LMFDB - Embedded newform 98.6.c.d.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,6,Mod(67,98)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$15.7176143417$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.6.c.d.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 + 3.46410i) q^{2} +(5.00000 - 8.66025i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(42.0000 + 72.7461i) q^{5} +40.0000 q^{6} -64.0000 q^{8} +(71.5000 + 123.842i) q^{9} +(-168.000 + 290.985i) q^{10} +(168.000 - 290.985i) q^{11} +(80.0000 + 138.564i) q^{12} -584.000 q^{13} +840.000 q^{15} +(-128.000 - 221.703i) q^{16} +(-729.000 + 1262.67i) q^{17} +(-286.000 + 495.367i) q^{18} +(235.000 + 407.032i) q^{19} -1344.00 q^{20} +1344.00 q^{22} +(2100.00 + 3637.31i) q^{23} +(-320.000 + 554.256i) q^{24} +(-1965.50 + 3404.35i) q^{25} +(-1168.00 - 2023.04i) q^{26} +3860.00 q^{27} +4866.00 q^{29} +(1680.00 + 2909.85i) q^{30} +(-3686.00 + 6384.34i) q^{31} +(512.000 - 886.810i) q^{32} +(-1680.00 - 2909.85i) q^{33} -5832.00 q^{34} -2288.00 q^{36} +(-7165.00 - 12410.1i) q^{37} +(-940.000 + 1628.13i) q^{38} +(-2920.00 + 5057.59i) q^{39} +(-2688.00 - 4655.75i) q^{40} -6222.00 q^{41} +3704.00 q^{43} +(2688.00 + 4655.75i) q^{44} +(-6006.00 + 10402.7i) q^{45} +(-8400.00 + 14549.2i) q^{46} +(-906.000 - 1569.24i) q^{47} -2560.00 q^{48} -15724.0 q^{50} +(7290.00 + 12626.7i) q^{51} +(4672.00 - 8092.14i) q^{52} +(18621.0 - 32252.5i) q^{53} +(7720.00 + 13371.4i) q^{54} +28224.0 q^{55} +4700.00 q^{57} +(9732.00 + 16856.3i) q^{58} +(17151.0 - 29706.4i) q^{59} +(-6720.00 + 11639.4i) q^{60} +(12238.0 + 21196.8i) q^{61} -29488.0 q^{62} +4096.00 q^{64} +(-24528.0 - 42483.7i) q^{65} +(6720.00 - 11639.4i) q^{66} +(8726.00 - 15113.9i) q^{67} +(-11664.0 - 20202.6i) q^{68} +42000.0 q^{69} +28224.0 q^{71} +(-4576.00 - 7925.86i) q^{72} +(1801.00 - 3119.42i) q^{73} +(28660.0 - 49640.6i) q^{74} +(19655.0 + 34043.5i) q^{75} -7520.00 q^{76} -23360.0 q^{78} +(-21436.0 - 37128.2i) q^{79} +(10752.0 - 18623.0i) q^{80} +(1925.50 - 3335.06i) q^{81} +(-12444.0 - 21553.6i) q^{82} +35202.0 q^{83} -122472. q^{85} +(7408.00 + 12831.0i) q^{86} +(24330.0 - 42140.8i) q^{87} +(-10752.0 + 18623.0i) q^{88} +(13365.0 + 23148.9i) q^{89} -48048.0 q^{90} -67200.0 q^{92} +(36860.0 + 63843.4i) q^{93} +(3624.00 - 6276.95i) q^{94} +(-19740.0 + 34190.7i) q^{95} +(-5120.00 - 8868.10i) q^{96} +16978.0 q^{97} +48048.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 10 q^{3} - 16 q^{4} + 84 q^{5} + 80 q^{6} - 128 q^{8} + 143 q^{9} - 336 q^{10} + 336 q^{11} + 160 q^{12} - 1168 q^{13} + 1680 q^{15} - 256 q^{16} - 1458 q^{17} - 572 q^{18} + 470 q^{19}+ \cdots + 96096 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 + 10 * q^3 - 16 * q^4 + 84 * q^5 + 80 * q^6 - 128 * q^8 + 143 * q^9 - 336 * q^10 + 336 * q^11 + 160 * q^12 - 1168 * q^13 + 1680 * q^15 - 256 * q^16 - 1458 * q^17 - 572 * q^18 + 470 * q^19 - 2688 * q^20 + 2688 * q^22 + 4200 * q^23 - 640 * q^24 - 3931 * q^25 - 2336 * q^26 + 7720 * q^27 + 9732 * q^29 + 3360 * q^30 - 7372 * q^31 + 1024 * q^32 - 3360 * q^33 - 11664 * q^34 - 4576 * q^36 - 14330 * q^37 - 1880 * q^38 - 5840 * q^39 - 5376 * q^40 - 12444 * q^41 + 7408 * q^43 + 5376 * q^44 - 12012 * q^45 - 16800 * q^46 - 1812 * q^47 - 5120 * q^48 - 31448 * q^50 + 14580 * q^51 + 9344 * q^52 + 37242 * q^53 + 15440 * q^54 + 56448 * q^55 + 9400 * q^57 + 19464 * q^58 + 34302 * q^59 - 13440 * q^60 + 24476 * q^61 - 58976 * q^62 + 8192 * q^64 - 49056 * q^65 + 13440 * q^66 + 17452 * q^67 - 23328 * q^68 + 84000 * q^69 + 56448 * q^71 - 9152 * q^72 + 3602 * q^73 + 57320 * q^74 + 39310 * q^75 - 15040 * q^76 - 46720 * q^78 - 42872 * q^79 + 21504 * q^80 + 3851 * q^81 - 24888 * q^82 + 70404 * q^83 - 244944 * q^85 + 14816 * q^86 + 48660 * q^87 - 21504 * q^88 + 26730 * q^89 - 96096 * q^90 - 134400 * q^92 + 73720 * q^93 + 7248 * q^94 - 39480 * q^95 - 10240 * q^96 + 33956 * q^97 + 96096 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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
$3$	5.00000	−	8.66025i	0.320750	−	0.555556i	−0.659893	−	0.751360i	$-0.729398\pi$
$3$	5.00000	−	8.66025i	0.320750	−	0.555556i	0.980643	+	0.195804i	$0.0627317\pi$
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	42.0000	+	72.7461i	0.751319	+	1.30132i	0.947184	+	0.320692i	$0.103915\pi$
$5$	42.0000	+	72.7461i	0.751319	+	1.30132i	−0.195865	+	0.980631i	$0.562751\pi$
$6$	40.0000			0.453609
$7$		0			0
$7$		0			0
$8$	−64.0000			−0.353553
$9$	71.5000	+	123.842i	0.294239	+	0.509636i
$10$	−168.000	+	290.985i	−0.531263	+	0.920174i
$11$	168.000	−	290.985i	0.418627	−	0.725084i	−0.577174	−	0.816621i	$-0.695845\pi$
$11$	168.000	−	290.985i	0.418627	−	0.725084i	0.995802	+	0.0915372i	$0.0291780\pi$
$12$	80.0000	+	138.564i	0.160375	+	0.277778i
$13$	−584.000			−0.958417			−0.479208	−	0.877701i	$-0.659076\pi$
$13$	−584.000			−0.958417			−0.479208	+	0.877701i	$0.659076\pi$
$14$		0			0
$15$	840.000			0.963943
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	−729.000	+	1262.67i	−0.611794	+	1.05966i	0.379144	+	0.925338i	$0.376219\pi$
$17$	−729.000	+	1262.67i	−0.611794	+	1.05966i	−0.990938	+	0.134321i	$0.957115\pi$
$18$	−286.000	+	495.367i	−0.208058	+	0.360367i
$19$	235.000	+	407.032i	0.149343	+	0.258669i	0.930985	−	0.365058i	$-0.118951\pi$
$19$	235.000	+	407.032i	0.149343	+	0.258669i	−0.781642	+	0.623727i	$0.785618\pi$
$20$	−1344.00			−0.751319
$21$		0			0
$22$	1344.00			0.592028
$23$	2100.00	+	3637.31i	0.827751	+	1.43371i	0.899799	+	0.436306i	$0.143713\pi$
$23$	2100.00	+	3637.31i	0.827751	+	1.43371i	−0.0720476	+	0.997401i	$0.522953\pi$
$24$	−320.000	+	554.256i	−0.113402	+	0.196419i
$25$	−1965.50	+	3404.35i	−0.628960	+	1.08939i
$26$	−1168.00	−	2023.04i	−0.338852	−	0.586908i
$27$	3860.00			1.01901
$28$		0			0
$29$	4866.00			1.07443			0.537214	−	0.843446i	$-0.319477\pi$
$29$	4866.00			1.07443			0.537214	+	0.843446i	$0.319477\pi$
$30$	1680.00	+	2909.85i	0.340805	+	0.590292i
$31$	−3686.00	+	6384.34i	−0.688892	+	1.19320i	0.283305	+	0.959030i	$0.408569\pi$
$31$	−3686.00	+	6384.34i	−0.688892	+	1.19320i	−0.972197	+	0.234166i	$0.924764\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$	−1680.00	−	2909.85i	−0.268550	−	0.465141i
$34$	−5832.00			−0.865207
$35$		0			0
$36$	−2288.00			−0.294239
$37$	−7165.00	−	12410.1i	−0.860423	−	1.49030i	−0.871521	−	0.490358i	$-0.836866\pi$
$37$	−7165.00	−	12410.1i	−0.860423	−	1.49030i	0.0110986	−	0.999938i	$-0.496467\pi$
$38$	−940.000	+	1628.13i	−0.105601	+	0.182907i
$39$	−2920.00	+	5057.59i	−0.307412	+	0.532454i
$40$	−2688.00	−	4655.75i	−0.265631	−	0.460087i
$41$	−6222.00			−0.578057			−0.289028	−	0.957321i	$-0.593332\pi$
$41$	−6222.00			−0.578057			−0.289028	+	0.957321i	$0.593332\pi$
$42$		0			0
$43$	3704.00			0.305492			0.152746	−	0.988265i	$-0.451188\pi$
$43$	3704.00			0.305492			0.152746	+	0.988265i	$0.451188\pi$
$44$	2688.00	+	4655.75i	0.209314	+	0.362542i
$45$	−6006.00	+	10402.7i	−0.442134	+	0.765799i
$46$	−8400.00	+	14549.2i	−0.585308	+	1.01378i
$47$	−906.000	−	1569.24i	−0.0598251	−	0.103620i	0.834562	−	0.550915i	$-0.185721\pi$
$47$	−906.000	−	1569.24i	−0.0598251	−	0.103620i	−0.894387	+	0.447294i	$0.852388\pi$
$48$	−2560.00			−0.160375
$49$		0			0
$50$	−15724.0			−0.889484
$51$	7290.00	+	12626.7i	0.392466	+	0.679771i
$52$	4672.00	−	8092.14i	0.239604	−	0.415007i
$53$	18621.0	−	32252.5i	0.910570	−	1.57715i	0.0973091	−	0.995254i	$-0.468976\pi$
$53$	18621.0	−	32252.5i	0.910570	−	1.57715i	0.813261	−	0.581899i	$-0.197690\pi$
$54$	7720.00	+	13371.4i	0.360274	+	0.624013i
$55$	28224.0			1.25809
$56$		0			0
$57$	4700.00			0.191607
$58$	9732.00	+	16856.3i	0.379867	+	0.657950i
$59$	17151.0	−	29706.4i	0.641445	−	1.11102i	−0.343665	−	0.939092i	$-0.611669\pi$
$59$	17151.0	−	29706.4i	0.641445	−	1.11102i	0.985110	−	0.171923i	$-0.0549981\pi$
$60$	−6720.00	+	11639.4i	−0.240986	+	0.417399i
$61$	12238.0	+	21196.8i	0.421101	+	0.729368i	0.996047	−	0.0888232i	$-0.0283106\pi$
$61$	12238.0	+	21196.8i	0.421101	+	0.729368i	−0.574947	+	0.818191i	$0.694977\pi$
$62$	−29488.0			−0.974240
$63$		0			0
$64$	4096.00			0.125000
$65$	−24528.0	−	42483.7i	−0.720077	−	1.24721i
$66$	6720.00	−	11639.4i	0.189893	−	0.328905i
$67$	8726.00	−	15113.9i	0.237481	−	0.411329i	−0.722510	−	0.691360i	$-0.757012\pi$
$67$	8726.00	−	15113.9i	0.237481	−	0.411329i	0.959991	+	0.280032i	$0.0903450\pi$
$68$	−11664.0	−	20202.6i	−0.305897	−	0.529829i
$69$	42000.0			1.06201
$70$		0			0
$71$	28224.0			0.664466			0.332233	−	0.943197i	$-0.392198\pi$
$71$	28224.0			0.664466			0.332233	+	0.943197i	$0.392198\pi$
$72$	−4576.00	−	7925.86i	−0.104029	−	0.180184i
$73$	1801.00	−	3119.42i	0.0395555	−	0.0685121i	−0.845570	−	0.533865i	$-0.820739\pi$
$73$	1801.00	−	3119.42i	0.0395555	−	0.0685121i	0.885125	+	0.465353i	$0.154072\pi$
$74$	28660.0	−	49640.6i	0.608411	−	1.05380i
$75$	19655.0	+	34043.5i	0.403478	+	0.698844i
$76$	−7520.00			−0.149343
$77$		0			0
$78$	−23360.0			−0.434747
$79$	−21436.0	−	37128.2i	−0.386435	−	0.669324i	0.605532	−	0.795821i	$-0.292960\pi$
$79$	−21436.0	−	37128.2i	−0.386435	−	0.669324i	−0.991967	+	0.126496i	$0.959627\pi$
$80$	10752.0	−	18623.0i	0.187830	−	0.325331i
$81$	1925.50	−	3335.06i	0.0326085	−	0.0564796i
$82$	−12444.0	−	21553.6i	−0.204374	−	0.353986i
$83$	35202.0			0.560883			0.280441	−	0.959871i	$-0.409519\pi$
$83$	35202.0			0.560883			0.280441	+	0.959871i	$0.409519\pi$
$84$		0			0
$85$	−122472.			−1.83861
$86$	7408.00	+	12831.0i	0.108008	+	0.187075i
$87$	24330.0	−	42140.8i	0.344623	−	0.596904i
$88$	−10752.0	+	18623.0i	−0.148007	+	0.256356i
$89$	13365.0	+	23148.9i	0.178852	+	0.309781i	0.941488	−	0.337048i	$-0.109428\pi$
$89$	13365.0	+	23148.9i	0.178852	+	0.309781i	−0.762636	+	0.646828i	$0.776095\pi$
$90$	−48048.0			−0.625272
$91$		0			0
$92$	−67200.0			−0.827751
$93$	36860.0	+	63843.4i	0.441924	+	0.765435i
$94$	3624.00	−	6276.95i	0.0423027	−	0.0732705i
$95$	−19740.0	+	34190.7i	−0.224408	+	0.388686i
$96$	−5120.00	−	8868.10i	−0.0567012	−	0.0982093i
$97$	16978.0			0.183213			0.0916067	−	0.995795i	$-0.470800\pi$
$97$	16978.0			0.183213			0.0916067	+	0.995795i	$0.470800\pi$
$98$		0			0
$99$	48048.0			0.492705
$100$	−31448.0	−	54469.5i	−0.314480	−	0.544695i
$101$	49602.0	−	85913.2i	0.483833	−	0.838024i	−0.515994	−	0.856592i	$-0.672577\pi$
$101$	49602.0	−	85913.2i	0.483833	−	0.838024i	0.999828	+	0.0185682i	$0.00591077\pi$
$102$	−29160.0	+	50506.6i	−0.277515	+	0.480671i
$103$	−65822.0	−	114007.i	−0.611333	−	1.05886i	−0.991016	−	0.133743i	$-0.957300\pi$
$103$	−65822.0	−	114007.i	−0.611333	−	1.05886i	0.379683	−	0.925117i	$-0.376033\pi$
$104$	37376.0			0.338852
$105$		0			0
$106$	148968.			1.28774
$107$	−24426.0	−	42307.1i	−0.206250	−	0.357235i	0.744281	−	0.667867i	$-0.232793\pi$
$107$	−24426.0	−	42307.1i	−0.206250	−	0.357235i	−0.950530	+	0.310632i	$0.899459\pi$
$108$	−30880.0	+	53485.7i	−0.254752	+	0.441244i
$109$	28187.0	−	48821.3i	0.227239	−	0.393589i	−0.729750	−	0.683714i	$-0.760364\pi$
$109$	28187.0	−	48821.3i	0.227239	−	0.393589i	0.956989	+	0.290125i	$0.0936969\pi$
$110$	56448.0	+	97770.8i	0.444802	+	0.770420i
$111$	−143300.			−1.10392
$112$		0			0
$113$	8742.00			0.0644043			0.0322021	−	0.999481i	$-0.489748\pi$
$113$	8742.00			0.0644043			0.0322021	+	0.999481i	$0.489748\pi$
$114$	9400.00	+	16281.3i	0.0677432	+	0.117335i
$115$	−176400.	+	305534.i	−1.24381	+	2.15434i
$116$	−38928.0	+	67425.3i	−0.268607	+	0.465241i
$117$	−41756.0	−	72323.5i	−0.282003	−	0.488444i
$118$	137208.			0.907140
$119$		0			0
$120$	−53760.0			−0.340805
$121$	24077.5	+	41703.5i	0.149502	+	0.258946i
$122$	−48952.0	+	84787.4i	−0.297763	+	0.515741i
$123$	−31110.0	+	53884.1i	−0.185412	+	0.321143i
$124$	−58976.0	−	102149.i	−0.344446	−	0.596598i
$125$	−67704.0			−0.387560
$126$		0			0
$127$	315992.			1.73847			0.869234	−	0.494401i	$-0.164612\pi$
$127$	315992.			1.73847			0.869234	+	0.494401i	$0.164612\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$	18520.0	−	32077.6i	0.0979866	−	0.169718i
$130$	98112.0	−	169935.i	0.509171	−	0.881910i
$131$	−12333.0	−	21361.4i	−0.0627900	−	0.108755i	0.832922	−	0.553391i	$-0.186667\pi$
$131$	−12333.0	−	21361.4i	−0.0627900	−	0.108755i	−0.895712	+	0.444636i	$0.853333\pi$
$132$	53760.0			0.268550
$133$		0			0
$134$	69808.0			0.335848
$135$	162120.	+	280800.i	0.765600	+	1.32606i
$136$	46656.0	−	80810.6i	0.216302	−	0.374646i
$137$	−151617.	+	262608.i	−0.690155	+	1.19538i	0.281632	+	0.959522i	$0.409124\pi$
$137$	−151617.	+	262608.i	−0.690155	+	1.19538i	−0.971787	+	0.235861i	$0.924209\pi$
$138$	84000.0	+	145492.i	0.375475	+	0.650343i
$139$	−250586.			−1.10007			−0.550034	−	0.835142i	$-0.685385\pi$
$139$	−250586.			−1.10007			−0.550034	+	0.835142i	$0.685385\pi$
$140$		0			0
$141$	−18120.0			−0.0767557
$142$	56448.0	+	97770.8i	0.234924	+	0.406901i
$143$	−98112.0	+	169935.i	−0.401220	+	0.694933i
$144$	18304.0	−	31703.5i	0.0735597	−	0.127409i
$145$	204372.	+	353983.i	0.807238	+	1.39818i
$146$	14408.0			0.0559399
$147$		0			0
$148$	229280.			0.860423
$149$	30297.0	+	52475.9i	0.111798	+	0.193640i	0.916495	−	0.400046i	$-0.131006\pi$
$149$	30297.0	+	52475.9i	0.111798	+	0.193640i	−0.804697	+	0.593685i	$0.797672\pi$
$150$	−78620.0	+	136174.i	−0.285302	+	0.494158i
$151$	−62224.0	+	107775.i	−0.222083	+	0.384659i	−0.955440	−	0.295184i	$-0.904619\pi$
$151$	−62224.0	+	107775.i	−0.222083	+	0.384659i	0.733357	+	0.679843i	$0.237952\pi$
$152$	−15040.0	−	26050.0i	−0.0528006	−	0.0914533i
$153$	−208494.			−0.720054
$154$		0			0
$155$	−619248.			−2.07031
$156$	−46720.0	−	80921.4i	−0.153706	−	0.266227i
$157$	38020.0	−	65852.6i	0.123101	−	0.213218i	−0.797888	−	0.602806i	$-0.794049\pi$
$157$	38020.0	−	65852.6i	0.123101	−	0.213218i	0.920989	+	0.389588i	$0.127383\pi$
$158$	85744.0	−	148513.i	0.273251	−	0.473284i
$159$	−186210.	−	322525.i	−0.584131	−	1.01174i
$160$	86016.0			0.265631
$161$		0			0
$162$	15404.0			0.0461154
$163$	−62128.0	−	107609.i	−0.183155	−	0.317233i	0.759798	−	0.650159i	$-0.225298\pi$
$163$	−62128.0	−	107609.i	−0.183155	−	0.317233i	−0.942953	+	0.332925i	$0.891964\pi$
$164$	49776.0	−	86214.6i	0.144514	−	0.250306i
$165$	141120.	−	244427.i	0.403533	−	0.698939i
$166$	70404.0	+	121943.i	0.198302	+	0.343469i
$167$	72420.0			0.200940			0.100470	−	0.994940i	$-0.467965\pi$
$167$	72420.0			0.200940			0.100470	+	0.994940i	$0.467965\pi$
$168$		0			0
$169$	−30237.0			−0.0814370
$170$	−244944.	−	424255.i	−0.650047	−	1.12591i
$171$	−33605.0	+	58205.6i	−0.0878848	+	0.152221i
$172$	−29632.0	+	51324.1i	−0.0763730	+	0.132282i
$173$	−220776.	−	382395.i	−0.560837	−	0.971398i	−0.997424	−	0.0717359i	$-0.977146\pi$
$173$	−220776.	−	382395.i	−0.560837	−	0.971398i	0.436587	−	0.899662i	$-0.356187\pi$
$174$	194640.			0.487370
$175$		0			0
$176$	−86016.0			−0.209314
$177$	−171510.	−	297064.i	−0.411487	−	0.712717i
$178$	−53460.0	+	92595.4i	−0.126468	+	0.219048i
$179$	5346.00	−	9259.54i	0.0124709	−	0.0216002i	−0.859723	−	0.510761i	$-0.829364\pi$
$179$	5346.00	−	9259.54i	0.0124709	−	0.0216002i	0.872193	+	0.489161i	$0.162697\pi$
$180$	−96096.0	−	166443.i	−0.221067	−	0.382899i
$181$	546064.			1.23893			0.619465	−	0.785024i	$-0.287349\pi$
$181$	546064.			1.23893			0.619465	+	0.785024i	$0.287349\pi$
$182$		0			0
$183$	244760.			0.540272
$184$	−134400.	−	232788.i	−0.292654	−	0.506892i
$185$	601860.	−	1.04245e6i	1.29290	−	2.23937i
$186$	−147440.	+	255374.i	−0.312488	+	0.541245i
$187$	244944.	+	424255.i	0.512227	+	0.887204i
$188$	28992.0			0.0598251
$189$		0			0
$190$	−157920.			−0.317361
$191$	287988.	+	498810.i	0.571204	+	0.989354i	0.996443	+	0.0842727i	$0.0268567\pi$
$191$	287988.	+	498810.i	0.571204	+	0.989354i	−0.425239	+	0.905081i	$0.639810\pi$
$192$	20480.0	−	35472.4i	0.0400938	−	0.0694444i
$193$	206969.	−	358481.i	0.399956	−	0.692744i	−0.593764	−	0.804639i	$-0.702359\pi$
$193$	206969.	−	358481.i	0.399956	−	0.692744i	0.993720	+	0.111895i	$0.0356921\pi$
$194$	33956.0	+	58813.5i	0.0647757	+	0.112195i
$195$	−490560.			−0.923859
$196$		0			0
$197$	−494946.			−0.908641			−0.454320	−	0.890838i	$-0.650118\pi$
$197$	−494946.			−0.908641			−0.454320	+	0.890838i	$0.650118\pi$
$198$	96096.0	+	166443.i	0.174198	+	0.301719i
$199$	260182.	−	450648.i	0.465741	−	0.806687i	−0.533494	−	0.845804i	$-0.679121\pi$
$199$	260182.	−	450648.i	0.465741	−	0.806687i	0.999235	+	0.0391169i	$0.0124545\pi$
$200$	125792.	−	217878.i	0.222371	−	0.385158i
$201$	−87260.0	−	151139.i	−0.152344	−	0.263867i
$202$	396816.			0.684244
$203$		0			0
$204$	−233280.			−0.392466
$205$	−261324.	−	452626.i	−0.434305	−	0.752238i
$206$	263288.	−	456028.i	0.432278	−	0.748727i
$207$	−300300.	+	520135.i	−0.487113	+	0.843704i
$208$	74752.0	+	129474.i	0.119802	+	0.207503i
$209$	157920.			0.250076
$210$		0			0
$211$	183284.			0.283412			0.141706	−	0.989909i	$-0.454741\pi$
$211$	183284.			0.283412			0.141706	+	0.989909i	$0.454741\pi$
$212$	297936.	+	516040.i	0.455285	+	0.788577i
$213$	141120.	−	244427.i	0.213128	−	0.369148i
$214$	97704.0	−	169228.i	0.145840	−	0.252603i
$215$	155568.	+	269452.i	0.229522	+	0.397544i
$216$	−247040.			−0.360274
$217$		0			0
$218$	225496.			0.321364
$219$	−18010.0	−	31194.2i	−0.0253748	−	0.0439505i
$220$	−225792.	+	391083.i	−0.314523	+	0.544769i
$221$	425736.	−	737396.i	0.586354	−	1.01559i
$222$	−286600.	−	496406.i	−0.390296	−	0.676012i
$223$	1.27746e6			1.72023			0.860115	−	0.510100i	$-0.170392\pi$
$223$	1.27746e6			1.72023			0.860115	+	0.510100i	$0.170392\pi$
$224$		0			0
$225$	−562133.			−0.740257
$226$	17484.0	+	30283.2i	0.0227703	+	0.0394394i
$227$	−643821.	+	1.11513e6i	−0.829279	+	1.43635i	0.0693262	+	0.997594i	$0.477915\pi$
$227$	−643821.	+	1.11513e6i	−0.829279	+	1.43635i	−0.898605	+	0.438759i	$0.855418\pi$
$228$	−37600.0	+	65125.1i	−0.0479017	+	0.0829681i
$229$	175468.	+	303919.i	0.221110	+	0.382974i	0.955145	−	0.296137i	$-0.0956985\pi$
$229$	175468.	+	303919.i	0.221110	+	0.382974i	−0.734035	+	0.679112i	$0.762365\pi$
$230$	−1.41120e6			−1.75901
$231$		0			0
$232$	−311424.			−0.379867
$233$	−418077.	−	724131.i	−0.504506	−	0.873830i	−0.999986	−	0.00521110i	$-0.998341\pi$
$233$	−418077.	−	724131.i	−0.504506	−	0.873830i	0.495480	−	0.868619i	$-0.334992\pi$
$234$	167024.	−	289294.i	0.199406	−	0.345382i
$235$	76104.0	−	131816.i	0.0898955	−	0.155704i
$236$	274416.	+	475302.i	0.320722	+	0.555508i
$237$	−428720.			−0.495796
$238$		0			0
$239$	774336.			0.876869			0.438434	−	0.898763i	$-0.355533\pi$
$239$	774336.			0.876869			0.438434	+	0.898763i	$0.355533\pi$
$240$	−107520.	−	186230.i	−0.120493	−	0.208700i
$241$	−576425.	+	998397.i	−0.639293	+	1.10729i	0.346295	+	0.938126i	$0.387440\pi$
$241$	−576425.	+	998397.i	−0.639293	+	1.10729i	−0.985588	+	0.169163i	$0.945894\pi$
$242$	−96310.0	+	166814.i	−0.105714	+	0.183102i
$243$	449735.	+	778964.i	0.488586	+	0.846256i
$244$	−391616.			−0.421101
$245$		0			0
$246$	−248880.			−0.262212
$247$	−137240.	−	237707.i	−0.143133	−	0.247913i
$248$	235904.	−	408598.i	0.243560	−	0.421858i
$249$	176010.	−	304858.i	0.179903	−	0.311602i
$250$	−135408.	−	234534.i	−0.137023	−	0.237331i
$251$	−1.35801e6			−1.36056			−0.680282	−	0.732951i	$-0.738142\pi$
$251$	−1.35801e6			−1.36056			−0.680282	+	0.732951i	$0.738142\pi$
$252$		0			0
$253$	1.41120e6			1.38608
$254$	631984.	+	1.09463e6i	0.614641	+	1.06459i
$255$	−612360.	+	1.06064e6i	−0.589734	+	1.02145i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−158871.	−	275173.i	−0.150042	−	0.259880i	0.781201	−	0.624280i	$-0.214607\pi$
$257$	−158871.	−	275173.i	−0.150042	−	0.259880i	−0.931243	+	0.364400i	$0.881274\pi$
$258$	148160.			0.138574
$259$		0			0
$260$	784896.			0.720077
$261$	347919.	+	602613.i	0.316138	+	0.547567i
$262$	49332.0	−	85445.5i	0.0443992	−	0.0769017i
$263$	−525504.	+	910200.i	−0.468475	+	0.811423i	−0.999351	−	0.0360268i	$-0.988530\pi$
$263$	−525504.	+	910200.i	−0.468475	+	0.811423i	0.530876	+	0.847450i	$0.321863\pi$
$264$	107520.	+	186230.i	0.0949466	+	0.164452i
$265$	3.12833e6			2.73651
$266$		0			0
$267$	267300.			0.229467
$268$	139616.	+	241822.i	0.118740	+	0.205664i
$269$	594792.	−	1.03021e6i	0.501169	−	0.868051i	−0.498830	−	0.866700i	$-0.666237\pi$
$269$	594792.	−	1.03021e6i	0.501169	−	0.868051i	0.999999	−	0.00135066i	$-0.000429930\pi$
$270$	−648480.	+	1.12320e6i	−0.541361	+	0.937665i
$271$	−715040.	−	1.23849e6i	−0.591435	−	1.02440i	−0.994039	−	0.109022i	$-0.965228\pi$
$271$	−715040.	−	1.23849e6i	−0.591435	−	1.02440i	0.402604	−	0.915374i	$-0.368105\pi$
$272$	373248.			0.305897
$273$		0			0
$274$	−1.21294e6			−0.976026
$275$	660408.	+	1.14386e6i	0.526600	+	0.912097i
$276$	−336000.	+	581969.i	−0.265501	+	0.459862i
$277$	−31651.0	+	54821.1i	−0.0247849	+	0.0429288i	−0.878152	−	0.478382i	$-0.841223\pi$
$277$	−31651.0	+	54821.1i	−0.0247849	+	0.0429288i	0.853367	+	0.521311i	$0.174557\pi$
$278$	−501172.	−	868055.i	−0.388933	−	0.673652i
$279$	−1.05420e6			−0.810795
$280$		0			0
$281$	−496614.			−0.375192			−0.187596	−	0.982246i	$-0.560070\pi$
$281$	−496614.			−0.375192			−0.187596	+	0.982246i	$0.560070\pi$
$282$	−36240.0	−	62769.5i	−0.0271372	−	0.0470031i
$283$	−579209.	+	1.00322e6i	−0.429902	+	0.744612i	−0.996864	−	0.0791320i	$-0.974785\pi$
$283$	−579209.	+	1.00322e6i	−0.429902	+	0.744612i	0.566962	+	0.823744i	$0.308118\pi$
$284$	−225792.	+	391083.i	−0.166116	+	0.287722i
$285$	197400.	+	341907.i	0.143958	+	0.249342i
$286$	−784896.			−0.567410
$287$		0			0
$288$	146432.			0.104029
$289$	−352954.	−	611333.i	−0.248584	−	0.430560i
$290$	−817488.	+	1.41593e6i	−0.570803	+	0.988660i
$291$	84890.0	−	147034.i	0.0587657	−	0.101785i
$292$	28816.0	+	49910.8i	0.0197777	+	0.0342560i
$293$	−1.43886e6			−0.979151			−0.489575	−	0.871961i	$-0.662848\pi$
$293$	−1.43886e6			−0.979151			−0.489575	+	0.871961i	$0.662848\pi$
$294$		0			0
$295$	2.88137e6			1.92772
$296$	458560.	+	794249.i	0.304205	+	0.526899i
$297$	648480.	−	1.12320e6i	0.426585	−	0.738867i
$298$	−121188.	+	209904.i	−0.0790531	+	0.136924i
$299$	−1.22640e6	−	2.12419e6i	−0.793331	−	1.37409i
$300$	−628960.			−0.403478
$301$		0			0
$302$	−497792.			−0.314073
$303$	−496020.	−	859132.i	−0.310379	−	0.537593i
$304$	60160.0	−	104200.i	0.0373357	−	0.0646673i
$305$	−1.02799e6	+	1.78053e6i	−0.632762	+	1.09598i
$306$	−416988.	−	722244.i	−0.254577	−	0.440941i
$307$	989098.			0.598954			0.299477	−	0.954104i	$-0.403188\pi$
$307$	989098.			0.598954			0.299477	+	0.954104i	$0.403188\pi$
$308$		0			0
$309$	−1.31644e6			−0.784341
$310$	−1.23850e6	−	2.14514e6i	−0.731965	−	1.26780i
$311$	−1.11025e6	+	1.92301e6i	−0.650909	+	1.12741i	0.331993	+	0.943282i	$0.392279\pi$
$311$	−1.11025e6	+	1.92301e6i	−0.650909	+	1.12741i	−0.982903	+	0.184126i	$0.941054\pi$
$312$	186880.	−	323686.i	0.108687	−	0.188251i
$313$	1.16504e6	+	2.01791e6i	0.672171	+	1.16423i	0.977287	+	0.211919i	$0.0679713\pi$
$313$	1.16504e6	+	2.01791e6i	0.672171	+	1.16423i	−0.305116	+	0.952315i	$0.598695\pi$
$314$	304160.			0.174092
$315$		0			0
$316$	685952.			0.386435
$317$	−213771.	−	370262.i	−0.119481	−	0.206948i	0.800081	−	0.599892i	$-0.204790\pi$
$317$	−213771.	−	370262.i	−0.119481	−	0.206948i	−0.919562	+	0.392944i	$0.871457\pi$
$318$	744840.	−	1.29010e6i	0.413043	−	0.715411i
$319$	817488.	−	1.41593e6i	0.449785	−	0.779050i
$320$	172032.	+	297968.i	0.0939149	+	0.162665i
$321$	−488520.			−0.264618
$322$		0			0
$323$	−685260.			−0.365468
$324$	30808.0	+	53361.0i	0.0163043	+	0.0282398i
$325$	1.14785e6	−	1.98814e6i	0.602806	−	1.04409i
$326$	248512.	−	430435.i	0.129510	−	0.224318i
$327$	−281870.	−	488213.i	−0.145774	−	0.252488i
$328$	398208.			0.204374
$329$		0			0
$330$	1.12896e6			0.570681
$331$	198308.	+	343480.i	0.0994879	+	0.172318i	0.911473	−	0.411360i	$-0.134946\pi$
$331$	198308.	+	343480.i	0.0994879	+	0.172318i	−0.811985	+	0.583678i	$0.801613\pi$
$332$	−281616.	+	487773.i	−0.140221	+	0.242869i
$333$	1.02460e6	−	1.77465e6i	0.506339	−	0.877005i
$334$	144840.	+	250870.i	0.0710432	+	0.123050i
$335$	1.46597e6			0.713695
$336$		0			0
$337$	−3.21819e6			−1.54361			−0.771805	−	0.635860i	$-0.780646\pi$
$337$	−3.21819e6			−1.54361			−0.771805	+	0.635860i	$0.780646\pi$
$338$	−60474.0	−	104744.i	−0.0287923	−	0.0498698i
$339$	43710.0	−	75707.9i	0.0206577	−	0.0357802i
$340$	979776.	−	1.69702e6i	0.459652	−	0.796141i
$341$	1.23850e6	+	2.14514e6i	0.576778	+	0.999009i
$342$	−268840.			−0.124288
$343$		0			0
$344$	−237056.			−0.108008
$345$	1.76400e6	+	3.05534e6i	0.797904	+	1.38201i
$346$	883104.	−	1.52958e6i	0.396572	−	0.686882i
$347$	−1.39009e6	+	2.40771e6i	−0.619755	+	1.07345i	0.369776	+	0.929121i	$0.379435\pi$
$347$	−1.39009e6	+	2.40771e6i	−0.619755	+	1.07345i	−0.989530	+	0.144326i	$0.953899\pi$
$348$	389280.	+	674253.i	0.172311	+	0.298452i
$349$	338800.			0.148895			0.0744475	−	0.997225i	$-0.476281\pi$
$349$	338800.			0.148895			0.0744475	+	0.997225i	$0.476281\pi$
$350$		0			0
$351$	−2.25424e6			−0.976635
$352$	−172032.	−	297968.i	−0.0740036	−	0.128178i
$353$	−181023.	+	313541.i	−0.0773209	+	0.133924i	−0.902093	−	0.431541i	$-0.857970\pi$
$353$	−181023.	+	313541.i	−0.0773209	+	0.133924i	0.824772	+	0.565465i	$0.191303\pi$
$354$	686040.	−	1.18826e6i	0.290965	−	0.503967i
$355$	1.18541e6	+	2.05319e6i	0.499226	+	0.864684i
$356$	−427680.			−0.178852
$357$		0			0
$358$	42768.0			0.0176365
$359$	−438264.	−	759096.i	−0.179473	−	0.310857i	0.762227	−	0.647310i	$-0.224106\pi$
$359$	−438264.	−	759096.i	−0.179473	−	0.310857i	−0.941700	+	0.336453i	$0.890773\pi$
$360$	384384.	−	665773.i	0.156318	−	0.270751i
$361$	1.12760e6	−	1.95306e6i	0.455394	−	0.788765i
$362$	1.09213e6	+	1.89162e6i	0.438028	+	0.758687i
$363$	481550.			0.191812
$364$		0			0
$365$	302568.			0.118875
$366$	489520.	+	847874.i	0.191015	+	0.330848i
$367$	1.49031e6	−	2.58129e6i	0.577578	−	1.00039i	−0.418178	−	0.908365i	$-0.637331\pi$
$367$	1.49031e6	−	2.58129e6i	0.577578	−	1.00039i	0.995756	−	0.0920298i	$-0.0293355\pi$
$368$	537600.	−	931151.i	0.206938	−	0.358427i
$369$	−444873.	−	770543.i	−0.170087	−	0.294599i
$370$	4.81488e6			1.82844
$371$		0			0
$372$	−1.17952e6			−0.441924
$373$	−1.95721e6	−	3.38998e6i	−0.728391	−	1.26161i	−0.957563	−	0.288225i	$-0.906935\pi$
$373$	−1.95721e6	−	3.38998e6i	−0.728391	−	1.26161i	0.229172	−	0.973386i	$-0.426398\pi$
$374$	−979776.	+	1.69702e6i	−0.362199	+	0.627348i
$375$	−338520.	+	586334.i	−0.124310	+	0.215311i
$376$	57984.0	+	100431.i	0.0211514	+	0.0366353i
$377$	−2.84174e6			−1.02975
$378$		0			0
$379$	3.60661e6			1.28974			0.644868	−	0.764294i	$-0.276912\pi$
$379$	3.60661e6			1.28974			0.644868	+	0.764294i	$0.276912\pi$
$380$	−315840.	−	547051.i	−0.112204	−	0.194343i
$381$	1.57996e6	−	2.73657e6i	0.557614	−	0.965816i
$382$	−1.15195e6	+	1.99524e6i	−0.403902	+	0.699579i
$383$	−1.33322e6	−	2.30920e6i	−0.464413	−	0.804387i	0.534762	−	0.845003i	$-0.320401\pi$
$383$	−1.33322e6	−	2.30920e6i	−0.464413	−	0.804387i	−0.999175	+	0.0406161i	$0.987068\pi$
$384$	163840.			0.0567012
$385$		0			0
$386$	1.65575e6			0.565623
$387$	264836.	+	458709.i	0.0898876	+	0.155690i
$388$	−135824.	+	235254.i	−0.0458033	+	0.0793337i
$389$	106683.	−	184780.i	0.0357455	−	0.0619130i	−0.847599	−	0.530637i	$-0.821953\pi$
$389$	106683.	−	184780.i	0.0357455	−	0.0619130i	0.883345	+	0.468724i	$0.155286\pi$
$390$	−981120.	−	1.69935e6i	−0.326633	−	0.565746i
$391$	−6.12360e6			−2.02565
$392$		0			0
$393$	−246660.			−0.0805596
$394$	−989892.	−	1.71454e6i	−0.321253	−	0.556427i
$395$	1.80062e6	−	3.11877e6i	0.580671	−	1.00575i
$396$	−384384.	+	665773.i	−0.123176	+	0.213348i
$397$	−2.04704e6	−	3.54558e6i	−0.651854	−	1.12904i	−0.982673	−	0.185349i	$-0.940658\pi$
$397$	−2.04704e6	−	3.54558e6i	−0.651854	−	1.12904i	0.330819	−	0.943694i	$-0.392675\pi$
$398$	2.08146e6			0.658657
$399$		0			0
$400$	1.00634e6			0.314480
$401$	−471183.	−	816113.i	−0.146328	−	0.253448i	0.783539	−	0.621342i	$-0.213412\pi$
$401$	−471183.	−	816113.i	−0.146328	−	0.253448i	−0.929868	+	0.367894i	$0.880079\pi$
$402$	349040.	−	604555.i	0.107723	−	0.186582i
$403$	2.15262e6	−	3.72845e6i	0.660246	−	1.14358i
$404$	793632.	+	1.37461e6i	0.241917	+	0.419012i
$405$	323484.			0.0979976
$406$		0			0
$407$	−4.81488e6			−1.44079
$408$	−466560.	−	808106.i	−0.138758	−	0.240335i
$409$	−2.42280e6	+	4.19642e6i	−0.716160	+	1.24043i	0.246350	+	0.969181i	$0.420769\pi$
$409$	−2.42280e6	+	4.19642e6i	−0.716160	+	1.24043i	−0.962510	+	0.271245i	$0.912565\pi$
$410$	1.04530e6	−	1.81051e6i	0.307100	−	0.531913i
$411$	1.51617e6	+	2.62608e6i	0.442734	+	0.766839i
$412$	2.10630e6			0.611333
$413$		0			0
$414$	−2.40240e6			−0.688881
$415$	1.47848e6	+	2.56081e6i	0.421402	+	0.729889i
$416$	−299008.	+	517897.i	−0.0847129	+	0.146727i
$417$	−1.25293e6	+	2.17014e6i	−0.352847	+	0.611149i
$418$	315840.	+	547051.i	0.0884151	+	0.153139i
$419$	1.73485e6			0.482754			0.241377	−	0.970431i	$-0.422401\pi$
$419$	1.73485e6			0.482754			0.241377	+	0.970431i	$0.422401\pi$
$420$		0			0
$421$	−1.65145e6			−0.454109			−0.227055	−	0.973882i	$-0.572910\pi$
$421$	−1.65145e6			−0.454109			−0.227055	+	0.973882i	$0.572910\pi$
$422$	366568.	+	634914.i	0.100201	+	0.173554i
$423$	129558.	−	224401.i	0.0352057	−	0.0609781i
$424$	−1.19174e6	+	2.06416e6i	−0.321935	+	0.557608i
$425$	−2.86570e6	−	4.96354e6i	−0.769588	−	1.33297i
$426$	1.12896e6			0.301408
$427$		0			0
$428$	781632.			0.206250
$429$	981120.	+	1.69935e6i	0.257382	+	0.445799i
$430$	−622272.	+	1.07781e6i	−0.162296	+	0.281106i
$431$	−2.07180e6	+	3.58846e6i	−0.537223	+	0.930498i	0.461829	+	0.886969i	$0.347193\pi$
$431$	−2.07180e6	+	3.58846e6i	−0.537223	+	0.930498i	−0.999052	+	0.0435287i	$0.986140\pi$
$432$	−494080.	−	855772.i	−0.127376	−	0.220622i
$433$	3.03966e6			0.779121			0.389561	−	0.921001i	$-0.372627\pi$
$433$	3.03966e6			0.779121			0.389561	+	0.921001i	$0.372627\pi$
$434$		0			0
$435$	4.08744e6			1.03569
$436$	450992.	+	781141.i	0.113619	+	0.196795i
$437$	−987000.	+	1.70953e6i	−0.247237	+	0.428227i
$438$	72040.0	−	124777.i	0.0179427	−	0.0310777i
$439$	1.27136e6	+	2.20205e6i	0.314852	+	0.545339i	0.979406	−	0.201901i	$-0.0647119\pi$
$439$	1.27136e6	+	2.20205e6i	0.314852	+	0.545339i	−0.664554	+	0.747240i	$0.731379\pi$
$440$	−1.80634e6			−0.444802
$441$		0			0
$442$	3.40589e6			0.829229
$443$	1.21605e6	+	2.10626e6i	0.294403	+	0.509921i	0.974846	−	0.222880i	$-0.0715459\pi$
$443$	1.21605e6	+	2.10626e6i	0.294403	+	0.509921i	−0.680443	+	0.732801i	$0.738213\pi$
$444$	1.14640e6	−	1.98562e6i	0.275981	−	0.478013i
$445$	−1.12266e6	+	1.94450e6i	−0.268750	+	0.465488i
$446$	2.55493e6	+	4.42527e6i	0.608193	+	1.05342i
$447$	605940.			0.143437
$448$		0			0
$449$	1.82853e6			0.428042			0.214021	−	0.976829i	$-0.431344\pi$
$449$	1.82853e6			0.428042			0.214021	+	0.976829i	$0.431344\pi$
$450$	−1.12427e6	−	1.94729e6i	−0.261721	−	0.453313i
$451$	−1.04530e6	+	1.81051e6i	−0.241990	+	0.419139i
$452$	−69936.0	+	121133.i	−0.0161011	+	0.0278879i
$453$	622240.	+	1.07775e6i	0.142466	+	0.246759i
$454$	−5.15057e6			−1.17278
$455$		0			0
$456$	−300800.			−0.0677432
$457$	−790315.	−	1.36887e6i	−0.177015	−	0.306599i	0.763842	−	0.645403i	$-0.223311\pi$
$457$	−790315.	−	1.36887e6i	−0.177015	−	0.306599i	−0.940857	+	0.338805i	$0.889977\pi$
$458$	−701872.	+	1.21568e6i	−0.156349	+	0.270804i
$459$	−2.81394e6	+	4.87389e6i	−0.623423	+	1.07980i
$460$	−2.82240e6	−	4.88854e6i	−0.621905	−	1.07717i
$461$	−5.09604e6			−1.11681			−0.558407	−	0.829567i	$-0.688587\pi$
$461$	−5.09604e6			−1.11681			−0.558407	+	0.829567i	$0.688587\pi$
$462$		0			0
$463$	−7.02338e6			−1.52263			−0.761313	−	0.648384i	$-0.775445\pi$
$463$	−7.02338e6			−1.52263			−0.761313	+	0.648384i	$0.775445\pi$
$464$	−622848.	−	1.07880e6i	−0.134303	−	0.232620i
$465$	−3.09624e6	+	5.36284e6i	−0.664052	+	1.15017i
$466$	1.67231e6	−	2.89652e6i	0.356740	−	0.617891i
$467$	−2.12422e6	−	3.67927e6i	−0.450722	−	0.780673i	0.547709	−	0.836669i	$-0.315500\pi$
$467$	−2.12422e6	−	3.67927e6i	−0.450722	−	0.780673i	−0.998431	+	0.0559960i	$0.982167\pi$
$468$	1.33619e6			0.282003
$469$		0			0
$470$	608832.			0.127131
$471$	−380200.	−	658526.i	−0.0789696	−	0.136779i
$472$	−1.09766e6	+	1.90121e6i	−0.226785	+	0.392803i
$473$	622272.	−	1.07781e6i	0.127887	−	0.221507i
$474$	−857440.	−	1.48513e6i	−0.175290	−	0.303612i
$475$	−1.84757e6			−0.375722
$476$		0			0
$477$	5.32561e6			1.07170
$478$	1.54867e6	+	2.68238e6i	0.310020	+	0.536970i
$479$	279642.	−	484354.i	0.0556883	−	0.0964549i	−0.836837	−	0.547452i	$-0.815598\pi$
$479$	279642.	−	484354.i	0.0556883	−	0.0964549i	0.892526	+	0.450997i	$0.148931\pi$
$480$	430080.	−	744920.i	0.0852013	−	0.147573i
$481$	4.18436e6	+	7.24752e6i	0.824644	+	1.42832i
$482$	−4.61140e6			−0.904097
$483$		0			0
$484$	−770480.			−0.149502
$485$	713076.	+	1.23508e6i	0.137652	+	0.238420i
$486$	−1.79894e6	+	3.11586e6i	−0.345482	+	0.598393i
$487$	660284.	−	1.14365e6i	0.126156	−	0.218509i	−0.796028	−	0.605260i	$-0.793069\pi$
$487$	660284.	−	1.14365e6i	0.126156	−	0.218509i	0.922184	+	0.386751i	$0.126403\pi$
$488$	−783232.	−	1.35660e6i	−0.148882	−	0.257870i
$489$	−1.24256e6			−0.234988
$490$		0			0
$491$	6.27193e6			1.17408			0.587040	−	0.809558i	$-0.300293\pi$
$491$	6.27193e6			1.17408			0.587040	+	0.809558i	$0.300293\pi$
$492$	−497760.	−	862146.i	−0.0927059	−	0.160571i
$493$	−3.54731e6	+	6.14413e6i	−0.657328	+	1.13853i
$494$	548960.	−	950827.i	0.101210	−	0.175301i
$495$	2.01802e6	+	3.49531e6i	0.370179	+	0.641169i
$496$	1.88723e6			0.344446
$497$		0			0
$498$	1.40808e6			0.254422
$499$	1.96893e6	+	3.41028e6i	0.353979	+	0.613110i	0.986943	−	0.161071i	$-0.0514949\pi$
$499$	1.96893e6	+	3.41028e6i	0.353979	+	0.613110i	−0.632963	+	0.774182i	$0.718162\pi$
$500$	541632.	−	938134.i	0.0968901	−	0.167819i
$501$	362100.	−	627176.i	0.0644517	−	0.111634i
$502$	−2.71602e6	−	4.70428e6i	−0.481032	−	0.833171i
$503$	7.59830e6			1.33905			0.669525	−	0.742790i	$-0.266498\pi$
$503$	7.59830e6			1.33905			0.669525	+	0.742790i	$0.266498\pi$
$504$		0			0
$505$	8.33314e6			1.45405
$506$	2.82240e6	+	4.88854e6i	0.490052	+	0.848795i
$507$	−151185.	+	261860.i	−0.0261209	+	0.0452428i
$508$	−2.52794e6	+	4.37851e6i	−0.434617	+	0.752779i
$509$	−3.91332e6	−	6.77807e6i	−0.669501	−	1.15961i	−0.978044	−	0.208399i	$-0.933175\pi$
$509$	−3.91332e6	−	6.77807e6i	−0.669501	−	1.15961i	0.308543	−	0.951210i	$-0.400158\pi$
$510$	−4.89888e6			−0.834010
$511$		0			0
$512$	−262144.			−0.0441942
$513$	907100.	+	1.57114e6i	0.152181	+	0.263586i
$514$	635484.	−	1.10069e6i	0.106095	−	0.183763i
$515$	5.52905e6	−	9.57659e6i	0.918612	−	1.59108i
$516$	296320.	+	513241.i	0.0489933	+	0.0848589i
$517$	−608832.			−0.100178
$518$		0			0
$519$	−4.41552e6			−0.719554
$520$	1.56979e6	+	2.71896e6i	0.254586	+	0.440955i
$521$	4.47227e6	−	7.74620e6i	0.721828	−	1.25024i	−0.238438	−	0.971158i	$-0.576635\pi$
$521$	4.47227e6	−	7.74620e6i	0.721828	−	1.25024i	0.960266	−	0.279085i	$-0.0900312\pi$
$522$	−1.39168e6	+	2.41045e6i	−0.223543	+	0.387189i
$523$	2.03740e6	+	3.52889e6i	0.325704	+	0.564135i	0.981655	−	0.190668i	$-0.0610655\pi$
$523$	2.03740e6	+	3.52889e6i	0.325704	+	0.564135i	−0.655951	+	0.754804i	$0.727732\pi$
$524$	394656.			0.0627900
$525$		0			0
$526$	−4.20403e6			−0.662524
$527$	−5.37419e6	−	9.30837e6i	−0.842920	−	1.45998i
$528$	−430080.	+	744920.i	−0.0671374	+	0.116285i
$529$	−5.60183e6	+	9.70265e6i	−0.870343	+	1.50748i
$530$	6.25666e6	+	1.08368e7i	0.967504	+	1.67577i
$531$	4.90519e6			0.754952
$532$		0			0
$533$	3.63365e6			0.554019
$534$	534600.	+	925954.i	0.0811289	+	0.140519i
$535$	2.05178e6	−	3.55379e6i	0.309918	−	0.536794i
$536$	−558464.	+	967288.i	−0.0839621	+	0.145427i
$537$	−53460.0	−	92595.4i	−0.00800006	−	0.0138565i
$538$	4.75834e6			0.708760
$539$		0			0
$540$	−5.18784e6			−0.765600
$541$	5.93379e6	+	1.02776e7i	0.871644	+	1.50973i	0.860296	+	0.509795i	$0.170279\pi$
$541$	5.93379e6	+	1.02776e7i	0.871644	+	1.50973i	0.0113479	+	0.999936i	$0.496388\pi$
$542$	2.86016e6	−	4.95394e6i	0.418208	−	0.724357i
$543$	2.73032e6	−	4.72905e6i	0.397387	−	0.688295i
$544$	746496.	+	1.29297e6i	0.108151	+	0.187323i
$545$	4.73542e6			0.682915
$546$		0			0
$547$	−5.37801e6			−0.768516			−0.384258	−	0.923226i	$-0.625543\pi$
$547$	−5.37801e6			−0.768516			−0.384258	+	0.923226i	$0.625543\pi$
$548$	−2.42587e6	−	4.20173e6i	−0.345077	−	0.597692i
$549$	−1.75003e6	+	3.03115e6i	−0.247808	+	0.429216i
$550$	−2.64163e6	+	4.57544e6i	−0.372362	+	0.644950i
$551$	1.14351e6	+	1.98062e6i	0.160458	+	0.277921i
$552$	−2.68800e6			−0.375475
$553$		0			0
$554$	−253208.			−0.0350512
$555$	−6.01860e6	−	1.04245e7i	−0.829398	−	1.43656i
$556$	2.00469e6	−	3.47222e6i	0.275017	−	0.476344i
$557$	2.82439e6	−	4.89199e6i	0.385733	−	0.668109i	−0.606138	−	0.795360i	$-0.707282\pi$
$557$	2.82439e6	−	4.89199e6i	0.385733	−	0.668109i	0.991871	+	0.127251i	$0.0406153\pi$
$558$	−2.10839e6	−	3.65184e6i	−0.286659	−	0.496508i
$559$	−2.16314e6			−0.292789
$560$		0			0
$561$	4.89888e6			0.657188
$562$	−993228.	−	1.72032e6i	−0.132650	−	0.229757i
$563$	2.28204e6	−	3.95260e6i	0.303425	−	0.525548i	−0.673484	−	0.739202i	$-0.735203\pi$
$563$	2.28204e6	−	3.95260e6i	0.303425	−	0.525548i	0.976909	+	0.213654i	$0.0685364\pi$
$564$	144960.	−	251078.i	0.0191889	−	0.0332362i
$565$	367164.	+	635947.i	0.0483881	+	0.0838107i
$566$	−4.63367e6			−0.607973
$567$		0			0
$568$	−1.80634e6			−0.234924
$569$	−4.00083e6	−	6.92964e6i	−0.518047	−	0.897284i	−0.999780	−	0.0209657i	$-0.993326\pi$
$569$	−4.00083e6	−	6.92964e6i	−0.518047	−	0.897284i	0.481733	−	0.876318i	$-0.340007\pi$
$570$	−789600.	+	1.36763e6i	−0.101793	+	0.176311i
$571$	6.85818e6	−	1.18787e7i	0.880275	−	1.52468i	0.0292397	−	0.999572i	$-0.490691\pi$
$571$	6.85818e6	−	1.18787e7i	0.880275	−	1.52468i	0.851035	−	0.525109i	$-0.175975\pi$
$572$	−1.56979e6	−	2.71896e6i	−0.200610	−	0.347466i
$573$	5.75976e6			0.732855
$574$		0			0
$575$	−1.65102e7			−2.08249
$576$	292864.	+	507255.i	0.0367798	+	0.0637045i
$577$	3.04898e6	−	5.28100e6i	0.381255	−	0.660353i	−0.609987	−	0.792412i	$-0.708825\pi$
$577$	3.04898e6	−	5.28100e6i	0.381255	−	0.660353i	0.991242	+	0.132058i	$0.0421586\pi$
$578$	1.41181e6	−	2.44533e6i	0.175775	−	0.304452i
$579$	−2.06969e6	−	3.58481e6i	−0.256572	−	0.444395i
$580$	−6.53990e6			−0.807238
$581$		0			0
$582$	679120.			0.0831073
$583$	−6.25666e6	−	1.08368e7i	−0.762379	−	1.32048i
$584$	−115264.	+	199643.i	−0.0139850	+	0.0242227i
$585$	3.50750e6	−	6.07518e6i	0.423749	−	0.733954i
$586$	−2.87772e6	−	4.98436e6i	−0.346182	−	0.599605i
$587$	8.08462e6			0.968422			0.484211	−	0.874951i	$-0.339107\pi$
$587$	8.08462e6			0.968422			0.484211	+	0.874951i	$0.339107\pi$
$588$		0			0
$589$	−3.46484e6			−0.411524
$590$	5.76274e6	+	9.98135e6i	0.681552	+	1.18048i
$591$	−2.47473e6	+	4.28636e6i	−0.291447	+	0.504800i
$592$	−1.83424e6	+	3.17700e6i	−0.215106	+	0.372574i
$593$	707877.	+	1.22608e6i	0.0826649	+	0.143180i	0.904394	−	0.426699i	$-0.140324\pi$
$593$	707877.	+	1.22608e6i	0.0826649	+	0.143180i	−0.821729	+	0.569879i	$0.806990\pi$
$594$	5.18784e6			0.603282
$595$		0			0
$596$	−969504.			−0.111798
$597$	−2.60182e6	−	4.50648e6i	−0.298773	−	0.517490i
$598$	4.90560e6	−	8.49675e6i	0.560969	−	0.971628i
$599$	−4.37730e6	+	7.58171e6i	−0.498470	+	0.863376i	−0.999998	−	0.00176549i	$-0.999438\pi$
$599$	−4.37730e6	+	7.58171e6i	−0.498470	+	0.863376i	0.501528	+	0.865141i	$0.332771\pi$
$600$	−1.25792e6	−	2.17878e6i	−0.142651	−	0.247079i
$601$	−8.70276e6			−0.982813			−0.491407	−	0.870930i	$-0.663517\pi$
$601$	−8.70276e6			−0.982813			−0.491407	+	0.870930i	$0.663517\pi$
$602$		0			0
$603$	2.49564e6			0.279504
$604$	−995584.	−	1.72440e6i	−0.111042	−	0.192330i
$605$	−2.02251e6	+	3.50309e6i	−0.224648	+	0.389101i
$606$	1.98408e6	−	3.43653e6i	0.219471	−	0.380135i
$607$	−8.47890e6	−	1.46859e7i	−0.934045	−	1.61781i	−0.776329	−	0.630328i	$-0.782920\pi$
$607$	−8.47890e6	−	1.46859e7i	−0.934045	−	1.61781i	−0.157716	−	0.987485i	$-0.550413\pi$
$608$	481280.			0.0528006
$609$		0			0
$610$	−8.22394e6			−0.894860
$611$	529104.	+	916435.i	0.0573374	+	0.0993113i
$612$	1.66795e6	−	2.88898e6i	0.180013	−	0.311792i
$613$	−8.83717e6	+	1.53064e7i	−0.949866	+	1.64522i	−0.204163	+	0.978937i	$0.565447\pi$
$613$	−8.83717e6	+	1.53064e7i	−0.949866	+	1.64522i	−0.745703	+	0.666279i	$0.767886\pi$
$614$	1.97820e6	+	3.42634e6i	0.211762	+	0.366783i
$615$	−5.22648e6			−0.557213
$616$		0			0
$617$	−9.70636e6			−1.02646			−0.513232	−	0.858250i	$-0.671552\pi$
$617$	−9.70636e6			−1.02646			−0.513232	+	0.858250i	$0.671552\pi$
$618$	−2.63288e6	−	4.56028e6i	−0.277306	−	0.480309i
$619$	7.43696e6	−	1.28812e7i	0.780133	−	1.35123i	−0.151731	−	0.988422i	$-0.548485\pi$
$619$	7.43696e6	−	1.28812e7i	0.780133	−	1.35123i	0.931864	−	0.362808i	$-0.118182\pi$
$620$	4.95398e6	−	8.58055e6i	0.517577	−	0.896471i
$621$	8.10600e6	+	1.40400e7i	0.843485	+	1.46096i
$622$	−8.88202e6			−0.920525
$623$		0			0
$624$	1.49504e6			0.153706
$625$	3.29862e6	+	5.71338e6i	0.337779	+	0.585050i
$626$	−4.66016e6	+	8.07163e6i	−0.475297	+	0.823238i
$627$	789600.	−	1.36763e6i	0.0802118	−	0.138931i
$628$	608320.	+	1.05364e6i	0.0615507	+	0.106609i
$629$	2.08931e7			2.10561
$630$		0			0
$631$	1.26353e7			1.26331			0.631656	−	0.775248i	$-0.282375\pi$
$631$	1.26353e7			1.26331			0.631656	+	0.775248i	$0.282375\pi$
$632$	1.37190e6	+	2.37621e6i	0.136625	+	0.236642i
$633$	916420.	−	1.58729e6i	0.0909045	−	0.157451i
$634$	855084.	−	1.48105e6i	0.0844862	−	0.146334i
$635$	1.32717e7	+	2.29872e7i	1.30614	+	2.26231i
$636$	5.95872e6			0.584131
$637$		0			0
$638$	6.53990e6			0.636092
$639$	2.01802e6	+	3.49531e6i	0.195512	+	0.338636i
$640$	−688128.	+	1.19187e6i	−0.0664078	+	0.115022i
$641$	−3.11699e6	+	5.39879e6i	−0.299634	+	0.518981i	−0.976052	−	0.217537i	$-0.930198\pi$
$641$	−3.11699e6	+	5.39879e6i	−0.299634	+	0.518981i	0.676419	+	0.736517i	$0.263531\pi$
$642$	−977040.	−	1.69228e6i	−0.0935567	−	0.162045i
$643$	−1.06874e7			−1.01940			−0.509701	−	0.860352i	$-0.670244\pi$
$643$	−1.06874e7			−1.01940			−0.509701	+	0.860352i	$0.670244\pi$
$644$		0			0
$645$	3.11136e6			0.294477
$646$	−1.37052e6	−	2.37381e6i	−0.129212	−	0.223802i
$647$	9.16292e6	−	1.58706e7i	0.860544	−	1.49051i	−0.0108606	−	0.999941i	$-0.503457\pi$
$647$	9.16292e6	−	1.58706e7i	0.860544	−	1.49051i	0.871405	−	0.490565i	$-0.163210\pi$
$648$	−123232.	+	213444.i	−0.0115288	+	0.0199686i
$649$	−5.76274e6	−	9.98135e6i	−0.537053	−	0.930203i
$650$	9.18282e6			0.852496
$651$		0			0
$652$	1.98810e6			0.183155
$653$	3.64428e6	+	6.31208e6i	0.334448	+	0.579282i	0.983379	−	0.181566i	$-0.0581167\pi$
$653$	3.64428e6	+	6.31208e6i	0.334448	+	0.579282i	−0.648930	+	0.760848i	$0.724783\pi$
$654$	1.12748e6	−	1.95285e6i	0.103078	−	0.178536i
$655$	1.03597e6	−	1.79436e6i	0.0943506	−	0.163420i
$656$	796416.	+	1.37943e6i	0.0722571	+	0.125153i
$657$	515086.			0.0465550
$658$		0			0
$659$	4.54337e6			0.407534			0.203767	−	0.979019i	$-0.434681\pi$
$659$	4.54337e6			0.407534			0.203767	+	0.979019i	$0.434681\pi$
$660$	2.25792e6	+	3.91083e6i	0.201766	+	0.349470i
$661$	−1.05010e7	+	1.81883e7i	−0.934821	+	1.61916i	−0.159868	+	0.987138i	$0.551107\pi$
$661$	−1.05010e7	+	1.81883e7i	−0.934821	+	1.61916i	−0.774953	+	0.632019i	$0.782226\pi$
$662$	−793232.	+	1.37392e6i	−0.0703486	+	0.121847i
$663$	−4.25736e6	−	7.37396e6i	−0.376146	−	0.651504i
$664$	−2.25293e6			−0.198302
$665$		0			0
$666$	8.19676e6			0.716072
$667$	1.02186e7	+	1.76991e7i	0.889358	+	1.54041i
$668$	−579360.	+	1.00348e6i	−0.0502351	+	0.0870098i
$669$	6.38732e6	−	1.10632e7i	0.551764	−	0.955683i
$670$	2.93194e6	+	5.07826e6i	0.252329	+	0.437047i
$671$	8.22394e6			0.705137
$672$		0			0
$673$	3.46923e6			0.295253			0.147627	−	0.989043i	$-0.452837\pi$
$673$	3.46923e6			0.295253			0.147627	+	0.989043i	$0.452837\pi$
$674$	−6.43639e6	−	1.11482e7i	−0.545748	−	0.945264i
$675$	−7.58683e6	+	1.31408e7i	−0.640916	+	1.11010i
$676$	241896.	−	418976.i	0.0203593	−	0.0352633i
$677$	−9.04582e6	−	1.56678e7i	−0.758536	−	1.31382i	−0.943597	−	0.331096i	$-0.892582\pi$
$677$	−9.04582e6	−	1.56678e7i	−0.758536	−	1.31382i	0.185061	−	0.982727i	$-0.440752\pi$
$678$	349680.			0.0292144
$679$		0			0
$680$	7.83821e6			0.650047
$681$	6.43821e6	+	1.11513e7i	0.531983	+	0.921421i
$682$	−4.95398e6	+	8.58055e6i	−0.407844	+	0.706406i
$683$	−2.33876e6	+	4.05085e6i	−0.191838	+	0.332272i	−0.945859	−	0.324577i	$-0.894778\pi$
$683$	−2.33876e6	+	4.05085e6i	−0.191838	+	0.332272i	0.754022	+	0.656850i	$0.228111\pi$
$684$	−537680.	−	931289.i	−0.0439424	−	0.0761104i
$685$	−2.54717e7			−2.07411
$686$		0			0
$687$	3.50936e6			0.283685
$688$	−474112.	−	821186.i	−0.0381865	−	0.0661410i
$689$	−1.08747e7	+	1.88355e7i	−0.872706	+	1.51157i
$690$	−7.05600e6	+	1.22214e7i	−0.564204	+	0.977229i
$691$	8.44802e6	+	1.46324e7i	0.673069	+	1.16579i	0.977029	+	0.213105i	$0.0683578\pi$
$691$	8.44802e6	+	1.46324e7i	0.673069	+	1.16579i	−0.303960	+	0.952685i	$0.598309\pi$
$692$	7.06483e6			0.560837
$693$		0			0
$694$	−1.11207e7			−0.876466
$695$	−1.05246e7	−	1.82292e7i	−0.826502	−	1.43154i
$696$	−1.55712e6	+	2.69701e6i	−0.121843	+	0.211037i
$697$	4.53584e6	−	7.85630e6i	0.353652	−	0.612542i
$698$	677600.	+	1.17364e6i	0.0526423	+	0.0911791i
$699$	−8.36154e6			−0.647282
$700$		0			0
$701$	2.40964e6			0.185207			0.0926035	−	0.995703i	$-0.470481\pi$
$701$	2.40964e6			0.185207			0.0926035	+	0.995703i	$0.470481\pi$
$702$	−4.50848e6	−	7.80892e6i	−0.345293	−	0.598064i
$703$	3.36755e6	−	5.83277e6i	0.256996	−	0.445129i
$704$	688128.	−	1.19187e6i	0.0523284	−	0.0906355i
$705$	−761040.	−	1.31816e6i	−0.0576680	−	0.0998839i
$706$	−1.44818e6			−0.109348
$707$		0			0
$708$	5.48832e6			0.411487
$709$	2.88505e6	+	4.99705e6i	0.215545	+	0.373335i	0.953441	−	0.301580i	$-0.0975139\pi$
$709$	2.88505e6	+	4.99705e6i	0.215545	+	0.373335i	−0.737896	+	0.674914i	$0.764181\pi$
$710$	−4.74163e6	+	8.21275e6i	−0.353006	+	0.611424i
$711$	3.06535e6	−	5.30934e6i	0.227408	−	0.393882i
$712$	−855360.	−	1.48153e6i	−0.0632338	−	0.109524i
$713$	−3.09624e7			−2.28092
$714$		0			0
$715$	−1.64828e7			−1.20578
$716$	85536.0	+	148153.i	0.00623543	+	0.0108001i
$717$	3.87168e6	−	6.70595e6i	0.281256	−	0.487149i
$718$	1.75306e6	−	3.03638e6i	0.126907	−	0.219809i
$719$	−7.18580e6	−	1.24462e7i	−0.518385	−	0.897870i	−0.999772	−	0.0213614i	$-0.993200\pi$
$719$	−7.18580e6	−	1.24462e7i	−0.518385	−	0.897870i	0.481386	−	0.876508i	$-0.340133\pi$
$720$	3.07507e6			0.221067
$721$		0			0
$722$	9.02080e6			0.644024
$723$	5.76425e6	+	9.98397e6i	0.410107	+	0.710326i
$724$	−4.36851e6	+	7.56648e6i	−0.309733	+	0.536473i
$725$	−9.56412e6	+	1.65655e7i	−0.675772	+	1.17047i
$726$	963100.	+	1.66814e6i	0.0678156	+	0.117460i
$727$	1.40705e7			0.987353			0.493676	−	0.869646i	$-0.335653\pi$
$727$	1.40705e7			0.987353			0.493676	+	0.869646i	$0.335653\pi$
$728$		0			0
$729$	9.93049e6			0.692073
$730$	605136.	+	1.04813e6i	0.0420287	+	0.0727958i
$731$	−2.70022e6	+	4.67691e6i	−0.186898	+	0.323717i
$732$	−1.95808e6	+	3.39149e6i	−0.135068	+	0.233945i
$733$	−1.87500e6	−	3.24760e6i	−0.128897	−	0.223256i	0.794353	−	0.607457i	$-0.207810\pi$
$733$	−1.87500e6	−	3.24760e6i	−0.128897	−	0.223256i	−0.923249	+	0.384201i	$0.874477\pi$
$734$	1.19225e7			0.816819
$735$		0			0
$736$	4.30080e6			0.292654
$737$	−2.93194e6	−	5.07826e6i	−0.198832	−	0.344387i
$738$	1.77949e6	−	3.08217e6i	0.120269	−	0.208313i
$739$	−1.30659e7	+	2.26308e7i	−0.880093	+	1.52437i	−0.0288556	+	0.999584i	$0.509186\pi$
$739$	−1.30659e7	+	2.26308e7i	−0.880093	+	1.52437i	−0.851237	+	0.524782i	$0.824147\pi$
$740$	9.62976e6	+	1.66792e7i	0.646452	+	1.11969i
$741$	−2.74480e6			−0.183639
$742$		0			0
$743$	−159072.			−0.0105711			−0.00528557	−	0.999986i	$-0.501682\pi$
$743$	−159072.			−0.0105711			−0.00528557	+	0.999986i	$0.501682\pi$
$744$	−2.35904e6	−	4.08598e6i	−0.156244	−	0.270622i
$745$	−2.54495e6	+	4.40798e6i	−0.167992	+	0.290970i
$746$	7.82883e6	−	1.35599e7i	0.515050	−	0.892093i
$747$	2.51694e6	+	4.35947e6i	0.165033	+	0.285846i
$748$	−7.83821e6			−0.512227
$749$		0			0
$750$	−2.70816e6			−0.175801
$751$	1.32655e7	+	2.29766e7i	0.858272	+	1.48657i	0.873576	+	0.486687i	$0.161795\pi$
$751$	1.32655e7	+	2.29766e7i	0.858272	+	1.48657i	−0.0153049	+	0.999883i	$0.504872\pi$
$752$	−231936.	+	401725.i	−0.0149563	+	0.0259050i
$753$	−6.79005e6	+	1.17607e7i	−0.436401	+	0.755868i
$754$	−5.68349e6	−	9.84409e6i	−0.364071	−	0.630590i
$755$	−1.04536e7			−0.667421
$756$		0			0
$757$	−1.52032e7			−0.964260			−0.482130	−	0.876100i	$-0.660137\pi$
$757$	−1.52032e7			−0.964260			−0.482130	+	0.876100i	$0.660137\pi$
$758$	7.21322e6	+	1.24937e7i	0.455991	+	0.789799i
$759$	7.05600e6	−	1.22214e7i	0.444584	−	0.770043i
$760$	1.26336e6	−	2.18820e6i	0.0793402	−	0.137421i
$761$	2.35690e6	+	4.08227e6i	0.147530	+	0.255529i	0.930314	−	0.366764i	$-0.119534\pi$
$761$	2.35690e6	+	4.08227e6i	0.147530	+	0.255529i	−0.782784	+	0.622293i	$0.786201\pi$
$762$	1.26397e7			0.788585
$763$		0			0
$764$	−9.21562e6			−0.571204
$765$	−8.75675e6	−	1.51671e7i	−0.540990	−	0.937022i
$766$	5.33287e6	−	9.23681e6i	0.328389	−	0.568787i
$767$	−1.00162e7	+	1.73485e7i	−0.614772	+	1.06482i
$768$	327680.	+	567558.i	0.0200469	+	0.0347222i
$769$	1.58977e6			0.0969434			0.0484717	−	0.998825i	$-0.484565\pi$
$769$	1.58977e6			0.0969434			0.0484717	+	0.998825i	$0.484565\pi$
$770$		0			0
$771$	−3.17742e6			−0.192504
$772$	3.31150e6	+	5.73569e6i	0.199978	+	0.346372i
$773$	−4.84547e6	+	8.39261e6i	−0.291667	+	0.505182i	−0.974204	−	0.225669i	$-0.927543\pi$
$773$	−4.84547e6	+	8.39261e6i	−0.291667	+	0.505182i	0.682537	+	0.730851i	$0.260877\pi$
$774$	−1.05934e6	+	1.83484e6i	−0.0635601	+	0.110089i
$775$	−1.44897e7	−	2.50968e7i	−0.866571	−	1.50094i
$776$	−1.08659e6			−0.0647757
$777$		0			0
$778$	853464.			0.0505518
$779$	−1.46217e6	−	2.53255e6i	−0.0863285	−	0.149525i
$780$	3.92448e6	−	6.79740e6i	0.230965	−	0.400043i
$781$	4.74163e6	−	8.21275e6i	0.278164	−	0.481793i
$782$	−1.22472e7	−	2.12128e7i	−0.716176	−	1.24045i
$783$	1.87828e7			1.09485
$784$		0			0
$785$	6.38736e6			0.369954
$786$	−493320.	−	854455.i	−0.0284821	−	0.0493325i
$787$	−785849.	+	1.36113e6i	−0.0452275	+	0.0783363i	−0.887753	−	0.460320i	$-0.847735\pi$
$787$	−785849.	+	1.36113e6i	−0.0452275	+	0.0783363i	0.842525	+	0.538656i	$0.181068\pi$
$788$	3.95957e6	−	6.85817e6i	0.227160	−	0.393453i
$789$	5.25504e6	+	9.10200e6i	0.300527	+	0.520528i
$790$	1.44050e7			0.821193
$791$		0			0
$792$	−3.07507e6			−0.174198
$793$	−7.14699e6	−	1.23790e7i	−0.403590	−	0.699038i
$794$	8.18816e6	−	1.41823e7i	0.460930	−	0.798354i
$795$	1.56416e7	−	2.70921e7i	0.877737	−	1.52029i
$796$	4.16291e6	+	7.21038e6i	0.232871	+	0.403344i
$797$	2.25298e6			0.125635			0.0628175	−	0.998025i	$-0.479991\pi$
$797$	2.25298e6			0.125635			0.0628175	+	0.998025i	$0.479991\pi$
$798$		0			0
$799$	2.64190e6			0.146403
$800$	2.01267e6	+	3.48605e6i	0.111185	+	0.192579i
$801$	−1.91120e6	+	3.31029e6i	−0.105250	+	0.182299i
$802$	1.88473e6	−	3.26445e6i	0.103470	−	0.179215i
$803$	−605136.	−	1.04813e6i	−0.0331180	−	0.0573621i
$804$	2.79232e6			0.152344
$805$		0			0
$806$	1.72210e7			0.933728
$807$	−5.94792e6	−	1.03021e7i	−0.321500	−	0.556855i
$808$	−3.17453e6	+	5.49844e6i	−0.171061	+	0.296286i
$809$	1.18969e7	−	2.06060e7i	0.639090	−	1.10694i	−0.346542	−	0.938034i	$-0.612644\pi$
$809$	1.18969e7	−	2.06060e7i	0.639090	−	1.10694i	0.985633	−	0.168903i	$-0.0540223\pi$
$810$	646968.	+	1.12058e6i	0.0346474	+	0.0600110i
$811$	−5.32300e6			−0.284187			−0.142093	−	0.989853i	$-0.545383\pi$
$811$	−5.32300e6			−0.284187			−0.142093	+	0.989853i	$0.545383\pi$
$812$		0			0
$813$	−1.43008e7			−0.758812
$814$	−9.62976e6	−	1.66792e7i	−0.509395	−	0.882298i
$815$	5.21875e6	−	9.03914e6i	0.275215	−	0.476687i
$816$	1.86624e6	−	3.23242e6i	0.0981165	−	0.169943i
$817$	870440.	+	1.50765e6i	0.0456230	+	0.0790213i
$818$	−1.93824e7			−1.01280
$819$		0			0
$820$	8.36237e6			0.434305
$821$	−7.44012e6	−	1.28867e7i	−0.385232	−	0.667241i	0.606569	−	0.795031i	$-0.292545\pi$
$821$	−7.44012e6	−	1.28867e7i	−0.385232	−	0.667241i	−0.991801	+	0.127789i	$0.959212\pi$
$822$	−6.06468e6	+	1.05043e7i	−0.313061	+	0.542237i
$823$	−1.00300e7	+	1.73725e7i	−0.516182	+	0.894054i	0.483641	+	0.875266i	$0.339314\pi$
$823$	−1.00300e7	+	1.73725e7i	−0.516182	+	0.894054i	−0.999824	+	0.0187873i	$0.994019\pi$
$824$	4.21261e6	+	7.29645e6i	0.216139	+	0.374364i
$825$	1.32082e7			0.675628
$826$		0			0
$827$	1.21539e7			0.617949			0.308975	−	0.951070i	$-0.400014\pi$
$827$	1.21539e7			0.617949			0.308975	+	0.951070i	$0.400014\pi$
$828$	−4.80480e6	−	8.32216e6i	−0.243556	−	0.421852i
$829$	1.60599e7	−	2.78165e7i	0.811625	−	1.40578i	−0.100101	−	0.994977i	$-0.531917\pi$
$829$	1.60599e7	−	2.78165e7i	0.811625	−	1.40578i	0.911726	−	0.410799i	$-0.134750\pi$
$830$	−5.91394e6	+	1.02432e7i	−0.297976	+	0.516110i
$831$	316510.	+	548211.i	0.0158996	+	0.0275388i
$832$	−2.39206e6			−0.119802
$833$		0			0
$834$	−1.00234e7			−0.499001
$835$	3.04164e6	+	5.26828e6i	0.150970	+	0.261488i
$836$	−1.26336e6	+	2.18820e6i	−0.0625189	+	0.108286i
$837$	−1.42280e7	+	2.46435e7i	−0.701987	+	1.21588i
$838$	3.46969e6	+	6.00968e6i	0.170679	+	0.295625i
$839$	1.01320e6			0.0496922			0.0248461	−	0.999691i	$-0.492090\pi$
$839$	1.01320e6			0.0496922			0.0248461	+	0.999691i	$0.492090\pi$
$840$		0			0
$841$	3.16681e6			0.154394
$842$	−3.30290e6	−	5.72079e6i	−0.160552	−	0.278084i
$843$	−2.48307e6	+	4.30080e6i	−0.120343	+	0.208440i
$844$	−1.46627e6	+	2.53966e6i	−0.0708530	+	0.122721i
$845$	−1.26995e6	−	2.19962e6i	−0.0611852	−	0.105976i
$846$	1.03646e6			0.0497884
$847$		0			0
$848$	−9.53395e6			−0.455285
$849$	5.79209e6	+	1.00322e7i	0.275782	+	0.477669i
$850$	1.14628e7	−	1.98541e7i	0.544181	−	0.942549i
$851$	3.00930e7	−	5.21226e7i	1.42443	−	2.46719i
$852$	2.25792e6	+	3.91083e6i	0.106564	+	0.184574i
$853$	−234824.			−0.0110502			−0.00552510	−	0.999985i	$-0.501759\pi$
$853$	−234824.			−0.0110502			−0.00552510	+	0.999985i	$0.501759\pi$
$854$		0			0
$855$	−5.64564e6			−0.264118
$856$	1.56326e6	+	2.70765e6i	0.0729202	+	0.126302i
$857$	1.41901e7	−	2.45780e7i	0.659985	−	1.14313i	−0.320634	−	0.947203i	$-0.603896\pi$
$857$	1.41901e7	−	2.45780e7i	0.659985	−	1.14313i	0.980619	−	0.195924i	$-0.0627707\pi$
$858$	−3.92448e6	+	6.79740e6i	−0.181997	+	0.315228i
$859$	2.00041e7	+	3.46481e7i	0.924986	+	1.60212i	0.791583	+	0.611061i	$0.209257\pi$
$859$	2.00041e7	+	3.46481e7i	0.924986	+	1.60212i	0.133403	+	0.991062i	$0.457410\pi$
$860$	−4.97818e6			−0.229522
$861$		0			0
$862$	−1.65744e7			−0.759748
$863$	1.04015e7	+	1.80160e7i	0.475411	+	0.823437i	0.999603	−	0.0281634i	$-0.00896587\pi$
$863$	1.04015e7	+	1.80160e7i	0.475411	+	0.823437i	−0.524192	+	0.851600i	$0.675633\pi$
$864$	1.97632e6	−	3.42309e6i	0.0900685	−	0.156003i
$865$	1.85452e7	−	3.21212e7i	0.842735	−	1.45966i
$866$	6.07932e6	+	1.05297e7i	0.275461	+	0.477112i
$867$	−7.05907e6			−0.318933
$868$		0			0
$869$	−1.44050e7			−0.647088
$870$	8.17488e6	+	1.41593e7i	0.366170	+	0.634226i
$871$	−5.09598e6	+	8.82650e6i	−0.227605	+	0.394224i
$872$	−1.80397e6	+	3.12456e6i	−0.0803411	+	0.139155i
$873$	1.21393e6	+	2.10258e6i	0.0539085	+	0.0933722i
$874$	−7.89600e6			−0.349646
$875$		0			0
$876$	576320.			0.0253748
$877$	−1.51779e7	−	2.62890e7i	−0.666367	−	1.15418i	−0.978913	−	0.204279i	$-0.934515\pi$
$877$	−1.51779e7	−	2.62890e7i	−0.666367	−	1.15418i	0.312545	−	0.949903i	$-0.398818\pi$
$878$	−5.08542e6	+	8.80821e6i	−0.222634	+	0.385613i
$879$	−7.19430e6	+	1.24609e7i	−0.314063	+	0.543973i
$880$	−3.61267e6	−	6.25733e6i	−0.157261	−	0.272385i
$881$	2.58936e7			1.12396			0.561981	−	0.827150i	$-0.310039\pi$
$881$	2.58936e7			1.12396			0.561981	+	0.827150i	$0.310039\pi$
$882$		0			0
$883$	−1.88813e7			−0.814950			−0.407475	−	0.913216i	$-0.633591\pi$
$883$	−1.88813e7			−0.814950			−0.407475	+	0.913216i	$0.633591\pi$
$884$	6.81178e6	+	1.17983e7i	0.293177	+	0.507797i
$885$	1.44068e7	−	2.49534e7i	0.618316	−	1.07095i
$886$	−4.86420e6	+	8.42504e6i	−0.208174	+	0.360568i
$887$	−1.17216e7	−	2.03023e7i	−0.500238	−	0.866437i	−1.00000		0.000274324i	$-0.999913\pi$
$887$	−1.17216e7	−	2.03023e7i	−0.500238	−	0.866437i	0.499762	−	0.866163i	$-0.333421\pi$
$888$	9.17120e6			0.390296
$889$		0			0
$890$	−8.98128e6			−0.380070
$891$	−646968.	−	1.12058e6i	−0.0273016	−	0.0472878i
$892$	−1.02197e7	+	1.77011e7i	−0.430057	+	0.744881i
$893$	425820.	−	737542.i	0.0178689	−	0.0309498i
$894$	1.21188e6	+	2.09904e6i	0.0507126	+	0.0878368i
$895$	898128.			0.0374784
$896$		0			0
$897$	−2.45280e7			−1.01784
$898$	3.65706e6	+	6.33421e6i	0.151336	+	0.262121i
$899$	−1.79361e7	+	3.10662e7i	−0.740164	+	1.28200i
$900$	4.49706e6	−	7.78914e6i	0.185064	−	0.320541i
$901$	2.71494e7	+	4.70242e7i	1.11416	+	1.92979i
$902$	−8.36237e6			−0.342226
$903$		0			0
$904$	−559488.			−0.0227703
$905$	2.29347e7	+	3.97240e7i	0.930832	+	1.61225i
$906$	−2.48896e6	+	4.31101e6i	−0.100739	+	0.174485i
$907$	2.80437e6	−	4.85730e6i	0.113192	−	0.196055i	−0.803863	−	0.594814i	$-0.797226\pi$
$907$	2.80437e6	−	4.85730e6i	0.113192	−	0.196055i	0.917056	+	0.398759i	$0.130559\pi$
$908$	−1.03011e7	−	1.78421e7i	−0.414639	−	0.718176i
$909$	1.41862e7			0.569450
$910$		0			0
$911$	2.16215e7			0.863156			0.431578	−	0.902076i	$-0.357957\pi$
$911$	2.16215e7			0.863156			0.431578	+	0.902076i	$0.357957\pi$
$912$	−601600.	−	1.04200e6i	−0.0239508	−	0.0414841i
$913$	5.91394e6	−	1.02432e7i	0.234801	−	0.406687i
$914$	3.16126e6	−	5.47546e6i	0.125168	−	0.216798i
$915$	1.02799e7	+	1.78053e7i	0.405917	+	0.703068i
$916$	−5.61498e6			−0.221110
$917$		0			0
$918$	−2.25115e7			−0.881654
$919$	−2.25848e7	−	3.91180e7i	−0.882119	−	1.52787i	−0.848981	−	0.528423i	$-0.822783\pi$
$919$	−2.25848e7	−	3.91180e7i	−0.882119	−	1.52787i	−0.0331374	−	0.999451i	$-0.510550\pi$
$920$	1.12896e7	−	1.95542e7i	0.439753	−	0.761675i
$921$	4.94549e6	−	8.56584e6i	0.192115	−	0.332752i
$922$	−1.01921e7	−	1.76532e7i	−0.394853	−	0.683906i
$923$	−1.64828e7			−0.636835
$924$		0			0
$925$	5.63312e7			2.16469
$926$	−1.40468e7	−	2.43297e7i	−0.538330	−	0.932415i
$927$	9.41255e6	−	1.63030e7i	0.359756	−	0.623115i
$928$	2.49139e6	−	4.31522e6i	0.0949669	−	0.164487i
$929$	−1.14364e7	−	1.98085e7i	−0.434762	−	0.753030i	0.562514	−	0.826788i	$-0.309834\pi$
$929$	−1.14364e7	−	1.98085e7i	−0.434762	−	0.753030i	−0.997276	+	0.0737577i	$0.976501\pi$
$930$	−2.47699e7			−0.939112
$931$		0			0
$932$	1.33785e7			0.504506
$933$	1.11025e7	+	1.92301e7i	0.417559	+	0.723233i
$934$	8.49690e6	−	1.47171e7i	0.318708	−	0.552019i
$935$	−2.05753e7	+	3.56375e7i	−0.769692	+	1.33315i
$936$	2.67238e6	+	4.62870e6i	0.0997032	+	0.172691i
$937$	1.79616e7			0.668336			0.334168	−	0.942514i	$-0.391545\pi$
$937$	1.79616e7			0.668336			0.334168	+	0.942514i	$0.391545\pi$
$938$		0			0
$939$	2.33008e7			0.862395
$940$	1.21766e6	+	2.10906e6i	0.0449477	+	0.0778518i
$941$	−8.98487e6	+	1.55623e7i	−0.330779	+	0.572926i	−0.982665	−	0.185391i	$-0.940645\pi$
$941$	−8.98487e6	+	1.55623e7i	−0.330779	+	0.572926i	0.651886	+	0.758317i	$0.273978\pi$
$942$	1.52080e6	−	2.63410e6i	0.0558399	−	0.0967176i
$943$	−1.30662e7	−	2.26313e7i	−0.478487	−	0.828764i
$944$	−8.78131e6			−0.320722
$945$		0			0
$946$	4.97818e6			0.180860
$947$	−2.16058e7	−	3.74223e7i	−0.782879	−	1.35599i	−0.930258	−	0.366907i	$-0.880417\pi$
$947$	−2.16058e7	−	3.74223e7i	−0.782879	−	1.35599i	0.147378	−	0.989080i	$-0.452916\pi$
$948$	3.42976e6	−	5.94052e6i	0.123949	−	0.214686i
$949$	−1.05178e6	+	1.82174e6i	−0.0379106	+	0.0656631i
$950$	−3.69514e6	−	6.40017e6i	−0.132838	−	0.230082i
$951$	−4.27542e6			−0.153295
$952$		0			0
$953$	−7.50965e6			−0.267848			−0.133924	−	0.990992i	$-0.542758\pi$
$953$	−7.50965e6			−0.267848			−0.133924	+	0.990992i	$0.542758\pi$
$954$	1.06512e7	+	1.84484e7i	0.378903	+	0.656279i
$955$	−2.41910e7	+	4.19000e7i	−0.858312	+	1.48664i
$956$	−6.19469e6	+	1.07295e7i	−0.219217	+	0.379695i
$957$	−8.17488e6	−	1.41593e7i	−0.288537	−	0.499761i
$958$	2.23714e6			0.0787551
$959$		0			0
$960$	3.44064e6			0.120493
$961$	−1.28586e7	−	2.22718e7i	−0.449144	−	0.777941i
$962$	−1.67374e7	+	2.89901e7i	−0.583111	+	1.00998i
$963$	3.49292e6	−	6.04991e6i	0.121373	−	0.210224i
$964$	−9.22280e6	−	1.59744e7i	−0.319647	−	0.553644i
$965$	3.47708e7			1.20198
$966$		0			0
$967$	−1.69305e7			−0.582242			−0.291121	−	0.956686i	$-0.594028\pi$
$967$	−1.69305e7			−0.582242			−0.291121	+	0.956686i	$0.594028\pi$
$968$	−1.54096e6	−	2.66902e6i	−0.0528571	−	0.0915511i
$969$	−3.42630e6	+	5.93453e6i	−0.117224	+	0.203038i
$970$	−2.85230e6	+	4.94034e6i	−0.0973344	+	0.168588i
$971$	1.43072e7	+	2.47808e7i	0.486974	+	0.843464i	0.999888	−	0.0149760i	$-0.00476719\pi$
$971$	1.43072e7	+	2.47808e7i	0.486974	+	0.843464i	−0.512914	+	0.858440i	$0.671434\pi$
$972$	−1.43915e7			−0.488586
$973$		0			0
$974$	5.28227e6			0.178412
$975$	−1.14785e7	−	1.98814e7i	−0.386700	−	0.669784i
$976$	3.13293e6	−	5.42639e6i	0.105275	−	0.182342i
$977$	−1.84722e7	+	3.19949e7i	−0.619132	+	1.07237i	0.370512	+	0.928828i	$0.379182\pi$
$977$	−1.84722e7	+	3.19949e7i	−0.619132	+	1.07237i	−0.989644	+	0.143541i	$0.954151\pi$
$978$	−2.48512e6	−	4.30435e6i	−0.0830807	−	0.143900i
$979$	8.98128e6			0.299489
$980$		0			0
$981$	8.06148e6			0.267450
$982$	1.25439e7	+	2.17266e7i	0.415100	+	0.718974i
$983$	−1.94394e7	+	3.36700e7i	−0.641650	+	1.11137i	0.343415	+	0.939184i	$0.388416\pi$
$983$	−1.94394e7	+	3.36700e7i	−0.641650	+	1.11137i	−0.985064	+	0.172186i	$0.944917\pi$
$984$	1.99104e6	−	3.44858e6i	0.0655529	−	0.113541i
$985$	−2.07877e7	−	3.60054e7i	−0.682679	−	1.18243i
$986$	−2.83785e7			−0.929603
$987$		0			0
$988$	4.39168e6			0.143133
$989$	7.77840e6	+	1.34726e7i	0.252871	+	0.437986i
$990$	−8.07206e6	+	1.39812e7i	−0.261756	+	0.453375i
$991$	−1.24606e7	+	2.15824e7i	−0.403046	+	0.698096i	−0.994092	−	0.108542i	$-0.965382\pi$
$991$	−1.24606e7	+	2.15824e7i	−0.403046	+	0.698096i	0.591046	+	0.806638i	$0.298715\pi$
$992$	3.77446e6	+	6.53756e6i	0.121780	+	0.210929i
$993$	3.96616e6			0.127643
$994$		0			0
$995$	4.37106e7			1.39968
$996$	2.81616e6	+	4.87773e6i	0.0899516	+	0.155801i
$997$	5.09781e6	−	8.82967e6i	0.162422	−	0.281324i	−0.773314	−	0.634023i	$-0.781403\pi$
$997$	5.09781e6	−	8.82967e6i	0.162422	−	0.281324i	0.935737	+	0.352699i	$0.114736\pi$
$998$	−7.87570e6	+	1.36411e7i	−0.250301	+	0.433534i
$999$	−2.76569e7	−	4.79032e7i	−0.876778	−	1.51862i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.6.c.d.67.1		2
7.2	even	3	inner	98.6.c.d.79.1		2
7.3	odd	6		14.6.a.a.1.1	✓	1
7.4	even	3		98.6.a.a.1.1		1
7.5	odd	6		98.6.c.c.79.1		2
7.6	odd	2		98.6.c.c.67.1		2
21.11	odd	6		882.6.a.x.1.1		1
21.17	even	6		126.6.a.f.1.1		1
28.3	even	6		112.6.a.c.1.1		1
28.11	odd	6		784.6.a.i.1.1		1
35.3	even	12		350.6.c.d.99.2		2
35.17	even	12		350.6.c.d.99.1		2
35.24	odd	6		350.6.a.i.1.1		1
56.3	even	6		448.6.a.l.1.1		1
56.45	odd	6		448.6.a.e.1.1		1
84.59	odd	6		1008.6.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.6.a.a.1.1	✓	1	7.3	odd	6
98.6.a.a.1.1		1	7.4	even	3
98.6.c.c.67.1		2	7.6	odd	2
98.6.c.c.79.1		2	7.5	odd	6
98.6.c.d.67.1		2	1.1	even	1	trivial
98.6.c.d.79.1		2	7.2	even	3	inner
112.6.a.c.1.1		1	28.3	even	6
126.6.a.f.1.1		1	21.17	even	6
350.6.a.i.1.1		1	35.24	odd	6
350.6.c.d.99.1		2	35.17	even	12
350.6.c.d.99.2		2	35.3	even	12
448.6.a.e.1.1		1	56.45	odd	6
448.6.a.l.1.1		1	56.3	even	6
784.6.a.i.1.1		1	28.11	odd	6
882.6.a.x.1.1		1	21.11	odd	6
1008.6.a.b.1.1		1	84.59	odd	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} +(5.00000 - 8.66025i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(42.0000 + 72.7461i) q^{5} +40.0000 q^{6} -64.0000 q^{8} +(71.5000 + 123.842i) q^{9} +(-168.000 + 290.985i) q^{10} +(168.000 - 290.985i) q^{11} +(80.0000 + 138.564i) q^{12} -584.000 q^{13} +840.000 q^{15} +(-128.000 - 221.703i) q^{16} +(-729.000 + 1262.67i) q^{17} +(-286.000 + 495.367i) q^{18} +(235.000 + 407.032i) q^{19} -1344.00 q^{20} +1344.00 q^{22} +(2100.00 + 3637.31i) q^{23} +(-320.000 + 554.256i) q^{24} +(-1965.50 + 3404.35i) q^{25} +(-1168.00 - 2023.04i) q^{26} +3860.00 q^{27} +4866.00 q^{29} +(1680.00 + 2909.85i) q^{30} +(-3686.00 + 6384.34i) q^{31} +(512.000 - 886.810i) q^{32} +(-1680.00 - 2909.85i) q^{33} -5832.00 q^{34} -2288.00 q^{36} +(-7165.00 - 12410.1i) q^{37} +(-940.000 + 1628.13i) q^{38} +(-2920.00 + 5057.59i) q^{39} +(-2688.00 - 4655.75i) q^{40} -6222.00 q^{41} +3704.00 q^{43} +(2688.00 + 4655.75i) q^{44} +(-6006.00 + 10402.7i) q^{45} +(-8400.00 + 14549.2i) q^{46} +(-906.000 - 1569.24i) q^{47} -2560.00 q^{48} -15724.0 q^{50} +(7290.00 + 12626.7i) q^{51} +(4672.00 - 8092.14i) q^{52} +(18621.0 - 32252.5i) q^{53} +(7720.00 + 13371.4i) q^{54} +28224.0 q^{55} +4700.00 q^{57} +(9732.00 + 16856.3i) q^{58} +(17151.0 - 29706.4i) q^{59} +(-6720.00 + 11639.4i) q^{60} +(12238.0 + 21196.8i) q^{61} -29488.0 q^{62} +4096.00 q^{64} +(-24528.0 - 42483.7i) q^{65} +(6720.00 - 11639.4i) q^{66} +(8726.00 - 15113.9i) q^{67} +(-11664.0 - 20202.6i) q^{68} +42000.0 q^{69} +28224.0 q^{71} +(-4576.00 - 7925.86i) q^{72} +(1801.00 - 3119.42i) q^{73} +(28660.0 - 49640.6i) q^{74} +(19655.0 + 34043.5i) q^{75} -7520.00 q^{76} -23360.0 q^{78} +(-21436.0 - 37128.2i) q^{79} +(10752.0 - 18623.0i) q^{80} +(1925.50 - 3335.06i) q^{81} +(-12444.0 - 21553.6i) q^{82} +35202.0 q^{83} -122472. q^{85} +(7408.00 + 12831.0i) q^{86} +(24330.0 - 42140.8i) q^{87} +(-10752.0 + 18623.0i) q^{88} +(13365.0 + 23148.9i) q^{89} -48048.0 q^{90} -67200.0 q^{92} +(36860.0 + 63843.4i) q^{93} +(3624.00 - 6276.95i) q^{94} +(-19740.0 + 34190.7i) q^{95} +(-5120.00 - 8868.10i) q^{96} +16978.0 q^{97} +48048.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 10 q^{3} - 16 q^{4} + 84 q^{5} + 80 q^{6} - 128 q^{8} + 143 q^{9} - 336 q^{10} + 336 q^{11} + 160 q^{12} - 1168 q^{13} + 1680 q^{15} - 256 q^{16} - 1458 q^{17} - 572 q^{18} + 470 q^{19}+ \cdots + 96096 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 10 * q^3 - 16 * q^4 + 84 * q^5 + 80 * q^6 - 128 * q^8 + 143 * q^9 - 336 * q^10 + 336 * q^11 + 160 * q^12 - 1168 * q^13 + 1680 * q^15 - 256 * q^16 - 1458 * q^17 - 572 * q^18 + 470 * q^19 - 2688 * q^20 + 2688 * q^22 + 4200 * q^23 - 640 * q^24 - 3931 * q^25 - 2336 * q^26 + 7720 * q^27 + 9732 * q^29 + 3360 * q^30 - 7372 * q^31 + 1024 * q^32 - 3360 * q^33 - 11664 * q^34 - 4576 * q^36 - 14330 * q^37 - 1880 * q^38 - 5840 * q^39 - 5376 * q^40 - 12444 * q^41 + 7408 * q^43 + 5376 * q^44 - 12012 * q^45 - 16800 * q^46 - 1812 * q^47 - 5120 * q^48 - 31448 * q^50 + 14580 * q^51 + 9344 * q^52 + 37242 * q^53 + 15440 * q^54 + 56448 * q^55 + 9400 * q^57 + 19464 * q^58 + 34302 * q^59 - 13440 * q^60 + 24476 * q^61 - 58976 * q^62 + 8192 * q^64 - 49056 * q^65 + 13440 * q^66 + 17452 * q^67 - 23328 * q^68 + 84000 * q^69 + 56448 * q^71 - 9152 * q^72 + 3602 * q^73 + 57320 * q^74 + 39310 * q^75 - 15040 * q^76 - 46720 * q^78 - 42872 * q^79 + 21504 * q^80 + 3851 * q^81 - 24888 * q^82 + 70404 * q^83 - 244944 * q^85 + 14816 * q^86 + 48660 * q^87 - 21504 * q^88 + 26730 * q^89 - 96096 * q^90 - 134400 * q^92 + 73720 * q^93 + 7248 * q^94 - 39480 * q^95 - 10240 * q^96 + 33956 * q^97 + 96096 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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