LMFDB - Embedded newform 309.6.a.b.1.19

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			1.19
Root			$10.3537$ 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)

$f(q)$	$=$	$q+10.3537 q^{2} -9.00000 q^{3} +75.1995 q^{4} +62.7780 q^{5} -93.1835 q^{6} -127.343 q^{7} +447.275 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+10.3537 q^{2} -9.00000 q^{3} +75.1995 q^{4} +62.7780 q^{5} -93.1835 q^{6} -127.343 q^{7} +447.275 q^{8} +81.0000 q^{9} +649.986 q^{10} +50.6386 q^{11} -676.795 q^{12} +307.042 q^{13} -1318.48 q^{14} -565.002 q^{15} +2224.58 q^{16} +1096.71 q^{17} +838.651 q^{18} +877.231 q^{19} +4720.87 q^{20} +1146.09 q^{21} +524.298 q^{22} +4432.04 q^{23} -4025.48 q^{24} +816.079 q^{25} +3179.02 q^{26} -729.000 q^{27} -9576.15 q^{28} -2210.94 q^{29} -5849.87 q^{30} +1897.76 q^{31} +8719.86 q^{32} -455.747 q^{33} +11355.0 q^{34} -7994.36 q^{35} +6091.16 q^{36} -1569.47 q^{37} +9082.60 q^{38} -2763.38 q^{39} +28079.1 q^{40} -8122.47 q^{41} +11866.3 q^{42} +11240.4 q^{43} +3808.00 q^{44} +5085.02 q^{45} +45888.1 q^{46} +13720.4 q^{47} -20021.2 q^{48} -590.682 q^{49} +8449.45 q^{50} -9870.35 q^{51} +23089.4 q^{52} +6888.05 q^{53} -7547.86 q^{54} +3178.99 q^{55} -56957.5 q^{56} -7895.08 q^{57} -22891.5 q^{58} -45177.3 q^{59} -42487.9 q^{60} +36224.1 q^{61} +19648.9 q^{62} -10314.8 q^{63} +19096.4 q^{64} +19275.5 q^{65} -4718.68 q^{66} -8970.44 q^{67} +82471.7 q^{68} -39888.3 q^{69} -82771.4 q^{70} +24541.9 q^{71} +36229.3 q^{72} -64472.2 q^{73} -16249.8 q^{74} -7344.71 q^{75} +65967.3 q^{76} -6448.49 q^{77} -28611.2 q^{78} +42433.5 q^{79} +139655. q^{80} +6561.00 q^{81} -84097.8 q^{82} +54588.4 q^{83} +86185.4 q^{84} +68849.0 q^{85} +116380. q^{86} +19898.5 q^{87} +22649.4 q^{88} -116061. q^{89} +52648.9 q^{90} -39099.7 q^{91} +333287. q^{92} -17079.8 q^{93} +142057. q^{94} +55070.8 q^{95} -78478.7 q^{96} +21242.6 q^{97} -6115.75 q^{98} +4101.73 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	10.3537	1.83030	0.915148	−	0.403118i	$-0.132074\pi$
$2$	10.3537	1.83030	0.915148	+	0.403118i	$0.132074\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	75.1995	2.34998
$5$	62.7780	1.12301	0.561504	−	0.827474i	$-0.310223\pi$
$5$	62.7780	1.12301	0.561504	+	0.827474i	$0.310223\pi$
$6$	−93.1835	−1.05672
$7$	−127.343	−0.982270	−0.491135	−	0.871083i	$-0.663418\pi$
$7$	−127.343	−0.982270	−0.491135	+	0.871083i	$0.663418\pi$
$8$	447.275	2.47087
$9$	81.0000	0.333333
$10$	649.986	2.05544
$11$	50.6386	0.126183	0.0630914	−	0.998008i	$-0.479904\pi$
$11$	50.6386	0.126183	0.0630914	+	0.998008i	$0.479904\pi$
$12$	−676.795	−1.35676
$13$	307.042	0.503894	0.251947	−	0.967741i	$-0.418929\pi$
$13$	307.042	0.503894	0.251947	+	0.967741i	$0.418929\pi$
$14$	−1318.48	−1.79785
$15$	−565.002	−0.648369
$16$	2224.58	2.17244
$17$	1096.71	0.920381	0.460191	−	0.887820i	$-0.347781\pi$
$17$	1096.71	0.920381	0.460191	+	0.887820i	$0.347781\pi$
$18$	838.651	0.610099
$19$	877.231	0.557481	0.278740	−	0.960366i	$-0.410083\pi$
$19$	877.231	0.557481	0.278740	+	0.960366i	$0.410083\pi$
$20$	4720.87	2.63905
$21$	1146.09	0.567114
$22$	524.298	0.230952
$23$	4432.04	1.74696	0.873482	−	0.486856i	$-0.161857\pi$
$23$	4432.04	1.74696	0.873482	+	0.486856i	$0.161857\pi$
$24$	−4025.48	−1.42656
$25$	816.079	0.261145
$26$	3179.02	0.922275
$27$	−729.000	−0.192450
$28$	−9576.15	−2.30832
$29$	−2210.94	−0.488182	−0.244091	−	0.969752i	$-0.578490\pi$
$29$	−2210.94	−0.488182	−0.244091	+	0.969752i	$0.578490\pi$
$30$	−5849.87	−1.18671
$31$	1897.76	0.354680	0.177340	−	0.984150i	$-0.443251\pi$
$31$	1897.76	0.354680	0.177340	+	0.984150i	$0.443251\pi$
$32$	8719.86	1.50534
$33$	−455.747	−0.0728516
$34$	11355.0	1.68457
$35$	−7994.36	−1.10310
$36$	6091.16	0.783328
$37$	−1569.47	−0.188472	−0.0942362	−	0.995550i	$-0.530041\pi$
$37$	−1569.47	−0.188472	−0.0942362	+	0.995550i	$0.530041\pi$
$38$	9082.60	1.02036
$39$	−2763.38	−0.290923
$40$	28079.1	2.77481
$41$	−8122.47	−0.754620	−0.377310	−	0.926087i	$-0.623151\pi$
$41$	−8122.47	−0.754620	−0.377310	+	0.926087i	$0.623151\pi$
$42$	11866.3	1.03799
$43$	11240.4	0.927070	0.463535	−	0.886079i	$-0.346581\pi$
$43$	11240.4	0.927070	0.463535	+	0.886079i	$0.346581\pi$
$44$	3808.00	0.296527
$45$	5085.02	0.374336
$46$	45888.1	3.19746
$47$	13720.4	0.905985	0.452993	−	0.891514i	$-0.350356\pi$
$47$	13720.4	0.905985	0.452993	+	0.891514i	$0.350356\pi$
$48$	−20021.2	−1.25426
$49$	−590.682	−0.0351450
$50$	8449.45	0.477973
$51$	−9870.35	−0.531382
$52$	23089.4	1.18414
$53$	6888.05	0.336827	0.168413	−	0.985716i	$-0.446136\pi$
$53$	6888.05	0.336827	0.168413	+	0.985716i	$0.446136\pi$
$54$	−7547.86	−0.352241
$55$	3178.99	0.141704
$56$	−56957.5	−2.42706
$57$	−7895.08	−0.321862
$58$	−22891.5	−0.893518
$59$	−45177.3	−1.68963	−0.844813	−	0.535062i	$-0.820288\pi$
$59$	−45177.3	−1.68963	−0.844813	+	0.535062i	$0.820288\pi$
$60$	−42487.9	−1.52366
$61$	36224.1	1.24645	0.623223	−	0.782044i	$-0.285823\pi$
$61$	36224.1	1.24645	0.623223	+	0.782044i	$0.285823\pi$
$62$	19648.9	0.649169
$63$	−10314.8	−0.327423
$64$	19096.4	0.582776
$65$	19275.5	0.565877
$66$	−4718.68	−0.133340
$67$	−8970.44	−0.244133	−0.122067	−	0.992522i	$-0.538952\pi$
$67$	−8970.44	−0.244133	−0.122067	+	0.992522i	$0.538952\pi$
$68$	82471.7	2.16288
$69$	−39888.3	−1.00861
$70$	−82771.4	−2.01899
$71$	24541.9	0.577779	0.288889	−	0.957363i	$-0.406714\pi$
$71$	24541.9	0.577779	0.288889	+	0.957363i	$0.406714\pi$
$72$	36229.3	0.823623
$73$	−64472.2	−1.41601	−0.708004	−	0.706209i	$-0.750404\pi$
$73$	−64472.2	−1.41601	−0.708004	+	0.706209i	$0.750404\pi$
$74$	−16249.8	−0.344960
$75$	−7344.71	−0.150772
$76$	65967.3	1.31007
$77$	−6448.49	−0.123946
$78$	−28611.2	−0.532476
$79$	42433.5	0.764964	0.382482	−	0.923963i	$-0.375069\pi$
$79$	42433.5	0.764964	0.382482	+	0.923963i	$0.375069\pi$
$80$	139655.	2.43967
$81$	6561.00	0.111111
$82$	−84097.8	−1.38118
$83$	54588.4	0.869771	0.434885	−	0.900486i	$-0.356789\pi$
$83$	54588.4	0.869771	0.434885	+	0.900486i	$0.356789\pi$
$84$	86185.4	1.33271
$85$	68849.0	1.03359
$86$	116380.	1.69681
$87$	19898.5	0.281852
$88$	22649.4	0.311781
$89$	−116061.	−1.55314	−0.776572	−	0.630028i	$-0.783043\pi$
$89$	−116061.	−1.55314	−0.776572	+	0.630028i	$0.783043\pi$
$90$	52648.9	0.685145
$91$	−39099.7	−0.494960
$92$	333287.	4.10534
$93$	−17079.8	−0.204775
$94$	142057.	1.65822
$95$	55070.8	0.626055
$96$	−78478.7	−0.869108
$97$	21242.6	0.229233	0.114617	−	0.993410i	$-0.463436\pi$
$97$	21242.6	0.229233	0.114617	+	0.993410i	$0.463436\pi$
$98$	−6115.75	−0.0643257
$99$	4101.73	0.0420609
$100$	61368.7	0.613687
$101$	24746.9	0.241389	0.120694	−	0.992690i	$-0.461488\pi$
$101$	24746.9	0.241389	0.120694	+	0.992690i	$0.461488\pi$
$102$	−102195.	−0.972587
$103$	10609.0	0.0985329
$103$	10609.0	0.0985329
$104$	137332.	1.24506
$105$	71949.2	0.636873
$106$	71316.9	0.616493
$107$	−30290.6	−0.255770	−0.127885	−	0.991789i	$-0.540819\pi$
$107$	−30290.6	−0.255770	−0.127885	+	0.991789i	$0.540819\pi$
$108$	−54820.4	−0.452255
$109$	13600.6	0.109646	0.0548228	−	0.998496i	$-0.482541\pi$
$109$	13600.6	0.109646	0.0548228	+	0.998496i	$0.482541\pi$
$110$	32914.4	0.259361
$111$	14125.2	0.108815
$112$	−283285.	−2.13392
$113$	−144358.	−1.06352	−0.531760	−	0.846895i	$-0.678469\pi$
$113$	−144358.	−1.06352	−0.531760	+	0.846895i	$0.678469\pi$
$114$	−81743.4	−0.589102
$115$	278235.	1.96185
$116$	−166262.	−1.14722
$117$	24870.4	0.167965
$118$	−467753.	−3.09251
$119$	−139658.	−0.904063
$120$	−252712.	−1.60203
$121$	−158487.	−0.984078
$122$	375054.	2.28136
$123$	73102.2	0.435680
$124$	142710.	0.833492
$125$	−144949.	−0.829739
$126$	−106797.	−0.599282
$127$	284468.	1.56504	0.782518	−	0.622629i	$-0.213935\pi$
$127$	284468.	1.56504	0.782518	+	0.622629i	$0.213935\pi$
$128$	−81316.6	−0.438686
$129$	−101164.	−0.535244
$130$	199573.	1.03572
$131$	−168454.	−0.857638	−0.428819	−	0.903390i	$-0.641070\pi$
$131$	−168454.	−0.857638	−0.428819	+	0.903390i	$0.641070\pi$
$132$	−34272.0	−0.171200
$133$	−111710.	−0.547597
$134$	−92877.5	−0.446836
$135$	−45765.2	−0.216123
$136$	490529.	2.27414
$137$	−367414.	−1.67246	−0.836228	−	0.548382i	$-0.815244\pi$
$137$	−367414.	−1.67246	−0.836228	+	0.548382i	$0.815244\pi$
$138$	−412993.	−1.84606
$139$	−98601.8	−0.432860	−0.216430	−	0.976298i	$-0.569441\pi$
$139$	−98601.8	−0.432860	−0.216430	+	0.976298i	$0.569441\pi$
$140$	−601172.	−2.59226
$141$	−123483.	−0.523071
$142$	254099.	1.05751
$143$	15548.2	0.0635827
$144$	180191.	0.724147
$145$	−138798.	−0.548232
$146$	−667527.	−2.59171
$147$	5316.14	0.0202910
$148$	−118023.	−0.442907
$149$	93418.5	0.344721	0.172360	−	0.985034i	$-0.444861\pi$
$149$	93418.5	0.344721	0.172360	+	0.985034i	$0.444861\pi$
$150$	−76045.1	−0.275958
$151$	−237261.	−0.846805	−0.423403	−	0.905942i	$-0.639164\pi$
$151$	−237261.	−0.846805	−0.423403	+	0.905942i	$0.639164\pi$
$152$	392364.	1.37746
$153$	88833.2	0.306794
$154$	−66765.8	−0.226857
$155$	119137.	0.398308
$156$	−207804.	−0.683665
$157$	58575.6	0.189657	0.0948283	−	0.995494i	$-0.469770\pi$
$157$	58575.6	0.189657	0.0948283	+	0.995494i	$0.469770\pi$
$158$	439344.	1.40011
$159$	−61992.4	−0.194467
$160$	547415.	1.69051
$161$	−564390.	−1.71599
$162$	67930.7	0.203366
$163$	−240020.	−0.707586	−0.353793	−	0.935324i	$-0.615108\pi$
$163$	−240020.	−0.707586	−0.353793	+	0.935324i	$0.615108\pi$
$164$	−610806.	−1.77335
$165$	−28610.9	−0.0818129
$166$	565192.	1.59194
$167$	−151977.	−0.421682	−0.210841	−	0.977520i	$-0.567620\pi$
$167$	−151977.	−0.421682	−0.210841	+	0.977520i	$0.567620\pi$
$168$	512618.	1.40127
$169$	−277018.	−0.746091
$170$	712843.	1.89178
$171$	71055.7	0.185827
$172$	845276.	2.17860
$173$	−474931.	−1.20647	−0.603233	−	0.797565i	$-0.706121\pi$
$173$	−474931.	−1.20647	−0.603233	+	0.797565i	$0.706121\pi$
$174$	206023.	0.515873
$175$	−103922.	−0.256515
$176$	112650.	0.274125
$177$	406596.	0.975506
$178$	−1.20166e6	−2.84271
$179$	−187909.	−0.438344	−0.219172	−	0.975686i	$-0.570336\pi$
$179$	−187909.	−0.438344	−0.219172	+	0.975686i	$0.570336\pi$
$180$	382391.	0.879683
$181$	76252.2	0.173004	0.0865020	−	0.996252i	$-0.472431\pi$
$181$	76252.2	0.173004	0.0865020	+	0.996252i	$0.472431\pi$
$182$	−404827.	−0.905923
$183$	−326017.	−0.719636
$184$	1.98234e6	4.31652
$185$	−98528.0	−0.211656
$186$	−176840.	−0.374798
$187$	55535.6	0.116136
$188$	1.03176e6	2.12905
$189$	92833.3	0.189038
$190$	570188.	1.14587
$191$	−435006.	−0.862802	−0.431401	−	0.902160i	$-0.641981\pi$
$191$	−435006.	−0.862802	−0.431401	+	0.902160i	$0.641981\pi$
$192$	−171868.	−0.336466
$193$	77595.8	0.149950	0.0749748	−	0.997185i	$-0.476112\pi$
$193$	77595.8	0.149950	0.0749748	+	0.997185i	$0.476112\pi$
$194$	219940.	0.419565
$195$	−173479.	−0.326709
$196$	−44419.0	−0.0825902
$197$	−226743.	−0.416264	−0.208132	−	0.978101i	$-0.566738\pi$
$197$	−226743.	−0.416264	−0.208132	+	0.978101i	$0.566738\pi$
$198$	42468.1	0.0769839
$199$	1.07650e6	1.92699	0.963497	−	0.267720i	$-0.0862703\pi$
$199$	1.07650e6	1.92699	0.963497	+	0.267720i	$0.0862703\pi$
$200$	365012.	0.645256
$201$	80734.0	0.140950
$202$	256222.	0.441812
$203$	281549.	0.479527
$204$	−742245.	−1.24874
$205$	−509913.	−0.847444
$206$	109843.	0.180344
$207$	358995.	0.582321
$208$	683039.	1.09468
$209$	44421.8	0.0703445
$210$	744942.	1.16567
$211$	−144952.	−0.224140	−0.112070	−	0.993700i	$-0.535748\pi$
$211$	−144952.	−0.224140	−0.112070	+	0.993700i	$0.535748\pi$
$212$	517978.	0.791537
$213$	−220877.	−0.333581
$214$	−313621.	−0.468134
$215$	705653.	1.04111
$216$	−326064.	−0.475519
$217$	−241667.	−0.348392
$218$	140817.	0.200684
$219$	580250.	0.817532
$220$	239058.	0.333002
$221$	336734.	0.463775
$222$	146248.	0.199163
$223$	560533.	0.754813	0.377406	−	0.926048i	$-0.376816\pi$
$223$	560533.	0.754813	0.377406	+	0.926048i	$0.376816\pi$
$224$	−1.11042e6	−1.47865
$225$	66102.4	0.0870484
$226$	−1.49465e6	−1.94656
$227$	−355873.	−0.458385	−0.229193	−	0.973381i	$-0.573609\pi$
$227$	−355873.	−0.458385	−0.229193	+	0.973381i	$0.573609\pi$
$228$	−593706.	−0.756370
$229$	−792287.	−0.998375	−0.499187	−	0.866494i	$-0.666368\pi$
$229$	−792287.	−0.998375	−0.499187	+	0.866494i	$0.666368\pi$
$230$	2.88076e6	3.59077
$231$	58036.4	0.0715600
$232$	−988899.	−1.20624
$233$	−235570.	−0.284269	−0.142135	−	0.989847i	$-0.545397\pi$
$233$	−235570.	−0.284269	−0.142135	+	0.989847i	$0.545397\pi$
$234$	257501.	0.307425
$235$	861337.	1.01743
$236$	−3.39731e6	−3.97059
$237$	−381901.	−0.441652
$238$	−1.44598e6	−1.65470
$239$	−1.49278e6	−1.69044	−0.845220	−	0.534418i	$-0.820531\pi$
$239$	−1.49278e6	−1.69044	−0.845220	+	0.534418i	$0.820531\pi$
$240$	−1.25689e6	−1.40854
$241$	−1.01603e6	−1.12685	−0.563423	−	0.826168i	$-0.690516\pi$
$241$	−1.01603e6	−1.12685	−0.563423	+	0.826168i	$0.690516\pi$
$242$	−1.64093e6	−1.80115
$243$	−59049.0	−0.0641500
$244$	2.72404e6	2.92913
$245$	−37081.8	−0.0394681
$246$	756880.	0.797424
$247$	269347.	0.280911
$248$	848820.	0.876368
$249$	−491295.	−0.502162
$250$	−1.50077e6	−1.51867
$251$	1.81217e6	1.81558	0.907791	−	0.419423i	$-0.137768\pi$
$251$	1.81217e6	1.81558	0.907791	+	0.419423i	$0.137768\pi$
$252$	−775668.	−0.769440
$253$	224432.	0.220437
$254$	2.94530e6	2.86448
$255$	−619641.	−0.596746
$256$	−1.45301e6	−1.38570
$257$	1.35229e6	1.27713	0.638566	−	0.769567i	$-0.279528\pi$
$257$	1.35229e6	1.27713	0.638566	+	0.769567i	$0.279528\pi$
$258$	−1.04742e6	−0.979655
$259$	199861.	0.185131
$260$	1.44951e6	1.32980
$261$	−179086.	−0.162727
$262$	−1.74413e6	−1.56973
$263$	−20029.1	−0.0178555	−0.00892776	−	0.999960i	$-0.502842\pi$
$263$	−20029.1	−0.0178555	−0.00892776	+	0.999960i	$0.502842\pi$
$264$	−203845.	−0.180007
$265$	432418.	0.378259
$266$	−1.15661e6	−1.00226
$267$	1.04455e6	0.896708
$268$	−674573.	−0.573709
$269$	1.65370e6	1.39340	0.696698	−	0.717364i	$-0.254652\pi$
$269$	1.65370e6	1.39340	0.696698	+	0.717364i	$0.254652\pi$
$270$	−473840.	−0.395569
$271$	1.44733e6	1.19713	0.598567	−	0.801073i	$-0.295737\pi$
$271$	1.44733e6	1.19713	0.598567	+	0.801073i	$0.295737\pi$
$272$	2.43971e6	1.99947
$273$	351897.	0.285765
$274$	−3.80411e6	−3.06109
$275$	41325.1	0.0329520
$276$	−2.99958e6	−2.37022
$277$	472495.	0.369997	0.184998	−	0.982739i	$-0.440772\pi$
$277$	472495.	0.369997	0.184998	+	0.982739i	$0.440772\pi$
$278$	−1.02090e6	−0.792263
$279$	153718.	0.118227
$280$	−3.57568e6	−2.72561
$281$	−1.40270e6	−1.05974	−0.529869	−	0.848079i	$-0.677759\pi$
$281$	−1.40270e6	−1.05974	−0.529869	+	0.848079i	$0.677759\pi$
$282$	−1.27851e6	−0.957374
$283$	−1.38798e6	−1.03019	−0.515094	−	0.857134i	$-0.672243\pi$
$283$	−1.38798e6	−1.03019	−0.515094	+	0.857134i	$0.672243\pi$
$284$	1.84553e6	1.35777
$285$	−495637.	−0.361453
$286$	160981.	0.116375
$287$	1.03434e6	0.741241
$288$	706308.	0.501780
$289$	−217094.	−0.152898
$290$	−1.43708e6	−1.00343
$291$	−191183.	−0.132348
$292$	−4.84828e6	−3.32760
$293$	2.01582e6	1.37178	0.685889	−	0.727706i	$-0.259414\pi$
$293$	2.01582e6	1.37178	0.685889	+	0.727706i	$0.259414\pi$
$294$	55041.8	0.0371385
$295$	−2.83614e6	−1.89746
$296$	−701984.	−0.465691
$297$	−36915.5	−0.0242839
$298$	967229.	0.630941
$299$	1.36082e6	0.880285
$300$	−552318.	−0.354312
$301$	−1.43140e6	−0.910633
$302$	−2.45653e6	−1.54990
$303$	−222722.	−0.139366
$304$	1.95147e6	1.21109
$305$	2.27408e6	1.39977
$306$	919754.	0.561523
$307$	−1.68703e6	−1.02159	−0.510795	−	0.859702i	$-0.670649\pi$
$307$	−1.68703e6	−1.02159	−0.510795	+	0.859702i	$0.670649\pi$
$308$	−484923.	−0.291270
$309$	−95481.0	−0.0568880
$310$	1.23352e6	0.729022
$311$	1.06191e6	0.622571	0.311285	−	0.950317i	$-0.399241\pi$
$311$	1.06191e6	0.622571	0.311285	+	0.950317i	$0.399241\pi$
$312$	−1.23599e6	−0.718834
$313$	2.82010e6	1.62706	0.813532	−	0.581521i	$-0.197542\pi$
$313$	2.82010e6	1.62706	0.813532	+	0.581521i	$0.197542\pi$
$314$	606476.	0.347128
$315$	−647543.	−0.367699
$316$	3.19098e6	1.79765
$317$	−672981.	−0.376144	−0.188072	−	0.982155i	$-0.560224\pi$
$317$	−672981.	−0.376144	−0.188072	+	0.982155i	$0.560224\pi$
$318$	−641852.	−0.355932
$319$	−111959.	−0.0616002
$320$	1.19883e6	0.654462
$321$	272616.	0.147669
$322$	−5.84354e6	−3.14077
$323$	962064.	0.513095
$324$	493384.	0.261109
$325$	250570.	0.131589
$326$	−2.48510e6	−1.29509
$327$	−122405.	−0.0633039
$328$	−3.63298e6	−1.86457
$329$	−1.74720e6	−0.889922
$330$	−296229.	−0.149742
$331$	217687.	0.109210	0.0546051	−	0.998508i	$-0.482610\pi$
$331$	217687.	0.109210	0.0546051	+	0.998508i	$0.482610\pi$
$332$	4.10502e6	2.04395
$333$	−127127.	−0.0628241
$334$	−1.57352e6	−0.771804
$335$	−563147.	−0.274163
$336$	2.54957e6	1.23202
$337$	569712.	0.273263	0.136631	−	0.990622i	$-0.456372\pi$
$337$	569712.	0.273263	0.136631	+	0.990622i	$0.456372\pi$
$338$	−2.86817e6	−1.36557
$339$	1.29923e6	0.614024
$340$	5.17741e6	2.42893
$341$	96099.8	0.0447545
$342$	735691.	0.340118
$343$	2.21548e6	1.01679
$344$	5.02757e6	2.29067
$345$	−2.50411e6	−1.13268
$346$	−4.91730e6	−2.20819
$347$	1.62019e6	0.722342	0.361171	−	0.932500i	$-0.382377\pi$
$347$	1.62019e6	0.722342	0.361171	+	0.932500i	$0.382377\pi$
$348$	1.49635e6	0.662348
$349$	−618021.	−0.271606	−0.135803	−	0.990736i	$-0.543361\pi$
$349$	−618021.	−0.271606	−0.135803	+	0.990736i	$0.543361\pi$
$350$	−1.07598e6	−0.469499
$351$	−223833.	−0.0969744
$352$	441561.	0.189948
$353$	−1.05362e6	−0.450038	−0.225019	−	0.974354i	$-0.572244\pi$
$353$	−1.05362e6	−0.450038	−0.225019	+	0.974354i	$0.572244\pi$
$354$	4.20978e6	1.78546
$355$	1.54069e6	0.648850
$356$	−8.72774e6	−3.64986
$357$	1.25692e6	0.521961
$358$	−1.94556e6	−0.802299
$359$	727235.	0.297809	0.148905	−	0.988852i	$-0.452425\pi$
$359$	727235.	0.297809	0.148905	+	0.988852i	$0.452425\pi$
$360$	2.27440e6	0.924935
$361$	−1.70656e6	−0.689215
$362$	789494.	0.316648
$363$	1.42638e6	0.568158
$364$	−2.94028e6	−1.16315
$365$	−4.04744e6	−1.59019
$366$	−3.37549e6	−1.31715
$367$	−301960.	−0.117026	−0.0585132	−	0.998287i	$-0.518636\pi$
$367$	−301960.	−0.117026	−0.0585132	+	0.998287i	$0.518636\pi$
$368$	9.85942e6	3.79518
$369$	−657920.	−0.251540
$370$	−1.02013e6	−0.387393
$371$	−877147.	−0.330855
$372$	−1.28439e6	−0.481217
$373$	2.44421e6	0.909633	0.454816	−	0.890585i	$-0.349705\pi$
$373$	2.44421e6	0.909633	0.454816	+	0.890585i	$0.349705\pi$
$374$	575000.	0.212564
$375$	1.30455e6	0.479050
$376$	6.13678e6	2.23857
$377$	−678851.	−0.245992
$378$	961170.	0.345996
$379$	−1.00289e6	−0.358637	−0.179318	−	0.983791i	$-0.557389\pi$
$379$	−1.00289e6	−0.358637	−0.179318	+	0.983791i	$0.557389\pi$
$380$	4.14130e6	1.47122
$381$	−2.56021e6	−0.903573
$382$	−4.50393e6	−1.57918
$383$	4.39731e6	1.53176	0.765879	−	0.642984i	$-0.222304\pi$
$383$	4.39731e6	1.53176	0.765879	+	0.642984i	$0.222304\pi$
$384$	731849.	0.253276
$385$	−404823.	−0.139192
$386$	803405.	0.274452
$387$	910476.	0.309023
$388$	1.59743e6	0.538695
$389$	−142833.	−0.0478578	−0.0239289	−	0.999714i	$-0.507618\pi$
$389$	−142833.	−0.0478578	−0.0239289	+	0.999714i	$0.507618\pi$
$390$	−1.79616e6	−0.597974
$391$	4.86064e6	1.60787
$392$	−264197.	−0.0868387
$393$	1.51609e6	0.495158
$394$	−2.34764e6	−0.761886
$395$	2.66389e6	0.859060
$396$	308448.	0.0988425
$397$	−1.79795e6	−0.572534	−0.286267	−	0.958150i	$-0.592414\pi$
$397$	−1.79795e6	−0.572534	−0.286267	+	0.958150i	$0.592414\pi$
$398$	1.11457e7	3.52697
$399$	1.00539e6	0.316155
$400$	1.81543e6	0.567323
$401$	5.45682e6	1.69465	0.847323	−	0.531078i	$-0.178213\pi$
$401$	5.45682e6	1.69465	0.847323	+	0.531078i	$0.178213\pi$
$402$	835897.	0.257981
$403$	582691.	0.178721
$404$	1.86095e6	0.567259
$405$	411887.	0.124779
$406$	2.91507e6	0.877677
$407$	−79475.6	−0.0237820
$408$	−4.41476e6	−1.31298
$409$	3.21298e6	0.949728	0.474864	−	0.880059i	$-0.342497\pi$
$409$	3.21298e6	0.949728	0.474864	+	0.880059i	$0.342497\pi$
$410$	−5.27949e6	−1.55107
$411$	3.30673e6	0.965593
$412$	797791.	0.231551
$413$	5.75303e6	1.65967
$414$	3.71693e6	1.06582
$415$	3.42695e6	0.976759
$416$	2.67736e6	0.758531
$417$	887416.	0.249912
$418$	459930.	0.128751
$419$	5.01707e6	1.39610	0.698048	−	0.716051i	$-0.254052\pi$
$419$	5.01707e6	1.39610	0.698048	+	0.716051i	$0.254052\pi$
$420$	5.41055e6	1.49664
$421$	−4.32359e6	−1.18888	−0.594442	−	0.804139i	$-0.702627\pi$
$421$	−4.32359e6	−1.18888	−0.594442	+	0.804139i	$0.702627\pi$
$422$	−1.50079e6	−0.410242
$423$	1.11135e6	0.301995
$424$	3.08085e6	0.832255
$425$	894998.	0.240353
$426$	−2.28689e6	−0.610551
$427$	−4.61290e6	−1.22435
$428$	−2.27784e6	−0.601055
$429$	−139934.	−0.0367095
$430$	7.30613e6	1.90553
$431$	2.58461e6	0.670195	0.335097	−	0.942184i	$-0.391231\pi$
$431$	2.58461e6	0.670195	0.335097	+	0.942184i	$0.391231\pi$
$432$	−1.62172e6	−0.418086
$433$	−5.36541e6	−1.37526	−0.687628	−	0.726063i	$-0.741348\pi$
$433$	−5.36541e6	−1.37526	−0.687628	+	0.726063i	$0.741348\pi$
$434$	−2.50215e6	−0.637660
$435$	1.24919e6	0.316522
$436$	1.02276e6	0.257665
$437$	3.88792e6	0.973899
$438$	6.00775e6	1.49633
$439$	2.27523e6	0.563460	0.281730	−	0.959494i	$-0.409092\pi$
$439$	2.27523e6	0.563460	0.281730	+	0.959494i	$0.409092\pi$
$440$	1.42188e6	0.350133
$441$	−47845.2	−0.0117150
$442$	3.48645e6	0.848845
$443$	111087.	0.0268938	0.0134469	−	0.999910i	$-0.495720\pi$
$443$	111087.	0.0268938	0.0134469	+	0.999910i	$0.495720\pi$
$444$	1.06221e6	0.255713
$445$	−7.28609e6	−1.74419
$446$	5.80360e6	1.38153
$447$	−840767.	−0.199025
$448$	−2.43180e6	−0.572444
$449$	−878855.	−0.205732	−0.102866	−	0.994695i	$-0.532801\pi$
$449$	−878855.	−0.205732	−0.102866	+	0.994695i	$0.532801\pi$
$450$	684405.	0.159324
$451$	−411311.	−0.0952201
$452$	−1.08557e7	−2.49926
$453$	2.13535e6	0.488903
$454$	−3.68461e6	−0.838981
$455$	−2.45460e6	−0.555844
$456$	−3.53127e6	−0.795279
$457$	33633.3	0.00753319	0.00376659	−	0.999993i	$-0.498801\pi$
$457$	33633.3	0.00753319	0.00376659	+	0.999993i	$0.498801\pi$
$458$	−8.20311e6	−1.82732
$459$	−799498.	−0.177127
$460$	2.09231e7	4.61032
$461$	−4.39628e6	−0.963458	−0.481729	−	0.876320i	$-0.659991\pi$
$461$	−4.39628e6	−0.963458	−0.481729	+	0.876320i	$0.659991\pi$
$462$	600892.	0.130976
$463$	−6.06026e6	−1.31383	−0.656914	−	0.753966i	$-0.728139\pi$
$463$	−6.06026e6	−1.31383	−0.656914	+	0.753966i	$0.728139\pi$
$464$	−4.91841e6	−1.06055
$465$	−1.07224e6	−0.229963
$466$	−2.43902e6	−0.520297
$467$	5.79284e6	1.22913	0.614567	−	0.788865i	$-0.289331\pi$
$467$	5.79284e6	1.22913	0.614567	+	0.788865i	$0.289331\pi$
$468$	1.87024e6	0.394714
$469$	1.14233e6	0.239805
$470$	8.91805e6	1.86219
$471$	−527181.	−0.109498
$472$	−2.02067e7	−4.17484
$473$	569200.	0.116980
$474$	−3.95410e6	−0.808354
$475$	715890.	0.145583
$476$	−1.05022e7	−2.12453
$477$	557932.	0.112276
$478$	−1.54558e7	−3.09401
$479$	−6.26166e6	−1.24696	−0.623478	−	0.781841i	$-0.714281\pi$
$479$	−6.26166e6	−1.24696	−0.623478	+	0.781841i	$0.714281\pi$
$480$	−4.92674e6	−0.976015
$481$	−481892.	−0.0949701
$482$	−1.05197e7	−2.06246
$483$	5.07951e6	0.990728
$484$	−1.19181e7	−2.31257
$485$	1.33357e6	0.257431
$486$	−611377.	−0.117414
$487$	2.41113e6	0.460679	0.230339	−	0.973110i	$-0.426016\pi$
$487$	2.41113e6	0.460679	0.230339	+	0.973110i	$0.426016\pi$
$488$	1.62022e7	3.07981
$489$	2.16018e6	0.408525
$490$	−383935.	−0.0722383
$491$	−7.17398e6	−1.34294	−0.671470	−	0.741032i	$-0.734337\pi$
$491$	−7.17398e6	−1.34294	−0.671470	+	0.741032i	$0.734337\pi$
$492$	5.49725e6	1.02384
$493$	−2.42475e6	−0.449314
$494$	2.78874e6	0.514151
$495$	257498.	0.0472347
$496$	4.22171e6	0.770521
$497$	−3.12524e6	−0.567535
$498$	−5.08673e6	−0.919106
$499$	−690871.	−0.124207	−0.0621035	−	0.998070i	$-0.519781\pi$
$499$	−690871.	−0.124207	−0.0621035	+	0.998070i	$0.519781\pi$
$500$	−1.09001e7	−1.94987
$501$	1.36779e6	0.243458
$502$	1.87627e7	3.32305
$503$	−3.73736e6	−0.658635	−0.329317	−	0.944219i	$-0.606819\pi$
$503$	−3.73736e6	−0.658635	−0.329317	+	0.944219i	$0.606819\pi$
$504$	−4.61356e6	−0.809021
$505$	1.55356e6	0.271081
$506$	2.32371e6	0.403464
$507$	2.49317e6	0.430756
$508$	2.13918e7	3.67781
$509$	1.29912e6	0.222256	0.111128	−	0.993806i	$-0.464554\pi$
$509$	1.29912e6	0.222256	0.111128	+	0.993806i	$0.464554\pi$
$510$	−6.41559e6	−1.09222
$511$	8.21011e6	1.39090
$512$	−1.24420e7	−2.09756
$513$	−639501.	−0.107287
$514$	1.40012e7	2.33753
$515$	666012.	0.110653
$516$	−7.60748e6	−1.25781
$517$	694780.	0.114320
$518$	2.06931e6	0.338844
$519$	4.27438e6	0.696553
$520$	8.62144e6	1.39821
$521$	1.05497e7	1.70272	0.851361	−	0.524580i	$-0.175778\pi$
$521$	1.05497e7	1.70272	0.851361	+	0.524580i	$0.175778\pi$
$522$	−1.85421e6	−0.297839
$523$	−1.16809e7	−1.86734	−0.933669	−	0.358137i	$-0.883412\pi$
$523$	−1.16809e7	−1.86734	−0.933669	+	0.358137i	$0.883412\pi$
$524$	−1.26677e7	−2.01544
$525$	935300.	0.148099
$526$	−207376.	−0.0326809
$527$	2.08128e6	0.326441
$528$	−1.01385e6	−0.158266
$529$	1.32066e7	2.05188
$530$	4.47713e6	0.692326
$531$	−3.65936e6	−0.563208
$532$	−8.40050e6	−1.28684
$533$	−2.49394e6	−0.380249
$534$	1.08150e7	1.64124
$535$	−1.90159e6	−0.287231
$536$	−4.01226e6	−0.603222
$537$	1.69118e6	0.253078
$538$	1.71219e7	2.55033
$539$	−29911.3	−0.00443469
$540$	−3.44152e6	−0.507885
$541$	6.86525e6	1.00847	0.504235	−	0.863566i	$-0.331775\pi$
$541$	6.86525e6	1.00847	0.504235	+	0.863566i	$0.331775\pi$
$542$	1.49852e7	2.19111
$543$	−686270.	−0.0998839
$544$	9.56312e6	1.38549
$545$	853817.	0.123133
$546$	3.64345e6	0.523035
$547$	−1.94454e6	−0.277875	−0.138937	−	0.990301i	$-0.544369\pi$
$547$	−1.94454e6	−0.277875	−0.138937	+	0.990301i	$0.544369\pi$
$548$	−2.76294e7	−3.93025
$549$	2.93415e6	0.415482
$550$	427868.	0.0603120
$551$	−1.93951e6	−0.272152
$552$	−1.78411e7	−2.49215
$553$	−5.40362e6	−0.751401
$554$	4.89208e6	0.677203
$555$	886752.	0.122200
$556$	−7.41480e6	−1.01721
$557$	−1.01902e7	−1.39170	−0.695850	−	0.718187i	$-0.744972\pi$
$557$	−1.01902e7	−1.39170	−0.695850	+	0.718187i	$0.744972\pi$
$558$	1.59156e6	0.216390
$559$	3.45129e6	0.467145
$560$	−1.77841e7	−2.39641
$561$	−499821.	−0.0670513
$562$	−1.45231e7	−1.93964
$563$	1.25174e7	1.66434	0.832170	−	0.554521i	$-0.187099\pi$
$563$	1.25174e7	1.66434	0.832170	+	0.554521i	$0.187099\pi$
$564$	−9.28588e6	−1.22921
$565$	−9.06253e6	−1.19434
$566$	−1.43707e7	−1.88555
$567$	−835499.	−0.109141
$568$	1.09770e7	1.42762
$569$	8.32892e6	1.07847	0.539235	−	0.842156i	$-0.318714\pi$
$569$	8.32892e6	1.07847	0.539235	+	0.842156i	$0.318714\pi$
$570$	−5.13169e6	−0.661566
$571$	−2.00526e6	−0.257383	−0.128692	−	0.991685i	$-0.541078\pi$
$571$	−2.00526e6	−0.257383	−0.128692	+	0.991685i	$0.541078\pi$
$572$	1.16921e6	0.149418
$573$	3.91505e6	0.498139
$574$	1.07093e7	1.35669
$575$	3.61689e6	0.456211
$576$	1.54681e6	0.194259
$577$	9.19302e6	1.14953	0.574763	−	0.818320i	$-0.305094\pi$
$577$	9.19302e6	1.14953	0.574763	+	0.818320i	$0.305094\pi$
$578$	−2.24773e6	−0.279849
$579$	−698362.	−0.0865734
$580$	−1.04376e7	−1.28834
$581$	−6.95146e6	−0.854350
$582$	−1.97946e6	−0.242236
$583$	348801.	0.0425017
$584$	−2.88368e7	−3.49877
$585$	1.56131e6	0.188626
$586$	2.08713e7	2.51076
$587$	−9.89906e6	−1.18577	−0.592883	−	0.805289i	$-0.702010\pi$
$587$	−9.89906e6	−1.18577	−0.592883	+	0.805289i	$0.702010\pi$
$588$	399771.	0.0476835
$589$	1.66477e6	0.197727
$590$	−2.93646e7	−3.47292
$591$	2.04069e6	0.240330
$592$	−3.49140e6	−0.409445
$593$	1.09980e7	1.28433	0.642163	−	0.766568i	$-0.278037\pi$
$593$	1.09980e7	1.28433	0.642163	+	0.766568i	$0.278037\pi$
$594$	−382213.	−0.0444467
$595$	−8.76746e6	−1.01527
$596$	7.02502e6	0.810088
$597$	−9.68848e6	−1.11255
$598$	1.40896e7	1.61118
$599$	5.49676e6	0.625950	0.312975	−	0.949761i	$-0.398674\pi$
$599$	5.49676e6	0.625950	0.312975	+	0.949761i	$0.398674\pi$
$600$	−3.28511e6	−0.372539
$601$	−5.28758e6	−0.597133	−0.298566	−	0.954389i	$-0.596508\pi$
$601$	−5.28758e6	−0.597133	−0.298566	+	0.954389i	$0.596508\pi$
$602$	−1.48203e7	−1.66673
$603$	−726606.	−0.0813778
$604$	−1.78419e7	−1.98998
$605$	−9.94948e6	−1.10513
$606$	−2.30600e6	−0.255081
$607$	−1.24220e7	−1.36842	−0.684209	−	0.729286i	$-0.739852\pi$
$607$	−1.24220e7	−1.36842	−0.684209	+	0.729286i	$0.739852\pi$
$608$	7.64933e6	0.839198
$609$	−2.53394e6	−0.276855
$610$	2.35452e7	2.56199
$611$	4.21273e6	0.456520
$612$	6.68021e6	0.720960
$613$	−2.41864e6	−0.259968	−0.129984	−	0.991516i	$-0.541493\pi$
$613$	−2.41864e6	−0.259968	−0.129984	+	0.991516i	$0.541493\pi$
$614$	−1.74670e7	−1.86981
$615$	4.58921e6	0.489272
$616$	−2.88425e6	−0.306253
$617$	−1.57501e6	−0.166560	−0.0832798	−	0.996526i	$-0.526540\pi$
$617$	−1.57501e6	−0.166560	−0.0832798	+	0.996526i	$0.526540\pi$
$618$	−988583.	−0.104122
$619$	−1.02681e7	−1.07712	−0.538560	−	0.842587i	$-0.681032\pi$
$619$	−1.02681e7	−1.07712	−0.538560	+	0.842587i	$0.681032\pi$
$620$	8.95908e6	0.936018
$621$	−3.23096e6	−0.336203
$622$	1.09948e7	1.13949
$623$	1.47796e7	1.52561
$624$	−6.14735e6	−0.632014
$625$	−1.16499e7	−1.19295
$626$	2.91986e7	2.97801
$627$	−399796.	−0.0406134
$628$	4.40486e6	0.445690
$629$	−1.72124e6	−0.173467
$630$	−6.70448e6	−0.672998
$631$	1.24728e7	1.24707	0.623536	−	0.781794i	$-0.285695\pi$
$631$	1.24728e7	1.24707	0.623536	+	0.781794i	$0.285695\pi$
$632$	1.89794e7	1.89013
$633$	1.30457e6	0.129407
$634$	−6.96785e6	−0.688456
$635$	1.78583e7	1.75755
$636$	−4.66180e6	−0.456994
$637$	−181364.	−0.0177093
$638$	−1.15919e6	−0.112747
$639$	1.98789e6	0.192593
$640$	−5.10489e6	−0.492648
$641$	1.83075e7	1.75988	0.879942	−	0.475080i	$-0.157581\pi$
$641$	1.83075e7	1.75988	0.879942	+	0.475080i	$0.157581\pi$
$642$	2.82259e6	0.270277
$643$	−1.02273e7	−0.975511	−0.487756	−	0.872980i	$-0.662184\pi$
$643$	−1.02273e7	−0.975511	−0.487756	+	0.872980i	$0.662184\pi$
$644$	−4.24419e7	−4.03255
$645$	−6.35088e6	−0.601083
$646$	9.96094e6	0.939116
$647$	−1.63976e7	−1.54000	−0.769998	−	0.638046i	$-0.779743\pi$
$647$	−1.63976e7	−1.54000	−0.769998	+	0.638046i	$0.779743\pi$
$648$	2.93457e6	0.274541
$649$	−2.28772e6	−0.213202
$650$	2.59433e6	0.240848
$651$	2.17500e6	0.201144
$652$	−1.80494e7	−1.66282
$653$	1.43388e7	1.31592	0.657962	−	0.753051i	$-0.271419\pi$
$653$	1.43388e7	1.31592	0.657962	+	0.753051i	$0.271419\pi$
$654$	−1.26735e6	−0.115865
$655$	−1.05752e7	−0.963134
$656$	−1.80691e7	−1.63937
$657$	−5.22225e6	−0.472003
$658$	−1.80900e7	−1.62882
$659$	4.19773e6	0.376531	0.188266	−	0.982118i	$-0.439713\pi$
$659$	4.19773e6	0.376531	0.188266	+	0.982118i	$0.439713\pi$
$660$	−2.15153e6	−0.192259
$661$	1.99042e7	1.77191	0.885953	−	0.463776i	$-0.153506\pi$
$661$	1.99042e7	1.77191	0.885953	+	0.463776i	$0.153506\pi$
$662$	2.25387e6	0.199887
$663$	−3.03061e6	−0.267760
$664$	2.44160e7	2.14909
$665$	−7.01290e6	−0.614955
$666$	−1.31624e6	−0.114987
$667$	−9.79898e6	−0.852837
$668$	−1.14286e7	−0.990947
$669$	−5.04480e6	−0.435791
$670$	−5.83066e6	−0.501800
$671$	1.83434e6	0.157280
$672$	9.99374e6	0.853699
$673$	5.40964e6	0.460395	0.230197	−	0.973144i	$-0.426063\pi$
$673$	5.40964e6	0.460395	0.230197	+	0.973144i	$0.426063\pi$
$674$	5.89863e6	0.500152
$675$	−594921.	−0.0502574
$676$	−2.08316e7	−1.75330
$677$	2.08335e7	1.74699	0.873494	−	0.486835i	$-0.161849\pi$
$677$	2.08335e7	1.74699	0.873494	+	0.486835i	$0.161849\pi$
$678$	1.34518e7	1.12385
$679$	−2.70510e6	−0.225169
$680$	3.07945e7	2.55388
$681$	3.20286e6	0.264649
$682$	994991.	0.0819140
$683$	−1.56895e7	−1.28694	−0.643469	−	0.765472i	$-0.722505\pi$
$683$	−1.56895e7	−1.28694	−0.643469	+	0.765472i	$0.722505\pi$
$684$	5.34335e6	0.436690
$685$	−2.30655e7	−1.87818
$686$	2.29384e7	1.86103
$687$	7.13058e6	0.576412
$688$	2.50053e7	2.01400
$689$	2.11492e6	0.169725
$690$	−2.59269e7	−2.07313
$691$	2.22105e7	1.76955	0.884774	−	0.466020i	$-0.154312\pi$
$691$	2.22105e7	1.76955	0.884774	+	0.466020i	$0.154312\pi$
$692$	−3.57146e7	−2.83518
$693$	−522327.	−0.0413152
$694$	1.67750e7	1.32210
$695$	−6.19002e6	−0.486105
$696$	8.90009e6	0.696420
$697$	−8.90796e6	−0.694539
$698$	−6.39882e6	−0.497120
$699$	2.12013e6	0.164123
$700$	−7.81489e6	−0.602807
$701$	1.36791e7	1.05138	0.525692	−	0.850675i	$-0.323806\pi$
$701$	1.36791e7	1.05138	0.525692	+	0.850675i	$0.323806\pi$
$702$	−2.31751e6	−0.177492
$703$	−1.37679e6	−0.105070
$704$	967015.	0.0735363
$705$	−7.75204e6	−0.587412
$706$	−1.09089e7	−0.823702
$707$	−3.15135e6	−0.237109
$708$	3.05758e7	2.29242
$709$	−3.89157e6	−0.290743	−0.145372	−	0.989377i	$-0.546438\pi$
$709$	−3.89157e6	−0.290743	−0.145372	+	0.989377i	$0.546438\pi$
$710$	1.59519e7	1.18759
$711$	3.43711e6	0.254988
$712$	−5.19113e7	−3.83762
$713$	8.41094e6	0.619613
$714$	1.30138e7	0.955344
$715$	976083.	0.0714039
$716$	−1.41307e7	−1.03010
$717$	1.34350e7	0.975977
$718$	7.52958e6	0.545079
$719$	2.59114e7	1.86926	0.934629	−	0.355624i	$-0.115731\pi$
$719$	2.59114e7	1.86926	0.934629	+	0.355624i	$0.115731\pi$
$720$	1.13120e7	0.813222
$721$	−1.35099e6	−0.0967860
$722$	−1.76693e7	−1.26147
$723$	9.14429e6	0.650585
$724$	5.73413e6	0.406557
$725$	−1.80430e6	−0.127487
$726$	1.47683e7	1.03990
$727$	5.00922e6	0.351507	0.175753	−	0.984434i	$-0.443764\pi$
$727$	5.00922e6	0.351507	0.175753	+	0.984434i	$0.443764\pi$
$728$	−1.74883e7	−1.22298
$729$	531441.	0.0370370
$730$	−4.19060e7	−2.91051
$731$	1.23275e7	0.853258
$732$	−2.45163e7	−1.69113
$733$	−5.76439e6	−0.396272	−0.198136	−	0.980175i	$-0.563489\pi$
$733$	−5.76439e6	−0.396272	−0.198136	+	0.980175i	$0.563489\pi$
$734$	−3.12641e6	−0.214193
$735$	333737.	0.0227869
$736$	3.86467e7	2.62977
$737$	−454251.	−0.0308054
$738$	−6.81192e6	−0.460393
$739$	−2.52997e7	−1.70413	−0.852067	−	0.523432i	$-0.824651\pi$
$739$	−2.52997e7	−1.70413	−0.852067	+	0.523432i	$0.824651\pi$
$740$	−7.40926e6	−0.497388
$741$	−2.42412e6	−0.162184
$742$	−9.08173e6	−0.605562
$743$	−2.31172e7	−1.53626	−0.768129	−	0.640295i	$-0.778812\pi$
$743$	−2.31172e7	−1.53626	−0.768129	+	0.640295i	$0.778812\pi$
$744$	−7.63938e6	−0.505971
$745$	5.86463e6	0.387124
$746$	2.53066e7	1.66490
$747$	4.42166e6	0.289924
$748$	4.17625e6	0.272918
$749$	3.85731e6	0.251235
$750$	1.35069e7	0.876804
$751$	9.19915e6	0.595179	0.297590	−	0.954694i	$-0.403817\pi$
$751$	9.19915e6	0.595179	0.297590	+	0.954694i	$0.403817\pi$
$752$	3.05220e7	1.96820
$753$	−1.63096e7	−1.04823
$754$	−7.02864e6	−0.450239
$755$	−1.48948e7	−0.950968
$756$	6.98101e6	0.444236
$757$	−1.77288e7	−1.12445	−0.562224	−	0.826985i	$-0.690054\pi$
$757$	−1.77288e7	−1.12445	−0.562224	+	0.826985i	$0.690054\pi$
$758$	−1.03836e7	−0.656411
$759$	−2.01989e6	−0.127269
$760$	2.46318e7	1.54690
$761$	2.24520e7	1.40538	0.702690	−	0.711496i	$-0.251982\pi$
$761$	2.24520e7	1.40538	0.702690	+	0.711496i	$0.251982\pi$
$762$	−2.65077e7	−1.65381
$763$	−1.73194e6	−0.107702
$764$	−3.27122e7	−2.02757
$765$	5.57677e6	0.344532
$766$	4.55285e7	2.80357
$767$	−1.38713e7	−0.851392
$768$	1.30771e7	0.800036
$769$	3.18501e6	0.194220	0.0971102	−	0.995274i	$-0.469040\pi$
$769$	3.18501e6	0.194220	0.0971102	+	0.995274i	$0.469040\pi$
$770$	−4.19143e6	−0.254762
$771$	−1.21706e7	−0.737352
$772$	5.83517e6	0.352379
$773$	−2.30921e7	−1.39000	−0.694999	−	0.719011i	$-0.744595\pi$
$773$	−2.30921e7	−1.39000	−0.694999	+	0.719011i	$0.744595\pi$
$774$	9.42681e6	0.565604
$775$	1.54872e6	0.0926230
$776$	9.50128e6	0.566406
$777$	−1.79875e6	−0.106885
$778$	−1.47885e6	−0.0875940
$779$	−7.12529e6	−0.420687
$780$	−1.30456e7	−0.767761
$781$	1.24277e6	0.0729057
$782$	5.03257e7	2.94288
$783$	1.61178e6	0.0939508
$784$	−1.31402e6	−0.0763504
$785$	3.67726e6	0.212986
$786$	1.56972e7	0.906285
$787$	1.37466e7	0.791149	0.395574	−	0.918434i	$-0.370546\pi$
$787$	1.37466e7	0.791149	0.395574	+	0.918434i	$0.370546\pi$
$788$	−1.70510e7	−0.978214
$789$	180262.	0.0103089
$790$	2.75812e7	1.57233
$791$	1.83831e7	1.04466
$792$	1.83460e6	0.103927
$793$	1.11223e7	0.628076
$794$	−1.86155e7	−1.04791
$795$	−3.89176e6	−0.218388
$796$	8.09520e7	4.52840
$797$	1.17631e6	0.0655956	0.0327978	−	0.999462i	$-0.489558\pi$
$797$	1.17631e6	0.0655956	0.0327978	+	0.999462i	$0.489558\pi$
$798$	1.04095e7	0.578658
$799$	1.50472e7	0.833852
$800$	7.11609e6	0.393112
$801$	−9.40095e6	−0.517715
$802$	5.64984e7	3.10170
$803$	−3.26478e6	−0.178676
$804$	6.07116e6	0.331231
$805$	−3.54313e7	−1.92707
$806$	6.03302e6	0.327113
$807$	−1.48833e7	−0.804478
$808$	1.10687e7	0.596440
$809$	−2.42473e7	−1.30254	−0.651272	−	0.758844i	$-0.725764\pi$
$809$	−2.42473e7	−1.30254	−0.651272	+	0.758844i	$0.725764\pi$
$810$	4.26456e6	0.228382
$811$	1.43498e7	0.766115	0.383057	−	0.923725i	$-0.374871\pi$
$811$	1.43498e7	0.766115	0.383057	+	0.923725i	$0.374871\pi$
$812$	2.11723e7	1.12688
$813$	−1.30259e7	−0.691166
$814$	−822868.	−0.0435280
$815$	−1.50680e7	−0.794624
$816$	−2.19574e7	−1.15440
$817$	9.86047e6	0.516824
$818$	3.32663e7	1.73828
$819$	−3.16708e6	−0.164987
$820$	−3.83452e7	−1.99148
$821$	−2.55905e7	−1.32501	−0.662507	−	0.749055i	$-0.730508\pi$
$821$	−2.55905e7	−1.32501	−0.662507	+	0.749055i	$0.730508\pi$
$822$	3.42370e7	1.76732
$823$	−2.61908e7	−1.34787	−0.673937	−	0.738789i	$-0.735398\pi$
$823$	−2.61908e7	−1.34787	−0.673937	+	0.738789i	$0.735398\pi$
$824$	4.74514e6	0.243462
$825$	−371926.	−0.0190249
$826$	5.95652e7	3.03769
$827$	4.80365e6	0.244235	0.122117	−	0.992516i	$-0.461032\pi$
$827$	4.80365e6	0.244235	0.122117	+	0.992516i	$0.461032\pi$
$828$	2.69963e7	1.36845
$829$	1.62257e7	0.820006	0.410003	−	0.912084i	$-0.365528\pi$
$829$	1.62257e7	0.820006	0.410003	+	0.912084i	$0.365528\pi$
$830$	3.54817e7	1.78776
$831$	−4.25245e6	−0.213618
$832$	5.86340e6	0.293657
$833$	−647804.	−0.0323468
$834$	9.18806e6	0.457413
$835$	−9.54079e6	−0.473552
$836$	3.34049e6	0.165308
$837$	−1.38347e6	−0.0682582
$838$	5.19454e7	2.55527
$839$	−9.40193e6	−0.461118	−0.230559	−	0.973058i	$-0.574055\pi$
$839$	−9.40193e6	−0.461118	−0.230559	+	0.973058i	$0.574055\pi$
$840$	3.21811e7	1.57363
$841$	−1.56229e7	−0.761678
$842$	−4.47652e7	−2.17601
$843$	1.26243e7	0.611840
$844$	−1.09003e7	−0.526725
$845$	−1.73907e7	−0.837865
$846$	1.15066e7	0.552740
$847$	2.01822e7	0.966631
$848$	1.53230e7	0.731736
$849$	1.24918e7	0.594779
$850$	9.26656e6	0.439918
$851$	−6.95594e6	−0.329255
$852$	−1.66098e7	−0.783909
$853$	−3.17955e7	−1.49621	−0.748105	−	0.663580i	$-0.769036\pi$
$853$	−3.17955e7	−1.49621	−0.748105	+	0.663580i	$0.769036\pi$
$854$	−4.77607e7	−2.24092
$855$	4.46074e6	0.208685
$856$	−1.35483e7	−0.631974
$857$	−2.98610e7	−1.38884	−0.694420	−	0.719570i	$-0.744339\pi$
$857$	−2.98610e7	−1.38884	−0.694420	+	0.719570i	$0.744339\pi$
$858$	−1.44883e6	−0.0671893
$859$	−2.82408e7	−1.30585	−0.652925	−	0.757422i	$-0.726459\pi$
$859$	−2.82408e7	−1.30585	−0.652925	+	0.757422i	$0.726459\pi$
$860$	5.30647e7	2.44658
$861$	−9.30908e6	−0.427956
$862$	2.67603e7	1.22665
$863$	−5.37342e6	−0.245598	−0.122799	−	0.992432i	$-0.539187\pi$
$863$	−5.37342e6	−0.245598	−0.122799	+	0.992432i	$0.539187\pi$
$864$	−6.35678e6	−0.289703
$865$	−2.98152e7	−1.35487
$866$	−5.55520e7	−2.51712
$867$	1.95384e6	0.0882758
$868$	−1.81732e7	−0.818715
$869$	2.14877e6	0.0965252
$870$	1.29337e7	0.579329
$871$	−2.75430e6	−0.123017
$872$	6.08320e6	0.270920
$873$	1.72065e6	0.0764111
$874$	4.02545e7	1.78252
$875$	1.84583e7	0.815028
$876$	4.36345e7	1.92119
$877$	−1.22230e7	−0.536635	−0.268318	−	0.963330i	$-0.586468\pi$
$877$	−1.22230e7	−0.536635	−0.268318	+	0.963330i	$0.586468\pi$
$878$	2.35571e7	1.03130
$879$	−1.81424e7	−0.791996
$880$	7.07192e6	0.307844
$881$	−1.99648e7	−0.866613	−0.433307	−	0.901247i	$-0.642653\pi$
$881$	−1.99648e7	−0.866613	−0.433307	+	0.901247i	$0.642653\pi$
$882$	−495376.	−0.0214419
$883$	3.28905e7	1.41961	0.709804	−	0.704400i	$-0.248784\pi$
$883$	3.28905e7	1.41961	0.709804	+	0.704400i	$0.248784\pi$
$884$	2.53223e7	1.08986
$885$	2.55253e7	1.09550
$886$	1.15016e6	0.0492237
$887$	2.48149e7	1.05902	0.529509	−	0.848304i	$-0.322376\pi$
$887$	2.48149e7	1.05902	0.529509	+	0.848304i	$0.322376\pi$
$888$	6.31785e6	0.268867
$889$	−3.62251e7	−1.53729
$890$	−7.54381e7	−3.19239
$891$	332240.	0.0140203
$892$	4.21518e7	1.77380
$893$	1.20359e7	0.505069
$894$	−8.70506e6	−0.364274
$895$	−1.17965e7	−0.492263
$896$	1.03551e7	0.430909
$897$	−1.22474e7	−0.508233
$898$	−9.09942e6	−0.376550
$899$	−4.19583e6	−0.173149
$900$	4.97087e6	0.204562
$901$	7.55416e6	0.310009
$902$	−4.25859e6	−0.174281
$903$	1.28826e7	0.525754
$904$	−6.45679e7	−2.62782
$905$	4.78696e6	0.194285
$906$	2.21088e7	0.894838
$907$	−1.22234e7	−0.493370	−0.246685	−	0.969096i	$-0.579341\pi$
$907$	−1.22234e7	−0.493370	−0.246685	+	0.969096i	$0.579341\pi$
$908$	−2.67615e7	−1.07720
$909$	2.00450e6	0.0804628
$910$	−2.54143e7	−1.01736
$911$	−2.91026e7	−1.16181	−0.580906	−	0.813970i	$-0.697302\pi$
$911$	−2.91026e7	−1.16181	−0.580906	+	0.813970i	$0.697302\pi$
$912$	−1.75632e7	−0.699226
$913$	2.76428e6	0.109750
$914$	348230.	0.0137880
$915$	−2.04667e7	−0.808156
$916$	−5.95795e7	−2.34616
$917$	2.14515e7	0.842433
$918$	−8.27778e6	−0.324196
$919$	4.98486e6	0.194699	0.0973495	−	0.995250i	$-0.468964\pi$
$919$	4.98486e6	0.194699	0.0973495	+	0.995250i	$0.468964\pi$
$920$	1.24447e8	4.84749
$921$	1.51833e7	0.589816
$922$	−4.55178e7	−1.76341
$923$	7.53537e6	0.291139
$924$	4.36431e6	0.168165
$925$	−1.28081e6	−0.0492187
$926$	−6.27462e7	−2.40469
$927$	859329.	0.0328443
$928$	−1.92791e7	−0.734880
$929$	6.76418e6	0.257144	0.128572	−	0.991700i	$-0.458961\pi$
$929$	6.76418e6	0.257144	0.128572	+	0.991700i	$0.458961\pi$
$930$	−1.11016e7	−0.420901
$931$	−518165.	−0.0195927
$932$	−1.77147e7	−0.668028
$933$	−9.55723e6	−0.359441
$934$	5.99774e7	2.24968
$935$	3.48642e6	0.130422
$936$	1.11239e7	0.415019
$937$	−3.59257e6	−0.133677	−0.0668385	−	0.997764i	$-0.521291\pi$
$937$	−3.59257e6	−0.133677	−0.0668385	+	0.997764i	$0.521291\pi$
$938$	1.18273e7	0.438914
$939$	−2.53809e7	−0.939385
$940$	6.47721e7	2.39094
$941$	−4.09791e7	−1.50865	−0.754325	−	0.656501i	$-0.772036\pi$
$941$	−4.09791e7	−1.50865	−0.754325	+	0.656501i	$0.772036\pi$
$942$	−5.45828e6	−0.200414
$943$	−3.59991e7	−1.31829
$944$	−1.00501e8	−3.67061
$945$	5.82789e6	0.212291
$946$	5.89334e6	0.214108
$947$	9.57043e6	0.346782	0.173391	−	0.984853i	$-0.444528\pi$
$947$	9.57043e6	0.346782	0.173391	+	0.984853i	$0.444528\pi$
$948$	−2.87188e7	−1.03788
$949$	−1.97957e7	−0.713518
$950$	7.41212e6	0.266461
$951$	6.05683e6	0.217167
$952$	−6.24656e7	−2.23382
$953$	−7.26918e6	−0.259270	−0.129635	−	0.991562i	$-0.541381\pi$
$953$	−7.26918e6	−0.259270	−0.129635	+	0.991562i	$0.541381\pi$
$954$	5.77667e6	0.205498
$955$	−2.73088e7	−0.968933
$956$	−1.12256e8	−3.97251
$957$	1.00763e6	0.0355649
$958$	−6.48315e7	−2.28230
$959$	4.67878e7	1.64280
$960$	−1.07895e7	−0.377854
$961$	−2.50277e7	−0.874202
$962$	−4.98937e6	−0.173823
$963$	−2.45354e6	−0.0852566
$964$	−7.64051e7	−2.64807
$965$	4.87131e6	0.168394
$966$	5.25919e7	1.81333
$967$	−5.23366e7	−1.79986	−0.899931	−	0.436033i	$-0.856383\pi$
$967$	−5.23366e7	−1.79986	−0.899931	+	0.436033i	$0.856383\pi$
$968$	−7.08872e7	−2.43153
$969$	−8.65858e6	−0.296236
$970$	1.38074e7	0.471174
$971$	−4.74586e7	−1.61535	−0.807675	−	0.589628i	$-0.799274\pi$
$971$	−4.74586e7	−1.61535	−0.807675	+	0.589628i	$0.799274\pi$
$972$	−4.44045e6	−0.150752
$973$	1.25563e7	0.425186
$974$	2.49642e7	0.843178
$975$	−2.25513e6	−0.0759732
$976$	8.05834e7	2.70783
$977$	−5.36352e7	−1.79768	−0.898842	−	0.438272i	$-0.855591\pi$
$977$	−5.36352e7	−1.79768	−0.898842	+	0.438272i	$0.855591\pi$
$978$	2.23659e7	0.747722
$979$	−5.87717e6	−0.195980
$980$	−2.78854e6	−0.0927494
$981$	1.10165e6	0.0365485
$982$	−7.42774e7	−2.45798
$983$	2.87346e7	0.948466	0.474233	−	0.880399i	$-0.342725\pi$
$983$	2.87346e7	0.948466	0.474233	+	0.880399i	$0.342725\pi$
$984$	3.26968e7	1.07651
$985$	−1.42345e7	−0.467468
$986$	−2.51052e7	−0.822378
$987$	1.57248e7	0.513797
$988$	2.02547e7	0.660137
$989$	4.98181e7	1.61956
$990$	2.66606e6	0.0864535
$991$	4.54790e7	1.47105	0.735523	−	0.677499i	$-0.236936\pi$
$991$	4.54790e7	1.47105	0.735523	+	0.677499i	$0.236936\pi$
$992$	1.65482e7	0.533914
$993$	−1.95919e6	−0.0630526
$994$	−3.23579e7	−1.03876
$995$	6.75804e7	2.16403
$996$	−3.69451e7	−1.18007
$997$	3.79990e7	1.21069	0.605346	−	0.795962i	$-0.293035\pi$
$997$	3.79990e7	1.21069	0.605346	+	0.795962i	$0.293035\pi$
$998$	−7.15309e6	−0.227336
$999$	1.14414e6	0.0362715

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.b.1.19	✓	20
3.2	odd	2		927.6.a.c.1.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.b.1.19	✓	20	1.1	even	1	trivial
927.6.a.c.1.2		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)

\(f(q)\)	\(=\)	\(q+10.3537 q^{2} -9.00000 q^{3} +75.1995 q^{4} +62.7780 q^{5} -93.1835 q^{6} -127.343 q^{7} +447.275 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+10.3537 q^{2} -9.00000 q^{3} +75.1995 q^{4} +62.7780 q^{5} -93.1835 q^{6} -127.343 q^{7} +447.275 q^{8} +81.0000 q^{9} +649.986 q^{10} +50.6386 q^{11} -676.795 q^{12} +307.042 q^{13} -1318.48 q^{14} -565.002 q^{15} +2224.58 q^{16} +1096.71 q^{17} +838.651 q^{18} +877.231 q^{19} +4720.87 q^{20} +1146.09 q^{21} +524.298 q^{22} +4432.04 q^{23} -4025.48 q^{24} +816.079 q^{25} +3179.02 q^{26} -729.000 q^{27} -9576.15 q^{28} -2210.94 q^{29} -5849.87 q^{30} +1897.76 q^{31} +8719.86 q^{32} -455.747 q^{33} +11355.0 q^{34} -7994.36 q^{35} +6091.16 q^{36} -1569.47 q^{37} +9082.60 q^{38} -2763.38 q^{39} +28079.1 q^{40} -8122.47 q^{41} +11866.3 q^{42} +11240.4 q^{43} +3808.00 q^{44} +5085.02 q^{45} +45888.1 q^{46} +13720.4 q^{47} -20021.2 q^{48} -590.682 q^{49} +8449.45 q^{50} -9870.35 q^{51} +23089.4 q^{52} +6888.05 q^{53} -7547.86 q^{54} +3178.99 q^{55} -56957.5 q^{56} -7895.08 q^{57} -22891.5 q^{58} -45177.3 q^{59} -42487.9 q^{60} +36224.1 q^{61} +19648.9 q^{62} -10314.8 q^{63} +19096.4 q^{64} +19275.5 q^{65} -4718.68 q^{66} -8970.44 q^{67} +82471.7 q^{68} -39888.3 q^{69} -82771.4 q^{70} +24541.9 q^{71} +36229.3 q^{72} -64472.2 q^{73} -16249.8 q^{74} -7344.71 q^{75} +65967.3 q^{76} -6448.49 q^{77} -28611.2 q^{78} +42433.5 q^{79} +139655. q^{80} +6561.00 q^{81} -84097.8 q^{82} +54588.4 q^{83} +86185.4 q^{84} +68849.0 q^{85} +116380. q^{86} +19898.5 q^{87} +22649.4 q^{88} -116061. q^{89} +52648.9 q^{90} -39099.7 q^{91} +333287. q^{92} -17079.8 q^{93} +142057. q^{94} +55070.8 q^{95} -78478.7 q^{96} +21242.6 q^{97} -6115.75 q^{98} +4101.73 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9}+O(q^{10}) \) 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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