LMFDB - Embedded newform 1045.6.a.h.1.14

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			1.14
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)

$f(q)$	$=$	$q-2.87435 q^{2} +1.31331 q^{3} -23.7381 q^{4} +25.0000 q^{5} -3.77492 q^{6} -104.963 q^{7} +160.211 q^{8} -241.275 q^{9} +O(q^{10})$	\(q-2.87435 q^{2} +1.31331 q^{3} -23.7381 q^{4} +25.0000 q^{5} -3.77492 q^{6} -104.963 q^{7} +160.211 q^{8} -241.275 q^{9} -71.8588 q^{10} +121.000 q^{11} -31.1755 q^{12} -700.590 q^{13} +301.700 q^{14} +32.8328 q^{15} +299.117 q^{16} -2236.66 q^{17} +693.510 q^{18} +361.000 q^{19} -593.453 q^{20} -137.849 q^{21} -347.796 q^{22} +1360.39 q^{23} +210.407 q^{24} +625.000 q^{25} +2013.74 q^{26} -636.004 q^{27} +2491.62 q^{28} -6286.52 q^{29} -94.3730 q^{30} -7800.35 q^{31} -5986.52 q^{32} +158.911 q^{33} +6428.96 q^{34} -2624.07 q^{35} +5727.42 q^{36} -2183.65 q^{37} -1037.64 q^{38} -920.093 q^{39} +4005.27 q^{40} +4277.11 q^{41} +396.226 q^{42} -21488.7 q^{43} -2872.31 q^{44} -6031.88 q^{45} -3910.24 q^{46} +23985.5 q^{47} +392.834 q^{48} -5789.78 q^{49} -1796.47 q^{50} -2937.44 q^{51} +16630.7 q^{52} -3796.11 q^{53} +1828.10 q^{54} +3025.00 q^{55} -16816.2 q^{56} +474.105 q^{57} +18069.7 q^{58} -28435.3 q^{59} -779.388 q^{60} +31382.7 q^{61} +22420.9 q^{62} +25325.0 q^{63} +7635.60 q^{64} -17514.8 q^{65} -456.765 q^{66} -60627.9 q^{67} +53094.1 q^{68} +1786.62 q^{69} +7542.51 q^{70} -40029.3 q^{71} -38654.9 q^{72} +12922.3 q^{73} +6276.59 q^{74} +820.820 q^{75} -8569.46 q^{76} -12700.5 q^{77} +2644.67 q^{78} -84471.1 q^{79} +7477.93 q^{80} +57794.6 q^{81} -12293.9 q^{82} +84397.8 q^{83} +3272.27 q^{84} -55916.6 q^{85} +61766.2 q^{86} -8256.15 q^{87} +19385.5 q^{88} -90713.2 q^{89} +17337.7 q^{90} +73536.0 q^{91} -32293.1 q^{92} -10244.3 q^{93} -68942.9 q^{94} +9025.00 q^{95} -7862.16 q^{96} -70683.3 q^{97} +16641.9 q^{98} -29194.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.87435	−0.508118	−0.254059	−	0.967189i	$-0.581766\pi$
$2$	−2.87435	−0.508118	−0.254059	+	0.967189i	$0.581766\pi$
$3$	1.31331	0.0842490	0.0421245	−	0.999112i	$-0.486587\pi$
$3$	1.31331	0.0842490	0.0421245	+	0.999112i	$0.486587\pi$
$4$	−23.7381	−0.741816
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−3.77492	−0.0428084
$7$	−104.963	−0.809638	−0.404819	−	0.914397i	$-0.632665\pi$
$7$	−104.963	−0.809638	−0.404819	+	0.914397i	$0.632665\pi$
$8$	160.211	0.885048
$9$	−241.275	−0.992902
$10$	−71.8588	−0.227237
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−31.1755	−0.0624972
$13$	−700.590	−1.14976	−0.574878	−	0.818239i	$-0.694951\pi$
$13$	−700.590	−1.14976	−0.574878	+	0.818239i	$0.694951\pi$
$14$	301.700	0.411392
$15$	32.8328	0.0376773
$16$	299.117	0.292107
$17$	−2236.66	−1.87706	−0.938530	−	0.345197i	$-0.887812\pi$
$17$	−2236.66	−1.87706	−0.938530	+	0.345197i	$0.887812\pi$
$18$	693.510	0.504512
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−593.453	−0.331750
$21$	−137.849	−0.0682112
$22$	−347.796	−0.153203
$23$	1360.39	0.536222	0.268111	−	0.963388i	$-0.413601\pi$
$23$	1360.39	0.536222	0.268111	+	0.963388i	$0.413601\pi$
$24$	210.407	0.0745644
$25$	625.000	0.200000
$26$	2013.74	0.584212
$27$	−636.004	−0.167900
$28$	2491.62	0.600602
$29$	−6286.52	−1.38808	−0.694041	−	0.719936i	$-0.744171\pi$
$29$	−6286.52	−1.38808	−0.694041	+	0.719936i	$0.744171\pi$
$30$	−94.3730	−0.0191445
$31$	−7800.35	−1.45784	−0.728920	−	0.684599i	$-0.759977\pi$
$31$	−7800.35	−1.45784	−0.728920	+	0.684599i	$0.759977\pi$
$32$	−5986.52	−1.03347
$33$	158.911	0.0254020
$34$	6428.96	0.953769
$35$	−2624.07	−0.362081
$36$	5727.42	0.736550
$37$	−2183.65	−0.262228	−0.131114	−	0.991367i	$-0.541855\pi$
$37$	−2183.65	−0.262228	−0.131114	+	0.991367i	$0.541855\pi$
$38$	−1037.64	−0.116570
$39$	−920.093	−0.0968658
$40$	4005.27	0.395806
$41$	4277.11	0.397366	0.198683	−	0.980064i	$-0.436334\pi$
$41$	4277.11	0.397366	0.198683	+	0.980064i	$0.436334\pi$
$42$	396.226	0.0346593
$43$	−21488.7	−1.77231	−0.886155	−	0.463389i	$-0.846633\pi$
$43$	−21488.7	−1.77231	−0.886155	+	0.463389i	$0.846633\pi$
$44$	−2872.31	−0.223666
$45$	−6031.88	−0.444039
$46$	−3910.24	−0.272464
$47$	23985.5	1.58382	0.791908	−	0.610640i	$-0.209088\pi$
$47$	23985.5	1.58382	0.791908	+	0.610640i	$0.209088\pi$
$48$	392.834	0.0246097
$49$	−5789.78	−0.344486
$50$	−1796.47	−0.101624
$51$	−2937.44	−0.158140
$52$	16630.7	0.852907
$53$	−3796.11	−0.185630	−0.0928151	−	0.995683i	$-0.529587\pi$
$53$	−3796.11	−0.185630	−0.0928151	+	0.995683i	$0.529587\pi$
$54$	1828.10	0.0853130
$55$	3025.00	0.134840
$56$	−16816.2	−0.716569
$57$	474.105	0.0193280
$58$	18069.7	0.705310
$59$	−28435.3	−1.06348	−0.531738	−	0.846909i	$-0.678461\pi$
$59$	−28435.3	−1.06348	−0.531738	+	0.846909i	$0.678461\pi$
$60$	−779.388	−0.0279496
$61$	31382.7	1.07985	0.539927	−	0.841712i	$-0.318452\pi$
$61$	31382.7	1.07985	0.539927	+	0.841712i	$0.318452\pi$
$62$	22420.9	0.740755
$63$	25325.0	0.803891
$64$	7635.60	0.233020
$65$	−17514.8	−0.514187
$66$	−456.765	−0.0129072
$67$	−60627.9	−1.65001	−0.825003	−	0.565128i	$-0.808827\pi$
$67$	−60627.9	−1.65001	−0.825003	+	0.565128i	$0.808827\pi$
$68$	53094.1	1.39243
$69$	1786.62	0.0451761
$70$	7542.51	0.183980
$71$	−40029.3	−0.942393	−0.471196	−	0.882028i	$-0.656178\pi$
$71$	−40029.3	−0.942393	−0.471196	+	0.882028i	$0.656178\pi$
$72$	−38654.9	−0.878766
$73$	12922.3	0.283813	0.141906	−	0.989880i	$-0.454677\pi$
$73$	12922.3	0.283813	0.141906	+	0.989880i	$0.454677\pi$
$74$	6276.59	0.133243
$75$	820.820	0.0168498
$76$	−8569.46	−0.170184
$77$	−12700.5	−0.244115
$78$	2644.67	0.0492193
$79$	−84471.1	−1.52279	−0.761395	−	0.648288i	$-0.775485\pi$
$79$	−84471.1	−1.52279	−0.761395	+	0.648288i	$0.775485\pi$
$80$	7477.93	0.130634
$81$	57794.6	0.978757
$82$	−12293.9	−0.201909
$83$	84397.8	1.34473	0.672366	−	0.740219i	$-0.265278\pi$
$83$	84397.8	1.34473	0.672366	+	0.740219i	$0.265278\pi$
$84$	3272.27	0.0506001
$85$	−55916.6	−0.839447
$86$	61766.2	0.900543
$87$	−8256.15	−0.116944
$88$	19385.5	0.266852
$89$	−90713.2	−1.21393	−0.606967	−	0.794727i	$-0.707614\pi$
$89$	−90713.2	−1.21393	−0.606967	+	0.794727i	$0.707614\pi$
$90$	17337.7	0.225624
$91$	73536.0	0.930886
$92$	−32293.1	−0.397778
$93$	−10244.3	−0.122821
$94$	−68942.9	−0.804766
$95$	9025.00	0.102598
$96$	−7862.16	−0.0870690
$97$	−70683.3	−0.762760	−0.381380	−	0.924418i	$-0.624551\pi$
$97$	−70683.3	−0.762760	−0.381380	+	0.924418i	$0.624551\pi$
$98$	16641.9	0.175040
$99$	−29194.3	−0.299371
$100$	−14836.3	−0.148363
$101$	14406.4	0.140525	0.0702624	−	0.997529i	$-0.477616\pi$
$101$	14406.4	0.140525	0.0702624	+	0.997529i	$0.477616\pi$
$102$	8443.22	0.0803540
$103$	7970.62	0.0740285	0.0370142	−	0.999315i	$-0.488215\pi$
$103$	7970.62	0.0740285	0.0370142	+	0.999315i	$0.488215\pi$
$104$	−112242.	−1.01759
$105$	−3446.23	−0.0305050
$106$	10911.3	0.0943221
$107$	13229.5	0.111708	0.0558542	−	0.998439i	$-0.482212\pi$
$107$	13229.5	0.111708	0.0558542	+	0.998439i	$0.482212\pi$
$108$	15097.5	0.124551
$109$	−87645.9	−0.706587	−0.353293	−	0.935513i	$-0.614938\pi$
$109$	−87645.9	−0.706587	−0.353293	+	0.935513i	$0.614938\pi$
$110$	−8694.91	−0.0685147
$111$	−2867.82	−0.0220925
$112$	−31396.2	−0.236501
$113$	−249433.	−1.83763	−0.918815	−	0.394689i	$-0.870852\pi$
$113$	−249433.	−1.83763	−0.918815	+	0.394689i	$0.870852\pi$
$114$	−1362.75	−0.00982093
$115$	34009.8	0.239806
$116$	149230.	1.02970
$117$	169035.	1.14160
$118$	81733.0	0.540371
$119$	234767.	1.51974
$120$	5260.17	0.0333462
$121$	14641.0	0.0909091
$122$	−90204.8	−0.548694
$123$	5617.17	0.0334777
$124$	185165.	1.08145
$125$	15625.0	0.0894427
$126$	−72792.8	−0.408472
$127$	228006.	1.25440	0.627201	−	0.778858i	$-0.284201\pi$
$127$	228006.	1.25440	0.627201	+	0.778858i	$0.284201\pi$
$128$	169621.	0.915071
$129$	−28221.4	−0.149315
$130$	50343.6	0.261268
$131$	−247254.	−1.25882	−0.629411	−	0.777072i	$-0.716704\pi$
$131$	−247254.	−1.25882	−0.629411	+	0.777072i	$0.716704\pi$
$132$	−3772.24	−0.0188436
$133$	−37891.6	−0.185744
$134$	174266.	0.838399
$135$	−15900.1	−0.0750871
$136$	−358338.	−1.66129
$137$	−164714.	−0.749770	−0.374885	−	0.927071i	$-0.622318\pi$
$137$	−164714.	−0.749770	−0.374885	+	0.927071i	$0.622318\pi$
$138$	−5135.37	−0.0229548
$139$	−5052.73	−0.0221814	−0.0110907	−	0.999938i	$-0.503530\pi$
$139$	−5052.73	−0.0221814	−0.0110907	+	0.999938i	$0.503530\pi$
$140$	62290.5	0.268598
$141$	31500.5	0.133435
$142$	115058.	0.478847
$143$	−84771.4	−0.346665
$144$	−72169.5	−0.290033
$145$	−157163.	−0.620769
$146$	−37143.2	−0.144210
$147$	−7603.79	−0.0290226
$148$	51835.8	0.194525
$149$	236807.	0.873834	0.436917	−	0.899502i	$-0.356070\pi$
$149$	236807.	0.873834	0.436917	+	0.899502i	$0.356070\pi$
$150$	−2359.32	−0.00856169
$151$	−96769.5	−0.345379	−0.172690	−	0.984976i	$-0.555246\pi$
$151$	−96769.5	−0.345379	−0.172690	+	0.984976i	$0.555246\pi$
$152$	57836.1	0.203044
$153$	539651.	1.86374
$154$	36505.7	0.124039
$155$	−195009.	−0.651966
$156$	21841.3	0.0718566
$157$	−304727.	−0.986648	−0.493324	−	0.869846i	$-0.664218\pi$
$157$	−304727.	−0.986648	−0.493324	+	0.869846i	$0.664218\pi$
$158$	242799.	0.773758
$159$	−4985.47	−0.0156392
$160$	−149663.	−0.462183
$161$	−142791.	−0.434146
$162$	−166122.	−0.497324
$163$	−253427.	−0.747109	−0.373555	−	0.927608i	$-0.621861\pi$
$163$	−253427.	−0.747109	−0.373555	+	0.927608i	$0.621861\pi$
$164$	−101530.	−0.294772
$165$	3972.77	0.0113601
$166$	−242589.	−0.683283
$167$	−280548.	−0.778423	−0.389212	−	0.921148i	$-0.627253\pi$
$167$	−280548.	−0.778423	−0.389212	+	0.921148i	$0.627253\pi$
$168$	−22084.9	−0.0603702
$169$	119534.	0.321940
$170$	160724.	0.426538
$171$	−87100.4	−0.227787
$172$	510102.	1.31473
$173$	−340010.	−0.863728	−0.431864	−	0.901939i	$-0.642144\pi$
$173$	−340010.	−0.863728	−0.431864	+	0.901939i	$0.642144\pi$
$174$	23731.1	0.0594216
$175$	−65601.8	−0.161928
$176$	36193.2	0.0880734
$177$	−37344.4	−0.0895967
$178$	260742.	0.616822
$179$	−464156.	−1.08276	−0.541378	−	0.840779i	$-0.682097\pi$
$179$	−464156.	−1.08276	−0.541378	+	0.840779i	$0.682097\pi$
$180$	143185.	0.329395
$181$	676257.	1.53432	0.767159	−	0.641457i	$-0.221670\pi$
$181$	676257.	1.53432	0.767159	+	0.641457i	$0.221670\pi$
$182$	−211368.	−0.473000
$183$	41215.2	0.0909766
$184$	217950.	0.474582
$185$	−54591.4	−0.117272
$186$	29445.7	0.0624078
$187$	−270636.	−0.565955
$188$	−569371.	−1.17490
$189$	66756.9	0.135938
$190$	−25941.0	−0.0521318
$191$	277329.	0.550062	0.275031	−	0.961435i	$-0.411312\pi$
$191$	277329.	0.550062	0.275031	+	0.961435i	$0.411312\pi$
$192$	10027.9	0.0196317
$193$	708452.	1.36904	0.684521	−	0.728993i	$-0.260011\pi$
$193$	708452.	1.36904	0.684521	+	0.728993i	$0.260011\pi$
$194$	203169.	0.387572
$195$	−23002.3	−0.0433197
$196$	137438.	0.255545
$197$	868129.	1.59374	0.796872	−	0.604148i	$-0.206487\pi$
$197$	868129.	1.59374	0.796872	+	0.604148i	$0.206487\pi$
$198$	83914.7	0.152116
$199$	−468267.	−0.838225	−0.419113	−	0.907934i	$-0.637659\pi$
$199$	−468267.	−0.838225	−0.419113	+	0.907934i	$0.637659\pi$
$200$	100132.	0.177010
$201$	−79623.4	−0.139011
$202$	−41409.1	−0.0714032
$203$	659851.	1.12384
$204$	69729.2	0.117311
$205$	106928.	0.177707
$206$	−22910.3	−0.0376152
$207$	−328229.	−0.532416
$208$	−209559.	−0.335851
$209$	43681.0	0.0691714
$210$	9905.66	0.0155001
$211$	166190.	0.256980	0.128490	−	0.991711i	$-0.458987\pi$
$211$	166190.	0.256980	0.128490	+	0.991711i	$0.458987\pi$
$212$	90112.4	0.137703
$213$	−52570.9	−0.0793956
$214$	−38026.4	−0.0567610
$215$	−537218.	−0.792601
$216$	−101895.	−0.148600
$217$	818747.	1.18032
$218$	251925.	0.359030
$219$	16971.0	0.0239109
$220$	−71807.8	−0.100026
$221$	1.56698e6	2.15816
$222$	8243.12	0.0112256
$223$	989122.	1.33195	0.665974	−	0.745975i	$-0.268016\pi$
$223$	989122.	1.33195	0.665974	+	0.745975i	$0.268016\pi$
$224$	628362.	0.836739
$225$	−150797.	−0.198580
$226$	716958.	0.933733
$227$	−1.34851e6	−1.73696	−0.868482	−	0.495721i	$-0.834904\pi$
$227$	−1.34851e6	−1.73696	−0.868482	+	0.495721i	$0.834904\pi$
$228$	−11254.4	−0.0143378
$229$	687762.	0.866662	0.433331	−	0.901235i	$-0.357338\pi$
$229$	687762.	0.866662	0.433331	+	0.901235i	$0.357338\pi$
$230$	−97756.1	−0.121850
$231$	−16679.7	−0.0205664
$232$	−1.00717e6	−1.22852
$233$	615328.	0.742535	0.371267	−	0.928526i	$-0.378923\pi$
$233$	615328.	0.742535	0.371267	+	0.928526i	$0.378923\pi$
$234$	−485866.	−0.580066
$235$	599639.	0.708304
$236$	675000.	0.788903
$237$	−110937.	−0.128294
$238$	−674802.	−0.772207
$239$	460491.	0.521466	0.260733	−	0.965411i	$-0.416036\pi$
$239$	460491.	0.521466	0.260733	+	0.965411i	$0.416036\pi$
$240$	9820.85	0.0110058
$241$	−319572.	−0.354426	−0.177213	−	0.984173i	$-0.556708\pi$
$241$	−319572.	−0.354426	−0.177213	+	0.984173i	$0.556708\pi$
$242$	−42083.4	−0.0461926
$243$	230451.	0.250359
$244$	−744965.	−0.801053
$245$	−144745.	−0.154059
$246$	−16145.7	−0.0170106
$247$	−252913.	−0.263772
$248$	−1.24970e6	−1.29026
$249$	110841.	0.113292
$250$	−44911.7	−0.0454475
$251$	407679.	0.408446	0.204223	−	0.978924i	$-0.434533\pi$
$251$	407679.	0.408446	0.204223	+	0.978924i	$0.434533\pi$
$252$	−601166.	−0.596339
$253$	164607.	0.161677
$254$	−655369.	−0.637384
$255$	−73435.9	−0.0707225
$256$	−731890.	−0.697985
$257$	−1.94944e6	−1.84110	−0.920548	−	0.390629i	$-0.872258\pi$
$257$	−1.94944e6	−1.84110	−0.920548	+	0.390629i	$0.872258\pi$
$258$	81118.2	0.0758698
$259$	229203.	0.212310
$260$	415767.	0.381432
$261$	1.51678e6	1.37823
$262$	710694.	0.639631
$263$	−1.15967e6	−1.03382	−0.516909	−	0.856040i	$-0.672918\pi$
$263$	−1.15967e6	−1.03382	−0.516909	+	0.856040i	$0.672918\pi$
$264$	25459.2	0.0224820
$265$	−94902.7	−0.0830164
$266$	108914.	0.0943798
$267$	−119135.	−0.102273
$268$	1.43919e6	1.22400
$269$	487480.	0.410748	0.205374	−	0.978684i	$-0.434159\pi$
$269$	487480.	0.410748	0.205374	+	0.978684i	$0.434159\pi$
$270$	45702.5	0.0381531
$271$	1.27712e6	1.05635	0.528177	−	0.849134i	$-0.322876\pi$
$271$	1.27712e6	1.05635	0.528177	+	0.849134i	$0.322876\pi$
$272$	−669024.	−0.548302
$273$	96575.7	0.0784262
$274$	473445.	0.380972
$275$	75625.0	0.0603023
$276$	−42410.9	−0.0335124
$277$	−444119.	−0.347776	−0.173888	−	0.984765i	$-0.555633\pi$
$277$	−444119.	−0.347776	−0.173888	+	0.984765i	$0.555633\pi$
$278$	14523.3	0.0112708
$279$	1.88203e6	1.44749
$280$	−420405.	−0.320459
$281$	981617.	0.741611	0.370805	−	0.928711i	$-0.379082\pi$
$281$	981617.	0.741611	0.370805	+	0.928711i	$0.379082\pi$
$282$	−90543.5	−0.0678007
$283$	1.67942e6	1.24650	0.623252	−	0.782021i	$-0.285811\pi$
$283$	1.67942e6	1.24650	0.623252	+	0.782021i	$0.285811\pi$
$284$	950219.	0.699082
$285$	11852.6	0.00864376
$286$	243663.	0.176147
$287$	−448938.	−0.321722
$288$	1.44440e6	1.02614
$289$	3.58281e6	2.52336
$290$	451741.	0.315424
$291$	−92829.2	−0.0642617
$292$	−306750.	−0.210537
$293$	−2.78836e6	−1.89749	−0.948747	−	0.316036i	$-0.897648\pi$
$293$	−2.78836e6	−1.89749	−0.948747	+	0.316036i	$0.897648\pi$
$294$	21856.0	0.0147469
$295$	−710882.	−0.475601
$296$	−349845.	−0.232085
$297$	−76956.5	−0.0506237
$298$	−680666.	−0.444011
$299$	−953078.	−0.616524
$300$	−19484.7	−0.0124994
$301$	2.25552e6	1.43493
$302$	278150.	0.175493
$303$	18920.1	0.0118391
$304$	107981.	0.0670138
$305$	784566.	0.482925
$306$	−1.55115e6	−0.946999
$307$	2.07091e6	1.25405	0.627026	−	0.778999i	$-0.284272\pi$
$307$	2.07091e6	1.25405	0.627026	+	0.778999i	$0.284272\pi$
$308$	301486.	0.181088
$309$	10467.9	0.00623682
$310$	560523.	0.331276
$311$	−2.27640e6	−1.33459	−0.667295	−	0.744793i	$-0.732548\pi$
$311$	−2.27640e6	−1.33459	−0.667295	+	0.744793i	$0.732548\pi$
$312$	−147409.	−0.0857309
$313$	2.42308e6	1.39800	0.699000	−	0.715121i	$-0.253629\pi$
$313$	2.42308e6	1.39800	0.699000	+	0.715121i	$0.253629\pi$
$314$	875894.	0.501334
$315$	633124.	0.359511
$316$	2.00518e6	1.12963
$317$	1.73435e6	0.969370	0.484685	−	0.874689i	$-0.338934\pi$
$317$	1.73435e6	0.969370	0.484685	+	0.874689i	$0.338934\pi$
$318$	14330.0	0.00794654
$319$	−760668.	−0.418522
$320$	190890.	0.104210
$321$	17374.5	0.00941131
$322$	410431.	0.220597
$323$	−807435.	−0.430627
$324$	−1.37193e6	−0.726057
$325$	−437869.	−0.229951
$326$	728439.	0.379620
$327$	−115106.	−0.0595292
$328$	685239.	0.351688
$329$	−2.51759e6	−1.28232
$330$	−11419.1	−0.00577229
$331$	−1.77220e6	−0.889086	−0.444543	−	0.895757i	$-0.646634\pi$
$331$	−1.77220e6	−0.889086	−0.444543	+	0.895757i	$0.646634\pi$
$332$	−2.00344e6	−0.997544
$333$	526862.	0.260367
$334$	806393.	0.395531
$335$	−1.51570e6	−0.737906
$336$	−41233.0	−0.0199249
$337$	542695.	0.260304	0.130152	−	0.991494i	$-0.458453\pi$
$337$	542695.	0.260304	0.130152	+	0.991494i	$0.458453\pi$
$338$	−343583.	−0.163583
$339$	−327583.	−0.154818
$340$	1.32735e6	0.622715
$341$	−943842.	−0.439555
$342$	250357.	0.115743
$343$	2.37182e6	1.08855
$344$	−3.44273e6	−1.56858
$345$	44665.5	0.0202034
$346$	977309.	0.438876
$347$	1.40624e6	0.626953	0.313476	−	0.949596i	$-0.398506\pi$
$347$	1.40624e6	0.626953	0.313476	+	0.949596i	$0.398506\pi$
$348$	195985.	0.0867512
$349$	1.94337e6	0.854067	0.427033	−	0.904236i	$-0.359559\pi$
$349$	1.94337e6	0.854067	0.427033	+	0.904236i	$0.359559\pi$
$350$	188563.	0.0822784
$351$	445578.	0.193044
$352$	−724368.	−0.311604
$353$	−2.22411e6	−0.949989	−0.474994	−	0.879989i	$-0.657550\pi$
$353$	−2.22411e6	−0.949989	−0.474994	+	0.879989i	$0.657550\pi$
$354$	107341.	0.0455257
$355$	−1.00073e6	−0.421451
$356$	2.15336e6	0.900516
$357$	308322.	0.128036
$358$	1.33415e6	0.550169
$359$	4.11243e6	1.68408	0.842040	−	0.539415i	$-0.181355\pi$
$359$	4.11243e6	1.68408	0.842040	+	0.539415i	$0.181355\pi$
$360$	−966373.	−0.392996
$361$	130321.	0.0526316
$362$	−1.94380e6	−0.779615
$363$	19228.2	0.00765900
$364$	−1.74561e6	−0.690546
$365$	323057.	0.126925
$366$	−118467.	−0.0462269
$367$	−2.45160e6	−0.950132	−0.475066	−	0.879950i	$-0.657576\pi$
$367$	−2.45160e6	−0.950132	−0.475066	+	0.879950i	$0.657576\pi$
$368$	406916.	0.156634
$369$	−1.03196e6	−0.394545
$370$	156915.	0.0595881
$371$	398451.	0.150293
$372$	243180.	0.0911109
$373$	885966.	0.329720	0.164860	−	0.986317i	$-0.447283\pi$
$373$	885966.	0.329720	0.164860	+	0.986317i	$0.447283\pi$
$374$	777904.	0.287572
$375$	20520.5	0.00753546
$376$	3.84275e6	1.40175
$377$	4.40427e6	1.59596
$378$	−191883.	−0.0690727
$379$	−3.96337e6	−1.41732	−0.708658	−	0.705552i	$-0.750699\pi$
$379$	−3.96337e6	−1.41732	−0.708658	+	0.705552i	$0.750699\pi$
$380$	−214236.	−0.0761087
$381$	299443.	0.105682
$382$	−797140.	−0.279496
$383$	3.58485e6	1.24875	0.624373	−	0.781127i	$-0.285355\pi$
$383$	3.58485e6	1.24875	0.624373	+	0.781127i	$0.285355\pi$
$384$	222765.	0.0770938
$385$	−317513.	−0.109172
$386$	−2.03634e6	−0.695635
$387$	5.18470e6	1.75973
$388$	1.67789e6	0.565827
$389$	57829.5	0.0193765	0.00968825	−	0.999953i	$-0.496916\pi$
$389$	57829.5	0.0193765	0.00968825	+	0.999953i	$0.496916\pi$
$390$	66116.8	0.0220115
$391$	−3.04274e6	−1.00652
$392$	−927586.	−0.304887
$393$	−324721.	−0.106055
$394$	−2.49531e6	−0.809810
$395$	−2.11178e6	−0.681013
$396$	693017.	0.222078
$397$	5.02763e6	1.60098	0.800492	−	0.599344i	$-0.204572\pi$
$397$	5.02763e6	1.60098	0.800492	+	0.599344i	$0.204572\pi$
$398$	1.34596e6	0.425918
$399$	−49763.5	−0.0156487
$400$	186948.	0.0584213
$401$	3.36735e6	1.04575	0.522874	−	0.852410i	$-0.324860\pi$
$401$	3.36735e6	1.04575	0.522874	+	0.852410i	$0.324860\pi$
$402$	228865.	0.0706342
$403$	5.46485e6	1.67616
$404$	−341981.	−0.104243
$405$	1.44487e6	0.437713
$406$	−1.89664e6	−0.571045
$407$	−264222.	−0.0790648
$408$	−470609.	−0.139962
$409$	−1.75620e6	−0.519117	−0.259559	−	0.965727i	$-0.583577\pi$
$409$	−1.75620e6	−0.519117	−0.259559	+	0.965727i	$0.583577\pi$
$410$	−307348.	−0.0902964
$411$	−216320.	−0.0631673
$412$	−189207.	−0.0549155
$413$	2.98465e6	0.861030
$414$	943445.	0.270530
$415$	2.10994e6	0.601383
$416$	4.19410e6	1.18824
$417$	−6635.80	−0.00186876
$418$	−125555.	−0.0351473
$419$	−4.33895e6	−1.20740	−0.603698	−	0.797213i	$-0.706307\pi$
$419$	−4.33895e6	−1.20740	−0.603698	+	0.797213i	$0.706307\pi$
$420$	81806.9	0.0226291
$421$	1.42406e6	0.391583	0.195792	−	0.980646i	$-0.437272\pi$
$421$	1.42406e6	0.391583	0.195792	+	0.980646i	$0.437272\pi$
$422$	−477690.	−0.130576
$423$	−5.78712e6	−1.57257
$424$	−608178.	−0.164292
$425$	−1.39791e6	−0.375412
$426$	151107.	0.0403424
$427$	−3.29402e6	−0.874291
$428$	−314044.	−0.0828670
$429$	−111331.	−0.0292061
$430$	1.54415e6	0.402735
$431$	−4.97152e6	−1.28913	−0.644564	−	0.764550i	$-0.722961\pi$
$431$	−4.97152e6	−1.28913	−0.644564	+	0.764550i	$0.722961\pi$
$432$	−190240.	−0.0490447
$433$	1.61103e6	0.412937	0.206469	−	0.978453i	$-0.433803\pi$
$433$	1.61103e6	0.412937	0.206469	+	0.978453i	$0.433803\pi$
$434$	−2.35337e6	−0.599743
$435$	−206404.	−0.0522991
$436$	2.08055e6	0.524157
$437$	491102.	0.123018
$438$	−48780.6	−0.0121496
$439$	2.58212e6	0.639464	0.319732	−	0.947508i	$-0.396407\pi$
$439$	2.58212e6	0.639464	0.319732	+	0.947508i	$0.396407\pi$
$440$	484638.	0.119340
$441$	1.39693e6	0.342041
$442$	−4.50406e6	−1.09660
$443$	2.04491e6	0.495069	0.247535	−	0.968879i	$-0.420380\pi$
$443$	2.04491e6	0.495069	0.247535	+	0.968879i	$0.420380\pi$
$444$	68076.6	0.0163885
$445$	−2.26783e6	−0.542888
$446$	−2.84308e6	−0.676787
$447$	311001.	0.0736196
$448$	−801455.	−0.188662
$449$	3.99341e6	0.934821	0.467410	−	0.884040i	$-0.345187\pi$
$449$	3.99341e6	0.934821	0.467410	+	0.884040i	$0.345187\pi$
$450$	433444.	0.100902
$451$	517530.	0.119810
$452$	5.92107e6	1.36318
$453$	−127089.	−0.0290978
$454$	3.87610e6	0.882583
$455$	1.83840e6	0.416305
$456$	75956.8	0.0171063
$457$	2.06457e6	0.462422	0.231211	−	0.972904i	$-0.425731\pi$
$457$	2.06457e6	0.462422	0.231211	+	0.972904i	$0.425731\pi$
$458$	−1.97687e6	−0.440367
$459$	1.42253e6	0.315158
$460$	−807328.	−0.177892
$461$	654314.	0.143395	0.0716975	−	0.997426i	$-0.477158\pi$
$461$	654314.	0.143395	0.0716975	+	0.997426i	$0.477158\pi$
$462$	47943.4	0.0104502
$463$	5.14314e6	1.11500	0.557502	−	0.830176i	$-0.311760\pi$
$463$	5.14314e6	1.11500	0.557502	+	0.830176i	$0.311760\pi$
$464$	−1.88040e6	−0.405468
$465$	−256107.	−0.0549274
$466$	−1.76867e6	−0.377295
$467$	5.21815e6	1.10720	0.553598	−	0.832784i	$-0.313254\pi$
$467$	5.21815e6	1.10720	0.553598	+	0.832784i	$0.313254\pi$
$468$	−4.01257e6	−0.846854
$469$	6.36369e6	1.33591
$470$	−1.72357e6	−0.359902
$471$	−400202.	−0.0831241
$472$	−4.55564e6	−0.941227
$473$	−2.60014e6	−0.534372
$474$	318871.	0.0651883
$475$	225625.	0.0458831
$476$	−5.57292e6	−1.12737
$477$	915907.	0.184313
$478$	−1.32361e6	−0.264966
$479$	−6.73871e6	−1.34196	−0.670978	−	0.741477i	$-0.734125\pi$
$479$	−6.73871e6	−1.34196	−0.670978	+	0.741477i	$0.734125\pi$
$480$	−196554.	−0.0389385
$481$	1.52985e6	0.301499
$482$	918561.	0.180090
$483$	−187529.	−0.0365763
$484$	−347550.	−0.0674378
$485$	−1.76708e6	−0.341116
$486$	−662398.	−0.127212
$487$	−2.46628e6	−0.471217	−0.235608	−	0.971848i	$-0.575708\pi$
$487$	−2.46628e6	−0.471217	−0.235608	+	0.971848i	$0.575708\pi$
$488$	5.02784e6	0.955723
$489$	−332829.	−0.0629432
$490$	416047.	0.0782802
$491$	5.29370e6	0.990958	0.495479	−	0.868620i	$-0.334992\pi$
$491$	5.29370e6	0.990958	0.495479	+	0.868620i	$0.334992\pi$
$492$	−133341.	−0.0248343
$493$	1.40608e7	2.60551
$494$	726961.	0.134027
$495$	−729858.	−0.133883
$496$	−2.33322e6	−0.425844
$497$	4.20159e6	0.762997
$498$	−318595.	−0.0575659
$499$	−5.18541e6	−0.932249	−0.466124	−	0.884719i	$-0.654350\pi$
$499$	−5.18541e6	−0.932249	−0.466124	+	0.884719i	$0.654350\pi$
$500$	−370908.	−0.0663500
$501$	−368447.	−0.0655814
$502$	−1.17181e6	−0.207539
$503$	−8.92681e6	−1.57317	−0.786586	−	0.617481i	$-0.788153\pi$
$503$	−8.92681e6	−1.57317	−0.786586	+	0.617481i	$0.788153\pi$
$504$	4.05733e6	0.711483
$505$	360161.	0.0628446
$506$	−473140.	−0.0821510
$507$	156985.	0.0271231
$508$	−5.41242e6	−0.930535
$509$	1.03050e7	1.76300	0.881501	−	0.472183i	$-0.156534\pi$
$509$	1.03050e7	1.76300	0.881501	+	0.472183i	$0.156534\pi$
$510$	211081.	0.0359354
$511$	−1.35636e6	−0.229786
$512$	−3.32417e6	−0.560413
$513$	−229598.	−0.0385189
$514$	5.60337e6	0.935495
$515$	199265.	0.0331065
$516$	669923.	0.110764
$517$	2.90225e6	0.477539
$518$	−658809.	−0.107879
$519$	−446539.	−0.0727682
$520$	−2.80606e6	−0.455080
$521$	−8.51590e6	−1.37447	−0.687236	−	0.726434i	$-0.741176\pi$
$521$	−8.51590e6	−1.37447	−0.687236	+	0.726434i	$0.741176\pi$
$522$	−4.35976e6	−0.700303
$523$	−1.87239e6	−0.299324	−0.149662	−	0.988737i	$-0.547819\pi$
$523$	−1.87239e6	−0.299324	−0.149662	+	0.988737i	$0.547819\pi$
$524$	5.86934e6	0.933815
$525$	−86155.6	−0.0136422
$526$	3.33329e6	0.525302
$527$	1.74467e7	2.73645
$528$	47532.9	0.00742010
$529$	−4.58568e6	−0.712466
$530$	272784.	0.0421821
$531$	6.86073e6	1.05593
$532$	899475.	0.137788
$533$	−2.99650e6	−0.456874
$534$	342435.	0.0519667
$535$	330739.	0.0499575
$536$	−9.71326e6	−1.46034
$537$	−609581.	−0.0912212
$538$	−1.40119e6	−0.208709
$539$	−700564.	−0.103867
$540$	377438.	0.0557008
$541$	9.74053e6	1.43083	0.715417	−	0.698697i	$-0.246237\pi$
$541$	9.74053e6	1.43083	0.715417	+	0.698697i	$0.246237\pi$
$542$	−3.67090e6	−0.536753
$543$	888136.	0.129265
$544$	1.33898e7	1.93989
$545$	−2.19115e6	−0.315995
$546$	−277593.	−0.0398498
$547$	−2.64055e6	−0.377334	−0.188667	−	0.982041i	$-0.560417\pi$
$547$	−2.64055e6	−0.377334	−0.188667	+	0.982041i	$0.560417\pi$
$548$	3.90999e6	0.556191
$549$	−7.57186e6	−1.07219
$550$	−217373.	−0.0306407
$551$	−2.26943e6	−0.318448
$552$	286236.	0.0399831
$553$	8.86633e6	1.23291
$554$	1.27655e6	0.176711
$555$	−71695.5	−0.00988005
$556$	119942.	0.0164545
$557$	5.79305e6	0.791169	0.395584	−	0.918430i	$-0.370542\pi$
$557$	5.79305e6	0.791169	0.395584	+	0.918430i	$0.370542\pi$
$558$	−5.40962e6	−0.735497
$559$	1.50548e7	2.03773
$560$	−784905.	−0.105766
$561$	−355430.	−0.0476811
$562$	−2.82151e6	−0.376826
$563$	1.33082e7	1.76949	0.884743	−	0.466080i	$-0.154334\pi$
$563$	1.33082e7	1.76949	0.884743	+	0.466080i	$0.154334\pi$
$564$	−747762.	−0.0989841
$565$	−6.23583e6	−0.821813
$566$	−4.82724e6	−0.633371
$567$	−6.06629e6	−0.792439
$568$	−6.41313e6	−0.834063
$569$	−8.64789e6	−1.11977	−0.559886	−	0.828570i	$-0.689155\pi$
$569$	−8.64789e6	−1.11977	−0.559886	+	0.828570i	$0.689155\pi$
$570$	−34068.6	−0.00439205
$571$	−2.37797e6	−0.305222	−0.152611	−	0.988286i	$-0.548768\pi$
$571$	−2.37797e6	−0.305222	−0.152611	+	0.988286i	$0.548768\pi$
$572$	2.01231e6	0.257161
$573$	364219.	0.0463421
$574$	1.29040e6	0.163473
$575$	850245.	0.107244
$576$	−1.84228e6	−0.231366
$577$	−3.15806e6	−0.394894	−0.197447	−	0.980314i	$-0.563265\pi$
$577$	−3.15806e6	−0.394894	−0.197447	+	0.980314i	$0.563265\pi$
$578$	−1.02982e7	−1.28216
$579$	930418.	0.115340
$580$	3.73075e6	0.460496
$581$	−8.85864e6	−1.08875
$582$	266824.	0.0326526
$583$	−459329.	−0.0559696
$584$	2.07029e6	0.251188
$585$	4.22588e6	0.510537
$586$	8.01474e6	0.964152
$587$	1.52974e7	1.83241	0.916207	−	0.400705i	$-0.131235\pi$
$587$	1.52974e7	1.83241	0.916207	+	0.400705i	$0.131235\pi$
$588$	180499.	0.0215294
$589$	−2.81593e6	−0.334451
$590$	2.04332e6	0.241661
$591$	1.14012e6	0.134271
$592$	−653168.	−0.0765986
$593$	−1.15903e7	−1.35349	−0.676747	−	0.736216i	$-0.736611\pi$
$593$	−1.15903e7	−1.35349	−0.676747	+	0.736216i	$0.736611\pi$
$594$	221200.	0.0257228
$595$	5.86917e6	0.679648
$596$	−5.62135e6	−0.648224
$597$	−614980.	−0.0706196
$598$	2.73948e6	0.313267
$599$	−3.50010e6	−0.398578	−0.199289	−	0.979941i	$-0.563863\pi$
$599$	−3.50010e6	−0.398578	−0.199289	+	0.979941i	$0.563863\pi$
$600$	131504.	0.0149129
$601$	−5.56103e6	−0.628014	−0.314007	−	0.949421i	$-0.601671\pi$
$601$	−5.56103e6	−0.628014	−0.314007	+	0.949421i	$0.601671\pi$
$602$	−6.48316e6	−0.729114
$603$	1.46280e7	1.63830
$604$	2.29712e6	0.256208
$605$	366025.	0.0406558
$606$	−54383.1	−0.00601564
$607$	−9.35377e6	−1.03042	−0.515211	−	0.857064i	$-0.672286\pi$
$607$	−9.35377e6	−1.03042	−0.515211	+	0.857064i	$0.672286\pi$
$608$	−2.16113e6	−0.237095
$609$	866590.	0.0946827
$610$	−2.25512e6	−0.245383
$611$	−1.68040e7	−1.82100
$612$	−1.28103e7	−1.38255
$613$	6.33257e6	0.680657	0.340329	−	0.940307i	$-0.389462\pi$
$613$	6.33257e6	0.680657	0.340329	+	0.940307i	$0.389462\pi$
$614$	−5.95252e6	−0.637206
$615$	140429.	0.0149717
$616$	−2.03476e6	−0.216054
$617$	−6.83377e6	−0.722683	−0.361341	−	0.932434i	$-0.617681\pi$
$617$	−6.83377e6	−0.722683	−0.361341	+	0.932434i	$0.617681\pi$
$618$	−30088.4	−0.00316904
$619$	−1.15111e7	−1.20751	−0.603756	−	0.797169i	$-0.706330\pi$
$619$	−1.15111e7	−1.20751	−0.603756	+	0.797169i	$0.706330\pi$
$620$	4.62914e6	0.483638
$621$	−865215.	−0.0900316
$622$	6.54318e6	0.678130
$623$	9.52152e6	0.982848
$624$	−275216.	−0.0282951
$625$	390625.	0.0400000
$626$	−6.96479e6	−0.710350
$627$	57366.8	0.00582762
$628$	7.23365e6	0.731911
$629$	4.88410e6	0.492218
$630$	−1.81982e6	−0.182674
$631$	−1.81446e7	−1.81415	−0.907076	−	0.420967i	$-0.861691\pi$
$631$	−1.81446e7	−1.81415	−0.907076	+	0.420967i	$0.861691\pi$
$632$	−1.35332e7	−1.34774
$633$	218260.	0.0216503
$634$	−4.98514e6	−0.492555
$635$	5.70014e6	0.560985
$636$	118346.	0.0116014
$637$	4.05627e6	0.396075
$638$	2.18643e6	0.212659
$639$	9.65807e6	0.935704
$640$	4.24053e6	0.409232
$641$	1.86630e6	0.179406	0.0897029	−	0.995969i	$-0.471408\pi$
$641$	1.86630e6	0.179406	0.0897029	+	0.995969i	$0.471408\pi$
$642$	−49940.4	−0.00478206
$643$	−220809.	−0.0210615	−0.0105308	−	0.999945i	$-0.503352\pi$
$643$	−220809.	−0.0210615	−0.0105308	+	0.999945i	$0.503352\pi$
$644$	3.38958e6	0.322056
$645$	−705535.	−0.0667758
$646$	2.32085e6	0.218810
$647$	−1.81118e7	−1.70098	−0.850492	−	0.525988i	$-0.823696\pi$
$647$	−1.81118e7	−1.70098	−0.850492	+	0.525988i	$0.823696\pi$
$648$	9.25932e6	0.866247
$649$	−3.44067e6	−0.320650
$650$	1.25859e6	0.116842
$651$	1.07527e6	0.0994409
$652$	6.01588e6	0.554217
$653$	−1.34466e7	−1.23404	−0.617021	−	0.786946i	$-0.711661\pi$
$653$	−1.34466e7	−1.23404	−0.617021	+	0.786946i	$0.711661\pi$
$654$	330856.	0.0302479
$655$	−6.18134e6	−0.562963
$656$	1.27936e6	0.116073
$657$	−3.11783e6	−0.281798
$658$	7.23645e6	0.651569
$659$	−230666.	−0.0206905	−0.0103452	−	0.999946i	$-0.503293\pi$
$659$	−230666.	−0.0206905	−0.0103452	+	0.999946i	$0.503293\pi$
$660$	−94306.0	−0.00842712
$661$	−1.66894e7	−1.48572	−0.742861	−	0.669446i	$-0.766532\pi$
$661$	−1.66894e7	−1.48572	−0.742861	+	0.669446i	$0.766532\pi$
$662$	5.09394e6	0.451761
$663$	2.05794e6	0.181823
$664$	1.35214e7	1.19015
$665$	−947291.	−0.0830671
$666$	−1.51439e6	−0.132297
$667$	−8.55213e6	−0.744320
$668$	6.65968e6	0.577447
$669$	1.29902e6	0.112215
$670$	4.35665e6	0.374943
$671$	3.79730e6	0.325588
$672$	825235.	0.0704944
$673$	−1.42207e7	−1.21027	−0.605137	−	0.796121i	$-0.706882\pi$
$673$	−1.42207e7	−1.21027	−0.605137	+	0.796121i	$0.706882\pi$
$674$	−1.55990e6	−0.132265
$675$	−397503.	−0.0335800
$676$	−2.83751e6	−0.238820
$677$	1.25619e7	1.05338	0.526689	−	0.850058i	$-0.323433\pi$
$677$	1.25619e7	1.05338	0.526689	+	0.850058i	$0.323433\pi$
$678$	941589.	0.0786661
$679$	7.41913e6	0.617559
$680$	−8.95844e6	−0.742951
$681$	−1.77102e6	−0.146337
$682$	2.71293e6	0.223346
$683$	−1.17113e7	−0.960625	−0.480312	−	0.877098i	$-0.659477\pi$
$683$	−1.17113e7	−0.960625	−0.480312	+	0.877098i	$0.659477\pi$
$684$	2.06760e6	0.168976
$685$	−4.11784e6	−0.335307
$686$	−6.81746e6	−0.553111
$687$	903246.	0.0730154
$688$	−6.42765e6	−0.517703
$689$	2.65952e6	0.213430
$690$	−128384.	−0.0102657
$691$	1.41951e7	1.13095	0.565476	−	0.824765i	$-0.308692\pi$
$691$	1.41951e7	1.13095	0.565476	+	0.824765i	$0.308692\pi$
$692$	8.07120e6	0.640727
$693$	3.06432e6	0.242382
$694$	−4.04202e6	−0.318566
$695$	−126318.	−0.00991982
$696$	−1.32273e6	−0.103501
$697$	−9.56645e6	−0.745880
$698$	−5.58593e6	−0.433967
$699$	808117.	0.0625578
$700$	1.55726e6	0.120120
$701$	−1.78879e6	−0.137487	−0.0687437	−	0.997634i	$-0.521899\pi$
$701$	−1.78879e6	−0.137487	−0.0687437	+	0.997634i	$0.521899\pi$
$702$	−1.28075e6	−0.0980892
$703$	−788299.	−0.0601593
$704$	923908.	0.0702582
$705$	787512.	0.0596739
$706$	6.39286e6	0.482707
$707$	−1.51214e6	−0.113774
$708$	886485.	0.0664643
$709$	−1.92852e7	−1.44081	−0.720406	−	0.693552i	$-0.756045\pi$
$709$	−1.92852e7	−1.44081	−0.720406	+	0.693552i	$0.756045\pi$
$710$	2.87646e6	0.214147
$711$	2.03808e7	1.51198
$712$	−1.45332e7	−1.07439
$713$	−1.06115e7	−0.781725
$714$	−886225.	−0.0650577
$715$	−2.11929e6	−0.155033
$716$	1.10182e7	0.803206
$717$	604768.	0.0439330
$718$	−1.18206e7	−0.855712
$719$	−1.24487e7	−0.898053	−0.449027	−	0.893518i	$-0.648229\pi$
$719$	−1.24487e7	−0.898053	−0.449027	+	0.893518i	$0.648229\pi$
$720$	−1.80424e6	−0.129707
$721$	−836619.	−0.0599363
$722$	−374588.	−0.0267431
$723$	−419697.	−0.0298600
$724$	−1.60531e7	−1.13818
$725$	−3.92907e6	−0.277616
$726$	−55268.6	−0.00389168
$727$	−3.54630e6	−0.248851	−0.124426	−	0.992229i	$-0.539709\pi$
$727$	−3.54630e6	−0.248851	−0.124426	+	0.992229i	$0.539709\pi$
$728$	1.17813e7	0.823880
$729$	−1.37414e7	−0.957664
$730$	−928579.	−0.0644929
$731$	4.80631e7	3.32673
$732$	−978371.	−0.0674879
$733$	−2.61383e7	−1.79687	−0.898436	−	0.439104i	$-0.855296\pi$
$733$	−2.61383e7	−1.79687	−0.898436	+	0.439104i	$0.855296\pi$
$734$	7.04675e6	0.482780
$735$	−190095.	−0.0129793
$736$	−8.14401e6	−0.554171
$737$	−7.33598e6	−0.497496
$738$	2.96621e6	0.200476
$739$	−2.73983e7	−1.84549	−0.922747	−	0.385406i	$-0.874061\pi$
$739$	−2.73983e7	−1.84549	−0.922747	+	0.385406i	$0.874061\pi$
$740$	1.29590e6	0.0869943
$741$	−332154.	−0.0222225
$742$	−1.14529e6	−0.0763668
$743$	2.04331e7	1.35788	0.678942	−	0.734192i	$-0.262439\pi$
$743$	2.04331e7	1.35788	0.678942	+	0.734192i	$0.262439\pi$
$744$	−1.64125e6	−0.108703
$745$	5.92018e6	0.390790
$746$	−2.54658e6	−0.167537
$747$	−2.03631e7	−1.33519
$748$	6.42439e6	0.419834
$749$	−1.38861e6	−0.0904433
$750$	−58983.1	−0.00382890
$751$	−1.21680e7	−0.787259	−0.393630	−	0.919269i	$-0.628781\pi$
$751$	−1.21680e7	−0.787259	−0.393630	+	0.919269i	$0.628781\pi$
$752$	7.17449e6	0.462643
$753$	535410.	0.0344111
$754$	−1.26594e7	−0.810934
$755$	−2.41924e6	−0.154458
$756$	−1.58468e6	−0.100841
$757$	−291153.	−0.0184664	−0.00923320	−	0.999957i	$-0.502939\pi$
$757$	−291153.	−0.0184664	−0.00923320	+	0.999957i	$0.502939\pi$
$758$	1.13921e7	0.720164
$759$	216181.	0.0136211
$760$	1.44590e6	0.0908041
$761$	−1.47077e7	−0.920625	−0.460312	−	0.887757i	$-0.652263\pi$
$761$	−1.47077e7	−0.920625	−0.460312	+	0.887757i	$0.652263\pi$
$762$	−860703.	−0.0536990
$763$	9.19958e6	0.572080
$764$	−6.58326e6	−0.408045
$765$	1.34913e7	0.833489
$766$	−1.03041e7	−0.634510
$767$	1.99215e7	1.22274
$768$	−961199.	−0.0588045
$769$	−4.46035e6	−0.271990	−0.135995	−	0.990710i	$-0.543423\pi$
$769$	−4.46035e6	−0.271990	−0.135995	+	0.990710i	$0.543423\pi$
$770$	912644.	0.0554721
$771$	−2.56022e6	−0.155110
$772$	−1.68173e7	−1.01558
$773$	−1.96218e7	−1.18111	−0.590553	−	0.806999i	$-0.701090\pi$
$773$	−1.96218e7	−1.18111	−0.590553	+	0.806999i	$0.701090\pi$
$774$	−1.49026e7	−0.894151
$775$	−4.87522e6	−0.291568
$776$	−1.13242e7	−0.675079
$777$	301015.	0.0178869
$778$	−166222.	−0.00984555
$779$	1.54404e6	0.0911620
$780$	546032.	0.0321352
$781$	−4.84354e6	−0.284142
$782$	8.74590e6	0.511432
$783$	3.99825e6	0.233059
$784$	−1.73182e6	−0.100627
$785$	−7.61818e6	−0.441243
$786$	933363.	0.0538882
$787$	−1.43195e7	−0.824124	−0.412062	−	0.911156i	$-0.635191\pi$
$787$	−1.43195e7	−0.824124	−0.412062	+	0.911156i	$0.635191\pi$
$788$	−2.06077e7	−1.18226
$789$	−1.52300e6	−0.0870981
$790$	6.06999e6	0.346035
$791$	2.61812e7	1.48781
$792$	−4.67724e6	−0.264958
$793$	−2.19864e7	−1.24157
$794$	−1.44512e7	−0.813489
$795$	−124637.	−0.00699404
$796$	1.11158e7	0.621809
$797$	−2.82658e7	−1.57622	−0.788108	−	0.615537i	$-0.788939\pi$
$797$	−2.82658e7	−1.57622	−0.788108	+	0.615537i	$0.788939\pi$
$798$	143038.	0.00795140
$799$	−5.36476e7	−2.97292
$800$	−3.74157e6	−0.206695
$801$	2.18868e7	1.20532
$802$	−9.67893e6	−0.531363
$803$	1.56360e6	0.0855728
$804$	1.89011e6	0.103121
$805$	−3.56977e6	−0.194156
$806$	−1.57079e7	−0.851688
$807$	640212.	0.0346051
$808$	2.30807e6	0.124371
$809$	3.15687e7	1.69584	0.847921	−	0.530122i	$-0.177854\pi$
$809$	3.15687e7	1.69584	0.847921	+	0.530122i	$0.177854\pi$
$810$	−4.15305e6	−0.222410
$811$	−1.93982e7	−1.03564	−0.517822	−	0.855488i	$-0.673257\pi$
$811$	−1.93982e7	−1.03564	−0.517822	+	0.855488i	$0.673257\pi$
$812$	−1.56636e7	−0.833685
$813$	1.67726e6	0.0889967
$814$	759467.	0.0401743
$815$	−6.33568e6	−0.334117
$816$	−878637.	−0.0461938
$817$	−7.75743e6	−0.406596
$818$	5.04793e6	0.263773
$819$	−1.77424e7	−0.924279
$820$	−2.53826e6	−0.131826
$821$	−3.61407e7	−1.87128	−0.935641	−	0.352953i	$-0.885177\pi$
$821$	−3.61407e7	−1.87128	−0.935641	+	0.352953i	$0.885177\pi$
$822$	621780.	0.0320965
$823$	1.62382e7	0.835677	0.417839	−	0.908521i	$-0.362788\pi$
$823$	1.62382e7	0.835677	0.417839	+	0.908521i	$0.362788\pi$
$824$	1.27698e6	0.0655188
$825$	99319.2	0.00508040
$826$	−8.57893e6	−0.437505
$827$	−9.55771e6	−0.485948	−0.242974	−	0.970033i	$-0.578123\pi$
$827$	−9.55771e6	−0.485948	−0.242974	+	0.970033i	$0.578123\pi$
$828$	7.79153e6	0.394954
$829$	1.47823e7	0.747058	0.373529	−	0.927618i	$-0.378148\pi$
$829$	1.47823e7	0.747058	0.373529	+	0.927618i	$0.378148\pi$
$830$	−6.06472e6	−0.305573
$831$	−583266.	−0.0292998
$832$	−5.34943e6	−0.267916
$833$	1.29498e7	0.646622
$834$	19073.6	0.000949551 0
$835$	−7.01370e6	−0.348121
$836$	−1.03690e6	−0.0513125
$837$	4.96105e6	0.244771
$838$	1.24717e7	0.613500
$839$	5.08927e6	0.249603	0.124802	−	0.992182i	$-0.460171\pi$
$839$	5.08927e6	0.249603	0.124802	+	0.992182i	$0.460171\pi$
$840$	−552123.	−0.0269984
$841$	1.90091e7	0.926770
$842$	−4.09326e6	−0.198971
$843$	1.28917e6	0.0624799
$844$	−3.94505e6	−0.190632
$845$	2.98835e6	0.143976
$846$	1.66342e7	0.799054
$847$	−1.53676e6	−0.0736035
$848$	−1.13548e6	−0.0542238
$849$	2.20560e6	0.105017
$850$	4.01810e6	0.190754
$851$	−2.97063e6	−0.140613
$852$	1.24793e6	0.0588969
$853$	−4.14507e6	−0.195056	−0.0975281	−	0.995233i	$-0.531094\pi$
$853$	−4.14507e6	−0.195056	−0.0975281	+	0.995233i	$0.531094\pi$
$854$	9.46816e6	0.444243
$855$	−2.17751e6	−0.101870
$856$	2.11952e6	0.0988673
$857$	−9.73809e6	−0.452920	−0.226460	−	0.974020i	$-0.572715\pi$
$857$	−9.73809e6	−0.452920	−0.226460	+	0.974020i	$0.572715\pi$
$858$	320005.	0.0148402
$859$	−1.06094e7	−0.490576	−0.245288	−	0.969450i	$-0.578883\pi$
$859$	−1.06094e7	−0.490576	−0.245288	+	0.969450i	$0.578883\pi$
$860$	1.27525e7	0.587964
$861$	−589595.	−0.0271048
$862$	1.42899e7	0.655030
$863$	7.03410e6	0.321500	0.160750	−	0.986995i	$-0.448609\pi$
$863$	7.03410e6	0.321500	0.160750	+	0.986995i	$0.448609\pi$
$864$	3.80745e6	0.173520
$865$	−8.50026e6	−0.386271
$866$	−4.63067e6	−0.209821
$867$	4.70534e6	0.212590
$868$	−1.94355e7	−0.875582
$869$	−1.02210e7	−0.459139
$870$	593277.	0.0265742
$871$	4.24754e7	1.89711
$872$	−1.40418e7	−0.625364
$873$	1.70541e7	0.757346
$874$	−1.41160e6	−0.0625076
$875$	−1.64005e6	−0.0724162
$876$	−402859.	−0.0177375
$877$	1.11289e7	0.488600	0.244300	−	0.969700i	$-0.421442\pi$
$877$	1.11289e7	0.488600	0.244300	+	0.969700i	$0.421442\pi$
$878$	−7.42193e6	−0.324923
$879$	−3.66199e6	−0.159862
$880$	904829.	0.0393876
$881$	1.04157e7	0.452116	0.226058	−	0.974114i	$-0.427416\pi$
$881$	1.04157e7	0.452116	0.226058	+	0.974114i	$0.427416\pi$
$882$	−4.01527e6	−0.173797
$883$	2.79619e7	1.20688	0.603441	−	0.797408i	$-0.293796\pi$
$883$	2.79619e7	1.20688	0.603441	+	0.797408i	$0.293796\pi$
$884$	−3.71973e7	−1.60096
$885$	−933609.	−0.0400689
$886$	−5.87780e6	−0.251554
$887$	−2.99268e7	−1.27718	−0.638588	−	0.769549i	$-0.720481\pi$
$887$	−2.99268e7	−1.27718	−0.638588	+	0.769549i	$0.720481\pi$
$888$	−459456.	−0.0195529
$889$	−2.39322e7	−1.01561
$890$	6.51854e6	0.275851
$891$	6.99315e6	0.295106
$892$	−2.34799e7	−0.988061
$893$	8.65878e6	0.363352
$894$	−893927.	−0.0374075
$895$	−1.16039e7	−0.484224
$896$	−1.78039e7	−0.740877
$897$	−1.25169e6	−0.0519415
$898$	−1.14785e7	−0.474999
$899$	4.90370e7	2.02360
$900$	3.57964e6	0.147310
$901$	8.49061e6	0.348439
$902$	−1.48756e6	−0.0608778
$903$	2.96220e6	0.120891
$904$	−3.99619e7	−1.62639
$905$	1.69064e7	0.686168
$906$	365297.	0.0147851
$907$	−4.52998e7	−1.82843	−0.914214	−	0.405232i	$-0.867191\pi$
$907$	−4.52998e7	−1.82843	−0.914214	+	0.405232i	$0.867191\pi$
$908$	3.20112e7	1.28851
$909$	−3.47591e6	−0.139527
$910$	−5.28421e6	−0.211532
$911$	2.98447e6	0.119144	0.0595719	−	0.998224i	$-0.481026\pi$
$911$	2.98447e6	0.119144	0.0595719	+	0.998224i	$0.481026\pi$
$912$	141813.	0.00564585
$913$	1.02121e7	0.405452
$914$	−5.93429e6	−0.234965
$915$	1.03038e6	0.0406860
$916$	−1.63262e7	−0.642903
$917$	2.59525e7	1.01919
$918$	−4.08884e6	−0.160138
$919$	3.82805e7	1.49516	0.747581	−	0.664170i	$-0.231215\pi$
$919$	3.82805e7	1.49516	0.747581	+	0.664170i	$0.231215\pi$
$920$	5.44874e6	0.212240
$921$	2.71975e6	0.105653
$922$	−1.88073e6	−0.0728616
$923$	2.80441e7	1.08352
$924$	395945.	0.0152565
$925$	−1.36478e6	−0.0524457
$926$	−1.47832e7	−0.566554
$927$	−1.92311e6	−0.0735030
$928$	3.76343e7	1.43454
$929$	−5.75878e6	−0.218923	−0.109462	−	0.993991i	$-0.534913\pi$
$929$	−5.75878e6	−0.218923	−0.109462	+	0.993991i	$0.534913\pi$
$930$	736142.	0.0279096
$931$	−2.09011e6	−0.0790306
$932$	−1.46067e7	−0.550824
$933$	−2.98963e6	−0.112438
$934$	−1.49988e7	−0.562587
$935$	−6.76591e6	−0.253103
$936$	2.70813e7	1.01037
$937$	3.21817e7	1.19746	0.598729	−	0.800952i	$-0.295673\pi$
$937$	3.21817e7	1.19746	0.598729	+	0.800952i	$0.295673\pi$
$938$	−1.82915e7	−0.678799
$939$	3.18226e6	0.117780
$940$	−1.42343e7	−0.525431
$941$	−1.96559e7	−0.723633	−0.361817	−	0.932249i	$-0.617843\pi$
$941$	−1.96559e7	−0.723633	−0.361817	+	0.932249i	$0.617843\pi$
$942$	1.15032e6	0.0422369
$943$	5.81854e6	0.213076
$944$	−8.50548e6	−0.310648
$945$	1.66892e6	0.0607934
$946$	7.47371e6	0.271524
$947$	2.60124e7	0.942551	0.471276	−	0.881986i	$-0.343794\pi$
$947$	2.60124e7	0.942551	0.471276	+	0.881986i	$0.343794\pi$
$948$	2.63343e6	0.0951702
$949$	−9.05323e6	−0.326316
$950$	−648525.	−0.0233141
$951$	2.27775e6	0.0816684
$952$	3.76122e7	1.34504
$953$	2.99498e7	1.06822	0.534112	−	0.845414i	$-0.320646\pi$
$953$	2.99498e7	1.06822	0.534112	+	0.845414i	$0.320646\pi$
$954$	−2.63264e6	−0.0936527
$955$	6.93322e6	0.245995
$956$	−1.09312e7	−0.386832
$957$	−998994.	−0.0352601
$958$	1.93694e7	0.681872
$959$	1.72888e7	0.607042
$960$	250698.	0.00877956
$961$	3.22163e7	1.12530
$962$	−4.39732e6	−0.153197
$963$	−3.19196e6	−0.110915
$964$	7.58603e6	0.262919
$965$	1.77113e7	0.612254
$966$	539023.	0.0185851
$967$	3.41109e7	1.17308	0.586539	−	0.809921i	$-0.300490\pi$
$967$	3.41109e7	1.17308	0.586539	+	0.809921i	$0.300490\pi$
$968$	2.34565e6	0.0804590
$969$	−1.06041e6	−0.0362799
$970$	5.07922e6	0.173328
$971$	−2.60768e7	−0.887577	−0.443788	−	0.896132i	$-0.646366\pi$
$971$	−2.60768e7	−0.887577	−0.443788	+	0.896132i	$0.646366\pi$
$972$	−5.47048e6	−0.185720
$973$	530349.	0.0179589
$974$	7.08897e6	0.239434
$975$	−575058.	−0.0193732
$976$	9.38709e6	0.315432
$977$	2.73280e7	0.915948	0.457974	−	0.888966i	$-0.348575\pi$
$977$	2.73280e7	0.915948	0.457974	+	0.888966i	$0.348575\pi$
$978$	956667.	0.0319826
$979$	−1.09763e7	−0.366015
$980$	3.43596e6	0.114283
$981$	2.11468e7	0.701572
$982$	−1.52159e7	−0.503524
$983$	3.42405e7	1.13020	0.565101	−	0.825022i	$-0.308837\pi$
$983$	3.42405e7	1.13020	0.565101	+	0.825022i	$0.308837\pi$
$984$	899932.	0.0296293
$985$	2.17032e7	0.712744
$986$	−4.04157e7	−1.32391
$987$	−3.30638e6	−0.108034
$988$	6.00368e6	0.195670
$989$	−2.92331e7	−0.950352
$990$	2.09787e6	0.0680283
$991$	3.37915e6	0.109301	0.0546504	−	0.998506i	$-0.482596\pi$
$991$	3.37915e6	0.109301	0.0546504	+	0.998506i	$0.482596\pi$
$992$	4.66969e7	1.50664
$993$	−2.32746e6	−0.0749046
$994$	−1.20768e7	−0.387693
$995$	−1.17067e7	−0.374866
$996$	−2.63115e6	−0.0840420
$997$	3.30410e7	1.05273	0.526363	−	0.850260i	$-0.323555\pi$
$997$	3.30410e7	1.05273	0.526363	+	0.850260i	$0.323555\pi$
$998$	1.49047e7	0.473693
$999$	1.38881e6	0.0440281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.h.1.14	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.h.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-2.87435 q^{2} +1.31331 q^{3} -23.7381 q^{4} +25.0000 q^{5} -3.77492 q^{6} -104.963 q^{7} +160.211 q^{8} -241.275 q^{9} +O(q^{10})\)	\(q-2.87435 q^{2} +1.31331 q^{3} -23.7381 q^{4} +25.0000 q^{5} -3.77492 q^{6} -104.963 q^{7} +160.211 q^{8} -241.275 q^{9} -71.8588 q^{10} +121.000 q^{11} -31.1755 q^{12} -700.590 q^{13} +301.700 q^{14} +32.8328 q^{15} +299.117 q^{16} -2236.66 q^{17} +693.510 q^{18} +361.000 q^{19} -593.453 q^{20} -137.849 q^{21} -347.796 q^{22} +1360.39 q^{23} +210.407 q^{24} +625.000 q^{25} +2013.74 q^{26} -636.004 q^{27} +2491.62 q^{28} -6286.52 q^{29} -94.3730 q^{30} -7800.35 q^{31} -5986.52 q^{32} +158.911 q^{33} +6428.96 q^{34} -2624.07 q^{35} +5727.42 q^{36} -2183.65 q^{37} -1037.64 q^{38} -920.093 q^{39} +4005.27 q^{40} +4277.11 q^{41} +396.226 q^{42} -21488.7 q^{43} -2872.31 q^{44} -6031.88 q^{45} -3910.24 q^{46} +23985.5 q^{47} +392.834 q^{48} -5789.78 q^{49} -1796.47 q^{50} -2937.44 q^{51} +16630.7 q^{52} -3796.11 q^{53} +1828.10 q^{54} +3025.00 q^{55} -16816.2 q^{56} +474.105 q^{57} +18069.7 q^{58} -28435.3 q^{59} -779.388 q^{60} +31382.7 q^{61} +22420.9 q^{62} +25325.0 q^{63} +7635.60 q^{64} -17514.8 q^{65} -456.765 q^{66} -60627.9 q^{67} +53094.1 q^{68} +1786.62 q^{69} +7542.51 q^{70} -40029.3 q^{71} -38654.9 q^{72} +12922.3 q^{73} +6276.59 q^{74} +820.820 q^{75} -8569.46 q^{76} -12700.5 q^{77} +2644.67 q^{78} -84471.1 q^{79} +7477.93 q^{80} +57794.6 q^{81} -12293.9 q^{82} +84397.8 q^{83} +3272.27 q^{84} -55916.6 q^{85} +61766.2 q^{86} -8256.15 q^{87} +19385.5 q^{88} -90713.2 q^{89} +17337.7 q^{90} +73536.0 q^{91} -32293.1 q^{92} -10244.3 q^{93} -68942.9 q^{94} +9025.00 q^{95} -7862.16 q^{96} -70683.3 q^{97} +16641.9 q^{98} -29194.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) \) 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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