LMFDB - Embedded newform 8.6.b.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,6,Mod(5,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	8.b (of order $2$, degree $1$, 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:	$1.28307055850$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.218489.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 8x + 64 $ x^4 - x^3 - 2x^2 - 8x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.4
Root			$-1.88600 + 2.10784i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.6.b.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.77200 + 4.21569i) q^{2} -3.25452i q^{3} +(-3.54400 + 31.8031i) q^{4} -73.9600i q^{5} +(13.7200 - 12.2760i) q^{6} -112.704 q^{7} +(-147.440 + 105.021i) q^{8} +232.408 q^{9} +O(q^{10})$	\(q+(3.77200 + 4.21569i) q^{2} -3.25452i q^{3} +(-3.54400 + 31.8031i) q^{4} -73.9600i q^{5} +(13.7200 - 12.2760i) q^{6} -112.704 q^{7} +(-147.440 + 105.021i) q^{8} +232.408 q^{9} +(311.792 - 278.977i) q^{10} +575.407i q^{11} +(103.504 + 11.5340i) q^{12} -117.735i q^{13} +(-425.120 - 475.125i) q^{14} -240.704 q^{15} +(-998.880 - 225.421i) q^{16} -223.408 q^{17} +(876.644 + 979.759i) q^{18} -1752.26i q^{19} +(2352.16 + 262.115i) q^{20} +366.797i q^{21} +(-2425.74 + 2170.44i) q^{22} +2361.15 q^{23} +(341.793 + 479.846i) q^{24} -2345.08 q^{25} +(496.336 - 444.098i) q^{26} -1547.22i q^{27} +(399.424 - 3584.34i) q^{28} +3865.52i q^{29} +(-907.936 - 1014.73i) q^{30} -1591.55 q^{31} +(-2817.47 - 5061.25i) q^{32} +1872.67 q^{33} +(-842.696 - 941.818i) q^{34} +8335.59i q^{35} +(-823.655 + 7391.31i) q^{36} -4736.44i q^{37} +(7386.97 - 6609.52i) q^{38} -383.172 q^{39} +(7767.36 + 10904.7i) q^{40} +8153.88 q^{41} +(-1546.30 + 1383.56i) q^{42} -4920.23i q^{43} +(-18299.8 - 2039.25i) q^{44} -17188.9i q^{45} +(8906.27 + 9953.88i) q^{46} -21062.0 q^{47} +(-733.636 + 3250.87i) q^{48} -4104.79 q^{49} +(-8845.65 - 9886.12i) q^{50} +727.085i q^{51} +(3744.36 + 417.255i) q^{52} +12709.0i q^{53} +(6522.61 - 5836.13i) q^{54} +42557.1 q^{55} +(16617.1 - 11836.3i) q^{56} -5702.75 q^{57} +(-16295.8 + 14580.7i) q^{58} +14111.1i q^{59} +(853.056 - 7655.15i) q^{60} +42030.6i q^{61} +(-6003.33 - 6709.48i) q^{62} -26193.3 q^{63} +(10709.1 - 30968.6i) q^{64} -8707.71 q^{65} +(7063.73 + 7894.60i) q^{66} -54153.4i q^{67} +(791.759 - 7105.08i) q^{68} -7684.41i q^{69} +(-35140.2 + 31441.9i) q^{70} +43879.9 q^{71} +(-34266.3 + 24407.8i) q^{72} -31290.6 q^{73} +(19967.4 - 17865.9i) q^{74} +7632.11i q^{75} +(55727.3 + 6210.01i) q^{76} -64850.7i q^{77} +(-1445.33 - 1615.33i) q^{78} -50211.5 q^{79} +(-16672.1 + 73877.2i) q^{80} +51439.7 q^{81} +(30756.4 + 34374.2i) q^{82} +43707.0i q^{83} +(-11665.3 - 1299.93i) q^{84} +16523.3i q^{85} +(20742.1 - 18559.1i) q^{86} +12580.4 q^{87} +(-60429.9 - 84838.1i) q^{88} +64418.7 q^{89} +(72463.0 - 64836.6i) q^{90} +13269.3i q^{91} +(-8367.93 + 75092.1i) q^{92} +5179.73i q^{93} +(-79446.0 - 88790.8i) q^{94} -129597. q^{95} +(-16471.9 + 9169.52i) q^{96} -62350.9 q^{97} +(-15483.3 - 17304.5i) q^{98} +133729. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 20 q^{4} - 116 q^{6} + 96 q^{7} - 248 q^{8} - 164 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 20 * q^4 - 116 * q^6 + 96 * q^7 - 248 * q^8 - 164 * q^9	\( 4 q - 2 q^{2} + 20 q^{4} - 116 q^{6} + 96 q^{7} - 248 q^{8} - 164 q^{9} + 632 q^{10} + 1576 q^{12} - 2384 q^{14} - 416 q^{15} - 3312 q^{16} + 200 q^{17} + 4754 q^{18} + 4624 q^{20} - 5636 q^{22} + 2336 q^{23} - 7792 q^{24} + 1556 q^{25} + 5608 q^{26} + 5152 q^{28} - 2128 q^{30} - 12928 q^{31} + 5408 q^{32} - 2352 q^{33} - 4772 q^{34} - 10164 q^{36} + 15980 q^{38} + 35104 q^{39} + 16032 q^{40} - 4568 q^{41} - 26144 q^{42} - 29112 q^{44} + 29200 q^{46} - 54720 q^{47} + 35616 q^{48} + 9828 q^{49} - 47498 q^{50} - 36560 q^{52} + 23288 q^{54} + 85472 q^{55} + 40768 q^{56} - 2032 q^{57} + 3784 q^{58} + 2592 q^{60} + 34496 q^{62} - 153440 q^{63} - 41920 q^{64} - 19520 q^{65} + 43224 q^{66} + 10344 q^{68} - 68928 q^{70} + 206688 q^{71} - 83272 q^{72} + 39976 q^{73} + 17464 q^{74} + 99944 q^{76} - 174064 q^{78} - 247872 q^{79} - 35520 q^{80} + 29684 q^{81} + 161132 q^{82} + 196672 q^{84} - 18500 q^{86} + 307872 q^{87} - 167216 q^{88} - 84632 q^{89} + 142280 q^{90} - 49056 q^{92} - 98784 q^{94} - 259744 q^{95} - 115648 q^{96} - 99576 q^{97} - 117042 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 20 * q^4 - 116 * q^6 + 96 * q^7 - 248 * q^8 - 164 * q^9 + 632 * q^10 + 1576 * q^12 - 2384 * q^14 - 416 * q^15 - 3312 * q^16 + 200 * q^17 + 4754 * q^18 + 4624 * q^20 - 5636 * q^22 + 2336 * q^23 - 7792 * q^24 + 1556 * q^25 + 5608 * q^26 + 5152 * q^28 - 2128 * q^30 - 12928 * q^31 + 5408 * q^32 - 2352 * q^33 - 4772 * q^34 - 10164 * q^36 + 15980 * q^38 + 35104 * q^39 + 16032 * q^40 - 4568 * q^41 - 26144 * q^42 - 29112 * q^44 + 29200 * q^46 - 54720 * q^47 + 35616 * q^48 + 9828 * q^49 - 47498 * q^50 - 36560 * q^52 + 23288 * q^54 + 85472 * q^55 + 40768 * q^56 - 2032 * q^57 + 3784 * q^58 + 2592 * q^60 + 34496 * q^62 - 153440 * q^63 - 41920 * q^64 - 19520 * q^65 + 43224 * q^66 + 10344 * q^68 - 68928 * q^70 + 206688 * q^71 - 83272 * q^72 + 39976 * q^73 + 17464 * q^74 + 99944 * q^76 - 174064 * q^78 - 247872 * q^79 - 35520 * q^80 + 29684 * q^81 + 161132 * q^82 + 196672 * q^84 - 18500 * q^86 + 307872 * q^87 - 167216 * q^88 - 84632 * q^89 + 142280 * q^90 - 49056 * q^92 - 98784 * q^94 - 259744 * q^95 - 115648 * q^96 - 99576 * q^97 - 117042 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

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 $

$2$	3.77200	+	4.21569i	0.666802	+	0.745235i
$2$	3.77200	+	4.21569i	0.666802	+	0.745235i
$3$		−	3.25452i		−	0.208777i	−0.994537	−	0.104389i	$-0.966711\pi$
$3$		−	3.25452i		−	0.208777i	0.994537	−	0.104389i	$-0.0332886\pi$
$4$	−3.54400	+	31.8031i	−0.110750	+	0.993848i
$5$		−	73.9600i		−	1.32304i	−0.749929	−	0.661518i	$-0.769912\pi$
$5$		−	73.9600i		−	1.32304i	0.749929	−	0.661518i	$-0.230088\pi$
$6$	13.7200	−	12.2760i	0.155588	−	0.139213i
$7$	−112.704			−0.869350			−0.434675	−	0.900587i	$-0.643137\pi$
$7$	−112.704			−0.869350			−0.434675	+	0.900587i	$0.643137\pi$
$8$	−147.440	+	105.021i	−0.814499	+	0.580165i
$9$	232.408			0.956412
$10$	311.792	−	278.977i	0.985973	−	0.882204i
$11$			575.407i			1.43382i	0.697167	+	0.716909i	$0.254443\pi$
$11$			575.407i			1.43382i	−0.697167	+	0.716909i	$0.745557\pi$
$12$	103.504	+	11.5340i	0.207493	+	0.0231221i
$13$		−	117.735i		−	0.193219i	−0.995322	−	0.0966093i	$-0.969200\pi$
$13$		−	117.735i		−	0.193219i	0.995322	−	0.0966093i	$-0.0307997\pi$
$14$	−425.120	−	475.125i	−0.579684	−	0.647870i
$15$	−240.704			−0.276220
$16$	−998.880	−	225.421i	−0.975469	−	0.220138i
$17$	−223.408			−0.187489			−0.0937447	−	0.995596i	$-0.529884\pi$
$17$	−223.408			−0.187489			−0.0937447	+	0.995596i	$0.529884\pi$
$18$	876.644	+	979.759i	0.637737	+	0.712752i
$19$		−	1752.26i		−	1.11356i	−0.830660	−	0.556781i	$-0.812036\pi$
$19$		−	1752.26i		−	1.11356i	0.830660	−	0.556781i	$-0.187964\pi$
$20$	2352.16	+	262.115i	1.31490	+	0.146526i
$21$			366.797i			0.181501i
$22$	−2425.74	+	2170.44i	−1.06853	+	0.956072i
$23$	2361.15			0.930689			0.465344	−	0.885130i	$-0.345930\pi$
$23$	2361.15			0.930689			0.465344	+	0.885130i	$0.345930\pi$
$24$	341.793	+	479.846i	0.121125	+	0.170049i
$25$	−2345.08			−0.750426
$26$	496.336	−	444.098i	0.143993	−	0.128839i
$27$		−	1547.22i		−	0.408455i
$28$	399.424	−	3584.34i	0.0962806	−	0.864002i
$29$			3865.52i			0.853518i	0.904365	+	0.426759i	$0.140345\pi$
$29$			3865.52i			0.853518i	−0.904365	+	0.426759i	$0.859655\pi$
$30$	−907.936	−	1014.73i	−0.184184	−	0.205849i
$31$	−1591.55			−0.297452			−0.148726	−	0.988878i	$-0.547517\pi$
$31$	−1591.55			−0.297452			−0.148726	+	0.988878i	$0.547517\pi$
$32$	−2817.47	−	5061.25i	−0.486390	−	0.873742i
$33$	1872.67			0.299349
$34$	−842.696	−	941.818i	−0.125018	−	0.139724i
$35$			8335.59i			1.15018i
$36$	−823.655	+	7391.31i	−0.105923	+	0.950528i
$37$		−	4736.44i		−	0.568785i	−0.958708	−	0.284392i	$-0.908208\pi$
$37$		−	4736.44i		−	0.568785i	0.958708	−	0.284392i	$-0.0917918\pi$
$38$	7386.97	−	6609.52i	0.829865	−	0.742525i
$39$	−383.172			−0.0403397
$40$	7767.36	+	10904.7i	0.767580	+	1.07761i
$41$	8153.88			0.757538			0.378769	−	0.925491i	$-0.376347\pi$
$41$	8153.88			0.757538			0.378769	+	0.925491i	$0.376347\pi$
$42$	−1546.30	+	1383.56i	−0.135261	+	0.121025i
$43$		−	4920.23i		−	0.405802i	−0.979199	−	0.202901i	$-0.934963\pi$
$43$		−	4920.23i		−	0.405802i	0.979199	−	0.202901i	$-0.0650370\pi$
$44$	−18299.8	−	2039.25i	−1.42500	−	0.158795i
$45$		−	17188.9i		−	1.26537i
$46$	8906.27	+	9953.88i	0.620585	+	0.693582i
$47$	−21062.0			−1.39077			−0.695385	−	0.718637i	$-0.744766\pi$
$47$	−21062.0			−1.39077			−0.695385	+	0.718637i	$0.744766\pi$
$48$	−733.636	+	3250.87i	−0.0459598	+	0.203656i
$49$	−4104.79			−0.244231
$50$	−8845.65	−	9886.12i	−0.500386	−	0.559244i
$51$			727.085i			0.0391435i
$52$	3744.36	+	417.255i	0.192030	+	0.0213990i
$53$			12709.0i			0.621470i	0.950497	+	0.310735i	$0.100575\pi$
$53$			12709.0i			0.621470i	−0.950497	+	0.310735i	$0.899425\pi$
$54$	6522.61	−	5836.13i	0.304395	−	0.272358i
$55$	42557.1			1.89699
$56$	16617.1	−	11836.3i	0.708084	−	0.504366i
$57$	−5702.75			−0.232486
$58$	−16295.8	+	14580.7i	−0.636071	+	0.569127i
$59$			14111.1i			0.527752i	0.964557	+	0.263876i	$0.0850010\pi$
$59$			14111.1i			0.527752i	−0.964557	+	0.263876i	$0.914999\pi$
$60$	853.056	−	7655.15i	0.0305914	−	0.274521i
$61$			42030.6i			1.44624i	0.690721	+	0.723121i	$0.257293\pi$
$61$			42030.6i			1.44624i	−0.690721	+	0.723121i	$0.742707\pi$
$62$	−6003.33	−	6709.48i	−0.198341	−	0.221671i
$63$	−26193.3			−0.831456
$64$	10709.1	−	30968.6i	0.326817	−	0.945088i
$65$	−8707.71			−0.255635
$66$	7063.73	+	7894.60i	0.199606	+	0.223085i
$67$		−	54153.4i		−	1.47380i	−0.676001	−	0.736901i	$-0.736289\pi$
$67$		−	54153.4i		−	1.47380i	0.676001	−	0.736901i	$-0.263711\pi$
$68$	791.759	−	7105.08i	0.0207645	−	0.186336i
$69$		−	7684.41i		−	0.194307i
$70$	−35140.2	+	31441.9i	−0.857155	+	0.766943i
$71$	43879.9			1.03305			0.516523	−	0.856273i	$-0.327226\pi$
$71$	43879.9			1.03305			0.516523	+	0.856273i	$0.327226\pi$
$72$	−34266.3	+	24407.8i	−0.778996	+	0.554877i
$73$	−31290.6			−0.687238			−0.343619	−	0.939109i	$-0.611653\pi$
$73$	−31290.6			−0.687238			−0.343619	+	0.939109i	$0.611653\pi$
$74$	19967.4	−	17865.9i	0.423878	−	0.379267i
$75$			7632.11i			0.156672i
$76$	55727.3	+	6210.01i	1.10671	+	0.123327i
$77$		−	64850.7i		−	1.24649i
$78$	−1445.33	−	1615.33i	−0.0268986	−	0.0300625i
$79$	−50211.5			−0.905180			−0.452590	−	0.891719i	$-0.649500\pi$
$79$	−50211.5			−0.905180			−0.452590	+	0.891719i	$0.649500\pi$
$80$	−16672.1	+	73877.2i	−0.291250	+	1.29058i
$81$	51439.7			0.871136
$82$	30756.4	+	34374.2i	0.505128	+	0.564544i
$83$			43707.0i			0.696395i	0.937421	+	0.348197i	$0.113206\pi$
$83$			43707.0i			0.696395i	−0.937421	+	0.348197i	$0.886794\pi$
$84$	−11665.3	−	1299.93i	−0.180384	−	0.0201012i
$85$			16523.3i			0.248055i
$86$	20742.1	−	18559.1i	0.302418	−	0.270590i
$87$	12580.4			0.178195
$88$	−60429.9	−	84838.1i	−0.831851	−	1.16784i
$89$	64418.7			0.862059			0.431030	−	0.902338i	$-0.358150\pi$
$89$	64418.7			0.862059			0.431030	+	0.902338i	$0.358150\pi$
$90$	72463.0	−	64836.6i	0.942997	−	0.843750i
$91$			13269.3i			0.167974i
$92$	−8367.93	+	75092.1i	−0.103074	+	0.924963i
$93$			5179.73i			0.0621012i
$94$	−79446.0	−	88790.8i	−0.927368	−	1.03645i
$95$	−129597.			−1.47328
$96$	−16471.9	+	9169.52i	−0.182417	+	0.101547i
$97$	−62350.9			−0.672843			−0.336421	−	0.941712i	$-0.609217\pi$
$97$	−62350.9			−0.672843			−0.336421	+	0.941712i	$0.609217\pi$
$98$	−15483.3	−	17304.5i	−0.162854	−	0.182010i
$99$			133729.i			1.37132i
$100$	8310.98	−	74581.0i	0.0831098	−	0.745810i
$101$		−	49960.5i		−	0.487330i	−0.969859	−	0.243665i	$-0.921650\pi$
$101$		−	49960.5i		−	0.487330i	0.969859	−	0.243665i	$-0.0783497\pi$
$102$	−3065.16	+	2742.57i	−0.0291711	+	0.0261010i
$103$	159260.			1.47915			0.739577	−	0.673072i	$-0.235026\pi$
$103$	159260.			1.47915			0.739577	+	0.673072i	$0.235026\pi$
$104$	12364.7	+	17358.9i	0.112099	+	0.157376i
$105$	27128.3			0.240132
$106$	−53576.9	+	47938.2i	−0.463141	+	0.414397i
$107$		−	135565.i		−	1.14469i	−0.820012	−	0.572346i	$-0.806033\pi$
$107$		−	135565.i		−	1.14469i	0.820012	−	0.572346i	$-0.193967\pi$
$108$	49206.6	+	5483.37i	0.405942	+	0.0452364i
$109$			115137.i			0.928218i	0.885778	+	0.464109i	$0.153625\pi$
$109$			115137.i			0.928218i	−0.885778	+	0.464109i	$0.846375\pi$
$110$	160526.	+	179407.i	1.26492	+	1.41370i
$111$	−15414.8			−0.118749
$112$	112578.	+	25405.9i	0.848023	+	0.191377i
$113$	−19192.0			−0.141392			−0.0706960	−	0.997498i	$-0.522522\pi$
$113$	−19192.0			−0.141392			−0.0706960	+	0.997498i	$0.522522\pi$
$114$	−21510.8	−	24041.0i	−0.155022	−	0.173257i
$115$		−	174631.i		−	1.23134i
$116$	−122936.	−	13699.4i	−0.848267	−	0.0945272i
$117$		−	27362.7i		−	0.184797i
$118$	−59487.9	+	53227.0i	−0.393299	+	0.351906i
$119$	25179.0			0.162994
$120$	35489.4	−	25279.0i	0.224981	−	0.160253i
$121$	−170043.			−1.05583
$122$	−177188.	+	158540.i	−1.07779	+	0.964357i
$123$		−	26536.9i		−	0.158157i
$124$	5640.46	−	50616.3i	0.0329428	−	0.295622i
$125$		−	57682.8i		−	0.330196i
$126$	−98801.3	−	110423.i	−0.554417	−	0.619630i
$127$	102000.			0.561163			0.280582	−	0.959830i	$-0.409473\pi$
$127$	102000.			0.561163			0.280582	+	0.959830i	$0.409473\pi$
$128$	170949.	−	71667.4i	0.922234	−	0.386631i
$129$	−16013.0			−0.0847223
$130$	−32845.5	−	36709.0i	−0.170458	−	0.190508i
$131$		−	11296.1i		−	0.0575111i	−0.999586	−	0.0287556i	$-0.990846\pi$
$131$		−	11296.1i		−	0.0575111i	0.999586	−	0.0287556i	$-0.00915444\pi$
$132$	−6636.76	+	59556.9i	−0.0331529	+	0.297507i
$133$			197487.i			0.968074i
$134$	228294.	−	204267.i	1.09833	−	0.982734i
$135$	−114433.			−0.540400
$136$	32939.3	−	23462.6i	0.152710	−	0.108775i
$137$	102753.			0.467727			0.233863	−	0.972269i	$-0.424863\pi$
$137$	102753.			0.467727			0.233863	+	0.972269i	$0.424863\pi$
$138$	32395.1	−	28985.6i	0.144804	−	0.129564i
$139$			343928.i			1.50984i	0.655818	+	0.754919i	$0.272324\pi$
$139$			343928.i			1.50984i	−0.655818	+	0.754919i	$0.727676\pi$
$140$	−265098.	−	29541.4i	−1.14311	−	0.127383i
$141$			68546.7i			0.290361i
$142$	165515.	+	184984.i	0.688837	+	0.769862i
$143$	67745.8			0.277040
$144$	−232148.	−	52389.7i	−0.932950	−	0.210542i
$145$	285894.			1.12924
$146$	−118028.	−	131911.i	−0.458252	−	0.512154i
$147$			13359.1i			0.0509900i
$148$	150634.	+	16786.0i	0.565286	+	0.0629930i
$149$		−	186446.i		−	0.687998i	−0.938970	−	0.343999i	$-0.888218\pi$
$149$		−	186446.i		−	0.687998i	0.938970	−	0.343999i	$-0.111782\pi$
$150$	−32174.6	+	28788.3i	−0.116757	+	0.104469i
$151$	−285769.			−1.01994			−0.509968	−	0.860194i	$-0.670343\pi$
$151$	−285769.			−1.01994			−0.509968	+	0.860194i	$0.670343\pi$
$152$	184024.	+	258353.i	0.646050	+	0.906994i
$153$	−51921.9			−0.179317
$154$	273390.	−	244617.i	0.928927	−	0.831161i
$155$			117711.i			0.393539i
$156$	1357.96	−	12186.1i	0.00446762	−	0.0400915i
$157$		−	480654.i		−	1.55626i	−0.628101	−	0.778132i	$-0.716167\pi$
$157$		−	480654.i		−	1.55626i	0.628101	−	0.778132i	$-0.283833\pi$
$158$	−189398.	−	211676.i	−0.603576	−	0.674572i
$159$	41361.5			0.129749
$160$	−374330.	+	208380.i	−1.15599	+	0.643512i
$161$	−266112.			−0.809094
$162$	194031.	+	216854.i	0.580875	+	0.649201i
$163$		−	176613.i		−	0.520659i	−0.965520	−	0.260329i	$-0.916169\pi$
$163$		−	176613.i		−	0.520659i	0.965520	−	0.260329i	$-0.0838312\pi$
$164$	−28897.4	+	259319.i	−0.0838974	+	0.752878i
$165$		−	138503.i		−	0.396049i
$166$	−184255.	+	164863.i	−0.518978	+	0.464358i
$167$	−218853.			−0.607240			−0.303620	−	0.952793i	$-0.598195\pi$
$167$	−218853.			−0.607240			−0.303620	+	0.952793i	$0.598195\pi$
$168$	−38521.5	−	54080.6i	−0.105300	−	0.147832i
$169$	357431.			0.962667
$170$	−69656.9	+	62325.8i	−0.184859	+	0.165404i
$171$		−	407239.i		−	1.06502i
$172$	156479.	+	17437.3i	0.403306	+	0.0449426i
$173$			522746.i			1.32793i	0.747764	+	0.663965i	$0.231128\pi$
$173$			522746.i			1.32793i	−0.747764	+	0.663965i	$0.768872\pi$
$174$	47453.2	+	53035.0i	0.118821	+	0.132797i
$175$	264300.			0.652383
$176$	129709.	−	574763.i	0.315637	−	1.39864i
$177$	45924.7			0.110183
$178$	242988.	+	271569.i	0.574823	+	0.642437i
$179$			411059.i			0.958897i	0.877570	+	0.479449i	$0.159163\pi$
$179$			411059.i			0.958897i	−0.877570	+	0.479449i	$0.840837\pi$
$180$	546661.	+	60917.5i	1.25758	+	0.140140i
$181$			133094.i			0.301970i	0.988536	+	0.150985i	$0.0482445\pi$
$181$			133094.i			0.301970i	−0.988536	+	0.150985i	$0.951755\pi$
$182$	−55939.0	+	50051.7i	−0.125180	+	0.112006i
$183$	136789.			0.301943
$184$	−348128.	+	247971.i	−0.758045	+	0.539953i
$185$	−350307.			−0.752523
$186$	−21836.1	+	19538.0i	−0.0462800	+	0.0414092i
$187$		−	128551.i		−	0.268825i
$188$	74643.9	−	669838.i	0.154028	−	1.38221i
$189$			174378.i			0.355090i
$190$	−488840.	−	546340.i	−0.982388	−	1.09794i
$191$	833447.			1.65308			0.826541	−	0.562877i	$-0.190305\pi$
$191$	833447.			1.65308			0.826541	+	0.562877i	$0.190305\pi$
$192$	−100788.	−	34853.0i	−0.197313	−	0.0682319i
$193$	−597550.			−1.15473			−0.577366	−	0.816486i	$-0.695919\pi$
$193$	−597550.			−1.15473			−0.577366	+	0.816486i	$0.695919\pi$
$194$	−235188.	−	262852.i	−0.448653	−	0.501426i
$195$			28339.4i			0.0533709i
$196$	14547.4	−	130545.i	0.0270486	−	0.242729i
$197$			688179.i			1.26339i	0.775219	+	0.631693i	$0.217640\pi$
$197$			688179.i			1.26339i	−0.775219	+	0.631693i	$0.782360\pi$
$198$	−563761.	+	504427.i	−1.02196	+	0.914399i
$199$	−977514.			−1.74981			−0.874904	−	0.484296i	$-0.839076\pi$
$199$	−977514.			−1.74981			−0.874904	+	0.484296i	$0.839076\pi$
$200$	345759.	−	246283.i	0.611221	−	0.435371i
$201$	−176243.			−0.307696
$202$	210618.	−	188451.i	0.363175	−	0.324952i
$203$		−	435659.i		−	0.742005i
$204$	−23123.6	−	2576.79i	−0.0389027	−	0.00433515i
$205$		−	603061.i		−	1.00225i
$206$	600729.	+	671390.i	0.986303	+	1.10232i
$207$	548751.			0.890122
$208$	−26540.0	+	117604.i	−0.0425347	+	0.188479i
$209$	1.00826e6			1.59664
$210$	102328.	+	114364.i	0.160120	+	0.178955i
$211$			44234.7i			0.0684001i	0.999415	+	0.0342000i	$0.0108883\pi$
$211$			44234.7i			0.0684001i	−0.999415	+	0.0342000i	$0.989112\pi$
$212$	−404185.	−	45040.6i	−0.617647	−	0.0688279i
$213$		−	142808.i		−	0.215677i
$214$	571501.	−	511352.i	0.853065	−	0.763284i
$215$	−363900.			−0.536891
$216$	162491.	+	228123.i	0.236971	+	0.332686i
$217$	179374.			0.258589
$218$	−485383.	+	434298.i	−0.691741	+	0.618938i
$219$			101836.i			0.143480i
$220$	−150823.	+	1.35345e6i	−0.210092	+	1.88532i
$221$			26303.1i			0.0362264i
$222$	−58144.8	−	64984.1i	−0.0791823	−	0.0884962i
$223$	−73883.6			−0.0994915			−0.0497458	−	0.998762i	$-0.515841\pi$
$223$	−73883.6			−0.0994915			−0.0497458	+	0.998762i	$0.515841\pi$
$224$	317541.	+	570424.i	0.422843	+	0.759587i
$225$	−545016.			−0.717716
$226$	−72392.4	−	80907.5i	−0.0942804	−	0.105370i
$227$		−	195146.i		−	0.251359i	−0.992071	−	0.125680i	$-0.959889\pi$
$227$		−	195146.i		−	0.251359i	0.992071	−	0.125680i	$-0.0401111\pi$
$228$	20210.6	−	181366.i	0.0257479	−	0.231056i
$229$		−	1.55451e6i		−	1.95886i	−0.201779	−	0.979431i	$-0.564672\pi$
$229$		−	1.55451e6i		−	1.95886i	0.201779	−	0.979431i	$-0.435328\pi$
$230$	736189.	−	658708.i	0.917634	−	0.821057i
$231$	−211058.			−0.260239
$232$	−405961.	−	569932.i	−0.495181	−	0.695189i
$233$	−56457.4			−0.0681289			−0.0340644	−	0.999420i	$-0.510845\pi$
$233$	−56457.4			−0.0681289			−0.0340644	+	0.999420i	$0.510845\pi$
$234$	115352.	−	103212.i	0.137717	−	0.123223i
$235$			1.55775e6i			1.84004i
$236$	−448777.	−	50009.7i	−0.524506	−	0.0584486i
$237$			163414.i			0.188981i
$238$	94975.2	+	106147.i	0.108685	+	0.121469i
$239$	−551027.			−0.623990			−0.311995	−	0.950084i	$-0.600997\pi$
$239$	−551027.			−0.623990			−0.311995	+	0.950084i	$0.600997\pi$
$240$	240434.	+	54259.7i	0.269444	+	0.0608064i
$241$	1.31586e6			1.45938			0.729689	−	0.683779i	$-0.239665\pi$
$241$	1.31586e6			1.45938			0.729689	+	0.683779i	$0.239665\pi$
$242$	−641401.	−	716846.i	−0.704030	−	0.786842i
$243$		−	543387.i		−	0.590328i
$244$	−1.33671e6	−	148957.i	−1.43735	−	0.160172i
$245$			303591.i			0.323127i
$246$	111871.	−	100097.i	0.117864	−	0.105459i
$247$	−206303.			−0.215161
$248$	234658.	−	167146.i	0.242274	−	0.172571i
$249$	142245.			0.145391
$250$	243172.	−	217580.i	0.246073	−	0.220175i
$251$			95208.0i			0.0953870i	0.998862	+	0.0476935i	$0.0151871\pi$
$251$			95208.0i			0.0953870i	−0.998862	+	0.0476935i	$0.984813\pi$
$252$	92829.3	−	833031.i	0.0920839	−	0.826342i
$253$			1.35862e6i			1.33444i
$254$	384743.	+	429998.i	0.374185	+	0.418199i
$255$	53775.2			0.0517883
$256$	946947.	+	450337.i	0.903079	+	0.429475i
$257$	−1.73166e6			−1.63542			−0.817711	−	0.575630i	$-0.804757\pi$
$257$	−1.73166e6			−1.63542			−0.817711	+	0.575630i	$0.804757\pi$
$258$	−60401.0	−	67505.7i	−0.0564930	−	0.0631380i
$259$			533816.i			0.494473i
$260$	30860.2	−	276933.i	0.0283116	−	0.254063i
$261$			898377.i			0.816315i
$262$	47621.0	−	42609.1i	0.0428593	−	0.0383485i
$263$	1.51692e6			1.35230			0.676150	−	0.736764i	$-0.263647\pi$
$263$	1.51692e6			1.35230			0.676150	+	0.736764i	$0.263647\pi$
$264$	−276107.	+	196670.i	−0.243819	+	0.173672i
$265$	939954.			0.822227
$266$	−832541.	+	744920.i	−0.721443	+	0.645514i
$267$		−	209652.i		−	0.179978i
$268$	1.72225e6	+	191920.i	1.46473	+	0.163224i
$269$		−	1.89610e6i		−	1.59765i	−0.601565	−	0.798824i	$-0.705456\pi$
$269$		−	1.89610e6i		−	1.59765i	0.601565	−	0.798824i	$-0.294544\pi$
$270$	−431640.	−	482412.i	−0.360340	−	0.402725i
$271$	476326.			0.393986			0.196993	−	0.980405i	$-0.436882\pi$
$271$	476326.			0.393986			0.196993	+	0.980405i	$0.436882\pi$
$272$	223158.	+	50360.9i	0.182890	+	0.0412735i
$273$	43185.0			0.0350693
$274$	387584.	+	433173.i	0.311881	+	0.348566i
$275$		−	1.34938e6i		−	1.07597i
$276$	244388.	+	27233.6i	0.193111	+	0.0215195i
$277$			842760.i			0.659940i	0.943991	+	0.329970i	$0.107039\pi$
$277$			842760.i			0.659940i	−0.943991	+	0.329970i	$0.892961\pi$
$278$	−1.44989e6	+	1.29730e6i	−1.12518	+	1.00676i
$279$	−369889.			−0.284486
$280$	−875413.	−	1.22900e6i	−0.667295	−	0.936821i
$281$	−1.64465e6			−1.24254			−0.621268	−	0.783598i	$-0.713382\pi$
$281$	−1.64465e6			−1.24254			−0.621268	+	0.783598i	$0.713382\pi$
$282$	−288971.	+	258558.i	−0.216387	+	0.193614i
$283$		−	2.22864e6i		−	1.65415i	−0.562092	−	0.827074i	$-0.690003\pi$
$283$		−	2.22864e6i		−	1.65415i	0.562092	−	0.827074i	$-0.309997\pi$
$284$	−155510.	+	1.39552e6i	−0.114410	+	1.02669i
$285$			421776.i			0.307588i
$286$	255537.	+	285595.i	0.184731	+	0.206460i
$287$	−918975.			−0.658565
$288$	−654804.	−	1.17628e6i	−0.465190	−	0.835657i
$289$	−1.36995e6			−0.964848
$290$	1.07839e6	+	1.20524e6i	0.752976	+	0.841545i
$291$			202922.i			0.140474i
$292$	110894.	−	995140.i	0.0761117	−	0.683010i
$293$		−	692080.i		−	0.470964i	−0.971879	−	0.235482i	$-0.924333\pi$
$293$		−	692080.i		−	0.470964i	0.971879	−	0.235482i	$-0.0756668\pi$
$294$	−56317.9	+	50390.6i	−0.0379995	+	0.0340002i
$295$	1.04366e6			0.698236
$296$	497426.	+	698341.i	0.329989	+	0.463275i
$297$	890284.			0.585649
$298$	785997.	−	703274.i	0.512720	−	0.458758i
$299$		−	277991.i		−	0.179826i
$300$	−242725.	−	27048.2i	−0.155708	−	0.0173514i
$301$			554530.i			0.352784i
$302$	−1.07792e6	−	1.20471e6i	−0.680095	−	0.760091i
$303$	−162597.			−0.101743
$304$	−394996.	+	1.75030e6i	−0.245137	+	1.08624i
$305$	3.10858e6			1.91343
$306$	−195849.	−	218886.i	−0.119569	−	0.133633i
$307$			2.91707e6i			1.76645i	0.468952	+	0.883223i	$0.344632\pi$
$307$			2.91707e6i			1.76645i	−0.468952	+	0.883223i	$0.655368\pi$
$308$	2.06246e6	+	229831.i	1.23882	+	0.138049i
$309$		−	518314.i		−	0.308814i
$310$	−496233.	+	444007.i	−0.293279	+	0.262413i
$311$	1.10725e6			0.649151			0.324575	−	0.945860i	$-0.394779\pi$
$311$	1.10725e6			0.649151			0.324575	+	0.945860i	$0.394779\pi$
$312$	56494.9	−	40241.2i	0.0328566	−	0.0234037i
$313$	−1.65389e6			−0.954213			−0.477107	−	0.878845i	$-0.658314\pi$
$313$	−1.65389e6			−0.954213			−0.477107	+	0.878845i	$0.658314\pi$
$314$	2.02629e6	−	1.81303e6i	1.15978	−	1.03772i
$315$			1.93726e6i			1.10005i
$316$	177950.	−	1.59688e6i	0.100249	−	0.899612i
$317$			459259.i			0.256691i	0.991730	+	0.128345i	$0.0409666\pi$
$317$			459259.i			0.256691i	−0.991730	+	0.128345i	$0.959033\pi$
$318$	156016.	+	174367.i	0.0865168	+	0.0966934i
$319$	−2.22425e6			−1.22379
$320$	−2.29044e6	−	792047.i	−1.25039	−	0.432390i
$321$	−441199.			−0.238986
$322$	−1.00377e6	−	1.12184e6i	−0.539505	−	0.602965i
$323$			391469.i			0.208781i
$324$	−182303.	+	1.63594e6i	−0.0964784	+	0.865777i
$325$			276099.i			0.144996i
$326$	744544.	−	666184.i	0.388013	−	0.347176i
$327$	374717.			0.193791
$328$	−1.20221e6	+	856329.i	−0.617014	+	0.439497i
$329$	2.37378e6			1.20907
$330$	583885.	−	522433.i	0.295150	−	0.264086i
$331$		−	1.55618e6i		−	0.780711i	−0.920664	−	0.390356i	$-0.872352\pi$
$331$		−	1.55618e6i		−	0.780711i	0.920664	−	0.390356i	$-0.127648\pi$
$332$	−1.39002e6	−	154898.i	−0.692111	−	0.0771258i
$333$		−	1.10079e6i		−	0.543993i
$334$	−825513.	−	922614.i	−0.404909	−	0.452537i
$335$	−4.00519e6			−1.94989
$336$	82683.8	−	366386.i	0.0399551	−	0.177048i
$337$	919178.			0.440885			0.220442	−	0.975400i	$-0.429250\pi$
$337$	919178.			0.440885			0.220442	+	0.975400i	$0.429250\pi$
$338$	1.34823e6	+	1.50682e6i	0.641908	+	0.717413i
$339$			62460.8i			0.0295194i
$340$	−525492.	−	58558.5i	−0.246529	−	0.0274722i
$341$		−	915790.i		−	0.426491i
$342$	1.71679e6	−	1.53611e6i	0.793693	−	0.710160i
$343$	2.35684e6			1.08167
$344$	516728.	+	725439.i	0.235432	+	0.330525i
$345$	−568339.			−0.257075
$346$	−2.20373e6	+	1.97180e6i	−0.989620	+	0.885466i
$347$			1.87289e6i			0.835003i	0.908676	+	0.417502i	$0.137094\pi$
$347$			1.87289e6i			0.835003i	−0.908676	+	0.417502i	$0.862906\pi$
$348$	−44584.9	+	400096.i	−0.0197351	+	0.177099i
$349$		−	2.41450e6i		−	1.06112i	−0.847649	−	0.530558i	$-0.821982\pi$
$349$		−	2.41450e6i		−	1.06112i	0.847649	−	0.530558i	$-0.178018\pi$
$350$	996941.	+	1.11421e6i	0.435010	+	0.486178i
$351$	−182163.			−0.0789210
$352$	2.91228e6	−	1.62120e6i	1.25279	−	0.697395i
$353$	−2.43268e6			−1.03908			−0.519539	−	0.854447i	$-0.673896\pi$
$353$	−2.43268e6			−1.03908			−0.519539	+	0.854447i	$0.673896\pi$
$354$	173228.	+	193604.i	0.0734701	+	0.0821120i
$355$		−	3.24535e6i		−	1.36676i
$356$	−228300.	+	2.04872e6i	−0.0954732	+	0.856756i
$357$		−	81945.5i		−	0.0340294i
$358$	−1.73290e6	+	1.55052e6i	−0.714604	+	0.639395i
$359$	2.14148e6			0.876958			0.438479	−	0.898741i	$-0.355517\pi$
$359$	2.14148e6			0.876958			0.438479	+	0.898741i	$0.355517\pi$
$360$	1.80520e6	+	2.53433e6i	0.734123	+	1.03064i
$361$	−594310.			−0.240019
$362$	−561085.	+	502033.i	−0.225039	+	0.201354i
$363$			553407.i			0.220434i
$364$	−422004.	−	47026.3i	−0.166941	−	0.0186032i
$365$			2.31425e6i			0.909241i
$366$	515970.	+	576661.i	0.201336	+	0.225018i
$367$	1.43273e6			0.555262			0.277631	−	0.960688i	$-0.410451\pi$
$367$	1.43273e6			0.555262			0.277631	+	0.960688i	$0.410451\pi$
$368$	−2.35851e6	−	532253.i	−0.907858	−	0.204880i
$369$	1.89503e6			0.724519
$370$	−1.32136e6	−	1.47679e6i	−0.501784	−	0.560806i
$371$		−	1.43235e6i		−	0.540275i
$372$	−164732.	−	18357.0i	−0.0617191	−	0.00687771i
$373$			2.57608e6i			0.958711i	0.877621	+	0.479356i	$0.159130\pi$
$373$			2.57608e6i			0.958711i	−0.877621	+	0.479356i	$0.840870\pi$
$374$	541929.	−	484893.i	0.200338	−	0.179253i
$375$	−187730.			−0.0689374
$376$	3.10538e6	−	2.21196e6i	1.13278	−	0.806876i
$377$	455108.			0.164915
$378$	−735124.	+	657756.i	−0.264625	+	0.236775i
$379$		−	1.88270e6i		−	0.673260i	−0.941637	−	0.336630i	$-0.890713\pi$
$379$		−	1.88270e6i		−	0.673260i	0.941637	−	0.336630i	$-0.109287\pi$
$380$	459292.	−	4.12159e6i	0.163166	−	1.46422i
$381$		−	331960.i		−	0.117158i
$382$	3.14376e6	+	3.51355e6i	1.10228	+	1.23193i
$383$	−929245.			−0.323693			−0.161847	−	0.986816i	$-0.551745\pi$
$383$	−929245.			−0.323693			−0.161847	+	0.986816i	$0.551745\pi$
$384$	−233243.	−	556356.i	−0.0807198	−	0.192542i
$385$	−4.79636e6			−1.64915
$386$	−2.25396e6	−	2.51908e6i	−0.769977	−	0.860546i
$387$		−	1.14350e6i		−	0.388114i
$388$	220972.	−	1.98296e6i	0.0745174	−	0.668703i
$389$			1.88218e6i			0.630647i	0.948984	+	0.315324i	$0.102113\pi$
$389$			1.88218e6i			0.630647i	−0.948984	+	0.315324i	$0.897887\pi$
$390$	−119470.	+	106896.i	−0.0397738	+	0.0355878i
$391$	−527501.			−0.174494
$392$	605211.	−	431090.i	0.198926	−	0.141694i
$393$	−36763.5			−0.0120070
$394$	−2.90115e6	+	2.59581e6i	−0.941519	+	0.842428i
$395$			3.71364e6i			1.19759i
$396$	−4.25301e6	−	473937.i	−1.36288	−	0.151874i
$397$			4.38186e6i			1.39535i	0.716417	+	0.697673i	$0.245781\pi$
$397$			4.38186e6i			1.39535i	−0.716417	+	0.697673i	$0.754219\pi$
$398$	−3.68719e6	−	4.12089e6i	−1.16678	−	1.30402i
$399$	642724.			0.202112
$400$	2.34245e6	+	528630.i	0.732017	+	0.165197i
$401$	1.43544e6			0.445784			0.222892	−	0.974843i	$-0.428450\pi$
$401$	1.43544e6			0.445784			0.222892	+	0.974843i	$0.428450\pi$
$402$	−664790.	−	742986.i	−0.205173	−	0.229306i
$403$			187382.i			0.0574732i
$404$	1.58890e6	+	177060.i	0.484332	+	0.0539718i
$405$		−	3.80448e6i		−	1.15254i
$406$	1.83660e6	−	1.64331e6i	0.552968	−	0.494771i
$407$	2.72538e6			0.815533
$408$	−76359.3	−	107202.i	−0.0227097	−	0.0318824i
$409$	−479384.			−0.141702			−0.0708509	−	0.997487i	$-0.522571\pi$
$409$	−479384.			−0.141702			−0.0708509	+	0.997487i	$0.522571\pi$
$410$	2.54231e6	−	2.27475e6i	0.746912	−	0.668303i
$411$		−	334411.i		−	0.0976508i
$412$	−564418.	+	5.06497e6i	−0.163816	+	1.47005i
$413$		−	1.59038e6i		−	0.458801i
$414$	2.06989e6	+	2.31336e6i	0.593535	+	0.663350i
$415$	3.23257e6			0.921356
$416$	−595889.	+	331717.i	−0.168823	+	0.0939796i
$417$	1.11932e6			0.315220
$418$	3.80317e6	+	4.25052e6i	1.06464	+	1.18987i
$419$			4.82901e6i			1.34376i	0.740658	+	0.671882i	$0.234514\pi$
$419$			4.82901e6i			1.34376i	−0.740658	+	0.671882i	$0.765486\pi$
$420$	−96142.9	+	862766.i	−0.0265946	+	0.238655i
$421$		−	918869.i		−	0.252667i	−0.991988	−	0.126333i	$-0.959679\pi$
$421$		−	918869.i		−	0.252667i	0.991988	−	0.126333i	$-0.0403209\pi$
$422$	−186479.	+	166853.i	−0.0509741	+	0.0456093i
$423$	−4.89498e6			−1.33015
$424$	−1.33471e6	−	1.87381e6i	−0.360555	−	0.506186i
$425$	523910.			0.140697
$426$	602033.	−	538671.i	0.160730	−	0.143814i
$427$		−	4.73702e6i		−	1.25729i
$428$	4.31140e6	+	480444.i	1.13765	+	0.126775i
$429$		−	220480.i		−	0.0578397i
$430$	−1.37263e6	−	1.53409e6i	−0.358000	−	0.400110i
$431$	−4.81272e6			−1.24795			−0.623975	−	0.781444i	$-0.714483\pi$
$431$	−4.81272e6			−1.24795			−0.623975	+	0.781444i	$0.714483\pi$
$432$	−348777.	+	1.54549e6i	−0.0899162	+	0.398435i
$433$	5.84598e6			1.49843			0.749217	−	0.662324i	$-0.230430\pi$
$433$	5.84598e6			1.49843			0.749217	+	0.662324i	$0.230430\pi$
$434$	676600.	+	756186.i	0.172428	+	0.192710i
$435$		−	930445.i		−	0.235759i
$436$	−3.66173e6	−	408047.i	−0.922508	−	0.102800i
$437$		−	4.13735e6i		−	1.03638i
$438$	−429308.	+	384125.i	−0.106926	+	0.0956726i
$439$	−2.28777e6			−0.566568			−0.283284	−	0.959036i	$-0.591424\pi$
$439$	−2.28777e6			−0.566568			−0.283284	+	0.959036i	$0.591424\pi$
$440$	−6.27462e6	+	4.46940e6i	−1.54510	+	1.10057i
$441$	−953988.			−0.233586
$442$	−110885.	+	99215.2i	−0.0269972	+	0.0241559i
$443$		−	982970.i		−	0.237975i	−0.992896	−	0.118987i	$-0.962035\pi$
$443$		−	982970.i		−	0.237975i	0.992896	−	0.118987i	$-0.0379648\pi$
$444$	54630.2	−	490240.i	0.0131515	−	0.118019i
$445$		−	4.76441e6i		−	1.14054i
$446$	−278689.	−	311470.i	−0.0663411	−	0.0741446i
$447$	−606791.			−0.143638
$448$	−1.20696e6	+	3.49029e6i	−0.284118	+	0.821612i
$449$	−2.86769e6			−0.671299			−0.335650	−	0.941987i	$-0.608956\pi$
$449$	−2.86769e6			−0.671299			−0.335650	+	0.941987i	$0.608956\pi$
$450$	−2.05580e6	−	2.29762e6i	−0.478575	−	0.534867i
$451$			4.69180e6i			1.08617i
$452$	68016.6	−	610367.i	0.0156592	−	0.140522i
$453$			930040.i			0.212939i
$454$	822673.	−	736091.i	0.187322	−	0.167607i
$455$	981395.			0.222236
$456$	840814.	−	598910.i	0.189360	−	0.134881i
$457$	−451218.			−0.101064			−0.0505319	−	0.998722i	$-0.516092\pi$
$457$	−451218.			−0.101064			−0.0505319	+	0.998722i	$0.516092\pi$
$458$	6.55331e6	−	5.86360e6i	1.45981	−	1.30617i
$459$			345662.i			0.0765809i
$460$	5.55381e6	+	618892.i	1.22376	+	0.136371i
$461$		−	242143.i		−	0.0530665i	−0.999648	−	0.0265332i	$-0.991553\pi$
$461$		−	242143.i		−	0.0530665i	0.999648	−	0.0265332i	$-0.00844678\pi$
$462$	−796111.	−	889753.i	−0.173528	−	0.193939i
$463$	4.80106e6			1.04084			0.520421	−	0.853910i	$-0.325775\pi$
$463$	4.80106e6			1.04084			0.520421	+	0.853910i	$0.325775\pi$
$464$	871368.	−	3.86119e6i	0.187891	−	0.832580i
$465$	383093.			0.0821621
$466$	−212957.	−	238007.i	−0.0454285	−	0.0507720i
$467$		−	306183.i		−	0.0649664i	−0.999472	−	0.0324832i	$-0.989658\pi$
$467$		−	306183.i		−	0.0649664i	0.999472	−	0.0324832i	$-0.0103415\pi$
$468$	870219.	+	96973.4i	0.183660	+	0.0204662i
$469$			6.10331e6i			1.28125i
$470$	−6.56697e6	+	5.87582e6i	−1.37126	+	1.22694i
$471$	−1.56430e6			−0.324913
$472$	−1.48196e6	−	2.08054e6i	−0.306183	−	0.429854i
$473$	2.83114e6			0.581846
$474$	−688902.	+	616398.i	−0.140835	+	0.126013i
$475$			4.10919e6i			0.835645i
$476$	−89234.5	+	800771.i	−0.0180516	+	0.161991i
$477$			2.95366e6i			0.594381i
$478$	−2.07847e6	−	2.32296e6i	−0.416078	−	0.465019i
$479$	3.99196e6			0.794964			0.397482	−	0.917610i	$-0.369884\pi$
$479$	3.99196e6			0.794964			0.397482	+	0.917610i	$0.369884\pi$
$480$	678177.	+	1.21826e6i	0.134351	+	0.241345i
$481$	−557647.			−0.109900
$482$	4.96343e6	+	5.54726e6i	0.973116	+	1.08758i
$483$			866064.i			0.168920i
$484$	602632.	−	5.40789e6i	0.116933	−	1.04934i
$485$			4.61147e6i			0.890195i
$486$	2.29075e6	−	2.04966e6i	0.439933	−	0.393632i
$487$	−6.45190e6			−1.23272			−0.616361	−	0.787464i	$-0.711394\pi$
$487$	−6.45190e6			−1.23272			−0.616361	+	0.787464i	$0.711394\pi$
$488$	−4.41410e6	−	6.19700e6i	−0.839060	−	1.17796i
$489$	−574790.			−0.108702
$490$	−1.27984e6	+	1.14514e6i	−0.240805	+	0.215462i
$491$		−	4.37221e6i		−	0.818459i	−0.912432	−	0.409229i	$-0.865798\pi$
$491$		−	4.37221e6i		−	0.818459i	0.912432	−	0.409229i	$-0.134202\pi$
$492$	843958.	+	94047.0i	0.157184	+	0.0175159i
$493$		−	863588.i		−	0.160025i
$494$	−778175.	−	869708.i	−0.143470	−	0.160345i
$495$	9.89062e6			1.81431
$496$	1.58977e6	+	358769.i	0.290155	+	0.0654803i
$497$	−4.94544e6			−0.898078
$498$	536549.	+	599661.i	0.0969473	+	0.108351i
$499$		−	5.17114e6i		−	0.929683i	−0.885394	−	0.464842i	$-0.846111\pi$
$499$		−	5.17114e6i		−	0.929683i	0.885394	−	0.464842i	$-0.153889\pi$
$500$	1.83449e6	+	204428.i	0.328164	+	0.0365692i
$501$			712260.i			0.126778i
$502$	−401367.	+	359125.i	−0.0710857	+	0.0636043i
$503$	−4.16421e6			−0.733859			−0.366929	−	0.930249i	$-0.619591\pi$
$503$	−4.16421e6			−0.733859			−0.366929	+	0.930249i	$0.619591\pi$
$504$	3.86195e6	−	2.75085e6i	0.677220	−	0.482382i
$505$	−3.69508e6			−0.644755
$506$	−5.72753e6	+	5.12474e6i	−0.994469	+	0.889806i
$507$		−	1.16327e6i		−	0.200983i
$508$	−361487.	+	3.24391e6i	−0.0621489	+	0.557711i
$509$			4.71340e6i			0.806381i	0.915116	+	0.403190i	$0.132099\pi$
$509$			4.71340e6i			0.806381i	−0.915116	+	0.403190i	$0.867901\pi$
$510$	202840.	+	226699.i	0.0345326	+	0.0385945i
$511$	3.52658e6			0.597450
$512$	1.67341e6	+	5.69070e6i	0.282115	+	0.959381i
$513$	−2.71114e6			−0.454839
$514$	−6.53182e6	−	7.30013e6i	−1.09050	−	1.21877i
$515$		−	1.17789e7i		−	1.95697i
$516$	56750.0	−	509263.i	0.00938301	−	0.0842011i
$517$		−	1.21192e7i		−	1.99411i
$518$	−2.25040e6	+	2.01356e6i	−0.368498	+	0.329715i
$519$	1.70128e6			0.277242
$520$	1.28387e6	−	914494.i	0.208215	−	0.148311i
$521$	2.34479e6			0.378451			0.189225	−	0.981934i	$-0.439402\pi$
$521$	2.34479e6			0.378451			0.189225	+	0.981934i	$0.439402\pi$
$522$	−3.78728e6	+	3.38868e6i	−0.608346	+	0.544320i
$523$			8.17020e6i			1.30611i	0.757312	+	0.653053i	$0.226512\pi$
$523$			8.17020e6i			1.30611i	−0.757312	+	0.653053i	$0.773488\pi$
$524$	359253.	+	40033.6i	0.0571573	+	0.00636936i
$525$		−	860169.i		−	0.136203i
$526$	5.72182e6	+	6.39485e6i	0.901716	+	1.00778i
$527$	355565.			0.0557690
$528$	−1.87058e6	−	422140.i	−0.292005	−	0.0658979i
$529$	−861301.			−0.133818
$530$	3.54551e6	+	3.96255e6i	0.548263	+	0.612753i
$531$			3.27953e6i			0.504749i
$532$	−6.28070e6	−	699893.i	−0.962119	−	0.107214i
$533$		−	960000.i		−	0.146370i
$534$	883826.	−	790807.i	0.134126	−	0.120010i
$535$	−1.00264e7			−1.51447
$536$	5.68725e6	+	7.98438e6i	0.855048	+	1.20041i
$537$	1.33780e6			0.200196
$538$	7.99337e6	−	7.15210e6i	1.19062	−	1.06531i
$539$		−	2.36193e6i		−	0.350183i
$540$	405550.	−	3.63932e6i	0.0598494	−	0.537076i
$541$			3.53355e6i			0.519060i	0.965735	+	0.259530i	$0.0835677\pi$
$541$			3.53355e6i			0.519060i	−0.965735	+	0.259530i	$0.916432\pi$
$542$	1.79670e6	+	2.00804e6i	0.262711	+	0.293612i
$543$	433158.			0.0630445
$544$	629447.	+	1.13072e6i	0.0911930	+	0.163817i
$545$	8.51556e6			1.22807
$546$	162894.	+	182055.i	0.0233843	+	0.0261348i
$547$		−	657235.i		−	0.0939187i	−0.998897	−	0.0469594i	$-0.985047\pi$
$547$		−	657235.i		−	0.0939187i	0.998897	−	0.0469594i	$-0.0149531\pi$
$548$	−364156.	+	3.26786e6i	−0.0518008	+	0.464850i
$549$			9.76826e6i			1.38320i
$550$	5.68855e6	−	5.08985e6i	0.801853	−	0.717461i
$551$	6.77338e6			0.950444
$552$	807026.	+	1.13299e6i	0.112730	+	0.158263i
$553$	5.65903e6			0.786918
$554$	−3.55281e6	+	3.17889e6i	−0.491810	+	0.440049i
$555$			1.14008e6i			0.157110i
$556$	−1.09380e7	−	1.21888e6i	−1.50055	−	0.167215i
$557$		−	1.35929e7i		−	1.85641i	−0.372065	−	0.928207i	$-0.621350\pi$
$557$		−	1.35929e7i		−	1.85641i	0.372065	−	0.928207i	$-0.378650\pi$
$558$	−1.39522e6	−	1.55934e6i	−0.189696	−	0.212009i
$559$	−579286.			−0.0784085
$560$	1.87902e6	−	8.32626e6i	0.253198	−	1.12197i
$561$	−418370.			−0.0561247
$562$	−6.20364e6	−	6.93335e6i	−0.828525	−	0.925981i
$563$			1.18702e7i			1.57829i	0.614206	+	0.789146i	$0.289477\pi$
$563$			1.18702e7i			1.57829i	−0.614206	+	0.789146i	$0.710523\pi$
$564$	−2.18000e6	−	242930.i	−0.288575	−	0.0321575i
$565$			1.41944e6i			0.187067i
$566$	9.39526e6	−	8.40645e6i	1.23273	−	1.10299i
$567$	−5.79746e6			−0.757322
$568$	−6.46965e6	+	4.60831e6i	−0.841414	+	0.599337i
$569$	−1.16590e7			−1.50966			−0.754831	−	0.655920i	$-0.772281\pi$
$569$	−1.16590e7			−1.50966			−0.754831	+	0.655920i	$0.772281\pi$
$570$	−1.77807e6	+	1.59094e6i	−0.229225	+	0.205100i
$571$			1.14849e7i			1.47414i	0.675819	+	0.737068i	$0.263790\pi$
$571$			1.14849e7i			1.47414i	−0.675819	+	0.737068i	$0.736210\pi$
$572$	−240092.	+	2.15453e6i	−0.0306822	+	0.275336i
$573$		−	2.71247e6i		−	0.345126i
$574$	−3.46638e6	−	3.87411e6i	−0.439133	−	0.490786i
$575$	−5.53709e6			−0.698413
$576$	2.48889e6	−	7.19736e6i	0.312571	−	0.903893i
$577$	7.93609e6			0.992355			0.496178	−	0.868221i	$-0.334736\pi$
$577$	7.93609e6			0.992355			0.496178	+	0.868221i	$0.334736\pi$
$578$	−5.16744e6	−	5.77526e6i	−0.643362	−	0.719038i
$579$			1.94474e6i			0.241082i
$580$	−1.01321e6	+	9.09231e6i	−0.125063	+	1.12229i
$581$		−	4.92595e6i		−	0.605411i
$582$	−855456.	+	765423.i	−0.104686	+	0.0936685i
$583$	−7.31282e6			−0.891074
$584$	4.61349e6	−	3.28618e6i	0.559754	−	0.398712i
$585$	−2.02374e6			−0.244493
$586$	2.91759e6	−	2.61053e6i	0.350978	−	0.314039i
$587$		−	7.16597e6i		−	0.858381i	−0.903214	−	0.429190i	$-0.858799\pi$
$587$		−	7.16597e6i		−	0.858381i	0.903214	−	0.429190i	$-0.141201\pi$
$588$	−424862.	−	47344.8i	−0.0506763	−	0.00564714i
$589$			2.78881e6i			0.331231i
$590$	3.93667e6	+	4.39972e6i	0.465585	+	0.520349i
$591$	2.23969e6			0.263766
$592$	−1.06769e6	+	4.73114e6i	−0.125211	+	0.554832i
$593$	−1.99624e6			−0.233118			−0.116559	−	0.993184i	$-0.537186\pi$
$593$	−1.99624e6			−0.233118			−0.116559	+	0.993184i	$0.537186\pi$
$594$	3.35815e6	+	3.75316e6i	0.390512	+	0.436446i
$595$		−	1.86224e6i		−	0.215647i
$596$	5.92957e6	+	660765.i	0.683766	+	0.0761958i
$597$			3.18134e6i			0.365320i
$598$	1.17192e6	−	1.04858e6i	0.134013	−	0.119909i
$599$	1.20579e7			1.37311			0.686555	−	0.727078i	$-0.259122\pi$
$599$	1.20579e7			1.37311			0.686555	+	0.727078i	$0.259122\pi$
$600$	−801532.	−	1.12528e6i	−0.0908956	−	0.127609i
$601$	1.50698e7			1.70185			0.850924	−	0.525289i	$-0.176043\pi$
$601$	1.50698e7			1.70185			0.850924	+	0.525289i	$0.176043\pi$
$602$	−2.33772e6	+	2.09169e6i	−0.262907	+	0.235237i
$603$		−	1.25857e7i		−	1.40956i
$604$	1.01277e6	−	9.08835e6i	0.112958	−	1.01366i
$605$			1.25764e7i			1.39690i
$606$	−613317.	−	685458.i	−0.0678427	−	0.0758227i
$607$	4.03809e6			0.444841			0.222420	−	0.974951i	$-0.428604\pi$
$607$	4.03809e6			0.444841			0.222420	+	0.974951i	$0.428604\pi$
$608$	−8.86862e6	+	4.93694e6i	−0.972965	+	0.541625i
$609$	−1.41786e6			−0.154914
$610$	1.17256e7	+	1.31048e7i	1.27588	+	1.42596i
$611$			2.47975e6i			0.268723i
$612$	184011.	−	1.65128e6i	0.0198594	−	0.178214i
$613$		−	1.07407e7i		−	1.15447i	−0.816578	−	0.577236i	$-0.804131\pi$
$613$		−	1.07407e7i		−	1.15447i	0.816578	−	0.577236i	$-0.195869\pi$
$614$	−1.22974e7	+	1.10032e7i	−1.31642	+	1.17787i
$615$	−1.96267e6			−0.209247
$616$	6.81070e6	+	9.56160e6i	0.723169	+	1.01526i
$617$	−9.37637e6			−0.991567			−0.495783	−	0.868446i	$-0.665119\pi$
$617$	−9.37637e6			−0.991567			−0.495783	+	0.868446i	$0.665119\pi$
$618$	2.18505e6	−	1.95508e6i	0.230139	−	0.205918i
$619$		−	4.03378e6i		−	0.423141i	−0.977363	−	0.211571i	$-0.932142\pi$
$619$		−	4.03378e6i		−	0.423141i	0.977363	−	0.211571i	$-0.0678579\pi$
$620$	−3.74358e6	−	417169.i	−0.391119	−	0.0435845i
$621$		−	3.65323e6i		−	0.380144i
$622$	4.17656e6	+	4.66783e6i	0.432855	+	0.483770i
$623$	−7.26025e6			−0.749431
$624$	382743.	+	86375.0i	0.0393501	+	0.00888028i
$625$	−1.15946e7			−1.18729
$626$	−6.23847e6	−	6.97227e6i	−0.636271	−	0.711113i
$627$		−	3.28141e6i		−	0.333343i
$628$	1.52863e7	+	1.70344e6i	1.54669	+	0.172356i
$629$			1.05816e6i			0.106641i
$630$	−8.16688e6	+	7.30735e6i	−0.819794	+	0.733514i
$631$	3.01348e6			0.301297			0.150648	−	0.988587i	$-0.451864\pi$
$631$	3.01348e6			0.301297			0.150648	+	0.988587i	$0.451864\pi$
$632$	7.40318e6	−	5.27326e6i	0.737268	−	0.525154i
$633$	143962.			0.0142804
$634$	−1.93609e6	+	1.73233e6i	−0.191295	+	0.171162i
$635$		−	7.54389e6i		−	0.742440i
$636$	−146585.	+	1.31543e6i	−0.0143697	+	0.128951i
$637$			483280.i			0.0471900i
$638$	−8.38986e6	−	9.37672e6i	−0.816024	−	0.912010i
$639$	1.01980e7			0.988017
$640$	−5.30052e6	−	1.26434e7i	−0.511527	−	1.22015i
$641$	−2.09755e6			−0.201636			−0.100818	−	0.994905i	$-0.532146\pi$
$641$	−2.09755e6			−0.201636			−0.100818	+	0.994905i	$0.532146\pi$
$642$	−1.66421e6	−	1.85996e6i	−0.159356	−	0.178101i
$643$			3.48456e6i			0.332369i	0.986095	+	0.166185i	$0.0531448\pi$
$643$			3.48456e6i			0.332369i	−0.986095	+	0.166185i	$0.946855\pi$
$644$	943100.	−	8.46318e6i	0.0896073	−	0.804117i
$645$			1.18432e6i			0.112091i
$646$	−1.65031e6	+	1.47662e6i	−0.155591	+	0.139216i
$647$	9.25999e6			0.869660			0.434830	−	0.900513i	$-0.356808\pi$
$647$	9.25999e6			0.869660			0.434830	+	0.900513i	$0.356808\pi$
$648$	−7.58427e6	+	5.40226e6i	−0.709539	+	0.505403i
$649$	−8.11962e6			−0.756700
$650$	−1.16395e6	+	1.04145e6i	−0.108056	+	0.0966838i
$651$		−	583777.i		−	0.0539876i
$652$	5.61684e6	+	625917.i	0.517456	+	0.0576630i
$653$			1.12475e7i			1.03222i	0.856523	+	0.516109i	$0.172620\pi$
$653$			1.12475e7i			1.03222i	−0.856523	+	0.516109i	$0.827380\pi$
$654$	1.41343e6	+	1.57969e6i	0.129220	+	0.144420i
$655$	−835462.			−0.0760893
$656$	−8.14474e6	−	1.83805e6i	−0.738955	−	0.166763i
$657$	−7.27220e6			−0.657283
$658$	8.95388e6	+	1.00071e7i	0.806207	+	0.901038i
$659$		−	6.37278e6i		−	0.571630i	−0.958285	−	0.285815i	$-0.907736\pi$
$659$		−	6.37278e6i		−	0.571630i	0.958285	−	0.285815i	$-0.0922643\pi$
$660$	4.40483e6	+	490855.i	0.393613	+	0.0438625i
$661$			4.13736e6i			0.368315i	0.982897	+	0.184158i	$0.0589556\pi$
$661$			4.13736e6i			0.368315i	−0.982897	+	0.184158i	$0.941044\pi$
$662$	6.56037e6	−	5.86992e6i	0.581813	−	0.520580i
$663$	85603.7			0.00756326
$664$	−4.59016e6	−	6.44416e6i	−0.404024	−	0.567213i
$665$	1.46061e7			1.28080
$666$	4.64057e6	−	4.15217e6i	0.405402	−	0.362735i
$667$			9.12707e6i			0.794359i
$668$	775615.	−	6.96020e6i	0.0672519	−	0.603505i
$669$			240456.i			0.0207716i
$670$	−1.51076e7	−	1.68846e7i	−1.30019	−	1.45313i
$671$	−2.41847e7			−2.07365
$672$	1.85645e6	−	1.03344e6i	0.158585	−	0.0882801i
$673$	1.50812e7			1.28350			0.641752	−	0.766913i	$-0.278208\pi$
$673$	1.50812e7			1.28350			0.641752	+	0.766913i	$0.278208\pi$
$674$	3.46714e6	+	3.87497e6i	0.293983	+	0.328563i
$675$			3.62837e6i			0.306515i
$676$	−1.26674e6	+	1.13674e7i	−0.106615	+	0.956745i
$677$			1.85553e7i			1.55595i	0.628295	+	0.777975i	$0.283753\pi$
$677$			1.85553e7i			1.55595i	−0.628295	+	0.777975i	$0.716247\pi$
$678$	−263315.	+	235602.i	−0.0219989	+	0.0196836i
$679$	7.02720e6			0.584935
$680$	−1.73529e6	−	2.43619e6i	−0.143913	−	0.202041i
$681$	−635105.			−0.0524781
$682$	3.86068e6	−	3.45436e6i	0.317836	−	0.284385i
$683$			2.31850e7i			1.90176i	0.309558	+	0.950881i	$0.399819\pi$
$683$			2.31850e7i			1.90176i	−0.309558	+	0.950881i	$0.600181\pi$
$684$	1.29515e7	+	1.44326e6i	1.05847	+	0.117951i
$685$		−	7.59960e6i		−	0.618820i
$686$	8.89002e6	+	9.93571e6i	0.721261	+	0.806100i
$687$	−5.05917e6			−0.408966
$688$	−1.10912e6	+	4.91472e6i	−0.0893323	+	0.395847i
$689$	1.49629e6			0.120080
$690$	−2.14378e6	−	2.39594e6i	−0.171418	−	0.191581i
$691$		−	1.04315e7i		−	0.831099i	−0.909571	−	0.415549i	$-0.863589\pi$
$691$		−	1.04315e7i		−	0.831099i	0.909571	−	0.415549i	$-0.136411\pi$
$692$	−1.66250e7	−	1.85261e6i	−1.31976	−	0.147068i
$693$		−	1.50718e7i		−	1.19216i
$694$	−7.89551e6	+	7.06454e6i	−0.622273	+	0.556782i
$695$	2.54369e7			1.99757
$696$	−1.85485e6	+	1.32121e6i	−0.145140	+	0.103383i
$697$	−1.82164e6			−0.142030
$698$	1.01788e7	−	9.10748e6i	0.790781	−	0.707554i
$699$			183742.i			0.0142238i
$700$	−936681.	+	8.40558e6i	−0.0722514	+	0.648369i
$701$		−	1.93026e7i		−	1.48362i	−0.670613	−	0.741808i	$-0.733969\pi$
$701$		−	1.93026e7i		−	1.48362i	0.670613	−	0.741808i	$-0.266031\pi$
$702$	−687120.	−	767942.i	−0.0526247	−	0.0588147i
$703$	−8.29947e6			−0.633377
$704$	1.78196e7	+	6.16211e6i	1.35508	+	0.468595i
$705$	5.06971e6			0.384159
$706$	−9.17607e6	−	1.02554e7i	−0.692859	−	0.774357i
$707$			5.63075e6i			0.423660i
$708$	−162757.	+	1.46055e6i	−0.0122027	+	0.109505i
$709$		−	5.90966e6i		−	0.441517i	−0.975329	−	0.220758i	$-0.929147\pi$
$709$		−	5.90966e6i		−	0.441517i	0.975329	−	0.220758i	$-0.0708532\pi$
$710$	1.36814e7	−	1.22415e7i	1.01856	−	0.911356i
$711$	−1.16695e7			−0.865725
$712$	−9.49790e6	+	6.76533e6i	−0.702146	+	0.500137i
$713$	−3.75790e6			−0.276835
$714$	345456.	−	309099.i	0.0253599	−	0.0226909i
$715$		−	5.01048e6i		−	0.366534i
$716$	−1.30730e7	−	1.45680e6i	−0.952998	−	0.106198i
$717$			1.79333e6i			0.130275i
$718$	8.07768e6	+	9.02782e6i	0.584757	+	0.653540i
$719$	−2.58536e7			−1.86509			−0.932543	−	0.361058i	$-0.882416\pi$
$719$	−2.58536e7			−1.86509			−0.932543	+	0.361058i	$0.882416\pi$
$720$	−3.87474e6	+	1.71697e7i	−0.278555	+	1.23433i
$721$	−1.79492e7			−1.28590
$722$	−2.24174e6	−	2.50542e6i	−0.160045	−	0.178870i
$723$		−	4.28250e6i		−	0.304685i
$724$	−4.23282e6	−	471687.i	−0.300112	−	0.0334432i
$725$		−	9.06495e6i		−	0.640502i
$726$	−2.33299e6	+	2.08745e6i	−0.164275	+	0.146986i
$727$	−497513.			−0.0349115			−0.0174558	−	0.999848i	$-0.505557\pi$
$727$	−497513.			−0.0349115			−0.0174558	+	0.999848i	$0.505557\pi$
$728$	−1.39355e6	−	1.95642e6i	−0.0974530	−	0.136815i
$729$	1.07314e7			0.747889
$730$	−9.75617e6	+	8.72937e6i	−0.677598	+	0.606284i
$731$			1.09922e6i			0.0760836i
$732$	−484782.	+	4.35033e6i	−0.0334402	+	0.300085i
$733$		−	9.66956e6i		−	0.664732i	−0.943150	−	0.332366i	$-0.892153\pi$
$733$		−	9.66956e6i		−	0.664732i	0.943150	−	0.332366i	$-0.107847\pi$
$734$	5.40424e6	+	6.03992e6i	0.370250	+	0.413800i
$735$	988041.			0.0674616
$736$	−6.65249e6	−	1.19504e7i	−0.452678	−	0.813182i
$737$	3.11603e7			2.11316
$738$	7.14805e6	+	7.98884e6i	0.483110	+	0.539936i
$739$		−	1.83759e7i		−	1.23776i	−0.785485	−	0.618881i	$-0.787586\pi$
$739$		−	1.83759e7i		−	1.23776i	0.785485	−	0.618881i	$-0.212414\pi$
$740$	1.24149e6	−	1.11409e7i	0.0833420	−	0.747894i
$741$			671416.i			0.0449207i
$742$	6.03834e6	−	5.40283e6i	0.402631	−	0.360256i
$743$	1.51555e7			1.00716			0.503578	−	0.863950i	$-0.332017\pi$
$743$	1.51555e7			1.00716			0.503578	+	0.863950i	$0.332017\pi$
$744$	−543981.	−	763700.i	−0.0360289	−	0.0505813i
$745$	−1.37895e7			−0.910246
$746$	−1.08600e7	+	9.71699e6i	−0.714465	+	0.639271i
$747$			1.01579e7i			0.666040i
$748$	4.08832e6	+	455584.i	0.267172	+	0.0297724i
$749$			1.52788e7i			0.995138i
$750$	−708116.	−	791409.i	−0.0459676	−	0.0513745i
$751$	7.70448e6			0.498475			0.249238	−	0.968442i	$-0.419820\pi$
$751$	7.70448e6			0.498475			0.249238	+	0.968442i	$0.419820\pi$
$752$	2.10384e7	+	4.74782e6i	1.35665	+	0.306161i
$753$	309856.			0.0199147
$754$	1.71667e6	+	1.91859e6i	0.109966	+	0.122901i
$755$			2.11355e7i			1.34941i
$756$	−5.54578e6	−	617998.i	−0.352905	−	0.0393262i
$757$			1.96934e7i			1.24905i	0.781005	+	0.624525i	$0.214707\pi$
$757$			1.96934e7i			1.24905i	−0.781005	+	0.624525i	$0.785293\pi$
$758$	7.93686e6	−	7.10154e6i	0.501737	−	0.448931i
$759$	4.42167e6			0.278600
$760$	1.91078e7	−	1.36104e7i	1.19999	−	0.854747i
$761$	−6.73562e6			−0.421615			−0.210807	−	0.977528i	$-0.567609\pi$
$761$	−6.73562e6			−0.421615			−0.210807	+	0.977528i	$0.567609\pi$
$762$	1.39944e6	−	1.25215e6i	0.0873104	−	0.0781213i
$763$		−	1.29765e7i		−	0.806946i
$764$	−2.95374e6	+	2.65062e7i	−0.183079	+	1.64291i
$765$			3.84014e6i			0.237243i
$766$	−3.50512e6	−	3.91741e6i	−0.215839	−	0.241227i
$767$	1.66137e6			0.101972
$768$	1.46563e6	−	3.08185e6i	0.0896646	−	0.188542i
$769$	−6.67796e6			−0.407219			−0.203609	−	0.979052i	$-0.565267\pi$
$769$	−6.67796e6			−0.407219			−0.203609	+	0.979052i	$0.565267\pi$
$770$	−1.80919e7	−	2.02199e7i	−1.09966	−	1.22900i
$771$			5.63571e6i			0.341439i
$772$	2.11772e6	−	1.90040e7i	0.127887	−	1.14763i
$773$		−	2.85469e6i		−	0.171835i	−0.996302	−	0.0859173i	$-0.972618\pi$
$773$		−	2.85469e6i		−	0.171835i	0.996302	−	0.0859173i	$-0.0273821\pi$
$774$	4.82064e6	−	4.31329e6i	0.289236	−	0.258795i
$775$	3.73232e6			0.223215
$776$	9.19302e6	−	6.54816e6i	0.548030	−	0.390360i
$777$	1.73731e6			0.103235
$778$	−7.93466e6	+	7.09957e6i	−0.469980	+	0.420517i
$779$		−	1.42877e7i		−	0.843565i
$780$	−901282.	−	100435.i	−0.0530425	−	0.00591083i
$781$			2.52488e7i			1.48120i
$782$	−1.98973e6	−	2.22378e6i	−0.116353	−	0.130039i
$783$	5.98082e6			0.348623
$784$	4.10020e6	+	925307.i	0.238240	+	0.0537645i
$785$	−3.55492e7			−2.05899
$786$	−138672.	−	154983.i	−0.00800630	−	0.00894805i
$787$			1.38785e7i			0.798738i	0.916790	+	0.399369i	$0.130771\pi$
$787$			1.38785e7i			0.798738i	−0.916790	+	0.399369i	$0.869229\pi$
$788$	−2.18863e7	−	2.43891e6i	−1.25561	−	0.139920i
$789$		−	4.93684e6i		−	0.282330i
$790$	−1.56555e7	+	1.40079e7i	−0.892483	+	0.798553i
$791$	2.16302e6			0.122919
$792$	−1.40444e7	−	1.97171e7i	−0.795592	−	1.11694i
$793$	4.94849e6			0.279441
$794$	−1.84725e7	+	1.65284e7i	−1.03986	+	0.930419i
$795$		−	3.05910e6i		−	0.171662i
$796$	3.46431e6	−	3.10880e7i	0.193791	−	1.73904i
$797$		−	8.67764e6i		−	0.483900i	−0.970289	−	0.241950i	$-0.922213\pi$
$797$		−	8.67764e6i		−	0.483900i	0.970289	−	0.241950i	$-0.0777871\pi$
$798$	2.42435e6	+	2.70952e6i	0.134769	+	0.150621i
$799$	4.70543e6			0.260755
$800$	6.60720e6	+	1.18690e7i	0.365000	+	0.655678i
$801$	1.49714e7			0.824484
$802$	5.41448e6	+	6.05136e6i	0.297249	+	0.332214i
$803$		−	1.80049e7i		−	0.985373i
$804$	624607.	−	5.60509e6i	0.0340774	−	0.305803i
$805$			1.96816e7i			1.07046i
$806$	−789944.	+	706805.i	−0.0428310	+	0.0383232i
$807$	−6.17089e6			−0.333553
$808$	5.24690e6	+	7.36617e6i	0.282732	+	0.396930i
$809$	7.54612e6			0.405371			0.202685	−	0.979244i	$-0.435033\pi$
$809$	7.54612e6			0.405371			0.202685	+	0.979244i	$0.435033\pi$
$810$	1.60385e7	−	1.43505e7i	0.858917	−	0.768519i
$811$		−	2.53731e7i		−	1.35463i	−0.735692	−	0.677316i	$-0.763143\pi$
$811$		−	2.53731e7i		−	1.35463i	0.735692	−	0.677316i	$-0.236857\pi$
$812$	1.38553e7	+	1.54398e6i	0.737441	+	0.0821772i
$813$		−	1.55021e6i		−	0.0822554i
$814$	1.02802e7	+	1.14894e7i	0.543799	+	0.607764i
$815$	−1.30623e7			−0.688851
$816$	163900.	−	726271.i	0.00861696	−	0.0381833i
$817$	−8.62152e6			−0.451886
$818$	−1.80824e6	−	2.02093e6i	−0.0944871	−	0.105601i
$819$			3.08388e6i			0.160653i
$820$	1.91792e7	+	2.13725e6i	0.996085	+	0.110999i
$821$		−	1.52925e7i		−	0.791812i	−0.918291	−	0.395906i	$-0.870431\pi$
$821$		−	1.52925e7i		−	0.791812i	0.918291	−	0.395906i	$-0.129569\pi$
$822$	1.40977e6	−	1.26140e6i	0.0727728	−	0.0651137i
$823$	4.47750e6			0.230428			0.115214	−	0.993341i	$-0.463245\pi$
$823$	4.47750e6			0.230428			0.115214	+	0.993341i	$0.463245\pi$
$824$	−2.34813e7	+	1.67257e7i	−1.20477	+	0.858154i
$825$	−4.39157e6			−0.224639
$826$	6.70452e6	−	5.99890e6i	0.341915	−	0.305930i
$827$			8.21663e6i			0.417763i	0.977941	+	0.208882i	$0.0669823\pi$
$827$			8.21663e6i			0.417763i	−0.977941	+	0.208882i	$0.933018\pi$
$828$	−1.94478e6	+	1.74520e7i	−0.0985811	+	0.884646i
$829$		−	1.58318e7i		−	0.800098i	−0.916494	−	0.400049i	$-0.868993\pi$
$829$		−	1.58318e7i		−	0.800098i	0.916494	−	0.400049i	$-0.131007\pi$
$830$	1.21933e7	+	1.36275e7i	0.614362	+	0.686627i
$831$	2.74278e6			0.137781
$832$	−3.64611e6	−	1.26084e6i	−0.182609	−	0.0631471i
$833$	917045.			0.0457908
$834$	4.22207e6	+	4.71870e6i	0.210189	+	0.234913i
$835$			1.61863e7i			0.803401i
$836$	−3.57329e6	+	3.20659e7i	−0.176828	+	1.58682i
$837$			2.46249e6i			0.121495i
$838$	−2.03576e7	+	1.82150e7i	−1.00142	+	0.896024i
$839$	1.29263e7			0.633970			0.316985	−	0.948430i	$-0.397329\pi$
$839$	1.29263e7			0.633970			0.316985	+	0.948430i	$0.397329\pi$
$840$	−3.99980e6	+	2.84905e6i	−0.195587	+	0.139316i
$841$	5.56893e6			0.271508
$842$	3.87366e6	−	3.46598e6i	0.188296	−	0.168479i
$843$			5.35256e6i			0.259413i
$844$	−1.40680e6	−	156768.i	−0.0679793	−	0.00757532i
$845$		−	2.64356e7i		−	1.27364i
$846$	−1.84639e7	−	2.06357e7i	−0.886946	−	0.991274i
$847$	1.91645e7			0.917886
$848$	2.86486e6	−	1.26947e7i	0.136809	−	0.606224i
$849$	−7.25316e6			−0.345349
$850$	1.97619e6	+	2.20864e6i	0.0938170	+	0.104852i
$851$		−	1.11835e7i		−	0.529362i
$852$	4.54174e6	+	506111.i	0.214350	+	0.0238862i
$853$			8.07995e6i			0.380221i	0.981763	+	0.190110i	$0.0608846\pi$
$853$			8.07995e6i			0.380221i	−0.981763	+	0.190110i	$0.939115\pi$
$854$	1.99698e7	−	1.78681e7i	0.936977	−	0.838364i
$855$	−3.01194e7			−1.40906
$856$	1.42372e7	+	1.99877e7i	0.664111	+	0.932351i
$857$	1.51474e7			0.704510			0.352255	−	0.935904i	$-0.385415\pi$
$857$	1.51474e7			0.704510			0.352255	+	0.935904i	$0.385415\pi$
$858$	929474.	−	831651.i	0.0431042	−	0.0385676i
$859$			1.27089e7i			0.587658i	0.955858	+	0.293829i	$0.0949297\pi$
$859$			1.27089e7i			0.587658i	−0.955858	+	0.293829i	$0.905070\pi$
$860$	1.28966e6	−	1.15732e7i	0.0594608	−	0.533588i
$861$			2.99082e6i			0.137494i
$862$	−1.81536e7	−	2.02889e7i	−0.832136	−	0.930016i
$863$	−3.10500e7			−1.41917			−0.709585	−	0.704620i	$-0.751118\pi$
$863$	−3.10500e7			−1.41917			−0.709585	+	0.704620i	$0.751118\pi$
$864$	−7.83089e6	+	4.35926e6i	−0.356884	+	0.198668i
$865$	3.86623e7			1.75690
$866$	2.20511e7	+	2.46448e7i	0.999159	+	1.11669i
$867$			4.45851e6i			0.201438i
$868$	−635703.	+	5.70467e6i	−0.0286388	+	0.256999i
$869$		−	2.88920e7i		−	1.29786i
$870$	3.92247e6	−	3.50964e6i	0.175696	−	0.157204i
$871$	−6.37578e6			−0.284766
$872$	−1.20919e7	−	1.69759e7i	−0.538520	−	0.756033i
$873$	−1.44909e7			−0.643515
$874$	1.74418e7	−	1.56061e7i	0.772346	−	0.691060i
$875$			6.50108e6i			0.287055i
$876$	−3.23870e6	−	360907.i	−0.142597	−	0.0158904i
$877$			1.45850e7i			0.640336i	0.947361	+	0.320168i	$0.103739\pi$
$877$			1.45850e7i			0.640336i	−0.947361	+	0.320168i	$0.896261\pi$
$878$	−8.62949e6	−	9.64454e6i	−0.377789	−	0.422226i
$879$	−2.25239e6			−0.0983265
$880$	−4.25095e7	−	9.59327e6i	−1.85046	−	0.417599i
$881$	5.73224e6			0.248820			0.124410	−	0.992231i	$-0.460296\pi$
$881$	5.73224e6			0.248820			0.124410	+	0.992231i	$0.460296\pi$
$882$	−3.59844e6	−	4.02171e6i	−0.155755	−	0.174076i
$883$			522077.i			0.0225337i	0.999937	+	0.0112669i	$0.00358643\pi$
$883$			522077.i			0.0225337i	−0.999937	+	0.0112669i	$0.996414\pi$
$884$	−836520.	−	93218.1i	−0.0360036	−	0.00401208i
$885$		−	3.39659e6i		−	0.145776i
$886$	4.14389e6	−	3.70776e6i	0.177347	−	0.158682i
$887$	−2.52815e7			−1.07893			−0.539466	−	0.842007i	$-0.681374\pi$
$887$	−2.52815e7			−1.07893			−0.539466	+	0.842007i	$0.681374\pi$
$888$	2.27276e6	−	1.61888e6i	0.0967212	−	0.0688943i
$889$	−1.14958e7			−0.487847
$890$	2.00853e7	−	1.79714e7i	0.849967	−	0.760512i
$891$			2.95988e7i			1.24905i
$892$	261844.	−	2.34973e6i	0.0110187	−	0.0988795i
$893$			3.69061e7i			1.54871i
$894$	−2.28882e6	−	2.55804e6i	−0.0957784	−	0.107044i
$895$	3.04020e7			1.26866
$896$	−1.92666e7	+	8.07721e6i	−0.801744	+	0.336118i
$897$	−904728.			−0.0375437
$898$	−1.08169e7	−	1.20893e7i	−0.447624	−	0.500276i
$899$		−	6.15217e6i		−	0.253880i
$900$	1.93154e6	−	1.73332e7i	0.0794872	−	0.713301i
$901$		−	2.83928e6i		−	0.116519i
$902$	−1.97792e7	+	1.76975e7i	−0.809453	+	0.724261i
$903$	1.80473e6			0.0736533
$904$	2.82967e6	−	2.01557e6i	0.115164	−	0.0820307i
$905$	9.84367e6			0.399517
$906$	−3.92076e6	+	3.50811e6i	−0.158690	+	0.141988i
$907$			1.27692e7i			0.515402i	0.966225	+	0.257701i	$0.0829649\pi$
$907$			1.27692e7i			0.515402i	−0.966225	+	0.257701i	$0.917035\pi$
$908$	6.20625e6	+	691598.i	0.249813	+	0.0278381i
$909$		−	1.16112e7i		−	0.466088i
$910$	3.70182e6	+	4.13725e6i	0.148188	+	0.165618i
$911$	3.33197e7			1.33017			0.665083	−	0.746770i	$-0.268396\pi$
$911$	3.33197e7			1.33017			0.665083	+	0.746770i	$0.268396\pi$
$912$	5.69637e6	+	1.28552e6i	0.226783	+	0.0511790i
$913$	−2.51493e7			−0.998503
$914$	−1.70200e6	−	1.90219e6i	−0.0673896	−	0.0753163i
$915$		−	1.01169e7i		−	0.399481i
$916$	4.94382e7	+	5.50918e6i	1.94681	+	0.216944i
$917$			1.27312e6i			0.0499973i
$918$	−1.45720e6	+	1.30384e6i	−0.0570707	+	0.0510643i
$919$	−2.91253e7			−1.13758			−0.568789	−	0.822484i	$-0.692588\pi$
$919$	−2.91253e7			−1.13758			−0.568789	+	0.822484i	$0.692588\pi$
$920$	1.83399e7	+	2.57476e7i	0.714378	+	1.00292i
$921$	9.49365e6			0.368794
$922$	1.02080e6	−	913365.i	0.0395470	−	0.0353848i
$923$		−	5.16622e6i		−	0.199604i
$924$	747990.	−	6.71230e6i	0.0288214	−	0.258638i
$925$			1.11073e7i			0.426831i
$926$	1.81096e7	+	2.02398e7i	0.694036	+	0.775672i
$927$	3.70133e7			1.41468
$928$	1.95644e7	−	1.08910e7i	0.745754	−	0.415143i
$929$	1.84988e7			0.703242			0.351621	−	0.936143i	$-0.385631\pi$
$929$	1.84988e7			0.703242			0.351621	+	0.936143i	$0.385631\pi$
$930$	1.44503e6	+	1.61500e6i	0.0547859	+	0.0612301i
$931$			7.19266e6i			0.271966i
$932$	200085.	−	1.79552e6i	0.00754528	−	0.0677098i
$933$		−	3.60357e6i		−	0.135528i
$934$	1.29077e6	−	1.15492e6i	0.0484152	−	0.0433197i
$935$	−9.50761e6			−0.355666
$936$	2.87366e6	+	4.03435e6i	0.107213	+	0.150517i
$937$	−3.42891e7			−1.27587			−0.637936	−	0.770089i	$-0.720212\pi$
$937$	−3.42891e7			−1.27587			−0.637936	+	0.770089i	$0.720212\pi$
$938$	−2.57296e7	+	2.30217e7i	−0.954831	+	0.854339i
$939$			5.38261e6i			0.199218i
$940$	−4.95413e7	−	5.52066e6i	−1.82872	−	0.203785i
$941$		−	1.23906e7i		−	0.456161i	−0.973642	−	0.228080i	$-0.926755\pi$
$941$		−	1.23906e7i		−	0.456161i	0.973642	−	0.228080i	$-0.0732449\pi$
$942$	−5.90053e6	−	6.59458e6i	−0.216652	−	0.242136i
$943$	1.92525e7			0.705032
$944$	3.18093e6	−	1.40953e7i	0.116178	−	0.514806i
$945$	1.28970e7			0.469797
$946$	1.06791e7	+	1.19352e7i	0.387976	+	0.433612i
$947$		−	5.12809e7i		−	1.85815i	−0.369893	−	0.929074i	$-0.620606\pi$
$947$		−	5.12809e7i		−	1.85815i	0.369893	−	0.929074i	$-0.379394\pi$
$948$	−5.19708e6	−	579140.i	−0.187819	−	0.0209297i
$949$			3.68402e6i			0.132787i
$950$	−1.73230e7	+	1.54999e7i	−0.622752	+	0.557210i
$951$	1.49467e6			0.0535912
$952$	−3.71239e6	+	2.64433e6i	−0.132758	+	0.0945633i
$953$	−1.10363e7			−0.393634			−0.196817	−	0.980440i	$-0.563060\pi$
$953$	−1.10363e7			−0.393634			−0.196817	+	0.980440i	$0.563060\pi$
$954$	−1.24517e7	+	1.11412e7i	−0.442954	+	0.396335i
$955$		−	6.16417e7i		−	2.18709i
$956$	1.95284e6	−	1.75244e7i	0.0691070	−	0.620152i
$957$			7.23885e6i			0.255499i
$958$	1.50577e7	+	1.68289e7i	0.530084	+	0.592435i
$959$	−1.15807e7			−0.406618
$960$	−2.57773e6	+	7.45428e6i	−0.0902733	+	0.261052i
$961$	−2.60961e7			−0.911523
$962$	−2.10345e6	−	2.35087e6i	−0.0732814	−	0.0819012i
$963$		−	3.15065e7i		−	1.09480i
$964$	−4.66342e6	+	4.18486e7i	−0.161626	+	1.45040i
$965$			4.41948e7i			1.52775i
$966$	−3.65105e6	+	3.26680e6i	−0.125885	+	0.112637i
$967$	−4.54331e7			−1.56245			−0.781225	−	0.624249i	$-0.785405\pi$
$967$	−4.54331e7			−1.56245			−0.781225	+	0.624249i	$0.785405\pi$
$968$	2.50711e7	−	1.78581e7i	0.859973	−	0.612557i
$969$	1.27404e6			0.0435887
$970$	−1.94405e7	+	1.73945e7i	−0.663405	+	0.593584i
$971$			6.77731e6i			0.230680i	0.993326	+	0.115340i	$0.0367957\pi$
$971$			6.77731e6i			0.230680i	−0.993326	+	0.115340i	$0.963204\pi$
$972$	1.72814e7	+	1.92576e6i	0.586696	+	0.0653789i
$973$		−	3.87621e7i		−	1.31258i
$974$	−2.43366e7	−	2.71992e7i	−0.821981	−	0.918667i
$975$	898569.			0.0302719
$976$	9.47458e6	−	4.19835e7i	0.318372	−	1.41076i
$977$	−4.58953e7			−1.53827			−0.769134	−	0.639087i	$-0.779312\pi$
$977$	−4.58953e7			−1.53827			−0.769134	+	0.639087i	$0.779312\pi$
$978$	−2.16811e6	−	2.42313e6i	−0.0724826	−	0.0810084i
$979$			3.70670e7i			1.23604i
$980$	−9.65514e6	−	1.07593e6i	−0.321139	−	0.0357863i
$981$			2.67589e7i			0.887759i
$982$	1.84318e7	−	1.64920e7i	0.609944	−	0.545750i
$983$	4.96160e7			1.63771			0.818857	−	0.573998i	$-0.194608\pi$
$983$	4.96160e7			1.63771			0.818857	+	0.573998i	$0.194608\pi$
$984$	2.78694e6	+	3.91261e6i	0.0917571	+	0.128819i
$985$	5.08977e7			1.67151
$986$	3.64061e6	−	3.25745e6i	0.119257	−	0.106705i
$987$		−	7.72549e6i		−	0.252425i
$988$	731138.	−	6.56108e6i	0.0238291	−	0.213837i
$989$		−	1.16174e7i		−	0.377676i
$990$	3.73074e7	+	4.16958e7i	1.20978	+	1.35208i
$991$	2.24227e7			0.725276			0.362638	−	0.931930i	$-0.381876\pi$
$991$	2.24227e7			0.725276			0.362638	+	0.931930i	$0.381876\pi$
$992$	4.48415e6	+	8.05524e6i	0.144678	+	0.259896i
$993$	−5.06462e6			−0.162995
$994$	−1.86542e7	−	2.08484e7i	−0.598840	−	0.669279i
$995$			7.22970e7i			2.31506i
$996$	−504117.	+	4.52384e6i	−0.0161021	+	0.144497i
$997$		−	5.13276e7i		−	1.63536i	−0.575675	−	0.817679i	$-0.695260\pi$
$997$		−	5.13276e7i		−	1.63536i	0.575675	−	0.817679i	$-0.304740\pi$
$998$	2.17999e7	−	1.95056e7i	0.692832	−	0.619915i
$999$	−7.32834e6			−0.232323

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.6.b.a.5.4	yes	4
3.2	odd	2		72.6.d.b.37.1		4
4.3	odd	2		32.6.b.a.17.3		4
5.2	odd	4		200.6.f.a.149.2		8
5.3	odd	4		200.6.f.a.149.7		8
5.4	even	2		200.6.d.a.101.1		4
8.3	odd	2		32.6.b.a.17.2		4
8.5	even	2	inner	8.6.b.a.5.3	✓	4
12.11	even	2		288.6.d.b.145.4		4
16.3	odd	4		256.6.a.n.1.2		4
16.5	even	4		256.6.a.k.1.2		4
16.11	odd	4		256.6.a.n.1.3		4
16.13	even	4		256.6.a.k.1.3		4
20.3	even	4		800.6.f.a.49.3		8
20.7	even	4		800.6.f.a.49.6		8
20.19	odd	2		800.6.d.a.401.2		4
24.5	odd	2		72.6.d.b.37.2		4
24.11	even	2		288.6.d.b.145.1		4
40.3	even	4		800.6.f.a.49.5		8
40.13	odd	4		200.6.f.a.149.1		8
40.19	odd	2		800.6.d.a.401.3		4
40.27	even	4		800.6.f.a.49.4		8
40.29	even	2		200.6.d.a.101.2		4
40.37	odd	4		200.6.f.a.149.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.6.b.a.5.3	✓	4	8.5	even	2	inner
8.6.b.a.5.4	yes	4	1.1	even	1	trivial
32.6.b.a.17.2		4	8.3	odd	2
32.6.b.a.17.3		4	4.3	odd	2
72.6.d.b.37.1		4	3.2	odd	2
72.6.d.b.37.2		4	24.5	odd	2
200.6.d.a.101.1		4	5.4	even	2
200.6.d.a.101.2		4	40.29	even	2
200.6.f.a.149.1		8	40.13	odd	4
200.6.f.a.149.2		8	5.2	odd	4
200.6.f.a.149.7		8	5.3	odd	4
200.6.f.a.149.8		8	40.37	odd	4
256.6.a.k.1.2		4	16.5	even	4
256.6.a.k.1.3		4	16.13	even	4
256.6.a.n.1.2		4	16.3	odd	4
256.6.a.n.1.3		4	16.11	odd	4
288.6.d.b.145.1		4	24.11	even	2
288.6.d.b.145.4		4	12.11	even	2
800.6.d.a.401.2		4	20.19	odd	2
800.6.d.a.401.3		4	40.19	odd	2
800.6.f.a.49.3		8	20.3	even	4
800.6.f.a.49.4		8	40.27	even	4
800.6.f.a.49.5		8	40.3	even	4
800.6.f.a.49.6		8	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.77200 + 4.21569i) q^{2} -3.25452i q^{3} +(-3.54400 + 31.8031i) q^{4} -73.9600i q^{5} +(13.7200 - 12.2760i) q^{6} -112.704 q^{7} +(-147.440 + 105.021i) q^{8} +232.408 q^{9} +O(q^{10})\)	\(q+(3.77200 + 4.21569i) q^{2} -3.25452i q^{3} +(-3.54400 + 31.8031i) q^{4} -73.9600i q^{5} +(13.7200 - 12.2760i) q^{6} -112.704 q^{7} +(-147.440 + 105.021i) q^{8} +232.408 q^{9} +(311.792 - 278.977i) q^{10} +575.407i q^{11} +(103.504 + 11.5340i) q^{12} -117.735i q^{13} +(-425.120 - 475.125i) q^{14} -240.704 q^{15} +(-998.880 - 225.421i) q^{16} -223.408 q^{17} +(876.644 + 979.759i) q^{18} -1752.26i q^{19} +(2352.16 + 262.115i) q^{20} +366.797i q^{21} +(-2425.74 + 2170.44i) q^{22} +2361.15 q^{23} +(341.793 + 479.846i) q^{24} -2345.08 q^{25} +(496.336 - 444.098i) q^{26} -1547.22i q^{27} +(399.424 - 3584.34i) q^{28} +3865.52i q^{29} +(-907.936 - 1014.73i) q^{30} -1591.55 q^{31} +(-2817.47 - 5061.25i) q^{32} +1872.67 q^{33} +(-842.696 - 941.818i) q^{34} +8335.59i q^{35} +(-823.655 + 7391.31i) q^{36} -4736.44i q^{37} +(7386.97 - 6609.52i) q^{38} -383.172 q^{39} +(7767.36 + 10904.7i) q^{40} +8153.88 q^{41} +(-1546.30 + 1383.56i) q^{42} -4920.23i q^{43} +(-18299.8 - 2039.25i) q^{44} -17188.9i q^{45} +(8906.27 + 9953.88i) q^{46} -21062.0 q^{47} +(-733.636 + 3250.87i) q^{48} -4104.79 q^{49} +(-8845.65 - 9886.12i) q^{50} +727.085i q^{51} +(3744.36 + 417.255i) q^{52} +12709.0i q^{53} +(6522.61 - 5836.13i) q^{54} +42557.1 q^{55} +(16617.1 - 11836.3i) q^{56} -5702.75 q^{57} +(-16295.8 + 14580.7i) q^{58} +14111.1i q^{59} +(853.056 - 7655.15i) q^{60} +42030.6i q^{61} +(-6003.33 - 6709.48i) q^{62} -26193.3 q^{63} +(10709.1 - 30968.6i) q^{64} -8707.71 q^{65} +(7063.73 + 7894.60i) q^{66} -54153.4i q^{67} +(791.759 - 7105.08i) q^{68} -7684.41i q^{69} +(-35140.2 + 31441.9i) q^{70} +43879.9 q^{71} +(-34266.3 + 24407.8i) q^{72} -31290.6 q^{73} +(19967.4 - 17865.9i) q^{74} +7632.11i q^{75} +(55727.3 + 6210.01i) q^{76} -64850.7i q^{77} +(-1445.33 - 1615.33i) q^{78} -50211.5 q^{79} +(-16672.1 + 73877.2i) q^{80} +51439.7 q^{81} +(30756.4 + 34374.2i) q^{82} +43707.0i q^{83} +(-11665.3 - 1299.93i) q^{84} +16523.3i q^{85} +(20742.1 - 18559.1i) q^{86} +12580.4 q^{87} +(-60429.9 - 84838.1i) q^{88} +64418.7 q^{89} +(72463.0 - 64836.6i) q^{90} +13269.3i q^{91} +(-8367.93 + 75092.1i) q^{92} +5179.73i q^{93} +(-79446.0 - 88790.8i) q^{94} -129597. q^{95} +(-16471.9 + 9169.52i) q^{96} -62350.9 q^{97} +(-15483.3 - 17304.5i) q^{98} +133729. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 20 q^{4} - 116 q^{6} + 96 q^{7} - 248 q^{8} - 164 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 20 * q^4 - 116 * q^6 + 96 * q^7 - 248 * q^8 - 164 * q^9	\( 4 q - 2 q^{2} + 20 q^{4} - 116 q^{6} + 96 q^{7} - 248 q^{8} - 164 q^{9} + 632 q^{10} + 1576 q^{12} - 2384 q^{14} - 416 q^{15} - 3312 q^{16} + 200 q^{17} + 4754 q^{18} + 4624 q^{20} - 5636 q^{22} + 2336 q^{23} - 7792 q^{24} + 1556 q^{25} + 5608 q^{26} + 5152 q^{28} - 2128 q^{30} - 12928 q^{31} + 5408 q^{32} - 2352 q^{33} - 4772 q^{34} - 10164 q^{36} + 15980 q^{38} + 35104 q^{39} + 16032 q^{40} - 4568 q^{41} - 26144 q^{42} - 29112 q^{44} + 29200 q^{46} - 54720 q^{47} + 35616 q^{48} + 9828 q^{49} - 47498 q^{50} - 36560 q^{52} + 23288 q^{54} + 85472 q^{55} + 40768 q^{56} - 2032 q^{57} + 3784 q^{58} + 2592 q^{60} + 34496 q^{62} - 153440 q^{63} - 41920 q^{64} - 19520 q^{65} + 43224 q^{66} + 10344 q^{68} - 68928 q^{70} + 206688 q^{71} - 83272 q^{72} + 39976 q^{73} + 17464 q^{74} + 99944 q^{76} - 174064 q^{78} - 247872 q^{79} - 35520 q^{80} + 29684 q^{81} + 161132 q^{82} + 196672 q^{84} - 18500 q^{86} + 307872 q^{87} - 167216 q^{88} - 84632 q^{89} + 142280 q^{90} - 49056 q^{92} - 98784 q^{94} - 259744 q^{95} - 115648 q^{96} - 99576 q^{97} - 117042 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 20 * q^4 - 116 * q^6 + 96 * q^7 - 248 * q^8 - 164 * q^9 + 632 * q^10 + 1576 * q^12 - 2384 * q^14 - 416 * q^15 - 3312 * q^16 + 200 * q^17 + 4754 * q^18 + 4624 * q^20 - 5636 * q^22 + 2336 * q^23 - 7792 * q^24 + 1556 * q^25 + 5608 * q^26 + 5152 * q^28 - 2128 * q^30 - 12928 * q^31 + 5408 * q^32 - 2352 * q^33 - 4772 * q^34 - 10164 * q^36 + 15980 * q^38 + 35104 * q^39 + 16032 * q^40 - 4568 * q^41 - 26144 * q^42 - 29112 * q^44 + 29200 * q^46 - 54720 * q^47 + 35616 * q^48 + 9828 * q^49 - 47498 * q^50 - 36560 * q^52 + 23288 * q^54 + 85472 * q^55 + 40768 * q^56 - 2032 * q^57 + 3784 * q^58 + 2592 * q^60 + 34496 * q^62 - 153440 * q^63 - 41920 * q^64 - 19520 * q^65 + 43224 * q^66 + 10344 * q^68 - 68928 * q^70 + 206688 * q^71 - 83272 * q^72 + 39976 * q^73 + 17464 * q^74 + 99944 * q^76 - 174064 * q^78 - 247872 * q^79 - 35520 * q^80 + 29684 * q^81 + 161132 * q^82 + 196672 * q^84 - 18500 * q^86 + 307872 * q^87 - 167216 * q^88 - 84632 * q^89 + 142280 * q^90 - 49056 * q^92 - 98784 * q^94 - 259744 * q^95 - 115648 * q^96 - 99576 * q^97 - 117042 * q^98

Introduction

L-functions

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