LMFDB - Embedded newform 177.6.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,6,Mod(1,177)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, 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("177.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.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:	$28.3879361069$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 269 x^{10} + 143 x^{9} + 25384 x^{8} + 8539 x^{7} - 1009736 x^{6} - 720516 x^{5} + \cdots + 49172480 $ x^12 - 2x^11 - 269x^10 + 143x^9 + 25384x^8 + 8539x^7 - 1009736x^6 - 720516x^5 + 15565376x^4 + 6775664x^3 - 75006848x^2 + 21512960*x + 49172480
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.38446$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.615542 q^{2} +9.00000 q^{3} -31.6211 q^{4} +61.9372 q^{5} +5.53988 q^{6} -209.534 q^{7} -39.1615 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+0.615542 q^{2} +9.00000 q^{3} -31.6211 q^{4} +61.9372 q^{5} +5.53988 q^{6} -209.534 q^{7} -39.1615 q^{8} +81.0000 q^{9} +38.1250 q^{10} +1.45515 q^{11} -284.590 q^{12} +351.120 q^{13} -128.977 q^{14} +557.435 q^{15} +987.770 q^{16} +689.107 q^{17} +49.8589 q^{18} +2735.73 q^{19} -1958.52 q^{20} -1885.80 q^{21} +0.895706 q^{22} -1310.96 q^{23} -352.453 q^{24} +711.222 q^{25} +216.129 q^{26} +729.000 q^{27} +6625.69 q^{28} +508.995 q^{29} +343.125 q^{30} +4218.33 q^{31} +1861.18 q^{32} +13.0964 q^{33} +424.174 q^{34} -12977.9 q^{35} -2561.31 q^{36} +4022.89 q^{37} +1683.95 q^{38} +3160.08 q^{39} -2425.55 q^{40} +7333.96 q^{41} -1160.79 q^{42} +5250.80 q^{43} -46.0135 q^{44} +5016.92 q^{45} -806.951 q^{46} +25394.3 q^{47} +8889.93 q^{48} +27097.3 q^{49} +437.787 q^{50} +6201.96 q^{51} -11102.8 q^{52} -16562.5 q^{53} +448.730 q^{54} +90.1280 q^{55} +8205.64 q^{56} +24621.5 q^{57} +313.308 q^{58} -3481.00 q^{59} -17626.7 q^{60} -4267.66 q^{61} +2596.56 q^{62} -16972.2 q^{63} -30463.0 q^{64} +21747.4 q^{65} +8.06136 q^{66} +13390.6 q^{67} -21790.3 q^{68} -11798.6 q^{69} -7988.46 q^{70} +54112.6 q^{71} -3172.08 q^{72} -32575.3 q^{73} +2476.26 q^{74} +6401.00 q^{75} -86506.7 q^{76} -304.903 q^{77} +1945.16 q^{78} +59592.4 q^{79} +61179.7 q^{80} +6561.00 q^{81} +4514.36 q^{82} +94095.2 q^{83} +59631.2 q^{84} +42681.4 q^{85} +3232.09 q^{86} +4580.95 q^{87} -56.9858 q^{88} -136311. q^{89} +3088.12 q^{90} -73571.4 q^{91} +41454.0 q^{92} +37965.0 q^{93} +15631.3 q^{94} +169443. q^{95} +16750.6 q^{96} +135175. q^{97} +16679.6 q^{98} +117.867 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9}+O(q^{10}) $ 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9} + 601 q^{10} + 1480 q^{11} + 1782 q^{12} + 472 q^{13} + 1065 q^{14} + 1422 q^{15} + 6370 q^{16} + 1565 q^{17} + 1782 q^{18} + 3939 q^{19} + 8033 q^{20} + 3717 q^{21} - 1738 q^{22} + 7245 q^{23} + 6507 q^{24} + 9690 q^{25} + 3764 q^{26} + 8748 q^{27} + 12154 q^{28} + 10003 q^{29} + 5409 q^{30} + 7295 q^{31} + 11628 q^{32} + 13320 q^{33} - 16344 q^{34} + 11015 q^{35} + 16038 q^{36} + 6741 q^{37} + 3035 q^{38} + 4248 q^{39} + 5572 q^{40} + 34025 q^{41} + 9585 q^{42} - 6336 q^{43} + 41168 q^{44} + 12798 q^{45} + 2345 q^{46} + 66167 q^{47} + 57330 q^{48} + 28319 q^{49} + 31173 q^{50} + 14085 q^{51} + 16440 q^{52} + 62290 q^{53} + 16038 q^{54} + 55764 q^{55} + 107306 q^{56} + 35451 q^{57} + 37952 q^{58} - 41772 q^{59} + 72297 q^{60} + 68469 q^{61} + 99190 q^{62} + 33453 q^{63} + 68525 q^{64} + 80156 q^{65} - 15642 q^{66} + 113310 q^{67} + 33887 q^{68} + 65205 q^{69} + 32034 q^{70} + 84520 q^{71} + 58563 q^{72} + 135895 q^{73} - 31962 q^{74} + 87210 q^{75} - 61848 q^{76} - 3799 q^{77} + 33876 q^{78} + 14122 q^{79} + 77609 q^{80} + 78732 q^{81} - 1501 q^{82} + 114463 q^{83} + 109386 q^{84} - 101097 q^{85} - 203536 q^{86} + 90027 q^{87} - 244967 q^{88} + 189109 q^{89} + 48681 q^{90} - 168249 q^{91} - 71946 q^{92} + 65655 q^{93} - 472284 q^{94} + 21923 q^{95} + 104652 q^{96} - 76192 q^{97} - 17544 q^{98} + 119880 q^{99}+O(q^{100}) \) 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9 + 601 * q^10 + 1480 * q^11 + 1782 * q^12 + 472 * q^13 + 1065 * q^14 + 1422 * q^15 + 6370 * q^16 + 1565 * q^17 + 1782 * q^18 + 3939 * q^19 + 8033 * q^20 + 3717 * q^21 - 1738 * q^22 + 7245 * q^23 + 6507 * q^24 + 9690 * q^25 + 3764 * q^26 + 8748 * q^27 + 12154 * q^28 + 10003 * q^29 + 5409 * q^30 + 7295 * q^31 + 11628 * q^32 + 13320 * q^33 - 16344 * q^34 + 11015 * q^35 + 16038 * q^36 + 6741 * q^37 + 3035 * q^38 + 4248 * q^39 + 5572 * q^40 + 34025 * q^41 + 9585 * q^42 - 6336 * q^43 + 41168 * q^44 + 12798 * q^45 + 2345 * q^46 + 66167 * q^47 + 57330 * q^48 + 28319 * q^49 + 31173 * q^50 + 14085 * q^51 + 16440 * q^52 + 62290 * q^53 + 16038 * q^54 + 55764 * q^55 + 107306 * q^56 + 35451 * q^57 + 37952 * q^58 - 41772 * q^59 + 72297 * q^60 + 68469 * q^61 + 99190 * q^62 + 33453 * q^63 + 68525 * q^64 + 80156 * q^65 - 15642 * q^66 + 113310 * q^67 + 33887 * q^68 + 65205 * q^69 + 32034 * q^70 + 84520 * q^71 + 58563 * q^72 + 135895 * q^73 - 31962 * q^74 + 87210 * q^75 - 61848 * q^76 - 3799 * q^77 + 33876 * q^78 + 14122 * q^79 + 77609 * q^80 + 78732 * q^81 - 1501 * q^82 + 114463 * q^83 + 109386 * q^84 - 101097 * q^85 - 203536 * q^86 + 90027 * q^87 - 244967 * q^88 + 189109 * q^89 + 48681 * q^90 - 168249 * q^91 - 71946 * q^92 + 65655 * q^93 - 472284 * q^94 + 21923 * q^95 + 104652 * q^96 - 76192 * q^97 - 17544 * q^98 + 119880 * 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 $

$2$	0.615542	0.108813	0.0544067	−	0.998519i	$-0.482673\pi$
$2$	0.615542	0.108813	0.0544067	+	0.998519i	$0.482673\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−31.6211	−0.988160
$5$	61.9372	1.10797	0.553984	−	0.832528i	$-0.313107\pi$
$5$	61.9372	1.10797	0.553984	+	0.832528i	$0.313107\pi$
$6$	5.53988	0.0628235
$7$	−209.534	−1.61625	−0.808125	−	0.589011i	$-0.799518\pi$
$7$	−209.534	−1.61625	−0.808125	+	0.589011i	$0.799518\pi$
$8$	−39.1615	−0.216339
$9$	81.0000	0.333333
$10$	38.1250	0.120562
$11$	1.45515	0.00362599	0.00181299	−	0.999998i	$-0.499423\pi$
$11$	1.45515	0.00362599	0.00181299	+	0.999998i	$0.499423\pi$
$12$	−284.590	−0.570514
$13$	351.120	0.576231	0.288116	−	0.957596i	$-0.406971\pi$
$13$	351.120	0.576231	0.288116	+	0.957596i	$0.406971\pi$
$14$	−128.977	−0.175870
$15$	557.435	0.639685
$16$	987.770	0.964619
$17$	689.107	0.578315	0.289157	−	0.957282i	$-0.406625\pi$
$17$	689.107	0.578315	0.289157	+	0.957282i	$0.406625\pi$
$18$	49.8589	0.0362712
$19$	2735.73	1.73856	0.869278	−	0.494323i	$-0.164584\pi$
$19$	2735.73	1.73856	0.869278	+	0.494323i	$0.164584\pi$
$20$	−1958.52	−1.09485
$21$	−1885.80	−0.933143
$22$	0.895706	0.000394556 0
$23$	−1310.96	−0.516737	−0.258369	−	0.966046i	$-0.583185\pi$
$23$	−1310.96	−0.516737	−0.258369	+	0.966046i	$0.583185\pi$
$24$	−352.453	−0.124903
$25$	711.222	0.227591
$26$	216.129	0.0627017
$27$	729.000	0.192450
$28$	6625.69	1.59711
$29$	508.995	0.112388	0.0561938	−	0.998420i	$-0.482104\pi$
$29$	508.995	0.112388	0.0561938	+	0.998420i	$0.482104\pi$
$30$	343.125	0.0696064
$31$	4218.33	0.788381	0.394191	−	0.919029i	$-0.371025\pi$
$31$	4218.33	0.788381	0.394191	+	0.919029i	$0.371025\pi$
$32$	1861.18	0.321302
$33$	13.0964	0.00209346
$34$	424.174	0.0629285
$35$	−12977.9	−1.79075
$36$	−2561.31	−0.329387
$37$	4022.89	0.483096	0.241548	−	0.970389i	$-0.422345\pi$
$37$	4022.89	0.483096	0.241548	+	0.970389i	$0.422345\pi$
$38$	1683.95	0.189178
$39$	3160.08	0.332687
$40$	−2425.55	−0.239696
$41$	7333.96	0.681364	0.340682	−	0.940179i	$-0.389342\pi$
$41$	7333.96	0.681364	0.340682	+	0.940179i	$0.389342\pi$
$42$	−1160.79	−0.101538
$43$	5250.80	0.433066	0.216533	−	0.976275i	$-0.430525\pi$
$43$	5250.80	0.433066	0.216533	+	0.976275i	$0.430525\pi$
$44$	−46.0135	−0.00358305
$45$	5016.92	0.369322
$46$	−806.951	−0.0562280
$47$	25394.3	1.67684	0.838420	−	0.545024i	$-0.183479\pi$
$47$	25394.3	1.67684	0.838420	+	0.545024i	$0.183479\pi$
$48$	8889.93	0.556923
$49$	27097.3	1.61227
$50$	437.787	0.0247650
$51$	6201.96	0.333890
$52$	−11102.8	−0.569408
$53$	−16562.5	−0.809911	−0.404956	−	0.914336i	$-0.632713\pi$
$53$	−16562.5	−0.809911	−0.404956	+	0.914336i	$0.632713\pi$
$54$	448.730	0.0209412
$55$	90.1280	0.00401747
$56$	8205.64	0.349657
$57$	24621.5	1.00376
$58$	313.308	0.0122293
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−17626.7	−0.632111
$61$	−4267.66	−0.146847	−0.0734235	−	0.997301i	$-0.523392\pi$
$61$	−4267.66	−0.146847	−0.0734235	+	0.997301i	$0.523392\pi$
$62$	2596.56	0.0857865
$63$	−16972.2	−0.538750
$64$	−30463.0	−0.929657
$65$	21747.4	0.638445
$66$	8.06136	0.000227797 0
$67$	13390.6	0.364429	0.182215	−	0.983259i	$-0.441673\pi$
$67$	13390.6	0.364429	0.182215	+	0.983259i	$0.441673\pi$
$68$	−21790.3	−0.571467
$69$	−11798.6	−0.298338
$70$	−7988.46	−0.194858
$71$	54112.6	1.27395	0.636976	−	0.770884i	$-0.280185\pi$
$71$	54112.6	1.27395	0.636976	+	0.770884i	$0.280185\pi$
$72$	−3172.08	−0.0721129
$73$	−32575.3	−0.715453	−0.357726	−	0.933826i	$-0.616448\pi$
$73$	−32575.3	−0.715453	−0.357726	+	0.933826i	$0.616448\pi$
$74$	2476.26	0.0525674
$75$	6401.00	0.131400
$76$	−86506.7	−1.71797
$77$	−304.903	−0.00586050
$78$	1945.16	0.0362009
$79$	59592.4	1.07429	0.537147	−	0.843489i	$-0.319502\pi$
$79$	59592.4	1.07429	0.537147	+	0.843489i	$0.319502\pi$
$80$	61179.7	1.06877
$81$	6561.00	0.111111
$82$	4514.36	0.0741415
$83$	94095.2	1.49924	0.749622	−	0.661867i	$-0.230236\pi$
$83$	94095.2	1.49924	0.749622	+	0.661867i	$0.230236\pi$
$84$	59631.2	0.922094
$85$	42681.4	0.640754
$86$	3232.09	0.0471235
$87$	4580.95	0.0648870
$88$	−56.9858	−0.000784441 0
$89$	−136311.	−1.82414	−0.912068	−	0.410040i	$-0.865515\pi$
$89$	−136311.	−1.82414	−0.912068	+	0.410040i	$0.865515\pi$
$90$	3088.12	0.0401873
$91$	−73571.4	−0.931334
$92$	41454.0	0.510619
$93$	37965.0	0.455172
$94$	15631.3	0.182463
$95$	169443.	1.92626
$96$	16750.6	0.185504
$97$	135175.	1.45870	0.729350	−	0.684141i	$-0.239823\pi$
$97$	135175.	1.45870	0.729350	+	0.684141i	$0.239823\pi$
$98$	16679.6	0.175436
$99$	117.867	0.00120866
$100$	−22489.6	−0.224896
$101$	−25496.8	−0.248704	−0.124352	−	0.992238i	$-0.539685\pi$
$101$	−25496.8	−0.248704	−0.124352	+	0.992238i	$0.539685\pi$
$102$	3817.57	0.0363318
$103$	62339.3	0.578987	0.289493	−	0.957180i	$-0.406513\pi$
$103$	62339.3	0.578987	0.289493	+	0.957180i	$0.406513\pi$
$104$	−13750.4	−0.124661
$105$	−116801.	−1.03389
$106$	−10194.9	−0.0881293
$107$	−16258.7	−0.137286	−0.0686429	−	0.997641i	$-0.521867\pi$
$107$	−16258.7	−0.137286	−0.0686429	+	0.997641i	$0.521867\pi$
$108$	−23051.8	−0.190171
$109$	−209396.	−1.68812	−0.844059	−	0.536250i	$-0.819840\pi$
$109$	−209396.	−1.68812	−0.844059	+	0.536250i	$0.819840\pi$
$110$	55.4776	0.000437155 0
$111$	36206.0	0.278916
$112$	−206971.	−1.55907
$113$	−143342.	−1.05603	−0.528017	−	0.849234i	$-0.677064\pi$
$113$	−143342.	−1.05603	−0.528017	+	0.849234i	$0.677064\pi$
$114$	15155.6	0.109222
$115$	−81197.2	−0.572528
$116$	−16095.0	−0.111057
$117$	28440.7	0.192077
$118$	−2142.70	−0.0141663
$119$	−144391.	−0.934702
$120$	−21830.0	−0.138389
$121$	−161049.	−0.999987
$122$	−2626.92	−0.0159789
$123$	66005.7	0.393386
$124$	−133388.	−0.779046
$125$	−149503.	−0.855804
$126$	−10447.1	−0.0586233
$127$	79745.4	0.438729	0.219365	−	0.975643i	$-0.429602\pi$
$127$	79745.4	0.438729	0.219365	+	0.975643i	$0.429602\pi$
$128$	−78309.0	−0.422461
$129$	47257.2	0.250031
$130$	13386.4	0.0694714
$131$	−5118.41	−0.0260589	−0.0130295	−	0.999915i	$-0.504148\pi$
$131$	−5118.41	−0.0260589	−0.0130295	+	0.999915i	$0.504148\pi$
$132$	−414.121	−0.00206868
$133$	−573227.	−2.80994
$134$	8242.49	0.0396548
$135$	45152.3	0.213228
$136$	−26986.4	−0.125112
$137$	−237403.	−1.08065	−0.540324	−	0.841457i	$-0.681698\pi$
$137$	−237403.	−1.08065	−0.540324	+	0.841457i	$0.681698\pi$
$138$	−7262.56	−0.0324632
$139$	−60191.4	−0.264239	−0.132120	−	0.991234i	$-0.542178\pi$
$139$	−60191.4	−0.264239	−0.132120	+	0.991234i	$0.542178\pi$
$140$	410377.	1.76955
$141$	228549.	0.968125
$142$	33308.6	0.138623
$143$	510.932	0.00208941
$144$	80009.4	0.321540
$145$	31525.7	0.124522
$146$	−20051.4	−0.0778509
$147$	243876.	0.930842
$148$	−127208.	−0.477376
$149$	−226647.	−0.836343	−0.418171	−	0.908368i	$-0.637329\pi$
$149$	−226647.	−0.836343	−0.418171	+	0.908368i	$0.637329\pi$
$150$	3940.09	0.0142981
$151$	−294492.	−1.05107	−0.525534	−	0.850773i	$-0.676134\pi$
$151$	−294492.	−1.05107	−0.525534	+	0.850773i	$0.676134\pi$
$152$	−107135.	−0.376117
$153$	55817.7	0.192772
$154$	−187.681	−0.000637702 0
$155$	261272.	0.873500
$156$	−99925.1	−0.328748
$157$	527580.	1.70820	0.854101	−	0.520108i	$-0.174108\pi$
$157$	527580.	1.70820	0.854101	+	0.520108i	$0.174108\pi$
$158$	36681.6	0.116898
$159$	−149063.	−0.467602
$160$	115276.	0.355992
$161$	274690.	0.835177
$162$	4038.57	0.0120904
$163$	138581.	0.408540	0.204270	−	0.978915i	$-0.434518\pi$
$163$	138581.	0.408540	0.204270	+	0.978915i	$0.434518\pi$
$164$	−231908.	−0.673296
$165$	811.152	0.00231949
$166$	57919.5	0.163138
$167$	201512.	0.559126	0.279563	−	0.960127i	$-0.409810\pi$
$167$	201512.	0.559126	0.279563	+	0.960127i	$0.409810\pi$
$168$	73850.8	0.201875
$169$	−248008.	−0.667958
$170$	26272.2	0.0697227
$171$	221594.	0.579519
$172$	−166036.	−0.427939
$173$	463291.	1.17690	0.588449	−	0.808535i	$-0.299739\pi$
$173$	463291.	1.17690	0.588449	+	0.808535i	$0.299739\pi$
$174$	2819.77	0.00706058
$175$	−149025.	−0.367844
$176$	1437.35	0.00349770
$177$	−31329.0	−0.0751646
$178$	−83905.4	−0.198490
$179$	−235004.	−0.548205	−0.274103	−	0.961700i	$-0.588381\pi$
$179$	−235004.	−0.548205	−0.274103	+	0.961700i	$0.588381\pi$
$180$	−158640.	−0.364949
$181$	345261.	0.783341	0.391670	−	0.920106i	$-0.371897\pi$
$181$	345261.	0.783341	0.391670	+	0.920106i	$0.371897\pi$
$182$	−45286.3	−0.101342
$183$	−38408.9	−0.0847822
$184$	51339.1	0.111790
$185$	249167.	0.535255
$186$	23369.0	0.0495288
$187$	1002.75	0.00209696
$188$	−802996.	−1.65699
$189$	−152750.	−0.311048
$190$	104300.	0.209603
$191$	973228.	1.93033	0.965164	−	0.261646i	$-0.0842654\pi$
$191$	973228.	1.93033	0.965164	+	0.261646i	$0.0842654\pi$
$192$	−274167.	−0.536738
$193$	−493451.	−0.953567	−0.476783	−	0.879021i	$-0.658197\pi$
$193$	−493451.	−0.953567	−0.476783	+	0.879021i	$0.658197\pi$
$194$	83205.7	0.158726
$195$	195726.	0.368607
$196$	−856848.	−1.59318
$197$	339146.	0.622616	0.311308	−	0.950309i	$-0.399233\pi$
$197$	339146.	0.622616	0.311308	+	0.950309i	$0.399233\pi$
$198$	72.5522	0.000131519 0
$199$	−589702.	−1.05560	−0.527801	−	0.849368i	$-0.676983\pi$
$199$	−589702.	−1.05560	−0.527801	+	0.849368i	$0.676983\pi$
$200$	−27852.5	−0.0492368
$201$	120516.	0.210403
$202$	−15694.4	−0.0270623
$203$	−106652.	−0.181646
$204$	−196113.	−0.329937
$205$	454245.	0.754929
$206$	38372.4	0.0630015
$207$	−106188.	−0.172246
$208$	346825.	0.555844
$209$	3980.89	0.00630398
$210$	−71896.2	−0.112501
$211$	779769.	1.20576	0.602879	−	0.797833i	$-0.294020\pi$
$211$	779769.	1.20576	0.602879	+	0.797833i	$0.294020\pi$
$212$	523726.	0.800322
$213$	487014.	0.735516
$214$	−10007.9	−0.0149385
$215$	325220.	0.479823
$216$	−28548.7	−0.0416344
$217$	−883882.	−1.27422
$218$	−128892.	−0.183690
$219$	−293177.	−0.413067
$220$	−2849.95	−0.00396991
$221$	241959.	0.333243
$222$	22286.3	0.0303498
$223$	148653.	0.200176	0.100088	−	0.994979i	$-0.468088\pi$
$223$	148653.	0.200176	0.100088	+	0.994979i	$0.468088\pi$
$224$	−389980.	−0.519305
$225$	57609.0	0.0758637
$226$	−88233.2	−0.114911
$227$	−705507.	−0.908733	−0.454367	−	0.890815i	$-0.650134\pi$
$227$	−705507.	−0.908733	−0.454367	+	0.890815i	$0.650134\pi$
$228$	−778561.	−0.991871
$229$	221449.	0.279052	0.139526	−	0.990218i	$-0.455442\pi$
$229$	221449.	0.279052	0.139526	+	0.990218i	$0.455442\pi$
$230$	−49980.3	−0.0622987
$231$	−2744.13	−0.00338356
$232$	−19933.0	−0.0243138
$233$	−303806.	−0.366612	−0.183306	−	0.983056i	$-0.558680\pi$
$233$	−303806.	−0.366612	−0.183306	+	0.983056i	$0.558680\pi$
$234$	17506.4	0.0209006
$235$	1.57285e6	1.85788
$236$	110073.	0.128647
$237$	536332.	0.620244
$238$	−88878.8	−0.101708
$239$	1.12989e6	1.27950	0.639751	−	0.768583i	$-0.279038\pi$
$239$	1.12989e6	1.27950	0.639751	+	0.768583i	$0.279038\pi$
$240$	550618.	0.617052
$241$	−1.30930e6	−1.45210	−0.726049	−	0.687643i	$-0.758645\pi$
$241$	−1.30930e6	−1.45210	−0.726049	+	0.687643i	$0.758645\pi$
$242$	−99132.3	−0.108812
$243$	59049.0	0.0641500
$244$	134948.	0.145108
$245$	1.67834e6	1.78634
$246$	40629.2	0.0428056
$247$	960568.	1.00181
$248$	−165196.	−0.170557
$249$	846856.	0.865588
$250$	−92025.2	−0.0931230
$251$	−948490.	−0.950273	−0.475136	−	0.879912i	$-0.657601\pi$
$251$	−948490.	−0.950273	−0.475136	+	0.879912i	$0.657601\pi$
$252$	536681.	0.532371
$253$	−1907.64	−0.00187368
$254$	49086.7	0.0477396
$255$	384133.	0.369939
$256$	926614.	0.883688
$257$	1.82976e6	1.72807	0.864036	−	0.503431i	$-0.167929\pi$
$257$	1.82976e6	1.72807	0.864036	+	0.503431i	$0.167929\pi$
$258$	29088.8	0.0272067
$259$	−842930.	−0.780804
$260$	−687676.	−0.630886
$261$	41228.6	0.0374625
$262$	−3150.60	−0.00283556
$263$	1.23847e6	1.10407	0.552033	−	0.833822i	$-0.313852\pi$
$263$	1.23847e6	1.10407	0.552033	+	0.833822i	$0.313852\pi$
$264$	−512.872	−0.000452897 0
$265$	−1.02584e6	−0.897355
$266$	−352845.	−0.305760
$267$	−1.22680e6	−1.05316
$268$	−423426.	−0.360115
$269$	1.19822e6	1.00962	0.504808	−	0.863232i	$-0.331563\pi$
$269$	1.19822e6	1.00962	0.504808	+	0.863232i	$0.331563\pi$
$270$	27793.1	0.0232021
$271$	−907388.	−0.750533	−0.375267	−	0.926917i	$-0.622449\pi$
$271$	−907388.	−0.750533	−0.375267	+	0.926917i	$0.622449\pi$
$272$	680679.	0.557854
$273$	−662142.	−0.537706
$274$	−146131.	−0.117589
$275$	1034.94	0.000825243 0
$276$	373086.	0.294806
$277$	196862.	0.154157	0.0770783	−	0.997025i	$-0.475441\pi$
$277$	196862.	0.154157	0.0770783	+	0.997025i	$0.475441\pi$
$278$	−37050.3	−0.0287528
$279$	341685.	0.262794
$280$	508235.	0.387409
$281$	2.31407e6	1.74828	0.874140	−	0.485674i	$-0.161426\pi$
$281$	2.31407e6	1.74828	0.874140	+	0.485674i	$0.161426\pi$
$282$	140681.	0.105345
$283$	42804.6	0.0317705	0.0158852	−	0.999874i	$-0.494943\pi$
$283$	42804.6	0.0317705	0.0158852	+	0.999874i	$0.494943\pi$
$284$	−1.71110e6	−1.25887
$285$	1.52499e6	1.11213
$286$	314.500	0.000227356 0
$287$	−1.53671e6	−1.10125
$288$	150756.	0.107101
$289$	−944988.	−0.665552
$290$	19405.4	0.0135496
$291$	1.21657e6	0.842181
$292$	1.03007e6	0.706981
$293$	−943192.	−0.641846	−0.320923	−	0.947105i	$-0.603993\pi$
$293$	−943192.	−0.641846	−0.320923	+	0.947105i	$0.603993\pi$
$294$	150116.	0.101288
$295$	−215604.	−0.144245
$296$	−157542.	−0.104512
$297$	1060.80	0.000697821 0
$298$	−139511.	−0.0910054
$299$	−460304.	−0.297760
$300$	−202407.	−0.129844
$301$	−1.10022e6	−0.699944
$302$	−181272.	−0.114370
$303$	−229471.	−0.143589
$304$	2.70227e6	1.67704
$305$	−264327.	−0.162702
$306$	34358.1	0.0209762
$307$	−1.05157e6	−0.636784	−0.318392	−	0.947959i	$-0.603143\pi$
$307$	−1.05157e6	−0.636784	−0.318392	+	0.947959i	$0.603143\pi$
$308$	9641.37	0.00579111
$309$	561053.	0.334278
$310$	160824.	0.0950486
$311$	−616781.	−0.361601	−0.180801	−	0.983520i	$-0.557869\pi$
$311$	−616781.	−0.361601	−0.180801	+	0.983520i	$0.557869\pi$
$312$	−123753.	−0.0719731
$313$	1.22803e6	0.708516	0.354258	−	0.935148i	$-0.384733\pi$
$313$	1.22803e6	0.708516	0.354258	+	0.935148i	$0.384733\pi$
$314$	324747.	0.185875
$315$	−1.05121e6	−0.596917
$316$	−1.88438e6	−1.06157
$317$	−2.46036e6	−1.37515	−0.687577	−	0.726112i	$-0.741325\pi$
$317$	−2.46036e6	−1.37515	−0.687577	+	0.726112i	$0.741325\pi$
$318$	−91754.5	−0.0508815
$319$	740.664	0.000407516 0
$320$	−1.88679e6	−1.03003
$321$	−146328.	−0.0792620
$322$	169083.	0.0908785
$323$	1.88521e6	1.00543
$324$	−207466.	−0.109796
$325$	249724.	0.131145
$326$	85302.3	0.0444546
$327$	−1.88457e6	−0.974635
$328$	−287209.	−0.147405
$329$	−5.32096e6	−2.71019
$330$	499.298	0.000252392 0
$331$	58317.0	0.0292567	0.0146283	−	0.999893i	$-0.495343\pi$
$331$	58317.0	0.0292567	0.0146283	+	0.999893i	$0.495343\pi$
$332$	−2.97539e6	−1.48149
$333$	325854.	0.161032
$334$	124039.	0.0608405
$335$	829378.	0.403776
$336$	−1.86274e6	−0.900127
$337$	2.05912e6	0.987658	0.493829	−	0.869559i	$-0.335597\pi$
$337$	2.05912e6	0.987658	0.493829	+	0.869559i	$0.335597\pi$
$338$	−152659.	−0.0726828
$339$	−1.29008e6	−0.609702
$340$	−1.34963e6	−0.633167
$341$	6138.30	0.00285866
$342$	136400.	0.0630595
$343$	−2.15617e6	−0.989574
$344$	−205629.	−0.0936890
$345$	−730775.	−0.330549
$346$	285175.	0.128062
$347$	−3.05058e6	−1.36006	−0.680030	−	0.733184i	$-0.738033\pi$
$347$	−3.05058e6	−1.36006	−0.680030	+	0.733184i	$0.738033\pi$
$348$	−144855.	−0.0641187
$349$	−2.54878e6	−1.12013	−0.560065	−	0.828449i	$-0.689224\pi$
$349$	−2.54878e6	−1.12013	−0.560065	+	0.828449i	$0.689224\pi$
$350$	−91731.2	−0.0400264
$351$	255966.	0.110896
$352$	2708.30	0.00116504
$353$	−139978.	−0.0597891	−0.0298945	−	0.999553i	$-0.509517\pi$
$353$	−139978.	−0.0597891	−0.0298945	+	0.999553i	$0.509517\pi$
$354$	−19284.3	−0.00817892
$355$	3.35159e6	1.41150
$356$	4.31032e6	1.80254
$357$	−1.29952e6	−0.539650
$358$	−144655.	−0.0596521
$359$	−587724.	−0.240679	−0.120339	−	0.992733i	$-0.538398\pi$
$359$	−587724.	−0.240679	−0.120339	+	0.992733i	$0.538398\pi$
$360$	−196470.	−0.0798987
$361$	5.00810e6	2.02258
$362$	212522.	0.0852380
$363$	−1.44944e6	−0.577343
$364$	2.32641e6	0.920307
$365$	−2.01762e6	−0.792698
$366$	−23642.3	−0.00922544
$367$	360316.	0.139643	0.0698214	−	0.997560i	$-0.477757\pi$
$367$	360316.	0.139643	0.0698214	+	0.997560i	$0.477757\pi$
$368$	−1.29493e6	−0.498455
$369$	594051.	0.227121
$370$	153372.	0.0582429
$371$	3.47041e6	1.30902
$372$	−1.20049e6	−0.449783
$373$	5.26924e6	1.96099	0.980497	−	0.196535i	$-0.0629690\pi$
$373$	5.26924e6	1.96099	0.980497	+	0.196535i	$0.0629690\pi$
$374$	617.237	0.000228178 0
$375$	−1.34552e6	−0.494098
$376$	−994478.	−0.362765
$377$	178718.	0.0647612
$378$	−94024.1	−0.0338462
$379$	3.43445e6	1.22817	0.614086	−	0.789239i	$-0.289525\pi$
$379$	3.43445e6	1.22817	0.614086	+	0.789239i	$0.289525\pi$
$380$	−5.35799e6	−1.90346
$381$	717709.	0.253300
$382$	599062.	0.210046
$383$	−3.55421e6	−1.23807	−0.619036	−	0.785363i	$-0.712476\pi$
$383$	−3.55421e6	−1.23807	−0.619036	+	0.785363i	$0.712476\pi$
$384$	−704781.	−0.243908
$385$	−18884.8	−0.00649324
$386$	−303740.	−0.103761
$387$	425315.	0.144355
$388$	−4.27437e6	−1.44143
$389$	4.52272e6	1.51539	0.757697	−	0.652606i	$-0.226324\pi$
$389$	4.52272e6	1.51539	0.757697	+	0.652606i	$0.226324\pi$
$390$	120478.	0.0401094
$391$	−903392.	−0.298837
$392$	−1.06117e6	−0.348795
$393$	−46065.7	−0.0150451
$394$	208758.	0.0677491
$395$	3.69099e6	1.19028
$396$	−3727.09	−0.00119435
$397$	407622.	0.129802	0.0649011	−	0.997892i	$-0.479327\pi$
$397$	407622.	0.129802	0.0649011	+	0.997892i	$0.479327\pi$
$398$	−362987.	−0.114864
$399$	−5.15904e6	−1.62232
$400$	702524.	0.219539
$401$	3.00347e6	0.932743	0.466372	−	0.884589i	$-0.345561\pi$
$401$	3.00347e6	0.932743	0.466372	+	0.884589i	$0.345561\pi$
$402$	74182.4	0.0228947
$403$	1.48114e6	0.454290
$404$	806237.	0.245759
$405$	406370.	0.123107
$406$	−65648.5	−0.0197656
$407$	5853.91	0.00175170
$408$	−242878.	−0.0722333
$409$	−4.77645e6	−1.41188	−0.705938	−	0.708274i	$-0.749474\pi$
$409$	−4.77645e6	−1.41188	−0.705938	+	0.708274i	$0.749474\pi$
$410$	279607.	0.0821464
$411$	−2.13662e6	−0.623912
$412$	−1.97124e6	−0.572131
$413$	729387.	0.210418
$414$	−65363.0	−0.0187427
$415$	5.82799e6	1.66111
$416$	653497.	0.185144
$417$	−541722.	−0.152559
$418$	2450.41	0.000685958 0
$419$	−2.95949e6	−0.823535	−0.411768	−	0.911289i	$-0.635088\pi$
$419$	−2.95949e6	−0.823535	−0.411768	+	0.911289i	$0.635088\pi$
$420$	3.69339e6	1.02165
$421$	1.17118e6	0.322047	0.161024	−	0.986951i	$-0.448520\pi$
$421$	1.17118e6	0.322047	0.161024	+	0.986951i	$0.448520\pi$
$422$	479981.	0.131203
$423$	2.05694e6	0.558947
$424$	648614.	0.175215
$425$	490108.	0.131619
$426$	299777.	0.0800341
$427$	894218.	0.237342
$428$	514117.	0.135660
$429$	4598.39	0.00120632
$430$	200187.	0.0522112
$431$	−2.43477e6	−0.631341	−0.315671	−	0.948869i	$-0.602229\pi$
$431$	−2.43477e6	−0.631341	−0.315671	+	0.948869i	$0.602229\pi$
$432$	720084.	0.185641
$433$	−229760.	−0.0588917	−0.0294459	−	0.999566i	$-0.509374\pi$
$433$	−229760.	−0.0588917	−0.0294459	+	0.999566i	$0.509374\pi$
$434$	−544066.	−0.138652
$435$	283732.	0.0718927
$436$	6.62134e6	1.66813
$437$	−3.58643e6	−0.898377
$438$	−180463.	−0.0449472
$439$	−2.63343e6	−0.652168	−0.326084	−	0.945341i	$-0.605729\pi$
$439$	−2.63343e6	−0.652168	−0.326084	+	0.945341i	$0.605729\pi$
$440$	−3529.54	−0.000869134 0
$441$	2.19489e6	0.537422
$442$	148936.	0.0362613
$443$	−5.30123e6	−1.28342	−0.641708	−	0.766949i	$-0.721774\pi$
$443$	−5.30123e6	−1.28342	−0.641708	+	0.766949i	$0.721774\pi$
$444$	−1.14487e6	−0.275613
$445$	−8.44275e6	−2.02108
$446$	91502.4	0.0217819
$447$	−2.03982e6	−0.482863
$448$	6.38302e6	1.50256
$449$	2.32172e6	0.543494	0.271747	−	0.962369i	$-0.412399\pi$
$449$	2.32172e6	0.543494	0.271747	+	0.962369i	$0.412399\pi$
$450$	35460.8	0.00825500
$451$	10672.0	0.00247062
$452$	4.53264e6	1.04353
$453$	−2.65043e6	−0.606834
$454$	−434269.	−0.0988824
$455$	−4.55681e6	−1.03189
$456$	−964216.	−0.217151
$457$	−3.05394e6	−0.684022	−0.342011	−	0.939696i	$-0.611108\pi$
$457$	−3.05394e6	−0.684022	−0.342011	+	0.939696i	$0.611108\pi$
$458$	136311.	0.0303647
$459$	502359.	0.111297
$460$	2.56755e6	0.565749
$461$	4.33222e6	0.949419	0.474710	−	0.880143i	$-0.342553\pi$
$461$	4.33222e6	0.949419	0.474710	+	0.880143i	$0.342553\pi$
$462$	−1689.13	−0.000368177 0
$463$	−6.38768e6	−1.38481	−0.692406	−	0.721508i	$-0.743449\pi$
$463$	−6.38768e6	−1.38481	−0.692406	+	0.721508i	$0.743449\pi$
$464$	502770.	0.108411
$465$	2.35144e6	0.504316
$466$	−187006.	−0.0398924
$467$	595087.	0.126266	0.0631332	−	0.998005i	$-0.479891\pi$
$467$	595087.	0.126266	0.0631332	+	0.998005i	$0.479891\pi$
$468$	−899326.	−0.189803
$469$	−2.80578e6	−0.589009
$470$	968158.	0.202163
$471$	4.74822e6	0.986230
$472$	136321.	0.0281649
$473$	7640.71	0.00157029
$474$	330135.	0.0674909
$475$	1.94571e6	0.395680
$476$	4.56581e6	0.923635
$477$	−1.34157e6	−0.269970
$478$	695494.	0.139227
$479$	854216.	0.170110	0.0850548	−	0.996376i	$-0.472893\pi$
$479$	854216.	0.170110	0.0850548	+	0.996376i	$0.472893\pi$
$480$	1.03749e6	0.205532
$481$	1.41251e6	0.278375
$482$	−805928.	−0.158008
$483$	2.47221e6	0.482190
$484$	5.09254e6	0.988147
$485$	8.37235e6	1.61619
$486$	36347.1	0.00698039
$487$	−6.99300e6	−1.33611	−0.668054	−	0.744113i	$-0.732872\pi$
$487$	−6.99300e6	−1.33611	−0.668054	+	0.744113i	$0.732872\pi$
$488$	167128.	0.0317687
$489$	1.24723e6	0.235871
$490$	1.03309e6	0.194378
$491$	6.08880e6	1.13980	0.569899	−	0.821715i	$-0.306982\pi$
$491$	6.08880e6	1.13980	0.569899	+	0.821715i	$0.306982\pi$
$492$	−2.08717e6	−0.388728
$493$	350752.	0.0649954
$494$	591270.	0.109010
$495$	7300.37	0.00133916
$496$	4.16674e6	0.760487
$497$	−1.13384e7	−2.05902
$498$	521276.	0.0941877
$499$	1.04489e7	1.87853	0.939264	−	0.343196i	$-0.111510\pi$
$499$	1.04489e7	1.87853	0.939264	+	0.343196i	$0.111510\pi$
$500$	4.72744e6	0.845671
$501$	1.81361e6	0.322812
$502$	−583835.	−0.103403
$503$	3.92622e6	0.691918	0.345959	−	0.938250i	$-0.387554\pi$
$503$	3.92622e6	0.691918	0.345959	+	0.938250i	$0.387554\pi$
$504$	664657.	0.116552
$505$	−1.57920e6	−0.275556
$506$	−1174.23	−0.000203882 0
$507$	−2.23207e6	−0.385646
$508$	−2.52164e6	−0.433534
$509$	−5.65513e6	−0.967493	−0.483746	−	0.875208i	$-0.660724\pi$
$509$	−5.65513e6	−0.967493	−0.483746	+	0.875208i	$0.660724\pi$
$510$	236450.	0.0402544
$511$	6.82561e6	1.15635
$512$	3.07626e6	0.518618
$513$	1.99435e6	0.334585
$514$	1.12629e6	0.188037
$515$	3.86112e6	0.641498
$516$	−1.49433e6	−0.247071
$517$	36952.5	0.00608020
$518$	−518859.	−0.0849620
$519$	4.16962e6	0.679482
$520$	−851659.	−0.138120
$521$	−1.00145e7	−1.61634	−0.808172	−	0.588947i	$-0.799543\pi$
$521$	−1.00145e7	−1.61634	−0.808172	+	0.588947i	$0.799543\pi$
$522$	25377.9	0.00407643
$523$	−9.06776e6	−1.44959	−0.724796	−	0.688964i	$-0.758066\pi$
$523$	−9.06776e6	−1.44959	−0.724796	+	0.688964i	$0.758066\pi$
$524$	161850.	0.0257504
$525$	−1.34123e6	−0.212375
$526$	762328.	0.120137
$527$	2.90688e6	0.455933
$528$	12936.2	0.00201940
$529$	−4.71773e6	−0.732983
$530$	−631447.	−0.0976443
$531$	−281961.	−0.0433963
$532$	1.81261e7	2.77667
$533$	2.57510e6	0.392623
$534$	−755148.	−0.114599
$535$	−1.00702e6	−0.152108
$536$	−524396.	−0.0788402
$537$	−2.11504e6	−0.316506
$538$	737555.	0.109860
$539$	39430.7	0.00584605
$540$	−1.42776e6	−0.210704
$541$	1.13999e7	1.67459	0.837296	−	0.546750i	$-0.184135\pi$
$541$	1.13999e7	1.67459	0.837296	+	0.546750i	$0.184135\pi$
$542$	−558536.	−0.0816681
$543$	3.10735e6	0.452262
$544$	1.28255e6	0.185814
$545$	−1.29694e7	−1.87038
$546$	−407576.	−0.0585096
$547$	9.29969e6	1.32892	0.664462	−	0.747322i	$-0.268661\pi$
$547$	9.29969e6	1.32892	0.664462	+	0.747322i	$0.268661\pi$
$548$	7.50694e6	1.06785
$549$	−345680.	−0.0489490
$550$	637.046	8.97975e−5 0
$551$	1.39247e6	0.195392
$552$	462052.	0.0645421
$553$	−1.24866e7	−1.73633
$554$	121177.	0.0167743
$555$	2.24250e6	0.309029
$556$	1.90332e6	0.261110
$557$	−5.55080e6	−0.758084	−0.379042	−	0.925379i	$-0.623746\pi$
$557$	−5.55080e6	−0.758084	−0.379042	+	0.925379i	$0.623746\pi$
$558$	210321.	0.0285955
$559$	1.84366e6	0.249546
$560$	−1.28192e7	−1.72739
$561$	9024.79	0.00121068
$562$	1.42441e6	0.190236
$563$	361373.	0.0480490	0.0240245	−	0.999711i	$-0.492352\pi$
$563$	361373.	0.0480490	0.0240245	+	0.999711i	$0.492352\pi$
$564$	−7.22697e6	−0.956662
$565$	−8.87823e6	−1.17005
$566$	26348.0	0.00345706
$567$	−1.37475e6	−0.179583
$568$	−2.11913e6	−0.275605
$569$	6.95770e6	0.900917	0.450459	−	0.892797i	$-0.351261\pi$
$569$	6.95770e6	0.900917	0.450459	+	0.892797i	$0.351261\pi$
$570$	938696.	0.121015
$571$	−1.46705e7	−1.88302	−0.941511	−	0.336982i	$-0.890594\pi$
$571$	−1.46705e7	−1.88302	−0.941511	+	0.336982i	$0.890594\pi$
$572$	−16156.2	−0.00206467
$573$	8.75905e6	1.11448
$574$	−945911.	−0.119831
$575$	−932384.	−0.117605
$576$	−2.46750e6	−0.309886
$577$	−1.16193e7	−1.45291	−0.726457	−	0.687212i	$-0.758834\pi$
$577$	−1.16193e7	−1.45291	−0.726457	+	0.687212i	$0.758834\pi$
$578$	−581680.	−0.0724210
$579$	−4.44106e6	−0.550542
$580$	−996879.	−0.123047
$581$	−1.97161e7	−2.42315
$582$	748851.	0.0916406
$583$	−24101.0	−0.00293673
$584$	1.27570e6	0.154780
$585$	1.76154e6	0.212815
$586$	−580574.	−0.0698415
$587$	1.26219e7	1.51192	0.755959	−	0.654619i	$-0.227171\pi$
$587$	1.26219e7	1.51192	0.755959	+	0.654619i	$0.227171\pi$
$588$	−7.71163e6	−0.919820
$589$	1.15402e7	1.37064
$590$	−132713.	−0.0156958
$591$	3.05231e6	0.359468
$592$	3.97369e6	0.466004
$593$	8.70200e6	1.01621	0.508103	−	0.861296i	$-0.330347\pi$
$593$	8.70200e6	1.01621	0.508103	+	0.861296i	$0.330347\pi$
$594$	652.970	7.59324e−5 0
$595$	−8.94319e6	−1.03562
$596$	7.16683e6	0.826440
$597$	−5.30732e6	−0.609452
$598$	−283336.	−0.0324003
$599$	314477.	0.0358115	0.0179057	−	0.999840i	$-0.494300\pi$
$599$	314477.	0.0358115	0.0179057	+	0.999840i	$0.494300\pi$
$600$	−250673.	−0.0284269
$601$	−1.33321e7	−1.50561	−0.752803	−	0.658246i	$-0.771299\pi$
$601$	−1.33321e7	−1.50561	−0.752803	+	0.658246i	$0.771299\pi$
$602$	−677231.	−0.0761633
$603$	1.08464e6	0.121476
$604$	9.31216e6	1.03862
$605$	−9.97492e6	−1.10795
$606$	−141249.	−0.0156244
$607$	4.65927e6	0.513270	0.256635	−	0.966508i	$-0.417386\pi$
$607$	4.65927e6	0.513270	0.256635	+	0.966508i	$0.417386\pi$
$608$	5.09168e6	0.558602
$609$	−959864.	−0.104874
$610$	−162704.	−0.0177041
$611$	8.91644e6	0.966248
$612$	−1.76502e6	−0.190489
$613$	3.95032e6	0.424601	0.212301	−	0.977204i	$-0.431904\pi$
$613$	3.95032e6	0.424601	0.212301	+	0.977204i	$0.431904\pi$
$614$	−647286.	−0.0692907
$615$	4.08821e6	0.435858
$616$	11940.4	0.00126785
$617$	9.77175e6	1.03338	0.516689	−	0.856173i	$-0.327164\pi$
$617$	9.77175e6	1.03338	0.516689	+	0.856173i	$0.327164\pi$
$618$	345352.	0.0363740
$619$	1.29372e7	1.35710	0.678552	−	0.734553i	$-0.262608\pi$
$619$	1.29372e7	1.35710	0.678552	+	0.734553i	$0.262608\pi$
$620$	−8.26170e6	−0.863158
$621$	−955690.	−0.0994461
$622$	−379655.	−0.0393471
$623$	2.85618e7	2.94826
$624$	3.12143e6	0.320916
$625$	−1.14824e7	−1.17579
$626$	755907.	0.0770961
$627$	35828.1	0.00363961
$628$	−1.66827e7	−1.68798
$629$	2.77220e6	0.279382
$630$	−647066.	−0.0649527
$631$	−1.78566e7	−1.78536	−0.892680	−	0.450690i	$-0.851178\pi$
$631$	−1.78566e7	−1.78536	−0.892680	+	0.450690i	$0.851178\pi$
$632$	−2.33373e6	−0.232411
$633$	7.01792e6	0.696144
$634$	−1.51446e6	−0.149635
$635$	4.93921e6	0.486097
$636$	4.71353e6	0.462066
$637$	9.51441e6	0.929038
$638$	455.910	4.43432e−5 0
$639$	4.38312e6	0.424650
$640$	−4.85025e6	−0.468073
$641$	−1.43521e7	−1.37966	−0.689828	−	0.723973i	$-0.742314\pi$
$641$	−1.43521e7	−1.37966	−0.689828	+	0.723973i	$0.742314\pi$
$642$	−90071.0	−0.00862477
$643$	−1.09103e6	−0.104066	−0.0520329	−	0.998645i	$-0.516570\pi$
$643$	−1.09103e6	−0.104066	−0.0520329	+	0.998645i	$0.516570\pi$
$644$	−8.68601e6	−0.825288
$645$	2.92698e6	0.277026
$646$	1.16043e6	0.109405
$647$	−6.11094e6	−0.573914	−0.286957	−	0.957943i	$-0.592644\pi$
$647$	−6.11094e6	−0.573914	−0.286957	+	0.957943i	$0.592644\pi$
$648$	−256938.	−0.0240376
$649$	−5065.38	−0.000472063 0
$650$	153716.	0.0142704
$651$	−7.95494e6	−0.735672
$652$	−4.38208e6	−0.403702
$653$	9.26459e6	0.850243	0.425122	−	0.905136i	$-0.360231\pi$
$653$	9.26459e6	0.850243	0.425122	+	0.905136i	$0.360231\pi$
$654$	−1.16003e6	−0.106053
$655$	−317020.	−0.0288724
$656$	7.24427e6	0.657256
$657$	−2.63860e6	−0.238484
$658$	−3.27528e6	−0.294906
$659$	1.26244e7	1.13239	0.566196	−	0.824271i	$-0.308415\pi$
$659$	1.26244e7	1.13239	0.566196	+	0.824271i	$0.308415\pi$
$660$	−25649.5	−0.00229203
$661$	6.62521e6	0.589788	0.294894	−	0.955530i	$-0.404716\pi$
$661$	6.62521e6	0.589788	0.294894	+	0.955530i	$0.404716\pi$
$662$	35896.5	0.00318352
$663$	2.17763e6	0.192398
$664$	−3.68490e6	−0.324344
$665$	−3.55041e7	−3.11332
$666$	200577.	0.0175225
$667$	−667272.	−0.0580748
$668$	−6.37203e6	−0.552506
$669$	1.33788e6	0.115572
$670$	510517.	0.0439363
$671$	−6210.08	−0.000532465 0
$672$	−3.50982e6	−0.299821
$673$	−4.38372e6	−0.373083	−0.186541	−	0.982447i	$-0.559728\pi$
$673$	−4.38372e6	−0.373083	−0.186541	+	0.982447i	$0.559728\pi$
$674$	1.26747e6	0.107470
$675$	518481.	0.0437999
$676$	7.84229e6	0.660049
$677$	1.24543e7	1.04435	0.522177	−	0.852837i	$-0.325120\pi$
$677$	1.24543e7	1.04435	0.522177	+	0.852837i	$0.325120\pi$
$678$	−794099.	−0.0663438
$679$	−2.83236e7	−2.35762
$680$	−1.67147e6	−0.138620
$681$	−6.34956e6	−0.524657
$682$	3778.38	0.000311061 0
$683$	−5.99410e6	−0.491668	−0.245834	−	0.969312i	$-0.579062\pi$
$683$	−5.99410e6	−0.491668	−0.245834	+	0.969312i	$0.579062\pi$
$684$	−7.00704e6	−0.572657
$685$	−1.47041e7	−1.19732
$686$	−1.32722e6	−0.107679
$687$	1.99304e6	0.161111
$688$	5.18658e6	0.417744
$689$	−5.81544e6	−0.466696
$690$	−449823.	−0.0359682
$691$	−1.41412e7	−1.12666	−0.563329	−	0.826232i	$-0.690480\pi$
$691$	−1.41412e7	−1.12666	−0.563329	+	0.826232i	$0.690480\pi$
$692$	−1.46498e7	−1.16296
$693$	−24697.1	−0.00195350
$694$	−1.87776e6	−0.147993
$695$	−3.72809e6	−0.292768
$696$	−179397.	−0.0140376
$697$	5.05388e6	0.394043
$698$	−1.56888e6	−0.121885
$699$	−2.73426e6	−0.211664
$700$	4.71234e6	0.363489
$701$	1.48140e7	1.13861	0.569307	−	0.822125i	$-0.307212\pi$
$701$	1.48140e7	1.13861	0.569307	+	0.822125i	$0.307212\pi$
$702$	157558.	0.0120670
$703$	1.10055e7	0.839890
$704$	−44328.3	−0.00337092
$705$	1.41557e7	1.07265
$706$	−86162.1	−0.00650586
$707$	5.34244e6	0.401968
$708$	990658.	0.0742746
$709$	−7.25689e6	−0.542170	−0.271085	−	0.962555i	$-0.587382\pi$
$709$	−7.25689e6	−0.542170	−0.271085	+	0.962555i	$0.587382\pi$
$710$	2.06304e6	0.153590
$711$	4.82699e6	0.358098
$712$	5.33815e6	0.394631
$713$	−5.53006e6	−0.407386
$714$	−799909.	−0.0587212
$715$	31645.7	0.00231499
$716$	7.43109e6	0.541714
$717$	1.01690e7	0.738720
$718$	−361769.	−0.0261891
$719$	−4.63110e6	−0.334089	−0.167044	−	0.985949i	$-0.553422\pi$
$719$	−4.63110e6	−0.334089	−0.167044	+	0.985949i	$0.553422\pi$
$720$	4.95556e6	0.356255
$721$	−1.30622e7	−0.935787
$722$	3.08270e6	0.220084
$723$	−1.17837e7	−0.838369
$724$	−1.09175e7	−0.774066
$725$	362009.	0.0255784
$726$	−892191.	−0.0628227
$727$	−1.27291e7	−0.893224	−0.446612	−	0.894728i	$-0.647369\pi$
$727$	−1.27291e7	−0.893224	−0.446612	+	0.894728i	$0.647369\pi$
$728$	2.88116e6	0.201483
$729$	531441.	0.0370370
$730$	−1.24193e6	−0.0862562
$731$	3.61836e6	0.250449
$732$	1.21453e6	0.0837783
$733$	−7.43767e6	−0.511302	−0.255651	−	0.966769i	$-0.582290\pi$
$733$	−7.43767e6	−0.511302	−0.255651	+	0.966769i	$0.582290\pi$
$734$	221790.	0.0151950
$735$	1.51050e7	1.03134
$736$	−2.43993e6	−0.166029
$737$	19485.4	0.00132142
$738$	365663.	0.0247138
$739$	1.96771e6	0.132541	0.0662705	−	0.997802i	$-0.478890\pi$
$739$	1.96771e6	0.132541	0.0662705	+	0.997802i	$0.478890\pi$
$740$	−7.87892e6	−0.528917
$741$	8.64511e6	0.578396
$742$	2.13618e6	0.142439
$743$	1.30961e7	0.870300	0.435150	−	0.900358i	$-0.356695\pi$
$743$	1.30961e7	0.870300	0.435150	+	0.900358i	$0.356695\pi$
$744$	−1.48676e6	−0.0984712
$745$	−1.40379e7	−0.926640
$746$	3.24344e6	0.213383
$747$	7.62171e6	0.499748
$748$	−31708.2	−0.00207213
$749$	3.40674e6	0.221888
$750$	−828227.	−0.0537646
$751$	−2.49792e7	−1.61614	−0.808068	−	0.589089i	$-0.799487\pi$
$751$	−2.49792e7	−1.61614	−0.808068	+	0.589089i	$0.799487\pi$
$752$	2.50837e7	1.61751
$753$	−8.53641e6	−0.548640
$754$	110008.	0.00704689
$755$	−1.82400e7	−1.16455
$756$	4.83013e6	0.307365
$757$	−553214.	−0.0350876	−0.0175438	−	0.999846i	$-0.505585\pi$
$757$	−553214.	−0.0350876	−0.0175438	+	0.999846i	$0.505585\pi$
$758$	2.11405e6	0.133642
$759$	−17168.8	−0.00108177
$760$	−6.63565e6	−0.416725
$761$	−6.91848e6	−0.433061	−0.216530	−	0.976276i	$-0.569474\pi$
$761$	−6.91848e6	−0.433061	−0.216530	+	0.976276i	$0.569474\pi$
$762$	441780.	0.0275625
$763$	4.38756e7	2.72842
$764$	−3.07745e7	−1.90747
$765$	3.45719e6	0.213585
$766$	−2.18776e6	−0.134719
$767$	−1.22225e6	−0.0750189
$768$	8.33952e6	0.510197
$769$	−1.29851e7	−0.791825	−0.395912	−	0.918288i	$-0.629572\pi$
$769$	−1.29851e7	−0.791825	−0.395912	+	0.918288i	$0.629572\pi$
$770$	−11624.4	−0.000706552 0
$771$	1.64679e7	0.997702
$772$	1.56035e7	0.942276
$773$	−5.40829e6	−0.325545	−0.162773	−	0.986664i	$-0.552044\pi$
$773$	−5.40829e6	−0.325545	−0.162773	+	0.986664i	$0.552044\pi$
$774$	261799.	0.0157078
$775$	3.00017e6	0.179429
$776$	−5.29364e6	−0.315573
$777$	−7.58637e6	−0.450798
$778$	2.78392e6	0.164895
$779$	2.00637e7	1.18459
$780$	−6.18909e6	−0.364242
$781$	78742.0	0.00461933
$782$	−556075.	−0.0325175
$783$	371057.	0.0216290
$784$	2.67659e7	1.55522
$785$	3.26768e7	1.89263
$786$	−28355.4	−0.00163711
$787$	4.47738e6	0.257684	0.128842	−	0.991665i	$-0.458874\pi$
$787$	4.47738e6	0.257684	0.128842	+	0.991665i	$0.458874\pi$
$788$	−1.07242e7	−0.615244
$789$	1.11462e7	0.637433
$790$	2.27196e6	0.129519
$791$	3.00350e7	1.70682
$792$	−4615.85	−0.000261480 0
$793$	−1.49846e6	−0.0846178
$794$	250909.	0.0141242
$795$	−9.23255e6	−0.518088
$796$	1.86470e7	1.04310
$797$	−2.50186e7	−1.39514	−0.697570	−	0.716516i	$-0.745736\pi$
$797$	−2.50186e7	−1.39514	−0.697570	+	0.716516i	$0.745736\pi$
$798$	−3.17561e6	−0.176530
$799$	1.74994e7	0.969742
$800$	1.32371e6	0.0731255
$801$	−1.10412e7	−0.608045
$802$	1.84876e6	0.101495
$803$	−47401.9	−0.00259422
$804$	−3.81083e6	−0.207912
$805$	1.70136e7	0.925348
$806$	911703.	0.0494328
$807$	1.07840e7	0.582902
$808$	998492.	0.0538042
$809$	−3.51699e7	−1.88929	−0.944646	−	0.328090i	$-0.893595\pi$
$809$	−3.51699e7	−1.88929	−0.944646	+	0.328090i	$0.893595\pi$
$810$	250138.	0.0133958
$811$	−2.65046e6	−0.141504	−0.0707521	−	0.997494i	$-0.522540\pi$
$811$	−2.65046e6	−0.141504	−0.0707521	+	0.997494i	$0.522540\pi$
$812$	3.37244e6	0.179496
$813$	−8.16649e6	−0.433321
$814$	3603.32	0.000190609 0
$815$	8.58332e6	0.452649
$816$	6.12611e6	0.322077
$817$	1.43648e7	0.752910
$818$	−2.94010e6	−0.153631
$819$	−5.95928e6	−0.310445
$820$	−1.43637e7	−0.745990
$821$	9.39154e6	0.486272	0.243136	−	0.969992i	$-0.421824\pi$
$821$	9.39154e6	0.486272	0.243136	+	0.969992i	$0.421824\pi$
$822$	−1.31518e6	−0.0678901
$823$	−1.99606e6	−0.102725	−0.0513623	−	0.998680i	$-0.516356\pi$
$823$	−1.99606e6	−0.102725	−0.0513623	+	0.998680i	$0.516356\pi$
$824$	−2.44130e6	−0.125257
$825$	9314.42	0.000476454 0
$826$	448968.	0.0228963
$827$	6.93283e6	0.352490	0.176245	−	0.984346i	$-0.443605\pi$
$827$	6.93283e6	0.352490	0.176245	+	0.984346i	$0.443605\pi$
$828$	3.35777e6	0.170206
$829$	−3.01802e7	−1.52523	−0.762616	−	0.646851i	$-0.776085\pi$
$829$	−3.01802e7	−1.52523	−0.762616	+	0.646851i	$0.776085\pi$
$830$	3.58738e6	0.180751
$831$	1.77176e6	0.0890024
$832$	−1.06962e7	−0.535697
$833$	1.86730e7	0.932397
$834$	−333453.	−0.0166004
$835$	1.24811e7	0.619493
$836$	−125880.	−0.00622934
$837$	3.07516e6	0.151724
$838$	−1.82169e6	−0.0896117
$839$	−1.09044e7	−0.534809	−0.267404	−	0.963584i	$-0.586166\pi$
$839$	−1.09044e7	−0.534809	−0.267404	+	0.963584i	$0.586166\pi$
$840$	4.57411e6	0.223671
$841$	−2.02521e7	−0.987369
$842$	720913.	0.0350431
$843$	2.08266e7	1.00937
$844$	−2.46572e7	−1.19148
$845$	−1.53609e7	−0.740075
$846$	1.26613e6	0.0608210
$847$	3.37452e7	1.61623
$848$	−1.63600e7	−0.781256
$849$	385241.	0.0183427
$850$	301682.	0.0143220
$851$	−5.27384e6	−0.249634
$852$	−1.53999e7	−0.726807
$853$	8.47613e6	0.398864	0.199432	−	0.979912i	$-0.436090\pi$
$853$	8.47613e6	0.398864	0.199432	+	0.979912i	$0.436090\pi$
$854$	550429.	0.0258260
$855$	1.37249e7	0.642088
$856$	636713.	0.0297002
$857$	2.96420e7	1.37865	0.689327	−	0.724450i	$-0.257906\pi$
$857$	2.96420e7	1.37865	0.689327	+	0.724450i	$0.257906\pi$
$858$	2830.50	0.000131264 0
$859$	−58116.2	−0.00268729	−0.00134364	−	0.999999i	$-0.500428\pi$
$859$	−58116.2	−0.00268729	−0.00134364	+	0.999999i	$0.500428\pi$
$860$	−1.02838e7	−0.474142
$861$	−1.38304e7	−0.635810
$862$	−1.49870e6	−0.0686984
$863$	6.44367e6	0.294514	0.147257	−	0.989098i	$-0.452956\pi$
$863$	6.44367e6	0.294514	0.147257	+	0.989098i	$0.452956\pi$
$864$	1.35680e6	0.0618346
$865$	2.86950e7	1.30396
$866$	−141427.	−0.00640821
$867$	−8.50490e6	−0.384257
$868$	2.79493e7	1.25913
$869$	86715.9	0.00389538
$870$	174649.	0.00782289
$871$	4.70171e6	0.209996
$872$	8.20027e6	0.365205
$873$	1.09491e7	0.486233
$874$	−2.20760e6	−0.0977555
$875$	3.13259e7	1.38319
$876$	9.27059e6	0.408176
$877$	−1.86307e7	−0.817957	−0.408979	−	0.912544i	$-0.634115\pi$
$877$	−1.86307e7	−0.817957	−0.408979	+	0.912544i	$0.634115\pi$
$878$	−1.62098e6	−0.0709647
$879$	−8.48873e6	−0.370570
$880$	89025.7	0.00387533
$881$	6.95060e6	0.301705	0.150853	−	0.988556i	$-0.451798\pi$
$881$	6.95060e6	0.301705	0.150853	+	0.988556i	$0.451798\pi$
$882$	1.35104e6	0.0584787
$883$	−1.75323e7	−0.756722	−0.378361	−	0.925658i	$-0.623512\pi$
$883$	−1.75323e7	−0.756722	−0.378361	+	0.925658i	$0.623512\pi$
$884$	−7.65101e6	−0.329297
$885$	−1.94043e6	−0.0832799
$886$	−3.26313e6	−0.139653
$887$	4.14544e6	0.176914	0.0884568	−	0.996080i	$-0.471806\pi$
$887$	4.14544e6	0.176914	0.0884568	+	0.996080i	$0.471806\pi$
$888$	−1.41788e6	−0.0603402
$889$	−1.67093e7	−0.709096
$890$	−5.19687e6	−0.219921
$891$	9547.24	0.000402887 0
$892$	−4.70058e6	−0.197806
$893$	6.94719e7	2.91528
$894$	−1.25560e6	−0.0525420
$895$	−1.45555e7	−0.607393
$896$	1.64084e7	0.682803
$897$	−4.14273e6	−0.171912
$898$	1.42912e6	0.0591395
$899$	2.14711e6	0.0886042
$900$	−1.82166e6	−0.0749655
$901$	−1.14134e7	−0.468384
$902$	6569.07	0.000268836 0
$903$	−9.90198e6	−0.404113
$904$	5.61349e6	0.228461
$905$	2.13845e7	0.867916
$906$	−1.63145e6	−0.0660318
$907$	6.52626e6	0.263418	0.131709	−	0.991288i	$-0.457953\pi$
$907$	6.52626e6	0.263418	0.131709	+	0.991288i	$0.457953\pi$
$908$	2.23089e7	0.897974
$909$	−2.06524e6	−0.0829013
$910$	−2.80491e6	−0.112283
$911$	4.12964e6	0.164860	0.0824302	−	0.996597i	$-0.473732\pi$
$911$	4.12964e6	0.164860	0.0824302	+	0.996597i	$0.473732\pi$
$912$	2.43204e7	0.968242
$913$	136923.	0.00543623
$914$	−1.87983e6	−0.0744308
$915$	−2.37894e6	−0.0939358
$916$	−7.00248e6	−0.275748
$917$	1.07248e6	0.0421178
$918$	309223.	0.0121106
$919$	−3.37200e7	−1.31704	−0.658520	−	0.752563i	$-0.728817\pi$
$919$	−3.37200e7	−1.31704	−0.658520	+	0.752563i	$0.728817\pi$
$920$	3.17980e6	0.123860
$921$	−9.46413e6	−0.367648
$922$	2.66666e6	0.103310
$923$	1.90000e7	0.734090
$924$	86772.3	0.00334350
$925$	2.86117e6	0.109948
$926$	−3.93188e6	−0.150686
$927$	5.04948e6	0.192996
$928$	947331.	0.0361104
$929$	−2.85561e7	−1.08557	−0.542787	−	0.839870i	$-0.682631\pi$
$929$	−2.85561e7	−1.08557	−0.542787	+	0.839870i	$0.682631\pi$
$930$	1.44741e6	0.0548763
$931$	7.41309e7	2.80301
$932$	9.60669e6	0.362272
$933$	−5.55103e6	−0.208771
$934$	366301.	0.0137395
$935$	62107.9	0.00232337
$936$	−1.11378e6	−0.0415537
$937$	1.16758e7	0.434446	0.217223	−	0.976122i	$-0.430300\pi$
$937$	1.16758e7	0.434446	0.217223	+	0.976122i	$0.430300\pi$
$938$	−1.72708e6	−0.0640922
$939$	1.10523e7	0.409062
$940$	−4.97354e7	−1.83589
$941$	−1.56740e7	−0.577040	−0.288520	−	0.957474i	$-0.593163\pi$
$941$	−1.56740e7	−0.577040	−0.288520	+	0.957474i	$0.593163\pi$
$942$	2.92273e6	0.107315
$943$	−9.61453e6	−0.352086
$944$	−3.43843e6	−0.125583
$945$	−9.46092e6	−0.344630
$946$	4703.18	0.000170869 0
$947$	−2.91932e7	−1.05781	−0.528904	−	0.848681i	$-0.677397\pi$
$947$	−2.91932e7	−1.05781	−0.528904	+	0.848681i	$0.677397\pi$
$948$	−1.69594e7	−0.612900
$949$	−1.14378e7	−0.412266
$950$	1.19767e6	0.0430553
$951$	−2.21433e7	−0.793945
$952$	5.65457e6	0.202212
$953$	−4.07979e7	−1.45514	−0.727571	−	0.686032i	$-0.759351\pi$
$953$	−4.07979e7	−1.45514	−0.727571	+	0.686032i	$0.759351\pi$
$954$	−825790.	−0.0293764
$955$	6.02790e7	2.13874
$956$	−3.57283e7	−1.26435
$957$	6665.98	0.000235279 0
$958$	525806.	0.0185102
$959$	4.97439e7	1.74660
$960$	−1.69812e7	−0.594688
$961$	−1.08349e7	−0.378455
$962$	869462.	0.0302910
$963$	−1.31695e6	−0.0457619
$964$	4.14015e7	1.43490
$965$	−3.05630e7	−1.05652
$966$	1.52175e6	0.0524687
$967$	−2.00499e7	−0.689519	−0.344760	−	0.938691i	$-0.612040\pi$
$967$	−2.00499e7	−0.689519	−0.344760	+	0.938691i	$0.612040\pi$
$968$	6.30691e6	0.216336
$969$	1.69669e7	0.580487
$970$	5.15353e6	0.175863
$971$	−5.07323e7	−1.72678	−0.863388	−	0.504540i	$-0.831662\pi$
$971$	−5.07323e7	−1.72678	−0.863388	+	0.504540i	$0.831662\pi$
$972$	−1.86719e6	−0.0633905
$973$	1.26121e7	0.427077
$974$	−4.30449e6	−0.145386
$975$	2.24752e6	0.0757167
$976$	−4.21546e6	−0.141651
$977$	4.01142e7	1.34450	0.672252	−	0.740322i	$-0.265327\pi$
$977$	4.01142e7	1.34450	0.672252	+	0.740322i	$0.265327\pi$
$978$	767721.	0.0256659
$979$	−198354.	−0.00661429
$980$	−5.30708e7	−1.76519
$981$	−1.69611e7	−0.562706
$982$	3.74791e6	0.124025
$983$	−5.36333e7	−1.77032	−0.885159	−	0.465289i	$-0.845950\pi$
$983$	−5.36333e7	−1.77032	−0.885159	+	0.465289i	$0.845950\pi$
$984$	−2.58488e6	−0.0851045
$985$	2.10057e7	0.689839
$986$	215903.	0.00707238
$987$	−4.78887e7	−1.56473
$988$	−3.03742e7	−0.989949
$989$	−6.88359e6	−0.223782
$990$	4493.68	0.000145718 0
$991$	4.34550e7	1.40558	0.702790	−	0.711397i	$-0.251937\pi$
$991$	4.34550e7	1.40558	0.702790	+	0.711397i	$0.251937\pi$
$992$	7.85107e6	0.253308
$993$	524853.	0.0168913
$994$	−6.97927e6	−0.224050
$995$	−3.65245e7	−1.16957
$996$	−2.67785e7	−0.855339
$997$	3.48232e7	1.10951	0.554754	−	0.832015i	$-0.312812\pi$
$997$	3.48232e7	1.10951	0.554754	+	0.832015i	$0.312812\pi$
$998$	6.43171e6	0.204409
$999$	2.93268e6	0.0929719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.c.1.6	✓	12
3.2	odd	2		531.6.a.c.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.c.1.6	✓	12	1.1	even	1	trivial
531.6.a.c.1.7		12	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+0.615542 q^{2} +9.00000 q^{3} -31.6211 q^{4} +61.9372 q^{5} +5.53988 q^{6} -209.534 q^{7} -39.1615 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+0.615542 q^{2} +9.00000 q^{3} -31.6211 q^{4} +61.9372 q^{5} +5.53988 q^{6} -209.534 q^{7} -39.1615 q^{8} +81.0000 q^{9} +38.1250 q^{10} +1.45515 q^{11} -284.590 q^{12} +351.120 q^{13} -128.977 q^{14} +557.435 q^{15} +987.770 q^{16} +689.107 q^{17} +49.8589 q^{18} +2735.73 q^{19} -1958.52 q^{20} -1885.80 q^{21} +0.895706 q^{22} -1310.96 q^{23} -352.453 q^{24} +711.222 q^{25} +216.129 q^{26} +729.000 q^{27} +6625.69 q^{28} +508.995 q^{29} +343.125 q^{30} +4218.33 q^{31} +1861.18 q^{32} +13.0964 q^{33} +424.174 q^{34} -12977.9 q^{35} -2561.31 q^{36} +4022.89 q^{37} +1683.95 q^{38} +3160.08 q^{39} -2425.55 q^{40} +7333.96 q^{41} -1160.79 q^{42} +5250.80 q^{43} -46.0135 q^{44} +5016.92 q^{45} -806.951 q^{46} +25394.3 q^{47} +8889.93 q^{48} +27097.3 q^{49} +437.787 q^{50} +6201.96 q^{51} -11102.8 q^{52} -16562.5 q^{53} +448.730 q^{54} +90.1280 q^{55} +8205.64 q^{56} +24621.5 q^{57} +313.308 q^{58} -3481.00 q^{59} -17626.7 q^{60} -4267.66 q^{61} +2596.56 q^{62} -16972.2 q^{63} -30463.0 q^{64} +21747.4 q^{65} +8.06136 q^{66} +13390.6 q^{67} -21790.3 q^{68} -11798.6 q^{69} -7988.46 q^{70} +54112.6 q^{71} -3172.08 q^{72} -32575.3 q^{73} +2476.26 q^{74} +6401.00 q^{75} -86506.7 q^{76} -304.903 q^{77} +1945.16 q^{78} +59592.4 q^{79} +61179.7 q^{80} +6561.00 q^{81} +4514.36 q^{82} +94095.2 q^{83} +59631.2 q^{84} +42681.4 q^{85} +3232.09 q^{86} +4580.95 q^{87} -56.9858 q^{88} -136311. q^{89} +3088.12 q^{90} -73571.4 q^{91} +41454.0 q^{92} +37965.0 q^{93} +15631.3 q^{94} +169443. q^{95} +16750.6 q^{96} +135175. q^{97} +16679.6 q^{98} +117.867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9}+O(q^{10}) \) 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9} + 601 q^{10} + 1480 q^{11} + 1782 q^{12} + 472 q^{13} + 1065 q^{14} + 1422 q^{15} + 6370 q^{16} + 1565 q^{17} + 1782 q^{18} + 3939 q^{19} + 8033 q^{20} + 3717 q^{21} - 1738 q^{22} + 7245 q^{23} + 6507 q^{24} + 9690 q^{25} + 3764 q^{26} + 8748 q^{27} + 12154 q^{28} + 10003 q^{29} + 5409 q^{30} + 7295 q^{31} + 11628 q^{32} + 13320 q^{33} - 16344 q^{34} + 11015 q^{35} + 16038 q^{36} + 6741 q^{37} + 3035 q^{38} + 4248 q^{39} + 5572 q^{40} + 34025 q^{41} + 9585 q^{42} - 6336 q^{43} + 41168 q^{44} + 12798 q^{45} + 2345 q^{46} + 66167 q^{47} + 57330 q^{48} + 28319 q^{49} + 31173 q^{50} + 14085 q^{51} + 16440 q^{52} + 62290 q^{53} + 16038 q^{54} + 55764 q^{55} + 107306 q^{56} + 35451 q^{57} + 37952 q^{58} - 41772 q^{59} + 72297 q^{60} + 68469 q^{61} + 99190 q^{62} + 33453 q^{63} + 68525 q^{64} + 80156 q^{65} - 15642 q^{66} + 113310 q^{67} + 33887 q^{68} + 65205 q^{69} + 32034 q^{70} + 84520 q^{71} + 58563 q^{72} + 135895 q^{73} - 31962 q^{74} + 87210 q^{75} - 61848 q^{76} - 3799 q^{77} + 33876 q^{78} + 14122 q^{79} + 77609 q^{80} + 78732 q^{81} - 1501 q^{82} + 114463 q^{83} + 109386 q^{84} - 101097 q^{85} - 203536 q^{86} + 90027 q^{87} - 244967 q^{88} + 189109 q^{89} + 48681 q^{90} - 168249 q^{91} - 71946 q^{92} + 65655 q^{93} - 472284 q^{94} + 21923 q^{95} + 104652 q^{96} - 76192 q^{97} - 17544 q^{98} + 119880 q^{99}+O(q^{100}) \) 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9 + 601 * q^10 + 1480 * q^11 + 1782 * q^12 + 472 * q^13 + 1065 * q^14 + 1422 * q^15 + 6370 * q^16 + 1565 * q^17 + 1782 * q^18 + 3939 * q^19 + 8033 * q^20 + 3717 * q^21 - 1738 * q^22 + 7245 * q^23 + 6507 * q^24 + 9690 * q^25 + 3764 * q^26 + 8748 * q^27 + 12154 * q^28 + 10003 * q^29 + 5409 * q^30 + 7295 * q^31 + 11628 * q^32 + 13320 * q^33 - 16344 * q^34 + 11015 * q^35 + 16038 * q^36 + 6741 * q^37 + 3035 * q^38 + 4248 * q^39 + 5572 * q^40 + 34025 * q^41 + 9585 * q^42 - 6336 * q^43 + 41168 * q^44 + 12798 * q^45 + 2345 * q^46 + 66167 * q^47 + 57330 * q^48 + 28319 * q^49 + 31173 * q^50 + 14085 * q^51 + 16440 * q^52 + 62290 * q^53 + 16038 * q^54 + 55764 * q^55 + 107306 * q^56 + 35451 * q^57 + 37952 * q^58 - 41772 * q^59 + 72297 * q^60 + 68469 * q^61 + 99190 * q^62 + 33453 * q^63 + 68525 * q^64 + 80156 * q^65 - 15642 * q^66 + 113310 * q^67 + 33887 * q^68 + 65205 * q^69 + 32034 * q^70 + 84520 * q^71 + 58563 * q^72 + 135895 * q^73 - 31962 * q^74 + 87210 * q^75 - 61848 * q^76 - 3799 * q^77 + 33876 * q^78 + 14122 * q^79 + 77609 * q^80 + 78732 * q^81 - 1501 * q^82 + 114463 * q^83 + 109386 * q^84 - 101097 * q^85 - 203536 * q^86 + 90027 * q^87 - 244967 * q^88 + 189109 * q^89 + 48681 * q^90 - 168249 * q^91 - 71946 * q^92 + 65655 * q^93 - 472284 * q^94 + 21923 * q^95 + 104652 * q^96 - 76192 * q^97 - 17544 * q^98 + 119880 * q^99

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