LMFDB - Embedded newform 845.2.d.a.844.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(844,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("845.844");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			844.3
Root			$-0.854638 - 0.854638i$ of defining polynomial
Character	$\chi$	$=$	845.844
Dual form			845.2.d.a.844.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.53919 q^{2} -3.17009i q^{3} +0.369102 q^{4} +(-2.17009 + 0.539189i) q^{5} +4.87936i q^{6} -1.70928 q^{7} +2.51026 q^{8} -7.04945 q^{9} +(3.34017 - 0.829914i) q^{10} +2.53919i q^{11} -1.17009i q^{12} +2.63090 q^{14} +(1.70928 + 6.87936i) q^{15} -4.60197 q^{16} -0.921622i q^{17} +10.8504 q^{18} +0.539189i q^{19} +(-0.800984 + 0.199016i) q^{20} +5.41855i q^{21} -3.90829i q^{22} +2.82991i q^{23} -7.95774i q^{24} +(4.41855 - 2.34017i) q^{25} +12.8371i q^{27} -0.630898 q^{28} +5.12783 q^{29} +(-2.63090 - 10.5886i) q^{30} +0.879362i q^{31} +2.06278 q^{32} +8.04945 q^{33} +1.41855i q^{34} +(3.70928 - 0.921622i) q^{35} -2.60197 q^{36} -6.04945 q^{37} -0.829914i q^{38} +(-5.44748 + 1.35350i) q^{40} +1.26180i q^{41} -8.34017i q^{42} +6.43188i q^{43} +0.937221i q^{44} +(15.2979 - 3.80098i) q^{45} -4.35577i q^{46} +5.70928 q^{47} +14.5886i q^{48} -4.07838 q^{49} +(-6.80098 + 3.60197i) q^{50} -2.92162 q^{51} -8.49693i q^{53} -19.7587i q^{54} +(-1.36910 - 5.51026i) q^{55} -4.29072 q^{56} +1.70928 q^{57} -7.89269 q^{58} -4.72261i q^{59} +(0.630898 + 2.53919i) q^{60} +8.04945 q^{61} -1.35350i q^{62} +12.0494 q^{63} +6.02893 q^{64} -12.3896 q^{66} -7.86603 q^{67} -0.340173i q^{68} +8.97107 q^{69} +(-5.70928 + 1.41855i) q^{70} -14.4813i q^{71} -17.6959 q^{72} +1.95055 q^{73} +9.31124 q^{74} +(-7.41855 - 14.0072i) q^{75} +0.199016i q^{76} -4.34017i q^{77} -0.496928 q^{79} +(9.98667 - 2.48133i) q^{80} +19.5464 q^{81} -1.94214i q^{82} +8.63090 q^{83} +2.00000i q^{84} +(0.496928 + 2.00000i) q^{85} -9.89988i q^{86} -16.2557i q^{87} +6.37402i q^{88} +12.8371i q^{89} +(-23.5464 + 5.85043i) q^{90} +1.04453i q^{92} +2.78765 q^{93} -8.78765 q^{94} +(-0.290725 - 1.17009i) q^{95} -6.53919i q^{96} -5.91548 q^{97} +6.27739 q^{98} -17.8999i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 10 q^{4} - 2 q^{5} + 4 q^{7} - 18 q^{8} - 6 q^{9} - 2 q^{10} + 8 q^{14} - 4 q^{15} + 10 q^{16} + 10 q^{18} + 14 q^{20} - 2 q^{25} + 4 q^{28} - 12 q^{29} - 8 q^{30} - 22 q^{32} + 12 q^{33}+ \cdots + 50 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 10 * q^4 - 2 * q^5 + 4 * q^7 - 18 * q^8 - 6 * q^9 - 2 * q^10 + 8 * q^14 - 4 * q^15 + 10 * q^16 + 10 * q^18 + 14 * q^20 - 2 * q^25 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 22 * q^32 + 12 * q^33 + 8 * q^35 + 22 * q^36 - 34 * q^40 + 38 * q^45 + 20 * q^47 - 18 * q^49 - 22 * q^50 - 24 * q^51 - 16 * q^55 - 40 * q^56 - 4 * q^57 - 24 * q^58 - 4 * q^60 + 12 * q^61 + 36 * q^63 + 66 * q^64 - 16 * q^66 - 20 * q^67 + 24 * q^69 - 20 * q^70 - 90 * q^72 + 48 * q^73 + 4 * q^74 - 16 * q^75 + 32 * q^79 + 58 * q^80 + 46 * q^81 + 44 * q^83 - 32 * q^85 - 70 * q^90 - 4 * q^93 - 32 * q^94 - 16 * q^95 + 28 * q^97 + 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.53919			−1.08837			−0.544185	−	0.838965i	$-0.683161\pi$
$2$	−1.53919			−1.08837			−0.544185	+	0.838965i	$0.683161\pi$
$3$		−	3.17009i		−	1.83025i	−0.403170	−	0.915125i	$-0.632092\pi$
$3$		−	3.17009i		−	1.83025i	0.403170	−	0.915125i	$-0.367908\pi$
$4$	0.369102			0.184551
$5$	−2.17009	+	0.539189i	−0.970492	+	0.241133i
$5$	−2.17009	+	0.539189i	−0.970492	+	0.241133i
$6$			4.87936i			1.99199i
$7$	−1.70928			−0.646045			−0.323023	−	0.946391i	$-0.604699\pi$
$7$	−1.70928			−0.646045			−0.323023	+	0.946391i	$0.604699\pi$
$8$	2.51026			0.887511
$9$	−7.04945			−2.34982
$10$	3.34017	−	0.829914i	1.05626	−	0.262442i
$11$			2.53919i			0.765594i	0.923832	+	0.382797i	$0.125039\pi$
$11$			2.53919i			0.765594i	−0.923832	+	0.382797i	$0.874961\pi$
$12$		−	1.17009i		−	0.337775i
$13$		0			0
$13$		0			0
$14$	2.63090			0.703137
$15$	1.70928	+	6.87936i	0.441333	+	1.77624i
$16$	−4.60197			−1.15049
$17$		−	0.921622i		−	0.223526i	−0.993735	−	0.111763i	$-0.964350\pi$
$17$		−	0.921622i		−	0.223526i	0.993735	−	0.111763i	$-0.0356498\pi$
$18$	10.8504			2.55747
$19$			0.539189i			0.123698i	0.998086	+	0.0618492i	$0.0196998\pi$
$19$			0.539189i			0.123698i	−0.998086	+	0.0618492i	$0.980300\pi$
$20$	−0.800984	+	0.199016i	−0.179105	+	0.0445013i
$21$			5.41855i			1.18242i
$22$		−	3.90829i		−	0.833250i
$23$			2.82991i			0.590078i	0.955485	+	0.295039i	$0.0953326\pi$
$23$			2.82991i			0.590078i	−0.955485	+	0.295039i	$0.904667\pi$
$24$		−	7.95774i		−	1.62437i
$25$	4.41855	−	2.34017i	0.883710	−	0.468035i
$26$		0			0
$27$			12.8371i			2.47050i
$28$	−0.630898			−0.119228
$29$	5.12783			0.952213			0.476107	−	0.879388i	$-0.342048\pi$
$29$	5.12783			0.952213			0.476107	+	0.879388i	$0.342048\pi$
$30$	−2.63090	−	10.5886i	−0.480334	−	1.93321i
$31$			0.879362i			0.157938i	0.996877	+	0.0789690i	$0.0251628\pi$
$31$			0.879362i			0.157938i	−0.996877	+	0.0789690i	$0.974837\pi$
$32$	2.06278			0.364651
$33$	8.04945			1.40123
$34$			1.41855i			0.243279i
$35$	3.70928	−	0.921622i	0.626982	−	0.155783i
$36$	−2.60197			−0.433661
$37$	−6.04945			−0.994523			−0.497262	−	0.867601i	$-0.665661\pi$
$37$	−6.04945			−0.994523			−0.497262	+	0.867601i	$0.665661\pi$
$38$		−	0.829914i		−	0.134630i
$39$		0			0
$40$	−5.44748	+	1.35350i	−0.861322	+	0.214008i
$41$			1.26180i			0.197059i	0.995134	+	0.0985297i	$0.0314139\pi$
$41$			1.26180i			0.197059i	−0.995134	+	0.0985297i	$0.968586\pi$
$42$		−	8.34017i		−	1.28692i
$43$			6.43188i			0.980853i	0.871483	+	0.490426i	$0.163159\pi$
$43$			6.43188i			0.980853i	−0.871483	+	0.490426i	$0.836841\pi$
$44$			0.937221i			0.141291i
$45$	15.2979	−	3.80098i	2.28048	−	0.566617i
$46$		−	4.35577i		−	0.642223i
$47$	5.70928			0.832783			0.416392	−	0.909185i	$-0.363295\pi$
$47$	5.70928			0.832783			0.416392	+	0.909185i	$0.363295\pi$
$48$			14.5886i			2.10569i
$49$	−4.07838			−0.582625
$50$	−6.80098	+	3.60197i	−0.961804	+	0.509395i
$51$	−2.92162			−0.409109
$52$		0			0
$53$		−	8.49693i		−	1.16714i	−0.812062	−	0.583571i	$-0.801655\pi$
$53$		−	8.49693i		−	1.16714i	0.812062	−	0.583571i	$-0.198345\pi$
$54$		−	19.7587i		−	2.68882i
$55$	−1.36910	−	5.51026i	−0.184610	−	0.743003i
$56$	−4.29072			−0.573372
$57$	1.70928			0.226399
$58$	−7.89269			−1.03636
$59$		−	4.72261i		−	0.614831i	−0.951575	−	0.307415i	$-0.900536\pi$
$59$		−	4.72261i		−	0.614831i	0.951575	−	0.307415i	$-0.0994641\pi$
$60$	0.630898	+	2.53919i	0.0814485	+	0.327808i
$61$	8.04945			1.03063			0.515313	−	0.857002i	$-0.327676\pi$
$61$	8.04945			1.03063			0.515313	+	0.857002i	$0.327676\pi$
$62$		−	1.35350i		−	0.171895i
$63$	12.0494			1.51809
$64$	6.02893			0.753616
$65$		0			0
$66$	−12.3896			−1.52506
$67$	−7.86603			−0.960989			−0.480494	−	0.876998i	$-0.659543\pi$
$67$	−7.86603			−0.960989			−0.480494	+	0.876998i	$0.659543\pi$
$68$		−	0.340173i		−	0.0412520i
$69$	8.97107			1.07999
$70$	−5.70928	+	1.41855i	−0.682389	+	0.169549i
$71$		−	14.4813i		−	1.71862i	−0.511457	−	0.859309i	$-0.670894\pi$
$71$		−	14.4813i		−	1.71862i	0.511457	−	0.859309i	$-0.329106\pi$
$72$	−17.6959			−2.08549
$73$	1.95055			0.228295			0.114147	−	0.993464i	$-0.463586\pi$
$73$	1.95055			0.228295			0.114147	+	0.993464i	$0.463586\pi$
$74$	9.31124			1.08241
$75$	−7.41855	−	14.0072i	−0.856620	−	1.61741i
$76$			0.199016i			0.0228287i
$77$		−	4.34017i		−	0.494609i
$78$		0			0
$79$	−0.496928			−0.0559088			−0.0279544	−	0.999609i	$-0.508899\pi$
$79$	−0.496928			−0.0559088			−0.0279544	+	0.999609i	$0.508899\pi$
$80$	9.98667	−	2.48133i	1.11654	−	0.277421i
$81$	19.5464			2.17182
$82$		−	1.94214i		−	0.214474i
$83$	8.63090			0.947364			0.473682	−	0.880696i	$-0.342925\pi$
$83$	8.63090			0.947364			0.473682	+	0.880696i	$0.342925\pi$
$84$			2.00000i			0.218218i
$85$	0.496928	+	2.00000i	0.0538995	+	0.216930i
$86$		−	9.89988i		−	1.06753i
$87$		−	16.2557i		−	1.74279i
$88$			6.37402i			0.679473i
$89$			12.8371i			1.36073i	0.732873	+	0.680365i	$0.238179\pi$
$89$			12.8371i			1.36073i	−0.732873	+	0.680365i	$0.761821\pi$
$90$	−23.5464	+	5.85043i	−2.48201	+	0.616690i
$91$		0			0
$92$			1.04453i			0.108900i
$93$	2.78765			0.289066
$94$	−8.78765			−0.906377
$95$	−0.290725	−	1.17009i	−0.0298277	−	0.120048i
$96$		−	6.53919i		−	0.667403i
$97$	−5.91548			−0.600626			−0.300313	−	0.953841i	$-0.597091\pi$
$97$	−5.91548			−0.600626			−0.300313	+	0.953841i	$0.597091\pi$
$98$	6.27739			0.634113
$99$		−	17.8999i		−	1.79901i
$100$	1.63090	−	0.863763i	0.163090	−	0.0863763i
$101$	16.4391			1.63575			0.817874	−	0.575397i	$-0.195152\pi$
$101$	16.4391			1.63575			0.817874	+	0.575397i	$0.195152\pi$
$102$	4.49693			0.445262
$103$		−	10.1906i		−	1.00411i	−0.864836	−	0.502055i	$-0.832577\pi$
$103$		−	10.1906i		−	1.00411i	0.864836	−	0.502055i	$-0.167423\pi$
$104$		0			0
$105$	−2.92162	−	11.7587i	−0.285121	−	1.14753i
$106$			13.0784i			1.27028i
$107$			9.75154i			0.942717i	0.881942	+	0.471358i	$0.156236\pi$
$107$			9.75154i			0.942717i	−0.881942	+	0.471358i	$0.843764\pi$
$108$			4.73820i			0.455934i
$109$			16.8638i			1.61526i	0.589693	+	0.807628i	$0.299249\pi$
$109$			16.8638i			1.61526i	−0.589693	+	0.807628i	$0.700751\pi$
$110$	2.10731	+	8.48133i	0.200924	+	0.808663i
$111$			19.1773i			1.82023i
$112$	7.86603			0.743270
$113$			11.7587i			1.10617i	0.833126	+	0.553084i	$0.186549\pi$
$113$			11.7587i			1.10617i	−0.833126	+	0.553084i	$0.813451\pi$
$114$	−2.63090			−0.246406
$115$	−1.52586	−	6.14116i	−0.142287	−	0.572666i
$116$	1.89269			0.175732
$117$		0			0
$118$			7.26898i			0.669164i
$119$			1.57531i			0.144408i
$120$	4.29072	+	17.2690i	0.391688	+	1.57644i
$121$	4.55252			0.413865
$122$	−12.3896			−1.12170
$123$	4.00000			0.360668
$124$			0.324575i			0.0291477i
$125$	−8.32684	+	7.46081i	−0.744775	+	0.667315i
$126$	−18.5464			−1.65224
$127$			18.0072i			1.59788i	0.601411	+	0.798940i	$0.294605\pi$
$127$			18.0072i			1.59788i	−0.601411	+	0.798940i	$0.705395\pi$
$128$	−13.4052			−1.18487
$129$	20.3896			1.79521
$130$		0			0
$131$	14.2557			1.24552			0.622761	−	0.782412i	$-0.286011\pi$
$131$	14.2557			1.24552			0.622761	+	0.782412i	$0.286011\pi$
$132$	2.97107			0.258599
$133$		−	0.921622i		−	0.0799148i
$134$	12.1073			1.04591
$135$	−6.92162	−	27.8576i	−0.595718	−	2.39760i
$136$		−	2.31351i		−	0.198382i
$137$	13.7854			1.17776			0.588882	−	0.808219i	$-0.299568\pi$
$137$	13.7854			1.17776			0.588882	+	0.808219i	$0.299568\pi$
$138$	−13.8082			−1.17543
$139$	6.65368			0.564358			0.282179	−	0.959362i	$-0.408943\pi$
$139$	6.65368			0.564358			0.282179	+	0.959362i	$0.408943\pi$
$140$	1.36910	−	0.340173i	0.115710	−	0.0287499i
$141$		−	18.0989i		−	1.52420i
$142$			22.2895i			1.87049i
$143$		0			0
$144$	32.4413			2.70344
$145$	−11.1278	+	2.76487i	−0.924116	+	0.229610i
$146$	−3.00227			−0.248469
$147$			12.9288i			1.06635i
$148$	−2.23287			−0.183540
$149$			9.07838i			0.743730i	0.928287	+	0.371865i	$0.121282\pi$
$149$			9.07838i			0.743730i	−0.928287	+	0.371865i	$0.878718\pi$
$150$	11.4186	+	21.5597i	0.932321	+	1.76034i
$151$		−	3.27739i		−	0.266711i	−0.991068	−	0.133355i	$-0.957425\pi$
$151$		−	3.27739i		−	0.266711i	0.991068	−	0.133355i	$-0.0425751\pi$
$152$			1.35350i			0.109784i
$153$			6.49693i			0.525246i
$154$			6.68035i			0.538318i
$155$	−0.474142	−	1.90829i	−0.0380840	−	0.153278i
$156$		0			0
$157$			12.8371i			1.02451i	0.858833	+	0.512256i	$0.171190\pi$
$157$			12.8371i			1.02451i	−0.858833	+	0.512256i	$0.828810\pi$
$158$	0.764867			0.0608495
$159$	−26.9360			−2.13616
$160$	−4.47641	+	1.11223i	−0.353891	+	0.0879293i
$161$		−	4.83710i		−	0.381217i
$162$	−30.0856			−2.36375
$163$	−12.0494			−0.943786			−0.471893	−	0.881656i	$-0.656429\pi$
$163$	−12.0494			−0.943786			−0.471893	+	0.881656i	$0.656429\pi$
$164$			0.465732i			0.0363675i
$165$	−17.4680	+	4.34017i	−1.35988	+	0.337882i
$166$	−13.2846			−1.03108
$167$	8.72979			0.675532			0.337766	−	0.941230i	$-0.390329\pi$
$167$	8.72979			0.675532			0.337766	+	0.941230i	$0.390329\pi$
$168$			13.6020i			1.04941i
$169$		0			0
$170$	−0.764867	−	3.07838i	−0.0586626	−	0.236101i
$171$		−	3.80098i		−	0.290669i
$172$			2.37402i			0.181018i
$173$			0.863763i			0.0656707i	0.999461	+	0.0328354i	$0.0104537\pi$
$173$			0.863763i			0.0656707i	−0.999461	+	0.0328354i	$0.989546\pi$
$174$			25.0205i			1.89680i
$175$	−7.55252	+	4.00000i	−0.570917	+	0.302372i
$176$		−	11.6853i		−	0.880810i
$177$	−14.9711			−1.12529
$178$		−	19.7587i		−	1.48098i
$179$	19.9155			1.48855			0.744276	−	0.667872i	$-0.232795\pi$
$179$	19.9155			1.48855			0.744276	+	0.667872i	$0.232795\pi$
$180$	5.64650	−	1.40295i	0.420865	−	0.104570i
$181$	−14.3896			−1.06957			−0.534786	−	0.844987i	$-0.679608\pi$
$181$	−14.3896			−1.06957			−0.534786	+	0.844987i	$0.679608\pi$
$182$		0			0
$183$		−	25.5174i		−	1.88630i
$184$			7.10382i			0.523700i
$185$	13.1278	−	3.26180i	0.965177	−	0.239812i
$186$	−4.29072			−0.314611
$187$	2.34017			0.171130
$188$	2.10731			0.153691
$189$		−	21.9421i		−	1.59606i
$190$	0.447480	+	1.80098i	0.0324636	+	0.130657i
$191$	1.47641			0.106829			0.0534146	−	0.998572i	$-0.482990\pi$
$191$	1.47641			0.106829			0.0534146	+	0.998572i	$0.482990\pi$
$192$		−	19.1122i		−	1.37931i
$193$	17.7321			1.27638			0.638191	−	0.769878i	$-0.279683\pi$
$193$	17.7321			1.27638			0.638191	+	0.769878i	$0.279683\pi$
$194$	9.10504			0.653704
$195$		0			0
$196$	−1.50534			−0.107524
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$			27.5513i			1.95799i
$199$	−5.39189			−0.382221			−0.191110	−	0.981569i	$-0.561209\pi$
$199$	−5.39189			−0.382221			−0.191110	+	0.981569i	$0.561209\pi$
$200$	11.0917	−	5.87444i	0.784302	−	0.415386i
$201$			24.9360i			1.75885i
$202$	−25.3028			−1.78030
$203$	−8.76487			−0.615173
$204$	−1.07838			−0.0755015
$205$	−0.680346	−	2.73820i	−0.0475174	−	0.191245i
$206$			15.6853i			1.09284i
$207$		−	19.9493i		−	1.38657i
$208$		0			0
$209$	−1.36910			−0.0947028
$210$	4.49693	+	18.0989i	0.310318	+	1.24894i
$211$	−22.7526			−1.56635			−0.783176	−	0.621800i	$-0.786402\pi$
$211$	−22.7526			−1.56635			−0.783176	+	0.621800i	$0.786402\pi$
$212$		−	3.13624i		−	0.215398i
$213$	−45.9071			−3.14550
$214$		−	15.0095i		−	1.02603i
$215$	−3.46800	−	13.9577i	−0.236516	−	0.951910i
$216$			32.2245i			2.19260i
$217$		−	1.50307i		−	0.102035i
$218$		−	25.9565i		−	1.75800i
$219$		−	6.18342i		−	0.417837i
$220$	−0.505339	−	2.03385i	−0.0340699	−	0.137122i
$221$		0			0
$222$		−	29.5174i		−	1.98108i
$223$	8.76099			0.586679			0.293340	−	0.956008i	$-0.405233\pi$
$223$	8.76099			0.586679			0.293340	+	0.956008i	$0.405233\pi$
$224$	−3.52586			−0.235581
$225$	−31.1483	+	16.4969i	−2.07656	+	1.09980i
$226$		−	18.0989i		−	1.20392i
$227$	17.2267			1.14338			0.571689	−	0.820470i	$-0.306288\pi$
$227$	17.2267			1.14338			0.571689	+	0.820470i	$0.306288\pi$
$228$	0.630898			0.0417822
$229$			3.07838i			0.203425i	0.994814	+	0.101712i	$0.0324322\pi$
$229$			3.07838i			0.203425i	−0.994814	+	0.101712i	$0.967568\pi$
$230$	2.34858	+	9.45240i	0.154861	+	0.623273i
$231$	−13.7587			−0.905258
$232$	12.8722			0.845100
$233$			18.9360i			1.24054i	0.784389	+	0.620269i	$0.212977\pi$
$233$			18.9360i			1.24054i	−0.784389	+	0.620269i	$0.787023\pi$
$234$		0			0
$235$	−12.3896	+	3.07838i	−0.808210	+	0.200811i
$236$		−	1.74313i		−	0.113468i
$237$			1.57531i			0.102327i
$238$		−	2.42469i		−	0.157170i
$239$		−	6.63809i		−	0.429382i	−0.976682	−	0.214691i	$-0.931126\pi$
$239$		−	6.63809i		−	0.429382i	0.976682	−	0.214691i	$-0.0688745\pi$
$240$	−7.86603	−	31.6586i	−0.507750	−	2.04355i
$241$			9.47641i			0.610429i	0.952284	+	0.305215i	$0.0987282\pi$
$241$			9.47641i			0.610429i	−0.952284	+	0.305215i	$0.901272\pi$
$242$	−7.00719			−0.450439
$243$		−	23.4524i		−	1.50447i
$244$	2.97107			0.190203
$245$	8.85043	−	2.19902i	0.565433	−	0.140490i
$246$	−6.15676			−0.392540
$247$		0			0
$248$			2.20743i			0.140172i
$249$		−	27.3607i		−	1.73391i
$250$	12.8166	−	11.4836i	0.810592	−	0.726286i
$251$	−29.4596			−1.85947			−0.929736	−	0.368226i	$-0.879965\pi$
$251$	−29.4596			−1.85947			−0.929736	+	0.368226i	$0.879965\pi$
$252$	4.44748			0.280165
$253$	−7.18568			−0.451760
$254$		−	27.7165i		−	1.73909i
$255$	6.34017	−	1.57531i	0.397037	−	0.0986495i
$256$	8.57531			0.535957
$257$			20.4657i			1.27662i	0.769781	+	0.638309i	$0.220366\pi$
$257$			20.4657i			1.27662i	−0.769781	+	0.638309i	$0.779634\pi$
$258$	−31.3835			−1.95385
$259$	10.3402			0.642507
$260$		0			0
$261$	−36.1483			−2.23753
$262$	−21.9421			−1.35559
$263$		−	9.14342i		−	0.563808i	−0.959443	−	0.281904i	$-0.909034\pi$
$263$		−	9.14342i		−	0.563808i	0.959443	−	0.281904i	$-0.0909659\pi$
$264$	20.2062			1.24361
$265$	4.58145	+	18.4391i	0.281436	+	1.13270i
$266$			1.41855i			0.0869769i
$267$	40.6947			2.49048
$268$	−2.90337			−0.177352
$269$	−11.3919			−0.694576			−0.347288	−	0.937759i	$-0.612897\pi$
$269$	−11.3919			−0.694576			−0.347288	+	0.937759i	$0.612897\pi$
$270$	10.6537	+	42.8781i	0.648363	+	2.60948i
$271$			21.1350i			1.28386i	0.766763	+	0.641930i	$0.221866\pi$
$271$			21.1350i			1.28386i	−0.766763	+	0.641930i	$0.778134\pi$
$272$			4.24128i			0.257165i
$273$		0			0
$274$	−21.2183			−1.28185
$275$	5.94214	+	11.2195i	0.358325	+	0.676563i
$276$	3.31124			0.199313
$277$			13.0784i			0.785804i	0.919580	+	0.392902i	$0.128529\pi$
$277$			13.0784i			0.785804i	−0.919580	+	0.392902i	$0.871471\pi$
$278$	−10.2413			−0.614231
$279$		−	6.19902i		−	0.371125i
$280$	9.31124	−	2.31351i	0.556453	−	0.138259i
$281$			0.680346i			0.0405860i	0.999794	+	0.0202930i	$0.00645991\pi$
$281$			0.680346i			0.0405860i	−0.999794	+	0.0202930i	$0.993540\pi$
$282$			27.8576i			1.65890i
$283$		−	19.2956i		−	1.14701i	−0.819203	−	0.573504i	$-0.805584\pi$
$283$		−	19.2956i		−	1.14701i	0.819203	−	0.573504i	$-0.194416\pi$
$284$		−	5.34509i		−	0.317173i
$285$	−3.70928	+	0.921622i	−0.219719	+	0.0545922i
$286$		0			0
$287$		−	2.15676i		−	0.127309i
$288$	−14.5415			−0.856864
$289$	16.1506			0.950036
$290$	17.1278	−	4.25565i	1.00578	−	0.249900i
$291$			18.7526i			1.09930i
$292$	0.719953			0.0421321
$293$	9.46800			0.553126			0.276563	−	0.960996i	$-0.410804\pi$
$293$	9.46800			0.553126			0.276563	+	0.960996i	$0.410804\pi$
$294$		−	19.8999i		−	1.16058i
$295$	2.54638	+	10.2485i	0.148256	+	0.596689i
$296$	−15.1857			−0.882650
$297$	−32.5958			−1.89140
$298$		−	13.9733i		−	0.809454i
$299$		0			0
$300$	−2.73820	−	5.17009i	−0.158090	−	0.298495i
$301$		−	10.9939i		−	0.633675i
$302$			5.04453i			0.290280i
$303$		−	52.1133i		−	2.99383i
$304$		−	2.48133i		−	0.142314i
$305$	−17.4680	+	4.34017i	−1.00021	+	0.248518i
$306$		−	10.0000i		−	0.571662i
$307$	−0.264063			−0.0150709			−0.00753543	−	0.999972i	$-0.502399\pi$
$307$	−0.264063			−0.0150709			−0.00753543	+	0.999972i	$0.502399\pi$
$308$		−	1.60197i		−	0.0912806i
$309$	−32.3051			−1.83777
$310$	0.729794	+	2.93722i	0.0414495	+	0.166823i
$311$	−13.0472			−0.739838			−0.369919	−	0.929064i	$-0.620615\pi$
$311$	−13.0472			−0.739838			−0.369919	+	0.929064i	$0.620615\pi$
$312$		0			0
$313$			33.7009i			1.90489i	0.304718	+	0.952443i	$0.401438\pi$
$313$			33.7009i			1.90489i	−0.304718	+	0.952443i	$0.598562\pi$
$314$		−	19.7587i		−	1.11505i
$315$	−26.1483	+	6.49693i	−1.47329	+	0.366060i
$316$	−0.183417			−0.0103180
$317$	13.9506			0.783541			0.391771	−	0.920063i	$-0.371863\pi$
$317$	13.9506			0.783541			0.391771	+	0.920063i	$0.371863\pi$
$318$	41.4596			2.32494
$319$			13.0205i			0.729009i
$320$	−13.0833	+	3.25073i	−0.731379	+	0.181721i
$321$	30.9132			1.72541
$322$			7.44521i			0.414905i
$323$	0.496928			0.0276498
$324$	7.21461			0.400812
$325$		0			0
$326$	18.5464			1.02719
$327$	53.4596			2.95632
$328$			3.16743i			0.174892i
$329$	−9.75872			−0.538016
$330$	26.8865	−	6.68035i	1.48006	−	0.367741i
$331$		−	18.4547i		−	1.01436i	−0.861840	−	0.507180i	$-0.830688\pi$
$331$		−	18.4547i		−	1.01436i	0.861840	−	0.507180i	$-0.169312\pi$
$332$	3.18568			0.174837
$333$	42.6453			2.33695
$334$	−13.4368			−0.735229
$335$	17.0700	−	4.24128i	0.932632	−	0.231726i
$336$		−	24.9360i		−	1.36037i
$337$			15.8576i			0.863820i	0.901917	+	0.431910i	$0.142160\pi$
$337$			15.8576i			0.863820i	−0.901917	+	0.431910i	$0.857840\pi$
$338$		0			0
$339$	37.2762			2.02456
$340$	0.183417	+	0.738205i	0.00994721	+	0.0400348i
$341$	−2.23287			−0.120916
$342$			5.85043i			0.316355i
$343$	18.9360			1.02245
$344$			16.1457i			0.870517i
$345$	−19.4680	+	4.83710i	−1.04812	+	0.260421i
$346$		−	1.32950i		−	0.0714741i
$347$			9.72487i			0.522059i	0.965331	+	0.261029i	$0.0840619\pi$
$347$			9.72487i			0.522059i	−0.965331	+	0.261029i	$0.915938\pi$
$348$		−	6.00000i		−	0.321634i
$349$		−	30.9093i		−	1.65454i	−0.561805	−	0.827269i	$-0.689893\pi$
$349$		−	30.9093i		−	1.65454i	0.561805	−	0.827269i	$-0.310107\pi$
$350$	11.6248	−	6.15676i	0.621369	−	0.329092i
$351$		0			0
$352$			5.23779i			0.279175i
$353$	5.95055			0.316716			0.158358	−	0.987382i	$-0.449380\pi$
$353$	5.95055			0.316716			0.158358	+	0.987382i	$0.449380\pi$
$354$	23.0433			1.22474
$355$	7.80817	+	31.4257i	0.414415	+	1.66791i
$356$			4.73820i			0.251124i
$357$	4.99386			0.264303
$358$	−30.6537			−1.62010
$359$			10.9783i			0.579410i	0.957116	+	0.289705i	$0.0935573\pi$
$359$			10.9783i			0.579410i	−0.957116	+	0.289705i	$0.906443\pi$
$360$	38.4017	−	9.54146i	2.02395	−	0.502879i
$361$	18.7093			0.984699
$362$	22.1483			1.16409
$363$		−	14.4319i		−	0.757477i
$364$		0			0
$365$	−4.23287	+	1.05172i	−0.221558	+	0.0550493i
$366$			39.2762i			2.05300i
$367$			10.3740i			0.541520i	0.962647	+	0.270760i	$0.0872749\pi$
$367$			10.3740i			0.541520i	−0.962647	+	0.270760i	$0.912725\pi$
$368$		−	13.0232i		−	0.678880i
$369$		−	8.89496i		−	0.463053i
$370$	−20.2062	+	5.02052i	−1.05047	+	0.261004i
$371$			14.5236i			0.754027i
$372$	1.02893			0.0533475
$373$		−	23.9877i		−	1.24204i	−0.783796	−	0.621018i	$-0.786719\pi$
$373$		−	23.9877i		−	1.24204i	0.783796	−	0.621018i	$-0.213281\pi$
$374$	−3.60197			−0.186253
$375$	23.6514	+	26.3968i	1.22135	+	1.36313i
$376$	14.3318			0.739104
$377$		0			0
$378$			33.7731i			1.73710i
$379$		−	29.7575i		−	1.52854i	−0.644896	−	0.764270i	$-0.723099\pi$
$379$		−	29.7575i		−	1.52854i	0.644896	−	0.764270i	$-0.276901\pi$
$380$	−0.107307	−	0.431882i	−0.00550474	−	0.0221551i
$381$	57.0843			2.92452
$382$	−2.27247			−0.116270
$383$	12.4163			0.634442			0.317221	−	0.948352i	$-0.397250\pi$
$383$	12.4163			0.634442			0.317221	+	0.948352i	$0.397250\pi$
$384$			42.4957i			2.16860i
$385$	2.34017	+	9.41855i	0.119266	+	0.480014i
$386$	−27.2930			−1.38918
$387$		−	45.3412i		−	2.30482i
$388$	−2.18342			−0.110846
$389$	−16.8371			−0.853675			−0.426837	−	0.904328i	$-0.640372\pi$
$389$	−16.8371			−0.853675			−0.426837	+	0.904328i	$0.640372\pi$
$390$		0			0
$391$	2.60811			0.131898
$392$	−10.2378			−0.517086
$393$		−	45.1917i		−	2.27962i
$394$	3.07838			0.155086
$395$	1.07838	−	0.267938i	0.0542591	−	0.0134814i
$396$		−	6.60689i		−	0.332009i
$397$	−3.89269			−0.195369			−0.0976843	−	0.995217i	$-0.531144\pi$
$397$	−3.89269			−0.195369			−0.0976843	+	0.995217i	$0.531144\pi$
$398$	8.29914			0.415998
$399$	−2.92162			−0.146264
$400$	−20.3340	+	10.7694i	−1.01670	+	0.538470i
$401$			9.10504i			0.454684i	0.973815	+	0.227342i	$0.0730035\pi$
$401$			9.10504i			0.454684i	−0.973815	+	0.227342i	$0.926996\pi$
$402$		−	38.3812i		−	1.91428i
$403$		0			0
$404$	6.06770			0.301879
$405$	−42.4173	+	10.5392i	−2.10773	+	0.523697i
$406$	13.4908			0.669536
$407$		−	15.3607i		−	0.761401i
$408$	−7.33403			−0.363089
$409$			19.4186i			0.960186i	0.877218	+	0.480093i	$0.159397\pi$
$409$			19.4186i			0.960186i	−0.877218	+	0.480093i	$0.840603\pi$
$410$	1.04718	+	4.21461i	0.0517166	+	0.208145i
$411$		−	43.7009i		−	2.15560i
$412$		−	3.76138i		−	0.185310i
$413$			8.07223i			0.397209i
$414$			30.7058i			1.50911i
$415$	−18.7298	+	4.65368i	−0.919409	+	0.228440i
$416$		0			0
$417$		−	21.0928i		−	1.03292i
$418$	2.10731			0.103072
$419$	16.7792			0.819720			0.409860	−	0.912149i	$-0.365578\pi$
$419$	16.7792			0.819720			0.409860	+	0.912149i	$0.365578\pi$
$420$	−1.07838	−	4.34017i	−0.0526194	−	0.211779i
$421$		−	19.0205i		−	0.927003i	−0.886096	−	0.463502i	$-0.846593\pi$
$421$		−	19.0205i		−	0.927003i	0.886096	−	0.463502i	$-0.153407\pi$
$422$	35.0205			1.70477
$423$	−40.2472			−1.95689
$424$		−	21.3295i		−	1.03585i
$425$	−2.15676	−	4.07223i	−0.104618	−	0.197532i
$426$	70.6596			3.42347
$427$	−13.7587			−0.665831
$428$			3.59932i			0.173979i
$429$		0			0
$430$	5.33791	+	21.4836i	0.257417	+	1.03603i
$431$			8.02997i			0.386790i	0.981121	+	0.193395i	$0.0619499\pi$
$431$			8.02997i			0.386790i	−0.981121	+	0.193395i	$0.938050\pi$
$432$		−	59.0759i		−	2.84229i
$433$			13.0472i			0.627008i	0.949587	+	0.313504i	$0.101503\pi$
$433$			13.0472i			0.627008i	−0.949587	+	0.313504i	$0.898497\pi$
$434$			2.31351i			0.111052i
$435$	8.76487	+	35.2762i	0.420243	+	1.69136i
$436$			6.22446i			0.298097i
$437$	−1.52586			−0.0729917
$438$			9.51745i			0.454761i
$439$	−7.70086			−0.367542			−0.183771	−	0.982969i	$-0.558831\pi$
$439$	−7.70086			−0.367542			−0.183771	+	0.982969i	$0.558831\pi$
$440$	−3.43680	−	13.8322i	−0.163843	−	0.659423i
$441$	28.7503			1.36906
$442$		0			0
$443$		−	6.39084i		−	0.303638i	−0.988408	−	0.151819i	$-0.951487\pi$
$443$		−	6.39084i		−	0.303638i	0.988408	−	0.151819i	$-0.0485131\pi$
$444$			7.07838i			0.335925i
$445$	−6.92162	−	27.8576i	−0.328116	−	1.32058i
$446$	−13.4848			−0.638525
$447$	28.7792			1.36121
$448$	−10.3051			−0.486870
$449$			31.6163i			1.49207i	0.665908	+	0.746034i	$0.268044\pi$
$449$			31.6163i			1.49207i	−0.665908	+	0.746034i	$0.731956\pi$
$450$	47.9432	−	25.3919i	2.26006	−	1.19699i
$451$	−3.20394			−0.150867
$452$			4.34017i			0.204145i
$453$	−10.3896			−0.488147
$454$	−26.5152			−1.24442
$455$		0			0
$456$	4.29072			0.200932
$457$	−35.6430			−1.66731			−0.833655	−	0.552286i	$-0.813756\pi$
$457$	−35.6430			−1.66731			−0.833655	+	0.552286i	$0.813756\pi$
$458$		−	4.73820i		−	0.221402i
$459$	11.8310			0.552222
$460$	−0.563198	−	2.26672i	−0.0262592	−	0.105686i
$461$		−	14.9795i		−	0.697664i	−0.937185	−	0.348832i	$-0.886578\pi$
$461$		−	14.9795i		−	0.697664i	0.937185	−	0.348832i	$-0.113422\pi$
$462$	21.1773			0.985256
$463$	−9.09663			−0.422756			−0.211378	−	0.977404i	$-0.567795\pi$
$463$	−9.09663			−0.422756			−0.211378	+	0.977404i	$0.567795\pi$
$464$	−23.5981			−1.09551
$465$	−6.04945	+	1.50307i	−0.280536	+	0.0697033i
$466$		−	29.1461i		−	1.35017i
$467$			1.87709i			0.0868616i	0.999056	+	0.0434308i	$0.0138288\pi$
$467$			1.87709i			0.0868616i	−0.999056	+	0.0434308i	$0.986171\pi$
$468$		0			0
$469$	13.4452			0.620842
$470$	19.0700	−	4.73820i	0.879632	−	0.218557i
$471$	40.6947			1.87511
$472$		−	11.8550i		−	0.545669i
$473$	−16.3318			−0.750935
$474$		−	2.42469i		−	0.111370i
$475$	1.26180	+	2.38243i	0.0578951	+	0.109314i
$476$			0.581449i			0.0266507i
$477$			59.8987i			2.74257i
$478$			10.2173i			0.467327i
$479$		−	15.7431i		−	0.719322i	−0.933083	−	0.359661i	$-0.882892\pi$
$479$		−	15.7431i		−	0.719322i	0.933083	−	0.359661i	$-0.117108\pi$
$480$	3.52586	+	14.1906i	0.160933	+	0.647710i
$481$		0			0
$482$		−	14.5860i		−	0.664373i
$483$	−15.3340			−0.697723
$484$	1.68035			0.0763794
$485$	12.8371	−	3.18956i	0.582903	−	0.144830i
$486$			36.0977i			1.63742i
$487$	4.94441			0.224053			0.112026	−	0.993705i	$-0.464266\pi$
$487$	4.94441			0.224053			0.112026	+	0.993705i	$0.464266\pi$
$488$	20.2062			0.914692
$489$			38.1978i			1.72736i
$490$	−13.6225	+	3.38470i	−0.615401	+	0.152905i
$491$	−39.4863			−1.78199			−0.890995	−	0.454014i	$-0.849992\pi$
$491$	−39.4863			−1.78199			−0.890995	+	0.454014i	$0.849992\pi$
$492$	1.47641			0.0665617
$493$		−	4.72592i		−	0.212845i
$494$		0			0
$495$	9.65142	+	38.8443i	0.433799	+	1.74592i
$496$		−	4.04680i		−	0.181706i
$497$			24.7526i			1.11030i
$498$			42.1133i			1.88714i
$499$		−	1.67089i		−	0.0747993i	−0.999300	−	0.0373997i	$-0.988093\pi$
$499$		−	1.67089i		−	0.0747993i	0.999300	−	0.0373997i	$-0.0119075\pi$
$500$	−3.07346	+	2.75380i	−0.137449	+	0.123154i
$501$		−	27.6742i		−	1.23639i
$502$	45.3439			2.02380
$503$			9.08557i			0.405105i	0.979271	+	0.202553i	$0.0649237\pi$
$503$			9.08557i			0.405105i	−0.979271	+	0.202553i	$0.935076\pi$
$504$	30.2472			1.34732
$505$	−35.6742	+	8.86376i	−1.58748	+	0.394432i
$506$	11.0601			0.491683
$507$		0			0
$508$			6.64650i			0.294891i
$509$			19.5441i			0.866277i	0.901327	+	0.433139i	$0.142594\pi$
$509$			19.5441i			0.866277i	−0.901327	+	0.433139i	$0.857406\pi$
$510$	−9.75872	+	2.42469i	−0.432124	+	0.107367i
$511$	−3.33403			−0.147489
$512$	13.6114			0.601546
$513$	−6.92162			−0.305597
$514$		−	31.5006i		−	1.38943i
$515$	5.49466	+	22.1145i	0.242124	+	0.974481i
$516$	7.52586			0.331307
$517$			14.4969i			0.637574i
$518$	−15.9155			−0.699286
$519$	2.73820			0.120194
$520$		0			0
$521$	6.50534			0.285004			0.142502	−	0.989795i	$-0.454485\pi$
$521$	6.50534			0.285004			0.142502	+	0.989795i	$0.454485\pi$
$522$	55.6391			2.43526
$523$			36.5452i			1.59801i	0.601326	+	0.799004i	$0.294639\pi$
$523$			36.5452i			1.59801i	−0.601326	+	0.799004i	$0.705361\pi$
$524$	5.26180			0.229863
$525$	12.6803	+	23.9421i	0.553416	+	1.04492i
$526$			14.0735i			0.613632i
$527$	0.810439			0.0353033
$528$	−37.0433			−1.61210
$529$	14.9916			0.651808
$530$	−7.05172	−	28.3812i	−0.306307	−	1.23280i
$531$			33.2918i			1.44474i
$532$		−	0.340173i		−	0.0147484i
$533$		0			0
$534$	−62.6369			−2.71056
$535$	−5.25792	−	21.1617i	−0.227320	−	0.914899i
$536$	−19.7458			−0.852888
$537$		−	63.1338i		−	2.72442i
$538$	17.5343			0.755956
$539$		−	10.3558i		−	0.446055i
$540$	−2.55479	−	10.2823i	−0.109941	−	0.442480i
$541$		−	20.3402i		−	0.874492i	−0.899342	−	0.437246i	$-0.855954\pi$
$541$		−	20.3402i		−	0.874492i	0.899342	−	0.437246i	$-0.144046\pi$
$542$		−	32.5308i		−	1.39732i
$543$			45.6163i			1.95758i
$544$		−	1.90110i		−	0.0815091i
$545$	−9.09275	−	36.5958i	−0.389491	−	1.56759i
$546$		0			0
$547$			11.5948i			0.495757i	0.968791	+	0.247879i	$0.0797334\pi$
$547$			11.5948i			0.495757i	−0.968791	+	0.247879i	$0.920267\pi$
$548$	5.08822			0.217358
$549$	−56.7442			−2.42178
$550$	−9.14608	−	17.2690i	−0.389990	−	0.736352i
$551$			2.76487i			0.117787i
$552$	22.5197			0.958503
$553$	0.849388			0.0361196
$554$		−	20.1301i		−	0.855246i
$555$	−10.3402	−	41.6163i	−0.438916	−	1.76652i
$556$	2.45589			0.104153
$557$	−10.7298			−0.454636			−0.227318	−	0.973821i	$-0.572996\pi$
$557$	−10.7298			−0.454636			−0.227318	+	0.973821i	$0.572996\pi$
$558$			9.54146i			0.403922i
$559$		0			0
$560$	−17.0700	+	4.24128i	−0.721338	+	0.179227i
$561$		−	7.41855i		−	0.313211i
$562$		−	1.04718i		−	0.0441727i
$563$		−	10.2485i		−	0.431921i	−0.976402	−	0.215961i	$-0.930712\pi$
$563$		−	10.2485i		−	0.431921i	0.976402	−	0.215961i	$-0.0692883\pi$
$564$		−	6.68035i		−	0.281293i
$565$	−6.34017	−	25.5174i	−0.266733	−	1.07353i
$566$			29.6996i			1.24837i
$567$	−33.4101			−1.40309
$568$		−	36.3519i		−	1.52529i
$569$	−8.84551			−0.370823			−0.185412	−	0.982661i	$-0.559362\pi$
$569$	−8.84551			−0.370823			−0.185412	+	0.982661i	$0.559362\pi$
$570$	5.70928	−	1.41855i	0.239135	−	0.0594166i
$571$	−9.29299			−0.388900			−0.194450	−	0.980912i	$-0.562292\pi$
$571$	−9.29299			−0.388900			−0.194450	+	0.980912i	$0.562292\pi$
$572$		0			0
$573$		−	4.68035i		−	0.195524i
$574$			3.31965i			0.138560i
$575$	6.62249	+	12.5041i	0.276177	+	0.521458i
$576$	−42.5006			−1.77086
$577$	−19.5259			−0.812872			−0.406436	−	0.913679i	$-0.633229\pi$
$577$	−19.5259			−0.812872			−0.406436	+	0.913679i	$0.633229\pi$
$578$	−24.8588			−1.03399
$579$		−	56.2122i		−	2.33610i
$580$	−4.10731	+	1.02052i	−0.170547	+	0.0423747i
$581$	−14.7526			−0.612040
$582$		−	28.8638i		−	1.19644i
$583$	21.5753			0.893558
$584$	4.89639			0.202614
$585$		0			0
$586$	−14.5730			−0.602007
$587$	22.5029			0.928794			0.464397	−	0.885627i	$-0.346271\pi$
$587$	22.5029			0.928794			0.464397	+	0.885627i	$0.346271\pi$
$588$			4.77205i			0.196796i
$589$	−0.474142			−0.0195367
$590$	−3.91935	−	15.7743i	−0.161357	−	0.649419i
$591$			6.34017i			0.260800i
$592$	27.8394			1.14419
$593$	4.43907			0.182291			0.0911454	−	0.995838i	$-0.470947\pi$
$593$	4.43907			0.182291			0.0911454	+	0.995838i	$0.470947\pi$
$594$	50.1711			2.05855
$595$	−0.849388	−	3.41855i	−0.0348215	−	0.140147i
$596$			3.35085i			0.137256i
$597$			17.0928i			0.699560i
$598$		0			0
$599$	−33.3607			−1.36308			−0.681540	−	0.731780i	$-0.738690\pi$
$599$	−33.3607			−1.36308			−0.681540	+	0.731780i	$0.738690\pi$
$600$	−18.6225	−	35.1617i	−0.760260	−	1.43547i
$601$	13.3197			0.543320			0.271660	−	0.962393i	$-0.412427\pi$
$601$	13.3197			0.543320			0.271660	+	0.962393i	$0.412427\pi$
$602$			16.9216i			0.689674i
$603$	55.4512			2.25815
$604$		−	1.20969i		−	0.0492217i
$605$	−9.87936	+	2.45467i	−0.401653	+	0.0997964i
$606$			80.2122i			3.25840i
$607$		−	14.1184i		−	0.573047i	−0.958073	−	0.286523i	$-0.907500\pi$
$607$		−	14.1184i		−	0.573047i	0.958073	−	0.286523i	$-0.0924996\pi$
$608$			1.11223i			0.0451068i
$609$			27.7854i			1.12592i
$610$	26.8865	−	6.68035i	1.08860	−	0.270479i
$611$		0			0
$612$			2.39803i			0.0969347i
$613$	26.8104			1.08286			0.541432	−	0.840745i	$-0.317882\pi$
$613$	26.8104			1.08286			0.541432	+	0.840745i	$0.317882\pi$
$614$	0.406442			0.0164027
$615$	−8.68035	+	2.15676i	−0.350025	+	0.0869688i
$616$		−	10.8950i		−	0.438970i
$617$	14.8950			0.599649			0.299824	−	0.953994i	$-0.403072\pi$
$617$	14.8950			0.599649			0.299824	+	0.953994i	$0.403072\pi$
$618$	49.7237			2.00018
$619$			45.3184i			1.82150i	0.412956	+	0.910751i	$0.364496\pi$
$619$			45.3184i			1.82150i	−0.412956	+	0.910751i	$0.635504\pi$
$620$	−0.175007	−	0.704355i	−0.00702845	−	0.0282876i
$621$	−36.3279			−1.45779
$622$	20.0821			0.805218
$623$		−	21.9421i		−	0.879093i
$624$		0			0
$625$	14.0472	−	20.6803i	0.561887	−	0.827214i
$626$		−	51.8720i		−	2.07322i
$627$			4.34017i			0.173330i
$628$			4.73820i			0.189075i
$629$			5.57531i			0.222302i
$630$	40.2472	−	10.0000i	1.60349	−	0.398410i
$631$		−	37.8876i		−	1.50828i	−0.656713	−	0.754141i	$-0.728054\pi$
$631$		−	37.8876i		−	1.50828i	0.656713	−	0.754141i	$-0.271946\pi$
$632$	−1.24742			−0.0496197
$633$			72.1276i			2.86682i
$634$	−21.4725			−0.852783
$635$	−9.70928	−	39.0772i	−0.385301	−	1.55073i
$636$	−9.94214			−0.394232
$637$		0			0
$638$		−	20.0410i		−	0.793432i
$639$			102.085i			4.03844i
$640$	29.0905	−	7.22795i	1.14990	−	0.285710i
$641$	8.47027			0.334555			0.167278	−	0.985910i	$-0.446502\pi$
$641$	8.47027			0.334555			0.167278	+	0.985910i	$0.446502\pi$
$642$	−47.5813			−1.87788
$643$	−34.1750			−1.34773			−0.673865	−	0.738854i	$-0.735367\pi$
$643$	−34.1750			−1.34773			−0.673865	+	0.738854i	$0.735367\pi$
$644$		−	1.78539i		−	0.0703541i
$645$	−44.2472	+	10.9939i	−1.74223	+	0.432883i
$646$	−0.764867			−0.0300933
$647$		−	13.8238i		−	0.543468i	−0.962372	−	0.271734i	$-0.912403\pi$
$647$		−	13.8238i		−	0.543468i	0.962372	−	0.271734i	$-0.0875972\pi$
$648$	49.0665			1.92751
$649$	11.9916			0.470711
$650$		0			0
$651$	−4.76487			−0.186750
$652$	−4.44748			−0.174177
$653$		−	42.8781i		−	1.67795i	−0.544169	−	0.838976i	$-0.683155\pi$
$653$		−	42.8781i		−	1.67795i	0.544169	−	0.838976i	$-0.316845\pi$
$654$	−82.2844			−3.21757
$655$	−30.9360	+	7.68649i	−1.20877	+	0.300336i
$656$		−	5.80674i		−	0.226715i
$657$	−13.7503			−0.536451
$658$	15.0205			0.585561
$659$	23.2495			0.905672			0.452836	−	0.891594i	$-0.350412\pi$
$659$	23.2495			0.905672			0.452836	+	0.891594i	$0.350412\pi$
$660$	−6.44748	+	1.60197i	−0.250968	+	0.0623565i
$661$		−	27.0661i		−	1.05275i	−0.850253	−	0.526374i	$-0.823551\pi$
$661$		−	27.0661i		−	1.05275i	0.850253	−	0.526374i	$-0.176449\pi$
$662$			28.4052i			1.10400i
$663$		0			0
$664$	21.6658			0.840796
$665$	0.496928	+	2.00000i	0.0192701	+	0.0775567i
$666$	−65.6391			−2.54346
$667$			14.5113i			0.561880i
$668$	3.22219			0.124670
$669$		−	27.7731i		−	1.07377i
$670$	−26.2739	+	6.52813i	−1.01505	+	0.252203i
$671$			20.4391i			0.789042i
$672$			11.1773i			0.431173i
$673$		−	16.1711i		−	0.623351i	−0.950189	−	0.311676i	$-0.899110\pi$
$673$		−	16.1711i		−	0.623351i	0.950189	−	0.311676i	$-0.100890\pi$
$674$		−	24.4079i		−	0.940156i
$675$	30.0410	+	56.7214i	1.15628	+	2.18321i
$676$		0			0
$677$		−	43.1194i		−	1.65721i	−0.559831	−	0.828607i	$-0.689134\pi$
$677$		−	43.1194i		−	1.65721i	0.559831	−	0.828607i	$-0.310866\pi$
$678$	−57.3751			−2.20348
$679$	10.1112			0.388032
$680$	1.24742	+	5.02052i	0.0478363	+	0.192528i
$681$		−	54.6102i		−	2.09267i
$682$	3.43680			0.131602
$683$	−17.7093			−0.677627			−0.338813	−	0.940854i	$-0.610026\pi$
$683$	−17.7093			−0.677627			−0.338813	+	0.940854i	$0.610026\pi$
$684$		−	1.40295i		−	0.0536432i
$685$	−29.9155	+	7.43293i	−1.14301	+	0.283998i
$686$	−29.1461			−1.11280
$687$	9.75872			0.372319
$688$		−	29.5993i		−	1.12846i
$689$		0			0
$690$	29.9649	−	7.44521i	1.14075	−	0.283434i
$691$		−	24.8794i		−	0.946456i	−0.880940	−	0.473228i	$-0.843089\pi$
$691$		−	24.8794i		−	0.946456i	0.880940	−	0.473228i	$-0.156911\pi$
$692$			0.318817i			0.0121196i
$693$			30.5958i			1.16224i
$694$		−	14.9684i		−	0.568193i
$695$	−14.4391	+	3.58759i	−0.547705	+	0.136085i
$696$		−	40.8059i		−	1.54674i
$697$	1.16290			0.0440479
$698$			47.5753i			1.80075i
$699$	60.0288			2.27050
$700$	−2.78765	+	1.47641i	−0.105363	+	0.0558030i
$701$	−33.0661			−1.24889			−0.624445	−	0.781069i	$-0.714675\pi$
$701$	−33.0661			−1.24889			−0.624445	+	0.781069i	$0.714675\pi$
$702$		0			0
$703$		−	3.26180i		−	0.123021i
$704$			15.3086i			0.576964i
$705$	9.75872	+	39.2762i	0.367535	+	1.47923i
$706$	−9.15902			−0.344704
$707$	−28.0989			−1.05677
$708$	−5.52586			−0.207674
$709$			2.18342i			0.0820000i	0.999159	+	0.0410000i	$0.0130544\pi$
$709$			2.18342i			0.0820000i	−0.999159	+	0.0410000i	$0.986946\pi$
$710$	−12.0183	−	48.3701i	−0.451037	−	1.81530i
$711$	3.50307			0.131375
$712$			32.2245i			1.20766i
$713$	−2.48852			−0.0931957
$714$	−7.68649			−0.287660
$715$		0			0
$716$	7.35085			0.274714
$717$	−21.0433			−0.785877
$718$		−	16.8976i		−	0.630613i
$719$	5.20847			0.194243			0.0971216	−	0.995273i	$-0.469036\pi$
$719$	5.20847			0.194243			0.0971216	+	0.995273i	$0.469036\pi$
$720$	−70.4005	+	17.4920i	−2.62367	+	0.651889i
$721$			17.4186i			0.648701i
$722$	−28.7971			−1.07172
$723$	30.0410			1.11724
$724$	−5.31124			−0.197391
$725$	22.6576	−	12.0000i	0.841481	−	0.445669i
$726$			22.2134i			0.824416i
$727$		−	3.52464i		−	0.130721i	−0.997862	−	0.0653607i	$-0.979180\pi$
$727$		−	3.52464i		−	0.130721i	0.997862	−	0.0653607i	$-0.0208198\pi$
$728$		0			0
$729$	−15.7070			−0.581741
$730$	6.51518	−	1.61879i	0.241138	−	0.0599141i
$731$	5.92777			0.219246
$732$		−	9.41855i		−	0.348120i
$733$	21.8310			0.806345			0.403172	−	0.915124i	$-0.367907\pi$
$733$	21.8310			0.806345			0.403172	+	0.915124i	$0.367907\pi$
$734$		−	15.9676i		−	0.589374i
$735$	−6.97107	−	28.0566i	−0.257132	−	1.03488i
$736$			5.83749i			0.215173i
$737$		−	19.9733i		−	0.735727i
$738$			13.6910i			0.503974i
$739$			50.3533i			1.85228i	0.377184	+	0.926139i	$0.376893\pi$
$739$			50.3533i			1.85228i	−0.377184	+	0.926139i	$0.623107\pi$
$740$	4.84551	−	1.20394i	0.178125	−	0.0442576i
$741$		0			0
$742$		−	22.3545i		−	0.820661i
$743$	−30.7877			−1.12949			−0.564745	−	0.825266i	$-0.691025\pi$
$743$	−30.7877			−1.12949			−0.564745	+	0.825266i	$0.691025\pi$
$744$	6.99773			0.256549
$745$	−4.89496	−	19.7009i	−0.179337	−	0.721784i
$746$			36.9216i			1.35180i
$747$	−60.8431			−2.22613
$748$	0.863763			0.0315823
$749$		−	16.6681i		−	0.609038i
$750$	−36.4040	−	40.6297i	−1.32929	−	1.48359i
$751$	10.6225			0.387620			0.193810	−	0.981039i	$-0.437915\pi$
$751$	10.6225			0.387620			0.193810	+	0.981039i	$0.437915\pi$
$752$	−26.2739			−0.958111
$753$			93.3894i			3.40330i
$754$		0			0
$755$	1.76713	+	7.11223i	0.0643126	+	0.258840i
$756$		−	8.09890i		−	0.294554i
$757$			7.98562i			0.290242i	0.989414	+	0.145121i	$0.0463572\pi$
$757$			7.98562i			0.290242i	−0.989414	+	0.145121i	$0.953643\pi$
$758$			45.8024i			1.66362i
$759$			22.7792i			0.826834i
$760$	−0.729794	−	2.93722i	−0.0264724	−	0.106544i
$761$			48.9360i			1.77393i	0.461838	+	0.886964i	$0.347190\pi$
$761$			48.9360i			1.77393i	−0.461838	+	0.886964i	$0.652810\pi$
$762$	−87.8636			−3.18296
$763$		−	28.8248i		−	1.04353i
$764$	0.544946			0.0197155
$765$	−3.50307	−	14.0989i	−0.126654	−	0.509747i
$766$	−19.1110			−0.690509
$767$		0			0
$768$		−	27.1845i		−	0.980935i
$769$			7.99547i			0.288324i	0.989554	+	0.144162i	$0.0460486\pi$
$769$			7.99547i			0.288324i	−0.989554	+	0.144162i	$0.953951\pi$
$770$	−3.60197	−	14.4969i	−0.129806	−	0.522433i
$771$	64.8781			2.33653
$772$	6.54495			0.235558
$773$	−26.6141			−0.957242			−0.478621	−	0.878022i	$-0.658863\pi$
$773$	−26.6141			−0.957242			−0.478621	+	0.878022i	$0.658863\pi$
$774$			69.7887i			2.50850i
$775$	2.05786	+	3.88550i	0.0739205	+	0.139571i
$776$	−14.8494			−0.533062
$777$		−	32.7792i		−	1.17595i
$778$	25.9155			0.929115
$779$	−0.680346			−0.0243759
$780$		0			0
$781$	36.7708			1.31576
$782$	−4.01438			−0.143554
$783$			65.8264i			2.35244i
$784$	18.7686			0.670306
$785$	−6.92162	−	27.8576i	−0.247043	−	0.994281i
$786$			69.5585i			2.48107i
$787$	−9.25792			−0.330009			−0.165005	−	0.986293i	$-0.552764\pi$
$787$	−9.25792			−0.330009			−0.165005	+	0.986293i	$0.552764\pi$
$788$	−0.738205			−0.0262975
$789$	−28.9854			−1.03191
$790$	−1.65983	+	0.412408i	−0.0590540	+	0.0146728i
$791$		−	20.0989i		−	0.714634i
$792$		−	44.9333i		−	1.59664i
$793$		0			0
$794$	5.99159			0.212634
$795$	58.4534	−	14.5236i	2.07313	−	0.515099i
$796$	−1.99016			−0.0705393
$797$			15.9421i			0.564700i	0.959312	+	0.282350i	$0.0911139\pi$
$797$			15.9421i			0.564700i	−0.959312	+	0.282350i	$0.908886\pi$
$798$	4.49693			0.159190
$799$		−	5.26180i		−	0.186149i
$800$	9.11450	−	4.82726i	0.322246	−	0.170669i
$801$		−	90.4945i		−	3.19747i
$802$		−	14.0144i		−	0.494865i
$803$			4.95282i			0.174781i
$804$			9.20394i			0.324598i
$805$	2.60811	+	10.4969i	0.0919238	+	0.369968i
$806$		0			0
$807$			36.1133i			1.27125i
$808$	41.2663			1.45174
$809$	−17.9239			−0.630170			−0.315085	−	0.949063i	$-0.602033\pi$
$809$	−17.9239			−0.630170			−0.315085	+	0.949063i	$0.602033\pi$
$810$	65.2883	−	16.2218i	2.29400	−	0.569976i
$811$			7.43415i			0.261048i	0.991445	+	0.130524i	$0.0416660\pi$
$811$			7.43415i			0.261048i	−0.991445	+	0.130524i	$0.958334\pi$
$812$	−3.23513			−0.113531
$813$	66.9998			2.34979
$814$			23.6430i			0.828687i
$815$	26.1483	−	6.49693i	0.915937	−	0.227577i
$816$	13.4452			0.470677
$817$	−3.46800			−0.121330
$818$		−	29.8888i		−	1.04504i
$819$		0			0
$820$	−0.251117	−	1.01068i	−0.00876940	−	0.0352944i
$821$			20.4801i			0.714761i	0.933959	+	0.357380i	$0.116330\pi$
$821$			20.4801i			0.714761i	−0.933959	+	0.357380i	$0.883670\pi$
$822$			67.2639i			2.34610i
$823$			3.75154i			0.130770i	0.997860	+	0.0653852i	$0.0208276\pi$
$823$			3.75154i			0.130770i	−0.997860	+	0.0653852i	$0.979172\pi$
$824$		−	25.5811i		−	0.891159i
$825$	35.5669	−	18.8371i	1.23828	−	0.655824i
$826$		−	12.4247i		−	0.432310i
$827$	48.1483			1.67428			0.837141	−	0.546987i	$-0.184225\pi$
$827$	48.1483			1.67428			0.837141	+	0.546987i	$0.184225\pi$
$828$		−	7.36334i		−	0.255894i
$829$	36.5608			1.26981			0.634904	−	0.772591i	$-0.281040\pi$
$829$	36.5608			1.26981			0.634904	+	0.772591i	$0.281040\pi$
$830$	28.8287	−	7.16290i	1.00066	−	0.248628i
$831$	41.4596			1.43822
$832$		0			0
$833$			3.75872i			0.130232i
$834$			32.4657i			1.12420i
$835$	−18.9444	+	4.70701i	−0.655598	+	0.162893i
$836$	−0.505339			−0.0174775
$837$	−11.2885			−0.390186
$838$	−25.8264			−0.892159
$839$			45.2294i			1.56149i	0.624849	+	0.780746i	$0.285161\pi$
$839$			45.2294i			1.56149i	−0.624849	+	0.780746i	$0.714839\pi$
$840$	−7.33403	−	29.5174i	−0.253048	−	1.01845i
$841$	−2.70540			−0.0932896
$842$			29.2762i			1.00892i
$843$	2.15676			0.0742826
$844$	−8.39803			−0.289072
$845$		0			0
$846$	61.9481			2.12982
$847$	−7.78151			−0.267376
$848$			39.1026i			1.34279i
$849$	−61.1689			−2.09931
$850$	3.31965	+	6.26794i	0.113863	+	0.214989i
$851$		−	17.1194i		−	0.586846i
$852$	−16.9444			−0.580506
$853$	−37.2534			−1.27553			−0.637766	−	0.770230i	$-0.720141\pi$
$853$	−37.2534			−1.27553			−0.637766	+	0.770230i	$0.720141\pi$
$854$	21.1773			0.724671
$855$	2.04945	+	8.24846i	0.0700897	+	0.282092i
$856$			24.4789i			0.836671i
$857$			10.8371i			0.370188i	0.982721	+	0.185094i	$0.0592590\pi$
$857$			10.8371i			0.370188i	−0.982721	+	0.185094i	$0.940741\pi$
$858$		0			0
$859$	−14.6081			−0.498422			−0.249211	−	0.968449i	$-0.580171\pi$
$859$	−14.6081			−0.498422			−0.249211	+	0.968449i	$0.580171\pi$
$860$	−1.28005	−	5.15183i	−0.0436492	−	0.175676i
$861$	−6.83710			−0.233008
$862$		−	12.3596i		−	0.420971i
$863$	10.3440			0.352116			0.176058	−	0.984380i	$-0.443665\pi$
$863$	10.3440			0.352116			0.176058	+	0.984380i	$0.443665\pi$
$864$			26.4801i			0.900872i
$865$	−0.465732	−	1.87444i	−0.0158354	−	0.0637329i
$866$		−	20.0821i		−	0.682417i
$867$		−	51.1988i		−	1.73880i
$868$		−	0.554787i		−	0.0188307i
$869$		−	1.26180i		−	0.0428035i
$870$	−13.4908	−	54.2967i	−0.457380	−	1.84083i
$871$		0			0
$872$			42.3324i			1.43356i
$873$	41.7009			1.41136
$874$	2.34858			0.0794420
$875$	14.2329	−	12.7526i	0.481159	−	0.431116i
$876$		−	2.28231i		−	0.0771122i
$877$	38.0677			1.28545			0.642727	−	0.766095i	$-0.277803\pi$
$877$	38.0677			1.28545			0.642727	+	0.766095i	$0.277803\pi$
$878$	11.8531			0.400022
$879$		−	30.0144i		−	1.01236i
$880$	6.30057	+	25.3580i	0.212392	+	0.854819i
$881$	−12.0494			−0.405956			−0.202978	−	0.979183i	$-0.565062\pi$
$881$	−12.0494			−0.405956			−0.202978	+	0.979183i	$0.565062\pi$
$882$	−44.2522			−1.49005
$883$			0.320699i			0.0107924i	0.999985	+	0.00539619i	$0.00171767\pi$
$883$			0.320699i			0.0107924i	−0.999985	+	0.00539619i	$0.998282\pi$
$884$		0			0
$885$	32.4885	−	8.07223i	1.09209	−	0.271345i
$886$			9.83672i			0.330471i
$887$		−	3.62144i		−	0.121596i	−0.998150	−	0.0607981i	$-0.980635\pi$
$887$		−	3.62144i		−	0.121596i	0.998150	−	0.0607981i	$-0.0193646\pi$
$888$			48.1399i			1.61547i
$889$		−	30.7792i		−	1.03230i
$890$	10.6537	+	42.8781i	0.357112	+	1.43728i
$891$			49.6319i			1.66273i
$892$	3.23370			0.108272
$893$			3.07838i			0.103014i
$894$	−44.2967			−1.48150
$895$	−43.2183	+	10.7382i	−1.44463	+	0.358939i
$896$	22.9132			0.765477
$897$		0			0
$898$		−	48.6635i		−	1.62392i
$899$			4.50921i			0.150391i
$900$	−11.4969	+	6.08906i	−0.383231	+	0.202969i
$901$	−7.83096			−0.260887
$902$	4.93146			0.164200
$903$	−34.8515			−1.15978
$904$			29.5174i			0.981736i
$905$	31.2267	−	7.75872i	1.03801	−	0.257909i
$906$	15.9916			0.531285
$907$			10.9333i			0.363036i	0.983388	+	0.181518i	$0.0581010\pi$
$907$			10.9333i			0.363036i	−0.983388	+	0.181518i	$0.941899\pi$
$908$	6.35842			0.211012
$909$	−115.886			−3.84371
$910$		0			0
$911$	−37.5897			−1.24540			−0.622701	−	0.782460i	$-0.713965\pi$
$911$	−37.5897			−1.24540			−0.622701	+	0.782460i	$0.713965\pi$
$912$	−7.86603			−0.260470
$913$			21.9155i			0.725297i
$914$	54.8613			1.81465
$915$	13.7587	+	55.3751i	0.454849	+	1.83064i
$916$			1.13624i			0.0375423i
$917$	−24.3668			−0.804664
$918$	−18.2101			−0.601022
$919$	−33.6742			−1.11081			−0.555405	−	0.831580i	$-0.687437\pi$
$919$	−33.6742			−1.11081			−0.555405	+	0.831580i	$0.687437\pi$
$920$	−3.83030	−	15.4159i	−0.126281	−	0.508247i
$921$			0.837101i			0.0275834i
$922$			23.0563i			0.759317i
$923$		0			0
$924$	−5.07838			−0.167066
$925$	−26.7298	+	14.1568i	−0.878870	+	0.465471i
$926$	14.0014			0.460116
$927$			71.8381i			2.35947i
$928$	10.5776			0.347226
$929$			43.2039i			1.41748i	0.705472	+	0.708738i	$0.250735\pi$
$929$			43.2039i			1.41748i	−0.705472	+	0.708738i	$0.749265\pi$
$930$	9.31124	−	2.31351i	0.305328	−	0.0758630i
$931$		−	2.19902i		−	0.0720698i
$932$			6.98932i			0.228943i
$933$			41.3607i			1.35409i
$934$		−	2.88920i		−	0.0945376i
$935$	−5.07838	+	1.26180i	−0.166081	+	0.0412651i
$936$		0			0
$937$			27.5630i			0.900445i	0.892916	+	0.450222i	$0.148655\pi$
$937$			27.5630i			0.900445i	−0.892916	+	0.450222i	$0.851345\pi$
$938$	−20.6947			−0.675707
$939$	106.835			3.48642
$940$	−4.57304	+	1.13624i	−0.149156	+	0.0370600i
$941$			58.1666i			1.89618i	0.318007	+	0.948088i	$0.396987\pi$
$941$			58.1666i			1.89618i	−0.318007	+	0.948088i	$0.603013\pi$
$942$	−62.6369			−2.04082
$943$	−3.57077			−0.116280
$944$			21.7333i			0.707358i
$945$	11.8310	+	47.6163i	0.384861	+	1.54896i
$946$	25.1377			0.817296
$947$	48.5152			1.57653			0.788266	−	0.615335i	$-0.210979\pi$
$947$	48.5152			1.57653			0.788266	+	0.615335i	$0.210979\pi$
$948$			0.581449i			0.0188846i
$949$		0			0
$950$	−1.94214	−	3.66701i	−0.0630114	−	0.118974i
$951$		−	44.2245i		−	1.43408i
$952$			3.95443i			0.128164i
$953$		−	23.0349i		−	0.746173i	−0.927796	−	0.373087i	$-0.878299\pi$
$953$		−	23.0349i		−	0.746173i	0.927796	−	0.373087i	$-0.121701\pi$
$954$		−	92.1953i		−	2.98493i
$955$	−3.20394	+	0.796064i	−0.103677	+	0.0257600i
$956$		−	2.45013i		−	0.0792430i
$957$	41.2762			1.33427
$958$			24.2316i			0.782889i
$959$	−23.5630			−0.760890
$960$	10.3051	+	41.4752i	0.332596	+	1.33861i
$961$	30.2267			0.975056
$962$		0			0
$963$		−	68.7429i		−	2.21521i
$964$			3.49777i			0.112655i
$965$	−38.4801	+	9.56093i	−1.23872	+	0.307777i
$966$	23.6020			0.759381
$967$	−54.9998			−1.76868			−0.884338	−	0.466848i	$-0.845389\pi$
$967$	−54.9998			−1.76868			−0.884338	+	0.466848i	$0.845389\pi$
$968$	11.4280			0.367310
$969$		−	1.57531i		−	0.0506061i
$970$	−19.7587	+	4.90934i	−0.634414	+	0.157629i
$971$	9.70540			0.311461			0.155731	−	0.987800i	$-0.450227\pi$
$971$	9.70540			0.311461			0.155731	+	0.987800i	$0.450227\pi$
$972$		−	8.65634i		−	0.277652i
$973$	−11.3730			−0.364601
$974$	−7.61038			−0.243852
$975$		0			0
$976$	−37.0433			−1.18573
$977$	−32.2062			−1.03037			−0.515184	−	0.857080i	$-0.672276\pi$
$977$	−32.2062			−1.03037			−0.515184	+	0.857080i	$0.672276\pi$
$978$		−	58.7936i		−	1.88001i
$979$	−32.5958			−1.04177
$980$	3.26672	−	0.811662i	0.104351	−	0.0259276i
$981$		−	118.880i		−	3.79555i
$982$	60.7768			1.93947
$983$	−44.0782			−1.40588			−0.702938	−	0.711251i	$-0.748129\pi$
$983$	−44.0782			−1.40588			−0.702938	+	0.711251i	$0.748129\pi$
$984$	10.0410			0.320097
$985$	4.34017	−	1.07838i	0.138289	−	0.0343600i
$986$			7.27408i			0.231654i
$987$			30.9360i			0.984704i
$988$		0			0
$989$	−18.2017			−0.578779
$990$	−14.8554	−	59.7887i	−0.472134	−	1.90021i
$991$	12.0677			0.383343			0.191672	−	0.981459i	$-0.438609\pi$
$991$	12.0677			0.383343			0.191672	+	0.981459i	$0.438609\pi$
$992$			1.81393i			0.0575923i
$993$	−58.5029			−1.85653
$994$		−	38.0989i		−	1.20842i
$995$	11.7009	−	2.90725i	0.370942	−	0.0921659i
$996$		−	10.0989i		−	0.319996i
$997$			45.7587i			1.44919i	0.689173	+	0.724597i	$0.257974\pi$
$997$			45.7587i			1.44919i	−0.689173	+	0.724597i	$0.742026\pi$
$998$			2.57182i			0.0814094i
$999$		−	77.6574i		−	2.45697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.d.a.844.3		6
5.4	even	2		845.2.d.b.844.4		6
13.2	odd	12		845.2.n.f.529.2		12
13.3	even	3		845.2.l.e.654.4		12
13.4	even	6		845.2.l.d.699.3		12
13.5	odd	4		65.2.b.a.14.5	yes	6
13.6	odd	12		845.2.n.f.484.5		12
13.7	odd	12		845.2.n.g.484.2		12
13.8	odd	4		845.2.b.c.339.2		6
13.9	even	3		845.2.l.e.699.3		12
13.10	even	6		845.2.l.d.654.4		12
13.11	odd	12		845.2.n.g.529.5		12
13.12	even	2		845.2.d.b.844.3		6
39.5	even	4		585.2.c.b.469.2		6
52.31	even	4		1040.2.d.c.209.6		6
65.4	even	6		845.2.l.e.699.4		12
65.8	even	4		4225.2.a.ba.1.2		3
65.9	even	6		845.2.l.d.699.4		12
65.18	even	4		325.2.a.k.1.2		3
65.19	odd	12		845.2.n.f.484.2		12
65.24	odd	12		845.2.n.g.529.2		12
65.29	even	6		845.2.l.d.654.3		12
65.34	odd	4		845.2.b.c.339.5		6
65.44	odd	4		65.2.b.a.14.2	✓	6
65.47	even	4		4225.2.a.bh.1.2		3
65.49	even	6		845.2.l.e.654.3		12
65.54	odd	12		845.2.n.f.529.5		12
65.57	even	4		325.2.a.j.1.2		3
65.59	odd	12		845.2.n.g.484.5		12
65.64	even	2	inner	845.2.d.a.844.4		6
195.44	even	4		585.2.c.b.469.5		6
195.83	odd	4		2925.2.a.bf.1.2		3
195.122	odd	4		2925.2.a.bj.1.2		3
260.83	odd	4		5200.2.a.cb.1.1		3
260.187	odd	4		5200.2.a.cj.1.3		3
260.239	even	4		1040.2.d.c.209.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.2	✓	6	65.44	odd	4
65.2.b.a.14.5	yes	6	13.5	odd	4
325.2.a.j.1.2		3	65.57	even	4
325.2.a.k.1.2		3	65.18	even	4
585.2.c.b.469.2		6	39.5	even	4
585.2.c.b.469.5		6	195.44	even	4
845.2.b.c.339.2		6	13.8	odd	4
845.2.b.c.339.5		6	65.34	odd	4
845.2.d.a.844.3		6	1.1	even	1	trivial
845.2.d.a.844.4		6	65.64	even	2	inner
845.2.d.b.844.3		6	13.12	even	2
845.2.d.b.844.4		6	5.4	even	2
845.2.l.d.654.3		12	65.29	even	6
845.2.l.d.654.4		12	13.10	even	6
845.2.l.d.699.3		12	13.4	even	6
845.2.l.d.699.4		12	65.9	even	6
845.2.l.e.654.3		12	65.49	even	6
845.2.l.e.654.4		12	13.3	even	3
845.2.l.e.699.3		12	13.9	even	3
845.2.l.e.699.4		12	65.4	even	6
845.2.n.f.484.2		12	65.19	odd	12
845.2.n.f.484.5		12	13.6	odd	12
845.2.n.f.529.2		12	13.2	odd	12
845.2.n.f.529.5		12	65.54	odd	12
845.2.n.g.484.2		12	13.7	odd	12
845.2.n.g.484.5		12	65.59	odd	12
845.2.n.g.529.2		12	65.24	odd	12
845.2.n.g.529.5		12	13.11	odd	12
1040.2.d.c.209.1		6	260.239	even	4
1040.2.d.c.209.6		6	52.31	even	4
2925.2.a.bf.1.2		3	195.83	odd	4
2925.2.a.bj.1.2		3	195.122	odd	4
4225.2.a.ba.1.2		3	65.8	even	4
4225.2.a.bh.1.2		3	65.47	even	4
5200.2.a.cb.1.1		3	260.83	odd	4
5200.2.a.cj.1.3		3	260.187	odd	4

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.53919 q^{2} -3.17009i q^{3} +0.369102 q^{4} +(-2.17009 + 0.539189i) q^{5} +4.87936i q^{6} -1.70928 q^{7} +2.51026 q^{8} -7.04945 q^{9} +(3.34017 - 0.829914i) q^{10} +2.53919i q^{11} -1.17009i q^{12} +2.63090 q^{14} +(1.70928 + 6.87936i) q^{15} -4.60197 q^{16} -0.921622i q^{17} +10.8504 q^{18} +0.539189i q^{19} +(-0.800984 + 0.199016i) q^{20} +5.41855i q^{21} -3.90829i q^{22} +2.82991i q^{23} -7.95774i q^{24} +(4.41855 - 2.34017i) q^{25} +12.8371i q^{27} -0.630898 q^{28} +5.12783 q^{29} +(-2.63090 - 10.5886i) q^{30} +0.879362i q^{31} +2.06278 q^{32} +8.04945 q^{33} +1.41855i q^{34} +(3.70928 - 0.921622i) q^{35} -2.60197 q^{36} -6.04945 q^{37} -0.829914i q^{38} +(-5.44748 + 1.35350i) q^{40} +1.26180i q^{41} -8.34017i q^{42} +6.43188i q^{43} +0.937221i q^{44} +(15.2979 - 3.80098i) q^{45} -4.35577i q^{46} +5.70928 q^{47} +14.5886i q^{48} -4.07838 q^{49} +(-6.80098 + 3.60197i) q^{50} -2.92162 q^{51} -8.49693i q^{53} -19.7587i q^{54} +(-1.36910 - 5.51026i) q^{55} -4.29072 q^{56} +1.70928 q^{57} -7.89269 q^{58} -4.72261i q^{59} +(0.630898 + 2.53919i) q^{60} +8.04945 q^{61} -1.35350i q^{62} +12.0494 q^{63} +6.02893 q^{64} -12.3896 q^{66} -7.86603 q^{67} -0.340173i q^{68} +8.97107 q^{69} +(-5.70928 + 1.41855i) q^{70} -14.4813i q^{71} -17.6959 q^{72} +1.95055 q^{73} +9.31124 q^{74} +(-7.41855 - 14.0072i) q^{75} +0.199016i q^{76} -4.34017i q^{77} -0.496928 q^{79} +(9.98667 - 2.48133i) q^{80} +19.5464 q^{81} -1.94214i q^{82} +8.63090 q^{83} +2.00000i q^{84} +(0.496928 + 2.00000i) q^{85} -9.89988i q^{86} -16.2557i q^{87} +6.37402i q^{88} +12.8371i q^{89} +(-23.5464 + 5.85043i) q^{90} +1.04453i q^{92} +2.78765 q^{93} -8.78765 q^{94} +(-0.290725 - 1.17009i) q^{95} -6.53919i q^{96} -5.91548 q^{97} +6.27739 q^{98} -17.8999i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 10 q^{4} - 2 q^{5} + 4 q^{7} - 18 q^{8} - 6 q^{9} - 2 q^{10} + 8 q^{14} - 4 q^{15} + 10 q^{16} + 10 q^{18} + 14 q^{20} - 2 q^{25} + 4 q^{28} - 12 q^{29} - 8 q^{30} - 22 q^{32} + 12 q^{33}+ \cdots + 50 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 10 * q^4 - 2 * q^5 + 4 * q^7 - 18 * q^8 - 6 * q^9 - 2 * q^10 + 8 * q^14 - 4 * q^15 + 10 * q^16 + 10 * q^18 + 14 * q^20 - 2 * q^25 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 22 * q^32 + 12 * q^33 + 8 * q^35 + 22 * q^36 - 34 * q^40 + 38 * q^45 + 20 * q^47 - 18 * q^49 - 22 * q^50 - 24 * q^51 - 16 * q^55 - 40 * q^56 - 4 * q^57 - 24 * q^58 - 4 * q^60 + 12 * q^61 + 36 * q^63 + 66 * q^64 - 16 * q^66 - 20 * q^67 + 24 * q^69 - 20 * q^70 - 90 * q^72 + 48 * q^73 + 4 * q^74 - 16 * q^75 + 32 * q^79 + 58 * q^80 + 46 * q^81 + 44 * q^83 - 32 * q^85 - 70 * q^90 - 4 * q^93 - 32 * q^94 - 16 * q^95 + 28 * q^97 + 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more