LMFDB - Embedded newform 207.4.i.b.190.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,4,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, 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:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			190.6
Character	$\chi$	$=$	207.190
Dual form			207.4.i.b.73.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62255 - 3.55289i) q^{2} +(-4.75146 - 5.48347i) q^{4} +(-2.37866 + 1.52867i) q^{5} +(-5.05798 + 35.1790i) q^{7} +(2.78946 - 0.819058i) q^{8} +O(q^{10})$	\(q+(1.62255 - 3.55289i) q^{2} +(-4.75146 - 5.48347i) q^{4} +(-2.37866 + 1.52867i) q^{5} +(-5.05798 + 35.1790i) q^{7} +(2.78946 - 0.819058i) q^{8} +(1.57171 + 10.9315i) q^{10} +(16.7703 + 36.7219i) q^{11} +(4.13183 + 28.7375i) q^{13} +(116.780 + 75.0501i) q^{14} +(9.87673 - 68.6942i) q^{16} +(12.6250 - 14.5700i) q^{17} +(13.0159 + 15.0211i) q^{19} +(19.6845 + 5.77990i) q^{20} +157.679 q^{22} +(-110.272 - 2.66697i) q^{23} +(-48.6057 + 106.432i) q^{25} +(108.805 + 31.9481i) q^{26} +(216.936 - 139.416i) q^{28} +(36.9991 - 42.6992i) q^{29} +(248.910 - 73.0866i) q^{31} +(-208.472 - 133.977i) q^{32} +(-31.2809 - 68.4957i) q^{34} +(-41.7460 - 91.4109i) q^{35} +(99.4353 + 63.9032i) q^{37} +(74.4871 - 21.8714i) q^{38} +(-5.38310 + 6.21242i) q^{40} +(-395.946 + 254.459i) q^{41} +(229.814 + 67.4796i) q^{43} +(121.680 - 266.442i) q^{44} +(-188.397 + 387.456i) q^{46} +260.363 q^{47} +(-882.874 - 259.235i) q^{49} +(299.274 + 345.381i) q^{50} +(137.949 - 159.202i) q^{52} +(68.1967 - 474.319i) q^{53} +(-96.0266 - 61.7125i) q^{55} +(14.7046 + 102.273i) q^{56} +(-91.6726 - 200.735i) q^{58} +(23.2951 + 162.021i) q^{59} +(564.446 - 165.736i) q^{61} +(144.201 - 1002.94i) q^{62} +(-347.191 + 223.126i) q^{64} +(-53.7584 - 62.0405i) q^{65} +(151.955 - 332.736i) q^{67} -139.881 q^{68} -392.508 q^{70} +(-301.536 + 660.271i) q^{71} +(-122.521 - 141.397i) q^{73} +(388.380 - 249.596i) q^{74} +(20.5235 - 142.744i) q^{76} +(-1376.66 + 404.225i) q^{77} +(61.3565 + 426.744i) q^{79} +(81.5175 + 178.498i) q^{80} +(261.622 + 1819.62i) q^{82} +(356.030 + 228.807i) q^{83} +(-7.75778 + 53.9565i) q^{85} +(612.633 - 707.016i) q^{86} +(76.8574 + 88.6982i) q^{88} +(681.570 + 200.127i) q^{89} -1031.85 q^{91} +(509.328 + 617.345i) q^{92} +(422.451 - 925.039i) q^{94} +(-53.9226 - 15.8331i) q^{95} +(-430.031 + 276.364i) q^{97} +(-2353.54 + 2716.13i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8}+O(q^{10}) $ 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8	$ 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8} - 78 q^{10} - 10 q^{11} + 50 q^{13} + 224 q^{14} + 260 q^{16} + 662 q^{17} - 4 q^{19} + 735 q^{20} + 622 q^{22} + 438 q^{23} - 754 q^{25} + 40 q^{26} + 672 q^{28} - 1302 q^{29} + 1528 q^{31} - 1588 q^{32} + 29 q^{34} - 950 q^{35} + 316 q^{37} - 3122 q^{38} - 1939 q^{40} + 1500 q^{41} - 1316 q^{43} + 2901 q^{44} - 1980 q^{46} + 1440 q^{47} - 2310 q^{49} - 195 q^{50} + 6189 q^{52} + 148 q^{53} - 606 q^{55} + 432 q^{56} - 2623 q^{58} - 5264 q^{59} + 1482 q^{61} + 2299 q^{62} - 6780 q^{64} + 1446 q^{65} + 388 q^{67} - 5604 q^{68} + 2984 q^{70} + 3316 q^{71} + 2072 q^{73} + 6556 q^{74} + 9841 q^{76} - 9338 q^{77} + 268 q^{79} - 7980 q^{80} + 7742 q^{82} + 3494 q^{83} - 3842 q^{85} + 4792 q^{86} - 7960 q^{88} + 2754 q^{89} - 5436 q^{91} + 17609 q^{92} - 10961 q^{94} + 2396 q^{95} - 5654 q^{97} - 14411 q^{98}+O(q^{100}) $ 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8 - 78 * q^10 - 10 * q^11 + 50 * q^13 + 224 * q^14 + 260 * q^16 + 662 * q^17 - 4 * q^19 + 735 * q^20 + 622 * q^22 + 438 * q^23 - 754 * q^25 + 40 * q^26 + 672 * q^28 - 1302 * q^29 + 1528 * q^31 - 1588 * q^32 + 29 * q^34 - 950 * q^35 + 316 * q^37 - 3122 * q^38 - 1939 * q^40 + 1500 * q^41 - 1316 * q^43 + 2901 * q^44 - 1980 * q^46 + 1440 * q^47 - 2310 * q^49 - 195 * q^50 + 6189 * q^52 + 148 * q^53 - 606 * q^55 + 432 * q^56 - 2623 * q^58 - 5264 * q^59 + 1482 * q^61 + 2299 * q^62 - 6780 * q^64 + 1446 * q^65 + 388 * q^67 - 5604 * q^68 + 2984 * q^70 + 3316 * q^71 + 2072 * q^73 + 6556 * q^74 + 9841 * q^76 - 9338 * q^77 + 268 * q^79 - 7980 * q^80 + 7742 * q^82 + 3494 * q^83 - 3842 * q^85 + 4792 * q^86 - 7960 * q^88 + 2754 * q^89 - 5436 * q^91 + 17609 * q^92 - 10961 * q^94 + 2396 * q^95 - 5654 * q^97 - 14411 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{11}\right)$	$1$

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 $

$2$	1.62255	−	3.55289i	0.573658	−	1.25614i	−0.371169	−	0.928565i	$-0.621043\pi$
$2$	1.62255	−	3.55289i	0.573658	−	1.25614i	0.944827	−	0.327570i	$-0.106230\pi$
$3$		0			0
$3$		0			0
$4$	−4.75146	−	5.48347i	−0.593932	−	0.685434i
$5$	−2.37866	+	1.52867i	−0.212754	+	0.136729i	−0.642678	−	0.766136i	$-0.722177\pi$
$5$	−2.37866	+	1.52867i	−0.212754	+	0.136729i	0.429924	+	0.902865i	$0.358540\pi$
$6$		0			0
$7$	−5.05798	+	35.1790i	−0.273105	+	1.89949i	0.142253	+	0.989830i	$0.454565\pi$
$7$	−5.05798	+	35.1790i	−0.273105	+	1.89949i	−0.415359	+	0.909658i	$0.636344\pi$
$8$	2.78946	−	0.819058i	0.123278	−	0.0361976i
$9$		0			0
$10$	1.57171	+	10.9315i	0.0497017	+	0.345683i
$11$	16.7703	+	36.7219i	0.459676	+	1.00655i	0.987561	+	0.157235i	$0.0502580\pi$
$11$	16.7703	+	36.7219i	0.459676	+	1.00655i	−0.527885	+	0.849316i	$0.677015\pi$
$12$		0			0
$13$	4.13183	+	28.7375i	0.0881509	+	0.613103i	0.985230	+	0.171234i	$0.0547754\pi$
$13$	4.13183	+	28.7375i	0.0881509	+	0.613103i	−0.897079	+	0.441869i	$0.854316\pi$
$14$	116.780	+	75.0501i	2.22935	+	1.43271i
$15$		0			0
$16$	9.87673	−	68.6942i	0.154324	−	1.07335i
$17$	12.6250	−	14.5700i	0.180118	−	0.207867i	−0.658510	−	0.752572i	$-0.728813\pi$
$17$	12.6250	−	14.5700i	0.180118	−	0.207867i	0.838628	+	0.544705i	$0.183358\pi$
$18$		0			0
$19$	13.0159	+	15.0211i	0.157160	+	0.181372i	0.828869	−	0.559443i	$-0.188985\pi$
$19$	13.0159	+	15.0211i	0.157160	+	0.181372i	−0.671709	+	0.740815i	$0.734439\pi$
$20$	19.6845	+	5.77990i	0.220080	+	0.0646213i
$21$		0			0
$22$	157.679			1.52806
$23$	−110.272	−	2.66697i	−0.999708	−	0.0241784i
$23$	−110.272	−	2.66697i	−0.999708	−	0.0241784i
$24$		0			0
$25$	−48.6057	+	106.432i	−0.388846	+	0.851453i
$26$	108.805	+	31.9481i	0.820709	+	0.240982i
$27$		0			0
$28$	216.936	−	139.416i	1.46418	−	0.940971i
$29$	36.9991	−	42.6992i	0.236916	−	0.273415i	−0.624824	−	0.780765i	$-0.714829\pi$
$29$	36.9991	−	42.6992i	0.236916	−	0.273415i	0.861740	+	0.507350i	$0.169375\pi$
$30$		0			0
$31$	248.910	−	73.0866i	1.44212	−	0.423443i	0.535189	−	0.844732i	$-0.320240\pi$
$31$	248.910	−	73.0866i	1.44212	−	0.423443i	0.906927	+	0.421289i	$0.138422\pi$
$32$	−208.472	−	133.977i	−1.15165	−	0.740123i
$33$		0			0
$34$	−31.2809	−	68.4957i	−0.157783	−	0.345497i
$35$	−41.7460	−	91.4109i	−0.201610	−	0.441465i
$36$		0			0
$37$	99.4353	+	63.9032i	0.441813	+	0.283936i	0.742574	−	0.669764i	$-0.233605\pi$
$37$	99.4353	+	63.9032i	0.441813	+	0.283936i	−0.300762	+	0.953699i	$0.597241\pi$
$38$	74.4871	−	21.8714i	0.317984	−	0.0933687i
$39$		0			0
$40$	−5.38310	+	6.21242i	−0.0212786	+	0.0245568i
$41$	−395.946	+	254.459i	−1.50820	+	0.969263i	−0.514467	+	0.857510i	$0.672010\pi$
$41$	−395.946	+	254.459i	−1.50820	+	0.969263i	−0.993736	+	0.111753i	$0.964354\pi$
$42$		0			0
$43$	229.814	+	67.4796i	0.815032	+	0.239315i	0.662575	−	0.748995i	$-0.269463\pi$
$43$	229.814	+	67.4796i	0.815032	+	0.239315i	0.152456	+	0.988310i	$0.451282\pi$
$44$	121.680	−	266.442i	0.416908	−	0.912901i
$45$		0			0
$46$	−188.397	+	387.456i	−0.603861	+	1.24190i
$47$	260.363			0.808038			0.404019	−	0.914751i	$-0.367613\pi$
$47$	260.363			0.808038			0.404019	+	0.914751i	$0.367613\pi$
$48$		0			0
$49$	−882.874	−	259.235i	−2.57398	−	0.755787i
$50$	299.274	+	345.381i	0.846476	+	0.976885i
$51$		0			0
$52$	137.949	−	159.202i	0.367886	−	0.424563i
$53$	68.1967	−	474.319i	0.176746	−	1.22930i	−0.687484	−	0.726199i	$-0.741285\pi$
$53$	68.1967	−	474.319i	0.176746	−	1.22930i	0.864230	−	0.503096i	$-0.167806\pi$
$54$		0			0
$55$	−96.0266	−	61.7125i	−0.235422	−	0.151297i
$56$	14.7046	+	102.273i	0.0350891	+	0.244050i
$57$		0			0
$58$	−91.6726	−	200.735i	−0.207538	−	0.454445i
$59$	23.2951	+	162.021i	0.0514028	+	0.357515i	0.999248	+	0.0387825i	$0.0123479\pi$
$59$	23.2951	+	162.021i	0.0514028	+	0.357515i	−0.947845	+	0.318732i	$0.896743\pi$
$60$		0			0
$61$	564.446	−	165.736i	1.18475	−	0.347875i	0.370748	−	0.928734i	$-0.379101\pi$
$61$	564.446	−	165.736i	1.18475	−	0.347875i	0.814004	+	0.580859i	$0.197283\pi$
$62$	144.201	−	1002.94i	0.295379	−	2.05440i
$63$		0			0
$64$	−347.191	+	223.126i	−0.678108	+	0.435793i
$65$	−53.7584	−	62.0405i	−0.102583	−	0.118387i
$66$		0			0
$67$	151.955	−	332.736i	0.277079	−	0.606718i	−0.719017	−	0.694992i	$-0.755408\pi$
$67$	151.955	−	332.736i	0.277079	−	0.606718i	0.996096	+	0.0882739i	$0.0281351\pi$
$68$	−139.881			−0.249457
$69$		0			0
$70$	−392.508			−0.670195
$71$	−301.536	+	660.271i	−0.504024	+	1.10366i	0.471117	+	0.882071i	$0.343851\pi$
$71$	−301.536	+	660.271i	−0.504024	+	1.10366i	−0.975141	+	0.221587i	$0.928876\pi$
$72$		0			0
$73$	−122.521	−	141.397i	−0.196439	−	0.226703i	0.648981	−	0.760804i	$-0.275195\pi$
$73$	−122.521	−	141.397i	−0.196439	−	0.226703i	−0.845420	+	0.534102i	$0.820650\pi$
$74$	388.380	−	249.596i	0.610111	−	0.392095i
$75$		0			0
$76$	20.5235	−	142.744i	0.0309764	−	0.215446i
$77$	−1376.66	+	404.225i	−2.03747	+	0.598256i
$78$		0			0
$79$	61.3565	+	426.744i	0.0873816	+	0.607753i	0.985713	+	0.168434i	$0.0538710\pi$
$79$	61.3565	+	426.744i	0.0873816	+	0.607753i	−0.898331	+	0.439319i	$0.855220\pi$
$80$	81.5175	+	178.498i	0.113924	+	0.249459i
$81$		0			0
$82$	261.622	+	1819.62i	0.352333	+	2.45053i
$83$	356.030	+	228.807i	0.470836	+	0.302588i	0.754458	−	0.656348i	$-0.227900\pi$
$83$	356.030	+	228.807i	0.470836	+	0.302588i	−0.283622	+	0.958936i	$0.591536\pi$
$84$		0			0
$85$	−7.75778	+	53.9565i	−0.00989941	+	0.0688519i
$86$	612.633	−	707.016i	0.768161	−	0.886505i
$87$		0			0
$88$	76.8574	+	88.6982i	0.0931026	+	0.107446i
$89$	681.570	+	200.127i	0.811756	+	0.238353i	0.661163	−	0.750243i	$-0.270063\pi$
$89$	681.570	+	200.127i	0.811756	+	0.238353i	0.150594	+	0.988596i	$0.451882\pi$
$90$		0			0
$91$	−1031.85			−1.18866
$92$	509.328	+	617.345i	0.577186	+	0.699594i
$93$		0			0
$94$	422.451	−	925.039i	0.463537	−	1.01500i
$95$	−53.9226	−	15.8331i	−0.0582352	−	0.0170994i
$96$		0			0
$97$	−430.031	+	276.364i	−0.450134	+	0.289284i	−0.746000	−	0.665946i	$-0.768028\pi$
$97$	−430.031	+	276.364i	−0.450134	+	0.289284i	0.295866	+	0.955229i	$0.404392\pi$
$98$	−2353.54	+	2716.13i	−2.42595	+	2.79970i
$99$		0			0
$100$	814.563	−	239.177i	0.814563	−	0.239177i
$101$	−333.241	−	214.161i	−0.328304	−	0.210988i	0.366096	−	0.930577i	$-0.380694\pi$
$101$	−333.241	−	214.161i	−0.328304	−	0.210988i	−0.694401	+	0.719589i	$0.744330\pi$
$102$		0			0
$103$	−650.036	−	1423.38i	−0.621845	−	1.36165i	−0.914170	−	0.405331i	$-0.867156\pi$
$103$	−650.036	−	1423.38i	−0.621845	−	1.36165i	0.292325	−	0.956319i	$-0.405571\pi$
$104$	35.0632	+	76.7777i	0.0330599	+	0.0723911i
$105$		0			0
$106$	−1574.55	−	1011.90i	−1.44277	−	0.927212i
$107$	−145.621	+	42.7583i	−0.131568	+	0.0386318i	−0.346853	−	0.937919i	$-0.612750\pi$
$107$	−145.621	+	42.7583i	−0.131568	+	0.0386318i	0.215286	+	0.976551i	$0.430932\pi$
$108$		0			0
$109$	−1396.85	+	1612.05i	−1.22747	+	1.41657i	−0.350129	+	0.936702i	$0.613862\pi$
$109$	−1396.85	+	1612.05i	−1.22747	+	1.41657i	−0.877339	+	0.479872i	$0.840683\pi$
$110$	−375.066	+	241.040i	−0.325101	+	0.208930i
$111$		0			0
$112$	2366.64	+	694.907i	1.99666	+	0.586273i
$113$	59.2416	−	129.721i	0.0493184	−	0.107992i	−0.883369	−	0.468679i	$-0.844730\pi$
$113$	59.2416	−	129.721i	0.0493184	−	0.107992i	0.932687	+	0.360686i	$0.117458\pi$
$114$		0			0
$115$	266.376	−	162.226i	0.215998	−	0.131545i
$116$	−409.939			−0.328120
$117$		0			0
$118$	613.440	+	180.122i	0.478574	+	0.140522i
$119$	448.701	+	517.829i	0.345650	+	0.398902i
$120$		0			0
$121$	−195.633	+	225.772i	−0.146982	+	0.169626i
$122$	326.999	−	2274.33i	0.242665	−	1.68777i
$123$		0			0
$124$	−1583.45	−	1017.62i	−1.14676	−	0.736979i
$125$	−97.3824	−	677.309i	−0.0696812	−	0.484643i
$126$		0			0
$127$	−86.7772	−	190.016i	−0.0606317	−	0.132765i	0.876891	−	0.480690i	$-0.159614\pi$
$127$	−86.7772	−	190.016i	−0.0606317	−	0.132765i	−0.937522	+	0.347925i	$0.886886\pi$
$128$	−52.7295	−	366.742i	−0.0364115	−	0.253248i
$129$		0			0
$130$	−307.649	+	90.3338i	−0.207558	+	0.0609446i
$131$	285.666	−	1986.85i	0.190525	−	1.32513i	−0.640098	−	0.768293i	$-0.721106\pi$
$131$	285.666	−	1986.85i	0.190525	−	1.32513i	0.830623	−	0.556835i	$-0.187984\pi$
$132$		0			0
$133$	−594.261	+	381.909i	−0.387436	+	0.248990i
$134$	−935.617	−	1079.76i	−0.603172	−	0.696097i
$135$		0			0
$136$	23.2831	−	50.9830i	0.0146802	−	0.0321452i
$137$	2966.11			1.84972			0.924862	−	0.380303i	$-0.124180\pi$
$137$	2966.11			1.84972			0.924862	+	0.380303i	$0.124180\pi$
$138$		0			0
$139$	876.374			0.534770			0.267385	−	0.963590i	$-0.413840\pi$
$139$	876.374			0.534770			0.267385	+	0.963590i	$0.413840\pi$
$140$	−302.895	+	663.248i	−0.182852	+	0.400391i
$141$		0			0
$142$	1856.61	+	2142.64i	1.09721	+	1.26624i
$143$	−986.002	+	633.665i	−0.576599	+	0.370558i
$144$		0			0
$145$	−22.7351	+	158.126i	−0.0130210	+	0.0905633i
$146$	−701.165	+	205.881i	−0.397458	+	0.116704i
$147$		0			0
$148$	−122.051	−	848.885i	−0.0677875	−	0.471472i
$149$	−256.408	−	561.456i	−0.140978	−	0.308700i	0.825952	−	0.563741i	$-0.190638\pi$
$149$	−256.408	−	561.456i	−0.140978	−	0.308700i	−0.966930	+	0.255041i	$0.917911\pi$
$150$		0			0
$151$	−422.072	−	2935.58i	−0.227469	−	1.58208i	−0.708716	−	0.705494i	$-0.750725\pi$
$151$	−422.072	−	2935.58i	−0.227469	−	1.58208i	0.481247	−	0.876585i	$-0.340184\pi$
$152$	48.6103	+	31.2399i	0.0259396	+	0.0166704i
$153$		0			0
$154$	−797.539	+	5547.00i	−0.417321	+	2.90253i
$155$	−480.347	+	554.350i	−0.248919	+	0.287268i
$156$		0			0
$157$	−1883.98	−	2174.23i	−0.957695	−	1.10524i	−0.994376	−	0.105912i	$-0.966224\pi$
$157$	−1883.98	−	2174.23i	−0.957695	−	1.10524i	0.0366806	−	0.999327i	$-0.488322\pi$
$158$	1615.73	+	474.421i	0.813547	+	0.238879i
$159$		0			0
$160$	700.689			0.346215
$161$	651.574	−	3865.77i	0.318952	−	1.89233i
$162$		0			0
$163$	1254.49	−	2746.94i	0.602815	−	1.31998i	−0.324566	−	0.945863i	$-0.605218\pi$
$163$	1254.49	−	2746.94i	0.602815	−	1.31998i	0.927381	−	0.374118i	$-0.122054\pi$
$164$	3276.64	+	962.107i	1.56014	+	0.458097i
$165$		0			0
$166$	1390.60	−	893.685i	0.650190	−	0.417852i
$167$	−1430.71	+	1651.13i	−0.662946	+	0.765081i	−0.983255	−	0.182232i	$-0.941668\pi$
$167$	−1430.71	+	1651.13i	−0.662946	+	0.765081i	0.320309	+	0.947313i	$0.396213\pi$
$168$		0			0
$169$	1299.24	−	381.490i	0.591368	−	0.173641i
$170$	179.114	+	115.110i	0.0808084	+	0.0519324i
$171$		0			0
$172$	−721.931	−	1580.81i	−0.320039	−	0.700788i
$173$	−1083.89	−	2373.39i	−0.476339	−	1.04304i	−0.983454	−	0.181158i	$-0.942015\pi$
$173$	−1083.89	−	2373.39i	−0.476339	−	1.04304i	0.507115	−	0.861878i	$-0.330712\pi$
$174$		0			0
$175$	−3498.31	−	2248.23i	−1.51113	−	0.971144i
$176$	2688.21	−	789.331i	1.15132	−	0.338057i
$177$		0			0
$178$	1816.91	−	2096.83i	0.765074	−	0.882943i
$179$	603.858	−	388.076i	0.252148	−	0.162046i	−0.408461	−	0.912776i	$-0.633934\pi$
$179$	603.858	−	388.076i	0.252148	−	0.162046i	0.660609	+	0.750730i	$0.270298\pi$
$180$		0			0
$181$	3871.65	+	1136.82i	1.58993	+	0.466846i	0.952722	−	0.303845i	$-0.0982704\pi$
$181$	3871.65	+	1136.82i	1.58993	+	0.466846i	0.637210	+	0.770691i	$0.280089\pi$
$182$	−1674.24	+	3666.06i	−0.681882	+	1.49311i
$183$		0			0
$184$	−309.783	+	82.8797i	−0.124117	+	0.0332064i
$185$	−334.210			−0.132819
$186$		0			0
$187$	746.763	+	219.269i	0.292025	+	0.0857463i
$188$	−1237.10	−	1427.69i	−0.479920	−	0.553857i
$189$		0			0
$190$	−143.745	+	165.891i	−0.0548863	+	0.0633421i
$191$	386.831	−	2690.47i	0.146545	−	1.01924i	−0.775274	−	0.631625i	$-0.782388\pi$
$191$	386.831	−	2690.47i	0.146545	−	1.01924i	0.921820	−	0.387619i	$-0.126702\pi$
$192$		0			0
$193$	3297.96	+	2119.47i	1.23001	+	0.790481i	0.983893	−	0.178758i	$-0.0572079\pi$
$193$	3297.96	+	2119.47i	1.23001	+	0.790481i	0.246120	+	0.969239i	$0.420844\pi$
$194$	284.144	+	1976.26i	0.105156	+	0.731379i
$195$		0			0
$196$	2773.43	+	6072.96i	1.01072	+	2.21318i
$197$	564.436	+	3925.74i	0.204134	+	1.41978i	0.791850	+	0.610716i	$0.209118\pi$
$197$	564.436	+	3925.74i	0.204134	+	1.41978i	−0.587716	+	0.809068i	$0.699973\pi$
$198$		0			0
$199$	−908.100	+	266.642i	−0.323485	+	0.0949837i	−0.439443	−	0.898270i	$-0.644824\pi$
$199$	−908.100	+	266.642i	−0.323485	+	0.0949837i	0.115958	+	0.993254i	$0.463006\pi$
$200$	−48.4097	+	336.697i	−0.0171154	+	0.119040i
$201$		0			0
$202$	−1301.59	+	836.482i	−0.453364	+	0.291360i
$203$	1314.97	+	1517.56i	0.454646	+	0.524689i
$204$		0			0
$205$	552.836	−	1210.54i	0.188350	−	0.412429i
$206$	−6111.83			−2.06714
$207$		0			0
$208$	2014.91			0.671676
$209$	−333.323	+	729.875i	−0.110318	+	0.241562i
$210$		0			0
$211$	−752.475	−	868.402i	−0.245509	−	0.283333i	0.619598	−	0.784919i	$-0.287296\pi$
$211$	−752.475	−	868.402i	−0.245509	−	0.283333i	−0.865108	+	0.501586i	$0.832750\pi$
$212$	−2924.95	+	1879.75i	−0.947577	+	0.608971i
$213$		0			0
$214$	−84.3624	+	586.754i	−0.0269481	+	0.187428i
$215$	−649.805	+	190.800i	−0.206122	+	0.0605230i
$216$		0			0
$217$	1312.13	+	9126.08i	0.410476	+	2.85493i
$218$	3460.98	+	7578.48i	1.07526	+	2.35449i
$219$		0			0
$220$	117.867	+	819.784i	0.0361209	+	0.251226i
$221$	470.869	+	302.609i	0.143322	+	0.0921073i
$222$		0			0
$223$	516.270	−	3590.74i	0.155031	−	1.07827i	−0.752594	−	0.658485i	$-0.771198\pi$
$223$	516.270	−	3590.74i	0.155031	−	1.07827i	0.907625	−	0.419782i	$-0.137893\pi$
$224$	5767.61	−	6656.17i	1.72038	−	1.98542i
$225$		0			0
$226$	−364.761	−	420.957i	−0.107361	−	0.123901i
$227$	2253.53	+	661.697i	0.658909	+	0.193473i	0.594058	−	0.804422i	$-0.297525\pi$
$227$	2253.53	+	661.697i	0.658909	+	0.193473i	0.0648503	+	0.997895i	$0.479343\pi$
$228$		0			0
$229$	4589.89			1.32449			0.662246	−	0.749286i	$-0.269603\pi$
$229$	4589.89			1.32449			0.662246	+	0.749286i	$0.269603\pi$
$230$	−144.161	−	1209.62i	−0.0413292	−	0.346784i
$231$		0			0
$232$	68.2341	−	149.412i	0.0193094	−	0.0422818i
$233$	−3958.08	−	1162.20i	−1.11289	−	0.326773i	−0.326927	−	0.945050i	$-0.606013\pi$
$233$	−3958.08	−	1162.20i	−1.11289	−	0.326773i	−0.785961	+	0.618276i	$0.787831\pi$
$234$		0			0
$235$	−619.314	+	398.009i	−0.171913	+	0.110482i
$236$	777.753	−	897.575i	0.214523	−	0.247573i
$237$		0			0
$238$	2567.83	−	753.982i	0.699360	−	0.205351i
$239$	2083.19	+	1338.78i	0.563808	+	0.362338i	0.791287	−	0.611446i	$-0.209412\pi$
$239$	2083.19	+	1338.78i	0.563808	+	0.362338i	−0.227478	+	0.973783i	$0.573048\pi$
$240$		0			0
$241$	−1079.56	−	2363.90i	−0.288550	−	0.631836i	0.708735	−	0.705475i	$-0.249266\pi$
$241$	−1079.56	−	2363.90i	−0.288550	−	0.631836i	−0.997285	+	0.0736387i	$0.976539\pi$
$242$	484.719	+	1061.39i	0.128756	+	0.281936i
$243$		0			0
$244$	−3590.75	−	2307.64i	−0.942108	−	0.605456i
$245$	2496.34	−	732.992i	0.650961	−	0.191139i
$246$		0			0
$247$	−377.889	+	436.107i	−0.0973462	+	0.112344i
$248$	634.462	−	407.744i	0.162453	−	0.104402i
$249$		0			0
$250$	−2564.41	−	752.979i	−0.648750	−	0.190490i
$251$	1002.89	−	2196.03i	0.252200	−	0.552241i	−0.740611	−	0.671934i	$-0.765464\pi$
$251$	1002.89	−	2196.03i	0.252200	−	0.552241i	0.992811	+	0.119693i	$0.0381912\pi$
$252$		0			0
$253$	−1751.36	−	4094.12i	−0.435205	−	1.01737i
$254$	−815.904			−0.201553
$255$		0			0
$256$	−4556.46	−	1337.90i	−1.11242	−	0.326635i
$257$	−3009.87	−	3473.57i	−0.730547	−	0.843096i	0.261986	−	0.965072i	$-0.415622\pi$
$257$	−3009.87	−	3473.57i	−0.730547	−	0.843096i	−0.992533	+	0.121976i	$0.961077\pi$
$258$		0			0
$259$	−2750.99	+	3174.82i	−0.659994	+	0.761674i
$260$	−84.7667	+	589.566i	−0.0202193	+	0.140628i
$261$		0			0
$262$	−6595.54	−	4238.70i	−1.55524	−	0.999495i
$263$	1106.74	+	7697.58i	0.259486	+	1.80476i	0.536502	+	0.843899i	$0.319745\pi$
$263$	1106.74	+	7697.58i	0.259486	+	1.80476i	−0.277016	+	0.960865i	$0.589346\pi$
$264$		0			0
$265$	562.861	+	1232.49i	0.130476	+	0.285704i
$266$	392.660	+	2731.01i	0.0905095	+	0.629507i
$267$		0			0
$268$	−2546.56	+	747.736i	−0.580432	+	0.170430i
$269$	−249.838	+	1737.66i	−0.0566279	+	0.393855i	0.941720	+	0.336398i	$0.109209\pi$
$269$	−249.838	+	1737.66i	−0.0566279	+	0.393855i	−0.998348	+	0.0574579i	$0.981701\pi$
$270$		0			0
$271$	−1154.87	+	742.191i	−0.258869	+	0.166365i	−0.663638	−	0.748054i	$-0.730988\pi$
$271$	−1154.87	+	742.191i	−0.258869	+	0.166365i	0.404769	+	0.914419i	$0.367352\pi$
$272$	−876.181	−	1011.17i	−0.195317	−	0.225408i
$273$		0			0
$274$	4812.67	−	10538.3i	1.06111	−	2.32350i
$275$	−4723.50			−1.03577
$276$		0			0
$277$	−4955.58			−1.07492			−0.537458	−	0.843290i	$-0.680615\pi$
$277$	−4955.58			−1.07492			−0.537458	+	0.843290i	$0.680615\pi$
$278$	1421.96	−	3113.66i	0.306775	−	0.671744i
$279$		0			0
$280$	−191.319	−	220.794i	−0.0408340	−	0.0471249i
$281$	372.209	−	239.204i	0.0790182	−	0.0507819i	−0.500535	−	0.865716i	$-0.666863\pi$
$281$	372.209	−	239.204i	0.0790182	−	0.0507819i	0.579553	+	0.814934i	$0.303227\pi$
$282$		0			0
$283$	−380.680	+	2647.69i	−0.0799614	+	0.556144i	0.909979	+	0.414655i	$0.136098\pi$
$283$	−380.680	+	2647.69i	−0.0799614	+	0.556144i	−0.989940	+	0.141488i	$0.954811\pi$
$284$	5053.31	−	1483.79i	1.05584	−	0.310023i
$285$		0			0
$286$	651.504	+	4531.31i	0.134700	+	0.936859i
$287$	−6948.92	−	15216.0i	−1.42921	−	3.12952i
$288$		0			0
$289$	646.298	+	4495.10i	0.131549	+	0.914940i
$290$	524.916	+	337.343i	0.106290	+	0.0683085i
$291$		0			0
$292$	−193.193	+	1343.69i	−0.0387183	+	0.269292i
$293$	4463.25	−	5150.87i	0.889918	−	1.02702i	−0.109536	−	0.993983i	$-0.534937\pi$
$293$	4463.25	−	5150.87i	0.889918	−	1.02702i	0.999454	−	0.0330373i	$-0.0105180\pi$
$294$		0			0
$295$	−303.088	−	349.783i	−0.0598186	−	0.0690344i
$296$	329.711	+	96.8118i	0.0647434	+	0.0190104i
$297$		0			0
$298$	−2410.83			−0.468642
$299$	−378.982	−	3179.96i	−0.0733013	−	0.615055i
$300$		0			0
$301$	−3536.26	+	7743.33i	−0.677165	+	1.48278i
$302$	−11114.6	−	3263.55i	−2.11780	−	0.621841i
$303$		0			0
$304$	1160.42	−	745.754i	0.218929	−	0.140697i
$305$	−1089.27	+	1257.08i	−0.204496	+	0.236001i
$306$		0			0
$307$	2353.33	−	691.000i	0.437497	−	0.128461i	−0.0555646	−	0.998455i	$-0.517696\pi$
$307$	2353.33	−	691.000i	0.437497	−	0.128461i	0.493062	+	0.869994i	$0.335878\pi$
$308$	8757.71	+	5628.24i	1.62018	+	1.04123i
$309$		0			0
$310$	1190.16	+	2606.08i	0.218053	+	0.477469i
$311$	972.039	+	2128.47i	0.177232	+	0.388085i	0.977311	−	0.211811i	$-0.0679361\pi$
$311$	972.039	+	2128.47i	0.177232	+	0.388085i	−0.800078	+	0.599896i	$0.795209\pi$
$312$		0			0
$313$	2227.66	+	1431.63i	0.402283	+	0.258532i	0.726101	−	0.687588i	$-0.241330\pi$
$313$	2227.66	+	1431.63i	0.402283	+	0.258532i	−0.323818	+	0.946119i	$0.604967\pi$
$314$	−10781.7	+	3165.78i	−1.93772	+	0.568966i
$315$		0			0
$316$	2048.51	−	2364.10i	0.364676	−	0.420858i
$317$	−8340.84	+	5360.33i	−1.47782	+	0.949736i	−0.480466	+	0.877013i	$0.659532\pi$
$317$	−8340.84	+	5360.33i	−1.47782	+	0.949736i	−0.997352	+	0.0727225i	$0.976831\pi$
$318$		0			0
$319$	2188.48	+	642.596i	0.384111	+	0.112785i
$320$	484.763	−	1061.48i	0.0846846	−	0.185433i
$321$		0			0
$322$	−12677.4	−	8587.37i	−2.19405	−	1.48620i
$323$	383.182			0.0660088
$324$		0			0
$325$	−3259.41	−	957.048i	−0.556306	−	0.163346i
$326$	−7724.10	−	8914.09i	−1.31227	−	1.51443i
$327$		0			0
$328$	−896.056	+	1034.10i	−0.150843	+	0.174082i
$329$	−1316.91	+	9159.30i	−0.220679	+	1.53486i
$330$		0			0
$331$	5519.03	+	3546.87i	0.916475	+	0.588983i	0.911633	−	0.411005i	$-0.134822\pi$
$331$	5519.03	+	3546.87i	0.916475	+	0.588983i	0.00484243	+	0.999988i	$0.498459\pi$
$332$	−437.007	−	3039.45i	−0.0722405	−	0.502444i
$333$		0			0
$334$	3544.88	+	7762.21i	0.580741	+	1.27164i
$335$	147.194	+	1023.75i	0.0240061	+	0.166966i
$336$		0			0
$337$	−3295.78	+	967.727i	−0.532737	+	0.156426i	−0.537027	−	0.843565i	$-0.680453\pi$
$337$	−3295.78	+	967.727i	−0.532737	+	0.156426i	0.00428986	+	0.999991i	$0.498634\pi$
$338$	752.683	−	5235.02i	0.121126	−	0.842449i
$339$		0			0
$340$	332.730	−	213.833i	0.0530730	−	0.0341080i
$341$	6858.18	+	7914.76i	1.08912	+	1.25692i
$342$		0			0
$343$	8521.08	−	18658.6i	1.34138	−	2.93722i
$344$	696.327			0.109138
$345$		0			0
$346$	−10191.0			−1.58345
$347$	−1345.72	+	2946.72i	−0.208191	+	0.455874i	−0.984706	−	0.174224i	$-0.944258\pi$
$347$	−1345.72	+	2946.72i	−0.208191	+	0.455874i	0.776515	+	0.630098i	$0.216985\pi$
$348$		0			0
$349$	3030.48	+	3497.36i	0.464808	+	0.536417i	0.938960	−	0.344026i	$-0.111791\pi$
$349$	3030.48	+	3497.36i	0.464808	+	0.536417i	−0.474152	+	0.880443i	$0.657245\pi$
$350$	−13663.9	+	8781.25i	−2.08676	+	1.34108i
$351$		0			0
$352$	1423.73	−	9902.29i	0.215583	−	1.49941i
$353$	7316.72	−	2148.38i	1.10320	−	0.323929i	0.321077	−	0.947053i	$-0.395955\pi$
$353$	7316.72	−	2148.38i	1.10320	−	0.323929i	0.782123	+	0.623124i	$0.214137\pi$
$354$		0			0
$355$	−292.087	−	2031.51i	−0.0436686	−	0.303722i
$356$	−2141.06	−	4688.27i	−0.318753	−	0.697971i
$357$		0			0
$358$	−399.001	−	2775.11i	−0.0589046	−	0.409690i
$359$	−2351.87	−	1511.45i	−0.345757	−	0.222204i	0.356223	−	0.934401i	$-0.384064\pi$
$359$	−2351.87	−	1511.45i	−0.345757	−	0.222204i	−0.701980	+	0.712196i	$0.747701\pi$
$360$		0			0
$361$	919.917	−	6398.16i	0.134118	−	0.932812i
$362$	10320.9	−	11911.0i	1.49850	−	1.72936i
$363$		0			0
$364$	4902.81	+	5658.15i	0.705982	+	0.814746i
$365$	507.587	+	149.041i	0.0727899	+	0.0213730i
$366$		0			0
$367$	4203.81			0.597921			0.298960	−	0.954266i	$-0.403360\pi$
$367$	4203.81			0.597921			0.298960	+	0.954266i	$0.403360\pi$
$368$	−1272.33	+	7548.69i	−0.180231	+	1.06930i
$369$		0			0
$370$	−542.272	+	1187.41i	−0.0761929	+	0.166839i
$371$	16341.1	+	4798.19i	2.28676	+	0.671454i
$372$		0			0
$373$	−8594.20	+	5523.16i	−1.19301	+	0.766698i	−0.977732	−	0.209856i	$-0.932701\pi$
$373$	−8594.20	+	5523.16i	−1.19301	+	0.766698i	−0.215273	+	0.976554i	$0.569064\pi$
$374$	1990.70	−	2297.39i	0.275231	−	0.317634i
$375$		0			0
$376$	726.270	−	213.252i	0.0996130	−	0.0292490i
$377$	1379.94	+	886.834i	0.188516	+	0.121152i
$378$		0			0
$379$	3241.27	+	7097.40i	0.439296	+	0.961924i	0.991727	+	0.128365i	$0.0409729\pi$
$379$	3241.27	+	7097.40i	0.439296	+	0.961924i	−0.552431	+	0.833558i	$0.686300\pi$
$380$	169.391	+	370.914i	0.0228673	+	0.0500723i
$381$		0			0
$382$	−8931.28	−	5739.79i	−1.19624	−	0.768778i
$383$	2398.76	−	704.341i	0.320029	−	0.0939690i	−0.117773	−	0.993041i	$-0.537575\pi$
$383$	2398.76	−	704.341i	0.320029	−	0.0939690i	0.437802	+	0.899072i	$0.355757\pi$
$384$		0			0
$385$	2656.69	−	3065.98i	0.351681	−	0.405862i
$386$	12881.4	−	8278.34i	1.69856	−	1.09160i
$387$		0			0
$388$	3558.71	+	1044.93i	0.465634	+	0.136722i
$389$	−5968.24	+	13068.6i	−0.777897	+	1.70336i	−0.0694586	+	0.997585i	$0.522127\pi$
$389$	−5968.24	+	13068.6i	−0.777897	+	1.70336i	−0.708439	+	0.705772i	$0.750600\pi$
$390$		0			0
$391$	−1431.04	+	1572.99i	−0.185091	+	0.203452i
$392$	−2675.06			−0.344671
$393$		0			0
$394$	14863.5	+	4364.33i	1.90054	+	0.558050i
$395$	−798.298	−	921.285i	−0.101688	−	0.117354i
$396$		0			0
$397$	618.365	−	713.632i	0.0781735	−	0.0902170i	−0.715315	−	0.698802i	$-0.753717\pi$
$397$	618.365	−	713.632i	0.0781735	−	0.0902170i	0.793489	+	0.608585i	$0.208262\pi$
$398$	−526.087	+	3659.02i	−0.0662572	+	0.460829i
$399$		0			0
$400$	6831.17	+	4390.12i	0.853896	+	0.548766i
$401$	746.923	+	5194.97i	0.0930164	+	0.646943i	0.981983	+	0.188971i	$0.0605151\pi$
$401$	746.923	+	5194.97i	0.0930164	+	0.646943i	−0.888966	+	0.457973i	$0.848576\pi$
$402$		0			0
$403$	3128.78	+	6851.07i	0.386738	+	0.846839i
$404$	409.035	+	2844.90i	0.0503719	+	0.350344i
$405$		0			0
$406$	7525.34	−	2209.64i	0.919892	−	0.270105i
$407$	−679.083	+	4723.13i	−0.0827049	+	0.575226i
$408$		0			0
$409$	−5195.32	+	3338.83i	−0.628098	+	0.403654i	−0.815605	−	0.578609i	$-0.803596\pi$
$409$	−5195.32	+	3338.83i	−0.628098	+	0.403654i	0.187507	+	0.982263i	$0.439959\pi$
$410$	−3403.92	−	3928.33i	−0.410018	−	0.473186i
$411$		0			0
$412$	−4716.45	+	10327.6i	−0.563988	+	1.23496i
$413$	−5817.57			−0.693133
$414$		0			0
$415$	−1196.65			−0.141545
$416$	2988.78	−	6544.51i	0.352252	−	0.771325i
$417$		0			0
$418$	2052.33	+	2368.52i	0.240150	+	0.277148i
$419$	4096.44	−	2632.62i	0.477624	−	0.306950i	−0.279587	−	0.960120i	$-0.590198\pi$
$419$	4096.44	−	2632.62i	0.477624	−	0.306950i	0.757211	+	0.653170i	$0.226561\pi$
$420$		0			0
$421$	−635.435	+	4419.55i	−0.0735611	+	0.511629i	0.919413	+	0.393294i	$0.128665\pi$
$421$	−635.435	+	4419.55i	−0.0735611	+	0.511629i	−0.992974	+	0.118335i	$0.962244\pi$
$422$	−4306.26	+	1264.43i	−0.496743	+	0.145857i
$423$		0			0
$424$	−198.263	−	1378.95i	−0.0227087	−	0.157942i
$425$	937.063	+	2051.88i	0.106951	+	0.234190i
$426$		0			0
$427$	2975.48	+	20694.9i	0.337222	+	2.34543i
$428$	926.377	+	595.347i	0.104622	+	0.0672364i
$429$		0			0
$430$	−376.450	+	2618.26i	−0.0422186	+	0.293637i
$431$	−6559.17	+	7569.69i	−0.733049	+	0.845984i	−0.992811	−	0.119689i	$-0.961810\pi$
$431$	−6559.17	+	7569.69i	−0.733049	+	0.845984i	0.259762	+	0.965673i	$0.416356\pi$
$432$		0			0
$433$	−6403.47	−	7390.00i	−0.710696	−	0.820187i	0.279460	−	0.960157i	$-0.409845\pi$
$433$	−6403.47	−	7390.00i	−0.710696	−	0.820187i	−0.990156	+	0.139971i	$0.955299\pi$
$434$	34553.0	+	10145.7i	3.82165	+	1.12214i
$435$		0			0
$436$	15476.7			1.70000
$437$	−1395.22	−	1691.12i	−0.152729	−	0.185119i
$438$		0			0
$439$	5343.80	−	11701.3i	0.580970	−	1.27215i	−0.359777	−	0.933038i	$-0.617147\pi$
$439$	5343.80	−	11701.3i	0.580970	−	1.27215i	0.940747	−	0.339109i	$-0.110125\pi$
$440$	−318.408	−	93.4930i	−0.0344989	−	0.0101298i
$441$		0			0
$442$	1839.15	−	1181.95i	0.197917	−	0.127193i
$443$	9274.39	−	10703.2i	0.994672	−	1.14791i	0.00567383	−	0.999984i	$-0.498194\pi$
$443$	9274.39	−	10703.2i	0.994672	−	1.14791i	0.988998	−	0.147929i	$-0.0472606\pi$
$444$		0			0
$445$	−1927.15	+	565.863i	−0.205294	+	0.0602797i
$446$	−11919.8	−	7660.40i	−1.26551	−	0.813297i
$447$		0			0
$448$	−6093.27	−	13342.4i	−0.642589	−	1.40707i
$449$	4636.98	+	10153.6i	0.487378	+	1.06721i	0.980369	+	0.197174i	$0.0631764\pi$
$449$	4636.98	+	10153.6i	0.487378	+	1.06721i	−0.492991	+	0.870035i	$0.664096\pi$
$450$		0			0
$451$	−15984.3	−	10272.5i	−1.66890	−	1.07254i
$452$	−992.805	+	291.514i	−0.103313	+	0.0303355i
$453$		0			0
$454$	6007.40	−	6932.91i	0.621016	−	0.716691i
$455$	2454.43	−	1577.37i	0.252891	−	0.162523i
$456$		0			0
$457$	853.103	+	250.494i	0.0873227	+	0.0256403i	0.325102	−	0.945679i	$-0.394601\pi$
$457$	853.103	+	250.494i	0.0873227	+	0.0256403i	−0.237779	+	0.971319i	$0.576420\pi$
$458$	7447.33	−	16307.4i	0.759805	−	1.66374i
$459$		0			0
$460$	−2155.24	−	689.859i	−0.218453	−	0.0699236i
$461$	−3838.43			−0.387795			−0.193897	−	0.981022i	$-0.562113\pi$
$461$	−3838.43			−0.387795			−0.193897	+	0.981022i	$0.562113\pi$
$462$		0			0
$463$	14.0140	+	4.11487i	0.00140666	+	0.000413033i	0.282436	−	0.959286i	$-0.408858\pi$
$463$	14.0140	+	4.11487i	0.00140666	+	0.000413033i	−0.281029	+	0.959699i	$0.590676\pi$
$464$	−2567.76	−	2963.35i	−0.256907	−	0.296487i
$465$		0			0
$466$	−10551.3	+	12176.9i	−1.04889	+	1.21048i
$467$	−176.826	+	1229.85i	−0.0175214	+	0.121864i	−0.996705	−	0.0811128i	$-0.974153\pi$
$467$	−176.826	+	1229.85i	−0.0175214	+	0.121864i	0.979183	+	0.202977i	$0.0650617\pi$
$468$		0			0
$469$	10936.7	+	7028.61i	1.07678	+	0.692006i
$470$	409.214	+	2846.14i	0.0401609	+	0.279325i
$471$		0			0
$472$	197.685	+	432.871i	0.0192780	+	0.0422129i
$473$	1376.08	+	9570.87i	0.133768	+	0.930378i
$474$		0			0
$475$	−2231.36	+	655.188i	−0.215541	+	0.0632886i
$476$	707.516	−	4920.89i	0.0681281	−	0.473841i
$477$		0			0
$478$	8136.62	−	5229.09i	0.778578	−	0.500362i
$479$	−9294.34	−	10726.2i	−0.886575	−	1.02316i	−0.999563	−	0.0295655i	$-0.990588\pi$
$479$	−9294.34	−	10726.2i	−0.886575	−	1.02316i	0.112988	−	0.993596i	$-0.463958\pi$
$480$		0			0
$481$	−1425.57	+	3121.56i	−0.135136	+	0.295906i
$482$	−10150.3			−0.959200
$483$		0			0
$484$	2167.56			0.203565
$485$	600.427	−	1314.75i	0.0562144	−	0.123092i
$486$		0			0
$487$	−231.571	−	267.247i	−0.0215472	−	0.0248668i	0.744874	−	0.667205i	$-0.232510\pi$
$487$	−231.571	−	267.247i	−0.0215472	−	0.0248668i	−0.766421	+	0.642339i	$0.777964\pi$
$488$	1438.75	−	924.628i	0.133461	−	0.0857703i
$489$		0			0
$490$	1446.20	−	10058.5i	0.133332	−	0.927344i
$491$	−739.251	+	217.064i	−0.0679469	+	0.0199510i	−0.315529	−	0.948916i	$-0.602182\pi$
$491$	−739.251	+	217.064i	−0.0679469	+	0.0199510i	0.247582	+	0.968867i	$0.420364\pi$
$492$		0			0
$493$	−155.015	−	1078.15i	−0.0141613	−	0.0984940i
$494$	936.297	+	2050.20i	0.0852753	+	0.186727i
$495$		0			0
$496$	−2562.21	−	17820.5i	−0.231949	−	1.61324i
$497$	−21702.5	−	13947.4i	−1.95873	−	1.25880i
$498$		0			0
$499$	962.791	−	6696.36i	0.0863736	−	0.600742i	−0.899959	−	0.435975i	$-0.856404\pi$
$499$	962.791	−	6696.36i	0.0863736	−	0.600742i	0.986333	−	0.164767i	$-0.0526872\pi$
$500$	−3251.30	+	3752.20i	−0.290805	+	0.335607i
$501$		0			0
$502$	−6175.01	−	7126.34i	−0.549012	−	0.633594i
$503$	−4431.95	−	1301.34i	−0.392864	−	0.115355i	0.0793331	−	0.996848i	$-0.474721\pi$
$503$	−4431.95	−	1301.34i	−0.392864	−	0.115355i	−0.472198	+	0.881493i	$0.656539\pi$
$504$		0			0
$505$	1120.05			0.0986962
$506$	−17387.6	−	420.526i	−1.52761	−	0.0369460i
$507$		0			0
$508$	−629.627	+	1378.69i	−0.0549905	+	0.120412i
$509$	17119.9	+	5026.86i	1.49082	+	0.437744i	0.922802	−	0.385273i	$-0.125893\pi$
$509$	17119.9	+	5026.86i	1.49082	+	0.437744i	0.568016	+	0.823017i	$0.307711\pi$
$510$		0			0
$511$	5593.92	−	3595.00i	0.484267	−	0.311220i
$512$	−10205.4	+	11777.7i	−0.880898	+	1.01661i
$513$		0			0
$514$	−17224.9	+	5057.68i	−1.47813	+	0.434017i
$515$	3722.10	+	2392.05i	0.318476	+	0.204672i
$516$		0			0
$517$	4366.36	+	9561.00i	0.371436	+	0.813331i
$518$	6816.14	+	14925.3i	0.578154	+	1.26598i
$519$		0			0
$520$	−200.771	−	129.028i	−0.0169316	−	0.0108812i
$521$	18723.3	−	5497.67i	1.57444	−	0.462298i	0.626151	−	0.779702i	$-0.284629\pi$
$521$	18723.3	−	5497.67i	1.57444	−	0.462298i	0.948290	+	0.317404i	$0.102811\pi$
$522$		0			0
$523$	10409.1	−	12012.8i	0.870284	−	1.00436i	−0.129634	−	0.991562i	$-0.541380\pi$
$523$	10409.1	−	12012.8i	0.870284	−	1.00436i	0.999918	−	0.0127995i	$-0.00407432\pi$
$524$	−12252.2	+	7873.99i	−1.02145	+	0.656444i
$525$		0			0
$526$	29144.4	+	8557.56i	2.41588	+	0.709368i
$527$	2077.61	−	4549.34i	0.171731	−	0.376039i
$528$		0			0
$529$	12152.8	+	588.184i	0.998831	+	0.0483426i
$530$	5292.18			0.433731
$531$		0			0
$532$	4917.79	+	1443.99i	0.400777	+	0.117679i
$533$	−8948.48	−	10327.1i	−0.727208	−	0.839242i
$534$		0			0
$535$	281.020	−	324.315i	0.0227095	−	0.0262081i
$536$	151.343	−	1052.61i	0.0121959	−	0.0848244i
$537$		0			0
$538$	5768.34	+	3707.09i	0.462251	+	0.297071i
$539$	−5286.47	−	36768.2i	−0.422457	−	2.93825i
$540$		0			0
$541$	2976.17	+	6516.90i	0.236517	+	0.517899i	0.990253	−	0.139277i	$-0.0444779\pi$
$541$	2976.17	+	6516.90i	0.236517	+	0.517899i	−0.753737	+	0.657176i	$0.771751\pi$
$542$	763.084	+	5307.37i	0.0604747	+	0.420611i
$543$		0			0
$544$	−4583.99	+	1345.98i	−0.361281	+	0.106082i
$545$	858.335	−	5969.85i	0.0674624	−	0.469211i
$546$		0			0
$547$	−5533.25	+	3556.01i	−0.432513	+	0.277960i	−0.738729	−	0.674003i	$-0.764574\pi$
$547$	−5533.25	+	3556.01i	−0.432513	+	0.277960i	0.306215	+	0.951962i	$0.400937\pi$
$548$	−14093.4	−	16264.6i	−1.09861	−	1.26786i
$549$		0			0
$550$	−7664.11	+	16782.1i	−0.594180	+	1.30107i
$551$	1122.96			0.0868237
$552$		0			0
$553$	−15322.8			−1.17828
$554$	−8040.67	+	17606.6i	−0.616634	+	1.35024i
$555$		0			0
$556$	−4164.05	−	4805.57i	−0.317617	−	0.366550i
$557$	908.665	−	583.964i	0.0691227	−	0.0444225i	−0.505623	−	0.862755i	$-0.668737\pi$
$557$	908.665	−	583.964i	0.0691227	−	0.0444225i	0.574746	+	0.818332i	$0.305101\pi$
$558$		0			0
$559$	−989.640	+	6883.10i	−0.0748789	+	0.520794i
$560$	−6691.71	+	1964.86i	−0.504958	+	0.148269i
$561$		0			0
$562$	−245.938	−	1710.54i	−0.0184596	−	0.128389i
$563$	−8536.63	−	18692.6i	−0.639034	−	1.39929i	−0.900832	−	0.434167i	$-0.857043\pi$
$563$	−8536.63	−	18692.6i	−0.639034	−	1.39929i	0.261798	−	0.965123i	$-0.415684\pi$
$564$		0			0
$565$	57.3852	+	399.123i	0.00427295	+	0.0297190i
$566$	8789.26	+	5648.52i	0.652721	+	0.419478i
$567$		0			0
$568$	−300.320	+	2088.77i	−0.0221851	+	0.154301i
$569$	−2737.44	+	3159.17i	−0.201686	+	0.232758i	−0.847578	−	0.530671i	$-0.821940\pi$
$569$	−2737.44	+	3159.17i	−0.201686	+	0.232758i	0.645892	+	0.763429i	$0.276486\pi$
$570$		0			0
$571$	65.8051	+	75.9431i	0.00482287	+	0.00556588i	0.758156	−	0.652073i	$-0.226101\pi$
$571$	65.8051	+	75.9431i	0.00482287	+	0.00556588i	−0.753333	+	0.657639i	$0.771555\pi$
$572$	8159.63	+	2395.88i	0.596453	+	0.175135i
$573$		0			0
$574$	−65335.8			−4.75098
$575$	5643.69	−	11606.8i	0.409319	−	0.841802i
$576$		0			0
$577$	3344.01	−	7322.35i	0.241270	−	0.528308i	−0.749798	−	0.661667i	$-0.769849\pi$
$577$	3344.01	−	7322.35i	0.241270	−	0.528308i	0.991068	+	0.133360i	$0.0425765\pi$
$578$	17019.2	+	4997.30i	1.22475	+	0.359620i
$579$		0			0
$580$	975.107	−	626.663i	0.0698088	−	0.0448634i
$581$	−9849.99	+	11367.5i	−0.703350	+	0.811709i
$582$		0			0
$583$	18561.5	−	5450.16i	1.31859	−	0.387174i
$584$	−457.580	−	294.069i	−0.0324226	−	0.0208368i
$585$		0			0
$586$	−11058.6	−	24215.0i	−0.779568	−	1.70702i
$587$	7033.90	+	15402.1i	0.494583	+	1.08299i	0.978192	+	0.207702i	$0.0665984\pi$
$587$	7033.90	+	15402.1i	0.494583	+	1.08299i	−0.483609	+	0.875284i	$0.660674\pi$
$588$		0			0
$589$	4337.62	+	2787.62i	0.303444	+	0.195012i
$590$	−1734.51	+	509.299i	−0.121032	+	0.0355382i
$591$		0			0
$592$	5371.87	−	6199.47i	0.372944	−	0.430400i
$593$	3859.68	−	2480.46i	0.267281	−	0.171771i	−0.400135	−	0.916456i	$-0.631037\pi$
$593$	3859.68	−	2480.46i	0.267281	−	0.171771i	0.667416	+	0.744685i	$0.267400\pi$
$594$		0			0
$595$	−1858.90	−	545.822i	−0.128080	−	0.0376076i
$596$	−1860.42	+	4073.74i	−0.127862	+	0.279978i
$597$		0			0
$598$	−11912.9	−	3813.15i	−0.814643	−	0.260755i
$599$	−1406.87			−0.0959649			−0.0479824	−	0.998848i	$-0.515279\pi$
$599$	−1406.87			−0.0959649			−0.0479824	+	0.998848i	$0.515279\pi$
$600$		0			0
$601$	6091.73	+	1788.69i	0.413456	+	0.121402i	0.481844	−	0.876257i	$-0.339967\pi$
$601$	6091.73	+	1788.69i	0.413456	+	0.121402i	−0.0683879	+	0.997659i	$0.521786\pi$
$602$	21773.4	+	25127.9i	1.47412	+	1.70122i
$603$		0			0
$604$	−14091.7	+	16262.7i	−0.949311	+	1.09556i
$605$	120.212	−	836.093i	0.00807821	−	0.0561852i
$606$		0			0
$607$	−21839.9	−	14035.7i	−1.46039	−	0.938533i	−0.998673	−	0.0515044i	$-0.983598\pi$
$607$	−21839.9	−	14035.7i	−1.46039	−	0.938533i	−0.461714	−	0.887029i	$-0.652765\pi$
$608$	−700.961	−	4875.29i	−0.0467561	−	0.325196i
$609$		0			0
$610$	2698.88	+	5909.73i	0.179139	+	0.392259i
$611$	1075.77	+	7482.16i	0.0712293	+	0.495411i
$612$		0			0
$613$	−5386.85	+	1581.72i	−0.354931	+	0.104217i	−0.454337	−	0.890830i	$-0.650124\pi$
$613$	−5386.85	+	1581.72i	−0.354931	+	0.104217i	0.0994060	+	0.995047i	$0.468306\pi$
$614$	1363.35	−	9482.30i	0.0896096	−	0.623248i
$615$		0			0
$616$	−3509.06	+	2255.13i	−0.229519	+	0.147503i
$617$	12634.8	+	14581.3i	0.824403	+	0.951412i	0.999450	−	0.0331481i	$-0.0105533\pi$
$617$	12634.8	+	14581.3i	0.824403	+	0.951412i	−0.175047	+	0.984560i	$0.556008\pi$
$618$		0			0
$619$	−3817.34	+	8358.81i	−0.247871	+	0.542761i	−0.992142	−	0.125116i	$-0.960070\pi$
$619$	−3817.34	+	8358.81i	−0.247871	+	0.542761i	0.744271	+	0.667877i	$0.232797\pi$
$620$	5322.12			0.344744
$621$		0			0
$622$	9139.39			0.589158
$623$	−10487.6	+	22964.7i	−0.674444	+	1.47683i
$624$		0			0
$625$	−8310.74	−	9591.10i	−0.531887	−	0.613830i
$626$	8700.89	−	5591.72i	0.555523	−	0.357013i
$627$		0			0
$628$	−2970.68	+	20661.5i	−0.188763	+	1.31287i
$629$	2186.44	−	641.996i	0.138599	−	0.0406965i
$630$		0			0
$631$	−357.438	−	2486.04i	−0.0225505	−	0.156842i	0.975435	−	0.220289i	$-0.0706999\pi$
$631$	−357.438	−	2486.04i	−0.0225505	−	0.156842i	−0.997985	+	0.0634463i	$0.979791\pi$
$632$	520.679	+	1140.13i	0.0327714	+	0.0717593i
$633$		0			0
$634$	5511.23	+	38331.5i	0.345235	+	2.40116i
$635$	496.885	+	319.329i	0.0310524	+	0.0199562i
$636$		0			0
$637$	3801.88	−	26442.7i	0.236477	−	1.64474i
$638$	5833.99	−	6732.78i	0.362022	−	0.417795i
$639$		0			0
$640$	686.054	+	791.748i	0.0423729	+	0.0489009i
$641$	1549.43	+	454.953i	0.0954738	+	0.0280336i	0.329121	−	0.944288i	$-0.393248\pi$
$641$	1549.43	+	454.953i	0.0954738	+	0.0280336i	−0.233647	+	0.972322i	$0.575066\pi$
$642$		0			0
$643$	−7455.77			−0.457274			−0.228637	−	0.973512i	$-0.573427\pi$
$643$	−7455.77			−0.457274			−0.228637	+	0.973512i	$0.573427\pi$
$644$	−24293.8	+	14795.1i	−1.48650	+	0.905295i
$645$		0			0
$646$	621.732	−	1361.40i	0.0378665	−	0.0829160i
$647$	−30210.5	−	8870.59i	−1.83570	−	0.539009i	−0.835747	−	0.549114i	$-0.814965\pi$
$647$	−30210.5	−	8870.59i	−1.83570	−	0.539009i	−0.999949	+	0.0101049i	$0.996783\pi$
$648$		0			0
$649$	−5559.05	+	3572.59i	−0.336228	+	0.216081i
$650$	−8688.83	+	10027.4i	−0.524314	+	0.605090i
$651$		0			0
$652$	−21023.4	+	6173.03i	−1.26279	+	0.370789i
$653$	−12830.8	−	8245.84i	−0.768923	−	0.494157i	0.0964173	−	0.995341i	$-0.469262\pi$
$653$	−12830.8	−	8245.84i	−0.768923	−	0.494157i	−0.865341	+	0.501184i	$0.832898\pi$
$654$		0			0
$655$	2357.74	+	5162.73i	0.140648	+	0.307976i
$656$	13569.2	+	29712.4i	0.807603	+	1.76840i
$657$		0			0
$658$	30405.2	+	19540.2i	1.80140	+	1.15769i
$659$	−1174.99	+	345.009i	−0.0694557	+	0.0203940i	−0.316276	−	0.948667i	$-0.602432\pi$
$659$	−1174.99	+	345.009i	−0.0694557	+	0.0203940i	0.246820	+	0.969061i	$0.420614\pi$
$660$		0			0
$661$	−11287.3	+	13026.3i	−0.664186	+	0.766511i	−0.983455	−	0.181153i	$-0.942017\pi$
$661$	−11287.3	+	13026.3i	−0.664186	+	0.766511i	0.319269	+	0.947664i	$0.396563\pi$
$662$	21556.5	−	13853.5i	1.26559	−	0.813343i
$663$		0			0
$664$	1180.54	+	346.637i	0.0689965	+	0.0202592i
$665$	829.733	−	1816.86i	0.0483845	−	0.105947i
$666$		0			0
$667$	−4193.83	+	4609.84i	−0.243457	+	0.267607i
$668$	15851.9			0.918157
$669$		0			0
$670$	3876.12	+	1138.13i	0.223504	+	0.0656266i
$671$	15552.1	+	17948.1i	0.894756	+	1.03260i
$672$		0			0
$673$	1915.69	−	2210.82i	0.109724	−	0.126629i	−0.698231	−	0.715873i	$-0.746029\pi$
$673$	1915.69	−	2210.82i	0.109724	−	0.126629i	0.807955	+	0.589244i	$0.200574\pi$
$674$	−1909.33	+	13279.7i	−0.109117	+	0.758925i
$675$		0			0
$676$	−8265.15	−	5311.69i	−0.470252	−	0.302213i
$677$	−3334.53	−	23192.2i	−0.189301	−	1.31662i	−0.833824	−	0.552030i	$-0.813853\pi$
$677$	−3334.53	−	23192.2i	−0.189301	−	1.31662i	0.644523	−	0.764585i	$-0.277056\pi$
$678$		0			0
$679$	−7547.12	−	16525.9i	−0.426557	−	0.934029i
$680$	22.5536	+	156.863i	0.00127190	+	0.00884623i
$681$		0			0
$682$	39248.0	−	11524.3i	2.20364	−	0.647047i
$683$	597.766	−	4157.55i	0.0334888	−	0.232920i	−0.966202	−	0.257786i	$-0.917007\pi$
$683$	597.766	−	4157.55i	0.0334888	−	0.232920i	0.999691	+	0.0248664i	$0.00791603\pi$
$684$		0			0
$685$	−7055.38	+	4534.22i	−0.393536	+	0.252910i
$686$	−52465.9	−	60548.9i	−2.92005	−	3.36992i
$687$		0			0
$688$	6905.27	−	15120.4i	0.382647	−	0.837879i
$689$	13912.5			0.769266
$690$		0			0
$691$	18363.9			1.01099			0.505497	−	0.862829i	$-0.331309\pi$
$691$	18363.9			1.01099			0.505497	+	0.862829i	$0.331309\pi$
$692$	−7864.35	+	17220.5i	−0.432020	+	0.945992i
$693$		0			0
$694$	8285.87	+	9562.40i	0.453209	+	0.523032i
$695$	−2084.60	+	1339.69i	−0.113774	+	0.0731184i
$696$		0			0
$697$	−1291.34	+	8981.46i	−0.0701764	+	0.488088i
$698$	17342.9	−	5092.32i	0.940454	−	0.276142i
$699$		0			0
$700$	4293.98	+	29865.3i	0.231853	+	1.61257i
$701$	6687.83	+	14644.3i	0.360336	+	0.789026i	0.999796	+	0.0202017i	$0.00643085\pi$
$701$	6687.83	+	14644.3i	0.360336	+	0.789026i	−0.639460	+	0.768825i	$0.720842\pi$
$702$		0			0
$703$	334.340	+	2325.38i	0.0179372	+	0.124756i
$704$	−14016.1	−	9007.61i	−0.750358	−	0.482226i
$705$		0			0
$706$	4238.78	−	29481.3i	0.225961	−	1.57159i
$707$	9219.50	−	10639.9i	0.490432	−	0.565988i
$708$		0			0
$709$	−8533.27	−	9847.92i	−0.452008	−	0.521645i	0.483312	−	0.875448i	$-0.339434\pi$
$709$	−8533.27	−	9847.92i	−0.452008	−	0.521645i	−0.935320	+	0.353803i	$0.884888\pi$
$710$	−7691.65	−	2258.47i	−0.406567	−	0.119379i
$711$		0			0
$712$	2065.13			0.108699
$713$	−27642.7	+	7395.56i	−1.45193	+	0.388452i
$714$		0			0
$715$	1376.70	−	3014.55i	0.0720078	−	0.157675i
$716$	−4997.21	−	1467.31i	−0.260830	−	0.0765867i
$717$		0			0
$718$	−9186.04	+	5903.51i	−0.477465	+	0.306848i
$719$	5950.17	−	6866.87i	0.308629	−	0.356177i	−0.580153	−	0.814508i	$-0.697007\pi$
$719$	5950.17	−	6866.87i	0.308629	−	0.356177i	0.888782	+	0.458331i	$0.151553\pi$
$720$		0			0
$721$	53361.0	−	15668.2i	2.75627	−	0.809313i
$722$	−21239.3	−	13649.7i	−1.09480	−	0.703586i
$723$		0			0
$724$	−12162.3	−	26631.6i	−0.624319	−	1.36707i
$725$	2746.18	+	6013.29i	0.140677	+	0.308039i
$726$		0			0
$727$	7880.84	+	5064.71i	0.402042	+	0.258376i	0.726000	−	0.687695i	$-0.241377\pi$
$727$	7880.84	+	5064.71i	0.402042	+	0.258376i	−0.323958	+	0.946071i	$0.605014\pi$
$728$	−2878.31	+	845.149i	−0.146535	+	0.0430265i
$729$		0			0
$730$	1353.11	−	1561.57i	0.0686039	−	0.0791731i
$731$	3884.58	−	2496.47i	0.196548	−	0.126314i
$732$		0			0
$733$	315.711	+	92.7010i	0.0159087	+	0.00467120i	0.289677	−	0.957124i	$-0.406452\pi$
$733$	315.711	+	92.7010i	0.0159087	+	0.00467120i	−0.273769	+	0.961796i	$0.588270\pi$
$734$	6820.88	−	14935.6i	0.343002	−	0.751069i
$735$		0			0
$736$	22631.2	+	15329.8i	1.13342	+	0.767751i
$737$	14767.0			0.738060
$738$		0			0
$739$	−25145.7	−	7383.44i	−1.25169	−	0.367530i	−0.412295	−	0.911050i	$-0.635273\pi$
$739$	−25145.7	−	7383.44i	−1.25169	−	0.367530i	−0.839396	+	0.543521i	$0.817091\pi$
$740$	1587.98	+	1832.63i	0.0788858	+	0.0910390i
$741$		0			0
$742$	43561.7	−	50272.9i	2.15526	−	2.48730i
$743$	2906.91	−	20218.0i	0.143532	−	0.998286i	−0.782987	−	0.622038i	$-0.786305\pi$
$743$	2906.91	−	20218.0i	0.143532	−	0.998286i	0.926519	−	0.376248i	$-0.122786\pi$
$744$		0			0
$745$	1468.19	+	943.549i	0.0722018	+	0.0464013i
$746$	5678.64	+	39495.8i	0.278700	+	1.93840i
$747$		0			0
$748$	−2345.85	−	5136.70i	−0.114670	−	0.251092i
$749$	−767.644	−	5339.08i	−0.0374488	−	0.260462i
$750$		0			0
$751$	7360.12	−	2161.13i	0.357622	−	0.105007i	−0.0979858	−	0.995188i	$-0.531240\pi$
$751$	7360.12	−	2161.13i	0.357622	−	0.105007i	0.455608	+	0.890180i	$0.349422\pi$
$752$	2571.53	−	17885.4i	0.124700	−	0.867305i
$753$		0			0
$754$	5389.84	−	3463.84i	0.260327	−	0.167302i
$755$	5491.51	+	6337.53i	0.264710	+	0.305492i
$756$		0			0
$757$	−8835.49	+	19347.0i	−0.424216	+	0.928903i	0.570014	+	0.821635i	$0.306938\pi$
$757$	−8835.49	+	19347.0i	−0.424216	+	0.928903i	−0.994230	+	0.107268i	$0.965790\pi$
$758$	30475.4			1.46031
$759$		0			0
$760$	−163.383			−0.00779806
$761$	−9893.98	+	21664.8i	−0.471296	+	1.03199i	0.513469	+	0.858108i	$0.328360\pi$
$761$	−9893.98	+	21664.8i	−0.471296	+	1.03199i	−0.984766	+	0.173887i	$0.944367\pi$
$762$		0			0
$763$	−49645.1	−	57293.5i	−2.35554	−	2.71843i
$764$	−16591.1	+	10662.5i	−0.785663	+	0.504915i
$765$		0			0
$766$	1389.67	−	9665.37i	0.0655494	−	0.455906i
$767$	−4559.83	+	1338.89i	−0.214662	+	0.0630305i
$768$		0			0
$769$	−4441.28	−	30889.8i	−0.208266	−	1.44852i	−0.778812	−	0.627257i	$-0.784178\pi$
$769$	−4441.28	−	30889.8i	−0.208266	−	1.44852i	0.570546	−	0.821266i	$-0.306732\pi$
$770$	−6582.48	−	14413.6i	−0.308073	−	0.674585i
$771$		0			0
$772$	−4048.06	−	28154.9i	−0.188721	−	1.31259i
$773$	−14194.6	−	9122.30i	−0.660470	−	0.424458i	0.167009	−	0.985955i	$-0.446589\pi$
$773$	−14194.6	−	9122.30i	−0.660470	−	0.424458i	−0.827479	+	0.561497i	$0.810226\pi$
$774$		0			0
$775$	−4319.72	+	30044.3i	−0.200218	+	1.39255i
$776$	−973.193	+	1123.12i	−0.0450201	+	0.0519560i
$777$		0			0
$778$	36747.6	+	42409.0i	1.69340	+	1.95429i
$779$	−8975.82	−	2635.54i	−0.412827	−	0.121217i
$780$		0			0
$781$	−29303.2			−1.34258
$782$	3266.73	+	7636.57i	0.149384	+	0.349211i
$783$		0			0
$784$	−26527.8	+	58087.9i	−1.20845	+	2.64613i
$785$	7805.04	+	2291.77i	0.354871	+	0.104200i
$786$		0			0
$787$	7005.87	−	4502.40i	0.317322	−	0.203930i	−0.372278	−	0.928121i	$-0.621423\pi$
$787$	7005.87	−	4502.40i	0.317322	−	0.203930i	0.689599	+	0.724191i	$0.257787\pi$
$788$	18844.8	−	21748.1i	0.851926	−	0.983176i
$789$		0			0
$790$	−4568.50	+	1341.43i	−0.205747	+	0.0604127i
$791$	4263.81	+	2740.18i	0.191661	+	0.123173i
$792$		0			0
$793$	7095.03	+	15536.0i	0.317720	+	0.695710i
$794$	−1532.12	−	3354.89i	−0.0684800	−	0.149950i
$795$		0			0
$796$	5776.92	+	3712.60i	0.257233	+	0.165314i
$797$	15689.7	−	4606.92i	0.697313	−	0.204750i	0.0861825	−	0.996279i	$-0.472533\pi$
$797$	15689.7	−	4606.92i	0.697313	−	0.204750i	0.611131	+	0.791530i	$0.290715\pi$
$798$		0			0
$799$	3287.07	−	3793.48i	0.145542	−	0.167965i
$800$	24392.2	−	15675.9i	1.07799	−	0.692785i
$801$		0			0
$802$	19669.1	+	5775.36i	0.866008	+	0.254283i
$803$	3137.65	−	6870.49i	0.137889	−	0.301936i
$804$		0			0
$805$	4359.62	+	10191.4i	0.190877	+	0.446210i
$806$	29417.7			1.28560
$807$		0			0
$808$	−1104.97	−	324.449i	−0.0481099	−	0.0141263i
$809$	−8932.84	−	10309.0i	−0.388210	−	0.448018i	0.527683	−	0.849442i	$-0.323061\pi$
$809$	−8932.84	−	10309.0i	−0.388210	−	0.448018i	−0.915893	+	0.401423i	$0.868516\pi$
$810$		0			0
$811$	−21306.4	+	24588.9i	−0.922525	+	1.06465i	0.0751952	+	0.997169i	$0.476042\pi$
$811$	−21306.4	+	24588.9i	−0.922525	+	1.06465i	−0.997720	+	0.0674821i	$0.978503\pi$
$812$	2073.46	−	14421.3i	0.0896113	−	0.623260i
$813$		0			0
$814$	15678.9	+	10076.2i	0.675117	+	0.433871i
$815$	1215.18	+	8451.73i	0.0522279	+	0.363253i
$816$		0			0
$817$	1977.61	+	4330.37i	0.0846854	+	0.185435i
$818$	3432.83	+	23875.8i	0.146731	+	1.02054i
$819$		0			0
$820$	−9264.75	+	2720.38i	−0.394560	+	0.115853i
$821$	−493.692	+	3433.70i	−0.0209866	+	0.145965i	−0.997620	−	0.0689451i	$-0.978037\pi$
$821$	−493.692	+	3433.70i	−0.0209866	+	0.145965i	0.976634	+	0.214910i	$0.0689458\pi$
$822$		0			0
$823$	32233.9	−	20715.4i	1.36525	−	0.877393i	0.366654	−	0.930357i	$-0.380503\pi$
$823$	32233.9	−	20715.4i	1.36525	−	0.877393i	0.998596	+	0.0529637i	$0.0168668\pi$
$824$	−2979.08	−	3438.04i	−0.125948	−	0.145352i
$825$		0			0
$826$	−9439.29	+	20669.2i	−0.397621	+	0.870669i
$827$	−18851.3			−0.792651			−0.396325	−	0.918110i	$-0.629715\pi$
$827$	−18851.3			−0.792651			−0.396325	+	0.918110i	$0.629715\pi$
$828$		0			0
$829$	−2598.99			−0.108886			−0.0544430	−	0.998517i	$-0.517338\pi$
$829$	−2598.99			−0.108886			−0.0544430	+	0.998517i	$0.517338\pi$
$830$	−1941.62	+	4251.55i	−0.0811982	+	0.177799i
$831$		0			0
$832$	−7846.62	−	9055.48i	−0.326962	−	0.377334i
$833$	−14923.3	+	9590.63i	−0.620723	+	0.398914i
$834$		0			0
$835$	879.143	−	6114.58i	0.0364359	−	0.253418i
$836$	5586.02	−	1640.20i	0.231096	−	0.0678560i
$837$		0			0
$838$	−2706.74	−	18825.8i	−0.111578	−	0.776044i
$839$	3950.78	+	8650.99i	0.162570	+	0.355978i	0.973333	−	0.229396i	$-0.0736750\pi$
$839$	3950.78	+	8650.99i	0.162570	+	0.355978i	−0.810764	+	0.585374i	$0.800948\pi$
$840$		0			0
$841$	3016.63	+	20981.1i	0.123688	+	0.860269i
$842$	14671.1	+	9428.57i	0.600476	+	0.385903i
$843$		0			0
$844$	−1186.51	+	8252.35i	−0.0483902	+	0.336561i
$845$	−2507.27	+	2893.54i	−0.102074	+	0.117800i
$846$		0			0
$847$	−6952.93	−	8024.11i	−0.282061	−	0.325516i
$848$	−31909.4	−	9369.44i	−1.29218	−	0.379419i
$849$		0			0
$850$	8810.54			0.355528
$851$	−10794.5	−	7311.92i	−0.434818	−	0.294535i
$852$		0			0
$853$	−5327.96	+	11666.6i	−0.213864	+	0.468296i	−0.985911	−	0.167268i	$-0.946505\pi$
$853$	−5327.96	+	11666.6i	−0.213864	+	0.468296i	0.772048	+	0.635565i	$0.219233\pi$
$854$	78354.6	+	23007.0i	3.13963	+	0.921877i
$855$		0			0
$856$	−371.183	+	238.545i	−0.0148210	+	0.00952487i
$857$	19135.3	−	22083.3i	0.762718	−	0.880224i	−0.233018	−	0.972473i	$-0.574860\pi$
$857$	19135.3	−	22083.3i	0.762718	−	0.880224i	0.995736	+	0.0922485i	$0.0294054\pi$
$858$		0			0
$859$	−31234.5	+	9171.28i	−1.24064	+	0.364284i	−0.835255	−	0.549863i	$-0.814680\pi$
$859$	−31234.5	+	9171.28i	−1.24064	+	0.364284i	−0.405383	+	0.914147i	$0.632862\pi$
$860$	4133.77	+	2656.61i	0.163907	+	0.105337i
$861$		0			0
$862$	16251.7	+	35586.2i	0.642151	+	1.40611i
$863$	−2923.80	−	6402.22i	−0.115327	−	0.252531i	0.843162	−	0.537659i	$-0.180691\pi$
$863$	−2923.80	−	6402.22i	−0.115327	−	0.252531i	−0.958489	+	0.285128i	$0.907964\pi$
$864$		0			0
$865$	6206.34	+	3988.57i	0.243956	+	0.156781i
$866$	−36645.8	+	10760.2i	−1.43796	+	0.422224i
$867$		0			0
$868$	43808.1	−	50557.2i	1.71307	−	1.97699i
$869$	−14641.9	+	9409.76i	−0.571567	+	0.367324i
$870$		0			0
$871$	10189.8	+	2992.01i	0.396406	+	0.116395i
$872$	−2576.09	+	5640.84i	−0.100043	+	0.219063i
$873$		0			0
$874$	−8272.17	+	2213.15i	−0.320149	+	0.0856530i
$875$	24319.6			0.939604
$876$		0			0
$877$	−4180.26	−	1227.44i	−0.160955	−	0.0472606i	0.200262	−	0.979742i	$-0.435821\pi$
$877$	−4180.26	−	1227.44i	−0.160955	−	0.0472606i	−0.361217	+	0.932482i	$0.617639\pi$
$878$	−32902.8	−	37971.9i	−1.26471	−	1.45955i
$879$		0			0
$880$	−5187.72	+	5986.95i	−0.198725	+	0.229341i
$881$	2041.30	−	14197.6i	0.0780627	−	0.542938i	−0.912836	−	0.408327i	$-0.866112\pi$
$881$	2041.30	−	14197.6i	0.0780627	−	0.542938i	0.990898	−	0.134611i	$-0.0429786\pi$
$882$		0			0
$883$	9699.68	+	6233.61i	0.369672	+	0.237574i	0.712266	−	0.701910i	$-0.247669\pi$
$883$	9699.68	+	6233.61i	0.369672	+	0.237574i	−0.342594	+	0.939484i	$0.611305\pi$
$884$	−577.965	−	4019.84i	−0.0219899	−	0.152943i
$885$		0			0
$886$	−22979.2	−	50317.4i	−0.871332	−	1.90795i
$887$	3829.88	+	26637.4i	0.144977	+	1.00834i	0.924286	+	0.381700i	$0.124661\pi$
$887$	3829.88	+	26637.4i	0.144977	+	1.00834i	−0.779309	+	0.626640i	$0.784430\pi$
$888$		0			0
$889$	7123.48	−	2091.64i	0.268744	−	0.0789104i
$890$	−1116.45	+	7765.10i	−0.0420490	+	0.292457i
$891$		0			0
$892$	−22142.7	+	14230.3i	−0.831159	+	0.534154i
$893$	3388.84	+	3910.93i	0.126991	+	0.146556i
$894$		0			0
$895$	−843.132	+	1846.20i	−0.0314892	+	0.0689516i
$896$	13168.3			0.490985
$897$		0			0
$898$	43598.2			1.62015
$899$	6088.70	−	13332.4i	0.225884	−	0.494617i
$900$		0			0
$901$	−6049.84	−	6981.89i	−0.223695	−	0.258158i
$902$	−62432.4	+	40122.9i	−2.30463	+	1.48109i
$903$		0			0
$904$	59.0027	−	410.373i	0.00217080	−	0.0150982i
$905$	−10947.2	+	3214.38i	−0.402095	+	0.118066i
$906$		0			0
$907$	−2779.01	−	19328.5i	−0.101737	−	0.707598i	−0.975300	−	0.220886i	$-0.929105\pi$
$907$	−2779.01	−	19328.5i	−0.101737	−	0.707598i	0.873563	−	0.486712i	$-0.161804\pi$
$908$	−7079.17	−	15501.2i	−0.258734	−	0.566548i
$909$		0			0
$910$	−1621.77	−	11279.7i	−0.0590783	−	0.410899i
$911$	17424.4	+	11198.0i	0.633695	+	0.407251i	0.817676	−	0.575679i	$-0.195262\pi$
$911$	17424.4	+	11198.0i	0.633695	+	0.407251i	−0.183981	+	0.982930i	$0.558899\pi$
$912$		0			0
$913$	−2431.47	+	16911.3i	−0.0881380	+	0.613013i
$914$	2274.18	−	2624.54i	0.0823010	−	0.0949804i
$915$		0			0
$916$	−21808.7	−	25168.6i	−0.786658	−	0.907852i
$917$	68450.5	+	20098.9i	2.46503	+	0.723799i
$918$		0			0
$919$	44407.6			1.59399			0.796993	−	0.603989i	$-0.206423\pi$
$919$	44407.6			1.59399			0.796993	+	0.603989i	$0.206423\pi$
$920$	610.172	−	670.699i	0.0218661	−	0.0240351i
$921$		0			0
$922$	−6228.04	+	13637.5i	−0.222462	+	0.487123i
$923$	−20220.4	−	5937.25i	−0.721087	−	0.211730i
$924$		0			0
$925$	−11634.4	+	7477.00i	−0.413555	+	0.265776i
$926$	37.3580	−	43.1135i	0.00132577	−	0.00153002i
$927$		0			0
$928$	−13433.9	+	3944.56i	−0.475205	+	0.139533i
$929$	4254.52	+	2734.21i	0.150254	+	0.0965626i	0.613608	−	0.789611i	$-0.289718\pi$
$929$	4254.52	+	2734.21i	0.150254	+	0.0965626i	−0.463353	+	0.886174i	$0.653354\pi$
$930$		0			0
$931$	−7597.36	−	16635.9i	−0.267447	−	0.585628i
$932$	12433.8	+	27226.2i	0.436998	+	0.956892i
$933$		0			0
$934$	4082.61	+	2623.73i	0.143027	+	0.0919177i
$935$	−2111.49	+	619.988i	−0.0738534	+	0.0216853i
$936$		0			0
$937$	−19065.1	+	22002.3i	−0.664705	+	0.767111i	−0.983538	−	0.180700i	$-0.942164\pi$
$937$	−19065.1	+	22002.3i	−0.664705	+	0.767111i	0.318833	+	0.947811i	$0.396709\pi$
$938$	42717.2	−	27452.7i	1.48696	−	0.955610i
$939$		0			0
$940$	5125.12	+	1504.87i	0.177833	+	0.0522164i
$941$	−6697.49	+	14665.5i	−0.232021	+	0.508055i	−0.989452	−	0.144860i	$-0.953727\pi$
$941$	−6697.49	+	14665.5i	−0.232021	+	0.508055i	0.757431	+	0.652915i	$0.226454\pi$
$942$		0			0
$943$	44340.3	−	27003.7i	1.53120	−	0.932514i
$944$	11360.0			0.391670
$945$		0			0
$946$	36237.0	+	10640.1i	1.24542	+	0.365688i
$947$	−4839.63	−	5585.23i	−0.166069	−	0.191653i	0.666615	−	0.745402i	$-0.267742\pi$
$947$	−4839.63	−	5585.23i	−0.166069	−	0.191653i	−0.832684	+	0.553748i	$0.813197\pi$
$948$		0			0
$949$	3557.16	−	4105.18i	0.121676	−	0.140421i
$950$	−1292.69	+	8990.86i	−0.0441478	+	0.307055i
$951$		0			0
$952$	1675.76	+	1076.95i	0.0570502	+	0.0366640i
$953$	2641.94	+	18375.1i	0.0898016	+	0.624584i	0.984167	+	0.177246i	$0.0567188\pi$
$953$	2641.94	+	18375.1i	0.0898016	+	0.624584i	−0.894365	+	0.447338i	$0.852372\pi$
$954$		0			0
$955$	3192.71	+	6991.05i	0.108182	+	0.236885i
$956$	−2556.99	−	17784.3i	−0.0865053	−	0.601658i
$957$		0			0
$958$	−53189.7	+	15617.9i	−1.79382	+	0.526713i
$959$	−15002.5	+	104345.i	−0.505169	+	3.51353i
$960$		0			0
$961$	31552.8	−	20277.8i	1.05914	−	0.680668i
$962$	8777.49	+	10129.8i	0.294176	+	0.339498i
$963$		0			0
$964$	−7832.93	+	17151.7i	−0.261703	+	0.573050i
$965$	−11084.7			−0.369771
$966$		0			0
$967$	−8814.70			−0.293135			−0.146568	−	0.989201i	$-0.546823\pi$
$967$	−8814.70			−0.293135			−0.146568	+	0.989201i	$0.546823\pi$
$968$	−360.788	+	790.016i	−0.0119795	+	0.0262315i
$969$		0			0
$970$	−3696.94	−	4266.50i	−0.122373	−	0.141226i
$971$	−22588.1	+	14516.5i	−0.746537	+	0.479770i	−0.857776	−	0.514024i	$-0.828154\pi$
$971$	−22588.1	+	14516.5i	−0.746537	+	0.479770i	0.111239	+	0.993794i	$0.464518\pi$
$972$		0			0
$973$	−4432.68	+	30830.0i	−0.146048	+	1.01579i
$974$	−1325.23	+	389.124i	−0.0435967	+	0.0128012i
$975$		0			0
$976$	−5810.24	−	40411.1i	−0.190554	−	1.32533i
$977$	−1221.27	−	2674.20i	−0.0399916	−	0.0875693i	0.888582	−	0.458718i	$-0.151691\pi$
$977$	−1221.27	−	2674.20i	−0.0399916	−	0.0875693i	−0.928573	+	0.371149i	$0.878964\pi$
$978$		0			0
$979$	4081.11	+	28384.7i	0.133231	+	0.926639i
$980$	−15880.6	−	10205.8i	−0.517640	−	0.332667i
$981$		0			0
$982$	−428.268	+	2978.67i	−0.0139171	+	0.0967956i
$983$	5943.08	−	6858.69i	0.192833	−	0.222541i	−0.651097	−	0.758995i	$-0.725691\pi$
$983$	5943.08	−	6858.69i	0.192833	−	0.222541i	0.843930	+	0.536453i	$0.180236\pi$
$984$		0			0
$985$	−7343.77	−	8475.16i	−0.237555	−	0.274153i
$986$	−4082.08	−	1198.61i	−0.131846	−	0.0387134i
$987$		0			0
$988$	4186.91			0.134821
$989$	−25162.1	−	8054.01i	−0.809007	−	0.258951i
$990$		0			0
$991$	12147.6	−	26599.5i	0.389386	−	0.852636i	−0.608851	−	0.793284i	$-0.708369\pi$
$991$	12147.6	−	26599.5i	0.389386	−	0.852636i	0.998237	−	0.0593517i	$-0.0189033\pi$
$992$	−61682.6	−	18111.6i	−1.97422	−	0.579683i
$993$		0			0
$994$	−84766.8	+	54476.3i	−2.70487	+	1.73831i
$995$	1752.45	−	2022.44i	0.0558357	−	0.0644378i
$996$		0			0
$997$	−29843.5	+	8762.85i	−0.947998	+	0.278357i	−0.718953	−	0.695059i	$-0.755378\pi$
$997$	−29843.5	+	8762.85i	−0.947998	+	0.278357i	−0.229045	+	0.973416i	$0.573560\pi$
$998$	−22229.2	−	14285.9i	−0.705064	−	0.453117i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.i.b.190.6		60
3.2	odd	2		69.4.e.b.52.1	yes	60
23.4	even	11	inner	207.4.i.b.73.6		60
69.2	odd	22		1587.4.a.w.1.6		30
69.44	even	22		1587.4.a.v.1.6		30
69.50	odd	22		69.4.e.b.4.1	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.4.e.b.4.1	✓	60	69.50	odd	22
69.4.e.b.52.1	yes	60	3.2	odd	2
207.4.i.b.73.6		60	23.4	even	11	inner
207.4.i.b.190.6		60	1.1	even	1	trivial
1587.4.a.v.1.6		30	69.44	even	22
1587.4.a.w.1.6		30	69.2	odd	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.62255 - 3.55289i) q^{2} +(-4.75146 - 5.48347i) q^{4} +(-2.37866 + 1.52867i) q^{5} +(-5.05798 + 35.1790i) q^{7} +(2.78946 - 0.819058i) q^{8} +O(q^{10})\)	\(q+(1.62255 - 3.55289i) q^{2} +(-4.75146 - 5.48347i) q^{4} +(-2.37866 + 1.52867i) q^{5} +(-5.05798 + 35.1790i) q^{7} +(2.78946 - 0.819058i) q^{8} +(1.57171 + 10.9315i) q^{10} +(16.7703 + 36.7219i) q^{11} +(4.13183 + 28.7375i) q^{13} +(116.780 + 75.0501i) q^{14} +(9.87673 - 68.6942i) q^{16} +(12.6250 - 14.5700i) q^{17} +(13.0159 + 15.0211i) q^{19} +(19.6845 + 5.77990i) q^{20} +157.679 q^{22} +(-110.272 - 2.66697i) q^{23} +(-48.6057 + 106.432i) q^{25} +(108.805 + 31.9481i) q^{26} +(216.936 - 139.416i) q^{28} +(36.9991 - 42.6992i) q^{29} +(248.910 - 73.0866i) q^{31} +(-208.472 - 133.977i) q^{32} +(-31.2809 - 68.4957i) q^{34} +(-41.7460 - 91.4109i) q^{35} +(99.4353 + 63.9032i) q^{37} +(74.4871 - 21.8714i) q^{38} +(-5.38310 + 6.21242i) q^{40} +(-395.946 + 254.459i) q^{41} +(229.814 + 67.4796i) q^{43} +(121.680 - 266.442i) q^{44} +(-188.397 + 387.456i) q^{46} +260.363 q^{47} +(-882.874 - 259.235i) q^{49} +(299.274 + 345.381i) q^{50} +(137.949 - 159.202i) q^{52} +(68.1967 - 474.319i) q^{53} +(-96.0266 - 61.7125i) q^{55} +(14.7046 + 102.273i) q^{56} +(-91.6726 - 200.735i) q^{58} +(23.2951 + 162.021i) q^{59} +(564.446 - 165.736i) q^{61} +(144.201 - 1002.94i) q^{62} +(-347.191 + 223.126i) q^{64} +(-53.7584 - 62.0405i) q^{65} +(151.955 - 332.736i) q^{67} -139.881 q^{68} -392.508 q^{70} +(-301.536 + 660.271i) q^{71} +(-122.521 - 141.397i) q^{73} +(388.380 - 249.596i) q^{74} +(20.5235 - 142.744i) q^{76} +(-1376.66 + 404.225i) q^{77} +(61.3565 + 426.744i) q^{79} +(81.5175 + 178.498i) q^{80} +(261.622 + 1819.62i) q^{82} +(356.030 + 228.807i) q^{83} +(-7.75778 + 53.9565i) q^{85} +(612.633 - 707.016i) q^{86} +(76.8574 + 88.6982i) q^{88} +(681.570 + 200.127i) q^{89} -1031.85 q^{91} +(509.328 + 617.345i) q^{92} +(422.451 - 925.039i) q^{94} +(-53.9226 - 15.8331i) q^{95} +(-430.031 + 276.364i) q^{97} +(-2353.54 + 2716.13i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8}+O(q^{10}) \) 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8	\( 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8} - 78 q^{10} - 10 q^{11} + 50 q^{13} + 224 q^{14} + 260 q^{16} + 662 q^{17} - 4 q^{19} + 735 q^{20} + 622 q^{22} + 438 q^{23} - 754 q^{25} + 40 q^{26} + 672 q^{28} - 1302 q^{29} + 1528 q^{31} - 1588 q^{32} + 29 q^{34} - 950 q^{35} + 316 q^{37} - 3122 q^{38} - 1939 q^{40} + 1500 q^{41} - 1316 q^{43} + 2901 q^{44} - 1980 q^{46} + 1440 q^{47} - 2310 q^{49} - 195 q^{50} + 6189 q^{52} + 148 q^{53} - 606 q^{55} + 432 q^{56} - 2623 q^{58} - 5264 q^{59} + 1482 q^{61} + 2299 q^{62} - 6780 q^{64} + 1446 q^{65} + 388 q^{67} - 5604 q^{68} + 2984 q^{70} + 3316 q^{71} + 2072 q^{73} + 6556 q^{74} + 9841 q^{76} - 9338 q^{77} + 268 q^{79} - 7980 q^{80} + 7742 q^{82} + 3494 q^{83} - 3842 q^{85} + 4792 q^{86} - 7960 q^{88} + 2754 q^{89} - 5436 q^{91} + 17609 q^{92} - 10961 q^{94} + 2396 q^{95} - 5654 q^{97} - 14411 q^{98}+O(q^{100}) \) 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8 - 78 * q^10 - 10 * q^11 + 50 * q^13 + 224 * q^14 + 260 * q^16 + 662 * q^17 - 4 * q^19 + 735 * q^20 + 622 * q^22 + 438 * q^23 - 754 * q^25 + 40 * q^26 + 672 * q^28 - 1302 * q^29 + 1528 * q^31 - 1588 * q^32 + 29 * q^34 - 950 * q^35 + 316 * q^37 - 3122 * q^38 - 1939 * q^40 + 1500 * q^41 - 1316 * q^43 + 2901 * q^44 - 1980 * q^46 + 1440 * q^47 - 2310 * q^49 - 195 * q^50 + 6189 * q^52 + 148 * q^53 - 606 * q^55 + 432 * q^56 - 2623 * q^58 - 5264 * q^59 + 1482 * q^61 + 2299 * q^62 - 6780 * q^64 + 1446 * q^65 + 388 * q^67 - 5604 * q^68 + 2984 * q^70 + 3316 * q^71 + 2072 * q^73 + 6556 * q^74 + 9841 * q^76 - 9338 * q^77 + 268 * q^79 - 7980 * q^80 + 7742 * q^82 + 3494 * q^83 - 3842 * q^85 + 4792 * q^86 - 7960 * q^88 + 2754 * q^89 - 5436 * q^91 + 17609 * q^92 - 10961 * q^94 + 2396 * q^95 - 5654 * q^97 - 14411 * q^98

Introduction

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