LMFDB - Embedded newform 309.6.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [309,6,Mod(1,309)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(309, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("309.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 309 = 3 \cdot 103 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	309.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:	$49.5586003222$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	309.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.35356 q^{2} -9.00000 q^{3} -30.1679 q^{4} -30.1704 q^{5} -12.1820 q^{6} +2.34390 q^{7} -84.1477 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+1.35356 q^{2} -9.00000 q^{3} -30.1679 q^{4} -30.1704 q^{5} -12.1820 q^{6} +2.34390 q^{7} -84.1477 q^{8} +81.0000 q^{9} -40.8373 q^{10} +90.6470 q^{11} +271.511 q^{12} +356.752 q^{13} +3.17260 q^{14} +271.534 q^{15} +851.474 q^{16} +1286.67 q^{17} +109.638 q^{18} +2083.15 q^{19} +910.178 q^{20} -21.0951 q^{21} +122.696 q^{22} -4862.73 q^{23} +757.329 q^{24} -2214.75 q^{25} +482.884 q^{26} -729.000 q^{27} -70.7105 q^{28} +4161.97 q^{29} +367.536 q^{30} -657.847 q^{31} +3845.24 q^{32} -815.823 q^{33} +1741.57 q^{34} -70.7164 q^{35} -2443.60 q^{36} +3972.03 q^{37} +2819.65 q^{38} -3210.77 q^{39} +2538.77 q^{40} -4384.59 q^{41} -28.5534 q^{42} -4071.80 q^{43} -2734.63 q^{44} -2443.80 q^{45} -6581.97 q^{46} -8091.34 q^{47} -7663.27 q^{48} -16801.5 q^{49} -2997.78 q^{50} -11580.0 q^{51} -10762.5 q^{52} +14314.3 q^{53} -986.742 q^{54} -2734.86 q^{55} -197.234 q^{56} -18748.3 q^{57} +5633.45 q^{58} -16761.2 q^{59} -8191.60 q^{60} +22998.5 q^{61} -890.432 q^{62} +189.856 q^{63} -22042.4 q^{64} -10763.4 q^{65} -1104.26 q^{66} +37913.5 q^{67} -38816.0 q^{68} +43764.5 q^{69} -95.7186 q^{70} -47353.1 q^{71} -6815.96 q^{72} -75718.3 q^{73} +5376.36 q^{74} +19932.7 q^{75} -62844.1 q^{76} +212.468 q^{77} -4345.95 q^{78} -61404.1 q^{79} -25689.3 q^{80} +6561.00 q^{81} -5934.78 q^{82} +6366.43 q^{83} +636.394 q^{84} -38819.2 q^{85} -5511.40 q^{86} -37457.7 q^{87} -7627.74 q^{88} +75663.0 q^{89} -3307.82 q^{90} +836.191 q^{91} +146698. q^{92} +5920.62 q^{93} -10952.1 q^{94} -62849.4 q^{95} -34607.2 q^{96} +44894.4 q^{97} -22741.8 q^{98} +7342.41 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9}+O(q^{10}) $ 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9	\( 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9} - 355 q^{10} - 708 q^{11} - 3078 q^{12} - 133 q^{13} - 2748 q^{14} + 477 q^{15} + 3678 q^{16} - 2006 q^{17} - 648 q^{18} - 4788 q^{19} - 2785 q^{20} - 90 q^{21} + 3609 q^{22} - 5695 q^{23} + 2376 q^{24} + 18477 q^{25} + 2432 q^{26} - 16038 q^{27} + 7635 q^{28} - 978 q^{29} + 3195 q^{30} - 6009 q^{31} + 22809 q^{32} + 6372 q^{33} - 4078 q^{34} - 22822 q^{35} + 27702 q^{36} + 13640 q^{37} - 5454 q^{38} + 1197 q^{39} - 13351 q^{40} - 24618 q^{41} + 24732 q^{42} + 1257 q^{43} - 65465 q^{44} - 4293 q^{45} - 6175 q^{46} - 63834 q^{47} - 33102 q^{48} + 18022 q^{49} - 41643 q^{50} + 18054 q^{51} - 40853 q^{52} - 13316 q^{53} + 5832 q^{54} - 35934 q^{55} - 251195 q^{56} + 43092 q^{57} - 103895 q^{58} - 138587 q^{59} + 25065 q^{60} - 53985 q^{61} - 218186 q^{62} + 810 q^{63} + 23758 q^{64} - 114073 q^{65} - 32481 q^{66} - 102785 q^{67} - 338669 q^{68} + 51255 q^{69} - 104184 q^{70} - 108740 q^{71} - 21384 q^{72} + 69762 q^{73} - 221377 q^{74} - 166293 q^{75} - 223267 q^{76} - 140360 q^{77} - 21888 q^{78} - 238938 q^{79} - 864251 q^{80} + 144342 q^{81} - 660293 q^{82} - 305455 q^{83} - 68715 q^{84} - 201204 q^{85} - 794679 q^{86} + 8802 q^{87} - 420823 q^{88} - 438448 q^{89} - 28755 q^{90} - 294186 q^{91} - 1251930 q^{92} + 54081 q^{93} - 826416 q^{94} - 652572 q^{95} - 205281 q^{96} - 284729 q^{97} - 887529 q^{98} - 57348 q^{99}+O(q^{100}) \) 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9 - 355 * q^10 - 708 * q^11 - 3078 * q^12 - 133 * q^13 - 2748 * q^14 + 477 * q^15 + 3678 * q^16 - 2006 * q^17 - 648 * q^18 - 4788 * q^19 - 2785 * q^20 - 90 * q^21 + 3609 * q^22 - 5695 * q^23 + 2376 * q^24 + 18477 * q^25 + 2432 * q^26 - 16038 * q^27 + 7635 * q^28 - 978 * q^29 + 3195 * q^30 - 6009 * q^31 + 22809 * q^32 + 6372 * q^33 - 4078 * q^34 - 22822 * q^35 + 27702 * q^36 + 13640 * q^37 - 5454 * q^38 + 1197 * q^39 - 13351 * q^40 - 24618 * q^41 + 24732 * q^42 + 1257 * q^43 - 65465 * q^44 - 4293 * q^45 - 6175 * q^46 - 63834 * q^47 - 33102 * q^48 + 18022 * q^49 - 41643 * q^50 + 18054 * q^51 - 40853 * q^52 - 13316 * q^53 + 5832 * q^54 - 35934 * q^55 - 251195 * q^56 + 43092 * q^57 - 103895 * q^58 - 138587 * q^59 + 25065 * q^60 - 53985 * q^61 - 218186 * q^62 + 810 * q^63 + 23758 * q^64 - 114073 * q^65 - 32481 * q^66 - 102785 * q^67 - 338669 * q^68 + 51255 * q^69 - 104184 * q^70 - 108740 * q^71 - 21384 * q^72 + 69762 * q^73 - 221377 * q^74 - 166293 * q^75 - 223267 * q^76 - 140360 * q^77 - 21888 * q^78 - 238938 * q^79 - 864251 * q^80 + 144342 * q^81 - 660293 * q^82 - 305455 * q^83 - 68715 * q^84 - 201204 * q^85 - 794679 * q^86 + 8802 * q^87 - 420823 * q^88 - 438448 * q^89 - 28755 * q^90 - 294186 * q^91 - 1251930 * q^92 + 54081 * q^93 - 826416 * q^94 - 652572 * q^95 - 205281 * q^96 - 284729 * q^97 - 887529 * q^98 - 57348 * 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 $

$2$	1.35356	0.239277	0.119639	−	0.992818i	$-0.461826\pi$
$2$	1.35356	0.239277	0.119639	+	0.992818i	$0.461826\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−30.1679	−0.942747
$5$	−30.1704	−0.539705	−0.269852	−	0.962902i	$-0.586975\pi$
$5$	−30.1704	−0.539705	−0.269852	+	0.962902i	$0.586975\pi$
$6$	−12.1820	−0.138147
$7$	2.34390	0.0180798	0.00903990	−	0.999959i	$-0.497122\pi$
$7$	2.34390	0.0180798	0.00903990	+	0.999959i	$0.497122\pi$
$8$	−84.1477	−0.464855
$9$	81.0000	0.333333
$10$	−40.8373	−0.129139
$11$	90.6470	0.225877	0.112938	−	0.993602i	$-0.463974\pi$
$11$	90.6470	0.225877	0.112938	+	0.993602i	$0.463974\pi$
$12$	271.511	0.544295
$13$	356.752	0.585475	0.292737	−	0.956193i	$-0.405434\pi$
$13$	356.752	0.585475	0.292737	+	0.956193i	$0.405434\pi$
$14$	3.17260	0.00432608
$15$	271.534	0.311599
$16$	851.474	0.831517
$17$	1286.67	1.07980	0.539900	−	0.841729i	$-0.318462\pi$
$17$	1286.67	1.07980	0.539900	+	0.841729i	$0.318462\pi$
$18$	109.638	0.0797590
$19$	2083.15	1.32384	0.661920	−	0.749574i	$-0.269742\pi$
$19$	2083.15	1.32384	0.661920	+	0.749574i	$0.269742\pi$
$20$	910.178	0.508805
$21$	−21.0951	−0.0104384
$22$	122.696	0.0540472
$23$	−4862.73	−1.91673	−0.958363	−	0.285552i	$-0.907823\pi$
$23$	−4862.73	−1.91673	−0.958363	+	0.285552i	$0.907823\pi$
$24$	757.329	0.268384
$25$	−2214.75	−0.708719
$26$	482.884	0.140091
$27$	−729.000	−0.192450
$28$	−70.7105	−0.0170447
$29$	4161.97	0.918975	0.459487	−	0.888184i	$-0.348033\pi$
$29$	4161.97	0.918975	0.459487	+	0.888184i	$0.348033\pi$
$30$	367.536	0.0745584
$31$	−657.847	−0.122948	−0.0614739	−	0.998109i	$-0.519580\pi$
$31$	−657.847	−0.122948	−0.0614739	+	0.998109i	$0.519580\pi$
$32$	3845.24	0.663818
$33$	−815.823	−0.130410
$34$	1741.57	0.258371
$35$	−70.7164	−0.00975776
$36$	−2443.60	−0.314249
$37$	3972.03	0.476988	0.238494	−	0.971144i	$-0.423346\pi$
$37$	3972.03	0.476988	0.238494	+	0.971144i	$0.423346\pi$
$38$	2819.65	0.316765
$39$	−3210.77	−0.338024
$40$	2538.77	0.250884
$41$	−4384.59	−0.407351	−0.203676	−	0.979038i	$-0.565289\pi$
$41$	−4384.59	−0.407351	−0.203676	+	0.979038i	$0.565289\pi$
$42$	−28.5534	−0.00249766
$43$	−4071.80	−0.335826	−0.167913	−	0.985802i	$-0.553703\pi$
$43$	−4071.80	−0.335826	−0.167913	+	0.985802i	$0.553703\pi$
$44$	−2734.63	−0.212945
$45$	−2443.80	−0.179902
$46$	−6581.97	−0.458629
$47$	−8091.34	−0.534288	−0.267144	−	0.963657i	$-0.586080\pi$
$47$	−8091.34	−0.534288	−0.267144	+	0.963657i	$0.586080\pi$
$48$	−7663.27	−0.480077
$49$	−16801.5	−0.999673
$50$	−2997.78	−0.169580
$51$	−11580.0	−0.623423
$52$	−10762.5	−0.551954
$53$	14314.3	0.699971	0.349985	−	0.936755i	$-0.386187\pi$
$53$	14314.3	0.699971	0.349985	+	0.936755i	$0.386187\pi$
$54$	−986.742	−0.0460489
$55$	−2734.86	−0.121907
$56$	−197.234	−0.00840448
$57$	−18748.3	−0.764320
$58$	5633.45	0.219890
$59$	−16761.2	−0.626868	−0.313434	−	0.949610i	$-0.601479\pi$
$59$	−16761.2	−0.626868	−0.313434	+	0.949610i	$0.601479\pi$
$60$	−8191.60	−0.293759
$61$	22998.5	0.791361	0.395681	−	0.918388i	$-0.370509\pi$
$61$	22998.5	0.791361	0.395681	+	0.918388i	$0.370509\pi$
$62$	−890.432	−0.0294186
$63$	189.856	0.00602660
$64$	−22042.4	−0.672681
$65$	−10763.4	−0.315983
$66$	−1104.26	−0.0312041
$67$	37913.5	1.03183	0.515914	−	0.856640i	$-0.327452\pi$
$67$	37913.5	1.03183	0.515914	+	0.856640i	$0.327452\pi$
$68$	−38816.0	−1.01798
$69$	43764.5	1.10662
$70$	−95.7186	−0.00233481
$71$	−47353.1	−1.11481	−0.557407	−	0.830239i	$-0.688204\pi$
$71$	−47353.1	−1.11481	−0.557407	+	0.830239i	$0.688204\pi$
$72$	−6815.96	−0.154952
$73$	−75718.3	−1.66301	−0.831503	−	0.555520i	$-0.812519\pi$
$73$	−75718.3	−1.66301	−0.831503	+	0.555520i	$0.812519\pi$
$74$	5376.36	0.114132
$75$	19932.7	0.409179
$76$	−62844.1	−1.24805
$77$	212.468	0.00408381
$78$	−4345.95	−0.0808814
$79$	−61404.1	−1.10695	−0.553477	−	0.832864i	$-0.686699\pi$
$79$	−61404.1	−1.10695	−0.553477	+	0.832864i	$0.686699\pi$
$80$	−25689.3	−0.448774
$81$	6561.00	0.111111
$82$	−5934.78	−0.0974698
$83$	6366.43	0.101438	0.0507190	−	0.998713i	$-0.483849\pi$
$83$	6366.43	0.101438	0.0507190	+	0.998713i	$0.483849\pi$
$84$	636.394	0.00984075
$85$	−38819.2	−0.582773
$86$	−5511.40	−0.0803556
$87$	−37457.7	−0.530570
$88$	−7627.74	−0.105000
$89$	75663.0	1.01253	0.506266	−	0.862378i	$-0.331026\pi$
$89$	75663.0	1.01253	0.506266	+	0.862378i	$0.331026\pi$
$90$	−3307.82	−0.0430463
$91$	836.191	0.0105853
$92$	146698.	1.80699
$93$	5920.62	0.0709839
$94$	−10952.1	−0.127843
$95$	−62849.4	−0.714483
$96$	−34607.2	−0.383255
$97$	44894.4	0.484465	0.242233	−	0.970218i	$-0.422120\pi$
$97$	44894.4	0.484465	0.242233	+	0.970218i	$0.422120\pi$
$98$	−22741.8	−0.239199
$99$	7342.41	0.0752923
$100$	66814.2	0.668142
$101$	−51213.2	−0.499550	−0.249775	−	0.968304i	$-0.580357\pi$
$101$	−51213.2	−0.499550	−0.249775	+	0.968304i	$0.580357\pi$
$102$	−15674.2	−0.149171
$103$	−10609.0	−0.0985329
$103$	−10609.0	−0.0985329
$104$	−30019.9	−0.272161
$105$	636.448	0.00563364
$106$	19375.2	0.167487
$107$	70031.4	0.591335	0.295668	−	0.955291i	$-0.404458\pi$
$107$	70031.4	0.591335	0.295668	+	0.955291i	$0.404458\pi$
$108$	21992.4	0.181432
$109$	−85495.3	−0.689249	−0.344625	−	0.938741i	$-0.611994\pi$
$109$	−85495.3	−0.689249	−0.344625	+	0.938741i	$0.611994\pi$
$110$	−3701.78	−0.0291695
$111$	−35748.2	−0.275389
$112$	1995.77	0.0150337
$113$	−131820.	−0.971147	−0.485574	−	0.874196i	$-0.661389\pi$
$113$	−131820.	−0.971147	−0.485574	+	0.874196i	$0.661389\pi$
$114$	−25376.9	−0.182884
$115$	146710.	1.03447
$116$	−125558.	−0.866360
$117$	28896.9	0.195158
$118$	−22687.3	−0.149995
$119$	3015.82	0.0195226
$120$	−22848.9	−0.144848
$121$	−152834.	−0.948980
$122$	31129.7	0.189355
$123$	39461.3	0.235184
$124$	19845.9	0.115909
$125$	161102.	0.922204
$126$	256.980	0.00144203
$127$	−113172.	−0.622630	−0.311315	−	0.950307i	$-0.600769\pi$
$127$	−113172.	−0.622630	−0.311315	+	0.950307i	$0.600769\pi$
$128$	−152883.	−0.824775
$129$	36646.2	0.193890
$130$	−14568.8	−0.0756076
$131$	−236321.	−1.20316	−0.601580	−	0.798812i	$-0.705462\pi$
$131$	−236321.	−1.20316	−0.601580	+	0.798812i	$0.705462\pi$
$132$	24611.7	0.122944
$133$	4882.68	0.0239348
$134$	51318.1	0.246893
$135$	21994.2	0.103866
$136$	−108270.	−0.501950
$137$	157898.	0.718747	0.359373	−	0.933194i	$-0.382990\pi$
$137$	157898.	0.718747	0.359373	+	0.933194i	$0.382990\pi$
$138$	59237.7	0.264789
$139$	239621.	1.05193	0.525967	−	0.850505i	$-0.323704\pi$
$139$	239621.	1.05193	0.525967	+	0.850505i	$0.323704\pi$
$140$	2133.36	0.00919909
$141$	72822.0	0.308471
$142$	−64095.0	−0.266749
$143$	32338.5	0.132245
$144$	68969.4	0.277172
$145$	−125568.	−0.495975
$146$	−102489.	−0.397919
$147$	151214.	0.577162
$148$	−119828.	−0.449679
$149$	−240700.	−0.888200	−0.444100	−	0.895977i	$-0.646477\pi$
$149$	−240700.	−0.888200	−0.444100	+	0.895977i	$0.646477\pi$
$150$	26980.0	0.0979071
$151$	−169034.	−0.603296	−0.301648	−	0.953419i	$-0.597537\pi$
$151$	−169034.	−0.603296	−0.301648	+	0.953419i	$0.597537\pi$
$152$	−175292.	−0.615393
$153$	104220.	0.359933
$154$	287.587	0.000977162 0
$155$	19847.5	0.0663555
$156$	96862.1	0.318671
$157$	163809.	0.530381	0.265191	−	0.964196i	$-0.414565\pi$
$157$	163809.	0.530381	0.265191	+	0.964196i	$0.414565\pi$
$158$	−83113.8	−0.264869
$159$	−128829.	−0.404128
$160$	−116013.	−0.358266
$161$	−11397.7	−0.0346540
$162$	8880.68	0.0265863
$163$	353465.	1.04202	0.521011	−	0.853550i	$-0.325555\pi$
$163$	353465.	1.04202	0.521011	+	0.853550i	$0.325555\pi$
$164$	132274.	0.384029
$165$	24613.7	0.0703830
$166$	8617.32	0.0242718
$167$	−223568.	−0.620323	−0.310162	−	0.950684i	$-0.600383\pi$
$167$	−223568.	−0.620323	−0.310162	+	0.950684i	$0.600383\pi$
$168$	1775.10	0.00485233
$169$	−244021.	−0.657220
$170$	−52544.0	−0.139444
$171$	168735.	0.441280
$172$	122838.	0.316599
$173$	73229.5	0.186025	0.0930124	−	0.995665i	$-0.470350\pi$
$173$	73229.5	0.186025	0.0930124	+	0.995665i	$0.470350\pi$
$174$	−50701.1	−0.126953
$175$	−5191.14	−0.0128135
$176$	77183.6	0.187821
$177$	150851.	0.361922
$178$	102414.	0.242275
$179$	−588272.	−1.37229	−0.686145	−	0.727465i	$-0.740698\pi$
$179$	−588272.	−1.37229	−0.686145	+	0.727465i	$0.740698\pi$
$180$	73724.4	0.169602
$181$	339424.	0.770098	0.385049	−	0.922896i	$-0.374185\pi$
$181$	339424.	0.770098	0.385049	+	0.922896i	$0.374185\pi$
$182$	1131.83	0.00253281
$183$	−206986.	−0.456893
$184$	409187.	0.890999
$185$	−119838.	−0.257433
$186$	8013.89	0.0169848
$187$	116632.	0.243902
$188$	244098.	0.503698
$189$	−1708.70	−0.00347946
$190$	−85070.1	−0.170959
$191$	−208169.	−0.412889	−0.206444	−	0.978458i	$-0.566189\pi$
$191$	−208169.	−0.412889	−0.206444	+	0.978458i	$0.566189\pi$
$192$	198382.	0.388373
$193$	−208721.	−0.403341	−0.201670	−	0.979453i	$-0.564637\pi$
$193$	−208721.	−0.403341	−0.201670	+	0.979453i	$0.564637\pi$
$194$	60767.0	0.115921
$195$	96870.2	0.182433
$196$	506866.	0.942438
$197$	−840038.	−1.54217	−0.771087	−	0.636730i	$-0.780287\pi$
$197$	−840038.	−1.54217	−0.771087	+	0.636730i	$0.780287\pi$
$198$	9938.36	0.0180157
$199$	839125.	1.50208	0.751041	−	0.660255i	$-0.229552\pi$
$199$	839125.	1.50208	0.751041	+	0.660255i	$0.229552\pi$
$200$	186366.	0.329451
$201$	−341222.	−0.595726
$202$	−69319.9	−0.119531
$203$	9755.23	0.0166149
$204$	349344.	0.587730
$205$	132285.	0.219849
$206$	−14359.9	−0.0235767
$207$	−393881.	−0.638909
$208$	303765.	0.486832
$209$	188831.	0.299025
$210$	861.467	0.00134800
$211$	−133467.	−0.206380	−0.103190	−	0.994662i	$-0.532905\pi$
$211$	−133467.	−0.206380	−0.103190	+	0.994662i	$0.532905\pi$
$212$	−431832.	−0.659895
$213$	426178.	0.643638
$214$	94791.4	0.141493
$215$	122848.	0.181247
$216$	61343.7	0.0894613
$217$	−1541.93	−0.00222287
$218$	−115723.	−0.164921
$219$	681465.	0.960137
$220$	82504.9	0.114927
$221$	459021.	0.632196
$222$	−48387.2	−0.0658943
$223$	282093.	0.379865	0.189933	−	0.981797i	$-0.439173\pi$
$223$	282093.	0.379865	0.189933	+	0.981797i	$0.439173\pi$
$224$	9012.86	0.0120017
$225$	−179394.	−0.236240
$226$	−178426.	−0.232373
$227$	−1.04654e6	−1.34800	−0.674000	−	0.738732i	$-0.735425\pi$
$227$	−1.04654e6	−1.34800	−0.674000	+	0.738732i	$0.735425\pi$
$228$	565597.	0.720560
$229$	−291162.	−0.366898	−0.183449	−	0.983029i	$-0.558726\pi$
$229$	−291162.	−0.366898	−0.183449	+	0.983029i	$0.558726\pi$
$230$	198581.	0.247524
$231$	−1912.21	−0.00235779
$232$	−350220.	−0.427190
$233$	147693.	0.178226	0.0891130	−	0.996022i	$-0.471597\pi$
$233$	147693.	0.178226	0.0891130	+	0.996022i	$0.471597\pi$
$234$	39113.6	0.0466969
$235$	244119.	0.288358
$236$	505651.	0.590977
$237$	552637.	0.639100
$238$	4082.07	0.00467131
$239$	244466.	0.276837	0.138418	−	0.990374i	$-0.455798\pi$
$239$	244466.	0.276837	0.138418	+	0.990374i	$0.455798\pi$
$240$	231204.	0.259100
$241$	873102.	0.968328	0.484164	−	0.874977i	$-0.339124\pi$
$241$	873102.	0.968328	0.484164	+	0.874977i	$0.339124\pi$
$242$	−206869.	−0.227069
$243$	−59049.0	−0.0641500
$244$	−693816.	−0.746053
$245$	506908.	0.539528
$246$	53413.1	0.0562742
$247$	743166.	0.775075
$248$	55356.3	0.0571528
$249$	−57297.9	−0.0585653
$250$	218061.	0.220662
$251$	−171468.	−0.171791	−0.0858953	−	0.996304i	$-0.527375\pi$
$251$	−171468.	−0.171791	−0.0858953	+	0.996304i	$0.527375\pi$
$252$	−5727.55	−0.00568156
$253$	−440792.	−0.432944
$254$	−153185.	−0.148981
$255$	349373.	0.336464
$256$	498421.	0.475331
$257$	−707179.	−0.667877	−0.333939	−	0.942595i	$-0.608378\pi$
$257$	−707179.	−0.667877	−0.333939	+	0.942595i	$0.608378\pi$
$258$	49602.6	0.0463933
$259$	9310.03	0.00862386
$260$	324708.	0.297892
$261$	337119.	0.306325
$262$	−319873.	−0.287889
$263$	−1.44955e6	−1.29224	−0.646119	−	0.763236i	$-0.723609\pi$
$263$	−1.44955e6	−1.29224	−0.646119	+	0.763236i	$0.723609\pi$
$264$	68649.6	0.0606218
$265$	−431868.	−0.377778
$266$	6608.98	0.00572704
$267$	−680967.	−0.584585
$268$	−1.14377e6	−0.972752
$269$	619968.	0.522382	0.261191	−	0.965287i	$-0.415885\pi$
$269$	619968.	0.522382	0.261191	+	0.965287i	$0.415885\pi$
$270$	29770.4	0.0248528
$271$	2.09776e6	1.73513	0.867565	−	0.497324i	$-0.165684\pi$
$271$	2.09776e6	1.73513	0.867565	+	0.497324i	$0.165684\pi$
$272$	1.09556e6	0.897873
$273$	−7525.72	−0.00611141
$274$	213724.	0.171980
$275$	−200760.	−0.160083
$276$	−1.32028e6	−1.04326
$277$	1.58191e6	1.23874	0.619372	−	0.785097i	$-0.287387\pi$
$277$	1.58191e6	1.23874	0.619372	+	0.785097i	$0.287387\pi$
$278$	324340.	0.251703
$279$	−53285.6	−0.0409826
$280$	5950.62	0.00453594
$281$	−1.01014e6	−0.763162	−0.381581	−	0.924335i	$-0.624620\pi$
$281$	−1.01014e6	−0.763162	−0.381581	+	0.924335i	$0.624620\pi$
$282$	98568.6	0.0738101
$283$	−968210.	−0.718627	−0.359313	−	0.933217i	$-0.616989\pi$
$283$	−968210.	−0.718627	−0.359313	+	0.933217i	$0.616989\pi$
$284$	1.42854e6	1.05099
$285$	565644.	0.412507
$286$	43772.0	0.0316432
$287$	−10277.0	−0.00736484
$288$	311465.	0.221273
$289$	235652.	0.165969
$290$	−169964.	−0.118675
$291$	−404049.	−0.279706
$292$	2.28426e6	1.56779
$293$	1.69575e6	1.15396	0.576982	−	0.816757i	$-0.304230\pi$
$293$	1.69575e6	1.15396	0.576982	+	0.816757i	$0.304230\pi$
$294$	204676.	0.138101
$295$	505693.	0.338323
$296$	−334237.	−0.221730
$297$	−66081.7	−0.0434700
$298$	−325801.	−0.212526
$299$	−1.73479e6	−1.12219
$300$	−601328.	−0.385752
$301$	−9543.88	−0.00607168
$302$	−228796.	−0.144355
$303$	460919.	0.288415
$304$	1.77374e6	1.10080
$305$	−693874.	−0.427101
$306$	141067.	0.0861238
$307$	1.86086e6	1.12685	0.563427	−	0.826166i	$-0.309483\pi$
$307$	1.86086e6	1.12685	0.563427	+	0.826166i	$0.309483\pi$
$308$	−6409.70	−0.00385000
$309$	95481.0	0.0568880
$310$	26864.7	0.0158773
$311$	−896388.	−0.525527	−0.262764	−	0.964860i	$-0.584634\pi$
$311$	−896388.	−0.525527	−0.262764	+	0.964860i	$0.584634\pi$
$312$	270179.	0.157132
$313$	−1.83541e6	−1.05894	−0.529471	−	0.848328i	$-0.677609\pi$
$313$	−1.83541e6	−1.05894	−0.529471	+	0.848328i	$0.677609\pi$
$314$	221724.	0.126908
$315$	−5728.03	−0.00325259
$316$	1.85243e6	1.04358
$317$	−2.76319e6	−1.54441	−0.772206	−	0.635373i	$-0.780846\pi$
$317$	−2.76319e6	−1.54441	−0.772206	+	0.635373i	$0.780846\pi$
$318$	−174377.	−0.0966986
$319$	377270.	0.207575
$320$	665029.	0.363049
$321$	−630283.	−0.341407
$322$	−15427.5	−0.00829192
$323$	2.68031e6	1.42948
$324$	−197932.	−0.104750
$325$	−790115.	−0.414937
$326$	478434.	0.249332
$327$	769458.	0.397938
$328$	368953.	0.189359
$329$	−18965.3	−0.00965983
$330$	33316.0	0.0168410
$331$	−3.28209e6	−1.64657	−0.823287	−	0.567626i	$-0.807862\pi$
$331$	−3.28209e6	−1.64657	−0.823287	+	0.567626i	$0.807862\pi$
$332$	−192062.	−0.0956304
$333$	321734.	0.158996
$334$	−302611.	−0.148429
$335$	−1.14387e6	−0.556882
$336$	−17961.9	−0.00867970
$337$	−3.92720e6	−1.88368	−0.941842	−	0.336056i	$-0.890907\pi$
$337$	−3.92720e6	−1.88368	−0.941842	+	0.336056i	$0.890907\pi$
$338$	−330296.	−0.157258
$339$	1.18638e6	0.560692
$340$	1.17109e6	0.549408
$341$	−59631.9	−0.0277711
$342$	228392.	0.105588
$343$	−78774.9	−0.0361537
$344$	342632.	0.156110
$345$	−1.32039e6	−0.597249
$346$	99120.1	0.0445114
$347$	−3.64861e6	−1.62668	−0.813342	−	0.581785i	$-0.802354\pi$
$347$	−3.64861e6	−1.62668	−0.813342	+	0.581785i	$0.802354\pi$
$348$	1.13002e6	0.500193
$349$	−1.04735e6	−0.460286	−0.230143	−	0.973157i	$-0.573919\pi$
$349$	−1.04735e6	−0.460286	−0.230143	+	0.973157i	$0.573919\pi$
$350$	−7026.50	−0.00306598
$351$	−260072.	−0.112675
$352$	348560.	0.149941
$353$	−3.11622e6	−1.33104	−0.665521	−	0.746379i	$-0.731790\pi$
$353$	−3.11622e6	−1.33104	−0.665521	+	0.746379i	$0.731790\pi$
$354$	204185.	0.0865997
$355$	1.42866e6	0.601670
$356$	−2.28259e6	−0.954560
$357$	−27142.3	−0.0112714
$358$	−796259.	−0.328357
$359$	122234.	0.0500559	0.0250279	−	0.999687i	$-0.492033\pi$
$359$	122234.	0.0500559	0.0250279	+	0.999687i	$0.492033\pi$
$360$	205640.	0.0836281
$361$	1.86340e6	0.752553
$362$	459429.	0.184267
$363$	1.37551e6	0.547894
$364$	−25226.1	−0.00997922
$365$	2.28445e6	0.897532
$366$	−280168.	−0.109324
$367$	855020.	0.331369	0.165684	−	0.986179i	$-0.447017\pi$
$367$	855020.	0.331369	0.165684	+	0.986179i	$0.447017\pi$
$368$	−4.14048e6	−1.59379
$369$	−355152.	−0.135784
$370$	−162207.	−0.0615978
$371$	33551.2	0.0126553
$372$	−178613.	−0.0669198
$373$	3.61097e6	1.34385	0.671927	−	0.740618i	$-0.265467\pi$
$373$	3.61097e6	1.34385	0.671927	+	0.740618i	$0.265467\pi$
$374$	157869.	0.0583602
$375$	−1.44992e6	−0.532435
$376$	680867.	0.248366
$377$	1.48479e6	0.538036
$378$	−2312.82	−0.000832555 0
$379$	−3.76089e6	−1.34491	−0.672454	−	0.740139i	$-0.734760\pi$
$379$	−3.76089e6	−1.34491	−0.672454	+	0.740139i	$0.734760\pi$
$380$	1.89603e6	0.673576
$381$	1.01855e6	0.359476
$382$	−281769.	−0.0987948
$383$	−395818.	−0.137879	−0.0689395	−	0.997621i	$-0.521962\pi$
$383$	−395818.	−0.137879	−0.0689395	+	0.997621i	$0.521962\pi$
$384$	1.37595e6	0.476184
$385$	−6410.23	−0.00220405
$386$	−282515.	−0.0965102
$387$	−329816.	−0.111942
$388$	−1.35437e6	−0.456728
$389$	−4.89264e6	−1.63934	−0.819671	−	0.572834i	$-0.805844\pi$
$389$	−4.89264e6	−1.63934	−0.819671	+	0.572834i	$0.805844\pi$
$390$	131119.	0.0436521
$391$	−6.25670e6	−2.06968
$392$	1.41381e6	0.464703
$393$	2.12689e6	0.694645
$394$	−1.13704e6	−0.369007
$395$	1.85259e6	0.597428
$396$	−221505.	−0.0709816
$397$	2.13853e6	0.680987	0.340494	−	0.940247i	$-0.389406\pi$
$397$	2.13853e6	0.680987	0.340494	+	0.940247i	$0.389406\pi$
$398$	1.13580e6	0.359414
$399$	−43944.1	−0.0138188
$400$	−1.88580e6	−0.589312
$401$	−2.50823e6	−0.778945	−0.389473	−	0.921038i	$-0.627343\pi$
$401$	−2.50823e6	−0.778945	−0.389473	+	0.921038i	$0.627343\pi$
$402$	−461862.	−0.142544
$403$	−234688.	−0.0719828
$404$	1.54499e6	0.470949
$405$	−197948.	−0.0599672
$406$	13204.2	0.00397556
$407$	360052.	0.107741
$408$	974430.	0.289801
$409$	1.20719e6	0.356834	0.178417	−	0.983955i	$-0.442902\pi$
$409$	1.20719e6	0.356834	0.178417	+	0.983955i	$0.442902\pi$
$410$	179055.	0.0526049
$411$	−1.42108e6	−0.414969
$412$	320051.	0.0928916
$413$	−39286.6	−0.0113336
$414$	−533139.	−0.152876
$415$	−192078.	−0.0547466
$416$	1.37180e6	0.388648
$417$	−2.15659e6	−0.607334
$418$	255593.	0.0715498
$419$	−6.33572e6	−1.76303	−0.881517	−	0.472152i	$-0.843477\pi$
$419$	−6.33572e6	−1.76303	−0.881517	+	0.472152i	$0.843477\pi$
$420$	−19200.3	−0.00531110
$421$	2.07823e6	0.571462	0.285731	−	0.958310i	$-0.407764\pi$
$421$	2.07823e6	0.571462	0.285731	+	0.958310i	$0.407764\pi$
$422$	−180655.	−0.0493820
$423$	−655398.	−0.178096
$424$	−1.20451e6	−0.325385
$425$	−2.84964e6	−0.765275
$426$	576855.	0.154008
$427$	53906.1	0.0143077
$428$	−2.11270e6	−0.557479
$429$	−291047.	−0.0763518
$430$	166281.	0.0433683
$431$	−5.46075e6	−1.41599	−0.707994	−	0.706219i	$-0.750400\pi$
$431$	−5.46075e6	−1.41599	−0.707994	+	0.706219i	$0.750400\pi$
$432$	−620724.	−0.160026
$433$	−4.36961e6	−1.12001	−0.560007	−	0.828488i	$-0.689201\pi$
$433$	−4.36961e6	−1.12001	−0.560007	+	0.828488i	$0.689201\pi$
$434$	−2087.08	−0.000531882 0
$435$	1.13011e6	0.286351
$436$	2.57921e6	0.649787
$437$	−1.01298e7	−2.53744
$438$	922400.	0.229739
$439$	2.60563e6	0.645285	0.322642	−	0.946521i	$-0.395429\pi$
$439$	2.60563e6	0.645285	0.322642	+	0.946521i	$0.395429\pi$
$440$	230132.	0.0566690
$441$	−1.36092e6	−0.333224
$442$	621310.	0.151270
$443$	7.34904e6	1.77919	0.889593	−	0.456753i	$-0.150988\pi$
$443$	7.34904e6	1.77919	0.889593	+	0.456753i	$0.150988\pi$
$444$	1.07845e6	0.259622
$445$	−2.28278e6	−0.546468
$446$	381828.	0.0908930
$447$	2.16630e6	0.512803
$448$	−51665.2	−0.0121619
$449$	3.29164e6	0.770543	0.385272	−	0.922803i	$-0.374108\pi$
$449$	3.29164e6	0.770543	0.385272	+	0.922803i	$0.374108\pi$
$450$	−242820.	−0.0565267
$451$	−397450.	−0.0920113
$452$	3.97673e6	0.915545
$453$	1.52130e6	0.348313
$454$	−1.41655e6	−0.322545
$455$	−25228.2	−0.00571292
$456$	1.57763e6	0.355297
$457$	4.97494e6	1.11429	0.557144	−	0.830416i	$-0.311897\pi$
$457$	4.97494e6	1.11429	0.557144	+	0.830416i	$0.311897\pi$
$458$	−394103.	−0.0877903
$459$	−937980.	−0.207808
$460$	−4.42594e6	−0.975240
$461$	−6.09182e6	−1.33504	−0.667520	−	0.744592i	$-0.732644\pi$
$461$	−6.09182e6	−1.33504	−0.667520	+	0.744592i	$0.732644\pi$
$462$	−2588.28	−0.000564165 0
$463$	−7.38220e6	−1.60042	−0.800209	−	0.599721i	$-0.795278\pi$
$463$	−7.38220e6	−1.60042	−0.800209	+	0.599721i	$0.795278\pi$
$464$	3.54381e6	0.764143
$465$	−178628.	−0.0383104
$466$	199911.	0.0426454
$467$	−5.96085e6	−1.26478	−0.632391	−	0.774649i	$-0.717926\pi$
$467$	−5.96085e6	−1.26478	−0.632391	+	0.774649i	$0.717926\pi$
$468$	−871759.	−0.183985
$469$	88865.5	0.0186552
$470$	330428.	0.0689974
$471$	−1.47428e6	−0.306216
$472$	1.41042e6	0.291402
$473$	−369096.	−0.0758555
$474$	748024.	0.152922
$475$	−4.61364e6	−0.938231
$476$	−90980.8	−0.0184048
$477$	1.15946e6	0.233324
$478$	330898.	0.0662406
$479$	−25697.4	−0.00511741	−0.00255870	−	0.999997i	$-0.500814\pi$
$479$	−25697.4	−0.00511741	−0.00255870	+	0.999997i	$0.500814\pi$
$480$	1.04411e6	0.206845
$481$	1.41703e6	0.279265
$482$	1.18179e6	0.231699
$483$	102580.	0.0200075
$484$	4.61068e6	0.894647
$485$	−1.35448e6	−0.261468
$486$	−79926.1	−0.0153496
$487$	2.39390e6	0.457386	0.228693	−	0.973499i	$-0.426555\pi$
$487$	2.39390e6	0.457386	0.228693	+	0.973499i	$0.426555\pi$
$488$	−1.93527e6	−0.367868
$489$	−3.18118e6	−0.601612
$490$	686129.	0.129097
$491$	801309.	0.150002	0.0750009	−	0.997183i	$-0.476104\pi$
$491$	801309.	0.150002	0.0750009	+	0.997183i	$0.476104\pi$
$492$	−1.19046e6	−0.221719
$493$	5.35506e6	0.992309
$494$	1.00592e6	0.185458
$495$	−221524.	−0.0406356
$496$	−560140.	−0.102233
$497$	−110991.	−0.0201556
$498$	−77555.9	−0.0140133
$499$	−4.43842e6	−0.797952	−0.398976	−	0.916961i	$-0.630634\pi$
$499$	−4.43842e6	−0.797952	−0.398976	+	0.916961i	$0.630634\pi$
$500$	−4.86012e6	−0.869404
$501$	2.01211e6	0.358144
$502$	−232092.	−0.0411056
$503$	2.90816e6	0.512506	0.256253	−	0.966610i	$-0.417512\pi$
$503$	2.90816e6	0.512506	0.256253	+	0.966610i	$0.417512\pi$
$504$	−15975.9	−0.00280149
$505$	1.54512e6	0.269609
$506$	−596636.	−0.103594
$507$	2.19619e6	0.379446
$508$	3.41416e6	0.586982
$509$	−361638.	−0.0618700	−0.0309350	−	0.999521i	$-0.509848\pi$
$509$	−361638.	−0.0618700	−0.0309350	+	0.999521i	$0.509848\pi$
$510$	472896.	0.0805082
$511$	−177476.	−0.0300668
$512$	5.56691e6	0.938511
$513$	−1.51861e6	−0.254773
$514$	−957206.	−0.159808
$515$	320078.	0.0531787
$516$	−1.10554e6	−0.182789
$517$	−733456.	−0.120683
$518$	12601.6	0.00206349
$519$	−659065.	−0.107401
$520$	905711.	0.146886
$521$	797065.	0.128647	0.0643235	−	0.997929i	$-0.479511\pi$
$521$	797065.	0.128647	0.0643235	+	0.997929i	$0.479511\pi$
$522$	456310.	0.0732965
$523$	1.14112e6	0.182422	0.0912109	−	0.995832i	$-0.470926\pi$
$523$	1.14112e6	0.182422	0.0912109	+	0.995832i	$0.470926\pi$
$524$	7.12930e6	1.13428
$525$	46720.3	0.00739788
$526$	−1.96204e6	−0.309203
$527$	−846429.	−0.132759
$528$	−694652.	−0.108438
$529$	1.72098e7	2.67384
$530$	−584557.	−0.0903935
$531$	−1.35766e6	−0.208956
$532$	−147300.	−0.0225644
$533$	−1.56421e6	−0.238494
$534$	−921726.	−0.139878
$535$	−2.11288e6	−0.319146
$536$	−3.19034e6	−0.479650
$537$	5.29445e6	0.792292
$538$	839161.	0.124994
$539$	−1.52301e6	−0.225803
$540$	−663519.	−0.0979195
$541$	28618.2	0.00420387	0.00210194	−	0.999998i	$-0.499331\pi$
$541$	28618.2	0.00420387	0.00210194	+	0.999998i	$0.499331\pi$
$542$	2.83943e6	0.415177
$543$	−3.05481e6	−0.444616
$544$	4.94754e6	0.716791
$545$	2.57943e6	0.371991
$546$	−10186.5	−0.00146232
$547$	3.92812e6	0.561328	0.280664	−	0.959806i	$-0.409445\pi$
$547$	3.92812e6	0.561328	0.280664	+	0.959806i	$0.409445\pi$
$548$	−4.76346e6	−0.677596
$549$	1.86288e6	0.263787
$550$	−271740.	−0.0383042
$551$	8.66998e6	1.21658
$552$	−3.68268e6	−0.514419
$553$	−143925.	−0.0200135
$554$	2.14120e6	0.296403
$555$	1.07854e6	0.148629
$556$	−7.22886e6	−0.991706
$557$	3.39648e6	0.463865	0.231933	−	0.972732i	$-0.425495\pi$
$557$	3.39648e6	0.463865	0.231933	+	0.972732i	$0.425495\pi$
$558$	−72125.0	−0.00980619
$559$	−1.45262e6	−0.196618
$560$	−60213.2	−0.00811375
$561$	−1.04969e6	−0.140817
$562$	−1.36728e6	−0.182607
$563$	3.22487e6	0.428787	0.214394	−	0.976747i	$-0.431222\pi$
$563$	3.22487e6	0.428787	0.214394	+	0.976747i	$0.431222\pi$
$564$	−2.19689e6	−0.290810
$565$	3.97706e6	0.524133
$566$	−1.31053e6	−0.171951
$567$	15378.3	0.00200887
$568$	3.98465e6	0.518226
$569$	1.22617e7	1.58771	0.793854	−	0.608108i	$-0.208071\pi$
$569$	1.22617e7	1.58771	0.793854	+	0.608108i	$0.208071\pi$
$570$	765631.	0.0987034
$571$	−1.01202e7	−1.29897	−0.649486	−	0.760373i	$-0.725016\pi$
$571$	−1.01202e7	−1.29897	−0.649486	+	0.760373i	$0.725016\pi$
$572$	−975585.	−0.124674
$573$	1.87352e6	0.238381
$574$	−13910.5	−0.00176224
$575$	1.07697e7	1.35842
$576$	−1.78544e6	−0.224227
$577$	−2.93781e6	−0.367353	−0.183677	−	0.982987i	$-0.558800\pi$
$577$	−2.93781e6	−0.367353	−0.183677	+	0.982987i	$0.558800\pi$
$578$	318969.	0.0397126
$579$	1.87849e6	0.232869
$580$	3.78813e6	0.467579
$581$	14922.3	0.00183398
$582$	−546903.	−0.0669273
$583$	1.29755e6	0.158107
$584$	6.37152e6	0.773056
$585$	−871832.	−0.105328
$586$	2.29529e6	0.276117
$587$	−1.23384e7	−1.47796	−0.738982	−	0.673725i	$-0.764693\pi$
$587$	−1.23384e7	−1.47796	−0.738982	+	0.673725i	$0.764693\pi$
$588$	−4.56179e6	−0.544117
$589$	−1.37039e6	−0.162763
$590$	684484.	0.0809530
$591$	7.56034e6	0.890374
$592$	3.38208e6	0.396624
$593$	3.18008e6	0.371365	0.185682	−	0.982610i	$-0.440550\pi$
$593$	3.18008e6	0.371365	0.185682	+	0.982610i	$0.440550\pi$
$594$	−89445.2	−0.0104014
$595$	−90988.4	−0.0105364
$596$	7.26142e6	0.837348
$597$	−7.55212e6	−0.867228
$598$	−2.34813e6	−0.268515
$599$	3.48950e6	0.397371	0.198685	−	0.980063i	$-0.436333\pi$
$599$	3.48950e6	0.397371	0.198685	+	0.980063i	$0.436333\pi$
$600$	−1.67729e6	−0.190209
$601$	1.19639e6	0.135110	0.0675548	−	0.997716i	$-0.478480\pi$
$601$	1.19639e6	0.135110	0.0675548	+	0.997716i	$0.478480\pi$
$602$	−12918.2	−0.00145281
$603$	3.07100e6	0.343943
$604$	5.09939e6	0.568755
$605$	4.61107e6	0.512169
$606$	623879.	0.0690111
$607$	2.00596e6	0.220978	0.110489	−	0.993877i	$-0.464758\pi$
$607$	2.00596e6	0.220978	0.110489	+	0.993877i	$0.464758\pi$
$608$	8.01020e6	0.878789
$609$	−87797.1	−0.00959261
$610$	−939197.	−0.102196
$611$	−2.88660e6	−0.312812
$612$	−3.14410e6	−0.339326
$613$	−1.18178e6	−0.127023	−0.0635117	−	0.997981i	$-0.520230\pi$
$613$	−1.18178e6	−0.127023	−0.0635117	+	0.997981i	$0.520230\pi$
$614$	2.51878e6	0.269630
$615$	−1.19056e6	−0.126930
$616$	−17878.6	−0.00189838
$617$	−4.16707e6	−0.440674	−0.220337	−	0.975424i	$-0.570716\pi$
$617$	−4.16707e6	−0.440674	−0.220337	+	0.975424i	$0.570716\pi$
$618$	129239.	0.0136120
$619$	−1.66984e7	−1.75166	−0.875828	−	0.482624i	$-0.839684\pi$
$619$	−1.66984e7	−1.75166	−0.875828	+	0.482624i	$0.839684\pi$
$620$	−598758.	−0.0625564
$621$	3.54493e6	0.368874
$622$	−1.21331e6	−0.125747
$623$	177346.	0.0183064
$624$	−2.73389e6	−0.281073
$625$	2.06056e6	0.211001
$626$	−2.48433e6	−0.253380
$627$	−1.69948e6	−0.172642
$628$	−4.94177e6	−0.500015
$629$	5.11067e6	0.515052
$630$	−7753.20	−0.000778269 0
$631$	412844.	0.0412774	0.0206387	−	0.999787i	$-0.493430\pi$
$631$	412844.	0.0412774	0.0206387	+	0.999787i	$0.493430\pi$
$632$	5.16701e6	0.514573
$633$	1.20120e6	0.119154
$634$	−3.74013e6	−0.369542
$635$	3.41445e6	0.336036
$636$	3.88649e6	0.380991
$637$	−5.99397e6	−0.585283
$638$	510656.	0.0496680
$639$	−3.83560e6	−0.371605
$640$	4.61255e6	0.445135
$641$	4.97943e6	0.478668	0.239334	−	0.970937i	$-0.423071\pi$
$641$	4.97943e6	0.478668	0.239334	+	0.970937i	$0.423071\pi$
$642$	−853123.	−0.0816910
$643$	−1.37021e7	−1.30695	−0.653477	−	0.756947i	$-0.726690\pi$
$643$	−1.37021e7	−1.30695	−0.653477	+	0.756947i	$0.726690\pi$
$644$	343846.	0.0326700
$645$	−1.10563e6	−0.104643
$646$	3.62795e6	0.342043
$647$	8.87267e6	0.833285	0.416642	−	0.909070i	$-0.363207\pi$
$647$	8.87267e6	0.833285	0.416642	+	0.909070i	$0.363207\pi$
$648$	−552093.	−0.0516505
$649$	−1.51936e6	−0.141595
$650$	−1.06946e6	−0.0992849
$651$	13877.3	0.00128338
$652$	−1.06633e7	−0.982363
$653$	1.48082e7	1.35900	0.679500	−	0.733676i	$-0.262197\pi$
$653$	1.48082e7	1.35900	0.679500	+	0.733676i	$0.262197\pi$
$654$	1.04150e6	0.0952174
$655$	7.12989e6	0.649351
$656$	−3.73336e6	−0.338720
$657$	−6.13318e6	−0.554335
$658$	−25670.5	−0.00231137
$659$	2.09667e7	1.88068	0.940342	−	0.340231i	$-0.110505\pi$
$659$	2.09667e7	1.88068	0.940342	+	0.340231i	$0.110505\pi$
$660$	−742544.	−0.0663533
$661$	−5.75011e6	−0.511885	−0.255943	−	0.966692i	$-0.582386\pi$
$661$	−5.75011e6	−0.511885	−0.255943	+	0.966692i	$0.582386\pi$
$662$	−4.44250e6	−0.393987
$663$	−4.13119e6	−0.364998
$664$	−535721.	−0.0471540
$665$	−147313.	−0.0129177
$666$	435485.	0.0380441
$667$	−2.02385e7	−1.76142
$668$	6.74457e6	0.584808
$669$	−2.53883e6	−0.219315
$670$	−1.54829e6	−0.133249
$671$	2.08475e6	0.178750
$672$	−81115.7	−0.00692918
$673$	2.18893e7	1.86292	0.931459	−	0.363846i	$-0.118537\pi$
$673$	2.18893e7	1.86292	0.931459	+	0.363846i	$0.118537\pi$
$674$	−5.31568e6	−0.450722
$675$	1.61455e6	0.136393
$676$	7.36160e6	0.619591
$677$	6.53435e6	0.547937	0.273969	−	0.961739i	$-0.411664\pi$
$677$	6.53435e6	0.547937	0.273969	+	0.961739i	$0.411664\pi$
$678$	1.60583e6	0.134161
$679$	105228.	0.00875904
$680$	3.26655e6	0.270905
$681$	9.41883e6	0.778268
$682$	−80715.1	−0.00664498
$683$	7.24482e6	0.594259	0.297130	−	0.954837i	$-0.403971\pi$
$683$	7.24482e6	0.594259	0.297130	+	0.954837i	$0.403971\pi$
$684$	−5.09037e6	−0.416015
$685$	−4.76385e6	−0.387911
$686$	−106626.	−0.00865075
$687$	2.62045e6	0.211829
$688$	−3.46703e6	−0.279246
$689$	5.10665e6	0.409815
$690$	−1.78723e6	−0.142908
$691$	6.87193e6	0.547500	0.273750	−	0.961801i	$-0.411736\pi$
$691$	6.87193e6	0.547500	0.273750	+	0.961801i	$0.411736\pi$
$692$	−2.20918e6	−0.175374
$693$	17209.9	0.00136127
$694$	−4.93859e6	−0.389228
$695$	−7.22947e6	−0.567733
$696$	3.15198e6	0.246638
$697$	−5.64150e6	−0.439858
$698$	−1.41765e6	−0.110136
$699$	−1.32924e6	−0.102899
$700$	156606.	0.0120799
$701$	−6.80957e6	−0.523389	−0.261694	−	0.965151i	$-0.584281\pi$
$701$	−6.80957e6	−0.523389	−0.261694	+	0.965151i	$0.584281\pi$
$702$	−352022.	−0.0269605
$703$	8.27431e6	0.631456
$704$	−1.99808e6	−0.151943
$705$	−2.19707e6	−0.166483
$706$	−4.21798e6	−0.318488
$707$	−120039.	−0.00903176
$708$	−4.55086e6	−0.341201
$709$	2.27569e7	1.70019	0.850095	−	0.526630i	$-0.176544\pi$
$709$	2.27569e7	1.70019	0.850095	+	0.526630i	$0.176544\pi$
$710$	1.93377e6	0.143966
$711$	−4.97373e6	−0.368985
$712$	−6.36686e6	−0.470680
$713$	3.19893e6	0.235657
$714$	−36738.7	−0.00269698
$715$	−975666.	−0.0713734
$716$	1.77469e7	1.29372
$717$	−2.20019e6	−0.159832
$718$	165450.	0.0119772
$719$	−3.40138e6	−0.245377	−0.122688	−	0.992445i	$-0.539152\pi$
$719$	−3.40138e6	−0.245377	−0.122688	+	0.992445i	$0.539152\pi$
$720$	−2.08083e6	−0.149591
$721$	−24866.4	−0.00178146
$722$	2.52221e6	0.180069
$723$	−7.85792e6	−0.559065
$724$	−1.02397e7	−0.726007
$725$	−9.21770e6	−0.651295
$726$	1.86182e6	0.131098
$727$	−1.78630e7	−1.25349	−0.626743	−	0.779226i	$-0.715612\pi$
$727$	−1.78630e7	−1.25349	−0.626743	+	0.779226i	$0.715612\pi$
$728$	−70363.5	−0.00492061
$729$	531441.	0.0370370
$730$	3.09213e6	0.214759
$731$	−5.23904e6	−0.362626
$732$	6.24434e6	0.430734
$733$	−9.35429e6	−0.643059	−0.321530	−	0.946900i	$-0.604197\pi$
$733$	−9.35429e6	−0.643059	−0.321530	+	0.946900i	$0.604197\pi$
$734$	1.15732e6	0.0792889
$735$	−4.56218e6	−0.311497
$736$	−1.86984e7	−1.27236
$737$	3.43675e6	0.233066
$738$	−480717.	−0.0324899
$739$	2.14934e7	1.44775	0.723874	−	0.689932i	$-0.242360\pi$
$739$	2.14934e7	1.44775	0.723874	+	0.689932i	$0.242360\pi$
$740$	3.61525e6	0.242694
$741$	−6.68850e6	−0.447490
$742$	45413.5	0.00302813
$743$	52728.8	0.00350409	0.00175205	−	0.999998i	$-0.499442\pi$
$743$	52728.8	0.00350409	0.00175205	+	0.999998i	$0.499442\pi$
$744$	−498207.	−0.0329972
$745$	7.26203e6	0.479366
$746$	4.88765e6	0.321553
$747$	515681.	0.0338127
$748$	−3.51856e6	−0.229938
$749$	164147.	0.0106912
$750$	−1.96255e6	−0.127399
$751$	−7.02339e6	−0.454409	−0.227204	−	0.973847i	$-0.572959\pi$
$751$	−7.02339e6	−0.454409	−0.227204	+	0.973847i	$0.572959\pi$
$752$	−6.88956e6	−0.444270
$753$	1.54322e6	0.0991834
$754$	2.00975e6	0.128740
$755$	5.09981e6	0.325602
$756$	51547.9	0.00328025
$757$	−1.14024e7	−0.723194	−0.361597	−	0.932334i	$-0.617768\pi$
$757$	−1.14024e7	−0.723194	−0.361597	+	0.932334i	$0.617768\pi$
$758$	−5.09057e6	−0.321806
$759$	3.96713e6	0.249961
$760$	5.28863e6	0.332131
$761$	1.37673e7	0.861762	0.430881	−	0.902409i	$-0.358203\pi$
$761$	1.37673e7	0.861762	0.430881	+	0.902409i	$0.358203\pi$
$762$	1.37866e6	0.0860142
$763$	−200392.	−0.0124615
$764$	6.28003e6	0.389249
$765$	−3.14436e6	−0.194258
$766$	−535761.	−0.0329913
$767$	−5.97960e6	−0.367015
$768$	−4.48579e6	−0.274433
$769$	−6.43976e6	−0.392693	−0.196347	−	0.980535i	$-0.562908\pi$
$769$	−6.43976e6	−0.392693	−0.196347	+	0.980535i	$0.562908\pi$
$770$	−8676.60	−0.000527379 0
$771$	6.36461e6	0.385599
$772$	6.29666e6	0.380248
$773$	−822426.	−0.0495049	−0.0247525	−	0.999694i	$-0.507880\pi$
$773$	−822426.	−0.0495049	−0.0247525	+	0.999694i	$0.507880\pi$
$774$	−446424.	−0.0267852
$775$	1.45696e6	0.0871354
$776$	−3.77776e6	−0.225206
$777$	−83790.2	−0.00497899
$778$	−6.62247e6	−0.392257
$779$	−9.13374e6	−0.539268
$780$	−2.92237e6	−0.171988
$781$	−4.29242e6	−0.251811
$782$	−8.46879e6	−0.495227
$783$	−3.03407e6	−0.176857
$784$	−1.43060e7	−0.831246
$785$	−4.94218e6	−0.286249
$786$	2.87886e6	0.166213
$787$	1.49062e7	0.857886	0.428943	−	0.903332i	$-0.358886\pi$
$787$	1.49062e7	0.857886	0.428943	+	0.903332i	$0.358886\pi$
$788$	2.53422e7	1.45388
$789$	1.30459e7	0.746074
$790$	2.50758e6	0.142951
$791$	−308973.	−0.0175582
$792$	−617847.	−0.0350000
$793$	8.20476e6	0.463322
$794$	2.89462e6	0.162945
$795$	3.88681e6	0.218110
$796$	−2.53146e7	−1.41608
$797$	3.22338e7	1.79749	0.898744	−	0.438474i	$-0.144481\pi$
$797$	3.22338e7	1.79749	0.898744	+	0.438474i	$0.144481\pi$
$798$	−59480.8	−0.00330651
$799$	−1.04108e7	−0.576925
$800$	−8.51624e6	−0.470460
$801$	6.12870e6	0.337510
$802$	−3.39503e6	−0.186384
$803$	−6.86364e6	−0.375635
$804$	1.02939e7	0.561619
$805$	343874.	0.0187030
$806$	−317663.	−0.0172238
$807$	−5.57971e6	−0.301598
$808$	4.30947e6	0.232218
$809$	−4.38412e6	−0.235511	−0.117756	−	0.993043i	$-0.537570\pi$
$809$	−4.38412e6	−0.235511	−0.117756	+	0.993043i	$0.537570\pi$
$810$	−267934.	−0.0143488
$811$	1.28188e7	0.684379	0.342190	−	0.939631i	$-0.388831\pi$
$811$	1.28188e7	0.684379	0.342190	+	0.939631i	$0.388831\pi$
$812$	−294295.	−0.0156636
$813$	−1.88798e7	−1.00178
$814$	487351.	0.0257799
$815$	−1.06642e7	−0.562384
$816$	−9.86006e6	−0.518387
$817$	−8.48215e6	−0.444581
$818$	1.63399e6	0.0853821
$819$	67731.4	0.00352842
$820$	−3.99075e6	−0.207262
$821$	−2.01921e7	−1.04550	−0.522749	−	0.852487i	$-0.675093\pi$
$821$	−2.01921e7	−1.04550	−0.522749	+	0.852487i	$0.675093\pi$
$822$	−1.92352e6	−0.0992925
$823$	2.68387e7	1.38122	0.690608	−	0.723230i	$-0.257343\pi$
$823$	2.68387e7	1.38122	0.690608	+	0.723230i	$0.257343\pi$
$824$	892723.	0.0458035
$825$	1.80684e6	0.0924241
$826$	−53176.6	−0.00271188
$827$	−3.43809e6	−0.174805	−0.0874024	−	0.996173i	$-0.527857\pi$
$827$	−3.43809e6	−0.174805	−0.0874024	+	0.996173i	$0.527857\pi$
$828$	1.18826e7	0.602329
$829$	2.43596e7	1.23107	0.615537	−	0.788108i	$-0.288939\pi$
$829$	2.43596e7	1.23107	0.615537	+	0.788108i	$0.288939\pi$
$830$	−259988.	−0.0130996
$831$	−1.42372e7	−0.715190
$832$	−7.86368e6	−0.393838
$833$	−2.16179e7	−1.07945
$834$	−2.91906e6	−0.145321
$835$	6.74513e6	0.334791
$836$	−5.69663e6	−0.281905
$837$	479570.	0.0236613
$838$	−8.57575e6	−0.421854
$839$	3.60992e6	0.177048	0.0885242	−	0.996074i	$-0.471785\pi$
$839$	3.60992e6	0.177048	0.0885242	+	0.996074i	$0.471785\pi$
$840$	−53555.6	−0.00261883
$841$	−3.18919e6	−0.155486
$842$	2.81299e6	0.136738
$843$	9.09128e6	0.440612
$844$	4.02642e6	0.194564
$845$	7.36221e6	0.354704
$846$	−887118.	−0.0426143
$847$	−358228.	−0.0171574
$848$	1.21882e7	0.582038
$849$	8.71389e6	0.414899
$850$	−3.85714e6	−0.183113
$851$	−1.93149e7	−0.914256
$852$	−1.28569e7	−0.606788
$853$	−9.94502e6	−0.467986	−0.233993	−	0.972238i	$-0.575179\pi$
$853$	−9.94502e6	−0.467986	−0.233993	+	0.972238i	$0.575179\pi$
$854$	72964.9	0.00342349
$855$	−5.09080e6	−0.238161
$856$	−5.89298e6	−0.274885
$857$	2.43866e7	1.13422	0.567112	−	0.823641i	$-0.308061\pi$
$857$	2.43866e7	1.13422	0.567112	+	0.823641i	$0.308061\pi$
$858$	−393948.	−0.0182692
$859$	−3.82010e6	−0.176641	−0.0883206	−	0.996092i	$-0.528150\pi$
$859$	−3.82010e6	−0.176641	−0.0883206	+	0.996092i	$0.528150\pi$
$860$	−3.70606e6	−0.170870
$861$	92493.3	0.00425209
$862$	−7.39143e6	−0.338813
$863$	−3.42036e7	−1.56331	−0.781655	−	0.623711i	$-0.785624\pi$
$863$	−3.42036e7	−1.56331	−0.781655	+	0.623711i	$0.785624\pi$
$864$	−2.80318e6	−0.127752
$865$	−2.20936e6	−0.100398
$866$	−5.91451e6	−0.267993
$867$	−2.12087e6	−0.0958223
$868$	46516.7	0.00209560
$869$	−5.56610e6	−0.250035
$870$	1.52967e6	0.0685173
$871$	1.35257e7	0.604109
$872$	7.19423e6	0.320401
$873$	3.63644e6	0.161488
$874$	−1.37112e7	−0.607151
$875$	377608.	0.0166733
$876$	−2.05584e7	−0.905166
$877$	3.99684e7	1.75476	0.877381	−	0.479795i	$-0.159289\pi$
$877$	3.99684e7	1.75476	0.877381	+	0.479795i	$0.159289\pi$
$878$	3.52686e6	0.154402
$879$	−1.52617e7	−0.666242
$880$	−2.32866e6	−0.101368
$881$	1.01815e7	0.441949	0.220975	−	0.975280i	$-0.429076\pi$
$881$	1.01815e7	0.441949	0.220975	+	0.975280i	$0.429076\pi$
$882$	−1.84208e6	−0.0797329
$883$	−5.36748e6	−0.231669	−0.115835	−	0.993269i	$-0.536954\pi$
$883$	−5.36748e6	−0.231669	−0.115835	+	0.993269i	$0.536954\pi$
$884$	−1.38477e7	−0.596000
$885$	−4.55124e6	−0.195331
$886$	9.94734e6	0.425719
$887$	−4.52840e7	−1.93257	−0.966287	−	0.257468i	$-0.917112\pi$
$887$	−4.52840e7	−1.93257	−0.966287	+	0.257468i	$0.917112\pi$
$888$	3.00813e6	0.128016
$889$	−265264.	−0.0112570
$890$	−3.08987e6	−0.130757
$891$	594735.	0.0250974
$892$	−8.51014e6	−0.358117
$893$	−1.68554e7	−0.707312
$894$	2.93221e6	0.122702
$895$	1.77484e7	0.740631
$896$	−358343.	−0.0149118
$897$	1.56131e7	0.647899
$898$	4.45542e6	0.184373
$899$	−2.73794e6	−0.112986
$900$	5.41195e6	0.222714
$901$	1.84177e7	0.755829
$902$	−537971.	−0.0220162
$903$	85894.9	0.00350549
$904$	1.10923e7	0.451442
$905$	−1.02406e7	−0.415625
$906$	2.05917e6	0.0833434
$907$	−2.81873e7	−1.13772	−0.568859	−	0.822435i	$-0.692615\pi$
$907$	−2.81873e7	−1.13772	−0.568859	+	0.822435i	$0.692615\pi$
$908$	3.15718e7	1.27082
$909$	−4.14827e6	−0.166517
$910$	−34147.8	−0.00136697
$911$	−4.00124e7	−1.59735	−0.798673	−	0.601766i	$-0.794464\pi$
$911$	−4.00124e7	−1.59735	−0.798673	+	0.601766i	$0.794464\pi$
$912$	−1.59637e7	−0.635545
$913$	577098.	0.0229125
$914$	6.73386e6	0.266623
$915$	6.24487e6	0.246587
$916$	8.78373e6	0.345892
$917$	−553912.	−0.0217529
$918$	−1.26961e6	−0.0497236
$919$	1.72054e7	0.672011	0.336005	−	0.941860i	$-0.390924\pi$
$919$	1.72054e7	0.672011	0.336005	+	0.941860i	$0.390924\pi$
$920$	−1.23453e7	−0.480876
$921$	−1.67477e7	−0.650590
$922$	−8.24561e6	−0.319445
$923$	−1.68933e7	−0.652695
$924$	57687.3	0.00222280
$925$	−8.79703e6	−0.338051
$926$	−9.99222e6	−0.382943
$927$	−859329.	−0.0328443
$928$	1.60038e7	0.610032
$929$	2.40182e7	0.913064	0.456532	−	0.889707i	$-0.349091\pi$
$929$	2.40182e7	0.913064	0.456532	+	0.889707i	$0.349091\pi$
$930$	−241782.	−0.00916679
$931$	−3.50000e7	−1.32341
$932$	−4.45560e6	−0.168022
$933$	8.06749e6	0.303413
$934$	−8.06834e6	−0.302633
$935$	−3.51885e6	−0.131635
$936$	−2.43161e6	−0.0907202
$937$	−3.98189e7	−1.48163	−0.740817	−	0.671707i	$-0.765561\pi$
$937$	−3.98189e7	−1.48163	−0.740817	+	0.671707i	$0.765561\pi$
$938$	120284.	0.00446377
$939$	1.65187e7	0.611380
$940$	−7.36455e6	−0.271848
$941$	−4.11598e7	−1.51530	−0.757651	−	0.652660i	$-0.773653\pi$
$941$	−4.11598e7	−1.51530	−0.757651	+	0.652660i	$0.773653\pi$
$942$	−1.99552e6	−0.0732704
$943$	2.13211e7	0.780781
$944$	−1.42717e7	−0.521251
$945$	51552.3	0.00187788
$946$	−499592.	−0.0181505
$947$	5.82775e6	0.211167	0.105583	−	0.994410i	$-0.466329\pi$
$947$	5.82775e6	0.211167	0.105583	+	0.994410i	$0.466329\pi$
$948$	−1.66719e7	−0.602509
$949$	−2.70127e7	−0.973648
$950$	−6.24482e6	−0.224497
$951$	2.48687e7	0.891666
$952$	−253774.	−0.00907516
$953$	2.20401e7	0.786105	0.393052	−	0.919516i	$-0.371419\pi$
$953$	2.20401e7	0.786105	0.393052	+	0.919516i	$0.371419\pi$
$954$	1.56939e6	0.0558290
$955$	6.28055e6	0.222838
$956$	−7.37502e6	−0.260987
$957$	−3.39543e6	−0.119844
$958$	−34782.8	−0.00122448
$959$	370098.	0.0129948
$960$	−5.98526e6	−0.209607
$961$	−2.81964e7	−0.984884
$962$	1.91803e6	0.0668216
$963$	5.67255e6	0.197112
$964$	−2.63397e7	−0.912888
$965$	6.29719e6	0.217685
$966$	138847.	0.00478734
$967$	−2.58949e7	−0.890530	−0.445265	−	0.895399i	$-0.646891\pi$
$967$	−2.58949e7	−0.890530	−0.445265	+	0.895399i	$0.646891\pi$
$968$	1.28606e7	0.441138
$969$	−2.41228e7	−0.825313
$970$	−1.83337e6	−0.0625633
$971$	−4.12561e6	−0.140424	−0.0702119	−	0.997532i	$-0.522368\pi$
$971$	−4.12561e6	−0.140424	−0.0702119	+	0.997532i	$0.522368\pi$
$972$	1.78138e6	0.0604772
$973$	561648.	0.0190187
$974$	3.24027e6	0.109442
$975$	7.11104e6	0.239564
$976$	1.95826e7	0.658031
$977$	2.28958e7	0.767397	0.383698	−	0.923459i	$-0.374650\pi$
$977$	2.28958e7	0.767397	0.383698	+	0.923459i	$0.374650\pi$
$978$	−4.30591e6	−0.143952
$979$	6.85863e6	0.228707
$980$	−1.52924e7	−0.508638
$981$	−6.92512e6	−0.229750
$982$	1.08462e6	0.0358920
$983$	3.10291e7	1.02420	0.512101	−	0.858926i	$-0.328868\pi$
$983$	3.10291e7	1.02420	0.512101	+	0.858926i	$0.328868\pi$
$984$	−3.32058e6	−0.109327
$985$	2.53443e7	0.832318
$986$	7.24837e6	0.237437
$987$	170687.	0.00557710
$988$	−2.24198e7	−0.730699
$989$	1.98000e7	0.643688
$990$	−299844.	−0.00972317
$991$	−3.93332e7	−1.27226	−0.636129	−	0.771582i	$-0.719466\pi$
$991$	−3.93332e7	−1.27226	−0.636129	+	0.771582i	$0.719466\pi$
$992$	−2.52958e6	−0.0816149
$993$	2.95388e7	0.950649
$994$	−150232.	−0.00482278
$995$	−2.53167e7	−0.810681
$996$	1.72856e6	0.0552122
$997$	3.50353e7	1.11627	0.558133	−	0.829751i	$-0.311518\pi$
$997$	3.50353e7	1.11627	0.558133	+	0.829751i	$0.311518\pi$
$998$	−6.00765e6	−0.190932
$999$	−2.89561e6	−0.0917964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.c.1.13	✓	22
3.2	odd	2		927.6.a.d.1.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.c.1.13	✓	22	1.1	even	1	trivial
927.6.a.d.1.10		22	3.2	odd	2

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:	\( N \)	\(=\)	\( 309 = 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	309.a (trivial)

\(f(q)\)	\(=\)	\(q+1.35356 q^{2} -9.00000 q^{3} -30.1679 q^{4} -30.1704 q^{5} -12.1820 q^{6} +2.34390 q^{7} -84.1477 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+1.35356 q^{2} -9.00000 q^{3} -30.1679 q^{4} -30.1704 q^{5} -12.1820 q^{6} +2.34390 q^{7} -84.1477 q^{8} +81.0000 q^{9} -40.8373 q^{10} +90.6470 q^{11} +271.511 q^{12} +356.752 q^{13} +3.17260 q^{14} +271.534 q^{15} +851.474 q^{16} +1286.67 q^{17} +109.638 q^{18} +2083.15 q^{19} +910.178 q^{20} -21.0951 q^{21} +122.696 q^{22} -4862.73 q^{23} +757.329 q^{24} -2214.75 q^{25} +482.884 q^{26} -729.000 q^{27} -70.7105 q^{28} +4161.97 q^{29} +367.536 q^{30} -657.847 q^{31} +3845.24 q^{32} -815.823 q^{33} +1741.57 q^{34} -70.7164 q^{35} -2443.60 q^{36} +3972.03 q^{37} +2819.65 q^{38} -3210.77 q^{39} +2538.77 q^{40} -4384.59 q^{41} -28.5534 q^{42} -4071.80 q^{43} -2734.63 q^{44} -2443.80 q^{45} -6581.97 q^{46} -8091.34 q^{47} -7663.27 q^{48} -16801.5 q^{49} -2997.78 q^{50} -11580.0 q^{51} -10762.5 q^{52} +14314.3 q^{53} -986.742 q^{54} -2734.86 q^{55} -197.234 q^{56} -18748.3 q^{57} +5633.45 q^{58} -16761.2 q^{59} -8191.60 q^{60} +22998.5 q^{61} -890.432 q^{62} +189.856 q^{63} -22042.4 q^{64} -10763.4 q^{65} -1104.26 q^{66} +37913.5 q^{67} -38816.0 q^{68} +43764.5 q^{69} -95.7186 q^{70} -47353.1 q^{71} -6815.96 q^{72} -75718.3 q^{73} +5376.36 q^{74} +19932.7 q^{75} -62844.1 q^{76} +212.468 q^{77} -4345.95 q^{78} -61404.1 q^{79} -25689.3 q^{80} +6561.00 q^{81} -5934.78 q^{82} +6366.43 q^{83} +636.394 q^{84} -38819.2 q^{85} -5511.40 q^{86} -37457.7 q^{87} -7627.74 q^{88} +75663.0 q^{89} -3307.82 q^{90} +836.191 q^{91} +146698. q^{92} +5920.62 q^{93} -10952.1 q^{94} -62849.4 q^{95} -34607.2 q^{96} +44894.4 q^{97} -22741.8 q^{98} +7342.41 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9}+O(q^{10}) \) 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9	\( 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9} - 355 q^{10} - 708 q^{11} - 3078 q^{12} - 133 q^{13} - 2748 q^{14} + 477 q^{15} + 3678 q^{16} - 2006 q^{17} - 648 q^{18} - 4788 q^{19} - 2785 q^{20} - 90 q^{21} + 3609 q^{22} - 5695 q^{23} + 2376 q^{24} + 18477 q^{25} + 2432 q^{26} - 16038 q^{27} + 7635 q^{28} - 978 q^{29} + 3195 q^{30} - 6009 q^{31} + 22809 q^{32} + 6372 q^{33} - 4078 q^{34} - 22822 q^{35} + 27702 q^{36} + 13640 q^{37} - 5454 q^{38} + 1197 q^{39} - 13351 q^{40} - 24618 q^{41} + 24732 q^{42} + 1257 q^{43} - 65465 q^{44} - 4293 q^{45} - 6175 q^{46} - 63834 q^{47} - 33102 q^{48} + 18022 q^{49} - 41643 q^{50} + 18054 q^{51} - 40853 q^{52} - 13316 q^{53} + 5832 q^{54} - 35934 q^{55} - 251195 q^{56} + 43092 q^{57} - 103895 q^{58} - 138587 q^{59} + 25065 q^{60} - 53985 q^{61} - 218186 q^{62} + 810 q^{63} + 23758 q^{64} - 114073 q^{65} - 32481 q^{66} - 102785 q^{67} - 338669 q^{68} + 51255 q^{69} - 104184 q^{70} - 108740 q^{71} - 21384 q^{72} + 69762 q^{73} - 221377 q^{74} - 166293 q^{75} - 223267 q^{76} - 140360 q^{77} - 21888 q^{78} - 238938 q^{79} - 864251 q^{80} + 144342 q^{81} - 660293 q^{82} - 305455 q^{83} - 68715 q^{84} - 201204 q^{85} - 794679 q^{86} + 8802 q^{87} - 420823 q^{88} - 438448 q^{89} - 28755 q^{90} - 294186 q^{91} - 1251930 q^{92} + 54081 q^{93} - 826416 q^{94} - 652572 q^{95} - 205281 q^{96} - 284729 q^{97} - 887529 q^{98} - 57348 q^{99}+O(q^{100}) \) 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9 - 355 * q^10 - 708 * q^11 - 3078 * q^12 - 133 * q^13 - 2748 * q^14 + 477 * q^15 + 3678 * q^16 - 2006 * q^17 - 648 * q^18 - 4788 * q^19 - 2785 * q^20 - 90 * q^21 + 3609 * q^22 - 5695 * q^23 + 2376 * q^24 + 18477 * q^25 + 2432 * q^26 - 16038 * q^27 + 7635 * q^28 - 978 * q^29 + 3195 * q^30 - 6009 * q^31 + 22809 * q^32 + 6372 * q^33 - 4078 * q^34 - 22822 * q^35 + 27702 * q^36 + 13640 * q^37 - 5454 * q^38 + 1197 * q^39 - 13351 * q^40 - 24618 * q^41 + 24732 * q^42 + 1257 * q^43 - 65465 * q^44 - 4293 * q^45 - 6175 * q^46 - 63834 * q^47 - 33102 * q^48 + 18022 * q^49 - 41643 * q^50 + 18054 * q^51 - 40853 * q^52 - 13316 * q^53 + 5832 * q^54 - 35934 * q^55 - 251195 * q^56 + 43092 * q^57 - 103895 * q^58 - 138587 * q^59 + 25065 * q^60 - 53985 * q^61 - 218186 * q^62 + 810 * q^63 + 23758 * q^64 - 114073 * q^65 - 32481 * q^66 - 102785 * q^67 - 338669 * q^68 + 51255 * q^69 - 104184 * q^70 - 108740 * q^71 - 21384 * q^72 + 69762 * q^73 - 221377 * q^74 - 166293 * q^75 - 223267 * q^76 - 140360 * q^77 - 21888 * q^78 - 238938 * q^79 - 864251 * q^80 + 144342 * q^81 - 660293 * q^82 - 305455 * q^83 - 68715 * q^84 - 201204 * q^85 - 794679 * q^86 + 8802 * q^87 - 420823 * q^88 - 438448 * q^89 - 28755 * q^90 - 294186 * q^91 - 1251930 * q^92 + 54081 * q^93 - 826416 * q^94 - 652572 * q^95 - 205281 * q^96 - 284729 * q^97 - 887529 * q^98 - 57348 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more