LMFDB - Embedded newform 309.6.a.b.1.5

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:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 475 x^{18} + 1732 x^{17} + 94501 x^{16} - 304042 x^{15} - 10274267 x^{14} + \cdots - 108537388253184 $ x^20 - 4x^19 - 475x^18 + 1732x^17 + 94501x^16 - 304042x^15 - 10274267x^14 + 27738506x^13 + 668854800x^12 - 1394251104x^11 - 26886918880x^10 + 36931823776x^9 + 663067133248x^8 - 391924258816x^7 - 9543181747968x^6 - 2051078115840x^5 + 69736119883776x^4 + 68811719589888x^3 - 164566613229568x^2 - 286519559659520*x - 108537388253184
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-6.26481$ of defining polynomial
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)

$f(q)$	$=$	$q-6.26481 q^{2} -9.00000 q^{3} +7.24778 q^{4} +1.70135 q^{5} +56.3832 q^{6} +91.2954 q^{7} +155.068 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-6.26481 q^{2} -9.00000 q^{3} +7.24778 q^{4} +1.70135 q^{5} +56.3832 q^{6} +91.2954 q^{7} +155.068 q^{8} +81.0000 q^{9} -10.6586 q^{10} -101.256 q^{11} -65.2300 q^{12} +544.224 q^{13} -571.948 q^{14} -15.3121 q^{15} -1203.40 q^{16} +2165.29 q^{17} -507.449 q^{18} +2325.47 q^{19} +12.3310 q^{20} -821.658 q^{21} +634.348 q^{22} +851.789 q^{23} -1395.61 q^{24} -3122.11 q^{25} -3409.46 q^{26} -729.000 q^{27} +661.689 q^{28} -2055.46 q^{29} +95.9276 q^{30} -6499.37 q^{31} +2576.89 q^{32} +911.302 q^{33} -13565.1 q^{34} +155.325 q^{35} +587.070 q^{36} +3665.19 q^{37} -14568.6 q^{38} -4898.02 q^{39} +263.825 q^{40} -1525.44 q^{41} +5147.53 q^{42} +12218.6 q^{43} -733.880 q^{44} +137.809 q^{45} -5336.29 q^{46} +7056.11 q^{47} +10830.6 q^{48} -8472.16 q^{49} +19559.4 q^{50} -19487.6 q^{51} +3944.42 q^{52} +4055.77 q^{53} +4567.04 q^{54} -172.271 q^{55} +14157.0 q^{56} -20929.2 q^{57} +12877.0 q^{58} -40388.9 q^{59} -110.979 q^{60} -23962.7 q^{61} +40717.3 q^{62} +7394.92 q^{63} +22365.1 q^{64} +925.916 q^{65} -5709.13 q^{66} -28613.5 q^{67} +15693.5 q^{68} -7666.10 q^{69} -973.083 q^{70} +55223.9 q^{71} +12560.5 q^{72} +63334.2 q^{73} -22961.7 q^{74} +28098.9 q^{75} +16854.5 q^{76} -9244.18 q^{77} +30685.1 q^{78} -28230.6 q^{79} -2047.40 q^{80} +6561.00 q^{81} +9556.61 q^{82} +88528.0 q^{83} -5955.20 q^{84} +3683.91 q^{85} -76546.9 q^{86} +18499.1 q^{87} -15701.5 q^{88} +29113.2 q^{89} -863.349 q^{90} +49685.2 q^{91} +6173.58 q^{92} +58494.3 q^{93} -44205.2 q^{94} +3956.43 q^{95} -23192.0 q^{96} -45891.2 q^{97} +53076.4 q^{98} -8201.72 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9}+O(q^{10}) $ 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9} + 445 q^{10} + 1712 q^{11} - 2934 q^{12} - 809 q^{13} + 388 q^{14} - 873 q^{15} + 3934 q^{16} + 2040 q^{17} + 324 q^{18} + 5320 q^{19} + 4415 q^{20} - 90 q^{21} + 705 q^{22} + 653 q^{23} - 2808 q^{24} + 5977 q^{25} - 1655 q^{26} - 14580 q^{27} - 9206 q^{28} - 706 q^{29} - 4005 q^{30} + 9091 q^{31} - 16762 q^{32} - 15408 q^{33} - 17698 q^{34} + 15988 q^{35} + 26406 q^{36} - 50 q^{37} + 3877 q^{38} + 7281 q^{39} + 30485 q^{40} + 37084 q^{41} - 3492 q^{42} + 2533 q^{43} + 64525 q^{44} + 7857 q^{45} + 13966 q^{46} + 23282 q^{47} - 35406 q^{48} + 32910 q^{49} + 85769 q^{50} - 18360 q^{51} + 58531 q^{52} + 67436 q^{53} - 2916 q^{54} + 27254 q^{55} + 130668 q^{56} - 47880 q^{57} - 26963 q^{58} + 162695 q^{59} - 39735 q^{60} + 44895 q^{61} + 115286 q^{62} + 810 q^{63} + 44238 q^{64} + 64945 q^{65} - 6345 q^{66} - 4127 q^{67} + 231174 q^{68} - 5877 q^{69} + 290034 q^{70} + 140618 q^{71} + 25272 q^{72} - 52974 q^{73} + 558413 q^{74} - 53793 q^{75} + 224357 q^{76} + 210380 q^{77} + 14895 q^{78} + 170742 q^{79} + 760913 q^{80} + 131220 q^{81} + 576206 q^{82} + 239285 q^{83} + 82854 q^{84} + 268116 q^{85} + 776443 q^{86} + 6354 q^{87} + 381839 q^{88} + 408810 q^{89} + 36045 q^{90} + 413782 q^{91} + 645628 q^{92} - 81819 q^{93} + 447752 q^{94} + 568618 q^{95} + 150858 q^{96} + 275859 q^{97} + 768726 q^{98} + 138672 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9 + 445 * q^10 + 1712 * q^11 - 2934 * q^12 - 809 * q^13 + 388 * q^14 - 873 * q^15 + 3934 * q^16 + 2040 * q^17 + 324 * q^18 + 5320 * q^19 + 4415 * q^20 - 90 * q^21 + 705 * q^22 + 653 * q^23 - 2808 * q^24 + 5977 * q^25 - 1655 * q^26 - 14580 * q^27 - 9206 * q^28 - 706 * q^29 - 4005 * q^30 + 9091 * q^31 - 16762 * q^32 - 15408 * q^33 - 17698 * q^34 + 15988 * q^35 + 26406 * q^36 - 50 * q^37 + 3877 * q^38 + 7281 * q^39 + 30485 * q^40 + 37084 * q^41 - 3492 * q^42 + 2533 * q^43 + 64525 * q^44 + 7857 * q^45 + 13966 * q^46 + 23282 * q^47 - 35406 * q^48 + 32910 * q^49 + 85769 * q^50 - 18360 * q^51 + 58531 * q^52 + 67436 * q^53 - 2916 * q^54 + 27254 * q^55 + 130668 * q^56 - 47880 * q^57 - 26963 * q^58 + 162695 * q^59 - 39735 * q^60 + 44895 * q^61 + 115286 * q^62 + 810 * q^63 + 44238 * q^64 + 64945 * q^65 - 6345 * q^66 - 4127 * q^67 + 231174 * q^68 - 5877 * q^69 + 290034 * q^70 + 140618 * q^71 + 25272 * q^72 - 52974 * q^73 + 558413 * q^74 - 53793 * q^75 + 224357 * q^76 + 210380 * q^77 + 14895 * q^78 + 170742 * q^79 + 760913 * q^80 + 131220 * q^81 + 576206 * q^82 + 239285 * q^83 + 82854 * q^84 + 268116 * q^85 + 776443 * q^86 + 6354 * q^87 + 381839 * q^88 + 408810 * q^89 + 36045 * q^90 + 413782 * q^91 + 645628 * q^92 - 81819 * q^93 + 447752 * q^94 + 568618 * q^95 + 150858 * q^96 + 275859 * q^97 + 768726 * q^98 + 138672 * 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 $

$2$	−6.26481	−1.10747	−0.553736	−	0.832692i	$-0.686798\pi$
$2$	−6.26481	−1.10747	−0.553736	+	0.832692i	$0.686798\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	7.24778	0.226493
$5$	1.70135	0.0304347	0.0152173	−	0.999884i	$-0.495156\pi$
$5$	1.70135	0.0304347	0.0152173	+	0.999884i	$0.495156\pi$
$6$	56.3832	0.639399
$7$	91.2954	0.704212	0.352106	−	0.935960i	$-0.385466\pi$
$7$	91.2954	0.704212	0.352106	+	0.935960i	$0.385466\pi$
$8$	155.068	0.856637
$9$	81.0000	0.333333
$10$	−10.6586	−0.0337055
$11$	−101.256	−0.252312	−0.126156	−	0.992010i	$-0.540264\pi$
$11$	−101.256	−0.252312	−0.126156	+	0.992010i	$0.540264\pi$
$12$	−65.2300	−0.130766
$13$	544.224	0.893140	0.446570	−	0.894749i	$-0.352645\pi$
$13$	544.224	0.893140	0.446570	+	0.894749i	$0.352645\pi$
$14$	−571.948	−0.779895
$15$	−15.3121	−0.0175715
$16$	−1203.40	−1.17519
$17$	2165.29	1.81716	0.908580	−	0.417712i	$-0.137168\pi$
$17$	2165.29	1.81716	0.908580	+	0.417712i	$0.137168\pi$
$18$	−507.449	−0.369157
$19$	2325.47	1.47784	0.738918	−	0.673795i	$-0.235337\pi$
$19$	2325.47	1.47784	0.738918	+	0.673795i	$0.235337\pi$
$20$	12.3310	0.00689325
$21$	−821.658	−0.406577
$22$	634.348	0.279428
$23$	851.789	0.335747	0.167874	−	0.985809i	$-0.446310\pi$
$23$	851.789	0.335747	0.167874	+	0.985809i	$0.446310\pi$
$24$	−1395.61	−0.494579
$25$	−3122.11	−0.999074
$26$	−3409.46	−0.989127
$27$	−729.000	−0.192450
$28$	661.689	0.159499
$29$	−2055.46	−0.453851	−0.226926	−	0.973912i	$-0.572867\pi$
$29$	−2055.46	−0.453851	−0.226926	+	0.973912i	$0.572867\pi$
$30$	95.9276	0.0194599
$31$	−6499.37	−1.21469	−0.607347	−	0.794437i	$-0.707766\pi$
$31$	−6499.37	−1.21469	−0.607347	+	0.794437i	$0.707766\pi$
$32$	2576.89	0.444857
$33$	911.302	0.145672
$34$	−13565.1	−2.01245
$35$	155.325	0.0214325
$36$	587.070	0.0754977
$37$	3665.19	0.440141	0.220071	−	0.975484i	$-0.429371\pi$
$37$	3665.19	0.440141	0.220071	+	0.975484i	$0.429371\pi$
$38$	−14568.6	−1.63666
$39$	−4898.02	−0.515655
$40$	263.825	0.0260715
$41$	−1525.44	−0.141722	−0.0708609	−	0.997486i	$-0.522575\pi$
$41$	−1525.44	−0.141722	−0.0708609	+	0.997486i	$0.522575\pi$
$42$	5147.53	0.450273
$43$	12218.6	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$43$	12218.6	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$44$	−733.880	−0.0571470
$45$	137.809	0.0101449
$46$	−5336.29	−0.371830
$47$	7056.11	0.465930	0.232965	−	0.972485i	$-0.425157\pi$
$47$	7056.11	0.465930	0.232965	+	0.972485i	$0.425157\pi$
$48$	10830.6	0.678499
$49$	−8472.16	−0.504085
$50$	19559.4	1.10645
$51$	−19487.6	−1.04914
$52$	3944.42	0.202290
$53$	4055.77	0.198328	0.0991638	−	0.995071i	$-0.468383\pi$
$53$	4055.77	0.198328	0.0991638	+	0.995071i	$0.468383\pi$
$54$	4567.04	0.213133
$55$	−172.271	−0.00767903
$56$	14157.0	0.603254
$57$	−20929.2	−0.853229
$58$	12877.0	0.502627
$59$	−40388.9	−1.51054	−0.755269	−	0.655414i	$-0.772494\pi$
$59$	−40388.9	−1.51054	−0.755269	+	0.655414i	$0.772494\pi$
$60$	−110.979	−0.00397982
$61$	−23962.7	−0.824538	−0.412269	−	0.911062i	$-0.635264\pi$
$61$	−23962.7	−0.824538	−0.412269	+	0.911062i	$0.635264\pi$
$62$	40717.3	1.34524
$63$	7394.92	0.234737
$64$	22365.1	0.682527
$65$	925.916	0.0271824
$66$	−5709.13	−0.161328
$67$	−28613.5	−0.778726	−0.389363	−	0.921084i	$-0.627305\pi$
$67$	−28613.5	−0.778726	−0.389363	+	0.921084i	$0.627305\pi$
$68$	15693.5	0.411574
$69$	−7666.10	−0.193844
$70$	−973.083	−0.0237358
$71$	55223.9	1.30011	0.650057	−	0.759885i	$-0.274745\pi$
$71$	55223.9	1.30011	0.650057	+	0.759885i	$0.274745\pi$
$72$	12560.5	0.285546
$73$	63334.2	1.39101	0.695507	−	0.718519i	$-0.255180\pi$
$73$	63334.2	1.39101	0.695507	+	0.718519i	$0.255180\pi$
$74$	−22961.7	−0.487444
$75$	28098.9	0.576815
$76$	16854.5	0.334720
$77$	−9244.18	−0.177681
$78$	30685.1	0.571073
$79$	−28230.6	−0.508924	−0.254462	−	0.967083i	$-0.581898\pi$
$79$	−28230.6	−0.508924	−0.254462	+	0.967083i	$0.581898\pi$
$80$	−2047.40	−0.0357666
$81$	6561.00	0.111111
$82$	9556.61	0.156953
$83$	88528.0	1.41054	0.705270	−	0.708939i	$-0.250826\pi$
$83$	88528.0	1.41054	0.705270	+	0.708939i	$0.250826\pi$
$84$	−5955.20	−0.0920870
$85$	3683.91	0.0553046
$86$	−76546.9	−1.11604
$87$	18499.1	0.262031
$88$	−15701.5	−0.216140
$89$	29113.2	0.389597	0.194798	−	0.980843i	$-0.437595\pi$
$89$	29113.2	0.389597	0.194798	+	0.980843i	$0.437595\pi$
$90$	−863.349	−0.0112352
$91$	49685.2	0.628960
$92$	6173.58	0.0760444
$93$	58494.3	0.701304
$94$	−44205.2	−0.516004
$95$	3956.43	0.0449775
$96$	−23192.0	−0.256838
$97$	−45891.2	−0.495222	−0.247611	−	0.968860i	$-0.579646\pi$
$97$	−45891.2	−0.495222	−0.247611	+	0.968860i	$0.579646\pi$
$98$	53076.4	0.558260
$99$	−8201.72	−0.0841040
$100$	−22628.3	−0.226283
$101$	160840.	1.56888	0.784441	−	0.620203i	$-0.212950\pi$
$101$	160840.	1.56888	0.784441	+	0.620203i	$0.212950\pi$
$102$	122086.	1.16189
$103$	10609.0	0.0985329
$103$	10609.0	0.0985329
$104$	84391.7	0.765097
$105$	−1397.93	−0.0123740
$106$	−25408.6	−0.219642
$107$	126524.	1.06835	0.534174	−	0.845375i	$-0.320623\pi$
$107$	126524.	1.06835	0.534174	+	0.845375i	$0.320623\pi$
$108$	−5283.63	−0.0435886
$109$	−58584.0	−0.472294	−0.236147	−	0.971717i	$-0.575885\pi$
$109$	−58584.0	−0.472294	−0.236147	+	0.971717i	$0.575885\pi$
$110$	1079.25	0.00850431
$111$	−32986.7	−0.254116
$112$	−109865.	−0.827586
$113$	199695.	1.47120	0.735599	−	0.677417i	$-0.236901\pi$
$113$	199695.	1.47120	0.735599	+	0.677417i	$0.236901\pi$
$114$	131117.	0.944927
$115$	1449.19	0.0102184
$116$	−14897.5	−0.102794
$117$	44082.2	0.297713
$118$	253029.	1.67288
$119$	197681.	1.27967
$120$	−2374.42	−0.0150524
$121$	−150798.	−0.936339
$122$	150121.	0.913152
$123$	13729.0	0.0818231
$124$	−47106.0	−0.275120
$125$	−10628.5	−0.0608411
$126$	−46327.8	−0.259965
$127$	77729.6	0.427639	0.213819	−	0.976873i	$-0.431410\pi$
$127$	77729.6	0.427639	0.213819	+	0.976873i	$0.431410\pi$
$128$	−222573.	−1.20074
$129$	−109967.	−0.581820
$130$	−5800.68	−0.0301038
$131$	146073.	0.743692	0.371846	−	0.928295i	$-0.378725\pi$
$131$	146073.	0.743692	0.371846	+	0.928295i	$0.378725\pi$
$132$	6604.92	0.0329938
$133$	212304.	1.04071
$134$	179258.	0.862417
$135$	−1240.28	−0.00585715
$136$	335766.	1.55665
$137$	−236299.	−1.07563	−0.537813	−	0.843064i	$-0.680749\pi$
$137$	−236299.	−1.07563	−0.537813	+	0.843064i	$0.680749\pi$
$138$	48026.6	0.214676
$139$	−41252.7	−0.181099	−0.0905494	−	0.995892i	$-0.528862\pi$
$139$	−41252.7	−0.181099	−0.0905494	+	0.995892i	$0.528862\pi$
$140$	1125.76	0.00485431
$141$	−63505.0	−0.269005
$142$	−345967.	−1.43984
$143$	−55105.8	−0.225350
$144$	−97475.3	−0.391731
$145$	−3497.05	−0.0138128
$146$	−396777.	−1.54051
$147$	76249.4	0.291034
$148$	26564.5	0.0996890
$149$	−128893.	−0.475624	−0.237812	−	0.971311i	$-0.576430\pi$
$149$	−128893.	−0.475624	−0.237812	+	0.971311i	$0.576430\pi$
$150$	−176034.	−0.638807
$151$	−40827.4	−0.145717	−0.0728583	−	0.997342i	$-0.523212\pi$
$151$	−40827.4	−0.145717	−0.0728583	+	0.997342i	$0.523212\pi$
$152$	360605.	1.26597
$153$	175388.	0.605720
$154$	57913.0	0.196777
$155$	−11057.7	−0.0369688
$156$	−35499.8	−0.116792
$157$	−146039.	−0.472847	−0.236423	−	0.971650i	$-0.575975\pi$
$157$	−146039.	−0.472847	−0.236423	+	0.971650i	$0.575975\pi$
$158$	176859.	0.563619
$159$	−36501.9	−0.114504
$160$	4384.19	0.0135391
$161$	77764.4	0.236437
$162$	−41103.4	−0.123052
$163$	−180218.	−0.531288	−0.265644	−	0.964071i	$-0.585585\pi$
$163$	−180218.	−0.531288	−0.265644	+	0.964071i	$0.585585\pi$
$164$	−11056.1	−0.0320990
$165$	1550.44	0.00443349
$166$	−554610.	−1.56213
$167$	259937.	0.721235	0.360617	−	0.932714i	$-0.382566\pi$
$167$	259937.	0.721235	0.360617	+	0.932714i	$0.382566\pi$
$168$	−127413.	−0.348289
$169$	−75112.9	−0.202301
$170$	−23079.0	−0.0612483
$171$	188363.	0.492612
$172$	88557.5	0.228247
$173$	−171103.	−0.434652	−0.217326	−	0.976099i	$-0.569733\pi$
$173$	−171103.	−0.434652	−0.217326	+	0.976099i	$0.569733\pi$
$174$	−115893.	−0.290192
$175$	−285034.	−0.703560
$176$	121851.	0.296516
$177$	363500.	0.872110
$178$	−182389.	−0.431467
$179$	656747.	1.53202	0.766012	−	0.642826i	$-0.222238\pi$
$179$	656747.	1.53202	0.766012	+	0.642826i	$0.222238\pi$
$180$	998.812	0.00229775
$181$	−422589.	−0.958786	−0.479393	−	0.877600i	$-0.659143\pi$
$181$	−422589.	−0.958786	−0.479393	+	0.877600i	$0.659143\pi$
$182$	−311268.	−0.696556
$183$	215664.	0.476047
$184$	132085.	0.287613
$185$	6235.76	0.0133955
$186$	−366455.	−0.776674
$187$	−219248.	−0.458491
$188$	51141.2	0.105530
$189$	−66554.3	−0.135526
$190$	−24786.3	−0.0498113
$191$	156906.	0.311213	0.155606	−	0.987819i	$-0.450267\pi$
$191$	156906.	0.311213	0.155606	+	0.987819i	$0.450267\pi$
$192$	−201286.	−0.394057
$193$	731181.	1.41297	0.706483	−	0.707730i	$-0.250281\pi$
$193$	731181.	1.41297	0.706483	+	0.707730i	$0.250281\pi$
$194$	287499.	0.548445
$195$	−8333.24	−0.0156938
$196$	−61404.4	−0.114172
$197$	−408293.	−0.749561	−0.374780	−	0.927114i	$-0.622282\pi$
$197$	−408293.	−0.749561	−0.374780	+	0.927114i	$0.622282\pi$
$198$	51382.2	0.0931428
$199$	−246738.	−0.441676	−0.220838	−	0.975310i	$-0.570879\pi$
$199$	−246738.	−0.441676	−0.220838	+	0.975310i	$0.570879\pi$
$200$	−484138.	−0.855843
$201$	257522.	0.449598
$202$	−1.00763e6	−1.73749
$203$	−187654.	−0.319608
$204$	−141242.	−0.237622
$205$	−2595.31	−0.00431325
$206$	−66463.3	−0.109122
$207$	68994.9	0.111916
$208$	−654919.	−1.04961
$209$	−235467.	−0.372876
$210$	8757.75	0.0137039
$211$	−697741.	−1.07892	−0.539459	−	0.842012i	$-0.681371\pi$
$211$	−697741.	−1.07892	−0.539459	+	0.842012i	$0.681371\pi$
$212$	29395.3	0.0449199
$213$	−497015.	−0.750621
$214$	−792647.	−1.18316
$215$	20788.1	0.0306703
$216$	−113044.	−0.164860
$217$	−593362.	−0.855402
$218$	367017.	0.523053
$219$	−570008.	−0.803102
$220$	−1248.59	−0.00173925
$221$	1.17840e6	1.62298
$222$	206655.	0.281426
$223$	1.05522e6	1.42096	0.710480	−	0.703718i	$-0.248478\pi$
$223$	1.05522e6	1.42096	0.710480	+	0.703718i	$0.248478\pi$
$224$	235258.	0.313274
$225$	−252891.	−0.333025
$226$	−1.25105e6	−1.62931
$227$	695825.	0.896263	0.448132	−	0.893968i	$-0.352090\pi$
$227$	695825.	0.896263	0.448132	+	0.893968i	$0.352090\pi$
$228$	−151690.	−0.193251
$229$	−338838.	−0.426976	−0.213488	−	0.976946i	$-0.568482\pi$
$229$	−338838.	−0.426976	−0.213488	+	0.976946i	$0.568482\pi$
$230$	−9078.89	−0.0113165
$231$	83197.6	0.102584
$232$	−318735.	−0.388786
$233$	515106.	0.621595	0.310797	−	0.950476i	$-0.399404\pi$
$233$	515106.	0.621595	0.310797	+	0.950476i	$0.399404\pi$
$234$	−276166.	−0.329709
$235$	12004.9	0.0141804
$236$	−292730.	−0.342127
$237$	254076.	0.293827
$238$	−1.23843e6	−1.41719
$239$	143814.	0.162857	0.0814286	−	0.996679i	$-0.474052\pi$
$239$	143814.	0.162857	0.0814286	+	0.996679i	$0.474052\pi$
$240$	18426.6	0.0206499
$241$	1.02372e6	1.13537	0.567687	−	0.823244i	$-0.307838\pi$
$241$	1.02372e6	1.13537	0.567687	+	0.823244i	$0.307838\pi$
$242$	944722.	1.03697
$243$	−59049.0	−0.0641500
$244$	−173676.	−0.186752
$245$	−14414.1	−0.0153417
$246$	−86009.5	−0.0906167
$247$	1.26558e6	1.31991
$248$	−1.00784e6	−1.04055
$249$	−796752.	−0.814375
$250$	66585.5	0.0673798
$251$	−237003.	−0.237448	−0.118724	−	0.992927i	$-0.537880\pi$
$251$	−237003.	−0.237448	−0.118724	+	0.992927i	$0.537880\pi$
$252$	53596.8	0.0531664
$253$	−86248.5	−0.0847130
$254$	−486961.	−0.473598
$255$	−33155.2	−0.0319301
$256$	678696.	0.647255
$257$	1.59147e6	1.50303	0.751514	−	0.659718i	$-0.229324\pi$
$257$	1.59147e6	1.50303	0.751514	+	0.659718i	$0.229324\pi$
$258$	688922.	0.644349
$259$	334615.	0.309953
$260$	6710.84	0.00615663
$261$	−166492.	−0.151284
$262$	−915121.	−0.823617
$263$	−1.61877e6	−1.44310	−0.721549	−	0.692364i	$-0.756569\pi$
$263$	−1.61877e6	−1.44310	−0.721549	+	0.692364i	$0.756569\pi$
$264$	141314.	0.124788
$265$	6900.28	0.00603603
$266$	−1.33005e6	−1.15256
$267$	−262019.	−0.224934
$268$	−207385.	−0.176376
$269$	−1.00311e6	−0.845216	−0.422608	−	0.906312i	$-0.638885\pi$
$269$	−1.00311e6	−0.845216	−0.422608	+	0.906312i	$0.638885\pi$
$270$	7770.14	0.00648663
$271$	−1.91998e6	−1.58808	−0.794041	−	0.607865i	$-0.792026\pi$
$271$	−1.91998e6	−1.58808	−0.794041	+	0.607865i	$0.792026\pi$
$272$	−2.60570e6	−2.13551
$273$	−447166.	−0.363130
$274$	1.48037e6	1.19123
$275$	316131.	0.252078
$276$	−55562.2	−0.0439043
$277$	1.28876e6	1.00919	0.504595	−	0.863356i	$-0.331642\pi$
$277$	1.28876e6	1.00919	0.504595	+	0.863356i	$0.331642\pi$
$278$	258440.	0.200562
$279$	−526449.	−0.404898
$280$	24086.0	0.0183598
$281$	1.94810e6	1.47179	0.735896	−	0.677095i	$-0.236761\pi$
$281$	1.94810e6	1.47179	0.735896	+	0.677095i	$0.236761\pi$
$282$	397846.	0.297915
$283$	−1.92514e6	−1.42888	−0.714442	−	0.699695i	$-0.753319\pi$
$283$	−1.92514e6	−1.42888	−0.714442	+	0.699695i	$0.753319\pi$
$284$	400251.	0.294467
$285$	−35607.9	−0.0259677
$286$	345227.	0.249569
$287$	−139266.	−0.0998022
$288$	208728.	0.148286
$289$	3.26861e6	2.30207
$290$	21908.4	0.0152973
$291$	413021.	0.285917
$292$	459033.	0.315055
$293$	−2.26844e6	−1.54368	−0.771841	−	0.635816i	$-0.780664\pi$
$293$	−2.26844e6	−1.54368	−0.771841	+	0.635816i	$0.780664\pi$
$294$	−477688.	−0.322311
$295$	−68715.6	−0.0459727
$296$	568353.	0.377041
$297$	73815.5	0.0485575
$298$	807489.	0.526740
$299$	463564.	0.299869
$300$	203655.	0.130645
$301$	1.11550e6	0.709664
$302$	255775.	0.161377
$303$	−1.44756e6	−0.905795
$304$	−2.79846e6	−1.73674
$305$	−40768.9	−0.0250945
$306$	−1.09877e6	−0.670817
$307$	1.17066e6	0.708899	0.354449	−	0.935075i	$-0.384668\pi$
$307$	1.17066e6	0.708899	0.354449	+	0.935075i	$0.384668\pi$
$308$	−66999.8	−0.0402436
$309$	−95481.0	−0.0568880
$310$	69274.3	0.0409419
$311$	−812017.	−0.476063	−0.238031	−	0.971257i	$-0.576502\pi$
$311$	−812017.	−0.476063	−0.238031	+	0.971257i	$0.576502\pi$
$312$	−759525.	−0.441729
$313$	1.33486e6	0.770149	0.385075	−	0.922885i	$-0.374176\pi$
$313$	1.33486e6	0.770149	0.385075	+	0.922885i	$0.374176\pi$
$314$	914907.	0.523664
$315$	12581.4	0.00714416
$316$	−204609.	−0.115268
$317$	2.73769e6	1.53016	0.765078	−	0.643938i	$-0.222700\pi$
$317$	2.73769e6	1.53016	0.765078	+	0.643938i	$0.222700\pi$
$318$	228677.	0.126810
$319$	208127.	0.114512
$320$	38050.8	0.0207725
$321$	−1.13871e6	−0.616811
$322$	−487179.	−0.261848
$323$	5.03530e6	2.68546
$324$	47552.7	0.0251659
$325$	−1.69913e6	−0.892313
$326$	1.12903e6	0.588386
$327$	527256.	0.272679
$328$	−236547.	−0.121404
$329$	644190.	0.328114
$330$	−9713.22	−0.00490997
$331$	1.27288e6	0.638584	0.319292	−	0.947656i	$-0.396555\pi$
$331$	1.27288e6	0.638584	0.319292	+	0.947656i	$0.396555\pi$
$332$	641632.	0.319478
$333$	296880.	0.146714
$334$	−1.62845e6	−0.798747
$335$	−48681.6	−0.0237003
$336$	988783.	0.477807
$337$	157893.	0.0757335	0.0378667	−	0.999283i	$-0.487944\pi$
$337$	157893.	0.0757335	0.0378667	+	0.999283i	$0.487944\pi$
$338$	470568.	0.224043
$339$	−1.79726e6	−0.849397
$340$	26700.2	0.0125261
$341$	658098.	0.306482
$342$	−1.18006e6	−0.545554
$343$	−2.30787e6	−1.05920
$344$	1.89471e6	0.863268
$345$	−13042.7	−0.00589957
$346$	1.07193e6	0.481365
$347$	1.82273e6	0.812640	0.406320	−	0.913731i	$-0.366812\pi$
$347$	1.82273e6	0.812640	0.406320	+	0.913731i	$0.366812\pi$
$348$	134078.	0.0593483
$349$	1.63819e6	0.719946	0.359973	−	0.932963i	$-0.382786\pi$
$349$	1.63819e6	0.719946	0.359973	+	0.932963i	$0.382786\pi$
$350$	1.78568e6	0.779173
$351$	−396740.	−0.171885
$352$	−260925.	−0.112243
$353$	−1.47151e6	−0.628531	−0.314266	−	0.949335i	$-0.601758\pi$
$353$	−1.47151e6	−0.628531	−0.314266	+	0.949335i	$0.601758\pi$
$354$	−2.27726e6	−0.965837
$355$	93955.2	0.0395685
$356$	211006.	0.0882410
$357$	−1.77913e6	−0.738815
$358$	−4.11439e6	−1.69667
$359$	1.93003e6	0.790364	0.395182	−	0.918603i	$-0.370682\pi$
$359$	1.93003e6	0.790364	0.395182	+	0.918603i	$0.370682\pi$
$360$	21369.8	0.00869048
$361$	2.93170e6	1.18400
$362$	2.64744e6	1.06183
$363$	1.35718e6	0.540595
$364$	360107.	0.142455
$365$	107754.	0.0423350
$366$	−1.35109e6	−0.527209
$367$	2.74759e6	1.06485	0.532424	−	0.846478i	$-0.321281\pi$
$367$	2.74759e6	1.06485	0.532424	+	0.846478i	$0.321281\pi$
$368$	−1.02504e6	−0.394568
$369$	−123561.	−0.0472406
$370$	−39065.9	−0.0148352
$371$	370273.	0.139665
$372$	423954.	0.158841
$373$	4.13303e6	1.53814	0.769071	−	0.639163i	$-0.220719\pi$
$373$	4.13303e6	1.53814	0.769071	+	0.639163i	$0.220719\pi$
$374$	1.37354e6	0.507766
$375$	95656.6	0.0351267
$376$	1.09418e6	0.399133
$377$	−1.11863e6	−0.405353
$378$	416950.	0.150091
$379$	4.04096e6	1.44506	0.722530	−	0.691339i	$-0.242979\pi$
$379$	4.04096e6	1.44506	0.722530	+	0.691339i	$0.242979\pi$
$380$	28675.4	0.0101871
$381$	−699567.	−0.246897
$382$	−982988.	−0.344659
$383$	1.07498e6	0.374457	0.187228	−	0.982316i	$-0.440050\pi$
$383$	1.07498e6	0.374457	0.187228	+	0.982316i	$0.440050\pi$
$384$	2.00316e6	0.693246
$385$	−15727.6	−0.00540767
$386$	−4.58071e6	−1.56482
$387$	989704.	0.335914
$388$	−332609.	−0.112164
$389$	148009.	0.0495922	0.0247961	−	0.999693i	$-0.492106\pi$
$389$	148009.	0.0495922	0.0247961	+	0.999693i	$0.492106\pi$
$390$	52206.1	0.0173804
$391$	1.84437e6	0.610106
$392$	−1.31376e6	−0.431818
$393$	−1.31466e6	−0.429371
$394$	2.55788e6	0.830117
$395$	−48030.2	−0.0154889
$396$	−59444.3	−0.0190490
$397$	−1.65802e6	−0.527974	−0.263987	−	0.964526i	$-0.585038\pi$
$397$	−1.65802e6	−0.527974	−0.263987	+	0.964526i	$0.585038\pi$
$398$	1.54577e6	0.489144
$399$	−1.91074e6	−0.600854
$400$	3.75714e6	1.17411
$401$	−3.95357e6	−1.22780	−0.613901	−	0.789383i	$-0.710401\pi$
$401$	−3.95357e6	−1.22780	−0.613901	+	0.789383i	$0.710401\pi$
$402$	−1.61332e6	−0.497916
$403$	−3.53711e6	−1.08489
$404$	1.16573e6	0.355341
$405$	11162.6	0.00338163
$406$	1.17561e6	0.353956
$407$	−371121.	−0.111053
$408$	−3.02190e6	−0.898730
$409$	−1.79839e6	−0.531590	−0.265795	−	0.964030i	$-0.585634\pi$
$409$	−1.79839e6	−0.531590	−0.265795	+	0.964030i	$0.585634\pi$
$410$	16259.1	0.00477681
$411$	2.12669e6	0.621013
$412$	76891.7	0.0223170
$413$	−3.68732e6	−1.06374
$414$	−432239.	−0.123943
$415$	150617.	0.0429293
$416$	1.40241e6	0.397320
$417$	371274.	0.104557
$418$	1.47515e6	0.412949
$419$	2.15955e6	0.600937	0.300468	−	0.953792i	$-0.402857\pi$
$419$	2.15955e6	0.600937	0.300468	+	0.953792i	$0.402857\pi$
$420$	−10131.9	−0.00280264
$421$	6.41303e6	1.76343	0.881714	−	0.471784i	$-0.156390\pi$
$421$	6.41303e6	1.76343	0.881714	+	0.471784i	$0.156390\pi$
$422$	4.37121e6	1.19487
$423$	571545.	0.155310
$424$	628919.	0.169895
$425$	−6.76025e6	−1.81548
$426$	3.11370e6	0.831292
$427$	−2.18768e6	−0.580650
$428$	917017.	0.241974
$429$	495953.	0.130106
$430$	−130233.	−0.0339665
$431$	−1.97099e6	−0.511082	−0.255541	−	0.966798i	$-0.582254\pi$
$431$	−1.97099e6	−0.511082	−0.255541	+	0.966798i	$0.582254\pi$
$432$	877278.	0.226166
$433$	−3.87304e6	−0.992734	−0.496367	−	0.868113i	$-0.665333\pi$
$433$	−3.87304e6	−0.992734	−0.496367	+	0.868113i	$0.665333\pi$
$434$	3.71730e6	0.947334
$435$	31473.5	0.00797483
$436$	−424604.	−0.106971
$437$	1.98081e6	0.496179
$438$	3.57099e6	0.889413
$439$	6.40780e6	1.58689	0.793446	−	0.608640i	$-0.208285\pi$
$439$	6.40780e6	1.58689	0.793446	+	0.608640i	$0.208285\pi$
$440$	−26713.8	−0.00657814
$441$	−686245.	−0.168028
$442$	−7.38245e6	−1.79740
$443$	3.55501e6	0.860659	0.430329	−	0.902672i	$-0.358397\pi$
$443$	3.55501e6	0.860659	0.430329	+	0.902672i	$0.358397\pi$
$444$	−239080.	−0.0575554
$445$	49531.8	0.0118572
$446$	−6.61076e6	−1.57367
$447$	1.16004e6	0.274602
$448$	2.04183e6	0.480644
$449$	−5.56581e6	−1.30290	−0.651452	−	0.758689i	$-0.725840\pi$
$449$	−5.56581e6	−1.30290	−0.651452	+	0.758689i	$0.725840\pi$
$450$	1.58431e6	0.368815
$451$	154460.	0.0357581
$452$	1.44735e6	0.333217
$453$	367446.	0.0841295
$454$	−4.35921e6	−0.992586
$455$	84531.8	0.0191422
$456$	−3.24545e6	−0.730907
$457$	−6.74512e6	−1.51077	−0.755386	−	0.655280i	$-0.772551\pi$
$457$	−6.74512e6	−1.51077	−0.755386	+	0.655280i	$0.772551\pi$
$458$	2.12275e6	0.472864
$459$	−1.57849e6	−0.349712
$460$	10503.4	0.00231439
$461$	−377364.	−0.0827004	−0.0413502	−	0.999145i	$-0.513166\pi$
$461$	−377364.	−0.0827004	−0.0413502	+	0.999145i	$0.513166\pi$
$462$	−521217.	−0.113609
$463$	3.75487e6	0.814035	0.407017	−	0.913420i	$-0.366569\pi$
$463$	3.75487e6	0.814035	0.407017	+	0.913420i	$0.366569\pi$
$464$	2.47354e6	0.533363
$465$	99519.2	0.0213439
$466$	−3.22704e6	−0.688398
$467$	1.36686e6	0.290023	0.145012	−	0.989430i	$-0.453678\pi$
$467$	1.36686e6	0.290023	0.145012	+	0.989430i	$0.453678\pi$
$468$	319498.	0.0674301
$469$	−2.61228e6	−0.548388
$470$	−75208.4	−0.0157044
$471$	1.31435e6	0.272998
$472$	−6.26302e6	−1.29398
$473$	−1.23720e6	−0.254265
$474$	−1.59173e6	−0.325405
$475$	−7.26036e6	−1.47647
$476$	1.43275e6	0.289836
$477$	328517.	0.0661092
$478$	−900968.	−0.180360
$479$	3.34958e6	0.667039	0.333520	−	0.942743i	$-0.391764\pi$
$479$	3.34958e6	0.667039	0.333520	+	0.942743i	$0.391764\pi$
$480$	−39457.7	−0.00781679
$481$	1.99468e6	0.393108
$482$	−6.41341e6	−1.25739
$483$	−699879.	−0.136507
$484$	−1.09295e6	−0.212074
$485$	−78077.0	−0.0150719
$486$	369930.	0.0710443
$487$	−1.90202e6	−0.363407	−0.181704	−	0.983353i	$-0.558161\pi$
$487$	−1.90202e6	−0.363407	−0.181704	+	0.983353i	$0.558161\pi$
$488$	−3.71584e6	−0.706330
$489$	1.62196e6	0.306739
$490$	90301.5	0.0169905
$491$	5.80845e6	1.08732	0.543659	−	0.839306i	$-0.317039\pi$
$491$	5.80845e6	1.08732	0.543659	+	0.839306i	$0.317039\pi$
$492$	99504.8	0.0185324
$493$	−4.45065e6	−0.824720
$494$	−7.92859e6	−1.46177
$495$	−13954.0	−0.00255968
$496$	7.82133e6	1.42750
$497$	5.04169e6	0.915556
$498$	4.99149e6	0.901898
$499$	1.01136e7	1.81826	0.909128	−	0.416517i	$-0.136750\pi$
$499$	1.01136e7	1.81826	0.909128	+	0.416517i	$0.136750\pi$
$500$	−77033.1	−0.0137801
$501$	−2.33943e6	−0.416405
$502$	1.48477e6	0.262967
$503$	−4.96453e6	−0.874899	−0.437449	−	0.899243i	$-0.644118\pi$
$503$	−4.96453e6	−0.874899	−0.437449	+	0.899243i	$0.644118\pi$
$504$	1.14671e6	0.201085
$505$	273645.	0.0477484
$506$	540330.	0.0938173
$507$	676016.	0.116798
$508$	563367.	0.0968573
$509$	9.22436e6	1.57813	0.789063	−	0.614312i	$-0.210566\pi$
$509$	9.22436e6	1.57813	0.789063	+	0.614312i	$0.210566\pi$
$510$	207711.	0.0353617
$511$	5.78212e6	0.979569
$512$	2.87045e6	0.483921
$513$	−1.69527e6	−0.284410
$514$	−9.97028e6	−1.66456
$515$	18049.6	0.00299882
$516$	−797018.	−0.131778
$517$	−714472.	−0.117560
$518$	−2.09630e6	−0.343264
$519$	1.53993e6	0.250947
$520$	143580.	0.0232855
$521$	3.85258e6	0.621810	0.310905	−	0.950441i	$-0.399368\pi$
$521$	3.85258e6	0.621810	0.310905	+	0.950441i	$0.399368\pi$
$522$	1.04304e6	0.167542
$523$	539315.	0.0862161	0.0431081	−	0.999070i	$-0.486274\pi$
$523$	539315.	0.0862161	0.0431081	+	0.999070i	$0.486274\pi$
$524$	1.05871e6	0.168441
$525$	2.56530e6	0.406201
$526$	1.01413e7	1.59819
$527$	−1.40730e7	−2.20729
$528$	−1.09666e6	−0.171193
$529$	−5.71080e6	−0.887274
$530$	−43228.9	−0.00668474
$531$	−3.27150e6	−0.503513
$532$	1.53874e6	0.235714
$533$	−830183.	−0.126577
$534$	1.64150e6	0.249108
$535$	215261.	0.0325148
$536$	−4.43704e6	−0.667085
$537$	−5.91072e6	−0.884515
$538$	6.28429e6	0.936053
$539$	857855.	0.127187
$540$	−8989.31	−0.00132661
$541$	−1.08409e7	−1.59248	−0.796240	−	0.604981i	$-0.793181\pi$
$541$	−1.08409e7	−1.59248	−0.796240	+	0.604981i	$0.793181\pi$
$542$	1.20283e7	1.75875
$543$	3.80330e6	0.553556
$544$	5.57970e6	0.808376
$545$	−99671.9	−0.0143741
$546$	2.80141e6	0.402157
$547$	−528142.	−0.0754713	−0.0377357	−	0.999288i	$-0.512014\pi$
$547$	−528142.	−0.0754713	−0.0377357	+	0.999288i	$0.512014\pi$
$548$	−1.71265e6	−0.243622
$549$	−1.94098e6	−0.274846
$550$	−1.98050e6	−0.279170
$551$	−4.77990e6	−0.670718
$552$	−1.18877e6	−0.166054
$553$	−2.57733e6	−0.358391
$554$	−8.07384e6	−1.11765
$555$	−56121.9	−0.00773392
$556$	−298991.	−0.0410176
$557$	8.30871e6	1.13474	0.567369	−	0.823464i	$-0.307961\pi$
$557$	8.30871e6	1.13474	0.567369	+	0.823464i	$0.307961\pi$
$558$	3.29810e6	0.448413
$559$	6.64964e6	0.900054
$560$	−186918.	−0.0251873
$561$	1.97323e6	0.264710
$562$	−1.22045e7	−1.62997
$563$	−3.37931e6	−0.449322	−0.224661	−	0.974437i	$-0.572127\pi$
$563$	−3.37931e6	−0.449322	−0.224661	+	0.974437i	$0.572127\pi$
$564$	−460270.	−0.0609278
$565$	339751.	0.0447755
$566$	1.20606e7	1.58245
$567$	598989.	0.0782458
$568$	8.56345e6	1.11373
$569$	−2.18697e6	−0.283180	−0.141590	−	0.989925i	$-0.545221\pi$
$569$	−2.18697e6	−0.283180	−0.141590	+	0.989925i	$0.545221\pi$
$570$	223077.	0.0287585
$571$	1.07274e7	1.37690	0.688451	−	0.725283i	$-0.258291\pi$
$571$	1.07274e7	1.37690	0.688451	+	0.725283i	$0.258291\pi$
$572$	−399395.	−0.0510402
$573$	−1.41216e6	−0.179679
$574$	872474.	0.110528
$575$	−2.65937e6	−0.335436
$576$	1.81157e6	0.227509
$577$	4.80586e6	0.600941	0.300470	−	0.953791i	$-0.402856\pi$
$577$	4.80586e6	0.600941	0.300470	+	0.953791i	$0.402856\pi$
$578$	−2.04772e7	−2.54947
$579$	−6.58063e6	−0.815777
$580$	−25345.9	−0.00312851
$581$	8.08219e6	0.993319
$582$	−2.58750e6	−0.316645
$583$	−410670.	−0.0500405
$584$	9.82110e6	1.19159
$585$	74999.2	0.00906081
$586$	1.42113e7	1.70958
$587$	−1.20191e7	−1.43972	−0.719859	−	0.694120i	$-0.755794\pi$
$587$	−1.20191e7	−1.43972	−0.719859	+	0.694120i	$0.755794\pi$
$588$	552639.	0.0659171
$589$	−1.51141e7	−1.79512
$590$	430490.	0.0509135
$591$	3.67464e6	0.432759
$592$	−4.41068e6	−0.517251
$593$	−1.61256e6	−0.188312	−0.0941561	−	0.995557i	$-0.530015\pi$
$593$	−1.61256e6	−0.188312	−0.0941561	+	0.995557i	$0.530015\pi$
$594$	−462439.	−0.0537760
$595$	336324.	0.0389462
$596$	−934188.	−0.107726
$597$	2.22065e6	0.255002
$598$	−2.90414e6	−0.332097
$599$	3.70730e6	0.422173	0.211086	−	0.977467i	$-0.432300\pi$
$599$	3.70730e6	0.422173	0.211086	+	0.977467i	$0.432300\pi$
$600$	4.35724e6	0.494121
$601$	1.10575e7	1.24874	0.624369	−	0.781129i	$-0.285356\pi$
$601$	1.10575e7	1.24874	0.624369	+	0.781129i	$0.285356\pi$
$602$	−6.98838e6	−0.785933
$603$	−2.31770e6	−0.259575
$604$	−295908.	−0.0330038
$605$	−256561.	−0.0284972
$606$	9.06868e6	1.00314
$607$	−3.94984e6	−0.435119	−0.217560	−	0.976047i	$-0.569810\pi$
$607$	−3.94984e6	−0.435119	−0.217560	+	0.976047i	$0.569810\pi$
$608$	5.99247e6	0.657426
$609$	1.68888e6	0.184526
$610$	255409.	0.0277915
$611$	3.84011e6	0.416141
$612$	1.27118e6	0.137191
$613$	−9.28851e6	−0.998378	−0.499189	−	0.866493i	$-0.666369\pi$
$613$	−9.28851e6	−0.998378	−0.499189	+	0.866493i	$0.666369\pi$
$614$	−7.33395e6	−0.785085
$615$	23357.8	0.00249026
$616$	−1.43348e6	−0.152208
$617$	−1.41112e7	−1.49228	−0.746141	−	0.665788i	$-0.768096\pi$
$617$	−1.41112e7	−1.49228	−0.746141	+	0.665788i	$0.768096\pi$
$618$	598170.	0.0630019
$619$	−1.56339e7	−1.63999	−0.819993	−	0.572373i	$-0.806023\pi$
$619$	−1.56339e7	−1.63999	−0.819993	+	0.572373i	$0.806023\pi$
$620$	−80143.8	−0.00837318
$621$	−620954.	−0.0646146
$622$	5.08713e6	0.527226
$623$	2.65790e6	0.274359
$624$	5.89427e6	0.605994
$625$	9.73850e6	0.997222
$626$	−8.36264e6	−0.852919
$627$	2.11920e6	0.215280
$628$	−1.05846e6	−0.107097
$629$	7.93618e6	0.799806
$630$	−78819.7	−0.00791195
$631$	6.70740e6	0.670626	0.335313	−	0.942107i	$-0.391158\pi$
$631$	6.70740e6	0.670626	0.335313	+	0.942107i	$0.391158\pi$
$632$	−4.37766e6	−0.435963
$633$	6.27967e6	0.622913
$634$	−1.71511e7	−1.69460
$635$	132245.	0.0130150
$636$	−264558.	−0.0259345
$637$	−4.61075e6	−0.450218
$638$	−1.30387e6	−0.126819
$639$	4.47314e6	0.433371
$640$	−378675.	−0.0365440
$641$	−1.80533e7	−1.73545	−0.867723	−	0.497049i	$-0.834417\pi$
$641$	−1.80533e7	−1.73545	−0.867723	+	0.497049i	$0.834417\pi$
$642$	7.13382e6	0.683101
$643$	3.32010e6	0.316682	0.158341	−	0.987384i	$-0.449385\pi$
$643$	3.32010e6	0.316682	0.158341	+	0.987384i	$0.449385\pi$
$644$	563619.	0.0535514
$645$	−187092.	−0.0177075
$646$	−3.15452e7	−2.97407
$647$	1.88247e7	1.76794	0.883968	−	0.467547i	$-0.154862\pi$
$647$	1.88247e7	1.76794	0.883968	+	0.467547i	$0.154862\pi$
$648$	1.01740e6	0.0951819
$649$	4.08961e6	0.381127
$650$	1.06447e7	0.988211
$651$	5.34026e6	0.493867
$652$	−1.30618e6	−0.120333
$653$	1.69202e7	1.55282	0.776412	−	0.630226i	$-0.217038\pi$
$653$	1.69202e7	1.55282	0.776412	+	0.630226i	$0.217038\pi$
$654$	−3.30316e6	−0.301985
$655$	248522.	0.0226340
$656$	1.83572e6	0.166551
$657$	5.13007e6	0.463671
$658$	−4.03573e6	−0.363377
$659$	−1.25506e7	−1.12578	−0.562889	−	0.826533i	$-0.690310\pi$
$659$	−1.25506e7	−1.12578	−0.562889	+	0.826533i	$0.690310\pi$
$660$	11237.3	0.00100416
$661$	−1.28516e7	−1.14407	−0.572036	−	0.820229i	$-0.693846\pi$
$661$	−1.28516e7	−1.14407	−0.572036	+	0.820229i	$0.693846\pi$
$662$	−7.97435e6	−0.707213
$663$	−1.06056e7	−0.937026
$664$	1.37278e7	1.20832
$665$	361204.	0.0316737
$666$	−1.85990e6	−0.162481
$667$	−1.75082e6	−0.152379
$668$	1.88397e6	0.163355
$669$	−9.49700e6	−0.820391
$670$	304981.	0.0262474
$671$	2.42636e6	0.208041
$672$	−2.11732e6	−0.180869
$673$	−8.35020e6	−0.710655	−0.355328	−	0.934742i	$-0.615631\pi$
$673$	−8.35020e6	−0.710655	−0.355328	+	0.934742i	$0.615631\pi$
$674$	−989168.	−0.0838726
$675$	2.27601e6	0.192272
$676$	−544402.	−0.0458198
$677$	−9.67315e6	−0.811141	−0.405571	−	0.914064i	$-0.632927\pi$
$677$	−9.67315e6	−0.811141	−0.405571	+	0.914064i	$0.632927\pi$
$678$	1.12595e7	0.940683
$679$	−4.18965e6	−0.348742
$680$	571256.	0.0473760
$681$	−6.26243e6	−0.517458
$682$	−4.12286e6	−0.339420
$683$	5.89204e6	0.483297	0.241648	−	0.970364i	$-0.422312\pi$
$683$	5.89204e6	0.483297	0.241648	+	0.970364i	$0.422312\pi$
$684$	1.36521e6	0.111573
$685$	−402028.	−0.0327363
$686$	1.44584e7	1.17303
$687$	3.04954e6	0.246515
$688$	−1.47038e7	−1.18429
$689$	2.20725e6	0.177134
$690$	81710.0	0.00653360
$691$	−8.23195e6	−0.655854	−0.327927	−	0.944703i	$-0.606350\pi$
$691$	−8.23195e6	−0.655854	−0.327927	+	0.944703i	$0.606350\pi$
$692$	−1.24012e6	−0.0984458
$693$	−748779.	−0.0592271
$694$	−1.14190e7	−0.899975
$695$	−70185.3	−0.00551168
$696$	2.86862e6	0.224466
$697$	−3.30302e6	−0.257531
$698$	−1.02629e7	−0.797319
$699$	−4.63596e6	−0.358878
$700$	−2.06586e6	−0.159352
$701$	−2.14986e7	−1.65240	−0.826200	−	0.563377i	$-0.809502\pi$
$701$	−2.14986e7	−1.65240	−0.826200	+	0.563377i	$0.809502\pi$
$702$	2.48550e6	0.190358
$703$	8.52327e6	0.650456
$704$	−2.26459e6	−0.172210
$705$	−108044.	−0.00818707
$706$	9.21873e6	0.696080
$707$	1.46839e7	1.10483
$708$	2.63457e6	0.197527
$709$	2.02203e7	1.51068	0.755338	−	0.655335i	$-0.227473\pi$
$709$	2.02203e7	1.51068	0.755338	+	0.655335i	$0.227473\pi$
$710$	−588611.	−0.0438210
$711$	−2.28668e6	−0.169641
$712$	4.51452e6	0.333743
$713$	−5.53609e6	−0.407830
$714$	1.11459e7	0.818217
$715$	−93754.3	−0.00685845
$716$	4.75996e6	0.346993
$717$	−1.29433e6	−0.0940257
$718$	−1.20912e7	−0.875305
$719$	−1.29911e7	−0.937179	−0.468589	−	0.883416i	$-0.655238\pi$
$719$	−1.29911e7	−0.937179	−0.468589	+	0.883416i	$0.655238\pi$
$720$	−165840.	−0.0119222
$721$	968553.	0.0693881
$722$	−1.83665e7	−1.31125
$723$	−9.21349e6	−0.655509
$724$	−3.06283e6	−0.217159
$725$	6.41736e6	0.453431
$726$	−8.50250e6	−0.598694
$727$	66426.4	0.00466128	0.00233064	−	0.999997i	$-0.499258\pi$
$727$	66426.4	0.00466128	0.00233064	+	0.999997i	$0.499258\pi$
$728$	7.70457e6	0.538790
$729$	531441.	0.0370370
$730$	−675056.	−0.0468849
$731$	2.64567e7	1.83123
$732$	1.56309e6	0.107821
$733$	−5.79955e6	−0.398689	−0.199345	−	0.979929i	$-0.563881\pi$
$733$	−5.79955e6	−0.398689	−0.199345	+	0.979929i	$0.563881\pi$
$734$	−1.72131e7	−1.17929
$735$	129727.	0.00885751
$736$	2.19496e6	0.149360
$737$	2.89729e6	0.196482
$738$	774085.	0.0523176
$739$	1.80702e7	1.21717	0.608585	−	0.793489i	$-0.291738\pi$
$739$	1.80702e7	1.21717	0.608585	+	0.793489i	$0.291738\pi$
$740$	45195.5	0.00303400
$741$	−1.13902e7	−0.762053
$742$	−2.31969e6	−0.154675
$743$	−1.08492e7	−0.720984	−0.360492	−	0.932762i	$-0.617391\pi$
$743$	−1.08492e7	−0.720984	−0.360492	+	0.932762i	$0.617391\pi$
$744$	9.07058e6	0.600762
$745$	−219292.	−0.0144755
$746$	−2.58926e7	−1.70345
$747$	7.17077e6	0.470180
$748$	−1.58906e6	−0.103845
$749$	1.15510e7	0.752344
$750$	−599270.	−0.0389018
$751$	−1.31252e7	−0.849193	−0.424596	−	0.905383i	$-0.639584\pi$
$751$	−1.31252e7	−0.849193	−0.424596	+	0.905383i	$0.639584\pi$
$752$	−8.49131e6	−0.547558
$753$	2.13302e6	0.137091
$754$	7.00800e6	0.448917
$755$	−69461.6	−0.00443483
$756$	−482371.	−0.0306957
$757$	2.32461e7	1.47438	0.737192	−	0.675683i	$-0.236151\pi$
$757$	2.32461e7	1.47438	0.737192	+	0.675683i	$0.236151\pi$
$758$	−2.53158e7	−1.60036
$759$	776237.	0.0489091
$760$	613516.	0.0385293
$761$	−2.29635e7	−1.43740	−0.718698	−	0.695322i	$-0.755262\pi$
$761$	−2.29635e7	−1.43740	−0.718698	+	0.695322i	$0.755262\pi$
$762$	4.38265e6	0.273432
$763$	−5.34845e6	−0.332596
$764$	1.13722e6	0.0704876
$765$	298397.	0.0184349
$766$	−6.73451e6	−0.414700
$767$	−2.19806e7	−1.34912
$768$	−6.10826e6	−0.373693
$769$	1.13374e7	0.691347	0.345673	−	0.938355i	$-0.387650\pi$
$769$	1.13374e7	0.691347	0.345673	+	0.938355i	$0.387650\pi$
$770$	98530.3	0.00598884
$771$	−1.43233e7	−0.867773
$772$	5.29944e6	0.320027
$773$	−1.30866e7	−0.787734	−0.393867	−	0.919167i	$-0.628863\pi$
$773$	−1.30866e7	−0.787734	−0.393867	+	0.919167i	$0.628863\pi$
$774$	−6.20030e6	−0.372015
$775$	2.02917e7	1.21357
$776$	−7.11625e6	−0.424226
$777$	−3.01153e6	−0.178951
$778$	−927247.	−0.0549220
$779$	−3.54737e6	−0.209442
$780$	−60397.5	−0.00355453
$781$	−5.59174e6	−0.328034
$782$	−1.15546e7	−0.675675
$783$	1.49843e6	0.0873437
$784$	1.01954e7	0.592398
$785$	−248464.	−0.0143909
$786$	8.23609e6	0.475516
$787$	9.29341e6	0.534858	0.267429	−	0.963578i	$-0.413826\pi$
$787$	9.29341e6	0.534858	0.267429	+	0.963578i	$0.413826\pi$
$788$	−2.95922e6	−0.169770
$789$	1.45689e7	0.833172
$790$	300900.	0.0171535
$791$	1.82312e7	1.03604
$792$	−1.27182e6	−0.0720466
$793$	−1.30411e7	−0.736428
$794$	1.03872e7	0.584716
$795$	−62102.5	−0.00348491
$796$	−1.78831e6	−0.100037
$797$	−7.89262e6	−0.440125	−0.220062	−	0.975486i	$-0.570626\pi$
$797$	−7.89262e6	−0.440125	−0.220062	+	0.975486i	$0.570626\pi$
$798$	1.19704e7	0.665429
$799$	1.52785e7	0.846669
$800$	−8.04532e6	−0.444445
$801$	2.35817e6	0.129866
$802$	2.47683e7	1.35976
$803$	−6.41296e6	−0.350970
$804$	1.86646e6	0.101831
$805$	132304.	0.00719589
$806$	2.21593e7	1.20149
$807$	9.02799e6	0.487986
$808$	2.49411e7	1.34396
$809$	−1.81342e7	−0.974152	−0.487076	−	0.873360i	$-0.661937\pi$
$809$	−1.81342e7	−0.974152	−0.487076	+	0.873360i	$0.661937\pi$
$810$	−69931.2	−0.00374506
$811$	−3.25324e6	−0.173686	−0.0868429	−	0.996222i	$-0.527678\pi$
$811$	−3.25324e6	−0.173686	−0.0868429	+	0.996222i	$0.527678\pi$
$812$	−1.36007e6	−0.0723890
$813$	1.72798e7	0.916879
$814$	2.32500e6	0.122988
$815$	−306614.	−0.0161696
$816$	2.34513e7	1.23294
$817$	2.84139e7	1.48928
$818$	1.12666e7	0.588721
$819$	4.02450e6	0.209653
$820$	−18810.3	−0.000976923 0
$821$	2.93009e7	1.51713	0.758567	−	0.651596i	$-0.225900\pi$
$821$	2.93009e7	1.51713	0.758567	+	0.651596i	$0.225900\pi$
$822$	−1.33233e7	−0.687754
$823$	−1.59844e7	−0.822617	−0.411308	−	0.911496i	$-0.634928\pi$
$823$	−1.59844e7	−0.822617	−0.411308	+	0.911496i	$0.634928\pi$
$824$	1.64511e6	0.0844069
$825$	−2.84518e6	−0.145538
$826$	2.31003e7	1.17806
$827$	2.17953e7	1.10815	0.554075	−	0.832466i	$-0.313072\pi$
$827$	2.17953e7	1.10815	0.554075	+	0.832466i	$0.313072\pi$
$828$	500060.	0.0253481
$829$	−2.79748e7	−1.41378	−0.706888	−	0.707326i	$-0.749901\pi$
$829$	−2.79748e7	−1.41378	−0.706888	+	0.707326i	$0.749901\pi$
$830$	−943586.	−0.0475430
$831$	−1.15989e7	−0.582656
$832$	1.21716e7	0.609592
$833$	−1.83446e7	−0.916003
$834$	−2.32596e6	−0.115794
$835$	442243.	0.0219505
$836$	−1.70661e6	−0.0844539
$837$	4.73804e6	0.233768
$838$	−1.35292e7	−0.665520
$839$	2.71638e7	1.33225	0.666124	−	0.745841i	$-0.267952\pi$
$839$	2.71638e7	1.33225	0.666124	+	0.745841i	$0.267952\pi$
$840$	−216774.	−0.0106001
$841$	−1.62862e7	−0.794019
$842$	−4.01764e7	−1.95295
$843$	−1.75329e7	−0.849739
$844$	−5.05708e6	−0.244367
$845$	−127793.	−0.00615696
$846$	−3.58062e6	−0.172001
$847$	−1.37672e7	−0.659381
$848$	−4.88070e6	−0.233073
$849$	1.73263e7	0.824967
$850$	4.23517e7	2.01059
$851$	3.12196e6	0.147776
$852$	−3.60226e6	−0.170011
$853$	−1.38147e6	−0.0650084	−0.0325042	−	0.999472i	$-0.510348\pi$
$853$	−1.38147e6	−0.0650084	−0.0325042	+	0.999472i	$0.510348\pi$
$854$	1.37054e7	0.643053
$855$	320471.	0.0149925
$856$	1.96198e7	0.915186
$857$	−6.12050e6	−0.284666	−0.142333	−	0.989819i	$-0.545460\pi$
$857$	−6.12050e6	−0.284666	−0.142333	+	0.989819i	$0.545460\pi$
$858$	−3.10705e6	−0.144089
$859$	2.22725e7	1.02988	0.514940	−	0.857226i	$-0.327814\pi$
$859$	2.22725e7	1.02988	0.514940	+	0.857226i	$0.327814\pi$
$860$	150667.	0.00694661
$861$	1.25339e6	0.0576208
$862$	1.23478e7	0.566009
$863$	8.54525e6	0.390569	0.195284	−	0.980747i	$-0.437437\pi$
$863$	8.54525e6	0.390569	0.195284	+	0.980747i	$0.437437\pi$
$864$	−1.87855e6	−0.0856128
$865$	−291106.	−0.0132285
$866$	2.42639e7	1.09942
$867$	−2.94175e7	−1.32910
$868$	−4.30056e6	−0.193743
$869$	2.85851e6	0.128408
$870$	−197175.	−0.00883190
$871$	−1.55722e7	−0.695511
$872$	−9.08449e6	−0.404585
$873$	−3.71719e6	−0.165074
$874$	−1.24094e7	−0.549504
$875$	−970334.	−0.0428451
$876$	−4.13130e6	−0.181897
$877$	2.94740e7	1.29402	0.647010	−	0.762482i	$-0.276019\pi$
$877$	2.94740e7	1.29402	0.647010	+	0.762482i	$0.276019\pi$
$878$	−4.01436e7	−1.75744
$879$	2.04159e7	0.891245
$880$	207311.	0.00902436
$881$	−37683.7	−0.00163574	−0.000817868	−	1.00000i	$-0.500260\pi$
$881$	−37683.7	−0.00163574	−0.000817868		1.00000i	$0.500260\pi$
$882$	4.29919e6	0.186087
$883$	4.14788e7	1.79029	0.895146	−	0.445772i	$-0.147071\pi$
$883$	4.14788e7	1.79029	0.895146	+	0.445772i	$0.147071\pi$
$884$	8.54080e6	0.367593
$885$	618441.	0.0265424
$886$	−2.22714e7	−0.953155
$887$	9.73466e6	0.415443	0.207722	−	0.978188i	$-0.433395\pi$
$887$	9.73466e6	0.415443	0.207722	+	0.978188i	$0.433395\pi$
$888$	−5.11517e6	−0.217685
$889$	7.09635e6	0.301149
$890$	−310307.	−0.0131316
$891$	−664339.	−0.0280347
$892$	7.64802e6	0.321838
$893$	1.64088e7	0.688568
$894$	−7.26741e6	−0.304113
$895$	1.11736e6	0.0466266
$896$	−2.03199e7	−0.845574
$897$	−4.17208e6	−0.173130
$898$	3.48687e7	1.44293
$899$	1.33592e7	0.551290
$900$	−1.83290e6	−0.0754278
$901$	8.78189e6	0.360393
$902$	−967662.	−0.0396011
$903$	−1.00395e7	−0.409725
$904$	3.09663e7	1.26028
$905$	−718972.	−0.0291803
$906$	−2.30198e6	−0.0931710
$907$	−1.00618e7	−0.406123	−0.203062	−	0.979166i	$-0.565089\pi$
$907$	−1.00618e7	−0.406123	−0.203062	+	0.979166i	$0.565089\pi$
$908$	5.04319e6	0.202998
$909$	1.30280e7	0.522961
$910$	−529575.	−0.0211994
$911$	1.36382e7	0.544455	0.272228	−	0.962233i	$-0.412240\pi$
$911$	1.36382e7	0.544455	0.272228	+	0.962233i	$0.412240\pi$
$912$	2.51862e7	1.00271
$913$	−8.96397e6	−0.355896
$914$	4.22568e7	1.67314
$915$	366920.	0.0144883
$916$	−2.45582e6	−0.0967072
$917$	1.33358e7	0.523717
$918$	9.88895e6	0.387297
$919$	4.05194e7	1.58261	0.791305	−	0.611421i	$-0.209402\pi$
$919$	4.05194e7	1.58261	0.791305	+	0.611421i	$0.209402\pi$
$920$	224723.	0.00875341
$921$	−1.05359e7	−0.409283
$922$	2.36411e6	0.0915883
$923$	3.00542e7	1.16118
$924$	602998.	0.0232347
$925$	−1.14431e7	−0.439733
$926$	−2.35236e7	−0.901520
$927$	859329.	0.0328443
$928$	−5.29668e6	−0.201899
$929$	7.01400e6	0.266641	0.133320	−	0.991073i	$-0.457436\pi$
$929$	7.01400e6	0.266641	0.133320	+	0.991073i	$0.457436\pi$
$930$	−623469.	−0.0236378
$931$	−1.97017e7	−0.744955
$932$	3.73338e6	0.140787
$933$	7.30816e6	0.274855
$934$	−8.56314e6	−0.321193
$935$	−373017.	−0.0139540
$936$	6.83573e6	0.255032
$937$	−3.66746e7	−1.36463	−0.682317	−	0.731056i	$-0.739028\pi$
$937$	−3.66746e7	−1.36463	−0.682317	+	0.731056i	$0.739028\pi$
$938$	1.63654e7	0.607324
$939$	−1.20137e7	−0.444646
$940$	87009.0	0.00321177
$941$	1.73619e7	0.639181	0.319590	−	0.947556i	$-0.396455\pi$
$941$	1.73619e7	0.639181	0.319590	+	0.947556i	$0.396455\pi$
$942$	−8.23416e6	−0.302338
$943$	−1.29936e6	−0.0475827
$944$	4.86039e7	1.77518
$945$	−113232.	−0.00412468
$946$	7.75082e6	0.281592
$947$	5.79106e6	0.209838	0.104919	−	0.994481i	$-0.466542\pi$
$947$	5.79106e6	0.209838	0.104919	+	0.994481i	$0.466542\pi$
$948$	1.84149e6	0.0665499
$949$	3.44680e7	1.24237
$950$	4.54847e7	1.63515
$951$	−2.46392e7	−0.883436
$952$	3.06539e7	1.09621
$953$	−1.70178e7	−0.606976	−0.303488	−	0.952835i	$-0.598151\pi$
$953$	−1.70178e7	−0.606976	−0.303488	+	0.952835i	$0.598151\pi$
$954$	−2.05810e6	−0.0732141
$955$	266953.	0.00947166
$956$	1.04233e6	0.0368861
$957$	−1.87314e6	−0.0661136
$958$	−2.09845e7	−0.738727
$959$	−2.15730e7	−0.757469
$960$	−342457.	−0.0119930
$961$	1.36126e7	0.475480
$962$	−1.24963e7	−0.435355
$963$	1.02484e7	0.356116
$964$	7.41971e6	0.257155
$965$	1.24400e6	0.0430032
$966$	4.38461e6	0.151178
$967$	4.38461e7	1.50787	0.753936	−	0.656948i	$-0.228153\pi$
$967$	4.38461e7	1.50787	0.753936	+	0.656948i	$0.228153\pi$
$968$	−2.33840e7	−0.802102
$969$	−4.53177e7	−1.55045
$970$	489137.	0.0166917
$971$	2.03499e7	0.692649	0.346325	−	0.938115i	$-0.387430\pi$
$971$	2.03499e7	0.692649	0.346325	+	0.938115i	$0.387430\pi$
$972$	−427974.	−0.0145295
$973$	−3.76618e6	−0.127532
$974$	1.19158e7	0.402463
$975$	1.52921e7	0.515177
$976$	2.88367e7	0.968992
$977$	−3.76339e7	−1.26137	−0.630686	−	0.776039i	$-0.717226\pi$
$977$	−3.76339e7	−1.26137	−0.630686	+	0.776039i	$0.717226\pi$
$978$	−1.01613e7	−0.339705
$979$	−2.94788e6	−0.0982999
$980$	−104470.	−0.00347478
$981$	−4.74530e6	−0.157431
$982$	−3.63888e7	−1.20417
$983$	1.44233e7	0.476082	0.238041	−	0.971255i	$-0.423495\pi$
$983$	1.44233e7	0.476082	0.238041	+	0.971255i	$0.423495\pi$
$984$	2.12892e6	0.0700927
$985$	−694650.	−0.0228126
$986$	2.78825e7	0.913354
$987$	−5.79771e6	−0.189437
$988$	9.17262e6	0.298952
$989$	1.04076e7	0.338346
$990$	87419.0	0.00283477
$991$	4.27200e7	1.38181	0.690903	−	0.722948i	$-0.257213\pi$
$991$	4.27200e7	1.38181	0.690903	+	0.722948i	$0.257213\pi$
$992$	−1.67481e7	−0.540365
$993$	−1.14559e7	−0.368686
$994$	−3.15852e7	−1.01395
$995$	−419788.	−0.0134423
$996$	−5.77468e6	−0.184451
$997$	2.26936e7	0.723045	0.361522	−	0.932363i	$-0.382257\pi$
$997$	2.26936e7	0.723045	0.361522	+	0.932363i	$0.382257\pi$
$998$	−6.33598e7	−2.01367
$999$	−2.67192e6	−0.0847052

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.b.1.5	✓	20
3.2	odd	2		927.6.a.c.1.16		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.b.1.5	✓	20	1.1	even	1	trivial
927.6.a.c.1.16		20	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)

\(f(q)\)	\(=\)	\(q-6.26481 q^{2} -9.00000 q^{3} +7.24778 q^{4} +1.70135 q^{5} +56.3832 q^{6} +91.2954 q^{7} +155.068 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-6.26481 q^{2} -9.00000 q^{3} +7.24778 q^{4} +1.70135 q^{5} +56.3832 q^{6} +91.2954 q^{7} +155.068 q^{8} +81.0000 q^{9} -10.6586 q^{10} -101.256 q^{11} -65.2300 q^{12} +544.224 q^{13} -571.948 q^{14} -15.3121 q^{15} -1203.40 q^{16} +2165.29 q^{17} -507.449 q^{18} +2325.47 q^{19} +12.3310 q^{20} -821.658 q^{21} +634.348 q^{22} +851.789 q^{23} -1395.61 q^{24} -3122.11 q^{25} -3409.46 q^{26} -729.000 q^{27} +661.689 q^{28} -2055.46 q^{29} +95.9276 q^{30} -6499.37 q^{31} +2576.89 q^{32} +911.302 q^{33} -13565.1 q^{34} +155.325 q^{35} +587.070 q^{36} +3665.19 q^{37} -14568.6 q^{38} -4898.02 q^{39} +263.825 q^{40} -1525.44 q^{41} +5147.53 q^{42} +12218.6 q^{43} -733.880 q^{44} +137.809 q^{45} -5336.29 q^{46} +7056.11 q^{47} +10830.6 q^{48} -8472.16 q^{49} +19559.4 q^{50} -19487.6 q^{51} +3944.42 q^{52} +4055.77 q^{53} +4567.04 q^{54} -172.271 q^{55} +14157.0 q^{56} -20929.2 q^{57} +12877.0 q^{58} -40388.9 q^{59} -110.979 q^{60} -23962.7 q^{61} +40717.3 q^{62} +7394.92 q^{63} +22365.1 q^{64} +925.916 q^{65} -5709.13 q^{66} -28613.5 q^{67} +15693.5 q^{68} -7666.10 q^{69} -973.083 q^{70} +55223.9 q^{71} +12560.5 q^{72} +63334.2 q^{73} -22961.7 q^{74} +28098.9 q^{75} +16854.5 q^{76} -9244.18 q^{77} +30685.1 q^{78} -28230.6 q^{79} -2047.40 q^{80} +6561.00 q^{81} +9556.61 q^{82} +88528.0 q^{83} -5955.20 q^{84} +3683.91 q^{85} -76546.9 q^{86} +18499.1 q^{87} -15701.5 q^{88} +29113.2 q^{89} -863.349 q^{90} +49685.2 q^{91} +6173.58 q^{92} +58494.3 q^{93} -44205.2 q^{94} +3956.43 q^{95} -23192.0 q^{96} -45891.2 q^{97} +53076.4 q^{98} -8201.72 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9}+O(q^{10}) \) 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9} + 445 q^{10} + 1712 q^{11} - 2934 q^{12} - 809 q^{13} + 388 q^{14} - 873 q^{15} + 3934 q^{16} + 2040 q^{17} + 324 q^{18} + 5320 q^{19} + 4415 q^{20} - 90 q^{21} + 705 q^{22} + 653 q^{23} - 2808 q^{24} + 5977 q^{25} - 1655 q^{26} - 14580 q^{27} - 9206 q^{28} - 706 q^{29} - 4005 q^{30} + 9091 q^{31} - 16762 q^{32} - 15408 q^{33} - 17698 q^{34} + 15988 q^{35} + 26406 q^{36} - 50 q^{37} + 3877 q^{38} + 7281 q^{39} + 30485 q^{40} + 37084 q^{41} - 3492 q^{42} + 2533 q^{43} + 64525 q^{44} + 7857 q^{45} + 13966 q^{46} + 23282 q^{47} - 35406 q^{48} + 32910 q^{49} + 85769 q^{50} - 18360 q^{51} + 58531 q^{52} + 67436 q^{53} - 2916 q^{54} + 27254 q^{55} + 130668 q^{56} - 47880 q^{57} - 26963 q^{58} + 162695 q^{59} - 39735 q^{60} + 44895 q^{61} + 115286 q^{62} + 810 q^{63} + 44238 q^{64} + 64945 q^{65} - 6345 q^{66} - 4127 q^{67} + 231174 q^{68} - 5877 q^{69} + 290034 q^{70} + 140618 q^{71} + 25272 q^{72} - 52974 q^{73} + 558413 q^{74} - 53793 q^{75} + 224357 q^{76} + 210380 q^{77} + 14895 q^{78} + 170742 q^{79} + 760913 q^{80} + 131220 q^{81} + 576206 q^{82} + 239285 q^{83} + 82854 q^{84} + 268116 q^{85} + 776443 q^{86} + 6354 q^{87} + 381839 q^{88} + 408810 q^{89} + 36045 q^{90} + 413782 q^{91} + 645628 q^{92} - 81819 q^{93} + 447752 q^{94} + 568618 q^{95} + 150858 q^{96} + 275859 q^{97} + 768726 q^{98} + 138672 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9 + 445 * q^10 + 1712 * q^11 - 2934 * q^12 - 809 * q^13 + 388 * q^14 - 873 * q^15 + 3934 * q^16 + 2040 * q^17 + 324 * q^18 + 5320 * q^19 + 4415 * q^20 - 90 * q^21 + 705 * q^22 + 653 * q^23 - 2808 * q^24 + 5977 * q^25 - 1655 * q^26 - 14580 * q^27 - 9206 * q^28 - 706 * q^29 - 4005 * q^30 + 9091 * q^31 - 16762 * q^32 - 15408 * q^33 - 17698 * q^34 + 15988 * q^35 + 26406 * q^36 - 50 * q^37 + 3877 * q^38 + 7281 * q^39 + 30485 * q^40 + 37084 * q^41 - 3492 * q^42 + 2533 * q^43 + 64525 * q^44 + 7857 * q^45 + 13966 * q^46 + 23282 * q^47 - 35406 * q^48 + 32910 * q^49 + 85769 * q^50 - 18360 * q^51 + 58531 * q^52 + 67436 * q^53 - 2916 * q^54 + 27254 * q^55 + 130668 * q^56 - 47880 * q^57 - 26963 * q^58 + 162695 * q^59 - 39735 * q^60 + 44895 * q^61 + 115286 * q^62 + 810 * q^63 + 44238 * q^64 + 64945 * q^65 - 6345 * q^66 - 4127 * q^67 + 231174 * q^68 - 5877 * q^69 + 290034 * q^70 + 140618 * q^71 + 25272 * q^72 - 52974 * q^73 + 558413 * q^74 - 53793 * q^75 + 224357 * q^76 + 210380 * q^77 + 14895 * q^78 + 170742 * q^79 + 760913 * q^80 + 131220 * q^81 + 576206 * q^82 + 239285 * q^83 + 82854 * q^84 + 268116 * q^85 + 776443 * q^86 + 6354 * q^87 + 381839 * q^88 + 408810 * q^89 + 36045 * q^90 + 413782 * q^91 + 645628 * q^92 - 81819 * q^93 + 447752 * q^94 + 568618 * q^95 + 150858 * q^96 + 275859 * q^97 + 768726 * q^98 + 138672 * q^99

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