LMFDB - Embedded newform 1045.6.a.g.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.a (trivial)

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:	yes
Analytic conductor:	$167.601091705$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00103 q^{2} +20.9100 q^{3} -30.9979 q^{4} -25.0000 q^{5} -20.9316 q^{6} +215.274 q^{7} +63.0630 q^{8} +194.229 q^{9} +O(q^{10})$	\(q-1.00103 q^{2} +20.9100 q^{3} -30.9979 q^{4} -25.0000 q^{5} -20.9316 q^{6} +215.274 q^{7} +63.0630 q^{8} +194.229 q^{9} +25.0258 q^{10} -121.000 q^{11} -648.168 q^{12} +358.187 q^{13} -215.496 q^{14} -522.751 q^{15} +928.806 q^{16} +493.249 q^{17} -194.430 q^{18} +361.000 q^{19} +774.948 q^{20} +4501.38 q^{21} +121.125 q^{22} +4068.66 q^{23} +1318.65 q^{24} +625.000 q^{25} -358.557 q^{26} -1019.79 q^{27} -6673.04 q^{28} +5193.54 q^{29} +523.291 q^{30} -5910.79 q^{31} -2947.78 q^{32} -2530.11 q^{33} -493.759 q^{34} -5381.85 q^{35} -6020.71 q^{36} -216.642 q^{37} -361.373 q^{38} +7489.69 q^{39} -1576.58 q^{40} +1370.66 q^{41} -4506.03 q^{42} -9477.87 q^{43} +3750.75 q^{44} -4855.74 q^{45} -4072.87 q^{46} -7230.29 q^{47} +19421.4 q^{48} +29535.8 q^{49} -625.646 q^{50} +10313.8 q^{51} -11103.0 q^{52} +6824.30 q^{53} +1020.85 q^{54} +3025.00 q^{55} +13575.8 q^{56} +7548.52 q^{57} -5198.91 q^{58} -22283.4 q^{59} +16204.2 q^{60} +38837.3 q^{61} +5916.90 q^{62} +41812.5 q^{63} -26770.9 q^{64} -8954.66 q^{65} +2532.73 q^{66} +34334.1 q^{67} -15289.7 q^{68} +85075.8 q^{69} +5387.41 q^{70} +7978.42 q^{71} +12248.7 q^{72} -13829.1 q^{73} +216.866 q^{74} +13068.8 q^{75} -11190.3 q^{76} -26048.1 q^{77} -7497.43 q^{78} +67664.0 q^{79} -23220.1 q^{80} -68521.7 q^{81} -1372.08 q^{82} -63429.8 q^{83} -139534. q^{84} -12331.2 q^{85} +9487.67 q^{86} +108597. q^{87} -7630.63 q^{88} -40857.6 q^{89} +4860.76 q^{90} +77108.2 q^{91} -126120. q^{92} -123595. q^{93} +7237.76 q^{94} -9025.00 q^{95} -61638.2 q^{96} -41947.3 q^{97} -29566.3 q^{98} -23501.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) $ 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00103	−0.176959	−0.0884797	−	0.996078i	$-0.528201\pi$
$2$	−1.00103	−0.176959	−0.0884797	+	0.996078i	$0.528201\pi$
$3$	20.9100	1.34138	0.670690	−	0.741738i	$-0.265998\pi$
$3$	20.9100	1.34138	0.670690	+	0.741738i	$0.265998\pi$
$4$	−30.9979	−0.968685
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−20.9316	−0.237370
$7$	215.274	1.66053	0.830264	−	0.557371i	$-0.188190\pi$
$7$	215.274	1.66053	0.830264	+	0.557371i	$0.188190\pi$
$8$	63.0630	0.348377
$9$	194.229	0.799298
$10$	25.0258	0.0791387
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−648.168	−1.29937
$13$	358.187	0.587829	0.293914	−	0.955832i	$-0.405042\pi$
$13$	358.187	0.587829	0.293914	+	0.955832i	$0.405042\pi$
$14$	−215.496	−0.293846
$15$	−522.751	−0.599883
$16$	928.806	0.907037
$17$	493.249	0.413946	0.206973	−	0.978347i	$-0.433639\pi$
$17$	493.249	0.413946	0.206973	+	0.978347i	$0.433639\pi$
$18$	−194.430	−0.141443
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	774.948	0.433209
$21$	4501.38	2.22740
$22$	121.125	0.0533553
$23$	4068.66	1.60373	0.801866	−	0.597503i	$-0.203841\pi$
$23$	4068.66	1.60373	0.801866	+	0.597503i	$0.203841\pi$
$24$	1318.65	0.467306
$25$	625.000	0.200000
$26$	−358.557	−0.104022
$27$	−1019.79	−0.269217
$28$	−6673.04	−1.60853
$29$	5193.54	1.14675	0.573375	−	0.819293i	$-0.305634\pi$
$29$	5193.54	1.14675	0.573375	+	0.819293i	$0.305634\pi$
$30$	523.291	0.106155
$31$	−5910.79	−1.10469	−0.552346	−	0.833615i	$-0.686267\pi$
$31$	−5910.79	−1.10469	−0.552346	+	0.833615i	$0.686267\pi$
$32$	−2947.78	−0.508886
$33$	−2530.11	−0.404441
$34$	−493.759	−0.0732516
$35$	−5381.85	−0.742610
$36$	−6020.71	−0.774268
$37$	−216.642	−0.0260159	−0.0130079	−	0.999915i	$-0.504141\pi$
$37$	−216.642	−0.0260159	−0.0130079	+	0.999915i	$0.504141\pi$
$38$	−361.373	−0.0405973
$39$	7489.69	0.788501
$40$	−1576.58	−0.155799
$41$	1370.66	0.127342	0.0636709	−	0.997971i	$-0.479719\pi$
$41$	1370.66	0.127342	0.0636709	+	0.997971i	$0.479719\pi$
$42$	−4506.03	−0.394159
$43$	−9477.87	−0.781699	−0.390850	−	0.920455i	$-0.627819\pi$
$43$	−9477.87	−0.781699	−0.390850	+	0.920455i	$0.627819\pi$
$44$	3750.75	0.292070
$45$	−4855.74	−0.357457
$46$	−4072.87	−0.283796
$47$	−7230.29	−0.477431	−0.238716	−	0.971090i	$-0.576726\pi$
$47$	−7230.29	−0.477431	−0.238716	+	0.971090i	$0.576726\pi$
$48$	19421.4	1.21668
$49$	29535.8	1.75735
$50$	−625.646	−0.0353919
$51$	10313.8	0.555259
$52$	−11103.0	−0.569421
$53$	6824.30	0.333709	0.166855	−	0.985981i	$-0.446639\pi$
$53$	6824.30	0.333709	0.166855	+	0.985981i	$0.446639\pi$
$54$	1020.85	0.0476405
$55$	3025.00	0.134840
$56$	13575.8	0.578490
$57$	7548.52	0.307733
$58$	−5198.91	−0.202928
$59$	−22283.4	−0.833397	−0.416698	−	0.909045i	$-0.636813\pi$
$59$	−22283.4	−0.833397	−0.416698	+	0.909045i	$0.636813\pi$
$60$	16204.2	0.581098
$61$	38837.3	1.33636	0.668181	−	0.743999i	$-0.267073\pi$
$61$	38837.3	1.33636	0.668181	+	0.743999i	$0.267073\pi$
$62$	5916.90	0.195486
$63$	41812.5	1.32726
$64$	−26770.9	−0.816985
$65$	−8954.66	−0.262885
$66$	2532.73	0.0715696
$67$	34334.1	0.934412	0.467206	−	0.884148i	$-0.345261\pi$
$67$	34334.1	0.934412	0.467206	+	0.884148i	$0.345261\pi$
$68$	−15289.7	−0.400983
$69$	85075.8	2.15121
$70$	5387.41	0.131412
$71$	7978.42	0.187833	0.0939163	−	0.995580i	$-0.470061\pi$
$71$	7978.42	0.187833	0.0939163	+	0.995580i	$0.470061\pi$
$72$	12248.7	0.278457
$73$	−13829.1	−0.303730	−0.151865	−	0.988401i	$-0.548528\pi$
$73$	−13829.1	−0.303730	−0.151865	+	0.988401i	$0.548528\pi$
$74$	216.866	0.00460375
$75$	13068.8	0.268276
$76$	−11190.3	−0.222232
$77$	−26048.1	−0.500668
$78$	−7497.43	−0.139533
$79$	67664.0	1.21980	0.609902	−	0.792477i	$-0.291209\pi$
$79$	67664.0	1.21980	0.609902	+	0.792477i	$0.291209\pi$
$80$	−23220.1	−0.405639
$81$	−68521.7	−1.16042
$82$	−1372.08	−0.0225343
$83$	−63429.8	−1.01064	−0.505322	−	0.862931i	$-0.668626\pi$
$83$	−63429.8	−1.01064	−0.505322	+	0.862931i	$0.668626\pi$
$84$	−139534.	−2.15765
$85$	−12331.2	−0.185122
$86$	9487.67	0.138329
$87$	108597.	1.53823
$88$	−7630.63	−0.105040
$89$	−40857.6	−0.546762	−0.273381	−	0.961906i	$-0.588142\pi$
$89$	−40857.6	−0.546762	−0.273381	+	0.961906i	$0.588142\pi$
$90$	4860.76	0.0632554
$91$	77108.2	0.976106
$92$	−126120.	−1.55351
$93$	−123595.	−1.48181
$94$	7237.76	0.0844860
$95$	−9025.00	−0.102598
$96$	−61638.2	−0.682609
$97$	−41947.3	−0.452662	−0.226331	−	0.974050i	$-0.572673\pi$
$97$	−41947.3	−0.452662	−0.226331	+	0.974050i	$0.572673\pi$
$98$	−29566.3	−0.310980
$99$	−23501.8	−0.240997
$100$	−19373.7	−0.193737
$101$	85207.7	0.831142	0.415571	−	0.909561i	$-0.363582\pi$
$101$	85207.7	0.831142	0.415571	+	0.909561i	$0.363582\pi$
$102$	−10324.5	−0.0982582
$103$	−58001.4	−0.538698	−0.269349	−	0.963043i	$-0.586809\pi$
$103$	−58001.4	−0.538698	−0.269349	+	0.963043i	$0.586809\pi$
$104$	22588.3	0.204786
$105$	−112535.	−0.996122
$106$	−6831.36	−0.0590530
$107$	72077.7	0.608613	0.304307	−	0.952574i	$-0.401575\pi$
$107$	72077.7	0.608613	0.304307	+	0.952574i	$0.401575\pi$
$108$	31611.5	0.260787
$109$	−96047.2	−0.774316	−0.387158	−	0.922013i	$-0.626543\pi$
$109$	−96047.2	−0.774316	−0.387158	+	0.922013i	$0.626543\pi$
$110$	−3028.13	−0.0238612
$111$	−4529.99	−0.0348971
$112$	199948.	1.50616
$113$	19342.1	0.142498	0.0712488	−	0.997459i	$-0.477302\pi$
$113$	19342.1	0.142498	0.0712488	+	0.997459i	$0.477302\pi$
$114$	−7556.32	−0.0544563
$115$	−101717.	−0.717211
$116$	−160989.	−1.11084
$117$	69570.4	0.469851
$118$	22306.5	0.147477
$119$	106184.	0.687369
$120$	−32966.3	−0.208986
$121$	14641.0	0.0909091
$122$	−38877.4	−0.236482
$123$	28660.6	0.170814
$124$	183222.	1.07010
$125$	−15625.0	−0.0894427
$126$	−41855.7	−0.234871
$127$	225735.	1.24191	0.620954	−	0.783847i	$-0.286745\pi$
$127$	225735.	1.24191	0.620954	+	0.783847i	$0.286745\pi$
$128$	121128.	0.653459
$129$	−198183.	−1.04856
$130$	8963.92	0.0465200
$131$	−65053.2	−0.331200	−0.165600	−	0.986193i	$-0.552956\pi$
$131$	−65053.2	−0.331200	−0.165600	+	0.986193i	$0.552956\pi$
$132$	78428.3	0.391776
$133$	77713.8	0.380951
$134$	−34369.6	−0.165353
$135$	25494.8	0.120398
$136$	31105.8	0.144209
$137$	80157.5	0.364874	0.182437	−	0.983218i	$-0.441601\pi$
$137$	80157.5	0.364874	0.182437	+	0.983218i	$0.441601\pi$
$138$	−85163.8	−0.380678
$139$	356628.	1.56559	0.782795	−	0.622279i	$-0.213793\pi$
$139$	356628.	1.56559	0.782795	+	0.622279i	$0.213793\pi$
$140$	166826.	0.719356
$141$	−151186.	−0.640416
$142$	−7986.66	−0.0332387
$143$	−43340.6	−0.177237
$144$	180401.	0.724993
$145$	−129839.	−0.512842
$146$	13843.4	0.0537480
$147$	617595.	2.35728
$148$	6715.45	0.0252012
$149$	124456.	0.459252	0.229626	−	0.973279i	$-0.426250\pi$
$149$	124456.	0.459252	0.229626	+	0.973279i	$0.426250\pi$
$150$	−13082.3	−0.0474739
$151$	333419.	1.19000	0.595002	−	0.803724i	$-0.297151\pi$
$151$	333419.	1.19000	0.595002	+	0.803724i	$0.297151\pi$
$152$	22765.8	0.0799233
$153$	95803.4	0.330866
$154$	26075.1	0.0885979
$155$	147770.	0.494034
$156$	−232165.	−0.763810
$157$	−295925.	−0.958147	−0.479074	−	0.877775i	$-0.659027\pi$
$157$	−295925.	−0.958147	−0.479074	+	0.877775i	$0.659027\pi$
$158$	−67734.0	−0.215856
$159$	142696.	0.447631
$160$	73694.6	0.227581
$161$	875876.	2.66304
$162$	68592.5	0.205347
$163$	−109549.	−0.322953	−0.161476	−	0.986877i	$-0.551626\pi$
$163$	−109549.	−0.322953	−0.161476	+	0.986877i	$0.551626\pi$
$164$	−42487.7	−0.123354
$165$	63252.8	0.180872
$166$	63495.3	0.178843
$167$	−414785.	−1.15089	−0.575443	−	0.817842i	$-0.695170\pi$
$167$	−414785.	−1.15089	−0.575443	+	0.817842i	$0.695170\pi$
$168$	283871.	0.775975
$169$	−242995.	−0.654457
$170$	12344.0	0.0327591
$171$	70116.8	0.183372
$172$	293794.	0.757221
$173$	627454.	1.59392	0.796960	−	0.604032i	$-0.206440\pi$
$173$	627454.	1.59392	0.796960	+	0.604032i	$0.206440\pi$
$174$	−108709.	−0.272204
$175$	134546.	0.332106
$176$	−112385.	−0.273482
$177$	−465947.	−1.11790
$178$	40899.9	0.0967546
$179$	118803.	0.277137	0.138568	−	0.990353i	$-0.455750\pi$
$179$	118803.	0.277137	0.138568	+	0.990353i	$0.455750\pi$
$180$	150518.	0.346263
$181$	−864622.	−1.96169	−0.980844	−	0.194797i	$-0.937595\pi$
$181$	−864622.	−1.96169	−0.980844	+	0.194797i	$0.937595\pi$
$182$	−77187.9	−0.172731
$183$	812089.	1.79257
$184$	256582.	0.558704
$185$	5416.05	0.0116347
$186$	123723.	0.262221
$187$	−59683.1	−0.124809
$188$	224124.	0.462481
$189$	−219535.	−0.447043
$190$	9034.33	0.0181557
$191$	−238853.	−0.473748	−0.236874	−	0.971540i	$-0.576123\pi$
$191$	−238853.	−0.473748	−0.236874	+	0.971540i	$0.576123\pi$
$192$	−559781.	−1.09589
$193$	772367.	1.49255	0.746277	−	0.665635i	$-0.231839\pi$
$193$	772367.	1.49255	0.746277	+	0.665635i	$0.231839\pi$
$194$	41990.6	0.0801028
$195$	−187242.	−0.352629
$196$	−915549.	−1.70232
$197$	1.00800e6	1.85052	0.925261	−	0.379330i	$-0.123846\pi$
$197$	1.00800e6	1.85052	0.925261	+	0.379330i	$0.123846\pi$
$198$	23526.1	0.0426468
$199$	434490.	0.777763	0.388882	−	0.921288i	$-0.372861\pi$
$199$	434490.	0.777763	0.388882	+	0.921288i	$0.372861\pi$
$200$	39414.4	0.0696755
$201$	717927.	1.25340
$202$	−85295.7	−0.147078
$203$	1.11803e6	1.90421
$204$	−319708.	−0.537871
$205$	−34266.6	−0.0569490
$206$	58061.4	0.0953277
$207$	790254.	1.28186
$208$	332686.	0.533182
$209$	−43681.0	−0.0691714
$210$	112651.	0.176273
$211$	208741.	0.322776	0.161388	−	0.986891i	$-0.448403\pi$
$211$	208741.	0.322776	0.161388	+	0.986891i	$0.448403\pi$
$212$	−211539.	−0.323259
$213$	166829.	0.251955
$214$	−72152.2	−0.107700
$215$	236947.	0.349587
$216$	−64311.3	−0.0937892
$217$	−1.27244e6	−1.83437
$218$	96146.5	0.137023
$219$	−289168.	−0.407418
$220$	−93768.7	−0.130618
$221$	176675.	0.243329
$222$	4534.67	0.00617538
$223$	228012.	0.307041	0.153520	−	0.988145i	$-0.450939\pi$
$223$	228012.	0.307041	0.153520	+	0.988145i	$0.450939\pi$
$224$	−634580.	−0.845019
$225$	121393.	0.159860
$226$	−19362.1	−0.0252163
$227$	34236.9	0.0440991	0.0220495	−	0.999757i	$-0.492981\pi$
$227$	34236.9	0.0440991	0.0220495	+	0.999757i	$0.492981\pi$
$228$	−233989.	−0.298097
$229$	553169.	0.697058	0.348529	−	0.937298i	$-0.386681\pi$
$229$	553169.	0.697058	0.348529	+	0.937298i	$0.386681\pi$
$230$	101822.	0.126917
$231$	−544667.	−0.671586
$232$	327520.	0.399502
$233$	668484.	0.806679	0.403340	−	0.915050i	$-0.367849\pi$
$233$	668484.	0.806679	0.403340	+	0.915050i	$0.367849\pi$
$234$	−69642.3	−0.0831445
$235$	180757.	0.213514
$236$	690740.	0.807299
$237$	1.41486e6	1.63622
$238$	−106293.	−0.121636
$239$	365379.	0.413761	0.206880	−	0.978366i	$-0.433669\pi$
$239$	365379.	0.413761	0.206880	+	0.978366i	$0.433669\pi$
$240$	−485534.	−0.544116
$241$	−1.20780e6	−1.33953	−0.669764	−	0.742574i	$-0.733605\pi$
$241$	−1.20780e6	−1.33953	−0.669764	+	0.742574i	$0.733605\pi$
$242$	−14656.1	−0.0160872
$243$	−1.18498e6	−1.28735
$244$	−1.20388e6	−1.29451
$245$	−738395.	−0.785912
$246$	−28690.2	−0.0302271
$247$	129305.	0.134857
$248$	−372753.	−0.384850
$249$	−1.32632e6	−1.35566
$250$	15641.2	0.0158277
$251$	−547437.	−0.548466	−0.274233	−	0.961663i	$-0.588424\pi$
$251$	−547437.	−0.548466	−0.274233	+	0.961663i	$0.588424\pi$
$252$	−1.29610e6	−1.28569
$253$	−492308.	−0.483544
$254$	−225968.	−0.219767
$255$	−257846.	−0.248319
$256$	735417.	0.701349
$257$	872440.	0.823954	0.411977	−	0.911194i	$-0.364838\pi$
$257$	872440.	0.823954	0.411977	+	0.911194i	$0.364838\pi$
$258$	198387.	0.185552
$259$	−46637.3	−0.0432001
$260$	277576.	0.254653
$261$	1.00874e6	0.916595
$262$	65120.4	0.0586090
$263$	239379.	0.213401	0.106701	−	0.994291i	$-0.465971\pi$
$263$	239379.	0.213401	0.106701	+	0.994291i	$0.465971\pi$
$264$	−159557.	−0.140898
$265$	−170608.	−0.149239
$266$	−77794.2	−0.0674129
$267$	−854334.	−0.733415
$268$	−1.06429e6	−0.905152
$269$	744211.	0.627069	0.313535	−	0.949577i	$-0.398487\pi$
$269$	744211.	0.627069	0.313535	+	0.949577i	$0.398487\pi$
$270$	−25521.2	−0.0213055
$271$	2.06708e6	1.70976	0.854879	−	0.518827i	$-0.173631\pi$
$271$	2.06708e6	1.70976	0.854879	+	0.518827i	$0.173631\pi$
$272$	458132.	0.375464
$273$	1.61233e6	1.30933
$274$	−80240.3	−0.0645678
$275$	−75625.0	−0.0603023
$276$	−2.63718e6	−2.08385
$277$	282225.	0.221002	0.110501	−	0.993876i	$-0.464755\pi$
$277$	282225.	0.221002	0.110501	+	0.993876i	$0.464755\pi$
$278$	−356996.	−0.277046
$279$	−1.14805e6	−0.882979
$280$	−339396.	−0.258709
$281$	−1.08118e6	−0.816830	−0.408415	−	0.912796i	$-0.633918\pi$
$281$	−1.08118e6	−0.816830	−0.408415	+	0.912796i	$0.633918\pi$
$282$	151342.	0.113328
$283$	−2.23821e6	−1.66125	−0.830623	−	0.556835i	$-0.812016\pi$
$283$	−2.23821e6	−1.66125	−0.830623	+	0.556835i	$0.812016\pi$
$284$	−247314.	−0.181951
$285$	−188713.	−0.137623
$286$	43385.4	0.0313638
$287$	295068.	0.211455
$288$	−572546.	−0.406752
$289$	−1.17656e6	−0.828649
$290$	129973.	0.0907522
$291$	−877118.	−0.607192
$292$	428675.	0.294219
$293$	2.40856e6	1.63903	0.819517	−	0.573055i	$-0.194242\pi$
$293$	2.40856e6	1.63903	0.819517	+	0.573055i	$0.194242\pi$
$294$	−618233.	−0.417142
$295$	557086.	0.372706
$296$	−13662.1	−0.00906334
$297$	123395.	0.0811721
$298$	−124585.	−0.0812690
$299$	1.45734e6	0.942720
$300$	−405105.	−0.259875
$301$	−2.04034e6	−1.29803
$302$	−333764.	−0.210582
$303$	1.78170e6	1.11488
$304$	335299.	0.208088
$305$	−970932.	−0.597639
$306$	−95902.5	−0.0585499
$307$	2.37896e6	1.44060	0.720298	−	0.693665i	$-0.244005\pi$
$307$	2.37896e6	1.44060	0.720298	+	0.693665i	$0.244005\pi$
$308$	807438.	0.484990
$309$	−1.21281e6	−0.722599
$310$	−147923.	−0.0874239
$311$	1.10620e6	0.648535	0.324268	−	0.945965i	$-0.394882\pi$
$311$	1.10620e6	0.648535	0.324268	+	0.945965i	$0.394882\pi$
$312$	472323.	0.274696
$313$	−2.01895e6	−1.16484	−0.582419	−	0.812889i	$-0.697894\pi$
$313$	−2.01895e6	−1.16484	−0.582419	+	0.812889i	$0.697894\pi$
$314$	296231.	0.169553
$315$	−1.04531e6	−0.593567
$316$	−2.09744e6	−1.18161
$317$	1.69832e6	0.949229	0.474614	−	0.880194i	$-0.342588\pi$
$317$	1.69832e6	0.949229	0.474614	+	0.880194i	$0.342588\pi$
$318$	−142844.	−0.0792125
$319$	−628418.	−0.345758
$320$	669274.	0.365367
$321$	1.50715e6	0.816381
$322$	−876782.	−0.471250
$323$	178063.	0.0949657
$324$	2.12403e6	1.12408
$325$	223867.	0.117566
$326$	109662.	0.0571495
$327$	−2.00835e6	−1.03865
$328$	86438.2	0.0443630
$329$	−1.55649e6	−0.792788
$330$	−63318.2	−0.0320069
$331$	371997.	0.186625	0.0933124	−	0.995637i	$-0.470254\pi$
$331$	371997.	0.186625	0.0933124	+	0.995637i	$0.470254\pi$
$332$	1.96619e6	0.978995
$333$	−42078.3	−0.0207944
$334$	415214.	0.203660
$335$	−858352.	−0.417882
$336$	4.18091e6	2.02033
$337$	1.94768e6	0.934207	0.467103	−	0.884203i	$-0.345298\pi$
$337$	1.94768e6	0.934207	0.467103	+	0.884203i	$0.345298\pi$
$338$	243247.	0.115812
$339$	404444.	0.191143
$340$	382242.	0.179325
$341$	715206.	0.333077
$342$	−70189.3	−0.0324493
$343$	2.74018e6	1.25760
$344$	−597704.	−0.272326
$345$	−2.12690e6	−0.962052
$346$	−628103.	−0.282059
$347$	831624.	0.370769	0.185384	−	0.982666i	$-0.440647\pi$
$347$	831624.	0.370769	0.185384	+	0.982666i	$0.440647\pi$
$348$	−3.36629e6	−1.49006
$349$	936033.	0.411365	0.205683	−	0.978619i	$-0.434059\pi$
$349$	936033.	0.411365	0.205683	+	0.978619i	$0.434059\pi$
$350$	−134685.	−0.0587692
$351$	−365276.	−0.158254
$352$	356682.	0.153435
$353$	409320.	0.174834	0.0874170	−	0.996172i	$-0.472139\pi$
$353$	409320.	0.174834	0.0874170	+	0.996172i	$0.472139\pi$
$354$	466429.	0.197823
$355$	−199460.	−0.0840013
$356$	1.26650e6	0.529640
$357$	2.22030e6	0.922022
$358$	−118926.	−0.0490420
$359$	888106.	0.363688	0.181844	−	0.983327i	$-0.441793\pi$
$359$	888106.	0.363688	0.181844	+	0.983327i	$0.441793\pi$
$360$	−306218.	−0.124530
$361$	130321.	0.0526316
$362$	865515.	0.347139
$363$	306144.	0.121944
$364$	−2.39019e6	−0.945540
$365$	345729.	0.135832
$366$	−812928.	−0.317212
$367$	2.40658e6	0.932686	0.466343	−	0.884604i	$-0.345571\pi$
$367$	2.40658e6	0.932686	0.466343	+	0.884604i	$0.345571\pi$
$368$	3.77900e6	1.45464
$369$	266223.	0.101784
$370$	−5421.65	−0.00205886
$371$	1.46909e6	0.554134
$372$	3.83119e6	1.43541
$373$	−1.03502e6	−0.385190	−0.192595	−	0.981278i	$-0.561690\pi$
$373$	−1.03502e6	−0.385190	−0.192595	+	0.981278i	$0.561690\pi$
$374$	59744.8	0.0220862
$375$	−326719.	−0.119977
$376$	−455964.	−0.166326
$377$	1.86026e6	0.674092
$378$	219762.	0.0791084
$379$	−421852.	−0.150856	−0.0754280	−	0.997151i	$-0.524032\pi$
$379$	−421852.	−0.150856	−0.0754280	+	0.997151i	$0.524032\pi$
$380$	279756.	0.0993850
$381$	4.72012e6	1.66587
$382$	239100.	0.0838341
$383$	3.12262e6	1.08773	0.543867	−	0.839171i	$-0.316960\pi$
$383$	3.12262e6	1.08773	0.543867	+	0.839171i	$0.316960\pi$
$384$	2.53278e6	0.876537
$385$	651203.	0.223905
$386$	−773165.	−0.264122
$387$	−1.84088e6	−0.624811
$388$	1.30028e6	0.438487
$389$	−2.11173e6	−0.707563	−0.353781	−	0.935328i	$-0.615104\pi$
$389$	−2.11173e6	−0.707563	−0.353781	+	0.935328i	$0.615104\pi$
$390$	187436.	0.0624009
$391$	2.00686e6	0.663859
$392$	1.86262e6	0.612222
$393$	−1.36026e6	−0.444265
$394$	−1.00904e6	−0.327467
$395$	−1.69160e6	−0.545513
$396$	728506.	0.233451
$397$	2.21166e6	0.704274	0.352137	−	0.935948i	$-0.385455\pi$
$397$	2.21166e6	0.704274	0.352137	+	0.935948i	$0.385455\pi$
$398$	−434940.	−0.137633
$399$	1.62500e6	0.511000
$400$	580503.	0.181407
$401$	−5.40497e6	−1.67854	−0.839272	−	0.543712i	$-0.817018\pi$
$401$	−5.40497e6	−1.67854	−0.839272	+	0.543712i	$0.817018\pi$
$402$	−718669.	−0.221801
$403$	−2.11717e6	−0.649370
$404$	−2.64126e6	−0.805115
$405$	1.71304e6	0.518956
$406$	−1.11919e6	−0.336968
$407$	26213.7	0.00784408
$408$	650423.	0.193440
$409$	−1.69005e6	−0.499563	−0.249782	−	0.968302i	$-0.580359\pi$
$409$	−1.69005e6	−0.499563	−0.249782	+	0.968302i	$0.580359\pi$
$410$	34302.0	0.0100777
$411$	1.67610e6	0.489434
$412$	1.79792e6	0.521829
$413$	−4.79704e6	−1.38388
$414$	−791071.	−0.226837
$415$	1.58574e6	0.451973
$416$	−1.05586e6	−0.299138
$417$	7.45710e6	2.10005
$418$	43726.1	0.0122405
$419$	−4.31247e6	−1.20003	−0.600013	−	0.799990i	$-0.704838\pi$
$419$	−4.31247e6	−1.20003	−0.600013	+	0.799990i	$0.704838\pi$
$420$	3.48834e6	0.964929
$421$	−6.82023e6	−1.87540	−0.937700	−	0.347447i	$-0.887049\pi$
$421$	−6.82023e6	−1.87540	−0.937700	+	0.347447i	$0.887049\pi$
$422$	−208957.	−0.0571183
$423$	−1.40433e6	−0.381610
$424$	430361.	0.116257
$425$	308280.	0.0827892
$426$	−167001.	−0.0445857
$427$	8.36065e6	2.21907
$428$	−2.23426e6	−0.589555
$429$	−906253.	−0.237742
$430$	−237192.	−0.0618626
$431$	1.24019e6	0.321586	0.160793	−	0.986988i	$-0.448595\pi$
$431$	1.24019e6	0.321586	0.160793	+	0.986988i	$0.448595\pi$
$432$	−947190.	−0.244190
$433$	−3.80376e6	−0.974975	−0.487488	−	0.873130i	$-0.662087\pi$
$433$	−3.80376e6	−0.974975	−0.487488	+	0.873130i	$0.662087\pi$
$434$	1.27375e6	0.324610
$435$	−2.71493e6	−0.687915
$436$	2.97726e6	0.750069
$437$	1.46879e6	0.367922
$438$	289467.	0.0720964
$439$	7.94872e6	1.96850	0.984251	−	0.176775i	$-0.0565663\pi$
$439$	7.94872e6	1.96850	0.984251	+	0.176775i	$0.0565663\pi$
$440$	190766.	0.0469752
$441$	5.73672e6	1.40465
$442$	−176858.	−0.0430594
$443$	−2.58268e6	−0.625261	−0.312630	−	0.949875i	$-0.601210\pi$
$443$	−2.58268e6	−0.625261	−0.312630	+	0.949875i	$0.601210\pi$
$444$	140420.	0.0338044
$445$	1.02144e6	0.244519
$446$	−228248.	−0.0543338
$447$	2.60239e6	0.616032
$448$	−5.76308e6	−1.35663
$449$	−4.05879e6	−0.950125	−0.475063	−	0.879952i	$-0.657575\pi$
$449$	−4.05879e6	−0.950125	−0.475063	+	0.879952i	$0.657575\pi$
$450$	−121519.	−0.0282887
$451$	−165850.	−0.0383950
$452$	−599565.	−0.138035
$453$	6.97181e6	1.59625
$454$	−34272.3	−0.00780375
$455$	−1.92770e6	−0.436528
$456$	476033.	0.107207
$457$	1.49723e6	0.335351	0.167675	−	0.985842i	$-0.446374\pi$
$457$	1.49723e6	0.335351	0.167675	+	0.985842i	$0.446374\pi$
$458$	−553740.	−0.123351
$459$	−503012.	−0.111441
$460$	3.15300e6	0.694752
$461$	6.50339e6	1.42524	0.712619	−	0.701552i	$-0.247509\pi$
$461$	6.50339e6	1.42524	0.712619	+	0.701552i	$0.247509\pi$
$462$	545230.	0.118843
$463$	8.13083e6	1.76272	0.881358	−	0.472449i	$-0.156630\pi$
$463$	8.13083e6	1.76272	0.881358	+	0.472449i	$0.156630\pi$
$464$	4.82379e6	1.04014
$465$	3.08987e6	0.662686
$466$	−669175.	−0.142750
$467$	9.07258e6	1.92503	0.962517	−	0.271220i	$-0.0874272\pi$
$467$	9.07258e6	1.92503	0.962517	+	0.271220i	$0.0874272\pi$
$468$	−2.15654e6	−0.455137
$469$	7.39123e6	1.55162
$470$	−180944.	−0.0377833
$471$	−6.18780e6	−1.28524
$472$	−1.40526e6	−0.290337
$473$	1.14682e6	0.235691
$474$	−1.41632e6	−0.289544
$475$	225625.	0.0458831
$476$	−3.29147e6	−0.665844
$477$	1.32548e6	0.266733
$478$	−365757.	−0.0732189
$479$	−4.12586e6	−0.821630	−0.410815	−	0.911719i	$-0.634756\pi$
$479$	−4.12586e6	−0.821630	−0.410815	+	0.911719i	$0.634756\pi$
$480$	1.54096e6	0.305272
$481$	−77598.3	−0.0152929
$482$	1.20905e6	0.237042
$483$	1.83146e7	3.57215
$484$	−453841.	−0.0880623
$485$	1.04868e6	0.202437
$486$	1.18621e6	0.227808
$487$	−4.55944e6	−0.871142	−0.435571	−	0.900154i	$-0.643454\pi$
$487$	−4.55944e6	−0.871142	−0.435571	+	0.900154i	$0.643454\pi$
$488$	2.44920e6	0.465559
$489$	−2.29067e6	−0.433202
$490$	739158.	0.139074
$491$	1.76202e6	0.329843	0.164921	−	0.986307i	$-0.447263\pi$
$491$	1.76202e6	0.329843	0.164921	+	0.986307i	$0.447263\pi$
$492$	−888420.	−0.165465
$493$	2.56171e6	0.474692
$494$	−129439.	−0.0238642
$495$	587544.	0.107777
$496$	−5.48998e6	−1.00200
$497$	1.71754e6	0.311901
$498$	1.32769e6	0.239896
$499$	9.48685e6	1.70557	0.852787	−	0.522258i	$-0.174910\pi$
$499$	9.48685e6	1.70557	0.852787	+	0.522258i	$0.174910\pi$
$500$	484343.	0.0866419
$501$	−8.67318e6	−1.54377
$502$	548003.	0.0970563
$503$	−2.95594e6	−0.520925	−0.260463	−	0.965484i	$-0.583875\pi$
$503$	−2.95594e6	−0.520925	−0.260463	+	0.965484i	$0.583875\pi$
$504$	2.63682e6	0.462386
$505$	−2.13019e6	−0.371698
$506$	492817.	0.0855676
$507$	−5.08104e6	−0.877875
$508$	−6.99731e6	−1.20302
$509$	4.76638e6	0.815444	0.407722	−	0.913106i	$-0.366323\pi$
$509$	4.76638e6	0.815444	0.407722	+	0.913106i	$0.366323\pi$
$510$	258113.	0.0439424
$511$	−2.97705e6	−0.504353
$512$	−4.61226e6	−0.777569
$513$	−368146.	−0.0617627
$514$	−873342.	−0.145806
$515$	1.45004e6	0.240913
$516$	6.14325e6	1.01572
$517$	874865.	0.143951
$518$	46685.6	0.00764466
$519$	1.31201e7	2.13805
$520$	−564708.	−0.0915832
$521$	−6.88472e6	−1.11120	−0.555600	−	0.831450i	$-0.687511\pi$
$521$	−6.88472e6	−1.11120	−0.555600	+	0.831450i	$0.687511\pi$
$522$	−1.00978e6	−0.162200
$523$	−1.13799e7	−1.81922	−0.909608	−	0.415468i	$-0.863618\pi$
$523$	−1.13799e7	−1.81922	−0.909608	+	0.415468i	$0.863618\pi$
$524$	2.01651e6	0.320829
$525$	2.81336e6	0.445479
$526$	−239627.	−0.0377634
$527$	−2.91549e6	−0.457283
$528$	−2.34998e6	−0.366843
$529$	1.01177e7	1.57196
$530$	170784.	0.0264093
$531$	−4.32810e6	−0.666133
$532$	−2.40897e6	−0.369022
$533$	490953.	0.0748552
$534$	855217.	0.129785
$535$	−1.80194e6	−0.272180
$536$	2.16521e6	0.325528
$537$	2.48417e6	0.371745
$538$	−744981.	−0.110966
$539$	−3.57383e6	−0.529861
$540$	−790287.	−0.116627
$541$	−2.81668e6	−0.413756	−0.206878	−	0.978367i	$-0.566330\pi$
$541$	−2.81668e6	−0.413756	−0.206878	+	0.978367i	$0.566330\pi$
$542$	−2.06922e6	−0.302558
$543$	−1.80793e7	−2.63137
$544$	−1.45399e6	−0.210651
$545$	2.40118e6	0.346285
$546$	−1.61400e6	−0.231698
$547$	−3.31243e6	−0.473346	−0.236673	−	0.971589i	$-0.576057\pi$
$547$	−3.31243e6	−0.473346	−0.236673	+	0.971589i	$0.576057\pi$
$548$	−2.48472e6	−0.353448
$549$	7.54334e6	1.06815
$550$	75703.2	0.0106711
$551$	1.87487e6	0.263082
$552$	5.36514e6	0.749434
$553$	1.45663e7	2.02552
$554$	−282516.	−0.0391083
$555$	113250.	0.0156065
$556$	−1.10547e7	−1.51656
$557$	1.32041e7	1.80332	0.901658	−	0.432450i	$-0.142351\pi$
$557$	1.32041e7	1.80332	0.901658	+	0.432450i	$0.142351\pi$
$558$	1.14924e6	0.156251
$559$	−3.39485e6	−0.459505
$560$	−4.99869e6	−0.673575
$561$	−1.24798e6	−0.167417
$562$	1.08230e6	0.144546
$563$	−1.33119e7	−1.76999	−0.884994	−	0.465602i	$-0.845838\pi$
$563$	−1.33119e7	−1.76999	−0.884994	+	0.465602i	$0.845838\pi$
$564$	4.68644e6	0.620362
$565$	−483553.	−0.0637269
$566$	2.24052e6	0.293973
$567$	−1.47509e7	−1.92691
$568$	503143.	0.0654366
$569$	−8.23495e6	−1.06630	−0.533151	−	0.846020i	$-0.678992\pi$
$569$	−8.23495e6	−1.06630	−0.533151	+	0.846020i	$0.678992\pi$
$570$	188908.	0.0243536
$571$	935036.	0.120016	0.0600078	−	0.998198i	$-0.480887\pi$
$571$	935036.	0.120016	0.0600078	+	0.998198i	$0.480887\pi$
$572$	1.34347e6	0.171687
$573$	−4.99442e6	−0.635475
$574$	−295373.	−0.0374189
$575$	2.54291e6	0.320747
$576$	−5.19971e6	−0.653014
$577$	1.23563e7	1.54508	0.772539	−	0.634967i	$-0.218986\pi$
$577$	1.23563e7	1.54508	0.772539	+	0.634967i	$0.218986\pi$
$578$	1.17778e6	0.146637
$579$	1.61502e7	2.00208
$580$	4.02473e6	0.496782
$581$	−1.36548e7	−1.67820
$582$	878025.	0.107448
$583$	−825740.	−0.100617
$584$	−872108.	−0.105813
$585$	−1.73926e6	−0.210124
$586$	−2.41105e6	−0.290043
$587$	2.53804e6	0.304021	0.152010	−	0.988379i	$-0.451425\pi$
$587$	2.53804e6	0.304021	0.152010	+	0.988379i	$0.451425\pi$
$588$	−1.91442e7	−2.28346
$589$	−2.13380e6	−0.253434
$590$	−557661.	−0.0659539
$591$	2.10773e7	2.48225
$592$	−201218.	−0.0235973
$593$	5.19481e6	0.606643	0.303321	−	0.952888i	$-0.401904\pi$
$593$	5.19481e6	0.606643	0.303321	+	0.952888i	$0.401904\pi$
$594$	−123523.	−0.0143642
$595$	−2.65459e6	−0.307401
$596$	−3.85789e6	−0.444871
$597$	9.08521e6	1.04328
$598$	−1.45885e6	−0.166823
$599$	−5.75228e6	−0.655048	−0.327524	−	0.944843i	$-0.606214\pi$
$599$	−5.75228e6	−0.655048	−0.327524	+	0.944843i	$0.606214\pi$
$600$	824156.	0.0934612
$601$	−5.67148e6	−0.640487	−0.320244	−	0.947335i	$-0.603765\pi$
$601$	−5.67148e6	−0.640487	−0.320244	+	0.947335i	$0.603765\pi$
$602$	2.04245e6	0.229699
$603$	6.66869e6	0.746874
$604$	−1.03353e7	−1.15274
$605$	−366025.	−0.0406558
$606$	−1.78354e6	−0.197288
$607$	−5.49507e6	−0.605343	−0.302672	−	0.953095i	$-0.597879\pi$
$607$	−5.49507e6	−0.605343	−0.302672	+	0.953095i	$0.597879\pi$
$608$	−1.06415e6	−0.116746
$609$	2.33781e7	2.55427
$610$	971936.	0.105758
$611$	−2.58979e6	−0.280648
$612$	−2.96971e6	−0.320505
$613$	−8.71499e6	−0.936732	−0.468366	−	0.883534i	$-0.655157\pi$
$613$	−8.71499e6	−0.936732	−0.468366	+	0.883534i	$0.655157\pi$
$614$	−2.38142e6	−0.254927
$615$	−716515.	−0.0763902
$616$	−1.64267e6	−0.174421
$617$	2.56629e6	0.271389	0.135695	−	0.990751i	$-0.456673\pi$
$617$	2.56629e6	0.271389	0.135695	+	0.990751i	$0.456673\pi$
$618$	1.21407e6	0.127871
$619$	−9.25147e6	−0.970475	−0.485237	−	0.874382i	$-0.661267\pi$
$619$	−9.25147e6	−0.970475	−0.485237	+	0.874382i	$0.661267\pi$
$620$	−4.58056e6	−0.478563
$621$	−4.14920e6	−0.431753
$622$	−1.10735e6	−0.114764
$623$	−8.79558e6	−0.907913
$624$	6.95647e6	0.715200
$625$	390625.	0.0400000
$626$	2.02104e6	0.206129
$627$	−913371.	−0.0927851
$628$	9.17306e6	0.928143
$629$	−106858.	−0.0107692
$630$	1.04639e6	0.105037
$631$	−2.53963e6	−0.253921	−0.126960	−	0.991908i	$-0.540522\pi$
$631$	−2.53963e6	−0.253921	−0.126960	+	0.991908i	$0.540522\pi$
$632$	4.26710e6	0.424952
$633$	4.36478e6	0.432965
$634$	−1.70007e6	−0.167975
$635$	−5.64337e6	−0.555398
$636$	−4.42329e6	−0.433614
$637$	1.05793e7	1.03302
$638$	629068.	0.0611851
$639$	1.54964e6	0.150134
$640$	−3.02819e6	−0.292236
$641$	−9.17000e6	−0.881504	−0.440752	−	0.897629i	$-0.645288\pi$
$641$	−9.17000e6	−0.881504	−0.440752	+	0.897629i	$0.645288\pi$
$642$	−1.50870e6	−0.144466
$643$	−1.96698e7	−1.87617	−0.938086	−	0.346403i	$-0.887403\pi$
$643$	−1.96698e7	−1.87617	−0.938086	+	0.346403i	$0.887403\pi$
$644$	−2.71504e7	−2.57965
$645$	4.95457e6	0.468928
$646$	−178247.	−0.0168051
$647$	9.83265e6	0.923443	0.461721	−	0.887025i	$-0.347232\pi$
$647$	9.83265e6	0.923443	0.461721	+	0.887025i	$0.347232\pi$
$648$	−4.32119e6	−0.404264
$649$	2.69629e6	0.251279
$650$	−224098.	−0.0208044
$651$	−2.66067e7	−2.46059
$652$	3.39579e6	0.312840
$653$	−1.80175e7	−1.65353	−0.826764	−	0.562549i	$-0.809821\pi$
$653$	−1.80175e7	−1.65353	−0.826764	+	0.562549i	$0.809821\pi$
$654$	2.01043e6	0.183799
$655$	1.62633e6	0.148117
$656$	1.27308e6	0.115504
$657$	−2.68603e6	−0.242771
$658$	1.55810e6	0.140291
$659$	1.26835e7	1.13769	0.568846	−	0.822444i	$-0.307390\pi$
$659$	1.26835e7	1.13769	0.568846	+	0.822444i	$0.307390\pi$
$660$	−1.96071e6	−0.175208
$661$	−5.19634e6	−0.462587	−0.231294	−	0.972884i	$-0.574296\pi$
$661$	−5.19634e6	−0.462587	−0.231294	+	0.972884i	$0.574296\pi$
$662$	−372381.	−0.0330250
$663$	3.69428e6	0.326397
$664$	−4.00007e6	−0.352085
$665$	−1.94285e6	−0.170367
$666$	42121.8	0.00367977
$667$	2.11308e7	1.83908
$668$	1.28575e7	1.11485
$669$	4.76774e6	0.411858
$670$	859240.	0.0739481
$671$	−4.69931e6	−0.402928
$672$	−1.32691e7	−1.13349
$673$	−1.56017e7	−1.32780	−0.663901	−	0.747820i	$-0.731101\pi$
$673$	−1.56017e7	−1.32780	−0.663901	+	0.747820i	$0.731101\pi$
$674$	−1.94969e6	−0.165317
$675$	−637371.	−0.0538435
$676$	7.53235e6	0.633963
$677$	−1.04613e7	−0.877229	−0.438614	−	0.898675i	$-0.644531\pi$
$677$	−1.04613e7	−0.877229	−0.438614	+	0.898675i	$0.644531\pi$
$678$	−404862.	−0.0338246
$679$	−9.03015e6	−0.751658
$680$	−777644.	−0.0644924
$681$	715894.	0.0591536
$682$	−715945.	−0.0589412
$683$	−7.85958e6	−0.644685	−0.322343	−	0.946623i	$-0.604470\pi$
$683$	−7.85958e6	−0.644685	−0.322343	+	0.946623i	$0.604470\pi$
$684$	−2.17348e6	−0.177629
$685$	−2.00394e6	−0.163176
$686$	−2.74301e6	−0.222545
$687$	1.15668e7	0.935019
$688$	−8.80310e6	−0.709030
$689$	2.44437e6	0.196164
$690$	2.12909e6	0.170244
$691$	−1.27513e7	−1.01592	−0.507962	−	0.861380i	$-0.669601\pi$
$691$	−1.27513e7	−1.01592	−0.507962	+	0.861380i	$0.669601\pi$
$692$	−1.94498e7	−1.54401
$693$	−5.05931e6	−0.400183
$694$	−832483.	−0.0656110
$695$	−8.91569e6	−0.700153
$696$	6.84846e6	0.535883
$697$	676078.	0.0527127
$698$	−937001.	−0.0727950
$699$	1.39780e7	1.08206
$700$	−4.17065e6	−0.321706
$701$	6.33463e6	0.486885	0.243442	−	0.969915i	$-0.421723\pi$
$701$	6.33463e6	0.486885	0.243442	+	0.969915i	$0.421723\pi$
$702$	365654.	0.0280045
$703$	−78207.8	−0.00596845
$704$	3.23928e6	0.246330
$705$	3.77964e6	0.286403
$706$	−409743.	−0.0309385
$707$	1.83430e7	1.38013
$708$	1.44434e7	1.08289
$709$	3.53573e6	0.264158	0.132079	−	0.991239i	$-0.457835\pi$
$709$	3.53573e6	0.264158	0.132079	+	0.991239i	$0.457835\pi$
$710$	199667.	0.0148648
$711$	1.31423e7	0.974987
$712$	−2.57661e6	−0.190479
$713$	−2.40490e7	−1.77163
$714$	−2.22260e6	−0.163160
$715$	1.08351e6	0.0792628
$716$	−3.68264e6	−0.268458
$717$	7.64009e6	0.555010
$718$	−889024.	−0.0643579
$719$	1.26915e7	0.915569	0.457784	−	0.889063i	$-0.348643\pi$
$719$	1.26915e7	0.915569	0.457784	+	0.889063i	$0.348643\pi$
$720$	−4.51004e6	−0.324227
$721$	−1.24862e7	−0.894523
$722$	−130456.	−0.00931365
$723$	−2.52551e7	−1.79682
$724$	2.68015e7	1.90026
$725$	3.24596e6	0.229350
$726$	−306460.	−0.0215791
$727$	−8.45564e6	−0.593349	−0.296675	−	0.954979i	$-0.595878\pi$
$727$	−8.45564e6	−0.593349	−0.296675	+	0.954979i	$0.595878\pi$
$728$	4.86268e6	0.340053
$729$	−8.12722e6	−0.566400
$730$	−346086.	−0.0240368
$731$	−4.67495e6	−0.323581
$732$	−2.51731e7	−1.73644
$733$	−581744.	−0.0399919	−0.0199959	−	0.999800i	$-0.506365\pi$
$733$	−581744.	−0.0399919	−0.0199959	+	0.999800i	$0.506365\pi$
$734$	−2.40907e6	−0.165048
$735$	−1.54399e7	−1.05421
$736$	−1.19935e7	−0.816117
$737$	−4.15443e6	−0.281736
$738$	−266498.	−0.0180117
$739$	−2.39451e7	−1.61290	−0.806448	−	0.591306i	$-0.798613\pi$
$739$	−2.39451e7	−1.61290	−0.806448	+	0.591306i	$0.798613\pi$
$740$	−167886.	−0.0112703
$741$	2.70378e6	0.180895
$742$	−1.47061e6	−0.0980592
$743$	2.57392e7	1.71050	0.855250	−	0.518215i	$-0.173403\pi$
$743$	2.57392e7	1.71050	0.855250	+	0.518215i	$0.173403\pi$
$744$	−7.79427e6	−0.516230
$745$	−3.11141e6	−0.205384
$746$	1.03609e6	0.0681630
$747$	−1.23199e7	−0.807805
$748$	1.85005e6	0.120901
$749$	1.55164e7	1.01062
$750$	327057.	0.0212310
$751$	−2.23981e7	−1.44914	−0.724570	−	0.689201i	$-0.757962\pi$
$751$	−2.23981e7	−1.44914	−0.724570	+	0.689201i	$0.757962\pi$
$752$	−6.71553e6	−0.433048
$753$	−1.14469e7	−0.735701
$754$	−1.86218e6	−0.119287
$755$	−8.33548e6	−0.532186
$756$	6.80513e6	0.433044
$757$	−2.10103e7	−1.33257	−0.666287	−	0.745695i	$-0.732118\pi$
$757$	−2.10103e7	−1.33257	−0.666287	+	0.745695i	$0.732118\pi$
$758$	422288.	0.0266954
$759$	−1.02942e7	−0.648615
$760$	−569144.	−0.0357428
$761$	8.56799e6	0.536312	0.268156	−	0.963376i	$-0.413586\pi$
$761$	8.56799e6	0.536312	0.268156	+	0.963376i	$0.413586\pi$
$762$	−4.72500e6	−0.294791
$763$	−2.06764e7	−1.28577
$764$	7.40395e6	0.458912
$765$	−2.39509e6	−0.147968
$766$	−3.12585e6	−0.192485
$767$	−7.98162e6	−0.489895
$768$	1.53776e7	0.940775
$769$	2.16046e7	1.31744	0.658719	−	0.752389i	$-0.271098\pi$
$769$	2.16046e7	1.31744	0.658719	+	0.752389i	$0.271098\pi$
$770$	−651876.	−0.0396222
$771$	1.82428e7	1.10523
$772$	−2.39418e7	−1.44582
$773$	1.08623e7	0.653844	0.326922	−	0.945051i	$-0.393989\pi$
$773$	1.08623e7	0.653844	0.326922	+	0.945051i	$0.393989\pi$
$774$	1.84278e6	0.110566
$775$	−3.69425e6	−0.220939
$776$	−2.64532e6	−0.157697
$777$	−975188.	−0.0579477
$778$	2.11391e6	0.125210
$779$	494810.	0.0292142
$780$	5.80412e6	0.341586
$781$	−965388.	−0.0566336
$782$	−2.00894e6	−0.117476
$783$	−5.29634e6	−0.308725
$784$	2.74330e7	1.59398
$785$	7.39812e6	0.428496
$786$	1.36167e6	0.0786169
$787$	1.69976e6	0.0978253	0.0489126	−	0.998803i	$-0.484424\pi$
$787$	1.69976e6	0.0978253	0.0489126	+	0.998803i	$0.484424\pi$
$788$	−3.12459e7	−1.79257
$789$	5.00543e6	0.286252
$790$	1.69335e6	0.0965336
$791$	4.16385e6	0.236621
$792$	−1.48209e6	−0.0839581
$793$	1.39110e7	0.785552
$794$	−2.21395e6	−0.124628
$795$	−3.56741e6	−0.200187
$796$	−1.34683e7	−0.753408
$797$	3.03624e7	1.69313	0.846566	−	0.532284i	$-0.178666\pi$
$797$	3.03624e7	1.69313	0.846566	+	0.532284i	$0.178666\pi$
$798$	−1.62668e6	−0.0904262
$799$	−3.56633e6	−0.197631
$800$	−1.84236e6	−0.101777
$801$	−7.93575e6	−0.437026
$802$	5.41056e6	0.297034
$803$	1.67333e6	0.0915782
$804$	−2.22543e7	−1.21415
$805$	−2.18969e7	−1.19095
$806$	2.11935e6	0.114912
$807$	1.55615e7	0.841138
$808$	5.37346e6	0.289551
$809$	−2.03212e7	−1.09164	−0.545819	−	0.837903i	$-0.683782\pi$
$809$	−2.03212e7	−1.09164	−0.545819	+	0.837903i	$0.683782\pi$
$810$	−1.71481e6	−0.0918341
$811$	2.98243e7	1.59227	0.796137	−	0.605116i	$-0.206873\pi$
$811$	2.98243e7	1.59227	0.796137	+	0.605116i	$0.206873\pi$
$812$	−3.46567e7	−1.84458
$813$	4.32228e7	2.29343
$814$	−26240.8	−0.00138808
$815$	2.73872e6	0.144429
$816$	9.57956e6	0.503640
$817$	−3.42151e6	−0.179334
$818$	1.69179e6	0.0884024
$819$	1.49767e7	0.780200
$820$	1.06219e6	0.0551657
$821$	−3.89714e6	−0.201785	−0.100892	−	0.994897i	$-0.532170\pi$
$821$	−3.89714e6	−0.201785	−0.100892	+	0.994897i	$0.532170\pi$
$822$	−1.67783e6	−0.0866099
$823$	−1.07144e6	−0.0551402	−0.0275701	−	0.999620i	$-0.508777\pi$
$823$	−1.07144e6	−0.0551402	−0.0275701	+	0.999620i	$0.508777\pi$
$824$	−3.65775e6	−0.187670
$825$	−1.58132e6	−0.0808882
$826$	4.80199e6	0.244890
$827$	7.83323e6	0.398269	0.199135	−	0.979972i	$-0.436187\pi$
$827$	7.83323e6	0.398269	0.199135	+	0.979972i	$0.436187\pi$
$828$	−2.44962e7	−1.24172
$829$	−1.56234e7	−0.789567	−0.394784	−	0.918774i	$-0.629180\pi$
$829$	−1.56234e7	−0.789567	−0.394784	+	0.918774i	$0.629180\pi$
$830$	−1.58738e6	−0.0799810
$831$	5.90133e6	0.296447
$832$	−9.58899e6	−0.480247
$833$	1.45685e7	0.727449
$834$	−7.46481e6	−0.371624
$835$	1.03696e7	0.514692
$836$	1.35402e6	0.0670054
$837$	6.02779e6	0.297402
$838$	4.31692e6	0.212356
$839$	−2.99595e7	−1.46936	−0.734682	−	0.678412i	$-0.762668\pi$
$839$	−2.99595e7	−1.46936	−0.734682	+	0.678412i	$0.762668\pi$
$840$	−7.09677e6	−0.347026
$841$	6.46171e6	0.315034
$842$	6.82728e6	0.331870
$843$	−2.26075e7	−1.09568
$844$	−6.47054e6	−0.312669
$845$	6.07488e6	0.292682
$846$	1.40579e6	0.0675295
$847$	3.15182e6	0.150957
$848$	6.33845e6	0.302687
$849$	−4.68010e7	−2.22836
$850$	−308599.	−0.0146503
$851$	−881443.	−0.0417225
$852$	−5.17135e6	−0.244065
$853$	2.15278e7	1.01304	0.506521	−	0.862228i	$-0.330931\pi$
$853$	2.15278e7	1.01304	0.506521	+	0.862228i	$0.330931\pi$
$854$	−8.36929e6	−0.392685
$855$	−1.75292e6	−0.0820063
$856$	4.54544e6	0.212027
$857$	−1.44182e7	−0.670593	−0.335296	−	0.942113i	$-0.608836\pi$
$857$	−1.44182e7	−0.670593	−0.335296	+	0.942113i	$0.608836\pi$
$858$	907190.	0.0420707
$859$	−3.53055e7	−1.63252	−0.816262	−	0.577681i	$-0.803958\pi$
$859$	−3.53055e7	−1.63252	−0.816262	+	0.577681i	$0.803958\pi$
$860$	−7.34486e6	−0.338639
$861$	6.16988e6	0.283641
$862$	−1.24148e6	−0.0569076
$863$	2.96014e6	0.135296	0.0676479	−	0.997709i	$-0.478451\pi$
$863$	2.96014e6	0.135296	0.0676479	+	0.997709i	$0.478451\pi$
$864$	3.00613e6	0.137001
$865$	−1.56864e7	−0.712823
$866$	3.80769e6	0.172531
$867$	−2.46020e7	−1.11153
$868$	3.94430e7	1.77693
$869$	−8.18735e6	−0.367785
$870$	2.71773e6	0.121733
$871$	1.22980e7	0.549275
$872$	−6.05703e6	−0.269754
$873$	−8.14739e6	−0.361812
$874$	−1.47031e6	−0.0651072
$875$	−3.36365e6	−0.148522
$876$	8.96361e6	0.394660
$877$	8.05269e6	0.353543	0.176771	−	0.984252i	$-0.443435\pi$
$877$	8.05269e6	0.353543	0.176771	+	0.984252i	$0.443435\pi$
$878$	−7.95694e6	−0.348345
$879$	5.03630e7	2.19857
$880$	2.80964e6	0.122305
$881$	2.18416e7	0.948078	0.474039	−	0.880504i	$-0.342796\pi$
$881$	2.18416e7	0.948078	0.474039	+	0.880504i	$0.342796\pi$
$882$	−5.74265e6	−0.248566
$883$	−1.95771e7	−0.844979	−0.422489	−	0.906368i	$-0.638844\pi$
$883$	−1.95771e7	−0.844979	−0.422489	+	0.906368i	$0.638844\pi$
$884$	−5.47656e6	−0.235710
$885$	1.16487e7	0.499941
$886$	2.58535e6	0.110646
$887$	3.68028e7	1.57062	0.785311	−	0.619101i	$-0.212503\pi$
$887$	3.68028e7	1.57062	0.785311	+	0.619101i	$0.212503\pi$
$888$	−285675.	−0.0121574
$889$	4.85948e7	2.06222
$890$	−1.02250e6	−0.0432700
$891$	8.29112e6	0.349880
$892$	−7.06791e6	−0.297426
$893$	−2.61013e6	−0.109530
$894$	−2.60508e6	−0.109013
$895$	−2.97007e6	−0.123939
$896$	2.60756e7	1.08509
$897$	3.04730e7	1.26455
$898$	4.06299e6	0.168134
$899$	−3.06979e7	−1.26681
$900$	−3.76294e6	−0.154854
$901$	3.36608e6	0.138138
$902$	166022.	0.00679436
$903$	−4.26635e7	−1.74115
$904$	1.21977e6	0.0496430
$905$	2.16155e7	0.877293
$906$	−6.97901e6	−0.282471
$907$	−9.84271e6	−0.397280	−0.198640	−	0.980073i	$-0.563652\pi$
$907$	−9.84271e6	−0.397280	−0.198640	+	0.980073i	$0.563652\pi$
$908$	−1.06127e6	−0.0427181
$909$	1.65498e7	0.664330
$910$	1.92970e6	0.0772477
$911$	−3.58221e7	−1.43006	−0.715031	−	0.699093i	$-0.753587\pi$
$911$	−3.58221e7	−1.43006	−0.715031	+	0.699093i	$0.753587\pi$
$912$	7.01111e6	0.279126
$913$	7.67500e6	0.304720
$914$	−1.49878e6	−0.0593435
$915$	−2.03022e7	−0.801661
$916$	−1.71471e7	−0.675230
$917$	−1.40043e7	−0.549967
$918$	503532.	0.0197206
$919$	−2.75882e7	−1.07754	−0.538772	−	0.842452i	$-0.681112\pi$
$919$	−2.75882e7	−1.07754	−0.538772	+	0.842452i	$0.681112\pi$
$920$	−6.41456e6	−0.249860
$921$	4.97442e7	1.93238
$922$	−6.51011e6	−0.252209
$923$	2.85776e6	0.110413
$924$	1.68836e7	0.650555
$925$	−135401.	−0.00520317
$926$	−8.13923e6	−0.311929
$927$	−1.12656e7	−0.430581
$928$	−1.53094e7	−0.583565
$929$	1.76452e7	0.670793	0.335396	−	0.942077i	$-0.391130\pi$
$929$	1.76452e7	0.670793	0.335396	+	0.942077i	$0.391130\pi$
$930$	−3.09307e6	−0.117269
$931$	1.06624e7	0.403164
$932$	−2.07216e7	−0.781418
$933$	2.31307e7	0.869932
$934$	−9.08196e6	−0.340653
$935$	1.49208e6	0.0558165
$936$	4.38732e6	0.163685
$937$	−3.39805e7	−1.26439	−0.632195	−	0.774810i	$-0.717846\pi$
$937$	−3.39805e7	−1.26439	−0.632195	+	0.774810i	$0.717846\pi$
$938$	−7.39887e6	−0.274573
$939$	−4.22164e7	−1.56249
$940$	−5.60310e6	−0.206828
$941$	−2.50852e6	−0.0923513	−0.0461757	−	0.998933i	$-0.514703\pi$
$941$	−2.50852e6	−0.0923513	−0.0461757	+	0.998933i	$0.514703\pi$
$942$	6.19419e6	0.227435
$943$	5.57677e6	0.204222
$944$	−2.06970e7	−0.755921
$945$	5.48837e6	0.199924
$946$	−1.14801e6	−0.0417078
$947$	−3.17240e7	−1.14951	−0.574754	−	0.818326i	$-0.694902\pi$
$947$	−3.17240e7	−1.14951	−0.574754	+	0.818326i	$0.694902\pi$
$948$	−4.38576e7	−1.58498
$949$	−4.95342e6	−0.178542
$950$	−225858.	−0.00811945
$951$	3.55119e7	1.27328
$952$	6.69626e6	0.239464
$953$	−4.35483e6	−0.155324	−0.0776621	−	0.996980i	$-0.524746\pi$
$953$	−4.35483e6	−0.155324	−0.0776621	+	0.996980i	$0.524746\pi$
$954$	−1.32685e6	−0.0472010
$955$	5.97132e6	0.211866
$956$	−1.13260e7	−0.400804
$957$	−1.31402e7	−0.463792
$958$	4.13013e6	0.145395
$959$	1.72558e7	0.605883
$960$	1.39945e7	0.490095
$961$	6.30832e6	0.220346
$962$	77678.5	0.00270622
$963$	1.39996e7	0.486463
$964$	3.74392e7	1.29758
$965$	−1.93092e7	−0.667491
$966$	−1.83335e7	−0.632126
$967$	−7.58823e6	−0.260960	−0.130480	−	0.991451i	$-0.541652\pi$
$967$	−7.58823e6	−0.260960	−0.130480	+	0.991451i	$0.541652\pi$
$968$	923306.	0.0316707
$969$	3.72330e6	0.127385
$970$	−1.04977e6	−0.0358231
$971$	−1.32091e7	−0.449599	−0.224800	−	0.974405i	$-0.572173\pi$
$971$	−1.32091e7	−0.449599	−0.224800	+	0.974405i	$0.572173\pi$
$972$	3.67319e7	1.24703
$973$	7.67726e7	2.59971
$974$	4.56415e6	0.154157
$975$	4.68106e6	0.157700
$976$	3.60723e7	1.21213
$977$	1.15389e7	0.386746	0.193373	−	0.981125i	$-0.438057\pi$
$977$	1.15389e7	0.386746	0.193373	+	0.981125i	$0.438057\pi$
$978$	2.29304e6	0.0766592
$979$	4.94377e6	0.164855
$980$	2.28887e7	0.761301
$981$	−1.86552e7	−0.618910
$982$	−1.76384e6	−0.0583688
$983$	2.68420e6	0.0885993	0.0442997	−	0.999018i	$-0.485894\pi$
$983$	2.68420e6	0.0885993	0.0442997	+	0.999018i	$0.485894\pi$
$984$	1.80743e6	0.0595076
$985$	−2.52000e7	−0.827579
$986$	−2.56435e6	−0.0840013
$987$	−3.25463e7	−1.06343
$988$	−4.00820e6	−0.130634
$989$	−3.85623e7	−1.25364
$990$	−588151.	−0.0190722
$991$	3.77126e7	1.21984	0.609919	−	0.792464i	$-0.291202\pi$
$991$	3.77126e7	1.21984	0.609919	+	0.792464i	$0.291202\pi$
$992$	1.74237e7	0.562163
$993$	7.77847e6	0.250335
$994$	−1.71932e6	−0.0551938
$995$	−1.08623e7	−0.347826
$996$	4.11131e7	1.31320
$997$	−3.55594e7	−1.13296	−0.566482	−	0.824074i	$-0.691696\pi$
$997$	−3.55594e7	−1.13296	−0.566482	+	0.824074i	$0.691696\pi$
$998$	−9.49666e6	−0.301818
$999$	220930.	0.00700392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.g.1.18	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.g.1.18	✓	39	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00103 q^{2} +20.9100 q^{3} -30.9979 q^{4} -25.0000 q^{5} -20.9316 q^{6} +215.274 q^{7} +63.0630 q^{8} +194.229 q^{9} +O(q^{10})\)	\(q-1.00103 q^{2} +20.9100 q^{3} -30.9979 q^{4} -25.0000 q^{5} -20.9316 q^{6} +215.274 q^{7} +63.0630 q^{8} +194.229 q^{9} +25.0258 q^{10} -121.000 q^{11} -648.168 q^{12} +358.187 q^{13} -215.496 q^{14} -522.751 q^{15} +928.806 q^{16} +493.249 q^{17} -194.430 q^{18} +361.000 q^{19} +774.948 q^{20} +4501.38 q^{21} +121.125 q^{22} +4068.66 q^{23} +1318.65 q^{24} +625.000 q^{25} -358.557 q^{26} -1019.79 q^{27} -6673.04 q^{28} +5193.54 q^{29} +523.291 q^{30} -5910.79 q^{31} -2947.78 q^{32} -2530.11 q^{33} -493.759 q^{34} -5381.85 q^{35} -6020.71 q^{36} -216.642 q^{37} -361.373 q^{38} +7489.69 q^{39} -1576.58 q^{40} +1370.66 q^{41} -4506.03 q^{42} -9477.87 q^{43} +3750.75 q^{44} -4855.74 q^{45} -4072.87 q^{46} -7230.29 q^{47} +19421.4 q^{48} +29535.8 q^{49} -625.646 q^{50} +10313.8 q^{51} -11103.0 q^{52} +6824.30 q^{53} +1020.85 q^{54} +3025.00 q^{55} +13575.8 q^{56} +7548.52 q^{57} -5198.91 q^{58} -22283.4 q^{59} +16204.2 q^{60} +38837.3 q^{61} +5916.90 q^{62} +41812.5 q^{63} -26770.9 q^{64} -8954.66 q^{65} +2532.73 q^{66} +34334.1 q^{67} -15289.7 q^{68} +85075.8 q^{69} +5387.41 q^{70} +7978.42 q^{71} +12248.7 q^{72} -13829.1 q^{73} +216.866 q^{74} +13068.8 q^{75} -11190.3 q^{76} -26048.1 q^{77} -7497.43 q^{78} +67664.0 q^{79} -23220.1 q^{80} -68521.7 q^{81} -1372.08 q^{82} -63429.8 q^{83} -139534. q^{84} -12331.2 q^{85} +9487.67 q^{86} +108597. q^{87} -7630.63 q^{88} -40857.6 q^{89} +4860.76 q^{90} +77108.2 q^{91} -126120. q^{92} -123595. q^{93} +7237.76 q^{94} -9025.00 q^{95} -61638.2 q^{96} -41947.3 q^{97} -29566.3 q^{98} -23501.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * q^99

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