LMFDB - Embedded newform 177.6.a.c.1.10

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			1.10
Root			$-7.23155$ 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)

$f(q)$	$=$	$q+9.23155 q^{2} +9.00000 q^{3} +53.2215 q^{4} +89.5822 q^{5} +83.0840 q^{6} -121.386 q^{7} +195.908 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+9.23155 q^{2} +9.00000 q^{3} +53.2215 q^{4} +89.5822 q^{5} +83.0840 q^{6} -121.386 q^{7} +195.908 q^{8} +81.0000 q^{9} +826.983 q^{10} +542.050 q^{11} +478.994 q^{12} -202.326 q^{13} -1120.58 q^{14} +806.240 q^{15} +105.442 q^{16} -431.232 q^{17} +747.756 q^{18} +362.462 q^{19} +4767.70 q^{20} -1092.47 q^{21} +5003.96 q^{22} +1693.68 q^{23} +1763.17 q^{24} +4899.97 q^{25} -1867.79 q^{26} +729.000 q^{27} -6460.34 q^{28} -7671.32 q^{29} +7442.84 q^{30} -2429.08 q^{31} -5295.65 q^{32} +4878.45 q^{33} -3980.94 q^{34} -10874.0 q^{35} +4310.94 q^{36} +2539.77 q^{37} +3346.09 q^{38} -1820.94 q^{39} +17549.8 q^{40} +6567.27 q^{41} -10085.2 q^{42} +779.187 q^{43} +28848.7 q^{44} +7256.16 q^{45} +15635.3 q^{46} -13880.3 q^{47} +948.975 q^{48} -2072.46 q^{49} +45234.3 q^{50} -3881.09 q^{51} -10768.1 q^{52} +14568.1 q^{53} +6729.80 q^{54} +48558.0 q^{55} -23780.4 q^{56} +3262.16 q^{57} -70818.2 q^{58} -3481.00 q^{59} +42909.3 q^{60} +19600.2 q^{61} -22424.2 q^{62} -9832.26 q^{63} -52261.2 q^{64} -18124.8 q^{65} +45035.7 q^{66} -56140.8 q^{67} -22950.8 q^{68} +15243.2 q^{69} -100384. q^{70} -37168.2 q^{71} +15868.5 q^{72} +82040.6 q^{73} +23446.1 q^{74} +44099.7 q^{75} +19290.8 q^{76} -65797.3 q^{77} -16810.1 q^{78} +77491.2 q^{79} +9445.69 q^{80} +6561.00 q^{81} +60626.0 q^{82} -63660.2 q^{83} -58143.1 q^{84} -38630.7 q^{85} +7193.11 q^{86} -69041.9 q^{87} +106192. q^{88} -15534.4 q^{89} +66985.6 q^{90} +24559.6 q^{91} +90140.5 q^{92} -21861.7 q^{93} -128137. q^{94} +32470.2 q^{95} -47660.9 q^{96} -93095.6 q^{97} -19132.0 q^{98} +43906.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	9.23155	1.63192	0.815961	−	0.578106i	$-0.196208\pi$
$2$	9.23155	1.63192	0.815961	+	0.578106i	$0.196208\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	53.2215	1.66317
$5$	89.5822	1.60249	0.801247	−	0.598333i	$-0.204170\pi$
$5$	89.5822	1.60249	0.801247	+	0.598333i	$0.204170\pi$
$6$	83.0840	0.942191
$7$	−121.386	−0.936318	−0.468159	−	0.883644i	$-0.655083\pi$
$7$	−121.386	−0.936318	−0.468159	+	0.883644i	$0.655083\pi$
$8$	195.908	1.08225
$9$	81.0000	0.333333
$10$	826.983	2.61515
$11$	542.050	1.35070	0.675348	−	0.737499i	$-0.263993\pi$
$11$	542.050	1.35070	0.675348	+	0.737499i	$0.263993\pi$
$12$	478.994	0.960233
$13$	−202.326	−0.332043	−0.166021	−	0.986122i	$-0.553092\pi$
$13$	−202.326	−0.332043	−0.166021	+	0.986122i	$0.553092\pi$
$14$	−1120.58	−1.52800
$15$	806.240	0.925201
$16$	105.442	0.102970
$17$	−431.232	−0.361900	−0.180950	−	0.983492i	$-0.557917\pi$
$17$	−431.232	−0.361900	−0.180950	+	0.983492i	$0.557917\pi$
$18$	747.756	0.543974
$19$	362.462	0.230345	0.115173	−	0.993346i	$-0.463258\pi$
$19$	362.462	0.230345	0.115173	+	0.993346i	$0.463258\pi$
$20$	4767.70	2.66523
$21$	−1092.47	−0.540583
$22$	5003.96	2.20423
$23$	1693.68	0.667595	0.333797	−	0.942645i	$-0.391670\pi$
$23$	1693.68	0.667595	0.333797	+	0.942645i	$0.391670\pi$
$24$	1763.17	0.624835
$25$	4899.97	1.56799
$26$	−1867.79	−0.541868
$27$	729.000	0.192450
$28$	−6460.34	−1.55726
$29$	−7671.32	−1.69385	−0.846925	−	0.531712i	$-0.821549\pi$
$29$	−7671.32	−1.69385	−0.846925	+	0.531712i	$0.821549\pi$
$30$	7442.84	1.50986
$31$	−2429.08	−0.453980	−0.226990	−	0.973897i	$-0.572889\pi$
$31$	−2429.08	−0.453980	−0.226990	+	0.973897i	$0.572889\pi$
$32$	−5295.65	−0.914207
$33$	4878.45	0.779825
$34$	−3980.94	−0.590593
$35$	−10874.0	−1.50044
$36$	4310.94	0.554391
$37$	2539.77	0.304994	0.152497	−	0.988304i	$-0.451269\pi$
$37$	2539.77	0.304994	0.152497	+	0.988304i	$0.451269\pi$
$38$	3346.09	0.375905
$39$	−1820.94	−0.191705
$40$	17549.8	1.73429
$41$	6567.27	0.610134	0.305067	−	0.952331i	$-0.401321\pi$
$41$	6567.27	0.610134	0.305067	+	0.952331i	$0.401321\pi$
$42$	−10085.2	−0.882190
$43$	779.187	0.0642645	0.0321322	−	0.999484i	$-0.489770\pi$
$43$	779.187	0.0642645	0.0321322	+	0.999484i	$0.489770\pi$
$44$	28848.7	2.24644
$45$	7256.16	0.534165
$46$	15635.3	1.08946
$47$	−13880.3	−0.916549	−0.458275	−	0.888811i	$-0.651532\pi$
$47$	−13880.3	−0.916549	−0.458275	+	0.888811i	$0.651532\pi$
$48$	948.975	0.0594500
$49$	−2072.46	−0.123309
$50$	45234.3	2.55884
$51$	−3881.09	−0.208943
$52$	−10768.1	−0.552244
$53$	14568.1	0.712382	0.356191	−	0.934413i	$-0.384075\pi$
$53$	14568.1	0.712382	0.356191	+	0.934413i	$0.384075\pi$
$54$	6729.80	0.314064
$55$	48558.0	2.16448
$56$	−23780.4	−1.01333
$57$	3262.16	0.132990
$58$	−70818.2	−2.76423
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	42909.3	1.53877
$61$	19600.2	0.674429	0.337214	−	0.941428i	$-0.390515\pi$
$61$	19600.2	0.674429	0.337214	+	0.941428i	$0.390515\pi$
$62$	−22424.2	−0.740861
$63$	−9832.26	−0.312106
$64$	−52261.2	−1.59489
$65$	−18124.8	−0.532097
$66$	45035.7	1.27261
$67$	−56140.8	−1.52789	−0.763944	−	0.645283i	$-0.776740\pi$
$67$	−56140.8	−1.52789	−0.763944	+	0.645283i	$0.776740\pi$
$68$	−22950.8	−0.601903
$69$	15243.2	0.385436
$70$	−100384.	−2.44861
$71$	−37168.2	−0.875036	−0.437518	−	0.899210i	$-0.644142\pi$
$71$	−37168.2	−0.875036	−0.437518	+	0.899210i	$0.644142\pi$
$72$	15868.5	0.360749
$73$	82040.6	1.80186	0.900931	−	0.433962i	$-0.142885\pi$
$73$	82040.6	1.80186	0.900931	+	0.433962i	$0.142885\pi$
$74$	23446.1	0.497726
$75$	44099.7	0.905280
$76$	19290.8	0.383104
$77$	−65797.3	−1.26468
$78$	−16810.1	−0.312848
$79$	77491.2	1.39696	0.698481	−	0.715629i	$-0.253860\pi$
$79$	77491.2	1.39696	0.698481	+	0.715629i	$0.253860\pi$
$80$	9445.69	0.165009
$81$	6561.00	0.111111
$82$	60626.0	0.995691
$83$	−63660.2	−1.01432	−0.507158	−	0.861853i	$-0.669304\pi$
$83$	−63660.2	−1.01432	−0.507158	+	0.861853i	$0.669304\pi$
$84$	−58143.1	−0.899083
$85$	−38630.7	−0.579943
$86$	7193.11	0.104875
$87$	−69041.9	−0.977945
$88$	106192.	1.46179
$89$	−15534.4	−0.207883	−0.103941	−	0.994583i	$-0.533145\pi$
$89$	−15534.4	−0.207883	−0.103941	+	0.994583i	$0.533145\pi$
$90$	66985.6	0.871716
$91$	24559.6	0.310897
$92$	90140.5	1.11033
$93$	−21861.7	−0.262106
$94$	−128137.	−1.49574
$95$	32470.2	0.369127
$96$	−47660.9	−0.527818
$97$	−93095.6	−1.00461	−0.502307	−	0.864689i	$-0.667515\pi$
$97$	−93095.6	−1.00461	−0.502307	+	0.864689i	$0.667515\pi$
$98$	−19132.0	−0.201231
$99$	43906.1	0.450232
$100$	260784.	2.60784
$101$	−77938.5	−0.760236	−0.380118	−	0.924938i	$-0.624117\pi$
$101$	−77938.5	−0.760236	−0.380118	+	0.924938i	$0.624117\pi$
$102$	−35828.5	−0.340979
$103$	75407.0	0.700356	0.350178	−	0.936683i	$-0.386121\pi$
$103$	75407.0	0.700356	0.350178	+	0.936683i	$0.386121\pi$
$104$	−39637.2	−0.359352
$105$	−97866.2	−0.866282
$106$	134486.	1.16255
$107$	−154511.	−1.30467	−0.652333	−	0.757933i	$-0.726210\pi$
$107$	−154511.	−1.30467	−0.652333	+	0.757933i	$0.726210\pi$
$108$	38798.5	0.320078
$109$	−186965.	−1.50728	−0.753641	−	0.657286i	$-0.771704\pi$
$109$	−186965.	−1.50728	−0.753641	+	0.657286i	$0.771704\pi$
$110$	448266.	3.53227
$111$	22858.0	0.176088
$112$	−12799.1	−0.0964130
$113$	−160142.	−1.17980	−0.589901	−	0.807476i	$-0.700833\pi$
$113$	−160142.	−1.17980	−0.589901	+	0.807476i	$0.700833\pi$
$114$	30114.8	0.217029
$115$	151724.	1.06982
$116$	−408279.	−2.81717
$117$	−16388.4	−0.110681
$118$	−32135.0	−0.212458
$119$	52345.5	0.338854
$120$	157948.	1.00130
$121$	132767.	0.824380
$122$	180940.	1.10062
$123$	59105.4	0.352261
$124$	−129279.	−0.755048
$125$	159006.	0.910201
$126$	−90767.0	−0.509333
$127$	277139.	1.52472	0.762358	−	0.647156i	$-0.224042\pi$
$127$	277139.	1.52472	0.762358	+	0.647156i	$0.224042\pi$
$128$	−312991.	−1.68852
$129$	7012.69	0.0371031
$130$	−167320.	−0.868341
$131$	36895.9	0.187845	0.0939226	−	0.995580i	$-0.470059\pi$
$131$	36895.9	0.187845	0.0939226	+	0.995580i	$0.470059\pi$
$132$	259639.	1.29698
$133$	−43997.8	−0.215676
$134$	−518266.	−2.49340
$135$	65305.4	0.308400
$136$	−84481.7	−0.391665
$137$	289045.	1.31572	0.657860	−	0.753140i	$-0.271462\pi$
$137$	289045.	1.31572	0.657860	+	0.753140i	$0.271462\pi$
$138$	140718.	0.629002
$139$	−303040.	−1.33034	−0.665170	−	0.746692i	$-0.731641\pi$
$139$	−303040.	−1.33034	−0.665170	+	0.746692i	$0.731641\pi$
$140$	−578732.	−2.49550
$141$	−124923.	−0.529170
$142$	−343120.	−1.42799
$143$	−109671.	−0.448489
$144$	8540.77	0.0343235
$145$	−687214.	−2.71439
$146$	757362.	2.94050
$147$	−18652.1	−0.0711925
$148$	135171.	0.507257
$149$	246895.	0.911059	0.455530	−	0.890221i	$-0.349450\pi$
$149$	246895.	0.911059	0.455530	+	0.890221i	$0.349450\pi$
$150$	407109.	1.47735
$151$	528032.	1.88459	0.942297	−	0.334777i	$-0.108661\pi$
$151$	528032.	1.88459	0.942297	+	0.334777i	$0.108661\pi$
$152$	71009.1	0.249290
$153$	−34929.8	−0.120633
$154$	−607411.	−2.06386
$155$	−217602.	−0.727501
$156$	−96913.0	−0.318838
$157$	−289375.	−0.936940	−0.468470	−	0.883479i	$-0.655195\pi$
$157$	−289375.	−0.936940	−0.468470	+	0.883479i	$0.655195\pi$
$158$	715364.	2.27973
$159$	131113.	0.411294
$160$	−474396.	−1.46501
$161$	−205589.	−0.625081
$162$	60568.2	0.181325
$163$	−282099.	−0.831634	−0.415817	−	0.909448i	$-0.636504\pi$
$163$	−282099.	−0.831634	−0.415817	+	0.909448i	$0.636504\pi$
$164$	349520.	1.01476
$165$	437022.	1.24967
$166$	−587683.	−1.65528
$167$	616710.	1.71116	0.855578	−	0.517674i	$-0.173202\pi$
$167$	616710.	1.71116	0.855578	+	0.517674i	$0.173202\pi$
$168$	−214024.	−0.585044
$169$	−330357.	−0.889748
$170$	−356622.	−0.946423
$171$	29359.5	0.0767817
$172$	41469.5	0.106883
$173$	−332590.	−0.844877	−0.422438	−	0.906392i	$-0.638826\pi$
$173$	−332590.	−0.844877	−0.422438	+	0.906392i	$0.638826\pi$
$174$	−637364.	−1.59593
$175$	−594787.	−1.46814
$176$	57154.7	0.139082
$177$	−31329.0	−0.0751646
$178$	−143406.	−0.339249
$179$	220129.	0.513506	0.256753	−	0.966477i	$-0.417347\pi$
$179$	220129.	0.513506	0.256753	+	0.966477i	$0.417347\pi$
$180$	386184.	0.888409
$181$	−610281.	−1.38463	−0.692314	−	0.721596i	$-0.743409\pi$
$181$	−610281.	−1.38463	−0.692314	+	0.721596i	$0.743409\pi$
$182$	226723.	0.507361
$183$	176402.	0.389382
$184$	331806.	0.722502
$185$	227519.	0.488751
$186$	−201817.	−0.427736
$187$	−233749.	−0.488817
$188$	−738733.	−1.52438
$189$	−88490.3	−0.180194
$190$	299750.	0.602387
$191$	348513.	0.691250	0.345625	−	0.938373i	$-0.387667\pi$
$191$	348513.	0.691250	0.345625	+	0.938373i	$0.387667\pi$
$192$	−470351.	−0.920808
$193$	126850.	0.245131	0.122566	−	0.992460i	$-0.460888\pi$
$193$	126850.	0.245131	0.122566	+	0.992460i	$0.460888\pi$
$194$	−859416.	−1.63945
$195$	−163123.	−0.307206
$196$	−110299.	−0.205084
$197$	344780.	0.632961	0.316481	−	0.948599i	$-0.397499\pi$
$197$	344780.	0.632961	0.316481	+	0.948599i	$0.397499\pi$
$198$	405321.	0.734744
$199$	508413.	0.910089	0.455045	−	0.890469i	$-0.349623\pi$
$199$	508413.	0.910089	0.455045	+	0.890469i	$0.349623\pi$
$200$	959941.	1.69695
$201$	−505267.	−0.882126
$202$	−719493.	−1.24065
$203$	931190.	1.58598
$204$	−206558.	−0.347509
$205$	588310.	0.977736
$206$	696124.	1.14293
$207$	137188.	0.222532
$208$	−21333.6	−0.0341906
$209$	196473.	0.311126
$210$	−903456.	−1.41371
$211$	798353.	1.23449	0.617247	−	0.786770i	$-0.288248\pi$
$211$	798353.	1.23449	0.617247	+	0.786770i	$0.288248\pi$
$212$	775336.	1.18481
$213$	−334514.	−0.505202
$214$	−1.42637e6	−2.12911
$215$	69801.3	0.102983
$216$	142817.	0.208278
$217$	294856.	0.425070
$218$	−1.72598e6	−2.45977
$219$	738365.	1.04031
$220$	2.58433e6	3.59991
$221$	87249.6	0.120166
$222$	211015.	0.287362
$223$	633080.	0.852504	0.426252	−	0.904604i	$-0.359834\pi$
$223$	633080.	0.852504	0.426252	+	0.904604i	$0.359834\pi$
$224$	642818.	0.855988
$225$	396897.	0.522663
$226$	−1.47836e6	−1.92535
$227$	1.05889e6	1.36392	0.681958	−	0.731392i	$-0.261129\pi$
$227$	1.05889e6	1.36392	0.681958	+	0.731392i	$0.261129\pi$
$228$	173617.	0.221185
$229$	327031.	0.412097	0.206049	−	0.978542i	$-0.433939\pi$
$229$	327031.	0.412097	0.206049	+	0.978542i	$0.433939\pi$
$230$	1.40065e6	1.74586
$231$	−592175.	−0.730164
$232$	−1.50287e6	−1.83316
$233$	1.17104e6	1.41313	0.706564	−	0.707649i	$-0.250244\pi$
$233$	1.17104e6	1.41313	0.706564	+	0.707649i	$0.250244\pi$
$234$	−151291.	−0.180623
$235$	−1.24343e6	−1.46877
$236$	−185264.	−0.216527
$237$	697421.	0.806536
$238$	483230.	0.552983
$239$	571554.	0.647235	0.323618	−	0.946188i	$-0.395101\pi$
$239$	571554.	0.647235	0.323618	+	0.946188i	$0.395101\pi$
$240$	85011.2	0.0952683
$241$	482157.	0.534744	0.267372	−	0.963593i	$-0.413845\pi$
$241$	482157.	0.534744	0.267372	+	0.963593i	$0.413845\pi$
$242$	1.22565e6	1.34533
$243$	59049.0	0.0641500
$244$	1.04315e6	1.12169
$245$	−185655.	−0.197602
$246$	545634.	0.574863
$247$	−73335.7	−0.0764844
$248$	−475875.	−0.491319
$249$	−572942.	−0.585615
$250$	1.46787e6	1.48538
$251$	−526100.	−0.527089	−0.263545	−	0.964647i	$-0.584892\pi$
$251$	−526100.	−0.527089	−0.263545	+	0.964647i	$0.584892\pi$
$252$	−523288.	−0.519086
$253$	918062.	0.901718
$254$	2.55843e6	2.48822
$255$	−347677.	−0.334830
$256$	−1.21703e6	−1.16065
$257$	−214918.	−0.202974	−0.101487	−	0.994837i	$-0.532360\pi$
$257$	−214918.	−0.202974	−0.101487	+	0.994837i	$0.532360\pi$
$258$	64738.0	0.0605494
$259$	−308293.	−0.285571
$260$	−964631.	−0.884969
$261$	−621377.	−0.564617
$262$	340607.	0.306549
$263$	−439795.	−0.392068	−0.196034	−	0.980597i	$-0.562806\pi$
$263$	−439795.	−0.392068	−0.196034	+	0.980597i	$0.562806\pi$
$264$	955725.	0.843963
$265$	1.30504e6	1.14159
$266$	−406168.	−0.351967
$267$	−139809.	−0.120021
$268$	−2.98790e6	−2.54114
$269$	860184.	0.724788	0.362394	−	0.932025i	$-0.381960\pi$
$269$	860184.	0.724788	0.362394	+	0.932025i	$0.381960\pi$
$270$	602870.	0.503286
$271$	−2.12669e6	−1.75906	−0.879532	−	0.475840i	$-0.842144\pi$
$271$	−2.12669e6	−1.75906	−0.879532	+	0.475840i	$0.842144\pi$
$272$	−45469.8	−0.0372650
$273$	221036.	0.179497
$274$	2.66833e6	2.14715
$275$	2.65603e6	2.11788
$276$	811264.	0.641047
$277$	2.44085e6	1.91136	0.955680	−	0.294409i	$-0.0951226\pi$
$277$	2.44085e6	1.91136	0.955680	+	0.294409i	$0.0951226\pi$
$278$	−2.79753e6	−2.17101
$279$	−196755.	−0.151327
$280$	−2.13030e6	−1.62385
$281$	−1.75576e6	−1.32647	−0.663237	−	0.748409i	$-0.730818\pi$
$281$	−1.75576e6	−1.32647	−0.663237	+	0.748409i	$0.730818\pi$
$282$	−1.15323e6	−0.863564
$283$	1.52824e6	1.13429	0.567145	−	0.823618i	$-0.308048\pi$
$283$	1.52824e6	1.13429	0.567145	+	0.823618i	$0.308048\pi$
$284$	−1.97815e6	−1.45534
$285$	292232.	0.213115
$286$	−1.01243e6	−0.731899
$287$	−797174.	−0.571279
$288$	−428948.	−0.304736
$289$	−1.23390e6	−0.869028
$290$	−6.34405e6	−4.42967
$291$	−837860.	−0.580015
$292$	4.36632e6	2.99681
$293$	2.08785e6	1.42079	0.710397	−	0.703802i	$-0.248516\pi$
$293$	2.08785e6	1.42079	0.710397	+	0.703802i	$0.248516\pi$
$294$	−172188.	−0.116181
$295$	−311836.	−0.208627
$296$	497561.	0.330078
$297$	395155.	0.259942
$298$	2.27922e6	1.48678
$299$	−342677.	−0.221670
$300$	2.34705e6	1.50564
$301$	−94582.4	−0.0601719
$302$	4.87455e6	3.07551
$303$	−701447.	−0.438923
$304$	38218.6	0.0237187
$305$	1.75583e6	1.08077
$306$	−322456.	−0.196864
$307$	3.15846e6	1.91262	0.956311	−	0.292352i	$-0.0944380\pi$
$307$	3.15846e6	1.91262	0.956311	+	0.292352i	$0.0944380\pi$
$308$	−3.50183e6	−2.10338
$309$	678663.	0.404350
$310$	−2.00880e6	−1.18723
$311$	3.00584e6	1.76224	0.881120	−	0.472892i	$-0.156790\pi$
$311$	3.00584e6	1.76224	0.881120	+	0.472892i	$0.156790\pi$
$312$	−356735.	−0.207472
$313$	−1.02498e6	−0.591365	−0.295683	−	0.955286i	$-0.595547\pi$
$313$	−1.02498e6	−0.591365	−0.295683	+	0.955286i	$0.595547\pi$
$314$	−2.67138e6	−1.52901
$315$	−880795.	−0.500148
$316$	4.12420e6	2.32339
$317$	−1.16894e6	−0.653345	−0.326673	−	0.945138i	$-0.605927\pi$
$317$	−1.16894e6	−0.653345	−0.326673	+	0.945138i	$0.605927\pi$
$318$	1.21037e6	0.671200
$319$	−4.15824e6	−2.28788
$320$	−4.68167e6	−2.55580
$321$	−1.39060e6	−0.753249
$322$	−1.89791e6	−1.02008
$323$	−156305.	−0.0833620
$324$	349186.	0.184797
$325$	−991393.	−0.520640
$326$	−2.60421e6	−1.35716
$327$	−1.68269e6	−0.870230
$328$	1.28658e6	0.660315
$329$	1.68488e6	0.858181
$330$	4.03439e6	2.03936
$331$	3.00630e6	1.50821	0.754105	−	0.656754i	$-0.228071\pi$
$331$	3.00630e6	1.50821	0.754105	+	0.656754i	$0.228071\pi$
$332$	−3.38809e6	−1.68698
$333$	205722.	0.101665
$334$	5.69319e6	2.79247
$335$	−5.02921e6	−2.44843
$336$	−115192.	−0.0556641
$337$	−969092.	−0.464826	−0.232413	−	0.972617i	$-0.574662\pi$
$337$	−969092.	−0.464826	−0.232413	+	0.972617i	$0.574662\pi$
$338$	−3.04971e6	−1.45200
$339$	−1.44128e6	−0.681159
$340$	−2.05599e6	−0.964546
$341$	−1.31668e6	−0.613190
$342$	271033.	0.125302
$343$	2.29170e6	1.05177
$344$	152649.	0.0695500
$345$	1.36552e6	0.617659
$346$	−3.07032e6	−1.37877
$347$	−2.01845e6	−0.899902	−0.449951	−	0.893053i	$-0.648559\pi$
$347$	−2.01845e6	−0.899902	−0.449951	+	0.893053i	$0.648559\pi$
$348$	−3.67451e6	−1.62649
$349$	−2.28363e6	−1.00360	−0.501802	−	0.864983i	$-0.667329\pi$
$349$	−2.28363e6	−1.00360	−0.501802	+	0.864983i	$0.667329\pi$
$350$	−5.49081e6	−2.39589
$351$	−147496.	−0.0639016
$352$	−2.87051e6	−1.23482
$353$	483424.	0.206486	0.103243	−	0.994656i	$-0.467078\pi$
$353$	483424.	0.206486	0.103243	+	0.994656i	$0.467078\pi$
$354$	−289215.	−0.122663
$355$	−3.32961e6	−1.40224
$356$	−826763.	−0.345745
$357$	471110.	0.195637
$358$	2.03214e6	0.838002
$359$	2.19256e6	0.897875	0.448938	−	0.893563i	$-0.351803\pi$
$359$	2.19256e6	0.897875	0.448938	+	0.893563i	$0.351803\pi$
$360$	1.42154e6	0.578098
$361$	−2.34472e6	−0.946941
$362$	−5.63384e6	−2.25961
$363$	1.19491e6	0.475956
$364$	1.30710e6	0.517076
$365$	7.34937e6	2.88747
$366$	1.62846e6	0.635441
$367$	−2.55829e6	−0.991482	−0.495741	−	0.868470i	$-0.665103\pi$
$367$	−2.55829e6	−0.991482	−0.495741	+	0.868470i	$0.665103\pi$
$368$	178585.	0.0687425
$369$	531949.	0.203378
$370$	2.10035e6	0.797604
$371$	−1.76836e6	−0.667016
$372$	−1.16351e6	−0.435927
$373$	1.33933e6	0.498444	0.249222	−	0.968446i	$-0.419825\pi$
$373$	1.33933e6	0.498444	0.249222	+	0.968446i	$0.419825\pi$
$374$	−2.15787e6	−0.797712
$375$	1.43105e6	0.525505
$376$	−2.71927e6	−0.991932
$377$	1.55211e6	0.562431
$378$	−816903.	−0.294063
$379$	−124784.	−0.0446234	−0.0223117	−	0.999751i	$-0.507103\pi$
$379$	−124784.	−0.0446234	−0.0223117	+	0.999751i	$0.507103\pi$
$380$	1.72811e6	0.613922
$381$	2.49425e6	0.880295
$382$	3.21731e6	1.12807
$383$	2.20676e6	0.768703	0.384351	−	0.923187i	$-0.374425\pi$
$383$	2.20676e6	0.768703	0.384351	+	0.923187i	$0.374425\pi$
$384$	−2.81692e6	−0.974869
$385$	−5.89426e6	−2.02664
$386$	1.17102e6	0.400035
$387$	63114.2	0.0214215
$388$	−4.95469e6	−1.67085
$389$	3.70241e6	1.24054	0.620269	−	0.784389i	$-0.287023\pi$
$389$	3.70241e6	1.24054	0.620269	+	0.784389i	$0.287023\pi$
$390$	−1.50588e6	−0.501337
$391$	−730371.	−0.241603
$392$	−406010.	−0.133451
$393$	332063.	0.108452
$394$	3.18286e6	1.03294
$395$	6.94183e6	2.23862
$396$	2.33675e6	0.748814
$397$	2.11382e6	0.673118	0.336559	−	0.941662i	$-0.390737\pi$
$397$	2.11382e6	0.673118	0.336559	+	0.941662i	$0.390737\pi$
$398$	4.69344e6	1.48520
$399$	−395980.	−0.124521
$400$	516661.	0.161456
$401$	−2.67664e6	−0.831245	−0.415623	−	0.909537i	$-0.636436\pi$
$401$	−2.67664e6	−0.831245	−0.415623	+	0.909537i	$0.636436\pi$
$402$	−4.66440e6	−1.43956
$403$	491466.	0.150741
$404$	−4.14801e6	−1.26440
$405$	587749.	0.178055
$406$	8.59633e6	2.58820
$407$	1.37669e6	0.411954
$408$	−760335.	−0.226128
$409$	3.98828e6	1.17890	0.589451	−	0.807804i	$-0.299344\pi$
$409$	3.98828e6	1.17890	0.589451	+	0.807804i	$0.299344\pi$
$410$	5.43101e6	1.59559
$411$	2.60140e6	0.759632
$412$	4.01328e6	1.16481
$413$	422544.	0.121898
$414$	1.26646e6	0.363154
$415$	−5.70282e6	−1.62543
$416$	1.07145e6	0.303556
$417$	−2.72736e6	−0.768072
$418$	1.81375e6	0.507734
$419$	−3.00819e6	−0.837087	−0.418543	−	0.908197i	$-0.637459\pi$
$419$	−3.00819e6	−0.837087	−0.418543	+	0.908197i	$0.637459\pi$
$420$	−5.20859e6	−1.44078
$421$	−7.18527e6	−1.97578	−0.987888	−	0.155170i	$-0.950407\pi$
$421$	−7.18527e6	−1.97578	−0.987888	+	0.155170i	$0.950407\pi$
$422$	7.37003e6	2.01460
$423$	−1.12431e6	−0.305516
$424$	2.85400e6	0.770973
$425$	−2.11302e6	−0.567456
$426$	−3.08808e6	−0.824451
$427$	−2.37919e6	−0.631480
$428$	−8.22330e6	−2.16988
$429$	−987039.	−0.258935
$430$	644374.	0.168061
$431$	3.00434e6	0.779032	0.389516	−	0.921020i	$-0.372642\pi$
$431$	3.00434e6	0.779032	0.389516	+	0.921020i	$0.372642\pi$
$432$	76867.0	0.0198167
$433$	1.50180e6	0.384938	0.192469	−	0.981303i	$-0.438350\pi$
$433$	1.50180e6	0.384938	0.192469	+	0.981303i	$0.438350\pi$
$434$	2.72198e6	0.693681
$435$	−6.18492e6	−1.56715
$436$	−9.95057e6	−2.50687
$437$	613897.	0.153777
$438$	6.81626e6	1.69770
$439$	1.12031e6	0.277445	0.138722	−	0.990331i	$-0.455700\pi$
$439$	1.12031e6	0.277445	0.138722	+	0.990331i	$0.455700\pi$
$440$	9.51289e6	2.34251
$441$	−167869.	−0.0411030
$442$	805449.	0.196102
$443$	−312245.	−0.0755937	−0.0377969	−	0.999285i	$-0.512034\pi$
$443$	−312245.	−0.0755937	−0.0377969	+	0.999285i	$0.512034\pi$
$444$	1.21654e6	0.292865
$445$	−1.39160e6	−0.333131
$446$	5.84431e6	1.39122
$447$	2.22205e6	0.526000
$448$	6.34378e6	1.49332
$449$	−7.57161e6	−1.77244	−0.886222	−	0.463261i	$-0.846679\pi$
$449$	−7.57161e6	−1.77244	−0.886222	+	0.463261i	$0.846679\pi$
$450$	3.66398e6	0.852946
$451$	3.55979e6	0.824105
$452$	−8.52300e6	−1.96221
$453$	4.75229e6	1.08807
$454$	9.77522e6	2.22580
$455$	2.20010e6	0.498212
$456$	639082.	0.143928
$457$	529334.	0.118560	0.0592801	−	0.998241i	$-0.481119\pi$
$457$	529334.	0.118560	0.0592801	+	0.998241i	$0.481119\pi$
$458$	3.01900e6	0.672511
$459$	−314368.	−0.0696477
$460$	8.07498e6	1.77929
$461$	−2.93740e6	−0.643740	−0.321870	−	0.946784i	$-0.604311\pi$
$461$	−2.93740e6	−0.643740	−0.321870	+	0.946784i	$0.604311\pi$
$462$	−5.46670e6	−1.19157
$463$	5.29725e6	1.14841	0.574206	−	0.818711i	$-0.305311\pi$
$463$	5.29725e6	1.14841	0.574206	+	0.818711i	$0.305311\pi$
$464$	−808877.	−0.174416
$465$	−1.95842e6	−0.420023
$466$	1.08105e7	2.30612
$467$	−6.50929e6	−1.38115	−0.690576	−	0.723260i	$-0.742643\pi$
$467$	−6.50929e6	−1.38115	−0.690576	+	0.723260i	$0.742643\pi$
$468$	−872217.	−0.184081
$469$	6.81470e6	1.43059
$470$	−1.14788e7	−2.39691
$471$	−2.60437e6	−0.540942
$472$	−681954.	−0.140896
$473$	422359.	0.0868018
$474$	6.43827e6	1.31621
$475$	1.77605e6	0.361179
$476$	2.78591e6	0.563572
$477$	1.18001e6	0.237461
$478$	5.27633e6	1.05624
$479$	4.95192e6	0.986131	0.493065	−	0.869992i	$-0.335876\pi$
$479$	4.95192e6	0.986131	0.493065	+	0.869992i	$0.335876\pi$
$480$	−4.26956e6	−0.845825
$481$	−513863.	−0.101271
$482$	4.45106e6	0.872661
$483$	−1.85030e6	−0.360891
$484$	7.06608e6	1.37109
$485$	−8.33970e6	−1.60989
$486$	545114.	0.104688
$487$	−5.32846e6	−1.01807	−0.509037	−	0.860745i	$-0.669998\pi$
$487$	−5.32846e6	−1.01807	−0.509037	+	0.860745i	$0.669998\pi$
$488$	3.83983e6	0.729898
$489$	−2.53889e6	−0.480144
$490$	−1.71388e6	−0.322472
$491$	−7.43544e6	−1.39188	−0.695942	−	0.718098i	$-0.745013\pi$
$491$	−7.43544e6	−1.39188	−0.695942	+	0.718098i	$0.745013\pi$
$492$	3.14568e6	0.585871
$493$	3.30812e6	0.613005
$494$	−677002.	−0.124817
$495$	3.93320e6	0.721495
$496$	−256126.	−0.0467465
$497$	4.51170e6	0.819312
$498$	−5.28914e6	−0.955679
$499$	2.82668e6	0.508188	0.254094	−	0.967179i	$-0.418223\pi$
$499$	2.82668e6	0.508188	0.254094	+	0.967179i	$0.418223\pi$
$500$	8.46252e6	1.51382
$501$	5.55039e6	0.987936
$502$	−4.85672e6	−0.860169
$503$	−7.04752e6	−1.24199	−0.620993	−	0.783816i	$-0.713270\pi$
$503$	−7.04752e6	−1.24199	−0.620993	+	0.783816i	$0.713270\pi$
$504$	−1.92621e6	−0.337776
$505$	−6.98190e6	−1.21828
$506$	8.47513e6	1.47153
$507$	−2.97321e6	−0.513696
$508$	1.47498e7	2.53587
$509$	−3.11157e6	−0.532334	−0.266167	−	0.963927i	$-0.585757\pi$
$509$	−3.11157e6	−0.532334	−0.266167	+	0.963927i	$0.585757\pi$
$510$	−3.20959e6	−0.546418
$511$	−9.95857e6	−1.68712
$512$	−1.21940e6	−0.205576
$513$	264235.	0.0443299
$514$	−1.98402e6	−0.331237
$515$	6.75512e6	1.12232
$516$	373226.	0.0617089
$517$	−7.52384e6	−1.23798
$518$	−2.84602e6	−0.466030
$519$	−2.99331e6	−0.487790
$520$	−3.55079e6	−0.575860
$521$	−1.27221e6	−0.205336	−0.102668	−	0.994716i	$-0.532738\pi$
$521$	−1.27221e6	−0.205336	−0.102668	+	0.994716i	$0.532738\pi$
$522$	−5.73627e6	−0.921411
$523$	−2.80084e6	−0.447748	−0.223874	−	0.974618i	$-0.571870\pi$
$523$	−2.80084e6	−0.447748	−0.223874	+	0.974618i	$0.571870\pi$
$524$	1.96366e6	0.312419
$525$	−5.35309e6	−0.847629
$526$	−4.05999e6	−0.639824
$527$	1.04750e6	0.164296
$528$	514392.	0.0802988
$529$	−3.56778e6	−0.554317
$530$	1.20476e7	1.86298
$531$	−281961.	−0.0433963
$532$	−2.34163e6	−0.358707
$533$	−1.32873e6	−0.202590
$534$	−1.29066e6	−0.195865
$535$	−1.38414e7	−2.09072
$536$	−1.09984e7	−1.65355
$537$	1.98117e6	0.296473
$538$	7.94083e6	1.18280
$539$	−1.12337e6	−0.166553
$540$	3.47565e6	0.512923
$541$	−9.35654e6	−1.37443	−0.687214	−	0.726455i	$-0.741167\pi$
$541$	−9.35654e6	−1.37443	−0.687214	+	0.726455i	$0.741167\pi$
$542$	−1.96327e7	−2.87066
$543$	−5.49253e6	−0.799415
$544$	2.28366e6	0.330852
$545$	−1.67488e7	−2.41541
$546$	2.04051e6	0.292925
$547$	5.63105e6	0.804676	0.402338	−	0.915491i	$-0.368198\pi$
$547$	5.63105e6	0.804676	0.402338	+	0.915491i	$0.368198\pi$
$548$	1.53834e7	2.18827
$549$	1.58762e6	0.224810
$550$	2.45193e7	3.45621
$551$	−2.78057e6	−0.390170
$552$	2.98625e6	0.417137
$553$	−9.40634e6	−1.30800
$554$	2.25329e7	3.11919
$555$	2.04767e6	0.282180
$556$	−1.61282e7	−2.21259
$557$	−1.18592e7	−1.61964	−0.809818	−	0.586681i	$-0.800434\pi$
$557$	−1.18592e7	−1.61964	−0.809818	+	0.586681i	$0.800434\pi$
$558$	−1.81636e6	−0.246954
$559$	−157650.	−0.0213385
$560$	−1.14657e6	−0.154501
$561$	−2.10375e6	−0.282219
$562$	−1.62084e7	−2.16470
$563$	1.16587e7	1.55017	0.775085	−	0.631856i	$-0.217707\pi$
$563$	1.16587e7	1.55017	0.775085	+	0.631856i	$0.217707\pi$
$564$	−6.64860e6	−0.880101
$565$	−1.43459e7	−1.89063
$566$	1.41080e7	1.85107
$567$	−796413.	−0.104035
$568$	−7.28153e6	−0.947005
$569$	−6.42402e6	−0.831814	−0.415907	−	0.909407i	$-0.636536\pi$
$569$	−6.42402e6	−0.831814	−0.415907	+	0.909407i	$0.636536\pi$
$570$	2.69775e6	0.347788
$571$	1.91324e6	0.245573	0.122786	−	0.992433i	$-0.460817\pi$
$571$	1.91324e6	0.245573	0.122786	+	0.992433i	$0.460817\pi$
$572$	−5.83686e6	−0.745914
$573$	3.13662e6	0.399094
$574$	−7.35915e6	−0.932283
$575$	8.29900e6	1.04678
$576$	−4.23316e6	−0.531628
$577$	3.05466e6	0.381965	0.190983	−	0.981593i	$-0.438833\pi$
$577$	3.05466e6	0.381965	0.190983	+	0.981593i	$0.438833\pi$
$578$	−1.13908e7	−1.41819
$579$	1.14165e6	0.141526
$580$	−3.65746e7	−4.51449
$581$	7.72746e6	0.949721
$582$	−7.73475e6	−0.946539
$583$	7.89663e6	0.962211
$584$	1.60724e7	1.95006
$585$	−1.46811e6	−0.177366
$586$	1.92741e7	2.31862
$587$	1.06077e7	1.27065	0.635325	−	0.772245i	$-0.280866\pi$
$587$	1.06077e7	1.27065	0.635325	+	0.772245i	$0.280866\pi$
$588$	−992693.	−0.118405
$589$	−880449.	−0.104572
$590$	−2.87873e6	−0.340463
$591$	3.10302e6	0.365440
$592$	267798.	0.0314053
$593$	−8.48186e6	−0.990500	−0.495250	−	0.868751i	$-0.664923\pi$
$593$	−8.48186e6	−0.990500	−0.495250	+	0.868751i	$0.664923\pi$
$594$	3.64789e6	0.424205
$595$	4.68923e6	0.543011
$596$	1.31401e7	1.51525
$597$	4.57572e6	0.525440
$598$	−3.16344e6	−0.361748
$599$	1.50366e7	1.71231	0.856155	−	0.516718i	$-0.172847\pi$
$599$	1.50366e7	1.71231	0.856155	+	0.516718i	$0.172847\pi$
$600$	8.63947e6	0.979736
$601$	1.00070e7	1.13010	0.565050	−	0.825057i	$-0.308857\pi$
$601$	1.00070e7	1.13010	0.565050	+	0.825057i	$0.308857\pi$
$602$	−873142.	−0.0981960
$603$	−4.54740e6	−0.509296
$604$	2.81027e7	3.13441
$605$	1.18936e7	1.32107
$606$	−6.47544e6	−0.716288
$607$	9.84700e6	1.08476	0.542378	−	0.840134i	$-0.317524\pi$
$607$	9.84700e6	1.08476	0.542378	+	0.840134i	$0.317524\pi$
$608$	−1.91947e6	−0.210583
$609$	8.38071e6	0.915667
$610$	1.62090e7	1.76373
$611$	2.80836e6	0.304333
$612$	−1.85902e6	−0.200634
$613$	5.23546e6	0.562735	0.281368	−	0.959600i	$-0.409212\pi$
$613$	5.23546e6	0.562735	0.281368	+	0.959600i	$0.409212\pi$
$614$	2.91575e7	3.12125
$615$	5.29479e6	0.564496
$616$	−1.28902e7	−1.36870
$617$	−1.58209e7	−1.67308	−0.836542	−	0.547902i	$-0.815427\pi$
$617$	−1.58209e7	−1.67308	−0.836542	+	0.547902i	$0.815427\pi$
$618$	6.26511e6	0.659869
$619$	−1.50849e7	−1.58240	−0.791198	−	0.611560i	$-0.790542\pi$
$619$	−1.50849e7	−1.58240	−0.791198	+	0.611560i	$0.790542\pi$
$620$	−1.15811e7	−1.20996
$621$	1.23470e6	0.128479
$622$	2.77486e7	2.87584
$623$	1.88565e6	0.194644
$624$	−192003.	−0.0197399
$625$	−1.06833e6	−0.109397
$626$	−9.46218e6	−0.965062
$627$	1.76825e6	0.179629
$628$	−1.54010e7	−1.55829
$629$	−1.09523e6	−0.110377
$630$	−8.13111e6	−0.816203
$631$	7.96398e6	0.796264	0.398132	−	0.917328i	$-0.369659\pi$
$631$	7.96398e6	0.796264	0.398132	+	0.917328i	$0.369659\pi$
$632$	1.51811e7	1.51186
$633$	7.18517e6	0.712735
$634$	−1.07911e7	−1.06621
$635$	2.48268e7	2.44335
$636$	6.97802e6	0.684053
$637$	419312.	0.0409439
$638$	−3.83870e7	−3.73364
$639$	−3.01063e6	−0.291679
$640$	−2.80384e7	−2.70585
$641$	9.73869e6	0.936172	0.468086	−	0.883683i	$-0.344944\pi$
$641$	9.73869e6	0.936172	0.468086	+	0.883683i	$0.344944\pi$
$642$	−1.28374e7	−1.22924
$643$	2.84747e6	0.271601	0.135801	−	0.990736i	$-0.456639\pi$
$643$	2.84747e6	0.271601	0.135801	+	0.990736i	$0.456639\pi$
$644$	−1.09418e7	−1.03962
$645$	628212.	0.0594575
$646$	−1.44294e6	−0.136040
$647$	−1.48035e7	−1.39028	−0.695140	−	0.718874i	$-0.744658\pi$
$647$	−1.48035e7	−1.39028	−0.695140	+	0.718874i	$0.744658\pi$
$648$	1.28535e6	0.120250
$649$	−1.88688e6	−0.175846
$650$	−9.15209e6	−0.849644
$651$	2.65370e6	0.245414
$652$	−1.50137e7	−1.38315
$653$	−4.55203e6	−0.417755	−0.208878	−	0.977942i	$-0.566981\pi$
$653$	−4.55203e6	−0.417755	−0.208878	+	0.977942i	$0.566981\pi$
$654$	−1.55338e7	−1.42015
$655$	3.30522e6	0.301021
$656$	692463.	0.0628257
$657$	6.64529e6	0.600621
$658$	1.55540e7	1.40049
$659$	1.78757e7	1.60343	0.801714	−	0.597708i	$-0.203922\pi$
$659$	1.78757e7	1.60343	0.801714	+	0.597708i	$0.203922\pi$
$660$	2.32590e7	2.07841
$661$	3.89590e6	0.346820	0.173410	−	0.984850i	$-0.444521\pi$
$661$	3.89590e6	0.346820	0.173410	+	0.984850i	$0.444521\pi$
$662$	2.77528e7	2.46128
$663$	785247.	0.0693781
$664$	−1.24715e7	−1.09774
$665$	−3.94142e6	−0.345620
$666$	1.89913e6	0.165909
$667$	−1.29928e7	−1.13081
$668$	3.28222e7	2.84595
$669$	5.69772e6	0.492193
$670$	−4.64274e7	−3.99565
$671$	1.06243e7	0.910949
$672$	5.78536e6	0.494205
$673$	−2.23886e6	−0.190541	−0.0952706	−	0.995451i	$-0.530372\pi$
$673$	−2.23886e6	−0.190541	−0.0952706	+	0.995451i	$0.530372\pi$
$674$	−8.94622e6	−0.758560
$675$	3.57208e6	0.301760
$676$	−1.75821e7	−1.47980
$677$	8.27181e6	0.693631	0.346816	−	0.937933i	$-0.387263\pi$
$677$	8.27181e6	0.693631	0.346816	+	0.937933i	$0.387263\pi$
$678$	−1.33052e7	−1.11160
$679$	1.13005e7	0.940639
$680$	−7.56805e6	−0.627642
$681$	9.53004e6	0.787457
$682$	−1.21550e7	−1.00068
$683$	−1.20134e7	−0.985403	−0.492702	−	0.870198i	$-0.663991\pi$
$683$	−1.20134e7	−0.985403	−0.492702	+	0.870198i	$0.663991\pi$
$684$	1.56255e6	0.127701
$685$	2.58933e7	2.10844
$686$	2.11559e7	1.71641
$687$	2.94328e6	0.237925
$688$	82158.8	0.00661733
$689$	−2.94751e6	−0.236541
$690$	1.26058e7	1.00797
$691$	6.53362e6	0.520545	0.260273	−	0.965535i	$-0.416188\pi$
$691$	6.53362e6	0.520545	0.260273	+	0.965535i	$0.416188\pi$
$692$	−1.77009e7	−1.40518
$693$	−5.32958e6	−0.421560
$694$	−1.86335e7	−1.46857
$695$	−2.71470e7	−2.13186
$696$	−1.35258e7	−1.05838
$697$	−2.83202e6	−0.220808
$698$	−2.10814e7	−1.63780
$699$	1.05393e7	0.815870
$700$	−3.16555e7	−2.44177
$701$	−7.08221e6	−0.544344	−0.272172	−	0.962249i	$-0.587742\pi$
$701$	−7.08221e6	−0.544344	−0.272172	+	0.962249i	$0.587742\pi$
$702$	−1.36162e6	−0.104283
$703$	920573.	0.0702538
$704$	−2.83282e7	−2.15421
$705$	−1.11909e7	−0.847992
$706$	4.46275e6	0.336970
$707$	9.46064e6	0.711823
$708$	−1.66738e6	−0.125012
$709$	−7.79243e6	−0.582180	−0.291090	−	0.956696i	$-0.594018\pi$
$709$	−7.79243e6	−0.582180	−0.291090	+	0.956696i	$0.594018\pi$
$710$	−3.07375e7	−2.28835
$711$	6.27679e6	0.465654
$712$	−3.04330e6	−0.224980
$713$	−4.11409e6	−0.303075
$714$	4.34907e6	0.319265
$715$	−9.82457e6	−0.718701
$716$	1.17156e7	0.854049
$717$	5.14398e6	0.373682
$718$	2.02408e7	1.46526
$719$	−8.35425e6	−0.602678	−0.301339	−	0.953517i	$-0.597434\pi$
$719$	−8.35425e6	−0.602678	−0.301339	+	0.953517i	$0.597434\pi$
$720$	765101.	0.0550032
$721$	−9.15335e6	−0.655755
$722$	−2.16454e7	−1.54533
$723$	4.33942e6	0.308735
$724$	−3.24801e7	−2.30288
$725$	−3.75892e7	−2.65594
$726$	1.10308e7	0.776724
$727$	1.48925e7	1.04503	0.522517	−	0.852629i	$-0.324993\pi$
$727$	1.48925e7	1.04503	0.522517	+	0.852629i	$0.324993\pi$
$728$	4.81140e6	0.336468
$729$	531441.	0.0370370
$730$	6.78461e7	4.71214
$731$	−336011.	−0.0232573
$732$	9.38838e6	0.647609
$733$	−495642.	−0.0340728	−0.0170364	−	0.999855i	$-0.505423\pi$
$733$	−495642.	−0.0340728	−0.0170364	+	0.999855i	$0.505423\pi$
$734$	−2.36170e7	−1.61802
$735$	−1.67090e6	−0.114086
$736$	−8.96916e6	−0.610320
$737$	−3.04311e7	−2.06371
$738$	4.91071e6	0.331897
$739$	−1.10697e7	−0.745633	−0.372816	−	0.927905i	$-0.621608\pi$
$739$	−1.10697e7	−0.745633	−0.372816	+	0.927905i	$0.621608\pi$
$740$	1.21089e7	0.812877
$741$	−660021.	−0.0441583
$742$	−1.63247e7	−1.08852
$743$	−8.05234e6	−0.535119	−0.267559	−	0.963541i	$-0.586217\pi$
$743$	−8.05234e6	−0.535119	−0.267559	+	0.963541i	$0.586217\pi$
$744$	−4.28287e6	−0.283663
$745$	2.21174e7	1.45997
$746$	1.23641e7	0.813423
$747$	−5.15648e6	−0.338105
$748$	−1.24405e7	−0.812988
$749$	1.87554e7	1.22158
$750$	1.32108e7	0.857584
$751$	−2.48039e7	−1.60480	−0.802399	−	0.596788i	$-0.796443\pi$
$751$	−2.48039e7	−1.60480	−0.802399	+	0.596788i	$0.796443\pi$
$752$	−1.46357e6	−0.0943774
$753$	−4.73490e6	−0.304315
$754$	1.43284e7	0.917844
$755$	4.73023e7	3.02005
$756$	−4.70959e6	−0.299694
$757$	4.14819e6	0.263099	0.131549	−	0.991310i	$-0.458005\pi$
$757$	4.14819e6	0.263099	0.131549	+	0.991310i	$0.458005\pi$
$758$	−1.15195e6	−0.0728219
$759$	8.26256e6	0.520607
$760$	6.36115e6	0.399486
$761$	−4.38843e6	−0.274693	−0.137346	−	0.990523i	$-0.543857\pi$
$761$	−4.38843e6	−0.274693	−0.137346	+	0.990523i	$0.543857\pi$
$762$	2.30258e7	1.43657
$763$	2.26950e7	1.41130
$764$	1.85484e7	1.14967
$765$	−3.12909e6	−0.193314
$766$	2.03718e7	1.25446
$767$	704298.	0.0432283
$768$	−1.09533e7	−0.670104
$769$	6.58376e6	0.401475	0.200737	−	0.979645i	$-0.435666\pi$
$769$	6.58376e6	0.401475	0.200737	+	0.979645i	$0.435666\pi$
$770$	−5.44132e7	−3.30733
$771$	−1.93426e6	−0.117187
$772$	6.75117e6	0.407695
$773$	1.53957e7	0.926723	0.463361	−	0.886169i	$-0.346643\pi$
$773$	1.53957e7	0.926723	0.463361	+	0.886169i	$0.346643\pi$
$774$	582642.	0.0349582
$775$	−1.19024e7	−0.711837
$776$	−1.82381e7	−1.08724
$777$	−2.77464e6	−0.164875
$778$	3.41789e7	2.02446
$779$	2.38039e6	0.140541
$780$	−8.68168e6	−0.510937
$781$	−2.01470e7	−1.18191
$782$	−6.74246e6	−0.394277
$783$	−5.59239e6	−0.325982
$784$	−218523.	−0.0126972
$785$	−2.59228e7	−1.50144
$786$	3.06546e6	0.176986
$787$	−3.16211e7	−1.81987	−0.909935	−	0.414750i	$-0.863869\pi$
$787$	−3.16211e7	−1.81987	−0.909935	+	0.414750i	$0.863869\pi$
$788$	1.83497e7	1.05272
$789$	−3.95816e6	−0.226360
$790$	6.40839e7	3.65326
$791$	1.94390e7	1.10467
$792$	8.60153e6	0.487262
$793$	−3.96564e6	−0.223939
$794$	1.95138e7	1.09848
$795$	1.17454e7	0.659096
$796$	2.70585e7	1.51364
$797$	2.35875e6	0.131534	0.0657668	−	0.997835i	$-0.479051\pi$
$797$	2.35875e6	0.131534	0.0657668	+	0.997835i	$0.479051\pi$
$798$	−3.65551e6	−0.203208
$799$	5.98565e6	0.331699
$800$	−2.59485e7	−1.43347
$801$	−1.25828e6	−0.0692943
$802$	−2.47095e7	−1.35653
$803$	4.44701e7	2.43377
$804$	−2.68911e7	−1.46713
$805$	−1.84172e7	−1.00169
$806$	4.53700e6	0.245998
$807$	7.74166e6	0.418456
$808$	−1.52687e7	−0.822763
$809$	−101171.	−0.00543479	−0.00271740	−	0.999996i	$-0.500865\pi$
$809$	−101171.	−0.00543479	−0.00271740	+	0.999996i	$0.500865\pi$
$810$	5.42583e6	0.290572
$811$	2.38375e7	1.27265	0.636324	−	0.771422i	$-0.280454\pi$
$811$	2.38375e7	1.27265	0.636324	+	0.771422i	$0.280454\pi$
$812$	4.95594e7	2.63776
$813$	−1.91402e7	−1.01560
$814$	1.27089e7	0.672277
$815$	−2.52710e7	−1.33269
$816$	−409229.	−0.0215150
$817$	282426.	0.0148030
$818$	3.68180e7	1.92388
$819$	1.98932e6	0.103632
$820$	3.13108e7	1.62614
$821$	8.77488e6	0.454343	0.227171	−	0.973855i	$-0.427052\pi$
$821$	8.77488e6	0.454343	0.227171	+	0.973855i	$0.427052\pi$
$822$	2.40150e7	1.23966
$823$	−2.52557e6	−0.129975	−0.0649875	−	0.997886i	$-0.520701\pi$
$823$	−2.52557e6	−0.129975	−0.0649875	+	0.997886i	$0.520701\pi$
$824$	1.47728e7	0.757957
$825$	2.39043e7	1.22276
$826$	3.90074e6	0.198928
$827$	−653924.	−0.0332478	−0.0166239	−	0.999862i	$-0.505292\pi$
$827$	−653924.	−0.0332478	−0.0166239	+	0.999862i	$0.505292\pi$
$828$	7.30138e6	0.370108
$829$	−2.14350e7	−1.08327	−0.541636	−	0.840613i	$-0.682195\pi$
$829$	−2.14350e7	−1.08327	−0.541636	+	0.840613i	$0.682195\pi$
$830$	−5.26459e7	−2.65258
$831$	2.19677e7	1.10352
$832$	1.05738e7	0.529570
$833$	893710.	0.0446256
$834$	−2.51777e7	−1.25343
$835$	5.52462e7	2.74212
$836$	1.04566e7	0.517457
$837$	−1.77080e6	−0.0873686
$838$	−2.77703e7	−1.36606
$839$	−6.47262e6	−0.317450	−0.158725	−	0.987323i	$-0.550738\pi$
$839$	−6.47262e6	−0.317450	−0.158725	+	0.987323i	$0.550738\pi$
$840$	−1.91727e7	−0.937531
$841$	3.83380e7	1.86913
$842$	−6.63311e7	−3.22431
$843$	−1.58018e7	−0.765841
$844$	4.24895e7	2.05318
$845$	−2.95941e7	−1.42582
$846$	−1.03791e7	−0.498579
$847$	−1.61161e7	−0.771882
$848$	1.53608e6	0.0733542
$849$	1.37541e7	0.654883
$850$	−1.95065e7	−0.926045
$851$	4.30158e6	0.203612
$852$	−1.78033e7	−0.840238
$853$	−9.71818e6	−0.457312	−0.228656	−	0.973507i	$-0.573433\pi$
$853$	−9.71818e6	−0.457312	−0.228656	+	0.973507i	$0.573433\pi$
$854$	−2.19636e7	−1.03053
$855$	2.63008e6	0.123042
$856$	−3.02698e7	−1.41197
$857$	6.76227e6	0.314514	0.157257	−	0.987558i	$-0.449735\pi$
$857$	6.76227e6	0.314514	0.157257	+	0.987558i	$0.449735\pi$
$858$	−9.11190e6	−0.422562
$859$	2.19326e7	1.01416	0.507080	−	0.861899i	$-0.330725\pi$
$859$	2.19326e7	1.01416	0.507080	+	0.861899i	$0.330725\pi$
$860$	3.71493e6	0.171279
$861$	−7.17456e6	−0.329828
$862$	2.77347e7	1.27132
$863$	8.93392e6	0.408333	0.204167	−	0.978936i	$-0.434552\pi$
$863$	8.93392e6	0.408333	0.204167	+	0.978936i	$0.434552\pi$
$864$	−3.86053e6	−0.175939
$865$	−2.97941e7	−1.35391
$866$	1.38639e7	0.628190
$867$	−1.11051e7	−0.501734
$868$	1.56927e7	0.706965
$869$	4.20041e7	1.88687
$870$	−5.70964e7	−2.55747
$871$	1.13588e7	0.507324
$872$	−3.66279e7	−1.63125
$873$	−7.54074e6	−0.334872
$874$	5.66722e6	0.250952
$875$	−1.93010e7	−0.852238
$876$	3.92969e7	1.73021
$877$	−4.03113e7	−1.76981	−0.884907	−	0.465767i	$-0.845778\pi$
$877$	−4.03113e7	−1.76981	−0.884907	+	0.465767i	$0.845778\pi$
$878$	1.03422e7	0.452769
$879$	1.87907e7	0.820295
$880$	5.12004e6	0.222878
$881$	5.96563e6	0.258950	0.129475	−	0.991583i	$-0.458671\pi$
$881$	5.96563e6	0.258950	0.129475	+	0.991583i	$0.458671\pi$
$882$	−1.54969e6	−0.0670770
$883$	3.38326e7	1.46027	0.730136	−	0.683302i	$-0.239457\pi$
$883$	3.38326e7	1.46027	0.730136	+	0.683302i	$0.239457\pi$
$884$	4.64356e6	0.199857
$885$	−2.80652e6	−0.120451
$886$	−2.88250e6	−0.123363
$887$	−3.81525e7	−1.62822	−0.814112	−	0.580708i	$-0.802776\pi$
$887$	−3.81525e7	−1.62822	−0.814112	+	0.580708i	$0.802776\pi$
$888$	4.47805e6	0.190571
$889$	−3.36408e7	−1.42762
$890$	−1.28467e7	−0.543644
$891$	3.55639e6	0.150077
$892$	3.36935e7	1.41786
$893$	−5.03110e6	−0.211123
$894$	2.05130e7	0.858392
$895$	1.97197e7	0.822891
$896$	3.79927e7	1.58099
$897$	−3.08409e6	−0.127981
$898$	−6.98977e7	−2.89249
$899$	1.86342e7	0.768975
$900$	2.11235e7	0.869279
$901$	−6.28223e6	−0.257811
$902$	3.28624e7	1.34488
$903$	−851242.	−0.0347403
$904$	−3.13730e7	−1.27684
$905$	−5.46703e7	−2.21886
$906$	4.38710e7	1.77565
$907$	−9.47966e6	−0.382626	−0.191313	−	0.981529i	$-0.561275\pi$
$907$	−9.47966e6	−0.382626	−0.191313	+	0.981529i	$0.561275\pi$
$908$	5.63559e7	2.26843
$909$	−6.31302e6	−0.253412
$910$	2.03103e7	0.813043
$911$	1.83383e7	0.732087	0.366043	−	0.930598i	$-0.380712\pi$
$911$	1.83383e7	0.732087	0.366043	+	0.930598i	$0.380712\pi$
$912$	343968.	0.0136940
$913$	−3.45070e7	−1.37003
$914$	4.88657e6	0.193481
$915$	1.58025e7	0.623982
$916$	1.74051e7	0.685389
$917$	−4.47865e6	−0.175883
$918$	−2.90211e6	−0.113660
$919$	−1.14654e7	−0.447816	−0.223908	−	0.974610i	$-0.571882\pi$
$919$	−1.14654e7	−0.447816	−0.223908	+	0.974610i	$0.571882\pi$
$920$	2.97239e7	1.15781
$921$	2.84261e7	1.10425
$922$	−2.71168e7	−1.05053
$923$	7.52011e6	0.290549
$924$	−3.15165e7	−1.21439
$925$	1.24448e7	0.478227
$926$	4.89018e7	1.87412
$927$	6.10797e6	0.233452
$928$	4.06246e7	1.54853
$929$	3.21954e7	1.22392	0.611962	−	0.790887i	$-0.290380\pi$
$929$	3.21954e7	1.22392	0.611962	+	0.790887i	$0.290380\pi$
$930$	−1.80792e7	−0.685445
$931$	−751187.	−0.0284036
$932$	6.23244e7	2.35027
$933$	2.70526e7	1.01743
$934$	−6.00908e7	−2.25393
$935$	−2.09398e7	−0.783327
$936$	−3.21062e6	−0.119784
$937$	1.18294e7	0.440165	0.220082	−	0.975481i	$-0.429367\pi$
$937$	1.18294e7	0.440165	0.220082	+	0.975481i	$0.429367\pi$
$938$	6.29103e7	2.33461
$939$	−9.22484e6	−0.341425
$940$	−6.61773e7	−2.44281
$941$	3.64458e7	1.34176	0.670878	−	0.741568i	$-0.265917\pi$
$941$	3.64458e7	1.34176	0.670878	+	0.741568i	$0.265917\pi$
$942$	−2.40424e7	−0.882776
$943$	1.11229e7	0.407322
$944$	−367042.	−0.0134056
$945$	−7.92716e6	−0.288761
$946$	3.89903e6	0.141654
$947$	−2.71277e7	−0.982965	−0.491483	−	0.870887i	$-0.663545\pi$
$947$	−2.71277e7	−0.982965	−0.491483	+	0.870887i	$0.663545\pi$
$948$	3.71178e7	1.34141
$949$	−1.65990e7	−0.598295
$950$	1.63957e7	0.589416
$951$	−1.05204e7	−0.377209
$952$	1.02549e7	0.366723
$953$	2.81557e7	1.00423	0.502117	−	0.864800i	$-0.332555\pi$
$953$	2.81557e7	1.00423	0.502117	+	0.864800i	$0.332555\pi$
$954$	1.08934e7	0.387517
$955$	3.12205e7	1.10773
$956$	3.04190e7	1.07646
$957$	−3.74242e7	−1.32091
$958$	4.57139e7	1.60929
$959$	−3.50860e7	−1.23193
$960$	−4.21351e7	−1.47559
$961$	−2.27287e7	−0.793902
$962$	−4.74375e6	−0.165266
$963$	−1.25154e7	−0.434889
$964$	2.56611e7	0.889372
$965$	1.13635e7	0.392821
$966$	−1.70812e7	−0.588946
$967$	−5.11650e7	−1.75957	−0.879785	−	0.475372i	$-0.842313\pi$
$967$	−5.11650e7	−1.75957	−0.879785	+	0.475372i	$0.842313\pi$
$968$	2.60101e7	0.892183
$969$	−1.40675e6	−0.0481290
$970$	−7.69884e7	−2.62722
$971$	−6.44355e6	−0.219319	−0.109660	−	0.993969i	$-0.534976\pi$
$971$	−6.44355e6	−0.219319	−0.109660	+	0.993969i	$0.534976\pi$
$972$	3.14268e6	0.106693
$973$	3.67848e7	1.24562
$974$	−4.91899e7	−1.66142
$975$	−8.92253e6	−0.300591
$976$	2.06668e6	0.0694462
$977$	3.15126e7	1.05620	0.528102	−	0.849181i	$-0.322904\pi$
$977$	3.15126e7	1.05620	0.528102	+	0.849181i	$0.322904\pi$
$978$	−2.34379e7	−0.783558
$979$	−8.42041e6	−0.280787
$980$	−9.88085e6	−0.328647
$981$	−1.51442e7	−0.502427
$982$	−6.86407e7	−2.27145
$983$	1.64341e6	0.0542454	0.0271227	−	0.999632i	$-0.491366\pi$
$983$	1.64341e6	0.0542454	0.0271227	+	0.999632i	$0.491366\pi$
$984$	1.15792e7	0.381233
$985$	3.08862e7	1.01432
$986$	3.05391e7	1.00038
$987$	1.51639e7	0.495471
$988$	−3.90304e6	−0.127207
$989$	1.31970e6	0.0429026
$990$	3.63095e7	1.17742
$991$	−4.16969e7	−1.34871	−0.674357	−	0.738405i	$-0.735579\pi$
$991$	−4.16969e7	−1.34871	−0.674357	+	0.738405i	$0.735579\pi$
$992$	1.28635e7	0.415032
$993$	2.70567e7	0.870765
$994$	4.16500e7	1.33705
$995$	4.55448e7	1.45841
$996$	−3.04928e7	−0.973979
$997$	−4.32397e6	−0.137767	−0.0688835	−	0.997625i	$-0.521944\pi$
$997$	−4.32397e6	−0.137767	−0.0688835	+	0.997625i	$0.521944\pi$
$998$	2.60946e7	0.829324
$999$	1.85150e6	0.0586961

Twists

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

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

\(f(q)\)	\(=\)	\(q+9.23155 q^{2} +9.00000 q^{3} +53.2215 q^{4} +89.5822 q^{5} +83.0840 q^{6} -121.386 q^{7} +195.908 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+9.23155 q^{2} +9.00000 q^{3} +53.2215 q^{4} +89.5822 q^{5} +83.0840 q^{6} -121.386 q^{7} +195.908 q^{8} +81.0000 q^{9} +826.983 q^{10} +542.050 q^{11} +478.994 q^{12} -202.326 q^{13} -1120.58 q^{14} +806.240 q^{15} +105.442 q^{16} -431.232 q^{17} +747.756 q^{18} +362.462 q^{19} +4767.70 q^{20} -1092.47 q^{21} +5003.96 q^{22} +1693.68 q^{23} +1763.17 q^{24} +4899.97 q^{25} -1867.79 q^{26} +729.000 q^{27} -6460.34 q^{28} -7671.32 q^{29} +7442.84 q^{30} -2429.08 q^{31} -5295.65 q^{32} +4878.45 q^{33} -3980.94 q^{34} -10874.0 q^{35} +4310.94 q^{36} +2539.77 q^{37} +3346.09 q^{38} -1820.94 q^{39} +17549.8 q^{40} +6567.27 q^{41} -10085.2 q^{42} +779.187 q^{43} +28848.7 q^{44} +7256.16 q^{45} +15635.3 q^{46} -13880.3 q^{47} +948.975 q^{48} -2072.46 q^{49} +45234.3 q^{50} -3881.09 q^{51} -10768.1 q^{52} +14568.1 q^{53} +6729.80 q^{54} +48558.0 q^{55} -23780.4 q^{56} +3262.16 q^{57} -70818.2 q^{58} -3481.00 q^{59} +42909.3 q^{60} +19600.2 q^{61} -22424.2 q^{62} -9832.26 q^{63} -52261.2 q^{64} -18124.8 q^{65} +45035.7 q^{66} -56140.8 q^{67} -22950.8 q^{68} +15243.2 q^{69} -100384. q^{70} -37168.2 q^{71} +15868.5 q^{72} +82040.6 q^{73} +23446.1 q^{74} +44099.7 q^{75} +19290.8 q^{76} -65797.3 q^{77} -16810.1 q^{78} +77491.2 q^{79} +9445.69 q^{80} +6561.00 q^{81} +60626.0 q^{82} -63660.2 q^{83} -58143.1 q^{84} -38630.7 q^{85} +7193.11 q^{86} -69041.9 q^{87} +106192. q^{88} -15534.4 q^{89} +66985.6 q^{90} +24559.6 q^{91} +90140.5 q^{92} -21861.7 q^{93} -128137. q^{94} +32470.2 q^{95} -47660.9 q^{96} -93095.6 q^{97} -19132.0 q^{98} +43906.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9}+O(q^{10}) \) 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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