LMFDB - Embedded newform 177.6.a.b.1.2

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:	$1$
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} - 4 x^{11} - 283 x^{10} + 1045 x^{9} + 27968 x^{8} - 94393 x^{7} - 1130486 x^{6} + \cdots - 50564480 $ x^12 - 4x^11 - 283x^10 + 1045x^9 + 27968x^8 - 94393x^7 - 1130486x^6 + 3566264x^5 + 15496192x^4 - 53008480x^3 - 16576192x^2 + 120303168*x - 50564480
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			1.2
Root			$8.94324$ 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)

$f(q)$	$=$	$q-8.94324 q^{2} -9.00000 q^{3} +47.9816 q^{4} +48.3356 q^{5} +80.4892 q^{6} -32.5863 q^{7} -142.927 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-8.94324 q^{2} -9.00000 q^{3} +47.9816 q^{4} +48.3356 q^{5} +80.4892 q^{6} -32.5863 q^{7} -142.927 q^{8} +81.0000 q^{9} -432.277 q^{10} -607.250 q^{11} -431.834 q^{12} -114.450 q^{13} +291.427 q^{14} -435.021 q^{15} -257.180 q^{16} +1477.59 q^{17} -724.402 q^{18} +1197.95 q^{19} +2319.22 q^{20} +293.277 q^{21} +5430.79 q^{22} -815.109 q^{23} +1286.34 q^{24} -788.665 q^{25} +1023.55 q^{26} -729.000 q^{27} -1563.54 q^{28} +7054.74 q^{29} +3890.50 q^{30} -2013.45 q^{31} +6873.69 q^{32} +5465.25 q^{33} -13214.4 q^{34} -1575.08 q^{35} +3886.51 q^{36} +2888.36 q^{37} -10713.6 q^{38} +1030.05 q^{39} -6908.46 q^{40} +7977.13 q^{41} -2622.85 q^{42} -11709.8 q^{43} -29136.8 q^{44} +3915.19 q^{45} +7289.72 q^{46} +2217.46 q^{47} +2314.62 q^{48} -15745.1 q^{49} +7053.22 q^{50} -13298.3 q^{51} -5491.47 q^{52} -16868.6 q^{53} +6519.62 q^{54} -29351.8 q^{55} +4657.46 q^{56} -10781.6 q^{57} -63092.2 q^{58} -3481.00 q^{59} -20873.0 q^{60} -11356.2 q^{61} +18006.8 q^{62} -2639.49 q^{63} -53243.2 q^{64} -5532.00 q^{65} -48877.1 q^{66} -29351.9 q^{67} +70896.9 q^{68} +7335.98 q^{69} +14086.3 q^{70} +61841.8 q^{71} -11577.1 q^{72} -6951.65 q^{73} -25831.3 q^{74} +7097.99 q^{75} +57479.7 q^{76} +19788.1 q^{77} -9211.96 q^{78} -74447.1 q^{79} -12431.0 q^{80} +6561.00 q^{81} -71341.4 q^{82} -64837.6 q^{83} +14071.9 q^{84} +71420.1 q^{85} +104724. q^{86} -63492.7 q^{87} +86792.4 q^{88} -6479.60 q^{89} -35014.5 q^{90} +3729.49 q^{91} -39110.2 q^{92} +18121.1 q^{93} -19831.3 q^{94} +57903.9 q^{95} -61863.2 q^{96} +34765.8 q^{97} +140812. q^{98} -49187.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9} - 863 q^{10} + 492 q^{11} - 1782 q^{12} - 974 q^{13} - 967 q^{14} - 324 q^{15} + 6370 q^{16} - 1463 q^{17} - 324 q^{18} - 3189 q^{19} - 835 q^{20} + 3699 q^{21} - 2726 q^{22} - 2617 q^{23} + 621 q^{24} + 8642 q^{25} + 2414 q^{26} - 8748 q^{27} - 20458 q^{28} - 1963 q^{29} + 7767 q^{30} - 11929 q^{31} - 14382 q^{32} - 4428 q^{33} - 20744 q^{34} + 1829 q^{35} + 16038 q^{36} - 28105 q^{37} - 23475 q^{38} + 8766 q^{39} - 100576 q^{40} - 7585 q^{41} + 8703 q^{42} - 33146 q^{43} + 26014 q^{44} + 2916 q^{45} - 142851 q^{46} - 79215 q^{47} - 57330 q^{48} - 32569 q^{49} - 136019 q^{50} + 13167 q^{51} - 248218 q^{52} - 12220 q^{53} + 2916 q^{54} - 117770 q^{55} - 186728 q^{56} + 28701 q^{57} - 188072 q^{58} - 41772 q^{59} + 7515 q^{60} - 54195 q^{61} + 36230 q^{62} - 33291 q^{63} + 45197 q^{64} + 42368 q^{65} + 24534 q^{66} + 24224 q^{67} - 209639 q^{68} + 23553 q^{69} - 35684 q^{70} + 60254 q^{71} - 5589 q^{72} - 15385 q^{73} + 214638 q^{74} - 77778 q^{75} - 167504 q^{76} - 17169 q^{77} - 21726 q^{78} - 27054 q^{79} + 216899 q^{80} + 78732 q^{81} + 37917 q^{82} - 117595 q^{83} + 184122 q^{84} - 121585 q^{85} + 306756 q^{86} + 17667 q^{87} - 105799 q^{88} - 36033 q^{89} - 69903 q^{90} - 32217 q^{91} - 30906 q^{92} + 107361 q^{93} + 128392 q^{94} - 50721 q^{95} + 129438 q^{96} - 196914 q^{97} + 574100 q^{98} + 39852 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9 - 863 * q^10 + 492 * q^11 - 1782 * q^12 - 974 * q^13 - 967 * q^14 - 324 * q^15 + 6370 * q^16 - 1463 * q^17 - 324 * q^18 - 3189 * q^19 - 835 * q^20 + 3699 * q^21 - 2726 * q^22 - 2617 * q^23 + 621 * q^24 + 8642 * q^25 + 2414 * q^26 - 8748 * q^27 - 20458 * q^28 - 1963 * q^29 + 7767 * q^30 - 11929 * q^31 - 14382 * q^32 - 4428 * q^33 - 20744 * q^34 + 1829 * q^35 + 16038 * q^36 - 28105 * q^37 - 23475 * q^38 + 8766 * q^39 - 100576 * q^40 - 7585 * q^41 + 8703 * q^42 - 33146 * q^43 + 26014 * q^44 + 2916 * q^45 - 142851 * q^46 - 79215 * q^47 - 57330 * q^48 - 32569 * q^49 - 136019 * q^50 + 13167 * q^51 - 248218 * q^52 - 12220 * q^53 + 2916 * q^54 - 117770 * q^55 - 186728 * q^56 + 28701 * q^57 - 188072 * q^58 - 41772 * q^59 + 7515 * q^60 - 54195 * q^61 + 36230 * q^62 - 33291 * q^63 + 45197 * q^64 + 42368 * q^65 + 24534 * q^66 + 24224 * q^67 - 209639 * q^68 + 23553 * q^69 - 35684 * q^70 + 60254 * q^71 - 5589 * q^72 - 15385 * q^73 + 214638 * q^74 - 77778 * q^75 - 167504 * q^76 - 17169 * q^77 - 21726 * q^78 - 27054 * q^79 + 216899 * q^80 + 78732 * q^81 + 37917 * q^82 - 117595 * q^83 + 184122 * q^84 - 121585 * q^85 + 306756 * q^86 + 17667 * q^87 - 105799 * q^88 - 36033 * q^89 - 69903 * q^90 - 32217 * q^91 - 30906 * q^92 + 107361 * q^93 + 128392 * q^94 - 50721 * q^95 + 129438 * q^96 - 196914 * q^97 + 574100 * q^98 + 39852 * 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 $

$2$	−8.94324	−1.58096	−0.790478	−	0.612490i	$-0.790168\pi$
$2$	−8.94324	−1.58096	−0.790478	+	0.612490i	$0.790168\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	47.9816	1.49942
$5$	48.3356	0.864654	0.432327	−	0.901717i	$-0.357693\pi$
$5$	48.3356	0.864654	0.432327	+	0.901717i	$0.357693\pi$
$6$	80.4892	0.912766
$7$	−32.5863	−0.251357	−0.125678	−	0.992071i	$-0.540111\pi$
$7$	−32.5863	−0.251357	−0.125678	+	0.992071i	$0.540111\pi$
$8$	−142.927	−0.789567
$9$	81.0000	0.333333
$10$	−432.277	−1.36698
$11$	−607.250	−1.51316	−0.756582	−	0.653899i	$-0.773132\pi$
$11$	−607.250	−1.51316	−0.756582	+	0.653899i	$0.773132\pi$
$12$	−431.834	−0.865693
$13$	−114.450	−0.187826	−0.0939131	−	0.995580i	$-0.529938\pi$
$13$	−114.450	−0.187826	−0.0939131	+	0.995580i	$0.529938\pi$
$14$	291.427	0.397384
$15$	−435.021	−0.499208
$16$	−257.180	−0.251153
$17$	1477.59	1.24003	0.620013	−	0.784592i	$-0.287127\pi$
$17$	1477.59	1.24003	0.620013	+	0.784592i	$0.287127\pi$
$18$	−724.402	−0.526985
$19$	1197.95	0.761300	0.380650	−	0.924719i	$-0.375700\pi$
$19$	1197.95	0.761300	0.380650	+	0.924719i	$0.375700\pi$
$20$	2319.22	1.29648
$21$	293.277	0.145121
$22$	5430.79	2.39225
$23$	−815.109	−0.321289	−0.160645	−	0.987012i	$-0.551357\pi$
$23$	−815.109	−0.321289	−0.160645	+	0.987012i	$0.551357\pi$
$24$	1286.34	0.455857
$25$	−788.665	−0.252373
$26$	1023.55	0.296945
$27$	−729.000	−0.192450
$28$	−1563.54	−0.376890
$29$	7054.74	1.55771	0.778854	−	0.627205i	$-0.215801\pi$
$29$	7054.74	1.55771	0.778854	+	0.627205i	$0.215801\pi$
$30$	3890.50	0.789227
$31$	−2013.45	−0.376302	−0.188151	−	0.982140i	$-0.560249\pi$
$31$	−2013.45	−0.376302	−0.188151	+	0.982140i	$0.560249\pi$
$32$	6873.69	1.18663
$33$	5465.25	0.873626
$34$	−13214.4	−1.96043
$35$	−1575.08	−0.217337
$36$	3886.51	0.499808
$37$	2888.36	0.346855	0.173427	−	0.984847i	$-0.444516\pi$
$37$	2888.36	0.346855	0.173427	+	0.984847i	$0.444516\pi$
$38$	−10713.6	−1.20358
$39$	1030.05	0.108441
$40$	−6908.46	−0.682702
$41$	7977.13	0.741117	0.370559	−	0.928809i	$-0.379166\pi$
$41$	7977.13	0.741117	0.370559	+	0.928809i	$0.379166\pi$
$42$	−2622.85	−0.229430
$43$	−11709.8	−0.965784	−0.482892	−	0.875680i	$-0.660414\pi$
$43$	−11709.8	−0.965784	−0.482892	+	0.875680i	$0.660414\pi$
$44$	−29136.8	−2.26887
$45$	3915.19	0.288218
$46$	7289.72	0.507944
$47$	2217.46	0.146424	0.0732119	−	0.997316i	$-0.476675\pi$
$47$	2217.46	0.146424	0.0732119	+	0.997316i	$0.476675\pi$
$48$	2314.62	0.145003
$49$	−15745.1	−0.936820
$50$	7053.22	0.398990
$51$	−13298.3	−0.715929
$52$	−5491.47	−0.281631
$53$	−16868.6	−0.824878	−0.412439	−	0.910985i	$-0.635323\pi$
$53$	−16868.6	−0.824878	−0.412439	+	0.910985i	$0.635323\pi$
$54$	6519.62	0.304255
$55$	−29351.8	−1.30836
$56$	4657.46	0.198463
$57$	−10781.6	−0.439537
$58$	−63092.2	−2.46267
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−20873.0	−0.748525
$61$	−11356.2	−0.390758	−0.195379	−	0.980728i	$-0.562594\pi$
$61$	−11356.2	−0.390758	−0.195379	+	0.980728i	$0.562594\pi$
$62$	18006.8	0.594917
$63$	−2639.49	−0.0837855
$64$	−53243.2	−1.62486
$65$	−5532.00	−0.162405
$66$	−48877.1	−1.38116
$67$	−29351.9	−0.798821	−0.399410	−	0.916772i	$-0.630785\pi$
$67$	−29351.9	−0.798821	−0.399410	+	0.916772i	$0.630785\pi$
$68$	70896.9	1.85932
$69$	7335.98	0.185496
$70$	14086.3	0.343600
$71$	61841.8	1.45592	0.727958	−	0.685622i	$-0.240470\pi$
$71$	61841.8	1.45592	0.727958	+	0.685622i	$0.240470\pi$
$72$	−11577.1	−0.263189
$73$	−6951.65	−0.152680	−0.0763398	−	0.997082i	$-0.524323\pi$
$73$	−6951.65	−0.152680	−0.0763398	+	0.997082i	$0.524323\pi$
$74$	−25831.3	−0.548362
$75$	7097.99	0.145708
$76$	57479.7	1.14151
$77$	19788.1	0.380344
$78$	−9211.96	−0.171441
$79$	−74447.1	−1.34208	−0.671042	−	0.741419i	$-0.734153\pi$
$79$	−74447.1	−1.34208	−0.671042	+	0.741419i	$0.734153\pi$
$80$	−12431.0	−0.217160
$81$	6561.00	0.111111
$82$	−71341.4	−1.17167
$83$	−64837.6	−1.03307	−0.516537	−	0.856265i	$-0.672779\pi$
$83$	−64837.6	−1.03307	−0.516537	+	0.856265i	$0.672779\pi$
$84$	14071.9	0.217598
$85$	71420.1	1.07219
$86$	104724.	1.52686
$87$	−63492.7	−0.899343
$88$	86792.4	1.19474
$89$	−6479.60	−0.0867108	−0.0433554	−	0.999060i	$-0.513805\pi$
$89$	−6479.60	−0.0867108	−0.0433554	+	0.999060i	$0.513805\pi$
$90$	−35014.5	−0.455660
$91$	3729.49	0.0472114
$92$	−39110.2	−0.481749
$93$	18121.1	0.217258
$94$	−19831.3	−0.231490
$95$	57903.9	0.658262
$96$	−61863.2	−0.685100
$97$	34765.8	0.375166	0.187583	−	0.982249i	$-0.439935\pi$
$97$	34765.8	0.375166	0.187583	+	0.982249i	$0.439935\pi$
$98$	140812.	1.48107
$99$	−49187.3	−0.504388
$100$	−37841.4	−0.378414
$101$	−10413.0	−0.101571	−0.0507857	−	0.998710i	$-0.516173\pi$
$101$	−10413.0	−0.101571	−0.0507857	+	0.998710i	$0.516173\pi$
$102$	118930.	1.13185
$103$	−187352.	−1.74007	−0.870033	−	0.492993i	$-0.835903\pi$
$103$	−187352.	−1.74007	−0.870033	+	0.492993i	$0.835903\pi$
$104$	16357.9	0.148301
$105$	14175.7	0.125479
$106$	150860.	1.30410
$107$	18946.3	0.159979	0.0799897	−	0.996796i	$-0.474511\pi$
$107$	18946.3	0.159979	0.0799897	+	0.996796i	$0.474511\pi$
$108$	−34978.6	−0.288564
$109$	12701.4	0.102396	0.0511981	−	0.998689i	$-0.483696\pi$
$109$	12701.4	0.102396	0.0511981	+	0.998689i	$0.483696\pi$
$110$	262501.	2.06847
$111$	−25995.3	−0.200257
$112$	8380.57	0.0631289
$113$	−90034.0	−0.663301	−0.331650	−	0.943402i	$-0.607605\pi$
$113$	−90034.0	−0.663301	−0.331650	+	0.943402i	$0.607605\pi$
$114$	96422.3	0.694889
$115$	−39398.8	−0.277804
$116$	338497.	2.33566
$117$	−9270.42	−0.0626087
$118$	31131.4	0.205823
$119$	−48149.1	−0.311689
$120$	62176.2	0.394158
$121$	207702.	1.28967
$122$	101561.	0.617772
$123$	−71794.1	−0.427884
$124$	−96608.5	−0.564236
$125$	−189170.	−1.08287
$126$	23605.6	0.132461
$127$	−75773.2	−0.416875	−0.208438	−	0.978036i	$-0.566838\pi$
$127$	−75773.2	−0.416875	−0.208438	+	0.978036i	$0.566838\pi$
$128$	256209.	1.38220
$129$	105389.	0.557595
$130$	49474.0	0.256755
$131$	−279838.	−1.42472	−0.712358	−	0.701816i	$-0.752373\pi$
$131$	−279838.	−1.42472	−0.712358	+	0.701816i	$0.752373\pi$
$132$	262231.	1.30993
$133$	−39036.9	−0.191358
$134$	262501.	1.26290
$135$	−35236.7	−0.166403
$136$	−211187.	−0.979083
$137$	−309329.	−1.40805	−0.704026	−	0.710174i	$-0.748616\pi$
$137$	−309329.	−1.40805	−0.704026	+	0.710174i	$0.748616\pi$
$138$	−65607.4	−0.293262
$139$	440414.	1.93341	0.966706	−	0.255889i	$-0.0823682\pi$
$139$	440414.	1.93341	0.966706	+	0.255889i	$0.0823682\pi$
$140$	−75574.8	−0.325880
$141$	−19957.2	−0.0845378
$142$	−553066.	−2.30174
$143$	69499.6	0.284212
$144$	−20831.6	−0.0837176
$145$	340995.	1.34688
$146$	62170.3	0.241380
$147$	141706.	0.540873
$148$	138588.	0.520082
$149$	−35329.4	−0.130368	−0.0651840	−	0.997873i	$-0.520763\pi$
$149$	−35329.4	−0.130368	−0.0651840	+	0.997873i	$0.520763\pi$
$150$	−63479.0	−0.230357
$151$	−277734.	−0.991258	−0.495629	−	0.868534i	$-0.665062\pi$
$151$	−277734.	−0.991258	−0.495629	+	0.868534i	$0.665062\pi$
$152$	−171220.	−0.601097
$153$	119684.	0.413342
$154$	−176969.	−0.601307
$155$	−97321.4	−0.325371
$156$	49423.2	0.162600
$157$	123296.	0.399208	0.199604	−	0.979877i	$-0.436034\pi$
$157$	123296.	0.399208	0.199604	+	0.979877i	$0.436034\pi$
$158$	665798.	2.12178
$159$	151818.	0.476244
$160$	332244.	1.02602
$161$	26561.4	0.0807582
$162$	−58676.6	−0.175662
$163$	−516622.	−1.52301	−0.761507	−	0.648157i	$-0.775540\pi$
$163$	−516622.	−1.52301	−0.761507	+	0.648157i	$0.775540\pi$
$164$	382755.	1.11125
$165$	264167.	0.755384
$166$	579858.	1.63325
$167$	265123.	0.735625	0.367812	−	0.929900i	$-0.380107\pi$
$167$	265123.	0.735625	0.367812	+	0.929900i	$0.380107\pi$
$168$	−41917.2	−0.114583
$169$	−358194.	−0.964721
$170$	−638727.	−1.69509
$171$	97034.2	0.253767
$172$	−561856.	−1.44812
$173$	−571531.	−1.45186	−0.725930	−	0.687769i	$-0.758590\pi$
$173$	−571531.	−1.45186	−0.725930	+	0.687769i	$0.758590\pi$
$174$	567830.	1.42182
$175$	25699.7	0.0634356
$176$	156173.	0.380035
$177$	31329.0	0.0751646
$178$	57948.6	0.137086
$179$	70392.7	0.164208	0.0821041	−	0.996624i	$-0.473836\pi$
$179$	70392.7	0.164208	0.0821041	+	0.996624i	$0.473836\pi$
$180$	187857.	0.432161
$181$	−69490.3	−0.157662	−0.0788312	−	0.996888i	$-0.525119\pi$
$181$	−69490.3	−0.157662	−0.0788312	+	0.996888i	$0.525119\pi$
$182$	−33353.8	−0.0746391
$183$	102206.	0.225604
$184$	116501.	0.253679
$185$	139611.	0.299909
$186$	−162061.	−0.343476
$187$	−897265.	−1.87636
$188$	106397.	0.219551
$189$	23755.4	0.0483736
$190$	−517848.	−1.04068
$191$	−790909.	−1.56871	−0.784356	−	0.620311i	$-0.787007\pi$
$191$	−790909.	−1.56871	−0.784356	+	0.620311i	$0.787007\pi$
$192$	479189.	0.938110
$193$	−970964.	−1.87633	−0.938166	−	0.346185i	$-0.887477\pi$
$193$	−970964.	−1.87633	−0.938166	+	0.346185i	$0.887477\pi$
$194$	−310919.	−0.593121
$195$	49788.0	0.0937644
$196$	−755476.	−1.40469
$197$	−619957.	−1.13814	−0.569070	−	0.822289i	$-0.692697\pi$
$197$	−619957.	−1.13814	−0.569070	+	0.822289i	$0.692697\pi$
$198$	439894.	0.797416
$199$	−175483.	−0.314124	−0.157062	−	0.987589i	$-0.550202\pi$
$199$	−175483.	−0.314124	−0.157062	+	0.987589i	$0.550202\pi$
$200$	112721.	0.199265
$201$	264167.	0.461199
$202$	93125.7	0.160580
$203$	−229888.	−0.391540
$204$	−638072.	−1.07348
$205$	385580.	0.640810
$206$	1.67554e6	2.75097
$207$	−66023.8	−0.107096
$208$	29434.2	0.0471731
$209$	−727458.	−1.15197
$210$	−126777.	−0.198377
$211$	561184.	0.867759	0.433880	−	0.900971i	$-0.357144\pi$
$211$	561184.	0.867759	0.433880	+	0.900971i	$0.357144\pi$
$212$	−809383.	−1.23684
$213$	−556576.	−0.840573
$214$	−169441.	−0.252921
$215$	−566003.	−0.835069
$216$	104194.	0.151952
$217$	65611.0	0.0945861
$218$	−113591.	−0.161884
$219$	62564.9	0.0881496
$220$	−1.40835e6	−1.96179
$221$	−169109.	−0.232909
$222$	232482.	0.316597
$223$	−346056.	−0.465998	−0.232999	−	0.972477i	$-0.574854\pi$
$223$	−346056.	−0.465998	−0.232999	+	0.972477i	$0.574854\pi$
$224$	−223988.	−0.298267
$225$	−63881.9	−0.0841243
$226$	805196.	1.04865
$227$	−69353.3	−0.0893310	−0.0446655	−	0.999002i	$-0.514222\pi$
$227$	−69353.3	−0.0893310	−0.0446655	+	0.999002i	$0.514222\pi$
$228$	−517317.	−0.659052
$229$	1.03395e6	1.30289	0.651447	−	0.758694i	$-0.274162\pi$
$229$	1.03395e6	1.30289	0.651447	+	0.758694i	$0.274162\pi$
$230$	352353.	0.439196
$231$	−178093.	−0.219592
$232$	−1.00831e6	−1.22991
$233$	1.08238e6	1.30614	0.653069	−	0.757298i	$-0.273481\pi$
$233$	1.08238e6	1.30614	0.653069	+	0.757298i	$0.273481\pi$
$234$	82907.6	0.0989817
$235$	107182.	0.126606
$236$	−167024.	−0.195208
$237$	670024.	0.774853
$238$	430609.	0.492766
$239$	526608.	0.596338	0.298169	−	0.954513i	$-0.403624\pi$
$239$	526608.	0.596338	0.298169	+	0.954513i	$0.403624\pi$
$240$	111879.	0.125378
$241$	1.09725e6	1.21692	0.608461	−	0.793584i	$-0.291787\pi$
$241$	1.09725e6	1.21692	0.608461	+	0.793584i	$0.291787\pi$
$242$	−1.85753e6	−2.03891
$243$	−59049.0	−0.0641500
$244$	−544888.	−0.585912
$245$	−761051.	−0.810025
$246$	642072.	0.676466
$247$	−137105.	−0.142992
$248$	287776.	0.297116
$249$	583538.	0.596446
$250$	1.69179e6	1.71197
$251$	729854.	0.731226	0.365613	−	0.930767i	$-0.380859\pi$
$251$	729854.	0.731226	0.365613	+	0.930767i	$0.380859\pi$
$252$	−126647.	−0.125630
$253$	494975.	0.486163
$254$	677658.	0.659062
$255$	−642781.	−0.619031
$256$	−587557.	−0.560338
$257$	722806.	0.682636	0.341318	−	0.939948i	$-0.389127\pi$
$257$	722806.	0.682636	0.341318	+	0.939948i	$0.389127\pi$
$258$	−942515.	−0.881534
$259$	−94121.1	−0.0871842
$260$	−265434.	−0.243513
$261$	571434.	0.519236
$262$	2.50266e6	2.25241
$263$	−1.30671e6	−1.16490	−0.582452	−	0.812865i	$-0.697906\pi$
$263$	−1.30671e6	−1.16490	−0.582452	+	0.812865i	$0.697906\pi$
$264$	−781131.	−0.689786
$265$	−815356.	−0.713235
$266$	349116.	0.302528
$267$	58316.4	0.0500625
$268$	−1.40835e6	−1.19777
$269$	2.09858e6	1.76825	0.884127	−	0.467246i	$-0.154754\pi$
$269$	2.09858e6	1.76825	0.884127	+	0.467246i	$0.154754\pi$
$270$	315130.	0.263076
$271$	1.04873e6	0.867440	0.433720	−	0.901048i	$-0.357201\pi$
$271$	1.04873e6	0.867440	0.433720	+	0.901048i	$0.357201\pi$
$272$	−380006.	−0.311436
$273$	−33565.4	−0.0272575
$274$	2.76640e6	2.22607
$275$	478917.	0.381881
$276$	351992.	0.278138
$277$	−191493.	−0.149953	−0.0749763	−	0.997185i	$-0.523888\pi$
$277$	−191493.	−0.149953	−0.0749763	+	0.997185i	$0.523888\pi$
$278$	−3.93873e6	−3.05664
$279$	−163090.	−0.125434
$280$	225121.	0.171602
$281$	−1.21812e6	−0.920292	−0.460146	−	0.887843i	$-0.652203\pi$
$281$	−1.21812e6	−0.920292	−0.460146	+	0.887843i	$0.652203\pi$
$282$	178482.	0.133651
$283$	798367.	0.592566	0.296283	−	0.955100i	$-0.404253\pi$
$283$	798367.	0.592566	0.296283	+	0.955100i	$0.404253\pi$
$284$	2.96727e6	2.18303
$285$	−521135.	−0.380048
$286$	−621552.	−0.449327
$287$	−259945.	−0.186285
$288$	556769.	0.395543
$289$	763404.	0.537662
$290$	−3.04960e6	−2.12936
$291$	−312893.	−0.216602
$292$	−333551.	−0.228931
$293$	−1.05915e6	−0.720754	−0.360377	−	0.932807i	$-0.617352\pi$
$293$	−1.05915e6	−0.720754	−0.360377	+	0.932807i	$0.617352\pi$
$294$	−1.26731e6	−0.855097
$295$	−168256.	−0.112568
$296$	−412825.	−0.273865
$297$	442685.	0.291209
$298$	315960.	0.206106
$299$	93288.9	0.0603465
$300$	340572.	0.218477
$301$	381581.	0.242756
$302$	2.48384e6	1.56714
$303$	93716.8	0.0586423
$304$	−308090.	−0.191203
$305$	−548909.	−0.337871
$306$	−1.07037e6	−0.653475
$307$	80118.4	0.0485161	0.0242581	−	0.999706i	$-0.492278\pi$
$307$	80118.4	0.0485161	0.0242581	+	0.999706i	$0.492278\pi$
$308$	949462.	0.570296
$309$	1.68617e6	1.00463
$310$	870369.	0.514398
$311$	2.98406e6	1.74947	0.874736	−	0.484600i	$-0.161035\pi$
$311$	2.98406e6	1.74947	0.874736	+	0.484600i	$0.161035\pi$
$312$	−147221.	−0.0856218
$313$	678550.	0.391491	0.195745	−	0.980655i	$-0.437287\pi$
$313$	678550.	0.391491	0.195745	+	0.980655i	$0.437287\pi$
$314$	−1.10266e6	−0.631130
$315$	−127582.	−0.0724455
$316$	−3.57209e6	−2.01235
$317$	1.81380e6	1.01377	0.506887	−	0.862013i	$-0.330796\pi$
$317$	1.81380e6	1.01377	0.506887	+	0.862013i	$0.330796\pi$
$318$	−1.35774e6	−0.752921
$319$	−4.28399e6	−2.35707
$320$	−2.57355e6	−1.40494
$321$	−170516.	−0.0923642
$322$	−237545.	−0.127675
$323$	1.77008e6	0.944031
$324$	314807.	0.166603
$325$	90262.4	0.0474022
$326$	4.62027e6	2.40782
$327$	−114312.	−0.0591185
$328$	−1.14015e6	−0.585161
$329$	−72258.9	−0.0368046
$330$	−2.36250e6	−1.19423
$331$	−2.91425e6	−1.46203	−0.731016	−	0.682360i	$-0.760954\pi$
$331$	−2.91425e6	−1.46203	−0.731016	+	0.682360i	$0.760954\pi$
$332$	−3.11101e6	−1.54902
$333$	233957.	0.115618
$334$	−2.37106e6	−1.16299
$335$	−1.41874e6	−0.690704
$336$	−75425.1	−0.0364475
$337$	−1.92879e6	−0.925145	−0.462572	−	0.886582i	$-0.653073\pi$
$337$	−1.92879e6	−0.925145	−0.462572	+	0.886582i	$0.653073\pi$
$338$	3.20342e6	1.52518
$339$	810306.	0.382957
$340$	3.42685e6	1.60767
$341$	1.22267e6	0.569407
$342$	−867801.	−0.401194
$343$	1.06075e6	0.486833
$344$	1.67365e6	0.762551
$345$	354589.	0.160390
$346$	5.11134e6	2.29533
$347$	−2.63458e6	−1.17459	−0.587297	−	0.809372i	$-0.699808\pi$
$347$	−2.63458e6	−1.17459	−0.587297	+	0.809372i	$0.699808\pi$
$348$	−3.04648e6	−1.34850
$349$	−338492.	−0.148759	−0.0743797	−	0.997230i	$-0.523698\pi$
$349$	−338492.	−0.148759	−0.0743797	+	0.997230i	$0.523698\pi$
$350$	−229839.	−0.100289
$351$	83433.8	0.0361472
$352$	−4.17405e6	−1.79556
$353$	−1.24130e6	−0.530200	−0.265100	−	0.964221i	$-0.585405\pi$
$353$	−1.24130e6	−0.530200	−0.265100	+	0.964221i	$0.585405\pi$
$354$	−280183.	−0.118832
$355$	2.98916e6	1.25886
$356$	−310901.	−0.130016
$357$	433342.	0.179953
$358$	−629539.	−0.259606
$359$	−1.85276e6	−0.758723	−0.379361	−	0.925249i	$-0.623856\pi$
$359$	−1.85276e6	−0.758723	−0.379361	+	0.925249i	$0.623856\pi$
$360$	−559585.	−0.227567
$361$	−1.04101e6	−0.420422
$362$	621469.	0.249257
$363$	−1.86932e6	−0.744589
$364$	178947.	0.0707898
$365$	−336013.	−0.132015
$366$	−914050.	−0.356671
$367$	2.21751e6	0.859410	0.429705	−	0.902969i	$-0.358618\pi$
$367$	2.21751e6	0.859410	0.429705	+	0.902969i	$0.358618\pi$
$368$	209630.	0.0806927
$369$	646147.	0.247039
$370$	−1.24857e6	−0.474144
$371$	549687.	0.207339
$372$	869476.	0.325762
$373$	−1.99276e6	−0.741623	−0.370811	−	0.928708i	$-0.620920\pi$
$373$	−1.99276e6	−0.741623	−0.370811	+	0.928708i	$0.620920\pi$
$374$	8.02445e6	2.96645
$375$	1.70253e6	0.625195
$376$	−316935.	−0.115611
$377$	−807413.	−0.292578
$378$	−212451.	−0.0764766
$379$	1.04393e6	0.373312	0.186656	−	0.982425i	$-0.440235\pi$
$379$	1.04393e6	0.373312	0.186656	+	0.982425i	$0.440235\pi$
$380$	2.77832e6	0.987013
$381$	681959.	0.240683
$382$	7.07329e6	2.48007
$383$	1.07017e6	0.372783	0.186391	−	0.982476i	$-0.440321\pi$
$383$	1.07017e6	0.372783	0.186391	+	0.982476i	$0.440321\pi$
$384$	−2.30588e6	−0.798012
$385$	956469.	0.328866
$386$	8.68356e6	2.96640
$387$	−948497.	−0.321928
$388$	1.66812e6	0.562533
$389$	1.68363e6	0.564122	0.282061	−	0.959396i	$-0.408982\pi$
$389$	1.68363e6	0.564122	0.282061	+	0.959396i	$0.408982\pi$
$390$	−445266.	−0.148237
$391$	−1.20439e6	−0.398407
$392$	2.25040e6	0.739682
$393$	2.51854e6	0.822560
$394$	5.54442e6	1.79935
$395$	−3.59845e6	−1.16044
$396$	−2.36008e6	−0.756291
$397$	−812204.	−0.258636	−0.129318	−	0.991603i	$-0.541279\pi$
$397$	−812204.	−0.258636	−0.129318	+	0.991603i	$0.541279\pi$
$398$	1.56938e6	0.496617
$399$	351332.	0.110481
$400$	202829.	0.0633841
$401$	−2.25492e6	−0.700279	−0.350139	−	0.936698i	$-0.613866\pi$
$401$	−2.25492e6	−0.700279	−0.350139	+	0.936698i	$0.613866\pi$
$402$	−2.36251e6	−0.729136
$403$	230439.	0.0706794
$404$	−499631.	−0.152299
$405$	317130.	0.0960727
$406$	2.05594e6	0.619008
$407$	−1.75396e6	−0.524848
$408$	1.90068e6	0.565274
$409$	949748.	0.280737	0.140369	−	0.990099i	$-0.455171\pi$
$409$	949748.	0.280737	0.140369	+	0.990099i	$0.455171\pi$
$410$	−3.44833e6	−1.01309
$411$	2.78396e6	0.812939
$412$	−8.98945e6	−2.60910
$413$	113433.	0.0327238
$414$	590467.	0.169315
$415$	−3.13397e6	−0.893252
$416$	−786691.	−0.222880
$417$	−3.96373e6	−1.11626
$418$	6.50583e6	1.82122
$419$	−328196.	−0.0913267	−0.0456634	−	0.998957i	$-0.514540\pi$
$419$	−328196.	−0.0913267	−0.0456634	+	0.998957i	$0.514540\pi$
$420$	680174.	0.188147
$421$	6.14766e6	1.69046	0.845230	−	0.534403i	$-0.179463\pi$
$421$	6.14766e6	1.69046	0.845230	+	0.534403i	$0.179463\pi$
$422$	−5.01880e6	−1.37189
$423$	179614.	0.0488079
$424$	2.41098e6	0.651297
$425$	−1.16532e6	−0.312949
$426$	4.97759e6	1.32891
$427$	370057.	0.0982197
$428$	909071.	0.239877
$429$	−625496.	−0.164090
$430$	5.06190e6	1.32021
$431$	3.28062e6	0.850674	0.425337	−	0.905035i	$-0.360156\pi$
$431$	3.28062e6	0.850674	0.425337	+	0.905035i	$0.360156\pi$
$432$	187485.	0.0483344
$433$	−1.79870e6	−0.461040	−0.230520	−	0.973068i	$-0.574043\pi$
$433$	−1.79870e6	−0.461040	−0.230520	+	0.973068i	$0.574043\pi$
$434$	−586775.	−0.149536
$435$	−3.06896e6	−0.777621
$436$	609431.	0.153535
$437$	−976463.	−0.244598
$438$	−559533.	−0.139361
$439$	1.62646e6	0.402794	0.201397	−	0.979510i	$-0.435452\pi$
$439$	1.62646e6	0.402794	0.201397	+	0.979510i	$0.435452\pi$
$440$	4.19517e6	1.03304
$441$	−1.27536e6	−0.312273
$442$	1.51238e6	0.368219
$443$	3.82966e6	0.927151	0.463576	−	0.886057i	$-0.346566\pi$
$443$	3.82966e6	0.927151	0.463576	+	0.886057i	$0.346566\pi$
$444$	−1.24729e6	−0.300269
$445$	−313196.	−0.0749748
$446$	3.09486e6	0.736723
$447$	317965.	0.0752680
$448$	1.73500e6	0.408418
$449$	−4.45166e6	−1.04209	−0.521046	−	0.853529i	$-0.674458\pi$
$449$	−4.45166e6	−1.04209	−0.521046	+	0.853529i	$0.674458\pi$
$450$	571311.	0.132997
$451$	−4.84411e6	−1.12143
$452$	−4.31997e6	−0.994569
$453$	2.49961e6	0.572303
$454$	620243.	0.141228
$455$	180268.	0.0408215
$456$	1.54098e6	0.347044
$457$	−1.17886e6	−0.264042	−0.132021	−	0.991247i	$-0.542147\pi$
$457$	−1.17886e6	−0.264042	−0.132021	+	0.991247i	$0.542147\pi$
$458$	−9.24683e6	−2.05982
$459$	−1.07716e6	−0.238643
$460$	−1.89042e6	−0.416546
$461$	1.73221e6	0.379620	0.189810	−	0.981821i	$-0.439213\pi$
$461$	1.73221e6	0.379620	0.189810	+	0.981821i	$0.439213\pi$
$462$	1.59272e6	0.347165
$463$	1.35619e6	0.294015	0.147007	−	0.989135i	$-0.453036\pi$
$463$	1.35619e6	0.294015	0.147007	+	0.989135i	$0.453036\pi$
$464$	−1.81434e6	−0.391223
$465$	875893.	0.187853
$466$	−9.67997e6	−2.06495
$467$	−3.59227e6	−0.762214	−0.381107	−	0.924531i	$-0.624457\pi$
$467$	−3.59227e6	−0.762214	−0.381107	+	0.924531i	$0.624457\pi$
$468$	−444809.	−0.0938770
$469$	956471.	0.200789
$470$	−958558.	−0.200158
$471$	−1.10966e6	−0.230483
$472$	497528.	0.102793
$473$	7.11080e6	1.46139
$474$	−5.99218e6	−1.22501
$475$	−944784.	−0.192131
$476$	−2.31027e6	−0.467353
$477$	−1.36636e6	−0.274959
$478$	−4.70958e6	−0.942784
$479$	−5.70119e6	−1.13534	−0.567671	−	0.823255i	$-0.692156\pi$
$479$	−5.70119e6	−1.13534	−0.567671	+	0.823255i	$0.692156\pi$
$480$	−2.99020e6	−0.592375
$481$	−330572.	−0.0651484
$482$	−9.81296e6	−1.92390
$483$	−239053.	−0.0466257
$484$	9.96586e6	1.93375
$485$	1.68043e6	0.324389
$486$	528089.	0.101418
$487$	−2.32159e6	−0.443571	−0.221786	−	0.975095i	$-0.571189\pi$
$487$	−2.32159e6	−0.443571	−0.221786	+	0.975095i	$0.571189\pi$
$488$	1.62310e6	0.308530
$489$	4.64960e6	0.879312
$490$	6.80626e6	1.28061
$491$	−7.27492e6	−1.36183	−0.680917	−	0.732360i	$-0.738419\pi$
$491$	−7.27492e6	−1.36183	−0.680917	+	0.732360i	$0.738419\pi$
$492$	−3.44479e6	−0.641580
$493$	1.04240e7	1.93160
$494$	1.22617e6	0.226064
$495$	−2.37750e6	−0.436121
$496$	517820.	0.0945093
$497$	−2.01520e6	−0.365954
$498$	−5.21872e6	−0.942955
$499$	2.13472e6	0.383786	0.191893	−	0.981416i	$-0.438537\pi$
$499$	2.13472e6	0.383786	0.191893	+	0.981416i	$0.438537\pi$
$500$	−9.07665e6	−1.62368
$501$	−2.38611e6	−0.424713
$502$	−6.52726e6	−1.15604
$503$	6.73329e6	1.18661	0.593304	−	0.804979i	$-0.297823\pi$
$503$	6.73329e6	1.18661	0.593304	+	0.804979i	$0.297823\pi$
$504$	377254.	0.0661543
$505$	−503318.	−0.0878242
$506$	−4.42668e6	−0.768603
$507$	3.22375e6	0.556982
$508$	−3.63571e6	−0.625073
$509$	−1.65266e6	−0.282742	−0.141371	−	0.989957i	$-0.545151\pi$
$509$	−1.65266e6	−0.282742	−0.141371	+	0.989957i	$0.545151\pi$
$510$	5.74854e6	0.978661
$511$	226529.	0.0383770
$512$	−2.94403e6	−0.496327
$513$	−873308.	−0.146512
$514$	−6.46423e6	−1.07922
$515$	−9.05579e6	−1.50456
$516$	5.05671e6	0.836072
$517$	−1.34655e6	−0.221563
$518$	841748.	0.137834
$519$	5.14378e6	0.838231
$520$	790671.	0.128229
$521$	−4.60489e6	−0.743233	−0.371617	−	0.928386i	$-0.621196\pi$
$521$	−4.60489e6	−0.743233	−0.371617	+	0.928386i	$0.621196\pi$
$522$	−5.11047e6	−0.820890
$523$	−797422.	−0.127478	−0.0637388	−	0.997967i	$-0.520302\pi$
$523$	−797422.	−0.127478	−0.0637388	+	0.997967i	$0.520302\pi$
$524$	−1.34271e7	−2.13625
$525$	−231297.	−0.0366245
$526$	1.16862e7	1.84166
$527$	−2.97505e6	−0.466624
$528$	−1.40556e6	−0.219414
$529$	−5.77194e6	−0.896773
$530$	7.29192e6	1.12759
$531$	−281961.	−0.0433963
$532$	−1.87305e6	−0.286926
$533$	−912979.	−0.139201
$534$	−521537.	−0.0791466
$535$	915780.	0.138327
$536$	4.19518e6	0.630722
$537$	−633534.	−0.0948057
$538$	−1.87681e7	−2.79553
$539$	9.56124e6	1.41756
$540$	−1.69071e6	−0.249508
$541$	−7.75717e6	−1.13949	−0.569745	−	0.821822i	$-0.692958\pi$
$541$	−7.75717e6	−1.13949	−0.569745	+	0.821822i	$0.692958\pi$
$542$	−9.37902e6	−1.37138
$543$	625413.	0.0910264
$544$	1.01565e7	1.47145
$545$	613929.	0.0885374
$546$	300184.	0.0430929
$547$	6.87407e6	0.982304	0.491152	−	0.871074i	$-0.336576\pi$
$547$	6.87407e6	0.982304	0.491152	+	0.871074i	$0.336576\pi$
$548$	−1.48421e7	−2.11127
$549$	−919851.	−0.130253
$550$	−4.28307e6	−0.603738
$551$	8.45125e6	1.18588
$552$	−1.04851e6	−0.146462
$553$	2.42596e6	0.337342
$554$	1.71257e6	0.237068
$555$	−1.25650e6	−0.173153
$556$	2.11318e7	2.89900
$557$	−1.03785e7	−1.41741	−0.708707	−	0.705503i	$-0.750721\pi$
$557$	−1.03785e7	−1.41741	−0.708707	+	0.705503i	$0.750721\pi$
$558$	1.45855e6	0.198306
$559$	1.34019e6	0.181399
$560$	405080.	0.0545847
$561$	8.07538e6	1.08332
$562$	1.08940e7	1.45494
$563$	−1.17737e7	−1.56546	−0.782730	−	0.622361i	$-0.786173\pi$
$563$	−1.17737e7	−1.56546	−0.782730	+	0.622361i	$0.786173\pi$
$564$	−957575.	−0.126758
$565$	−4.35185e6	−0.573526
$566$	−7.13999e6	−0.936821
$567$	−213799.	−0.0279285
$568$	−8.83885e6	−1.14954
$569$	−1.71606e6	−0.222204	−0.111102	−	0.993809i	$-0.535438\pi$
$569$	−1.71606e6	−0.222204	−0.111102	+	0.993809i	$0.535438\pi$
$570$	4.66063e6	0.600839
$571$	−1.38827e7	−1.78190	−0.890950	−	0.454102i	$-0.849960\pi$
$571$	−1.38827e7	−1.78190	−0.890950	+	0.454102i	$0.849960\pi$
$572$	3.33470e6	0.426154
$573$	7.11819e6	0.905697
$574$	2.32475e6	0.294508
$575$	642848.	0.0810846
$576$	−4.31270e6	−0.541618
$577$	4.75324e6	0.594360	0.297180	−	0.954821i	$-0.403954\pi$
$577$	4.75324e6	0.594360	0.297180	+	0.954821i	$0.403954\pi$
$578$	−6.82730e6	−0.850021
$579$	8.73868e6	1.08330
$580$	1.63615e7	2.01954
$581$	2.11282e6	0.259670
$582$	2.79827e6	0.342439
$583$	1.02435e7	1.24818
$584$	993578.	0.120551
$585$	−448092.	−0.0541349
$586$	9.47221e6	1.13948
$587$	−1.92855e6	−0.231013	−0.115506	−	0.993307i	$-0.536849\pi$
$587$	−1.92855e6	−0.231013	−0.115506	+	0.993307i	$0.536849\pi$
$588$	6.79928e6	0.810998
$589$	−2.41202e6	−0.286479
$590$	1.50476e6	0.177966
$591$	5.57961e6	0.657105
$592$	−742830.	−0.0871135
$593$	1.17565e7	1.37291	0.686453	−	0.727174i	$-0.259167\pi$
$593$	1.17565e7	1.37291	0.686453	+	0.727174i	$0.259167\pi$
$594$	−3.95904e6	−0.460388
$595$	−2.32732e6	−0.269503
$596$	−1.69516e6	−0.195477
$597$	1.57934e6	0.181360
$598$	−834305.	−0.0954052
$599$	1.36231e7	1.55135	0.775673	−	0.631136i	$-0.217411\pi$
$599$	1.36231e7	1.55135	0.775673	+	0.631136i	$0.217411\pi$
$600$	−1.01449e6	−0.115046
$601$	5.50257e6	0.621411	0.310706	−	0.950506i	$-0.399435\pi$
$601$	5.50257e6	0.621411	0.310706	+	0.950506i	$0.399435\pi$
$602$	−3.41257e6	−0.383787
$603$	−2.37750e6	−0.266274
$604$	−1.33261e7	−1.48632
$605$	1.00394e7	1.11512
$606$	−838132.	−0.0927109
$607$	529691.	0.0583513	0.0291757	−	0.999574i	$-0.490712\pi$
$607$	529691.	0.0583513	0.0291757	+	0.999574i	$0.490712\pi$
$608$	8.23436e6	0.903380
$609$	2.06899e6	0.226056
$610$	4.90902e6	0.534159
$611$	−253788.	−0.0275022
$612$	5.74265e6	0.619774
$613$	−6.94496e6	−0.746480	−0.373240	−	0.927735i	$-0.621753\pi$
$613$	−6.94496e6	−0.746480	−0.373240	+	0.927735i	$0.621753\pi$
$614$	−716518.	−0.0767019
$615$	−3.47022e6	−0.369972
$616$	−2.82824e6	−0.300307
$617$	1.72574e7	1.82500	0.912501	−	0.409075i	$-0.134148\pi$
$617$	1.72574e7	1.82500	0.912501	+	0.409075i	$0.134148\pi$
$618$	−1.50798e7	−1.58827
$619$	−1.09446e7	−1.14809	−0.574043	−	0.818825i	$-0.694626\pi$
$619$	−1.09446e7	−1.14809	−0.574043	+	0.818825i	$0.694626\pi$
$620$	−4.66963e6	−0.487869
$621$	594214.	0.0618321
$622$	−2.66872e7	−2.76584
$623$	211146.	0.0217953
$624$	−264908.	−0.0272354
$625$	−6.67905e6	−0.683935
$626$	−6.06844e6	−0.618930
$627$	6.54712e6	0.665091
$628$	5.91592e6	0.598581
$629$	4.26780e6	0.430108
$630$	1.14099e6	0.114533
$631$	−1.74968e7	−1.74939	−0.874694	−	0.484676i	$-0.838937\pi$
$631$	−1.74968e7	−1.74939	−0.874694	+	0.484676i	$0.838937\pi$
$632$	1.06405e7	1.05967
$633$	−5.05066e6	−0.501001
$634$	−1.62212e7	−1.60273
$635$	−3.66255e6	−0.360453
$636$	7.28444e6	0.714091
$637$	1.80202e6	0.175959
$638$	3.83128e7	3.72642
$639$	5.00919e6	0.485305
$640$	1.23840e7	1.19512
$641$	−1.02308e6	−0.0983478	−0.0491739	−	0.998790i	$-0.515659\pi$
$641$	−1.02308e6	−0.0983478	−0.0491739	+	0.998790i	$0.515659\pi$
$642$	1.52497e6	0.146024
$643$	1.59762e7	1.52387	0.761933	−	0.647655i	$-0.224250\pi$
$643$	1.59762e7	1.52387	0.761933	+	0.647655i	$0.224250\pi$
$644$	1.27446e6	0.121091
$645$	5.09402e6	0.482127
$646$	−1.58302e7	−1.49247
$647$	1.48605e7	1.39564	0.697820	−	0.716273i	$-0.254153\pi$
$647$	1.48605e7	1.39564	0.697820	+	0.716273i	$0.254153\pi$
$648$	−937743.	−0.0877296
$649$	2.11384e6	0.196997
$650$	−807239.	−0.0749408
$651$	−590499.	−0.0546093
$652$	−2.47883e7	−2.28364
$653$	1.12385e7	1.03140	0.515699	−	0.856770i	$-0.327532\pi$
$653$	1.12385e7	1.03140	0.515699	+	0.856770i	$0.327532\pi$
$654$	1.02232e6	0.0934638
$655$	−1.35261e7	−1.23189
$656$	−2.05156e6	−0.186134
$657$	−563084.	−0.0508932
$658$	646229.	0.0581864
$659$	1.66209e7	1.49088	0.745439	−	0.666574i	$-0.232240\pi$
$659$	1.66209e7	1.49088	0.745439	+	0.666574i	$0.232240\pi$
$660$	1.26751e7	1.13264
$661$	5.12621e6	0.456344	0.228172	−	0.973621i	$-0.426725\pi$
$661$	5.12621e6	0.456344	0.228172	+	0.973621i	$0.426725\pi$
$662$	2.60628e7	2.31141
$663$	1.52198e6	0.134470
$664$	9.26703e6	0.815681
$665$	−1.88687e6	−0.165458
$666$	−2.09234e6	−0.182787
$667$	−5.75038e6	−0.500475
$668$	1.27210e7	1.10301
$669$	3.11450e6	0.269044
$670$	1.26882e7	1.09197
$671$	6.89605e6	0.591281
$672$	2.01589e6	0.172204
$673$	2.11025e6	0.179596	0.0897978	−	0.995960i	$-0.471378\pi$
$673$	2.11025e6	0.179596	0.0897978	+	0.995960i	$0.471378\pi$
$674$	1.72496e7	1.46261
$675$	574937.	0.0485692
$676$	−1.71867e7	−1.44653
$677$	4.85784e6	0.407354	0.203677	−	0.979038i	$-0.434711\pi$
$677$	4.85784e6	0.407354	0.203677	+	0.979038i	$0.434711\pi$
$678$	−7.24676e6	−0.605438
$679$	−1.13289e6	−0.0943005
$680$	−1.02078e7	−0.846568
$681$	624179.	0.0515753
$682$	−1.09346e7	−0.900208
$683$	−1.60898e7	−1.31977	−0.659887	−	0.751365i	$-0.729396\pi$
$683$	−1.60898e7	−1.31977	−0.659887	+	0.751365i	$0.729396\pi$
$684$	4.65585e6	0.380504
$685$	−1.49516e7	−1.21748
$686$	−9.48658e6	−0.769661
$687$	−9.30552e6	−0.752227
$688$	3.01154e6	0.242559
$689$	1.93061e6	0.154934
$690$	−3.17118e6	−0.253570
$691$	5.42126e6	0.431922	0.215961	−	0.976402i	$-0.430712\pi$
$691$	5.42126e6	0.431922	0.215961	+	0.976402i	$0.430712\pi$
$692$	−2.74229e7	−2.17695
$693$	1.60283e6	0.126781
$694$	2.35617e7	1.85698
$695$	2.12877e7	1.67173
$696$	9.07481e6	0.710091
$697$	1.17869e7	0.919004
$698$	3.02721e6	0.235182
$699$	−9.74140e6	−0.754099
$700$	1.23311e6	0.0951168
$701$	1.47704e7	1.13527	0.567633	−	0.823282i	$-0.307859\pi$
$701$	1.47704e7	1.13527	0.567633	+	0.823282i	$0.307859\pi$
$702$	−746169.	−0.0571471
$703$	3.46012e6	0.264060
$704$	3.23320e7	2.45867
$705$	−964642.	−0.0730960
$706$	1.11012e7	0.838223
$707$	339321.	0.0255306
$708$	1.50321e6	0.112704
$709$	2.41386e7	1.80341	0.901707	−	0.432347i	$-0.142314\pi$
$709$	2.41386e7	1.80341	0.901707	+	0.432347i	$0.142314\pi$
$710$	−2.67328e7	−1.99021
$711$	−6.03021e6	−0.447362
$712$	926108.	0.0684639
$713$	1.64118e6	0.120902
$714$	−3.87548e6	−0.284499
$715$	3.35931e6	0.245745
$716$	3.37755e6	0.246218
$717$	−4.73947e6	−0.344296
$718$	1.65697e7	1.19951
$719$	1.09977e7	0.793374	0.396687	−	0.917954i	$-0.370160\pi$
$719$	1.09977e7	0.793374	0.396687	+	0.917954i	$0.370160\pi$
$720$	−1.00691e6	−0.0723868
$721$	6.10512e6	0.437377
$722$	9.30997e6	0.664669
$723$	−9.87524e6	−0.702590
$724$	−3.33425e6	−0.236403
$725$	−5.56383e6	−0.393123
$726$	1.67178e7	1.17716
$727$	−1.70462e7	−1.19616	−0.598082	−	0.801435i	$-0.704070\pi$
$727$	−1.70462e7	−1.19616	−0.598082	+	0.801435i	$0.704070\pi$
$728$	−533045.	−0.0372765
$729$	531441.	0.0370370
$730$	3.00504e6	0.208710
$731$	−1.73023e7	−1.19760
$732$	4.90399e6	0.338276
$733$	−337753.	−0.0232188	−0.0116094	−	0.999933i	$-0.503695\pi$
$733$	−337753.	−0.0232188	−0.0116094	+	0.999933i	$0.503695\pi$
$734$	−1.98317e7	−1.35869
$735$	6.84946e6	0.467668
$736$	−5.60280e6	−0.381251
$737$	1.78240e7	1.20875
$738$	−5.77865e6	−0.390558
$739$	−805741.	−0.0542731	−0.0271365	−	0.999632i	$-0.508639\pi$
$739$	−805741.	−0.0542731	−0.0271365	+	0.999632i	$0.508639\pi$
$740$	6.69875e6	0.449691
$741$	1.23395e6	0.0825565
$742$	−4.91598e6	−0.327793
$743$	−2.67091e7	−1.77495	−0.887477	−	0.460851i	$-0.847544\pi$
$743$	−2.67091e7	−1.77495	−0.887477	+	0.460851i	$0.847544\pi$
$744$	−2.58999e6	−0.171540
$745$	−1.70767e6	−0.112723
$746$	1.78217e7	1.17247
$747$	−5.25185e6	−0.344358
$748$	−4.30521e7	−2.81346
$749$	−617389.	−0.0402119
$750$	−1.52261e7	−0.988406
$751$	−3.82078e6	−0.247202	−0.123601	−	0.992332i	$-0.539444\pi$
$751$	−3.82078e6	−0.247202	−0.123601	+	0.992332i	$0.539444\pi$
$752$	−570288.	−0.0367747
$753$	−6.56868e6	−0.422174
$754$	7.22089e6	0.462554
$755$	−1.34245e7	−0.857096
$756$	1.13982e6	0.0725325
$757$	8.80899e6	0.558710	0.279355	−	0.960188i	$-0.409879\pi$
$757$	8.80899e6	0.558710	0.279355	+	0.960188i	$0.409879\pi$
$758$	−9.33609e6	−0.590190
$759$	−4.45478e6	−0.280686
$760$	−8.27602e6	−0.519741
$761$	2.10564e6	0.131802	0.0659012	−	0.997826i	$-0.479008\pi$
$761$	2.10564e6	0.131802	0.0659012	+	0.997826i	$0.479008\pi$
$762$	−6.09892e6	−0.380509
$763$	−413891.	−0.0257380
$764$	−3.79491e7	−2.35216
$765$	5.78503e6	0.357398
$766$	−9.57079e6	−0.589353
$767$	398399.	0.0244529
$768$	5.28801e6	0.323511
$769$	−6.98302e6	−0.425821	−0.212911	−	0.977072i	$-0.568294\pi$
$769$	−6.98302e6	−0.425821	−0.212911	+	0.977072i	$0.568294\pi$
$770$	−8.55393e6	−0.519923
$771$	−6.50525e6	−0.394120
$772$	−4.65884e7	−2.81342
$773$	−1.43123e7	−0.861511	−0.430756	−	0.902469i	$-0.641753\pi$
$773$	−1.43123e7	−0.861511	−0.430756	+	0.902469i	$0.641753\pi$
$774$	8.48264e6	0.508954
$775$	1.58794e6	0.0949684
$776$	−4.96897e6	−0.296219
$777$	847090.	0.0503358
$778$	−1.50571e7	−0.891852
$779$	9.55623e6	0.564213
$780$	2.38890e6	0.140593
$781$	−3.75534e7	−2.20304
$782$	1.07712e7	0.629864
$783$	−5.14291e6	−0.299781
$784$	4.04934e6	0.235285
$785$	5.95958e6	0.345177
$786$	−2.25239e7	−1.30043
$787$	−1.83449e7	−1.05579	−0.527897	−	0.849308i	$-0.677019\pi$
$787$	−1.83449e7	−1.05579	−0.527897	+	0.849308i	$0.677019\pi$
$788$	−2.97465e7	−1.70655
$789$	1.17604e7	0.672557
$790$	3.21818e7	1.83460
$791$	2.93388e6	0.166725
$792$	7.03018e6	0.398248
$793$	1.29971e6	0.0733946
$794$	7.26373e6	0.408892
$795$	7.33820e6	0.411786
$796$	−8.41993e6	−0.471005
$797$	−1.80668e7	−1.00748	−0.503740	−	0.863855i	$-0.668043\pi$
$797$	−1.80668e7	−1.00748	−0.503740	+	0.863855i	$0.668043\pi$
$798$	−3.14205e6	−0.174665
$799$	3.27649e6	0.181569
$800$	−5.42104e6	−0.299473
$801$	−524847.	−0.0289036
$802$	2.01663e7	1.10711
$803$	4.22139e6	0.231029
$804$	1.26752e7	0.691533
$805$	1.28386e6	0.0698279
$806$	−2.06087e6	−0.111741
$807$	−1.88872e7	−1.02090
$808$	1.48829e6	0.0801974
$809$	1.71475e7	0.921150	0.460575	−	0.887621i	$-0.347643\pi$
$809$	1.71475e7	0.921150	0.460575	+	0.887621i	$0.347643\pi$
$810$	−2.83617e6	−0.151887
$811$	−2.71687e7	−1.45050	−0.725249	−	0.688487i	$-0.758275\pi$
$811$	−2.71687e7	−1.45050	−0.725249	+	0.688487i	$0.758275\pi$
$812$	−1.10304e7	−0.587085
$813$	−9.43854e6	−0.500817
$814$	1.56861e7	0.829762
$815$	−2.49712e7	−1.31688
$816$	3.42006e6	0.179808
$817$	−1.40278e7	−0.735251
$818$	−8.49383e6	−0.443834
$819$	302089.	0.0157371
$820$	1.85007e7	0.960846
$821$	2.36514e7	1.22462	0.612308	−	0.790619i	$-0.290241\pi$
$821$	2.36514e7	1.22462	0.612308	+	0.790619i	$0.290241\pi$
$822$	−2.48976e7	−1.28522
$823$	−3.65582e7	−1.88142	−0.940708	−	0.339216i	$-0.889838\pi$
$823$	−3.65582e7	−1.88142	−0.940708	+	0.339216i	$0.889838\pi$
$824$	2.67777e7	1.37390
$825$	−4.31025e6	−0.220479
$826$	−1.01446e6	−0.0517350
$827$	3.43682e7	1.74740	0.873702	−	0.486461i	$-0.161712\pi$
$827$	3.43682e7	1.74740	0.873702	+	0.486461i	$0.161712\pi$
$828$	−3.16793e6	−0.160583
$829$	−6.66101e6	−0.336631	−0.168315	−	0.985733i	$-0.553833\pi$
$829$	−6.66101e6	−0.336631	−0.168315	+	0.985733i	$0.553833\pi$
$830$	2.80278e7	1.41219
$831$	1.72344e6	0.0865751
$832$	6.09367e6	0.305190
$833$	−2.32648e7	−1.16168
$834$	3.54486e7	1.76475
$835$	1.28149e7	0.636061
$836$	−3.49045e7	−1.72729
$837$	1.46781e6	0.0724194
$838$	2.93513e6	0.144384
$839$	2.74300e7	1.34531	0.672654	−	0.739957i	$-0.265154\pi$
$839$	2.74300e7	1.34531	0.672654	+	0.739957i	$0.265154\pi$
$840$	−2.02609e6	−0.0990743
$841$	2.92582e7	1.42645
$842$	−5.49800e7	−2.67254
$843$	1.09631e7	0.531331
$844$	2.69265e7	1.30114
$845$	−1.73136e7	−0.834151
$846$	−1.60633e6	−0.0771632
$847$	−6.76824e6	−0.324166
$848$	4.33828e6	0.207171
$849$	−7.18530e6	−0.342118
$850$	1.04217e7	0.494758
$851$	−2.35433e6	−0.111441
$852$	−2.67054e7	−1.26038
$853$	3.05075e7	1.43560	0.717800	−	0.696249i	$-0.245149\pi$
$853$	3.05075e7	1.43560	0.717800	+	0.696249i	$0.245149\pi$
$854$	−3.30950e6	−0.155281
$855$	4.69021e6	0.219421
$856$	−2.70793e6	−0.126314
$857$	3.59631e7	1.67265	0.836324	−	0.548235i	$-0.184700\pi$
$857$	3.59631e7	1.67265	0.836324	+	0.548235i	$0.184700\pi$
$858$	5.59396e6	0.259419
$859$	2.39847e7	1.10905	0.554525	−	0.832167i	$-0.312900\pi$
$859$	2.39847e7	1.10905	0.554525	+	0.832167i	$0.312900\pi$
$860$	−2.71577e7	−1.25212
$861$	2.33951e6	0.107552
$862$	−2.93394e7	−1.34488
$863$	−7.98871e6	−0.365132	−0.182566	−	0.983194i	$-0.558440\pi$
$863$	−7.98871e6	−0.365132	−0.182566	+	0.983194i	$0.558440\pi$
$864$	−5.01092e6	−0.228367
$865$	−2.76253e7	−1.25536
$866$	1.60862e7	0.728885
$867$	−6.87063e6	−0.310420
$868$	3.14812e6	0.141825
$869$	4.52080e7	2.03079
$870$	2.74464e7	1.22939
$871$	3.35932e6	0.150039
$872$	−1.81537e6	−0.0808487
$873$	2.81603e6	0.125055
$874$	8.73274e6	0.386698
$875$	6.16434e6	0.272186
$876$	3.00196e6	0.132174
$877$	1.96183e7	0.861316	0.430658	−	0.902515i	$-0.358281\pi$
$877$	1.96183e7	0.861316	0.430658	+	0.902515i	$0.358281\pi$
$878$	−1.45459e7	−0.636800
$879$	9.53232e6	0.416128
$880$	7.54872e6	0.328599
$881$	2.55652e7	1.10971	0.554854	−	0.831947i	$-0.312774\pi$
$881$	2.55652e7	1.10971	0.554854	+	0.831947i	$0.312774\pi$
$882$	1.14058e7	0.493690
$883$	1.76039e7	0.759812	0.379906	−	0.925025i	$-0.375956\pi$
$883$	1.76039e7	0.759812	0.379906	+	0.925025i	$0.375956\pi$
$884$	−8.11412e6	−0.349229
$885$	1.51431e6	0.0649914
$886$	−3.42495e7	−1.46579
$887$	3.35376e7	1.43127	0.715637	−	0.698473i	$-0.246137\pi$
$887$	3.35376e7	1.43127	0.715637	+	0.698473i	$0.246137\pi$
$888$	3.71542e6	0.158116
$889$	2.46917e6	0.104784
$890$	2.80098e6	0.118532
$891$	−3.98417e6	−0.168129
$892$	−1.66043e7	−0.698729
$893$	2.65642e6	0.111472
$894$	−2.84364e6	−0.118995
$895$	3.40248e6	0.141983
$896$	−8.34892e6	−0.347424
$897$	−839600.	−0.0348411
$898$	3.98122e7	1.64750
$899$	−1.42044e7	−0.586169
$900$	−3.06515e6	−0.126138
$901$	−2.49248e7	−1.02287
$902$	4.33221e7	1.77293
$903$	−3.43423e6	−0.140155
$904$	1.28683e7	0.523720
$905$	−3.35886e6	−0.136323
$906$	−2.23546e7	−0.904787
$907$	−4.58984e7	−1.85259	−0.926296	−	0.376798i	$-0.877025\pi$
$907$	−4.58984e7	−1.85259	−0.926296	+	0.376798i	$0.877025\pi$
$908$	−3.32768e6	−0.133945
$909$	−843451.	−0.0338571
$910$	−1.61218e6	−0.0645370
$911$	−3.40938e7	−1.36107	−0.680534	−	0.732716i	$-0.738252\pi$
$911$	−3.40938e7	−1.36107	−0.680534	+	0.732716i	$0.738252\pi$
$912$	2.77281e6	0.110391
$913$	3.93727e7	1.56321
$914$	1.05429e7	0.417439
$915$	4.94018e6	0.195070
$916$	4.96103e7	1.95359
$917$	9.11889e6	0.358112
$918$	9.63330e6	0.377284
$919$	−4.71301e7	−1.84081	−0.920406	−	0.390965i	$-0.872141\pi$
$919$	−4.71301e7	−1.84081	−0.920406	+	0.390965i	$0.872141\pi$
$920$	5.63115e6	0.219345
$921$	−721065.	−0.0280108
$922$	−1.54916e7	−0.600162
$923$	−7.07777e6	−0.273459
$924$	−8.54516e6	−0.329261
$925$	−2.27795e6	−0.0875367
$926$	−1.21288e7	−0.464825
$927$	−1.51755e7	−0.580022
$928$	4.84921e7	1.84842
$929$	3.41936e7	1.29989	0.649944	−	0.759982i	$-0.274792\pi$
$929$	3.41936e7	1.29989	0.649944	+	0.759982i	$0.274792\pi$
$930$	−7.83332e6	−0.296988
$931$	−1.88619e7	−0.713201
$932$	5.19342e7	1.95845
$933$	−2.68566e7	−1.01006
$934$	3.21265e7	1.20503
$935$	−4.33699e7	−1.62240
$936$	1.32499e6	0.0494338
$937$	−4.54494e7	−1.69114	−0.845569	−	0.533866i	$-0.820739\pi$
$937$	−4.54494e7	−1.69114	−0.845569	+	0.533866i	$0.820739\pi$
$938$	−8.55395e6	−0.317438
$939$	−6.10695e6	−0.226027
$940$	5.14278e6	0.189836
$941$	−5.33355e7	−1.96355	−0.981776	−	0.190043i	$-0.939137\pi$
$941$	−5.33355e7	−1.96355	−0.981776	+	0.190043i	$0.939137\pi$
$942$	9.92397e6	0.364383
$943$	−6.50223e6	−0.238113
$944$	895245.	0.0326973
$945$	1.14823e6	0.0418265
$946$	−6.35936e7	−2.31039
$947$	2.21988e7	0.804367	0.402183	−	0.915559i	$-0.368251\pi$
$947$	2.21988e7	0.804367	0.402183	+	0.915559i	$0.368251\pi$
$948$	3.21488e7	1.16183
$949$	795614.	0.0286772
$950$	8.44943e6	0.303752
$951$	−1.63242e7	−0.585303
$952$	6.88180e6	0.246099
$953$	−43754.2	−0.00156059	−0.000780293	−	1.00000i	$-0.500248\pi$
$953$	−43754.2	−0.00156059	−0.000780293		1.00000i	$0.500248\pi$
$954$	1.22197e7	0.434699
$955$	−3.82291e7	−1.35639
$956$	2.52675e7	0.894163
$957$	3.85559e7	1.36085
$958$	5.09871e7	1.79493
$959$	1.00799e7	0.353923
$960$	2.31619e7	0.811141
$961$	−2.45752e7	−0.858397
$962$	2.95639e6	0.102997
$963$	1.53465e6	0.0533265
$964$	5.26477e7	1.82468
$965$	−4.69322e7	−1.62238
$966$	2.13791e6	0.0737133
$967$	4.71228e7	1.62056	0.810280	−	0.586043i	$-0.199315\pi$
$967$	4.71228e7	1.62056	0.810280	+	0.586043i	$0.199315\pi$
$968$	−2.96862e7	−1.01828
$969$	−1.59307e7	−0.545037
$970$	−1.50285e7	−0.512845
$971$	−3.47681e7	−1.18340	−0.591701	−	0.806157i	$-0.701543\pi$
$971$	−3.47681e7	−1.18340	−0.591701	+	0.806157i	$0.701543\pi$
$972$	−2.83326e6	−0.0961881
$973$	−1.43515e7	−0.485976
$974$	2.07626e7	0.701267
$975$	−812362.	−0.0273677
$976$	2.92059e6	0.0981400
$977$	−4.21133e7	−1.41151	−0.705753	−	0.708458i	$-0.749391\pi$
$977$	−4.21133e7	−1.41151	−0.705753	+	0.708458i	$0.749391\pi$
$978$	−4.15825e7	−1.39015
$979$	3.93474e6	0.131208
$980$	−3.65164e7	−1.21457
$981$	1.02881e6	0.0341321
$982$	6.50613e7	2.15300
$983$	−1.65545e7	−0.546427	−0.273214	−	0.961953i	$-0.588087\pi$
$983$	−1.65545e7	−0.546427	−0.273214	+	0.961953i	$0.588087\pi$
$984$	1.02613e7	0.337843
$985$	−2.99660e7	−0.984098
$986$	−9.32242e7	−3.05377
$987$	650330.	0.0212491
$988$	−6.57853e6	−0.214406
$989$	9.54480e6	0.310296
$990$	2.12625e7	0.689489
$991$	5.06855e6	0.163946	0.0819728	−	0.996635i	$-0.473878\pi$
$991$	5.06855e6	0.163946	0.0819728	+	0.996635i	$0.473878\pi$
$992$	−1.38398e7	−0.446531
$993$	2.62283e7	0.844105
$994$	1.80224e7	0.578557
$995$	−8.48207e6	−0.271609
$996$	2.79991e7	0.894325
$997$	3.70847e6	0.118156	0.0590782	−	0.998253i	$-0.481184\pi$
$997$	3.70847e6	0.118156	0.0590782	+	0.998253i	$0.481184\pi$
$998$	−1.90913e7	−0.606749
$999$	−2.10562e6	−0.0667522

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.b.1.2	✓	12
3.2	odd	2		531.6.a.d.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.b.1.2	✓	12	1.1	even	1	trivial
531.6.a.d.1.11		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)

\(f(q)\)	\(=\)	\(q-8.94324 q^{2} -9.00000 q^{3} +47.9816 q^{4} +48.3356 q^{5} +80.4892 q^{6} -32.5863 q^{7} -142.927 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-8.94324 q^{2} -9.00000 q^{3} +47.9816 q^{4} +48.3356 q^{5} +80.4892 q^{6} -32.5863 q^{7} -142.927 q^{8} +81.0000 q^{9} -432.277 q^{10} -607.250 q^{11} -431.834 q^{12} -114.450 q^{13} +291.427 q^{14} -435.021 q^{15} -257.180 q^{16} +1477.59 q^{17} -724.402 q^{18} +1197.95 q^{19} +2319.22 q^{20} +293.277 q^{21} +5430.79 q^{22} -815.109 q^{23} +1286.34 q^{24} -788.665 q^{25} +1023.55 q^{26} -729.000 q^{27} -1563.54 q^{28} +7054.74 q^{29} +3890.50 q^{30} -2013.45 q^{31} +6873.69 q^{32} +5465.25 q^{33} -13214.4 q^{34} -1575.08 q^{35} +3886.51 q^{36} +2888.36 q^{37} -10713.6 q^{38} +1030.05 q^{39} -6908.46 q^{40} +7977.13 q^{41} -2622.85 q^{42} -11709.8 q^{43} -29136.8 q^{44} +3915.19 q^{45} +7289.72 q^{46} +2217.46 q^{47} +2314.62 q^{48} -15745.1 q^{49} +7053.22 q^{50} -13298.3 q^{51} -5491.47 q^{52} -16868.6 q^{53} +6519.62 q^{54} -29351.8 q^{55} +4657.46 q^{56} -10781.6 q^{57} -63092.2 q^{58} -3481.00 q^{59} -20873.0 q^{60} -11356.2 q^{61} +18006.8 q^{62} -2639.49 q^{63} -53243.2 q^{64} -5532.00 q^{65} -48877.1 q^{66} -29351.9 q^{67} +70896.9 q^{68} +7335.98 q^{69} +14086.3 q^{70} +61841.8 q^{71} -11577.1 q^{72} -6951.65 q^{73} -25831.3 q^{74} +7097.99 q^{75} +57479.7 q^{76} +19788.1 q^{77} -9211.96 q^{78} -74447.1 q^{79} -12431.0 q^{80} +6561.00 q^{81} -71341.4 q^{82} -64837.6 q^{83} +14071.9 q^{84} +71420.1 q^{85} +104724. q^{86} -63492.7 q^{87} +86792.4 q^{88} -6479.60 q^{89} -35014.5 q^{90} +3729.49 q^{91} -39110.2 q^{92} +18121.1 q^{93} -19831.3 q^{94} +57903.9 q^{95} -61863.2 q^{96} +34765.8 q^{97} +140812. q^{98} -49187.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9} - 863 q^{10} + 492 q^{11} - 1782 q^{12} - 974 q^{13} - 967 q^{14} - 324 q^{15} + 6370 q^{16} - 1463 q^{17} - 324 q^{18} - 3189 q^{19} - 835 q^{20} + 3699 q^{21} - 2726 q^{22} - 2617 q^{23} + 621 q^{24} + 8642 q^{25} + 2414 q^{26} - 8748 q^{27} - 20458 q^{28} - 1963 q^{29} + 7767 q^{30} - 11929 q^{31} - 14382 q^{32} - 4428 q^{33} - 20744 q^{34} + 1829 q^{35} + 16038 q^{36} - 28105 q^{37} - 23475 q^{38} + 8766 q^{39} - 100576 q^{40} - 7585 q^{41} + 8703 q^{42} - 33146 q^{43} + 26014 q^{44} + 2916 q^{45} - 142851 q^{46} - 79215 q^{47} - 57330 q^{48} - 32569 q^{49} - 136019 q^{50} + 13167 q^{51} - 248218 q^{52} - 12220 q^{53} + 2916 q^{54} - 117770 q^{55} - 186728 q^{56} + 28701 q^{57} - 188072 q^{58} - 41772 q^{59} + 7515 q^{60} - 54195 q^{61} + 36230 q^{62} - 33291 q^{63} + 45197 q^{64} + 42368 q^{65} + 24534 q^{66} + 24224 q^{67} - 209639 q^{68} + 23553 q^{69} - 35684 q^{70} + 60254 q^{71} - 5589 q^{72} - 15385 q^{73} + 214638 q^{74} - 77778 q^{75} - 167504 q^{76} - 17169 q^{77} - 21726 q^{78} - 27054 q^{79} + 216899 q^{80} + 78732 q^{81} + 37917 q^{82} - 117595 q^{83} + 184122 q^{84} - 121585 q^{85} + 306756 q^{86} + 17667 q^{87} - 105799 q^{88} - 36033 q^{89} - 69903 q^{90} - 32217 q^{91} - 30906 q^{92} + 107361 q^{93} + 128392 q^{94} - 50721 q^{95} + 129438 q^{96} - 196914 q^{97} + 574100 q^{98} + 39852 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9 - 863 * q^10 + 492 * q^11 - 1782 * q^12 - 974 * q^13 - 967 * q^14 - 324 * q^15 + 6370 * q^16 - 1463 * q^17 - 324 * q^18 - 3189 * q^19 - 835 * q^20 + 3699 * q^21 - 2726 * q^22 - 2617 * q^23 + 621 * q^24 + 8642 * q^25 + 2414 * q^26 - 8748 * q^27 - 20458 * q^28 - 1963 * q^29 + 7767 * q^30 - 11929 * q^31 - 14382 * q^32 - 4428 * q^33 - 20744 * q^34 + 1829 * q^35 + 16038 * q^36 - 28105 * q^37 - 23475 * q^38 + 8766 * q^39 - 100576 * q^40 - 7585 * q^41 + 8703 * q^42 - 33146 * q^43 + 26014 * q^44 + 2916 * q^45 - 142851 * q^46 - 79215 * q^47 - 57330 * q^48 - 32569 * q^49 - 136019 * q^50 + 13167 * q^51 - 248218 * q^52 - 12220 * q^53 + 2916 * q^54 - 117770 * q^55 - 186728 * q^56 + 28701 * q^57 - 188072 * q^58 - 41772 * q^59 + 7515 * q^60 - 54195 * q^61 + 36230 * q^62 - 33291 * q^63 + 45197 * q^64 + 42368 * q^65 + 24534 * q^66 + 24224 * q^67 - 209639 * q^68 + 23553 * q^69 - 35684 * q^70 + 60254 * q^71 - 5589 * q^72 - 15385 * q^73 + 214638 * q^74 - 77778 * q^75 - 167504 * q^76 - 17169 * q^77 - 21726 * q^78 - 27054 * q^79 + 216899 * q^80 + 78732 * q^81 + 37917 * q^82 - 117595 * q^83 + 184122 * q^84 - 121585 * q^85 + 306756 * q^86 + 17667 * q^87 - 105799 * q^88 - 36033 * q^89 - 69903 * q^90 - 32217 * q^91 - 30906 * q^92 + 107361 * q^93 + 128392 * q^94 - 50721 * q^95 + 129438 * q^96 - 196914 * q^97 + 574100 * q^98 + 39852 * q^99

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