LMFDB - Embedded newform 309.6.a.b.1.10

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			1.10
Root			$-1.45649$ 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)

$f(q)$	$=$	$q-1.45649 q^{2} -9.00000 q^{3} -29.8786 q^{4} +91.7313 q^{5} +13.1084 q^{6} +87.1582 q^{7} +90.1255 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-1.45649 q^{2} -9.00000 q^{3} -29.8786 q^{4} +91.7313 q^{5} +13.1084 q^{6} +87.1582 q^{7} +90.1255 q^{8} +81.0000 q^{9} -133.606 q^{10} +570.684 q^{11} +268.908 q^{12} +338.619 q^{13} -126.945 q^{14} -825.582 q^{15} +824.850 q^{16} +544.959 q^{17} -117.975 q^{18} -214.840 q^{19} -2740.81 q^{20} -784.424 q^{21} -831.194 q^{22} +1470.31 q^{23} -811.129 q^{24} +5289.64 q^{25} -493.194 q^{26} -729.000 q^{27} -2604.17 q^{28} -8136.74 q^{29} +1202.45 q^{30} -626.132 q^{31} -4085.40 q^{32} -5136.15 q^{33} -793.726 q^{34} +7995.13 q^{35} -2420.17 q^{36} +14145.0 q^{37} +312.911 q^{38} -3047.57 q^{39} +8267.33 q^{40} -7014.39 q^{41} +1142.50 q^{42} -10471.3 q^{43} -17051.3 q^{44} +7430.24 q^{45} -2141.49 q^{46} -5753.19 q^{47} -7423.65 q^{48} -9210.45 q^{49} -7704.29 q^{50} -4904.63 q^{51} -10117.5 q^{52} +13760.9 q^{53} +1061.78 q^{54} +52349.6 q^{55} +7855.17 q^{56} +1933.56 q^{57} +11851.1 q^{58} +9280.13 q^{59} +24667.3 q^{60} +18376.1 q^{61} +911.953 q^{62} +7059.81 q^{63} -20444.9 q^{64} +31061.9 q^{65} +7480.74 q^{66} +52396.2 q^{67} -16282.6 q^{68} -13232.8 q^{69} -11644.8 q^{70} +19934.1 q^{71} +7300.16 q^{72} +13927.8 q^{73} -20602.0 q^{74} -47606.7 q^{75} +6419.12 q^{76} +49739.8 q^{77} +4438.74 q^{78} +45890.3 q^{79} +75664.6 q^{80} +6561.00 q^{81} +10216.4 q^{82} -11465.1 q^{83} +23437.5 q^{84} +49989.8 q^{85} +15251.2 q^{86} +73230.7 q^{87} +51433.1 q^{88} +23677.2 q^{89} -10822.0 q^{90} +29513.4 q^{91} -43930.9 q^{92} +5635.19 q^{93} +8379.44 q^{94} -19707.5 q^{95} +36768.6 q^{96} +15055.0 q^{97} +13414.9 q^{98} +46225.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.45649	−0.257473	−0.128736	−	0.991679i	$-0.541092\pi$
$2$	−1.45649	−0.257473	−0.128736	+	0.991679i	$0.541092\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−29.8786	−0.933708
$5$	91.7313	1.64094	0.820470	−	0.571690i	$-0.193712\pi$
$5$	91.7313	1.64094	0.820470	+	0.571690i	$0.193712\pi$
$6$	13.1084	0.148652
$7$	87.1582	0.672300	0.336150	−	0.941808i	$-0.390875\pi$
$7$	87.1582	0.672300	0.336150	+	0.941808i	$0.390875\pi$
$8$	90.1255	0.497878
$9$	81.0000	0.333333
$10$	−133.606	−0.422498
$11$	570.684	1.42205	0.711023	−	0.703169i	$-0.248232\pi$
$11$	570.684	1.42205	0.711023	+	0.703169i	$0.248232\pi$
$12$	268.908	0.539076
$13$	338.619	0.555715	0.277858	−	0.960622i	$-0.410376\pi$
$13$	338.619	0.555715	0.277858	+	0.960622i	$0.410376\pi$
$14$	−126.945	−0.173099
$15$	−825.582	−0.947397
$16$	824.850	0.805518
$17$	544.959	0.457343	0.228671	−	0.973504i	$-0.426562\pi$
$17$	544.959	0.457343	0.228671	+	0.973504i	$0.426562\pi$
$18$	−117.975	−0.0858243
$19$	−214.840	−0.136531	−0.0682654	−	0.997667i	$-0.521746\pi$
$19$	−214.840	−0.136531	−0.0682654	+	0.997667i	$0.521746\pi$
$20$	−2740.81	−1.53216
$21$	−784.424	−0.388152
$22$	−831.194	−0.366139
$23$	1470.31	0.579548	0.289774	−	0.957095i	$-0.406420\pi$
$23$	1470.31	0.579548	0.289774	+	0.957095i	$0.406420\pi$
$24$	−811.129	−0.287450
$25$	5289.64	1.69268
$26$	−493.194	−0.143082
$27$	−729.000	−0.192450
$28$	−2604.17	−0.627731
$29$	−8136.74	−1.79662	−0.898309	−	0.439365i	$-0.855204\pi$
$29$	−8136.74	−1.79662	−0.898309	+	0.439365i	$0.855204\pi$
$30$	1202.45	0.243929
$31$	−626.132	−0.117020	−0.0585102	−	0.998287i	$-0.518635\pi$
$31$	−626.132	−0.117020	−0.0585102	+	0.998287i	$0.518635\pi$
$32$	−4085.40	−0.705277
$33$	−5136.15	−0.821019
$34$	−793.726	−0.117753
$35$	7995.13	1.10320
$36$	−2420.17	−0.311236
$37$	14145.0	1.69863	0.849313	−	0.527890i	$-0.177017\pi$
$37$	14145.0	1.69863	0.849313	+	0.527890i	$0.177017\pi$
$38$	312.911	0.0351530
$39$	−3047.57	−0.320842
$40$	8267.33	0.816987
$41$	−7014.39	−0.651674	−0.325837	−	0.945426i	$-0.605646\pi$
$41$	−7014.39	−0.651674	−0.325837	+	0.945426i	$0.605646\pi$
$42$	1142.50	0.0999388
$43$	−10471.3	−0.863630	−0.431815	−	0.901962i	$-0.642127\pi$
$43$	−10471.3	−0.863630	−0.431815	+	0.901962i	$0.642127\pi$
$44$	−17051.3	−1.32778
$45$	7430.24	0.546980
$46$	−2141.49	−0.149218
$47$	−5753.19	−0.379895	−0.189948	−	0.981794i	$-0.560832\pi$
$47$	−5753.19	−0.379895	−0.189948	+	0.981794i	$0.560832\pi$
$48$	−7423.65	−0.465066
$49$	−9210.45	−0.548013
$50$	−7704.29	−0.435820
$51$	−4904.63	−0.264047
$52$	−10117.5	−0.518876
$53$	13760.9	0.672910	0.336455	−	0.941700i	$-0.390772\pi$
$53$	13760.9	0.672910	0.336455	+	0.941700i	$0.390772\pi$
$54$	1061.78	0.0495507
$55$	52349.6	2.33349
$56$	7855.17	0.334723
$57$	1933.56	0.0788261
$58$	11851.1	0.462580
$59$	9280.13	0.347076	0.173538	−	0.984827i	$-0.444480\pi$
$59$	9280.13	0.347076	0.173538	+	0.984827i	$0.444480\pi$
$60$	24667.3	0.884592
$61$	18376.1	0.632310	0.316155	−	0.948708i	$-0.397608\pi$
$61$	18376.1	0.632310	0.316155	+	0.948708i	$0.397608\pi$
$62$	911.953	0.0301296
$63$	7059.81	0.224100
$64$	−20444.9	−0.623928
$65$	31061.9	0.911896
$66$	7480.74	0.211390
$67$	52396.2	1.42598	0.712989	−	0.701175i	$-0.247341\pi$
$67$	52396.2	1.42598	0.712989	+	0.701175i	$0.247341\pi$
$68$	−16282.6	−0.427024
$69$	−13232.8	−0.334602
$70$	−11644.8	−0.284045
$71$	19934.1	0.469300	0.234650	−	0.972080i	$-0.424606\pi$
$71$	19934.1	0.469300	0.234650	+	0.972080i	$0.424606\pi$
$72$	7300.16	0.165959
$73$	13927.8	0.305898	0.152949	−	0.988234i	$-0.451123\pi$
$73$	13927.8	0.305898	0.152949	+	0.988234i	$0.451123\pi$
$74$	−20602.0	−0.437350
$75$	−47606.7	−0.977271
$76$	6419.12	0.127480
$77$	49739.8	0.956042
$78$	4438.74	0.0826083
$79$	45890.3	0.827282	0.413641	−	0.910440i	$-0.364257\pi$
$79$	45890.3	0.827282	0.413641	+	0.910440i	$0.364257\pi$
$80$	75664.6	1.32181
$81$	6561.00	0.111111
$82$	10216.4	0.167788
$83$	−11465.1	−0.182676	−0.0913380	−	0.995820i	$-0.529114\pi$
$83$	−11465.1	−0.182676	−0.0913380	+	0.995820i	$0.529114\pi$
$84$	23437.5	0.362421
$85$	49989.8	0.750472
$86$	15251.2	0.222361
$87$	73230.7	1.03728
$88$	51433.1	0.708005
$89$	23677.2	0.316852	0.158426	−	0.987371i	$-0.449358\pi$
$89$	23677.2	0.316852	0.158426	+	0.987371i	$0.449358\pi$
$90$	−10822.0	−0.140833
$91$	29513.4	0.373607
$92$	−43930.9	−0.541129
$93$	5635.19	0.0675618
$94$	8379.44	0.0978128
$95$	−19707.5	−0.224039
$96$	36768.6	0.407192
$97$	15055.0	0.162461	0.0812307	−	0.996695i	$-0.474115\pi$
$97$	15055.0	0.162461	0.0812307	+	0.996695i	$0.474115\pi$
$98$	13414.9	0.141099
$99$	46225.4	0.474015
$100$	−158047.	−1.58047
$101$	−29285.2	−0.285657	−0.142829	−	0.989747i	$-0.545620\pi$
$101$	−29285.2	−0.285657	−0.142829	+	0.989747i	$0.545620\pi$
$102$	7143.53	0.0679849
$103$	10609.0	0.0985329
$103$	10609.0	0.0985329
$104$	30518.2	0.276678
$105$	−71956.2	−0.636935
$106$	−20042.6	−0.173256
$107$	2133.62	0.0180160	0.00900798	−	0.999959i	$-0.497133\pi$
$107$	2133.62	0.0180160	0.00900798	+	0.999959i	$0.497133\pi$
$108$	21781.5	0.179692
$109$	−190478.	−1.53561	−0.767803	−	0.640687i	$-0.778650\pi$
$109$	−190478.	−1.53561	−0.767803	+	0.640687i	$0.778650\pi$
$110$	−76246.5	−0.600811
$111$	−127305.	−0.980702
$112$	71892.4	0.541549
$113$	−142352.	−1.04874	−0.524369	−	0.851491i	$-0.675699\pi$
$113$	−142352.	−1.04874	−0.524369	+	0.851491i	$0.675699\pi$
$114$	−2816.20	−0.0202956
$115$	134874.	0.951004
$116$	243115.	1.67752
$117$	27428.1	0.185238
$118$	−13516.4	−0.0893626
$119$	47497.6	0.307471
$120$	−74405.9	−0.471688
$121$	164629.	1.02222
$122$	−26764.6	−0.162803
$123$	63129.5	0.376244
$124$	18708.0	0.109263
$125$	198565.	1.13665
$126$	−10282.5	−0.0576997
$127$	−32988.2	−0.181488	−0.0907442	−	0.995874i	$-0.528925\pi$
$127$	−32988.2	−0.181488	−0.0907442	+	0.995874i	$0.528925\pi$
$128$	160510.	0.865921
$129$	94241.3	0.498617
$130$	−45241.3	−0.234788
$131$	−204524.	−1.04128	−0.520638	−	0.853777i	$-0.674306\pi$
$131$	−204524.	−1.04128	−0.520638	+	0.853777i	$0.674306\pi$
$132$	153461.	0.766592
$133$	−18725.0	−0.0917896
$134$	−76314.4	−0.367151
$135$	−66872.1	−0.315799
$136$	49114.7	0.227701
$137$	257566.	1.17243	0.586216	−	0.810155i	$-0.300617\pi$
$137$	257566.	1.17243	0.586216	+	0.810155i	$0.300617\pi$
$138$	19273.4	0.0861511
$139$	110072.	0.483215	0.241608	−	0.970374i	$-0.422325\pi$
$139$	110072.	0.483215	0.241608	+	0.970374i	$0.422325\pi$
$140$	−238884.	−1.03007
$141$	51778.7	0.219333
$142$	−29033.8	−0.120832
$143$	193244.	0.790253
$144$	66812.9	0.268506
$145$	−746394.	−2.94814
$146$	−20285.7	−0.0787605
$147$	82894.1	0.316395
$148$	−422633.	−1.58602
$149$	356035.	1.31379	0.656897	−	0.753980i	$-0.271869\pi$
$149$	356035.	1.31379	0.656897	+	0.753980i	$0.271869\pi$
$150$	69338.6	0.251621
$151$	337485.	1.20451	0.602257	−	0.798302i	$-0.294268\pi$
$151$	337485.	1.20451	0.602257	+	0.798302i	$0.294268\pi$
$152$	−19362.5	−0.0679756
$153$	44141.7	0.152448
$154$	−72445.3	−0.246155
$155$	−57435.9	−0.192024
$156$	91057.2	0.299573
$157$	−109303.	−0.353901	−0.176950	−	0.984220i	$-0.556623\pi$
$157$	−109303.	−0.353901	−0.176950	+	0.984220i	$0.556623\pi$
$158$	−66838.7	−0.213003
$159$	−123848.	−0.388505
$160$	−374759.	−1.15732
$161$	128150.	0.389630
$162$	−9556.01	−0.0286081
$163$	−360424.	−1.06254	−0.531269	−	0.847203i	$-0.678285\pi$
$163$	−360424.	−1.06254	−0.531269	+	0.847203i	$0.678285\pi$
$164$	209580.	0.608473
$165$	−471146.	−1.34724
$166$	16698.7	0.0470341
$167$	556434.	1.54391	0.771956	−	0.635676i	$-0.219279\pi$
$167$	556434.	1.54391	0.771956	+	0.635676i	$0.219279\pi$
$168$	−70696.5	−0.193252
$169$	−256630.	−0.691180
$170$	−72809.5	−0.193226
$171$	−17402.0	−0.0455102
$172$	312867.	0.806377
$173$	749292.	1.90343	0.951713	−	0.306989i	$-0.0993213\pi$
$173$	749292.	1.90343	0.951713	+	0.306989i	$0.0993213\pi$
$174$	−106660.	−0.267071
$175$	461035.	1.13799
$176$	470729.	1.14548
$177$	−83521.2	−0.200384
$178$	−34485.6	−0.0815807
$179$	328640.	0.766634	0.383317	−	0.923617i	$-0.374782\pi$
$179$	328640.	0.766634	0.383317	+	0.923617i	$0.374782\pi$
$180$	−222005.	−0.510719
$181$	−316231.	−0.717478	−0.358739	−	0.933438i	$-0.616793\pi$
$181$	−316231.	−0.717478	−0.358739	+	0.933438i	$0.616793\pi$
$182$	−42985.9	−0.0961938
$183$	−165385.	−0.365064
$184$	132512.	0.288544
$185$	1.29754e6	2.78734
$186$	−8207.58	−0.0173953
$187$	310999.	0.650362
$188$	171897.	0.354711
$189$	−63538.3	−0.129384
$190$	28703.8	0.0576839
$191$	−730746.	−1.44938	−0.724691	−	0.689074i	$-0.758018\pi$
$191$	−730746.	−1.44938	−0.724691	+	0.689074i	$0.758018\pi$
$192$	184004.	0.360225
$193$	−570606.	−1.10266	−0.551332	−	0.834286i	$-0.685880\pi$
$193$	−570606.	−1.10266	−0.551332	+	0.834286i	$0.685880\pi$
$194$	−21927.4	−0.0418294
$195$	−279557.	−0.526483
$196$	275196.	0.511684
$197$	−706887.	−1.29773	−0.648865	−	0.760904i	$-0.724756\pi$
$197$	−706887.	−1.29773	−0.648865	+	0.760904i	$0.724756\pi$
$198$	−67326.7	−0.122046
$199$	−271135.	−0.485348	−0.242674	−	0.970108i	$-0.578024\pi$
$199$	−271135.	−0.485348	−0.242674	+	0.970108i	$0.578024\pi$
$200$	476731.	0.842749
$201$	−471566.	−0.823289
$202$	42653.5	0.0735490
$203$	−709184.	−1.20787
$204$	146544.	0.246543
$205$	−643439.	−1.06936
$206$	−15451.9	−0.0253696
$207$	119095.	0.193183
$208$	279310.	0.447639
$209$	−122606.	−0.194153
$210$	104803.	0.163994
$211$	34172.1	0.0528404	0.0264202	−	0.999651i	$-0.491589\pi$
$211$	34172.1	0.0528404	0.0264202	+	0.999651i	$0.491589\pi$
$212$	−411157.	−0.628301
$213$	−179407.	−0.270951
$214$	−3107.59	−0.00463862
$215$	−960542.	−1.41716
$216$	−65701.5	−0.0958166
$217$	−54572.5	−0.0786728
$218$	277429.	0.395377
$219$	−125351.	−0.176610
$220$	−1.56413e6	−2.17880
$221$	184533.	0.254152
$222$	185418.	0.252504
$223$	−848656.	−1.14280	−0.571399	−	0.820672i	$-0.693599\pi$
$223$	−848656.	−1.14280	−0.571399	+	0.820672i	$0.693599\pi$
$224$	−356076.	−0.474157
$225$	428461.	0.564228
$226$	207333.	0.270022
$227$	557995.	0.718729	0.359365	−	0.933197i	$-0.382993\pi$
$227$	557995.	0.718729	0.359365	+	0.933197i	$0.382993\pi$
$228$	−57772.1	−0.0736005
$229$	−147838.	−0.186293	−0.0931464	−	0.995652i	$-0.529692\pi$
$229$	−147838.	−0.186293	−0.0931464	+	0.995652i	$0.529692\pi$
$230$	−196442.	−0.244858
$231$	−447658.	−0.551971
$232$	−733328.	−0.894495
$233$	42511.3	0.0512997	0.0256499	−	0.999671i	$-0.491835\pi$
$233$	42511.3	0.0512997	0.0256499	+	0.999671i	$0.491835\pi$
$234$	−39948.7	−0.0476939
$235$	−527748.	−0.623385
$236$	−277278.	−0.324067
$237$	−413013.	−0.477631
$238$	−69179.7	−0.0791656
$239$	−1.06602e6	−1.20718	−0.603589	−	0.797296i	$-0.706263\pi$
$239$	−1.06602e6	−1.20718	−0.603589	+	0.797296i	$0.706263\pi$
$240$	−680981.	−0.763145
$241$	1.60179e6	1.77649	0.888244	−	0.459372i	$-0.151926\pi$
$241$	1.60179e6	1.77649	0.888244	+	0.459372i	$0.151926\pi$
$242$	−239780.	−0.263193
$243$	−59049.0	−0.0641500
$244$	−549054.	−0.590392
$245$	−844887.	−0.899256
$246$	−91947.3	−0.0968726
$247$	−72748.7	−0.0758722
$248$	−56430.4	−0.0582619
$249$	103186.	0.105468
$250$	−289207.	−0.292657
$251$	−13527.0	−0.0135524	−0.00677620	−	0.999977i	$-0.502157\pi$
$251$	−13527.0	−0.0135524	−0.00677620	+	0.999977i	$0.502157\pi$
$252$	−210938.	−0.209244
$253$	839083.	0.824145
$254$	48046.8	0.0467284
$255$	−449908.	−0.433285
$256$	420455.	0.400977
$257$	529963.	0.500510	0.250255	−	0.968180i	$-0.419486\pi$
$257$	529963.	0.500510	0.250255	+	0.968180i	$0.419486\pi$
$258$	−137261.	−0.128380
$259$	1.23285e6	1.14199
$260$	−928089.	−0.851444
$261$	−659076.	−0.598872
$262$	297887.	0.268100
$263$	1.03710e6	0.924553	0.462276	−	0.886736i	$-0.347033\pi$
$263$	1.03710e6	0.924553	0.462276	+	0.886736i	$0.347033\pi$
$264$	−462898.	−0.408767
$265$	1.26230e6	1.10420
$266$	27272.8	0.0236333
$267$	−213095.	−0.182934
$268$	−1.56553e6	−1.33145
$269$	−1.09033e6	−0.918706	−0.459353	−	0.888254i	$-0.651919\pi$
$269$	−1.09033e6	−0.918706	−0.459353	+	0.888254i	$0.651919\pi$
$270$	97398.4	0.0813097
$271$	1.41103e6	1.16711	0.583557	−	0.812072i	$-0.301660\pi$
$271$	1.41103e6	1.16711	0.583557	+	0.812072i	$0.301660\pi$
$272$	449510.	0.368398
$273$	−265620.	−0.215702
$274$	−375142.	−0.301869
$275$	3.01871e6	2.40707
$276$	395378.	0.312421
$277$	−572362.	−0.448200	−0.224100	−	0.974566i	$-0.571944\pi$
$277$	−572362.	−0.448200	−0.224100	+	0.974566i	$0.571944\pi$
$278$	−160319.	−0.124415
$279$	−50716.7	−0.0390068
$280$	720565.	0.549260
$281$	−2.04977e6	−1.54860	−0.774300	−	0.632818i	$-0.781898\pi$
$281$	−2.04977e6	−1.54860	−0.774300	+	0.632818i	$0.781898\pi$
$282$	−75415.0	−0.0564722
$283$	2.54030e6	1.88547	0.942733	−	0.333549i	$-0.108246\pi$
$283$	2.54030e6	1.88547	0.942733	+	0.333549i	$0.108246\pi$
$284$	−595604.	−0.438189
$285$	177368.	0.129349
$286$	−281458.	−0.203469
$287$	−611361.	−0.438120
$288$	−330917.	−0.235092
$289$	−1.12288e6	−0.790838
$290$	1.08711e6	0.759067
$291$	−135495.	−0.0937972
$292$	−416145.	−0.285619
$293$	170376.	0.115942	0.0579709	−	0.998318i	$-0.481537\pi$
$293$	170376.	0.115942	0.0579709	+	0.998318i	$0.481537\pi$
$294$	−120734.	−0.0814633
$295$	851279.	0.569530
$296$	1.27482e6	0.845708
$297$	−416028.	−0.273673
$298$	−518561.	−0.338267
$299$	497875.	0.322064
$300$	1.42242e6	0.912486
$301$	−912655.	−0.580618
$302$	−491542.	−0.310130
$303$	263567.	0.164924
$304$	−177211.	−0.109978
$305$	1.68567e6	1.03758
$306$	−64291.8	−0.0392511
$307$	1.27670e6	0.773113	0.386556	−	0.922266i	$-0.373665\pi$
$307$	1.27670e6	0.773113	0.386556	+	0.922266i	$0.373665\pi$
$308$	−1.48616e6	−0.892663
$309$	−95481.0	−0.0568880
$310$	83654.7	0.0494409
$311$	2.73085e6	1.60102	0.800509	−	0.599321i	$-0.204563\pi$
$311$	2.73085e6	1.60102	0.800509	+	0.599321i	$0.204563\pi$
$312$	−274663.	−0.159740
$313$	248252.	0.143229	0.0716146	−	0.997432i	$-0.477185\pi$
$313$	248252.	0.143229	0.0716146	+	0.997432i	$0.477185\pi$
$314$	159198.	0.0911199
$315$	647606.	0.367735
$316$	−1.37114e6	−0.772439
$317$	887223.	0.495889	0.247945	−	0.968774i	$-0.420245\pi$
$317$	887223.	0.495889	0.247945	+	0.968774i	$0.420245\pi$
$318$	180383.	0.100029
$319$	−4.64351e6	−2.55487
$320$	−1.87544e6	−1.02383
$321$	−19202.6	−0.0104015
$322$	−186648.	−0.100319
$323$	−117079.	−0.0624413
$324$	−196034.	−0.103745
$325$	1.79117e6	0.940650
$326$	524953.	0.273575
$327$	1.71431e6	0.886582
$328$	−632175.	−0.324454
$329$	−501437.	−0.255404
$330$	686218.	0.346879
$331$	2.20980e6	1.10862	0.554312	−	0.832309i	$-0.312982\pi$
$331$	2.20980e6	1.10862	0.554312	+	0.832309i	$0.312982\pi$
$332$	342561.	0.170566
$333$	1.14574e6	0.566209
$334$	−810439.	−0.397516
$335$	4.80638e6	2.33994
$336$	−647032.	−0.312664
$337$	2.15818e6	1.03517	0.517587	−	0.855630i	$-0.326830\pi$
$337$	2.15818e6	1.03517	0.517587	+	0.855630i	$0.326830\pi$
$338$	373779.	0.177960
$339$	1.28117e6	0.605489
$340$	−1.49363e6	−0.700721
$341$	−357323.	−0.166409
$342$	25345.8	0.0117177
$343$	−2.26763e6	−1.04073
$344$	−943726.	−0.429982
$345$	−1.21386e6	−0.549062
$346$	−1.09133e6	−0.490081
$347$	1.63773e6	0.730161	0.365081	−	0.930976i	$-0.381041\pi$
$347$	1.63773e6	0.730161	0.365081	+	0.930976i	$0.381041\pi$
$348$	−2.18803e6	−0.968514
$349$	−1.70866e6	−0.750918	−0.375459	−	0.926839i	$-0.622515\pi$
$349$	−1.70866e6	−0.750918	−0.375459	+	0.926839i	$0.622515\pi$
$350$	−671492.	−0.293002
$351$	−246853.	−0.106947
$352$	−2.33147e6	−1.00294
$353$	−2.54911e6	−1.08881	−0.544404	−	0.838823i	$-0.683244\pi$
$353$	−2.54911e6	−1.08881	−0.544404	+	0.838823i	$0.683244\pi$
$354$	121648.	0.0515935
$355$	1.82858e6	0.770093
$356$	−707444.	−0.295847
$357$	−427479.	−0.177519
$358$	−478660.	−0.197388
$359$	4.77096e6	1.95375	0.976877	−	0.213803i	$-0.0685851\pi$
$359$	4.77096e6	1.95375	0.976877	+	0.213803i	$0.0685851\pi$
$360$	669654.	0.272329
$361$	−2.42994e6	−0.981359
$362$	460587.	0.184731
$363$	−1.48166e6	−0.590177
$364$	−881820.	−0.348840
$365$	1.27762e6	0.501960
$366$	240882.	0.0939942
$367$	−1.35333e6	−0.524491	−0.262245	−	0.965001i	$-0.584463\pi$
$367$	−1.35333e6	−0.524491	−0.262245	+	0.965001i	$0.584463\pi$
$368$	1.21279e6	0.466836
$369$	−568165.	−0.217225
$370$	−1.88985e6	−0.717666
$371$	1.19937e6	0.452397
$372$	−168372.	−0.0630830
$373$	1.20226e6	0.447430	0.223715	−	0.974655i	$-0.428181\pi$
$373$	1.20226e6	0.447430	0.223715	+	0.974655i	$0.428181\pi$
$374$	−452967.	−0.167451
$375$	−1.78708e6	−0.656246
$376$	−518509.	−0.189141
$377$	−2.75525e6	−0.998408
$378$	92542.7	0.0333129
$379$	4.32034e6	1.54497	0.772485	−	0.635033i	$-0.219013\pi$
$379$	4.32034e6	1.54497	0.772485	+	0.635033i	$0.219013\pi$
$380$	588834.	0.209187
$381$	296893.	0.104782
$382$	1.06432e6	0.373177
$383$	−522974.	−0.182172	−0.0910862	−	0.995843i	$-0.529034\pi$
$383$	−522974.	−0.182172	−0.0910862	+	0.995843i	$0.529034\pi$
$384$	−1.44459e6	−0.499940
$385$	4.56269e6	1.56881
$386$	831080.	0.283906
$387$	−848171.	−0.287877
$388$	−449822.	−0.151692
$389$	1.54499e6	0.517670	0.258835	−	0.965922i	$-0.416661\pi$
$389$	1.54499e6	0.517670	0.258835	+	0.965922i	$0.416661\pi$
$390$	407172.	0.135555
$391$	801260.	0.265052
$392$	−830096.	−0.272843
$393$	1.84072e6	0.601181
$394$	1.02957e6	0.334130
$395$	4.20958e6	1.35752
$396$	−1.38115e6	−0.442592
$397$	−4.18413e6	−1.33238	−0.666191	−	0.745781i	$-0.732076\pi$
$397$	−4.18413e6	−1.33238	−0.666191	+	0.745781i	$0.732076\pi$
$398$	394905.	0.124964
$399$	168525.	0.0529947
$400$	4.36316e6	1.36349
$401$	−2.41558e6	−0.750170	−0.375085	−	0.926990i	$-0.622386\pi$
$401$	−2.41558e6	−0.750170	−0.375085	+	0.926990i	$0.622386\pi$
$402$	686830.	0.211975
$403$	−212020.	−0.0650301
$404$	875002.	0.266720
$405$	601849.	0.182327
$406$	1.03292e6	0.310993
$407$	8.07230e6	2.41553
$408$	−442032.	−0.131463
$409$	954487.	0.282138	0.141069	−	0.990000i	$-0.454946\pi$
$409$	954487.	0.282138	0.141069	+	0.990000i	$0.454946\pi$
$410$	937161.	0.275331
$411$	−2.31810e6	−0.676903
$412$	−316983.	−0.0920009
$413$	808840.	0.233339
$414$	−173461.	−0.0497394
$415$	−1.05171e6	−0.299760
$416$	−1.38339e6	−0.391933
$417$	−990650.	−0.278985
$418$	178573.	0.0499892
$419$	−6.10512e6	−1.69887	−0.849433	−	0.527696i	$-0.823056\pi$
$419$	−6.10512e6	−1.69887	−0.849433	+	0.527696i	$0.823056\pi$
$420$	2.14995e6	0.594711
$421$	−6.01672e6	−1.65445	−0.827226	−	0.561869i	$-0.810082\pi$
$421$	−6.01672e6	−1.65445	−0.827226	+	0.561869i	$0.810082\pi$
$422$	−49771.3	−0.0136050
$423$	−466008.	−0.126632
$424$	1.24021e6	0.335027
$425$	2.88264e6	0.774136
$426$	261304.	0.0697624
$427$	1.60163e6	0.425102
$428$	−63749.7	−0.0168216
$429$	−1.73920e6	−0.456253
$430$	1.39902e6	0.364881
$431$	−3.39728e6	−0.880923	−0.440462	−	0.897772i	$-0.645185\pi$
$431$	−3.39728e6	−0.880923	−0.440462	+	0.897772i	$0.645185\pi$
$432$	−601316.	−0.155022
$433$	75813.1	0.0194323	0.00971616	−	0.999953i	$-0.496907\pi$
$433$	75813.1	0.0194323	0.00971616	+	0.999953i	$0.496907\pi$
$434$	79484.2	0.0202561
$435$	6.71755e6	1.70211
$436$	5.69124e6	1.43381
$437$	−315881.	−0.0791262
$438$	182571.	0.0454724
$439$	1.40402e6	0.347707	0.173853	−	0.984772i	$-0.444378\pi$
$439$	1.40402e6	0.347707	0.173853	+	0.984772i	$0.444378\pi$
$440$	4.71803e6	1.16179
$441$	−746047.	−0.182671
$442$	−268770.	−0.0654374
$443$	1.72777e6	0.418290	0.209145	−	0.977885i	$-0.432932\pi$
$443$	1.72777e6	0.418290	0.209145	+	0.977885i	$0.432932\pi$
$444$	3.80369e6	0.915689
$445$	2.17194e6	0.519935
$446$	1.23606e6	0.294240
$447$	−3.20432e6	−0.758520
$448$	−1.78194e6	−0.419467
$449$	6.19819e6	1.45094	0.725470	−	0.688254i	$-0.241623\pi$
$449$	6.19819e6	1.45094	0.725470	+	0.688254i	$0.241623\pi$
$450$	−624047.	−0.145273
$451$	−4.00300e6	−0.926710
$452$	4.25328e6	0.979214
$453$	−3.03736e6	−0.695426
$454$	−812712.	−0.185053
$455$	2.70730e6	0.613067
$456$	174263.	0.0392457
$457$	−1.14035e6	−0.255417	−0.127708	−	0.991812i	$-0.540762\pi$
$457$	−1.14035e6	−0.255417	−0.127708	+	0.991812i	$0.540762\pi$
$458$	215324.	0.0479654
$459$	−397275.	−0.0880156
$460$	−4.02984e6	−0.887960
$461$	3.58743e6	0.786196	0.393098	−	0.919496i	$-0.371403\pi$
$461$	3.58743e6	0.786196	0.393098	+	0.919496i	$0.371403\pi$
$462$	652008.	0.142118
$463$	7.93860e6	1.72104	0.860520	−	0.509416i	$-0.170138\pi$
$463$	7.93860e6	1.72104	0.860520	+	0.509416i	$0.170138\pi$
$464$	−6.71159e6	−1.44721
$465$	516923.	0.110865
$466$	−61917.2	−0.0132083
$467$	2.69996e6	0.572882	0.286441	−	0.958098i	$-0.407528\pi$
$467$	2.69996e6	0.572882	0.286441	+	0.958098i	$0.407528\pi$
$468$	−819515.	−0.172959
$469$	4.56676e6	0.958685
$470$	768658.	0.160505
$471$	983724.	0.204325
$472$	836376.	0.172801
$473$	−5.97577e6	−1.22812
$474$	601548.	0.122977
$475$	−1.13642e6	−0.231103
$476$	−1.41917e6	−0.287088
$477$	1.11463e6	0.224303
$478$	1.55265e6	0.310816
$479$	−6.06348e6	−1.20749	−0.603745	−	0.797178i	$-0.706325\pi$
$479$	−6.06348e6	−1.20749	−0.603745	+	0.797178i	$0.706325\pi$
$480$	3.37283e6	0.668177
$481$	4.78975e6	0.943953
$482$	−2.33298e6	−0.457398
$483$	−1.15335e6	−0.224953
$484$	−4.91889e6	−0.954451
$485$	1.38101e6	0.266590
$486$	86004.1	0.0165169
$487$	1.20267e6	0.229787	0.114893	−	0.993378i	$-0.463347\pi$
$487$	1.20267e6	0.229787	0.114893	+	0.993378i	$0.463347\pi$
$488$	1.65616e6	0.314813
$489$	3.24382e6	0.613457
$490$	1.23057e6	0.231534
$491$	2.05826e6	0.385298	0.192649	−	0.981268i	$-0.438292\pi$
$491$	2.05826e6	0.385298	0.192649	+	0.981268i	$0.438292\pi$
$492$	−1.88622e6	−0.351302
$493$	−4.43419e6	−0.821670
$494$	105958.	0.0195351
$495$	4.24032e6	0.777831
$496$	−516465.	−0.0942620
$497$	1.73742e6	0.315510
$498$	−150289.	−0.0271552
$499$	−4.87731e6	−0.876858	−0.438429	−	0.898766i	$-0.644465\pi$
$499$	−4.87731e6	−0.876858	−0.438429	+	0.898766i	$0.644465\pi$
$500$	−5.93285e6	−1.06130
$501$	−5.00790e6	−0.891378
$502$	19701.9	0.00348938
$503$	8.99614e6	1.58539	0.792695	−	0.609618i	$-0.208677\pi$
$503$	8.99614e6	1.58539	0.792695	+	0.609618i	$0.208677\pi$
$504$	636269.	0.111574
$505$	−2.68637e6	−0.468746
$506$	−1.22211e6	−0.212195
$507$	2.30967e6	0.399053
$508$	985642.	0.169457
$509$	−9.99456e6	−1.70989	−0.854947	−	0.518715i	$-0.826411\pi$
$509$	−9.99456e6	−1.70989	−0.854947	+	0.518715i	$0.826411\pi$
$510$	655286.	0.111559
$511$	1.21392e6	0.205655
$512$	−5.74872e6	−0.969162
$513$	156618.	0.0262754
$514$	−771884.	−0.128868
$515$	973178.	0.161687
$516$	−2.81580e6	−0.465562
$517$	−3.28325e6	−0.540229
$518$	−1.79563e6	−0.294031
$519$	−6.74363e6	−1.09894
$520$	2.79947e6	0.454012
$521$	8.73179e6	1.40932	0.704659	−	0.709546i	$-0.251100\pi$
$521$	8.73179e6	1.40932	0.704659	+	0.709546i	$0.251100\pi$
$522$	959936.	0.154193
$523$	5.27617e6	0.843460	0.421730	−	0.906721i	$-0.361423\pi$
$523$	5.27617e6	0.843460	0.421730	+	0.906721i	$0.361423\pi$
$524$	6.11090e6	0.972248
$525$	−4.14931e6	−0.657019
$526$	−1.51052e6	−0.238047
$527$	−341216.	−0.0535184
$528$	−4.23656e6	−0.661345
$529$	−4.27453e6	−0.664124
$530$	−1.83853e6	−0.284303
$531$	751691.	0.115692
$532$	559479.	0.0857046
$533$	−2.37520e6	−0.362145
$534$	310370.	0.0471007
$535$	195720.	0.0295631
$536$	4.72223e6	0.709963
$537$	−2.95776e6	−0.442616
$538$	1.58805e6	0.236542
$539$	−5.25626e6	−0.779300
$540$	1.99805e6	0.294864
$541$	2.05185e6	0.301406	0.150703	−	0.988579i	$-0.451846\pi$
$541$	2.05185e6	0.301406	0.150703	+	0.988579i	$0.451846\pi$
$542$	−2.05515e6	−0.300501
$543$	2.84608e6	0.414236
$544$	−2.22638e6	−0.322553
$545$	−1.74728e7	−2.51984
$546$	386873.	0.0555375
$547$	2.68321e6	0.383431	0.191715	−	0.981451i	$-0.438595\pi$
$547$	2.68321e6	0.383431	0.191715	+	0.981451i	$0.438595\pi$
$548$	−7.69573e6	−1.09471
$549$	1.48847e6	0.210770
$550$	−4.39671e6	−0.619757
$551$	1.74810e6	0.245294
$552$	−1.19261e6	−0.166591
$553$	3.99972e6	0.556181
$554$	833639.	0.115399
$555$	−1.16778e7	−1.60927
$556$	−3.28881e6	−0.451182
$557$	−5.26167e6	−0.718597	−0.359299	−	0.933223i	$-0.616984\pi$
$557$	−5.26167e6	−0.718597	−0.359299	+	0.933223i	$0.616984\pi$
$558$	73868.2	0.0100432
$559$	−3.54576e6	−0.479932
$560$	6.59479e6	0.888650
$561$	−2.79899e6	−0.375487
$562$	2.98546e6	0.398723
$563$	−1.42342e7	−1.89261	−0.946307	−	0.323269i	$-0.895218\pi$
$563$	−1.42342e7	−1.89261	−0.946307	+	0.323269i	$0.895218\pi$
$564$	−1.54708e6	−0.204793
$565$	−1.30581e7	−1.72091
$566$	−3.69991e6	−0.485456
$567$	571845.	0.0747000
$568$	1.79657e6	0.233654
$569$	−7.06417e6	−0.914704	−0.457352	−	0.889286i	$-0.651202\pi$
$569$	−7.06417e6	−0.914704	−0.457352	+	0.889286i	$0.651202\pi$
$570$	−258334.	−0.0333038
$571$	−1.07660e7	−1.38186	−0.690930	−	0.722921i	$-0.742799\pi$
$571$	−1.07660e7	−1.38186	−0.690930	+	0.722921i	$0.742799\pi$
$572$	−5.77387e6	−0.737865
$573$	6.57671e6	0.836801
$574$	890440.	0.112804
$575$	7.77741e6	0.980992
$576$	−1.65603e6	−0.207976
$577$	−977086.	−0.122178	−0.0610890	−	0.998132i	$-0.519457\pi$
$577$	−977086.	−0.122178	−0.0610890	+	0.998132i	$0.519457\pi$
$578$	1.63546e6	0.203619
$579$	5.13545e6	0.636623
$580$	2.23012e7	2.75270
$581$	−999275.	−0.122813
$582$	197346.	0.0241502
$583$	7.85311e6	0.956909
$584$	1.25525e6	0.152300
$585$	2.51602e6	0.303965
$586$	−248151.	−0.0298519
$587$	−1.48868e7	−1.78323	−0.891613	−	0.452799i	$-0.850426\pi$
$587$	−1.48868e7	−1.78323	−0.891613	+	0.452799i	$0.850426\pi$
$588$	−2.47676e6	−0.295421
$589$	134518.	0.0159769
$590$	−1.23988e6	−0.146639
$591$	6.36198e6	0.749244
$592$	1.16675e7	1.36827
$593$	−4.68871e6	−0.547541	−0.273770	−	0.961795i	$-0.588271\pi$
$593$	−4.68871e6	−0.547541	−0.273770	+	0.961795i	$0.588271\pi$
$594$	605940.	0.0704634
$595$	4.35702e6	0.504542
$596$	−1.06379e7	−1.22670
$597$	2.44022e6	0.280216
$598$	−725148.	−0.0829228
$599$	−6.54814e6	−0.745677	−0.372839	−	0.927896i	$-0.621616\pi$
$599$	−6.54814e6	−0.745677	−0.372839	+	0.927896i	$0.621616\pi$
$600$	−4.29058e6	−0.486561
$601$	2.90845e6	0.328454	0.164227	−	0.986423i	$-0.447487\pi$
$601$	2.90845e6	0.328454	0.164227	+	0.986423i	$0.447487\pi$
$602$	1.32927e6	0.149493
$603$	4.24409e6	0.475326
$604$	−1.00836e7	−1.12466
$605$	1.51016e7	1.67740
$606$	−383882.	−0.0424635
$607$	5.26607e6	0.580116	0.290058	−	0.957009i	$-0.406325\pi$
$607$	5.26607e6	0.580116	0.290058	+	0.957009i	$0.406325\pi$
$608$	877706.	0.0962919
$609$	6.38265e6	0.697362
$610$	−2.45515e6	−0.267149
$611$	−1.94814e6	−0.211114
$612$	−1.31889e6	−0.142341
$613$	139306.	0.0149733	0.00748666	−	0.999972i	$-0.497617\pi$
$613$	139306.	0.0149733	0.00748666	+	0.999972i	$0.497617\pi$
$614$	−1.85950e6	−0.199056
$615$	5.79095e6	0.617394
$616$	4.48282e6	0.475992
$617$	3.71960e6	0.393354	0.196677	−	0.980468i	$-0.436985\pi$
$617$	3.71960e6	0.393354	0.196677	+	0.980468i	$0.436985\pi$
$618$	139067.	0.0146471
$619$	−4.77619e6	−0.501019	−0.250510	−	0.968114i	$-0.580598\pi$
$619$	−4.77619e6	−0.501019	−0.250510	+	0.968114i	$0.580598\pi$
$620$	1.71611e6	0.179294
$621$	−1.07186e6	−0.111534
$622$	−3.97744e6	−0.412219
$623$	2.06366e6	0.213019
$624$	−2.51379e6	−0.258444
$625$	1.68451e6	0.172494
$626$	−361576.	−0.0368777
$627$	1.10345e6	0.112094
$628$	3.26581e6	0.330440
$629$	7.70843e6	0.776854
$630$	−943230.	−0.0946817
$631$	1.34302e7	1.34279	0.671394	−	0.741101i	$-0.265696\pi$
$631$	1.34302e7	1.34279	0.671394	+	0.741101i	$0.265696\pi$
$632$	4.13589e6	0.411885
$633$	−307549.	−0.0305074
$634$	−1.29223e6	−0.127678
$635$	−3.02605e6	−0.297812
$636$	3.70041e6	0.362750
$637$	−3.11883e6	−0.304539
$638$	6.76321e6	0.657811
$639$	1.61466e6	0.156433
$640$	1.47238e7	1.42092
$641$	1.80982e7	1.73977	0.869884	−	0.493256i	$-0.164193\pi$
$641$	1.80982e7	1.73977	0.869884	+	0.493256i	$0.164193\pi$
$642$	27968.3	0.00267811
$643$	−1.82861e7	−1.74419	−0.872093	−	0.489340i	$-0.837238\pi$
$643$	−1.82861e7	−1.74419	−0.872093	+	0.489340i	$0.837238\pi$
$644$	−3.82894e6	−0.363801
$645$	8.64488e6	0.818200
$646$	170524.	0.0160770
$647$	1.20419e7	1.13092	0.565461	−	0.824775i	$-0.308698\pi$
$647$	1.20419e7	1.13092	0.565461	+	0.824775i	$0.308698\pi$
$648$	591313.	0.0553197
$649$	5.29602e6	0.493558
$650$	−2.60882e6	−0.242192
$651$	491153.	0.0454218
$652$	1.07690e7	0.992101
$653$	−3.43861e6	−0.315573	−0.157787	−	0.987473i	$-0.550436\pi$
$653$	−3.43861e6	−0.315573	−0.157787	+	0.987473i	$0.550436\pi$
$654$	−2.49686e6	−0.228271
$655$	−1.87613e7	−1.70867
$656$	−5.78582e6	−0.524935
$657$	1.12815e6	0.101966
$658$	730337.	0.0657595
$659$	1.55056e6	0.139083	0.0695416	−	0.997579i	$-0.477846\pi$
$659$	1.55056e6	0.139083	0.0695416	+	0.997579i	$0.477846\pi$
$660$	1.40772e7	1.25793
$661$	−1.68743e7	−1.50218	−0.751092	−	0.660197i	$-0.770473\pi$
$661$	−1.68743e7	−1.50218	−0.751092	+	0.660197i	$0.770473\pi$
$662$	−3.21855e6	−0.285441
$663$	−1.66080e6	−0.146735
$664$	−1.03329e6	−0.0909503
$665$	−1.71767e6	−0.150621
$666$	−1.66876e6	−0.145783
$667$	−1.19635e7	−1.04123
$668$	−1.66255e7	−1.44156
$669$	7.63791e6	0.659795
$670$	−7.00042e6	−0.602473
$671$	1.04870e7	0.899174
$672$	3.20468e6	0.273755
$673$	−2.06760e7	−1.75966	−0.879830	−	0.475288i	$-0.842344\pi$
$673$	−2.06760e7	−1.75966	−0.879830	+	0.475288i	$0.842344\pi$
$674$	−3.14337e6	−0.266530
$675$	−3.85614e6	−0.325757
$676$	7.66777e6	0.645360
$677$	−1.90811e7	−1.60004	−0.800020	−	0.599973i	$-0.795178\pi$
$677$	−1.90811e7	−1.60004	−0.800020	+	0.599973i	$0.795178\pi$
$678$	−1.86600e6	−0.155897
$679$	1.31216e6	0.109223
$680$	4.50536e6	0.373643
$681$	−5.02195e6	−0.414959
$682$	520437.	0.0428457
$683$	−1.54801e7	−1.26976	−0.634882	−	0.772609i	$-0.718951\pi$
$683$	−1.54801e7	−1.26976	−0.634882	+	0.772609i	$0.718951\pi$
$684$	519949.	0.0424933
$685$	2.36269e7	1.92389
$686$	3.30278e6	0.267960
$687$	1.33054e6	0.107556
$688$	−8.63721e6	−0.695669
$689$	4.65969e6	0.373946
$690$	1.76798e6	0.141369
$691$	−7.10650e6	−0.566188	−0.283094	−	0.959092i	$-0.591361\pi$
$691$	−7.10650e6	−0.566188	−0.283094	+	0.959092i	$0.591361\pi$
$692$	−2.23878e7	−1.77724
$693$	4.02892e6	0.318681
$694$	−2.38533e6	−0.187997
$695$	1.00971e7	0.792927
$696$	6.59995e6	0.516437
$697$	−3.82255e6	−0.298038
$698$	2.48864e6	0.193341
$699$	−382602.	−0.0296179
$700$	−1.37751e7	−1.06255
$701$	2.83574e6	0.217957	0.108979	−	0.994044i	$-0.465242\pi$
$701$	2.83574e6	0.217957	0.108979	+	0.994044i	$0.465242\pi$
$702$	359538.	0.0275361
$703$	−3.03890e6	−0.231915
$704$	−1.16676e7	−0.887255
$705$	4.74973e6	0.359912
$706$	3.71274e6	0.280339
$707$	−2.55245e6	−0.192047
$708$	2.49550e6	0.187100
$709$	−1.31067e7	−0.979214	−0.489607	−	0.871943i	$-0.662860\pi$
$709$	−1.31067e7	−0.979214	−0.489607	+	0.871943i	$0.662860\pi$
$710$	−2.66330e6	−0.198278
$711$	3.71712e6	0.275761
$712$	2.13392e6	0.157753
$713$	−920609.	−0.0678190
$714$	622617.	0.0457063
$715$	1.77265e7	1.29676
$716$	−9.81933e6	−0.715812
$717$	9.59420e6	0.696965
$718$	−6.94884e6	−0.503039
$719$	−2.79106e6	−0.201348	−0.100674	−	0.994919i	$-0.532100\pi$
$719$	−2.79106e6	−0.201348	−0.100674	+	0.994919i	$0.532100\pi$
$720$	6.12883e6	0.440602
$721$	924661.	0.0662437
$722$	3.53918e6	0.252674
$723$	−1.44161e7	−1.02566
$724$	9.44856e6	0.669914
$725$	−4.30404e7	−3.04110
$726$	2.15802e6	0.151955
$727$	−1.87537e7	−1.31599	−0.657993	−	0.753024i	$-0.728595\pi$
$727$	−1.87537e7	−1.31599	−0.657993	+	0.753024i	$0.728595\pi$
$728$	2.65991e6	0.186011
$729$	531441.	0.0370370
$730$	−1.86084e6	−0.129241
$731$	−5.70641e6	−0.394975
$732$	4.94149e6	0.340863
$733$	1.90982e7	1.31290	0.656451	−	0.754369i	$-0.272057\pi$
$733$	1.90982e7	1.31290	0.656451	+	0.754369i	$0.272057\pi$
$734$	1.97110e6	0.135042
$735$	7.60398e6	0.519186
$736$	−6.00681e6	−0.408742
$737$	2.99017e7	2.02781
$738$	827526.	0.0559294
$739$	−2.47726e7	−1.66863	−0.834315	−	0.551288i	$-0.814137\pi$
$739$	−2.47726e7	−1.66863	−0.834315	+	0.551288i	$0.814137\pi$
$740$	−3.87686e7	−2.60256
$741$	654738.	0.0438049
$742$	−1.74687e6	−0.116480
$743$	−3.98988e6	−0.265148	−0.132574	−	0.991173i	$-0.542324\pi$
$743$	−3.98988e6	−0.265148	−0.132574	+	0.991173i	$0.542324\pi$
$744$	507874.	0.0336375
$745$	3.26596e7	2.15586
$746$	−1.75107e6	−0.115201
$747$	−928671.	−0.0608920
$748$	−9.29224e6	−0.607248
$749$	185962.	0.0121121
$750$	2.60287e6	0.168966
$751$	1.22633e7	0.793429	0.396715	−	0.917942i	$-0.370150\pi$
$751$	1.22633e7	0.793429	0.396715	+	0.917942i	$0.370150\pi$
$752$	−4.74552e6	−0.306012
$753$	121743.	0.00782449
$754$	4.01299e6	0.257063
$755$	3.09579e7	1.97653
$756$	1.89844e6	0.120807
$757$	1.21349e7	0.769657	0.384829	−	0.922988i	$-0.374261\pi$
$757$	1.21349e7	0.769657	0.384829	+	0.922988i	$0.374261\pi$
$758$	−6.29252e6	−0.397788
$759$	−7.55175e6	−0.475820
$760$	−1.77615e6	−0.111544
$761$	7.41604e6	0.464206	0.232103	−	0.972691i	$-0.425439\pi$
$761$	7.41604e6	0.464206	0.232103	+	0.972691i	$0.425439\pi$
$762$	−432422.	−0.0269786
$763$	−1.66017e7	−1.03239
$764$	2.18337e7	1.35330
$765$	4.04918e6	0.250157
$766$	761704.	0.0469045
$767$	3.14243e6	0.192875
$768$	−3.78409e6	−0.231504
$769$	−1.27779e7	−0.779192	−0.389596	−	0.920986i	$-0.627385\pi$
$769$	−1.27779e7	−0.779192	−0.389596	+	0.920986i	$0.627385\pi$
$770$	−6.64550e6	−0.403925
$771$	−4.76967e6	−0.288970
$772$	1.70489e7	1.02957
$773$	−1.23544e7	−0.743660	−0.371830	−	0.928301i	$-0.621270\pi$
$773$	−1.23544e7	−0.743660	−0.371830	+	0.928301i	$0.621270\pi$
$774$	1.23535e6	0.0741204
$775$	−3.31201e6	−0.198079
$776$	1.35684e6	0.0808859
$777$	−1.10956e7	−0.659326
$778$	−2.25026e6	−0.133286
$779$	1.50697e6	0.0889735
$780$	8.35280e6	0.491581
$781$	1.13761e7	0.667367
$782$	−1.16702e6	−0.0682438
$783$	5.93169e6	0.345759
$784$	−7.59724e6	−0.441434
$785$	−1.00265e7	−0.580730
$786$	−2.68098e6	−0.154788
$787$	1.73534e6	0.0998727	0.0499364	−	0.998752i	$-0.484098\pi$
$787$	1.73534e6	0.0998727	0.0499364	+	0.998752i	$0.484098\pi$
$788$	2.11208e7	1.21170
$789$	−9.33391e6	−0.533791
$790$	−6.13120e6	−0.349525
$791$	−1.24071e7	−0.705066
$792$	4.16608e6	0.236002
$793$	6.22251e6	0.351384
$794$	6.09413e6	0.343052
$795$	−1.13607e7	−0.637513
$796$	8.10115e6	0.453173
$797$	−7.00668e6	−0.390721	−0.195360	−	0.980732i	$-0.562588\pi$
$797$	−7.00668e6	−0.390721	−0.195360	+	0.980732i	$0.562588\pi$
$798$	−245455.	−0.0136447
$799$	−3.13525e6	−0.173742
$800$	−2.16103e7	−1.19381
$801$	1.91786e6	0.105617
$802$	3.51825e6	0.193149
$803$	7.94839e6	0.435001
$804$	1.40898e7	0.768711
$805$	1.17553e7	0.639360
$806$	308804.	0.0167435
$807$	9.81295e6	0.530415
$808$	−2.63934e6	−0.142222
$809$	−5.49444e6	−0.295157	−0.147578	−	0.989050i	$-0.547148\pi$
$809$	−5.49444e6	−0.295157	−0.147578	+	0.989050i	$0.547148\pi$
$810$	−876586.	−0.0469442
$811$	−3.39945e7	−1.81492	−0.907458	−	0.420142i	$-0.861980\pi$
$811$	−3.39945e7	−1.81492	−0.907458	+	0.420142i	$0.861980\pi$
$812$	2.11894e7	1.12779
$813$	−1.26993e7	−0.673834
$814$	−1.17572e7	−0.621932
$815$	−3.30622e7	−1.74356
$816$	−4.04559e6	−0.212694
$817$	2.24964e6	0.117912
$818$	−1.39020e6	−0.0726429
$819$	2.39058e6	0.124536
$820$	1.92251e7	0.998467
$821$	2.93656e7	1.52048	0.760241	−	0.649641i	$-0.225081\pi$
$821$	2.93656e7	1.52048	0.760241	+	0.649641i	$0.225081\pi$
$822$	3.37628e6	0.174284
$823$	−1.56256e7	−0.804149	−0.402074	−	0.915607i	$-0.631711\pi$
$823$	−1.56256e7	−0.804149	−0.402074	+	0.915607i	$0.631711\pi$
$824$	956141.	0.0490573
$825$	−2.71684e7	−1.38973
$826$	−1.17806e6	−0.0600785
$827$	2.17380e7	1.10524	0.552619	−	0.833434i	$-0.313629\pi$
$827$	2.17380e7	1.10524	0.552619	+	0.833434i	$0.313629\pi$
$828$	−3.55840e6	−0.180376
$829$	−1.57955e6	−0.0798267	−0.0399134	−	0.999203i	$-0.512708\pi$
$829$	−1.57955e6	−0.0798267	−0.0399134	+	0.999203i	$0.512708\pi$
$830$	1.53180e6	0.0771802
$831$	5.15126e6	0.258768
$832$	−6.92301e6	−0.346726
$833$	−5.01932e6	−0.250630
$834$	1.44287e6	0.0718310
$835$	5.10424e7	2.53347
$836$	3.66329e6	0.181282
$837$	456450.	0.0225206
$838$	8.89203e6	0.437412
$839$	3.51998e7	1.72637	0.863187	−	0.504885i	$-0.168465\pi$
$839$	3.51998e7	1.72637	0.863187	+	0.504885i	$0.168465\pi$
$840$	−6.48509e6	−0.317116
$841$	4.56954e7	2.22783
$842$	8.76327e6	0.425977
$843$	1.84479e7	0.894085
$844$	−1.02102e6	−0.0493375
$845$	−2.35410e7	−1.13419
$846$	678735.	0.0326043
$847$	1.43488e7	0.687236
$848$	1.13507e7	0.542041
$849$	−2.28627e7	−1.08857
$850$	−4.19852e6	−0.199319
$851$	2.07975e7	0.984436
$852$	5.36043e6	0.252989
$853$	−3.22689e7	−1.51849	−0.759245	−	0.650805i	$-0.774431\pi$
$853$	−3.22689e7	−1.51849	−0.759245	+	0.650805i	$0.774431\pi$
$854$	−2.33276e6	−0.109452
$855$	−1.59631e6	−0.0746796
$856$	192293.	0.00896974
$857$	−2.81363e7	−1.30862	−0.654312	−	0.756224i	$-0.727042\pi$
$857$	−2.81363e7	−1.30862	−0.654312	+	0.756224i	$0.727042\pi$
$858$	2.53312e6	0.117473
$859$	2.52190e7	1.16612	0.583061	−	0.812428i	$-0.301855\pi$
$859$	2.52190e7	1.16612	0.583061	+	0.812428i	$0.301855\pi$
$860$	2.86997e7	1.32322
$861$	5.50225e6	0.252949
$862$	4.94809e6	0.226814
$863$	−2.15981e7	−0.987163	−0.493581	−	0.869700i	$-0.664312\pi$
$863$	−2.15981e7	−0.987163	−0.493581	+	0.869700i	$0.664312\pi$
$864$	2.97826e6	0.135731
$865$	6.87336e7	3.12341
$866$	−110421.	−0.00500330
$867$	1.01059e7	0.456590
$868$	1.63055e6	0.0734574
$869$	2.61889e7	1.17643
$870$	−9.78402e6	−0.438247
$871$	1.77423e7	0.792438
$872$	−1.71670e7	−0.764543
$873$	1.21945e6	0.0541538
$874$	460077.	0.0203729
$875$	1.73066e7	0.764171
$876$	3.74530e6	0.164902
$877$	−1.33664e7	−0.586835	−0.293418	−	0.955984i	$-0.594793\pi$
$877$	−1.33664e7	−0.586835	−0.293418	+	0.955984i	$0.594793\pi$
$878$	−2.04494e6	−0.0895251
$879$	−1.53339e6	−0.0669390
$880$	4.31806e7	1.87967
$881$	−3.01856e7	−1.31027	−0.655134	−	0.755513i	$-0.727388\pi$
$881$	−3.01856e7	−1.31027	−0.655134	+	0.755513i	$0.727388\pi$
$882$	1.08661e6	0.0470328
$883$	5.61640e6	0.242413	0.121207	−	0.992627i	$-0.461324\pi$
$883$	5.61640e6	0.242413	0.121207	+	0.992627i	$0.461324\pi$
$884$	−5.51361e6	−0.237304
$885$	−7.66151e6	−0.328819
$886$	−2.51648e6	−0.107698
$887$	8.72958e6	0.372550	0.186275	−	0.982498i	$-0.440359\pi$
$887$	8.72958e6	0.372550	0.186275	+	0.982498i	$0.440359\pi$
$888$	−1.14734e7	−0.488270
$889$	−2.87519e6	−0.122015
$890$	−3.16341e6	−0.133869
$891$	3.74426e6	0.158005
$892$	2.53567e7	1.06704
$893$	1.23601e6	0.0518674
$894$	4.66705e6	0.195298
$895$	3.01466e7	1.25800
$896$	1.39898e7	0.582159
$897$	−4.48087e6	−0.185944
$898$	−9.02759e6	−0.373578
$899$	5.09468e6	0.210241
$900$	−1.28018e7	−0.526824
$901$	7.49912e6	0.307750
$902$	5.83031e6	0.238603
$903$	8.21390e6	0.335220
$904$	−1.28295e7	−0.522143
$905$	−2.90083e7	−1.17734
$906$	4.42388e6	0.179053
$907$	1.81084e7	0.730908	0.365454	−	0.930829i	$-0.380914\pi$
$907$	1.81084e7	0.730908	0.365454	+	0.930829i	$0.380914\pi$
$908$	−1.66721e7	−0.671083
$909$	−2.37210e6	−0.0952190
$910$	−3.94315e6	−0.157848
$911$	666038.	0.0265890	0.0132945	−	0.999912i	$-0.495768\pi$
$911$	666038.	0.0265890	0.0132945	+	0.999912i	$0.495768\pi$
$912$	1.59489e6	0.0634958
$913$	−6.54293e6	−0.259774
$914$	1.66091e6	0.0657629
$915$	−1.51710e7	−0.599048
$916$	4.41719e6	0.173943
$917$	−1.78259e7	−0.700050
$918$	578626.	0.0226616
$919$	−1.80403e7	−0.704620	−0.352310	−	0.935883i	$-0.614604\pi$
$919$	−1.80403e7	−0.704620	−0.352310	+	0.935883i	$0.614604\pi$
$920$	1.21555e7	0.473484
$921$	−1.14903e7	−0.446357
$922$	−5.22505e6	−0.202424
$923$	6.75006e6	0.260797
$924$	1.33754e7	0.515379
$925$	7.48217e7	2.87524
$926$	−1.15625e7	−0.443122
$927$	859329.	0.0328443
$928$	3.32418e7	1.26711
$929$	4.06610e7	1.54575	0.772874	−	0.634559i	$-0.218818\pi$
$929$	4.06610e7	1.54575	0.772874	+	0.634559i	$0.218818\pi$
$930$	−752892.	−0.0285447
$931$	1.97877e6	0.0748206
$932$	−1.27018e6	−0.0478989
$933$	−2.45776e7	−0.924348
$934$	−3.93246e6	−0.147502
$935$	2.85284e7	1.06721
$936$	2.47197e6	0.0922261
$937$	−9.24622e6	−0.344045	−0.172023	−	0.985093i	$-0.555030\pi$
$937$	−9.24622e6	−0.344045	−0.172023	+	0.985093i	$0.555030\pi$
$938$	−6.65143e6	−0.246836
$939$	−2.23427e6	−0.0826934
$940$	1.57684e7	0.582060
$941$	3.37750e7	1.24343	0.621715	−	0.783243i	$-0.286436\pi$
$941$	3.37750e7	1.24343	0.621715	+	0.783243i	$0.286436\pi$
$942$	−1.43278e6	−0.0526081
$943$	−1.03133e7	−0.377676
$944$	7.65472e6	0.279576
$945$	−5.82845e6	−0.212312
$946$	8.70364e6	0.316208
$947$	−4.13252e7	−1.49741	−0.748704	−	0.662904i	$-0.769324\pi$
$947$	−4.13252e7	−1.49741	−0.748704	+	0.662904i	$0.769324\pi$
$948$	1.23403e7	0.445968
$949$	4.71623e6	0.169992
$950$	1.65519e6	0.0595029
$951$	−7.98500e6	−0.286302
$952$	4.28075e6	0.153083
$953$	−2.49988e6	−0.0891635	−0.0445817	−	0.999006i	$-0.514196\pi$
$953$	−2.49988e6	−0.0891635	−0.0445817	+	0.999006i	$0.514196\pi$
$954$	−1.62345e6	−0.0577520
$955$	−6.70323e7	−2.37835
$956$	3.18513e7	1.12715
$957$	4.17916e7	1.47506
$958$	8.83139e6	0.310896
$959$	2.24490e7	0.788225
$960$	1.68789e7	0.591108
$961$	−2.82371e7	−0.986306
$962$	−6.97621e6	−0.243042
$963$	172823.	0.00600532
$964$	−4.78592e7	−1.65872
$965$	−5.23424e7	−1.80940
$966$	1.67983e6	0.0579194
$967$	9.44958e6	0.324972	0.162486	−	0.986711i	$-0.448049\pi$
$967$	9.44958e6	0.324972	0.162486	+	0.986711i	$0.448049\pi$
$968$	1.48373e7	0.508938
$969$	1.05371e6	0.0360505
$970$	−2.01143e6	−0.0686396
$971$	−1.20350e7	−0.409635	−0.204818	−	0.978800i	$-0.565660\pi$
$971$	−1.20350e7	−0.409635	−0.204818	+	0.978800i	$0.565660\pi$
$972$	1.76430e6	0.0598974
$973$	9.59370e6	0.324866
$974$	−1.75168e6	−0.0591638
$975$	−1.61205e7	−0.543085
$976$	1.51576e7	0.509337
$977$	−2.57033e7	−0.861496	−0.430748	−	0.902472i	$-0.641750\pi$
$977$	−2.57033e7	−0.861496	−0.430748	+	0.902472i	$0.641750\pi$
$978$	−4.72458e6	−0.157949
$979$	1.35122e7	0.450578
$980$	2.52441e7	0.839642
$981$	−1.54288e7	−0.511868
$982$	−2.99783e6	−0.0992038
$983$	4.12772e7	1.36247	0.681233	−	0.732066i	$-0.261444\pi$
$983$	4.12772e7	1.36247	0.681233	+	0.732066i	$0.261444\pi$
$984$	5.68957e6	0.187323
$985$	−6.48436e7	−2.12950
$986$	6.45835e6	0.211558
$987$	4.51294e6	0.147457
$988$	2.17363e6	0.0708425
$989$	−1.53960e7	−0.500515
$990$	−6.17597e6	−0.200270
$991$	−1.30029e7	−0.420586	−0.210293	−	0.977638i	$-0.567442\pi$
$991$	−1.30029e7	−0.420586	−0.210293	+	0.977638i	$0.567442\pi$
$992$	2.55800e6	0.0825318
$993$	−1.98882e7	−0.640064
$994$	−2.53053e6	−0.0812354
$995$	−2.48716e7	−0.796426
$996$	−3.08305e6	−0.0984763
$997$	−4.81976e7	−1.53563	−0.767817	−	0.640670i	$-0.778657\pi$
$997$	−4.81976e7	−1.53563	−0.767817	+	0.640670i	$0.778657\pi$
$998$	7.10375e6	0.225767
$999$	−1.03117e7	−0.326901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.b.1.10	✓	20
3.2	odd	2		927.6.a.c.1.11		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.b.1.10	✓	20	1.1	even	1	trivial
927.6.a.c.1.11		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)

\(f(q)\)	\(=\)	\(q-1.45649 q^{2} -9.00000 q^{3} -29.8786 q^{4} +91.7313 q^{5} +13.1084 q^{6} +87.1582 q^{7} +90.1255 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-1.45649 q^{2} -9.00000 q^{3} -29.8786 q^{4} +91.7313 q^{5} +13.1084 q^{6} +87.1582 q^{7} +90.1255 q^{8} +81.0000 q^{9} -133.606 q^{10} +570.684 q^{11} +268.908 q^{12} +338.619 q^{13} -126.945 q^{14} -825.582 q^{15} +824.850 q^{16} +544.959 q^{17} -117.975 q^{18} -214.840 q^{19} -2740.81 q^{20} -784.424 q^{21} -831.194 q^{22} +1470.31 q^{23} -811.129 q^{24} +5289.64 q^{25} -493.194 q^{26} -729.000 q^{27} -2604.17 q^{28} -8136.74 q^{29} +1202.45 q^{30} -626.132 q^{31} -4085.40 q^{32} -5136.15 q^{33} -793.726 q^{34} +7995.13 q^{35} -2420.17 q^{36} +14145.0 q^{37} +312.911 q^{38} -3047.57 q^{39} +8267.33 q^{40} -7014.39 q^{41} +1142.50 q^{42} -10471.3 q^{43} -17051.3 q^{44} +7430.24 q^{45} -2141.49 q^{46} -5753.19 q^{47} -7423.65 q^{48} -9210.45 q^{49} -7704.29 q^{50} -4904.63 q^{51} -10117.5 q^{52} +13760.9 q^{53} +1061.78 q^{54} +52349.6 q^{55} +7855.17 q^{56} +1933.56 q^{57} +11851.1 q^{58} +9280.13 q^{59} +24667.3 q^{60} +18376.1 q^{61} +911.953 q^{62} +7059.81 q^{63} -20444.9 q^{64} +31061.9 q^{65} +7480.74 q^{66} +52396.2 q^{67} -16282.6 q^{68} -13232.8 q^{69} -11644.8 q^{70} +19934.1 q^{71} +7300.16 q^{72} +13927.8 q^{73} -20602.0 q^{74} -47606.7 q^{75} +6419.12 q^{76} +49739.8 q^{77} +4438.74 q^{78} +45890.3 q^{79} +75664.6 q^{80} +6561.00 q^{81} +10216.4 q^{82} -11465.1 q^{83} +23437.5 q^{84} +49989.8 q^{85} +15251.2 q^{86} +73230.7 q^{87} +51433.1 q^{88} +23677.2 q^{89} -10822.0 q^{90} +29513.4 q^{91} -43930.9 q^{92} +5635.19 q^{93} +8379.44 q^{94} -19707.5 q^{95} +36768.6 q^{96} +15055.0 q^{97} +13414.9 q^{98} +46225.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9}+O(q^{10}) \) 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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