LMFDB - Embedded newform 1045.6.a.a.1.11

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:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-5.42281 q^{2} -30.3382 q^{3} -2.59316 q^{4} -25.0000 q^{5} +164.518 q^{6} +20.9364 q^{7} +187.592 q^{8} +677.408 q^{9} +O(q^{10})$	\(q-5.42281 q^{2} -30.3382 q^{3} -2.59316 q^{4} -25.0000 q^{5} +164.518 q^{6} +20.9364 q^{7} +187.592 q^{8} +677.408 q^{9} +135.570 q^{10} +121.000 q^{11} +78.6720 q^{12} +1153.10 q^{13} -113.534 q^{14} +758.456 q^{15} -934.294 q^{16} +16.3441 q^{17} -3673.45 q^{18} +361.000 q^{19} +64.8291 q^{20} -635.173 q^{21} -656.160 q^{22} +323.700 q^{23} -5691.21 q^{24} +625.000 q^{25} -6253.05 q^{26} -13179.2 q^{27} -54.2915 q^{28} -469.198 q^{29} -4112.96 q^{30} +4835.25 q^{31} -936.448 q^{32} -3670.92 q^{33} -88.6307 q^{34} -523.410 q^{35} -1756.63 q^{36} -5225.44 q^{37} -1957.63 q^{38} -34983.1 q^{39} -4689.80 q^{40} +3497.42 q^{41} +3444.42 q^{42} -2345.21 q^{43} -313.773 q^{44} -16935.2 q^{45} -1755.36 q^{46} +14593.7 q^{47} +28344.8 q^{48} -16368.7 q^{49} -3389.25 q^{50} -495.850 q^{51} -2990.18 q^{52} -24006.7 q^{53} +71468.0 q^{54} -3025.00 q^{55} +3927.50 q^{56} -10952.1 q^{57} +2544.37 q^{58} +29478.5 q^{59} -1966.80 q^{60} +2740.47 q^{61} -26220.6 q^{62} +14182.5 q^{63} +34975.6 q^{64} -28827.6 q^{65} +19906.7 q^{66} +11068.1 q^{67} -42.3828 q^{68} -9820.47 q^{69} +2838.35 q^{70} -43179.1 q^{71} +127076. q^{72} +57334.5 q^{73} +28336.5 q^{74} -18961.4 q^{75} -936.132 q^{76} +2533.31 q^{77} +189706. q^{78} -84305.7 q^{79} +23357.4 q^{80} +235222. q^{81} -18965.8 q^{82} -21325.6 q^{83} +1647.11 q^{84} -408.602 q^{85} +12717.6 q^{86} +14234.6 q^{87} +22698.6 q^{88} -92868.1 q^{89} +91836.3 q^{90} +24141.8 q^{91} -839.406 q^{92} -146693. q^{93} -79139.0 q^{94} -9025.00 q^{95} +28410.2 q^{96} +103715. q^{97} +88764.1 q^{98} +81966.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) $ 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9 + 100 * q^10 + 4235 * q^11 - 568 * q^12 - 717 * q^13 - 2585 * q^14 + 675 * q^15 + 3356 * q^16 - 3349 * q^17 - 5533 * q^18 + 12635 * q^19 - 13000 * q^20 + 289 * q^21 - 484 * q^22 - 820 * q^23 - 21748 * q^24 + 21875 * q^25 - 6267 * q^26 - 13650 * q^27 - 6487 * q^28 - 13357 * q^29 + 7275 * q^30 - 15341 * q^31 - 16405 * q^32 - 3267 * q^33 - 1255 * q^34 - 2925 * q^35 + 23487 * q^36 - 511 * q^37 - 1444 * q^38 - 33584 * q^39 + 12450 * q^40 - 36855 * q^41 + 16330 * q^42 + 10991 * q^43 + 62920 * q^44 - 51150 * q^45 - 20443 * q^46 - 33594 * q^47 + 36221 * q^48 + 23422 * q^49 - 2500 * q^50 - 53530 * q^51 + 89382 * q^52 + 13103 * q^53 + 65776 * q^54 - 105875 * q^55 + 130911 * q^56 - 9747 * q^57 + 127808 * q^58 - 161139 * q^59 + 14200 * q^60 - 91587 * q^61 + 131818 * q^62 + 16590 * q^63 - 23186 * q^64 + 17925 * q^65 - 35211 * q^66 + 39210 * q^67 + 26300 * q^68 - 23174 * q^69 + 64625 * q^70 - 167772 * q^71 + 135820 * q^72 - 5106 * q^73 - 256965 * q^74 - 16875 * q^75 + 187720 * q^76 + 14157 * q^77 + 492812 * q^78 - 156897 * q^79 - 83900 * q^80 + 31279 * q^81 + 46818 * q^82 - 185627 * q^83 + 165864 * q^84 + 83725 * q^85 - 159946 * q^86 - 112092 * q^87 - 60258 * q^88 - 144420 * q^89 + 138325 * q^90 - 442480 * q^91 - 205876 * q^92 + 125910 * q^93 - 110044 * q^94 - 315875 * q^95 - 554286 * q^96 + 41200 * q^97 + 41052 * q^98 + 247566 * 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 $

$2$	−5.42281	−0.958626	−0.479313	−	0.877644i	$-0.659114\pi$
$2$	−5.42281	−0.958626	−0.479313	+	0.877644i	$0.659114\pi$
$3$	−30.3382	−1.94620	−0.973099	−	0.230388i	$-0.926001\pi$
$3$	−30.3382	−1.94620	−0.973099	+	0.230388i	$0.926001\pi$
$4$	−2.59316	−0.0810364
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	164.518	1.86568
$7$	20.9364	0.161494	0.0807471	−	0.996735i	$-0.474269\pi$
$7$	20.9364	0.161494	0.0807471	+	0.996735i	$0.474269\pi$
$8$	187.592	1.03631
$9$	677.408	2.78769
$10$	135.570	0.428711
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	78.6720	0.157713
$13$	1153.10	1.89238	0.946192	−	0.323605i	$-0.104895\pi$
$13$	1153.10	1.89238	0.946192	+	0.323605i	$0.104895\pi$
$14$	−113.534	−0.154813
$15$	758.456	0.870366
$16$	−934.294	−0.912397
$17$	16.3441	0.0137163	0.00685816	−	0.999976i	$-0.497817\pi$
$17$	16.3441	0.0137163	0.00685816	+	0.999976i	$0.497817\pi$
$18$	−3673.45	−2.67235
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	64.8291	0.0362406
$21$	−635.173	−0.314300
$22$	−656.160	−0.289037
$23$	323.700	0.127592	0.0637959	−	0.997963i	$-0.479679\pi$
$23$	323.700	0.127592	0.0637959	+	0.997963i	$0.479679\pi$
$24$	−5691.21	−2.01686
$25$	625.000	0.200000
$26$	−6253.05	−1.81409
$27$	−13179.2	−3.47919
$28$	−54.2915	−0.0130869
$29$	−469.198	−0.103600	−0.0518002	−	0.998657i	$-0.516496\pi$
$29$	−469.198	−0.103600	−0.0518002	+	0.998657i	$0.516496\pi$
$30$	−4112.96	−0.834355
$31$	4835.25	0.903680	0.451840	−	0.892099i	$-0.350768\pi$
$31$	4835.25	0.903680	0.451840	+	0.892099i	$0.350768\pi$
$32$	−936.448	−0.161662
$33$	−3670.92	−0.586801
$34$	−88.6307	−0.0131488
$35$	−523.410	−0.0722224
$36$	−1756.63	−0.225904
$37$	−5225.44	−0.627507	−0.313753	−	0.949505i	$-0.601586\pi$
$37$	−5225.44	−0.627507	−0.313753	+	0.949505i	$0.601586\pi$
$38$	−1957.63	−0.219924
$39$	−34983.1	−3.68296
$40$	−4689.80	−0.463452
$41$	3497.42	0.324928	0.162464	−	0.986714i	$-0.448056\pi$
$41$	3497.42	0.324928	0.162464	+	0.986714i	$0.448056\pi$
$42$	3444.42	0.301296
$43$	−2345.21	−0.193424	−0.0967121	−	0.995312i	$-0.530833\pi$
$43$	−2345.21	−0.193424	−0.0967121	+	0.995312i	$0.530833\pi$
$44$	−313.773	−0.0244334
$45$	−16935.2	−1.24669
$46$	−1755.36	−0.122313
$47$	14593.7	0.963655	0.481828	−	0.876266i	$-0.339973\pi$
$47$	14593.7	0.963655	0.481828	+	0.876266i	$0.339973\pi$
$48$	28344.8	1.77570
$49$	−16368.7	−0.973920
$50$	−3389.25	−0.191725
$51$	−495.850	−0.0266947
$52$	−2990.18	−0.153352
$53$	−24006.7	−1.17393	−0.586967	−	0.809611i	$-0.699678\pi$
$53$	−24006.7	−1.17393	−0.586967	+	0.809611i	$0.699678\pi$
$54$	71468.0	3.33524
$55$	−3025.00	−0.134840
$56$	3927.50	0.167358
$57$	−10952.1	−0.446488
$58$	2544.37	0.0993139
$59$	29478.5	1.10249	0.551246	−	0.834343i	$-0.314153\pi$
$59$	29478.5	1.10249	0.551246	+	0.834343i	$0.314153\pi$
$60$	−1966.80	−0.0705313
$61$	2740.47	0.0942975	0.0471487	−	0.998888i	$-0.484987\pi$
$61$	2740.47	0.0942975	0.0471487	+	0.998888i	$0.484987\pi$
$62$	−26220.6	−0.866291
$63$	14182.5	0.450195
$64$	34975.6	1.06737
$65$	−28827.6	−0.846300
$66$	19906.7	0.562522
$67$	11068.1	0.301223	0.150611	−	0.988593i	$-0.451876\pi$
$67$	11068.1	0.301223	0.150611	+	0.988593i	$0.451876\pi$
$68$	−42.3828	−0.00111152
$69$	−9820.47	−0.248319
$70$	2838.35	0.0692343
$71$	−43179.1	−1.01655	−0.508274	−	0.861195i	$-0.669716\pi$
$71$	−43179.1	−1.01655	−0.508274	+	0.861195i	$0.669716\pi$
$72$	127076.	2.88891
$73$	57334.5	1.25924	0.629621	−	0.776903i	$-0.283210\pi$
$73$	57334.5	1.25924	0.629621	+	0.776903i	$0.283210\pi$
$74$	28336.5	0.601544
$75$	−18961.4	−0.389240
$76$	−936.132	−0.0185910
$77$	2533.31	0.0486923
$78$	189706.	3.53058
$79$	−84305.7	−1.51981	−0.759905	−	0.650034i	$-0.774754\pi$
$79$	−84305.7	−1.51981	−0.759905	+	0.650034i	$0.774754\pi$
$80$	23357.4	0.408036
$81$	235222.	3.98351
$82$	−18965.8	−0.311485
$83$	−21325.6	−0.339786	−0.169893	−	0.985462i	$-0.554342\pi$
$83$	−21325.6	−0.339786	−0.169893	+	0.985462i	$0.554342\pi$
$84$	1647.11	0.0254697
$85$	−408.602	−0.00613413
$86$	12717.6	0.185421
$87$	14234.6	0.201627
$88$	22698.6	0.312459
$89$	−92868.1	−1.24277	−0.621386	−	0.783504i	$-0.713430\pi$
$89$	−92868.1	−1.24277	−0.621386	+	0.783504i	$0.713430\pi$
$90$	91836.3	1.19511
$91$	24141.8	0.305609
$92$	−839.406	−0.0103396
$93$	−146693.	−1.75874
$94$	−79139.0	−0.923785
$95$	−9025.00	−0.102598
$96$	28410.2	0.314627
$97$	103715.	1.11921	0.559605	−	0.828760i	$-0.310953\pi$
$97$	103715.	1.11921	0.559605	+	0.828760i	$0.310953\pi$
$98$	88764.1	0.933625
$99$	81966.3	0.840519
$100$	−1620.73	−0.0162073
$101$	−133183.	−1.29911	−0.649555	−	0.760314i	$-0.725045\pi$
$101$	−133183.	−1.29911	−0.649555	+	0.760314i	$0.725045\pi$
$102$	2688.90	0.0255902
$103$	−63009.8	−0.585214	−0.292607	−	0.956233i	$-0.594523\pi$
$103$	−63009.8	−0.585214	−0.292607	+	0.956233i	$0.594523\pi$
$104$	216313.	1.96110
$105$	15879.3	0.140559
$106$	130184.	1.12536
$107$	25529.8	0.215570	0.107785	−	0.994174i	$-0.465624\pi$
$107$	25529.8	0.215570	0.107785	+	0.994174i	$0.465624\pi$
$108$	34175.7	0.281941
$109$	−24338.8	−0.196216	−0.0981078	−	0.995176i	$-0.531279\pi$
$109$	−24338.8	−0.196216	−0.0981078	+	0.995176i	$0.531279\pi$
$110$	16404.0	0.129261
$111$	158530.	1.22125
$112$	−19560.8	−0.147347
$113$	−11775.0	−0.0867493	−0.0433746	−	0.999059i	$-0.513811\pi$
$113$	−11775.0	−0.0867493	−0.0433746	+	0.999059i	$0.513811\pi$
$114$	59391.1	0.428015
$115$	−8092.49	−0.0570608
$116$	1216.71	0.00839539
$117$	781120.	5.27537
$118$	−159856.	−1.05688
$119$	342.186	0.00221511
$120$	142280.	0.901969
$121$	14641.0	0.0909091
$122$	−14861.0	−0.0903960
$123$	−106105.	−0.632375
$124$	−12538.6	−0.0732310
$125$	−15625.0	−0.0894427
$126$	−76908.9	−0.431569
$127$	71216.5	0.391806	0.195903	−	0.980623i	$-0.437236\pi$
$127$	71216.5	0.391806	0.195903	+	0.980623i	$0.437236\pi$
$128$	−159700.	−0.861547
$129$	71149.5	0.376442
$130$	156326.	0.811285
$131$	67744.4	0.344902	0.172451	−	0.985018i	$-0.444831\pi$
$131$	67744.4	0.344902	0.172451	+	0.985018i	$0.444831\pi$
$132$	9519.31	0.0475522
$133$	7558.04	0.0370493
$134$	−60020.4	−0.288760
$135$	329479.	1.55594
$136$	3066.02	0.0142144
$137$	−161791.	−0.736465	−0.368233	−	0.929734i	$-0.620037\pi$
$137$	−161791.	−0.736465	−0.368233	+	0.929734i	$0.620037\pi$
$138$	53254.5	0.238045
$139$	−296399.	−1.30119	−0.650593	−	0.759427i	$-0.725480\pi$
$139$	−296399.	−1.30119	−0.650593	+	0.759427i	$0.725480\pi$
$140$	1357.29	0.00585264
$141$	−442748.	−1.87546
$142$	234152.	0.974489
$143$	139525.	0.570575
$144$	−632898.	−2.54348
$145$	11729.9	0.0463315
$146$	−310914.	−1.20714
$147$	496596.	1.89544
$148$	13550.4	0.0508509
$149$	−366016.	−1.35062	−0.675311	−	0.737533i	$-0.735991\pi$
$149$	−366016.	−1.35062	−0.675311	+	0.737533i	$0.735991\pi$
$150$	102824.	0.373135
$151$	36458.5	0.130124	0.0650619	−	0.997881i	$-0.479276\pi$
$151$	36458.5	0.130124	0.0650619	+	0.997881i	$0.479276\pi$
$152$	67720.7	0.237746
$153$	11071.6	0.0382368
$154$	−13737.6	−0.0466777
$155$	−120881.	−0.404138
$156$	90716.8	0.298453
$157$	194892.	0.631023	0.315511	−	0.948922i	$-0.397824\pi$
$157$	194892.	0.631023	0.315511	+	0.948922i	$0.397824\pi$
$158$	457174.	1.45693
$159$	728322.	2.28471
$160$	23411.2	0.0722976
$161$	6777.11	0.0206053
$162$	−1.27556e6	−3.81869
$163$	−479787.	−1.41442	−0.707212	−	0.707002i	$-0.750047\pi$
$163$	−479787.	−1.41442	−0.707212	+	0.707002i	$0.750047\pi$
$164$	−9069.37	−0.0263310
$165$	91773.1	0.262425
$166$	115645.	0.325728
$167$	−614359.	−1.70463	−0.852316	−	0.523027i	$-0.824803\pi$
$167$	−614359.	−1.70463	−0.852316	+	0.523027i	$0.824803\pi$
$168$	−119153.	−0.325712
$169$	958352.	2.58112
$170$	2215.77	0.00588033
$171$	244544.	0.639539
$172$	6081.52	0.0156744
$173$	555934.	1.41224	0.706120	−	0.708093i	$-0.250444\pi$
$173$	555934.	1.41224	0.706120	+	0.708093i	$0.250444\pi$
$174$	−77191.6	−0.193285
$175$	13085.3	0.0322988
$176$	−113050.	−0.275098
$177$	−894325.	−2.14567
$178$	503606.	1.19135
$179$	37496.6	0.0874700	0.0437350	−	0.999043i	$-0.486074\pi$
$179$	37496.6	0.0874700	0.0437350	+	0.999043i	$0.486074\pi$
$180$	43915.7	0.101027
$181$	117005.	0.265465	0.132733	−	0.991152i	$-0.457625\pi$
$181$	117005.	0.265465	0.132733	+	0.991152i	$0.457625\pi$
$182$	−130916.	−0.292965
$183$	−83140.9	−0.183522
$184$	60723.5	0.132225
$185$	130636.	0.280630
$186$	795488.	1.68597
$187$	1977.63	0.00413563
$188$	−37843.9	−0.0780911
$189$	−275924.	−0.561869
$190$	48940.8	0.0983529
$191$	−488691.	−0.969285	−0.484642	−	0.874712i	$-0.661050\pi$
$191$	−488691.	−0.969285	−0.484642	+	0.874712i	$0.661050\pi$
$192$	−1.06110e6	−2.07731
$193$	285999.	0.552677	0.276339	−	0.961060i	$-0.410879\pi$
$193$	285999.	0.552677	0.276339	+	0.961060i	$0.410879\pi$
$194$	−562425.	−1.07290
$195$	874577.	1.64707
$196$	42446.6	0.0789229
$197$	960329.	1.76301	0.881504	−	0.472176i	$-0.156531\pi$
$197$	960329.	1.76301	0.881504	+	0.472176i	$0.156531\pi$
$198$	−444488.	−0.805743
$199$	160539.	0.287373	0.143687	−	0.989623i	$-0.454104\pi$
$199$	160539.	0.287373	0.143687	+	0.989623i	$0.454104\pi$
$200$	117245.	0.207262
$201$	−335788.	−0.586239
$202$	722227.	1.24536
$203$	−9823.32	−0.0167309
$204$	1285.82	0.00216324
$205$	−87435.4	−0.145312
$206$	341690.	0.561001
$207$	219277.	0.355686
$208$	−1.07734e6	−1.72661
$209$	43681.0	0.0691714
$210$	−86110.6	−0.134744
$211$	−763777.	−1.18103	−0.590515	−	0.807027i	$-0.701075\pi$
$211$	−763777.	−1.18103	−0.590515	+	0.807027i	$0.701075\pi$
$212$	62253.4	0.0951313
$213$	1.30998e6	1.97840
$214$	−138443.	−0.206651
$215$	58630.3	0.0865019
$216$	−2.47230e6	−3.60552
$217$	101233.	0.145939
$218$	131985.	0.188097
$219$	−1.73943e6	−2.45073
$220$	7844.32	0.0109269
$221$	18846.4	0.0259566
$222$	−859680.	−1.17072
$223$	532270.	0.716754	0.358377	−	0.933577i	$-0.383330\pi$
$223$	532270.	0.716754	0.358377	+	0.933577i	$0.383330\pi$
$224$	−19605.9	−0.0261075
$225$	423380.	0.557537
$226$	63853.7	0.0831601
$227$	−1.09486e6	−1.41024	−0.705120	−	0.709088i	$-0.749107\pi$
$227$	−1.09486e6	−1.41024	−0.705120	+	0.709088i	$0.749107\pi$
$228$	28400.6	0.0361818
$229$	−1.21708e6	−1.53367	−0.766835	−	0.641844i	$-0.778170\pi$
$229$	−1.21708e6	−1.53367	−0.766835	+	0.641844i	$0.778170\pi$
$230$	43884.0	0.0546999
$231$	−76856.0	−0.0947649
$232$	−88017.8	−0.107362
$233$	1.10705e6	1.33591	0.667956	−	0.744200i	$-0.267169\pi$
$233$	1.10705e6	1.33591	0.667956	+	0.744200i	$0.267169\pi$
$234$	−4.23586e6	−5.05711
$235$	−364843.	−0.430960
$236$	−76442.5	−0.0893419
$237$	2.55768e6	2.95785
$238$	−1855.61	−0.00212346
$239$	−1.35907e6	−1.53904	−0.769518	−	0.638625i	$-0.779503\pi$
$239$	−1.35907e6	−1.53904	−0.769518	+	0.638625i	$0.779503\pi$
$240$	−708621.	−0.794119
$241$	−259248.	−0.287524	−0.143762	−	0.989612i	$-0.545920\pi$
$241$	−259248.	−0.287524	−0.143762	+	0.989612i	$0.545920\pi$
$242$	−79395.3	−0.0871478
$243$	−3.93368e6	−4.27350
$244$	−7106.48	−0.00764152
$245$	409217.	0.435550
$246$	575389.	0.606211
$247$	416270.	0.434143
$248$	907055.	0.936493
$249$	646980.	0.661291
$250$	84731.4	0.0857421
$251$	53188.5	0.0532885	0.0266442	−	0.999645i	$-0.491518\pi$
$251$	53188.5	0.0532885	0.0266442	+	0.999645i	$0.491518\pi$
$252$	−36777.5	−0.0364822
$253$	39167.7	0.0384704
$254$	−386194.	−0.375596
$255$	12396.2	0.0119382
$256$	−253199.	−0.241469
$257$	−330031.	−0.311690	−0.155845	−	0.987782i	$-0.549810\pi$
$257$	−330031.	−0.311690	−0.155845	+	0.987782i	$0.549810\pi$
$258$	−385830.	−0.360867
$259$	−109402.	−0.101339
$260$	74754.6	0.0685811
$261$	−317838.	−0.288805
$262$	−367365.	−0.330632
$263$	981072.	0.874604	0.437302	−	0.899315i	$-0.355934\pi$
$263$	981072.	0.874604	0.437302	+	0.899315i	$0.355934\pi$
$264$	−688636.	−0.608107
$265$	600169.	0.524999
$266$	−40985.8	−0.0355164
$267$	2.81745e6	2.41868
$268$	−28701.5	−0.0244100
$269$	−92160.5	−0.0776541	−0.0388270	−	0.999246i	$-0.512362\pi$
$269$	−92160.5	−0.0776541	−0.0388270	+	0.999246i	$0.512362\pi$
$270$	−1.78670e6	−1.49157
$271$	−1.04776e6	−0.866642	−0.433321	−	0.901240i	$-0.642658\pi$
$271$	−1.04776e6	−0.866642	−0.433321	+	0.901240i	$0.642658\pi$
$272$	−15270.2	−0.0125147
$273$	−732420.	−0.594776
$274$	877360.	0.705994
$275$	75625.0	0.0603023
$276$	25466.1	0.0201228
$277$	−856167.	−0.670439	−0.335219	−	0.942140i	$-0.608810\pi$
$277$	−856167.	−0.670439	−0.335219	+	0.942140i	$0.608810\pi$
$278$	1.60731e6	1.24735
$279$	3.27544e6	2.51918
$280$	−98187.6	−0.0748448
$281$	530447.	0.400753	0.200376	−	0.979719i	$-0.435784\pi$
$281$	530447.	0.400753	0.200376	+	0.979719i	$0.435784\pi$
$282$	2.40094e6	1.79787
$283$	2.40036e6	1.78160	0.890799	−	0.454398i	$-0.150146\pi$
$283$	2.40036e6	1.78160	0.890799	+	0.454398i	$0.150146\pi$
$284$	111970.	0.0823773
$285$	273802.	0.199676
$286$	−756619.	−0.546968
$287$	73223.3	0.0524741
$288$	−634357.	−0.450664
$289$	−1.41959e6	−0.999812
$290$	−63609.2	−0.0444145
$291$	−3.14652e6	−2.17820
$292$	−148678.	−0.102044
$293$	2.06955e6	1.40834	0.704170	−	0.710032i	$-0.251319\pi$
$293$	2.06955e6	1.40834	0.704170	+	0.710032i	$0.251319\pi$
$294$	−2.69295e6	−1.81702
$295$	−736962.	−0.493049
$296$	−980251.	−0.650291
$297$	−1.59468e6	−1.04902
$298$	1.98483e6	1.29474
$299$	373259.	0.241453
$300$	49170.0	0.0315426
$301$	−49100.3	−0.0312369
$302$	−197707.	−0.124740
$303$	4.04054e6	2.52833
$304$	−337280.	−0.209318
$305$	−68511.7	−0.0421711
$306$	−60039.1	−0.0366548
$307$	−1.85033e6	−1.12048	−0.560238	−	0.828331i	$-0.689290\pi$
$307$	−1.85033e6	−1.12048	−0.560238	+	0.828331i	$0.689290\pi$
$308$	−6569.27	−0.00394585
$309$	1.91160e6	1.13894
$310$	655516.	0.387417
$311$	−2.06757e6	−1.21216	−0.606079	−	0.795404i	$-0.707259\pi$
$311$	−2.06757e6	−1.21216	−0.606079	+	0.795404i	$0.707259\pi$
$312$	−6.56255e6	−3.81668
$313$	−1.49084e6	−0.860142	−0.430071	−	0.902795i	$-0.641512\pi$
$313$	−1.49084e6	−0.860142	−0.430071	+	0.902795i	$0.641512\pi$
$314$	−1.05686e6	−0.604915
$315$	−354562.	−0.201333
$316$	218618.	0.123160
$317$	1.72370e6	0.963415	0.481707	−	0.876332i	$-0.340017\pi$
$317$	1.72370e6	0.963415	0.481707	+	0.876332i	$0.340017\pi$
$318$	−3.94955e6	−2.19018
$319$	−56772.9	−0.0312367
$320$	−874390.	−0.477343
$321$	−774528.	−0.419541
$322$	−36750.9	−0.0197528
$323$	5900.21	0.00314674
$324$	−609969.	−0.322809
$325$	720689.	0.378477
$326$	2.60179e6	1.35590
$327$	738397.	0.381874
$328$	656088.	0.336726
$329$	305540.	0.155625
$330$	−497668.	−0.251568
$331$	−3.33706e6	−1.67415	−0.837075	−	0.547088i	$-0.815736\pi$
$331$	−3.33706e6	−1.67415	−0.837075	+	0.547088i	$0.815736\pi$
$332$	55300.7	0.0275350
$333$	−3.53975e6	−1.74929
$334$	3.33155e6	1.63410
$335$	−276704.	−0.134711
$336$	593439.	0.286766
$337$	−839982.	−0.402898	−0.201449	−	0.979499i	$-0.564565\pi$
$337$	−839982.	−0.402898	−0.201449	+	0.979499i	$0.564565\pi$
$338$	−5.19696e6	−2.47433
$339$	357233.	0.168831
$340$	1059.57	0.000497087 0
$341$	585066.	0.272470
$342$	−1.32612e6	−0.613079
$343$	−694579.	−0.318777
$344$	−439943.	−0.200447
$345$	245512.	0.111052
$346$	−3.01472e6	−1.35381
$347$	−2.91056e6	−1.29763	−0.648817	−	0.760944i	$-0.724736\pi$
$347$	−2.91056e6	−1.29763	−0.648817	+	0.760944i	$0.724736\pi$
$348$	−36912.7	−0.0163391
$349$	−1.53441e6	−0.674340	−0.337170	−	0.941444i	$-0.609470\pi$
$349$	−1.53441e6	−0.674340	−0.337170	+	0.941444i	$0.609470\pi$
$350$	−70958.8	−0.0309625
$351$	−1.51969e7	−6.58397
$352$	−113310.	−0.0487430
$353$	1.64910e6	0.704386	0.352193	−	0.935927i	$-0.385436\pi$
$353$	1.64910e6	0.704386	0.352193	+	0.935927i	$0.385436\pi$
$354$	4.84975e6	2.05689
$355$	1.07948e6	0.454614
$356$	240822.	0.100710
$357$	−10381.3	−0.00431104
$358$	−203337.	−0.0838510
$359$	1.07636e6	0.440778	0.220389	−	0.975412i	$-0.429267\pi$
$359$	1.07636e6	0.440778	0.220389	+	0.975412i	$0.429267\pi$
$360$	−3.17691e6	−1.29196
$361$	130321.	0.0526316
$362$	−634495.	−0.254482
$363$	−444182.	−0.176927
$364$	−62603.7	−0.0247655
$365$	−1.43336e6	−0.563150
$366$	450857.	0.175928
$367$	2.56276e6	0.993215	0.496608	−	0.867975i	$-0.334579\pi$
$367$	2.56276e6	0.993215	0.496608	+	0.867975i	$0.334579\pi$
$368$	−302431.	−0.116414
$369$	2.36918e6	0.905798
$370$	−708413.	−0.269019
$371$	−502615.	−0.189584
$372$	380399.	0.142522
$373$	1.14889e6	0.427568	0.213784	−	0.976881i	$-0.431421\pi$
$373$	1.14889e6	0.427568	0.213784	+	0.976881i	$0.431421\pi$
$374$	−10724.3	−0.00396452
$375$	474035.	0.174073
$376$	2.73767e6	0.998645
$377$	−541033.	−0.196052
$378$	1.49628e6	0.538622
$379$	4.74051e6	1.69522	0.847611	−	0.530618i	$-0.178040\pi$
$379$	4.74051e6	1.69522	0.847611	+	0.530618i	$0.178040\pi$
$380$	23403.3	0.00831415
$381$	−2.16058e6	−0.762533
$382$	2.65008e6	0.929181
$383$	3.06724e6	1.06844	0.534220	−	0.845345i	$-0.320605\pi$
$383$	3.06724e6	1.06844	0.534220	+	0.845345i	$0.320605\pi$
$384$	4.84500e6	1.67674
$385$	−63332.6	−0.0217759
$386$	−1.55092e6	−0.529811
$387$	−1.58866e6	−0.539206
$388$	−268949.	−0.0906966
$389$	3.55609e6	1.19151	0.595757	−	0.803165i	$-0.296852\pi$
$389$	3.55609e6	1.19151	0.595757	+	0.803165i	$0.296852\pi$
$390$	−4.74266e6	−1.57892
$391$	5290.57	0.00175009
$392$	−3.07063e6	−1.00928
$393$	−2.05525e6	−0.671247
$394$	−5.20768e6	−1.69007
$395$	2.10764e6	0.679680
$396$	−212552.	−0.0681126
$397$	−262468.	−0.0835796	−0.0417898	−	0.999126i	$-0.513306\pi$
$397$	−262468.	−0.0835796	−0.0417898	+	0.999126i	$0.513306\pi$
$398$	−870569.	−0.275484
$399$	−229298.	−0.0721053
$400$	−583934.	−0.182479
$401$	−5.13312e6	−1.59412	−0.797059	−	0.603902i	$-0.793612\pi$
$401$	−5.13312e6	−1.59412	−0.797059	+	0.603902i	$0.793612\pi$
$402$	1.82091e6	0.561984
$403$	5.57554e6	1.71011
$404$	345366.	0.105275
$405$	−5.88055e6	−1.78148
$406$	53270.0	0.0160386
$407$	−632278.	−0.189200
$408$	−93017.5	−0.0276640
$409$	4.60864e6	1.36227	0.681137	−	0.732156i	$-0.261486\pi$
$409$	4.60864e6	1.36227	0.681137	+	0.732156i	$0.261486\pi$
$410$	474145.	0.139300
$411$	4.90844e6	1.43331
$412$	163395.	0.0474236
$413$	617174.	0.178046
$414$	−1.18909e6	−0.340970
$415$	533140.	0.151957
$416$	−1.07982e6	−0.305927
$417$	8.99221e6	2.53236
$418$	−236874.	−0.0663095
$419$	−3.49247e6	−0.971848	−0.485924	−	0.874001i	$-0.661517\pi$
$419$	−3.49247e6	−0.971848	−0.485924	+	0.874001i	$0.661517\pi$
$420$	−41177.7	−0.0113904
$421$	−2.50057e6	−0.687596	−0.343798	−	0.939044i	$-0.611714\pi$
$421$	−2.50057e6	−0.687596	−0.343798	+	0.939044i	$0.611714\pi$
$422$	4.14182e6	1.13217
$423$	9.88591e6	2.68637
$424$	−4.50348e6	−1.21656
$425$	10215.0	0.00274327
$426$	−7.10375e6	−1.89655
$427$	57375.5	0.0152285
$428$	−66202.9	−0.0174690
$429$	−4.23295e6	−1.11045
$430$	−317941.	−0.0829230
$431$	−224717.	−0.0582697	−0.0291348	−	0.999575i	$-0.509275\pi$
$431$	−224717.	−0.0582697	−0.0291348	+	0.999575i	$0.509275\pi$
$432$	1.23132e7	3.17440
$433$	2.18043e6	0.558885	0.279443	−	0.960162i	$-0.409850\pi$
$433$	2.18043e6	0.558885	0.279443	+	0.960162i	$0.409850\pi$
$434$	−548966.	−0.139901
$435$	−355866.	−0.0901702
$436$	63114.6	0.0159006
$437$	116856.	0.0292716
$438$	9.43258e6	2.34934
$439$	2.51643e6	0.623196	0.311598	−	0.950214i	$-0.399136\pi$
$439$	2.51643e6	0.623196	0.311598	+	0.950214i	$0.399136\pi$
$440$	−567466.	−0.139736
$441$	−1.10883e7	−2.71498
$442$	−102200.	−0.0248826
$443$	−6.79085e6	−1.64405	−0.822024	−	0.569453i	$-0.807155\pi$
$443$	−6.79085e6	−1.64405	−0.822024	+	0.569453i	$0.807155\pi$
$444$	−411095.	−0.0989658
$445$	2.32170e6	0.555785
$446$	−2.88640e6	−0.687099
$447$	1.11043e7	2.62858
$448$	732263.	0.172374
$449$	2.61409e6	0.611933	0.305967	−	0.952042i	$-0.401020\pi$
$449$	2.61409e6	0.611933	0.305967	+	0.952042i	$0.401020\pi$
$450$	−2.29591e6	−0.534470
$451$	423187.	0.0979696
$452$	30534.6	0.00702984
$453$	−1.10609e6	−0.253246
$454$	5.93720e6	1.35189
$455$	−603545.	−0.136673
$456$	−2.05453e6	−0.462700
$457$	−4.25864e6	−0.953851	−0.476925	−	0.878944i	$-0.658249\pi$
$457$	−4.25864e6	−0.953851	−0.476925	+	0.878944i	$0.658249\pi$
$458$	6.60002e6	1.47022
$459$	−215401.	−0.0477217
$460$	20985.2	0.00462400
$461$	8.81193e6	1.93116	0.965581	−	0.260103i	$-0.0837566\pi$
$461$	8.81193e6	1.93116	0.965581	+	0.260103i	$0.0837566\pi$
$462$	416775.	0.0908441
$463$	−4.42727e6	−0.959807	−0.479903	−	0.877321i	$-0.659328\pi$
$463$	−4.42727e6	−0.959807	−0.479903	+	0.877321i	$0.659328\pi$
$464$	438369.	0.0945246
$465$	3.66732e6	0.786533
$466$	−6.00333e6	−1.28064
$467$	−7.05596e6	−1.49715	−0.748573	−	0.663053i	$-0.769261\pi$
$467$	−7.05596e6	−1.49715	−0.748573	+	0.663053i	$0.769261\pi$
$468$	−2.02557e6	−0.427497
$469$	231727.	0.0486457
$470$	1.97848e6	0.413129
$471$	−5.91268e6	−1.22810
$472$	5.52993e6	1.14252
$473$	−283771.	−0.0583196
$474$	−1.38698e7	−2.83547
$475$	225625.	0.0458831
$476$	−887.344	−0.000179504 0
$477$	−1.62624e7	−3.27256
$478$	7.37000e6	1.47536
$479$	4.57258e6	0.910589	0.455294	−	0.890341i	$-0.349534\pi$
$479$	4.57258e6	0.910589	0.455294	+	0.890341i	$0.349534\pi$
$480$	−710254.	−0.140705
$481$	−6.02546e6	−1.18748
$482$	1.40585e6	0.275628
$483$	−205605.	−0.0401021
$484$	−37966.5	−0.00736694
$485$	−2.59287e6	−0.500525
$486$	2.13316e7	4.09669
$487$	6.00072e6	1.14652	0.573259	−	0.819374i	$-0.305679\pi$
$487$	6.00072e6	1.14652	0.573259	+	0.819374i	$0.305679\pi$
$488$	514090.	0.0977214
$489$	1.45559e7	2.75275
$490$	−2.21910e6	−0.417530
$491$	−6.85198e6	−1.28266	−0.641331	−	0.767264i	$-0.721618\pi$
$491$	−6.85198e6	−1.28266	−0.641331	+	0.767264i	$0.721618\pi$
$492$	275149.	0.0512454
$493$	−7668.60	−0.00142102
$494$	−2.25735e6	−0.416181
$495$	−2.04916e6	−0.375891
$496$	−4.51755e6	−0.824515
$497$	−904015.	−0.164167
$498$	−3.50845e6	−0.633931
$499$	1.38946e6	0.249802	0.124901	−	0.992169i	$-0.460139\pi$
$499$	1.38946e6	0.249802	0.124901	+	0.992169i	$0.460139\pi$
$500$	40518.2	0.00724811
$501$	1.86385e7	3.31755
$502$	−288431.	−0.0510837
$503$	−5.15697e6	−0.908814	−0.454407	−	0.890794i	$-0.650149\pi$
$503$	−5.15697e6	−0.908814	−0.454407	+	0.890794i	$0.650149\pi$
$504$	2.66052e6	0.466542
$505$	3.32958e6	0.580980
$506$	−212399.	−0.0368787
$507$	−2.90747e7	−5.02337
$508$	−184676.	−0.0317506
$509$	452046.	0.0773371	0.0386686	−	0.999252i	$-0.487688\pi$
$509$	452046.	0.0773371	0.0386686	+	0.999252i	$0.487688\pi$
$510$	−67222.5	−0.0114443
$511$	1.20038e6	0.203360
$512$	6.48344e6	1.09303
$513$	−4.75767e6	−0.798181
$514$	1.78970e6	0.298794
$515$	1.57524e6	0.261716
$516$	−184502.	−0.0305055
$517$	1.76584e6	0.290553
$518$	593265.	0.0971459
$519$	−1.68661e7	−2.74850
$520$	−5.40782e6	−0.877029
$521$	−7.25183e6	−1.17045	−0.585225	−	0.810871i	$-0.698994\pi$
$521$	−7.25183e6	−1.17045	−0.585225	+	0.810871i	$0.698994\pi$
$522$	1.72358e6	0.276856
$523$	86380.4	0.0138090	0.00690448	−	0.999976i	$-0.497802\pi$
$523$	86380.4	0.0138090	0.00690448	+	0.999976i	$0.497802\pi$
$524$	−175672.	−0.0279496
$525$	−396983.	−0.0628599
$526$	−5.32017e6	−0.838419
$527$	79027.7	0.0123952
$528$	3.42972e6	0.535395
$529$	−6.33156e6	−0.983720
$530$	−3.25460e6	−0.503278
$531$	1.99690e7	3.07340
$532$	−19599.2	−0.00300234
$533$	4.03288e6	0.614890
$534$	−1.52785e7	−2.31861
$535$	−638244.	−0.0964056
$536$	2.07630e6	0.312160
$537$	−1.13758e6	−0.170234
$538$	499769.	0.0744412
$539$	−1.98061e6	−0.293648
$540$	−854393.	−0.126088
$541$	3.22184e6	0.473273	0.236636	−	0.971598i	$-0.423955\pi$
$541$	3.22184e6	0.473273	0.236636	+	0.971598i	$0.423955\pi$
$542$	5.68182e6	0.830786
$543$	−3.54972e6	−0.516648
$544$	−15305.4	−0.00221741
$545$	608471.	0.0877503
$546$	3.97177e6	0.570168
$547$	1.13733e7	1.62524	0.812620	−	0.582794i	$-0.198040\pi$
$547$	1.13733e7	1.62524	0.812620	+	0.582794i	$0.198040\pi$
$548$	419550.	0.0596804
$549$	1.85641e6	0.262872
$550$	−410100.	−0.0578073
$551$	−169380.	−0.0237675
$552$	−1.84224e6	−0.257335
$553$	−1.76506e6	−0.245440
$554$	4.64283e6	0.642700
$555$	−3.96326e6	−0.546161
$556$	768610.	0.105443
$557$	1.73931e6	0.237541	0.118770	−	0.992922i	$-0.462105\pi$
$557$	1.73931e6	0.237541	0.118770	+	0.992922i	$0.462105\pi$
$558$	−1.77621e7	−2.41495
$559$	−2.70427e6	−0.366033
$560$	489019.	0.0658955
$561$	−59997.8	−0.00804875
$562$	−2.87651e6	−0.384172
$563$	1.86541e6	0.248030	0.124015	−	0.992280i	$-0.460423\pi$
$563$	1.86541e6	0.248030	0.124015	+	0.992280i	$0.460423\pi$
$564$	1.14812e6	0.151981
$565$	294376.	0.0387954
$566$	−1.30167e7	−1.70789
$567$	4.92470e6	0.643313
$568$	−8.10006e6	−1.05346
$569$	1.12524e7	1.45702	0.728508	−	0.685037i	$-0.240214\pi$
$569$	1.12524e7	1.45702	0.728508	+	0.685037i	$0.240214\pi$
$570$	−1.48478e6	−0.191414
$571$	1.05738e7	1.35719	0.678595	−	0.734513i	$-0.262589\pi$
$571$	1.05738e7	1.35719	0.678595	+	0.734513i	$0.262589\pi$
$572$	−361812.	−0.0462374
$573$	1.48260e7	1.88642
$574$	−397076.	−0.0503030
$575$	202312.	0.0255183
$576$	2.36927e7	2.97549
$577$	−9.42989e6	−1.17915	−0.589573	−	0.807715i	$-0.700704\pi$
$577$	−9.42989e6	−1.17915	−0.589573	+	0.807715i	$0.700704\pi$
$578$	7.69816e6	0.958446
$579$	−8.67671e6	−1.07562
$580$	−30417.7	−0.00375453
$581$	−446481.	−0.0548735
$582$	1.70630e7	2.08808
$583$	−2.90482e6	−0.353954
$584$	1.07555e7	1.30496
$585$	−1.95280e7	−2.35922
$586$	−1.12228e7	−1.35007
$587$	−1.42201e7	−1.70337	−0.851684	−	0.524055i	$-0.824419\pi$
$587$	−1.42201e7	−1.70337	−0.851684	+	0.524055i	$0.824419\pi$
$588$	−1.28776e6	−0.153600
$589$	1.74553e6	0.207319
$590$	3.99640e6	0.472650
$591$	−2.91347e7	−3.43116
$592$	4.88210e6	0.572535
$593$	1.41463e7	1.65198	0.825991	−	0.563684i	$-0.190616\pi$
$593$	1.41463e7	1.65198	0.825991	+	0.563684i	$0.190616\pi$
$594$	8.64763e6	1.00561
$595$	−8554.65	−0.000990626 0
$596$	949139.	0.109450
$597$	−4.87045e6	−0.559285
$598$	−2.02411e6	−0.231463
$599$	−2.68996e6	−0.306323	−0.153161	−	0.988201i	$-0.548945\pi$
$599$	−2.68996e6	−0.306323	−0.153161	+	0.988201i	$0.548945\pi$
$600$	−3.55701e6	−0.403373
$601$	1.24949e7	1.41106	0.705530	−	0.708680i	$-0.250709\pi$
$601$	1.24949e7	1.41106	0.705530	+	0.708680i	$0.250709\pi$
$602$	266261.	0.0299445
$603$	7.49764e6	0.839714
$604$	−94542.9	−0.0105448
$605$	−366025.	−0.0406558
$606$	−2.19111e7	−2.42372
$607$	−8.57974e6	−0.945154	−0.472577	−	0.881289i	$-0.656676\pi$
$607$	−8.57974e6	−0.945154	−0.472577	+	0.881289i	$0.656676\pi$
$608$	−338058.	−0.0370879
$609$	298022.	0.0325615
$610$	371526.	0.0404263
$611$	1.68281e7	1.82361
$612$	−28710.5	−0.00309857
$613$	4.40994e6	0.474003	0.237002	−	0.971509i	$-0.423835\pi$
$613$	4.40994e6	0.474003	0.237002	+	0.971509i	$0.423835\pi$
$614$	1.00340e7	1.07412
$615$	2.65263e6	0.282807
$616$	475228.	0.0504603
$617$	7.74075e6	0.818597	0.409299	−	0.912400i	$-0.365773\pi$
$617$	7.74075e6	0.818597	0.409299	+	0.912400i	$0.365773\pi$
$618$	−1.03663e7	−1.09182
$619$	4.17696e6	0.438161	0.219081	−	0.975707i	$-0.429694\pi$
$619$	4.17696e6	0.438161	0.219081	+	0.975707i	$0.429694\pi$
$620$	313465.	0.0327499
$621$	−4.26609e6	−0.443916
$622$	1.12120e7	1.16201
$623$	−1.94432e6	−0.200701
$624$	3.26845e7	3.36032
$625$	390625.	0.0400000
$626$	8.08454e6	0.824555
$627$	−1.32520e6	−0.134621
$628$	−505387.	−0.0511358
$629$	−85404.9	−0.00860709
$630$	1.92272e6	0.193003
$631$	−3.42449e6	−0.342392	−0.171196	−	0.985237i	$-0.554763\pi$
$631$	−3.42449e6	−0.342392	−0.171196	+	0.985237i	$0.554763\pi$
$632$	−1.58151e7	−1.57499
$633$	2.31717e7	2.29852
$634$	−9.34729e6	−0.923554
$635$	−1.78041e6	−0.175221
$636$	−1.88866e6	−0.185144
$637$	−1.88747e7	−1.84303
$638$	307869.	0.0299443
$639$	−2.92499e7	−2.83382
$640$	3.99249e6	0.385295
$641$	1.14569e7	1.10134	0.550672	−	0.834722i	$-0.314371\pi$
$641$	1.14569e7	1.10134	0.550672	+	0.834722i	$0.314371\pi$
$642$	4.20012e6	0.402183
$643$	−5.22825e6	−0.498688	−0.249344	−	0.968415i	$-0.580215\pi$
$643$	−5.22825e6	−0.498688	−0.249344	+	0.968415i	$0.580215\pi$
$644$	−17574.1	−0.00166978
$645$	−1.77874e6	−0.168350
$646$	−31995.7	−0.00301655
$647$	−1.84387e7	−1.73168	−0.865842	−	0.500317i	$-0.833217\pi$
$647$	−1.84387e7	−1.73168	−0.865842	+	0.500317i	$0.833217\pi$
$648$	4.41258e7	4.12814
$649$	3.56690e6	0.332414
$650$	−3.90816e6	−0.362818
$651$	−3.07122e6	−0.284027
$652$	1.24417e6	0.114620
$653$	−1.01728e7	−0.933591	−0.466795	−	0.884365i	$-0.654592\pi$
$653$	−1.01728e7	−0.933591	−0.466795	+	0.884365i	$0.654592\pi$
$654$	−4.00418e6	−0.366075
$655$	−1.69361e6	−0.154245
$656$	−3.26762e6	−0.296464
$657$	3.88388e7	3.51037
$658$	−1.65689e6	−0.149186
$659$	−664762.	−0.0596283	−0.0298142	−	0.999555i	$-0.509492\pi$
$659$	−664762.	−0.0596283	−0.0298142	+	0.999555i	$0.509492\pi$
$660$	−237983.	−0.0212660
$661$	2.77236e6	0.246801	0.123400	−	0.992357i	$-0.460620\pi$
$661$	2.77236e6	0.246801	0.123400	+	0.992357i	$0.460620\pi$
$662$	1.80962e7	1.60488
$663$	−571766.	−0.0505166
$664$	−4.00051e6	−0.352124
$665$	−188951.	−0.0165690
$666$	1.91954e7	1.67692
$667$	−151879.	−0.0132185
$668$	1.59313e6	0.138137
$669$	−1.61481e7	−1.39494
$670$	1.50051e6	0.129137
$671$	331597.	0.0284318
$672$	594807.	0.0508104
$673$	1.37127e7	1.16704	0.583519	−	0.812099i	$-0.301675\pi$
$673$	1.37127e7	1.16704	0.583519	+	0.812099i	$0.301675\pi$
$674$	4.55506e6	0.386229
$675$	−8.23697e6	−0.695838
$676$	−2.48516e6	−0.209165
$677$	−1.05702e7	−0.886367	−0.443183	−	0.896431i	$-0.646151\pi$
$677$	−1.05702e7	−0.886367	−0.443183	+	0.896431i	$0.646151\pi$
$678$	−1.93721e6	−0.161846
$679$	2.17141e6	0.180746
$680$	−76650.4	−0.00635686
$681$	3.32160e7	2.74460
$682$	−3.17270e6	−0.261197
$683$	−1.94910e7	−1.59876	−0.799378	−	0.600828i	$-0.794838\pi$
$683$	−1.94910e7	−1.59876	−0.799378	+	0.600828i	$0.794838\pi$
$684$	−634143.	−0.0518259
$685$	4.04477e6	0.329357
$686$	3.76657e6	0.305588
$687$	3.69242e7	2.98483
$688$	2.19112e6	0.176480
$689$	−2.76822e7	−2.22153
$690$	−1.33136e6	−0.106457
$691$	−8.97654e6	−0.715177	−0.357589	−	0.933879i	$-0.616401\pi$
$691$	−8.97654e6	−0.715177	−0.357589	+	0.933879i	$0.616401\pi$
$692$	−1.44163e6	−0.114443
$693$	1.71608e6	0.135739
$694$	1.57834e7	1.24395
$695$	7.40997e6	0.581908
$696$	2.67030e6	0.208948
$697$	57162.0	0.00445683
$698$	8.32084e6	0.646440
$699$	−3.35860e7	−2.59995
$700$	−33932.2	−0.00261738
$701$	−1.79155e7	−1.37700	−0.688498	−	0.725238i	$-0.741730\pi$
$701$	−1.79155e7	−1.37700	−0.688498	+	0.725238i	$0.741730\pi$
$702$	8.24099e7	6.31156
$703$	−1.88638e6	−0.143960
$704$	4.23205e6	0.321824
$705$	1.10687e7	0.838733
$706$	−8.94276e6	−0.675243
$707$	−2.78838e6	−0.209799
$708$	2.31913e6	0.173877
$709$	3.50611e6	0.261945	0.130972	−	0.991386i	$-0.458190\pi$
$709$	3.50611e6	0.261945	0.130972	+	0.991386i	$0.458190\pi$
$710$	−5.85380e6	−0.435805
$711$	−5.71093e7	−4.23675
$712$	−1.74213e7	−1.28790
$713$	1.56517e6	0.115302
$714$	56295.9	0.00413267
$715$	−3.48813e6	−0.255169
$716$	−97234.7	−0.00708825
$717$	4.12319e7	2.99527
$718$	−5.83687e6	−0.422541
$719$	−1.54857e6	−0.111714	−0.0558572	−	0.998439i	$-0.517789\pi$
$719$	−1.54857e6	−0.111714	−0.0558572	+	0.998439i	$0.517789\pi$
$720$	1.58225e7	1.13748
$721$	−1.31920e6	−0.0945087
$722$	−706706.	−0.0504540
$723$	7.86514e6	0.559578
$724$	−303413.	−0.0215123
$725$	−293249.	−0.0207201
$726$	2.40871e6	0.169607
$727$	2.34000e7	1.64203	0.821014	−	0.570908i	$-0.193409\pi$
$727$	2.34000e7	1.64203	0.821014	+	0.570908i	$0.193409\pi$
$728$	4.52881e6	0.316706
$729$	6.21820e7	4.33357
$730$	7.77285e6	0.539850
$731$	−38330.3	−0.00265307
$732$	215598.	0.0148719
$733$	−5.27862e6	−0.362878	−0.181439	−	0.983402i	$-0.558075\pi$
$733$	−5.27862e6	−0.362878	−0.181439	+	0.983402i	$0.558075\pi$
$734$	−1.38974e7	−0.952122
$735$	−1.24149e7	−0.847667
$736$	−303128.	−0.0206268
$737$	1.33925e6	0.0908221
$738$	−1.28476e7	−0.868322
$739$	1.13782e7	0.766412	0.383206	−	0.923663i	$-0.374820\pi$
$739$	1.13782e7	0.766412	0.383206	+	0.923663i	$0.374820\pi$
$740$	−338760.	−0.0227412
$741$	−1.26289e7	−0.844928
$742$	2.72558e6	0.181740
$743$	−1.35881e7	−0.903001	−0.451500	−	0.892271i	$-0.649111\pi$
$743$	−1.35881e7	−0.903001	−0.451500	+	0.892271i	$0.649111\pi$
$744$	−2.75184e7	−1.82260
$745$	9.15039e6	0.604017
$746$	−6.23019e6	−0.409877
$747$	−1.44461e7	−0.947217
$748$	−5128.32	−0.000335136 0
$749$	534502.	0.0348132
$750$	−2.57060e6	−0.166871
$751$	6.09011e6	0.394026	0.197013	−	0.980401i	$-0.436876\pi$
$751$	6.09011e6	0.394026	0.197013	+	0.980401i	$0.436876\pi$
$752$	−1.36348e7	−0.879236
$753$	−1.61364e6	−0.103710
$754$	2.93392e6	0.187940
$755$	−911463.	−0.0581931
$756$	715516.	0.0455318
$757$	−1.18109e7	−0.749105	−0.374553	−	0.927206i	$-0.622204\pi$
$757$	−1.18109e7	−0.749105	−0.374553	+	0.927206i	$0.622204\pi$
$758$	−2.57069e7	−1.62508
$759$	−1.18828e6	−0.0748709
$760$	−1.69302e6	−0.106323
$761$	−3.04966e6	−0.190893	−0.0954466	−	0.995435i	$-0.530428\pi$
$761$	−3.04966e6	−0.190893	−0.0954466	+	0.995435i	$0.530428\pi$
$762$	1.17164e7	0.730984
$763$	−509568.	−0.0316877
$764$	1.26726e6	0.0785473
$765$	−276790.	−0.0171000
$766$	−1.66330e7	−1.02423
$767$	3.39917e7	2.08634
$768$	7.68161e6	0.469947
$769$	−1.17392e7	−0.715854	−0.357927	−	0.933750i	$-0.616516\pi$
$769$	−1.17392e7	−0.715854	−0.357927	+	0.933750i	$0.616516\pi$
$770$	343441.	0.0208749
$771$	1.00126e7	0.606610
$772$	−741643.	−0.0447870
$773$	−1.74496e7	−1.05036	−0.525178	−	0.850993i	$-0.676001\pi$
$773$	−1.74496e7	−1.05036	−0.525178	+	0.850993i	$0.676001\pi$
$774$	8.61502e6	0.516897
$775$	3.02203e6	0.180736
$776$	1.94561e7	1.15985
$777$	3.31906e6	0.197225
$778$	−1.92840e7	−1.14222
$779$	1.26257e6	0.0745437
$780$	−2.26792e6	−0.133472
$781$	−5.22467e6	−0.306501
$782$	−28689.7	−0.00167768
$783$	6.18363e6	0.360445
$784$	1.52932e7	0.888601
$785$	−4.87230e6	−0.282202
$786$	1.11452e7	0.643475
$787$	1.22285e7	0.703776	0.351888	−	0.936042i	$-0.385540\pi$
$787$	1.22285e7	0.703776	0.351888	+	0.936042i	$0.385540\pi$
$788$	−2.49029e6	−0.142868
$789$	−2.97640e7	−1.70215
$790$	−1.14293e7	−0.651558
$791$	−246527.	−0.0140095
$792$	1.53762e7	0.871038
$793$	3.16004e6	0.178447
$794$	1.42331e6	0.0801216
$795$	−1.82081e7	−1.02175
$796$	−416303.	−0.0232877
$797$	4.81189e6	0.268331	0.134165	−	0.990959i	$-0.457165\pi$
$797$	4.81189e6	0.268331	0.134165	+	0.990959i	$0.457165\pi$
$798$	1.24344e6	0.0691220
$799$	238521.	0.0132178
$800$	−585280.	−0.0323325
$801$	−6.29096e7	−3.46446
$802$	2.78359e7	1.52816
$803$	6.93748e6	0.379676
$804$	870752.	0.0475067
$805$	−169428.	−0.00921498
$806$	−3.02351e7	−1.63936
$807$	2.79599e6	0.151130
$808$	−2.49841e7	−1.34628
$809$	1.69722e7	0.911730	0.455865	−	0.890049i	$-0.349330\pi$
$809$	1.69722e7	0.911730	0.455865	+	0.890049i	$0.349330\pi$
$810$	3.18891e7	1.70777
$811$	2.56616e6	0.137004	0.0685018	−	0.997651i	$-0.478178\pi$
$811$	2.56616e6	0.137004	0.0685018	+	0.997651i	$0.478178\pi$
$812$	25473.5	0.00135581
$813$	3.17873e7	1.68666
$814$	3.42872e6	0.181372
$815$	1.19947e7	0.632549
$816$	463270.	0.0243561
$817$	−846621.	−0.0443746
$818$	−2.49918e7	−1.30591
$819$	1.63539e7	0.851943
$820$	226734.	0.0117756
$821$	−1.26385e7	−0.654391	−0.327195	−	0.944957i	$-0.606104\pi$
$821$	−1.26385e7	−0.654391	−0.327195	+	0.944957i	$0.606104\pi$
$822$	−2.66175e7	−1.37400
$823$	−1.57339e7	−0.809725	−0.404863	−	0.914377i	$-0.632681\pi$
$823$	−1.57339e7	−0.809725	−0.404863	+	0.914377i	$0.632681\pi$
$824$	−1.18201e7	−0.606463
$825$	−2.29433e6	−0.117360
$826$	−3.34681e6	−0.170680
$827$	2.66712e7	1.35606	0.678030	−	0.735034i	$-0.262834\pi$
$827$	2.66712e7	1.35606	0.678030	+	0.735034i	$0.262834\pi$
$828$	−568620.	−0.0288235
$829$	−339310.	−0.0171479	−0.00857395	−	0.999963i	$-0.502729\pi$
$829$	−339310.	−0.0171479	−0.00857395	+	0.999963i	$0.502729\pi$
$830$	−2.89111e6	−0.145670
$831$	2.59746e7	1.30481
$832$	4.03304e7	2.01988
$833$	−267531.	−0.0133586
$834$	−4.87630e7	−2.42759
$835$	1.53590e7	0.762335
$836$	−113272.	−0.00560540
$837$	−6.37245e7	−3.14408
$838$	1.89390e7	0.931638
$839$	2.73539e7	1.34157	0.670786	−	0.741651i	$-0.265957\pi$
$839$	2.73539e7	1.34157	0.670786	+	0.741651i	$0.265957\pi$
$840$	2.97884e6	0.145663
$841$	−2.02910e7	−0.989267
$842$	1.35601e7	0.659147
$843$	−1.60928e7	−0.779944
$844$	1.98060e6	0.0957063
$845$	−2.39588e7	−1.15431
$846$	−5.36094e7	−2.57522
$847$	306530.	0.0146813
$848$	2.24294e7	1.07109
$849$	−7.28225e7	−3.46734
$850$	−55394.2	−0.00262977
$851$	−1.69147e6	−0.0800647
$852$	−3.39699e6	−0.160323
$853$	3.98898e7	1.87711	0.938555	−	0.345131i	$-0.112165\pi$
$853$	3.98898e7	1.87711	0.938555	+	0.345131i	$0.112165\pi$
$854$	−311136.	−0.0145984
$855$	−6.11360e6	−0.286011
$856$	4.78918e6	0.223397
$857$	−2.82176e7	−1.31240	−0.656202	−	0.754586i	$-0.727838\pi$
$857$	−2.82176e7	−1.31240	−0.656202	+	0.754586i	$0.727838\pi$
$858$	2.29545e7	1.06451
$859$	−2.62636e7	−1.21443	−0.607214	−	0.794539i	$-0.707713\pi$
$859$	−2.62636e7	−1.21443	−0.607214	+	0.794539i	$0.707713\pi$
$860$	−152038.	−0.00700980
$861$	−2.22147e6	−0.102125
$862$	1.21860e6	0.0558588
$863$	2.85510e7	1.30495	0.652475	−	0.757810i	$-0.273731\pi$
$863$	2.85510e7	1.30495	0.652475	+	0.757810i	$0.273731\pi$
$864$	1.23416e7	0.562454
$865$	−1.38984e7	−0.631573
$866$	−1.18241e7	−0.535762
$867$	4.30678e7	1.94583
$868$	−262513.	−0.0118264
$869$	−1.02010e7	−0.458240
$870$	1.92979e6	0.0864395
$871$	1.27627e7	0.570029
$872$	−4.56577e6	−0.203340
$873$	7.02572e7	3.12000
$874$	−633685.	−0.0280605
$875$	−327131.	−0.0144445
$876$	4.51062e6	0.198598
$877$	1.19679e7	0.525434	0.262717	−	0.964873i	$-0.415381\pi$
$877$	1.19679e7	0.525434	0.262717	+	0.964873i	$0.415381\pi$
$878$	−1.36461e7	−0.597411
$879$	−6.27865e7	−2.74091
$880$	2.82624e6	0.123028
$881$	1.97610e7	0.857766	0.428883	−	0.903360i	$-0.358907\pi$
$881$	1.97610e7	0.857766	0.428883	+	0.903360i	$0.358907\pi$
$882$	6.01295e7	2.60265
$883$	3.71532e7	1.60359	0.801797	−	0.597597i	$-0.203878\pi$
$883$	3.71532e7	1.60359	0.801797	+	0.597597i	$0.203878\pi$
$884$	−48871.8	−0.00210343
$885$	2.23581e7	0.959571
$886$	3.68254e7	1.57603
$887$	2.71027e7	1.15666	0.578328	−	0.815805i	$-0.303706\pi$
$887$	2.71027e7	1.15666	0.578328	+	0.815805i	$0.303706\pi$
$888$	2.97391e7	1.26560
$889$	1.49102e6	0.0632745
$890$	−1.25901e7	−0.532790
$891$	2.84619e7	1.20107
$892$	−1.38026e6	−0.0580831
$893$	5.26834e6	0.221078
$894$	−6.02163e7	−2.51982
$895$	−937414.	−0.0391178
$896$	−3.34353e6	−0.139135
$897$	−1.13240e7	−0.469915
$898$	−1.41757e7	−0.586615
$899$	−2.26869e6	−0.0936216
$900$	−1.09789e6	−0.0451808
$901$	−392368.	−0.0161021
$902$	−2.29486e6	−0.0939162
$903$	1.48962e6	0.0607932
$904$	−2.20890e6	−0.0898991
$905$	−2.92512e6	−0.118720
$906$	5.99809e6	0.242769
$907$	−2.31154e7	−0.933002	−0.466501	−	0.884521i	$-0.654486\pi$
$907$	−2.31154e7	−0.933002	−0.466501	+	0.884521i	$0.654486\pi$
$908$	2.83914e6	0.114281
$909$	−9.02193e7	−3.62151
$910$	3.27291e6	0.131018
$911$	−2.64314e7	−1.05517	−0.527587	−	0.849501i	$-0.676903\pi$
$911$	−2.64314e7	−1.05517	−0.527587	+	0.849501i	$0.676903\pi$
$912$	1.02325e7	0.407375
$913$	−2.58040e6	−0.102449
$914$	2.30938e7	0.914386
$915$	2.07852e6	0.0820733
$916$	3.15610e6	0.124283
$917$	1.41832e6	0.0556996
$918$	1.16808e6	0.0457473
$919$	1.58691e7	0.619816	0.309908	−	0.950767i	$-0.399702\pi$
$919$	1.58691e7	0.619816	0.309908	+	0.950767i	$0.399702\pi$
$920$	−1.51809e6	−0.0591326
$921$	5.61357e7	2.18067
$922$	−4.77854e7	−1.85126
$923$	−4.97899e7	−1.92370
$924$	199300.	0.00767940
$925$	−3.26590e6	−0.125501
$926$	2.40082e7	0.920096
$927$	−4.26833e7	−1.63139
$928$	439379.	0.0167483
$929$	−3.31495e7	−1.26019	−0.630097	−	0.776516i	$-0.716985\pi$
$929$	−3.31495e7	−1.26019	−0.630097	+	0.776516i	$0.716985\pi$
$930$	−1.98872e7	−0.753991
$931$	−5.90909e6	−0.223432
$932$	−2.87077e6	−0.108257
$933$	6.27264e7	2.35910
$934$	3.82631e7	1.43520
$935$	−49440.8	−0.00184951
$936$	1.46532e8	5.46692
$937$	−1.65911e7	−0.617341	−0.308671	−	0.951169i	$-0.599884\pi$
$937$	−1.65911e7	−0.617341	−0.308671	+	0.951169i	$0.599884\pi$
$938$	−1.25661e6	−0.0466331
$939$	4.52294e7	1.67401
$940$	946098.	0.0349234
$941$	−4.64616e7	−1.71049	−0.855244	−	0.518225i	$-0.826593\pi$
$941$	−4.64616e7	−1.71049	−0.855244	+	0.518225i	$0.826593\pi$
$942$	3.20633e7	1.17728
$943$	1.13211e6	0.0414582
$944$	−2.75416e7	−1.00591
$945$	6.89810e6	0.251276
$946$	1.53883e6	0.0559067
$947$	−4.36551e7	−1.58183	−0.790915	−	0.611925i	$-0.790395\pi$
$947$	−4.36551e7	−1.58183	−0.790915	+	0.611925i	$0.790395\pi$
$948$	−6.63249e6	−0.239693
$949$	6.61126e7	2.38297
$950$	−1.22352e6	−0.0439848
$951$	−5.22940e7	−1.87500
$952$	64191.4	0.00229554
$953$	1.95869e7	0.698607	0.349303	−	0.937010i	$-0.386418\pi$
$953$	1.95869e7	0.698607	0.349303	+	0.937010i	$0.386418\pi$
$954$	8.81876e7	3.13716
$955$	1.22173e7	0.433477
$956$	3.52430e6	0.124718
$957$	1.72239e6	0.0607927
$958$	−2.47962e7	−0.872914
$959$	−3.38732e6	−0.118935
$960$	2.65274e7	0.929003
$961$	−5.24949e6	−0.183362
$962$	3.26749e7	1.13835
$963$	1.72941e7	0.600940
$964$	672274.	0.0232999
$965$	−7.14998e6	−0.247165
$966$	1.11496e6	0.0384429
$967$	−2.47905e7	−0.852549	−0.426274	−	0.904594i	$-0.640174\pi$
$967$	−2.47905e7	−0.852549	−0.426274	+	0.904594i	$0.640174\pi$
$968$	2.74654e6	0.0942100
$969$	−179002.	−0.00612418
$970$	1.40606e7	0.479817
$971$	−3.87645e7	−1.31943	−0.659715	−	0.751516i	$-0.729323\pi$
$971$	−3.87645e7	−1.31943	−0.659715	+	0.751516i	$0.729323\pi$
$972$	1.02007e7	0.346309
$973$	−6.20552e6	−0.210134
$974$	−3.25407e7	−1.09908
$975$	−2.18644e7	−0.736591
$976$	−2.56040e6	−0.0860367
$977$	1.87494e7	0.628422	0.314211	−	0.949353i	$-0.398260\pi$
$977$	1.87494e7	0.628422	0.314211	+	0.949353i	$0.398260\pi$
$978$	−7.89337e7	−2.63886
$979$	−1.12370e7	−0.374710
$980$	−1.06117e6	−0.0352954
$981$	−1.64873e7	−0.546987
$982$	3.71570e7	1.22959
$983$	−4.36796e7	−1.44177	−0.720883	−	0.693057i	$-0.756263\pi$
$983$	−4.36796e7	−1.44177	−0.720883	+	0.693057i	$0.756263\pi$
$984$	−1.99045e7	−0.655336
$985$	−2.40082e7	−0.788441
$986$	41585.4	0.00136222
$987$	−9.26955e6	−0.302877
$988$	−1.07946e6	−0.0351814
$989$	−759144.	−0.0246793
$990$	1.11122e7	0.360339
$991$	5.32799e7	1.72337	0.861686	−	0.507441i	$-0.169409\pi$
$991$	5.32799e7	1.72337	0.861686	+	0.507441i	$0.169409\pi$
$992$	−4.52796e6	−0.146091
$993$	1.01241e8	3.25823
$994$	4.90230e6	0.157374
$995$	−4.01346e6	−0.128517
$996$	−1.67773e6	−0.0535886
$997$	−1.22394e7	−0.389963	−0.194981	−	0.980807i	$-0.562465\pi$
$997$	−1.22394e7	−0.389963	−0.194981	+	0.980807i	$0.562465\pi$
$998$	−7.53479e6	−0.239467
$999$	6.88668e7	2.18321

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.a.1.11	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.a.1.11	✓	35	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)

\(f(q)\)	\(=\)	\(q-5.42281 q^{2} -30.3382 q^{3} -2.59316 q^{4} -25.0000 q^{5} +164.518 q^{6} +20.9364 q^{7} +187.592 q^{8} +677.408 q^{9} +O(q^{10})\)	\(q-5.42281 q^{2} -30.3382 q^{3} -2.59316 q^{4} -25.0000 q^{5} +164.518 q^{6} +20.9364 q^{7} +187.592 q^{8} +677.408 q^{9} +135.570 q^{10} +121.000 q^{11} +78.6720 q^{12} +1153.10 q^{13} -113.534 q^{14} +758.456 q^{15} -934.294 q^{16} +16.3441 q^{17} -3673.45 q^{18} +361.000 q^{19} +64.8291 q^{20} -635.173 q^{21} -656.160 q^{22} +323.700 q^{23} -5691.21 q^{24} +625.000 q^{25} -6253.05 q^{26} -13179.2 q^{27} -54.2915 q^{28} -469.198 q^{29} -4112.96 q^{30} +4835.25 q^{31} -936.448 q^{32} -3670.92 q^{33} -88.6307 q^{34} -523.410 q^{35} -1756.63 q^{36} -5225.44 q^{37} -1957.63 q^{38} -34983.1 q^{39} -4689.80 q^{40} +3497.42 q^{41} +3444.42 q^{42} -2345.21 q^{43} -313.773 q^{44} -16935.2 q^{45} -1755.36 q^{46} +14593.7 q^{47} +28344.8 q^{48} -16368.7 q^{49} -3389.25 q^{50} -495.850 q^{51} -2990.18 q^{52} -24006.7 q^{53} +71468.0 q^{54} -3025.00 q^{55} +3927.50 q^{56} -10952.1 q^{57} +2544.37 q^{58} +29478.5 q^{59} -1966.80 q^{60} +2740.47 q^{61} -26220.6 q^{62} +14182.5 q^{63} +34975.6 q^{64} -28827.6 q^{65} +19906.7 q^{66} +11068.1 q^{67} -42.3828 q^{68} -9820.47 q^{69} +2838.35 q^{70} -43179.1 q^{71} +127076. q^{72} +57334.5 q^{73} +28336.5 q^{74} -18961.4 q^{75} -936.132 q^{76} +2533.31 q^{77} +189706. q^{78} -84305.7 q^{79} +23357.4 q^{80} +235222. q^{81} -18965.8 q^{82} -21325.6 q^{83} +1647.11 q^{84} -408.602 q^{85} +12717.6 q^{86} +14234.6 q^{87} +22698.6 q^{88} -92868.1 q^{89} +91836.3 q^{90} +24141.8 q^{91} -839.406 q^{92} -146693. q^{93} -79139.0 q^{94} -9025.00 q^{95} +28410.2 q^{96} +103715. q^{97} +88764.1 q^{98} +81966.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9 + 100 * q^10 + 4235 * q^11 - 568 * q^12 - 717 * q^13 - 2585 * q^14 + 675 * q^15 + 3356 * q^16 - 3349 * q^17 - 5533 * q^18 + 12635 * q^19 - 13000 * q^20 + 289 * q^21 - 484 * q^22 - 820 * q^23 - 21748 * q^24 + 21875 * q^25 - 6267 * q^26 - 13650 * q^27 - 6487 * q^28 - 13357 * q^29 + 7275 * q^30 - 15341 * q^31 - 16405 * q^32 - 3267 * q^33 - 1255 * q^34 - 2925 * q^35 + 23487 * q^36 - 511 * q^37 - 1444 * q^38 - 33584 * q^39 + 12450 * q^40 - 36855 * q^41 + 16330 * q^42 + 10991 * q^43 + 62920 * q^44 - 51150 * q^45 - 20443 * q^46 - 33594 * q^47 + 36221 * q^48 + 23422 * q^49 - 2500 * q^50 - 53530 * q^51 + 89382 * q^52 + 13103 * q^53 + 65776 * q^54 - 105875 * q^55 + 130911 * q^56 - 9747 * q^57 + 127808 * q^58 - 161139 * q^59 + 14200 * q^60 - 91587 * q^61 + 131818 * q^62 + 16590 * q^63 - 23186 * q^64 + 17925 * q^65 - 35211 * q^66 + 39210 * q^67 + 26300 * q^68 - 23174 * q^69 + 64625 * q^70 - 167772 * q^71 + 135820 * q^72 - 5106 * q^73 - 256965 * q^74 - 16875 * q^75 + 187720 * q^76 + 14157 * q^77 + 492812 * q^78 - 156897 * q^79 - 83900 * q^80 + 31279 * q^81 + 46818 * q^82 - 185627 * q^83 + 165864 * q^84 + 83725 * q^85 - 159946 * q^86 - 112092 * q^87 - 60258 * q^88 - 144420 * q^89 + 138325 * q^90 - 442480 * q^91 - 205876 * q^92 + 125910 * q^93 - 110044 * q^94 - 315875 * q^95 - 554286 * q^96 + 41200 * q^97 + 41052 * q^98 + 247566 * q^99

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