LMFDB - Embedded newform 165.4.c.b.34.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,4,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	165.c (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:	$9.73531515095$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 66x^{12} + 1705x^{10} + 22060x^{8} + 151880x^{6} + 537860x^{4} + 825344x^{2} + 262144 $ x^14 + 66x^12 + 1705x^10 + 22060x^8 + 151880x^6 + 537860x^4 + 825344x^2 + 262144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.8
Root			$-0.647712i$ of defining polynomial
Character	$\chi$	$=$	165.34
Dual form			165.4.c.b.34.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.352288i q^{2} +3.00000i q^{3} +7.87589 q^{4} +(10.7402 + 3.10602i) q^{5} -1.05686 q^{6} +19.8486i q^{7} +5.59288i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+0.352288i q^{2} +3.00000i q^{3} +7.87589 q^{4} +(10.7402 + 3.10602i) q^{5} -1.05686 q^{6} +19.8486i q^{7} +5.59288i q^{8} -9.00000 q^{9} +(-1.09421 + 3.78365i) q^{10} +11.0000 q^{11} +23.6277i q^{12} -25.5286i q^{13} -6.99242 q^{14} +(-9.31806 + 32.2207i) q^{15} +61.0368 q^{16} -77.3644i q^{17} -3.17059i q^{18} -96.1609 q^{19} +(84.5889 + 24.4627i) q^{20} -59.5458 q^{21} +3.87517i q^{22} +173.860i q^{23} -16.7786 q^{24} +(105.705 + 66.7188i) q^{25} +8.99340 q^{26} -27.0000i q^{27} +156.326i q^{28} +189.619 q^{29} +(-11.3510 - 3.28264i) q^{30} -275.829 q^{31} +66.2456i q^{32} +33.0000i q^{33} +27.2545 q^{34} +(-61.6502 + 213.179i) q^{35} -70.8830 q^{36} +269.805i q^{37} -33.8763i q^{38} +76.5857 q^{39} +(-17.3716 + 60.0689i) q^{40} +306.118 q^{41} -20.9773i q^{42} -477.907i q^{43} +86.6348 q^{44} +(-96.6621 - 27.9542i) q^{45} -61.2487 q^{46} -257.405i q^{47} +183.111i q^{48} -50.9676 q^{49} +(-23.5042 + 37.2387i) q^{50} +232.093 q^{51} -201.060i q^{52} -495.761i q^{53} +9.51177 q^{54} +(118.143 + 34.1662i) q^{55} -111.011 q^{56} -288.483i q^{57} +66.8003i q^{58} -102.064 q^{59} +(-73.3880 + 253.767i) q^{60} -585.738 q^{61} -97.1710i q^{62} -178.638i q^{63} +464.957 q^{64} +(79.2923 - 274.183i) q^{65} -11.6255 q^{66} +474.381i q^{67} -609.314i q^{68} -521.580 q^{69} +(-75.1003 - 21.7186i) q^{70} +453.954 q^{71} -50.3359i q^{72} -655.838i q^{73} -95.0491 q^{74} +(-200.156 + 317.116i) q^{75} -757.353 q^{76} +218.335i q^{77} +26.9802i q^{78} -482.235 q^{79} +(655.550 + 189.582i) q^{80} +81.0000 q^{81} +107.842i q^{82} -523.492i q^{83} -468.977 q^{84} +(240.295 - 830.912i) q^{85} +168.361 q^{86} +568.856i q^{87} +61.5217i q^{88} +750.979 q^{89} +(9.84791 - 34.0529i) q^{90} +506.707 q^{91} +1369.30i q^{92} -827.486i q^{93} +90.6806 q^{94} +(-1032.79 - 298.678i) q^{95} -198.737 q^{96} -572.084i q^{97} -17.9553i q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9}+O(q^{10}) $ 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9	$ 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9} - 48 q^{10} + 154 q^{11} - 84 q^{14} - 86 q^{16} - 116 q^{19} + 442 q^{20} - 204 q^{21} + 450 q^{24} + 162 q^{25} - 400 q^{26} - 128 q^{29} + 246 q^{30} - 696 q^{31} - 412 q^{34} + 672 q^{35} + 234 q^{36} + 480 q^{39} + 1612 q^{40} - 664 q^{41} - 286 q^{44} + 126 q^{45} - 656 q^{46} + 834 q^{49} + 1908 q^{50} - 972 q^{51} + 270 q^{54} - 154 q^{55} - 3236 q^{56} + 664 q^{59} + 108 q^{60} + 44 q^{61} - 1122 q^{64} - 2328 q^{65} - 330 q^{66} + 1944 q^{69} + 1220 q^{70} - 1032 q^{71} - 3256 q^{74} + 84 q^{75} + 5588 q^{76} - 3492 q^{79} - 510 q^{80} + 1134 q^{81} - 1008 q^{84} - 1068 q^{85} + 2540 q^{86} + 4452 q^{89} + 432 q^{90} + 2144 q^{91} - 9472 q^{94} - 932 q^{95} + 450 q^{96} - 1386 q^{99}+O(q^{100}) $ 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9 - 48 * q^10 + 154 * q^11 - 84 * q^14 - 86 * q^16 - 116 * q^19 + 442 * q^20 - 204 * q^21 + 450 * q^24 + 162 * q^25 - 400 * q^26 - 128 * q^29 + 246 * q^30 - 696 * q^31 - 412 * q^34 + 672 * q^35 + 234 * q^36 + 480 * q^39 + 1612 * q^40 - 664 * q^41 - 286 * q^44 + 126 * q^45 - 656 * q^46 + 834 * q^49 + 1908 * q^50 - 972 * q^51 + 270 * q^54 - 154 * q^55 - 3236 * q^56 + 664 * q^59 + 108 * q^60 + 44 * q^61 - 1122 * q^64 - 2328 * q^65 - 330 * q^66 + 1944 * q^69 + 1220 * q^70 - 1032 * q^71 - 3256 * q^74 + 84 * q^75 + 5588 * q^76 - 3492 * q^79 - 510 * q^80 + 1134 * q^81 - 1008 * q^84 - 1068 * q^85 + 2540 * q^86 + 4452 * q^89 + 432 * q^90 + 2144 * q^91 - 9472 * q^94 - 932 * q^95 + 450 * q^96 - 1386 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			0.352288i			0.124553i	0.998059	+	0.0622763i	$0.0198360\pi$
$2$			0.352288i			0.124553i	−0.998059	+	0.0622763i	$0.980164\pi$
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	7.87589			0.984487
$5$	10.7402	+	3.10602i	0.960636	+	0.277811i
$5$	10.7402	+	3.10602i	0.960636	+	0.277811i
$6$	−1.05686			−0.0719104
$7$			19.8486i			1.07172i	0.844305	+	0.535862i	$0.180013\pi$
$7$			19.8486i			1.07172i	−0.844305	+	0.535862i	$0.819987\pi$
$8$			5.59288i			0.247173i
$9$	−9.00000			−0.333333
$10$	−1.09421	+	3.78365i	−0.0346020	+	0.119650i
$11$	11.0000			0.301511
$11$	11.0000			0.301511
$12$			23.6277i			0.568394i
$13$		−	25.5286i		−	0.544643i	−0.962206	−	0.272321i	$-0.912209\pi$
$13$		−	25.5286i		−	0.544643i	0.962206	−	0.272321i	$-0.0877913\pi$
$14$	−6.99242			−0.133486
$15$	−9.31806	+	32.2207i	−0.160394	+	0.554623i
$16$	61.0368			0.953701
$17$		−	77.3644i		−	1.10374i	−0.833929	−	0.551871i	$-0.813914\pi$
$17$		−	77.3644i		−	1.10374i	0.833929	−	0.551871i	$-0.186086\pi$
$18$		−	3.17059i		−	0.0415175i
$19$	−96.1609			−1.16110			−0.580548	−	0.814226i	$-0.697162\pi$
$19$	−96.1609			−1.16110			−0.580548	+	0.814226i	$0.697162\pi$
$20$	84.5889	+	24.4627i	0.945733	+	0.273501i
$21$	−59.5458			−0.618760
$22$			3.87517i			0.0375540i
$23$			173.860i			1.57619i	0.615556	+	0.788094i	$0.288932\pi$
$23$			173.860i			1.57619i	−0.615556	+	0.788094i	$0.711068\pi$
$24$	−16.7786			−0.142705
$25$	105.705	+	66.7188i	0.845642	+	0.533750i
$26$	8.99340			0.0678366
$27$		−	27.0000i		−	0.192450i
$28$			156.326i			1.05510i
$29$	189.619			1.21418			0.607091	−	0.794632i	$-0.292336\pi$
$29$	189.619			1.21418			0.607091	+	0.794632i	$0.292336\pi$
$30$	−11.3510	−	3.28264i	−0.0690797	−	0.0199775i
$31$	−275.829			−1.59807			−0.799037	−	0.601282i	$-0.794657\pi$
$31$	−275.829			−1.59807			−0.799037	+	0.601282i	$0.794657\pi$
$32$			66.2456i			0.365959i
$33$			33.0000i			0.174078i
$34$	27.2545			0.137474
$35$	−61.6502	+	213.179i	−0.297737	+	1.02954i
$36$	−70.8830			−0.328162
$37$			269.805i			1.19880i	0.800449	+	0.599401i	$0.204595\pi$
$37$			269.805i			1.19880i	−0.800449	+	0.599401i	$0.795405\pi$
$38$		−	33.8763i		−	0.144618i
$39$	76.5857			0.314450
$40$	−17.3716	+	60.0689i	−0.0686673	+	0.237443i
$41$	306.118			1.16604			0.583020	−	0.812458i	$-0.301871\pi$
$41$	306.118			1.16604			0.583020	+	0.812458i	$0.301871\pi$
$42$		−	20.9773i		−	0.0770682i
$43$		−	477.907i		−	1.69489i	−0.530887	−	0.847443i	$-0.678141\pi$
$43$		−	477.907i		−	1.69489i	0.530887	−	0.847443i	$-0.321859\pi$
$44$	86.6348			0.296834
$45$	−96.6621	−	27.9542i	−0.320212	−	0.0926036i
$46$	−61.2487			−0.196318
$47$		−	257.405i		−	0.798859i	−0.916764	−	0.399429i	$-0.869208\pi$
$47$		−	257.405i		−	0.798859i	0.916764	−	0.399429i	$-0.130792\pi$
$48$			183.111i			0.550619i
$49$	−50.9676			−0.148594
$50$	−23.5042	+	37.2387i	−0.0664799	+	0.105327i
$51$	232.093			0.637246
$52$		−	201.060i		−	0.536193i
$53$		−	495.761i		−	1.28487i	−0.766341	−	0.642434i	$-0.777925\pi$
$53$		−	495.761i		−	1.28487i	0.766341	−	0.642434i	$-0.222075\pi$
$54$	9.51177			0.0239701
$55$	118.143	+	34.1662i	0.289643	+	0.0837631i
$56$	−111.011			−0.264901
$57$		−	288.483i		−	0.670359i
$58$			66.8003i			0.151229i
$59$	−102.064			−0.225214			−0.112607	−	0.993640i	$-0.535920\pi$
$59$	−102.064			−0.225214			−0.112607	+	0.993640i	$0.535920\pi$
$60$	−73.3880	+	253.767i	−0.157906	+	0.546019i
$61$	−585.738			−1.22944			−0.614721	−	0.788744i	$-0.710732\pi$
$61$	−585.738			−1.22944			−0.614721	+	0.788744i	$0.710732\pi$
$62$		−	97.1710i		−	0.199044i
$63$		−	178.638i		−	0.357242i
$64$	464.957			0.908120
$65$	79.2923	−	274.183i	0.151308	−	0.523203i
$66$	−11.6255			−0.0216818
$67$			474.381i			0.864997i	0.901635	+	0.432499i	$0.142368\pi$
$67$			474.381i			0.864997i	−0.901635	+	0.432499i	$0.857632\pi$
$68$		−	609.314i		−	1.08662i
$69$	−521.580			−0.910012
$70$	−75.1003	−	21.7186i	−0.128231	−	0.0370839i
$71$	453.954			0.758794			0.379397	−	0.925234i	$-0.376131\pi$
$71$	453.954			0.758794			0.379397	+	0.925234i	$0.376131\pi$
$72$		−	50.3359i		−	0.0823909i
$73$		−	655.838i		−	1.05151i	−0.850637	−	0.525753i	$-0.823784\pi$
$73$		−	655.838i		−	1.05151i	0.850637	−	0.525753i	$-0.176216\pi$
$74$	−95.0491			−0.149314
$75$	−200.156	+	317.116i	−0.308161	+	0.488232i
$76$	−757.353			−1.14308
$77$			218.335i			0.323137i
$78$			26.9802i			0.0391655i
$79$	−482.235			−0.686781			−0.343390	−	0.939193i	$-0.611575\pi$
$79$	−482.235			−0.686781			−0.343390	+	0.939193i	$0.611575\pi$
$80$	655.550	+	189.582i	0.916159	+	0.264948i
$81$	81.0000			0.111111
$82$			107.842i			0.145233i
$83$		−	523.492i		−	0.692297i	−0.938180	−	0.346149i	$-0.887489\pi$
$83$		−	523.492i		−	0.692297i	0.938180	−	0.346149i	$-0.112511\pi$
$84$	−468.977			−0.609161
$85$	240.295	−	830.912i	0.306632	−	1.06029i
$86$	168.361			0.211102
$87$			568.856i			0.701008i
$88$			61.5217i			0.0745254i
$89$	750.979			0.894423			0.447211	−	0.894428i	$-0.352417\pi$
$89$	750.979			0.894423			0.447211	+	0.894428i	$0.352417\pi$
$90$	9.84791	−	34.0529i	0.0115340	−	0.0398832i
$91$	506.707			0.583707
$92$			1369.30i			1.55174i
$93$		−	827.486i		−	0.922648i
$94$	90.6806			0.0994999
$95$	−1032.79	−	298.678i	−1.11539	−	0.322565i
$96$	−198.737			−0.211286
$97$		−	572.084i		−	0.598829i	−0.954123	−	0.299414i	$-0.903209\pi$
$97$		−	572.084i		−	0.598829i	0.954123	−	0.299414i	$-0.0967913\pi$
$98$		−	17.9553i		−	0.0185077i
$99$	−99.0000			−0.100504
$100$	832.524	+	525.470i	0.832524	+	0.525470i
$101$	79.5187			0.0783407			0.0391703	−	0.999233i	$-0.487529\pi$
$101$	79.5187			0.0783407			0.0391703	+	0.999233i	$0.487529\pi$
$102$			81.7636i			0.0793706i
$103$		−	1026.44i		−	0.981925i	−0.871181	−	0.490963i	$-0.836645\pi$
$103$		−	1026.44i		−	0.981925i	0.871181	−	0.490963i	$-0.163355\pi$
$104$	142.778			0.134621
$105$	−639.536	−	184.951i	−0.594403	−	0.171898i
$106$	174.650			0.160034
$107$		−	1087.33i		−	0.982397i	−0.871048	−	0.491199i	$-0.836559\pi$
$107$		−	1087.33i		−	0.982397i	0.871048	−	0.491199i	$-0.163441\pi$
$108$		−	212.649i		−	0.189465i
$109$	−1330.39			−1.16907			−0.584534	−	0.811369i	$-0.698723\pi$
$109$	−1330.39			−1.16907			−0.584534	+	0.811369i	$0.698723\pi$
$110$	−12.0363	+	41.6202i	−0.0104329	+	0.0360757i
$111$	−809.416			−0.692129
$112$			1211.50i			1.02210i
$113$		−	1460.20i		−	1.21561i	−0.794086	−	0.607805i	$-0.792050\pi$
$113$		−	1460.20i		−	1.21561i	0.794086	−	0.607805i	$-0.207950\pi$
$114$	101.629			0.0834950
$115$	−540.012	+	1867.30i	−0.437882	+	1.51414i
$116$	1493.42			1.19535
$117$			229.757i			0.181548i
$118$		−	35.9560i		−	0.0280510i
$119$	1535.58			1.18291
$120$	−180.207	−	52.1148i	−0.137088	−	0.0396451i
$121$	121.000			0.0909091
$122$		−	206.348i		−	0.153130i
$123$			918.354i			0.673213i
$124$	−2172.40			−1.57328
$125$	928.070	+	1044.90i	0.664073	+	0.747668i
$126$	62.9318			0.0444953
$127$			1022.85i			0.714674i	0.933975	+	0.357337i	$0.116315\pi$
$127$			1022.85i			0.714674i	−0.933975	+	0.357337i	$0.883685\pi$
$128$			693.763i			0.479067i
$129$	1433.72			0.978542
$130$	96.5913	+	27.9337i	0.0651663	+	0.0188457i
$131$	1308.85			0.872936			0.436468	−	0.899720i	$-0.356229\pi$
$131$	1308.85			0.872936			0.436468	+	0.899720i	$0.356229\pi$
$132$			259.904i			0.171377i
$133$		−	1908.66i		−	1.24438i
$134$	−167.118			−0.107738
$135$	83.8625	−	289.986i	0.0534647	−	0.184874i
$136$	432.690			0.272815
$137$			1405.87i			0.876725i	0.898798	+	0.438363i	$0.144441\pi$
$137$			1405.87i			0.876725i	−0.898798	+	0.438363i	$0.855559\pi$
$138$		−	183.746i		−	0.113344i
$139$	725.138			0.442485			0.221242	−	0.975219i	$-0.428989\pi$
$139$	725.138			0.442485			0.221242	+	0.975219i	$0.428989\pi$
$140$	−485.550	+	1678.97i	−0.293118	+	1.01357i
$141$	772.215			0.461221
$142$			159.922i			0.0945098i
$143$		−	280.814i		−	0.164216i
$144$	−549.332			−0.317900
$145$	2036.55	+	588.959i	1.16639	+	0.337313i
$146$	231.044			0.130968
$147$		−	152.903i		−	0.0857905i
$148$			2124.96i			1.18021i
$149$	−2812.26			−1.54624			−0.773118	−	0.634262i	$-0.781304\pi$
$149$	−2812.26			−1.54624			−0.773118	+	0.634262i	$0.781304\pi$
$150$	−111.716	−	70.5126i	−0.0608105	−	0.0383822i
$151$	−469.633			−0.253100			−0.126550	−	0.991960i	$-0.540390\pi$
$151$	−469.633			−0.253100			−0.126550	+	0.991960i	$0.540390\pi$
$152$		−	537.817i		−	0.286992i
$153$			696.279i			0.367914i
$154$	−76.9167			−0.0402475
$155$	−2962.46	−	856.729i	−1.53517	−	0.443962i
$156$	603.181			0.309571
$157$			276.945i			0.140781i	0.997520	+	0.0703906i	$0.0224246\pi$
$157$			276.945i			0.140781i	−0.997520	+	0.0703906i	$0.977575\pi$
$158$		−	169.885i		−	0.0855402i
$159$	1487.28			0.741819
$160$	−205.760	+	711.493i	−0.101667	+	0.351553i
$161$	−3450.88			−1.68924
$162$			28.5353i			0.0138392i
$163$			2654.73i			1.27567i	0.770172	+	0.637836i	$0.220170\pi$
$163$			2654.73i			1.27567i	−0.770172	+	0.637836i	$0.779830\pi$
$164$	2410.95			1.14795
$165$	−102.499	+	354.428i	−0.0483607	+	0.167225i
$166$	184.420			0.0862274
$167$			3219.81i			1.49196i	0.665970	+	0.745978i	$0.268018\pi$
$167$			3219.81i			1.49196i	−0.665970	+	0.745978i	$0.731982\pi$
$168$		−	333.033i		−	0.152941i
$169$	1545.29			0.703365
$170$	292.720	+	84.6531i	0.132062	+	0.0381917i
$171$	865.449			0.387032
$172$		−	3763.94i		−	1.66859i
$173$		−	2540.33i		−	1.11640i	−0.829706	−	0.558201i	$-0.811492\pi$
$173$		−	2540.33i		−	1.11640i	0.829706	−	0.558201i	$-0.188508\pi$
$174$	−200.401			−0.0873123
$175$	−1324.28	+	2098.10i	−0.572033	+	0.906296i
$176$	671.405			0.287552
$177$		−	306.193i		−	0.130028i
$178$			264.561i			0.111403i
$179$	86.1324			0.0359656			0.0179828	−	0.999838i	$-0.494276\pi$
$179$	86.1324			0.0359656			0.0179828	+	0.999838i	$0.494276\pi$
$180$	−761.300	−	220.164i	−0.315244	−	0.0911670i
$181$	1745.36			0.716748			0.358374	−	0.933578i	$-0.383331\pi$
$181$	1745.36			0.716748			0.358374	+	0.933578i	$0.383331\pi$
$182$			178.507i			0.0727021i
$183$		−	1757.21i		−	0.709819i
$184$	−972.378			−0.389591
$185$	−838.020	+	2897.77i	−0.333040	+	1.15161i
$186$	291.513			0.114918
$187$		−	851.008i		−	0.332791i
$188$		−	2027.29i		−	0.786466i
$189$	535.913			0.206253
$190$	105.221	−	363.840i	0.0401763	−	0.138925i
$191$	−5019.02			−1.90138			−0.950690	−	0.310144i	$-0.899623\pi$
$191$	−5019.02			−1.90138			−0.950690	+	0.310144i	$0.899623\pi$
$192$			1394.87i			0.524303i
$193$		−	4275.03i		−	1.59442i	−0.603700	−	0.797211i	$-0.706308\pi$
$193$		−	4275.03i		−	1.59442i	0.603700	−	0.797211i	$-0.293692\pi$
$194$	201.538			0.0745856
$195$	822.549	+	237.877i	0.302071	+	0.0873575i
$196$	−401.415			−0.146288
$197$			2006.68i			0.725735i	0.931841	+	0.362867i	$0.118202\pi$
$197$			2006.68i			0.725735i	−0.931841	+	0.362867i	$0.881798\pi$
$198$		−	34.8765i		−	0.0125180i
$199$	3668.78			1.30690			0.653450	−	0.756970i	$-0.273321\pi$
$199$	3668.78			1.30690			0.653450	+	0.756970i	$0.273321\pi$
$200$	−373.150	+	591.197i	−0.131929	+	0.209020i
$201$	−1423.14			−0.499406
$202$			28.0135i			0.00975753i
$203$			3763.67i			1.30127i
$204$	1827.94			0.627360
$205$	3287.78	+	950.809i	1.12014	+	0.323938i
$206$	361.603			0.122301
$207$		−	1564.74i		−	0.525396i
$208$		−	1558.18i		−	0.519426i
$209$	−1057.77			−0.350084
$210$	65.1558	−	225.301i	0.0214104	−	0.0740344i
$211$	1600.30			0.522129			0.261064	−	0.965321i	$-0.415927\pi$
$211$	1600.30			0.522129			0.261064	+	0.965321i	$0.415927\pi$
$212$		−	3904.56i		−	1.26494i
$213$			1361.86i			0.438090i
$214$	383.054			0.122360
$215$	1484.39	−	5132.83i	0.470858	−	1.62817i
$216$	151.008			0.0475684
$217$		−	5474.81i		−	1.71269i
$218$		−	468.681i		−	0.145610i
$219$	1967.51			0.607088
$220$	930.478	+	269.089i	0.285149	+	0.0824637i
$221$	−1975.00			−0.601145
$222$		−	285.147i		−	0.0862064i
$223$		−	3904.42i		−	1.17246i	−0.810143	−	0.586232i	$-0.800611\pi$
$223$		−	3904.42i		−	1.17246i	0.810143	−	0.586232i	$-0.199389\pi$
$224$	−1314.88			−0.392207
$225$	−951.348	−	600.469i	−0.281881	−	0.177917i
$226$	514.410			0.151407
$227$			1364.98i			0.399107i	0.979887	+	0.199553i	$0.0639491\pi$
$227$			1364.98i			0.399107i	−0.979887	+	0.199553i	$0.936051\pi$
$228$		−	2272.06i		−	0.659960i
$229$	−5045.66			−1.45601			−0.728005	−	0.685571i	$-0.759552\pi$
$229$	−5045.66			−1.45601			−0.728005	+	0.685571i	$0.759552\pi$
$230$	−657.826	−	190.240i	−0.188590	−	0.0545393i
$231$	−655.004			−0.186563
$232$			1060.51i			0.300113i
$233$			6083.69i			1.71054i	0.518182	+	0.855270i	$0.326609\pi$
$233$			6083.69i			1.71054i	−0.518182	+	0.855270i	$0.673391\pi$
$234$	−80.9406			−0.0226122
$235$	799.505	−	2764.59i	0.221932	−	0.767412i
$236$	−803.848			−0.221720
$237$		−	1446.70i		−	0.396513i
$238$			540.965i			0.147334i
$239$	−3413.30			−0.923799			−0.461900	−	0.886932i	$-0.652832\pi$
$239$	−3413.30			−0.923799			−0.461900	+	0.886932i	$0.652832\pi$
$240$	−568.745	+	1966.65i	−0.152968	+	0.528945i
$241$	979.432			0.261787			0.130894	−	0.991396i	$-0.458215\pi$
$241$	979.432			0.261787			0.130894	+	0.991396i	$0.458215\pi$
$242$			42.6268i			0.0113230i
$243$			243.000i			0.0641500i
$244$	−4613.21			−1.21037
$245$	−547.404	−	158.306i	−0.142744	−	0.0412809i
$246$	−323.525			−0.0838504
$247$			2454.85i			0.632383i
$248$		−	1542.68i		−	0.395000i
$249$	1570.48			0.399698
$250$	−368.105	+	326.948i	−0.0931239	+	0.0827119i
$251$	−2414.09			−0.607075			−0.303537	−	0.952820i	$-0.598168\pi$
$251$	−2414.09			−0.607075			−0.303537	+	0.952820i	$0.598168\pi$
$252$		−	1406.93i		−	0.351700i
$253$			1912.46i			0.475238i
$254$	−360.339			−0.0890145
$255$	2492.73	+	720.886i	0.612161	+	0.177034i
$256$	3475.25			0.848451
$257$		−	2888.26i		−	0.701029i	−0.936557	−	0.350514i	$-0.886007\pi$
$257$		−	2888.26i		−	0.701029i	0.936557	−	0.350514i	$-0.113993\pi$
$258$			505.082i			0.121880i
$259$	−5355.26			−1.28479
$260$	624.497	−	2159.44i	0.148960	−	0.515086i
$261$	−1706.57			−0.404727
$262$			461.091i			0.108726i
$263$		−	3916.08i		−	0.918158i	−0.888395	−	0.459079i	$-0.848179\pi$
$263$		−	3916.08i		−	0.918158i	0.888395	−	0.459079i	$-0.151821\pi$
$264$	−184.565			−0.0430273
$265$	1539.84	−	5324.59i	0.356950	−	1.23429i
$266$	672.398			0.154990
$267$			2252.94i			0.516395i
$268$			3736.17i			0.851578i
$269$	3495.41			0.792263			0.396131	−	0.918194i	$-0.370353\pi$
$269$	3495.41			0.792263			0.396131	+	0.918194i	$0.370353\pi$
$270$	102.159	+	29.5437i	0.0230266	+	0.00665917i
$271$	774.974			0.173713			0.0868567	−	0.996221i	$-0.472318\pi$
$271$	774.974			0.173713			0.0868567	+	0.996221i	$0.472318\pi$
$272$		−	4722.08i		−	1.05264i
$273$			1520.12i			0.337003i
$274$	−495.270			−0.109198
$275$	1162.76	+	733.906i	0.254971	+	0.160932i
$276$	−4107.91			−0.895895
$277$			7491.71i			1.62503i	0.582940	+	0.812515i	$0.301902\pi$
$277$			7491.71i			1.62503i	−0.582940	+	0.812515i	$0.698098\pi$
$278$			255.457i			0.0551126i
$279$	2482.46			0.532691
$280$	−1192.28	−	344.802i	−0.254474	−	0.0735924i
$281$	−125.514			−0.0266461			−0.0133230	−	0.999911i	$-0.504241\pi$
$281$	−125.514			−0.0266461			−0.0133230	+	0.999911i	$0.504241\pi$
$282$			272.042i			0.0574463i
$283$		−	8.28147i		−	0.00173951i	−1.00000		0.000869757i	$-0.999723\pi$
$283$		−	8.28147i		−	0.00173951i	1.00000		0.000869757i	$-0.000276852\pi$
$284$	3575.29			0.747023
$285$	896.033	−	3098.37i	0.186233	−	0.643971i
$286$	98.9274			0.0204535
$287$			6076.02i			1.24967i
$288$		−	596.210i		−	0.121986i
$289$	−1072.25			−0.218247
$290$	−207.483	+	717.451i	−0.0420132	+	0.145276i
$291$	1716.25			0.345734
$292$		−	5165.31i		−	1.03519i
$293$		−	3055.93i		−	0.609316i	−0.952462	−	0.304658i	$-0.901458\pi$
$293$		−	3055.93i		−	0.609316i	0.952462	−	0.304658i	$-0.0985421\pi$
$294$	53.8658			0.0106854
$295$	−1096.19	−	317.014i	−0.216349	−	0.0625670i
$296$	−1508.99			−0.296312
$297$		−	297.000i		−	0.0580259i
$298$		−	990.724i		−	0.192588i
$299$	4438.40			0.858458
$300$	−1576.41	+	2497.57i	−0.303380	+	0.480658i
$301$	9485.78			1.81645
$302$		−	165.446i		−	0.0315243i
$303$			238.556i			0.0452300i
$304$	−5869.36			−1.10734
$305$	−6290.96	−	1819.31i	−1.18105	−	0.341553i
$306$	−245.291			−0.0458246
$307$			8063.04i			1.49896i	0.662024	+	0.749482i	$0.269698\pi$
$307$			8063.04i			1.49896i	−0.662024	+	0.749482i	$0.730302\pi$
$308$			1719.58i			0.318124i
$309$	3079.33			0.566915
$310$	301.815	−	1043.64i	0.0552966	−	0.191209i
$311$	−6633.87			−1.20956			−0.604778	−	0.796394i	$-0.706738\pi$
$311$	−6633.87			−1.20956			−0.604778	+	0.796394i	$0.706738\pi$
$312$			428.335i			0.0777234i
$313$			4751.78i			0.858104i	0.903280	+	0.429052i	$0.141152\pi$
$313$			4751.78i			0.858104i	−0.903280	+	0.429052i	$0.858848\pi$
$314$	−97.5644			−0.0175346
$315$	554.852	−	1918.61i	0.0992456	−	0.343179i
$316$	−3798.03			−0.676126
$317$		−	1207.20i		−	0.213890i	−0.994265	−	0.106945i	$-0.965893\pi$
$317$		−	1207.20i		−	0.213890i	0.994265	−	0.106945i	$-0.0341069\pi$
$318$			523.951i			0.0923954i
$319$	2085.80			0.366090
$320$	4993.75	+	1444.17i	0.872372	+	0.252285i
$321$	3262.00			0.567187
$322$		−	1215.70i		−	0.210399i
$323$			7439.43i			1.28155i
$324$	637.947			0.109387
$325$	1703.23	−	2698.51i	0.290703	−	0.460573i
$326$	−935.230			−0.158888
$327$		−	3991.18i		−	0.674962i
$328$			1712.08i			0.288213i
$329$	5109.13			0.856157
$330$	−124.861	−	36.1090i	−0.0208283	−	0.00602344i
$331$	2437.37			0.404744			0.202372	−	0.979309i	$-0.435135\pi$
$331$	2437.37			0.404744			0.202372	+	0.979309i	$0.435135\pi$
$332$		−	4122.97i		−	0.681558i
$333$		−	2428.25i		−	0.399601i
$334$	−1134.30			−0.185827
$335$	−1473.44	+	5094.96i	−0.240306	+	0.830947i
$336$	−3634.49			−0.590112
$337$		−	4057.48i		−	0.655861i	−0.944702	−	0.327930i	$-0.893649\pi$
$337$		−	4057.48i		−	0.655861i	0.944702	−	0.327930i	$-0.106351\pi$
$338$			544.387i			0.0876058i
$339$	4380.59			0.701833
$340$	1892.54	−	6544.17i	0.301875	−	1.04385i
$341$	−3034.11			−0.481837
$342$			304.887i			0.0482058i
$343$			5796.44i			0.912473i
$344$	2672.88			0.418930
$345$	−5601.89	−	1620.04i	−0.874190	−	0.252811i
$346$	894.926			0.139051
$347$			7263.85i			1.12376i	0.827219	+	0.561879i	$0.189921\pi$
$347$			7263.85i			1.12376i	−0.827219	+	0.561879i	$0.810079\pi$
$348$			4480.25i			0.690133i
$349$	−5331.58			−0.817745			−0.408872	−	0.912592i	$-0.634078\pi$
$349$	−5331.58			−0.817745			−0.408872	+	0.912592i	$0.634078\pi$
$350$	−739.136	−	466.526i	−0.112881	−	0.0712482i
$351$	−689.272			−0.104817
$352$			728.702i			0.110341i
$353$			6448.09i			0.972231i	0.873895	+	0.486115i	$0.161586\pi$
$353$			6448.09i			0.972231i	−0.873895	+	0.486115i	$0.838414\pi$
$354$	107.868			0.0161953
$355$	4875.57	+	1409.99i	0.728925	+	0.210801i
$356$	5914.63			0.880547
$357$			4606.73i			0.682952i
$358$			30.3434i			0.00447960i
$359$	1845.68			0.271341			0.135670	−	0.990754i	$-0.456681\pi$
$359$	1845.68			0.271341			0.135670	+	0.990754i	$0.456681\pi$
$360$	156.344	−	540.620i	0.0228891	−	0.0791477i
$361$	2387.93			0.348145
$362$			614.868i			0.0892727i
$363$			363.000i			0.0524864i
$364$	3990.77			0.574652
$365$	2037.04	−	7043.85i	0.292120	−	1.01011i
$366$	619.044			0.0884098
$367$			11384.6i			1.61926i	0.586938	+	0.809632i	$0.300333\pi$
$367$			11384.6i			1.61926i	−0.586938	+	0.809632i	$0.699667\pi$
$368$			10611.9i			1.50321i
$369$	−2755.06			−0.388680
$370$	−1020.85	−	295.224i	−0.143436	−	0.0414810i
$371$	9840.17			1.37702
$372$		−	6517.19i		−	0.908335i
$373$			3543.87i			0.491943i	0.969277	+	0.245972i	$0.0791070\pi$
$373$			3543.87i			0.491943i	−0.969277	+	0.245972i	$0.920893\pi$
$374$	299.800			0.0414499
$375$	−3134.69	+	2784.21i	−0.431666	+	0.383403i
$376$	1439.64			0.197456
$377$		−	4840.69i		−	0.661295i
$378$			188.795i			0.0256894i
$379$	−9256.66			−1.25457			−0.627286	−	0.778789i	$-0.715834\pi$
$379$	−9256.66			−1.25457			−0.627286	+	0.778789i	$0.715834\pi$
$380$	−8134.15	−	2352.35i	−1.09809	−	0.317561i
$381$	−3068.56			−0.412617
$382$		−	1768.14i		−	0.236822i
$383$			3260.36i			0.434978i	0.976063	+	0.217489i	$0.0697867\pi$
$383$			3260.36i			0.434978i	−0.976063	+	0.217489i	$0.930213\pi$
$384$	−2081.29			−0.276590
$385$	−678.152	+	2344.97i	−0.0897710	+	0.310417i
$386$	1506.04			0.198589
$387$			4301.16i			0.564962i
$388$		−	4505.68i		−	0.589539i
$389$	−139.121			−0.0181329			−0.00906646	−	0.999959i	$-0.502886\pi$
$389$	−139.121			−0.0181329			−0.00906646	+	0.999959i	$0.502886\pi$
$390$	−83.8011	+	289.774i	−0.0108806	+	0.0376238i
$391$	13450.6			1.73970
$392$		−	285.056i		−	0.0367283i
$393$			3926.54i			0.503990i
$394$	−706.927			−0.0903921
$395$	−5179.32	−	1497.83i	−0.659746	−	0.190795i
$396$	−779.713			−0.0989446
$397$		−	1324.39i		−	0.167428i	−0.996490	−	0.0837141i	$-0.973322\pi$
$397$		−	1324.39i		−	0.167428i	0.996490	−	0.0837141i	$-0.0266783\pi$
$398$			1292.47i			0.162778i
$399$	5725.99			0.718441
$400$	6451.92	+	4072.30i	0.806490	+	0.509038i
$401$	−638.767			−0.0795473			−0.0397737	−	0.999209i	$-0.512664\pi$
$401$	−638.767			−0.0795473			−0.0397737	+	0.999209i	$0.512664\pi$
$402$		−	501.355i		−	0.0622023i
$403$			7041.51i			0.870379i
$404$	626.281			0.0771253
$405$	869.959	+	251.588i	0.106737	+	0.0308679i
$406$	−1325.89			−0.162076
$407$			2967.86i			0.361453i
$408$			1298.07i			0.157510i
$409$	−7828.03			−0.946384			−0.473192	−	0.880959i	$-0.656898\pi$
$409$	−7828.03			−0.946384			−0.473192	+	0.880959i	$0.656898\pi$
$410$	−334.958	+	1158.24i	−0.0403473	+	0.139516i
$411$	−4217.60			−0.506178
$412$		−	8084.15i		−	0.966692i
$413$		−	2025.84i		−	0.241368i
$414$	551.238			0.0654394
$415$	1625.98	−	5622.42i	0.192328	−	0.665046i
$416$	1691.16			0.199317
$417$			2175.41i			0.255469i
$418$		−	372.640i		−	0.0436038i
$419$	−3829.62			−0.446513			−0.223257	−	0.974760i	$-0.571669\pi$
$419$	−3829.62			−0.446513			−0.223257	+	0.974760i	$0.571669\pi$
$420$	−5036.92	−	1456.65i	−0.585182	−	0.169232i
$421$	−16051.8			−1.85824			−0.929120	−	0.369779i	$-0.879433\pi$
$421$	−16051.8			−1.85824			−0.929120	+	0.369779i	$0.879433\pi$
$422$			563.766i			0.0650324i
$423$			2316.64i			0.266286i
$424$	2772.73			0.317584
$425$	5161.66	−	8177.82i	0.589123	−	0.933371i
$426$	−479.767			−0.0545652
$427$		−	11626.1i		−	1.31762i
$428$		−	8563.72i		−	0.967157i
$429$	842.443			0.0948101
$430$	1808.23	+	522.931i	0.202792	+	0.0586465i
$431$	1613.07			0.180276			0.0901379	−	0.995929i	$-0.471269\pi$
$431$	1613.07			0.180276			0.0901379	+	0.995929i	$0.471269\pi$
$432$		−	1647.99i		−	0.183540i
$433$		−	1137.16i		−	0.126209i	−0.998007	−	0.0631044i	$-0.979900\pi$
$433$		−	1137.16i		−	0.126209i	0.998007	−	0.0631044i	$-0.0201001\pi$
$434$	1928.71			0.213320
$435$	−1766.88	+	6109.64i	−0.194748	+	0.673414i
$436$	−10478.0			−1.15093
$437$		−	16718.5i		−	1.83011i
$438$			693.131i			0.0756143i
$439$	−15605.6			−1.69662			−0.848309	−	0.529502i	$-0.822379\pi$
$439$	−15605.6			−1.69662			−0.848309	+	0.529502i	$0.822379\pi$
$440$	−191.088	+	660.758i	−0.0207040	+	0.0715918i
$441$	458.708			0.0495312
$442$		−	695.769i		−	0.0748741i
$443$			417.501i			0.0447767i	0.999749	+	0.0223884i	$0.00712703\pi$
$443$			417.501i			0.0447767i	−0.999749	+	0.0223884i	$0.992873\pi$
$444$	−6374.87			−0.681392
$445$	8065.69	+	2332.56i	0.859214	+	0.248480i
$446$	1375.48			0.146033
$447$		−	8436.78i		−	0.892720i
$448$			9228.76i			0.973254i
$449$	2601.70			0.273456			0.136728	−	0.990609i	$-0.456341\pi$
$449$	2601.70			0.273456			0.136728	+	0.990609i	$0.456341\pi$
$450$	211.538	−	335.148i	0.0221600	−	0.0351090i
$451$	3367.30			0.351574
$452$		−	11500.4i		−	1.19675i
$453$		−	1408.90i		−	0.146128i
$454$	−480.867			−0.0497097
$455$	5442.15	+	1573.84i	0.560730	+	0.162160i
$456$	1613.45			0.165695
$457$		−	6957.44i		−	0.712156i	−0.934456	−	0.356078i	$-0.884114\pi$
$457$		−	6957.44i		−	0.712156i	0.934456	−	0.356078i	$-0.115886\pi$
$458$		−	1777.52i		−	0.181350i
$459$	−2088.84			−0.212415
$460$	−4253.08	+	14706.6i	−0.431089	+	1.49065i
$461$	3120.45			0.315258			0.157629	−	0.987498i	$-0.449615\pi$
$461$	3120.45			0.315258			0.157629	+	0.987498i	$0.449615\pi$
$462$		−	230.750i		−	0.0232369i
$463$		−	76.4453i		−	0.00767325i	−0.999993	−	0.00383662i	$-0.998779\pi$
$463$		−	76.4453i		−	0.00767325i	0.999993	−	0.00383662i	$-0.00122124\pi$
$464$	11573.7			1.15797
$465$	2570.19	−	8887.39i	0.256322	−	0.886329i
$466$	−2143.21			−0.213052
$467$		−	9038.75i		−	0.895639i	−0.894124	−	0.447819i	$-0.852201\pi$
$467$		−	9038.75i		−	0.895639i	0.894124	−	0.447819i	$-0.147799\pi$
$468$			1809.54i			0.178731i
$469$	−9415.80			−0.927039
$470$	973.931	+	281.656i	0.0955831	+	0.0276421i
$471$	−830.836			−0.0812800
$472$		−	570.834i		−	0.0556668i
$473$		−	5256.97i		−	0.511027i
$474$	509.656			0.0493867
$475$	−10164.7	−	6415.74i	−0.981872	−	0.619735i
$476$	12094.0			1.16456
$477$			4461.85i			0.428289i
$478$		−	1202.46i		−	0.115062i
$479$	7767.93			0.740972			0.370486	−	0.928838i	$-0.379191\pi$
$479$	7767.93			0.740972			0.370486	+	0.928838i	$0.379191\pi$
$480$	−2134.48	−	617.280i	−0.202969	−	0.0586976i
$481$	6887.74			0.652919
$482$			345.042i			0.0326063i
$483$		−	10352.6i		−	0.975282i
$484$	952.983			0.0894988
$485$	1776.91	−	6144.32i	0.166361	−	0.575256i
$486$	−85.6059			−0.00799005
$487$			311.944i			0.0290258i	0.999895	+	0.0145129i	$0.00461976\pi$
$487$			311.944i			0.0290258i	−0.999895	+	0.0145129i	$0.995380\pi$
$488$		−	3275.96i		−	0.303885i
$489$	−7964.20			−0.736510
$490$	55.7694	−	192.844i	0.00514164	−	0.0177792i
$491$	12908.1			1.18642			0.593211	−	0.805047i	$-0.297860\pi$
$491$	12908.1			1.18642			0.593211	+	0.805047i	$0.297860\pi$
$492$			7232.86i			0.662769i
$493$		−	14669.7i		−	1.34014i
$494$	−864.814			−0.0787648
$495$	−1063.28	−	307.496i	−0.0965475	−	0.0279210i
$496$	−16835.7			−1.52408
$497$			9010.35i			0.813219i
$498$			553.259i			0.0497834i
$499$	14175.0			1.27166			0.635831	−	0.771828i	$-0.280657\pi$
$499$	14175.0			1.27166			0.635831	+	0.771828i	$0.280657\pi$
$500$	7309.38	+	8229.50i	0.653771	+	0.736069i
$501$	−9659.44			−0.861382
$502$		−	850.453i		−	0.0756127i
$503$			7144.07i			0.633277i	0.948546	+	0.316639i	$0.102554\pi$
$503$			7144.07i			0.633277i	−0.948546	+	0.316639i	$0.897446\pi$
$504$	999.099			0.0883004
$505$	854.049	+	246.987i	0.0752568	+	0.0217639i
$506$	−673.736			−0.0591921
$507$			4635.88i			0.406088i
$508$			8055.89i			0.703587i
$509$	−8333.89			−0.725724			−0.362862	−	0.931843i	$-0.618200\pi$
$509$	−8333.89			−0.725724			−0.362862	+	0.931843i	$0.618200\pi$
$510$	−253.959	+	878.160i	−0.0220500	+	0.0762462i
$511$	13017.5			1.12693
$512$			6774.40i			0.584744i
$513$			2596.35i			0.223453i
$514$	1017.50			0.0873149
$515$	3188.15	−	11024.2i	0.272790	−	0.943273i
$516$	11291.8			0.963362
$517$		−	2831.45i		−	0.240865i
$518$		−	1886.59i		−	0.160023i
$519$	7620.98			0.644555
$520$	1533.47	+	443.472i	0.129322	+	0.0373991i
$521$	−11728.3			−0.986232			−0.493116	−	0.869963i	$-0.664142\pi$
$521$	−11728.3			−0.986232			−0.493116	+	0.869963i	$0.664142\pi$
$522$		−	601.203i		−	0.0504098i
$523$			15253.6i			1.27532i	0.770316	+	0.637662i	$0.220099\pi$
$523$			15253.6i			1.27532i	−0.770316	+	0.637662i	$0.779901\pi$
$524$	10308.3			0.859393
$525$	−6294.31	−	3972.83i	−0.523250	−	0.330263i
$526$	1379.59			0.114359
$527$			21339.3i			1.76386i
$528$			2014.22i			0.166018i
$529$	−18060.3			−1.48437
$530$	1875.79	+	542.468i	0.153734	+	0.0444591i
$531$	918.579			0.0750714
$532$		−	15032.4i		−	1.22507i
$533$		−	7814.76i		−	0.635075i
$534$	−793.682			−0.0643183
$535$	3377.28	−	11678.2i	0.272921	−	0.943726i
$536$	−2653.15			−0.213804
$537$			258.397i			0.0207647i
$538$			1231.39i			0.0986783i
$539$	−560.643			−0.0448026
$540$	660.492	−	2283.90i	0.0526353	−	0.182006i
$541$	−22147.6			−1.76008			−0.880039	−	0.474902i	$-0.842483\pi$
$541$	−22147.6			−1.76008			−0.880039	+	0.474902i	$0.842483\pi$
$542$			273.014i			0.0216364i
$543$			5236.07i			0.413814i
$544$	5125.05			0.403924
$545$	−14288.7	−	4132.22i	−1.12305	−	0.324780i
$546$	−535.520			−0.0419746
$547$			2806.38i			0.219364i	0.993967	+	0.109682i	$0.0349833\pi$
$547$			2806.38i			0.219364i	−0.993967	+	0.109682i	$0.965017\pi$
$548$			11072.5i			0.863124i
$549$	5271.64			0.409814
$550$	−258.546	+	409.625i	−0.0200445	+	0.0317572i
$551$	−18233.9			−1.40978
$552$		−	2917.13i		−	0.224930i
$553$		−	9571.69i		−	0.736040i
$554$	−2639.24			−0.202402
$555$	−8693.32	−	2514.06i	−0.664884	−	0.192281i
$556$	5711.11			0.435621
$557$		−	8190.23i		−	0.623036i	−0.950240	−	0.311518i	$-0.899163\pi$
$557$		−	8190.23i		−	0.623036i	0.950240	−	0.311518i	$-0.100837\pi$
$558$			874.539i			0.0663480i
$559$	−12200.3			−0.923107
$560$	−3762.93	+	13011.8i	−0.283952	+	0.981870i
$561$	2553.02			0.192137
$562$		−	44.2171i		−	0.00331883i
$563$		−	21508.4i		−	1.61007i	−0.593226	−	0.805036i	$-0.702146\pi$
$563$		−	21508.4i		−	1.61007i	0.593226	−	0.805036i	$-0.297854\pi$
$564$	6081.88			0.454066
$565$	4535.40	−	15682.9i	0.337710	−	1.16776i
$566$	2.91746			0.000216661
$567$			1607.74i			0.119081i
$568$			2538.91i			0.187553i
$569$	7128.25			0.525188			0.262594	−	0.964906i	$-0.415422\pi$
$569$	7128.25			0.525188			0.262594	+	0.964906i	$0.415422\pi$
$570$	1091.52	+	315.662i	0.0802082	+	0.0231958i
$571$	14565.4			1.06750			0.533750	−	0.845642i	$-0.320782\pi$
$571$	14565.4			1.06750			0.533750	+	0.845642i	$0.320782\pi$
$572$		−	2211.66i		−	0.161668i
$573$		−	15057.1i		−	1.09776i
$574$	−2140.51			−0.155650
$575$	−11599.7	+	18377.9i	−0.841290	+	1.33289i
$576$	−4184.62			−0.302707
$577$			15188.8i			1.09587i	0.836520	+	0.547937i	$0.184587\pi$
$577$			15188.8i			1.09587i	−0.836520	+	0.547937i	$0.815413\pi$
$578$		−	377.739i		−	0.0271832i
$579$	12825.1			0.920540
$580$	16039.6	+	4638.58i	1.14829	+	0.332080i
$581$	10390.6			0.741952
$582$			604.615i			0.0430620i
$583$		−	5453.37i		−	0.387402i
$584$	3668.02			0.259904
$585$	−713.630	+	2467.65i	−0.0504359	+	0.174401i
$586$	1076.57			0.0758918
$587$		−	10096.8i		−	0.709948i	−0.934876	−	0.354974i	$-0.884490\pi$
$587$		−	10096.8i		−	0.709948i	0.934876	−	0.354974i	$-0.115510\pi$
$588$		−	1204.25i		−	0.0844596i
$589$	26523.9			1.85552
$590$	111.680	−	386.176i	0.00779287	−	0.0269468i
$591$	−6020.03			−0.419003
$592$			16468.1i			1.14330i
$593$		−	566.942i		−	0.0392605i	−0.999807	−	0.0196303i	$-0.993751\pi$
$593$		−	566.942i		−	0.0392605i	0.999807	−	0.0196303i	$-0.00624891\pi$
$594$	104.629			0.00722727
$595$	16492.4	+	4769.53i	1.13634	+	0.328625i
$596$	−22149.0			−1.52225
$597$			11006.3i			0.754539i
$598$			1563.59i			0.106923i
$599$	−3326.86			−0.226931			−0.113466	−	0.993542i	$-0.536195\pi$
$599$	−3326.86			−0.226931			−0.113466	+	0.993542i	$0.536195\pi$
$600$	−1773.59	−	1119.45i	−0.120678	−	0.0761690i
$601$	−27089.1			−1.83858			−0.919290	−	0.393581i	$-0.871236\pi$
$601$	−27089.1			−1.83858			−0.919290	+	0.393581i	$0.871236\pi$
$602$			3341.73i			0.226243i
$603$		−	4269.43i		−	0.288332i
$604$	−3698.78			−0.249174
$605$	1299.57	+	375.828i	0.0873305	+	0.0252555i
$606$	−84.0404			−0.00563351
$607$			732.349i			0.0489706i	0.999700	+	0.0244853i	$0.00779469\pi$
$607$			732.349i			0.0489706i	−0.999700	+	0.0244853i	$0.992205\pi$
$608$		−	6370.24i		−	0.424913i
$609$	−11291.0			−0.751288
$610$	640.921	−	2216.23i	0.0425412	−	0.147102i
$611$	−6571.18			−0.435092
$612$			5483.82i			0.362206i
$613$		−	7678.49i		−	0.505924i	−0.967476	−	0.252962i	$-0.918595\pi$
$613$		−	7678.49i		−	0.505924i	0.967476	−	0.252962i	$-0.0814047\pi$
$614$	−2840.51			−0.186700
$615$	−2852.43	+	9863.34i	−0.187026	+	0.646713i
$616$	−1221.12			−0.0798707
$617$			21512.8i			1.40368i	0.712334	+	0.701841i	$0.247638\pi$
$617$			21512.8i			1.40368i	−0.712334	+	0.701841i	$0.752362\pi$
$618$			1084.81i			0.0706107i
$619$	11921.8			0.774112			0.387056	−	0.922056i	$-0.373492\pi$
$619$	11921.8			0.774112			0.387056	+	0.922056i	$0.373492\pi$
$620$	−23332.0	−	6747.51i	−1.51135	−	0.437075i
$621$	4694.22			0.303337
$622$		−	2337.03i		−	0.150653i
$623$			14905.9i			0.958575i
$624$	4674.55			0.299891
$625$	6722.21	+	14105.1i	0.430222	+	0.902723i
$626$	−1673.99			−0.106879
$627$		−	3173.31i		−	0.202121i
$628$			2181.19i			0.138597i
$629$	20873.3			1.32317
$630$	675.902	+	195.467i	0.0427438	+	0.0123613i
$631$	6522.97			0.411530			0.205765	−	0.978601i	$-0.434032\pi$
$631$	6522.97			0.411530			0.205765	+	0.978601i	$0.434032\pi$
$632$		−	2697.08i		−	0.169753i
$633$			4800.90i			0.301451i
$634$	425.282			0.0266405
$635$	−3177.01	+	10985.7i	−0.198544	+	0.686542i
$636$	11713.7			0.730311
$637$			1301.13i			0.0809304i
$638$			734.803i			0.0455974i
$639$	−4085.58			−0.252931
$640$	−2154.84	+	7451.18i	−0.133090	+	0.460209i
$641$	2973.80			0.183242			0.0916209	−	0.995794i	$-0.470795\pi$
$641$	2973.80			0.183242			0.0916209	+	0.995794i	$0.470795\pi$
$642$			1149.16i			0.0706446i
$643$		−	25884.2i		−	1.58752i	−0.608234	−	0.793758i	$-0.708122\pi$
$643$		−	25884.2i		−	1.58752i	0.608234	−	0.793758i	$-0.291878\pi$
$644$	−27178.8			−1.66303
$645$	15398.5	+	4453.16i	0.940023	+	0.271850i
$646$	−2620.82			−0.159620
$647$			13929.9i			0.846433i	0.906028	+	0.423217i	$0.139099\pi$
$647$			13929.9i			0.846433i	−0.906028	+	0.423217i	$0.860901\pi$
$648$			453.023i			0.0274636i
$649$	−1122.71			−0.0679047
$650$	950.650	+	600.029i	0.0573655	+	0.0362078i
$651$	16424.4			0.988824
$652$			20908.4i			1.25588i
$653$			18254.9i			1.09398i	0.837140	+	0.546989i	$0.184226\pi$
$653$			18254.9i			1.09398i	−0.837140	+	0.546989i	$0.815774\pi$
$654$	1406.04			0.0840682
$655$	14057.3	+	4065.31i	0.838573	+	0.242511i
$656$	18684.5			1.11205
$657$			5902.54i			0.350502i
$658$			1799.88i			0.106636i
$659$	−24637.9			−1.45638			−0.728192	−	0.685373i	$-0.759639\pi$
$659$	−24637.9			−1.45638			−0.728192	+	0.685373i	$0.759639\pi$
$660$	−807.268	+	2791.44i	−0.0476104	+	0.164631i
$661$	22721.6			1.33702			0.668508	−	0.743705i	$-0.266933\pi$
$661$	22721.6			1.33702			0.668508	+	0.743705i	$0.266933\pi$
$662$			858.657i			0.0504118i
$663$		−	5925.01i		−	0.347071i
$664$	2927.83			0.171117
$665$	5928.34	−	20499.5i	0.345701	−	1.19539i
$666$	855.442			0.0497713
$667$			32967.1i			1.91378i
$668$			25358.9i			1.46881i
$669$	11713.3			0.676923
$670$	−1794.89	−	519.073i	−0.103497	−	0.0299307i
$671$	−6443.11			−0.370691
$672$		−	3944.65i		−	0.226441i
$673$			10281.6i			0.588898i	0.955667	+	0.294449i	$0.0951361\pi$
$673$			10281.6i			0.588898i	−0.955667	+	0.294449i	$0.904864\pi$
$674$	1429.40			0.0816891
$675$	1801.41	−	2854.04i	0.102720	−	0.162744i
$676$	12170.6			0.692453
$677$			18937.3i			1.07507i	0.843243	+	0.537533i	$0.180644\pi$
$677$			18937.3i			1.07507i	−0.843243	+	0.537533i	$0.819356\pi$
$678$			1543.23i			0.0874150i
$679$	11355.1			0.641779
$680$	4647.19	+	1343.94i	0.262076	+	0.0757910i
$681$	−4094.95			−0.230424
$682$		−	1068.88i		−	0.0600140i
$683$		−	9590.55i		−	0.537294i	−0.963239	−	0.268647i	$-0.913423\pi$
$683$		−	9590.55i		−	0.537294i	0.963239	−	0.268647i	$-0.0865766\pi$
$684$	6816.18			0.381028
$685$	−4366.65	+	15099.3i	−0.243564	+	0.842214i
$686$	−2042.01			−0.113651
$687$		−	15137.0i		−	0.840628i
$688$		−	29169.9i		−	1.61641i
$689$	−12656.1			−0.699794
$690$	570.719	−	1973.48i	0.0314883	−	0.108883i
$691$	−29379.5			−1.61744			−0.808718	−	0.588197i	$-0.799838\pi$
$691$	−29379.5			−1.61744			−0.808718	+	0.588197i	$0.799838\pi$
$692$		−	20007.3i		−	1.09908i
$693$		−	1965.01i		−	0.107712i
$694$	−2558.97			−0.139967
$695$	7788.15	+	2252.29i	0.425067	+	0.122927i
$696$	−3181.54			−0.173270
$697$		−	23682.6i		−	1.28701i
$698$		−	1878.25i		−	0.101852i
$699$	−18251.1			−0.987581
$700$	−10429.8	+	16524.4i	−0.563159	+	0.892236i
$701$	9839.37			0.530140			0.265070	−	0.964229i	$-0.414605\pi$
$701$	9839.37			0.530140			0.265070	+	0.964229i	$0.414605\pi$
$702$		−	242.822i		−	0.0130552i
$703$		−	25944.7i		−	1.39193i
$704$	5114.53			0.273808
$705$	8293.77	+	2398.51i	0.443066	+	0.128132i
$706$	−2271.58			−0.121094
$707$			1578.34i			0.0839596i
$708$		−	2411.54i		−	0.128010i
$709$	−2732.03			−0.144716			−0.0723579	−	0.997379i	$-0.523052\pi$
$709$	−2732.03			−0.144716			−0.0723579	+	0.997379i	$0.523052\pi$
$710$	−496.722	+	1717.60i	−0.0262558	+	0.0907895i
$711$	4340.11			0.228927
$712$			4200.14i			0.221077i
$713$		−	47955.5i		−	2.51886i
$714$	−1622.89			−0.0850634
$715$	872.215	−	3016.01i	0.0456210	−	0.157752i
$716$	678.370			0.0354076
$717$		−	10239.9i		−	0.533356i
$718$			650.211i			0.0337962i
$719$	12352.7			0.640719			0.320359	−	0.947296i	$-0.396196\pi$
$719$	12352.7			0.640719			0.320359	+	0.947296i	$0.396196\pi$
$720$	−5899.95	−	1706.23i	−0.305386	−	0.0883161i
$721$	20373.4			1.05235
$722$			841.238i			0.0433624i
$723$			2938.30i			0.151143i
$724$	13746.2			0.705628
$725$	20043.7	+	12651.1i	1.02676	+	0.648070i
$726$	−127.880			−0.00653731
$727$			4292.36i			0.218975i	0.993988	+	0.109488i	$0.0349210\pi$
$727$			4292.36i			0.218975i	−0.993988	+	0.109488i	$0.965079\pi$
$728$			2833.95i			0.144276i
$729$	−729.000			−0.0370370
$730$	2481.46	+	717.626i	0.125812	+	0.0363843i
$731$	−36972.9			−1.87072
$732$		−	13839.6i		−	0.698807i
$733$			28377.0i			1.42991i	0.699168	+	0.714957i	$0.253554\pi$
$733$			28377.0i			1.42991i	−0.699168	+	0.714957i	$0.746446\pi$
$734$	−4010.65			−0.201683
$735$	474.919	−	1642.21i	0.0238335	−	0.0824134i
$736$	−11517.5			−0.576819
$737$			5218.19i			0.260806i
$738$		−	970.575i		−	0.0484110i
$739$	−15807.4			−0.786853			−0.393426	−	0.919356i	$-0.628710\pi$
$739$	−15807.4			−0.786853			−0.393426	+	0.919356i	$0.628710\pi$
$740$	−6600.16	+	22822.5i	−0.327874	+	1.13375i
$741$	−7364.56			−0.365106
$742$			3466.57i			0.171512i
$743$		−	12809.5i		−	0.632481i	−0.948679	−	0.316241i	$-0.897579\pi$
$743$		−	12809.5i		−	0.632481i	0.948679	−	0.316241i	$-0.102421\pi$
$744$	4628.03			0.228053
$745$	−30204.3	−	8734.93i	−1.48537	−	0.429561i
$746$	−1248.46			−0.0612728
$747$			4711.43i			0.230766i
$748$		−	6702.45i		−	0.327628i
$749$	21582.1			1.05286
$750$	−980.843	−	1104.31i	−0.0477538	−	0.0537651i
$751$	2792.75			0.135697			0.0678487	−	0.997696i	$-0.478386\pi$
$751$	2792.75			0.135697			0.0678487	+	0.997696i	$0.478386\pi$
$752$		−	15711.2i		−	0.761872i
$753$		−	7242.26i		−	0.350495i
$754$	1705.32			0.0823660
$755$	−5043.97	−	1458.69i	−0.243137	−	0.0703141i
$756$	4220.79			0.203054
$757$		−	19648.3i		−	0.943366i	−0.881768	−	0.471683i	$-0.843647\pi$
$757$		−	19648.3i		−	0.943366i	0.881768	−	0.471683i	$-0.156353\pi$
$758$		−	3261.01i		−	0.156260i
$759$	−5737.38			−0.274379
$760$	1670.47	−	5776.28i	0.0797294	−	0.275694i
$761$	3048.76			0.145226			0.0726132	−	0.997360i	$-0.476866\pi$
$761$	3048.76			0.145226			0.0726132	+	0.997360i	$0.476866\pi$
$762$		−	1081.02i		−	0.0513925i
$763$		−	26406.4i		−	1.25292i
$764$	−39529.3			−1.87188
$765$	−2162.66	+	7478.20i	−0.102211	+	0.353431i
$766$	−1148.59			−0.0541776
$767$			2605.56i			0.122661i
$768$			10425.8i			0.489853i
$769$	−1792.84			−0.0840722			−0.0420361	−	0.999116i	$-0.513384\pi$
$769$	−1792.84			−0.0840722			−0.0420361	+	0.999116i	$0.513384\pi$
$770$	−826.103	−	238.905i	−0.0386632	−	0.0111812i
$771$	8664.77			0.404739
$772$		−	33669.7i		−	1.56969i
$773$		−	17731.5i		−	0.825044i	−0.910948	−	0.412522i	$-0.864648\pi$
$773$		−	17731.5i		−	0.825044i	0.910948	−	0.412522i	$-0.135352\pi$
$774$	−1515.25			−0.0703674
$775$	−29156.5	−	18402.9i	−1.35140	−	0.852972i
$776$	3199.60			0.148014
$777$		−	16065.8i		−	0.741772i
$778$		−	49.0106i		−	0.00225850i
$779$	−29436.6			−1.35388
$780$	6478.31	+	1873.49i	0.297385	+	0.0860023i
$781$	4993.49			0.228785
$782$			4738.47i			0.216685i
$783$		−	5119.70i		−	0.233669i
$784$	−3110.90			−0.141714
$785$	−860.197	+	2974.46i	−0.0391105	+	0.135239i
$786$	−1383.27			−0.0627732
$787$			7735.83i			0.350385i	0.984534	+	0.175192i	$0.0560547\pi$
$787$			7735.83i			0.350385i	−0.984534	+	0.175192i	$0.943945\pi$
$788$			15804.4i			0.714476i
$789$	11748.2			0.530099
$790$	527.668	−	1824.61i	0.0237640	−	0.0821730i
$791$	28982.9			1.30280
$792$		−	553.695i		−	0.0248418i
$793$			14953.0i			0.669607i
$794$	466.565			0.0208536
$795$	15973.8	+	4619.53i	0.712618	+	0.206085i
$796$	28894.9			1.28663
$797$		−	25823.4i		−	1.14769i	−0.818963	−	0.573846i	$-0.805451\pi$
$797$		−	25823.4i		−	1.14769i	0.818963	−	0.573846i	$-0.194549\pi$
$798$			2017.19i			0.0894836i
$799$	−19914.0			−0.881734
$800$	−4419.82	+	7002.51i	−0.195330	+	0.309470i
$801$	−6758.81			−0.298141
$802$		−	225.030i		−	0.00990782i
$803$		−	7214.21i		−	0.317041i
$804$	−11208.5			−0.491659
$805$	−37063.3	−	10718.5i	−1.62274	−	0.469289i
$806$	−2480.64			−0.108408
$807$			10486.2i			0.457413i
$808$			444.739i			0.0193637i
$809$	−3169.71			−0.137752			−0.0688759	−	0.997625i	$-0.521941\pi$
$809$	−3169.71			−0.137752			−0.0688759	+	0.997625i	$0.521941\pi$
$810$	−88.6312	+	306.476i	−0.00384467	+	0.0132944i
$811$	23051.5			0.998085			0.499043	−	0.866577i	$-0.333685\pi$
$811$	23051.5			0.998085			0.499043	+	0.866577i	$0.333685\pi$
$812$			29642.2i			1.28108i
$813$			2324.92i			0.100293i
$814$	−1045.54			−0.0450198
$815$	−8245.65	+	28512.4i	−0.354396	+	1.22546i
$816$	14166.2			0.607742
$817$			45955.9i			1.96793i
$818$		−	2757.72i		−	0.117875i
$819$	−4560.36			−0.194569
$820$	25894.2	+	7488.47i	1.10276	+	0.318913i
$821$	6922.35			0.294265			0.147133	−	0.989117i	$-0.452996\pi$
$821$	6922.35			0.294265			0.147133	+	0.989117i	$0.452996\pi$
$822$		−	1485.81i		−	0.0630457i
$823$		−	6344.57i		−	0.268722i	−0.990932	−	0.134361i	$-0.957102\pi$
$823$		−	6344.57i		−	0.268722i	0.990932	−	0.134361i	$-0.0428981\pi$
$824$	5740.77			0.242705
$825$	−2201.72	+	3488.27i	−0.0929140	+	0.147207i
$826$	713.677			0.0300630
$827$		−	40602.9i		−	1.70726i	−0.520882	−	0.853629i	$-0.674397\pi$
$827$		−	40602.9i		−	1.70726i	0.520882	−	0.853629i	$-0.325603\pi$
$828$		−	12323.7i		−	0.517245i
$829$	20652.2			0.865238			0.432619	−	0.901577i	$-0.357590\pi$
$829$	20652.2			0.865238			0.432619	+	0.901577i	$0.357590\pi$
$830$	1980.71	+	572.811i	0.0828331	+	0.0239549i
$831$	−22475.1			−0.938212
$832$		−	11869.7i		−	0.494601i
$833$			3943.08i			0.164009i
$834$	−766.372			−0.0318193
$835$	−10000.8	+	34581.6i	−0.414482	+	1.43323i
$836$	−8330.89			−0.344653
$837$			7447.37i			0.307549i
$838$		−	1349.13i		−	0.0556143i
$839$	30274.0			1.24574			0.622870	−	0.782326i	$-0.285967\pi$
$839$	30274.0			1.24574			0.622870	+	0.782326i	$0.285967\pi$
$840$	1034.41	−	3576.85i	0.0424886	−	0.146920i
$841$	11566.2			0.474238
$842$		−	5654.87i		−	0.231448i
$843$		−	376.542i		−	0.0153841i
$844$	12603.8			0.514029
$845$	16596.8	+	4799.71i	0.675677	+	0.195402i
$846$	−816.125			−0.0331666
$847$			2401.68i			0.0974295i
$848$		−	30259.7i		−	1.22538i
$849$	24.8444			0.00100431
$850$	2880.95	+	1818.39i	0.116254	+	0.0733767i
$851$	−46908.3			−1.88954
$852$			10725.9i			0.431294i
$853$			19771.8i			0.793639i	0.917897	+	0.396820i	$0.129886\pi$
$853$			19771.8i			0.793639i	−0.917897	+	0.396820i	$0.870114\pi$
$854$	4095.73			0.164113
$855$	9295.12	+	2688.10i	0.371797	+	0.107522i
$856$	6081.33			0.242822
$857$		−	26489.4i		−	1.05585i	−0.849292	−	0.527923i	$-0.822971\pi$
$857$		−	26489.4i		−	1.05585i	0.849292	−	0.527923i	$-0.177029\pi$
$858$			296.782i			0.0118088i
$859$	24876.2			0.988085			0.494043	−	0.869438i	$-0.335519\pi$
$859$	24876.2			0.988085			0.494043	+	0.869438i	$0.335519\pi$
$860$	11690.9	−	40425.6i	0.463553	−	1.60291i
$861$	−18228.1			−0.721499
$862$			568.265i			0.0224538i
$863$		−	13871.8i		−	0.547162i	−0.961849	−	0.273581i	$-0.911792\pi$
$863$		−	13871.8i		−	0.547162i	0.961849	−	0.273581i	$-0.0882082\pi$
$864$	1788.63			0.0704288
$865$	7890.31	−	27283.7i	0.310149	−	1.07246i
$866$	400.608			0.0157196
$867$		−	3216.74i		−	0.126005i
$868$		−	43119.1i		−	1.68612i
$869$	−5304.58			−0.207072
$870$	−2152.35	−	622.449i	−0.0838754	−	0.0242563i
$871$	12110.3			0.471114
$872$		−	7440.72i		−	0.288962i
$873$			5148.76i			0.199610i
$874$	5889.74			0.227944
$875$	−20739.8	+	18420.9i	−0.801294	+	0.711703i
$876$	15495.9			0.597670
$877$			34035.3i			1.31048i	0.755421	+	0.655240i	$0.227432\pi$
$877$			34035.3i			1.31048i	−0.755421	+	0.655240i	$0.772568\pi$
$878$		−	5497.66i		−	0.211318i
$879$	9167.80			0.351789
$880$	7211.05	+	2085.40i	0.276232	+	0.0798849i
$881$	−642.501			−0.0245703			−0.0122851	−	0.999925i	$-0.503911\pi$
$881$	−642.501			−0.0245703			−0.0122851	+	0.999925i	$0.503911\pi$
$882$			161.597i			0.00616923i
$883$		−	37886.4i		−	1.44392i	−0.691937	−	0.721958i	$-0.743242\pi$
$883$		−	37886.4i		−	1.44392i	0.691937	−	0.721958i	$-0.256758\pi$
$884$	−15554.9			−0.591819
$885$	951.041	−	3288.58i	0.0361231	−	0.124909i
$886$	−147.081			−0.00557705
$887$			17674.7i			0.669063i	0.942385	+	0.334532i	$0.108578\pi$
$887$			17674.7i			0.669063i	−0.942385	+	0.334532i	$0.891422\pi$
$888$		−	4526.97i		−	0.171076i
$889$	−20302.2			−0.765934
$890$	−821.731	+	2841.44i	−0.0309488	+	0.107017i
$891$	891.000			0.0335013
$892$		−	30750.8i		−	1.15428i
$893$			24752.3i			0.927552i
$894$	2972.17			0.111191
$895$	925.082	+	267.529i	0.0345498	+	0.00999163i
$896$	−13770.2			−0.513428
$897$			13315.2i			0.495631i
$898$			916.547i			0.0340597i
$899$	−52302.2			−1.94035
$900$	−7492.71	−	4729.23i	−0.277508	−	0.175157i
$901$	−38354.2			−1.41816
$902$			1186.26i			0.0437894i
$903$			28457.4i			1.04873i
$904$	8166.72			0.300466
$905$	18745.5	+	5421.11i	0.688533	+	0.199120i
$906$	496.338			0.0182006
$907$		−	46463.4i		−	1.70098i	−0.525989	−	0.850491i	$-0.676305\pi$
$907$		−	46463.4i		−	1.70098i	0.525989	−	0.850491i	$-0.323695\pi$
$908$			10750.5i			0.392915i
$909$	−715.668			−0.0261136
$910$	−554.445	+	1917.20i	−0.0201974	+	0.0698403i
$911$	15455.9			0.562103			0.281051	−	0.959693i	$-0.409317\pi$
$911$	15455.9			0.562103			0.281051	+	0.959693i	$0.409317\pi$
$912$		−	17608.1i		−	0.639322i
$913$		−	5758.41i		−	0.208736i
$914$	2451.02			0.0887008
$915$	5457.94	−	18872.9i	0.197195	−	0.681878i
$916$	−39739.1			−1.43342
$917$			25978.8i			0.935546i
$918$		−	735.872i		−	0.0264569i
$919$	35769.7			1.28393			0.641965	−	0.766734i	$-0.278119\pi$
$919$	35769.7			1.28393			0.641965	+	0.766734i	$0.278119\pi$
$920$	−10443.6	−	3020.23i	−0.374255	−	0.108232i
$921$	−24189.1			−0.865428
$922$			1099.30i			0.0392661i
$923$		−	11588.8i		−	0.413272i
$924$	−5158.74			−0.183669
$925$	−18001.1	+	28519.8i	−0.639861	+	1.01376i
$926$	26.9307			0.000955722
$927$			9237.98i			0.327308i
$928$			12561.4i			0.444340i
$929$	50926.4			1.79854			0.899268	−	0.437398i	$-0.144100\pi$
$929$	50926.4			1.79854			0.899268	+	0.437398i	$0.144100\pi$
$930$	3130.92	+	905.445i	0.110394	+	0.0319255i
$931$	4901.09			0.172531
$932$			47914.5i			1.68400i
$933$		−	19901.6i		−	0.698338i
$934$	3184.24			0.111554
$935$	2643.25	−	9140.03i	0.0924529	−	0.319691i
$936$	−1285.00			−0.0448736
$937$		−	15370.9i		−	0.535906i	−0.963432	−	0.267953i	$-0.913653\pi$
$937$		−	15370.9i		−	0.535906i	0.963432	−	0.267953i	$-0.0863472\pi$
$938$		−	3317.07i		−	0.115465i
$939$	−14255.3			−0.495426
$940$	6296.81	−	21773.6i	0.218489	−	0.755507i
$941$	35629.1			1.23430			0.617149	−	0.786846i	$-0.288287\pi$
$941$	35629.1			1.23430			0.617149	+	0.786846i	$0.288287\pi$
$942$		−	292.693i		−	0.0101236i
$943$			53221.7i			1.83790i
$944$	−6229.68			−0.214787
$945$	5755.83	+	1664.56i	0.198134	+	0.0572995i
$946$	1851.97			0.0636497
$947$		−	22204.2i		−	0.761920i	−0.924591	−	0.380960i	$-0.875593\pi$
$947$		−	22204.2i		−	0.761920i	0.924591	−	0.380960i	$-0.124407\pi$
$948$		−	11394.1i		−	0.390362i
$949$	−16742.6			−0.572695
$950$	2260.19	−	3580.91i	0.0771896	−	0.122295i
$951$	3621.60			0.123489
$952$			8588.30i			0.292383i
$953$			50757.0i			1.72527i	0.505827	+	0.862635i	$0.331187\pi$
$953$			50757.0i			1.72527i	−0.505827	+	0.862635i	$0.668813\pi$
$954$	−1571.85			−0.0533445
$955$	−53905.4	−	15589.2i	−1.82653	−	0.528224i
$956$	−26882.8			−0.909468
$957$			6257.41i			0.211362i
$958$			2736.55i			0.0922900i
$959$	−27904.5			−0.939608
$960$	−4332.50	+	14981.2i	−0.145657	+	0.503664i
$961$	46290.4			1.55384
$962$			2426.47i			0.0813227i
$963$			9786.00i			0.327466i
$964$	7713.90			0.257726
$965$	13278.3	−	45914.9i	0.442948	−	1.53166i
$966$	3647.11			0.121474
$967$			33405.1i			1.11089i	0.831552	+	0.555447i	$0.187453\pi$
$967$			33405.1i			1.11089i	−0.831552	+	0.555447i	$0.812547\pi$
$968$			676.739i			0.0224703i
$969$	−22318.3			−0.739904
$970$	2164.57	+	625.982i	0.0716496	+	0.0207207i
$971$	48382.3			1.59903			0.799516	−	0.600644i	$-0.205089\pi$
$971$	48382.3			1.59903			0.799516	+	0.600644i	$0.205089\pi$
$972$			1913.84i			0.0631548i
$973$			14393.0i			0.474222i
$974$	−109.894			−0.00361523
$975$	8095.52	+	5109.70i	0.265912	+	0.167837i
$976$	−35751.6			−1.17252
$977$			14604.6i			0.478241i	0.970990	+	0.239121i	$0.0768592\pi$
$977$			14604.6i			0.478241i	−0.970990	+	0.239121i	$0.923141\pi$
$978$		−	2805.69i		−	0.0917342i
$979$	8260.77			0.269679
$980$	−4311.29	−	1246.80i	−0.140530	−	0.0406405i
$981$	11973.5			0.389689
$982$			4547.35i			0.147772i
$983$			22492.6i			0.729809i	0.931045	+	0.364904i	$0.118898\pi$
$983$			22492.6i			0.729809i	−0.931045	+	0.364904i	$0.881102\pi$
$984$	−5136.25			−0.166400
$985$	−6232.77	+	21552.2i	−0.201617	+	0.697167i
$986$	5167.96			0.166918
$987$			15327.4i			0.494302i
$988$			19334.2i			0.622572i
$989$	83088.8			2.67146
$990$	108.327	−	374.582i	0.00347764	−	0.0120252i
$991$	22276.1			0.714049			0.357025	−	0.934095i	$-0.383791\pi$
$991$	22276.1			0.714049			0.357025	+	0.934095i	$0.383791\pi$
$992$		−	18272.4i		−	0.584829i
$993$			7312.12i			0.233679i
$994$	−3174.24			−0.101288
$995$	39403.6	+	11395.3i	1.25545	+	0.363071i
$996$	12368.9			0.393497
$997$		−	25955.4i		−	0.824490i	−0.911073	−	0.412245i	$-0.864745\pi$
$997$		−	25955.4i		−	0.824490i	0.911073	−	0.412245i	$-0.135255\pi$
$998$			4993.68i			0.158389i
$999$	7284.74			0.230710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.4.c.b.34.8	yes	14
3.2	odd	2		495.4.c.d.199.7		14
5.2	odd	4		825.4.a.ba.1.4		7
5.3	odd	4		825.4.a.bd.1.4		7
5.4	even	2	inner	165.4.c.b.34.7	✓	14
15.2	even	4		2475.4.a.bs.1.4		7
15.8	even	4		2475.4.a.bo.1.4		7
15.14	odd	2		495.4.c.d.199.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.b.34.7	✓	14	5.4	even	2	inner
165.4.c.b.34.8	yes	14	1.1	even	1	trivial
495.4.c.d.199.7		14	3.2	odd	2
495.4.c.d.199.8		14	15.14	odd	2
825.4.a.ba.1.4		7	5.2	odd	4
825.4.a.bd.1.4		7	5.3	odd	4
2475.4.a.bo.1.4		7	15.8	even	4
2475.4.a.bs.1.4		7	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.352288i q^{2} +3.00000i q^{3} +7.87589 q^{4} +(10.7402 + 3.10602i) q^{5} -1.05686 q^{6} +19.8486i q^{7} +5.59288i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+0.352288i q^{2} +3.00000i q^{3} +7.87589 q^{4} +(10.7402 + 3.10602i) q^{5} -1.05686 q^{6} +19.8486i q^{7} +5.59288i q^{8} -9.00000 q^{9} +(-1.09421 + 3.78365i) q^{10} +11.0000 q^{11} +23.6277i q^{12} -25.5286i q^{13} -6.99242 q^{14} +(-9.31806 + 32.2207i) q^{15} +61.0368 q^{16} -77.3644i q^{17} -3.17059i q^{18} -96.1609 q^{19} +(84.5889 + 24.4627i) q^{20} -59.5458 q^{21} +3.87517i q^{22} +173.860i q^{23} -16.7786 q^{24} +(105.705 + 66.7188i) q^{25} +8.99340 q^{26} -27.0000i q^{27} +156.326i q^{28} +189.619 q^{29} +(-11.3510 - 3.28264i) q^{30} -275.829 q^{31} +66.2456i q^{32} +33.0000i q^{33} +27.2545 q^{34} +(-61.6502 + 213.179i) q^{35} -70.8830 q^{36} +269.805i q^{37} -33.8763i q^{38} +76.5857 q^{39} +(-17.3716 + 60.0689i) q^{40} +306.118 q^{41} -20.9773i q^{42} -477.907i q^{43} +86.6348 q^{44} +(-96.6621 - 27.9542i) q^{45} -61.2487 q^{46} -257.405i q^{47} +183.111i q^{48} -50.9676 q^{49} +(-23.5042 + 37.2387i) q^{50} +232.093 q^{51} -201.060i q^{52} -495.761i q^{53} +9.51177 q^{54} +(118.143 + 34.1662i) q^{55} -111.011 q^{56} -288.483i q^{57} +66.8003i q^{58} -102.064 q^{59} +(-73.3880 + 253.767i) q^{60} -585.738 q^{61} -97.1710i q^{62} -178.638i q^{63} +464.957 q^{64} +(79.2923 - 274.183i) q^{65} -11.6255 q^{66} +474.381i q^{67} -609.314i q^{68} -521.580 q^{69} +(-75.1003 - 21.7186i) q^{70} +453.954 q^{71} -50.3359i q^{72} -655.838i q^{73} -95.0491 q^{74} +(-200.156 + 317.116i) q^{75} -757.353 q^{76} +218.335i q^{77} +26.9802i q^{78} -482.235 q^{79} +(655.550 + 189.582i) q^{80} +81.0000 q^{81} +107.842i q^{82} -523.492i q^{83} -468.977 q^{84} +(240.295 - 830.912i) q^{85} +168.361 q^{86} +568.856i q^{87} +61.5217i q^{88} +750.979 q^{89} +(9.84791 - 34.0529i) q^{90} +506.707 q^{91} +1369.30i q^{92} -827.486i q^{93} +90.6806 q^{94} +(-1032.79 - 298.678i) q^{95} -198.737 q^{96} -572.084i q^{97} -17.9553i q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9}+O(q^{10}) \) 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9	\( 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9} - 48 q^{10} + 154 q^{11} - 84 q^{14} - 86 q^{16} - 116 q^{19} + 442 q^{20} - 204 q^{21} + 450 q^{24} + 162 q^{25} - 400 q^{26} - 128 q^{29} + 246 q^{30} - 696 q^{31} - 412 q^{34} + 672 q^{35} + 234 q^{36} + 480 q^{39} + 1612 q^{40} - 664 q^{41} - 286 q^{44} + 126 q^{45} - 656 q^{46} + 834 q^{49} + 1908 q^{50} - 972 q^{51} + 270 q^{54} - 154 q^{55} - 3236 q^{56} + 664 q^{59} + 108 q^{60} + 44 q^{61} - 1122 q^{64} - 2328 q^{65} - 330 q^{66} + 1944 q^{69} + 1220 q^{70} - 1032 q^{71} - 3256 q^{74} + 84 q^{75} + 5588 q^{76} - 3492 q^{79} - 510 q^{80} + 1134 q^{81} - 1008 q^{84} - 1068 q^{85} + 2540 q^{86} + 4452 q^{89} + 432 q^{90} + 2144 q^{91} - 9472 q^{94} - 932 q^{95} + 450 q^{96} - 1386 q^{99}+O(q^{100}) \) 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9 - 48 * q^10 + 154 * q^11 - 84 * q^14 - 86 * q^16 - 116 * q^19 + 442 * q^20 - 204 * q^21 + 450 * q^24 + 162 * q^25 - 400 * q^26 - 128 * q^29 + 246 * q^30 - 696 * q^31 - 412 * q^34 + 672 * q^35 + 234 * q^36 + 480 * q^39 + 1612 * q^40 - 664 * q^41 - 286 * q^44 + 126 * q^45 - 656 * q^46 + 834 * q^49 + 1908 * q^50 - 972 * q^51 + 270 * q^54 - 154 * q^55 - 3236 * q^56 + 664 * q^59 + 108 * q^60 + 44 * q^61 - 1122 * q^64 - 2328 * q^65 - 330 * q^66 + 1944 * q^69 + 1220 * q^70 - 1032 * q^71 - 3256 * q^74 + 84 * q^75 + 5588 * q^76 - 3492 * q^79 - 510 * q^80 + 1134 * q^81 - 1008 * q^84 - 1068 * q^85 + 2540 * q^86 + 4452 * q^89 + 432 * q^90 + 2144 * q^91 - 9472 * q^94 - 932 * q^95 + 450 * q^96 - 1386 * q^99

Introduction

L-functions

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