LMFDB - Embedded newform 309.6.a.c.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:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-1.37411 q^{2} -9.00000 q^{3} -30.1118 q^{4} +53.5472 q^{5} +12.3670 q^{6} -13.2336 q^{7} +85.3483 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-1.37411 q^{2} -9.00000 q^{3} -30.1118 q^{4} +53.5472 q^{5} +12.3670 q^{6} -13.2336 q^{7} +85.3483 q^{8} +81.0000 q^{9} -73.5796 q^{10} -774.562 q^{11} +271.006 q^{12} +547.241 q^{13} +18.1844 q^{14} -481.925 q^{15} +846.301 q^{16} +975.548 q^{17} -111.303 q^{18} -1048.57 q^{19} -1612.40 q^{20} +119.103 q^{21} +1064.33 q^{22} +1592.22 q^{23} -768.135 q^{24} -257.695 q^{25} -751.967 q^{26} -729.000 q^{27} +398.488 q^{28} +4648.98 q^{29} +662.216 q^{30} +1244.78 q^{31} -3894.05 q^{32} +6971.06 q^{33} -1340.51 q^{34} -708.624 q^{35} -2439.06 q^{36} +9334.84 q^{37} +1440.85 q^{38} -4925.17 q^{39} +4570.16 q^{40} +8501.22 q^{41} -163.660 q^{42} -7417.20 q^{43} +23323.5 q^{44} +4337.33 q^{45} -2187.88 q^{46} +7465.45 q^{47} -7616.71 q^{48} -16631.9 q^{49} +354.100 q^{50} -8779.93 q^{51} -16478.4 q^{52} -21815.6 q^{53} +1001.72 q^{54} -41475.7 q^{55} -1129.47 q^{56} +9437.14 q^{57} -6388.20 q^{58} +5551.80 q^{59} +14511.6 q^{60} -7439.97 q^{61} -1710.47 q^{62} -1071.92 q^{63} -21730.8 q^{64} +29303.2 q^{65} -9578.98 q^{66} -66196.5 q^{67} -29375.5 q^{68} -14330.0 q^{69} +973.725 q^{70} -43163.9 q^{71} +6913.21 q^{72} -9786.78 q^{73} -12827.1 q^{74} +2319.25 q^{75} +31574.4 q^{76} +10250.3 q^{77} +6767.70 q^{78} +1214.54 q^{79} +45317.1 q^{80} +6561.00 q^{81} -11681.6 q^{82} -55107.0 q^{83} -3586.40 q^{84} +52237.9 q^{85} +10192.0 q^{86} -41840.8 q^{87} -66107.6 q^{88} -52380.5 q^{89} -5959.95 q^{90} -7241.97 q^{91} -47944.6 q^{92} -11203.1 q^{93} -10258.3 q^{94} -56148.1 q^{95} +35046.5 q^{96} -76345.2 q^{97} +22854.0 q^{98} -62739.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9}+O(q^{10}) $ 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9	\( 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9} - 355 q^{10} - 708 q^{11} - 3078 q^{12} - 133 q^{13} - 2748 q^{14} + 477 q^{15} + 3678 q^{16} - 2006 q^{17} - 648 q^{18} - 4788 q^{19} - 2785 q^{20} - 90 q^{21} + 3609 q^{22} - 5695 q^{23} + 2376 q^{24} + 18477 q^{25} + 2432 q^{26} - 16038 q^{27} + 7635 q^{28} - 978 q^{29} + 3195 q^{30} - 6009 q^{31} + 22809 q^{32} + 6372 q^{33} - 4078 q^{34} - 22822 q^{35} + 27702 q^{36} + 13640 q^{37} - 5454 q^{38} + 1197 q^{39} - 13351 q^{40} - 24618 q^{41} + 24732 q^{42} + 1257 q^{43} - 65465 q^{44} - 4293 q^{45} - 6175 q^{46} - 63834 q^{47} - 33102 q^{48} + 18022 q^{49} - 41643 q^{50} + 18054 q^{51} - 40853 q^{52} - 13316 q^{53} + 5832 q^{54} - 35934 q^{55} - 251195 q^{56} + 43092 q^{57} - 103895 q^{58} - 138587 q^{59} + 25065 q^{60} - 53985 q^{61} - 218186 q^{62} + 810 q^{63} + 23758 q^{64} - 114073 q^{65} - 32481 q^{66} - 102785 q^{67} - 338669 q^{68} + 51255 q^{69} - 104184 q^{70} - 108740 q^{71} - 21384 q^{72} + 69762 q^{73} - 221377 q^{74} - 166293 q^{75} - 223267 q^{76} - 140360 q^{77} - 21888 q^{78} - 238938 q^{79} - 864251 q^{80} + 144342 q^{81} - 660293 q^{82} - 305455 q^{83} - 68715 q^{84} - 201204 q^{85} - 794679 q^{86} + 8802 q^{87} - 420823 q^{88} - 438448 q^{89} - 28755 q^{90} - 294186 q^{91} - 1251930 q^{92} + 54081 q^{93} - 826416 q^{94} - 652572 q^{95} - 205281 q^{96} - 284729 q^{97} - 887529 q^{98} - 57348 q^{99}+O(q^{100}) \) 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9 - 355 * q^10 - 708 * q^11 - 3078 * q^12 - 133 * q^13 - 2748 * q^14 + 477 * q^15 + 3678 * q^16 - 2006 * q^17 - 648 * q^18 - 4788 * q^19 - 2785 * q^20 - 90 * q^21 + 3609 * q^22 - 5695 * q^23 + 2376 * q^24 + 18477 * q^25 + 2432 * q^26 - 16038 * q^27 + 7635 * q^28 - 978 * q^29 + 3195 * q^30 - 6009 * q^31 + 22809 * q^32 + 6372 * q^33 - 4078 * q^34 - 22822 * q^35 + 27702 * q^36 + 13640 * q^37 - 5454 * q^38 + 1197 * q^39 - 13351 * q^40 - 24618 * q^41 + 24732 * q^42 + 1257 * q^43 - 65465 * q^44 - 4293 * q^45 - 6175 * q^46 - 63834 * q^47 - 33102 * q^48 + 18022 * q^49 - 41643 * q^50 + 18054 * q^51 - 40853 * q^52 - 13316 * q^53 + 5832 * q^54 - 35934 * q^55 - 251195 * q^56 + 43092 * q^57 - 103895 * q^58 - 138587 * q^59 + 25065 * q^60 - 53985 * q^61 - 218186 * q^62 + 810 * q^63 + 23758 * q^64 - 114073 * q^65 - 32481 * q^66 - 102785 * q^67 - 338669 * q^68 + 51255 * q^69 - 104184 * q^70 - 108740 * q^71 - 21384 * q^72 + 69762 * q^73 - 221377 * q^74 - 166293 * q^75 - 223267 * q^76 - 140360 * q^77 - 21888 * q^78 - 238938 * q^79 - 864251 * q^80 + 144342 * q^81 - 660293 * q^82 - 305455 * q^83 - 68715 * q^84 - 201204 * q^85 - 794679 * q^86 + 8802 * q^87 - 420823 * q^88 - 438448 * q^89 - 28755 * q^90 - 294186 * q^91 - 1251930 * q^92 + 54081 * q^93 - 826416 * q^94 - 652572 * q^95 - 205281 * q^96 - 284729 * q^97 - 887529 * q^98 - 57348 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.37411	−0.242910	−0.121455	−	0.992597i	$-0.538756\pi$
$2$	−1.37411	−0.242910	−0.121455	+	0.992597i	$0.538756\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−30.1118	−0.940995
$5$	53.5472	0.957882	0.478941	−	0.877847i	$-0.341021\pi$
$5$	53.5472	0.957882	0.478941	+	0.877847i	$0.341021\pi$
$6$	12.3670	0.140244
$7$	−13.2336	−0.102078	−0.0510392	−	0.998697i	$-0.516253\pi$
$7$	−13.2336	−0.102078	−0.0510392	+	0.998697i	$0.516253\pi$
$8$	85.3483	0.471487
$9$	81.0000	0.333333
$10$	−73.5796	−0.232679
$11$	−774.562	−1.93008	−0.965039	−	0.262107i	$-0.915583\pi$
$11$	−774.562	−1.93008	−0.965039	+	0.262107i	$0.915583\pi$
$12$	271.006	0.543284
$13$	547.241	0.898090	0.449045	−	0.893509i	$-0.351764\pi$
$13$	547.241	0.898090	0.449045	+	0.893509i	$0.351764\pi$
$14$	18.1844	0.0247959
$15$	−481.925	−0.553033
$16$	846.301	0.826466
$17$	975.548	0.818703	0.409351	−	0.912377i	$-0.365755\pi$
$17$	975.548	0.818703	0.409351	+	0.912377i	$0.365755\pi$
$18$	−111.303	−0.0809700
$19$	−1048.57	−0.666368	−0.333184	−	0.942862i	$-0.608123\pi$
$19$	−1048.57	−0.666368	−0.333184	+	0.942862i	$0.608123\pi$
$20$	−1612.40	−0.901362
$21$	119.103	0.0589349
$22$	1064.33	0.468835
$23$	1592.22	0.627600	0.313800	−	0.949489i	$-0.398398\pi$
$23$	1592.22	0.627600	0.313800	+	0.949489i	$0.398398\pi$
$24$	−768.135	−0.272213
$25$	−257.695	−0.0824624
$26$	−751.967	−0.218155
$27$	−729.000	−0.192450
$28$	398.488	0.0960552
$29$	4648.98	1.02651	0.513255	−	0.858236i	$-0.328440\pi$
$29$	4648.98	1.02651	0.513255	+	0.858236i	$0.328440\pi$
$30$	662.216	0.134337
$31$	1244.78	0.232643	0.116321	−	0.993212i	$-0.462890\pi$
$31$	1244.78	0.232643	0.116321	+	0.993212i	$0.462890\pi$
$32$	−3894.05	−0.672244
$33$	6971.06	1.11433
$34$	−1340.51	−0.198871
$35$	−708.624	−0.0977790
$36$	−2439.06	−0.313665
$37$	9334.84	1.12099	0.560496	−	0.828157i	$-0.310610\pi$
$37$	9334.84	1.12099	0.560496	+	0.828157i	$0.310610\pi$
$38$	1440.85	0.161867
$39$	−4925.17	−0.518513
$40$	4570.16	0.451629
$41$	8501.22	0.789808	0.394904	−	0.918722i	$-0.370778\pi$
$41$	8501.22	0.789808	0.394904	+	0.918722i	$0.370778\pi$
$42$	−163.660	−0.0143159
$43$	−7417.20	−0.611743	−0.305872	−	0.952073i	$-0.598948\pi$
$43$	−7417.20	−0.611743	−0.305872	+	0.952073i	$0.598948\pi$
$44$	23323.5	1.81619
$45$	4337.33	0.319294
$46$	−2187.88	−0.152450
$47$	7465.45	0.492960	0.246480	−	0.969148i	$-0.420726\pi$
$47$	7465.45	0.492960	0.246480	+	0.969148i	$0.420726\pi$
$48$	−7616.71	−0.477160
$49$	−16631.9	−0.989580
$50$	354.100	0.0200309
$51$	−8779.93	−0.472678
$52$	−16478.4	−0.845098
$53$	−21815.6	−1.06679	−0.533394	−	0.845867i	$-0.679084\pi$
$53$	−21815.6	−1.06679	−0.533394	+	0.845867i	$0.679084\pi$
$54$	1001.72	0.0467481
$55$	−41475.7	−1.84879
$56$	−1129.47	−0.0481286
$57$	9437.14	0.384728
$58$	−6388.20	−0.249349
$59$	5551.80	0.207637	0.103818	−	0.994596i	$-0.466894\pi$
$59$	5551.80	0.207637	0.103818	+	0.994596i	$0.466894\pi$
$60$	14511.6	0.520401
$61$	−7439.97	−0.256004	−0.128002	−	0.991774i	$-0.540856\pi$
$61$	−7439.97	−0.256004	−0.128002	+	0.991774i	$0.540856\pi$
$62$	−1710.47	−0.0565113
$63$	−1071.92	−0.0340261
$64$	−21730.8	−0.663171
$65$	29303.2	0.860264
$66$	−9578.98	−0.270682
$67$	−66196.5	−1.80156	−0.900778	−	0.434280i	$-0.857003\pi$
$67$	−66196.5	−1.80156	−0.900778	+	0.434280i	$0.857003\pi$
$68$	−29375.5	−0.770395
$69$	−14330.0	−0.362345
$70$	973.725	0.0237515
$71$	−43163.9	−1.01619	−0.508095	−	0.861301i	$-0.669650\pi$
$71$	−43163.9	−1.01619	−0.508095	+	0.861301i	$0.669650\pi$
$72$	6913.21	0.157162
$73$	−9786.78	−0.214948	−0.107474	−	0.994208i	$-0.534276\pi$
$73$	−9786.78	−0.214948	−0.107474	+	0.994208i	$0.534276\pi$
$74$	−12827.1	−0.272300
$75$	2319.25	0.0476097
$76$	31574.4	0.627048
$77$	10250.3	0.197019
$78$	6767.70	0.125952
$79$	1214.54	0.0218950	0.0109475	−	0.999940i	$-0.496515\pi$
$79$	1214.54	0.0218950	0.0109475	+	0.999940i	$0.496515\pi$
$80$	45317.1	0.791656
$81$	6561.00	0.111111
$82$	−11681.6	−0.191852
$83$	−55107.0	−0.878035	−0.439017	−	0.898479i	$-0.644673\pi$
$83$	−55107.0	−0.878035	−0.439017	+	0.898479i	$0.644673\pi$
$84$	−3586.40	−0.0554575
$85$	52237.9	0.784221
$86$	10192.0	0.148599
$87$	−41840.8	−0.592655
$88$	−66107.6	−0.910007
$89$	−52380.5	−0.700962	−0.350481	−	0.936570i	$-0.613982\pi$
$89$	−52380.5	−0.700962	−0.350481	+	0.936570i	$0.613982\pi$
$90$	−5959.95	−0.0775597
$91$	−7241.97	−0.0916755
$92$	−47944.6	−0.590569
$93$	−11203.1	−0.134316
$94$	−10258.3	−0.119745
$95$	−56148.1	−0.638301
$96$	35046.5	0.388120
$97$	−76345.2	−0.823858	−0.411929	−	0.911216i	$-0.635145\pi$
$97$	−76345.2	−0.823858	−0.411929	+	0.911216i	$0.635145\pi$
$98$	22854.0	0.240379
$99$	−62739.6	−0.643359
$100$	7759.67	0.0775967
$101$	−33267.1	−0.324498	−0.162249	−	0.986750i	$-0.551875\pi$
$101$	−33267.1	−0.324498	−0.162249	+	0.986750i	$0.551875\pi$
$102$	12064.6	0.114818
$103$	−10609.0	−0.0985329
$103$	−10609.0	−0.0985329
$104$	46706.0	0.423438
$105$	6377.61	0.0564527
$106$	29977.0	0.259133
$107$	−189535.	−1.60041	−0.800205	−	0.599727i	$-0.795276\pi$
$107$	−189535.	−1.60041	−0.800205	+	0.599727i	$0.795276\pi$
$108$	21951.5	0.181095
$109$	45063.9	0.363297	0.181649	−	0.983363i	$-0.441857\pi$
$109$	45063.9	0.363297	0.181649	+	0.983363i	$0.441857\pi$
$110$	56992.0	0.449089
$111$	−84013.6	−0.647205
$112$	−11199.6	−0.0843642
$113$	−36393.5	−0.268119	−0.134060	−	0.990973i	$-0.542801\pi$
$113$	−36393.5	−0.268119	−0.134060	+	0.990973i	$0.542801\pi$
$114$	−12967.6	−0.0934542
$115$	85258.9	0.601167
$116$	−139989.	−0.965940
$117$	44326.5	0.299363
$118$	−7628.77	−0.0504370
$119$	−12910.0	−0.0835718
$120$	−41131.5	−0.260748
$121$	438896.	2.72520
$122$	10223.3	0.0621859
$123$	−76511.0	−0.455996
$124$	−37482.7	−0.218916
$125$	−181134.	−1.03687
$126$	1472.94	0.00826528
$127$	83395.8	0.458812	0.229406	−	0.973331i	$-0.426322\pi$
$127$	83395.8	0.458812	0.229406	+	0.973331i	$0.426322\pi$
$128$	154470.	0.833335
$129$	66754.8	0.353190
$130$	−40265.7	−0.208967
$131$	81595.5	0.415421	0.207710	−	0.978190i	$-0.433399\pi$
$131$	81595.5	0.415421	0.207710	+	0.978190i	$0.433399\pi$
$132$	−209911.	−1.04858
$133$	13876.4	0.0680217
$134$	90961.0	0.437616
$135$	−39035.9	−0.184344
$136$	83261.4	0.386008
$137$	−101963.	−0.464130	−0.232065	−	0.972700i	$-0.574548\pi$
$137$	−101963.	−0.464130	−0.232065	+	0.972700i	$0.574548\pi$
$138$	19690.9	0.0880173
$139$	−51271.2	−0.225080	−0.112540	−	0.993647i	$-0.535899\pi$
$139$	−51271.2	−0.225080	−0.112540	+	0.993647i	$0.535899\pi$
$140$	21338.0	0.0920095
$141$	−67189.0	−0.284610
$142$	59311.8	0.246843
$143$	−423872.	−1.73338
$144$	68550.4	0.275489
$145$	248940.	0.983275
$146$	13448.1	0.0522130
$147$	149687.	0.571334
$148$	−281089.	−1.05485
$149$	310665.	1.14637	0.573187	−	0.819424i	$-0.305707\pi$
$149$	310665.	1.14637	0.573187	+	0.819424i	$0.305707\pi$
$150$	−3186.90	−0.0115649
$151$	−285335.	−1.01839	−0.509194	−	0.860652i	$-0.670056\pi$
$151$	−285335.	−1.01839	−0.509194	+	0.860652i	$0.670056\pi$
$152$	−89493.8	−0.314184
$153$	79019.4	0.272901
$154$	−14085.0	−0.0478579
$155$	66654.7	0.222844
$156$	148306.	0.487918
$157$	−187740.	−0.607866	−0.303933	−	0.952693i	$-0.598300\pi$
$157$	−187740.	−0.607866	−0.303933	+	0.952693i	$0.598300\pi$
$158$	−1668.91	−0.00531852
$159$	196341.	0.615910
$160$	−208516.	−0.643930
$161$	−21070.8	−0.0640644
$162$	−9015.52	−0.0269900
$163$	−54600.2	−0.160963	−0.0804814	−	0.996756i	$-0.525646\pi$
$163$	−54600.2	−0.160963	−0.0804814	+	0.996756i	$0.525646\pi$
$164$	−255987.	−0.743205
$165$	373281.	1.06740
$166$	75722.9	0.213283
$167$	−37637.8	−0.104432	−0.0522160	−	0.998636i	$-0.516628\pi$
$167$	−37637.8	−0.104432	−0.0522160	+	0.998636i	$0.516628\pi$
$168$	10165.2	0.0277871
$169$	−71820.8	−0.193434
$170$	−71780.4	−0.190495
$171$	−84934.3	−0.222123
$172$	223346.	0.575647
$173$	−391970.	−0.995720	−0.497860	−	0.867257i	$-0.665881\pi$
$173$	−391970.	−0.995720	−0.497860	+	0.867257i	$0.665881\pi$
$174$	57493.8	0.143962
$175$	3410.24	0.00841762
$176$	−655513.	−1.59514
$177$	−49966.2	−0.119879
$178$	71976.4	0.170271
$179$	−854899.	−1.99426	−0.997131	−	0.0756937i	$-0.975883\pi$
$179$	−854899.	−1.99426	−0.997131	+	0.0756937i	$0.975883\pi$
$180$	−130605.	−0.300454
$181$	397095.	0.900944	0.450472	−	0.892790i	$-0.351256\pi$
$181$	397095.	0.900944	0.450472	+	0.892790i	$0.351256\pi$
$182$	9951.25	0.0222689
$183$	66959.7	0.147804
$184$	135893.	0.295905
$185$	499855.	1.07378
$186$	15394.2	0.0326268
$187$	−755623.	−1.58016
$188$	−224798.	−0.463872
$189$	9647.31	0.0196450
$190$	77153.4	0.155050
$191$	−397489.	−0.788391	−0.394195	−	0.919027i	$-0.628977\pi$
$191$	−397489.	−0.788391	−0.394195	+	0.919027i	$0.628977\pi$
$192$	195577.	0.382882
$193$	−218097.	−0.421460	−0.210730	−	0.977544i	$-0.567584\pi$
$193$	−218097.	−0.421460	−0.210730	+	0.977544i	$0.567584\pi$
$194$	104906.	0.200123
$195$	−263729.	−0.496674
$196$	500816.	0.931190
$197$	170740.	0.313451	0.156726	−	0.987642i	$-0.449906\pi$
$197$	170740.	0.313451	0.156726	+	0.987642i	$0.449906\pi$
$198$	86210.9	0.156278
$199$	828187.	1.48250	0.741252	−	0.671227i	$-0.234233\pi$
$199$	828187.	1.48250	0.741252	+	0.671227i	$0.234233\pi$
$200$	−21993.8	−0.0388800
$201$	595768.	1.04013
$202$	45712.6	0.0788238
$203$	−61522.9	−0.104784
$204$	264380.	0.444788
$205$	455217.	0.756543
$206$	14577.9	0.0239346
$207$	128970.	0.209200
$208$	463130.	0.742241
$209$	812184.	1.28614
$210$	−8763.52	−0.0137129
$211$	1.10999e6	1.71637	0.858185	−	0.513340i	$-0.171592\pi$
$211$	1.10999e6	1.71637	0.858185	+	0.513340i	$0.171592\pi$
$212$	656908.	1.00384
$213$	388475.	0.586698
$214$	260442.	0.388756
$215$	−397171.	−0.585978
$216$	−62218.9	−0.0907377
$217$	−16473.0	−0.0237478
$218$	−61922.6	−0.0882486
$219$	88081.0	0.124100
$220$	1.24891e6	1.73970
$221$	533859.	0.735269
$222$	115444.	0.157213
$223$	78657.7	0.105920	0.0529601	−	0.998597i	$-0.483134\pi$
$223$	78657.7	0.105920	0.0529601	+	0.998597i	$0.483134\pi$
$224$	51532.4	0.0686215
$225$	−20873.3	−0.0274875
$226$	50008.6	0.0651289
$227$	1.07619e6	1.38619	0.693097	−	0.720844i	$-0.256246\pi$
$227$	1.07619e6	1.38619	0.693097	+	0.720844i	$0.256246\pi$
$228$	−284170.	−0.362027
$229$	−441450.	−0.556280	−0.278140	−	0.960541i	$-0.589718\pi$
$229$	−441450.	−0.556280	−0.278140	+	0.960541i	$0.589718\pi$
$230$	−117155.	−0.146030
$231$	−92252.4	−0.113749
$232$	396783.	0.483986
$233$	−848455.	−1.02386	−0.511928	−	0.859028i	$-0.671069\pi$
$233$	−848455.	−1.02386	−0.511928	+	0.859028i	$0.671069\pi$
$234$	−60909.3	−0.0727184
$235$	399754.	0.472197
$236$	−167175.	−0.195385
$237$	−10930.9	−0.0126411
$238$	17739.8	0.0203004
$239$	252084.	0.285463	0.142732	−	0.989761i	$-0.454411\pi$
$239$	252084.	0.285463	0.142732	+	0.989761i	$0.454411\pi$
$240$	−407854.	−0.457063
$241$	−158826.	−0.176149	−0.0880744	−	0.996114i	$-0.528071\pi$
$241$	−158826.	−0.176149	−0.0880744	+	0.996114i	$0.528071\pi$
$242$	−603090.	−0.661978
$243$	−59049.0	−0.0641500
$244$	224031.	0.240898
$245$	−890591.	−0.947901
$246$	105134.	0.110766
$247$	−573821.	−0.598458
$248$	106240.	0.109688
$249$	495963.	0.506934
$250$	248897.	0.251866
$251$	−725843.	−0.727207	−0.363604	−	0.931554i	$-0.618454\pi$
$251$	−725843.	−0.727207	−0.363604	+	0.931554i	$0.618454\pi$
$252$	32277.6	0.0320184
$253$	−1.23327e6	−1.21132
$254$	−114595.	−0.111450
$255$	−470141.	−0.452770
$256$	483127.	0.460745
$257$	1.43298e6	1.35334	0.676670	−	0.736287i	$-0.263423\pi$
$257$	1.43298e6	1.35334	0.676670	+	0.736287i	$0.263423\pi$
$258$	−91728.3	−0.0857934
$259$	−123534.	−0.114429
$260$	−882373.	−0.809504
$261$	376568.	0.342170
$262$	−112121.	−0.100910
$263$	608768.	0.542704	0.271352	−	0.962480i	$-0.412529\pi$
$263$	608768.	0.542704	0.271352	+	0.962480i	$0.412529\pi$
$264$	594968.	0.525393
$265$	−1.16817e6	−1.02186
$266$	−19067.6	−0.0165232
$267$	471424.	0.404701
$268$	1.99330e6	1.69525
$269$	−1.55686e6	−1.31181	−0.655904	−	0.754844i	$-0.727712\pi$
$269$	−1.55686e6	−1.31181	−0.655904	+	0.754844i	$0.727712\pi$
$270$	53639.5	0.0447791
$271$	−914045.	−0.756040	−0.378020	−	0.925798i	$-0.623395\pi$
$271$	−914045.	−0.756040	−0.378020	+	0.925798i	$0.623395\pi$
$272$	825607.	0.676630
$273$	65177.8	0.0529289
$274$	140108.	0.112742
$275$	199601.	0.159159
$276$	431502.	0.340965
$277$	−1.29658e6	−1.01531	−0.507655	−	0.861561i	$-0.669487\pi$
$277$	−1.29658e6	−1.01531	−0.507655	+	0.861561i	$0.669487\pi$
$278$	70452.1	0.0546742
$279$	100828.	0.0775476
$280$	−60479.8	−0.0461015
$281$	1.15475e6	0.872414	0.436207	−	0.899846i	$-0.356322\pi$
$281$	1.15475e6	0.872414	0.436207	+	0.899846i	$0.356322\pi$
$282$	92324.9	0.0691347
$283$	1.60544e6	1.19159	0.595796	−	0.803136i	$-0.296837\pi$
$283$	1.60544e6	1.19159	0.595796	+	0.803136i	$0.296837\pi$
$284$	1.29974e6	0.956230
$285$	505333.	0.368523
$286$	582445.	0.421056
$287$	−112502.	−0.0806223
$288$	−315418.	−0.224081
$289$	−468163.	−0.329726
$290$	−342070.	−0.238847
$291$	687107.	0.475655
$292$	294698.	0.202265
$293$	−2.41338e6	−1.64231	−0.821157	−	0.570702i	$-0.806671\pi$
$293$	−2.41338e6	−1.64231	−0.821157	+	0.570702i	$0.806671\pi$
$294$	−205686.	−0.138783
$295$	297284.	0.198891
$296$	796713.	0.528534
$297$	564656.	0.371444
$298$	−426887.	−0.278466
$299$	871327.	0.563642
$300$	−69837.0	−0.0448005
$301$	98156.4	0.0624457
$302$	392081.	0.247377
$303$	299404.	0.187349
$304$	−887407.	−0.550730
$305$	−398390.	−0.245221
$306$	−108581.	−0.0662904
$307$	−1.28675e6	−0.779200	−0.389600	−	0.920984i	$-0.627387\pi$
$307$	−1.28675e6	−0.779200	−0.389600	+	0.920984i	$0.627387\pi$
$308$	−308654.	−0.185394
$309$	95481.0	0.0568880
$310$	−91590.7	−0.0541311
$311$	886549.	0.519759	0.259879	−	0.965641i	$-0.416317\pi$
$311$	886549.	0.519759	0.259879	+	0.965641i	$0.416317\pi$
$312$	−420354.	−0.244472
$313$	−441339.	−0.254631	−0.127316	−	0.991862i	$-0.540636\pi$
$313$	−441339.	−0.254631	−0.127316	+	0.991862i	$0.540636\pi$
$314$	257975.	0.147657
$315$	−57398.5	−0.0325930
$316$	−36572.1	−0.0206031
$317$	−2.12860e6	−1.18972	−0.594861	−	0.803829i	$-0.702793\pi$
$317$	−2.12860e6	−1.18972	−0.594861	+	0.803829i	$0.702793\pi$
$318$	−269793.	−0.149611
$319$	−3.60093e6	−1.98124
$320$	−1.16362e6	−0.635239
$321$	1.70582e6	0.923997
$322$	28953.6	0.0155619
$323$	−1.02293e6	−0.545557
$324$	−197564.	−0.104555
$325$	−141021.	−0.0740586
$326$	75026.5	0.0390995
$327$	−405575.	−0.209750
$328$	725565.	0.372384
$329$	−98794.9	−0.0503205
$330$	−512928.	−0.259282
$331$	2.39033e6	1.19919	0.599596	−	0.800303i	$-0.295328\pi$
$331$	2.39033e6	1.19919	0.599596	+	0.800303i	$0.295328\pi$
$332$	1.65937e6	0.826226
$333$	756122.	0.373664
$334$	51718.4	0.0253676
$335$	−3.54464e6	−1.72568
$336$	100797.	0.0487077
$337$	−69925.7	−0.0335399	−0.0167700	−	0.999859i	$-0.505338\pi$
$337$	−69925.7	−0.0335399	−0.0167700	+	0.999859i	$0.505338\pi$
$338$	98689.4	0.0469871
$339$	327542.	0.154799
$340$	−1.57298e6	−0.737947
$341$	−964163.	−0.449019
$342$	116709.	0.0539558
$343$	442517.	0.203093
$344$	−633046.	−0.288429
$345$	−767330.	−0.347084
$346$	538608.	0.241870
$347$	−3.29775e6	−1.47026	−0.735130	−	0.677926i	$-0.762879\pi$
$347$	−3.29775e6	−1.47026	−0.735130	+	0.677926i	$0.762879\pi$
$348$	1.25990e6	0.557686
$349$	1.62611e6	0.714638	0.357319	−	0.933982i	$-0.383691\pi$
$349$	1.62611e6	0.714638	0.357319	+	0.933982i	$0.383691\pi$
$350$	−4686.03	−0.00204472
$351$	−398938.	−0.172838
$352$	3.01619e6	1.29748
$353$	372586.	0.159144	0.0795718	−	0.996829i	$-0.474645\pi$
$353$	372586.	0.159144	0.0795718	+	0.996829i	$0.474645\pi$
$354$	68658.9	0.0291198
$355$	−2.31131e6	−0.973390
$356$	1.57727e6	0.659602
$357$	116190.	0.0482502
$358$	1.17472e6	0.484426
$359$	−37081.9	−0.0151854	−0.00759269	−	0.999971i	$-0.502417\pi$
$359$	−37081.9	−0.0151854	−0.00759269	+	0.999971i	$0.502417\pi$
$360$	370183.	0.150543
$361$	−1.37660e6	−0.555954
$362$	−545651.	−0.218848
$363$	−3.95006e6	−1.57339
$364$	218069.	0.0862662
$365$	−524055.	−0.205894
$366$	−92009.8	−0.0359030
$367$	1.66873e6	0.646725	0.323363	−	0.946275i	$-0.395187\pi$
$367$	1.66873e6	0.646725	0.323363	+	0.946275i	$0.395187\pi$
$368$	1.34750e6	0.518690
$369$	688599.	0.263269
$370$	−686854.	−0.260832
$371$	288700.	0.108896
$372$	337345.	0.126391
$373$	783617.	0.291630	0.145815	−	0.989312i	$-0.453420\pi$
$373$	783617.	0.291630	0.145815	+	0.989312i	$0.453420\pi$
$374$	1.03831e6	0.383837
$375$	1.63021e6	0.598638
$376$	637163.	0.232424
$377$	2.54411e6	0.921898
$378$	−13256.4	−0.00477196
$379$	−2.91576e6	−1.04269	−0.521344	−	0.853347i	$-0.674569\pi$
$379$	−2.91576e6	−1.04269	−0.521344	+	0.853347i	$0.674569\pi$
$380$	1.69072e6	0.600638
$381$	−750562.	−0.264895
$382$	546192.	0.191508
$383$	−210253.	−0.0732395	−0.0366197	−	0.999329i	$-0.511659\pi$
$383$	−210253.	−0.0732395	−0.0366197	+	0.999329i	$0.511659\pi$
$384$	−1.39023e6	−0.481126
$385$	548873.	0.188721
$386$	299689.	0.102377
$387$	−600793.	−0.203914
$388$	2.29889e6	0.775246
$389$	−3.12003e6	−1.04540	−0.522702	−	0.852515i	$-0.675076\pi$
$389$	−3.12003e6	−1.04540	−0.522702	+	0.852515i	$0.675076\pi$
$390$	362392.	0.120647
$391$	1.55329e6	0.513818
$392$	−1.41950e6	−0.466574
$393$	−734360.	−0.239843
$394$	−234615.	−0.0761404
$395$	65035.4	0.0209728
$396$	1.88920e6	0.605398
$397$	4.46005e6	1.42025	0.710123	−	0.704078i	$-0.248639\pi$
$397$	4.46005e6	1.42025	0.710123	+	0.704078i	$0.248639\pi$
$398$	−1.13802e6	−0.360115
$399$	−124888.	−0.0392723
$400$	−218087.	−0.0681523
$401$	−4.09620e6	−1.27210	−0.636048	−	0.771649i	$-0.719432\pi$
$401$	−4.09620e6	−1.27210	−0.636048	+	0.771649i	$0.719432\pi$
$402$	−818649.	−0.252658
$403$	681196.	0.208934
$404$	1.00173e6	0.305351
$405$	351323.	0.106431
$406$	84539.0	0.0254532
$407$	−7.23042e6	−2.16360
$408$	−749352.	−0.222862
$409$	−3.76026e6	−1.11150	−0.555750	−	0.831349i	$-0.687569\pi$
$409$	−3.76026e6	−1.11150	−0.555750	+	0.831349i	$0.687569\pi$
$410$	−625516.	−0.183772
$411$	917664.	0.267966
$412$	319456.	0.0927190
$413$	−73470.4	−0.0211952
$414$	−177218.	−0.0508168
$415$	−2.95083e6	−0.841054
$416$	−2.13098e6	−0.603736
$417$	461441.	0.129950
$418$	−1.11603e6	−0.312417
$419$	−2.02166e6	−0.562564	−0.281282	−	0.959625i	$-0.590760\pi$
$419$	−2.02166e6	−0.562564	−0.281282	+	0.959625i	$0.590760\pi$
$420$	−192042.	−0.0531217
$421$	−3.50126e6	−0.962762	−0.481381	−	0.876511i	$-0.659865\pi$
$421$	−3.50126e6	−0.962762	−0.481381	+	0.876511i	$0.659865\pi$
$422$	−1.52524e6	−0.416924
$423$	604701.	0.164320
$424$	−1.86193e6	−0.502976
$425$	−251394.	−0.0675122
$426$	−533807.	−0.142515
$427$	98457.7	0.0261324
$428$	5.70726e6	1.50598
$429$	3.81485e6	1.00077
$430$	545755.	0.142340
$431$	−6.83268e6	−1.77173	−0.885865	−	0.463943i	$-0.846434\pi$
$431$	−6.83268e6	−1.77173	−0.885865	+	0.463943i	$0.846434\pi$
$432$	−616953.	−0.159053
$433$	4.80850e6	1.23251	0.616254	−	0.787547i	$-0.288649\pi$
$433$	4.80850e6	1.23251	0.616254	+	0.787547i	$0.288649\pi$
$434$	22635.7	0.00576858
$435$	−2.24046e6	−0.567694
$436$	−1.35696e6	−0.341861
$437$	−1.66955e6	−0.418213
$438$	−121033.	−0.0301452
$439$	7.82826e6	1.93867	0.969336	−	0.245741i	$-0.0790313\pi$
$439$	7.82826e6	1.93867	0.969336	+	0.245741i	$0.0790313\pi$
$440$	−3.53988e6	−0.871679
$441$	−1.34718e6	−0.329860
$442$	−733580.	−0.178604
$443$	−5.65940e6	−1.37013	−0.685064	−	0.728483i	$-0.740226\pi$
$443$	−5.65940e6	−1.37013	−0.685064	+	0.728483i	$0.740226\pi$
$444$	2.52980e6	0.609017
$445$	−2.80483e6	−0.671439
$446$	−108084.	−0.0257291
$447$	−2.79598e6	−0.661860
$448$	287577.	0.0676954
$449$	1.34902e6	0.315794	0.157897	−	0.987456i	$-0.449529\pi$
$449$	1.34902e6	0.315794	0.157897	+	0.987456i	$0.449529\pi$
$450$	28682.1	0.00667698
$451$	−6.58473e6	−1.52439
$452$	1.09588e6	0.252299
$453$	2.56802e6	0.587967
$454$	−1.47880e6	−0.336720
$455$	−387788.	−0.0878143
$456$	805444.	0.181394
$457$	−1.85905e6	−0.416389	−0.208195	−	0.978087i	$-0.566759\pi$
$457$	−1.85905e6	−0.416389	−0.208195	+	0.978087i	$0.566759\pi$
$458$	606600.	0.135126
$459$	−711174.	−0.157559
$460$	−2.56730e6	−0.565695
$461$	−3.94552e6	−0.864672	−0.432336	−	0.901712i	$-0.642311\pi$
$461$	−3.94552e6	−0.864672	−0.432336	+	0.901712i	$0.642311\pi$
$462$	126765.	0.0276308
$463$	−610505.	−0.132354	−0.0661769	−	0.997808i	$-0.521080\pi$
$463$	−610505.	−0.132354	−0.0661769	+	0.997808i	$0.521080\pi$
$464$	3.93444e6	0.848375
$465$	−599893.	−0.128659
$466$	1.16587e6	0.248705
$467$	1.03019e6	0.218588	0.109294	−	0.994009i	$-0.465141\pi$
$467$	1.03019e6	0.218588	0.109294	+	0.994009i	$0.465141\pi$
$468$	−1.33475e6	−0.281699
$469$	876019.	0.183900
$470$	−549305.	−0.114701
$471$	1.68966e6	0.350951
$472$	473837.	0.0978980
$473$	5.74509e6	1.18071
$474$	15020.2	0.00307065
$475$	270211.	0.0549503
$476$	388745.	0.0786406
$477$	−1.76706e6	−0.355596
$478$	−346390.	−0.0693419
$479$	8.51549e6	1.69578	0.847892	−	0.530168i	$-0.177871\pi$
$479$	8.51549e6	1.69578	0.847892	+	0.530168i	$0.177871\pi$
$480$	1.87664e6	0.371773
$481$	5.10841e6	1.00675
$482$	218244.	0.0427883
$483$	189637.	0.0369876
$484$	−1.32160e7	−2.56440
$485$	−4.08807e6	−0.789159
$486$	81139.6	0.0155827
$487$	3.30567e6	0.631593	0.315796	−	0.948827i	$-0.397728\pi$
$487$	3.30567e6	0.631593	0.315796	+	0.948827i	$0.397728\pi$
$488$	−634989.	−0.120703
$489$	491402.	0.0929319
$490$	1.22377e6	0.230255
$491$	−1.00382e7	−1.87911	−0.939556	−	0.342395i	$-0.888762\pi$
$491$	−1.00382e7	−1.87911	−0.939556	+	0.342395i	$0.888762\pi$
$492$	2.30389e6	0.429090
$493$	4.53531e6	0.840406
$494$	788491.	0.145372
$495$	−3.35953e6	−0.616262
$496$	1.05346e6	0.192271
$497$	571215.	0.103731
$498$	−681506.	−0.123139
$499$	7.73757e6	1.39108	0.695542	−	0.718486i	$-0.255164\pi$
$499$	7.73757e6	1.39108	0.695542	+	0.718486i	$0.255164\pi$
$500$	5.45427e6	0.975690
$501$	338740.	0.0602938
$502$	997386.	0.176646
$503$	1.85196e6	0.326371	0.163186	−	0.986595i	$-0.447823\pi$
$503$	1.85196e6	0.326371	0.163186	+	0.986595i	$0.447823\pi$
$504$	−91486.8	−0.0160429
$505$	−1.78136e6	−0.310830
$506$	1.69465e6	0.294241
$507$	646387.	0.111679
$508$	−2.51120e6	−0.431740
$509$	9.43035e6	1.61337	0.806684	−	0.590983i	$-0.201260\pi$
$509$	9.43035e6	1.61337	0.806684	+	0.590983i	$0.201260\pi$
$510$	646024.	0.109982
$511$	129515.	0.0219415
$512$	−5.60691e6	−0.945255
$513$	764408.	0.128243
$514$	−1.96907e6	−0.328740
$515$	−568082.	−0.0943829
$516$	−2.01011e6	−0.332350
$517$	−5.78246e6	−0.951450
$518$	169749.	0.0277960
$519$	3.52773e6	0.574879
$520$	2.50098e6	0.405604
$521$	6.09179e6	0.983220	0.491610	−	0.870815i	$-0.336409\pi$
$521$	6.09179e6	0.983220	0.491610	+	0.870815i	$0.336409\pi$
$522$	−517444.	−0.0831165
$523$	8.14725e6	1.30244	0.651218	−	0.758890i	$-0.274258\pi$
$523$	8.14725e6	1.30244	0.651218	+	0.758890i	$0.274258\pi$
$524$	−2.45699e6	−0.390909
$525$	−30692.1	−0.00485992
$526$	−836513.	−0.131828
$527$	1.21435e6	0.190465
$528$	5.89962e6	0.920956
$529$	−3.90118e6	−0.606118
$530$	1.60518e6	0.248219
$531$	449696.	0.0692122
$532$	−417844.	−0.0640080
$533$	4.65221e6	0.709319
$534$	−647788.	−0.0983059
$535$	−1.01491e7	−1.53300
$536$	−5.64976e6	−0.849411
$537$	7.69409e6	1.15139
$538$	2.13930e6	0.318651
$539$	1.28824e7	1.90997
$540$	1.17544e6	0.173467
$541$	−3.84806e6	−0.565261	−0.282630	−	0.959229i	$-0.591207\pi$
$541$	−3.84806e6	−0.565261	−0.282630	+	0.959229i	$0.591207\pi$
$542$	1.25600e6	0.183650
$543$	−3.57385e6	−0.520160
$544$	−3.79884e6	−0.550368
$545$	2.41305e6	0.347996
$546$	−89561.2	−0.0128570
$547$	3.60848e6	0.515652	0.257826	−	0.966191i	$-0.416994\pi$
$547$	3.60848e6	0.515652	0.257826	+	0.966191i	$0.416994\pi$
$548$	3.07028e6	0.436744
$549$	−602637.	−0.0853346
$550$	−274273.	−0.0386613
$551$	−4.87479e6	−0.684033
$552$	−1.22304e6	−0.170841
$553$	−16072.8	−0.00223501
$554$	1.78163e6	0.246629
$555$	−4.49869e6	−0.619946
$556$	1.54387e6	0.211799
$557$	−1.09136e7	−1.49049	−0.745244	−	0.666792i	$-0.767667\pi$
$557$	−1.09136e7	−1.49049	−0.745244	+	0.666792i	$0.767667\pi$
$558$	−138548.	−0.0188371
$559$	−4.05899e6	−0.549400
$560$	−599709.	−0.0808110
$561$	6.80061e6	0.912306
$562$	−1.58675e6	−0.211918
$563$	5.18168e6	0.688969	0.344484	−	0.938792i	$-0.388054\pi$
$563$	5.18168e6	0.688969	0.344484	+	0.938792i	$0.388054\pi$
$564$	2.02319e6	0.267817
$565$	−1.94877e6	−0.256827
$566$	−2.20604e6	−0.289450
$567$	−86825.8	−0.0113420
$568$	−3.68397e6	−0.479121
$569$	1.09387e7	1.41640	0.708198	−	0.706014i	$-0.249508\pi$
$569$	1.09387e7	1.41640	0.708198	+	0.706014i	$0.249508\pi$
$570$	−694381.	−0.0895181
$571$	−707551.	−0.0908171	−0.0454085	−	0.998969i	$-0.514459\pi$
$571$	−707551.	−0.0908171	−0.0454085	+	0.998969i	$0.514459\pi$
$572$	1.27636e7	1.63110
$573$	3.57740e6	0.455178
$574$	154590.	0.0195840
$575$	−410307.	−0.0517534
$576$	−1.76019e6	−0.221057
$577$	5.47208e6	0.684247	0.342123	−	0.939655i	$-0.388854\pi$
$577$	5.47208e6	0.684247	0.342123	+	0.939655i	$0.388854\pi$
$578$	643306.	0.0800937
$579$	1.96287e6	0.243330
$580$	−7.49604e6	−0.925256
$581$	729265.	0.0896283
$582$	−944158.	−0.115541
$583$	1.68976e7	2.05898
$584$	−835285.	−0.101345
$585$	2.37356e6	0.286755
$586$	3.31624e6	0.398935
$587$	−1.16809e7	−1.39921	−0.699604	−	0.714530i	$-0.746640\pi$
$587$	−1.16809e7	−1.39921	−0.699604	+	0.714530i	$0.746640\pi$
$588$	−4.50734e6	−0.537623
$589$	−1.30524e6	−0.155026
$590$	−408499.	−0.0483127
$591$	−1.53666e6	−0.180971
$592$	7.90009e6	0.926462
$593$	6.39235e6	0.746490	0.373245	−	0.927733i	$-0.378245\pi$
$593$	6.39235e6	0.746490	0.373245	+	0.927733i	$0.378245\pi$
$594$	−775898.	−0.0902274
$595$	−691296.	−0.0800519
$596$	−9.35469e6	−1.07873
$597$	−7.45368e6	−0.855924
$598$	−1.19730e6	−0.136914
$599$	1.91534e6	0.218112	0.109056	−	0.994036i	$-0.465217\pi$
$599$	1.91534e6	0.218112	0.109056	+	0.994036i	$0.465217\pi$
$600$	197944.	0.0224474
$601$	8.17110e6	0.922771	0.461386	−	0.887200i	$-0.347352\pi$
$601$	8.17110e6	0.922771	0.461386	+	0.887200i	$0.347352\pi$
$602$	−134877.	−0.0151687
$603$	−5.36191e6	−0.600519
$604$	8.59197e6	0.958298
$605$	2.35017e7	2.61042
$606$	−411413.	−0.0455089
$607$	−1.45158e7	−1.59907	−0.799537	−	0.600617i	$-0.794922\pi$
$607$	−1.45158e7	−1.59907	−0.799537	+	0.600617i	$0.794922\pi$
$608$	4.08319e6	0.447962
$609$	553706.	0.0604973
$610$	547430.	0.0595667
$611$	4.08540e6	0.442722
$612$	−2.37942e6	−0.256798
$613$	1.11597e7	1.19950	0.599751	−	0.800187i	$-0.295266\pi$
$613$	1.11597e7	1.19950	0.599751	+	0.800187i	$0.295266\pi$
$614$	1.76813e6	0.189276
$615$	−4.09695e6	−0.436790
$616$	874843.	0.0928920
$617$	−1.07196e7	−1.13361	−0.566805	−	0.823852i	$-0.691821\pi$
$617$	−1.07196e7	−1.13361	−0.566805	+	0.823852i	$0.691821\pi$
$618$	−131201.	−0.0138187
$619$	1.00697e7	1.05631	0.528155	−	0.849148i	$-0.322884\pi$
$619$	1.00697e7	1.05631	0.528155	+	0.849148i	$0.322884\pi$
$620$	−2.00710e6	−0.209695
$621$	−1.16073e6	−0.120782
$622$	−1.21821e6	−0.126255
$623$	693184.	0.0715530
$624$	−4.16817e6	−0.428533
$625$	−8.89392e6	−0.910738
$626$	606447.	0.0618525
$627$	−7.30965e6	−0.742554
$628$	5.65319e6	0.571998
$629$	9.10659e6	0.917760
$630$	78871.7	0.00791717
$631$	−1.97408e7	−1.97375	−0.986874	−	0.161490i	$-0.948370\pi$
$631$	−1.97408e7	−1.97375	−0.986874	+	0.161490i	$0.948370\pi$
$632$	103659.	0.0103232
$633$	−9.98987e6	−0.990947
$634$	2.92492e6	0.288995
$635$	4.46561e6	0.439488
$636$	−5.91217e6	−0.579568
$637$	−9.10163e6	−0.888732
$638$	4.94806e6	0.481264
$639$	−3.49628e6	−0.338730
$640$	8.27145e6	0.798236
$641$	−8.15452e6	−0.783887	−0.391943	−	0.919989i	$-0.628197\pi$
$641$	−8.15452e6	−0.783887	−0.391943	+	0.919989i	$0.628197\pi$
$642$	−2.34398e6	−0.224448
$643$	1.51153e7	1.44175	0.720875	−	0.693065i	$-0.243740\pi$
$643$	1.51153e7	1.44175	0.720875	+	0.693065i	$0.243740\pi$
$644$	634481.	0.0602842
$645$	3.57454e6	0.338314
$646$	1.40562e6	0.132521
$647$	−7.70464e6	−0.723588	−0.361794	−	0.932258i	$-0.617836\pi$
$647$	−7.70464e6	−0.723588	−0.361794	+	0.932258i	$0.617836\pi$
$648$	559970.	0.0523875
$649$	−4.30022e6	−0.400755
$650$	193778.	0.0179896
$651$	148257.	0.0137108
$652$	1.64411e6	0.151465
$653$	−1.60071e6	−0.146903	−0.0734513	−	0.997299i	$-0.523401\pi$
$653$	−1.60071e6	−0.146903	−0.0734513	+	0.997299i	$0.523401\pi$
$654$	557303.	0.0509504
$655$	4.36921e6	0.397924
$656$	7.19459e6	0.652749
$657$	−792729.	−0.0716492
$658$	135755.	0.0122234
$659$	−529187.	−0.0474674	−0.0237337	−	0.999718i	$-0.507555\pi$
$659$	−529187.	−0.0474674	−0.0237337	+	0.999718i	$0.507555\pi$
$660$	−1.12402e7	−1.00442
$661$	3.17067e6	0.282258	0.141129	−	0.989991i	$-0.454927\pi$
$661$	3.17067e6	0.282258	0.141129	+	0.989991i	$0.454927\pi$
$662$	−3.28458e6	−0.291296
$663$	−4.80473e6	−0.424508
$664$	−4.70329e6	−0.413982
$665$	743042.	0.0651567
$666$	−1.03899e6	−0.0907668
$667$	7.40220e6	0.644238
$668$	1.13334e6	0.0982699
$669$	−707919.	−0.0611531
$670$	4.87071e6	0.419185
$671$	5.76272e6	0.494107
$672$	−463792.	−0.0396187
$673$	−4.60171e6	−0.391635	−0.195817	−	0.980640i	$-0.562736\pi$
$673$	−4.60171e6	−0.391635	−0.195817	+	0.980640i	$0.562736\pi$
$674$	96085.3	0.00814718
$675$	187860.	0.0158699
$676$	2.16265e6	0.182021
$677$	1.36936e7	1.14828	0.574138	−	0.818759i	$-0.305337\pi$
$677$	1.36936e7	1.14828	0.574138	+	0.818759i	$0.305337\pi$
$678$	−450077.	−0.0376022
$679$	1.01032e6	0.0840981
$680$	4.45841e6	0.369750
$681$	−9.68570e6	−0.800319
$682$	1.32486e6	0.109071
$683$	1.42838e7	1.17164	0.585819	−	0.810442i	$-0.300773\pi$
$683$	1.42838e7	1.17164	0.585819	+	0.810442i	$0.300773\pi$
$684$	2.55753e6	0.209016
$685$	−5.45982e6	−0.444582
$686$	−608066.	−0.0493333
$687$	3.97305e6	0.321168
$688$	−6.27719e6	−0.505585
$689$	−1.19384e7	−0.958071
$690$	1.05439e6	0.0843102
$691$	−1.57319e7	−1.25339	−0.626695	−	0.779265i	$-0.715593\pi$
$691$	−1.57319e7	−1.25339	−0.626695	+	0.779265i	$0.715593\pi$
$692$	1.18029e7	0.936967
$693$	830271.	0.0656730
$694$	4.53146e6	0.357141
$695$	−2.74543e6	−0.215600
$696$	−3.57104e6	−0.279429
$697$	8.29335e6	0.646618
$698$	−2.23445e6	−0.173593
$699$	7.63610e6	0.591124
$700$	−102688.	−0.00792094
$701$	−1.56619e7	−1.20379	−0.601893	−	0.798577i	$-0.705587\pi$
$701$	−1.56619e7	−1.20379	−0.601893	+	0.798577i	$0.705587\pi$
$702$	548184.	0.0419840
$703$	−9.78825e6	−0.746993
$704$	1.68318e7	1.27997
$705$	−3.59779e6	−0.272623
$706$	−511973.	−0.0386576
$707$	440244.	0.0331242
$708$	1.50457e6	0.112806
$709$	−1.51974e7	−1.13541	−0.567707	−	0.823230i	$-0.692169\pi$
$709$	−1.51974e7	−1.13541	−0.567707	+	0.823230i	$0.692169\pi$
$710$	3.17598e6	0.236446
$711$	98378.0	0.00729834
$712$	−4.47059e6	−0.330495
$713$	1.98197e6	0.146007
$714$	−159658.	−0.0117205
$715$	−2.26972e7	−1.66038
$716$	2.57426e7	1.87659
$717$	−2.26875e6	−0.164812
$718$	50954.5	0.00368868
$719$	−9.32908e6	−0.673002	−0.336501	−	0.941683i	$-0.609244\pi$
$719$	−9.32908e6	−0.673002	−0.336501	+	0.941683i	$0.609244\pi$
$720$	3.67068e6	0.263885
$721$	140395.	0.0100581
$722$	1.89159e6	0.135047
$723$	1.42944e6	0.101700
$724$	−1.19573e7	−0.847784
$725$	−1.19802e6	−0.0846484
$726$	5.42781e6	0.382193
$727$	−725901.	−0.0509380	−0.0254690	−	0.999676i	$-0.508108\pi$
$727$	−725901.	−0.0509380	−0.0254690	+	0.999676i	$0.508108\pi$
$728$	−618090.	−0.0432238
$729$	531441.	0.0370370
$730$	720108.	0.0500138
$731$	−7.23584e6	−0.500836
$732$	−2.01628e6	−0.139083
$733$	−9.70009e6	−0.666831	−0.333416	−	0.942780i	$-0.608201\pi$
$733$	−9.70009e6	−0.666831	−0.333416	+	0.942780i	$0.608201\pi$
$734$	−2.29301e6	−0.157096
$735$	8.01531e6	0.547271
$736$	−6.20018e6	−0.421901
$737$	5.12733e7	3.47714
$738$	−946208.	−0.0639508
$739$	2.47619e7	1.66791	0.833956	−	0.551831i	$-0.186071\pi$
$739$	2.47619e7	1.66791	0.833956	+	0.551831i	$0.186071\pi$
$740$	−1.50515e7	−1.01042
$741$	5.16439e6	0.345520
$742$	−396704.	−0.0264519
$743$	4.09368e6	0.272045	0.136023	−	0.990706i	$-0.456568\pi$
$743$	4.09368e6	0.272045	0.136023	+	0.990706i	$0.456568\pi$
$744$	−956162.	−0.0633285
$745$	1.66352e7	1.09809
$746$	−1.07677e6	−0.0708398
$747$	−4.46367e6	−0.292678
$748$	2.27532e7	1.48692
$749$	2.50824e6	0.163367
$750$	−2.24008e6	−0.145415
$751$	2.53873e7	1.64254	0.821271	−	0.570539i	$-0.193266\pi$
$751$	2.53873e7	1.64254	0.821271	+	0.570539i	$0.193266\pi$
$752$	6.31802e6	0.407414
$753$	6.53259e6	0.419853
$754$	−3.49588e6	−0.223938
$755$	−1.52789e7	−0.975495
$756$	−290498.	−0.0184858
$757$	−2.65364e7	−1.68307	−0.841536	−	0.540201i	$-0.818348\pi$
$757$	−2.65364e7	−1.68307	−0.841536	+	0.540201i	$0.818348\pi$
$758$	4.00657e6	0.253279
$759$	1.10995e7	0.699354
$760$	−4.79214e6	−0.300951
$761$	2.02831e7	1.26961	0.634807	−	0.772670i	$-0.281079\pi$
$761$	2.02831e7	1.26961	0.634807	+	0.772670i	$0.281079\pi$
$762$	1.03135e6	0.0643457
$763$	−596358.	−0.0370848
$764$	1.19691e7	0.741872
$765$	4.23127e6	0.261407
$766$	288910.	0.0177906
$767$	3.03817e6	0.186476
$768$	−4.34814e6	−0.266011
$769$	1.13755e7	0.693675	0.346837	−	0.937925i	$-0.387256\pi$
$769$	1.13755e7	0.693675	0.346837	+	0.937925i	$0.387256\pi$
$770$	−754210.	−0.0458422
$771$	−1.28968e7	−0.781351
$772$	6.56730e6	0.396592
$773$	−1.02132e6	−0.0614768	−0.0307384	−	0.999527i	$-0.509786\pi$
$773$	−1.02132e6	−0.0614768	−0.0307384	+	0.999527i	$0.509786\pi$
$774$	825554.	0.0495329
$775$	−320775.	−0.0191843
$776$	−6.51593e6	−0.388439
$777$	1.11180e6	0.0660656
$778$	4.28725e6	0.253939
$779$	−8.91413e6	−0.526303
$780$	7.94136e6	0.467367
$781$	3.34332e7	1.96133
$782$	−2.13438e6	−0.124812
$783$	−3.38911e6	−0.197552
$784$	−1.40756e7	−0.817854
$785$	−1.00530e7	−0.582264
$786$	1.00909e6	0.0582604
$787$	−3.48861e6	−0.200778	−0.100389	−	0.994948i	$-0.532009\pi$
$787$	−3.48861e6	−0.200778	−0.100389	+	0.994948i	$0.532009\pi$
$788$	−5.14130e6	−0.294956
$789$	−5.47891e6	−0.313330
$790$	−89365.6	−0.00509451
$791$	481618.	0.0273692
$792$	−5.35471e6	−0.303336
$793$	−4.07145e6	−0.229914
$794$	−6.12859e6	−0.344992
$795$	1.05135e7	0.589969
$796$	−2.49382e7	−1.39503
$797$	−2.75851e7	−1.53825	−0.769127	−	0.639096i	$-0.779309\pi$
$797$	−2.75851e7	−1.53825	−0.769127	+	0.639096i	$0.779309\pi$
$798$	171609.	0.00953965
$799$	7.28290e6	0.403587
$800$	1.00348e6	0.0554348
$801$	−4.24282e6	−0.233654
$802$	5.62861e6	0.309005
$803$	7.58047e6	0.414866
$804$	−1.79397e7	−0.978756
$805$	−1.12828e6	−0.0613661
$806$	−936037.	−0.0507522
$807$	1.40118e7	0.757373
$808$	−2.83929e6	−0.152997
$809$	−940587.	−0.0505275	−0.0252637	−	0.999681i	$-0.508043\pi$
$809$	−940587.	−0.0505275	−0.0252637	+	0.999681i	$0.508043\pi$
$810$	−482756.	−0.0258532
$811$	2.20005e7	1.17457	0.587287	−	0.809379i	$-0.300196\pi$
$811$	2.20005e7	1.17457	0.587287	+	0.809379i	$0.300196\pi$
$812$	1.85257e6	0.0986015
$813$	8.22641e6	0.436500
$814$	9.93537e6	0.525561
$815$	−2.92369e6	−0.154183
$816$	−7.43046e6	−0.390652
$817$	7.77747e6	0.407646
$818$	5.16700e6	0.269995
$819$	−586600.	−0.0305585
$820$	−1.37074e7	−0.711903
$821$	−1.13416e7	−0.587243	−0.293622	−	0.955922i	$-0.594861\pi$
$821$	−1.13416e7	−0.587243	−0.293622	+	0.955922i	$0.594861\pi$
$822$	−1.26097e6	−0.0650915
$823$	−3.43137e7	−1.76591	−0.882953	−	0.469461i	$-0.844448\pi$
$823$	−3.43137e7	−1.76591	−0.882953	+	0.469461i	$0.844448\pi$
$824$	−905460.	−0.0464570
$825$	−1.79641e6	−0.0918904
$826$	100956.	0.00514853
$827$	4.68484e6	0.238194	0.119097	−	0.992883i	$-0.462000\pi$
$827$	4.68484e6	0.238194	0.119097	+	0.992883i	$0.462000\pi$
$828$	−3.88351e6	−0.196856
$829$	−4.04565e6	−0.204457	−0.102229	−	0.994761i	$-0.532597\pi$
$829$	−4.04565e6	−0.204457	−0.102229	+	0.994761i	$0.532597\pi$
$830$	4.05475e6	0.204300
$831$	1.16692e7	0.586189
$832$	−1.18920e7	−0.595587
$833$	−1.62252e7	−0.810172
$834$	−634069.	−0.0315661
$835$	−2.01540e6	−0.100033
$836$	−2.44563e7	−1.21025
$837$	−907448.	−0.0447721
$838$	2.77797e6	0.136653
$839$	3.05868e6	0.150013	0.0750065	−	0.997183i	$-0.476102\pi$
$839$	3.05868e6	0.150013	0.0750065	+	0.997183i	$0.476102\pi$
$840$	544318.	0.0266167
$841$	1.10189e6	0.0537216
$842$	4.81111e6	0.233865
$843$	−1.03928e7	−0.503688
$844$	−3.34237e7	−1.61510
$845$	−3.84580e6	−0.185287
$846$	−830924.	−0.0399150
$847$	−5.80818e6	−0.278184
$848$	−1.84626e7	−0.881663
$849$	−1.44489e7	−0.687966
$850$	345442.	0.0163994
$851$	1.48631e7	0.703535
$852$	−1.16977e7	−0.552079
$853$	3.32975e7	1.56689	0.783446	−	0.621460i	$-0.213460\pi$
$853$	3.32975e7	1.56689	0.783446	+	0.621460i	$0.213460\pi$
$854$	−135291.	−0.00634783
$855$	−4.54799e6	−0.212767
$856$	−1.61765e7	−0.754572
$857$	−78442.4	−0.00364837	−0.00182419	−	0.999998i	$-0.500581\pi$
$857$	−78442.4	−0.00364837	−0.00182419	+	0.999998i	$0.500581\pi$
$858$	−5.24201e6	−0.243097
$859$	−3.51051e7	−1.62326	−0.811629	−	0.584174i	$-0.801419\pi$
$859$	−3.51051e7	−1.62326	−0.811629	+	0.584174i	$0.801419\pi$
$860$	1.19595e7	0.551402
$861$	1.01252e6	0.0465473
$862$	9.38883e6	0.430371
$863$	1.01934e7	0.465901	0.232951	−	0.972489i	$-0.425162\pi$
$863$	1.01934e7	0.465901	0.232951	+	0.972489i	$0.425162\pi$
$864$	2.83876e6	0.129373
$865$	−2.09889e7	−0.953782
$866$	−6.60739e6	−0.299389
$867$	4.21347e6	0.190367
$868$	496032.	0.0223465
$869$	−940740.	−0.0422591
$870$	3.07863e6	0.137899
$871$	−3.62254e7	−1.61796
$872$	3.84613e6	0.171290
$873$	−6.18396e6	−0.274619
$874$	2.29415e6	0.101588
$875$	2.39706e6	0.105842
$876$	−2.65228e6	−0.116778
$877$	5.71535e6	0.250925	0.125462	−	0.992098i	$-0.459959\pi$
$877$	5.71535e6	0.250925	0.125462	+	0.992098i	$0.459959\pi$
$878$	−1.07569e7	−0.470923
$879$	2.17204e7	0.948191
$880$	−3.51009e7	−1.52796
$881$	−1.75420e7	−0.761445	−0.380722	−	0.924689i	$-0.624325\pi$
$881$	−1.75420e7	−0.761445	−0.380722	+	0.924689i	$0.624325\pi$
$882$	1.85117e6	0.0801263
$883$	−6.93125e6	−0.299164	−0.149582	−	0.988749i	$-0.547793\pi$
$883$	−6.93125e6	−0.299164	−0.149582	+	0.988749i	$0.547793\pi$
$884$	−1.60755e7	−0.691884
$885$	−2.67555e6	−0.114830
$886$	7.77662e6	0.332818
$887$	−3.74508e7	−1.59828	−0.799138	−	0.601148i	$-0.794710\pi$
$887$	−3.74508e7	−1.59828	−0.799138	+	0.601148i	$0.794710\pi$
$888$	−7.17042e6	−0.305149
$889$	−1.10363e6	−0.0468348
$890$	3.85414e6	0.163099
$891$	−5.08190e6	−0.214453
$892$	−2.36853e6	−0.0996704
$893$	−7.82805e6	−0.328492
$894$	3.84198e6	0.160772
$895$	−4.57775e7	−1.91027
$896$	−2.04420e6	−0.0850654
$897$	−7.84194e6	−0.325419
$898$	−1.85370e6	−0.0767095
$899$	5.78698e6	0.238810
$900$	628533.	0.0258656
$901$	−2.12822e7	−0.873382
$902$	9.04812e6	0.370290
$903$	−883408.	−0.0360530
$904$	−3.10613e6	−0.126415
$905$	2.12633e7	0.862998
$906$	−3.52873e6	−0.142823
$907$	3.22974e7	1.30361	0.651807	−	0.758385i	$-0.274011\pi$
$907$	3.22974e7	1.30361	0.651807	+	0.758385i	$0.274011\pi$
$908$	−3.24060e7	−1.30440
$909$	−2.69464e6	−0.108166
$910$	532862.	0.0213310
$911$	2.92722e7	1.16858	0.584292	−	0.811544i	$-0.301372\pi$
$911$	2.92722e7	1.16858	0.584292	+	0.811544i	$0.301372\pi$
$912$	7.98666e6	0.317964
$913$	4.26838e7	1.69467
$914$	2.55453e6	0.101145
$915$	3.58551e6	0.141579
$916$	1.32929e7	0.523456
$917$	−1.07980e6	−0.0424055
$918$	977230.	0.0382728
$919$	2.08070e7	0.812684	0.406342	−	0.913721i	$-0.366804\pi$
$919$	2.08070e7	0.812684	0.406342	+	0.913721i	$0.366804\pi$
$920$	7.27670e6	0.283442
$921$	1.15808e7	0.449871
$922$	5.42156e6	0.210038
$923$	−2.36210e7	−0.912630
$924$	2.77789e6	0.107037
$925$	−2.40554e6	−0.0924397
$926$	838899.	0.0321501
$927$	−859329.	−0.0328443
$928$	−1.81034e7	−0.690065
$929$	4.03830e7	1.53518	0.767591	−	0.640940i	$-0.221455\pi$
$929$	4.03830e7	1.53518	0.767591	+	0.640940i	$0.221455\pi$
$930$	824316.	0.0312526
$931$	1.74397e7	0.659424
$932$	2.55485e7	0.963444
$933$	−7.97894e6	−0.300083
$934$	−1.41559e6	−0.0530971
$935$	−4.04615e7	−1.51361
$936$	3.78319e6	0.141146
$937$	−4.37728e7	−1.62875	−0.814377	−	0.580336i	$-0.802921\pi$
$937$	−4.37728e7	−1.62875	−0.814377	+	0.580336i	$0.802921\pi$
$938$	−1.20374e6	−0.0446711
$939$	3.97205e6	0.147011
$940$	−1.20373e7	−0.444335
$941$	−1.96886e6	−0.0724837	−0.0362419	−	0.999343i	$-0.511539\pi$
$941$	−1.96886e6	−0.0724837	−0.0362419	+	0.999343i	$0.511539\pi$
$942$	−2.32177e6	−0.0852496
$943$	1.35358e7	0.495684
$944$	4.69850e6	0.171605
$945$	516587.	0.0188176
$946$	−7.89436e6	−0.286807
$947$	−1.78631e7	−0.647265	−0.323632	−	0.946183i	$-0.604904\pi$
$947$	−1.78631e7	−0.647265	−0.323632	+	0.946183i	$0.604904\pi$
$948$	329149.	0.0118952
$949$	−5.35572e6	−0.193042
$950$	−371299.	−0.0133480
$951$	1.91574e7	0.686886
$952$	−1.10185e6	−0.0394030
$953$	−5.01719e7	−1.78949	−0.894744	−	0.446580i	$-0.852642\pi$
$953$	−5.01719e7	−1.78949	−0.894744	+	0.446580i	$0.852642\pi$
$954$	2.42814e6	0.0863778
$955$	−2.12844e7	−0.755185
$956$	−7.59070e6	−0.268619
$957$	3.24083e7	1.14387
$958$	−1.17012e7	−0.411923
$959$	1.34933e6	0.0473776
$960$	1.04726e7	0.366756
$961$	−2.70797e7	−0.945877
$962$	−7.01949e6	−0.244550
$963$	−1.53524e7	−0.533470
$964$	4.78255e6	0.165755
$965$	−1.16785e7	−0.403709
$966$	−260582.	−0.00898466
$967$	4.31137e6	0.148269	0.0741343	−	0.997248i	$-0.476381\pi$
$967$	4.31137e6	0.148269	0.0741343	+	0.997248i	$0.476381\pi$
$968$	3.74590e7	1.28490
$969$	9.20638e6	0.314978
$970$	5.61745e6	0.191695
$971$	1.26800e6	0.0431589	0.0215794	−	0.999767i	$-0.493131\pi$
$971$	1.26800e6	0.0431589	0.0215794	+	0.999767i	$0.493131\pi$
$972$	1.77807e6	0.0603648
$973$	678504.	0.0229758
$974$	−4.54234e6	−0.153420
$975$	1.26919e6	0.0427578
$976$	−6.29645e6	−0.211578
$977$	−1.23823e7	−0.415016	−0.207508	−	0.978233i	$-0.566535\pi$
$977$	−1.23823e7	−0.415016	−0.207508	+	0.978233i	$0.566535\pi$
$978$	−675239.	−0.0225741
$979$	4.05720e7	1.35291
$980$	2.68173e7	0.891970
$981$	3.65017e6	0.121099
$982$	1.37936e7	0.456455
$983$	−2.91743e7	−0.962980	−0.481490	−	0.876452i	$-0.659904\pi$
$983$	−2.91743e7	−0.962980	−0.481490	+	0.876452i	$0.659904\pi$
$984$	−6.53008e6	−0.214996
$985$	9.14265e6	0.300249
$986$	−6.23199e6	−0.204143
$987$	889154.	0.0290525
$988$	1.72788e7	0.563146
$989$	−1.18098e7	−0.383930
$990$	4.61635e6	0.149696
$991$	1.76406e7	0.570597	0.285299	−	0.958439i	$-0.407907\pi$
$991$	1.76406e7	0.570597	0.285299	+	0.958439i	$0.407907\pi$
$992$	−4.84726e6	−0.156393
$993$	−2.15130e7	−0.692354
$994$	−784910.	−0.0251973
$995$	4.43471e7	1.42006
$996$	−1.49344e7	−0.477022
$997$	−5.24868e7	−1.67229	−0.836147	−	0.548506i	$-0.815197\pi$
$997$	−5.24868e7	−1.67229	−0.836147	+	0.548506i	$0.815197\pi$
$998$	−1.06322e7	−0.337908
$999$	−6.80510e6	−0.215735

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.37411 q^{2} -9.00000 q^{3} -30.1118 q^{4} +53.5472 q^{5} +12.3670 q^{6} -13.2336 q^{7} +85.3483 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-1.37411 q^{2} -9.00000 q^{3} -30.1118 q^{4} +53.5472 q^{5} +12.3670 q^{6} -13.2336 q^{7} +85.3483 q^{8} +81.0000 q^{9} -73.5796 q^{10} -774.562 q^{11} +271.006 q^{12} +547.241 q^{13} +18.1844 q^{14} -481.925 q^{15} +846.301 q^{16} +975.548 q^{17} -111.303 q^{18} -1048.57 q^{19} -1612.40 q^{20} +119.103 q^{21} +1064.33 q^{22} +1592.22 q^{23} -768.135 q^{24} -257.695 q^{25} -751.967 q^{26} -729.000 q^{27} +398.488 q^{28} +4648.98 q^{29} +662.216 q^{30} +1244.78 q^{31} -3894.05 q^{32} +6971.06 q^{33} -1340.51 q^{34} -708.624 q^{35} -2439.06 q^{36} +9334.84 q^{37} +1440.85 q^{38} -4925.17 q^{39} +4570.16 q^{40} +8501.22 q^{41} -163.660 q^{42} -7417.20 q^{43} +23323.5 q^{44} +4337.33 q^{45} -2187.88 q^{46} +7465.45 q^{47} -7616.71 q^{48} -16631.9 q^{49} +354.100 q^{50} -8779.93 q^{51} -16478.4 q^{52} -21815.6 q^{53} +1001.72 q^{54} -41475.7 q^{55} -1129.47 q^{56} +9437.14 q^{57} -6388.20 q^{58} +5551.80 q^{59} +14511.6 q^{60} -7439.97 q^{61} -1710.47 q^{62} -1071.92 q^{63} -21730.8 q^{64} +29303.2 q^{65} -9578.98 q^{66} -66196.5 q^{67} -29375.5 q^{68} -14330.0 q^{69} +973.725 q^{70} -43163.9 q^{71} +6913.21 q^{72} -9786.78 q^{73} -12827.1 q^{74} +2319.25 q^{75} +31574.4 q^{76} +10250.3 q^{77} +6767.70 q^{78} +1214.54 q^{79} +45317.1 q^{80} +6561.00 q^{81} -11681.6 q^{82} -55107.0 q^{83} -3586.40 q^{84} +52237.9 q^{85} +10192.0 q^{86} -41840.8 q^{87} -66107.6 q^{88} -52380.5 q^{89} -5959.95 q^{90} -7241.97 q^{91} -47944.6 q^{92} -11203.1 q^{93} -10258.3 q^{94} -56148.1 q^{95} +35046.5 q^{96} -76345.2 q^{97} +22854.0 q^{98} -62739.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9}+O(q^{10}) \) 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9	\( 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9} - 355 q^{10} - 708 q^{11} - 3078 q^{12} - 133 q^{13} - 2748 q^{14} + 477 q^{15} + 3678 q^{16} - 2006 q^{17} - 648 q^{18} - 4788 q^{19} - 2785 q^{20} - 90 q^{21} + 3609 q^{22} - 5695 q^{23} + 2376 q^{24} + 18477 q^{25} + 2432 q^{26} - 16038 q^{27} + 7635 q^{28} - 978 q^{29} + 3195 q^{30} - 6009 q^{31} + 22809 q^{32} + 6372 q^{33} - 4078 q^{34} - 22822 q^{35} + 27702 q^{36} + 13640 q^{37} - 5454 q^{38} + 1197 q^{39} - 13351 q^{40} - 24618 q^{41} + 24732 q^{42} + 1257 q^{43} - 65465 q^{44} - 4293 q^{45} - 6175 q^{46} - 63834 q^{47} - 33102 q^{48} + 18022 q^{49} - 41643 q^{50} + 18054 q^{51} - 40853 q^{52} - 13316 q^{53} + 5832 q^{54} - 35934 q^{55} - 251195 q^{56} + 43092 q^{57} - 103895 q^{58} - 138587 q^{59} + 25065 q^{60} - 53985 q^{61} - 218186 q^{62} + 810 q^{63} + 23758 q^{64} - 114073 q^{65} - 32481 q^{66} - 102785 q^{67} - 338669 q^{68} + 51255 q^{69} - 104184 q^{70} - 108740 q^{71} - 21384 q^{72} + 69762 q^{73} - 221377 q^{74} - 166293 q^{75} - 223267 q^{76} - 140360 q^{77} - 21888 q^{78} - 238938 q^{79} - 864251 q^{80} + 144342 q^{81} - 660293 q^{82} - 305455 q^{83} - 68715 q^{84} - 201204 q^{85} - 794679 q^{86} + 8802 q^{87} - 420823 q^{88} - 438448 q^{89} - 28755 q^{90} - 294186 q^{91} - 1251930 q^{92} + 54081 q^{93} - 826416 q^{94} - 652572 q^{95} - 205281 q^{96} - 284729 q^{97} - 887529 q^{98} - 57348 q^{99}+O(q^{100}) \) 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9 - 355 * q^10 - 708 * q^11 - 3078 * q^12 - 133 * q^13 - 2748 * q^14 + 477 * q^15 + 3678 * q^16 - 2006 * q^17 - 648 * q^18 - 4788 * q^19 - 2785 * q^20 - 90 * q^21 + 3609 * q^22 - 5695 * q^23 + 2376 * q^24 + 18477 * q^25 + 2432 * q^26 - 16038 * q^27 + 7635 * q^28 - 978 * q^29 + 3195 * q^30 - 6009 * q^31 + 22809 * q^32 + 6372 * q^33 - 4078 * q^34 - 22822 * q^35 + 27702 * q^36 + 13640 * q^37 - 5454 * q^38 + 1197 * q^39 - 13351 * q^40 - 24618 * q^41 + 24732 * q^42 + 1257 * q^43 - 65465 * q^44 - 4293 * q^45 - 6175 * q^46 - 63834 * q^47 - 33102 * q^48 + 18022 * q^49 - 41643 * q^50 + 18054 * q^51 - 40853 * q^52 - 13316 * q^53 + 5832 * q^54 - 35934 * q^55 - 251195 * q^56 + 43092 * q^57 - 103895 * q^58 - 138587 * q^59 + 25065 * q^60 - 53985 * q^61 - 218186 * q^62 + 810 * q^63 + 23758 * q^64 - 114073 * q^65 - 32481 * q^66 - 102785 * q^67 - 338669 * q^68 + 51255 * q^69 - 104184 * q^70 - 108740 * q^71 - 21384 * q^72 + 69762 * q^73 - 221377 * q^74 - 166293 * q^75 - 223267 * q^76 - 140360 * q^77 - 21888 * q^78 - 238938 * q^79 - 864251 * q^80 + 144342 * q^81 - 660293 * q^82 - 305455 * q^83 - 68715 * q^84 - 201204 * q^85 - 794679 * q^86 + 8802 * q^87 - 420823 * q^88 - 438448 * q^89 - 28755 * q^90 - 294186 * q^91 - 1251930 * q^92 + 54081 * q^93 - 826416 * q^94 - 652572 * q^95 - 205281 * q^96 - 284729 * q^97 - 887529 * q^98 - 57348 * q^99

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