LMFDB - Embedded newform 22.7.b.a.21.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,7,Mod(21,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("22.21");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	22.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:	$5.06118983964$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 1781x^{4} + 14500x^{3} + 786532x^{2} - 11444432x + 42080676 $ x^6 - 2x^5 - 1781x^4 + 14500x^3 + 786532x^2 - 11444432*x + 42080676
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.3
Root			$25.9852 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.7.b.a.21.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685i q^{2} +16.9852 q^{3} -32.0000 q^{4} +175.767 q^{5} -96.0828i q^{6} -412.125i q^{7} +181.019i q^{8} -440.503 q^{9} +O(q^{10})$	\(q-5.65685i q^{2} +16.9852 q^{3} -32.0000 q^{4} +175.767 q^{5} -96.0828i q^{6} -412.125i q^{7} +181.019i q^{8} -440.503 q^{9} -994.286i q^{10} +(1259.88 - 429.258i) q^{11} -543.526 q^{12} -1853.71i q^{13} -2331.33 q^{14} +2985.43 q^{15} +1024.00 q^{16} +8103.56i q^{17} +2491.86i q^{18} +9527.12i q^{19} -5624.53 q^{20} -7000.02i q^{21} +(-2428.25 - 7126.96i) q^{22} +219.542 q^{23} +3074.65i q^{24} +15268.9 q^{25} -10486.1 q^{26} -19864.2 q^{27} +13188.0i q^{28} +6798.33i q^{29} -16888.1i q^{30} +6235.97 q^{31} -5792.62i q^{32} +(21399.3 - 7291.04i) q^{33} +45840.6 q^{34} -72437.7i q^{35} +14096.1 q^{36} -59358.7 q^{37} +53893.5 q^{38} -31485.6i q^{39} +31817.1i q^{40} -33300.1i q^{41} -39598.1 q^{42} +131981. i q^{43} +(-40316.2 + 13736.3i) q^{44} -77425.7 q^{45} -1241.92i q^{46} +75062.8 q^{47} +17392.8 q^{48} -52197.7 q^{49} -86373.8i q^{50} +137640. i q^{51} +59318.6i q^{52} -231249. q^{53} +112369. i q^{54} +(221445. - 75449.3i) q^{55} +74602.5 q^{56} +161820. i q^{57} +38457.2 q^{58} +128524. q^{59} -95533.7 q^{60} -268328. i q^{61} -35276.0i q^{62} +181542. i q^{63} -32768.0 q^{64} -325819. i q^{65} +(-41244.3 - 121053. i) q^{66} +181664. q^{67} -259314. i q^{68} +3728.97 q^{69} -409770. q^{70} +162021. q^{71} -79739.6i q^{72} +331034. i q^{73} +335784. i q^{74} +259345. q^{75} -304868. i q^{76} +(-176908. - 519228. i) q^{77} -178109. q^{78} -94241.5i q^{79} +179985. q^{80} -16271.3 q^{81} -188374. q^{82} -676011. i q^{83} +224001. i q^{84} +1.42433e6i q^{85} +746596. q^{86} +115471. i q^{87} +(77704.1 + 228063. i) q^{88} +288260. q^{89} +437986. i q^{90} -763958. q^{91} -7025.36 q^{92} +105919. q^{93} -424619. i q^{94} +1.67455e6i q^{95} -98388.8i q^{96} -1.47936e6 q^{97} +295275. i q^{98} +(-554981. + 189090. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 52 q^{3} - 192 q^{4} + 368 q^{5} - 346 q^{9}+O(q^{10}) $ 6 * q - 52 * q^3 - 192 * q^4 + 368 * q^5 - 346 * q^9	$ 6 q - 52 q^{3} - 192 q^{4} + 368 q^{5} - 346 q^{9} - 1166 q^{11} + 1664 q^{12} + 2208 q^{14} - 6512 q^{15} + 6144 q^{16} - 11776 q^{20} + 1056 q^{22} + 2156 q^{23} + 59862 q^{25} - 1824 q^{26} - 57472 q^{27} - 78468 q^{31} + 142208 q^{33} + 28704 q^{34} + 11072 q^{36} - 205920 q^{37} + 101472 q^{38} - 344160 q^{42} + 37312 q^{44} + 368716 q^{45} + 493460 q^{47} - 53248 q^{48} - 270762 q^{49} - 531700 q^{53} + 274956 q^{55} - 70656 q^{56} + 509184 q^{58} - 833380 q^{59} + 208384 q^{60} - 196608 q^{64} + 193248 q^{66} + 537420 q^{67} + 398860 q^{69} + 96096 q^{70} - 460372 q^{71} - 211428 q^{75} + 249744 q^{77} - 1866912 q^{78} + 376832 q^{80} + 485654 q^{81} + 428640 q^{82} + 1055808 q^{86} - 33792 q^{88} + 2377952 q^{89} - 5068656 q^{91} - 68992 q^{92} + 699868 q^{93} + 1351632 q^{97} - 2470930 q^{99}+O(q^{100}) $ 6 * q - 52 * q^3 - 192 * q^4 + 368 * q^5 - 346 * q^9 - 1166 * q^11 + 1664 * q^12 + 2208 * q^14 - 6512 * q^15 + 6144 * q^16 - 11776 * q^20 + 1056 * q^22 + 2156 * q^23 + 59862 * q^25 - 1824 * q^26 - 57472 * q^27 - 78468 * q^31 + 142208 * q^33 + 28704 * q^34 + 11072 * q^36 - 205920 * q^37 + 101472 * q^38 - 344160 * q^42 + 37312 * q^44 + 368716 * q^45 + 493460 * q^47 - 53248 * q^48 - 270762 * q^49 - 531700 * q^53 + 274956 * q^55 - 70656 * q^56 + 509184 * q^58 - 833380 * q^59 + 208384 * q^60 - 196608 * q^64 + 193248 * q^66 + 537420 * q^67 + 398860 * q^69 + 96096 * q^70 - 460372 * q^71 - 211428 * q^75 + 249744 * q^77 - 1866912 * q^78 + 376832 * q^80 + 485654 * q^81 + 428640 * q^82 + 1055808 * q^86 - 33792 * q^88 + 2377952 * q^89 - 5068656 * q^91 - 68992 * q^92 + 699868 * q^93 + 1351632 * q^97 - 2470930 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$-1$

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 $

$2$		−	5.65685i		−	0.707107i
$2$		−	5.65685i		−	0.707107i
$3$	16.9852			0.629081			0.314541	−	0.949244i	$-0.398150\pi$
$3$	16.9852			0.629081			0.314541	+	0.949244i	$0.398150\pi$
$4$	−32.0000			−0.500000
$5$	175.767			1.40613			0.703066	−	0.711124i	$-0.251814\pi$
$5$	175.767			1.40613			0.703066	+	0.711124i	$0.251814\pi$
$6$		−	96.0828i		−	0.444828i
$7$		−	412.125i		−	1.20153i	−0.799426	−	0.600765i	$-0.794863\pi$
$7$		−	412.125i		−	1.20153i	0.799426	−	0.600765i	$-0.205137\pi$
$8$			181.019i			0.353553i
$9$	−440.503			−0.604257
$10$		−	994.286i		−	0.994286i
$11$	1259.88	−	429.258i	0.946567	−	0.322508i
$11$	1259.88	−	429.258i	0.946567	−	0.322508i
$12$	−543.526			−0.314541
$13$		−	1853.71i		−	0.843744i	−0.906655	−	0.421872i	$-0.861373\pi$
$13$		−	1853.71i		−	0.843744i	0.906655	−	0.421872i	$-0.138627\pi$
$14$	−2331.33			−0.849610
$15$	2985.43			0.884572
$16$	1024.00			0.250000
$17$			8103.56i			1.64941i	0.565563	+	0.824705i	$0.308659\pi$
$17$			8103.56i			1.64941i	−0.565563	+	0.824705i	$0.691341\pi$
$18$			2491.86i			0.427274i
$19$			9527.12i			1.38900i	0.719495	+	0.694498i	$0.244373\pi$
$19$			9527.12i			1.38900i	−0.719495	+	0.694498i	$0.755627\pi$
$20$	−5624.53			−0.703066
$21$		−	7000.02i		−	0.755860i
$22$	−2428.25	−	7126.96i	−0.228048	−	0.669324i
$23$	219.542			0.0180441			0.00902205	−	0.999959i	$-0.497128\pi$
$23$	219.542			0.0180441			0.00902205	+	0.999959i	$0.497128\pi$
$24$			3074.65i			0.222414i
$25$	15268.9			0.977208
$26$	−10486.1			−0.596617
$27$	−19864.2			−1.00921
$28$			13188.0i			0.600765i
$29$			6798.33i			0.278746i	0.990240	+	0.139373i	$0.0445087\pi$
$29$			6798.33i			0.278746i	−0.990240	+	0.139373i	$0.955491\pi$
$30$		−	16888.1i		−	0.625487i
$31$	6235.97			0.209324			0.104662	−	0.994508i	$-0.466624\pi$
$31$	6235.97			0.209324			0.104662	+	0.994508i	$0.466624\pi$
$32$		−	5792.62i		−	0.176777i
$33$	21399.3	−	7291.04i	0.595467	−	0.202884i
$34$	45840.6			1.16631
$35$		−	72437.7i		−	1.68951i
$36$	14096.1			0.302128
$37$	−59358.7			−1.17187			−0.585935	−	0.810358i	$-0.699273\pi$
$37$	−59358.7			−1.17187			−0.585935	+	0.810358i	$0.699273\pi$
$38$	53893.5			0.982168
$39$		−	31485.6i		−	0.530784i
$40$			31817.1i			0.497143i
$41$		−	33300.1i		−	0.483163i	−0.970380	−	0.241582i	$-0.922334\pi$
$41$		−	33300.1i		−	0.483163i	0.970380	−	0.241582i	$-0.0776662\pi$
$42$	−39598.1			−0.534474
$43$			131981.i			1.65999i	0.557771	+	0.829995i	$0.311657\pi$
$43$			131981.i			1.65999i	−0.557771	+	0.829995i	$0.688343\pi$
$44$	−40316.2	+	13736.3i	−0.473283	+	0.161254i
$45$	−77425.7			−0.849665
$46$		−	1241.92i		−	0.0127591i
$47$	75062.8			0.722988			0.361494	−	0.932374i	$-0.382267\pi$
$47$	75062.8			0.722988			0.361494	+	0.932374i	$0.382267\pi$
$48$	17392.8			0.157270
$49$	−52197.7			−0.443673
$50$		−	86373.8i		−	0.690990i
$51$			137640.i			1.03761i
$52$			59318.6i			0.421872i
$53$	−231249.			−1.55329			−0.776645	−	0.629938i	$-0.783080\pi$
$53$	−231249.			−1.55329			−0.776645	+	0.629938i	$0.783080\pi$
$54$			112369.i			0.713618i
$55$	221445.	−	75449.3i	1.33100	−	0.453489i
$56$	74602.5			0.424805
$57$			161820.i			0.873791i
$58$	38457.2			0.197103
$59$	128524.			0.625788			0.312894	−	0.949788i	$-0.398701\pi$
$59$	128524.			0.625788			0.312894	+	0.949788i	$0.398701\pi$
$60$	−95533.7			−0.442286
$61$		−	268328.i		−	1.18216i	−0.806613	−	0.591079i	$-0.798702\pi$
$61$		−	268328.i		−	1.18216i	0.806613	−	0.591079i	$-0.201298\pi$
$62$		−	35276.0i		−	0.148014i
$63$			181542.i			0.726032i
$64$	−32768.0			−0.125000
$65$		−	325819.i		−	1.18642i
$66$	−41244.3	−	121053.i	−0.143461	−	0.421059i
$67$	181664.			0.604010			0.302005	−	0.953306i	$-0.402344\pi$
$67$	181664.			0.604010			0.302005	+	0.953306i	$0.402344\pi$
$68$		−	259314.i		−	0.824705i
$69$	3728.97			0.0113512
$70$	−409770.			−1.19466
$71$	162021.			0.452684			0.226342	−	0.974048i	$-0.427323\pi$
$71$	162021.			0.452684			0.226342	+	0.974048i	$0.427323\pi$
$72$		−	79739.6i		−	0.213637i
$73$			331034.i			0.850950i	0.904970	+	0.425475i	$0.139893\pi$
$73$			331034.i			0.850950i	−0.904970	+	0.425475i	$0.860107\pi$
$74$			335784.i			0.828637i
$75$	259345.			0.614743
$76$		−	304868.i		−	0.694498i
$77$	−176908.	−	519228.i	−0.387503	−	1.13733i
$78$	−178109.			−0.375321
$79$		−	94241.5i		−	0.191144i	−0.995423	−	0.0955720i	$-0.969532\pi$
$79$		−	94241.5i		−	0.191144i	0.995423	−	0.0955720i	$-0.0304680\pi$
$80$	179985.			0.351533
$81$	−16271.3			−0.0306173
$82$	−188374.			−0.341648
$83$		−	676011.i		−	1.18228i	−0.806570	−	0.591138i	$-0.798679\pi$
$83$		−	676011.i		−	1.18228i	0.806570	−	0.591138i	$-0.201321\pi$
$84$			224001.i			0.377930i
$85$			1.42433e6i			2.31929i
$86$	746596.			1.17379
$87$			115471.i			0.175354i
$88$	77704.1	+	228063.i	0.114024	+	0.334662i
$89$	288260.			0.408898			0.204449	−	0.978877i	$-0.434460\pi$
$89$	288260.			0.408898			0.204449	+	0.978877i	$0.434460\pi$
$90$			437986.i			0.600804i
$91$	−763958.			−1.01378
$92$	−7025.36			−0.00902205
$93$	105919.			0.131682
$94$		−	424619.i		−	0.511230i
$95$			1.67455e6i			1.95311i
$96$		−	98388.8i		−	0.111207i
$97$	−1.47936e6			−1.62091			−0.810453	−	0.585804i	$-0.800779\pi$
$97$	−1.47936e6			−1.62091			−0.810453	+	0.585804i	$0.800779\pi$
$98$			295275.i			0.313724i
$99$	−554981.	+	189090.i	−0.571969	+	0.194878i
$100$	−488604.			−0.488604
$101$		−	1.80675e6i		−	1.75362i	−0.480838	−	0.876809i	$-0.659668\pi$
$101$		−	1.80675e6i		−	1.75362i	0.480838	−	0.876809i	$-0.340332\pi$
$102$	778612.			0.733704
$103$	1.25034e6			1.14424			0.572119	−	0.820171i	$-0.306122\pi$
$103$	1.25034e6			1.14424			0.572119	+	0.820171i	$0.306122\pi$
$104$	335557.			0.298309
$105$		−	1.23037e6i		−	1.06284i
$106$			1.30814e6i			1.09834i
$107$		−	1.19558e6i		−	0.975953i	−0.872857	−	0.487976i	$-0.837735\pi$
$107$		−	1.19558e6i		−	0.975953i	0.872857	−	0.487976i	$-0.162265\pi$
$108$	635656.			0.504604
$109$			643224.i			0.496687i	0.968672	+	0.248343i	$0.0798862\pi$
$109$			643224.i			0.496687i	−0.968672	+	0.248343i	$0.920114\pi$
$110$	−426806.	−	1.25268e6i	−0.320665	−	0.941158i
$111$	−1.00822e6			−0.737202
$112$		−	422016.i		−	0.300382i
$113$	−1.33637e6			−0.926169			−0.463084	−	0.886314i	$-0.653257\pi$
$113$	−1.33637e6			−0.926169			−0.463084	+	0.886314i	$0.653257\pi$
$114$	915392.			0.617864
$115$	38588.2			0.0253724
$116$		−	217547.i		−	0.139373i
$117$			816563.i			0.509838i
$118$		−	727040.i		−	0.442499i
$119$	3.33967e6			1.98182
$120$			540420.i			0.312743i
$121$	1.40304e6	−	1.08163e6i	0.791977	−	0.610551i
$122$	−1.51789e6			−0.835912
$123$		−	565609.i		−	0.303949i
$124$	−199551.			−0.104662
$125$	−62595.1			−0.0320487
$126$	1.02696e6			0.513382
$127$		−	2.16447e6i		−	1.05667i	−0.849035	−	0.528337i	$-0.822816\pi$
$127$		−	2.16447e6i		−	1.05667i	0.849035	−	0.528337i	$-0.177184\pi$
$128$			185364.i			0.0883883i
$129$			2.24172e6i			1.04427i
$130$	−1.84311e6			−0.838923
$131$			2.78752e6i			1.23995i	0.784622	+	0.619974i	$0.212857\pi$
$131$			2.78752e6i			1.23995i	−0.784622	+	0.619974i	$0.787143\pi$
$132$	−684778.	+	233313.i	−0.297734	+	0.101442i
$133$	3.92636e6			1.66892
$134$		−	1.02765e6i		−	0.427099i
$135$	−3.49147e6			−1.41908
$136$	−1.46690e6			−0.583155
$137$	−2.96546e6			−1.15327			−0.576634	−	0.817003i	$-0.695634\pi$
$137$	−2.96546e6			−1.15327			−0.576634	+	0.817003i	$0.695634\pi$
$138$		−	21094.3i		−	0.00802651i
$139$			789181.i			0.293855i	0.989147	+	0.146927i	$0.0469383\pi$
$139$			789181.i			0.293855i	−0.989147	+	0.146927i	$0.953062\pi$
$140$			2.31801e6i			0.844755i
$141$	1.27496e6			0.454818
$142$		−	916526.i		−	0.320096i
$143$	−795719.	−	2.33545e6i	−0.272114	−	0.798660i
$144$	−451075.			−0.151064
$145$			1.19492e6i			0.391954i
$146$	1.87261e6			0.601713
$147$	−886589.			−0.279107
$148$	1.89948e6			0.585935
$149$			5.69493e6i			1.72159i	0.508953	+	0.860794i	$0.330033\pi$
$149$			5.69493e6i			1.72159i	−0.508953	+	0.860794i	$0.669967\pi$
$150$		−	1.46708e6i		−	0.434689i
$151$			2.77930e6i			0.807244i	0.914926	+	0.403622i	$0.132249\pi$
$151$			2.77930e6i			0.807244i	−0.914926	+	0.403622i	$0.867751\pi$
$152$	−1.72459e6			−0.491084
$153$		−	3.56964e6i		−	0.996667i
$154$	−2.93720e6	+	1.00074e6i	−0.804212	+	0.274006i
$155$	1.09607e6			0.294337
$156$			1.00754e6i			0.265392i
$157$	7.04317e6			1.81999			0.909996	−	0.414617i	$-0.136085\pi$
$157$	7.04317e6			1.81999			0.909996	+	0.414617i	$0.136085\pi$
$158$	−533110.			−0.135159
$159$	−3.92781e6			−0.977146
$160$		−	1.01815e6i		−	0.248571i
$161$		−	90478.9i		−	0.0216805i
$162$			92044.3i			0.0216497i
$163$	−697459.			−0.161048			−0.0805241	−	0.996753i	$-0.525659\pi$
$163$	−697459.			−0.161048			−0.0805241	+	0.996753i	$0.525659\pi$
$164$			1.06560e6i			0.241582i
$165$	3.76128e6	−	1.28152e6i	0.837306	−	0.285282i
$166$	−3.82409e6			−0.835996
$167$			708308.i			0.152080i	0.997105	+	0.0760401i	$0.0242277\pi$
$167$			708308.i			0.152080i	−0.997105	+	0.0760401i	$0.975772\pi$
$168$	1.26714e6			0.267237
$169$	1.39058e6			0.288096
$170$	8.05725e6			1.63999
$171$		−	4.19672e6i		−	0.839310i
$172$		−	4.22339e6i		−	0.829995i
$173$		−	6.46711e6i		−	1.24903i	−0.781014	−	0.624514i	$-0.785297\pi$
$173$		−	6.46711e6i		−	1.24903i	0.781014	−	0.624514i	$-0.214703\pi$
$174$	653203.			0.123994
$175$		−	6.29268e6i		−	1.17414i
$176$	1.29012e6	−	439561.i	0.236642	−	0.0806271i
$177$	2.18300e6			0.393672
$178$		−	1.63065e6i		−	0.289135i
$179$	−1.08249e7			−1.88741			−0.943705	−	0.330790i	$-0.892685\pi$
$179$	−1.08249e7			−1.88741			−0.943705	+	0.330790i	$0.892685\pi$
$180$	2.47762e6			0.424832
$181$	−3.56684e6			−0.601517			−0.300759	−	0.953700i	$-0.597240\pi$
$181$	−3.56684e6			−0.601517			−0.300759	+	0.953700i	$0.597240\pi$
$182$			4.32160e6i			0.716853i
$183$		−	4.55760e6i		−	0.743674i
$184$			39741.4i			0.00637955i
$185$	−1.04333e7			−1.64780
$186$		−	599169.i		−	0.0931131i
$187$	3.47852e6	+	1.02095e7i	0.531949	+	1.56128i
$188$	−2.40201e6			−0.361494
$189$			8.18654e6i			1.21259i
$190$	9.47268e6			1.38106
$191$	−3.27361e6			−0.469815			−0.234907	−	0.972018i	$-0.575479\pi$
$191$	−3.27361e6			−0.469815			−0.234907	+	0.972018i	$0.575479\pi$
$192$	−556571.			−0.0786352
$193$		−	2.87534e6i		−	0.399961i	−0.979800	−	0.199981i	$-0.935912\pi$
$193$		−	2.87534e6i		−	0.399961i	0.979800	−	0.199981i	$-0.0640879\pi$
$194$			8.36851e6i			1.14615i
$195$		−	5.53411e6i		−	0.746352i
$196$	1.67033e6			0.221837
$197$			6.01219e6i			0.786383i	0.919457	+	0.393192i	$0.128629\pi$
$197$			6.01219e6i			0.786383i	−0.919457	+	0.393192i	$0.871371\pi$
$198$	1.06965e6	+	3.13945e6i	0.137799	+	0.404443i
$199$	4.86533e6			0.617381			0.308690	−	0.951163i	$-0.400109\pi$
$199$	4.86533e6			0.617381			0.308690	+	0.951163i	$0.400109\pi$
$200$			2.76396e6i			0.345495i
$201$	3.08559e6			0.379971
$202$	−1.02205e7			−1.24000
$203$	2.80176e6			0.334922
$204$		−	4.40450e6i		−	0.518807i
$205$		−	5.85304e6i		−	0.679392i
$206$		−	7.07299e6i		−	0.809098i
$207$	−96709.1			−0.0109033
$208$		−	1.89819e6i		−	0.210936i
$209$	4.08960e6	+	1.20030e7i	0.447962	+	1.31478i
$210$	−6.96002e6			−0.751541
$211$		−	4.94713e6i		−	0.526630i	−0.964710	−	0.263315i	$-0.915184\pi$
$211$		−	4.94713e6i		−	0.526630i	0.964710	−	0.263315i	$-0.0848158\pi$
$212$	7.39998e6			0.776645
$213$	2.75195e6			0.284775
$214$	−6.76324e6			−0.690103
$215$			2.31978e7i			2.33417i
$216$		−	3.59581e6i		−	0.356809i
$217$		−	2.57000e6i		−	0.251509i
$218$	3.63862e6			0.351211
$219$			5.62268e6i			0.535317i
$220$	−7.08623e6	+	2.41438e6i	−0.665499	+	0.226745i
$221$	1.50216e7			1.39168
$222$			5.70335e6i			0.521280i
$223$	−1.37738e7			−1.24205			−0.621027	−	0.783789i	$-0.713284\pi$
$223$	−1.37738e7			−1.24205			−0.621027	+	0.783789i	$0.713284\pi$
$224$	−2.38728e6			−0.212402
$225$	−6.72599e6			−0.590484
$226$			7.55963e6i			0.654900i
$227$		−	1.60283e7i		−	1.37028i	−0.728411	−	0.685140i	$-0.759741\pi$
$227$		−	1.60283e7i		−	1.37028i	0.728411	−	0.685140i	$-0.240259\pi$
$228$		−	5.17824e6i		−	0.436895i
$229$	−4.33803e6			−0.361232			−0.180616	−	0.983554i	$-0.557809\pi$
$229$	−4.33803e6			−0.361232			−0.180616	+	0.983554i	$0.557809\pi$
$230$		−	218288.i		−	0.0179410i
$231$	−3.00482e6	−	8.81918e6i	−0.243771	−	0.715472i
$232$	−1.23063e6			−0.0985516
$233$		−	6.96714e6i		−	0.550791i	−0.961331	−	0.275395i	$-0.911191\pi$
$233$		−	6.96714e6i		−	0.550791i	0.961331	−	0.275395i	$-0.0888088\pi$
$234$	4.61918e6			0.360510
$235$	1.31935e7			1.01662
$236$	−4.11276e6			−0.312894
$237$		−	1.60071e6i		−	0.120245i
$238$		−	1.88921e7i		−	1.40136i
$239$		−	4.71730e6i		−	0.345541i	−0.984962	−	0.172771i	$-0.944728\pi$
$239$		−	4.71730e6i		−	0.345541i	0.984962	−	0.172771i	$-0.0552719\pi$
$240$	3.05708e6			0.221143
$241$		−	6.19630e6i		−	0.442671i	−0.975198	−	0.221336i	$-0.928958\pi$
$241$		−	6.19630e6i		−	0.442671i	0.975198	−	0.221336i	$-0.0710416\pi$
$242$	−6.11861e6	−	7.93677e6i	−0.431725	−	0.560012i
$243$	1.42047e7			0.989947
$244$			8.58648e6i			0.591079i
$245$	−9.17461e6			−0.623864
$246$	−3.19957e6			−0.214924
$247$	1.76605e7			1.17196
$248$			1.12883e6i			0.0740072i
$249$		−	1.14822e7i		−	0.743748i
$250$			354091.i			0.0226619i
$251$	8.78682e6			0.555662			0.277831	−	0.960630i	$-0.410384\pi$
$251$	8.78682e6			0.555662			0.277831	+	0.960630i	$0.410384\pi$
$252$		−	5.80935e6i		−	0.363016i
$253$	276597.	−	94240.5i	0.0170799	−	0.00581937i
$254$	−1.22441e7			−0.747182
$255$			2.41926e7i			1.45902i
$256$	1.04858e6			0.0625000
$257$	5.89939e6			0.347542			0.173771	−	0.984786i	$-0.444405\pi$
$257$	5.89939e6			0.347542			0.173771	+	0.984786i	$0.444405\pi$
$258$	1.26811e7			0.738410
$259$			2.44632e7i			1.40804i
$260$			1.04262e7i			0.593208i
$261$		−	2.99469e6i		−	0.168434i
$262$	1.57686e7			0.876776
$263$		−	1.62207e7i		−	0.891666i	−0.895116	−	0.445833i	$-0.852908\pi$
$263$		−	1.62207e7i		−	0.891666i	0.895116	−	0.445833i	$-0.147092\pi$
$264$	1.31982e6	+	3.87369e6i	0.0717303	+	0.210530i
$265$	−4.06459e7			−2.18413
$266$		−	2.22108e7i		−	1.18010i
$267$	4.89616e6			0.257230
$268$	−5.81324e6			−0.302005
$269$	−9.03612e6			−0.464221			−0.232111	−	0.972689i	$-0.574563\pi$
$269$	−9.03612e6			−0.464221			−0.232111	+	0.972689i	$0.574563\pi$
$270$			1.97507e7i			1.00344i
$271$		−	2.17153e6i		−	0.109108i	−0.998511	−	0.0545542i	$-0.982626\pi$
$271$		−	2.17153e6i		−	0.109108i	0.998511	−	0.0545542i	$-0.0173738\pi$
$272$			8.29804e6i			0.412353i
$273$	−1.29760e7			−0.637752
$274$			1.67752e7i			0.815484i
$275$	1.92370e7	−	6.55429e6i	0.924992	−	0.315158i
$276$	−119327.			−0.00567560
$277$		−	2.28964e6i		−	0.107728i	−0.998548	−	0.0538639i	$-0.982846\pi$
$277$		−	2.28964e6i		−	0.107728i	0.998548	−	0.0538639i	$-0.0171537\pi$
$278$	4.46428e6			0.207787
$279$	−2.74696e6			−0.126485
$280$	1.31126e7			0.597332
$281$			8.71219e6i			0.392653i	0.980539	+	0.196326i	$0.0629012\pi$
$281$			8.71219e6i			0.392653i	−0.980539	+	0.196326i	$0.937099\pi$
$282$		−	7.21224e6i		−	0.321605i
$283$			1.05751e7i			0.466581i	0.972407	+	0.233290i	$0.0749492\pi$
$283$			1.05751e7i			0.466581i	−0.972407	+	0.233290i	$0.925051\pi$
$284$	−5.18466e6			−0.226342
$285$			2.84425e7i			1.22867i
$286$	−1.32113e7	+	4.50127e6i	−0.564738	+	0.192414i
$287$	−1.37238e7			−0.580535
$288$			2.55167e6i			0.106818i
$289$	−4.15300e7			−1.72056
$290$	6.75949e6			0.277153
$291$	−2.51272e7			−1.01968
$292$		−	1.05931e7i		−	0.425475i
$293$			1.52726e6i			0.0607170i	0.999539	+	0.0303585i	$0.00966489\pi$
$293$			1.52726e6i			0.0607170i	−0.999539	+	0.0303585i	$0.990335\pi$
$294$			5.01530e6i			0.197358i
$295$	2.25902e7			0.879941
$296$		−	1.07451e7i		−	0.414319i
$297$	−2.50266e7	+	8.52689e6i	−0.955283	+	0.325478i
$298$	3.22154e7			1.21735
$299$		−	406967.i		−	0.0152246i
$300$	−8.29903e6			−0.307372
$301$	5.43926e7			1.99453
$302$	1.57221e7			0.570808
$303$		−	3.06881e7i		−	1.10317i
$304$			9.75577e6i			0.347249i
$305$		−	4.71630e7i		−	1.66227i
$306$	−2.01929e7			−0.704750
$307$		−	7.67760e6i		−	0.265345i	−0.991160	−	0.132672i	$-0.957644\pi$
$307$		−	7.67760e6i		−	0.265345i	0.991160	−	0.132672i	$-0.0423558\pi$
$308$	5.66106e6	+	1.66153e7i	0.193752	+	0.568664i
$309$	2.12373e7			0.719819
$310$		−	6.20034e6i		−	0.208128i
$311$	2.19337e7			0.729172			0.364586	−	0.931170i	$-0.381210\pi$
$311$	2.19337e7			0.729172			0.364586	+	0.931170i	$0.381210\pi$
$312$	5.69949e6			0.187660
$313$	−3.09060e7			−1.00788			−0.503941	−	0.863738i	$-0.668117\pi$
$313$	−3.09060e7			−1.00788			−0.503941	+	0.863738i	$0.668117\pi$
$314$		−	3.98422e7i		−	1.28693i
$315$			3.19090e7i			1.02090i
$316$			3.01573e6i			0.0955720i
$317$	4.89664e7			1.53717			0.768583	−	0.639750i	$-0.220962\pi$
$317$	4.89664e7			1.53717			0.768583	+	0.639750i	$0.220962\pi$
$318$			2.22191e7i			0.690947i
$319$	2.91824e6	+	8.56509e6i	0.0898979	+	0.263852i
$320$	−5.75952e6			−0.175767
$321$		−	2.03072e7i		−	0.613954i
$322$	−511826.			−0.0153304
$323$	−7.72035e7			−2.29102
$324$	520681.			0.0153086
$325$		−	2.83040e7i		−	0.824513i
$326$			3.94542e6i			0.113878i
$327$			1.09253e7i			0.312457i
$328$	6.02796e6			0.170824
$329$		−	3.09352e7i		−	0.868692i
$330$	−7.24938e6	−	2.12770e7i	−0.201725	−	0.592065i
$331$	2.46737e7			0.680377			0.340188	−	0.940357i	$-0.389509\pi$
$331$	2.46737e7			0.680377			0.340188	+	0.940357i	$0.389509\pi$
$332$			2.16323e7i			0.591138i
$333$	2.61477e7			0.708110
$334$	4.00679e6			0.107537
$335$	3.19304e7			0.849317
$336$		−	7.16802e6i		−	0.188965i
$337$			5.73399e7i			1.49819i	0.662462	+	0.749095i	$0.269512\pi$
$337$			5.73399e7i			1.49819i	−0.662462	+	0.749095i	$0.730488\pi$
$338$		−	7.86633e6i		−	0.203715i
$339$	−2.26984e7			−0.582635
$340$		−	4.55787e7i		−	1.15964i
$341$	7.85658e6	−	2.67684e6i	0.198139	−	0.0675087i
$342$	−2.37403e7			−0.593481
$343$		−	2.69741e7i		−	0.668443i
$344$	−2.38911e7			−0.586895
$345$	655428.			0.0159613
$346$	−3.65835e7			−0.883196
$347$		−	7.09887e7i		−	1.69903i	−0.527566	−	0.849514i	$-0.676895\pi$
$347$		−	7.09887e7i		−	1.69903i	0.527566	−	0.849514i	$-0.323105\pi$
$348$		−	3.69507e6i		−	0.0876769i
$349$			7.62194e7i			1.79304i	0.443005	+	0.896519i	$0.353912\pi$
$349$			7.62194e7i			1.79304i	−0.443005	+	0.896519i	$0.646088\pi$
$350$	−3.55968e7			−0.830245
$351$			3.68225e7i			0.851513i
$352$	−2.48653e6	−	7.29801e6i	−0.0570119	−	0.167331i
$353$	−6.84796e6			−0.155682			−0.0778408	−	0.996966i	$-0.524803\pi$
$353$	−6.84796e6			−0.155682			−0.0778408	+	0.996966i	$0.524803\pi$
$354$		−	1.23489e7i		−	0.278368i
$355$	2.84778e7			0.636533
$356$	−9.22433e6			−0.204449
$357$	5.67250e7			1.24672
$358$			6.12351e7i			1.33460i
$359$			1.85553e7i			0.401036i	0.979690	+	0.200518i	$0.0642626\pi$
$359$			1.85553e7i			0.401036i	−0.979690	+	0.200518i	$0.935737\pi$
$360$		−	1.40155e7i		−	0.300402i
$361$	−4.37201e7			−0.929307
$362$			2.01771e7i			0.425337i
$363$	2.38308e7	−	1.83717e7i	0.498218	−	0.384086i
$364$	2.44466e7			0.506892
$365$			5.81847e7i			1.19655i
$366$	−2.57817e7			−0.525857
$367$	−3.44501e7			−0.696934			−0.348467	−	0.937321i	$-0.613298\pi$
$367$	−3.44501e7			−0.696934			−0.348467	+	0.937321i	$0.613298\pi$
$368$	224811.			0.00451102
$369$			1.46688e7i			0.291955i
$370$			5.90196e7i			1.16517i
$371$			9.53035e7i			1.86632i
$372$	−3.38941e6			−0.0658409
$373$			2.21873e6i			0.0427540i	0.999771	+	0.0213770i	$0.00680503\pi$
$373$			2.21873e6i			0.0427540i	−0.999771	+	0.0213770i	$0.993195\pi$
$374$	5.77537e7	−	1.96775e7i	1.10399	−	0.376144i
$375$	−1.06319e6			−0.0201612
$376$			1.35878e7i			0.255615i
$377$	1.26021e7			0.235190
$378$	4.63101e7			0.857433
$379$	−4.32864e7			−0.795122			−0.397561	−	0.917576i	$-0.630143\pi$
$379$	−4.32864e7			−0.795122			−0.397561	+	0.917576i	$0.630143\pi$
$380$		−	5.35855e7i		−	0.976555i
$381$		−	3.67640e7i		−	0.664734i
$382$			1.85183e7i			0.332209i
$383$	−1.83762e7			−0.327085			−0.163542	−	0.986536i	$-0.552292\pi$
$383$	−1.83762e7			−0.327085			−0.163542	+	0.986536i	$0.552292\pi$
$384$			3.14844e6i			0.0556035i
$385$	−3.10945e7	−	9.12629e7i	−0.544881	−	1.59923i
$386$	−1.62654e7			−0.282815
$387$		−	5.81380e7i		−	1.00306i
$388$	4.73394e7			0.810453
$389$	9.86287e6			0.167554			0.0837769	−	0.996485i	$-0.473302\pi$
$389$	9.86287e6			0.167554			0.0837769	+	0.996485i	$0.473302\pi$
$390$	−3.13056e7			−0.527751
$391$			1.77907e6i			0.0297621i
$392$		−	9.44880e6i		−	0.156862i
$393$			4.73465e7i			0.780028i
$394$	3.40101e7			0.556057
$395$		−	1.65645e7i		−	0.268774i
$396$	1.77594e7	−	6.05087e6i	0.285985	−	0.0974389i
$397$	−8.82757e7			−1.41081			−0.705406	−	0.708803i	$-0.749235\pi$
$397$	−8.82757e7			−1.41081			−0.705406	+	0.708803i	$0.749235\pi$
$398$		−	2.75225e7i		−	0.436554i
$399$	6.66900e7			1.04989
$400$	1.56353e7			0.244302
$401$	8.24767e7			1.27908			0.639541	−	0.768757i	$-0.279125\pi$
$401$	8.24767e7			1.27908			0.639541	+	0.768757i	$0.279125\pi$
$402$		−	1.74548e7i		−	0.268680i
$403$		−	1.15597e7i		−	0.176616i
$404$			5.78162e7i			0.876809i
$405$	−2.85995e6			−0.0430520
$406$		−	1.58492e7i		−	0.236825i
$407$	−7.47849e7	+	2.54802e7i	−1.10925	+	0.377938i
$408$	−2.49156e7			−0.366852
$409$		−	8.96469e7i		−	1.31028i	−0.755506	−	0.655142i	$-0.772609\pi$
$409$		−	8.96469e7i		−	1.31028i	0.755506	−	0.655142i	$-0.227391\pi$
$410$	−3.31098e7			−0.480402
$411$	−5.03689e7			−0.725499
$412$	−4.00109e7			−0.572119
$413$		−	5.29678e7i		−	0.751903i
$414$			547069.i			0.00770977i
$415$		−	1.18820e8i		−	1.66244i
$416$	−1.07378e7			−0.149154
$417$			1.34044e7i			0.184858i
$418$	6.78994e7	−	2.31342e7i	0.929687	−	0.316757i
$419$	1.01853e8			1.38463			0.692315	−	0.721595i	$-0.256591\pi$
$419$	1.01853e8			1.38463			0.692315	+	0.721595i	$0.256591\pi$
$420$			3.93718e7i			0.531419i
$421$	5.27316e7			0.706683			0.353342	−	0.935494i	$-0.385045\pi$
$421$	5.27316e7			0.706683			0.353342	+	0.935494i	$0.385045\pi$
$422$	−2.79852e7			−0.372384
$423$	−3.30654e7			−0.436870
$424$		−	4.18606e7i		−	0.549171i
$425$			1.23732e8i			1.61182i
$426$		−	1.55674e7i		−	0.201366i
$427$	−1.10584e8			−1.42040
$428$			3.82587e7i			0.487976i
$429$	−1.35154e7	−	3.96680e7i	−0.171182	−	0.502422i
$430$	1.31227e8			1.65050
$431$			1.47790e6i			0.0184592i	0.999957	+	0.00922959i	$0.00293791\pi$
$431$			1.47790e6i			0.0184592i	−0.999957	+	0.00922959i	$0.997062\pi$
$432$	−2.03410e7			−0.252302
$433$	2.90742e7			0.358133			0.179066	−	0.983837i	$-0.442692\pi$
$433$	2.90742e7			0.358133			0.179066	+	0.983837i	$0.442692\pi$
$434$	−1.45381e7			−0.177844
$435$			2.02959e7i			0.246571i
$436$		−	2.05832e7i		−	0.248343i
$437$			2.09161e6i			0.0250632i
$438$	3.18067e7			0.378526
$439$			5.95615e7i			0.703999i	0.936000	+	0.352000i	$0.114498\pi$
$439$			5.95615e7i			0.703999i	−0.936000	+	0.352000i	$0.885502\pi$
$440$	1.36578e7	+	4.00858e7i	0.160333	+	0.470579i
$441$	2.29933e7			0.268093
$442$		−	8.49750e7i		−	0.984067i
$443$	−8.59153e7			−0.988233			−0.494116	−	0.869396i	$-0.664508\pi$
$443$	−8.59153e7			−0.988233			−0.494116	+	0.869396i	$0.664508\pi$
$444$	3.22630e7			0.368601
$445$	5.06665e7			0.574965
$446$			7.79166e7i			0.878264i
$447$			9.67295e7i			1.08302i
$448$			1.35045e7i			0.150191i
$449$	1.20600e8			1.33232			0.666162	−	0.745807i	$-0.267936\pi$
$449$	1.20600e8			1.33232			0.666162	+	0.745807i	$0.267936\pi$
$450$			3.80479e7i			0.417535i
$451$	−1.42944e7	−	4.19541e7i	−0.155824	−	0.457346i
$452$	4.27637e7			0.463084
$453$			4.72070e7i			0.507822i
$454$	−9.06697e7			−0.968935
$455$	−1.34278e8			−1.42551
$456$	−2.92925e7			−0.308932
$457$			5.87263e7i			0.615296i	0.951500	+	0.307648i	$0.0995420\pi$
$457$			5.87263e7i			0.615296i	−0.951500	+	0.307648i	$0.900458\pi$
$458$			2.45396e7i			0.255430i
$459$		−	1.60971e8i		−	1.66460i
$460$	−1.23482e6			−0.0126862
$461$			4.94494e7i			0.504729i	0.967632	+	0.252364i	$0.0812081\pi$
$461$			4.94494e7i			0.504729i	−0.967632	+	0.252364i	$0.918792\pi$
$462$	−4.98888e7	+	1.69978e7i	−0.505915	+	0.172372i
$463$	−1.06727e8			−1.07531			−0.537653	−	0.843166i	$-0.680689\pi$
$463$	−1.06727e8			−1.07531			−0.537653	+	0.843166i	$0.680689\pi$
$464$			6.96150e6i			0.0696865i
$465$	1.86170e7			0.185162
$466$	−3.94121e7			−0.389468
$467$	3.59851e7			0.353324			0.176662	−	0.984272i	$-0.443470\pi$
$467$	3.59851e7			0.353324			0.176662	+	0.984272i	$0.443470\pi$
$468$		−	2.61300e7i		−	0.254919i
$469$		−	7.48681e7i		−	0.725735i
$470$		−	7.46339e7i		−	0.718857i
$471$	1.19630e8			1.14492
$472$			2.32653e7i			0.221250i
$473$	5.66539e7	+	1.66280e8i	0.535360	+	1.57129i
$474$	−9.05498e6			−0.0850262
$475$			1.45468e8i			1.35734i
$476$	−1.06870e8			−0.990908
$477$	1.01866e8			0.938586
$478$	−2.66851e7			−0.244335
$479$		−	9.11006e7i		−	0.828924i	−0.910067	−	0.414462i	$-0.863970\pi$
$479$		−	9.11006e7i		−	0.828924i	0.910067	−	0.414462i	$-0.136030\pi$
$480$		−	1.72935e7i		−	0.156372i
$481$			1.10034e8i			0.988759i
$482$	−3.50516e7			−0.313016
$483$		−	1.53680e6i		−	0.0136388i
$484$	−4.48971e7	+	3.46121e7i	−0.395988	+	0.305276i
$485$	−2.60021e8			−2.27921
$486$		−	8.03537e7i		−	0.699998i
$487$	2.02981e8			1.75739			0.878694	−	0.477386i	$-0.158416\pi$
$487$	2.02981e8			1.75739			0.878694	+	0.477386i	$0.158416\pi$
$488$	4.85725e7			0.417956
$489$	−1.18465e7			−0.101312
$490$			5.18995e7i			0.441138i
$491$		−	2.26588e7i		−	0.191422i	−0.995409	−	0.0957111i	$-0.969488\pi$
$491$		−	2.26588e7i		−	0.191422i	0.995409	−	0.0957111i	$-0.0305125\pi$
$492$			1.80995e7i			0.151975i
$493$	−5.50907e7			−0.459767
$494$		−	9.99027e7i		−	0.828698i
$495$	−9.75471e7	+	3.32356e7i	−0.804264	+	0.274024i
$496$	6.38563e6			0.0523310
$497$		−	6.67727e7i		−	0.543913i
$498$	−6.49530e7			−0.525910
$499$	1.96136e8			1.57854			0.789269	−	0.614048i	$-0.210460\pi$
$499$	1.96136e8			1.57854			0.789269	+	0.614048i	$0.210460\pi$
$500$	2.00304e6			0.0160243
$501$			1.20307e7i			0.0956708i
$502$		−	4.97058e7i		−	0.392912i
$503$			4.99226e7i			0.392277i	0.980576	+	0.196139i	$0.0628403\pi$
$503$			4.99226e7i			0.392277i	−0.980576	+	0.196139i	$0.937160\pi$
$504$	−3.28626e7			−0.256691
$505$		−	3.17567e8i		−	2.46582i
$506$	−533105.	−	1.56467e6i	−0.00411491	−	0.0120773i
$507$	2.36194e7			0.181236
$508$			6.92632e7i			0.528337i
$509$	−6.80263e7			−0.515850			−0.257925	−	0.966165i	$-0.583039\pi$
$509$	−6.80263e7			−0.515850			−0.257925	+	0.966165i	$0.583039\pi$
$510$	1.36854e8			1.03168
$511$	1.36427e8			1.02244
$512$		−	5.93164e6i		−	0.0441942i
$513$		−	1.89249e8i		−	1.40178i
$514$		−	3.33720e7i		−	0.245749i
$515$	2.19768e8			1.60895
$516$		−	7.17351e7i		−	0.522134i
$517$	9.45702e7	−	3.22213e7i	0.684357	−	0.233170i
$518$	1.38385e8			0.995632
$519$		−	1.09845e8i		−	0.785740i
$520$	5.89796e7			0.419461
$521$	−2.00252e7			−0.141600			−0.0708000	−	0.997491i	$-0.522555\pi$
$521$	−2.00252e7			−0.141600			−0.0708000	+	0.997491i	$0.522555\pi$
$522$	−1.69405e7			−0.119101
$523$			2.66789e8i			1.86493i	0.361262	+	0.932464i	$0.382346\pi$
$523$			2.66789e8i			1.86493i	−0.361262	+	0.932464i	$0.617654\pi$
$524$		−	8.92005e7i		−	0.619974i
$525$		−	1.06882e8i		−	0.738632i
$526$	−9.17581e7			−0.630503
$527$			5.05335e7i			0.345261i
$528$	2.19129e7	−	7.46602e6i	0.148867	−	0.0507210i
$529$	−1.47988e8			−0.999674
$530$			2.29928e8i			1.54441i
$531$	−5.66151e7			−0.378137
$532$	−1.25644e8			−0.834459
$533$	−6.17286e7			−0.407666
$534$		−	2.76969e7i		−	0.181889i
$535$		−	2.10144e8i		−	1.37232i
$536$			3.28846e7i			0.213550i
$537$	−1.83864e8			−1.18733
$538$			5.11160e7i			0.328254i
$539$	−6.57629e7	+	2.24063e7i	−0.419966	+	0.143088i
$540$	1.11727e8			0.709540
$541$			2.06398e8i			1.30351i	0.758431	+	0.651753i	$0.225966\pi$
$541$			2.06398e8i			1.30351i	−0.758431	+	0.651753i	$0.774034\pi$
$542$	−1.22840e7			−0.0771513
$543$	−6.05835e7			−0.378403
$544$	4.69408e7			0.291577
$545$			1.13057e8i			0.698408i
$546$			7.34032e7i			0.450959i
$547$			1.40391e8i			0.857781i	0.903357	+	0.428890i	$0.141095\pi$
$547$			1.40391e8i			0.857781i	−0.903357	+	0.428890i	$0.858905\pi$
$548$	9.48947e7			0.576634
$549$			1.18199e8i			0.714327i
$550$	−3.70767e7	−	1.08821e8i	−0.222850	−	0.654068i
$551$	−6.47685e7			−0.387177
$552$			675016.i			0.00401326i
$553$	−3.88392e7			−0.229665
$554$	−1.29522e7			−0.0761751
$555$	−1.77211e8			−1.03660
$556$		−	2.52538e7i		−	0.146927i
$557$		−	2.17888e8i		−	1.26086i	−0.776246	−	0.630430i	$-0.782878\pi$
$557$		−	2.17888e8i		−	1.26086i	0.776246	−	0.630430i	$-0.217122\pi$
$558$			1.55392e7i			0.0894387i
$559$	2.44654e8			1.40061
$560$		−	7.41762e7i		−	0.422377i
$561$	5.90833e7	+	1.73411e8i	0.334639	+	0.982170i
$562$	4.92836e7			0.277647
$563$			9.17850e7i			0.514335i	0.966367	+	0.257168i	$0.0827893\pi$
$563$			9.17850e7i			0.514335i	−0.966367	+	0.257168i	$0.917211\pi$
$564$	−4.07986e7			−0.227409
$565$	−2.34888e8			−1.30232
$566$	5.98220e7			0.329922
$567$			6.70580e6i			0.0367876i
$568$			2.93288e7i			0.160048i
$569$		−	2.89969e8i		−	1.57403i	−0.616931	−	0.787017i	$-0.711624\pi$
$569$		−	2.89969e8i		−	1.57403i	0.616931	−	0.787017i	$-0.288376\pi$
$570$	1.60895e8			0.868798
$571$		−	1.72236e8i		−	0.925160i	−0.886578	−	0.462580i	$-0.846924\pi$
$571$		−	1.72236e8i		−	0.925160i	0.886578	−	0.462580i	$-0.153076\pi$
$572$	2.54630e7	+	7.47343e7i	0.136057	+	0.399330i
$573$	−5.56029e7			−0.295552
$574$			7.76335e7i			0.410500i
$575$	3.35217e6			0.0176328
$576$	1.44344e7			0.0755321
$577$	1.38310e8			0.719988			0.359994	−	0.932955i	$-0.382779\pi$
$577$	1.38310e8			0.719988			0.359994	+	0.932955i	$0.382779\pi$
$578$			2.34929e8i			1.21662i
$579$		−	4.88383e7i		−	0.251608i
$580$		−	3.82374e7i		−	0.195977i
$581$	−2.78601e8			−1.42054
$582$			1.42141e8i			0.721024i
$583$	−2.91346e8	+	9.92657e7i	−1.47029	+	0.500949i
$584$	−5.99236e7			−0.300856
$585$			1.43524e8i			0.716900i
$586$	8.63949e6			0.0429334
$587$	8.51407e7			0.420942			0.210471	−	0.977600i	$-0.432500\pi$
$587$	8.51407e7			0.420942			0.210471	+	0.977600i	$0.432500\pi$
$588$	2.83708e7			0.139553
$589$			5.94108e7i			0.290750i
$590$		−	1.27789e8i		−	0.622212i
$591$			1.02118e8i			0.494699i
$592$	−6.07834e7			−0.292968
$593$			3.19267e8i			1.53105i	0.643406	+	0.765525i	$0.277521\pi$
$593$			3.19267e8i			1.53105i	−0.643406	+	0.765525i	$0.722479\pi$
$594$	4.82354e7	+	1.41572e8i	0.230148	+	0.675487i
$595$	5.87003e8			2.78670
$596$		−	1.82238e8i		−	0.860794i
$597$	8.26386e7			0.388383
$598$	−2.30215e6			−0.0107654
$599$	1.44229e7			0.0671076			0.0335538	−	0.999437i	$-0.489317\pi$
$599$	1.44229e7			0.0671076			0.0335538	+	0.999437i	$0.489317\pi$
$600$			4.69464e7i			0.217345i
$601$			7.86679e7i			0.362388i	0.983447	+	0.181194i	$0.0579963\pi$
$601$			7.86679e7i			0.362388i	−0.983447	+	0.181194i	$0.942004\pi$
$602$		−	3.07691e8i		−	1.41034i
$603$	−8.00234e7			−0.364977
$604$		−	8.89377e7i		−	0.403622i
$605$	2.46607e8	−	1.90114e8i	1.11362	−	0.858516i
$606$	−1.73598e8			−0.780058
$607$			3.71631e7i			0.166167i	0.996543	+	0.0830837i	$0.0264769\pi$
$607$			3.71631e7i			0.166167i	−0.996543	+	0.0830837i	$0.973523\pi$
$608$	5.51870e7			0.245542
$609$	4.75885e7			0.210693
$610$	−2.66794e8			−1.17540
$611$		−	1.39144e8i		−	0.610017i
$612$			1.14229e8i			0.498334i
$613$		−	2.11808e8i		−	0.919518i	−0.888044	−	0.459759i	$-0.847936\pi$
$613$		−	2.11808e8i		−	0.919518i	0.888044	−	0.459759i	$-0.152064\pi$
$614$	−4.34311e7			−0.187627
$615$		−	9.94151e7i		−	0.427393i
$616$	9.39903e7	−	3.20238e7i	0.402106	−	0.137003i
$617$	1.28156e8			0.545609			0.272805	−	0.962069i	$-0.412049\pi$
$617$	1.28156e8			0.545609			0.272805	+	0.962069i	$0.412049\pi$
$618$		−	1.20136e8i		−	0.508989i
$619$	−7.02259e7			−0.296091			−0.148046	−	0.988981i	$-0.547298\pi$
$619$	−7.02259e7			−0.296091			−0.148046	+	0.988981i	$0.547298\pi$
$620$	−3.50744e7			−0.147169
$621$	−4.36104e6			−0.0182102
$622$		−	1.24076e8i		−	0.515603i
$623$		−	1.18799e8i		−	0.491303i
$624$		−	3.22412e7i		−	0.132696i
$625$	−2.49578e8			−1.02227
$626$			1.74831e8i			0.712680i
$627$	6.94626e7	+	2.03874e8i	0.281805	+	0.827101i
$628$	−2.25382e8			−0.909996
$629$		−	4.81017e8i		−	1.93290i
$630$	1.80505e8			0.721883
$631$	9.23666e7			0.367643			0.183822	−	0.982960i	$-0.441153\pi$
$631$	9.23666e7			0.367643			0.183822	+	0.982960i	$0.441153\pi$
$632$	1.70595e7			0.0675796
$633$		−	8.40279e7i		−	0.331293i
$634$		−	2.76996e8i		−	1.08694i
$635$		−	3.80442e8i		−	1.48582i
$636$	1.25690e8			0.488573
$637$			9.67592e7i			0.374347i
$638$	4.84515e7	−	1.65081e7i	0.186571	−	0.0635674i
$639$	−7.13705e7			−0.273537
$640$			3.25808e7i			0.124286i
$641$	1.83403e8			0.696359			0.348179	−	0.937428i	$-0.386800\pi$
$641$	1.83403e8			0.696359			0.348179	+	0.937428i	$0.386800\pi$
$642$	−1.14875e8			−0.434131
$643$	−3.44975e8			−1.29764			−0.648820	−	0.760942i	$-0.724737\pi$
$643$	−3.44975e8			−1.29764			−0.648820	+	0.760942i	$0.724737\pi$
$644$			2.89532e6i			0.0108403i
$645$			3.94019e8i			1.46838i
$646$			4.36729e8i			1.62000i
$647$	−2.10601e7			−0.0777585			−0.0388793	−	0.999244i	$-0.512379\pi$
$647$	−2.10601e7			−0.0777585			−0.0388793	+	0.999244i	$0.512379\pi$
$648$		−	2.94542e6i		−	0.0108248i
$649$	1.61925e8	−	5.51699e7i	0.592350	−	0.201822i
$650$	−1.60112e8			−0.583019
$651$		−	4.36519e7i		−	0.158220i
$652$	2.23187e7			0.0805241
$653$	1.81407e7			0.0651502			0.0325751	−	0.999469i	$-0.489629\pi$
$653$	1.81407e7			0.0651502			0.0325751	+	0.999469i	$0.489629\pi$
$654$	6.18028e7			0.220940
$655$			4.89952e8i			1.74353i
$656$		−	3.40993e7i		−	0.120791i
$657$		−	1.45822e8i		−	0.514192i
$658$	−1.74996e8			−0.614258
$659$			1.83188e8i			0.640089i	0.947403	+	0.320044i	$0.103698\pi$
$659$			1.83188e8i			0.640089i	−0.947403	+	0.320044i	$0.896302\pi$
$660$	−1.20361e8	+	4.10087e7i	−0.418653	+	0.142641i
$661$	−9.60760e7			−0.332668			−0.166334	−	0.986070i	$-0.553193\pi$
$661$	−9.60760e7			−0.332668			−0.166334	+	0.986070i	$0.553193\pi$
$662$		−	1.39575e8i		−	0.481099i
$663$	2.55145e8			0.875480
$664$	1.22371e8			0.417998
$665$	6.90123e8			2.34672
$666$		−	1.47914e8i		−	0.500710i
$667$			1.49252e6i			0.00502972i
$668$		−	2.26658e7i		−	0.0760401i
$669$	−2.33951e8			−0.781353
$670$		−	1.80626e8i		−	0.600558i
$671$	−1.15182e8	−	3.38061e8i	−0.381256	−	1.11899i
$672$	−4.05484e7			−0.133618
$673$			2.46880e8i			0.809918i	0.914335	+	0.404959i	$0.132714\pi$
$673$			2.46880e8i			0.809918i	−0.914335	+	0.404959i	$0.867286\pi$
$674$	3.24363e8			1.05938
$675$	−3.03305e8			−0.986206
$676$	−4.44987e7			−0.144048
$677$			9.99216e7i			0.322028i	0.986952	+	0.161014i	$0.0514764\pi$
$677$			9.99216e7i			0.322028i	−0.986952	+	0.161014i	$0.948524\pi$
$678$			1.28402e8i			0.411985i
$679$			6.09680e8i			1.94757i
$680$	−2.57832e8			−0.819993
$681$		−	2.72244e8i		−	0.862018i
$682$	−1.51425e7	−	4.44435e7i	−0.0477359	−	0.140105i
$683$	2.69471e8			0.845765			0.422883	−	0.906184i	$-0.361018\pi$
$683$	2.69471e8			0.845765			0.422883	+	0.906184i	$0.361018\pi$
$684$			1.34295e8i			0.419655i
$685$	−5.21228e8			−1.62165
$686$	−1.52588e8			−0.472660
$687$	−7.36823e7			−0.227244
$688$			1.35148e8i			0.414998i
$689$			4.28668e8i			1.31058i
$690$		−	3.70766e6i		−	0.0112863i
$691$	5.36169e8			1.62505			0.812527	−	0.582923i	$-0.198091\pi$
$691$	5.36169e8			1.62505			0.812527	+	0.582923i	$0.198091\pi$
$692$			2.06947e8i			0.624514i
$693$	7.79285e7	+	2.28721e8i	0.234151	+	0.687238i
$694$	−4.01573e8			−1.20139
$695$			1.38712e8i			0.413198i
$696$	−2.09025e7			−0.0619970
$697$	2.69849e8			0.796935
$698$	4.31162e8			1.26787
$699$		−	1.18338e8i		−	0.346492i
$700$			2.01366e8i			0.587072i
$701$			3.77121e8i			1.09478i	0.836877	+	0.547390i	$0.184379\pi$
$701$			3.77121e8i			1.09478i	−0.836877	+	0.547390i	$0.815621\pi$
$702$	2.08299e8			0.602111
$703$		−	5.65518e8i		−	1.62772i
$704$	−4.12838e7	+	1.40659e7i	−0.118321	+	0.0403135i
$705$	2.24095e8			0.639535
$706$			3.87379e7i			0.110084i
$707$	−7.44608e8			−2.10702
$708$	−6.98561e7			−0.196836
$709$	−3.76660e8			−1.05684			−0.528422	−	0.848982i	$-0.677216\pi$
$709$	−3.76660e8			−1.05684			−0.528422	+	0.848982i	$0.677216\pi$
$710$		−	1.61095e8i		−	0.450097i
$711$			4.15137e7i			0.115500i
$712$			5.21807e7i			0.144567i
$713$	1.36906e6			0.00377706
$714$		−	3.20885e8i		−	0.881567i
$715$	−1.39861e8	−	4.10493e8i	−0.382629	−	1.12302i
$716$	3.46398e8			0.943705
$717$		−	8.01243e7i		−	0.217374i
$718$	1.04964e8			0.283575
$719$	−6.49391e8			−1.74711			−0.873554	−	0.486728i	$-0.838190\pi$
$719$	−6.49391e8			−1.74711			−0.873554	+	0.486728i	$0.838190\pi$
$720$	−7.92839e7			−0.212416
$721$		−	5.15296e8i		−	1.37484i
$722$			2.47318e8i			0.657120i
$723$		−	1.05245e8i		−	0.278476i
$724$	1.14139e8			0.300759
$725$			1.03803e8i			0.272393i
$726$	−1.03926e8	−	1.34808e8i	−0.271590	−	0.352293i
$727$	5.51243e8			1.43463			0.717314	−	0.696750i	$-0.245371\pi$
$727$	5.51243e8			1.43463			0.717314	+	0.696750i	$0.245371\pi$
$728$		−	1.38291e8i		−	0.358427i
$729$	2.53131e8			0.653375
$730$	3.29142e8			0.846088
$731$	−1.06951e9			−2.73801
$732$			1.45843e8i			0.371837i
$733$		−	7.28139e8i		−	1.84885i	−0.381361	−	0.924426i	$-0.624545\pi$
$733$		−	7.28139e8i		−	1.84885i	0.381361	−	0.924426i	$-0.375455\pi$
$734$			1.94879e8i			0.492807i
$735$	−1.55833e8			−0.392461
$736$		−	1.27173e6i		−	0.00318977i
$737$	2.28875e8	−	7.79807e7i	0.571735	−	0.194798i
$738$	8.29793e7			0.206443
$739$		−	2.49677e8i		−	0.618649i	−0.950957	−	0.309325i	$-0.899897\pi$
$739$		−	2.49677e8i		−	0.618649i	0.950957	−	0.309325i	$-0.100103\pi$
$740$	3.33865e8			0.823902
$741$	2.99967e8			0.737256
$742$	5.39118e8			1.31969
$743$		−	5.49838e8i		−	1.34050i	−0.742134	−	0.670252i	$-0.766186\pi$
$743$		−	5.49838e8i		−	1.34050i	0.742134	−	0.670252i	$-0.233814\pi$
$744$			1.91734e7i			0.0465566i
$745$			1.00098e9i			2.42078i
$746$	1.25510e7			0.0302317
$747$			2.97785e8i			0.714399i
$748$	−1.11313e8	−	3.26704e8i	−0.265974	−	0.780639i
$749$	−4.92730e8			−1.17264
$750$			6.01431e6i			0.0142561i
$751$	1.81933e8			0.429528			0.214764	−	0.976666i	$-0.431102\pi$
$751$	1.81933e8			0.429528			0.214764	+	0.976666i	$0.431102\pi$
$752$	7.68643e7			0.180747
$753$	1.49246e8			0.349557
$754$		−	7.12883e7i		−	0.166305i
$755$			4.88508e8i			1.13509i
$756$		−	2.61969e8i		−	0.606297i
$757$	2.89733e8			0.667897			0.333949	−	0.942591i	$-0.391619\pi$
$757$	2.89733e8			0.667897			0.333949	+	0.942591i	$0.391619\pi$
$758$			2.44865e8i			0.562236i
$759$	4.69806e6	−	1.60069e6i	0.0107447	−	0.00366086i
$760$	−3.03126e8			−0.690529
$761$		−	2.58513e8i		−	0.586581i	−0.956023	−	0.293290i	$-0.905250\pi$
$761$		−	2.58513e8i		−	0.586581i	0.956023	−	0.293290i	$-0.0947503\pi$
$762$	−2.07969e8			−0.470038
$763$	2.65088e8			0.596784
$764$	1.04756e8			0.234907
$765$		−	6.27423e8i		−	1.40145i
$766$			1.03952e8i			0.231284i
$767$		−	2.38245e8i		−	0.528005i
$768$	1.78103e7			0.0393176
$769$			1.83751e8i			0.404064i	0.979379	+	0.202032i	$0.0647545\pi$
$769$			1.83751e8i			0.404064i	−0.979379	+	0.202032i	$0.935246\pi$
$770$	−5.16261e8	+	1.75897e8i	−1.13083	+	0.385289i
$771$	1.00202e8			0.218632
$772$			9.20110e7i			0.199981i
$773$	−3.75387e6			−0.00812720			−0.00406360	−	0.999992i	$-0.501293\pi$
$773$	−3.75387e6			−0.00812720			−0.00406360	+	0.999992i	$0.501293\pi$
$774$	−3.28878e8			−0.709271
$775$	9.52162e7			0.204553
$776$		−	2.67792e8i		−	0.573077i
$777$			4.15512e8i			0.885770i
$778$		−	5.57928e7i		−	0.118478i
$779$	3.17254e8			0.671112
$780$			1.77091e8i			0.373176i
$781$	2.04126e8	−	6.95487e7i	0.428495	−	0.145994i
$782$	1.00640e7			0.0210450
$783$		−	1.35044e8i		−	0.281313i
$784$	−5.34505e7			−0.110918
$785$	1.23795e9			2.55915
$786$	2.67832e8			0.551563
$787$		−	6.46196e8i		−	1.32568i	−0.748759	−	0.662842i	$-0.769350\pi$
$787$		−	6.46196e8i		−	1.32568i	0.748759	−	0.662842i	$-0.230650\pi$
$788$		−	1.92390e8i		−	0.393192i
$789$		−	2.75512e8i		−	0.560930i
$790$	−9.37029e7			−0.190052
$791$			5.50749e8i			1.11282i
$792$	−3.42289e7	−	1.00462e8i	−0.0688997	−	0.202222i
$793$	−4.97400e8			−0.997439
$794$			4.99363e8i			0.997595i
$795$	−6.90378e8			−1.37400
$796$	−1.55691e8			−0.308690
$797$	−4.26209e8			−0.841875			−0.420937	−	0.907090i	$-0.638299\pi$
$797$	−4.26209e8			−0.841875			−0.420937	+	0.907090i	$0.638299\pi$
$798$		−	3.77256e8i		−	0.742381i
$799$			6.08276e8i			1.19250i
$800$		−	8.84468e7i		−	0.172748i
$801$	−1.26980e8			−0.247079
$802$		−	4.66559e8i		−	0.904447i
$803$	1.42099e8	+	4.17063e8i	0.274438	+	0.805481i
$804$	−9.87390e7			−0.189986
$805$		−	1.59032e7i		−	0.0304857i
$806$	−6.53913e7			−0.124886
$807$	−1.53480e8			−0.292033
$808$	3.27058e8			0.619998
$809$			4.48232e8i			0.846559i	0.905999	+	0.423280i	$0.139121\pi$
$809$			4.48232e8i			0.846559i	−0.905999	+	0.423280i	$0.860879\pi$
$810$			1.61783e7i			0.0304423i
$811$			5.87947e8i			1.10224i	0.834426	+	0.551119i	$0.185799\pi$
$811$			5.87947e8i			1.10224i	−0.834426	+	0.551119i	$0.814201\pi$
$812$	−8.96564e7			−0.167461
$813$		−	3.68839e7i		−	0.0686380i
$814$	1.44138e8	+	4.23047e8i	0.267242	+	0.784361i
$815$	−1.22590e8			−0.226455
$816$			1.40944e8i			0.259403i
$817$	−1.25740e9			−2.30572
$818$	−5.07120e8			−0.926511
$819$	3.36526e8			0.612585
$820$			1.87297e8i			0.339696i
$821$			6.93632e8i			1.25343i	0.779249	+	0.626714i	$0.215601\pi$
$821$			6.93632e8i			1.25343i	−0.779249	+	0.626714i	$0.784399\pi$
$822$			2.84930e8i			0.513005i
$823$	3.30681e8			0.593211			0.296606	−	0.955000i	$-0.404145\pi$
$823$	3.30681e8			0.593211			0.296606	+	0.955000i	$0.404145\pi$
$824$			2.26336e8i			0.404549i
$825$	3.26743e8	−	1.11326e8i	0.581896	−	0.198260i
$826$	−2.99631e8			−0.531676
$827$			4.07604e7i			0.0720646i	0.999351	+	0.0360323i	$0.0114719\pi$
$827$			4.07604e7i			0.0720646i	−0.999351	+	0.0360323i	$0.988528\pi$
$828$	3.09469e6			0.00545163
$829$	−2.93862e7			−0.0515798			−0.0257899	−	0.999667i	$-0.508210\pi$
$829$	−2.93862e7			−0.0515798			−0.0257899	+	0.999667i	$0.508210\pi$
$830$	−6.72148e8			−1.17552
$831$		−	3.88900e7i		−	0.0677696i
$832$			6.07422e7i			0.105468i
$833$		−	4.22987e8i		−	0.731800i
$834$	7.58267e7			0.130715
$835$			1.24497e8i			0.213845i
$836$	−1.30867e8	−	3.84097e8i	−0.223981	−	0.657388i
$837$	−1.23873e8			−0.211251
$838$		−	5.76170e8i		−	0.979082i
$839$	1.05633e9			1.78861			0.894305	−	0.447458i	$-0.147671\pi$
$839$	1.05633e9			1.78861			0.894305	+	0.447458i	$0.147671\pi$
$840$	2.22721e8			0.375770
$841$	5.48606e8			0.922301
$842$		−	2.98295e8i		−	0.499700i
$843$			1.47978e8i			0.247010i
$844$			1.58308e8i			0.263315i
$845$	2.44418e8			0.405101
$846$			1.87046e8i			0.308914i
$847$	−4.45766e8	−	5.78225e8i	−0.733595	−	0.951584i
$848$	−2.36799e8			−0.388323
$849$			1.79621e8i			0.293517i
$850$	6.99935e8			1.13973
$851$	−1.30318e7			−0.0211453
$852$	−8.80624e7			−0.142387
$853$			5.94560e8i			0.957962i	0.877825	+	0.478981i	$0.158994\pi$
$853$			5.94560e8i			0.957962i	−0.877825	+	0.478981i	$0.841006\pi$
$854$			6.25560e8i			1.00437i
$855$		−	7.37644e8i		−	1.18018i
$856$	2.16424e8			0.345051
$857$		−	7.06965e7i		−	0.112320i	−0.998422	−	0.0561598i	$-0.982114\pi$
$857$		−	7.06965e7i		−	0.112320i	0.998422	−	0.0561598i	$-0.0178856\pi$
$858$	−2.24396e8	+	7.64549e7i	−0.355266	+	0.121044i
$859$	1.00322e9			1.58277			0.791386	−	0.611317i	$-0.209360\pi$
$859$	1.00322e9			1.58277			0.791386	+	0.611317i	$0.209360\pi$
$860$		−	7.42330e8i		−	1.16708i
$861$	−2.33101e8			−0.365204
$862$	8.36025e6			0.0130526
$863$	1.96468e7			0.0305674			0.0152837	−	0.999883i	$-0.495135\pi$
$863$	1.96468e7			0.0305674			0.0152837	+	0.999883i	$0.495135\pi$
$864$			1.15066e8i			0.178404i
$865$		−	1.13670e9i		−	1.75630i
$866$		−	1.64469e8i		−	0.253238i
$867$	−7.05396e8			−1.08237
$868$			8.22399e7i			0.125754i
$869$	−4.04539e7	−	1.18733e8i	−0.0616455	−	0.180931i
$870$	1.14811e8			0.174352
$871$		−	3.36751e8i		−	0.509629i
$872$	−1.16436e8			−0.175605
$873$	6.51661e8			0.979443
$874$	1.18319e7			0.0177223
$875$			2.57970e7i			0.0385075i
$876$		−	1.79926e8i		−	0.267658i
$877$			5.09819e8i			0.755818i	0.925843	+	0.377909i	$0.123357\pi$
$877$			5.09819e8i			0.755818i	−0.925843	+	0.377909i	$0.876643\pi$
$878$	3.36931e8			0.497803
$879$			2.59408e7i			0.0381959i
$880$	2.26759e8	−	7.72601e7i	0.332749	−	0.113372i
$881$	−3.28419e8			−0.480287			−0.240144	−	0.970737i	$-0.577195\pi$
$881$	−3.28419e8			−0.480287			−0.240144	+	0.970737i	$0.577195\pi$
$882$		−	1.30070e8i		−	0.189570i
$883$	7.99892e8			1.16185			0.580924	−	0.813958i	$-0.302692\pi$
$883$	7.99892e8			1.16185			0.580924	+	0.813958i	$0.302692\pi$
$884$	−4.80691e8			−0.695840
$885$	3.83699e8			0.553555
$886$			4.86010e8i			0.698786i
$887$		−	3.53129e8i		−	0.506013i	−0.967465	−	0.253007i	$-0.918581\pi$
$887$		−	3.53129e8i		−	0.506013i	0.967465	−	0.253007i	$-0.0814195\pi$
$888$		−	1.82507e8i		−	0.260640i
$889$	−8.92033e8			−1.26963
$890$		−	2.86613e8i		−	0.406561i
$891$	−2.04999e7	+	6.98459e6i	−0.0289813	+	0.00987433i
$892$	4.40763e8			0.621027
$893$			7.15132e8i			1.00423i
$894$	5.47185e8			0.765810
$895$	−1.90266e9			−2.65395
$896$	7.63930e7			0.106201
$897$		−	6.91242e6i		−	0.00957751i
$898$		−	6.82219e8i		−	0.942095i
$899$			4.23942e7i			0.0583482i
$900$	2.15232e8			0.295242
$901$		−	1.87394e9i		−	2.56201i
$902$	−2.37328e8	+	8.08611e7i	−0.323393	+	0.110184i
$903$	9.23868e8			1.25472
$904$		−	2.41908e8i		−	0.327450i
$905$	−6.26931e8			−0.845813
$906$	2.67043e8			0.359085
$907$	−1.07465e8			−0.144028			−0.0720140	−	0.997404i	$-0.522943\pi$
$907$	−1.07465e8			−0.144028			−0.0720140	+	0.997404i	$0.522943\pi$
$908$			5.12905e8i			0.685140i
$909$			7.95881e8i			1.05964i
$910$			7.59592e8i			1.00799i
$911$	−2.64437e8			−0.349758			−0.174879	−	0.984590i	$-0.555953\pi$
$911$	−2.64437e8			−0.349758			−0.174879	+	0.984590i	$0.555953\pi$
$912$			1.65704e8i			0.218448i
$913$	−2.90183e8	−	8.51692e8i	−0.381294	−	1.11910i
$914$	3.32206e8			0.435080
$915$		−	8.01073e8i		−	1.04570i
$916$	1.38817e8			0.180616
$917$	1.14880e9			1.48983
$918$	−9.10589e8			−1.17705
$919$			1.39166e9i			1.79303i	0.443015	+	0.896514i	$0.353909\pi$
$919$			1.39166e9i			1.79303i	−0.443015	+	0.896514i	$0.646091\pi$
$920$			6.98521e6i			0.00897049i
$921$		−	1.30406e8i		−	0.166923i
$922$	2.79728e8			0.356897
$923$		−	3.00338e8i		−	0.381949i
$924$	9.61541e7	+	2.82214e8i	0.121886	+	0.357736i
$925$	−9.06341e8			−1.14516
$926$			6.03740e8i			0.760356i
$927$	−5.50778e8			−0.691413
$928$	3.93802e7			0.0492758
$929$	−1.25707e9			−1.56788			−0.783939	−	0.620838i	$-0.786793\pi$
$929$	−1.25707e9			−1.56788			−0.783939	+	0.620838i	$0.786793\pi$
$930$		−	1.05314e8i		−	0.130929i
$931$		−	4.97294e8i		−	0.616260i
$932$			2.22949e8i			0.275395i
$933$	3.72548e8			0.458709
$934$		−	2.03563e8i		−	0.249837i
$935$	6.11407e8	+	1.79449e9i	0.747990	+	2.19536i
$936$	−1.47814e8			−0.180255
$937$		−	2.03959e8i		−	0.247927i	−0.992287	−	0.123963i	$-0.960439\pi$
$937$		−	2.03959e8i		−	0.247927i	0.992287	−	0.123963i	$-0.0395605\pi$
$938$	−4.23518e8			−0.513172
$939$	−5.24944e8			−0.634040
$940$	−4.22193e8			−0.508309
$941$			9.16620e7i			0.110007i	0.998486	+	0.0550035i	$0.0175170\pi$
$941$			9.16620e7i			0.110007i	−0.998486	+	0.0550035i	$0.982483\pi$
$942$		−	6.76728e8i		−	0.809583i
$943$		−	7.31079e6i		−	0.00871824i
$944$	1.31608e8			0.156447
$945$			1.43892e9i			1.70507i
$946$	9.40622e8	−	3.20483e8i	1.11107	−	0.378557i
$947$	1.18415e9			1.39430			0.697150	−	0.716925i	$-0.254451\pi$
$947$	1.18415e9			1.39430			0.697150	+	0.716925i	$0.254451\pi$
$948$			5.12227e7i			0.0601226i
$949$	6.13640e8			0.717984
$950$	8.22893e8			0.959782
$951$	8.31704e8			0.967002
$952$			6.04546e8i			0.700678i
$953$		−	1.10796e9i		−	1.28011i	−0.768330	−	0.640054i	$-0.778912\pi$
$953$		−	1.10796e9i		−	1.28011i	0.768330	−	0.640054i	$-0.221088\pi$
$954$		−	5.76241e8i		−	0.663681i
$955$	−5.75391e8			−0.660622
$956$			1.50954e8i			0.172771i
$957$	4.95669e7	+	1.45480e8i	0.0565531	+	0.165984i
$958$	−5.15343e8			−0.586138
$959$			1.22214e9i			1.38569i
$960$	−9.78265e7			−0.110571
$961$	−8.48616e8			−0.956183
$962$	6.22444e8			0.699158
$963$			5.26658e8i			0.589726i
$964$			1.98282e8i			0.221336i
$965$		−	5.05389e8i		−	0.562398i
$966$	−8.69346e6			−0.00964409
$967$			2.09973e8i			0.232212i	0.993237	+	0.116106i	$0.0370412\pi$
$967$			2.09973e8i			0.232212i	−0.993237	+	0.116106i	$0.962959\pi$
$968$	1.95796e8	+	2.53977e8i	0.215862	+	0.280006i
$969$	−1.31132e9			−1.44124
$970$			1.47090e9i			1.61164i
$971$	6.83482e8			0.746568			0.373284	−	0.927717i	$-0.378232\pi$
$971$	6.83482e8			0.746568			0.373284	+	0.927717i	$0.378232\pi$
$972$	−4.54549e8			−0.494974
$973$	3.25241e8			0.353075
$974$		−	1.14823e9i		−	1.24266i
$975$		−	4.80749e8i		−	0.518686i
$976$		−	2.74767e8i		−	0.295540i
$977$	−1.51580e9			−1.62539			−0.812696	−	0.582688i	$-0.802001\pi$
$977$	−1.51580e9			−1.62539			−0.812696	+	0.582688i	$0.802001\pi$
$978$			6.70138e7i			0.0716387i
$979$	3.63174e8	−	1.23738e8i	0.387049	−	0.131873i
$980$	2.93588e8			0.311932
$981$		−	2.83342e8i		−	0.300126i
$982$	−1.28177e8			−0.135356
$983$	−2.07821e7			−0.0218790			−0.0109395	−	0.999940i	$-0.503482\pi$
$983$	−2.07821e7			−0.0218790			−0.0109395	+	0.999940i	$0.503482\pi$
$984$	1.02386e8			0.107462
$985$			1.05674e9i			1.10576i
$986$			3.11640e8i			0.325104i
$987$		−	5.25441e8i		−	0.546478i
$988$	−5.65135e8			−0.585978
$989$			2.89754e7i			0.0299530i
$990$	1.88009e8	+	5.51810e8i	0.193764	+	0.568701i
$991$	8.23277e7			0.0845912			0.0422956	−	0.999105i	$-0.486533\pi$
$991$	8.23277e7			0.0845912			0.0422956	+	0.999105i	$0.486533\pi$
$992$		−	3.61226e7i		−	0.0370036i
$993$	4.19087e8			0.428012
$994$	−3.77723e8			−0.384605
$995$	8.55162e8			0.868119
$996$			3.67430e8i			0.371874i
$997$			1.31565e8i			0.132756i	0.997795	+	0.0663782i	$0.0211444\pi$
$997$			1.31565e8i			0.132756i	−0.997795	+	0.0663782i	$0.978856\pi$
$998$		−	1.10951e9i		−	1.11619i
$999$	1.17912e9			1.18266

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.7.b.a.21.3	✓	6
3.2	odd	2		198.7.d.a.109.4		6
4.3	odd	2		176.7.h.e.65.2		6
11.10	odd	2	inner	22.7.b.a.21.6	yes	6
33.32	even	2		198.7.d.a.109.1		6
44.43	even	2		176.7.h.e.65.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.7.b.a.21.3	✓	6	1.1	even	1	trivial
22.7.b.a.21.6	yes	6	11.10	odd	2	inner
176.7.h.e.65.1		6	44.43	even	2
176.7.h.e.65.2		6	4.3	odd	2
198.7.d.a.109.1		6	33.32	even	2
198.7.d.a.109.4		6	3.2	odd	2

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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	22.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.65685i q^{2} +16.9852 q^{3} -32.0000 q^{4} +175.767 q^{5} -96.0828i q^{6} -412.125i q^{7} +181.019i q^{8} -440.503 q^{9} +O(q^{10})\)	\(q-5.65685i q^{2} +16.9852 q^{3} -32.0000 q^{4} +175.767 q^{5} -96.0828i q^{6} -412.125i q^{7} +181.019i q^{8} -440.503 q^{9} -994.286i q^{10} +(1259.88 - 429.258i) q^{11} -543.526 q^{12} -1853.71i q^{13} -2331.33 q^{14} +2985.43 q^{15} +1024.00 q^{16} +8103.56i q^{17} +2491.86i q^{18} +9527.12i q^{19} -5624.53 q^{20} -7000.02i q^{21} +(-2428.25 - 7126.96i) q^{22} +219.542 q^{23} +3074.65i q^{24} +15268.9 q^{25} -10486.1 q^{26} -19864.2 q^{27} +13188.0i q^{28} +6798.33i q^{29} -16888.1i q^{30} +6235.97 q^{31} -5792.62i q^{32} +(21399.3 - 7291.04i) q^{33} +45840.6 q^{34} -72437.7i q^{35} +14096.1 q^{36} -59358.7 q^{37} +53893.5 q^{38} -31485.6i q^{39} +31817.1i q^{40} -33300.1i q^{41} -39598.1 q^{42} +131981. i q^{43} +(-40316.2 + 13736.3i) q^{44} -77425.7 q^{45} -1241.92i q^{46} +75062.8 q^{47} +17392.8 q^{48} -52197.7 q^{49} -86373.8i q^{50} +137640. i q^{51} +59318.6i q^{52} -231249. q^{53} +112369. i q^{54} +(221445. - 75449.3i) q^{55} +74602.5 q^{56} +161820. i q^{57} +38457.2 q^{58} +128524. q^{59} -95533.7 q^{60} -268328. i q^{61} -35276.0i q^{62} +181542. i q^{63} -32768.0 q^{64} -325819. i q^{65} +(-41244.3 - 121053. i) q^{66} +181664. q^{67} -259314. i q^{68} +3728.97 q^{69} -409770. q^{70} +162021. q^{71} -79739.6i q^{72} +331034. i q^{73} +335784. i q^{74} +259345. q^{75} -304868. i q^{76} +(-176908. - 519228. i) q^{77} -178109. q^{78} -94241.5i q^{79} +179985. q^{80} -16271.3 q^{81} -188374. q^{82} -676011. i q^{83} +224001. i q^{84} +1.42433e6i q^{85} +746596. q^{86} +115471. i q^{87} +(77704.1 + 228063. i) q^{88} +288260. q^{89} +437986. i q^{90} -763958. q^{91} -7025.36 q^{92} +105919. q^{93} -424619. i q^{94} +1.67455e6i q^{95} -98388.8i q^{96} -1.47936e6 q^{97} +295275. i q^{98} +(-554981. + 189090. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 52 q^{3} - 192 q^{4} + 368 q^{5} - 346 q^{9}+O(q^{10}) \) 6 * q - 52 * q^3 - 192 * q^4 + 368 * q^5 - 346 * q^9	\( 6 q - 52 q^{3} - 192 q^{4} + 368 q^{5} - 346 q^{9} - 1166 q^{11} + 1664 q^{12} + 2208 q^{14} - 6512 q^{15} + 6144 q^{16} - 11776 q^{20} + 1056 q^{22} + 2156 q^{23} + 59862 q^{25} - 1824 q^{26} - 57472 q^{27} - 78468 q^{31} + 142208 q^{33} + 28704 q^{34} + 11072 q^{36} - 205920 q^{37} + 101472 q^{38} - 344160 q^{42} + 37312 q^{44} + 368716 q^{45} + 493460 q^{47} - 53248 q^{48} - 270762 q^{49} - 531700 q^{53} + 274956 q^{55} - 70656 q^{56} + 509184 q^{58} - 833380 q^{59} + 208384 q^{60} - 196608 q^{64} + 193248 q^{66} + 537420 q^{67} + 398860 q^{69} + 96096 q^{70} - 460372 q^{71} - 211428 q^{75} + 249744 q^{77} - 1866912 q^{78} + 376832 q^{80} + 485654 q^{81} + 428640 q^{82} + 1055808 q^{86} - 33792 q^{88} + 2377952 q^{89} - 5068656 q^{91} - 68992 q^{92} + 699868 q^{93} + 1351632 q^{97} - 2470930 q^{99}+O(q^{100}) \) 6 * q - 52 * q^3 - 192 * q^4 + 368 * q^5 - 346 * q^9 - 1166 * q^11 + 1664 * q^12 + 2208 * q^14 - 6512 * q^15 + 6144 * q^16 - 11776 * q^20 + 1056 * q^22 + 2156 * q^23 + 59862 * q^25 - 1824 * q^26 - 57472 * q^27 - 78468 * q^31 + 142208 * q^33 + 28704 * q^34 + 11072 * q^36 - 205920 * q^37 + 101472 * q^38 - 344160 * q^42 + 37312 * q^44 + 368716 * q^45 + 493460 * q^47 - 53248 * q^48 - 270762 * q^49 - 531700 * q^53 + 274956 * q^55 - 70656 * q^56 + 509184 * q^58 - 833380 * q^59 + 208384 * q^60 - 196608 * q^64 + 193248 * q^66 + 537420 * q^67 + 398860 * q^69 + 96096 * q^70 - 460372 * q^71 - 211428 * q^75 + 249744 * q^77 - 1866912 * q^78 + 376832 * q^80 + 485654 * q^81 + 428640 * q^82 + 1055808 * q^86 - 33792 * q^88 + 2377952 * q^89 - 5068656 * q^91 - 68992 * q^92 + 699868 * q^93 + 1351632 * q^97 - 2470930 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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