LMFDB - Embedded newform 294.4.e.l.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("294.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.e (of order $3$, degree $2$, not 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:	$17.3465615417$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{1345})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 337x^{2} + 336x + 112896 $ x^4 - x^3 + 337x^2 + 336x + 112896
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$-8.91856 - 15.4474i$ of defining polynomial
Character	$\chi$	$=$	294.67
Dual form			294.4.e.l.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-7.91856 - 13.7153i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-7.91856 - 13.7153i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-15.8371 + 27.4307i) q^{10} +(-25.9186 + 44.8923i) q^{11} +(6.00000 + 10.3923i) q^{12} -38.8371 q^{13} -47.5114 q^{15} +(-8.00000 - 13.8564i) q^{16} +(13.6742 - 23.6845i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(38.2557 + 66.2608i) q^{19} +63.3485 q^{20} +103.674 q^{22} +(-73.6742 - 127.608i) q^{23} +(12.0000 - 20.7846i) q^{24} +(-62.9072 + 108.958i) q^{25} +(38.8371 + 67.2679i) q^{26} -27.0000 q^{27} +240.208 q^{29} +(47.5114 + 82.2921i) q^{30} +(-148.337 + 256.927i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(77.7557 + 134.677i) q^{33} -54.6970 q^{34} +36.0000 q^{36} +(80.7670 + 139.893i) q^{37} +(76.5114 - 132.522i) q^{38} +(-58.2557 + 100.902i) q^{39} +(-63.3485 - 109.723i) q^{40} +102.977 q^{41} -328.557 q^{43} +(-103.674 - 179.569i) q^{44} +(-71.2670 + 123.438i) q^{45} +(-147.348 + 255.215i) q^{46} +(33.9773 + 58.8504i) q^{47} -48.0000 q^{48} +251.629 q^{50} +(-41.0227 - 71.0534i) q^{51} +(77.6742 - 134.536i) q^{52} +(33.2443 - 57.5808i) q^{53} +(27.0000 + 46.7654i) q^{54} +820.951 q^{55} +229.534 q^{57} +(-240.208 - 416.053i) q^{58} +(-230.964 + 400.041i) q^{59} +(95.0227 - 164.584i) q^{60} +(92.6742 + 160.516i) q^{61} +593.348 q^{62} +64.0000 q^{64} +(307.534 + 532.665i) q^{65} +(155.511 - 269.354i) q^{66} +(-272.604 + 472.164i) q^{67} +(54.6970 + 94.7379i) q^{68} -442.045 q^{69} -130.742 q^{71} +(-36.0000 - 62.3538i) q^{72} +(90.6496 - 157.010i) q^{73} +(161.534 - 279.785i) q^{74} +(188.722 + 326.875i) q^{75} -306.045 q^{76} +233.023 q^{78} +(204.848 + 354.808i) q^{79} +(-126.697 + 219.446i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-102.977 - 178.362i) q^{82} -347.928 q^{83} -433.121 q^{85} +(328.557 + 569.077i) q^{86} +(360.312 - 624.080i) q^{87} +(-207.348 + 359.138i) q^{88} +(578.580 + 1002.13i) q^{89} +285.068 q^{90} +589.394 q^{92} +(445.011 + 770.782i) q^{93} +(67.9546 - 117.701i) q^{94} +(605.860 - 1049.38i) q^{95} +(48.0000 + 83.1384i) q^{96} -1618.30 q^{97} +466.534 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 5 q^{5} - 24 q^{6} + 32 q^{8} - 18 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 5 * q^5 - 24 * q^6 + 32 * q^8 - 18 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 5 q^{5} - 24 q^{6} + 32 q^{8} - 18 q^{9} + 10 q^{10} - 67 q^{11} + 24 q^{12} - 82 q^{13} + 30 q^{15} - 32 q^{16} - 92 q^{17} - 36 q^{18} + 43 q^{19} - 40 q^{20} + 268 q^{22} - 148 q^{23} + 48 q^{24} - 435 q^{25} + 82 q^{26} - 108 q^{27} + 154 q^{29} - 30 q^{30} - 520 q^{31} - 64 q^{32} + 201 q^{33} + 368 q^{34} + 144 q^{36} - 7 q^{37} + 86 q^{38} - 123 q^{39} + 40 q^{40} + 852 q^{41} - 214 q^{43} - 268 q^{44} + 45 q^{45} - 296 q^{46} + 576 q^{47} - 192 q^{48} + 1740 q^{50} + 276 q^{51} + 164 q^{52} + 243 q^{53} + 108 q^{54} + 1010 q^{55} + 258 q^{57} - 154 q^{58} - 7 q^{59} - 60 q^{60} + 224 q^{61} + 2080 q^{62} + 256 q^{64} + 570 q^{65} + 402 q^{66} - 687 q^{67} - 368 q^{68} - 888 q^{69} + 944 q^{71} - 144 q^{72} - 921 q^{73} - 14 q^{74} + 1305 q^{75} - 344 q^{76} + 492 q^{78} + 526 q^{79} + 80 q^{80} - 162 q^{81} - 852 q^{82} + 442 q^{83} - 5840 q^{85} + 214 q^{86} + 231 q^{87} - 536 q^{88} + 774 q^{89} - 180 q^{90} + 1184 q^{92} + 1560 q^{93} + 1152 q^{94} + 1910 q^{95} + 192 q^{96} - 3906 q^{97} + 1206 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 5 * q^5 - 24 * q^6 + 32 * q^8 - 18 * q^9 + 10 * q^10 - 67 * q^11 + 24 * q^12 - 82 * q^13 + 30 * q^15 - 32 * q^16 - 92 * q^17 - 36 * q^18 + 43 * q^19 - 40 * q^20 + 268 * q^22 - 148 * q^23 + 48 * q^24 - 435 * q^25 + 82 * q^26 - 108 * q^27 + 154 * q^29 - 30 * q^30 - 520 * q^31 - 64 * q^32 + 201 * q^33 + 368 * q^34 + 144 * q^36 - 7 * q^37 + 86 * q^38 - 123 * q^39 + 40 * q^40 + 852 * q^41 - 214 * q^43 - 268 * q^44 + 45 * q^45 - 296 * q^46 + 576 * q^47 - 192 * q^48 + 1740 * q^50 + 276 * q^51 + 164 * q^52 + 243 * q^53 + 108 * q^54 + 1010 * q^55 + 258 * q^57 - 154 * q^58 - 7 * q^59 - 60 * q^60 + 224 * q^61 + 2080 * q^62 + 256 * q^64 + 570 * q^65 + 402 * q^66 - 687 * q^67 - 368 * q^68 - 888 * q^69 + 944 * q^71 - 144 * q^72 - 921 * q^73 - 14 * q^74 + 1305 * q^75 - 344 * q^76 + 492 * q^78 + 526 * q^79 + 80 * q^80 - 162 * q^81 - 852 * q^82 + 442 * q^83 - 5840 * q^85 + 214 * q^86 + 231 * q^87 - 536 * q^88 + 774 * q^89 - 180 * q^90 + 1184 * q^92 + 1560 * q^93 + 1152 * q^94 + 1910 * q^95 + 192 * q^96 - 3906 * q^97 + 1206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−7.91856	−	13.7153i	−0.708258	−	1.22674i	−0.965503	−	0.260392i	$-0.916148\pi$
$5$	−7.91856	−	13.7153i	−0.708258	−	1.22674i	0.257245	−	0.966346i	$-0.417185\pi$
$6$	−6.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−15.8371	+	27.4307i	−0.500814	+	0.867435i
$11$	−25.9186	+	44.8923i	−0.710431	+	1.23050i	0.254265	+	0.967135i	$0.418167\pi$
$11$	−25.9186	+	44.8923i	−0.710431	+	1.23050i	−0.964696	+	0.263368i	$0.915167\pi$
$12$	6.00000	+	10.3923i	0.144338	+	0.250000i
$13$	−38.8371			−0.828575			−0.414288	−	0.910146i	$-0.635969\pi$
$13$	−38.8371			−0.828575			−0.414288	+	0.910146i	$0.635969\pi$
$14$		0			0
$15$	−47.5114			−0.817825
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	13.6742	−	23.6845i	0.195088	−	0.337902i	−0.751842	−	0.659344i	$-0.770834\pi$
$17$	13.6742	−	23.6845i	0.195088	−	0.337902i	0.946929	+	0.321442i	$0.104168\pi$
$18$	−9.00000	+	15.5885i	−0.117851	+	0.204124i
$19$	38.2557	+	66.2608i	0.461919	+	0.800067i	0.999057	−	0.0434278i	$-0.0138279\pi$
$19$	38.2557	+	66.2608i	0.461919	+	0.800067i	−0.537138	+	0.843494i	$0.680495\pi$
$20$	63.3485			0.708258
$21$		0			0
$22$	103.674			1.00470
$23$	−73.6742	−	127.608i	−0.667919	−	1.15687i	−0.978485	−	0.206318i	$-0.933852\pi$
$23$	−73.6742	−	127.608i	−0.667919	−	1.15687i	0.310566	−	0.950552i	$-0.399481\pi$
$24$	12.0000	−	20.7846i	0.102062	−	0.176777i
$25$	−62.9072	+	108.958i	−0.503258	+	0.871668i
$26$	38.8371	+	67.2679i	0.292946	+	0.507397i
$27$	−27.0000			−0.192450
$28$		0			0
$29$	240.208			1.53812			0.769061	−	0.639175i	$-0.220724\pi$
$29$	240.208			1.53812			0.769061	+	0.639175i	$0.220724\pi$
$30$	47.5114	+	82.2921i	0.289145	+	0.500814i
$31$	−148.337	+	256.927i	−0.859424	+	1.48857i	0.0130559	+	0.999915i	$0.495844\pi$
$31$	−148.337	+	256.927i	−0.859424	+	1.48857i	−0.872480	+	0.488651i	$0.837489\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	77.7557	+	134.677i	0.410167	+	0.710431i
$34$	−54.6970			−0.275896
$35$		0			0
$36$	36.0000			0.166667
$37$	80.7670	+	139.893i	0.358865	+	0.621573i	0.987772	−	0.155908i	$-0.0498304\pi$
$37$	80.7670	+	139.893i	0.358865	+	0.621573i	−0.628906	+	0.777481i	$0.716497\pi$
$38$	76.5114	−	132.522i	0.326626	−	0.565733i
$39$	−58.2557	+	100.902i	−0.239189	+	0.414288i
$40$	−63.3485	−	109.723i	−0.250407	−	0.433717i
$41$	102.977			0.392252			0.196126	−	0.980579i	$-0.437164\pi$
$41$	102.977			0.392252			0.196126	+	0.980579i	$0.437164\pi$
$42$		0			0
$43$	−328.557			−1.16522			−0.582610	−	0.812752i	$-0.697968\pi$
$43$	−328.557			−1.16522			−0.582610	+	0.812752i	$0.697968\pi$
$44$	−103.674	−	179.569i	−0.355215	−	0.615251i
$45$	−71.2670	+	123.438i	−0.236086	+	0.408913i
$46$	−147.348	+	255.215i	−0.472290	+	0.818031i
$47$	33.9773	+	58.8504i	0.105449	+	0.182643i	0.913921	−	0.405891i	$-0.133039\pi$
$47$	33.9773	+	58.8504i	0.105449	+	0.182643i	−0.808473	+	0.588534i	$0.799705\pi$
$48$	−48.0000			−0.144338
$49$		0			0
$50$	251.629			0.711714
$51$	−41.0227	−	71.0534i	−0.112634	−	0.195088i
$52$	77.6742	−	134.536i	0.207144	−	0.358784i
$53$	33.2443	−	57.5808i	0.0861596	−	0.149233i	−0.819725	−	0.572757i	$-0.805874\pi$
$53$	33.2443	−	57.5808i	0.0861596	−	0.149233i	0.905885	+	0.423524i	$0.139207\pi$
$54$	27.0000	+	46.7654i	0.0680414	+	0.117851i
$55$	820.951			2.01267
$56$		0			0
$57$	229.534			0.533378
$58$	−240.208	−	416.053i	−0.543809	−	0.941904i
$59$	−230.964	+	400.041i	−0.509643	+	0.882728i	0.490294	+	0.871557i	$0.336889\pi$
$59$	−230.964	+	400.041i	−0.509643	+	0.882728i	−0.999938	+	0.0111711i	$0.996444\pi$
$60$	95.0227	−	164.584i	0.204456	−	0.354129i
$61$	92.6742	+	160.516i	0.194520	+	0.336919i	0.946743	−	0.321990i	$-0.104352\pi$
$61$	92.6742	+	160.516i	0.194520	+	0.336919i	−0.752223	+	0.658909i	$0.771018\pi$
$62$	593.348			1.21541
$63$		0			0
$64$	64.0000			0.125000
$65$	307.534	+	532.665i	0.586845	+	1.01644i
$66$	155.511	−	269.354i	0.290032	−	0.502351i
$67$	−272.604	+	472.164i	−0.497073	+	0.860956i	−0.999994	−	0.00337637i	$-0.998925\pi$
$67$	−272.604	+	472.164i	−0.497073	+	0.860956i	0.502921	+	0.864332i	$0.332259\pi$
$68$	54.6970	+	94.7379i	0.0975438	+	0.168951i
$69$	−442.045			−0.771247
$70$		0			0
$71$	−130.742			−0.218539			−0.109270	−	0.994012i	$-0.534851\pi$
$71$	−130.742			−0.218539			−0.109270	+	0.994012i	$0.534851\pi$
$72$	−36.0000	−	62.3538i	−0.0589256	−	0.102062i
$73$	90.6496	−	157.010i	0.145339	−	0.251734i	−0.784160	−	0.620558i	$-0.786906\pi$
$73$	90.6496	−	157.010i	0.145339	−	0.251734i	0.929499	+	0.368824i	$0.120239\pi$
$74$	161.534	−	279.785i	0.253756	−	0.439519i
$75$	188.722	+	326.875i	0.290556	+	0.503258i
$76$	−306.045			−0.461919
$77$		0			0
$78$	233.023			0.338264
$79$	204.848	+	354.808i	0.291737	+	0.505304i	0.974221	−	0.225597i	$-0.0724333\pi$
$79$	204.848	+	354.808i	0.291737	+	0.505304i	−0.682483	+	0.730901i	$0.739100\pi$
$80$	−126.697	+	219.446i	−0.177064	+	0.306685i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−102.977	−	178.362i	−0.138682	−	0.240205i
$83$	−347.928			−0.460121			−0.230061	−	0.973176i	$-0.573892\pi$
$83$	−347.928			−0.460121			−0.230061	+	0.973176i	$0.573892\pi$
$84$		0			0
$85$	−433.121			−0.552689
$86$	328.557	+	569.077i	0.411967	+	0.713548i
$87$	360.312	−	624.080i	0.444018	−	0.769061i
$88$	−207.348	+	359.138i	−0.251175	+	0.435048i
$89$	578.580	+	1002.13i	0.689093	+	1.19354i	0.972132	+	0.234436i	$0.0753243\pi$
$89$	578.580	+	1002.13i	0.689093	+	1.19354i	−0.283038	+	0.959109i	$0.591342\pi$
$90$	285.068			0.333876
$91$		0			0
$92$	589.394			0.667919
$93$	445.011	+	770.782i	0.496188	+	0.859424i
$94$	67.9546	−	117.701i	0.0745636	−	0.129148i
$95$	605.860	−	1049.38i	0.654315	−	1.13331i
$96$	48.0000	+	83.1384i	0.0510310	+	0.0883883i
$97$	−1618.30			−1.69395			−0.846976	−	0.531631i	$-0.821579\pi$
$97$	−1618.30			−1.69395			−0.846976	+	0.531631i	$0.821579\pi$
$98$		0			0
$99$	466.534			0.473621
$100$	−251.629	−	435.834i	−0.251629	−	0.435834i
$101$	359.371	−	622.449i	0.354047	−	0.613228i	−0.632907	−	0.774228i	$-0.718139\pi$
$101$	359.371	−	622.449i	0.354047	−	0.613228i	0.986954	+	0.161000i	$0.0514719\pi$
$102$	−82.0454	+	142.107i	−0.0796442	+	0.137948i
$103$	−805.790	−	1395.67i	−0.770843	−	1.33514i	−0.937102	−	0.349057i	$-0.886502\pi$
$103$	−805.790	−	1395.67i	−0.770843	−	1.33514i	0.166259	−	0.986082i	$-0.446831\pi$
$104$	−310.697			−0.292946
$105$		0			0
$106$	−132.977			−0.121848
$107$	−467.335	−	809.448i	−0.422234	−	0.731330i	0.573924	−	0.818909i	$-0.305420\pi$
$107$	−467.335	−	809.448i	−0.422234	−	0.731330i	−0.996158	+	0.0875784i	$0.972087\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	598.509	−	1036.65i	0.525934	−	0.910944i	−0.473610	−	0.880735i	$-0.657049\pi$
$109$	598.509	−	1036.65i	0.525934	−	0.910944i	0.999544	−	0.0302095i	$-0.00961746\pi$
$110$	−820.951	−	1421.93i	−0.711587	−	1.23251i
$111$	484.602			0.414382
$112$		0			0
$113$	−2384.64			−1.98521			−0.992604	−	0.121400i	$-0.961262\pi$
$113$	−2384.64			−1.98521			−0.992604	+	0.121400i	$0.961262\pi$
$114$	−229.534	−	397.565i	−0.188578	−	0.326626i
$115$	−1166.79	+	2020.94i	−0.946118	+	1.63872i
$116$	−480.417	+	832.106i	−0.384531	+	0.666027i
$117$	174.767	+	302.705i	0.138096	+	0.239189i
$118$	923.856			0.720744
$119$		0			0
$120$	−380.091			−0.289145
$121$	−678.044	−	1174.41i	−0.509424	−	0.882349i
$122$	185.348	−	321.033i	0.137546	−	0.238237i
$123$	154.466	−	267.543i	0.113234	−	0.196126i
$124$	−593.348	−	1027.71i	−0.429712	−	0.744283i
$125$	12.8977			0.00922883
$126$		0			0
$127$	−2673.92			−1.86829			−0.934143	−	0.356898i	$-0.883834\pi$
$127$	−2673.92			−1.86829			−0.934143	+	0.356898i	$0.883834\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	−492.835	+	853.616i	−0.336370	+	0.582610i
$130$	615.068	−	1065.33i	0.414962	−	0.718735i
$131$	−19.4299	−	33.6536i	−0.0129588	−	0.0224453i	0.859473	−	0.511181i	$-0.170792\pi$
$131$	−19.4299	−	33.6536i	−0.0129588	−	0.0224453i	−0.872432	+	0.488735i	$0.837458\pi$
$132$	−622.045			−0.410167
$133$		0			0
$134$	1090.42			0.702968
$135$	213.801	+	370.314i	0.136304	+	0.236086i
$136$	109.394	−	189.476i	0.0689739	−	0.119466i
$137$	384.072	−	665.232i	0.239514	−	0.414851i	−0.721061	−	0.692872i	$-0.756345\pi$
$137$	384.072	−	665.232i	0.239514	−	0.414851i	0.960575	+	0.278021i	$0.0896784\pi$
$138$	442.045	+	765.645i	0.272677	+	0.472290i
$139$	−1052.55			−0.642274			−0.321137	−	0.947033i	$-0.604065\pi$
$139$	−1052.55			−0.642274			−0.321137	+	0.947033i	$0.604065\pi$
$140$		0			0
$141$	203.864			0.121762
$142$	130.742	+	226.453i	0.0772652	+	0.133827i
$143$	1006.60	−	1743.49i	0.588646	−	1.01956i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	−1902.10	−	3294.54i	−1.08939	−	1.88687i
$146$	−362.598			−0.205540
$147$		0			0
$148$	−646.136			−0.358865
$149$	−180.489	−	312.615i	−0.0992363	−	0.171882i	0.812132	−	0.583473i	$-0.198307\pi$
$149$	−180.489	−	312.615i	−0.0992363	−	0.171882i	−0.911369	+	0.411591i	$0.864973\pi$
$150$	377.443	−	653.751i	0.205454	−	0.355857i
$151$	−774.195	+	1340.95i	−0.417239	+	0.722679i	−0.995661	−	0.0930587i	$-0.970336\pi$
$151$	−774.195	+	1340.95i	−0.417239	+	0.722679i	0.578422	+	0.815738i	$0.303669\pi$
$152$	306.045	+	530.086i	0.163313	+	0.282866i
$153$	−246.136			−0.130058
$154$		0			0
$155$	4698.47			2.43477
$156$	−233.023	−	403.607i	−0.119595	−	0.207144i
$157$	−483.534	+	837.506i	−0.245798	+	0.425734i	−0.962356	−	0.271794i	$-0.912383\pi$
$157$	−483.534	+	837.506i	−0.245798	+	0.425734i	0.716558	+	0.697528i	$0.245717\pi$
$158$	409.697	−	709.616i	0.206289	−	0.357304i
$159$	−99.7330	−	172.743i	−0.0497443	−	0.0861596i
$160$	506.788			0.250407
$161$		0			0
$162$	162.000			0.0785674
$163$	663.250	+	1148.78i	0.318710	+	0.552022i	0.980219	−	0.197915i	$-0.0634170\pi$
$163$	663.250	+	1148.78i	0.318710	+	0.552022i	−0.661509	+	0.749937i	$0.730084\pi$
$164$	−205.955	+	356.724i	−0.0980631	+	0.169850i
$165$	1231.43	−	2132.89i	0.581008	−	1.00634i
$166$	347.928	+	602.629i	0.162677	+	0.281766i
$167$	−1416.70			−0.656451			−0.328225	−	0.944599i	$-0.606451\pi$
$167$	−1416.70			−0.656451			−0.328225	+	0.944599i	$0.606451\pi$
$168$		0			0
$169$	−688.678			−0.313463
$170$	433.121	+	750.188i	0.195405	+	0.338452i
$171$	344.301	−	596.347i	0.153973	−	0.266689i
$172$	657.114	−	1138.15i	0.291305	−	0.504555i
$173$	−518.299	−	897.721i	−0.227778	−	0.394523i	0.729371	−	0.684118i	$-0.239813\pi$
$173$	−518.299	−	897.721i	−0.227778	−	0.394523i	−0.957149	+	0.289595i	$0.906479\pi$
$174$	−1441.25			−0.627936
$175$		0			0
$176$	829.394			0.355215
$177$	692.892	+	1200.12i	0.294243	+	0.509643i
$178$	1157.16	−	2004.26i	0.487263	−	0.843964i
$179$	383.716	−	664.615i	0.160225	−	0.277518i	−0.774724	−	0.632299i	$-0.782111\pi$
$179$	383.716	−	664.615i	0.160225	−	0.277518i	0.934949	+	0.354781i	$0.115445\pi$
$180$	−285.068	−	493.753i	−0.118043	−	0.204456i
$181$	3957.71			1.62527			0.812636	−	0.582772i	$-0.198032\pi$
$181$	3957.71			1.62527			0.812636	+	0.582772i	$0.198032\pi$
$182$		0			0
$183$	556.045			0.224612
$184$	−589.394	−	1020.86i	−0.236145	−	0.409015i
$185$	1279.12	−	2215.50i	0.508338	−	0.880468i
$186$	890.023	−	1541.56i	0.350858	−	0.607704i
$187$	708.833	+	1227.74i	0.277193	+	0.480112i
$188$	−271.818			−0.105449
$189$		0			0
$190$	−2423.44			−0.925341
$191$	902.648	+	1563.43i	0.341954	+	0.592282i	0.984796	−	0.173717i	$-0.0555778\pi$
$191$	902.648	+	1563.43i	0.341954	+	0.592282i	−0.642841	+	0.765999i	$0.722244\pi$
$192$	96.0000	−	166.277i	0.0360844	−	0.0625000i
$193$	−1685.42	+	2919.23i	−0.628597	+	1.08876i	0.359237	+	0.933247i	$0.383037\pi$
$193$	−1685.42	+	2919.23i	−0.628597	+	1.08876i	−0.987833	+	0.155515i	$0.950296\pi$
$194$	1618.30	+	2802.98i	0.598903	+	1.03733i
$195$	1845.20			0.677630
$196$		0			0
$197$	−4612.31			−1.66809			−0.834044	−	0.551697i	$-0.813980\pi$
$197$	−4612.31			−1.66809			−0.834044	+	0.551697i	$0.813980\pi$
$198$	−466.534	−	808.061i	−0.167450	−	0.290032i
$199$	−1114.93	+	1931.12i	−0.397163	+	0.687906i	−0.993375	−	0.114921i	$-0.963339\pi$
$199$	−1114.93	+	1931.12i	−0.397163	+	0.687906i	0.596212	+	0.802827i	$0.296672\pi$
$200$	−503.258	+	871.668i	−0.177928	+	0.308181i
$201$	817.812	+	1416.49i	0.286985	+	0.497073i
$202$	−1437.48			−0.500698
$203$		0			0
$204$	328.182			0.112634
$205$	−815.432	−	1412.37i	−0.277816	−	0.481191i
$206$	−1611.58	+	2791.34i	−0.545068	+	0.944086i
$207$	−663.068	+	1148.47i	−0.222640	+	0.385623i
$208$	310.697	+	538.143i	0.103572	+	0.179392i
$209$	−3966.13			−1.31265
$210$		0			0
$211$	912.614			0.297758			0.148879	−	0.988855i	$-0.452434\pi$
$211$	912.614			0.297758			0.148879	+	0.988855i	$0.452434\pi$
$212$	132.977	+	230.323i	0.0430798	+	0.0746164i
$213$	−196.114	+	339.679i	−0.0630868	+	0.109270i
$214$	−934.670	+	1618.90i	−0.298564	+	0.517129i
$215$	2601.70	+	4506.27i	0.825276	+	1.42942i
$216$	−216.000			−0.0680414
$217$		0			0
$218$	−2394.04			−0.743783
$219$	−271.949	−	471.029i	−0.0839114	−	0.145339i
$220$	−1641.90	+	2843.86i	−0.503168	+	0.871513i
$221$	−531.068	+	919.837i	−0.161645	+	0.279977i
$222$	−484.602	−	839.356i	−0.146506	−	0.253756i
$223$	4319.47			1.29710			0.648549	−	0.761173i	$-0.275376\pi$
$223$	4319.47			1.29710			0.648549	+	0.761173i	$0.275376\pi$
$224$		0			0
$225$	1132.33			0.335505
$226$	2384.64	+	4130.32i	0.701877	+	1.21569i
$227$	1030.64	−	1785.12i	0.301349	−	0.521951i	−0.675093	−	0.737733i	$-0.735897\pi$
$227$	1030.64	−	1785.12i	0.301349	−	0.521951i	0.976442	+	0.215782i	$0.0692299\pi$
$228$	−459.068	+	795.129i	−0.133344	+	0.230959i
$229$	−1737.32	−	3009.12i	−0.501332	−	0.868333i	−0.999999	−	0.00153905i	$-0.999510\pi$
$229$	−1737.32	−	3009.12i	−0.501332	−	0.868333i	0.498667	−	0.866794i	$-0.333823\pi$
$230$	4667.15			1.33801
$231$		0			0
$232$	1921.67			0.543809
$233$	−388.049	−	672.121i	−0.109107	−	0.188979i	0.806302	−	0.591505i	$-0.201466\pi$
$233$	−388.049	−	672.121i	−0.109107	−	0.188979i	−0.915409	+	0.402525i	$0.868132\pi$
$234$	349.534	−	605.411i	0.0976485	−	0.169132i
$235$	538.102	−	932.020i	0.149370	−	0.258716i
$236$	−923.856	−	1600.17i	−0.254822	−	0.441364i
$237$	1229.09			0.336869
$238$		0			0
$239$	2006.80			0.543133			0.271567	−	0.962420i	$-0.412458\pi$
$239$	2006.80			0.543133			0.271567	+	0.962420i	$0.412458\pi$
$240$	380.091	+	658.337i	0.102228	+	0.177064i
$241$	402.824	−	697.711i	0.107669	−	0.186488i	−0.807157	−	0.590337i	$-0.798995\pi$
$241$	402.824	−	697.711i	0.107669	−	0.186488i	0.914825	+	0.403850i	$0.132328\pi$
$242$	−1356.09	+	2348.81i	−0.360217	+	0.623915i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	−741.394			−0.194520
$245$		0			0
$246$	−617.864			−0.160136
$247$	−1485.74	−	2573.38i	−0.382734	−	0.662915i
$248$	−1186.70	+	2055.42i	−0.303852	+	0.526287i
$249$	−521.892	+	903.944i	−0.132826	+	0.230061i
$250$	−12.8977	−	22.3394i	−0.00326289	−	0.00565148i
$251$	−1421.78			−0.357539			−0.178769	−	0.983891i	$-0.557212\pi$
$251$	−1421.78			−0.357539			−0.178769	+	0.983891i	$0.557212\pi$
$252$		0			0
$253$	7638.12			1.89804
$254$	2673.92	+	4631.37i	0.660539	+	1.14409i
$255$	−649.682	+	1125.28i	−0.159548	+	0.276345i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−732.909	−	1269.44i	−0.177890	−	0.308114i	0.763268	−	0.646082i	$-0.223594\pi$
$257$	−732.909	−	1269.44i	−0.177890	−	0.308114i	−0.941157	+	0.337968i	$0.890260\pi$
$258$	1971.34			0.475699
$259$		0			0
$260$	−2460.27			−0.586845
$261$	−1080.94	−	1872.24i	−0.256354	−	0.444018i
$262$	−38.8598	+	67.3072i	−0.00916324	+	0.0158712i
$263$	−3495.69	+	6054.72i	−0.819596	+	1.41958i	0.0863847	+	0.996262i	$0.472469\pi$
$263$	−3495.69	+	6054.72i	−0.819596	+	1.41958i	−0.905980	+	0.423320i	$0.860865\pi$
$264$	622.045	+	1077.41i	0.145016	+	0.251175i
$265$	−1052.99			−0.244093
$266$		0			0
$267$	3471.48			0.795696
$268$	−1090.42	−	1888.66i	−0.248537	−	0.430478i
$269$	404.479	−	700.578i	0.0916786	−	0.158792i	−0.816539	−	0.577290i	$-0.804110\pi$
$269$	404.479	−	700.578i	0.0916786	−	0.158792i	0.908218	+	0.418498i	$0.137443\pi$
$270$	427.602	−	740.629i	0.0963816	−	0.166938i
$271$	3330.88	+	5769.26i	0.746630	+	1.29320i	0.949429	+	0.313981i	$0.101663\pi$
$271$	3330.88	+	5769.26i	0.746630	+	1.29320i	−0.202799	+	0.979220i	$0.565004\pi$
$272$	−437.576			−0.0975438
$273$		0			0
$274$	−1536.29			−0.338725
$275$	−3260.93	−	5648.09i	−0.715059	−	1.23852i
$276$	884.091	−	1531.29i	0.192812	−	0.333960i
$277$	3765.73	−	6522.44i	0.816827	−	1.41479i	−0.0911823	−	0.995834i	$-0.529065\pi$
$277$	3765.73	−	6522.44i	0.816827	−	1.41479i	0.908009	−	0.418951i	$-0.137602\pi$
$278$	1052.55	+	1823.07i	0.227078	+	0.393311i
$279$	2670.07			0.572949
$280$		0			0
$281$	1690.19			0.358819			0.179410	−	0.983774i	$-0.442581\pi$
$281$	1690.19			0.358819			0.179410	+	0.983774i	$0.442581\pi$
$282$	−203.864	−	353.102i	−0.0430493	−	0.0745636i
$283$	1589.12	−	2752.43i	0.333792	−	0.578145i	−0.649460	−	0.760396i	$-0.725005\pi$
$283$	1589.12	−	2752.43i	0.333792	−	0.578145i	0.983252	+	0.182251i	$0.0583384\pi$
$284$	261.485	−	452.905i	0.0546348	−	0.0946302i
$285$	−1817.58	−	3148.14i	−0.377769	−	0.654315i
$286$	−4026.41			−0.832470
$287$		0			0
$288$	288.000			0.0589256
$289$	2082.53	+	3607.05i	0.423882	+	0.734184i
$290$	−3804.21	+	6589.08i	−0.770313	+	1.33422i
$291$	−2427.45	+	4204.46i	−0.489002	+	0.846976i
$292$	362.598	+	628.039i	0.0726694	+	0.125867i
$293$	2176.53			0.433974			0.216987	−	0.976174i	$-0.430377\pi$
$293$	2176.53			0.433974			0.216987	+	0.976174i	$0.430377\pi$
$294$		0			0
$295$	7315.61			1.44383
$296$	646.136	+	1119.14i	0.126878	+	0.219759i
$297$	699.801	−	1212.09i	0.136722	−	0.236810i
$298$	−360.977	+	625.231i	−0.0701706	+	0.121539i
$299$	2861.30	+	4955.91i	0.553421	+	0.958554i
$300$	−1509.77			−0.290556
$301$		0			0
$302$	3096.78			0.590065
$303$	−1078.11	−	1867.35i	−0.204409	−	0.354047i
$304$	612.091	−	1060.17i	0.115480	−	0.200017i
$305$	1467.69	−	2542.12i	0.275541	−	0.477250i
$306$	246.136	+	426.321i	0.0459826	+	0.0796442i
$307$	−623.504			−0.115913			−0.0579564	−	0.998319i	$-0.518458\pi$
$307$	−623.504			−0.115913			−0.0579564	+	0.998319i	$0.518458\pi$
$308$		0			0
$309$	−4834.74			−0.890093
$310$	−4698.47	−	8137.98i	−0.860822	−	1.49099i
$311$	233.996	−	405.293i	0.0426647	−	0.0738973i	−0.843905	−	0.536493i	$-0.819749\pi$
$311$	233.996	−	405.293i	0.0426647	−	0.0738973i	0.886569	+	0.462596i	$0.153082\pi$
$312$	−466.045	+	807.214i	−0.0845661	+	0.146473i
$313$	1806.41	+	3128.79i	0.326211	+	0.565014i	0.981757	−	0.190141i	$-0.0608946\pi$
$313$	1806.41	+	3128.79i	0.326211	+	0.565014i	−0.655546	+	0.755156i	$0.727561\pi$
$314$	1934.14			0.347610
$315$		0			0
$316$	−1638.79			−0.291737
$317$	−2265.87	−	3924.60i	−0.401463	−	0.695355i	0.592439	−	0.805615i	$-0.298165\pi$
$317$	−2265.87	−	3924.60i	−0.401463	−	0.695355i	−0.993903	+	0.110260i	$0.964832\pi$
$318$	−199.466	+	345.485i	−0.0351745	+	0.0609240i
$319$	−6225.85	+	10783.5i	−1.09273	+	1.89266i
$320$	−506.788	−	877.782i	−0.0885322	−	0.153342i
$321$	−2804.01			−0.487553
$322$		0			0
$323$	2092.47			0.360459
$324$	−162.000	−	280.592i	−0.0277778	−	0.0481125i
$325$	2443.13	−	4231.63i	0.416987	−	0.722242i
$326$	1326.50	−	2297.57i	0.225362	−	0.390339i
$327$	−1795.53	−	3109.95i	−0.303648	−	0.525934i
$328$	823.818			0.138682
$329$		0			0
$330$	−4925.70			−0.821670
$331$	618.528	+	1071.32i	0.102711	+	0.177901i	0.912801	−	0.408405i	$-0.133915\pi$
$331$	618.528	+	1071.32i	0.102711	+	0.177901i	−0.810090	+	0.586306i	$0.800582\pi$
$332$	695.856	−	1205.26i	0.115030	−	0.199238i
$333$	726.903	−	1259.03i	0.119622	−	0.207191i
$334$	1416.70	+	2453.79i	0.232090	+	0.401992i
$335$	8634.53			1.40822
$336$		0			0
$337$	−1867.83			−0.301921			−0.150960	−	0.988540i	$-0.548237\pi$
$337$	−1867.83			−0.301921			−0.150960	+	0.988540i	$0.548237\pi$
$338$	688.678	+	1192.83i	0.110826	+	0.191956i
$339$	−3576.97	+	6195.49i	−0.573080	+	0.992604i
$340$	866.242	−	1500.38i	0.138172	−	0.239322i
$341$	−7689.37	−	13318.4i	−1.22112	−	2.11505i
$342$	−1377.20			−0.217751
$343$		0			0
$344$	−2628.45			−0.411967
$345$	3500.36	+	6062.81i	0.546241	+	0.946118i
$346$	−1036.60	+	1795.44i	−0.161063	+	0.278970i
$347$	31.6819	−	54.8746i	0.00490136	−	0.00848940i	−0.863564	−	0.504239i	$-0.831773\pi$
$347$	31.6819	−	54.8746i	0.00490136	−	0.00848940i	0.868466	+	0.495749i	$0.165107\pi$
$348$	1441.25	+	2496.32i	0.222009	+	0.384531i
$349$	−1223.79			−0.187702			−0.0938508	−	0.995586i	$-0.529918\pi$
$349$	−1223.79			−0.187702			−0.0938508	+	0.995586i	$0.529918\pi$
$350$		0			0
$351$	1048.60			0.159459
$352$	−829.394	−	1436.55i	−0.125588	−	0.217524i
$353$	−2257.81	+	3910.64i	−0.340428	+	0.589638i	−0.984512	−	0.175316i	$-0.943905\pi$
$353$	−2257.81	+	3910.64i	−0.340428	+	0.589638i	0.644085	+	0.764954i	$0.277238\pi$
$354$	1385.78	−	2400.25i	0.208061	−	0.360372i
$355$	1035.29	+	1793.18i	0.154782	+	0.268090i
$356$	−4628.64			−0.689093
$357$		0			0
$358$	−1534.86			−0.226592
$359$	−1114.25	−	1929.93i	−0.163810	−	0.283727i	0.772422	−	0.635109i	$-0.219045\pi$
$359$	−1114.25	−	1929.93i	−0.163810	−	0.283727i	−0.936232	+	0.351383i	$0.885712\pi$
$360$	−570.136	+	987.505i	−0.0834690	+	0.144572i
$361$	502.506	−	870.365i	0.0732622	−	0.126894i
$362$	−3957.71	−	6854.95i	−0.574620	−	0.995271i
$363$	−4068.26			−0.588232
$364$		0			0
$365$	−2871.26			−0.411749
$366$	−556.045	−	963.099i	−0.0794125	−	0.137546i
$367$	−718.670	+	1244.77i	−0.102219	+	0.177048i	−0.912598	−	0.408857i	$-0.865928\pi$
$367$	−718.670	+	1244.77i	−0.102219	+	0.177048i	0.810380	+	0.585905i	$0.199261\pi$
$368$	−1178.79	+	2041.72i	−0.166980	+	0.289217i
$369$	−463.398	−	802.628i	−0.0653754	−	0.113234i
$370$	−5116.47			−0.718899
$371$		0			0
$372$	−3560.09			−0.496188
$373$	6118.71	+	10597.9i	0.849370	+	1.47115i	0.881771	+	0.471677i	$0.156351\pi$
$373$	6118.71	+	10597.9i	0.849370	+	1.47115i	−0.0324014	+	0.999475i	$0.510315\pi$
$374$	1417.67	−	2455.47i	0.196005	−	0.339490i
$375$	19.3465	−	33.5092i	0.00266413	−	0.00461442i
$376$	271.818	+	470.803i	0.0372818	+	0.0645740i
$377$	−9329.00			−1.27445
$378$		0			0
$379$	−10647.0			−1.44301			−0.721503	−	0.692411i	$-0.756549\pi$
$379$	−10647.0			−1.44301			−0.721503	+	0.692411i	$0.756549\pi$
$380$	2423.44	+	4197.52i	0.327157	+	0.566653i
$381$	−4010.89	+	6947.06i	−0.539328	+	0.934143i
$382$	1805.30	−	3126.86i	0.241798	−	0.418807i
$383$	−3357.41	−	5815.20i	−0.447925	−	0.775829i	0.550326	−	0.834950i	$-0.314504\pi$
$383$	−3357.41	−	5815.20i	−0.447925	−	0.775829i	−0.998251	+	0.0591208i	$0.981170\pi$
$384$	−384.000			−0.0510310
$385$		0			0
$386$	6741.68			0.888970
$387$	1478.51	+	2560.85i	0.194203	+	0.336370i
$388$	3236.60	−	5605.95i	0.423488	−	0.733503i
$389$	5326.54	−	9225.83i	0.694258	−	1.20249i	−0.276173	−	0.961108i	$-0.589066\pi$
$389$	5326.54	−	9225.83i	0.694258	−	1.20249i	0.970430	−	0.241381i	$-0.0776005\pi$
$390$	−1845.20	−	3195.99i	−0.239578	−	0.414962i
$391$	−4029.76			−0.521211
$392$		0			0
$393$	−116.580			−0.0149635
$394$	4612.31	+	7988.76i	0.589758	+	1.02149i
$395$	3244.21	−	5619.14i	0.413250	−	0.715771i
$396$	−933.068	+	1616.12i	−0.118405	+	0.205084i
$397$	1610.52	+	2789.50i	0.203601	+	0.352648i	0.949686	−	0.313203i	$-0.101402\pi$
$397$	1610.52	+	2789.50i	0.203601	+	0.352648i	−0.746085	+	0.665851i	$0.768069\pi$
$398$	4459.73			0.561673
$399$		0			0
$400$	2013.03			0.251629
$401$	−6242.50	−	10812.3i	−0.777395	−	1.34649i	−0.933438	−	0.358738i	$-0.883207\pi$
$401$	−6242.50	−	10812.3i	−0.777395	−	1.34649i	0.156043	−	0.987750i	$-0.450126\pi$
$402$	1635.62	−	2832.99i	0.202929	−	0.351484i
$403$	5760.99	−	9978.32i	0.712097	−	1.23339i
$404$	1437.48	+	2489.80i	0.177024	+	0.306614i
$405$	1282.81			0.157391
$406$		0			0
$407$	−8373.46			−1.01980
$408$	−328.182	−	568.428i	−0.0398221	−	0.0689739i
$409$	3518.69	−	6094.56i	0.425399	−	0.736813i	−0.571059	−	0.820909i	$-0.693467\pi$
$409$	3518.69	−	6094.56i	0.425399	−	0.736813i	0.996458	+	0.0840967i	$0.0268004\pi$
$410$	−1630.86	+	2824.74i	−0.196445	+	0.340253i
$411$	−1152.22	−	1995.70i	−0.138284	−	0.239514i
$412$	6446.32			0.770843
$413$		0			0
$414$	2652.27			0.314860
$415$	2755.09	+	4771.95i	0.325884	+	0.564448i
$416$	621.394	−	1076.29i	0.0732364	−	0.126849i
$417$	−1578.82	+	2734.60i	−0.185408	+	0.321137i
$418$	3966.13	+	6869.54i	0.464090	+	0.803828i
$419$	1549.66			0.180682			0.0903410	−	0.995911i	$-0.471204\pi$
$419$	1549.66			0.180682			0.0903410	+	0.995911i	$0.471204\pi$
$420$		0			0
$421$	5531.63			0.640369			0.320184	−	0.947355i	$-0.396255\pi$
$421$	5531.63			0.640369			0.320184	+	0.947355i	$0.396255\pi$
$422$	−912.614	−	1580.69i	−0.105273	−	0.182339i
$423$	305.795	−	529.653i	0.0351496	−	0.0608809i
$424$	265.955	−	460.647i	0.0304620	−	0.0527618i
$425$	1720.42	+	2979.85i	0.196359	+	0.340103i
$426$	784.454			0.0892182
$427$		0			0
$428$	3738.68			0.422234
$429$	−3019.81	−	5230.46i	−0.339855	−	0.588646i
$430$	5203.39	−	9012.54i	0.583558	−	1.01075i
$431$	1014.97	−	1757.97i	0.113432	−	0.196470i	−0.803720	−	0.595008i	$-0.797149\pi$
$431$	1014.97	−	1757.97i	0.113432	−	0.196470i	0.917152	+	0.398538i	$0.130482\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	327.739			0.0363744			0.0181872	−	0.999835i	$-0.494211\pi$
$433$	327.739			0.0363744			0.0181872	+	0.999835i	$0.494211\pi$
$434$		0			0
$435$	−11412.6			−1.25792
$436$	2394.04	+	4146.60i	0.262967	+	0.455472i
$437$	5636.92	−	9763.43i	0.617049	−	1.06876i
$438$	−543.898	+	942.058i	−0.0593343	+	0.102770i
$439$	3954.34	+	6849.12i	0.429910	+	0.744625i	0.996865	−	0.0791234i	$-0.0252121\pi$
$439$	3954.34	+	6849.12i	0.429910	+	0.744625i	−0.566955	+	0.823749i	$0.691879\pi$
$440$	6567.61			0.711587
$441$		0			0
$442$	2124.27			0.228600
$443$	1460.41	+	2529.51i	0.156628	+	0.271288i	0.933651	−	0.358185i	$-0.116604\pi$
$443$	1460.41	+	2529.51i	0.156628	+	0.271288i	−0.777023	+	0.629473i	$0.783271\pi$
$444$	−969.205	+	1678.71i	−0.103596	+	0.179433i
$445$	9163.03	−	15870.8i	0.976111	−	1.69067i
$446$	−4319.47	−	7481.53i	−0.458593	−	0.794307i
$447$	−1082.93			−0.114588
$448$		0			0
$449$	−10240.2			−1.07631			−0.538156	−	0.842845i	$-0.680879\pi$
$449$	−10240.2			−1.07631			−0.538156	+	0.842845i	$0.680879\pi$
$450$	−1132.33	−	1961.25i	−0.118619	−	0.205454i
$451$	−2669.02	+	4622.88i	−0.278668	+	0.482668i
$452$	4769.29	−	8260.65i	0.496302	−	0.859620i
$453$	2322.59	+	4022.84i	0.240893	+	0.417239i
$454$	−4122.57			−0.426171
$455$		0			0
$456$	1836.27			0.188578
$457$	−2946.31	−	5103.17i	−0.301582	−	0.522355i	0.674913	−	0.737897i	$-0.264181\pi$
$457$	−2946.31	−	5103.17i	−0.301582	−	0.522355i	−0.976494	+	0.215543i	$0.930848\pi$
$458$	−3474.63	+	6018.24i	−0.354495	+	0.614004i
$459$	−369.205	+	639.481i	−0.0375446	+	0.0650292i
$460$	−4667.15	−	8083.74i	−0.473059	−	0.819362i
$461$	12643.4			1.27735			0.638677	−	0.769475i	$-0.279482\pi$
$461$	12643.4			1.27735			0.638677	+	0.769475i	$0.279482\pi$
$462$		0			0
$463$	15093.2			1.51499			0.757494	−	0.652842i	$-0.226423\pi$
$463$	15093.2			1.51499			0.757494	+	0.652842i	$0.226423\pi$
$464$	−1921.67	−	3328.42i	−0.192265	−	0.333013i
$465$	7047.70	−	12207.0i	0.702858	−	1.21739i
$466$	−776.099	+	1344.24i	−0.0771504	+	0.133628i
$467$	−1410.12	−	2442.39i	−0.139727	−	0.242014i	0.787666	−	0.616102i	$-0.211289\pi$
$467$	−1410.12	−	2442.39i	−0.139727	−	0.242014i	−0.927393	+	0.374088i	$0.877956\pi$
$468$	−1398.14			−0.138096
$469$		0			0
$470$	−2152.41			−0.211241
$471$	1450.60	+	2512.52i	0.141911	+	0.245798i
$472$	−1847.71	+	3200.33i	−0.180186	+	0.312091i
$473$	8515.72	−	14749.7i	0.827808	−	1.43381i
$474$	−1229.09	−	2128.85i	−0.119101	−	0.206289i
$475$	−9626.23			−0.929856
$476$		0			0
$477$	−598.398			−0.0574397
$478$	−2006.80	−	3475.87i	−0.192027	−	0.332600i
$479$	−8224.25	+	14244.8i	−0.784500	+	1.35879i	0.144798	+	0.989461i	$0.453747\pi$
$479$	−8224.25	+	14244.8i	−0.784500	+	1.35879i	−0.929297	+	0.369332i	$0.879586\pi$
$480$	760.182	−	1316.67i	0.0722862	−	0.125203i
$481$	−3136.76	−	5433.03i	−0.297347	−	0.515020i
$482$	−1611.30			−0.152267
$483$		0			0
$484$	5424.35			0.509424
$485$	12814.6	+	22195.5i	1.19975	+	2.07804i
$486$	243.000	−	420.888i	0.0226805	−	0.0392837i
$487$	−3165.53	+	5482.87i	−0.294546	+	0.510169i	−0.974879	−	0.222734i	$-0.928502\pi$
$487$	−3165.53	+	5482.87i	−0.294546	+	0.510169i	0.680333	+	0.732903i	$0.261835\pi$
$488$	741.394	+	1284.13i	0.0687732	+	0.119119i
$489$	3979.50			0.368015
$490$		0			0
$491$	−9286.90			−0.853588			−0.426794	−	0.904349i	$-0.640357\pi$
$491$	−9286.90			−0.853588			−0.426794	+	0.904349i	$0.640357\pi$
$492$	617.864	+	1070.17i	0.0566168	+	0.0980631i
$493$	3284.67	−	5689.21i	0.300069	−	0.519735i
$494$	−2971.48	+	5146.76i	−0.270634	+	0.468752i
$495$	−3694.28	−	6398.68i	−0.335445	−	0.581008i
$496$	4746.79			0.429712
$497$		0			0
$498$	2087.57			0.187844
$499$	121.725	+	210.835i	0.0109202	+	0.0189143i	0.871434	−	0.490513i	$-0.163191\pi$
$499$	121.725	+	210.835i	0.0109202	+	0.0189143i	−0.860514	+	0.509427i	$0.829857\pi$
$500$	−25.7954	+	44.6789i	−0.00230721	+	0.00399620i
$501$	−2125.05	+	3680.69i	−0.189501	+	0.328225i
$502$	1421.78	+	2462.60i	0.126409	+	0.218947i
$503$	−8499.30			−0.753409			−0.376705	−	0.926333i	$-0.622943\pi$
$503$	−8499.30			−0.753409			−0.376705	+	0.926333i	$0.622943\pi$
$504$		0			0
$505$	−11382.8			−1.00303
$506$	−7638.12	−	13229.6i	−0.671059	−	1.16231i
$507$	−1033.02	+	1789.24i	−0.0904890	+	0.156731i
$508$	5347.85	−	9262.75i	0.467072	−	0.808992i
$509$	−3841.55	−	6653.76i	−0.334526	−	0.579416i	0.648868	−	0.760901i	$-0.275243\pi$
$509$	−3841.55	−	6653.76i	−0.334526	−	0.579416i	−0.983394	+	0.181485i	$0.941910\pi$
$510$	2598.73			0.225634
$511$		0			0
$512$	512.000			0.0441942
$513$	−1032.90	−	1789.04i	−0.0888963	−	0.153973i
$514$	−1465.82	+	2538.87i	−0.125787	+	0.217869i
$515$	−12761.4	+	22103.4i	−1.09191	+	1.89124i
$516$	−1971.34	−	3414.46i	−0.168185	−	0.291305i
$517$	−3522.57			−0.299656
$518$		0			0
$519$	−3109.80			−0.263015
$520$	2460.27	+	4261.32i	0.207481	+	0.359368i
$521$	−10765.3	+	18646.1i	−0.905253	+	1.56794i	−0.0846750	+	0.996409i	$0.526985\pi$
$521$	−10765.3	+	18646.1i	−0.905253	+	1.56794i	−0.820578	+	0.571535i	$0.806348\pi$
$522$	−2161.87	+	3744.48i	−0.181270	+	0.313968i
$523$	−8423.53	−	14590.0i	−0.704274	−	1.21984i	−0.966953	−	0.254955i	$-0.917939\pi$
$523$	−8423.53	−	14590.0i	−0.704274	−	1.21984i	0.262679	−	0.964883i	$-0.415394\pi$
$524$	155.439			0.0129588
$525$		0			0
$526$	13982.8			1.15908
$527$	4056.80	+	7026.58i	0.335326	+	0.580802i
$528$	1244.09	−	2154.83i	0.102542	−	0.177608i
$529$	−4772.29	+	8265.84i	−0.392232	+	0.679366i
$530$	1052.99	+	1823.83i	0.0862998	+	0.149476i
$531$	4157.35			0.339762
$532$		0			0
$533$	−3999.34			−0.325011
$534$	−3471.48	−	6012.77i	−0.281321	−	0.487263i
$535$	−7401.24	+	12819.3i	−0.598100	+	1.03594i
$536$	−2180.83	+	3777.31i	−0.175742	+	0.304394i
$537$	−1151.15	−	1993.85i	−0.0925059	−	0.160225i
$538$	−1617.92			−0.129653
$539$		0			0
$540$	−1710.41			−0.136304
$541$	−8720.02	−	15103.5i	−0.692981	−	1.20028i	−0.970856	−	0.239662i	$-0.922963\pi$
$541$	−8720.02	−	15103.5i	−0.692981	−	1.20028i	0.277875	−	0.960617i	$-0.410370\pi$
$542$	6661.77	−	11538.5i	0.527947	−	0.914432i
$543$	5936.56	−	10282.4i	0.469175	−	0.812636i
$544$	437.576	+	757.903i	0.0344870	+	0.0597332i
$545$	−18957.3			−1.48999
$546$		0			0
$547$	11520.7			0.900530			0.450265	−	0.892895i	$-0.351329\pi$
$547$	11520.7			0.900530			0.450265	+	0.892895i	$0.351329\pi$
$548$	1536.29	+	2660.93i	0.119757	+	0.207426i
$549$	834.068	−	1444.65i	0.0648400	−	0.112306i
$550$	−6521.86	+	11296.2i	−0.505623	+	0.875765i
$551$	9189.33	+	15916.4i	0.710488	+	1.23060i
$552$	−3536.36			−0.272677
$553$		0			0
$554$	−15062.9			−1.15517
$555$	−3837.35	−	6646.49i	−0.293489	−	0.508338i
$556$	2105.10	−	3646.14i	0.160568	−	0.278113i
$557$	−5746.51	+	9953.25i	−0.437141	+	0.757151i	−0.997468	−	0.0711212i	$-0.977342\pi$
$557$	−5746.51	+	9953.25i	−0.437141	+	0.757151i	0.560327	+	0.828272i	$0.310676\pi$
$558$	−2670.07	−	4624.69i	−0.202568	−	0.350858i
$559$	12760.2			0.965472
$560$		0			0
$561$	4253.00			0.320075
$562$	−1690.19	−	2927.49i	−0.126862	−	0.219731i
$563$	9055.65	−	15684.8i	0.677886	−	1.17413i	−0.297730	−	0.954650i	$-0.596230\pi$
$563$	9055.65	−	15684.8i	0.677886	−	1.17413i	0.975616	−	0.219483i	$-0.0704372\pi$
$564$	−407.727	+	706.204i	−0.0304405	+	0.0527244i
$565$	18882.9	+	32706.2i	1.40604	+	2.43533i
$566$	−6356.46			−0.472053
$567$		0			0
$568$	−1045.94			−0.0772652
$569$	−2208.81	−	3825.77i	−0.162738	−	0.281871i	0.773112	−	0.634270i	$-0.218699\pi$
$569$	−2208.81	−	3825.77i	−0.162738	−	0.281871i	−0.935850	+	0.352399i	$0.885366\pi$
$570$	−3635.16	+	6296.28i	−0.267123	+	0.462670i
$571$	−6609.87	+	11448.6i	−0.484439	+	0.839073i	−0.999840	−	0.0178762i	$-0.994310\pi$
$571$	−6609.87	+	11448.6i	−0.484439	+	0.839073i	0.515401	+	0.856949i	$0.327643\pi$
$572$	4026.41	+	6973.95i	0.294323	+	0.509782i
$573$	5415.89			0.394855
$574$		0			0
$575$	18538.6			1.34454
$576$	−288.000	−	498.831i	−0.0208333	−	0.0360844i
$577$	−8748.20	+	15152.3i	−0.631182	+	1.09324i	0.356128	+	0.934437i	$0.384097\pi$
$577$	−8748.20	+	15152.3i	−0.631182	+	1.09324i	−0.987310	+	0.158803i	$0.949237\pi$
$578$	4165.06	−	7214.10i	0.299730	−	0.519147i
$579$	5056.26	+	8757.70i	0.362921	+	0.628597i
$580$	15216.8			1.08939
$581$		0			0
$582$	9709.80			0.691553
$583$	1723.29	+	2984.83i	0.122421	+	0.212039i
$584$	725.197	−	1256.08i	0.0513850	−	0.0890015i
$585$	2767.81	−	4793.98i	0.195615	−	0.338815i
$586$	−2176.53	−	3769.87i	−0.153433	−	0.265754i
$587$	4280.53			0.300982			0.150491	−	0.988611i	$-0.451915\pi$
$587$	4280.53			0.300982			0.150491	+	0.988611i	$0.451915\pi$
$588$		0			0
$589$	−22699.0			−1.58794
$590$	−7315.61	−	12671.0i	−0.510473	−	0.884165i
$591$	−6918.47	+	11983.1i	−0.481536	+	0.834044i
$592$	1292.27	−	2238.28i	0.0897164	−	0.155393i
$593$	−795.466	−	1377.79i	−0.0550858	−	0.0954114i	0.837168	−	0.546946i	$-0.184210\pi$
$593$	−795.466	−	1377.79i	−0.0550858	−	0.0954114i	−0.892253	+	0.451535i	$0.850877\pi$
$594$	−2799.20			−0.193355
$595$		0			0
$596$	1443.91			0.0992363
$597$	3344.80	+	5793.36i	0.229302	+	0.397163i
$598$	5722.59	−	9911.82i	0.391328	−	0.677800i
$599$	6961.42	−	12057.5i	0.474851	−	0.822467i	−0.524734	−	0.851266i	$-0.675835\pi$
$599$	6961.42	−	12057.5i	0.474851	−	0.822467i	0.999585	+	0.0287997i	$0.00916851\pi$
$600$	1509.77	+	2615.00i	0.102727	+	0.177928i
$601$	−12559.7			−0.852446			−0.426223	−	0.904618i	$-0.640156\pi$
$601$	−12559.7			−0.852446			−0.426223	+	0.904618i	$0.640156\pi$
$602$		0			0
$603$	4906.87			0.331382
$604$	−3096.78	−	5363.78i	−0.208620	−	0.361340i
$605$	−10738.3	+	18599.2i	−0.721607	+	1.24986i
$606$	−2156.23	+	3734.70i	−0.144539	+	0.250349i
$607$	3839.19	+	6649.66i	0.256718	+	0.444648i	0.965361	−	0.260919i	$-0.0840256\pi$
$607$	3839.19	+	6649.66i	0.256718	+	0.444648i	−0.708643	+	0.705567i	$0.750692\pi$
$608$	−2448.36			−0.163313
$609$		0			0
$610$	−5870.77			−0.389673
$611$	−1319.58	−	2285.58i	−0.0873723	−	0.151333i
$612$	492.273	−	852.641i	0.0325146	−	0.0563170i
$613$	−3079.19	+	5333.31i	−0.202883	+	0.351403i	−0.949456	−	0.313900i	$-0.898364\pi$
$613$	−3079.19	+	5333.31i	−0.202883	+	0.351403i	0.746573	+	0.665303i	$0.231698\pi$
$614$	623.504	+	1079.94i	0.0409814	+	0.0709818i
$615$	−4892.59			−0.320794
$616$		0			0
$617$	8813.12			0.575045			0.287523	−	0.957774i	$-0.407168\pi$
$617$	8813.12			0.575045			0.287523	+	0.957774i	$0.407168\pi$
$618$	4834.74	+	8374.01i	0.314695	+	0.545068i
$619$	11595.0	−	20083.1i	0.752894	−	1.30405i	−0.193521	−	0.981096i	$-0.561991\pi$
$619$	11595.0	−	20083.1i	0.752894	−	1.30405i	0.946415	−	0.322954i	$-0.104676\pi$
$620$	−9396.93	+	16276.0i	−0.608693	+	1.05429i
$621$	1989.20	+	3445.40i	0.128541	+	0.222640i
$622$	−935.985			−0.0603369
$623$		0			0
$624$	1864.18			0.119595
$625$	7761.27	+	13442.9i	0.496721	+	0.860346i
$626$	3612.81	−	6257.57i	0.230666	−	0.399525i
$627$	−5949.19	+	10304.3i	−0.378928	+	0.656323i
$628$	−1934.14	−	3350.02i	−0.122899	−	0.212867i
$629$	4417.71			0.280041
$630$		0			0
$631$	7936.94			0.500736			0.250368	−	0.968151i	$-0.419448\pi$
$631$	7936.94			0.500736			0.250368	+	0.968151i	$0.419448\pi$
$632$	1638.79	+	2838.46i	0.103145	+	0.178652i
$633$	1368.92	−	2371.04i	0.0859553	−	0.148879i
$634$	−4531.74	+	7849.20i	−0.283877	+	0.491690i
$635$	21173.6	+	36673.8i	1.32323	+	2.29190i
$636$	797.864			0.0497443
$637$		0			0
$638$	24903.4			1.54535
$639$	588.341	+	1019.04i	0.0364232	+	0.0630868i
$640$	−1013.58	+	1755.56i	−0.0626017	+	0.108429i
$641$	−16057.3	+	27812.1i	−0.989432	+	1.71375i	−0.369146	+	0.929371i	$0.620350\pi$
$641$	−16057.3	+	27812.1i	−0.989432	+	1.71375i	−0.620286	+	0.784376i	$0.712984\pi$
$642$	2804.01	+	4856.69i	0.172376	+	0.298564i
$643$	24786.7			1.52021			0.760104	−	0.649802i	$-0.225148\pi$
$643$	24786.7			1.52021			0.760104	+	0.649802i	$0.225148\pi$
$644$		0			0
$645$	15610.2			0.952946
$646$	−2092.47	−	3624.26i	−0.127441	−	0.220735i
$647$	3772.80	−	6534.67i	0.229249	−	0.397070i	−0.728337	−	0.685219i	$-0.759706\pi$
$647$	3772.80	−	6534.67i	0.229249	−	0.397070i	0.957586	+	0.288149i	$0.0930398\pi$
$648$	−324.000	+	561.184i	−0.0196419	+	0.0340207i
$649$	−11972.5	−	20737.0i	−0.724133	−	1.25423i
$650$	−9772.54			−0.589708
$651$		0			0
$652$	−5306.00			−0.318710
$653$	2444.49	+	4233.99i	0.146494	+	0.253735i	0.929929	−	0.367738i	$-0.119868\pi$
$653$	2444.49	+	4233.99i	0.146494	+	0.253735i	−0.783435	+	0.621473i	$0.786534\pi$
$654$	−3591.06	+	6219.89i	−0.214712	+	0.371892i
$655$	−307.714	+	532.976i	−0.0183563	+	0.0317941i
$656$	−823.818	−	1426.89i	−0.0490316	−	0.0849251i
$657$	−1631.69			−0.0968926
$658$		0			0
$659$	25895.9			1.53075			0.765374	−	0.643586i	$-0.222554\pi$
$659$	25895.9			1.53075			0.765374	+	0.643586i	$0.222554\pi$
$660$	4925.70	+	8531.57i	0.290504	+	0.503168i
$661$	4091.68	−	7087.00i	0.240769	−	0.417023i	−0.720165	−	0.693803i	$-0.755934\pi$
$661$	4091.68	−	7087.00i	0.240769	−	0.417023i	0.960933	+	0.276780i	$0.0892672\pi$
$662$	1237.06	−	2142.65i	0.0726278	−	0.125795i
$663$	1593.20	+	2759.51i	0.0933257	+	0.161645i
$664$	−2783.42			−0.162677
$665$		0			0
$666$	−2907.61			−0.169171
$667$	−17697.2	−	30652.4i	−1.02734	−	1.77941i
$668$	2833.39	−	4907.58i	0.164113	−	0.284252i
$669$	6479.20	−	11222.3i	0.374440	−	0.648549i
$670$	−8634.53	−	14955.4i	−0.497882	−	0.862357i
$671$	−9607.93			−0.552772
$672$		0			0
$673$	−4635.02			−0.265478			−0.132739	−	0.991151i	$-0.542377\pi$
$673$	−4635.02			−0.265478			−0.132739	+	0.991151i	$0.542377\pi$
$674$	1867.83	+	3235.18i	0.106745	+	0.184888i
$675$	1698.49	−	2941.88i	0.0968520	−	0.167753i
$676$	1377.36	−	2385.65i	0.0783657	−	0.135733i
$677$	−12192.9	−	21118.7i	−0.692187	−	1.19890i	−0.971120	−	0.238593i	$-0.923314\pi$
$677$	−12192.9	−	21118.7i	−0.692187	−	1.19890i	0.278932	−	0.960311i	$-0.410020\pi$
$678$	14307.9			0.810458
$679$		0			0
$680$	−3464.97			−0.195405
$681$	−3091.93	−	5355.37i	−0.173984	−	0.301349i
$682$	−15378.7	+	26636.8i	−0.863464	+	1.49556i
$683$	9196.71	−	15929.2i	0.515230	−	0.892405i	−0.484613	−	0.874728i	$-0.661040\pi$
$683$	9196.71	−	15929.2i	0.515230	−	0.892405i	0.999844	−	0.0176767i	$-0.00562697\pi$
$684$	1377.20	+	2385.39i	0.0769864	+	0.133344i
$685$	−12165.2			−0.678552
$686$		0			0
$687$	−10423.9			−0.578889
$688$	2628.45	+	4552.62i	0.145652	+	0.252277i
$689$	−1291.11	+	2236.27i	−0.0713897	+	0.123651i
$690$	7000.73	−	12125.6i	0.386251	−	0.669006i
$691$	−7449.44	−	12902.8i	−0.410116	−	0.710341i	0.584786	−	0.811187i	$-0.301178\pi$
$691$	−7449.44	−	12902.8i	−0.410116	−	0.710341i	−0.994902	+	0.100846i	$0.967845\pi$
$692$	4146.39			0.227778
$693$		0			0
$694$	−126.727			−0.00693157
$695$	8334.67	+	14436.1i	0.454895	+	0.787902i
$696$	2882.50	−	4992.64i	0.156984	−	0.271904i
$697$	1408.14	−	2438.96i	0.0765236	−	0.132543i
$698$	1223.79	+	2119.66i	0.0663625	+	0.114943i
$699$	−2328.30			−0.125986
$700$		0			0
$701$	−5725.70			−0.308497			−0.154249	−	0.988032i	$-0.549296\pi$
$701$	−5725.70			−0.308497			−0.154249	+	0.988032i	$0.549296\pi$
$702$	−1048.60	−	1816.23i	−0.0563774	−	0.0976485i
$703$	−6179.60	+	10703.4i	−0.331533	+	0.574232i
$704$	−1658.79	+	2873.10i	−0.0888039	+	0.153813i
$705$	−1614.31	−	2796.06i	−0.0862387	−	0.149370i
$706$	9031.23			0.481437
$707$		0			0
$708$	−5543.14			−0.294243
$709$	11728.4	+	20314.2i	0.621255	+	1.07604i	0.989252	+	0.146218i	$0.0467101\pi$
$709$	11728.4	+	20314.2i	0.621255	+	1.07604i	−0.367998	+	0.929827i	$0.619957\pi$
$710$	2070.58	−	3586.36i	0.109447	−	0.189568i
$711$	1843.64	−	3193.27i	0.0972458	−	0.168435i
$712$	4628.64	+	8017.03i	0.243631	+	0.421982i
$713$	43714.5			2.29610
$714$		0			0
$715$	−31883.4			−1.66765
$716$	1534.86	+	2658.46i	0.0801125	+	0.138759i
$717$	3010.19	−	5213.81i	0.156789	−	0.271567i
$718$	−2228.49	+	3859.86i	−0.115831	+	0.200625i
$719$	−4229.50	−	7325.71i	−0.219379	−	0.379976i	0.735239	−	0.677808i	$-0.237070\pi$
$719$	−4229.50	−	7325.71i	−0.219379	−	0.379976i	−0.954618	+	0.297832i	$0.903737\pi$
$720$	2280.55			0.118043
$721$		0			0
$722$	−2010.02			−0.103608
$723$	−1208.47	−	2093.13i	−0.0621626	−	0.107669i
$724$	−7915.42	+	13709.9i	−0.406318	+	0.703763i
$725$	−15110.8	+	26172.7i	−0.774072	+	1.34073i
$726$	4068.26	+	7046.44i	0.207972	+	0.360217i
$727$	11822.2			0.603111			0.301555	−	0.953449i	$-0.402494\pi$
$727$	11822.2			0.603111			0.301555	+	0.953449i	$0.402494\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	2871.26	+	4973.16i	0.145575	+	0.252144i
$731$	−4492.77	+	7781.70i	−0.227320	+	0.393730i
$732$	−1112.09	+	1926.20i	−0.0561531	+	0.0972600i
$733$	2514.48	+	4355.20i	0.126704	+	0.219458i	0.922398	−	0.386241i	$-0.126227\pi$
$733$	2514.48	+	4355.20i	0.126704	+	0.219458i	−0.795694	+	0.605699i	$0.792893\pi$
$734$	2874.68			0.144559
$735$		0			0
$736$	4715.15			0.236145
$737$	−14131.0	−	24475.6i	−0.706272	−	1.22330i
$738$	−926.795	+	1605.26i	−0.0462274	+	0.0800682i
$739$	8871.95	−	15366.7i	0.441624	−	0.764914i	−0.556187	−	0.831057i	$-0.687736\pi$
$739$	8871.95	−	15366.7i	0.441624	−	0.764914i	0.997810	+	0.0661431i	$0.0210694\pi$
$740$	5116.47	+	8861.99i	0.254169	+	0.440234i
$741$	−8914.44			−0.441944
$742$		0			0
$743$	−13202.3			−0.651877			−0.325938	−	0.945391i	$-0.605680\pi$
$743$	−13202.3			−0.651877			−0.325938	+	0.945391i	$0.605680\pi$
$744$	3560.09	+	6166.26i	0.175429	+	0.303852i
$745$	−2858.42	+	4950.93i	−0.140570	+	0.243474i
$746$	12237.4	−	21195.8i	0.600595	−	1.04026i
$747$	1565.68	+	2711.83i	0.0766869	+	0.132826i
$748$	−5670.67			−0.277193
$749$		0			0
$750$	−77.3861			−0.00376766
$751$	−7800.49	−	13510.8i	−0.379020	−	0.656482i	0.611900	−	0.790935i	$-0.290406\pi$
$751$	−7800.49	−	13510.8i	−0.379020	−	0.656482i	−0.990920	+	0.134453i	$0.957072\pi$
$752$	543.636	−	941.606i	0.0263622	−	0.0456607i
$753$	−2132.68	+	3693.90i	−0.103213	+	0.178769i
$754$	9329.00	+	16158.3i	0.450586	+	0.780439i
$755$	24522.0			1.18205
$756$		0			0
$757$	2948.08			0.141545			0.0707725	−	0.997492i	$-0.477454\pi$
$757$	2948.08			0.141545			0.0707725	+	0.997492i	$0.477454\pi$
$758$	10647.0	+	18441.1i	0.510180	+	0.883657i
$759$	11457.2	−	19844.4i	0.547917	−	0.949021i
$760$	4846.88	−	8395.04i	0.231335	−	0.400684i
$761$	848.515	+	1469.67i	0.0404187	+	0.0700073i	0.885527	−	0.464588i	$-0.153797\pi$
$761$	848.515	+	1469.67i	0.0404187	+	0.0700073i	−0.845108	+	0.534595i	$0.820464\pi$
$762$	16043.5			0.762725
$763$		0			0
$764$	−7221.18			−0.341954
$765$	1949.05	+	3375.85i	0.0921149	+	0.159548i
$766$	−6714.81	+	11630.4i	−0.316731	+	0.548594i
$767$	8969.98	−	15536.5i	0.422278	−	0.731407i
$768$	384.000	+	665.108i	0.0180422	+	0.0312500i
$769$	96.7799			0.00453833			0.00226916	−	0.999997i	$-0.499278\pi$
$769$	96.7799			0.00453833			0.00226916	+	0.999997i	$0.499278\pi$
$770$		0			0
$771$	−4397.45			−0.205409
$772$	−6741.68	−	11676.9i	−0.314298	−	0.544381i
$773$	18163.4	−	31459.9i	0.845138	−	1.46382i	−0.0403629	−	0.999185i	$-0.512851\pi$
$773$	18163.4	−	31459.9i	0.845138	−	1.46382i	0.885501	−	0.464637i	$-0.153815\pi$
$774$	2957.01	−	5121.69i	0.137322	−	0.237849i
$775$	−18662.9	−	32325.2i	−0.865023	−	1.49826i
$776$	−12946.4			−0.598903
$777$		0			0
$778$	−21306.2			−0.981828
$779$	3939.47	+	6823.35i	0.181189	+	0.313828i
$780$	−3690.41	+	6391.98i	−0.169407	+	0.293422i
$781$	3388.66	−	5869.32i	0.155257	−	0.268913i
$782$	4029.76	+	6979.74i	0.184276	+	0.319175i
$783$	−6485.62			−0.296012
$784$		0			0
$785$	15315.6			0.696352
$786$	116.580	+	201.922i	0.00529040	+	0.00916324i
$787$	3548.23	−	6145.72i	0.160713	−	0.278362i	−0.774412	−	0.632682i	$-0.781954\pi$
$787$	3548.23	−	6145.72i	0.160713	−	0.278362i	0.935124	+	0.354319i	$0.115287\pi$
$788$	9224.62	−	15977.5i	0.417022	−	0.722304i
$789$	10487.1	+	18164.2i	0.473194	+	0.819596i
$790$	−12976.8			−0.584424
$791$		0			0
$792$	3732.27			0.167450
$793$	−3599.20	−	6234.00i	−0.161174	−	0.279162i
$794$	3221.04	−	5579.01i	0.143968	−	0.249360i
$795$	−1579.48	+	2735.74i	−0.0704635	+	0.122046i
$796$	−4459.73	−	7724.47i	−0.198581	−	0.343953i
$797$	−40289.6			−1.79063			−0.895314	−	0.445436i	$-0.853049\pi$
$797$	−40289.6			−1.79063			−0.895314	+	0.445436i	$0.853049\pi$
$798$		0			0
$799$	1858.45			0.0822871
$800$	−2013.03	−	3486.67i	−0.0889642	−	0.154091i
$801$	5207.22	−	9019.16i	0.229698	−	0.397848i
$802$	−12485.0	+	21624.7i	−0.549702	+	0.952111i
$803$	4699.02	+	8138.93i	0.206506	+	0.357680i
$804$	−6542.50			−0.286985
$805$		0			0
$806$	−23043.9			−1.00706
$807$	−1213.44	−	2101.74i	−0.0529306	−	0.0916786i
$808$	2874.97	−	4979.59i	0.125175	−	0.216809i
$809$	5782.98	−	10016.4i	0.251321	−	0.435301i	−0.712569	−	0.701602i	$-0.752468\pi$
$809$	5782.98	−	10016.4i	0.251321	−	0.435301i	0.963890	+	0.266301i	$0.0858017\pi$
$810$	−1282.81	−	2221.89i	−0.0556460	−	0.0963816i
$811$	−18014.2			−0.779981			−0.389991	−	0.920819i	$-0.627522\pi$
$811$	−18014.2			−0.779981			−0.389991	+	0.920819i	$0.627522\pi$
$812$		0			0
$813$	19985.3			0.862134
$814$	8373.46	+	14503.3i	0.360552	+	0.624495i
$815$	10504.0	−	18193.4i	0.451458	−	0.781948i
$816$	−656.364	+	1136.86i	−0.0281585	+	0.0487719i
$817$	−12569.2	−	21770.4i	−0.538237	−	0.932253i
$818$	−14074.8			−0.601605
$819$		0			0
$820$	6523.45			0.277816
$821$	8396.22	+	14542.7i	0.356918	+	0.618201i	0.987444	−	0.157967i	$-0.0504941\pi$
$821$	8396.22	+	14542.7i	0.356918	+	0.618201i	−0.630526	+	0.776168i	$0.717161\pi$
$822$	−2304.43	+	3991.39i	−0.0977814	+	0.169362i
$823$	4409.52	−	7637.50i	0.186763	−	0.323483i	−0.757406	−	0.652944i	$-0.773534\pi$
$823$	4409.52	−	7637.50i	0.186763	−	0.323483i	0.944169	+	0.329461i	$0.106867\pi$
$824$	−6446.32	−	11165.4i	−0.272534	−	0.472043i
$825$	−19565.6			−0.825680
$826$		0			0
$827$	8250.13			0.346898			0.173449	−	0.984843i	$-0.444509\pi$
$827$	8250.13			0.346898			0.173449	+	0.984843i	$0.444509\pi$
$828$	−2652.27	−	4593.87i	−0.111320	−	0.192812i
$829$	−10775.2	+	18663.3i	−0.451435	+	0.781909i	−0.998475	−	0.0551975i	$-0.982421\pi$
$829$	−10775.2	+	18663.3i	−0.451435	+	0.781909i	0.547040	+	0.837106i	$0.315754\pi$
$830$	5510.18	−	9543.91i	0.230435	−	0.399125i
$831$	−11297.2	−	19567.3i	−0.471595	−	0.816827i
$832$	−2485.58			−0.103572
$833$		0			0
$834$	6315.30			0.262207
$835$	11218.2	+	19430.5i	0.464936	+	0.805293i
$836$	7932.26	−	13739.1i	0.328161	−	0.568392i
$837$	4005.10	−	6937.04i	0.165396	−	0.286475i
$838$	−1549.66	−	2684.09i	−0.0638808	−	0.110645i
$839$	−30130.4			−1.23983			−0.619916	−	0.784669i	$-0.712833\pi$
$839$	−30130.4			−1.23983			−0.619916	+	0.784669i	$0.712833\pi$
$840$		0			0
$841$	33311.0			1.36582
$842$	−5531.63	−	9581.07i	−0.226405	−	0.392144i
$843$	2535.28	−	4391.24i	0.103582	−	0.179410i
$844$	−1825.23	+	3161.39i	−0.0744395	+	0.128933i
$845$	5453.34	+	9445.46i	0.222012	+	0.384537i
$846$	−1223.18			−0.0497091
$847$		0			0
$848$	−1063.82			−0.0430798
$849$	−4767.35	−	8257.29i	−0.192715	−	0.333792i
$850$	3440.83	−	5959.70i	0.138847	−	0.240489i
$851$	11900.9	−	20613.0i	0.479386	−	0.830321i
$852$	−784.454	−	1358.72i	−0.0315434	−	0.0546348i
$853$	40738.6			1.63525			0.817623	−	0.575754i	$-0.195291\pi$
$853$	40738.6			1.63525			0.817623	+	0.575754i	$0.195291\pi$
$854$		0			0
$855$	−10905.5			−0.436210
$856$	−3738.68	−	6475.59i	−0.149282	−	0.258564i
$857$	−18254.1	+	31617.0i	−0.727594	+	1.26023i	0.230303	+	0.973119i	$0.426028\pi$
$857$	−18254.1	+	31617.0i	−0.727594	+	1.26023i	−0.957897	+	0.287111i	$0.907305\pi$
$858$	−6039.61	+	10460.9i	−0.240314	+	0.416235i
$859$	−10990.4	−	19036.0i	−0.436541	−	0.756110i	0.560879	−	0.827897i	$-0.310463\pi$
$859$	−10990.4	−	19036.0i	−0.436541	−	0.756110i	−0.997420	+	0.0717871i	$0.977130\pi$
$860$	−20813.6			−0.825276
$861$		0			0
$862$	−4059.86			−0.160417
$863$	11713.0	+	20287.6i	0.462012	+	0.800228i	0.999061	−	0.0433226i	$-0.0137943\pi$
$863$	11713.0	+	20287.6i	0.462012	+	0.800228i	−0.537049	+	0.843551i	$0.680461\pi$
$864$	432.000	−	748.246i	0.0170103	−	0.0294628i
$865$	−8208.37	+	14217.3i	−0.322651	+	0.558847i
$866$	−327.739	−	567.660i	−0.0128603	−	0.0222747i
$867$	12495.2			0.489456
$868$		0			0
$869$	−21237.5			−0.829037
$870$	11412.6	+	19767.2i	0.444740	+	0.770313i
$871$	10587.2	−	18337.5i	0.411863	−	0.713367i
$872$	4788.08	−	8293.19i	0.185946	−	0.322068i
$873$	7282.35	+	12613.4i	0.282325	+	0.489002i
$874$	−22547.7			−0.872639
$875$		0			0
$876$	2175.59			0.0839114
$877$	−153.701	−	266.217i	−0.00591802	−	0.0102503i	0.863051	−	0.505116i	$-0.168550\pi$
$877$	−153.701	−	266.217i	−0.00591802	−	0.0102503i	−0.868969	+	0.494866i	$0.835217\pi$
$878$	7908.68	−	13698.2i	0.303992	−	0.526530i
$879$	3264.80	−	5654.80i	0.125278	−	0.216987i
$880$	−6567.61	−	11375.4i	−0.251584	−	0.435756i
$881$	19941.7			0.762605			0.381302	−	0.924450i	$-0.375476\pi$
$881$	19941.7			0.762605			0.381302	+	0.924450i	$0.375476\pi$
$882$		0			0
$883$	−37524.1			−1.43011			−0.715056	−	0.699068i	$-0.753599\pi$
$883$	−37524.1			−1.43011			−0.715056	+	0.699068i	$0.753599\pi$
$884$	−2124.27	−	3679.35i	−0.0808224	−	0.139989i
$885$	10973.4	−	19006.5i	0.416799	−	0.721917i
$886$	2920.82	−	5059.01i	0.110753	−	0.191829i
$887$	−1440.10	−	2494.33i	−0.0545140	−	0.0944210i	0.837481	−	0.546467i	$-0.184028\pi$
$887$	−1440.10	−	2494.33i	−0.0545140	−	0.0944210i	−0.891995	+	0.452046i	$0.850694\pi$
$888$	3876.82			0.146506
$889$		0			0
$890$	−36652.1			−1.38043
$891$	−2099.40	−	3636.27i	−0.0789368	−	0.136722i
$892$	−8638.93	+	14963.1i	−0.324274	+	0.561660i
$893$	−2599.65	+	4502.72i	−0.0974176	+	0.168732i
$894$	1082.93	+	1875.69i	0.0405130	+	0.0701706i
$895$	−12153.9			−0.453922
$896$		0			0
$897$	17167.8			0.639036
$898$	10240.2	+	17736.5i	0.380534	+	0.659104i
$899$	−35631.8	+	61716.1i	−1.32190	+	2.28960i
$900$	−2264.66	+	3922.50i	−0.0838763	+	0.145278i
$901$	−909.182	−	1574.75i	−0.0336174	−	0.0582270i
$902$	10676.1			0.394096
$903$		0			0
$904$	−19077.2			−0.701877
$905$	−31339.4	−	54281.4i	−1.15111	−	1.99378i
$906$	4645.17	−	8045.67i	0.170337	−	0.295033i
$907$	−9159.62	+	15864.9i	−0.335326	+	0.580801i	−0.983547	−	0.180651i	$-0.942180\pi$
$907$	−9159.62	+	15864.9i	−0.335326	+	0.580801i	0.648222	+	0.761452i	$0.275513\pi$
$908$	4122.57	+	7140.50i	0.150674	+	0.260975i
$909$	−6468.68			−0.236031
$910$		0			0
$911$	46150.7			1.67842			0.839210	−	0.543807i	$-0.183018\pi$
$911$	46150.7			1.67842			0.839210	+	0.543807i	$0.183018\pi$
$912$	−1836.27	−	3180.52i	−0.0666722	−	0.115480i
$913$	9017.79	−	15619.3i	0.326884	−	0.566180i
$914$	−5892.63	+	10206.3i	−0.213250	+	0.369360i
$915$	−4403.08	−	7626.36i	−0.159083	−	0.275541i
$916$	13898.5			0.501332
$917$		0			0
$918$	1476.82			0.0530961
$919$	−23632.1	−	40932.1i	−0.848261	−	1.46923i	−0.882758	−	0.469827i	$-0.844316\pi$
$919$	−23632.1	−	40932.1i	−0.848261	−	1.46923i	0.0344969	−	0.999405i	$-0.489017\pi$
$920$	−9334.30	+	16167.5i	−0.334503	+	0.579376i
$921$	−935.256	+	1619.91i	−0.0334612	+	0.0579564i
$922$	−12643.4	−	21899.0i	−0.451613	−	0.782217i
$923$	5077.66			0.181076
$924$		0			0
$925$	−20323.3			−0.722407
$926$	−15093.2	−	26142.2i	−0.535629	−	0.927737i
$927$	−7252.11	+	12561.0i	−0.256948	+	0.445046i
$928$	−3843.33	+	6656.85i	−0.135952	+	0.235476i
$929$	−26635.7	−	46134.4i	−0.940678	−	1.62930i	−0.764182	−	0.645001i	$-0.776857\pi$
$929$	−26635.7	−	46134.4i	−0.940678	−	1.62930i	−0.176496	−	0.984301i	$-0.556476\pi$
$930$	−28190.8			−0.993992
$931$		0			0
$932$	3104.39			0.109107
$933$	−701.989	−	1215.88i	−0.0246324	−	0.0426647i
$934$	−2820.23	+	4884.79i	−0.0988018	+	0.171130i
$935$	11225.9	−	19443.8i	0.392648	−	0.680086i
$936$	1398.14	+	2421.64i	0.0488243	+	0.0845661i
$937$	−17197.8			−0.599602			−0.299801	−	0.954002i	$-0.596920\pi$
$937$	−17197.8			−0.599602			−0.299801	+	0.954002i	$0.596920\pi$
$938$		0			0
$939$	10838.4			0.376676
$940$	2152.41	+	3728.08i	0.0746849	+	0.129358i
$941$	14417.4	−	24971.7i	0.499463	−	0.865096i	−0.500537	−	0.865715i	$-0.666864\pi$
$941$	14417.4	−	24971.7i	0.499463	−	0.865096i	1.00000		0.000619696i	$0.000197256\pi$
$942$	2901.20	−	5025.03i	0.100346	−	0.173805i
$943$	−7586.77	−	13140.7i	−0.261993	−	0.453785i
$944$	7390.85			0.254822
$945$		0			0
$946$	−34062.9			−1.17070
$947$	25920.6	+	44895.8i	0.889448	+	1.54057i	0.840530	+	0.541766i	$0.182244\pi$
$947$	25920.6	+	44895.8i	0.889448	+	1.54057i	0.0489180	+	0.998803i	$0.484423\pi$
$948$	−2458.18	+	4257.70i	−0.0842173	+	0.145869i
$949$	−3520.57	+	6097.81i	−0.120424	+	0.208581i
$950$	9626.23	+	16673.1i	0.328754	+	0.569418i
$951$	−13595.2			−0.463570
$952$		0			0
$953$	−5887.31			−0.200114			−0.100057	−	0.994982i	$-0.531903\pi$
$953$	−5887.31			−0.200114			−0.100057	+	0.994982i	$0.531903\pi$
$954$	598.398	+	1036.46i	0.0203080	+	0.0351745i
$955$	14295.3	−	24760.3i	0.484384	−	0.838977i
$956$	−4013.59	+	6951.74i	−0.135783	+	0.235184i
$957$	18677.6	+	32350.5i	0.630888	+	1.09273i
$958$	32897.0			1.10945
$959$		0			0
$960$	−3040.73			−0.102228
$961$	−29112.3	−	50424.0i	−0.977218	−	1.69259i
$962$	−6273.52	+	10866.1i	−0.210256	+	0.364174i
$963$	−4206.02	+	7285.04i	−0.140745	+	0.243777i
$964$	1611.30	+	2790.85i	0.0538344	+	0.0932439i
$965$	53384.4			1.78083
$966$		0			0
$967$	−36620.0			−1.21781			−0.608904	−	0.793244i	$-0.708391\pi$
$967$	−36620.0			−1.21781			−0.608904	+	0.793244i	$0.708391\pi$
$968$	−5424.35	−	9395.25i	−0.180109	−	0.311957i
$969$	3138.70	−	5436.40i	0.104055	−	0.180229i
$970$	25629.2	−	44391.1i	0.848355	−	1.46939i
$971$	−21182.4	−	36689.1i	−0.700079	−	1.21257i	−0.968438	−	0.249254i	$-0.919815\pi$
$971$	−21182.4	−	36689.1i	−0.700079	−	1.21257i	0.268359	−	0.963319i	$-0.413519\pi$
$972$	−972.000			−0.0320750
$973$		0			0
$974$	12662.1			0.416551
$975$	−7329.40	−	12694.9i	−0.240747	−	0.416987i
$976$	1482.79	−	2568.26i	0.0486300	−	0.0842296i
$977$	−2511.16	+	4349.46i	−0.0822304	+	0.142427i	−0.904208	−	0.427093i	$-0.859538\pi$
$977$	−2511.16	+	4349.46i	−0.0822304	+	0.142427i	0.821977	+	0.569520i	$0.192871\pi$
$978$	−3979.50	−	6892.70i	−0.130113	−	0.225362i
$979$	−59983.8			−1.95821
$980$		0			0
$981$	−10773.2			−0.350623
$982$	9286.90	+	16085.4i	0.301789	+	0.522714i
$983$	14146.4	−	24502.3i	0.459003	−	0.795016i	−0.539906	−	0.841725i	$-0.681540\pi$
$983$	14146.4	−	24502.3i	0.459003	−	0.795016i	0.998909	+	0.0467095i	$0.0148735\pi$
$984$	1235.73	−	2140.34i	0.0400341	−	0.0693411i
$985$	36522.9	+	63259.4i	1.18144	+	2.04631i
$986$	−13138.7			−0.424361
$987$		0			0
$988$	11885.9			0.382734
$989$	24206.2	+	41926.3i	0.778273	+	1.34801i
$990$	−7388.56	+	12797.4i	−0.237196	+	0.410835i
$991$	−18200.5	+	31524.2i	−0.583410	+	1.01050i	0.411662	+	0.911337i	$0.364948\pi$
$991$	−18200.5	+	31524.2i	−0.583410	+	1.01050i	−0.995072	+	0.0991586i	$0.968385\pi$
$992$	−4746.79	−	8221.68i	−0.151926	−	0.263144i
$993$	3711.17			0.118601
$994$		0			0
$995$	35314.6			1.12517
$996$	−2087.57	−	3615.77i	−0.0664128	−	0.115030i
$997$	−1178.60	+	2041.39i	−0.0374389	+	0.0648460i	−0.884138	−	0.467226i	$-0.845253\pi$
$997$	−1178.60	+	2041.39i	−0.0374389	+	0.0648460i	0.846699	+	0.532072i	$0.178587\pi$
$998$	243.451	−	421.669i	0.00772174	−	0.0133745i
$999$	−2180.71	−	3777.10i	−0.0690637	−	0.119622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.e.l.67.1		4
3.2	odd	2		882.4.g.bf.361.2		4
7.2	even	3	inner	294.4.e.l.79.1		4
7.3	odd	6		294.4.a.n.1.1		2
7.4	even	3		294.4.a.m.1.2		2
7.5	odd	6		42.4.e.c.37.2	yes	4
7.6	odd	2		42.4.e.c.25.2	✓	4
21.2	odd	6		882.4.g.bf.667.2		4
21.5	even	6		126.4.g.g.37.1		4
21.11	odd	6		882.4.a.z.1.1		2
21.17	even	6		882.4.a.v.1.2		2
21.20	even	2		126.4.g.g.109.1		4
28.3	even	6		2352.4.a.bq.1.1		2
28.11	odd	6		2352.4.a.ca.1.2		2
28.19	even	6		336.4.q.j.289.2		4
28.27	even	2		336.4.q.j.193.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.e.c.25.2	✓	4	7.6	odd	2
42.4.e.c.37.2	yes	4	7.5	odd	6
126.4.g.g.37.1		4	21.5	even	6
126.4.g.g.109.1		4	21.20	even	2
294.4.a.m.1.2		2	7.4	even	3
294.4.a.n.1.1		2	7.3	odd	6
294.4.e.l.67.1		4	1.1	even	1	trivial
294.4.e.l.79.1		4	7.2	even	3	inner
336.4.q.j.193.2		4	28.27	even	2
336.4.q.j.289.2		4	28.19	even	6
882.4.a.v.1.2		2	21.17	even	6
882.4.a.z.1.1		2	21.11	odd	6
882.4.g.bf.361.2		4	3.2	odd	2
882.4.g.bf.667.2		4	21.2	odd	6
2352.4.a.bq.1.1		2	28.3	even	6
2352.4.a.ca.1.2		2	28.11	odd	6

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-7.91856 - 13.7153i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-7.91856 - 13.7153i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-15.8371 + 27.4307i) q^{10} +(-25.9186 + 44.8923i) q^{11} +(6.00000 + 10.3923i) q^{12} -38.8371 q^{13} -47.5114 q^{15} +(-8.00000 - 13.8564i) q^{16} +(13.6742 - 23.6845i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(38.2557 + 66.2608i) q^{19} +63.3485 q^{20} +103.674 q^{22} +(-73.6742 - 127.608i) q^{23} +(12.0000 - 20.7846i) q^{24} +(-62.9072 + 108.958i) q^{25} +(38.8371 + 67.2679i) q^{26} -27.0000 q^{27} +240.208 q^{29} +(47.5114 + 82.2921i) q^{30} +(-148.337 + 256.927i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(77.7557 + 134.677i) q^{33} -54.6970 q^{34} +36.0000 q^{36} +(80.7670 + 139.893i) q^{37} +(76.5114 - 132.522i) q^{38} +(-58.2557 + 100.902i) q^{39} +(-63.3485 - 109.723i) q^{40} +102.977 q^{41} -328.557 q^{43} +(-103.674 - 179.569i) q^{44} +(-71.2670 + 123.438i) q^{45} +(-147.348 + 255.215i) q^{46} +(33.9773 + 58.8504i) q^{47} -48.0000 q^{48} +251.629 q^{50} +(-41.0227 - 71.0534i) q^{51} +(77.6742 - 134.536i) q^{52} +(33.2443 - 57.5808i) q^{53} +(27.0000 + 46.7654i) q^{54} +820.951 q^{55} +229.534 q^{57} +(-240.208 - 416.053i) q^{58} +(-230.964 + 400.041i) q^{59} +(95.0227 - 164.584i) q^{60} +(92.6742 + 160.516i) q^{61} +593.348 q^{62} +64.0000 q^{64} +(307.534 + 532.665i) q^{65} +(155.511 - 269.354i) q^{66} +(-272.604 + 472.164i) q^{67} +(54.6970 + 94.7379i) q^{68} -442.045 q^{69} -130.742 q^{71} +(-36.0000 - 62.3538i) q^{72} +(90.6496 - 157.010i) q^{73} +(161.534 - 279.785i) q^{74} +(188.722 + 326.875i) q^{75} -306.045 q^{76} +233.023 q^{78} +(204.848 + 354.808i) q^{79} +(-126.697 + 219.446i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-102.977 - 178.362i) q^{82} -347.928 q^{83} -433.121 q^{85} +(328.557 + 569.077i) q^{86} +(360.312 - 624.080i) q^{87} +(-207.348 + 359.138i) q^{88} +(578.580 + 1002.13i) q^{89} +285.068 q^{90} +589.394 q^{92} +(445.011 + 770.782i) q^{93} +(67.9546 - 117.701i) q^{94} +(605.860 - 1049.38i) q^{95} +(48.0000 + 83.1384i) q^{96} -1618.30 q^{97} +466.534 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 5 q^{5} - 24 q^{6} + 32 q^{8} - 18 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 5 * q^5 - 24 * q^6 + 32 * q^8 - 18 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 5 q^{5} - 24 q^{6} + 32 q^{8} - 18 q^{9} + 10 q^{10} - 67 q^{11} + 24 q^{12} - 82 q^{13} + 30 q^{15} - 32 q^{16} - 92 q^{17} - 36 q^{18} + 43 q^{19} - 40 q^{20} + 268 q^{22} - 148 q^{23} + 48 q^{24} - 435 q^{25} + 82 q^{26} - 108 q^{27} + 154 q^{29} - 30 q^{30} - 520 q^{31} - 64 q^{32} + 201 q^{33} + 368 q^{34} + 144 q^{36} - 7 q^{37} + 86 q^{38} - 123 q^{39} + 40 q^{40} + 852 q^{41} - 214 q^{43} - 268 q^{44} + 45 q^{45} - 296 q^{46} + 576 q^{47} - 192 q^{48} + 1740 q^{50} + 276 q^{51} + 164 q^{52} + 243 q^{53} + 108 q^{54} + 1010 q^{55} + 258 q^{57} - 154 q^{58} - 7 q^{59} - 60 q^{60} + 224 q^{61} + 2080 q^{62} + 256 q^{64} + 570 q^{65} + 402 q^{66} - 687 q^{67} - 368 q^{68} - 888 q^{69} + 944 q^{71} - 144 q^{72} - 921 q^{73} - 14 q^{74} + 1305 q^{75} - 344 q^{76} + 492 q^{78} + 526 q^{79} + 80 q^{80} - 162 q^{81} - 852 q^{82} + 442 q^{83} - 5840 q^{85} + 214 q^{86} + 231 q^{87} - 536 q^{88} + 774 q^{89} - 180 q^{90} + 1184 q^{92} + 1560 q^{93} + 1152 q^{94} + 1910 q^{95} + 192 q^{96} - 3906 q^{97} + 1206 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 5 * q^5 - 24 * q^6 + 32 * q^8 - 18 * q^9 + 10 * q^10 - 67 * q^11 + 24 * q^12 - 82 * q^13 + 30 * q^15 - 32 * q^16 - 92 * q^17 - 36 * q^18 + 43 * q^19 - 40 * q^20 + 268 * q^22 - 148 * q^23 + 48 * q^24 - 435 * q^25 + 82 * q^26 - 108 * q^27 + 154 * q^29 - 30 * q^30 - 520 * q^31 - 64 * q^32 + 201 * q^33 + 368 * q^34 + 144 * q^36 - 7 * q^37 + 86 * q^38 - 123 * q^39 + 40 * q^40 + 852 * q^41 - 214 * q^43 - 268 * q^44 + 45 * q^45 - 296 * q^46 + 576 * q^47 - 192 * q^48 + 1740 * q^50 + 276 * q^51 + 164 * q^52 + 243 * q^53 + 108 * q^54 + 1010 * q^55 + 258 * q^57 - 154 * q^58 - 7 * q^59 - 60 * q^60 + 224 * q^61 + 2080 * q^62 + 256 * q^64 + 570 * q^65 + 402 * q^66 - 687 * q^67 - 368 * q^68 - 888 * q^69 + 944 * q^71 - 144 * q^72 - 921 * q^73 - 14 * q^74 + 1305 * q^75 - 344 * q^76 + 492 * q^78 + 526 * q^79 + 80 * q^80 - 162 * q^81 - 852 * q^82 + 442 * q^83 - 5840 * q^85 + 214 * q^86 + 231 * q^87 - 536 * q^88 + 774 * q^89 - 180 * q^90 + 1184 * q^92 + 1560 * q^93 + 1152 * q^94 + 1910 * q^95 + 192 * q^96 - 3906 * q^97 + 1206 * q^99

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