LMFDB - Embedded newform 177.6.a.c.1.7

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			1.7
Root			$-0.689340$ 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)

$f(q)$	$=$	$q+2.68934 q^{2} +9.00000 q^{3} -24.7675 q^{4} -83.5049 q^{5} +24.2041 q^{6} -48.3401 q^{7} -152.667 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+2.68934 q^{2} +9.00000 q^{3} -24.7675 q^{4} -83.5049 q^{5} +24.2041 q^{6} -48.3401 q^{7} -152.667 q^{8} +81.0000 q^{9} -224.573 q^{10} +19.9993 q^{11} -222.907 q^{12} +611.920 q^{13} -130.003 q^{14} -751.544 q^{15} +381.985 q^{16} +1525.25 q^{17} +217.837 q^{18} -1272.41 q^{19} +2068.20 q^{20} -435.061 q^{21} +53.7850 q^{22} +3308.46 q^{23} -1374.00 q^{24} +3848.06 q^{25} +1645.66 q^{26} +729.000 q^{27} +1197.26 q^{28} -2171.14 q^{29} -2021.16 q^{30} +7163.58 q^{31} +5912.63 q^{32} +179.994 q^{33} +4101.91 q^{34} +4036.64 q^{35} -2006.16 q^{36} -5908.05 q^{37} -3421.93 q^{38} +5507.28 q^{39} +12748.4 q^{40} +2583.15 q^{41} -1170.03 q^{42} -5333.76 q^{43} -495.332 q^{44} -6763.89 q^{45} +8897.58 q^{46} -10520.3 q^{47} +3437.87 q^{48} -14470.2 q^{49} +10348.7 q^{50} +13727.2 q^{51} -15155.7 q^{52} +6041.06 q^{53} +1960.53 q^{54} -1670.04 q^{55} +7379.94 q^{56} -11451.7 q^{57} -5838.93 q^{58} -3481.00 q^{59} +18613.8 q^{60} +134.207 q^{61} +19265.3 q^{62} -3915.55 q^{63} +3677.55 q^{64} -51098.3 q^{65} +484.065 q^{66} +49806.2 q^{67} -37776.5 q^{68} +29776.2 q^{69} +10855.9 q^{70} +64703.4 q^{71} -12366.0 q^{72} +43618.4 q^{73} -15888.8 q^{74} +34632.5 q^{75} +31514.3 q^{76} -966.770 q^{77} +14810.9 q^{78} +74841.5 q^{79} -31897.6 q^{80} +6561.00 q^{81} +6946.96 q^{82} +5270.76 q^{83} +10775.4 q^{84} -127366. q^{85} -14344.3 q^{86} -19540.2 q^{87} -3053.23 q^{88} +85402.3 q^{89} -18190.4 q^{90} -29580.3 q^{91} -81942.2 q^{92} +64472.3 q^{93} -28292.8 q^{94} +106252. q^{95} +53213.7 q^{96} +47381.9 q^{97} -38915.4 q^{98} +1619.94 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.68934	0.475413	0.237706	−	0.971337i	$-0.423604\pi$
$2$	2.68934	0.475413	0.237706	+	0.971337i	$0.423604\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−24.7675	−0.773983
$5$	−83.5049	−1.49378	−0.746890	−	0.664948i	$-0.768454\pi$
$5$	−83.5049	−1.49378	−0.746890	+	0.664948i	$0.768454\pi$
$6$	24.2041	0.274480
$7$	−48.3401	−0.372875	−0.186437	−	0.982467i	$-0.559694\pi$
$7$	−48.3401	−0.372875	−0.186437	+	0.982467i	$0.559694\pi$
$8$	−152.667	−0.843374
$9$	81.0000	0.333333
$10$	−224.573	−0.710162
$11$	19.9993	0.0498349	0.0249174	−	0.999690i	$-0.492068\pi$
$11$	19.9993	0.0498349	0.0249174	+	0.999690i	$0.492068\pi$
$12$	−222.907	−0.446859
$13$	611.920	1.00424	0.502119	−	0.864799i	$-0.332554\pi$
$13$	611.920	1.00424	0.502119	+	0.864799i	$0.332554\pi$
$14$	−130.003	−0.177269
$15$	−751.544	−0.862434
$16$	381.985	0.373032
$17$	1525.25	1.28002	0.640012	−	0.768365i	$-0.278929\pi$
$17$	1525.25	1.28002	0.640012	+	0.768365i	$0.278929\pi$
$18$	217.837	0.158471
$19$	−1272.41	−0.808615	−0.404308	−	0.914623i	$-0.632487\pi$
$19$	−1272.41	−0.808615	−0.404308	+	0.914623i	$0.632487\pi$
$20$	2068.20	1.15616
$21$	−435.061	−0.215279
$22$	53.7850	0.0236921
$23$	3308.46	1.30409	0.652044	−	0.758181i	$-0.273912\pi$
$23$	3308.46	1.30409	0.652044	+	0.758181i	$0.273912\pi$
$24$	−1374.00	−0.486922
$25$	3848.06	1.23138
$26$	1645.66	0.477427
$27$	729.000	0.192450
$28$	1197.26	0.288599
$29$	−2171.14	−0.479394	−0.239697	−	0.970848i	$-0.577048\pi$
$29$	−2171.14	−0.479394	−0.239697	+	0.970848i	$0.577048\pi$
$30$	−2021.16	−0.410012
$31$	7163.58	1.33883	0.669416	−	0.742888i	$-0.266544\pi$
$31$	7163.58	1.33883	0.669416	+	0.742888i	$0.266544\pi$
$32$	5912.63	1.02072
$33$	179.994	0.0287722
$34$	4101.91	0.608540
$35$	4036.64	0.556993
$36$	−2006.16	−0.257994
$37$	−5908.05	−0.709480	−0.354740	−	0.934965i	$-0.615431\pi$
$37$	−5908.05	−0.709480	−0.354740	+	0.934965i	$0.615431\pi$
$38$	−3421.93	−0.384426
$39$	5507.28	0.579797
$40$	12748.4	1.25982
$41$	2583.15	0.239988	0.119994	−	0.992775i	$-0.461712\pi$
$41$	2583.15	0.239988	0.119994	+	0.992775i	$0.461712\pi$
$42$	−1170.03	−0.102346
$43$	−5333.76	−0.439908	−0.219954	−	0.975510i	$-0.570591\pi$
$43$	−5333.76	−0.439908	−0.219954	+	0.975510i	$0.570591\pi$
$44$	−495.332	−0.0385713
$45$	−6763.89	−0.497927
$46$	8897.58	0.619980
$47$	−10520.3	−0.694680	−0.347340	−	0.937739i	$-0.612915\pi$
$47$	−10520.3	−0.694680	−0.347340	+	0.937739i	$0.612915\pi$
$48$	3437.87	0.215370
$49$	−14470.2	−0.860965
$50$	10348.7	0.585413
$51$	13727.2	0.739022
$52$	−15155.7	−0.777262
$53$	6041.06	0.295409	0.147705	−	0.989032i	$-0.452812\pi$
$53$	6041.06	0.295409	0.147705	+	0.989032i	$0.452812\pi$
$54$	1960.53	0.0914932
$55$	−1670.04	−0.0744424
$56$	7379.94	0.314473
$57$	−11451.7	−0.466854
$58$	−5838.93	−0.227910
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	18613.8	0.667509
$61$	134.207	0.00461798	0.00230899	−	0.999997i	$-0.499265\pi$
$61$	134.207	0.00461798	0.00230899	+	0.999997i	$0.499265\pi$
$62$	19265.3	0.636498
$63$	−3915.55	−0.124292
$64$	3677.55	0.112230
$65$	−51098.3	−1.50011
$66$	484.065	0.0136787
$67$	49806.2	1.35549	0.677745	−	0.735297i	$-0.262957\pi$
$67$	49806.2	1.35549	0.677745	+	0.735297i	$0.262957\pi$
$68$	−37776.5	−0.990717
$69$	29776.2	0.752915
$70$	10855.9	0.264801
$71$	64703.4	1.52329	0.761643	−	0.647997i	$-0.224393\pi$
$71$	64703.4	1.52329	0.761643	+	0.647997i	$0.224393\pi$
$72$	−12366.0	−0.281125
$73$	43618.4	0.957993	0.478996	−	0.877817i	$-0.341001\pi$
$73$	43618.4	0.957993	0.478996	+	0.877817i	$0.341001\pi$
$74$	−15888.8	−0.337296
$75$	34632.5	0.710937
$76$	31514.3	0.625854
$77$	−966.770	−0.0185822
$78$	14810.9	0.275643
$79$	74841.5	1.34920	0.674598	−	0.738185i	$-0.264317\pi$
$79$	74841.5	1.34920	0.674598	+	0.738185i	$0.264317\pi$
$80$	−31897.6	−0.557228
$81$	6561.00	0.111111
$82$	6946.96	0.114093
$83$	5270.76	0.0839804	0.0419902	−	0.999118i	$-0.486630\pi$
$83$	5270.76	0.0839804	0.0419902	+	0.999118i	$0.486630\pi$
$84$	10775.4	0.166622
$85$	−127366.	−1.91208
$86$	−14344.3	−0.209138
$87$	−19540.2	−0.276778
$88$	−3053.23	−0.0420294
$89$	85402.3	1.14286	0.571432	−	0.820649i	$-0.306388\pi$
$89$	85402.3	1.14286	0.571432	+	0.820649i	$0.306388\pi$
$90$	−18190.4	−0.236721
$91$	−29580.3	−0.374455
$92$	−81942.2	−1.00934
$93$	64472.3	0.772975
$94$	−28292.8	−0.330260
$95$	106252.	1.20789
$96$	53213.7	0.589312
$97$	47381.9	0.511309	0.255654	−	0.966768i	$-0.417709\pi$
$97$	47381.9	0.511309	0.255654	+	0.966768i	$0.417709\pi$
$98$	−38915.4	−0.409313
$99$	1619.94	0.0166116
$100$	−95306.6	−0.953066
$101$	111845.	1.09097	0.545484	−	0.838121i	$-0.316346\pi$
$101$	111845.	1.09097	0.545484	+	0.838121i	$0.316346\pi$
$102$	36917.2	0.351341
$103$	−161601.	−1.50089	−0.750447	−	0.660930i	$-0.770162\pi$
$103$	−161601.	−1.50089	−0.750447	+	0.660930i	$0.770162\pi$
$104$	−93420.0	−0.846947
$105$	36329.7	0.321580
$106$	16246.5	0.140441
$107$	−181209.	−1.53010	−0.765052	−	0.643969i	$-0.777287\pi$
$107$	−181209.	−1.53010	−0.765052	+	0.643969i	$0.777287\pi$
$108$	−18055.5	−0.148953
$109$	−69858.3	−0.563186	−0.281593	−	0.959534i	$-0.590863\pi$
$109$	−69858.3	−0.563186	−0.281593	+	0.959534i	$0.590863\pi$
$110$	−4491.30	−0.0353908
$111$	−53172.5	−0.409618
$112$	−18465.2	−0.139094
$113$	152141.	1.12086	0.560428	−	0.828203i	$-0.310637\pi$
$113$	152141.	1.12086	0.560428	+	0.828203i	$0.310637\pi$
$114$	−30797.4	−0.221948
$115$	−276273.	−1.94802
$116$	53773.6	0.371043
$117$	49565.5	0.334746
$118$	−9361.59	−0.0618934
$119$	−73730.7	−0.477289
$120$	114736.	0.727355
$121$	−160651.	−0.997516
$122$	360.929	0.00219545
$123$	23248.3	0.138557
$124$	−177424.	−1.03623
$125$	−60379.0	−0.345630
$126$	−10530.2	−0.0590898
$127$	275370.	1.51498	0.757491	−	0.652846i	$-0.226425\pi$
$127$	275370.	1.51498	0.757491	+	0.652846i	$0.226425\pi$
$128$	−179314.	−0.967363
$129$	−48003.8	−0.253981
$130$	−137421.	−0.713171
$131$	10248.5	0.0521775	0.0260888	−	0.999660i	$-0.491695\pi$
$131$	10248.5	0.0521775	0.0260888	+	0.999660i	$0.491695\pi$
$132$	−4457.99	−0.0222692
$133$	61508.3	0.301512
$134$	133946.	0.644417
$135$	−60875.0	−0.287478
$136$	−232855.	−1.07954
$137$	391127.	1.78039	0.890197	−	0.455576i	$-0.150567\pi$
$137$	391127.	1.78039	0.890197	+	0.455576i	$0.150567\pi$
$138$	80078.2	0.357945
$139$	−45851.0	−0.201285	−0.100643	−	0.994923i	$-0.532090\pi$
$139$	−45851.0	−0.201285	−0.100643	+	0.994923i	$0.532090\pi$
$140$	−99977.2	−0.431103
$141$	−94683.0	−0.401074
$142$	174009.	0.724189
$143$	12238.0	0.0500460
$144$	30940.8	0.124344
$145$	181301.	0.716109
$146$	117305.	0.455442
$147$	−130232.	−0.497078
$148$	146327.	0.549125
$149$	188439.	0.695354	0.347677	−	0.937614i	$-0.386971\pi$
$149$	188439.	0.695354	0.347677	+	0.937614i	$0.386971\pi$
$150$	93138.7	0.337988
$151$	−70211.4	−0.250591	−0.125295	−	0.992119i	$-0.539988\pi$
$151$	−70211.4	−0.250591	−0.125295	+	0.992119i	$0.539988\pi$
$152$	194254.	0.681965
$153$	123545.	0.426675
$154$	−2599.97	−0.00883419
$155$	−598194.	−1.99992
$156$	−136401.	−0.448753
$157$	−409601.	−1.32621	−0.663105	−	0.748527i	$-0.730762\pi$
$157$	−409601.	−1.32621	−0.663105	+	0.748527i	$0.730762\pi$
$158$	201274.	0.641425
$159$	54369.6	0.170554
$160$	−493733.	−1.52473
$161$	−159932.	−0.486261
$162$	17644.8	0.0528236
$163$	−447613.	−1.31957	−0.659787	−	0.751452i	$-0.729354\pi$
$163$	−447613.	−1.31957	−0.659787	+	0.751452i	$0.729354\pi$
$164$	−63978.0	−0.185747
$165$	−15030.4	−0.0429793
$166$	14174.9	0.0399254
$167$	−64777.2	−0.179734	−0.0898672	−	0.995954i	$-0.528644\pi$
$167$	−64777.2	−0.179734	−0.0898672	+	0.995954i	$0.528644\pi$
$168$	66419.5	0.181561
$169$	3153.10	0.00849222
$170$	−342529.	−0.909025
$171$	−103065.	−0.269538
$172$	132104.	0.340481
$173$	436181.	1.10803	0.554014	−	0.832507i	$-0.313095\pi$
$173$	436181.	1.10803	0.554014	+	0.832507i	$0.313095\pi$
$174$	−52550.4	−0.131584
$175$	−186016.	−0.459150
$176$	7639.44	0.0185900
$177$	−31329.0	−0.0751646
$178$	229676.	0.543332
$179$	248687.	0.580123	0.290061	−	0.957008i	$-0.406324\pi$
$179$	248687.	0.580123	0.290061	+	0.957008i	$0.406324\pi$
$180$	167524.	0.385387
$181$	−509737.	−1.15651	−0.578256	−	0.815856i	$-0.696266\pi$
$181$	−509737.	−1.15651	−0.578256	+	0.815856i	$0.696266\pi$
$182$	−79551.5	−0.178020
$183$	1207.87	0.00266619
$184$	−505093.	−1.09983
$185$	493351.	1.05981
$186$	173388.	0.367482
$187$	30503.9	0.0637899
$188$	260562.	0.537671
$189$	−35240.0	−0.0717598
$190$	285748.	0.574248
$191$	582176.	1.15471	0.577353	−	0.816495i	$-0.304086\pi$
$191$	582176.	1.15471	0.577353	+	0.816495i	$0.304086\pi$
$192$	33097.9	0.0647960
$193$	33922.3	0.0655529	0.0327765	−	0.999463i	$-0.489565\pi$
$193$	33922.3	0.0655529	0.0327765	+	0.999463i	$0.489565\pi$
$194$	127426.	0.243083
$195$	−459885.	−0.866089
$196$	358391.	0.666372
$197$	51381.6	0.0943283	0.0471642	−	0.998887i	$-0.484982\pi$
$197$	51381.6	0.0943283	0.0471642	+	0.998887i	$0.484982\pi$
$198$	4356.58	0.00789738
$199$	293133.	0.524725	0.262363	−	0.964969i	$-0.415498\pi$
$199$	293133.	0.524725	0.262363	+	0.964969i	$0.415498\pi$
$200$	−587472.	−1.03851
$201$	448256.	0.782593
$202$	300789.	0.518660
$203$	104953.	0.178754
$204$	−339989.	−0.571991
$205$	−215705.	−0.358489
$206$	−434599.	−0.713544
$207$	267985.	0.434696
$208$	233744.	0.374613
$209$	−25447.3	−0.0402972
$210$	97703.0	0.152883
$211$	−257285.	−0.397839	−0.198920	−	0.980016i	$-0.563743\pi$
$211$	−257285.	−0.397839	−0.198920	+	0.980016i	$0.563743\pi$
$212$	−149622.	−0.228642
$213$	582331.	0.879469
$214$	−487333.	−0.727430
$215$	445395.	0.657126
$216$	−111294.	−0.162307
$217$	−346289.	−0.499217
$218$	−187873.	−0.267746
$219$	392565.	0.553098
$220$	41362.6	0.0576171
$221$	933330.	1.28545
$222$	−142999.	−0.194738
$223$	−269708.	−0.363188	−0.181594	−	0.983374i	$-0.558126\pi$
$223$	−269708.	−0.363188	−0.181594	+	0.983374i	$0.558126\pi$
$224$	−285817.	−0.380600
$225$	311693.	0.410460
$226$	409159.	0.532869
$227$	474834.	0.611614	0.305807	−	0.952094i	$-0.401074\pi$
$227$	474834.	0.611614	0.305807	+	0.952094i	$0.401074\pi$
$228$	283628.	0.361337
$229$	735574.	0.926910	0.463455	−	0.886120i	$-0.346610\pi$
$229$	735574.	0.926910	0.463455	+	0.886120i	$0.346610\pi$
$230$	−742991.	−0.926113
$231$	−8700.93	−0.0107284
$232$	331461.	0.404308
$233$	147473.	0.177960	0.0889800	−	0.996033i	$-0.471639\pi$
$233$	147473.	0.177960	0.0889800	+	0.996033i	$0.471639\pi$
$234$	133299.	0.159142
$235$	878499.	1.03770
$236$	86215.5	0.100764
$237$	673574.	0.778959
$238$	−198287.	−0.226909
$239$	−951198.	−1.07715	−0.538575	−	0.842577i	$-0.681037\pi$
$239$	−951198.	−1.07715	−0.538575	+	0.842577i	$0.681037\pi$
$240$	−287078.	−0.321716
$241$	341256.	0.378475	0.189238	−	0.981931i	$-0.439398\pi$
$241$	341256.	0.378475	0.189238	+	0.981931i	$0.439398\pi$
$242$	−432045.	−0.474232
$243$	59049.0	0.0641500
$244$	−3323.98	−0.00357424
$245$	1.20833e6	1.28609
$246$	62522.7	0.0658718
$247$	−778611.	−0.812042
$248$	−1.09364e6	−1.12914
$249$	47436.8	0.0484861
$250$	−162380.	−0.164317
$251$	1.54946e6	1.55238	0.776188	−	0.630502i	$-0.217151\pi$
$251$	1.54946e6	1.55238	0.776188	+	0.630502i	$0.217151\pi$
$252$	96978.2	0.0961995
$253$	66167.0	0.0649890
$254$	740564.	0.720242
$255$	−1.14629e6	−1.10394
$256$	−599918.	−0.572126
$257$	−819098.	−0.773576	−0.386788	−	0.922169i	$-0.626416\pi$
$257$	−819098.	−0.773576	−0.386788	+	0.922169i	$0.626416\pi$
$258$	−129099.	−0.120746
$259$	285596.	0.264547
$260$	1.26557e6	1.16106
$261$	−175862.	−0.159798
$262$	27561.8	0.0248058
$263$	1.22245e6	1.08979	0.544894	−	0.838505i	$-0.316570\pi$
$263$	1.22245e6	1.08979	0.544894	+	0.838505i	$0.316570\pi$
$264$	−27479.1	−0.0242657
$265$	−504458.	−0.441276
$266$	165417.	0.143343
$267$	768621.	0.659833
$268$	−1.23357e6	−1.04913
$269$	−1.60210e6	−1.34992	−0.674961	−	0.737853i	$-0.735840\pi$
$269$	−1.60210e6	−1.34992	−0.674961	+	0.737853i	$0.735840\pi$
$270$	−163714.	−0.136671
$271$	1.62601e6	1.34493	0.672465	−	0.740129i	$-0.265235\pi$
$271$	1.62601e6	1.34493	0.672465	+	0.740129i	$0.265235\pi$
$272$	582622.	0.477490
$273$	−266223.	−0.216191
$274$	1.05187e6	0.846422
$275$	76958.6	0.0613656
$276$	−737480.	−0.582743
$277$	1.36348e6	1.06770	0.533851	−	0.845579i	$-0.320744\pi$
$277$	1.36348e6	1.06770	0.533851	+	0.845579i	$0.320744\pi$
$278$	−123309.	−0.0956935
$279$	580250.	0.446277
$280$	−616261.	−0.469753
$281$	1.74237e6	1.31636	0.658179	−	0.752862i	$-0.271327\pi$
$281$	1.74237e6	1.31636	0.658179	+	0.752862i	$0.271327\pi$
$282$	−254635.	−0.190676
$283$	−1.23647e6	−0.917735	−0.458868	−	0.888505i	$-0.651745\pi$
$283$	−1.23647e6	−0.917735	−0.458868	+	0.888505i	$0.651745\pi$
$284$	−1.60254e6	−1.17900
$285$	956269.	0.697378
$286$	32912.1	0.0237925
$287$	−124870.	−0.0894854
$288$	478923.	0.340239
$289$	906525.	0.638462
$290$	487579.	0.340447
$291$	426437.	0.295204
$292$	−1.08032e6	−0.741470
$293$	2.68981e6	1.83042	0.915212	−	0.402972i	$-0.132023\pi$
$293$	2.68981e6	1.83042	0.915212	+	0.402972i	$0.132023\pi$
$294$	−350238.	−0.236317
$295$	290680.	0.194474
$296$	901964.	0.598357
$297$	14579.5	0.00959073
$298$	506777.	0.330580
$299$	2.02451e6	1.30961
$300$	−857760.	−0.550253
$301$	257835.	0.164031
$302$	−188822.	−0.119134
$303$	1.00660e6	0.629871
$304$	−486040.	−0.301640
$305$	−11207.0	−0.00689825
$306$	332255.	0.202847
$307$	−1.87388e6	−1.13474	−0.567369	−	0.823463i	$-0.692039\pi$
$307$	−1.87388e6	−1.13474	−0.567369	+	0.823463i	$0.692039\pi$
$308$	23944.4	0.0143823
$309$	−1.45441e6	−0.866542
$310$	−1.60875e6	−0.950788
$311$	−1.66629e6	−0.976898	−0.488449	−	0.872592i	$-0.662437\pi$
$311$	−1.66629e6	−0.976898	−0.488449	+	0.872592i	$0.662437\pi$
$312$	−840780.	−0.488985
$313$	−1.52243e6	−0.878368	−0.439184	−	0.898397i	$-0.644732\pi$
$313$	−1.52243e6	−0.878368	−0.439184	+	0.898397i	$0.644732\pi$
$314$	−1.10156e6	−0.630497
$315$	326968.	0.185664
$316$	−1.85363e6	−1.04425
$317$	−1.08948e6	−0.608933	−0.304466	−	0.952523i	$-0.598478\pi$
$317$	−1.08948e6	−0.608933	−0.304466	+	0.952523i	$0.598478\pi$
$318$	146218.	0.0810837
$319$	−43421.3	−0.0238905
$320$	−307093.	−0.167647
$321$	−1.63088e6	−0.883405
$322$	−430110.	−0.231175
$323$	−1.94074e6	−1.03505
$324$	−162499.	−0.0859981
$325$	2.35471e6	1.23660
$326$	−1.20378e6	−0.627342
$327$	−628725.	−0.325156
$328$	−394361.	−0.202400
$329$	508555.	0.259029
$330$	−40421.7	−0.0204329
$331$	3.01617e6	1.51317	0.756583	−	0.653898i	$-0.226867\pi$
$331$	3.01617e6	1.51317	0.756583	+	0.653898i	$0.226867\pi$
$332$	−130543.	−0.0649994
$333$	−478552.	−0.236493
$334$	−174208.	−0.0854480
$335$	−4.15906e6	−2.02480
$336$	−166187.	−0.0803061
$337$	−2.89211e6	−1.38720	−0.693602	−	0.720359i	$-0.743977\pi$
$337$	−2.89211e6	−1.38720	−0.693602	+	0.720359i	$0.743977\pi$
$338$	8479.77	0.00403731
$339$	1.36927e6	0.647127
$340$	3.15452e6	1.47991
$341$	143267.	0.0667205
$342$	−277177.	−0.128142
$343$	1.51195e6	0.693906
$344$	814289.	0.371007
$345$	−2.48645e6	−1.12469
$346$	1.17304e6	0.526771
$347$	−2.45959e6	−1.09658	−0.548289	−	0.836289i	$-0.684721\pi$
$347$	−2.45959e6	−1.09658	−0.548289	+	0.836289i	$0.684721\pi$
$348$	483962.	0.214222
$349$	1.57913e6	0.693992	0.346996	−	0.937867i	$-0.387202\pi$
$349$	1.57913e6	0.693992	0.346996	+	0.937867i	$0.387202\pi$
$350$	−500260.	−0.218286
$351$	446090.	0.193266
$352$	118249.	0.0508674
$353$	−932705.	−0.398389	−0.199195	−	0.979960i	$-0.563833\pi$
$353$	−932705.	−0.398389	−0.199195	+	0.979960i	$0.563833\pi$
$354$	−84254.3	−0.0357342
$355$	−5.40305e6	−2.27545
$356$	−2.11520e6	−0.884557
$357$	−663576.	−0.275563
$358$	668803.	0.275798
$359$	−94646.8	−0.0387587	−0.0193794	−	0.999812i	$-0.506169\pi$
$359$	−94646.8	−0.0387587	−0.0193794	+	0.999812i	$0.506169\pi$
$360$	1.03262e6	0.419938
$361$	−857080.	−0.346141
$362$	−1.37086e6	−0.549820
$363$	−1.44586e6	−0.575916
$364$	732629.	0.289821
$365$	−3.64235e6	−1.43103
$366$	3248.36	0.00126754
$367$	3.17308e6	1.22975	0.614873	−	0.788626i	$-0.289207\pi$
$367$	3.17308e6	1.22975	0.614873	+	0.788626i	$0.289207\pi$
$368$	1.26378e6	0.486467
$369$	209235.	0.0799960
$370$	1.32679e6	0.503845
$371$	−292026.	−0.110151
$372$	−1.59681e6	−0.598269
$373$	−2.35041e6	−0.874723	−0.437362	−	0.899286i	$-0.644087\pi$
$373$	−2.35041e6	−0.874723	−0.437362	+	0.899286i	$0.644087\pi$
$374$	82035.4	0.0303265
$375$	−543411.	−0.199549
$376$	1.60611e6	0.585875
$377$	−1.32856e6	−0.481425
$378$	−94772.2	−0.0341155
$379$	998577.	0.357095	0.178547	−	0.983931i	$-0.442860\pi$
$379$	998577.	0.357095	0.178547	+	0.983931i	$0.442860\pi$
$380$	−2.63159e6	−0.934889
$381$	2.47833e6	0.874675
$382$	1.56567e6	0.548961
$383$	−3.24360e6	−1.12987	−0.564937	−	0.825134i	$-0.691100\pi$
$383$	−3.24360e6	−1.12987	−0.564937	+	0.825134i	$0.691100\pi$
$384$	−1.61383e6	−0.558507
$385$	80730.0	0.0277577
$386$	91228.6	0.0311647
$387$	−432034.	−0.146636
$388$	−1.17353e6	−0.395744
$389$	−434588.	−0.145614	−0.0728070	−	0.997346i	$-0.523196\pi$
$389$	−434588.	−0.145614	−0.0728070	+	0.997346i	$0.523196\pi$
$390$	−1.23679e6	−0.411749
$391$	5.04623e6	1.66926
$392$	2.20913e6	0.726115
$393$	92236.8	0.0301247
$394$	138183.	0.0448449
$395$	−6.24963e6	−2.01540
$396$	−40121.9	−0.0128571
$397$	2.29030e6	0.729315	0.364658	−	0.931142i	$-0.381186\pi$
$397$	2.29030e6	0.729315	0.364658	+	0.931142i	$0.381186\pi$
$398$	788334.	0.249461
$399$	553575.	0.174078
$400$	1.46990e6	0.459344
$401$	1.95111e6	0.605928	0.302964	−	0.953002i	$-0.402024\pi$
$401$	1.95111e6	0.605928	0.302964	+	0.953002i	$0.402024\pi$
$402$	1.20551e6	0.372054
$403$	4.38354e6	1.34450
$404$	−2.77011e6	−0.844391
$405$	−547875.	−0.165976
$406$	282255.	0.0849818
$407$	−118157.	−0.0353568
$408$	−2.09570e6	−0.623272
$409$	1.46908e6	0.434247	0.217123	−	0.976144i	$-0.430333\pi$
$409$	1.46908e6	0.434247	0.217123	+	0.976144i	$0.430333\pi$
$410$	−580105.	−0.170430
$411$	3.52014e6	1.02791
$412$	4.00244e6	1.16167
$413$	168272.	0.0485441
$414$	720704.	0.206660
$415$	−440134.	−0.125448
$416$	3.61806e6	1.02504
$417$	−412659.	−0.116212
$418$	−68436.3	−0.0191578
$419$	−3.97963e6	−1.10741	−0.553703	−	0.832714i	$-0.686786\pi$
$419$	−3.97963e6	−1.10741	−0.553703	+	0.832714i	$0.686786\pi$
$420$	−899795.	−0.248897
$421$	828909.	0.227930	0.113965	−	0.993485i	$-0.463645\pi$
$421$	828909.	0.227930	0.113965	+	0.993485i	$0.463645\pi$
$422$	−691926.	−0.189138
$423$	−852147.	−0.231560
$424$	−922271.	−0.249140
$425$	5.86925e6	1.57620
$426$	1.56608e6	0.418111
$427$	−6487.61	−0.00172193
$428$	4.48809e6	1.18427
$429$	110142.	0.0288941
$430$	1.19782e6	0.312406
$431$	6.65314e6	1.72518	0.862588	−	0.505907i	$-0.168842\pi$
$431$	6.65314e6	1.72518	0.862588	+	0.505907i	$0.168842\pi$
$432$	278467.	0.0717901
$433$	−532462.	−0.136480	−0.0682400	−	0.997669i	$-0.521738\pi$
$433$	−532462.	−0.136480	−0.0682400	+	0.997669i	$0.521738\pi$
$434$	−931288.	−0.237334
$435$	1.63171e6	0.413446
$436$	1.73021e6	0.435896
$437$	−4.20971e6	−1.05450
$438$	1.05574e6	0.262950
$439$	4.04363e6	1.00141	0.500703	−	0.865619i	$-0.333075\pi$
$439$	4.04363e6	1.00141	0.500703	+	0.865619i	$0.333075\pi$
$440$	254960.	0.0627827
$441$	−1.17209e6	−0.286988
$442$	2.51004e6	0.611118
$443$	1.66963e6	0.404214	0.202107	−	0.979363i	$-0.435221\pi$
$443$	1.66963e6	0.404214	0.202107	+	0.979363i	$0.435221\pi$
$444$	1.31695e6	0.317038
$445$	−7.13151e6	−1.70719
$446$	−725336.	−0.172664
$447$	1.69595e6	0.401463
$448$	−177773.	−0.0418477
$449$	−4.07437e6	−0.953772	−0.476886	−	0.878965i	$-0.658235\pi$
$449$	−4.07437e6	−0.953772	−0.476886	+	0.878965i	$0.658235\pi$
$450$	838248.	0.195138
$451$	51661.2	0.0119598
$452$	−3.76814e6	−0.867524
$453$	−631902.	−0.144679
$454$	1.27699e6	0.290769
$455$	2.47010e6	0.559353
$456$	1.74829e6	0.393733
$457$	−6.80572e6	−1.52435	−0.762173	−	0.647373i	$-0.775868\pi$
$457$	−6.80572e6	−1.52435	−0.762173	+	0.647373i	$0.775868\pi$
$458$	1.97821e6	0.440665
$459$	1.11191e6	0.246341
$460$	6.84257e6	1.50773
$461$	6.87814e6	1.50737	0.753683	−	0.657239i	$-0.228276\pi$
$461$	6.87814e6	1.50737	0.753683	+	0.657239i	$0.228276\pi$
$462$	−23399.8	−0.00510042
$463$	−2.39491e6	−0.519202	−0.259601	−	0.965716i	$-0.583591\pi$
$463$	−2.39491e6	−0.519202	−0.259601	+	0.965716i	$0.583591\pi$
$464$	−829343.	−0.178829
$465$	−5.38375e6	−1.15465
$466$	396605.	0.0846044
$467$	5.32072e6	1.12896	0.564480	−	0.825447i	$-0.309077\pi$
$467$	5.32072e6	1.12896	0.564480	+	0.825447i	$0.309077\pi$
$468$	−1.22761e6	−0.259087
$469$	−2.40764e6	−0.505428
$470$	2.36258e6	0.493336
$471$	−3.68641e6	−0.765687
$472$	531434.	0.109798
$473$	−106671.	−0.0219228
$474$	1.81147e6	0.370327
$475$	−4.89630e6	−0.995712
$476$	1.82612e6	0.369413
$477$	489326.	0.0984697
$478$	−2.55810e6	−0.512091
$479$	−476392.	−0.0948693	−0.0474347	−	0.998874i	$-0.515105\pi$
$479$	−476392.	−0.0948693	−0.0474347	+	0.998874i	$0.515105\pi$
$480$	−4.44360e6	−0.880302
$481$	−3.61526e6	−0.712486
$482$	917753.	0.179932
$483$	−1.43938e6	−0.280743
$484$	3.97892e6	0.772061
$485$	−3.95662e6	−0.763783
$486$	158803.	0.0304977
$487$	−3.24904e6	−0.620774	−0.310387	−	0.950610i	$-0.600459\pi$
$487$	−3.24904e6	−0.620774	−0.310387	+	0.950610i	$0.600459\pi$
$488$	−20489.0	−0.00389468
$489$	−4.02852e6	−0.761857
$490$	3.24962e6	0.611424
$491$	−1.12407e6	−0.210421	−0.105211	−	0.994450i	$-0.533552\pi$
$491$	−1.12407e6	−0.210421	−0.105211	+	0.994450i	$0.533552\pi$
$492$	−575802.	−0.107241
$493$	−3.31153e6	−0.613636
$494$	−2.09395e6	−0.386055
$495$	−135273.	−0.0248141
$496$	2.73638e6	0.499428
$497$	−3.12777e6	−0.567994
$498$	127574.	0.0230509
$499$	876516.	0.157583	0.0787913	−	0.996891i	$-0.474894\pi$
$499$	876516.	0.157583	0.0787913	+	0.996891i	$0.474894\pi$
$500$	1.49543e6	0.267512
$501$	−582995.	−0.103770
$502$	4.16703e6	0.738019
$503$	−1.53970e6	−0.271342	−0.135671	−	0.990754i	$-0.543319\pi$
$503$	−1.53970e6	−0.271342	−0.135671	+	0.990754i	$0.543319\pi$
$504$	597775.	0.104824
$505$	−9.33958e6	−1.62967
$506$	177946.	0.0308966
$507$	28377.9	0.00490299
$508$	−6.82022e6	−1.17257
$509$	3.23654e6	0.553715	0.276858	−	0.960911i	$-0.410707\pi$
$509$	3.23654e6	0.553715	0.276858	+	0.960911i	$0.410707\pi$
$510$	−3.08277e6	−0.524826
$511$	−2.10852e6	−0.357211
$512$	4.12467e6	0.695367
$513$	−927585.	−0.155618
$514$	−2.20283e6	−0.367768
$515$	1.34944e7	2.24201
$516$	1.18893e6	0.196577
$517$	−210400.	−0.0346193
$518$	768065.	0.125769
$519$	3.92562e6	0.639721
$520$	7.80102e6	1.26515
$521$	8.43608e6	1.36159	0.680795	−	0.732474i	$-0.261634\pi$
$521$	8.43608e6	1.36159	0.680795	+	0.732474i	$0.261634\pi$
$522$	−472953.	−0.0759700
$523$	1.04546e7	1.67129	0.835645	−	0.549270i	$-0.185094\pi$
$523$	1.04546e7	1.67129	0.835645	+	0.549270i	$0.185094\pi$
$524$	−253830.	−0.0403845
$525$	−1.67414e6	−0.265090
$526$	3.28759e6	0.518099
$527$	1.09262e7	1.71374
$528$	68755.0	0.0107330
$529$	4.50958e6	0.700644
$530$	−1.35666e6	−0.209788
$531$	−281961.	−0.0433963
$532$	−1.52340e6	−0.233365
$533$	1.58068e6	0.241005
$534$	2.06708e6	0.313693
$535$	1.51318e7	2.28564
$536$	−7.60376e6	−1.14318
$537$	2.23818e6	0.334934
$538$	−4.30859e6	−0.641770
$539$	−289395.	−0.0429061
$540$	1.50772e6	0.222503
$541$	−7.11362e6	−1.04496	−0.522478	−	0.852653i	$-0.674992\pi$
$541$	−7.11362e6	−1.04496	−0.522478	+	0.852653i	$0.674992\pi$
$542$	4.37289e6	0.639397
$543$	−4.58764e6	−0.667712
$544$	9.01823e6	1.30654
$545$	5.83351e6	0.841276
$546$	−715963.	−0.102780
$547$	−3.99245e6	−0.570520	−0.285260	−	0.958450i	$-0.592080\pi$
$547$	−3.99245e6	−0.570520	−0.285260	+	0.958450i	$0.592080\pi$
$548$	−9.68721e6	−1.37799
$549$	10870.8	0.00153933
$550$	206968.	0.0291740
$551$	2.76257e6	0.387645
$552$	−4.54584e6	−0.634989
$553$	−3.61785e6	−0.503081
$554$	3.66686e6	0.507599
$555$	4.44016e6	0.611880
$556$	1.13561e6	0.155791
$557$	−1.13329e6	−0.154776	−0.0773881	−	0.997001i	$-0.524658\pi$
$557$	−1.13329e6	−0.154776	−0.0773881	+	0.997001i	$0.524658\pi$
$558$	1.56049e6	0.212166
$559$	−3.26383e6	−0.441772
$560$	1.54193e6	0.207776
$561$	274535.	0.0368291
$562$	4.68582e6	0.625813
$563$	−1.33775e7	−1.77871	−0.889353	−	0.457222i	$-0.848844\pi$
$563$	−1.33775e7	−1.77871	−0.889353	+	0.457222i	$0.848844\pi$
$564$	2.34506e6	0.310424
$565$	−1.27045e7	−1.67431
$566$	−3.32529e6	−0.436303
$567$	−317160.	−0.0414305
$568$	−9.87807e6	−1.28470
$569$	−9.96665e6	−1.29053	−0.645266	−	0.763958i	$-0.723253\pi$
$569$	−9.96665e6	−1.29053	−0.645266	+	0.763958i	$0.723253\pi$
$570$	2.57173e6	0.331542
$571$	−5.30435e6	−0.680835	−0.340417	−	0.940274i	$-0.610568\pi$
$571$	−5.30435e6	−0.680835	−0.340417	+	0.940274i	$0.610568\pi$
$572$	−303104.	−0.0387348
$573$	5.23959e6	0.666669
$574$	−335817.	−0.0425425
$575$	1.27312e7	1.60583
$576$	297882.	0.0374100
$577$	1.35522e7	1.69461	0.847307	−	0.531103i	$-0.178222\pi$
$577$	1.35522e7	1.69461	0.847307	+	0.531103i	$0.178222\pi$
$578$	2.43795e6	0.303533
$579$	305301.	0.0378470
$580$	−4.49035e6	−0.554256
$581$	−254789.	−0.0313142
$582$	1.14683e6	0.140344
$583$	120817.	0.0147217
$584$	−6.65909e6	−0.807946
$585$	−4.13896e6	−0.500037
$586$	7.23380e6	0.870207
$587$	−1.53895e7	−1.84344	−0.921720	−	0.387857i	$-0.873215\pi$
$587$	−1.53895e7	−1.84344	−0.921720	+	0.387857i	$0.873215\pi$
$588$	3.22552e6	0.384730
$589$	−9.11499e6	−1.08260
$590$	781738.	0.0924552
$591$	462435.	0.0544605
$592$	−2.25679e6	−0.264659
$593$	9.50339e6	1.10979	0.554896	−	0.831920i	$-0.312758\pi$
$593$	9.50339e6	1.10979	0.554896	+	0.831920i	$0.312758\pi$
$594$	39209.2	0.00455955
$595$	6.15687e6	0.712964
$596$	−4.66716e6	−0.538192
$597$	2.63820e6	0.302950
$598$	5.44461e6	0.622606
$599$	5.58939e6	0.636498	0.318249	−	0.948007i	$-0.396905\pi$
$599$	5.58939e6	0.636498	0.318249	+	0.948007i	$0.396905\pi$
$600$	−5.28725e6	−0.599586
$601$	−1.67571e7	−1.89240	−0.946200	−	0.323581i	$-0.895113\pi$
$601$	−1.67571e7	−1.89240	−0.946200	+	0.323581i	$0.895113\pi$
$602$	693405.	0.0779822
$603$	4.03430e6	0.451830
$604$	1.73896e6	0.193953
$605$	1.34151e7	1.49007
$606$	2.70710e6	0.299449
$607$	−1.00054e7	−1.10220	−0.551101	−	0.834439i	$-0.685792\pi$
$607$	−1.00054e7	−1.10220	−0.551101	+	0.834439i	$0.685792\pi$
$608$	−7.52327e6	−0.825368
$609$	944578.	0.103204
$610$	−30139.4	−0.00327951
$611$	−6.43761e6	−0.697624
$612$	−3.05990e6	−0.330239
$613$	1.22753e7	1.31941	0.659704	−	0.751525i	$-0.270682\pi$
$613$	1.22753e7	1.31941	0.659704	+	0.751525i	$0.270682\pi$
$614$	−5.03950e6	−0.539469
$615$	−1.94135e6	−0.206974
$616$	147594.	0.0156717
$617$	−3.39106e6	−0.358611	−0.179305	−	0.983793i	$-0.557385\pi$
$617$	−3.39106e6	−0.358611	−0.179305	+	0.983793i	$0.557385\pi$
$618$	−3.91139e6	−0.411965
$619$	−1.36685e7	−1.43382	−0.716908	−	0.697168i	$-0.754443\pi$
$619$	−1.36685e7	−1.43382	−0.716908	+	0.697168i	$0.754443\pi$
$620$	1.48157e7	1.54790
$621$	2.41187e6	0.250972
$622$	−4.48122e6	−0.464430
$623$	−4.12836e6	−0.426145
$624$	2.10370e6	0.216283
$625$	−6.98325e6	−0.715084
$626$	−4.09433e6	−0.417587
$627$	−229025.	−0.0232656
$628$	1.01448e7	1.02646
$629$	−9.01125e6	−0.908151
$630$	879327.	0.0882671
$631$	1.06988e7	1.06969	0.534847	−	0.844949i	$-0.320369\pi$
$631$	1.06988e7	1.06969	0.534847	+	0.844949i	$0.320369\pi$
$632$	−1.14258e7	−1.13788
$633$	−2.31556e6	−0.229693
$634$	−2.92997e6	−0.289494
$635$	−2.29947e7	−2.26305
$636$	−1.34660e6	−0.132006
$637$	−8.85462e6	−0.864613
$638$	−116775.	−0.0113579
$639$	5.24097e6	0.507762
$640$	1.49736e7	1.44503
$641$	−5.09674e6	−0.489945	−0.244972	−	0.969530i	$-0.578779\pi$
$641$	−5.09674e6	−0.489945	−0.244972	+	0.969530i	$0.578779\pi$
$642$	−4.38600e6	−0.419982
$643$	540230.	0.0515289	0.0257645	−	0.999668i	$-0.491798\pi$
$643$	540230.	0.0515289	0.0257645	+	0.999668i	$0.491798\pi$
$644$	3.96110e6	0.376358
$645$	4.00855e6	0.379392
$646$	−5.21930e6	−0.492075
$647$	1.70813e6	0.160421	0.0802105	−	0.996778i	$-0.474441\pi$
$647$	1.70813e6	0.160421	0.0802105	+	0.996778i	$0.474441\pi$
$648$	−1.00165e6	−0.0937082
$649$	−69617.6	−0.00648795
$650$	6.33260e6	0.587894
$651$	−3.11660e6	−0.288223
$652$	1.10862e7	1.02133
$653$	−1.69268e6	−0.155343	−0.0776716	−	0.996979i	$-0.524749\pi$
$653$	−1.69268e6	−0.155343	−0.0776716	+	0.996979i	$0.524749\pi$
$654$	−1.69086e6	−0.154583
$655$	−855802.	−0.0779417
$656$	986724.	0.0895233
$657$	3.53309e6	0.319331
$658$	1.36768e6	0.123145
$659$	1.08698e7	0.975005	0.487502	−	0.873122i	$-0.337908\pi$
$659$	1.08698e7	0.975005	0.487502	+	0.873122i	$0.337908\pi$
$660$	372264.	0.0332653
$661$	1.45109e7	1.29178	0.645892	−	0.763429i	$-0.276486\pi$
$661$	1.45109e7	1.29178	0.645892	+	0.763429i	$0.276486\pi$
$662$	8.11152e6	0.719378
$663$	8.39997e6	0.742154
$664$	−804671.	−0.0708269
$665$	−5.13624e6	−0.450393
$666$	−1.28699e6	−0.112432
$667$	−7.18313e6	−0.625172
$668$	1.60437e6	0.139111
$669$	−2.42737e6	−0.209687
$670$	−1.11851e7	−0.962618
$671$	2684.06	0.000230136 0
$672$	−2.57236e6	−0.219739
$673$	−1.88349e7	−1.60297	−0.801484	−	0.598016i	$-0.795956\pi$
$673$	−1.88349e7	−1.60297	−0.801484	+	0.598016i	$0.795956\pi$
$674$	−7.77787e6	−0.659494
$675$	2.80524e6	0.236979
$676$	−78094.3	−0.00657284
$677$	−8.52740e6	−0.715064	−0.357532	−	0.933901i	$-0.616382\pi$
$677$	−8.52740e6	−0.715064	−0.357532	+	0.933901i	$0.616382\pi$
$678$	3.68243e6	0.307652
$679$	−2.29045e6	−0.190654
$680$	1.94445e7	1.61259
$681$	4.27351e6	0.353115
$682$	385293.	0.0317198
$683$	1.61614e7	1.32564	0.662821	−	0.748778i	$-0.269359\pi$
$683$	1.61614e7	1.32564	0.662821	+	0.748778i	$0.269359\pi$
$684$	2.55266e6	0.208618
$685$	−3.26610e7	−2.65952
$686$	4.06614e6	0.329892
$687$	6.62016e6	0.535152
$688$	−2.03742e6	−0.164100
$689$	3.69665e6	0.296661
$690$	−6.68692e6	−0.534692
$691$	−2.32191e7	−1.84991	−0.924953	−	0.380081i	$-0.875896\pi$
$691$	−2.32191e7	−1.84991	−0.924953	+	0.380081i	$0.875896\pi$
$692$	−1.08031e7	−0.857595
$693$	−78308.3	−0.00619405
$694$	−6.61468e6	−0.521327
$695$	3.82878e6	0.300676
$696$	2.98315e6	0.233427
$697$	3.93994e6	0.307191
$698$	4.24682e6	0.329932
$699$	1.32726e6	0.102745
$700$	4.60714e6	0.355374
$701$	−1.45476e7	−1.11814	−0.559070	−	0.829121i	$-0.688842\pi$
$701$	−1.45476e7	−1.11814	−0.559070	+	0.829121i	$0.688842\pi$
$702$	1.19969e6	0.0918809
$703$	7.51744e6	0.573696
$704$	73548.5	0.00559296
$705$	7.90649e6	0.599116
$706$	−2.50836e6	−0.189399
$707$	−5.40659e6	−0.406795
$708$	775939.	0.0581761
$709$	2.04913e7	1.53092	0.765462	−	0.643481i	$-0.222510\pi$
$709$	2.04913e7	1.53092	0.765462	+	0.643481i	$0.222510\pi$
$710$	−1.45306e7	−1.08178
$711$	6.06216e6	0.449732
$712$	−1.30381e7	−0.963861
$713$	2.37005e7	1.74595
$714$	−1.78458e6	−0.131006
$715$	−1.02193e6	−0.0747578
$716$	−6.15933e6	−0.449005
$717$	−8.56079e6	−0.621893
$718$	−254537.	−0.0184264
$719$	5.74561e6	0.414490	0.207245	−	0.978289i	$-0.433550\pi$
$719$	5.74561e6	0.414490	0.207245	+	0.978289i	$0.433550\pi$
$720$	−2.58371e6	−0.185743
$721$	7.81180e6	0.559645
$722$	−2.30498e6	−0.164560
$723$	3.07130e6	0.218513
$724$	1.26249e7	0.895120
$725$	−8.35467e6	−0.590316
$726$	−3.88841e6	−0.273798
$727$	−2.22394e7	−1.56058	−0.780292	−	0.625416i	$-0.784929\pi$
$727$	−2.22394e7	−1.56058	−0.780292	+	0.625416i	$0.784929\pi$
$728$	4.51593e6	0.315805
$729$	531441.	0.0370370
$730$	−9.79551e6	−0.680330
$731$	−8.13530e6	−0.563093
$732$	−29915.8	−0.00206359
$733$	1.66373e7	1.14373	0.571866	−	0.820347i	$-0.306220\pi$
$733$	1.66373e7	1.14373	0.571866	+	0.820347i	$0.306220\pi$
$734$	8.53349e6	0.584637
$735$	1.08750e7	0.742525
$736$	1.95617e7	1.33111
$737$	996090.	0.0675507
$738$	562704.	0.0380311
$739$	−6.69365e6	−0.450871	−0.225435	−	0.974258i	$-0.572380\pi$
$739$	−6.69365e6	−0.450871	−0.225435	+	0.974258i	$0.572380\pi$
$740$	−1.22190e7	−0.820272
$741$	−7.00750e6	−0.468832
$742$	−785357.	−0.0523669
$743$	2.73131e7	1.81509	0.907547	−	0.419951i	$-0.137953\pi$
$743$	2.73131e7	1.81509	0.907547	+	0.419951i	$0.137953\pi$
$744$	−9.84278e6	−0.651907
$745$	−1.57356e7	−1.03871
$746$	−6.32104e6	−0.415854
$747$	426932.	0.0279935
$748$	−755504.	−0.0493723
$749$	8.75968e6	0.570537
$750$	−1.46142e6	−0.0948683
$751$	−3.14794e6	−0.203670	−0.101835	−	0.994801i	$-0.532471\pi$
$751$	−3.14794e6	−0.203670	−0.101835	+	0.994801i	$0.532471\pi$
$752$	−4.01861e6	−0.259138
$753$	1.39452e7	0.896264
$754$	−3.57296e6	−0.228876
$755$	5.86299e6	0.374328
$756$	872804.	0.0555408
$757$	8.68258e6	0.550692	0.275346	−	0.961345i	$-0.411208\pi$
$757$	8.68258e6	0.550692	0.275346	+	0.961345i	$0.411208\pi$
$758$	2.68551e6	0.169767
$759$	595503.	0.0375214
$760$	−1.62212e7	−1.01871
$761$	−9.78953e6	−0.612774	−0.306387	−	0.951907i	$-0.599120\pi$
$761$	−9.78953e6	−0.612774	−0.306387	+	0.951907i	$0.599120\pi$
$762$	6.66507e6	0.415832
$763$	3.37696e6	0.209998
$764$	−1.44190e7	−0.893722
$765$	−1.03166e7	−0.637358
$766$	−8.72314e6	−0.537157
$767$	−2.13009e6	−0.130741
$768$	−5.39926e6	−0.330317
$769$	−2.96608e7	−1.80870	−0.904351	−	0.426789i	$-0.859645\pi$
$769$	−2.96608e7	−1.80870	−0.904351	+	0.426789i	$0.859645\pi$
$770$	217110.	0.0131963
$771$	−7.37188e6	−0.446624
$772$	−840169.	−0.0507368
$773$	−7.78504e6	−0.468611	−0.234305	−	0.972163i	$-0.575282\pi$
$773$	−7.78504e6	−0.468611	−0.234305	+	0.972163i	$0.575282\pi$
$774$	−1.16189e6	−0.0697126
$775$	2.75659e7	1.64861
$776$	−7.23365e6	−0.431224
$777$	2.57036e6	0.152736
$778$	−1.16875e6	−0.0692268
$779$	−3.28681e6	−0.194058
$780$	1.13902e7	0.670338
$781$	1.29402e6	0.0759127
$782$	1.35710e7	0.793589
$783$	−1.58276e6	−0.0922594
$784$	−5.52741e6	−0.321168
$785$	3.42037e7	1.98106
$786$	248056.	0.0143217
$787$	−2.25929e6	−0.130028	−0.0650138	−	0.997884i	$-0.520709\pi$
$787$	−2.25929e6	−0.130028	−0.0650138	+	0.997884i	$0.520709\pi$
$788$	−1.27259e6	−0.0730085
$789$	1.10021e7	0.629190
$790$	−1.68074e7	−0.958148
$791$	−7.35451e6	−0.417939
$792$	−247312.	−0.0140098
$793$	82124.2	0.00463755
$794$	6.15938e6	0.346726
$795$	−4.54012e6	−0.254771
$796$	−7.26016e6	−0.406128
$797$	−1.95399e7	−1.08962	−0.544812	−	0.838558i	$-0.683399\pi$
$797$	−1.95399e7	−1.08962	−0.544812	+	0.838558i	$0.683399\pi$
$798$	1.48875e6	0.0827589
$799$	−1.60461e7	−0.889208
$800$	2.27522e7	1.25689
$801$	6.91759e6	0.380955
$802$	5.24720e6	0.288066
$803$	872338.	0.0477415
$804$	−1.11022e7	−0.605713
$805$	1.33551e7	0.726367
$806$	1.17888e7	0.639195
$807$	−1.44189e7	−0.779378
$808$	−1.70750e7	−0.920094
$809$	−2.92703e7	−1.57237	−0.786187	−	0.617989i	$-0.787948\pi$
$809$	−2.92703e7	−1.57237	−0.786187	+	0.617989i	$0.787948\pi$
$810$	−1.47342e6	−0.0789069
$811$	3.63592e6	0.194116	0.0970581	−	0.995279i	$-0.469057\pi$
$811$	3.63592e6	0.194116	0.0970581	+	0.995279i	$0.469057\pi$
$812$	−2.59942e6	−0.138352
$813$	1.46341e7	0.776496
$814$	−317764.	−0.0168091
$815$	3.73779e7	1.97115
$816$	5.24360e6	0.275679
$817$	6.78671e6	0.355717
$818$	3.95085e6	0.206446
$819$	−2.39600e6	−0.124818
$820$	5.34247e6	0.277465
$821$	1.26564e6	0.0655318	0.0327659	−	0.999463i	$-0.489568\pi$
$821$	1.26564e6	0.0655318	0.0327659	+	0.999463i	$0.489568\pi$
$822$	9.46685e6	0.488682
$823$	2.48803e7	1.28043	0.640216	−	0.768195i	$-0.278845\pi$
$823$	2.48803e7	1.28043	0.640216	+	0.768195i	$0.278845\pi$
$824$	2.46711e7	1.26581
$825$	692627.	0.0354295
$826$	452541.	0.0230785
$827$	1.44783e7	0.736131	0.368065	−	0.929800i	$-0.380020\pi$
$827$	1.44783e7	0.736131	0.368065	+	0.929800i	$0.380020\pi$
$828$	−6.63732e6	−0.336447
$829$	476856.	0.0240991	0.0120495	−	0.999927i	$-0.496164\pi$
$829$	476856.	0.0240991	0.0120495	+	0.999927i	$0.496164\pi$
$830$	−1.18367e6	−0.0596397
$831$	1.22713e7	0.616438
$832$	2.25037e6	0.112705
$833$	−2.20707e7	−1.10206
$834$	−1.10978e6	−0.0552486
$835$	5.40921e6	0.268484
$836$	630264.	0.0311894
$837$	5.22225e6	0.257658
$838$	−1.07026e7	−0.526475
$839$	2.73963e7	1.34365	0.671827	−	0.740708i	$-0.265510\pi$
$839$	2.73963e7	1.34365	0.671827	+	0.740708i	$0.265510\pi$
$840$	−5.54635e6	−0.271212
$841$	−1.57973e7	−0.770181
$842$	2.22922e6	0.108361
$843$	1.56813e7	0.759999
$844$	6.37228e6	0.307921
$845$	−263299.	−0.0126855
$846$	−2.29171e6	−0.110087
$847$	7.76589e6	0.371949
$848$	2.30760e6	0.110197
$849$	−1.11282e7	−0.529855
$850$	1.57844e7	0.749343
$851$	−1.95466e7	−0.925223
$852$	−1.44228e7	−0.680694
$853$	2.87120e6	0.135111	0.0675556	−	0.997716i	$-0.478480\pi$
$853$	2.87120e6	0.135111	0.0675556	+	0.997716i	$0.478480\pi$
$854$	−17447.4	−0.000818626 0
$855$	8.60642e6	0.402631
$856$	2.76647e7	1.29045
$857$	2.66310e7	1.23861	0.619305	−	0.785150i	$-0.287414\pi$
$857$	2.66310e7	1.23861	0.619305	+	0.785150i	$0.287414\pi$
$858$	296209.	0.0137366
$859$	7.47800e6	0.345782	0.172891	−	0.984941i	$-0.444689\pi$
$859$	7.47800e6	0.345782	0.172891	+	0.984941i	$0.444689\pi$
$860$	−1.10313e7	−0.508604
$861$	−1.12383e6	−0.0516644
$862$	1.78926e7	0.820171
$863$	−3.33536e7	−1.52446	−0.762230	−	0.647306i	$-0.775895\pi$
$863$	−3.33536e7	−1.52446	−0.762230	+	0.647306i	$0.775895\pi$
$864$	4.31031e6	0.196437
$865$	−3.64232e7	−1.65515
$866$	−1.43197e6	−0.0648843
$867$	8.15873e6	0.368616
$868$	8.57669e6	0.386385
$869$	1.49678e6	0.0672370
$870$	4.38821e6	0.196557
$871$	3.04774e7	1.36123
$872$	1.06651e7	0.474976
$873$	3.83793e6	0.170436
$874$	−1.13213e7	−0.501325
$875$	2.91873e6	0.128877
$876$	−9.72284e6	−0.428088
$877$	2.97763e7	1.30729	0.653645	−	0.756802i	$-0.273239\pi$
$877$	2.97763e7	1.30729	0.653645	+	0.756802i	$0.273239\pi$
$878$	1.08747e7	0.476081
$879$	2.42083e7	1.05680
$880$	−637930.	−0.0277694
$881$	1.74483e7	0.757380	0.378690	−	0.925523i	$-0.376375\pi$
$881$	1.74483e7	0.757380	0.378690	+	0.925523i	$0.376375\pi$
$882$	−3.15214e6	−0.136438
$883$	3.08101e7	1.32981	0.664907	−	0.746926i	$-0.268471\pi$
$883$	3.08101e7	1.32981	0.664907	+	0.746926i	$0.268471\pi$
$884$	−2.31162e7	−0.994915
$885$	2.61612e6	0.112279
$886$	4.49021e6	0.192169
$887$	−110509.	−0.00471615	−0.00235807	−	0.999997i	$-0.500751\pi$
$887$	−110509.	−0.00471615	−0.00235807	+	0.999997i	$0.500751\pi$
$888$	8.11768e6	0.345461
$889$	−1.33114e7	−0.564898
$890$	−1.91790e7	−0.811618
$891$	131216.	0.00553721
$892$	6.67997e6	0.281101
$893$	1.33861e7	0.561729
$894$	4.56100e6	0.190860
$895$	−2.07665e7	−0.866576
$896$	8.66806e6	0.360705
$897$	1.82206e7	0.756105
$898$	−1.09574e7	−0.453435
$899$	−1.55531e7	−0.641828
$900$	−7.71984e6	−0.317689
$901$	9.21412e6	0.378131
$902$	138934.	0.00568583
$903$	2.32051e6	0.0947031
$904$	−2.32269e7	−0.945301
$905$	4.25655e7	1.72757
$906$	−1.69940e6	−0.0687821
$907$	3.31400e7	1.33763	0.668813	−	0.743431i	$-0.266803\pi$
$907$	3.31400e7	1.33763	0.668813	+	0.743431i	$0.266803\pi$
$908$	−1.17604e7	−0.473379
$909$	9.05943e6	0.363656
$910$	6.64293e6	0.265923
$911$	−2.55670e7	−1.02067	−0.510334	−	0.859976i	$-0.670478\pi$
$911$	−2.55670e7	−1.02067	−0.510334	+	0.859976i	$0.670478\pi$
$912$	−4.37436e6	−0.174152
$913$	105412.	0.00418515
$914$	−1.83029e7	−0.724694
$915$	−100863.	−0.00398270
$916$	−1.82183e7	−0.717412
$917$	−495415.	−0.0194557
$918$	2.99029e6	0.117114
$919$	4.08635e7	1.59605	0.798026	−	0.602623i	$-0.205878\pi$
$919$	4.08635e7	1.59605	0.798026	+	0.602623i	$0.205878\pi$
$920$	4.21777e7	1.64291
$921$	−1.68649e7	−0.655142
$922$	1.84976e7	0.716620
$923$	3.95933e7	1.52974
$924$	215500.	0.00830361
$925$	−2.27345e7	−0.873639
$926$	−6.44072e6	−0.246835
$927$	−1.30897e7	−0.500298
$928$	−1.28371e7	−0.489326
$929$	−1.44490e7	−0.549287	−0.274644	−	0.961546i	$-0.588560\pi$
$929$	−1.44490e7	−0.549287	−0.274644	+	0.961546i	$0.588560\pi$
$930$	−1.44787e7	−0.548938
$931$	1.84120e7	0.696189
$932$	−3.65253e6	−0.137738
$933$	−1.49966e7	−0.564013
$934$	1.43092e7	0.536722
$935$	−2.54723e6	−0.0952880
$936$	−7.56702e6	−0.282316
$937$	−9.49392e6	−0.353262	−0.176631	−	0.984277i	$-0.556520\pi$
$937$	−9.49392e6	−0.353262	−0.176631	+	0.984277i	$0.556520\pi$
$938$	−6.47496e6	−0.240287
$939$	−1.37019e7	−0.507126
$940$	−2.17582e7	−0.803162
$941$	4.83451e6	0.177983	0.0889915	−	0.996032i	$-0.471636\pi$
$941$	4.83451e6	0.177983	0.0889915	+	0.996032i	$0.471636\pi$
$942$	−9.91401e6	−0.364017
$943$	8.54625e6	0.312965
$944$	−1.32969e6	−0.0485647
$945$	2.94271e6	0.107193
$946$	−286876.	−0.0104224
$947$	−2.50321e7	−0.907030	−0.453515	−	0.891249i	$-0.649830\pi$
$947$	−2.50321e7	−0.907030	−0.453515	+	0.891249i	$0.649830\pi$
$948$	−1.66827e7	−0.602901
$949$	2.66910e7	0.962052
$950$	−1.31678e7	−0.473374
$951$	−9.80528e6	−0.351567
$952$	1.12562e7	0.402533
$953$	−1.73815e7	−0.619949	−0.309975	−	0.950745i	$-0.600321\pi$
$953$	−1.73815e7	−0.619949	−0.309975	+	0.950745i	$0.600321\pi$
$954$	1.31596e6	0.0468137
$955$	−4.86145e7	−1.72488
$956$	2.35588e7	0.833696
$957$	−390792.	−0.0137932
$958$	−1.28118e6	−0.0451021
$959$	−1.89071e7	−0.663864
$960$	−2.76384e6	−0.0967909
$961$	2.26878e7	0.792472
$962$	−9.72265e6	−0.338725
$963$	−1.46779e7	−0.510034
$964$	−8.45204e6	−0.292933
$965$	−2.83268e6	−0.0979216
$966$	−3.87099e6	−0.133469
$967$	−5.09719e6	−0.175293	−0.0876465	−	0.996152i	$-0.527935\pi$
$967$	−5.09719e6	−0.175293	−0.0876465	+	0.996152i	$0.527935\pi$
$968$	2.45261e7	0.841279
$969$	−1.74666e7	−0.597585
$970$	−1.06407e7	−0.363112
$971$	393529.	0.0133946	0.00669729	−	0.999978i	$-0.497868\pi$
$971$	393529.	0.0133946	0.00669729	+	0.999978i	$0.497868\pi$
$972$	−1.46249e6	−0.0496510
$973$	2.21644e6	0.0750541
$974$	−8.73778e6	−0.295124
$975$	2.11923e7	0.713949
$976$	51265.2	0.00172266
$977$	−5.44154e7	−1.82384	−0.911918	−	0.410373i	$-0.865398\pi$
$977$	−5.44154e7	−1.82384	−0.911918	+	0.410373i	$0.865398\pi$
$978$	−1.08341e7	−0.362196
$979$	1.70799e6	0.0569545
$980$	−2.99274e7	−0.995413
$981$	−5.65852e6	−0.187729
$982$	−3.02301e6	−0.100037
$983$	−6.93627e6	−0.228951	−0.114475	−	0.993426i	$-0.536519\pi$
$983$	−6.93627e6	−0.228951	−0.114475	+	0.993426i	$0.536519\pi$
$984$	−3.54925e6	−0.116855
$985$	−4.29061e6	−0.140906
$986$	−8.90582e6	−0.291730
$987$	4.57699e6	0.149550
$988$	1.92842e7	0.628506
$989$	−1.76465e7	−0.573679
$990$	−363796.	−0.0117969
$991$	2.32589e7	0.752326	0.376163	−	0.926554i	$-0.377243\pi$
$991$	2.32589e7	0.752326	0.376163	+	0.926554i	$0.377243\pi$
$992$	4.23556e7	1.36657
$993$	2.71456e7	0.873626
$994$	−8.41164e6	−0.270032
$995$	−2.44780e7	−0.783824
$996$	−1.17489e6	−0.0375274
$997$	−4.77014e7	−1.51982	−0.759912	−	0.650026i	$-0.774758\pi$
$997$	−4.77014e7	−1.51982	−0.759912	+	0.650026i	$0.774758\pi$
$998$	2.35725e6	0.0749168
$999$	−4.30697e6	−0.136539

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.c.1.7	✓	12	1.1	even	1	trivial
531.6.a.c.1.6		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)

\(f(q)\)	\(=\)	\(q+2.68934 q^{2} +9.00000 q^{3} -24.7675 q^{4} -83.5049 q^{5} +24.2041 q^{6} -48.3401 q^{7} -152.667 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+2.68934 q^{2} +9.00000 q^{3} -24.7675 q^{4} -83.5049 q^{5} +24.2041 q^{6} -48.3401 q^{7} -152.667 q^{8} +81.0000 q^{9} -224.573 q^{10} +19.9993 q^{11} -222.907 q^{12} +611.920 q^{13} -130.003 q^{14} -751.544 q^{15} +381.985 q^{16} +1525.25 q^{17} +217.837 q^{18} -1272.41 q^{19} +2068.20 q^{20} -435.061 q^{21} +53.7850 q^{22} +3308.46 q^{23} -1374.00 q^{24} +3848.06 q^{25} +1645.66 q^{26} +729.000 q^{27} +1197.26 q^{28} -2171.14 q^{29} -2021.16 q^{30} +7163.58 q^{31} +5912.63 q^{32} +179.994 q^{33} +4101.91 q^{34} +4036.64 q^{35} -2006.16 q^{36} -5908.05 q^{37} -3421.93 q^{38} +5507.28 q^{39} +12748.4 q^{40} +2583.15 q^{41} -1170.03 q^{42} -5333.76 q^{43} -495.332 q^{44} -6763.89 q^{45} +8897.58 q^{46} -10520.3 q^{47} +3437.87 q^{48} -14470.2 q^{49} +10348.7 q^{50} +13727.2 q^{51} -15155.7 q^{52} +6041.06 q^{53} +1960.53 q^{54} -1670.04 q^{55} +7379.94 q^{56} -11451.7 q^{57} -5838.93 q^{58} -3481.00 q^{59} +18613.8 q^{60} +134.207 q^{61} +19265.3 q^{62} -3915.55 q^{63} +3677.55 q^{64} -51098.3 q^{65} +484.065 q^{66} +49806.2 q^{67} -37776.5 q^{68} +29776.2 q^{69} +10855.9 q^{70} +64703.4 q^{71} -12366.0 q^{72} +43618.4 q^{73} -15888.8 q^{74} +34632.5 q^{75} +31514.3 q^{76} -966.770 q^{77} +14810.9 q^{78} +74841.5 q^{79} -31897.6 q^{80} +6561.00 q^{81} +6946.96 q^{82} +5270.76 q^{83} +10775.4 q^{84} -127366. q^{85} -14344.3 q^{86} -19540.2 q^{87} -3053.23 q^{88} +85402.3 q^{89} -18190.4 q^{90} -29580.3 q^{91} -81942.2 q^{92} +64472.3 q^{93} -28292.8 q^{94} +106252. q^{95} +53213.7 q^{96} +47381.9 q^{97} -38915.4 q^{98} +1619.94 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9}+O(q^{10}) \) 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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