pi$
$132$	−62835.7	−	24.0850i	−0.313886	−	0.000120313i
$133$	−76316.3			−0.374100
$134$	265461.	−	83792.7i	1.27714	−	0.403129i
$135$	348231.	+	94453.0i	1.64450	+	0.446048i
$136$	−122491.	+	159950.i	−0.567881	+	0.741545i
$137$		−	89679.3i		−	0.408217i	−0.978948	−	0.204108i	$-0.934571\pi$
$137$		−	89679.3i		−	0.408217i	0.978948	−	0.204108i	$-0.0654295\pi$
$138$	−6308.22	+	19958.2i	−0.0281974	+	0.0892122i
$139$			301465.i			1.32343i	0.749756	+	0.661714i	$0.230171\pi$
$139$			301465.i			1.32343i	−0.749756	+	0.661714i	$0.769829\pi$
$140$	−122290.	+	85744.5i	−0.527315	+	0.369731i
$141$	254842.	+	178831.i	1.07950	+	0.757520i
$142$	52903.4	+	167602.i	0.220172	+	0.697522i
$143$	31931.7			0.130582
$144$	248832.	+	190.756i	1.00000	+	0.000766604i
$145$	697815.			2.75626
$146$	−78256.5	−	247922.i	−0.303835	−	0.962572i
$147$	30637.2	+	21499.1i	0.116938	+	0.0820590i
$148$	73067.7	−	51232.1i	0.274202	−	0.192259i
$149$			133822.i			0.493811i	0.969040	+	0.246905i	$0.0794137\pi$
$149$			133822.i			0.493811i	−0.969040	+	0.246905i	$0.920586\pi$
$150$	−158071.	+	500111.i	−0.573619	+	1.81484i
$151$			173559.i			0.619447i	0.950827	+	0.309724i	$0.100237\pi$
$151$			173559.i			0.619447i	−0.950827	+	0.309724i	$0.899763\pi$
$152$	−171416.	+	223837.i	−0.601786	+	0.785819i
$153$	254325.	−	91978.6i	0.878334	−	0.317657i
$154$	−33296.6	+	10510.1i	−0.113135	+	0.0357111i
$155$	−725788.			−2.42650
$156$	−126451.	−	48.4689i	−0.416017	−	0.000159460i
$157$	52362.6			0.169540			0.0847700	−	0.996401i	$-0.472984\pi$
$157$	52362.6			0.169540			0.0847700	+	0.996401i	$0.472984\pi$
$158$	441252.	−	139281.i	1.40619	−	0.443864i
$159$	169846.	−	242039.i	0.532799	−	0.759264i
$160$	−23187.9	+	551270.i	−0.0716079	+	1.70241i
$161$			11631.0i			0.0353632i
$162$	−281041.	−	180535.i	−0.841362	−	0.540473i
$163$		−	215621.i		−	0.635655i	−0.948149	−	0.317827i	$-0.897047\pi$
$163$		−	215621.i		−	0.635655i	0.948149	−	0.317827i	$-0.102953\pi$
$164$	−332675.	−	474465.i	−0.965853	−	1.37751i
$165$	−107437.	+	153103.i	−0.307216	+	0.437798i
$166$	−98041.7	−	310603.i	−0.276147	−	0.874853i
$167$	−127451.			−0.353632			−0.176816	−	0.984244i	$-0.556580\pi$
$167$	−127451.			−0.353632			−0.176816	+	0.984244i	$0.556580\pi$
$168$	131872.	−	41569.8i	0.360478	−	0.113633i
$169$	−307033.			−0.826930
$170$	180511.	+	571872.i	0.479051	+	1.51767i
$171$	355906.	−	128716.i	0.930775	−	0.336623i
$172$	124435.	+	177470.i	0.320716	+	0.457409i
$173$			239913.i			0.609450i	0.952440	+	0.304725i	$0.0985645\pi$
$173$			239913.i			0.609450i	−0.952440	+	0.304725i	$0.901436\pi$
$174$	−615982.	−	194694.i	−1.54239	−	0.487506i
$175$			291448.i			0.719393i
$176$	−43962.1	+	121266.i	−0.106979	+	0.295093i
$177$	552339.	+	387593.i	1.32517	+	0.929914i
$178$	−649391.	+	204980.i	−1.53623	+	0.484911i
$179$	−249966.			−0.583106			−0.291553	−	0.956555i	$-0.594172\pi$
$179$	−249966.			−0.583106			−0.291553	+	0.956555i	$0.594172\pi$
$180$	425688.	−	606131.i	0.979287	−	1.39439i
$181$	−498914.			−1.13195			−0.565977	−	0.824421i	$-0.691501\pi$
$181$	−498914.			−1.13195			−0.565977	+	0.824421i	$0.691501\pi$
$182$	−67006.3	+	21150.5i	−0.149947	+	0.0473307i
$183$	−158057.	−	110913.i	−0.348887	−	0.244825i
$184$	34113.8	+	26124.6i	0.0742824	+	0.0568860i
$185$		−	265631.i		−	0.570623i
$186$	640675.	+	202499.i	1.35786	+	0.429181i
$187$			140193.i			0.293173i
$188$	523281.	−	366903.i	1.07979	−	0.757106i
$189$	−179139.	−	48589.0i	−0.364784	−	0.0989427i
$190$	252610.	+	800287.i	0.507653	+	1.60828i
$191$	272338.			0.540164			0.270082	−	0.962837i	$-0.412949\pi$
$191$	272338.			0.540164			0.270082	+	0.962837i	$0.412949\pi$
$192$	174276.	−	480153.i	0.341181	−	0.939998i
$193$	254707.			0.492207			0.246104	−	0.969244i	$-0.420850\pi$
$193$	254707.			0.492207			0.246104	+	0.969244i	$0.420850\pi$
$194$	43052.9	+	136395.i	0.0821293	+	0.260191i
$195$	−216207.	+	308105.i	−0.407177	+	0.580247i
$196$	62909.0	−	44109.2i	0.116969	−	0.0820142i
$197$		−	260028.i		−	0.477370i	−0.971097	−	0.238685i	$-0.923284\pi$
$197$		−	260028.i		−	0.477370i	0.971097	−	0.238685i	$-0.0767163\pi$
$198$	137554.	−	105173.i	0.249351	−	0.190652i
$199$		−	788079.i		−	1.41071i	−0.708855	−	0.705354i	$-0.750788\pi$
$199$		−	788079.i		−	1.41071i	0.708855	−	0.705354i	$-0.249212\pi$
$200$	854822.	+	654629.i	1.51113	+	1.15723i
$201$	−440633.	+	627924.i	−0.769285	+	1.09627i
$202$	690238.	−	217873.i	1.19020	−	0.375687i
$203$	−358974.			−0.611396
$204$	212.798	−	555172.i	0.000358008	−	0.934011i
$205$	−1.72487e6			−2.86664
$206$	−444398.	+	140274.i	−0.729632	+	0.230308i
$207$	−19617.0	−	54241.8i	−0.0318205	−	0.0879850i
$208$	−88469.7	+	244037.i	−0.141787	+	0.391109i
$209$			196189.i			0.310677i
$210$	124038.	−	392438.i	0.194092	−	0.614077i
$211$			215899.i			0.333845i	0.985970	+	0.166923i	$0.0533830\pi$
$211$			215899.i			0.333845i	−0.985970	+	0.166923i	$0.946617\pi$
$212$	−348470.	−	496992.i	−0.532508	−	0.759469i
$213$	−396446.	−	278199.i	−0.598736	−	0.420152i
$214$	−263490.	−	834755.i	−0.393305	−	1.24602i
$215$	645177.			0.951881
$216$	−544881.	+	416281.i	−0.794634	+	0.607088i
$217$	373364.			0.538249
$218$	90213.8	+	285803.i	0.128568	+	0.407311i
$219$	586437.	+	411521.i	0.826249	+	0.579804i
$220$	220426.	+	314374.i	0.307048	+	0.437915i
$221$			282126.i			0.388564i
$222$	−74112.5	+	234480.i	−0.100927	+	0.319318i
$223$			827504.i			1.11432i	0.830407	+	0.557158i	$0.188108\pi$
$223$			827504.i			1.11432i	−0.830407	+	0.557158i	$0.811892\pi$
$224$	11928.4	−	283588.i	0.0158841	−	0.377631i
$225$	−491561.	−	1.35919e6i	−0.647324	−	1.78988i
$226$	604287.	−	190743.i	0.786995	−	0.248415i
$227$	−1.00379e6			−1.29295			−0.646473	−	0.762937i	$-0.723757\pi$
$227$	−1.00379e6			−1.29295			−0.646473	+	0.762937i	$0.723757\pi$
$228$	297.794	−	776916.i	0.000379383	−	0.989777i
$229$	−461802.			−0.581925			−0.290962	−	0.956734i	$-0.593975\pi$
$229$	−461802.			−0.581925			−0.290962	+	0.956734i	$0.593975\pi$
$230$	121968.	−	38499.1i	0.152029	−	0.0479878i
$231$	55268.3	−	78760.0i	0.0681470	−	0.0971127i
$232$	−806300.	+	1.05288e6i	−0.983505	+	1.28427i
$233$			663502.i			0.800668i	0.916369	+	0.400334i	$0.131106\pi$
$233$			663502.i			0.800668i	−0.916369	+	0.400334i	$0.868894\pi$
$234$	276815.	−	211651.i	0.330484	−	0.252685i
$235$		−	1.90234e6i		−	2.24708i
$236$	1.13415e6	−	795217.i	1.32553	−	0.929406i
$237$	−732426.	+	1.04374e6i	−0.847018	+	1.20704i
$238$	−92859.6	−	294186.i	−0.106264	−	0.336650i
$239$	−1.20218e6			−1.36136			−0.680682	−	0.732579i	$-0.738316\pi$
$239$	−1.20218e6			−1.36136			−0.680682	+	0.732579i	$0.738316\pi$
$240$	−872421.	−	1.24527e6i	−0.977683	−	1.39552i
$241$	1.03987e6			1.15329			0.576644	−	0.816996i	$-0.304362\pi$
$241$	1.03987e6			1.15329			0.576644	+	0.816996i	$0.304362\pi$
$242$	−247214.	−	783192.i	−0.271353	−	0.859666i
$243$	917378.	−	75541.0i	0.996627	−	0.0820667i
$244$	−324546.	+	227558.i	−0.348981	+	0.244691i
$245$		−	228700.i		−	0.243417i
$246$	1.52260e6	+	481249.i	1.60416	+	0.507028i
$247$			394812.i			0.411763i
$248$	838622.	−	1.09508e6i	0.865839	−	1.13062i
$249$	734702.	+	515563.i	0.750953	+	0.526967i
$250$	1.45052e6	−	457856.i	1.46782	−	0.463317i
$251$	976908.			0.978745			0.489373	−	0.872075i	$-0.337226\pi$
$251$	976908.			0.978745			0.489373	+	0.872075i	$0.337226\pi$
$252$	−218985.	+	311809.i	−0.217226	+	0.309306i
$253$	29900.2			0.0293679
$254$	83189.8	−	26258.8i	0.0809070	−	0.0255383i
$255$	−1.35271e6	−	949239.i	−1.30273	−	0.914166i
$256$	−804974.	−	671959.i	−0.767683	−	0.640830i
$257$		−	559824.i		−	0.528711i	−0.964425	−	0.264356i	$-0.914841\pi$
$257$		−	559824.i		−	0.528711i	0.964425	−	0.264356i	$-0.0851593\pi$
$258$	−569517.	−	180008.i	−0.532669	−	0.168361i
$259$			136647.i			0.126576i
$260$	443588.	+	632649.i	0.406955	+	0.580403i
$261$	1.67410e6	−	605451.i	1.52118	−	0.550146i
$262$	−36899.7	−	116901.i	−0.0332100	−	0.105212i
$263$	1.53013e6			1.36408			0.682039	−	0.731316i	$-0.261094\pi$
$263$	1.53013e6			1.36408			0.682039	+	0.731316i	$0.261094\pi$
$264$	−106865.	−	339008.i	−0.0943680	−	0.299364i
$265$	−1.80677e6			−1.58048
$266$	−129949.	−	411688.i	−0.112608	−	0.356750i
$267$	1.07791e6	−	1.53608e6i	0.925348	−	1.31866i
$268$	904039.	+	1.28935e6i	0.768865	+	1.09656i
$269$		−	164637.i		−	0.138722i	−0.997592	−	0.0693612i	$-0.977904\pi$
$269$		−	164637.i		−	0.138722i	0.997592	−	0.0693612i	$-0.0220961\pi$
$270$	83431.8	+	2.03936e6i	0.0696502	+	1.70249i
$271$			1.37484e6i			1.13718i	0.822621	+	0.568590i	$0.192511\pi$
$271$			1.37484e6i			1.13718i	−0.822621	+	0.568590i	$0.807489\pi$
$272$	−1.07142e6	−	388419.i	−0.878091	−	0.318330i
$273$	111222.	−	158497.i	0.0903204	−	0.128711i
$274$	483774.	−	152703.i	0.389284	−	0.122877i
$275$	749236.			0.597430
$276$	−118406.	−	45.3852i	−0.0935623	−	3.58626e-5i
$277$	1.28296e6			1.00464			0.502322	−	0.864681i	$-0.332479\pi$
$277$	1.28296e6			1.00464			0.502322	+	0.864681i	$0.332479\pi$
$278$	−1.62625e6	+	513326.i	−1.26205	+	0.398365i
$279$	−1.74121e6	+	629722.i	−1.33918	+	0.484327i
$280$	−670780.	−	513688.i	−0.511311	−	0.391565i
$281$			2.53555e6i			1.91561i	0.287423	+	0.957804i	$0.407202\pi$
$281$			2.53555e6i			1.91561i	−0.287423	+	0.957804i	$0.592798\pi$
$282$	−530763.	+	1.67925e6i	−0.397446	+	1.25746i
$283$			2.22499e6i			1.65143i	0.564085	+	0.825717i	$0.309229\pi$
$283$			2.22499e6i			1.65143i	−0.564085	+	0.825717i	$0.690771\pi$
$284$	−814044.	+	570775.i	−0.598897	+	0.419922i
$285$	−1.89300e6	−	1.32838e6i	−1.38051	−	0.968746i
$286$	54372.4	+	172255.i	0.0393064	+	0.124525i
$287$	887319.			0.635880
$288$	422675.	+	1.34265e6i	0.300279	+	0.953851i
$289$	181206.			0.127623
$290$	1.18822e6	+	3.76436e6i	0.829662	+	2.62843i
$291$	−322629.	−	226399.i	−0.223342	−	0.156726i
$292$	1.20416e6	−	844309.i	0.826471	−	0.579488i
$293$		−	2.05621e6i		−	1.39926i	−0.714505	−	0.699630i	$-0.753348\pi$
$293$		−	2.05621e6i		−	1.39926i	0.714505	−	0.699630i	$-0.246652\pi$
$294$	−63808.5	+	201880.i	−0.0430537	+	0.136215i
$295$		−	4.12308e6i		−	2.75846i
$296$	400789.	+	306927.i	0.265880	+	0.203613i
$297$	−124909.	+	460519.i	−0.0821683	+	0.302940i
$298$	−721900.	+	227867.i	−0.470908	+	0.148642i
$299$	60171.3			0.0389235
$300$	−2.96701e6	−	1137.26i	−1.90334	−	0.000729552i
$301$	−331896.			−0.211147
$302$	−936262.	+	295531.i	−0.590718	+	0.186460i
$303$	−1.14571e6	+	1.63269e6i	−0.716917	+	1.02164i
$304$	−1.49937e6	−	543559.i	−0.930517	−	0.337336i
$305$			1.17986e6i			0.726240i
$306$	929235.	+	1.21533e6i	0.567312	+	0.741980i
$307$		−	565239.i		−	0.342283i	−0.985246	−	0.171142i	$-0.945254\pi$
$307$		−	565239.i		−	0.342283i	0.985246	−	0.171142i	$-0.0547456\pi$
$308$	−113393.	−	161722.i	−0.0681097	−	0.0971388i
$309$	737647.	−	1.05118e6i	0.439493	−	0.626299i
$310$	−1.23585e6	−	3.91526e6i	−0.730402	−	2.31396i
$311$	−1.85540e6			−1.08777			−0.543885	−	0.839160i	$-0.683047\pi$
$311$	−1.85540e6			−1.08777			−0.543885	+	0.839160i	$0.683047\pi$
$312$	−215055.	−	682221.i	−0.125073	−	0.396770i
$313$	761909.			0.439585			0.219792	−	0.975547i	$-0.429462\pi$
$313$	761909.			0.439585			0.219792	+	0.975547i	$0.429462\pi$
$314$	89161.5	+	282470.i	0.0510333	+	0.161677i
$315$	385729.	+	1.06656e6i	0.219031	+	0.605630i
$316$	1.50270e6	+	2.14317e6i	0.846555	+	1.20737i
$317$		−	422323.i		−	0.236046i	−0.993011	−	0.118023i	$-0.962344\pi$
$317$		−	422323.i		−	0.236046i	0.993011	−	0.118023i	$-0.0376557\pi$
$318$	1.59489e6	+	504098.i	0.884428	+	0.279542i
$319$			922826.i			0.507742i
$320$	−3.01331e6	+	813600.i	−1.64501	+	0.444157i
$321$	1.97454e6	+	1.38559e6i	1.06955	+	0.750539i
$322$	−62743.3	+	19804.9i	−0.0337231	+	0.0106447i
$323$	−1.73339e6			−0.924463
$324$	495346.	−	1.82349e6i	0.262148	−	0.965028i
$325$	1.50777e6			0.791819
$326$	1.16316e6	−	367152.i	0.606174	−	0.191338i
$327$	−676042.	−	474399.i	−0.349626	−	0.245344i
$328$	1.99303e6	−	2.60252e6i	1.02289	−	1.33570i
$329$			978612.i			0.498449i
$330$	−1.00885e6	−	318869.i	−0.509968	−	0.161186i
$331$			2.39137e6i			1.19971i	0.800107	+	0.599857i	$0.204776\pi$
$331$			2.39137e6i			1.19971i	−0.800107	+	0.599857i	$0.795224\pi$
$332$	1.50860e6	−	1.05777e6i	0.751155	−	0.526679i
$333$	−230472.	−	637263.i	−0.113896	−	0.314926i
$334$	−217020.	−	687533.i	−0.106447	−	0.337231i
$335$	4.68731e6			2.28198
$336$	448796.	+	640599.i	0.216870	+	0.309555i
$337$	3.18329e6			1.52687			0.763433	−	0.645887i	$-0.223512\pi$
$337$	3.18329e6			1.52687			0.763433	+	0.645887i	$0.223512\pi$
$338$	−522807.	−	1.65629e6i	−0.248914	−	0.788578i
$339$	−1.00304e6	+	1.42938e6i	−0.474046	+	0.675538i
$340$	−2.77759e6	+	1.94753e6i	−1.30308	+	0.913666i
$341$		−	959819.i		−	0.446996i
$342$	1.30039e6	+	1.70076e6i	0.601183	+	0.786280i
$343$			117649.i			0.0539949i
$344$	−745478.	+	973454.i	−0.339656	+	0.443526i
$345$	−202452.	+	288503.i	−0.0915743	+	0.130498i
$346$	−1.29421e6	+	408516.i	−0.581184	+	0.183450i
$347$	−1.00648e6			−0.448727			−0.224364	−	0.974506i	$-0.572030\pi$
$347$	−1.00648e6			−0.448727			−0.224364	+	0.974506i	$0.572030\pi$
$348$	1400.75	−	3.65443e6i	0.000620030	−	1.61760i
$349$	2.58212e6			1.13478			0.567392	−	0.823448i	$-0.307953\pi$
$349$	2.58212e6			1.13478			0.567392	+	0.823448i	$0.307953\pi$
$350$	−1.57222e6	+	496269.i	−0.686028	+	0.216545i
$351$	−251369.	+	926752.i	−0.108904	+	0.401509i
$352$	−729028.	−	30664.8i	−0.313608	−	0.0131912i
$353$		−	1.19755e6i		−	0.511514i	−0.966741	−	0.255757i	$-0.917675\pi$
$353$		−	1.19755e6i		−	0.511514i	0.966741	−	0.255757i	$-0.0823248\pi$
$354$	−1.15036e6	+	3.63957e6i	−0.487895	+	1.54363i
$355$			2.95938e6i			1.24632i
$356$	−2.21153e6	−	3.15410e6i	−0.924842	−	1.31902i
$357$	695869.	+	488313.i	0.288973	+	0.202781i
$358$	−425634.	−	1.34844e6i	−0.175521	−	0.556062i
$359$	−1.99676e6			−0.817693			−0.408846	−	0.912603i	$-0.634069\pi$
$359$	−1.99676e6			−0.817693			−0.408846	+	0.912603i	$0.634069\pi$
$360$	3.99462e6	+	1.26427e6i	1.62450	+	0.514142i
$361$	50369.4			0.0203422
$362$	−849536.	−	2.69139e6i	−0.340730	−	1.07946i
$363$	1.85257e6	+	1.30000e6i	0.737917	+	0.517819i
$364$	−228193.	−	325451.i	−0.0902710	−	0.128745i
$365$		−	4.37762e6i		−	1.71991i
$366$	329187.	−	1.04150e6i	0.128452	−	0.406401i
$367$		−	4.38062e6i		−	1.69774i	−0.528604	−	0.848868i	$-0.677285\pi$
$367$		−	4.38062e6i		−	1.69774i	0.528604	−	0.848868i	$-0.322715\pi$
$368$	−82841.1	+	228511.i	−0.0318879	+	0.0879606i
$369$	−4.13807e6	+	1.49657e6i	−1.58209	+	0.572177i
$370$	1.43294e6	−	452308.i	0.544158	−	0.171763i
$371$	929448.			0.350583
$372$	−1456.90	+	3.80093e6i	−0.000545850	+	1.42407i
$373$	920904.			0.342722			0.171361	−	0.985208i	$-0.445184\pi$
$373$	920904.			0.342722			0.171361	+	0.985208i	$0.445184\pi$
$374$	−756273.	+	238717.i	−0.279576	+	0.0882480i
$375$	−2.40769e6	+	3.43107e6i	−0.884141	+	1.25994i
$376$	2.87028e6	+	2.19808e6i	1.04702	+	0.801816i
$377$			1.85710e6i			0.672949i
$378$	−42919.5	−	1.04910e6i	−0.0154499	−	0.377649i
$379$		−	5.33144e6i		−	1.90654i	−0.302114	−	0.953272i	$-0.597692\pi$
$379$		−	5.33144e6i		−	1.90654i	0.302114	−	0.953272i	$-0.402308\pi$
$380$	−3.88701e6	+	2.72541e6i	−1.38088	+	0.968217i
$381$	−138085.	+	196778.i	−0.0487343	+	0.0694486i
$382$	463730.	+	1.46913e6i	0.162595	+	0.515112i
$383$	2.10904e6			0.734663			0.367332	−	0.930090i	$-0.380271\pi$
$383$	2.10904e6			0.734663			0.367332	+	0.930090i	$0.380271\pi$
$384$	2.88694e6	+	122541.i	0.999100	+	0.0424084i
$385$	−587926.			−0.202149
$386$	433708.	+	1.37402e6i	0.148159	+	0.469379i
$387$	1.54782e6	−	559781.i	0.525342	−	0.189994i
$388$	−662471.	+	464497.i	−0.223402	+	0.156640i
$389$		−	3.67245e6i		−	1.23050i	−0.788332	−	0.615250i	$-0.789055\pi$
$389$		−	3.67245e6i		−	1.23050i	0.788332	−	0.615250i	$-0.210945\pi$
$390$	−2.03022e6	−	641695.i	−0.675900	−	0.213632i
$391$			264177.i			0.0873882i
$392$	345066.	+	264254.i	0.113419	+	0.0868574i
$393$	276518.	+	194041.i	0.0903112	+	0.0633742i
$394$	1.40272e6	−	442769.i	0.455230	−	0.143693i
$395$	7.79130e6			2.51256
$396$	801578.	+	562951.i	0.256867	+	0.180398i
$397$	−141806.			−0.0451564			−0.0225782	−	0.999745i	$-0.507187\pi$
$397$	−141806.			−0.0451564			−0.0225782	+	0.999745i	$0.507187\pi$
$398$	4.25129e6	−	1.34192e6i	1.34528	−	0.424637i
$399$	973809.	+	683352.i	0.306226	+	0.214888i
$400$	−2.07583e6	+	5.72601e6i	−0.648696	+	1.78938i
$401$		−	722310.i		−	0.224317i	−0.993690	−	0.112159i	$-0.964224\pi$
$401$		−	722310.i		−	0.224317i	0.993690	−	0.112159i	$-0.0357765\pi$
$402$	−4.13763e6	−	1.30778e6i	−1.27699	−	0.403619i
$403$		−	1.93155e6i		−	0.592438i
$404$	2.35063e6	+	3.35250e6i	0.716525	+	1.02192i
$405$	−3.59774e6	−	4.32338e6i	−1.08991	−	1.30974i
$406$	−611250.	−	1.93648e6i	−0.184036	−	0.583040i
$407$	351284.			0.105117
$408$	2.99523e6	−	944183.i	0.890801	−	0.280805i
$409$	−2.83896e6			−0.839171			−0.419586	−	0.907716i	$-0.637825\pi$
$409$	−2.83896e6			−0.839171			−0.419586	+	0.907716i	$0.637825\pi$
$410$	−2.93706e6	−	9.30482e6i	−0.862887	−	2.73368i
$411$	−803007.	+	1.14432e6i	−0.234485	+	0.334152i
$412$	−1.51342e6	−	2.15845e6i	−0.439253	−	0.626467i
$413$			2.12102e6i			0.611885i
$414$	259204.	−	198185.i	0.0743260	−	0.0568291i
$415$		−	5.48439e6i		−	1.56318i
$416$	−1.46710e6	−	61710.1i	−0.415649	−	0.0174833i
$417$	2.69938e6	−	3.84675e6i	0.760194	−	1.08331i
$418$	−1.05834e6	+	334065.i	−0.296268	+	0.0935168i
$419$	1.07343e6			0.298702			0.149351	−	0.988784i	$-0.452282\pi$
$419$	1.07343e6			0.298702			0.149351	+	0.988784i	$0.452282\pi$
$420$	2.32821e6	+	892.409i	0.644020	+	0.000246854i
$421$	−2.43807e6			−0.670411			−0.335205	−	0.942145i	$-0.608806\pi$
$421$	−2.43807e6			−0.670411			−0.335205	+	0.942145i	$0.608806\pi$
$422$	−1.16467e6	+	367627.i	−0.318362	+	0.100491i
$423$	−1.65054e6	−	4.56382e6i	−0.448514	−	1.24016i
$424$	2.08766e6	−	2.72609e6i	0.563955	−	0.736419i
$425$			6.61972e6i			1.77774i
$426$	825684.	−	2.61234e6i	0.220440	−	0.697437i
$427$		−	606949.i		−	0.161095i
$428$	4.05442e6	−	2.84279e6i	1.06984	−	0.750129i
$429$	−407454.	−	285923.i	−0.106890	−	0.0750078i
$430$	1.09859e6	+	3.48040e6i	0.286526	+	0.907734i
$431$	−3.31642e6			−0.859956			−0.429978	−	0.902839i	$-0.641479\pi$
$431$	−3.31642e6			−0.859956			−0.429978	+	0.902839i	$0.641479\pi$
$432$	−3.17343e6	−	2.23053e6i	−0.818125	−	0.575040i
$433$	1.96006e6			0.502399			0.251199	−	0.967935i	$-0.419175\pi$
$433$	1.96006e6			0.502399			0.251199	+	0.967935i	$0.419175\pi$
$434$	635753.	+	2.01411e6i	0.162018	+	0.513285i
$435$	−8.90424e6	−	6.24838e6i	−2.25618	−	1.58323i
$436$	−1.38815e6	+	973315.i	−0.349720	+	0.245210i
$437$			369693.i			0.0926058i
$438$	−1.22138e6	+	3.86426e6i	−0.304204	+	0.962455i
$439$			7.95801e6i			1.97080i	0.170244	+	0.985402i	$0.445545\pi$
$439$			7.95801e6i			1.97080i	−0.170244	+	0.985402i	$0.554455\pi$
$440$	−1.32055e6	+	1.72440e6i	−0.325181	+	0.424625i
$441$	−198429.	−	548664.i	−0.0485857	−	0.134341i
$442$	−1.52193e6	+	480396.i	−0.370543	+	0.116962i
$443$	1.08325e6			0.262252			0.131126	−	0.991366i	$-0.458141\pi$
$443$	1.08325e6			0.262252			0.131126	+	0.991366i	$0.458141\pi$
$444$	−1.39110e6	−	533.211i	−0.334889	−	0.000128364i
$445$	−1.14665e7			−2.74492
$446$	−4.46397e6	+	1.40905e6i	−1.06263	+	0.335420i
$447$	1.19827e6	−	1.70759e6i	0.283651	−	0.404217i
$448$	1.55012e6	−	418537.i	0.364898	−	0.0985232i
$449$			4.86396e6i			1.13861i	0.822127	+	0.569304i	$0.192787\pi$
$449$			4.86396e6i			1.13861i	−0.822127	+	0.569304i	$0.807213\pi$
$450$	6.49511e6	−	4.96611e6i	1.51201	−	1.15607i
$451$		−	2.28106e6i		−	0.528075i
$452$	2.05792e6	+	2.93503e6i	0.473787	+	0.675719i
$453$	1.55408e6	−	2.21464e6i	0.355818	−	0.507058i
$454$	−1.70923e6	−	5.41497e6i	−0.389190	−	1.23298i
$455$	−1.18315e6			−0.267923
$456$	4.19158e6	−	1.32130e6i	0.943986	−	0.297571i
$457$	831312.			0.186197			0.0930986	−	0.995657i	$-0.470323\pi$
$457$	831312.			0.186197			0.0930986	+	0.995657i	$0.470323\pi$
$458$	−786342.	−	2.49119e6i	−0.175165	−	0.554936i
$459$	−4.06882e6	−	1.10361e6i	−0.901441	−	0.244503i
$460$	415366.	+	592399.i	0.0915243	+	0.130533i
$461$			5.59883e6i			1.22700i	0.789694	+	0.613501i	$0.210239\pi$
$461$			5.59883e6i			1.22700i	−0.789694	+	0.613501i	$0.789761\pi$
$462$	518980.	+	164035.i	0.113122	+	0.0357545i
$463$			5.49551e6i			1.19139i	0.803209	+	0.595697i	$0.203124\pi$
$463$			5.49551e6i			1.19139i	−0.803209	+	0.595697i	$0.796876\pi$
$464$	−7.05267e6	−	2.55677e6i	−1.52075	−	0.551312i
$465$	9.26119e6	+	6.49886e6i	1.98625	+	1.39381i
$466$	−3.57926e6	+	1.12979e6i	−0.763533	+	0.241009i
$467$	4.50213e6			0.955270			0.477635	−	0.878558i	$-0.341494\pi$
$467$	4.50213e6			0.955270			0.477635	+	0.878558i	$0.341494\pi$
$468$	1.61310e6	+	1.13289e6i	0.340445	+	0.239096i
$469$	−2.41127e6			−0.506191
$470$	1.02622e7	−	3.23925e6i	2.14286	−	0.676394i
$471$	−668156.	−	468866.i	−0.138780	−	0.0973860i
$472$	6.22098e6	+	4.76407e6i	1.28530	+	0.984291i
$473$			853215.i			0.175350i
$474$	−6.87761e6	−	2.17381e6i	−1.40602	−	0.444403i
$475$			9.26374e6i			1.88388i
$476$	1.42886e6	−	1.00186e6i	0.289050	−	0.202670i
$477$	−4.33454e6	+	1.56762e6i	−0.872262	+	0.315461i
$478$	−2.04703e6	−	6.48515e6i	−0.409784	−	1.29823i
$479$	−1.82422e6			−0.363277			−0.181638	−	0.983365i	$-0.558140\pi$
$479$	−1.82422e6			−0.363277			−0.181638	+	0.983365i	$0.558140\pi$
$480$	5.23207e6	−	6.82668e6i	1.03650	−	1.35240i
$481$	706926.			0.139319
$482$	1.77067e6	+	5.60959e6i	0.347151	+	1.09980i
$483$	104146.	−	148413.i	0.0203131	−	0.0289471i
$484$	3.80398e6	−	2.66719e6i	0.738116	−	0.517536i
$485$			2.40835e6i			0.464907i
$486$	1.96959e6	+	4.82016e6i	0.378255	+	0.925701i
$487$			2.35880e6i			0.450680i	0.974280	+	0.225340i	$0.0723494\pi$
$487$			2.35880e6i			0.450680i	−0.974280	+	0.225340i	$0.927651\pi$
$488$	−1.78019e6	−	1.36328e6i	−0.338390	−	0.259141i
$489$	−1.93071e6	+	2.75136e6i	−0.365128	+	0.520325i
$490$	1.23372e6	−	389423.i	0.232127	−	0.0732709i
$491$	−3.02931e6			−0.567075			−0.283538	−	0.958961i	$-0.591508\pi$
$491$	−3.02931e6			−0.567075			−0.283538	+	0.958961i	$0.591508\pi$
$492$	−3462.40	+	9.03310e6i	−0.000644859	+	1.68238i
$493$	−8.15345e6			−1.51086
$494$	−2.12981e6	+	672274.i	−0.392666	+	0.123945i
$495$	2.74183e6	−	991606.i	0.502953	−	0.181897i
$496$	7.33540e6	+	2.65927e6i	1.33881	+	0.485353i
$497$		−	1.52238e6i		−	0.276460i
$498$	−1.53017e6	+	4.84123e6i	−0.276482	+	0.874747i
$499$			8.25397e6i			1.48392i	0.670443	+	0.741961i	$0.266104\pi$
$499$			8.25397e6i			1.48392i	−0.670443	+	0.741961i	$0.733896\pi$
$500$	4.93980e6	+	7.04519e6i	0.883658	+	1.26028i
$501$	1.62630e6	+	1.14122e6i	0.289471	+	0.203131i
$502$	1.66345e6	+	5.26993e6i	0.294612	+	0.933352i
$503$	−257244.			−0.0453341			−0.0226670	−	0.999743i	$-0.507216\pi$
$503$	−257244.			−0.0453341			−0.0226670	+	0.999743i	$0.507216\pi$
$504$	−2.05493e6	−	650372.i	−0.360348	−	0.114047i
$505$	1.21877e7			2.12664
$506$	50913.1	+	161296.i	0.00884002	+	0.0280058i
$507$	3.91780e6	+	2.74924e6i	0.676897	+	0.474999i
$508$	283306.	+	404054.i	0.0487076	+	0.0694673i
$509$		−	2.70538e6i		−	0.462844i	−0.972853	−	0.231422i	$-0.925662\pi$
$509$		−	2.70538e6i		−	0.462844i	0.972853	−	0.231422i	$-0.0743378\pi$
$510$	2.81731e6	−	8.91352e6i	0.479633	−	1.51748i
$511$			2.25196e6i			0.381512i
$512$	2.25419e6	−	5.48662e6i	0.380029	−	0.924975i
$513$	−5.69398e6	−	1.54441e6i	−0.955261	−	0.259102i
$514$	3.01997e6	−	953251.i	0.504190	−	0.159147i
$515$	−7.84684e6			−1.30370
$516$	1295.09	−	3.37877e6i	0.000214129	−	0.558643i
$517$	2.51575e6			0.413944
$518$	−737143.	+	232679.i	−0.120706	+	0.0381007i
$519$	2.14823e6	−	3.06133e6i	0.350076	−	0.498875i
$520$	−2.65749e6	+	3.47019e6i	−0.430987	+	0.562788i
$521$		−	2.26536e6i		−	0.365631i	−0.983147	−	0.182815i	$-0.941479\pi$
$521$		−	2.26536e6i		−	0.365631i	0.983147	−	0.182815i	$-0.0585211\pi$
$522$	6.11671e6	+	7.99996e6i	0.982520	+	1.28503i
$523$			900682.i			0.143985i	0.997405	+	0.0719925i	$0.0229358\pi$
$523$			900682.i			0.143985i	−0.997405	+	0.0719925i	$0.977064\pi$
$524$	567789.	−	398110.i	0.0903355	−	0.0633396i
$525$	2.60969e6	−	3.71893e6i	0.413229	−	0.588871i
$526$	2.60546e6	+	8.25428e6i	0.410601	+	1.30081i
$527$	8.48029e6			1.33010
$528$	1.64681e6	−	1.15373e6i	0.257074	−	0.180103i
$529$	−6.38000e6			−0.991246
$530$	−3.07651e6	−	9.74661e6i	−0.475739	−	1.50718i
$531$	−3.57735e6	−	9.89151e6i	−0.550586	−	1.52239i
$532$	1.99957e6	−	1.40202e6i	0.306308	−	0.214771i
$533$		−	4.59042e6i		−	0.699898i
$534$	1.01218e7	+	3.19920e6i	1.53604	+	0.485500i
$535$		−	1.47395e7i		−	2.22637i
$536$	−5.41602e6	+	7.07230e6i	−0.814269	+	1.06328i
$537$	3.18960e6	+	2.23824e6i	0.477311	+	0.334944i
$538$	888133.	−	280339.i	0.132289	−	0.0417569i
$539$	302444.			0.0448408
$540$	−1.08593e7	+	3.92264e6i	−1.60257	+	0.578888i
$541$	−9.12432e6			−1.34032			−0.670158	−	0.742219i	$-0.733774\pi$
$541$	−9.12432e6			−1.34032			−0.670158	+	0.742219i	$0.733774\pi$
$542$	−7.41657e6	+	2.34104e6i	−1.08444	+	0.342303i
$543$	6.36623e6	+	4.46738e6i	0.926579	+	0.650209i
$544$	270933.	−	6.44118e6i	0.0392522	−	0.933186i
$545$			5.04650e6i			0.727778i
$546$	1.04440e6	+	330104.i	0.149929	+	0.0473881i
$547$		−	2.15626e6i		−	0.308130i	−0.988061	−	0.154065i	$-0.950764\pi$
$547$		−	2.15626e6i		−	0.308130i	0.988061	−	0.154065i	$-0.0492365\pi$
$548$	1.64751e6	+	2.34970e6i	0.234357	+	0.334242i
$549$	1.02369e6	+	2.83055e6i	0.144957	+	0.400811i
$550$	1.27578e6	+	4.04175e6i	0.179832	+	0.569721i
$551$	−1.14101e7			−1.60106
$552$	−201373.	−	638817.i	−0.0281290	−	0.0892337i
$553$	−4.00804e6			−0.557339
$554$	2.18458e6	+	6.92090e6i	0.302408	+	0.958050i
$555$	−2.37851e6	+	3.38950e6i	−0.327773	+	0.467092i
$556$	−5.53827e6	−	7.89874e6i	−0.759779	−	1.08360i
$557$		−	962141.i		−	0.131402i	−0.997839	−	0.0657008i	$-0.979072\pi$
$557$		−	962141.i		−	0.131402i	0.997839	−	0.0657008i	$-0.0209283\pi$
$558$	−6.36191e6	−	8.32066e6i	−0.864972	−	1.13129i
$559$			1.71702e6i			0.232405i
$560$	1.62890e6	−	4.49321e6i	0.219495	−	0.605462i
$561$	1.25532e6	−	1.78889e6i	0.168402	−	0.239981i
$562$	−1.36780e7	+	4.31746e6i	−1.82676	+	0.576617i
$563$	2.91948e6			0.388182			0.194091	−	0.980984i	$-0.437824\pi$
$563$	2.91948e6			0.388182			0.194091	+	0.980984i	$0.437824\pi$
$564$	−9.96248e6	−	3818.64i	−1.31877	−	0.000505488i
$565$	1.06700e7			1.40619
$566$	−1.20027e7	+	3.78864e6i	−1.57484	+	0.497098i
$567$	1.85077e6	+	2.22405e6i	0.241766	+	0.290528i
$568$	−4.46517e6	−	3.41946e6i	−0.580721	−	0.444720i
$569$		−	4.77366e6i		−	0.618117i	−0.951043	−	0.309058i	$-0.899986\pi$
$569$		−	4.77366e6i		−	0.618117i	0.951043	−	0.309058i	$-0.100014\pi$
$570$	3.94258e6	−	1.24737e7i	0.508269	−	1.60808i
$571$		−	6.22029e6i		−	0.798400i	−0.916864	−	0.399200i	$-0.869288\pi$
$571$		−	6.22029e6i		−	0.798400i	0.916864	−	0.399200i	$-0.130712\pi$
$572$	−836647.	+	586623.i	−0.106918	+	0.0749668i
$573$	−3.47509e6	−	2.43858e6i	−0.442160	−	0.310277i
$574$	1.51090e6	+	4.78664e6i	0.191406	+	0.606388i
$575$	1.41184e6			0.178080
$576$	−6.52319e6	+	4.56634e6i	−0.819226	+	0.573471i
$577$	4.15487e6			0.519539			0.259769	−	0.965671i	$-0.416353\pi$
$577$	4.15487e6			0.519539			0.259769	+	0.965671i	$0.416353\pi$
$578$	308552.	+	977514.i	0.0384157	+	0.121704i
$579$	−3.25011e6	−	2.28070e6i	−0.402904	−	0.282730i
$580$	−1.82836e7	+	1.28197e7i	−2.25679	+	1.58237i
$581$			2.82131e6i			0.346745i
$582$	671943.	−	2.12592e6i	0.0822291	−	0.260160i
$583$		−	2.38936e6i		−	0.291146i
$584$	6.60503e6	+	5.05818e6i	0.801388	+	0.613708i
$585$	5.51768e6	−	1.99552e6i	0.666602	−	0.241082i
$586$	1.10922e7	−	3.50125e6i	1.33436	−	0.421191i
$587$	−1.07003e7			−1.28174			−0.640872	−	0.767648i	$-0.721427\pi$
$587$	−1.07003e7			−1.28174			−0.640872	+	0.767648i	$0.721427\pi$
$588$	−1.19769e6	−	459.078i	−0.142857	−	5.47574e-5i
$589$	1.18675e7			1.40951
$590$	2.22420e7	−	7.02067e6i	2.63053	−	0.830325i
$591$	−2.32835e6	+	3.31801e6i	−0.274208	+	0.390759i
$592$	−973264.	+	2.68468e6i	−0.114137	+	0.314838i
$593$		−	9.99589e6i		−	1.16731i	−0.812003	−	0.583653i	$-0.801623\pi$
$593$		−	9.99589e6i		−	1.16731i	0.812003	−	0.583653i	$-0.198377\pi$
$594$	−2.69696e6	+	110334.i	−0.313623	+	0.0128305i
$595$		−	5.19451e6i		−	0.601522i
$596$	−2.45846e6	−	3.50628e6i	−0.283496	−	0.404325i
$597$	−7.05663e6	+	1.00560e7i	−0.810329	+	1.15476i
$598$	102458.	+	324594.i	0.0117164	+	0.0371182i
$599$	2.27690e6			0.259285			0.129643	−	0.991561i	$-0.458617\pi$
$599$	2.27690e6			0.259285			0.129643	+	0.991561i	$0.458617\pi$
$600$	−5.04599e6	−	1.60074e7i	−0.572227	−	1.81528i
$601$	513853.			0.0580300			0.0290150	−	0.999579i	$-0.490763\pi$
$601$	513853.			0.0580300			0.0290150	+	0.999579i	$0.490763\pi$
$602$	−565142.	−	1.79041e6i	−0.0635574	−	0.201354i
$603$	1.12451e7	−	4.06689e6i	1.25942	−	0.455480i
$604$	−3.18848e6	−	4.54744e6i	−0.355624	−	0.507195i
$605$		−	1.38290e7i		−	1.53604i
$606$	−1.07584e7	−	3.40043e6i	−1.19006	−	0.376143i
$607$		−	5.78585e6i		−	0.637375i	−0.947860	−	0.318688i	$-0.896758\pi$
$607$		−	5.78585e6i		−	0.637375i	0.947860	−	0.318688i	$-0.103242\pi$
$608$	379148.	−	9.01389e6i	0.0415958	−	0.988902i
$609$	4.58057e6	+	3.21433e6i	0.500468	+	0.351194i
$610$	−6.36474e6	+	2.00903e6i	−0.692558	+	0.218606i
$611$	5.06272e6			0.548631
$612$	−4.97384e6	+	7.08219e6i	−0.536801	+	0.764344i
$613$	857841.			0.0922052			0.0461026	−	0.998937i	$-0.485320\pi$
$613$	857841.			0.0922052			0.0461026	+	0.998937i	$0.485320\pi$
$614$	3.04918e6	−	962471.i	0.326409	−	0.103031i
$615$	2.20097e7	+	1.54449e7i	2.34653	+	1.64663i
$616$	679327.	−	887073.i	0.0721319	−	0.0941906i
$617$			7.35207e6i			0.777493i	0.921345	+	0.388747i	$0.127092\pi$
$617$			7.35207e6i			0.777493i	−0.921345	+	0.388747i	$0.872908\pi$
$618$	6.92664e6	+	2.18931e6i	0.729544	+	0.230588i
$619$			7.48655e6i			0.785335i	0.919680	+	0.392668i	$0.128448\pi$
$619$			7.48655e6i			0.785335i	−0.919680	+	0.392668i	$0.871552\pi$
$620$	1.90165e7	−	1.33336e7i	1.98679	−	1.39305i
$621$	−235376.	+	867790.i	−0.0244925	+	0.0902996i
$622$	−3.15932e6	−	1.00089e7i	−0.327429	−	1.03732i
$623$	5.89864e6			0.608880
$624$	3.31405e6	−	2.32178e6i	0.340720	−	0.238704i
$625$	7.02490e6			0.719350
$626$	1.29736e6	+	4.11012e6i	0.132319	+	0.419197i
$627$	1.75672e6	−	2.50340e6i	0.178457	−	0.254309i
$628$	−1.37196e6	+	961963.i	−0.138817	+	0.0973328i
$629$			3.10370e6i			0.312790i
$630$	−5.09672e6	+	3.89691e6i	−0.511611	+	0.391173i
$631$			9.51591e6i			0.951430i	0.879600	+	0.475715i	$0.157811\pi$
$631$			9.51591e6i			0.951430i	−0.879600	+	0.475715i	$0.842189\pi$
$632$	−9.00256e6	+	1.17556e7i	−0.896547	+	1.17072i
$633$	1.93321e6	−	2.75491e6i	0.191765	−	0.273274i
$634$	2.27822e6	−	719120.i	0.225099	−	0.0710523i
$635$	1.46890e6			0.144564
$636$	−3626.80	+	9.46198e6i	−0.000355533	+	0.927555i
$637$	608641.			0.0594309
$638$	−4.97818e6	+	1.57136e6i	−0.484193	+	0.152835i
$639$	2.56768e6	+	7.09973e6i	0.248764	+	0.687843i
$640$	−9.51993e6	−	1.48699e7i	−0.918722	−	1.43502i
$641$			70110.8i			0.00673969i	0.999994	+	0.00336985i	$0.00107266\pi$
$641$			70110.8i			0.00673969i	−0.999994	+	0.00336985i	$0.998927\pi$
$642$	−4.11239e6	+	1.30110e7i	−0.393783	+	1.24587i
$643$		−	1.14165e7i		−	1.08894i	−0.838780	−	0.544471i	$-0.816731\pi$
$643$		−	1.14165e7i		−	1.08894i	0.838780	−	0.544471i	$-0.183269\pi$
$644$	−213675.	−	304745.i	−0.0203020	−	0.0289549i
$645$	−8.23257e6	−	5.77705e6i	−0.779177	−	0.546773i
$646$	−2.95156e6	−	9.35075e6i	−0.278273	−	0.881587i
$647$	−1.75365e7			−1.64696			−0.823478	−	0.567349i	$-0.807969\pi$
$647$	−1.75365e7			−1.64696			−0.823478	+	0.567349i	$0.807969\pi$
$648$	1.06802e7	−	432836.i	0.999180	−	0.0404935i
$649$	5.45258e6			0.508148
$650$	2.56738e6	+	8.13364e6i	0.238346	+	0.755095i
$651$	−4.76419e6	−	3.34318e6i	−0.440592	−	0.309177i
$652$	3.96120e6	+	5.64951e6i	0.364929	+	0.520465i
$653$		−	2.03918e7i		−	1.87143i	−0.352757	−	0.935715i	$-0.614756\pi$
$653$		−	2.03918e7i		−	1.87143i	0.352757	−	0.935715i	$-0.385244\pi$
$654$	1.40800e6	−	4.45470e6i	0.128724	−	0.407262i
$655$		−	2.06414e6i		−	0.187991i
$656$	1.74329e7	+	6.31989e6i	1.58165	+	0.573390i
$657$	−3.79819e6	−	1.05022e7i	−0.343292	−	0.949216i
$658$	−5.27912e6	+	1.66635e6i	−0.475332	+	0.150038i
$659$	1.21536e6			0.109016			0.0545082	−	0.998513i	$-0.482641\pi$
$659$	1.21536e6			0.109016			0.0545082	+	0.998513i	$0.482641\pi$
$660$	2294.14	−	5.98522e6i	0.000205003	−	0.534835i
$661$	−8.84880e6			−0.787736			−0.393868	−	0.919167i	$-0.628863\pi$
$661$	−8.84880e6			−0.787736			−0.393868	+	0.919167i	$0.628863\pi$
$662$	−1.29003e7	+	4.07196e6i	−1.14407	+	0.361126i
$663$	2.52622e6	−	3.59998e6i	0.223196	−	0.318065i
$664$	8.27494e6	+	6.33701e6i	0.728358	+	0.557782i
$665$		−	7.26927e6i		−	0.637436i
$666$	3.04527e6	−	2.32839e6i	0.266036	−	0.203409i
$667$			1.73895e6i			0.151347i
$668$	3.33936e6	−	2.34142e6i	0.289549	−	0.203020i
$669$	7.40965e6	−	1.05591e7i	0.640077	−	0.912141i
$670$	7.98141e6	+	2.52857e7i	0.686899	+	2.17614i
$671$	−1.56030e6			−0.133784
$672$	−2.69151e6	+	3.51182e6i	−0.229918	+	0.299991i
$673$	−1.82534e7			−1.55348			−0.776740	−	0.629822i	$-0.783128\pi$
$673$	−1.82534e7			−1.55348			−0.776740	+	0.629822i	$0.783128\pi$
$674$	5.42041e6	+	1.71722e7i	0.459602	+	1.45605i
$675$	−5.89804e6	+	2.17450e7i	−0.498251	+	1.83696i
$676$	8.04463e6	−	5.64056e6i	0.677079	−	0.474740i
$677$		−	1.42553e7i		−	1.19538i	−0.801728	−	0.597690i	$-0.796085\pi$
$677$		−	1.42553e7i		−	1.19538i	0.801728	−	0.597690i	$-0.203915\pi$
$678$	−9.41875e6	−	2.97700e6i	−0.786899	−	0.248716i
$679$		−	1.23892e6i		−	0.103126i
$680$	−1.52356e7	−	1.16675e7i	−1.26353	−	0.967622i
$681$	1.28086e7	+	8.98819e6i	1.05836	+	0.742685i
$682$	5.17774e6	−	1.63435e6i	0.426265	−	0.134550i
$683$	2.07371e6			0.170097			0.0850486	−	0.996377i	$-0.472895\pi$
$683$	2.07371e6			0.170097			0.0850486	+	0.996377i	$0.472895\pi$
$684$	−6.96047e6	+	9.91092e6i	−0.568851	+	0.809979i
$685$	8.54212e6			0.695567
$686$	−634657.	+	200329.i	−0.0514907	+	0.0162530i
$687$	5.89267e6	+	4.13507e6i	0.476344	+	0.334265i
$688$	−6.52067e6	−	2.36391e6i	−0.525196	−	0.190397i
$689$		−	4.80837e6i		−	0.385878i
$690$	−1.90106e6	−	600870.i	−0.152010	−	0.0480460i
$691$			2.10859e7i			1.67995i	0.542622	+	0.839977i	$0.317432\pi$
$691$			2.10859e7i			1.67995i	−0.542622	+	0.839977i	$0.682568\pi$
$692$	−4.40747e6	−	6.28598e6i	−0.349884	−	0.499009i
$693$	−1.41047e6	+	510107.i	−0.111566	+	0.0403486i
$694$	−1.71381e6	−	5.42946e6i	−0.135071	−	0.427916i
$695$	−2.87151e7			−2.25501
$696$	1.97162e7	−	6.21510e6i	1.54277	−	0.486323i
$697$	2.01539e7			1.57136
$698$	4.39676e6	+	1.39292e7i	0.341581	+	1.08215i
$699$	5.94113e6	−	8.46640e6i	0.459914	−	0.655399i
$700$	−5.35424e6	−	7.63628e6i	−0.413003	−	0.589029i
$701$			1.05688e7i			0.812324i	0.913801	+	0.406162i	$0.133133\pi$
$701$			1.05688e7i			0.812324i	−0.913801	+	0.406162i	$0.866867\pi$
$702$	−5.42738e6	+	222038.i	−0.415669	+	0.0170053i
$703$			4.34336e6i			0.331465i
$704$	−1.07595e6	−	3.98495e6i	−0.0818199	−	0.303034i
$705$	−1.70340e7	+	2.42742e7i	−1.29075	+	1.83938i
$706$	6.46019e6	−	2.03916e6i	0.487791	−	0.153971i
$707$	−6.26966e6			−0.471732
$708$	−2.15924e7	−	8276.42i	−1.61889	−	0.000620525i
$709$	6.21987e6			0.464693			0.232346	−	0.972633i	$-0.425360\pi$
$709$	6.21987e6			0.464693			0.232346	+	0.972633i	$0.425360\pi$
$710$	−1.59644e7	+	5.03915e6i	−1.18852	+	0.375156i
$711$	1.86918e7	−	6.76003e6i	1.38668	−	0.501504i
$712$	1.32491e7	−	1.73008e7i	0.979457	−	1.27899i
$713$		−	1.80866e6i		−	0.133240i
$714$	−1.44930e6	+	4.58534e6i	−0.106393	+	0.336610i
$715$			3.04156e6i			0.222500i
$716$	6.54938e6	−	4.59216e6i	0.477439	−	0.334761i
$717$	1.53400e7	+	1.07646e7i	1.11437	+	0.781985i
$718$	−3.40003e6	−	1.07715e7i	−0.246134	−	0.779769i
$719$	1.10651e7			0.798240			0.399120	−	0.916899i	$-0.369316\pi$
$719$	1.10651e7			0.798240			0.399120	+	0.916899i	$0.369316\pi$
$720$	−18169.8	+	2.37017e7i	−0.00130623	+	1.70392i
$721$	4.03661e6			0.289187
$722$	85767.5	+	271717.i	0.00612322	+	0.0193988i
$723$	−1.32690e7	−	9.31124e6i	−0.944042	−	0.662463i
$724$	1.30721e7	−	9.16563e6i	0.926829	−	0.649854i
$725$			4.35745e7i			3.07884i
$726$	−3.85837e6	+	1.22073e7i	−0.271683	+	0.859562i
$727$			2.86468e6i			0.201020i	0.994936	+	0.100510i	$0.0320475\pi$
$727$			2.86468e6i			0.201020i	−0.994936	+	0.100510i	$0.967953\pi$
$728$	1.36708e6	−	1.78515e6i	0.0956019	−	0.124838i
$729$	−1.23823e7	−	7.25048e6i	−0.862945	−	0.505298i
$730$	2.36150e7	−	7.45408e6i	1.64014	−	0.517711i
$731$	−7.53841e6			−0.521779
$732$	6.17887e6	+	2368.37i	0.426218	+	0.000163370i
$733$	−2.04741e6			−0.140749			−0.0703744	−	0.997521i	$-0.522419\pi$
$733$	−2.04741e6			−0.140749			−0.0703744	+	0.997521i	$0.522419\pi$
$734$	2.36312e7	−	7.45919e6i	1.61900	−	0.511036i
$735$	−2.04783e6	+	2.91825e6i	−0.139822	+	0.199253i
$736$	−1.37376e6	−	57784.0i	−0.0934796	−	0.00393200i
$737$			6.19874e6i			0.420373i
$738$	−1.51194e7	−	1.97745e7i	−1.02187	−	1.33649i
$739$		−	8.74430e6i		−	0.588998i	−0.955652	−	0.294499i	$-0.904847\pi$
$739$		−	8.74430e6i		−	0.588998i	0.955652	−	0.294499i	$-0.0951528\pi$
$740$	4.87995e6	+	6.95983e6i	0.327594	+	0.467218i
$741$	3.53523e6	−	5.03787e6i	0.236522	−	0.337055i
$742$	1.58264e6	+	5.01390e6i	0.105529	+	0.334323i
$743$	−1.54376e6			−0.102590			−0.0512952	−	0.998684i	$-0.516335\pi$
$743$	−1.54376e6			−0.102590			−0.0512952	+	0.998684i	$0.516335\pi$
$744$	−2.05066e7	+	6.46425e6i	−1.35819	+	0.428140i
$745$	−1.27468e7			−0.841413
$746$	1.56809e6	+	4.96781e6i	0.103163	+	0.326827i
$747$	−4.75847e6	−	1.31574e7i	−0.312008	−	0.862715i
$748$	−2.57552e6	−	3.67323e6i	−0.168310	−	0.240046i
$749$			7.58236e6i			0.493855i
$750$	−2.26086e7	−	7.14593e6i	−1.46764	−	0.463880i
$751$		−	2.06707e7i		−	1.33738i	−0.743542	−	0.668690i	$-0.766856\pi$
$751$		−	2.06707e7i		−	1.33738i	0.743542	−	0.668690i	$-0.233144\pi$
$752$	−6.97012e6	+	1.92266e7i	−0.449465	+	1.23982i
$753$	−1.24655e7	−	8.74744e6i	−0.801167	−	0.562204i
$754$	−1.00181e7	+	3.16222e6i	−0.641738	+	0.202565i
$755$	−1.65318e7			−1.05549
$756$	5.58629e6	−	2.01791e6i	0.355483	−	0.128409i
$757$	−2.04221e6			−0.129527			−0.0647635	−	0.997901i	$-0.520629\pi$
$757$	−2.04221e6			−0.129527			−0.0647635	+	0.997901i	$0.520629\pi$
$758$	2.87604e7	−	9.07822e6i	1.81812	−	0.573889i
$759$	−381531.	−	267732.i	−0.0240395	−	0.0168693i
$760$	−2.13209e7	−	1.63277e7i	−1.33897	−	1.02539i
$761$			2.76595e7i			1.73134i	0.500613	+	0.865671i	$0.333108\pi$
$761$			2.76595e7i			1.73134i	−0.500613	+	0.865671i	$0.666892\pi$
$762$	−1.29664e6	−	409832.i	−0.0808972	−	0.0255693i
$763$		−	2.59605e6i		−	0.161436i
$764$	−7.13558e6	+	5.00318e6i	−0.442278	+	0.310108i
$765$	8.76114e6	+	2.42249e7i	0.541261	+	1.49661i
$766$	3.59121e6	+	1.13772e7i	0.221141	+	0.700590i
$767$	1.09728e7			0.673487
$768$	4.25474e6	+	1.57822e7i	0.260298	+	0.965528i
$769$	2.00522e6			0.122277			0.0611387	−	0.998129i	$-0.480527\pi$
$769$	2.00522e6			0.122277			0.0611387	+	0.998129i	$0.480527\pi$
$770$	−1.00110e6	−	3.17156e6i	−0.0608488	−	0.192773i
$771$	−5.01278e6	+	7.14345e6i	−0.303699	+	0.432785i
$772$	−6.67362e6	+	4.67927e6i	−0.403012	+	0.282576i
$773$		−	8.35686e6i		−	0.503030i	−0.967853	−	0.251515i	$-0.919071\pi$
$773$		−	8.35686e6i		−	0.503030i	0.967853	−	0.251515i	$-0.0809288\pi$
$774$	5.65531e6	+	7.39651e6i	0.339316	+	0.443787i
$775$		−	4.53212e7i		−	2.71049i
$776$	−3.63376e6	−	2.78276e6i	−0.216622	−	0.165891i
$777$	1.22357e6	−	1.74364e6i	0.0727069	−	0.103611i
$778$	1.98110e7	−	6.25334e6i	1.17343	−	0.370393i
$779$	2.82036e7			1.66518
$780$	4616.75	−	1.20447e7i	0.000271707	−	0.708858i
$781$	−3.91364e6			−0.229590
$782$	−1.42510e6	+	449833.i	−0.0833353	+	0.0263047i
$783$	−2.67831e7	−	7.26455e6i	−1.56119	−	0.423452i
$784$	−837949.	+	2.31142e6i	−0.0486886	+	0.134304i
$785$			4.98764e6i			0.288882i
$786$	−575907.	+	1.82208e6i	−0.0332504	+	0.105199i
$787$			2.34910e7i			1.35196i	0.736919	+	0.675981i	$0.236280\pi$
$787$			2.34910e7i			1.35196i	−0.736919	+	0.675981i	$0.763720\pi$
$788$	4.77703e6	+	6.81304e6i	0.274058	+	0.390864i
$789$	−1.95247e7	−	1.37011e7i	−1.11659	−	0.783544i
$790$	1.32668e7	+	4.20301e7i	0.756307	+	2.39603i
$791$	−5.48894e6			−0.311923
$792$	−1.67193e6	+	5.28269e6i	−0.0947122	+	0.299255i
$793$	−3.13997e6			−0.177314
$794$	−241464.	−	764973.i	−0.0135925	−	0.0430621i
$795$	2.30547e7	+	1.61782e7i	1.29372	+	0.907846i
$796$	1.44779e7	+	2.06486e7i	0.809886	+	1.15507i
$797$		−	2.18636e7i		−	1.21920i	−0.792708	−	0.609601i	$-0.791330\pi$
$797$		−	2.18636e7i		−	1.21920i	0.792708	−	0.609601i	$-0.208670\pi$
$798$	−2.02817e6	+	6.41680e6i	−0.112745	+	0.356707i
$799$			2.22274e7i			1.23175i
$800$	−3.44236e7	−	1.44795e6i	−1.90165	−	0.0799885i
$801$	−2.75087e7	+	9.94874e6i	−1.51492	+	0.547882i
$802$	3.89650e6	−	1.22993e6i	0.213914	−	0.0675218i
$803$	5.78919e6			0.316832
$804$	9409.02	−	2.45473e7i	0.000513339	−	1.33925i
$805$	−1.10787e6			−0.0602560
$806$	1.04197e7	−	3.28898e6i	0.564961	−	0.178330i
$807$	−1.47419e6	+	2.10080e6i	−0.0796839	+	0.113553i
$808$	−1.40824e7	+	1.83890e7i	−0.758839	+	0.990900i
$809$		−	909145.i		−	0.0488385i	−0.999702	−	0.0244192i	$-0.992226\pi$
$809$		−	909145.i		−	0.0488385i	0.999702	−	0.0244192i	$-0.00777365\pi$
$810$	1.71963e7	−	2.67697e7i	0.920921	−	1.43361i
$811$			951938.i			0.0508226i	0.999677	+	0.0254113i	$0.00808953\pi$
$811$			951938.i			0.0508226i	−0.999677	+	0.0254113i	$0.991910\pi$
$812$	9.40553e6	−	6.59477e6i	0.500602	−	0.351002i
$813$	1.23106e7	−	1.75432e7i	0.653211	−	0.930856i
$814$	598156.	+	1.89500e6i	0.0316412	+	0.100242i
$815$	2.05383e7			1.08310
$816$	1.01936e7	+	1.45501e7i	0.535922	+	0.764961i
$817$	−1.05494e7			−0.552932
$818$	−4.83409e6	−	1.53147e7i	−0.252599	−	0.800251i
$819$	−2.83844e6	+	1.02654e6i	−0.147866	+	0.0534771i
$820$	4.51937e7	−	3.16879e7i	2.34716	−	1.64573i
$821$			1.08653e7i			0.562577i	0.959623	+	0.281289i	$0.0907619\pi$
$821$			1.08653e7i			0.562577i	−0.959623	+	0.281289i	$0.909238\pi$
$822$	−7.54038e6	−	2.38330e6i	−0.389237	−	0.123027i
$823$		−	8.20455e6i		−	0.422236i	−0.977461	−	0.211118i	$-0.932290\pi$
$823$		−	8.20455e6i		−	0.422236i	0.977461	−	0.211118i	$-0.0677104\pi$
$824$	9.06674e6	−	1.18395e7i	0.465193	−	0.607454i
$825$	−9.56038e6	−	6.70881e6i	−0.489035	−	0.343171i
$826$	−1.14418e7	+	3.61161e6i	−0.583506	+	0.184183i
$827$	−2.32831e6			−0.118379			−0.0591897	−	0.998247i	$-0.518852\pi$
$827$	−2.32831e6			−0.118379			−0.0591897	+	0.998247i	$0.518852\pi$
$828$	1.51047e6	+	1.06081e6i	0.0765663	+	0.0537727i
$829$	2.27580e7			1.15013			0.575066	−	0.818107i	$-0.304976\pi$
$829$	2.27580e7			1.15013			0.575066	+	0.818107i	$0.304976\pi$
$830$	2.95855e7	−	9.33866e6i	1.49068	−	0.470532i
$831$	−1.63707e7	−	1.14879e7i	−0.822367	−	0.577080i
$832$	−2.16524e6	−	8.01935e6i	−0.108442	−	0.401634i
$833$			2.67219e6i			0.133430i
$834$	2.53477e7	+	8.01168e6i	1.26190	+	0.398849i
$835$		−	1.21399e7i		−	0.602560i
$836$	−3.60422e6	−	5.14037e6i	−0.178359	−	0.254378i
$837$	2.78568e7	+	7.55577e6i	1.37441	+	0.372791i
$838$	1.82780e6	+	5.79060e6i	0.0899122	+	0.284848i
$839$	−2.95005e7			−1.44685			−0.723427	−	0.690401i	$-0.757434\pi$
$839$	−2.95005e7			−1.44685			−0.723427	+	0.690401i	$0.757434\pi$
$840$	3.95960e6	+	1.25611e7i	0.193621	+	0.614226i
$841$	−3.31591e7			−1.61664
$842$	−4.15147e6	−	1.31522e7i	−0.201800	−	0.639318i
$843$	2.27039e7	−	3.23541e7i	1.10035	−	1.56805i
$844$	−3.96633e6	−	5.65681e6i	−0.191660	−	0.273348i
$845$		−	2.92455e7i		−	1.40902i
$846$	2.18090e7	−	1.66750e7i	1.04763	−	0.801013i
$847$			7.11400e6i			0.340726i
$848$	1.82607e7	+	6.61995e6i	0.872020	+	0.316130i
$849$	1.99230e7	−	2.83912e7i	0.948605	−	1.35181i
$850$	−3.57101e7	+	1.12719e7i	−1.69529	+	0.535117i
$851$	661950.			0.0313330
$852$	1.54982e7	+	5940.48i	0.731445	+	0.000280364i
$853$	−3.80978e7			−1.79278			−0.896391	−	0.443264i	$-0.853820\pi$
$853$	−3.80978e7			−1.79278			−0.896391	+	0.443264i	$0.853820\pi$
$854$	3.27418e6	−	1.03349e6i	0.153624	−	0.0484913i
$855$	1.22605e7	+	3.39007e7i	0.573577	+	1.58596i
$856$	2.22392e7	+	1.70309e7i	1.03737	+	0.794426i
$857$		−	2.35915e7i		−	1.09724i	−0.836071	−	0.548621i	$-0.815153\pi$
$857$		−	2.35915e7i		−	1.09724i	0.836071	−	0.548621i	$-0.184847\pi$
$858$	848610.	−	2.68487e6i	0.0393541	−	0.124510i
$859$		−	1.17362e6i		−	0.0542681i	−0.999632	−	0.0271341i	$-0.991362\pi$
$859$		−	1.17362e6i		−	0.0542681i	0.999632	−	0.0271341i	$-0.00863810\pi$
$860$	−1.69044e7	+	1.18527e7i	−0.779387	+	0.546474i
$861$	−1.13223e7	−	7.94524e6i	−0.520509	−	0.365258i
$862$	−5.64710e6	−	1.78904e7i	−0.258855	−	0.820072i
$863$	3.37797e6			0.154394			0.0771968	−	0.997016i	$-0.475403\pi$
$863$	3.37797e6			0.154394			0.0771968	+	0.997016i	$0.475403\pi$
$864$	6.62894e6	−	2.09171e7i	0.302106	−	0.953274i
$865$	−2.28521e7			−1.03845
$866$	3.33753e6	+	1.05735e7i	0.151227	+	0.479098i
$867$	−2.31222e6	−	1.62256e6i	−0.104467	−	0.0733081i
$868$	−9.78257e6	+	6.85913e6i	−0.440711	+	0.309008i
$869$			1.03036e7i			0.462850i
$870$	1.85450e7	−	5.86734e7i	0.830670	−	2.62811i
$871$			1.24744e7i			0.557152i
$872$	−7.61425e6	−	5.83105e6i	−0.339106	−	0.259690i
$873$	2.08958e6	+	5.77777e6i	0.0927948	+	0.256581i
$874$	−1.99431e6	+	629503.i	−0.0883108	+	0.0278753i
$875$	−1.31755e7			−0.581766
$876$	−2.29254e7	−	8787.36i	−1.00939	−	0.000386900i
$877$	−946751.			−0.0415659			−0.0207829	−	0.999784i	$-0.506616\pi$
$877$	−946751.			−0.0415659			−0.0207829	+	0.999784i	$0.506616\pi$
$878$	−4.29295e7	+	1.35507e7i	−1.87940	+	0.593232i
$879$	−1.84117e7	+	2.62376e7i	−0.803753	+	1.14539i
$880$	−1.15508e7	−	4.18748e6i	−0.502814	−	0.182283i
$881$			1.57293e7i			0.682761i	0.939925	+	0.341380i	$0.110894\pi$
$881$			1.57293e7i			0.682761i	−0.939925	+	0.341380i	$0.889106\pi$
$882$	2.62188e6	−	2.00467e6i	0.113486	−	0.0867704i
$883$			3.73913e6i			0.161387i	0.996739	+	0.0806935i	$0.0257135\pi$
$883$			3.73913e6i			0.161387i	−0.996739	+	0.0806935i	$0.974287\pi$
$884$	−5.18299e6	−	7.39203e6i	−0.223074	−	0.318151i
$885$	−3.69190e7	+	5.26113e7i	−1.58450	+	2.25798i
$886$	1.84452e6	+	5.84358e6i	0.0789405	+	0.250089i
$887$	−2.41136e6			−0.102909			−0.0514545	−	0.998675i	$-0.516386\pi$
$887$	−2.41136e6			−0.102909			−0.0514545	+	0.998675i	$0.516386\pi$
$888$	−2.36585e6	−	7.50518e6i	−0.100682	−	0.319396i
$889$	−755641.			−0.0320672
$890$	−1.95247e7	−	6.18558e7i	−0.826248	−	2.61761i
$891$	5.71745e6	−	4.75784e6i	0.241273	−	0.200778i
$892$	−1.52022e7	−	2.16816e7i	−0.639728	−	0.912386i
$893$			3.11054e7i			1.30529i
$894$	1.12519e7	+	3.55641e6i	0.470851	+	0.148823i
$895$		−	2.38097e7i		−	0.993565i
$896$	4.89730e6	+	7.64946e6i	0.203792	+	0.318318i
$897$	−767796.	−	538786.i	−0.0318614	−	0.0223581i
$898$	−2.62386e7	+	8.28221e6i	−1.08580	+	0.342733i
$899$	5.58217e7			2.30358
$900$	3.78493e7	+	2.65817e7i	1.55759	+	1.09390i
$901$	2.11107e7			0.866347
$902$	1.23052e7	−	3.88412e6i	0.503583	−	0.158956i
$903$	4.23505e6	+	2.97186e6i	0.172838	+	0.121286i
$904$	−1.23288e7	+	1.60991e7i	−0.501766	+	0.655211i
$905$		−	4.75225e7i		−	1.92876i
$906$	1.45931e7	+	4.61246e6i	0.590646	+	0.186686i
$907$			3.65317e7i			1.47452i	0.675607	+	0.737262i	$0.263882\pi$
$907$			3.65317e7i			1.47452i	−0.675607	+	0.737262i	$0.736118\pi$
$908$	2.63006e7	−	1.84409e7i	1.05865	−	0.742279i
$909$	2.92390e7	−	1.05745e7i	1.17369	−	0.424474i
$910$	−2.01463e6	−	6.38248e6i	−0.0806476	−	0.255497i
$911$	7.00311e6			0.279573			0.139786	−	0.990182i	$-0.455358\pi$
$911$	7.00311e6			0.279573			0.139786	+	0.990182i	$0.455358\pi$
$912$	1.42651e7	+	2.03616e7i	0.567919	+	0.810633i
$913$	7.25284e6			0.287959
$914$	1.41553e6	+	4.48451e6i	0.0560473	+	0.177562i
$915$	1.05647e7	−	1.50552e7i	0.417162	−	0.594475i
$916$	1.20997e7	−	8.48384e6i	0.476472	−	0.334082i
$917$			1.06185e6i			0.0417003i
$918$	−974839.	−	2.38284e7i	−0.0381791	−	0.933231i
$919$		−	3.32983e7i		−	1.30057i	−0.759691	−	0.650285i	$-0.774650\pi$
$919$		−	3.32983e7i		−	1.30057i	0.759691	−	0.650285i	$-0.225350\pi$
$920$	−2.48842e6	+	3.24941e6i	−0.0969291	+	0.126571i
$921$	−5.06127e6	+	7.21254e6i	−0.196612	+	0.280181i
$922$	−3.02029e7	+	9.53352e6i	−1.17009	+	0.369340i
$923$	−7.87584e6			−0.304293
$924$	−1180.17	+	3.07895e6i	−4.54740e−5	+	0.118638i
$925$	1.65871e7			0.637406
$926$	−2.96455e7	+	9.35759e6i	−1.13614	+	0.358622i
$927$	−1.88250e7	+	6.80822e6i	−0.719508	+	0.260216i
$928$	1.78342e6	−	4.23992e7i	0.0679804	−	1.61617i
$929$		−	2.52854e7i		−	0.961237i	−0.876930	−	0.480618i	$-0.840412\pi$
$929$		−	2.52854e7i		−	0.961237i	0.876930	−	0.480618i	$-0.159588\pi$
$930$	−1.92884e7	+	6.10255e7i	−0.731289	+	2.31368i
$931$			3.73950e6i			0.141397i
$932$	−1.21893e7	−	1.73845e7i	−0.459662	−	0.655575i
$933$	2.36752e7	+	1.66136e7i	0.890410	+	0.624829i
$934$	7.66610e6	+	2.42867e7i	0.287546	+	0.910965i
$935$	−1.33537e7			−0.499542
$936$	−3.36461e6	+	1.06309e7i	−0.125529	+	0.396626i
$937$	2.12114e7			0.789260			0.394630	−	0.918840i	$-0.370873\pi$
$937$	2.12114e7			0.789260			0.394630	+	0.918840i	$0.370873\pi$
$938$	−4.10584e6	−	1.30076e7i	−0.152368	−	0.482714i
$939$	−9.72210e6	−	6.82230e6i	−0.359829	−	0.252503i
$940$	3.49482e7	+	4.98435e7i	1.29005	+	1.83988i
$941$			2.90310e7i			1.06878i	0.845239	+	0.534389i	$0.179458\pi$
$941$			2.90310e7i			1.06878i	−0.845239	+	0.534389i	$0.820542\pi$
$942$	1.39158e6	−	4.40274e6i	0.0510952	−	0.161657i
$943$		−	4.29837e6i		−	0.157407i
$944$	−1.51069e7	+	4.16712e7i	−0.551753	+	1.52197i
$945$	4.62820e6	−	1.70633e7i	0.168590	−	0.621562i
$946$	−4.60266e6	+	1.45283e6i	−0.167217	+	0.0527821i
$947$	−2.36138e7			−0.855639			−0.427820	−	0.903864i	$-0.640718\pi$
$947$	−2.36138e7			−0.855639			−0.427820	+	0.903864i	$0.640718\pi$
$948$	15639.8	−	4.08027e7i	0.000565209	−	1.47458i
$949$	1.16502e7			0.419921
$950$	−4.99732e7	+	1.57740e7i	−1.79650	+	0.567066i
$951$	−3.78157e6	+	5.38892e6i	−0.135588	+	0.193219i
$952$	7.83756e6	+	6.00206e6i	0.280278	+	0.214639i
$953$			1.35710e7i			0.484039i	0.970271	+	0.242020i	$0.0778099\pi$
$953$			1.35710e7i			0.484039i	−0.970271	+	0.242020i	$0.922190\pi$
$954$	−1.58373e7	−	2.07134e7i	−0.563390	−	0.736851i
$955$			2.59407e7i			0.920395i
$956$	3.14985e7	−	2.20854e7i	1.11467	−	0.781558i
$957$	8.26318e6	−	1.17754e7i	0.291654	−	0.415620i
$958$	−3.10622e6	−	9.84073e6i	−0.109350	−	0.346428i
$959$	−4.39428e6			−0.154291
$960$	4.57355e7	+	1.66001e7i	1.60168	+	0.581344i
$961$	−2.94303e7			−1.02798
$962$	1.20373e6	+	3.81351e6i	0.0419365	+	0.132858i
$963$	−1.27885e7	−	3.53608e7i	−0.444381	−	1.22873i
$964$	−2.72459e7	+	1.91037e7i	−0.944296	+	0.662102i
$965$			2.42613e7i			0.838681i
$966$	977953.	+	309103.i	0.0337190	+	0.0106576i
$967$			3.89108e7i			1.33815i	0.743196	+	0.669074i	$0.233309\pi$
$967$			3.89108e7i			1.33815i	−0.743196	+	0.669074i	$0.766691\pi$
$968$	2.08655e7	+	1.59789e7i	0.715714	+	0.548099i
$969$	2.21183e7	+	1.55211e7i	0.756733	+	0.531023i
$970$	−1.29918e7	+	4.10087e6i	−0.443345	+	0.139942i
$971$	−1.82151e7			−0.619987			−0.309993	−	0.950739i	$-0.600327\pi$
$971$	−1.82151e7			−0.619987			−0.309993	+	0.950739i	$0.600327\pi$
$972$	−2.26486e7	+	1.88326e7i	−0.768910	+	0.639358i
$973$	1.47718e7			0.500209
$974$	−1.27245e7	+	4.01649e6i	−0.429778	+	0.135659i
$975$	−1.92394e7	−	1.35009e7i	−0.648156	−	0.454831i
$976$	4.32297e6	−	1.19246e7i	0.145264	−	0.400699i
$977$		−	3.97089e7i		−	1.33092i	−0.746434	−	0.665459i	$-0.768236\pi$
$977$		−	3.97089e7i		−	1.33092i	0.746434	−	0.665459i	$-0.231764\pi$
$978$	−1.81297e7	−	5.73029e6i	−0.606100	−	0.191571i
$979$		−	1.51638e7i		−	0.505652i
$980$	4.20148e6	+	5.99220e6i	0.139745	+	0.199306i
$981$	4.37854e6	+	1.21068e7i	0.145264	+	0.401660i
$982$	−5.15823e6	−	1.63416e7i	−0.170695	−	0.540775i
$983$	1.30999e7			0.432399			0.216199	−	0.976349i	$-0.430634\pi$
$983$	1.30999e7			0.432399			0.216199	+	0.976349i	$0.430634\pi$
$984$	−4.87349e7	+	1.53626e7i	−1.60455	+	0.505798i
$985$	2.47682e7			0.813399
$986$	−1.38834e7	−	4.39837e7i	−0.454784	−	1.44079i
$987$	8.76270e6	−	1.24873e7i	0.286316	−	0.408013i
$988$	−7.25316e6	−	1.03445e7i	−0.236393	−	0.337146i
$989$			1.60778e6i			0.0522679i
$990$	1.00179e7	+	1.31023e7i	0.324855	+	0.424874i
$991$		−	7.15876e6i		−	0.231555i	−0.993275	−	0.115777i	$-0.963064\pi$
$991$		−	7.15876e6i		−	0.231555i	0.993275	−	0.115777i	$-0.0369359\pi$
$992$	−1.85491e6	+	4.40989e7i	−0.0598473	+	1.42281i
$993$	2.14129e7	−	3.05144e7i	0.689131	−	0.982044i
$994$	8.21249e6	−	2.59227e6i	0.263638	−	0.0832174i
$995$	7.50660e7			2.40373
$996$	−2.87215e7	−	11009.0i	−0.917402	−	0.000351642i
$997$	2.42531e7			0.772731			0.386366	−	0.922346i	$-0.373730\pi$
$997$	2.42531e7			0.772731			0.386366	+	0.922346i	$0.373730\pi$
$998$	−4.45260e7	+	1.40546e7i	−1.41510	+	0.446676i
$999$	−2.76533e6	+	1.01953e7i	−0.0876665	+	0.323211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.6.e.a.71.36	yes	60
3.2	odd	2	inner	84.6.e.a.71.25	✓	60
4.3	odd	2	inner	84.6.e.a.71.26	yes	60
12.11	even	2	inner	84.6.e.a.71.35	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.6.e.a.71.25	✓	60	3.2	odd	2	inner
84.6.e.a.71.26	yes	60	4.3	odd	2	inner
84.6.e.a.71.35	yes	60	12.11	even	2	inner
84.6.e.a.71.36	yes	60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	84.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.70277 + 5.39449i) q^{2} +(-12.7602 - 8.95421i) q^{3} +(-26.2011 + 18.3712i) q^{4} +95.2519i q^{5} +(26.5758 - 84.0817i) q^{6} -49.0000i q^{7} +(-143.718 - 110.060i) q^{8} +(82.6442 + 228.515i) q^{9} +(-513.836 + 162.192i) q^{10} -125.966 q^{11} +(498.831 + 0.191203i) q^{12} -253.495 q^{13} +(264.330 - 83.4357i) q^{14} +(852.905 - 1215.43i) q^{15} +(349.000 - 962.691i) q^{16} -1112.95i q^{17} +(-1092.00 + 834.932i) q^{18} -1557.48i q^{19} +(-1749.89 - 2495.71i) q^{20} +(-438.756 + 625.249i) q^{21} +(-214.491 - 679.523i) q^{22} -237.367 q^{23} +(848.362 + 2691.26i) q^{24} -5947.92 q^{25} +(-431.643 - 1367.48i) q^{26} +(991.613 - 3655.90i) q^{27} +(900.187 + 1283.86i) q^{28} -7326.00i q^{29} +(8008.94 + 2531.39i) q^{30} +7619.67i q^{31} +(5787.50 + 243.437i) q^{32} +(1607.35 + 1127.93i) q^{33} +(6003.79 - 1895.09i) q^{34} +4667.34 q^{35} +(-6363.45 - 4469.07i) q^{36} -2788.72 q^{37} +(8401.79 - 2652.02i) q^{38} +(3234.64 + 2269.85i) q^{39} +(10483.4 - 13689.4i) q^{40} +18108.6i q^{41} +(-4120.00 - 1302.21i) q^{42} -6773.38i q^{43} +(3300.45 - 2314.14i) q^{44} +(-21766.4 + 7872.02i) q^{45} +(-404.182 - 1280.48i) q^{46} -19971.7 q^{47} +(-13073.4 + 9159.09i) q^{48} -2401.00 q^{49} +(-10127.9 - 32086.0i) q^{50} +(-9965.56 + 14201.4i) q^{51} +(6641.85 - 4657.00i) q^{52} +18968.3i q^{53} +(21410.2 - 875.907i) q^{54} -11998.5i q^{55} +(-5392.94 + 7042.17i) q^{56} +(-13946.0 + 19873.7i) q^{57} +(39520.0 - 12474.5i) q^{58} -43286.1 q^{59} +(-18.2124 + 47514.6i) q^{60} +12386.7 q^{61} +(-41104.3 + 12974.6i) q^{62} +(11197.2 - 4049.57i) q^{63} +(8541.56 + 31635.2i) q^{64} -24145.9i q^{65} +(-3347.64 + 10591.4i) q^{66} -49209.6i q^{67} +(20446.1 + 29160.5i) q^{68} +(3028.85 + 2125.43i) q^{69} +(7947.41 + 25178.0i) q^{70} +31069.0 q^{71} +(13272.9 - 41937.4i) q^{72} -45958.4 q^{73} +(-4748.55 - 15043.7i) q^{74} +(75896.5 + 53259.0i) q^{75} +(28612.6 + 40807.6i) q^{76} +6172.33i q^{77} +(-6736.82 + 21314.3i) q^{78} -81796.8i q^{79} +(91698.2 + 33242.9i) q^{80} +(-45388.9 + 37770.8i) q^{81} +(-97686.5 + 30834.7i) q^{82} -57577.8 q^{83} +(9.36893 - 24442.7i) q^{84} +106010. q^{85} +(36539.0 - 11533.5i) q^{86} +(-65598.5 + 93481.0i) q^{87} +(18103.5 + 13863.8i) q^{88} +120380. i q^{89} +(-79528.8 - 104015. i) q^{90} +12421.2i q^{91} +(6219.29 - 4360.71i) q^{92} +(68228.2 - 97228.4i) q^{93} +(-34007.2 - 107737. i) q^{94} +148352. q^{95} +(-71669.8 - 54928.8i) q^{96} +25284.0 q^{97} +(-4088.35 - 12952.2i) q^{98} +(-10410.4 - 28785.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 20 q^{4} - 114 q^{6} + 44 q^{9} + 668 q^{10} + 786 q^{12} - 3004 q^{16} - 3320 q^{18} + 7120 q^{22} + 16466 q^{24} - 37500 q^{25} - 7448 q^{28} - 35236 q^{30} - 9424 q^{33} + 43360 q^{34} + 50524 q^{36}+ \cdots + 232584 q^{97}+O(q^{100}) \) 60 * q - 20 * q^4 - 114 * q^6 + 44 * q^9 + 668 * q^10 + 786 * q^12 - 3004 * q^16 - 3320 * q^18 + 7120 * q^22 + 16466 * q^24 - 37500 * q^25 - 7448 * q^28 - 35236 * q^30 - 9424 * q^33 + 43360 * q^34 + 50524 * q^36 - 15056 * q^37 - 35468 * q^40 - 20090 * q^42 + 36024 * q^45 + 124416 * q^46 + 88654 * q^48 - 144060 * q^49 - 140108 * q^52 + 19486 * q^54 - 65072 * q^57 + 115616 * q^58 + 164908 * q^60 - 169424 * q^61 + 20116 * q^64 - 98484 * q^66 + 142536 * q^69 + 35868 * q^70 + 121312 * q^72 + 107256 * q^73 + 214836 * q^76 + 263708 * q^78 - 114932 * q^81 - 479624 * q^82 + 40474 * q^84 - 383992 * q^85 - 107320 * q^88 + 423760 * q^90 + 545208 * q^93 - 448512 * q^94 - 751618 * q^96 + 232584 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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