LMFDB - Embedded newform 1045.6.a.h.1.5

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:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-8.55086 q^{2} +12.0717 q^{3} +41.1172 q^{4} +25.0000 q^{5} -103.224 q^{6} -150.646 q^{7} -77.9596 q^{8} -97.2734 q^{9} +O(q^{10})$	\(q-8.55086 q^{2} +12.0717 q^{3} +41.1172 q^{4} +25.0000 q^{5} -103.224 q^{6} -150.646 q^{7} -77.9596 q^{8} -97.2734 q^{9} -213.771 q^{10} +121.000 q^{11} +496.355 q^{12} -71.2149 q^{13} +1288.16 q^{14} +301.793 q^{15} -649.128 q^{16} +933.503 q^{17} +831.771 q^{18} +361.000 q^{19} +1027.93 q^{20} -1818.56 q^{21} -1034.65 q^{22} +2306.65 q^{23} -941.107 q^{24} +625.000 q^{25} +608.949 q^{26} -4107.69 q^{27} -6194.15 q^{28} +4095.48 q^{29} -2580.59 q^{30} +5443.15 q^{31} +8045.31 q^{32} +1460.68 q^{33} -7982.25 q^{34} -3766.16 q^{35} -3999.61 q^{36} +6724.50 q^{37} -3086.86 q^{38} -859.687 q^{39} -1948.99 q^{40} -11440.7 q^{41} +15550.3 q^{42} -13666.9 q^{43} +4975.18 q^{44} -2431.84 q^{45} -19723.9 q^{46} -20736.8 q^{47} -7836.09 q^{48} +5887.33 q^{49} -5344.29 q^{50} +11269.0 q^{51} -2928.16 q^{52} -19250.0 q^{53} +35124.3 q^{54} +3025.00 q^{55} +11744.3 q^{56} +4357.89 q^{57} -35019.8 q^{58} -46610.1 q^{59} +12408.9 q^{60} +16865.0 q^{61} -46543.6 q^{62} +14653.9 q^{63} -48022.2 q^{64} -1780.37 q^{65} -12490.1 q^{66} +45274.0 q^{67} +38383.0 q^{68} +27845.3 q^{69} +32203.9 q^{70} -16399.4 q^{71} +7583.40 q^{72} +9142.48 q^{73} -57500.3 q^{74} +7544.83 q^{75} +14843.3 q^{76} -18228.2 q^{77} +7351.06 q^{78} +92375.7 q^{79} -16228.2 q^{80} -25949.4 q^{81} +97827.9 q^{82} -16302.2 q^{83} -74774.1 q^{84} +23337.6 q^{85} +116863. q^{86} +49439.5 q^{87} -9433.11 q^{88} +56296.0 q^{89} +20794.3 q^{90} +10728.3 q^{91} +94843.0 q^{92} +65708.2 q^{93} +177318. q^{94} +9025.00 q^{95} +97120.7 q^{96} -90929.3 q^{97} -50341.7 q^{98} -11770.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) $ 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * 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 $

$2$	−8.55086	−1.51159	−0.755796	−	0.654807i	$-0.772750\pi$
$2$	−8.55086	−1.51159	−0.755796	+	0.654807i	$0.772750\pi$
$3$	12.0717	0.774402	0.387201	−	0.921995i	$-0.373442\pi$
$3$	12.0717	0.774402	0.387201	+	0.921995i	$0.373442\pi$
$4$	41.1172	1.28491
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−103.224	−1.17058
$7$	−150.646	−1.16202	−0.581010	−	0.813896i	$-0.697342\pi$
$7$	−150.646	−1.16202	−0.581010	+	0.813896i	$0.697342\pi$
$8$	−77.9596	−0.430670
$9$	−97.2734	−0.400302
$10$	−213.771	−0.676005
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	496.355	0.995037
$13$	−71.2149	−0.116873	−0.0584363	−	0.998291i	$-0.518611\pi$
$13$	−71.2149	−0.116873	−0.0584363	+	0.998291i	$0.518611\pi$
$14$	1288.16	1.75650
$15$	301.793	0.346323
$16$	−649.128	−0.633914
$17$	933.503	0.783417	0.391709	−	0.920089i	$-0.371884\pi$
$17$	933.503	0.783417	0.391709	+	0.920089i	$0.371884\pi$
$18$	831.771	0.605094
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	1027.93	0.574630
$21$	−1818.56	−0.899870
$22$	−1034.65	−0.455762
$23$	2306.65	0.909207	0.454603	−	0.890694i	$-0.349781\pi$
$23$	2306.65	0.909207	0.454603	+	0.890694i	$0.349781\pi$
$24$	−941.107	−0.333512
$25$	625.000	0.200000
$26$	608.949	0.176664
$27$	−4107.69	−1.08440
$28$	−6194.15	−1.49309
$29$	4095.48	0.904293	0.452147	−	0.891944i	$-0.350658\pi$
$29$	4095.48	0.904293	0.452147	+	0.891944i	$0.350658\pi$
$30$	−2580.59	−0.523499
$31$	5443.15	1.01729	0.508647	−	0.860975i	$-0.330146\pi$
$31$	5443.15	1.01729	0.508647	+	0.860975i	$0.330146\pi$
$32$	8045.31	1.38889
$33$	1460.68	0.233491
$34$	−7982.25	−1.18421
$35$	−3766.16	−0.519671
$36$	−3999.61	−0.514353
$37$	6724.50	0.807525	0.403762	−	0.914864i	$-0.367702\pi$
$37$	6724.50	0.807525	0.403762	+	0.914864i	$0.367702\pi$
$38$	−3086.86	−0.346783
$39$	−859.687	−0.0905063
$40$	−1948.99	−0.192602
$41$	−11440.7	−1.06290	−0.531451	−	0.847089i	$-0.678353\pi$
$41$	−11440.7	−1.06290	−0.531451	+	0.847089i	$0.678353\pi$
$42$	15550.3	1.36024
$43$	−13666.9	−1.12719	−0.563596	−	0.826050i	$-0.690583\pi$
$43$	−13666.9	−1.12719	−0.563596	+	0.826050i	$0.690583\pi$
$44$	4975.18	0.387415
$45$	−2431.84	−0.179021
$46$	−19723.9	−1.37435
$47$	−20736.8	−1.36930	−0.684648	−	0.728874i	$-0.740044\pi$
$47$	−20736.8	−1.36930	−0.684648	+	0.728874i	$0.740044\pi$
$48$	−7836.09	−0.490904
$49$	5887.33	0.350290
$50$	−5344.29	−0.302318
$51$	11269.0	0.606680
$52$	−2928.16	−0.150171
$53$	−19250.0	−0.941329	−0.470665	−	0.882312i	$-0.655986\pi$
$53$	−19250.0	−0.941329	−0.470665	+	0.882312i	$0.655986\pi$
$54$	35124.3	1.63917
$55$	3025.00	0.134840
$56$	11744.3	0.500447
$57$	4357.89	0.177660
$58$	−35019.8	−1.36692
$59$	−46610.1	−1.74321	−0.871605	−	0.490208i	$-0.836921\pi$
$59$	−46610.1	−1.74321	−0.871605	+	0.490208i	$0.836921\pi$
$60$	12408.9	0.444994
$61$	16865.0	0.580311	0.290155	−	0.956980i	$-0.406293\pi$
$61$	16865.0	0.580311	0.290155	+	0.956980i	$0.406293\pi$
$62$	−46543.6	−1.53773
$63$	14653.9	0.465159
$64$	−48022.2	−1.46552
$65$	−1780.37	−0.0522670
$66$	−12490.1	−0.352943
$67$	45274.0	1.23214	0.616072	−	0.787689i	$-0.288723\pi$
$67$	45274.0	1.23214	0.616072	+	0.787689i	$0.288723\pi$
$68$	38383.0	1.00662
$69$	27845.3	0.704091
$70$	32203.9	0.785531
$71$	−16399.4	−0.386083	−0.193042	−	0.981191i	$-0.561835\pi$
$71$	−16399.4	−0.386083	−0.193042	+	0.981191i	$0.561835\pi$
$72$	7583.40	0.172398
$73$	9142.48	0.200797	0.100398	−	0.994947i	$-0.467988\pi$
$73$	9142.48	0.200797	0.100398	+	0.994947i	$0.467988\pi$
$74$	−57500.3	−1.22065
$75$	7544.83	0.154880
$76$	14843.3	0.294779
$77$	−18228.2	−0.350362
$78$	7351.06	0.136809
$79$	92375.7	1.66529	0.832645	−	0.553807i	$-0.186825\pi$
$79$	92375.7	1.66529	0.832645	+	0.553807i	$0.186825\pi$
$80$	−16228.2	−0.283495
$81$	−25949.4	−0.439456
$82$	97827.9	1.60668
$83$	−16302.2	−0.259747	−0.129873	−	0.991531i	$-0.541457\pi$
$83$	−16302.2	−0.259747	−0.129873	+	0.991531i	$0.541457\pi$
$84$	−74774.1	−1.15625
$85$	23337.6	0.350355
$86$	116863.	1.70386
$87$	49439.5	0.700286
$88$	−9433.11	−0.129852
$89$	56296.0	0.753360	0.376680	−	0.926343i	$-0.377066\pi$
$89$	56296.0	0.753360	0.376680	+	0.926343i	$0.377066\pi$
$90$	20794.3	0.270606
$91$	10728.3	0.135808
$92$	94843.0	1.16825
$93$	65708.2	0.787794
$94$	177318.	2.06982
$95$	9025.00	0.102598
$96$	97120.7	1.07556
$97$	−90929.3	−0.981238	−0.490619	−	0.871374i	$-0.663229\pi$
$97$	−90929.3	−0.981238	−0.490619	+	0.871374i	$0.663229\pi$
$98$	−50341.7	−0.529496
$99$	−11770.1	−0.120696
$100$	25698.2	0.256982
$101$	8381.37	0.0817544	0.0408772	−	0.999164i	$-0.486985\pi$
$101$	8381.37	0.0817544	0.0408772	+	0.999164i	$0.486985\pi$
$102$	−96359.5	−0.917052
$103$	56329.3	0.523168	0.261584	−	0.965181i	$-0.415755\pi$
$103$	56329.3	0.523168	0.261584	+	0.965181i	$0.415755\pi$
$104$	5551.89	0.0503335
$105$	−45464.0	−0.402434
$106$	164604.	1.42291
$107$	77738.1	0.656409	0.328204	−	0.944607i	$-0.393557\pi$
$107$	77738.1	0.656409	0.328204	+	0.944607i	$0.393557\pi$
$108$	−168896.	−1.39335
$109$	−147584.	−1.18979	−0.594897	−	0.803802i	$-0.702807\pi$
$109$	−147584.	−1.18979	−0.594897	+	0.803802i	$0.702807\pi$
$110$	−25866.3	−0.203823
$111$	81176.4	0.625348
$112$	97788.7	0.736621
$113$	−104975.	−0.773371	−0.386686	−	0.922212i	$-0.626380\pi$
$113$	−104975.	−0.773371	−0.386686	+	0.922212i	$0.626380\pi$
$114$	−37263.7	−0.268549
$115$	57666.3	0.406610
$116$	168394.	1.16194
$117$	6927.32	0.0467843
$118$	398556.	2.63502
$119$	−140629.	−0.910347
$120$	−23527.7	−0.149151
$121$	14641.0	0.0909091
$122$	−144210.	−0.877194
$123$	−138109.	−0.823113
$124$	223807.	1.30713
$125$	15625.0	0.0894427
$126$	−125303.	−0.703131
$127$	209746.	1.15395	0.576973	−	0.816764i	$-0.304234\pi$
$127$	209746.	1.15395	0.576973	+	0.816764i	$0.304234\pi$
$128$	153181.	0.826381
$129$	−164983.	−0.872899
$130$	15223.7	0.0790064
$131$	−237616.	−1.20976	−0.604878	−	0.796319i	$-0.706778\pi$
$131$	−237616.	−1.20976	−0.604878	+	0.796319i	$0.706778\pi$
$132$	60059.0	0.300015
$133$	−54383.3	−0.266586
$134$	−387131.	−1.86250
$135$	−102692.	−0.484957
$136$	−72775.5	−0.337394
$137$	201445.	0.916971	0.458486	−	0.888702i	$-0.348392\pi$
$137$	201445.	0.916971	0.458486	+	0.888702i	$0.348392\pi$
$138$	−238101.	−1.06430
$139$	−8850.88	−0.0388552	−0.0194276	−	0.999811i	$-0.506184\pi$
$139$	−8850.88	−0.0388552	−0.0194276	+	0.999811i	$0.506184\pi$
$140$	−154854.	−0.667731
$141$	−250329.	−1.06039
$142$	140229.	0.583600
$143$	−8617.00	−0.0352384
$144$	63142.9	0.253757
$145$	102387.	0.404412
$146$	−78176.1	−0.303523
$147$	71070.2	0.271265
$148$	276493.	1.03760
$149$	401386.	1.48114	0.740571	−	0.671978i	$-0.234555\pi$
$149$	401386.	1.48114	0.740571	+	0.671978i	$0.234555\pi$
$150$	−64514.8	−0.234116
$151$	199291.	0.711289	0.355644	−	0.934621i	$-0.384261\pi$
$151$	199291.	0.711289	0.355644	+	0.934621i	$0.384261\pi$
$152$	−28143.4	−0.0988025
$153$	−90805.0	−0.313604
$154$	155867.	0.529605
$155$	136079.	0.454948
$156$	−35347.9	−0.116293
$157$	59385.0	0.192277	0.0961385	−	0.995368i	$-0.469351\pi$
$157$	59385.0	0.192277	0.0961385	+	0.995368i	$0.469351\pi$
$158$	−789891.	−2.51724
$159$	−232381.	−0.728967
$160$	201133.	0.621130
$161$	−347489.	−1.05652
$162$	221890.	0.664278
$163$	−291881.	−0.860473	−0.430237	−	0.902716i	$-0.641570\pi$
$163$	−291881.	−0.860473	−0.430237	+	0.902716i	$0.641570\pi$
$164$	−470410.	−1.36574
$165$	36517.0	0.104420
$166$	139398.	0.392631
$167$	472833.	1.31195	0.655974	−	0.754783i	$-0.272258\pi$
$167$	472833.	1.31195	0.655974	+	0.754783i	$0.272258\pi$
$168$	141774.	0.387547
$169$	−366221.	−0.986341
$170$	−199556.	−0.529594
$171$	−35115.7	−0.0918356
$172$	−561943.	−1.44834
$173$	−428214.	−1.08779	−0.543896	−	0.839153i	$-0.683051\pi$
$173$	−428214.	−1.08779	−0.543896	+	0.839153i	$0.683051\pi$
$174$	−422750.	−1.05855
$175$	−94154.0	−0.232404
$176$	−78544.5	−0.191132
$177$	−562664.	−1.34995
$178$	−481379.	−1.13877
$179$	272677.	0.636085	0.318043	−	0.948076i	$-0.396974\pi$
$179$	272677.	0.636085	0.318043	+	0.948076i	$0.396974\pi$
$180$	−99990.2	−0.230026
$181$	−116814.	−0.265033	−0.132516	−	0.991181i	$-0.542306\pi$
$181$	−116814.	−0.265033	−0.132516	+	0.991181i	$0.542306\pi$
$182$	−91735.9	−0.205287
$183$	203589.	0.449394
$184$	−179826.	−0.391568
$185$	168113.	0.361136
$186$	−561862.	−1.19082
$187$	112954.	0.236209
$188$	−852639.	−1.75942
$189$	618808.	1.26009
$190$	−77171.5	−0.155086
$191$	−184952.	−0.366840	−0.183420	−	0.983035i	$-0.558717\pi$
$191$	−184952.	−0.366840	−0.183420	+	0.983035i	$0.558717\pi$
$192$	−579711.	−1.13490
$193$	55195.5	0.106662	0.0533311	−	0.998577i	$-0.483016\pi$
$193$	55195.5	0.106662	0.0533311	+	0.998577i	$0.483016\pi$
$194$	777524.	1.48323
$195$	−21492.2	−0.0404756
$196$	242070.	0.450092
$197$	1.02034e6	1.87319	0.936593	−	0.350418i	$-0.113960\pi$
$197$	1.02034e6	1.87319	0.936593	+	0.350418i	$0.113960\pi$
$198$	100644.	0.182443
$199$	−551326.	−0.986906	−0.493453	−	0.869772i	$-0.664266\pi$
$199$	−551326.	−0.986906	−0.493453	+	0.869772i	$0.664266\pi$
$200$	−48724.8	−0.0861340
$201$	546535.	0.954175
$202$	−71667.9	−0.123579
$203$	−616968.	−1.05081
$204$	463349.	0.779530
$205$	−286018.	−0.475344
$206$	−481664.	−0.790817
$207$	−224376.	−0.363957
$208$	46227.6	0.0740871
$209$	43681.0	0.0691714
$210$	388757.	0.608316
$211$	275587.	0.426141	0.213071	−	0.977037i	$-0.431654\pi$
$211$	275587.	0.426141	0.213071	+	0.977037i	$0.431654\pi$
$212$	−791506.	−1.20952
$213$	−197968.	−0.298983
$214$	−664727.	−0.992222
$215$	−341672.	−0.504096
$216$	320234.	0.467017
$217$	−819991.	−1.18212
$218$	1.26197e6	1.79848
$219$	110366.	0.155497
$220$	124379.	0.173257
$221$	−66479.3	−0.0915600
$222$	−694127.	−0.945272
$223$	819552.	1.10361	0.551804	−	0.833974i	$-0.313940\pi$
$223$	819552.	1.10361	0.551804	+	0.833974i	$0.313940\pi$
$224$	−1.21200e6	−1.61392
$225$	−60795.9	−0.0800604
$226$	897623.	1.16902
$227$	−630266.	−0.811819	−0.405909	−	0.913913i	$-0.633045\pi$
$227$	−630266.	−0.811819	−0.405909	+	0.913913i	$0.633045\pi$
$228$	179184.	0.228277
$229$	−247601.	−0.312006	−0.156003	−	0.987757i	$-0.549861\pi$
$229$	−247601.	−0.312006	−0.156003	+	0.987757i	$0.549861\pi$
$230$	−493096.	−0.614628
$231$	−220046.	−0.271321
$232$	−319282.	−0.389452
$233$	1.10045e6	1.32795	0.663976	−	0.747754i	$-0.268868\pi$
$233$	1.10045e6	1.32795	0.663976	+	0.747754i	$0.268868\pi$
$234$	−59234.5	−0.0707189
$235$	−518420.	−0.612368
$236$	−1.91647e6	−2.23987
$237$	1.11513e6	1.28960
$238$	1.20250e6	1.37607
$239$	110119.	0.124700	0.0623502	−	0.998054i	$-0.480140\pi$
$239$	110119.	0.124700	0.0623502	+	0.998054i	$0.480140\pi$
$240$	−195902.	−0.219539
$241$	−1.09463e6	−1.21402	−0.607008	−	0.794696i	$-0.707630\pi$
$241$	−1.09463e6	−1.21402	−0.607008	+	0.794696i	$0.707630\pi$
$242$	−125193.	−0.137417
$243$	684914.	0.744081
$244$	693439.	0.745648
$245$	147183.	0.156654
$246$	1.18095e6	1.24421
$247$	−25708.6	−0.0268124
$248$	−424346.	−0.438118
$249$	−196795.	−0.201148
$250$	−133607.	−0.135201
$251$	389038.	0.389769	0.194885	−	0.980826i	$-0.437567\pi$
$251$	389038.	0.389769	0.194885	+	0.980826i	$0.437567\pi$
$252$	602526.	0.597688
$253$	279105.	0.274136
$254$	−1.79351e6	−1.74429
$255$	281725.	0.271315
$256$	226881.	0.216370
$257$	983830.	0.929153	0.464576	−	0.885533i	$-0.346207\pi$
$257$	983830.	0.929153	0.464576	+	0.885533i	$0.346207\pi$
$258$	1.41074e6	1.31947
$259$	−1.01302e6	−0.938360
$260$	−73203.9	−0.0671585
$261$	−398381.	−0.361991
$262$	2.03182e6	1.82866
$263$	−1.04245e6	−0.929321	−0.464660	−	0.885489i	$-0.653824\pi$
$263$	−1.04245e6	−0.929321	−0.464660	+	0.885489i	$0.653824\pi$
$264$	−113874.	−0.100558
$265$	−481251.	−0.420975
$266$	465024.	0.402969
$267$	679590.	0.583403
$268$	1.86154e6	1.58320
$269$	680363.	0.573271	0.286635	−	0.958040i	$-0.407463\pi$
$269$	680363.	0.573271	0.286635	+	0.958040i	$0.407463\pi$
$270$	878106.	0.733057
$271$	736325.	0.609041	0.304520	−	0.952506i	$-0.401504\pi$
$271$	736325.	0.609041	0.304520	+	0.952506i	$0.401504\pi$
$272$	−605963.	−0.496619
$273$	129509.	0.105170
$274$	−1.72253e6	−1.38609
$275$	75625.0	0.0603023
$276$	1.14492e6	0.904695
$277$	−836059.	−0.654693	−0.327347	−	0.944904i	$-0.606154\pi$
$277$	−836059.	−0.654693	−0.327347	+	0.944904i	$0.606154\pi$
$278$	75682.6	0.0587332
$279$	−529474.	−0.407225
$280$	293608.	0.223807
$281$	1.28526e6	0.971015	0.485508	−	0.874232i	$-0.338635\pi$
$281$	1.28526e6	0.971015	0.485508	+	0.874232i	$0.338635\pi$
$282$	2.14053e6	1.60287
$283$	706022.	0.524025	0.262013	−	0.965064i	$-0.415614\pi$
$283$	706022.	0.524025	0.262013	+	0.965064i	$0.415614\pi$
$284$	−674295.	−0.496083
$285$	108947.	0.0794519
$286$	73682.8	0.0532661
$287$	1.72350e6	1.23511
$288$	−782595.	−0.555976
$289$	−548430.	−0.386257
$290$	−875496.	−0.611307
$291$	−1.09767e6	−0.759873
$292$	375913.	0.258006
$293$	1.50033e6	1.02098	0.510491	−	0.859883i	$-0.329464\pi$
$293$	1.50033e6	1.02098	0.510491	+	0.859883i	$0.329464\pi$
$294$	−607711.	−0.410042
$295$	−1.16525e6	−0.779588
$296$	−524240.	−0.347777
$297$	−497030.	−0.326958
$298$	−3.43220e6	−2.23888
$299$	−164268.	−0.106261
$300$	310222.	0.199007
$301$	2.05886e6	1.30982
$302$	−1.70411e6	−1.07518
$303$	101178.	0.0633108
$304$	−234335.	−0.145430
$305$	421624.	0.259523
$306$	776461.	0.474041
$307$	1.18027e6	0.714720	0.357360	−	0.933967i	$-0.383677\pi$
$307$	1.18027e6	0.714720	0.357360	+	0.933967i	$0.383677\pi$
$308$	−749492.	−0.450184
$309$	679992.	0.405142
$310$	−1.16359e6	−0.687695
$311$	693645.	0.406664	0.203332	−	0.979110i	$-0.434823\pi$
$311$	693645.	0.406664	0.203332	+	0.979110i	$0.434823\pi$
$312$	67020.9	0.0389784
$313$	−292301.	−0.168643	−0.0843217	−	0.996439i	$-0.526872\pi$
$313$	−292301.	−0.168643	−0.0843217	+	0.996439i	$0.526872\pi$
$314$	−507792.	−0.290644
$315$	366347.	0.208025
$316$	3.79823e6	2.13975
$317$	2.66490e6	1.48948	0.744738	−	0.667357i	$-0.232574\pi$
$317$	2.66490e6	1.48948	0.744738	+	0.667357i	$0.232574\pi$
$318$	1.98706e6	1.10190
$319$	495553.	0.272655
$320$	−1.20055e6	−0.655401
$321$	938433.	0.508324
$322$	2.97133e6	1.59702
$323$	336994.	0.179728
$324$	−1.06697e6	−0.564662
$325$	−44509.3	−0.0233745
$326$	2.49584e6	1.30068
$327$	−1.78159e6	−0.921379
$328$	891913.	0.457760
$329$	3.12393e6	1.59115
$330$	−312251.	−0.157841
$331$	2.49691e6	1.25266	0.626331	−	0.779557i	$-0.284556\pi$
$331$	2.49691e6	1.25266	0.626331	+	0.779557i	$0.284556\pi$
$332$	−670299.	−0.333752
$333$	−654116.	−0.323254
$334$	−4.04313e6	−1.98313
$335$	1.13185e6	0.551032
$336$	1.18048e6	0.570440
$337$	419810.	0.201362	0.100681	−	0.994919i	$-0.467898\pi$
$337$	419810.	0.201362	0.100681	+	0.994919i	$0.467898\pi$
$338$	3.13151e6	1.49095
$339$	−1.26722e6	−0.598900
$340$	959575.	0.450175
$341$	658622.	0.306726
$342$	300269.	0.138818
$343$	1.64501e6	0.754976
$344$	1.06546e6	0.485448
$345$	696132.	0.314879
$346$	3.66160e6	1.64430
$347$	961596.	0.428715	0.214358	−	0.976755i	$-0.431234\pi$
$347$	961596.	0.428715	0.214358	+	0.976755i	$0.431234\pi$
$348$	2.03281e6	0.899806
$349$	94162.7	0.0413824	0.0206912	−	0.999786i	$-0.493413\pi$
$349$	94162.7	0.0413824	0.0206912	+	0.999786i	$0.493413\pi$
$350$	805097.	0.351300
$351$	292529.	0.126736
$352$	973482.	0.418766
$353$	−767720.	−0.327918	−0.163959	−	0.986467i	$-0.552427\pi$
$353$	−767720.	−0.327918	−0.163959	+	0.986467i	$0.552427\pi$
$354$	4.81126e6	2.04057
$355$	−409984.	−0.172662
$356$	2.31473e6	0.968001
$357$	−1.69763e6	−0.704974
$358$	−2.33162e6	−0.961502
$359$	1.78125e6	0.729439	0.364719	−	0.931118i	$-0.381165\pi$
$359$	1.78125e6	0.729439	0.364719	+	0.931118i	$0.381165\pi$
$360$	189585.	0.0770988
$361$	130321.	0.0526316
$362$	998863.	0.400622
$363$	176742.	0.0704001
$364$	441116.	0.174502
$365$	228562.	0.0897991
$366$	−1.74086e6	−0.679300
$367$	3.54586e6	1.37422	0.687111	−	0.726553i	$-0.258879\pi$
$367$	3.54586e6	1.37422	0.687111	+	0.726553i	$0.258879\pi$
$368$	−1.49731e6	−0.576359
$369$	1.11288e6	0.425482
$370$	−1.43751e6	−0.545891
$371$	2.89995e6	1.09384
$372$	2.70174e6	1.01225
$373$	1.45653e6	0.542061	0.271030	−	0.962571i	$-0.412636\pi$
$373$	1.45653e6	0.542061	0.271030	+	0.962571i	$0.412636\pi$
$374$	−965852.	−0.357052
$375$	188621.	0.0692646
$376$	1.61663e6	0.589715
$377$	−291659.	−0.105687
$378$	−5.29134e6	−1.90474
$379$	134543.	0.0481132	0.0240566	−	0.999711i	$-0.492342\pi$
$379$	134543.	0.0481132	0.0240566	+	0.999711i	$0.492342\pi$
$380$	371082.	0.131829
$381$	2.53200e6	0.893617
$382$	1.58150e6	0.554512
$383$	−1.48481e6	−0.517217	−0.258608	−	0.965982i	$-0.583264\pi$
$383$	−1.48481e6	−0.517217	−0.258608	+	0.965982i	$0.583264\pi$
$384$	1.84916e6	0.639950
$385$	−455705.	−0.156687
$386$	−471969.	−0.161230
$387$	1.32942e6	0.451218
$388$	−3.73876e6	−1.26080
$389$	−2.64085e6	−0.884851	−0.442425	−	0.896805i	$-0.645882\pi$
$389$	−2.64085e6	−0.884851	−0.442425	+	0.896805i	$0.645882\pi$
$390$	183777.	0.0611827
$391$	2.15327e6	0.712288
$392$	−458974.	−0.150859
$393$	−2.86844e6	−0.936836
$394$	−8.72482e6	−2.83149
$395$	2.30939e6	0.744741
$396$	−483953.	−0.155083
$397$	−704306.	−0.224277	−0.112139	−	0.993693i	$-0.535770\pi$
$397$	−704306.	−0.224277	−0.112139	+	0.993693i	$0.535770\pi$
$398$	4.71431e6	1.49180
$399$	−656501.	−0.206444
$400$	−405705.	−0.126783
$401$	1.61703e6	0.502179	0.251089	−	0.967964i	$-0.419211\pi$
$401$	1.61703e6	0.502179	0.251089	+	0.967964i	$0.419211\pi$
$402$	−4.67334e6	−1.44232
$403$	−387634.	−0.118894
$404$	344618.	0.105047
$405$	−648736.	−0.196531
$406$	5.27561e6	1.58839
$407$	813665.	0.243478
$408$	−878526.	−0.261279
$409$	3.28128e6	0.969919	0.484959	−	0.874537i	$-0.338834\pi$
$409$	3.28128e6	0.969919	0.484959	+	0.874537i	$0.338834\pi$
$410$	2.44570e6	0.718527
$411$	2.43179e6	0.710104
$412$	2.31610e6	0.672225
$413$	7.02164e6	2.02565
$414$	1.91861e6	0.550155
$415$	−407554.	−0.116162
$416$	−572946.	−0.162323
$417$	−106845.	−0.0300895
$418$	−373510.	−0.104559
$419$	−128186.	−0.0356701	−0.0178351	−	0.999841i	$-0.505677\pi$
$419$	−128186.	−0.0356701	−0.0178351	+	0.999841i	$0.505677\pi$
$420$	−1.86935e6	−0.517092
$421$	2.48599e6	0.683587	0.341794	−	0.939775i	$-0.388966\pi$
$421$	2.48599e6	0.683587	0.341794	+	0.939775i	$0.388966\pi$
$422$	−2.35651e6	−0.644152
$423$	2.01714e6	0.548132
$424$	1.50072e6	0.405402
$425$	583439.	0.156683
$426$	1.69280e6	0.451941
$427$	−2.54065e6	−0.674333
$428$	3.19637e6	0.843427
$429$	−104022.	−0.0272887
$430$	2.92159e6	0.761987
$431$	172232.	0.0446603	0.0223301	−	0.999751i	$-0.492892\pi$
$431$	172232.	0.0446603	0.0223301	+	0.999751i	$0.492892\pi$
$432$	2.66641e6	0.687414
$433$	1.96024e6	0.502446	0.251223	−	0.967929i	$-0.419167\pi$
$433$	1.96024e6	0.502446	0.251223	+	0.967929i	$0.419167\pi$
$434$	7.01163e6	1.78688
$435$	1.23599e6	0.313177
$436$	−6.06822e6	−1.52878
$437$	832702.	0.208586
$438$	−943720.	−0.235049
$439$	1.99952e6	0.495180	0.247590	−	0.968865i	$-0.420361\pi$
$439$	1.99952e6	0.495180	0.247590	+	0.968865i	$0.420361\pi$
$440$	−235828.	−0.0580715
$441$	−572680.	−0.140222
$442$	568455.	0.138401
$443$	−3.10911e6	−0.752708	−0.376354	−	0.926476i	$-0.622822\pi$
$443$	−3.10911e6	−0.752708	−0.376354	+	0.926476i	$0.622822\pi$
$444$	3.33774e6	0.803517
$445$	1.40740e6	0.336913
$446$	−7.00788e6	−1.66820
$447$	4.84542e6	1.14700
$448$	7.23437e6	1.70296
$449$	−8.32331e6	−1.94841	−0.974205	−	0.225666i	$-0.927544\pi$
$449$	−8.32331e6	−1.94841	−0.974205	+	0.225666i	$0.927544\pi$
$450$	519857.	0.121019
$451$	−1.38433e6	−0.320477
$452$	−4.31626e6	−0.993713
$453$	2.40579e6	0.550823
$454$	5.38931e6	1.22714
$455$	268207.	0.0607353
$456$	−339740.	−0.0765128
$457$	5.83535e6	1.30700	0.653501	−	0.756926i	$-0.273300\pi$
$457$	5.83535e6	1.30700	0.653501	+	0.756926i	$0.273300\pi$
$458$	2.11720e6	0.471626
$459$	−3.83454e6	−0.849535
$460$	2.37108e6	0.522457
$461$	4.38829e6	0.961709	0.480854	−	0.876801i	$-0.340327\pi$
$461$	4.38829e6	0.961709	0.480854	+	0.876801i	$0.340327\pi$
$462$	1.88158e6	0.410127
$463$	−8.33830e6	−1.80769	−0.903847	−	0.427855i	$-0.859269\pi$
$463$	−8.33830e6	−1.80769	−0.903847	+	0.427855i	$0.859269\pi$
$464$	−2.65849e6	−0.573244
$465$	1.64271e6	0.352312
$466$	−9.40983e6	−2.00732
$467$	1.15648e6	0.245384	0.122692	−	0.992445i	$-0.460847\pi$
$467$	1.15648e6	0.245384	0.122692	+	0.992445i	$0.460847\pi$
$468$	284832.	0.0601137
$469$	−6.82036e6	−1.43178
$470$	4.43294e6	0.925651
$471$	716879.	0.148900
$472$	3.63370e6	0.750749
$473$	−1.65369e6	−0.339861
$474$	−9.53535e6	−1.94935
$475$	225625.	0.0458831
$476$	−5.78226e6	−1.16971
$477$	1.87252e6	0.376816
$478$	−941612.	−0.188496
$479$	1.28731e6	0.256356	0.128178	−	0.991751i	$-0.459087\pi$
$479$	1.28731e6	0.256356	0.128178	+	0.991751i	$0.459087\pi$
$480$	2.42802e6	0.481004
$481$	−478885.	−0.0943775
$482$	9.36001e6	1.83510
$483$	−4.19479e6	−0.818168
$484$	601996.	0.116810
$485$	−2.27323e6	−0.438823
$486$	−5.85660e6	−1.12475
$487$	7.64647e6	1.46096	0.730480	−	0.682934i	$-0.239296\pi$
$487$	7.64647e6	1.46096	0.730480	+	0.682934i	$0.239296\pi$
$488$	−1.31479e6	−0.249923
$489$	−3.52351e6	−0.666352
$490$	−1.25854e6	−0.236798
$491$	5.66387e6	1.06025	0.530127	−	0.847918i	$-0.322144\pi$
$491$	5.66387e6	1.06025	0.530127	+	0.847918i	$0.322144\pi$
$492$	−5.67866e6	−1.05763
$493$	3.82314e6	0.708439
$494$	219830.	0.0405294
$495$	−294252.	−0.0539767
$496$	−3.53330e6	−0.644877
$497$	2.47050e6	0.448636
$498$	1.68277e6	0.304054
$499$	−3.51678e6	−0.632257	−0.316129	−	0.948716i	$-0.602383\pi$
$499$	−3.51678e6	−0.632257	−0.316129	+	0.948716i	$0.602383\pi$
$500$	642456.	0.114926
$501$	5.70791e6	1.01597
$502$	−3.32661e6	−0.589172
$503$	−9.49940e6	−1.67408	−0.837040	−	0.547141i	$-0.815716\pi$
$503$	−9.49940e6	−1.67408	−0.837040	+	0.547141i	$0.815716\pi$
$504$	−1.14241e6	−0.200330
$505$	209534.	0.0365617
$506$	−2.38659e6	−0.414382
$507$	−4.42092e6	−0.763824
$508$	8.62418e6	1.48272
$509$	−3.27119e6	−0.559643	−0.279822	−	0.960052i	$-0.590275\pi$
$509$	−3.27119e6	−0.559643	−0.279822	+	0.960052i	$0.590275\pi$
$510$	−2.40899e6	−0.410118
$511$	−1.37728e6	−0.233330
$512$	−6.84182e6	−1.15344
$513$	−1.48288e6	−0.248778
$514$	−8.41259e6	−1.40450
$515$	1.40823e6	0.233968
$516$	−6.78362e6	−1.12160
$517$	−2.50915e6	−0.412858
$518$	8.66221e6	1.41842
$519$	−5.16928e6	−0.842388
$520$	138797.	0.0225098
$521$	3.61278e6	0.583105	0.291553	−	0.956555i	$-0.405828\pi$
$521$	3.61278e6	0.583105	0.291553	+	0.956555i	$0.405828\pi$
$522$	3.40650e6	0.547182
$523$	5.79421e6	0.926275	0.463137	−	0.886287i	$-0.346724\pi$
$523$	5.79421e6	0.926275	0.463137	+	0.886287i	$0.346724\pi$
$524$	−9.77010e6	−1.55443
$525$	−1.13660e6	−0.179974
$526$	8.91384e6	1.40475
$527$	5.08120e6	0.796966
$528$	−948167.	−0.148013
$529$	−1.11570e6	−0.173343
$530$	4.11510e6	0.636343
$531$	4.53392e6	0.697811
$532$	−2.23609e6	−0.342539
$533$	814749.	0.124224
$534$	−5.81108e6	−0.881868
$535$	1.94345e6	0.293555
$536$	−3.52954e6	−0.530648
$537$	3.29168e6	0.492586
$538$	−5.81768e6	−0.866552
$539$	712366.	0.105616
$540$	−4.22241e6	−0.623126
$541$	−8.73015e6	−1.28241	−0.641207	−	0.767368i	$-0.721566\pi$
$541$	−8.73015e6	−1.28241	−0.641207	+	0.767368i	$0.721566\pi$
$542$	−6.29621e6	−0.920621
$543$	−1.41015e6	−0.205242
$544$	7.51032e6	1.08808
$545$	−3.68959e6	−0.532092
$546$	−1.10741e6	−0.158974
$547$	4.64429e6	0.663668	0.331834	−	0.943338i	$-0.392333\pi$
$547$	4.64429e6	0.663668	0.331834	+	0.943338i	$0.392333\pi$
$548$	8.28286e6	1.17823
$549$	−1.64051e6	−0.232300
$550$	−646659.	−0.0911524
$551$	1.47847e6	0.207459
$552$	−2.17081e6	−0.303231
$553$	−1.39161e7	−1.93510
$554$	7.14903e6	0.989629
$555$	2.02941e6	0.279664
$556$	−363923.	−0.0499255
$557$	1.09819e7	1.49982	0.749911	−	0.661539i	$-0.230096\pi$
$557$	1.09819e7	1.49982	0.749911	+	0.661539i	$0.230096\pi$
$558$	4.52746e6	0.615558
$559$	973285.	0.131738
$560$	2.44472e6	0.329427
$561$	1.36355e6	0.182921
$562$	−1.09901e7	−1.46778
$563$	130130.	0.0173024	0.00865119	−	0.999963i	$-0.497246\pi$
$563$	130130.	0.0173024	0.00865119	+	0.999963i	$0.497246\pi$
$564$	−1.02928e7	−1.36250
$565$	−2.62436e6	−0.345862
$566$	−6.03709e6	−0.792113
$567$	3.90919e6	0.510656
$568$	1.27849e6	0.166274
$569$	−2.55163e6	−0.330398	−0.165199	−	0.986260i	$-0.552827\pi$
$569$	−2.55163e6	−0.330398	−0.165199	+	0.986260i	$0.552827\pi$
$570$	−931593.	−0.120099
$571$	6.91946e6	0.888141	0.444070	−	0.895992i	$-0.353534\pi$
$571$	6.91946e6	0.888141	0.444070	+	0.895992i	$0.353534\pi$
$572$	−354307.	−0.0452782
$573$	−2.23269e6	−0.284081
$574$	−1.47374e7	−1.86699
$575$	1.44166e6	0.181841
$576$	4.67128e6	0.586651
$577$	2.32530e6	0.290764	0.145382	−	0.989376i	$-0.453559\pi$
$577$	2.32530e6	0.290764	0.145382	+	0.989376i	$0.453559\pi$
$578$	4.68955e6	0.583863
$579$	666305.	0.0825993
$580$	4.20986e6	0.519634
$581$	2.45586e6	0.301831
$582$	9.38605e6	1.14862
$583$	−2.32925e6	−0.283821
$584$	−712745.	−0.0864772
$585$	173183.	0.0209226
$586$	−1.28291e7	−1.54331
$587$	8.24919e6	0.988134	0.494067	−	0.869424i	$-0.335510\pi$
$587$	8.24919e6	0.988134	0.494067	+	0.869424i	$0.335510\pi$
$588$	2.92220e6	0.348552
$589$	1.96498e6	0.233383
$590$	9.96391e6	1.17842
$591$	1.23173e7	1.45060
$592$	−4.36506e6	−0.511901
$593$	1.53834e7	1.79646	0.898228	−	0.439530i	$-0.144855\pi$
$593$	1.53834e7	1.79646	0.898228	+	0.439530i	$0.144855\pi$
$594$	4.25003e6	0.494227
$595$	−3.51572e6	−0.407119
$596$	1.65039e7	1.90314
$597$	−6.65546e6	−0.764262
$598$	1.40463e6	0.160624
$599$	1.47994e7	1.68530	0.842652	−	0.538459i	$-0.180993\pi$
$599$	1.47994e7	1.68530	0.842652	+	0.538459i	$0.180993\pi$
$600$	−588192.	−0.0667023
$601$	3.39646e6	0.383566	0.191783	−	0.981437i	$-0.438573\pi$
$601$	3.39646e6	0.383566	0.191783	+	0.981437i	$0.438573\pi$
$602$	−1.76051e7	−1.97991
$603$	−4.40396e6	−0.493230
$604$	8.19429e6	0.913943
$605$	366025.	0.0406558
$606$	−865155.	−0.0957001
$607$	1.28066e7	1.41079	0.705393	−	0.708816i	$-0.250770\pi$
$607$	1.28066e7	1.41079	0.705393	+	0.708816i	$0.250770\pi$
$608$	2.90436e6	0.318633
$609$	−7.44787e6	−0.813746
$610$	−3.60525e6	−0.392293
$611$	1.47677e6	0.160033
$612$	−3.73365e6	−0.402953
$613$	9.28213e6	0.997692	0.498846	−	0.866691i	$-0.333757\pi$
$613$	9.28213e6	0.997692	0.498846	+	0.866691i	$0.333757\pi$
$614$	−1.00923e7	−1.08036
$615$	−3.45273e6	−0.368107
$616$	1.42106e6	0.150890
$617$	−1.39823e7	−1.47865	−0.739323	−	0.673351i	$-0.764854\pi$
$617$	−1.39823e7	−1.47865	−0.739323	+	0.673351i	$0.764854\pi$
$618$	−5.81451e6	−0.612410
$619$	−544051.	−0.0570706	−0.0285353	−	0.999593i	$-0.509084\pi$
$619$	−544051.	−0.0570706	−0.0285353	+	0.999593i	$0.509084\pi$
$620$	5.59518e6	0.584567
$621$	−9.47501e6	−0.985940
$622$	−5.93126e6	−0.614711
$623$	−8.48079e6	−0.875419
$624$	558047.	0.0573732
$625$	390625.	0.0400000
$626$	2.49942e6	0.254920
$627$	527305.	0.0535665
$628$	2.44174e6	0.247059
$629$	6.27734e6	0.632629
$630$	−3.13258e6	−0.314450
$631$	−1.66107e7	−1.66079	−0.830394	−	0.557177i	$-0.811885\pi$
$631$	−1.66107e7	−1.66079	−0.830394	+	0.557177i	$0.811885\pi$
$632$	−7.20157e6	−0.717191
$633$	3.32682e6	0.330004
$634$	−2.27872e7	−2.25148
$635$	5.24366e6	0.516060
$636$	−9.55485e6	−0.936658
$637$	−419265.	−0.0409393
$638$	−4.23740e6	−0.412143
$639$	1.59522e6	0.154550
$640$	3.82953e6	0.369569
$641$	−2.64658e6	−0.254414	−0.127207	−	0.991876i	$-0.540601\pi$
$641$	−2.64658e6	−0.254414	−0.127207	+	0.991876i	$0.540601\pi$
$642$	−8.02440e6	−0.768379
$643$	1.28930e7	1.22978	0.614891	−	0.788612i	$-0.289200\pi$
$643$	1.28930e7	1.22978	0.614891	+	0.788612i	$0.289200\pi$
$644$	−1.42878e7	−1.35753
$645$	−4.12457e6	−0.390372
$646$	−2.88159e6	−0.271676
$647$	−477187.	−0.0448155	−0.0224077	−	0.999749i	$-0.507133\pi$
$647$	−477187.	−0.0448155	−0.0224077	+	0.999749i	$0.507133\pi$
$648$	2.02301e6	0.189260
$649$	−5.63982e6	−0.525598
$650$	380593.	0.0353327
$651$	−9.89871e6	−0.915432
$652$	−1.20013e7	−1.10563
$653$	1.91774e7	1.75997	0.879987	−	0.474998i	$-0.157551\pi$
$653$	1.91774e7	1.75997	0.879987	+	0.474998i	$0.157551\pi$
$654$	1.52341e7	1.39275
$655$	−5.94040e6	−0.541019
$656$	7.42648e6	0.673789
$657$	−889321.	−0.0803795
$658$	−2.67122e7	−2.40517
$659$	−6.30280e6	−0.565354	−0.282677	−	0.959215i	$-0.591222\pi$
$659$	−6.30280e6	−0.565354	−0.282677	+	0.959215i	$0.591222\pi$
$660$	1.50147e6	0.134171
$661$	−310525.	−0.0276435	−0.0138218	−	0.999904i	$-0.504400\pi$
$661$	−310525.	−0.0276435	−0.0138218	+	0.999904i	$0.504400\pi$
$662$	−2.13508e7	−1.89351
$663$	−802520.	−0.0709042
$664$	1.27091e6	0.111865
$665$	−1.35958e6	−0.119221
$666$	5.59325e6	0.488628
$667$	9.44684e6	0.822190
$668$	1.94416e7	1.68574
$669$	9.89341e6	0.854635
$670$	−9.67829e6	−0.832936
$671$	2.04066e6	0.174970
$672$	−1.46309e7	−1.24982
$673$	−2.36403e6	−0.201194	−0.100597	−	0.994927i	$-0.532075\pi$
$673$	−2.36403e6	−0.201194	−0.100597	+	0.994927i	$0.532075\pi$
$674$	−3.58974e6	−0.304378
$675$	−2.56730e6	−0.216879
$676$	−1.50580e7	−1.26736
$677$	−1.33591e7	−1.12023	−0.560114	−	0.828415i	$-0.689243\pi$
$677$	−1.33591e7	−1.12023	−0.560114	+	0.828415i	$0.689243\pi$
$678$	1.08359e7	0.905292
$679$	1.36982e7	1.14022
$680$	−1.81939e6	−0.150887
$681$	−7.60840e6	−0.628674
$682$	−5.63178e6	−0.463644
$683$	−1.06444e6	−0.0873109	−0.0436554	−	0.999047i	$-0.513900\pi$
$683$	−1.06444e6	−0.0873109	−0.0436554	+	0.999047i	$0.513900\pi$
$684$	−1.44386e6	−0.118001
$685$	5.03613e6	0.410082
$686$	−1.40662e7	−1.14122
$687$	−2.98897e6	−0.241618
$688$	8.87155e6	0.714543
$689$	1.37089e6	0.110016
$690$	−5.95253e6	−0.475969
$691$	−1.67272e6	−0.133269	−0.0666343	−	0.997777i	$-0.521226\pi$
$691$	−1.67272e6	−0.133269	−0.0666343	+	0.997777i	$0.521226\pi$
$692$	−1.76070e7	−1.39772
$693$	1.77312e6	0.140251
$694$	−8.22247e6	−0.648042
$695$	−221272.	−0.0173766
$696$	−3.85428e6	−0.301592
$697$	−1.06799e7	−0.832696
$698$	−805172.	−0.0625533
$699$	1.32844e7	1.02837
$700$	−3.87134e6	−0.298619
$701$	1.53207e7	1.17756	0.588782	−	0.808292i	$-0.299608\pi$
$701$	1.53207e7	1.17756	0.588782	+	0.808292i	$0.299608\pi$
$702$	−2.50137e6	−0.191573
$703$	2.42755e6	0.185259
$704$	−5.81068e6	−0.441871
$705$	−6.25823e6	−0.474219
$706$	6.56466e6	0.495679
$707$	−1.26262e6	−0.0950003
$708$	−2.31352e7	−1.73456
$709$	−2.39436e7	−1.78885	−0.894426	−	0.447215i	$-0.852416\pi$
$709$	−2.39436e7	−1.78885	−0.894426	+	0.447215i	$0.852416\pi$
$710$	3.50571e6	0.260994
$711$	−8.98570e6	−0.666620
$712$	−4.38881e6	−0.324450
$713$	1.25555e7	0.924930
$714$	1.45162e7	1.06563
$715$	−215425.	−0.0157591
$716$	1.12117e7	0.817313
$717$	1.32933e6	0.0965682
$718$	−1.52312e7	−1.10261
$719$	−1.67724e7	−1.20996	−0.604982	−	0.796239i	$-0.706820\pi$
$719$	−1.67724e7	−1.20996	−0.604982	+	0.796239i	$0.706820\pi$
$720$	1.57857e6	0.113484
$721$	−8.48580e6	−0.607932
$722$	−1.11436e6	−0.0795575
$723$	−1.32141e7	−0.940135
$724$	−4.80307e6	−0.340544
$725$	2.55967e6	0.180859
$726$	−1.51130e6	−0.106416
$727$	1.04512e7	0.733381	0.366690	−	0.930343i	$-0.380491\pi$
$727$	1.04512e7	0.733381	0.366690	+	0.930343i	$0.380491\pi$
$728$	−836372.	−0.0584885
$729$	1.45738e7	1.01567
$730$	−1.95440e6	−0.135740
$731$	−1.27581e7	−0.883062
$732$	8.37101e6	0.577431
$733$	2.43966e7	1.67714	0.838569	−	0.544796i	$-0.183393\pi$
$733$	2.43966e7	1.67714	0.838569	+	0.544796i	$0.183393\pi$
$734$	−3.03202e7	−2.07726
$735$	1.77675e6	0.121313
$736$	1.85577e7	1.26279
$737$	5.47815e6	0.371506
$738$	−9.51606e6	−0.643156
$739$	−7.71931e6	−0.519957	−0.259978	−	0.965614i	$-0.583715\pi$
$739$	−7.71931e6	−0.519957	−0.259978	+	0.965614i	$0.583715\pi$
$740$	6.91231e6	0.464028
$741$	−310347.	−0.0207636
$742$	−2.47970e7	−1.65344
$743$	3.36291e6	0.223483	0.111741	−	0.993737i	$-0.464357\pi$
$743$	3.36291e6	0.223483	0.111741	+	0.993737i	$0.464357\pi$
$744$	−5.12259e6	−0.339279
$745$	1.00347e7	0.662387
$746$	−1.24546e7	−0.819375
$747$	1.58577e6	0.103977
$748$	4.64434e6	0.303508
$749$	−1.17110e7	−0.762760
$750$	−1.61287e6	−0.104700
$751$	−598478.	−0.0387211	−0.0193606	−	0.999813i	$-0.506163\pi$
$751$	−598478.	−0.0387211	−0.0193606	+	0.999813i	$0.506163\pi$
$752$	1.34608e7	0.868016
$753$	4.69636e6	0.301838
$754$	2.49393e6	0.159756
$755$	4.98228e6	0.318098
$756$	2.54436e7	1.61910
$757$	−6.30804e6	−0.400087	−0.200044	−	0.979787i	$-0.564108\pi$
$757$	−6.30804e6	−0.400087	−0.200044	+	0.979787i	$0.564108\pi$
$758$	−1.15046e6	−0.0727275
$759$	3.36928e6	0.212291
$760$	−703585.	−0.0441858
$761$	−1.49217e7	−0.934020	−0.467010	−	0.884252i	$-0.654669\pi$
$761$	−1.49217e7	−0.934020	−0.467010	+	0.884252i	$0.654669\pi$
$762$	−2.16508e7	−1.35078
$763$	2.22329e7	1.38257
$764$	−7.60472e6	−0.471357
$765$	−2.27013e6	−0.140248
$766$	1.26964e7	0.781821
$767$	3.31933e6	0.203734
$768$	2.73884e6	0.167557
$769$	−2.22535e7	−1.35701	−0.678503	−	0.734597i	$-0.737371\pi$
$769$	−2.22535e7	−1.35701	−0.678503	+	0.734597i	$0.737371\pi$
$770$	3.89667e6	0.236846
$771$	1.18765e7	0.719537
$772$	2.26948e6	0.137051
$773$	1.29560e7	0.779871	0.389935	−	0.920842i	$-0.372497\pi$
$773$	1.29560e7	0.779871	0.389935	+	0.920842i	$0.372497\pi$
$774$	−1.13677e7	−0.682057
$775$	3.40197e6	0.203459
$776$	7.08881e6	0.422590
$777$	−1.22289e7	−0.726667
$778$	2.25815e7	1.33753
$779$	−4.13010e6	−0.243847
$780$	−883697.	−0.0520076
$781$	−1.98432e6	−0.116408
$782$	−1.84123e7	−1.07669
$783$	−1.68229e7	−0.980612
$784$	−3.82163e6	−0.222054
$785$	1.48462e6	0.0859889
$786$	2.45276e7	1.41611
$787$	−9.80748e6	−0.564443	−0.282222	−	0.959349i	$-0.591071\pi$
$787$	−9.80748e6	−0.564443	−0.282222	+	0.959349i	$0.591071\pi$
$788$	4.19537e7	2.40688
$789$	−1.25842e7	−0.719667
$790$	−1.97473e7	−1.12574
$791$	1.58140e7	0.898673
$792$	917591.	0.0519800
$793$	−1.20104e6	−0.0678224
$794$	6.02242e6	0.339016
$795$	−5.80952e6	−0.326004
$796$	−2.26690e7	−1.26809
$797$	2.88620e7	1.60946	0.804730	−	0.593641i	$-0.202310\pi$
$797$	2.88620e7	1.60946	0.804730	+	0.593641i	$0.202310\pi$
$798$	5.61364e6	0.312060
$799$	−1.93579e7	−1.07273
$800$	5.02832e6	0.277778
$801$	−5.47611e6	−0.301572
$802$	−1.38270e7	−0.759089
$803$	1.10624e6	0.0605426
$804$	2.24720e7	1.22603
$805$	−8.68722e6	−0.472488
$806$	3.31460e6	0.179719
$807$	8.21315e6	0.443942
$808$	−653408.	−0.0352092
$809$	−1.10942e7	−0.595969	−0.297984	−	0.954571i	$-0.596314\pi$
$809$	−1.10942e7	−0.595969	−0.297984	+	0.954571i	$0.596314\pi$
$810$	5.54725e6	0.297074
$811$	−9.35372e6	−0.499381	−0.249691	−	0.968326i	$-0.580329\pi$
$811$	−9.35372e6	−0.499381	−0.249691	+	0.968326i	$0.580329\pi$
$812$	−2.53680e7	−1.35019
$813$	8.88871e6	0.471642
$814$	−6.95753e6	−0.368039
$815$	−7.29703e6	−0.384815
$816$	−7.31501e6	−0.384583
$817$	−4.93374e6	−0.258596
$818$	−2.80578e7	−1.46612
$819$	−1.04358e6	−0.0543643
$820$	−1.17602e7	−0.610775
$821$	−6.81016e6	−0.352614	−0.176307	−	0.984335i	$-0.556415\pi$
$821$	−6.81016e6	−0.352614	−0.176307	+	0.984335i	$0.556415\pi$
$822$	−2.07939e7	−1.07339
$823$	−2.18259e7	−1.12324	−0.561620	−	0.827395i	$-0.689822\pi$
$823$	−2.18259e7	−1.12324	−0.561620	+	0.827395i	$0.689822\pi$
$824$	−4.39141e6	−0.225313
$825$	912924.	0.0466982
$826$	−6.00410e7	−3.06195
$827$	−5.00263e6	−0.254352	−0.127176	−	0.991880i	$-0.540591\pi$
$827$	−5.00263e6	−0.254352	−0.127176	+	0.991880i	$0.540591\pi$
$828$	−9.22571e6	−0.467653
$829$	−1.56555e7	−0.791190	−0.395595	−	0.918425i	$-0.629462\pi$
$829$	−1.56555e7	−0.791190	−0.395595	+	0.918425i	$0.629462\pi$
$830$	3.48494e6	0.175590
$831$	−1.00927e7	−0.506995
$832$	3.41990e6	0.171279
$833$	5.49583e6	0.274423
$834$	913619.	0.0454831
$835$	1.18208e7	0.586721
$836$	1.79604e6	0.0888792
$837$	−2.23588e7	−1.10315
$838$	1.09610e6	0.0539187
$839$	2.18299e7	1.07065	0.535324	−	0.844647i	$-0.320189\pi$
$839$	2.18299e7	1.07065	0.535324	+	0.844647i	$0.320189\pi$
$840$	3.54436e6	0.173316
$841$	−3.73823e6	−0.182254
$842$	−2.12573e7	−1.03331
$843$	1.55153e7	0.751956
$844$	1.13314e7	0.547553
$845$	−9.15554e6	−0.441105
$846$	−1.72483e7	−0.828553
$847$	−2.20561e6	−0.105638
$848$	1.24957e7	0.596722
$849$	8.52290e6	0.405806
$850$	−4.98891e6	−0.236842
$851$	1.55111e7	0.734207
$852$	−8.13990e6	−0.384167
$853$	3.83498e7	1.80464	0.902319	−	0.431069i	$-0.141863\pi$
$853$	3.83498e7	1.80464	0.902319	+	0.431069i	$0.141863\pi$
$854$	2.17247e7	1.01932
$855$	−877893.	−0.0410701
$856$	−6.06043e6	−0.282696
$857$	−7.58808e6	−0.352923	−0.176461	−	0.984308i	$-0.556465\pi$
$857$	−7.58808e6	−0.352923	−0.176461	+	0.984308i	$0.556465\pi$
$858$	889478.	0.0412494
$859$	2.05770e7	0.951477	0.475738	−	0.879587i	$-0.342181\pi$
$859$	2.05770e7	0.951477	0.475738	+	0.879587i	$0.342181\pi$
$860$	−1.40486e7	−0.647718
$861$	2.08056e7	0.956474
$862$	−1.47273e6	−0.0675082
$863$	2.01101e7	0.919153	0.459576	−	0.888138i	$-0.348001\pi$
$863$	2.01101e7	0.919153	0.459576	+	0.888138i	$0.348001\pi$
$864$	−3.30476e7	−1.50611
$865$	−1.07054e7	−0.486475
$866$	−1.67617e7	−0.759493
$867$	−6.62049e6	−0.299118
$868$	−3.37157e7	−1.51891
$869$	1.11775e7	0.502104
$870$	−1.05687e7	−0.473397
$871$	−3.22418e6	−0.144004
$872$	1.15056e7	0.512409
$873$	8.84501e6	0.392792
$874$	−7.12031e6	−0.315297
$875$	−2.35385e6	−0.103934
$876$	4.53792e6	0.199800
$877$	−7.34179e6	−0.322332	−0.161166	−	0.986927i	$-0.551525\pi$
$877$	−7.34179e6	−0.322332	−0.161166	+	0.986927i	$0.551525\pi$
$878$	−1.70976e7	−0.748511
$879$	1.81116e7	0.790650
$880$	−1.96361e6	−0.0854769
$881$	−2.26545e7	−0.983364	−0.491682	−	0.870775i	$-0.663618\pi$
$881$	−2.26545e7	−0.983364	−0.491682	+	0.870775i	$0.663618\pi$
$882$	4.89691e6	0.211958
$883$	5.78873e6	0.249851	0.124926	−	0.992166i	$-0.460131\pi$
$883$	5.78873e6	0.249851	0.124926	+	0.992166i	$0.460131\pi$
$884$	−2.73344e6	−0.117647
$885$	−1.40666e7	−0.603714
$886$	2.65855e7	1.13779
$887$	2.24844e7	0.959558	0.479779	−	0.877389i	$-0.340717\pi$
$887$	2.24844e7	0.959558	0.479779	+	0.877389i	$0.340717\pi$
$888$	−6.32848e6	−0.269319
$889$	−3.15975e7	−1.34091
$890$	−1.20345e7	−0.509275
$891$	−3.13988e6	−0.132501
$892$	3.36977e7	1.41804
$893$	−7.48599e6	−0.314138
$894$	−4.14325e7	−1.73379
$895$	6.81692e6	0.284466
$896$	−2.30762e7	−0.960271
$897$	−1.98300e6	−0.0822889
$898$	7.11714e7	2.94520
$899$	2.22923e7	0.919932
$900$	−2.49976e6	−0.102871
$901$	−1.79699e7	−0.737454
$902$	1.18372e7	0.484431
$903$	2.48540e7	1.01433
$904$	8.18378e6	0.333068
$905$	−2.92036e6	−0.118526
$906$	−2.05716e7	−0.832620
$907$	1.32524e7	0.534903	0.267452	−	0.963571i	$-0.413818\pi$
$907$	1.32524e7	0.534903	0.267452	+	0.963571i	$0.413818\pi$
$908$	−2.59147e7	−1.04312
$909$	−815284.	−0.0327265
$910$	−2.29340e6	−0.0918070
$911$	1.78307e7	0.711826	0.355913	−	0.934519i	$-0.384170\pi$
$911$	1.78307e7	0.711826	0.355913	+	0.934519i	$0.384170\pi$
$912$	−2.82883e6	−0.112621
$913$	−1.97256e6	−0.0783166
$914$	−4.98972e7	−1.97565
$915$	5.08973e6	0.200975
$916$	−1.01806e7	−0.400900
$917$	3.57960e7	1.40576
$918$	3.27886e7	1.28415
$919$	1.08092e7	0.422186	0.211093	−	0.977466i	$-0.432298\pi$
$919$	1.08092e7	0.422186	0.211093	+	0.977466i	$0.432298\pi$
$920$	−4.49564e6	−0.175115
$921$	1.42479e7	0.553480
$922$	−3.75237e7	−1.45371
$923$	1.16788e6	0.0451225
$924$	−9.04767e6	−0.348623
$925$	4.20281e6	0.161505
$926$	7.12996e7	2.73250
$927$	−5.47934e6	−0.209425
$928$	3.29494e7	1.25596
$929$	1.75365e6	0.0666657	0.0333329	−	0.999444i	$-0.489388\pi$
$929$	1.75365e6	0.0666657	0.0333329	+	0.999444i	$0.489388\pi$
$930$	−1.40465e7	−0.532552
$931$	2.12532e6	0.0803621
$932$	4.52476e7	1.70630
$933$	8.37349e6	0.314921
$934$	−9.88888e6	−0.370920
$935$	2.82385e6	0.105636
$936$	−540051.	−0.0201486
$937$	5.03273e7	1.87264	0.936321	−	0.351145i	$-0.114208\pi$
$937$	5.03273e7	1.87264	0.936321	+	0.351145i	$0.114208\pi$
$938$	5.83199e7	2.16426
$939$	−3.52858e6	−0.130598
$940$	−2.13160e7	−0.786839
$941$	−3.20030e7	−1.17819	−0.589097	−	0.808063i	$-0.700516\pi$
$941$	−3.20030e7	−1.17819	−0.589097	+	0.808063i	$0.700516\pi$
$942$	−6.12993e6	−0.225076
$943$	−2.63897e7	−0.966398
$944$	3.02559e7	1.10505
$945$	1.54702e7	0.563529
$946$	1.41405e7	0.513732
$947$	1.41707e7	0.513473	0.256737	−	0.966481i	$-0.417353\pi$
$947$	1.41707e7	0.513473	0.256737	+	0.966481i	$0.417353\pi$
$948$	4.58512e7	1.65703
$949$	−651081.	−0.0234677
$950$	−1.92929e6	−0.0693566
$951$	3.21700e7	1.15345
$952$	1.09634e7	0.392059
$953$	−5.47820e6	−0.195392	−0.0976958	−	0.995216i	$-0.531147\pi$
$953$	−5.47820e6	−0.195392	−0.0976958	+	0.995216i	$0.531147\pi$
$954$	−1.60116e7	−0.569592
$955$	−4.62381e6	−0.164056
$956$	4.52778e6	0.160229
$957$	5.98217e6	0.211144
$958$	−1.10076e7	−0.387505
$959$	−3.03470e7	−1.06554
$960$	−1.44928e7	−0.507543
$961$	998763.	0.0348862
$962$	4.09488e6	0.142660
$963$	−7.56185e6	−0.262762
$964$	−4.50080e7	−1.55990
$965$	1.37989e6	0.0477008
$966$	3.58690e7	1.23674
$967$	−3.67623e7	−1.26426	−0.632130	−	0.774863i	$-0.717819\pi$
$967$	−3.67623e7	−1.26426	−0.632130	+	0.774863i	$0.717819\pi$
$968$	−1.14141e6	−0.0391518
$969$	4.06810e6	0.139182
$970$	1.94381e7	0.663322
$971$	−1.51254e7	−0.514823	−0.257412	−	0.966302i	$-0.582870\pi$
$971$	−1.51254e7	−0.514823	−0.257412	+	0.966302i	$0.582870\pi$
$972$	2.81617e7	0.956078
$973$	1.33335e6	0.0451505
$974$	−6.53839e7	−2.20838
$975$	−537304.	−0.0181013
$976$	−1.09475e7	−0.367867
$977$	1.01109e7	0.338887	0.169444	−	0.985540i	$-0.445803\pi$
$977$	1.01109e7	0.338887	0.169444	+	0.985540i	$0.445803\pi$
$978$	3.01290e7	1.00725
$979$	6.81182e6	0.227147
$980$	6.05175e6	0.201287
$981$	1.43560e7	0.476278
$982$	−4.84310e7	−1.60267
$983$	−1.46205e7	−0.482591	−0.241295	−	0.970452i	$-0.577572\pi$
$983$	−1.46205e7	−0.482591	−0.241295	+	0.970452i	$0.577572\pi$
$984$	1.07669e7	0.354490
$985$	2.55086e7	0.837715
$986$	−3.26911e7	−1.07087
$987$	3.77112e7	1.23219
$988$	−1.05706e6	−0.0344516
$989$	−3.15247e7	−1.02485
$990$	2.51611e6	0.0815908
$991$	−2.47379e7	−0.800163	−0.400082	−	0.916480i	$-0.631018\pi$
$991$	−2.47379e7	−0.800163	−0.400082	+	0.916480i	$0.631018\pi$
$992$	4.37918e7	1.41291
$993$	3.01421e7	0.970063
$994$	−2.11249e7	−0.678155
$995$	−1.37832e7	−0.441358
$996$	−8.09167e6	−0.258458
$997$	1.98844e7	0.633540	0.316770	−	0.948502i	$-0.397402\pi$
$997$	1.98844e7	0.633540	0.316770	+	0.948502i	$0.397402\pi$
$998$	3.00715e7	0.955715
$999$	−2.76222e7	−0.875677

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.h.1.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.h.1.5	✓	40	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)

\(f(q)\)	\(=\)	\(q-8.55086 q^{2} +12.0717 q^{3} +41.1172 q^{4} +25.0000 q^{5} -103.224 q^{6} -150.646 q^{7} -77.9596 q^{8} -97.2734 q^{9} +O(q^{10})\)	\(q-8.55086 q^{2} +12.0717 q^{3} +41.1172 q^{4} +25.0000 q^{5} -103.224 q^{6} -150.646 q^{7} -77.9596 q^{8} -97.2734 q^{9} -213.771 q^{10} +121.000 q^{11} +496.355 q^{12} -71.2149 q^{13} +1288.16 q^{14} +301.793 q^{15} -649.128 q^{16} +933.503 q^{17} +831.771 q^{18} +361.000 q^{19} +1027.93 q^{20} -1818.56 q^{21} -1034.65 q^{22} +2306.65 q^{23} -941.107 q^{24} +625.000 q^{25} +608.949 q^{26} -4107.69 q^{27} -6194.15 q^{28} +4095.48 q^{29} -2580.59 q^{30} +5443.15 q^{31} +8045.31 q^{32} +1460.68 q^{33} -7982.25 q^{34} -3766.16 q^{35} -3999.61 q^{36} +6724.50 q^{37} -3086.86 q^{38} -859.687 q^{39} -1948.99 q^{40} -11440.7 q^{41} +15550.3 q^{42} -13666.9 q^{43} +4975.18 q^{44} -2431.84 q^{45} -19723.9 q^{46} -20736.8 q^{47} -7836.09 q^{48} +5887.33 q^{49} -5344.29 q^{50} +11269.0 q^{51} -2928.16 q^{52} -19250.0 q^{53} +35124.3 q^{54} +3025.00 q^{55} +11744.3 q^{56} +4357.89 q^{57} -35019.8 q^{58} -46610.1 q^{59} +12408.9 q^{60} +16865.0 q^{61} -46543.6 q^{62} +14653.9 q^{63} -48022.2 q^{64} -1780.37 q^{65} -12490.1 q^{66} +45274.0 q^{67} +38383.0 q^{68} +27845.3 q^{69} +32203.9 q^{70} -16399.4 q^{71} +7583.40 q^{72} +9142.48 q^{73} -57500.3 q^{74} +7544.83 q^{75} +14843.3 q^{76} -18228.2 q^{77} +7351.06 q^{78} +92375.7 q^{79} -16228.2 q^{80} -25949.4 q^{81} +97827.9 q^{82} -16302.2 q^{83} -74774.1 q^{84} +23337.6 q^{85} +116863. q^{86} +49439.5 q^{87} -9433.11 q^{88} +56296.0 q^{89} +20794.3 q^{90} +10728.3 q^{91} +94843.0 q^{92} +65708.2 q^{93} +177318. q^{94} +9025.00 q^{95} +97120.7 q^{96} -90929.3 q^{97} -50341.7 q^{98} -11770.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * q^99

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