LMFDB - Embedded newform 845.2.c.h.506.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(506,845)]

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([0, 1]))

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

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

chi := DirichletCharacter("845.506");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.c (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:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 34x^{16} + 407x^{14} + 2175x^{12} + 5555x^{10} + 6664x^{8} + 3544x^{6} + 681x^{4} + 47x^{2} + 1 $ x^18 + 34x^16 + 407x^14 + 2175x^12 + 5555x^10 + 6664x^8 + 3544x^6 + 681x^4 + 47x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			506.7
Root			$-0.199774i$ of defining polynomial
Character	$\chi$	$=$	845.506
Dual form			845.2.c.h.506.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.04721i q^{2} -2.75868 q^{3} +0.903360 q^{4} +1.00000i q^{5} +2.88890i q^{6} -3.42366i q^{7} -3.04042i q^{8} +4.61031 q^{9} +O(q^{10})$	\(q-1.04721i q^{2} -2.75868 q^{3} +0.903360 q^{4} +1.00000i q^{5} +2.88890i q^{6} -3.42366i q^{7} -3.04042i q^{8} +4.61031 q^{9} +1.04721 q^{10} +2.38793i q^{11} -2.49208 q^{12} -3.58527 q^{14} -2.75868i q^{15} -1.37722 q^{16} +7.43316 q^{17} -4.82794i q^{18} +0.840998i q^{19} +0.903360i q^{20} +9.44477i q^{21} +2.50066 q^{22} -5.46920 q^{23} +8.38753i q^{24} -1.00000 q^{25} -4.44233 q^{27} -3.09279i q^{28} +1.65390 q^{29} -2.88890 q^{30} -8.10151i q^{31} -4.63860i q^{32} -6.58754i q^{33} -7.78405i q^{34} +3.42366 q^{35} +4.16477 q^{36} -6.39379i q^{37} +0.880698 q^{38} +3.04042 q^{40} -6.15846i q^{41} +9.89061 q^{42} -12.0911 q^{43} +2.15716i q^{44} +4.61031i q^{45} +5.72737i q^{46} -2.33083i q^{47} +3.79931 q^{48} -4.72142 q^{49} +1.04721i q^{50} -20.5057 q^{51} +4.35709 q^{53} +4.65203i q^{54} -2.38793 q^{55} -10.4093 q^{56} -2.32004i q^{57} -1.73197i q^{58} -5.11542i q^{59} -2.49208i q^{60} -8.84695 q^{61} -8.48395 q^{62} -15.7841i q^{63} -7.61201 q^{64} -6.89851 q^{66} +7.17992i q^{67} +6.71482 q^{68} +15.0878 q^{69} -3.58527i q^{70} +3.28070i q^{71} -14.0173i q^{72} -9.41601i q^{73} -6.69561 q^{74} +2.75868 q^{75} +0.759724i q^{76} +8.17546 q^{77} +5.89740 q^{79} -1.37722i q^{80} -1.57598 q^{81} -6.44917 q^{82} -5.14271i q^{83} +8.53203i q^{84} +7.43316i q^{85} +12.6619i q^{86} -4.56257 q^{87} +7.26031 q^{88} -6.03426i q^{89} +4.82794 q^{90} -4.94065 q^{92} +22.3495i q^{93} -2.44085 q^{94} -0.840998 q^{95} +12.7964i q^{96} -6.33475i q^{97} +4.94429i q^{98} +11.0091i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9}+O(q^{10}) $ 18 * q + 14 * q^3 - 34 * q^4 + 32 * q^9	$ 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9} - 6 q^{10} - 24 q^{12} - 4 q^{14} + 74 q^{16} + 2 q^{17} + 24 q^{22} - 28 q^{23} - 18 q^{25} + 44 q^{27} + 24 q^{29} + 4 q^{30} + 14 q^{35} - 6 q^{36} + 94 q^{38} + 24 q^{40} - 22 q^{42} - 78 q^{43} - 6 q^{48} - 32 q^{49} - 86 q^{51} - 16 q^{53} - 18 q^{55} + 58 q^{56} - 6 q^{61} + 20 q^{62} - 68 q^{64} - 98 q^{66} - 40 q^{68} + 26 q^{69} - 30 q^{74} - 14 q^{75} + 8 q^{77} + 78 q^{79} + 58 q^{81} + 8 q^{82} + 32 q^{87} - 84 q^{88} + 20 q^{90} - 54 q^{92} + 32 q^{94} + 8 q^{95}+O(q^{100}) $ 18 * q + 14 * q^3 - 34 * q^4 + 32 * q^9 - 6 * q^10 - 24 * q^12 - 4 * q^14 + 74 * q^16 + 2 * q^17 + 24 * q^22 - 28 * q^23 - 18 * q^25 + 44 * q^27 + 24 * q^29 + 4 * q^30 + 14 * q^35 - 6 * q^36 + 94 * q^38 + 24 * q^40 - 22 * q^42 - 78 * q^43 - 6 * q^48 - 32 * q^49 - 86 * q^51 - 16 * q^53 - 18 * q^55 + 58 * q^56 - 6 * q^61 + 20 * q^62 - 68 * q^64 - 98 * q^66 - 40 * q^68 + 26 * q^69 - 30 * q^74 - 14 * q^75 + 8 * q^77 + 78 * q^79 + 58 * q^81 + 8 * q^82 + 32 * q^87 - 84 * q^88 + 20 * q^90 - 54 * q^92 + 32 * q^94 + 8 * q^95

Display 100 coefficients 10 coefficients

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 $

$2$	− 1.04721i	− 0.740486i	−0.928935	−	0.370243i	$-0.879274\pi$
$2$	− 1.04721i	− 0.740486i	0.928935	−	0.370243i	$-0.120726\pi$
$3$	−2.75868	−1.59272	−0.796362	−	0.604820i	$-0.793245\pi$
$3$	−2.75868	−1.59272	−0.796362	+	0.604820i	$0.793245\pi$
$4$	0.903360	0.451680
$5$	1.00000i	0.447214i
$5$	1.00000i	0.447214i
$6$	2.88890i	1.17939i
$7$	− 3.42366i	− 1.29402i	−0.762481	−	0.647010i	$-0.776019\pi$
$7$	− 3.42366i	− 1.29402i	0.762481	−	0.647010i	$-0.223981\pi$
$8$	− 3.04042i	− 1.07495i
$9$	4.61031	1.53677
$10$	1.04721	0.331156
$11$	2.38793i	0.719989i	0.932954	+	0.359995i	$0.117221\pi$
$11$	2.38793i	0.719989i	−0.932954	+	0.359995i	$0.882779\pi$
$12$	−2.49208	−0.719402
$13$	0	0
$13$	0	0
$14$	−3.58527	−0.958204
$15$	− 2.75868i	− 0.712288i
$16$	−1.37722	−0.344305
$17$	7.43316	1.80281	0.901403	−	0.432981i	$-0.142538\pi$
$17$	7.43316	1.80281	0.901403	+	0.432981i	$0.142538\pi$
$18$	− 4.82794i	− 1.13796i
$19$	0.840998i	0.192938i	0.995336	+	0.0964691i	$0.0307549\pi$
$19$	0.840998i	0.192938i	−0.995336	+	0.0964691i	$0.969245\pi$
$20$	0.903360i	0.201997i
$21$	9.44477i	2.06102i
$22$	2.50066	0.533142
$23$	−5.46920	−1.14041	−0.570203	−	0.821504i	$-0.693135\pi$
$23$	−5.46920	−1.14041	−0.570203	+	0.821504i	$0.693135\pi$
$24$	8.38753i	1.71210i
$25$	−1.00000	−0.200000
$26$	0	0
$27$	−4.44233	−0.854926
$28$	− 3.09279i	− 0.584483i
$29$	1.65390	0.307121	0.153560	−	0.988139i	$-0.450926\pi$
$29$	1.65390	0.307121	0.153560	+	0.988139i	$0.450926\pi$
$30$	−2.88890	−0.527439
$31$	− 8.10151i	− 1.45507i	−0.686068	−	0.727537i	$-0.740665\pi$
$31$	− 8.10151i	− 1.45507i	0.686068	−	0.727537i	$-0.259335\pi$
$32$	− 4.63860i	− 0.819996i
$33$	− 6.58754i	− 1.14674i
$34$	− 7.78405i	− 1.33495i
$35$	3.42366	0.578703
$36$	4.16477	0.694128
$37$	− 6.39379i	− 1.05113i	−0.850753	−	0.525566i	$-0.823854\pi$
$37$	− 6.39379i	− 1.05113i	0.850753	−	0.525566i	$-0.176146\pi$
$38$	0.880698	0.142868
$39$	0	0
$40$	3.04042	0.480732
$41$	− 6.15846i	− 0.961789i	−0.876778	−	0.480895i	$-0.840312\pi$
$41$	− 6.15846i	− 0.961789i	0.876778	−	0.480895i	$-0.159688\pi$
$42$	9.89061	1.52615
$43$	−12.0911	−1.84388	−0.921938	−	0.387339i	$-0.873394\pi$
$43$	−12.0911	−1.84388	−0.921938	+	0.387339i	$0.873394\pi$
$44$	2.15716i	0.325205i
$45$	4.61031i	0.687264i
$46$	5.72737i	0.844455i
$47$	− 2.33083i	− 0.339986i	−0.985445	−	0.169993i	$-0.945625\pi$
$47$	− 2.33083i	− 0.339986i	0.985445	−	0.169993i	$-0.0543745\pi$
$48$	3.79931	0.548383
$49$	−4.72142	−0.674488
$50$	1.04721i	0.148097i
$51$	−20.5057	−2.87137
$52$	0	0
$53$	4.35709	0.598492	0.299246	−	0.954176i	$-0.403265\pi$
$53$	4.35709	0.598492	0.299246	+	0.954176i	$0.403265\pi$
$54$	4.65203i	0.633061i
$55$	−2.38793	−0.321989
$56$	−10.4093	−1.39101
$57$	− 2.32004i	− 0.307297i
$58$	− 1.73197i	− 0.227419i
$59$	− 5.11542i	− 0.665971i	−0.942932	−	0.332985i	$-0.891944\pi$
$59$	− 5.11542i	− 0.665971i	0.942932	−	0.332985i	$-0.108056\pi$
$60$	− 2.49208i	− 0.321726i
$61$	−8.84695	−1.13274	−0.566368	−	0.824153i	$-0.691652\pi$
$61$	−8.84695	−1.13274	−0.566368	+	0.824153i	$0.691652\pi$
$62$	−8.48395	−1.07746
$63$	− 15.7841i	− 1.98861i
$64$	−7.61201	−0.951501
$65$	0	0
$66$	−6.89851	−0.849148
$67$	7.17992i	0.877167i	0.898690	+	0.438584i	$0.144520\pi$
$67$	7.17992i	0.877167i	−0.898690	+	0.438584i	$0.855480\pi$
$68$	6.71482	0.814292
$69$	15.0878	1.81635
$70$	− 3.58527i	− 0.428522i
$71$	3.28070i	0.389348i	0.980868	+	0.194674i	$0.0623649\pi$
$71$	3.28070i	0.389348i	−0.980868	+	0.194674i	$0.937635\pi$
$72$	− 14.0173i	− 1.65195i
$73$	− 9.41601i	− 1.10206i	−0.834485	−	0.551030i	$-0.814235\pi$
$73$	− 9.41601i	− 1.10206i	0.834485	−	0.551030i	$-0.185765\pi$
$74$	−6.69561	−0.778349
$75$	2.75868	0.318545
$76$	0.759724i	0.0871464i
$77$	8.17546	0.931680
$78$	0	0
$79$	5.89740	0.663509	0.331755	−	0.943366i	$-0.392359\pi$
$79$	5.89740	0.663509	0.331755	+	0.943366i	$0.392359\pi$
$80$	− 1.37722i	− 0.153978i
$81$	−1.57598	−0.175109
$82$	−6.44917	−0.712192
$83$	− 5.14271i	− 0.564486i	−0.959343	−	0.282243i	$-0.908922\pi$
$83$	− 5.14271i	− 0.564486i	0.959343	−	0.282243i	$-0.0910784\pi$
$84$	8.53203i	0.930920i
$85$	7.43316i	0.806239i
$86$	12.6619i	1.36536i
$87$	−4.56257	−0.489158
$88$	7.26031	0.773952
$89$	− 6.03426i	− 0.639630i	−0.947480	−	0.319815i	$-0.896379\pi$
$89$	− 6.03426i	− 0.639630i	0.947480	−	0.319815i	$-0.103621\pi$
$90$	4.82794	0.508910
$91$	0	0
$92$	−4.94065	−0.515099
$93$	22.3495i	2.31753i
$94$	−2.44085	−0.251755
$95$	−0.840998	−0.0862846
$96$	12.7964i	1.30603i
$97$	− 6.33475i	− 0.643196i	−0.946876	−	0.321598i	$-0.895780\pi$
$97$	− 6.33475i	− 0.643196i	0.946876	−	0.321598i	$-0.104220\pi$
$98$	4.94429i	0.499449i
$99$	11.0091i	1.10646i
$100$	−0.903360	−0.0903360
$101$	−4.34957	−0.432799	−0.216399	−	0.976305i	$-0.569431\pi$
$101$	−4.34957	−0.432799	−0.216399	+	0.976305i	$0.569431\pi$
$102$	21.4737i	2.12621i
$103$	−2.11946	−0.208837	−0.104418	−	0.994533i	$-0.533298\pi$
$103$	−2.11946	−0.208837	−0.104418	+	0.994533i	$0.533298\pi$
$104$	0	0
$105$	−9.44477	−0.921715
$106$	− 4.56277i	− 0.443175i
$107$	4.79902	0.463939	0.231969	−	0.972723i	$-0.425483\pi$
$107$	4.79902	0.463939	0.231969	+	0.972723i	$0.425483\pi$
$108$	−4.01302	−0.386153
$109$	7.44950i	0.713533i	0.934194	+	0.356767i	$0.116121\pi$
$109$	7.44950i	0.713533i	−0.934194	+	0.356767i	$0.883879\pi$
$110$	2.50066i	0.238428i
$111$	17.6384i	1.67416i
$112$	4.71513i	0.445538i
$113$	8.60985	0.809947	0.404973	−	0.914328i	$-0.367281\pi$
$113$	8.60985	0.809947	0.404973	+	0.914328i	$0.367281\pi$
$114$	−2.42956	−0.227549
$115$	− 5.46920i	− 0.510005i
$116$	1.49406	0.138720
$117$	0	0
$118$	−5.35690	−0.493142
$119$	− 25.4486i	− 2.33287i
$120$	−8.38753	−0.765673
$121$	5.29777	0.481616
$122$	9.26457i	0.838775i
$123$	16.9892i	1.53186i
$124$	− 7.31858i	− 0.657228i
$125$	− 1.00000i	− 0.0894427i
$126$	−16.5292	−1.47254
$127$	−18.7179	−1.66095	−0.830474	−	0.557057i	$-0.811931\pi$
$127$	−18.7179	−1.66095	−0.830474	+	0.557057i	$0.811931\pi$
$128$	− 1.30586i	− 0.115423i
$129$	33.3555	2.93678
$130$	0	0
$131$	9.44189	0.824942	0.412471	−	0.910971i	$-0.364666\pi$
$131$	9.44189	0.824942	0.412471	+	0.910971i	$0.364666\pi$
$132$	− 5.95092i	− 0.517961i
$133$	2.87929	0.249666
$134$	7.51886	0.649530
$135$	− 4.44233i	− 0.382335i
$136$	− 22.5999i	− 1.93792i
$137$	15.6690i	1.33870i	0.742949	+	0.669348i	$0.233427\pi$
$137$	15.6690i	1.33870i	−0.742949	+	0.669348i	$0.766573\pi$
$138$	− 15.8000i	− 1.34498i
$139$	12.1555	1.03102	0.515509	−	0.856884i	$-0.327603\pi$
$139$	12.1555	1.03102	0.515509	+	0.856884i	$0.327603\pi$
$140$	3.09279	0.261389
$141$	6.43000i	0.541504i
$142$	3.43557	0.288307
$143$	0	0
$144$	−6.34941	−0.529117
$145$	1.65390i	0.137349i
$146$	−9.86050	−0.816061
$147$	13.0249	1.07427
$148$	− 5.77589i	− 0.474775i
$149$	− 0.777505i	− 0.0636957i	−0.999493	−	0.0318479i	$-0.989861\pi$
$149$	− 0.777505i	− 0.0636957i	0.999493	−	0.0318479i	$-0.0101392\pi$
$150$	− 2.88890i	− 0.235878i
$151$	− 7.75832i	− 0.631363i	−0.948865	−	0.315682i	$-0.897767\pi$
$151$	− 7.75832i	− 0.631363i	0.948865	−	0.315682i	$-0.102233\pi$
$152$	2.55698	0.207399
$153$	34.2692	2.77050
$154$	− 8.56139i	− 0.689897i
$155$	8.10151	0.650729
$156$	0	0
$157$	12.1350	0.968479	0.484240	−	0.874935i	$-0.339096\pi$
$157$	12.1350	0.968479	0.484240	+	0.874935i	$0.339096\pi$
$158$	− 6.17579i	− 0.491319i
$159$	−12.0198	−0.953233
$160$	4.63860	0.366713
$161$	18.7246i	1.47571i
$162$	1.65037i	0.129666i
$163$	− 0.186353i	− 0.0145963i	−0.999973	−	0.00729817i	$-0.997677\pi$
$163$	− 0.186353i	− 0.0145963i	0.999973	−	0.00729817i	$-0.00232310\pi$
$164$	− 5.56330i	− 0.434421i
$165$	6.58754	0.512839
$166$	−5.38548	−0.417994
$167$	− 7.42351i	− 0.574449i	−0.957863	−	0.287224i	$-0.907268\pi$
$167$	− 7.42351i	− 0.574449i	0.957863	−	0.287224i	$-0.0927325\pi$
$168$	28.7160	2.21549
$169$	0	0
$170$	7.78405	0.597009
$171$	3.87726i	0.296502i
$172$	−10.9226	−0.832842
$173$	−4.62865	−0.351910	−0.175955	−	0.984398i	$-0.556301\pi$
$173$	−4.62865	−0.351910	−0.175955	+	0.984398i	$0.556301\pi$
$174$	4.77795i	0.362215i
$175$	3.42366i	0.258804i
$176$	− 3.28871i	− 0.247896i
$177$	14.1118i	1.06071i
$178$	−6.31911	−0.473637
$179$	11.9605	0.893972	0.446986	−	0.894541i	$-0.352497\pi$
$179$	11.9605	0.893972	0.446986	+	0.894541i	$0.352497\pi$
$180$	4.16477i	0.310424i
$181$	−12.8070	−0.951935	−0.475968	−	0.879463i	$-0.657902\pi$
$181$	−12.8070	−0.951935	−0.475968	+	0.879463i	$0.657902\pi$
$182$	0	0
$183$	24.4059	1.80413
$184$	16.6286i	1.22588i
$185$	6.39379	0.470081
$186$	23.4045	1.71610
$187$	17.7499i	1.29800i
$188$	− 2.10558i	− 0.153565i
$189$	15.2090i	1.10629i
$190$	0.880698i	0.0638926i
$191$	17.5284	1.26831	0.634155	−	0.773206i	$-0.281348\pi$
$191$	17.5284	1.26831	0.634155	+	0.773206i	$0.281348\pi$
$192$	20.9991	1.51548
$193$	8.60151i	0.619151i	0.950875	+	0.309575i	$0.100187\pi$
$193$	8.60151i	0.619151i	−0.950875	+	0.309575i	$0.899813\pi$
$194$	−6.63379	−0.476278
$195$	0	0
$196$	−4.26514	−0.304653
$197$	8.12364i	0.578785i	0.957210	+	0.289393i	$0.0934533\pi$
$197$	8.12364i	0.578785i	−0.957210	+	0.289393i	$0.906547\pi$
$198$	11.5288	0.819317
$199$	−7.55978	−0.535898	−0.267949	−	0.963433i	$-0.586346\pi$
$199$	−7.55978	−0.535898	−0.267949	+	0.963433i	$0.586346\pi$
$200$	3.04042i	0.214990i
$201$	− 19.8071i	− 1.39709i
$202$	4.55490i	0.320481i
$203$	− 5.66237i	− 0.397420i
$204$	−18.5240	−1.29694
$205$	6.15846	0.430125
$206$	2.21951i	0.154641i
$207$	−25.2147	−1.75254
$208$	0	0
$209$	−2.00825	−0.138913
$210$	9.89061i	0.682517i
$211$	20.8167	1.43308	0.716540	−	0.697546i	$-0.245725\pi$
$211$	20.8167	1.43308	0.716540	+	0.697546i	$0.245725\pi$
$212$	3.93602	0.270327
$213$	− 9.05040i	− 0.620124i
$214$	− 5.02556i	− 0.343540i
$215$	− 12.0911i	− 0.824606i
$216$	13.5065i	0.919002i
$217$	−27.7368	−1.88290
$218$	7.80116	0.528361
$219$	25.9757i	1.75528i
$220$	−2.15716	−0.145436
$221$	0	0
$222$	18.4710	1.23969
$223$	17.7214i	1.18672i	0.804939	+	0.593358i	$0.202198\pi$
$223$	17.7214i	1.18672i	−0.804939	+	0.593358i	$0.797802\pi$
$224$	−15.8810	−1.06109
$225$	−4.61031	−0.307354
$226$	− 9.01629i	− 0.599755i
$227$	− 9.72267i	− 0.645316i	−0.946516	−	0.322658i	$-0.895424\pi$
$227$	− 9.72267i	− 0.645316i	0.946516	−	0.322658i	$-0.104576\pi$
$228$	− 2.09584i	− 0.138800i
$229$	21.5044i	1.42105i	0.703673	+	0.710524i	$0.251542\pi$
$229$	21.5044i	1.42105i	−0.703673	+	0.710524i	$0.748458\pi$
$230$	−5.72737	−0.377652
$231$	−22.5535	−1.48391
$232$	− 5.02853i	− 0.330139i
$233$	17.8626	1.17022	0.585111	−	0.810954i	$-0.301051\pi$
$233$	17.8626	1.17022	0.585111	+	0.810954i	$0.301051\pi$
$234$	0	0
$235$	2.33083	0.152046
$236$	− 4.62107i	− 0.300806i
$237$	−16.2690	−1.05679
$238$	−26.6499	−1.72746
$239$	− 4.80445i	− 0.310774i	−0.987854	−	0.155387i	$-0.950338\pi$
$239$	− 4.80445i	− 0.310774i	0.987854	−	0.155387i	$-0.0496625\pi$
$240$	3.79931i	0.245244i
$241$	− 21.0062i	− 1.35313i	−0.736383	−	0.676565i	$-0.763468\pi$
$241$	− 21.0062i	− 1.35313i	0.736383	−	0.676565i	$-0.236532\pi$
$242$	− 5.54786i	− 0.356630i
$243$	17.6746	1.13383
$244$	−7.99198	−0.511634
$245$	− 4.72142i	− 0.301640i
$246$	17.7912	1.13432
$247$	0	0
$248$	−24.6320	−1.56413
$249$	14.1871i	0.899070i
$250$	−1.04721	−0.0662311
$251$	0.294350	0.0185792	0.00928962	−	0.999957i	$-0.497043\pi$
$251$	0.294350	0.0185792	0.00928962	+	0.999957i	$0.497043\pi$
$252$	− 14.2587i	− 0.898216i
$253$	− 13.0601i	− 0.821080i
$254$	19.6015i	1.22991i
$255$	− 20.5057i	− 1.28412i
$256$	−16.5915	−1.03697
$257$	21.9428	1.36875	0.684376	−	0.729129i	$-0.260075\pi$
$257$	21.9428	1.36875	0.684376	+	0.729129i	$0.260075\pi$
$258$	− 34.9300i	− 2.17465i
$259$	−21.8901	−1.36019
$260$	0	0
$261$	7.62497	0.471974
$262$	− 9.88760i	− 0.610858i
$263$	−26.2189	−1.61673	−0.808363	−	0.588685i	$-0.799646\pi$
$263$	−26.2189	−1.61673	−0.808363	+	0.588685i	$0.799646\pi$
$264$	−20.0289	−1.23269
$265$	4.35709i	0.267654i
$266$	− 3.01521i	− 0.184874i
$267$	16.6466i	1.01875i
$268$	6.48606i	0.396199i
$269$	15.1362	0.922871	0.461436	−	0.887174i	$-0.347334\pi$
$269$	15.1362	0.922871	0.461436	+	0.887174i	$0.347334\pi$
$270$	−4.65203	−0.283113
$271$	11.5436i	0.701221i	0.936521	+	0.350611i	$0.114026\pi$
$271$	11.5436i	0.701221i	−0.936521	+	0.350611i	$0.885974\pi$
$272$	−10.2371	−0.620715
$273$	0	0
$274$	16.4087	0.991287
$275$	− 2.38793i	− 0.143998i
$276$	13.6297	0.820410
$277$	−26.6854	−1.60337	−0.801686	−	0.597745i	$-0.796063\pi$
$277$	−26.6854	−1.60337	−0.801686	+	0.597745i	$0.796063\pi$
$278$	− 12.7293i	− 0.763455i
$279$	− 37.3505i	− 2.23611i
$280$	− 10.4093i	− 0.622077i
$281$	20.4907i	1.22237i	0.791486	+	0.611187i	$0.209308\pi$
$281$	20.4907i	1.22237i	−0.791486	+	0.611187i	$0.790692\pi$
$282$	6.73353	0.400976
$283$	−23.3361	−1.38719	−0.693593	−	0.720367i	$-0.743973\pi$
$283$	−23.3361	−1.38719	−0.693593	+	0.720367i	$0.743973\pi$
$284$	2.96366i	0.175861i
$285$	2.32004	0.137428
$286$	0	0
$287$	−21.0844	−1.24457
$288$	− 21.3854i	− 1.26015i
$289$	38.2519	2.25011
$290$	1.73197	0.101705
$291$	17.4755i	1.02443i
$292$	− 8.50605i	− 0.497779i
$293$	12.6983i	0.741842i	0.928664	+	0.370921i	$0.120958\pi$
$293$	12.6983i	0.741842i	−0.928664	+	0.370921i	$0.879042\pi$
$294$	− 13.6397i	− 0.795485i
$295$	5.11542	0.297831
$296$	−19.4398	−1.12991
$297$	− 10.6080i	− 0.615537i
$298$	−0.814208	−0.0471658
$299$	0	0
$300$	2.49208	0.143880
$301$	41.3958i	2.38601i
$302$	−8.12456	−0.467516
$303$	11.9991	0.689329
$304$	− 1.15824i	− 0.0664296i
$305$	− 8.84695i	− 0.506575i
$306$	− 35.8869i	− 2.05152i
$307$	9.44324i	0.538954i	0.963007	+	0.269477i	$0.0868508\pi$
$307$	9.44324i	0.538954i	−0.963007	+	0.269477i	$0.913149\pi$
$308$	7.38539	0.420822
$309$	5.84691	0.332619
$310$	− 8.48395i	− 0.481856i
$311$	22.3785	1.26897	0.634485	−	0.772935i	$-0.281212\pi$
$311$	22.3785	1.26897	0.634485	+	0.772935i	$0.281212\pi$
$312$	0	0
$313$	−0.953510	−0.0538955	−0.0269478	−	0.999637i	$-0.508579\pi$
$313$	−0.953510	−0.0538955	−0.0269478	+	0.999637i	$0.508579\pi$
$314$	− 12.7078i	− 0.717145i
$315$	15.7841	0.889334
$316$	5.32747	0.299694
$317$	− 2.57505i	− 0.144629i	−0.997382	−	0.0723146i	$-0.976961\pi$
$317$	− 2.57505i	− 0.144629i	0.997382	−	0.0723146i	$-0.0230386\pi$
$318$	12.5872i	0.705856i
$319$	3.94939i	0.221124i
$320$	− 7.61201i	− 0.425524i
$321$	−13.2390	−0.738927
$322$	19.6086	1.09274
$323$	6.25127i	0.347830i
$324$	−1.42368	−0.0790931
$325$	0	0
$326$	−0.195150	−0.0108084
$327$	− 20.5508i	− 1.13646i
$328$	−18.7243	−1.03387
$329$	−7.97995	−0.439949
$330$	− 6.89851i	− 0.379751i
$331$	5.44348i	0.299201i	0.988747	+	0.149600i	$0.0477987\pi$
$331$	5.44348i	0.299201i	−0.988747	+	0.149600i	$0.952201\pi$
$332$	− 4.64572i	− 0.254967i
$333$	− 29.4773i	− 1.61535i
$334$	−7.77394	−0.425371
$335$	−7.17992	−0.392281
$336$	− 13.0075i	− 0.709618i
$337$	−7.28071	−0.396605	−0.198303	−	0.980141i	$-0.563543\pi$
$337$	−7.28071	−0.396605	−0.198303	+	0.980141i	$0.563543\pi$
$338$	0	0
$339$	−23.7518	−1.29002
$340$	6.71482i	0.364162i
$341$	19.3459	1.04764
$342$	4.06029	0.219555
$343$	− 7.80108i	− 0.421219i
$344$	36.7620i	1.98207i
$345$	15.0878i	0.812297i
$346$	4.84715i	0.260584i
$347$	−1.51723	−0.0814494	−0.0407247	−	0.999170i	$-0.512967\pi$
$347$	−1.51723	−0.0814494	−0.0407247	+	0.999170i	$0.512967\pi$
$348$	−4.12164	−0.220943
$349$	− 32.7914i	− 1.75529i	−0.479315	−	0.877643i	$-0.659115\pi$
$349$	− 32.7914i	− 1.75529i	0.479315	−	0.877643i	$-0.340885\pi$
$350$	3.58527	0.191641
$351$	0	0
$352$	11.0767	0.590388
$353$	− 9.97003i	− 0.530651i	−0.964159	−	0.265325i	$-0.914521\pi$
$353$	− 9.97003i	− 0.530651i	0.964159	−	0.265325i	$-0.0854794\pi$
$354$	14.7780	0.785440
$355$	−3.28070	−0.174122
$356$	− 5.45111i	− 0.288908i
$357$	70.2045i	3.71561i
$358$	− 12.5251i	− 0.661974i
$359$	8.06159i	0.425474i	0.977109	+	0.212737i	$0.0682378\pi$
$359$	8.06159i	0.425474i	−0.977109	+	0.212737i	$0.931762\pi$
$360$	14.0173	0.738774
$361$	18.2927	0.962775
$362$	13.4115i	0.704895i
$363$	−14.6149	−0.767081
$364$	0	0
$365$	9.41601	0.492856
$366$	− 25.5580i	− 1.33594i
$367$	−1.37366	−0.0717044	−0.0358522	−	0.999357i	$-0.511415\pi$
$367$	−1.37366	−0.0717044	−0.0358522	+	0.999357i	$0.511415\pi$
$368$	7.53228	0.392647
$369$	− 28.3924i	− 1.47805i
$370$	− 6.69561i	− 0.348088i
$371$	− 14.9172i	− 0.774461i
$372$	20.1896i	1.04678i
$373$	−6.14540	−0.318197	−0.159098	−	0.987263i	$-0.550859\pi$
$373$	−6.14540	−0.318197	−0.159098	+	0.987263i	$0.550859\pi$
$374$	18.5878	0.961152
$375$	2.75868i	0.142458i
$376$	−7.08668	−0.365468
$377$	0	0
$378$	15.9269	0.819194
$379$	− 30.8770i	− 1.58604i	−0.609194	−	0.793021i	$-0.708507\pi$
$379$	− 30.8770i	− 1.58604i	0.609194	−	0.793021i	$-0.291493\pi$
$380$	−0.759724	−0.0389730
$381$	51.6368	2.64543
$382$	− 18.3558i	− 0.939166i
$383$	33.5485i	1.71425i	0.515110	+	0.857124i	$0.327751\pi$
$383$	33.5485i	1.71425i	−0.515110	+	0.857124i	$0.672249\pi$
$384$	3.60245i	0.183837i
$385$	8.17546i	0.416660i
$386$	9.00756	0.458472
$387$	−55.7437	−2.83361
$388$	− 5.72256i	− 0.290519i
$389$	−27.3375	−1.38606	−0.693032	−	0.720907i	$-0.743726\pi$
$389$	−27.3375	−1.38606	−0.693032	+	0.720907i	$0.743726\pi$
$390$	0	0
$391$	−40.6534	−2.05593
$392$	14.3551i	0.725040i
$393$	−26.0471	−1.31390
$394$	8.50712	0.428583
$395$	5.89740i	0.296730i
$396$	9.94519i	0.499765i
$397$	18.5292i	0.929953i	0.885323	+	0.464977i	$0.153937\pi$
$397$	18.5292i	0.929953i	−0.885323	+	0.464977i	$0.846063\pi$
$398$	7.91664i	0.396825i
$399$	−7.94303	−0.397649
$400$	1.37722	0.0688610
$401$	35.2525i	1.76043i	0.474578	+	0.880214i	$0.342601\pi$
$401$	35.2525i	1.76043i	−0.474578	+	0.880214i	$0.657399\pi$
$402$	−20.7421	−1.03452
$403$	0	0
$404$	−3.92923	−0.195487
$405$	− 1.57598i	− 0.0783110i
$406$	−5.92966	−0.294284
$407$	15.2679	0.756804
$408$	62.3458i	3.08658i
$409$	− 1.81630i	− 0.0898103i	−0.998991	−	0.0449051i	$-0.985701\pi$
$409$	− 1.81630i	− 0.0898103i	0.998991	−	0.0449051i	$-0.0142986\pi$
$410$	− 6.44917i	− 0.318502i
$411$	− 43.2259i	− 2.13217i
$412$	−1.91464	−0.0943274
$413$	−17.5134	−0.861780
$414$	26.4050i	1.29773i
$415$	5.14271	0.252446
$416$	0	0
$417$	−33.5332	−1.64213
$418$	2.10305i	0.102863i
$419$	−5.92370	−0.289392	−0.144696	−	0.989476i	$-0.546220\pi$
$419$	−5.92370	−0.289392	−0.144696	+	0.989476i	$0.546220\pi$
$420$	−8.53203	−0.416320
$421$	2.22193i	0.108290i	0.998533	+	0.0541451i	$0.0172434\pi$
$421$	2.22193i	0.108290i	−0.998533	+	0.0541451i	$0.982757\pi$
$422$	− 21.7994i	− 1.06118i
$423$	− 10.7458i	− 0.522480i
$424$	− 13.2474i	− 0.643348i
$425$	−7.43316	−0.360561
$426$	−9.47764	−0.459193
$427$	30.2889i	1.46578i
$428$	4.33525	0.209552
$429$	0	0
$430$	−12.6619	−0.610609
$431$	2.91961i	0.140633i	0.997525	+	0.0703163i	$0.0224009\pi$
$431$	2.91961i	0.140633i	−0.997525	+	0.0703163i	$0.977599\pi$
$432$	6.11806	0.294355
$433$	−1.19163	−0.0572661	−0.0286330	−	0.999590i	$-0.509115\pi$
$433$	−1.19163	−0.0572661	−0.0286330	+	0.999590i	$0.509115\pi$
$434$	29.0461i	1.39426i
$435$	− 4.56257i	− 0.218758i
$436$	6.72959i	0.322289i
$437$	− 4.59958i	− 0.220028i
$438$	27.2019	1.29976
$439$	0.753548	0.0359649	0.0179825	−	0.999838i	$-0.494276\pi$
$439$	0.753548	0.0359649	0.0179825	+	0.999838i	$0.494276\pi$
$440$	7.26031i	0.346122i
$441$	−21.7672	−1.03653
$442$	0	0
$443$	20.0999	0.954977	0.477488	−	0.878638i	$-0.341547\pi$
$443$	20.0999	0.954977	0.477488	+	0.878638i	$0.341547\pi$
$444$	15.9338i	0.756186i
$445$	6.03426	0.286051
$446$	18.5580	0.878747
$447$	2.14489i	0.101450i
$448$	26.0609i	1.23126i
$449$	− 27.4311i	− 1.29455i	−0.762256	−	0.647276i	$-0.775908\pi$
$449$	− 27.4311i	− 1.29455i	0.762256	−	0.647276i	$-0.224092\pi$
$450$	4.82794i	0.227591i
$451$	14.7060	0.692478
$452$	7.77780	0.365837
$453$	21.4027i	1.00559i
$454$	−10.1816	−0.477848
$455$	0	0
$456$	−7.05390	−0.330329
$457$	− 15.2157i	− 0.711759i	−0.934532	−	0.355879i	$-0.884181\pi$
$457$	− 15.2157i	− 0.711759i	0.934532	−	0.355879i	$-0.115819\pi$
$458$	22.5195	1.05227
$459$	−33.0205	−1.54127
$460$	− 4.94065i	− 0.230359i
$461$	4.57978i	0.213301i	0.994297	+	0.106651i	$0.0340127\pi$
$461$	4.57978i	0.213301i	−0.994297	+	0.106651i	$0.965987\pi$
$462$	23.6181i	1.09881i
$463$	− 14.5795i	− 0.677566i	−0.940865	−	0.338783i	$-0.889985\pi$
$463$	− 14.5795i	− 0.677566i	0.940865	−	0.338783i	$-0.110015\pi$
$464$	−2.27778	−0.105743
$465$	−22.3495	−1.03643
$466$	− 18.7059i	− 0.866533i
$467$	38.3834	1.77617	0.888087	−	0.459676i	$-0.152035\pi$
$467$	38.3834	1.77617	0.888087	+	0.459676i	$0.152035\pi$
$468$	0	0
$469$	24.5816	1.13507
$470$	− 2.44085i	− 0.112588i
$471$	−33.4766	−1.54252
$472$	−15.5530	−0.715885
$473$	− 28.8727i	− 1.32757i
$474$	17.0370i	0.782536i
$475$	− 0.840998i	− 0.0385876i
$476$	− 22.9892i	− 1.05371i
$477$	20.0875	0.919744
$478$	−5.03125	−0.230124
$479$	− 30.9140i	− 1.41250i	−0.707964	−	0.706248i	$-0.750386\pi$
$479$	− 30.9140i	− 1.41250i	0.707964	−	0.706248i	$-0.249614\pi$
$480$	−12.7964	−0.584073
$481$	0	0
$482$	−21.9978	−1.00197
$483$	− 51.6553i	− 2.35040i
$484$	4.78580	0.217536
$485$	6.33475	0.287646
$486$	− 18.5089i	− 0.839582i
$487$	5.37275i	0.243463i	0.992563	+	0.121731i	$0.0388446\pi$
$487$	5.37275i	0.243463i	−0.992563	+	0.121731i	$0.961155\pi$
$488$	26.8984i	1.21763i
$489$	0.514089i	0.0232479i
$490$	−4.94429	−0.223360
$491$	0.638413	0.0288112	0.0144056	−	0.999896i	$-0.495414\pi$
$491$	0.638413	0.0288112	0.0144056	+	0.999896i	$0.495414\pi$
$492$	15.3474i	0.691913i
$493$	12.2937	0.553679
$494$	0	0
$495$	−11.0091	−0.494823
$496$	11.1576i	0.500989i
$497$	11.2320	0.503824
$498$	14.8568	0.665749
$499$	− 24.2542i	− 1.08577i	−0.839807	−	0.542885i	$-0.817332\pi$
$499$	− 24.2542i	− 1.08577i	0.839807	−	0.542885i	$-0.182668\pi$
$500$	− 0.903360i	− 0.0403995i
$501$	20.4791i	0.914938i
$502$	− 0.308245i	− 0.0137577i
$503$	2.66695	0.118914	0.0594568	−	0.998231i	$-0.481063\pi$
$503$	2.66695	0.118914	0.0594568	+	0.998231i	$0.481063\pi$
$504$	−47.9902	−2.13766
$505$	− 4.34957i	− 0.193553i
$506$	−13.6766	−0.607998
$507$	0	0
$508$	−16.9090	−0.750218
$509$	28.4006i	1.25884i	0.777067	+	0.629418i	$0.216707\pi$
$509$	28.4006i	1.25884i	−0.777067	+	0.629418i	$0.783293\pi$
$510$	−21.4737	−0.950871
$511$	−32.2372	−1.42609
$512$	14.7630i	0.652439i
$513$	− 3.73599i	− 0.164948i
$514$	− 22.9786i	− 1.01354i
$515$	− 2.11946i	− 0.0933946i
$516$	30.1320	1.32649
$517$	5.56586	0.244786
$518$	22.9235i	1.00720i
$519$	12.7690	0.560495
$520$	0	0
$521$	−10.4355	−0.457190	−0.228595	−	0.973522i	$-0.573413\pi$
$521$	−10.4355	−0.457190	−0.228595	+	0.973522i	$0.573413\pi$
$522$	− 7.98491i	− 0.349490i
$523$	34.3111	1.50032	0.750159	−	0.661257i	$-0.229977\pi$
$523$	34.3111	1.50032	0.750159	+	0.661257i	$0.229977\pi$
$524$	8.52943	0.372610
$525$	− 9.44477i	− 0.412203i
$526$	27.4566i	1.19716i
$527$	− 60.2198i	− 2.62322i
$528$	9.07249i	0.394830i
$529$	6.91210	0.300526
$530$	4.56277	0.198194
$531$	− 23.5837i	− 1.02344i
$532$	2.60103	0.112769
$533$	0	0
$534$	17.4324	0.754373
$535$	4.79902i	0.207480i
$536$	21.8300	0.942910
$537$	−32.9953	−1.42385
$538$	− 15.8507i	− 0.683374i
$539$	− 11.2744i	− 0.485624i
$540$	− 4.01302i	− 0.172693i
$541$	35.2810i	1.51685i	0.651761	+	0.758425i	$0.274031\pi$
$541$	35.2810i	1.51685i	−0.651761	+	0.758425i	$0.725969\pi$
$542$	12.0885	0.519245
$543$	35.3303	1.51617
$544$	− 34.4794i	− 1.47829i
$545$	−7.44950	−0.319102
$546$	0	0
$547$	32.8604	1.40501	0.702504	−	0.711679i	$-0.252065\pi$
$547$	32.8604	1.40501	0.702504	+	0.711679i	$0.252065\pi$
$548$	14.1548i	0.604663i
$549$	−40.7872	−1.74075
$550$	−2.50066	−0.106628
$551$	1.39092i	0.0592553i
$552$	− 45.8730i	− 1.95249i
$553$	− 20.1907i	− 0.858594i
$554$	27.9451i	1.18727i
$555$	−17.6384	−0.748709
$556$	10.9808	0.465691
$557$	− 18.5254i	− 0.784947i	−0.919763	−	0.392474i	$-0.871619\pi$
$557$	− 18.5254i	− 0.784947i	0.919763	−	0.392474i	$-0.128381\pi$
$558$	−39.1136	−1.65581
$559$	0	0
$560$	−4.71513	−0.199250
$561$	− 48.9663i	− 2.06736i
$562$	21.4580	0.905151
$563$	20.9662	0.883622	0.441811	−	0.897108i	$-0.354336\pi$
$563$	20.9662	0.883622	0.441811	+	0.897108i	$0.354336\pi$
$564$	5.80861i	0.244587i
$565$	8.60985i	0.362219i
$566$	24.4377i	1.02719i
$567$	5.39560i	0.226594i
$568$	9.97470	0.418529
$569$	22.1884	0.930188	0.465094	−	0.885261i	$-0.346021\pi$
$569$	22.1884	0.930188	0.465094	+	0.885261i	$0.346021\pi$
$570$	− 2.42956i	− 0.101763i
$571$	14.8506	0.621480	0.310740	−	0.950495i	$-0.399423\pi$
$571$	14.8506	0.621480	0.310740	+	0.950495i	$0.399423\pi$
$572$	0	0
$573$	−48.3552	−2.02007
$574$	22.0797i	0.921590i
$575$	5.46920	0.228081
$576$	−35.0937	−1.46224
$577$	− 26.9163i	− 1.12054i	−0.828311	−	0.560269i	$-0.810698\pi$
$577$	− 26.9163i	− 1.12054i	0.828311	−	0.560269i	$-0.189302\pi$
$578$	− 40.0576i	− 1.66618i
$579$	− 23.7288i	− 0.986136i
$580$	1.49406i	0.0620376i
$581$	−17.6069	−0.730456
$582$	18.3005	0.758580
$583$	10.4044i	0.430908i
$584$	−28.6286	−1.18466
$585$	0	0
$586$	13.2977	0.549324
$587$	11.6753i	0.481890i	0.970539	+	0.240945i	$0.0774573\pi$
$587$	11.6753i	0.481890i	−0.970539	+	0.240945i	$0.922543\pi$
$588$	11.7662	0.485228
$589$	6.81336	0.280739
$590$	− 5.35690i	− 0.220540i
$591$	− 22.4105i	− 0.921845i
$592$	8.80565i	0.361910i
$593$	16.9271i	0.695111i	0.937659	+	0.347556i	$0.112988\pi$
$593$	16.9271i	0.695111i	−0.937659	+	0.347556i	$0.887012\pi$
$594$	−11.1087	−0.455797
$595$	25.4486	1.04329
$596$	− 0.702367i	− 0.0287701i
$597$	20.8550	0.853538
$598$	0	0
$599$	6.57368	0.268593	0.134297	−	0.990941i	$-0.457123\pi$
$599$	6.57368	0.268593	0.134297	+	0.990941i	$0.457123\pi$
$600$	− 8.38753i	− 0.342419i
$601$	4.62956	0.188844	0.0944219	−	0.995532i	$-0.469900\pi$
$601$	4.62956	0.188844	0.0944219	+	0.995532i	$0.469900\pi$
$602$	43.3499	1.76681
$603$	33.1017i	1.34800i
$604$	− 7.00856i	− 0.285174i
$605$	5.29777i	0.215385i
$606$	− 12.5655i	− 0.510438i
$607$	−10.7891	−0.437915	−0.218958	−	0.975734i	$-0.570266\pi$
$607$	−10.7891	−0.437915	−0.218958	+	0.975734i	$0.570266\pi$
$608$	3.90105	0.158209
$609$	15.6207i	0.632981i
$610$	−9.26457	−0.375112
$611$	0	0
$612$	30.9574	1.25138
$613$	26.4860i	1.06976i	0.844928	+	0.534879i	$0.179643\pi$
$613$	26.4860i	1.06976i	−0.844928	+	0.534879i	$0.820357\pi$
$614$	9.88901	0.399088
$615$	−16.9892	−0.685071
$616$	− 24.8568i	− 1.00151i
$617$	28.3651i	1.14194i	0.820972	+	0.570968i	$0.193432\pi$
$617$	28.3651i	1.14194i	−0.820972	+	0.570968i	$0.806568\pi$
$618$	− 6.12292i	− 0.246300i
$619$	− 13.9696i	− 0.561485i	−0.959783	−	0.280742i	$-0.909419\pi$
$619$	− 13.9696i	− 0.561485i	0.959783	−	0.280742i	$-0.0905806\pi$
$620$	7.31858	0.293921
$621$	24.2959	0.974963
$622$	− 23.4349i	− 0.939655i
$623$	−20.6592	−0.827694
$624$	0	0
$625$	1.00000	0.0400000
$626$	0.998521i	0.0399089i
$627$	5.54011	0.221251
$628$	10.9623	0.437443
$629$	− 47.5260i	− 1.89499i
$630$	− 16.5292i	− 0.658539i
$631$	23.6090i	0.939859i	0.882704	+	0.469930i	$0.155721\pi$
$631$	23.6090i	0.939859i	−0.882704	+	0.469930i	$0.844279\pi$
$632$	− 17.9305i	− 0.713239i
$633$	−57.4266	−2.28250
$634$	−2.69661	−0.107096
$635$	− 18.7179i	− 0.742799i
$636$	−10.8582	−0.430556
$637$	0	0
$638$	4.13583	0.163739
$639$	15.1251i	0.598338i
$640$	1.30586	0.0516187
$641$	−37.9614	−1.49939	−0.749693	−	0.661785i	$-0.769799\pi$
$641$	−37.9614	−1.49939	−0.749693	+	0.661785i	$0.769799\pi$
$642$	13.8639i	0.547165i
$643$	− 50.6338i	− 1.99680i	−0.0565186	−	0.998402i	$-0.518000\pi$
$643$	− 50.6338i	− 1.99680i	0.0565186	−	0.998402i	$-0.482000\pi$
$644$	16.9151i	0.666548i
$645$	33.3555i	1.31337i
$646$	6.54637	0.257563
$647$	−34.3014	−1.34853	−0.674264	−	0.738490i	$-0.735539\pi$
$647$	−34.3014	−1.34853	−0.674264	+	0.738490i	$0.735539\pi$
$648$	4.79163i	0.188233i
$649$	12.2153	0.479492
$650$	0	0
$651$	76.5169	2.99893
$652$	− 0.168344i	− 0.00659287i
$653$	−19.2672	−0.753985	−0.376993	−	0.926216i	$-0.623042\pi$
$653$	−19.2672	−0.753985	−0.376993	+	0.926216i	$0.623042\pi$
$654$	−21.5209	−0.841534
$655$	9.44189i	0.368925i
$656$	8.48155i	0.331149i
$657$	− 43.4107i	− 1.69361i
$658$	8.35665i	0.325776i
$659$	−36.4980	−1.42176	−0.710880	−	0.703314i	$-0.751703\pi$
$659$	−36.4980	−1.42176	−0.710880	+	0.703314i	$0.751703\pi$
$660$	5.95092	0.231639
$661$	13.5048i	0.525276i	0.964895	+	0.262638i	$0.0845924\pi$
$661$	13.5048i	0.525276i	−0.964895	+	0.262638i	$0.915408\pi$
$662$	5.70044	0.221554
$663$	0	0
$664$	−15.6360	−0.606794
$665$	2.87929i	0.111654i
$666$	−30.8688	−1.19614
$667$	−9.04548	−0.350242
$668$	− 6.70610i	− 0.259467i
$669$	− 48.8878i	− 1.89011i
$670$	7.51886i	0.290479i
$671$	− 21.1259i	− 0.815557i
$672$	43.8105	1.69003
$673$	−3.45492	−0.133177	−0.0665887	−	0.997781i	$-0.521212\pi$
$673$	−3.45492	−0.133177	−0.0665887	+	0.997781i	$0.521212\pi$
$674$	7.62440i	0.293681i
$675$	4.44233	0.170985
$676$	0	0
$677$	9.65561	0.371095	0.185548	−	0.982635i	$-0.440594\pi$
$677$	9.65561	0.371095	0.185548	+	0.982635i	$0.440594\pi$
$678$	24.8730i	0.955243i
$679$	−21.6880	−0.832309
$680$	22.5999	0.866666
$681$	26.8217i	1.02781i
$682$	− 20.2591i	− 0.775761i
$683$	20.1271i	0.770144i	0.922887	+	0.385072i	$0.125823\pi$
$683$	20.1271i	0.770144i	−0.922887	+	0.385072i	$0.874177\pi$
$684$	3.50256i	0.133924i
$685$	−15.6690	−0.598683
$686$	−8.16934	−0.311907
$687$	− 59.3236i	− 2.26334i
$688$	16.6521	0.634855
$689$	0	0
$690$	15.8000	0.601495
$691$	9.23887i	0.351463i	0.984438	+	0.175732i	$0.0562291\pi$
$691$	9.23887i	0.351463i	−0.984438	+	0.175732i	$0.943771\pi$
$692$	−4.18134	−0.158951
$693$	37.6914	1.43178
$694$	1.58886i	0.0603121i
$695$	12.1555i	0.461085i
$696$	13.8721i	0.525820i
$697$	− 45.7768i	− 1.73392i
$698$	−34.3394	−1.29977
$699$	−49.2773	−1.86384
$700$	3.09279i	0.116897i
$701$	−8.20434	−0.309874	−0.154937	−	0.987924i	$-0.549517\pi$
$701$	−8.20434	−0.309874	−0.154937	+	0.987924i	$0.549517\pi$
$702$	0	0
$703$	5.37716	0.202804
$704$	− 18.1770i	− 0.685070i
$705$	−6.43000	−0.242168
$706$	−10.4407	−0.392940
$707$	14.8914i	0.560050i
$708$	12.7480i	0.479101i
$709$	− 32.8408i	− 1.23336i	−0.787213	−	0.616682i	$-0.788477\pi$
$709$	− 32.8408i	− 1.23336i	0.787213	−	0.616682i	$-0.211523\pi$
$710$	3.43557i	0.128935i
$711$	27.1888	1.01966
$712$	−18.3466	−0.687569
$713$	44.3087i	1.65938i
$714$	73.5185	2.75136
$715$	0	0
$716$	10.8047	0.403790
$717$	13.2539i	0.494977i
$718$	8.44214	0.315058
$719$	9.98530	0.372389	0.186194	−	0.982513i	$-0.440385\pi$
$719$	9.98530	0.372389	0.186194	+	0.982513i	$0.440385\pi$
$720$	− 6.34941i	− 0.236628i
$721$	7.25631i	0.270239i
$722$	− 19.1562i	− 0.712922i
$723$	57.9494i	2.15516i
$724$	−11.5693	−0.429970
$725$	−1.65390	−0.0614241
$726$	15.3048i	0.568013i
$727$	−19.8629	−0.736673	−0.368336	−	0.929693i	$-0.620073\pi$
$727$	−19.8629	−0.736673	−0.368336	+	0.929693i	$0.620073\pi$
$728$	0	0
$729$	−44.0306	−1.63076
$730$	− 9.86050i	− 0.364953i
$731$	−89.8751	−3.32415
$732$	22.0473	0.814892
$733$	13.4222i	0.495761i	0.968791	+	0.247881i	$0.0797341\pi$
$733$	13.4222i	0.495761i	−0.968791	+	0.247881i	$0.920266\pi$
$734$	1.43850i	0.0530961i
$735$	13.0249i	0.480430i
$736$	25.3694i	0.935129i
$737$	−17.1452	−0.631551
$738$	−29.7327	−1.09447
$739$	42.4122i	1.56016i	0.625681	+	0.780079i	$0.284821\pi$
$739$	42.4122i	1.56016i	−0.625681	+	0.780079i	$0.715179\pi$
$740$	5.77589	0.212326
$741$	0	0
$742$	−15.6213	−0.573477
$743$	15.1678i	0.556451i	0.960516	+	0.278225i	$0.0897462\pi$
$743$	15.1678i	0.556451i	−0.960516	+	0.278225i	$0.910254\pi$
$744$	67.9517	2.49123
$745$	0.777505	0.0284856
$746$	6.43549i	0.235620i
$747$	− 23.7095i	− 0.867485i
$748$	16.0345i	0.586281i
$749$	− 16.4302i	− 0.600346i
$750$	2.88890	0.105488
$751$	51.0088	1.86134	0.930669	−	0.365862i	$-0.119226\pi$
$751$	51.0088	1.86134	0.930669	+	0.365862i	$0.119226\pi$
$752$	3.21006i	0.117059i
$753$	−0.812018	−0.0295916
$754$	0	0
$755$	7.75832	0.282354
$756$	13.7392i	0.499690i
$757$	18.4750	0.671486	0.335743	−	0.941954i	$-0.391013\pi$
$757$	18.4750	0.671486	0.335743	+	0.941954i	$0.391013\pi$
$758$	−32.3345	−1.17444
$759$	36.0286i	1.30775i
$760$	2.55698i	0.0927516i
$761$	17.8713i	0.647835i	0.946085	+	0.323918i	$0.105000\pi$
$761$	17.8713i	0.647835i	−0.946085	+	0.323918i	$0.895000\pi$
$762$	− 54.0743i	− 1.95891i
$763$	25.5045	0.923326
$764$	15.8344	0.572870
$765$	34.2692i	1.23900i
$766$	35.1322	1.26938
$767$	0	0
$768$	45.7707	1.65161
$769$	− 19.7597i	− 0.712552i	−0.934381	−	0.356276i	$-0.884046\pi$
$769$	− 19.7597i	− 0.712552i	0.934381	−	0.356276i	$-0.115954\pi$
$770$	8.56139	0.308531
$771$	−60.5330	−2.18004
$772$	7.77027i	0.279658i
$773$	49.5340i	1.78161i	0.454383	+	0.890806i	$0.349860\pi$
$773$	49.5340i	1.78161i	−0.454383	+	0.890806i	$0.650140\pi$
$774$	58.3751i	2.09825i
$775$	8.10151i	0.291015i
$776$	−19.2603	−0.691404
$777$	60.3878	2.16640
$778$	28.6279i	1.02636i
$779$	5.17925	0.185566
$780$	0	0
$781$	−7.83410	−0.280326
$782$	42.5725i	1.52239i
$783$	−7.34714	−0.262565
$784$	6.50243	0.232230
$785$	12.1350i	0.433117i
$786$	27.2767i	0.972928i
$787$	37.7290i	1.34490i	0.740145	+	0.672448i	$0.234757\pi$
$787$	37.7290i	1.34490i	−0.740145	+	0.672448i	$0.765243\pi$
$788$	7.33857i	0.261426i
$789$	72.3295	2.57500
$790$	6.17579	0.219725
$791$	− 29.4772i	− 1.04809i
$792$	33.4723	1.18939
$793$	0	0
$794$	19.4039	0.688617
$795$	− 12.0198i	− 0.426299i
$796$	−6.82920	−0.242055
$797$	42.6042	1.50912	0.754559	−	0.656232i	$-0.227851\pi$
$797$	42.6042	1.50912	0.754559	+	0.656232i	$0.227851\pi$
$798$	8.31799i	0.294454i
$799$	− 17.3254i	− 0.612929i
$800$	4.63860i	0.163999i
$801$	− 27.8198i	− 0.982964i
$802$	36.9166	1.30357
$803$	22.4848	0.793472
$804$	− 17.8930i	− 0.631036i
$805$	−18.7246	−0.659957
$806$	0	0
$807$	−41.7560	−1.46988
$808$	13.2245i	0.465237i
$809$	−13.1167	−0.461157	−0.230579	−	0.973054i	$-0.574062\pi$
$809$	−13.1167	−0.461157	−0.230579	+	0.973054i	$0.574062\pi$
$810$	−1.65037	−0.0579882
$811$	− 38.4234i	− 1.34923i	−0.738171	−	0.674614i	$-0.764310\pi$
$811$	− 38.4234i	− 1.34923i	0.738171	−	0.674614i	$-0.235690\pi$
$812$	− 5.11516i	− 0.179507i
$813$	− 31.8450i	− 1.11685i
$814$	− 15.9887i	− 0.560403i
$815$	0.186353	0.00652768
$816$	28.2409	0.988628
$817$	− 10.1686i	− 0.355754i
$818$	−1.90204	−0.0665033
$819$	0	0
$820$	5.56330	0.194279
$821$	− 29.0515i	− 1.01390i	−0.861975	−	0.506951i	$-0.830772\pi$
$821$	− 29.0515i	− 1.01390i	0.861975	−	0.506951i	$-0.169228\pi$
$822$	−45.2664	−1.57885
$823$	25.2103	0.878777	0.439388	−	0.898297i	$-0.355195\pi$
$823$	25.2103	0.878777	0.439388	+	0.898297i	$0.355195\pi$
$824$	6.44404i	0.224489i
$825$	6.58754i	0.229349i
$826$	18.3402i	0.638136i
$827$	2.27577i	0.0791361i	0.999217	+	0.0395681i	$0.0125982\pi$
$827$	2.27577i	0.0791361i	−0.999217	+	0.0395681i	$0.987402\pi$
$828$	−22.7779	−0.791588
$829$	34.8474	1.21030	0.605149	−	0.796112i	$-0.293113\pi$
$829$	34.8474	1.21030	0.605149	+	0.796112i	$0.293113\pi$
$830$	− 5.38548i	− 0.186933i
$831$	73.6165	2.55373
$832$	0	0
$833$	−35.0950	−1.21597
$834$	35.1162i	1.21597i
$835$	7.42351	0.256901
$836$	−1.81417	−0.0627444
$837$	35.9896i	1.24398i
$838$	6.20333i	0.214290i
$839$	50.7285i	1.75134i	0.482907	+	0.875672i	$0.339581\pi$
$839$	50.7285i	1.75134i	−0.482907	+	0.875672i	$0.660419\pi$
$840$	28.7160i	0.990797i
$841$	−26.2646	−0.905677
$842$	2.32682	0.0801874
$843$	− 56.5273i	− 1.94690i
$844$	18.8050	0.647294
$845$	0	0
$846$	−11.2531	−0.386889
$847$	− 18.1377i	− 0.623220i
$848$	−6.00067	−0.206064
$849$	64.3767	2.20940
$850$	7.78405i	0.266991i
$851$	34.9689i	1.19872i
$852$	− 8.17578i	− 0.280097i
$853$	50.2475i	1.72044i	0.509921	+	0.860221i	$0.329674\pi$
$853$	50.2475i	1.72044i	−0.509921	+	0.860221i	$0.670326\pi$
$854$	31.7187	1.08539
$855$	−3.87726	−0.132600
$856$	− 14.5910i	− 0.498711i
$857$	44.5420	1.52153	0.760763	−	0.649030i	$-0.224825\pi$
$857$	44.5420	1.52153	0.760763	+	0.649030i	$0.224825\pi$
$858$	0	0
$859$	16.8945	0.576432	0.288216	−	0.957565i	$-0.406938\pi$
$859$	16.8945	0.576432	0.288216	+	0.957565i	$0.406938\pi$
$860$	− 10.9226i	− 0.372458i
$861$	58.1652	1.98226
$862$	3.05743	0.104137
$863$	48.4137i	1.64802i	0.566574	+	0.824011i	$0.308268\pi$
$863$	48.4137i	1.64802i	−0.566574	+	0.824011i	$0.691732\pi$
$864$	20.6062i	0.701036i
$865$	− 4.62865i	− 0.157379i
$866$	1.24788i	0.0424048i
$867$	−105.525	−3.58380
$868$	−25.0563	−0.850467
$869$	14.0826i	0.477719i
$870$	−4.77795	−0.161988
$871$	0	0
$872$	22.6496	0.767012
$873$	− 29.2052i	− 0.988445i
$874$	−4.81671	−0.162928
$875$	−3.42366	−0.115741
$876$	23.4655i	0.792824i
$877$	− 8.18430i	− 0.276364i	−0.990407	−	0.138182i	$-0.955874\pi$
$877$	− 8.18430i	− 0.276364i	0.990407	−	0.138182i	$-0.0441259\pi$
$878$	− 0.789120i	− 0.0266315i
$879$	− 35.0305i	− 1.18155i
$880$	3.28871	0.110862
$881$	15.6088	0.525874	0.262937	−	0.964813i	$-0.415309\pi$
$881$	15.6088	0.525874	0.262937	+	0.964813i	$0.415309\pi$
$882$	22.7947i	0.767538i
$883$	0.0864274	0.00290851	0.00145426	−	0.999999i	$-0.499537\pi$
$883$	0.0864274	0.00290851	0.00145426	+	0.999999i	$0.499537\pi$
$884$	0	0
$885$	−14.1118	−0.474363
$886$	− 21.0488i	− 0.707147i
$887$	52.4753	1.76195	0.880975	−	0.473163i	$-0.156888\pi$
$887$	52.4753	1.76195	0.880975	+	0.473163i	$0.156888\pi$
$888$	53.6281	1.79964
$889$	64.0838i	2.14930i
$890$	− 6.31911i	− 0.211817i
$891$	− 3.76333i	− 0.126076i
$892$	16.0089i	0.536016i
$893$	1.96022	0.0655963
$894$	2.24614	0.0751221
$895$	11.9605i	0.399797i
$896$	−4.47082	−0.149360
$897$	0	0
$898$	−28.7260	−0.958598
$899$	− 13.3991i	− 0.446883i
$900$	−4.16477	−0.138826
$901$	32.3869	1.07897
$902$	− 15.4002i	− 0.512770i
$903$	− 114.198i	− 3.80026i
$904$	− 26.1775i	− 0.870652i
$905$	− 12.8070i	− 0.425718i
$906$	22.4130	0.744624
$907$	−22.9724	−0.762787	−0.381393	−	0.924413i	$-0.624556\pi$
$907$	−22.9724	−0.762787	−0.381393	+	0.924413i	$0.624556\pi$
$908$	− 8.78307i	− 0.291477i
$909$	−20.0529	−0.665112
$910$	0	0
$911$	−7.20421	−0.238686	−0.119343	−	0.992853i	$-0.538079\pi$
$911$	−7.20421	−0.238686	−0.119343	+	0.992853i	$0.538079\pi$
$912$	3.19521i	0.105804i
$913$	12.2805	0.406424
$914$	−15.9339	−0.527048
$915$	24.4059i	0.806834i
$916$	19.4262i	0.641859i
$917$	− 32.3258i	− 1.06749i
$918$	34.5793i	1.14129i
$919$	−47.1095	−1.55400	−0.776999	−	0.629502i	$-0.783259\pi$
$919$	−47.1095	−1.55400	−0.776999	+	0.629502i	$0.783259\pi$
$920$	−16.6286	−0.548230
$921$	− 26.0509i	− 0.858405i
$922$	4.79597	0.157947
$923$	0	0
$924$	−20.3739	−0.670253
$925$	6.39379i	0.210226i
$926$	−15.2677	−0.501728
$927$	−9.77137	−0.320934
$928$	− 7.67176i	− 0.251838i
$929$	56.8858i	1.86636i	0.359406	+	0.933181i	$0.382979\pi$
$929$	56.8858i	1.86636i	−0.359406	+	0.933181i	$0.617021\pi$
$930$	23.4045i	0.767463i
$931$	− 3.97070i	− 0.130135i
$932$	16.1364	0.528566
$933$	−61.7352	−2.02112
$934$	− 40.1953i	− 1.31523i
$935$	−17.7499	−0.580484
$936$	0	0
$937$	−12.1029	−0.395385	−0.197693	−	0.980264i	$-0.563345\pi$
$937$	−12.1029	−0.395385	−0.197693	+	0.980264i	$0.563345\pi$
$938$	− 25.7420i	− 0.840505i
$939$	2.63043	0.0858407
$940$	2.10558	0.0686763
$941$	− 14.2400i	− 0.464210i	−0.972691	−	0.232105i	$-0.925439\pi$
$941$	− 14.2400i	− 0.464210i	0.972691	−	0.232105i	$-0.0745613\pi$
$942$	35.0569i	1.14221i
$943$	33.6818i	1.09683i
$944$	7.04506i	0.229297i
$945$	−15.2090	−0.494749
$946$	−30.2357	−0.983047
$947$	53.7892i	1.74791i	0.486004	+	0.873957i	$0.338454\pi$
$947$	53.7892i	1.74791i	−0.486004	+	0.873957i	$0.661546\pi$
$948$	−14.6968	−0.477330
$949$	0	0
$950$	−0.880698	−0.0285736
$951$	7.10374i	0.230355i
$952$	−77.3742	−2.50771
$953$	−45.8325	−1.48466	−0.742330	−	0.670034i	$-0.766280\pi$
$953$	−45.8325	−1.48466	−0.742330	+	0.670034i	$0.766280\pi$
$954$	− 21.0358i	− 0.681058i
$955$	17.5284i	0.567205i
$956$	− 4.34015i	− 0.140371i
$957$	− 10.8951i	− 0.352189i
$958$	−32.3733	−1.04593
$959$	53.6454	1.73230
$960$	20.9991i	0.677742i
$961$	−34.6345	−1.11724
$962$	0	0
$963$	22.1250	0.712967
$964$	− 18.9762i	− 0.611182i
$965$	−8.60151	−0.276893
$966$	−54.0937	−1.74044
$967$	34.6342i	1.11376i	0.830592	+	0.556881i	$0.188002\pi$
$967$	34.6342i	1.11376i	−0.830592	+	0.556881i	$0.811998\pi$
$968$	− 16.1074i	− 0.517712i
$969$	− 17.2453i	− 0.553998i
$970$	− 6.63379i	− 0.212998i
$971$	21.0966	0.677021	0.338511	−	0.940963i	$-0.390077\pi$
$971$	21.0966	0.677021	0.338511	+	0.940963i	$0.390077\pi$
$972$	15.9665	0.512127
$973$	− 41.6163i	− 1.33416i
$974$	5.62638	0.180281
$975$	0	0
$976$	12.1842	0.390006
$977$	37.8931i	1.21231i	0.795347	+	0.606154i	$0.207288\pi$
$977$	37.8931i	1.21231i	−0.795347	+	0.606154i	$0.792712\pi$
$978$	0.538357	0.0172148
$979$	14.4094	0.460526
$980$	− 4.26514i	− 0.136245i
$981$	34.3445i	1.09654i
$982$	− 0.668549i	− 0.0213343i
$983$	− 18.8772i	− 0.602089i	−0.953610	−	0.301045i	$-0.902665\pi$
$983$	− 18.8772i	− 0.602089i	0.953610	−	0.301045i	$-0.0973353\pi$
$984$	51.6542	1.64668
$985$	−8.12364	−0.258841
$986$	− 12.8740i	− 0.409992i
$987$	22.0141	0.700717
$988$	0	0
$989$	66.1286	2.10277
$990$	11.5288i	0.366409i
$991$	52.6982	1.67401	0.837007	−	0.547193i	$-0.184303\pi$
$991$	52.6982	1.67401	0.837007	+	0.547193i	$0.184303\pi$
$992$	−37.5797	−1.19316
$993$	− 15.0168i	− 0.476544i
$994$	− 11.7622i	− 0.373075i
$995$	− 7.55978i	− 0.239661i
$996$	12.8161i	0.406092i
$997$	53.7219	1.70139	0.850695	−	0.525659i	$-0.176181\pi$
$997$	53.7219	1.70139	0.850695	+	0.525659i	$0.176181\pi$
$998$	−25.3992	−0.803997
$999$	28.4033i	0.898640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.c.h.506.7		18
13.2	odd	12		845.2.e.o.191.7		18
13.3	even	3		845.2.m.j.316.12		36
13.4	even	6		845.2.m.j.361.12		36
13.5	odd	4		845.2.a.o.1.3	yes	9
13.6	odd	12		845.2.e.o.146.7		18
13.7	odd	12		845.2.e.p.146.3		18
13.8	odd	4		845.2.a.n.1.7	✓	9
13.9	even	3		845.2.m.j.361.7		36
13.10	even	6		845.2.m.j.316.7		36
13.11	odd	12		845.2.e.p.191.3		18
13.12	even	2	inner	845.2.c.h.506.12		18
39.5	even	4		7605.2.a.cp.1.7		9
39.8	even	4		7605.2.a.cs.1.3		9
65.34	odd	4		4225.2.a.bt.1.3		9
65.44	odd	4		4225.2.a.bs.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.7	✓	9	13.8	odd	4
845.2.a.o.1.3	yes	9	13.5	odd	4
845.2.c.h.506.7		18	1.1	even	1	trivial
845.2.c.h.506.12		18	13.12	even	2	inner
845.2.e.o.146.7		18	13.6	odd	12
845.2.e.o.191.7		18	13.2	odd	12
845.2.e.p.146.3		18	13.7	odd	12
845.2.e.p.191.3		18	13.11	odd	12
845.2.m.j.316.7		36	13.10	even	6
845.2.m.j.316.12		36	13.3	even	3
845.2.m.j.361.7		36	13.9	even	3
845.2.m.j.361.12		36	13.4	even	6
4225.2.a.bs.1.7		9	65.44	odd	4
4225.2.a.bt.1.3		9	65.34	odd	4
7605.2.a.cp.1.7		9	39.5	even	4
7605.2.a.cs.1.3		9	39.8	even	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.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.04721i q^{2} -2.75868 q^{3} +0.903360 q^{4} +1.00000i q^{5} +2.88890i q^{6} -3.42366i q^{7} -3.04042i q^{8} +4.61031 q^{9} +O(q^{10})\)	\(q-1.04721i q^{2} -2.75868 q^{3} +0.903360 q^{4} +1.00000i q^{5} +2.88890i q^{6} -3.42366i q^{7} -3.04042i q^{8} +4.61031 q^{9} +1.04721 q^{10} +2.38793i q^{11} -2.49208 q^{12} -3.58527 q^{14} -2.75868i q^{15} -1.37722 q^{16} +7.43316 q^{17} -4.82794i q^{18} +0.840998i q^{19} +0.903360i q^{20} +9.44477i q^{21} +2.50066 q^{22} -5.46920 q^{23} +8.38753i q^{24} -1.00000 q^{25} -4.44233 q^{27} -3.09279i q^{28} +1.65390 q^{29} -2.88890 q^{30} -8.10151i q^{31} -4.63860i q^{32} -6.58754i q^{33} -7.78405i q^{34} +3.42366 q^{35} +4.16477 q^{36} -6.39379i q^{37} +0.880698 q^{38} +3.04042 q^{40} -6.15846i q^{41} +9.89061 q^{42} -12.0911 q^{43} +2.15716i q^{44} +4.61031i q^{45} +5.72737i q^{46} -2.33083i q^{47} +3.79931 q^{48} -4.72142 q^{49} +1.04721i q^{50} -20.5057 q^{51} +4.35709 q^{53} +4.65203i q^{54} -2.38793 q^{55} -10.4093 q^{56} -2.32004i q^{57} -1.73197i q^{58} -5.11542i q^{59} -2.49208i q^{60} -8.84695 q^{61} -8.48395 q^{62} -15.7841i q^{63} -7.61201 q^{64} -6.89851 q^{66} +7.17992i q^{67} +6.71482 q^{68} +15.0878 q^{69} -3.58527i q^{70} +3.28070i q^{71} -14.0173i q^{72} -9.41601i q^{73} -6.69561 q^{74} +2.75868 q^{75} +0.759724i q^{76} +8.17546 q^{77} +5.89740 q^{79} -1.37722i q^{80} -1.57598 q^{81} -6.44917 q^{82} -5.14271i q^{83} +8.53203i q^{84} +7.43316i q^{85} +12.6619i q^{86} -4.56257 q^{87} +7.26031 q^{88} -6.03426i q^{89} +4.82794 q^{90} -4.94065 q^{92} +22.3495i q^{93} -2.44085 q^{94} -0.840998 q^{95} +12.7964i q^{96} -6.33475i q^{97} +4.94429i q^{98} +11.0091i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9}+O(q^{10}) \) 18 * q + 14 * q^3 - 34 * q^4 + 32 * q^9	\( 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9} - 6 q^{10} - 24 q^{12} - 4 q^{14} + 74 q^{16} + 2 q^{17} + 24 q^{22} - 28 q^{23} - 18 q^{25} + 44 q^{27} + 24 q^{29} + 4 q^{30} + 14 q^{35} - 6 q^{36} + 94 q^{38} + 24 q^{40} - 22 q^{42} - 78 q^{43} - 6 q^{48} - 32 q^{49} - 86 q^{51} - 16 q^{53} - 18 q^{55} + 58 q^{56} - 6 q^{61} + 20 q^{62} - 68 q^{64} - 98 q^{66} - 40 q^{68} + 26 q^{69} - 30 q^{74} - 14 q^{75} + 8 q^{77} + 78 q^{79} + 58 q^{81} + 8 q^{82} + 32 q^{87} - 84 q^{88} + 20 q^{90} - 54 q^{92} + 32 q^{94} + 8 q^{95}+O(q^{100}) \) 18 * q + 14 * q^3 - 34 * q^4 + 32 * q^9 - 6 * q^10 - 24 * q^12 - 4 * q^14 + 74 * q^16 + 2 * q^17 + 24 * q^22 - 28 * q^23 - 18 * q^25 + 44 * q^27 + 24 * q^29 + 4 * q^30 + 14 * q^35 - 6 * q^36 + 94 * q^38 + 24 * q^40 - 22 * q^42 - 78 * q^43 - 6 * q^48 - 32 * q^49 - 86 * q^51 - 16 * q^53 - 18 * q^55 + 58 * q^56 - 6 * q^61 + 20 * q^62 - 68 * q^64 - 98 * q^66 - 40 * q^68 + 26 * q^69 - 30 * q^74 - 14 * q^75 + 8 * q^77 + 78 * q^79 + 58 * q^81 + 8 * q^82 + 32 * q^87 - 84 * q^88 + 20 * q^90 - 54 * q^92 + 32 * q^94 + 8 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more