LMFDB - Embedded newform 98.6.c.f.79.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,6,Mod(67,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.67"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,8,-14,-32,-42,-112,0,-256,-652] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.7176143417$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{130})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 130x^{2} + 16900 $ x^4 + 130*x^2 + 16900
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$-5.70088 - 9.87421i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.6.c.f.67.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 - 3.46410i) q^{2} +(7.90175 + 13.6862i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-10.5000 + 18.1865i) q^{5} +63.2140 q^{6} -64.0000 q^{8} +(-3.37544 + 5.84643i) q^{9} +(42.0000 + 72.7461i) q^{10} +(312.937 + 542.023i) q^{11} +(126.428 - 218.980i) q^{12} +206.821 q^{13} -331.874 q^{15} +(-128.000 + 221.703i) q^{16} +(530.732 + 919.254i) q^{17} +(13.5018 + 23.3857i) q^{18} +(-941.989 + 1631.57i) q^{19} +336.000 q^{20} +2503.49 q^{22} +(-1858.68 + 3219.34i) q^{23} +(-505.712 - 875.919i) q^{24} +(1342.00 + 2324.41i) q^{25} +(413.642 - 716.449i) q^{26} +3733.56 q^{27} -123.747 q^{29} +(-663.747 + 1149.64i) q^{30} +(-4554.63 - 7888.85i) q^{31} +(512.000 + 886.810i) q^{32} +(-4945.50 + 8565.86i) q^{33} +4245.85 q^{34} +108.014 q^{36} +(3014.36 - 5221.03i) q^{37} +(3767.96 + 6526.29i) q^{38} +(1634.25 + 2830.60i) q^{39} +(672.000 - 1163.94i) q^{40} +17201.9 q^{41} +5401.98 q^{43} +(5006.99 - 8672.36i) q^{44} +(-70.8843 - 122.775i) q^{45} +(7434.74 + 12877.3i) q^{46} +(937.621 - 1624.01i) q^{47} -4045.70 q^{48} +10736.0 q^{50} +(-8387.42 + 14527.4i) q^{51} +(-1654.57 - 2865.80i) q^{52} +(-9353.62 - 16200.9i) q^{53} +(7467.13 - 12933.4i) q^{54} -13143.3 q^{55} -29773.5 q^{57} +(-247.495 + 428.673i) q^{58} +(-1267.39 - 2195.18i) q^{59} +(2654.99 + 4598.58i) q^{60} +(-1047.35 + 1814.07i) q^{61} -36437.1 q^{62} +4096.00 q^{64} +(-2171.62 + 3761.36i) q^{65} +(19782.0 + 34263.4i) q^{66} +(-29310.4 - 50767.1i) q^{67} +(8491.71 - 14708.1i) q^{68} -58747.5 q^{69} -31279.5 q^{71} +(216.028 - 374.172i) q^{72} +(-3575.24 - 6192.49i) q^{73} +(-12057.5 - 20884.1i) q^{74} +(-21208.3 + 36733.9i) q^{75} +30143.7 q^{76} +13074.0 q^{78} +(-1489.91 + 2580.59i) q^{79} +(-2688.00 - 4655.75i) q^{80} +(30321.9 + 52519.1i) q^{81} +(34403.7 - 59589.0i) q^{82} -45954.6 q^{83} -22290.7 q^{85} +(10804.0 - 18713.0i) q^{86} +(-977.821 - 1693.64i) q^{87} +(-20028.0 - 34689.4i) q^{88} +(49520.0 - 85771.1i) q^{89} -567.074 q^{90} +59477.9 q^{92} +(71979.2 - 124672. i) q^{93} +(-3750.48 - 6496.03i) q^{94} +(-19781.8 - 34263.0i) q^{95} +(-8091.40 + 14014.7i) q^{96} +115548. q^{97} -4225.20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} - 14 q^{3} - 32 q^{4} - 42 q^{5} - 112 q^{6} - 256 q^{8} - 652 q^{9} + 168 q^{10} + 294 q^{11} - 224 q^{12} + 280 q^{13} + 588 q^{15} - 512 q^{16} + 1302 q^{17} + 2608 q^{18} - 1442 q^{19}+ \cdots + 419832 q^{99}+O(q^{100}) $ 4 * q + 8 * q^2 - 14 * q^3 - 32 * q^4 - 42 * q^5 - 112 * q^6 - 256 * q^8 - 652 * q^9 + 168 * q^10 + 294 * q^11 - 224 * q^12 + 280 * q^13 + 588 * q^15 - 512 * q^16 + 1302 * q^17 + 2608 * q^18 - 1442 * q^19 + 1344 * q^20 + 2352 * q^22 - 2646 * q^23 + 896 * q^24 + 5368 * q^25 + 560 * q^26 + 31444 * q^27 + 3336 * q^29 + 1176 * q^30 - 14798 * q^31 + 2048 * q^32 - 19782 * q^33 + 10416 * q^34 + 20864 * q^36 - 5182 * q^37 + 5768 * q^38 + 5260 * q^39 + 2688 * q^40 + 10248 * q^41 - 9040 * q^43 + 4704 * q^44 - 13692 * q^45 + 10584 * q^46 - 14994 * q^47 + 7168 * q^48 + 42944 * q^50 - 9606 * q^51 - 2240 * q^52 - 24006 * q^53 + 62888 * q^54 - 12348 * q^55 - 85892 * q^57 + 6672 * q^58 + 38850 * q^59 - 4704 * q^60 - 23618 * q^61 - 118384 * q^62 + 16384 * q^64 - 2940 * q^65 + 79128 * q^66 - 32002 * q^67 + 20832 * q^68 - 181356 * q^69 - 178752 * q^71 + 41728 * q^72 - 47138 * q^73 + 20728 * q^74 + 37576 * q^75 + 46144 * q^76 + 42080 * q^78 + 40970 * q^79 - 10752 * q^80 - 139858 * q^81 + 20496 * q^82 - 136752 * q^83 - 54684 * q^85 - 18080 * q^86 - 55356 * q^87 - 18816 * q^88 + 123102 * q^89 - 109536 * q^90 + 84672 * q^92 - 25586 * q^93 + 59976 * q^94 - 30282 * q^95 + 14336 * q^96 + 87304 * q^97 + 419832 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$3$	7.90175	+	13.6862i	0.506898	+	0.877973i	0.999968	+	0.00798326i	$0.00254118\pi$
$3$	7.90175	+	13.6862i	0.506898	+	0.877973i	−0.493070	+	0.869989i	$0.664125\pi$
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−10.5000	+	18.1865i	−0.187830	+	0.325331i	−0.944526	−	0.328436i	$-0.893479\pi$
$5$	−10.5000	+	18.1865i	−0.187830	+	0.325331i	0.756697	+	0.653766i	$0.226812\pi$
$6$	63.2140			0.716862
$7$		0			0
$7$		0			0
$8$	−64.0000			−0.353553
$9$	−3.37544	+	5.84643i	−0.0138907	+	0.0240594i
$10$	42.0000	+	72.7461i	0.132816	+	0.230043i
$11$	312.937	+	542.023i	0.779785	+	1.35063i	0.932065	+	0.362290i	$0.118005\pi$
$11$	312.937	+	542.023i	0.779785	+	1.35063i	−0.152280	+	0.988337i	$0.548662\pi$
$12$	126.428	−	218.980i	0.253449	−	0.438986i
$13$	206.821			0.339419			0.169710	−	0.985494i	$-0.445717\pi$
$13$	206.821			0.339419			0.169710	+	0.985494i	$0.445717\pi$
$14$		0			0
$15$	−331.874			−0.380842
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	530.732	+	919.254i	0.445402	+	0.771460i	0.998080	−	0.0619354i	$-0.0197273\pi$
$17$	530.732	+	919.254i	0.445402	+	0.771460i	−0.552678	+	0.833395i	$0.686394\pi$
$18$	13.5018	+	23.3857i	0.00982221	+	0.0170126i
$19$	−941.989	+	1631.57i	−0.598635	+	1.03687i	0.394388	+	0.918944i	$0.370957\pi$
$19$	−941.989	+	1631.57i	−0.598635	+	1.03687i	−0.993023	+	0.117922i	$0.962377\pi$
$20$	336.000			0.187830
$21$		0			0
$22$	2503.49			1.10278
$23$	−1858.68	+	3219.34i	−0.732632	+	1.26896i	0.223122	+	0.974790i	$0.428375\pi$
$23$	−1858.68	+	3219.34i	−0.732632	+	1.26896i	−0.955754	+	0.294166i	$0.904958\pi$
$24$	−505.712	−	875.919i	−0.179215	−	0.310410i
$25$	1342.00	+	2324.41i	0.429440	+	0.743812i
$26$	413.642	−	716.449i	0.120003	−	0.207851i
$27$	3733.56			0.985631
$28$		0			0
$29$	−123.747			−0.0273238			−0.0136619	−	0.999907i	$-0.504349\pi$
$29$	−123.747			−0.0273238			−0.0136619	+	0.999907i	$0.504349\pi$
$30$	−663.747	+	1149.64i	−0.134648	+	0.233217i
$31$	−4554.63	−	7888.85i	−0.851234	−	1.47438i	−0.880095	−	0.474797i	$-0.842521\pi$
$31$	−4554.63	−	7888.85i	−0.851234	−	1.47438i	0.0288611	−	0.999583i	$-0.490812\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$	−4945.50	+	8565.86i	−0.790543	+	1.36926i
$34$	4245.85			0.629894
$35$		0			0
$36$	108.014			0.0138907
$37$	3014.36	−	5221.03i	0.361986	−	0.626977i	−0.626302	−	0.779581i	$-0.715432\pi$
$37$	3014.36	−	5221.03i	0.361986	−	0.626977i	0.988288	+	0.152603i	$0.0487656\pi$
$38$	3767.96	+	6526.29i	0.423299	+	0.733175i
$39$	1634.25	+	2830.60i	0.172051	+	0.298001i
$40$	672.000	−	1163.94i	0.0664078	−	0.115022i
$41$	17201.9			1.59814			0.799071	−	0.601236i	$-0.205325\pi$
$41$	17201.9			1.59814			0.799071	+	0.601236i	$0.205325\pi$
$42$		0			0
$43$	5401.98			0.445535			0.222767	−	0.974872i	$-0.428491\pi$
$43$	5401.98			0.445535			0.222767	+	0.974872i	$0.428491\pi$
$44$	5006.99	−	8672.36i	0.389893	−	0.675314i
$45$	−70.8843	−	122.775i	−0.00521817	−	0.00903814i
$46$	7434.74	+	12877.3i	0.518049	+	0.897288i
$47$	937.621	−	1624.01i	0.0619131	−	0.107237i	−0.833407	−	0.552659i	$-0.813613\pi$
$47$	937.621	−	1624.01i	0.0619131	−	0.107237i	0.895321	+	0.445422i	$0.146946\pi$
$48$	−4045.70			−0.253449
$49$		0			0
$50$	10736.0			0.607320
$51$	−8387.42	+	14527.4i	−0.451547	+	0.782102i
$52$	−1654.57	−	2865.80i	−0.0848548	−	0.146973i
$53$	−9353.62	−	16200.9i	−0.457393	−	0.792229i	0.541429	−	0.840747i	$-0.317884\pi$
$53$	−9353.62	−	16200.9i	−0.457393	−	0.792229i	−0.998822	+	0.0485180i	$0.984550\pi$
$54$	7467.13	−	12933.4i	0.348473	−	0.603573i
$55$	−13143.3			−0.585867
$56$		0			0
$57$	−29773.5			−1.21379
$58$	−247.495	+	428.673i	−0.00966042	+	0.0167323i
$59$	−1267.39	−	2195.18i	−0.0474002	−	0.0820995i	0.841352	−	0.540488i	$-0.181760\pi$
$59$	−1267.39	−	2195.18i	−0.0474002	−	0.0820995i	−0.888752	+	0.458388i	$0.848427\pi$
$60$	2654.99	+	4598.58i	0.0952105	+	0.164909i
$61$	−1047.35	+	1814.07i	−0.0360386	+	0.0624208i	−0.883482	−	0.468465i	$-0.844807\pi$
$61$	−1047.35	+	1814.07i	−0.0360386	+	0.0624208i	0.847444	+	0.530886i	$0.178141\pi$
$62$	−36437.1			−1.20383
$63$		0			0
$64$	4096.00			0.125000
$65$	−2171.62	+	3761.36i	−0.0637530	+	0.110423i
$66$	19782.0	+	34263.4i	0.558998	+	0.968213i
$67$	−29310.4	−	50767.1i	−0.797691	−	1.38164i	−0.921117	−	0.389287i	$-0.872722\pi$
$67$	−29310.4	−	50767.1i	−0.797691	−	1.38164i	0.123426	−	0.992354i	$-0.460612\pi$
$68$	8491.71	−	14708.1i	0.222701	−	0.385730i
$69$	−58747.5			−1.48548
$70$		0			0
$71$	−31279.5			−0.736401			−0.368201	−	0.929746i	$-0.620026\pi$
$71$	−31279.5			−0.736401			−0.368201	+	0.929746i	$0.620026\pi$
$72$	216.028	−	374.172i	0.00491110	−	0.00850628i
$73$	−3575.24	−	6192.49i	−0.0785231	−	0.136006i	0.824090	−	0.566459i	$-0.191687\pi$
$73$	−3575.24	−	6192.49i	−0.0785231	−	0.136006i	−0.902613	+	0.430453i	$0.858354\pi$
$74$	−12057.5	−	20884.1i	−0.255962	−	0.443340i
$75$	−21208.3	+	36733.9i	−0.435364	+	0.754073i
$76$	30143.7			0.598635
$77$		0			0
$78$	13074.0			0.243317
$79$	−1489.91	+	2580.59i	−0.0268591	+	0.0465213i	−0.879143	−	0.476559i	$-0.841884\pi$
$79$	−1489.91	+	2580.59i	−0.0268591	+	0.0465213i	0.852283	+	0.523080i	$0.175217\pi$
$80$	−2688.00	−	4655.75i	−0.0469574	−	0.0813327i
$81$	30321.9	+	52519.1i	0.513505	+	0.889416i
$82$	34403.7	−	59589.0i	0.565029	−	0.978659i
$83$	−45954.6			−0.732207			−0.366103	−	0.930574i	$-0.619308\pi$
$83$	−45954.6			−0.732207			−0.366103	+	0.930574i	$0.619308\pi$
$84$		0			0
$85$	−22290.7			−0.334639
$86$	10804.0	−	18713.0i	0.157520	−	0.272833i
$87$	−977.821	−	1693.64i	−0.0138504	−	0.0239895i
$88$	−20028.0	−	34689.4i	−0.275696	−	0.477519i
$89$	49520.0	−	85771.1i	0.662682	−	1.14780i	−0.317226	−	0.948350i	$-0.602751\pi$
$89$	49520.0	−	85771.1i	0.662682	−	1.14780i	0.979908	−	0.199450i	$-0.0639154\pi$
$90$	−567.074			−0.00737961
$91$		0			0
$92$	59477.9			0.732632
$93$	71979.2	−	124672.i	0.862977	−	1.49472i
$94$	−3750.48	−	6496.03i	−0.0437792	−	0.0758278i
$95$	−19781.8	−	34263.0i	−0.224883	−	0.389509i
$96$	−8091.40	+	14014.7i	−0.0896077	+	0.155205i
$97$	115548.			1.24691			0.623454	−	0.781860i	$-0.285729\pi$
$97$	115548.			1.24691			0.623454	+	0.781860i	$0.285729\pi$
$98$		0			0
$99$	−4225.20			−0.0433271
$100$	21472.0	−	37190.6i	0.214720	−	0.371906i
$101$	5475.73	+	9484.25i	0.0534120	+	0.0925123i	0.891495	−	0.453030i	$-0.149657\pi$
$101$	5475.73	+	9484.25i	0.0534120	+	0.0925123i	−0.838083	+	0.545542i	$0.816324\pi$
$102$	33549.7	+	58109.8i	0.319292	+	0.553030i
$103$	−68862.2	+	119273.i	−0.639570	+	1.10777i	0.345957	+	0.938250i	$0.387554\pi$
$103$	−68862.2	+	119273.i	−0.639570	+	1.10777i	−0.985527	+	0.169517i	$0.945779\pi$
$104$	−13236.5			−0.120003
$105$		0			0
$106$	−74828.9			−0.646852
$107$	−37786.5	+	65448.1i	−0.319064	+	0.552634i	−0.980293	−	0.197550i	$-0.936702\pi$
$107$	−37786.5	+	65448.1i	−0.319064	+	0.552634i	0.661229	+	0.750184i	$0.270035\pi$
$108$	−29868.5	−	51733.8i	−0.246408	−	0.426791i
$109$	−22263.1	−	38560.9i	−0.179482	−	0.310871i	0.762221	−	0.647316i	$-0.224109\pi$
$109$	−22263.1	−	38560.9i	−0.179482	−	0.310871i	−0.941703	+	0.336445i	$0.890775\pi$
$110$	−26286.7	+	45529.9i	−0.207135	+	0.358769i
$111$	95275.0			0.733959
$112$		0			0
$113$	90456.5			0.666413			0.333207	−	0.942854i	$-0.391869\pi$
$113$	90456.5			0.666413			0.333207	+	0.942854i	$0.391869\pi$
$114$	−59547.0	+	103138.i	−0.429138	+	0.743290i
$115$	−39032.4	−	67606.0i	−0.275220	−	0.476695i
$116$	989.979	+	1714.69i	0.00683095	+	0.0118315i
$117$	−698.112	+	1209.17i	−0.00471477	+	0.00816622i
$118$	−10139.1			−0.0670340
$119$		0			0
$120$	21239.9			0.134648
$121$	−115333.	+	199763.i	−0.716130	+	1.24037i
$122$	4189.41	+	7256.27i	0.0254832	+	0.0441381i
$123$	135925.	+	235429.i	0.810095	+	1.40313i
$124$	−72874.1	+	126222.i	−0.425617	+	0.737190i
$125$	−121989.			−0.698306
$126$		0			0
$127$	187707.			1.03269			0.516346	−	0.856380i	$-0.327292\pi$
$127$	187707.			1.03269			0.516346	+	0.856380i	$0.327292\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$	42685.1	+	73932.8i	0.225841	+	0.391167i
$130$	8686.48	+	15045.4i	0.0450802	+	0.0780812i
$131$	77206.1	−	133725.i	0.393073	−	0.680823i	−0.599780	−	0.800165i	$-0.704745\pi$
$131$	77206.1	−	133725.i	0.393073	−	0.680823i	0.992853	+	0.119342i	$0.0380785\pi$
$132$	158256.			0.790543
$133$		0			0
$134$	−234483.			−1.12810
$135$	−39202.4	+	67900.6i	−0.185131	+	0.320656i
$136$	−33966.8	−	58832.3i	−0.157474	−	0.272752i
$137$	−54618.9	−	94602.7i	−0.248623	−	0.430628i	0.714521	−	0.699614i	$-0.246645\pi$
$137$	−54618.9	−	94602.7i	−0.248623	−	0.430628i	−0.963144	+	0.268986i	$0.913311\pi$
$138$	−117495.	+	203507.i	−0.525196	+	0.909666i
$139$	204695.			0.898609			0.449305	−	0.893379i	$-0.351672\pi$
$139$	204695.			0.898609			0.449305	+	0.893379i	$0.351672\pi$
$140$		0			0
$141$	29635.4			0.125534
$142$	−62559.1	+	108355.i	−0.260357	+	0.450952i
$143$	64721.9	+	112102.i	0.264674	+	0.458429i
$144$	−864.113	−	1496.69i	−0.00347268	−	0.00601485i
$145$	1299.35	−	2250.54i	0.00513222	−	0.00888926i
$146$	−28601.9			−0.111048
$147$		0			0
$148$	−96459.6			−0.361986
$149$	203154.	−	351873.i	0.749651	−	1.29843i	−0.198339	−	0.980134i	$-0.563555\pi$
$149$	203154.	−	351873.i	0.749651	−	1.29843i	0.947990	−	0.318300i	$-0.103112\pi$
$150$	84833.2	+	146935.i	0.307849	+	0.533210i
$151$	208419.	+	360992.i	0.743866	+	1.28841i	0.950723	+	0.310043i	$0.100343\pi$
$151$	208419.	+	360992.i	0.743866	+	1.28841i	−0.206856	+	0.978371i	$0.566323\pi$
$152$	60287.3	−	104421.i	0.211649	−	0.366588i
$153$	−7165.81			−0.0247478
$154$		0			0
$155$	191295.			0.639548
$156$	26148.0	−	45289.6i	0.0860254	−	0.149000i
$157$	59645.3	+	103309.i	0.193120	+	0.334493i	0.946283	−	0.323341i	$-0.104806\pi$
$157$	59645.3	+	103309.i	0.193120	+	0.334493i	−0.753163	+	0.657834i	$0.771473\pi$
$158$	5959.62	+	10322.4i	0.0189922	+	0.0328955i
$159$	147820.	−	256032.i	0.463703	−	0.803158i
$160$	−21504.0			−0.0664078
$161$		0			0
$162$	242576.			0.726205
$163$	−23686.2	+	41025.7i	−0.0698275	+	0.120945i	−0.898825	−	0.438307i	$-0.855578\pi$
$163$	−23686.2	+	41025.7i	−0.0698275	+	0.120945i	0.828998	+	0.559252i	$0.188912\pi$
$164$	−137615.	−	238356.i	−0.399536	−	0.692016i
$165$	−103856.	−	179883.i	−0.296975	−	0.514375i
$166$	−91909.2	+	159191.i	−0.258874	+	0.448383i
$167$	231669.			0.642802			0.321401	−	0.946943i	$-0.395846\pi$
$167$	231669.			0.642802			0.321401	+	0.946943i	$0.395846\pi$
$168$		0			0
$169$	−328518.			−0.884795
$170$	−44581.5	+	77217.3i	−0.118313	+	0.204924i
$171$	−6359.26	−	11014.6i	−0.0166309	−	0.0288056i
$172$	−43215.8	−	74852.0i	−0.111384	−	0.192922i
$173$	67169.6	−	116341.i	0.170631	−	0.295541i	−0.768010	−	0.640438i	$-0.778753\pi$
$173$	67169.6	−	116341.i	0.170631	−	0.295541i	0.938641	+	0.344897i	$0.112086\pi$
$174$	−7822.57			−0.0195874
$175$		0			0
$176$	−160224.			−0.389893
$177$	20029.2	−	34691.6i	0.0480541	−	0.0832321i
$178$	−198080.	−	343085.i	−0.468587	−	0.811617i
$179$	−23292.2	−	40343.2i	−0.0543347	−	0.0941105i	0.837579	−	0.546317i	$-0.183970\pi$
$179$	−23292.2	−	40343.2i	−0.0543347	−	0.0941105i	−0.891913	+	0.452206i	$0.850637\pi$
$180$	−1134.15	+	1964.40i	−0.00260909	+	0.00451907i
$181$	−829210.			−1.88134			−0.940672	−	0.339317i	$-0.889804\pi$
$181$	−829210.			−1.88134			−0.940672	+	0.339317i	$0.889804\pi$
$182$		0			0
$183$	−33103.7			−0.0730716
$184$	118956.	−	206037.i	0.259025	−	0.448644i
$185$	63301.6	+	109642.i	0.135983	+	0.235530i
$186$	−287917.	−	498686.i	−0.610217	−	1.05693i
$187$	−332171.	+	575337.i	−0.694636	+	1.20315i
$188$	−30003.9			−0.0619131
$189$		0			0
$190$	−158254.			−0.318032
$191$	235958.	−	408692.i	0.468006	−	0.810611i	−0.531325	−	0.847168i	$-0.678306\pi$
$191$	235958.	−	408692.i	0.468006	−	0.810611i	0.999332	+	0.0365572i	$0.0116391\pi$
$192$	32365.6	+	56058.8i	0.0633622	+	0.109747i
$193$	−344177.	−	596132.i	−0.665103	−	1.15199i	−0.979257	−	0.202620i	$-0.935054\pi$
$193$	−344177.	−	596132.i	−0.665103	−	1.15199i	0.314155	−	0.949372i	$-0.398279\pi$
$194$	231097.	−	400271.i	0.440849	−	0.763573i
$195$	−68638.5			−0.129265
$196$		0			0
$197$	311915.			0.572625			0.286313	−	0.958136i	$-0.407570\pi$
$197$	311915.			0.572625			0.286313	+	0.958136i	$0.407570\pi$
$198$	−8450.40	+	14636.5i	−0.0153184	+	0.0265323i
$199$	−143606.	−	248733.i	−0.257063	−	0.445246i	0.708391	−	0.705820i	$-0.249421\pi$
$199$	−143606.	−	248733.i	−0.257063	−	0.445246i	−0.965454	+	0.260574i	$0.916088\pi$
$200$	−85888.0	−	148762.i	−0.151830	−	0.262977i
$201$	463207.	−	802298.i	0.808695	−	1.40070i
$202$	43805.9			0.0755360
$203$		0			0
$204$	268397.			0.451547
$205$	−180619.	+	312842.i	−0.300179	+	0.519925i
$206$	275449.	+	477091.i	0.452244	+	0.783310i
$207$	−12547.8	−	21733.4i	−0.0203536	−	0.0352534i
$208$	−26473.1	+	45852.7i	−0.0424274	+	0.0734864i
$209$	−1.17913e6			−1.86723
$210$		0			0
$211$	−460493.			−0.712061			−0.356031	−	0.934474i	$-0.615870\pi$
$211$	−460493.			−0.712061			−0.356031	+	0.934474i	$0.615870\pi$
$212$	−149658.	+	259215.i	−0.228697	+	0.396114i
$213$	−247163.	−	428099.i	−0.373280	−	0.646540i
$214$	151146.	+	261793.i	0.225612	+	0.390771i
$215$	−56720.8	+	98243.3i	−0.0836847	+	0.144946i
$216$	−238948.			−0.348473
$217$		0			0
$218$	−178105.			−0.253825
$219$	56501.3	−	97863.1i	0.0796064	−	0.137882i
$220$	105147.	+	182120.i	0.146467	+	0.253688i
$221$	109766.	+	190121.i	0.151178	+	0.261848i
$222$	190550.	−	330042.i	0.259494	−	0.449456i
$223$	1.19776e6			1.61290			0.806449	−	0.591304i	$-0.201387\pi$
$223$	1.19776e6			1.61290			0.806449	+	0.591304i	$0.201387\pi$
$224$		0			0
$225$	−18119.4			−0.0238609
$226$	180913.	−	313350.i	0.235613	−	0.408093i
$227$	447281.	+	774713.i	0.576123	+	0.997875i	0.995919	+	0.0902559i	$0.0287685\pi$
$227$	447281.	+	774713.i	0.576123	+	0.997875i	−0.419795	+	0.907619i	$0.637898\pi$
$228$	238188.	+	412553.i	0.303447	+	0.525585i
$229$	−129628.	+	224522.i	−0.163347	+	0.282925i	−0.936067	−	0.351822i	$-0.885562\pi$
$229$	−129628.	+	224522.i	−0.163347	+	0.282925i	0.772720	+	0.634747i	$0.218896\pi$
$230$	−312259.			−0.389220
$231$		0			0
$232$	7919.83			0.00966042
$233$	−105657.	+	183004.i	−0.127500	+	0.220836i	−0.922707	−	0.385501i	$-0.874029\pi$
$233$	−105657.	+	183004.i	−0.127500	+	0.220836i	0.795207	+	0.606337i	$0.207362\pi$
$234$	2792.45	+	4836.66i	0.00333385	+	0.00577439i
$235$	19690.0	+	34104.2i	0.0232582	+	0.0402845i
$236$	−20278.2	+	35122.9i	−0.0237001	+	0.0410498i
$237$	−47091.5			−0.0544592
$238$		0			0
$239$	463.018			0.000524328			0.000262164	−	1.00000i	$-0.499917\pi$
$239$	463.018			0.000524328			0.000262164		1.00000i	$0.499917\pi$
$240$	42479.8	−	73577.2i	0.0476052	−	0.0824547i
$241$	143197.	+	248025.i	0.158815	+	0.275076i	0.934442	−	0.356116i	$-0.115899\pi$
$241$	143197.	+	248025.i	0.158815	+	0.275076i	−0.775626	+	0.631192i	$0.782566\pi$
$242$	461334.	+	799053.i	0.506380	+	0.877076i
$243$	−25565.0	+	44279.8i	−0.0277734	+	0.0481050i
$244$	33515.3			0.0360386
$245$		0			0
$246$	1.08740e6			1.14565
$247$	−194823.	+	337444.i	−0.203188	+	0.351932i
$248$	291496.	+	504887.i	0.300957	+	0.521272i
$249$	−363122.	−	628946.i	−0.371154	−	0.642858i
$250$	−243978.	+	422582.i	−0.246888	+	0.427623i
$251$	1.37168e6			1.37426			0.687129	−	0.726535i	$-0.258870\pi$
$251$	1.37168e6			1.37426			0.687129	+	0.726535i	$0.258870\pi$
$252$		0			0
$253$	−2.32660e6			−2.28518
$254$	375414.	−	650236.i	0.365112	−	0.632392i
$255$	−176136.	−	305076.i	−0.169628	−	0.293804i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−379612.	+	657507.i	−0.358515	+	0.620965i	−0.987713	−	0.156279i	$-0.950050\pi$
$257$	−379612.	+	657507.i	−0.358515	+	0.620965i	0.629198	+	0.777245i	$0.283383\pi$
$258$	341481.			0.319387
$259$		0			0
$260$	69491.9			0.0637530
$261$	417.702	−	723.481i	0.000379547	−	0.000657394i
$262$	−308825.	−	534900.i	−0.277945	−	0.481415i
$263$	536222.	+	928764.i	0.478030	+	0.827973i	0.999683	−	0.0251852i	$-0.00801754\pi$
$263$	536222.	+	928764.i	0.478030	+	0.827973i	−0.521652	+	0.853158i	$0.674684\pi$
$264$	316512.	−	548215.i	0.279499	−	0.484107i
$265$	392852.			0.343648
$266$		0			0
$267$	1.56518e6			1.34365
$268$	−468966.	+	812273.i	−0.398845	+	0.690820i
$269$	−883056.	−	1.52950e6i	−0.744059	−	1.28875i	−0.950633	−	0.310317i	$-0.899565\pi$
$269$	−883056.	−	1.52950e6i	−0.744059	−	1.28875i	0.206574	−	0.978431i	$-0.433769\pi$
$270$	156810.	+	271602.i	0.130907	+	0.226738i
$271$	−1.02586e6	+	1.77684e6i	−0.848522	+	1.46968i	0.0340046	+	0.999422i	$0.489174\pi$
$271$	−1.02586e6	+	1.77684e6i	−0.848522	+	1.46968i	−0.882527	+	0.470262i	$0.844159\pi$
$272$	−271735.			−0.222701
$273$		0			0
$274$	−436951.			−0.351606
$275$	−839922.	+	1.45479e6i	−0.669742	+	1.16003i
$276$	469980.	+	814029.i	0.371370	+	0.643231i
$277$	−435341.	−	754033.i	−0.340903	−	0.590461i	0.643698	−	0.765280i	$-0.277399\pi$
$277$	−435341.	−	754033.i	−0.340903	−	0.590461i	−0.984601	+	0.174819i	$0.944066\pi$
$278$	409391.	−	709085.i	0.317706	−	0.550284i
$279$	61495.6			0.0472970
$280$		0			0
$281$	2.35412e6			1.77854			0.889270	−	0.457383i	$-0.151213\pi$
$281$	2.35412e6			1.77854			0.889270	+	0.457383i	$0.151213\pi$
$282$	59270.8	−	102660.i	0.0443831	−	0.0768739i
$283$	−1.09518e6	−	1.89690e6i	−0.812863	−	1.40792i	−0.910852	−	0.412733i	$-0.864574\pi$
$283$	−1.09518e6	−	1.89690e6i	−0.812863	−	1.40792i	0.0979887	−	0.995188i	$-0.468759\pi$
$284$	250236.	+	433422.i	0.184100	+	0.318871i
$285$	312622.	−	541476.i	0.227985	−	0.394882i
$286$	517775.			0.374306
$287$		0			0
$288$	−6912.90			−0.00491110
$289$	146576.	−	253878.i	0.103233	−	0.178805i
$290$	−5197.39	−	9002.14i	−0.00362903	−	0.00628566i
$291$	913035.	+	1.58142e6i	0.632055	+	1.09475i
$292$	−57203.8	+	99079.9i	−0.0392616	+	0.0680030i
$293$	807700.			0.549644			0.274822	−	0.961495i	$-0.411381\pi$
$293$	807700.			0.549644			0.274822	+	0.961495i	$0.411381\pi$
$294$		0			0
$295$	53230.4			0.0356127
$296$	−192919.	+	334146.i	−0.127981	+	0.221670i
$297$	1.16837e6	+	2.02368e6i	0.768580	+	1.33122i
$298$	−812615.	−	1.40749e6i	−0.530083	−	0.918131i
$299$	−384415.	+	665826.i	−0.248669	+	0.430708i
$300$	678666.			0.435364
$301$		0			0
$302$	1.66735e6			1.05199
$303$	−86535.8	+	149884.i	−0.0541488	+	0.0937885i
$304$	−241149.	−	417683.i	−0.149659	−	0.259217i
$305$	−21994.4	−	38095.4i	−0.0135383	−	0.0234489i
$306$	−14331.6	+	24823.1i	−0.00874967	+	0.0151549i
$307$	−211516.			−0.128085			−0.0640424	−	0.997947i	$-0.520399\pi$
$307$	−211516.			−0.128085			−0.0640424	+	0.997947i	$0.520399\pi$
$308$		0			0
$309$	−2.17653e6			−1.29679
$310$	382589.	−	662664.i	0.226114	−	0.391642i
$311$	−145855.	−	252627.i	−0.0855104	−	0.148108i	0.820098	−	0.572223i	$-0.193919\pi$
$311$	−145855.	−	252627.i	−0.0855104	−	0.148108i	−0.905609	+	0.424114i	$0.860585\pi$
$312$	−104592.	−	181159.i	−0.0608292	−	0.105359i
$313$	−997988.	+	1.72857e6i	−0.575791	+	0.997299i	0.420165	+	0.907448i	$0.361972\pi$
$313$	−997988.	+	1.72857e6i	−0.575791	+	0.997299i	−0.995955	+	0.0898507i	$0.971361\pi$
$314$	477162.			0.273113
$315$		0			0
$316$	47677.0			0.0268591
$317$	1.40479e6	−	2.43316e6i	0.785167	−	1.35995i	−0.143733	−	0.989617i	$-0.545911\pi$
$317$	1.40479e6	−	2.43316e6i	0.785167	−	1.35995i	0.928899	−	0.370332i	$-0.120756\pi$
$318$	−591280.	−	1.02413e6i	−0.327888	−	0.567918i
$319$	−38725.1	−	67073.9i	−0.0213067	−	0.0369043i
$320$	−43008.0	+	74492.0i	−0.0234787	+	0.0406663i
$321$	−1.19432e6			−0.646930
$322$		0			0
$323$	−1.99977e6			−1.06653
$324$	485151.	−	840306.i	0.256752	−	0.444708i
$325$	277554.	+	480737.i	0.145760	+	0.252464i
$326$	94744.8	+	164103.i	0.0493755	+	0.0855209i
$327$	351836.	−	609397.i	0.181958	−	0.315160i
$328$	−1.10092e6			−0.565029
$329$		0			0
$330$	−830844.			−0.419986
$331$	−690248.	+	1.19554e6i	−0.346286	+	0.599785i	−0.985587	−	0.169172i	$-0.945891\pi$
$331$	−690248.	+	1.19554e6i	−0.346286	+	0.599785i	0.639301	+	0.768957i	$0.279224\pi$
$332$	367637.	+	636766.i	0.183052	+	0.317055i
$333$	20349.6	+	35246.6i	0.0100565	+	0.0174183i
$334$	463338.	−	802526.i	0.227265	−	0.393634i
$335$	1.23104e6			0.599320
$336$		0			0
$337$	566429.			0.271688			0.135844	−	0.990730i	$-0.456625\pi$
$337$	566429.			0.271688			0.135844	+	0.990730i	$0.456625\pi$
$338$	−657036.	+	1.13802e6i	−0.312822	+	0.541824i
$339$	714765.	+	1.23801e6i	0.337803	+	0.585092i
$340$	178326.	+	308869.i	0.0836598	+	0.144903i
$341$	2.85062e6	−	4.93743e6i	1.32756	−	2.29940i
$342$	−50874.1			−0.0235197
$343$		0			0
$344$	−345727.			−0.157520
$345$	616848.	−	1.06841e6i	0.279017	−	0.483272i
$346$	−268678.	−	465365.i	−0.120654	−	0.208979i
$347$	−270104.	−	467833.i	−0.120422	−	0.208577i	0.799512	−	0.600650i	$-0.205092\pi$
$347$	−270104.	−	467833.i	−0.120422	−	0.208577i	−0.919934	+	0.392073i	$0.871758\pi$
$348$	−15645.1	+	27098.2i	−0.00692518	+	0.0119948i
$349$	−1.73807e6			−0.763841			−0.381921	−	0.924195i	$-0.624737\pi$
$349$	−1.73807e6			−0.763841			−0.381921	+	0.924195i	$0.624737\pi$
$350$		0			0
$351$	772180.			0.334542
$352$	−320447.	+	555031.i	−0.137848	+	0.238759i
$353$	537109.	+	930300.i	0.229417	+	0.397362i	0.957635	−	0.287983i	$-0.0929847\pi$
$353$	537109.	+	930300.i	0.229417	+	0.397362i	−0.728219	+	0.685345i	$0.759651\pi$
$354$	−80116.8	−	138766.i	−0.0339794	−	0.0588540i
$355$	328435.	−	568866.i	0.138318	−	0.239574i
$356$	−1.58464e6			−0.662682
$357$		0			0
$358$	−186337.			−0.0768409
$359$	−60601.9	+	104966.i	−0.0248170	+	0.0429844i	−0.878167	−	0.478354i	$-0.841234\pi$
$359$	−60601.9	+	104966.i	−0.0248170	+	0.0429844i	0.853350	+	0.521338i	$0.174567\pi$
$360$	4536.59	+	7857.61i	0.00184490	+	0.00319547i
$361$	−536639.	−	929486.i	−0.216728	−	0.375383i
$362$	−1.65842e6	+	2.87247e6i	−0.665156	+	1.15208i
$363$	−3.64535e6			−1.45202
$364$		0			0
$365$	150160.			0.0589959
$366$	−66207.4	+	114675.i	−0.0258347	+	0.0447470i
$367$	−276914.	−	479630.i	−0.107320	−	0.185884i	0.807364	−	0.590054i	$-0.200894\pi$
$367$	−276914.	−	479630.i	−0.107320	−	0.185884i	−0.914684	+	0.404171i	$0.867560\pi$
$368$	−475823.	−	824150.i	−0.183158	−	0.317239i
$369$	−58063.8	+	100570.i	−0.0221993	+	0.0384504i
$370$	506413.			0.192309
$371$		0			0
$372$	−2.30333e6			−0.862977
$373$	250739.	−	434293.i	0.0933146	−	0.161626i	−0.815589	−	0.578631i	$-0.803587\pi$
$373$	250739.	−	434293.i	0.0933146	−	0.161626i	0.908904	+	0.417006i	$0.136920\pi$
$374$	1.32868e6	+	2.30135e6i	0.491182	+	0.850752i
$375$	−963927.	−	1.66957e6i	−0.353970	−	0.613093i
$376$	−60007.7	+	103936.i	−0.0218896	+	0.0379139i
$377$	−25593.6			−0.00927422
$378$		0			0
$379$	999004.			0.357248			0.178624	−	0.983917i	$-0.442835\pi$
$379$	999004.			0.357248			0.178624	+	0.983917i	$0.442835\pi$
$380$	−316508.	+	548209.i	−0.112441	+	0.194754i
$381$	1.48321e6	+	2.56900e6i	0.523469	+	0.906676i
$382$	−943833.	−	1.63477e6i	−0.330930	−	0.573188i
$383$	326232.	−	565050.i	0.113640	−	0.196829i	−0.803596	−	0.595176i	$-0.797082\pi$
$383$	326232.	−	565050.i	0.113640	−	0.196829i	0.917235	+	0.398346i	$0.130416\pi$
$384$	258925.			0.0896077
$385$		0			0
$386$	−2.75342e6			−0.940597
$387$	−18234.1	+	31582.3i	−0.00618879	+	0.0107193i
$388$	−924387.	−	1.60109e6i	−0.311727	−	0.539927i
$389$	39626.5	+	68635.1i	0.0132774	+	0.0229971i	0.872588	−	0.488457i	$-0.162440\pi$
$389$	39626.5	+	68635.1i	0.0132774	+	0.0229971i	−0.859310	+	0.511454i	$0.829107\pi$
$390$	−137277.	+	237771.i	−0.0457021	+	0.0791583i
$391$	−3.94585e6			−1.30526
$392$		0			0
$393$	2.44026e6			0.796992
$394$	623830.	−	1.08050e6i	0.202454	−	0.350660i
$395$	−31288.0	−	54192.4i	−0.0100899	−	0.0174762i
$396$	33801.6	+	58546.1i	0.0108318	+	0.0187612i
$397$	2.00443e6	−	3.47177e6i	0.638284	−	1.10554i	−0.347525	−	0.937671i	$-0.612978\pi$
$397$	2.00443e6	−	3.47177e6i	0.638284	−	1.10554i	0.985809	−	0.167870i	$-0.0536889\pi$
$398$	−1.14885e6			−0.363542
$399$		0			0
$400$	−687104.			−0.214720
$401$	−337209.	+	584063.i	−0.104722	+	0.181384i	−0.913625	−	0.406559i	$-0.866729\pi$
$401$	−337209.	+	584063.i	−0.104722	+	0.181384i	0.808903	+	0.587943i	$0.200062\pi$
$402$	−1.85283e6	−	3.20919e6i	−0.571834	−	0.990445i
$403$	−941994.	−	1.63158e6i	−0.288925	−	0.500433i
$404$	87611.7	−	151748.i	0.0267060	−	0.0462561i
$405$	−1.27352e6			−0.385806
$406$		0			0
$407$	3.77322e6			1.12908
$408$	536795.	−	929756.i	0.159646	−	0.276515i
$409$	−1.42706e6	−	2.47175e6i	−0.421828	−	0.730627i	0.574291	−	0.818652i	$-0.305278\pi$
$409$	−1.42706e6	−	2.47175e6i	−0.421828	−	0.730627i	−0.996118	+	0.0880244i	$0.971945\pi$
$410$	722478.	+	1.25137e6i	0.212258	+	0.367642i
$411$	863171.	−	1.49506e6i	0.252053	−	0.436569i
$412$	2.20359e6			0.639570
$413$		0			0
$414$	−100382.			−0.0287843
$415$	482523.	−	835755.i	0.137530	−	0.238209i
$416$	105892.	+	183411.i	0.0300007	+	0.0519627i
$417$	1.61745e6	+	2.80151e6i	0.455503	+	0.788954i
$418$	−2.35827e6	+	4.08464e6i	−0.660164	+	1.14344i
$419$	4.66553e6			1.29827			0.649136	−	0.760672i	$-0.275130\pi$
$419$	4.66553e6			1.29827			0.649136	+	0.760672i	$0.275130\pi$
$420$		0			0
$421$	−3.73317e6			−1.02653			−0.513266	−	0.858229i	$-0.671565\pi$
$421$	−3.73317e6			−1.02653			−0.513266	+	0.858229i	$0.671565\pi$
$422$	−920987.	+	1.59520e6i	−0.251752	+	0.436047i
$423$	6329.77	+	10963.5i	0.00172003	+	0.00297919i
$424$	598631.	+	1.03686e6i	0.161713	+	0.280095i
$425$	−1.42448e6	+	2.46728e6i	−0.382547	+	0.662591i
$426$	−1.97731e6			−0.527898
$427$		0			0
$428$	1.20917e6			0.319064
$429$	−1.02283e6	+	1.77160e6i	−0.268325	+	0.464753i
$430$	226883.	+	392973.i	0.0591740	+	0.102492i
$431$	−482335.	−	835429.i	−0.125071	−	0.216629i	0.796690	−	0.604388i	$-0.206582\pi$
$431$	−482335.	−	835429.i	−0.125071	−	0.216629i	−0.921761	+	0.387760i	$0.873249\pi$
$432$	−477896.	+	827741.i	−0.123204	+	0.213395i
$433$	6.18096e6			1.58429			0.792147	−	0.610330i	$-0.208963\pi$
$433$	6.18096e6			1.58429			0.792147	+	0.610330i	$0.208963\pi$
$434$		0			0
$435$	41068.5			0.0104060
$436$	−356210.	+	616974.i	−0.0897409	+	0.155436i
$437$	−3.50172e6	−	6.06516e6i	−0.877158	−	1.51928i
$438$	−226005.	−	391452.i	−0.0562902	−	0.0974975i
$439$	−107567.	+	186312.i	−0.0266391	+	0.0461402i	−0.879038	−	0.476752i	$-0.841814\pi$
$439$	−107567.	+	186312.i	−0.0266391	+	0.0461402i	0.852399	+	0.522893i	$0.175147\pi$
$440$	841174.			0.207135
$441$		0			0
$442$	878132.			0.213798
$443$	3.59934e6	−	6.23423e6i	0.871391	−	1.50929i	0.0108335	−	0.999941i	$-0.496552\pi$
$443$	3.59934e6	−	6.23423e6i	0.871391	−	1.50929i	0.860558	−	0.509353i	$-0.170115\pi$
$444$	−762200.	−	1.32017e6i	−0.183490	−	0.317813i
$445$	1.03992e6	+	1.80119e6i	0.248943	+	0.431182i
$446$	2.39551e6	−	4.14915e6i	0.570245	−	0.987694i
$447$	6.42109e6			1.51999
$448$		0			0
$449$	3.92153e6			0.917994			0.458997	−	0.888438i	$-0.348209\pi$
$449$	3.92153e6			0.917994			0.458997	+	0.888438i	$0.348209\pi$
$450$	−36238.7	+	62767.3i	−0.00843610	+	0.0146118i
$451$	5.38309e6	+	9.32379e6i	1.24621	+	2.15850i
$452$	−723652.	−	1.25340e6i	−0.166603	−	0.288565i
$453$	−3.29375e6	+	5.70494e6i	−0.754128	+	1.30619i
$454$	3.57824e6			0.814761
$455$		0			0
$456$	1.90550e6			0.429138
$457$	−660839.	+	1.14461e6i	−0.148015	+	0.256369i	−0.930494	−	0.366308i	$-0.880622\pi$
$457$	−660839.	+	1.14461e6i	−0.148015	+	0.256369i	0.782479	+	0.622677i	$0.213955\pi$
$458$	518512.	+	898090.i	0.115504	+	0.200058i
$459$	1.98152e6	+	3.43209e6i	0.439002	+	0.760375i
$460$	−624518.	+	1.08170e6i	−0.137610	+	0.238348i
$461$	75459.1			0.0165371			0.00826855	−	0.999966i	$-0.497368\pi$
$461$	75459.1			0.0165371			0.00826855	+	0.999966i	$0.497368\pi$
$462$		0			0
$463$	−3.28757e6			−0.712727			−0.356363	−	0.934347i	$-0.615984\pi$
$463$	−3.28757e6			−0.712727			−0.356363	+	0.934347i	$0.615984\pi$
$464$	15839.7	−	27435.1i	0.00341547	−	0.00591577i
$465$	1.51156e6	+	2.61810e6i	0.324186	+	0.561506i
$466$	422630.	+	732016.i	0.0901561	+	0.156155i
$467$	−321691.	+	557185.i	−0.0682569	+	0.118224i	−0.898134	−	0.439722i	$-0.855077\pi$
$467$	−321691.	+	557185.i	−0.0682569	+	0.118224i	0.829877	+	0.557946i	$0.188410\pi$
$468$	22339.6			0.00471477
$469$		0			0
$470$	157520.			0.0328921
$471$	−942605.	+	1.63264e6i	−0.195784	+	0.339108i
$472$	81112.9	+	140492.i	0.0167585	+	0.0290266i
$473$	1.69048e6	+	2.92799e6i	0.347422	+	0.601752i
$474$	−94182.9	+	163130.i	−0.0192542	+	0.0333493i
$475$	−5.05660e6			−1.02831
$476$		0			0
$477$	126290.			0.0254141
$478$	926.036	−	1603.94i	0.000185378	−	0.000321084i
$479$	−3.71324e6	−	6.43152e6i	−0.739459	−	1.28078i	−0.952739	−	0.303790i	$-0.901748\pi$
$479$	−3.71324e6	−	6.43152e6i	−0.739459	−	1.28078i	0.213280	−	0.976991i	$-0.431585\pi$
$480$	−169919.	−	294309.i	−0.0336620	−	0.0583043i
$481$	623434.	−	1.07982e6i	0.122865	−	0.212808i
$482$	1.14558e6			0.224599
$483$		0			0
$484$	3.69067e6			0.716130
$485$	−1.21326e6	+	2.10143e6i	−0.234207	+	0.405658i
$486$	102260.	+	177119.i	0.0196388	+	0.0340154i
$487$	2.08542e6	+	3.61206e6i	0.398448	+	0.690132i	0.993535	−	0.113529i	$-0.0362156\pi$
$487$	2.08542e6	+	3.61206e6i	0.398448	+	0.690132i	−0.595087	+	0.803662i	$0.702882\pi$
$488$	67030.6	−	116100.i	0.0127416	−	0.0220691i
$489$	−748651.			−0.141582
$490$		0			0
$491$	−3.73674e6			−0.699502			−0.349751	−	0.936843i	$-0.613734\pi$
$491$	−3.73674e6			−0.699502			−0.349751	+	0.936843i	$0.613734\pi$
$492$	2.17480e6	−	3.76686e6i	0.405048	−	0.701563i
$493$	−65676.6	−	113755.i	−0.0121701	−	0.0210792i
$494$	779293.	+	1.34978e6i	0.143676	+	0.248854i
$495$	44364.6	−	76841.7i	0.00813811	−	0.0140956i
$496$	2.33197e6			0.425617
$497$		0			0
$498$	−2.90498e6			−0.524891
$499$	−4.35431e6	+	7.54188e6i	−0.782831	+	1.35590i	0.147456	+	0.989069i	$0.452892\pi$
$499$	−4.35431e6	+	7.54188e6i	−0.782831	+	1.35590i	−0.930286	+	0.366834i	$0.880442\pi$
$500$	975912.	+	1.69033e6i	0.174576	+	0.302375i
$501$	1.83059e6	+	3.17068e6i	0.325835	+	0.564363i
$502$	2.74336e6	−	4.75164e6i	0.485874	−	0.841558i
$503$	−3.28384e6			−0.578711			−0.289355	−	0.957222i	$-0.593441\pi$
$503$	−3.28384e6			−0.578711			−0.289355	+	0.957222i	$0.593441\pi$
$504$		0			0
$505$	−229981.			−0.0401294
$506$	−4.65321e6	+	8.05959e6i	−0.807934	+	1.39938i
$507$	−2.59587e6	−	4.49618e6i	−0.448500	−	0.776826i
$508$	−1.50166e6	−	2.60094e6i	−0.258173	−	0.447169i
$509$	−4.71851e6	+	8.17271e6i	−0.807255	+	1.39821i	0.107503	+	0.994205i	$0.465714\pi$
$509$	−4.71851e6	+	8.17271e6i	−0.807255	+	1.39821i	−0.914758	+	0.404002i	$0.867619\pi$
$510$	−1.40909e6			−0.239890
$511$		0			0
$512$	−262144.			−0.0441942
$513$	−3.51698e6	+	6.09159e6i	−0.590033	+	1.02197i
$514$	1.51845e6	+	2.63003e6i	0.253508	+	0.439089i
$515$	−1.44611e6	−	2.50473e6i	−0.240260	−	0.416143i
$516$	682962.	−	1.18292e6i	0.112920	−	0.195584i
$517$	1.17366e6			0.193116
$518$		0			0
$519$	2.12303e6			0.345970
$520$	138984.	−	240727.i	0.0225401	−	0.0390406i
$521$	2.95363e6	+	5.11584e6i	0.476719	+	0.825701i	0.999644	−	0.0266776i	$-0.00849276\pi$
$521$	2.95363e6	+	5.11584e6i	0.476719	+	0.825701i	−0.522926	+	0.852378i	$0.675159\pi$
$522$	−1670.81	−	2893.92i	−0.000268380	−	0.000464848i
$523$	327168.	−	566672.i	0.0523019	−	0.0905895i	−0.838689	−	0.544610i	$-0.816678\pi$
$523$	327168.	−	566672.i	0.0523019	−	0.0905895i	0.890991	+	0.454021i	$0.150011\pi$
$524$	−2.47060e6			−0.393073
$525$		0			0
$526$	4.28978e6			0.676037
$527$	4.83457e6	−	8.37373e6i	0.758284	−	1.31339i
$528$	−1.26605e6	−	2.19286e6i	−0.197636	−	0.342315i
$529$	−3.69124e6	−	6.39342e6i	−0.573500	−	0.993331i
$530$	785704.	−	1.36088e6i	0.121498	−	0.210441i
$531$	17112.0			0.00263369
$532$		0			0
$533$	3.55771e6			0.542440
$534$	3.13036e6	−	5.42194e6i	0.475052	−	0.822814i
$535$	−793516.	−	1.37441e6i	−0.119859	−	0.207602i
$536$	1.87586e6	+	3.24909e6i	0.282026	+	0.488484i
$537$	368098.	−	637565.i	0.0550843	−	0.0954088i
$538$	−7.06445e6			−1.05226
$539$		0			0
$540$	1.25448e6			0.185131
$541$	431558.	−	747480.i	0.0633936	−	0.109801i	−0.832587	−	0.553895i	$-0.813141\pi$
$541$	431558.	−	747480.i	0.0633936	−	0.109801i	0.895980	+	0.444094i	$0.146474\pi$
$542$	4.10342e6	+	7.10734e6i	0.599996	+	1.03922i
$543$	−6.55222e6	−	1.13488e7i	−0.953649	−	1.65177i
$544$	−543469.	+	941316.i	−0.0787368	+	0.136376i
$545$	935052.			0.134848
$546$		0			0
$547$	−5.45692e6			−0.779794			−0.389897	−	0.920859i	$-0.627489\pi$
$547$	−5.45692e6			−0.779794			−0.389897	+	0.920859i	$0.627489\pi$
$548$	−873903.	+	1.51364e6i	−0.124312	+	0.215314i
$549$	−7070.55	−	12246.6i	−0.00100120	−	0.00173414i
$550$	3.35969e6	+	5.81915e6i	0.473579	+	0.820263i
$551$	116569.	−	201903.i	0.0163570	−	0.0283311i
$552$	3.75984e6			0.525196
$553$		0			0
$554$	−3.48273e6			−0.482109
$555$	−1.00039e6	+	1.73272e6i	−0.137859	+	0.238779i
$556$	−1.63756e6	−	2.83634e6i	−0.224652	−	0.389109i
$557$	−5.58881e6	−	9.68010e6i	−0.763275	−	1.32203i	−0.941154	−	0.337979i	$-0.890257\pi$
$557$	−5.58881e6	−	9.68010e6i	−0.763275	−	1.32203i	0.177879	−	0.984052i	$-0.443077\pi$
$558$	122991.	−	213027.i	0.0167220	−	0.0289634i
$559$	1.11724e6			0.151223
$560$		0			0
$561$	−1.04989e7			−1.40844
$562$	4.70825e6	−	8.15493e6i	0.628809	−	1.08913i
$563$	440132.	+	762332.i	0.0585211	+	0.101361i	0.893802	−	0.448462i	$-0.148028\pi$
$563$	440132.	+	762332.i	0.0585211	+	0.101361i	−0.835281	+	0.549824i	$0.814695\pi$
$564$	−237083.	−	410640.i	−0.0313836	−	0.0543580i
$565$	−949793.	+	1.64509e6i	−0.125172	+	0.216805i
$566$	−8.76140e6			−1.14956
$567$		0			0
$568$	2.00189e6			0.260357
$569$	774858.	−	1.34209e6i	0.100332	−	0.173781i	−0.811489	−	0.584367i	$-0.801343\pi$
$569$	774858.	−	1.34209e6i	0.100332	−	0.173781i	0.911822	+	0.410587i	$0.134676\pi$
$570$	−1.25049e6	−	2.16591e6i	−0.161210	−	0.279224i
$571$	5.48507e6	+	9.50043e6i	0.704032	+	1.21942i	0.967040	+	0.254625i	$0.0819521\pi$
$571$	5.48507e6	+	9.50043e6i	0.704032	+	1.21942i	−0.263008	+	0.964794i	$0.584715\pi$
$572$	1.03555e6	−	1.79363e6i	0.132337	−	0.229214i
$573$	7.45794e6			0.948926
$574$		0			0
$575$	−9.97742e6			−1.25849
$576$	−13825.8	+	23947.0i	−0.00173634	+	0.00300743i
$577$	−6.29341e6	−	1.09005e7i	−0.786948	−	1.36303i	−0.927828	−	0.373008i	$-0.878326\pi$
$577$	−6.29341e6	−	1.09005e7i	−0.786948	−	1.36303i	0.140880	−	0.990027i	$-0.455007\pi$
$578$	−586306.	−	1.01551e6i	−0.0729969	−	0.126434i
$579$	5.43921e6	−	9.42098e6i	0.674278	−	1.16788i
$580$	−41579.1			−0.00513222
$581$		0			0
$582$	7.30428e6			0.893861
$583$	5.85418e6	−	1.01397e7i	0.713337	−	1.23554i
$584$	228815.	+	396319.i	0.0277621	+	0.0480854i
$585$	−14660.4	−	25392.5i	−0.00177115	−	0.00306772i
$586$	1.61540e6	−	2.79796e6i	0.194328	−	0.336587i
$587$	−1.19962e7			−1.43697			−0.718484	−	0.695544i	$-0.755164\pi$
$587$	−1.19962e7			−1.43697			−0.718484	+	0.695544i	$0.755164\pi$
$588$		0			0
$589$	1.71617e7			2.03831
$590$	106461.	−	184395.i	0.0125910	−	0.0218082i
$591$	2.46467e6	+	4.26894e6i	0.290262	+	0.502749i
$592$	771677.	+	1.33658e6i	0.0904964	+	0.156744i
$593$	2.66154e6	−	4.60993e6i	0.310811	−	0.538341i	−0.667727	−	0.744406i	$-0.732733\pi$
$593$	2.66154e6	−	4.60993e6i	0.310811	−	0.538341i	0.978538	+	0.206065i	$0.0660659\pi$
$594$	9.34696e6			1.08694
$595$		0			0
$596$	−6.50092e6			−0.749651
$597$	2.26948e6	−	3.93085e6i	0.260609	−	0.451388i
$598$	1.53766e6	+	2.66331e6i	0.175836	+	0.304557i
$599$	−3.77757e6	−	6.54293e6i	−0.430175	−	0.745085i	0.566713	−	0.823915i	$-0.308215\pi$
$599$	−3.77757e6	−	6.54293e6i	−0.430175	−	0.745085i	−0.996888	+	0.0788305i	$0.974881\pi$
$600$	1.35733e6	−	2.35097e6i	0.153925	−	0.266605i
$601$	−4.44758e6			−0.502270			−0.251135	−	0.967952i	$-0.580804\pi$
$601$	−4.44758e6			−0.502270			−0.251135	+	0.967952i	$0.580804\pi$
$602$		0			0
$603$	395742.			0.0443219
$604$	3.33470e6	−	5.77588e6i	0.371933	−	0.644207i
$605$	−2.42200e6	−	4.19503e6i	−0.269021	−	0.465958i
$606$	346143.	+	599537.i	0.0382890	+	0.0663185i
$607$	2.78660e6	−	4.82653e6i	0.306975	−	0.531696i	−0.670724	−	0.741707i	$-0.734017\pi$
$607$	2.78660e6	−	4.82653e6i	0.306975	−	0.531696i	0.977699	+	0.210011i	$0.0673499\pi$
$608$	−1.92919e6			−0.211649
$609$		0			0
$610$	−175955.			−0.0191460
$611$	193920.	−	335879.i	0.0210145	−	0.0363982i
$612$	57326.5	+	99292.4i	0.00618695	+	0.0107161i
$613$	5.56323e6	+	9.63580e6i	0.597965	+	1.03571i	0.993121	+	0.117092i	$0.0373573\pi$
$613$	5.56323e6	+	9.63580e6i	0.597965	+	1.03571i	−0.395156	+	0.918614i	$0.629309\pi$
$614$	−423032.	+	732713.i	−0.0452848	+	0.0784356i
$615$	−5.70884e6			−0.608640
$616$		0			0
$617$	−1.07454e7			−1.13634			−0.568170	−	0.822911i	$-0.692349\pi$
$617$	−1.07454e7			−1.13634			−0.568170	+	0.822911i	$0.692349\pi$
$618$	−4.35306e6	+	7.53972e6i	−0.458483	+	0.794116i
$619$	6.78781e6	+	1.17568e7i	0.712038	+	1.23329i	0.964091	+	0.265572i	$0.0855610\pi$
$619$	6.78781e6	+	1.17568e7i	0.712038	+	1.23329i	−0.252053	+	0.967713i	$0.581106\pi$
$620$	−1.53036e6	−	2.65065e6i	−0.159887	−	0.276933i
$621$	−6.93952e6	+	1.20196e7i	−0.722105	+	1.25072i
$622$	−1.16684e6			−0.120930
$623$		0			0
$624$	−836736.			−0.0860254
$625$	−2.91287e6	+	5.04523e6i	−0.298277	+	0.516632i
$626$	3.99195e6	+	6.91427e6i	0.407145	+	0.705197i
$627$	−9.31722e6	−	1.61379e7i	−0.946493	−	1.63937i
$628$	954324.	−	1.65294e6i	0.0965599	−	0.167247i
$629$	6.39927e6			0.644917
$630$		0			0
$631$	1.27986e7			1.27964			0.639820	−	0.768525i	$-0.279009\pi$
$631$	1.27986e7			1.27964			0.639820	+	0.768525i	$0.279009\pi$
$632$	95353.9	−	165158.i	0.00949611	−	0.0164478i
$633$	−3.63871e6	−	6.30242e6i	−0.360942	−	0.625170i
$634$	−5.61914e6	−	9.73264e6i	−0.555197	−	0.961629i
$635$	−1.97092e6	+	3.41374e6i	−0.193970	+	0.335966i
$636$	−4.73024e6			−0.463703
$637$		0			0
$638$	−309801.			−0.0301322
$639$	105582.	−	182874.i	0.0102291	−	0.0177174i
$640$	172032.	+	297968.i	0.0166020	+	0.0287554i
$641$	442417.	+	766288.i	0.0425291	+	0.0736626i	0.886506	−	0.462716i	$-0.153125\pi$
$641$	442417.	+	766288.i	0.0425291	+	0.0736626i	−0.843977	+	0.536379i	$0.819792\pi$
$642$	−2.38864e6	+	4.13724e6i	−0.228724	+	0.396162i
$643$	−6.66271e6			−0.635511			−0.317756	−	0.948173i	$-0.602929\pi$
$643$	−6.66271e6			−0.635511			−0.317756	+	0.948173i	$0.602929\pi$
$644$		0			0
$645$	−1.79277e6			−0.169678
$646$	−3.99955e6	+	6.92742e6i	−0.377077	+	0.653116i
$647$	−8.45887e6	−	1.46512e7i	−0.794423	−	1.37598i	−0.923205	−	0.384308i	$-0.874440\pi$
$647$	−8.45887e6	−	1.46512e7i	−0.794423	−	1.37598i	0.128782	−	0.991673i	$-0.458893\pi$
$648$	−1.94060e6	−	3.36123e6i	−0.181551	−	0.314456i
$649$	793226.	−	1.37391e6i	0.0739239	−	0.128040i
$650$	2.22043e6			0.206136
$651$		0			0
$652$	757959.			0.0698275
$653$	−4.74654e6	+	8.22124e6i	−0.435606	+	0.754492i	−0.997345	−	0.0728230i	$-0.976799\pi$
$653$	−4.74654e6	+	8.22124e6i	−0.435606	+	0.754492i	0.561739	+	0.827315i	$0.310133\pi$
$654$	−1.40734e6	−	2.43759e6i	−0.128664	−	0.222852i
$655$	1.62133e6	+	2.80822e6i	0.147662	+	0.255758i
$656$	−2.20184e6	+	3.81369e6i	−0.199768	+	0.346008i
$657$	48272.0			0.00436297
$658$		0			0
$659$	−4.97563e6			−0.446308			−0.223154	−	0.974783i	$-0.571635\pi$
$659$	−4.97563e6			−0.446308			−0.223154	+	0.974783i	$0.571635\pi$
$660$	−1.66169e6	+	2.87813e6i	−0.148487	+	0.257188i
$661$	1.05765e7	+	1.83191e7i	0.941543	+	1.63080i	0.762530	+	0.646953i	$0.223957\pi$
$661$	1.05765e7	+	1.83191e7i	0.941543	+	1.63080i	0.179013	+	0.983847i	$0.442710\pi$
$662$	2.76099e6	+	4.78218e6i	0.244861	+	0.424112i
$663$	−1.73470e6	+	3.00458e6i	−0.153264	+	0.265461i
$664$	2.94110e6			0.258874
$665$		0			0
$666$	162797.			0.0142220
$667$	230007.	−	398384.i	0.0200183	−	0.0346727i
$668$	−1.85335e6	−	3.21010e6i	−0.160700	−	0.278341i
$669$	9.46438e6	+	1.63928e7i	0.817574	+	1.41608i
$670$	2.46207e6	−	4.26443e6i	0.211892	−	0.367007i
$671$	−1.31102e6			−0.112410
$672$		0			0
$673$	417573.			0.0355382			0.0177691	−	0.999842i	$-0.494344\pi$
$673$	417573.			0.0355382			0.0177691	+	0.999842i	$0.494344\pi$
$674$	1.13286e6	−	1.96217e6i	0.0960562	−	0.166374i
$675$	5.01044e6	+	8.67834e6i	0.423269	+	0.733124i
$676$	2.62814e6	+	4.55208e6i	0.221199	+	0.383127i
$677$	1.31234e6	−	2.27304e6i	0.110046	−	0.190605i	−0.805743	−	0.592266i	$-0.798233\pi$
$677$	1.31234e6	−	2.27304e6i	0.110046	−	0.190605i	0.915789	+	0.401661i	$0.131567\pi$
$678$	5.71812e6			0.477726
$679$		0			0
$680$	1.42661e6			0.118313
$681$	−7.06860e6	+	1.22432e7i	−0.584071	+	1.01164i
$682$	−1.14025e7	−	1.97497e7i	−0.938726	−	1.62592i
$683$	4.37227e6	+	7.57300e6i	0.358637	+	0.621178i	0.987733	−	0.156149i	$-0.0499081\pi$
$683$	4.37227e6	+	7.57300e6i	0.358637	+	0.621178i	−0.629096	+	0.777328i	$0.716575\pi$
$684$	−101748.	+	176233.i	−0.00831546	+	0.0144028i
$685$	2.29399e6			0.186795
$686$		0			0
$687$	−4.09716e6			−0.331200
$688$	−691453.	+	1.19763e6i	−0.0556919	+	0.0964611i
$689$	−1.93452e6	−	3.35069e6i	−0.155248	−	0.268898i
$690$	−2.46739e6	−	4.27365e6i	−0.197295	−	0.341725i
$691$	2.19834e6	−	3.80763e6i	0.175146	−	0.303361i	−0.765066	−	0.643952i	$-0.777294\pi$
$691$	2.19834e6	−	3.80763e6i	0.175146	−	0.303361i	0.940212	+	0.340591i	$0.110627\pi$
$692$	−2.14943e6			−0.170631
$693$		0			0
$694$	−2.16083e6			−0.170303
$695$	−2.14930e6	+	3.72270e6i	−0.168786	+	0.292345i
$696$	62580.6	+	108393.i	0.00489684	+	0.00848158i
$697$	9.12957e6	+	1.58129e7i	0.711817	+	1.23290i
$698$	−3.47614e6	+	6.02084e6i	−0.270059	+	0.467755i
$699$	−3.33951e6			−0.258518
$700$		0			0
$701$	6.51339e6			0.500624			0.250312	−	0.968165i	$-0.419467\pi$
$701$	6.51339e6			0.500624			0.250312	+	0.968165i	$0.419467\pi$
$702$	1.54436e6	−	2.67491e6i	0.118278	−	0.204864i
$703$	5.67900e6	+	9.83631e6i	0.433394	+	0.750661i
$704$	1.28179e6	+	2.22012e6i	0.0974731	+	0.168828i
$705$	−311172.	+	538965.i	−0.0235791	+	0.0408402i
$706$	4.29687e6			0.324445
$707$		0			0
$708$	−640934.			−0.0480541
$709$	5.23256e6	−	9.06305e6i	0.390929	−	0.677110i	−0.601643	−	0.798765i	$-0.705487\pi$
$709$	5.23256e6	−	9.06305e6i	0.390929	−	0.677110i	0.992572	+	0.121655i	$0.0388203\pi$
$710$	−1.31374e6	−	2.27547e6i	−0.0978056	−	0.169404i
$711$	−10058.2	−	17421.3i	−0.000746183	−	0.00129243i
$712$	−3.16928e6	+	5.48935e6i	−0.234294	+	0.405808i
$713$	3.38625e7			2.49457
$714$		0			0
$715$	−2.71832e6			−0.198855
$716$	−372675.	+	645492.i	−0.0271674	+	0.0470553i
$717$	3658.66	+	6336.98i	0.000265781	+	0.000460346i
$718$	242408.	+	419862.i	0.0175483	+	0.0303946i
$719$	−8.40746e6	+	1.45621e7i	−0.606516	+	1.05052i	0.385294	+	0.922794i	$0.374100\pi$
$719$	−8.40746e6	+	1.45621e7i	−0.606516	+	1.05052i	−0.991810	+	0.127723i	$0.959233\pi$
$720$	36292.7			0.00260909
$721$		0			0
$722$	−4.29311e6			−0.306499
$723$	−2.26302e6	+	3.91967e6i	−0.161006	+	0.278871i
$724$	6.63368e6	+	1.14899e7i	0.470336	+	0.814646i
$725$	−166069.	−	287640.i	−0.0117339	−	0.0203238i
$726$	−7.29069e6	+	1.26278e7i	−0.513366	+	0.889176i
$727$	1.71928e7			1.20646			0.603228	−	0.797569i	$-0.293881\pi$
$727$	1.71928e7			1.20646			0.603228	+	0.797569i	$0.293881\pi$
$728$		0			0
$729$	1.39284e7			0.970696
$730$	300320.	−	520169.i	0.0208582	−	0.0361275i
$731$	2.86700e6	+	4.96579e6i	0.198442	+	0.343712i
$732$	264830.	+	458698.i	0.0182679	+	0.0316409i
$733$	9.86827e6	−	1.70923e7i	0.678393	−	1.17501i	−0.297072	−	0.954855i	$-0.596010\pi$
$733$	9.86827e6	−	1.70923e7i	0.678393	−	1.17501i	0.975465	−	0.220155i	$-0.0706564\pi$
$734$	−2.21531e6			−0.151773
$735$		0			0
$736$	−3.80659e6			−0.259025
$737$	1.83446e7	−	3.17738e7i	1.24405	−	2.15477i
$738$	232255.	+	402278.i	0.0156973	+	0.0271885i
$739$	−6.43593e6	−	1.11474e7i	−0.433511	−	0.750863i	0.563662	−	0.826006i	$-0.309392\pi$
$739$	−6.43593e6	−	1.11474e7i	−0.433511	−	0.750863i	−0.997173	+	0.0751426i	$0.976059\pi$
$740$	1.01283e6	−	1.75427e6i	0.0679916	−	0.117765i
$741$	−6.15778e6			−0.411983
$742$		0			0
$743$	2.45606e7			1.63218			0.816089	−	0.577927i	$-0.196138\pi$
$743$	2.45606e7			1.63218			0.816089	+	0.577927i	$0.196138\pi$
$744$	−4.60667e6	+	7.97898e6i	−0.305109	+	0.528464i
$745$	4.26623e6	+	7.38933e6i	0.281614	+	0.487769i
$746$	−1.00296e6	−	1.73717e6i	−0.0659834	−	0.114287i
$747$	155117.	−	268671.i	0.0101709	−	0.0176165i
$748$	1.06295e7			0.694636
$749$		0			0
$750$	−7.71142e6			−0.500589
$751$	162983.	−	282294.i	0.0105449	−	0.0182643i	−0.860705	−	0.509104i	$-0.829977\pi$
$751$	162983.	−	282294.i	0.0105449	−	0.0182643i	0.871250	+	0.490840i	$0.163310\pi$
$752$	240031.	+	415746.i	0.0154783	+	0.0268092i
$753$	1.08387e7	+	1.87731e7i	0.696609	+	1.20656i
$754$	−51187.1	+	88658.7i	−0.00327893	+	0.00567928i
$755$	−8.75360e6			−0.558881
$756$		0			0
$757$	1.84659e7			1.17120			0.585599	−	0.810601i	$-0.300859\pi$
$757$	1.84659e7			1.17120			0.585599	+	0.810601i	$0.300859\pi$
$758$	1.99801e6	−	3.46065e6i	0.126306	−	0.218769i
$759$	−1.83842e7	−	3.18424e7i	−1.15835	−	2.00633i
$760$	1.26603e6	+	2.19283e6i	0.0795081	+	0.137712i
$761$	2.56313e6	−	4.43947e6i	0.160439	−	0.277888i	−0.774587	−	0.632467i	$-0.782042\pi$
$761$	2.56313e6	−	4.43947e6i	0.160439	−	0.277888i	0.935026	+	0.354579i	$0.115376\pi$
$762$	1.18657e7			0.740298
$763$		0			0
$764$	−7.55066e6			−0.468006
$765$	75241.0	−	130321.i	0.00464837	−	0.00805122i
$766$	−1.30493e6	−	2.26020e6i	−0.0803553	−	0.139179i
$767$	−262123.	−	454010.i	−0.0160885	−	0.0278662i
$768$	517849.	−	896941.i	0.0316811	−	0.0548733i
$769$	−1.63432e6			−0.0996602			−0.0498301	−	0.998758i	$-0.515868\pi$
$769$	−1.63432e6			−0.0996602			−0.0498301	+	0.998758i	$0.515868\pi$
$770$		0			0
$771$	−1.19984e7			−0.726921
$772$	−5.50683e6	+	9.53811e6i	−0.332551	+	0.575996i
$773$	−2.14128e6	−	3.70881e6i	−0.128892	−	0.223247i	0.794356	−	0.607453i	$-0.207809\pi$
$773$	−2.14128e6	−	3.70881e6i	−0.128892	−	0.223247i	−0.923248	+	0.384206i	$0.874475\pi$
$774$	72936.2	+	126329.i	0.00437614	+	0.00757969i
$775$	1.22246e7	−	2.11737e7i	0.731108	−	1.26632i
$776$	−7.39510e6			−0.440849
$777$		0			0
$778$	317012.			0.0187770
$779$	−1.62040e7	+	2.80661e7i	−0.956704	+	1.65706i
$780$	549108.	+	951082.i	0.0323163	+	0.0559734i
$781$	−9.78852e6	−	1.69542e7i	−0.574235	−	0.994604i
$782$	−7.89170e6	+	1.36688e7i	−0.461481	+	0.799308i
$783$	−462019.			−0.0269312
$784$		0			0
$785$	−2.50510e6			−0.145095
$786$	4.88051e6	−	8.45329e6i	0.281779	−	0.488056i
$787$	−3.91482e6	−	6.78066e6i	−0.225307	−	0.390243i	0.731105	−	0.682265i	$-0.239005\pi$
$787$	−3.91482e6	−	6.78066e6i	−0.225307	−	0.390243i	−0.956411	+	0.292022i	$0.905672\pi$
$788$	−2.49532e6	−	4.32202e6i	−0.143156	−	0.247954i
$789$	−8.47419e6	+	1.46777e7i	−0.484625	+	0.839395i
$790$	−250304.			−0.0142692
$791$		0			0
$792$	270413.			0.0153184
$793$	−216615.	+	375187.i	−0.0122322	+	0.0211868i
$794$	−8.01771e6	−	1.38871e7i	−0.451335	−	0.781736i
$795$	3.10422e6	+	5.37666e6i	0.174195	+	0.301714i
$796$	−2.29769e6	+	3.97972e6i	−0.128531	+	0.222623i
$797$	3.68238e6			0.205344			0.102672	−	0.994715i	$-0.467261\pi$
$797$	3.68238e6			0.205344			0.102672	+	0.994715i	$0.467261\pi$
$798$		0			0
$799$	1.99050e6			0.110305
$800$	−1.37421e6	+	2.38020e6i	−0.0759150	+	0.131489i
$801$	334304.	+	579031.i	0.0184102	+	0.0318875i
$802$	1.34884e6	+	2.33625e6i	0.0740497	+	0.128258i
$803$	2.23765e6	−	3.87572e6i	0.122462	−	0.212111i
$804$	−1.48226e7			−0.808695
$805$		0			0
$806$	−7.53595e6			−0.408602
$807$	1.39554e7	−	2.41714e7i	0.754324	−	1.30653i
$808$	−350447.	−	606992.i	−0.0188840	−	0.0327080i
$809$	−1.04091e7	−	1.80290e7i	−0.559165	−	0.968502i	−0.997566	−	0.0697227i	$-0.977789\pi$
$809$	−1.04091e7	−	1.80290e7i	−0.559165	−	0.968502i	0.438402	−	0.898779i	$-0.355545\pi$
$810$	−2.54704e6	+	4.41161e6i	−0.136403	+	0.236257i
$811$	−3.03542e7			−1.62057			−0.810283	−	0.586039i	$-0.800687\pi$
$811$	−3.03542e7			−1.62057			−0.810283	+	0.586039i	$0.800687\pi$
$812$		0			0
$813$	−3.24243e7			−1.72046
$814$	7.54644e6	−	1.30708e7i	0.399191	−	0.691420i
$815$	−497410.	−	861540.i	−0.0262314	−	0.0454341i
$816$	−2.14718e6	−	3.71902e6i	−0.112887	−	0.195526i
$817$	−5.08861e6	+	8.81373e6i	−0.266713	+	0.461960i
$818$	−1.14165e7			−0.596555
$819$		0			0
$820$	5.77982e6			0.300179
$821$	−1.37193e7	+	2.37626e7i	−0.710355	+	1.23037i	0.254369	+	0.967107i	$0.418132\pi$
$821$	−1.37193e7	+	2.37626e7i	−0.710355	+	1.23037i	−0.964724	+	0.263264i	$0.915201\pi$
$822$	−3.45268e6	−	5.98022e6i	−0.178228	−	0.308701i
$823$	−7.95629e6	−	1.37807e7i	−0.409459	−	0.709204i	0.585370	−	0.810766i	$-0.300949\pi$
$823$	−7.95629e6	−	1.37807e7i	−0.409459	−	0.709204i	−0.994829	+	0.101562i	$0.967616\pi$
$824$	4.40718e6	−	7.63346e6i	0.226122	−	0.391655i
$825$	−2.65474e7			−1.35796
$826$		0			0
$827$	1.40824e7			0.716001			0.358001	−	0.933721i	$-0.383459\pi$
$827$	1.40824e7			0.716001			0.358001	+	0.933721i	$0.383459\pi$
$828$	−200764.	+	347734.i	−0.0101768	+	0.0176267i
$829$	1.09441e7	+	1.89558e7i	0.553089	+	0.957978i	0.998049	+	0.0624281i	$0.0198844\pi$
$829$	1.09441e7	+	1.89558e7i	0.553089	+	0.957978i	−0.444960	+	0.895550i	$0.646782\pi$
$830$	−1.93009e6	−	3.34302e6i	−0.0972486	−	0.168439i
$831$	6.87992e6	−	1.19164e7i	0.345605	−	0.598606i
$832$	847139.			0.0424274
$833$		0			0
$834$	1.29396e7			0.644179
$835$	−2.43253e6	+	4.21326e6i	−0.120737	+	0.209123i
$836$	9.43306e6	+	1.63385e7i	0.466807	+	0.808533i
$837$	−1.70050e7	−	2.94535e7i	−0.839003	−	1.45320i
$838$	9.33106e6	−	1.61619e7i	0.459009	−	0.795026i
$839$	1.98669e7			0.974372			0.487186	−	0.873298i	$-0.338023\pi$
$839$	1.98669e7			0.974372			0.487186	+	0.873298i	$0.338023\pi$
$840$		0			0
$841$	−2.04958e7			−0.999253
$842$	−7.46635e6	+	1.29321e7i	−0.362934	+	0.628620i
$843$	1.86017e7	+	3.22191e7i	0.901538	+	1.56151i
$844$	3.68395e6	+	6.38078e6i	0.178015	+	0.308332i
$845$	3.44944e6	−	5.97460e6i	0.166191	−	0.287851i
$846$	50638.1			0.00243249
$847$		0			0
$848$	4.78905e6			0.228697
$849$	1.73076e7	−	2.99777e7i	0.824077	−	1.42734i
$850$	5.69793e6	+	9.86911e6i	0.270502	+	0.468523i
$851$	1.12055e7	+	1.94085e7i	0.530405	+	0.918688i
$852$	−3.95461e6	+	6.84959e6i	−0.186640	+	0.323270i
$853$	−8.75258e6			−0.411873			−0.205937	−	0.978565i	$-0.566024\pi$
$853$	−8.75258e6			−0.411873			−0.205937	+	0.978565i	$0.566024\pi$
$854$		0			0
$855$	267089.			0.0124951
$856$	2.41834e6	−	4.18868e6i	0.112806	−	0.195386i
$857$	−977384.	−	1.69288e6i	−0.0454583	−	0.0787361i	0.842401	−	0.538851i	$-0.181141\pi$
$857$	−977384.	−	1.69288e6i	−0.0454583	−	0.0787361i	−0.887859	+	0.460115i	$0.847808\pi$
$858$	4.09133e6	+	7.08640e6i	0.189735	+	0.328630i
$859$	2.49225e6	−	4.31670e6i	0.115241	−	0.199604i	−0.802635	−	0.596471i	$-0.796569\pi$
$859$	2.49225e6	−	4.31670e6i	0.115241	−	0.199604i	0.917876	+	0.396867i	$0.129902\pi$
$860$	1.81506e6			0.0836847
$861$		0			0
$862$	−3.85868e6			−0.176877
$863$	8.49654e6	−	1.47164e7i	0.388343	−	0.672629i	−0.603884	−	0.797072i	$-0.706381\pi$
$863$	8.49654e6	−	1.47164e7i	0.388343	−	0.672629i	0.992227	+	0.124443i	$0.0397144\pi$
$864$	1.91159e6	+	3.31096e6i	0.0871183	+	0.150893i
$865$	1.41056e6	+	2.44316e6i	0.0640991	+	0.111023i
$866$	1.23619e7	−	2.14115e7i	0.560133	−	0.970179i
$867$	4.63285e6			0.209315
$868$		0			0
$869$	−1.86498e6			−0.0837772
$870$	82137.0	−	142265.i	0.00367909	−	0.00637237i
$871$	−6.06200e6	−	1.04997e7i	−0.270751	−	0.468955i
$872$	1.42484e6	+	2.46790e6i	0.0634564	+	0.109910i
$873$	−390027.	+	675546.i	−0.0173204	+	0.0299999i
$874$	−2.80138e7			−1.24049
$875$		0			0
$876$	−1.80804e6			−0.0796064
$877$	−9.09797e6	+	1.57581e7i	−0.399434	+	0.691840i	−0.993656	−	0.112461i	$-0.964127\pi$
$877$	−9.09797e6	+	1.57581e7i	−0.399434	+	0.691840i	0.594222	+	0.804301i	$0.297460\pi$
$878$	430269.	+	745249.i	0.0188367	+	0.0326261i
$879$	6.38225e6	+	1.10544e7i	0.278613	+	0.482572i
$880$	1.68235e6	−	2.91391e6i	0.0732334	−	0.126844i
$881$	−1.77637e7			−0.771068			−0.385534	−	0.922694i	$-0.625983\pi$
$881$	−1.77637e7			−0.771068			−0.385534	+	0.922694i	$0.625983\pi$
$882$		0			0
$883$	1.71479e6			0.0740131			0.0370065	−	0.999315i	$-0.488218\pi$
$883$	1.71479e6			0.0740131			0.0370065	+	0.999315i	$0.488218\pi$
$884$	1.75626e6	−	3.04194e6i	0.0755891	−	0.130924i
$885$	420613.	+	728523.i	0.0180520	+	0.0312669i
$886$	−1.43973e7	−	2.49369e7i	−0.616167	−	1.06723i
$887$	−1.21218e7	+	2.09955e7i	−0.517318	+	0.896021i	0.482480	+	0.875907i	$0.339736\pi$
$887$	−1.21218e7	+	2.09955e7i	−0.517318	+	0.896021i	−0.999798	+	0.0201139i	$0.993597\pi$
$888$	−6.09760e6			−0.259494
$889$		0			0
$890$	8.31936e6			0.352058
$891$	−1.89777e7	+	3.28704e7i	−0.800847	+	1.38711i
$892$	−9.58206e6	−	1.65966e7i	−0.403224	−	0.698405i
$893$	1.76646e6	+	3.05960e6i	0.0741267	+	0.128391i
$894$	1.28422e7	−	2.22433e7i	0.537396	−	0.930798i
$895$	978272.			0.0408227
$896$		0			0
$897$	−1.21502e7			−0.504200
$898$	7.84306e6	−	1.35846e7i	0.324560	−	0.562154i
$899$	563624.	+	976225.i	0.0232589	+	0.0402857i
$900$	144955.	+	251069.i	0.00596522	+	0.0103321i
$901$	9.92852e6	−	1.71967e7i	0.407448	−	0.705721i
$902$	4.30647e7			1.76240
$903$		0			0
$904$	−5.78921e6			−0.235613
$905$	8.70671e6	−	1.50805e7i	0.353372	−	0.612059i
$906$	1.31750e7	+	2.28198e7i	0.533249	+	0.923615i
$907$	9.52161e6	+	1.64919e7i	0.384319	+	0.665661i	0.991675	−	0.128770i	$-0.0411028\pi$
$907$	9.52161e6	+	1.64919e7i	0.384319	+	0.665661i	−0.607355	+	0.794430i	$0.707769\pi$
$908$	7.15649e6	−	1.23954e7i	0.288062	−	0.498937i
$909$	−73932.0			−0.00296772
$910$		0			0
$911$	−3.18731e7			−1.27242			−0.636208	−	0.771518i	$-0.719498\pi$
$911$	−3.18731e7			−1.27242			−0.636208	+	0.771518i	$0.719498\pi$
$912$	3.81101e6	−	6.60085e6i	0.151723	−	0.262793i
$913$	−1.43809e7	−	2.49084e7i	−0.570964	−	0.988939i
$914$	2.64336e6	+	4.57843e6i	0.104662	+	0.181280i
$915$	347589.	−	602041.i	0.0137250	−	0.0237724i
$916$	4.14810e6			0.163347
$917$		0			0
$918$	1.58522e7			0.620843
$919$	1.47429e7	−	2.55355e7i	0.575830	−	0.997367i	−0.420121	−	0.907468i	$-0.638012\pi$
$919$	1.47429e7	−	2.55355e7i	0.575830	−	0.997367i	0.995951	−	0.0898988i	$-0.0286544\pi$
$920$	2.49807e6	+	4.32679e6i	0.0973050	+	0.168537i
$921$	−1.67135e6	−	2.89486e6i	−0.0649259	−	0.112455i
$922$	150918.	−	261398.i	0.00584675	−	0.0101269i
$923$	−6.46927e6			−0.249949
$924$		0			0
$925$	1.61811e7			0.621804
$926$	−6.57515e6	+	1.13885e7i	−0.251987	+	0.436454i
$927$	−464881.	−	805197.i	−0.0177681	−	0.0307753i
$928$	−63358.6	−	109740.i	−0.00241510	−	0.00418308i
$929$	−4.86935e6	+	8.43397e6i	−0.185111	+	0.320621i	−0.943614	−	0.331048i	$-0.892598\pi$
$929$	−4.86935e6	+	8.43397e6i	−0.185111	+	0.320621i	0.758503	+	0.651670i	$0.225931\pi$
$930$	1.20925e7			0.458468
$931$		0			0
$932$	3.38104e6			0.127500
$933$	2.30501e6	−	3.99240e6i	0.0866901	−	0.150152i
$934$	1.28676e6	+	2.22874e6i	0.0482649	+	0.0835973i
$935$	−6.97559e6	−	1.20821e7i	−0.260947	−	0.451973i
$936$	44679.2	−	77386.6i	0.00166692	−	0.00288720i
$937$	−2.66734e7			−0.992498			−0.496249	−	0.868180i	$-0.665290\pi$
$937$	−2.66734e7			−0.992498			−0.496249	+	0.868180i	$0.665290\pi$
$938$		0			0
$939$	−3.15434e7			−1.16747
$940$	315041.	−	545666.i	0.0116291	−	0.0201422i
$941$	1.61432e6	+	2.79609e6i	0.0594315	+	0.102938i	0.894210	−	0.447647i	$-0.147738\pi$
$941$	1.61432e6	+	2.79609e6i	0.0594315	+	0.102938i	−0.834779	+	0.550585i	$0.814405\pi$
$942$	3.77042e6	+	6.53056e6i	0.138440	+	0.239786i
$943$	−3.19728e7	+	5.53785e7i	−1.17085	+	2.02797i
$944$	648903.			0.0237001
$945$		0			0
$946$	1.35238e7			0.491328
$947$	2.29622e6	−	3.97717e6i	0.0832029	−	0.144112i	−0.821421	−	0.570322i	$-0.806818\pi$
$947$	2.29622e6	−	3.97717e6i	0.0832029	−	0.144112i	0.904624	+	0.426210i	$0.140152\pi$
$948$	376732.	+	652518.i	0.0136148	+	0.0235815i
$949$	−739434.	−	1.28074e6i	−0.0266523	−	0.0461631i
$950$	−1.01132e7	+	1.75166e7i	−0.363563	+	0.629709i
$951$	4.44011e7			1.59200
$952$		0			0
$953$	2.97125e7			1.05976			0.529880	−	0.848073i	$-0.322237\pi$
$953$	2.97125e7			1.05976			0.529880	+	0.848073i	$0.322237\pi$
$954$	252581.	−	437482.i	0.00898523	−	0.0155629i
$955$	4.95512e6	+	8.58253e6i	0.175811	+	0.304514i
$956$	−3704.14	−	6415.77i	−0.000131082	−	0.000227041i
$957$	611993.	−	1.06000e6i	0.0216006	−	0.0374134i
$958$	−2.97059e7			−1.04575
$959$		0			0
$960$	−1.35935e6			−0.0476052
$961$	−2.71748e7	+	4.70681e7i	−0.949199	+	1.64406i
$962$	−2.49373e6	−	4.31928e6i	−0.0868786	−	0.150478i
$963$	−255092.	−	441833.i	−0.00886403	−	0.0153530i
$964$	2.29116e6	−	3.96840e6i	0.0794077	−	0.137538i
$965$	1.44554e7			0.499704
$966$		0			0
$967$	7.64435e6			0.262890			0.131445	−	0.991323i	$-0.458038\pi$
$967$	7.64435e6			0.262890			0.131445	+	0.991323i	$0.458038\pi$
$968$	7.38134e6	−	1.27849e7i	0.253190	−	0.438538i
$969$	−1.58017e7	−	2.73694e7i	−0.540624	−	0.936388i
$970$	4.85303e6	+	8.40570e6i	0.165609	+	0.286843i
$971$	−2.49810e7	+	4.32684e7i	−0.850281	+	1.47273i	0.0306743	+	0.999529i	$0.490235\pi$
$971$	−2.49810e7	+	4.32684e7i	−0.850281	+	1.47273i	−0.880955	+	0.473200i	$0.843099\pi$
$972$	818079.			0.0277734
$973$		0			0
$974$	1.66834e7			0.563491
$975$	−4.38632e6	+	7.59734e6i	−0.147771	+	0.255947i
$976$	−268122.	−	464401.i	−0.00900966	−	0.0156052i
$977$	−2.02697e7	−	3.51082e7i	−0.679378	−	1.17672i	−0.975169	−	0.221464i	$-0.928916\pi$
$977$	−2.02697e7	−	3.51082e7i	−0.679378	−	1.17672i	0.295791	−	0.955253i	$-0.404417\pi$
$978$	−1.49730e6	+	2.59340e6i	−0.0500567	+	0.0867007i
$979$	6.19865e7			2.06700
$980$		0			0
$981$	300592.			0.00997251
$982$	−7.47348e6	+	1.29445e7i	−0.247311	+	0.428356i
$983$	−2.06528e7	−	3.57717e7i	−0.681703	−	1.18074i	−0.974461	−	0.224558i	$-0.927906\pi$
$983$	−2.06528e7	−	3.57717e7i	−0.681703	−	1.18074i	0.292757	−	0.956187i	$-0.405427\pi$
$984$	−8.69919e6	−	1.50674e7i	−0.286412	−	0.496080i
$985$	−3.27511e6	+	5.67265e6i	−0.107556	+	0.186292i
$986$	−525413.			−0.0172111
$987$		0			0
$988$	6.23434e6			0.203188
$989$	−1.00406e7	+	1.73908e7i	−0.326413	+	0.565364i
$990$	−177458.	−	307367.i	−0.00575451	−	0.00996711i
$991$	9.20419e6	+	1.59421e7i	0.297715	+	0.515658i	0.975613	−	0.219498i	$-0.0704420\pi$
$991$	9.20419e6	+	1.59421e7i	0.297715	+	0.515658i	−0.677897	+	0.735156i	$0.737109\pi$
$992$	4.66394e6	−	8.07819e6i	0.150478	−	0.260636i
$993$	−2.18167e7			−0.702126
$994$		0			0
$995$	6.03144e6			0.193136
$996$	−5.80995e6	+	1.00631e7i	−0.185577	+	0.321429i
$997$	−1.69854e7	−	2.94196e7i	−0.541175	−	0.937343i	−0.998837	−	0.0482164i	$-0.984646\pi$
$997$	−1.69854e7	−	2.94196e7i	−0.541175	−	0.937343i	0.457662	−	0.889126i	$-0.348687\pi$
$998$	1.74172e7	+	3.01675e7i	0.553545	+	0.958768i
$999$	1.12543e7	−	1.94931e7i	0.356784	−	0.617968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.6.c.f.79.2		4
7.2	even	3		98.6.a.f.1.1		2
7.3	odd	6		14.6.c.b.11.1	yes	4
7.4	even	3	inner	98.6.c.f.67.2		4
7.5	odd	6		98.6.a.c.1.2		2
7.6	odd	2		14.6.c.b.9.1	✓	4
21.2	odd	6		882.6.a.bl.1.2		2
21.5	even	6		882.6.a.bt.1.2		2
21.17	even	6		126.6.g.e.109.2		4
21.20	even	2		126.6.g.e.37.2		4
28.3	even	6		112.6.i.b.81.2		4
28.19	even	6		784.6.a.bc.1.1		2
28.23	odd	6		784.6.a.r.1.2		2
28.27	even	2		112.6.i.b.65.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.6.c.b.9.1	✓	4	7.6	odd	2
14.6.c.b.11.1	yes	4	7.3	odd	6
98.6.a.c.1.2		2	7.5	odd	6
98.6.a.f.1.1		2	7.2	even	3
98.6.c.f.67.2		4	7.4	even	3	inner
98.6.c.f.79.2		4	1.1	even	1	trivial
112.6.i.b.65.2		4	28.27	even	2
112.6.i.b.81.2		4	28.3	even	6
126.6.g.e.37.2		4	21.20	even	2
126.6.g.e.109.2		4	21.17	even	6
784.6.a.r.1.2		2	28.23	odd	6
784.6.a.bc.1.1		2	28.19	even	6
882.6.a.bl.1.2		2	21.2	odd	6
882.6.a.bt.1.2		2	21.5	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(7.90175 + 13.6862i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-10.5000 + 18.1865i) q^{5} +63.2140 q^{6} -64.0000 q^{8} +(-3.37544 + 5.84643i) q^{9} +(42.0000 + 72.7461i) q^{10} +(312.937 + 542.023i) q^{11} +(126.428 - 218.980i) q^{12} +206.821 q^{13} -331.874 q^{15} +(-128.000 + 221.703i) q^{16} +(530.732 + 919.254i) q^{17} +(13.5018 + 23.3857i) q^{18} +(-941.989 + 1631.57i) q^{19} +336.000 q^{20} +2503.49 q^{22} +(-1858.68 + 3219.34i) q^{23} +(-505.712 - 875.919i) q^{24} +(1342.00 + 2324.41i) q^{25} +(413.642 - 716.449i) q^{26} +3733.56 q^{27} -123.747 q^{29} +(-663.747 + 1149.64i) q^{30} +(-4554.63 - 7888.85i) q^{31} +(512.000 + 886.810i) q^{32} +(-4945.50 + 8565.86i) q^{33} +4245.85 q^{34} +108.014 q^{36} +(3014.36 - 5221.03i) q^{37} +(3767.96 + 6526.29i) q^{38} +(1634.25 + 2830.60i) q^{39} +(672.000 - 1163.94i) q^{40} +17201.9 q^{41} +5401.98 q^{43} +(5006.99 - 8672.36i) q^{44} +(-70.8843 - 122.775i) q^{45} +(7434.74 + 12877.3i) q^{46} +(937.621 - 1624.01i) q^{47} -4045.70 q^{48} +10736.0 q^{50} +(-8387.42 + 14527.4i) q^{51} +(-1654.57 - 2865.80i) q^{52} +(-9353.62 - 16200.9i) q^{53} +(7467.13 - 12933.4i) q^{54} -13143.3 q^{55} -29773.5 q^{57} +(-247.495 + 428.673i) q^{58} +(-1267.39 - 2195.18i) q^{59} +(2654.99 + 4598.58i) q^{60} +(-1047.35 + 1814.07i) q^{61} -36437.1 q^{62} +4096.00 q^{64} +(-2171.62 + 3761.36i) q^{65} +(19782.0 + 34263.4i) q^{66} +(-29310.4 - 50767.1i) q^{67} +(8491.71 - 14708.1i) q^{68} -58747.5 q^{69} -31279.5 q^{71} +(216.028 - 374.172i) q^{72} +(-3575.24 - 6192.49i) q^{73} +(-12057.5 - 20884.1i) q^{74} +(-21208.3 + 36733.9i) q^{75} +30143.7 q^{76} +13074.0 q^{78} +(-1489.91 + 2580.59i) q^{79} +(-2688.00 - 4655.75i) q^{80} +(30321.9 + 52519.1i) q^{81} +(34403.7 - 59589.0i) q^{82} -45954.6 q^{83} -22290.7 q^{85} +(10804.0 - 18713.0i) q^{86} +(-977.821 - 1693.64i) q^{87} +(-20028.0 - 34689.4i) q^{88} +(49520.0 - 85771.1i) q^{89} -567.074 q^{90} +59477.9 q^{92} +(71979.2 - 124672. i) q^{93} +(-3750.48 - 6496.03i) q^{94} +(-19781.8 - 34263.0i) q^{95} +(-8091.40 + 14014.7i) q^{96} +115548. q^{97} -4225.20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 14 q^{3} - 32 q^{4} - 42 q^{5} - 112 q^{6} - 256 q^{8} - 652 q^{9} + 168 q^{10} + 294 q^{11} - 224 q^{12} + 280 q^{13} + 588 q^{15} - 512 q^{16} + 1302 q^{17} + 2608 q^{18} - 1442 q^{19}+ \cdots + 419832 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 - 14 * q^3 - 32 * q^4 - 42 * q^5 - 112 * q^6 - 256 * q^8 - 652 * q^9 + 168 * q^10 + 294 * q^11 - 224 * q^12 + 280 * q^13 + 588 * q^15 - 512 * q^16 + 1302 * q^17 + 2608 * q^18 - 1442 * q^19 + 1344 * q^20 + 2352 * q^22 - 2646 * q^23 + 896 * q^24 + 5368 * q^25 + 560 * q^26 + 31444 * q^27 + 3336 * q^29 + 1176 * q^30 - 14798 * q^31 + 2048 * q^32 - 19782 * q^33 + 10416 * q^34 + 20864 * q^36 - 5182 * q^37 + 5768 * q^38 + 5260 * q^39 + 2688 * q^40 + 10248 * q^41 - 9040 * q^43 + 4704 * q^44 - 13692 * q^45 + 10584 * q^46 - 14994 * q^47 + 7168 * q^48 + 42944 * q^50 - 9606 * q^51 - 2240 * q^52 - 24006 * q^53 + 62888 * q^54 - 12348 * q^55 - 85892 * q^57 + 6672 * q^58 + 38850 * q^59 - 4704 * q^60 - 23618 * q^61 - 118384 * q^62 + 16384 * q^64 - 2940 * q^65 + 79128 * q^66 - 32002 * q^67 + 20832 * q^68 - 181356 * q^69 - 178752 * q^71 + 41728 * q^72 - 47138 * q^73 + 20728 * q^74 + 37576 * q^75 + 46144 * q^76 + 42080 * q^78 + 40970 * q^79 - 10752 * q^80 - 139858 * q^81 + 20496 * q^82 - 136752 * q^83 - 54684 * q^85 - 18080 * q^86 - 55356 * q^87 - 18816 * q^88 + 123102 * q^89 - 109536 * q^90 + 84672 * q^92 - 25586 * q^93 + 59976 * q^94 - 30282 * q^95 + 14336 * q^96 + 87304 * q^97 + 419832 * q^99

Introduction

L-functions

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