LMFDB - Embedded newform 450.2.h.a.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(91,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.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:	$3.59326809096$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			271.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	450.271
Dual form			450.2.h.a.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.80902 - 1.31433i) q^{5} -3.00000 q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.80902 - 1.31433i) q^{5} -3.00000 q^{7} +(-0.809017 + 0.587785i) q^{8} +(-1.80902 + 1.31433i) q^{10} +(-1.30902 + 4.02874i) q^{11} +(0.309017 + 0.951057i) q^{13} +(-0.927051 + 2.85317i) q^{14} +(0.309017 + 0.951057i) q^{16} +(0.927051 - 0.673542i) q^{17} +(-4.73607 + 3.44095i) q^{19} +(0.690983 + 2.12663i) q^{20} +(3.42705 + 2.48990i) q^{22} +(0.545085 - 1.67760i) q^{23} +(1.54508 + 4.75528i) q^{25} +1.00000 q^{26} +(2.42705 + 1.76336i) q^{28} +(-7.66312 - 5.56758i) q^{29} +(0.190983 - 0.138757i) q^{31} +1.00000 q^{32} +(-0.354102 - 1.08981i) q^{34} +(5.42705 + 3.94298i) q^{35} +(-2.57295 - 7.91872i) q^{37} +(1.80902 + 5.56758i) q^{38} +2.23607 q^{40} +(-0.454915 - 1.40008i) q^{41} -6.23607 q^{43} +(3.42705 - 2.48990i) q^{44} +(-1.42705 - 1.03681i) q^{46} +(-9.66312 - 7.02067i) q^{47} +2.00000 q^{49} +5.00000 q^{50} +(0.309017 - 0.951057i) q^{52} +(8.47214 + 6.15537i) q^{53} +(7.66312 - 5.56758i) q^{55} +(2.42705 - 1.76336i) q^{56} +(-7.66312 + 5.56758i) q^{58} +(1.38197 + 4.25325i) q^{59} +(-2.73607 + 8.42075i) q^{61} +(-0.0729490 - 0.224514i) q^{62} +(0.309017 - 0.951057i) q^{64} +(0.690983 - 2.12663i) q^{65} +(8.28115 - 6.01661i) q^{67} -1.14590 q^{68} +(5.42705 - 3.94298i) q^{70} +(-2.42705 - 1.76336i) q^{71} +(2.38197 - 7.33094i) q^{73} -8.32624 q^{74} +5.85410 q^{76} +(3.92705 - 12.0862i) q^{77} +(5.85410 + 4.25325i) q^{79} +(0.690983 - 2.12663i) q^{80} -1.47214 q^{82} +(-3.66312 + 2.66141i) q^{83} -2.56231 q^{85} +(-1.92705 + 5.93085i) q^{86} +(-1.30902 - 4.02874i) q^{88} +(-1.38197 + 4.25325i) q^{89} +(-0.927051 - 2.85317i) q^{91} +(-1.42705 + 1.03681i) q^{92} +(-9.66312 + 7.02067i) q^{94} +13.0902 q^{95} +(-7.73607 - 5.62058i) q^{97} +(0.618034 - 1.90211i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} - 5 q^{5} - 12 q^{7} - q^{8}+O(q^{10}) $ 4 * q - q^2 - q^4 - 5 * q^5 - 12 * q^7 - q^8	$ 4 q - q^{2} - q^{4} - 5 q^{5} - 12 q^{7} - q^{8} - 5 q^{10} - 3 q^{11} - q^{13} + 3 q^{14} - q^{16} - 3 q^{17} - 10 q^{19} + 5 q^{20} + 7 q^{22} - 9 q^{23} - 5 q^{25} + 4 q^{26} + 3 q^{28} - 15 q^{29} + 3 q^{31} + 4 q^{32} + 12 q^{34} + 15 q^{35} - 17 q^{37} + 5 q^{38} - 13 q^{41} - 16 q^{43} + 7 q^{44} + q^{46} - 23 q^{47} + 8 q^{49} + 20 q^{50} - q^{52} + 16 q^{53} + 15 q^{55} + 3 q^{56} - 15 q^{58} + 10 q^{59} - 2 q^{61} - 7 q^{62} - q^{64} + 5 q^{65} + 13 q^{67} - 18 q^{68} + 15 q^{70} - 3 q^{71} + 14 q^{73} - 2 q^{74} + 10 q^{76} + 9 q^{77} + 10 q^{79} + 5 q^{80} + 12 q^{82} + q^{83} + 30 q^{85} - q^{86} - 3 q^{88} - 10 q^{89} + 3 q^{91} + q^{92} - 23 q^{94} + 30 q^{95} - 22 q^{97} - 2 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^4 - 5 * q^5 - 12 * q^7 - q^8 - 5 * q^10 - 3 * q^11 - q^13 + 3 * q^14 - q^16 - 3 * q^17 - 10 * q^19 + 5 * q^20 + 7 * q^22 - 9 * q^23 - 5 * q^25 + 4 * q^26 + 3 * q^28 - 15 * q^29 + 3 * q^31 + 4 * q^32 + 12 * q^34 + 15 * q^35 - 17 * q^37 + 5 * q^38 - 13 * q^41 - 16 * q^43 + 7 * q^44 + q^46 - 23 * q^47 + 8 * q^49 + 20 * q^50 - q^52 + 16 * q^53 + 15 * q^55 + 3 * q^56 - 15 * q^58 + 10 * q^59 - 2 * q^61 - 7 * q^62 - q^64 + 5 * q^65 + 13 * q^67 - 18 * q^68 + 15 * q^70 - 3 * q^71 + 14 * q^73 - 2 * q^74 + 10 * q^76 + 9 * q^77 + 10 * q^79 + 5 * q^80 + 12 * q^82 + q^83 + 30 * q^85 - q^86 - 3 * q^88 - 10 * q^89 + 3 * q^91 + q^92 - 23 * q^94 + 30 * q^95 - 22 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$6$		0			0
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$		0			0
$10$	−1.80902	+	1.31433i	−0.572061	+	0.415627i
$11$	−1.30902	+	4.02874i	−0.394683	+	1.21471i	0.534524	+	0.845153i	$0.320491\pi$
$11$	−1.30902	+	4.02874i	−0.394683	+	1.21471i	−0.929208	+	0.369558i	$0.879509\pi$
$12$		0			0
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i	0.984720	−	0.174143i	$-0.0557156\pi$
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i	−0.899014	+	0.437919i	$0.855716\pi$
$14$	−0.927051	+	2.85317i	−0.247765	+	0.762542i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.927051	−	0.673542i	0.224843	−	0.163358i	−0.469661	−	0.882847i	$-0.655624\pi$
$17$	0.927051	−	0.673542i	0.224843	−	0.163358i	0.694504	+	0.719489i	$0.255624\pi$
$18$		0			0
$19$	−4.73607	+	3.44095i	−1.08653	+	0.789409i	−0.978810	−	0.204772i	$-0.934355\pi$
$19$	−4.73607	+	3.44095i	−1.08653	+	0.789409i	−0.107719	+	0.994181i	$0.534355\pi$
$20$	0.690983	+	2.12663i	0.154508	+	0.475528i
$21$		0			0
$22$	3.42705	+	2.48990i	0.730650	+	0.530848i
$23$	0.545085	−	1.67760i	0.113658	−	0.349804i	−0.878007	−	0.478648i	$-0.841127\pi$
$23$	0.545085	−	1.67760i	0.113658	−	0.349804i	0.991665	+	0.128845i	$0.0411269\pi$
$24$		0			0
$25$	1.54508	+	4.75528i	0.309017	+	0.951057i
$26$	1.00000			0.196116
$27$		0			0
$28$	2.42705	+	1.76336i	0.458670	+	0.333243i
$29$	−7.66312	−	5.56758i	−1.42301	−	1.03387i	−0.991266	−	0.131875i	$-0.957900\pi$
$29$	−7.66312	−	5.56758i	−1.42301	−	1.03387i	−0.431739	−	0.901998i	$-0.642100\pi$
$30$		0			0
$31$	0.190983	−	0.138757i	0.0343016	−	0.0249215i	−0.570502	−	0.821296i	$-0.693251\pi$
$31$	0.190983	−	0.138757i	0.0343016	−	0.0249215i	0.604804	+	0.796374i	$0.293251\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−0.354102	−	1.08981i	−0.0607280	−	0.186902i
$35$	5.42705	+	3.94298i	0.917339	+	0.666486i
$36$		0			0
$37$	−2.57295	−	7.91872i	−0.422990	−	1.30183i	−0.904906	−	0.425612i	$-0.860059\pi$
$37$	−2.57295	−	7.91872i	−0.422990	−	1.30183i	0.481915	−	0.876218i	$-0.339941\pi$
$38$	1.80902	+	5.56758i	0.293461	+	0.903181i
$39$		0			0
$40$	2.23607			0.353553
$41$	−0.454915	−	1.40008i	−0.0710458	−	0.218656i	0.909229	−	0.416297i	$-0.136672\pi$
$41$	−0.454915	−	1.40008i	−0.0710458	−	0.218656i	−0.980275	+	0.197640i	$0.936672\pi$
$42$		0			0
$43$	−6.23607			−0.950991			−0.475496	−	0.879718i	$-0.657731\pi$
$43$	−6.23607			−0.950991			−0.475496	+	0.879718i	$0.657731\pi$
$44$	3.42705	−	2.48990i	0.516647	−	0.375366i
$45$		0			0
$46$	−1.42705	−	1.03681i	−0.210407	−	0.152870i
$47$	−9.66312	−	7.02067i	−1.40951	−	1.02407i	−0.993393	−	0.114759i	$-0.963391\pi$
$47$	−9.66312	−	7.02067i	−1.40951	−	1.02407i	−0.416117	−	0.909311i	$-0.636609\pi$
$48$		0			0
$49$	2.00000			0.285714
$50$	5.00000			0.707107
$51$		0			0
$52$	0.309017	−	0.951057i	0.0428529	−	0.131888i
$53$	8.47214	+	6.15537i	1.16374	+	0.845505i	0.990246	−	0.139331i	$-0.0444951\pi$
$53$	8.47214	+	6.15537i	1.16374	+	0.845505i	0.173491	+	0.984835i	$0.444495\pi$
$54$		0			0
$55$	7.66312	−	5.56758i	1.03329	−	0.750733i
$56$	2.42705	−	1.76336i	0.324328	−	0.235638i
$57$		0			0
$58$	−7.66312	+	5.56758i	−1.00622	+	0.731059i
$59$	1.38197	+	4.25325i	0.179917	+	0.553727i	0.999824	−	0.0187700i	$-0.00597502\pi$
$59$	1.38197	+	4.25325i	0.179917	+	0.553727i	−0.819907	+	0.572496i	$0.805975\pi$
$60$		0			0
$61$	−2.73607	+	8.42075i	−0.350318	+	1.07817i	0.608357	+	0.793663i	$0.291829\pi$
$61$	−2.73607	+	8.42075i	−0.350318	+	1.07817i	−0.958675	+	0.284504i	$0.908171\pi$
$62$	−0.0729490	−	0.224514i	−0.00926453	−	0.0285133i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.690983	−	2.12663i	0.0857059	−	0.263776i
$66$		0			0
$67$	8.28115	−	6.01661i	1.01170	−	0.735046i	0.0471381	−	0.998888i	$-0.484990\pi$
$67$	8.28115	−	6.01661i	1.01170	−	0.735046i	0.964566	+	0.263843i	$0.0849899\pi$
$68$	−1.14590			−0.138961
$69$		0			0
$70$	5.42705	−	3.94298i	0.648657	−	0.471277i
$71$	−2.42705	−	1.76336i	−0.288038	−	0.209272i	0.434378	−	0.900731i	$-0.356968\pi$
$71$	−2.42705	−	1.76336i	−0.288038	−	0.209272i	−0.722416	+	0.691459i	$0.756968\pi$
$72$		0			0
$73$	2.38197	−	7.33094i	0.278788	−	0.858021i	−0.709404	−	0.704802i	$-0.751036\pi$
$73$	2.38197	−	7.33094i	0.278788	−	0.858021i	0.988192	−	0.153219i	$-0.0489641\pi$
$74$	−8.32624			−0.967905
$75$		0			0
$76$	5.85410			0.671512
$77$	3.92705	−	12.0862i	0.447529	−	1.37735i
$78$		0			0
$79$	5.85410	+	4.25325i	0.658638	+	0.478528i	0.866203	−	0.499693i	$-0.166554\pi$
$79$	5.85410	+	4.25325i	0.658638	+	0.478528i	−0.207565	+	0.978221i	$0.566554\pi$
$80$	0.690983	−	2.12663i	0.0772542	−	0.237764i
$81$		0			0
$82$	−1.47214			−0.162570
$83$	−3.66312	+	2.66141i	−0.402080	+	0.292128i	−0.770387	−	0.637576i	$-0.779937\pi$
$83$	−3.66312	+	2.66141i	−0.402080	+	0.292128i	0.368308	+	0.929704i	$0.379937\pi$
$84$		0			0
$85$	−2.56231			−0.277921
$86$	−1.92705	+	5.93085i	−0.207799	+	0.639540i
$87$		0			0
$88$	−1.30902	−	4.02874i	−0.139542	−	0.429465i
$89$	−1.38197	+	4.25325i	−0.146488	+	0.450844i	−0.997199	−	0.0747893i	$-0.976172\pi$
$89$	−1.38197	+	4.25325i	−0.146488	+	0.450844i	0.850711	+	0.525633i	$0.176172\pi$
$90$		0			0
$91$	−0.927051	−	2.85317i	−0.0971813	−	0.299093i
$92$	−1.42705	+	1.03681i	−0.148780	+	0.108095i
$93$		0			0
$94$	−9.66312	+	7.02067i	−0.996675	+	0.724126i
$95$	13.0902			1.34302
$96$		0			0
$97$	−7.73607	−	5.62058i	−0.785479	−	0.570684i	0.121140	−	0.992635i	$-0.461345\pi$
$97$	−7.73607	−	5.62058i	−0.785479	−	0.570684i	−0.906618	+	0.421952i	$0.861345\pi$
$98$	0.618034	−	1.90211i	0.0624309	−	0.192142i
$99$		0			0
$100$	1.54508	−	4.75528i	0.154508	−	0.475528i
$101$	−0.618034			−0.0614967			−0.0307483	−	0.999527i	$-0.509789\pi$
$101$	−0.618034			−0.0614967			−0.0307483	+	0.999527i	$0.509789\pi$
$102$		0			0
$103$	10.6353	+	7.72696i	1.04792	+	0.761360i	0.971816	−	0.235739i	$-0.0757511\pi$
$103$	10.6353	+	7.72696i	1.04792	+	0.761360i	0.0761065	+	0.997100i	$0.475751\pi$
$104$	−0.809017	−	0.587785i	−0.0793306	−	0.0576371i
$105$		0			0
$106$	8.47214	−	6.15537i	0.822887	−	0.597862i
$107$	1.09017			0.105391			0.0526954	−	0.998611i	$-0.483219\pi$
$107$	1.09017			0.105391			0.0526954	+	0.998611i	$0.483219\pi$
$108$		0			0
$109$	−4.63525	−	14.2658i	−0.443977	−	1.36642i	−0.883602	−	0.468239i	$-0.844889\pi$
$109$	−4.63525	−	14.2658i	−0.443977	−	1.36642i	0.439625	−	0.898181i	$-0.355111\pi$
$110$	−2.92705	−	9.00854i	−0.279083	−	0.858930i
$111$		0			0
$112$	−0.927051	−	2.85317i	−0.0875981	−	0.269599i
$113$	−1.16312	−	3.57971i	−0.109417	−	0.336751i	0.881325	−	0.472511i	$-0.156652\pi$
$113$	−1.16312	−	3.57971i	−0.109417	−	0.336751i	−0.990742	+	0.135760i	$0.956652\pi$
$114$		0			0
$115$	−3.19098	+	2.31838i	−0.297561	+	0.216191i
$116$	2.92705	+	9.00854i	0.271770	+	0.836422i
$117$		0			0
$118$	4.47214			0.411693
$119$	−2.78115	+	2.02063i	−0.254948	+	0.185230i
$120$		0			0
$121$	−5.61803	−	4.08174i	−0.510730	−	0.371067i
$122$	7.16312	+	5.20431i	0.648518	+	0.471176i
$123$		0			0
$124$	−0.236068			−0.0211995
$125$	3.45492	−	10.6331i	0.309017	−	0.951057i
$126$		0			0
$127$	−1.09017	+	3.35520i	−0.0967369	+	0.297726i	−0.987702	−	0.156345i	$-0.950029\pi$
$127$	−1.09017	+	3.35520i	−0.0967369	+	0.297726i	0.890966	+	0.454071i	$0.150029\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	−1.80902	−	1.31433i	−0.158661	−	0.115274i
$131$	−13.2812	+	9.64932i	−1.16038	+	0.843065i	−0.989826	−	0.142283i	$-0.954556\pi$
$131$	−13.2812	+	9.64932i	−1.16038	+	0.843065i	−0.170554	+	0.985348i	$0.554556\pi$
$132$		0			0
$133$	14.2082	−	10.3229i	1.23201	−	0.895106i
$134$	−3.16312	−	9.73508i	−0.273252	−	0.840983i
$135$		0			0
$136$	−0.354102	+	1.08981i	−0.0303640	+	0.0934508i
$137$	−1.57295	−	4.84104i	−0.134386	−	0.413598i	0.861108	−	0.508422i	$-0.169771\pi$
$137$	−1.57295	−	4.84104i	−0.134386	−	0.413598i	−0.995494	+	0.0948243i	$0.969771\pi$
$138$		0			0
$139$	−1.64590	+	5.06555i	−0.139603	+	0.429655i	−0.996278	−	0.0862030i	$-0.972527\pi$
$139$	−1.64590	+	5.06555i	−0.139603	+	0.429655i	0.856674	+	0.515858i	$0.172527\pi$
$140$	−2.07295	−	6.37988i	−0.175196	−	0.539198i
$141$		0			0
$142$	−2.42705	+	1.76336i	−0.203674	+	0.147978i
$143$	−4.23607			−0.354238
$144$		0			0
$145$	6.54508	+	20.1437i	0.543540	+	1.67284i
$146$	−6.23607	−	4.53077i	−0.516101	−	0.374969i
$147$		0			0
$148$	−2.57295	+	7.91872i	−0.211495	+	0.650915i
$149$	−2.23607			−0.183186			−0.0915929	−	0.995797i	$-0.529196\pi$
$149$	−2.23607			−0.183186			−0.0915929	+	0.995797i	$0.529196\pi$
$150$		0			0
$151$	−9.70820			−0.790042			−0.395021	−	0.918672i	$-0.629263\pi$
$151$	−9.70820			−0.790042			−0.395021	+	0.918672i	$0.629263\pi$
$152$	1.80902	−	5.56758i	0.146731	−	0.451591i
$153$		0			0
$154$	−10.2812	−	7.46969i	−0.828479	−	0.601925i
$155$	−0.527864			−0.0423991
$156$		0			0
$157$	4.56231			0.364112			0.182056	−	0.983288i	$-0.441725\pi$
$157$	4.56231			0.364112			0.182056	+	0.983288i	$0.441725\pi$
$158$	5.85410	−	4.25325i	0.465727	−	0.338371i
$159$		0			0
$160$	−1.80902	−	1.31433i	−0.143015	−	0.103907i
$161$	−1.63525	+	5.03280i	−0.128876	+	0.396640i
$162$		0			0
$163$	0.572949	+	1.76336i	0.0448768	+	0.138117i	0.970984	−	0.239143i	$-0.0768664\pi$
$163$	0.572949	+	1.76336i	0.0448768	+	0.138117i	−0.926108	+	0.377260i	$0.876866\pi$
$164$	−0.454915	+	1.40008i	−0.0355229	+	0.109328i
$165$		0			0
$166$	1.39919	+	4.30625i	0.108598	+	0.334230i
$167$	10.8262	−	7.86572i	0.837759	−	0.608668i	−0.0839844	−	0.996467i	$-0.526765\pi$
$167$	10.8262	−	7.86572i	0.837759	−	0.608668i	0.921744	+	0.387799i	$0.126765\pi$
$168$		0			0
$169$	9.70820	−	7.05342i	0.746785	−	0.542571i
$170$	−0.791796	+	2.43690i	−0.0607280	+	0.186902i
$171$		0			0
$172$	5.04508	+	3.66547i	0.384684	+	0.279489i
$173$	0.381966	−	1.17557i	0.0290403	−	0.0893770i	−0.935486	−	0.353364i	$-0.885038\pi$
$173$	0.381966	−	1.17557i	0.0290403	−	0.0893770i	0.964526	+	0.263987i	$0.0850377\pi$
$174$		0			0
$175$	−4.63525	−	14.2658i	−0.350392	−	1.07840i
$176$	−4.23607			−0.319306
$177$		0			0
$178$	3.61803	+	2.62866i	0.271183	+	0.197026i
$179$	9.04508	+	6.57164i	0.676061	+	0.491187i	0.872049	−	0.489419i	$-0.162791\pi$
$179$	9.04508	+	6.57164i	0.676061	+	0.491187i	−0.195987	+	0.980606i	$0.562791\pi$
$180$		0			0
$181$	−4.38197	+	3.18368i	−0.325709	+	0.236641i	−0.738608	−	0.674136i	$-0.764516\pi$
$181$	−4.38197	+	3.18368i	−0.325709	+	0.236641i	0.412899	+	0.910777i	$0.364516\pi$
$182$	−3.00000			−0.222375
$183$		0			0
$184$	0.545085	+	1.67760i	0.0401842	+	0.123674i
$185$	−5.75329	+	17.7068i	−0.422990	+	1.30183i
$186$		0			0
$187$	1.50000	+	4.61653i	0.109691	+	0.337594i
$188$	3.69098	+	11.3597i	0.269193	+	0.828490i
$189$		0			0
$190$	4.04508	−	12.4495i	0.293461	−	0.903181i
$191$	4.21885	+	12.9843i	0.305265	+	0.939509i	0.979578	+	0.201064i	$0.0644398\pi$
$191$	4.21885	+	12.9843i	0.305265	+	0.939509i	−0.674313	+	0.738446i	$0.735560\pi$
$192$		0			0
$193$	−14.6525			−1.05471			−0.527354	−	0.849646i	$-0.676816\pi$
$193$	−14.6525			−1.05471			−0.527354	+	0.849646i	$0.676816\pi$
$194$	−7.73607	+	5.62058i	−0.555417	+	0.403534i
$195$		0			0
$196$	−1.61803	−	1.17557i	−0.115574	−	0.0839693i
$197$	9.70820	+	7.05342i	0.691681	+	0.502536i	0.877212	−	0.480103i	$-0.159401\pi$
$197$	9.70820	+	7.05342i	0.691681	+	0.502536i	−0.185531	+	0.982638i	$0.559401\pi$
$198$		0			0
$199$	2.56231			0.181637			0.0908185	−	0.995867i	$-0.471052\pi$
$199$	2.56231			0.181637			0.0908185	+	0.995867i	$0.471052\pi$
$200$	−4.04508	−	2.93893i	−0.286031	−	0.207813i
$201$		0			0
$202$	−0.190983	+	0.587785i	−0.0134375	+	0.0413564i
$203$	22.9894	+	16.7027i	1.61354	+	1.17230i
$204$		0			0
$205$	−1.01722	+	3.13068i	−0.0710458	+	0.218656i
$206$	10.6353	−	7.72696i	0.740993	−	0.538363i
$207$		0			0
$208$	−0.809017	+	0.587785i	−0.0560952	+	0.0407556i
$209$	−7.66312	−	23.5847i	−0.530069	−	1.63138i
$210$		0			0
$211$	−6.88197	+	21.1805i	−0.473774	+	1.45813i	0.373830	+	0.927497i	$0.378044\pi$
$211$	−6.88197	+	21.1805i	−0.473774	+	1.45813i	−0.847604	+	0.530629i	$0.821956\pi$
$212$	−3.23607	−	9.95959i	−0.222254	−	0.684028i
$213$		0			0
$214$	0.336881	−	1.03681i	0.0230287	−	0.0708751i
$215$	11.2812	+	8.19624i	0.769368	+	0.558979i
$216$		0			0
$217$	−0.572949	+	0.416272i	−0.0388943	+	0.0282584i
$218$	−15.0000			−1.01593
$219$		0			0
$220$	−9.47214			−0.638611
$221$	0.927051	+	0.673542i	0.0623602	+	0.0453073i
$222$		0			0
$223$	−2.78115	+	8.55951i	−0.186240	+	0.573187i	−0.999968	−	0.00805911i	$-0.997435\pi$
$223$	−2.78115	+	8.55951i	−0.186240	+	0.573187i	0.813728	+	0.581246i	$0.197435\pi$
$224$	−3.00000			−0.200446
$225$		0			0
$226$	−3.76393			−0.250373
$227$	−9.07295	+	27.9237i	−0.602193	+	1.85336i	−0.0871483	+	0.996195i	$0.527775\pi$
$227$	−9.07295	+	27.9237i	−0.602193	+	1.85336i	−0.515044	+	0.857163i	$0.672225\pi$
$228$		0			0
$229$	2.07295	+	1.50609i	0.136984	+	0.0995249i	0.654167	−	0.756350i	$-0.273019\pi$
$229$	2.07295	+	1.50609i	0.136984	+	0.0995249i	−0.517183	+	0.855875i	$0.673019\pi$
$230$	1.21885	+	3.75123i	0.0803684	+	0.247348i
$231$		0			0
$232$	9.47214			0.621876
$233$	11.5623	−	8.40051i	0.757472	−	0.550336i	−0.140662	−	0.990058i	$-0.544923\pi$
$233$	11.5623	−	8.40051i	0.757472	−	0.550336i	0.898134	+	0.439722i	$0.144923\pi$
$234$		0			0
$235$	8.25329	+	25.4010i	0.538385	+	1.65698i
$236$	1.38197	−	4.25325i	0.0899583	−	0.276863i
$237$		0			0
$238$	1.06231	+	3.26944i	0.0688591	+	0.211926i
$239$	2.13525	−	6.57164i	0.138118	−	0.425084i	−0.857944	−	0.513743i	$-0.828258\pi$
$239$	2.13525	−	6.57164i	0.138118	−	0.425084i	0.996062	+	0.0886595i	$0.0282583\pi$
$240$		0			0
$241$	4.82624	+	14.8536i	0.310885	+	0.956807i	0.977415	+	0.211328i	$0.0677789\pi$
$241$	4.82624	+	14.8536i	0.310885	+	0.956807i	−0.666530	+	0.745478i	$0.732221\pi$
$242$	−5.61803	+	4.08174i	−0.361141	+	0.262384i
$243$		0			0
$244$	7.16312	−	5.20431i	0.458572	−	0.333172i
$245$	−3.61803	−	2.62866i	−0.231148	−	0.167939i
$246$		0			0
$247$	−4.73607	−	3.44095i	−0.301349	−	0.218943i
$248$	−0.0729490	+	0.224514i	−0.00463227	+	0.0142567i
$249$		0			0
$250$	−9.04508	−	6.57164i	−0.572061	−	0.415627i
$251$	−0.819660			−0.0517365			−0.0258682	−	0.999665i	$-0.508235\pi$
$251$	−0.819660			−0.0517365			−0.0258682	+	0.999665i	$0.508235\pi$
$252$		0			0
$253$	6.04508	+	4.39201i	0.380051	+	0.276123i
$254$	2.85410	+	2.07363i	0.179082	+	0.130111i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−25.7426			−1.60578			−0.802891	−	0.596126i	$-0.796706\pi$
$257$	−25.7426			−1.60578			−0.802891	+	0.596126i	$0.796706\pi$
$258$		0			0
$259$	7.71885	+	23.7562i	0.479626	+	1.47614i
$260$	−1.80902	+	1.31433i	−0.112190	+	0.0815111i
$261$		0			0
$262$	5.07295	+	15.6129i	0.313408	+	0.964570i
$263$	−1.42705	−	4.39201i	−0.0879957	−	0.270823i	0.897369	−	0.441280i	$-0.145476\pi$
$263$	−1.42705	−	4.39201i	−0.0879957	−	0.270823i	−0.985365	+	0.170457i	$0.945476\pi$
$264$		0			0
$265$	−7.23607	−	22.2703i	−0.444508	−	1.36806i
$266$	−5.42705	−	16.7027i	−0.332754	−	1.02411i
$267$		0			0
$268$	−10.2361			−0.625267
$269$	1.54508	−	1.12257i	0.0942055	−	0.0684443i	−0.539685	−	0.841867i	$-0.681457\pi$
$269$	1.54508	−	1.12257i	0.0942055	−	0.0684443i	0.633891	+	0.773422i	$0.281457\pi$
$270$		0			0
$271$	−23.0623	−	16.7557i	−1.40094	−	1.01784i	−0.994564	−	0.104131i	$-0.966794\pi$
$271$	−23.0623	−	16.7557i	−1.40094	−	1.01784i	−0.406372	−	0.913708i	$-0.633206\pi$
$272$	0.927051	+	0.673542i	0.0562107	+	0.0408395i
$273$		0			0
$274$	−5.09017			−0.307508
$275$	−21.1803			−1.27722
$276$		0			0
$277$	0.0901699	−	0.277515i	0.00541779	−	0.0166742i	−0.948311	−	0.317342i	$-0.897210\pi$
$277$	0.0901699	−	0.277515i	0.00541779	−	0.0166742i	0.953729	+	0.300668i	$0.0972096\pi$
$278$	4.30902	+	3.13068i	0.258438	+	0.187766i
$279$		0			0
$280$	−6.70820			−0.400892
$281$	2.57295	−	1.86936i	0.153489	−	0.111516i	−0.508390	−	0.861127i	$-0.669759\pi$
$281$	2.57295	−	1.86936i	0.153489	−	0.111516i	0.661879	+	0.749610i	$0.269759\pi$
$282$		0			0
$283$	9.94427	−	7.22494i	0.591126	−	0.429478i	−0.251592	−	0.967833i	$-0.580954\pi$
$283$	9.94427	−	7.22494i	0.591126	−	0.429478i	0.842718	+	0.538355i	$0.180954\pi$
$284$	0.927051	+	2.85317i	0.0550104	+	0.169304i
$285$		0			0
$286$	−1.30902	+	4.02874i	−0.0774038	+	0.238224i
$287$	1.36475	+	4.20025i	0.0805584	+	0.247933i
$288$		0			0
$289$	−4.84752	+	14.9191i	−0.285148	+	0.877597i
$290$	21.1803			1.24375
$291$		0			0
$292$	−6.23607	+	4.53077i	−0.364938	+	0.265143i
$293$	−8.56231			−0.500215			−0.250108	−	0.968218i	$-0.580466\pi$
$293$	−8.56231			−0.500215			−0.250108	+	0.968218i	$0.580466\pi$
$294$		0			0
$295$	3.09017	−	9.51057i	0.179917	−	0.553727i
$296$	6.73607	+	4.89404i	0.391526	+	0.284460i
$297$		0			0
$298$	−0.690983	+	2.12663i	−0.0400276	+	0.123192i
$299$	1.76393			0.102011
$300$		0			0
$301$	18.7082			1.07832
$302$	−3.00000	+	9.23305i	−0.172631	+	0.531302i
$303$		0			0
$304$	−4.73607	−	3.44095i	−0.271632	−	0.197352i
$305$	16.0172	−	11.6372i	0.917143	−	0.666344i
$306$		0			0
$307$	−23.1246			−1.31979			−0.659896	−	0.751357i	$-0.729400\pi$
$307$	−23.1246			−1.31979			−0.659896	+	0.751357i	$0.729400\pi$
$308$	−10.2812	+	7.46969i	−0.585823	+	0.425625i
$309$		0			0
$310$	−0.163119	+	0.502029i	−0.00926453	+	0.0285133i
$311$	3.06231	−	9.42481i	0.173647	−	0.534432i	−0.825922	−	0.563785i	$-0.809345\pi$
$311$	3.06231	−	9.42481i	0.173647	−	0.534432i	0.999569	+	0.0293530i	$0.00934470\pi$
$312$		0			0
$313$	−5.11803	−	15.7517i	−0.289288	−	0.890338i	−0.985080	−	0.172095i	$-0.944946\pi$
$313$	−5.11803	−	15.7517i	−0.289288	−	0.890338i	0.695792	−	0.718243i	$-0.255054\pi$
$314$	1.40983	−	4.33901i	0.0795613	−	0.244865i
$315$		0			0
$316$	−2.23607	−	6.88191i	−0.125789	−	0.387138i
$317$	6.78115	−	4.92680i	0.380867	−	0.276716i	−0.380835	−	0.924643i	$-0.624364\pi$
$317$	6.78115	−	4.92680i	0.380867	−	0.276716i	0.761703	+	0.647926i	$0.224364\pi$
$318$		0			0
$319$	32.4615	−	23.5847i	1.81749	−	1.32049i
$320$	−1.80902	+	1.31433i	−0.101127	+	0.0734732i
$321$		0			0
$322$	4.28115	+	3.11044i	0.238579	+	0.173338i
$323$	−2.07295	+	6.37988i	−0.115342	+	0.354986i
$324$		0			0
$325$	−4.04508	+	2.93893i	−0.224381	+	0.163022i
$326$	1.85410			0.102689
$327$		0			0
$328$	1.19098	+	0.865300i	0.0657610	+	0.0477782i
$329$	28.9894	+	21.0620i	1.59823	+	1.16119i
$330$		0			0
$331$	12.5902	−	9.14729i	0.692018	−	0.502781i	−0.185305	−	0.982681i	$-0.559327\pi$
$331$	12.5902	−	9.14729i	0.692018	−	0.502781i	0.877323	+	0.479900i	$0.159327\pi$
$332$	4.52786			0.248499
$333$		0			0
$334$	−4.13525	−	12.7270i	−0.226271	−	0.696391i
$335$	−22.8885			−1.25053
$336$		0			0
$337$	−1.41641	−	4.35926i	−0.0771567	−	0.237464i	0.905038	−	0.425331i	$-0.139842\pi$
$337$	−1.41641	−	4.35926i	−0.0771567	−	0.237464i	−0.982194	+	0.187868i	$0.939842\pi$
$338$	−3.70820	−	11.4127i	−0.201700	−	0.620768i
$339$		0			0
$340$	2.07295	+	1.50609i	0.112421	+	0.0816790i
$341$	0.309017	+	0.951057i	0.0167342	+	0.0515026i
$342$		0			0
$343$	15.0000			0.809924
$344$	5.04508	−	3.66547i	0.272013	−	0.197629i
$345$		0			0
$346$	−1.00000	−	0.726543i	−0.0537603	−	0.0390592i
$347$	−17.0623	−	12.3965i	−0.915953	−	0.665478i	0.0265607	−	0.999647i	$-0.491544\pi$
$347$	−17.0623	−	12.3965i	−0.915953	−	0.665478i	−0.942513	+	0.334169i	$0.891544\pi$
$348$		0			0
$349$	−17.7639			−0.950881			−0.475441	−	0.879748i	$-0.657711\pi$
$349$	−17.7639			−0.950881			−0.475441	+	0.879748i	$0.657711\pi$
$350$	−15.0000			−0.801784
$351$		0			0
$352$	−1.30902	+	4.02874i	−0.0697708	+	0.214733i
$353$	−17.1803	−	12.4822i	−0.914417	−	0.664363i	0.0277109	−	0.999616i	$-0.491178\pi$
$353$	−17.1803	−	12.4822i	−0.914417	−	0.664363i	−0.942128	+	0.335253i	$0.891178\pi$
$354$		0			0
$355$	2.07295	+	6.37988i	0.110021	+	0.338609i
$356$	3.61803	−	2.62866i	0.191755	−	0.139318i
$357$		0			0
$358$	9.04508	−	6.57164i	0.478048	−	0.347322i
$359$	2.50000	+	7.69421i	0.131945	+	0.406085i	0.995102	−	0.0988502i	$-0.0315165\pi$
$359$	2.50000	+	7.69421i	0.131945	+	0.406085i	−0.863157	+	0.504935i	$0.831516\pi$
$360$		0			0
$361$	4.71885	−	14.5231i	0.248360	−	0.764375i
$362$	1.67376	+	5.15131i	0.0879710	+	0.270747i
$363$		0			0
$364$	−0.927051	+	2.85317i	−0.0485907	+	0.149547i
$365$	−13.9443	+	10.1311i	−0.729877	+	0.530286i
$366$		0			0
$367$	−28.7533	+	20.8905i	−1.50091	+	1.09047i	−0.530892	+	0.847440i	$0.678143\pi$
$367$	−28.7533	+	20.8905i	−1.50091	+	1.09047i	−0.970018	+	0.243035i	$0.921857\pi$
$368$	1.76393			0.0919513
$369$		0			0
$370$	15.0623	+	10.9434i	0.783052	+	0.568921i
$371$	−25.4164	−	18.4661i	−1.31955	−	0.958712i
$372$		0			0
$373$	−3.63525	+	11.1882i	−0.188226	+	0.579301i	−0.999989	−	0.00468631i	$-0.998508\pi$
$373$	−3.63525	+	11.1882i	−0.188226	+	0.579301i	0.811763	+	0.583987i	$0.198508\pi$
$374$	4.85410			0.251000
$375$		0			0
$376$	11.9443			0.615979
$377$	2.92705	−	9.00854i	0.150751	−	0.463963i
$378$		0			0
$379$	−7.66312	−	5.56758i	−0.393628	−	0.285987i	0.373313	−	0.927706i	$-0.378222\pi$
$379$	−7.66312	−	5.56758i	−0.393628	−	0.285987i	−0.766941	+	0.641718i	$0.778222\pi$
$380$	−10.5902	−	7.69421i	−0.543264	−	0.394705i
$381$		0			0
$382$	13.6525			0.698521
$383$	9.16312	−	6.65740i	0.468214	−	0.340177i	−0.328531	−	0.944493i	$-0.606554\pi$
$383$	9.16312	−	6.65740i	0.468214	−	0.340177i	0.796745	+	0.604316i	$0.206554\pi$
$384$		0			0
$385$	−22.9894	+	16.7027i	−1.17165	+	0.851251i
$386$	−4.52786	+	13.9353i	−0.230462	+	0.709290i
$387$		0			0
$388$	2.95492	+	9.09429i	0.150013	+	0.461693i
$389$	−5.62868	+	17.3233i	−0.285385	+	0.878326i	0.700898	+	0.713262i	$0.252783\pi$
$389$	−5.62868	+	17.3233i	−0.285385	+	0.878326i	−0.986283	+	0.165064i	$0.947217\pi$
$390$		0			0
$391$	−0.624612	−	1.92236i	−0.0315880	−	0.0972178i
$392$	−1.61803	+	1.17557i	−0.0817231	+	0.0593753i
$393$		0			0
$394$	9.70820	−	7.05342i	0.489092	−	0.355346i
$395$	−5.00000	−	15.3884i	−0.251577	−	0.774275i
$396$		0			0
$397$	8.28115	+	6.01661i	0.415619	+	0.301965i	0.775873	−	0.630889i	$-0.217310\pi$
$397$	8.28115	+	6.01661i	0.415619	+	0.301965i	−0.360254	+	0.932854i	$0.617310\pi$
$398$	0.791796	−	2.43690i	0.0396892	−	0.122151i
$399$		0			0
$400$	−4.04508	+	2.93893i	−0.202254	+	0.146946i
$401$	14.1803			0.708132			0.354066	−	0.935220i	$-0.384799\pi$
$401$	14.1803			0.708132			0.354066	+	0.935220i	$0.384799\pi$
$402$		0			0
$403$	0.190983	+	0.138757i	0.00951354	+	0.00691199i
$404$	0.500000	+	0.363271i	0.0248759	+	0.0180734i
$405$		0			0
$406$	22.9894	−	16.7027i	1.14094	−	0.828943i
$407$	35.2705			1.74829
$408$		0			0
$409$	−2.07295	−	6.37988i	−0.102501	−	0.315465i	0.886635	−	0.462470i	$-0.153037\pi$
$409$	−2.07295	−	6.37988i	−0.102501	−	0.315465i	−0.989136	+	0.147005i	$0.953037\pi$
$410$	2.66312	+	1.93487i	0.131522	+	0.0955564i
$411$		0			0
$412$	−4.06231	−	12.5025i	−0.200135	−	0.615954i
$413$	−4.14590	−	12.7598i	−0.204006	−	0.627867i
$414$		0			0
$415$	10.1246			0.496998
$416$	0.309017	+	0.951057i	0.0151508	+	0.0466294i
$417$		0			0
$418$	−24.7984			−1.21293
$419$	18.4164	−	13.3803i	0.899700	−	0.653671i	−0.0386886	−	0.999251i	$-0.512318\pi$
$419$	18.4164	−	13.3803i	0.899700	−	0.653671i	0.938389	+	0.345581i	$0.112318\pi$
$420$		0			0
$421$	−17.2082	−	12.5025i	−0.838677	−	0.609334i	0.0833241	−	0.996522i	$-0.473446\pi$
$421$	−17.2082	−	12.5025i	−0.838677	−	0.609334i	−0.922001	+	0.387188i	$0.873446\pi$
$422$	18.0172	+	13.0903i	0.877065	+	0.637225i
$423$		0			0
$424$	−10.4721			−0.508572
$425$	4.63525	+	3.36771i	0.224843	+	0.163358i
$426$		0			0
$427$	8.20820	−	25.2623i	0.397223	−	1.22253i
$428$	−0.881966	−	0.640786i	−0.0426314	−	0.0309736i
$429$		0			0
$430$	11.2812	−	8.19624i	0.544026	−	0.395258i
$431$	21.0902	−	15.3229i	1.01588	−	0.738078i	0.0504440	−	0.998727i	$-0.483936\pi$
$431$	21.0902	−	15.3229i	1.01588	−	0.738078i	0.965434	+	0.260649i	$0.0839364\pi$
$432$		0			0
$433$	17.2812	−	12.5555i	0.830479	−	0.603378i	−0.0892157	−	0.996012i	$-0.528436\pi$
$433$	17.2812	−	12.5555i	0.830479	−	0.603378i	0.919695	+	0.392634i	$0.128436\pi$
$434$	0.218847	+	0.673542i	0.0105050	+	0.0323310i
$435$		0			0
$436$	−4.63525	+	14.2658i	−0.221988	+	0.683210i
$437$	3.19098	+	9.82084i	0.152645	+	0.469794i
$438$		0			0
$439$	7.92705	−	24.3970i	0.378338	−	1.16440i	−0.562862	−	0.826551i	$-0.690300\pi$
$439$	7.92705	−	24.3970i	0.378338	−	1.16440i	0.941199	−	0.337852i	$-0.109700\pi$
$440$	−2.92705	+	9.00854i	−0.139542	+	0.429465i
$441$		0			0
$442$	0.927051	−	0.673542i	0.0440953	−	0.0320371i
$443$	−19.4164			−0.922501			−0.461251	−	0.887270i	$-0.652599\pi$
$443$	−19.4164			−0.922501			−0.461251	+	0.887270i	$0.652599\pi$
$444$		0			0
$445$	8.09017	−	5.87785i	0.383511	−	0.278637i
$446$	7.28115	+	5.29007i	0.344773	+	0.250492i
$447$		0			0
$448$	−0.927051	+	2.85317i	−0.0437990	+	0.134800i
$449$	3.94427			0.186142			0.0930709	−	0.995659i	$-0.470332\pi$
$449$	3.94427			0.186142			0.0930709	+	0.995659i	$0.470332\pi$
$450$		0			0
$451$	6.23607			0.293645
$452$	−1.16312	+	3.57971i	−0.0547085	+	0.168375i
$453$		0			0
$454$	23.7533	+	17.2578i	1.11480	+	0.809947i
$455$	−2.07295	+	6.37988i	−0.0971813	+	0.299093i
$456$		0			0
$457$	40.2148			1.88117			0.940584	−	0.339561i	$-0.110278\pi$
$457$	40.2148			1.88117			0.940584	+	0.339561i	$0.110278\pi$
$458$	2.07295	−	1.50609i	0.0968625	−	0.0703748i
$459$		0			0
$460$	3.94427			0.183903
$461$	−1.79837	+	5.53483i	−0.0837586	+	0.257783i	−0.984161	−	0.177275i	$-0.943272\pi$
$461$	−1.79837	+	5.53483i	−0.0837586	+	0.257783i	0.900403	+	0.435057i	$0.143272\pi$
$462$		0			0
$463$	−10.8090	−	33.2667i	−0.502338	−	1.54604i	−0.805201	−	0.593002i	$-0.797943\pi$
$463$	−10.8090	−	33.2667i	−0.502338	−	1.54604i	0.302863	−	0.953034i	$-0.402057\pi$
$464$	2.92705	−	9.00854i	0.135885	−	0.418211i
$465$		0			0
$466$	−4.41641	−	13.5923i	−0.204586	−	0.629651i
$467$	−15.5172	+	11.2739i	−0.718051	+	0.521695i	−0.885761	−	0.464142i	$-0.846363\pi$
$467$	−15.5172	+	11.2739i	−0.718051	+	0.521695i	0.167710	+	0.985836i	$0.446363\pi$
$468$		0			0
$469$	−24.8435	+	18.0498i	−1.14716	+	0.833464i
$470$	26.7082			1.23196
$471$		0			0
$472$	−3.61803	−	2.62866i	−0.166534	−	0.120994i
$473$	8.16312	−	25.1235i	0.375341	−	1.15518i
$474$		0			0
$475$	−23.6803	−	17.2048i	−1.08653	−	0.789409i
$476$	3.43769			0.157566
$477$		0			0
$478$	−5.59017	−	4.06150i	−0.255688	−	0.185769i
$479$	−12.2984	−	8.93529i	−0.561927	−	0.408264i	0.270237	−	0.962794i	$-0.412898\pi$
$479$	−12.2984	−	8.93529i	−0.561927	−	0.408264i	−0.832164	+	0.554530i	$0.812898\pi$
$480$		0			0
$481$	6.73607	−	4.89404i	0.307138	−	0.223149i
$482$	15.6180			0.711382
$483$		0			0
$484$	2.14590	+	6.60440i	0.0975408	+	0.300200i
$485$	6.60739	+	20.3355i	0.300026	+	0.923386i
$486$		0			0
$487$	6.83688	+	21.0418i	0.309809	+	0.953493i	0.977839	+	0.209359i	$0.0671377\pi$
$487$	6.83688	+	21.0418i	0.309809	+	0.953493i	−0.668030	+	0.744134i	$0.732862\pi$
$488$	−2.73607	−	8.42075i	−0.123856	−	0.381190i
$489$		0			0
$490$	−3.61803	+	2.62866i	−0.163446	+	0.118751i
$491$	−5.94427	−	18.2946i	−0.268261	−	0.825623i	−0.990924	−	0.134423i	$-0.957082\pi$
$491$	−5.94427	−	18.2946i	−0.268261	−	0.825623i	0.722663	−	0.691201i	$-0.242918\pi$
$492$		0			0
$493$	−10.8541			−0.488844
$494$	−4.73607	+	3.44095i	−0.213086	+	0.154816i
$495$		0			0
$496$	0.190983	+	0.138757i	0.00857539	+	0.00623039i
$497$	7.28115	+	5.29007i	0.326604	+	0.237292i
$498$		0			0
$499$	34.1459			1.52858			0.764290	−	0.644873i	$-0.223090\pi$
$499$	34.1459			1.52858			0.764290	+	0.644873i	$0.223090\pi$
$500$	−9.04508	+	6.57164i	−0.404508	+	0.293893i
$501$		0			0
$502$	−0.253289	+	0.779543i	−0.0113048	+	0.0347927i
$503$	−24.6803	−	17.9313i	−1.10044	−	0.799518i	−0.119310	−	0.992857i	$-0.538068\pi$
$503$	−24.6803	−	17.9313i	−1.10044	−	0.799518i	−0.981132	+	0.193339i	$0.938068\pi$
$504$		0			0
$505$	1.11803	+	0.812299i	0.0497519	+	0.0361468i
$506$	6.04508	−	4.39201i	0.268737	−	0.195249i
$507$		0			0
$508$	2.85410	−	2.07363i	0.126630	−	0.0920023i
$509$	0.590170	+	1.81636i	0.0261588	+	0.0805086i	0.963284	−	0.268486i	$-0.0865232\pi$
$509$	0.590170	+	1.81636i	0.0261588	+	0.0805086i	−0.937125	+	0.348994i	$0.886523\pi$
$510$		0			0
$511$	−7.14590	+	21.9928i	−0.316116	+	0.972905i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	−7.95492	+	24.4827i	−0.350876	+	1.07989i
$515$	−9.08359	−	27.9564i	−0.400271	−	1.23191i
$516$		0			0
$517$	40.9336	−	29.7400i	1.80026	−	1.30796i
$518$	24.9787			1.09750
$519$		0			0
$520$	0.690983	+	2.12663i	0.0303016	+	0.0932588i
$521$	−18.9721	−	13.7841i	−0.831184	−	0.603891i	0.0887098	−	0.996058i	$-0.471726\pi$
$521$	−18.9721	−	13.7841i	−0.831184	−	0.603891i	−0.919894	+	0.392167i	$0.871726\pi$
$522$		0			0
$523$	−1.43769	+	4.42477i	−0.0628660	+	0.193482i	−0.977557	−	0.210673i	$-0.932434\pi$
$523$	−1.43769	+	4.42477i	−0.0628660	+	0.193482i	0.914691	+	0.404155i	$0.132434\pi$
$524$	16.4164			0.717154
$525$		0			0
$526$	−4.61803			−0.201356
$527$	0.0835921	−	0.257270i	0.00364133	−	0.0112069i
$528$		0			0
$529$	16.0902	+	11.6902i	0.699573	+	0.508269i
$530$	−23.4164			−1.01714
$531$		0			0
$532$	−17.5623			−0.761423
$533$	1.19098	−	0.865300i	0.0515872	−	0.0374803i
$534$		0			0
$535$	−1.97214	−	1.43284i	−0.0852629	−	0.0619471i
$536$	−3.16312	+	9.73508i	−0.136626	+	0.420491i
$537$		0			0
$538$	−0.590170	−	1.81636i	−0.0254440	−	0.0783087i
$539$	−2.61803	+	8.05748i	−0.112767	+	0.347060i
$540$		0			0
$541$	4.72542	+	14.5434i	0.203162	+	0.625268i	0.999784	+	0.0207902i	$0.00661819\pi$
$541$	4.72542	+	14.5434i	0.203162	+	0.625268i	−0.796622	+	0.604478i	$0.793382\pi$
$542$	−23.0623	+	16.7557i	−0.990611	+	0.719721i
$543$		0			0
$544$	0.927051	−	0.673542i	0.0397470	−	0.0288779i
$545$	−10.3647	+	31.8994i	−0.443977	+	1.36642i
$546$		0			0
$547$	−6.78115	−	4.92680i	−0.289941	−	0.210655i	0.433301	−	0.901249i	$-0.357349\pi$
$547$	−6.78115	−	4.92680i	−0.289941	−	0.210655i	−0.723242	+	0.690595i	$0.757349\pi$
$548$	−1.57295	+	4.84104i	−0.0671931	+	0.206799i
$549$		0			0
$550$	−6.54508	+	20.1437i	−0.279083	+	0.858930i
$551$	55.4508			2.36229
$552$		0			0
$553$	−17.5623	−	12.7598i	−0.746825	−	0.542600i
$554$	−0.236068	−	0.171513i	−0.0100296	−	0.00728691i
$555$		0			0
$556$	4.30902	−	3.13068i	0.182743	−	0.132771i
$557$	−24.8885			−1.05456			−0.527281	−	0.849691i	$-0.676788\pi$
$557$	−24.8885			−1.05456			−0.527281	+	0.849691i	$0.676788\pi$
$558$		0			0
$559$	−1.92705	−	5.93085i	−0.0815056	−	0.250848i
$560$	−2.07295	+	6.37988i	−0.0875981	+	0.269599i
$561$		0			0
$562$	−0.982779	−	3.02468i	−0.0414560	−	0.127589i
$563$	8.69756	+	26.7683i	0.366558	+	1.12815i	0.948999	+	0.315278i	$0.102098\pi$
$563$	8.69756	+	26.7683i	0.366558	+	1.12815i	−0.582441	+	0.812873i	$0.697902\pi$
$564$		0			0
$565$	−2.60081	+	8.00448i	−0.109417	+	0.336751i
$566$	−3.79837	−	11.6902i	−0.159658	−	0.491375i
$567$		0			0
$568$	3.00000			0.125877
$569$	14.3713	−	10.4414i	0.602477	−	0.437725i	−0.244280	−	0.969705i	$-0.578552\pi$
$569$	14.3713	−	10.4414i	0.602477	−	0.437725i	0.846757	+	0.531979i	$0.178552\pi$
$570$		0			0
$571$	−14.0172	−	10.1841i	−0.586602	−	0.426192i	0.254496	−	0.967074i	$-0.418090\pi$
$571$	−14.0172	−	10.1841i	−0.586602	−	0.426192i	−0.841098	+	0.540882i	$0.818090\pi$
$572$	3.42705	+	2.48990i	0.143292	+	0.104108i
$573$		0			0
$574$	4.41641			0.184337
$575$	8.81966			0.367805
$576$		0			0
$577$	−13.2877	+	40.8954i	−0.553175	+	1.70250i	0.147538	+	0.989056i	$0.452865\pi$
$577$	−13.2877	+	40.8954i	−0.553175	+	1.70250i	−0.700714	+	0.713443i	$0.747135\pi$
$578$	12.6910	+	9.22054i	0.527875	+	0.383524i
$579$		0			0
$580$	6.54508	−	20.1437i	0.271770	−	0.836422i
$581$	10.9894	−	7.98424i	0.455915	−	0.331242i
$582$		0			0
$583$	−35.8885	+	26.0746i	−1.48635	+	1.07990i
$584$	2.38197	+	7.33094i	0.0985665	+	0.303356i
$585$		0			0
$586$	−2.64590	+	8.14324i	−0.109301	+	0.336394i
$587$	10.5623	+	32.5074i	0.435953	+	1.34173i	0.892107	+	0.451824i	$0.149227\pi$
$587$	10.5623	+	32.5074i	0.435953	+	1.34173i	−0.456154	+	0.889901i	$0.650773\pi$
$588$		0			0
$589$	−0.427051	+	1.31433i	−0.0175963	+	0.0541559i
$590$	−8.09017	−	5.87785i	−0.333067	−	0.241987i
$591$		0			0
$592$	6.73607	−	4.89404i	0.276851	−	0.201144i
$593$	−29.0132			−1.19143			−0.595714	−	0.803197i	$-0.703131\pi$
$593$	−29.0132			−1.19143			−0.595714	+	0.803197i	$0.703131\pi$
$594$		0			0
$595$	7.68692			0.315133
$596$	1.80902	+	1.31433i	0.0741002	+	0.0538370i
$597$		0			0
$598$	0.545085	−	1.67760i	0.0222902	−	0.0686021i
$599$	−8.94427			−0.365453			−0.182727	−	0.983164i	$-0.558492\pi$
$599$	−8.94427			−0.365453			−0.182727	+	0.983164i	$0.558492\pi$
$600$		0			0
$601$	38.8328			1.58402			0.792012	−	0.610506i	$-0.209034\pi$
$601$	38.8328			1.58402			0.792012	+	0.610506i	$0.209034\pi$
$602$	5.78115	−	17.7926i	0.235622	−	0.725171i
$603$		0			0
$604$	7.85410	+	5.70634i	0.319579	+	0.232188i
$605$	4.79837	+	14.7679i	0.195082	+	0.600400i
$606$		0			0
$607$	−33.8541			−1.37410			−0.687048	−	0.726612i	$-0.741094\pi$
$607$	−33.8541			−1.37410			−0.687048	+	0.726612i	$0.741094\pi$
$608$	−4.73607	+	3.44095i	−0.192073	+	0.139549i
$609$		0			0
$610$	−6.11803	−	18.8294i	−0.247712	−	0.762379i
$611$	3.69098	−	11.3597i	0.149321	−	0.459563i
$612$		0			0
$613$	−6.62461	−	20.3885i	−0.267566	−	0.823482i	−0.991091	−	0.133185i	$-0.957480\pi$
$613$	−6.62461	−	20.3885i	−0.267566	−	0.823482i	0.723526	−	0.690297i	$-0.242520\pi$
$614$	−7.14590	+	21.9928i	−0.288385	+	0.887558i
$615$		0			0
$616$	3.92705	+	12.0862i	0.158225	+	0.486968i
$617$	11.6180	−	8.44100i	0.467724	−	0.339822i	−0.328829	−	0.944389i	$-0.606654\pi$
$617$	11.6180	−	8.44100i	0.467724	−	0.339822i	0.796554	+	0.604568i	$0.206654\pi$
$618$		0			0
$619$	−37.9894	+	27.6009i	−1.52692	+	1.10937i	−0.569002	+	0.822336i	$0.692670\pi$
$619$	−37.9894	+	27.6009i	−1.52692	+	1.10937i	−0.957920	+	0.287037i	$0.907330\pi$
$620$	0.427051	+	0.310271i	0.0171508	+	0.0124608i
$621$		0			0
$622$	−8.01722	−	5.82485i	−0.321461	−	0.233555i
$623$	4.14590	−	12.7598i	0.166102	−	0.511209i
$624$		0			0
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$	−16.5623			−0.661963
$627$		0			0
$628$	−3.69098	−	2.68166i	−0.147286	−	0.107010i
$629$	−7.71885	−	5.60807i	−0.307771	−	0.223608i
$630$		0			0
$631$	36.2705	−	26.3521i	1.44391	−	1.04906i	0.456698	−	0.889622i	$-0.349032\pi$
$631$	36.2705	−	26.3521i	1.44391	−	1.04906i	0.987208	−	0.159438i	$-0.0509681\pi$
$632$	−7.23607			−0.287835
$633$		0			0
$634$	−2.59017	−	7.97172i	−0.102869	−	0.316598i
$635$	6.38197	−	4.63677i	0.253261	−	0.184005i
$636$		0			0
$637$	0.618034	+	1.90211i	0.0244874	+	0.0753645i
$638$	−12.3992	−	38.1608i	−0.490889	−	1.51080i
$639$		0			0
$640$	0.690983	+	2.12663i	0.0273135	+	0.0840623i
$641$	9.38197	+	28.8747i	0.370565	+	1.14048i	0.946422	+	0.322932i	$0.104669\pi$
$641$	9.38197	+	28.8747i	0.370565	+	1.14048i	−0.575857	+	0.817551i	$0.695331\pi$
$642$		0			0
$643$	−31.7639			−1.25265			−0.626324	−	0.779563i	$-0.715441\pi$
$643$	−31.7639			−1.25265			−0.626324	+	0.779563i	$0.715441\pi$
$644$	4.28115	−	3.11044i	0.168701	−	0.122568i
$645$		0			0
$646$	5.42705	+	3.94298i	0.213524	+	0.155135i
$647$	−19.1353	−	13.9026i	−0.752284	−	0.546567i	0.144250	−	0.989541i	$-0.453923\pi$
$647$	−19.1353	−	13.9026i	−0.752284	−	0.546567i	−0.896534	+	0.442975i	$0.853923\pi$
$648$		0			0
$649$	−18.9443			−0.743628
$650$	1.54508	+	4.75528i	0.0606032	+	0.186518i
$651$		0			0
$652$	0.572949	−	1.76336i	0.0224384	−	0.0690583i
$653$	−6.95492	−	5.05304i	−0.272167	−	0.197741i	0.443327	−	0.896360i	$-0.353798\pi$
$653$	−6.95492	−	5.05304i	−0.272167	−	0.197741i	−0.715494	+	0.698619i	$0.753798\pi$
$654$		0			0
$655$	36.7082			1.43431
$656$	1.19098	−	0.865300i	0.0465001	−	0.0337843i
$657$		0			0
$658$	28.9894	−	21.0620i	1.13012	−	0.821082i
$659$	7.92705	+	24.3970i	0.308794	+	0.950370i	0.978234	+	0.207504i	$0.0665341\pi$
$659$	7.92705	+	24.3970i	0.308794	+	0.950370i	−0.669440	+	0.742866i	$0.733466\pi$
$660$		0			0
$661$	−8.42705	+	25.9358i	−0.327774	+	1.00879i	0.642398	+	0.766371i	$0.277939\pi$
$661$	−8.42705	+	25.9358i	−0.327774	+	1.00879i	−0.970173	+	0.242415i	$0.922061\pi$
$662$	−4.80902	−	14.8006i	−0.186908	−	0.575243i
$663$		0			0
$664$	1.39919	−	4.30625i	0.0542990	−	0.167115i
$665$	−39.2705			−1.52285
$666$		0			0
$667$	−13.5172	+	9.82084i	−0.523389	+	0.380264i
$668$	−13.3820			−0.517764
$669$		0			0
$670$	−7.07295	+	21.7683i	−0.273252	+	0.840983i
$671$	−30.3435	−	22.0458i	−1.17140	−	0.851069i
$672$		0			0
$673$	1.00000	−	3.07768i	0.0385472	−	0.118636i	−0.929931	−	0.367733i	$-0.880134\pi$
$673$	1.00000	−	3.07768i	0.0385472	−	0.118636i	0.968478	+	0.249097i	$0.0801339\pi$
$674$	−4.58359			−0.176553
$675$		0			0
$676$	−12.0000			−0.461538
$677$	−2.59017	+	7.97172i	−0.0995483	+	0.306378i	−0.988412	−	0.151793i	$-0.951495\pi$
$677$	−2.59017	+	7.97172i	−0.0995483	+	0.306378i	0.888864	+	0.458171i	$0.151495\pi$
$678$		0			0
$679$	23.2082	+	16.8617i	0.890649	+	0.647094i
$680$	2.07295	−	1.50609i	0.0794940	−	0.0577557i
$681$		0			0
$682$	1.00000			0.0382920
$683$	−9.19098	+	6.67764i	−0.351683	+	0.255513i	−0.749575	−	0.661920i	$-0.769742\pi$
$683$	−9.19098	+	6.67764i	−0.351683	+	0.255513i	0.397892	+	0.917432i	$0.369742\pi$
$684$		0			0
$685$	−3.51722	+	10.8249i	−0.134386	+	0.413598i
$686$	4.63525	−	14.2658i	0.176975	−	0.544673i
$687$		0			0
$688$	−1.92705	−	5.93085i	−0.0734681	−	0.226112i
$689$	−3.23607	+	9.95959i	−0.123284	+	0.379430i
$690$		0			0
$691$	−9.97214	−	30.6911i	−0.379358	−	1.16754i	−0.940491	−	0.339818i	$-0.889634\pi$
$691$	−9.97214	−	30.6911i	−0.379358	−	1.16754i	0.561133	−	0.827725i	$-0.310366\pi$
$692$	−1.00000	+	0.726543i	−0.0380143	+	0.0276190i
$693$		0			0
$694$	−17.0623	+	12.3965i	−0.647676	+	0.470564i
$695$	9.63525	−	7.00042i	0.365486	−	0.265541i
$696$		0			0
$697$	−1.36475	−	0.991545i	−0.0516934	−	0.0375575i
$698$	−5.48936	+	16.8945i	−0.207775	+	0.639466i
$699$		0			0
$700$	−4.63525	+	14.2658i	−0.175196	+	0.539198i
$701$	−18.1803			−0.686662			−0.343331	−	0.939214i	$-0.611555\pi$
$701$	−18.1803			−0.686662			−0.343331	+	0.939214i	$0.611555\pi$
$702$		0			0
$703$	39.4336	+	28.6502i	1.48727	+	1.08056i
$704$	3.42705	+	2.48990i	0.129162	+	0.0938416i
$705$		0			0
$706$	−17.1803	+	12.4822i	−0.646591	+	0.469776i
$707$	1.85410			0.0697307
$708$		0			0
$709$	3.78115	+	11.6372i	0.142004	+	0.437044i	0.996614	−	0.0822274i	$-0.0262034\pi$
$709$	3.78115	+	11.6372i	0.142004	+	0.437044i	−0.854609	+	0.519271i	$0.826203\pi$
$710$	6.70820			0.251754
$711$		0			0
$712$	−1.38197	−	4.25325i	−0.0517914	−	0.159397i
$713$	−0.128677	−	0.396027i	−0.00481900	−	0.0148313i
$714$		0			0
$715$	7.66312	+	5.56758i	0.286584	+	0.208216i
$716$	−3.45492	−	10.6331i	−0.129116	−	0.397379i
$717$		0			0
$718$	8.09017			0.301922
$719$	9.30902	−	6.76340i	0.347168	−	0.252232i	−0.400512	−	0.916291i	$-0.631168\pi$
$719$	9.30902	−	6.76340i	0.347168	−	0.252232i	0.747680	+	0.664059i	$0.231168\pi$
$720$		0			0
$721$	−31.9058	−	23.1809i	−1.18823	−	0.863302i
$722$	−12.3541	−	8.97578i	−0.459772	−	0.334044i
$723$		0			0
$724$	5.41641			0.201299
$725$	14.6353	−	45.0427i	0.543540	−	1.67284i
$726$		0			0
$727$	0.819660	−	2.52265i	0.0303995	−	0.0935601i	−0.934706	−	0.355423i	$-0.884337\pi$
$727$	0.819660	−	2.52265i	0.0303995	−	0.0935601i	0.965105	+	0.261863i	$0.0843368\pi$
$728$	2.42705	+	1.76336i	0.0899525	+	0.0653543i
$729$		0			0
$730$	5.32624	+	16.3925i	0.197133	+	0.606713i
$731$	−5.78115	+	4.20025i	−0.213824	+	0.155352i
$732$		0			0
$733$	−25.7082	+	18.6781i	−0.949554	+	0.689891i	−0.950701	−	0.310108i	$-0.899635\pi$
$733$	−25.7082	+	18.6781i	−0.949554	+	0.689891i	0.00114721	+	0.999999i	$0.499635\pi$
$734$	10.9828	+	33.8015i	0.405382	+	1.24764i
$735$		0			0
$736$	0.545085	−	1.67760i	0.0200921	−	0.0618371i
$737$	13.3992	+	41.2385i	0.493565	+	1.51904i
$738$		0			0
$739$	9.27051	−	28.5317i	0.341021	−	1.04956i	−0.622658	−	0.782494i	$-0.713947\pi$
$739$	9.27051	−	28.5317i	0.341021	−	1.04956i	0.963679	−	0.267062i	$-0.0860527\pi$
$740$	15.0623	−	10.9434i	0.553701	−	0.402288i
$741$		0			0
$742$	−25.4164	+	18.4661i	−0.933066	+	0.677912i
$743$	−15.2705			−0.560221			−0.280110	−	0.959968i	$-0.590371\pi$
$743$	−15.2705			−0.560221			−0.280110	+	0.959968i	$0.590371\pi$
$744$		0			0
$745$	4.04508	+	2.93893i	0.148200	+	0.107674i
$746$	9.51722	+	6.91467i	0.348450	+	0.253164i
$747$		0			0
$748$	1.50000	−	4.61653i	0.0548454	−	0.168797i
$749$	−3.27051			−0.119502
$750$		0			0
$751$	7.85410			0.286600			0.143300	−	0.989679i	$-0.454229\pi$
$751$	7.85410			0.286600			0.143300	+	0.989679i	$0.454229\pi$
$752$	3.69098	−	11.3597i	0.134596	−	0.414245i
$753$		0			0
$754$	−7.66312	−	5.56758i	−0.279074	−	0.202759i
$755$	17.5623	+	12.7598i	0.639158	+	0.464375i
$756$		0			0
$757$	−16.4164			−0.596664			−0.298332	−	0.954462i	$-0.596430\pi$
$757$	−16.4164			−0.596664			−0.298332	+	0.954462i	$0.596430\pi$
$758$	−7.66312	+	5.56758i	−0.278337	+	0.202224i
$759$		0			0
$760$	−10.5902	+	7.69421i	−0.384146	+	0.279098i
$761$	−8.31966	+	25.6053i	−0.301587	+	0.928191i	0.679341	+	0.733823i	$0.262266\pi$
$761$	−8.31966	+	25.6053i	−0.301587	+	0.928191i	−0.980929	+	0.194368i	$0.937734\pi$
$762$		0			0
$763$	13.9058	+	42.7975i	0.503422	+	1.54938i
$764$	4.21885	−	12.9843i	0.152633	−	0.469755i
$765$		0			0
$766$	−3.50000	−	10.7719i	−0.126460	−	0.389204i
$767$	−3.61803	+	2.62866i	−0.130640	+	0.0949153i
$768$		0			0
$769$	−2.76393	+	2.00811i	−0.0996699	+	0.0724144i	−0.636504	−	0.771273i	$-0.719620\pi$
$769$	−2.76393	+	2.00811i	−0.0996699	+	0.0724144i	0.536834	+	0.843688i	$0.319620\pi$
$770$	8.78115	+	27.0256i	0.316451	+	0.973935i
$771$		0			0
$772$	11.8541	+	8.61251i	0.426638	+	0.309971i
$773$	−9.51722	+	29.2910i	−0.342311	+	1.05352i	0.620697	+	0.784050i	$0.286850\pi$
$773$	−9.51722	+	29.2910i	−0.342311	+	1.05352i	−0.963008	+	0.269473i	$0.913150\pi$
$774$		0			0
$775$	0.954915	+	0.693786i	0.0343016	+	0.0249215i
$776$	9.56231			0.343267
$777$		0			0
$778$	14.7361	+	10.7064i	0.528314	+	0.383842i
$779$	6.97214	+	5.06555i	0.249803	+	0.181492i
$780$		0			0
$781$	10.2812	−	7.46969i	0.367889	−	0.267287i
$782$	−2.02129			−0.0722810
$783$		0			0
$784$	0.618034	+	1.90211i	0.0220726	+	0.0679326i
$785$	−8.25329	−	5.99637i	−0.294573	−	0.214019i
$786$		0			0
$787$	−3.52786	−	10.8576i	−0.125755	−	0.387033i	0.868283	−	0.496069i	$-0.165224\pi$
$787$	−3.52786	−	10.8576i	−0.125755	−	0.387033i	−0.994038	+	0.109036i	$0.965224\pi$
$788$	−3.70820	−	11.4127i	−0.132099	−	0.406560i
$789$		0			0
$790$	−16.1803			−0.575671
$791$	3.48936	+	10.7391i	0.124067	+	0.381840i
$792$		0			0
$793$	−8.85410			−0.314418
$794$	8.28115	−	6.01661i	0.293887	−	0.213521i
$795$		0			0
$796$	−2.07295	−	1.50609i	−0.0734737	−	0.0533818i
$797$	4.54508	+	3.30220i	0.160995	+	0.116970i	0.665366	−	0.746517i	$-0.268276\pi$
$797$	4.54508	+	3.30220i	0.160995	+	0.116970i	−0.504371	+	0.863487i	$0.668276\pi$
$798$		0			0
$799$	−13.6869			−0.484208
$800$	1.54508	+	4.75528i	0.0546270	+	0.168125i
$801$		0			0
$802$	4.38197	−	13.4863i	0.154733	−	0.476218i
$803$	26.4164	+	19.1926i	0.932215	+	0.677294i
$804$		0			0
$805$	9.57295	−	6.95515i	0.337402	−	0.245137i
$806$	0.190983	−	0.138757i	0.00672709	−	0.00488752i
$807$		0			0
$808$	0.500000	−	0.363271i	0.0175899	−	0.0127798i
$809$	0.690983	+	2.12663i	0.0242937	+	0.0747682i	0.962468	−	0.271394i	$-0.0874847\pi$
$809$	0.690983	+	2.12663i	0.0242937	+	0.0747682i	−0.938175	+	0.346162i	$0.887485\pi$
$810$		0			0
$811$	12.6525	−	38.9403i	0.444289	−	1.36738i	−0.438974	−	0.898500i	$-0.644658\pi$
$811$	12.6525	−	38.9403i	0.444289	−	1.36738i	0.883262	−	0.468880i	$-0.155342\pi$
$812$	−8.78115	−	27.0256i	−0.308158	−	0.948413i
$813$		0			0
$814$	10.8992	−	33.5442i	0.382016	−	1.17573i
$815$	1.28115	−	3.94298i	0.0448768	−	0.138117i
$816$		0			0
$817$	29.5344	−	21.4580i	1.03328	−	0.750721i
$818$	−6.70820			−0.234547
$819$		0			0
$820$	2.66312	−	1.93487i	0.0930001	−	0.0675686i
$821$	31.6803	+	23.0171i	1.10565	+	0.803303i	0.981973	−	0.189020i	$-0.0605310\pi$
$821$	31.6803	+	23.0171i	1.10565	+	0.803303i	0.123678	+	0.992322i	$0.460531\pi$
$822$		0			0
$823$	−6.43769	+	19.8132i	−0.224404	+	0.690644i	0.773948	+	0.633250i	$0.218279\pi$
$823$	−6.43769	+	19.8132i	−0.224404	+	0.690644i	−0.998352	+	0.0573946i	$0.981721\pi$
$824$	−13.1459			−0.457959
$825$		0			0
$826$	−13.4164			−0.466817
$827$	1.55573	−	4.78804i	0.0540980	−	0.166496i	−0.920357	−	0.391079i	$-0.872102\pi$
$827$	1.55573	−	4.78804i	0.0540980	−	0.166496i	0.974455	+	0.224583i	$0.0721019\pi$
$828$		0			0
$829$	−43.2148	−	31.3974i	−1.50091	−	1.09048i	−0.970017	−	0.243038i	$-0.921856\pi$
$829$	−43.2148	−	31.3974i	−1.50091	−	1.09048i	−0.530895	−	0.847438i	$-0.678144\pi$
$830$	3.12868	−	9.62908i	0.108598	−	0.334230i
$831$		0			0
$832$	1.00000			0.0346688
$833$	1.85410	−	1.34708i	0.0642408	−	0.0466737i
$834$		0			0
$835$	−29.9230			−1.03553
$836$	−7.66312	+	23.5847i	−0.265035	+	0.815692i
$837$		0			0
$838$	−7.03444	−	21.6498i	−0.243001	−	0.747879i
$839$	17.0729	−	52.5451i	0.589424	−	1.81406i	0.00869515	−	0.999962i	$-0.497232\pi$
$839$	17.0729	−	52.5451i	0.589424	−	1.81406i	0.580729	−	0.814097i	$-0.302768\pi$
$840$		0			0
$841$	18.7639	+	57.7494i	0.647032	+	1.99136i
$842$	−17.2082	+	12.5025i	−0.593034	+	0.430864i
$843$		0			0
$844$	18.0172	−	13.0903i	0.620178	−	0.450586i
$845$	−26.8328			−0.923077
$846$		0			0
$847$	16.8541	+	12.2452i	0.579114	+	0.420751i
$848$	−3.23607	+	9.95959i	−0.111127	+	0.342014i
$849$		0			0
$850$	4.63525	−	3.36771i	0.158988	−	0.115511i
$851$	−14.6869			−0.503461
$852$		0			0
$853$	14.6803	+	10.6659i	0.502645	+	0.365193i	0.810026	−	0.586393i	$-0.199453\pi$
$853$	14.6803	+	10.6659i	0.502645	+	0.365193i	−0.307381	+	0.951586i	$0.599453\pi$
$854$	−21.4894	−	15.6129i	−0.735351	−	0.534264i
$855$		0			0
$856$	−0.881966	+	0.640786i	−0.0301450	+	0.0219016i
$857$	56.3394			1.92452			0.962259	−	0.272137i	$-0.0877304\pi$
$857$	56.3394			1.92452			0.962259	+	0.272137i	$0.0877304\pi$
$858$		0			0
$859$	10.6287	+	32.7117i	0.362646	+	1.11611i	0.951442	+	0.307828i	$0.0996020\pi$
$859$	10.6287	+	32.7117i	0.362646	+	1.11611i	−0.588796	+	0.808281i	$0.700398\pi$
$860$	−4.30902	−	13.2618i	−0.146936	−	0.452223i
$861$		0			0
$862$	−8.05573	−	24.7930i	−0.274379	−	0.844452i
$863$	3.47214	+	10.6861i	0.118193	+	0.363760i	0.992600	−	0.121433i	$-0.0387491\pi$
$863$	3.47214	+	10.6861i	0.118193	+	0.363760i	−0.874407	+	0.485194i	$0.838749\pi$
$864$		0			0
$865$	−2.23607	+	1.62460i	−0.0760286	+	0.0552380i
$866$	−6.60081	−	20.3152i	−0.224305	−	0.690339i
$867$		0			0
$868$	0.708204			0.0240380
$869$	−24.7984	+	18.0171i	−0.841227	+	0.611187i
$870$		0			0
$871$	8.28115	+	6.01661i	0.280596	+	0.203865i
$872$	12.1353	+	8.81678i	0.410952	+	0.298574i
$873$		0			0
$874$	10.3262			0.349290
$875$	−10.3647	+	31.8994i	−0.350392	+	1.07840i
$876$		0			0
$877$	1.37132	−	4.22050i	0.0463063	−	0.142516i	−0.925230	−	0.379406i	$-0.876128\pi$
$877$	1.37132	−	4.22050i	0.0463063	−	0.142516i	0.971536	+	0.236890i	$0.0761282\pi$
$878$	−20.7533	−	15.0781i	−0.700390	−	0.508863i
$879$		0			0
$880$	7.66312	+	5.56758i	0.258324	+	0.187683i
$881$	30.8885	−	22.4418i	1.04066	−	0.756085i	0.0702469	−	0.997530i	$-0.477621\pi$
$881$	30.8885	−	22.4418i	1.04066	−	0.756085i	0.970415	+	0.241445i	$0.0776213\pi$
$882$		0			0
$883$	33.7254	−	24.5030i	1.13495	−	0.824590i	0.148543	−	0.988906i	$-0.452542\pi$
$883$	33.7254	−	24.5030i	1.13495	−	0.824590i	0.986408	+	0.164316i	$0.0525416\pi$
$884$	−0.354102	−	1.08981i	−0.0119097	−	0.0366544i
$885$		0			0
$886$	−6.00000	+	18.4661i	−0.201574	+	0.620381i
$887$	−10.2533	−	31.5564i	−0.344272	−	1.05956i	−0.961973	−	0.273146i	$-0.911936\pi$
$887$	−10.2533	−	31.5564i	−0.344272	−	1.05956i	0.617701	−	0.786413i	$-0.288064\pi$
$888$		0			0
$889$	3.27051	−	10.0656i	0.109689	−	0.337589i
$890$	−3.09017	−	9.51057i	−0.103583	−	0.318795i
$891$		0			0
$892$	7.28115	−	5.29007i	0.243791	−	0.177125i
$893$	69.9230			2.33988
$894$		0			0
$895$	−7.72542	−	23.7764i	−0.258232	−	0.794758i
$896$	2.42705	+	1.76336i	0.0810821	+	0.0589096i
$897$		0			0
$898$	1.21885	−	3.75123i	0.0406735	−	0.125180i
$899$	−2.23607			−0.0745770
$900$		0			0
$901$	12.0000			0.399778
$902$	1.92705	−	5.93085i	0.0641638	−	0.197476i
$903$		0			0
$904$	3.04508	+	2.21238i	0.101278	+	0.0735828i
$905$	12.1115			0.402598
$906$		0			0
$907$	25.6180			0.850633			0.425316	−	0.905045i	$-0.360163\pi$
$907$	25.6180			0.850633			0.425316	+	0.905045i	$0.360163\pi$
$908$	23.7533	−	17.2578i	0.788281	−	0.572719i
$909$		0			0
$910$	5.42705	+	3.94298i	0.179905	+	0.130709i
$911$	5.07295	−	15.6129i	0.168074	−	0.517280i	−0.831175	−	0.556010i	$-0.812331\pi$
$911$	5.07295	−	15.6129i	0.168074	−	0.517280i	0.999250	+	0.0387308i	$0.0123315\pi$
$912$		0			0
$913$	−5.92705	−	18.2416i	−0.196157	−	0.603708i
$914$	12.4271	−	38.2465i	0.411050	−	1.26508i
$915$		0			0
$916$	−0.791796	−	2.43690i	−0.0261617	−	0.0805174i
$917$	39.8435	−	28.9480i	1.31575	−	0.955946i
$918$		0			0
$919$	4.57295	−	3.32244i	0.150848	−	0.109597i	−0.509801	−	0.860292i	$-0.670281\pi$
$919$	4.57295	−	3.32244i	0.150848	−	0.109597i	0.660649	+	0.750695i	$0.270281\pi$
$920$	1.21885	−	3.75123i	0.0401842	−	0.123674i
$921$		0			0
$922$	4.70820	+	3.42071i	0.155056	+	0.112655i
$923$	0.927051	−	2.85317i	0.0305143	−	0.0939132i
$924$		0			0
$925$	33.6803	−	24.4702i	1.10740	−	0.804575i
$926$	−34.9787			−1.14947
$927$		0			0
$928$	−7.66312	−	5.56758i	−0.251554	−	0.182765i
$929$	−42.7877	−	31.0871i	−1.40382	−	1.01993i	−0.994185	−	0.107685i	$-0.965656\pi$
$929$	−42.7877	−	31.0871i	−1.40382	−	1.01993i	−0.409635	−	0.912250i	$-0.634344\pi$
$930$		0			0
$931$	−9.47214	+	6.88191i	−0.310437	+	0.225545i
$932$	−14.2918			−0.468143
$933$		0			0
$934$	5.92705	+	18.2416i	0.193939	+	0.596883i
$935$	3.35410	−	10.3229i	0.109691	−	0.337594i
$936$		0			0
$937$	12.9549	+	39.8711i	0.423219	+	1.30253i	0.904690	+	0.426071i	$0.140103\pi$
$937$	12.9549	+	39.8711i	0.423219	+	1.30253i	−0.481471	+	0.876462i	$0.659897\pi$
$938$	9.48936	+	29.2052i	0.309838	+	0.953585i
$939$		0			0
$940$	8.25329	−	25.4010i	0.269193	−	0.828490i
$941$	2.89919	+	8.92278i	0.0945108	+	0.290874i	0.987126	−	0.159945i	$-0.0511318\pi$
$941$	2.89919	+	8.92278i	0.0945108	+	0.290874i	−0.892615	+	0.450820i	$0.851132\pi$
$942$		0			0
$943$	−2.59675			−0.0845617
$944$	−3.61803	+	2.62866i	−0.117757	+	0.0855555i
$945$		0			0
$946$	−21.3713	−	15.5272i	−0.694842	−	0.504832i
$947$	−31.8607	−	23.1481i	−1.03533	−	0.752213i	−0.0659639	−	0.997822i	$-0.521012\pi$
$947$	−31.8607	−	23.1481i	−1.03533	−	0.752213i	−0.969369	+	0.245609i	$0.921012\pi$
$948$		0			0
$949$	7.70820			0.250219
$950$	−23.6803	+	17.2048i	−0.768292	+	0.558197i
$951$		0			0
$952$	1.06231	−	3.26944i	0.0344295	−	0.105963i
$953$	36.0967	+	26.2258i	1.16929	+	0.849538i	0.990924	−	0.134427i	$-0.0429193\pi$
$953$	36.0967	+	26.2258i	1.16929	+	0.849538i	0.178365	+	0.983964i	$0.442919\pi$
$954$		0			0
$955$	9.43363	−	29.0337i	0.305265	−	0.939509i
$956$	−5.59017	+	4.06150i	−0.180799	+	0.131358i
$957$		0			0
$958$	−12.2984	+	8.93529i	−0.397342	+	0.288686i
$959$	4.71885	+	14.5231i	0.152380	+	0.468976i
$960$		0			0
$961$	−9.56231	+	29.4298i	−0.308461	+	0.949347i
$962$	−2.57295	−	7.91872i	−0.0829552	−	0.255310i
$963$		0			0
$964$	4.82624	−	14.8536i	0.155443	−	0.478403i
$965$	26.5066	+	19.2582i	0.853277	+	0.619942i
$966$		0			0
$967$	10.6180	−	7.71445i	0.341453	−	0.248080i	−0.403822	−	0.914838i	$-0.632318\pi$
$967$	10.6180	−	7.71445i	0.341453	−	0.248080i	0.745275	+	0.666758i	$0.232318\pi$
$968$	6.94427			0.223197
$969$		0			0
$970$	21.3820			0.686534
$971$	4.90983	+	3.56720i	0.157564	+	0.114477i	0.663774	−	0.747934i	$-0.268954\pi$
$971$	4.90983	+	3.56720i	0.157564	+	0.114477i	−0.506210	+	0.862410i	$0.668954\pi$
$972$		0			0
$973$	4.93769	−	15.1967i	0.158295	−	0.487183i
$974$	22.1246			0.708918
$975$		0			0
$976$	−8.85410			−0.283413
$977$	−15.4549	+	47.5653i	−0.494447	+	1.52175i	0.323371	+	0.946272i	$0.395184\pi$
$977$	−15.4549	+	47.5653i	−0.494447	+	1.52175i	−0.817817	+	0.575478i	$0.804816\pi$
$978$		0			0
$979$	−15.3262	−	11.1352i	−0.489829	−	0.355881i
$980$	1.38197	+	4.25325i	0.0441453	+	0.135865i
$981$		0			0
$982$	−19.2361			−0.613848
$983$	31.1353	−	22.6211i	0.993060	−	0.721501i	0.0324712	−	0.999473i	$-0.489662\pi$
$983$	31.1353	−	22.6211i	0.993060	−	0.721501i	0.960589	+	0.277972i	$0.0896623\pi$
$984$		0			0
$985$	−8.29180	−	25.5195i	−0.264199	−	0.813120i
$986$	−3.35410	+	10.3229i	−0.106816	+	0.328747i
$987$		0			0
$988$	1.80902	+	5.56758i	0.0575525	+	0.177128i
$989$	−3.39919	+	10.4616i	−0.108088	+	0.332660i
$990$		0			0
$991$	−1.06637	−	3.28195i	−0.0338744	−	0.104255i	0.932690	−	0.360680i	$-0.117455\pi$
$991$	−1.06637	−	3.28195i	−0.0338744	−	0.104255i	−0.966564	+	0.256425i	$0.917455\pi$
$992$	0.190983	−	0.138757i	0.00606372	−	0.00440555i
$993$		0			0
$994$	7.28115	−	5.29007i	0.230944	−	0.167791i
$995$	−4.63525	−	3.36771i	−0.146947	−	0.106764i
$996$		0			0
$997$	−22.0451	−	16.0167i	−0.698175	−	0.507254i	0.181162	−	0.983453i	$-0.442014\pi$
$997$	−22.0451	−	16.0167i	−0.698175	−	0.507254i	−0.879337	+	0.476199i	$0.842014\pi$
$998$	10.5517	−	32.4747i	0.334007	−	1.02797i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.a.271.1		4
3.2	odd	2		50.2.d.a.21.1	✓	4
12.11	even	2		400.2.u.c.321.1		4
15.2	even	4		250.2.e.b.149.1		8
15.8	even	4		250.2.e.b.149.2		8
15.14	odd	2		250.2.d.a.101.1		4
25.6	even	5	inner	450.2.h.a.181.1		4
75.8	even	20		250.2.e.b.99.1		8
75.17	even	20		250.2.e.b.99.2		8
75.38	even	20		1250.2.b.b.1249.4		4
75.41	odd	10		1250.2.a.a.1.2		2
75.44	odd	10		250.2.d.a.151.1		4
75.56	odd	10		50.2.d.a.31.1	yes	4
75.59	odd	10		1250.2.a.d.1.1		2
75.62	even	20		1250.2.b.b.1249.1		4
300.59	even	10		10000.2.a.a.1.2		2
300.131	even	10		400.2.u.c.81.1		4
300.191	even	10		10000.2.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.a.21.1	✓	4	3.2	odd	2
50.2.d.a.31.1	yes	4	75.56	odd	10
250.2.d.a.101.1		4	15.14	odd	2
250.2.d.a.151.1		4	75.44	odd	10
250.2.e.b.99.1		8	75.8	even	20
250.2.e.b.99.2		8	75.17	even	20
250.2.e.b.149.1		8	15.2	even	4
250.2.e.b.149.2		8	15.8	even	4
400.2.u.c.81.1		4	300.131	even	10
400.2.u.c.321.1		4	12.11	even	2
450.2.h.a.181.1		4	25.6	even	5	inner
450.2.h.a.271.1		4	1.1	even	1	trivial
1250.2.a.a.1.2		2	75.41	odd	10
1250.2.a.d.1.1		2	75.59	odd	10
1250.2.b.b.1249.1		4	75.62	even	20
1250.2.b.b.1249.4		4	75.38	even	20
10000.2.a.a.1.2		2	300.59	even	10
10000.2.a.n.1.1		2	300.191	even	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.80902 - 1.31433i) q^{5} -3.00000 q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.80902 - 1.31433i) q^{5} -3.00000 q^{7} +(-0.809017 + 0.587785i) q^{8} +(-1.80902 + 1.31433i) q^{10} +(-1.30902 + 4.02874i) q^{11} +(0.309017 + 0.951057i) q^{13} +(-0.927051 + 2.85317i) q^{14} +(0.309017 + 0.951057i) q^{16} +(0.927051 - 0.673542i) q^{17} +(-4.73607 + 3.44095i) q^{19} +(0.690983 + 2.12663i) q^{20} +(3.42705 + 2.48990i) q^{22} +(0.545085 - 1.67760i) q^{23} +(1.54508 + 4.75528i) q^{25} +1.00000 q^{26} +(2.42705 + 1.76336i) q^{28} +(-7.66312 - 5.56758i) q^{29} +(0.190983 - 0.138757i) q^{31} +1.00000 q^{32} +(-0.354102 - 1.08981i) q^{34} +(5.42705 + 3.94298i) q^{35} +(-2.57295 - 7.91872i) q^{37} +(1.80902 + 5.56758i) q^{38} +2.23607 q^{40} +(-0.454915 - 1.40008i) q^{41} -6.23607 q^{43} +(3.42705 - 2.48990i) q^{44} +(-1.42705 - 1.03681i) q^{46} +(-9.66312 - 7.02067i) q^{47} +2.00000 q^{49} +5.00000 q^{50} +(0.309017 - 0.951057i) q^{52} +(8.47214 + 6.15537i) q^{53} +(7.66312 - 5.56758i) q^{55} +(2.42705 - 1.76336i) q^{56} +(-7.66312 + 5.56758i) q^{58} +(1.38197 + 4.25325i) q^{59} +(-2.73607 + 8.42075i) q^{61} +(-0.0729490 - 0.224514i) q^{62} +(0.309017 - 0.951057i) q^{64} +(0.690983 - 2.12663i) q^{65} +(8.28115 - 6.01661i) q^{67} -1.14590 q^{68} +(5.42705 - 3.94298i) q^{70} +(-2.42705 - 1.76336i) q^{71} +(2.38197 - 7.33094i) q^{73} -8.32624 q^{74} +5.85410 q^{76} +(3.92705 - 12.0862i) q^{77} +(5.85410 + 4.25325i) q^{79} +(0.690983 - 2.12663i) q^{80} -1.47214 q^{82} +(-3.66312 + 2.66141i) q^{83} -2.56231 q^{85} +(-1.92705 + 5.93085i) q^{86} +(-1.30902 - 4.02874i) q^{88} +(-1.38197 + 4.25325i) q^{89} +(-0.927051 - 2.85317i) q^{91} +(-1.42705 + 1.03681i) q^{92} +(-9.66312 + 7.02067i) q^{94} +13.0902 q^{95} +(-7.73607 - 5.62058i) q^{97} +(0.618034 - 1.90211i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} - 5 q^{5} - 12 q^{7} - q^{8}+O(q^{10}) \) 4 * q - q^2 - q^4 - 5 * q^5 - 12 * q^7 - q^8	\( 4 q - q^{2} - q^{4} - 5 q^{5} - 12 q^{7} - q^{8} - 5 q^{10} - 3 q^{11} - q^{13} + 3 q^{14} - q^{16} - 3 q^{17} - 10 q^{19} + 5 q^{20} + 7 q^{22} - 9 q^{23} - 5 q^{25} + 4 q^{26} + 3 q^{28} - 15 q^{29} + 3 q^{31} + 4 q^{32} + 12 q^{34} + 15 q^{35} - 17 q^{37} + 5 q^{38} - 13 q^{41} - 16 q^{43} + 7 q^{44} + q^{46} - 23 q^{47} + 8 q^{49} + 20 q^{50} - q^{52} + 16 q^{53} + 15 q^{55} + 3 q^{56} - 15 q^{58} + 10 q^{59} - 2 q^{61} - 7 q^{62} - q^{64} + 5 q^{65} + 13 q^{67} - 18 q^{68} + 15 q^{70} - 3 q^{71} + 14 q^{73} - 2 q^{74} + 10 q^{76} + 9 q^{77} + 10 q^{79} + 5 q^{80} + 12 q^{82} + q^{83} + 30 q^{85} - q^{86} - 3 q^{88} - 10 q^{89} + 3 q^{91} + q^{92} - 23 q^{94} + 30 q^{95} - 22 q^{97} - 2 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^4 - 5 * q^5 - 12 * q^7 - q^8 - 5 * q^10 - 3 * q^11 - q^13 + 3 * q^14 - q^16 - 3 * q^17 - 10 * q^19 + 5 * q^20 + 7 * q^22 - 9 * q^23 - 5 * q^25 + 4 * q^26 + 3 * q^28 - 15 * q^29 + 3 * q^31 + 4 * q^32 + 12 * q^34 + 15 * q^35 - 17 * q^37 + 5 * q^38 - 13 * q^41 - 16 * q^43 + 7 * q^44 + q^46 - 23 * q^47 + 8 * q^49 + 20 * q^50 - q^52 + 16 * q^53 + 15 * q^55 + 3 * q^56 - 15 * q^58 + 10 * q^59 - 2 * q^61 - 7 * q^62 - q^64 + 5 * q^65 + 13 * q^67 - 18 * q^68 + 15 * q^70 - 3 * q^71 + 14 * q^73 - 2 * q^74 + 10 * q^76 + 9 * q^77 + 10 * q^79 + 5 * q^80 + 12 * q^82 + q^83 + 30 * q^85 - q^86 - 3 * q^88 - 10 * q^89 + 3 * q^91 + q^92 - 23 * q^94 + 30 * q^95 - 22 * q^97 - 2 * q^98

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