LMFDB - Embedded newform 225.4.h.a.136.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.5
Character	$\chi$	$=$	225.136
Dual form			225.4.h.a.91.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08389 - 0.787491i) q^{2} +(-1.91746 + 5.90135i) q^{4} +(3.83217 + 10.5031i) q^{5} -12.2101 q^{7} +(5.88101 + 18.0999i) q^{8} +O(q^{10})$	\(q+(1.08389 - 0.787491i) q^{2} +(-1.91746 + 5.90135i) q^{4} +(3.83217 + 10.5031i) q^{5} -12.2101 q^{7} +(5.88101 + 18.0999i) q^{8} +(12.4247 + 8.36635i) q^{10} +(-2.00821 + 1.45905i) q^{11} +(-69.2682 - 50.3263i) q^{13} +(-13.2344 + 9.61535i) q^{14} +(-19.5320 - 14.1909i) q^{16} +(1.71458 + 5.27694i) q^{17} +(-7.45887 - 22.9561i) q^{19} +(-69.3303 + 2.47571i) q^{20} +(-1.02769 + 3.16290i) q^{22} +(-83.6143 + 60.7493i) q^{23} +(-95.6289 + 80.4991i) q^{25} -114.710 q^{26} +(23.4124 - 72.0561i) q^{28} +(35.3035 - 108.653i) q^{29} +(47.5487 + 146.340i) q^{31} -184.596 q^{32} +(6.01395 + 4.36939i) q^{34} +(-46.7912 - 128.244i) q^{35} +(277.229 + 201.419i) q^{37} +(-26.1623 - 19.0080i) q^{38} +(-167.567 + 131.130i) q^{40} +(28.0530 + 20.3817i) q^{41} -154.740 q^{43} +(-4.75970 - 14.6489i) q^{44} +(-42.7890 + 131.691i) q^{46} +(-104.613 + 321.965i) q^{47} -193.913 q^{49} +(-40.2588 + 162.559i) q^{50} +(429.812 - 312.277i) q^{52} +(-199.512 + 614.036i) q^{53} +(-23.0204 - 15.5011i) q^{55} +(-71.8077 - 221.001i) q^{56} +(-47.2982 - 145.569i) q^{58} +(536.260 + 389.616i) q^{59} +(289.370 - 210.239i) q^{61} +(166.779 + 121.172i) q^{62} +(-43.8256 + 31.8411i) q^{64} +(263.133 - 920.387i) q^{65} +(-164.205 - 505.370i) q^{67} -34.4287 q^{68} +(-151.707 - 102.154i) q^{70} +(196.164 - 603.732i) q^{71} +(-779.001 + 565.977i) q^{73} +459.101 q^{74} +149.774 q^{76} +(24.5205 - 17.8152i) q^{77} +(175.752 - 540.908i) q^{79} +(74.1975 - 259.528i) q^{80} +46.4568 q^{82} +(98.8352 + 304.184i) q^{83} +(-48.8535 + 38.2305i) q^{85} +(-167.721 + 121.856i) q^{86} +(-38.2190 - 27.7677i) q^{88} +(-1079.81 + 784.525i) q^{89} +(845.772 + 614.489i) q^{91} +(-198.176 - 609.922i) q^{92} +(140.156 + 431.355i) q^{94} +(212.525 - 166.313i) q^{95} +(123.390 - 379.754i) q^{97} +(-210.180 + 152.705i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) $ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8	$ 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) $ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 + 165 * q^10 - 19 * q^11 + 4 * q^13 + 24 * q^14 - 66 * q^16 - 208 * q^17 + 42 * q^19 - 295 * q^20 - 89 * q^22 - 32 * q^23 + 95 * q^25 - 206 * q^26 - 482 * q^28 + 716 * q^29 + 637 * q^31 + 844 * q^32 - 90 * q^34 - 430 * q^35 + 216 * q^37 - 2314 * q^38 - 500 * q^40 + 38 * q^41 - 1392 * q^43 - 603 * q^44 + 1622 * q^46 + 536 * q^47 + 162 * q^49 + 2265 * q^50 - 1922 * q^52 - 1672 * q^53 - 1000 * q^55 - 3000 * q^56 - 827 * q^58 - 973 * q^59 - 2712 * q^61 - 1057 * q^62 + 4439 * q^64 + 4360 * q^65 + 2768 * q^67 + 1370 * q^68 + 3230 * q^70 + 1074 * q^71 - 1018 * q^73 + 1414 * q^74 - 11408 * q^76 - 1607 * q^77 - 1820 * q^79 + 1290 * q^80 + 1772 * q^82 - 4045 * q^83 + 1850 * q^85 + 3986 * q^86 + 2407 * q^88 - 4542 * q^89 + 4412 * q^91 + 1089 * q^92 + 5137 * q^94 + 720 * q^95 - 5977 * q^97 + 10689 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.08389	−	0.787491i	0.383212	−	0.278420i	−0.379456	−	0.925210i	$-0.623889\pi$
$2$	1.08389	−	0.787491i	0.383212	−	0.278420i	0.762668	+	0.646790i	$0.223889\pi$
$3$		0			0
$3$		0			0
$4$	−1.91746	+	5.90135i	−0.239683	+	0.737669i
$5$	3.83217	+	10.5031i	0.342760	+	0.939423i
$5$	3.83217	+	10.5031i	0.342760	+	0.939423i
$6$		0			0
$7$	−12.2101			−0.659284			−0.329642	−	0.944106i	$-0.606928\pi$
$7$	−12.2101			−0.659284			−0.329642	+	0.944106i	$0.606928\pi$
$8$	5.88101	+	18.0999i	0.259906	+	0.799909i
$9$		0			0
$10$	12.4247	+	8.36635i	0.392904	+	0.264567i
$11$	−2.00821	+	1.45905i	−0.0550454	+	0.0399928i	−0.614968	−	0.788552i	$-0.710831\pi$
$11$	−2.00821	+	1.45905i	−0.0550454	+	0.0399928i	0.559922	+	0.828545i	$0.310831\pi$
$12$		0			0
$13$	−69.2682	−	50.3263i	−1.47781	−	1.07369i	−0.978254	−	0.207411i	$-0.933496\pi$
$13$	−69.2682	−	50.3263i	−1.47781	−	1.07369i	−0.499557	−	0.866281i	$-0.666504\pi$
$14$	−13.2344	+	9.61535i	−0.252646	+	0.183558i
$15$		0			0
$16$	−19.5320	−	14.1909i	−0.305188	−	0.221732i
$17$	1.71458	+	5.27694i	0.0244616	+	0.0752850i	0.962542	−	0.271132i	$-0.0873981\pi$
$17$	1.71458	+	5.27694i	0.0244616	+	0.0752850i	−0.938080	+	0.346417i	$0.887398\pi$
$18$		0			0
$19$	−7.45887	−	22.9561i	−0.0900623	−	0.277183i	0.895873	−	0.444310i	$-0.146551\pi$
$19$	−7.45887	−	22.9561i	−0.0900623	−	0.277183i	−0.985935	+	0.167127i	$0.946551\pi$
$20$	−69.3303	+	2.47571i	−0.775137	+	0.0276793i
$21$		0			0
$22$	−1.02769	+	3.16290i	−0.00995927	+	0.0306515i
$23$	−83.6143	+	60.7493i	−0.758034	+	0.550744i	−0.898307	−	0.439369i	$-0.855202\pi$
$23$	−83.6143	+	60.7493i	−0.758034	+	0.550744i	0.140273	+	0.990113i	$0.455202\pi$
$24$		0			0
$25$	−95.6289	+	80.4991i	−0.765031	+	0.643993i
$26$	−114.710			−0.865253
$27$		0			0
$28$	23.4124	−	72.0561i	0.158019	−	0.486333i
$29$	35.3035	−	108.653i	0.226059	−	0.695737i	−0.772124	−	0.635472i	$-0.780806\pi$
$29$	35.3035	−	108.653i	0.226059	−	0.695737i	0.998182	−	0.0602646i	$-0.0191945\pi$
$30$		0			0
$31$	47.5487	+	146.340i	0.275484	+	0.847852i	0.989091	+	0.147306i	$0.0470602\pi$
$31$	47.5487	+	146.340i	0.275484	+	0.847852i	−0.713607	+	0.700546i	$0.752940\pi$
$32$	−184.596			−1.01976
$33$		0			0
$34$	6.01395	+	4.36939i	0.0303348	+	0.0220395i
$35$	−46.7912	−	128.244i	−0.225976	−	0.619346i
$36$		0			0
$37$	277.229	+	201.419i	1.23179	+	0.894948i	0.997023	−	0.0771043i	$-0.0245674\pi$
$37$	277.229	+	201.419i	1.23179	+	0.894948i	0.234767	+	0.972052i	$0.424567\pi$
$38$	−26.1623	−	19.0080i	−0.111686	−	0.0811449i
$39$		0			0
$40$	−167.567	+	131.130i	−0.662368	+	0.518339i
$41$	28.0530	+	20.3817i	0.106857	+	0.0776363i	0.639931	−	0.768433i	$-0.278963\pi$
$41$	28.0530	+	20.3817i	0.106857	+	0.0776363i	−0.533073	+	0.846069i	$0.678963\pi$
$42$		0			0
$43$	−154.740			−0.548783			−0.274391	−	0.961618i	$-0.588476\pi$
$43$	−154.740			−0.548783			−0.274391	+	0.961618i	$0.588476\pi$
$44$	−4.75970	−	14.6489i	−0.0163080	−	0.0501908i
$45$		0			0
$46$	−42.7890	+	131.691i	−0.137150	+	0.422104i
$47$	−104.613	+	321.965i	−0.324666	+	0.999221i	0.646924	+	0.762554i	$0.276055\pi$
$47$	−104.613	+	321.965i	−0.324666	+	0.999221i	−0.971591	+	0.236667i	$0.923945\pi$
$48$		0			0
$49$	−193.913			−0.565345
$50$	−40.2588	+	162.559i	−0.113869	+	0.459786i
$51$		0			0
$52$	429.812	−	312.277i	1.14624	−	0.832789i
$53$	−199.512	+	614.036i	−0.517078	+	1.59140i	0.262390	+	0.964962i	$0.415489\pi$
$53$	−199.512	+	614.036i	−0.517078	+	1.59140i	−0.779469	+	0.626441i	$0.784511\pi$
$54$		0			0
$55$	−23.0204	−	15.5011i	−0.0564375	−	0.0380030i
$56$	−71.8077	−	221.001i	−0.171352	−	0.527367i
$57$		0			0
$58$	−47.2982	−	145.569i	−0.107079	−	0.329554i
$59$	536.260	+	389.616i	1.18331	+	0.859724i	0.992541	−	0.121912i	$-0.0389025\pi$
$59$	536.260	+	389.616i	1.18331	+	0.859724i	0.190767	+	0.981635i	$0.438903\pi$
$60$		0			0
$61$	289.370	−	210.239i	0.607377	−	0.441285i	−0.241113	−	0.970497i	$-0.577512\pi$
$61$	289.370	−	210.239i	0.607377	−	0.441285i	0.848490	+	0.529212i	$0.177512\pi$
$62$	166.779	+	121.172i	0.341628	+	0.248207i
$63$		0			0
$64$	−43.8256	+	31.8411i	−0.0855968	+	0.0621897i
$65$	263.133	−	920.387i	0.502117	−	1.75631i
$66$		0			0
$67$	−164.205	−	505.370i	−0.299415	−	0.921504i	−0.981703	−	0.190420i	$-0.939015\pi$
$67$	−164.205	−	505.370i	−0.299415	−	0.921504i	0.682288	−	0.731083i	$-0.260985\pi$
$68$	−34.4287			−0.0613984
$69$		0			0
$70$	−151.707	−	102.154i	−0.259035	−	0.174425i
$71$	196.164	−	603.732i	0.327893	−	1.00915i	−0.642224	−	0.766517i	$-0.721988\pi$
$71$	196.164	−	603.732i	0.327893	−	1.00915i	0.970118	−	0.242635i	$-0.0780118\pi$
$72$		0			0
$73$	−779.001	+	565.977i	−1.24897	+	0.907433i	−0.998162	−	0.0606028i	$-0.980698\pi$
$73$	−779.001	+	565.977i	−1.24897	+	0.907433i	−0.250812	+	0.968036i	$0.580698\pi$
$74$	459.101			0.721208
$75$		0			0
$76$	149.774			0.226056
$77$	24.5205	−	17.8152i	0.0362905	−	0.0263666i
$78$		0			0
$79$	175.752	−	540.908i	0.250299	−	0.770340i	−0.744421	−	0.667711i	$-0.767274\pi$
$79$	175.752	−	540.908i	0.250299	−	0.770340i	0.994720	−	0.102630i	$-0.0327257\pi$
$80$	74.1975	−	259.528i	0.103694	−	0.362702i
$81$		0			0
$82$	46.4568			0.0625645
$83$	98.8352	+	304.184i	0.130706	+	0.402271i	0.994897	−	0.100892i	$-0.0321696\pi$
$83$	98.8352	+	304.184i	0.130706	+	0.402271i	−0.864192	+	0.503163i	$0.832170\pi$
$84$		0			0
$85$	−48.8535	+	38.2305i	−0.0623400	+	0.0487844i
$86$	−167.721	+	121.856i	−0.210300	+	0.152792i
$87$		0			0
$88$	−38.2190	−	27.7677i	−0.0462973	−	0.0336369i
$89$	−1079.81	+	784.525i	−1.28606	+	0.934376i	−0.999718	−	0.0237515i	$-0.992439\pi$
$89$	−1079.81	+	784.525i	−1.28606	+	0.934376i	−0.286341	+	0.958128i	$0.592439\pi$
$90$		0			0
$91$	845.772	+	614.489i	0.974296	+	0.707868i
$92$	−198.176	−	609.922i	−0.224579	−	0.691182i
$93$		0			0
$94$	140.156	+	431.355i	0.153787	+	0.473307i
$95$	212.525	−	166.313i	0.229523	−	0.179614i
$96$		0			0
$97$	123.390	−	379.754i	0.129158	−	0.397507i	−0.865478	−	0.500947i	$-0.832985\pi$
$97$	123.390	−	379.754i	0.129158	−	0.397507i	0.994636	+	0.103440i	$0.0329850\pi$
$98$	−210.180	+	152.705i	−0.216647	+	0.157403i
$99$		0			0
$100$	−291.688	−	718.694i	−0.291688	−	0.718694i
$101$	131.408			0.129461			0.0647307	−	0.997903i	$-0.479381\pi$
$101$	131.408			0.129461			0.0647307	+	0.997903i	$0.479381\pi$
$102$		0			0
$103$	5.82218	−	17.9188i	0.00556967	−	0.0171417i	−0.948233	−	0.317575i	$-0.897131\pi$
$103$	5.82218	−	17.9188i	0.00556967	−	0.0171417i	0.953803	+	0.300434i	$0.0971314\pi$
$104$	503.533	−	1549.72i	0.474764	−	1.46117i
$105$		0			0
$106$	267.299	+	822.661i	0.244928	+	0.753810i
$107$	1832.09			1.65528			0.827640	−	0.561259i	$-0.189683\pi$
$107$	1832.09			1.65528			0.827640	+	0.561259i	$0.189683\pi$
$108$		0			0
$109$	1082.18	+	786.250i	0.950954	+	0.690909i	0.951032	−	0.309091i	$-0.100025\pi$
$109$	1082.18	+	786.250i	0.950954	+	0.690909i	−7.79623e−5		1.00000i	$0.500025\pi$
$110$	−37.1584	+	1.32689i	−0.0322083	+	0.00115013i
$111$		0			0
$112$	238.488	+	173.272i	0.201206	+	0.146184i
$113$	29.3061	+	21.2921i	0.0243972	+	0.0177256i	0.599917	−	0.800062i	$-0.295200\pi$
$113$	29.3061	+	21.2921i	0.0243972	+	0.0177256i	−0.575520	+	0.817788i	$0.695200\pi$
$114$		0			0
$115$	−958.478	−	645.405i	−0.777205	−	0.523342i
$116$	573.506	+	416.677i	0.459041	+	0.333513i
$117$		0			0
$118$	888.065			0.692822
$119$	−20.9352	−	64.4319i	−0.0161271	−	0.0496342i
$120$		0			0
$121$	−409.398	+	1260.00i	−0.307586	+	0.946654i
$122$	148.083	−	455.752i	0.109892	−	0.338212i
$123$		0			0
$124$	−954.776			−0.691463
$125$	−1211.95	−	695.911i	−0.867204	−	0.497953i
$126$		0			0
$127$	1130.69	−	821.496i	0.790021	−	0.573984i	−0.117949	−	0.993020i	$-0.537632\pi$
$127$	1130.69	−	821.496i	0.790021	−	0.573984i	0.907970	+	0.419036i	$0.137632\pi$
$128$	433.920	−	1335.47i	0.299637	−	0.922187i
$129$		0			0
$130$	−439.590	−	1204.81i	−0.296574	−	0.812838i
$131$	877.005	+	2699.14i	0.584918	+	1.80019i	0.599598	+	0.800301i	$0.295327\pi$
$131$	877.005	+	2699.14i	0.584918	+	1.80019i	−0.0146799	+	0.999892i	$0.504673\pi$
$132$		0			0
$133$	91.0736	+	280.296i	0.0593766	+	0.182742i
$134$	−575.953	−	418.455i	−0.371304	−	0.269768i
$135$		0			0
$136$	−85.4284	+	62.0674i	−0.0538634	+	0.0391341i
$137$	−655.541	−	476.279i	−0.408808	−	0.297016i	0.364311	−	0.931277i	$-0.381304\pi$
$137$	−655.541	−	476.279i	−0.408808	−	0.297016i	−0.773119	+	0.634261i	$0.781304\pi$
$138$		0			0
$139$	2540.67	−	1845.91i	1.55034	−	1.12639i	0.606927	−	0.794758i	$-0.292402\pi$
$139$	2540.67	−	1845.91i	1.55034	−	1.12639i	0.943410	−	0.331628i	$-0.107598\pi$
$140$	846.530	−	30.2287i	0.511035	−	0.0182485i
$141$		0			0
$142$	−262.813	−	808.855i	−0.155315	−	0.478012i
$143$	212.534			0.124287
$144$		0			0
$145$	1276.48	−	45.5818i	0.731075	−	0.0261059i
$146$	−398.648	+	1226.91i	−0.225975	+	0.695479i
$147$		0			0
$148$	−1720.22	+	1249.81i	−0.955414	+	0.694149i
$149$	1008.26			0.554362			0.277181	−	0.960818i	$-0.410600\pi$
$149$	1008.26			0.554362			0.277181	+	0.960818i	$0.410600\pi$
$150$		0			0
$151$	−2162.97			−1.16570			−0.582848	−	0.812581i	$-0.698062\pi$
$151$	−2162.97			−1.16570			−0.582848	+	0.812581i	$0.698062\pi$
$152$	371.636	−	270.009i	0.198314	−	0.144083i
$153$		0			0
$154$	12.5482	−	38.6193i	0.00656598	−	0.0202080i
$155$	−1354.80	+	1060.21i	−0.702067	+	0.549406i
$156$		0			0
$157$	−2618.64			−1.33115			−0.665575	−	0.746331i	$-0.731814\pi$
$157$	−2618.64			−1.33115			−0.665575	+	0.746331i	$0.731814\pi$
$158$	−235.465	−	724.686i	−0.118561	−	0.364892i
$159$		0			0
$160$	−707.405	−	1938.83i	−0.349533	−	0.957987i
$161$	1020.94	−	741.756i	0.499759	−	0.363096i
$162$		0			0
$163$	261.518	+	190.004i	0.125667	+	0.0913022i	0.648843	−	0.760922i	$-0.275253\pi$
$163$	261.518	+	190.004i	0.125667	+	0.0913022i	−0.523176	+	0.852224i	$0.675253\pi$
$164$	−174.070	+	126.469i	−0.0828818	+	0.0602171i
$165$		0			0
$166$	346.668	+	251.869i	0.162088	+	0.117764i
$167$	−49.1296	−	151.205i	−0.0227650	−	0.0700636i	0.939029	−	0.343839i	$-0.111727\pi$
$167$	−49.1296	−	151.205i	−0.0227650	−	0.0700636i	−0.961794	+	0.273775i	$0.911727\pi$
$168$		0			0
$169$	1586.44	+	4882.55i	0.722092	+	2.22237i
$170$	−22.8455	+	79.9092i	−0.0103069	+	0.0360515i
$171$		0			0
$172$	296.709	−	913.176i	0.131534	−	0.404820i
$173$	−2663.82	+	1935.38i	−1.17067	+	0.850545i	−0.991089	−	0.133198i	$-0.957475\pi$
$173$	−2663.82	+	1935.38i	−1.17067	+	0.850545i	−0.179585	+	0.983743i	$0.557475\pi$
$174$		0			0
$175$	1167.64	−	982.903i	0.504373	−	0.424574i
$176$	59.9297			0.0256669
$177$		0			0
$178$	−552.583	+	1700.67i	−0.232684	+	0.716129i
$179$	−871.102	+	2680.98i	−0.363739	+	1.11947i	0.587028	+	0.809566i	$0.300298\pi$
$179$	−871.102	+	2680.98i	−0.363739	+	1.11947i	−0.950767	+	0.309906i	$0.899702\pi$
$180$		0			0
$181$	129.046	+	397.161i	0.0529938	+	0.163098i	0.974051	−	0.226330i	$-0.0726727\pi$
$181$	129.046	+	397.161i	0.0529938	+	0.163098i	−0.921057	+	0.389428i	$0.872673\pi$
$182$	1400.63			0.570447
$183$		0			0
$184$	−1591.29	−	1156.14i	−0.637563	−	0.463217i
$185$	−1053.13	+	3683.63i	−0.418526	+	1.46392i
$186$		0			0
$187$	−11.1426	−	8.09555i	−0.00435736	−	0.00316580i
$188$	−1699.43	−	1234.71i	−0.659277	−	0.478992i
$189$		0			0
$190$	99.3841	−	347.626i	0.0379478	−	0.132734i
$191$	421.982	+	306.588i	0.159861	+	0.116146i	0.664840	−	0.746986i	$-0.268500\pi$
$191$	421.982	+	306.588i	0.159861	+	0.116146i	−0.504979	+	0.863132i	$0.668500\pi$
$192$		0			0
$193$	−4528.65			−1.68901			−0.844506	−	0.535547i	$-0.820106\pi$
$193$	−4528.65			−1.68901			−0.844506	+	0.535547i	$0.820106\pi$
$194$	−165.312	−	508.779i	−0.0611791	−	0.188290i
$195$		0			0
$196$	371.822	−	1144.35i	0.135504	−	0.417037i
$197$	859.280	−	2644.59i	0.310767	−	0.956444i	−0.666694	−	0.745331i	$-0.732291\pi$
$197$	859.280	−	2644.59i	0.310767	−	0.956444i	0.977462	−	0.211112i	$-0.0677086\pi$
$198$		0			0
$199$	4988.03			1.77685			0.888423	−	0.459026i	$-0.151801\pi$
$199$	4988.03			1.77685			0.888423	+	0.459026i	$0.151801\pi$
$200$	−2019.42	−	1257.46i	−0.713972	−	0.444578i
$201$		0			0
$202$	142.432	−	103.483i	0.0496112	−	0.0360446i
$203$	−431.060	+	1326.67i	−0.149037	+	0.458688i
$204$		0			0
$205$	−106.567	+	372.749i	−0.0363070	+	0.126995i
$206$	−7.80032	−	24.0069i	−0.00263822	−	0.00811961i
$207$		0			0
$208$	638.776	+	1965.95i	0.212938	+	0.655356i
$209$	48.4731	+	35.2178i	0.0160428	+	0.0116558i
$210$		0			0
$211$	−3035.52	+	2205.44i	−0.990398	+	0.719566i	−0.960008	−	0.279972i	$-0.909675\pi$
$211$	−3035.52	+	2205.44i	−0.990398	+	0.719566i	−0.0303898	+	0.999538i	$0.509675\pi$
$212$	−3241.08	−	2354.79i	−1.04999	−	0.762865i
$213$		0			0
$214$	1985.78	−	1442.76i	0.634324	−	0.460863i
$215$	−592.991	−	1625.25i	−0.188101	−	0.515539i
$216$		0			0
$217$	−580.575	−	1786.83i	−0.181622	−	0.558975i
$218$	1792.13			0.556780
$219$		0			0
$220$	135.618	−	106.128i	0.0415607	−	0.0325235i
$221$	146.803	−	451.812i	0.0446833	−	0.137521i
$222$		0			0
$223$	−1324.82	+	962.540i	−0.397833	+	0.289042i	−0.768658	−	0.639660i	$-0.779075\pi$
$223$	−1324.82	+	962.540i	−0.397833	+	0.289042i	0.370825	+	0.928703i	$0.379075\pi$
$224$	2253.94			0.672312
$225$		0			0
$226$	48.5319			0.0142845
$227$	−3068.69	+	2229.54i	−0.897252	+	0.651892i	−0.937759	−	0.347287i	$-0.887103\pi$
$227$	−3068.69	+	2229.54i	−0.897252	+	0.651892i	0.0405064	+	0.999179i	$0.487103\pi$
$228$		0			0
$229$	27.8795	−	85.8041i	0.00804509	−	0.0247603i	−0.946953	−	0.321371i	$-0.895856\pi$
$229$	27.8795	−	85.8041i	0.00804509	−	0.0247603i	0.954998	+	0.296611i	$0.0958564\pi$
$230$	−1547.13	+	55.2465i	−0.443543	+	0.0158385i
$231$		0			0
$232$	2174.23			0.615280
$233$	−1118.15	−	3441.31i	−0.314388	−	0.967587i	−0.976006	−	0.217746i	$-0.930130\pi$
$233$	−1118.15	−	3441.31i	−0.314388	−	0.967587i	0.661617	−	0.749842i	$-0.269870\pi$
$234$		0			0
$235$	−3782.51	+	135.070i	−1.04997	+	0.0374935i
$236$	−3327.52	+	2417.59i	−0.917810	+	0.666828i
$237$		0			0
$238$	−73.4310	−	53.3507i	−0.0199993	−	0.0145303i
$239$	−1189.87	+	864.489i	−0.322034	+	0.233971i	−0.737043	−	0.675846i	$-0.763778\pi$
$239$	−1189.87	+	864.489i	−0.322034	+	0.233971i	0.415009	+	0.909817i	$0.363778\pi$
$240$		0			0
$241$	3192.76	+	2319.68i	0.853377	+	0.620014i	0.926075	−	0.377340i	$-0.123161\pi$
$241$	3192.76	+	2319.68i	0.853377	+	0.620014i	−0.0726983	+	0.997354i	$0.523161\pi$
$242$	548.494	+	1688.09i	0.145696	+	0.448408i
$243$		0			0
$244$	685.840	+	2110.80i	0.179944	+	0.553811i
$245$	−743.109	−	2036.69i	−0.193778	−	0.531098i
$246$		0			0
$247$	−638.630	+	1965.50i	−0.164514	+	0.506323i
$248$	−2369.10	+	1721.25i	−0.606605	+	0.440724i
$249$		0			0
$250$	−1861.65	+	200.113i	−0.470963	+	0.0506251i
$251$	−3410.52			−0.857649			−0.428825	−	0.903388i	$-0.641072\pi$
$251$	−3410.52			−0.857649			−0.428825	+	0.903388i	$0.641072\pi$
$252$		0			0
$253$	79.2789	−	243.995i	0.0197005	−	0.0606318i
$254$	578.623	−	1780.82i	0.142937	−	0.439915i
$255$		0			0
$256$	−715.268	−	2201.37i	−0.174626	−	0.537443i
$257$	6919.87			1.67957			0.839785	−	0.542918i	$-0.182681\pi$
$257$	6919.87			1.67957			0.839785	+	0.542918i	$0.182681\pi$
$258$		0			0
$259$	−3385.00	−	2459.35i	−0.812099	−	0.590024i
$260$	4926.98	+	3317.65i	1.17522	+	0.791353i
$261$		0			0
$262$	3076.13	+	2234.94i	0.725358	+	0.527003i
$263$	3081.19	+	2238.62i	0.722413	+	0.524863i	0.887154	−	0.461473i	$-0.152679\pi$
$263$	3081.19	+	2238.62i	0.722413	+	0.524863i	−0.164742	+	0.986337i	$0.552679\pi$
$264$		0			0
$265$	−7213.83	+	257.598i	−1.67223	+	0.0597138i
$266$	319.444	+	232.090i	0.0736330	+	0.0534975i
$267$		0			0
$268$	3297.22			0.751529
$269$	−799.222	−	2459.75i	−0.181150	−	0.557523i	0.818711	−	0.574206i	$-0.194689\pi$
$269$	−799.222	−	2459.75i	−0.181150	−	0.557523i	−0.999861	+	0.0166834i	$0.994689\pi$
$270$		0			0
$271$	329.230	−	1013.27i	0.0737981	−	0.227127i	−0.907353	−	0.420370i	$-0.861900\pi$
$271$	329.230	−	1013.27i	0.0737981	−	0.227127i	0.981151	+	0.193242i	$0.0619004\pi$
$272$	41.3950	−	127.401i	0.00922772	−	0.0284000i
$273$		0			0
$274$	−1085.60			−0.239356
$275$	74.5909	−	301.187i	0.0163564	−	0.0660446i
$276$		0			0
$277$	1996.88	−	1450.82i	0.433144	−	0.314698i	−0.349761	−	0.936839i	$-0.613737\pi$
$277$	1996.88	−	1450.82i	0.433144	−	0.314698i	0.782905	+	0.622141i	$0.213737\pi$
$278$	1300.17	−	4001.51i	0.280500	−	0.863290i
$279$		0			0
$280$	2046.01	−	1601.12i	0.436688	−	0.341732i
$281$	−960.683	−	2956.68i	−0.203948	−	0.627689i	−0.999755	−	0.0221378i	$-0.992953\pi$
$281$	−960.683	−	2956.68i	−0.203948	−	0.627689i	0.795806	−	0.605551i	$-0.207047\pi$
$282$		0			0
$283$	−1994.41	−	6138.15i	−0.418923	−	1.28931i	−0.908695	−	0.417461i	$-0.862920\pi$
$283$	−1994.41	−	6138.15i	−0.418923	−	1.28931i	0.489772	−	0.871851i	$-0.337080\pi$
$284$	3186.69	+	2315.27i	0.665829	+	0.483753i
$285$		0			0
$286$	230.363	−	167.369i	0.0476282	−	0.0346039i
$287$	−342.530	−	248.863i	−0.0704493	−	0.0511844i
$288$		0			0
$289$	3949.79	−	2869.69i	0.803948	−	0.584102i
$290$	1347.67	−	1054.62i	0.272888	−	0.213550i
$291$		0			0
$292$	−1846.32	−	5682.39i	−0.370027	−	1.13883i
$293$	−835.063			−0.166501			−0.0832507	−	0.996529i	$-0.526530\pi$
$293$	−835.063			−0.166501			−0.0832507	+	0.996529i	$0.526530\pi$
$294$		0			0
$295$	−2037.12	+	7125.46i	−0.402054	+	1.40631i
$296$	−2015.27	+	6202.36i	−0.395727	+	1.21792i
$297$		0			0
$298$	1092.84	−	793.996i	0.212438	−	0.154346i
$299$	8849.10			1.71156
$300$		0			0
$301$	1889.39			0.361803
$302$	−2344.42	+	1703.32i	−0.446709	+	0.324553i
$303$		0			0
$304$	−180.079	+	554.227i	−0.0339745	+	0.104563i
$305$	3317.07	+	2233.60i	0.622738	+	0.419329i
$306$		0			0
$307$	2681.88			0.498577			0.249289	−	0.968429i	$-0.419803\pi$
$307$	2681.88			0.498577			0.249289	+	0.968429i	$0.419803\pi$
$308$	58.1164	+	178.864i	0.0107516	+	0.0330900i
$309$		0			0
$310$	−633.552	+	2216.04i	−0.116075	+	0.406009i
$311$	6580.24	−	4780.83i	1.19978	−	0.871691i	0.205516	−	0.978654i	$-0.434113\pi$
$311$	6580.24	−	4780.83i	1.19978	−	0.871691i	0.994263	+	0.106963i	$0.0341126\pi$
$312$		0			0
$313$	−6248.59	−	4539.87i	−1.12841	−	0.819835i	−0.142944	−	0.989731i	$-0.545657\pi$
$313$	−6248.59	−	4539.87i	−1.12841	−	0.819835i	−0.985462	+	0.169895i	$0.945657\pi$
$314$	−2838.32	+	2062.16i	−0.510113	+	0.370619i
$315$		0			0
$316$	2855.09	+	2074.34i	0.508263	+	0.369275i
$317$	−995.186	−	3062.87i	−0.176326	−	0.542674i	0.823366	−	0.567511i	$-0.192093\pi$
$317$	−995.186	−	3062.87i	−0.176326	−	0.542674i	−0.999692	+	0.0248365i	$0.992093\pi$
$318$		0			0
$319$	87.6335	+	269.708i	0.0153810	+	0.0473378i
$320$	−502.377	−	338.282i	−0.0877616	−	0.0590955i
$321$		0			0
$322$	522.458	−	1607.96i	0.0904206	−	0.278286i
$323$	108.349	−	78.7200i	0.0186647	−	0.0135607i
$324$		0			0
$325$	10675.3	−	763.379i	1.82202	−	0.130291i
$326$	433.083			0.0735774
$327$		0			0
$328$	−203.927	+	627.622i	−0.0343292	+	0.105654i
$329$	1277.33	−	3931.22i	0.214047	−	0.658770i
$330$		0			0
$331$	1297.25	+	3992.52i	0.215417	+	0.662987i	0.999124	+	0.0418550i	$0.0133268\pi$
$331$	1297.25	+	3992.52i	0.215417	+	0.662987i	−0.783706	+	0.621132i	$0.786673\pi$
$332$	−1984.61			−0.328071
$333$		0			0
$334$	−172.324	−	125.201i	−0.0282309	−	0.0205110i
$335$	4678.67	−	3661.31i	0.763054	−	0.597131i
$336$		0			0
$337$	−1039.69	−	755.378i	−0.168058	−	0.122101i	0.500577	−	0.865692i	$-0.333121\pi$
$337$	−1039.69	−	755.378i	−0.168058	−	0.122101i	−0.668635	+	0.743591i	$0.733121\pi$
$338$	5564.48	+	4042.83i	0.895467	+	0.650595i
$339$		0			0
$340$	−131.937	−	361.607i	−0.0210449	−	0.0576791i
$341$	−309.006	−	224.506i	−0.0490721	−	0.0356530i
$342$		0			0
$343$	6555.77			1.03201
$344$	−910.028	−	2800.78i	−0.142632	−	0.438976i
$345$		0			0
$346$	−1363.19	+	4195.47i	−0.211808	+	0.651878i
$347$	96.1696	−	295.980i	0.0148780	−	0.0457897i	−0.943342	−	0.331822i	$-0.892337\pi$
$347$	96.1696	−	295.980i	0.0148780	−	0.0457897i	0.958220	+	0.286033i	$0.0923366\pi$
$348$		0			0
$349$	−3853.76			−0.591081			−0.295540	−	0.955330i	$-0.595500\pi$
$349$	−3853.76			−0.591081			−0.295540	+	0.955330i	$0.595500\pi$
$350$	491.564	−	1984.86i	0.0750719	−	0.303129i
$351$		0			0
$352$	370.709	−	269.336i	0.0561331	−	0.0407831i
$353$	−371.671	+	1143.89i	−0.0560398	+	0.172473i	−0.975159	−	0.221508i	$-0.928902\pi$
$353$	−371.671	+	1143.89i	−0.0560398	+	0.172473i	0.919119	+	0.393980i	$0.128902\pi$
$354$		0			0
$355$	7092.77	−	253.276i	1.06041	−	0.0378661i
$356$	−2559.27	−	7876.61i	−0.381014	−	1.17264i
$357$		0			0
$358$	1167.07	+	3591.86i	0.172295	+	0.530268i
$359$	8830.61	+	6415.81i	1.29822	+	0.943213i	0.999937	−	0.0112636i	$-0.00358538\pi$
$359$	8830.61	+	6415.81i	1.29822	+	0.943213i	0.298285	+	0.954477i	$0.403585\pi$
$360$		0			0
$361$	5077.70	−	3689.17i	0.740298	−	0.537858i
$362$	452.632	+	328.856i	0.0657177	+	0.0477467i
$363$		0			0
$364$	−5248.05	+	3812.93i	−0.755694	+	0.549044i
$365$	−8929.76	−	6012.98i	−1.28056	−	0.862284i
$366$		0			0
$367$	−44.8963	−	138.177i	−0.00638575	−	0.0196533i	0.947813	−	0.318827i	$-0.103289\pi$
$367$	−44.8963	−	138.177i	−0.00638575	−	0.0196533i	−0.954199	+	0.299174i	$0.903289\pi$
$368$	2495.24			0.353461
$369$		0			0
$370$	1759.35	+	4821.97i	0.247201	+	0.677520i
$371$	2436.07	−	7497.45i	0.340901	−	1.04919i
$372$		0			0
$373$	2847.26	−	2068.66i	0.395243	−	0.287161i	−0.372358	−	0.928089i	$-0.621451\pi$
$373$	2847.26	−	2068.66i	0.395243	−	0.287161i	0.767601	+	0.640929i	$0.221451\pi$
$374$	−18.4525			−0.00255122
$375$		0			0
$376$	−6442.75			−0.883669
$377$	−7913.51	+	5749.50i	−1.08108	+	0.785450i
$378$		0			0
$379$	−124.955	+	384.571i	−0.0169354	+	0.0521217i	−0.959167	−	0.282840i	$-0.908723\pi$
$379$	−124.955	+	384.571i	−0.0169354	+	0.0521217i	0.942232	+	0.334962i	$0.108723\pi$
$380$	573.959	+	1573.08i	0.0774828	+	0.212362i
$381$		0			0
$382$	698.816			0.0935982
$383$	1292.81	+	3978.86i	0.172479	+	0.530836i	0.999509	−	0.0313212i	$-0.00997146\pi$
$383$	1292.81	+	3978.86i	0.172479	+	0.530836i	−0.827030	+	0.562158i	$0.809971\pi$
$384$		0			0
$385$	281.081	+	189.270i	0.0372083	+	0.0250547i
$386$	−4908.55	+	3566.27i	−0.647250	+	0.470255i
$387$		0			0
$388$	2004.47	+	1456.33i	0.262272	+	0.190551i
$389$	−8299.40	+	6029.87i	−1.08174	+	0.785929i	−0.977985	−	0.208674i	$-0.933085\pi$
$389$	−8299.40	+	6029.87i	−1.08174	+	0.785929i	−0.103754	+	0.994603i	$0.533085\pi$
$390$		0			0
$391$	−463.934	−	337.067i	−0.0600054	−	0.0435965i
$392$	−1140.41	−	3509.81i	−0.146937	−	0.452225i
$393$		0			0
$394$	−1151.23	−	3543.12i	−0.147203	−	0.453045i
$395$	6354.70	−	226.920i	0.809468	−	0.0289053i
$396$		0			0
$397$	−3149.37	+	9692.75i	−0.398142	+	1.22535i	0.528346	+	0.849029i	$0.322812\pi$
$397$	−3149.37	+	9692.75i	−0.398142	+	1.22535i	−0.926488	+	0.376325i	$0.877188\pi$
$398$	5406.47	−	3928.03i	0.680909	−	0.494710i
$399$		0			0
$400$	3010.18	−	215.255i	0.376273	−	0.0269069i
$401$	−5912.32			−0.736277			−0.368139	−	0.929771i	$-0.620005\pi$
$401$	−5912.32			−0.736277			−0.368139	+	0.929771i	$0.620005\pi$
$402$		0			0
$403$	4071.13	−	12529.6i	0.503219	−	1.54875i
$404$	−251.970	+	775.485i	−0.0310297	+	0.0954996i
$405$		0			0
$406$	577.516	+	1777.41i	0.0705952	+	0.217270i
$407$	−850.616			−0.103596
$408$		0			0
$409$	−4576.30	−	3324.88i	−0.553260	−	0.401967i	0.275726	−	0.961236i	$-0.411082\pi$
$409$	−4576.30	−	3324.88i	−0.553260	−	0.401967i	−0.828986	+	0.559269i	$0.811082\pi$
$410$	178.030	+	487.939i	0.0214446	+	0.0587746i
$411$		0			0
$412$	94.5814	+	68.7174i	0.0113099	+	0.00821714i
$413$	−6547.80	−	4757.25i	−0.780136	−	0.566802i
$414$		0			0
$415$	−2816.11	+	2203.76i	−0.333102	+	0.260670i
$416$	12786.7	+	9290.05i	1.50701	+	1.09491i
$417$		0			0
$418$	80.2731			0.00939303
$419$	−4234.75	−	13033.2i	−0.493749	−	1.51960i	−0.818897	−	0.573940i	$-0.805414\pi$
$419$	−4234.75	−	13033.2i	−0.493749	−	1.51960i	0.325148	−	0.945663i	$-0.394586\pi$
$420$		0			0
$421$	2847.48	−	8763.66i	0.329639	−	1.01452i	−0.639664	−	0.768654i	$-0.720927\pi$
$421$	2847.48	−	8763.66i	0.329639	−	1.01452i	0.969303	−	0.245869i	$-0.0790734\pi$
$422$	−1553.41	+	4780.89i	−0.179191	+	0.551493i
$423$		0			0
$424$	−12287.3			−1.40737
$425$	−588.752	−	366.606i	−0.0671969	−	0.0418423i
$426$		0			0
$427$	−3533.23	+	2567.04i	−0.400434	+	0.290932i
$428$	−3512.97	+	10811.8i	−0.396743	+	1.22105i
$429$		0			0
$430$	−1922.60	−	1294.61i	−0.215619	−	0.145190i
$431$	−2337.94	−	7195.44i	−0.261287	−	0.804158i	−0.992526	−	0.122036i	$-0.961058\pi$
$431$	−2337.94	−	7195.44i	−0.261287	−	0.804158i	0.731239	−	0.682121i	$-0.238942\pi$
$432$		0			0
$433$	1250.50	+	3848.63i	0.138788	+	0.427144i	0.996160	−	0.0875525i	$-0.0279046\pi$
$433$	1250.50	+	3848.63i	0.138788	+	0.427144i	−0.857372	+	0.514697i	$0.827905\pi$
$434$	−2036.39	−	1479.52i	−0.225230	−	0.163639i
$435$		0			0
$436$	−6714.97	+	4878.71i	−0.737589	+	0.535890i
$437$	2018.23	+	1466.33i	0.220927	+	0.160513i
$438$		0			0
$439$	−3157.92	+	2294.36i	−0.343324	+	0.249440i	−0.746063	−	0.665875i	$-0.768058\pi$
$439$	−3157.92	+	2294.36i	−0.343324	+	0.249440i	0.402739	+	0.915315i	$0.368058\pi$
$440$	145.185	−	507.828i	0.0157305	−	0.0550221i
$441$		0			0
$442$	−196.680	−	605.320i	−0.0211654	−	0.0651405i
$443$	−2288.91			−0.245484			−0.122742	−	0.992439i	$-0.539169\pi$
$443$	−2288.91			−0.245484			−0.122742	+	0.992439i	$0.539169\pi$
$444$		0			0
$445$	−12377.9	−	8334.84i	−1.31858	−	0.887887i
$446$	−677.968	+	2086.57i	−0.0719792	+	0.221529i
$447$		0			0
$448$	535.115	−	388.784i	0.0564326	−	0.0410007i
$449$	−10025.3			−1.05373			−0.526863	−	0.849950i	$-0.676632\pi$
$449$	−10025.3			−1.05373			−0.526863	+	0.849950i	$0.676632\pi$
$450$		0			0
$451$	−86.0745			−0.00898690
$452$	−181.846	+	132.119i	−0.0189232	+	0.0137485i
$453$		0			0
$454$	−1570.38	+	4833.13i	−0.162338	+	0.499626i
$455$	−3212.88	+	11238.0i	−0.331038	+	1.15791i
$456$		0			0
$457$	−3293.06			−0.337075			−0.168537	−	0.985695i	$-0.553904\pi$
$457$	−3293.06			−0.337075			−0.168537	+	0.985695i	$0.553904\pi$
$458$	−37.3518	−	114.957i	−0.00381077	−	0.0117283i
$459$		0			0
$460$	5646.61	−	4418.77i	0.572336	−	0.447884i
$461$	−672.561	+	488.644i	−0.0679486	+	0.0493676i	−0.621241	−	0.783620i	$-0.713371\pi$
$461$	−672.561	+	488.644i	−0.0679486	+	0.0493676i	0.553292	+	0.832987i	$0.313371\pi$
$462$		0			0
$463$	7302.69	+	5305.71i	0.733012	+	0.532565i	0.890515	−	0.454954i	$-0.150344\pi$
$463$	7302.69	+	5305.71i	0.733012	+	0.532565i	−0.157503	+	0.987519i	$0.550344\pi$
$464$	−2231.43	+	1621.23i	−0.223258	+	0.162206i
$465$		0			0
$466$	−3921.95	−	2849.46i	−0.389873	−	0.283259i
$467$	−406.581	−	1251.33i	−0.0402876	−	0.123992i	0.928890	−	0.370356i	$-0.120764\pi$
$467$	−406.581	−	1251.33i	−0.0402876	−	0.123992i	−0.969177	+	0.246364i	$0.920764\pi$
$468$		0			0
$469$	2004.95	+	6170.62i	0.197399	+	0.607532i
$470$	−3993.45	+	3125.09i	−0.391924	+	0.306702i
$471$		0			0
$472$	−3898.25	+	11997.6i	−0.380152	+	1.16999i
$473$	310.751	−	225.774i	0.0302080	−	0.0219474i
$474$		0			0
$475$	2561.23	+	1594.83i	0.247404	+	0.154054i
$476$	420.378			0.0404790
$477$		0			0
$478$	−608.906	+	1874.02i	−0.0582651	+	0.179321i
$479$	−2883.48	+	8874.45i	−0.275052	+	0.846522i	0.714154	+	0.699989i	$0.246812\pi$
$479$	−2883.48	+	8874.45i	−0.275052	+	0.846522i	−0.989206	+	0.146533i	$0.953188\pi$
$480$		0			0
$481$	−9066.51	−	27903.8i	−0.859454	−	2.64513i
$482$	5287.32			0.499649
$483$		0			0
$484$	−6650.67	−	4831.99i	−0.624593	−	0.453794i
$485$	4461.43	−	159.313i	0.417698	−	0.0149155i
$486$		0			0
$487$	1662.91	+	1208.18i	0.154731	+	0.112418i	0.662457	−	0.749100i	$-0.269514\pi$
$487$	1662.91	+	1208.18i	0.154731	+	0.112418i	−0.507726	+	0.861519i	$0.669514\pi$
$488$	5507.09	+	4001.14i	0.510849	+	0.371154i
$489$		0			0
$490$	−2409.32	−	1622.35i	−0.222126	−	0.149572i
$491$	2888.29	+	2098.47i	0.265472	+	0.192877i	0.712556	−	0.701615i	$-0.247537\pi$
$491$	2888.29	+	2098.47i	0.265472	+	0.192877i	−0.447084	+	0.894492i	$0.647537\pi$
$492$		0			0
$493$	633.886			0.0579083
$494$	855.611	+	2633.30i	0.0779266	+	0.239833i
$495$		0			0
$496$	1147.97	−	3533.07i	0.103922	−	0.319838i
$497$	−2395.19	+	7371.63i	−0.216175	+	0.665317i
$498$		0			0
$499$	−316.957			−0.0284347			−0.0142174	−	0.999899i	$-0.504526\pi$
$499$	−316.957			−0.0284347			−0.0142174	+	0.999899i	$0.504526\pi$
$500$	6430.69	−	5817.78i	0.575179	−	0.520358i
$501$		0			0
$502$	−3696.62	+	2685.75i	−0.328662	+	0.238787i
$503$	3270.63	−	10066.0i	0.289921	−	0.892285i	−0.694959	−	0.719049i	$-0.744578\pi$
$503$	3270.63	−	10066.0i	0.289921	−	0.892285i	0.984880	−	0.173236i	$-0.0554223\pi$
$504$		0			0
$505$	503.578	+	1380.19i	0.0443741	+	0.121619i
$506$	−106.215	−	326.895i	−0.00933165	−	0.0287199i
$507$		0			0
$508$	2679.87	+	8247.79i	0.234055	+	0.720348i
$509$	−11989.3	−	8710.74i	−1.04404	−	0.758540i	−0.0729705	−	0.997334i	$-0.523248\pi$
$509$	−11989.3	−	8710.74i	−1.04404	−	0.758540i	−0.971070	+	0.238794i	$0.923248\pi$
$510$		0			0
$511$	9511.68	−	6910.64i	0.823428	−	0.598256i
$512$	6579.32	+	4780.15i	0.567905	+	0.412607i
$513$		0			0
$514$	7500.37	−	5449.34i	0.643632	−	0.467626i
$515$	210.514	−	7.51724i	0.0180124	−	0.000643202i
$516$		0			0
$517$	−259.679	−	799.209i	−0.0220903	−	0.0679868i
$518$	−5605.67			−0.475481
$519$		0			0
$520$	18206.4	−	650.131i	1.53539	−	0.0548272i
$521$	−1266.26	+	3897.16i	−0.106480	+	0.327711i	−0.990075	−	0.140541i	$-0.955116\pi$
$521$	−1266.26	+	3897.16i	−0.106480	+	0.327711i	0.883595	+	0.468252i	$0.155116\pi$
$522$		0			0
$523$	−4884.26	+	3548.62i	−0.408363	+	0.296693i	−0.772939	−	0.634481i	$-0.781214\pi$
$523$	−4884.26	+	3548.62i	−0.408363	+	0.296693i	0.364576	+	0.931174i	$0.381214\pi$
$524$	−17610.2			−1.46814
$525$		0			0
$526$	5102.56			0.422970
$527$	−690.700	+	501.823i	−0.0570918	+	0.0414796i
$528$		0			0
$529$	−458.945	+	1412.49i	−0.0377204	+	0.116092i
$530$	−7616.13	+	5960.03i	−0.624195	+	0.488467i
$531$		0			0
$532$	−1828.75			−0.149035
$533$	−917.446	−	2823.61i	−0.0745573	−	0.229464i
$534$		0			0
$535$	7020.89	+	19242.6i	0.567364	+	1.55501i
$536$	8181.44	−	5944.17i	0.659300	−	0.479009i
$537$		0			0
$538$	−2803.30	−	2036.72i	−0.224645	−	0.163214i
$539$	389.419	−	282.930i	0.0311196	−	0.0226097i
$540$		0			0
$541$	−3971.18	−	2885.23i	−0.315590	−	0.229290i	0.418701	−	0.908124i	$-0.362485\pi$
$541$	−3971.18	−	2885.23i	−0.315590	−	0.229290i	−0.734291	+	0.678834i	$0.762485\pi$
$542$	−441.089	−	1357.53i	−0.0349564	−	0.107585i
$543$		0			0
$544$	−316.505	−	974.104i	−0.0249450	−	0.0767727i
$545$	−4110.94	+	14379.3i	−0.323107	+	1.13016i
$546$		0			0
$547$	−5430.58	+	16713.6i	−0.424488	+	1.30644i	0.478995	+	0.877817i	$0.341001\pi$
$547$	−5430.58	+	16713.6i	−0.424488	+	1.30644i	−0.903484	+	0.428623i	$0.858999\pi$
$548$	4067.66	−	2955.33i	0.317084	−	0.230375i
$549$		0			0
$550$	−156.334	−	385.193i	−0.0121202	−	0.0298630i
$551$	−2757.57			−0.213206
$552$		0			0
$553$	−2145.95	+	6604.54i	−0.165018	+	0.507873i
$554$	1021.89	−	3145.05i	0.0783680	−	0.241192i
$555$		0			0
$556$	6021.68	+	18532.8i	0.459310	+	1.41361i
$557$	23625.5			1.79721			0.898603	−	0.438764i	$-0.144583\pi$
$557$	23625.5			1.79721			0.898603	+	0.438764i	$0.144583\pi$
$558$		0			0
$559$	10718.6	+	7787.50i	0.810997	+	0.589224i
$560$	−905.959	+	3168.87i	−0.0683638	+	0.239123i
$561$		0			0
$562$	−3369.63	−	2448.18i	−0.252917	−	0.183755i
$563$	−18736.1	−	13612.6i	−1.40254	−	1.01901i	−0.994355	−	0.106109i	$-0.966161\pi$
$563$	−18736.1	−	13612.6i	−1.40254	−	1.01901i	−0.408188	−	0.912898i	$-0.633839\pi$
$564$		0			0
$565$	−111.327	+	389.399i	−0.00828947	+	0.0289950i
$566$	−6995.45	−	5082.49i	−0.519507	−	0.377444i
$567$		0			0
$568$	12081.1			0.892452
$569$	2625.00	+	8078.93i	0.193402	+	0.595231i	0.999992	+	0.00411844i	$0.00131094\pi$
$569$	2625.00	+	8078.93i	0.193402	+	0.595231i	−0.806589	+	0.591112i	$0.798689\pi$
$570$		0			0
$571$	4777.92	−	14704.9i	0.350174	−	1.07773i	−0.608580	−	0.793492i	$-0.708261\pi$
$571$	4777.92	−	14704.9i	0.350174	−	1.07773i	0.958755	−	0.284234i	$-0.0917393\pi$
$572$	−407.526	+	1254.24i	−0.0297894	+	0.0916823i
$573$		0			0
$574$	−567.242			−0.0412478
$575$	3105.68	−	12540.3i	0.225245	−	0.909505i
$576$		0			0
$577$	−21389.0	+	15540.0i	−1.54322	+	1.12121i	−0.594937	+	0.803772i	$0.702823\pi$
$577$	−21389.0	+	15540.0i	−1.54322	+	1.12121i	−0.948278	+	0.317440i	$0.897177\pi$
$578$	2021.28	−	6220.85i	0.145457	−	0.447670i
$579$		0			0
$580$	−2178.61	+	7620.35i	−0.155969	+	0.545548i
$581$	−1206.79	−	3714.11i	−0.0861722	−	0.265211i
$582$		0			0
$583$	−495.248	−	1524.22i	−0.0351819	−	0.108279i
$584$	−14825.4	−	10771.3i	−1.05048	−	0.763219i
$585$		0			0
$586$	−905.115	+	657.605i	−0.0638054	+	0.0463573i
$587$	−4812.71	−	3496.64i	−0.338402	−	0.245863i	0.405585	−	0.914057i	$-0.367068\pi$
$587$	−4812.71	−	3496.64i	−0.338402	−	0.245863i	−0.743987	+	0.668194i	$0.767068\pi$
$588$		0			0
$589$	3004.73	−	2183.06i	0.210200	−	0.152719i
$590$	3403.22	+	9327.41i	0.237472	+	0.650853i
$591$		0			0
$592$	−2556.55	−	7868.24i	−0.177489	−	0.546255i
$593$	11755.3			0.814054			0.407027	−	0.913416i	$-0.366566\pi$
$593$	11755.3			0.814054			0.407027	+	0.913416i	$0.366566\pi$
$594$		0			0
$595$	596.506	−	466.798i	0.0410998	−	0.0321628i
$596$	−1933.30	+	5950.10i	−0.132871	+	0.408936i
$597$		0			0
$598$	9591.43	−	6968.58i	0.655891	−	0.476533i
$599$	10184.4			0.694698			0.347349	−	0.937736i	$-0.387082\pi$
$599$	10184.4			0.694698			0.347349	+	0.937736i	$0.387082\pi$
$600$		0			0
$601$	−16384.2			−1.11202			−0.556012	−	0.831174i	$-0.687669\pi$
$601$	−16384.2			−1.11202			−0.556012	+	0.831174i	$0.687669\pi$
$602$	2047.89	−	1487.88i	0.138648	−	0.100733i
$603$		0			0
$604$	4147.42	−	12764.4i	0.279398	−	0.859897i
$605$	−14802.7	+	528.589i	−0.994737	+	0.0355210i
$606$		0			0
$607$	20161.1			1.34813			0.674066	−	0.738672i	$-0.264547\pi$
$607$	20161.1			1.34813			0.674066	+	0.738672i	$0.264547\pi$
$608$	1376.88	+	4237.61i	0.0918420	+	0.282661i
$609$		0			0
$610$	5354.27	−	191.195i	0.355390	−	0.0126906i
$611$	23449.6	−	17037.1i	1.55265	−	1.12807i
$612$		0			0
$613$	2555.01	+	1856.32i	0.168346	+	0.122310i	0.668768	−	0.743471i	$-0.266822\pi$
$613$	2555.01	+	1856.32i	0.168346	+	0.122310i	−0.500422	+	0.865781i	$0.666822\pi$
$614$	2906.86	−	2111.96i	0.191061	−	0.138814i
$615$		0			0
$616$	466.658	+	339.047i	0.0305230	+	0.0221763i
$617$	−2032.29	−	6254.74i	−0.132604	−	0.408114i	0.862605	−	0.505877i	$-0.168831\pi$
$617$	−2032.29	−	6254.74i	−0.132604	−	0.408114i	−0.995210	+	0.0977634i	$0.968831\pi$
$618$		0			0
$619$	−6522.15	−	20073.1i	−0.423502	−	1.30340i	−0.904422	−	0.426639i	$-0.859697\pi$
$619$	−6522.15	−	20073.1i	−0.423502	−	1.30340i	0.480920	−	0.876764i	$-0.340303\pi$
$620$	−3658.86	−	10028.1i	−0.237006	−	0.649576i
$621$		0			0
$622$	3367.39	−	10363.8i	0.217074	−	0.668085i
$623$	13184.5	−	9579.13i	0.847877	−	0.616019i
$624$		0			0
$625$	2664.79	−	15396.1i	0.170546	−	0.985350i
$626$	−10347.9			−0.660678
$627$		0			0
$628$	5021.16	−	15453.5i	0.319054	−	0.981947i
$629$	−587.542	+	1808.27i	−0.0372446	+	0.114627i
$630$		0			0
$631$	−8297.74	−	25537.8i	−0.523499	−	1.61116i	−0.767265	−	0.641331i	$-0.778383\pi$
$631$	−8297.74	−	25537.8i	−0.523499	−	1.61116i	0.243765	−	0.969834i	$-0.421617\pi$
$632$	10824.0			0.681257
$633$		0			0
$634$	−3490.65	−	2536.11i	−0.218662	−	0.158867i
$635$	12961.2	+	8727.62i	0.810001	+	0.545425i
$636$		0			0
$637$	13432.0	+	9758.94i	0.835473	+	0.607007i
$638$	307.378	+	223.323i	0.0190740	+	0.0138581i
$639$		0			0
$640$	15689.4	−	560.251i	0.969027	−	0.0346029i
$641$	20566.4	+	14942.4i	1.26728	+	0.920732i	0.999091	−	0.0426350i	$-0.0135753\pi$
$641$	20566.4	+	14942.4i	1.26728	+	0.920732i	0.268188	+	0.963367i	$0.413575\pi$
$642$		0			0
$643$	−10481.7			−0.642856			−0.321428	−	0.946934i	$-0.604163\pi$
$643$	−10481.7			−0.642856			−0.321428	+	0.946934i	$0.604163\pi$
$644$	2419.74	+	7447.21i	0.148061	+	0.455685i
$645$		0			0
$646$	55.4467	−	170.647i	0.00337697	−	0.0103932i
$647$	−5847.14	+	17995.7i	−0.355294	+	1.09348i	0.600545	+	0.799591i	$0.294950\pi$
$647$	−5847.14	+	17995.7i	−0.355294	+	1.09348i	−0.955839	+	0.293891i	$0.905050\pi$
$648$		0			0
$649$	−1645.40			−0.0995184
$650$	10969.6	−	9234.09i	0.661946	−	0.557217i
$651$		0			0
$652$	−1622.73	+	1178.98i	−0.0974710	+	0.0708168i
$653$	3911.37	−	12037.9i	0.234401	−	0.721411i	−0.762800	−	0.646635i	$-0.776176\pi$
$653$	3911.37	−	12037.9i	0.234401	−	0.721411i	0.997200	−	0.0747761i	$-0.0238242\pi$
$654$		0			0
$655$	−24988.5	+	19554.8i	−1.49066	+	1.16652i
$656$	−258.699	−	796.193i	−0.0153971	−	0.0473874i
$657$		0			0
$658$	−1711.32	−	5266.89i	−0.101389	−	0.312044i
$659$	9820.27	+	7134.84i	0.580491	+	0.421751i	0.838901	−	0.544284i	$-0.183199\pi$
$659$	9820.27	+	7134.84i	0.580491	+	0.421751i	−0.258410	+	0.966035i	$0.583199\pi$
$660$		0			0
$661$	−3379.82	+	2455.59i	−0.198880	+	0.144495i	−0.682768	−	0.730635i	$-0.739224\pi$
$661$	−3379.82	+	2455.59i	−0.198880	+	0.144495i	0.483888	+	0.875130i	$0.339224\pi$
$662$	4550.14	+	3305.87i	0.267139	+	0.194088i
$663$		0			0
$664$	−4924.44	+	3577.81i	−0.287809	+	0.209105i
$665$	−2594.96	+	2030.69i	−0.151320	+	0.118416i
$666$		0			0
$667$	3648.72	+	11229.6i	0.211813	+	0.651892i
$668$	986.519			0.0571401
$669$		0			0
$670$	2187.91	−	7652.87i	0.126159	−	0.441278i
$671$	−274.366	+	844.411i	−0.0157851	+	0.0485814i
$672$		0			0
$673$	−6124.43	+	4449.66i	−0.350787	+	0.254862i	−0.749199	−	0.662345i	$-0.769561\pi$
$673$	−6124.43	+	4449.66i	−0.350787	+	0.254862i	0.398412	+	0.917206i	$0.369561\pi$
$674$	−1721.76			−0.0983972
$675$		0			0
$676$	−31855.6			−1.81245
$677$	−26966.3	+	19592.1i	−1.53087	+	1.11224i	−0.575114	+	0.818073i	$0.695042\pi$
$677$	−26966.3	+	19592.1i	−1.53087	+	1.11224i	−0.955754	+	0.294168i	$0.904958\pi$
$678$		0			0
$679$	−1506.60	+	4636.84i	−0.0851517	+	0.262070i
$680$	−979.275	−	659.408i	−0.0552257	−	0.0371870i
$681$		0			0
$682$	−511.724			−0.0287315
$683$	10789.5	+	33206.6i	0.604463	+	1.86035i	0.500440	+	0.865771i	$0.333172\pi$
$683$	10789.5	+	33206.6i	0.604463	+	1.86035i	0.104023	+	0.994575i	$0.466828\pi$
$684$		0			0
$685$	2490.24	−	8710.38i	0.138901	−	0.485849i
$686$	7105.72	−	5162.61i	0.395478	−	0.287331i
$687$		0			0
$688$	3022.39	+	2195.90i	0.167482	+	0.121683i
$689$	44722.0	−	32492.5i	2.47282	−	1.79661i
$690$		0			0
$691$	27262.3	+	19807.2i	1.50088	+	1.09045i	0.970031	+	0.242982i	$0.0781257\pi$
$691$	27262.3	+	19807.2i	1.50088	+	1.09045i	0.530846	+	0.847468i	$0.321874\pi$
$692$	−6313.57	−	19431.2i	−0.346829	−	1.06743i
$693$		0			0
$694$	−128.844	−	396.542i	−0.00704735	−	0.0216895i
$695$	29124.0	+	19611.0i	1.58955	+	1.07034i
$696$		0			0
$697$	−59.4539	+	182.980i	−0.00323095	+	0.00994386i
$698$	−4177.05	+	3034.80i	−0.226510	+	0.164569i
$699$		0			0
$700$	3561.54	+	8775.33i	0.192305	+	0.473823i
$701$	−23077.6			−1.24341			−0.621704	−	0.783252i	$-0.713559\pi$
$701$	−23077.6			−1.24341			−0.621704	+	0.783252i	$0.713559\pi$
$702$		0			0
$703$	2555.96	−	7866.45i	0.137127	−	0.422032i
$704$	41.5532	−	127.888i	0.00222457	−	0.00684651i
$705$		0			0
$706$	497.950	+	1532.53i	0.0265447	+	0.0816963i
$707$	−1604.51			−0.0853518
$708$		0			0
$709$	15178.3	+	11027.7i	0.803997	+	0.584138i	0.912084	−	0.410003i	$-0.134472\pi$
$709$	15178.3	+	11027.7i	0.803997	+	0.584138i	−0.108087	+	0.994141i	$0.534472\pi$
$710$	7488.32	−	5860.02i	0.395819	−	0.309750i
$711$		0			0
$712$	−20550.2	−	14930.6i	−1.08167	−	0.785880i
$713$	−12865.8	−	9347.55i	−0.675776	−	0.490980i
$714$		0			0
$715$	814.467	+	2232.26i	0.0426005	+	0.116758i
$716$	−14151.1	−	10281.4i	−0.738618	−	0.536637i
$717$		0			0
$718$	14623.8			0.760104
$719$	4136.61	+	12731.2i	0.214561	+	0.660351i	0.999184	+	0.0403783i	$0.0128563\pi$
$719$	4136.61	+	12731.2i	0.214561	+	0.660351i	−0.784623	+	0.619973i	$0.787144\pi$
$720$		0			0
$721$	−71.0894	+	218.791i	−0.00367199	+	0.0113012i
$722$	2598.48	−	7997.29i	0.133941	−	0.412227i
$723$		0			0
$724$	−2591.23			−0.133014
$725$	5370.44	+	13232.3i	0.275108	+	0.677841i
$726$		0			0
$727$	8138.17	−	5912.73i	0.415169	−	0.301638i	−0.360522	−	0.932751i	$-0.617401\pi$
$727$	8138.17	−	5912.73i	0.415169	−	0.301638i	0.775691	+	0.631113i	$0.217401\pi$
$728$	−6148.19	+	18922.2i	−0.313004	+	0.963328i
$729$		0			0
$730$	−14414.0	+	514.710i	−0.730804	+	0.0260963i
$731$	−265.314	−	816.554i	−0.0134241	−	0.0413151i
$732$		0			0
$733$	−884.238	−	2721.40i	−0.0445567	−	0.137131i	0.926303	−	0.376779i	$-0.122968\pi$
$733$	−884.238	−	2721.40i	−0.0445567	−	0.137131i	−0.970860	+	0.239647i	$0.922968\pi$
$734$	−157.475	−	114.413i	−0.00791897	−	0.00575347i
$735$		0			0
$736$	15434.9	−	11214.1i	0.773013	−	0.561627i
$737$	1067.12	+	775.307i	0.0533349	+	0.0387501i
$738$		0			0
$739$	−24379.0	+	17712.4i	−1.21353	+	0.881680i	−0.995546	−	0.0942726i	$-0.969947\pi$
$739$	−24379.0	+	17712.4i	−1.21353	+	0.881680i	−0.217982	+	0.975953i	$0.569947\pi$
$740$	−19719.1	−	13278.1i	−0.979577	−	0.659611i
$741$		0			0
$742$	−3263.75	−	10044.8i	−0.161477	−	0.496975i
$743$	−1183.79			−0.0584508			−0.0292254	−	0.999573i	$-0.509304\pi$
$743$	−1183.79			−0.0584508			−0.0292254	+	0.999573i	$0.509304\pi$
$744$		0			0
$745$	3863.83	+	10589.8i	0.190013	+	0.520781i
$746$	1457.06	−	4484.38i	0.0715106	−	0.220087i
$747$		0			0
$748$	69.1401	−	50.2333i	0.00337970	−	0.00245549i
$749$	−22370.0			−1.09130
$750$		0			0
$751$	33092.2			1.60793			0.803964	−	0.594679i	$-0.202721\pi$
$751$	33092.2			1.60793			0.803964	+	0.594679i	$0.202721\pi$
$752$	6612.26	−	4804.08i	0.320644	−	0.232961i
$753$		0			0
$754$	−4049.68	+	12463.6i	−0.195598	+	0.601988i
$755$	−8288.88	−	22717.8i	−0.399554	−	1.09508i
$756$		0			0
$757$	14001.4			0.672246			0.336123	−	0.941818i	$-0.390884\pi$
$757$	14001.4			0.672246			0.336123	+	0.941818i	$0.390884\pi$
$758$	167.409	+	515.233i	0.00802188	+	0.0246888i
$759$		0			0
$760$	4260.10	+	2868.60i	0.203329	+	0.136914i
$761$	−13651.0	+	9918.02i	−0.650260	+	0.472441i	−0.863360	−	0.504589i	$-0.831644\pi$
$761$	−13651.0	+	9918.02i	−0.650260	+	0.472441i	0.213100	+	0.977030i	$0.431644\pi$
$762$		0			0
$763$	−13213.5	−	9600.19i	−0.626949	−	0.455505i
$764$	−2618.41	+	1902.39i	−0.123993	+	0.0900864i
$765$		0			0
$766$	4534.58	+	3294.56i	0.213892	+	0.155401i
$767$	−17537.9	−	53976.0i	−0.825627	−	2.54102i
$768$		0			0
$769$	2146.67	+	6606.78i	0.100665	+	0.309813i	0.988688	−	0.149984i	$-0.0479221\pi$
$769$	2146.67	+	6606.78i	0.100665	+	0.309813i	−0.888024	+	0.459797i	$0.847922\pi$
$770$	453.708	−	16.2015i	0.0212344	−	0.000758260i
$771$		0			0
$772$	8683.52	−	26725.1i	0.404827	−	1.24593i
$773$	−6808.98	+	4947.01i	−0.316820	+	0.230183i	−0.734817	−	0.678265i	$-0.762732\pi$
$773$	−6808.98	+	4947.01i	−0.316820	+	0.230183i	0.417997	+	0.908448i	$0.362732\pi$
$774$		0			0
$775$	−16327.3	−	10166.7i	−0.756765	−	0.471224i
$776$	7599.16			0.351539
$777$		0			0
$778$	−4247.16	+	13071.4i	−0.195717	+	0.602356i
$779$	258.640	−	796.012i	0.0118957	−	0.0366111i
$780$		0			0
$781$	486.937	+	1498.64i	0.0223098	+	0.0686625i
$782$	−768.290			−0.0351330
$783$		0			0
$784$	3787.52	+	2751.80i	0.172537	+	0.125355i
$785$	−10035.1	−	27503.8i	−0.456265	−	1.25051i
$786$		0			0
$787$	10033.4	+	7289.66i	0.454448	+	0.330176i	0.791349	−	0.611364i	$-0.209379\pi$
$787$	10033.4	+	7289.66i	0.454448	+	0.330176i	−0.336901	+	0.941540i	$0.609379\pi$
$788$	13959.0	+	10141.8i	0.631053	+	0.458487i
$789$		0			0
$790$	6709.09	−	5250.23i	0.302150	−	0.236449i
$791$	−357.831	−	259.979i	−0.0160847	−	0.0116862i
$792$		0			0
$793$	−30624.7			−1.37139
$794$	4219.39	+	12986.0i	0.188590	+	0.580421i
$795$		0			0
$796$	−9564.38	+	29436.1i	−0.425880	+	1.31072i
$797$	−10310.5	+	31732.5i	−0.458240	+	1.41032i	0.409048	+	0.912513i	$0.365861\pi$
$797$	−10310.5	+	31732.5i	−0.458240	+	1.41032i	−0.867289	+	0.497806i	$0.834139\pi$
$798$		0			0
$799$	−1878.35			−0.0831682
$800$	17652.8	−	14859.9i	0.780149	−	0.656719i
$801$		0			0
$802$	−6408.29	+	4655.90i	−0.282151	+	0.204994i
$803$	738.609	−	2273.21i	0.0324595	−	0.0999000i
$804$		0			0
$805$	11703.1	+	7880.46i	0.512399	+	0.345031i
$806$	−5454.33	−	16786.7i	−0.238363	−	0.733607i
$807$		0			0
$808$	772.812	+	2378.47i	0.0336478	+	0.103557i
$809$	11812.8	+	8582.52i	0.513371	+	0.372986i	0.814101	−	0.580724i	$-0.197230\pi$
$809$	11812.8	+	8582.52i	0.513371	+	0.372986i	−0.300730	+	0.953709i	$0.597230\pi$
$810$		0			0
$811$	−4741.12	+	3444.63i	−0.205282	+	0.149146i	−0.685676	−	0.727907i	$-0.740493\pi$
$811$	−4741.12	+	3444.63i	−0.205282	+	0.149146i	0.480395	+	0.877052i	$0.340493\pi$
$812$	−7002.57	−	5087.67i	−0.302638	−	0.219879i
$813$		0			0
$814$	−921.973	+	669.853i	−0.0396992	+	0.0288431i
$815$	−993.444	+	3474.87i	−0.0426979	+	0.149349i
$816$		0			0
$817$	1154.19	+	3552.22i	0.0494246	+	0.152113i
$818$	−7578.50			−0.323932
$819$		0			0
$820$	−1995.39	−	1343.62i	−0.0849779	−	0.0572210i
$821$	−4761.16	+	14653.3i	−0.202394	+	0.622905i	0.797416	+	0.603430i	$0.206200\pi$
$821$	−4761.16	+	14653.3i	−0.202394	+	0.622905i	−0.999810	+	0.0194753i	$0.993800\pi$
$822$		0			0
$823$	33713.6	−	24494.3i	1.42792	−	1.03745i	0.437525	−	0.899206i	$-0.355855\pi$
$823$	33713.6	−	24494.3i	1.42792	−	1.03745i	0.990399	−	0.138241i	$-0.0441447\pi$
$824$	358.569			0.0151594
$825$		0			0
$826$	−10843.4			−0.456767
$827$	−12428.2	+	9029.60i	−0.522576	+	0.379673i	−0.817573	−	0.575825i	$-0.804681\pi$
$827$	−12428.2	+	9029.60i	−0.522576	+	0.379673i	0.294998	+	0.955498i	$0.404681\pi$
$828$		0			0
$829$	4586.20	−	14114.9i	0.192142	−	0.591351i	−0.807856	−	0.589379i	$-0.799372\pi$
$829$	4586.20	−	14114.9i	0.192142	−	0.591351i	0.999998	−	0.00197177i	$-0.000627633\pi$
$830$	−1316.91	+	4606.28i	−0.0550729	+	0.192634i
$831$		0			0
$832$	4638.16			0.193268
$833$	−332.480	−	1023.27i	−0.0138292	−	0.0425620i
$834$		0			0
$835$	1399.85	−	1095.46i	0.0580164	−	0.0454010i
$836$	−300.778	+	218.528i	−0.0124433	+	0.00904060i
$837$		0			0
$838$	−14853.5	−	10791.7i	−0.612299	−	0.444861i
$839$	3570.89	−	2594.40i	0.146938	−	0.106757i	−0.511888	−	0.859052i	$-0.671054\pi$
$839$	3570.89	−	2594.40i	0.146938	−	0.106757i	0.658825	+	0.752296i	$0.271054\pi$
$840$		0			0
$841$	9171.97	+	6663.83i	0.376070	+	0.273231i
$842$	−3814.94	−	11741.2i	−0.156142	−	0.480556i
$843$		0			0
$844$	−7194.54	−	22142.5i	−0.293420	−	0.903053i
$845$	−45202.3	+	35373.2i	−1.84024	+	1.44009i
$846$		0			0
$847$	4998.79	−	15384.7i	0.202787	−	0.624113i
$848$	12610.6	−	9162.13i	0.510672	−	0.371025i
$849$		0			0
$850$	−926.840	+	66.2775i	−0.0374004	+	0.00267447i
$851$	−35416.4			−1.42663
$852$		0			0
$853$	−1784.63	+	5492.53i	−0.0716350	+	0.220470i	−0.980464	−	0.196699i	$-0.936978\pi$
$853$	−1784.63	+	5492.53i	−0.0716350	+	0.220470i	0.908829	+	0.417169i	$0.136978\pi$
$854$	−1808.11	+	5564.78i	−0.0724498	+	0.222977i
$855$		0			0
$856$	10774.5	+	33160.7i	0.430218	+	1.32407i
$857$	4100.45			0.163441			0.0817203	−	0.996655i	$-0.473959\pi$
$857$	4100.45			0.163441			0.0817203	+	0.996655i	$0.473959\pi$
$858$		0			0
$859$	7956.07	+	5780.42i	0.316016	+	0.229599i	0.734473	−	0.678637i	$-0.237429\pi$
$859$	7956.07	+	5780.42i	0.316016	+	0.229599i	−0.418458	+	0.908236i	$0.637429\pi$
$860$	10728.2	−	383.092i	0.425381	−	0.0151899i
$861$		0			0
$862$	−8200.41	−	5957.94i	−0.324022	−	0.235416i
$863$	13882.1	+	10086.0i	0.547571	+	0.397834i	0.826889	−	0.562365i	$-0.190108\pi$
$863$	13882.1	+	10086.0i	0.547571	+	0.397834i	−0.279318	+	0.960199i	$0.590108\pi$
$864$		0			0
$865$	−30535.7	−	20561.6i	−1.20028	−	0.808226i
$866$	4386.16	+	3186.73i	0.172111	+	0.125046i
$867$		0			0
$868$	11657.9			0.455870
$869$	436.266	+	1342.69i	0.0170303	+	0.0524138i
$870$		0			0
$871$	−14059.2	+	43269.8i	−0.546933	+	1.68329i
$872$	−7866.72	+	24211.3i	−0.305505	+	0.940249i
$873$		0			0
$874$	3342.26			0.129352
$875$	14798.1	+	8497.15i	0.571733	+	0.328293i
$876$		0			0
$877$	7136.71	−	5185.12i	0.274789	−	0.199646i	−0.441853	−	0.897088i	$-0.645679\pi$
$877$	7136.71	−	5185.12i	0.274789	−	0.199646i	0.716641	+	0.697442i	$0.245679\pi$
$878$	−1616.04	+	4973.67i	−0.0621171	+	0.191177i
$879$		0			0
$880$	229.661	+	629.446i	0.00879758	+	0.0241121i
$881$	9227.88	+	28400.5i	0.352889	+	1.08608i	0.957223	+	0.289350i	$0.0934391\pi$
$881$	9227.88	+	28400.5i	0.352889	+	1.08608i	−0.604335	+	0.796731i	$0.706561\pi$
$882$		0			0
$883$	2159.26	+	6645.52i	0.0822932	+	0.253272i	0.983734	−	0.179629i	$-0.0574898\pi$
$883$	2159.26	+	6645.52i	0.0822932	+	0.253272i	−0.901441	+	0.432902i	$0.857490\pi$
$884$	2384.81	+	1732.67i	0.0907352	+	0.0659230i
$885$		0			0
$886$	−2480.92	+	1802.49i	−0.0940723	+	0.0683476i
$887$	35503.0	+	25794.4i	1.34394	+	0.976428i	0.999289	+	0.0376958i	$0.0120018\pi$
$887$	35503.0	+	25794.4i	1.34394	+	0.976428i	0.344648	+	0.938732i	$0.387998\pi$
$888$		0			0
$889$	−13805.9	+	10030.5i	−0.520848	+	0.378418i
$890$	−19979.9	+	713.461i	−0.752503	+	0.0268711i
$891$		0			0
$892$	−3139.98	−	9663.87i	−0.117864	−	0.362747i
$893$	8171.33			0.306207
$894$		0			0
$895$	−31496.7	+	1124.71i	−1.17633	+	0.0420057i
$896$	−5298.21	+	16306.2i	−0.197546	+	0.607983i
$897$		0			0
$898$	−10866.3	+	7894.83i	−0.403801	+	0.293379i
$899$	17578.9			0.652157
$900$		0			0
$901$	−3582.31			−0.132457
$902$	−93.2951	+	67.7829i	−0.00344389	+	0.00250213i
$903$		0			0
$904$	−213.036	+	655.657i	−0.00783790	+	0.0241226i
$905$	−3676.89	+	2877.36i	−0.135054	+	0.105687i
$906$		0			0
$907$	20572.4			0.753138			0.376569	−	0.926389i	$-0.377104\pi$
$907$	20572.4			0.753138			0.376569	+	0.926389i	$0.377104\pi$
$908$	−7273.16	−	22384.5i	−0.265824	−	0.818122i
$909$		0			0
$910$	5367.44	+	14710.9i	0.195526	+	0.535891i
$911$	−5933.73	+	4311.11i	−0.215799	+	0.156787i	−0.690434	−	0.723396i	$-0.742580\pi$
$911$	−5933.73	+	4311.11i	−0.215799	+	0.156787i	0.474634	+	0.880183i	$0.342580\pi$
$912$		0			0
$913$	−642.302	−	466.660i	−0.0232827	−	0.0169159i
$914$	−3569.31	+	2593.26i	−0.129171	+	0.0938483i
$915$		0			0
$916$	452.902	+	329.053i	0.0163366	+	0.0118692i
$917$	−10708.3	−	32956.8i	−0.385627	−	1.18684i
$918$		0			0
$919$	−12333.6	−	37958.9i	−0.442707	−	1.36251i	−0.884978	−	0.465632i	$-0.845827\pi$
$919$	−12333.6	−	37958.9i	−0.442707	−	1.36251i	0.442271	−	0.896882i	$-0.354173\pi$
$920$	6044.93	−	21144.0i	0.216625	−	0.757713i
$921$		0			0
$922$	−344.178	+	1059.27i	−0.0122938	+	0.0378365i
$923$	−43971.5	+	31947.2i	−1.56808	+	1.13928i
$924$		0			0
$925$	−42725.2	+	3055.24i	−1.51870	+	0.108601i
$926$	12093.5			0.429176
$927$		0			0
$928$	−6516.90	+	20057.0i	−0.230526	+	0.709485i
$929$	−6378.19	+	19630.0i	−0.225255	+	0.693263i	0.773011	+	0.634393i	$0.218750\pi$
$929$	−6378.19	+	19630.0i	−0.225255	+	0.693263i	−0.998266	+	0.0588699i	$0.981250\pi$
$930$		0			0
$931$	1446.38	+	4451.49i	0.0509163	+	0.156704i
$932$	22452.4			0.789112
$933$		0			0
$934$	−1426.10	−	1036.12i	−0.0499607	−	0.0362986i
$935$	42.3279	−	148.055i	0.00148050	−	0.00517851i
$936$		0			0
$937$	−21497.0	−	15618.5i	−0.749494	−	0.544539i	0.146176	−	0.989259i	$-0.453303\pi$
$937$	−21497.0	−	15618.5i	−0.749494	−	0.544539i	−0.895670	+	0.444719i	$0.853303\pi$
$938$	7032.45	+	5109.37i	0.244795	+	0.177854i
$939$		0			0
$940$	6455.74	−	22580.9i	0.224003	−	0.783519i
$941$	10502.5	+	7630.51i	0.363838	+	0.264344i	0.754651	−	0.656126i	$-0.227806\pi$
$941$	10502.5	+	7630.51i	0.363838	+	0.264344i	−0.390813	+	0.920470i	$0.627806\pi$
$942$		0			0
$943$	−3583.81			−0.123759
$944$	−4945.28	−	15220.0i	−0.170503	−	0.524755i
$945$		0			0
$946$	159.025	−	489.428i	0.00546547	−	0.0168210i
$947$	−14382.2	+	44263.9i	−0.493516	+	1.51888i	0.325742	+	0.945459i	$0.394386\pi$
$947$	−14382.2	+	44263.9i	−0.493516	+	1.51888i	−0.819257	+	0.573426i	$0.805614\pi$
$948$		0			0
$949$	82443.5			2.82005
$950$	4032.00	−	288.324i	0.137700	−	0.00984682i
$951$		0			0
$952$	1043.09	−	757.849i	0.0355113	−	0.0258005i
$953$	11512.2	−	35430.8i	0.391307	−	1.20432i	−0.540493	−	0.841349i	$-0.681762\pi$
$953$	11512.2	−	35430.8i	0.391307	−	1.20432i	0.931800	−	0.362972i	$-0.118238\pi$
$954$		0			0
$955$	−1603.00	+	5607.00i	−0.0543163	+	0.189988i
$956$	−2820.12	−	8679.45i	−0.0954072	−	0.293633i
$957$		0			0
$958$	3863.18	+	11889.6i	0.130286	+	0.400978i
$959$	8004.23	+	5815.41i	0.269520	+	0.195818i
$960$		0			0
$961$	4946.94	−	3594.16i	0.166055	−	0.120646i
$962$	−31801.1	−	23104.9i	−1.06581	−	0.774356i
$963$		0			0
$964$	−19811.2	+	14393.7i	−0.661905	+	0.480902i
$965$	−17354.5	−	47564.7i	−0.578925	−	1.58670i
$966$		0			0
$967$	−9790.75	−	30132.8i	−0.325594	−	1.00207i	−0.971172	−	0.238380i	$-0.923384\pi$
$967$	−9790.75	−	30132.8i	−0.325594	−	1.00207i	0.645578	−	0.763694i	$-0.276616\pi$
$968$	−25213.5			−0.837181
$969$		0			0
$970$	4710.24	−	3686.02i	0.155914	−	0.122011i
$971$	−8373.85	+	25772.1i	−0.276756	+	0.851766i	0.711994	+	0.702186i	$0.247792\pi$
$971$	−8373.85	+	25772.1i	−0.276756	+	0.851766i	−0.988750	+	0.149581i	$0.952208\pi$
$972$		0			0
$973$	−31021.9	+	22538.7i	−1.02211	+	0.742608i
$974$	2753.84			0.0905943
$975$		0			0
$976$	−8635.46			−0.283211
$977$	40154.6	−	29174.1i	1.31490	−	0.955333i	0.314923	−	0.949117i	$-0.398021\pi$
$977$	40154.6	−	29174.1i	1.31490	−	0.955333i	0.999981	−	0.00621630i	$-0.00197872\pi$
$978$		0			0
$979$	1023.82	−	3150.99i	0.0334233	−	0.102866i
$980$	13444.1	−	480.074i	0.438220	−	0.0156484i
$981$		0			0
$982$	4783.11			0.155433
$983$	−10741.8	−	33059.7i	−0.348534	−	1.07268i	−0.959665	−	0.281147i	$-0.909285\pi$
$983$	−10741.8	−	33059.7i	−0.348534	−	1.07268i	0.611131	−	0.791530i	$-0.290715\pi$
$984$		0			0
$985$	31069.2	−	1109.45i	1.00502	−	0.0358884i
$986$	687.061	−	499.179i	0.0221912	−	0.0161228i
$987$		0			0
$988$	−10374.6	−	7537.56i	−0.334068	−	0.242714i
$989$	12938.5	−	9400.36i	0.415996	−	0.302239i
$990$		0			0
$991$	−15805.8	−	11483.6i	−0.506646	−	0.368100i	0.304904	−	0.952383i	$-0.401376\pi$
$991$	−15805.8	−	11483.6i	−0.506646	−	0.368100i	−0.811550	+	0.584283i	$0.801376\pi$
$992$	−8777.33	−	27013.8i	−0.280928	−	0.864607i
$993$		0			0
$994$	3208.97	+	9876.21i	0.102397	+	0.315145i
$995$	19115.0	+	52389.7i	0.609031	+	1.66921i
$996$		0			0
$997$	10317.8	−	31755.1i	0.327753	−	1.00872i	−0.642430	−	0.766344i	$-0.722074\pi$
$997$	10317.8	−	31755.1i	0.327753	−	1.00872i	0.970183	−	0.242375i	$-0.0779264\pi$
$998$	−343.546	+	249.601i	−0.0108965	+	0.00791680i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.a.136.5		28
3.2	odd	2		75.4.g.b.61.3	yes	28
25.16	even	5	inner	225.4.h.a.91.5		28
75.29	odd	10		1875.4.a.f.1.6		14
75.41	odd	10		75.4.g.b.16.3	✓	28
75.71	odd	10		1875.4.a.g.1.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.16.3	✓	28	75.41	odd	10
75.4.g.b.61.3	yes	28	3.2	odd	2
225.4.h.a.91.5		28	25.16	even	5	inner
225.4.h.a.136.5		28	1.1	even	1	trivial
1875.4.a.f.1.6		14	75.29	odd	10
1875.4.a.g.1.9		14	75.71	odd	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.08389 - 0.787491i) q^{2} +(-1.91746 + 5.90135i) q^{4} +(3.83217 + 10.5031i) q^{5} -12.2101 q^{7} +(5.88101 + 18.0999i) q^{8} +O(q^{10})\)	\(q+(1.08389 - 0.787491i) q^{2} +(-1.91746 + 5.90135i) q^{4} +(3.83217 + 10.5031i) q^{5} -12.2101 q^{7} +(5.88101 + 18.0999i) q^{8} +(12.4247 + 8.36635i) q^{10} +(-2.00821 + 1.45905i) q^{11} +(-69.2682 - 50.3263i) q^{13} +(-13.2344 + 9.61535i) q^{14} +(-19.5320 - 14.1909i) q^{16} +(1.71458 + 5.27694i) q^{17} +(-7.45887 - 22.9561i) q^{19} +(-69.3303 + 2.47571i) q^{20} +(-1.02769 + 3.16290i) q^{22} +(-83.6143 + 60.7493i) q^{23} +(-95.6289 + 80.4991i) q^{25} -114.710 q^{26} +(23.4124 - 72.0561i) q^{28} +(35.3035 - 108.653i) q^{29} +(47.5487 + 146.340i) q^{31} -184.596 q^{32} +(6.01395 + 4.36939i) q^{34} +(-46.7912 - 128.244i) q^{35} +(277.229 + 201.419i) q^{37} +(-26.1623 - 19.0080i) q^{38} +(-167.567 + 131.130i) q^{40} +(28.0530 + 20.3817i) q^{41} -154.740 q^{43} +(-4.75970 - 14.6489i) q^{44} +(-42.7890 + 131.691i) q^{46} +(-104.613 + 321.965i) q^{47} -193.913 q^{49} +(-40.2588 + 162.559i) q^{50} +(429.812 - 312.277i) q^{52} +(-199.512 + 614.036i) q^{53} +(-23.0204 - 15.5011i) q^{55} +(-71.8077 - 221.001i) q^{56} +(-47.2982 - 145.569i) q^{58} +(536.260 + 389.616i) q^{59} +(289.370 - 210.239i) q^{61} +(166.779 + 121.172i) q^{62} +(-43.8256 + 31.8411i) q^{64} +(263.133 - 920.387i) q^{65} +(-164.205 - 505.370i) q^{67} -34.4287 q^{68} +(-151.707 - 102.154i) q^{70} +(196.164 - 603.732i) q^{71} +(-779.001 + 565.977i) q^{73} +459.101 q^{74} +149.774 q^{76} +(24.5205 - 17.8152i) q^{77} +(175.752 - 540.908i) q^{79} +(74.1975 - 259.528i) q^{80} +46.4568 q^{82} +(98.8352 + 304.184i) q^{83} +(-48.8535 + 38.2305i) q^{85} +(-167.721 + 121.856i) q^{86} +(-38.2190 - 27.7677i) q^{88} +(-1079.81 + 784.525i) q^{89} +(845.772 + 614.489i) q^{91} +(-198.176 - 609.922i) q^{92} +(140.156 + 431.355i) q^{94} +(212.525 - 166.313i) q^{95} +(123.390 - 379.754i) q^{97} +(-210.180 + 152.705i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) \) 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 + 165 * q^10 - 19 * q^11 + 4 * q^13 + 24 * q^14 - 66 * q^16 - 208 * q^17 + 42 * q^19 - 295 * q^20 - 89 * q^22 - 32 * q^23 + 95 * q^25 - 206 * q^26 - 482 * q^28 + 716 * q^29 + 637 * q^31 + 844 * q^32 - 90 * q^34 - 430 * q^35 + 216 * q^37 - 2314 * q^38 - 500 * q^40 + 38 * q^41 - 1392 * q^43 - 603 * q^44 + 1622 * q^46 + 536 * q^47 + 162 * q^49 + 2265 * q^50 - 1922 * q^52 - 1672 * q^53 - 1000 * q^55 - 3000 * q^56 - 827 * q^58 - 973 * q^59 - 2712 * q^61 - 1057 * q^62 + 4439 * q^64 + 4360 * q^65 + 2768 * q^67 + 1370 * q^68 + 3230 * q^70 + 1074 * q^71 - 1018 * q^73 + 1414 * q^74 - 11408 * q^76 - 1607 * q^77 - 1820 * q^79 + 1290 * q^80 + 1772 * q^82 - 4045 * q^83 + 1850 * q^85 + 3986 * q^86 + 2407 * q^88 - 4542 * q^89 + 4412 * q^91 + 1089 * q^92 + 5137 * q^94 + 720 * q^95 - 5977 * q^97 + 10689 * q^98

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