LMFDB - Embedded newform 1045.6.a.a.1.15

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			1.15
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54765 q^{2} +26.9200 q^{3} -25.5095 q^{4} -25.0000 q^{5} -68.5826 q^{6} +6.38524 q^{7} +146.514 q^{8} +481.684 q^{9} +O(q^{10})$	\(q-2.54765 q^{2} +26.9200 q^{3} -25.5095 q^{4} -25.0000 q^{5} -68.5826 q^{6} +6.38524 q^{7} +146.514 q^{8} +481.684 q^{9} +63.6912 q^{10} +121.000 q^{11} -686.714 q^{12} -96.3795 q^{13} -16.2674 q^{14} -672.999 q^{15} +443.037 q^{16} -980.988 q^{17} -1227.16 q^{18} +361.000 q^{19} +637.737 q^{20} +171.890 q^{21} -308.266 q^{22} -2802.67 q^{23} +3944.15 q^{24} +625.000 q^{25} +245.541 q^{26} +6425.37 q^{27} -162.884 q^{28} +348.228 q^{29} +1714.57 q^{30} +2478.78 q^{31} -5817.15 q^{32} +3257.32 q^{33} +2499.21 q^{34} -159.631 q^{35} -12287.5 q^{36} +2747.01 q^{37} -919.702 q^{38} -2594.53 q^{39} -3662.85 q^{40} -4187.57 q^{41} -437.916 q^{42} -16588.7 q^{43} -3086.65 q^{44} -12042.1 q^{45} +7140.21 q^{46} +12393.2 q^{47} +11926.5 q^{48} -16766.2 q^{49} -1592.28 q^{50} -26408.2 q^{51} +2458.59 q^{52} -22695.1 q^{53} -16369.6 q^{54} -3025.00 q^{55} +935.527 q^{56} +9718.11 q^{57} -887.164 q^{58} +5085.55 q^{59} +17167.9 q^{60} +11282.2 q^{61} -6315.07 q^{62} +3075.67 q^{63} +642.883 q^{64} +2409.49 q^{65} -8298.50 q^{66} +44586.4 q^{67} +25024.5 q^{68} -75447.6 q^{69} +406.684 q^{70} -14308.1 q^{71} +70573.5 q^{72} +50131.9 q^{73} -6998.41 q^{74} +16825.0 q^{75} -9208.92 q^{76} +772.614 q^{77} +6609.96 q^{78} +39291.6 q^{79} -11075.9 q^{80} +55921.5 q^{81} +10668.5 q^{82} +2995.06 q^{83} -4384.83 q^{84} +24524.7 q^{85} +42262.3 q^{86} +9374.29 q^{87} +17728.2 q^{88} -53706.8 q^{89} +30679.1 q^{90} -615.406 q^{91} +71494.5 q^{92} +66728.7 q^{93} -31573.5 q^{94} -9025.00 q^{95} -156597. q^{96} -50915.4 q^{97} +42714.5 q^{98} +58283.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.54765	−0.450365	−0.225183	−	0.974317i	$-0.572298\pi$
$2$	−2.54765	−0.450365	−0.225183	+	0.974317i	$0.572298\pi$
$3$	26.9200	1.72692	0.863458	−	0.504421i	$-0.168294\pi$
$3$	26.9200	1.72692	0.863458	+	0.504421i	$0.168294\pi$
$4$	−25.5095	−0.797171
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−68.5826	−0.777743
$7$	6.38524	0.0492529	0.0246265	−	0.999697i	$-0.492160\pi$
$7$	6.38524	0.0492529	0.0246265	+	0.999697i	$0.492160\pi$
$8$	146.514	0.809383
$9$	481.684	1.98224
$10$	63.6912	0.201409
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−686.714	−1.37665
$13$	−96.3795	−0.158171	−0.0790854	−	0.996868i	$-0.525200\pi$
$13$	−96.3795	−0.158171	−0.0790854	+	0.996868i	$0.525200\pi$
$14$	−16.2674	−0.0221818
$15$	−672.999	−0.772300
$16$	443.037	0.432653
$17$	−980.988	−0.823268	−0.411634	−	0.911349i	$-0.635042\pi$
$17$	−980.988	−0.823268	−0.411634	+	0.911349i	$0.635042\pi$
$18$	−1227.16	−0.892732
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	637.737	0.356506
$21$	171.890	0.0850557
$22$	−308.266	−0.135790
$23$	−2802.67	−1.10472	−0.552359	−	0.833606i	$-0.686272\pi$
$23$	−2802.67	−1.10472	−0.552359	+	0.833606i	$0.686272\pi$
$24$	3944.15	1.39774
$25$	625.000	0.200000
$26$	245.541	0.0712346
$27$	6425.37	1.69625
$28$	−162.884	−0.0392630
$29$	348.228	0.0768899	0.0384449	−	0.999261i	$-0.487760\pi$
$29$	348.228	0.0768899	0.0384449	+	0.999261i	$0.487760\pi$
$30$	1714.57	0.347817
$31$	2478.78	0.463270	0.231635	−	0.972803i	$-0.425593\pi$
$31$	2478.78	0.463270	0.231635	+	0.972803i	$0.425593\pi$
$32$	−5817.15	−1.00424
$33$	3257.32	0.520685
$34$	2499.21	0.370771
$35$	−159.631	−0.0220266
$36$	−12287.5	−1.58018
$37$	2747.01	0.329880	0.164940	−	0.986304i	$-0.447257\pi$
$37$	2747.01	0.329880	0.164940	+	0.986304i	$0.447257\pi$
$38$	−919.702	−0.103321
$39$	−2594.53	−0.273148
$40$	−3662.85	−0.361967
$41$	−4187.57	−0.389047	−0.194524	−	0.980898i	$-0.562316\pi$
$41$	−4187.57	−0.389047	−0.194524	+	0.980898i	$0.562316\pi$
$42$	−437.916	−0.0383061
$43$	−16588.7	−1.36818	−0.684088	−	0.729399i	$-0.739800\pi$
$43$	−16588.7	−1.36818	−0.684088	+	0.729399i	$0.739800\pi$
$44$	−3086.65	−0.240356
$45$	−12042.1	−0.886485
$46$	7140.21	0.497527
$47$	12393.2	0.818348	0.409174	−	0.912456i	$-0.365817\pi$
$47$	12393.2	0.818348	0.409174	+	0.912456i	$0.365817\pi$
$48$	11926.5	0.747156
$49$	−16766.2	−0.997574
$50$	−1592.28	−0.0900730
$51$	−26408.2	−1.42172
$52$	2458.59	0.126089
$53$	−22695.1	−1.10980	−0.554898	−	0.831918i	$-0.687243\pi$
$53$	−22695.1	−1.10980	−0.554898	+	0.831918i	$0.687243\pi$
$54$	−16369.6	−0.763930
$55$	−3025.00	−0.134840
$56$	935.527	0.0398645
$57$	9718.11	0.396182
$58$	−887.164	−0.0346285
$59$	5085.55	0.190199	0.0950994	−	0.995468i	$-0.469683\pi$
$59$	5085.55	0.190199	0.0950994	+	0.995468i	$0.469683\pi$
$60$	17167.9	0.615656
$61$	11282.2	0.388213	0.194106	−	0.980981i	$-0.437819\pi$
$61$	11282.2	0.388213	0.194106	+	0.980981i	$0.437819\pi$
$62$	−6315.07	−0.208641
$63$	3075.67	0.0976311
$64$	642.883	0.0196192
$65$	2409.49	0.0707361
$66$	−8298.50	−0.234498
$67$	44586.4	1.21343	0.606716	−	0.794919i	$-0.292487\pi$
$67$	44586.4	1.21343	0.606716	+	0.794919i	$0.292487\pi$
$68$	25024.5	0.656286
$69$	−75447.6	−1.90776
$70$	406.684	0.00992000
$71$	−14308.1	−0.336851	−0.168425	−	0.985714i	$-0.553868\pi$
$71$	−14308.1	−0.336851	−0.168425	+	0.985714i	$0.553868\pi$
$72$	70573.5	1.60439
$73$	50131.9	1.10105	0.550525	−	0.834818i	$-0.314427\pi$
$73$	50131.9	1.10105	0.550525	+	0.834818i	$0.314427\pi$
$74$	−6998.41	−0.148566
$75$	16825.0	0.345383
$76$	−9208.92	−0.182884
$77$	772.614	0.0148503
$78$	6609.96	0.123016
$79$	39291.6	0.708325	0.354162	−	0.935184i	$-0.384766\pi$
$79$	39291.6	0.708325	0.354162	+	0.935184i	$0.384766\pi$
$80$	−11075.9	−0.193488
$81$	55921.5	0.947035
$82$	10668.5	0.175213
$83$	2995.06	0.0477211	0.0238606	−	0.999715i	$-0.492404\pi$
$83$	2995.06	0.0477211	0.0238606	+	0.999715i	$0.492404\pi$
$84$	−4384.83	−0.0678039
$85$	24524.7	0.368177
$86$	42262.3	0.616179
$87$	9374.29	0.132782
$88$	17728.2	0.244038
$89$	−53706.8	−0.718711	−0.359355	−	0.933201i	$-0.617003\pi$
$89$	−53706.8	−0.718711	−0.359355	+	0.933201i	$0.617003\pi$
$90$	30679.1	0.399242
$91$	−615.406	−0.00779037
$92$	71494.5	0.880650
$93$	66728.7	0.800028
$94$	−31573.5	−0.368555
$95$	−9025.00	−0.102598
$96$	−156597.	−1.73423
$97$	−50915.4	−0.549440	−0.274720	−	0.961524i	$-0.588585\pi$
$97$	−50915.4	−0.549440	−0.274720	+	0.961524i	$0.588585\pi$
$98$	42714.5	0.449273
$99$	58283.8	0.597668
$100$	−15943.4	−0.159434
$101$	−12483.8	−0.121771	−0.0608853	−	0.998145i	$-0.519392\pi$
$101$	−12483.8	−0.121771	−0.0608853	+	0.998145i	$0.519392\pi$
$102$	67278.7	0.640291
$103$	31407.5	0.291702	0.145851	−	0.989307i	$-0.453408\pi$
$103$	31407.5	0.291702	0.145851	+	0.989307i	$0.453408\pi$
$104$	−14120.9	−0.128021
$105$	−4297.26	−0.0380381
$106$	57819.3	0.499813
$107$	−121372.	−1.02485	−0.512423	−	0.858733i	$-0.671252\pi$
$107$	−121372.	−1.02485	−0.512423	+	0.858733i	$0.671252\pi$
$108$	−163908.	−1.35220
$109$	−119019.	−0.959511	−0.479756	−	0.877402i	$-0.659275\pi$
$109$	−119019.	−0.959511	−0.479756	+	0.877402i	$0.659275\pi$
$110$	7706.64	0.0607272
$111$	73949.3	0.569674
$112$	2828.90	0.0213094
$113$	23715.6	0.174718	0.0873590	−	0.996177i	$-0.472157\pi$
$113$	23715.6	0.174718	0.0873590	+	0.996177i	$0.472157\pi$
$114$	−24758.3	−0.178426
$115$	70066.6	0.494045
$116$	−8883.12	−0.0612944
$117$	−46424.5	−0.313532
$118$	−12956.2	−0.0856589
$119$	−6263.84	−0.0405484
$120$	−98603.8	−0.625087
$121$	14641.0	0.0909091
$122$	−28743.1	−0.174837
$123$	−112729.	−0.671852
$124$	−63232.4	−0.369305
$125$	−15625.0	−0.0894427
$126$	−7835.73	−0.0439696
$127$	56732.4	0.312120	0.156060	−	0.987748i	$-0.450121\pi$
$127$	56732.4	0.312120	0.156060	+	0.987748i	$0.450121\pi$
$128$	184511.	0.995399
$129$	−446568.	−2.36273
$130$	−6138.53	−0.0318571
$131$	−381084.	−1.94018	−0.970091	−	0.242742i	$-0.921953\pi$
$131$	−381084.	−1.94018	−0.970091	+	0.242742i	$0.921953\pi$
$132$	−83092.4	−0.415075
$133$	2305.07	0.0112994
$134$	−113591.	−0.546487
$135$	−160634.	−0.758584
$136$	−143729.	−0.666340
$137$	182345.	0.830026	0.415013	−	0.909815i	$-0.363777\pi$
$137$	182345.	0.830026	0.415013	+	0.909815i	$0.363777\pi$
$138$	192214.	0.859187
$139$	−12635.0	−0.0554676	−0.0277338	−	0.999615i	$-0.508829\pi$
$139$	−12635.0	−0.0554676	−0.0277338	+	0.999615i	$0.508829\pi$
$140$	4072.10	0.0175590
$141$	333624.	1.41322
$142$	36452.1	0.151706
$143$	−11661.9	−0.0476903
$144$	213404.	0.857623
$145$	−8705.71	−0.0343862
$146$	−127719.	−0.495875
$147$	−451346.	−1.72273
$148$	−70074.7	−0.262971
$149$	−271873.	−1.00323	−0.501615	−	0.865091i	$-0.667261\pi$
$149$	−271873.	−1.00323	−0.501615	+	0.865091i	$0.667261\pi$
$150$	−42864.1	−0.155549
$151$	186540.	0.665779	0.332889	−	0.942966i	$-0.391976\pi$
$151$	186540.	0.665779	0.332889	+	0.942966i	$0.391976\pi$
$152$	52891.6	0.185685
$153$	−472527.	−1.63192
$154$	−1968.35	−0.00668806
$155$	−61969.5	−0.207181
$156$	66185.1	0.217745
$157$	−82268.8	−0.266371	−0.133185	−	0.991091i	$-0.542521\pi$
$157$	−82268.8	−0.266371	−0.133185	+	0.991091i	$0.542521\pi$
$158$	−100101.	−0.319005
$159$	−610952.	−1.91653
$160$	145429.	0.449108
$161$	−17895.7	−0.0544106
$162$	−142468.	−0.426511
$163$	−190074.	−0.560342	−0.280171	−	0.959950i	$-0.590391\pi$
$163$	−190074.	−0.560342	−0.280171	+	0.959950i	$0.590391\pi$
$164$	106823.	0.310137
$165$	−81432.9	−0.232857
$166$	−7630.37	−0.0214919
$167$	−560337.	−1.55474	−0.777371	−	0.629042i	$-0.783447\pi$
$167$	−560337.	−1.55474	−0.777371	+	0.629042i	$0.783447\pi$
$168$	25184.3	0.0688426
$169$	−362004.	−0.974982
$170$	−62480.4	−0.165814
$171$	173888.	0.454757
$172$	423170.	1.09067
$173$	−595398.	−1.51249	−0.756244	−	0.654289i	$-0.772968\pi$
$173$	−595398.	−1.51249	−0.756244	+	0.654289i	$0.772968\pi$
$174$	−23882.4	−0.0598005
$175$	3990.77	0.00985059
$176$	53607.5	0.130450
$177$	136903.	0.328457
$178$	136826.	0.323682
$179$	−537052.	−1.25280	−0.626402	−	0.779500i	$-0.715473\pi$
$179$	−537052.	−1.25280	−0.626402	+	0.779500i	$0.715473\pi$
$180$	307188.	0.706680
$181$	−443739.	−1.00677	−0.503387	−	0.864061i	$-0.667913\pi$
$181$	−443739.	−1.00677	−0.503387	+	0.864061i	$0.667913\pi$
$182$	1567.84	0.00350851
$183$	303717.	0.670411
$184$	−410630.	−0.894141
$185$	−68675.2	−0.147527
$186$	−170001.	−0.360305
$187$	−118700.	−0.248225
$188$	−316144.	−0.652364
$189$	41027.5	0.0835451
$190$	22992.5	0.0462065
$191$	883817.	1.75299	0.876494	−	0.481413i	$-0.159876\pi$
$191$	883817.	1.75299	0.876494	+	0.481413i	$0.159876\pi$
$192$	17306.4	0.0338808
$193$	136857.	0.264468	0.132234	−	0.991219i	$-0.457785\pi$
$193$	136857.	0.264468	0.132234	+	0.991219i	$0.457785\pi$
$194$	129715.	0.247449
$195$	64863.3	0.122155
$196$	427698.	0.795237
$197$	−582102.	−1.06864	−0.534322	−	0.845281i	$-0.679433\pi$
$197$	−582102.	−1.06864	−0.534322	+	0.845281i	$0.679433\pi$
$198$	−148487.	−0.269169
$199$	−738508.	−1.32197	−0.660986	−	0.750398i	$-0.729862\pi$
$199$	−738508.	−1.32197	−0.660986	+	0.750398i	$0.729862\pi$
$200$	91571.3	0.161877
$201$	1.20026e6	2.09550
$202$	31804.3	0.0548412
$203$	2223.52	0.00378705
$204$	673658.	1.13335
$205$	104689.	0.173987
$206$	−80015.3	−0.131373
$207$	−1.35000e6	−2.18982
$208$	−42699.7	−0.0684331
$209$	43681.0	0.0691714
$210$	10947.9	0.0171310
$211$	1727.65	0.00267147	0.00133574	−	0.999999i	$-0.499575\pi$
$211$	1727.65	0.00267147	0.00133574	+	0.999999i	$0.499575\pi$
$212$	578941.	0.884698
$213$	−385175.	−0.581713
$214$	309213.	0.461555
$215$	414718.	0.611867
$216$	941407.	1.37291
$217$	15827.6	0.0228174
$218$	303219.	0.432130
$219$	1.34955e6	1.90142
$220$	77166.2	0.107491
$221$	94547.1	0.130217
$222$	−188397.	−0.256562
$223$	−200979.	−0.270638	−0.135319	−	0.990802i	$-0.543206\pi$
$223$	−200979.	−0.270638	−0.135319	+	0.990802i	$0.543206\pi$
$224$	−37143.9	−0.0494615
$225$	301053.	0.396448
$226$	−60419.0	−0.0786868
$227$	1.16283e6	1.49779	0.748894	−	0.662690i	$-0.230585\pi$
$227$	1.16283e6	1.49779	0.748894	+	0.662690i	$0.230585\pi$
$228$	−247904.	−0.315825
$229$	−350822.	−0.442077	−0.221039	−	0.975265i	$-0.570945\pi$
$229$	−350822.	−0.442077	−0.221039	+	0.975265i	$0.570945\pi$
$230$	−178505.	−0.222501
$231$	20798.7	0.0256453
$232$	51020.3	0.0622334
$233$	−450191.	−0.543259	−0.271630	−	0.962402i	$-0.587563\pi$
$233$	−450191.	−0.543259	−0.271630	+	0.962402i	$0.587563\pi$
$234$	118273.	0.141204
$235$	−309830.	−0.365976
$236$	−129730.	−0.151621
$237$	1.05773e6	1.22322
$238$	15958.1	0.0182616
$239$	−655437.	−0.742227	−0.371113	−	0.928588i	$-0.621024\pi$
$239$	−655437.	−0.742227	−0.371113	+	0.928588i	$0.621024\pi$
$240$	−298163.	−0.334138
$241$	557337.	0.618123	0.309062	−	0.951042i	$-0.399985\pi$
$241$	557337.	0.618123	0.309062	+	0.951042i	$0.399985\pi$
$242$	−37300.1	−0.0409423
$243$	−55961.9	−0.0607962
$244$	−287803.	−0.309472
$245$	419156.	0.446129
$246$	287194.	0.302579
$247$	−34793.0	−0.0362869
$248$	363176.	0.374963
$249$	80627.0	0.0824104
$250$	39807.0	0.0402819
$251$	608371.	0.609515	0.304757	−	0.952430i	$-0.401425\pi$
$251$	608371.	0.609515	0.304757	+	0.952430i	$0.401425\pi$
$252$	−78458.7	−0.0778287
$253$	−339123.	−0.333085
$254$	−144534.	−0.140568
$255$	660204.	0.635811
$256$	−490642.	−0.467912
$257$	1.23307e6	1.16454	0.582271	−	0.812995i	$-0.302164\pi$
$257$	1.23307e6	1.16454	0.582271	+	0.812995i	$0.302164\pi$
$258$	1.13770e6	1.06409
$259$	17540.3	0.0162475
$260$	−61464.7	−0.0563888
$261$	167736.	0.152414
$262$	970869.	0.873790
$263$	1.25864e6	1.12205	0.561023	−	0.827800i	$-0.310408\pi$
$263$	1.25864e6	1.12205	0.561023	+	0.827800i	$0.310408\pi$
$264$	477242.	0.421434
$265$	567379.	0.496316
$266$	−5872.51	−0.00508885
$267$	−1.44578e6	−1.24115
$268$	−1.13738e6	−0.967313
$269$	190012.	0.160104	0.0800518	−	0.996791i	$-0.474491\pi$
$269$	190012.	0.160104	0.0800518	+	0.996791i	$0.474491\pi$
$270$	409240.	0.341640
$271$	1.33733e6	1.10615	0.553076	−	0.833131i	$-0.313454\pi$
$271$	1.33733e6	1.10615	0.553076	+	0.833131i	$0.313454\pi$
$272$	−434614.	−0.356190
$273$	−16566.7	−0.0134533
$274$	−464551.	−0.373815
$275$	75625.0	0.0603023
$276$	1.92463e6	1.52081
$277$	−786716.	−0.616053	−0.308027	−	0.951378i	$-0.599669\pi$
$277$	−786716.	−0.616053	−0.308027	+	0.951378i	$0.599669\pi$
$278$	32189.7	0.0249807
$279$	1.19399e6	0.918312
$280$	−23388.2	−0.0178279
$281$	−511693.	−0.386584	−0.193292	−	0.981141i	$-0.561916\pi$
$281$	−511693.	−0.386584	−0.193292	+	0.981141i	$0.561916\pi$
$282$	−849957.	−0.636464
$283$	−1.30223e6	−0.966544	−0.483272	−	0.875470i	$-0.660552\pi$
$283$	−1.30223e6	−0.966544	−0.483272	+	0.875470i	$0.660552\pi$
$284$	364993.	0.268528
$285$	−242953.	−0.177178
$286$	29710.5	0.0214780
$287$	−26738.6	−0.0191617
$288$	−2.80203e6	−1.99063
$289$	−457519.	−0.322229
$290$	22179.1	0.0154863
$291$	−1.37064e6	−0.948837
$292$	−1.27884e6	−0.877726
$293$	−1.01198e6	−0.688658	−0.344329	−	0.938849i	$-0.611894\pi$
$293$	−1.01198e6	−0.688658	−0.344329	+	0.938849i	$0.611894\pi$
$294$	1.14987e6	0.775856
$295$	−127139.	−0.0850595
$296$	402475.	0.266999
$297$	777470.	0.511437
$298$	692637.	0.451820
$299$	270119.	0.174734
$300$	−429196.	−0.275330
$301$	−105923.	−0.0673867
$302$	−475239.	−0.299843
$303$	−336063.	−0.210288
$304$	159936.	0.0992575
$305$	−282055.	−0.173614
$306$	1.20383e6	0.734958
$307$	−843618.	−0.510857	−0.255429	−	0.966828i	$-0.582217\pi$
$307$	−843618.	−0.510857	−0.255429	+	0.966828i	$0.582217\pi$
$308$	−19709.0	−0.0118382
$309$	845488.	0.503746
$310$	157877.	0.0933069
$311$	−806905.	−0.473066	−0.236533	−	0.971623i	$-0.576011\pi$
$311$	−806905.	−0.473066	−0.236533	+	0.971623i	$0.576011\pi$
$312$	−380135.	−0.221081
$313$	−2.82068e6	−1.62740	−0.813698	−	0.581288i	$-0.802549\pi$
$313$	−2.82068e6	−1.62740	−0.813698	+	0.581288i	$0.802549\pi$
$314$	209592.	0.119964
$315$	−76891.7	−0.0436620
$316$	−1.00231e6	−0.564656
$317$	14811.0	0.00827822	0.00413911	−	0.999991i	$-0.498682\pi$
$317$	14811.0	0.00827822	0.00413911	+	0.999991i	$0.498682\pi$
$318$	1.55649e6	0.863136
$319$	42135.6	0.0231832
$320$	−16072.1	−0.00877399
$321$	−3.26733e6	−1.76982
$322$	45591.9	0.0245046
$323$	−354137.	−0.188871
$324$	−1.42653e6	−0.754949
$325$	−60237.2	−0.0316341
$326$	484241.	0.252358
$327$	−3.20399e6	−1.65700
$328$	−613537.	−0.314888
$329$	79133.4	0.0403060
$330$	207462.	0.104871
$331$	−2.01099e6	−1.00888	−0.504441	−	0.863446i	$-0.668301\pi$
$331$	−2.01099e6	−1.00888	−0.504441	+	0.863446i	$0.668301\pi$
$332$	−76402.5	−0.0380419
$333$	1.32319e6	0.653900
$334$	1.42754e6	0.700202
$335$	−1.11466e6	−0.542663
$336$	76153.8	0.0367996
$337$	1.38778e6	0.665652	0.332826	−	0.942988i	$-0.391998\pi$
$337$	1.38778e6	0.665652	0.332826	+	0.942988i	$0.391998\pi$
$338$	922259.	0.439098
$339$	638422.	0.301723
$340$	−625612.	−0.293500
$341$	299933.	0.139681
$342$	−443006.	−0.204807
$343$	−214373.	−0.0983864
$344$	−2.43048e6	−1.10738
$345$	1.88619e6	0.853175
$346$	1.51687e6	0.681172
$347$	−1.93627e6	−0.863263	−0.431632	−	0.902050i	$-0.642062\pi$
$347$	−1.93627e6	−0.863263	−0.431632	+	0.902050i	$0.642062\pi$
$348$	−239133.	−0.105850
$349$	−1.42990e6	−0.628410	−0.314205	−	0.949355i	$-0.601738\pi$
$349$	−1.42990e6	−0.628410	−0.314205	+	0.949355i	$0.601738\pi$
$350$	−10167.1	−0.00443636
$351$	−619274.	−0.268296
$352$	−703875.	−0.302788
$353$	−772223.	−0.329842	−0.164921	−	0.986307i	$-0.552737\pi$
$353$	−772223.	−0.329842	−0.164921	+	0.986307i	$0.552737\pi$
$354$	−348780.	−0.147926
$355$	357704.	0.150644
$356$	1.37003e6	0.572935
$357$	−168622.	−0.0700237
$358$	1.36822e6	0.564220
$359$	1.63524e6	0.669646	0.334823	−	0.942281i	$-0.391323\pi$
$359$	1.63524e6	0.669646	0.334823	+	0.942281i	$0.391323\pi$
$360$	−1.76434e6	−0.717506
$361$	130321.	0.0526316
$362$	1.13049e6	0.453415
$363$	394135.	0.156992
$364$	15698.7	0.00621026
$365$	−1.25330e6	−0.492405
$366$	−773764.	−0.301930
$367$	−2.48246e6	−0.962093	−0.481046	−	0.876695i	$-0.659743\pi$
$367$	−2.48246e6	−0.962093	−0.481046	+	0.876695i	$0.659743\pi$
$368$	−1.24168e6	−0.477960
$369$	−2.01709e6	−0.771185
$370$	174960.	0.0664409
$371$	−144914.	−0.0546607
$372$	−1.70221e6	−0.637759
$373$	−796585.	−0.296456	−0.148228	−	0.988953i	$-0.547357\pi$
$373$	−796585.	−0.296456	−0.148228	+	0.988953i	$0.547357\pi$
$374$	302405.	0.111792
$375$	−420624.	−0.154460
$376$	1.81577e6	0.662357
$377$	−33562.1	−0.0121617
$378$	−104524.	−0.0376258
$379$	−4.35621e6	−1.55780	−0.778898	−	0.627151i	$-0.784221\pi$
$379$	−4.35621e6	−1.55780	−0.778898	+	0.627151i	$0.784221\pi$
$380$	230223.	0.0817880
$381$	1.52723e6	0.539006
$382$	−2.25166e6	−0.789484
$383$	32389.8	0.0112827	0.00564133	−	0.999984i	$-0.498204\pi$
$383$	32389.8	0.0112827	0.00564133	+	0.999984i	$0.498204\pi$
$384$	4.96703e6	1.71897
$385$	−19315.3	−0.00664126
$386$	−348664.	−0.119107
$387$	−7.99053e6	−2.71205
$388$	1.29883e6	0.437998
$389$	−3.14598e6	−1.05410	−0.527049	−	0.849835i	$-0.676702\pi$
$389$	−3.14598e6	−1.05410	−0.527049	+	0.849835i	$0.676702\pi$
$390$	−165249.	−0.0550145
$391$	2.74938e6	0.909480
$392$	−2.45649e6	−0.807420
$393$	−1.02588e7	−3.35053
$394$	1.48299e6	0.481280
$395$	−982291.	−0.316772
$396$	−1.48679e6	−0.476444
$397$	−468935.	−0.149326	−0.0746631	−	0.997209i	$-0.523788\pi$
$397$	−468935.	−0.149326	−0.0746631	+	0.997209i	$0.523788\pi$
$398$	1.88146e6	0.595370
$399$	62052.4	0.0195131
$400$	276898.	0.0865307
$401$	−1.58612e6	−0.492577	−0.246288	−	0.969197i	$-0.579211\pi$
$401$	−1.58612e6	−0.492577	−0.246288	+	0.969197i	$0.579211\pi$
$402$	−3.05785e6	−0.943738
$403$	−238904.	−0.0732757
$404$	318455.	0.0970721
$405$	−1.39804e6	−0.423527
$406$	−5664.75	−0.00170556
$407$	332388.	0.0994624
$408$	−3.86917e6	−1.15071
$409$	3.80467e6	1.12463	0.562313	−	0.826924i	$-0.309911\pi$
$409$	3.80467e6	1.12463	0.562313	+	0.826924i	$0.309911\pi$
$410$	−266711.	−0.0783578
$411$	4.90871e6	1.43339
$412$	−801189.	−0.232537
$413$	32472.4	0.00936784
$414$	3.43933e6	0.986217
$415$	−74876.6	−0.0213415
$416$	560654.	0.158841
$417$	−340135.	−0.0957880
$418$	−111284.	−0.0311524
$419$	−4.96255e6	−1.38092	−0.690461	−	0.723369i	$-0.742592\pi$
$419$	−4.96255e6	−1.38092	−0.690461	+	0.723369i	$0.742592\pi$
$420$	109621.	0.0303228
$421$	3.93446e6	1.08188	0.540941	−	0.841060i	$-0.318068\pi$
$421$	3.93446e6	1.08188	0.540941	+	0.841060i	$0.318068\pi$
$422$	−4401.46	−0.00120314
$423$	5.96960e6	1.62216
$424$	−3.32516e6	−0.898250
$425$	−613118.	−0.164654
$426$	981290.	0.261983
$427$	72039.6	0.0191206
$428$	3.09614e6	0.816978
$429$	−313938.	−0.0823571
$430$	−1.05656e6	−0.275564
$431$	3.28565e6	0.851978	0.425989	−	0.904728i	$-0.359926\pi$
$431$	3.28565e6	0.851978	0.425989	+	0.904728i	$0.359926\pi$
$432$	2.84668e6	0.733886
$433$	4.34170e6	1.11286	0.556430	−	0.830895i	$-0.312171\pi$
$433$	4.34170e6	1.11286	0.556430	+	0.830895i	$0.312171\pi$
$434$	−40323.2	−0.0102762
$435$	−234357.	−0.0593821
$436$	3.03611e6	0.764895
$437$	−1.01176e6	−0.253440
$438$	−3.43818e6	−0.856334
$439$	−4.66780e6	−1.15598	−0.577991	−	0.816043i	$-0.696163\pi$
$439$	−4.66780e6	−1.15598	−0.577991	+	0.816043i	$0.696163\pi$
$440$	−443205.	−0.109137
$441$	−8.07603e6	−1.97743
$442$	−240873.	−0.0586452
$443$	6.57990e6	1.59298	0.796489	−	0.604653i	$-0.206688\pi$
$443$	6.57990e6	1.59298	0.796489	+	0.604653i	$0.206688\pi$
$444$	−1.88641e6	−0.454128
$445$	1.34267e6	0.321417
$446$	512025.	0.121886
$447$	−7.31881e6	−1.73249
$448$	4104.96	0.000966304 0
$449$	7.21023e6	1.68785	0.843924	−	0.536463i	$-0.180240\pi$
$449$	7.21023e6	1.68785	0.843924	+	0.536463i	$0.180240\pi$
$450$	−766977.	−0.178546
$451$	−506696.	−0.117302
$452$	−604972.	−0.139280
$453$	5.02165e6	1.14974
$454$	−2.96248e6	−0.674552
$455$	15385.1	0.00348396
$456$	1.42384e6	0.320663
$457$	−3.63010e6	−0.813071	−0.406535	−	0.913635i	$-0.633263\pi$
$457$	−3.63010e6	−0.813071	−0.406535	+	0.913635i	$0.633263\pi$
$458$	893772.	0.199096
$459$	−6.30321e6	−1.39647
$460$	−1.78736e6	−0.393839
$461$	1.08283e6	0.237305	0.118653	−	0.992936i	$-0.462143\pi$
$461$	1.08283e6	0.237305	0.118653	+	0.992936i	$0.462143\pi$
$462$	−52987.9	−0.0115497
$463$	4.83470e6	1.04813	0.524067	−	0.851677i	$-0.324414\pi$
$463$	4.83470e6	1.04813	0.524067	+	0.851677i	$0.324414\pi$
$464$	154278.	0.0332667
$465$	−1.66822e6	−0.357783
$466$	1.14693e6	0.244665
$467$	−5.46540e6	−1.15966	−0.579829	−	0.814739i	$-0.696880\pi$
$467$	−5.46540e6	−1.15966	−0.579829	+	0.814739i	$0.696880\pi$
$468$	1.18426e6	0.249939
$469$	284695.	0.0597651
$470$	789337.	0.164823
$471$	−2.21467e6	−0.460000
$472$	745104.	0.153944
$473$	−2.00724e6	−0.412521
$474$	−2.69472e6	−0.550894
$475$	225625.	0.0458831
$476$	159787.	0.0323240
$477$	−1.09319e7	−2.19988
$478$	1.66983e6	0.334273
$479$	8.19442e6	1.63185	0.815924	−	0.578160i	$-0.196229\pi$
$479$	8.19442e6	1.63185	0.815924	+	0.578160i	$0.196229\pi$
$480$	3.91494e6	0.775571
$481$	−264755.	−0.0521773
$482$	−1.41990e6	−0.278381
$483$	−481751.	−0.0939626
$484$	−373484.	−0.0724701
$485$	1.27289e6	0.245717
$486$	142571.	0.0273805
$487$	29086.4	0.00555734	0.00277867	−	0.999996i	$-0.499116\pi$
$487$	29086.4	0.00555734	0.00277867	+	0.999996i	$0.499116\pi$
$488$	1.65300e6	0.314213
$489$	−5.11678e6	−0.967664
$490$	−1.06786e6	−0.200921
$491$	−4.61023e6	−0.863015	−0.431508	−	0.902109i	$-0.642018\pi$
$491$	−4.61023e6	−0.863015	−0.431508	+	0.902109i	$0.642018\pi$
$492$	2.87566e6	0.535581
$493$	−341608.	−0.0633010
$494$	88640.3	0.0163423
$495$	−1.45709e6	−0.267285
$496$	1.09819e6	0.200435
$497$	−91360.9	−0.0165909
$498$	−205409.	−0.0371148
$499$	−1.75272e6	−0.315109	−0.157554	−	0.987510i	$-0.550361\pi$
$499$	−1.75272e6	−0.315109	−0.157554	+	0.987510i	$0.550361\pi$
$500$	398586.	0.0713012
$501$	−1.50843e7	−2.68491
$502$	−1.54992e6	−0.274504
$503$	−2.03556e6	−0.358726	−0.179363	−	0.983783i	$-0.557404\pi$
$503$	−2.03556e6	−0.358726	−0.179363	+	0.983783i	$0.557404\pi$
$504$	450629.	0.0790210
$505$	312094.	0.0544575
$506$	863965.	0.150010
$507$	−9.74513e6	−1.68371
$508$	−1.44721e6	−0.248813
$509$	3.74763e6	0.641153	0.320577	−	0.947223i	$-0.396123\pi$
$509$	3.74763e6	0.641153	0.320577	+	0.947223i	$0.396123\pi$
$510$	−1.68197e6	−0.286347
$511$	320104.	0.0542300
$512$	−4.65437e6	−0.784668
$513$	2.31956e6	0.389145
$514$	−3.14143e6	−0.524469
$515$	−785187.	−0.130453
$516$	1.13917e7	1.88350
$517$	1.49957e6	0.246741
$518$	−44686.5	−0.00731732
$519$	−1.60281e7	−2.61194
$520$	353024.	0.0572526
$521$	7.72774e6	1.24726	0.623632	−	0.781718i	$-0.285656\pi$
$521$	7.72774e6	1.24726	0.623632	+	0.781718i	$0.285656\pi$
$522$	−427333.	−0.0686420
$523$	−5.37438e6	−0.859160	−0.429580	−	0.903029i	$-0.641338\pi$
$523$	−5.37438e6	−0.859160	−0.429580	+	0.903029i	$0.641338\pi$
$524$	9.72125e6	1.54666
$525$	107431.	0.0170111
$526$	−3.20656e6	−0.505330
$527$	−2.43166e6	−0.381395
$528$	1.44311e6	0.225276
$529$	1.41859e6	0.220403
$530$	−1.44548e6	−0.223523
$531$	2.44963e6	0.377019
$532$	−58801.2	−0.00900755
$533$	403596.	0.0615359
$534$	3.68335e6	0.558972
$535$	3.03430e6	0.458325
$536$	6.53253e6	0.982131
$537$	−1.44574e7	−2.16349
$538$	−484085.	−0.0721050
$539$	−2.02871e6	−0.300780
$540$	4.09770e6	0.604722
$541$	5.15010e6	0.756524	0.378262	−	0.925699i	$-0.376522\pi$
$541$	5.15010e6	0.756524	0.378262	+	0.925699i	$0.376522\pi$
$542$	−3.40704e6	−0.498172
$543$	−1.19454e7	−1.73861
$544$	5.70656e6	0.826755
$545$	2.97547e6	0.429106
$546$	42206.2	0.00605890
$547$	2.22078e6	0.317349	0.158675	−	0.987331i	$-0.449278\pi$
$547$	2.22078e6	0.317349	0.158675	+	0.987331i	$0.449278\pi$
$548$	−4.65152e6	−0.661673
$549$	5.43446e6	0.769530
$550$	−192666.	−0.0271580
$551$	125710.	0.0176397
$552$	−1.10541e7	−1.54411
$553$	250886.	0.0348871
$554$	2.00428e6	0.277449
$555$	−1.84873e6	−0.254766
$556$	322313.	0.0442172
$557$	−5.99128e6	−0.818242	−0.409121	−	0.912480i	$-0.634165\pi$
$557$	−5.99128e6	−0.818242	−0.409121	+	0.912480i	$0.634165\pi$
$558$	−3.04187e6	−0.413576
$559$	1.59881e6	0.216405
$560$	−70722.4	−0.00952987
$561$	−3.19539e6	−0.428663
$562$	1.30361e6	0.174104
$563$	−1.25277e6	−0.166572	−0.0832860	−	0.996526i	$-0.526542\pi$
$563$	−1.25277e6	−0.166572	−0.0832860	+	0.996526i	$0.526542\pi$
$564$	−8.51057e6	−1.12658
$565$	−592889.	−0.0781362
$566$	3.31763e6	0.435298
$567$	357072.	0.0466442
$568$	−2.09634e6	−0.272641
$569$	−1.00551e7	−1.30199	−0.650995	−	0.759082i	$-0.725648\pi$
$569$	−1.00551e7	−1.30199	−0.650995	+	0.759082i	$0.725648\pi$
$570$	618958.	0.0797947
$571$	−1.04462e7	−1.34081	−0.670405	−	0.741995i	$-0.733880\pi$
$571$	−1.04462e7	−1.34081	−0.670405	+	0.741995i	$0.733880\pi$
$572$	297489.	0.0380173
$573$	2.37923e7	3.02726
$574$	68120.6	0.00862977
$575$	−1.75167e6	−0.220944
$576$	309667.	0.0388900
$577$	2.36201e6	0.295354	0.147677	−	0.989036i	$-0.452820\pi$
$577$	2.36201e6	0.295354	0.147677	+	0.989036i	$0.452820\pi$
$578$	1.16560e6	0.145121
$579$	3.68418e6	0.456715
$580$	222078.	0.0274117
$581$	19124.2	0.00235041
$582$	3.49192e6	0.427323
$583$	−2.74611e6	−0.334616
$584$	7.34503e6	0.891172
$585$	1.16061e6	0.140216
$586$	2.57817e6	0.310147
$587$	1.19997e7	1.43740	0.718698	−	0.695322i	$-0.244738\pi$
$587$	1.19997e7	1.43740	0.718698	+	0.695322i	$0.244738\pi$
$588$	1.15136e7	1.37331
$589$	894840.	0.106281
$590$	323905.	0.0383078
$591$	−1.56702e7	−1.84546
$592$	1.21703e6	0.142723
$593$	−5.26363e6	−0.614679	−0.307340	−	0.951600i	$-0.599439\pi$
$593$	−5.26363e6	−0.614679	−0.307340	+	0.951600i	$0.599439\pi$
$594$	−1.98072e6	−0.230334
$595$	156596.	0.0181338
$596$	6.93534e6	0.799746
$597$	−1.98806e7	−2.28294
$598$	−688170.	−0.0786942
$599$	−8.90988e6	−1.01462	−0.507312	−	0.861763i	$-0.669361\pi$
$599$	−8.90988e6	−1.01462	−0.507312	+	0.861763i	$0.669361\pi$
$600$	2.46509e6	0.279547
$601$	8.42091e6	0.950983	0.475491	−	0.879720i	$-0.342270\pi$
$601$	8.42091e6	0.950983	0.475491	+	0.879720i	$0.342270\pi$
$602$	269855.	0.0303486
$603$	2.14766e7	2.40531
$604$	−4.75854e6	−0.530740
$605$	−366025.	−0.0406558
$606$	856170.	0.0947062
$607$	−5.17122e6	−0.569667	−0.284834	−	0.958577i	$-0.591938\pi$
$607$	−5.17122e6	−0.569667	−0.284834	+	0.958577i	$0.591938\pi$
$608$	−2.09999e6	−0.230387
$609$	59857.1	0.00653992
$610$	718578.	0.0781897
$611$	−1.19445e6	−0.129439
$612$	1.20539e7	1.30092
$613$	4.72736e6	0.508122	0.254061	−	0.967188i	$-0.418234\pi$
$613$	4.72736e6	0.508122	0.254061	+	0.967188i	$0.418234\pi$
$614$	2.14924e6	0.230072
$615$	2.81823e6	0.300461
$616$	113199.	0.0120196
$617$	1.26513e7	1.33790	0.668948	−	0.743309i	$-0.266745\pi$
$617$	1.26513e7	1.33790	0.668948	+	0.743309i	$0.266745\pi$
$618$	−2.15401e6	−0.226870
$619$	7.15682e6	0.750747	0.375373	−	0.926874i	$-0.377515\pi$
$619$	7.15682e6	0.750747	0.375373	+	0.926874i	$0.377515\pi$
$620$	1.58081e6	0.165158
$621$	−1.80082e7	−1.87387
$622$	2.05571e6	0.213052
$623$	−342931.	−0.0353986
$624$	−1.14947e6	−0.118178
$625$	390625.	0.0400000
$626$	7.18611e6	0.732922
$627$	1.17589e6	0.119453
$628$	2.09864e6	0.212343
$629$	−2.69478e6	−0.271579
$630$	195893.	0.0196638
$631$	9.14471e6	0.914317	0.457158	−	0.889385i	$-0.348867\pi$
$631$	9.14471e6	0.914317	0.457158	+	0.889385i	$0.348867\pi$
$632$	5.75678e6	0.573306
$633$	46508.4	0.00461341
$634$	−37733.3	−0.00372822
$635$	−1.41831e6	−0.139584
$636$	1.55851e7	1.52780
$637$	1.61592e6	0.157787
$638$	−107347.	−0.0104409
$639$	−6.89201e6	−0.667719
$640$	−4.61278e6	−0.445156
$641$	−7.96449e6	−0.765619	−0.382810	−	0.923827i	$-0.625043\pi$
$641$	−7.96449e6	−0.765619	−0.382810	+	0.923827i	$0.625043\pi$
$642$	8.32401e6	0.797067
$643$	1.71934e7	1.63996	0.819981	−	0.572391i	$-0.193984\pi$
$643$	1.71934e7	1.63996	0.819981	+	0.572391i	$0.193984\pi$
$644$	456510.	0.0433746
$645$	1.11642e7	1.05664
$646$	902216.	0.0850608
$647$	1.01235e7	0.950761	0.475381	−	0.879780i	$-0.342310\pi$
$647$	1.01235e7	0.950761	0.475381	+	0.879780i	$0.342310\pi$
$648$	8.19328e6	0.766514
$649$	615351.	0.0573471
$650$	153463.	0.0142469
$651$	426079.	0.0394037
$652$	4.84868e6	0.446689
$653$	8.64564e6	0.793440	0.396720	−	0.917940i	$-0.370148\pi$
$653$	8.64564e6	0.793440	0.396720	+	0.917940i	$0.370148\pi$
$654$	8.16263e6	0.746253
$655$	9.52710e6	0.867676
$656$	−1.85525e6	−0.168323
$657$	2.41478e7	2.18255
$658$	−201604.	−0.0181524
$659$	−1.47406e7	−1.32222	−0.661108	−	0.750291i	$-0.729913\pi$
$659$	−1.47406e7	−1.32222	−0.661108	+	0.750291i	$0.729913\pi$
$660$	2.07731e6	0.185627
$661$	1.09487e7	0.974669	0.487335	−	0.873215i	$-0.337969\pi$
$661$	1.09487e7	0.974669	0.487335	+	0.873215i	$0.337969\pi$
$662$	5.12331e6	0.454365
$663$	2.54520e6	0.224874
$664$	438819.	0.0386247
$665$	−57626.8	−0.00505324
$666$	−3.37103e6	−0.294494
$667$	−975968.	−0.0849417
$668$	1.42939e7	1.23940
$669$	−5.41035e6	−0.467369
$670$	2.83976e6	0.244397
$671$	1.36515e6	0.117050
$672$	−999912.	−0.0854159
$673$	−5.06638e6	−0.431182	−0.215591	−	0.976484i	$-0.569168\pi$
$673$	−5.06638e6	−0.431182	−0.215591	+	0.976484i	$0.569168\pi$
$674$	−3.53559e6	−0.299786
$675$	4.01586e6	0.339249
$676$	9.23453e6	0.777228
$677$	1.19496e6	0.100203	0.0501017	−	0.998744i	$-0.484045\pi$
$677$	1.19496e6	0.100203	0.0501017	+	0.998744i	$0.484045\pi$
$678$	−1.62648e6	−0.135886
$679$	−325107.	−0.0270615
$680$	3.59321e6	0.297996
$681$	3.13033e7	2.58655
$682$	−764123.	−0.0629075
$683$	5.68119e6	0.466002	0.233001	−	0.972477i	$-0.425145\pi$
$683$	5.68119e6	0.466002	0.233001	+	0.972477i	$0.425145\pi$
$684$	−4.43579e6	−0.362519
$685$	−4.55862e6	−0.371199
$686$	546148.	0.0443098
$687$	−9.44412e6	−0.763430
$688$	−7.34942e6	−0.591946
$689$	2.18735e6	0.175537
$690$	−4.80535e6	−0.384240
$691$	−1.42487e7	−1.13522	−0.567610	−	0.823297i	$-0.692132\pi$
$691$	−1.42487e7	−1.13522	−0.567610	+	0.823297i	$0.692132\pi$
$692$	1.51883e7	1.20571
$693$	372156.	0.0294369
$694$	4.93295e6	0.388784
$695$	315876.	0.0248059
$696$	1.37347e6	0.107472
$697$	4.10795e6	0.320290
$698$	3.64289e6	0.283014
$699$	−1.21191e7	−0.938163
$700$	−101803.	−0.00785260
$701$	−1.00778e7	−0.774584	−0.387292	−	0.921957i	$-0.626589\pi$
$701$	−1.00778e7	−0.774584	−0.387292	+	0.921957i	$0.626589\pi$
$702$	1.57769e6	0.120831
$703$	991670.	0.0756796
$704$	77788.8	0.00591542
$705$	−8.34060e6	−0.632011
$706$	1.96735e6	0.148549
$707$	−79711.9	−0.00599756
$708$	−3.49232e6	−0.261837
$709$	−1.02505e7	−0.765825	−0.382913	−	0.923785i	$-0.625079\pi$
$709$	−1.02505e7	−0.765825	−0.382913	+	0.923785i	$0.625079\pi$
$710$	−911303.	−0.0678449
$711$	1.89262e7	1.40407
$712$	−7.86880e6	−0.581712
$713$	−6.94720e6	−0.511783
$714$	429591.	0.0315362
$715$	291548.	0.0213277
$716$	1.36999e7	0.998700
$717$	−1.76444e7	−1.28176
$718$	−4.16602e6	−0.301585
$719$	−1.35603e7	−0.978243	−0.489121	−	0.872216i	$-0.662682\pi$
$719$	−1.35603e7	−0.978243	−0.489121	+	0.872216i	$0.662682\pi$
$720$	−5.33510e6	−0.383540
$721$	200544.	0.0143672
$722$	−332012.	−0.0237034
$723$	1.50035e7	1.06745
$724$	1.13196e7	0.802571
$725$	217643.	0.0153780
$726$	−1.00412e6	−0.0707039
$727$	1.98764e7	1.39477	0.697384	−	0.716698i	$-0.254347\pi$
$727$	1.98764e7	1.39477	0.697384	+	0.716698i	$0.254347\pi$
$728$	−90165.6	−0.00630540
$729$	−1.50954e7	−1.05202
$730$	3.19297e6	0.221762
$731$	1.62734e7	1.12638
$732$	−7.74765e6	−0.534432
$733$	6.71440e6	0.461580	0.230790	−	0.973004i	$-0.425869\pi$
$733$	6.71440e6	0.461580	0.230790	+	0.973004i	$0.425869\pi$
$734$	6.32444e6	0.433293
$735$	1.12837e7	0.770427
$736$	1.63035e7	1.10940
$737$	5.39495e6	0.365863
$738$	5.13883e6	0.347315
$739$	2.43176e7	1.63798	0.818992	−	0.573804i	$-0.194533\pi$
$739$	2.43176e7	1.63798	0.818992	+	0.573804i	$0.194533\pi$
$740$	1.75187e6	0.117604
$741$	−936626.	−0.0626644
$742$	369190.	0.0246173
$743$	−1.29743e7	−0.862206	−0.431103	−	0.902303i	$-0.641875\pi$
$743$	−1.29743e7	−0.862206	−0.431103	+	0.902303i	$0.641875\pi$
$744$	9.77669e6	0.647529
$745$	6.79683e6	0.448658
$746$	2.02942e6	0.133513
$747$	1.44268e6	0.0945948
$748$	3.02796e6	0.197878
$749$	−774989.	−0.0504767
$750$	1.07160e6	0.0695634
$751$	1.69145e7	1.09436	0.547178	−	0.837016i	$-0.315702\pi$
$751$	1.69145e7	1.09436	0.547178	+	0.837016i	$0.315702\pi$
$752$	5.49064e6	0.354061
$753$	1.63773e7	1.05258
$754$	85504.4	0.00547722
$755$	−4.66350e6	−0.297745
$756$	−1.04659e6	−0.0665997
$757$	−1.34880e7	−0.855478	−0.427739	−	0.903902i	$-0.640690\pi$
$757$	−1.34880e7	−0.855478	−0.427739	+	0.903902i	$0.640690\pi$
$758$	1.10981e7	0.701577
$759$	−9.12917e6	−0.575210
$760$	−1.32229e6	−0.0830410
$761$	−1.69539e7	−1.06123	−0.530614	−	0.847613i	$-0.678039\pi$
$761$	−1.69539e7	−1.06123	−0.530614	+	0.847613i	$0.678039\pi$
$762$	−3.89086e6	−0.242749
$763$	−759965.	−0.0472587
$764$	−2.25457e7	−1.39743
$765$	1.18132e7	0.729815
$766$	−82517.8	−0.00508131
$767$	−490142.	−0.0300839
$768$	−1.32081e7	−0.808046
$769$	1.51313e6	0.0922699	0.0461350	−	0.998935i	$-0.485310\pi$
$769$	1.51313e6	0.0922699	0.0461350	+	0.998935i	$0.485310\pi$
$770$	49208.7	0.00299099
$771$	3.31942e7	2.01107
$772$	−3.49115e6	−0.210827
$773$	−1.81107e7	−1.09015	−0.545077	−	0.838386i	$-0.683499\pi$
$773$	−1.81107e7	−1.09015	−0.545077	+	0.838386i	$0.683499\pi$
$774$	2.03571e7	1.22141
$775$	1.54924e6	0.0926540
$776$	−7.45983e6	−0.444707
$777$	472184.	0.0280581
$778$	8.01485e6	0.474729
$779$	−1.51171e6	−0.0892535
$780$	−1.65463e6	−0.0973787
$781$	−1.73129e6	−0.101564
$782$	−7.00446e6	−0.409598
$783$	2.23750e6	0.130424
$784$	−7.42806e6	−0.431604
$785$	2.05672e6	0.119125
$786$	2.61357e7	1.50896
$787$	−2.09721e6	−0.120699	−0.0603496	−	0.998177i	$-0.519222\pi$
$787$	−2.09721e6	−0.120699	−0.0603496	+	0.998177i	$0.519222\pi$
$788$	1.48491e7	0.851893
$789$	3.38824e7	1.93768
$790$	2.50253e6	0.142663
$791$	151430.	0.00860537
$792$	8.53939e6	0.483742
$793$	−1.08737e6	−0.0614039
$794$	1.19468e6	0.0672513
$795$	1.52738e7	0.857096
$796$	1.88390e7	1.05384
$797$	3.39953e7	1.89572	0.947858	−	0.318693i	$-0.103244\pi$
$797$	3.39953e7	1.89572	0.947858	+	0.318693i	$0.103244\pi$
$798$	−158088.	−0.00878802
$799$	−1.21576e7	−0.673720
$800$	−3.63572e6	−0.200847
$801$	−2.58697e7	−1.42466
$802$	4.04087e6	0.221839
$803$	6.06596e6	0.331979
$804$	−3.06181e7	−1.67047
$805$	447392.	0.0243332
$806$	608643.	0.0330008
$807$	5.11512e6	0.276485
$808$	−1.82905e6	−0.0985591
$809$	4.38209e6	0.235402	0.117701	−	0.993049i	$-0.462448\pi$
$809$	4.38209e6	0.235402	0.117701	+	0.993049i	$0.462448\pi$
$810$	3.56171e6	0.190742
$811$	4.24135e6	0.226439	0.113220	−	0.993570i	$-0.463884\pi$
$811$	4.24135e6	0.226439	0.113220	+	0.993570i	$0.463884\pi$
$812$	−56720.9	−0.00301893
$813$	3.60008e7	1.91023
$814$	−846808.	−0.0447944
$815$	4.75184e6	0.250593
$816$	−1.16998e7	−0.615110
$817$	−5.98853e6	−0.313881
$818$	−9.69296e6	−0.506493
$819$	−296431.	−0.0154424
$820$	−2.67057e6	−0.138698
$821$	2.14745e7	1.11190	0.555950	−	0.831216i	$-0.312354\pi$
$821$	2.14745e7	1.11190	0.555950	+	0.831216i	$0.312354\pi$
$822$	−1.25057e7	−0.645547
$823$	1.49955e7	0.771721	0.385860	−	0.922557i	$-0.373905\pi$
$823$	1.49955e7	0.771721	0.385860	+	0.922557i	$0.373905\pi$
$824$	4.60164e6	0.236099
$825$	2.03582e6	0.104137
$826$	−82728.4	−0.00421895
$827$	−1.39884e7	−0.711219	−0.355609	−	0.934635i	$-0.615727\pi$
$827$	−1.39884e7	−0.711219	−0.355609	+	0.934635i	$0.615727\pi$
$828$	3.44378e7	1.74566
$829$	−1.36695e6	−0.0690821	−0.0345411	−	0.999403i	$-0.510997\pi$
$829$	−1.36695e6	−0.0690821	−0.0345411	+	0.999403i	$0.510997\pi$
$830$	190759.	0.00961149
$831$	−2.11784e7	−1.06387
$832$	−61960.7	−0.00310319
$833$	1.64475e7	0.821271
$834$	866544.	0.0431396
$835$	1.40084e7	0.695302
$836$	−1.11428e6	−0.0551415
$837$	1.59271e7	0.785819
$838$	1.26428e7	0.621919
$839$	1.81182e6	0.0888605	0.0444303	−	0.999012i	$-0.485853\pi$
$839$	1.81182e6	0.0888605	0.0444303	+	0.999012i	$0.485853\pi$
$840$	−629609.	−0.0307874
$841$	−2.03899e7	−0.994088
$842$	−1.00236e7	−0.487242
$843$	−1.37748e7	−0.667598
$844$	−44071.6	−0.00212962
$845$	9.05010e6	0.436025
$846$	−1.52085e7	−0.730565
$847$	93486.3	0.00447754
$848$	−1.00548e7	−0.480157
$849$	−3.50560e7	−1.66914
$850$	1.56201e6	0.0741543
$851$	−7.69894e6	−0.364424
$852$	9.82561e6	0.463725
$853$	9.95533e6	0.468472	0.234236	−	0.972180i	$-0.424741\pi$
$853$	9.95533e6	0.468472	0.234236	+	0.972180i	$0.424741\pi$
$854$	−183532.	−0.00861125
$855$	−4.34720e6	−0.203374
$856$	−1.77827e7	−0.829494
$857$	−3.35263e7	−1.55931	−0.779656	−	0.626208i	$-0.784606\pi$
$857$	−3.35263e7	−1.55931	−0.779656	+	0.626208i	$0.784606\pi$
$858$	799805.	0.0370908
$859$	1.28509e7	0.594225	0.297113	−	0.954842i	$-0.403976\pi$
$859$	1.28509e7	0.594225	0.297113	+	0.954842i	$0.403976\pi$
$860$	−1.05793e7	−0.487763
$861$	−719803.	−0.0330907
$862$	−8.37069e6	−0.383701
$863$	−6.42105e6	−0.293480	−0.146740	−	0.989175i	$-0.546878\pi$
$863$	−6.42105e6	−0.293480	−0.146740	+	0.989175i	$0.546878\pi$
$864$	−3.73774e7	−1.70343
$865$	1.48850e7	0.676406
$866$	−1.10611e7	−0.501193
$867$	−1.23164e7	−0.556463
$868$	−403754.	−0.0181894
$869$	4.75429e6	0.213568
$870$	597060.	0.0267436
$871$	−4.29721e6	−0.191929
$872$	−1.74379e7	−0.776612
$873$	−2.45252e7	−1.08912
$874$	2.57762e6	0.114140
$875$	−99769.4	−0.00440532
$876$	−3.44263e7	−1.51576
$877$	1.44237e7	0.633253	0.316626	−	0.948550i	$-0.397450\pi$
$877$	1.44237e7	0.633253	0.316626	+	0.948550i	$0.397450\pi$
$878$	1.18919e7	0.520614
$879$	−2.72425e7	−1.18925
$880$	−1.34019e6	−0.0583390
$881$	6.75986e6	0.293426	0.146713	−	0.989179i	$-0.453131\pi$
$881$	6.75986e6	0.293426	0.146713	+	0.989179i	$0.453131\pi$
$882$	2.05749e7	0.890566
$883$	3.02966e7	1.30765	0.653825	−	0.756645i	$-0.273163\pi$
$883$	3.02966e7	1.30765	0.653825	+	0.756645i	$0.273163\pi$
$884$	−2.41185e6	−0.103805
$885$	−3.42257e6	−0.146891
$886$	−1.67633e7	−0.717422
$887$	1.04748e7	0.447031	0.223515	−	0.974700i	$-0.428247\pi$
$887$	1.04748e7	0.447031	0.223515	+	0.974700i	$0.428247\pi$
$888$	1.08346e7	0.461085
$889$	362250.	0.0153728
$890$	−3.42065e6	−0.144755
$891$	6.76650e6	0.285542
$892$	5.12688e6	0.215745
$893$	4.47394e6	0.187742
$894$	1.86458e7	0.780255
$895$	1.34263e7	0.560271
$896$	1.17815e6	0.0490263
$897$	7.27160e6	0.301751
$898$	−1.83691e7	−0.760148
$899$	863182.	0.0356208
$900$	−7.67970e6	−0.316037
$901$	2.22637e7	0.913660
$902$	1.29088e6	0.0528288
$903$	−2.85144e6	−0.116371
$904$	3.47466e6	0.141414
$905$	1.10935e7	0.450243
$906$	−1.27934e7	−0.517805
$907$	2.05902e7	0.831080	0.415540	−	0.909575i	$-0.363593\pi$
$907$	2.05902e7	0.831080	0.415540	+	0.909575i	$0.363593\pi$
$908$	−2.96631e7	−1.19399
$909$	−6.01324e6	−0.241379
$910$	−39196.0	−0.00156905
$911$	7.65653e6	0.305658	0.152829	−	0.988253i	$-0.451162\pi$
$911$	7.65653e6	0.305658	0.152829	+	0.988253i	$0.451162\pi$
$912$	4.30548e6	0.171409
$913$	362403.	0.0143885
$914$	9.24823e6	0.366179
$915$	−7.59292e6	−0.299817
$916$	8.94929e6	0.352411
$917$	−2.43331e6	−0.0955596
$918$	1.60584e7	0.628919
$919$	6.38282e6	0.249301	0.124650	−	0.992201i	$-0.460219\pi$
$919$	6.38282e6	0.249301	0.124650	+	0.992201i	$0.460219\pi$
$920$	1.02657e7	0.399872
$921$	−2.27102e7	−0.882208
$922$	−2.75867e6	−0.106874
$923$	1.37901e6	0.0532799
$924$	−530565.	−0.0204437
$925$	1.71688e6	0.0659759
$926$	−1.23171e7	−0.472043
$927$	1.51285e7	0.578224
$928$	−2.02570e6	−0.0772155
$929$	1.16326e7	0.442217	0.221109	−	0.975249i	$-0.429032\pi$
$929$	1.16326e7	0.442217	0.221109	+	0.975249i	$0.429032\pi$
$930$	4.25003e6	0.161133
$931$	−6.05261e6	−0.228859
$932$	1.14841e7	0.433071
$933$	−2.17219e7	−0.816945
$934$	1.39239e7	0.522269
$935$	2.96749e6	0.111009
$936$	−6.80183e6	−0.253768
$937$	−4.82076e7	−1.79377	−0.896884	−	0.442265i	$-0.854175\pi$
$937$	−4.82076e7	−1.79377	−0.896884	+	0.442265i	$0.854175\pi$
$938$	−725303.	−0.0269161
$939$	−7.59326e7	−2.81038
$940$	7.90359e6	0.291746
$941$	6.56944e6	0.241854	0.120927	−	0.992661i	$-0.461413\pi$
$941$	6.56944e6	0.241854	0.120927	+	0.992661i	$0.461413\pi$
$942$	5.64221e6	0.207168
$943$	1.17364e7	0.429788
$944$	2.25309e6	0.0822901
$945$	−1.02569e6	−0.0373625
$946$	5.11374e6	0.185785
$947$	3.07970e7	1.11592	0.557961	−	0.829867i	$-0.311584\pi$
$947$	3.07970e7	1.11592	0.557961	+	0.829867i	$0.311584\pi$
$948$	−2.69821e7	−0.975114
$949$	−4.83169e6	−0.174154
$950$	−574813.	−0.0206642
$951$	398712.	0.0142958
$952$	−917741.	−0.0328192
$953$	−2.44273e7	−0.871249	−0.435625	−	0.900128i	$-0.643472\pi$
$953$	−2.44273e7	−0.871249	−0.435625	+	0.900128i	$0.643472\pi$
$954$	2.78506e7	0.990750
$955$	−2.20954e7	−0.783960
$956$	1.67199e7	0.591682
$957$	1.13429e6	0.0400354
$958$	−2.08765e7	−0.734927
$959$	1.16431e6	0.0408812
$960$	−432660.	−0.0151519
$961$	−2.24848e7	−0.785381
$962$	674503.	0.0234988
$963$	−5.84630e7	−2.03149
$964$	−1.42174e7	−0.492750
$965$	−3.42142e6	−0.118274
$966$	1.22733e6	0.0423175
$967$	−1.77828e7	−0.611553	−0.305777	−	0.952103i	$-0.598916\pi$
$967$	−1.77828e7	−0.611553	−0.305777	+	0.952103i	$0.598916\pi$
$968$	2.14511e6	0.0735803
$969$	−9.53335e6	−0.326164
$970$	−3.24287e6	−0.110662
$971$	−4.25409e7	−1.44797	−0.723984	−	0.689817i	$-0.757691\pi$
$971$	−4.25409e7	−1.44797	−0.723984	+	0.689817i	$0.757691\pi$
$972$	1.42756e6	0.0484650
$973$	−80677.7	−0.00273194
$974$	−74101.9	−0.00250283
$975$	−1.62158e6	−0.0546295
$976$	4.99844e6	0.167961
$977$	−1.61740e7	−0.542103	−0.271051	−	0.962565i	$-0.587371\pi$
$977$	−1.61740e7	−0.542103	−0.271051	+	0.962565i	$0.587371\pi$
$978$	1.30358e7	0.435802
$979$	−6.49852e6	−0.216699
$980$	−1.06924e7	−0.355641
$981$	−5.73296e7	−1.90198
$982$	1.17452e7	0.388672
$983$	2.54406e7	0.839737	0.419868	−	0.907585i	$-0.362076\pi$
$983$	2.54406e7	0.839737	0.419868	+	0.907585i	$0.362076\pi$
$984$	−1.65164e7	−0.543786
$985$	1.45525e7	0.477913
$986$	870297.	0.0285086
$987$	2.13027e6	0.0696052
$988$	887551.	0.0289268
$989$	4.64927e7	1.51145
$990$	3.71217e6	0.120376
$991$	3.01983e7	0.976785	0.488392	−	0.872624i	$-0.337583\pi$
$991$	3.01983e7	0.976785	0.488392	+	0.872624i	$0.337583\pi$
$992$	−1.44194e7	−0.465232
$993$	−5.41358e7	−1.74226
$994$	232756.	0.00747195
$995$	1.84627e7	0.591204
$996$	−2.05675e6	−0.0656952
$997$	1.28718e7	0.410112	0.205056	−	0.978750i	$-0.434262\pi$
$997$	1.28718e7	0.410112	0.205056	+	0.978750i	$0.434262\pi$
$998$	4.46531e6	0.141914
$999$	1.76505e7	0.559557

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.a.1.15	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.a.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.54765 q^{2} +26.9200 q^{3} -25.5095 q^{4} -25.0000 q^{5} -68.5826 q^{6} +6.38524 q^{7} +146.514 q^{8} +481.684 q^{9} +O(q^{10})\)	\(q-2.54765 q^{2} +26.9200 q^{3} -25.5095 q^{4} -25.0000 q^{5} -68.5826 q^{6} +6.38524 q^{7} +146.514 q^{8} +481.684 q^{9} +63.6912 q^{10} +121.000 q^{11} -686.714 q^{12} -96.3795 q^{13} -16.2674 q^{14} -672.999 q^{15} +443.037 q^{16} -980.988 q^{17} -1227.16 q^{18} +361.000 q^{19} +637.737 q^{20} +171.890 q^{21} -308.266 q^{22} -2802.67 q^{23} +3944.15 q^{24} +625.000 q^{25} +245.541 q^{26} +6425.37 q^{27} -162.884 q^{28} +348.228 q^{29} +1714.57 q^{30} +2478.78 q^{31} -5817.15 q^{32} +3257.32 q^{33} +2499.21 q^{34} -159.631 q^{35} -12287.5 q^{36} +2747.01 q^{37} -919.702 q^{38} -2594.53 q^{39} -3662.85 q^{40} -4187.57 q^{41} -437.916 q^{42} -16588.7 q^{43} -3086.65 q^{44} -12042.1 q^{45} +7140.21 q^{46} +12393.2 q^{47} +11926.5 q^{48} -16766.2 q^{49} -1592.28 q^{50} -26408.2 q^{51} +2458.59 q^{52} -22695.1 q^{53} -16369.6 q^{54} -3025.00 q^{55} +935.527 q^{56} +9718.11 q^{57} -887.164 q^{58} +5085.55 q^{59} +17167.9 q^{60} +11282.2 q^{61} -6315.07 q^{62} +3075.67 q^{63} +642.883 q^{64} +2409.49 q^{65} -8298.50 q^{66} +44586.4 q^{67} +25024.5 q^{68} -75447.6 q^{69} +406.684 q^{70} -14308.1 q^{71} +70573.5 q^{72} +50131.9 q^{73} -6998.41 q^{74} +16825.0 q^{75} -9208.92 q^{76} +772.614 q^{77} +6609.96 q^{78} +39291.6 q^{79} -11075.9 q^{80} +55921.5 q^{81} +10668.5 q^{82} +2995.06 q^{83} -4384.83 q^{84} +24524.7 q^{85} +42262.3 q^{86} +9374.29 q^{87} +17728.2 q^{88} -53706.8 q^{89} +30679.1 q^{90} -615.406 q^{91} +71494.5 q^{92} +66728.7 q^{93} -31573.5 q^{94} -9025.00 q^{95} -156597. q^{96} -50915.4 q^{97} +42714.5 q^{98} +58283.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) \) 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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