LMFDB - Embedded newform 309.6.a.c.1.6

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			1.6
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)

$f(q)$	$=$	$q-7.25337 q^{2} -9.00000 q^{3} +20.6114 q^{4} +11.4457 q^{5} +65.2804 q^{6} +191.311 q^{7} +82.6057 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-7.25337 q^{2} -9.00000 q^{3} +20.6114 q^{4} +11.4457 q^{5} +65.2804 q^{6} +191.311 q^{7} +82.6057 q^{8} +81.0000 q^{9} -83.0197 q^{10} -523.919 q^{11} -185.503 q^{12} -192.015 q^{13} -1387.65 q^{14} -103.011 q^{15} -1258.73 q^{16} -1253.73 q^{17} -587.523 q^{18} +966.656 q^{19} +235.911 q^{20} -1721.80 q^{21} +3800.18 q^{22} +2691.88 q^{23} -743.451 q^{24} -2994.00 q^{25} +1392.75 q^{26} -729.000 q^{27} +3943.20 q^{28} -1828.21 q^{29} +747.177 q^{30} +10414.1 q^{31} +6486.69 q^{32} +4715.27 q^{33} +9093.78 q^{34} +2189.68 q^{35} +1669.52 q^{36} +5525.54 q^{37} -7011.51 q^{38} +1728.13 q^{39} +945.477 q^{40} -3797.76 q^{41} +12488.9 q^{42} -16891.9 q^{43} -10798.7 q^{44} +927.099 q^{45} -19525.2 q^{46} -13791.8 q^{47} +11328.6 q^{48} +19793.0 q^{49} +21716.6 q^{50} +11283.6 q^{51} -3957.69 q^{52} +7604.18 q^{53} +5287.71 q^{54} -5996.60 q^{55} +15803.4 q^{56} -8699.90 q^{57} +13260.7 q^{58} -1350.43 q^{59} -2123.20 q^{60} -20761.2 q^{61} -75537.5 q^{62} +15496.2 q^{63} -6770.87 q^{64} -2197.74 q^{65} -34201.6 q^{66} +50745.4 q^{67} -25841.2 q^{68} -24226.9 q^{69} -15882.6 q^{70} +54409.6 q^{71} +6691.06 q^{72} -53396.6 q^{73} -40078.8 q^{74} +26946.0 q^{75} +19924.1 q^{76} -100232. q^{77} -12534.8 q^{78} +85612.3 q^{79} -14407.1 q^{80} +6561.00 q^{81} +27546.5 q^{82} -70102.0 q^{83} -35488.8 q^{84} -14349.8 q^{85} +122523. q^{86} +16453.9 q^{87} -43278.6 q^{88} -36332.6 q^{89} -6724.59 q^{90} -36734.6 q^{91} +55483.5 q^{92} -93727.1 q^{93} +100037. q^{94} +11064.0 q^{95} -58380.2 q^{96} -1854.26 q^{97} -143566. q^{98} -42437.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−7.25337	−1.28223	−0.641114	−	0.767446i	$-0.721527\pi$
$2$	−7.25337	−1.28223	−0.641114	+	0.767446i	$0.721527\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	20.6114	0.644107
$5$	11.4457	0.204746	0.102373	−	0.994746i	$-0.467356\pi$
$5$	11.4457	0.204746	0.102373	+	0.994746i	$0.467356\pi$
$6$	65.2804	0.740294
$7$	191.311	1.47569	0.737845	−	0.674970i	$-0.235843\pi$
$7$	191.311	1.47569	0.737845	+	0.674970i	$0.235843\pi$
$8$	82.6057	0.456336
$9$	81.0000	0.333333
$10$	−83.0197	−0.262531
$11$	−523.919	−1.30552	−0.652758	−	0.757567i	$-0.726388\pi$
$11$	−523.919	−1.30552	−0.652758	+	0.757567i	$0.726388\pi$
$12$	−185.503	−0.371875
$13$	−192.015	−0.315120	−0.157560	−	0.987509i	$-0.550363\pi$
$13$	−192.015	−0.315120	−0.157560	+	0.987509i	$0.550363\pi$
$14$	−1387.65	−1.89217
$15$	−103.011	−0.118210
$16$	−1258.73	−1.22923
$17$	−1253.73	−1.05216	−0.526081	−	0.850435i	$-0.676339\pi$
$17$	−1253.73	−1.05216	−0.526081	+	0.850435i	$0.676339\pi$
$18$	−587.523	−0.427409
$19$	966.656	0.614310	0.307155	−	0.951659i	$-0.400623\pi$
$19$	966.656	0.614310	0.307155	+	0.951659i	$0.400623\pi$
$20$	235.911	0.131878
$21$	−1721.80	−0.851991
$22$	3800.18	1.67397
$23$	2691.88	1.06105	0.530525	−	0.847669i	$-0.321995\pi$
$23$	2691.88	1.06105	0.530525	+	0.847669i	$0.321995\pi$
$24$	−743.451	−0.263466
$25$	−2994.00	−0.958079
$26$	1392.75	0.404055
$27$	−729.000	−0.192450
$28$	3943.20	0.950502
$29$	−1828.21	−0.403675	−0.201837	−	0.979419i	$-0.564691\pi$
$29$	−1828.21	−0.403675	−0.201837	+	0.979419i	$0.564691\pi$
$30$	747.177	0.151572
$31$	10414.1	1.94634	0.973169	−	0.230090i	$-0.0739019\pi$
$31$	10414.1	1.94634	0.973169	+	0.230090i	$0.0739019\pi$
$32$	6486.69	1.11982
$33$	4715.27	0.753740
$34$	9093.78	1.34911
$35$	2189.68	0.302142
$36$	1669.52	0.214702
$37$	5525.54	0.663546	0.331773	−	0.943359i	$-0.392353\pi$
$37$	5525.54	0.663546	0.331773	+	0.943359i	$0.392353\pi$
$38$	−7011.51	−0.787686
$39$	1728.13	0.181935
$40$	945.477	0.0934331
$41$	−3797.76	−0.352832	−0.176416	−	0.984316i	$-0.556450\pi$
$41$	−3797.76	−0.352832	−0.176416	+	0.984316i	$0.556450\pi$
$42$	12488.9	1.09245
$43$	−16891.9	−1.39318	−0.696589	−	0.717471i	$-0.745300\pi$
$43$	−16891.9	−1.39318	−0.696589	+	0.717471i	$0.745300\pi$
$44$	−10798.7	−0.840891
$45$	927.099	0.0682488
$46$	−19525.2	−1.36051
$47$	−13791.8	−0.910705	−0.455353	−	0.890311i	$-0.650487\pi$
$47$	−13791.8	−0.910705	−0.455353	+	0.890311i	$0.650487\pi$
$48$	11328.6	0.709698
$49$	19793.0	1.17766
$50$	21716.6	1.22847
$51$	11283.6	0.607466
$52$	−3957.69	−0.202971
$53$	7604.18	0.371845	0.185923	−	0.982564i	$-0.440473\pi$
$53$	7604.18	0.371845	0.185923	+	0.982564i	$0.440473\pi$
$54$	5287.71	0.246765
$55$	−5996.60	−0.267299
$56$	15803.4	0.673411
$57$	−8699.90	−0.354672
$58$	13260.7	0.517603
$59$	−1350.43	−0.0505058	−0.0252529	−	0.999681i	$-0.508039\pi$
$59$	−1350.43	−0.0505058	−0.0252529	+	0.999681i	$0.508039\pi$
$60$	−2123.20	−0.0761400
$61$	−20761.2	−0.714379	−0.357190	−	0.934032i	$-0.616265\pi$
$61$	−20761.2	−0.714379	−0.357190	+	0.934032i	$0.616265\pi$
$62$	−75537.5	−2.49565
$63$	15496.2	0.491897
$64$	−6770.87	−0.206631
$65$	−2197.74	−0.0645196
$66$	−34201.6	−0.966466
$67$	50745.4	1.38105	0.690525	−	0.723308i	$-0.257379\pi$
$67$	50745.4	1.38105	0.690525	+	0.723308i	$0.257379\pi$
$68$	−25841.2	−0.677704
$69$	−24226.9	−0.612598
$70$	−15882.6	−0.387415
$71$	54409.6	1.28094	0.640471	−	0.767982i	$-0.278739\pi$
$71$	54409.6	1.28094	0.640471	+	0.767982i	$0.278739\pi$
$72$	6691.06	0.152112
$73$	−53396.6	−1.17275	−0.586376	−	0.810039i	$-0.699446\pi$
$73$	−53396.6	−1.17275	−0.586376	+	0.810039i	$0.699446\pi$
$74$	−40078.8	−0.850816
$75$	26946.0	0.553147
$76$	19924.1	0.395681
$77$	−100232.	−1.92654
$78$	−12534.8	−0.233282
$79$	85612.3	1.54336	0.771682	−	0.636008i	$-0.219416\pi$
$79$	85612.3	1.54336	0.771682	+	0.636008i	$0.219416\pi$
$80$	−14407.1	−0.251681
$81$	6561.00	0.111111
$82$	27546.5	0.452410
$83$	−70102.0	−1.11695	−0.558477	−	0.829520i	$-0.688614\pi$
$83$	−70102.0	−1.11695	−0.558477	+	0.829520i	$0.688614\pi$
$84$	−35488.8	−0.548773
$85$	−14349.8	−0.215426
$86$	122523.	1.78637
$87$	16453.9	0.233062
$88$	−43278.6	−0.595754
$89$	−36332.6	−0.486207	−0.243104	−	0.970000i	$-0.578165\pi$
$89$	−36332.6	−0.486207	−0.243104	+	0.970000i	$0.578165\pi$
$90$	−6724.59	−0.0875104
$91$	−36734.6	−0.465020
$92$	55483.5	0.683430
$93$	−93727.1	−1.12372
$94$	100037.	1.16773
$95$	11064.0	0.125778
$96$	−58380.2	−0.646528
$97$	−1854.26	−0.0200097	−0.0100048	−	0.999950i	$-0.503185\pi$
$97$	−1854.26	−0.0200097	−0.0100048	+	0.999950i	$0.503185\pi$
$98$	−143566.	−1.51003
$99$	−42437.4	−0.435172
$100$	−61710.5	−0.617105
$101$	−146661.	−1.43058	−0.715289	−	0.698829i	$-0.753705\pi$
$101$	−146661.	−1.43058	−0.715289	+	0.698829i	$0.753705\pi$
$102$	−81844.0	−0.778909
$103$	−10609.0	−0.0985329
$103$	−10609.0	−0.0985329
$104$	−15861.5	−0.143801
$105$	−19707.2	−0.174442
$106$	−55155.9	−0.476790
$107$	−63881.5	−0.539406	−0.269703	−	0.962944i	$-0.586926\pi$
$107$	−63881.5	−0.539406	−0.269703	+	0.962944i	$0.586926\pi$
$108$	−15025.7	−0.123958
$109$	34500.1	0.278134	0.139067	−	0.990283i	$-0.455590\pi$
$109$	34500.1	0.278134	0.139067	+	0.990283i	$0.455590\pi$
$110$	43495.5	0.342739
$111$	−49729.9	−0.383098
$112$	−240810.	−1.81397
$113$	−39698.0	−0.292464	−0.146232	−	0.989250i	$-0.546715\pi$
$113$	−39698.0	−0.292464	−0.146232	+	0.989250i	$0.546715\pi$
$114$	63103.6	0.454770
$115$	30810.4	0.217246
$116$	−37682.0	−0.260010
$117$	−15553.2	−0.105040
$118$	9795.16	0.0647599
$119$	−239853.	−1.55266
$120$	−8509.29	−0.0539436
$121$	113440.	0.704371
$122$	150589.	0.915997
$123$	34179.8	0.203707
$124$	214650.	1.25365
$125$	−70036.0	−0.400909
$126$	−112400.	−0.630724
$127$	−287554.	−1.58201	−0.791006	−	0.611808i	$-0.790442\pi$
$127$	−287554.	−1.58201	−0.791006	+	0.611808i	$0.790442\pi$
$128$	−158462.	−0.854873
$129$	152027.	0.804352
$130$	15941.0	0.0827289
$131$	−390941.	−1.99037	−0.995184	−	0.0980252i	$-0.968747\pi$
$131$	−390941.	−1.99037	−0.995184	+	0.0980252i	$0.968747\pi$
$132$	97188.3	0.485489
$133$	184932.	0.906532
$134$	−368075.	−1.77082
$135$	−8343.89	−0.0394034
$136$	−103565.	−0.480139
$137$	225505.	1.02649	0.513245	−	0.858242i	$-0.328443\pi$
$137$	225505.	1.02649	0.513245	+	0.858242i	$0.328443\pi$
$138$	175727.	0.785490
$139$	152525.	0.669584	0.334792	−	0.942292i	$-0.391334\pi$
$139$	152525.	0.669584	0.334792	+	0.942292i	$0.391334\pi$
$140$	45132.5	0.194612
$141$	124127.	0.525796
$142$	−394653.	−1.64246
$143$	100600.	0.411394
$144$	−101958.	−0.409744
$145$	−20925.1	−0.0826509
$146$	387305.	1.50374
$147$	−178137.	−0.679925
$148$	113889.	0.427394
$149$	−272628.	−1.00602	−0.503008	−	0.864282i	$-0.667773\pi$
$149$	−272628.	−1.00602	−0.503008	+	0.864282i	$0.667773\pi$
$150$	−195449.	−0.709260
$151$	151251.	0.539829	0.269914	−	0.962884i	$-0.413005\pi$
$151$	151251.	0.539829	0.269914	+	0.962884i	$0.413005\pi$
$152$	79851.3	0.280332
$153$	−101552.	−0.350720
$154$	727017.	2.47026
$155$	119197.	0.398506
$156$	35619.2	0.117185
$157$	533048.	1.72591	0.862954	−	0.505283i	$-0.168612\pi$
$157$	533048.	1.72591	0.862954	+	0.505283i	$0.168612\pi$
$158$	−620978.	−1.97894
$159$	−68437.6	−0.214685
$160$	74244.5	0.229279
$161$	514987.	1.56578
$162$	−47589.4	−0.142470
$163$	−243.964	−0.000719213 0	−0.000359606	−	1.00000i	$-0.500114\pi$
$163$	−243.964	−0.000719213 0	−0.000359606		1.00000i	$0.500114\pi$
$164$	−78277.1	−0.227261
$165$	53969.4	0.154325
$166$	508476.	1.43219
$167$	−443670.	−1.23103	−0.615515	−	0.788125i	$-0.711052\pi$
$167$	−443670.	−1.23103	−0.615515	+	0.788125i	$0.711052\pi$
$168$	−142231.	−0.388794
$169$	−334423.	−0.900699
$170$	104084.	0.276225
$171$	78299.1	0.204770
$172$	−348165.	−0.897355
$173$	−2264.44	−0.00575236	−0.00287618	−	0.999996i	$-0.500916\pi$
$173$	−2264.44	−0.00575236	−0.00287618	+	0.999996i	$0.500916\pi$
$174$	−119346.	−0.298838
$175$	−572785.	−1.41383
$176$	659475.	1.60478
$177$	12153.8	0.0291595
$178$	263534.	0.623428
$179$	59057.0	0.137765	0.0688825	−	0.997625i	$-0.478057\pi$
$179$	59057.0	0.137765	0.0688825	+	0.997625i	$0.478057\pi$
$180$	19108.8	0.0439595
$181$	230001.	0.521836	0.260918	−	0.965361i	$-0.415975\pi$
$181$	230001.	0.521836	0.260918	+	0.965361i	$0.415975\pi$
$182$	266449.	0.596261
$183$	186851.	0.412447
$184$	222365.	0.484196
$185$	63243.5	0.135858
$186$	679838.	1.44086
$187$	656853.	1.37361
$188$	−284269.	−0.586591
$189$	−139466.	−0.283997
$190$	−80251.4	−0.161276
$191$	−174007.	−0.345131	−0.172565	−	0.984998i	$-0.555206\pi$
$191$	−174007.	−0.345131	−0.172565	+	0.984998i	$0.555206\pi$
$192$	60937.9	0.119298
$193$	−283019.	−0.546918	−0.273459	−	0.961884i	$-0.588168\pi$
$193$	−283019.	−0.546918	−0.273459	+	0.961884i	$0.588168\pi$
$194$	13449.6	0.0256570
$195$	19779.6	0.0372504
$196$	407962.	0.758541
$197$	−818128.	−1.50195	−0.750975	−	0.660331i	$-0.770416\pi$
$197$	−818128.	−1.50195	−0.750975	+	0.660331i	$0.770416\pi$
$198$	307814.	0.557989
$199$	414659.	0.742265	0.371132	−	0.928580i	$-0.378970\pi$
$199$	414659.	0.742265	0.371132	+	0.928580i	$0.378970\pi$
$200$	−247321.	−0.437206
$201$	−456708.	−0.797350
$202$	1.06379e6	1.83432
$203$	−349758.	−0.595699
$204$	232571.	0.391273
$205$	−43467.8	−0.0722410
$206$	76951.0	0.126342
$207$	218042.	0.353684
$208$	241696.	0.387356
$209$	−506449.	−0.801992
$210$	142943.	0.223674
$211$	−863129.	−1.33466	−0.667328	−	0.744764i	$-0.732562\pi$
$211$	−863129.	−1.33466	−0.667328	+	0.744764i	$0.732562\pi$
$212$	156733.	0.239508
$213$	−489686.	−0.739552
$214$	463357.	0.691641
$215$	−193339.	−0.285248
$216$	−60219.5	−0.0878219
$217$	1.99234e6	2.87219
$218$	−250242.	−0.356631
$219$	480569.	0.677089
$220$	−123598.	−0.172169
$221$	240735.	0.331557
$222$	360709.	0.491219
$223$	252360.	0.339827	0.169914	−	0.985459i	$-0.445651\pi$
$223$	252360.	0.339827	0.169914	+	0.985459i	$0.445651\pi$
$224$	1.24098e6	1.65251
$225$	−242514.	−0.319360
$226$	287944.	0.375005
$227$	−43700.1	−0.0562882	−0.0281441	−	0.999604i	$-0.508960\pi$
$227$	−43700.1	−0.0562882	−0.0281441	+	0.999604i	$0.508960\pi$
$228$	−179317.	−0.228447
$229$	−1.23342e6	−1.55426	−0.777129	−	0.629341i	$-0.783325\pi$
$229$	−1.23342e6	−1.55426	−0.777129	+	0.629341i	$0.783325\pi$
$230$	−223479.	−0.278559
$231$	902084.	1.11229
$232$	−151021.	−0.184211
$233$	145773.	0.175908	0.0879542	−	0.996125i	$-0.471967\pi$
$233$	145773.	0.175908	0.0879542	+	0.996125i	$0.471967\pi$
$234$	112813.	0.134685
$235$	−157857.	−0.186463
$236$	−27834.2	−0.0325311
$237$	−770511.	−0.891062
$238$	1.73974e6	1.99087
$239$	−470975.	−0.533339	−0.266669	−	0.963788i	$-0.585923\pi$
$239$	−470975.	−0.533339	−0.266669	+	0.963788i	$0.585923\pi$
$240$	129664.	0.145308
$241$	−1.46629e6	−1.62621	−0.813106	−	0.582115i	$-0.802225\pi$
$241$	−1.46629e6	−1.62621	−0.813106	+	0.582115i	$0.802225\pi$
$242$	−822820.	−0.903164
$243$	−59049.0	−0.0641500
$244$	−427919.	−0.460136
$245$	226544.	0.241122
$246$	−247919.	−0.261199
$247$	−185612.	−0.193582
$248$	860266.	0.888185
$249$	630918.	0.644873
$250$	507997.	0.514057
$251$	−1.57741e6	−1.58038	−0.790188	−	0.612864i	$-0.790017\pi$
$251$	−1.57741e6	−1.58038	−0.790188	+	0.612864i	$0.790017\pi$
$252$	319399.	0.316834
$253$	−1.41033e6	−1.38522
$254$	2.08574e6	2.02850
$255$	129148.	0.124376
$256$	1.36606e6	1.30277
$257$	−150820.	−0.142438	−0.0712189	−	0.997461i	$-0.522689\pi$
$257$	−150820.	−0.142438	−0.0712189	+	0.997461i	$0.522689\pi$
$258$	−1.10271e6	−1.03136
$259$	1.05710e6	0.979188
$260$	−45298.4	−0.0415575
$261$	−148085.	−0.134558
$262$	2.83564e6	2.55210
$263$	−536036.	−0.477865	−0.238932	−	0.971036i	$-0.576797\pi$
$263$	−536036.	−0.477865	−0.238932	+	0.971036i	$0.576797\pi$
$264$	389508.	0.343959
$265$	87034.8	0.0761340
$266$	−1.34138e6	−1.16238
$267$	326993.	0.280712
$268$	1.04593e6	0.889544
$269$	943719.	0.795174	0.397587	−	0.917564i	$-0.369848\pi$
$269$	943719.	0.795174	0.397587	+	0.917564i	$0.369848\pi$
$270$	60521.3	0.0505242
$271$	−1.19496e6	−0.988392	−0.494196	−	0.869351i	$-0.664537\pi$
$271$	−1.19496e6	−0.988392	−0.494196	+	0.869351i	$0.664537\pi$
$272$	1.57812e6	1.29335
$273$	330611.	0.268479
$274$	−1.63567e6	−1.31619
$275$	1.56861e6	1.25079
$276$	−499351.	−0.394578
$277$	−800699.	−0.627003	−0.313502	−	0.949588i	$-0.601502\pi$
$277$	−800699.	−0.627003	−0.313502	+	0.949588i	$0.601502\pi$
$278$	−1.10632e6	−0.858559
$279$	843544.	0.648780
$280$	180880.	0.137878
$281$	2.07006e6	1.56393	0.781965	−	0.623322i	$-0.214217\pi$
$281$	2.07006e6	1.56393	0.781965	+	0.623322i	$0.214217\pi$
$282$	−900337.	−0.674190
$283$	−2.00252e6	−1.48631	−0.743157	−	0.669117i	$-0.766672\pi$
$283$	−2.00252e6	−1.48631	−0.743157	+	0.669117i	$0.766672\pi$
$284$	1.12146e6	0.825063
$285$	−99576.2	−0.0726178
$286$	−729690.	−0.527501
$287$	−726554.	−0.520670
$288$	525422.	0.373273
$289$	151986.	0.107043
$290$	151778.	0.105977
$291$	16688.3	0.0115526
$292$	−1.10058e6	−0.755378
$293$	321446.	0.218745	0.109373	−	0.994001i	$-0.465116\pi$
$293$	321446.	0.218745	0.109373	+	0.994001i	$0.465116\pi$
$294$	1.29209e6	0.871818
$295$	−15456.5	−0.0103409
$296$	456441.	0.302800
$297$	381937.	0.251247
$298$	1.97747e6	1.28994
$299$	−516881.	−0.334358
$300$	555395.	0.356286
$301$	−3.23160e6	−2.05590
$302$	−1.09708e6	−0.692183
$303$	1.31995e6	0.825944
$304$	−1.21676e6	−0.755131
$305$	−237626.	−0.146266
$306$	736596.	0.449703
$307$	2.07922e6	1.25908	0.629542	−	0.776966i	$-0.283242\pi$
$307$	2.07922e6	1.25908	0.629542	+	0.776966i	$0.283242\pi$
$308$	−2.06591e6	−1.24090
$309$	95481.0	0.0568880
$310$	−864577.	−0.510975
$311$	−1.46467e6	−0.858694	−0.429347	−	0.903140i	$-0.641256\pi$
$311$	−1.46467e6	−0.858694	−0.429347	+	0.903140i	$0.641256\pi$
$312$	142754.	0.0830234
$313$	2.05440e6	1.18529	0.592644	−	0.805465i	$-0.298084\pi$
$313$	2.05440e6	1.18529	0.592644	+	0.805465i	$0.298084\pi$
$314$	−3.86640e6	−2.21300
$315$	177364.	0.100714
$316$	1.76459e6	0.994091
$317$	−140610.	−0.0785904	−0.0392952	−	0.999228i	$-0.512511\pi$
$317$	−140610.	−0.0785904	−0.0392952	+	0.999228i	$0.512511\pi$
$318$	496403.	0.275275
$319$	957834.	0.527004
$320$	−77497.1	−0.0423069
$321$	574934.	0.311426
$322$	−3.73539e6	−2.00769
$323$	−1.21193e6	−0.646354
$324$	135231.	0.0715674
$325$	574891.	0.301910
$326$	1769.56	0.000922194 0
$327$	−310501.	−0.160581
$328$	−313716.	−0.161010
$329$	−2.63854e6	−1.34392
$330$	−391460.	−0.197880
$331$	−1.16887e6	−0.586401	−0.293201	−	0.956051i	$-0.594720\pi$
$331$	−1.16887e6	−0.586401	−0.293201	+	0.956051i	$0.594720\pi$
$332$	−1.44490e6	−0.719437
$333$	447569.	0.221182
$334$	3.21810e6	1.57846
$335$	580815.	0.282765
$336$	2.16729e6	1.04730
$337$	−2.02793e6	−0.972698	−0.486349	−	0.873765i	$-0.661672\pi$
$337$	−2.02793e6	−0.972698	−0.486349	+	0.873765i	$0.661672\pi$
$338$	2.42570e6	1.15490
$339$	357282.	0.168854
$340$	−295769.	−0.138757
$341$	−5.45615e6	−2.54098
$342$	−567933.	−0.262562
$343$	571255.	0.262177
$344$	−1.39536e6	−0.635757
$345$	−277293.	−0.125427
$346$	16424.9	0.00737584
$347$	1.27207e6	0.567136	0.283568	−	0.958952i	$-0.408482\pi$
$347$	1.27207e6	0.567136	0.283568	+	0.958952i	$0.408482\pi$
$348$	339138.	0.150117
$349$	−1.84771e6	−0.812025	−0.406012	−	0.913868i	$-0.633081\pi$
$349$	−1.84771e6	−0.812025	−0.406012	+	0.913868i	$0.633081\pi$
$350$	4.15462e6	1.81285
$351$	139979.	0.0606449
$352$	−3.39850e6	−1.46194
$353$	−1.39294e6	−0.594971	−0.297485	−	0.954726i	$-0.596148\pi$
$353$	−1.39294e6	−0.594971	−0.297485	+	0.954726i	$0.596148\pi$
$354$	−88156.4	−0.0373892
$355$	622754.	0.262268
$356$	−748866.	−0.313169
$357$	2.15868e6	0.896431
$358$	−428363.	−0.176646
$359$	−3.00206e6	−1.22937	−0.614686	−	0.788772i	$-0.710717\pi$
$359$	−3.00206e6	−1.22937	−0.614686	+	0.788772i	$0.710717\pi$
$360$	76583.6	0.0311444
$361$	−1.54168e6	−0.622623
$362$	−1.66829e6	−0.669112
$363$	−1.02096e6	−0.406669
$364$	−757151.	−0.299522
$365$	−611159.	−0.240117
$366$	−1.35530e6	−0.528851
$367$	1.45667e6	0.564541	0.282270	−	0.959335i	$-0.408912\pi$
$367$	1.45667e6	0.564541	0.282270	+	0.959335i	$0.408912\pi$
$368$	−3.38836e6	−1.30428
$369$	−307618.	−0.117611
$370$	−458729.	−0.174201
$371$	1.45476e6	0.548729
$372$	−1.93185e6	−0.723795
$373$	−3.28100e6	−1.22105	−0.610527	−	0.791996i	$-0.709042\pi$
$373$	−3.28100e6	−1.22105	−0.610527	+	0.791996i	$0.709042\pi$
$374$	−4.76440e6	−1.76128
$375$	630324.	0.231465
$376$	−1.13928e6	−0.415588
$377$	351044.	0.127206
$378$	1.01160e6	0.364149
$379$	−2.02619e6	−0.724574	−0.362287	−	0.932067i	$-0.618004\pi$
$379$	−2.02619e6	−0.724574	−0.362287	+	0.932067i	$0.618004\pi$
$380$	228045.	0.0810143
$381$	2.58798e6	0.913375
$382$	1.26214e6	0.442536
$383$	1.62490e6	0.566017	0.283008	−	0.959117i	$-0.408668\pi$
$383$	1.62490e6	0.566017	0.283008	+	0.959117i	$0.408668\pi$
$384$	1.42616e6	0.493561
$385$	−1.14722e6	−0.394451
$386$	2.05284e6	0.701273
$387$	−1.36824e6	−0.464393
$388$	−38218.8	−0.0128884
$389$	5.40065e6	1.80956	0.904779	−	0.425882i	$-0.140036\pi$
$389$	5.40065e6	1.80956	0.904779	+	0.425882i	$0.140036\pi$
$390$	−143469.	−0.0477635
$391$	−3.37490e6	−1.11640
$392$	1.63501e6	0.537411
$393$	3.51847e6	1.14914
$394$	5.93418e6	1.92584
$395$	979890.	0.315998
$396$	−874695.	−0.280297
$397$	−679795.	−0.216472	−0.108236	−	0.994125i	$-0.534520\pi$
$397$	−679795.	−0.216472	−0.108236	+	0.994125i	$0.534520\pi$
$398$	−3.00768e6	−0.951752
$399$	−1.66439e6	−0.523387
$400$	3.76865e6	1.17770
$401$	2.63367e6	0.817899	0.408950	−	0.912557i	$-0.365895\pi$
$401$	2.63367e6	0.817899	0.408950	+	0.912557i	$0.365895\pi$
$402$	3.31268e6	1.02238
$403$	−1.99966e6	−0.613330
$404$	−3.02289e6	−0.921444
$405$	75095.0	0.0227496
$406$	2.53692e6	0.763822
$407$	−2.89494e6	−0.866269
$408$	932088.	0.277208
$409$	3.83572e6	1.13380	0.566902	−	0.823785i	$-0.308142\pi$
$409$	3.83572e6	1.13380	0.566902	+	0.823785i	$0.308142\pi$
$410$	315288.	0.0926293
$411$	−2.02954e6	−0.592644
$412$	−218666.	−0.0634657
$413$	−258352.	−0.0745310
$414$	−1.58154e6	−0.453503
$415$	−802364.	−0.228692
$416$	−1.24554e6	−0.352878
$417$	−1.37273e6	−0.386585
$418$	3.67346e6	1.02834
$419$	4.46076e6	1.24129	0.620646	−	0.784091i	$-0.286871\pi$
$419$	4.46076e6	1.24129	0.620646	+	0.784091i	$0.286871\pi$
$420$	−406192.	−0.112359
$421$	−4.30869e6	−1.18479	−0.592394	−	0.805649i	$-0.701817\pi$
$421$	−4.30869e6	−1.18479	−0.592394	+	0.805649i	$0.701817\pi$
$422$	6.26060e6	1.71133
$423$	−1.11714e6	−0.303568
$424$	628148.	0.169687
$425$	3.75367e6	1.00805
$426$	3.55188e6	0.948274
$427$	−3.97186e6	−1.05420
$428$	−1.31669e6	−0.347435
$429$	−905400.	−0.237519
$430$	1.40236e6	0.365753
$431$	317146.	0.0822369	0.0411184	−	0.999154i	$-0.486908\pi$
$431$	317146.	0.0822369	0.0411184	+	0.999154i	$0.486908\pi$
$432$	917618.	0.236566
$433$	−511518.	−0.131112	−0.0655558	−	0.997849i	$-0.520882\pi$
$433$	−511518.	−0.131112	−0.0655558	+	0.997849i	$0.520882\pi$
$434$	−1.44512e7	−3.68281
$435$	188326.	0.0477185
$436$	711096.	0.179148
$437$	2.60212e6	0.651815
$438$	−3.48575e6	−0.868182
$439$	−3.29196e6	−0.815254	−0.407627	−	0.913148i	$-0.633644\pi$
$439$	−3.29196e6	−0.815254	−0.407627	+	0.913148i	$0.633644\pi$
$440$	−495353.	−0.121978
$441$	1.60323e6	0.392555
$442$	−1.74614e6	−0.425132
$443$	−4.92105e6	−1.19137	−0.595687	−	0.803216i	$-0.703120\pi$
$443$	−4.92105e6	−1.19137	−0.595687	+	0.803216i	$0.703120\pi$
$444$	−1.02500e6	−0.246756
$445$	−415851.	−0.0995491
$446$	−1.83046e6	−0.435735
$447$	2.45365e6	0.580824
$448$	−1.29534e6	−0.304923
$449$	−5.52278e6	−1.29283	−0.646415	−	0.762986i	$-0.723733\pi$
$449$	−5.52278e6	−1.29283	−0.646415	+	0.762986i	$0.723733\pi$
$450$	1.75904e6	0.409492
$451$	1.98972e6	0.460627
$452$	−818232.	−0.188378
$453$	−1.36126e6	−0.311670
$454$	316973.	0.0721743
$455$	−420452.	−0.0952111
$456$	−718661.	−0.161850
$457$	−8.23785e6	−1.84511	−0.922557	−	0.385860i	$-0.873905\pi$
$457$	−8.23785e6	−1.84511	−0.922557	+	0.385860i	$0.873905\pi$
$458$	8.94647e6	1.99291
$459$	913970.	0.202489
$460$	635045.	0.139930
$461$	−1.18024e6	−0.258654	−0.129327	−	0.991602i	$-0.541282\pi$
$461$	−1.18024e6	−0.258654	−0.129327	+	0.991602i	$0.541282\pi$
$462$	−6.54315e6	−1.42620
$463$	8.97679e6	1.94611	0.973057	−	0.230563i	$-0.0740567\pi$
$463$	8.97679e6	1.94611	0.973057	+	0.230563i	$0.0740567\pi$
$464$	2.30123e6	0.496210
$465$	−1.07277e6	−0.230077
$466$	−1.05734e6	−0.225555
$467$	3.15371e6	0.669159	0.334580	−	0.942368i	$-0.391406\pi$
$467$	3.15371e6	0.669159	0.334580	+	0.942368i	$0.391406\pi$
$468$	−320573.	−0.0676570
$469$	9.70816e6	2.03800
$470$	1.14499e6	0.239089
$471$	−4.79743e6	−0.996453
$472$	−111553.	−0.0230476
$473$	8.84996e6	1.81882
$474$	5.58880e6	1.14254
$475$	−2.89416e6	−0.588558
$476$	−4.94371e6	−1.00008
$477$	615938.	0.123948
$478$	3.41616e6	0.683861
$479$	5.58715e6	1.11263	0.556316	−	0.830971i	$-0.312215\pi$
$479$	5.58715e6	1.11263	0.556316	+	0.830971i	$0.312215\pi$
$480$	−668200.	−0.132374
$481$	−1.06099e6	−0.209096
$482$	1.06355e7	2.08517
$483$	−4.63488e6	−0.904005
$484$	2.33815e6	0.453690
$485$	−21223.2	−0.00409691
$486$	428304.	0.0822549
$487$	4.80653e6	0.918353	0.459177	−	0.888345i	$-0.348145\pi$
$487$	4.80653e6	0.918353	0.459177	+	0.888345i	$0.348145\pi$
$488$	−1.71500e6	−0.325997
$489$	2195.68	0.000415238 0
$490$	−1.64321e6	−0.309174
$491$	4.39203e6	0.822169	0.411084	−	0.911597i	$-0.365150\pi$
$491$	4.39203e6	0.822169	0.411084	+	0.911597i	$0.365150\pi$
$492$	704494.	0.131209
$493$	2.29209e6	0.424731
$494$	1.34631e6	0.248215
$495$	−485724.	−0.0890998
$496$	−1.31086e7	−2.39250
$497$	1.04092e7	1.89027
$498$	−4.57628e6	−0.826874
$499$	−7.49926e6	−1.34824	−0.674119	−	0.738622i	$-0.735477\pi$
$499$	−7.49926e6	−1.34824	−0.674119	+	0.738622i	$0.735477\pi$
$500$	−1.44354e6	−0.258228
$501$	3.99303e6	0.710736
$502$	1.14416e7	2.02640
$503$	−276786.	−0.0487780	−0.0243890	−	0.999703i	$-0.507764\pi$
$503$	−276786.	−0.0487780	−0.0243890	+	0.999703i	$0.507764\pi$
$504$	1.28007e6	0.224470
$505$	−1.67863e6	−0.292905
$506$	1.02296e7	1.77616
$507$	3.00981e6	0.520019
$508$	−5.92689e6	−1.01898
$509$	8.69147e6	1.48696	0.743479	−	0.668760i	$-0.233174\pi$
$509$	8.69147e6	1.48696	0.743479	+	0.668760i	$0.233174\pi$
$510$	−936759.	−0.159479
$511$	−1.02154e7	−1.73062
$512$	−4.83771e6	−0.815577
$513$	−704692.	−0.118224
$514$	1.09395e6	0.182638
$515$	−121427.	−0.0201742
$516$	3.13349e6	0.518088
$517$	7.22581e6	1.18894
$518$	−7.66753e6	−1.25554
$519$	20380.0	0.00332113
$520$	−181545.	−0.0294426
$521$	−8.41882e6	−1.35880	−0.679402	−	0.733766i	$-0.737761\pi$
$521$	−8.41882e6	−1.35880	−0.679402	+	0.733766i	$0.737761\pi$
$522$	1.07412e6	0.172534
$523$	3.19867e6	0.511347	0.255673	−	0.966763i	$-0.417703\pi$
$523$	3.19867e6	0.511347	0.255673	+	0.966763i	$0.417703\pi$
$524$	−8.05785e6	−1.28201
$525$	5.15507e6	0.816274
$526$	3.88807e6	0.612731
$527$	−1.30565e7	−2.04786
$528$	−5.93527e6	−0.926522
$529$	809878.	0.125829
$530$	−631296.	−0.0976210
$531$	−109385.	−0.0168353
$532$	3.81171e6	0.583903
$533$	729225.	0.111184
$534$	−2.37180e6	−0.359936
$535$	−731167.	−0.110441
$536$	4.19186e6	0.630223
$537$	−531513.	−0.0795387
$538$	−6.84515e6	−1.01959
$539$	−1.03699e7	−1.53746
$540$	−171979.	−0.0253800
$541$	−8.23265e6	−1.20933	−0.604667	−	0.796478i	$-0.706694\pi$
$541$	−8.23265e6	−1.20933	−0.604667	+	0.796478i	$0.706694\pi$
$542$	8.66747e6	1.26734
$543$	−2.07001e6	−0.301282
$544$	−8.13257e6	−1.17823
$545$	394877.	0.0569469
$546$	−2.39805e6	−0.344251
$547$	8.09242e6	1.15641	0.578203	−	0.815893i	$-0.303754\pi$
$547$	8.09242e6	1.15641	0.578203	+	0.815893i	$0.303754\pi$
$548$	4.64797e6	0.661169
$549$	−1.68166e6	−0.238126
$550$	−1.13777e7	−1.60379
$551$	−1.76725e6	−0.247982
$552$	−2.00128e6	−0.279551
$553$	1.63786e7	2.27753
$554$	5.80777e6	0.803961
$555$	−569192.	−0.0784379
$556$	3.14376e6	0.431284
$557$	5.22944e6	0.714196	0.357098	−	0.934067i	$-0.383766\pi$
$557$	5.22944e6	0.714196	0.357098	+	0.934067i	$0.383766\pi$
$558$	−6.11854e6	−0.831883
$559$	3.24349e6	0.439018
$560$	−2.75623e6	−0.371403
$561$	−5.91168e6	−0.793056
$562$	−1.50149e7	−2.00531
$563$	−7.95665e6	−1.05794	−0.528968	−	0.848642i	$-0.677421\pi$
$563$	−7.95665e6	−1.05794	−0.528968	+	0.848642i	$0.677421\pi$
$564$	2.55842e6	0.338669
$565$	−454370.	−0.0598809
$566$	1.45250e7	1.90579
$567$	1.25519e6	0.163966
$568$	4.49454e6	0.584540
$569$	6.53157e6	0.845741	0.422870	−	0.906190i	$-0.361023\pi$
$569$	6.53157e6	0.845741	0.422870	+	0.906190i	$0.361023\pi$
$570$	722263.	0.0931125
$571$	9.49100e6	1.21821	0.609104	−	0.793090i	$-0.291529\pi$
$571$	9.49100e6	1.21821	0.609104	+	0.793090i	$0.291529\pi$
$572$	2.07351e6	0.264982
$573$	1.56606e6	0.199261
$574$	5.26996e6	0.667618
$575$	−8.05948e6	−1.01657
$576$	−548441.	−0.0688769
$577$	−5.84404e6	−0.730758	−0.365379	−	0.930859i	$-0.619061\pi$
$577$	−5.84404e6	−0.730758	−0.365379	+	0.930859i	$0.619061\pi$
$578$	−1.10241e6	−0.137254
$579$	2.54717e6	0.315763
$580$	−431296.	−0.0532360
$581$	−1.34113e7	−1.64828
$582$	−121047.	−0.0148131
$583$	−3.98397e6	−0.485450
$584$	−4.41086e6	−0.535169
$585$	−178017.	−0.0215065
$586$	−2.33157e6	−0.280481
$587$	−1.55898e7	−1.86744	−0.933719	−	0.358006i	$-0.883457\pi$
$587$	−1.55898e7	−1.86744	−0.933719	+	0.358006i	$0.883457\pi$
$588$	−3.67165e6	−0.437944
$589$	1.00669e7	1.19566
$590$	112112.	0.0132594
$591$	7.36315e6	0.867151
$592$	−6.95519e6	−0.815652
$593$	1.05517e7	1.23221	0.616106	−	0.787664i	$-0.288709\pi$
$593$	1.05517e7	1.23221	0.616106	+	0.787664i	$0.288709\pi$
$594$	−2.77033e6	−0.322155
$595$	−2.74528e6	−0.317902
$596$	−5.61925e6	−0.647981
$597$	−3.73193e6	−0.428547
$598$	3.74913e6	0.428723
$599$	−1.46403e7	−1.66718	−0.833590	−	0.552384i	$-0.813718\pi$
$599$	−1.46403e7	−1.66718	−0.833590	+	0.552384i	$0.813718\pi$
$600$	2.22589e6	0.252421
$601$	7.63349e6	0.862059	0.431029	−	0.902338i	$-0.358150\pi$
$601$	7.63349e6	0.862059	0.431029	+	0.902338i	$0.358150\pi$
$602$	2.34400e7	2.63613
$603$	4.11038e6	0.460350
$604$	3.11750e6	0.347707
$605$	1.29839e6	0.144217
$606$	−9.57408e6	−1.05905
$607$	1.08822e7	1.19880	0.599400	−	0.800450i	$-0.295406\pi$
$607$	1.08822e7	1.19880	0.599400	+	0.800450i	$0.295406\pi$
$608$	6.27040e6	0.687917
$609$	3.14782e6	0.343927
$610$	1.72359e6	0.187547
$611$	2.64824e6	0.286981
$612$	−2.09314e6	−0.225901
$613$	−1.09089e7	−1.17254	−0.586271	−	0.810115i	$-0.699405\pi$
$613$	−1.09089e7	−1.17254	−0.586271	+	0.810115i	$0.699405\pi$
$614$	−1.50814e7	−1.61443
$615$	391211.	0.0417083
$616$	−8.27969e6	−0.879149
$617$	9.50244e6	1.00490	0.502449	−	0.864607i	$-0.332432\pi$
$617$	9.50244e6	1.00490	0.502449	+	0.864607i	$0.332432\pi$
$618$	−692559.	−0.0729434
$619$	−1.16146e7	−1.21837	−0.609184	−	0.793029i	$-0.708503\pi$
$619$	−1.16146e7	−1.21837	−0.609184	+	0.793029i	$0.708503\pi$
$620$	2.45681e6	0.256680
$621$	−1.96238e6	−0.204199
$622$	1.06238e7	1.10104
$623$	−6.95083e6	−0.717491
$624$	−2.17526e6	−0.223640
$625$	8.55463e6	0.875994
$626$	−1.49013e7	−1.51981
$627$	4.55804e6	0.463030
$628$	1.09869e7	1.11167
$629$	−6.92755e6	−0.698157
$630$	−1.28649e6	−0.129138
$631$	1.05482e7	1.05464	0.527320	−	0.849667i	$-0.323197\pi$
$631$	1.05482e7	1.05464	0.527320	+	0.849667i	$0.323197\pi$
$632$	7.07206e6	0.704293
$633$	7.76816e6	0.770565
$634$	1.01990e6	0.100771
$635$	−3.29124e6	−0.323911
$636$	−1.41060e6	−0.138280
$637$	−3.80055e6	−0.371105
$638$	−6.94753e6	−0.675739
$639$	4.40718e6	0.426981
$640$	−1.81371e6	−0.175032
$641$	1.27999e7	1.23044	0.615219	−	0.788356i	$-0.289067\pi$
$641$	1.27999e7	1.23044	0.615219	+	0.788356i	$0.289067\pi$
$642$	−4.17021e6	−0.399319
$643$	1.14817e7	1.09516	0.547582	−	0.836752i	$-0.315548\pi$
$643$	1.14817e7	1.09516	0.547582	+	0.836752i	$0.315548\pi$
$644$	1.06146e7	1.00853
$645$	1.74005e6	0.164688
$646$	8.79056e6	0.828772
$647$	−6.80144e6	−0.638764	−0.319382	−	0.947626i	$-0.603475\pi$
$647$	−6.80144e6	−0.638764	−0.319382	+	0.947626i	$0.603475\pi$
$648$	541976.	0.0507040
$649$	707514.	0.0659361
$650$	−4.16990e6	−0.387117
$651$	−1.79311e7	−1.65826
$652$	−5028.45	−0.000463250 0
$653$	1.06049e7	0.973250	0.486625	−	0.873611i	$-0.338228\pi$
$653$	1.06049e7	0.973250	0.486625	+	0.873611i	$0.338228\pi$
$654$	2.25218e6	0.205901
$655$	−4.47458e6	−0.407520
$656$	4.78037e6	0.433712
$657$	−4.32512e6	−0.390918
$658$	1.91383e7	1.72321
$659$	−1.13370e7	−1.01692	−0.508459	−	0.861086i	$-0.669785\pi$
$659$	−1.13370e7	−1.01692	−0.508459	+	0.861086i	$0.669785\pi$
$660$	1.11238e6	0.0994020
$661$	−1.62530e7	−1.44688	−0.723438	−	0.690390i	$-0.757439\pi$
$661$	−1.62530e7	−1.44688	−0.723438	+	0.690390i	$0.757439\pi$
$662$	8.47822e6	0.751900
$663$	−2.16661e6	−0.191425
$664$	−5.79082e6	−0.509706
$665$	2.11667e6	0.185609
$666$	−3.24639e6	−0.283605
$667$	−4.92133e6	−0.428319
$668$	−9.14466e6	−0.792915
$669$	−2.27124e6	−0.196199
$670$	−4.21287e6	−0.362569
$671$	1.08772e7	0.932633
$672$	−1.11688e7	−0.954076
$673$	1.98563e7	1.68990	0.844951	−	0.534844i	$-0.179630\pi$
$673$	1.98563e7	1.68990	0.844951	+	0.534844i	$0.179630\pi$
$674$	1.47093e7	1.24722
$675$	2.18262e6	0.184382
$676$	−6.89294e6	−0.580146
$677$	−1.87258e6	−0.157025	−0.0785124	−	0.996913i	$-0.525017\pi$
$677$	−1.87258e6	−0.157025	−0.0785124	+	0.996913i	$0.525017\pi$
$678$	−2.59150e6	−0.216509
$679$	−354740.	−0.0295281
$680$	−1.18537e6	−0.0983067
$681$	393300.	0.0324980
$682$	3.95755e7	3.25811
$683$	1.97802e7	1.62248	0.811240	−	0.584713i	$-0.198793\pi$
$683$	1.97802e7	1.62248	0.811240	+	0.584713i	$0.198793\pi$
$684$	1.61386e6	0.131894
$685$	2.58105e6	0.210170
$686$	−4.14352e6	−0.336170
$687$	1.11008e7	0.897352
$688$	2.12624e7	1.71254
$689$	−1.46011e6	−0.117176
$690$	2.01131e6	0.160826
$691$	−570965.	−0.0454899	−0.0227449	−	0.999741i	$-0.507241\pi$
$691$	−570965.	−0.0454899	−0.0227449	+	0.999741i	$0.507241\pi$
$692$	−46673.4	−0.00370514
$693$	−8.11875e6	−0.642179
$694$	−9.22680e6	−0.727197
$695$	1.74575e6	0.137095
$696$	1.35919e6	0.106354
$697$	4.76137e6	0.371236
$698$	1.34021e7	1.04120
$699$	−1.31196e6	−0.101561
$700$	−1.18059e7	−0.910656
$701$	−5.93279e6	−0.455999	−0.228000	−	0.973661i	$-0.573218\pi$
$701$	−5.93279e6	−0.455999	−0.228000	+	0.973661i	$0.573218\pi$
$702$	−1.01532e6	−0.0777605
$703$	5.34130e6	0.407623
$704$	3.54739e6	0.269760
$705$	1.42071e6	0.107655
$706$	1.01035e7	0.762887
$707$	−2.80579e7	−2.11109
$708$	250508.	0.0187819
$709$	−2.55951e7	−1.91223	−0.956117	−	0.292986i	$-0.905351\pi$
$709$	−2.55951e7	−1.91223	−0.956117	+	0.292986i	$0.905351\pi$
$710$	−4.51707e6	−0.336287
$711$	6.93460e6	0.514455
$712$	−3.00128e6	−0.221874
$713$	2.80336e7	2.06516
$714$	−1.56577e7	−1.14943
$715$	1.15143e6	0.0842314
$716$	1.21725e6	0.0887354
$717$	4.23877e6	0.307923
$718$	2.17751e7	1.57633
$719$	−1.09069e7	−0.786829	−0.393415	−	0.919361i	$-0.628706\pi$
$719$	−1.09069e7	−0.786829	−0.393415	+	0.919361i	$0.628706\pi$
$720$	−1.16697e6	−0.0838936
$721$	−2.02962e6	−0.145404
$722$	1.11823e7	0.798344
$723$	1.31966e7	0.938894
$724$	4.74065e6	0.336118
$725$	5.47366e6	0.386752
$726$	7.40538e6	0.521442
$727$	−3.47673e6	−0.243969	−0.121985	−	0.992532i	$-0.538926\pi$
$727$	−3.47673e6	−0.243969	−0.121985	+	0.992532i	$0.538926\pi$
$728$	−3.03448e6	−0.212205
$729$	531441.	0.0370370
$730$	4.43297e6	0.307884
$731$	2.11779e7	1.46585
$732$	3.85127e6	0.265660
$733$	−1.24172e7	−0.853618	−0.426809	−	0.904342i	$-0.640362\pi$
$733$	−1.24172e7	−0.853618	−0.426809	+	0.904342i	$0.640362\pi$
$734$	−1.05658e7	−0.723870
$735$	−2.03890e6	−0.139212
$736$	1.74614e7	1.18819
$737$	−2.65865e7	−1.80298
$738$	2.23127e6	0.150803
$739$	−1.21921e7	−0.821232	−0.410616	−	0.911808i	$-0.634686\pi$
$739$	−1.21921e7	−0.821232	−0.410616	+	0.911808i	$0.634686\pi$
$740$	1.30354e6	0.0875073
$741$	1.67051e6	0.111764
$742$	−1.05519e7	−0.703595
$743$	1.17270e7	0.779318	0.389659	−	0.920959i	$-0.372593\pi$
$743$	1.17270e7	0.779318	0.389659	+	0.920959i	$0.372593\pi$
$744$	−7.74239e6	−0.512794
$745$	−3.12041e6	−0.205978
$746$	2.37983e7	1.56567
$747$	−5.67826e6	−0.372318
$748$	1.35387e7	0.884753
$749$	−1.22213e7	−0.795997
$750$	−4.57197e6	−0.296791
$751$	−7.90567e6	−0.511492	−0.255746	−	0.966744i	$-0.582321\pi$
$751$	−7.90567e6	−0.511492	−0.255746	+	0.966744i	$0.582321\pi$
$752$	1.73603e7	1.11947
$753$	1.41967e7	0.912431
$754$	−2.54625e6	−0.163107
$755$	1.73117e6	0.110528
$756$	−2.87459e6	−0.182924
$757$	1.29389e7	0.820652	0.410326	−	0.911939i	$-0.365415\pi$
$757$	1.29389e7	0.820652	0.410326	+	0.911939i	$0.365415\pi$
$758$	1.46967e7	0.929069
$759$	1.26929e7	0.799756
$760$	913951.	0.0573969
$761$	2.08136e7	1.30282	0.651412	−	0.758725i	$-0.274177\pi$
$761$	2.08136e7	1.30282	0.651412	+	0.758725i	$0.274177\pi$
$762$	−1.87716e7	−1.17115
$763$	6.60026e6	0.410440
$764$	−3.58653e6	−0.222301
$765$	−1.16233e6	−0.0718087
$766$	−1.17860e7	−0.725762
$767$	259302.	0.0159154
$768$	−1.22945e7	−0.752156
$769$	1.37826e7	0.840457	0.420228	−	0.907418i	$-0.361950\pi$
$769$	1.37826e7	0.840457	0.420228	+	0.907418i	$0.361950\pi$
$770$	8.32119e6	0.505776
$771$	1.35738e6	0.0822365
$772$	−5.83342e6	−0.352273
$773$	1.50894e7	0.908284	0.454142	−	0.890929i	$-0.349946\pi$
$773$	1.50894e7	0.908284	0.454142	+	0.890929i	$0.349946\pi$
$774$	9.92436e6	0.595457
$775$	−3.11799e7	−1.86475
$776$	−153172.	−0.00913115
$777$	−9.51389e6	−0.565335
$778$	−3.91729e7	−2.32026
$779$	−3.67112e6	−0.216748
$780$	407686.	0.0239933
$781$	−2.85062e7	−1.67229
$782$	2.44794e7	1.43147
$783$	1.33277e6	0.0776872
$784$	−2.49141e7	−1.44762
$785$	6.10109e6	0.353373
$786$	−2.55208e7	−1.47346
$787$	1.26305e6	0.0726915	0.0363457	−	0.999339i	$-0.488428\pi$
$787$	1.26305e6	0.0726915	0.0363457	+	0.999339i	$0.488428\pi$
$788$	−1.68628e7	−0.967416
$789$	4.82433e6	0.275895
$790$	−7.10750e6	−0.405181
$791$	−7.59467e6	−0.431587
$792$	−3.50557e6	−0.198585
$793$	3.98646e6	0.225115
$794$	4.93081e6	0.277566
$795$	−783314.	−0.0439560
$796$	8.54671e6	0.478098
$797$	1.04719e7	0.583958	0.291979	−	0.956425i	$-0.405686\pi$
$797$	1.04719e7	0.583958	0.291979	+	0.956425i	$0.405686\pi$
$798$	1.20724e7	0.671101
$799$	1.72913e7	0.958209
$800$	−1.94211e7	−1.07288
$801$	−2.94294e6	−0.162069
$802$	−1.91030e7	−1.04873
$803$	2.79755e7	1.53105
$804$	−9.41341e6	−0.513578
$805$	5.89437e6	0.320588
$806$	1.45043e7	0.786429
$807$	−8.49348e6	−0.459094
$808$	−1.21150e7	−0.652824
$809$	1.45591e7	0.782102	0.391051	−	0.920369i	$-0.372112\pi$
$809$	1.45591e7	0.782102	0.391051	+	0.920369i	$0.372112\pi$
$810$	−544692.	−0.0291701
$811$	−4.70326e6	−0.251100	−0.125550	−	0.992087i	$-0.540070\pi$
$811$	−4.70326e6	−0.251100	−0.125550	+	0.992087i	$0.540070\pi$
$812$	−7.20900e6	−0.383694
$813$	1.07546e7	0.570648
$814$	2.09980e7	1.11075
$815$	−2792.33	−0.000147256 0
$816$	−1.42030e7	−0.746717
$817$	−1.63286e7	−0.855844
$818$	−2.78219e7	−1.45380
$819$	−2.97550e6	−0.155007
$820$	−895934.	−0.0465309
$821$	1.82307e7	0.943940	0.471970	−	0.881615i	$-0.343543\pi$
$821$	1.82307e7	0.943940	0.471970	+	0.881615i	$0.343543\pi$
$822$	1.47210e7	0.759904
$823$	−2.57538e7	−1.32538	−0.662691	−	0.748893i	$-0.730586\pi$
$823$	−2.57538e7	−1.32538	−0.662691	+	0.748893i	$0.730586\pi$
$824$	−876364.	−0.0449641
$825$	−1.41175e7	−0.722142
$826$	1.87392e6	0.0955656
$827$	−2.17026e7	−1.10344	−0.551720	−	0.834029i	$-0.686028\pi$
$827$	−2.17026e7	−1.10344	−0.551720	+	0.834029i	$0.686028\pi$
$828$	4.49416e6	0.227810
$829$	−2.41485e7	−1.22040	−0.610202	−	0.792246i	$-0.708912\pi$
$829$	−2.41485e7	−1.22040	−0.610202	+	0.792246i	$0.708912\pi$
$830$	5.81984e6	0.293235
$831$	7.20629e6	0.362001
$832$	1.30011e6	0.0651135
$833$	−2.48151e7	−1.23909
$834$	9.95691e6	0.495689
$835$	−5.07810e6	−0.252049
$836$	−1.04386e7	−0.516568
$837$	−7.59190e6	−0.374573
$838$	−3.23556e7	−1.59162
$839$	2.14289e7	1.05098	0.525490	−	0.850799i	$-0.323882\pi$
$839$	2.14289e7	1.05098	0.525490	+	0.850799i	$0.323882\pi$
$840$	−1.62792e6	−0.0796041
$841$	−1.71688e7	−0.837047
$842$	3.12526e7	1.51917
$843$	−1.86306e7	−0.902936
$844$	−1.77903e7	−0.859661
$845$	−3.82770e6	−0.184415
$846$	8.10303e6	0.389244
$847$	2.17023e7	1.03943
$848$	−9.57164e6	−0.457085
$849$	1.80227e7	0.858124
$850$	−2.72268e7	−1.29255
$851$	1.48741e7	0.704056
$852$	−1.00931e7	−0.476351
$853$	−8.63422e6	−0.406303	−0.203152	−	0.979147i	$-0.565118\pi$
$853$	−8.63422e6	−0.406303	−0.203152	+	0.979147i	$0.565118\pi$
$854$	2.88094e7	1.35173
$855$	896185.	0.0419259
$856$	−5.27698e6	−0.246151
$857$	1.84543e7	0.858314	0.429157	−	0.903230i	$-0.358811\pi$
$857$	1.84543e7	0.858314	0.429157	+	0.903230i	$0.358811\pi$
$858$	6.56721e6	0.304553
$859$	−1.30920e6	−0.0605373	−0.0302686	−	0.999542i	$-0.509636\pi$
$859$	−1.30920e6	−0.0605373	−0.0302686	+	0.999542i	$0.509636\pi$
$860$	−3.98498e6	−0.183730
$861$	6.53898e6	0.300609
$862$	−2.30038e6	−0.105446
$863$	−3.66050e7	−1.67307	−0.836534	−	0.547915i	$-0.815422\pi$
$863$	−3.66050e7	−1.67307	−0.836534	+	0.547915i	$0.815422\pi$
$864$	−4.72880e6	−0.215509
$865$	−25918.1	−0.00117777
$866$	3.71023e6	0.168115
$867$	−1.36787e6	−0.0618014
$868$	4.10649e7	1.85000
$869$	−4.48539e7	−2.01489
$870$	−1.36600e6	−0.0611860
$871$	−9.74386e6	−0.435197
$872$	2.84990e6	0.126923
$873$	−150195.	−0.00666990
$874$	−1.88742e7	−0.835774
$875$	−1.33987e7	−0.591618
$876$	9.90521e6	0.436118
$877$	1.03563e7	0.454682	0.227341	−	0.973815i	$-0.426997\pi$
$877$	1.03563e7	0.454682	0.227341	+	0.973815i	$0.426997\pi$
$878$	2.38778e7	1.04534
$879$	−2.89301e6	−0.126293
$880$	7.54812e6	0.328573
$881$	3.55532e6	0.154326	0.0771630	−	0.997018i	$-0.475414\pi$
$881$	3.55532e6	0.154326	0.0771630	+	0.997018i	$0.475414\pi$
$882$	−1.16288e7	−0.503344
$883$	7.99119e6	0.344913	0.172457	−	0.985017i	$-0.444830\pi$
$883$	7.99119e6	0.344913	0.172457	+	0.985017i	$0.444830\pi$
$884$	4.96189e6	0.213558
$885$	139109.	0.00597031
$886$	3.56942e7	1.52761
$887$	−45288.3	−0.00193275	−0.000966377	−	1.00000i	$-0.500308\pi$
$887$	−45288.3	−0.00193275	−0.000966377		1.00000i	$0.500308\pi$
$888$	−4.10797e6	−0.174822
$889$	−5.50123e7	−2.33456
$890$	3.01632e6	0.127645
$891$	−3.43743e6	−0.145057
$892$	5.20149e6	0.218885
$893$	−1.33320e7	−0.559456
$894$	−1.77973e7	−0.744748
$895$	675947.	0.0282069
$896$	−3.03157e7	−1.26153
$897$	4.65192e6	0.193042
$898$	4.00588e7	1.65770
$899$	−1.90392e7	−0.785688
$900$	−4.99855e6	−0.205702
$901$	−9.53360e6	−0.391241
$902$	−1.44321e7	−0.590629
$903$	2.90844e7	1.18697
$904$	−3.27928e6	−0.133462
$905$	2.63252e6	0.106844
$906$	9.87372e6	0.399632
$907$	−1.46918e7	−0.593004	−0.296502	−	0.955032i	$-0.595820\pi$
$907$	−1.46918e7	−0.593004	−0.296502	+	0.955032i	$0.595820\pi$
$908$	−900720.	−0.0362556
$909$	−1.18795e7	−0.476859
$910$	3.04969e6	0.122082
$911$	5.24186e6	0.209261	0.104631	−	0.994511i	$-0.466634\pi$
$911$	5.24186e6	0.209261	0.104631	+	0.994511i	$0.466634\pi$
$912$	1.09509e7	0.435975
$913$	3.67277e7	1.45820
$914$	5.97522e7	2.36586
$915$	2.13864e6	0.0844470
$916$	−2.54226e7	−1.00111
$917$	−7.47915e7	−2.93717
$918$	−6.62937e6	−0.259636
$919$	−3.06404e7	−1.19675	−0.598377	−	0.801215i	$-0.704188\pi$
$919$	−3.06404e7	−1.19675	−0.598377	+	0.801215i	$0.704188\pi$
$920$	2.54511e6	0.0991373
$921$	−1.87130e7	−0.726933
$922$	8.56073e6	0.331653
$923$	−1.04474e7	−0.403651
$924$	1.85932e7	0.716431
$925$	−1.65435e7	−0.635729
$926$	−6.51120e7	−2.49536
$927$	−859329.	−0.0328443
$928$	−1.18590e7	−0.452043
$929$	1.31316e7	0.499204	0.249602	−	0.968349i	$-0.419700\pi$
$929$	1.31316e7	0.499204	0.249602	+	0.968349i	$0.419700\pi$
$930$	7.78119e6	0.295011
$931$	1.91330e7	0.723451
$932$	3.00458e6	0.113304
$933$	1.31820e7	0.495767
$934$	−2.28750e7	−0.858014
$935$	7.51812e6	0.281242
$936$	−1.28478e6	−0.0479336
$937$	−2.09974e7	−0.781296	−0.390648	−	0.920540i	$-0.627749\pi$
$937$	−2.09974e7	−0.781296	−0.390648	+	0.920540i	$0.627749\pi$
$938$	−7.04169e7	−2.61318
$939$	−1.84896e7	−0.684326
$940$	−3.25365e6	−0.120102
$941$	−4.95313e7	−1.82350	−0.911751	−	0.410744i	$-0.865269\pi$
$941$	−4.95313e7	−1.82350	−0.911751	+	0.410744i	$0.865269\pi$
$942$	3.47976e7	1.27768
$943$	−1.02231e7	−0.374372
$944$	1.69983e6	0.0620834
$945$	−1.59628e6	−0.0581473
$946$	−6.41921e7	−2.33213
$947$	−1.89914e6	−0.0688149	−0.0344074	−	0.999408i	$-0.510954\pi$
$947$	−1.89914e6	−0.0688149	−0.0344074	+	0.999408i	$0.510954\pi$
$948$	−1.58813e7	−0.573939
$949$	1.02529e7	0.369558
$950$	2.09925e7	0.754665
$951$	1.26549e6	0.0453742
$952$	−1.98132e7	−0.708537
$953$	−1.28794e7	−0.459370	−0.229685	−	0.973265i	$-0.573770\pi$
$953$	−1.28794e7	−0.459370	−0.229685	+	0.973265i	$0.573770\pi$
$954$	−4.46763e6	−0.158930
$955$	−1.99163e6	−0.0706642
$956$	−9.70746e6	−0.343527
$957$	−8.62051e6	−0.304266
$958$	−4.05256e7	−1.42665
$959$	4.31416e7	1.51478
$960$	697474.	0.0244259
$961$	7.98248e7	2.78824
$962$	7.69572e6	0.268109
$963$	−5.17440e6	−0.179802
$964$	−3.02223e7	−1.04745
$965$	−3.23934e6	−0.111979
$966$	3.36185e7	1.15914
$967$	8.25605e6	0.283927	0.141963	−	0.989872i	$-0.454658\pi$
$967$	8.25605e6	0.283927	0.141963	+	0.989872i	$0.454658\pi$
$968$	9.37076e6	0.321430
$969$	1.09073e7	0.373172
$970$	153940.	0.00525317
$971$	4.95337e7	1.68598	0.842990	−	0.537930i	$-0.180793\pi$
$971$	4.95337e7	1.68598	0.842990	+	0.537930i	$0.180793\pi$
$972$	−1.21708e6	−0.0413195
$973$	2.91798e7	0.988100
$974$	−3.48636e7	−1.17754
$975$	−5.17402e6	−0.174308
$976$	2.61329e7	0.878139
$977$	−4.01765e6	−0.134659	−0.0673295	−	0.997731i	$-0.521448\pi$
$977$	−4.01765e6	−0.134659	−0.0673295	+	0.997731i	$0.521448\pi$
$978$	−15926.1	−0.000532429 0
$979$	1.90353e7	0.634751
$980$	4.66939e6	0.155308
$981$	2.79451e6	0.0927114
$982$	−3.18570e7	−1.05421
$983$	1.36159e6	0.0449431	0.0224716	−	0.999747i	$-0.492846\pi$
$983$	1.36159e6	0.0449431	0.0224716	+	0.999747i	$0.492846\pi$
$984$	2.82345e6	0.0929591
$985$	−9.36401e6	−0.307519
$986$	−1.66254e7	−0.544602
$987$	2.37468e7	0.775912
$988$	−3.82573e6	−0.124687
$989$	−4.54709e7	−1.47823
$990$	3.52314e6	0.114246
$991$	2.75323e7	0.890549	0.445274	−	0.895394i	$-0.353106\pi$
$991$	2.75323e7	0.890549	0.445274	+	0.895394i	$0.353106\pi$
$992$	6.75532e7	2.17955
$993$	1.05198e7	0.338559
$994$	−7.55016e7	−2.42376
$995$	4.74605e6	0.151976
$996$	1.30041e7	0.415367
$997$	5.77614e7	1.84035	0.920174	−	0.391510i	$-0.128047\pi$
$997$	5.77614e7	1.84035	0.920174	+	0.391510i	$0.128047\pi$
$998$	5.43949e7	1.72875
$999$	−4.02812e6	−0.127699

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.c.1.6	✓	22
3.2	odd	2		927.6.a.d.1.17		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.c.1.6	✓	22	1.1	even	1	trivial
927.6.a.d.1.17		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)

\(f(q)\)	\(=\)	\(q-7.25337 q^{2} -9.00000 q^{3} +20.6114 q^{4} +11.4457 q^{5} +65.2804 q^{6} +191.311 q^{7} +82.6057 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-7.25337 q^{2} -9.00000 q^{3} +20.6114 q^{4} +11.4457 q^{5} +65.2804 q^{6} +191.311 q^{7} +82.6057 q^{8} +81.0000 q^{9} -83.0197 q^{10} -523.919 q^{11} -185.503 q^{12} -192.015 q^{13} -1387.65 q^{14} -103.011 q^{15} -1258.73 q^{16} -1253.73 q^{17} -587.523 q^{18} +966.656 q^{19} +235.911 q^{20} -1721.80 q^{21} +3800.18 q^{22} +2691.88 q^{23} -743.451 q^{24} -2994.00 q^{25} +1392.75 q^{26} -729.000 q^{27} +3943.20 q^{28} -1828.21 q^{29} +747.177 q^{30} +10414.1 q^{31} +6486.69 q^{32} +4715.27 q^{33} +9093.78 q^{34} +2189.68 q^{35} +1669.52 q^{36} +5525.54 q^{37} -7011.51 q^{38} +1728.13 q^{39} +945.477 q^{40} -3797.76 q^{41} +12488.9 q^{42} -16891.9 q^{43} -10798.7 q^{44} +927.099 q^{45} -19525.2 q^{46} -13791.8 q^{47} +11328.6 q^{48} +19793.0 q^{49} +21716.6 q^{50} +11283.6 q^{51} -3957.69 q^{52} +7604.18 q^{53} +5287.71 q^{54} -5996.60 q^{55} +15803.4 q^{56} -8699.90 q^{57} +13260.7 q^{58} -1350.43 q^{59} -2123.20 q^{60} -20761.2 q^{61} -75537.5 q^{62} +15496.2 q^{63} -6770.87 q^{64} -2197.74 q^{65} -34201.6 q^{66} +50745.4 q^{67} -25841.2 q^{68} -24226.9 q^{69} -15882.6 q^{70} +54409.6 q^{71} +6691.06 q^{72} -53396.6 q^{73} -40078.8 q^{74} +26946.0 q^{75} +19924.1 q^{76} -100232. q^{77} -12534.8 q^{78} +85612.3 q^{79} -14407.1 q^{80} +6561.00 q^{81} +27546.5 q^{82} -70102.0 q^{83} -35488.8 q^{84} -14349.8 q^{85} +122523. q^{86} +16453.9 q^{87} -43278.6 q^{88} -36332.6 q^{89} -6724.59 q^{90} -36734.6 q^{91} +55483.5 q^{92} -93727.1 q^{93} +100037. q^{94} +11064.0 q^{95} -58380.2 q^{96} -1854.26 q^{97} -143566. q^{98} -42437.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9}+O(q^{10}) \) 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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