LMFDB - Embedded newform 80.6.q.a.29.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(29,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("80.29");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.q (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.6
Character	$\chi$	$=$	80.29
Dual form			80.6.q.a.69.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.44124 + 1.54691i) q^{2} +(9.88218 - 9.88218i) q^{3} +(27.2142 - 16.8342i) q^{4} +(27.0375 + 48.9282i) q^{5} +(-38.4845 + 69.0581i) q^{6} -163.839 q^{7} +(-122.038 + 133.697i) q^{8} +47.6849i q^{9} +O(q^{10})$	\(q+(-5.44124 + 1.54691i) q^{2} +(9.88218 - 9.88218i) q^{3} +(27.2142 - 16.8342i) q^{4} +(27.0375 + 48.9282i) q^{5} +(-38.4845 + 69.0581i) q^{6} -163.839 q^{7} +(-122.038 + 133.697i) q^{8} +47.6849i q^{9} +(-222.805 - 224.406i) q^{10} +(237.296 - 237.296i) q^{11} +(102.577 - 435.294i) q^{12} +(-496.001 + 496.001i) q^{13} +(891.486 - 253.443i) q^{14} +(750.708 + 216.328i) q^{15} +(457.221 - 916.256i) q^{16} +595.429i q^{17} +(-73.7640 - 259.465i) q^{18} +(424.045 + 424.045i) q^{19} +(1559.47 + 876.386i) q^{20} +(-1619.08 + 1619.08i) q^{21} +(-924.111 + 1658.26i) q^{22} -4158.82 q^{23} +(115.213 + 2527.21i) q^{24} +(-1662.94 + 2645.80i) q^{25} +(1931.59 - 3466.13i) q^{26} +(2872.60 + 2872.60i) q^{27} +(-4458.73 + 2758.09i) q^{28} +(3202.25 + 3202.25i) q^{29} +(-4419.42 - 15.8166i) q^{30} -7965.53 q^{31} +(-1070.49 + 5692.85i) q^{32} -4690.01i q^{33} +(-921.073 - 3239.87i) q^{34} +(-4429.80 - 8016.34i) q^{35} +(802.736 + 1297.70i) q^{36} +(7883.67 + 7883.67i) q^{37} +(-2963.29 - 1651.37i) q^{38} +9803.15i q^{39} +(-9841.14 - 2356.27i) q^{40} +10819.2i q^{41} +(6305.25 - 11314.4i) q^{42} +(14859.6 + 14859.6i) q^{43} +(2463.13 - 10452.5i) q^{44} +(-2333.14 + 1289.28i) q^{45} +(22629.1 - 6433.30i) q^{46} -10242.4i q^{47} +(-4536.27 - 13573.0i) q^{48} +10036.1 q^{49} +(4955.67 - 16968.8i) q^{50} +(5884.14 + 5884.14i) q^{51} +(-5148.49 + 21848.0i) q^{52} +(-25488.4 - 25488.4i) q^{53} +(-20074.2 - 11186.9i) q^{54} +(18026.4 + 5194.58i) q^{55} +(19994.5 - 21904.7i) q^{56} +8380.99 q^{57} +(-22377.8 - 12470.6i) q^{58} +(1433.11 - 1433.11i) q^{59} +(24071.6 - 6750.36i) q^{60} +(-6070.84 - 6070.84i) q^{61} +(43342.3 - 12321.9i) q^{62} -7812.63i q^{63} +(-2981.52 - 32632.1i) q^{64} +(-37679.1 - 10857.8i) q^{65} +(7255.01 + 25519.5i) q^{66} +(27935.2 - 27935.2i) q^{67} +(10023.6 + 16204.1i) q^{68} +(-41098.2 + 41098.2i) q^{69} +(36504.1 + 36766.3i) q^{70} +17162.5i q^{71} +(-6375.30 - 5819.36i) q^{72} -22459.0 q^{73} +(-55092.2 - 30701.6i) q^{74} +(9712.76 + 42579.8i) q^{75} +(18678.5 + 4401.59i) q^{76} +(-38878.3 + 38878.3i) q^{77} +(-15164.6 - 53341.3i) q^{78} +3182.60 q^{79} +(57192.9 - 2402.28i) q^{80} +45187.7 q^{81} +(-16736.2 - 58869.7i) q^{82} +(-24530.3 + 24530.3i) q^{83} +(-16806.1 + 71318.0i) q^{84} +(-29133.3 + 16098.9i) q^{85} +(-103841. - 57868.1i) q^{86} +63290.4 q^{87} +(2766.56 + 60684.8i) q^{88} -36437.3i q^{89} +(10700.8 - 10624.4i) q^{90} +(81264.2 - 81264.2i) q^{91} +(-113179. + 70010.2i) q^{92} +(-78716.8 + 78716.8i) q^{93} +(15844.0 + 55731.2i) q^{94} +(-9282.65 + 32212.9i) q^{95} +(45679.0 + 66836.5i) q^{96} -32621.8i q^{97} +(-54609.0 + 15524.9i) q^{98} +(11315.4 + 11315.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−5.44124	+	1.54691i	−0.961884	+	0.273457i
$2$	−5.44124	+	1.54691i	−0.961884	+	0.273457i
$3$	9.88218	−	9.88218i	0.633942	−	0.633942i	−0.315112	−	0.949054i	$-0.602042\pi$
$3$	9.88218	−	9.88218i	0.633942	−	0.633942i	0.949054	+	0.315112i	$0.102042\pi$
$4$	27.2142	−	16.8342i	0.850443	−	0.526068i
$5$	27.0375	+	48.9282i	0.483662	+	0.875255i
$5$	27.0375	+	48.9282i	0.483662	+	0.875255i
$6$	−38.4845	+	69.0581i	−0.436423	+	0.783135i
$7$	−163.839			−1.26378			−0.631890	−	0.775058i	$-0.717721\pi$
$7$	−163.839			−1.26378			−0.631890	+	0.775058i	$0.717721\pi$
$8$	−122.038	+	133.697i	−0.674170	+	0.738576i
$9$			47.6849i			0.196234i
$10$	−222.805	−	224.406i	−0.704572	−	0.709633i
$11$	237.296	−	237.296i	0.591302	−	0.591302i	−0.346681	−	0.937983i	$-0.612691\pi$
$11$	237.296	−	237.296i	0.591302	−	0.591302i	0.937983	+	0.346681i	$0.112691\pi$
$12$	102.577	−	435.294i	0.205635	−	0.872628i
$13$	−496.001	+	496.001i	−0.814000	+	0.814000i	−0.985231	−	0.171231i	$-0.945226\pi$
$13$	−496.001	+	496.001i	−0.814000	+	0.814000i	0.171231	+	0.985231i	$0.445226\pi$
$14$	891.486	−	253.443i	1.21561	−	0.345589i
$15$	750.708	+	216.328i	0.861475	+	0.248247i
$16$	457.221	−	916.256i	0.446505	−	0.894781i
$17$			595.429i			0.499698i	0.968285	+	0.249849i	$0.0803810\pi$
$17$			595.429i			0.499698i	−0.968285	+	0.249849i	$0.919619\pi$
$18$	−73.7640	−	259.465i	−0.0536616	−	0.188754i
$19$	424.045	+	424.045i	0.269481	+	0.269481i	0.828891	−	0.559410i	$-0.188972\pi$
$19$	424.045	+	424.045i	0.269481	+	0.269481i	−0.559410	+	0.828891i	$0.688972\pi$
$20$	1559.47	+	876.386i	0.871770	+	0.489915i
$21$	−1619.08	+	1619.08i	−0.801164	+	0.801164i
$22$	−924.111	+	1658.26i	−0.407068	+	0.730459i
$23$	−4158.82			−1.63927			−0.819634	−	0.572887i	$-0.805823\pi$
$23$	−4158.82			−1.63927			−0.819634	+	0.572887i	$0.805823\pi$
$24$	115.213	+	2527.21i	0.0408294	+	0.895600i
$25$	−1662.94	+	2645.80i	−0.532142	+	0.846655i
$26$	1931.59	−	3466.13i	0.560380	−	1.00557i
$27$	2872.60	+	2872.60i	0.758343	+	0.758343i
$28$	−4458.73	+	2758.09i	−1.07477	+	0.664834i
$29$	3202.25	+	3202.25i	0.707066	+	0.707066i	0.965917	−	0.258851i	$-0.0833439\pi$
$29$	3202.25	+	3202.25i	0.707066	+	0.707066i	−0.258851	+	0.965917i	$0.583344\pi$
$30$	−4419.42	−	15.8166i	−0.896524	−	0.00320856i
$31$	−7965.53			−1.48871			−0.744355	−	0.667784i	$-0.767243\pi$
$31$	−7965.53			−1.48871			−0.744355	+	0.667784i	$0.767243\pi$
$32$	−1070.49	+	5692.85i	−0.184802	+	0.982776i
$33$		−	4690.01i		−	0.749702i
$34$	−921.073	−	3239.87i	−0.136646	−	0.480652i
$35$	−4429.80	−	8016.34i	−0.611243	−	1.10613i
$36$	802.736	+	1297.70i	0.103232	+	0.166886i
$37$	7883.67	+	7883.67i	0.946725	+	0.946725i	0.998651	−	0.0519256i	$-0.0165359\pi$
$37$	7883.67	+	7883.67i	0.946725	+	0.946725i	−0.0519256	+	0.998651i	$0.516536\pi$
$38$	−2963.29	−	1651.37i	−0.332901	−	0.185518i
$39$			9803.15i			1.03206i
$40$	−9841.14	−	2356.27i	−0.972513	−	0.232849i
$41$			10819.2i			1.00516i	0.864531	+	0.502579i	$0.167615\pi$
$41$			10819.2i			1.00516i	−0.864531	+	0.502579i	$0.832385\pi$
$42$	6305.25	−	11314.4i	0.551543	−	0.989710i
$43$	14859.6	+	14859.6i	1.22556	+	1.22556i	0.965626	+	0.259936i	$0.0837015\pi$
$43$	14859.6	+	14859.6i	1.22556	+	1.22556i	0.259936	+	0.965626i	$0.416298\pi$
$44$	2463.13	−	10452.5i	0.191803	−	0.813933i
$45$	−2333.14	+	1289.28i	−0.171755	+	0.0949110i
$46$	22629.1	−	6433.30i	1.57679	−	0.448270i
$47$		−	10242.4i		−	0.676326i	−0.941088	−	0.338163i	$-0.890195\pi$
$47$		−	10242.4i		−	0.676326i	0.941088	−	0.338163i	$-0.109805\pi$
$48$	−4536.27	−	13573.0i	−0.284181	−	0.850298i
$49$	10036.1			0.597140
$50$	4955.67	−	16968.8i	0.280335	−	0.959902i
$51$	5884.14	+	5884.14i	0.316780	+	0.316780i
$52$	−5148.49	+	21848.0i	−0.264041	+	1.12048i
$53$	−25488.4	−	25488.4i	−1.24639	−	1.24639i	−0.957303	−	0.289086i	$-0.906649\pi$
$53$	−25488.4	−	25488.4i	−1.24639	−	1.24639i	−0.289086	−	0.957303i	$-0.593351\pi$
$54$	−20074.2	−	11186.9i	−0.936813	−	0.522064i
$55$	18026.4	+	5194.58i	0.803530	+	0.231549i
$56$	19994.5	−	21904.7i	0.852003	−	0.933397i
$57$	8380.99			0.341671
$58$	−22377.8	−	12470.6i	−0.873468	−	0.486764i
$59$	1433.11	−	1433.11i	0.0535982	−	0.0535982i	−0.679800	−	0.733398i	$-0.737933\pi$
$59$	1433.11	−	1433.11i	0.0535982	−	0.0535982i	0.733398	+	0.679800i	$0.237933\pi$
$60$	24071.6	−	6750.36i	0.863230	−	0.242075i
$61$	−6070.84	−	6070.84i	−0.208893	−	0.208893i	0.594904	−	0.803797i	$-0.297190\pi$
$61$	−6070.84	−	6070.84i	−0.208893	−	0.208893i	−0.803797	+	0.594904i	$0.797190\pi$
$62$	43342.3	−	12321.9i	1.43197	−	0.407098i
$63$		−	7812.63i		−	0.247997i
$64$	−2981.52	−	32632.1i	−0.0909887	−	0.995852i
$65$	−37679.1	−	10857.8i	−1.10616	−	0.318756i
$66$	7255.01	+	25519.5i	0.205011	+	0.721127i
$67$	27935.2	−	27935.2i	0.760263	−	0.760263i	−0.216106	−	0.976370i	$-0.569336\pi$
$67$	27935.2	−	27935.2i	0.760263	−	0.760263i	0.976370	+	0.216106i	$0.0693358\pi$
$68$	10023.6	+	16204.1i	0.262875	+	0.424965i
$69$	−41098.2	+	41098.2i	−1.03920	+	1.03920i
$70$	36504.1	+	36766.3i	0.890423	+	0.896820i
$71$			17162.5i			0.404049i	0.979380	+	0.202024i	$0.0647520\pi$
$71$			17162.5i			0.404049i	−0.979380	+	0.202024i	$0.935248\pi$
$72$	−6375.30	−	5819.36i	−0.144934	−	0.132295i
$73$	−22459.0			−0.493269			−0.246635	−	0.969109i	$-0.579325\pi$
$73$	−22459.0			−0.493269			−0.246635	+	0.969109i	$0.579325\pi$
$74$	−55092.2	−	30701.6i	−1.16953	−	0.651752i
$75$	9712.76	+	42579.8i	0.199384	+	0.874078i
$76$	18678.5	+	4401.59i	0.370944	+	0.0874129i
$77$	−38878.3	+	38878.3i	−0.747275	+	0.747275i
$78$	−15164.6	−	53341.3i	−0.282224	−	0.992721i
$79$	3182.60			0.0573738			0.0286869	−	0.999588i	$-0.490867\pi$
$79$	3182.60			0.0573738			0.0286869	+	0.999588i	$0.490867\pi$
$80$	57192.9	−	2402.28i	0.999119	−	0.0419662i
$81$	45187.7			0.765258
$82$	−16736.2	−	58869.7i	−0.274867	−	0.966845i
$83$	−24530.3	+	24530.3i	−0.390848	+	0.390848i	−0.874990	−	0.484142i	$-0.839132\pi$
$83$	−24530.3	+	24530.3i	−0.390848	+	0.390848i	0.484142	+	0.874990i	$0.339132\pi$
$84$	−16806.1	+	71318.0i	−0.259877	+	1.10281i
$85$	−29133.3	+	16098.9i	−0.437363	+	0.241685i
$86$	−103841.	−	57868.1i	−1.51399	−	0.843710i
$87$	63290.4			0.896478
$88$	2766.56	+	60684.8i	0.0380831	+	0.835359i
$89$		−	36437.3i		−	0.487608i	−0.969824	−	0.243804i	$-0.921605\pi$
$89$		−	36437.3i		−	0.487608i	0.969824	−	0.243804i	$-0.0783954\pi$
$90$	10700.8	−	10624.4i	0.139254	−	0.138261i
$91$	81264.2	−	81264.2i	1.02872	−	1.02872i
$92$	−113179.	+	70010.2i	−1.39410	+	0.862367i
$93$	−78716.8	+	78716.8i	−0.943757	+	0.943757i
$94$	15844.0	+	55731.2i	0.184946	+	0.650547i
$95$	−9282.65	+	32212.9i	−0.105527	+	0.366203i
$96$	45679.0	+	66836.5i	0.505869	+	0.740177i
$97$		−	32621.8i		−	0.352029i	−0.984388	−	0.176014i	$-0.943679\pi$
$97$		−	32621.8i		−	0.352029i	0.984388	−	0.176014i	$-0.0563206\pi$
$98$	−54609.0	+	15524.9i	−0.574379	+	0.163292i
$99$	11315.4	+	11315.4i	0.116034	+	0.116034i
$100$	−715.767	+	99997.4i	−0.00715767	+	0.999974i
$101$	62763.5	−	62763.5i	0.612215	−	0.612215i	−0.331308	−	0.943523i	$-0.607490\pi$
$101$	62763.5	−	62763.5i	0.612215	−	0.612215i	0.943523	+	0.331308i	$0.107490\pi$
$102$	−41119.2	−	22914.8i	−0.391331	−	0.218080i
$103$	89216.5			0.828614			0.414307	−	0.910137i	$-0.364024\pi$
$103$	89216.5			0.828614			0.414307	+	0.910137i	$0.364024\pi$
$104$	−5782.71	−	126845.i	−0.0524262	−	1.14998i
$105$	−122995.	−	35442.9i	−1.08871	−	0.313730i
$106$	178117.	+	99260.5i	1.53972	+	0.858048i
$107$	−15708.7	−	15708.7i	−0.132642	−	0.132642i	0.637669	−	0.770311i	$-0.279899\pi$
$107$	−15708.7	−	15708.7i	−0.132642	−	0.132642i	−0.770311	+	0.637669i	$0.779899\pi$
$108$	126533.	+	29817.6i	1.04387	+	0.245987i
$109$	34699.7	+	34699.7i	0.279743	+	0.279743i	0.833006	−	0.553264i	$-0.186618\pi$
$109$	34699.7	+	34699.7i	0.279743	+	0.279743i	−0.553264	+	0.833006i	$0.686618\pi$
$110$	−106121.	−	379.796i	−0.836222	−	0.00299274i
$111$	155816.			1.20034
$112$	−74910.5	+	150118.i	−0.564284	+	1.13081i
$113$		−	186059.i		−	1.37074i	−0.728195	−	0.685370i	$-0.759640\pi$
$113$		−	186059.i		−	1.37074i	0.728195	−	0.685370i	$-0.240360\pi$
$114$	−45603.0	+	12964.6i	−0.328648	+	0.0934323i
$115$	−112444.	−	203484.i	−0.792852	−	1.43478i
$116$	141054.	+	33239.3i	0.973284	+	0.229354i
$117$	−23651.8	−	23651.8i	−0.159735	−	0.159735i
$118$	−5581.01	+	10014.8i	−0.0368984	+	0.0662120i
$119$		−	97554.4i		−	0.631509i
$120$	−120537.	+	73966.8i	−0.764130	+	0.468904i
$121$			48432.0i			0.300724i
$122$	42423.9	+	23641.9i	0.258054	+	0.143808i
$123$	106917.	+	106917.i	0.637212	+	0.637212i
$124$	−216775.	+	134093.i	−1.26606	+	0.783163i
$125$	−174416.	−	9828.96i	−0.998416	−	0.0562643i
$126$	12085.4	+	42510.4i	0.0678164	+	0.238544i
$127$		−	17509.6i		−	0.0963313i	−0.998839	−	0.0481657i	$-0.984662\pi$
$127$		−	17509.6i		−	0.0963313i	0.998839	−	0.0481657i	$-0.0153375\pi$
$128$	66701.9	+	172947.i	0.359843	+	0.933013i
$129$	293690.			1.55387
$130$	221817.	+	793.858i	1.15116	+	0.00411988i
$131$	−120437.	−	120437.i	−0.613170	−	0.613170i	0.330600	−	0.943771i	$-0.392749\pi$
$131$	−120437.	−	120437.i	−0.613170	−	0.613170i	−0.943771	+	0.330600i	$0.892749\pi$
$132$	−78952.5	−	127635.i	−0.394394	−	0.637579i
$133$	−69475.1	−	69475.1i	−0.340565	−	0.340565i
$134$	−108789.	+	195215.i	−0.523386	+	0.939185i
$135$	−62883.2	+	218219.i	−0.296962	+	1.03053i
$136$	−79606.8	−	72664.9i	−0.369065	−	0.336882i
$137$	−149328.			−0.679734			−0.339867	−	0.940473i	$-0.610382\pi$
$137$	−149328.			−0.679734			−0.339867	+	0.940473i	$0.610382\pi$
$138$	160050.	−	287200.i	0.715415	−	1.28377i
$139$	207476.	−	207476.i	0.910815	−	0.910815i	−0.0855210	−	0.996336i	$-0.527255\pi$
$139$	207476.	−	207476.i	0.910815	−	0.910815i	0.996336	+	0.0855210i	$0.0272555\pi$
$140$	−255502.	−	143586.i	−1.10173	−	0.619144i
$141$	−101217.	−	101217.i	−0.428751	−	0.428751i
$142$	−26548.7	−	93385.1i	−0.110490	−	0.388648i
$143$			235399.i			0.962639i
$144$	43691.6	+	21802.5i	0.175587	+	0.0876195i
$145$	−70099.4	+	243261.i	−0.276882	+	0.960844i
$146$	122205.	−	34742.0i	0.474468	−	0.134888i
$147$	99178.8	−	99178.8i	0.378552	−	0.378552i
$148$	347262.	+	81832.4i	1.30318	+	0.307094i
$149$	−305179.	+	305179.i	−1.12613	+	1.12613i	−0.135332	+	0.990800i	$0.543210\pi$
$149$	−305179.	+	305179.i	−1.12613	+	1.12613i	−0.990800	+	0.135332i	$0.956790\pi$
$150$	−118716.	−	216662.i	−0.430807	−	0.786239i
$151$			106699.i			0.380817i	0.981705	+	0.190409i	$0.0609813\pi$
$151$			106699.i			0.380817i	−0.981705	+	0.190409i	$0.939019\pi$
$152$	−108443.	+	4943.80i	−0.380709	+	0.0173561i
$153$	−28393.0			−0.0980578
$154$	151405.	−	271687.i	0.514445	−	0.923140i
$155$	−215368.	−	389739.i	−0.720033	−	1.30300i
$156$	165028.	+	266785.i	0.542933	+	0.877706i
$157$	215938.	−	215938.i	0.699164	−	0.699164i	−0.265066	−	0.964230i	$-0.585394\pi$
$157$	215938.	−	215938.i	0.699164	−	0.699164i	0.964230	+	0.265066i	$0.0853939\pi$
$158$	−17317.3	+	4923.18i	−0.0551870	+	0.0156893i
$159$	−503763.			−1.58028
$160$	−307484.	+	101543.i	−0.949561	+	0.313583i
$161$	681375.			2.07168
$162$	−245877.	+	69901.2i	−0.736090	+	0.209265i
$163$	−201066.	+	201066.i	−0.592748	+	0.592748i	−0.938373	−	0.345624i	$-0.887667\pi$
$163$	−201066.	+	201066.i	−0.592748	+	0.592748i	0.345624	+	0.938373i	$0.387667\pi$
$164$	182132.	+	294434.i	0.528781	+	0.854829i
$165$	229474.	−	126806.i	0.656181	−	0.362603i
$166$	95529.1	−	171421.i	0.269070	−	0.482830i
$167$	668460.			1.85475			0.927373	−	0.374138i	$-0.122061\pi$
$167$	668460.			1.85475			0.927373	+	0.374138i	$0.122061\pi$
$168$	−18876.3	−	414056.i	−0.0515994	−	1.13184i
$169$		−	120742.i		−	0.325192i
$170$	133618.	−	132665.i	0.354602	−	0.352073i
$171$	−20220.6	+	20220.6i	−0.0528814	+	0.0528814i
$172$	654540.	+	154242.i	1.68700	+	0.397541i
$173$	493566.	−	493566.i	1.25381	−	1.25381i	0.299805	−	0.954000i	$-0.403078\pi$
$173$	493566.	−	493566.i	1.25381	−	1.25381i	0.954000	−	0.299805i	$-0.0969218\pi$
$174$	−344378.	+	97904.3i	−0.862308	+	0.245148i
$175$	272454.	−	433484.i	0.672510	−	1.06999i
$176$	−108927.	−	325921.i	−0.265066	−	0.793105i
$177$		−	28324.5i		−	0.0679563i
$178$	56365.1	+	198264.i	0.133340	+	0.469023i
$179$	−248593.	−	248593.i	−0.579905	−	0.579905i	0.354972	−	0.934877i	$-0.384490\pi$
$179$	−248593.	−	248593.i	−0.579905	−	0.579905i	−0.934877	+	0.354972i	$0.884490\pi$
$180$	−41790.4	+	74363.2i	−0.0961380	+	0.171071i
$181$	−616940.	+	616940.i	−1.39974	+	1.39974i	−0.598956	+	0.800782i	$0.704418\pi$
$181$	−616940.	+	616940.i	−1.39974	+	1.39974i	−0.800782	+	0.598956i	$0.795582\pi$
$182$	−316470.	+	567886.i	−0.708197	+	1.27082i
$183$	−119986.			−0.264852
$184$	507533.	−	556019.i	1.10515	−	1.21072i
$185$	−172579.	+	598889.i	−0.370731	+	1.28652i
$186$	306549.	−	550085.i	0.649708	−	1.16586i
$187$	141293.	+	141293.i	0.295472	+	0.295472i
$188$	−172422.	−	278738.i	−0.355793	−	0.575176i
$189$	−470643.	−	470643.i	−0.958379	−	0.958379i
$190$	678.691	−	189638.i	0.00136392	−	0.381101i
$191$	413626.			0.820399			0.410199	−	0.911996i	$-0.365459\pi$
$191$	413626.			0.820399			0.410199	+	0.911996i	$0.365459\pi$
$192$	−351940.	−	293012.i	−0.688994	−	0.573631i
$193$			340061.i			0.657148i	0.944478	+	0.328574i	$0.106568\pi$
$193$			340061.i			0.657148i	−0.944478	+	0.328574i	$0.893432\pi$
$194$	50462.8	+	177503.i	0.0962648	+	0.338611i
$195$	−479651.	+	265053.i	−0.903314	+	0.499168i
$196$	273125.	−	168950.i	0.507833	−	0.314136i
$197$	315890.	+	315890.i	0.579922	+	0.579922i	0.934882	−	0.354959i	$-0.115505\pi$
$197$	315890.	+	315890.i	0.579922	+	0.579922i	−0.354959	+	0.934882i	$0.615505\pi$
$198$	−79074.0	−	44066.1i	−0.143341	−	0.0798807i
$199$			823192.i			1.47356i	0.676132	+	0.736781i	$0.263655\pi$
$199$			823192.i			1.47356i	−0.676132	+	0.736781i	$0.736345\pi$
$200$	−150792.	−	545217.i	−0.266565	−	0.963817i
$201$		−	552121.i		−	0.963926i
$202$	−244422.	+	438601.i	−0.421465	+	0.756294i
$203$	−524652.	−	524652.i	−0.893576	−	0.893576i
$204$	259187.	+	61077.3i	0.436051	+	0.102755i
$205$	−529363.	+	292524.i	−0.879769	+	0.486157i
$206$	−485448.	+	138010.i	−0.797031	+	0.226590i
$207$		−	198313.i		−	0.321680i
$208$	227682.	+	681246.i	0.364897	+	1.09181i
$209$	201249.			0.318689
$210$	724072.	+	2591.37i	1.13301	+	0.00405491i
$211$	291079.	+	291079.i	0.450095	+	0.450095i	0.895386	−	0.445291i	$-0.146900\pi$
$211$	291079.	+	291079.i	0.450095	+	0.450095i	−0.445291	+	0.895386i	$0.646900\pi$
$212$	−1.12272e6	−	264570.i	−1.71567	−	0.404297i
$213$	169603.	+	169603.i	0.256144	+	0.256144i
$214$	109775.	+	61175.1i	0.163859	+	0.0913146i
$215$	−325286.	+	1.12882e6i	−0.479921	+	1.66544i
$216$	−734623.	+	33490.7i	−1.07135	+	0.0488416i
$217$	1.30506e6			1.88140
$218$	−242486.	−	135132.i	−0.345578	−	0.192583i
$219$	−221944.	+	221944.i	−0.312704	+	0.312704i
$220$	578020.	−	162093.i	0.805167	−	0.225792i
$221$	−295334.	−	295334.i	−0.406754	−	0.406754i
$222$	−847830.	+	241032.i	−1.15459	+	0.328241i
$223$			708720.i			0.954361i	0.878805	+	0.477180i	$0.158341\pi$
$223$			708720.i			0.954361i	−0.878805	+	0.477180i	$0.841659\pi$
$224$	175387.	−	932708.i	0.233549	−	1.24201i
$225$	−126165.	−	79297.2i	−0.166143	−	0.104424i
$226$	287816.	+	1.01239e6i	0.374838	+	1.31849i
$227$	86489.9	−	86489.9i	0.111404	−	0.111404i	−0.649207	−	0.760611i	$-0.724899\pi$
$227$	86489.9	−	86489.9i	0.111404	−	0.111404i	0.760611	+	0.649207i	$0.224899\pi$
$228$	228082.	−	141087.i	0.290572	−	0.179742i
$229$	−218491.	+	218491.i	−0.275324	+	0.275324i	−0.831239	−	0.555915i	$-0.812368\pi$
$229$	−218491.	+	218491.i	−0.275324	+	0.275324i	0.555915	+	0.831239i	$0.312368\pi$
$230$	926606.	+	933262.i	1.15498	+	1.16328i
$231$			768405.i			0.947459i
$232$	−818925.	+	37333.9i	−0.998905	+	0.0455390i
$233$	−145626.			−0.175731			−0.0878654	−	0.996132i	$-0.528005\pi$
$233$	−145626.			−0.175731			−0.0878654	+	0.996132i	$0.528005\pi$
$234$	165282.	+	92107.8i	0.197327	+	0.109966i
$235$	501141.	−	276929.i	0.591957	−	0.327113i
$236$	14875.7	−	63126.2i	0.0173859	−	0.0737784i
$237$	31451.0	−	31451.0i	0.0363717	−	0.0363717i
$238$	150907.	+	530817.i	0.172690	+	0.607438i
$239$	117219.			0.132740			0.0663700	−	0.997795i	$-0.478858\pi$
$239$	117219.			0.132740			0.0663700	+	0.997795i	$0.478858\pi$
$240$	541451.	−	588931.i	0.606780	−	0.659988i
$241$	636706.			0.706149			0.353075	−	0.935595i	$-0.385136\pi$
$241$	636706.			0.706149			0.353075	+	0.935595i	$0.385136\pi$
$242$	−74919.7	−	263530.i	−0.0822352	−	0.289262i
$243$	−251489.	+	251489.i	−0.273214	+	0.273214i
$244$	−267410.	−	63015.2i	−0.287543	−	0.0677596i
$245$	271352.	+	491050.i	0.288814	+	0.522649i
$246$	−747151.	−	416370.i	−0.787174	−	0.438674i
$247$	−420654.			−0.438715
$248$	972096.	−	1.06496e6i	1.00364	−	1.09953i
$249$			484826.i			0.495550i
$250$	964244.	−	216324.i	0.975746	−	0.218904i
$251$	−447833.	+	447833.i	−0.448675	+	0.448675i	−0.894914	−	0.446239i	$-0.852763\pi$
$251$	−447833.	+	447833.i	−0.448675	+	0.448675i	0.446239	+	0.894914i	$0.352763\pi$
$252$	−131519.	−	212614.i	−0.130463	−	0.210907i
$253$	−986872.	+	986872.i	−0.969303	+	0.969303i
$254$	27085.7	+	95274.0i	0.0263425	+	0.0926596i
$255$	−128808.	+	446993.i	−0.124049	+	0.430478i
$256$	−630474.	−	837863.i	−0.601266	−	0.799049i
$257$		−	1.21057e6i		−	1.14330i	−0.820499	−	0.571648i	$-0.806304\pi$
$257$		−	1.21057e6i		−	1.14330i	0.820499	−	0.571648i	$-0.193696\pi$
$258$	−1.59804e6	+	454311.i	−1.49464	+	0.424917i
$259$	−1.29165e6	−	1.29165e6i	−1.19645	−	1.19645i
$260$	−1.20819e6	+	338811.i	−1.10841	+	0.310831i
$261$	−152699.	+	152699.i	−0.138750	+	0.138750i
$262$	841630.	+	469021.i	0.757475	+	0.422123i
$263$	−1.53871e6			−1.37173			−0.685865	−	0.727729i	$-0.740576\pi$
$263$	−1.53871e6			−1.37173			−0.685865	+	0.727729i	$0.740576\pi$
$264$	627038.	+	572359.i	0.553712	+	0.505427i
$265$	557960.	−	1.93625e6i	0.488077	−	1.69374i
$266$	485502.	+	270559.i	0.420714	+	0.234454i
$267$	−360080.	−	360080.i	−0.309116	−	0.309116i
$268$	289967.	−	1.23050e6i	0.246610	−	1.04651i
$269$	1.35292e6	+	1.35292e6i	1.13997	+	1.13997i	0.988455	+	0.151512i	$0.0484143\pi$
$269$	1.35292e6	+	1.35292e6i	1.13997	+	1.13997i	0.151512	+	0.988455i	$0.451586\pi$
$270$	4597.64	−	1.28466e6i	0.00383818	−	1.07245i
$271$	−1.01384e6			−0.838585			−0.419293	−	0.907851i	$-0.637722\pi$
$271$	−1.01384e6			−0.838585			−0.419293	+	0.907851i	$0.637722\pi$
$272$	545566.	+	272243.i	0.447121	+	0.223118i
$273$		−	1.60614e6i		−	1.30429i
$274$	812528.	−	230996.i	0.653826	−	0.185878i
$275$	233228.	+	1.02245e6i	0.185972	+	0.815285i
$276$	−426599.	+	1.81031e6i	−0.337091	+	1.43047i
$277$	1.23565e6	+	1.23565e6i	0.967604	+	0.967604i	0.999491	−	0.0318878i	$-0.0101519\pi$
$277$	1.23565e6	+	1.23565e6i	0.967604	+	0.967604i	−0.0318878	+	0.999491i	$0.510152\pi$
$278$	−807980.	+	1.44987e6i	−0.627030	+	1.12517i
$279$		−	379835.i		−	0.292136i
$280$	1.61236e6	+	386048.i	1.22904	+	0.294270i
$281$			347325.i			0.262404i	0.991356	+	0.131202i	$0.0418836\pi$
$281$			347325.i			0.262404i	−0.991356	+	0.131202i	$0.958116\pi$
$282$	707319.	+	394173.i	0.529654	+	0.295164i
$283$	−103590.	−	103590.i	−0.0768867	−	0.0768867i	0.667618	−	0.744504i	$-0.267314\pi$
$283$	−103590.	−	103590.i	−0.0768867	−	0.0768867i	−0.744504	+	0.667618i	$0.767314\pi$
$284$	288916.	+	467062.i	0.212557	+	0.343620i
$285$	226601.	+	410067.i	0.165253	+	0.299049i
$286$	−364139.	−	1.28086e6i	−0.263240	−	0.925948i
$287$		−	1.77260e6i		−	1.27030i
$288$	−271463.	−	51046.1i	−0.192854	−	0.0362645i
$289$	1.06532e6			0.750302
$290$	5125.25	−	1.43208e6i	0.00357865	−	0.999936i
$291$	−322374.	−	322374.i	−0.223166	−	0.223166i
$292$	−611204.	+	378079.i	−0.419497	+	0.259493i
$293$	−18953.9	−	18953.9i	−0.0128982	−	0.0128982i	0.700628	−	0.713526i	$-0.252903\pi$
$293$	−18953.9	−	18953.9i	−0.0128982	−	0.0128982i	−0.713526	+	0.700628i	$0.752903\pi$
$294$	−386235.	+	693076.i	−0.260606	+	0.467641i
$295$	108867.	+	31371.8i	0.0728355	+	0.0209886i
$296$	−2.01612e6	+	91913.0i	−1.33748	+	0.0609744i
$297$	1.36332e6			0.896820
$298$	1.18847e6	−	2.13264e6i	0.775260	−	1.39116i
$299$	2.06278e6	−	2.06278e6i	1.33437	−	1.33437i
$300$	981120.	+	995266.i	0.629389	+	0.638464i
$301$	−2.43457e6	−	2.43457e6i	−1.54884	−	1.54884i
$302$	−165053.	−	580573.i	−0.104137	−	0.366302i
$303$		−	1.24048e6i		−	0.776218i
$304$	582417.	−	194652.i	0.361451	−	0.120802i
$305$	132895.	−	461176.i	0.0818009	−	0.283868i
$306$	154493.	−	43921.3i	0.0943203	−	0.0268146i
$307$	692796.	−	692796.i	0.419527	−	0.419527i	−0.465514	−	0.885041i	$-0.654131\pi$
$307$	692796.	−	692796.i	0.419527	−	0.419527i	0.885041	+	0.465514i	$0.154131\pi$
$308$	−403556.	+	1.71252e6i	−0.242397	+	1.02863i
$309$	881654.	−	881654.i	0.525294	−	0.525294i
$310$	1.77476e6	+	1.78751e6i	1.04890	+	1.05644i
$311$		−	2.00419e6i		−	1.17500i	−0.809223	−	0.587501i	$-0.800112\pi$
$311$		−	2.00419e6i		−	1.17500i	0.809223	−	0.587501i	$-0.199888\pi$
$312$	−1.31065e6	−	1.19636e6i	−0.762253	−	0.695783i
$313$	1.12863e6			0.651163			0.325581	−	0.945514i	$-0.394440\pi$
$313$	1.12863e6			0.651163			0.325581	+	0.945514i	$0.394440\pi$
$314$	−840932.	+	1.50900e6i	−0.481323	+	0.863706i
$315$	382258.	−	211234.i	0.217060	−	0.119947i
$316$	86611.7	−	53576.4i	0.0487931	−	0.0301825i
$317$	1.63164e6	−	1.63164e6i	0.911960	−	0.911960i	−0.0844667	−	0.996426i	$-0.526919\pi$
$317$	1.63164e6	−	1.63164e6i	0.911960	−	0.911960i	0.996426	+	0.0844667i	$0.0269187\pi$
$318$	2.74110e6	−	779274.i	1.52004	−	0.432138i
$319$	1.51976e6			0.836179
$320$	1.51602e6	−	1.02817e6i	0.827616	−	0.561294i
$321$	−310473.			−0.168175
$322$	−3.70753e6	+	1.05402e6i	−1.99271	+	0.566514i
$323$	−252489.	+	252489.i	−0.134659	+	0.134659i
$324$	1.22975e6	−	760698.i	0.650808	−	0.402578i
$325$	−487498.	−	2.13714e6i	−0.256014	−	1.12234i
$326$	783019.	−	1.40508e6i	0.408064	−	0.732247i
$327$	685817.			0.354682
$328$	−1.44648e6	−	1.32035e6i	−0.742385	−	0.677647i
$329$			1.67810e6i			0.854727i
$330$	−1.05246e6	+	1.04496e6i	−0.532014	+	0.528219i
$331$	−284625.	+	284625.i	−0.142792	+	0.142792i	−0.774889	−	0.632097i	$-0.782194\pi$
$331$	−284625.	+	284625.i	−0.142792	+	0.142792i	0.632097	+	0.774889i	$0.282194\pi$
$332$	−254624.	+	1.08052e6i	−0.126781	+	0.538006i
$333$	−375932.	+	375932.i	−0.185780	+	0.185780i
$334$	−3.63725e6	+	1.03405e6i	−1.78405	+	0.507193i
$335$	2.12212e6	+	611520.i	1.03313	+	0.297713i
$336$	743216.	+	2.22378e6i	0.359142	+	1.07459i
$337$			2.40590e6i			1.15399i	0.816746	+	0.576997i	$0.195776\pi$
$337$			2.40590e6i			1.15399i	−0.816746	+	0.576997i	$0.804224\pi$
$338$	186776.	+	656984.i	0.0889261	+	0.312797i
$339$	−1.83867e6	−	1.83867e6i	−0.868970	−	0.868970i
$340$	−521826.	+	928554.i	−0.244810	+	0.435622i
$341$	−1.89019e6	+	1.89019e6i	−0.880277	+	0.880277i
$342$	78745.6	−	141304.i	0.0364050	−	0.0653266i
$343$	1.10933e6			0.509127
$344$	−3.80010e6	+	173243.i	−1.73141	+	0.0789330i
$345$	−3.12206e6	−	899668.i	−1.41219	−	0.406944i
$346$	−1.92211e6	+	3.44911e6i	−0.863154	+	1.54888i
$347$	1.00476e6	+	1.00476e6i	0.447958	+	0.447958i	0.894675	−	0.446717i	$-0.147407\pi$
$347$	1.00476e6	+	1.00476e6i	0.447958	+	0.447958i	−0.446717	+	0.894675i	$0.647407\pi$
$348$	1.72240e6	−	1.06544e6i	0.762403	−	0.471609i
$349$	1.80200e6	+	1.80200e6i	0.791940	+	0.791940i	0.981809	−	0.189869i	$-0.0608064\pi$
$349$	1.80200e6	+	1.80200e6i	0.791940	+	0.791940i	−0.189869	+	0.981809i	$0.560806\pi$
$350$	−811930.	+	2.78015e6i	−0.354282	+	1.21311i
$351$	−2.84963e6			−1.23458
$352$	1.09687e6	+	1.60491e6i	0.471843	+	0.690391i
$353$			3.43150e6i			1.46571i	0.680387	+	0.732853i	$0.261812\pi$
$353$			3.43150e6i			1.46571i	−0.680387	+	0.732853i	$0.738188\pi$
$354$	43815.4	+	154121.i	0.0185831	+	0.0653661i
$355$	−839729.	+	464031.i	−0.353646	+	0.195423i
$356$	−613392.	−	991611.i	−0.256515	−	0.414683i
$357$	−964050.	−	964050.i	−0.400340	−	0.400340i
$358$	1.73721e6	+	968105.i	0.716380	+	0.399222i
$359$			316777.i			0.129723i	0.997894	+	0.0648616i	$0.0206606\pi$
$359$			316777.i			0.129723i	−0.997894	+	0.0648616i	$0.979339\pi$
$360$	112359.	−	469273.i	0.0456930	−	0.190840i
$361$		−	2.11647e6i		−	0.854760i
$362$	2.40257e6	−	4.31127e6i	0.963618	−	1.72915i
$363$	478614.	+	478614.i	0.190642	+	0.190642i
$364$	843522.	−	3.57955e6i	0.333690	−	1.41604i
$365$	−607237.	−	1.09888e6i	−0.238576	−	0.431736i
$366$	652874.	−	185608.i	0.254757	−	0.0724257i
$367$			1.11458e6i			0.431962i	0.976398	+	0.215981i	$0.0692950\pi$
$367$			1.11458e6i			0.431962i	−0.976398	+	0.215981i	$0.930705\pi$
$368$	−1.90150e6	+	3.81054e6i	−0.731942	+	1.46679i
$369$	−515911.			−0.197246
$370$	12617.9	−	3.52566e6i	0.00479163	−	1.33886i
$371$	4.17599e6	+	4.17599e6i	1.57516	+	1.57516i
$372$	−817080.	+	3.46734e6i	−0.306131	+	1.29909i
$373$	−2.48426e6	−	2.48426e6i	−0.924540	−	0.924540i	0.0728059	−	0.997346i	$-0.476805\pi$
$373$	−2.48426e6	−	2.48426e6i	−0.924540	−	0.924540i	−0.997346	+	0.0728059i	$0.976805\pi$
$374$	−987377.	−	550242.i	−0.365009	−	0.203411i
$375$	−1.82074e6	+	1.62648e6i	−0.668606	+	0.597270i
$376$	1.36937e6	+	1.24996e6i	0.499518	+	0.455959i
$377$	−3.17664e6			−1.15110
$378$	3.28892e6	+	1.83284e6i	1.18393	+	0.659774i
$379$	−1.78873e6	+	1.78873e6i	−0.639658	+	0.639658i	−0.950471	−	0.310813i	$-0.899399\pi$
$379$	−1.78873e6	+	1.78873e6i	−0.639658	+	0.639658i	0.310813	+	0.950471i	$0.399399\pi$
$380$	289659.	+	1.03291e6i	0.102903	+	0.366948i
$381$	−173033.	−	173033.i	−0.0610685	−	0.0610685i
$382$	−2.25064e6	+	639841.i	−0.789128	+	0.224344i
$383$			1.74920e6i			0.609315i	0.952462	+	0.304657i	$0.0985420\pi$
$383$			1.74920e6i			0.609315i	−0.952462	+	0.304657i	$0.901458\pi$
$384$	2.36825e6	+	1.04993e6i	0.819596	+	0.363356i
$385$	−2.95342e6	−	851073.i	−1.01549	−	0.292627i
$386$	−526042.	−	1.85035e6i	−0.179702	−	0.632101i
$387$	−708577.	+	708577.i	−0.240497	+	0.240497i
$388$	−549161.	−	887774.i	−0.185191	−	0.299380i
$389$	4.08115e6	−	4.08115e6i	1.36744	−	1.36744i	0.503373	−	0.864069i	$-0.332092\pi$
$389$	4.08115e6	−	4.08115e6i	1.36744	−	1.36744i	0.864069	−	0.503373i	$-0.167908\pi$
$390$	2.19988e6	−	2.18419e6i	0.732383	−	0.727159i
$391$		−	2.47628e6i		−	0.819140i
$392$	−1.22479e6	+	1.34179e6i	−0.402574	+	0.441033i
$393$	−2.38036e6			−0.777429
$394$	−2.20748e6	−	1.23018e6i	−0.716402	−	0.399234i
$395$	86049.6	+	155719.i	0.0277496	+	0.0502167i
$396$	498426.	+	117454.i	0.159721	+	0.0376383i
$397$	−1.35042e6	+	1.35042e6i	−0.430024	+	0.430024i	−0.888636	−	0.458612i	$-0.848347\pi$
$397$	−1.35042e6	+	1.35042e6i	−0.430024	+	0.430024i	0.458612	+	0.888636i	$0.348347\pi$
$398$	−1.27340e6	−	4.47918e6i	−0.402956	−	1.41740i
$399$	−1.37313e6			−0.431797
$400$	1.66390e6	+	2.73340e6i	0.519967	+	0.854186i
$401$	2.67527e6			0.830819			0.415409	−	0.909635i	$-0.363638\pi$
$401$	2.67527e6			0.830819			0.415409	+	0.909635i	$0.363638\pi$
$402$	854079.	+	3.00422e6i	0.263592	+	0.927186i
$403$	3.95091e6	−	3.95091e6i	1.21181	−	1.21181i
$404$	651485.	−	2.76463e6i	0.198587	−	0.842720i
$405$	1.22177e6	+	2.21096e6i	0.370126	+	0.669796i
$406$	3.66635e6	+	2.04317e6i	1.10387	+	0.615162i
$407$	3.74153e6			1.11960
$408$	−1.50478e6	+	68601.2i	−0.447530	+	0.0204024i
$409$			6.03650e6i			1.78434i	0.451703	+	0.892169i	$0.350817\pi$
$409$			6.03650e6i			1.78434i	−0.451703	+	0.892169i	$0.649183\pi$
$410$	2.42788e6	−	2.41057e6i	0.713293	−	0.708205i
$411$	−1.47568e6	+	1.47568e6i	−0.430912	+	0.430912i
$412$	2.42795e6	−	1.50189e6i	0.704689	−	0.435907i
$413$	−234799.	+	234799.i	−0.0677363	+	0.0677363i
$414$	306771.	+	1.07907e6i	0.0879658	+	0.309419i
$415$	−1.86346e6	−	536985.i	−0.531130	−	0.153053i
$416$	−2.29270e6	−	3.35462e6i	−0.649551	−	0.950408i
$417$		−	4.10063e6i		−	1.15481i
$418$	−1.09504e6	+	311313.i	−0.306542	+	0.0871478i
$419$	−436288.	−	436288.i	−0.121405	−	0.121405i	0.643794	−	0.765199i	$-0.277359\pi$
$419$	−436288.	−	436288.i	−0.121405	−	0.121405i	−0.765199	+	0.643794i	$0.777359\pi$
$420$	−3.94386e6	+	1.10597e6i	−1.09093	+	0.305929i
$421$	−984309.	+	984309.i	−0.270661	+	0.270661i	−0.829366	−	0.558705i	$-0.811298\pi$
$421$	−984309.	+	984309.i	−0.270661	+	0.270661i	0.558705	+	0.829366i	$0.311298\pi$
$422$	−2.03410e6	−	1.13356e6i	−0.556021	−	0.309858i
$423$	488406.			0.132718
$424$	6.51827e6	−	297161.i	1.76083	−	0.0802744i
$425$	−1.57539e6	−	990165.i	−0.423072	−	0.265910i
$426$	−1.18521e6	−	660489.i	−0.316425	−	0.176336i
$427$	994638.	+	994638.i	0.263995	+	0.263995i
$428$	−691944.	−	163057.i	−0.182584	−	0.0430258i
$429$	2.32625e6	+	2.32625e6i	0.610258	+	0.610258i
$430$	23783.0	−	6.64536e6i	0.00620290	−	1.73320i
$431$	5.09258e6			1.32052			0.660260	−	0.751037i	$-0.270446\pi$
$431$	5.09258e6			1.32052			0.660260	+	0.751037i	$0.270446\pi$
$432$	3.94545e6	−	1.31862e6i	1.01716	−	0.339947i
$433$			5.21971e6i			1.33791i	0.743303	+	0.668955i	$0.233258\pi$
$433$			5.21971e6i			1.33791i	−0.743303	+	0.668955i	$0.766742\pi$
$434$	−7.10115e6	+	2.01881e6i	−1.80969	+	0.514483i
$435$	1.71122e6	+	3.09669e6i	0.433593	+	0.784647i
$436$	1.52846e6	+	360182.i	0.385069	+	0.0907415i
$437$	−1.76353e6	−	1.76353e6i	−0.441752	−	0.441752i
$438$	864325.	−	1.55098e6i	0.215274	−	0.386296i
$439$		−	5.84926e6i		−	1.44857i	−0.689501	−	0.724285i	$-0.742170\pi$
$439$		−	5.84926e6i		−	1.44857i	0.689501	−	0.724285i	$-0.257830\pi$
$440$	−2.89440e6	+	1.77613e6i	−0.712733	+	0.437364i
$441$			478571.i			0.117179i
$442$	2.06383e6	+	1.15013e6i	0.502481	+	0.280021i
$443$	1.42750e6	+	1.42750e6i	0.345595	+	0.345595i	0.858466	−	0.512871i	$-0.171418\pi$
$443$	1.42750e6	+	1.42750e6i	0.345595	+	0.345595i	−0.512871	+	0.858466i	$0.671418\pi$
$444$	4.24039e6	−	2.62303e6i	1.02082	−	0.631460i
$445$	1.78281e6	−	985175.i	0.426782	−	0.235838i
$446$	−1.09632e6	−	3.85631e6i	−0.260977	−	0.917984i
$447$			6.03168e6i			1.42781i
$448$	488488.	+	5.34640e6i	0.114990	+	1.25854i
$449$	−6.76907e6			−1.58458			−0.792288	−	0.610148i	$-0.791110\pi$
$449$	−6.76907e6			−1.58458			−0.792288	+	0.610148i	$0.791110\pi$
$450$	809157.	+	236310.i	0.188366	+	0.0550112i
$451$	2.56735e6	+	2.56735e6i	0.594351	+	0.594351i
$452$	−3.13215e6	−	5.06345e6i	−0.721102	−	1.16574i
$453$	1.05442e6	+	1.05442e6i	0.241416	+	0.241416i
$454$	−336820.	+	604404.i	−0.0766935	+	0.137622i
$455$	6.17330e6	+	1.77893e6i	1.39794	+	0.402838i
$456$	−1.02280e6	+	1.12051e6i	−0.230345	+	0.252350i
$457$	−3.13327e6			−0.701790			−0.350895	−	0.936415i	$-0.614123\pi$
$457$	−3.13327e6			−0.701790			−0.350895	+	0.936415i	$0.614123\pi$
$458$	850875.	−	1.52684e6i	0.189541	−	0.340119i
$459$	−1.71043e6	+	1.71043e6i	−0.378943	+	0.378943i
$460$	−6.48555e6	−	3.64473e6i	−1.42907	−	0.803102i
$461$	1.55863e6	+	1.55863e6i	0.341579	+	0.341579i	0.856961	−	0.515382i	$-0.172350\pi$
$461$	1.55863e6	+	1.55863e6i	0.341579	+	0.341579i	−0.515382	+	0.856961i	$0.672350\pi$
$462$	−1.18865e6	−	4.18108e6i	−0.259089	−	0.911346i
$463$		−	4.60180e6i		−	0.997643i	−0.866705	−	0.498822i	$-0.833766\pi$
$463$		−	4.60180e6i		−	0.997643i	0.866705	−	0.498822i	$-0.166234\pi$
$464$	4.39821e6	−	1.46994e6i	0.948378	−	0.316961i
$465$	−5.97978e6	−	1.72317e6i	−1.28249	−	0.369568i
$466$	792384.	−	225269.i	0.169033	−	0.0480548i
$467$	1.16841e6	−	1.16841e6i	0.247915	−	0.247915i	−0.572199	−	0.820115i	$-0.693910\pi$
$467$	1.16841e6	−	1.16841e6i	0.247915	−	0.247915i	0.820115	+	0.572199i	$0.193910\pi$
$468$	−1.04182e6	−	245505.i	−0.219876	−	0.0518138i
$469$	−4.57686e6	+	4.57686e6i	−0.960806	+	0.960806i
$470$	−2.29845e6	+	2.28205e6i	−0.479943	+	0.476520i
$471$		−	4.26787e6i		−	0.886459i
$472$	16708.2	+	366496.i	0.00345202	+	0.0757206i
$473$	7.05224e6			1.44935
$474$	−122481.	+	219784.i	−0.0250393	+	0.0449315i
$475$	−1.82710e6	+	416775.i	−0.371560	+	0.0847555i
$476$	−1.64225e6	−	2.65486e6i	−0.332216	−	0.537062i
$477$	1.21541e6	−	1.21541e6i	0.244584	−	0.244584i
$478$	−637814.	+	181326.i	−0.127680	+	0.0362987i
$479$	−4.22399e6			−0.841170			−0.420585	−	0.907253i	$-0.638175\pi$
$479$	−4.22399e6			−0.841170			−0.420585	+	0.907253i	$0.638175\pi$
$480$	−2.03514e6	+	4.04209e6i	−0.403174	+	0.800760i
$481$	−7.82062e6			−1.54127
$482$	−3.46447e6	+	984925.i	−0.679234	+	0.193102i
$483$	6.73348e6	−	6.73348e6i	1.31332	−	1.31332i
$484$	815312.	+	1.31804e6i	0.158202	+	0.255749i
$485$	1.59613e6	−	882013.i	0.308115	−	0.170263i
$486$	979381.	−	1.75744e6i	0.188088	−	0.337512i
$487$	−1.97208e6			−0.376793			−0.188396	−	0.982093i	$-0.560329\pi$
$487$	−1.97208e6			−0.376793			−0.188396	+	0.982093i	$0.560329\pi$
$488$	1.55252e6	−	70777.8i	0.295113	−	0.0134539i
$489$			3.97395e6i			0.751537i
$490$	−2.23610e6	−	2.25216e6i	−0.420728	−	0.423750i
$491$	−4.36328e6	+	4.36328e6i	−0.816788	+	0.816788i	−0.985641	−	0.168853i	$-0.945994\pi$
$491$	−4.36328e6	+	4.36328e6i	−0.816788	+	0.816788i	0.168853	+	0.985641i	$0.445994\pi$
$492$	4.70951e6	+	1.10980e6i	0.877129	+	0.206695i
$493$	−1.90671e6	+	1.90671e6i	−0.353320	+	0.353320i
$494$	2.28888e6	−	650713.i	0.421993	−	0.119970i
$495$	−247703.	+	859586.i	−0.0454379	+	0.157680i
$496$	−3.64201e6	+	7.29846e6i	−0.664717	+	1.33207i
$497$		−	2.81188e6i		−	0.510629i
$498$	−749980.	−	2.63805e6i	−0.135512	−	0.476662i
$499$	−4.15338e6	−	4.15338e6i	−0.746706	−	0.746706i	0.227153	−	0.973859i	$-0.427058\pi$
$499$	−4.15338e6	−	4.15338e6i	−0.746706	−	0.746706i	−0.973859	+	0.227153i	$0.927058\pi$
$500$	−4.91205e6	+	2.66866e6i	−0.878694	+	0.477385i
$501$	6.60585e6	−	6.60585e6i	1.17580	−	1.17580i
$502$	1.74401e6	−	3.12952e6i	0.308880	−	0.554266i
$503$	−932727.			−0.164375			−0.0821873	−	0.996617i	$-0.526191\pi$
$503$	−932727.			−0.164375			−0.0821873	+	0.996617i	$0.526191\pi$
$504$	1.04452e6	+	953437.i	0.183164	+	0.167192i
$505$	4.76788e6	+	1.37394e6i	0.831949	+	0.239739i
$506$	3.84321e6	−	6.89640e6i	0.667294	−	1.19742i
$507$	−1.19319e6	−	1.19319e6i	−0.206153	−	0.206153i
$508$	−294760.	−	476510.i	−0.0506768	−	0.0819242i
$509$	7.04290e6	+	7.04290e6i	1.20492	+	1.20492i	0.972653	+	0.232263i	$0.0746130\pi$
$509$	7.04290e6	+	7.04290e6i	1.20492	+	1.20492i	0.232263	+	0.972653i	$0.425387\pi$
$510$	9417.66	−	2.63145e6i	0.00160331	−	0.447992i
$511$	3.67966e6			0.623384
$512$	4.72665e6	+	3.58373e6i	0.796854	+	0.604172i
$513$			2.43623e6i			0.408719i
$514$	1.87265e6	+	6.58703e6i	0.312642	+	1.09972i
$515$	2.41220e6	+	4.36521e6i	0.400769	+	0.725248i
$516$	7.99253e6	−	4.94403e6i	1.32148	−	0.817442i
$517$	−2.43048e6	−	2.43048e6i	−0.399912	−	0.399912i
$518$	9.02624e6	+	5.03011e6i	1.47803	+	0.823670i
$519$		−	9.75503e6i		−	1.58968i
$520$	6.04993e6	−	3.71250e6i	0.981165	−	0.602086i
$521$		−	1.66237e6i		−	0.268307i	−0.990961	−	0.134154i	$-0.957168\pi$
$521$		−	1.66237e6i		−	0.268307i	0.990961	−	0.134154i	$-0.0428315\pi$
$522$	594660.	−	1.06708e6i	0.0955196	−	0.171404i
$523$	−4.48967e6	−	4.48967e6i	−0.717728	−	0.717728i	0.250412	−	0.968139i	$-0.419434\pi$
$523$	−4.48967e6	−	4.48967e6i	−0.717728	−	0.717728i	−0.968139	+	0.250412i	$0.919434\pi$
$524$	−5.30504e6	−	1.25013e6i	−0.844035	−	0.198897i
$525$	−1.59133e6	−	6.97621e6i	−0.251977	−	1.10464i
$526$	8.37252e6	−	2.38025e6i	1.31945	−	0.375109i
$527$		−	4.74291e6i		−	0.743906i
$528$	−4.29725e6	−	2.14437e6i	−0.670820	−	0.334746i
$529$	1.08594e7			1.68720
$530$	−40794.6	+	1.13987e7i	−0.00630832	+	1.76265i
$531$	68337.8	+	68337.8i	0.0105178	+	0.0105178i
$532$	−3.06026e6	−	721150.i	−0.468791	−	0.110471i
$533$	−5.36632e6	−	5.36632e6i	−0.818198	−	0.818198i
$534$	2.51629e6	+	1.40227e6i	0.381863	+	0.212804i
$535$	343875.	−	1.19333e6i	0.0519417	−	0.180250i
$536$	325686.	+	7.14398e6i	0.0489652	+	1.07406i
$537$	−4.91329e6			−0.735253
$538$	−9.45442e6	−	5.26873e6i	−1.40825	−	0.784785i
$539$	2.38153e6	−	2.38153e6i	0.353090	−	0.353090i
$540$	1.96223e6	+	6.99724e6i	0.289578	+	1.03263i
$541$	6.23116e6	+	6.23116e6i	0.915326	+	0.915326i	0.996685	−	0.0813592i	$-0.0259261\pi$
$541$	6.23116e6	+	6.23116e6i	0.915326	+	0.915326i	−0.0813592	+	0.996685i	$0.525926\pi$
$542$	5.51656e6	−	1.56832e6i	0.806622	−	0.229317i
$543$			1.21934e7i			1.77471i
$544$	−3.38969e6	−	637400.i	−0.491091	−	0.0923453i
$545$	−759599.	+	2.63599e6i	−0.109545	+	0.380147i
$546$	2.48454e6	+	8.73937e6i	0.356668	+	1.25458i
$547$	−9.49271e6	+	9.49271e6i	−1.35651	+	1.35651i	−0.478323	+	0.878184i	$0.658755\pi$
$547$	−9.49271e6	+	9.49271e6i	−1.35651	+	1.35651i	−0.878184	+	0.478323i	$0.841245\pi$
$548$	−4.06383e6	+	2.51381e6i	−0.578075	+	0.357586i
$549$	289487.	−	289487.i	0.0409919	−	0.0409919i
$550$	−2.85068e6	−	5.20260e6i	−0.401829	−	0.733354i
$551$			2.71580e6i			0.381082i
$552$	−479150.	−	1.05102e7i	−0.0669304	−	1.46813i
$553$	−521433.			−0.0725079
$554$	−8.63493e6	−	4.81205e6i	−1.19532	−	0.666125i
$555$	4.21287e6	+	7.62379e6i	0.580558	+	1.05060i
$556$	2.15360e6	−	9.13896e6i	0.295445	−	1.25375i
$557$	−4.42158e6	+	4.42158e6i	−0.603864	+	0.603864i	−0.941336	−	0.337471i	$-0.890428\pi$
$557$	−4.42158e6	+	4.42158e6i	−0.603864	+	0.603864i	0.337471	+	0.941336i	$0.390428\pi$
$558$	587570.	+	2.06677e6i	0.0798866	+	0.281001i
$559$	−1.47407e7			−1.99522
$560$	−9.37041e6	+	393587.i	−1.26267	+	0.0530360i
$561$	2.79257e6			0.374625
$562$	−537279.	−	1.88988e6i	−0.0717561	−	0.252402i
$563$	−6.86061e6	+	6.86061e6i	−0.912203	+	0.912203i	−0.996445	−	0.0842422i	$-0.973153\pi$
$563$	−6.86061e6	+	6.86061e6i	−0.912203	+	0.912203i	0.0842422	+	0.996445i	$0.473153\pi$
$564$	−4.45844e6	−	1.05063e6i	−0.590181	−	0.139076i
$565$	9.10355e6	−	5.03058e6i	1.19975	−	0.662975i
$566$	723901.	+	403413.i	0.0949813	+	0.0529309i
$567$	−7.40350e6			−0.967118
$568$	−2.29456e6	−	2.09447e6i	−0.298421	−	0.272398i
$569$		−	8.36508e6i		−	1.08315i	−0.840652	−	0.541576i	$-0.817828\pi$
$569$		−	8.36508e6i		−	1.08315i	0.840652	−	0.541576i	$-0.182172\pi$
$570$	−1.86733e6	−	1.88074e6i	−0.240732	−	0.242461i
$571$	1.99214e6	−	1.99214e6i	0.255700	−	0.255700i	−0.567603	−	0.823302i	$-0.692129\pi$
$571$	1.99214e6	−	1.99214e6i	0.255700	−	0.255700i	0.823302	+	0.567603i	$0.192129\pi$
$572$	3.96274e6	+	6.40617e6i	0.506414	+	0.818670i
$573$	4.08753e6	−	4.08753e6i	0.520085	−	0.520085i
$574$	2.74204e6	+	9.64513e6i	0.347372	+	1.22188i
$575$	6.91587e6	−	1.10034e7i	0.872323	−	1.38790i
$576$	1.55606e6	−	142173.i	0.195420	−	0.0178551i
$577$			1.28538e7i			1.60728i	0.595116	+	0.803640i	$0.297106\pi$
$577$			1.28538e7i			1.60728i	−0.595116	+	0.803640i	$0.702894\pi$
$578$	−5.79667e6	+	1.64795e6i	−0.721703	+	0.205175i
$579$	3.36054e6	+	3.36054e6i	0.416594	+	0.416594i
$580$	2.18741e6	+	7.80022e6i	0.269997	+	0.962801i
$581$	4.01901e6	−	4.01901e6i	0.493945	−	0.493945i
$582$	2.25280e6	+	1.25543e6i	0.275686	+	0.153634i
$583$	−1.20966e7			−1.47398
$584$	2.74085e6	−	3.00269e6i	0.332547	−	0.364317i
$585$	517753.	−	1.79672e6i	0.0625509	−	0.217066i
$586$	132452.	+	73812.6i	0.0159337	+	0.00887946i
$587$	2.91883e6	+	2.91883e6i	0.349634	+	0.349634i	0.859973	−	0.510339i	$-0.170480\pi$
$587$	2.91883e6	+	2.91883e6i	0.349634	+	0.349634i	−0.510339	+	0.859973i	$0.670480\pi$
$588$	1.02948e6	−	4.36866e6i	0.122793	−	0.521081i
$589$	−3.37775e6	−	3.37775e6i	−0.401180	−	0.401180i
$590$	−640903.	−	2293.72i	−0.0757988	−	0.000271275i
$591$	6.24336e6			0.735275
$592$	1.08280e7	−	3.61888e6i	1.26983	−	0.424394i
$593$		−	8.87365e6i		−	1.03625i	−0.855304	−	0.518126i	$-0.826630\pi$
$593$		−	8.87365e6i		−	1.03625i	0.855304	−	0.518126i	$-0.173370\pi$
$594$	−7.41812e6	+	2.10892e6i	−0.862637	+	0.245242i
$595$	4.77316e6	−	2.63763e6i	0.552731	−	0.305437i
$596$	−3.16776e6	+	1.34426e7i	−0.365289	+	1.55013i
$597$	8.13493e6	+	8.13493e6i	0.934153	+	0.934153i
$598$	−8.03315e6	+	1.44150e7i	−0.918613	+	1.64840i
$599$		−	1.22845e7i		−	1.39891i	−0.714674	−	0.699457i	$-0.753425\pi$
$599$		−	1.22845e7i		−	1.39891i	0.714674	−	0.699457i	$-0.246575\pi$
$600$	−6.87809e6	−	3.89778e6i	−0.779991	−	0.442017i
$601$		−	1.98834e6i		−	0.224546i	−0.993677	−	0.112273i	$-0.964187\pi$
$601$		−	1.98834e6i		−	0.224546i	0.993677	−	0.112273i	$-0.0358131\pi$
$602$	1.70132e7	+	9.48104e6i	1.91335	+	1.06626i
$603$	1.33208e6	+	1.33208e6i	0.149190	+	0.149190i
$604$	1.79618e6	+	2.90371e6i	0.200336	+	0.323863i
$605$	−2.36969e6	+	1.30948e6i	−0.263211	+	0.145449i
$606$	1.91891e6	+	6.74976e6i	0.212262	+	0.746632i
$607$		−	1.23636e7i		−	1.36198i	−0.732291	−	0.680992i	$-0.761549\pi$
$607$		−	1.23636e7i		−	1.36198i	0.732291	−	0.680992i	$-0.238451\pi$
$608$	−2.86796e6	+	1.96009e6i	−0.314640	+	0.215039i
$609$	−1.03694e7			−1.13295
$610$	−9716.46	+	2.71494e6i	−0.00105726	+	0.295417i
$611$	5.08023e6	+	5.08023e6i	0.550529	+	0.550529i
$612$	−772691.	+	477972.i	−0.0833926	+	0.0515851i
$613$	−3.15327e6	−	3.15327e6i	−0.338930	−	0.338930i	0.517035	−	0.855964i	$-0.327036\pi$
$613$	−3.15327e6	−	3.15327e6i	−0.338930	−	0.338930i	−0.855964	+	0.517035i	$0.827036\pi$
$614$	−2.69798e6	+	4.84136e6i	−0.288813	+	0.518258i
$615$	−2.34049e6	+	8.12203e6i	−0.249527	+	0.865918i
$616$	−453269.	−	9.94252e6i	−0.0481287	−	1.05571i
$617$	8.75164e6			0.925500			0.462750	−	0.886489i	$-0.346863\pi$
$617$	8.75164e6			0.925500			0.462750	+	0.886489i	$0.346863\pi$
$618$	−3.43345e6	+	6.16113e6i	−0.361626	+	0.648917i
$619$	−493918.	+	493918.i	−0.0518117	+	0.0518117i	−0.732538	−	0.680726i	$-0.761664\pi$
$619$	−493918.	+	493918.i	−0.0518117	+	0.0518117i	0.680726	+	0.732538i	$0.261664\pi$
$620$	−1.24220e7	−	6.98088e6i	−1.29781	−	0.729341i
$621$	−1.19466e7	−	1.19466e7i	−1.24313	−	1.24313i
$622$	3.10030e6	+	1.09053e7i	0.321313	+	1.13022i
$623$			5.96984e6i			0.616230i
$624$	8.98220e6	+	4.48221e6i	0.923466	+	0.460819i
$625$	−4.23487e6	−	8.79962e6i	−0.433651	−	0.901081i
$626$	−6.14113e6	+	1.74588e6i	−0.626343	+	0.178065i
$627$	1.98878e6	−	1.98878e6i	0.202031	−	0.202031i
$628$	2.24143e6	−	9.51169e6i	0.226791	−	0.962406i
$629$	−4.69417e6	+	4.69417e6i	−0.473077	+	0.473077i
$630$	−1.75320e6	+	1.74069e6i	−0.175987	+	0.174731i
$631$			1.18020e7i			1.18000i	0.807405	+	0.589998i	$0.200872\pi$
$631$			1.18020e7i			1.18000i	−0.807405	+	0.589998i	$0.799128\pi$
$632$	−388397.	+	425502.i	−0.0386797	+	0.0423749i
$633$	5.75298e6			0.570668
$634$	−6.35414e6	+	1.14021e7i	−0.627818	+	1.12658i
$635$	856715.	−	473417.i	0.0843144	−	0.0465918i
$636$	−1.37095e7	+	8.48044e6i	−1.34394	+	0.831334i
$637$	−4.97793e6	+	4.97793e6i	−0.486072	+	0.486072i
$638$	−8.26939e6	+	2.35093e6i	−0.804307	+	0.228659i
$639$	−818390.			−0.0792882
$640$	−6.65852e6	+	7.93966e6i	−0.642581	+	0.766218i
$641$	−3.59254e6			−0.345348			−0.172674	−	0.984979i	$-0.555241\pi$
$641$	−3.59254e6			−0.345348			−0.172674	+	0.984979i	$0.555241\pi$
$642$	1.68936e6	−	480273.i	0.161765	−	0.0459887i
$643$	1.33720e7	−	1.33720e7i	1.27546	−	1.27546i	0.332283	−	0.943180i	$-0.392181\pi$
$643$	1.33720e7	−	1.33720e7i	1.27546	−	1.27546i	0.943180	−	0.332283i	$-0.107819\pi$
$644$	1.85431e7	−	1.14704e7i	1.76184	−	1.08984i
$645$	7.94066e6	+	1.43697e7i	0.751549	+	1.36003i
$646$	983276.	−	1.76443e6i	0.0927031	−	0.166350i
$647$	−1.96424e7			−1.84474			−0.922368	−	0.386313i	$-0.873748\pi$
$647$	−1.96424e7			−1.84474			−0.922368	+	0.386313i	$0.873748\pi$
$648$	−5.51461e6	+	6.04144e6i	−0.515914	+	0.565201i
$649$		−	680144.i		−	0.0633854i
$650$	5.95855e6	+	1.08746e7i	0.553168	+	1.00955i
$651$	1.28969e7	−	1.28969e7i	1.19270	−	1.19270i
$652$	−2.08707e6	+	8.85664e6i	−0.192273	+	0.815924i
$653$	8.31532e6	−	8.31532e6i	0.763125	−	0.763125i	−0.213761	−	0.976886i	$-0.568571\pi$
$653$	8.31532e6	−	8.31532e6i	0.763125	−	0.763125i	0.976886	+	0.213761i	$0.0685713\pi$
$654$	−3.73169e6	+	1.06089e6i	−0.341163	+	0.0969902i
$655$	2.63645e6	−	9.14908e6i	0.240113	−	0.833248i
$656$	9.91312e6	+	4.94675e6i	0.899396	+	0.448808i
$657$		−	1.07096e6i		−	0.0967962i
$658$	−2.59586e6	−	9.13093e6i	−0.233731	−	0.822148i
$659$	−581499.	−	581499.i	−0.0521597	−	0.0521597i	0.680546	−	0.732706i	$-0.261743\pi$
$659$	−581499.	−	581499.i	−0.0521597	−	0.0521597i	−0.732706	+	0.680546i	$0.761743\pi$
$660$	4.11026e6	−	7.31393e6i	0.367290	−	0.653568i
$661$	3.80968e6	−	3.80968e6i	0.339144	−	0.339144i	−0.516901	−	0.856045i	$-0.672914\pi$
$661$	3.80968e6	−	3.80968e6i	0.339144	−	0.339144i	0.856045	+	0.516901i	$0.172914\pi$
$662$	1.10842e6	−	1.98900e6i	0.0983016	−	0.176396i
$663$	−5.83708e6			−0.515718
$664$	−285990.	−	6.27324e6i	−0.0251728	−	0.552169i
$665$	1.52086e6	−	5.27773e6i	0.133363	−	0.462799i
$666$	1.46400e6	−	2.62707e6i	0.127896	−	0.229501i
$667$	−1.33176e7	−	1.33176e7i	−1.15907	−	1.15907i
$668$	1.81916e7	−	1.12530e7i	1.57735	−	0.975722i
$669$	7.00370e6	+	7.00370e6i	0.605010	+	0.605010i
$670$	−1.24929e7	−	44710.6i	−1.07517	−	0.00384790i
$671$	−2.88117e6			−0.247038
$672$	−7.48399e6	−	1.09504e7i	−0.639308	−	0.935421i
$673$			7.04618e6i			0.599675i	0.953990	+	0.299837i	$0.0969324\pi$
$673$			7.04618e6i			0.599675i	−0.953990	+	0.299837i	$0.903068\pi$
$674$	−3.72171e6	−	1.30911e7i	−0.315568	−	1.11001i
$675$	−1.23773e7	+	2.82335e6i	−1.04560	+	0.238509i
$676$	−2.03259e6	−	3.28588e6i	−0.171073	−	0.276557i
$677$	3.32338e6	+	3.32338e6i	0.278682	+	0.278682i	0.832583	−	0.553901i	$-0.186861\pi$
$677$	3.32338e6	+	3.32338e6i	0.278682	+	0.278682i	−0.553901	+	0.832583i	$0.686861\pi$
$678$	1.28489e7	+	7.16040e6i	1.07347	+	0.598223i
$679$			5.34471e6i			0.444887i
$680$	1.40299e6	−	5.85970e6i	0.116354	−	0.485963i
$681$		−	1.70942e6i		−	0.141247i
$682$	7.36103e6	−	1.32089e7i	0.606007	−	1.08744i
$683$	5.72466e6	+	5.72466e6i	0.469568	+	0.469568i	0.901775	−	0.432207i	$-0.142265\pi$
$683$	5.72466e6	+	5.72466e6i	0.469568	+	0.469568i	−0.432207	+	0.901775i	$0.642265\pi$
$684$	−209889.	+	890682.i	−0.0171534	+	0.0727918i
$685$	−4.03746e6	−	7.30634e6i	−0.328762	−	0.594941i
$686$	−6.03614e6	+	1.71603e6i	−0.489721	+	0.139224i
$687$			4.31833e6i			0.349079i
$688$	2.04093e7	−	6.82106e6i	1.64383	−	0.549390i
$689$	2.52846e7			2.02912
$690$	1.83796e7	+	65778.3i	1.46964	+	0.00525968i
$691$	−5.74923e6	−	5.74923e6i	−0.458052	−	0.458052i	0.439964	−	0.898016i	$-0.354991\pi$
$691$	−5.74923e6	−	5.74923e6i	−0.458052	−	0.458052i	−0.898016	+	0.439964i	$0.854991\pi$
$692$	5.12321e6	−	2.17408e7i	0.406703	−	1.72588i
$693$	−1.85391e6	−	1.85391e6i	−0.146641	−	0.146641i
$694$	−7.02139e6	−	3.91286e6i	−0.553381	−	0.308387i
$695$	1.57611e7	+	4.54179e6i	1.23772	+	0.356668i
$696$	−7.72383e6	+	8.46171e6i	−0.604379	+	0.662117i
$697$	−6.44205e6			−0.502275
$698$	−1.25927e7	−	7.01760e6i	−0.978316	−	0.545193i
$699$	−1.43910e6	+	1.43910e6i	−0.111403	+	0.111403i
$700$	117270.	−	1.63835e7i	0.00904572	−	1.26375i
$701$	2.26596e6	+	2.26596e6i	0.174163	+	0.174163i	0.788806	−	0.614642i	$-0.210700\pi$
$701$	2.26596e6	+	2.26596e6i	0.174163	+	0.174163i	−0.614642	+	0.788806i	$0.710700\pi$
$702$	1.55055e7	−	4.40811e6i	1.18753	−	0.337605i
$703$			6.68607e6i			0.510249i
$704$	−8.45097e6	−	7.03597e6i	−0.642651	−	0.535047i
$705$	2.21571e6	−	7.68903e6i	0.167896	−	0.582638i
$706$	−5.30821e6	−	1.86716e7i	−0.400808	−	1.40984i
$707$	−1.02831e7	+	1.02831e7i	−0.773705	+	0.773705i
$708$	−476820.	−	770829.i	−0.0357496	−	0.0577929i
$709$	3.48993e6	−	3.48993e6i	0.260736	−	0.260736i	−0.564617	−	0.825353i	$-0.690976\pi$
$709$	3.48993e6	−	3.48993e6i	0.260736	−	0.260736i	0.825353	+	0.564617i	$0.190976\pi$
$710$	3.85135e6	−	3.82389e6i	0.286726	−	0.284681i
$711$			151762.i			0.0112587i
$712$	4.87154e6	+	4.44673e6i	0.360136	+	0.328731i
$713$	3.31272e7			2.44040
$714$	6.73692e6	+	3.75433e6i	0.494557	+	0.275605i
$715$	−1.15176e7	+	6.36460e6i	−0.842555	+	0.465592i
$716$	−1.09501e7	−	2.58039e6i	−0.798245	−	0.188106i
$717$	1.15838e6	−	1.15838e6i	0.0841495	−	0.0841495i
$718$	−490024.	−	1.72366e6i	−0.0354737	−	0.124779i
$719$	1.18415e7			0.854249			0.427124	−	0.904193i	$-0.359527\pi$
$719$	1.18415e7			0.854249			0.427124	+	0.904193i	$0.359527\pi$
$720$	114553.	+	2.72724e6i	0.00823520	+	0.196061i
$721$	−1.46171e7			−1.04719
$722$	3.27398e6	+	1.15162e7i	0.233740	+	0.822180i
$723$	6.29205e6	−	6.29205e6i	0.447658	−	0.447658i
$724$	−6.40383e6	+	2.71752e7i	−0.454039	+	1.92675i
$725$	−1.37977e7	+	3.14735e6i	−0.974901	+	0.222382i
$726$	−3.34462e6	−	1.86388e6i	−0.235508	−	0.131243i
$727$	1.67492e7			1.17533			0.587663	−	0.809106i	$-0.300048\pi$
$727$	1.67492e7			1.17533			0.587663	+	0.809106i	$0.300048\pi$
$728$	947432.	+	2.07821e7i	0.0662551	+	1.45332i
$729$			1.59511e7i			1.11166i
$730$	5.00399e6	+	5.03993e6i	0.347543	+	0.350040i
$731$	−8.84783e6	+	8.84783e6i	−0.612411	+	0.612411i
$732$	−3.26533e6	+	2.01987e6i	−0.225242	+	0.139330i
$733$	−1.86231e6	+	1.86231e6i	−0.128024	+	0.128024i	−0.768215	−	0.640191i	$-0.778855\pi$
$733$	−1.86231e6	+	1.86231e6i	−0.128024	+	0.128024i	0.640191	+	0.768215i	$0.278855\pi$
$734$	−1.72415e6	−	6.06469e6i	−0.118123	−	0.415498i
$735$	7.53420e6	+	2.17109e6i	0.514421	+	0.148238i
$736$	4.45196e6	−	2.36755e7i	0.302940	−	1.61103i
$737$		−	1.32578e7i		−	0.899090i
$738$	2.80719e6	−	798065.i	0.189728	−	0.0539383i
$739$	−2.97620e6	−	2.97620e6i	−0.200471	−	0.200471i	0.599731	−	0.800202i	$-0.295274\pi$
$739$	−2.97620e6	−	2.97620e6i	−0.200471	−	0.200471i	−0.800202	+	0.599731i	$0.795274\pi$
$740$	5.38521e6	+	1.92035e7i	0.361513	+	1.28914i
$741$	−4.15698e6	+	4.15698e6i	−0.278120	+	0.278120i
$742$	−2.91825e7	−	1.62627e7i	−1.94586	−	1.08438i
$743$	−5.66812e6			−0.376675			−0.188338	−	0.982104i	$-0.560310\pi$
$743$	−5.66812e6			−0.376675			−0.188338	+	0.982104i	$0.560310\pi$
$744$	−917732.	−	2.01306e7i	−0.0607832	−	1.33329i
$745$	−2.31832e7	−	6.68058e6i	−1.53032	−	0.440985i
$746$	1.73604e7	+	9.67455e6i	1.14212	+	0.636479i
$747$	−1.16972e6	−	1.16972e6i	−0.0766976	−	0.0766976i
$748$	6.22373e6	+	1.46662e6i	0.406721	+	0.0958438i
$749$	2.57370e6	+	2.57370e6i	0.167631	+	0.167631i
$750$	7.39109e6	−	1.16666e7i	0.479794	−	0.757340i
$751$	−2.91172e7			−1.88386			−0.941931	−	0.335806i	$-0.890991\pi$
$751$	−2.91172e7			−1.88386			−0.941931	+	0.335806i	$0.890991\pi$
$752$	−9.38463e6	−	4.68303e6i	−0.605163	−	0.301983i
$753$			8.85113e6i			0.568868i
$754$	1.72849e7	−	4.91396e6i	1.10723	−	0.314777i
$755$	−5.22058e6	+	2.88487e6i	−0.333312	+	0.184187i
$756$	−2.07311e7	−	4.88527e6i	−1.31922	−	0.310874i
$757$	1.10040e7	+	1.10040e7i	0.697929	+	0.697929i	0.963963	−	0.266035i	$-0.0857136\pi$
$757$	1.10040e7	+	1.10040e7i	0.697929	+	0.697929i	−0.266035	+	0.963963i	$0.585714\pi$
$758$	6.96592e6	−	1.24999e7i	0.440358	−	0.790196i
$759$			1.95049e7i			1.22896i
$760$	−3.17392e6	−	5.17226e6i	−0.199325	−	0.324822i
$761$			1.24303e7i			0.778072i	0.921223	+	0.389036i	$0.127192\pi$
$761$			1.24303e7i			0.778072i	−0.921223	+	0.389036i	$0.872808\pi$
$762$	1.20918e6	+	673849.i	0.0754404	+	0.0420412i
$763$	−5.68515e6	−	5.68515e6i	−0.353533	−	0.353533i
$764$	1.12565e7	−	6.96306e6i	0.697702	−	0.431585i
$765$	−767676.	−	1.38922e6i	−0.0474269	−	0.0858256i
$766$	−2.70584e6	−	9.51780e6i	−0.166621	−	0.586090i
$767$			1.42165e6i			0.0872578i
$768$	−1.45104e7	−	2.04946e6i	−0.887719	−	0.125382i
$769$	1.98520e7			1.21056			0.605282	−	0.796011i	$-0.293060\pi$
$769$	1.98520e7			1.21056			0.605282	+	0.796011i	$0.293060\pi$
$770$	1.73868e7	+	62225.3i	1.05680	+	0.00378216i
$771$	−1.19631e7	−	1.19631e7i	−0.724784	−	0.724784i
$772$	5.72465e6	+	9.25447e6i	0.345705	+	0.558867i
$773$	−1.84624e7	−	1.84624e7i	−1.11132	−	1.11132i	−0.992973	−	0.118345i	$-0.962241\pi$
$773$	−1.84624e7	−	1.84624e7i	−1.11132	−	1.11132i	−0.118345	−	0.992973i	$-0.537759\pi$
$774$	2.75944e6	−	4.95164e6i	0.165565	−	0.297096i
$775$	1.32462e7	−	2.10752e7i	0.792205	−	1.26043i
$776$	4.36142e6	+	3.98109e6i	0.260000	+	0.237327i
$777$	−2.55286e7			−1.51696
$778$	−1.58934e7	+	2.85197e7i	−0.941384	+	1.68926i
$779$	−4.58782e6	+	4.58782e6i	−0.270871	+	0.270871i
$780$	−8.59135e6	+	1.52877e7i	−0.505621	+	0.899718i
$781$	4.07259e6	+	4.07259e6i	0.238915	+	0.238915i
$782$	3.83057e6	+	1.34740e7i	0.224000	+	0.787918i
$783$			1.83976e7i			1.07240i
$784$	4.58873e6	−	9.19566e6i	0.266626	−	0.534309i
$785$	1.64039e7	+	4.72702e6i	0.950106	+	0.273787i
$786$	1.29521e7	−	3.68219e6i	0.747797	−	0.212594i
$787$	−8.89693e6	+	8.89693e6i	−0.512040	+	0.512040i	−0.915151	−	0.403111i	$-0.867929\pi$
$787$	−8.89693e6	+	8.89693e6i	−0.512040	+	0.512040i	0.403111	+	0.915151i	$0.367929\pi$
$788$	1.39144e7	+	3.27893e6i	0.798269	+	0.188112i
$789$	−1.52059e7	+	1.52059e7i	−0.869598	+	0.869598i
$790$	−709099.	−	714193.i	−0.0404240	−	0.0407144i
$791$			3.04837e7i			1.73231i
$792$	−2.89375e6	+	131923.i	−0.163926	+	0.00747321i
$793$	6.02229e6			0.340078
$794$	5.25899e6	−	9.43694e6i	0.296040	−	0.531227i
$795$	−1.36205e7	−	2.46482e7i	−0.764321	−	1.38315i
$796$	1.38578e7	+	2.24025e7i	0.775194	+	1.25318i
$797$	6.97802e6	−	6.97802e6i	0.389123	−	0.389123i	−0.485252	−	0.874375i	$-0.661272\pi$
$797$	6.97802e6	−	6.97802e6i	0.389123	−	0.389123i	0.874375	+	0.485252i	$0.161272\pi$
$798$	7.47153e6	−	2.12410e6i	0.415339	−	0.118078i
$799$	6.09861e6			0.337959
$800$	−1.32820e7	−	1.22992e7i	−0.733731	−	0.679440i
$801$	1.73751e6			0.0956854
$802$	−1.45568e7	+	4.13839e6i	−0.799152	+	0.227193i
$803$	−5.32945e6	+	5.32945e6i	−0.291671	+	0.291671i
$804$	−9.29449e6	−	1.50255e7i	−0.507091	−	0.819764i
$805$	1.84227e7	+	3.33385e7i	1.00199	+	1.81324i
$806$	−1.53862e7	+	2.76096e7i	−0.834244	+	1.49700i
$807$	2.67397e7			1.44535
$808$	731738.	+	1.60508e7i	0.0394301	+	0.864904i
$809$		−	3.03763e6i		−	0.163179i	−0.996666	−	0.0815894i	$-0.974000\pi$
$809$		−	3.03763e6i		−	0.163179i	0.996666	−	0.0815894i	$-0.0259996\pi$
$810$	−1.00681e7	−	1.01404e7i	−0.539179	−	0.543052i
$811$	1.27080e6	−	1.27080e6i	0.0678460	−	0.0678460i	−0.672370	−	0.740216i	$-0.734723\pi$
$811$	1.27080e6	−	1.27080e6i	0.0678460	−	0.0678460i	0.740216	+	0.672370i	$0.234723\pi$
$812$	−2.31101e7	−	5.44588e6i	−1.23002	−	0.289853i
$813$	−1.00190e7	+	1.00190e7i	−0.531615	+	0.531615i
$814$	−2.03586e7	+	5.78780e6i	−1.07693	+	0.306163i
$815$	−1.52742e7	−	4.40148e6i	−0.805496	−	0.232116i
$816$	8.08173e6	−	2.70102e6i	0.424893	−	0.142005i
$817$			1.26023e7i			0.660532i
$818$	−9.33790e6	−	3.28460e7i	−0.487939	−	1.71633i
$819$	3.87507e6	+	3.87507e6i	0.201869	+	0.201869i
$820$	−9.48176e6	+	1.68722e7i	−0.492441	+	0.876266i
$821$	−2.12317e7	+	2.12317e7i	−1.09933	+	1.09933i	−0.104836	+	0.994490i	$0.533432\pi$
$821$	−2.12317e7	+	2.12317e7i	−1.09933	+	1.09933i	−0.994490	+	0.104836i	$0.966568\pi$
$822$	5.74681e6	−	1.03123e7i	0.296652	−	0.532324i
$823$	3.24062e7			1.66774			0.833871	−	0.551960i	$-0.186120\pi$
$823$	3.24062e7			1.66774			0.833871	+	0.551960i	$0.186120\pi$
$824$	−1.08878e7	+	1.19279e7i	−0.558627	+	0.611994i
$825$	1.24088e7	+	7.79922e6i	0.634740	+	0.398948i
$826$	914386.	−	1.64081e6i	0.0466315	−	0.0836774i
$827$	2.03549e6	+	2.03549e6i	0.103492	+	0.103492i	0.756957	−	0.653465i	$-0.226685\pi$
$827$	2.03549e6	+	2.03549e6i	0.103492	+	0.103492i	−0.653465	+	0.756957i	$0.726685\pi$
$828$	−3.33843e6	−	5.39691e6i	−0.169226	−	0.273571i
$829$	−1.43533e7	−	1.43533e7i	−0.725381	−	0.725381i	0.244315	−	0.969696i	$-0.421437\pi$
$829$	−1.43533e7	−	1.43533e7i	−0.725381	−	0.725381i	−0.969696	+	0.244315i	$0.921437\pi$
$830$	1.09702e7	+	39261.1i	0.552739	+	0.00197819i
$831$	2.44219e7			1.22681
$832$	1.76644e7	+	1.47067e7i	0.884688	+	0.736559i
$833$			5.97580e6i			0.298390i
$834$	6.34329e6	+	2.23125e7i	0.315791	+	1.11079i
$835$	1.80735e7	+	3.27066e7i	0.897071	+	1.62338i
$836$	5.47682e6	−	3.38786e6i	0.271027	−	0.167652i
$837$	−2.28818e7	−	2.28818e7i	−1.12895	−	1.12895i
$838$	3.04884e6	+	1.69905e6i	0.149977	+	0.0835788i
$839$		−	1.91574e7i		−	0.939574i	−0.882780	−	0.469787i	$-0.844331\pi$
$839$		−	1.91574e7i		−	0.939574i	0.882780	−	0.469787i	$-0.155669\pi$
$840$	1.97486e7	−	1.21186e7i	0.965692	−	0.592591i
$841$		−	2358.56i		−	0.000114989i
$842$	3.83323e6	−	6.87849e6i	0.186331	−	0.334359i
$843$	3.43233e6	+	3.43233e6i	0.166349	+	0.166349i
$844$	1.28215e7	+	3.02139e6i	0.619560	+	0.145999i
$845$	5.90768e6	−	3.26456e6i	0.284626	−	0.157283i
$846$	−2.65753e6	+	755519.i	−0.127659	+	0.0362927i
$847$		−	7.93503e6i		−	0.380050i
$848$	−3.50078e7	+	1.17001e7i	−1.67176	+	0.558727i
$849$	−2.04739e6			−0.0974835
$850$	1.01037e7	+	2.95075e6i	0.479662	+	0.140083i
$851$	−3.27867e7	−	3.27867e7i	−1.55194	−	1.55194i
$852$	7.47072e6	+	1.76047e6i	0.352585	+	0.0830865i
$853$	−1.19015e7	−	1.19015e7i	−0.560054	−	0.560054i	0.369269	−	0.929323i	$-0.379608\pi$
$853$	−1.19015e7	−	1.19015e7i	−0.560054	−	0.560054i	−0.929323	+	0.369269i	$0.879608\pi$
$854$	−6.95068e6	−	3.87345e6i	−0.326124	−	0.181741i
$855$	−1.53607e6	−	442642.i	−0.0718614	−	0.0207080i
$856$	4.01727e6	−	183143.i	0.187390	−	0.00854290i
$857$	−2.43863e7			−1.13421			−0.567106	−	0.823645i	$-0.691937\pi$
$857$	−2.43863e7			−1.13421			−0.567106	+	0.823645i	$0.691937\pi$
$858$	−1.62562e7	−	9.05920e6i	−0.753877	−	0.420118i
$859$	2.15288e7	−	2.15288e7i	0.995489	−	0.995489i	−0.00450137	−	0.999990i	$-0.501433\pi$
$859$	2.15288e7	−	2.15288e7i	0.995489	−	0.995489i	0.999990	+	0.00450137i	$0.00143283\pi$
$860$	1.01503e7	+	3.61958e7i	0.467988	+	1.66883i
$861$	−1.75171e7	−	1.75171e7i	−0.805296	−	0.805296i
$862$	−2.77100e7	+	7.87775e6i	−1.27019	+	0.361105i
$863$			3.26254e7i			1.49118i	0.666407	+	0.745588i	$0.267831\pi$
$863$			3.26254e7i			1.49118i	−0.666407	+	0.745588i	$0.732169\pi$
$864$	−1.94284e7	+	1.32782e7i	−0.885425	+	0.605138i
$865$	3.74941e7	+	1.08045e7i	1.70382	+	0.490981i
$866$	−8.07441e6	−	2.84017e7i	−0.365861	−	1.28691i
$867$	1.05277e7	−	1.05277e7i	0.475648	−	0.475648i
$868$	3.55162e7	−	2.19696e7i	1.60003	−	0.989746i
$869$	755218.	−	755218.i	0.0339252	−	0.0339252i
$870$	−1.41014e7	−	1.42027e7i	−0.631633	−	0.636171i
$871$			2.77117e7i			1.23771i
$872$	−8.87389e6	+	404551.i	−0.395206	+	0.0180170i
$873$	1.55557e6			0.0690801
$874$	1.23238e7	+	6.86776e6i	0.545715	+	0.304114i
$875$	2.85761e7	+	1.61036e6i	1.26178	+	0.0711056i
$876$	−2.30378e6	+	9.77628e6i	−0.101433	+	0.430441i
$877$	−1.01553e7	+	1.01553e7i	−0.445857	+	0.445857i	−0.893975	−	0.448118i	$-0.852095\pi$
$877$	−1.01553e7	+	1.01553e7i	−0.445857	+	0.445857i	0.448118	+	0.893975i	$0.352095\pi$
$878$	9.04826e6	+	3.18272e7i	0.396122	+	1.39336i
$879$	−374611.			−0.0163534
$880$	1.30016e7	−	1.41417e7i	0.565966	−	0.615596i
$881$	−1.25018e7			−0.542668			−0.271334	−	0.962485i	$-0.587465\pi$
$881$	−1.25018e7			−0.542668			−0.271334	+	0.962485i	$0.587465\pi$
$882$	−740305.	−	2.60402e6i	−0.0320435	−	0.112713i
$883$	2.78147e7	−	2.78147e7i	1.20053	−	1.20053i	0.226520	−	0.974006i	$-0.427265\pi$
$883$	2.78147e7	−	2.78147e7i	1.20053	−	1.20053i	0.974006	−	0.226520i	$-0.0727350\pi$
$884$	−1.30090e7	−	3.06556e6i	−0.559902	−	0.131941i
$885$	1.38587e6	−	765826.i	0.0594791	−	0.0328679i
$886$	−9.97560e6	−	5.55917e6i	−0.426928	−	0.237917i
$887$	9.78546e6			0.417611			0.208806	−	0.977957i	$-0.433042\pi$
$887$	9.78546e6			0.417611			0.208806	+	0.977957i	$0.433042\pi$
$888$	−1.90154e7	+	2.08320e7i	−0.809233	+	0.886541i
$889$			2.86875e6i			0.121742i
$890$	−8.17674e6	+	8.11842e6i	−0.346023	+	0.343555i
$891$	1.07229e7	−	1.07229e7i	0.452498	−	0.452498i
$892$	1.19307e7	+	1.92872e7i	0.502058	+	0.811629i
$893$	4.34323e6	−	4.34323e6i	0.182257	−	0.182257i
$894$	−9.33044e6	−	3.28198e7i	−0.390443	−	1.37338i
$895$	5.44188e6	−	1.88846e7i	0.227086	−	0.788043i
$896$	−1.09284e7	−	2.83354e7i	−0.454763	−	1.17912i
$897$		−	4.07695e7i		−	1.69182i
$898$	3.68321e7	−	1.04711e7i	1.52418	−	0.433313i
$899$	−2.55076e7	−	2.55076e7i	−1.05262	−	1.05262i
$900$	−4.76837e6	−	34131.3i	−0.196229	−	0.00140458i
$901$	1.51766e7	−	1.51766e7i	0.622819	−	0.622819i
$902$	−1.79410e7	−	9.99810e6i	−0.734227	−	0.409168i
$903$	−4.81178e7			−1.96375
$904$	2.48755e7	+	2.27063e7i	1.01240	+	0.924112i
$905$	−4.68664e7	−	1.35052e7i	−1.90213	−	0.548127i
$906$	−7.36841e6	−	4.10625e6i	−0.298231	−	0.166197i
$907$	2.39944e7	+	2.39944e7i	0.968484	+	0.968484i	0.999518	−	0.0310344i	$-0.00988015\pi$
$907$	2.39944e7	+	2.39944e7i	0.968484	+	0.968484i	−0.0310344	+	0.999518i	$0.509880\pi$
$908$	897764.	−	3.80974e6i	0.0361366	−	0.153349i
$909$	2.99287e6	+	2.99287e6i	0.120137	+	0.120137i
$910$	−3.63422e7	−	130065.i	−1.45482	−	0.00520662i
$911$	1.54983e7			0.618710			0.309355	−	0.950947i	$-0.399887\pi$
$911$	1.54983e7			0.618710			0.309355	+	0.950947i	$0.399887\pi$
$912$	3.83197e6	−	7.67913e6i	0.152558	−	0.305721i
$913$			1.16419e7i			0.462218i
$914$	1.70489e7	−	4.84687e6i	0.675041	−	0.191909i
$915$	−3.24413e6	−	5.87071e6i	−0.128099	−	0.231813i
$916$	−2.26793e6	+	9.62415e6i	−0.0893081	+	0.378986i
$917$	1.97322e7	+	1.97322e7i	0.774912	+	0.774912i
$918$	6.66099e6	−	1.19527e7i	0.260875	−	0.468124i
$919$			3.09051e7i			1.20709i	0.797328	+	0.603547i	$0.206246\pi$
$919$			3.09051e7i			1.20709i	−0.797328	+	0.603547i	$0.793754\pi$
$920$	4.09275e7	+	9.79930e6i	1.59421	+	0.381703i
$921$		−	1.36927e7i		−	0.531911i
$922$	−1.08919e7	−	6.06983e6i	−0.421967	−	0.235152i
$923$	−8.51261e6	−	8.51261e6i	−0.328896	−	0.328896i
$924$	1.29355e7	+	2.09115e7i	0.498428	+	0.805759i
$925$	−3.39687e7	+	7.74850e6i	−1.30534	+	0.297758i
$926$	7.11855e6	+	2.50395e7i	0.272813	+	0.959617i
$927$			4.25428e6i			0.162602i
$928$	−2.16579e7	+	1.48019e7i	−0.825555	+	0.564220i
$929$	−1.10909e7			−0.421626			−0.210813	−	0.977526i	$-0.567611\pi$
$929$	−1.10909e7			−0.421626			−0.210813	+	0.977526i	$0.567611\pi$
$930$	3.52030e7	+	125987.i	1.33467	+	0.00477661i
$931$	4.25577e6	+	4.25577e6i	0.160918	+	0.160918i
$932$	−3.96308e6	+	2.45149e6i	−0.149449	+	0.0924464i
$933$	−1.98058e7	−	1.98058e7i	−0.744884	−	0.744884i
$934$	−4.55018e6	+	8.16503e6i	−0.170672	+	0.306260i
$935$	−3.09300e6	+	1.07334e7i	−0.115705	+	0.401523i
$936$	6.04857e6	−	275748.i	0.225664	−	0.0102878i
$937$	3.32920e7			1.23877			0.619385	−	0.785088i	$-0.287382\pi$
$937$	3.32920e7			1.23877			0.619385	+	0.785088i	$0.287382\pi$
$938$	1.78238e7	−	3.19838e7i	0.661445	−	1.18692i
$939$	1.11533e7	−	1.11533e7i	0.412800	−	0.412800i
$940$	8.97627e6	−	1.59727e7i	0.331342	−	0.589601i
$941$	1.47920e7	+	1.47920e7i	0.544567	+	0.544567i	0.924864	−	0.380297i	$-0.124178\pi$
$941$	1.47920e7	+	1.47920e7i	0.544567	+	0.544567i	−0.380297	+	0.924864i	$0.624178\pi$
$942$	6.60199e6	+	2.32225e7i	0.242408	+	0.852671i
$943$		−	4.49949e7i		−	1.64772i
$944$	−657848.	−	1.96835e6i	−0.0240268	−	0.0718905i
$945$	1.03027e7	−	3.57528e7i	0.375294	−	1.30236i
$946$	−3.83729e7	+	1.09092e7i	−1.39411	+	0.396336i
$947$	9.33246e6	−	9.33246e6i	0.338159	−	0.338159i	−0.517515	−	0.855674i	$-0.673143\pi$
$947$	9.33246e6	−	9.33246e6i	0.338159	−	0.338159i	0.855674	+	0.517515i	$0.173143\pi$
$948$	326461.	−	1.38536e6i	0.0117981	−	0.0500660i
$949$	1.11397e7	−	1.11397e7i	0.401521	−	0.401521i
$950$	9.29699e6	−	5.09413e6i	0.334221	−	0.183131i
$951$		−	3.22483e7i		−	1.15626i
$952$	1.30427e7	+	1.19053e7i	0.466417	+	0.425744i
$953$	−2.61757e7			−0.933612			−0.466806	−	0.884360i	$-0.654595\pi$
$953$	−2.61757e7			−0.933612			−0.466806	+	0.884360i	$0.654595\pi$
$954$	−4.73323e6	+	8.49349e6i	−0.168378	+	0.302145i
$955$	1.11834e7	+	2.02380e7i	0.396796	+	0.718058i
$956$	3.19000e6	−	1.97328e6i	0.112888	−	0.0698302i
$957$	1.50186e7	−	1.50186e7i	0.530089	−	0.530089i
$958$	2.29837e7	−	6.53411e6i	0.809108	−	0.230024i
$959$	2.44657e7			0.859034
$960$	4.82097e6	−	2.51421e7i	0.168833	−	0.880489i
$961$	3.48205e7			1.21626
$962$	4.25539e7	−	1.20978e7i	1.48252	−	0.421471i
$963$	749070.	−	749070.i	0.0260289	−	0.0260289i
$964$	1.73274e7	−	1.07184e7i	0.600540	−	0.371483i
$965$	−1.66386e7	+	9.19441e6i	−0.575172	+	0.317838i
$966$	−2.62224e7	+	4.70545e7i	−0.904127	+	1.62240i
$967$	2.21652e7			0.762264			0.381132	−	0.924521i	$-0.375534\pi$
$967$	2.21652e7			0.762264			0.381132	+	0.924521i	$0.375534\pi$
$968$	−6.47519e6	−	5.91054e6i	−0.222108	−	0.202740i
$969$			4.99029e6i			0.170732i
$970$	−7.32051e6	+	7.26830e6i	−0.249811	+	0.248030i
$971$	1.02205e7	−	1.02205e7i	0.347874	−	0.347874i	−0.511443	−	0.859317i	$-0.670889\pi$
$971$	1.02205e7	−	1.02205e7i	0.347874	−	0.347874i	0.859317	+	0.511443i	$0.170889\pi$
$972$	−2.61045e6	+	1.10777e7i	−0.0886237	+	0.376082i
$973$	−3.39926e7	+	3.39926e7i	−1.15107	+	1.15107i
$974$	1.07306e7	−	3.05063e6i	0.362431	−	0.103037i
$975$	−2.59372e7	−	1.63021e7i	−0.873798	−	0.549201i
$976$	−8.33816e6	+	2.78672e6i	−0.280185	+	0.0936418i
$977$		−	8.07408e6i		−	0.270618i	−0.990803	−	0.135309i	$-0.956797\pi$
$977$		−	8.07408e6i		−	0.270618i	0.990803	−	0.135309i	$-0.0432027\pi$
$978$	−6.14733e6	−	2.16232e7i	−0.205513	−	0.722891i
$979$	−8.64644e6	−	8.64644e6i	−0.288324	−	0.288324i
$980$	1.56510e7	+	8.79552e6i	0.520569	+	0.292547i
$981$	−1.65465e6	+	1.65465e6i	−0.0548951	+	0.0548951i
$982$	1.69921e7	−	3.04913e7i	0.562299	−	1.00901i
$983$	−1.27193e7			−0.419835			−0.209917	−	0.977719i	$-0.567320\pi$
$983$	−1.27193e7			−0.419835			−0.209917	+	0.977719i	$0.567320\pi$
$984$	−2.73423e7	+	1.24651e6i	−0.900219	+	0.0410400i
$985$	−6.91504e6	+	2.39968e7i	−0.227093	+	0.788066i
$986$	7.42537e6	−	1.33244e7i	0.243235	−	0.436470i
$987$	1.65833e7	+	1.65833e7i	0.541847	+	0.541847i
$988$	−1.14478e7	+	7.08137e6i	−0.373102	+	0.230794i
$989$	−6.17983e7	−	6.17983e7i	−2.00903	−	2.00903i
$990$	18110.5	−	5.06039e6i	0.000587277	−	0.164095i
$991$	−2.99875e7			−0.969966			−0.484983	−	0.874524i	$-0.661174\pi$
$991$	−2.99875e7			−0.969966			−0.484983	+	0.874524i	$0.661174\pi$
$992$	8.52700e6	−	4.53465e7i	0.275117	−	1.46307i
$993$			5.62543e6i			0.181043i
$994$	4.34971e6	+	1.53001e7i	0.139635	+	0.491166i
$995$	−4.02773e7	+	2.22571e7i	−1.28974	+	0.712706i
$996$	8.16164e6	+	1.31941e7i	0.260693	+	0.421437i
$997$	2.16097e7	+	2.16097e7i	0.688512	+	0.688512i	0.961903	−	0.273391i	$-0.0881453\pi$
$997$	2.16097e7	+	2.16097e7i	0.688512	+	0.688512i	−0.273391	+	0.961903i	$0.588145\pi$
$998$	2.90244e7	+	1.61746e7i	0.922437	+	0.514053i
$999$			4.52933e7i			1.43589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.q.a.29.6	✓	116
5.4	even	2	inner	80.6.q.a.29.53	yes	116
16.5	even	4	inner	80.6.q.a.69.53	yes	116
80.69	even	4	inner	80.6.q.a.69.6	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.q.a.29.6	✓	116	1.1	even	1	trivial
80.6.q.a.29.53	yes	116	5.4	even	2	inner
80.6.q.a.69.6	yes	116	80.69	even	4	inner
80.6.q.a.69.53	yes	116	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.44124 + 1.54691i) q^{2} +(9.88218 - 9.88218i) q^{3} +(27.2142 - 16.8342i) q^{4} +(27.0375 + 48.9282i) q^{5} +(-38.4845 + 69.0581i) q^{6} -163.839 q^{7} +(-122.038 + 133.697i) q^{8} +47.6849i q^{9} +O(q^{10})\)	\(q+(-5.44124 + 1.54691i) q^{2} +(9.88218 - 9.88218i) q^{3} +(27.2142 - 16.8342i) q^{4} +(27.0375 + 48.9282i) q^{5} +(-38.4845 + 69.0581i) q^{6} -163.839 q^{7} +(-122.038 + 133.697i) q^{8} +47.6849i q^{9} +(-222.805 - 224.406i) q^{10} +(237.296 - 237.296i) q^{11} +(102.577 - 435.294i) q^{12} +(-496.001 + 496.001i) q^{13} +(891.486 - 253.443i) q^{14} +(750.708 + 216.328i) q^{15} +(457.221 - 916.256i) q^{16} +595.429i q^{17} +(-73.7640 - 259.465i) q^{18} +(424.045 + 424.045i) q^{19} +(1559.47 + 876.386i) q^{20} +(-1619.08 + 1619.08i) q^{21} +(-924.111 + 1658.26i) q^{22} -4158.82 q^{23} +(115.213 + 2527.21i) q^{24} +(-1662.94 + 2645.80i) q^{25} +(1931.59 - 3466.13i) q^{26} +(2872.60 + 2872.60i) q^{27} +(-4458.73 + 2758.09i) q^{28} +(3202.25 + 3202.25i) q^{29} +(-4419.42 - 15.8166i) q^{30} -7965.53 q^{31} +(-1070.49 + 5692.85i) q^{32} -4690.01i q^{33} +(-921.073 - 3239.87i) q^{34} +(-4429.80 - 8016.34i) q^{35} +(802.736 + 1297.70i) q^{36} +(7883.67 + 7883.67i) q^{37} +(-2963.29 - 1651.37i) q^{38} +9803.15i q^{39} +(-9841.14 - 2356.27i) q^{40} +10819.2i q^{41} +(6305.25 - 11314.4i) q^{42} +(14859.6 + 14859.6i) q^{43} +(2463.13 - 10452.5i) q^{44} +(-2333.14 + 1289.28i) q^{45} +(22629.1 - 6433.30i) q^{46} -10242.4i q^{47} +(-4536.27 - 13573.0i) q^{48} +10036.1 q^{49} +(4955.67 - 16968.8i) q^{50} +(5884.14 + 5884.14i) q^{51} +(-5148.49 + 21848.0i) q^{52} +(-25488.4 - 25488.4i) q^{53} +(-20074.2 - 11186.9i) q^{54} +(18026.4 + 5194.58i) q^{55} +(19994.5 - 21904.7i) q^{56} +8380.99 q^{57} +(-22377.8 - 12470.6i) q^{58} +(1433.11 - 1433.11i) q^{59} +(24071.6 - 6750.36i) q^{60} +(-6070.84 - 6070.84i) q^{61} +(43342.3 - 12321.9i) q^{62} -7812.63i q^{63} +(-2981.52 - 32632.1i) q^{64} +(-37679.1 - 10857.8i) q^{65} +(7255.01 + 25519.5i) q^{66} +(27935.2 - 27935.2i) q^{67} +(10023.6 + 16204.1i) q^{68} +(-41098.2 + 41098.2i) q^{69} +(36504.1 + 36766.3i) q^{70} +17162.5i q^{71} +(-6375.30 - 5819.36i) q^{72} -22459.0 q^{73} +(-55092.2 - 30701.6i) q^{74} +(9712.76 + 42579.8i) q^{75} +(18678.5 + 4401.59i) q^{76} +(-38878.3 + 38878.3i) q^{77} +(-15164.6 - 53341.3i) q^{78} +3182.60 q^{79} +(57192.9 - 2402.28i) q^{80} +45187.7 q^{81} +(-16736.2 - 58869.7i) q^{82} +(-24530.3 + 24530.3i) q^{83} +(-16806.1 + 71318.0i) q^{84} +(-29133.3 + 16098.9i) q^{85} +(-103841. - 57868.1i) q^{86} +63290.4 q^{87} +(2766.56 + 60684.8i) q^{88} -36437.3i q^{89} +(10700.8 - 10624.4i) q^{90} +(81264.2 - 81264.2i) q^{91} +(-113179. + 70010.2i) q^{92} +(-78716.8 + 78716.8i) q^{93} +(15844.0 + 55731.2i) q^{94} +(-9282.65 + 32212.9i) q^{95} +(45679.0 + 66836.5i) q^{96} -32621.8i q^{97} +(-54609.0 + 15524.9i) q^{98} +(11315.4 + 11315.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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