LMFDB - Embedded newform 1045.6.a.f.1.16

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:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-2.29603 q^{2} -17.4404 q^{3} -26.7283 q^{4} +25.0000 q^{5} +40.0437 q^{6} -42.9271 q^{7} +134.842 q^{8} +61.1692 q^{9} +O(q^{10})$	\(q-2.29603 q^{2} -17.4404 q^{3} -26.7283 q^{4} +25.0000 q^{5} +40.0437 q^{6} -42.9271 q^{7} +134.842 q^{8} +61.1692 q^{9} -57.4007 q^{10} -121.000 q^{11} +466.153 q^{12} +174.640 q^{13} +98.5618 q^{14} -436.011 q^{15} +545.704 q^{16} -2224.00 q^{17} -140.446 q^{18} -361.000 q^{19} -668.206 q^{20} +748.668 q^{21} +277.819 q^{22} +406.959 q^{23} -2351.70 q^{24} +625.000 q^{25} -400.978 q^{26} +3171.21 q^{27} +1147.37 q^{28} +4559.01 q^{29} +1001.09 q^{30} -1873.99 q^{31} -5567.89 q^{32} +2110.29 q^{33} +5106.37 q^{34} -1073.18 q^{35} -1634.95 q^{36} -4086.47 q^{37} +828.866 q^{38} -3045.80 q^{39} +3371.04 q^{40} +2913.19 q^{41} -1718.96 q^{42} +20073.8 q^{43} +3234.12 q^{44} +1529.23 q^{45} -934.388 q^{46} +9677.30 q^{47} -9517.32 q^{48} -14964.3 q^{49} -1435.02 q^{50} +38787.6 q^{51} -4667.82 q^{52} -17841.2 q^{53} -7281.19 q^{54} -3025.00 q^{55} -5788.36 q^{56} +6296.00 q^{57} -10467.6 q^{58} -39863.6 q^{59} +11653.8 q^{60} -15442.3 q^{61} +4302.73 q^{62} -2625.81 q^{63} -4678.52 q^{64} +4366.00 q^{65} -4845.29 q^{66} -32587.1 q^{67} +59443.7 q^{68} -7097.54 q^{69} +2464.04 q^{70} -10606.5 q^{71} +8248.15 q^{72} -38969.2 q^{73} +9382.64 q^{74} -10900.3 q^{75} +9648.90 q^{76} +5194.18 q^{77} +6993.24 q^{78} -72120.6 q^{79} +13642.6 q^{80} -70171.4 q^{81} -6688.77 q^{82} -87588.5 q^{83} -20010.6 q^{84} -55600.1 q^{85} -46089.9 q^{86} -79511.2 q^{87} -16315.8 q^{88} +15968.3 q^{89} -3511.15 q^{90} -7496.79 q^{91} -10877.3 q^{92} +32683.2 q^{93} -22219.3 q^{94} -9025.00 q^{95} +97106.4 q^{96} +52926.3 q^{97} +34358.4 q^{98} -7401.47 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) $ 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9} + 200 q^{10} - 4598 q^{11} + 2312 q^{12} + 41 q^{13} + 23 q^{14} + 1575 q^{15} + 7196 q^{16} - 2431 q^{17} - 1689 q^{18} - 13718 q^{19} + 15400 q^{20} - 1577 q^{21} - 968 q^{22} + 9284 q^{23} + 7598 q^{24} + 23750 q^{25} + 13129 q^{26} + 9228 q^{27} - 1079 q^{28} - 559 q^{29} + 3725 q^{30} + 11147 q^{31} + 11051 q^{32} - 7623 q^{33} + 40895 q^{34} + 6875 q^{35} + 55887 q^{36} + 41579 q^{37} - 2888 q^{38} + 24982 q^{39} + 6600 q^{40} + 18597 q^{41} + 61360 q^{42} + 25353 q^{43} - 74536 q^{44} + 75725 q^{45} + 1611 q^{46} + 63516 q^{47} + 187737 q^{48} + 141609 q^{49} + 5000 q^{50} + 107546 q^{51} + 60018 q^{52} + 123045 q^{53} + 256696 q^{54} - 114950 q^{55} + 157335 q^{56} - 22743 q^{57} + 218938 q^{58} + 132925 q^{59} + 57800 q^{60} - 59107 q^{61} + 166982 q^{62} + 130582 q^{63} + 313126 q^{64} + 1025 q^{65} - 18029 q^{66} + 162534 q^{67} + 182980 q^{68} + 178552 q^{69} + 575 q^{70} + 157840 q^{71} + 98630 q^{72} - 63010 q^{73} + 122683 q^{74} + 39375 q^{75} - 222376 q^{76} - 33275 q^{77} + 277272 q^{78} - 16385 q^{79} + 179900 q^{80} + 290354 q^{81} + 362302 q^{82} + 138461 q^{83} + 446870 q^{84} - 60775 q^{85} + 643902 q^{86} + 291602 q^{87} - 31944 q^{88} + 224792 q^{89} - 42225 q^{90} + 498548 q^{91} + 581088 q^{92} + 134210 q^{93} + 35864 q^{94} - 342950 q^{95} + 377376 q^{96} + 292216 q^{97} - 58230 q^{98} - 366509 q^{99}+O(q^{100}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9 + 200 * q^10 - 4598 * q^11 + 2312 * q^12 + 41 * q^13 + 23 * q^14 + 1575 * q^15 + 7196 * q^16 - 2431 * q^17 - 1689 * q^18 - 13718 * q^19 + 15400 * q^20 - 1577 * q^21 - 968 * q^22 + 9284 * q^23 + 7598 * q^24 + 23750 * q^25 + 13129 * q^26 + 9228 * q^27 - 1079 * q^28 - 559 * q^29 + 3725 * q^30 + 11147 * q^31 + 11051 * q^32 - 7623 * q^33 + 40895 * q^34 + 6875 * q^35 + 55887 * q^36 + 41579 * q^37 - 2888 * q^38 + 24982 * q^39 + 6600 * q^40 + 18597 * q^41 + 61360 * q^42 + 25353 * q^43 - 74536 * q^44 + 75725 * q^45 + 1611 * q^46 + 63516 * q^47 + 187737 * q^48 + 141609 * q^49 + 5000 * q^50 + 107546 * q^51 + 60018 * q^52 + 123045 * q^53 + 256696 * q^54 - 114950 * q^55 + 157335 * q^56 - 22743 * q^57 + 218938 * q^58 + 132925 * q^59 + 57800 * q^60 - 59107 * q^61 + 166982 * q^62 + 130582 * q^63 + 313126 * q^64 + 1025 * q^65 - 18029 * q^66 + 162534 * q^67 + 182980 * q^68 + 178552 * q^69 + 575 * q^70 + 157840 * q^71 + 98630 * q^72 - 63010 * q^73 + 122683 * q^74 + 39375 * q^75 - 222376 * q^76 - 33275 * q^77 + 277272 * q^78 - 16385 * q^79 + 179900 * q^80 + 290354 * q^81 + 362302 * q^82 + 138461 * q^83 + 446870 * q^84 - 60775 * q^85 + 643902 * q^86 + 291602 * q^87 - 31944 * q^88 + 224792 * q^89 - 42225 * q^90 + 498548 * q^91 + 581088 * q^92 + 134210 * q^93 + 35864 * q^94 - 342950 * q^95 + 377376 * q^96 + 292216 * q^97 - 58230 * q^98 - 366509 * 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 $

$2$	−2.29603	−0.405884	−0.202942	−	0.979191i	$-0.565050\pi$
$2$	−2.29603	−0.405884	−0.202942	+	0.979191i	$0.565050\pi$
$3$	−17.4404	−1.11881	−0.559403	−	0.828896i	$-0.688969\pi$
$3$	−17.4404	−1.11881	−0.559403	+	0.828896i	$0.688969\pi$
$4$	−26.7283	−0.835258
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	40.0437	0.454105
$7$	−42.9271	−0.331121	−0.165560	−	0.986200i	$-0.552943\pi$
$7$	−42.9271	−0.331121	−0.165560	+	0.986200i	$0.552943\pi$
$8$	134.842	0.744902
$9$	61.1692	0.251725
$10$	−57.4007	−0.181517
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	466.153	0.934491
$13$	174.640	0.286606	0.143303	−	0.989679i	$-0.454228\pi$
$13$	174.640	0.286606	0.143303	+	0.989679i	$0.454228\pi$
$14$	98.5618	0.134397
$15$	−436.011	−0.500345
$16$	545.704	0.532914
$17$	−2224.00	−1.86644	−0.933218	−	0.359310i	$-0.883012\pi$
$17$	−2224.00	−1.86644	−0.933218	+	0.359310i	$0.883012\pi$
$18$	−140.446	−0.102171
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−668.206	−0.373539
$21$	748.668	0.370460
$22$	277.819	0.122379
$23$	406.959	0.160410	0.0802048	−	0.996778i	$-0.474443\pi$
$23$	406.959	0.160410	0.0802048	+	0.996778i	$0.474443\pi$
$24$	−2351.70	−0.833400
$25$	625.000	0.200000
$26$	−400.978	−0.116329
$27$	3171.21	0.837174
$28$	1147.37	0.276571
$29$	4559.01	1.00664	0.503322	−	0.864099i	$-0.332111\pi$
$29$	4559.01	1.00664	0.503322	+	0.864099i	$0.332111\pi$
$30$	1001.09	0.203082
$31$	−1873.99	−0.350238	−0.175119	−	0.984547i	$-0.556031\pi$
$31$	−1873.99	−0.350238	−0.175119	+	0.984547i	$0.556031\pi$
$32$	−5567.89	−0.961203
$33$	2110.29	0.337332
$34$	5106.37	0.757557
$35$	−1073.18	−0.148082
$36$	−1634.95	−0.210255
$37$	−4086.47	−0.490731	−0.245366	−	0.969431i	$-0.578908\pi$
$37$	−4086.47	−0.490731	−0.245366	+	0.969431i	$0.578908\pi$
$38$	828.866	0.0931162
$39$	−3045.80	−0.320656
$40$	3371.04	0.333130
$41$	2913.19	0.270651	0.135325	−	0.990801i	$-0.456792\pi$
$41$	2913.19	0.270651	0.135325	+	0.990801i	$0.456792\pi$
$42$	−1718.96	−0.150364
$43$	20073.8	1.65561	0.827805	−	0.561016i	$-0.189589\pi$
$43$	20073.8	1.65561	0.827805	+	0.561016i	$0.189589\pi$
$44$	3234.12	0.251840
$45$	1529.23	0.112575
$46$	−934.388	−0.0651077
$47$	9677.30	0.639013	0.319506	−	0.947584i	$-0.396483\pi$
$47$	9677.30	0.639013	0.319506	+	0.947584i	$0.396483\pi$
$48$	−9517.32	−0.596227
$49$	−14964.3	−0.890359
$50$	−1435.02	−0.0811768
$51$	38787.6	2.08818
$52$	−4667.82	−0.239390
$53$	−17841.2	−0.872437	−0.436219	−	0.899841i	$-0.643683\pi$
$53$	−17841.2	−0.872437	−0.436219	+	0.899841i	$0.643683\pi$
$54$	−7281.19	−0.339796
$55$	−3025.00	−0.134840
$56$	−5788.36	−0.246653
$57$	6296.00	0.256672
$58$	−10467.6	−0.408580
$59$	−39863.6	−1.49089	−0.745446	−	0.666566i	$-0.767764\pi$
$59$	−39863.6	−1.49089	−0.745446	+	0.666566i	$0.767764\pi$
$60$	11653.8	0.417917
$61$	−15442.3	−0.531360	−0.265680	−	0.964061i	$-0.585596\pi$
$61$	−15442.3	−0.531360	−0.265680	+	0.964061i	$0.585596\pi$
$62$	4302.73	0.142156
$63$	−2625.81	−0.0833514
$64$	−4678.52	−0.142777
$65$	4366.00	0.128174
$66$	−4845.29	−0.136918
$67$	−32587.1	−0.886867	−0.443433	−	0.896307i	$-0.646240\pi$
$67$	−32587.1	−0.886867	−0.443433	+	0.896307i	$0.646240\pi$
$68$	59443.7	1.55896
$69$	−7097.54	−0.179467
$70$	2464.04	0.0601040
$71$	−10606.5	−0.249703	−0.124852	−	0.992175i	$-0.539845\pi$
$71$	−10606.5	−0.249703	−0.124852	+	0.992175i	$0.539845\pi$
$72$	8248.15	0.187510
$73$	−38969.2	−0.855884	−0.427942	−	0.903806i	$-0.640761\pi$
$73$	−38969.2	−0.855884	−0.427942	+	0.903806i	$0.640761\pi$
$74$	9382.64	0.199180
$75$	−10900.3	−0.223761
$76$	9648.90	0.191621
$77$	5194.18	0.0998367
$78$	6993.24	0.130149
$79$	−72120.6	−1.30014	−0.650072	−	0.759872i	$-0.725261\pi$
$79$	−72120.6	−1.30014	−0.650072	+	0.759872i	$0.725261\pi$
$80$	13642.6	0.238326
$81$	−70171.4	−1.18836
$82$	−6688.77	−0.109853
$83$	−87588.5	−1.39557	−0.697786	−	0.716307i	$-0.745831\pi$
$83$	−87588.5	−1.39557	−0.697786	+	0.716307i	$0.745831\pi$
$84$	−20010.6	−0.309429
$85$	−55600.1	−0.834696
$86$	−46089.9	−0.671986
$87$	−79511.2	−1.12624
$88$	−16315.8	−0.224596
$89$	15968.3	0.213689	0.106845	−	0.994276i	$-0.465925\pi$
$89$	15968.3	0.213689	0.106845	+	0.994276i	$0.465925\pi$
$90$	−3511.15	−0.0456923
$91$	−7496.79	−0.0949012
$92$	−10877.3	−0.133983
$93$	32683.2	0.391848
$94$	−22219.3	−0.259365
$95$	−9025.00	−0.102598
$96$	97106.4	1.07540
$97$	52926.3	0.571140	0.285570	−	0.958358i	$-0.407817\pi$
$97$	52926.3	0.571140	0.285570	+	0.958358i	$0.407817\pi$
$98$	34358.4	0.361383
$99$	−7401.47	−0.0758979
$100$	−16705.2	−0.167052
$101$	−30320.7	−0.295757	−0.147879	−	0.989005i	$-0.547245\pi$
$101$	−30320.7	−0.295757	−0.147879	+	0.989005i	$0.547245\pi$
$102$	−89057.4	−0.847558
$103$	−99316.7	−0.922421	−0.461211	−	0.887291i	$-0.652585\pi$
$103$	−99316.7	−0.922421	−0.461211	+	0.887291i	$0.652585\pi$
$104$	23548.8	0.213493
$105$	18716.7	0.165675
$106$	40963.8	0.354108
$107$	−6342.60	−0.0535559	−0.0267780	−	0.999641i	$-0.508525\pi$
$107$	−6342.60	−0.0535559	−0.0267780	+	0.999641i	$0.508525\pi$
$108$	−84760.9	−0.699256
$109$	120793.	0.973814	0.486907	−	0.873454i	$-0.338125\pi$
$109$	120793.	0.973814	0.486907	+	0.873454i	$0.338125\pi$
$110$	6945.48	0.0547294
$111$	71269.8	0.549032
$112$	−23425.5	−0.176459
$113$	177711.	1.30923	0.654617	−	0.755961i	$-0.272830\pi$
$113$	177711.	1.30923	0.654617	+	0.755961i	$0.272830\pi$
$114$	−14455.8	−0.104179
$115$	10174.0	0.0717374
$116$	−121854.	−0.840807
$117$	10682.6	0.0721459
$118$	91527.9	0.605129
$119$	95470.0	0.618016
$120$	−58792.5	−0.372708
$121$	14641.0	0.0909091
$122$	35456.0	0.215670
$123$	−50807.4	−0.302806
$124$	50088.5	0.292539
$125$	15625.0	0.0894427
$126$	6028.94	0.0338310
$127$	−296934.	−1.63362	−0.816810	−	0.576907i	$-0.804260\pi$
$127$	−296934.	−1.63362	−0.816810	+	0.576907i	$0.804260\pi$
$128$	188914.	1.01915
$129$	−350096.	−1.85231
$130$	−10024.5	−0.0520238
$131$	−30821.8	−0.156921	−0.0784603	−	0.996917i	$-0.525000\pi$
$131$	−30821.8	−0.156921	−0.0784603	+	0.996917i	$0.525000\pi$
$132$	−56404.5	−0.281760
$133$	15496.7	0.0759643
$134$	74820.8	0.359965
$135$	79280.3	0.374396
$136$	−299888.	−1.39031
$137$	−329096.	−1.49803	−0.749016	−	0.662552i	$-0.769473\pi$
$137$	−329096.	−1.49803	−0.749016	+	0.662552i	$0.769473\pi$
$138$	16296.1	0.0728429
$139$	−309288.	−1.35777	−0.678886	−	0.734244i	$-0.737537\pi$
$139$	−309288.	−1.35777	−0.678886	+	0.734244i	$0.737537\pi$
$140$	28684.2	0.123686
$141$	−168776.	−0.714931
$142$	24352.7	0.101351
$143$	−21131.4	−0.0864150
$144$	33380.3	0.134148
$145$	113975.	0.450184
$146$	89474.4	0.347390
$147$	260983.	0.996138
$148$	109224.	0.409887
$149$	217491.	0.802556	0.401278	−	0.915956i	$-0.368566\pi$
$149$	217491.	0.802556	0.401278	+	0.915956i	$0.368566\pi$
$150$	25027.3	0.0908210
$151$	−231520.	−0.826318	−0.413159	−	0.910659i	$-0.635575\pi$
$151$	−231520.	−0.826318	−0.413159	+	0.910659i	$0.635575\pi$
$152$	−48677.8	−0.170892
$153$	−136040.	−0.469829
$154$	−11926.0	−0.0405221
$155$	−46849.7	−0.156631
$156$	81408.9	0.267831
$157$	394814.	1.27833	0.639166	−	0.769069i	$-0.279280\pi$
$157$	394814.	1.27833	0.639166	+	0.769069i	$0.279280\pi$
$158$	165591.	0.527708
$159$	311158.	0.976087
$160$	−139197.	−0.429863
$161$	−17469.5	−0.0531150
$162$	161116.	0.482336
$163$	−454517.	−1.33993	−0.669963	−	0.742394i	$-0.733690\pi$
$163$	−454517.	−1.33993	−0.669963	+	0.742394i	$0.733690\pi$
$164$	−77864.5	−0.226063
$165$	52757.4	0.150860
$166$	201106.	0.566440
$167$	−342372.	−0.949963	−0.474981	−	0.879996i	$-0.657545\pi$
$167$	−342372.	−0.949963	−0.474981	+	0.879996i	$0.657545\pi$
$168$	100952.	0.275956
$169$	−340794.	−0.917857
$170$	127659.	0.338790
$171$	−22082.1	−0.0577497
$172$	−536537.	−1.38286
$173$	−455036.	−1.15593	−0.577964	−	0.816062i	$-0.696152\pi$
$173$	−455036.	−1.15593	−0.577964	+	0.816062i	$0.696152\pi$
$174$	182560.	0.457122
$175$	−26829.4	−0.0662241
$176$	−66030.2	−0.160680
$177$	695239.	1.66802
$178$	−36663.6	−0.0867331
$179$	−162827.	−0.379833	−0.189917	−	0.981800i	$-0.560822\pi$
$179$	−162827.	−0.379833	−0.189917	+	0.981800i	$0.560822\pi$
$180$	−40873.6	−0.0940290
$181$	540669.	1.22669	0.613345	−	0.789815i	$-0.289823\pi$
$181$	540669.	1.22669	0.613345	+	0.789815i	$0.289823\pi$
$182$	17212.8	0.0385189
$183$	269321.	0.594488
$184$	54875.0	0.119489
$185$	−102162.	−0.219462
$186$	−75041.5	−0.159045
$187$	269104.	0.562752
$188$	−258657.	−0.533740
$189$	−136131.	−0.277206
$190$	20721.6	0.0416428
$191$	724912.	1.43781	0.718906	−	0.695108i	$-0.244643\pi$
$191$	724912.	1.43781	0.718906	+	0.695108i	$0.244643\pi$
$192$	81595.5	0.159740
$193$	879241.	1.69908	0.849542	−	0.527521i	$-0.176878\pi$
$193$	879241.	1.69908	0.849542	+	0.527521i	$0.176878\pi$
$194$	−121520.	−0.231817
$195$	−76145.0	−0.143402
$196$	399969.	0.743680
$197$	−744470.	−1.36673	−0.683363	−	0.730078i	$-0.739484\pi$
$197$	−744470.	−1.36673	−0.683363	+	0.730078i	$0.739484\pi$
$198$	16994.0	0.0308058
$199$	774930.	1.38717	0.693585	−	0.720374i	$-0.256030\pi$
$199$	774930.	1.38717	0.693585	+	0.720374i	$0.256030\pi$
$200$	84276.0	0.148980
$201$	568333.	0.992231
$202$	69617.1	0.120043
$203$	−195705.	−0.333320
$204$	−1.03673e6	−1.74417
$205$	72829.8	0.121039
$206$	228034.	0.374396
$207$	24893.3	0.0403791
$208$	95301.8	0.152736
$209$	43681.0	0.0691714
$210$	−42974.0	−0.0672447
$211$	59653.0	0.0922414	0.0461207	−	0.998936i	$-0.485314\pi$
$211$	59653.0	0.0922414	0.0461207	+	0.998936i	$0.485314\pi$
$212$	476864.	0.728710
$213$	184981.	0.279369
$214$	14562.8	0.0217375
$215$	501845.	0.740411
$216$	427611.	0.623613
$217$	80444.9	0.115971
$218$	−277344.	−0.395256
$219$	679641.	0.957567
$220$	80853.0	0.112626
$221$	−388400.	−0.534932
$222$	−163637.	−0.222844
$223$	−787591.	−1.06057	−0.530284	−	0.847820i	$-0.677915\pi$
$223$	−787591.	−1.06057	−0.530284	+	0.847820i	$0.677915\pi$
$224$	239013.	0.318274
$225$	38230.7	0.0503450
$226$	−408028.	−0.531397
$227$	998577.	1.28622	0.643112	−	0.765772i	$-0.277643\pi$
$227$	998577.	1.28622	0.643112	+	0.765772i	$0.277643\pi$
$228$	−168281.	−0.214387
$229$	−342704.	−0.431847	−0.215924	−	0.976410i	$-0.569276\pi$
$229$	−342704.	−0.431847	−0.215924	+	0.976410i	$0.569276\pi$
$230$	−23359.7	−0.0291171
$231$	−90588.8	−0.111698
$232$	614744.	0.749850
$233$	844500.	1.01908	0.509542	−	0.860446i	$-0.329815\pi$
$233$	844500.	1.01908	0.509542	+	0.860446i	$0.329815\pi$
$234$	−24527.5	−0.0292829
$235$	241932.	0.285775
$236$	1.06548e6	1.24528
$237$	1.25782e6	1.45461
$238$	−219202.	−0.250843
$239$	1.47569e6	1.67110	0.835548	−	0.549418i	$-0.185150\pi$
$239$	1.47569e6	1.67110	0.835548	+	0.549418i	$0.185150\pi$
$240$	−237933.	−0.266641
$241$	−1.46969e6	−1.62998	−0.814991	−	0.579474i	$-0.803258\pi$
$241$	−1.46969e6	−1.62998	−0.814991	+	0.579474i	$0.803258\pi$
$242$	−33616.1	−0.0368986
$243$	453217.	0.492369
$244$	412747.	0.443822
$245$	−374107.	−0.398181
$246$	116655.	0.122904
$247$	−63045.0	−0.0657519
$248$	−252692.	−0.260893
$249$	1.52758e6	1.56137
$250$	−35875.4	−0.0363034
$251$	609537.	0.610683	0.305342	−	0.952243i	$-0.401229\pi$
$251$	609537.	0.610683	0.305342	+	0.952243i	$0.401229\pi$
$252$	70183.5	0.0696199
$253$	−49242.0	−0.0483653
$254$	681769.	0.663060
$255$	969690.	0.933862
$256$	−284040.	−0.270881
$257$	133072.	0.125676	0.0628380	−	0.998024i	$-0.479985\pi$
$257$	133072.	0.125676	0.0628380	+	0.998024i	$0.479985\pi$
$258$	803829.	0.751821
$259$	175420.	0.162491
$260$	−116696.	−0.107058
$261$	278871.	0.253397
$262$	70767.7	0.0636916
$263$	1.21817e6	1.08597	0.542985	−	0.839743i	$-0.317294\pi$
$263$	1.21817e6	1.08597	0.542985	+	0.839743i	$0.317294\pi$
$264$	284556.	0.251280
$265$	−446030.	−0.390166
$266$	−35580.8	−0.0308327
$267$	−278494.	−0.239077
$268$	870996.	0.740763
$269$	−1.68344e6	−1.41846	−0.709230	−	0.704977i	$-0.750957\pi$
$269$	−1.68344e6	−1.41846	−0.709230	+	0.704977i	$0.750957\pi$
$270$	−182030.	−0.151961
$271$	1.41501e6	1.17041	0.585204	−	0.810886i	$-0.301015\pi$
$271$	1.41501e6	1.17041	0.585204	+	0.810886i	$0.301015\pi$
$272$	−1.21365e6	−0.994650
$273$	130747.	0.106176
$274$	755613.	0.608027
$275$	−75625.0	−0.0603023
$276$	189705.	0.149901
$277$	−1.99128e6	−1.55931	−0.779657	−	0.626207i	$-0.784607\pi$
$277$	−1.99128e6	−1.55931	−0.779657	+	0.626207i	$0.784607\pi$
$278$	710135.	0.551098
$279$	−114630.	−0.0881636
$280$	−144709.	−0.110306
$281$	−2.15260e6	−1.62629	−0.813143	−	0.582065i	$-0.802245\pi$
$281$	−2.15260e6	−1.62629	−0.813143	+	0.582065i	$0.802245\pi$
$282$	387515.	0.290179
$283$	889568.	0.660257	0.330129	−	0.943936i	$-0.392908\pi$
$283$	889568.	0.660257	0.330129	+	0.943936i	$0.392908\pi$
$284$	283492.	0.208567
$285$	157400.	0.114787
$286$	48518.4	0.0350745
$287$	−125055.	−0.0896181
$288$	−340583.	−0.241959
$289$	3.52633e6	2.48358
$290$	−261690.	−0.182723
$291$	−923059.	−0.638994
$292$	1.04158e6	0.714884
$293$	1.08247e6	0.736625	0.368312	−	0.929702i	$-0.379936\pi$
$293$	1.08247e6	0.736625	0.368312	+	0.929702i	$0.379936\pi$
$294$	−599225.	−0.404317
$295$	−996590.	−0.666747
$296$	−551026.	−0.365547
$297$	−383717.	−0.252417
$298$	−499365.	−0.325745
$299$	71071.2	0.0459744
$300$	291345.	0.186898
$301$	−861709.	−0.548207
$302$	531577.	0.335389
$303$	528806.	0.330895
$304$	−196999.	−0.122259
$305$	−386059.	−0.237631
$306$	312353.	0.190696
$307$	1.70046e6	1.02972	0.514862	−	0.857273i	$-0.327843\pi$
$307$	1.70046e6	1.02972	0.514862	+	0.857273i	$0.327843\pi$
$308$	−138831.	−0.0833894
$309$	1.73213e6	1.03201
$310$	107568.	0.0635740
$311$	−1.36603e6	−0.800862	−0.400431	−	0.916327i	$-0.631140\pi$
$311$	−1.36603e6	−0.800862	−0.400431	+	0.916327i	$0.631140\pi$
$312$	−410701.	−0.238858
$313$	955703.	0.551394	0.275697	−	0.961245i	$-0.411091\pi$
$313$	955703.	0.551394	0.275697	+	0.961245i	$0.411091\pi$
$314$	−906503.	−0.518854
$315$	−65645.4	−0.0372759
$316$	1.92766e6	1.08596
$317$	−1.90964e6	−1.06734	−0.533670	−	0.845693i	$-0.679188\pi$
$317$	−1.90964e6	−1.06734	−0.533670	+	0.845693i	$0.679188\pi$
$318$	−714428.	−0.396178
$319$	−551640.	−0.303514
$320$	−116963.	−0.0638519
$321$	110618.	0.0599187
$322$	40110.6	0.0215585
$323$	802865.	0.428190
$324$	1.87556e6	0.992587
$325$	109150.	0.0573212
$326$	1.04358e6	0.543855
$327$	−2.10669e6	−1.08951
$328$	392820.	0.201608
$329$	−415418.	−0.211590
$330$	−121132.	−0.0612315
$331$	−3.06110e6	−1.53570	−0.767851	−	0.640628i	$-0.778674\pi$
$331$	−3.06110e6	−1.53570	−0.767851	+	0.640628i	$0.778674\pi$
$332$	2.34109e6	1.16566
$333$	−249966.	−0.123529
$334$	786095.	0.385575
$335$	−814677.	−0.396619
$336$	408551.	0.197423
$337$	−2.76131e6	−1.32447	−0.662233	−	0.749298i	$-0.730391\pi$
$337$	−2.76131e6	−1.32447	−0.662233	+	0.749298i	$0.730391\pi$
$338$	782472.	0.372544
$339$	−3.09935e6	−1.46478
$340$	1.48609e6	0.697186
$341$	226753.	0.105601
$342$	50701.0	0.0234397
$343$	1.36385e6	0.625937
$344$	2.70678e6	1.23327
$345$	−177438.	−0.0802602
$346$	1.04478e6	0.469173
$347$	3.58508e6	1.59836	0.799182	−	0.601089i	$-0.205266\pi$
$347$	3.58508e6	1.59836	0.799182	+	0.601089i	$0.205266\pi$
$348$	2.12519e6	0.940699
$349$	1.94990e6	0.856938	0.428469	−	0.903556i	$-0.359053\pi$
$349$	1.94990e6	0.856938	0.428469	+	0.903556i	$0.359053\pi$
$350$	61601.1	0.0268793
$351$	553820.	0.239939
$352$	673714.	0.289814
$353$	3.77011e6	1.61034	0.805170	−	0.593045i	$-0.202074\pi$
$353$	3.77011e6	1.61034	0.805170	+	0.593045i	$0.202074\pi$
$354$	−1.59629e6	−0.677022
$355$	−265161.	−0.111671
$356$	−426804.	−0.178486
$357$	−1.66504e6	−0.691439
$358$	373855.	0.154168
$359$	−3.63771e6	−1.48968	−0.744839	−	0.667244i	$-0.767474\pi$
$359$	−3.63771e6	−1.48968	−0.744839	+	0.667244i	$0.767474\pi$
$360$	206204.	0.0838572
$361$	130321.	0.0526316
$362$	−1.24139e6	−0.497894
$363$	−255346.	−0.101710
$364$	200376.	0.0792670
$365$	−974231.	−0.382763
$366$	−618369.	−0.241293
$367$	4.70614e6	1.82390	0.911948	−	0.410306i	$-0.134578\pi$
$367$	4.70614e6	1.82390	0.911948	+	0.410306i	$0.134578\pi$
$368$	222079.	0.0854846
$369$	178198.	0.0681296
$370$	234566.	0.0890760
$371$	765870.	0.288882
$372$	−873565.	−0.327294
$373$	5.18798e6	1.93075	0.965375	−	0.260867i	$-0.0840086\pi$
$373$	5.18798e6	1.93075	0.965375	+	0.260867i	$0.0840086\pi$
$374$	−617871.	−0.228412
$375$	−272507.	−0.100069
$376$	1.30490e6	0.476002
$377$	796185.	0.288510
$378$	312560.	0.112513
$379$	4.70570e6	1.68278	0.841388	−	0.540432i	$-0.181739\pi$
$379$	4.70570e6	1.68278	0.841388	+	0.540432i	$0.181739\pi$
$380$	241223.	0.0856957
$381$	5.17867e6	1.82770
$382$	−1.66442e6	−0.583585
$383$	−287468.	−0.100136	−0.0500682	−	0.998746i	$-0.515944\pi$
$383$	−287468.	−0.100136	−0.0500682	+	0.998746i	$0.515944\pi$
$384$	−3.29475e6	−1.14024
$385$	129854.	0.0446483
$386$	−2.01876e6	−0.689631
$387$	1.22790e6	0.416758
$388$	−1.41463e6	−0.477049
$389$	−3.33803e6	−1.11845	−0.559225	−	0.829016i	$-0.688901\pi$
$389$	−3.33803e6	−1.11845	−0.559225	+	0.829016i	$0.688901\pi$
$390$	174831.	0.0582045
$391$	−905077.	−0.299394
$392$	−2.01781e6	−0.663230
$393$	537546.	0.175564
$394$	1.70932e6	0.554733
$395$	−1.80302e6	−0.581442
$396$	197828.	0.0633944
$397$	−3.48218e6	−1.10885	−0.554427	−	0.832232i	$-0.687063\pi$
$397$	−3.48218e6	−1.10885	−0.554427	+	0.832232i	$0.687063\pi$
$398$	−1.77926e6	−0.563030
$399$	−270269.	−0.0849893
$400$	341065.	0.106583
$401$	−5.29754e6	−1.64518	−0.822590	−	0.568635i	$-0.807472\pi$
$401$	−5.29754e6	−1.64518	−0.822590	+	0.568635i	$0.807472\pi$
$402$	−1.30491e6	−0.402731
$403$	−327273.	−0.100380
$404$	810419.	0.247034
$405$	−1.75429e6	−0.531451
$406$	449344.	0.135289
$407$	494462.	0.147961
$408$	5.23019e6	1.55549
$409$	−243902.	−0.0720953	−0.0360477	−	0.999350i	$-0.511477\pi$
$409$	−243902.	−0.0720953	−0.0360477	+	0.999350i	$0.511477\pi$
$410$	−167219.	−0.0491277
$411$	5.73958e6	1.67601
$412$	2.65456e6	0.770460
$413$	1.71123e6	0.493665
$414$	−57155.7	−0.0163892
$415$	−2.18971e6	−0.624118
$416$	−972376.	−0.275487
$417$	5.39413e6	1.51908
$418$	−100293.	−0.0280756
$419$	−1.19681e6	−0.333036	−0.166518	−	0.986038i	$-0.553252\pi$
$419$	−1.19681e6	−0.333036	−0.166518	+	0.986038i	$0.553252\pi$
$420$	−500265.	−0.138381
$421$	−86235.7	−0.0237127	−0.0118564	−	0.999930i	$-0.503774\pi$
$421$	−86235.7	−0.0237127	−0.0118564	+	0.999930i	$0.503774\pi$
$422$	−136965.	−0.0374393
$423$	591952.	0.160855
$424$	−2.40574e6	−0.649880
$425$	−1.39000e6	−0.373287
$426$	−424722.	−0.113392
$427$	662895.	0.175944
$428$	169527.	0.0447330
$429$	368542.	0.0966815
$430$	−1.15225e6	−0.300521
$431$	−4.71443e6	−1.22246	−0.611232	−	0.791452i	$-0.709326\pi$
$431$	−4.71443e6	−1.22246	−0.611232	+	0.791452i	$0.709326\pi$
$432$	1.73054e6	0.446142
$433$	6.27231e6	1.60771	0.803856	−	0.594824i	$-0.202778\pi$
$433$	6.27231e6	1.60771	0.803856	+	0.594824i	$0.202778\pi$
$434$	−184704.	−0.0470708
$435$	−1.98778e6	−0.503669
$436$	−3.22859e6	−0.813386
$437$	−146912.	−0.0368005
$438$	−1.56047e6	−0.388661
$439$	3.00420e6	0.743991	0.371995	−	0.928235i	$-0.378674\pi$
$439$	3.00420e6	0.743991	0.371995	+	0.928235i	$0.378674\pi$
$440$	−407896.	−0.100443
$441$	−915352.	−0.224126
$442$	891777.	0.217120
$443$	110627.	0.0267826	0.0133913	−	0.999910i	$-0.495737\pi$
$443$	110627.	0.0267826	0.0133913	+	0.999910i	$0.495737\pi$
$444$	−1.90492e6	−0.458584
$445$	399207.	0.0955648
$446$	1.80833e6	0.430468
$447$	−3.79314e6	−0.897904
$448$	200835.	0.0472765
$449$	1.86608e6	0.436832	0.218416	−	0.975856i	$-0.429911\pi$
$449$	1.86608e6	0.436832	0.218416	+	0.975856i	$0.429911\pi$
$450$	−87778.8	−0.0204342
$451$	−352496.	−0.0816043
$452$	−4.74990e6	−1.09355
$453$	4.03782e6	0.924488
$454$	−2.29276e6	−0.522058
$455$	−187420.	−0.0424411
$456$	848963.	0.191195
$457$	5.93745e6	1.32987	0.664936	−	0.746900i	$-0.268459\pi$
$457$	5.93745e6	1.32987	0.664936	+	0.746900i	$0.268459\pi$
$458$	786857.	0.175280
$459$	−7.05278e6	−1.56253
$460$	−271932.	−0.0599192
$461$	−7.62687e6	−1.67145	−0.835726	−	0.549146i	$-0.814953\pi$
$461$	−7.62687e6	−1.67145	−0.835726	+	0.549146i	$0.814953\pi$
$462$	207994.	0.0453363
$463$	−4.49269e6	−0.973989	−0.486994	−	0.873405i	$-0.661907\pi$
$463$	−4.49269e6	−0.973989	−0.486994	+	0.873405i	$0.661907\pi$
$464$	2.48787e6	0.536454
$465$	817080.	0.175240
$466$	−1.93900e6	−0.413630
$467$	5.98372e6	1.26964	0.634818	−	0.772662i	$-0.281075\pi$
$467$	5.98372e6	1.26964	0.634818	+	0.772662i	$0.281075\pi$
$468$	−285527.	−0.0602605
$469$	1.39887e6	0.293660
$470$	−555483.	−0.115992
$471$	−6.88573e6	−1.43020
$472$	−5.37527e6	−1.11057
$473$	−2.42893e6	−0.499185
$474$	−2.88798e6	−0.590402
$475$	−225625.	−0.0458831
$476$	−2.55175e6	−0.516203
$477$	−1.09133e6	−0.219614
$478$	−3.38823e6	−0.678271
$479$	5.73062e6	1.14120	0.570601	−	0.821227i	$-0.306710\pi$
$479$	5.73062e6	1.14120	0.570601	+	0.821227i	$0.306710\pi$
$480$	2.42766e6	0.480933
$481$	−713660.	−0.140647
$482$	3.37444e6	0.661583
$483$	304677.	0.0594253
$484$	−391328.	−0.0759326
$485$	1.32316e6	0.255422
$486$	−1.04060e6	−0.199845
$487$	9.30565e6	1.77797	0.888985	−	0.457937i	$-0.151411\pi$
$487$	9.30565e6	1.77797	0.888985	+	0.457937i	$0.151411\pi$
$488$	−2.08227e6	−0.395811
$489$	7.92698e6	1.49912
$490$	858959.	0.161615
$491$	−7.78869e6	−1.45801	−0.729006	−	0.684508i	$-0.760017\pi$
$491$	−7.78869e6	−1.45801	−0.729006	+	0.684508i	$0.760017\pi$
$492$	1.35799e6	0.252921
$493$	−1.01393e7	−1.87883
$494$	144753.	0.0266877
$495$	−185037.	−0.0339426
$496$	−1.02264e6	−0.186647
$497$	455304.	0.0826819
$498$	−3.50737e6	−0.633736
$499$	6.46608e6	1.16249	0.581246	−	0.813728i	$-0.302565\pi$
$499$	6.46608e6	1.16249	0.581246	+	0.813728i	$0.302565\pi$
$500$	−417629.	−0.0747078
$501$	5.97111e6	1.06282
$502$	−1.39951e6	−0.247867
$503$	6.47430e6	1.14097	0.570483	−	0.821310i	$-0.306756\pi$
$503$	6.47430e6	1.14097	0.570483	+	0.821310i	$0.306756\pi$
$504$	−354069.	−0.0620886
$505$	−758017.	−0.132267
$506$	113061.	0.0196307
$507$	5.94360e6	1.02690
$508$	7.93654e6	1.36449
$509$	−2.80901e6	−0.480572	−0.240286	−	0.970702i	$-0.577241\pi$
$509$	−2.80901e6	−0.480572	−0.240286	+	0.970702i	$0.577241\pi$
$510$	−2.22644e6	−0.379040
$511$	1.67284e6	0.283401
$512$	−5.39310e6	−0.909208
$513$	−1.14481e6	−0.192061
$514$	−305536.	−0.0510099
$515$	−2.48292e6	−0.412519
$516$	9.35745e6	1.54715
$517$	−1.17095e6	−0.192670
$518$	−402769.	−0.0659526
$519$	7.93603e6	1.29326
$520$	588719.	0.0954772
$521$	−9.09082e6	−1.46727	−0.733633	−	0.679546i	$-0.762177\pi$
$521$	−9.09082e6	−1.46727	−0.733633	+	0.679546i	$0.762177\pi$
$522$	−640295.	−0.102850
$523$	1.09999e7	1.75846	0.879231	−	0.476395i	$-0.158057\pi$
$523$	1.09999e7	1.75846	0.879231	+	0.476395i	$0.158057\pi$
$524$	823813.	0.131069
$525$	467917.	0.0740919
$526$	−2.79694e6	−0.440778
$527$	4.16776e6	0.653696
$528$	1.15160e6	0.179769
$529$	−6.27073e6	−0.974269
$530$	1.02410e6	0.158362
$531$	−2.43842e6	−0.375295
$532$	−414199.	−0.0634498
$533$	508760.	0.0775702
$534$	639429.	0.0970375
$535$	−158565.	−0.0239509
$536$	−4.39410e6	−0.660629
$537$	2.83977e6	0.424960
$538$	3.86523e6	0.575730
$539$	1.81068e6	0.268453
$540$	−2.11902e6	−0.312717
$541$	5.61819e6	0.825283	0.412642	−	0.910893i	$-0.364606\pi$
$541$	5.61819e6	0.825283	0.412642	+	0.910893i	$0.364606\pi$
$542$	−3.24891e6	−0.475050
$543$	−9.42951e6	−1.37243
$544$	1.23830e7	1.79402
$545$	3.01983e6	0.435503
$546$	−300199.	−0.0430951
$547$	−1.08682e7	−1.55306	−0.776530	−	0.630080i	$-0.783022\pi$
$547$	−1.08682e7	−1.55306	−0.776530	+	0.630080i	$0.783022\pi$
$548$	8.79616e6	1.25124
$549$	−944595.	−0.133757
$550$	173637.	0.0244757
$551$	−1.64580e6	−0.230940
$552$	−957044.	−0.133685
$553$	3.09593e6	0.430505
$554$	4.57204e6	0.632901
$555$	1.78174e6	0.245535
$556$	8.26674e6	1.13409
$557$	7.77309e6	1.06159	0.530794	−	0.847501i	$-0.321894\pi$
$557$	7.77309e6	1.06159	0.530794	+	0.847501i	$0.321894\pi$
$558$	263194.	0.0357842
$559$	3.50569e6	0.474508
$560$	−585637.	−0.0789148
$561$	−4.69330e6	−0.629609
$562$	4.94242e6	0.660083
$563$	−6.99632e6	−0.930248	−0.465124	−	0.885246i	$-0.653990\pi$
$563$	−6.99632e6	−0.930248	−0.465124	+	0.885246i	$0.653990\pi$
$564$	4.51110e6	0.597152
$565$	4.44277e6	0.585507
$566$	−2.04247e6	−0.267988
$567$	3.01226e6	0.393490
$568$	−1.43019e6	−0.186004
$569$	5.82561e6	0.754329	0.377164	−	0.926146i	$-0.376899\pi$
$569$	5.82561e6	0.754329	0.377164	+	0.926146i	$0.376899\pi$
$570$	−361395.	−0.0465902
$571$	−305769.	−0.0392468	−0.0196234	−	0.999807i	$-0.506247\pi$
$571$	−305769.	−0.0392468	−0.0196234	+	0.999807i	$0.506247\pi$
$572$	564807.	0.0721788
$573$	−1.26428e7	−1.60863
$574$	287129.	0.0363746
$575$	254349.	0.0320819
$576$	−286181.	−0.0359406
$577$	−7.36636e6	−0.921114	−0.460557	−	0.887630i	$-0.652350\pi$
$577$	−7.36636e6	−0.921114	−0.460557	+	0.887630i	$0.652350\pi$
$578$	−8.09656e6	−1.00805
$579$	−1.53344e7	−1.90094
$580$	−3.04636e6	−0.376020
$581$	3.75992e6	0.462103
$582$	2.11937e6	0.259358
$583$	2.15878e6	0.263050
$584$	−5.25468e6	−0.637550
$585$	267065.	0.0322646
$586$	−2.48538e6	−0.298984
$587$	−8.29202e6	−0.993265	−0.496632	−	0.867961i	$-0.665430\pi$
$587$	−8.29202e6	−0.993265	−0.496632	+	0.867961i	$0.665430\pi$
$588$	−6.97563e6	−0.832033
$589$	676510.	0.0803500
$590$	2.28820e6	0.270622
$591$	1.29839e7	1.52910
$592$	−2.23000e6	−0.261518
$593$	4.27298e6	0.498992	0.249496	−	0.968376i	$-0.419735\pi$
$593$	4.27298e6	0.498992	0.249496	+	0.968376i	$0.419735\pi$
$594$	881023.	0.102452
$595$	2.38675e6	0.276385
$596$	−5.81315e6	−0.670342
$597$	−1.35151e7	−1.55197
$598$	−163181.	−0.0186603
$599$	6.09398e6	0.693959	0.346979	−	0.937873i	$-0.387207\pi$
$599$	6.09398e6	0.693959	0.346979	+	0.937873i	$0.387207\pi$
$600$	−1.46981e6	−0.166680
$601$	−3.05021e6	−0.344464	−0.172232	−	0.985056i	$-0.555098\pi$
$601$	−3.05021e6	−0.344464	−0.172232	+	0.985056i	$0.555098\pi$
$602$	1.97851e6	0.222508
$603$	−1.99332e6	−0.223247
$604$	6.18814e6	0.690188
$605$	366025.	0.0406558
$606$	−1.21415e6	−0.134305
$607$	1.07848e7	1.18806	0.594030	−	0.804443i	$-0.297536\pi$
$607$	1.07848e7	1.18806	0.594030	+	0.804443i	$0.297536\pi$
$608$	2.01001e6	0.220515
$609$	3.41318e6	0.372921
$610$	886401.	0.0964507
$611$	1.69004e6	0.183145
$612$	3.63612e6	0.392428
$613$	−7.46446e6	−0.802319	−0.401160	−	0.916008i	$-0.631393\pi$
$613$	−7.46446e6	−0.802319	−0.401160	+	0.916008i	$0.631393\pi$
$614$	−3.90431e6	−0.417949
$615$	−1.27018e6	−0.135419
$616$	700392.	0.0743685
$617$	1.12507e6	0.118978	0.0594890	−	0.998229i	$-0.481053\pi$
$617$	1.12507e6	0.118978	0.0594890	+	0.998229i	$0.481053\pi$
$618$	−3.97701e6	−0.418876
$619$	7.09002e6	0.743740	0.371870	−	0.928285i	$-0.378717\pi$
$619$	7.09002e6	0.743740	0.371870	+	0.928285i	$0.378717\pi$
$620$	1.25221e6	0.130827
$621$	1.29055e6	0.134291
$622$	3.13643e6	0.325057
$623$	−685472.	−0.0707570
$624$	−1.66211e6	−0.170882
$625$	390625.	0.0400000
$626$	−2.19432e6	−0.223802
$627$	−761816.	−0.0773894
$628$	−1.05527e7	−1.06774
$629$	9.08831e6	0.915918
$630$	150724.	0.0151297
$631$	−5.80055e6	−0.579957	−0.289979	−	0.957033i	$-0.593648\pi$
$631$	−5.80055e6	−0.579957	−0.289979	+	0.957033i	$0.593648\pi$
$632$	−9.72486e6	−0.968480
$633$	−1.04037e6	−0.103200
$634$	4.38458e6	0.433217
$635$	−7.42336e6	−0.730577
$636$	−8.31672e6	−0.815285
$637$	−2.61336e6	−0.255182
$638$	1.26658e6	0.123192
$639$	−648788.	−0.0628565
$640$	4.72286e6	0.455780
$641$	7.29739e6	0.701491	0.350746	−	0.936471i	$-0.385928\pi$
$641$	7.29739e6	0.701491	0.350746	+	0.936471i	$0.385928\pi$
$642$	−253981.	−0.0243200
$643$	1.19448e7	1.13934	0.569669	−	0.821874i	$-0.307071\pi$
$643$	1.19448e7	1.13934	0.569669	+	0.821874i	$0.307071\pi$
$644$	466931.	0.0443647
$645$	−8.75239e6	−0.828376
$646$	−1.84340e6	−0.173795
$647$	2.72288e6	0.255722	0.127861	−	0.991792i	$-0.459189\pi$
$647$	2.72288e6	0.255722	0.127861	+	0.991792i	$0.459189\pi$
$648$	−9.46203e6	−0.885211
$649$	4.82349e6	0.449521
$650$	−250611.	−0.0232658
$651$	−1.40299e6	−0.129749
$652$	1.21484e7	1.11918
$653$	−4.28488e6	−0.393239	−0.196619	−	0.980480i	$-0.562996\pi$
$653$	−4.28488e6	−0.393239	−0.196619	+	0.980480i	$0.562996\pi$
$654$	4.83701e6	0.442214
$655$	−770545.	−0.0701770
$656$	1.58974e6	0.144234
$657$	−2.38372e6	−0.215447
$658$	953812.	0.0858811
$659$	1.45039e7	1.30098	0.650492	−	0.759513i	$-0.274563\pi$
$659$	1.45039e7	1.30098	0.650492	+	0.759513i	$0.274563\pi$
$660$	−1.41011e6	−0.126007
$661$	−5.58001e6	−0.496743	−0.248371	−	0.968665i	$-0.579895\pi$
$661$	−5.58001e6	−0.496743	−0.248371	+	0.968665i	$0.579895\pi$
$662$	7.02836e6	0.623317
$663$	6.77387e6	0.598485
$664$	−1.18106e7	−1.03956
$665$	387417.	0.0339723
$666$	573928.	0.0501386
$667$	1.85533e6	0.161475
$668$	9.15100e6	0.793464
$669$	1.37359e7	1.18657
$670$	1.87052e6	0.160981
$671$	1.86852e6	0.160211
$672$	−4.16850e6	−0.356087
$673$	−1.90955e7	−1.62515	−0.812575	−	0.582857i	$-0.801935\pi$
$673$	−1.90955e7	−1.62515	−0.812575	+	0.582857i	$0.801935\pi$
$674$	6.34005e6	0.537580
$675$	1.98201e6	0.167435
$676$	9.10883e6	0.766647
$677$	−2.39783e6	−0.201069	−0.100535	−	0.994934i	$-0.532055\pi$
$677$	−2.39783e6	−0.201069	−0.100535	+	0.994934i	$0.532055\pi$
$678$	7.11620e6	0.594530
$679$	−2.27197e6	−0.189116
$680$	−7.49721e6	−0.621766
$681$	−1.74156e7	−1.43904
$682$	−520630.	−0.0428616
$683$	1.77436e7	1.45542	0.727712	−	0.685883i	$-0.240584\pi$
$683$	1.77436e7	1.45542	0.727712	+	0.685883i	$0.240584\pi$
$684$	590215.	0.0482359
$685$	−8.22740e6	−0.669940
$686$	−3.13143e6	−0.254058
$687$	5.97691e6	0.483153
$688$	1.09543e7	0.882298
$689$	−3.11579e6	−0.250046
$690$	407404.	0.0325763
$691$	4.58978e6	0.365676	0.182838	−	0.983143i	$-0.441472\pi$
$691$	4.58978e6	0.365676	0.182838	+	0.983143i	$0.441472\pi$
$692$	1.21623e7	0.965498
$693$	317724.	0.0251314
$694$	−8.23145e6	−0.648750
$695$	−7.73221e6	−0.607214
$696$	−1.07214e7	−0.838937
$697$	−6.47895e6	−0.505153
$698$	−4.47703e6	−0.347818
$699$	−1.47285e7	−1.14016
$700$	717104.	0.0553143
$701$	−1.58436e7	−1.21775	−0.608875	−	0.793266i	$-0.708379\pi$
$701$	−1.58436e7	−1.21775	−0.608875	+	0.793266i	$0.708379\pi$
$702$	−1.27159e6	−0.0973875
$703$	1.47521e6	0.112581
$704$	566101.	0.0430489
$705$	−4.21941e6	−0.319727
$706$	−8.65628e6	−0.653611
$707$	1.30158e6	0.0979314
$708$	−1.85825e7	−1.39323
$709$	−2.38132e7	−1.77911	−0.889553	−	0.456832i	$-0.848984\pi$
$709$	−2.38132e7	−1.77911	−0.889553	+	0.456832i	$0.848984\pi$
$710$	608817.	0.0453254
$711$	−4.41156e6	−0.327279
$712$	2.15319e6	0.159178
$713$	−762636.	−0.0561815
$714$	3.82298e6	0.280644
$715$	−528286.	−0.0386460
$716$	4.35208e6	0.317259
$717$	−2.57367e7	−1.86963
$718$	8.35229e6	0.604637
$719$	−5.54101e6	−0.399730	−0.199865	−	0.979823i	$-0.564050\pi$
$719$	−5.54101e6	−0.399730	−0.199865	+	0.979823i	$0.564050\pi$
$720$	834507.	0.0599927
$721$	4.26338e6	0.305433
$722$	−299221.	−0.0213623
$723$	2.56320e7	1.82363
$724$	−1.44511e7	−1.02460
$725$	2.84938e6	0.201329
$726$	586280.	0.0412823
$727$	1.70934e7	1.19948	0.599738	−	0.800197i	$-0.295272\pi$
$727$	1.70934e7	1.19948	0.599738	+	0.800197i	$0.295272\pi$
$728$	−1.01088e6	−0.0706921
$729$	9.14735e6	0.637495
$730$	2.23686e6	0.155357
$731$	−4.46442e7	−3.09009
$732$	−7.19849e6	−0.496551
$733$	−7.99958e6	−0.549930	−0.274965	−	0.961454i	$-0.588666\pi$
$733$	−7.99958e6	−0.549930	−0.274965	+	0.961454i	$0.588666\pi$
$734$	−1.08054e7	−0.740290
$735$	6.52459e6	0.445487
$736$	−2.26590e6	−0.154186
$737$	3.94304e6	0.267400
$738$	−409146.	−0.0276527
$739$	−1.83611e7	−1.23677	−0.618383	−	0.785877i	$-0.712212\pi$
$739$	−1.83611e7	−1.23677	−0.618383	+	0.785877i	$0.712212\pi$
$740$	2.73060e6	0.183307
$741$	1.09953e6	0.0735636
$742$	−1.75846e6	−0.117253
$743$	1.92638e7	1.28018	0.640088	−	0.768302i	$-0.278898\pi$
$743$	1.92638e7	1.28018	0.640088	+	0.768302i	$0.278898\pi$
$744$	4.40706e6	0.291888
$745$	5.43727e6	0.358914
$746$	−1.19117e7	−0.783660
$747$	−5.35772e6	−0.351300
$748$	−7.19269e6	−0.470043
$749$	272269.	0.0177335
$750$	625683.	0.0406164
$751$	9.87002e6	0.638584	0.319292	−	0.947656i	$-0.396555\pi$
$751$	9.87002e6	0.638584	0.319292	+	0.947656i	$0.396555\pi$
$752$	5.28094e6	0.340539
$753$	−1.06306e7	−0.683235
$754$	−1.82806e6	−0.117102
$755$	−5.78801e6	−0.369540
$756$	3.63854e6	0.231538
$757$	−2.08939e7	−1.32519	−0.662597	−	0.748976i	$-0.730546\pi$
$757$	−2.08939e7	−1.32519	−0.662597	+	0.748976i	$0.730546\pi$
$758$	−1.08044e7	−0.683012
$759$	858802.	0.0541114
$760$	−1.21695e6	−0.0764253
$761$	−3.67811e6	−0.230231	−0.115115	−	0.993352i	$-0.536724\pi$
$761$	−3.67811e6	−0.230231	−0.115115	+	0.993352i	$0.536724\pi$
$762$	−1.18904e7	−0.741835
$763$	−5.18530e6	−0.322450
$764$	−1.93756e7	−1.20094
$765$	−3.40101e6	−0.210114
$766$	660034.	0.0406438
$767$	−6.96178e6	−0.427299
$768$	4.95378e6	0.303064
$769$	−1.54209e7	−0.940357	−0.470178	−	0.882571i	$-0.655810\pi$
$769$	−1.54209e7	−0.940357	−0.470178	+	0.882571i	$0.655810\pi$
$770$	−298149.	−0.0181220
$771$	−2.32083e6	−0.140607
$772$	−2.35006e7	−1.41917
$773$	−1.67803e7	−1.01007	−0.505035	−	0.863099i	$-0.668521\pi$
$773$	−1.67803e7	−1.01007	−0.505035	+	0.863099i	$0.668521\pi$
$774$	−2.81928e6	−0.169156
$775$	−1.17124e6	−0.0700475
$776$	7.13668e6	0.425443
$777$	−3.05940e6	−0.181796
$778$	7.66421e6	0.453961
$779$	−1.05166e6	−0.0620916
$780$	2.03522e6	0.119778
$781$	1.28338e6	0.0752884
$782$	2.07808e6	0.121519
$783$	1.44576e7	0.842735
$784$	−8.16606e6	−0.474485
$785$	9.87035e6	0.571687
$786$	−1.23422e6	−0.0712584
$787$	2.79269e7	1.60726	0.803629	−	0.595131i	$-0.202900\pi$
$787$	2.79269e7	1.60726	0.803629	+	0.595131i	$0.202900\pi$
$788$	1.98984e7	1.14157
$789$	−2.12454e7	−1.21499
$790$	4.13977e6	0.235998
$791$	−7.62860e6	−0.433515
$792$	−998027.	−0.0565365
$793$	−2.69685e6	−0.152291
$794$	7.99517e6	0.450066
$795$	7.77896e6	0.436519
$796$	−2.07125e7	−1.15865
$797$	2.94575e7	1.64267	0.821336	−	0.570445i	$-0.193229\pi$
$797$	2.94575e7	1.64267	0.821336	+	0.570445i	$0.193229\pi$
$798$	620545.	0.0344958
$799$	−2.15223e7	−1.19268
$800$	−3.47993e6	−0.192241
$801$	976766.	0.0537910
$802$	1.21633e7	0.667752
$803$	4.71528e6	0.258059
$804$	−1.51906e7	−0.828769
$805$	−436739.	−0.0237537
$806$	751429.	0.0407427
$807$	2.93600e7	1.58698
$808$	−4.08849e6	−0.220310
$809$	−775747.	−0.0416724	−0.0208362	−	0.999783i	$-0.506633\pi$
$809$	−775747.	−0.0416724	−0.0208362	+	0.999783i	$0.506633\pi$
$810$	4.02789e6	0.215707
$811$	6.76662e6	0.361260	0.180630	−	0.983551i	$-0.442186\pi$
$811$	6.76662e6	0.361260	0.180630	+	0.983551i	$0.442186\pi$
$812$	5.23085e6	0.278409
$813$	−2.46785e7	−1.30946
$814$	−1.13530e6	−0.0600550
$815$	−1.13629e7	−0.599233
$816$	2.11666e7	1.11282
$817$	−7.24664e6	−0.379823
$818$	560006.	0.0292624
$819$	−458572.	−0.0238890
$820$	−1.94661e6	−0.101099
$821$	1.57927e7	0.817711	0.408855	−	0.912599i	$-0.365928\pi$
$821$	1.57927e7	0.817711	0.408855	+	0.912599i	$0.365928\pi$
$822$	−1.31782e7	−0.680264
$823$	−2.16922e7	−1.11636	−0.558179	−	0.829721i	$-0.688500\pi$
$823$	−2.16922e7	−1.11636	−0.558179	+	0.829721i	$0.688500\pi$
$824$	−1.33920e7	−0.687113
$825$	1.31893e6	0.0674665
$826$	−3.92902e6	−0.200371
$827$	2.60919e7	1.32661	0.663303	−	0.748351i	$-0.269154\pi$
$827$	2.60919e7	1.32661	0.663303	+	0.748351i	$0.269154\pi$
$828$	−665355.	−0.0337270
$829$	−1.59544e7	−0.806294	−0.403147	−	0.915135i	$-0.632084\pi$
$829$	−1.59544e7	−0.806294	−0.403147	+	0.915135i	$0.632084\pi$
$830$	5.02764e6	0.253320
$831$	3.47289e7	1.74457
$832$	−817057.	−0.0409208
$833$	3.32806e7	1.66180
$834$	−1.23851e7	−0.616571
$835$	−8.55929e6	−0.424836
$836$	−1.16752e6	−0.0577760
$837$	−5.94281e6	−0.293210
$838$	2.74791e6	0.135174
$839$	1.51283e7	0.741970	0.370985	−	0.928639i	$-0.379020\pi$
$839$	1.51283e7	0.741970	0.370985	+	0.928639i	$0.379020\pi$
$840$	2.52379e6	0.123411
$841$	273418.	0.0133302
$842$	197999.	0.00962462
$843$	3.75422e7	1.81950
$844$	−1.59442e6	−0.0770454
$845$	−8.51985e6	−0.410478
$846$	−1.35914e6	−0.0652887
$847$	−628496.	−0.0301019
$848$	−9.73601e6	−0.464934
$849$	−1.55145e7	−0.738699
$850$	3.19148e6	0.151511
$851$	−1.66302e6	−0.0787180
$852$	−4.94423e6	−0.233345
$853$	2.40966e7	1.13392	0.566961	−	0.823745i	$-0.308119\pi$
$853$	2.40966e7	1.13392	0.566961	+	0.823745i	$0.308119\pi$
$854$	−1.52202e6	−0.0714130
$855$	−552052.	−0.0258264
$856$	−855246.	−0.0398939
$857$	−3.52467e7	−1.63933	−0.819664	−	0.572844i	$-0.805840\pi$
$857$	−3.52467e7	−1.63933	−0.819664	+	0.572844i	$0.805840\pi$
$858$	−846182.	−0.0392415
$859$	−3.81040e7	−1.76192	−0.880962	−	0.473187i	$-0.843103\pi$
$859$	−3.81040e7	−1.76192	−0.880962	+	0.473187i	$0.843103\pi$
$860$	−1.34134e7	−0.618435
$861$	2.18101e6	0.100265
$862$	1.08245e7	0.496178
$863$	720923.	0.0329505	0.0164752	−	0.999864i	$-0.494756\pi$
$863$	720923.	0.0329505	0.0164752	+	0.999864i	$0.494756\pi$
$864$	−1.76569e7	−0.804694
$865$	−1.13759e7	−0.516946
$866$	−1.44014e7	−0.652544
$867$	−6.15008e7	−2.77865
$868$	−2.15015e6	−0.0968657
$869$	8.72659e6	0.392008
$870$	4.56399e6	0.204431
$871$	−5.69101e6	−0.254181
$872$	1.62880e7	0.725396
$873$	3.23746e6	0.143770
$874$	337314.	0.0149367
$875$	−670736.	−0.0296163
$876$	−1.81656e7	−0.799816
$877$	1.26853e7	0.556931	0.278466	−	0.960446i	$-0.410174\pi$
$877$	1.26853e7	0.556931	0.278466	+	0.960446i	$0.410174\pi$
$878$	−6.89772e6	−0.301974
$879$	−1.88787e7	−0.824139
$880$	−1.65076e6	−0.0718581
$881$	2.37918e7	1.03273	0.516365	−	0.856369i	$-0.327285\pi$
$881$	2.37918e7	1.03273	0.516365	+	0.856369i	$0.327285\pi$
$882$	2.10167e6	0.0909690
$883$	1.90664e7	0.822939	0.411470	−	0.911424i	$-0.365016\pi$
$883$	1.90664e7	0.822939	0.411470	+	0.911424i	$0.365016\pi$
$884$	1.03813e7	0.446806
$885$	1.73810e7	0.745960
$886$	−254003.	−0.0108706
$887$	2.67408e7	1.14121	0.570605	−	0.821225i	$-0.306709\pi$
$887$	2.67408e7	1.14121	0.570605	+	0.821225i	$0.306709\pi$
$888$	9.61014e6	0.408975
$889$	1.27465e7	0.540925
$890$	−916590.	−0.0387882
$891$	8.49074e6	0.358304
$892$	2.10509e7	0.885849
$893$	−3.49350e6	−0.146600
$894$	8.70915e6	0.364445
$895$	−4.07067e6	−0.169867
$896$	−8.10954e6	−0.337463
$897$	−1.23951e6	−0.0514364
$898$	−4.28457e6	−0.177303
$899$	−8.54353e6	−0.352564
$900$	−1.02184e6	−0.0420511
$901$	3.96789e7	1.62835
$902$	809341.	0.0331219
$903$	1.50286e7	0.613337
$904$	2.39628e7	0.975251
$905$	1.35167e7	0.548593
$906$	−9.27094e6	−0.375235
$907$	−2.70499e7	−1.09181	−0.545906	−	0.837847i	$-0.683814\pi$
$907$	−2.70499e7	−1.09181	−0.545906	+	0.837847i	$0.683814\pi$
$908$	−2.66902e7	−1.07433
$909$	−1.85469e6	−0.0744495
$910$	430321.	0.0172262
$911$	−1.13217e7	−0.451975	−0.225987	−	0.974130i	$-0.572561\pi$
$911$	−1.13217e7	−0.451975	−0.225987	+	0.974130i	$0.572561\pi$
$912$	3.43575e6	0.136784
$913$	1.05982e7	0.420781
$914$	−1.36326e7	−0.539774
$915$	6.73303e6	0.265863
$916$	9.15987e6	0.360704
$917$	1.32309e6	0.0519596
$918$	1.61934e7	0.634207
$919$	−1.45507e7	−0.568324	−0.284162	−	0.958776i	$-0.591715\pi$
$919$	−1.45507e7	−0.568324	−0.284162	+	0.958776i	$0.591715\pi$
$920$	1.37187e6	0.0534373
$921$	−2.96568e7	−1.15206
$922$	1.75115e7	0.678416
$923$	−1.85231e6	−0.0715665
$924$	2.42128e6	0.0932965
$925$	−2.55404e6	−0.0981462
$926$	1.03153e7	0.395327
$927$	−6.07512e6	−0.232196
$928$	−2.53840e7	−0.967589
$929$	3.98939e7	1.51659	0.758294	−	0.651913i	$-0.226033\pi$
$929$	3.98939e7	1.51659	0.758294	+	0.651913i	$0.226033\pi$
$930$	−1.87604e6	−0.0711270
$931$	5.40210e6	0.204262
$932$	−2.25720e7	−0.851198
$933$	2.38241e7	0.896009
$934$	−1.37388e7	−0.515325
$935$	6.72761e6	0.251670
$936$	1.44046e6	0.0537416
$937$	1.50813e7	0.561164	0.280582	−	0.959830i	$-0.409472\pi$
$937$	1.50813e7	0.561164	0.280582	+	0.959830i	$0.409472\pi$
$938$	−3.21184e6	−0.119192
$939$	−1.66679e7	−0.616903
$940$	−6.46643e6	−0.238696
$941$	−4.61297e7	−1.69827	−0.849135	−	0.528176i	$-0.822876\pi$
$941$	−4.61297e7	−1.69827	−0.849135	+	0.528176i	$0.822876\pi$
$942$	1.58098e7	0.580497
$943$	1.18555e6	0.0434150
$944$	−2.17537e7	−0.794518
$945$	−3.40327e6	−0.123970
$946$	5.57688e6	0.202611
$947$	−1.63647e7	−0.592970	−0.296485	−	0.955038i	$-0.595814\pi$
$947$	−1.63647e7	−0.592970	−0.296485	+	0.955038i	$0.595814\pi$
$948$	−3.36192e7	−1.21497
$949$	−6.80559e6	−0.245302
$950$	518041.	0.0186232
$951$	3.33049e7	1.19415
$952$	1.28733e7	0.460361
$953$	3.89315e7	1.38857	0.694287	−	0.719698i	$-0.255720\pi$
$953$	3.89315e7	1.38857	0.694287	+	0.719698i	$0.255720\pi$
$954$	2.50572e6	0.0891379
$955$	1.81228e7	0.643009
$956$	−3.94427e7	−1.39580
$957$	9.62085e6	0.339573
$958$	−1.31577e7	−0.463196
$959$	1.41271e7	0.496030
$960$	2.03989e6	0.0714378
$961$	−2.51173e7	−0.877334
$962$	1.63858e6	0.0570862
$963$	−387971.	−0.0134814
$964$	3.92822e7	1.36146
$965$	2.19810e7	0.759854
$966$	−699546.	−0.0241198
$967$	−5.14566e7	−1.76960	−0.884800	−	0.465971i	$-0.845705\pi$
$967$	−5.14566e7	−1.76960	−0.884800	+	0.465971i	$0.845705\pi$
$968$	1.97422e6	0.0677184
$969$	−1.40023e7	−0.479061
$970$	−3.03801e6	−0.103672
$971$	7.59032e6	0.258352	0.129176	−	0.991622i	$-0.458767\pi$
$971$	7.59032e6	0.258352	0.129176	+	0.991622i	$0.458767\pi$
$972$	−1.21137e7	−0.411255
$973$	1.32769e7	0.449586
$974$	−2.13660e7	−0.721650
$975$	−1.90362e6	−0.0641313
$976$	−8.42695e6	−0.283169
$977$	−2.20767e7	−0.739943	−0.369971	−	0.929043i	$-0.620633\pi$
$977$	−2.20767e7	−0.739943	−0.369971	+	0.929043i	$0.620633\pi$
$978$	−1.82006e7	−0.608468
$979$	−1.93216e6	−0.0644298
$980$	9.99922e6	0.332584
$981$	7.38882e6	0.245133
$982$	1.78831e7	0.591784
$983$	1.70466e7	0.562669	0.281335	−	0.959610i	$-0.409223\pi$
$983$	1.70466e7	0.562669	0.281335	+	0.959610i	$0.409223\pi$
$984$	−6.85095e6	−0.225561
$985$	−1.86118e7	−0.611219
$986$	2.32800e7	0.762589
$987$	7.24508e6	0.236728
$988$	1.68508e6	0.0549198
$989$	8.16920e6	0.265576
$990$	424849.	0.0137768
$991$	2.89559e7	0.936599	0.468299	−	0.883570i	$-0.344867\pi$
$991$	2.89559e7	0.936599	0.468299	+	0.883570i	$0.344867\pi$
$992$	1.04342e7	0.336650
$993$	5.33869e7	1.71815
$994$	−1.04539e6	−0.0335593
$995$	1.93733e7	0.620362
$996$	−4.08296e7	−1.30415
$997$	−3.93579e7	−1.25399	−0.626995	−	0.779023i	$-0.715716\pi$
$997$	−3.93579e7	−1.25399	−0.626995	+	0.779023i	$0.715716\pi$
$998$	−1.48463e7	−0.471837
$999$	−1.29590e7	−0.410827

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.f.1.16	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.f.1.16	✓	38	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)

\(f(q)\)	\(=\)	\(q-2.29603 q^{2} -17.4404 q^{3} -26.7283 q^{4} +25.0000 q^{5} +40.0437 q^{6} -42.9271 q^{7} +134.842 q^{8} +61.1692 q^{9} +O(q^{10})\)	\(q-2.29603 q^{2} -17.4404 q^{3} -26.7283 q^{4} +25.0000 q^{5} +40.0437 q^{6} -42.9271 q^{7} +134.842 q^{8} +61.1692 q^{9} -57.4007 q^{10} -121.000 q^{11} +466.153 q^{12} +174.640 q^{13} +98.5618 q^{14} -436.011 q^{15} +545.704 q^{16} -2224.00 q^{17} -140.446 q^{18} -361.000 q^{19} -668.206 q^{20} +748.668 q^{21} +277.819 q^{22} +406.959 q^{23} -2351.70 q^{24} +625.000 q^{25} -400.978 q^{26} +3171.21 q^{27} +1147.37 q^{28} +4559.01 q^{29} +1001.09 q^{30} -1873.99 q^{31} -5567.89 q^{32} +2110.29 q^{33} +5106.37 q^{34} -1073.18 q^{35} -1634.95 q^{36} -4086.47 q^{37} +828.866 q^{38} -3045.80 q^{39} +3371.04 q^{40} +2913.19 q^{41} -1718.96 q^{42} +20073.8 q^{43} +3234.12 q^{44} +1529.23 q^{45} -934.388 q^{46} +9677.30 q^{47} -9517.32 q^{48} -14964.3 q^{49} -1435.02 q^{50} +38787.6 q^{51} -4667.82 q^{52} -17841.2 q^{53} -7281.19 q^{54} -3025.00 q^{55} -5788.36 q^{56} +6296.00 q^{57} -10467.6 q^{58} -39863.6 q^{59} +11653.8 q^{60} -15442.3 q^{61} +4302.73 q^{62} -2625.81 q^{63} -4678.52 q^{64} +4366.00 q^{65} -4845.29 q^{66} -32587.1 q^{67} +59443.7 q^{68} -7097.54 q^{69} +2464.04 q^{70} -10606.5 q^{71} +8248.15 q^{72} -38969.2 q^{73} +9382.64 q^{74} -10900.3 q^{75} +9648.90 q^{76} +5194.18 q^{77} +6993.24 q^{78} -72120.6 q^{79} +13642.6 q^{80} -70171.4 q^{81} -6688.77 q^{82} -87588.5 q^{83} -20010.6 q^{84} -55600.1 q^{85} -46089.9 q^{86} -79511.2 q^{87} -16315.8 q^{88} +15968.3 q^{89} -3511.15 q^{90} -7496.79 q^{91} -10877.3 q^{92} +32683.2 q^{93} -22219.3 q^{94} -9025.00 q^{95} +97106.4 q^{96} +52926.3 q^{97} +34358.4 q^{98} -7401.47 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9} + 200 q^{10} - 4598 q^{11} + 2312 q^{12} + 41 q^{13} + 23 q^{14} + 1575 q^{15} + 7196 q^{16} - 2431 q^{17} - 1689 q^{18} - 13718 q^{19} + 15400 q^{20} - 1577 q^{21} - 968 q^{22} + 9284 q^{23} + 7598 q^{24} + 23750 q^{25} + 13129 q^{26} + 9228 q^{27} - 1079 q^{28} - 559 q^{29} + 3725 q^{30} + 11147 q^{31} + 11051 q^{32} - 7623 q^{33} + 40895 q^{34} + 6875 q^{35} + 55887 q^{36} + 41579 q^{37} - 2888 q^{38} + 24982 q^{39} + 6600 q^{40} + 18597 q^{41} + 61360 q^{42} + 25353 q^{43} - 74536 q^{44} + 75725 q^{45} + 1611 q^{46} + 63516 q^{47} + 187737 q^{48} + 141609 q^{49} + 5000 q^{50} + 107546 q^{51} + 60018 q^{52} + 123045 q^{53} + 256696 q^{54} - 114950 q^{55} + 157335 q^{56} - 22743 q^{57} + 218938 q^{58} + 132925 q^{59} + 57800 q^{60} - 59107 q^{61} + 166982 q^{62} + 130582 q^{63} + 313126 q^{64} + 1025 q^{65} - 18029 q^{66} + 162534 q^{67} + 182980 q^{68} + 178552 q^{69} + 575 q^{70} + 157840 q^{71} + 98630 q^{72} - 63010 q^{73} + 122683 q^{74} + 39375 q^{75} - 222376 q^{76} - 33275 q^{77} + 277272 q^{78} - 16385 q^{79} + 179900 q^{80} + 290354 q^{81} + 362302 q^{82} + 138461 q^{83} + 446870 q^{84} - 60775 q^{85} + 643902 q^{86} + 291602 q^{87} - 31944 q^{88} + 224792 q^{89} - 42225 q^{90} + 498548 q^{91} + 581088 q^{92} + 134210 q^{93} + 35864 q^{94} - 342950 q^{95} + 377376 q^{96} + 292216 q^{97} - 58230 q^{98} - 366509 q^{99}+O(q^{100}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9 + 200 * q^10 - 4598 * q^11 + 2312 * q^12 + 41 * q^13 + 23 * q^14 + 1575 * q^15 + 7196 * q^16 - 2431 * q^17 - 1689 * q^18 - 13718 * q^19 + 15400 * q^20 - 1577 * q^21 - 968 * q^22 + 9284 * q^23 + 7598 * q^24 + 23750 * q^25 + 13129 * q^26 + 9228 * q^27 - 1079 * q^28 - 559 * q^29 + 3725 * q^30 + 11147 * q^31 + 11051 * q^32 - 7623 * q^33 + 40895 * q^34 + 6875 * q^35 + 55887 * q^36 + 41579 * q^37 - 2888 * q^38 + 24982 * q^39 + 6600 * q^40 + 18597 * q^41 + 61360 * q^42 + 25353 * q^43 - 74536 * q^44 + 75725 * q^45 + 1611 * q^46 + 63516 * q^47 + 187737 * q^48 + 141609 * q^49 + 5000 * q^50 + 107546 * q^51 + 60018 * q^52 + 123045 * q^53 + 256696 * q^54 - 114950 * q^55 + 157335 * q^56 - 22743 * q^57 + 218938 * q^58 + 132925 * q^59 + 57800 * q^60 - 59107 * q^61 + 166982 * q^62 + 130582 * q^63 + 313126 * q^64 + 1025 * q^65 - 18029 * q^66 + 162534 * q^67 + 182980 * q^68 + 178552 * q^69 + 575 * q^70 + 157840 * q^71 + 98630 * q^72 - 63010 * q^73 + 122683 * q^74 + 39375 * q^75 - 222376 * q^76 - 33275 * q^77 + 277272 * q^78 - 16385 * q^79 + 179900 * q^80 + 290354 * q^81 + 362302 * q^82 + 138461 * q^83 + 446870 * q^84 - 60775 * q^85 + 643902 * q^86 + 291602 * q^87 - 31944 * q^88 + 224792 * q^89 - 42225 * q^90 + 498548 * q^91 + 581088 * q^92 + 134210 * q^93 + 35864 * q^94 - 342950 * q^95 + 377376 * q^96 + 292216 * q^97 - 58230 * q^98 - 366509 * q^99

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