LMFDB - Embedded newform 1045.6.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$167.601091705$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.93899 q^{2} +3.69296 q^{3} +47.9055 q^{4} +25.0000 q^{5} -33.0113 q^{6} -46.2037 q^{7} -142.179 q^{8} -229.362 q^{9} +O(q^{10})$	\(q-8.93899 q^{2} +3.69296 q^{3} +47.9055 q^{4} +25.0000 q^{5} -33.0113 q^{6} -46.2037 q^{7} -142.179 q^{8} -229.362 q^{9} -223.475 q^{10} -121.000 q^{11} +176.913 q^{12} +121.188 q^{13} +413.014 q^{14} +92.3239 q^{15} -262.042 q^{16} -620.188 q^{17} +2050.26 q^{18} -361.000 q^{19} +1197.64 q^{20} -170.628 q^{21} +1081.62 q^{22} -2410.67 q^{23} -525.059 q^{24} +625.000 q^{25} -1083.30 q^{26} -1744.41 q^{27} -2213.41 q^{28} -1031.57 q^{29} -825.282 q^{30} -444.106 q^{31} +6892.10 q^{32} -446.848 q^{33} +5543.85 q^{34} -1155.09 q^{35} -10987.7 q^{36} -13786.3 q^{37} +3226.97 q^{38} +447.542 q^{39} -3554.47 q^{40} -7470.17 q^{41} +1525.24 q^{42} -4050.44 q^{43} -5796.56 q^{44} -5734.05 q^{45} +21548.9 q^{46} +7118.64 q^{47} -967.708 q^{48} -14672.2 q^{49} -5586.87 q^{50} -2290.33 q^{51} +5805.57 q^{52} -27921.4 q^{53} +15593.3 q^{54} -3025.00 q^{55} +6569.18 q^{56} -1333.16 q^{57} +9221.17 q^{58} +8163.77 q^{59} +4422.82 q^{60} +50046.3 q^{61} +3969.85 q^{62} +10597.4 q^{63} -53223.1 q^{64} +3029.70 q^{65} +3994.36 q^{66} -18153.2 q^{67} -29710.4 q^{68} -8902.49 q^{69} +10325.4 q^{70} +4545.37 q^{71} +32610.4 q^{72} +24723.1 q^{73} +123236. q^{74} +2308.10 q^{75} -17293.9 q^{76} +5590.65 q^{77} -4000.57 q^{78} -4008.44 q^{79} -6551.04 q^{80} +49292.9 q^{81} +66775.8 q^{82} -9863.82 q^{83} -8174.03 q^{84} -15504.7 q^{85} +36206.8 q^{86} -3809.53 q^{87} +17203.6 q^{88} +103749. q^{89} +51256.6 q^{90} -5599.34 q^{91} -115484. q^{92} -1640.06 q^{93} -63633.4 q^{94} -9025.00 q^{95} +25452.2 q^{96} +178627. q^{97} +131155. q^{98} +27752.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.93899	−1.58020	−0.790102	−	0.612975i	$-0.789973\pi$
$2$	−8.93899	−1.58020	−0.790102	+	0.612975i	$0.789973\pi$
$3$	3.69296	0.236903	0.118452	−	0.992960i	$-0.462207\pi$
$3$	3.69296	0.236903	0.118452	+	0.992960i	$0.462207\pi$
$4$	47.9055	1.49705
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−33.0113	−0.374355
$7$	−46.2037	−0.356395	−0.178198	−	0.983995i	$-0.557027\pi$
$7$	−46.2037	−0.356395	−0.178198	+	0.983995i	$0.557027\pi$
$8$	−142.179	−0.785434
$9$	−229.362	−0.943877
$10$	−223.475	−0.706689
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	176.913	0.354655
$13$	121.188	0.198885	0.0994423	−	0.995043i	$-0.468294\pi$
$13$	121.188	0.198885	0.0994423	+	0.995043i	$0.468294\pi$
$14$	413.014	0.563177
$15$	92.3239	0.105946
$16$	−262.042	−0.255900
$17$	−620.188	−0.520476	−0.260238	−	0.965544i	$-0.583801\pi$
$17$	−620.188	−0.520476	−0.260238	+	0.965544i	$0.583801\pi$
$18$	2050.26	1.49152
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	1197.64	0.669499
$21$	−170.628	−0.0844312
$22$	1081.62	0.476450
$23$	−2410.67	−0.950207	−0.475103	−	0.879930i	$-0.657589\pi$
$23$	−2410.67	−0.950207	−0.475103	+	0.879930i	$0.657589\pi$
$24$	−525.059	−0.186072
$25$	625.000	0.200000
$26$	−1083.30	−0.314278
$27$	−1744.41	−0.460511
$28$	−2213.41	−0.533540
$29$	−1031.57	−0.227773	−0.113887	−	0.993494i	$-0.536330\pi$
$29$	−1031.57	−0.227773	−0.113887	+	0.993494i	$0.536330\pi$
$30$	−825.282	−0.167417
$31$	−444.106	−0.0830007	−0.0415004	−	0.999138i	$-0.513214\pi$
$31$	−444.106	−0.0830007	−0.0415004	+	0.999138i	$0.513214\pi$
$32$	6892.10	1.18981
$33$	−446.848	−0.0714290
$34$	5543.85	0.822459
$35$	−1155.09	−0.159385
$36$	−10987.7	−1.41303
$37$	−13786.3	−1.65555	−0.827777	−	0.561057i	$-0.810395\pi$
$37$	−13786.3	−1.65555	−0.827777	+	0.561057i	$0.810395\pi$
$38$	3226.97	0.362524
$39$	447.542	0.0471164
$40$	−3554.47	−0.351257
$41$	−7470.17	−0.694018	−0.347009	−	0.937862i	$-0.612803\pi$
$41$	−7470.17	−0.694018	−0.347009	+	0.937862i	$0.612803\pi$
$42$	1525.24	0.133418
$43$	−4050.44	−0.334065	−0.167032	−	0.985951i	$-0.553418\pi$
$43$	−4050.44	−0.334065	−0.167032	+	0.985951i	$0.553418\pi$
$44$	−5796.56	−0.451376
$45$	−5734.05	−0.422115
$46$	21548.9	1.50152
$47$	7118.64	0.470059	0.235029	−	0.971988i	$-0.424481\pi$
$47$	7118.64	0.470059	0.235029	+	0.971988i	$0.424481\pi$
$48$	−967.708	−0.0606235
$49$	−14672.2	−0.872982
$50$	−5586.87	−0.316041
$51$	−2290.33	−0.123302
$52$	5805.57	0.297739
$53$	−27921.4	−1.36536	−0.682681	−	0.730716i	$-0.739186\pi$
$53$	−27921.4	−1.36536	−0.682681	+	0.730716i	$0.739186\pi$
$54$	15593.3	0.727701
$55$	−3025.00	−0.134840
$56$	6569.18	0.279925
$57$	−1333.16	−0.0543493
$58$	9221.17	0.359928
$59$	8163.77	0.305324	0.152662	−	0.988278i	$-0.451215\pi$
$59$	8163.77	0.305324	0.152662	+	0.988278i	$0.451215\pi$
$60$	4422.82	0.158606
$61$	50046.3	1.72206	0.861028	−	0.508558i	$-0.169821\pi$
$61$	50046.3	1.72206	0.861028	+	0.508558i	$0.169821\pi$
$62$	3969.85	0.131158
$63$	10597.4	0.336393
$64$	−53223.1	−1.62424
$65$	3029.70	0.0889439
$66$	3994.36	0.112872
$67$	−18153.2	−0.494045	−0.247022	−	0.969010i	$-0.579452\pi$
$67$	−18153.2	−0.494045	−0.247022	+	0.969010i	$0.579452\pi$
$68$	−29710.4	−0.779177
$69$	−8902.49	−0.225107
$70$	10325.4	0.251860
$71$	4545.37	0.107010	0.0535048	−	0.998568i	$-0.482961\pi$
$71$	4545.37	0.107010	0.0535048	+	0.998568i	$0.482961\pi$
$72$	32610.4	0.741353
$73$	24723.1	0.542995	0.271498	−	0.962439i	$-0.412481\pi$
$73$	24723.1	0.542995	0.271498	+	0.962439i	$0.412481\pi$
$74$	123236.	2.61611
$75$	2308.10	0.0473806
$76$	−17293.9	−0.343446
$77$	5590.65	0.107457
$78$	−4000.57	−0.0744535
$79$	−4008.44	−0.0722616	−0.0361308	−	0.999347i	$-0.511503\pi$
$79$	−4008.44	−0.0722616	−0.0361308	+	0.999347i	$0.511503\pi$
$80$	−6551.04	−0.114442
$81$	49292.9	0.834780
$82$	66775.8	1.09669
$83$	−9863.82	−0.157163	−0.0785815	−	0.996908i	$-0.525039\pi$
$83$	−9863.82	−0.157163	−0.0785815	+	0.996908i	$0.525039\pi$
$84$	−8174.03	−0.126397
$85$	−15504.7	−0.232764
$86$	36206.8	0.527891
$87$	−3809.53	−0.0539602
$88$	17203.6	0.236817
$89$	103749.	1.38838	0.694191	−	0.719790i	$-0.255762\pi$
$89$	103749.	1.38838	0.694191	+	0.719790i	$0.255762\pi$
$90$	51256.6	0.667027
$91$	−5599.34	−0.0708815
$92$	−115484.	−1.42250
$93$	−1640.06	−0.0196631
$94$	−63633.4	−0.742789
$95$	−9025.00	−0.102598
$96$	25452.2	0.281869
$97$	178627.	1.92760	0.963802	−	0.266618i	$-0.0859063\pi$
$97$	178627.	1.92760	0.963802	+	0.266618i	$0.0859063\pi$
$98$	131155.	1.37949
$99$	27752.8	0.284590
$100$	29940.9	0.299409
$101$	−117672.	−1.14781	−0.573904	−	0.818923i	$-0.694572\pi$
$101$	−117672.	−1.14781	−0.573904	+	0.818923i	$0.694572\pi$
$102$	20473.2	0.194843
$103$	15.2252	0.000141407 0	7.07035e−5	−	1.00000i	$-0.499977\pi$
$103$	15.2252	0.000141407 0	7.07035e−5		1.00000i	$0.499977\pi$
$104$	−17230.3	−0.156211
$105$	−4265.71	−0.0377588
$106$	249589.	2.15755
$107$	70313.4	0.593716	0.296858	−	0.954922i	$-0.404061\pi$
$107$	70313.4	0.593716	0.296858	+	0.954922i	$0.404061\pi$
$108$	−83566.9	−0.689405
$109$	−174865.	−1.40973	−0.704865	−	0.709342i	$-0.748992\pi$
$109$	−174865.	−1.40973	−0.704865	+	0.709342i	$0.748992\pi$
$110$	27040.4	0.213075
$111$	−50912.2	−0.392206
$112$	12107.3	0.0912015
$113$	43159.8	0.317968	0.158984	−	0.987281i	$-0.449178\pi$
$113$	43159.8	0.317968	0.158984	+	0.987281i	$0.449178\pi$
$114$	11917.1	0.0858830
$115$	−60266.7	−0.424945
$116$	−49417.7	−0.340987
$117$	−27795.9	−0.187723
$118$	−72975.9	−0.482474
$119$	28655.0	0.185495
$120$	−13126.5	−0.0832138
$121$	14641.0	0.0909091
$122$	−447363.	−2.72120
$123$	−27587.0	−0.164415
$124$	−21275.1	−0.124256
$125$	15625.0	0.0894427
$126$	−94729.8	−0.531570
$127$	−245257.	−1.34931	−0.674657	−	0.738131i	$-0.735708\pi$
$127$	−245257.	−1.34931	−0.674657	+	0.738131i	$0.735708\pi$
$128$	255213.	1.37682
$129$	−14958.1	−0.0791411
$130$	−27082.4	−0.140550
$131$	−146211.	−0.744392	−0.372196	−	0.928154i	$-0.621395\pi$
$131$	−146211.	−0.744392	−0.372196	+	0.928154i	$0.621395\pi$
$132$	−21406.4	−0.106932
$133$	16679.5	0.0817627
$134$	162271.	0.780692
$135$	−43610.3	−0.205947
$136$	88177.5	0.408800
$137$	228483.	1.04005	0.520023	−	0.854152i	$-0.325923\pi$
$137$	228483.	1.04005	0.520023	+	0.854152i	$0.325923\pi$
$138$	79579.3	0.355715
$139$	159736.	0.701238	0.350619	−	0.936518i	$-0.385971\pi$
$139$	159736.	0.701238	0.350619	+	0.936518i	$0.385971\pi$
$140$	−55335.3	−0.238606
$141$	26288.8	0.111358
$142$	−40631.0	−0.169097
$143$	−14663.7	−0.0599660
$144$	60102.4	0.241538
$145$	−25789.2	−0.101863
$146$	−221000.	−0.858043
$147$	−54183.8	−0.206812
$148$	−660439.	−2.47844
$149$	−478275.	−1.76487	−0.882434	−	0.470436i	$-0.844097\pi$
$149$	−478275.	−1.76487	−0.882434	+	0.470436i	$0.844097\pi$
$150$	−20632.0	−0.0748711
$151$	−354355.	−1.26472	−0.632362	−	0.774673i	$-0.717914\pi$
$151$	−354355.	−1.26472	−0.632362	+	0.774673i	$0.717914\pi$
$152$	51326.5	0.180191
$153$	142248.	0.491265
$154$	−49974.7	−0.169804
$155$	−11102.6	−0.0371191
$156$	21439.7	0.0705354
$157$	443242.	1.43513	0.717565	−	0.696491i	$-0.245257\pi$
$157$	443242.	1.43513	0.717565	+	0.696491i	$0.245257\pi$
$158$	35831.4	0.114188
$159$	−103113.	−0.323459
$160$	172303.	0.532098
$161$	111382.	0.338649
$162$	−440629.	−1.31912
$163$	116338.	0.342968	0.171484	−	0.985187i	$-0.445144\pi$
$163$	116338.	0.342968	0.171484	+	0.985187i	$0.445144\pi$
$164$	−357862.	−1.03898
$165$	−11171.2	−0.0319440
$166$	88172.6	0.248350
$167$	−217634.	−0.603860	−0.301930	−	0.953330i	$-0.597631\pi$
$167$	−217634.	−0.603860	−0.301930	+	0.953330i	$0.597631\pi$
$168$	24259.7	0.0663151
$169$	−356606.	−0.960445
$170$	138596.	0.367815
$171$	82799.7	0.216540
$172$	−194038.	−0.500111
$173$	−514139.	−1.30607	−0.653034	−	0.757329i	$-0.726504\pi$
$173$	−514139.	−1.30607	−0.653034	+	0.757329i	$0.726504\pi$
$174$	34053.4	0.0852682
$175$	−28877.3	−0.0712790
$176$	31707.0	0.0771568
$177$	30148.5	0.0723322
$178$	−927411.	−2.19393
$179$	554442.	1.29337	0.646686	−	0.762757i	$-0.276155\pi$
$179$	554442.	1.29337	0.646686	+	0.762757i	$0.276155\pi$
$180$	−274692.	−0.631925
$181$	743456.	1.68678	0.843391	−	0.537300i	$-0.180556\pi$
$181$	743456.	1.68678	0.843391	+	0.537300i	$0.180556\pi$
$182$	50052.4	0.112007
$183$	184819.	0.407961
$184$	342746.	0.746324
$185$	−344658.	−0.740387
$186$	14660.5	0.0310718
$187$	75042.7	0.156929
$188$	341022.	0.703700
$189$	80598.3	0.164124
$190$	80674.3	0.162126
$191$	−909987.	−1.80489	−0.902447	−	0.430801i	$-0.858231\pi$
$191$	−909987.	−1.80489	−0.902447	+	0.430801i	$0.858231\pi$
$192$	−196550.	−0.384788
$193$	−922858.	−1.78337	−0.891686	−	0.452655i	$-0.850477\pi$
$193$	−922858.	−1.78337	−0.891686	+	0.452655i	$0.850477\pi$
$194$	−1.59674e6	−3.04601
$195$	11188.5	0.0210711
$196$	−702879.	−1.30689
$197$	582010.	1.06848	0.534238	−	0.845334i	$-0.320599\pi$
$197$	582010.	1.06848	0.534238	+	0.845334i	$0.320599\pi$
$198$	−248082.	−0.449710
$199$	−544256.	−0.974250	−0.487125	−	0.873332i	$-0.661954\pi$
$199$	−544256.	−0.974250	−0.487125	+	0.873332i	$0.661954\pi$
$200$	−88861.7	−0.157087
$201$	−67039.0	−0.117041
$202$	1.05187e6	1.81377
$203$	47662.3	0.0811773
$204$	−109719.	−0.184589
$205$	−186754.	−0.310374
$206$	−136.098	−0.000223452 0
$207$	552916.	0.896878
$208$	−31756.3	−0.0508946
$209$	43681.0	0.0691714
$210$	38131.1	0.0596666
$211$	316670.	0.489667	0.244834	−	0.969565i	$-0.421267\pi$
$211$	316670.	0.489667	0.244834	+	0.969565i	$0.421267\pi$
$212$	−1.33759e6	−2.04401
$213$	16785.8	0.0253509
$214$	−628530.	−0.938192
$215$	−101261.	−0.149398
$216$	248018.	0.361701
$217$	20519.3	0.0295811
$218$	1.56311e6	2.22766
$219$	91301.3	0.128637
$220$	−144914.	−0.201862
$221$	−75159.3	−0.103515
$222$	455103.	0.619766
$223$	−839685.	−1.13072	−0.565359	−	0.824845i	$-0.691262\pi$
$223$	−839685.	−1.13072	−0.565359	+	0.824845i	$0.691262\pi$
$224$	−318441.	−0.424042
$225$	−143351.	−0.188775
$226$	−385805.	−0.502455
$227$	533594.	0.687300	0.343650	−	0.939098i	$-0.388337\pi$
$227$	533594.	0.687300	0.343650	+	0.939098i	$0.388337\pi$
$228$	−63865.5	−0.0813634
$229$	300739.	0.378967	0.189483	−	0.981884i	$-0.439319\pi$
$229$	300739.	0.378967	0.189483	+	0.981884i	$0.439319\pi$
$230$	538723.	0.671500
$231$	20646.0	0.0254570
$232$	146667.	0.178901
$233$	1.22367e6	1.47664	0.738322	−	0.674449i	$-0.235619\pi$
$233$	1.22367e6	1.47664	0.738322	+	0.674449i	$0.235619\pi$
$234$	248467.	0.296640
$235$	177966.	0.210217
$236$	391089.	0.457084
$237$	−14803.0	−0.0171190
$238$	−256146.	−0.293120
$239$	625171.	0.707953	0.353976	−	0.935254i	$-0.384829\pi$
$239$	625171.	0.707953	0.353976	+	0.935254i	$0.384829\pi$
$240$	−24192.7	−0.0271117
$241$	−573387.	−0.635924	−0.317962	−	0.948103i	$-0.602998\pi$
$241$	−573387.	−0.635924	−0.317962	+	0.948103i	$0.602998\pi$
$242$	−130876.	−0.143655
$243$	605929.	0.658273
$244$	2.39749e6	2.57800
$245$	−366805.	−0.390410
$246$	246600.	0.259810
$247$	−43748.9	−0.0456273
$248$	63142.3	0.0651916
$249$	−36426.7	−0.0372324
$250$	−139672.	−0.141338
$251$	559405.	0.560457	0.280228	−	0.959933i	$-0.409590\pi$
$251$	559405.	0.560457	0.280228	+	0.959933i	$0.409590\pi$
$252$	507672.	0.503596
$253$	291691.	0.286498
$254$	2.19235e6	2.13219
$255$	−57258.1	−0.0551425
$256$	−578207.	−0.551421
$257$	−432090.	−0.408076	−0.204038	−	0.978963i	$-0.565407\pi$
$257$	−432090.	−0.408076	−0.204038	+	0.978963i	$0.565407\pi$
$258$	133710.	0.125059
$259$	636978.	0.590032
$260$	145139.	0.133153
$261$	236603.	0.214990
$262$	1.30698e6	1.17629
$263$	869241.	0.774909	0.387454	−	0.921889i	$-0.373354\pi$
$263$	869241.	0.774909	0.387454	+	0.921889i	$0.373354\pi$
$264$	63532.2	0.0561027
$265$	−698036.	−0.610609
$266$	−149098.	−0.129202
$267$	383141.	0.328912
$268$	−869638.	−0.739608
$269$	−1.56705e6	−1.32039	−0.660194	−	0.751096i	$-0.729526\pi$
$269$	−1.56705e6	−1.32039	−0.660194	+	0.751096i	$0.729526\pi$
$270$	389832.	0.325438
$271$	−1.29851e6	−1.07404	−0.537021	−	0.843569i	$-0.680450\pi$
$271$	−1.29851e6	−1.07404	−0.537021	+	0.843569i	$0.680450\pi$
$272$	162515.	0.133190
$273$	−20678.1	−0.0167921
$274$	−2.04241e6	−1.64349
$275$	−75625.0	−0.0603023
$276$	−426478.	−0.336995
$277$	76427.6	0.0598481	0.0299241	−	0.999552i	$-0.490473\pi$
$277$	76427.6	0.0598481	0.0299241	+	0.999552i	$0.490473\pi$
$278$	−1.42788e6	−1.10810
$279$	101861.	0.0783425
$280$	164230.	0.125186
$281$	−1.15698e6	−0.874100	−0.437050	−	0.899437i	$-0.643977\pi$
$281$	−1.15698e6	−0.874100	−0.437050	+	0.899437i	$0.643977\pi$
$282$	−234995.	−0.175969
$283$	1.01950e6	0.756698	0.378349	−	0.925663i	$-0.376492\pi$
$283$	1.01950e6	0.756698	0.378349	+	0.925663i	$0.376492\pi$
$284$	217748.	0.160198
$285$	−33328.9	−0.0243058
$286$	131079.	0.0947585
$287$	345150.	0.247345
$288$	−1.58079e6	−1.12303
$289$	−1.03522e6	−0.729104
$290$	230529.	0.160965
$291$	659662.	0.456656
$292$	1.18437e6	0.812889
$293$	232619.	0.158298	0.0791490	−	0.996863i	$-0.474780\pi$
$293$	232619.	0.158298	0.0791490	+	0.996863i	$0.474780\pi$
$294$	484349.	0.326806
$295$	204094.	0.136545
$296$	1.96012e6	1.30033
$297$	211074.	0.138849
$298$	4.27530e6	2.78885
$299$	−292144.	−0.188981
$300$	110570.	0.0709310
$301$	187145.	0.119059
$302$	3.16757e6	1.99852
$303$	−434557.	−0.271919
$304$	94597.0	0.0587075
$305$	1.25116e6	0.770127
$306$	−1.27155e6	−0.776300
$307$	924323.	0.559729	0.279865	−	0.960039i	$-0.409710\pi$
$307$	924323.	0.559729	0.279865	+	0.960039i	$0.409710\pi$
$308$	267823.	0.160868
$309$	56.2261	3.34997e−5 0
$310$	99246.3	0.0586557
$311$	1.52615e6	0.894741	0.447371	−	0.894349i	$-0.352360\pi$
$311$	1.52615e6	0.894741	0.447371	+	0.894349i	$0.352360\pi$
$312$	−63630.9	−0.0370068
$313$	666982.	0.384816	0.192408	−	0.981315i	$-0.438370\pi$
$313$	666982.	0.384816	0.192408	+	0.981315i	$0.438370\pi$
$314$	−3.96213e6	−2.26780
$315$	264935.	0.150440
$316$	−192026.	−0.108179
$317$	1.71983e6	0.961252	0.480626	−	0.876926i	$-0.340410\pi$
$317$	1.71983e6	0.961252	0.480626	+	0.876926i	$0.340410\pi$
$318$	921722.	0.511131
$319$	124820.	0.0686762
$320$	−1.33058e6	−0.726382
$321$	259664.	0.140653
$322$	−995641.	−0.535135
$323$	223888.	0.119405
$324$	2.36140e6	1.24970
$325$	75742.5	0.0397769
$326$	−1.03995e6	−0.541960
$327$	−645767.	−0.333969
$328$	1.06210e6	0.545105
$329$	−328908.	−0.167527
$330$	99859.1	0.0504781
$331$	1.73022e6	0.868022	0.434011	−	0.900908i	$-0.357098\pi$
$331$	1.73022e6	0.868022	0.434011	+	0.900908i	$0.357098\pi$
$332$	−472531.	−0.235280
$333$	3.16206e6	1.56264
$334$	1.94543e6	0.954222
$335$	−453830.	−0.220944
$336$	44711.7	0.0216059
$337$	2.73853e6	1.31354	0.656770	−	0.754091i	$-0.271922\pi$
$337$	2.73853e6	1.31354	0.656770	+	0.754091i	$0.271922\pi$
$338$	3.18770e6	1.51770
$339$	159387.	0.0753277
$340$	−742760.	−0.348458
$341$	53736.8	0.0250257
$342$	−740145.	−0.342178
$343$	1.45446e6	0.667522
$344$	575886.	0.262386
$345$	−222562.	−0.100671
$346$	4.59588e6	2.06385
$347$	3.02682e6	1.34947	0.674734	−	0.738061i	$-0.264259\pi$
$347$	3.02682e6	1.34947	0.674734	+	0.738061i	$0.264259\pi$
$348$	−182497.	−0.0807809
$349$	−727645.	−0.319784	−0.159892	−	0.987135i	$-0.551115\pi$
$349$	−727645.	−0.319784	−0.159892	+	0.987135i	$0.551115\pi$
$350$	258134.	0.112635
$351$	−211402.	−0.0915885
$352$	−833945.	−0.358741
$353$	−4.54550e6	−1.94153	−0.970766	−	0.240027i	$-0.922844\pi$
$353$	−4.54550e6	−1.94153	−0.970766	+	0.240027i	$0.922844\pi$
$354$	−269497.	−0.114300
$355$	113634.	0.0478562
$356$	4.97015e6	2.07847
$357$	105822.	0.0439444
$358$	−4.95615e6	−2.04379
$359$	1.17510e6	0.481215	0.240608	−	0.970622i	$-0.422653\pi$
$359$	1.17510e6	0.481215	0.240608	+	0.970622i	$0.422653\pi$
$360$	815260.	0.331543
$361$	130321.	0.0526316
$362$	−6.64575e6	−2.66546
$363$	54068.6	0.0215367
$364$	−268239.	−0.106113
$365$	618078.	0.242835
$366$	−1.65209e6	−0.644661
$367$	3.55069e6	1.37609	0.688047	−	0.725666i	$-0.258468\pi$
$367$	3.55069e6	1.37609	0.688047	+	0.725666i	$0.258468\pi$
$368$	631696.	0.243158
$369$	1.71337e6	0.655068
$370$	3.08089e6	1.16996
$371$	1.29007e6	0.486609
$372$	−78567.9	−0.0294366
$373$	−1.31568e6	−0.489642	−0.244821	−	0.969568i	$-0.578729\pi$
$373$	−1.31568e6	−0.489642	−0.244821	+	0.969568i	$0.578729\pi$
$374$	−670806.	−0.247981
$375$	57702.4	0.0211893
$376$	−1.01212e6	−0.369200
$377$	−125014.	−0.0453006
$378$	−720467.	−0.259349
$379$	−3.32000e6	−1.18724	−0.593622	−	0.804744i	$-0.702303\pi$
$379$	−3.32000e6	−1.18724	−0.593622	+	0.804744i	$0.702303\pi$
$380$	−432347.	−0.153594
$381$	−905725.	−0.319657
$382$	8.13436e6	2.85210
$383$	1.19677e6	0.416881	0.208441	−	0.978035i	$-0.433161\pi$
$383$	1.19677e6	0.416881	0.208441	+	0.978035i	$0.433161\pi$
$384$	942490.	0.326174
$385$	139766.	0.0480563
$386$	8.24942e6	2.81809
$387$	929017.	0.315316
$388$	8.55721e6	2.88571
$389$	1.53618e6	0.514717	0.257359	−	0.966316i	$-0.417148\pi$
$389$	1.53618e6	0.514717	0.257359	+	0.966316i	$0.417148\pi$
$390$	−100014.	−0.0332966
$391$	1.49507e6	0.494560
$392$	2.08608e6	0.685670
$393$	−539951.	−0.176349
$394$	−5.20257e6	−1.68841
$395$	−100211.	−0.0323164
$396$	1.32951e6	0.426044
$397$	3.90312e6	1.24290	0.621449	−	0.783455i	$-0.286544\pi$
$397$	3.90312e6	1.24290	0.621449	+	0.783455i	$0.286544\pi$
$398$	4.86510e6	1.53951
$399$	61596.8	0.0193698
$400$	−163776.	−0.0511800
$401$	4.63418e6	1.43917	0.719585	−	0.694404i	$-0.244332\pi$
$401$	4.63418e6	1.43917	0.719585	+	0.694404i	$0.244332\pi$
$402$	599261.	0.184948
$403$	−53820.3	−0.0165076
$404$	−5.63712e6	−1.71832
$405$	1.23232e6	0.373325
$406$	−426052.	−0.128277
$407$	1.66814e6	0.499168
$408$	325635.	0.0968459
$409$	−1.67856e6	−0.496169	−0.248084	−	0.968738i	$-0.579801\pi$
$409$	−1.67856e6	−0.496169	−0.248084	+	0.968738i	$0.579801\pi$
$410$	1.66939e6	0.490455
$411$	843778.	0.246390
$412$	729.371	0.000211693 0
$413$	−377197.	−0.108816
$414$	−4.94251e6	−1.41725
$415$	−246596.	−0.0702854
$416$	835240.	0.236634
$417$	589897.	0.166126
$418$	−390464.	−0.109305
$419$	−5.40112e6	−1.50297	−0.751483	−	0.659752i	$-0.770661\pi$
$419$	−5.40112e6	−1.50297	−0.751483	+	0.659752i	$0.770661\pi$
$420$	−204351.	−0.0565266
$421$	3.27325e6	0.900064	0.450032	−	0.893012i	$-0.351413\pi$
$421$	3.27325e6	0.900064	0.450032	+	0.893012i	$0.351413\pi$
$422$	−2.83071e6	−0.773774
$423$	−1.63275e6	−0.443678
$424$	3.96983e6	1.07240
$425$	−387617.	−0.104095
$426$	−150048.	−0.0400596
$427$	−2.31232e6	−0.613732
$428$	3.36840e6	0.888820
$429$	−54152.6	−0.0142061
$430$	905170.	0.236080
$431$	7.52133e6	1.95030	0.975151	−	0.221543i	$-0.0711093\pi$
$431$	7.52133e6	1.95030	0.975151	+	0.221543i	$0.0711093\pi$
$432$	457109.	0.117845
$433$	5.78710e6	1.48334	0.741671	−	0.670764i	$-0.234034\pi$
$433$	5.78710e6	1.48334	0.741671	+	0.670764i	$0.234034\pi$
$434$	−183422.	−0.0467441
$435$	−95238.4	−0.0241317
$436$	−8.37697e6	−2.11043
$437$	870252.	0.217992
$438$	−816141.	−0.203273
$439$	−6.07506e6	−1.50449	−0.752244	−	0.658884i	$-0.771029\pi$
$439$	−6.07506e6	−1.50449	−0.752244	+	0.658884i	$0.771029\pi$
$440$	430090.	0.105908
$441$	3.36525e6	0.823988
$442$	671848.	0.163574
$443$	−3.99904e6	−0.968159	−0.484080	−	0.875024i	$-0.660846\pi$
$443$	−3.99904e6	−0.968159	−0.484080	+	0.875024i	$0.660846\pi$
$444$	−2.43897e6	−0.587151
$445$	2.59373e6	0.620904
$446$	7.50593e6	1.78677
$447$	−1.76625e6	−0.418103
$448$	2.45910e6	0.578871
$449$	2.68831e6	0.629308	0.314654	−	0.949206i	$-0.398112\pi$
$449$	2.68831e6	0.629308	0.314654	+	0.949206i	$0.398112\pi$
$450$	1.28142e6	0.298304
$451$	903891.	0.209254
$452$	2.06759e6	0.476013
$453$	−1.30862e6	−0.299617
$454$	−4.76979e6	−1.08607
$455$	−139983.	−0.0316992
$456$	189546.	0.0426878
$457$	3.42217e6	0.766499	0.383250	−	0.923645i	$-0.374805\pi$
$457$	3.42217e6	0.766499	0.383250	+	0.923645i	$0.374805\pi$
$458$	−2.68830e6	−0.598845
$459$	1.08186e6	0.239685
$460$	−2.88711e6	−0.636163
$461$	1.97403e6	0.432614	0.216307	−	0.976325i	$-0.430599\pi$
$461$	1.97403e6	0.432614	0.216307	+	0.976325i	$0.430599\pi$
$462$	−184554.	−0.0402272
$463$	4.60232e6	0.997756	0.498878	−	0.866672i	$-0.333746\pi$
$463$	4.60232e6	0.997756	0.498878	+	0.866672i	$0.333746\pi$
$464$	270314.	0.0582872
$465$	−41001.5	−0.00879362
$466$	−1.09384e7	−2.33340
$467$	7.87733e6	1.67142	0.835712	−	0.549167i	$-0.185055\pi$
$467$	7.87733e6	1.67142	0.835712	+	0.549167i	$0.185055\pi$
$468$	−1.33158e6	−0.281029
$469$	838746.	0.176075
$470$	−1.59084e6	−0.332185
$471$	1.63687e6	0.339987
$472$	−1.16071e6	−0.239812
$473$	490103.	0.100724
$474$	132324.	0.0270515
$475$	−225625.	−0.0458831
$476$	1.37273e6	0.277695
$477$	6.40412e6	1.28873
$478$	−5.58840e6	−1.11871
$479$	−2.22837e6	−0.443759	−0.221880	−	0.975074i	$-0.571219\pi$
$479$	−2.22837e6	−0.443759	−0.221880	+	0.975074i	$0.571219\pi$
$480$	636306.	0.126056
$481$	−1.67073e6	−0.329264
$482$	5.12550e6	1.00489
$483$	411328.	0.0802270
$484$	701384.	0.136095
$485$	4.46568e6	0.862051
$486$	−5.41639e6	−1.04021
$487$	237989.	0.0454709	0.0227355	−	0.999742i	$-0.492762\pi$
$487$	237989.	0.0454709	0.0227355	+	0.999742i	$0.492762\pi$
$488$	−7.11551e6	−1.35256
$489$	429632.	0.0812503
$490$	3.27887e6	0.616927
$491$	−7.93946e6	−1.48623	−0.743117	−	0.669162i	$-0.766653\pi$
$491$	−7.93946e6	−1.48623	−0.743117	+	0.669162i	$0.766653\pi$
$492$	−1.32157e6	−0.246137
$493$	639766.	0.118551
$494$	391070.	0.0721004
$495$	693820.	0.127272
$496$	116374.	0.0212399
$497$	−210013.	−0.0381377
$498$	325617.	0.0588348
$499$	−6.93260e6	−1.24636	−0.623182	−	0.782077i	$-0.714160\pi$
$499$	−6.93260e6	−1.24636	−0.623182	+	0.782077i	$0.714160\pi$
$500$	748523.	0.133900
$501$	−803714.	−0.143056
$502$	−5.00052e6	−0.885636
$503$	7.73779e6	1.36363	0.681816	−	0.731524i	$-0.261191\pi$
$503$	7.73779e6	1.36363	0.681816	+	0.731524i	$0.261191\pi$
$504$	−1.50672e6	−0.264214
$505$	−2.94179e6	−0.513315
$506$	−2.60742e6	−0.452726
$507$	−1.31693e6	−0.227532
$508$	−1.17492e7	−2.01998
$509$	2.91564e6	0.498815	0.249407	−	0.968399i	$-0.419764\pi$
$509$	2.91564e6	0.498815	0.249407	+	0.968399i	$0.419764\pi$
$510$	511830.	0.0871365
$511$	−1.14230e6	−0.193521
$512$	−2.99823e6	−0.505464
$513$	629733.	0.105648
$514$	3.86244e6	0.644844
$515$	380.631	6.32391e−5 0
$516$	−716574.	−0.118478
$517$	−861355.	−0.141728
$518$	−5.69394e6	−0.932371
$519$	−1.89869e6	−0.309412
$520$	−430759.	−0.0698595
$521$	2.49787e6	0.403158	0.201579	−	0.979472i	$-0.435393\pi$
$521$	2.49787e6	0.403158	0.201579	+	0.979472i	$0.435393\pi$
$522$	−2.11499e6	−0.339728
$523$	−6.42836e6	−1.02765	−0.513826	−	0.857895i	$-0.671772\pi$
$523$	−6.42836e6	−1.02765	−0.513826	+	0.857895i	$0.671772\pi$
$524$	−7.00431e6	−1.11439
$525$	−106643.	−0.0168862
$526$	−7.77013e6	−1.22451
$527$	275429.	0.0431999
$528$	117093.	0.0182787
$529$	−625016.	−0.0971073
$530$	6.23973e6	0.964886
$531$	−1.87246e6	−0.288188
$532$	799041.	0.122402
$533$	−905295.	−0.138030
$534$	−3.42489e6	−0.519749
$535$	1.75783e6	0.265518
$536$	2.58100e6	0.388039
$537$	2.04753e6	0.306404
$538$	1.40078e7	2.08648
$539$	1.77534e6	0.263214
$540$	−2.08917e6	−0.308311
$541$	179949.	0.0264336	0.0132168	−	0.999913i	$-0.495793\pi$
$541$	179949.	0.0264336	0.0132168	+	0.999913i	$0.495793\pi$
$542$	1.16073e7	1.69720
$543$	2.74555e6	0.399604
$544$	−4.27440e6	−0.619267
$545$	−4.37162e6	−0.630450
$546$	184841.	0.0265349
$547$	−5.65618e6	−0.808267	−0.404133	−	0.914700i	$-0.632427\pi$
$547$	−5.65618e6	−0.808267	−0.404133	+	0.914700i	$0.632427\pi$
$548$	1.09456e7	1.55700
$549$	−1.14787e7	−1.62541
$550$	676011.	0.0952899
$551$	372396.	0.0522548
$552$	1.26574e6	0.176807
$553$	185205.	0.0257537
$554$	−683185.	−0.0945723
$555$	−1.27280e6	−0.175400
$556$	7.65222e6	1.04979
$557$	−9.50093e6	−1.29756	−0.648781	−	0.760975i	$-0.724721\pi$
$557$	−9.50093e6	−1.29756	−0.648781	+	0.760975i	$0.724721\pi$
$558$	−910534.	−0.123797
$559$	−490865.	−0.0664404
$560$	302682.	0.0407866
$561$	277129.	0.0371771
$562$	1.03422e7	1.38126
$563$	8.80714e6	1.17102	0.585509	−	0.810666i	$-0.300895\pi$
$563$	8.80714e6	1.17102	0.585509	+	0.810666i	$0.300895\pi$
$564$	1.25938e6	0.166709
$565$	1.07900e6	0.142200
$566$	−9.11332e6	−1.19574
$567$	−2.27752e6	−0.297512
$568$	−646254.	−0.0840490
$569$	1.01529e7	1.31464	0.657322	−	0.753610i	$-0.271689\pi$
$569$	1.01529e7	1.31464	0.657322	+	0.753610i	$0.271689\pi$
$570$	297927.	0.0384081
$571$	7.35589e6	0.944159	0.472079	−	0.881556i	$-0.343504\pi$
$571$	7.35589e6	0.944159	0.472079	+	0.881556i	$0.343504\pi$
$572$	−702473.	−0.0897718
$573$	−3.36054e6	−0.427585
$574$	−3.08529e6	−0.390855
$575$	−1.50667e6	−0.190041
$576$	1.22074e7	1.53308
$577$	−1.49898e7	−1.87437	−0.937187	−	0.348827i	$-0.886580\pi$
$577$	−1.49898e7	−1.87437	−0.937187	+	0.348827i	$0.886580\pi$
$578$	9.25385e6	1.15213
$579$	−3.40807e6	−0.422486
$580$	−1.23544e6	−0.152494
$581$	455745.	0.0560121
$582$	−5.89671e6	−0.721609
$583$	3.37849e6	0.411672
$584$	−3.51510e6	−0.426487
$585$	−694898.	−0.0839521
$586$	−2.07937e6	−0.250143
$587$	2.17749e6	0.260832	0.130416	−	0.991459i	$-0.458369\pi$
$587$	2.17749e6	0.260832	0.130416	+	0.991459i	$0.458369\pi$
$588$	−2.59570e6	−0.309608
$589$	160322.	0.0190417
$590$	−1.82440e6	−0.215769
$591$	2.14934e6	0.253125
$592$	3.61259e6	0.423656
$593$	−6.49260e6	−0.758196	−0.379098	−	0.925356i	$-0.623766\pi$
$593$	−6.49260e6	−0.758196	−0.379098	+	0.925356i	$0.623766\pi$
$594$	−1.88679e6	−0.219410
$595$	716375.	0.0829560
$596$	−2.29120e7	−2.64209
$597$	−2.00991e6	−0.230803
$598$	2.61147e6	0.298629
$599$	1.40660e7	1.60179	0.800893	−	0.598808i	$-0.204359\pi$
$599$	1.40660e7	1.60179	0.800893	+	0.598808i	$0.204359\pi$
$600$	−328162.	−0.0372143
$601$	6.79327e6	0.767172	0.383586	−	0.923505i	$-0.374689\pi$
$601$	6.79327e6	0.767172	0.383586	+	0.923505i	$0.374689\pi$
$602$	−1.67289e6	−0.188138
$603$	4.16366e6	0.466318
$604$	−1.69755e7	−1.89335
$605$	366025.	0.0406558
$606$	3.88450e6	0.429688
$607$	−8.83851e6	−0.973660	−0.486830	−	0.873497i	$-0.661847\pi$
$607$	−8.83851e6	−0.973660	−0.486830	+	0.873497i	$0.661847\pi$
$608$	−2.48805e6	−0.272961
$609$	176015.	0.0192312
$610$	−1.11841e7	−1.21696
$611$	862693.	0.0934875
$612$	6.81443e6	0.735447
$613$	−806654.	−0.0867034	−0.0433517	−	0.999060i	$-0.513804\pi$
$613$	−806654.	−0.0867034	−0.0433517	+	0.999060i	$0.513804\pi$
$614$	−8.26251e6	−0.884486
$615$	−689675.	−0.0735287
$616$	−794871.	−0.0844005
$617$	7.96592e6	0.842409	0.421205	−	0.906966i	$-0.361607\pi$
$617$	7.96592e6	0.842409	0.421205	+	0.906966i	$0.361607\pi$
$618$	−502.604	−5.29364e−5 0
$619$	−1.16239e7	−1.21934	−0.609670	−	0.792655i	$-0.708698\pi$
$619$	−1.16239e7	−1.21934	−0.609670	+	0.792655i	$0.708698\pi$
$620$	−531877.	−0.0555689
$621$	4.20520e6	0.437580
$622$	−1.36423e7	−1.41387
$623$	−4.79359e6	−0.494813
$624$	−117275.	−0.0120571
$625$	390625.	0.0400000
$626$	−5.96215e6	−0.608088
$627$	161312.	0.0163869
$628$	2.12337e7	2.14846
$629$	8.55010e6	0.861677
$630$	−2.36825e6	−0.237725
$631$	−1.61018e7	−1.60991	−0.804955	−	0.593336i	$-0.797810\pi$
$631$	−1.61018e7	−1.60991	−0.804955	+	0.593336i	$0.797810\pi$
$632$	569915.	0.0567567
$633$	1.16945e6	0.116004
$634$	−1.53735e7	−1.51897
$635$	−6.13144e6	−0.603431
$636$	−4.93966e6	−0.484232
$637$	−1.77810e6	−0.173623
$638$	−1.11576e6	−0.108522
$639$	−1.04253e6	−0.101004
$640$	6.38033e6	0.615734
$641$	8.92735e6	0.858179	0.429089	−	0.903262i	$-0.358835\pi$
$641$	8.92735e6	0.858179	0.429089	+	0.903262i	$0.358835\pi$
$642$	−2.32113e6	−0.222261
$643$	−1.57185e6	−0.149928	−0.0749640	−	0.997186i	$-0.523884\pi$
$643$	−1.57185e6	−0.149928	−0.0749640	+	0.997186i	$0.523884\pi$
$644$	5.33580e6	0.506973
$645$	−373952.	−0.0353930
$646$	−2.00133e6	−0.188685
$647$	9.23252e6	0.867081	0.433540	−	0.901134i	$-0.357264\pi$
$647$	9.23252e6	0.867081	0.433540	+	0.901134i	$0.357264\pi$
$648$	−7.00841e6	−0.655665
$649$	−987817.	−0.0920587
$650$	−677061.	−0.0628557
$651$	75777.0	0.00700785
$652$	5.57324e6	0.513439
$653$	6.80077e6	0.624130	0.312065	−	0.950061i	$-0.398979\pi$
$653$	6.80077e6	0.624130	0.312065	+	0.950061i	$0.398979\pi$
$654$	5.77251e6	0.527740
$655$	−3.65528e6	−0.332902
$656$	1.95750e6	0.177599
$657$	−5.67054e6	−0.512521
$658$	2.94010e6	0.264726
$659$	−525211.	−0.0471107	−0.0235554	−	0.999723i	$-0.507499\pi$
$659$	−525211.	−0.0471107	−0.0235554	+	0.999723i	$0.507499\pi$
$660$	−535161.	−0.0478217
$661$	−837437.	−0.0745502	−0.0372751	−	0.999305i	$-0.511868\pi$
$661$	−837437.	−0.0745502	−0.0372751	+	0.999305i	$0.511868\pi$
$662$	−1.54664e7	−1.37165
$663$	−277560.	−0.0245230
$664$	1.40243e6	0.123441
$665$	416989.	0.0365654
$666$	−2.82656e7	−2.46929
$667$	2.48677e6	0.216432
$668$	−1.04259e7	−0.904006
$669$	−3.10092e6	−0.267871
$670$	4.05678e6	0.349136
$671$	−6.05560e6	−0.519219
$672$	−1.17599e6	−0.100457
$673$	−1.04564e7	−0.889907	−0.444953	−	0.895554i	$-0.646780\pi$
$673$	−1.04564e7	−0.889907	−0.444953	+	0.895554i	$0.646780\pi$
$674$	−2.44797e7	−2.07566
$675$	−1.09026e6	−0.0921021
$676$	−1.70834e7	−1.43783
$677$	1.48236e7	1.24303	0.621516	−	0.783401i	$-0.286517\pi$
$677$	1.48236e7	1.24303	0.621516	+	0.783401i	$0.286517\pi$
$678$	−1.42476e6	−0.119033
$679$	−8.25323e6	−0.686989
$680$	2.20444e6	0.182821
$681$	1.97054e6	0.162824
$682$	−480352.	−0.0395457
$683$	1.40802e7	1.15493	0.577467	−	0.816414i	$-0.304041\pi$
$683$	1.40802e7	1.15493	0.577467	+	0.816414i	$0.304041\pi$
$684$	3.96656e6	0.324171
$685$	5.71208e6	0.465123
$686$	−1.30014e7	−1.05482
$687$	1.11062e6	0.0897784
$688$	1.06138e6	0.0854872
$689$	−3.38374e6	−0.271550
$690$	1.98948e6	0.159081
$691$	1.91573e7	1.52630	0.763150	−	0.646222i	$-0.223652\pi$
$691$	1.91573e7	1.52630	0.763150	+	0.646222i	$0.223652\pi$
$692$	−2.46301e7	−1.95524
$693$	−1.28228e6	−0.101426
$694$	−2.70567e7	−2.13243
$695$	3.99340e6	0.313603
$696$	541635.	0.0423822
$697$	4.63291e6	0.361220
$698$	6.50441e6	0.505323
$699$	4.51897e6	0.349821
$700$	−1.38338e6	−0.106708
$701$	−3.09744e6	−0.238072	−0.119036	−	0.992890i	$-0.537980\pi$
$701$	−3.09744e6	−0.238072	−0.119036	+	0.992890i	$0.537980\pi$
$702$	1.88972e6	0.144729
$703$	4.97686e6	0.379810
$704$	6.43999e6	0.489727
$705$	657220.	0.0498010
$706$	4.06321e7	3.06802
$707$	5.43687e6	0.409073
$708$	1.44428e6	0.108285
$709$	−1.31030e7	−0.978938	−0.489469	−	0.872021i	$-0.662809\pi$
$709$	−1.31030e7	−0.978938	−0.489469	+	0.872021i	$0.662809\pi$
$710$	−1.01577e6	−0.0756225
$711$	919384.	0.0682061
$712$	−1.47509e7	−1.09048
$713$	1.07059e6	0.0788679
$714$	−945937.	−0.0694411
$715$	−366594.	−0.0268176
$716$	2.65608e7	1.93624
$717$	2.30873e6	0.167716
$718$	−1.05042e7	−0.760418
$719$	1.41672e7	1.02203	0.511014	−	0.859572i	$-0.329270\pi$
$719$	1.41672e7	1.02203	0.511014	+	0.859572i	$0.329270\pi$
$720$	1.50256e6	0.108019
$721$	−703.462	−5.03967e−5 0
$722$	−1.16494e6	−0.0831686
$723$	−2.11749e6	−0.150652
$724$	3.56156e7	2.52519
$725$	−644730.	−0.0455547
$726$	−483318.	−0.0340323
$727$	−1.55120e7	−1.08851	−0.544253	−	0.838921i	$-0.683187\pi$
$727$	−1.55120e7	−1.08851	−0.544253	+	0.838921i	$0.683187\pi$
$728$	796106.	0.0556727
$729$	−9.74052e6	−0.678834
$730$	−5.52499e6	−0.383729
$731$	2.51203e6	0.173873
$732$	8.85382e6	0.610736
$733$	−2.23658e7	−1.53753	−0.768766	−	0.639531i	$-0.779129\pi$
$733$	−2.23658e7	−1.53753	−0.768766	+	0.639531i	$0.779129\pi$
$734$	−3.17396e7	−2.17451
$735$	−1.35460e6	−0.0924893
$736$	−1.66146e7	−1.13056
$737$	2.19654e6	0.148960
$738$	−1.53158e7	−1.03514
$739$	2.06098e7	1.38823	0.694116	−	0.719863i	$-0.255796\pi$
$739$	2.06098e7	1.38823	0.694116	+	0.719863i	$0.255796\pi$
$740$	−1.65110e7	−1.10839
$741$	−161563.	−0.0108092
$742$	−1.15319e7	−0.768941
$743$	1.09623e7	0.728502	0.364251	−	0.931301i	$-0.381325\pi$
$743$	1.09623e7	0.728502	0.364251	+	0.931301i	$0.381325\pi$
$744$	233182.	0.0154441
$745$	−1.19569e7	−0.789273
$746$	1.17609e7	0.773735
$747$	2.26239e6	0.148342
$748$	3.59496e6	0.234931
$749$	−3.24874e6	−0.211597
$750$	−515801.	−0.0334834
$751$	971655.	0.0628655	0.0314327	−	0.999506i	$-0.489993\pi$
$751$	971655.	0.0628655	0.0314327	+	0.999506i	$0.489993\pi$
$752$	−1.86538e6	−0.120288
$753$	2.06586e6	0.132774
$754$	1.11750e6	0.0715842
$755$	−8.85886e6	−0.565602
$756$	3.86110e6	0.245701
$757$	2.81473e7	1.78524	0.892620	−	0.450810i	$-0.148865\pi$
$757$	2.81473e7	1.78524	0.892620	+	0.450810i	$0.148865\pi$
$758$	2.96774e7	1.87609
$759$	1.07720e6	0.0678723
$760$	1.28316e6	0.0805838
$761$	9.08791e6	0.568856	0.284428	−	0.958697i	$-0.408196\pi$
$761$	9.08791e6	0.568856	0.284428	+	0.958697i	$0.408196\pi$
$762$	8.09626e6	0.505123
$763$	8.07940e6	0.502421
$764$	−4.35933e7	−2.70201
$765$	3.55619e6	0.219701
$766$	−1.06979e7	−0.658758
$767$	989351.	0.0607242
$768$	−2.13529e6	−0.130633
$769$	2.67474e7	1.63104	0.815521	−	0.578728i	$-0.196451\pi$
$769$	2.67474e7	1.63104	0.815521	+	0.578728i	$0.196451\pi$
$770$	−1.24937e6	−0.0759388
$771$	−1.59569e6	−0.0966746
$772$	−4.42100e7	−2.66979
$773$	1.97603e7	1.18945	0.594723	−	0.803931i	$-0.297262\pi$
$773$	1.97603e7	1.18945	0.594723	+	0.803931i	$0.297262\pi$
$774$	−8.30447e6	−0.498264
$775$	−277566.	−0.0166001
$776$	−2.53970e7	−1.51401
$777$	2.35233e6	0.139780
$778$	−1.37319e7	−0.813359
$779$	2.69673e6	0.159219
$780$	535992.	0.0315444
$781$	−549989.	−0.0322646
$782$	−1.33644e7	−0.781506
$783$	1.79948e6	0.104892
$784$	3.84473e6	0.223396
$785$	1.10810e7	0.641810
$786$	4.82661e6	0.278667
$787$	−8.11421e6	−0.466992	−0.233496	−	0.972358i	$-0.575017\pi$
$787$	−8.11421e6	−0.466992	−0.233496	+	0.972358i	$0.575017\pi$
$788$	2.78814e7	1.59956
$789$	3.21007e6	0.183578
$790$	895785.	0.0510665
$791$	−1.99414e6	−0.113322
$792$	−3.94586e6	−0.223526
$793$	6.06501e6	0.342490
$794$	−3.48899e7	−1.96403
$795$	−2.57781e6	−0.144655
$796$	−2.60728e7	−1.45850
$797$	−1.51390e7	−0.844212	−0.422106	−	0.906546i	$-0.638709\pi$
$797$	−1.51390e7	−0.844212	−0.422106	+	0.906546i	$0.638709\pi$
$798$	−550613.	−0.0306083
$799$	−4.41489e6	−0.244655
$800$	4.30756e6	0.237962
$801$	−2.37961e7	−1.31046
$802$	−4.14249e7	−2.27418
$803$	−2.99150e6	−0.163719
$804$	−3.21153e6	−0.175215
$805$	2.78455e6	0.151448
$806$	481098.	0.0260853
$807$	−5.78703e6	−0.312804
$808$	1.67304e7	0.901526
$809$	−3.79985e6	−0.204124	−0.102062	−	0.994778i	$-0.532544\pi$
$809$	−3.79985e6	−0.204124	−0.102062	+	0.994778i	$0.532544\pi$
$810$	−1.10157e7	−0.589930
$811$	1.19461e7	0.637786	0.318893	−	0.947791i	$-0.396689\pi$
$811$	1.19461e7	0.637786	0.318893	+	0.947791i	$0.396689\pi$
$812$	2.28328e6	0.121526
$813$	−4.79533e6	−0.254444
$814$	−1.49115e7	−0.788788
$815$	2.90846e6	0.153380
$816$	600161.	0.0315531
$817$	1.46221e6	0.0766398
$818$	1.50046e7	0.784048
$819$	1.28428e6	0.0669034
$820$	−8.94655e6	−0.464645
$821$	−2.80369e7	−1.45169	−0.725843	−	0.687860i	$-0.758550\pi$
$821$	−2.80369e7	−1.45169	−0.725843	+	0.687860i	$0.758550\pi$
$822$	−7.54252e6	−0.389347
$823$	−3.46329e7	−1.78234	−0.891168	−	0.453673i	$-0.850113\pi$
$823$	−3.46329e7	−1.78234	−0.891168	+	0.453673i	$0.850113\pi$
$824$	−2164.70	−0.000111066 0
$825$	−279280.	−0.0142858
$826$	3.37176e6	0.171952
$827$	1.40753e7	0.715636	0.357818	−	0.933791i	$-0.383521\pi$
$827$	1.40753e7	0.715636	0.357818	+	0.933791i	$0.383521\pi$
$828$	2.64877e7	1.34267
$829$	−1.31165e7	−0.662875	−0.331438	−	0.943477i	$-0.607534\pi$
$829$	−1.31165e7	−0.662875	−0.331438	+	0.943477i	$0.607534\pi$
$830$	2.20431e6	0.111065
$831$	282244.	0.0141782
$832$	−6.45000e6	−0.323036
$833$	9.09953e6	0.454367
$834$	−5.27308e6	−0.262512
$835$	−5.44086e6	−0.270054
$836$	2.09256e6	0.103553
$837$	774703.	0.0382227
$838$	4.82806e7	2.37499
$839$	2.42236e7	1.18805	0.594023	−	0.804448i	$-0.297539\pi$
$839$	2.42236e7	1.18805	0.594023	+	0.804448i	$0.297539\pi$
$840$	606492.	0.0296570
$841$	−1.94470e7	−0.948119
$842$	−2.92595e7	−1.42229
$843$	−4.27268e6	−0.207077
$844$	1.51702e7	0.733054
$845$	−8.91516e6	−0.429524
$846$	1.45951e7	0.701101
$847$	−676469.	−0.0323996
$848$	7.31658e6	0.349396
$849$	3.76498e6	0.179264
$850$	3.46491e6	0.164492
$851$	3.32342e7	1.57312
$852$	804133.	0.0379515
$853$	3.50777e7	1.65067	0.825333	−	0.564647i	$-0.190988\pi$
$853$	3.50777e7	1.65067	0.825333	+	0.564647i	$0.190988\pi$
$854$	2.06698e7	0.969823
$855$	2.06999e6	0.0968397
$856$	−9.99707e6	−0.466324
$857$	2.44542e7	1.13737	0.568684	−	0.822556i	$-0.307453\pi$
$857$	2.44542e7	1.13737	0.568684	+	0.822556i	$0.307453\pi$
$858$	484069.	0.0224486
$859$	2.38256e7	1.10170	0.550848	−	0.834606i	$-0.314304\pi$
$859$	2.38256e7	1.10170	0.550848	+	0.834606i	$0.314304\pi$
$860$	−4.85095e6	−0.223656
$861$	1.27462e6	0.0585968
$862$	−6.72331e7	−3.08187
$863$	1.91145e7	0.873645	0.436823	−	0.899548i	$-0.356104\pi$
$863$	1.91145e7	0.873645	0.436823	+	0.899548i	$0.356104\pi$
$864$	−1.20227e7	−0.547919
$865$	−1.28535e7	−0.584091
$866$	−5.17308e7	−2.34398
$867$	−3.82304e6	−0.172727
$868$	982988.	0.0442842
$869$	485021.	0.0217877
$870$	851334.	0.0381331
$871$	−2.19995e6	−0.0982579
$872$	2.48620e7	1.10725
$873$	−4.09703e7	−1.81942
$874$	−7.77917e6	−0.344472
$875$	−721933.	−0.0318770
$876$	4.37383e6	0.192576
$877$	−2.32837e7	−1.02224	−0.511121	−	0.859509i	$-0.670770\pi$
$877$	−2.32837e7	−1.02224	−0.511121	+	0.859509i	$0.670770\pi$
$878$	5.43048e7	2.37740
$879$	859050.	0.0375013
$880$	792676.	0.0345056
$881$	−2.01012e6	−0.0872534	−0.0436267	−	0.999048i	$-0.513891\pi$
$881$	−2.01012e6	−0.0872534	−0.0436267	+	0.999048i	$0.513891\pi$
$882$	−3.00819e7	−1.30207
$883$	2.50369e7	1.08063	0.540316	−	0.841462i	$-0.318305\pi$
$883$	2.50369e7	1.08063	0.540316	+	0.841462i	$0.318305\pi$
$884$	−3.60054e6	−0.154966
$885$	753711.	0.0323480
$886$	3.57474e7	1.52989
$887$	−4.16739e7	−1.77850	−0.889252	−	0.457417i	$-0.848775\pi$
$887$	−4.16739e7	−1.77850	−0.889252	+	0.457417i	$0.848775\pi$
$888$	7.23863e6	0.308052
$889$	1.13318e7	0.480889
$890$	−2.31853e7	−0.981155
$891$	−5.96445e6	−0.251696
$892$	−4.02255e7	−1.69274
$893$	−2.56983e6	−0.107839
$894$	1.57885e7	0.660688
$895$	1.38610e7	0.578413
$896$	−1.17918e7	−0.490693
$897$	−1.07888e6	−0.0447703
$898$	−2.40307e7	−0.994435
$899$	458125.	0.0189054
$900$	−6.86731e6	−0.282605
$901$	1.73165e7	0.710639
$902$	−8.07987e6	−0.330665
$903$	691119.	0.0282055
$904$	−6.13641e6	−0.249743
$905$	1.85864e7	0.754352
$906$	1.16977e7	0.473456
$907$	4.14673e7	1.67374	0.836869	−	0.547403i	$-0.184383\pi$
$907$	4.14673e7	1.67374	0.836869	+	0.547403i	$0.184383\pi$
$908$	2.55621e7	1.02892
$909$	2.69894e7	1.08339
$910$	1.25131e6	0.0500912
$911$	4.28891e7	1.71218	0.856092	−	0.516823i	$-0.172885\pi$
$911$	4.28891e7	1.71218	0.856092	+	0.516823i	$0.172885\pi$
$912$	349343.	0.0139080
$913$	1.19352e6	0.0473864
$914$	−3.05908e7	−1.21123
$915$	4.62047e6	0.182446
$916$	1.44070e7	0.567330
$917$	6.75549e6	0.265298
$918$	−9.67076e6	−0.378751
$919$	−4.10843e7	−1.60467	−0.802337	−	0.596871i	$-0.796410\pi$
$919$	−4.10843e7	−1.60467	−0.802337	+	0.596871i	$0.796410\pi$
$920$	8.56864e6	0.333766
$921$	3.41348e6	0.132602
$922$	−1.76458e7	−0.683619
$923$	550844.	0.0212826
$924$	989057.	0.0381102
$925$	−8.61644e6	−0.331111
$926$	−4.11401e7	−1.57666
$927$	−3492.09	−0.000133471 0
$928$	−7.10967e6	−0.271007
$929$	−4.76099e7	−1.80991	−0.904957	−	0.425503i	$-0.860097\pi$
$929$	−4.76099e7	−1.80991	−0.904957	+	0.425503i	$0.860097\pi$
$930$	366512.	0.0138957
$931$	5.29667e6	0.200276
$932$	5.86206e7	2.21060
$933$	5.63602e6	0.211967
$934$	−7.04153e7	−2.64119
$935$	1.87607e6	0.0701810
$936$	3.95199e6	0.147444
$937$	1.24130e7	0.461878	0.230939	−	0.972968i	$-0.425820\pi$
$937$	1.24130e7	0.461878	0.230939	+	0.972968i	$0.425820\pi$
$938$	−7.49754e6	−0.278235
$939$	2.46314e6	0.0911642
$940$	8.52554e6	0.314704
$941$	−2.69214e7	−0.991112	−0.495556	−	0.868576i	$-0.665036\pi$
$941$	−2.69214e7	−0.991112	−0.495556	+	0.868576i	$0.665036\pi$
$942$	−1.46320e7	−0.537249
$943$	1.80081e7	0.659461
$944$	−2.13925e6	−0.0781324
$945$	2.01496e6	0.0733984
$946$	−4.38102e6	−0.159165
$947$	−4.31235e6	−0.156257	−0.0781285	−	0.996943i	$-0.524894\pi$
$947$	−4.31235e6	−0.156257	−0.0781285	+	0.996943i	$0.524894\pi$
$948$	−709144.	−0.0256279
$949$	2.99614e6	0.107993
$950$	2.01686e6	0.0725047
$951$	6.35125e6	0.227724
$952$	−4.07413e6	−0.145694
$953$	1.91128e7	0.681699	0.340850	−	0.940118i	$-0.389285\pi$
$953$	1.91128e7	0.681699	0.340850	+	0.940118i	$0.389285\pi$
$954$	−5.72463e7	−2.03646
$955$	−2.27497e7	−0.807173
$956$	2.99491e7	1.05984
$957$	460954.	0.0162696
$958$	1.99193e7	0.701231
$959$	−1.05568e7	−0.370668
$960$	−4.91376e6	−0.172082
$961$	−2.84319e7	−0.993111
$962$	1.49347e7	0.520305
$963$	−1.61272e7	−0.560395
$964$	−2.74684e7	−0.952007
$965$	−2.30715e7	−0.797548
$966$	−3.67686e6	−0.126775
$967$	2.56402e7	0.881770	0.440885	−	0.897564i	$-0.354665\pi$
$967$	2.56402e7	0.881770	0.440885	+	0.897564i	$0.354665\pi$
$968$	−2.08164e6	−0.0714031
$969$	826808.	0.0282875
$970$	−3.99186e7	−1.36222
$971$	−6.32134e6	−0.215160	−0.107580	−	0.994196i	$-0.534310\pi$
$971$	−6.32134e6	−0.215160	−0.107580	+	0.994196i	$0.534310\pi$
$972$	2.90273e7	0.985464
$973$	−7.38039e6	−0.249918
$974$	−2.12738e6	−0.0718533
$975$	279714.	0.00942328
$976$	−1.31142e7	−0.440674
$977$	3.61608e7	1.21200	0.605999	−	0.795466i	$-0.292774\pi$
$977$	3.61608e7	1.21200	0.605999	+	0.795466i	$0.292774\pi$
$978$	−3.84048e6	−0.128392
$979$	−1.25536e7	−0.418613
$980$	−1.75720e7	−0.584461
$981$	4.01073e7	1.33061
$982$	7.09707e7	2.34855
$983$	3.70645e7	1.22342	0.611708	−	0.791084i	$-0.290483\pi$
$983$	3.70645e7	1.22342	0.611708	+	0.791084i	$0.290483\pi$
$984$	3.92229e6	0.129137
$985$	1.45502e7	0.477837
$986$	−5.71886e6	−0.187334
$987$	−1.21464e6	−0.0396876
$988$	−2.09581e6	−0.0683061
$989$	9.76427e6	0.317431
$990$	−6.20205e6	−0.201116
$991$	3.42857e7	1.10899	0.554497	−	0.832186i	$-0.312911\pi$
$991$	3.42857e7	1.10899	0.554497	+	0.832186i	$0.312911\pi$
$992$	−3.06082e6	−0.0987549
$993$	6.38961e6	0.205637
$994$	1.87730e6	0.0602654
$995$	−1.36064e7	−0.435698
$996$	−1.74504e6	−0.0557386
$997$	−1.92000e7	−0.611736	−0.305868	−	0.952074i	$-0.598947\pi$
$997$	−1.92000e7	−0.611736	−0.305868	+	0.952074i	$0.598947\pi$
$998$	6.19704e7	1.96951
$999$	2.40490e7	0.762400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.f.1.5	✓	38

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

\(f(q)\)	\(=\)	\(q-8.93899 q^{2} +3.69296 q^{3} +47.9055 q^{4} +25.0000 q^{5} -33.0113 q^{6} -46.2037 q^{7} -142.179 q^{8} -229.362 q^{9} +O(q^{10})\)	\(q-8.93899 q^{2} +3.69296 q^{3} +47.9055 q^{4} +25.0000 q^{5} -33.0113 q^{6} -46.2037 q^{7} -142.179 q^{8} -229.362 q^{9} -223.475 q^{10} -121.000 q^{11} +176.913 q^{12} +121.188 q^{13} +413.014 q^{14} +92.3239 q^{15} -262.042 q^{16} -620.188 q^{17} +2050.26 q^{18} -361.000 q^{19} +1197.64 q^{20} -170.628 q^{21} +1081.62 q^{22} -2410.67 q^{23} -525.059 q^{24} +625.000 q^{25} -1083.30 q^{26} -1744.41 q^{27} -2213.41 q^{28} -1031.57 q^{29} -825.282 q^{30} -444.106 q^{31} +6892.10 q^{32} -446.848 q^{33} +5543.85 q^{34} -1155.09 q^{35} -10987.7 q^{36} -13786.3 q^{37} +3226.97 q^{38} +447.542 q^{39} -3554.47 q^{40} -7470.17 q^{41} +1525.24 q^{42} -4050.44 q^{43} -5796.56 q^{44} -5734.05 q^{45} +21548.9 q^{46} +7118.64 q^{47} -967.708 q^{48} -14672.2 q^{49} -5586.87 q^{50} -2290.33 q^{51} +5805.57 q^{52} -27921.4 q^{53} +15593.3 q^{54} -3025.00 q^{55} +6569.18 q^{56} -1333.16 q^{57} +9221.17 q^{58} +8163.77 q^{59} +4422.82 q^{60} +50046.3 q^{61} +3969.85 q^{62} +10597.4 q^{63} -53223.1 q^{64} +3029.70 q^{65} +3994.36 q^{66} -18153.2 q^{67} -29710.4 q^{68} -8902.49 q^{69} +10325.4 q^{70} +4545.37 q^{71} +32610.4 q^{72} +24723.1 q^{73} +123236. q^{74} +2308.10 q^{75} -17293.9 q^{76} +5590.65 q^{77} -4000.57 q^{78} -4008.44 q^{79} -6551.04 q^{80} +49292.9 q^{81} +66775.8 q^{82} -9863.82 q^{83} -8174.03 q^{84} -15504.7 q^{85} +36206.8 q^{86} -3809.53 q^{87} +17203.6 q^{88} +103749. q^{89} +51256.6 q^{90} -5599.34 q^{91} -115484. q^{92} -1640.06 q^{93} -63633.4 q^{94} -9025.00 q^{95} +25452.2 q^{96} +178627. q^{97} +131155. q^{98} +27752.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) \) 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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