LMFDB - Embedded newform 945.2.z.b.629.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(314,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3, 3]))

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

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

chi := DirichletCharacter("945.314");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.z (of order $6$, degree $2$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			629.3
Character	$\chi$	$=$	945.629
Dual form			945.2.z.b.314.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19580 + 2.07119i) q^{2} +(-1.85987 - 3.22139i) q^{4} +(-1.39933 - 1.74410i) q^{5} +(1.82814 + 1.91257i) q^{7} +4.11294 q^{8} +O(q^{10})$	\(q+(-1.19580 + 2.07119i) q^{2} +(-1.85987 - 3.22139i) q^{4} +(-1.39933 - 1.74410i) q^{5} +(1.82814 + 1.91257i) q^{7} +4.11294 q^{8} +(5.28567 - 0.812672i) q^{10} +(-3.27627 - 1.89156i) q^{11} +(-2.95115 - 5.11155i) q^{13} +(-6.14737 + 1.49937i) q^{14} +(-1.19851 + 2.07588i) q^{16} +1.69241i q^{17} +4.29448i q^{19} +(-3.01586 + 7.75159i) q^{20} +(7.83553 - 4.52384i) q^{22} +(3.30241 + 5.71995i) q^{23} +(-1.08377 + 4.88113i) q^{25} +14.1160 q^{26} +(2.76102 - 9.44629i) q^{28} +(6.21072 + 3.58576i) q^{29} +(3.85236 - 2.22416i) q^{31} +(1.24659 + 2.15915i) q^{32} +(-3.50529 - 2.02378i) q^{34} +(0.777540 - 5.86476i) q^{35} +4.73927i q^{37} +(-8.89467 - 5.13534i) q^{38} +(-5.75535 - 7.17338i) q^{40} +(-0.696581 - 1.20651i) q^{41} +(4.60768 + 2.66025i) q^{43} +14.0722i q^{44} -15.7961 q^{46} +(8.81141 + 5.08727i) q^{47} +(-0.315813 + 6.99287i) q^{49} +(-8.81376 - 8.08154i) q^{50} +(-10.9775 + 19.0137i) q^{52} -4.07705 q^{53} +(1.28551 + 8.36105i) q^{55} +(7.51903 + 7.86627i) q^{56} +(-14.8536 + 8.57571i) q^{58} +(-0.0684247 - 0.118515i) q^{59} +(-1.15878 - 0.669022i) q^{61} +10.6386i q^{62} -10.7567 q^{64} +(-4.78542 + 12.2998i) q^{65} +(-5.59511 + 3.23034i) q^{67} +(5.45192 - 3.14767i) q^{68} +(11.2172 + 8.62351i) q^{70} +0.186379i q^{71} +3.27524 q^{73} +(-9.81592 - 5.66722i) q^{74} +(13.8342 - 7.98719i) q^{76} +(-2.37176 - 9.72411i) q^{77} +(2.14428 - 3.71399i) q^{79} +(5.29765 - 0.814514i) q^{80} +3.33189 q^{82} +(4.86438 + 2.80845i) q^{83} +(2.95173 - 2.36823i) q^{85} +(-11.0197 + 6.36224i) q^{86} +(-13.4751 - 7.77986i) q^{88} -7.10637 q^{89} +(4.38105 - 14.9889i) q^{91} +(12.2841 - 21.2768i) q^{92} +(-21.0734 + 12.1667i) q^{94} +(7.49001 - 6.00939i) q^{95} +(-3.82861 + 6.63135i) q^{97} +(-14.1059 - 9.01618i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 52 q^{4}+O(q^{10}) $ 80 * q - 52 * q^4	$ 80 q - 52 q^{4} + 24 q^{11} + 12 q^{14} - 28 q^{16} - 22 q^{25} + 48 q^{29} - 24 q^{46} + 20 q^{49} + 42 q^{50} - 24 q^{56} + 128 q^{64} - 90 q^{65} - 6 q^{70} - 12 q^{74} - 32 q^{79} - 2 q^{85} - 156 q^{86} - 8 q^{91} + 24 q^{95}+O(q^{100}) $ 80 * q - 52 * q^4 + 24 * q^11 + 12 * q^14 - 28 * q^16 - 22 * q^25 + 48 * q^29 - 24 * q^46 + 20 * q^49 + 42 * q^50 - 24 * q^56 + 128 * q^64 - 90 * q^65 - 6 * q^70 - 12 * q^74 - 32 * q^79 - 2 * q^85 - 156 * q^86 - 8 * q^91 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.19580	+	2.07119i	−0.845558	+	1.46455i	0.0395778	+	0.999216i	$0.487399\pi$
$2$	−1.19580	+	2.07119i	−0.845558	+	1.46455i	−0.885136	+	0.465333i	$0.845935\pi$
$3$		0			0
$3$		0			0
$4$	−1.85987	−	3.22139i	−0.929937	−	1.61070i
$5$	−1.39933	−	1.74410i	−0.625798	−	0.779985i
$5$	−1.39933	−	1.74410i	−0.625798	−	0.779985i
$6$		0			0
$7$	1.82814	+	1.91257i	0.690972	+	0.722882i
$7$	1.82814	+	1.91257i	0.690972	+	0.722882i
$8$	4.11294			1.45415
$9$		0			0
$10$	5.28567	−	0.812672i	1.67148	−	0.256990i
$11$	−3.27627	−	1.89156i	−0.987833	−	0.570326i	−0.0832072	−	0.996532i	$-0.526516\pi$
$11$	−3.27627	−	1.89156i	−0.987833	−	0.570326i	−0.904626	+	0.426207i	$0.859850\pi$
$12$		0			0
$13$	−2.95115	−	5.11155i	−0.818503	−	1.41769i	−0.906785	−	0.421593i	$-0.861471\pi$
$13$	−2.95115	−	5.11155i	−0.818503	−	1.41769i	0.0882821	−	0.996096i	$-0.471862\pi$
$14$	−6.14737	+	1.49937i	−1.64295	+	0.400724i
$15$		0			0
$16$	−1.19851	+	2.07588i	−0.299627	+	0.518970i
$17$			1.69241i			0.410470i	0.978713	+	0.205235i	$0.0657958\pi$
$17$			1.69241i			0.410470i	−0.978713	+	0.205235i	$0.934204\pi$
$18$		0			0
$19$			4.29448i			0.985222i	0.870250	+	0.492611i	$0.163957\pi$
$19$			4.29448i			0.985222i	−0.870250	+	0.492611i	$0.836043\pi$
$20$	−3.01586	+	7.75159i	−0.674367	+	1.73331i
$21$		0			0
$22$	7.83553	−	4.52384i	1.67054	−	0.964487i
$23$	3.30241	+	5.71995i	0.688601	+	1.19269i	0.972291	+	0.233775i	$0.0751080\pi$
$23$	3.30241	+	5.71995i	0.688601	+	1.19269i	−0.283690	+	0.958916i	$0.591559\pi$
$24$		0			0
$25$	−1.08377	+	4.88113i	−0.216753	+	0.976226i
$26$	14.1160			2.76837
$27$		0			0
$28$	2.76102	−	9.44629i	0.521784	−	1.78518i
$29$	6.21072	+	3.58576i	1.15330	+	0.665859i	0.949690	−	0.313192i	$-0.101398\pi$
$29$	6.21072	+	3.58576i	1.15330	+	0.665859i	0.203613	+	0.979052i	$0.434732\pi$
$30$		0			0
$31$	3.85236	−	2.22416i	0.691904	−	0.399471i	−0.112421	−	0.993661i	$-0.535860\pi$
$31$	3.85236	−	2.22416i	0.691904	−	0.399471i	0.804325	+	0.594190i	$0.202527\pi$
$32$	1.24659	+	2.15915i	0.220368	+	0.381688i
$33$		0			0
$34$	−3.50529	−	2.02378i	−0.601153	−	0.347076i
$35$	0.777540	−	5.86476i	0.131428	−	0.991326i
$36$		0			0
$37$			4.73927i			0.779132i	0.920999	+	0.389566i	$0.127375\pi$
$37$			4.73927i			0.779132i	−0.920999	+	0.389566i	$0.872625\pi$
$38$	−8.89467	−	5.13534i	−1.44291	−	0.833062i
$39$		0			0
$40$	−5.75535	−	7.17338i	−0.910001	−	1.13421i
$41$	−0.696581	−	1.20651i	−0.108788	−	0.188426i	0.806492	−	0.591245i	$-0.201364\pi$
$41$	−0.696581	−	1.20651i	−0.108788	−	0.188426i	−0.915279	+	0.402820i	$0.868030\pi$
$42$		0			0
$43$	4.60768	+	2.66025i	0.702665	+	0.405684i	0.808339	−	0.588717i	$-0.200367\pi$
$43$	4.60768	+	2.66025i	0.702665	+	0.405684i	−0.105674	+	0.994401i	$0.533700\pi$
$44$			14.0722i			2.12147i
$45$		0			0
$46$	−15.7961			−2.32901
$47$	8.81141	+	5.08727i	1.28528	+	0.742055i	0.977808	−	0.209503i	$-0.0671848\pi$
$47$	8.81141	+	5.08727i	1.28528	+	0.742055i	0.307469	+	0.951558i	$0.400518\pi$
$48$		0			0
$49$	−0.315813	+	6.99287i	−0.0451162	+	0.998982i
$50$	−8.81376	−	8.08154i	−1.24645	−	1.14290i
$51$		0			0
$52$	−10.9775	+	19.0137i	−1.52231	+	2.63672i
$53$	−4.07705			−0.560026			−0.280013	−	0.959996i	$-0.590339\pi$
$53$	−4.07705			−0.560026			−0.280013	+	0.959996i	$0.590339\pi$
$54$		0			0
$55$	1.28551	+	8.36105i	0.173339	+	1.12740i
$56$	7.51903	+	7.86627i	1.00477	+	1.05118i
$57$		0			0
$58$	−14.8536	+	8.57571i	−1.95037	+	1.12605i
$59$	−0.0684247	−	0.118515i	−0.00890814	−	0.0154294i	0.861537	−	0.507695i	$-0.169502\pi$
$59$	−0.0684247	−	0.118515i	−0.00890814	−	0.0154294i	−0.870445	+	0.492265i	$0.836169\pi$
$60$		0			0
$61$	−1.15878	−	0.669022i	−0.148367	−	0.0856595i	0.423979	−	0.905672i	$-0.360633\pi$
$61$	−1.15878	−	0.669022i	−0.148367	−	0.0856595i	−0.572346	+	0.820013i	$0.693966\pi$
$62$			10.6386i			1.35110i
$63$		0			0
$64$	−10.7567			−1.34459
$65$	−4.78542	+	12.2998i	−0.593558	+	1.52561i
$66$		0			0
$67$	−5.59511	+	3.23034i	−0.683551	+	0.394648i	−0.801192	−	0.598408i	$-0.795800\pi$
$67$	−5.59511	+	3.23034i	−0.683551	+	0.394648i	0.117641	+	0.993056i	$0.462467\pi$
$68$	5.45192	−	3.14767i	0.661142	−	0.381711i
$69$		0			0
$70$	11.2172	+	8.62351i	1.34072	+	1.03071i
$71$			0.186379i			0.0221191i	0.999939	+	0.0110595i	$0.00352043\pi$
$71$			0.186379i			0.0221191i	−0.999939	+	0.0110595i	$0.996480\pi$
$72$		0			0
$73$	3.27524			0.383337			0.191669	−	0.981460i	$-0.438610\pi$
$73$	3.27524			0.383337			0.191669	+	0.981460i	$0.438610\pi$
$74$	−9.81592	−	5.66722i	−1.14108	−	0.658801i
$75$		0			0
$76$	13.8342	−	7.98719i	1.58689	−	0.916194i
$77$	−2.37176	−	9.72411i	−0.270287	−	1.10817i
$78$		0			0
$79$	2.14428	−	3.71399i	0.241250	−	0.417857i	−0.719821	−	0.694160i	$-0.755776\pi$
$79$	2.14428	−	3.71399i	0.241250	−	0.417857i	0.961071	+	0.276303i	$0.0891093\pi$
$80$	5.29765	−	0.814514i	0.592295	−	0.0910655i
$81$		0			0
$82$	3.33189			0.367945
$83$	4.86438	+	2.80845i	0.533936	+	0.308268i	0.742618	−	0.669716i	$-0.233584\pi$
$83$	4.86438	+	2.80845i	0.533936	+	0.308268i	−0.208682	+	0.977984i	$0.566917\pi$
$84$		0			0
$85$	2.95173	−	2.36823i	0.320160	−	0.256871i
$86$	−11.0197	+	6.36224i	−1.18829	+	0.686058i
$87$		0			0
$88$	−13.4751	−	7.77986i	−1.43645	−	0.829336i
$89$	−7.10637			−0.753274			−0.376637	−	0.926361i	$-0.622920\pi$
$89$	−7.10637			−0.753274			−0.376637	+	0.926361i	$0.622920\pi$
$90$		0			0
$91$	4.38105	−	14.9889i	0.459259	−	1.57126i
$92$	12.2841	−	21.2768i	1.28071	−	2.21825i
$93$		0			0
$94$	−21.0734	+	12.1667i	−2.17355	+	1.25490i
$95$	7.49001	−	6.00939i	0.768459	−	0.616550i
$96$		0			0
$97$	−3.82861	+	6.63135i	−0.388737	+	0.673312i	−0.992280	−	0.124019i	$-0.960422\pi$
$97$	−3.82861	+	6.63135i	−0.388737	+	0.673312i	0.603543	+	0.797330i	$0.293755\pi$
$98$	−14.1059	−	9.01618i	−1.42491	−	0.910772i
$99$		0			0
$100$	17.7397	−	5.58704i	1.77397	−	0.558704i
$101$	2.78778	−	4.82857i	0.277394	−	0.480461i	−0.693342	−	0.720609i	$-0.743862\pi$
$101$	2.78778	−	4.82857i	0.277394	−	0.480461i	0.970736	+	0.240148i	$0.0771958\pi$
$102$		0			0
$103$	1.52647	+	2.64393i	0.150408	+	0.260514i	0.931377	−	0.364055i	$-0.118608\pi$
$103$	1.52647	+	2.64393i	0.150408	+	0.260514i	−0.780970	+	0.624569i	$0.785275\pi$
$104$	−12.1379	−	21.0235i	−1.19022	−	2.06153i
$105$		0			0
$106$	4.87533	−	8.44432i	0.473534	−	0.820185i
$107$	−0.925234			−0.0894457			−0.0447229	−	0.998999i	$-0.514240\pi$
$107$	−0.925234			−0.0894457			−0.0447229	+	0.998999i	$0.514240\pi$
$108$		0			0
$109$	0.0228809			0.00219159			0.00109579	−	0.999999i	$-0.499651\pi$
$109$	0.0228809			0.00219159			0.00109579	+	0.999999i	$0.499651\pi$
$110$	−18.8545	−	7.33560i	−1.79771	−	0.699422i
$111$		0			0
$112$	−6.16130	+	1.50277i	−0.582188	+	0.141998i
$113$	1.15860	+	2.00675i	0.108992	+	0.188779i	0.915362	−	0.402632i	$-0.131904\pi$
$113$	1.15860	+	2.00675i	0.108992	+	0.188779i	−0.806370	+	0.591411i	$0.798571\pi$
$114$		0			0
$115$	5.35500	−	13.7638i	0.499356	−	1.28348i
$116$		−	26.6763i		−	2.47683i
$117$		0			0
$118$	0.327289			0.0301294
$119$	−3.23684	+	3.09396i	−0.296721	+	0.283623i
$120$		0			0
$121$	1.65597	+	2.86823i	0.150543	+	0.260748i
$122$	2.77134	−	1.60003i	0.250905	−	0.144860i
$123$		0			0
$124$	−14.3298	−	8.27332i	−1.28685	−	0.742966i
$125$	10.0297	−	4.94010i	0.897086	−	0.441856i
$126$		0			0
$127$			6.54669i			0.580925i	0.956886	+	0.290462i	$0.0938091\pi$
$127$			6.54669i			0.580925i	−0.956886	+	0.290462i	$0.906191\pi$
$128$	10.3697	−	17.9609i	0.916561	−	1.58753i
$129$		0			0
$130$	−19.7528	−	24.6196i	−1.73244	−	2.15928i
$131$	8.75164	+	15.1583i	0.764634	+	1.32439i	0.940440	+	0.339960i	$0.110414\pi$
$131$	8.75164	+	15.1583i	0.764634	+	1.32439i	−0.175806	+	0.984425i	$0.556253\pi$
$132$		0			0
$133$	−8.21348	+	7.85091i	−0.712199	+	0.680761i
$134$		−	15.4513i		−	1.33479i
$135$		0			0
$136$			6.96079i			0.596882i
$137$	−5.06016	+	8.76445i	−0.432318	+	0.748798i	−0.997073	−	0.0764617i	$-0.975638\pi$
$137$	−5.06016	+	8.76445i	−0.432318	+	0.748798i	0.564754	+	0.825259i	$0.308971\pi$
$138$		0			0
$139$	12.9351	−	7.46806i	1.09714	−	0.633432i	0.161669	−	0.986845i	$-0.448312\pi$
$139$	12.9351	−	7.46806i	1.09714	−	0.633432i	0.935468	+	0.353413i	$0.114979\pi$
$140$	−20.3388	+	8.40295i	−1.71895	+	0.710179i
$141$		0			0
$142$	−0.386025	−	0.222872i	−0.0323945	−	0.0187030i
$143$			22.3291i			1.86725i
$144$		0			0
$145$	−2.43691	−	15.8498i	−0.202374	−	1.31625i
$146$	−3.91653	+	6.78362i	−0.324134	+	0.561417i
$147$		0			0
$148$	15.2671	−	8.81445i	1.25495	−	0.724543i
$149$	10.7832	−	6.22566i	0.883390	−	0.510026i	0.0116156	−	0.999933i	$-0.496303\pi$
$149$	10.7832	−	6.22566i	0.883390	−	0.510026i	0.871775	+	0.489907i	$0.162969\pi$
$150$		0			0
$151$	4.72476	−	8.18352i	0.384495	−	0.665965i	−0.607204	−	0.794546i	$-0.707709\pi$
$151$	4.72476	−	8.18352i	0.384495	−	0.665965i	0.991699	+	0.128581i	$0.0410422\pi$
$152$			17.6630i			1.43266i
$153$		0			0
$154$	22.9766	+	6.71574i	1.85151	+	0.541170i
$155$	−9.26987	−	3.60657i	−0.744574	−	0.289687i
$156$		0			0
$157$	0.916356	+	1.58717i	0.0731332	+	0.126670i	0.900273	−	0.435326i	$-0.143367\pi$
$157$	0.916356	+	1.58717i	0.0731332	+	0.126670i	−0.827140	+	0.561996i	$0.810034\pi$
$158$	5.12825	+	8.88238i	0.407981	+	0.706645i
$159$		0			0
$160$	2.02140	−	5.19554i	0.159805	−	0.410743i
$161$	−4.90250	+	16.7729i	−0.386371	+	1.32189i
$162$		0			0
$163$			14.1821i			1.11083i	0.831575	+	0.555413i	$0.187440\pi$
$163$			14.1821i			1.11083i	−0.831575	+	0.555413i	$0.812560\pi$
$164$	−2.59111	+	4.48793i	−0.202331	+	0.350448i
$165$		0			0
$166$	−11.6337	+	6.71670i	−0.902947	+	0.521317i
$167$	−11.0072	+	6.35503i	−0.851765	+	0.491767i	−0.861246	−	0.508188i	$-0.830315\pi$
$167$	−11.0072	+	6.35503i	−0.851765	+	0.491767i	0.00948069	+	0.999955i	$0.496982\pi$
$168$		0			0
$169$	−10.9186	+	18.9116i	−0.839894	+	1.45474i
$170$	1.37537	+	8.94552i	0.105486	+	0.686090i
$171$		0			0
$172$		−	19.7909i		−	1.50904i
$173$	−8.48655	−	4.89971i	−0.645221	−	0.372518i	0.141402	−	0.989952i	$-0.454839\pi$
$173$	−8.48655	−	4.89971i	−0.645221	−	0.372518i	−0.786623	+	0.617434i	$0.788172\pi$
$174$		0			0
$175$	−11.3168	+	6.85061i	−0.855467	+	0.517858i
$176$	7.85329	−	4.53410i	0.591964	−	0.341770i
$177$		0			0
$178$	8.49779	−	14.7186i	0.636937	−	1.10321i
$179$		−	15.8558i		−	1.18512i	−0.805527	−	0.592559i	$-0.798118\pi$
$179$		−	15.8558i		−	1.18512i	0.805527	−	0.592559i	$-0.201882\pi$
$180$		0			0
$181$			17.3482i			1.28948i	0.764400	+	0.644742i	$0.223035\pi$
$181$			17.3482i			1.28948i	−0.764400	+	0.644742i	$0.776965\pi$
$182$	25.8059	+	26.9977i	1.91286	+	2.00120i
$183$		0			0
$184$	13.5826	+	23.5258i	1.00133	+	1.73435i
$185$	8.26577	−	6.63180i	0.607711	−	0.487579i
$186$		0			0
$187$	3.20129	−	5.54479i	0.234101	−	0.405475i
$188$		−	37.8467i		−	2.76026i
$189$		0			0
$190$	3.49001	+	22.6992i	0.253192	+	1.64677i
$191$	12.0714	+	6.96942i	0.873455	+	0.504289i	0.868495	−	0.495698i	$-0.165088\pi$
$191$	12.0714	+	6.96942i	0.873455	+	0.504289i	0.00496004	+	0.999988i	$0.498421\pi$
$192$		0			0
$193$	3.39661	−	1.96103i	0.244493	−	0.141158i	−0.372747	−	0.927933i	$-0.621584\pi$
$193$	3.39661	−	1.96103i	0.244493	−	0.141158i	0.617240	+	0.786775i	$0.288251\pi$
$194$	−9.15650	−	15.8595i	−0.657399	−	1.13865i
$195$		0			0
$196$	23.1142	−	11.9885i	1.65101	−	0.856321i
$197$	7.72054			0.550066			0.275033	−	0.961435i	$-0.411311\pi$
$197$	7.72054			0.550066			0.275033	+	0.961435i	$0.411311\pi$
$198$		0			0
$199$		−	13.1920i		−	0.935155i	−0.883952	−	0.467578i	$-0.845127\pi$
$199$		−	13.1920i		−	0.935155i	0.883952	−	0.467578i	$-0.154873\pi$
$200$	−4.45747	+	20.0758i	−0.315191	+	1.41957i
$201$		0			0
$202$	6.66725	+	11.5480i	0.469106	+	0.812515i
$203$	4.49606	+	18.4337i	0.315562	+	1.29379i
$204$		0			0
$205$	−1.12954	+	2.90321i	−0.0788902	+	0.202769i
$206$	−7.30141			−0.508714
$207$		0			0
$208$	14.1480			0.980984
$209$	8.12326	−	14.0699i	0.561898	−	0.973235i
$210$		0			0
$211$	7.44349	+	12.8925i	0.512431	+	0.887557i	0.999896	+	0.0144142i	$0.00458833\pi$
$211$	7.44349	+	12.8925i	0.512431	+	0.887557i	−0.487465	+	0.873143i	$0.662078\pi$
$212$	7.58279	+	13.1338i	0.520788	+	0.902032i
$213$		0			0
$214$	1.10639	−	1.91633i	0.0756316	−	0.130998i
$215$	−1.80792	−	11.7588i	−0.123299	−	0.801945i
$216$		0			0
$217$	11.2965	+	3.30181i	0.766857	+	0.224142i
$218$	−0.0273609	+	0.0473905i	−0.00185312	+	0.00320969i
$219$		0			0
$220$	24.5434	−	19.6916i	1.65471	−	1.32761i
$221$	8.65084	−	4.99456i	0.581918	−	0.335971i
$222$		0			0
$223$	−2.06408	+	3.57509i	−0.138221	+	0.239406i	−0.926823	−	0.375498i	$-0.877472\pi$
$223$	−2.06408	+	3.57509i	−0.138221	+	0.239406i	0.788602	+	0.614904i	$0.210805\pi$
$224$	−1.85059	+	6.33142i	−0.123648	+	0.423036i
$225$		0			0
$226$	−5.54181			−0.368636
$227$	−19.8410	−	11.4552i	−1.31690	−	0.760310i	−0.333668	−	0.942691i	$-0.608286\pi$
$227$	−19.8410	−	11.4552i	−1.31690	−	0.760310i	−0.983228	+	0.182380i	$0.941620\pi$
$228$		0			0
$229$	0.265499	−	0.153286i	0.0175447	−	0.0101294i	−0.491202	−	0.871046i	$-0.663442\pi$
$229$	0.265499	−	0.153286i	0.0175447	−	0.0101294i	0.508747	+	0.860916i	$0.330109\pi$
$230$	22.1039	+	27.5500i	1.45749	+	1.81659i
$231$		0			0
$232$	25.5444	+	14.7480i	1.67707	+	0.968256i
$233$	3.31647			0.217269			0.108635	−	0.994082i	$-0.465352\pi$
$233$	3.31647			0.217269			0.108635	+	0.994082i	$0.465352\pi$
$234$		0			0
$235$	−3.45734	−	22.4867i	−0.225532	−	1.46687i
$236$	−0.254523	+	0.440846i	−0.0165680	+	0.0286966i
$237$		0			0
$238$	−2.53755	−	10.4039i	−0.164485	−	0.674382i
$239$	−7.58220	+	4.37759i	−0.490452	+	0.283163i	−0.724762	−	0.688999i	$-0.758050\pi$
$239$	−7.58220	+	4.37759i	−0.490452	+	0.283163i	0.234310	+	0.972162i	$0.424717\pi$
$240$		0			0
$241$	7.34043	+	4.23800i	0.472839	+	0.272993i	0.717427	−	0.696633i	$-0.245320\pi$
$241$	7.34043	+	4.23800i	0.472839	+	0.272993i	−0.244589	+	0.969627i	$0.578653\pi$
$242$	−7.92084			−0.509171
$243$		0			0
$244$			4.97718i			0.318631i
$245$	12.6382	−	9.23451i	0.807425	−	0.589971i
$246$		0			0
$247$	21.9515	−	12.6737i	1.39674	−	0.806407i
$248$	15.8445	−	9.14785i	1.00613	−	0.580889i
$249$		0			0
$250$	−1.76167	+	26.6808i	−0.111418	+	1.68744i
$251$	−24.2894			−1.53313			−0.766567	−	0.642164i	$-0.778037\pi$
$251$	−24.2894			−1.53313			−0.766567	+	0.642164i	$0.778037\pi$
$252$		0			0
$253$		−	24.9868i		−	1.57091i
$254$	−13.5594	−	7.82853i	−0.850793	−	0.491205i
$255$		0			0
$256$	14.0435	+	24.3240i	0.877716	+	1.52025i
$257$	26.1668	−	15.1074i	1.63224	−	0.942374i	0.648839	−	0.760926i	$-0.275255\pi$
$257$	26.1668	−	15.1074i	1.63224	−	0.942374i	0.983401	−	0.181448i	$-0.0580784\pi$
$258$		0			0
$259$	−9.06417	+	8.66405i	−0.563220	+	0.538358i
$260$	48.5229	−	7.46041i	3.00926	−	0.462675i
$261$		0			0
$262$	−41.8608			−2.58617
$263$	4.01217	−	6.94928i	0.247401	−	0.428511i	−0.715403	−	0.698712i	$-0.753757\pi$
$263$	4.01217	−	6.94928i	0.247401	−	0.428511i	0.962804	+	0.270201i	$0.0870902\pi$
$264$		0			0
$265$	5.70512	+	7.11078i	0.350463	+	0.436812i
$266$	−6.43902	−	26.3998i	−0.394802	−	1.61867i
$267$		0			0
$268$	20.8124	+	12.0160i	1.27132	+	0.733996i
$269$	−10.6940			−0.652022			−0.326011	−	0.945366i	$-0.605705\pi$
$269$	−10.6940			−0.652022			−0.326011	+	0.945366i	$0.605705\pi$
$270$		0			0
$271$			29.8519i			1.81337i	0.421806	+	0.906686i	$0.361396\pi$
$271$			29.8519i			1.81337i	−0.421806	+	0.906686i	$0.638604\pi$
$272$	−3.51324	−	2.02837i	−0.213021	−	0.122988i
$273$		0			0
$274$	−12.1019	−	20.9611i	−0.731101	−	1.26630i
$275$	12.7837	−	13.9419i	0.770883	−	0.840729i
$276$		0			0
$277$	11.6697	+	6.73753i	0.701167	+	0.404819i	0.807782	−	0.589481i	$-0.200668\pi$
$277$	11.6697	+	6.73753i	0.701167	+	0.404819i	−0.106615	+	0.994300i	$0.534001\pi$
$278$			35.7212i			2.14241i
$279$		0			0
$280$	3.19798	−	24.1214i	0.191116	−	1.44153i
$281$	−8.96113	−	5.17371i	−0.534576	−	0.308638i	0.208302	−	0.978065i	$-0.433206\pi$
$281$	−8.96113	−	5.17371i	−0.534576	−	0.308638i	−0.742878	+	0.669427i	$0.766540\pi$
$282$		0			0
$283$	−13.0884	−	22.6698i	−0.778025	−	1.34758i	−0.933079	−	0.359672i	$-0.882889\pi$
$283$	−13.0884	−	22.6698i	−0.778025	−	1.34758i	0.155054	−	0.987906i	$-0.450445\pi$
$284$	0.600400	−	0.346641i	0.0356272	−	0.0205694i
$285$		0			0
$286$	−46.2477	−	26.7011i	−2.73468	−	1.57887i
$287$	1.03409	−	3.53793i	0.0610404	−	0.208838i
$288$		0			0
$289$	14.1357			0.831515
$290$	35.7419	+	13.9059i	2.09884	+	0.816581i
$291$		0			0
$292$	−6.09152	−	10.5508i	−0.356479	−	0.617441i
$293$	−22.6938	+	13.1023i	−1.32579	+	0.765443i	−0.984645	−	0.174570i	$-0.944147\pi$
$293$	−22.6938	+	13.1023i	−1.32579	+	0.765443i	−0.341141	+	0.940012i	$0.610813\pi$
$294$		0			0
$295$	−0.110954	+	0.285181i	−0.00645997	+	0.0166039i
$296$			19.4924i			1.13297i
$297$		0			0
$298$			29.7786i			1.72503i
$299$	19.4919	−	33.7609i	1.12724	−	1.95244i
$300$		0			0
$301$	3.33559	+	13.6758i	0.192260	+	0.788260i
$302$	11.2997	+	19.5717i	0.650226	+	1.12622i
$303$		0			0
$304$	−8.91483	−	5.14698i	−0.511301	−	0.295200i
$305$	0.454671	+	2.95721i	0.0260344	+	0.169329i
$306$		0			0
$307$	16.3222			0.931560			0.465780	−	0.884901i	$-0.345774\pi$
$307$	16.3222			0.931560			0.465780	+	0.884901i	$0.345774\pi$
$308$	−26.9140	+	25.7260i	−1.53357	+	1.46587i
$309$		0			0
$310$	18.5548	−	14.8869i	1.05384	−	0.845518i
$311$	9.11553	+	15.7886i	0.516894	+	0.895287i	0.999808	+	0.0196190i	$0.00624533\pi$
$311$	9.11553	+	15.7886i	0.516894	+	0.895287i	−0.482913	+	0.875668i	$0.660421\pi$
$312$		0			0
$313$	−8.59559	+	14.8880i	−0.485851	+	0.841519i	−0.999868	−	0.0162611i	$-0.994824\pi$
$313$	−8.59559	+	14.8880i	−0.485851	+	0.841519i	0.514016	+	0.857780i	$0.328157\pi$
$314$	−4.38311			−0.247353
$315$		0			0
$316$	−15.9523			−0.897388
$317$	9.67647	−	16.7601i	0.543484	−	0.941343i	−0.455216	−	0.890381i	$-0.650438\pi$
$317$	9.67647	−	16.7601i	0.543484	−	0.941343i	0.998701	−	0.0509617i	$-0.0162286\pi$
$318$		0			0
$319$	−13.5653	−	23.4959i	−0.759514	−	1.31552i
$320$	15.0522	+	18.7608i	0.841442	+	1.04876i
$321$		0			0
$322$	−28.8775	−	30.2111i	−1.60928	−	1.68360i
$323$	−7.26803			−0.404404
$324$		0			0
$325$	28.1485	−	8.86524i	1.56140	−	0.491755i
$326$	−29.3737	−	16.9589i	−1.62686	−	0.939267i
$327$		0			0
$328$	−2.86500	−	4.96232i	−0.158193	−	0.273999i
$329$	6.37875	+	26.1526i	0.351672	+	1.44184i
$330$		0			0
$331$	15.0255	−	26.0249i	0.825874	−	1.43046i	−0.0753758	−	0.997155i	$-0.524016\pi$
$331$	15.0255	−	26.0249i	0.825874	−	1.43046i	0.901250	−	0.433300i	$-0.142651\pi$
$332$		−	20.8935i		−	1.14668i
$333$		0			0
$334$		−	30.3974i		−	1.66327i
$335$	13.4634	+	5.23813i	0.735585	+	0.286189i
$336$		0			0
$337$	−25.2779	+	14.5942i	−1.37698	+	0.794997i	−0.991794	−	0.127844i	$-0.959194\pi$
$337$	−25.2779	+	14.5942i	−1.37698	+	0.794997i	−0.385181	+	0.922841i	$0.625861\pi$
$338$	−26.1130	−	45.2290i	−1.42036	−	2.46013i
$339$		0			0
$340$	−13.1189	−	5.10407i	−0.711470	−	0.276807i
$341$	−16.8285			−0.911315
$342$		0			0
$343$	−13.9517	+	12.1799i	−0.753320	+	0.657654i
$344$	18.9511	+	10.9414i	1.02178	+	0.589923i
$345$		0			0
$346$	20.2964	−	11.7182i	1.09114	−	0.629972i
$347$	−5.52222	−	9.56476i	−0.296448	−	0.513463i	0.678873	−	0.734256i	$-0.262469\pi$
$347$	−5.52222	−	9.56476i	−0.296448	−	0.513463i	−0.975321	+	0.220793i	$0.929136\pi$
$348$		0			0
$349$	0.210157	+	0.121334i	0.0112495	+	0.00649488i	0.505614	−	0.862760i	$-0.331266\pi$
$349$	0.210157	+	0.121334i	0.0112495	+	0.00649488i	−0.494365	+	0.869255i	$0.664599\pi$
$350$	−0.656312	−	31.6311i	−0.0350813	−	1.69075i
$351$		0			0
$352$		−	9.43197i		−	0.502726i
$353$	11.1362	+	6.42951i	0.592722	+	0.342208i	0.766173	−	0.642634i	$-0.222159\pi$
$353$	11.1362	+	6.42951i	0.592722	+	0.342208i	−0.173451	+	0.984842i	$0.555492\pi$
$354$		0			0
$355$	0.325063	−	0.260805i	0.0172526	−	0.0138421i
$356$	13.2169	+	22.8924i	0.700497	+	1.21330i
$357$		0			0
$358$	32.8403	+	18.9604i	1.73566	+	1.00209i
$359$			6.26078i			0.330431i	0.986257	+	0.165216i	$0.0528320\pi$
$359$			6.26078i			0.330431i	−0.986257	+	0.165216i	$0.947168\pi$
$360$		0			0
$361$	0.557410			0.0293373
$362$	−35.9314	−	20.7450i	−1.88851	−	1.09033i
$363$		0			0
$364$	−56.4334	+	13.7644i	−2.95791	+	0.721448i
$365$	−4.58313	−	5.71234i	−0.239892	−	0.298997i
$366$		0			0
$367$	−7.10475	+	12.3058i	−0.370865	+	0.642357i	−0.989699	−	0.143165i	$-0.954272\pi$
$367$	−7.10475	+	12.3058i	−0.370865	+	0.642357i	0.618834	+	0.785522i	$0.287605\pi$
$368$	−15.8319			−0.825295
$369$		0			0
$370$	3.85148	+	25.0502i	0.200229	+	1.30230i
$371$	−7.45341	−	7.79762i	−0.386962	−	0.404832i
$372$		0			0
$373$	−0.899536	+	0.519348i	−0.0465762	+	0.0268908i	−0.523107	−	0.852267i	$-0.675227\pi$
$373$	−0.899536	+	0.519348i	−0.0465762	+	0.0268908i	0.476531	+	0.879158i	$0.341894\pi$
$374$	7.65620	+	13.2609i	0.395893	+	0.685706i
$375$		0			0
$376$	36.2408	+	20.9237i	1.86898	+	1.07906i
$377$		−	42.3286i		−	2.18003i
$378$		0			0
$379$	36.2376			1.86140			0.930701	−	0.365781i	$-0.119198\pi$
$379$	36.2376			1.86140			0.930701	+	0.365781i	$0.119198\pi$
$380$	−33.2891	−	12.9516i	−1.70769	−	0.664402i
$381$		0			0
$382$	−28.8699	+	16.6681i	−1.47711	+	0.852812i
$383$	−5.69956	+	3.29064i	−0.291234	+	0.168144i	−0.638498	−	0.769623i	$-0.720444\pi$
$383$	−5.69956	+	3.29064i	−0.291234	+	0.168144i	0.347264	+	0.937767i	$0.387111\pi$
$384$		0			0
$385$	−13.6410	+	17.7438i	−0.695208	+	0.904307i
$386$			9.38002i			0.477430i
$387$		0			0
$388$	28.4829			1.44600
$389$	10.6037	+	6.12206i	0.537630	+	0.310401i	0.744118	−	0.668048i	$-0.232870\pi$
$389$	10.6037	+	6.12206i	0.537630	+	0.310401i	−0.206488	+	0.978449i	$0.566203\pi$
$390$		0			0
$391$	−9.68049	+	5.58904i	−0.489564	+	0.282650i
$392$	−1.29892	+	28.7613i	−0.0656055	+	1.45266i
$393$		0			0
$394$	−9.23222	+	15.9907i	−0.465113	+	0.805599i
$395$	−9.47812	+	1.45726i	−0.476896	+	0.0733228i
$396$		0			0
$397$	25.0713			1.25829			0.629145	−	0.777288i	$-0.283405\pi$
$397$	25.0713			1.25829			0.629145	+	0.777288i	$0.283405\pi$
$398$	27.3231	+	15.7750i	1.36958	+	0.790728i
$399$		0			0
$400$	−8.83374	−	8.09986i	−0.441687	−	0.404993i
$401$	9.99330	−	5.76963i	0.499042	−	0.288122i	−0.229276	−	0.973361i	$-0.573636\pi$
$401$	9.99330	−	5.76963i	0.499042	−	0.288122i	0.728318	+	0.685240i	$0.240303\pi$
$402$		0			0
$403$	−22.7378	−	13.1277i	−1.13265	−	0.653937i
$404$	−20.7397			−1.03184
$405$		0			0
$406$	−43.5560	−	12.7308i	−2.16165	−	0.631820i
$407$	8.96461	−	15.5272i	0.444359	−	0.769652i
$408$		0			0
$409$	−29.4907	+	17.0264i	−1.45822	+	0.841903i	−0.998924	−	0.0463804i	$-0.985231\pi$
$409$	−29.4907	+	17.0264i	−1.45822	+	0.841903i	−0.459295	+	0.888284i	$0.651898\pi$
$410$	−4.66240	−	5.81114i	−0.230259	−	0.286992i
$411$		0			0
$412$	5.67809	−	9.83473i	0.279739	−	0.484523i
$413$	0.101578	−	0.347529i	0.00499833	−	0.0171008i
$414$		0			0
$415$	−1.90864	−	12.4139i	−0.0936915	−	0.609375i
$416$	7.35775	−	12.7440i	0.360743	−	0.624826i
$417$		0			0
$418$	19.4276	+	33.6496i	0.950234	+	1.64585i
$419$	−13.3097	−	23.0531i	−0.650221	−	1.12622i	−0.983069	−	0.183235i	$-0.941343\pi$
$419$	−13.3097	−	23.0531i	−0.650221	−	1.12622i	0.332848	−	0.942980i	$-0.391990\pi$
$420$		0			0
$421$	0.915994	−	1.58655i	0.0446428	−	0.0773236i	−0.842841	−	0.538163i	$-0.819118\pi$
$421$	0.915994	−	1.58655i	0.0446428	−	0.0773236i	0.887483	+	0.460840i	$0.152452\pi$
$422$	−35.6037			−1.73316
$423$		0			0
$424$	−16.7687			−0.814359
$425$	−8.26087	−	1.83418i	−0.400711	−	0.0889707i
$426$		0			0
$427$	−0.838863	−	3.43931i	−0.0405954	−	0.166440i
$428$	1.72082	+	2.98054i	0.0831789	+	0.144070i
$429$		0			0
$430$	26.5166	+	10.3166i	1.27874	+	0.497513i
$431$			3.00440i			0.144717i	0.997379	+	0.0723584i	$0.0230525\pi$
$431$			3.00440i			0.144717i	−0.997379	+	0.0723584i	$0.976947\pi$
$432$		0			0
$433$	−31.3064			−1.50449			−0.752244	−	0.658884i	$-0.771029\pi$
$433$	−31.3064			−1.50449			−0.752244	+	0.658884i	$0.771029\pi$
$434$	−20.3470	+	19.4488i	−0.976689	+	0.933575i
$435$		0			0
$436$	−0.0425555	−	0.0737083i	−0.00203804	−	0.00352999i
$437$	−24.5642	+	14.1822i	−1.17507	+	0.678425i
$438$		0			0
$439$	11.6891	+	6.74871i	0.557891	+	0.322098i	0.752298	−	0.658822i	$-0.228945\pi$
$439$	11.6891	+	6.74871i	0.557891	+	0.322098i	−0.194408	+	0.980921i	$0.562279\pi$
$440$	5.28724	+	34.3885i	0.252059	+	1.63941i
$441$		0			0
$442$			23.8900i			1.13633i
$443$	12.2333	−	21.1888i	0.581224	−	1.00671i	−0.414111	−	0.910227i	$-0.635907\pi$
$443$	12.2333	−	21.1888i	0.581224	−	1.00671i	0.995335	−	0.0964829i	$-0.0307593\pi$
$444$		0			0
$445$	9.94414	+	12.3942i	0.471397	+	0.587542i
$446$	−4.93646	−	8.55019i	−0.233748	−	0.404863i
$447$		0			0
$448$	−19.6648	−	20.5729i	−0.929074	−	0.971980i
$449$			27.5369i			1.29955i	0.760128	+	0.649773i	$0.225136\pi$
$449$			27.5369i			1.29955i	−0.760128	+	0.649773i	$0.774864\pi$
$450$		0			0
$451$			5.27049i			0.248178i
$452$	4.30969	−	7.46461i	0.202711	−	0.351106i
$453$		0			0
$454$	47.4518	−	27.3963i	2.22702	−	1.28577i
$455$	−32.2727	+	13.3334i	−1.51297	+	0.625079i
$456$		0			0
$457$	−19.0575	−	11.0029i	−0.891473	−	0.514692i	−0.0170489	−	0.999855i	$-0.505427\pi$
$457$	−19.0575	−	11.0029i	−0.891473	−	0.514692i	−0.874424	+	0.485163i	$0.838760\pi$
$458$			0.733197i			0.0342600i
$459$		0			0
$460$	−54.2983	+	8.34837i	−2.53167	+	0.389245i
$461$	−2.95347	+	5.11555i	−0.137557	+	0.238255i	−0.926571	−	0.376119i	$-0.877258\pi$
$461$	−2.95347	+	5.11555i	−0.137557	+	0.238255i	0.789015	+	0.614374i	$0.210592\pi$
$462$		0			0
$463$	−18.6722	+	10.7804i	−0.867772	+	0.501009i	−0.866607	−	0.498991i	$-0.833704\pi$
$463$	−18.6722	+	10.7804i	−0.867772	+	0.501009i	−0.00116511	+	0.999999i	$0.500371\pi$
$464$	−14.8872	+	8.59514i	−0.691122	+	0.399020i
$465$		0			0
$466$	−3.96584	+	6.86903i	−0.183714	+	0.318202i
$467$			32.6959i			1.51299i	0.654001	+	0.756493i	$0.273089\pi$
$467$			32.6959i			1.51299i	−0.654001	+	0.756493i	$0.726911\pi$
$468$		0			0
$469$	−16.4069	−	4.79550i	−0.757598	−	0.221436i
$470$	50.7085	+	19.7288i	2.33901	+	0.910023i
$471$		0			0
$472$	−0.281427	−	0.487446i	−0.0129537	−	0.0224365i
$473$	−10.0640	−	17.4314i	−0.462744	−	0.801496i
$474$		0			0
$475$	−20.9619	−	4.65422i	−0.961800	−	0.213550i
$476$	15.9870	+	4.67278i	0.732762	+	0.214176i
$477$		0			0
$478$		−	20.9389i		−	0.957722i
$479$	−12.5685	+	21.7692i	−0.574268	+	0.994661i	0.421853	+	0.906664i	$0.361380\pi$
$479$	−12.5685	+	21.7692i	−0.574268	+	0.994661i	−0.996121	+	0.0879970i	$0.971953\pi$
$480$		0			0
$481$	24.2250	−	13.9863i	1.10457	−	0.637722i
$482$	−17.5554	+	10.1356i	−0.799625	+	0.461664i
$483$		0			0
$484$	6.15979	−	10.6691i	0.279991	−	0.484958i
$485$	16.9232	−	2.60195i	0.768444	−	0.118148i
$486$		0			0
$487$		−	37.5584i		−	1.70193i	−0.525220	−	0.850966i	$-0.676017\pi$
$487$		−	37.5584i		−	1.70193i	0.525220	−	0.850966i	$-0.323983\pi$
$488$	−4.76600	−	2.75165i	−0.215746	−	0.124561i
$489$		0			0
$490$	4.01363	+	37.2187i	0.181317	+	1.68137i
$491$	7.27036	−	4.19755i	0.328107	−	0.189433i	−0.326893	−	0.945061i	$-0.606002\pi$
$491$	7.27036	−	4.19755i	0.328107	−	0.189433i	0.655000	+	0.755629i	$0.272668\pi$
$492$		0			0
$493$	−6.06858	+	10.5111i	−0.273315	+	0.473396i
$494$			60.6207i			2.72746i
$495$		0			0
$496$			10.6627i			0.478770i
$497$	−0.356462	+	0.340726i	−0.0159895	+	0.0152837i
$498$		0			0
$499$	−18.0730	−	31.3033i	−0.809058	−	1.40133i	−0.913517	−	0.406800i	$-0.866644\pi$
$499$	−18.0730	−	31.3033i	−0.809058	−	1.40133i	0.104459	−	0.994529i	$-0.466689\pi$
$500$	−34.5680	−	23.1217i	−1.54593	−	1.03404i
$501$		0			0
$502$	29.0453	−	50.3079i	1.29635	−	2.24535i
$503$		−	1.08412i		−	0.0483387i	−0.999708	−	0.0241694i	$-0.992306\pi$
$503$		−	1.08412i		−	0.0483387i	0.999708	−	0.0241694i	$-0.00769409\pi$
$504$		0			0
$505$	−12.3225	+	1.89459i	−0.548345	+	0.0843082i
$506$	51.7523	+	29.8792i	2.30067	+	1.32829i
$507$		0			0
$508$	21.0895	−	12.1760i	0.935694	−	0.540223i
$509$	1.21404	+	2.10278i	0.0538115	+	0.0932042i	0.891676	−	0.452673i	$-0.149530\pi$
$509$	1.21404	+	2.10278i	0.0538115	+	0.0932042i	−0.837865	+	0.545878i	$0.816196\pi$
$510$		0			0
$511$	5.98759	+	6.26410i	0.264875	+	0.277108i
$512$	−25.6938			−1.13552
$513$		0			0
$514$			72.2617i			3.18733i
$515$	2.47524	−	6.36203i	0.109072	−	0.280345i
$516$		0			0
$517$	−19.2457	−	33.3346i	−0.846426	−	1.46605i
$518$	−7.10593	−	29.1341i	−0.312217	−	1.28008i
$519$		0			0
$520$	−19.6822	+	50.5885i	−0.863120	+	2.21845i
$521$	32.3550			1.41750			0.708749	−	0.705461i	$-0.249260\pi$
$521$	32.3550			1.41750			0.708749	+	0.705461i	$0.249260\pi$
$522$		0			0
$523$	−6.81216			−0.297875			−0.148938	−	0.988847i	$-0.547585\pi$
$523$	−6.81216			−0.297875			−0.148938	+	0.988847i	$0.547585\pi$
$524$	32.5539	−	56.3850i	1.42212	−	2.46319i
$525$		0			0
$526$	9.59550	+	16.6199i	0.418384	+	0.724662i
$527$	3.76419	+	6.51977i	0.163971	+	0.284006i
$528$		0			0
$529$	−10.3119	+	17.8607i	−0.448342	+	0.776551i
$530$	−21.5499	+	3.31331i	−0.936069	+	0.143921i
$531$		0			0
$532$	40.5669	+	11.8572i	1.75880	+	0.514073i
$533$	−4.11144	+	7.12122i	−0.178086	+	0.308454i
$534$		0			0
$535$	1.29470	+	1.61370i	0.0559750	+	0.0697663i
$536$	−23.0124	+	13.2862i	−0.993982	+	0.573876i
$537$		0			0
$538$	12.7878	−	22.1492i	0.551323	−	0.954919i
$539$	14.2621	−	22.3132i	0.614312	−	0.961096i
$540$		0			0
$541$	−35.4058			−1.52221			−0.761107	−	0.648626i	$-0.775344\pi$
$541$	−35.4058			−1.52221			−0.761107	+	0.648626i	$0.775344\pi$
$542$	−61.8288	−	35.6969i	−2.65577	−	1.53331i
$543$		0			0
$544$	−3.65417	+	2.10974i	−0.156671	+	0.0904543i
$545$	−0.0320178	−	0.0399065i	−0.00137149	−	0.00170941i
$546$		0			0
$547$	−21.3371	−	12.3190i	−0.912309	−	0.526722i	−0.0311353	−	0.999515i	$-0.509912\pi$
$547$	−21.3371	−	12.3190i	−0.912309	−	0.526722i	−0.881173	+	0.472794i	$0.843246\pi$
$548$	37.6450			1.60812
$549$		0			0
$550$	13.5896	+	43.1490i	0.579462	+	1.83988i
$551$	−15.3990	+	26.6719i	−0.656019	+	1.13626i
$552$		0			0
$553$	11.0233	−	2.68863i	0.468758	−	0.114332i
$554$	−27.9094	+	16.1135i	−1.18575	+	0.684596i
$555$		0			0
$556$	−48.1151	−	27.7793i	−2.04054	−	1.17810i
$557$	−34.2686			−1.45201			−0.726004	−	0.687690i	$-0.758625\pi$
$557$	−34.2686			−1.45201			−0.726004	+	0.687690i	$0.758625\pi$
$558$		0			0
$559$		−	31.4032i		−	1.32821i
$560$	11.2427	+	8.64305i	0.475089	+	0.365236i
$561$		0			0
$562$	21.4314	−	12.3734i	0.904031	−	0.521942i
$563$	14.8001	−	8.54484i	0.623750	−	0.360122i	−0.154578	−	0.987981i	$-0.549402\pi$
$563$	14.8001	−	8.54484i	0.623750	−	0.360122i	0.778328	+	0.627858i	$0.216068\pi$
$564$		0			0
$565$	1.87872	−	4.82881i	0.0790382	−	0.203150i
$566$	62.6044			2.63146
$567$		0			0
$568$			0.766565i			0.0321644i
$569$	−0.638402	−	0.368582i	−0.0267632	−	0.0154517i	0.486559	−	0.873648i	$-0.338252\pi$
$569$	−0.638402	−	0.368582i	−0.0267632	−	0.0154517i	−0.513322	+	0.858196i	$0.671585\pi$
$570$		0			0
$571$	9.04448	+	15.6655i	0.378500	+	0.655581i	0.990844	−	0.135010i	$-0.0431068\pi$
$571$	9.04448	+	15.6655i	0.378500	+	0.655581i	−0.612344	+	0.790591i	$0.709773\pi$
$572$	71.9308	−	41.5293i	3.00758	−	1.73643i
$573$		0			0
$574$	6.09115	+	6.37245i	0.254240	+	0.265981i
$575$	−31.4989	+	9.92042i	−1.31359	+	0.413710i
$576$		0			0
$577$	−8.90877			−0.370877			−0.185438	−	0.982656i	$-0.559371\pi$
$577$	−8.90877			−0.370877			−0.185438	+	0.982656i	$0.559371\pi$
$578$	−16.9035	+	29.2778i	−0.703094	+	1.21779i
$579$		0			0
$580$	−46.5260	+	37.3288i	−1.93189	+	1.54999i
$581$	3.52142	+	14.4377i	0.146093	+	0.598977i
$582$		0			0
$583$	13.3575	+	7.71197i	0.553212	+	0.319397i
$584$	13.4709			0.557428
$585$		0			0
$586$		−	62.6707i		−	2.58890i
$587$	11.0118	+	6.35769i	0.454507	+	0.262410i	0.709732	−	0.704472i	$-0.248816\pi$
$587$	11.0118	+	6.35769i	0.454507	+	0.262410i	−0.255225	+	0.966882i	$0.582149\pi$
$588$		0			0
$589$	9.55162	+	16.5439i	0.393568	+	0.681679i
$590$	−0.457984	−	0.570825i	−0.0188549	−	0.0235005i
$591$		0			0
$592$	−9.83816	−	5.68007i	−0.404346	−	0.233449i
$593$			23.7783i			0.976456i	0.872716	+	0.488228i	$0.162357\pi$
$593$			23.7783i			0.976456i	−0.872716	+	0.488228i	$0.837643\pi$
$594$		0			0
$595$	9.92558	+	1.31592i	0.406909	+	0.0539473i
$596$	−40.1106	−	23.1579i	−1.64299	−	0.948583i
$597$		0			0
$598$	46.6167	+	80.7425i	1.90630	+	3.30181i
$599$	−1.75148	+	1.01122i	−0.0715634	+	0.0413171i	−0.535355	−	0.844627i	$-0.679822\pi$
$599$	−1.75148	+	1.01122i	−0.0715634	+	0.0413171i	0.463791	+	0.885944i	$0.346489\pi$
$600$		0			0
$601$	38.6966	+	22.3415i	1.57847	+	0.911330i	0.995073	+	0.0991416i	$0.0316097\pi$
$601$	38.6966	+	22.3415i	1.57847	+	0.911330i	0.583396	+	0.812188i	$0.301724\pi$
$602$	−32.3138	−	9.44489i	−1.31701	−	0.384945i
$603$		0			0
$604$	−35.1498			−1.43022
$605$	2.68523	−	6.90177i	0.109170	−	0.280597i
$606$		0			0
$607$	−0.845887	−	1.46512i	−0.0343335	−	0.0594674i	0.848348	−	0.529439i	$-0.177598\pi$
$607$	−0.845887	−	1.46512i	−0.0343335	−	0.0594674i	−0.882682	+	0.469972i	$0.844264\pi$
$608$	−9.27245	+	5.35345i	−0.376048	+	0.217111i
$609$		0			0
$610$	−6.66862	−	2.59452i	−0.270005	−	0.105049i
$611$		−	60.0533i		−	2.42950i
$612$		0			0
$613$		−	0.247395i		−	0.00999217i	−0.999988	−	0.00499609i	$-0.998410\pi$
$613$		−	0.247395i		−	0.00999217i	0.999988	−	0.00499609i	$-0.00159031\pi$
$614$	−19.5181	+	33.8064i	−0.787688	+	1.36432i
$615$		0			0
$616$	−9.75490	−	39.9947i	−0.393036	−	1.61143i
$617$	−2.48021	−	4.29585i	−0.0998495	−	0.172944i	0.811773	−	0.583973i	$-0.198503\pi$
$617$	−2.48021	−	4.29585i	−0.0998495	−	0.172944i	−0.911622	+	0.411029i	$0.865169\pi$
$618$		0			0
$619$	−29.9212	−	17.2750i	−1.20263	−	0.694341i	−0.241494	−	0.970402i	$-0.577637\pi$
$619$	−29.9212	−	17.2750i	−1.20263	−	0.694341i	−0.961140	+	0.276061i	$0.910971\pi$
$620$	5.62259	+	36.5697i	0.225809	+	1.46867i
$621$		0			0
$622$	−43.6014			−1.74826
$623$	−12.9914	−	13.5914i	−0.520491	−	0.544528i
$624$		0			0
$625$	−22.6509	−	10.5800i	−0.906036	−	0.423201i
$626$	−20.5572	−	35.6061i	−0.821631	−	1.42311i
$627$		0			0
$628$	3.40861	−	5.90389i	0.136018	−	0.235591i
$629$	−8.02079			−0.319810
$630$		0			0
$631$	−38.6332			−1.53796			−0.768981	−	0.639271i	$-0.779236\pi$
$631$	−38.6332			−1.53796			−0.768981	+	0.639271i	$0.779236\pi$
$632$	8.81928	−	15.2754i	0.350812	−	0.607625i
$633$		0			0
$634$	23.1422	+	40.0835i	0.919095	+	1.59192i
$635$	11.4181	−	9.16096i	0.453113	−	0.363541i
$636$		0			0
$637$	36.6764	−	19.0227i	1.45317	−	0.753709i
$638$	64.8857			2.56885
$639$		0			0
$640$	−45.8361	+	7.04731i	−1.81183	+	0.278569i
$641$	29.9412	+	17.2865i	1.18261	+	0.682778i	0.956616	−	0.291352i	$-0.0941051\pi$
$641$	29.9412	+	17.2865i	1.18261	+	0.682778i	0.225990	+	0.974130i	$0.427438\pi$
$642$		0			0
$643$	9.93213	+	17.2030i	0.391685	+	0.678418i	0.992672	−	0.120841i	$-0.0385590\pi$
$643$	9.93213	+	17.2030i	0.391685	+	0.678418i	−0.600987	+	0.799259i	$0.705226\pi$
$644$	63.1503	−	15.4026i	2.48847	−	0.606949i
$645$		0			0
$646$	8.69110	−	15.0534i	0.341947	−	0.592269i
$647$		−	29.1502i		−	1.14601i	−0.819552	−	0.573005i	$-0.805777\pi$
$647$		−	29.1502i		−	1.14601i	0.819552	−	0.573005i	$-0.194223\pi$
$648$		0			0
$649$			0.517717i			0.0203222i
$650$	−15.2984	+	68.9018i	−0.600053	+	2.70255i
$651$		0			0
$652$	45.6860	−	26.3769i	1.78920	−	1.03300i
$653$	21.0534	+	36.4656i	0.823885	+	1.42701i	0.902769	+	0.430127i	$0.141531\pi$
$653$	21.0534	+	36.4656i	0.823885	+	1.42701i	−0.0788837	+	0.996884i	$0.525136\pi$
$654$		0			0
$655$	14.1912	−	36.4751i	0.554494	−	1.42520i
$656$	3.33944			0.130383
$657$		0			0
$658$	−61.7947	−	18.0617i	−2.40901	−	0.704120i
$659$	−33.1600	−	19.1449i	−1.29173	−	0.745781i	−0.312770	−	0.949829i	$-0.601257\pi$
$659$	−33.1600	−	19.1449i	−1.29173	−	0.745781i	−0.978961	+	0.204048i	$0.934590\pi$
$660$		0			0
$661$	32.4841	−	18.7547i	1.26348	−	0.729473i	0.289738	−	0.957106i	$-0.406432\pi$
$661$	32.4841	−	18.7547i	1.26348	−	0.729473i	0.973747	+	0.227633i	$0.0730986\pi$
$662$	35.9349	+	62.2410i	1.39665	+	2.41907i
$663$		0			0
$664$	20.0069	+	11.5510i	0.776420	+	0.448266i
$665$	25.1861	+	3.33913i	0.976676	+	0.129486i
$666$		0			0
$667$			47.3667i			1.83405i
$668$	40.9441	+	23.6391i	1.58418	+	0.914624i
$669$		0			0
$670$	−26.9487	+	21.6215i	−1.04112	+	0.835310i
$671$	2.53098	+	4.38379i	0.0977076	+	0.169234i
$672$		0			0
$673$	33.2297	+	19.1852i	1.28091	+	0.739534i	0.977015	−	0.213171i	$-0.0683790\pi$
$673$	33.2297	+	19.1852i	1.28091	+	0.739534i	0.303896	+	0.952705i	$0.401712\pi$
$674$		−	69.8070i		−	2.68886i
$675$		0			0
$676$	81.2290			3.12419
$677$	−5.84917	−	3.37702i	−0.224802	−	0.129789i	0.383370	−	0.923595i	$-0.374763\pi$
$677$	−5.84917	−	3.37702i	−0.224802	−	0.129789i	−0.608172	+	0.793806i	$0.708097\pi$
$678$		0			0
$679$	−19.6821	+	4.80056i	−0.755331	+	0.184229i
$680$	12.1403	−	9.74042i	0.465559	−	0.373528i
$681$		0			0
$682$	20.1235	−	34.8550i	0.770569	−	1.33467i
$683$	16.2830			0.623051			0.311525	−	0.950238i	$-0.399160\pi$
$683$	16.2830			0.623051			0.311525	+	0.950238i	$0.399160\pi$
$684$		0			0
$685$	22.3669	−	3.43891i	0.854595	−	0.131394i
$686$	−8.54349	−	43.4613i	−0.326192	−	1.65936i
$687$		0			0
$688$	−11.0447	+	6.37666i	−0.421076	+	0.243108i
$689$	12.0320	+	20.8400i	0.458383	+	0.793942i
$690$		0			0
$691$	−42.4779	−	24.5246i	−1.61594	−	0.932962i	−0.987956	−	0.154733i	$-0.950548\pi$
$691$	−42.4779	−	24.5246i	−1.61594	−	0.932962i	−0.627980	−	0.778229i	$-0.716118\pi$
$692$			36.4514i			1.38567i
$693$		0			0
$694$	26.4139			1.00266
$695$	−31.1254	−	12.1098i	−1.18065	−	0.459350i
$696$		0			0
$697$	2.04192	−	1.17890i	0.0773431	−	0.0446540i
$698$	−0.502612	+	0.290183i	−0.0190241	+	0.0109836i
$699$		0			0
$700$	43.1163	+	23.7145i	1.62964	+	0.896323i
$701$			42.6160i			1.60958i	0.593558	+	0.804791i	$0.297723\pi$
$701$			42.6160i			1.60958i	−0.593558	+	0.804791i	$0.702277\pi$
$702$		0			0
$703$	−20.3527			−0.767618
$704$	35.2419	+	20.3469i	1.32823	+	0.766854i
$705$		0			0
$706$	−26.6334	+	15.3768i	−1.00236	+	0.578714i
$707$	14.3314	−	3.49550i	0.538988	−	0.131462i
$708$		0			0
$709$	12.4370	−	21.5416i	0.467082	−	0.809010i	−0.532211	−	0.846612i	$-0.678639\pi$
$709$	12.4370	−	21.5416i	0.467082	−	0.809010i	0.999293	+	0.0376019i	$0.0119719\pi$
$710$	0.151465	+	0.985137i	0.00568438	+	0.0369715i
$711$		0			0
$712$	−29.2281			−1.09537
$713$	25.4442	+	14.6902i	0.952892	+	0.550152i
$714$		0			0
$715$	38.9442	−	31.2457i	1.45643	−	1.16852i
$716$	−51.0778	+	29.4898i	−1.90887	+	1.10208i
$717$		0			0
$718$	−12.9672	−	7.48664i	−0.483933	−	0.279399i
$719$	6.21418			0.231750			0.115875	−	0.993264i	$-0.463033\pi$
$719$	6.21418			0.231750			0.115875	+	0.993264i	$0.463033\pi$
$720$		0			0
$721$	−2.26608	+	7.75294i	−0.0843932	+	0.288735i
$722$	−0.666550	+	1.15450i	−0.0248064	+	0.0429660i
$723$		0			0
$724$	55.8855	−	32.2655i	2.07697	−	1.19914i
$725$	−24.2336	+	26.4292i	−0.900012	+	0.981557i
$726$		0			0
$727$	9.92998	−	17.1992i	0.368283	−	0.637884i	−0.621015	−	0.783799i	$-0.713279\pi$
$727$	9.92998	−	17.1992i	0.368283	−	0.637884i	0.989297	+	0.145915i	$0.0466126\pi$
$728$	18.0190	−	61.6485i	0.667829	−	2.28485i
$729$		0			0
$730$	17.3118	−	2.66169i	0.640739	−	0.0985137i
$731$	−4.50223	+	7.79809i	−0.166521	+	0.288423i
$732$		0			0
$733$	−19.0319	−	32.9642i	−0.702959	−	1.21756i	−0.967423	−	0.253165i	$-0.918529\pi$
$733$	−19.0319	−	32.9642i	−0.702959	−	1.21756i	0.264465	−	0.964395i	$-0.414805\pi$
$734$	−16.9917	−	29.4305i	−0.627175	−	1.08630i
$735$		0			0
$736$	−8.23350	+	14.2608i	−0.303491	+	0.525662i
$737$	24.4414			0.900312
$738$		0			0
$739$	29.6923			1.09225			0.546125	−	0.837704i	$-0.316102\pi$
$739$	29.6923			1.09225			0.546125	+	0.837704i	$0.316102\pi$
$740$	−36.7369	−	14.2930i	−1.35048	−	0.525421i
$741$		0			0
$742$	25.0631	−	6.11301i	0.920096	−	0.224416i
$743$	−8.10127	−	14.0318i	−0.297207	−	0.514777i	0.678289	−	0.734795i	$-0.262722\pi$
$743$	−8.10127	−	14.0318i	−0.297207	−	0.514777i	−0.975496	+	0.220018i	$0.929388\pi$
$744$		0			0
$745$	−25.9473	−	10.0952i	−0.950636	−	0.369858i
$746$		−	2.48414i		−	0.0909509i
$747$		0			0
$748$	−23.8160			−0.870798
$749$	−1.69146	−	1.76957i	−0.0618045	−	0.0646587i
$750$		0			0
$751$	−24.2550	−	42.0109i	−0.885079	−	1.53300i	−0.845624	−	0.533780i	$-0.820771\pi$
$751$	−24.2550	−	42.0109i	−0.885079	−	1.53300i	−0.0394551	−	0.999221i	$-0.512562\pi$
$752$	−21.1211	+	12.1943i	−0.770208	+	0.444680i
$753$		0			0
$754$	87.6703	+	50.6165i	3.19276	+	1.84334i
$755$	−20.8844	+	3.21097i	−0.760059	+	0.116859i
$756$		0			0
$757$		−	35.7942i		−	1.30096i	−0.759522	−	0.650482i	$-0.774567\pi$
$757$		−	35.7942i		−	1.30096i	0.759522	−	0.650482i	$-0.225433\pi$
$758$	−43.3329	+	75.0549i	−1.57392	+	2.72612i
$759$		0			0
$760$	30.8060	−	24.7163i	1.11745	−	0.896553i
$761$	−14.2570	−	24.6938i	−0.516815	−	0.895149i	−0.999809	−	0.0195261i	$-0.993784\pi$
$761$	−14.2570	−	24.6938i	−0.516815	−	0.895149i	0.482995	−	0.875623i	$-0.339549\pi$
$762$		0			0
$763$	0.0418294	+	0.0437612i	0.00151433	+	0.00158426i
$764$		−	51.8489i		−	1.87583i
$765$		0			0
$766$		−	15.7398i		−	0.568702i
$767$	−0.403864	+	0.699513i	−0.0145827	+	0.0252579i
$768$		0			0
$769$	13.1122	−	7.57032i	0.472838	−	0.272993i	−0.244589	−	0.969627i	$-0.578653\pi$
$769$	13.1122	−	7.57032i	0.472838	−	0.272993i	0.717427	+	0.696634i	$0.245320\pi$
$770$	−20.4388	−	49.4710i	−0.736564	−	1.78281i
$771$		0			0
$772$	−12.6345	−	7.29455i	−0.454727	−	0.262537i
$773$			19.8598i			0.714309i	0.934045	+	0.357154i	$0.116253\pi$
$773$			19.8598i			0.714309i	−0.934045	+	0.357154i	$0.883747\pi$
$774$		0			0
$775$	6.68136	+	21.2144i	0.240002	+	0.762042i
$776$	−15.7469	+	27.2744i	−0.565279	+	0.979093i
$777$		0			0
$778$	−25.3598	+	14.6415i	−0.909195	+	0.524924i
$779$	5.18135	−	2.99146i	0.185641	−	0.107180i
$780$		0			0
$781$	0.352546	−	0.610628i	0.0126151	−	0.0218500i
$782$		−	26.7335i		−	0.955987i
$783$		0			0
$784$	−14.1379	−	9.03662i	−0.504923	−	0.322736i
$785$	1.48591	−	3.81919i	0.0530344	−	0.136313i
$786$		0			0
$787$	17.3391	+	30.0322i	0.618072	+	1.07053i	0.989837	+	0.142206i	$0.0454195\pi$
$787$	17.3391	+	30.0322i	0.618072	+	1.07053i	−0.371765	+	0.928327i	$0.621247\pi$
$788$	−14.3592	−	24.8709i	−0.511527	−	0.885990i
$789$		0			0
$790$	8.31567	−	21.3735i	0.295858	−	0.760436i
$791$	−1.71996	+	5.88452i	−0.0611549	+	0.209229i
$792$		0			0
$793$			7.89755i			0.280450i
$794$	−29.9802	+	51.9272i	−1.06396	+	1.84283i
$795$		0			0
$796$	−42.4966	+	24.5354i	−1.50625	+	0.869635i
$797$	9.29069	−	5.36398i	0.329093	−	0.190002i	−0.326345	−	0.945251i	$-0.605817\pi$
$797$	9.29069	−	5.36398i	0.329093	−	0.190002i	0.655438	+	0.755249i	$0.272484\pi$
$798$		0			0
$799$	−8.60975	+	14.9125i	−0.304591	+	0.527567i
$800$	−11.8901	+	3.74474i	−0.420380	+	0.132397i
$801$		0			0
$802$			27.5973i			0.974495i
$803$	−10.7306	−	6.19529i	−0.378673	−	0.218627i
$804$		0			0
$805$	36.1139	−	14.9204i	1.27285	−	0.525874i
$806$	54.3797	−	31.3962i	1.91544	−	1.10588i
$807$		0			0
$808$	11.4660	−	19.8597i	0.403372	−	0.698660i
$809$		−	3.33520i		−	0.117260i	−0.998280	−	0.0586298i	$-0.981327\pi$
$809$		−	3.33520i		−	0.117260i	0.998280	−	0.0586298i	$-0.0186731\pi$
$810$		0			0
$811$			5.87612i			0.206338i	0.994664	+	0.103169i	$0.0328983\pi$
$811$			5.87612i			0.206338i	−0.994664	+	0.103169i	$0.967102\pi$
$812$	51.0201	−	48.7679i	1.79045	−	1.71142i
$813$		0			0
$814$	21.4397	+	37.1347i	0.751463	+	1.30157i
$815$	24.7349	−	19.8454i	0.866427	−	0.695152i
$816$		0			0
$817$	−11.4244	+	19.7876i	−0.399689	+	0.692281i
$818$		−	81.4408i		−	2.84751i
$819$		0			0
$820$	11.4532	−	1.76093i	0.399963	−	0.0614944i
$821$	21.8933	+	12.6401i	0.764082	+	0.441143i	0.830759	−	0.556632i	$-0.187907\pi$
$821$	21.8933	+	12.6401i	0.764082	+	0.441143i	−0.0666776	+	0.997775i	$0.521240\pi$
$822$		0			0
$823$	4.34252	−	2.50716i	0.151371	−	0.0873940i	−0.422401	−	0.906409i	$-0.638813\pi$
$823$	4.34252	−	2.50716i	0.151371	−	0.0873940i	0.573772	+	0.819015i	$0.305479\pi$
$824$	6.27829	+	10.8743i	0.218715	+	0.378825i
$825$		0			0
$826$	0.598330	+	0.625962i	0.0208186	+	0.0217800i
$827$	10.3675			0.360514			0.180257	−	0.983620i	$-0.442307\pi$
$827$	10.3675			0.360514			0.180257	+	0.983620i	$0.442307\pi$
$828$		0			0
$829$			42.0369i			1.46000i	0.683447	+	0.730000i	$0.260480\pi$
$829$			42.0369i			1.46000i	−0.683447	+	0.730000i	$0.739520\pi$
$830$	27.9939	+	10.8914i	0.971682	+	0.378046i
$831$		0			0
$832$	31.7447	+	54.9835i	1.10055	+	1.90621i
$833$	−11.8348	−	0.534486i	−0.410052	−	0.0185188i
$834$		0			0
$835$	26.4865	+	10.3049i	0.916604	+	0.356617i
$836$	−60.4329			−2.09012
$837$		0			0
$838$	63.6629			2.19920
$839$	−7.82462	+	13.5526i	−0.270136	+	0.467889i	−0.968896	−	0.247466i	$-0.920402\pi$
$839$	−7.82462	+	13.5526i	−0.270136	+	0.467889i	0.698760	+	0.715356i	$0.253735\pi$
$840$		0			0
$841$	11.2154	+	19.4256i	0.386738	+	0.669849i
$842$	2.19069	+	3.79439i	0.0754962	+	0.130763i
$843$		0			0
$844$	27.6879	−	47.9568i	0.953057	−	1.65074i
$845$	48.2625	−	7.42036i	1.66028	−	0.255268i
$846$		0			0
$847$	−2.45832	+	8.41067i	−0.0844690	+	0.288994i
$848$	4.88638	−	8.46346i	0.167799	−	0.290637i
$849$		0			0
$850$	13.6773	−	14.9165i	0.469127	−	0.511632i
$851$	−27.1084	+	15.6510i	−0.929264	+	0.536511i
$852$		0			0
$853$	−12.3530	+	21.3960i	−0.422958	+	0.732584i	−0.996227	−	0.0867827i	$-0.972341\pi$
$853$	−12.3530	+	21.3960i	−0.422958	+	0.732584i	0.573270	+	0.819367i	$0.305675\pi$
$854$	8.12655	+	2.37528i	0.278085	+	0.0812805i
$855$		0			0
$856$	−3.80543			−0.130067
$857$	5.67390	+	3.27583i	0.193817	+	0.111900i	0.593768	−	0.804636i	$-0.297640\pi$
$857$	5.67390	+	3.27583i	0.193817	+	0.111900i	−0.399951	+	0.916536i	$0.630973\pi$
$858$		0			0
$859$	−0.158205	+	0.0913399i	−0.00539790	+	0.00311648i	−0.502697	−	0.864463i	$-0.667659\pi$
$859$	−0.158205	+	0.0913399i	−0.00539790	+	0.00311648i	0.497299	+	0.867579i	$0.334325\pi$
$860$	−34.5173	+	27.6939i	−1.17703	+	0.944355i
$861$		0			0
$862$	−6.22266	−	3.59266i	−0.211945	−	0.122366i
$863$	0.0675885			0.00230074			0.00115037	−	0.999999i	$-0.499634\pi$
$863$	0.0675885			0.00230074			0.00115037	+	0.999999i	$0.499634\pi$
$864$		0			0
$865$	3.32987	+	21.6577i	0.113219	+	0.736384i
$866$	37.4362	−	64.8413i	1.27213	−	2.20340i
$867$		0			0
$868$	−10.3736	−	42.5315i	−0.352104	−	1.44361i
$869$	−14.0505	+	8.11204i	−0.476629	+	0.275182i
$870$		0			0
$871$	33.0240	+	19.0664i	1.11898	+	0.646042i
$872$	0.0941077			0.00318689
$873$		0			0
$874$		−	67.8361i		−	2.29459i
$875$	27.7840	+	10.1513i	0.939271	+	0.343177i
$876$		0			0
$877$	−42.8858	+	24.7601i	−1.44815	+	0.836090i	−0.998371	−	0.0570500i	$-0.981831\pi$
$877$	−42.8858	+	24.7601i	−1.44815	+	0.836090i	−0.449779	+	0.893140i	$0.648497\pi$
$878$	−27.9557	+	16.1402i	−0.943458	+	0.544706i
$879$		0			0
$880$	−18.8972	−	7.35223i	−0.637026	−	0.247844i
$881$	36.5690			1.23204			0.616021	−	0.787730i	$-0.288744\pi$
$881$	36.5690			1.23204			0.616021	+	0.787730i	$0.288744\pi$
$882$		0			0
$883$			11.8788i			0.399752i	0.979821	+	0.199876i	$0.0640539\pi$
$883$			11.8788i			0.399752i	−0.979821	+	0.199876i	$0.935946\pi$
$884$	−32.1789	−	18.5785i	−1.08229	−	0.624863i
$885$		0			0
$886$	29.2573	+	50.6751i	0.982917	+	1.70246i
$887$	−16.6515	+	9.61376i	−0.559103	+	0.322798i	−0.752785	−	0.658266i	$-0.771290\pi$
$887$	−16.6515	+	9.61376i	−0.559103	+	0.322798i	0.193682	+	0.981064i	$0.437957\pi$
$888$		0			0
$889$	−12.5210	+	11.9683i	−0.419940	+	0.401402i
$890$	−37.5619	+	5.77515i	−1.25908	+	0.193584i
$891$		0			0
$892$	15.3557			0.514148
$893$	−21.8472	+	37.8405i	−0.731089	+	1.26628i
$894$		0			0
$895$	−27.6541	+	22.1874i	−0.924374	+	0.741645i
$896$	53.3086	−	13.0022i	1.78091	−	0.434373i
$897$		0			0
$898$	−57.0340	−	32.9286i	−1.90325	−	1.09884i
$899$	31.9013			1.06397
$900$		0			0
$901$		−	6.90004i		−	0.229874i
$902$	−10.9162	−	6.30245i	−0.363469	−	0.209849i
$903$		0			0
$904$	4.76525	+	8.25366i	0.158490	+	0.274513i
$905$	30.2570	−	24.2759i	1.00578	−	0.806957i
$906$		0			0
$907$	41.0175	+	23.6815i	1.36196	+	0.786330i	0.989885	−	0.141871i	$-0.0453117\pi$
$907$	41.0175	+	23.6815i	1.36196	+	0.786330i	0.372079	+	0.928201i	$0.378645\pi$
$908$			85.2211i			2.82816i
$909$		0			0
$910$	10.9757	−	82.7867i	0.363842	−	2.74435i
$911$	−19.0907	−	11.0220i	−0.632503	−	0.365176i	0.149218	−	0.988804i	$-0.452324\pi$
$911$	−19.0907	−	11.0220i	−0.632503	−	0.365176i	−0.781721	+	0.623629i	$0.785658\pi$
$912$		0			0
$913$	−10.6247	−	18.4025i	−0.351626	−	0.609034i
$914$	45.5779	−	26.3144i	1.50758	−	0.870404i
$915$		0			0
$916$	−0.987588	−	0.570184i	−0.0326308	−	0.0188394i
$917$	−12.9920	+	44.4495i	−0.429033	+	1.46785i
$918$		0			0
$919$	−17.4481			−0.575558			−0.287779	−	0.957697i	$-0.592917\pi$
$919$	−17.4481			−0.575558			−0.287779	+	0.957697i	$0.592917\pi$
$920$	22.0248	−	56.6098i	0.726137	−	1.86637i
$921$		0			0
$922$	−7.06351	−	12.2344i	−0.232624	−	0.402917i
$923$	0.952684	−	0.550033i	0.0313580	−	0.0181045i
$924$		0			0
$925$	−23.1330	−	5.13627i	−0.760609	−	0.168880i
$926$		−	51.5649i		−	1.69453i
$927$		0			0
$928$			17.8799i			0.586936i
$929$	−8.59917	+	14.8942i	−0.282130	+	0.488663i	−0.971909	−	0.235357i	$-0.924374\pi$
$929$	−8.59917	+	14.8942i	−0.282130	+	0.488663i	0.689779	+	0.724020i	$0.257708\pi$
$930$		0			0
$931$	−30.0308	−	1.35626i	−0.984219	−	0.0444495i
$932$	−6.16822	−	10.6837i	−0.202047	−	0.349955i
$933$		0			0
$934$	−67.7193	−	39.0978i	−2.21584	−	1.27932i
$935$	−14.1503	+	2.17561i	−0.462765	+	0.0711502i
$936$		0			0
$937$	15.2037			0.496684			0.248342	−	0.968672i	$-0.420114\pi$
$937$	15.2037			0.496684			0.248342	+	0.968672i	$0.420114\pi$
$938$	29.5517	−	28.2472i	0.964897	−	0.922304i
$939$		0			0
$940$	−66.0084	+	52.9599i	−2.15296	+	1.72736i
$941$	−21.2055	−	36.7290i	−0.691280	−	1.19733i	−0.971419	−	0.237373i	$-0.923714\pi$
$941$	−21.2055	−	36.7290i	−0.691280	−	1.19733i	0.280139	−	0.959960i	$-0.409620\pi$
$942$		0			0
$943$	4.60080	−	7.96882i	0.149823	−	0.259500i
$944$	0.328031			0.0106765
$945$		0			0
$946$	48.1382			1.56511
$947$	−20.7389	+	35.9209i	−0.673925	+	1.16727i	0.302857	+	0.953036i	$0.402060\pi$
$947$	−20.7389	+	35.9209i	−0.673925	+	1.16727i	−0.976782	+	0.214236i	$0.931274\pi$
$948$		0			0
$949$	−9.66573	−	16.7415i	−0.313763	−	0.543453i
$950$	34.7060	−	37.8506i	1.12601	−	1.22803i
$951$		0			0
$952$	−13.3130	+	12.7253i	−0.431475	+	0.412429i
$953$	−28.9734			−0.938541			−0.469270	−	0.883055i	$-0.655483\pi$
$953$	−28.9734			−0.938541			−0.469270	+	0.883055i	$0.655483\pi$
$954$		0			0
$955$	−4.73646	−	30.8062i	−0.153268	−	0.996865i
$956$	28.2039	+	16.2835i	0.912178	+	0.526646i
$957$		0			0
$958$	−30.0587	−	52.0633i	−0.971154	−	1.68209i
$959$	−26.0133	+	6.34475i	−0.840012	+	0.204883i
$960$		0			0
$961$	−5.60621	+	9.71025i	−0.180846	+	0.313234i
$962$			66.8994i			2.15692i
$963$		0			0
$964$		−	31.5286i		−	1.01547i
$965$	−8.17321	−	3.17990i	−0.263105	−	0.102365i
$966$		0			0
$967$	12.3851	−	7.15052i	0.398277	−	0.229945i	−0.287463	−	0.957792i	$-0.592812\pi$
$967$	12.3851	−	7.15052i	0.398277	−	0.229945i	0.685740	+	0.727846i	$0.259479\pi$
$968$	6.81092	+	11.7969i	0.218911	+	0.379165i
$969$		0			0
$970$	−14.8477	+	38.1625i	−0.476730	+	1.22532i
$971$	−30.6812			−0.984608			−0.492304	−	0.870423i	$-0.663845\pi$
$971$	−30.6812			−0.984608			−0.492304	+	0.870423i	$0.663845\pi$
$972$		0			0
$973$	37.9302	+	11.0865i	1.21599	+	0.355417i
$974$	77.7904	+	44.9123i	2.49256	+	1.43908i
$975$		0			0
$976$	2.77762	−	1.60366i	0.0889094	−	0.0513319i
$977$	−16.7763	−	29.0574i	−0.536721	−	0.929628i	−0.999078	−	0.0429339i	$-0.986330\pi$
$977$	−16.7763	−	29.0574i	−0.536721	−	0.929628i	0.462357	−	0.886694i	$-0.347004\pi$
$978$		0			0
$979$	23.2824	+	13.4421i	0.744109	+	0.429611i
$980$	−53.2534	−	23.5376i	−1.70112	−	0.751881i
$981$		0			0
$982$			20.0777i			0.640705i
$983$	−26.6331	−	15.3766i	−0.849462	−	0.490437i	0.0110070	−	0.999939i	$-0.496496\pi$
$983$	−26.6331	−	15.3766i	−0.849462	−	0.490437i	−0.860469	+	0.509502i	$0.829830\pi$
$984$		0			0
$985$	−10.8036	−	13.4654i	−0.344230	−	0.429043i
$986$	−14.5136	−	25.1383i	−0.462207	−	0.800567i
$987$		0			0
$988$	−81.6539	−	47.1429i	−2.59776	−	1.49982i
$989$			35.1409i			1.11742i
$990$		0			0
$991$	18.1260			0.575791			0.287896	−	0.957662i	$-0.407044\pi$
$991$	18.1260			0.575791			0.287896	+	0.957662i	$0.407044\pi$
$992$	9.60462	+	5.54523i	0.304947	+	0.176061i
$993$		0			0
$994$	−0.279451	−	1.14574i	−0.00886364	−	0.0363406i
$995$	−23.0081	+	18.4599i	−0.729407	+	0.585218i
$996$		0			0
$997$	−13.5749	+	23.5125i	−0.429923	+	0.744648i	−0.996866	−	0.0791090i	$-0.974792\pi$
$997$	−13.5749	+	23.5125i	−0.429923	+	0.744648i	0.566943	+	0.823757i	$0.308126\pi$
$998$	86.4467			2.73642
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.z.b.629.3		80
3.2	odd	2		315.2.z.b.209.38	yes	80
5.4	even	2	inner	945.2.z.b.629.37		80
7.6	odd	2	inner	945.2.z.b.629.4		80
9.4	even	3		315.2.z.b.104.4	yes	80
9.5	odd	6	inner	945.2.z.b.314.38		80
15.14	odd	2		315.2.z.b.209.3	yes	80
21.20	even	2		315.2.z.b.209.37	yes	80
35.34	odd	2	inner	945.2.z.b.629.38		80
45.4	even	6		315.2.z.b.104.37	yes	80
45.14	odd	6	inner	945.2.z.b.314.4		80
63.13	odd	6		315.2.z.b.104.3	✓	80
63.41	even	6	inner	945.2.z.b.314.37		80
105.104	even	2		315.2.z.b.209.4	yes	80
315.104	even	6	inner	945.2.z.b.314.3		80
315.139	odd	6		315.2.z.b.104.38	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.z.b.104.3	✓	80	63.13	odd	6
315.2.z.b.104.4	yes	80	9.4	even	3
315.2.z.b.104.37	yes	80	45.4	even	6
315.2.z.b.104.38	yes	80	315.139	odd	6
315.2.z.b.209.3	yes	80	15.14	odd	2
315.2.z.b.209.4	yes	80	105.104	even	2
315.2.z.b.209.37	yes	80	21.20	even	2
315.2.z.b.209.38	yes	80	3.2	odd	2
945.2.z.b.314.3		80	315.104	even	6	inner
945.2.z.b.314.4		80	45.14	odd	6	inner
945.2.z.b.314.37		80	63.41	even	6	inner
945.2.z.b.314.38		80	9.5	odd	6	inner
945.2.z.b.629.3		80	1.1	even	1	trivial
945.2.z.b.629.4		80	7.6	odd	2	inner
945.2.z.b.629.37		80	5.4	even	2	inner
945.2.z.b.629.38		80	35.34	odd	2	inner

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.19580 + 2.07119i) q^{2} +(-1.85987 - 3.22139i) q^{4} +(-1.39933 - 1.74410i) q^{5} +(1.82814 + 1.91257i) q^{7} +4.11294 q^{8} +O(q^{10})\)	\(q+(-1.19580 + 2.07119i) q^{2} +(-1.85987 - 3.22139i) q^{4} +(-1.39933 - 1.74410i) q^{5} +(1.82814 + 1.91257i) q^{7} +4.11294 q^{8} +(5.28567 - 0.812672i) q^{10} +(-3.27627 - 1.89156i) q^{11} +(-2.95115 - 5.11155i) q^{13} +(-6.14737 + 1.49937i) q^{14} +(-1.19851 + 2.07588i) q^{16} +1.69241i q^{17} +4.29448i q^{19} +(-3.01586 + 7.75159i) q^{20} +(7.83553 - 4.52384i) q^{22} +(3.30241 + 5.71995i) q^{23} +(-1.08377 + 4.88113i) q^{25} +14.1160 q^{26} +(2.76102 - 9.44629i) q^{28} +(6.21072 + 3.58576i) q^{29} +(3.85236 - 2.22416i) q^{31} +(1.24659 + 2.15915i) q^{32} +(-3.50529 - 2.02378i) q^{34} +(0.777540 - 5.86476i) q^{35} +4.73927i q^{37} +(-8.89467 - 5.13534i) q^{38} +(-5.75535 - 7.17338i) q^{40} +(-0.696581 - 1.20651i) q^{41} +(4.60768 + 2.66025i) q^{43} +14.0722i q^{44} -15.7961 q^{46} +(8.81141 + 5.08727i) q^{47} +(-0.315813 + 6.99287i) q^{49} +(-8.81376 - 8.08154i) q^{50} +(-10.9775 + 19.0137i) q^{52} -4.07705 q^{53} +(1.28551 + 8.36105i) q^{55} +(7.51903 + 7.86627i) q^{56} +(-14.8536 + 8.57571i) q^{58} +(-0.0684247 - 0.118515i) q^{59} +(-1.15878 - 0.669022i) q^{61} +10.6386i q^{62} -10.7567 q^{64} +(-4.78542 + 12.2998i) q^{65} +(-5.59511 + 3.23034i) q^{67} +(5.45192 - 3.14767i) q^{68} +(11.2172 + 8.62351i) q^{70} +0.186379i q^{71} +3.27524 q^{73} +(-9.81592 - 5.66722i) q^{74} +(13.8342 - 7.98719i) q^{76} +(-2.37176 - 9.72411i) q^{77} +(2.14428 - 3.71399i) q^{79} +(5.29765 - 0.814514i) q^{80} +3.33189 q^{82} +(4.86438 + 2.80845i) q^{83} +(2.95173 - 2.36823i) q^{85} +(-11.0197 + 6.36224i) q^{86} +(-13.4751 - 7.77986i) q^{88} -7.10637 q^{89} +(4.38105 - 14.9889i) q^{91} +(12.2841 - 21.2768i) q^{92} +(-21.0734 + 12.1667i) q^{94} +(7.49001 - 6.00939i) q^{95} +(-3.82861 + 6.63135i) q^{97} +(-14.1059 - 9.01618i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 52 q^{4}+O(q^{10}) \) 80 * q - 52 * q^4	\( 80 q - 52 q^{4} + 24 q^{11} + 12 q^{14} - 28 q^{16} - 22 q^{25} + 48 q^{29} - 24 q^{46} + 20 q^{49} + 42 q^{50} - 24 q^{56} + 128 q^{64} - 90 q^{65} - 6 q^{70} - 12 q^{74} - 32 q^{79} - 2 q^{85} - 156 q^{86} - 8 q^{91} + 24 q^{95}+O(q^{100}) \) 80 * q - 52 * q^4 + 24 * q^11 + 12 * q^14 - 28 * q^16 - 22 * q^25 + 48 * q^29 - 24 * q^46 + 20 * q^49 + 42 * q^50 - 24 * q^56 + 128 * q^64 - 90 * q^65 - 6 * q^70 - 12 * q^74 - 32 * q^79 - 2 * q^85 - 156 * q^86 - 8 * q^91 + 24 * q^95

Introduction

L-functions

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