LMFDB - Embedded newform 177.6.d.b.176.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,6,Mod(176,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("177.176");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.d (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:	$28.3879361069$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.7
Character	$\chi$	$=$	177.176
Dual form			177.6.d.b.176.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.95283 q^{2} +(-15.5523 - 1.06177i) q^{3} +67.0588 q^{4} -97.9414i q^{5} +(154.789 + 10.5677i) q^{6} -155.750 q^{7} -348.934 q^{8} +(240.745 + 33.0259i) q^{9} +O(q^{10})$	\(q-9.95283 q^{2} +(-15.5523 - 1.06177i) q^{3} +67.0588 q^{4} -97.9414i q^{5} +(154.789 + 10.5677i) q^{6} -155.750 q^{7} -348.934 q^{8} +(240.745 + 33.0259i) q^{9} +974.794i q^{10} +637.985 q^{11} +(-1042.92 - 71.2012i) q^{12} -651.416i q^{13} +1550.16 q^{14} +(-103.992 + 1523.21i) q^{15} +1327.00 q^{16} +1943.14i q^{17} +(-2396.10 - 328.702i) q^{18} -604.694 q^{19} -6567.83i q^{20} +(2422.27 + 165.372i) q^{21} -6349.76 q^{22} -1689.09 q^{23} +(5426.71 + 370.489i) q^{24} -6467.52 q^{25} +6483.43i q^{26} +(-3709.07 - 769.245i) q^{27} -10444.4 q^{28} -6482.75i q^{29} +(1035.01 - 15160.2i) q^{30} +8950.46i q^{31} -2041.50 q^{32} +(-9922.11 - 677.396i) q^{33} -19339.7i q^{34} +15254.4i q^{35} +(16144.1 + 2214.68i) q^{36} +3363.48i q^{37} +6018.41 q^{38} +(-691.656 + 10131.0i) q^{39} +34175.1i q^{40} +2841.20i q^{41} +(-24108.4 - 1645.92i) q^{42} +8732.70i q^{43} +42782.5 q^{44} +(3234.61 - 23578.9i) q^{45} +16811.2 q^{46} +3956.62 q^{47} +(-20637.8 - 1408.97i) q^{48} +7451.21 q^{49} +64370.1 q^{50} +(2063.17 - 30220.2i) q^{51} -43683.1i q^{52} +14672.5i q^{53} +(36915.7 + 7656.16i) q^{54} -62485.2i q^{55} +54346.6 q^{56} +(9404.35 + 642.048i) q^{57} +64521.7i q^{58} +(26703.5 - 1358.34i) q^{59} +(-6973.55 + 102145. i) q^{60} +28285.7i q^{61} -89082.4i q^{62} +(-37496.2 - 5143.81i) q^{63} -22145.2 q^{64} -63800.6 q^{65} +(98753.0 + 6742.01i) q^{66} +47631.3i q^{67} +130304. i q^{68} +(26269.1 + 1793.43i) q^{69} -151825. i q^{70} -7395.45i q^{71} +(-84004.2 - 11523.9i) q^{72} +16012.4i q^{73} -33476.1i q^{74} +(100584. + 6867.04i) q^{75} -40550.0 q^{76} -99366.5 q^{77} +(6883.93 - 100832. i) q^{78} +20478.8 q^{79} -129968. i q^{80} +(56867.6 + 15901.7i) q^{81} -28278.0i q^{82} +58853.4 q^{83} +(162435. + 11089.6i) q^{84} +190314. q^{85} -86915.0i q^{86} +(-6883.22 + 100821. i) q^{87} -222615. q^{88} +75358.4 q^{89} +(-32193.5 + 234677. i) q^{90} +101458. i q^{91} -113268. q^{92} +(9503.36 - 139200. i) q^{93} -39379.5 q^{94} +59224.6i q^{95} +(31750.0 + 2167.61i) q^{96} -100295. i q^{97} -74160.6 q^{98} +(153592. + 21070.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9}+O(q^{10}) $ 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9	$ 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9} - 1244 q^{12} + 1116 q^{15} + 14724 q^{16} + 1784 q^{19} + 6388 q^{21} - 8140 q^{22} - 48208 q^{25} - 6458 q^{27} - 19092 q^{28} - 20832 q^{36} - 134984 q^{45} + 51180 q^{46} + 61720 q^{48} + 174556 q^{49} + 8332 q^{51} + 236784 q^{57} + 375208 q^{60} - 429890 q^{63} + 561472 q^{64} - 11596 q^{66} + 169948 q^{75} + 111488 q^{76} + 356264 q^{78} + 180260 q^{79} + 79554 q^{81} + 269308 q^{84} + 111028 q^{85} - 318764 q^{87} - 1242976 q^{88} - 513608 q^{94}+O(q^{100}) $ 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9 - 1244 * q^12 + 1116 * q^15 + 14724 * q^16 + 1784 * q^19 + 6388 * q^21 - 8140 * q^22 - 48208 * q^25 - 6458 * q^27 - 19092 * q^28 - 20832 * q^36 - 134984 * q^45 + 51180 * q^46 + 61720 * q^48 + 174556 * q^49 + 8332 * q^51 + 236784 * q^57 + 375208 * q^60 - 429890 * q^63 + 561472 * q^64 - 11596 * q^66 + 169948 * q^75 + 111488 * q^76 + 356264 * q^78 + 180260 * q^79 + 79554 * q^81 + 269308 * q^84 + 111028 * q^85 - 318764 * q^87 - 1242976 * q^88 - 513608 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−9.95283			−1.75943			−0.879714	−	0.475503i	$-0.842266\pi$
$2$	−9.95283			−1.75943			−0.879714	+	0.475503i	$0.842266\pi$
$3$	−15.5523	−	1.06177i	−0.997678	−	0.0681128i
$3$	−15.5523	−	1.06177i	−0.997678	−	0.0681128i
$4$	67.0588			2.09559
$5$		−	97.9414i		−	1.75203i	−0.482285	−	0.876014i	$-0.660193\pi$
$5$		−	97.9414i		−	1.75203i	0.482285	−	0.876014i	$-0.339807\pi$
$6$	154.789	+	10.5677i	1.75534	+	0.119840i
$7$	−155.750			−1.20139			−0.600695	−	0.799478i	$-0.705110\pi$
$7$	−155.750			−1.20139			−0.600695	+	0.799478i	$0.705110\pi$
$8$	−348.934			−1.92761
$9$	240.745	+	33.0259i	0.990721	+	0.135909i
$10$			974.794i			3.08257i
$11$	637.985			1.58975			0.794875	−	0.606773i	$-0.207536\pi$
$11$	637.985			1.58975			0.794875	+	0.606773i	$0.207536\pi$
$12$	−1042.92	−	71.2012i	−2.09072	−	0.142736i
$13$		−	651.416i		−	1.06905i	−0.845151	−	0.534527i	$-0.820490\pi$
$13$		−	651.416i		−	1.06905i	0.845151	−	0.534527i	$-0.179510\pi$
$14$	1550.16			2.11376
$15$	−103.992	+	1523.21i	−0.119336	+	1.74796i
$16$	1327.00			1.29590
$17$			1943.14i			1.63073i	0.578949	+	0.815364i	$0.303463\pi$
$17$			1943.14i			1.63073i	−0.578949	+	0.815364i	$0.696537\pi$
$18$	−2396.10	−	328.702i	−1.74310	−	0.239123i
$19$	−604.694			−0.384283			−0.192142	−	0.981367i	$-0.561543\pi$
$19$	−604.694			−0.384283			−0.192142	+	0.981367i	$0.561543\pi$
$20$		−	6567.83i		−	3.67153i
$21$	2422.27	+	165.372i	1.19860	+	0.0818301i
$22$	−6349.76			−2.79705
$23$	−1689.09			−0.665783			−0.332892	−	0.942965i	$-0.608024\pi$
$23$	−1689.09			−0.665783			−0.332892	+	0.942965i	$0.608024\pi$
$24$	5426.71	+	370.489i	1.92313	+	0.131295i
$25$	−6467.52			−2.06961
$26$			6483.43i			1.88092i
$27$	−3709.07	−	769.245i	−0.979163	−	0.203074i
$28$	−10444.4			−2.51762
$29$		−	6482.75i		−	1.43141i	−0.698402	−	0.715706i	$-0.746105\pi$
$29$		−	6482.75i		−	1.43141i	0.698402	−	0.715706i	$-0.253895\pi$
$30$	1035.01	−	15160.2i	0.209962	−	3.07541i
$31$			8950.46i			1.67279i	0.548128	+	0.836394i	$0.315341\pi$
$31$			8950.46i			1.67279i	−0.548128	+	0.836394i	$0.684659\pi$
$32$	−2041.50			−0.352432
$33$	−9922.11	−	677.396i	−1.58606	−	0.108282i
$34$		−	19339.7i		−	2.86915i
$35$			15254.4i			2.10487i
$36$	16144.1	+	2214.68i	2.07614	+	0.284810i
$37$			3363.48i			0.403910i	0.979395	+	0.201955i	$0.0647294\pi$
$37$			3363.48i			0.403910i	−0.979395	+	0.201955i	$0.935271\pi$
$38$	6018.41			0.676119
$39$	−691.656	+	10131.0i	−0.0728163	+	1.06657i
$40$			34175.1i			3.37722i
$41$			2841.20i			0.263963i	0.991252	+	0.131981i	$0.0421339\pi$
$41$			2841.20i			0.263963i	−0.991252	+	0.131981i	$0.957866\pi$
$42$	−24108.4	−	1645.92i	−2.10885	−	0.143974i
$43$			8732.70i			0.720240i	0.932906	+	0.360120i	$0.117264\pi$
$43$			8732.70i			0.720240i	−0.932906	+	0.360120i	$0.882736\pi$
$44$	42782.5			3.33146
$45$	3234.61	−	23578.9i	0.238117	−	1.73577i
$46$	16811.2			1.17140
$47$	3956.62			0.261264			0.130632	−	0.991431i	$-0.458299\pi$
$47$	3956.62			0.261264			0.130632	+	0.991431i	$0.458299\pi$
$48$	−20637.8	−	1408.97i	−1.29289	−	0.0882672i
$49$	7451.21			0.443340
$50$	64370.1			3.64132
$51$	2063.17	−	30220.2i	0.111073	−	1.62694i
$52$		−	43683.1i		−	2.24030i
$53$			14672.5i			0.717490i	0.933436	+	0.358745i	$0.116795\pi$
$53$			14672.5i			0.717490i	−0.933436	+	0.358745i	$0.883205\pi$
$54$	36915.7	+	7656.16i	1.72277	+	0.357295i
$55$		−	62485.2i		−	2.78529i
$56$	54346.6			2.31581
$57$	9404.35	+	642.048i	0.383391	+	0.0261746i
$58$			64521.7i			2.51847i
$59$	26703.5	−	1358.34i	0.998709	−	0.0508018i
$59$	26703.5	−	1358.34i	0.998709	−	0.0508018i
$60$	−6973.55	+	102145.i	−0.250078	+	3.66300i
$61$			28285.7i			0.973290i	0.873600	+	0.486645i	$0.161779\pi$
$61$			28285.7i			0.973290i	−0.873600	+	0.486645i	$0.838221\pi$
$62$		−	89082.4i		−	2.94315i
$63$	−37496.2	−	5143.81i	−1.19024	−	0.163280i
$64$	−22145.2			−0.675819
$65$	−63800.6			−1.87301
$66$	98753.0	+	6742.01i	2.79056	+	0.190515i
$67$			47631.3i			1.29630i	0.761513	+	0.648150i	$0.224457\pi$
$67$			47631.3i			1.29630i	−0.761513	+	0.648150i	$0.775543\pi$
$68$			130304.i			3.41733i
$69$	26269.1	+	1793.43i	0.664237	+	0.0453484i
$70$		−	151825.i		−	3.70337i
$71$		−	7395.45i		−	0.174108i	−0.996204	−	0.0870540i	$-0.972255\pi$
$71$		−	7395.45i		−	0.174108i	0.996204	−	0.0870540i	$-0.0277453\pi$
$72$	−84004.2	−	11523.9i	−1.90972	−	0.261980i
$73$			16012.4i			0.351681i	0.984419	+	0.175841i	$0.0562643\pi$
$73$			16012.4i			0.351681i	−0.984419	+	0.175841i	$0.943736\pi$
$74$		−	33476.1i		−	0.710650i
$75$	100584.	+	6867.04i	2.06480	+	0.140967i
$76$	−40550.0			−0.805299
$77$	−99366.5			−1.90991
$78$	6883.93	−	100832.i	0.128115	−	1.87656i
$79$	20478.8			0.369179			0.184589	−	0.982816i	$-0.440905\pi$
$79$	20478.8			0.369179			0.184589	+	0.982816i	$0.440905\pi$
$80$		−	129968.i		−	2.27045i
$81$	56867.6	+	15901.7i	0.963057	+	0.269296i
$82$		−	28278.0i		−	0.464423i
$83$	58853.4			0.937727			0.468864	−	0.883271i	$-0.344664\pi$
$83$	58853.4			0.937727			0.468864	+	0.883271i	$0.344664\pi$
$84$	162435.	+	11089.6i	2.51177	+	0.171482i
$85$	190314.			2.85708
$86$		−	86915.0i		−	1.26721i
$87$	−6883.22	+	100821.i	−0.0974975	+	1.42809i
$88$	−222615.			−3.06441
$89$	75358.4			1.00846			0.504228	−	0.863571i	$-0.331777\pi$
$89$	75358.4			1.00846			0.504228	+	0.863571i	$0.331777\pi$
$90$	−32193.5	+	234677.i	−0.418950	+	3.05397i
$91$			101458.i			1.28435i
$92$	−113268.			−1.39521
$93$	9503.36	−	139200.i	0.113938	−	1.66890i
$94$	−39379.5			−0.459675
$95$			59224.6i			0.673275i
$96$	31750.0	+	2167.61i	0.351613	+	0.0240051i
$97$		−	100295.i		−	1.08230i	−0.840926	−	0.541150i	$-0.817989\pi$
$97$		−	100295.i		−	1.08230i	0.840926	−	0.541150i	$-0.182011\pi$
$98$	−74160.6			−0.780024
$99$	153592.	+	21070.1i	1.57500	+	0.216062i
$100$	−433704.			−4.33704
$101$	−141030.			−1.37565			−0.687826	−	0.725875i	$-0.741435\pi$
$101$	−141030.			−1.37565			−0.687826	+	0.725875i	$0.741435\pi$
$102$	−20534.4	+	300776.i	−0.195426	+	2.86248i
$103$		−	53647.1i		−	0.498257i	−0.968470	−	0.249128i	$-0.919856\pi$
$103$		−	53647.1i		−	0.498257i	0.968470	−	0.249128i	$-0.0801441\pi$
$104$			227301.i			2.06072i
$105$	16196.7	−	237241.i	0.143369	−	2.09998i
$106$		−	146033.i		−	1.26237i
$107$			107650.i			0.908978i	0.890752	+	0.454489i	$0.150178\pi$
$107$			107650.i			0.908978i	−0.890752	+	0.454489i	$0.849822\pi$
$108$	−248725.	−	51584.6i	−2.05192	−	0.425560i
$109$			18877.0i			0.152183i	0.997101	+	0.0760917i	$0.0242442\pi$
$109$			18877.0i			0.152183i	−0.997101	+	0.0760917i	$0.975756\pi$
$110$			621904.i			4.90051i
$111$	3571.25	−	52309.7i	0.0275114	−	0.402972i
$112$	−206681.			−1.55688
$113$	−15698.1			−0.115651			−0.0578256	−	0.998327i	$-0.518417\pi$
$113$	−15698.1			−0.115651			−0.0578256	+	0.998327i	$0.518417\pi$
$114$	−93599.9	−	6390.19i	−0.674549	−	0.0460524i
$115$			165432.i			1.16647i
$116$		−	434726.i		−	2.99965i
$117$	21513.6	−	156825.i	0.145294	−	1.05914i
$118$	−265776.	+	13519.3i	−1.75716	+	0.0893821i
$119$		−	302645.i		−	1.95914i
$120$	36286.2	−	531500.i	0.230032	−	3.36938i
$121$	245974.			1.52731
$122$		−	281523.i		−	1.71243i
$123$	3016.71	−	44187.1i	0.0179792	−	0.263350i
$124$			600207.i			3.50547i
$125$			327371.i			1.87398i
$126$	373193.	+	51195.4i	2.09415	+	0.287280i
$127$	−44909.1			−0.247073			−0.123536	−	0.992340i	$-0.539424\pi$
$127$	−44909.1			−0.247073			−0.123536	+	0.992340i	$0.539424\pi$
$128$	285736.			1.54149
$129$	9272.15	−	135813.i	0.0490576	−	0.718567i
$130$	634996.			3.29543
$131$	151394.			0.770782			0.385391	−	0.922753i	$-0.374067\pi$
$131$	151394.			0.770782			0.385391	+	0.922753i	$0.374067\pi$
$132$	−665365.	−	45425.3i	−3.32372	−	0.226915i
$133$	94181.3			0.461674
$134$		−	474066.i		−	2.28075i
$135$	−75340.9	+	363271.i	−0.355792	+	1.71552i
$136$		−	678027.i		−	3.14340i
$137$		−	345873.i		−	1.57440i	−0.616697	−	0.787201i	$-0.711529\pi$
$137$		−	345873.i		−	1.57440i	0.616697	−	0.787201i	$-0.288471\pi$
$138$	−261452.	−	17849.7i	−1.16868	−	0.0797872i
$139$	−22047.5			−0.0967882			−0.0483941	−	0.998828i	$-0.515410\pi$
$139$	−22047.5			−0.0967882			−0.0483941	+	0.998828i	$0.515410\pi$
$140$			1.02294e6i			4.41094i
$141$	−61534.3	−	4201.03i	−0.260657	−	0.0177954i
$142$			73605.6i			0.306330i
$143$		−	415594.i		−	1.69953i
$144$	319469.	+	43825.4i	1.28387	+	0.176124i
$145$	−634930.			−2.50787
$146$		−	159369.i		−	0.618758i
$147$	−115883.	−	7911.50i	−0.442310	−	0.0301971i
$148$			225551.i			0.846428i
$149$	−424520.			−1.56651			−0.783254	−	0.621702i	$-0.786442\pi$
$149$	−424520.			−1.56651			−0.783254	+	0.621702i	$0.786442\pi$
$150$	−1.00110e6	−	68346.5i	−3.63286	−	0.248021i
$151$			95892.3i			0.342248i	0.985249	+	0.171124i	$0.0547399\pi$
$151$			95892.3i			0.342248i	−0.985249	+	0.171124i	$0.945260\pi$
$152$	210998.			0.740747
$153$	−64174.0	+	467801.i	−0.221631	+	1.61560i
$154$	988978.			3.36035
$155$	876620.			2.93077
$156$	−46381.6	+	679371.i	−0.152593	+	2.23509i
$157$		−	385672.i		−	1.24873i	−0.781132	−	0.624366i	$-0.785357\pi$
$157$		−	385672.i		−	1.24873i	0.781132	−	0.624366i	$-0.214643\pi$
$158$	−203822.			−0.649543
$159$	15578.9	−	228191.i	0.0488703	−	0.715824i
$160$			199948.i			0.617471i
$161$	263076.			0.799866
$162$	−565993.	−	158267.i	−1.69443	−	0.473808i
$163$	487203.			1.43628			0.718142	−	0.695896i	$-0.244993\pi$
$163$	487203.			1.43628			0.718142	+	0.695896i	$0.244993\pi$
$164$			190528.i			0.553157i
$165$	−66345.1	+	971785.i	−0.189714	+	2.77882i
$166$	−585758.			−1.64986
$167$		−	256.470i		−	0.000711615i	−1.00000		0.000355808i	$-0.999887\pi$
$167$		−	256.470i		−	0.000711615i	1.00000		0.000355808i	$-0.000113257\pi$
$168$	−845213.	−	57703.8i	−2.31043	−	0.157736i
$169$	−53049.4			−0.142878
$170$	−1.89416e6			−5.02683
$171$	−145577.	−	19970.6i	−0.380718	−	0.0522277i
$172$			585604.i			1.50933i
$173$	442665.			1.12450			0.562250	−	0.826967i	$-0.309936\pi$
$173$	442665.			1.12450			0.562250	+	0.826967i	$0.309936\pi$
$174$	68507.5	−	1.00346e6i	0.171540	−	2.51262i
$175$	1.00732e6			2.48640
$176$	846606.			2.06015
$177$	−416743.	−	7227.84i	−0.999850	−	0.0173411i
$178$	−750029.			−1.77430
$179$	−8484.97			−0.0197933			−0.00989664	−	0.999951i	$-0.503150\pi$
$179$	−8484.97			−0.0197933			−0.00989664	+	0.999951i	$0.503150\pi$
$180$	216909.	−	1.58117e6i	0.498995	−	3.63746i
$181$	−178227.			−0.404369			−0.202184	−	0.979347i	$-0.564804\pi$
$181$	−178227.			−0.404369			−0.202184	+	0.979347i	$0.564804\pi$
$182$		−	1.00980e6i		−	2.25973i
$183$	30033.0	−	439906.i	0.0662935	−	0.971029i
$184$	589380.			1.28337
$185$	329424.			0.707662
$186$	−94585.3	+	1.38543e6i	−0.200466	+	2.93632i
$187$			1.23969e6i			2.59245i
$188$	265326.			0.547501
$189$	577689.	+	119810.i	1.17636	+	0.243972i
$190$		−	589452.i		−	1.18458i
$191$	−161763.			−0.320845			−0.160423	−	0.987048i	$-0.551286\pi$
$191$	−161763.			−0.320845			−0.160423	+	0.987048i	$0.551286\pi$
$192$	344408.	+	23513.2i	0.674249	+	0.0460319i
$193$	−29421.5			−0.0568554			−0.0284277	−	0.999596i	$-0.509050\pi$
$193$	−29421.5			−0.0568554			−0.0284277	+	0.999596i	$0.509050\pi$
$194$			998214.i			1.90423i
$195$	992243.	+	67741.8i	1.86866	+	0.127576i
$196$	499669.			0.929056
$197$			102771.i			0.188671i	0.995540	+	0.0943356i	$0.0300727\pi$
$197$			102771.i			0.188671i	−0.995540	+	0.0943356i	$0.969927\pi$
$198$	−1.52867e6	−	209707.i	−2.77110	−	0.380145i
$199$	−14462.2			−0.0258883			−0.0129441	−	0.999916i	$-0.504120\pi$
$199$	−14462.2			−0.0258883			−0.0129441	+	0.999916i	$0.504120\pi$
$200$	2.25674e6			3.98938
$201$	50573.6	−	740774.i	0.0882946	−	1.29329i
$202$	1.40365e6			2.42036
$203$			1.00969e6i			1.71968i
$204$	138354.	−	2.02653e6i	0.232764	−	3.40939i
$205$	278271.			0.462470
$206$			533940.i			0.876647i
$207$	−406640.	−	55783.7i	−0.659605	−	0.0904861i
$208$		−	864428.i		−	1.38538i
$209$	−385786.			−0.610915
$210$	−161203.	+	2.36121e6i	−0.252247	+	3.69477i
$211$			569457.i			0.880552i	0.897862	+	0.440276i	$0.145119\pi$
$211$			569457.i			0.880552i	−0.897862	+	0.440276i	$0.854881\pi$
$212$			983923.i			1.50356i
$213$	−7852.29	+	115016.i	−0.0118590	+	0.173704i
$214$		−	1.07142e6i		−	1.59928i
$215$	855293.			1.26188
$216$	1.29422e6	+	268416.i	1.88744	+	0.391448i
$217$		−	1.39404e6i		−	2.00967i
$218$		−	187880.i		−	0.267756i
$219$	17001.5	−	249029.i	0.0239540	−	0.350864i
$220$		−	4.19018e6i		−	5.83681i
$221$	1.26579e6			1.74334
$222$	−35544.1	+	520629.i	−0.0484044	+	0.709000i
$223$	−604508.			−0.814030			−0.407015	−	0.913422i	$-0.633430\pi$
$223$	−604508.			−0.814030			−0.407015	+	0.913422i	$0.633430\pi$
$224$	317965.			0.423408
$225$	−1.55702e6	−	213596.i	−2.05040	−	0.281279i
$226$	156240.			0.203480
$227$	864660.			1.11373			0.556866	−	0.830602i	$-0.312004\pi$
$227$	864660.			1.11373			0.556866	+	0.830602i	$0.312004\pi$
$228$	630644.	+	43055.0i	0.803429	+	0.0548512i
$229$			505214.i			0.636629i	0.947985	+	0.318315i	$0.103117\pi$
$229$			505214.i			0.636629i	−0.947985	+	0.318315i	$0.896883\pi$
$230$		−	1.64651e6i		−	2.05232i
$231$	1.54537e6	+	105505.i	1.90548	+	0.130089i
$232$			2.26205e6i			2.75920i
$233$	−181647.			−0.219199			−0.109600	−	0.993976i	$-0.534957\pi$
$233$	−181647.			−0.219199			−0.109600	+	0.993976i	$0.534957\pi$
$234$	−214121.	+	1.56085e6i	−0.255635	+	1.86347i
$235$		−	387517.i		−	0.457742i
$236$	1.79071e6	−	91088.7i	2.09288	−	0.106460i
$237$	−318491.	−	21743.8i	−0.368321	−	0.0251458i
$238$			3.01217e6i			3.44697i
$239$		−	773579.i		−	0.876012i	−0.898972	−	0.438006i	$-0.855685\pi$
$239$		−	773579.i		−	0.876012i	0.898972	−	0.438006i	$-0.144315\pi$
$240$	−137997.	+	2.02130e6i	−0.154647	+	2.26518i
$241$	−264955.			−0.293852			−0.146926	−	0.989147i	$-0.546938\pi$
$241$	−264955.			−0.293852			−0.146926	+	0.989147i	$0.546938\pi$
$242$	−2.44814e6			−2.68719
$243$	−867535.	−	307688.i	−0.942478	−	0.334268i
$244$			1.89680e6i			2.03961i
$245$		−	729782.i		−	0.776744i
$246$	−30024.8	+	439787.i	−0.0316332	+	0.463345i
$247$			393907.i			0.410820i
$248$		−	3.12312e6i		−	3.22448i
$249$	−915303.	−	62489.0i	−0.935549	−	0.0638712i
$250$		−	3.25826e6i		−	3.29713i
$251$		−	331435.i		−	0.332058i	−0.986121	−	0.166029i	$-0.946905\pi$
$251$		−	331435.i		−	0.332058i	0.986121	−	0.166029i	$-0.0530946\pi$
$252$	−2.51445e6	−	344937.i	−2.49426	−	0.342168i
$253$	−1.07761e6			−1.05843
$254$	446973.			0.434707
$255$	−2.95981e6	−	202070.i	−2.85045	−	0.194604i
$256$	−2.13523e6			−2.03632
$257$			1.61393e6i			1.52423i	0.647441	+	0.762116i	$0.275839\pi$
$257$			1.61393e6i			1.52423i	−0.647441	+	0.762116i	$0.724161\pi$
$258$	−92284.1	+	1.35172e6i	−0.0863133	+	1.26427i
$259$		−	523863.i		−	0.485253i
$260$	−4.27839e6			−3.92506
$261$	214099.	−	1.56069e6i	0.194542	−	1.41813i
$262$	−1.50680e6			−1.35614
$263$			1.10742e6i			0.987240i	0.869678	+	0.493620i	$0.164327\pi$
$263$			1.10742e6i			0.987240i	−0.869678	+	0.493620i	$0.835673\pi$
$264$	3.46216e6	+	236366.i	3.05730	+	0.208726i
$265$	1.43705e6			1.25706
$266$	−937371.			−0.812283
$267$	−1.17199e6	−	80013.6i	−1.00611	−	0.0686887i
$268$			3.19410e6i			2.71651i
$269$	412175.			0.347297			0.173649	−	0.984808i	$-0.444444\pi$
$269$	412175.			0.347297			0.173649	+	0.984808i	$0.444444\pi$
$270$	749855.	−	3.61557e6i	0.625991	−	3.01834i
$271$	2.07215e6			1.71395			0.856975	−	0.515358i	$-0.172341\pi$
$271$	2.07215e6			1.71395			0.856975	+	0.515358i	$0.172341\pi$
$272$			2.57854e6i			2.11325i
$273$	107726.	−	1.57791e6i	0.0874808	−	1.28137i
$274$			3.44242e6i			2.77005i
$275$	−4.12618e6			−3.29016
$276$	1.76158e6	+	120265.i	1.39197	+	0.0950314i
$277$	1.66702e6			1.30539			0.652696	−	0.757620i	$-0.273638\pi$
$277$	1.66702e6			1.30539			0.652696	+	0.757620i	$0.273638\pi$
$278$	219435.			0.170292
$279$	−295597.	+	2.15478e6i	−0.227347	+	1.65727i
$280$		−	5.32278e6i		−	4.05736i
$281$			1.61261e6i			1.21833i	0.793044	+	0.609164i	$0.208495\pi$
$281$			1.61261e6i			1.21833i	−0.793044	+	0.609164i	$0.791505\pi$
$282$	612441.	+	41812.2i	0.458608	+	0.0313098i
$283$			806837.i			0.598853i	0.954119	+	0.299426i	$0.0967953\pi$
$283$			806837.i			0.598853i	−0.954119	+	0.299426i	$0.903205\pi$
$284$		−	495930.i		−	0.364858i
$285$	62883.1	−	921075.i	0.0458587	−	0.671712i
$286$			4.13633e6i			2.99020i
$287$		−	442519.i		−	0.317122i
$288$	−491482.	−	67422.6i	−0.349162	−	0.0478987i
$289$	−2.35593e6			−1.65927
$290$	6.31935e6			4.41243
$291$	−106490.	+	1.55981e6i	−0.0737185	+	1.07979i
$292$			1.07377e6i			0.736978i
$293$		−	1.83767e6i		−	1.25054i	−0.780407	−	0.625271i	$-0.784988\pi$
$293$		−	1.83767e6i		−	1.25054i	0.780407	−	0.625271i	$-0.215012\pi$
$294$	1.15336e6	+	78741.8i	0.778212	+	0.0531296i
$295$	−133038.	−	2.61538e6i	−0.0890062	−	1.74977i
$296$		−	1.17363e6i		−	0.778579i
$297$	−2.36633e6	−	490767.i	−1.55663	−	0.322838i
$298$	4.22518e6			2.75616
$299$			1.10030e6i			0.711758i
$300$	6.74507e6	+	460495.i	4.32697	+	0.295408i
$301$		−	1.36012e6i		−	0.865290i
$302$		−	954400.i		−	0.602161i
$303$	2.19334e6	+	149742.i	1.37246	+	0.0936996i
$304$	−802428.			−0.497992
$305$	2.77034e6			1.70523
$306$	638713.	−	4.65595e6i	0.389944	−	2.84253i
$307$	−571711.			−0.346203			−0.173102	−	0.984904i	$-0.555379\pi$
$307$	−571711.			−0.346203			−0.173102	+	0.984904i	$0.555379\pi$
$308$	−6.66340e6			−4.00238
$309$	−56961.1	+	834333.i	−0.0339377	+	0.497100i
$310$	−8.72485e6			−5.15649
$311$		−	361031.i		−	0.211662i	−0.994384	−	0.105831i	$-0.966250\pi$
$311$		−	361031.i		−	0.211662i	0.994384	−	0.105831i	$-0.0337503\pi$
$312$	241342.	−	3.53504e6i	0.140361	−	2.05593i
$313$		−	2.52393e6i		−	1.45618i	−0.685479	−	0.728092i	$-0.740407\pi$
$313$		−	2.52393e6i		−	1.45618i	0.685479	−	0.728092i	$-0.259593\pi$
$314$			3.83853e6i			2.19706i
$315$	−503792.	+	3.67243e6i	−0.286071	+	2.08534i
$316$	1.37328e6			0.773646
$317$		−	2.52519e6i		−	1.41138i	−0.708518	−	0.705692i	$-0.750636\pi$
$317$		−	2.52519e6i		−	1.41138i	0.708518	−	0.705692i	$-0.249364\pi$
$318$	−155054.	+	2.27115e6i	−0.0859837	+	1.25944i
$319$		−	4.13590e6i		−	2.27559i
$320$			2.16894e6i			1.18405i
$321$	114300.	−	1.67419e6i	0.0619130	−	0.906867i
$322$	−2.61835e6			−1.40731
$323$		−	1.17500e6i		−	0.626661i
$324$	3.81347e6	+	1.06635e6i	2.01817	+	0.564334i
$325$			4.21304e6i			2.21252i
$326$	−4.84904e6			−2.52704
$327$	20043.1	−	293580.i	0.0103656	−	0.151830i
$328$		−	991392.i		−	0.508816i
$329$	−616245.			−0.313880
$330$	660321.	−	9.67201e6i	0.333788	−	4.88913i
$331$	−40207.5			−0.0201715			−0.0100857	−	0.999949i	$-0.503210\pi$
$331$	−40207.5			−0.0201715			−0.0100857	+	0.999949i	$0.503210\pi$
$332$	3.94664e6			1.96509
$333$	−111082.	+	809742.i	−0.0548951	+	0.400162i
$334$			2552.60i			0.00125204i
$335$	4.66507e6			2.27115
$336$	3.21435e6	+	219448.i	1.55326	+	0.106043i
$337$			3.28467e6i			1.57550i	0.615997	+	0.787748i	$0.288753\pi$
$337$			3.28467e6i			1.57550i	−0.615997	+	0.787748i	$0.711247\pi$
$338$	527992.			0.251383
$339$	244141.	+	16667.8i	0.115383	+	0.00787733i
$340$	1.27622e7			5.98726
$341$			5.71026e6i			2.65932i
$342$	1.44890e6	+	198764.i	0.669845	+	0.0918908i
$343$	1.45717e6			0.668767
$344$		−	3.04713e6i		−	1.38834i
$345$	175651.	−	2.57284e6i	0.0794516	−	1.16376i
$346$	−4.40577e6			−1.97848
$347$	282772.			0.126070			0.0630351	−	0.998011i	$-0.479922\pi$
$347$	282772.			0.126070			0.0630351	+	0.998011i	$0.479922\pi$
$348$	−461580.	+	6.76096e6i	−0.204314	+	2.99268i
$349$		−	854662.i		−	0.375605i	−0.982207	−	0.187802i	$-0.939864\pi$
$349$		−	854662.i		−	0.375605i	0.982207	−	0.187802i	$-0.0601364\pi$
$350$	−1.00257e7			−4.37465
$351$	−501098.	+	2.41614e6i	−0.217098	+	1.04678i
$352$	−1.30245e6			−0.560279
$353$	−1.83697e6			−0.784631			−0.392316	−	0.919831i	$-0.628326\pi$
$353$	−1.83697e6			−0.784631			−0.392316	+	0.919831i	$0.628326\pi$
$354$	4.14777e6	+	71937.5i	1.75916	+	0.0305103i
$355$	−724321.			−0.305042
$356$	5.05344e6			2.11331
$357$	−321340.	+	4.70681e6i	−0.133443	+	1.95459i
$358$	84449.5			0.0348249
$359$			2.53506e6i			1.03813i	0.854734	+	0.519066i	$0.173720\pi$
$359$			2.53506e6i			1.03813i	−0.854734	+	0.519066i	$0.826280\pi$
$360$	−1.12866e6	+	8.22749e6i	−0.458996	+	3.34589i
$361$	−2.11044e6			−0.852326
$362$	1.77386e6			0.711458
$363$	−3.82545e6	−	261169.i	−1.52376	−	0.104029i
$364$			6.80367e6i			2.69147i
$365$	1.56828e6			0.616155
$366$	−298913.	+	4.37831e6i	−0.116639	+	1.70846i
$367$		−	3.58351e6i		−	1.38881i	−0.719583	−	0.694406i	$-0.755667\pi$
$367$		−	3.58351e6i		−	1.38881i	0.719583	−	0.694406i	$-0.244333\pi$
$368$	−2.24142e6			−0.862786
$369$	−93833.4	+	684006.i	−0.0358750	+	0.261513i
$370$	−3.27870e6			−1.24508
$371$		−	2.28526e6i		−	0.861986i
$372$	637284.	−	9.33457e6i	0.238768	−	3.49733i
$373$	3.01455e6			1.12189			0.560945	−	0.827853i	$-0.310438\pi$
$373$	3.01455e6			1.12189			0.560945	+	0.827853i	$0.310438\pi$
$374$		−	1.23385e7i		−	4.56123i
$375$	347594.	−	5.09135e6i	0.127642	−	1.86963i
$376$	−1.38060e6			−0.503614
$377$	−4.22297e6			−1.53026
$378$	−5.74964e6	−	1.19245e6i	−2.06972	−	0.429251i
$379$	−3.59767e6			−1.28654			−0.643270	−	0.765639i	$-0.722423\pi$
$379$	−3.59767e6			−1.28654			−0.643270	+	0.765639i	$0.722423\pi$
$380$			3.97153e6i			1.41091i
$381$	698438.	+	47683.3i	0.246499	+	0.0168288i
$382$	1.61000e6			0.564504
$383$		−	1.70800e6i		−	0.594965i	−0.954727	−	0.297482i	$-0.903853\pi$
$383$		−	1.70800e6i		−	0.594965i	0.954727	−	0.297482i	$-0.0961470\pi$
$384$	−4.44384e6	−	303387.i	−1.53791	−	0.104995i
$385$			9.73209e6i			3.34622i
$386$	292827.			0.100033
$387$	−288406.	+	2.10236e6i	−0.0978873	+	0.713557i
$388$		−	6.72563e6i		−	2.26805i
$389$			178222.i			0.0597156i	0.999554	+	0.0298578i	$0.00950545\pi$
$389$			178222.i			0.0597156i	−0.999554	+	0.0298578i	$0.990495\pi$
$390$	−9.87562e6	−	674222.i	−3.28778	−	0.224461i
$391$		−	3.28213e6i		−	1.08571i
$392$	−2.59998e6			−0.854584
$393$	−2.35452e6	−	160747.i	−0.768992	−	0.0525001i
$394$		−	1.02286e6i		−	0.331953i
$395$		−	2.00572e6i		−	0.646812i
$396$	1.02997e7	+	1.41293e6i	3.30055	+	0.452776i
$397$			1.69943e6i			0.541160i	0.962697	+	0.270580i	$0.0872155\pi$
$397$			1.69943e6i			0.541160i	−0.962697	+	0.270580i	$0.912784\pi$
$398$	143940.			0.0455485
$399$	−1.46473e6	−	99999.3i	−0.460602	−	0.0314459i
$400$	−8.58239e6			−2.68200
$401$	−182580.			−0.0567011			−0.0283505	−	0.999598i	$-0.509025\pi$
$401$	−182580.			−0.0567011			−0.0283505	+	0.999598i	$0.509025\pi$
$402$	−503351.	+	7.37280e6i	−0.155348	+	2.27545i
$403$	5.83047e6			1.78830
$404$	−9.45732e6			−2.88280
$405$	1.55743e6	−	5.56969e6i	0.471815	−	1.68730i
$406$		−	1.00493e7i		−	3.02566i
$407$			2.14585e6i			0.642116i
$408$	−719911.	+	1.05448e7i	−0.214106	+	3.13610i
$409$			4.30716e6i			1.27316i	0.771211	+	0.636580i	$0.219651\pi$
$409$			4.30716e6i			1.27316i	−0.771211	+	0.636580i	$0.780349\pi$
$410$	−2.76959e6			−0.813683
$411$	−367239.	+	5.37911e6i	−0.107237	+	1.57075i
$412$		−	3.59751e6i		−	1.04414i
$413$	−4.15909e6	+	211562.i	−1.19984	+	0.0610328i
$414$	4.04722e6	+	555206.i	1.16053	+	0.159204i
$415$		−	5.76419e6i		−	1.64292i
$416$			1.32987e6i			0.376769i
$417$	342888.	+	23409.5i	0.0965634	+	0.00659252i
$418$	3.83966e6			1.07486
$419$	3.01036e6			0.837689			0.418844	−	0.908058i	$-0.362435\pi$
$419$	3.01036e6			0.837689			0.418844	+	0.908058i	$0.362435\pi$
$420$	1.08613e6	−	1.59091e7i	0.300442	−	4.40070i
$421$			5.34313e6i			1.46923i	0.678483	+	0.734616i	$0.262638\pi$
$421$			5.34313e6i			1.46923i	−0.678483	+	0.734616i	$0.737362\pi$
$422$		−	5.66771e6i		−	1.54927i
$423$	952537.	+	130671.i	0.258840	+	0.0355082i
$424$		−	5.11975e6i		−	1.38304i
$425$		−	1.25673e7i		−	3.37496i
$426$	78152.5	−	1.14473e6i	0.0208650	−	0.305619i
$427$		−	4.40551e6i		−	1.16930i
$428$			7.21885e6i			1.90484i
$429$	−441266.	+	6.46342e6i	−0.115760	+	1.69558i
$430$	−8.51258e6			−2.22019
$431$	6.35167e6			1.64700			0.823502	−	0.567313i	$-0.192017\pi$
$431$	6.35167e6			1.64700			0.823502	+	0.567313i	$0.192017\pi$
$432$	−4.92193e6	−	1.02079e6i	−1.26889	−	0.263164i
$433$	4.41731e6			1.13224			0.566120	−	0.824323i	$-0.308444\pi$
$433$	4.41731e6			1.13224			0.566120	+	0.824323i	$0.308444\pi$
$434$			1.38746e7i			3.53587i
$435$	9.87459e6	+	674152.i	2.50205	+	0.170818i
$436$			1.26587e6i			0.318914i
$437$	1.02138e6			0.255849
$438$	−169213.	+	2.47854e6i	−0.0421453	+	0.617321i
$439$	1.48299e6			0.367263			0.183632	−	0.982995i	$-0.441215\pi$
$439$	1.48299e6			0.367263			0.183632	+	0.982995i	$0.441215\pi$
$440$			2.18032e7i			5.36894i
$441$	1.79384e6	+	246083.i	0.439226	+	0.0602539i
$442$	−1.25982e7			−3.06727
$443$	393210.			0.0951952			0.0475976	−	0.998867i	$-0.484843\pi$
$443$	393210.			0.0951952			0.0475976	+	0.998867i	$0.484843\pi$
$444$	239484.	−	3.50782e6i	0.0576526	−	0.844462i
$445$		−	7.38071e6i		−	1.76684i
$446$	6.01657e6			1.43223
$447$	6.60225e6	+	450744.i	1.56287	+	0.106699i
$448$	3.44913e6			0.811923
$449$		−	465305.i		−	0.108924i	−0.998516	−	0.0544618i	$-0.982656\pi$
$449$		−	465305.i		−	0.108924i	0.998516	−	0.0544618i	$-0.0173443\pi$
$450$	1.54968e7	+	2.12588e6i	3.60753	+	0.494889i
$451$			1.81265e6i			0.419635i
$452$	−1.05269e6			−0.242357
$453$	101816.	−	1.49134e6i	0.0233115	−	0.341454i
$454$	−8.60581e6			−1.95953
$455$	9.93697e6			2.25022
$456$	−3.28150e6	−	224032.i	−0.739027	−	0.0504544i
$457$			7.22237e6i			1.61767i	0.588037	+	0.808834i	$0.299901\pi$
$457$			7.22237e6i			1.61767i	−0.588037	+	0.808834i	$0.700099\pi$
$458$		−	5.02831e6i		−	1.12010i
$459$	1.49475e6	−	7.20723e6i	0.331159	−	1.59675i
$460$			1.10936e7i			2.44444i
$461$		−	2.52097e6i		−	0.552479i	−0.961089	−	0.276240i	$-0.910912\pi$
$461$		−	2.52097e6i		−	0.552479i	0.961089	−	0.276240i	$-0.0890883\pi$
$462$	−1.53808e7	−	1.05007e6i	−3.35255	−	0.228883i
$463$			1.40533e6i			0.304666i	0.988329	+	0.152333i	$0.0486787\pi$
$463$			1.40533e6i			0.304666i	−0.988329	+	0.152333i	$0.951321\pi$
$464$		−	8.60261e6i		−	1.85496i
$465$	−1.36334e7	−	930772.i	−2.92397	−	0.199623i
$466$	1.80790e6			0.385665
$467$	−5.91272e6			−1.25457			−0.627286	−	0.778789i	$-0.715834\pi$
$467$	−5.91272e6			−1.25457			−0.627286	+	0.778789i	$0.715834\pi$
$468$	1.44268e6	−	1.05165e7i	0.304477	−	2.21951i
$469$		−	7.41860e6i		−	1.55736i
$470$			3.85689e6i			0.805364i
$471$	−409497.	+	5.99808e6i	−0.0850547	+	1.24583i
$472$	−9.31777e6	+	473972.i	−1.92512	+	0.0979258i
$473$			5.57133e6i			1.14500i
$474$	3.16989e6	+	216413.i	0.648035	+	0.0442422i
$475$	3.91087e6			0.795315
$476$		−	2.02950e7i		−	4.10555i
$477$	−484575.	+	3.53235e6i	−0.0975135	+	0.710833i
$478$			7.69930e6i			1.54128i
$479$			5.22977e6i			1.04146i	0.853721	+	0.520731i	$0.174341\pi$
$479$			5.22977e6i			1.04146i	−0.853721	+	0.520731i	$0.825659\pi$
$480$	212299.	−	3.10964e6i	0.0420577	−	0.616037i
$481$	2.19102e6			0.431802
$482$	2.63705e6			0.517012
$483$	−4.09143e6	−	279327.i	−0.798008	−	0.0544811i
$484$	1.64947e7			3.20060
$485$	−9.82298e6			−1.89622
$486$	8.63443e6	+	3.06236e6i	1.65822	+	0.588120i
$487$	−5.95709e6			−1.13818			−0.569091	−	0.822274i	$-0.692705\pi$
$487$	−5.95709e6			−1.13818			−0.569091	+	0.822274i	$0.692705\pi$
$488$		−	9.86984e6i		−	1.87612i
$489$	−7.57710e6	−	517299.i	−1.43295	−	0.0978294i
$490$			7.26339e6i			1.36662i
$491$		−	2.21607e6i		−	0.414839i	−0.978252	−	0.207419i	$-0.933494\pi$
$491$		−	2.21607e6i		−	0.414839i	0.978252	−	0.207419i	$-0.0665065\pi$
$492$	202297.	−	2.96313e6i	0.0376771	−	0.551872i
$493$	1.25969e7			2.33424
$494$		−	3.92049e6i		−	0.722808i
$495$	2.06363e6	−	1.50430e7i	0.378547	−	2.75944i
$496$			1.18772e7i			2.16776i
$497$			1.15184e6i			0.209172i
$498$	9.10986e6	+	621942.i	1.64603	+	0.112377i
$499$	−1.44204e6			−0.259254			−0.129627	−	0.991563i	$-0.541378\pi$
$499$	−1.44204e6			−0.259254			−0.129627	+	0.991563i	$0.541378\pi$
$500$			2.19531e7i			3.92709i
$501$	−272.313	+	3988.69i	−4.84701e−5	+	0.000709963i
$502$			3.29872e6i			0.584233i
$503$	−2.73709e6			−0.482358			−0.241179	−	0.970481i	$-0.577534\pi$
$503$	−2.73709e6			−0.482358			−0.241179	+	0.970481i	$0.577534\pi$
$504$	1.30837e7	+	1.79485e6i	2.29432	+	0.314740i
$505$			1.38127e7i			2.41018i
$506$	1.07253e7			1.86223
$507$	825038.	+	56326.5i	0.142546	+	0.00973179i
$508$	−3.01155e6			−0.517763
$509$	2.70098e6			0.462091			0.231046	−	0.972943i	$-0.425785\pi$
$509$	2.70098e6			0.462091			0.231046	+	0.972943i	$0.425785\pi$
$510$	2.94584e7	+	2.01117e6i	5.01515	+	0.342391i
$511$		−	2.49394e6i		−	0.422506i
$512$	1.21080e7			2.04126
$513$	2.24285e6	+	465158.i	0.376276	+	0.0780381i
$514$		−	1.60631e7i		−	2.68178i
$515$	−5.25427e6			−0.872960
$516$	621779.	−	9.10746e6i	0.102804	−	1.50582i
$517$	2.52426e6			0.415345
$518$			5.21392e6i			0.853768i
$519$	−6.88444e6	−	470010.i	−1.12189	−	0.0765929i
$520$	2.22622e7			3.61043
$521$			4.10602e6i			0.662715i	0.943505	+	0.331357i	$0.107507\pi$
$521$			4.10602e6i			0.662715i	−0.943505	+	0.331357i	$0.892493\pi$
$522$	−2.13089e6	+	1.55333e7i	−0.342283	+	2.49510i
$523$	8.87108e6			1.41815			0.709075	−	0.705133i	$-0.249113\pi$
$523$	8.87108e6			1.41815			0.709075	+	0.705133i	$0.249113\pi$
$524$	1.01523e7			1.61524
$525$	−1.56661e7	−	1.06954e6i	−2.48063	−	0.169356i
$526$		−	1.10220e7i		−	1.73698i
$527$	−1.73920e7			−2.72786
$528$	−1.31666e7	−	898904.i	−2.05537	−	0.140323i
$529$	−3.58332e6			−0.556733
$530$	−1.43027e7			−2.21171
$531$	6.47361e6	+	554896.i	0.996346	+	0.0854034i
$532$	6.31569e6			0.967479
$533$	1.85080e6			0.282191
$534$	1.16646e7	+	796361.i	1.77018	+	0.120853i
$535$	1.05434e7			1.59256
$536$		−	1.66202e7i		−	2.49875i
$537$	131960.	+	9009.12i	0.0197473	+	0.00134818i
$538$	−4.10231e6			−0.611045
$539$	4.75376e6			0.704799
$540$	−5.05227e6	+	2.43605e7i	−0.745594	+	3.59503i
$541$		−	9.21589e6i		−	1.35377i	−0.736090	−	0.676883i	$-0.763330\pi$
$541$		−	9.21589e6i		−	1.35377i	0.736090	−	0.676883i	$-0.236670\pi$
$542$	−2.06238e7			−3.01557
$543$	2.77184e6	+	189237.i	0.403430	+	0.0275427i
$544$		−	3.96692e6i		−	0.574720i
$545$	1.84884e6			0.266630
$546$	−1.07218e6	+	1.57046e7i	−0.153916	+	2.25448i
$547$	4.40437e6			0.629384			0.314692	−	0.949194i	$-0.398099\pi$
$547$	4.40437e6			0.629384			0.314692	+	0.949194i	$0.398099\pi$
$548$		−	2.31938e7i		−	3.29930i
$549$	−934162.	+	6.80965e6i	−0.132279	+	0.964259i
$550$	4.10672e7			5.78879
$551$			3.92008e6i			0.550068i
$552$	−9.16619e6	−	625788.i	−1.28039	−	0.0874138i
$553$	−3.18958e6			−0.443528
$554$	−1.65915e7			−2.29674
$555$	−5.12328e6	−	349774.i	−0.706018	−	0.0482008i
$556$	−1.47848e6			−0.202828
$557$			4.28592e6i			0.585337i	0.956214	+	0.292669i	$0.0945433\pi$
$557$			4.28592e6i			0.585337i	−0.956214	+	0.292669i	$0.905457\pi$
$558$	2.94203e6	−	2.14462e7i	0.400001	−	2.91584i
$559$	5.68862e6			0.769976
$560$			2.02426e7i			2.72770i
$561$	1.31627e6	−	1.92800e7i	0.176579	−	2.58643i
$562$		−	1.60501e7i		−	2.14356i
$563$	5.76513e6			0.766546			0.383273	−	0.923635i	$-0.374797\pi$
$563$	5.76513e6			0.766546			0.383273	+	0.923635i	$0.374797\pi$
$564$	−4.12642e6	−	281716.i	−0.546230	−	0.0372919i
$565$			1.53749e6i			0.202624i
$566$		−	8.03031e6i		−	1.05364i
$567$	−8.85715e6	−	2.47669e6i	−1.15701	−	0.323530i
$568$			2.58052e6i			0.335612i
$569$	1.15448e7			1.49487			0.747437	−	0.664333i	$-0.231284\pi$
$569$	1.15448e7			1.49487			0.747437	+	0.664333i	$0.231284\pi$
$570$	−625864.	+	9.16730e6i	−0.0806851	+	1.18183i
$571$			2.93196e6i			0.376330i	0.982137	+	0.188165i	$0.0602539\pi$
$571$			2.93196e6i			0.376330i	−0.982137	+	0.188165i	$0.939746\pi$
$572$		−	2.78692e7i		−	3.56151i
$573$	2.51578e6	+	171756.i	0.320100	+	0.0218537i
$574$			4.40431e6i			0.557954i
$575$	1.09242e7			1.37791
$576$	−5.33136e6	−	731367.i	−0.669548	−	0.0918500i
$577$	−1.26665e7			−1.58386			−0.791930	−	0.610612i	$-0.790924\pi$
$577$	−1.26665e7			−1.58386			−0.791930	+	0.610612i	$0.790924\pi$
$578$	2.34481e7			2.91937
$579$	457571.	+	31239.0i	0.0567234	+	0.00387258i
$580$	−4.25776e7			−5.25547
$581$	−9.16645e6			−1.12658
$582$	1.05988e6	−	1.55245e7i	0.129702	−	1.89981i
$583$			9.36087e6i			1.14063i
$584$		−	5.58727e6i		−	0.677903i
$585$	−1.53597e7	−	2.10707e6i	−1.85564	−	0.254560i
$586$			1.82900e7i			2.20024i
$587$	1.61149e7			1.93033			0.965165	−	0.261644i	$-0.0842646\pi$
$587$	1.61149e7			1.93033			0.965165	+	0.261644i	$0.0842646\pi$
$588$	−7.77098e6	−	530535.i	−0.926899	−	0.0632806i
$589$		−	5.41229e6i		−	0.642825i
$590$	1.32410e6	+	2.60304e7i	0.156600	+	3.07859i
$591$	109120.	−	1.59832e6i	0.0128509	−	0.188233i
$592$			4.46333e6i			0.523426i
$593$			9.11826e6i			1.06482i	0.846487	+	0.532409i	$0.178713\pi$
$593$			9.11826e6i			1.06482i	−0.846487	+	0.532409i	$0.821287\pi$
$594$	2.35517e7	+	4.88452e6i	2.73877	+	0.568010i
$595$	−2.96414e7			−3.43247
$596$	−2.84678e7			−3.28275
$597$	224920.	+	15355.6i	0.0258281	+	0.00176332i
$598$		−	1.09511e7i		−	1.25229i
$599$			7.55326e6i			0.860136i	0.902796	+	0.430068i	$0.141510\pi$
$599$			7.55326e6i			0.860136i	−0.902796	+	0.430068i	$0.858490\pi$
$600$	−3.50973e7	−	2.39614e6i	−3.98012	−	0.271728i
$601$		−	8.62609e6i		−	0.974155i	−0.873359	−	0.487077i	$-0.838063\pi$
$601$		−	8.62609e6i		−	0.974155i	0.873359	−	0.487077i	$-0.161937\pi$
$602$			1.35371e7i			1.52241i
$603$	−1.57307e6	+	1.14670e7i	−0.176179	+	1.28427i
$604$			6.43042e6i			0.717211i
$605$		−	2.40911e7i		−	2.67589i
$606$	−2.18299e7	−	1.49036e6i	−2.41474	−	0.164858i
$607$	7.24442e6			0.798053			0.399027	−	0.916939i	$-0.369348\pi$
$607$	7.24442e6			0.798053			0.399027	+	0.916939i	$0.369348\pi$
$608$	1.23448e6			0.135434
$609$	1.07206e6	−	1.57030e7i	0.117133	−	1.71569i
$610$	−2.75727e7			−3.00023
$611$		−	2.57740e6i		−	0.279305i
$612$	−4.30343e6	+	3.13702e7i	−0.464447	+	3.38562i
$613$			1.75286e7i			1.88406i	0.335522	+	0.942032i	$0.391087\pi$
$613$			1.75286e7i			1.88406i	−0.335522	+	0.942032i	$0.608913\pi$
$614$	5.69015e6			0.609119
$615$	−4.32775e6	−	295461.i	−0.461396	−	0.0315002i
$616$	3.46723e7			3.68156
$617$			3.56163e6i			0.376648i	0.982107	+	0.188324i	$0.0603056\pi$
$617$			3.56163e6i			0.376648i	−0.982107	+	0.188324i	$0.939694\pi$
$618$	566924.	−	8.30398e6i	0.0597109	−	0.874611i
$619$	−3.47580e6			−0.364609			−0.182305	−	0.983242i	$-0.558356\pi$
$619$	−3.47580e6			−0.364609			−0.182305	+	0.983242i	$0.558356\pi$
$620$	5.87851e7			6.14169
$621$	6.26494e6	+	1.29932e6i	0.651910	+	0.135204i
$622$			3.59328e6i			0.372405i
$623$	−1.17371e7			−1.21155
$624$	−917827.	+	1.34438e7i	−0.0943625	+	1.38217i
$625$	1.18522e7			1.21366
$626$			2.51202e7i			2.56205i
$627$	5.99984e6	+	409617.i	0.609496	+	0.0416111i
$628$		−	2.58627e7i		−	2.61683i
$629$	−6.53570e6			−0.658667
$630$	5.01415e6	−	3.65511e7i	0.503322	−	3.66901i
$631$	−5.29472e6			−0.529382			−0.264691	−	0.964333i	$-0.585270\pi$
$631$	−5.29472e6			−0.529382			−0.264691	+	0.964333i	$0.585270\pi$
$632$	−7.14575e6			−0.711631
$633$	604635.	−	8.85634e6i	0.0599769	−	0.878507i
$634$			2.51328e7i			2.48323i
$635$			4.39846e6i			0.432879i
$636$	1.04470e6	−	1.53022e7i	0.102412	−	1.50007i
$637$		−	4.85383e6i		−	0.473954i
$638$			4.11639e7i			4.00373i
$639$	244242.	−	1.78042e6i	0.0236629	−	0.172492i
$640$		−	2.79854e7i		−	2.70073i
$641$			1.09862e7i			1.05610i	0.849215	+	0.528048i	$0.177076\pi$
$641$			1.09862e7i			1.05610i	−0.849215	+	0.528048i	$0.822924\pi$
$642$	−1.13760e6	+	1.66630e7i	−0.108932	+	1.59557i
$643$	−1.70326e7			−1.62463			−0.812314	−	0.583220i	$-0.801793\pi$
$643$	−1.70326e7			−1.62463			−0.812314	+	0.583220i	$0.801793\pi$
$644$	1.76416e7			1.67619
$645$	−1.33017e7	−	908127.i	−1.25895	−	0.0859503i
$646$			1.16946e7i			1.10257i
$647$		−	1.53045e7i		−	1.43733i	−0.695355	−	0.718666i	$-0.744753\pi$
$647$		−	1.53045e7i		−	1.43733i	0.695355	−	0.718666i	$-0.255247\pi$
$648$	−1.98430e7	−	5.54864e6i	−1.85640	−	0.519097i
$649$	1.70365e7	−	866602.i	1.58770	−	0.0807622i
$650$		−	4.19317e7i		−	3.89277i
$651$	−1.48015e6	+	2.16804e7i	−0.136884	+	2.00501i
$652$	3.26712e7			3.00986
$653$		−	7.50437e6i		−	0.688702i	−0.938841	−	0.344351i	$-0.888099\pi$
$653$		−	7.50437e6i		−	0.688702i	0.938841	−	0.344351i	$-0.111901\pi$
$654$	−199486.	+	2.92195e6i	−0.0182376	+	0.267134i
$655$		−	1.48278e7i		−	1.35043i
$656$			3.77027e6i			0.342069i
$657$	−528824.	+	3.85491e6i	−0.0477967	+	0.348418i
$658$	6.13338e6			0.552249
$659$	190355.			0.0170746			0.00853730	−	0.999964i	$-0.497282\pi$
$659$	190355.			0.0170746			0.00853730	+	0.999964i	$0.497282\pi$
$660$	−4.44902e6	+	6.51667e7i	−0.397562	+	5.82326i
$661$	−2.13768e6			−0.190300			−0.0951500	−	0.995463i	$-0.530333\pi$
$661$	−2.13768e6			−0.190300			−0.0951500	+	0.995463i	$0.530333\pi$
$662$	400179.			0.0354902
$663$	−1.96859e7	−	1.34398e6i	−1.73929	−	0.118744i
$664$	−2.05360e7			−1.80757
$665$		−	9.22425e6i		−	0.808867i
$666$	1.10558e6	−	8.05922e6i	0.0965839	−	0.704056i
$667$			1.09499e7i			0.953010i
$668$		−	17198.6i		−	0.00149125i
$669$	9.40147e6	+	641851.i	0.812139	+	0.0554458i
$670$	−4.64307e7			−3.99593
$671$			1.80459e7i			1.54729i
$672$	−4.94507e6	−	337607.i	−0.422425	−	0.0288395i
$673$		−	8.41942e6i		−	0.716546i	−0.933617	−	0.358273i	$-0.883366\pi$
$673$		−	8.41942e6i		−	0.716546i	0.933617	−	0.358273i	$-0.116634\pi$
$674$		−	3.26918e7i		−	2.77197i
$675$	2.39884e7	+	4.97510e6i	2.02648	+	0.420284i
$676$	−3.55743e6			−0.299412
$677$		−	8.35803e6i		−	0.700862i	−0.936589	−	0.350431i	$-0.886035\pi$
$677$		−	8.35803e6i		−	0.700862i	0.936589	−	0.350431i	$-0.113965\pi$
$678$	−2.42989e6	−	165892.i	−0.203008	−	0.0138596i
$679$			1.56209e7i			1.30027i
$680$	−6.64069e7			−5.50733
$681$	−1.34474e7	−	918073.i	−1.11115	−	0.0758594i
$682$		−	5.68332e7i		−	4.67888i
$683$	−1.62697e7			−1.33453			−0.667263	−	0.744823i	$-0.732534\pi$
$683$	−1.62697e7			−1.33453			−0.667263	+	0.744823i	$0.732534\pi$
$684$	−9.76223e6	−	1.33920e6i	−0.797827	−	0.109448i
$685$	−3.38753e7			−2.75840
$686$	−1.45030e7			−1.17665
$687$	536423.	−	7.85722e6i	0.0433626	−	0.635151i
$688$			1.15883e7i			0.933357i
$689$	9.55793e6			0.767036
$690$	−1.74822e6	+	2.56070e7i	−0.139789	+	2.04756i
$691$			5.24552e6i			0.417920i	0.977924	+	0.208960i	$0.0670079\pi$
$691$			5.24552e6i			0.417920i	−0.977924	+	0.208960i	$0.932992\pi$
$692$	2.96846e7			2.35649
$693$	−2.39220e7	−	3.28167e6i	−1.89219	−	0.259575i
$694$	−2.81438e6			−0.221812
$695$			2.15936e6i			0.169576i
$696$	2.40179e6	−	3.51800e7i	0.187937	−	2.75279i
$697$	−5.52085e6			−0.430451
$698$			8.50630e6i			0.660849i
$699$	2.82502e6	+	192868.i	0.218690	+	0.0149303i
$700$	6.75496e7			5.21048
$701$	1.25718e7			0.966282			0.483141	−	0.875542i	$-0.339496\pi$
$701$	1.25718e7			0.966282			0.483141	+	0.875542i	$0.339496\pi$
$702$	4.98734e6	−	2.40475e7i	0.381968	−	1.84173i
$703$		−	2.03387e6i		−	0.155216i
$704$	−1.41283e7			−1.07438
$705$	−411455.	+	6.02676e6i	−0.0311781	+	0.456679i
$706$	1.82831e7			1.38050
$707$	2.19655e7			1.65270
$708$	−2.79462e7	−	484690.i	−2.09527	−	0.0363397i
$709$	2.31592e6			0.173024			0.0865122	−	0.996251i	$-0.472428\pi$
$709$	2.31592e6			0.173024			0.0865122	+	0.996251i	$0.472428\pi$
$710$	7.20904e6			0.536700
$711$	4.93017e6	+	676331.i	0.365753	+	0.0501748i
$712$	−2.62951e7			−1.94390
$713$		−	1.51181e7i		−	1.11371i
$714$	3.19824e6	−	4.68460e7i	0.234783	−	3.43896i
$715$	−4.07038e7			−2.97763
$716$	−568992.			−0.0414785
$717$	−821366.	+	1.20309e7i	−0.0596676	+	0.873977i
$718$		−	2.52310e7i		−	1.82652i
$719$	5.70070e6			0.411250			0.205625	−	0.978631i	$-0.434077\pi$
$719$	5.70070e6			0.411250			0.205625	+	0.978631i	$0.434077\pi$
$720$	4.29232e6	−	3.12892e7i	0.308575	−	2.24938i
$721$			8.35556e6i			0.598601i
$722$	2.10049e7			1.49961
$723$	4.12065e6	+	281322.i	0.293170	+	0.0200151i
$724$	−1.19517e7			−0.847390
$725$			4.19273e7i			2.96246i
$726$	3.80741e7	+	2.59937e6i	2.68095	+	0.183032i
$727$	−7.61455e6			−0.534329			−0.267164	−	0.963651i	$-0.586087\pi$
$727$	−7.61455e6			−0.534329			−0.267164	+	0.963651i	$0.586087\pi$
$728$		−	3.54022e7i		−	2.47572i
$729$	1.31654e7	+	5.70636e6i	0.917522	+	0.397686i
$730$	−1.56088e7			−1.08408
$731$	−1.69688e7			−1.17452
$732$	2.01398e6	−	2.94996e7i	0.138924	−	2.03488i
$733$	−1.25719e7			−0.864256			−0.432128	−	0.901812i	$-0.642237\pi$
$733$	−1.25719e7			−0.864256			−0.432128	+	0.901812i	$0.642237\pi$
$734$			3.56661e7i			2.44352i
$735$	−774863.	+	1.13498e7i	−0.0529062	+	0.774940i
$736$	3.44828e6			0.234643
$737$			3.03881e7i			2.06079i
$738$	933908.	−	6.80780e6i	0.0631194	−	0.460114i
$739$			1.65513e7i			1.11486i	0.830224	+	0.557431i	$0.188213\pi$
$739$			1.65513e7i			1.11486i	−0.830224	+	0.557431i	$0.811787\pi$
$740$	2.20908e7			1.48297
$741$	418240.	−	6.12614e6i	0.0279821	−	0.409866i
$742$			2.27448e7i			1.51660i
$743$			542980.i			0.0360838i	0.999837	+	0.0180419i	$0.00574323\pi$
$743$			542980.i			0.0360838i	−0.999837	+	0.0180419i	$0.994257\pi$
$744$	−3.31605e6	+	4.85715e7i	−0.219628	+	3.21699i
$745$			4.15781e7i			2.74457i
$746$	−3.00033e7			−1.97388
$747$	1.41687e7	+	1.94369e6i	0.929026	+	0.127446i
$748$			8.31323e7i			5.43270i
$749$		−	1.67665e7i		−	1.09204i
$750$	−3.45954e6	+	5.06734e7i	−0.224577	+	3.28947i
$751$		−	1.90255e7i		−	1.23094i	−0.788161	−	0.615470i	$-0.788966\pi$
$751$		−	1.90255e7i		−	1.23094i	0.788161	−	0.615470i	$-0.211034\pi$
$752$	5.25043e6			0.338571
$753$	−351909.	+	5.15457e6i	−0.0226174	+	0.331287i
$754$	4.20305e7			2.69238
$755$	9.39183e6			0.599629
$756$	3.87391e7	+	8.03433e6i	2.46516	+	0.511264i
$757$	−2.10511e7			−1.33516			−0.667582	−	0.744536i	$-0.732671\pi$
$757$	−2.10511e7			−1.33516			−0.667582	+	0.744536i	$0.732671\pi$
$758$	3.58070e7			2.26358
$759$	1.67593e7	+	1.14418e6i	1.05597	+	0.0720926i
$760$		−	2.06655e7i		−	1.29781i
$761$		−	2.35573e7i		−	1.47457i	−0.675583	−	0.737284i	$-0.736108\pi$
$761$		−	2.35573e7i		−	1.47457i	0.675583	−	0.737284i	$-0.263892\pi$
$762$	−6.95143e6	−	474584.i	−0.433697	−	0.0296091i
$763$		−	2.94011e6i		−	0.182832i
$764$	−1.08476e7			−0.672359
$765$	4.58171e7	+	6.28529e6i	2.83057	+	0.388304i
$766$			1.69994e7i			1.04680i
$767$	−884845.	−	1.73951e7i	−0.0543099	−	1.06767i
$768$	3.32077e7	+	2.26713e6i	2.03159	+	0.138699i
$769$		−	2.62066e7i		−	1.59807i	−0.601285	−	0.799034i	$-0.705345\pi$
$769$		−	2.62066e7i		−	1.59807i	0.601285	−	0.799034i	$-0.294655\pi$
$770$		−	9.68619e7i		−	5.88743i
$771$	1.71362e6	−	2.51002e7i	0.103820	−	1.52069i
$772$	−1.97297e6			−0.119145
$773$	1.37293e7			0.826420			0.413210	−	0.910636i	$-0.364408\pi$
$773$	1.37293e7			0.826420			0.413210	+	0.910636i	$0.364408\pi$
$774$	2.87045e6	−	2.09244e7i	0.172226	−	1.25545i
$775$		−	5.78872e7i		−	3.46201i
$776$			3.49962e7i			2.08625i
$777$	−556224.	+	8.14726e6i	−0.0330520	+	0.484127i
$778$		−	1.77382e6i		−	0.105065i
$779$		−	1.71806e6i		−	0.101436i
$780$	6.65386e7	+	4.54268e6i	3.91595	+	0.267347i
$781$		−	4.71819e6i		−	0.276788i
$782$			3.26665e7i			1.91023i
$783$	−4.98683e6	+	2.40450e7i	−0.290683	+	1.40159i
$784$	9.88774e6			0.574522
$785$	−3.77733e7			−2.18782
$786$	2.34342e7	+	1.59988e6i	1.35299	+	0.0923702i
$787$	1.28467e7			0.739358			0.369679	−	0.929160i	$-0.379468\pi$
$787$	1.28467e7			0.739358			0.369679	+	0.929160i	$0.379468\pi$
$788$			6.89170e6i			0.395377i
$789$	1.17583e6	−	1.72229e7i	0.0672437	−	0.984947i
$790$			1.99626e7i			1.13802i
$791$	2.44498e6			0.138942
$792$	−5.35934e7	−	7.35206e6i	−3.03598	−	0.416482i
$793$	1.84257e7			1.04050
$794$		−	1.69141e7i		−	0.952133i
$795$	−2.23494e7	−	1.52582e6i	−1.25414	−	0.0856221i
$796$	−969820.			−0.0542511
$797$	2.64235e7			1.47348			0.736739	−	0.676177i	$-0.236365\pi$
$797$	2.64235e7			1.47348			0.736739	+	0.676177i	$0.236365\pi$
$798$	1.45782e7	+	995276.i	0.810396	+	0.0553269i
$799$			7.68826e6i			0.426050i
$800$	1.32035e7			0.729395
$801$	1.81422e7	+	2.48878e6i	0.999098	+	0.137058i
$802$	1.81718e6			0.0997615
$803$			1.02157e7i			0.559085i
$804$	3.39141e6	−	4.96754e7i	0.185029	−	2.71020i
$805$		−	2.57661e7i		−	1.40139i
$806$	−5.80297e7			−3.14639
$807$	−6.41026e6	−	437637.i	−0.346491	−	0.0236554i
$808$	4.92103e7			2.65172
$809$	1.57846e7			0.847932			0.423966	−	0.905678i	$-0.360638\pi$
$809$	1.57846e7			0.847932			0.423966	+	0.905678i	$0.360638\pi$
$810$	−1.55009e7	+	5.54342e7i	−0.830125	+	2.96869i
$811$			2.11732e7i			1.13041i	0.824951	+	0.565204i	$0.191203\pi$
$811$			2.11732e7i			1.13041i	−0.824951	+	0.565204i	$0.808797\pi$
$812$			6.77087e7i			3.60375i
$813$	−3.22266e7	−	2.20016e6i	−1.70997	−	0.116742i
$814$		−	2.13573e7i		−	1.12976i
$815$		−	4.77173e7i		−	2.51641i
$816$	2.73783e6	−	4.01021e7i	0.143940	−	2.10835i
$817$		−	5.28061e6i		−	0.276776i
$818$		−	4.28684e7i		−	2.24003i
$819$	−3.35076e6	+	2.44256e7i	−0.174555	+	1.27243i
$820$	1.86605e7			0.969147
$821$	−3.28563e7			−1.70122			−0.850611	−	0.525795i	$-0.823768\pi$
$821$	−3.28563e7			−1.70122			−0.850611	+	0.525795i	$0.823768\pi$
$822$	3.65507e6	−	5.35374e7i	0.188676	−	2.76361i
$823$			2.61111e7i			1.34377i	0.740655	+	0.671885i	$0.234515\pi$
$823$			2.61111e7i			1.34377i	−0.740655	+	0.671885i	$0.765485\pi$
$824$			1.87193e7i			0.960443i
$825$	6.41714e7	+	4.38107e6i	3.28251	+	0.224102i
$826$	4.13947e7	−	2.10564e6i	2.11103	−	0.107383i
$827$			2.80329e7i			1.42529i	0.701523	+	0.712647i	$0.252504\pi$
$827$			2.80329e7i			1.42529i	−0.701523	+	0.712647i	$0.747496\pi$
$828$	−2.72688e7	−	3.74079e6i	−1.38226	−	0.189621i
$829$	3.91207e7			1.97706			0.988531	−	0.151018i	$-0.0482550\pi$
$829$	3.91207e7			1.97706			0.988531	+	0.151018i	$0.0482550\pi$
$830$			5.73699e7i			2.89061i
$831$	−2.59259e7	−	1.76999e6i	−1.30236	−	0.0889139i
$832$			1.44258e7i			0.722487i
$833$			1.44787e7i			0.722966i
$834$	−3.41271e6	−	232990.i	−0.169896	−	0.0115991i
$835$	−25119.0			−0.00124677
$836$	−2.58703e7			−1.28022
$837$	6.88510e6	−	3.31978e7i	0.339701	−	1.63793i
$838$	−2.99616e7			−1.47385
$839$	1.67594e7			0.821967			0.410984	−	0.911643i	$-0.365185\pi$
$839$	1.67594e7			0.821967			0.410984	+	0.911643i	$0.365185\pi$
$840$	−5.65159e6	+	8.27813e7i	−0.276358	+	4.04794i
$841$	−2.15150e7			−1.04894
$842$		−	5.31793e7i		−	2.58501i
$843$	1.71223e6	−	2.50798e7i	0.0829837	−	1.21550i
$844$			3.81871e7i			1.84527i
$845$			5.19574e6i			0.250326i
$846$	−9.48044e6	−	1.30055e6i	−0.455410	−	0.0624741i
$847$	−3.83106e7			−1.83489
$848$			1.94705e7i			0.929793i
$849$	856679.	−	1.25481e7i	0.0407895	−	0.597462i
$850$			1.25080e8i			5.93800i
$851$		−	5.68121e6i		−	0.268916i
$852$	−526565.	+	7.71283e6i	−0.0248515	+	0.364011i
$853$	−2.75579e7			−1.29680			−0.648402	−	0.761298i	$-0.724562\pi$
$853$	−2.75579e7			−1.29680			−0.648402	+	0.761298i	$0.724562\pi$
$854$			4.38473e7i			2.05730i
$855$	−1.95595e6	+	1.42580e7i	−0.0915044	+	0.667028i
$856$		−	3.75626e7i		−	1.75215i
$857$	3.09058e6			0.143743			0.0718717	−	0.997414i	$-0.477103\pi$
$857$	3.09058e6			0.143743			0.0718717	+	0.997414i	$0.477103\pi$
$858$	4.39185e6	−	6.43293e7i	0.203671	−	2.98326i
$859$		−	2.09531e7i		−	0.968870i	−0.874827	−	0.484435i	$-0.839025\pi$
$859$		−	2.09531e7i		−	0.968870i	0.874827	−	0.484435i	$-0.160975\pi$
$860$	5.73549e7			2.64438
$861$	−469855.	+	6.88216e6i	−0.0216001	+	0.316386i
$862$	−6.32171e7			−2.89779
$863$	2.33264e6			0.106616			0.0533078	−	0.998578i	$-0.483024\pi$
$863$	2.33264e6			0.106616			0.0533078	+	0.998578i	$0.483024\pi$
$864$	7.57207e6	+	1.57042e6i	0.345088	+	0.0715699i
$865$		−	4.33552e7i		−	1.97016i
$866$	−4.39647e7			−1.99209
$867$	3.66400e7	+	2.50146e6i	1.65542	+	0.113018i
$868$		−	9.34825e7i		−	4.21144i
$869$	1.30652e7			0.586902
$870$	−9.82801e7	−	6.70972e6i	−4.40218	−	0.300543i
$871$	3.10278e7			1.38581
$872$		−	6.58683e6i		−	0.293350i
$873$	3.31232e6	−	2.41454e7i	0.147095	−	1.07226i
$874$	−1.01656e7			−0.450148
$875$		−	5.09881e7i		−	2.25138i
$876$	1.14010e6	−	1.66996e7i	0.0501977	−	0.735267i
$877$	−2.46159e7			−1.08073			−0.540363	−	0.841432i	$-0.681713\pi$
$877$	−2.46159e7			−1.08073			−0.540363	+	0.841432i	$0.681713\pi$
$878$	−1.47600e7			−0.646173
$879$	−1.95119e6	+	2.85799e7i	−0.0851780	+	1.24764i
$880$		−	8.29177e7i		−	3.60945i
$881$	−1.19451e7			−0.518502			−0.259251	−	0.965810i	$-0.583476\pi$
$881$	−1.19451e7			−0.518502			−0.259251	+	0.965810i	$0.583476\pi$
$882$	−1.78538e7	−	2.44922e6i	−0.772786	−	0.106012i
$883$	1.48652e7			0.641608			0.320804	−	0.947146i	$-0.396047\pi$
$883$	1.48652e7			0.641608			0.320804	+	0.947146i	$0.396047\pi$
$884$	8.48824e7			3.65331
$885$	−707905.	+	4.08163e7i	−0.0303820	+	1.75177i
$886$	−3.91355e6			−0.167489
$887$	−1.07545e7			−0.458967			−0.229484	−	0.973313i	$-0.573704\pi$
$887$	−1.07545e7			−0.458967			−0.229484	+	0.973313i	$0.573704\pi$
$888$	−1.24613e6	+	1.82526e7i	−0.0530312	+	0.776771i
$889$	6.99461e6			0.296831
$890$			7.34589e7i			3.10863i
$891$	3.62807e7	+	1.01450e7i	1.53102	+	0.428114i
$892$	−4.05376e7			−1.70587
$893$	−2.39254e6			−0.100399
$894$	−6.57110e7	−	4.48618e6i	−2.74976	−	0.187730i
$895$			831030.i			0.0346784i
$896$	−4.45035e7			−1.85193
$897$	1.16827e6	−	1.71121e7i	0.0484799	−	0.710105i
$898$			4.63110e6i			0.191643i
$899$	5.80236e7			2.39445
$900$	−1.04412e8	−	1.43235e7i	−4.29680	−	0.589444i
$901$	−2.85108e7			−1.17003
$902$		−	1.80409e7i		−	0.738317i
$903$	−1.44414e6	+	2.11530e7i	−0.0589373	+	0.863280i
$904$	5.47759e6			0.222930
$905$			1.74558e7i			0.708466i
$906$	−1.01336e6	+	1.48431e7i	−0.0410149	+	0.600763i
$907$	1.88753e7			0.761861			0.380930	−	0.924604i	$-0.375604\pi$
$907$	1.88753e7			0.761861			0.380930	+	0.924604i	$0.375604\pi$
$908$	5.79830e7			2.33392
$909$	−3.39524e7	−	4.65766e6i	−1.36289	−	0.186964i
$910$	−9.89009e7			−3.95910
$911$		−	2.88126e7i		−	1.15024i	−0.818071	−	0.575118i	$-0.804956\pi$
$911$		−	2.88126e7i		−	1.15024i	0.818071	−	0.575118i	$-0.195044\pi$
$912$	1.24796e7	+	851997.i	0.496835	+	0.0339196i
$913$	3.75476e7			1.49075
$914$		−	7.18830e7i		−	2.84617i
$915$	−4.30850e7	−	2.94147e6i	−1.70127	−	0.116148i
$916$			3.38790e7i			1.33411i
$917$	−2.35798e7			−0.926010
$918$	−1.48770e7	+	7.17323e7i	−0.582650	+	2.80936i
$919$		−	1.42478e7i		−	0.556491i	−0.960510	−	0.278245i	$-0.910247\pi$
$919$		−	1.42478e7i		−	0.556491i	0.960510	−	0.278245i	$-0.0897529\pi$
$920$		−	5.77247e7i		−	2.24850i
$921$	8.89140e6	+	607028.i	0.345399	+	0.0235809i
$922$			2.50908e7i			0.972047i
$923$	−4.81751e6			−0.186131
$924$	1.03631e8	+	7.07502e6i	3.99309	+	0.272614i
$925$		−	2.17534e7i		−	0.835934i
$926$		−	1.39870e7i		−	0.536039i
$927$	1.77175e6	−	1.29153e7i	0.0677177	−	0.493634i
$928$			1.32346e7i			0.504475i
$929$	967237.			0.0367700			0.0183850	−	0.999831i	$-0.494148\pi$
$929$	967237.			0.0367700			0.0183850	+	0.999831i	$0.494148\pi$
$930$	1.35691e8	+	9.26382e6i	5.14451	+	0.351223i
$931$	−4.50570e6			−0.170368
$932$	−1.21810e7			−0.459351
$933$	−383333.	+	5.61485e6i	−0.0144169	+	0.211171i
$934$	5.88483e7			2.20733
$935$	1.21417e8			4.54205
$936$	−7.50683e6	+	5.47217e7i	−0.280070	+	2.04160i
$937$			2.05057e7i			0.763001i	0.924369	+	0.381501i	$0.124593\pi$
$937$			2.05057e7i			0.763001i	−0.924369	+	0.381501i	$0.875407\pi$
$938$			7.38360e7i			2.74007i
$939$	−2.67984e6	+	3.92528e7i	−0.0991848	+	1.45280i
$940$		−	2.59864e7i		−	0.959238i
$941$	−1.26707e7			−0.466471			−0.233236	−	0.972420i	$-0.574931\pi$
$941$	−1.26707e7			−0.466471			−0.233236	+	0.972420i	$0.574931\pi$
$942$	4.07565e6	−	5.96978e7i	0.149648	−	2.19195i
$943$		−	4.79904e6i		−	0.175742i
$944$	3.54356e7	−	1.80252e6i	1.29422	−	0.0658339i
$945$	1.17344e7	−	5.65796e7i	0.427446	−	2.06101i
$946$		−	5.54505e7i		−	2.01455i
$947$			3.31493e7i			1.20116i	0.799566	+	0.600579i	$0.205063\pi$
$947$			3.31493e7i			1.20116i	−0.799566	+	0.600579i	$0.794937\pi$
$948$	−2.13576e7	−	1.45812e6i	−0.771849	−	0.0526952i
$949$	1.04307e7			0.375966
$950$	−3.89242e7			−1.39930
$951$	−2.68118e6	+	3.92724e7i	−0.0961334	+	1.40811i
$952$			1.05603e8i			3.77645i
$953$		−	1.31803e7i		−	0.470104i	−0.971983	−	0.235052i	$-0.924474\pi$
$953$		−	1.31803e7i		−	0.470104i	0.971983	−	0.235052i	$-0.0755261\pi$
$954$	4.82289e6	−	3.51568e7i	0.171568	−	1.25066i
$955$			1.58433e7i			0.562130i
$956$		−	5.18752e7i		−	1.83576i
$957$	−4.39139e6	+	6.43226e7i	−0.154997	+	2.27030i
$958$		−	5.20510e7i		−	1.83238i
$959$			5.38699e7i			1.89147i
$960$	2.30292e6	−	3.37318e7i	0.0806493	−	1.18130i
$961$	−5.14816e7			−1.79822
$962$	−2.18069e7			−0.759724
$963$	−3.55523e6	+	2.59161e7i	−0.123538	+	0.900543i
$964$	−1.77676e7			−0.615793
$965$			2.88158e6i			0.0996123i
$966$	4.07213e7	+	2.78010e6i	1.40404	+	0.0958556i
$967$		−	4.48466e7i		−	1.54228i	−0.636665	−	0.771140i	$-0.719687\pi$
$967$		−	4.48466e7i		−	1.54228i	0.636665	−	0.771140i	$-0.280313\pi$
$968$	−8.58288e7			−2.94405
$969$	−1.24759e6	+	1.82740e7i	−0.0426837	+	0.625206i
$970$	9.77665e7			3.33627
$971$			2.25586e7i			0.767829i	0.923369	+	0.383914i	$0.125424\pi$
$971$			2.25586e7i			0.767829i	−0.923369	+	0.383914i	$0.874576\pi$
$972$	−5.81758e7	−	2.06331e7i	−1.97504	−	0.700487i
$973$	3.43391e6			0.116280
$974$	5.92899e7			2.00255
$975$	4.47330e6	−	6.55223e7i	0.150701	−	2.20738i
$976$			3.75351e7i			1.26128i
$977$	−7.98168e6			−0.267521			−0.133760	−	0.991014i	$-0.542705\pi$
$977$	−7.98168e6			−0.267521			−0.133760	+	0.991014i	$0.542705\pi$
$978$	7.54136e7	+	5.14859e6i	2.52117	+	0.172124i
$979$	4.80775e7			1.60319
$980$		−	4.89383e7i		−	1.62773i
$981$	−623432.	+	4.54455e6i	−0.0206831	+	0.150771i
$982$			2.20561e7i			0.729879i
$983$	2.16858e7			0.715800			0.357900	−	0.933760i	$-0.383493\pi$
$983$	2.16858e7			0.715800			0.357900	+	0.933760i	$0.383493\pi$
$984$	−1.05263e6	+	1.54184e7i	−0.0346569	+	0.507634i
$985$	1.00655e7			0.330557
$986$	−1.25375e8			−4.10693
$987$	9.58400e6	+	654313.i	0.313151	+	0.0213793i
$988$			2.64149e7i			0.860909i
$989$		−	1.47503e7i		−	0.479524i
$990$	−2.05390e7	+	1.49720e8i	−0.666025	+	4.85504i
$991$			5.54087e7i			1.79223i	0.443822	+	0.896115i	$0.353622\pi$
$991$			5.54087e7i			1.79223i	−0.443822	+	0.896115i	$0.646378\pi$
$992$		−	1.82724e7i		−	0.589544i
$993$	625318.	+	42691.3i	0.0201246	+	0.00137394i
$994$		−	1.14641e7i		−	0.368023i
$995$			1.41645e6i			0.0453570i
$996$	−6.13791e7	−	4.19044e6i	−1.96052	−	0.133848i
$997$	5.14102e7			1.63799			0.818996	−	0.573799i	$-0.194531\pi$
$997$	5.14102e7			1.63799			0.818996	+	0.573799i	$0.194531\pi$
$998$	1.43524e7			0.456139
$999$	2.58734e6	−	1.24754e7i	0.0820238	−	0.395494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.d.b.176.7	✓	92
3.2	odd	2	inner	177.6.d.b.176.86	yes	92
59.58	odd	2	inner	177.6.d.b.176.85	yes	92
177.176	even	2	inner	177.6.d.b.176.8	yes	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.d.b.176.7	✓	92	1.1	even	1	trivial
177.6.d.b.176.8	yes	92	177.176	even	2	inner
177.6.d.b.176.85	yes	92	59.58	odd	2	inner
177.6.d.b.176.86	yes	92	3.2	odd	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-9.95283 q^{2} +(-15.5523 - 1.06177i) q^{3} +67.0588 q^{4} -97.9414i q^{5} +(154.789 + 10.5677i) q^{6} -155.750 q^{7} -348.934 q^{8} +(240.745 + 33.0259i) q^{9} +O(q^{10})\)	\(q-9.95283 q^{2} +(-15.5523 - 1.06177i) q^{3} +67.0588 q^{4} -97.9414i q^{5} +(154.789 + 10.5677i) q^{6} -155.750 q^{7} -348.934 q^{8} +(240.745 + 33.0259i) q^{9} +974.794i q^{10} +637.985 q^{11} +(-1042.92 - 71.2012i) q^{12} -651.416i q^{13} +1550.16 q^{14} +(-103.992 + 1523.21i) q^{15} +1327.00 q^{16} +1943.14i q^{17} +(-2396.10 - 328.702i) q^{18} -604.694 q^{19} -6567.83i q^{20} +(2422.27 + 165.372i) q^{21} -6349.76 q^{22} -1689.09 q^{23} +(5426.71 + 370.489i) q^{24} -6467.52 q^{25} +6483.43i q^{26} +(-3709.07 - 769.245i) q^{27} -10444.4 q^{28} -6482.75i q^{29} +(1035.01 - 15160.2i) q^{30} +8950.46i q^{31} -2041.50 q^{32} +(-9922.11 - 677.396i) q^{33} -19339.7i q^{34} +15254.4i q^{35} +(16144.1 + 2214.68i) q^{36} +3363.48i q^{37} +6018.41 q^{38} +(-691.656 + 10131.0i) q^{39} +34175.1i q^{40} +2841.20i q^{41} +(-24108.4 - 1645.92i) q^{42} +8732.70i q^{43} +42782.5 q^{44} +(3234.61 - 23578.9i) q^{45} +16811.2 q^{46} +3956.62 q^{47} +(-20637.8 - 1408.97i) q^{48} +7451.21 q^{49} +64370.1 q^{50} +(2063.17 - 30220.2i) q^{51} -43683.1i q^{52} +14672.5i q^{53} +(36915.7 + 7656.16i) q^{54} -62485.2i q^{55} +54346.6 q^{56} +(9404.35 + 642.048i) q^{57} +64521.7i q^{58} +(26703.5 - 1358.34i) q^{59} +(-6973.55 + 102145. i) q^{60} +28285.7i q^{61} -89082.4i q^{62} +(-37496.2 - 5143.81i) q^{63} -22145.2 q^{64} -63800.6 q^{65} +(98753.0 + 6742.01i) q^{66} +47631.3i q^{67} +130304. i q^{68} +(26269.1 + 1793.43i) q^{69} -151825. i q^{70} -7395.45i q^{71} +(-84004.2 - 11523.9i) q^{72} +16012.4i q^{73} -33476.1i q^{74} +(100584. + 6867.04i) q^{75} -40550.0 q^{76} -99366.5 q^{77} +(6883.93 - 100832. i) q^{78} +20478.8 q^{79} -129968. i q^{80} +(56867.6 + 15901.7i) q^{81} -28278.0i q^{82} +58853.4 q^{83} +(162435. + 11089.6i) q^{84} +190314. q^{85} -86915.0i q^{86} +(-6883.22 + 100821. i) q^{87} -222615. q^{88} +75358.4 q^{89} +(-32193.5 + 234677. i) q^{90} +101458. i q^{91} -113268. q^{92} +(9503.36 - 139200. i) q^{93} -39379.5 q^{94} +59224.6i q^{95} +(31750.0 + 2167.61i) q^{96} -100295. i q^{97} -74160.6 q^{98} +(153592. + 21070.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9}+O(q^{10}) \) 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9	\( 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9} - 1244 q^{12} + 1116 q^{15} + 14724 q^{16} + 1784 q^{19} + 6388 q^{21} - 8140 q^{22} - 48208 q^{25} - 6458 q^{27} - 19092 q^{28} - 20832 q^{36} - 134984 q^{45} + 51180 q^{46} + 61720 q^{48} + 174556 q^{49} + 8332 q^{51} + 236784 q^{57} + 375208 q^{60} - 429890 q^{63} + 561472 q^{64} - 11596 q^{66} + 169948 q^{75} + 111488 q^{76} + 356264 q^{78} + 180260 q^{79} + 79554 q^{81} + 269308 q^{84} + 111028 q^{85} - 318764 q^{87} - 1242976 q^{88} - 513608 q^{94}+O(q^{100}) \) 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9 - 1244 * q^12 + 1116 * q^15 + 14724 * q^16 + 1784 * q^19 + 6388 * q^21 - 8140 * q^22 - 48208 * q^25 - 6458 * q^27 - 19092 * q^28 - 20832 * q^36 - 134984 * q^45 + 51180 * q^46 + 61720 * q^48 + 174556 * q^49 + 8332 * q^51 + 236784 * q^57 + 375208 * q^60 - 429890 * q^63 + 561472 * q^64 - 11596 * q^66 + 169948 * q^75 + 111488 * q^76 + 356264 * q^78 + 180260 * q^79 + 79554 * q^81 + 269308 * q^84 + 111028 * q^85 - 318764 * q^87 - 1242976 * q^88 - 513608 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more