LMFDB - Embedded newform 304.2.k.b.77.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(77,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("304.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.k (of order $4$, degree $2$, 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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.28
Character	$\chi$	$=$	304.77
Dual form			304.2.k.b.229.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16214 + 0.805879i) q^{2} +(-1.57596 - 1.57596i) q^{3} +(0.701117 + 1.87308i) q^{4} +(-1.57740 + 1.57740i) q^{5} +(-0.561447 - 3.10152i) q^{6} +1.68609i q^{7} +(-0.694684 + 2.74179i) q^{8} +1.96732i q^{9} +O(q^{10})$	\(q+(1.16214 + 0.805879i) q^{2} +(-1.57596 - 1.57596i) q^{3} +(0.701117 + 1.87308i) q^{4} +(-1.57740 + 1.57740i) q^{5} +(-0.561447 - 3.10152i) q^{6} +1.68609i q^{7} +(-0.694684 + 2.74179i) q^{8} +1.96732i q^{9} +(-3.10435 + 0.561960i) q^{10} +(-2.67034 + 2.67034i) q^{11} +(1.84697 - 4.05684i) q^{12} +(4.96054 + 4.96054i) q^{13} +(-1.35878 + 1.95946i) q^{14} +4.97186 q^{15} +(-3.01687 + 2.62650i) q^{16} +0.745156 q^{17} +(-1.58542 + 2.28629i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(-4.06055 - 1.84866i) q^{20} +(2.65721 - 2.65721i) q^{21} +(-5.25526 + 0.951324i) q^{22} -9.28569i q^{23} +(5.41576 - 3.22616i) q^{24} +0.0235982i q^{25} +(1.76722 + 9.76241i) q^{26} +(-1.62747 + 1.62747i) q^{27} +(-3.15818 + 1.18215i) q^{28} +(-2.38928 - 2.38928i) q^{29} +(5.77797 + 4.00672i) q^{30} +4.12358 q^{31} +(-5.62265 + 0.621117i) q^{32} +8.41670 q^{33} +(0.865973 + 0.600506i) q^{34} +(-2.65964 - 2.65964i) q^{35} +(-3.68495 + 1.37932i) q^{36} +(-4.56212 + 4.56212i) q^{37} +(-0.251911 - 1.39160i) q^{38} -15.6352i q^{39} +(-3.22911 - 5.42071i) q^{40} +2.33941i q^{41} +(5.22943 - 0.946648i) q^{42} +(-2.19419 + 2.19419i) q^{43} +(-6.87398 - 3.12954i) q^{44} +(-3.10326 - 3.10326i) q^{45} +(7.48315 - 10.7912i) q^{46} +6.33222 q^{47} +(8.89374 + 0.615207i) q^{48} +4.15711 q^{49} +(-0.0190173 + 0.0274243i) q^{50} +(-1.17434 - 1.17434i) q^{51} +(-5.81357 + 12.7694i) q^{52} +(7.24655 - 7.24655i) q^{53} +(-3.20288 + 0.579795i) q^{54} -8.42439i q^{55} +(-4.62290 - 1.17130i) q^{56} +2.22875i q^{57} +(-0.851195 - 4.70214i) q^{58} +(8.10520 - 8.10520i) q^{59} +(3.48586 + 9.31270i) q^{60} +(2.83217 + 2.83217i) q^{61} +(4.79215 + 3.32310i) q^{62} -3.31707 q^{63} +(-7.03483 - 3.80936i) q^{64} -15.6495 q^{65} +(9.78135 + 6.78284i) q^{66} +(-3.09338 - 3.09338i) q^{67} +(0.522442 + 1.39574i) q^{68} +(-14.6339 + 14.6339i) q^{69} +(-0.947513 - 5.23421i) q^{70} +4.16634i q^{71} +(-5.39398 - 1.36667i) q^{72} -8.32181i q^{73} +(-8.97832 + 1.62528i) q^{74} +(0.0371899 - 0.0371899i) q^{75} +(0.828704 - 1.82023i) q^{76} +(-4.50242 - 4.50242i) q^{77} +(12.6001 - 18.1703i) q^{78} +5.53927 q^{79} +(0.615769 - 8.90187i) q^{80} +11.0316 q^{81} +(-1.88529 + 2.71872i) q^{82} +(5.44587 + 5.44587i) q^{83} +(6.84019 + 3.11416i) q^{84} +(-1.17541 + 1.17541i) q^{85} +(-4.31820 + 0.781695i) q^{86} +7.53083i q^{87} +(-5.46646 - 9.17654i) q^{88} +12.5226i q^{89} +(-1.10555 - 6.10725i) q^{90} +(-8.36390 + 8.36390i) q^{91} +(17.3929 - 6.51036i) q^{92} +(-6.49860 - 6.49860i) q^{93} +(7.35889 + 5.10300i) q^{94} +2.23079 q^{95} +(9.83995 + 7.88223i) q^{96} +3.33008 q^{97} +(4.83112 + 3.35013i) q^{98} +(-5.25340 - 5.25340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.16214	+	0.805879i	0.821754	+	0.569843i
$2$	1.16214	+	0.805879i	0.821754	+	0.569843i
$3$	−1.57596	−	1.57596i	−0.909883	−	0.909883i	0.0863796	−	0.996262i	$-0.472470\pi$
$3$	−1.57596	−	1.57596i	−0.909883	−	0.909883i	−0.996262	+	0.0863796i	$0.972470\pi$
$4$	0.701117	+	1.87308i	0.350559	+	0.936541i
$5$	−1.57740	+	1.57740i	−0.705436	+	0.705436i	−0.965572	−	0.260136i	$-0.916233\pi$
$5$	−1.57740	+	1.57740i	−0.705436	+	0.705436i	0.260136	+	0.965572i	$0.416233\pi$
$6$	−0.561447	−	3.10152i	−0.229210	−	1.26619i
$7$			1.68609i			0.637281i	0.947876	+	0.318641i	$0.103226\pi$
$7$			1.68609i			0.637281i	−0.947876	+	0.318641i	$0.896774\pi$
$8$	−0.694684	+	2.74179i	−0.245608	+	0.969369i
$9$			1.96732i			0.655773i
$10$	−3.10435	+	0.561960i	−0.981682	+	0.177707i
$11$	−2.67034	+	2.67034i	−0.805137	+	0.805137i	−0.983893	−	0.178757i	$-0.942792\pi$
$11$	−2.67034	+	2.67034i	−0.805137	+	0.805137i	0.178757	+	0.983893i	$0.442792\pi$
$12$	1.84697	−	4.05684i	0.533175	−	1.17111i
$13$	4.96054	+	4.96054i	1.37581	+	1.37581i	0.851579	+	0.524226i	$0.175645\pi$
$13$	4.96054	+	4.96054i	1.37581	+	1.37581i	0.524226	+	0.851579i	$0.324355\pi$
$14$	−1.35878	+	1.95946i	−0.363150	+	0.523688i
$15$	4.97186			1.28373
$16$	−3.01687	+	2.62650i	−0.754217	+	0.656625i
$17$	0.745156			0.180727			0.0903635	−	0.995909i	$-0.471197\pi$
$17$	0.745156			0.180727			0.0903635	+	0.995909i	$0.471197\pi$
$18$	−1.58542	+	2.28629i	−0.373687	+	0.538884i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$20$	−4.06055	−	1.84866i	−0.907966	−	0.413373i
$21$	2.65721	−	2.65721i	0.579851	−	0.579851i
$22$	−5.25526	+	0.951324i	−1.12043	+	0.202823i
$23$		−	9.28569i		−	1.93620i	−0.250563	−	0.968100i	$-0.580616\pi$
$23$		−	9.28569i		−	1.93620i	0.250563	−	0.968100i	$-0.419384\pi$
$24$	5.41576	−	3.22616i	1.10549	−	0.658538i
$25$			0.0235982i			0.00471964i
$26$	1.76722	+	9.76241i	0.346581	+	1.91457i
$27$	−1.62747	+	1.62747i	−0.313206	+	0.313206i
$28$	−3.15818	+	1.18215i	−0.596840	+	0.223405i
$29$	−2.38928	−	2.38928i	−0.443678	−	0.443678i	0.449568	−	0.893246i	$-0.351578\pi$
$29$	−2.38928	−	2.38928i	−0.443678	−	0.443678i	−0.893246	+	0.449568i	$0.851578\pi$
$30$	5.77797	+	4.00672i	1.05491	+	0.731523i
$31$	4.12358			0.740616			0.370308	−	0.928909i	$-0.379252\pi$
$31$	4.12358			0.740616			0.370308	+	0.928909i	$0.379252\pi$
$32$	−5.62265	+	0.621117i	−0.993954	+	0.109799i
$33$	8.41670			1.46516
$34$	0.865973	+	0.600506i	0.148513	+	0.102986i
$35$	−2.65964	−	2.65964i	−0.449561	−	0.449561i
$36$	−3.68495	+	1.37932i	−0.614158	+	0.229887i
$37$	−4.56212	+	4.56212i	−0.750008	+	0.750008i	−0.974480	−	0.224473i	$-0.927934\pi$
$37$	−4.56212	+	4.56212i	−0.750008	+	0.750008i	0.224473	+	0.974480i	$0.427934\pi$
$38$	−0.251911	−	1.39160i	−0.0408654	−	0.225747i
$39$		−	15.6352i		−	2.50364i
$40$	−3.22911	−	5.42071i	−0.510567	−	0.857089i
$41$			2.33941i			0.365355i	0.983173	+	0.182678i	$0.0584764\pi$
$41$			2.33941i			0.365355i	−0.983173	+	0.182678i	$0.941524\pi$
$42$	5.22943	−	0.946648i	0.806919	−	0.146071i
$43$	−2.19419	+	2.19419i	−0.334611	+	0.334611i	−0.854335	−	0.519723i	$-0.826035\pi$
$43$	−2.19419	+	2.19419i	−0.334611	+	0.334611i	0.519723	+	0.854335i	$0.326035\pi$
$44$	−6.87398	−	3.12954i	−1.03629	−	0.471796i
$45$	−3.10326	−	3.10326i	−0.462606	−	0.462606i
$46$	7.48315	−	10.7912i	1.10333	−	1.59108i
$47$	6.33222			0.923649			0.461824	−	0.886971i	$-0.347195\pi$
$47$	6.33222			0.923649			0.461824	+	0.886971i	$0.347195\pi$
$48$	8.89374	+	0.615207i	1.28370	+	0.0887975i
$49$	4.15711			0.593873
$50$	−0.0190173	+	0.0274243i	−0.00268945	+	0.00387839i
$51$	−1.17434	−	1.17434i	−0.164440	−	0.164440i
$52$	−5.81357	+	12.7694i	−0.806197	+	1.77080i
$53$	7.24655	−	7.24655i	0.995391	−	0.995391i	−0.00459887	−	0.999989i	$-0.501464\pi$
$53$	7.24655	−	7.24655i	0.995391	−	0.995391i	0.999989	+	0.00459887i	$0.00146387\pi$
$54$	−3.20288	+	0.579795i	−0.435857	+	0.0789001i
$55$		−	8.42439i		−	1.13594i
$56$	−4.62290	−	1.17130i	−0.617761	−	0.156521i
$57$			2.22875i			0.295205i
$58$	−0.851195	−	4.70214i	−0.111767	−	0.617421i
$59$	8.10520	−	8.10520i	1.05521	−	1.05521i	0.0568228	−	0.998384i	$-0.481903\pi$
$59$	8.10520	−	8.10520i	1.05521	−	1.05521i	0.998384	−	0.0568228i	$-0.0180970\pi$
$60$	3.48586	+	9.31270i	0.450022	+	1.20226i
$61$	2.83217	+	2.83217i	0.362622	+	0.362622i	0.864777	−	0.502155i	$-0.167459\pi$
$61$	2.83217	+	2.83217i	0.362622	+	0.362622i	−0.502155	+	0.864777i	$0.667459\pi$
$62$	4.79215	+	3.32310i	0.608604	+	0.422035i
$63$	−3.31707			−0.417912
$64$	−7.03483	−	3.80936i	−0.879353	−	0.476170i
$65$	−15.6495			−1.94109
$66$	9.78135	+	6.78284i	1.20400	+	0.834910i
$67$	−3.09338	−	3.09338i	−0.377917	−	0.377917i	0.492433	−	0.870350i	$-0.336108\pi$
$67$	−3.09338	−	3.09338i	−0.377917	−	0.377917i	−0.870350	+	0.492433i	$0.836108\pi$
$68$	0.522442	+	1.39574i	0.0633554	+	0.169258i
$69$	−14.6339	+	14.6339i	−1.76172	+	1.76172i
$70$	−0.947513	−	5.23421i	−0.113250	−	0.625608i
$71$			4.16634i			0.494454i	0.968958	+	0.247227i	$0.0795193\pi$
$71$			4.16634i			0.494454i	−0.968958	+	0.247227i	$0.920481\pi$
$72$	−5.39398	−	1.36667i	−0.635686	−	0.161063i
$73$		−	8.32181i		−	0.973994i	−0.873404	−	0.486997i	$-0.838092\pi$
$73$		−	8.32181i		−	0.973994i	0.873404	−	0.486997i	$-0.161908\pi$
$74$	−8.97832	+	1.62528i	−1.04371	+	0.188935i
$75$	0.0371899	−	0.0371899i	0.00429432	−	0.00429432i
$76$	0.828704	−	1.82023i	0.0950588	−	0.208795i
$77$	−4.50242	−	4.50242i	−0.513098	−	0.513098i
$78$	12.6001	−	18.1703i	1.42668	−	2.05738i
$79$	5.53927			0.623216			0.311608	−	0.950211i	$-0.399132\pi$
$79$	5.53927			0.623216			0.311608	+	0.950211i	$0.399132\pi$
$80$	0.615769	−	8.90187i	0.0688451	−	0.995259i
$81$	11.0316			1.22573
$82$	−1.88529	+	2.71872i	−0.208195	+	0.300232i
$83$	5.44587	+	5.44587i	0.597762	+	0.597762i	0.939716	−	0.341955i	$-0.111089\pi$
$83$	5.44587	+	5.44587i	0.597762	+	0.597762i	−0.341955	+	0.939716i	$0.611089\pi$
$84$	6.84019	+	3.11416i	0.746326	+	0.339782i
$85$	−1.17541	+	1.17541i	−0.127491	+	0.127491i
$86$	−4.31820	+	0.781695i	−0.465644	+	0.0842923i
$87$			7.53083i			0.807390i
$88$	−5.46646	−	9.17654i	−0.582727	−	0.978223i
$89$			12.5226i			1.32739i	0.748004	+	0.663694i	$0.231012\pi$
$89$			12.5226i			1.32739i	−0.748004	+	0.663694i	$0.768988\pi$
$90$	−1.10555	−	6.10725i	−0.116536	−	0.643761i
$91$	−8.36390	+	8.36390i	−0.876775	+	0.876775i
$92$	17.3929	−	6.51036i	1.81333	−	0.678752i
$93$	−6.49860	−	6.49860i	−0.673874	−	0.673874i
$94$	7.35889	+	5.10300i	0.759012	+	0.526334i
$95$	2.23079			0.228874
$96$	9.83995	+	7.88223i	1.00429	+	0.804477i
$97$	3.33008			0.338118			0.169059	−	0.985606i	$-0.445927\pi$
$97$	3.33008			0.338118			0.169059	+	0.985606i	$0.445927\pi$
$98$	4.83112	+	3.35013i	0.488017	+	0.338414i
$99$	−5.25340	−	5.25340i	−0.527987	−	0.527987i
$100$	−0.0442014	+	0.0165451i	−0.00442014	+	0.00165451i
$101$	5.75972	−	5.75972i	0.573114	−	0.573114i	−0.359883	−	0.932997i	$-0.617184\pi$
$101$	5.75972	−	5.75972i	0.573114	−	0.573114i	0.932997	+	0.359883i	$0.117184\pi$
$102$	−0.418366	−	2.31112i	−0.0414244	−	0.228835i
$103$			17.1116i			1.68606i	0.537869	+	0.843028i	$0.319229\pi$
$103$			17.1116i			1.68606i	−0.537869	+	0.843028i	$0.680771\pi$
$104$	−17.0468	+	10.1547i	−1.67157	+	0.995755i
$105$			8.38299i			0.818096i
$106$	14.2613	−	2.58163i	1.38518	−	0.250750i
$107$	−6.09993	+	6.09993i	−0.589702	+	0.589702i	−0.937551	−	0.347849i	$-0.886912\pi$
$107$	−6.09993	+	6.09993i	−0.589702	+	0.589702i	0.347849	+	0.937551i	$0.386912\pi$
$108$	−4.18942	−	1.90733i	−0.403127	−	0.183533i
$109$	8.30961	+	8.30961i	0.795916	+	0.795916i	0.982449	−	0.186533i	$-0.0597250\pi$
$109$	8.30961	+	8.30961i	0.795916	+	0.795916i	−0.186533	+	0.982449i	$0.559725\pi$
$110$	6.78904	−	9.79029i	0.647310	−	0.933467i
$111$	14.3795			1.36484
$112$	−4.42851	−	5.08671i	−0.418455	−	0.480649i
$113$	−8.64423			−0.813181			−0.406590	−	0.913611i	$-0.633282\pi$
$113$	−8.64423			−0.813181			−0.406590	+	0.913611i	$0.633282\pi$
$114$	−1.79610	+	2.59011i	−0.168220	+	0.242586i
$115$	14.6473	+	14.6473i	1.36587	+	1.36587i
$116$	2.80015	−	6.15048i	0.259987	−	0.571058i
$117$	−9.75896	+	9.75896i	−0.902216	+	0.902216i
$118$	15.9512	−	2.88753i	1.46842	−	0.265818i
$119$			1.25640i			0.115174i
$120$	−3.45387	+	13.6318i	−0.315294	+	1.24441i
$121$		−	3.26139i		−	0.296490i
$122$	1.00898	+	5.57375i	0.0913485	+	0.504623i
$123$	3.68683	−	3.68683i	0.332430	−	0.332430i
$124$	2.89111	+	7.72380i	0.259629	+	0.693617i
$125$	−7.92424	−	7.92424i	−0.708766	−	0.708766i
$126$	−3.85489	−	2.67316i	−0.343421	−	0.238144i
$127$	−18.5183			−1.64323			−0.821617	−	0.570040i	$-0.806928\pi$
$127$	−18.5183			−1.64323			−0.821617	+	0.570040i	$0.806928\pi$
$128$	−5.10554	−	10.0962i	−0.451270	−	0.892387i
$129$	6.91593			0.608914
$130$	−18.1869	−	12.6116i	−1.59509	−	1.10611i
$131$	7.55135	+	7.55135i	0.659764	+	0.659764i	0.955324	−	0.295560i	$-0.0955062\pi$
$131$	7.55135	+	7.55135i	0.659764	+	0.659764i	−0.295560	+	0.955324i	$0.595506\pi$
$132$	5.90110	+	15.7652i	0.513624	+	1.37218i
$133$	1.19224	−	1.19224i	0.103381	−	0.103381i
$134$	−1.10204	−	6.08782i	−0.0952014	−	0.525908i
$135$		−	5.13434i		−	0.441894i
$136$	−0.517648	+	2.04306i	−0.0443880	+	0.175191i
$137$		−	7.22190i		−	0.617009i	−0.951223	−	0.308504i	$-0.900172\pi$
$137$		−	7.22190i		−	0.617009i	0.951223	−	0.308504i	$-0.0998284\pi$
$138$	−28.7997	+	5.21342i	−2.45160	+	0.443796i
$139$	−2.08768	+	2.08768i	−0.177075	+	0.177075i	−0.790079	−	0.613005i	$-0.789961\pi$
$139$	−2.08768	+	2.08768i	−0.177075	+	0.177075i	0.613005	+	0.790079i	$0.289961\pi$
$140$	3.11700	−	6.84644i	0.263435	−	0.578630i
$141$	−9.97934	−	9.97934i	−0.840412	−	0.840412i
$142$	−3.35757	+	4.84185i	−0.281761	+	0.406319i
$143$	−26.4926			−2.21542
$144$	−5.16716	−	5.93514i	−0.430597	−	0.494595i
$145$	7.53771			0.625973
$146$	6.70637	−	9.67107i	0.555023	−	0.800383i
$147$	−6.55145	−	6.55145i	−0.540354	−	0.540354i
$148$	−11.7438	−	5.34664i	−0.965334	−	0.439491i
$149$	4.10195	−	4.10195i	0.336045	−	0.336045i	−0.518831	−	0.854877i	$-0.673633\pi$
$149$	4.10195	−	4.10195i	0.336045	−	0.336045i	0.854877	+	0.518831i	$0.173633\pi$
$150$	0.0731903	−	0.0132491i	0.00597596	−	0.00108179i
$151$		−	17.3656i		−	1.41319i	−0.707619	−	0.706594i	$-0.750231\pi$
$151$		−	17.3656i		−	1.41319i	0.707619	−	0.706594i	$-0.249769\pi$
$152$	2.42995	−	1.44752i	0.197095	−	0.117410i
$153$			1.46596i			0.118516i
$154$	−1.60402	−	8.86083i	−0.129255	−	0.714026i
$155$	−6.50454	+	6.50454i	−0.522457	+	0.522457i
$156$	29.2861	−	10.9621i	2.34476	−	0.877674i
$157$	−4.68861	−	4.68861i	−0.374192	−	0.374192i	0.494809	−	0.869001i	$-0.335238\pi$
$157$	−4.68861	−	4.68861i	−0.374192	−	0.374192i	−0.869001	+	0.494809i	$0.835238\pi$
$158$	6.43738	+	4.46398i	0.512130	+	0.355135i
$159$	−22.8406			−1.81138
$160$	7.88944	−	9.84894i	0.623715	−	0.778627i
$161$	15.6565			1.23390
$162$	12.8202	+	8.89015i	1.00725	+	0.698476i
$163$	−9.42345	−	9.42345i	−0.738101	−	0.738101i	0.234109	−	0.972210i	$-0.424783\pi$
$163$	−9.42345	−	9.42345i	−0.738101	−	0.738101i	−0.972210	+	0.234109i	$0.924783\pi$
$164$	−4.38191	+	1.64020i	−0.342170	+	0.128078i
$165$	−13.2765	+	13.2765i	−1.03358	+	1.03358i
$166$	1.94012	+	10.7176i	0.150583	+	0.831843i
$167$			2.49387i			0.192982i	0.995334	+	0.0964909i	$0.0307619\pi$
$167$			2.49387i			0.192982i	−0.995334	+	0.0964909i	$0.969238\pi$
$168$	5.43960	+	9.13144i	0.419674	+	0.704506i
$169$			36.2138i			2.78568i
$170$	−2.31323	+	0.418748i	−0.177417	+	0.0321165i
$171$	1.39110	−	1.39110i	0.106380	−	0.106380i
$172$	−5.64829	−	2.57152i	−0.430678	−	0.196076i
$173$	−1.03148	−	1.03148i	−0.0784222	−	0.0784222i	0.666808	−	0.745230i	$-0.267660\pi$
$173$	−1.03148	−	1.03148i	−0.0784222	−	0.0784222i	−0.745230	+	0.666808i	$0.767660\pi$
$174$	−6.06894	+	8.75184i	−0.460085	+	0.663476i
$175$	−0.0397887			−0.00300774
$176$	1.04242	−	15.0697i	0.0785750	−	1.13592i
$177$	−25.5470			−1.92023
$178$	−10.0917	+	14.5529i	−0.756403	+	1.09079i
$179$	0.977829	+	0.977829i	0.0730864	+	0.0730864i	0.742705	−	0.669619i	$-0.233542\pi$
$179$	0.977829	+	0.977829i	0.0730864	+	0.0730864i	−0.669619	+	0.742705i	$0.733542\pi$
$180$	3.63690	−	7.98840i	0.271079	−	0.595420i
$181$	9.98191	−	9.98191i	0.741949	−	0.741949i	−0.231004	−	0.972953i	$-0.574201\pi$
$181$	9.98191	−	9.98191i	0.741949	−	0.741949i	0.972953	+	0.231004i	$0.0742009\pi$
$182$	−16.4603	+	2.97969i	−1.22012	+	0.220869i
$183$		−	8.92678i		−	0.659887i
$184$	25.4594	+	6.45062i	1.87689	+	0.475546i
$185$		−	14.3926i		−	1.05817i
$186$	−2.31517	−	12.7893i	−0.169756	−	0.937761i
$187$	−1.98982	+	1.98982i	−0.145510	+	0.145510i
$188$	4.43963	+	11.8608i	0.323793	+	0.865035i
$189$	−2.74405	−	2.74405i	−0.199600	−	0.199600i
$190$	2.59247	+	1.79774i	0.188078	+	0.130422i
$191$	7.18058			0.519569			0.259784	−	0.965667i	$-0.416349\pi$
$191$	7.18058			0.519569			0.259784	+	0.965667i	$0.416349\pi$
$192$	5.08322	+	17.0900i	0.366850	+	1.23337i
$193$	13.9809			1.00637			0.503183	−	0.864180i	$-0.332162\pi$
$193$	13.9809			1.00637			0.503183	+	0.864180i	$0.332162\pi$
$194$	3.87000	+	2.68364i	0.277850	+	0.192674i
$195$	24.6631	+	24.6631i	1.76616	+	1.76616i
$196$	2.91462	+	7.78660i	0.208187	+	0.556186i
$197$	3.17726	−	3.17726i	0.226371	−	0.226371i	−0.584804	−	0.811175i	$-0.698829\pi$
$197$	3.17726	−	3.17726i	0.226371	−	0.226371i	0.811175	+	0.584804i	$0.198829\pi$
$198$	−1.87156	−	10.3388i	−0.133006	−	0.734745i
$199$		−	3.42039i		−	0.242465i	−0.992624	−	0.121233i	$-0.961315\pi$
$199$		−	3.42039i		−	0.242465i	0.992624	−	0.121233i	$-0.0386847\pi$
$200$	−0.0647014	−	0.0163933i	−0.00457508	−	0.00115918i
$201$			9.75011i			0.687720i
$202$	11.3352	−	2.05194i	0.797543	−	0.144374i
$203$	4.02853	−	4.02853i	0.282748	−	0.282748i
$204$	1.37628	−	3.02298i	0.0963591	−	0.211651i
$205$	−3.69020	−	3.69020i	−0.257735	−	0.257735i
$206$	−13.7899	+	19.8860i	−0.960787	+	1.38552i
$207$	18.2679			1.26971
$208$	−27.9941	−	1.93644i	−1.94104	−	0.134268i
$209$	3.77643			0.261221
$210$	−6.75568	+	9.74217i	−0.466186	+	0.672274i
$211$	9.02544	+	9.02544i	0.621337	+	0.621337i	0.945873	−	0.324536i	$-0.105208\pi$
$211$	9.02544	+	9.02544i	0.621337	+	0.621337i	−0.324536	+	0.945873i	$0.605208\pi$
$212$	18.6541	+	8.49270i	1.28117	+	0.583281i
$213$	6.56600	−	6.56600i	0.449895	−	0.449895i
$214$	−12.0047	+	2.17314i	−0.820627	+	0.148553i
$215$		−	6.92225i		−	0.472094i
$216$	−3.33160	−	5.59275i	−0.226686	−	0.380538i
$217$			6.95271i			0.471981i
$218$	2.96035	+	16.3534i	0.200500	+	1.10759i
$219$	−13.1149	+	13.1149i	−0.886220	+	0.886220i
$220$	15.7796	−	5.90649i	1.06386	−	0.398215i
$221$	3.69638	+	3.69638i	0.248645	+	0.248645i
$222$	16.7109	+	11.5881i	1.12156	+	0.777743i
$223$	10.1714			0.681130			0.340565	−	0.940221i	$-0.389382\pi$
$223$	10.1714			0.681130			0.340565	+	0.940221i	$0.389382\pi$
$224$	−1.04726	−	9.48029i	−0.0699728	−	0.633428i
$225$	−0.0464252			−0.00309502
$226$	−10.0458	−	6.96621i	−0.668235	−	0.463385i
$227$	−10.2101	−	10.2101i	−0.677668	−	0.677668i	0.281804	−	0.959472i	$-0.409067\pi$
$227$	−10.2101	−	10.2101i	−0.677668	−	0.677668i	−0.959472	+	0.281804i	$0.909067\pi$
$228$	−4.17463	+	1.56261i	−0.276471	+	0.103487i
$229$	15.8958	−	15.8958i	1.05042	−	1.05042i	0.0517648	−	0.998659i	$-0.483515\pi$
$229$	15.8958	−	15.8958i	1.05042	−	1.05042i	0.998659	−	0.0517648i	$-0.0164846\pi$
$230$	5.21818	+	28.8261i	0.344077	+	1.90073i
$231$			14.1913i			0.933719i
$232$	8.21070	−	4.89111i	0.539059	−	0.321117i
$233$		−	14.4046i		−	0.943674i	−0.881686	−	0.471837i	$-0.843591\pi$
$233$		−	14.4046i		−	0.943674i	0.881686	−	0.471837i	$-0.156409\pi$
$234$	−19.2058	+	3.47669i	−1.25552	+	0.227278i
$235$	−9.98846	+	9.98846i	−0.651575	+	0.651575i
$236$	20.8644	+	9.49900i	1.35816	+	0.618332i
$237$	−8.72968	−	8.72968i	−0.567054	−	0.567054i
$238$	−1.01251	+	1.46011i	−0.0656310	+	0.0946446i
$239$	4.89457			0.316603			0.158302	−	0.987391i	$-0.449398\pi$
$239$	4.89457			0.316603			0.158302	+	0.987391i	$0.449398\pi$
$240$	−14.9994	+	13.0586i	−0.968210	+	0.842928i
$241$	13.5680			0.873990			0.436995	−	0.899464i	$-0.356043\pi$
$241$	13.5680			0.873990			0.436995	+	0.899464i	$0.356043\pi$
$242$	2.62828	−	3.79017i	0.168953	−	0.243642i
$243$	−12.5030	−	12.5030i	−0.802069	−	0.802069i
$244$	−3.31920	+	7.29056i	−0.212490	+	0.466730i
$245$	−6.55743	+	6.55743i	−0.418939	+	0.418939i
$246$	7.25574	−	1.31346i	0.462609	−	0.0837429i
$247$		−	7.01526i		−	0.446370i
$248$	−2.86458	+	11.3060i	−0.181901	+	0.717931i
$249$		−	17.1650i		−	1.08779i
$250$	−2.82306	−	15.5950i	−0.178546	−	0.986316i
$251$	−16.3192	+	16.3192i	−1.03006	+	1.03006i	−0.0305248	+	0.999534i	$0.509718\pi$
$251$	−16.3192	+	16.3192i	−1.03006	+	1.03006i	−0.999534	+	0.0305248i	$0.990282\pi$
$252$	−2.32566	−	6.21315i	−0.146503	−	0.391392i
$253$	24.7959	+	24.7959i	1.55891	+	1.55891i
$254$	−21.5208	−	14.9235i	−1.35033	−	0.936385i
$255$	3.70481			0.232004
$256$	2.20300	−	15.8476i	0.137687	−	0.990476i
$257$	−25.3775			−1.58301			−0.791503	−	0.611165i	$-0.790701\pi$
$257$	−25.3775			−1.58301			−0.791503	+	0.611165i	$0.790701\pi$
$258$	8.03725	+	5.57341i	0.500377	+	0.346985i
$259$	−7.69213	−	7.69213i	−0.477966	−	0.477966i
$260$	−10.9722	−	29.3129i	−0.680464	−	1.81791i
$261$	4.70047	−	4.70047i	0.290952	−	0.290952i
$262$	2.69021	+	14.8612i	0.166202	+	0.918126i
$263$			9.72484i			0.599659i	0.953993	+	0.299830i	$0.0969299\pi$
$263$			9.72484i			0.599659i	−0.953993	+	0.299830i	$0.903070\pi$
$264$	−5.84695	+	23.0768i	−0.359855	+	1.42028i
$265$			22.8615i			1.40437i
$266$	2.34635	−	0.424744i	0.143864	−	0.0260427i
$267$	19.7351	−	19.7351i	1.20777	−	1.20777i
$268$	3.62533	−	7.96298i	0.221452	−	0.486416i
$269$	−19.6767	−	19.6767i	−1.19971	−	1.19971i	−0.974254	−	0.225453i	$-0.927614\pi$
$269$	−19.6767	−	19.6767i	−1.19971	−	1.19971i	−0.225453	−	0.974254i	$-0.572386\pi$
$270$	4.13766	−	5.96680i	0.251810	−	0.363128i
$271$	20.8174			1.26457			0.632285	−	0.774736i	$-0.282117\pi$
$271$	20.8174			1.26457			0.632285	+	0.774736i	$0.282117\pi$
$272$	−2.24804	+	1.95715i	−0.136307	+	0.118670i
$273$	26.3624			1.59552
$274$	5.81998	−	8.39283i	0.351598	−	0.507029i
$275$	−0.0630152	−	0.0630152i	−0.00379996	−	0.00379996i
$276$	−37.6706	−	17.1504i	−2.26750	−	1.03233i
$277$	19.8793	−	19.8793i	1.19443	−	1.19443i	0.218618	−	0.975810i	$-0.429845\pi$
$277$	19.8793	−	19.8793i	1.19443	−	1.19443i	0.975810	−	0.218618i	$-0.0701549\pi$
$278$	−4.10858	+	0.743748i	−0.246416	+	0.0446071i
$279$			8.11239i			0.485676i
$280$	9.13979	−	5.44457i	0.546207	−	0.325375i
$281$			1.38015i			0.0823329i	0.999152	+	0.0411664i	$0.0131074\pi$
$281$			1.38015i			0.0823329i	−0.999152	+	0.0411664i	$0.986893\pi$
$282$	−3.55520	−	19.6395i	−0.211709	−	1.16951i
$283$	2.30064	−	2.30064i	0.136759	−	0.136759i	−0.635413	−	0.772172i	$-0.719170\pi$
$283$	2.30064	−	2.30064i	0.136759	−	0.136759i	0.772172	+	0.635413i	$0.219170\pi$
$284$	−7.80390	+	2.92109i	−0.463076	+	0.173335i
$285$	−3.51563	−	3.51563i	−0.208248	−	0.208248i
$286$	−30.7880	−	21.3498i	−1.82053	−	1.26244i
$287$	−3.94446			−0.232834
$288$	−1.22194	−	11.0616i	−0.0720032	−	0.651808i
$289$	−16.4447			−0.967338
$290$	8.75984	+	6.07449i	0.514396	+	0.356706i
$291$	−5.24808	−	5.24808i	−0.307648	−	0.307648i
$292$	15.5874	−	5.83456i	0.912185	−	0.341442i
$293$	−17.2518	+	17.2518i	−1.00786	+	1.00786i	−0.00789162	+	0.999969i	$0.502512\pi$
$293$	−17.2518	+	17.2518i	−1.00786	+	1.00786i	−0.999969	+	0.00789162i	$0.997488\pi$
$294$	−2.33399	−	12.8933i	−0.136121	−	0.751955i
$295$			25.5703i			1.48876i
$296$	−9.33914	−	15.6776i	−0.542827	−	0.911242i
$297$		−	8.69177i		−	0.504347i
$298$	8.07270	−	1.46135i	0.467639	−	0.0846535i
$299$	46.0620	−	46.0620i	2.66383	−	2.66383i
$300$	0.0957343	+	0.0435853i	0.00552722	+	0.00251640i
$301$	−3.69960	−	3.69960i	−0.213242	−	0.213242i
$302$	13.9945	−	20.1811i	0.805295	−	1.16129i
$303$	−18.1542			−1.04293
$304$	3.99046	+	0.276032i	0.228869	+	0.0158315i
$305$	−8.93494			−0.511613
$306$	−1.18139	+	1.70364i	−0.0675354	+	0.0973909i
$307$	−0.402763	−	0.402763i	−0.0229869	−	0.0229869i	0.695520	−	0.718507i	$-0.255174\pi$
$307$	−0.402763	−	0.402763i	−0.0229869	−	0.0229869i	−0.718507	+	0.695520i	$0.755174\pi$
$308$	5.27668	−	11.5901i	0.300667	−	0.660409i
$309$	26.9673	−	26.9673i	1.53411	−	1.53411i
$310$	−12.8010	+	2.31728i	−0.727050	+	0.131613i
$311$			15.7246i			0.891658i	0.895118	+	0.445829i	$0.147091\pi$
$311$			15.7246i			0.891658i	−0.895118	+	0.445829i	$0.852909\pi$
$312$	42.8686	+	10.8616i	2.42695	+	0.614915i
$313$		−	17.1622i		−	0.970063i	−0.874497	−	0.485031i	$-0.838808\pi$
$313$		−	17.1622i		−	0.970063i	0.874497	−	0.485031i	$-0.161192\pi$
$314$	−1.67035	−	9.22726i	−0.0942632	−	0.520724i
$315$	5.23236	−	5.23236i	0.294810	−	0.294810i
$316$	3.88368	+	10.3755i	0.218474	+	0.583667i
$317$	1.89706	+	1.89706i	0.106550	+	0.106550i	0.758372	−	0.651822i	$-0.225995\pi$
$317$	1.89706	+	1.89706i	0.106550	+	0.106550i	−0.651822	+	0.758372i	$0.725995\pi$
$318$	−26.5439	−	18.4068i	−1.48851	−	1.03220i
$319$	12.7604			0.714443
$320$	17.1057	−	5.08787i	0.956235	−	0.284421i
$321$	19.2265			1.07312
$322$	18.1950	+	12.6172i	1.01397	+	0.703131i
$323$	−0.526905	−	0.526905i	−0.0293178	−	0.0293178i
$324$	7.73446	+	20.6631i	0.429692	+	1.14795i
$325$	−0.117060	+	0.117060i	−0.00649331	+	0.00649331i
$326$	−3.35716	−	18.5455i	−0.185936	−	1.02714i
$327$		−	26.1913i		−	1.44838i
$328$	−6.41418	−	1.62515i	−0.354164	−	0.0897341i
$329$			10.6767i			0.588624i
$330$	−26.1284	+	4.72985i	−1.43832	+	0.260369i
$331$	3.76461	−	3.76461i	0.206922	−	0.206922i	−0.596036	−	0.802958i	$-0.703258\pi$
$331$	3.76461	−	3.76461i	0.206922	−	0.206922i	0.802958	+	0.596036i	$0.203258\pi$
$332$	−6.38236	+	14.0188i	−0.350278	+	0.769379i
$333$	−8.97514	−	8.97514i	−0.491835	−	0.491835i
$334$	−2.00976	+	2.89822i	−0.109969	+	0.158584i
$335$	9.75902			0.533192
$336$	−1.03729	+	14.9956i	−0.0565890	+	0.818079i
$337$	1.11886			0.0609480			0.0304740	−	0.999536i	$-0.490298\pi$
$337$	1.11886			0.0609480			0.0304740	+	0.999536i	$0.490298\pi$
$338$	−29.1840	+	42.0854i	−1.58740	+	2.28914i
$339$	13.6230	+	13.6230i	0.739899	+	0.739899i
$340$	−3.02574	−	1.37754i	−0.164094	−	0.0747076i
$341$	−11.0113	+	11.0113i	−0.596297	+	0.596297i
$342$	2.73771	−	0.495590i	0.148039	−	0.0267984i
$343$			18.8119i			1.01575i
$344$	−4.49175	−	7.54029i	−0.242179	−	0.406545i
$345$		−	46.1671i		−	2.48556i
$346$	−0.367472	−	2.02997i	−0.0197554	−	0.109132i
$347$	−22.6290	+	22.6290i	−1.21479	+	1.21479i	−0.245354	+	0.969434i	$0.578904\pi$
$347$	−22.6290	+	22.6290i	−1.21479	+	1.21479i	−0.969434	+	0.245354i	$0.921096\pi$
$348$	−14.1059	+	5.28000i	−0.756153	+	0.283037i
$349$	−18.5059	−	18.5059i	−0.990597	−	0.990597i	0.00935911	−	0.999956i	$-0.497021\pi$
$349$	−18.5059	−	18.5059i	−0.990597	−	0.990597i	−0.999956	+	0.00935911i	$0.997021\pi$
$350$	−0.0462398	−	0.0320649i	−0.00247162	−	0.00171394i
$351$	−16.1462			−0.861821
$352$	13.3558	−	16.6730i	0.711865	−	0.888672i
$353$	−20.2998			−1.08045			−0.540225	−	0.841521i	$-0.681661\pi$
$353$	−20.2998			−1.08045			−0.540225	+	0.841521i	$0.681661\pi$
$354$	−29.6891	−	20.5878i	−1.57796	−	1.09423i
$355$	−6.57200	−	6.57200i	−0.348806	−	0.348806i
$356$	−23.4558	+	8.77979i	−1.24315	+	0.465328i
$357$	1.98004	−	1.98004i	0.104795	−	0.104795i
$358$	0.348358	+	1.92438i	0.0184113	+	0.101707i
$359$		−	0.916087i		−	0.0483492i	−0.999708	−	0.0241746i	$-0.992304\pi$
$359$		−	0.916087i		−	0.0483492i	0.999708	−	0.0241746i	$-0.00769577\pi$
$360$	10.6643	−	6.35269i	0.562056	−	0.334816i
$361$			1.00000i			0.0526316i
$362$	19.6445	−	3.55612i	1.03249	−	0.186905i
$363$	−5.13983	+	5.13983i	−0.269771	+	0.269771i
$364$	−21.5303	−	9.80219i	−1.12850	−	0.513774i
$365$	13.1268	+	13.1268i	0.687090	+	0.687090i
$366$	7.19391	−	10.3741i	0.376032	−	0.542264i
$367$	14.7129			0.768005			0.384003	−	0.923332i	$-0.374545\pi$
$367$	14.7129			0.768005			0.384003	+	0.923332i	$0.374545\pi$
$368$	24.3889	+	28.0137i	1.27136	+	1.46032i
$369$	−4.60238			−0.239590
$370$	11.5987	−	16.7262i	0.602988	−	0.869551i
$371$	12.2183	+	12.2183i	0.634344	+	0.634344i
$372$	7.61613	−	16.7287i	0.394878	−	0.867343i
$373$	−10.0488	+	10.0488i	−0.520308	+	0.520308i	−0.917664	−	0.397356i	$-0.869928\pi$
$373$	−10.0488	+	10.0488i	−0.520308	+	0.520308i	0.397356	+	0.917664i	$0.369928\pi$
$374$	−3.91599	+	0.708885i	−0.202491	+	0.0366556i
$375$			24.9766i			1.28979i
$376$	−4.39889	+	17.3616i	−0.226855	+	0.895357i
$377$		−	23.7042i		−	1.22083i
$378$	−0.977585	−	5.40033i	−0.0502816	−	0.277763i
$379$	−10.4995	+	10.4995i	−0.539325	+	0.539325i	−0.923331	−	0.384006i	$-0.874544\pi$
$379$	−10.4995	+	10.4995i	−0.539325	+	0.539325i	0.384006	+	0.923331i	$0.374544\pi$
$380$	1.56404	+	4.17844i	0.0802337	+	0.214350i
$381$	29.1842	+	29.1842i	1.49515	+	1.49515i
$382$	8.34481	+	5.78668i	0.426958	+	0.296072i
$383$	1.23106			0.0629044			0.0314522	−	0.999505i	$-0.489987\pi$
$383$	1.23106			0.0629044			0.0314522	+	0.999505i	$0.489987\pi$
$384$	−7.86511	+	23.9574i	−0.401365	+	1.22257i
$385$	14.2043			0.723916
$386$	16.2477	+	11.2669i	0.826984	+	0.573470i
$387$	−4.31668	−	4.31668i	−0.219429	−	0.219429i
$388$	2.33477	+	6.23750i	0.118530	+	0.316661i
$389$	2.75220	−	2.75220i	0.139542	−	0.139542i	−0.633885	−	0.773427i	$-0.718541\pi$
$389$	2.75220	−	2.75220i	0.139542	−	0.139542i	0.773427	+	0.633885i	$0.218541\pi$
$390$	8.78638	+	48.5373i	0.444916	+	2.45778i
$391$		−	6.91929i		−	0.349924i
$392$	−2.88788	+	11.3979i	−0.145860	+	0.575682i
$393$		−	23.8013i		−	1.20062i
$394$	6.25290	−	1.13192i	0.315017	−	0.0570253i
$395$	−8.73766	+	8.73766i	−0.439639	+	0.439639i
$396$	6.15680	−	13.5233i	0.309391	−	0.679572i
$397$	−9.87588	−	9.87588i	−0.495656	−	0.495656i	0.414427	−	0.910083i	$-0.363982\pi$
$397$	−9.87588	−	9.87588i	−0.495656	−	0.495656i	−0.910083	+	0.414427i	$0.863982\pi$
$398$	2.75642	−	3.97496i	0.138167	−	0.199247i
$399$	−3.75787			−0.188129
$400$	−0.0619807	−	0.0711927i	−0.00309904	−	0.00355964i
$401$	−11.5469			−0.576625			−0.288312	−	0.957536i	$-0.593094\pi$
$401$	−11.5469			−0.576625			−0.288312	+	0.957536i	$0.593094\pi$
$402$	−7.85741	+	11.3309i	−0.391892	+	0.565136i
$403$	20.4552	+	20.4552i	1.01894	+	1.01894i
$404$	14.8267	+	6.75019i	0.737655	+	0.335834i
$405$	−17.4013	+	17.4013i	−0.864678	+	0.864678i
$406$	7.92821	−	1.43519i	0.393471	−	0.0712273i
$407$		−	24.3648i		−	1.20772i
$408$	4.03559	−	2.40400i	0.199791	−	0.119016i
$409$		−	36.8887i		−	1.82403i	−0.410156	−	0.912015i	$-0.634526\pi$
$409$		−	36.8887i		−	1.82403i	0.410156	−	0.912015i	$-0.365474\pi$
$410$	−1.31466	−	7.26237i	−0.0649263	−	0.358663i
$411$	−11.3815	+	11.3815i	−0.561406	+	0.561406i
$412$	−32.0514	+	11.9972i	−1.57906	+	0.591062i
$413$	13.6661	+	13.6661i	0.672464	+	0.672464i
$414$	21.2298	+	14.7217i	1.04339	+	0.723534i
$415$	−17.1807			−0.843366
$416$	−30.9724	−	24.8103i	−1.51855	−	1.21642i
$417$	6.58021			0.322234
$418$	4.38872	+	3.04334i	0.214659	+	0.148855i
$419$	17.8976	+	17.8976i	0.874355	+	0.874355i	0.992943	−	0.118589i	$-0.0378370\pi$
$419$	17.8976	+	17.8976i	0.874355	+	0.874355i	−0.118589	+	0.992943i	$0.537837\pi$
$420$	−15.7020	+	5.87746i	−0.766180	+	0.286791i
$421$	20.8204	−	20.8204i	1.01473	−	1.01473i	0.0148362	−	0.999890i	$-0.495277\pi$
$421$	20.8204	−	20.8204i	1.01473	−	1.01473i	0.999890	−	0.0148362i	$-0.00472269\pi$
$422$	3.21537	+	17.7622i	0.156522	+	0.864650i
$423$			12.4575i			0.605704i
$424$	14.8345	+	24.9026i	0.720425	+	1.20938i
$425$			0.0175844i			0.000852967i
$426$	12.9220	−	2.33918i	0.626072	−	0.113334i
$427$	−4.77528	+	4.77528i	−0.231092	+	0.231092i
$428$	−15.7024	−	7.14889i	−0.759005	−	0.345555i
$429$	41.7514	+	41.7514i	2.01577	+	2.01577i
$430$	5.57850	−	8.04460i	0.269019	−	0.387945i
$431$	5.86431			0.282474			0.141237	−	0.989976i	$-0.454892\pi$
$431$	5.86431			0.282474			0.141237	+	0.989976i	$0.454892\pi$
$432$	0.635312	−	9.18439i	0.0305665	−	0.441884i
$433$	−1.10457			−0.0530822			−0.0265411	−	0.999648i	$-0.508449\pi$
$433$	−1.10457			−0.0530822			−0.0265411	+	0.999648i	$0.508449\pi$
$434$	−5.60305	+	8.07999i	−0.268955	+	0.387852i
$435$	−11.8792	−	11.8792i	−0.569562	−	0.569562i
$436$	−9.73856	+	21.3906i	−0.466393	+	1.02442i
$437$	−6.56598	+	6.56598i	−0.314093	+	0.314093i
$438$	−25.8102	+	4.67225i	−1.23326	+	0.223249i
$439$			20.5982i			0.983100i	0.870849	+	0.491550i	$0.163569\pi$
$439$			20.5982i			0.983100i	−0.870849	+	0.491550i	$0.836431\pi$
$440$	23.0979	+	5.85229i	1.10115	+	0.278997i
$441$			8.17836i			0.389446i
$442$	1.31686	+	7.27452i	0.0626365	+	0.346014i
$443$	25.4691	−	25.4691i	1.21007	−	1.21007i	0.239071	−	0.971002i	$-0.423157\pi$
$443$	25.4691	−	25.4691i	1.21007	−	1.21007i	0.971002	−	0.239071i	$-0.0768429\pi$
$444$	10.0817	+	26.9339i	0.478456	+	1.27823i
$445$	−19.7531	−	19.7531i	−0.936388	−	0.936388i
$446$	11.8206	+	8.19695i	0.559721	+	0.388137i
$447$	−12.9291			−0.611523
$448$	6.42291	−	11.8613i	0.303454	−	0.560396i
$449$	−18.4747			−0.871874			−0.435937	−	0.899977i	$-0.643583\pi$
$449$	−18.4747			−0.871874			−0.435937	+	0.899977i	$0.643583\pi$
$450$	−0.0539524	−	0.0374131i	−0.00254334	−	0.00176367i
$451$	−6.24702	−	6.24702i	−0.294161	−	0.294161i
$452$	−6.06062	−	16.1914i	−0.285068	−	0.761577i
$453$	−27.3675	+	27.3675i	−1.28584	+	1.28584i
$454$	−3.63741	−	20.0936i	−0.170712	−	0.943040i
$455$		−	26.3865i		−	1.23702i
$456$	−6.11076	−	1.54828i	−0.286163	−	0.0725047i
$457$		−	0.505944i		−	0.0236671i	−0.999930	−	0.0118335i	$-0.996233\pi$
$457$		−	0.505944i		−	0.0236671i	0.999930	−	0.0118335i	$-0.00376682\pi$
$458$	31.2832	−	5.66298i	1.46177	−	0.264614i
$459$	−1.21272	+	1.21272i	−0.0566048	+	0.0566048i
$460$	−17.1661	+	37.7050i	−0.800373	+	1.75801i
$461$	8.39485	+	8.39485i	0.390987	+	0.390987i	0.875039	−	0.484052i	$-0.160835\pi$
$461$	8.39485	+	8.39485i	0.390987	+	0.390987i	−0.484052	+	0.875039i	$0.660835\pi$
$462$	−11.4365	+	16.4922i	−0.532073	+	0.767287i
$463$	−6.77587			−0.314901			−0.157451	−	0.987527i	$-0.550327\pi$
$463$	−6.77587			−0.314901			−0.157451	+	0.987527i	$0.550327\pi$
$464$	13.4836	+	0.932700i	0.625960	+	0.0432995i
$465$	20.5018			0.950750
$466$	11.6083	−	16.7401i	0.537746	−	0.775468i
$467$	12.2684	+	12.2684i	0.567716	+	0.567716i	0.931488	−	0.363772i	$-0.118511\pi$
$467$	12.2684	+	12.2684i	0.567716	+	0.567716i	−0.363772	+	0.931488i	$0.618511\pi$
$468$	−25.1215	−	11.4372i	−1.16124	−	0.528682i
$469$	5.21571	−	5.21571i	0.240839	−	0.240839i
$470$	−19.6574	+	3.55845i	−0.906730	+	0.164139i
$471$			14.7782i			0.680942i
$472$	16.5922	+	27.8533i	0.763718	+	1.28205i
$473$		−	11.7185i		−	0.538816i
$474$	−3.11000	−	17.1801i	−0.142847	−	0.789110i
$475$	0.0166865	−	0.0166865i	0.000765627	−	0.000765627i
$476$	−2.35334	+	0.880883i	−0.107865	+	0.0403752i
$477$	14.2563	+	14.2563i	0.652750	+	0.652750i
$478$	5.68815	+	3.94443i	0.260170	+	0.180414i
$479$	4.99002			0.228000			0.114000	−	0.993481i	$-0.463634\pi$
$479$	4.99002			0.228000			0.114000	+	0.993481i	$0.463634\pi$
$480$	−27.9550	+	3.08810i	−1.27597	+	0.140952i
$481$	−45.2611			−2.06373
$482$	15.7678	+	10.9341i	0.718205	+	0.498037i
$483$	−24.6741	−	24.6741i	−1.12271	−	1.12271i
$484$	6.10884	−	2.28662i	0.277675	−	0.103937i
$485$	−5.25287	+	5.25287i	−0.238521	+	0.238521i
$486$	−4.45428	−	24.6061i	−0.202050	−	1.11616i
$487$			9.95097i			0.450922i	0.974252	+	0.225461i	$0.0723888\pi$
$487$			9.95097i			0.450922i	−0.974252	+	0.225461i	$0.927611\pi$
$488$	−9.73267	+	5.79775i	−0.440577	+	0.262452i
$489$			29.7020i			1.34317i
$490$	−12.9051	+	2.33613i	−0.582994	+	0.105535i
$491$	10.1145	−	10.1145i	0.456463	−	0.456463i	−0.441030	−	0.897493i	$-0.645387\pi$
$491$	10.1145	−	10.1145i	0.456463	−	0.456463i	0.897493	+	0.441030i	$0.145387\pi$
$492$	9.49064	+	4.32083i	0.427871	+	0.194798i
$493$	−1.78039	−	1.78039i	−0.0801846	−	0.0801846i
$494$	5.65345	−	8.15268i	0.254361	−	0.366806i
$495$	16.5735			0.744922
$496$	−12.4403	+	10.8306i	−0.558586	+	0.486307i
$497$	−7.02482			−0.315106
$498$	13.8329	−	19.9480i	0.619867	−	0.893893i
$499$	−21.1075	−	21.1075i	−0.944903	−	0.944903i	0.0536568	−	0.998559i	$-0.482912\pi$
$499$	−21.1075	−	21.1075i	−0.944903	−	0.944903i	−0.998559	+	0.0536568i	$0.982912\pi$
$500$	9.28693	−	20.3986i	0.415324	−	0.912252i
$501$	3.93025	−	3.93025i	0.175591	−	0.175591i
$502$	−32.1164	+	5.81382i	−1.43343	+	0.259483i
$503$		−	20.9971i		−	0.936214i	−0.883672	−	0.468107i	$-0.844936\pi$
$503$		−	20.9971i		−	0.936214i	0.883672	−	0.468107i	$-0.155064\pi$
$504$	2.30432	−	9.09472i	0.102642	−	0.405111i
$505$			18.1708i			0.808590i
$506$	8.83370	+	48.7987i	0.392706	+	2.16937i
$507$	57.0717	−	57.0717i	2.53464	−	2.53464i
$508$	−12.9835	−	34.6863i	−0.576050	−	1.53896i
$509$	30.7064	+	30.7064i	1.36104	+	1.36104i	0.872595	+	0.488444i	$0.162435\pi$
$509$	30.7064	+	30.7064i	1.36104	+	1.36104i	0.488444	+	0.872595i	$0.337565\pi$
$510$	4.30549	+	2.98563i	0.190650	+	0.132206i
$511$	14.0313			0.620708
$512$	15.3314	−	16.6417i	0.677560	−	0.735467i
$513$	2.30159			0.101617
$514$	−29.4921	−	20.4512i	−1.30084	−	0.902064i
$515$	−26.9919	−	26.9919i	−1.18941	−	1.18941i
$516$	4.84888	+	12.9541i	0.213460	+	0.570273i
$517$	−16.9091	+	16.9091i	−0.743663	+	0.743663i
$518$	−2.74037	−	15.1382i	−0.120405	−	0.665136i
$519$			3.25116i			0.142710i
$520$	10.8715	−	42.9077i	0.476746	−	1.88163i
$521$		−	6.56275i		−	0.287519i	−0.989613	−	0.143760i	$-0.954081\pi$
$521$		−	6.56275i		−	0.287519i	0.989613	−	0.143760i	$-0.0459192\pi$
$522$	9.25060	−	1.67457i	0.404888	−	0.0732941i
$523$	−13.0317	+	13.0317i	−0.569837	+	0.569837i	−0.932083	−	0.362246i	$-0.882010\pi$
$523$	−13.0317	+	13.0317i	−0.569837	+	0.569837i	0.362246	+	0.932083i	$0.382010\pi$
$524$	−8.84991	+	19.4387i	−0.386610	+	0.849182i
$525$	0.0627055	+	0.0627055i	0.00273669	+	0.00273669i
$526$	−7.83705	+	11.3016i	−0.341711	+	0.492772i
$527$	3.07271			0.133849
$528$	−25.3921	+	22.1065i	−1.10505	+	0.962060i
$529$	−63.2241			−2.74887
$530$	−18.4236	+	26.5681i	−0.800269	+	1.15405i
$531$	15.9455	+	15.9455i	0.691976	+	0.691976i
$532$	3.06907	+	1.39727i	0.133061	+	0.0605792i
$533$	−11.6048	+	11.6048i	−0.502658	+	0.502658i
$534$	38.8390	−	7.03075i	1.68073	−	0.304250i
$535$		−	19.2441i		−	0.831994i
$536$	10.6303	−	6.33248i	0.459160	−	0.273522i
$537$		−	3.08205i		−	0.133000i
$538$	−7.00993	−	38.7239i	−0.302220	−	1.66951i
$539$	−11.1009	+	11.1009i	−0.478148	+	0.478148i
$540$	9.61704	−	3.59978i	0.413852	−	0.154910i
$541$	28.8515	+	28.8515i	1.24042	+	1.24042i	0.959826	+	0.280595i	$0.0905318\pi$
$541$	28.8515	+	28.8515i	1.24042	+	1.24042i	0.280595	+	0.959826i	$0.409468\pi$
$542$	24.1927	+	16.7763i	1.03917	+	0.720606i
$543$	−31.4622			−1.35017
$544$	−4.18976	+	0.462829i	−0.179634	+	0.0198436i
$545$	−26.2152			−1.12294
$546$	30.6367	+	21.2449i	1.31113	+	0.909198i
$547$	0.123183	+	0.123183i	0.00526694	+	0.00526694i	0.709735	−	0.704468i	$-0.248815\pi$
$547$	0.123183	+	0.123183i	0.00526694	+	0.00526694i	−0.704468	+	0.709735i	$0.748815\pi$
$548$	13.5272	−	5.06340i	0.577854	−	0.216298i
$549$	−5.57178	+	5.57178i	−0.237798	+	0.237798i
$550$	−0.0224495	−	0.124015i	−0.000957252	−	0.00528801i
$551$			3.37895i			0.143948i
$552$	−29.9572	−	50.2890i	−1.27506	−	2.14044i
$553$			9.33969i			0.397164i
$554$	39.1227	−	7.08211i	1.66216	−	0.300890i
$555$	−22.6822	+	22.6822i	−0.962806	+	0.962806i
$556$	−5.37410	−	2.44668i	−0.227913	−	0.103763i
$557$	4.64693	+	4.64693i	0.196897	+	0.196897i	0.798668	−	0.601772i	$-0.205538\pi$
$557$	4.64693	+	4.64693i	0.196897	+	0.196897i	−0.601772	+	0.798668i	$0.705538\pi$
$558$	−6.53761	+	9.42770i	−0.276759	+	0.399106i
$559$	−21.7687			−0.920720
$560$	15.0093	+	1.03824i	0.634260	+	0.0438737i
$561$	6.27176			0.264794
$562$	−1.11223	+	1.60392i	−0.0469168	+	0.0676573i
$563$	0.0253124	+	0.0253124i	0.00106679	+	0.00106679i	0.707640	−	0.706573i	$-0.249760\pi$
$563$	0.0253124	+	0.0253124i	0.00106679	+	0.00106679i	−0.706573	+	0.707640i	$0.749760\pi$
$564$	11.6954	−	25.6888i	0.492466	−	1.08169i
$565$	13.6354	−	13.6354i	0.573647	−	0.573647i
$566$	4.52770	−	0.819618i	0.190313	−	0.0344511i
$567$			18.6003i			0.781138i
$568$	−11.4232	−	2.89429i	−0.479308	−	0.121442i
$569$			35.4165i			1.48474i	0.669992	+	0.742369i	$0.266298\pi$
$569$			35.4165i			1.48474i	−0.669992	+	0.742369i	$0.733702\pi$
$570$	−1.25247	−	6.91882i	−0.0524601	−	0.289798i
$571$	−8.52660	+	8.52660i	−0.356827	+	0.356827i	−0.862642	−	0.505815i	$-0.831192\pi$
$571$	−8.52660	+	8.52660i	−0.356827	+	0.356827i	0.505815	+	0.862642i	$0.331192\pi$
$572$	−18.5744	−	49.6228i	−0.776636	−	2.07483i
$573$	−11.3163	−	11.3163i	−0.472747	−	0.472747i
$574$	−4.58399	−	3.17876i	−0.191332	−	0.132679i
$575$	0.219126			0.00913818
$576$	7.49422	−	13.8398i	0.312259	−	0.576656i
$577$	−17.8216			−0.741924			−0.370962	−	0.928648i	$-0.620972\pi$
$577$	−17.8216			−0.741924			−0.370962	+	0.928648i	$0.620972\pi$
$578$	−19.1110	−	13.2525i	−0.794913	−	0.551230i
$579$	−22.0333	−	22.0333i	−0.915674	−	0.915674i
$580$	5.28482	+	14.1187i	0.219440	+	0.586249i
$581$	−9.18221	+	9.18221i	−0.380942	+	0.380942i
$582$	−1.86966	−	10.3283i	−0.0774999	−	0.428121i
$583$			38.7015i			1.60285i
$584$	22.8166	+	5.78103i	0.944160	+	0.239221i
$585$		−	30.7876i		−	1.27291i
$586$	−33.9518	+	6.14606i	−1.40254	+	0.253891i
$587$	22.0917	−	22.0917i	0.911821	−	0.911821i	−0.0845949	−	0.996415i	$-0.526960\pi$
$587$	22.0917	−	22.0917i	0.911821	−	0.911821i	0.996415	+	0.0845949i	$0.0269596\pi$
$588$	7.67806	−	16.8647i	0.316638	−	0.695490i
$589$	−2.91581	−	2.91581i	−0.120144	−	0.120144i
$590$	−20.6066	+	29.7162i	−0.848360	+	1.22340i
$591$	−10.0145			−0.411941
$592$	1.78091	−	25.7457i	0.0731949	−	1.05814i
$593$	18.7487			0.769917			0.384958	−	0.922934i	$-0.374216\pi$
$593$	18.7487			0.769917			0.384958	+	0.922934i	$0.374216\pi$
$594$	7.00451	−	10.1010i	0.287399	−	0.414449i
$595$	−1.98185	−	1.98185i	−0.0812479	−	0.0812479i
$596$	10.5592	+	4.80734i	0.432523	+	0.196916i
$597$	−5.39041	+	5.39041i	−0.220615	+	0.220615i
$598$	90.6507	−	16.4099i	3.70698	−	0.671050i
$599$			12.6985i			0.518846i	0.965764	+	0.259423i	$0.0835323\pi$
$599$			12.6985i			0.518846i	−0.965764	+	0.259423i	$0.916468\pi$
$600$	0.0761317	+	0.127802i	0.00310806	+	0.00521750i
$601$			40.7759i			1.66328i	0.555312	+	0.831642i	$0.312599\pi$
$601$			40.7759i			1.66328i	−0.555312	+	0.831642i	$0.687401\pi$
$602$	−1.31801	−	7.28087i	−0.0537179	−	0.296746i
$603$	6.08567	−	6.08567i	0.247828	−	0.247828i
$604$	32.5271	−	12.1753i	1.32351	−	0.495406i
$605$	5.14452	+	5.14452i	0.209155	+	0.209155i
$606$	−21.0977	−	14.6301i	−0.857034	−	0.594308i
$607$	23.2677			0.944405			0.472202	−	0.881490i	$-0.343459\pi$
$607$	23.2677			0.944405			0.472202	+	0.881490i	$0.343459\pi$
$608$	4.41501	+	3.53662i	0.179052	+	0.143429i
$609$	−12.6976			−0.514534
$610$	−10.3836	−	7.20048i	−0.420420	−	0.291539i
$611$	31.4112	+	31.4112i	1.27076	+	1.27076i
$612$	−2.74586	+	1.02781i	−0.110995	+	0.0415468i
$613$	13.5213	−	13.5213i	0.546120	−	0.546120i	−0.379196	−	0.925316i	$-0.623799\pi$
$613$	13.5213	−	13.5213i	0.546120	−	0.546120i	0.925316	+	0.379196i	$0.123799\pi$
$614$	−0.143487	−	0.792644i	−0.00579066	−	0.0319885i
$615$			11.6312i			0.469017i
$616$	15.4725	−	9.21693i	0.623403	−	0.371361i
$617$			20.0366i			0.806642i	0.915059	+	0.403321i	$0.132144\pi$
$617$			20.0366i			0.806642i	−0.915059	+	0.403321i	$0.867856\pi$
$618$	53.0720	−	9.60725i	2.13487	−	0.386460i
$619$	22.2313	−	22.2313i	0.893552	−	0.893552i	−0.101304	−	0.994856i	$-0.532301\pi$
$619$	22.2313	−	22.2313i	0.893552	−	0.893552i	0.994856	+	0.101304i	$0.0323013\pi$
$620$	−16.7440	−	7.62309i	−0.672455	−	0.306151i
$621$	15.1122	+	15.1122i	0.606430	+	0.606430i
$622$	−12.6721	+	18.2741i	−0.508105	+	0.732723i
$623$	−21.1141			−0.845920
$624$	41.0660	+	47.1695i	1.64395	+	1.88829i
$625$	24.8815			0.995258
$626$	13.8306	−	19.9448i	0.552783	−	0.797153i
$627$	−5.95151	−	5.95151i	−0.237680	−	0.237680i
$628$	5.49489	−	12.0694i	0.219270	−	0.481622i
$629$	−3.39949	+	3.39949i	−0.135547	+	0.135547i
$630$	10.2974	−	1.86406i	0.410257	−	0.0742660i
$631$		−	35.8471i		−	1.42705i	−0.700629	−	0.713526i	$-0.747097\pi$
$631$		−	35.8471i		−	1.42705i	0.700629	−	0.713526i	$-0.252903\pi$
$632$	−3.84804	+	15.1875i	−0.153067	+	0.604127i
$633$		−	28.4475i		−	1.13069i
$634$	0.675841	+	3.73345i	0.0268411	+	0.148274i
$635$	29.2108	−	29.2108i	1.15920	−	1.15920i
$636$	−16.0139	−	42.7823i	−0.634994	−	1.69643i
$637$	20.6215	+	20.6215i	0.817053	+	0.817053i
$638$	14.8293	+	10.2833i	0.587096	+	0.407120i
$639$	−8.19652			−0.324249
$640$	23.9793	+	7.87230i	0.947865	+	0.311180i
$641$	−35.8583			−1.41632			−0.708158	−	0.706054i	$-0.750474\pi$
$641$	−35.8583			−1.41632			−0.708158	+	0.706054i	$0.750474\pi$
$642$	22.3438	+	15.4943i	0.881840	+	0.611509i
$643$	−23.4956	−	23.4956i	−0.926574	−	0.926574i	0.0709085	−	0.997483i	$-0.477410\pi$
$643$	−23.4956	−	23.4956i	−0.926574	−	0.926574i	−0.997483	+	0.0709085i	$0.977410\pi$
$644$	10.9770	+	29.3259i	0.432556	+	1.15560i
$645$	−10.9092	+	10.9092i	−0.429550	+	0.429550i
$646$	−0.187713	−	1.03696i	−0.00738548	−	0.0407985i
$647$		−	28.2637i		−	1.11116i	−0.831463	−	0.555580i	$-0.812496\pi$
$647$		−	28.2637i		−	1.11116i	0.831463	−	0.555580i	$-0.187504\pi$
$648$	−7.66349	+	30.2464i	−0.301050	+	1.18819i
$649$			43.2872i			1.69917i
$650$	−0.230376	+	0.0417033i	−0.00903607	+	0.00163574i
$651$	10.9572	−	10.9572i	0.429447	−	0.429447i
$652$	11.0439	−	24.2578i	0.432514	−	0.950010i
$653$	−24.1245	−	24.1245i	−0.944066	−	0.944066i	0.0544504	−	0.998516i	$-0.482659\pi$
$653$	−24.1245	−	24.1245i	−0.944066	−	0.944066i	−0.998516	+	0.0544504i	$0.982659\pi$
$654$	21.1070	−	30.4378i	0.825349	−	1.19021i
$655$	−23.8230			−0.930843
$656$	−6.14447	−	7.05771i	−0.239901	−	0.275557i
$657$	16.3717			0.638719
$658$	−8.60411	+	12.4077i	−0.335423	+	0.483704i
$659$	−33.1834	−	33.1834i	−1.29264	−	1.29264i	−0.933146	−	0.359497i	$-0.882948\pi$
$659$	−33.1834	−	33.1834i	−1.29264	−	1.29264i	−0.359497	−	0.933146i	$-0.617052\pi$
$660$	−34.1764	−	15.5596i	−1.33032	−	0.605657i
$661$	7.71340	−	7.71340i	0.300017	−	0.300017i	−0.541004	−	0.841020i	$-0.681955\pi$
$661$	7.71340	−	7.71340i	0.300017	−	0.300017i	0.841020	+	0.541004i	$0.181955\pi$
$662$	7.40881	−	1.34117i	0.287951	−	0.0521259i
$663$		−	11.6507i		−	0.452476i
$664$	−18.7146	+	11.1483i	−0.726267	+	0.432637i
$665$			3.76130i			0.145857i
$666$	−3.19745	−	17.6632i	−0.123899	−	0.684436i
$667$	−22.1861	+	22.1861i	−0.859049	+	0.859049i
$668$	−4.67123	+	1.74850i	−0.180735	+	0.0676514i
$669$	−16.0298	−	16.0298i	−0.619748	−	0.619748i
$670$	11.3413	+	7.86459i	0.438153	+	0.303836i
$671$	−15.1257			−0.583920
$672$	−13.2901	+	16.5910i	−0.512678	+	0.640012i
$673$	17.0920			0.658848			0.329424	−	0.944182i	$-0.393145\pi$
$673$	17.0920			0.658848			0.329424	+	0.944182i	$0.393145\pi$
$674$	1.30026	+	0.901663i	0.0500842	+	0.0347307i
$675$	−0.0384053	−	0.0384053i	−0.00147822	−	0.00147822i
$676$	−67.8315	+	25.3902i	−2.60890	+	0.976545i
$677$	33.0966	−	33.0966i	1.27200	−	1.27200i	0.326970	−	0.945035i	$-0.393972\pi$
$677$	33.0966	−	33.0966i	1.27200	−	1.27200i	0.945035	−	0.326970i	$-0.106028\pi$
$678$	4.85327	+	26.8102i	0.186389	+	1.02964i
$679$			5.61480i			0.215476i
$680$	−2.40619	−	4.03927i	−0.0922733	−	0.154899i
$681$			32.1815i			1.23320i
$682$	−21.6705	+	3.92286i	−0.829805	+	0.150214i
$683$	−29.7256	+	29.7256i	−1.13742	+	1.13742i	−0.148508	+	0.988911i	$0.547447\pi$
$683$	−29.7256	+	29.7256i	−1.13742	+	1.13742i	−0.988911	+	0.148508i	$0.952553\pi$
$684$	3.58098	+	1.63032i	0.136922	+	0.0623370i
$685$	11.3919	+	11.3919i	0.435260	+	0.435260i
$686$	−15.1601	+	21.8619i	−0.578815	+	0.834692i
$687$	−50.1024			−1.91153
$688$	0.856544	−	12.3826i	0.0326555	−	0.472084i
$689$	71.8936			2.73893
$690$	37.2051	−	53.6525i	1.41638	−	2.04251i
$691$	−20.7907	−	20.7907i	−0.790915	−	0.790915i	0.190728	−	0.981643i	$-0.438915\pi$
$691$	−20.7907	−	20.7907i	−0.790915	−	0.790915i	−0.981643	+	0.190728i	$0.938915\pi$
$692$	1.20886	−	2.65524i	0.0459540	−	0.100937i
$693$	8.85770	−	8.85770i	0.336476	−	0.336476i
$694$	−44.5342	+	8.06171i	−1.69049	+	0.306018i
$695$		−	6.58622i		−	0.249830i
$696$	−20.6480	−	5.23155i	−0.782659	−	0.198301i
$697$			1.74323i			0.0660295i
$698$	−6.59283	−	36.4198i	−0.249542	−	1.37851i
$699$	−22.7011	+	22.7011i	−0.858633	+	0.858633i
$700$	−0.0278965	−	0.0745274i	−0.00105439	−	0.00281687i
$701$	0.922831	+	0.922831i	0.0348548	+	0.0348548i	0.724319	−	0.689465i	$-0.242154\pi$
$701$	0.922831	+	0.922831i	0.0348548	+	0.0348548i	−0.689465	+	0.724319i	$0.742154\pi$
$702$	−18.7641	−	13.0119i	−0.708205	−	0.491103i
$703$	6.45181			0.243335
$704$	28.9576	−	8.61309i	1.09138	−	0.324618i
$705$	31.4829			1.18571
$706$	−23.5911	−	16.3592i	−0.887864	−	0.615686i
$707$	9.71140	+	9.71140i	0.365235	+	0.365235i
$708$	−17.9114	−	47.8516i	−0.673153	−	1.79837i
$709$	13.2315	−	13.2315i	0.496920	−	0.496920i	−0.413558	−	0.910478i	$-0.635714\pi$
$709$	13.2315	−	13.2315i	0.496920	−	0.496920i	0.910478	+	0.413558i	$0.135714\pi$
$710$	−2.34132	−	12.9338i	−0.0878680	−	0.485397i
$711$			10.8975i			0.408688i
$712$	−34.3342	−	8.69922i	−1.28673	−	0.326017i
$713$		−	38.2903i		−	1.43398i
$714$	3.89675	−	0.705401i	0.145832	−	0.0263990i
$715$	41.7895	−	41.7895i	1.56284	−	1.56284i
$716$	−1.14598	+	2.51713i	−0.0428273	+	0.0940695i
$717$	−7.71366	−	7.71366i	−0.288072	−	0.288072i
$718$	0.738256	−	1.06462i	0.0275515	−	0.0397312i
$719$	−8.61798			−0.321396			−0.160698	−	0.987004i	$-0.551375\pi$
$719$	−8.61798			−0.321396			−0.160698	+	0.987004i	$0.551375\pi$
$720$	17.5128	+	1.21141i	0.652664	+	0.0451467i
$721$	−28.8517			−1.07449
$722$	−0.805879	+	1.16214i	−0.0299917	+	0.0432502i
$723$	−21.3826	−	21.3826i	−0.795229	−	0.795229i
$724$	25.6954	+	11.6984i	0.954963	+	0.434769i
$725$	0.0563827	−	0.0563827i	0.00209400	−	0.00209400i
$726$	−10.1153	+	1.83109i	−0.375412	+	0.0679583i
$727$		−	2.92019i		−	0.108304i	−0.998533	−	0.0541519i	$-0.982754\pi$
$727$		−	2.92019i		−	0.108304i	0.998533	−	0.0541519i	$-0.0172455\pi$
$728$	−17.1218	−	28.7423i	−0.634576	−	1.06526i
$729$			6.31374i			0.233842i
$730$	4.67652	+	25.8338i	0.173086	+	0.956153i
$731$	−1.63502	+	1.63502i	−0.0604733	+	0.0604733i
$732$	16.7206	−	6.25872i	0.618011	−	0.231329i
$733$	−17.0882	−	17.0882i	−0.631166	−	0.631166i	0.317195	−	0.948360i	$-0.397259\pi$
$733$	−17.0882	−	17.0882i	−0.631166	−	0.631166i	−0.948360	+	0.317195i	$0.897259\pi$
$734$	17.0983	+	11.8568i	0.631111	+	0.437642i
$735$	20.6686			0.762371
$736$	5.76750	+	52.2102i	0.212593	+	1.92449i
$737$	16.5207			0.608549
$738$	−5.34858	−	3.70896i	−0.196884	−	0.136529i
$739$	10.2614	+	10.2614i	0.377470	+	0.377470i	0.870189	−	0.492719i	$-0.163997\pi$
$739$	10.2614	+	10.2614i	0.377470	+	0.377470i	−0.492719	+	0.870189i	$0.663997\pi$
$740$	26.9585	−	10.0909i	0.991015	−	0.370949i
$741$	−11.0558	+	11.0558i	−0.406145	+	0.406145i
$742$	4.35285	+	24.0458i	0.159798	+	0.882751i
$743$			24.2443i			0.889436i	0.895671	+	0.444718i	$0.146696\pi$
$743$			24.2443i			0.889436i	−0.895671	+	0.444718i	$0.853304\pi$
$744$	22.3323	−	13.3033i	0.818741	−	0.487724i
$745$			12.9409i			0.474117i
$746$	−19.7762	+	3.57996i	−0.724059	+	0.131071i
$747$	−10.7138	+	10.7138i	−0.391996	+	0.391996i
$748$	−5.12219	−	2.33200i	−0.187286	−	0.0852662i
$749$	−10.2850	−	10.2850i	−0.375806	−	0.375806i
$750$	−20.1281	+	29.0262i	−0.734976	+	1.05989i
$751$	−38.6250			−1.40944			−0.704722	−	0.709483i	$-0.748928\pi$
$751$	−38.6250			−1.40944			−0.704722	+	0.709483i	$0.748928\pi$
$752$	−19.1035	+	16.6316i	−0.696632	+	0.606491i
$753$	51.4369			1.87447
$754$	19.1027	−	27.5475i	0.695680	−	1.00322i
$755$	27.3925	+	27.3925i	0.996915	+	0.996915i
$756$	3.21593	−	7.06374i	0.116962	−	0.256906i
$757$	−1.87274	+	1.87274i	−0.0680660	+	0.0680660i	−0.740320	−	0.672254i	$-0.765326\pi$
$757$	−1.87274	+	1.87274i	−0.0680660	+	0.0680660i	0.672254	+	0.740320i	$0.265326\pi$
$758$	−20.6632	+	3.74052i	−0.750522	+	0.135862i
$759$		−	78.1549i		−	2.83684i
$760$	−1.54969	+	6.11634i	−0.0562132	+	0.221863i
$761$			20.5292i			0.744181i	0.928196	+	0.372091i	$0.121359\pi$
$761$			20.5292i			0.744181i	−0.928196	+	0.372091i	$0.878641\pi$
$762$	10.3970	+	57.4349i	0.376645	+	2.08065i
$763$	−14.0107	+	14.0107i	−0.507222	+	0.507222i
$764$	5.03443	+	13.4498i	0.182139	+	0.486597i
$765$	−2.31241	−	2.31241i	−0.0836054	−	0.0836054i
$766$	1.43066	+	0.992088i	0.0516919	+	0.0358456i
$767$	80.4123			2.90352
$768$	−28.4471	+	21.5034i	−1.02650	+	0.775938i
$769$	−31.5640			−1.13823			−0.569113	−	0.822259i	$-0.692713\pi$
$769$	−31.5640			−1.13823			−0.569113	+	0.822259i	$0.692713\pi$
$770$	16.5073	+	11.4469i	0.594881	+	0.412518i
$771$	39.9940	+	39.9940i	1.44035	+	1.44035i
$772$	9.80223	+	26.1873i	0.352790	+	0.942502i
$773$	−24.0804	+	24.0804i	−0.866113	+	0.866113i	−0.992040	−	0.125927i	$-0.959810\pi$
$773$	−24.0804	+	24.0804i	−0.866113	+	0.866113i	0.125927	+	0.992040i	$0.459810\pi$
$774$	−1.53784	−	8.49529i	−0.0552766	−	0.305357i
$775$			0.0973091i			0.00349545i
$776$	−2.31335	+	9.13037i	−0.0830445	+	0.327761i
$777$			24.2450i			0.869786i
$778$	5.41636	−	0.980487i	0.194186	−	0.0351522i
$779$	1.65422	−	1.65422i	0.0592684	−	0.0592684i
$780$	−28.9043	+	63.4877i	−1.03494	+	2.27322i
$781$	−11.1255	−	11.1255i	−0.398103	−	0.398103i
$782$	5.57611	−	8.04116i	0.199401	−	0.287551i
$783$	7.77694			0.277925
$784$	−12.5414	+	10.9186i	−0.447909	+	0.389952i
$785$	14.7917			0.527937
$786$	19.1810	−	27.6603i	0.684162	−	0.986611i
$787$	−9.26918	−	9.26918i	−0.330410	−	0.330410i	0.522332	−	0.852742i	$-0.325062\pi$
$787$	−9.26918	−	9.26918i	−0.330410	−	0.330410i	−0.852742	+	0.522332i	$0.825062\pi$
$788$	8.17891	+	3.72364i	0.291362	+	0.132649i
$789$	15.3260	−	15.3260i	0.545620	−	0.545620i
$790$	−17.1958	+	3.11284i	−0.611800	+	0.110750i
$791$		−	14.5749i		−	0.518225i
$792$	18.0532	−	10.7543i	0.641492	−	0.382136i
$793$			28.0981i			0.997794i
$794$	−3.51834	−	19.4359i	−0.124861	−	0.689753i
$795$	36.0288	−	36.0288i	1.27781	−	1.27781i
$796$	6.40668	−	2.39810i	0.227079	−	0.0849983i
$797$	3.18216	+	3.18216i	0.112718	+	0.112718i	0.761216	−	0.648498i	$-0.224603\pi$
$797$	3.18216	+	3.18216i	0.112718	+	0.112718i	−0.648498	+	0.761216i	$0.724603\pi$
$798$	−4.36715	−	3.02839i	−0.154595	−	0.107204i
$799$	4.71849			0.166928
$800$	−0.0146573	−	0.132685i	−0.000518212	−	0.00469111i
$801$	−24.6359			−0.870466
$802$	−13.4191	−	9.30541i	−0.473844	−	0.328585i
$803$	22.2220	+	22.2220i	0.784198	+	0.784198i
$804$	−18.2628	+	6.83597i	−0.644078	+	0.241086i
$805$	−24.6966	+	24.6966i	−0.870441	+	0.870441i
$806$	7.28727	+	40.2560i	0.256683	+	1.41796i
$807$			62.0194i			2.18318i
$808$	11.7908	+	19.7931i	0.414798	+	0.696320i
$809$		−	49.6396i		−	1.74524i	−0.488402	−	0.872619i	$-0.662420\pi$
$809$		−	49.6396i		−	1.74524i	0.488402	−	0.872619i	$-0.337580\pi$
$810$	−34.2460	+	6.19932i	−1.20328	+	0.217822i
$811$	34.5423	−	34.5423i	1.21294	−	1.21294i	0.242891	−	0.970053i	$-0.421904\pi$
$811$	34.5423	−	34.5423i	1.21294	−	1.21294i	0.970053	−	0.242891i	$-0.0780959\pi$
$812$	10.3702	+	4.72130i	0.363924	+	0.165685i
$813$	−32.8075	−	32.8075i	−1.15061	−	1.15061i
$814$	19.6351	−	28.3152i	0.688209	−	0.992446i
$815$	29.7291			1.04137
$816$	6.62723	+	0.458425i	0.231999	+	0.0160481i
$817$	3.10306			0.108562
$818$	29.7279	−	42.8697i	1.03941	−	1.49890i
$819$	−16.4545	−	16.4545i	−0.574965	−	0.574965i
$820$	4.32478	−	9.49931i	0.151028	−	0.331730i
$821$	29.9868	−	29.9868i	1.04655	−	1.04655i	0.0476858	−	0.998862i	$-0.484815\pi$
$821$	29.9868	−	29.9868i	1.04655	−	1.04655i	0.998862	−	0.0476858i	$-0.0151846\pi$
$822$	−22.3989	+	4.05471i	−0.781250	+	0.141424i
$823$			18.6588i			0.650404i	0.945645	+	0.325202i	$0.105432\pi$
$823$			18.6588i			0.650404i	−0.945645	+	0.325202i	$0.894568\pi$
$824$	−46.9164	−	11.8872i	−1.63441	−	0.414109i
$825$			0.198619i			0.00691503i
$826$	4.86863	+	26.8950i	0.169401	+	0.935798i
$827$	33.8005	−	33.8005i	1.17536	−	1.17536i	0.194443	−	0.980914i	$-0.437710\pi$
$827$	33.8005	−	33.8005i	1.17536	−	1.17536i	0.980914	−	0.194443i	$-0.0622900\pi$
$828$	12.8080	+	34.2173i	0.445107	+	1.18913i
$829$	15.0301	+	15.0301i	0.522018	+	0.522018i	0.918181	−	0.396162i	$-0.129658\pi$
$829$	15.0301	+	15.0301i	0.522018	+	0.522018i	−0.396162	+	0.918181i	$0.629658\pi$
$830$	−19.9663	−	13.8455i	−0.693039	−	0.480586i
$831$	−62.6579			−2.17358
$832$	−16.0001	−	53.7930i	−0.554703	−	1.86494i
$833$	3.09770			0.107329
$834$	7.64709	+	5.30285i	0.264797	+	0.183623i
$835$	−3.93385	−	3.93385i	−0.136136	−	0.136136i
$836$	2.64772	+	7.07355i	0.0915732	+	0.244644i
$837$	−6.71098	+	6.71098i	−0.231966	+	0.231966i
$838$	6.37613	+	35.2227i	0.220260	+	1.21675i
$839$			23.2106i			0.801321i	0.916227	+	0.400660i	$0.131219\pi$
$839$			23.2106i			0.801321i	−0.916227	+	0.400660i	$0.868781\pi$
$840$	−22.9844	−	5.82353i	−0.793037	−	0.200931i
$841$		−	17.5827i		−	0.606300i
$842$	40.9749	−	7.41741i	1.41209	−	0.255621i
$843$	2.17507	−	2.17507i	0.0749133	−	0.0749133i
$844$	−10.5775	+	23.2333i	−0.364092	+	0.799722i
$845$	−57.1238	−	57.1238i	−1.96512	−	1.96512i
$846$	−10.0392	+	14.4773i	−0.345156	+	0.497740i
$847$	5.49899			0.188947
$848$	−2.82883	+	40.8950i	−0.0971424	+	1.40434i
$849$	−7.25145			−0.248869
$850$	−0.0141709	+	0.0204354i	−0.000486057	+	0.000700929i
$851$	42.3624	+	42.3624i	1.45217	+	1.45217i
$852$	16.9022	+	7.69512i	0.579059	+	0.263630i
$853$	−7.73580	+	7.73580i	−0.264869	+	0.264869i	−0.827029	−	0.562160i	$-0.809971\pi$
$853$	−7.73580	+	7.73580i	−0.264869	+	0.264869i	0.562160	+	0.827029i	$0.309971\pi$
$854$	−9.39783	+	1.70122i	−0.321587	+	0.0582147i
$855$			4.38867i			0.150089i
$856$	−12.4872	−	20.9622i	−0.426804	−	0.716475i
$857$		−	35.5955i		−	1.21592i	−0.793968	−	0.607959i	$-0.791988\pi$
$857$		−	35.5955i		−	1.21592i	0.793968	−	0.607959i	$-0.208012\pi$
$858$	14.8742	+	82.1673i	0.507796	+	2.80514i
$859$	15.6464	−	15.6464i	0.533848	−	0.533848i	−0.387867	−	0.921715i	$-0.626788\pi$
$859$	15.6464	−	15.6464i	0.533848	−	0.533848i	0.921715	+	0.387867i	$0.126788\pi$
$860$	12.9659	−	4.85331i	0.442135	−	0.165497i
$861$	6.21632	+	6.21632i	0.211852	+	0.211852i
$862$	6.81512	+	4.72592i	0.232124	+	0.160966i
$863$	12.0054			0.408668			0.204334	−	0.978901i	$-0.434497\pi$
$863$	12.0054			0.408668			0.204334	+	0.978901i	$0.434497\pi$
$864$	8.13983	−	10.1615i	0.276923	−	0.345702i
$865$	3.25413			0.110644
$866$	−1.28366	−	0.890149i	−0.0436205	−	0.0302485i
$867$	25.9163	+	25.9163i	0.880164	+	0.880164i
$868$	−13.0230	+	4.87467i	−0.442029	+	0.165457i
$869$	−14.7917	+	14.7917i	−0.501774	+	0.501774i
$870$	−4.23202	−	23.3784i	−0.143479	−	0.792600i
$871$		−	30.6897i		−	1.03988i
$872$	−28.5558	+	17.0106i	−0.967020	+	0.576053i
$873$			6.55132i			0.221729i
$874$	−12.9219	+	2.33917i	−0.437091	+	0.0791236i
$875$	13.3610	−	13.3610i	0.451683	−	0.451683i
$876$	−33.7603	−	15.3701i	−1.14065	−	0.519309i
$877$	16.1952	+	16.1952i	0.546872	+	0.546872i	0.925535	−	0.378663i	$-0.123616\pi$
$877$	16.1952	+	16.1952i	0.546872	+	0.546872i	−0.378663	+	0.925535i	$0.623616\pi$
$878$	−16.5997	+	23.9379i	−0.560212	+	0.807866i
$879$	54.3764			1.83407
$880$	22.1267	+	25.4153i	0.745890	+	0.856749i
$881$	27.9754			0.942517			0.471258	−	0.881995i	$-0.343800\pi$
$881$	27.9754			0.942517			0.471258	+	0.881995i	$0.343800\pi$
$882$	−6.59077	+	9.50436i	−0.221923	+	0.320028i
$883$	−5.09457	−	5.09457i	−0.171446	−	0.171446i	0.616169	−	0.787614i	$-0.288684\pi$
$883$	−5.09457	−	5.09457i	−0.171446	−	0.171446i	−0.787614	+	0.616169i	$0.788684\pi$
$884$	−4.33202	+	9.51521i	−0.145702	+	0.320031i
$885$	40.2979	−	40.2979i	1.35460	−	1.35460i
$886$	50.1235	−	9.07352i	1.68393	−	0.304831i
$887$			5.03188i			0.168954i	0.996425	+	0.0844769i	$0.0269219\pi$
$887$			5.03188i			0.168954i	−0.996425	+	0.0844769i	$0.973078\pi$
$888$	−9.98918	+	39.4255i	−0.335215	+	1.32303i
$889$		−	31.2235i		−	1.04720i
$890$	−7.03717	−	38.8744i	−0.235887	−	1.30307i
$891$	−29.4581	+	29.4581i	−0.986884	+	0.986884i
$892$	7.13137	+	19.0519i	0.238776	+	0.637906i
$893$	−4.47755	−	4.47755i	−0.149836	−	0.149836i
$894$	−15.0253	−	10.4193i	−0.502522	−	0.348472i
$895$	−3.08486			−0.103116
$896$	17.0231	−	8.60839i	0.568702	−	0.287586i
$897$	−145.184			−4.84755
$898$	−21.4701	−	14.8884i	−0.716466	−	0.496831i
$899$	−9.85237	−	9.85237i	−0.328595	−	0.328595i
$900$	−0.0325495	−	0.0869583i	−0.00108498	−	0.00289861i
$901$	5.39982	−	5.39982i	0.179894	−	0.179894i
$902$	−2.22554	−	12.2942i	−0.0741024	−	0.409353i
$903$			11.6609i			0.388050i
$904$	6.00501	−	23.7007i	0.199724	−	0.788273i
$905$			31.4910i			1.04680i
$906$	−53.8596	+	9.74983i	−1.78936	+	0.323916i
$907$	−21.1793	+	21.1793i	−0.703248	+	0.703248i	−0.965106	−	0.261858i	$-0.915665\pi$
$907$	−21.1793	+	21.1793i	−0.703248	+	0.703248i	0.261858	+	0.965106i	$0.415665\pi$
$908$	11.9659	−	26.2828i	0.397101	−	0.872226i
$909$	11.3312	+	11.3312i	0.375833	+	0.375833i
$910$	21.2643	−	30.6647i	0.704905	−	1.01652i
$911$	−8.55091			−0.283304			−0.141652	−	0.989916i	$-0.545241\pi$
$911$	−8.55091			−0.283304			−0.141652	+	0.989916i	$0.545241\pi$
$912$	−5.85381	−	6.72384i	−0.193839	−	0.222649i
$913$	−29.0846			−0.962560
$914$	0.407730	−	0.587976i	0.0134865	−	0.0194485i
$915$	14.0811	+	14.0811i	0.465508	+	0.465508i
$916$	40.9190	+	18.6293i	1.35200	+	0.615530i
$917$	−12.7322	+	12.7322i	−0.420455	+	0.420455i
$918$	−2.38665	+	0.432038i	−0.0787710	+	0.0142594i
$919$			5.69492i			0.187858i	0.995579	+	0.0939291i	$0.0299427\pi$
$919$			5.69492i			0.187858i	−0.995579	+	0.0939291i	$0.970057\pi$
$920$	−50.3350	+	29.9845i	−1.65950	+	0.988561i
$921$			1.26948i			0.0418308i
$922$	2.99072	+	16.5212i	0.0984941	+	0.544097i
$923$	−20.6673	+	20.6673i	−0.680272	+	0.680272i
$924$	−26.5815	+	9.94977i	−0.874466	+	0.327323i
$925$	−0.107658	−	0.107658i	−0.00353977	−	0.00353977i
$926$	−7.87447	−	5.46053i	−0.258771	−	0.179444i
$927$	−33.6640			−1.10567
$928$	14.9181	+	11.9501i	0.489711	+	0.392280i
$929$	49.3534			1.61923			0.809616	−	0.586960i	$-0.199676\pi$
$929$	49.3534			1.61923			0.809616	+	0.586960i	$0.199676\pi$
$930$	23.8259	+	16.5220i	0.781282	+	0.541778i
$931$	−2.93952	−	2.93952i	−0.0963388	−	0.0963388i
$932$	26.9809	−	10.0993i	0.883790	−	0.330813i
$933$	24.7813	−	24.7813i	0.811304	−	0.811304i
$934$	4.37071	+	24.1445i	0.143014	+	0.790031i
$935$		−	6.27749i		−	0.205296i
$936$	−19.9776	−	33.5364i	−0.652989	−	1.09617i
$937$		−	16.8032i		−	0.548936i	−0.961596	−	0.274468i	$-0.911498\pi$
$937$		−	16.8032i		−	0.548936i	0.961596	−	0.274468i	$-0.0885017\pi$
$938$	10.2646	−	1.85813i	0.335151	−	0.0606701i
$939$	−27.0469	+	27.0469i	−0.882643	+	0.882643i
$940$	−25.7123	−	11.7061i	−0.838642	−	0.381811i
$941$	29.3410	+	29.3410i	0.956489	+	0.956489i	0.999092	−	0.0426033i	$-0.0135651\pi$
$941$	29.3410	+	29.3410i	0.956489	+	0.956489i	−0.0426033	+	0.999092i	$0.513565\pi$
$942$	−11.9094	+	17.1742i	−0.388030	+	0.559566i
$943$	21.7231			0.707401
$944$	−3.16402	+	45.7406i	−0.102980	+	1.48873i
$945$	8.65695			0.281611
$946$	9.44367	−	13.6184i	0.307040	−	0.442774i
$947$	−6.93921	−	6.93921i	−0.225494	−	0.225494i	0.585313	−	0.810807i	$-0.300972\pi$
$947$	−6.93921	−	6.93921i	−0.225494	−	0.225494i	−0.810807	+	0.585313i	$0.800972\pi$
$948$	10.2309	−	22.4719i	0.332283	−	0.729854i
$949$	41.2806	−	41.2806i	1.34003	−	1.34003i
$950$	0.0328392	−	0.00594466i	0.00106544	−	0.000192870i
$951$		−	5.97941i		−	0.193896i
$952$	−3.44478	−	0.872801i	−0.111646	−	0.0282876i
$953$			58.9341i			1.90906i	0.298108	+	0.954532i	$0.403644\pi$
$953$			58.9341i			1.90906i	−0.298108	+	0.954532i	$0.596356\pi$
$954$	5.07889	+	28.0566i	0.164435	+	0.908365i
$955$	−11.3267	+	11.3267i	−0.366523	+	0.366523i
$956$	3.43167	+	9.16793i	0.110988	+	0.296512i
$957$	−20.1098	−	20.1098i	−0.650059	−	0.650059i
$958$	5.79908	+	4.02135i	0.187360	+	0.129924i
$959$	12.1768			0.393208
$960$	−34.9762	−	18.9396i	−1.12885	−	0.611272i
$961$	−13.9961			−0.451488
$962$	−52.5995	−	36.4750i	−1.69588	−	1.17600i
$963$	−12.0005	−	12.0005i	−0.386711	−	0.386711i
$964$	9.51274	+	25.4139i	0.306385	+	0.818527i
$965$	−22.0535	+	22.0535i	−0.709926	+	0.709926i
$966$	−8.79028	−	48.5589i	−0.282823	−	1.56236i
$967$		−	53.4092i		−	1.71752i	−0.512375	−	0.858762i	$-0.671234\pi$
$967$		−	53.4092i		−	1.71752i	0.512375	−	0.858762i	$-0.328766\pi$
$968$	8.94204	+	2.26563i	0.287408	+	0.0728202i
$969$			1.66077i			0.0533515i
$970$	−10.3377	+	1.87137i	−0.331925	+	0.0600860i
$971$	−26.3394	+	26.3394i	−0.845270	+	0.845270i	−0.989539	−	0.144268i	$-0.953917\pi$
$971$	−26.3394	+	26.3394i	−0.845270	+	0.845270i	0.144268	+	0.989539i	$0.453917\pi$
$972$	14.6531	−	32.1852i	0.469998	−	1.03234i
$973$	−3.52001	−	3.52001i	−0.112846	−	0.112846i
$974$	−8.01928	+	11.5644i	−0.256954	+	0.370547i
$975$	0.368964			0.0118163
$976$	−15.9830	−	1.10559i	−0.511602	−	0.0353891i
$977$	−6.77662			−0.216803			−0.108402	−	0.994107i	$-0.534573\pi$
$977$	−6.77662			−0.216803			−0.108402	+	0.994107i	$0.534573\pi$
$978$	−23.9362	+	34.5178i	−0.765396	+	1.10376i
$979$	−33.4394	−	33.4394i	−1.06873	−	1.06873i
$980$	−16.8801	−	7.68508i	−0.539216	−	0.245491i
$981$	−16.3477	+	16.3477i	−0.521940	+	0.521940i
$982$	19.9056	−	3.60337i	0.635212	−	0.114988i
$983$			26.6344i			0.849505i	0.905310	+	0.424752i	$0.139639\pi$
$983$			26.6344i			0.849505i	−0.905310	+	0.424752i	$0.860361\pi$
$984$	7.54733	+	12.6697i	0.240600	+	0.403895i
$985$			10.0237i			0.319380i
$986$	−0.634274	−	3.50383i	−0.0201994	−	0.111585i
$987$	16.8260	−	16.8260i	0.535579	−	0.535579i
$988$	13.1402	−	4.91852i	0.418044	−	0.156479i
$989$	20.3746	+	20.3746i	0.647874	+	0.647874i
$990$	19.2606	+	13.3562i	0.612143	+	0.424488i
$991$	−21.3636			−0.678638			−0.339319	−	0.940671i	$-0.610197\pi$
$991$	−21.3636			−0.678638			−0.339319	+	0.940671i	$0.610197\pi$
$992$	−23.1854	+	2.56122i	−0.736138	+	0.0813189i
$993$	−11.8658			−0.376549
$994$	−8.16379	−	5.66115i	−0.258940	−	0.179561i
$995$	5.39534	+	5.39534i	0.171044	+	0.171044i
$996$	32.1514	−	12.0347i	1.01876	−	0.381333i
$997$	−13.3210	+	13.3210i	−0.421880	+	0.421880i	−0.885851	−	0.463970i	$-0.846424\pi$
$997$	−13.3210	+	13.3210i	−0.421880	+	0.421880i	0.463970	+	0.885851i	$0.346424\pi$
$998$	−7.51969	−	41.5399i	−0.238032	−	1.31492i
$999$		−	14.8494i		−	0.469814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.77.28	✓	68
4.3	odd	2		1216.2.k.b.913.28		68
16.5	even	4	inner	304.2.k.b.229.28	yes	68
16.11	odd	4		1216.2.k.b.305.28		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.28	✓	68	1.1	even	1	trivial
304.2.k.b.229.28	yes	68	16.5	even	4	inner
1216.2.k.b.305.28		68	16.11	odd	4
1216.2.k.b.913.28		68	4.3	odd	2

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16214 + 0.805879i) q^{2} +(-1.57596 - 1.57596i) q^{3} +(0.701117 + 1.87308i) q^{4} +(-1.57740 + 1.57740i) q^{5} +(-0.561447 - 3.10152i) q^{6} +1.68609i q^{7} +(-0.694684 + 2.74179i) q^{8} +1.96732i q^{9} +O(q^{10})\)	\(q+(1.16214 + 0.805879i) q^{2} +(-1.57596 - 1.57596i) q^{3} +(0.701117 + 1.87308i) q^{4} +(-1.57740 + 1.57740i) q^{5} +(-0.561447 - 3.10152i) q^{6} +1.68609i q^{7} +(-0.694684 + 2.74179i) q^{8} +1.96732i q^{9} +(-3.10435 + 0.561960i) q^{10} +(-2.67034 + 2.67034i) q^{11} +(1.84697 - 4.05684i) q^{12} +(4.96054 + 4.96054i) q^{13} +(-1.35878 + 1.95946i) q^{14} +4.97186 q^{15} +(-3.01687 + 2.62650i) q^{16} +0.745156 q^{17} +(-1.58542 + 2.28629i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(-4.06055 - 1.84866i) q^{20} +(2.65721 - 2.65721i) q^{21} +(-5.25526 + 0.951324i) q^{22} -9.28569i q^{23} +(5.41576 - 3.22616i) q^{24} +0.0235982i q^{25} +(1.76722 + 9.76241i) q^{26} +(-1.62747 + 1.62747i) q^{27} +(-3.15818 + 1.18215i) q^{28} +(-2.38928 - 2.38928i) q^{29} +(5.77797 + 4.00672i) q^{30} +4.12358 q^{31} +(-5.62265 + 0.621117i) q^{32} +8.41670 q^{33} +(0.865973 + 0.600506i) q^{34} +(-2.65964 - 2.65964i) q^{35} +(-3.68495 + 1.37932i) q^{36} +(-4.56212 + 4.56212i) q^{37} +(-0.251911 - 1.39160i) q^{38} -15.6352i q^{39} +(-3.22911 - 5.42071i) q^{40} +2.33941i q^{41} +(5.22943 - 0.946648i) q^{42} +(-2.19419 + 2.19419i) q^{43} +(-6.87398 - 3.12954i) q^{44} +(-3.10326 - 3.10326i) q^{45} +(7.48315 - 10.7912i) q^{46} +6.33222 q^{47} +(8.89374 + 0.615207i) q^{48} +4.15711 q^{49} +(-0.0190173 + 0.0274243i) q^{50} +(-1.17434 - 1.17434i) q^{51} +(-5.81357 + 12.7694i) q^{52} +(7.24655 - 7.24655i) q^{53} +(-3.20288 + 0.579795i) q^{54} -8.42439i q^{55} +(-4.62290 - 1.17130i) q^{56} +2.22875i q^{57} +(-0.851195 - 4.70214i) q^{58} +(8.10520 - 8.10520i) q^{59} +(3.48586 + 9.31270i) q^{60} +(2.83217 + 2.83217i) q^{61} +(4.79215 + 3.32310i) q^{62} -3.31707 q^{63} +(-7.03483 - 3.80936i) q^{64} -15.6495 q^{65} +(9.78135 + 6.78284i) q^{66} +(-3.09338 - 3.09338i) q^{67} +(0.522442 + 1.39574i) q^{68} +(-14.6339 + 14.6339i) q^{69} +(-0.947513 - 5.23421i) q^{70} +4.16634i q^{71} +(-5.39398 - 1.36667i) q^{72} -8.32181i q^{73} +(-8.97832 + 1.62528i) q^{74} +(0.0371899 - 0.0371899i) q^{75} +(0.828704 - 1.82023i) q^{76} +(-4.50242 - 4.50242i) q^{77} +(12.6001 - 18.1703i) q^{78} +5.53927 q^{79} +(0.615769 - 8.90187i) q^{80} +11.0316 q^{81} +(-1.88529 + 2.71872i) q^{82} +(5.44587 + 5.44587i) q^{83} +(6.84019 + 3.11416i) q^{84} +(-1.17541 + 1.17541i) q^{85} +(-4.31820 + 0.781695i) q^{86} +7.53083i q^{87} +(-5.46646 - 9.17654i) q^{88} +12.5226i q^{89} +(-1.10555 - 6.10725i) q^{90} +(-8.36390 + 8.36390i) q^{91} +(17.3929 - 6.51036i) q^{92} +(-6.49860 - 6.49860i) q^{93} +(7.35889 + 5.10300i) q^{94} +2.23079 q^{95} +(9.83995 + 7.88223i) q^{96} +3.33008 q^{97} +(4.83112 + 3.35013i) q^{98} +(-5.25340 - 5.25340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Introduction

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