LMFDB - Embedded newform 177.6.a.c.1.3

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			1.3
Root			$7.96013$ 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)

$f(q)$	$=$	$q-5.96013 q^{2} +9.00000 q^{3} +3.52316 q^{4} +65.6425 q^{5} -53.6412 q^{6} +119.026 q^{7} +169.726 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-5.96013 q^{2} +9.00000 q^{3} +3.52316 q^{4} +65.6425 q^{5} -53.6412 q^{6} +119.026 q^{7} +169.726 q^{8} +81.0000 q^{9} -391.238 q^{10} +237.620 q^{11} +31.7085 q^{12} +999.008 q^{13} -709.408 q^{14} +590.783 q^{15} -1124.33 q^{16} -1276.40 q^{17} -482.771 q^{18} +1426.51 q^{19} +231.269 q^{20} +1071.23 q^{21} -1416.25 q^{22} +546.573 q^{23} +1527.53 q^{24} +1183.94 q^{25} -5954.22 q^{26} +729.000 q^{27} +419.346 q^{28} -1547.67 q^{29} -3521.14 q^{30} -7569.31 q^{31} +1269.92 q^{32} +2138.58 q^{33} +7607.51 q^{34} +7813.14 q^{35} +285.376 q^{36} -1012.21 q^{37} -8502.16 q^{38} +8991.07 q^{39} +11141.2 q^{40} +13264.9 q^{41} -6384.67 q^{42} -21794.0 q^{43} +837.174 q^{44} +5317.05 q^{45} -3257.65 q^{46} +23038.8 q^{47} -10119.0 q^{48} -2639.91 q^{49} -7056.46 q^{50} -11487.6 q^{51} +3519.67 q^{52} +19051.5 q^{53} -4344.94 q^{54} +15598.0 q^{55} +20201.7 q^{56} +12838.6 q^{57} +9224.33 q^{58} -3481.00 q^{59} +2081.42 q^{60} -7235.44 q^{61} +45114.1 q^{62} +9641.07 q^{63} +28409.6 q^{64} +65577.4 q^{65} -12746.2 q^{66} +69873.8 q^{67} -4496.96 q^{68} +4919.16 q^{69} -46567.3 q^{70} +17826.0 q^{71} +13747.8 q^{72} +9089.91 q^{73} +6032.93 q^{74} +10655.5 q^{75} +5025.81 q^{76} +28282.9 q^{77} -53588.0 q^{78} +31488.7 q^{79} -73803.8 q^{80} +6561.00 q^{81} -79060.3 q^{82} -102025. q^{83} +3774.12 q^{84} -83786.1 q^{85} +129895. q^{86} -13929.0 q^{87} +40330.2 q^{88} +104185. q^{89} -31690.3 q^{90} +118908. q^{91} +1925.67 q^{92} -68123.8 q^{93} -137314. q^{94} +93639.5 q^{95} +11429.3 q^{96} -117345. q^{97} +15734.2 q^{98} +19247.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.96013	−1.05361	−0.526806	−	0.849985i	$-0.676611\pi$
$2$	−5.96013	−1.05361	−0.526806	+	0.849985i	$0.676611\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	3.52316	0.110099
$5$	65.6425	1.17425	0.587125	−	0.809496i	$-0.300260\pi$
$5$	65.6425	1.17425	0.587125	+	0.809496i	$0.300260\pi$
$6$	−53.6412	−0.608303
$7$	119.026	0.918111	0.459055	−	0.888408i	$-0.348188\pi$
$7$	119.026	0.918111	0.459055	+	0.888408i	$0.348188\pi$
$8$	169.726	0.937611
$9$	81.0000	0.333333
$10$	−391.238	−1.23720
$11$	237.620	0.592109	0.296054	−	0.955171i	$-0.404329\pi$
$11$	237.620	0.592109	0.296054	+	0.955171i	$0.404329\pi$
$12$	31.7085	0.0635656
$13$	999.008	1.63950	0.819749	−	0.572723i	$-0.194113\pi$
$13$	999.008	1.63950	0.819749	+	0.572723i	$0.194113\pi$
$14$	−709.408	−0.967333
$15$	590.783	0.677953
$16$	−1124.33	−1.09798
$17$	−1276.40	−1.07118	−0.535592	−	0.844477i	$-0.679912\pi$
$17$	−1276.40	−1.07118	−0.535592	+	0.844477i	$0.679912\pi$
$18$	−482.771	−0.351204
$19$	1426.51	0.906546	0.453273	−	0.891372i	$-0.350256\pi$
$19$	1426.51	0.906546	0.453273	+	0.891372i	$0.350256\pi$
$20$	231.269	0.129283
$21$	1071.23	0.530072
$22$	−1416.25	−0.623853
$23$	546.573	0.215441	0.107721	−	0.994181i	$-0.465645\pi$
$23$	546.573	0.215441	0.107721	+	0.994181i	$0.465645\pi$
$24$	1527.53	0.541330
$25$	1183.94	0.378862
$26$	−5954.22	−1.72739
$27$	729.000	0.192450
$28$	419.346	0.101083
$29$	−1547.67	−0.341731	−0.170865	−	0.985294i	$-0.554656\pi$
$29$	−1547.67	−0.341731	−0.170865	+	0.985294i	$0.554656\pi$
$30$	−3521.14	−0.714300
$31$	−7569.31	−1.41466	−0.707330	−	0.706883i	$-0.750101\pi$
$31$	−7569.31	−1.41466	−0.707330	+	0.706883i	$0.750101\pi$
$32$	1269.92	0.219231
$33$	2138.58	0.341854
$34$	7607.51	1.12861
$35$	7813.14	1.07809
$36$	285.376	0.0366996
$37$	−1012.21	−0.121554	−0.0607769	−	0.998151i	$-0.519358\pi$
$37$	−1012.21	−0.121554	−0.0607769	+	0.998151i	$0.519358\pi$
$38$	−8502.16	−0.955148
$39$	8991.07	0.946564
$40$	11141.2	1.10099
$41$	13264.9	1.23237	0.616187	−	0.787600i	$-0.288676\pi$
$41$	13264.9	1.23237	0.616187	+	0.787600i	$0.288676\pi$
$42$	−6384.67	−0.558490
$43$	−21794.0	−1.79749	−0.898743	−	0.438476i	$-0.855518\pi$
$43$	−21794.0	−1.79749	−0.898743	+	0.438476i	$0.855518\pi$
$44$	837.174	0.0651905
$45$	5317.05	0.391417
$46$	−3257.65	−0.226992
$47$	23038.8	1.52130	0.760650	−	0.649163i	$-0.224881\pi$
$47$	23038.8	1.52130	0.760650	+	0.649163i	$0.224881\pi$
$48$	−10119.0	−0.633917
$49$	−2639.91	−0.157072
$50$	−7056.46	−0.399174
$51$	−11487.6	−0.618449
$52$	3519.67	0.180507
$53$	19051.5	0.931624	0.465812	−	0.884884i	$-0.345762\pi$
$53$	19051.5	0.931624	0.465812	+	0.884884i	$0.345762\pi$
$54$	−4344.94	−0.202768
$55$	15598.0	0.695283
$56$	20201.7	0.860831
$57$	12838.6	0.523394
$58$	9224.33	0.360052
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	2081.42	0.0746418
$61$	−7235.44	−0.248966	−0.124483	−	0.992222i	$-0.539727\pi$
$61$	−7235.44	−0.248966	−0.124483	+	0.992222i	$0.539727\pi$
$62$	45114.1	1.49050
$63$	9641.07	0.306037
$64$	28409.6	0.866992
$65$	65577.4	1.92518
$66$	−12746.2	−0.360182
$67$	69873.8	1.90164	0.950818	−	0.309752i	$-0.100246\pi$
$67$	69873.8	1.90164	0.950818	+	0.309752i	$0.100246\pi$
$68$	−4496.96	−0.117936
$69$	4919.16	0.124385
$70$	−46567.3	−1.13589
$71$	17826.0	0.419671	0.209836	−	0.977737i	$-0.432707\pi$
$71$	17826.0	0.419671	0.209836	+	0.977737i	$0.432707\pi$
$72$	13747.8	0.312537
$73$	9089.91	0.199642	0.0998212	−	0.995005i	$-0.468173\pi$
$73$	9089.91	0.199642	0.0998212	+	0.995005i	$0.468173\pi$
$74$	6032.93	0.128071
$75$	10655.5	0.218736
$76$	5025.81	0.0998096
$77$	28282.9	0.543622
$78$	−53588.0	−0.997312
$79$	31488.7	0.567658	0.283829	−	0.958875i	$-0.408395\pi$
$79$	31488.7	0.567658	0.283829	+	0.958875i	$0.408395\pi$
$80$	−73803.8	−1.28930
$81$	6561.00	0.111111
$82$	−79060.3	−1.29845
$83$	−102025.	−1.62560	−0.812798	−	0.582546i	$-0.802056\pi$
$83$	−102025.	−1.62560	−0.812798	+	0.582546i	$0.802056\pi$
$84$	3774.12	0.0583602
$85$	−83786.1	−1.25784
$86$	129895.	1.89385
$87$	−13929.0	−0.197298
$88$	40330.2	0.555168
$89$	104185.	1.39422	0.697111	−	0.716963i	$-0.254468\pi$
$89$	104185.	1.39422	0.697111	+	0.716963i	$0.254468\pi$
$90$	−31690.3	−0.412401
$91$	118908.	1.50524
$92$	1925.67	0.0237198
$93$	−68123.8	−0.816755
$94$	−137314.	−1.60286
$95$	93639.5	1.06451
$96$	11429.3	0.126573
$97$	−117345.	−1.26629	−0.633147	−	0.774032i	$-0.718237\pi$
$97$	−117345.	−1.26629	−0.633147	+	0.774032i	$0.718237\pi$
$98$	15734.2	0.165493
$99$	19247.2	0.197370
$100$	4171.22	0.0417122
$101$	109234.	1.06550	0.532751	−	0.846272i	$-0.321158\pi$
$101$	109234.	1.06550	0.532751	+	0.846272i	$0.321158\pi$
$102$	68467.6	0.651605
$103$	−162469.	−1.50896	−0.754481	−	0.656322i	$-0.772111\pi$
$103$	−162469.	−1.50896	−0.754481	+	0.656322i	$0.772111\pi$
$104$	169557.	1.53721
$105$	70318.3	0.622436
$106$	−113550.	−0.981570
$107$	−9555.85	−0.0806882	−0.0403441	−	0.999186i	$-0.512845\pi$
$107$	−9555.85	−0.0806882	−0.0403441	+	0.999186i	$0.512845\pi$
$108$	2568.38	0.0211885
$109$	−80849.6	−0.651796	−0.325898	−	0.945405i	$-0.605667\pi$
$109$	−80849.6	−0.651796	−0.325898	+	0.945405i	$0.605667\pi$
$110$	−92966.1	−0.732559
$111$	−9109.93	−0.0701791
$112$	−133824.	−1.00806
$113$	−131306.	−0.967359	−0.483679	−	0.875245i	$-0.660700\pi$
$113$	−131306.	−0.967359	−0.483679	+	0.875245i	$0.660700\pi$
$114$	−76519.5	−0.551455
$115$	35878.5	0.252982
$116$	−5452.70	−0.0376241
$117$	80919.7	0.546499
$118$	20747.2	0.137169
$119$	−151924.	−0.983466
$120$	100271.	0.635656
$121$	−104588.	−0.649407
$122$	43124.1	0.262314
$123$	119384.	0.711512
$124$	−26667.9	−0.155752
$125$	−127416.	−0.729371
$126$	−57462.0	−0.322444
$127$	−234331.	−1.28920	−0.644600	−	0.764520i	$-0.722976\pi$
$127$	−234331.	−1.28920	−0.644600	+	0.764520i	$0.722976\pi$
$128$	−209963.	−1.13270
$129$	−196146.	−1.03778
$130$	−390850.	−2.02839
$131$	135156.	0.688108	0.344054	−	0.938950i	$-0.388200\pi$
$131$	135156.	0.688108	0.344054	+	0.938950i	$0.388200\pi$
$132$	7534.57	0.0376377
$133$	169791.	0.832309
$134$	−416457.	−2.00359
$135$	47853.4	0.225984
$136$	−216638.	−1.00435
$137$	−133343.	−0.606971	−0.303486	−	0.952836i	$-0.598150\pi$
$137$	−133343.	−0.606971	−0.303486	+	0.952836i	$0.598150\pi$
$138$	−29318.8	−0.131054
$139$	197409.	0.866622	0.433311	−	0.901244i	$-0.357345\pi$
$139$	197409.	0.866622	0.433311	+	0.901244i	$0.357345\pi$
$140$	27527.0	0.118697
$141$	207349.	0.878323
$142$	−106246.	−0.442171
$143$	237384.	0.970761
$144$	−91070.6	−0.365992
$145$	−101593.	−0.401277
$146$	−54177.1	−0.210346
$147$	−23759.2	−0.0906857
$148$	−3566.20	−0.0133829
$149$	94205.2	0.347624	0.173812	−	0.984779i	$-0.444392\pi$
$149$	94205.2	0.347624	0.173812	+	0.984779i	$0.444392\pi$
$150$	−63508.1	−0.230463
$151$	−32019.8	−0.114281	−0.0571407	−	0.998366i	$-0.518198\pi$
$151$	−32019.8	−0.114281	−0.0571407	+	0.998366i	$0.518198\pi$
$152$	242115.	0.849987
$153$	−103388.	−0.357062
$154$	−168570.	−0.572766
$155$	−496869.	−1.66116
$156$	31677.0	0.104216
$157$	487099.	1.57713	0.788565	−	0.614951i	$-0.210824\pi$
$157$	487099.	1.57713	0.788565	+	0.614951i	$0.210824\pi$
$158$	−187677.	−0.598091
$159$	171464.	0.537873
$160$	83361.0	0.257432
$161$	65056.2	0.197799
$162$	−39104.4	−0.117068
$163$	349125.	1.02923	0.514615	−	0.857421i	$-0.327935\pi$
$163$	349125.	1.02923	0.514615	+	0.857421i	$0.327935\pi$
$164$	46734.2	0.135683
$165$	140382.	0.401422
$166$	608084.	1.71275
$167$	68091.2	0.188930	0.0944648	−	0.995528i	$-0.469886\pi$
$167$	68091.2	0.188930	0.0944648	+	0.995528i	$0.469886\pi$
$168$	181815.	0.497001
$169$	626725.	1.68795
$170$	499376.	1.32527
$171$	115547.	0.302182
$172$	−76783.7	−0.197901
$173$	15052.9	0.0382388	0.0191194	−	0.999817i	$-0.493914\pi$
$173$	15052.9	0.0382388	0.0191194	+	0.999817i	$0.493914\pi$
$174$	83018.9	0.207876
$175$	140920.	0.347837
$176$	−267163.	−0.650122
$177$	−31329.0	−0.0751646
$178$	−620959.	−1.46897
$179$	716413.	1.67121	0.835604	−	0.549332i	$-0.185118\pi$
$179$	716413.	1.67121	0.835604	+	0.549332i	$0.185118\pi$
$180$	18732.8	0.0430945
$181$	−702418.	−1.59367	−0.796837	−	0.604194i	$-0.793495\pi$
$181$	−702418.	−1.59367	−0.796837	+	0.604194i	$0.793495\pi$
$182$	−708704.	−1.58594
$183$	−65118.9	−0.143741
$184$	92767.5	0.202000
$185$	−66444.3	−0.142734
$186$	406027.	0.860543
$187$	−303298.	−0.634258
$188$	81169.3	0.167493
$189$	86769.6	0.176691
$190$	−558104.	−1.12158
$191$	−28509.8	−0.0565472	−0.0282736	−	0.999600i	$-0.509001\pi$
$191$	−28509.8	−0.0565472	−0.0282736	+	0.999600i	$0.509001\pi$
$192$	255686.	0.500558
$193$	−310039.	−0.599133	−0.299567	−	0.954075i	$-0.596842\pi$
$193$	−310039.	−0.599133	−0.299567	+	0.954075i	$0.596842\pi$
$194$	699390.	1.33418
$195$	590197.	1.11150
$196$	−9300.85	−0.0172935
$197$	664034.	1.21906	0.609530	−	0.792763i	$-0.291358\pi$
$197$	664034.	1.21906	0.609530	+	0.792763i	$0.291358\pi$
$198$	−114716.	−0.207951
$199$	326015.	0.583586	0.291793	−	0.956481i	$-0.405748\pi$
$199$	326015.	0.583586	0.291793	+	0.956481i	$0.405748\pi$
$200$	200946.	0.355225
$201$	628864.	1.09791
$202$	−651048.	−1.12263
$203$	−184213.	−0.313747
$204$	−40472.7	−0.0680905
$205$	870739.	1.44712
$206$	968338.	1.58986
$207$	44272.4	0.0718137
$208$	−1.12321e6	−1.80013
$209$	338967.	0.536774
$210$	−419106.	−0.655807
$211$	−775314.	−1.19887	−0.599434	−	0.800424i	$-0.704608\pi$
$211$	−775314.	−1.19887	−0.599434	+	0.800424i	$0.704608\pi$
$212$	67121.7	0.102571
$213$	160434.	0.242297
$214$	56954.1	0.0850141
$215$	−1.43061e6	−2.11070
$216$	123730.	0.180443
$217$	−900942.	−1.29882
$218$	481874.	0.686740
$219$	81809.2	0.115264
$220$	54954.2	0.0765499
$221$	−1.27513e6	−1.75620
$222$	54296.4	0.0739415
$223$	−855406.	−1.15189	−0.575944	−	0.817489i	$-0.695365\pi$
$223$	−855406.	−1.15189	−0.575944	+	0.817489i	$0.695365\pi$
$224$	151153.	0.201279
$225$	95899.4	0.126287
$226$	782599.	1.01922
$227$	255022.	0.328483	0.164241	−	0.986420i	$-0.447482\pi$
$227$	255022.	0.328483	0.164241	+	0.986420i	$0.447482\pi$
$228$	45232.3	0.0576251
$229$	504531.	0.635769	0.317884	−	0.948129i	$-0.397028\pi$
$229$	504531.	0.635769	0.317884	+	0.948129i	$0.397028\pi$
$230$	−213840.	−0.266545
$231$	254546.	0.313860
$232$	−262680.	−0.320410
$233$	315787.	0.381070	0.190535	−	0.981680i	$-0.438978\pi$
$233$	315787.	0.381070	0.190535	+	0.981680i	$0.438978\pi$
$234$	−482292.	−0.575798
$235$	1.51232e6	1.78638
$236$	−12264.1	−0.0143336
$237$	283398.	0.327738
$238$	905488.	1.03619
$239$	−1.31913e6	−1.49380	−0.746901	−	0.664935i	$-0.768459\pi$
$239$	−1.31913e6	−1.49380	−0.746901	+	0.664935i	$0.768459\pi$
$240$	−664234.	−0.744377
$241$	−101157.	−0.112190	−0.0560950	−	0.998425i	$-0.517865\pi$
$241$	−101157.	−0.112190	−0.0560950	+	0.998425i	$0.517865\pi$
$242$	623356.	0.684223
$243$	59049.0	0.0641500
$244$	−25491.6	−0.0274109
$245$	−173291.	−0.184442
$246$	−711542.	−0.749658
$247$	1.42509e6	1.48628
$248$	−1.28471e6	−1.32640
$249$	−918227.	−0.938538
$250$	759415.	0.768474
$251$	1.78020e6	1.78354	0.891771	−	0.452487i	$-0.149463\pi$
$251$	1.78020e6	1.78354	0.891771	+	0.452487i	$0.149463\pi$
$252$	33967.1	0.0336943
$253$	129877.	0.127565
$254$	1.39664e6	1.35832
$255$	−754075.	−0.726213
$256$	342297.	0.326440
$257$	−381509.	−0.360307	−0.180153	−	0.983639i	$-0.557659\pi$
$257$	−381509.	−0.360307	−0.180153	+	0.983639i	$0.557659\pi$
$258$	1.16905e6	1.09342
$259$	−120479.	−0.111600
$260$	231040.	0.211960
$261$	−125361.	−0.113910
$262$	−805547.	−0.724999
$263$	−225601.	−0.201118	−0.100559	−	0.994931i	$-0.532063\pi$
$263$	−225601.	−0.201118	−0.100559	+	0.994931i	$0.532063\pi$
$264$	362972.	0.320526
$265$	1.25059e6	1.09396
$266$	−1.01197e6	−0.876931
$267$	937669.	0.804954
$268$	246177.	0.209368
$269$	−562259.	−0.473757	−0.236879	−	0.971539i	$-0.576124\pi$
$269$	−562259.	−0.473757	−0.236879	+	0.971539i	$0.576124\pi$
$270$	−285213.	−0.238100
$271$	−1.36135e6	−1.12602	−0.563012	−	0.826449i	$-0.690358\pi$
$271$	−1.36135e6	−1.12602	−0.563012	+	0.826449i	$0.690358\pi$
$272$	1.43509e6	1.17614
$273$	1.07017e6	0.869051
$274$	794741.	0.639512
$275$	281329.	0.224327
$276$	17331.0	0.0136946
$277$	−2.03987e6	−1.59736	−0.798681	−	0.601755i	$-0.794468\pi$
$277$	−2.03987e6	−1.59736	−0.798681	+	0.601755i	$0.794468\pi$
$278$	−1.17658e6	−0.913083
$279$	−613114.	−0.471554
$280$	1.32609e6	1.01083
$281$	−667020.	−0.503933	−0.251967	−	0.967736i	$-0.581077\pi$
$281$	−667020.	−0.503933	−0.251967	+	0.967736i	$0.581077\pi$
$282$	−1.23583e6	−0.925411
$283$	1.41041e6	1.04684	0.523418	−	0.852076i	$-0.324657\pi$
$283$	1.41041e6	1.04684	0.523418	+	0.852076i	$0.324657\pi$
$284$	62804.0	0.0462053
$285$	842756.	0.614596
$286$	−1.41484e6	−1.02281
$287$	1.57886e6	1.13146
$288$	102864.	0.0730771
$289$	209339.	0.147437
$290$	605508.	0.422790
$291$	−1.05610e6	−0.731095
$292$	32025.2	0.0219804
$293$	928970.	0.632168	0.316084	−	0.948731i	$-0.397632\pi$
$293$	928970.	0.632168	0.316084	+	0.948731i	$0.397632\pi$
$294$	141608.	0.0955476
$295$	−228502.	−0.152874
$296$	−171799.	−0.113970
$297$	173225.	0.113951
$298$	−561475.	−0.366261
$299$	546031.	0.353215
$300$	37541.0	0.0240826
$301$	−2.59404e6	−1.65029
$302$	190842.	0.120408
$303$	983105.	0.615167
$304$	−1.60386e6	−0.995366
$305$	−474952.	−0.292348
$306$	616208.	0.376204
$307$	−756619.	−0.458175	−0.229087	−	0.973406i	$-0.573574\pi$
$307$	−756619.	−0.458175	−0.229087	+	0.973406i	$0.573574\pi$
$308$	99645.1	0.0598521
$309$	−1.46222e6	−0.871199
$310$	2.96140e6	1.75022
$311$	−1.45073e6	−0.850521	−0.425260	−	0.905071i	$-0.639818\pi$
$311$	−1.45073e6	−0.850521	−0.425260	+	0.905071i	$0.639818\pi$
$312$	1.52602e6	0.887509
$313$	−401791.	−0.231814	−0.115907	−	0.993260i	$-0.536977\pi$
$313$	−401791.	−0.231814	−0.115907	+	0.993260i	$0.536977\pi$
$314$	−2.90317e6	−1.66168
$315$	632864.	0.359364
$316$	110940.	0.0624985
$317$	−1.81917e6	−1.01678	−0.508388	−	0.861128i	$-0.669759\pi$
$317$	−1.81917e6	−1.01678	−0.508388	+	0.861128i	$0.669759\pi$
$318$	−1.02195e6	−0.566710
$319$	−367758.	−0.202342
$320$	1.86488e6	1.01807
$321$	−86002.7	−0.0465853
$322$	−387743.	−0.208403
$323$	−1.82079e6	−0.971078
$324$	23115.5	0.0122332
$325$	1.18277e6	0.621143
$326$	−2.08083e6	−1.08441
$327$	−727646.	−0.376314
$328$	2.25139e6	1.15549
$329$	2.74220e6	1.39672
$330$	−836695.	−0.422943
$331$	3.27514e6	1.64309	0.821543	−	0.570147i	$-0.193114\pi$
$331$	3.27514e6	1.64309	0.821543	+	0.570147i	$0.193114\pi$
$332$	−359451.	−0.178976
$333$	−81989.4	−0.0405179
$334$	−405833.	−0.199059
$335$	4.58669e6	2.23299
$336$	−1.20441e6	−0.582006
$337$	1.40437e6	0.673606	0.336803	−	0.941575i	$-0.390654\pi$
$337$	1.40437e6	0.673606	0.336803	+	0.941575i	$0.390654\pi$
$338$	−3.73536e6	−1.77845
$339$	−1.18175e6	−0.558505
$340$	−295192.	−0.138486
$341$	−1.79862e6	−0.837633
$342$	−688675.	−0.318383
$343$	−2.31468e6	−1.06232
$344$	−3.69900e6	−1.68534
$345$	322906.	0.146059
$346$	−89717.1	−0.0402888
$347$	4.10924e6	1.83205	0.916025	−	0.401120i	$-0.131379\pi$
$347$	4.10924e6	1.83205	0.916025	+	0.401120i	$0.131379\pi$
$348$	−49074.3	−0.0217223
$349$	65008.4	0.0285697	0.0142849	−	0.999898i	$-0.495453\pi$
$349$	65008.4	0.0285697	0.0142849	+	0.999898i	$0.495453\pi$
$350$	−839899.	−0.366486
$351$	728277.	0.315521
$352$	301759.	0.129809
$353$	2.87105e6	1.22632	0.613160	−	0.789959i	$-0.289898\pi$
$353$	2.87105e6	1.22632	0.613160	+	0.789959i	$0.289898\pi$
$354$	186725.	0.0791943
$355$	1.17015e6	0.492799
$356$	367062.	0.153502
$357$	−1.36732e6	−0.567805
$358$	−4.26991e6	−1.76081
$359$	−2.59406e6	−1.06229	−0.531146	−	0.847281i	$-0.678238\pi$
$359$	−2.59406e6	−1.06229	−0.531146	+	0.847281i	$0.678238\pi$
$360$	902439.	0.366996
$361$	−441179.	−0.178175
$362$	4.18651e6	1.67911
$363$	−941289.	−0.374935
$364$	418930.	0.165725
$365$	596685.	0.234430
$366$	388117.	0.151447
$367$	1.69904e6	0.658472	0.329236	−	0.944248i	$-0.393209\pi$
$367$	1.69904e6	0.658472	0.329236	+	0.944248i	$0.393209\pi$
$368$	−614528.	−0.236550
$369$	1.07445e6	0.410792
$370$	396017.	0.150387
$371$	2.26762e6	0.855334
$372$	−240011.	−0.0899237
$373$	1.30896e6	0.487142	0.243571	−	0.969883i	$-0.421681\pi$
$373$	1.30896e6	0.487142	0.243571	+	0.969883i	$0.421681\pi$
$374$	1.80770e6	0.668262
$375$	−1.14674e6	−0.421103
$376$	3.91027e6	1.42639
$377$	−1.54614e6	−0.560266
$378$	−517158.	−0.186163
$379$	−2.85503e6	−1.02097	−0.510485	−	0.859887i	$-0.670534\pi$
$379$	−2.85503e6	−1.02097	−0.510485	+	0.859887i	$0.670534\pi$
$380$	329907.	0.117201
$381$	−2.10898e6	−0.744320
$382$	169922.	0.0595788
$383$	−1.29291e6	−0.450371	−0.225186	−	0.974316i	$-0.572299\pi$
$383$	−1.29291e6	−0.450371	−0.225186	+	0.974316i	$0.572299\pi$
$384$	−1.88966e6	−0.653968
$385$	1.85656e6	0.638347
$386$	1.84788e6	0.631254
$387$	−1.76531e6	−0.599162
$388$	−413425.	−0.139417
$389$	−514685.	−0.172452	−0.0862259	−	0.996276i	$-0.527481\pi$
$389$	−514685.	−0.172452	−0.0862259	+	0.996276i	$0.527481\pi$
$390$	−3.51765e6	−1.17109
$391$	−697646.	−0.230777
$392$	−448061.	−0.147273
$393$	1.21640e6	0.397280
$394$	−3.95773e6	−1.28442
$395$	2.06700e6	0.666572
$396$	67811.1	0.0217302
$397$	−3.92612e6	−1.25022	−0.625112	−	0.780535i	$-0.714947\pi$
$397$	−3.92612e6	−1.25022	−0.625112	+	0.780535i	$0.714947\pi$
$398$	−1.94309e6	−0.614873
$399$	1.52812e6	0.480534
$400$	−1.33114e6	−0.415982
$401$	−2.41292e6	−0.749346	−0.374673	−	0.927157i	$-0.622245\pi$
$401$	−2.41292e6	−0.749346	−0.374673	+	0.927157i	$0.622245\pi$
$402$	−3.74811e6	−1.15677
$403$	−7.56181e6	−2.31933
$404$	384849.	0.117310
$405$	430681.	0.130472
$406$	1.09793e6	0.330567
$407$	−240523.	−0.0719730
$408$	−1.94974e6	−0.579864
$409$	3.67029e6	1.08491	0.542454	−	0.840086i	$-0.317495\pi$
$409$	3.67029e6	1.08491	0.542454	+	0.840086i	$0.317495\pi$
$410$	−5.18972e6	−1.52470
$411$	−1.20009e6	−0.350435
$412$	−572405.	−0.166135
$413$	−414328.	−0.119528
$414$	−263870.	−0.0756638
$415$	−6.69720e6	−1.90885
$416$	1.26866e6	0.359429
$417$	1.77668e6	0.500344
$418$	−2.02029e6	−0.565551
$419$	−1.90475e6	−0.530034	−0.265017	−	0.964244i	$-0.585378\pi$
$419$	−1.90475e6	−0.530034	−0.265017	+	0.964244i	$0.585378\pi$
$420$	247743.	0.0685295
$421$	4.91363e6	1.35113	0.675565	−	0.737300i	$-0.263900\pi$
$421$	4.91363e6	1.35113	0.675565	+	0.737300i	$0.263900\pi$
$422$	4.62097e6	1.26314
$423$	1.86614e6	0.507100
$424$	3.23354e6	0.873500
$425$	−1.51118e6	−0.405831
$426$	−956210.	−0.255287
$427$	−861202.	−0.228578
$428$	−33666.8	−0.00888367
$429$	2.13646e6	0.560469
$430$	8.52664e6	2.22386
$431$	−3.65588e6	−0.947979	−0.473990	−	0.880530i	$-0.657187\pi$
$431$	−3.65588e6	−0.947979	−0.473990	+	0.880530i	$0.657187\pi$
$432$	−819635.	−0.211306
$433$	−5.06298e6	−1.29774	−0.648869	−	0.760900i	$-0.724758\pi$
$433$	−5.06298e6	−1.29774	−0.648869	+	0.760900i	$0.724758\pi$
$434$	5.36973e6	1.36845
$435$	−914338.	−0.231677
$436$	−284846.	−0.0717619
$437$	779690.	0.195307
$438$	−487594.	−0.121443
$439$	−3.94551e6	−0.977108	−0.488554	−	0.872534i	$-0.662475\pi$
$439$	−3.94551e6	−0.977108	−0.488554	+	0.872534i	$0.662475\pi$
$440$	2.64738e6	0.651905
$441$	−213833.	−0.0523574
$442$	7.59996e6	1.85036
$443$	−3.37423e6	−0.816894	−0.408447	−	0.912782i	$-0.633930\pi$
$443$	−3.37423e6	−0.816894	−0.408447	+	0.912782i	$0.633930\pi$
$444$	−32095.8	−0.00772663
$445$	6.83900e6	1.63716
$446$	5.09833e6	1.21364
$447$	847847.	0.200701
$448$	3.38147e6	0.795995
$449$	−5.64111e6	−1.32053	−0.660266	−	0.751032i	$-0.729556\pi$
$449$	−5.64111e6	−1.32053	−0.660266	+	0.751032i	$0.729556\pi$
$450$	−571573.	−0.133058
$451$	3.15200e6	0.729700
$452$	−462611.	−0.106505
$453$	−288178.	−0.0659804
$454$	−1.51996e6	−0.346094
$455$	7.80539e6	1.76753
$456$	2.17903e6	0.490740
$457$	−134096.	−0.0300348	−0.0150174	−	0.999887i	$-0.504780\pi$
$457$	−134096.	−0.0300348	−0.0150174	+	0.999887i	$0.504780\pi$
$458$	−3.00707e6	−0.669854
$459$	−930495.	−0.206150
$460$	126406.	0.0278530
$461$	4.00954e6	0.878703	0.439351	−	0.898315i	$-0.355208\pi$
$461$	4.00954e6	0.878703	0.439351	+	0.898315i	$0.355208\pi$
$462$	−1.51713e6	−0.330687
$463$	8.02971e6	1.74079	0.870397	−	0.492351i	$-0.163862\pi$
$463$	8.02971e6	1.74079	0.870397	+	0.492351i	$0.163862\pi$
$464$	1.74009e6	0.375212
$465$	−4.47182e6	−0.959074
$466$	−1.88213e6	−0.401500
$467$	−1.17884e6	−0.250129	−0.125065	−	0.992149i	$-0.539914\pi$
$467$	−1.17884e6	−0.250129	−0.125065	+	0.992149i	$0.539914\pi$
$468$	285093.	0.0601689
$469$	8.31677e6	1.74591
$470$	−9.01365e6	−1.88216
$471$	4.38389e6	0.910557
$472$	−590815.	−0.122067
$473$	−5.17869e6	−1.06431
$474$	−1.68909e6	−0.345308
$475$	1.68890e6	0.343456
$476$	−535254.	−0.108278
$477$	1.54317e6	0.310541
$478$	7.86219e6	1.57389
$479$	−7.03708e6	−1.40137	−0.700686	−	0.713470i	$-0.747123\pi$
$479$	−7.03708e6	−1.40137	−0.700686	+	0.713470i	$0.747123\pi$
$480$	750249.	0.148629
$481$	−1.01121e6	−0.199287
$482$	602910.	0.118205
$483$	585506.	0.114199
$484$	−368479.	−0.0714990
$485$	−7.70281e6	−1.48694
$486$	−351940.	−0.0675893
$487$	−1.74859e6	−0.334093	−0.167046	−	0.985949i	$-0.553423\pi$
$487$	−1.74859e6	−0.334093	−0.167046	+	0.985949i	$0.553423\pi$
$488$	−1.22804e6	−0.233433
$489$	3.14213e6	0.594226
$490$	1.03284e6	0.194330
$491$	5.71036e6	1.06896	0.534478	−	0.845183i	$-0.320508\pi$
$491$	5.71036e6	1.06896	0.534478	+	0.845183i	$0.320508\pi$
$492$	420608.	0.0783366
$493$	1.97545e6	0.366057
$494$	−8.49373e6	−1.56596
$495$	1.26344e6	0.231761
$496$	8.51040e6	1.55327
$497$	2.12176e6	0.385305
$498$	5.47275e6	0.988855
$499$	−3.18564e6	−0.572724	−0.286362	−	0.958121i	$-0.592446\pi$
$499$	−3.18564e6	−0.572724	−0.286362	+	0.958121i	$0.592446\pi$
$500$	−448907.	−0.0803029
$501$	612821.	0.109079
$502$	−1.06102e7	−1.87916
$503$	7.57762e6	1.33541	0.667703	−	0.744428i	$-0.267278\pi$
$503$	7.57762e6	1.33541	0.667703	+	0.744428i	$0.267278\pi$
$504$	1.63634e6	0.286944
$505$	7.17039e6	1.25116
$506$	−774083.	−0.134404
$507$	5.64052e6	0.974539
$508$	−825586.	−0.141939
$509$	−6.23348e6	−1.06644	−0.533220	−	0.845977i	$-0.679018\pi$
$509$	−6.23348e6	−1.06644	−0.533220	+	0.845977i	$0.679018\pi$
$510$	4.49439e6	0.765147
$511$	1.08193e6	0.183294
$512$	4.67867e6	0.788764
$513$	1.03992e6	0.174465
$514$	2.27385e6	0.379624
$515$	−1.06649e7	−1.77190
$516$	−691053.	−0.114258
$517$	5.47448e6	0.900775
$518$	718073.	0.117583
$519$	135476.	0.0220772
$520$	1.11302e7	1.80507
$521$	−4.48711e6	−0.724224	−0.362112	−	0.932135i	$-0.617944\pi$
$521$	−4.48711e6	−0.724224	−0.362112	+	0.932135i	$0.617944\pi$
$522$	747170.	0.120017
$523$	−6.66955e6	−1.06621	−0.533104	−	0.846050i	$-0.678975\pi$
$523$	−6.66955e6	−1.06621	−0.533104	+	0.846050i	$0.678975\pi$
$524$	476176.	0.0757599
$525$	1.26828e6	0.200824
$526$	1.34461e6	0.211901
$527$	9.66147e6	1.51536
$528$	−2.40447e6	−0.375348
$529$	−6.13760e6	−0.953585
$530$	−7.45369e6	−1.15261
$531$	−281961.	−0.0433963
$532$	598200.	0.0916363
$533$	1.32517e7	2.02048
$534$	−5.58863e6	−0.848110
$535$	−627270.	−0.0947481
$536$	1.18594e7	1.78299
$537$	6.44772e6	0.964873
$538$	3.35114e6	0.499157
$539$	−627297.	−0.0930039
$540$	168595.	0.0248806
$541$	−5.56886e6	−0.818038	−0.409019	−	0.912526i	$-0.634129\pi$
$541$	−5.56886e6	−0.818038	−0.409019	+	0.912526i	$0.634129\pi$
$542$	8.11385e6	1.18639
$543$	−6.32177e6	−0.920108
$544$	−1.62093e6	−0.234837
$545$	−5.30717e6	−0.765371
$546$	−6.37834e6	−0.915643
$547$	1.15071e7	1.64437	0.822184	−	0.569222i	$-0.192756\pi$
$547$	1.15071e7	1.64437	0.822184	+	0.569222i	$0.192756\pi$
$548$	−469788.	−0.0668268
$549$	−586070.	−0.0829887
$550$	−1.67676e6	−0.236354
$551$	−2.20776e6	−0.309794
$552$	834908.	0.116625
$553$	3.74796e6	0.521173
$554$	1.21579e7	1.68300
$555$	−597999.	−0.0824077
$556$	695503.	0.0954140
$557$	3.88277e6	0.530277	0.265139	−	0.964210i	$-0.414582\pi$
$557$	3.88277e6	0.530277	0.265139	+	0.964210i	$0.414582\pi$
$558$	3.65424e6	0.496835
$559$	−2.17724e7	−2.94697
$560$	−8.78454e6	−1.18372
$561$	−2.72968e6	−0.366189
$562$	3.97553e6	0.530950
$563$	981269.	0.130472	0.0652360	−	0.997870i	$-0.479220\pi$
$563$	981269.	0.130472	0.0652360	+	0.997870i	$0.479220\pi$
$564$	730524.	0.0967023
$565$	−8.61924e6	−1.13592
$566$	−8.40621e6	−1.10296
$567$	780927.	0.102012
$568$	3.02554e6	0.393488
$569$	−8.63190e6	−1.11770	−0.558850	−	0.829268i	$-0.688757\pi$
$569$	−8.63190e6	−1.11770	−0.558850	+	0.829268i	$0.688757\pi$
$570$	−5.02293e6	−0.647545
$571$	1.06342e7	1.36494	0.682469	−	0.730915i	$-0.260906\pi$
$571$	1.06342e7	1.36494	0.682469	+	0.730915i	$0.260906\pi$
$572$	836344.	0.106880
$573$	−256588.	−0.0326475
$574$	−9.41019e6	−1.19212
$575$	647112.	0.0816225
$576$	2.30118e6	0.288997
$577$	3.83248e6	0.479225	0.239613	−	0.970869i	$-0.422980\pi$
$577$	3.83248e6	0.479225	0.239613	+	0.970869i	$0.422980\pi$
$578$	−1.24769e6	−0.155341
$579$	−2.79035e6	−0.345910
$580$	−357929.	−0.0441801
$581$	−1.21436e7	−1.49248
$582$	6.29451e6	0.770291
$583$	4.52703e6	0.551622
$584$	1.54279e6	0.187187
$585$	5.31177e6	0.641726
$586$	−5.53678e6	−0.666060
$587$	−3.74170e6	−0.448202	−0.224101	−	0.974566i	$-0.571945\pi$
$587$	−3.74170e6	−0.448202	−0.224101	+	0.974566i	$0.571945\pi$
$588$	−83707.6	−0.00998439
$589$	−1.07977e7	−1.28245
$590$	1.36190e6	0.161070
$591$	5.97631e6	0.703825
$592$	1.13806e6	0.133463
$593$	−411565.	−0.0480620	−0.0240310	−	0.999711i	$-0.507650\pi$
$593$	−411565.	−0.0480620	−0.0240310	+	0.999711i	$0.507650\pi$
$594$	−1.03244e6	−0.120061
$595$	−9.97269e6	−1.15483
$596$	331900.	0.0382729
$597$	2.93414e6	0.336934
$598$	−3.25442e6	−0.372152
$599$	6.06004e6	0.690094	0.345047	−	0.938585i	$-0.387863\pi$
$599$	6.06004e6	0.690094	0.345047	+	0.938585i	$0.387863\pi$
$600$	1.80851e6	0.205089
$601$	6.69768e6	0.756376	0.378188	−	0.925729i	$-0.376547\pi$
$601$	6.69768e6	0.756376	0.378188	+	0.925729i	$0.376547\pi$
$602$	1.54608e7	1.73877
$603$	5.65978e6	0.633878
$604$	−112811.	−0.0125822
$605$	−6.86540e6	−0.762566
$606$	−5.85943e6	−0.648148
$607$	−1.00236e6	−0.110421	−0.0552106	−	0.998475i	$-0.517583\pi$
$607$	−1.00236e6	−0.110421	−0.0552106	+	0.998475i	$0.517583\pi$
$608$	1.81155e6	0.198743
$609$	−1.65791e6	−0.181142
$610$	2.83078e6	0.308022
$611$	2.30159e7	2.49417
$612$	−364254.	−0.0393121
$613$	−1.24680e7	−1.34013	−0.670064	−	0.742303i	$-0.733733\pi$
$613$	−1.24680e7	−1.34013	−0.670064	+	0.742303i	$0.733733\pi$
$614$	4.50955e6	0.482739
$615$	7.83665e6	0.835492
$616$	4.80033e6	0.509705
$617$	−7.98964e6	−0.844917	−0.422459	−	0.906382i	$-0.638833\pi$
$617$	−7.98964e6	−0.844917	−0.422459	+	0.906382i	$0.638833\pi$
$618$	8.71504e6	0.917906
$619$	−8.83016e6	−0.926279	−0.463140	−	0.886285i	$-0.653277\pi$
$619$	−8.83016e6	−0.926279	−0.463140	+	0.886285i	$0.653277\pi$
$620$	−1.75055e6	−0.182892
$621$	398452.	0.0414617
$622$	8.64653e6	0.896119
$623$	1.24007e7	1.28005
$624$	−1.01089e7	−1.03931
$625$	−1.20637e7	−1.23533
$626$	2.39473e6	0.244242
$627$	3.05070e6	0.309906
$628$	1.71613e6	0.173640
$629$	1.29199e6	0.130207
$630$	−3.77195e6	−0.378630
$631$	−8.18563e6	−0.818425	−0.409212	−	0.912439i	$-0.634196\pi$
$631$	−8.18563e6	−0.818425	−0.409212	+	0.912439i	$0.634196\pi$
$632$	5.34444e6	0.532242
$633$	−6.97783e6	−0.692167
$634$	1.08425e7	1.07129
$635$	−1.53821e7	−1.51384
$636$	604095.	0.0592192
$637$	−2.63730e6	−0.257520
$638$	2.19189e6	0.213190
$639$	1.44391e6	0.139890
$640$	−1.37825e7	−1.33008
$641$	−1.08929e7	−1.04713	−0.523564	−	0.851986i	$-0.675398\pi$
$641$	−1.08929e7	−1.04713	−0.523564	+	0.851986i	$0.675398\pi$
$642$	512587.	0.0490829
$643$	4.87772e6	0.465254	0.232627	−	0.972566i	$-0.425268\pi$
$643$	4.87772e6	0.465254	0.232627	+	0.972566i	$0.425268\pi$
$644$	229204.	0.0217774
$645$	−1.28755e7	−1.21861
$646$	1.08522e7	1.02314
$647$	−5.09261e6	−0.478277	−0.239138	−	0.970985i	$-0.576865\pi$
$647$	−5.09261e6	−0.478277	−0.239138	+	0.970985i	$0.576865\pi$
$648$	1.11357e6	0.104179
$649$	−827156.	−0.0770860
$650$	−7.04946e6	−0.654444
$651$	−8.10848e6	−0.749871
$652$	1.23002e6	0.113317
$653$	−1.57557e7	−1.44595	−0.722976	−	0.690873i	$-0.757226\pi$
$653$	−1.57557e7	−1.44595	−0.722976	+	0.690873i	$0.757226\pi$
$654$	4.33687e6	0.396489
$655$	8.87198e6	0.808011
$656$	−1.49141e7	−1.35312
$657$	736283.	0.0665474
$658$	−1.63439e7	−1.47160
$659$	1.52866e7	1.37119	0.685596	−	0.727983i	$-0.259542\pi$
$659$	1.52866e7	1.37119	0.685596	+	0.727983i	$0.259542\pi$
$660$	494588.	0.0441961
$661$	−7.43781e6	−0.662127	−0.331064	−	0.943608i	$-0.607408\pi$
$661$	−7.43781e6	−0.662127	−0.331064	+	0.943608i	$0.607408\pi$
$662$	−1.95203e7	−1.73117
$663$	−1.14762e7	−1.01395
$664$	−1.73163e7	−1.52418
$665$	1.11455e7	0.977339
$666$	488667.	0.0426902
$667$	−845916.	−0.0736229
$668$	239896.	0.0208009
$669$	−7.69866e6	−0.665043
$670$	−2.73373e7	−2.35271
$671$	−1.71929e6	−0.147415
$672$	1.36038e6	0.116208
$673$	−2.00568e7	−1.70697	−0.853483	−	0.521121i	$-0.825514\pi$
$673$	−2.00568e7	−1.70697	−0.853483	+	0.521121i	$0.825514\pi$
$674$	−8.37021e6	−0.709719
$675$	863095.	0.0729120
$676$	2.20805e6	0.185841
$677$	2.08686e6	0.174993	0.0874965	−	0.996165i	$-0.472113\pi$
$677$	2.08686e6	0.174993	0.0874965	+	0.996165i	$0.472113\pi$
$678$	7.04339e6	0.588448
$679$	−1.39670e7	−1.16260
$680$	−1.42207e7	−1.17936
$681$	2.29520e6	0.189650
$682$	1.07200e7	0.882540
$683$	5.45861e6	0.447745	0.223872	−	0.974618i	$-0.428130\pi$
$683$	5.45861e6	0.447745	0.223872	+	0.974618i	$0.428130\pi$
$684$	407091.	0.0332699
$685$	−8.75296e6	−0.712736
$686$	1.37958e7	1.11927
$687$	4.54078e6	0.367061
$688$	2.45036e7	1.97360
$689$	1.90326e7	1.52739
$690$	−1.92456e6	−0.153890
$691$	655073.	0.0521908	0.0260954	−	0.999659i	$-0.491693\pi$
$691$	655073.	0.0521908	0.0260954	+	0.999659i	$0.491693\pi$
$692$	53033.7	0.00421004
$693$	2.29091e6	0.181207
$694$	−2.44916e7	−1.93027
$695$	1.29584e7	1.01763
$696$	−2.36412e6	−0.184989
$697$	−1.69313e7	−1.32010
$698$	−387459.	−0.0301014
$699$	2.84208e6	0.220011
$700$	496482.	0.0382965
$701$	−2.15464e7	−1.65607	−0.828037	−	0.560674i	$-0.810542\pi$
$701$	−2.15464e7	−1.65607	−0.828037	+	0.560674i	$0.810542\pi$
$702$	−4.34063e6	−0.332437
$703$	−1.44393e6	−0.110194
$704$	6.75069e6	0.513354
$705$	1.36109e7	1.03137
$706$	−1.71118e7	−1.29207
$707$	1.30016e7	0.978248
$708$	−110377.	−0.00827553
$709$	1.65045e7	1.23307	0.616533	−	0.787329i	$-0.288537\pi$
$709$	1.65045e7	1.23307	0.616533	+	0.787329i	$0.288537\pi$
$710$	−6.97423e6	−0.519219
$711$	2.55058e6	0.189219
$712$	1.76829e7	1.30724
$713$	−4.13719e6	−0.304776
$714$	8.14939e6	0.598246
$715$	1.55825e7	1.13992
$716$	2.52404e6	0.183998
$717$	−1.18722e7	−0.862447
$718$	1.54609e7	1.11924
$719$	3.65458e6	0.263642	0.131821	−	0.991274i	$-0.457918\pi$
$719$	3.65458e6	0.263642	0.131821	+	0.991274i	$0.457918\pi$
$720$	−5.97811e6	−0.429766
$721$	−1.93380e7	−1.38539
$722$	2.62948e6	0.187727
$723$	−910415.	−0.0647729
$724$	−2.47473e6	−0.175462
$725$	−1.83236e6	−0.129469
$726$	5.61021e6	0.395037
$727$	1.40192e7	0.983757	0.491878	−	0.870664i	$-0.336310\pi$
$727$	1.40192e7	0.983757	0.491878	+	0.870664i	$0.336310\pi$
$728$	2.01817e7	1.41133
$729$	531441.	0.0370370
$730$	−3.55632e6	−0.246998
$731$	2.78178e7	1.92544
$732$	−229425.	−0.0158257
$733$	−2.41229e7	−1.65833	−0.829163	−	0.559007i	$-0.811183\pi$
$733$	−2.41229e7	−1.65833	−0.829163	+	0.559007i	$0.811183\pi$
$734$	−1.01265e7	−0.693774
$735$	−1.55962e6	−0.106488
$736$	694106.	0.0472315
$737$	1.66034e7	1.12597
$738$	−6.40388e6	−0.432815
$739$	−1.00291e7	−0.675537	−0.337768	−	0.941229i	$-0.609672\pi$
$739$	−1.00291e7	−0.675537	−0.337768	+	0.941229i	$0.609672\pi$
$740$	−234094.	−0.0157149
$741$	1.28258e7	0.858104
$742$	−1.35153e7	−0.901190
$743$	4.51165e6	0.299822	0.149911	−	0.988699i	$-0.452101\pi$
$743$	4.51165e6	0.299822	0.149911	+	0.988699i	$0.452101\pi$
$744$	−1.15624e7	−0.765798
$745$	6.18387e6	0.408197
$746$	−7.80160e6	−0.513259
$747$	−8.26404e6	−0.541865
$748$	−1.06857e6	−0.0698310
$749$	−1.13739e6	−0.0740807
$750$	6.83474e6	0.443679
$751$	1.58055e7	1.02260	0.511302	−	0.859401i	$-0.329163\pi$
$751$	1.58055e7	1.02260	0.511302	+	0.859401i	$0.329163\pi$
$752$	−2.59031e7	−1.67035
$753$	1.60218e7	1.02973
$754$	9.21518e6	0.590304
$755$	−2.10186e6	−0.134195
$756$	305703.	0.0194534
$757$	7.71419e6	0.489272	0.244636	−	0.969615i	$-0.421331\pi$
$757$	7.71419e6	0.489272	0.244636	+	0.969615i	$0.421331\pi$
$758$	1.70163e7	1.07571
$759$	1.16889e6	0.0736495
$760$	1.58930e7	0.998097
$761$	−1.26944e7	−0.794603	−0.397302	−	0.917688i	$-0.630053\pi$
$761$	−1.26944e7	−0.794603	−0.397302	+	0.917688i	$0.630053\pi$
$762$	1.25698e7	0.784225
$763$	−9.62316e6	−0.598421
$764$	−100445.	−0.00622578
$765$	−6.78668e6	−0.419279
$766$	7.70590e6	0.474517
$767$	−3.47755e6	−0.213444
$768$	3.08067e6	0.188470
$769$	−3.29528e6	−0.200944	−0.100472	−	0.994940i	$-0.532035\pi$
$769$	−3.29528e6	−0.200944	−0.100472	+	0.994940i	$0.532035\pi$
$770$	−1.10653e7	−0.672571
$771$	−3.43358e6	−0.208023
$772$	−1.09232e6	−0.0659639
$773$	−5.51865e6	−0.332188	−0.166094	−	0.986110i	$-0.553116\pi$
$773$	−5.51865e6	−0.332188	−0.166094	+	0.986110i	$0.553116\pi$
$774$	1.05215e7	0.631284
$775$	−8.96164e6	−0.535961
$776$	−1.99164e7	−1.18729
$777$	−1.08431e6	−0.0644322
$778$	3.06759e6	0.181697
$779$	1.89224e7	1.11720
$780$	2.07936e6	0.122375
$781$	4.23583e6	0.248491
$782$	4.15806e6	0.243150
$783$	−1.12825e6	−0.0657661
$784$	2.96813e6	0.172462
$785$	3.19744e7	1.85194
$786$	−7.24992e6	−0.418579
$787$	1.63062e7	0.938459	0.469230	−	0.883076i	$-0.344532\pi$
$787$	1.63062e7	0.938459	0.469230	+	0.883076i	$0.344532\pi$
$788$	2.33950e6	0.134217
$789$	−2.03041e6	−0.116116
$790$	−1.23196e7	−0.702309
$791$	−1.56287e7	−0.888143
$792$	3.26675e6	0.185056
$793$	−7.22826e6	−0.408179
$794$	2.34002e7	1.31725
$795$	1.12553e7	0.631597
$796$	1.14860e6	0.0642521
$797$	3.19084e7	1.77934	0.889671	−	0.456602i	$-0.150934\pi$
$797$	3.19084e7	1.77934	0.889671	+	0.456602i	$0.150934\pi$
$798$	−9.10777e6	−0.506297
$799$	−2.94067e7	−1.62959
$800$	1.50352e6	0.0830584
$801$	8.43902e6	0.464741
$802$	1.43813e7	0.789520
$803$	2.15995e6	0.118210
$804$	2.21559e6	0.120879
$805$	4.27045e6	0.232265
$806$	4.50694e7	2.44368
$807$	−5.06033e6	−0.273524
$808$	1.85398e7	0.999025
$809$	1.70126e7	0.913900	0.456950	−	0.889492i	$-0.348942\pi$
$809$	1.70126e7	0.913900	0.456950	+	0.889492i	$0.348942\pi$
$810$	−2.56691e6	−0.137467
$811$	1.05241e7	0.561865	0.280932	−	0.959728i	$-0.409356\pi$
$811$	1.05241e7	0.561865	0.280932	+	0.959728i	$0.409356\pi$
$812$	−649010.	−0.0345431
$813$	−1.22522e7	−0.650110
$814$	1.43355e6	0.0758317
$815$	2.29175e7	1.20857
$816$	1.29158e7	0.679043
$817$	−3.10892e7	−1.62950
$818$	−2.18754e7	−1.14307
$819$	9.63151e6	0.501747
$820$	3.06775e6	0.159326
$821$	3.31358e7	1.71569	0.857847	−	0.513906i	$-0.171802\pi$
$821$	3.31358e7	1.71569	0.857847	+	0.513906i	$0.171802\pi$
$822$	7.15266e6	0.369223
$823$	2.83322e7	1.45808	0.729039	−	0.684472i	$-0.239967\pi$
$823$	2.83322e7	1.45808	0.729039	+	0.684472i	$0.239967\pi$
$824$	−2.75752e7	−1.41482
$825$	2.53196e6	0.129516
$826$	2.46945e6	0.125936
$827$	8.10406e6	0.412039	0.206020	−	0.978548i	$-0.433949\pi$
$827$	8.10406e6	0.412039	0.206020	+	0.978548i	$0.433949\pi$
$828$	155979.	0.00790661
$829$	−2.88681e7	−1.45892	−0.729461	−	0.684022i	$-0.760229\pi$
$829$	−2.88681e7	−1.45892	−0.729461	+	0.684022i	$0.760229\pi$
$830$	3.99162e7	2.01119
$831$	−1.83588e7	−0.922237
$832$	2.83814e7	1.42143
$833$	3.36959e6	0.168253
$834$	−1.05892e7	−0.527169
$835$	4.46968e6	0.221851
$836$	1.19423e6	0.0590981
$837$	−5.51803e6	−0.272252
$838$	1.13526e7	0.558450
$839$	−3.01221e7	−1.47734	−0.738671	−	0.674066i	$-0.764546\pi$
$839$	−3.01221e7	−1.47734	−0.738671	+	0.674066i	$0.764546\pi$
$840$	1.19348e7	0.583603
$841$	−1.81159e7	−0.883220
$842$	−2.92859e7	−1.42357
$843$	−6.00318e6	−0.290946
$844$	−2.73156e6	−0.131994
$845$	4.11398e7	1.98208
$846$	−1.11224e7	−0.534287
$847$	−1.24486e7	−0.596228
$848$	−2.14202e7	−1.02290
$849$	1.26937e7	0.604391
$850$	9.00686e6	0.427589
$851$	−553249.	−0.0261877
$852$	565236.	0.0266766
$853$	−3.03837e7	−1.42977	−0.714887	−	0.699240i	$-0.753522\pi$
$853$	−3.03837e7	−1.42977	−0.714887	+	0.699240i	$0.753522\pi$
$854$	5.13288e6	0.240833
$855$	7.58480e6	0.354837
$856$	−1.62187e6	−0.0756541
$857$	−3.42703e7	−1.59392	−0.796958	−	0.604035i	$-0.793559\pi$
$857$	−3.42703e7	−1.59392	−0.796958	+	0.604035i	$0.793559\pi$
$858$	−1.27336e7	−0.590517
$859$	−7.21405e6	−0.333577	−0.166789	−	0.985993i	$-0.553340\pi$
$859$	−7.21405e6	−0.333577	−0.166789	+	0.985993i	$0.553340\pi$
$860$	−5.04028e6	−0.232385
$861$	1.42097e7	0.653247
$862$	2.17895e7	0.998802
$863$	−3.87581e7	−1.77148	−0.885739	−	0.464184i	$-0.846348\pi$
$863$	−3.87581e7	−1.77148	−0.885739	+	0.464184i	$0.846348\pi$
$864$	925774.	0.0421911
$865$	988108.	0.0449019
$866$	3.01761e7	1.36731
$867$	1.88405e6	0.0851226
$868$	−3.17416e6	−0.142998
$869$	7.48235e6	0.336115
$870$	5.44957e6	0.244098
$871$	6.98045e7	3.11773
$872$	−1.37222e7	−0.611131
$873$	−9.50493e6	−0.422098
$874$	−4.64706e6	−0.205778
$875$	−1.51657e7	−0.669644
$876$	288227.	0.0126904
$877$	−4.06345e6	−0.178400	−0.0892002	−	0.996014i	$-0.528431\pi$
$877$	−4.06345e6	−0.178400	−0.0892002	+	0.996014i	$0.528431\pi$
$878$	2.35158e7	1.02949
$879$	8.36073e6	0.364982
$880$	−1.75373e7	−0.763405
$881$	−4.47103e7	−1.94074	−0.970372	−	0.241616i	$-0.922323\pi$
$881$	−4.47103e7	−1.94074	−0.970372	+	0.241616i	$0.922323\pi$
$882$	1.27447e6	0.0551644
$883$	−6.18489e6	−0.266950	−0.133475	−	0.991052i	$-0.542614\pi$
$883$	−6.18489e6	−0.266950	−0.133475	+	0.991052i	$0.542614\pi$
$884$	−4.49250e6	−0.193356
$885$	−2.05652e6	−0.0882620
$886$	2.01109e7	0.860690
$887$	4.16533e7	1.77763	0.888813	−	0.458270i	$-0.151531\pi$
$887$	4.16533e7	1.77763	0.888813	+	0.458270i	$0.151531\pi$
$888$	−1.54619e6	−0.0658007
$889$	−2.78914e7	−1.18363
$890$	−4.07613e7	−1.72494
$891$	1.55903e6	0.0657899
$892$	−3.01374e6	−0.126822
$893$	3.28650e7	1.37913
$894$	−5.05328e6	−0.211461
$895$	4.70272e7	1.96242
$896$	−2.49909e7	−1.03995
$897$	4.91428e6	0.203929
$898$	3.36218e7	1.39133
$899$	1.17148e7	0.483433
$900$	337869.	0.0139041
$901$	−2.43174e7	−0.997941
$902$	−1.87863e7	−0.768821
$903$	−2.33464e7	−0.952796
$904$	−2.22860e7	−0.907006
$905$	−4.61085e7	−1.87137
$906$	1.71758e6	0.0695178
$907$	2.48069e7	1.00128	0.500639	−	0.865656i	$-0.333098\pi$
$907$	2.48069e7	1.00128	0.500639	+	0.865656i	$0.333098\pi$
$908$	898483.	0.0361656
$909$	8.84794e6	0.355167
$910$	−4.65212e7	−1.86229
$911$	2.87038e7	1.14589	0.572946	−	0.819593i	$-0.305800\pi$
$911$	2.87038e7	1.14589	0.572946	+	0.819593i	$0.305800\pi$
$912$	−1.44348e7	−0.574675
$913$	−2.42432e7	−0.962529
$914$	799228.	0.0316450
$915$	−4.27457e6	−0.168787
$916$	1.77754e6	0.0699974
$917$	1.60870e7	0.631760
$918$	5.54587e6	0.217202
$919$	3.98850e7	1.55783	0.778917	−	0.627127i	$-0.215769\pi$
$919$	3.98850e7	1.55783	0.778917	+	0.627127i	$0.215769\pi$
$920$	6.08950e6	0.237198
$921$	−6.80957e6	−0.264527
$922$	−2.38974e7	−0.925812
$923$	1.78084e7	0.688050
$924$	896806.	0.0345556
$925$	−1.19840e6	−0.0460521
$926$	−4.78581e7	−1.83412
$927$	−1.31600e7	−0.502987
$928$	−1.96542e6	−0.0749180
$929$	−3.09058e7	−1.17490	−0.587451	−	0.809260i	$-0.699868\pi$
$929$	−3.09058e7	−1.17490	−0.587451	+	0.809260i	$0.699868\pi$
$930$	2.66526e7	1.01049
$931$	−3.76585e6	−0.142393
$932$	1.11257e6	0.0419553
$933$	−1.30566e7	−0.491048
$934$	7.02606e6	0.263539
$935$	−1.99093e7	−0.744777
$936$	1.37341e7	0.512403
$937$	−3.92068e7	−1.45886	−0.729428	−	0.684058i	$-0.760214\pi$
$937$	−3.92068e7	−1.45886	−0.729428	+	0.684058i	$0.760214\pi$
$938$	−4.95690e7	−1.83951
$939$	−3.61612e6	−0.133838
$940$	5.32816e6	0.196679
$941$	−4.21602e7	−1.55213	−0.776066	−	0.630652i	$-0.782788\pi$
$941$	−4.21602e7	−1.55213	−0.776066	+	0.630652i	$0.782788\pi$
$942$	−2.61285e7	−0.959374
$943$	7.25021e6	0.265504
$944$	3.91379e6	0.142944
$945$	5.69578e6	0.207479
$946$	3.08657e7	1.12137
$947$	5.32912e7	1.93099	0.965497	−	0.260416i	$-0.0838596\pi$
$947$	5.32912e7	1.93099	0.965497	+	0.260416i	$0.0838596\pi$
$948$	998458.	0.0360835
$949$	9.08090e6	0.327313
$950$	−1.00661e7	−0.361869
$951$	−1.63725e7	−0.587036
$952$	−2.57854e7	−0.922109
$953$	3.66273e7	1.30639	0.653194	−	0.757190i	$-0.273428\pi$
$953$	3.66273e7	1.30639	0.653194	+	0.757190i	$0.273428\pi$
$954$	−9.19752e6	−0.327190
$955$	−1.87146e6	−0.0664005
$956$	−4.64751e6	−0.164466
$957$	−3.30982e6	−0.116822
$958$	4.19419e7	1.47650
$959$	−1.58712e7	−0.557267
$960$	1.67839e7	0.587780
$961$	2.86654e7	1.00127
$962$	6.02695e6	0.209971
$963$	−774024.	−0.0268961
$964$	−356393.	−0.0123520
$965$	−2.03518e7	−0.703532
$966$	−3.48969e6	−0.120322
$967$	−3.44677e7	−1.18535	−0.592675	−	0.805442i	$-0.701928\pi$
$967$	−3.44677e7	−1.18535	−0.592675	+	0.805442i	$0.701928\pi$
$968$	−1.77512e7	−0.608891
$969$	−1.63871e7	−0.560652
$970$	4.59098e7	1.56666
$971$	9.21316e6	0.313589	0.156794	−	0.987631i	$-0.449884\pi$
$971$	9.21316e6	0.313589	0.156794	+	0.987631i	$0.449884\pi$
$972$	208039.	0.00706284
$973$	2.34967e7	0.795655
$974$	1.04219e7	0.352004
$975$	1.06449e7	0.358617
$976$	8.13501e6	0.273359
$977$	3.66542e6	0.122854	0.0614268	−	0.998112i	$-0.480435\pi$
$977$	3.66542e6	0.122854	0.0614268	+	0.998112i	$0.480435\pi$
$978$	−1.87275e7	−0.626084
$979$	2.47566e7	0.825531
$980$	−610531.	−0.0203069
$981$	−6.54881e6	−0.217265
$982$	−3.40345e7	−1.12626
$983$	−7.59961e6	−0.250846	−0.125423	−	0.992103i	$-0.540029\pi$
$983$	−7.59961e6	−0.250846	−0.125423	+	0.992103i	$0.540029\pi$
$984$	2.02625e7	0.667121
$985$	4.35889e7	1.43148
$986$	−1.17739e7	−0.385682
$987$	2.46798e7	0.806398
$988$	5.02083e6	0.163638
$989$	−1.19120e7	−0.387252
$990$	−7.53025e6	−0.244186
$991$	3.53749e7	1.14422	0.572112	−	0.820175i	$-0.306124\pi$
$991$	3.53749e7	1.14422	0.572112	+	0.820175i	$0.306124\pi$
$992$	−9.61245e6	−0.310138
$993$	2.94763e7	0.948636
$994$	−1.26459e7	−0.405962
$995$	2.14005e7	0.685276
$996$	−3.23506e6	−0.103332
$997$	3.58278e7	1.14152	0.570759	−	0.821118i	$-0.306649\pi$
$997$	3.58278e7	1.14152	0.570759	+	0.821118i	$0.306649\pi$
$998$	1.89868e7	0.603429
$999$	−737904.	−0.0233930

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.c.1.3	✓	12
3.2	odd	2		531.6.a.c.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.c.1.3	✓	12	1.1	even	1	trivial
531.6.a.c.1.10		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)

\(f(q)\)	\(=\)	\(q-5.96013 q^{2} +9.00000 q^{3} +3.52316 q^{4} +65.6425 q^{5} -53.6412 q^{6} +119.026 q^{7} +169.726 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-5.96013 q^{2} +9.00000 q^{3} +3.52316 q^{4} +65.6425 q^{5} -53.6412 q^{6} +119.026 q^{7} +169.726 q^{8} +81.0000 q^{9} -391.238 q^{10} +237.620 q^{11} +31.7085 q^{12} +999.008 q^{13} -709.408 q^{14} +590.783 q^{15} -1124.33 q^{16} -1276.40 q^{17} -482.771 q^{18} +1426.51 q^{19} +231.269 q^{20} +1071.23 q^{21} -1416.25 q^{22} +546.573 q^{23} +1527.53 q^{24} +1183.94 q^{25} -5954.22 q^{26} +729.000 q^{27} +419.346 q^{28} -1547.67 q^{29} -3521.14 q^{30} -7569.31 q^{31} +1269.92 q^{32} +2138.58 q^{33} +7607.51 q^{34} +7813.14 q^{35} +285.376 q^{36} -1012.21 q^{37} -8502.16 q^{38} +8991.07 q^{39} +11141.2 q^{40} +13264.9 q^{41} -6384.67 q^{42} -21794.0 q^{43} +837.174 q^{44} +5317.05 q^{45} -3257.65 q^{46} +23038.8 q^{47} -10119.0 q^{48} -2639.91 q^{49} -7056.46 q^{50} -11487.6 q^{51} +3519.67 q^{52} +19051.5 q^{53} -4344.94 q^{54} +15598.0 q^{55} +20201.7 q^{56} +12838.6 q^{57} +9224.33 q^{58} -3481.00 q^{59} +2081.42 q^{60} -7235.44 q^{61} +45114.1 q^{62} +9641.07 q^{63} +28409.6 q^{64} +65577.4 q^{65} -12746.2 q^{66} +69873.8 q^{67} -4496.96 q^{68} +4919.16 q^{69} -46567.3 q^{70} +17826.0 q^{71} +13747.8 q^{72} +9089.91 q^{73} +6032.93 q^{74} +10655.5 q^{75} +5025.81 q^{76} +28282.9 q^{77} -53588.0 q^{78} +31488.7 q^{79} -73803.8 q^{80} +6561.00 q^{81} -79060.3 q^{82} -102025. q^{83} +3774.12 q^{84} -83786.1 q^{85} +129895. q^{86} -13929.0 q^{87} +40330.2 q^{88} +104185. q^{89} -31690.3 q^{90} +118908. q^{91} +1925.67 q^{92} -68123.8 q^{93} -137314. q^{94} +93639.5 q^{95} +11429.3 q^{96} -117345. q^{97} +15734.2 q^{98} +19247.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9}+O(q^{10}) \) 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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