LMFDB - Embedded newform 230.6.b.b.139.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,6,Mod(139,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("230.139");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.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:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.3
Character	$\chi$	$=$	230.139
Dual form			230.6.b.b.139.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{2} -18.9029i q^{3} -16.0000 q^{4} +(-54.8757 + 10.6611i) q^{5} -75.6115 q^{6} -198.078i q^{7} +64.0000i q^{8} -114.319 q^{9} +O(q^{10})$	\(q-4.00000i q^{2} -18.9029i q^{3} -16.0000 q^{4} +(-54.8757 + 10.6611i) q^{5} -75.6115 q^{6} -198.078i q^{7} +64.0000i q^{8} -114.319 q^{9} +(42.6446 + 219.503i) q^{10} -532.364 q^{11} +302.446i q^{12} +1076.91i q^{13} -792.312 q^{14} +(201.526 + 1037.31i) q^{15} +256.000 q^{16} -1213.00i q^{17} +457.274i q^{18} -540.647 q^{19} +(878.011 - 170.578i) q^{20} -3744.24 q^{21} +2129.46i q^{22} +529.000i q^{23} +1209.78 q^{24} +(2897.68 - 1170.08i) q^{25} +4307.66 q^{26} -2432.45i q^{27} +3169.25i q^{28} -1606.70 q^{29} +(4149.23 - 806.105i) q^{30} -5036.63 q^{31} -1024.00i q^{32} +10063.2i q^{33} -4852.01 q^{34} +(2111.74 + 10869.7i) q^{35} +1829.10 q^{36} +5671.20i q^{37} +2162.59i q^{38} +20356.8 q^{39} +(-682.313 - 3512.04i) q^{40} +15130.2 q^{41} +14977.0i q^{42} +14382.5i q^{43} +8517.83 q^{44} +(6273.31 - 1218.77i) q^{45} +2116.00 q^{46} -19231.4i q^{47} -4839.13i q^{48} -22427.9 q^{49} +(-4680.30 - 11590.7i) q^{50} -22929.2 q^{51} -17230.6i q^{52} -13028.1i q^{53} -9729.80 q^{54} +(29213.9 - 5675.61i) q^{55} +12677.0 q^{56} +10219.8i q^{57} +6426.81i q^{58} +43452.0 q^{59} +(-3224.42 - 16596.9i) q^{60} -32248.3 q^{61} +20146.5i q^{62} +22644.0i q^{63} -4096.00 q^{64} +(-11481.1 - 59096.4i) q^{65} +40252.9 q^{66} -3750.65i q^{67} +19408.0i q^{68} +9999.62 q^{69} +(43478.7 - 8446.96i) q^{70} +49267.9 q^{71} -7316.39i q^{72} -74465.7i q^{73} +22684.8 q^{74} +(-22117.8 - 54774.5i) q^{75} +8650.35 q^{76} +105450. i q^{77} -81427.1i q^{78} +16724.6 q^{79} +(-14048.2 + 2729.25i) q^{80} -73759.7 q^{81} -60520.7i q^{82} +115706. i q^{83} +59907.9 q^{84} +(12932.0 + 66564.3i) q^{85} +57529.8 q^{86} +30371.3i q^{87} -34071.3i q^{88} +12822.3 q^{89} +(-4875.07 - 25093.2i) q^{90} +213313. q^{91} -8464.00i q^{92} +95206.8i q^{93} -76925.5 q^{94} +(29668.4 - 5763.92i) q^{95} -19356.5 q^{96} +90619.9i q^{97} +89711.7i q^{98} +60859.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 480 q^{4} - 30 q^{5} + 216 q^{6} - 3020 q^{9}+O(q^{10}) $ 30 * q - 480 * q^4 - 30 * q^5 + 216 * q^6 - 3020 * q^9	$ 30 q - 480 q^{4} - 30 q^{5} + 216 q^{6} - 3020 q^{9} + 80 q^{10} + 2074 q^{11} - 808 q^{14} - 3056 q^{15} + 7680 q^{16} - 1750 q^{19} + 480 q^{20} + 524 q^{21} - 3456 q^{24} + 12218 q^{25} + 10440 q^{26} - 27548 q^{29} + 16280 q^{30} + 31170 q^{31} - 25080 q^{34} + 20664 q^{35} + 48320 q^{36} - 47176 q^{39} - 1280 q^{40} + 71758 q^{41} - 33184 q^{44} - 9476 q^{45} + 63480 q^{46} - 212504 q^{49} + 50768 q^{50} - 129106 q^{51} - 52656 q^{54} + 137582 q^{55} + 12928 q^{56} - 212568 q^{59} + 48896 q^{60} + 7814 q^{61} - 122880 q^{64} + 50144 q^{65} - 54264 q^{66} - 28566 q^{69} + 11320 q^{70} + 268238 q^{71} - 41264 q^{74} + 61368 q^{75} + 28000 q^{76} + 93452 q^{79} - 7680 q^{80} + 412886 q^{81} - 8384 q^{84} + 67716 q^{85} + 248368 q^{86} - 349096 q^{89} - 40304 q^{90} + 348102 q^{91} - 98864 q^{94} + 60058 q^{95} + 55296 q^{96} - 578634 q^{99}+O(q^{100}) $ 30 * q - 480 * q^4 - 30 * q^5 + 216 * q^6 - 3020 * q^9 + 80 * q^10 + 2074 * q^11 - 808 * q^14 - 3056 * q^15 + 7680 * q^16 - 1750 * q^19 + 480 * q^20 + 524 * q^21 - 3456 * q^24 + 12218 * q^25 + 10440 * q^26 - 27548 * q^29 + 16280 * q^30 + 31170 * q^31 - 25080 * q^34 + 20664 * q^35 + 48320 * q^36 - 47176 * q^39 - 1280 * q^40 + 71758 * q^41 - 33184 * q^44 - 9476 * q^45 + 63480 * q^46 - 212504 * q^49 + 50768 * q^50 - 129106 * q^51 - 52656 * q^54 + 137582 * q^55 + 12928 * q^56 - 212568 * q^59 + 48896 * q^60 + 7814 * q^61 - 122880 * q^64 + 50144 * q^65 - 54264 * q^66 - 28566 * q^69 + 11320 * q^70 + 268238 * q^71 - 41264 * q^74 + 61368 * q^75 + 28000 * q^76 + 93452 * q^79 - 7680 * q^80 + 412886 * q^81 - 8384 * q^84 + 67716 * q^85 + 248368 * q^86 - 349096 * q^89 - 40304 * q^90 + 348102 * q^91 - 98864 * q^94 + 60058 * q^95 + 55296 * q^96 - 578634 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$		−	18.9029i		−	1.21262i	−0.795228	−	0.606310i	$-0.792649\pi$
$3$		−	18.9029i		−	1.21262i	0.795228	−	0.606310i	$-0.207351\pi$
$4$	−16.0000			−0.500000
$5$	−54.8757	+	10.6611i	−0.981646	+	0.190712i
$5$	−54.8757	+	10.6611i	−0.981646	+	0.190712i
$6$	−75.6115			−0.857452
$7$		−	198.078i		−	1.52789i	−0.645283	−	0.763944i	$-0.723261\pi$
$7$		−	198.078i		−	1.52789i	0.645283	−	0.763944i	$-0.276739\pi$
$8$			64.0000i			0.353553i
$9$	−114.319			−0.470447
$10$	42.6446	+	219.503i	0.134854	+	0.694129i
$11$	−532.364			−1.32656			−0.663281	−	0.748371i	$-0.730836\pi$
$11$	−532.364			−1.32656			−0.663281	+	0.748371i	$0.730836\pi$
$12$			302.446i			0.606310i
$13$			1076.91i			1.76735i	0.468100	+	0.883676i	$0.344939\pi$
$13$			1076.91i			1.76735i	−0.468100	+	0.883676i	$0.655061\pi$
$14$	−792.312			−1.08038
$15$	201.526	+	1037.31i	0.231262	+	1.19036i
$16$	256.000			0.250000
$17$		−	1213.00i		−	1.01798i	−0.860772	−	0.508990i	$-0.830019\pi$
$17$		−	1213.00i		−	1.01798i	0.860772	−	0.508990i	$-0.169981\pi$
$18$			457.274i			0.332656i
$19$	−540.647			−0.343581			−0.171791	−	0.985133i	$-0.554955\pi$
$19$	−540.647			−0.343581			−0.171791	+	0.985133i	$0.554955\pi$
$20$	878.011	−	170.578i	0.490823	−	0.0953562i
$21$	−3744.24			−1.85275
$22$			2129.46i			0.938020i
$23$			529.000i			0.208514i
$23$			529.000i			0.208514i
$24$	1209.78			0.428726
$25$	2897.68	−	1170.08i	0.927258	−	0.374424i
$26$	4307.66			1.24971
$27$		−	2432.45i		−	0.642147i
$28$			3169.25i			0.763944i
$29$	−1606.70			−0.354765			−0.177382	−	0.984142i	$-0.556763\pi$
$29$	−1606.70			−0.354765			−0.177382	+	0.984142i	$0.556763\pi$
$30$	4149.23	−	806.105i	0.841714	−	0.163527i
$31$	−5036.63			−0.941318			−0.470659	−	0.882315i	$-0.655984\pi$
$31$	−5036.63			−0.941318			−0.470659	+	0.882315i	$0.655984\pi$
$32$		−	1024.00i		−	0.176777i
$33$			10063.2i			1.60861i
$34$	−4852.01			−0.719821
$35$	2111.74	+	10869.7i	0.291387	+	1.49984i
$36$	1829.10			0.235223
$37$			5671.20i			0.681037i	0.940238	+	0.340519i	$0.110603\pi$
$37$			5671.20i			0.681037i	−0.940238	+	0.340519i	$0.889397\pi$
$38$			2162.59i			0.242949i
$39$	20356.8			2.14312
$40$	−682.313	−	3512.04i	−0.0674270	−	0.347064i
$41$	15130.2			1.40567			0.702836	−	0.711352i	$-0.251917\pi$
$41$	15130.2			1.40567			0.702836	+	0.711352i	$0.251917\pi$
$42$			14977.0i			1.31009i
$43$			14382.5i			1.18621i	0.805125	+	0.593105i	$0.202098\pi$
$43$			14382.5i			1.18621i	−0.805125	+	0.593105i	$0.797902\pi$
$44$	8517.83			0.663281
$45$	6273.31	−	1218.77i	0.461812	−	0.0897200i
$46$	2116.00			0.147442
$47$		−	19231.4i		−	1.26989i	−0.772558	−	0.634945i	$-0.781023\pi$
$47$		−	19231.4i		−	1.26989i	0.772558	−	0.634945i	$-0.218977\pi$
$48$		−	4839.13i		−	0.303155i
$49$	−22427.9			−1.33444
$50$	−4680.30	−	11590.7i	−0.264758	−	0.655670i
$51$	−22929.2			−1.23442
$52$		−	17230.6i		−	0.883676i
$53$		−	13028.1i		−	0.637076i	−0.947910	−	0.318538i	$-0.896808\pi$
$53$		−	13028.1i		−	0.637076i	0.947910	−	0.318538i	$-0.103192\pi$
$54$	−9729.80			−0.454066
$55$	29213.9	−	5675.61i	1.30221	−	0.252992i
$56$	12677.0			0.540190
$57$			10219.8i			0.416634i
$58$			6426.81i			0.250856i
$59$	43452.0			1.62510			0.812550	−	0.582891i	$-0.198079\pi$
$59$	43452.0			1.62510			0.812550	+	0.582891i	$0.198079\pi$
$60$	−3224.42	−	16596.9i	−0.115631	−	0.595182i
$61$	−32248.3			−1.10964			−0.554819	−	0.831971i	$-0.687213\pi$
$61$	−32248.3			−1.10964			−0.554819	+	0.831971i	$0.687213\pi$
$62$			20146.5i			0.665612i
$63$			22644.0i			0.718789i
$64$	−4096.00			−0.125000
$65$	−11481.1	−	59096.4i	−0.337056	−	1.73491i
$66$	40252.9			1.13746
$67$		−	3750.65i		−	0.102075i	−0.998697	−	0.0510375i	$-0.983747\pi$
$67$		−	3750.65i		−	0.102075i	0.998697	−	0.0510375i	$-0.0162528\pi$
$68$			19408.0i			0.508990i
$69$	9999.62			0.252849
$70$	43478.7	−	8446.96i	1.06055	−	0.206042i
$71$	49267.9			1.15989			0.579947	−	0.814654i	$-0.303073\pi$
$71$	49267.9			1.15989			0.579947	+	0.814654i	$0.303073\pi$
$72$		−	7316.39i		−	0.166328i
$73$		−	74465.7i		−	1.63550i	−0.575577	−	0.817748i	$-0.695223\pi$
$73$		−	74465.7i		−	1.63550i	0.575577	−	0.817748i	$-0.304777\pi$
$74$	22684.8			0.481566
$75$	−22117.8	−	54774.5i	−0.454034	−	1.12441i
$76$	8650.35			0.171791
$77$			105450.i			2.02684i
$78$		−	81427.1i		−	1.51542i
$79$	16724.6			0.301500			0.150750	−	0.988572i	$-0.451831\pi$
$79$	16724.6			0.301500			0.150750	+	0.988572i	$0.451831\pi$
$80$	−14048.2	+	2729.25i	−0.245411	+	0.0476781i
$81$	−73759.7			−1.24913
$82$		−	60520.7i		−	0.993961i
$83$			115706.i			1.84358i	0.387692	+	0.921789i	$0.373272\pi$
$83$			115706.i			1.84358i	−0.387692	+	0.921789i	$0.626728\pi$
$84$	59907.9			0.926373
$85$	12932.0	+	66564.3i	0.194141	+	0.999296i
$86$	57529.8			0.838777
$87$			30371.3i			0.430195i
$88$		−	34071.3i		−	0.469010i
$89$	12822.3			0.171589			0.0857947	−	0.996313i	$-0.472657\pi$
$89$	12822.3			0.171589			0.0857947	+	0.996313i	$0.472657\pi$
$90$	−4875.07	−	25093.2i	−0.0634416	−	0.326550i
$91$	213313.			2.70031
$92$		−	8464.00i		−	0.104257i
$93$			95206.8i			1.14146i
$94$	−76925.5			−0.897947
$95$	29668.4	−	5763.92i	0.337275	−	0.0655252i
$96$	−19356.5			−0.214363
$97$			90619.9i			0.977900i	0.872312	+	0.488950i	$0.162620\pi$
$97$			90619.9i			0.977900i	−0.872312	+	0.488950i	$0.837380\pi$
$98$			89711.7i			0.943591i
$99$	60859.1			0.624076
$100$	−46362.9	+	18721.2i	−0.463629	+	0.187212i
$101$	−80922.3			−0.789341			−0.394671	−	0.918823i	$-0.629141\pi$
$101$	−80922.3			−0.789341			−0.394671	+	0.918823i	$0.629141\pi$
$102$			91716.9i			0.872869i
$103$		−	28416.6i		−	0.263925i	−0.991255	−	0.131962i	$-0.957872\pi$
$103$		−	28416.6i		−	0.263925i	0.991255	−	0.131962i	$-0.0421278\pi$
$104$	−68922.5			−0.624853
$105$	205468.	−	39917.9i	1.81874	−	0.353342i
$106$	−52112.4			−0.450481
$107$			66121.7i			0.558322i	0.960244	+	0.279161i	$0.0900563\pi$
$107$			66121.7i			0.558322i	−0.960244	+	0.279161i	$0.909944\pi$
$108$			38919.2i			0.321073i
$109$	−226331.			−1.82465			−0.912323	−	0.409471i	$-0.865713\pi$
$109$	−226331.			−1.82465			−0.912323	+	0.409471i	$0.865713\pi$
$110$	−22702.5	−	116855.i	−0.178892	−	0.920804i
$111$	107202.			0.825839
$112$		−	50708.0i		−	0.381972i
$113$			49494.3i			0.364635i	0.983240	+	0.182318i	$0.0583599\pi$
$113$			49494.3i			0.364635i	−0.983240	+	0.182318i	$0.941640\pi$
$114$	40879.1			0.294604
$115$	−5639.75	−	29029.2i	−0.0397663	−	0.204687i
$116$	25707.2			0.177382
$117$		−	123111.i		−	0.831444i
$118$		−	173808.i		−	1.14912i
$119$	−240269.			−1.55536
$120$	−66387.7	+	12897.7i	−0.420857	+	0.0817633i
$121$	122361.			0.759765
$122$			128993.i			0.784633i
$123$		−	286004.i		−	1.70455i
$124$	80586.1			0.470659
$125$	−146538.	+	95101.3i	−0.838831	+	0.544391i
$126$	90576.0			0.508261
$127$		−	12787.0i		−	0.0703493i	−0.999381	−	0.0351746i	$-0.988801\pi$
$127$		−	12787.0i		−	0.0703493i	0.999381	−	0.0351746i	$-0.0111987\pi$
$128$			16384.0i			0.0883883i
$129$	271870.			1.43842
$130$	−236386.	+	45924.6i	−1.22677	+	0.238334i
$131$	117787.			0.599680			0.299840	−	0.953989i	$-0.403067\pi$
$131$	117787.			0.599680			0.299840	+	0.953989i	$0.403067\pi$
$132$		−	161011.i		−	0.804307i
$133$			107090.i			0.524954i
$134$	−15002.6			−0.0721779
$135$	25932.7	+	133482.i	0.122465	+	0.630361i
$136$	77632.1			0.359910
$137$			401401.i			1.82716i	0.406655	+	0.913582i	$0.366695\pi$
$137$			401401.i			1.82716i	−0.406655	+	0.913582i	$0.633305\pi$
$138$		−	39998.5i		−	0.178791i
$139$	−25364.3			−0.111349			−0.0556744	−	0.998449i	$-0.517731\pi$
$139$	−25364.3			−0.111349			−0.0556744	+	0.998449i	$0.517731\pi$
$140$	−33787.8	−	173915.i	−0.145694	−	0.749922i
$141$	−363528.			−1.53989
$142$		−	197072.i		−	0.820169i
$143$		−	573311.i		−	2.34450i
$144$	−29265.5			−0.117612
$145$	88168.9	−	17129.3i	0.348253	−	0.0676580i
$146$	−297863.			−1.15647
$147$			423952.i			1.61817i
$148$		−	90739.2i		−	0.340519i
$149$	−99206.6			−0.366079			−0.183039	−	0.983106i	$-0.558594\pi$
$149$	−99206.6			−0.366079			−0.183039	+	0.983106i	$0.558594\pi$
$150$	−219098.	+	88471.1i	−0.795079	+	0.321051i
$151$	−162103.			−0.578561			−0.289281	−	0.957244i	$-0.593416\pi$
$151$	−162103.			−0.578561			−0.289281	+	0.957244i	$0.593416\pi$
$152$		−	34601.4i		−	0.121474i
$153$			138669.i			0.478905i
$154$	421799.			1.43319
$155$	276389.	−	53696.3i	0.924041	−	0.179521i
$156$	−325708.			−1.07156
$157$			227377.i			0.736202i	0.929786	+	0.368101i	$0.119992\pi$
$157$			227377.i			0.736202i	−0.929786	+	0.368101i	$0.880008\pi$
$158$		−	66898.3i		−	0.213193i
$159$	−246268.			−0.772531
$160$	10917.0	+	56192.7i	0.0337135	+	0.173532i
$161$	104783.			0.318587
$162$			295039.i			0.883266i
$163$			601718.i			1.77388i	0.461885	+	0.886940i	$0.347173\pi$
$163$			601718.i			1.77388i	−0.461885	+	0.886940i	$0.652827\pi$
$164$	−242083.			−0.702836
$165$	−107285.	−	552226.i	−0.306783	−	1.57909i
$166$	462825.			1.30361
$167$			327376.i			0.908356i	0.890911	+	0.454178i	$0.150067\pi$
$167$			327376.i			0.908356i	−0.890911	+	0.454178i	$0.849933\pi$
$168$		−	239632.i		−	0.655045i
$169$	−788452.			−2.12353
$170$	266257.	−	51728.0i	0.706609	−	0.137279i
$171$	61806.0			0.161637
$172$		−	230119.i		−	0.593105i
$173$			599965.i			1.52409i	0.647525	+	0.762044i	$0.275804\pi$
$173$			599965.i			1.52409i	−0.647525	+	0.762044i	$0.724196\pi$
$174$	121485.			0.304194
$175$	−231766.	−	573967.i	−0.572078	−	1.41675i
$176$	−136285.			−0.331640
$177$		−	821368.i		−	1.97063i
$178$		−	51289.1i		−	0.121332i
$179$	−188490.			−0.439700			−0.219850	−	0.975534i	$-0.570557\pi$
$179$	−188490.			−0.439700			−0.219850	+	0.975534i	$0.570557\pi$
$180$	−100373.	+	19500.3i	−0.230906	+	0.0448600i
$181$	−370657.			−0.840960			−0.420480	−	0.907302i	$-0.638138\pi$
$181$	−370657.			−0.840960			−0.420480	+	0.907302i	$0.638138\pi$
$182$		−	853253.i		−	1.90941i
$183$			609585.i			1.34557i
$184$	−33856.0			−0.0737210
$185$	−60461.5	−	311211.i	−0.129882	−	0.668537i
$186$	380827.			0.807134
$187$			645759.i			1.35041i
$188$			307702.i			0.634945i
$189$	−481815.			−0.981128
$190$	−23055.7	−	118673.i	−0.0463333	−	0.238490i
$191$	470227.			0.932663			0.466331	−	0.884610i	$-0.345575\pi$
$191$	470227.			0.932663			0.466331	+	0.884610i	$0.345575\pi$
$192$			77426.2i			0.151577i
$193$			327255.i			0.632402i	0.948692	+	0.316201i	$0.102407\pi$
$193$			327255.i			0.632402i	−0.948692	+	0.316201i	$0.897593\pi$
$194$	362480.			0.691480
$195$	−1.11709e6	+	217027.i	−2.10379	+	0.408720i
$196$	358847.			0.667220
$197$		−	928652.i		−	1.70486i	−0.522845	−	0.852428i	$-0.675129\pi$
$197$		−	928652.i		−	1.70486i	0.522845	−	0.852428i	$-0.324871\pi$
$198$		−	243436.i		−	0.441289i
$199$	36141.1			0.0646947			0.0323474	−	0.999477i	$-0.489702\pi$
$199$	36141.1			0.0646947			0.0323474	+	0.999477i	$0.489702\pi$
$200$	74884.8	+	185452.i	0.132379	+	0.327835i
$201$	−70898.0			−0.123778
$202$			323689.i			0.558149i
$203$			318252.i			0.542040i
$204$	366868.			0.617211
$205$	−830278.	+	161305.i	−1.37987	+	0.268079i
$206$	−113667.			−0.186623
$207$		−	60474.5i		−	0.0980949i
$208$			275690.i			0.441838i
$209$	287821.			0.455782
$210$	−159672.	−	821872.i	−0.249850	−	1.28604i
$211$	142371.			0.220148			0.110074	−	0.993923i	$-0.464891\pi$
$211$	142371.			0.220148			0.110074	+	0.993923i	$0.464891\pi$
$212$			208450.i			0.318538i
$213$		−	931305.i		−	1.40651i
$214$	264487.			0.394793
$215$	−153333.	−	789247.i	−0.226225	−	1.16444i
$216$	155677.			0.227033
$217$			997647.i			1.43823i
$218$			905326.i			1.29022i
$219$	−1.40762e6			−1.98323
$220$	−467422.	+	90809.8i	−0.651107	+	0.126496i
$221$	1.30630e6			1.79913
$222$		−	428808.i		−	0.583956i
$223$			1.02478e6i			1.37997i	0.723823	+	0.689986i	$0.242383\pi$
$223$			1.02478e6i			1.37997i	−0.723823	+	0.689986i	$0.757617\pi$
$224$	−202832.			−0.270095
$225$	−331258.	+	133761.i	−0.436225	+	0.176147i
$226$	197977.			0.257836
$227$		−	1.48030e6i		−	1.90671i	−0.301856	−	0.953354i	$-0.597606\pi$
$227$		−	1.48030e6i		−	1.90671i	0.301856	−	0.953354i	$-0.402394\pi$
$228$		−	163516.i		−	0.208317i
$229$	−815672.			−1.02784			−0.513921	−	0.857837i	$-0.671808\pi$
$229$	−815672.			−1.02784			−0.513921	+	0.857837i	$0.671808\pi$
$230$	−116117.	+	22559.0i	−0.144736	+	0.0281190i
$231$	1.99330e6			2.45778
$232$		−	102829.i		−	0.125428i
$233$			139341.i			0.168146i	0.996460	+	0.0840732i	$0.0267930\pi$
$233$			139341.i			0.168146i	−0.996460	+	0.0840732i	$0.973207\pi$
$234$	−492445.			−0.587920
$235$	205029.	+	1.05534e6i	0.242184	+	1.24658i
$236$	−695233.			−0.812550
$237$		−	316142.i		−	0.365605i
$238$			961077.i			1.09980i
$239$	695042.			0.787075			0.393538	−	0.919309i	$-0.371251\pi$
$239$	695042.			0.787075			0.393538	+	0.919309i	$0.371251\pi$
$240$	51590.7	+	265551.i	0.0578154	+	0.297591i
$241$	−1.46929e6			−1.62954			−0.814772	−	0.579781i	$-0.803138\pi$
$241$	−1.46929e6			−1.62954			−0.814772	+	0.579781i	$0.803138\pi$
$242$		−	489443.i		−	0.537235i
$243$			803184.i			0.872569i
$244$	515972.			0.554819
$245$	1.23075e6	−	239107.i	1.30995	−	0.254494i
$246$	−1.14401e6			−1.20530
$247$		−	582230.i		−	0.607229i
$248$		−	322345.i		−	0.332806i
$249$	2.18718e6			2.23556
$250$	380405.	+	586151.i	0.384943	+	0.593143i
$251$	−396599.			−0.397345			−0.198672	−	0.980066i	$-0.563663\pi$
$251$	−396599.			−0.397345			−0.198672	+	0.980066i	$0.563663\pi$
$252$		−	362304.i		−	0.359395i
$253$		−	281621.i		−	0.276607i
$254$	−51148.0			−0.0497444
$255$	1.25826e6	−	244452.i	1.21177	−	0.235420i
$256$	65536.0			0.0625000
$257$			687968.i			0.649734i	0.945760	+	0.324867i	$0.105320\pi$
$257$			687968.i			0.649734i	−0.945760	+	0.324867i	$0.894680\pi$
$258$		−	1.08748e6i		−	1.01712i
$259$	1.12334e6			1.04055
$260$	183698.	+	945543.i	0.168528	+	0.867457i
$261$	183676.			0.166898
$262$		−	471149.i		−	0.424038i
$263$			836725.i			0.745922i	0.927847	+	0.372961i	$0.121657\pi$
$263$			836725.i			0.745922i	−0.927847	+	0.372961i	$0.878343\pi$
$264$	−644046.			−0.568731
$265$	138894.	+	714926.i	0.121498	+	0.625383i
$266$	428361.			0.371198
$267$		−	242378.i		−	0.208073i
$268$			60010.3i			0.0510375i
$269$	−1.34489e6			−1.13320			−0.566601	−	0.823992i	$-0.691742\pi$
$269$	−1.34489e6			−1.13320			−0.566601	+	0.823992i	$0.691742\pi$
$270$	533929.	−	103731.i	0.445732	−	0.0865961i
$271$	50553.5			0.0418146			0.0209073	−	0.999781i	$-0.493345\pi$
$271$	50553.5			0.0418146			0.0209073	+	0.999781i	$0.493345\pi$
$272$		−	310529.i		−	0.254495i
$273$		−	4.03223e6i		−	3.27445i
$274$	1.60561e6			1.29200
$275$	−1.54262e6	+	622906.i	−1.23006	+	0.496696i
$276$	−159994.			−0.126424
$277$		−	2.24449e6i		−	1.75759i	−0.477195	−	0.878797i	$-0.658347\pi$
$277$		−	2.24449e6i		−	1.75759i	0.477195	−	0.878797i	$-0.341653\pi$
$278$			101457.i			0.0787355i
$279$	575781.			0.442840
$280$	−695659.	+	135151.i	−0.530275	+	0.103021i
$281$	1.53408e6			1.15900			0.579499	−	0.814973i	$-0.303248\pi$
$281$	1.53408e6			1.15900			0.579499	+	0.814973i	$0.303248\pi$
$282$			1.45411e6i			1.08887i
$283$			158402.i			0.117569i	0.998271	+	0.0587846i	$0.0187225\pi$
$283$			158402.i			0.117569i	−0.998271	+	0.0587846i	$0.981277\pi$
$284$	−788287.			−0.579947
$285$	−108955.	−	560817.i	−0.0794572	−	0.408987i
$286$	−2.29324e6			−1.65781
$287$		−	2.99696e6i		−	2.14771i
$288$			117062.i			0.0831640i
$289$	−51517.3			−0.0362835
$290$	−68517.1	−	352675.i	−0.0478414	−	0.246252i
$291$	1.71298e6			1.18582
$292$			1.19145e6i			0.817748i
$293$			1.78893e6i			1.21737i	0.793411	+	0.608686i	$0.208303\pi$
$293$			1.78893e6i			1.21737i	−0.793411	+	0.608686i	$0.791697\pi$
$294$	1.69581e6			1.14422
$295$	−2.38446e6	+	463249.i	−1.59527	+	0.309927i
$296$	−362957.			−0.240783
$297$			1.29495e6i			0.851847i
$298$			396826.i			0.258857i
$299$	−569688.			−0.368518
$300$	353885.	+	876392.i	0.227017	+	0.562205i
$301$	2.84885e6			1.81240
$302$			648413.i			0.409105i
$303$			1.52966e6i			0.957171i
$304$	−138406.			−0.0858954
$305$	1.76964e6	−	343803.i	1.08927	−	0.211622i
$306$	554674.			0.338637
$307$		−	43869.1i		−	0.0265652i	−0.999912	−	0.0132826i	$-0.995772\pi$
$307$		−	43869.1i		−	0.0265652i	0.999912	−	0.0132826i	$-0.00422811\pi$
$308$		−	1.68720e6i		−	1.01342i
$309$	−537156.			−0.320040
$310$	−214785.	−	1.10555e6i	−0.126940	−	0.653395i
$311$	894338.			0.524325			0.262163	−	0.965024i	$-0.415564\pi$
$311$	894338.			0.524325			0.262163	+	0.965024i	$0.415564\pi$
$312$			1.30283e6i			0.757709i
$313$		−	2.82879e6i		−	1.63207i	−0.578000	−	0.816037i	$-0.696167\pi$
$313$		−	2.82879e6i		−	1.63207i	0.578000	−	0.816037i	$-0.303833\pi$
$314$	909507.			0.520573
$315$	−241411.	−	1.24260e6i	−0.137082	−	0.705597i
$316$	−267593.			−0.150750
$317$		−	2.26719e6i		−	1.26719i	−0.773666	−	0.633593i	$-0.781579\pi$
$317$		−	2.26719e6i		−	1.26719i	0.773666	−	0.633593i	$-0.218421\pi$
$318$			985074.i			0.546262i
$319$	855351.			0.470617
$320$	224771.	−	43668.1i	0.122706	−	0.0238390i
$321$	1.24989e6			0.677032
$322$		−	419133.i		−	0.225275i
$323$			655806.i			0.349759i
$324$	1.18015e6			0.624563
$325$	1.26007e6	+	3.12055e6i	0.661739	+	1.63879i
$326$	2.40687e6			1.25432
$327$			4.27831e6i			2.21260i
$328$			968331.i			0.496980i
$329$	−3.80932e6			−1.94025
$330$	−2.20890e6	+	429142.i	−1.11659	+	0.216928i
$331$	2.98383e6			1.49694			0.748469	−	0.663170i	$-0.230789\pi$
$331$	2.98383e6			1.49694			0.748469	+	0.663170i	$0.230789\pi$
$332$		−	1.85130e6i		−	0.921789i
$333$		−	648323.i		−	0.320392i
$334$	1.30950e6			0.642304
$335$	39986.2	+	205819.i	0.0194669	+	0.100201i
$336$	−958527.			−0.463187
$337$			1.69788e6i			0.814392i	0.913341	+	0.407196i	$0.133493\pi$
$337$			1.69788e6i			0.814392i	−0.913341	+	0.407196i	$0.866507\pi$
$338$			3.15381e6i			1.50156i
$339$	935584.			0.442164
$340$	−206912.	−	1.06503e6i	−0.0970707	−	0.499648i
$341$	2.68132e6			1.24872
$342$		−	247224.i		−	0.114294i
$343$			1.11338e6i			0.510986i
$344$	−920477.			−0.419389
$345$	−548736.	+	106607.i	−0.248208	+	0.0482214i
$346$	2.39986e6			1.07769
$347$			468874.i			0.209041i	0.994523	+	0.104521i	$0.0333308\pi$
$347$			468874.i			0.209041i	−0.994523	+	0.104521i	$0.966669\pi$
$348$		−	485940.i		−	0.215097i
$349$	−81411.5			−0.0357785			−0.0178893	−	0.999840i	$-0.505695\pi$
$349$	−81411.5			−0.0357785			−0.0178893	+	0.999840i	$0.505695\pi$
$350$	−2.29587e6	+	927065.i	−1.00179	+	0.404520i
$351$	2.61954e6			1.13490
$352$			545141.i			0.234505i
$353$		−	2.12949e6i		−	0.909575i	−0.890600	−	0.454787i	$-0.849715\pi$
$353$		−	2.12949e6i		−	0.909575i	0.890600	−	0.454787i	$-0.150285\pi$
$354$	−3.28547e6			−1.39344
$355$	−2.70361e6	+	525253.i	−1.13861	+	0.221206i
$356$	−205157.			−0.0857947
$357$			4.54178e6i			1.88606i
$358$			753961.i			0.310915i
$359$	−2.87936e6			−1.17913			−0.589563	−	0.807722i	$-0.700700\pi$
$359$	−2.87936e6			−1.17913			−0.589563	+	0.807722i	$0.700700\pi$
$360$	78001.1	+	401492.i	0.0317208	+	0.163275i
$361$	−2.18380e6			−0.881952
$362$			1.48263e6i			0.594649i
$363$		−	2.31297e6i		−	0.921305i
$364$	−3.41301e6			−1.35016
$365$	793890.	+	4.08636e6i	0.311909	+	1.60548i
$366$	2.43834e6			0.951461
$367$			421983.i			0.163542i	0.996651	+	0.0817711i	$0.0260576\pi$
$367$			421983.i			0.163542i	−0.996651	+	0.0817711i	$0.973942\pi$
$368$			135424.i			0.0521286i
$369$	−1.72966e6			−0.661294
$370$	−1.24484e6	+	241846.i	−0.472727	+	0.0918406i
$371$	−2.58058e6			−0.973380
$372$		−	1.52331e6i		−	0.570730i
$373$		−	1.73176e6i		−	0.644489i	−0.946656	−	0.322245i	$-0.895563\pi$
$373$		−	1.73176e6i		−	0.644489i	0.946656	−	0.322245i	$-0.104437\pi$
$374$	2.58304e6			0.954886
$375$	1.79769e6	+	2.76999e6i	0.660140	+	1.01718i
$376$	1.23081e6			0.448974
$377$		−	1.73028e6i		−	0.626994i
$378$			1.92726e6i			0.693762i
$379$	−1.22589e6			−0.438385			−0.219192	−	0.975682i	$-0.570342\pi$
$379$	−1.22589e6			−0.438385			−0.219192	+	0.975682i	$0.570342\pi$
$380$	−474694.	+	92222.7i	−0.168638	+	0.0327626i
$381$	−241711.			−0.0853069
$382$		−	1.88091e6i		−	0.659492i
$383$			2.80235e6i			0.976170i	0.872796	+	0.488085i	$0.162304\pi$
$383$			2.80235e6i			0.976170i	−0.872796	+	0.488085i	$0.837696\pi$
$384$	309705.			0.107181
$385$	−1.12421e6	−	5.78662e6i	−0.386543	−	1.98964i
$386$	1.30902e6			0.447175
$387$		−	1.64418e6i		−	0.558049i
$388$		−	1.44992e6i		−	0.488950i
$389$	2.06695e6			0.692558			0.346279	−	0.938131i	$-0.387445\pi$
$389$	2.06695e6			0.692558			0.346279	+	0.938131i	$0.387445\pi$
$390$	868106.	+	4.46837e6i	0.289009	+	1.48760i
$391$	641678.			0.212264
$392$		−	1.43539e6i		−	0.471796i
$393$		−	2.22652e6i		−	0.727184i
$394$	−3.71461e6			−1.20552
$395$	−917772.	+	178303.i	−0.295966	+	0.0574998i
$396$	−973746.			−0.312038
$397$		−	719946.i		−	0.229258i	−0.993408	−	0.114629i	$-0.963432\pi$
$397$		−	719946.i		−	0.229258i	0.993408	−	0.114629i	$-0.0365678\pi$
$398$		−	144564.i		−	0.0457461i
$399$	2.02431e6			0.636569
$400$	741806.	−	299539.i	0.231814	−	0.0936060i
$401$	2.72214e6			0.845374			0.422687	−	0.906276i	$-0.361087\pi$
$401$	2.72214e6			0.845374			0.422687	+	0.906276i	$0.361087\pi$
$402$			283592.i			0.0875243i
$403$		−	5.42402e6i		−	1.66364i
$404$	1.29476e6			0.394671
$405$	4.04761e6	−	786363.i	1.22620	−	0.238224i
$406$	1.27301e6			0.383280
$407$		−	3.01915e6i		−	0.903437i
$408$		−	1.46747e6i		−	0.436434i
$409$	−4.36017e6			−1.28883			−0.644414	−	0.764677i	$-0.722898\pi$
$409$	−4.36017e6			−1.28883			−0.644414	+	0.764677i	$0.722898\pi$
$410$	645220.	+	3.32111e6i	0.189561	+	0.975717i
$411$	7.58764e6			2.21565
$412$			454666.i			0.131962i
$413$		−	8.60690e6i		−	2.48297i
$414$	−241898.			−0.0693636
$415$	−1.23356e6	−	6.34946e6i	−0.351593	−	1.80974i
$416$	1.10276e6			0.312426
$417$			479458.i			0.135024i
$418$		−	1.15128e6i		−	0.322286i
$419$	−863502.			−0.240286			−0.120143	−	0.992757i	$-0.538335\pi$
$419$	−863502.			−0.240286			−0.120143	+	0.992757i	$0.538335\pi$
$420$	−3.28749e6	+	638687.i	−0.909370	+	0.176671i
$421$	−3.78080e6			−1.03963			−0.519815	−	0.854279i	$-0.673999\pi$
$421$	−3.78080e6			−1.03963			−0.519815	+	0.854279i	$0.673999\pi$
$422$		−	569482.i		−	0.155668i
$423$			2.19850e6i			0.597415i
$424$	833798.			0.225240
$425$	−1.41930e6	−	3.51489e6i	−0.381156	−	0.943930i
$426$	−3.72522e6			−0.994553
$427$			6.38767e6i			1.69540i
$428$		−	1.05795e6i		−	0.279161i
$429$	−1.08372e7			−2.84299
$430$	−3.15699e6	+	613334.i	−0.823382	+	0.159965i
$431$	−3.43384e6			−0.890403			−0.445202	−	0.895430i	$-0.646868\pi$
$431$	−3.43384e6			−0.890403			−0.445202	+	0.895430i	$0.646868\pi$
$432$		−	622707.i		−	0.160537i
$433$			4.17242e6i			1.06947i	0.845020	+	0.534734i	$0.179588\pi$
$433$			4.17242e6i			1.06947i	−0.845020	+	0.534734i	$0.820412\pi$
$434$	3.99059e6			1.01698
$435$	−323793.	−	1.66664e6i	−0.0820434	−	0.422299i
$436$	3.62130e6			0.912323
$437$		−	286002.i		−	0.0716417i
$438$			5.63046e6i			1.40236i
$439$	2.68448e6			0.664811			0.332405	−	0.943137i	$-0.392140\pi$
$439$	2.68448e6			0.664811			0.332405	+	0.943137i	$0.392140\pi$
$440$	363239.	+	1.86969e6i	0.0894461	+	0.460402i
$441$	2.56393e6			0.627783
$442$		−	5.22520e6i		−	1.27218i
$443$			3.36639e6i			0.814996i	0.913206	+	0.407498i	$0.133599\pi$
$443$			3.36639e6i			0.814996i	−0.913206	+	0.407498i	$0.866401\pi$
$444$	−1.71523e6			−0.412920
$445$	−703631.	+	136700.i	−0.168440	+	0.0327242i
$446$	4.09913e6			0.975787
$447$			1.87529e6i			0.443915i
$448$			811328.i			0.190986i
$449$	2.52502e6			0.591083			0.295541	−	0.955330i	$-0.404500\pi$
$449$	2.52502e6			0.591083			0.295541	+	0.955330i	$0.404500\pi$
$450$	535045.	+	1.32503e6i	0.124554	+	0.308458i
$451$	−8.05476e6			−1.86471
$452$		−	791908.i		−	0.182318i
$453$			3.06422e6i			0.701575i
$454$	−5.92119e6			−1.34825
$455$	−1.17057e7	+	2.27416e6i	−2.65075	+	0.514983i
$456$	−654066.			−0.147302
$457$		−	671371.i		−	0.150374i	−0.997169	−	0.0751869i	$-0.976045\pi$
$457$		−	671371.i		−	0.150374i	0.997169	−	0.0751869i	$-0.0239553\pi$
$458$			3.26269e6i			0.726795i
$459$	−2.95057e6			−0.653693
$460$	90235.9	+	464468.i	0.0198831	+	0.102344i
$461$	3.21429e6			0.704421			0.352211	−	0.935921i	$-0.385430\pi$
$461$	3.21429e6			0.704421			0.352211	+	0.935921i	$0.385430\pi$
$462$		−	7.97321e6i		−	1.73791i
$463$		−	5.58815e6i		−	1.21148i	−0.795663	−	0.605739i	$-0.792877\pi$
$463$		−	5.58815e6i		−	1.21148i	0.795663	−	0.605739i	$-0.207123\pi$
$464$	−411316.			−0.0886912
$465$	−1.01501e6	−	5.22454e6i	−0.217691	−	1.12051i
$466$	557362.			0.118897
$467$		−	3.49666e6i		−	0.741926i	−0.928648	−	0.370963i	$-0.879028\pi$
$467$		−	3.49666e6i		−	0.741926i	0.928648	−	0.370963i	$-0.120972\pi$
$468$			1.96978e6i			0.415722i
$469$	−742921.			−0.155959
$470$	4.22134e6	−	820114.i	0.881466	−	0.171250i
$471$	4.29807e6			0.892733
$472$			2.78093e6i			0.574560i
$473$		−	7.65670e6i		−	1.57358i
$474$	−1.26457e6			−0.258522
$475$	−1.56662e6	+	632598.i	−0.318589	+	0.128645i
$476$	3.84431e6			0.777679
$477$			1.48935e6i			0.299710i
$478$		−	2.78017e6i		−	0.556546i
$479$	−3.05191e6			−0.607762			−0.303881	−	0.952710i	$-0.598282\pi$
$479$	−3.05191e6			−0.607762			−0.303881	+	0.952710i	$0.598282\pi$
$480$	1.06220e6	−	206363.i	0.210428	−	0.0408817i
$481$	−6.10740e6			−1.20363
$482$			5.87718e6i			1.15226i
$483$		−	1.98071e6i		−	0.386324i
$484$	−1.95777e6			−0.379882
$485$	−966112.	−	4.97283e6i	−0.186498	−	0.959952i
$486$	3.21274e6			0.616999
$487$			562122.i			0.107401i	0.998557	+	0.0537005i	$0.0171016\pi$
$487$			562122.i			0.107401i	−0.998557	+	0.0537005i	$0.982898\pi$
$488$		−	2.06389e6i		−	0.392317i
$489$	1.13742e7			2.15104
$490$	−956430.	−	4.92299e6i	−0.179955	−	0.926273i
$491$	−9.87180e6			−1.84796			−0.923980	−	0.382441i	$-0.875084\pi$
$491$	−9.87180e6			−1.84796			−0.923980	+	0.382441i	$0.875084\pi$
$492$			4.57606e6i			0.852273i
$493$			1.94893e6i			0.361143i
$494$	−2.32892e6			−0.429376
$495$	−3.33968e6	+	648828.i	−0.612622	+	0.119019i
$496$	−1.28938e6			−0.235329
$497$		−	9.75890e6i		−	1.77219i
$498$		−	8.74872e6i		−	1.58078i
$499$	429238.			0.0771696			0.0385848	−	0.999255i	$-0.487715\pi$
$499$	429238.			0.0771696			0.0385848	+	0.999255i	$0.487715\pi$
$500$	2.34460e6	−	1.52162e6i	0.419416	−	0.272196i
$501$	6.18835e6			1.10149
$502$			1.58640e6i			0.280965i
$503$		−	2.64410e6i		−	0.465970i	−0.972480	−	0.232985i	$-0.925151\pi$
$503$		−	2.64410e6i		−	0.465970i	0.972480	−	0.232985i	$-0.0748493\pi$
$504$	−1.44922e6			−0.254130
$505$	4.44067e6	−	862725.i	0.774854	−	0.150537i
$506$	−1.12648e6			−0.195591
$507$			1.49040e7i			2.57503i
$508$			204592.i			0.0351746i
$509$	1.04433e7			1.78666			0.893332	−	0.449396i	$-0.148361\pi$
$509$	1.04433e7			1.78666			0.893332	+	0.449396i	$0.148361\pi$
$510$	−977807.	−	5.03303e6i	−0.166467	−	0.856848i
$511$	−1.47500e7			−2.49885
$512$		−	262144.i		−	0.0441942i
$513$			1.31510e6i			0.220630i
$514$	2.75187e6			0.459431
$515$	302954.	+	1.55938e6i	0.0503337	+	0.259080i
$516$	−4.34991e6			−0.719211
$517$			1.02381e7i			1.68459i
$518$		−	4.49336e6i		−	0.735779i
$519$	1.13411e7			1.84814
$520$	3.78217e6	−	734793.i	0.613384	−	0.119167i
$521$	5.53689e6			0.893658			0.446829	−	0.894619i	$-0.352553\pi$
$521$	5.53689e6			0.893658			0.446829	+	0.894619i	$0.352553\pi$
$522$		−	734703.i		−	0.118015i
$523$		−	5.01095e6i		−	0.801062i	−0.916283	−	0.400531i	$-0.868826\pi$
$523$		−	5.01095e6i		−	0.801062i	0.916283	−	0.400531i	$-0.131174\pi$
$524$	−1.88459e6			−0.299840
$525$	−1.08496e7	+	4.38105e6i	−1.71797	+	0.693713i
$526$	3.34690e6			0.527446
$527$			6.10945e6i			0.958243i
$528$			2.57618e6i			0.402154i
$529$	−279841.			−0.0434783
$530$	2.85970e6	−	555578.i	0.442213	−	0.0859123i
$531$	−4.96737e6			−0.764523
$532$		−	1.71344e6i		−	0.262477i
$533$			1.62939e7i			2.48432i
$534$	−969512.			−0.147130
$535$	−704933.	−	3.62847e6i	−0.106479	−	0.548074i
$536$	240041.			0.0360889
$537$			3.56301e6i			0.533189i
$538$			5.37958e6i			0.801295i
$539$	1.19398e7			1.77022
$540$	−414923.	−	2.13572e6i	−0.0612327	−	0.315180i
$541$	−6.51271e6			−0.956685			−0.478342	−	0.878173i	$-0.658762\pi$
$541$	−6.51271e6			−0.956685			−0.478342	+	0.878173i	$0.658762\pi$
$542$		−	202214.i		−	0.0295674i
$543$			7.00648e6i			1.01977i
$544$	−1.24211e6			−0.179955
$545$	1.24201e7	−	2.41295e6i	1.79116	−	0.347983i
$546$	−1.61289e7			−2.31539
$547$			1.03269e7i			1.47571i	0.674958	+	0.737856i	$0.264162\pi$
$547$			1.03269e7i			1.47571i	−0.674958	+	0.737856i	$0.735838\pi$
$548$		−	6.42242e6i		−	0.913582i
$549$	3.68657e6			0.522026
$550$	2.49163e6	+	6.17049e6i	0.351217	+	0.869787i
$551$	868658.			0.121891
$552$			639976.i			0.0893955i
$553$		−	3.31277e6i		−	0.460658i
$554$	−8.97797e6			−1.24281
$555$	−5.88278e6	+	1.14290e6i	−0.810682	+	0.157498i
$556$	405829.			0.0556744
$557$			8.30617e6i			1.13439i	0.823583	+	0.567195i	$0.191972\pi$
$557$			8.30617e6i			1.13439i	−0.823583	+	0.567195i	$0.808028\pi$
$558$		−	2.30312e6i		−	0.313135i
$559$	−1.54887e7			−2.09645
$560$	540605.	+	2.78264e6i	0.0728468	+	0.374961i
$561$	1.22067e7			1.63754
$562$		−	6.13633e6i		−	0.819535i
$563$		−	3.23698e6i		−	0.430397i	−0.976570	−	0.215198i	$-0.930960\pi$
$563$		−	3.23698e6i		−	0.430397i	0.976570	−	0.215198i	$-0.0690398\pi$
$564$	5.81645e6			0.769946
$565$	−527666.	−	2.71603e6i	−0.0695405	−	0.357943i
$566$	633606.			0.0831339
$567$			1.46102e7i			1.90852i
$568$			3.15315e6i			0.410085i
$569$	−1.30365e7			−1.68803			−0.844017	−	0.536316i	$-0.819816\pi$
$569$	−1.30365e7			−1.68803			−0.844017	+	0.536316i	$0.819816\pi$
$570$	−2.24327e6	+	435818.i	−0.289197	+	0.0561847i
$571$	−4.40476e6			−0.565369			−0.282685	−	0.959213i	$-0.591225\pi$
$571$	−4.40476e6			−0.565369			−0.282685	+	0.959213i	$0.591225\pi$
$572$			9.17297e6i			1.17225i
$573$		−	8.88865e6i		−	1.13096i
$574$	−1.19878e7			−1.51866
$575$	618970.	+	1.53287e6i	0.0780728	+	0.193347i
$576$	468249.			0.0588058
$577$			7.42629e6i			0.928608i	0.885676	+	0.464304i	$0.153695\pi$
$577$			7.42629e6i			0.928608i	−0.885676	+	0.464304i	$0.846305\pi$
$578$			206069.i			0.0256563i
$579$	6.18606e6			0.766863
$580$	−1.41070e6	+	274069.i	−0.174127	+	0.0338290i
$581$	2.29189e7			2.81678
$582$		−	6.85191e6i		−	0.838502i
$583$			6.93569e6i			0.845120i
$584$	4.76581e6			0.578235
$585$	1.31251e6	+	6.75581e6i	0.158567	+	0.816184i
$586$	7.15571e6			0.860812
$587$		−	1.40638e6i		−	0.168464i	−0.996446	−	0.0842320i	$-0.973156\pi$
$587$		−	1.40638e6i		−	0.168464i	0.996446	−	0.0842320i	$-0.0268437\pi$
$588$		−	6.78323e6i		−	0.809084i
$589$	2.72304e6			0.323419
$590$	1.85299e6	+	9.53784e6i	0.219151	+	1.12803i
$591$	−1.75542e7			−2.06734
$592$			1.45183e6i			0.170259i
$593$			1.56429e6i			0.182676i	0.995820	+	0.0913378i	$0.0291143\pi$
$593$			1.56429e6i			0.182676i	−0.995820	+	0.0913378i	$0.970886\pi$
$594$	5.17980e6			0.602347
$595$	1.31849e7	−	2.56154e6i	1.52681	−	0.296626i
$596$	1.58730e6			0.183039
$597$		−	683171.i		−	0.0784501i
$598$			2.27875e6i			0.260582i
$599$	−7.69381e6			−0.876142			−0.438071	−	0.898940i	$-0.644338\pi$
$599$	−7.69381e6			−0.876142			−0.438071	+	0.898940i	$0.644338\pi$
$600$	3.50557e6	−	1.41554e6i	0.397539	−	0.160525i
$601$	4.15186e6			0.468875			0.234437	−	0.972131i	$-0.424675\pi$
$601$	4.15186e6			0.468875			0.234437	+	0.972131i	$0.424675\pi$
$602$		−	1.13954e7i		−	1.28156i
$603$			428768.i			0.0480208i
$604$	2.59365e6			0.289281
$605$	−6.71463e6	+	1.30451e6i	−0.745820	+	0.144897i
$606$	6.11866e6			0.676822
$607$		−	2.19422e6i		−	0.241718i	−0.992670	−	0.120859i	$-0.961435\pi$
$607$		−	2.19422e6i		−	0.241718i	0.992670	−	0.120859i	$-0.0385649\pi$
$608$			553622.i			0.0607372i
$609$	6.01588e6			0.657289
$610$	−1.37521e6	−	7.07858e6i	−0.149639	−	0.770232i
$611$	2.07106e7			2.24434
$612$		−	2.21870e6i		−	0.239453i
$613$			7.39780e6i			0.795154i	0.917569	+	0.397577i	$0.130149\pi$
$613$			7.39780e6i			0.795154i	−0.917569	+	0.397577i	$0.869851\pi$
$614$	−175476.			−0.0187844
$615$	3.04913e6	+	1.56946e7i	0.325078	+	1.67326i
$616$	−6.74878e6			−0.716595
$617$			1.13455e6i			0.119981i	0.998199	+	0.0599903i	$0.0191070\pi$
$617$			1.13455e6i			0.119981i	−0.998199	+	0.0599903i	$0.980893\pi$
$618$			2.14862e6i			0.226302i
$619$	9.28863e6			0.974372			0.487186	−	0.873298i	$-0.338023\pi$
$619$	9.28863e6			0.974372			0.487186	+	0.873298i	$0.338023\pi$
$620$	−4.42222e6	+	859141.i	−0.462020	+	0.0897605i
$621$	1.28677e6			0.133897
$622$		−	3.57735e6i		−	0.370754i
$623$		−	2.53981e6i		−	0.262169i
$624$	5.21133e6			0.535781
$625$	7.02747e6	−	6.78101e6i	0.719613	−	0.694375i
$626$	−1.13152e7			−1.15405
$627$		−	5.44065e6i		−	0.552690i
$628$		−	3.63803e6i		−	0.368101i
$629$	6.87918e6			0.693282
$630$	−4.97042e6	+	965644.i	−0.498932	+	0.0969316i
$631$	7.38730e6			0.738605			0.369302	−	0.929309i	$-0.379597\pi$
$631$	7.38730e6			0.738605			0.369302	+	0.929309i	$0.379597\pi$
$632$			1.07037e6i			0.106596i
$633$		−	2.69121e6i		−	0.266956i
$634$	−9.06878e6			−0.896036
$635$	136324.	+	701696.i	0.0134165	+	0.0690581i
$636$	3.94029e6			0.386265
$637$		−	2.41530e7i		−	2.35842i
$638$		−	3.42140e6i		−	0.332776i
$639$	−5.63224e6			−0.545668
$640$	−174672.	−	899083.i	−0.0168568	−	0.0867661i
$641$	−6.25749e6			−0.601527			−0.300763	−	0.953699i	$-0.597241\pi$
$641$	−6.25749e6			−0.601527			−0.300763	+	0.953699i	$0.597241\pi$
$642$		−	4.99956e6i		−	0.478734i
$643$		−	4.78077e6i		−	0.456006i	−0.973660	−	0.228003i	$-0.926780\pi$
$643$		−	4.78077e6i		−	0.456006i	0.973660	−	0.228003i	$-0.0732196\pi$
$644$	−1.67653e6			−0.159293
$645$	−1.49190e7	+	2.89844e6i	−1.41202	+	0.274325i
$646$	2.62322e6			0.247317
$647$		−	9.76424e6i		−	0.917018i	−0.888690	−	0.458509i	$-0.848384\pi$
$647$		−	9.76424e6i		−	0.917018i	0.888690	−	0.458509i	$-0.151616\pi$
$648$		−	4.72062e6i		−	0.441633i
$649$	−2.31323e7			−2.15579
$650$	1.24822e7	−	5.04028e6i	1.15880	−	0.467920i
$651$	1.88584e7			1.74402
$652$		−	9.62749e6i		−	0.886940i
$653$			7.46223e6i			0.684835i	0.939548	+	0.342417i	$0.111246\pi$
$653$			7.46223e6i			0.684835i	−0.939548	+	0.342417i	$0.888754\pi$
$654$	1.71133e7			1.56455
$655$	−6.46365e6	+	1.25575e6i	−0.588674	+	0.114366i
$656$	3.87332e6			0.351418
$657$			8.51281e6i			0.769413i
$658$			1.52373e7i			1.37196i
$659$	1.96518e6			0.176274			0.0881370	−	0.996108i	$-0.471909\pi$
$659$	1.96518e6			0.176274			0.0881370	+	0.996108i	$0.471909\pi$
$660$	1.71657e6	+	8.83561e6i	0.153391	+	0.789545i
$661$	−1.08149e7			−0.962764			−0.481382	−	0.876511i	$-0.659865\pi$
$661$	−1.08149e7			−0.962764			−0.481382	+	0.876511i	$0.659865\pi$
$662$		−	1.19353e7i		−	1.05850i
$663$		−	2.46928e7i		−	2.18166i
$664$	−7.40520e6			−0.651803
$665$	−1.14171e6	−	5.87665e6i	−0.100115	−	0.515319i
$666$	−2.59329e6			−0.226551
$667$		−	849945.i		−	0.0739735i
$668$		−	5.23802e6i		−	0.454178i
$669$	1.93714e7			1.67338
$670$	823277.	−	159945.i	0.0708531	−	0.0137652i
$671$	1.71678e7			1.47200
$672$			3.83411e6i			0.327522i
$673$			2.30881e6i			0.196494i	0.995162	+	0.0982472i	$0.0313236\pi$
$673$			2.30881e6i			0.196494i	−0.995162	+	0.0982472i	$0.968676\pi$
$674$	6.79154e6			0.575862
$675$	−2.84615e6	−	7.04846e6i	−0.240435	−	0.595436i
$676$	1.26152e7			1.06176
$677$			1.19881e6i			0.100526i	0.998736	+	0.0502631i	$0.0160060\pi$
$677$			1.19881e6i			0.100526i	−0.998736	+	0.0502631i	$0.983994\pi$
$678$		−	3.74234e6i		−	0.312657i
$679$	1.79498e7			1.49412
$680$	−4.26012e6	+	827648.i	−0.353305	+	0.0686394i
$681$	−2.79818e7			−2.31211
$682$		−	1.07253e7i		−	0.882975i
$683$			5.08345e6i			0.416972i	0.978025	+	0.208486i	$0.0668535\pi$
$683$			5.08345e6i			0.416972i	−0.978025	+	0.208486i	$0.933146\pi$
$684$	−988895.			−0.0808184
$685$	−4.27940e6	−	2.20272e7i	−0.348463	−	1.79363i
$686$	4.45353e6			0.361322
$687$			1.54185e7i			1.24638i
$688$			3.68191e6i			0.296553i
$689$	1.40301e7			1.12594
$690$	426430.	+	2.19494e6i	0.0340977	+	0.175509i
$691$	1.29756e7			1.03379			0.516897	−	0.856048i	$-0.327087\pi$
$691$	1.29756e7			1.03379			0.516897	+	0.856048i	$0.327087\pi$
$692$		−	9.59943e6i		−	0.762044i
$693$		−	1.20549e7i		−	0.953518i
$694$	1.87549e6			0.147814
$695$	1.39188e6	−	270412.i	0.109305	−	0.0212356i
$696$	−1.94376e6			−0.152097
$697$		−	1.83529e7i		−	1.43095i
$698$			325646.i			0.0252992i
$699$	2.63394e6			0.203898
$700$	3.70826e6	+	9.18347e6i	0.286039	+	0.708373i
$701$	−2.27821e7			−1.75105			−0.875525	−	0.483172i	$-0.839485\pi$
$701$	−2.27821e7			−1.75105			−0.875525	+	0.483172i	$0.839485\pi$
$702$		−	1.04782e7i		−	0.802495i
$703$		−	3.06612e6i		−	0.233992i
$704$	2.18056e6			0.165820
$705$	1.99489e7	−	3.87563e6i	1.51163	−	0.293677i
$706$	−8.51795e6			−0.643167
$707$			1.60289e7i			1.20602i
$708$			1.31419e7i			0.985314i
$709$	−1.66007e7			−1.24026			−0.620128	−	0.784501i	$-0.712919\pi$
$709$	−1.66007e7			−1.24026			−0.620128	+	0.784501i	$0.712919\pi$
$710$	2.10101e6	+	1.08144e7i	0.156416	+	0.805116i
$711$	−1.91193e6			−0.141840
$712$			820626.i			0.0606660i
$713$		−	2.66438e6i		−	0.196278i
$714$	1.81671e7			1.33364
$715$	6.11215e6	+	3.14608e7i	0.447125	+	2.30147i
$716$	3.01584e6			0.219850
$717$		−	1.31383e7i		−	0.954423i
$718$			1.15174e7i			0.833768i
$719$	−2.44772e7			−1.76579			−0.882896	−	0.469568i	$-0.844410\pi$
$719$	−2.44772e7			−1.76579			−0.882896	+	0.469568i	$0.844410\pi$
$720$	1.60597e6	−	312004.i	0.115453	−	0.0224300i
$721$	−5.62871e6			−0.403247
$722$			8.73520e6i			0.623634i
$723$			2.77739e7i			1.97602i
$724$	5.93051e6			0.420480
$725$	−4.65571e6	+	1.87996e6i	−0.328958	+	0.132832i
$726$	−9.25188e6			−0.651461
$727$			1.02983e7i			0.722653i	0.932439	+	0.361326i	$0.117676\pi$
$727$			1.02983e7i			0.722653i	−0.932439	+	0.361326i	$0.882324\pi$
$728$			1.36520e7i			0.954705i
$729$	−2.74111e6			−0.191033
$730$	1.63454e7	−	3.17556e6i	1.13524	−	0.220553i
$731$	1.74459e7			1.20754
$732$		−	9.75335e6i		−	0.672785i
$733$			4.71628e6i			0.324220i	0.986773	+	0.162110i	$0.0518300\pi$
$733$			4.71628e6i			0.324220i	−0.986773	+	0.162110i	$0.948170\pi$
$734$	1.68793e6			0.115642
$735$	−4.51982e6	−	2.32647e7i	−0.308605	−	1.58847i
$736$	541696.			0.0368605
$737$			1.99671e6i			0.135409i
$738$			6.91864e6i			0.467605i
$739$	1.67061e7			1.12529			0.562644	−	0.826699i	$-0.309784\pi$
$739$	1.67061e7			1.12529			0.562644	+	0.826699i	$0.309784\pi$
$740$	967384.	+	4.97938e6i	0.0649411	+	0.334269i
$741$	−1.10058e7			−0.736338
$742$			1.03223e7i			0.688284i
$743$			1.81731e6i			0.120769i	0.998175	+	0.0603846i	$0.0192327\pi$
$743$			1.81731e6i			0.120769i	−0.998175	+	0.0603846i	$0.980767\pi$
$744$	−6.09324e6			−0.403567
$745$	5.44403e6	−	1.05766e6i	0.359360	−	0.0698158i
$746$	−6.92704e6			−0.455723
$747$		−	1.32274e7i		−	0.867305i
$748$		−	1.03321e7i		−	0.675206i
$749$	1.30973e7			0.853052
$750$	1.10799e7	−	7.19075e6i	0.719257	−	0.466789i
$751$	−2.80430e7			−1.81437			−0.907183	−	0.420736i	$-0.861772\pi$
$751$	−2.80430e7			−1.81437			−0.907183	+	0.420736i	$0.861772\pi$
$752$		−	4.92323e6i		−	0.317472i
$753$			7.49687e6i			0.481828i
$754$	−6.92112e6			−0.443351
$755$	8.89553e6	−	1.72821e6i	0.567942	−	0.110339i
$756$	7.70904e6			0.490564
$757$		−	1.83221e7i		−	1.16208i	−0.813876	−	0.581038i	$-0.802647\pi$
$757$		−	1.83221e7i		−	1.16208i	0.813876	−	0.581038i	$-0.197353\pi$
$758$			4.90358e6i			0.309985i
$759$	−5.32344e6			−0.335419
$760$	368891.	+	1.89878e6i	0.0231667	+	0.119245i
$761$	−3.00045e6			−0.187813			−0.0939063	−	0.995581i	$-0.529935\pi$
$761$	−3.00045e6			−0.187813			−0.0939063	+	0.995581i	$0.529935\pi$
$762$			966844.i			0.0603211i
$763$			4.48313e7i			2.78785i
$764$	−7.52364e6			−0.466331
$765$	−1.47837e6	−	7.60953e6i	−0.0913332	−	0.470115i
$766$	1.12094e7			0.690256
$767$			4.67941e7i			2.87212i
$768$		−	1.23882e6i		−	0.0757887i
$769$	2.82429e7			1.72224			0.861120	−	0.508402i	$-0.169764\pi$
$769$	2.82429e7			1.72224			0.861120	+	0.508402i	$0.169764\pi$
$770$	−2.31465e7	+	4.49686e6i	−1.40688	+	0.273327i
$771$	1.30046e7			0.787880
$772$		−	5.23608e6i		−	0.316201i
$773$		−	1.86927e7i		−	1.12518i	−0.826734	−	0.562592i	$-0.809804\pi$
$773$		−	1.86927e7i		−	1.12518i	0.826734	−	0.562592i	$-0.190196\pi$
$774$	−6.57672e6			−0.394600
$775$	−1.45946e7	+	5.89324e6i	−0.872844	+	0.352452i
$776$	−5.79968e6			−0.345740
$777$		−	2.12344e7i		−	1.26179i
$778$		−	8.26781e6i		−	0.489713i
$779$	−8.18008e6			−0.482963
$780$	1.78735e7	−	3.47242e6i	1.05189	−	0.204360i
$781$	−2.62285e7			−1.53867
$782$		−	2.56671e6i		−	0.150093i
$783$			3.90822e6i			0.227811i
$784$	−5.74155e6			−0.333610
$785$	−2.42410e6	−	1.24775e7i	−0.140403	−	0.722690i
$786$	−8.90606e6			−0.514197
$787$		−	1.05976e7i		−	0.609916i	−0.952366	−	0.304958i	$-0.901358\pi$
$787$		−	1.05976e7i		−	0.609916i	0.952366	−	0.304958i	$-0.0986425\pi$
$788$			1.48584e7i			0.852428i
$789$	1.58165e7			0.904520
$790$	713212.	+	3.67109e6i	0.0406585	+	0.209280i
$791$	9.80373e6			0.557122
$792$			3.89498e6i			0.220644i
$793$		−	3.47286e7i		−	1.96112i
$794$	−2.87978e6			−0.162110
$795$	1.35141e7	−	2.62550e6i	0.758352	−	0.147331i
$796$	−578258.			−0.0323474
$797$			1.19806e7i			0.668085i	0.942558	+	0.334042i	$0.108413\pi$
$797$			1.19806e7i			0.668085i	−0.942558	+	0.334042i	$0.891587\pi$
$798$		−	8.09726e6i		−	0.450122i
$799$	−2.33277e7			−1.29272
$800$	−1.19816e6	−	2.96722e6i	−0.0661895	−	0.163918i
$801$	−1.46582e6			−0.0807236
$802$		−	1.08885e7i		−	0.597770i
$803$			3.96429e7i			2.16958i
$804$	1.13437e6			0.0618890
$805$	−5.75005e6	+	1.11711e6i	−0.312739	+	0.0607584i
$806$	−2.16961e7			−1.17637
$807$			2.54224e7i			1.37414i
$808$		−	5.17903e6i		−	0.279074i
$809$	−2.31035e7			−1.24110			−0.620550	−	0.784167i	$-0.713091\pi$
$809$	−2.31035e7			−1.24110			−0.620550	+	0.784167i	$0.713091\pi$
$810$	−3.14545e6	−	1.61904e7i	−0.168450	−	0.867054i
$811$	2.36881e7			1.26467			0.632336	−	0.774694i	$-0.282096\pi$
$811$	2.36881e7			1.26467			0.632336	+	0.774694i	$0.282096\pi$
$812$		−	5.09204e6i		−	0.271020i
$813$		−	955607.i		−	0.0507052i
$814$	−1.20766e7			−0.638827
$815$	−6.41501e6	−	3.30197e7i	−0.338301	−	1.74132i
$816$	−5.86988e6			−0.308606
$817$		−	7.77583e6i		−	0.407560i
$818$			1.74407e7i			0.911338i
$819$	−2.43856e7			−1.27035
$820$	1.32845e7	−	2.58088e6i	0.689936	−	0.134040i
$821$	−3.32070e7			−1.71938			−0.859690	−	0.510816i	$-0.829343\pi$
$821$	−3.32070e7			−1.71938			−0.859690	+	0.510816i	$0.829343\pi$
$822$		−	3.03505e7i		−	1.56670i
$823$			3.68415e7i			1.89600i	0.318275	+	0.947999i	$0.396897\pi$
$823$			3.68415e7i			1.89600i	−0.318275	+	0.947999i	$0.603103\pi$
$824$	1.81867e6			0.0933114
$825$	1.17747e7	+	2.91600e7i	0.602304	+	1.49160i
$826$	−3.44276e7			−1.75572
$827$		−	1.62904e7i		−	0.828263i	−0.910217	−	0.414132i	$-0.864085\pi$
$827$		−	1.62904e7i		−	0.828263i	0.910217	−	0.414132i	$-0.135915\pi$
$828$			967592.i			0.0490474i
$829$	3.79361e6			0.191719			0.0958597	−	0.995395i	$-0.469440\pi$
$829$	3.79361e6			0.191719			0.0958597	+	0.995395i	$0.469440\pi$
$830$	−2.53978e7	+	4.93424e6i	−1.27968	+	0.248614i
$831$	−4.24273e7			−2.13129
$832$		−	4.41104e6i		−	0.220919i
$833$			2.72051e7i			1.35843i
$834$	1.91783e6			0.0954762
$835$	−3.49021e6	−	1.79650e7i	−0.173235	−	0.891684i
$836$	−4.60514e6			−0.227891
$837$			1.22514e7i			0.604464i
$838$			3.45401e6i			0.169908i
$839$	−2.23050e7			−1.09395			−0.546975	−	0.837149i	$-0.684221\pi$
$839$	−2.23050e7			−1.09395			−0.546975	+	0.837149i	$0.684221\pi$
$840$	2.55475e6	+	1.31499e7i	0.124925	+	0.643022i
$841$	−1.79297e7			−0.874142
$842$			1.51232e7i			0.735129i
$843$		−	2.89985e7i		−	1.40542i
$844$	−2.27793e6			−0.110074
$845$	4.32668e7	−	8.40580e6i	2.08455	−	0.404983i
$846$	8.79401e6			0.422436
$847$		−	2.42370e7i		−	1.16083i
$848$		−	3.33519e6i		−	0.159269i
$849$	2.99424e6			0.142567
$850$	−1.40596e7	+	5.67722e6i	−0.667459	+	0.269518i
$851$	−3.00007e6			−0.142006
$852$			1.49009e7i			0.703255i
$853$			1.68266e7i			0.791817i	0.918290	+	0.395909i	$0.129570\pi$
$853$			1.68266e7i			0.791817i	−0.918290	+	0.395909i	$0.870430\pi$
$854$	2.55507e7			1.19883
$855$	−3.39164e6	+	658922.i	−0.158670	+	0.0308261i
$856$	−4.23179e6			−0.197396
$857$			1.58433e7i			0.736874i	0.929653	+	0.368437i	$0.120107\pi$
$857$			1.58433e7i			0.736874i	−0.929653	+	0.368437i	$0.879893\pi$
$858$			4.33489e7i			2.01029i
$859$	−1.87805e7			−0.868408			−0.434204	−	0.900815i	$-0.642970\pi$
$859$	−1.87805e7			−0.868408			−0.434204	+	0.900815i	$0.642970\pi$
$860$	2.45333e6	+	1.26279e7i	0.113113	+	0.582219i
$861$	−5.66511e7			−2.60435
$862$			1.37354e7i			0.629610i
$863$		−	3.89526e7i		−	1.78037i	−0.455601	−	0.890184i	$-0.650576\pi$
$863$		−	3.89526e7i		−	1.78037i	0.455601	−	0.890184i	$-0.349424\pi$
$864$	−2.49083e6			−0.113517
$865$	−6.39631e6	−	3.29235e7i	−0.290663	−	1.49612i
$866$	1.66897e7			0.756229
$867$			973826.i			0.0439981i
$868$		−	1.59623e7i		−	0.719114i
$869$	−8.90356e6			−0.399958
$870$	−6.66658e6	+	1.29517e6i	−0.298610	+	0.0580135i
$871$	4.03912e6			0.180402
$872$		−	1.44852e7i		−	0.645110i
$873$		−	1.03595e7i		−	0.460050i
$874$	−1.14401e6			−0.0506583
$875$	1.88375e7	+	2.90259e7i	0.831769	+	1.28164i
$876$	2.25219e7			0.991617
$877$			1.00593e7i			0.441640i	0.975315	+	0.220820i	$0.0708733\pi$
$877$			1.00593e7i			0.441640i	−0.975315	+	0.220820i	$0.929127\pi$
$878$		−	1.07379e7i		−	0.470092i
$879$	3.38159e7			1.47621
$880$	7.47875e6	−	1.45296e6i	0.325553	−	0.0632479i
$881$	1.44749e7			0.628314			0.314157	−	0.949371i	$-0.398278\pi$
$881$	1.44749e7			0.628314			0.314157	+	0.949371i	$0.398278\pi$
$882$		−	1.02557e7i		−	0.443909i
$883$			8.54593e6i			0.368857i	0.982846	+	0.184428i	$0.0590433\pi$
$883$			8.54593e6i			0.368857i	−0.982846	+	0.184428i	$0.940957\pi$
$884$	−2.09008e7			−0.899564
$885$	8.75673e6	+	4.50731e7i	0.375823	+	1.93446i
$886$	1.34656e7			0.576289
$887$		−	2.67542e7i		−	1.14178i	−0.821027	−	0.570890i	$-0.806598\pi$
$887$		−	2.67542e7i		−	1.14178i	0.821027	−	0.570890i	$-0.193402\pi$
$888$			6.86093e6i			0.291978i
$889$	−2.53283e6			−0.107486
$890$	546801.	+	2.81453e6i	0.0231395	+	0.119105i
$891$	3.92670e7			1.65704
$892$		−	1.63965e7i		−	0.689986i
$893$			1.03974e7i			0.436310i
$894$	7.50116e6			0.313895
$895$	1.03435e7	−	2.00952e6i	0.431630	−	0.0838562i
$896$	3.24531e6			0.135047
$897$			1.07687e7i			0.446872i
$898$		−	1.01001e7i		−	0.417959i
$899$	8.09237e6			0.333946
$900$	5.30014e6	−	2.14018e6i	0.218113	−	0.0880733i
$901$	−1.58031e7			−0.648531
$902$			3.22191e7i			1.31855i
$903$		−	5.38514e7i		−	2.19775i
$904$	−3.16763e6			−0.128918
$905$	2.03400e7	−	3.95163e6i	0.825525	−	0.160382i
$906$	1.22569e7			0.496088
$907$		−	3.38983e7i		−	1.36823i	−0.729373	−	0.684116i	$-0.760188\pi$
$907$		−	3.38983e7i		−	1.36823i	0.729373	−	0.684116i	$-0.239812\pi$
$908$			2.36847e7i			0.953354i
$909$	9.25092e6			0.371343
$910$	9.09665e6	+	4.68228e7i	0.364148	+	1.87436i
$911$	−1.38860e7			−0.554348			−0.277174	−	0.960820i	$-0.589398\pi$
$911$	−1.38860e7			−0.554348			−0.277174	+	0.960820i	$0.589398\pi$
$912$			2.61626e6i			0.104158i
$913$		−	6.15979e7i		−	2.44562i
$914$	−2.68549e6			−0.106330
$915$	−6.49887e6	−	3.34514e7i	−0.256617	−	1.32087i
$916$	1.30507e7			0.513921
$917$		−	2.33311e7i		−	0.916244i
$918$			1.18023e7i			0.462231i
$919$	−3.17081e6			−0.123846			−0.0619229	−	0.998081i	$-0.519723\pi$
$919$	−3.17081e6			−0.123846			−0.0619229	+	0.998081i	$0.519723\pi$
$920$	1.85787e6	−	360944.i	0.0723679	−	0.0140595i
$921$	−829252.			−0.0322135
$922$		−	1.28572e7i		−	0.498101i
$923$			5.30573e7i			2.04994i
$924$	−3.18928e7			−1.22889
$925$	6.63573e6	+	1.64333e7i	0.254997	+	0.631497i
$926$	−2.23526e7			−0.856645
$927$			3.24855e6i			0.124162i
$928$			1.64526e6i			0.0627141i
$929$	−9.88554e6			−0.375804			−0.187902	−	0.982188i	$-0.560169\pi$
$929$	−9.88554e6			−0.375804			−0.187902	+	0.982188i	$0.560169\pi$
$930$	−2.08982e7	+	4.06006e6i	−0.792320	+	0.153931i
$931$	1.21256e7			0.458489
$932$		−	2.22945e6i		−	0.0840732i
$933$		−	1.69056e7i		−	0.635807i
$934$	−1.39866e7			−0.524621
$935$	−6.88453e6	−	3.54365e7i	−0.257540	−	1.32563i
$936$	7.87912e6			0.293960
$937$			1.90723e7i			0.709667i	0.934929	+	0.354834i	$0.115462\pi$
$937$			1.90723e7i			0.709667i	−0.934929	+	0.354834i	$0.884538\pi$
$938$			2.97168e6i			0.110280i
$939$	−5.34722e7			−1.97908
$940$	−3.28046e6	−	1.68854e7i	−0.121092	−	0.623291i
$941$	5.63987e6			0.207633			0.103816	−	0.994596i	$-0.466895\pi$
$941$	5.63987e6			0.207633			0.103816	+	0.994596i	$0.466895\pi$
$942$		−	1.71923e7i		−	0.631257i
$943$			8.00386e6i			0.293103i
$944$	1.11237e7			0.406275
$945$	2.64399e7	−	5.13670e6i	0.963120	−	0.187113i
$946$	−3.06268e7			−1.11269
$947$		−	4.00201e7i		−	1.45012i	−0.688687	−	0.725059i	$-0.741813\pi$
$947$		−	4.00201e7i		−	1.45012i	0.688687	−	0.725059i	$-0.258187\pi$
$948$			5.05828e6i			0.182802i
$949$	8.01932e7			2.89049
$950$	2.53039e6	+	6.26649e6i	0.0909659	+	0.225276i
$951$	−4.28565e7			−1.53662
$952$		−	1.53772e7i		−	0.549902i
$953$		−	3.37494e7i		−	1.20374i	−0.798593	−	0.601872i	$-0.794422\pi$
$953$		−	3.37494e7i		−	1.20374i	0.798593	−	0.601872i	$-0.205578\pi$
$954$	5.95741e6			0.211927
$955$	−2.58040e7	+	5.01316e6i	−0.915544	+	0.177870i
$956$	−1.11207e7			−0.393538
$957$		−	1.61686e7i		−	0.570679i
$958$			1.22077e7i			0.429752i
$959$	7.95088e7			2.79170
$960$	−825452.	−	4.24881e6i	−0.0289077	−	0.148795i
$961$	−3.26147e6			−0.113921
$962$			2.44296e7i			0.851096i
$963$		−	7.55893e6i		−	0.262661i
$964$	2.35087e7			0.814772
$965$	−3.48891e6	−	1.79583e7i	−0.120607	−	0.620794i
$966$	−7.92282e6			−0.273173
$967$			1.08019e7i			0.371478i	0.982599	+	0.185739i	$0.0594679\pi$
$967$			1.08019e7i			0.371478i	−0.982599	+	0.185739i	$0.940532\pi$
$968$			7.83109e6i			0.268617i
$969$	1.23966e7			0.424125
$970$	−1.98913e7	+	3.86445e6i	−0.678788	+	0.131874i
$971$	3.10125e7			1.05557			0.527787	−	0.849377i	$-0.323022\pi$
$971$	3.10125e7			1.05557			0.527787	+	0.849377i	$0.323022\pi$
$972$		−	1.28510e7i		−	0.436284i
$973$			5.02411e6i			0.170128i
$974$	2.24849e6			0.0759439
$975$	5.89874e7	−	2.38190e7i	1.98723	−	0.802438i
$976$	−8.25555e6			−0.277410
$977$			1.99742e7i			0.669473i	0.942312	+	0.334736i	$0.108647\pi$
$977$			1.99742e7i			0.669473i	−0.942312	+	0.334736i	$0.891353\pi$
$978$		−	4.54968e7i		−	1.52102i
$979$	−6.82613e6			−0.227624
$980$	−1.96920e7	+	3.82572e6i	−0.654974	+	0.127247i
$981$	2.58739e7			0.858399
$982$			3.94872e7i			1.30670i
$983$		−	3.77483e7i		−	1.24599i	−0.782227	−	0.622993i	$-0.785916\pi$
$983$		−	3.77483e7i		−	1.24599i	0.782227	−	0.622993i	$-0.214084\pi$
$984$	1.83042e7			0.602648
$985$	9.90050e6	+	5.09604e7i	0.325137	+	1.67356i
$986$	7.79573e6			0.255367
$987$			7.20070e7i			2.35278i
$988$			9.31569e6i			0.303615i
$989$	−7.60832e6			−0.247342
$990$	2.59531e6	+	1.33587e7i	0.0841592	+	0.433189i
$991$	−5.95198e7			−1.92521			−0.962604	−	0.270913i	$-0.912674\pi$
$991$	−5.95198e7			−1.92521			−0.962604	+	0.270913i	$0.912674\pi$
$992$			5.15751e6i			0.166403i
$993$		−	5.64029e7i		−	1.81522i
$994$	−3.90356e7			−1.25313
$995$	−1.98327e6	+	385306.i	−0.0635073	+	0.0123381i
$996$	−3.49949e7			−1.11778
$997$			1.30116e7i			0.414567i	0.978281	+	0.207283i	$0.0664622\pi$
$997$			1.30116e7i			0.414567i	−0.978281	+	0.207283i	$0.933538\pi$
$998$		−	1.71695e6i		−	0.0545672i
$999$	1.37949e7			0.437326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.b.b.139.3	✓	30
5.4	even	2	inner	230.6.b.b.139.28	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.b.b.139.3	✓	30	1.1	even	1	trivial
230.6.b.b.139.28	yes	30	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -18.9029i q^{3} -16.0000 q^{4} +(-54.8757 + 10.6611i) q^{5} -75.6115 q^{6} -198.078i q^{7} +64.0000i q^{8} -114.319 q^{9} +O(q^{10})\)	\(q-4.00000i q^{2} -18.9029i q^{3} -16.0000 q^{4} +(-54.8757 + 10.6611i) q^{5} -75.6115 q^{6} -198.078i q^{7} +64.0000i q^{8} -114.319 q^{9} +(42.6446 + 219.503i) q^{10} -532.364 q^{11} +302.446i q^{12} +1076.91i q^{13} -792.312 q^{14} +(201.526 + 1037.31i) q^{15} +256.000 q^{16} -1213.00i q^{17} +457.274i q^{18} -540.647 q^{19} +(878.011 - 170.578i) q^{20} -3744.24 q^{21} +2129.46i q^{22} +529.000i q^{23} +1209.78 q^{24} +(2897.68 - 1170.08i) q^{25} +4307.66 q^{26} -2432.45i q^{27} +3169.25i q^{28} -1606.70 q^{29} +(4149.23 - 806.105i) q^{30} -5036.63 q^{31} -1024.00i q^{32} +10063.2i q^{33} -4852.01 q^{34} +(2111.74 + 10869.7i) q^{35} +1829.10 q^{36} +5671.20i q^{37} +2162.59i q^{38} +20356.8 q^{39} +(-682.313 - 3512.04i) q^{40} +15130.2 q^{41} +14977.0i q^{42} +14382.5i q^{43} +8517.83 q^{44} +(6273.31 - 1218.77i) q^{45} +2116.00 q^{46} -19231.4i q^{47} -4839.13i q^{48} -22427.9 q^{49} +(-4680.30 - 11590.7i) q^{50} -22929.2 q^{51} -17230.6i q^{52} -13028.1i q^{53} -9729.80 q^{54} +(29213.9 - 5675.61i) q^{55} +12677.0 q^{56} +10219.8i q^{57} +6426.81i q^{58} +43452.0 q^{59} +(-3224.42 - 16596.9i) q^{60} -32248.3 q^{61} +20146.5i q^{62} +22644.0i q^{63} -4096.00 q^{64} +(-11481.1 - 59096.4i) q^{65} +40252.9 q^{66} -3750.65i q^{67} +19408.0i q^{68} +9999.62 q^{69} +(43478.7 - 8446.96i) q^{70} +49267.9 q^{71} -7316.39i q^{72} -74465.7i q^{73} +22684.8 q^{74} +(-22117.8 - 54774.5i) q^{75} +8650.35 q^{76} +105450. i q^{77} -81427.1i q^{78} +16724.6 q^{79} +(-14048.2 + 2729.25i) q^{80} -73759.7 q^{81} -60520.7i q^{82} +115706. i q^{83} +59907.9 q^{84} +(12932.0 + 66564.3i) q^{85} +57529.8 q^{86} +30371.3i q^{87} -34071.3i q^{88} +12822.3 q^{89} +(-4875.07 - 25093.2i) q^{90} +213313. q^{91} -8464.00i q^{92} +95206.8i q^{93} -76925.5 q^{94} +(29668.4 - 5763.92i) q^{95} -19356.5 q^{96} +90619.9i q^{97} +89711.7i q^{98} +60859.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 480 q^{4} - 30 q^{5} + 216 q^{6} - 3020 q^{9}+O(q^{10}) \) 30 * q - 480 * q^4 - 30 * q^5 + 216 * q^6 - 3020 * q^9	\( 30 q - 480 q^{4} - 30 q^{5} + 216 q^{6} - 3020 q^{9} + 80 q^{10} + 2074 q^{11} - 808 q^{14} - 3056 q^{15} + 7680 q^{16} - 1750 q^{19} + 480 q^{20} + 524 q^{21} - 3456 q^{24} + 12218 q^{25} + 10440 q^{26} - 27548 q^{29} + 16280 q^{30} + 31170 q^{31} - 25080 q^{34} + 20664 q^{35} + 48320 q^{36} - 47176 q^{39} - 1280 q^{40} + 71758 q^{41} - 33184 q^{44} - 9476 q^{45} + 63480 q^{46} - 212504 q^{49} + 50768 q^{50} - 129106 q^{51} - 52656 q^{54} + 137582 q^{55} + 12928 q^{56} - 212568 q^{59} + 48896 q^{60} + 7814 q^{61} - 122880 q^{64} + 50144 q^{65} - 54264 q^{66} - 28566 q^{69} + 11320 q^{70} + 268238 q^{71} - 41264 q^{74} + 61368 q^{75} + 28000 q^{76} + 93452 q^{79} - 7680 q^{80} + 412886 q^{81} - 8384 q^{84} + 67716 q^{85} + 248368 q^{86} - 349096 q^{89} - 40304 q^{90} + 348102 q^{91} - 98864 q^{94} + 60058 q^{95} + 55296 q^{96} - 578634 q^{99}+O(q^{100}) \) 30 * q - 480 * q^4 - 30 * q^5 + 216 * q^6 - 3020 * q^9 + 80 * q^10 + 2074 * q^11 - 808 * q^14 - 3056 * q^15 + 7680 * q^16 - 1750 * q^19 + 480 * q^20 + 524 * q^21 - 3456 * q^24 + 12218 * q^25 + 10440 * q^26 - 27548 * q^29 + 16280 * q^30 + 31170 * q^31 - 25080 * q^34 + 20664 * q^35 + 48320 * q^36 - 47176 * q^39 - 1280 * q^40 + 71758 * q^41 - 33184 * q^44 - 9476 * q^45 + 63480 * q^46 - 212504 * q^49 + 50768 * q^50 - 129106 * q^51 - 52656 * q^54 + 137582 * q^55 + 12928 * q^56 - 212568 * q^59 + 48896 * q^60 + 7814 * q^61 - 122880 * q^64 + 50144 * q^65 - 54264 * q^66 - 28566 * q^69 + 11320 * q^70 + 268238 * q^71 - 41264 * q^74 + 61368 * q^75 + 28000 * q^76 + 93452 * q^79 - 7680 * q^80 + 412886 * q^81 - 8384 * q^84 + 67716 * q^85 + 248368 * q^86 - 349096 * q^89 - 40304 * q^90 + 348102 * q^91 - 98864 * q^94 + 60058 * q^95 + 55296 * q^96 - 578634 * q^99

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