LMFDB - Embedded newform 375.2.i.d.274.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(49,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("375.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (of order $10$, degree $4$, 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:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			274.1
Character	$\chi$	$=$	375.274
Dual form			375.2.i.d.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.55553 - 0.830342i) q^{2} +(0.587785 - 0.809017i) q^{3} +(4.22323 + 3.06835i) q^{4} +(-2.17386 + 1.57940i) q^{6} +1.68704i q^{7} +(-5.08599 - 7.00026i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-2.55553 - 0.830342i) q^{2} +(0.587785 - 0.809017i) q^{3} +(4.22323 + 3.06835i) q^{4} +(-2.17386 + 1.57940i) q^{6} +1.68704i q^{7} +(-5.08599 - 7.00026i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(0.333373 - 1.02602i) q^{11} +(4.96470 - 1.61313i) q^{12} +(2.54620 - 0.827310i) q^{13} +(1.40082 - 4.31129i) q^{14} +(3.95852 + 12.1831i) q^{16} +(2.31098 + 3.18079i) q^{17} +2.68704i q^{18} +(-0.952655 + 0.692144i) q^{19} +(1.36485 + 0.991619i) q^{21} +(-1.70389 + 2.34520i) q^{22} +(3.86409 + 1.25552i) q^{23} -8.65280 q^{24} -7.19384 q^{26} +(-0.951057 - 0.309017i) q^{27} +(-5.17644 + 7.12476i) q^{28} +(4.81846 + 3.50082i) q^{29} +(5.74653 - 4.17510i) q^{31} -17.1155i q^{32} +(-0.634113 - 0.872782i) q^{33} +(-3.26463 - 10.0475i) q^{34} +(1.61313 - 4.96470i) q^{36} +(4.35761 - 1.41587i) q^{37} +(3.00925 - 0.977766i) q^{38} +(0.827310 - 2.54620i) q^{39} +(-3.47998 - 10.7103i) q^{41} +(-2.66452 - 3.66740i) q^{42} -2.58587i q^{43} +(4.55609 - 3.31019i) q^{44} +(-8.83229 - 6.41703i) q^{46} +(-1.12727 + 1.55155i) q^{47} +(12.1831 + 3.95852i) q^{48} +4.15389 q^{49} +3.93167 q^{51} +(13.2917 + 4.31872i) q^{52} +(1.49803 - 2.06187i) q^{53} +(2.17386 + 1.57940i) q^{54} +(11.8097 - 8.58028i) q^{56} +1.17755i q^{57} +(-9.40685 - 12.9474i) q^{58} +(-0.412843 - 1.27060i) q^{59} +(-2.24997 + 6.92470i) q^{61} +(-18.1522 + 5.89800i) q^{62} +(1.60447 - 0.521325i) q^{63} +(-6.29470 + 19.3731i) q^{64} +(0.895787 + 2.75695i) q^{66} +(-7.31502 - 10.0683i) q^{67} +20.5241i q^{68} +(3.28699 - 2.38814i) q^{69} +(4.84181 + 3.51778i) q^{71} +(-5.08599 + 7.00026i) q^{72} +(3.13911 + 1.01996i) q^{73} -12.3117 q^{74} -6.14702 q^{76} +(1.73093 + 0.562414i) q^{77} +(-4.22843 + 5.81994i) q^{78} +(-3.23934 - 2.35351i) q^{79} +(-0.809017 + 0.587785i) q^{81} +30.2600i q^{82} +(5.21649 + 7.17988i) q^{83} +(2.72142 + 8.37566i) q^{84} +(-2.14716 + 6.60827i) q^{86} +(5.66445 - 1.84049i) q^{87} +(-8.87792 + 2.88461i) q^{88} +(-4.77234 + 14.6877i) q^{89} +(1.39571 + 4.29555i) q^{91} +(12.4666 + 17.1587i) q^{92} -7.10310i q^{93} +(4.16908 - 3.02901i) q^{94} +(-13.8468 - 10.0603i) q^{96} +(6.32939 - 8.71166i) q^{97} +(-10.6154 - 3.44915i) q^{98} -1.07882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{4} + 6 q^{9}+O(q^{10}) $ 24 * q + 20 * q^4 + 6 * q^9	$ 24 q + 20 q^{4} + 6 q^{9} - 8 q^{11} - 12 q^{14} + 32 q^{16} - 14 q^{19} - 6 q^{21} - 12 q^{24} - 112 q^{26} + 2 q^{29} + 26 q^{31} + 50 q^{34} - 4 q^{39} + 16 q^{41} - 66 q^{44} - 44 q^{46} + 56 q^{49} + 52 q^{51} + 90 q^{56} + 44 q^{59} - 16 q^{61} - 98 q^{64} - 6 q^{66} - 12 q^{69} - 42 q^{71} + 88 q^{74} - 104 q^{76} - 20 q^{79} - 6 q^{81} + 12 q^{84} + 112 q^{86} - 114 q^{89} - 14 q^{91} + 46 q^{94} - 46 q^{96} - 12 q^{99}+O(q^{100}) $ 24 * q + 20 * q^4 + 6 * q^9 - 8 * q^11 - 12 * q^14 + 32 * q^16 - 14 * q^19 - 6 * q^21 - 12 * q^24 - 112 * q^26 + 2 * q^29 + 26 * q^31 + 50 * q^34 - 4 * q^39 + 16 * q^41 - 66 * q^44 - 44 * q^46 + 56 * q^49 + 52 * q^51 + 90 * q^56 + 44 * q^59 - 16 * q^61 - 98 * q^64 - 6 * q^66 - 12 * q^69 - 42 * q^71 + 88 * q^74 - 104 * q^76 - 20 * q^79 - 6 * q^81 + 12 * q^84 + 112 * q^86 - 114 * q^89 - 14 * q^91 + 46 * q^94 - 46 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	−2.55553	−	0.830342i	−1.80703	−	0.587140i	−0.807038	−	0.590500i	$-0.798931\pi$
$2$	−2.55553	−	0.830342i	−1.80703	−	0.587140i	−0.999994	+	0.00335992i	$0.998931\pi$
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$4$	4.22323	+	3.06835i	2.11161	+	1.53418i
$5$		0			0
$5$		0			0
$6$	−2.17386	+	1.57940i	−0.887476	+	0.644789i
$7$			1.68704i			0.637642i	0.947815	+	0.318821i	$0.103287\pi$
$7$			1.68704i			0.637642i	−0.947815	+	0.318821i	$0.896713\pi$
$8$	−5.08599	−	7.00026i	−1.79817	−	2.47497i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$		0			0
$11$	0.333373	−	1.02602i	0.100516	−	0.309356i	−0.888136	−	0.459581i	$-0.848000\pi$
$11$	0.333373	−	1.02602i	0.100516	−	0.309356i	0.988652	+	0.150225i	$0.0479998\pi$
$12$	4.96470	−	1.61313i	1.43319	−	0.465670i
$13$	2.54620	−	0.827310i	0.706189	−	0.229455i	0.0661638	−	0.997809i	$-0.478924\pi$
$13$	2.54620	−	0.827310i	0.706189	−	0.229455i	0.640025	+	0.768354i	$0.278924\pi$
$14$	1.40082	−	4.31129i	0.374385	−	1.15224i
$15$		0			0
$16$	3.95852	+	12.1831i	0.989631	+	3.04577i
$17$	2.31098	+	3.18079i	0.560494	+	0.771454i	0.991389	−	0.130948i	$-0.0418021\pi$
$17$	2.31098	+	3.18079i	0.560494	+	0.771454i	−0.430895	+	0.902402i	$0.641802\pi$
$18$			2.68704i			0.633342i
$19$	−0.952655	+	0.692144i	−0.218554	+	0.158789i	−0.691676	−	0.722208i	$-0.743127\pi$
$19$	−0.952655	+	0.692144i	−0.218554	+	0.158789i	0.473121	+	0.880997i	$0.343127\pi$
$20$		0			0
$21$	1.36485	+	0.991619i	0.297834	+	0.216389i
$22$	−1.70389	+	2.34520i	−0.363270	+	0.499999i
$23$	3.86409	+	1.25552i	0.805719	+	0.261794i	0.682783	−	0.730621i	$-0.260769\pi$
$23$	3.86409	+	1.25552i	0.805719	+	0.261794i	0.122935	+	0.992415i	$0.460769\pi$
$24$	−8.65280			−1.76625
$25$		0			0
$26$	−7.19384			−1.41083
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	−5.17644	+	7.12476i	−0.978256	+	1.34645i
$29$	4.81846	+	3.50082i	0.894766	+	0.650086i	0.937116	−	0.349017i	$-0.113484\pi$
$29$	4.81846	+	3.50082i	0.894766	+	0.650086i	−0.0423500	+	0.999103i	$0.513484\pi$
$30$		0			0
$31$	5.74653	−	4.17510i	1.03211	−	0.749870i	0.0633776	−	0.997990i	$-0.479813\pi$
$31$	5.74653	−	4.17510i	1.03211	−	0.749870i	0.968729	+	0.248120i	$0.0798128\pi$
$32$		−	17.1155i		−	3.02563i
$33$	−0.634113	−	0.872782i	−0.110385	−	0.151932i
$34$	−3.26463	−	10.0475i	−0.559879	−	1.72313i
$35$		0			0
$36$	1.61313	−	4.96470i	0.268855	−	0.827450i
$37$	4.35761	−	1.41587i	0.716387	−	0.232768i	0.0719311	−	0.997410i	$-0.477084\pi$
$37$	4.35761	−	1.41587i	0.716387	−	0.232768i	0.644456	+	0.764641i	$0.277084\pi$
$38$	3.00925	−	0.977766i	0.488165	−	0.158615i
$39$	0.827310	−	2.54620i	0.132476	−	0.407718i
$40$		0			0
$41$	−3.47998	−	10.7103i	−0.543481	−	1.67266i	−0.724574	−	0.689197i	$-0.757963\pi$
$41$	−3.47998	−	10.7103i	−0.543481	−	1.67266i	0.181093	−	0.983466i	$-0.442037\pi$
$42$	−2.66452	−	3.66740i	−0.411144	−	0.565892i
$43$		−	2.58587i		−	0.394342i	−0.980369	−	0.197171i	$-0.936825\pi$
$43$		−	2.58587i		−	0.394342i	0.980369	−	0.197171i	$-0.0631754\pi$
$44$	4.55609	−	3.31019i	0.686857	−	0.499031i
$45$		0			0
$46$	−8.83229	−	6.41703i	−1.30225	−	0.946140i
$47$	−1.12727	+	1.55155i	−0.164429	+	0.226317i	−0.883278	−	0.468849i	$-0.844669\pi$
$47$	−1.12727	+	1.55155i	−0.164429	+	0.226317i	0.718850	+	0.695166i	$0.244669\pi$
$48$	12.1831	+	3.95852i	1.75848	+	0.571364i
$49$	4.15389			0.593413
$50$		0			0
$51$	3.93167			0.550544
$52$	13.2917	+	4.31872i	1.84322	+	0.598899i
$53$	1.49803	−	2.06187i	0.205771	−	0.283219i	−0.693642	−	0.720320i	$-0.743995\pi$
$53$	1.49803	−	2.06187i	0.205771	−	0.283219i	0.899412	+	0.437101i	$0.143995\pi$
$54$	2.17386	+	1.57940i	0.295825	+	0.214930i
$55$		0			0
$56$	11.8097	−	8.58028i	1.57814	−	1.14659i
$57$			1.17755i			0.155970i
$58$	−9.40685	−	12.9474i	−1.23518	−	1.70008i
$59$	−0.412843	−	1.27060i	−0.0537476	−	0.165418i	0.920579	−	0.390555i	$-0.127717\pi$
$59$	−0.412843	−	1.27060i	−0.0537476	−	0.165418i	−0.974327	+	0.225137i	$0.927717\pi$
$60$		0			0
$61$	−2.24997	+	6.92470i	−0.288079	+	0.886617i	0.697379	+	0.716702i	$0.254349\pi$
$61$	−2.24997	+	6.92470i	−0.288079	+	0.886617i	−0.985459	+	0.169915i	$0.945651\pi$
$62$	−18.1522	+	5.89800i	−2.30533	+	0.749047i
$63$	1.60447	−	0.521325i	0.202145	−	0.0656807i
$64$	−6.29470	+	19.3731i	−0.786838	+	2.42164i
$65$		0			0
$66$	0.895787	+	2.75695i	0.110264	+	0.339357i
$67$	−7.31502	−	10.0683i	−0.893672	−	1.23003i	−0.972443	−	0.233141i	$-0.925100\pi$
$67$	−7.31502	−	10.0683i	−0.893672	−	1.23003i	0.0787711	−	0.996893i	$-0.474900\pi$
$68$			20.5241i			2.48891i
$69$	3.28699	−	2.38814i	0.395707	−	0.287498i
$70$		0			0
$71$	4.84181	+	3.51778i	0.574617	+	0.417484i	0.836779	−	0.547540i	$-0.184436\pi$
$71$	4.84181	+	3.51778i	0.574617	+	0.417484i	−0.262162	+	0.965024i	$0.584436\pi$
$72$	−5.08599	+	7.00026i	−0.599390	+	0.824989i
$73$	3.13911	+	1.01996i	0.367405	+	0.119377i	0.486900	−	0.873458i	$-0.338128\pi$
$73$	3.13911	+	1.01996i	0.367405	+	0.119377i	−0.119495	+	0.992835i	$0.538128\pi$
$74$	−12.3117			−1.43120
$75$		0			0
$76$	−6.14702			−0.705112
$77$	1.73093	+	0.562414i	0.197258	+	0.0640931i
$78$	−4.22843	+	5.81994i	−0.478776	+	0.658978i
$79$	−3.23934	−	2.35351i	−0.364454	−	0.264791i	0.390454	−	0.920623i	$-0.372318\pi$
$79$	−3.23934	−	2.35351i	−0.364454	−	0.264791i	−0.754907	+	0.655831i	$0.772318\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$			30.2600i			3.34166i
$83$	5.21649	+	7.17988i	0.572584	+	0.788094i	0.992858	−	0.119303i	$-0.0380661\pi$
$83$	5.21649	+	7.17988i	0.572584	+	0.788094i	−0.420274	+	0.907397i	$0.638066\pi$
$84$	2.72142	+	8.37566i	0.296931	+	0.913859i
$85$		0			0
$86$	−2.14716	+	6.60827i	−0.231534	+	0.712588i
$87$	5.66445	−	1.84049i	0.607292	−	0.197321i
$88$	−8.87792	+	2.88461i	−0.946389	+	0.307501i
$89$	−4.77234	+	14.6877i	−0.505867	+	1.55690i	0.293442	+	0.955977i	$0.405199\pi$
$89$	−4.77234	+	14.6877i	−0.505867	+	1.55690i	−0.799309	+	0.600920i	$0.794801\pi$
$90$		0			0
$91$	1.39571	+	4.29555i	0.146310	+	0.450296i
$92$	12.4666	+	17.1587i	1.29973	+	1.78892i
$93$		−	7.10310i		−	0.736557i
$94$	4.16908	−	3.02901i	0.430008	−	0.312419i
$95$		0			0
$96$	−13.8468	−	10.0603i	−1.41323	−	1.02677i
$97$	6.32939	−	8.71166i	0.642652	−	0.884535i	−0.356101	−	0.934447i	$-0.615894\pi$
$97$	6.32939	−	8.71166i	0.642652	−	0.884535i	0.998754	+	0.0499122i	$0.0158941\pi$
$98$	−10.6154	−	3.44915i	−1.07232	−	0.348416i
$99$	−1.07882			−0.108425
$100$		0			0
$101$	−13.5654			−1.34981			−0.674905	−	0.737905i	$-0.735815\pi$
$101$	−13.5654			−1.34981			−0.674905	+	0.737905i	$0.735815\pi$
$102$	−10.0475	−	3.26463i	−0.994850	−	0.323246i
$103$	−0.804700	+	1.10757i	−0.0792894	+	0.109133i	−0.846819	−	0.531880i	$-0.821486\pi$
$103$	−0.804700	+	1.10757i	−0.0792894	+	0.109133i	0.767530	+	0.641013i	$0.221486\pi$
$104$	−18.7413	−	13.6164i	−1.83774	−	1.33520i
$105$		0			0
$106$	−5.54032	+	4.02528i	−0.538124	+	0.390970i
$107$			11.0115i			1.06452i	0.846579	+	0.532262i	$0.178658\pi$
$107$			11.0115i			1.06452i	−0.846579	+	0.532262i	$0.821342\pi$
$108$	−3.06835	−	4.22323i	−0.295253	−	0.406380i
$109$	−1.06577	−	3.28010i	−0.102082	−	0.314176i	0.886952	−	0.461861i	$-0.152818\pi$
$109$	−1.06577	−	3.28010i	−0.102082	−	0.314176i	−0.989035	+	0.147684i	$0.952818\pi$
$110$		0			0
$111$	1.41587	−	4.35761i	0.134389	−	0.413606i
$112$	−20.5534	+	6.67820i	−1.94211	+	0.631030i
$113$	5.75574	−	1.87015i	0.541455	−	0.175929i	−0.0255053	−	0.999675i	$-0.508119\pi$
$113$	5.75574	−	1.87015i	0.541455	−	0.175929i	0.566960	+	0.823745i	$0.308119\pi$
$114$	0.977766	−	3.00925i	0.0915762	−	0.281842i
$115$		0			0
$116$	9.60772	+	29.5695i	0.892054	+	2.74546i
$117$	−1.57364	−	2.16593i	−0.145483	−	0.200240i
$118$			3.58986i			0.330473i
$119$	−5.36612	+	3.89872i	−0.491912	+	0.357395i
$120$		0			0
$121$	7.95761	+	5.78155i	0.723419	+	0.525595i
$122$	11.4997	−	15.8280i	1.04114	−	1.43300i
$123$	−10.7103	−	3.47998i	−0.965713	−	0.313779i
$124$	37.0796			3.32984
$125$		0			0
$126$	−4.53315			−0.403845
$127$	−19.2457	−	6.25332i	−1.70778	−	0.554893i	−0.717822	−	0.696227i	$-0.754861\pi$
$127$	−19.2457	−	6.25332i	−1.70778	−	0.554893i	−0.989962	+	0.141334i	$0.954861\pi$
$128$	12.0521	−	16.5882i	1.06526	−	1.46621i
$129$	−2.09201	−	1.51994i	−0.184192	−	0.133823i
$130$		0			0
$131$	2.46759	−	1.79281i	0.215595	−	0.156639i	−0.474747	−	0.880122i	$-0.657460\pi$
$131$	2.46759	−	1.79281i	0.215595	−	0.156639i	0.690341	+	0.723484i	$0.257460\pi$
$132$		−	5.63164i		−	0.490171i
$133$	−1.16768	−	1.60717i	−0.101250	−	0.139359i
$134$	10.3336	+	31.8037i	0.892691	+	2.74742i
$135$		0			0
$136$	10.5127	−	32.3549i	0.901460	−	2.77441i
$137$	19.5062	−	6.33795i	1.66653	−	0.541487i	0.684302	−	0.729199i	$-0.260107\pi$
$137$	19.5062	−	6.33795i	1.66653	−	0.541487i	0.982224	+	0.187711i	$0.0601069\pi$
$138$	−10.3830	+	3.37363i	−0.883858	+	0.287183i
$139$	−5.66068	+	17.4218i	−0.480133	+	1.47770i	0.358775	+	0.933424i	$0.383194\pi$
$139$	−5.66068	+	17.4218i	−0.480133	+	1.47770i	−0.838908	+	0.544273i	$0.816806\pi$
$140$		0			0
$141$	0.592639	+	1.82396i	0.0499092	+	0.153605i
$142$	−9.45242	−	13.0101i	−0.793230	−	1.09179i
$143$		−	2.88825i		−	0.241527i
$144$	10.3635	−	7.52956i	0.863629	−	0.627463i
$145$		0			0
$146$	−7.17517	−	5.21306i	−0.593821	−	0.431436i
$147$	2.44159	−	3.36057i	0.201379	−	0.277175i
$148$	22.7476	+	7.39114i	1.86984	+	0.607548i
$149$	−0.705938			−0.0578327			−0.0289163	−	0.999582i	$-0.509206\pi$
$149$	−0.705938			−0.0578327			−0.0289163	+	0.999582i	$0.509206\pi$
$150$		0			0
$151$	7.04538			0.573345			0.286673	−	0.958029i	$-0.407451\pi$
$151$	7.04538			0.573345			0.286673	+	0.958029i	$0.407451\pi$
$152$	9.69039	+	3.14860i	0.785994	+	0.255385i
$153$	2.31098	−	3.18079i	0.186831	−	0.257151i
$154$	−3.95645	−	2.87453i	−0.318820	−	0.231636i
$155$		0			0
$156$	11.3066	−	8.21470i	0.905249	−	0.657702i
$157$		−	5.12880i		−	0.409323i	−0.978833	−	0.204662i	$-0.934391\pi$
$157$		−	5.12880i		−	0.409323i	0.978833	−	0.204662i	$-0.0656094\pi$
$158$	6.32399	+	8.70423i	0.503110	+	0.692471i
$159$	−0.787563	−	2.42387i	−0.0624578	−	0.192225i
$160$		0			0
$161$	−2.11811	+	6.51888i	−0.166931	+	0.513760i
$162$	2.55553	−	0.830342i	0.200781	−	0.0652378i
$163$	−23.0739	+	7.49715i	−1.80728	+	0.587222i	−0.999996	−	0.00293441i	$-0.999066\pi$
$163$	−23.0739	+	7.49715i	−1.80728	+	0.587222i	−0.807289	+	0.590157i	$0.799066\pi$
$164$	18.1662	−	55.9097i	1.41854	−	4.36581i
$165$		0			0
$166$	−7.36913	−	22.6799i	−0.571955	−	1.76030i
$167$	−2.67377	−	3.68013i	−0.206903	−	0.284777i	0.692937	−	0.720998i	$-0.256317\pi$
$167$	−2.67377	−	3.68013i	−0.206903	−	0.284777i	−0.899840	+	0.436221i	$0.856317\pi$
$168$		−	14.5976i		−	1.12623i
$169$	−4.71853	+	3.42821i	−0.362964	+	0.263709i
$170$		0			0
$171$	0.952655	+	0.692144i	0.0728513	+	0.0529296i
$172$	7.93437	−	10.9207i	0.604990	−	0.832697i
$173$	2.54625	+	0.827327i	0.193588	+	0.0629005i	0.404206	−	0.914668i	$-0.367548\pi$
$173$	2.54625	+	0.827327i	0.193588	+	0.0629005i	−0.210618	+	0.977568i	$0.567548\pi$
$174$	−16.0039			−1.21325
$175$		0			0
$176$	13.8197			1.04170
$177$	−1.27060	−	0.412843i	−0.0955042	−	0.0310312i
$178$	24.3917	−	33.5723i	1.82823	−	2.51635i
$179$	−12.6422	−	9.18511i	−0.944924	−	0.686528i	0.00467674	−	0.999989i	$-0.498511\pi$
$179$	−12.6422	−	9.18511i	−0.944924	−	0.686528i	−0.949601	+	0.313461i	$0.898511\pi$
$180$		0			0
$181$	−0.164103	+	0.119228i	−0.0121977	+	0.00886215i	−0.593867	−	0.804563i	$-0.702400\pi$
$181$	−0.164103	+	0.119228i	−0.0121977	+	0.00886215i	0.581670	+	0.813425i	$0.302400\pi$
$182$		−	12.1363i		−	0.899603i
$183$	4.27970	+	5.89050i	0.316365	+	0.435439i
$184$	−10.8638	−	33.4352i	−0.800887	−	2.46488i
$185$		0			0
$186$	−5.89800	+	18.1522i	−0.432462	+	1.33098i
$187$	4.03396	−	1.31071i	0.294992	−	0.0958488i
$188$	−9.52141	+	3.09369i	−0.694420	+	0.225631i
$189$	0.521325	−	1.60447i	0.0379208	−	0.116708i
$190$		0			0
$191$	−2.44734	−	7.53213i	−0.177083	−	0.545006i	0.822639	−	0.568563i	$-0.192501\pi$
$191$	−2.44734	−	7.53213i	−0.177083	−	0.545006i	−0.999722	+	0.0235578i	$0.992501\pi$
$192$	11.9732	+	16.4798i	0.864094	+	1.18932i
$193$			16.4269i			1.18243i	0.806513	+	0.591216i	$0.201352\pi$
$193$			16.4269i			1.18243i	−0.806513	+	0.591216i	$0.798648\pi$
$194$	−23.4086	+	17.0073i	−1.68064	+	1.22106i
$195$		0			0
$196$	17.5428	+	12.7456i	1.25306	+	0.910400i
$197$	−10.0728	+	13.8640i	−0.717657	+	0.987770i	0.281942	+	0.959432i	$0.409022\pi$
$197$	−10.0728	+	13.8640i	−0.717657	+	0.987770i	−0.999598	+	0.0283382i	$0.990978\pi$
$198$	2.75695	+	0.895787i	0.195928	+	0.0636608i
$199$	2.01848			0.143086			0.0715430	−	0.997438i	$-0.477208\pi$
$199$	2.01848			0.143086			0.0715430	+	0.997438i	$0.477208\pi$
$200$		0			0
$201$	−12.4451			−0.877806
$202$	34.6668	+	11.2639i	2.43915	+	0.792528i
$203$	−5.90603	+	8.12895i	−0.414522	+	0.570541i
$204$	16.6043	+	12.0638i	1.16254	+	0.844632i
$205$		0			0
$206$	2.97610	−	2.16226i	0.207355	−	0.150652i
$207$		−	4.06295i		−	0.282394i
$208$	20.1584	+	27.7456i	1.39773	+	1.92381i
$209$	0.392562	+	1.20818i	0.0271541	+	0.0835717i
$210$		0			0
$211$	−7.36119	+	22.6554i	−0.506765	+	1.55966i	0.291018	+	0.956718i	$0.406006\pi$
$211$	−7.36119	+	22.6554i	−0.506765	+	1.55966i	−0.797783	+	0.602945i	$0.793994\pi$
$212$	12.6531	−	4.11123i	0.869017	−	0.282361i
$213$	5.69189	−	1.84941i	0.390002	−	0.126719i
$214$	9.14333	−	28.1403i	0.625025	−	1.92363i
$215$		0			0
$216$	2.67386	+	8.22930i	0.181933	+	0.559933i
$217$	7.04356	+	9.69463i	0.478148	+	0.658115i
$218$			9.26733i			0.627663i
$219$	2.67028	−	1.94007i	0.180441	−	0.131098i
$220$		0			0
$221$	8.51571	+	6.18702i	0.572828	+	0.416184i
$222$	−7.23662	+	9.96035i	−0.485690	+	0.668495i
$223$	−12.4695	−	4.05158i	−0.835017	−	0.271314i	−0.139860	−	0.990171i	$-0.544665\pi$
$223$	−12.4695	−	4.05158i	−0.835017	−	0.271314i	−0.695157	+	0.718858i	$0.744665\pi$
$224$	28.8746			1.92927
$225$		0			0
$226$	−16.2618			−1.08172
$227$	−24.9944	−	8.12118i	−1.65894	−	0.539022i	−0.678289	−	0.734795i	$-0.737278\pi$
$227$	−24.9944	−	8.12118i	−1.65894	−	0.539022i	−0.980649	+	0.195774i	$0.937278\pi$
$228$	−3.61313	+	4.97305i	−0.239285	+	0.329348i
$229$	1.61484	+	1.17325i	0.106711	+	0.0775304i	0.639861	−	0.768490i	$-0.278992\pi$
$229$	1.61484	+	1.17325i	0.106711	+	0.0775304i	−0.533150	+	0.846021i	$0.678992\pi$
$230$		0			0
$231$	1.47242	−	1.06978i	0.0968781	−	0.0703861i
$232$		−	51.5357i		−	3.38348i
$233$	−0.308910	−	0.425178i	−0.0202373	−	0.0278543i	0.798778	−	0.601625i	$-0.205480\pi$
$233$	−0.308910	−	0.425178i	−0.0202373	−	0.0278543i	−0.819016	+	0.573771i	$0.805480\pi$
$234$	2.22302	+	6.84175i	0.145323	+	0.447259i
$235$		0			0
$236$	2.15512	−	6.63278i	0.140286	−	0.431757i
$237$	−3.80807	+	1.23732i	−0.247361	+	0.0803723i
$238$	16.9505	−	5.50757i	1.09874	−	0.357002i
$239$	2.16612	−	6.66663i	0.140115	−	0.431229i	−0.856236	−	0.516585i	$-0.827203\pi$
$239$	2.16612	−	6.66663i	0.140115	−	0.431229i	0.996350	+	0.0853565i	$0.0272029\pi$
$240$		0			0
$241$	0.715542	+	2.20221i	0.0460921	+	0.141857i	0.971454	−	0.237228i	$-0.0762388\pi$
$241$	0.715542	+	2.20221i	0.0460921	+	0.141857i	−0.925362	+	0.379085i	$0.876239\pi$
$242$	−15.5353	−	21.3824i	−0.998644	−	1.37452i
$243$			1.00000i			0.0641500i
$244$	−30.7496	+	22.3409i	−1.96854	+	1.43023i
$245$		0			0
$246$	24.4808	+	17.7864i	1.56084	+	1.13402i
$247$	−1.85303	+	2.55048i	−0.117906	+	0.162283i
$248$	−58.4536	−	18.9927i	−3.71180	−	1.20604i
$249$	8.87482			0.562419
$250$		0			0
$251$	−6.17885			−0.390005			−0.195003	−	0.980803i	$-0.562472\pi$
$251$	−6.17885			−0.390005			−0.195003	+	0.980803i	$0.562472\pi$
$252$	8.37566	+	2.72142i	0.527617	+	0.171433i
$253$	2.57637	−	3.54607i	0.161975	−	0.222939i
$254$	43.9907	+	31.9611i	2.76022	+	2.00542i
$255$		0			0
$256$	−11.6138	+	8.43794i	−0.725864	+	0.527371i
$257$			13.2239i			0.824882i	0.910984	+	0.412441i	$0.135324\pi$
$257$			13.2239i			0.824882i	−0.910984	+	0.412441i	$0.864676\pi$
$258$	4.08413	+	5.62133i	0.254267	+	0.349969i
$259$	2.38864	+	7.35148i	0.148423	+	0.456799i
$260$		0			0
$261$	1.84049	−	5.66445i	0.113923	−	0.350620i
$262$	−7.79465	+	2.53264i	−0.481555	+	0.156467i
$263$	−6.63498	+	2.15583i	−0.409130	+	0.132934i	−0.506349	−	0.862329i	$-0.669005\pi$
$263$	−6.63498	+	2.15583i	−0.409130	+	0.132934i	0.0972190	+	0.995263i	$0.469005\pi$
$264$	−2.88461	+	8.87792i	−0.177536	+	0.546398i
$265$		0			0
$266$	1.64953	+	5.07674i	0.101139	+	0.311275i
$267$	9.07752	+	12.4941i	0.555535	+	0.764629i
$268$		−	64.9656i		−	3.96841i
$269$	19.1898	−	13.9422i	1.17002	−	0.850070i	0.179010	−	0.983847i	$-0.442711\pi$
$269$	19.1898	−	13.9422i	1.17002	−	0.850070i	0.991011	+	0.133777i	$0.0427107\pi$
$270$		0			0
$271$	−23.4542	−	17.0405i	−1.42474	−	1.03514i	−0.990966	−	0.134114i	$-0.957181\pi$
$271$	−23.4542	−	17.0405i	−1.42474	−	1.03514i	−0.433775	−	0.901021i	$-0.642819\pi$
$272$	−29.6037	+	40.7460i	−1.79499	+	2.47059i
$273$	4.29555	+	1.39571i	0.259978	+	0.0844721i
$274$	−55.1113			−3.32940
$275$		0			0
$276$	21.2094			1.27665
$277$	−8.16641	−	2.65343i	−0.490672	−	0.159429i	0.0532223	−	0.998583i	$-0.483051\pi$
$277$	−8.16641	−	2.65343i	−0.490672	−	0.159429i	−0.543894	+	0.839154i	$0.683051\pi$
$278$	28.9321	−	39.8216i	1.73523	−	2.38834i
$279$	−5.74653	−	4.17510i	−0.344036	−	0.249957i
$280$		0			0
$281$	−13.8877	+	10.0900i	−0.828471	+	0.601919i	−0.919126	−	0.393963i	$-0.871104\pi$
$281$	−13.8877	+	10.0900i	−0.828471	+	0.601919i	0.0906557	+	0.995882i	$0.471104\pi$
$282$		−	5.15327i		−	0.306872i
$283$	−5.65452	−	7.78278i	−0.336126	−	0.462638i	0.607179	−	0.794565i	$-0.292301\pi$
$283$	−5.65452	−	7.78278i	−0.336126	−	0.462638i	−0.943305	+	0.331927i	$0.892301\pi$
$284$	9.65426	+	29.7128i	0.572875	+	1.76313i
$285$		0			0
$286$	−2.39823	+	7.38100i	−0.141810	+	0.436447i
$287$	18.0687	−	5.87087i	1.06656	−	0.346546i
$288$	−16.2779	+	5.28899i	−0.959182	+	0.311657i
$289$	0.476498	−	1.46651i	0.0280293	−	0.0862654i
$290$		0			0
$291$	−3.32756	−	10.2412i	−0.195065	−	0.600348i
$292$	10.1276	+	13.9394i	0.592671	+	0.815742i
$293$		−	16.8202i		−	0.982649i	−0.870977	−	0.491324i	$-0.836513\pi$
$293$		−	16.8202i		−	0.982649i	0.870977	−	0.491324i	$-0.163487\pi$
$294$	−9.02998	+	6.56067i	−0.526639	+	0.382626i
$295$		0			0
$296$	−32.0743	−	23.3033i	−1.86428	−	1.35448i
$297$	−0.634113	+	0.872782i	−0.0367950	+	0.0506439i
$298$	1.80404	+	0.586170i	0.104505	+	0.0339559i
$299$	10.8775			0.629059
$300$		0			0
$301$	4.36247			0.251449
$302$	−18.0047	−	5.85008i	−1.03605	−	0.336634i
$303$	−7.97356	+	10.9747i	−0.458069	+	0.630478i
$304$	−12.2036	−	8.86641i	−0.699922	−	0.508523i
$305$		0			0
$306$	−8.54691	+	6.20969i	−0.488594	+	0.354984i
$307$			11.3212i			0.646134i	0.946376	+	0.323067i	$0.104714\pi$
$307$			11.3212i			0.646134i	−0.946376	+	0.323067i	$0.895286\pi$
$308$	5.58444	+	7.68632i	0.318203	+	0.437969i
$309$	0.423056	+	1.30203i	0.0240668	+	0.0740700i
$310$		0			0
$311$	5.73642	−	17.6549i	0.325283	−	1.00112i	−0.646030	−	0.763312i	$-0.723572\pi$
$311$	5.73642	−	17.6549i	0.325283	−	1.00112i	0.971313	−	0.237805i	$-0.0764280\pi$
$312$	−22.0318	+	7.15855i	−1.24730	+	0.405273i
$313$	−9.22478	+	2.99731i	−0.521416	+	0.169418i	−0.557888	−	0.829916i	$-0.688388\pi$
$313$	−9.22478	+	2.99731i	−0.521416	+	0.169418i	0.0364720	+	0.999335i	$0.488388\pi$
$314$	−4.25866	+	13.1068i	−0.240330	+	0.739660i
$315$		0			0
$316$	−6.45903	−	19.8789i	−0.363349	−	1.11827i
$317$	−4.39456	−	6.04859i	−0.246823	−	0.339723i	0.667573	−	0.744545i	$-0.267333\pi$
$317$	−4.39456	−	6.04859i	−0.246823	−	0.339723i	−0.914395	+	0.404822i	$0.867333\pi$
$318$			6.84822i			0.384029i
$319$	5.19825	−	3.77675i	0.291046	−	0.211457i
$320$		0			0
$321$	8.90851	+	6.47241i	0.497225	+	0.361255i
$322$	10.8258	−	14.9004i	0.603298	−	0.830369i
$323$	−4.40313	−	1.43066i	−0.244997	−	0.0796042i
$324$	−5.22020			−0.290011
$325$		0			0
$326$	65.1911			3.61060
$327$	−3.28010	−	1.06577i	−0.181390	−	0.0589371i
$328$	−57.2756	+	78.8331i	−3.16252	+	4.35283i
$329$	−2.61753	−	1.90175i	−0.144309	−	0.104847i
$330$		0			0
$331$	20.4333	−	14.8457i	1.12312	−	0.815993i	0.138439	−	0.990371i	$-0.455791\pi$
$331$	20.4333	−	14.8457i	1.12312	−	0.815993i	0.984679	+	0.174378i	$0.0557914\pi$
$332$			46.3283i			2.54259i
$333$	−2.69315	−	3.70681i	−0.147584	−	0.203132i
$334$	3.77714	+	11.6248i	0.206676	+	0.636083i
$335$		0			0
$336$	−6.67820	+	20.5534i	−0.364325	+	1.12128i
$337$	12.3866	−	4.02464i	0.674739	−	0.219236i	0.0484485	−	0.998826i	$-0.484572\pi$
$337$	12.3866	−	4.02464i	0.674739	−	0.219236i	0.626291	+	0.779590i	$0.284572\pi$
$338$	14.9049	−	4.84291i	0.810721	−	0.263419i
$339$	1.87015	−	5.75574i	0.101573	−	0.312609i
$340$		0			0
$341$	−2.36798	−	7.28790i	−0.128233	−	0.394662i
$342$	−1.85982	−	2.55982i	−0.100568	−	0.138419i
$343$			18.8171i			1.01603i
$344$	−18.1018	+	13.1517i	−0.975983	+	0.709093i
$345$		0			0
$346$	−5.82005	−	4.22852i	−0.312888	−	0.227326i
$347$	−3.52759	+	4.85531i	−0.189371	+	0.260647i	−0.893137	−	0.449785i	$-0.851500\pi$
$347$	−3.52759	+	4.85531i	−0.189371	+	0.260647i	0.703766	+	0.710432i	$0.251500\pi$
$348$	29.5695	+	9.60772i	1.58509	+	0.515028i
$349$	22.7183			1.21608			0.608042	−	0.793905i	$-0.291955\pi$
$349$	22.7183			1.21608			0.608042	+	0.793905i	$0.291955\pi$
$350$		0			0
$351$	−2.67723			−0.142900
$352$	−17.5608	−	5.70586i	−0.935996	−	0.304123i
$353$	2.85366	−	3.92772i	0.151885	−	0.209052i	−0.726294	−	0.687385i	$-0.758759\pi$
$353$	2.85366	−	3.92772i	0.151885	−	0.209052i	0.878179	+	0.478333i	$0.158759\pi$
$354$	2.90425	+	2.11006i	0.154359	+	0.112149i
$355$		0			0
$356$	−65.2218	+	47.3864i	−3.45675	+	2.51148i
$357$			6.63289i			0.351050i
$358$	24.6808	+	33.9702i	1.30442	+	1.79538i
$359$	−8.92780	−	27.4769i	−0.471191	−	1.45018i	−0.851026	−	0.525123i	$-0.824019\pi$
$359$	−8.92780	−	27.4769i	−0.471191	−	1.45018i	0.379835	−	0.925054i	$-0.375981\pi$
$360$		0			0
$361$	−5.44284	+	16.7513i	−0.286465	+	0.881649i
$362$	0.518371	−	0.168429i	0.0272450	−	0.00885242i
$363$	9.35474	−	3.03954i	0.490996	−	0.159534i
$364$	−7.28587	+	22.4236i	−0.381883	+	1.17532i
$365$		0			0
$366$	−6.04577	−	18.6070i	−0.316018	−	0.972602i
$367$	8.64570	+	11.8998i	0.451302	+	0.621163i	0.972677	−	0.232164i	$-0.0745807\pi$
$367$	8.64570	+	11.8998i	0.451302	+	0.621163i	−0.521375	+	0.853328i	$0.674581\pi$
$368$			52.0465i			2.71311i
$369$	−9.11070	+	6.61931i	−0.474284	+	0.344588i
$370$		0			0
$371$	3.47846	+	2.52725i	0.180592	+	0.131208i
$372$	21.7948	−	29.9980i	1.13001	−	1.55532i
$373$	31.4220	+	10.2096i	1.62697	+	0.528635i	0.973572	−	0.228378i	$-0.0733423\pi$
$373$	31.4220	+	10.2096i	1.62697	+	0.528635i	0.653399	+	0.757013i	$0.273342\pi$
$374$	−11.3972			−0.589337
$375$		0			0
$376$	16.5945			0.855797
$377$	15.1650	+	4.92742i	0.781039	+	0.253775i
$378$	−2.66452	+	3.66740i	−0.137048	+	0.188631i
$379$	−12.2612	−	8.90826i	−0.629814	−	0.457587i	0.226522	−	0.974006i	$-0.427265\pi$
$379$	−12.2612	−	8.90826i	−0.629814	−	0.457587i	−0.856336	+	0.516419i	$0.827265\pi$
$380$		0			0
$381$	−16.3714	+	11.8945i	−0.838733	+	0.609375i
$382$			21.2807i			1.08882i
$383$	−4.70705	−	6.47870i	−0.240519	−	0.331046i	0.671644	−	0.740874i	$-0.265589\pi$
$383$	−4.70705	−	6.47870i	−0.240519	−	0.331046i	−0.912163	+	0.409828i	$0.865589\pi$
$384$	−6.33615	−	19.5007i	−0.323340	−	0.995139i
$385$		0			0
$386$	13.6399	−	41.9793i	0.694253	−	2.13669i
$387$	−2.45931	+	0.799078i	−0.125014	+	0.0406194i
$388$	53.4609	−	17.3705i	2.71407	−	0.881854i
$389$	−0.332078	+	1.02203i	−0.0168370	+	0.0518191i	−0.959122	−	0.282993i	$-0.908673\pi$
$389$	−0.332078	+	1.02203i	−0.0168370	+	0.0518191i	0.942285	+	0.334812i	$0.108673\pi$
$390$		0			0
$391$	4.93629	+	15.1923i	0.249639	+	0.768309i
$392$	−21.1266	−	29.0783i	−1.06706	−	1.46868i
$393$		−	3.05011i		−	0.153858i
$394$	37.2532	−	27.0660i	1.87679	−	1.36357i
$395$		0			0
$396$	−4.55609	−	3.31019i	−0.228952	−	0.166344i
$397$	−14.2326	+	19.5894i	−0.714312	+	0.983166i	0.285382	+	0.958414i	$0.407880\pi$
$397$	−14.2326	+	19.5894i	−0.714312	+	0.983166i	−0.999694	+	0.0247517i	$0.992120\pi$
$398$	−5.15828	−	1.67603i	−0.258561	−	0.0840116i
$399$	−1.98657			−0.0994529
$400$		0			0
$401$	−1.99317			−0.0995340			−0.0497670	−	0.998761i	$-0.515848\pi$
$401$	−1.99317			−0.0995340			−0.0497670	+	0.998761i	$0.515848\pi$
$402$	31.8037	+	10.3336i	1.58622	+	0.515395i
$403$	11.1777	−	15.3848i	0.556801	−	0.766371i
$404$	−57.2899	−	41.6235i	−2.85028	−	2.07085i
$405$		0			0
$406$	21.8428	−	15.8698i	1.08404	−	0.787603i
$407$		−	4.94300i		−	0.245015i
$408$	−19.9964	−	27.5227i	−0.989971	−	1.36258i
$409$	−2.05953	−	6.33858i	−0.101837	−	0.313423i	0.887138	−	0.461504i	$-0.152690\pi$
$409$	−2.05953	−	6.33858i	−0.101837	−	0.313423i	−0.988975	+	0.148082i	$0.952690\pi$
$410$		0			0
$411$	6.33795	−	19.5062i	0.312628	−	0.962169i
$412$	−6.79686	+	2.20843i	−0.334857	+	0.108802i
$413$	2.14356	−	0.696484i	0.105477	−	0.0342717i
$414$	−3.37363	+	10.3830i	−0.165805	+	0.510295i
$415$		0			0
$416$	−14.1599	−	43.5796i	−0.694245	−	2.13667i
$417$	10.7673	+	14.8199i	0.527275	+	0.725732i
$418$		−	3.41351i		−	0.166960i
$419$	17.2758	−	12.5516i	0.843977	−	0.613185i	−0.0795021	−	0.996835i	$-0.525333\pi$
$419$	17.2758	−	12.5516i	0.843977	−	0.613185i	0.923479	+	0.383650i	$0.125333\pi$
$420$		0			0
$421$	−18.0708	−	13.1292i	−0.880717	−	0.639878i	0.0527243	−	0.998609i	$-0.483210\pi$
$421$	−18.0708	−	13.1292i	−0.880717	−	0.639878i	−0.933441	+	0.358731i	$0.883210\pi$
$422$	37.6235	−	51.7842i	1.83148	−	2.52082i
$423$	1.82396	+	0.592639i	0.0886838	+	0.0288151i
$424$	−22.0526			−1.07097
$425$		0			0
$426$	−16.0814			−0.779147
$427$	−11.6823	−	3.79580i	−0.565344	−	0.183692i
$428$	−33.7873	+	46.5042i	−1.63317	+	2.24786i
$429$	−2.33664	−	1.69767i	−0.112814	−	0.0819642i
$430$		0			0
$431$	24.6046	−	17.8763i	1.18516	−	0.861070i	0.192416	−	0.981313i	$-0.438368\pi$
$431$	24.6046	−	17.8763i	1.18516	−	0.861070i	0.992744	+	0.120244i	$0.0383677\pi$
$432$		−	12.8101i		−	0.616324i
$433$	0.338940	+	0.466511i	0.0162884	+	0.0224191i	0.817084	−	0.576519i	$-0.195589\pi$
$433$	0.338940	+	0.466511i	0.0162884	+	0.0224191i	−0.800795	+	0.598938i	$0.795589\pi$
$434$	−9.95017	−	30.6235i	−0.477624	−	1.46997i
$435$		0			0
$436$	5.56352	−	17.1227i	0.266444	−	0.820031i
$437$	−4.55015	+	1.47843i	−0.217663	+	0.0707230i
$438$	−8.43491	+	2.74067i	−0.403036	+	0.130954i
$439$	−3.95681	+	12.1778i	−0.188848	+	0.581215i	−0.999993	−	0.00363006i	$-0.998845\pi$
$439$	−3.95681	+	12.1778i	−0.188848	+	0.581215i	0.811145	+	0.584845i	$0.198845\pi$
$440$		0			0
$441$	−1.28362	−	3.95058i	−0.0611249	−	0.188123i
$442$	−16.6248	−	22.8821i	−0.790761	−	1.08839i
$443$		−	14.3147i		−	0.680110i	−0.940405	−	0.340055i	$-0.889554\pi$
$443$		−	14.3147i		−	0.680110i	0.940405	−	0.340055i	$-0.110446\pi$
$444$	19.3503	−	14.0588i	0.918323	−	0.667200i
$445$		0			0
$446$	28.5019	+	20.7078i	1.34960	+	0.980545i
$447$	−0.414940	+	0.571116i	−0.0196260	+	0.0270128i
$448$	−32.6833	−	10.6194i	−1.54414	−	0.501721i
$449$	11.9663			0.564724			0.282362	−	0.959308i	$-0.408882\pi$
$449$	11.9663			0.564724			0.282362	+	0.959308i	$0.408882\pi$
$450$		0			0
$451$	−12.1490			−0.572076
$452$	30.0461	+	9.76257i	1.41325	+	0.459193i
$453$	4.14117	−	5.69983i	0.194569	−	0.267802i
$454$	57.1306	+	41.5078i	2.68127	+	1.94806i
$455$		0			0
$456$	8.24313	−	5.98899i	0.386020	−	0.280460i
$457$		−	8.22154i		−	0.384587i	−0.981337	−	0.192294i	$-0.938407\pi$
$457$		−	8.22154i		−	0.384587i	0.981337	−	0.192294i	$-0.0615926\pi$
$458$	−3.15257	−	4.33913i	−0.147310	−	0.202754i
$459$	−1.21495	−	3.73924i	−0.0567091	−	0.174533i
$460$		0			0
$461$	0.393120	−	1.20990i	0.0183094	−	0.0563506i	−0.941484	−	0.337057i	$-0.890569\pi$
$461$	0.393120	−	1.20990i	0.0183094	−	0.0563506i	0.959794	+	0.280706i	$0.0905686\pi$
$462$	−4.65109	+	1.51123i	−0.216388	+	0.0703088i
$463$	31.0771	−	10.0976i	1.44428	−	0.469273i	0.521048	−	0.853527i	$-0.325541\pi$
$463$	31.0771	−	10.0976i	1.44428	−	0.469273i	0.923227	+	0.384254i	$0.125541\pi$
$464$	−23.5768	+	72.5618i	−1.09452	+	3.36860i
$465$		0			0
$466$	0.436385	+	1.34305i	0.0202151	+	0.0622158i
$467$	−8.48450	−	11.6779i	−0.392616	−	0.540389i	0.566256	−	0.824230i	$-0.308391\pi$
$467$	−8.48450	−	11.6779i	−0.392616	−	0.540389i	−0.958872	+	0.283840i	$0.908391\pi$
$468$		−	13.9757i		−	0.646026i
$469$	16.9856	−	12.3407i	0.784321	−	0.569843i
$470$		0			0
$471$	−4.14929	−	3.01464i	−0.191189	−	0.138907i
$472$	−6.79482	+	9.35227i	−0.312757	+	0.430473i
$473$	−2.65315	−	0.862060i	−0.121992	−	0.0396375i
$474$	10.7590			0.494178
$475$		0			0
$476$	−34.6250			−1.58703
$477$	−2.42387	−	0.787563i	−0.110981	−	0.0360600i
$478$	−11.0712	+	15.2382i	−0.506383	+	0.696977i
$479$	−13.6415	−	9.91113i	−0.623296	−	0.452851i	0.230775	−	0.973007i	$-0.425874\pi$
$479$	−13.6415	−	9.91113i	−0.623296	−	0.452851i	−0.854071	+	0.520156i	$0.825874\pi$
$480$		0			0
$481$	9.92398	−	7.21020i	0.452495	−	0.328757i
$482$		−	6.22196i		−	0.283403i
$483$	4.02889	+	5.54529i	0.183321	+	0.252320i
$484$	15.8670	+	48.8336i	0.721227	+	2.21971i
$485$		0			0
$486$	0.830342	−	2.55553i	0.0376651	−	0.115921i
$487$	−37.8744	+	12.3061i	−1.71625	+	0.557644i	−0.991354	−	0.131212i	$-0.958113\pi$
$487$	−37.8744	+	12.3061i	−1.71625	+	0.557644i	−0.724898	+	0.688856i	$0.758113\pi$
$488$	59.9181	−	19.4686i	2.71236	−	0.881301i
$489$	−7.49715	+	23.0739i	−0.339033	+	1.04344i
$490$		0			0
$491$	4.33411	+	13.3390i	0.195596	+	0.601981i	0.999969	+	0.00785739i	$0.00250111\pi$
$491$	4.33411	+	13.3390i	0.195596	+	0.601981i	−0.804374	+	0.594124i	$0.797499\pi$
$492$	−34.5541	−	47.5596i	−1.55782	−	2.14415i
$493$			23.4168i			1.05464i
$494$	6.85324	−	4.97917i	0.308342	−	0.224024i
$495$		0			0
$496$	73.6133	+	53.4832i	3.30534	+	2.40147i
$497$	−5.93464	+	8.16834i	−0.266205	+	0.366400i
$498$	−22.6799	−	7.36913i	−1.01631	−	0.330219i
$499$	−15.2315			−0.681857			−0.340929	−	0.940089i	$-0.610741\pi$
$499$	−15.2315			−0.681857			−0.340929	+	0.940089i	$0.610741\pi$
$500$		0			0
$501$	−4.54890			−0.203230
$502$	15.7902	+	5.13055i	0.704752	+	0.228988i
$503$	−13.9499	+	19.2004i	−0.621996	+	0.856104i	−0.997496	−	0.0707185i	$-0.977471\pi$
$503$	−13.9499	+	19.2004i	−0.621996	+	0.856104i	0.375501	+	0.926822i	$0.377471\pi$
$504$	−11.8097	−	8.58028i	−0.526048	−	0.382196i
$505$		0			0
$506$	−9.52843	+	6.92281i	−0.423590	+	0.307756i
$507$			5.83243i			0.259027i
$508$	−62.0918	−	85.4620i	−2.75488	−	3.79176i
$509$	3.86570	+	11.8974i	0.171344	+	0.527343i	0.999448	−	0.0332320i	$-0.0105800\pi$
$509$	3.86570	+	11.8974i	0.171344	+	0.527343i	−0.828103	+	0.560575i	$0.810580\pi$
$510$		0			0
$511$	−1.72071	+	5.29581i	−0.0761198	+	0.234273i
$512$	−2.31548	+	0.752345i	−0.102331	+	0.0332493i
$513$	1.11991	−	0.363882i	0.0494454	−	0.0160658i
$514$	10.9803	−	33.7940i	0.484321	−	1.49059i
$515$		0			0
$516$	−4.17134	−	12.8381i	−0.183633	−	0.565165i
$517$	1.21612	+	1.67384i	0.0534847	+	0.0736154i
$518$		−	20.7703i		−	0.912595i
$519$	2.16597	−	1.57367i	0.0950755	−	0.0690764i
$520$		0			0
$521$	22.6232	+	16.4367i	0.991141	+	0.720106i	0.960171	−	0.279414i	$-0.0901403\pi$
$521$	22.6232	+	16.4367i	0.991141	+	0.720106i	0.0309702	+	0.999520i	$0.490140\pi$
$522$	−9.40685	+	12.9474i	−0.411727	+	0.566693i
$523$	−14.9328	−	4.85196i	−0.652966	−	0.212162i	−0.0362446	−	0.999343i	$-0.511540\pi$
$523$	−14.9328	−	4.85196i	−0.652966	−	0.212162i	−0.616722	+	0.787181i	$0.711540\pi$
$524$	15.9222			0.695564
$525$		0			0
$526$	18.7460			0.817362
$527$	26.5602	+	8.62993i	1.15698	+	0.375926i
$528$	8.12302	−	11.1804i	0.353509	−	0.486564i
$529$	−5.25252	−	3.81618i	−0.228370	−	0.165921i
$530$		0			0
$531$	−1.08084	+	0.785274i	−0.0469043	+	0.0340780i
$532$		−	10.3703i		−	0.449609i
$533$	−17.7214	−	24.3915i	−0.767601	−	1.05651i
$534$	−12.8235	−	39.4666i	−0.554926	−	1.70789i
$535$		0			0
$536$	−33.2764	+	102.414i	−1.43732	+	4.42362i
$537$	−14.8618	+	4.82890i	−0.641335	+	0.208382i
$538$	−60.6168	+	19.6956i	−2.61338	+	0.849137i
$539$	1.38479	−	4.26196i	0.0596473	−	0.183576i
$540$		0			0
$541$	−7.40971	−	22.8048i	−0.318569	−	0.980453i	−0.974261	−	0.225425i	$-0.927623\pi$
$541$	−7.40971	−	22.8048i	−0.318569	−	0.980453i	0.655692	−	0.755028i	$-0.272377\pi$
$542$	45.7885	+	63.0224i	1.96678	+	2.70705i
$543$			0.202843i			0.00870482i
$544$	54.4409	−	39.5536i	2.33413	−	1.69585i
$545$		0			0
$546$	−9.81848	−	7.13354i	−0.420192	−	0.305287i
$547$	−3.30736	+	4.55219i	−0.141412	+	0.194637i	−0.873848	−	0.486198i	$-0.838383\pi$
$547$	−3.30736	+	4.55219i	−0.141412	+	0.194637i	0.732436	+	0.680836i	$0.238383\pi$
$548$	101.826	+	33.0853i	4.34980	+	1.41333i
$549$	7.28106			0.310748
$550$		0			0
$551$	−7.01341			−0.298781
$552$	−33.4352	−	10.8638i	−1.42310	−	0.462392i
$553$	3.97048	−	5.46490i	0.168842	−	0.232391i
$554$	18.6663	+	13.5618i	0.793053	+	0.576187i
$555$		0			0
$556$	−77.3626	+	56.2072i	−3.28090	+	2.38372i
$557$		−	42.4247i		−	1.79759i	−0.438366	−	0.898796i	$-0.644443\pi$
$557$		−	42.4247i		−	1.79759i	0.438366	−	0.898796i	$-0.355557\pi$
$558$	11.2187	+	15.4412i	0.474924	+	0.653677i
$559$	−2.13932	−	6.58414i	−0.0904835	−	0.278480i
$560$		0			0
$561$	1.31071	−	4.03396i	0.0553383	−	0.170314i
$562$	43.8686	−	14.2538i	1.85048	−	0.601259i
$563$	5.50279	−	1.78796i	0.231915	−	0.0753537i	−0.190754	−	0.981638i	$-0.561093\pi$
$563$	5.50279	−	1.78796i	0.231915	−	0.0753537i	0.422669	+	0.906284i	$0.361093\pi$
$564$	−3.09369	+	9.52141i	−0.130268	+	0.400924i
$565$		0			0
$566$	7.98793	+	24.5843i	0.335758	+	1.03336i
$567$	−0.991619	−	1.36485i	−0.0416441	−	0.0573181i
$568$		−	51.7853i		−	2.17286i
$569$	−17.8029	+	12.9346i	−0.746336	+	0.542245i	−0.894689	−	0.446690i	$-0.852603\pi$
$569$	−17.8029	+	12.9346i	−0.746336	+	0.542245i	0.148353	+	0.988934i	$0.452603\pi$
$570$		0			0
$571$	−27.1946	−	19.7580i	−1.13806	−	0.826847i	−0.151210	−	0.988502i	$-0.548317\pi$
$571$	−27.1946	−	19.7580i	−1.13806	−	0.826847i	−0.986847	+	0.161654i	$0.948317\pi$
$572$	8.86216	−	12.1977i	0.370546	−	0.510012i
$573$	−7.53213	−	2.44734i	−0.314659	−	0.102239i
$574$	−51.0499			−2.13078
$575$		0			0
$576$	20.3701			0.848754
$577$	38.2658	+	12.4333i	1.59303	+	0.517605i	0.965370	−	0.260886i	$-0.0840145\pi$
$577$	38.2658	+	12.4333i	1.59303	+	0.517605i	0.627656	+	0.778491i	$0.284015\pi$
$578$	−2.43541	+	3.35205i	−0.101300	+	0.139427i
$579$	13.2896	+	9.65547i	0.552297	+	0.401268i
$580$		0			0
$581$	−12.1128	+	8.80043i	−0.502522	+	0.365103i
$582$			28.9346i			1.19938i
$583$	−1.61611	−	2.22438i	−0.0669323	−	0.0921243i
$584$	−8.82549	−	27.1621i	−0.365201	−	1.12397i
$585$		0			0
$586$	−13.9665	+	42.9846i	−0.576952	+	1.77568i
$587$	2.68483	−	0.872353i	0.110815	−	0.0360059i	−0.253085	−	0.967444i	$-0.581445\pi$
$587$	2.68483	−	0.872353i	0.110815	−	0.0360059i	0.363899	+	0.931438i	$0.381445\pi$
$588$	20.6228	−	6.70076i	0.850471	−	0.276335i
$589$	−2.58469	+	7.95485i	−0.106500	+	0.327774i
$590$		0			0
$591$	5.29558	+	16.2981i	0.217831	+	0.670415i
$592$	34.4994	+	47.4844i	1.41792	+	1.95160i
$593$			24.6805i			1.01351i	0.862091	+	0.506754i	$0.169155\pi$
$593$			24.6805i			1.01351i	−0.862091	+	0.506754i	$0.830845\pi$
$594$	2.34520	−	1.70389i	0.0962248	−	0.0699114i
$595$		0			0
$596$	−2.98134	−	2.16607i	−0.122120	−	0.0887256i
$597$	1.18643	−	1.63298i	0.0485574	−	0.0668335i
$598$	−27.7976	−	9.03200i	−1.13673	−	0.369346i
$599$	7.71547			0.315245			0.157623	−	0.987499i	$-0.449617\pi$
$599$	7.71547			0.315245			0.157623	+	0.987499i	$0.449617\pi$
$600$		0			0
$601$	22.6506			0.923938			0.461969	−	0.886896i	$-0.347143\pi$
$601$	22.6506			0.923938			0.461969	+	0.886896i	$0.347143\pi$
$602$	−11.1484	−	3.62234i	−0.454376	−	0.147636i
$603$	−7.31502	+	10.0683i	−0.297891	+	0.410011i
$604$	29.7543	+	21.6177i	1.21068	+	0.879613i
$605$		0			0
$606$	29.4894	−	21.4253i	1.19792	−	0.870343i
$607$		−	24.6423i		−	1.00020i	−0.865968	−	0.500099i	$-0.833297\pi$
$607$		−	24.6423i		−	1.00020i	0.865968	−	0.500099i	$-0.166703\pi$
$608$	11.8464	+	16.3052i	0.480436	+	0.661264i
$609$	3.10498	+	9.55616i	0.125820	+	0.387235i
$610$		0			0
$611$	−1.58663	+	4.88315i	−0.0641883	+	0.197551i
$612$	19.5196	−	6.34229i	0.789031	−	0.256372i
$613$	−39.7574	+	12.9180i	−1.60579	+	0.521751i	−0.968529	−	0.248901i	$-0.919931\pi$
$613$	−39.7574	+	12.9180i	−1.60579	+	0.521751i	−0.637256	+	0.770652i	$0.719931\pi$
$614$	9.40045	−	28.9316i	0.379371	−	1.16758i
$615$		0			0
$616$	−4.86646	−	14.9774i	−0.196075	−	0.603458i
$617$	−9.36871	−	12.8949i	−0.377170	−	0.519130i	0.577662	−	0.816276i	$-0.303965\pi$
$617$	−9.36871	−	12.8949i	−0.377170	−	0.519130i	−0.954832	+	0.297146i	$0.903965\pi$
$618$		−	3.67866i		−	0.147977i
$619$	−38.1613	+	27.7258i	−1.53383	+	1.11440i	−0.579775	+	0.814777i	$0.696859\pi$
$619$	−38.1613	+	27.7258i	−1.53383	+	1.11440i	−0.954059	+	0.299619i	$0.903141\pi$
$620$		0			0
$621$	−3.28699	−	2.38814i	−0.131902	−	0.0958327i
$622$	−29.3192	+	40.3544i	−1.17559	+	1.61806i
$623$	−24.7788	−	8.05113i	−0.992743	−	0.322562i
$624$	34.2955			1.37292
$625$		0			0
$626$	26.0630			1.04169
$627$	1.20818	+	0.392562i	0.0482501	+	0.0156774i
$628$	15.7370	−	21.6601i	0.627974	−	0.864332i
$629$	14.5739	+	10.5886i	0.581101	+	0.422195i
$630$		0			0
$631$	−26.1825	+	19.0227i	−1.04231	+	0.757282i	−0.970735	−	0.240153i	$-0.922802\pi$
$631$	−26.1825	+	19.0227i	−1.04231	+	0.757282i	−0.0715741	+	0.997435i	$0.522802\pi$
$632$			34.6462i			1.37815i
$633$	14.0018	+	19.2718i	0.556522	+	0.765987i
$634$	6.20802	+	19.1063i	0.246552	+	0.758809i
$635$		0			0
$636$	4.11123	−	12.6531i	0.163021	−	0.501727i
$637$	10.5766	−	3.43656i	0.419061	−	0.136161i
$638$	−16.4203	+	5.33526i	−0.650084	+	0.211225i
$639$	1.84941	−	5.69189i	0.0731614	−	0.225168i
$640$		0			0
$641$	5.56360	+	17.1230i	0.219749	+	0.676317i	0.998782	+	0.0493350i	$0.0157102\pi$
$641$	5.56360	+	17.1230i	0.219749	+	0.676317i	−0.779033	+	0.626982i	$0.784290\pi$
$642$	−17.3916	−	23.9376i	−0.686394	−	0.944740i
$643$		−	21.8891i		−	0.863224i	−0.902059	−	0.431612i	$-0.857945\pi$
$643$		−	21.8891i		−	0.863224i	0.902059	−	0.431612i	$-0.142055\pi$
$644$	−28.9475	+	21.0316i	−1.14069	+	0.828761i
$645$		0			0
$646$	10.0644	+	7.31220i	0.395978	+	0.287695i
$647$	11.1834	−	15.3926i	0.439665	−	0.605147i	−0.530473	−	0.847702i	$-0.677985\pi$
$647$	11.1834	−	15.3926i	0.439665	−	0.605147i	0.970138	+	0.242555i	$0.0779855\pi$
$648$	8.22930	+	2.67386i	0.323278	+	0.105039i
$649$	−1.44129			−0.0565755
$650$		0			0
$651$	11.9832			0.469660
$652$	−120.450	−	39.1366i	−4.71719	−	1.53271i
$653$	1.36349	−	1.87669i	0.0533576	−	0.0734405i	−0.781504	−	0.623900i	$-0.785547\pi$
$653$	1.36349	−	1.87669i	0.0533576	−	0.0734405i	0.834862	+	0.550459i	$0.185547\pi$
$654$	7.49743	+	5.44720i	0.293173	+	0.213002i
$655$		0			0
$656$	116.709	−	84.7937i	4.55670	−	3.31064i
$657$		−	3.30065i		−	0.128771i
$658$	5.11007	+	7.03341i	0.199211	+	0.274191i
$659$	−2.22239	−	6.83980i	−0.0865719	−	0.266441i	0.898394	−	0.439191i	$-0.144735\pi$
$659$	−2.22239	−	6.83980i	−0.0865719	−	0.266441i	−0.984966	+	0.172750i	$0.944735\pi$
$660$		0			0
$661$	13.2943	−	40.9158i	0.517090	−	1.59144i	−0.262358	−	0.964971i	$-0.584500\pi$
$661$	13.2943	−	40.9158i	0.517090	−	1.59144i	0.779447	−	0.626468i	$-0.215500\pi$
$662$	−64.5450	+	20.9719i	−2.50861	+	0.815098i
$663$	10.0108	−	3.25271i	0.388788	−	0.126325i
$664$	23.7300	−	73.0336i	0.920904	−	2.83425i
$665$		0			0
$666$	3.80451	+	11.7091i	0.147422	+	0.453718i
$667$	14.2236	+	19.5772i	0.550742	+	0.758031i
$668$		−	23.7461i		−	0.918765i
$669$	−10.6072	+	7.70656i	−0.410097	+	0.297953i
$670$		0			0
$671$	6.35478	+	4.61702i	0.245324	+	0.178238i
$672$	16.9721	−	23.3601i	0.654713	−	0.901135i
$673$	28.3444	+	9.20966i	1.09260	+	0.355006i	0.799250	−	0.600999i	$-0.205231\pi$
$673$	28.3444	+	9.20966i	1.09260	+	0.355006i	0.293348	+	0.956006i	$0.405231\pi$
$674$	−34.9961			−1.34800
$675$		0			0
$676$	−30.4464			−1.17102
$677$	−25.4261	−	8.26144i	−0.977204	−	0.317513i	−0.223483	−	0.974708i	$-0.571743\pi$
$677$	−25.4261	−	8.26144i	−0.977204	−	0.317513i	−0.753721	+	0.657195i	$0.771743\pi$
$678$	−9.55846	+	13.1561i	−0.367091	+	0.505257i
$679$	14.6969	+	10.6780i	0.564017	+	0.409782i
$680$		0			0
$681$	−21.2615	+	15.4474i	−0.814743	+	0.591946i
$682$			20.5907i			0.788457i
$683$	16.7489	+	23.0529i	0.640880	+	0.882096i	0.998662	−	0.0517093i	$-0.0164669\pi$
$683$	16.7489	+	23.0529i	0.640880	+	0.882096i	−0.357782	+	0.933805i	$0.616467\pi$
$684$	1.89953	+	5.84617i	0.0726305	+	0.223534i
$685$		0			0
$686$	15.6246	−	48.0876i	0.596550	−	1.83599i
$687$	1.89835	−	0.616813i	0.0724267	−	0.0235329i
$688$	31.5039	−	10.2362i	1.20107	−	0.390253i
$689$	2.10849	−	6.48926i	0.0803270	−	0.247221i
$690$		0			0
$691$	10.7065	+	32.9512i	0.407294	+	1.25352i	0.918965	+	0.394340i	$0.129027\pi$
$691$	10.7065	+	32.9512i	0.407294	+	1.25352i	−0.511671	+	0.859182i	$0.670973\pi$
$692$	8.21486	+	11.3068i	0.312282	+	0.429820i
$693$		−	1.82001i		−	0.0691365i
$694$	13.0464	−	9.47878i	0.495235	−	0.359810i
$695$		0			0
$696$	−41.6932	−	30.2919i	−1.58038	−	1.14821i
$697$	26.0249	−	35.8203i	0.985765	−	1.35679i
$698$	−58.0574	−	18.8640i	−2.19750	−	0.714012i
$699$	−0.525548			−0.0198781
$700$		0			0
$701$	0.973305			0.0367612			0.0183806	−	0.999831i	$-0.494149\pi$
$701$	0.973305			0.0367612			0.0183806	+	0.999831i	$0.494149\pi$
$702$	6.84175	+	2.22302i	0.258225	+	0.0839024i
$703$	−3.17131	+	4.36494i	−0.119608	+	0.164627i
$704$	17.7786	+	12.9169i	0.670058	+	0.486826i
$705$		0			0
$706$	−10.5540	+	7.66790i	−0.397204	+	0.288585i
$707$		−	22.8854i		−	0.860696i
$708$	−4.09928	−	5.64218i	−0.154061	−	0.212046i
$709$	3.49938	+	10.7700i	0.131422	+	0.404475i	0.995016	−	0.0997119i	$-0.0317921\pi$
$709$	3.49938	+	10.7700i	0.131422	+	0.404475i	−0.863594	+	0.504187i	$0.831792\pi$
$710$		0			0
$711$	−1.23732	+	3.80807i	−0.0464030	+	0.142814i
$712$	127.090	−	41.2941i	4.76290	−	1.54756i
$713$	27.4470	−	8.91808i	1.02790	−	0.333985i
$714$	5.50757	−	16.9505i	0.206115	−	0.634358i
$715$		0			0
$716$	−25.2078	−	77.5816i	−0.942060	−	2.89936i
$717$	−4.12021	−	5.67098i	−0.153872	−	0.211787i
$718$			77.6312i			2.89717i
$719$	−24.8627	+	18.0638i	−0.927224	+	0.673667i	−0.945311	−	0.326169i	$-0.894242\pi$
$719$	−24.8627	+	18.0638i	−0.927224	+	0.673667i	0.0180878	+	0.999836i	$0.494242\pi$
$720$		0			0
$721$	−1.86852	−	1.35756i	−0.0695875	−	0.0505583i
$722$	27.8186	−	38.2891i	1.03530	−	1.42497i
$723$	2.20221	+	0.715542i	0.0819011	+	0.0266113i
$724$	−1.05888			−0.0393529
$725$		0			0
$726$	−26.4302			−0.980915
$727$	−6.24688	−	2.02973i	−0.231684	−	0.0752787i	0.190874	−	0.981615i	$-0.438868\pi$
$727$	−6.24688	−	2.02973i	−0.231684	−	0.0752787i	−0.422558	+	0.906336i	$0.638868\pi$
$728$	22.9714	−	31.6174i	0.851377	−	1.17182i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$		0			0
$731$	8.22510	−	5.97589i	0.304216	−	0.221026i
$732$			38.0086i			1.40484i
$733$	−18.7666	−	25.8300i	−0.693159	−	0.954051i	−0.999997	−	0.00228977i	$-0.999271\pi$
$733$	−18.7666	−	25.8300i	−0.693159	−	0.954051i	0.306838	−	0.951762i	$-0.400729\pi$
$734$	−12.2134	−	37.5891i	−0.450806	−	1.38744i
$735$		0			0
$736$	21.4889	−	66.1360i	0.792091	−	2.43781i
$737$	−12.7688	+	4.14885i	−0.470346	+	0.152825i
$738$	28.7789	−	9.35085i	1.05937	−	0.344209i
$739$	4.73017	−	14.5580i	0.174002	−	0.535524i	−0.825584	−	0.564279i	$-0.809154\pi$
$739$	4.73017	−	14.5580i	0.174002	−	0.535524i	0.999586	+	0.0287550i	$0.00915426\pi$
$740$		0			0
$741$	0.974196	+	2.99827i	0.0357880	+	0.110144i
$742$	−6.79082	−	9.34676i	−0.249299	−	0.343130i
$743$		−	16.5455i		−	0.606995i	−0.952832	−	0.303498i	$-0.901846\pi$
$743$		−	16.5455i		−	0.606995i	0.952832	−	0.303498i	$-0.0981545\pi$
$744$	−49.7236	+	36.1263i	−1.82295	+	1.32445i
$745$		0			0
$746$	−71.8225	−	52.1821i	−2.62961	−	1.91052i
$747$	5.21649	−	7.17988i	0.190861	−	0.262698i
$748$	21.0580	+	6.84217i	0.769959	+	0.250175i
$749$	−18.5769			−0.678786
$750$		0			0
$751$	46.0279			1.67958			0.839791	−	0.542911i	$-0.182678\pi$
$751$	46.0279			1.67958			0.839791	+	0.542911i	$0.182678\pi$
$752$	−23.3650	−	7.59174i	−0.852033	−	0.276842i
$753$	−3.63184	+	4.99879i	−0.132351	+	0.182166i
$754$	−34.6632	−	25.1843i	−1.26236	−	0.917159i
$755$		0			0
$756$	7.12476	−	5.17644i	0.259125	−	0.188265i
$757$		−	26.5282i		−	0.964184i	−0.876121	−	0.482092i	$-0.839877\pi$
$757$		−	26.5282i		−	0.964184i	0.876121	−	0.482092i	$-0.160123\pi$
$758$	23.9369	+	32.9463i	0.869427	+	1.19666i
$759$	−1.35448	−	4.16865i	−0.0491644	−	0.151312i
$760$		0			0
$761$	−8.78353	+	27.0329i	−0.318403	+	0.979943i	0.655928	+	0.754823i	$0.272277\pi$
$761$	−8.78353	+	27.0329i	−0.318403	+	0.979943i	−0.974331	+	0.225120i	$0.927723\pi$
$762$	51.7141	−	16.8029i	1.87341	−	0.608706i
$763$	5.53366	−	1.79800i	0.200332	−	0.0650918i
$764$	12.7756	−	39.3192i	0.462204	−	1.42252i
$765$		0			0
$766$	6.64947	+	20.4650i	0.240255	+	0.739429i
$767$	−2.10236	−	2.89365i	−0.0759119	−	0.104484i
$768$			14.3555i			0.518009i
$769$	−7.24841	+	5.26628i	−0.261384	+	0.189907i	−0.710757	−	0.703438i	$-0.751647\pi$
$769$	−7.24841	+	5.26628i	−0.261384	+	0.189907i	0.449373	+	0.893344i	$0.351647\pi$
$770$		0			0
$771$	10.6983	+	7.77279i	0.385291	+	0.279930i
$772$	−50.4034	+	69.3744i	−1.81406	+	2.49684i
$773$	−21.9734	−	7.13959i	−0.790329	−	0.256793i	−0.114085	−	0.993471i	$-0.536393\pi$
$773$	−21.9734	−	7.13959i	−0.790329	−	0.256793i	−0.676244	+	0.736678i	$0.736393\pi$
$774$	6.94834			0.249753
$775$		0			0
$776$	−93.1752			−3.34479
$777$	7.35148	+	2.38864i	0.263733	+	0.0856920i
$778$	1.69727	−	2.33609i	0.0608501	−	0.0837530i
$779$	10.7283	+	7.79455i	0.384380	+	0.279269i
$780$		0			0
$781$	5.22343	−	3.79504i	0.186909	−	0.135797i
$782$		−	42.9232i		−	1.53493i
$783$	−3.50082	−	4.81846i	−0.125109	−	0.172198i
$784$	16.4433	+	50.6072i	0.587260	+	1.80740i
$785$		0			0
$786$	−2.53264	+	7.79465i	−0.0903361	+	0.278026i
$787$	1.93436	−	0.628511i	0.0689524	−	0.0224040i	−0.274338	−	0.961633i	$-0.588459\pi$
$787$	1.93436	−	0.628511i	0.0689524	−	0.0224040i	0.343290	+	0.939229i	$0.388459\pi$
$788$	−85.0794	+	27.6440i	−3.03083	+	0.984776i
$789$	−2.15583	+	6.63498i	−0.0767497	+	0.236211i
$790$		0			0
$791$	3.15503	+	9.71018i	0.112180	+	0.345254i
$792$	5.48686	+	7.55201i	0.194967	+	0.268349i
$793$			19.4931i			0.692220i
$794$	52.6376	−	38.2435i	1.86804	−	1.35721i
$795$		0			0
$796$	8.52449	+	6.19340i	0.302142	+	0.219519i
$797$	−7.16646	+	9.86379i	−0.253849	+	0.349393i	−0.916855	−	0.399221i	$-0.869281\pi$
$797$	−7.16646	+	9.86379i	−0.253849	+	0.349393i	0.663006	+	0.748614i	$0.269281\pi$
$798$	5.07674	+	1.64953i	0.179715	+	0.0583928i
$799$	−7.54024			−0.266754
$800$		0			0
$801$	15.4436			0.545673
$802$	5.09359	+	1.65501i	0.179861	+	0.0584404i
$803$	2.09299	−	2.88075i	0.0738599	−	0.101659i
$804$	−52.5583	−	38.1858i	−1.85359	−	1.34671i
$805$		0			0
$806$	−41.3396	+	30.0350i	−1.45612	+	1.05794i
$807$		−	23.7199i		−	0.834979i
$808$	68.9936	+	94.9616i	2.42719	+	3.34074i
$809$	−2.72972	−	8.40121i	−0.0959718	−	0.295371i	0.891534	−	0.452954i	$-0.149630\pi$
$809$	−2.72972	−	8.40121i	−0.0959718	−	0.295371i	−0.987506	+	0.157583i	$0.949630\pi$
$810$		0			0
$811$	−4.30102	+	13.2372i	−0.151029	+	0.464820i	−0.997737	−	0.0672381i	$-0.978581\pi$
$811$	−4.30102	+	13.2372i	−0.151029	+	0.464820i	0.846708	+	0.532058i	$0.178581\pi$
$812$	−49.8850	+	16.2086i	−1.75062	+	0.568811i
$813$	−27.5721	+	8.95871i	−0.966995	+	0.314196i
$814$	−4.10438	+	12.6320i	−0.143858	+	0.442750i
$815$		0			0
$816$	15.5636	+	47.8998i	0.544835	+	1.67683i
$817$	1.78980	+	2.46344i	0.0626170	+	0.0861850i
$818$			17.9085i			0.626158i
$819$	3.65401	−	2.65479i	0.127681	−	0.0927660i
$820$		0			0
$821$	23.8603	+	17.3355i	0.832731	+	0.605015i	0.920331	−	0.391141i	$-0.127920\pi$
$821$	23.8603	+	17.3355i	0.832731	+	0.605015i	−0.0875994	+	0.996156i	$0.527920\pi$
$822$	−32.3936	+	44.5860i	−1.12986	+	1.55511i
$823$	39.9121	+	12.9682i	1.39125	+	0.452044i	0.906350	−	0.422527i	$-0.138857\pi$
$823$	39.9121	+	12.9682i	1.39125	+	0.452044i	0.484898	+	0.874571i	$0.338857\pi$
$824$	11.8460			0.412675
$825$		0			0
$826$	−6.05624			−0.210724
$827$	35.6336	+	11.5781i	1.23910	+	0.402609i	0.854004	−	0.520266i	$-0.174167\pi$
$827$	35.6336	+	11.5781i	1.23910	+	0.402609i	0.385099	+	0.922875i	$0.374167\pi$
$828$	12.4666	−	17.1587i	0.433243	−	0.596307i
$829$	−7.73108	−	5.61696i	−0.268512	−	0.195085i	0.445379	−	0.895342i	$-0.353069\pi$
$829$	−7.73108	−	5.61696i	−0.268512	−	0.195085i	−0.713891	+	0.700257i	$0.753069\pi$
$830$		0			0
$831$	−6.94677	+	5.04712i	−0.240981	+	0.175083i
$832$			54.5355i			1.89068i
$833$	9.59954	+	13.2126i	0.332604	+	0.457791i
$834$	−15.2105	−	46.8131i	−0.526696	−	1.62100i
$835$		0			0
$836$	−2.04925	+	6.30695i	−0.0708748	+	0.218130i
$837$	−6.75545	+	2.19498i	−0.233502	+	0.0758695i
$838$	−54.5708	+	17.7311i	−1.88512	+	0.612512i
$839$	−16.9128	+	52.0522i	−0.583895	+	1.79704i	0.0197702	+	0.999805i	$0.493707\pi$
$839$	−16.9128	+	52.0522i	−0.583895	+	1.79704i	−0.603665	+	0.797238i	$0.706293\pi$
$840$		0			0
$841$	2.00037	+	6.15651i	0.0689783	+	0.212294i
$842$	35.2787	+	48.5570i	1.21579	+	1.67338i
$843$			17.1661i			0.591233i
$844$	−100.603	+	73.0922i	−3.46289	+	2.51594i
$845$		0			0
$846$	−4.16908	−	3.02901i	−0.143336	−	0.104140i
$847$	−9.75371	+	13.4248i	−0.335141	+	0.461283i
$848$	31.0499	+	10.0887i	1.06626	+	0.346448i
$849$	−9.62005			−0.330159
$850$		0			0
$851$	18.6159			0.638144
$852$	29.7128	+	9.65426i	1.01794	+	0.330750i
$853$	8.99706	−	12.3834i	0.308053	−	0.423999i	−0.626720	−	0.779245i	$-0.715603\pi$
$853$	8.99706	−	12.3834i	0.308053	−	0.423999i	0.934773	+	0.355246i	$0.115603\pi$
$854$	26.7026	+	19.4005i	0.913743	+	0.663873i
$855$		0			0
$856$	77.0836	−	56.0045i	2.63466	−	1.91419i
$857$		−	8.66910i		−	0.296131i	−0.988978	−	0.148065i	$-0.952695\pi$
$857$		−	8.66910i		−	0.296131i	0.988978	−	0.148065i	$-0.0473046\pi$
$858$	4.56171	+	6.27865i	0.155734	+	0.214350i
$859$	9.39653	+	28.9195i	0.320605	+	0.986722i	0.973385	+	0.229174i	$0.0736026\pi$
$859$	9.39653	+	28.9195i	0.320605	+	0.986722i	−0.652780	+	0.757547i	$0.726397\pi$
$860$		0			0
$861$	5.87087	−	18.0687i	0.200079	−	0.615779i
$862$	−77.7211	+	25.2531i	−2.64719	+	0.860125i
$863$	−17.1595	+	5.57545i	−0.584115	+	0.189791i	−0.586143	−	0.810207i	$-0.699354\pi$
$863$	−17.1595	+	5.57545i	−0.584115	+	0.189791i	0.00202803	+	0.999998i	$0.499354\pi$
$864$	−5.28899	+	16.2779i	−0.179935	+	0.553784i
$865$		0			0
$866$	−0.478808	−	1.47362i	−0.0162706	−	0.0500756i
$867$	−0.906354	−	1.24749i	−0.0307814	−	0.0423669i
$868$			62.5548i			2.12325i
$869$	−3.49465	+	2.53901i	−0.118548	+	0.0861301i
$870$		0			0
$871$	−26.9551	−	19.5840i	−0.913338	−	0.663579i
$872$	−17.5411	+	24.1432i	−0.594015	+	0.817591i
$873$	−10.2412	−	3.32756i	−0.346611	−	0.112621i
$874$	12.8556			0.434848
$875$		0			0
$876$	17.2301			0.582149
$877$	21.2140	+	6.89285i	0.716346	+	0.232755i	0.644438	−	0.764656i	$-0.277091\pi$
$877$	21.2140	+	6.89285i	0.716346	+	0.232755i	0.0719076	+	0.997411i	$0.477091\pi$
$878$	20.2235	−	27.8352i	0.682509	−	0.939393i
$879$	−13.6079	−	9.88669i	−0.458982	−	0.333470i
$880$		0			0
$881$	−6.27761	+	4.56095i	−0.211498	+	0.153662i	−0.688491	−	0.725245i	$-0.741727\pi$
$881$	−6.27761	+	4.56095i	−0.211498	+	0.153662i	0.476993	+	0.878907i	$0.341727\pi$
$882$			11.1617i			0.375833i
$883$	−11.7279	−	16.1421i	−0.394675	−	0.543224i	0.564722	−	0.825281i	$-0.308983\pi$
$883$	−11.7279	−	16.1421i	−0.394675	−	0.543224i	−0.959398	+	0.282057i	$0.908983\pi$
$884$	16.9798	+	52.2584i	0.571092	+	1.75764i
$885$		0			0
$886$	−11.8861	+	36.5816i	−0.399320	+	1.22898i
$887$	−8.18183	+	2.65844i	−0.274719	+	0.0892616i	−0.443137	−	0.896454i	$-0.646134\pi$
$887$	−8.18183	+	2.65844i	−0.274719	+	0.0892616i	0.168418	+	0.985716i	$0.446134\pi$
$888$	−37.7056	+	12.2513i	−1.26532	+	0.411126i
$889$	10.5496	−	32.4684i	0.353823	−	1.08895i
$890$		0			0
$891$	0.333373	+	1.02602i	0.0111684	+	0.0343729i
$892$	−40.2297	−	55.3715i	−1.34699	−	1.85397i
$893$		−	2.25832i		−	0.0755719i
$894$	1.53461	−	1.11496i	0.0513251	−	0.0372899i
$895$		0			0
$896$	27.9851	+	20.3323i	0.934916	+	0.679256i
$897$	6.39360	−	8.80004i	0.213476	−	0.293825i
$898$	−30.5802	−	9.93611i	−1.02047	−	0.331572i
$899$	42.3057			1.41097
$900$		0			0
$901$	10.0203			0.333824
$902$	31.0472	+	10.0879i	1.03376	+	0.335889i
$903$	2.56420	−	3.52932i	0.0853312	−	0.117448i
$904$	−42.3652	−	30.7801i	−1.40905	−	1.02373i
$905$		0			0
$906$	−15.3157	+	11.1275i	−0.508830	+	0.369687i
$907$			6.26125i			0.207902i	0.994582	+	0.103951i	$0.0331484\pi$
$907$			6.26125i			0.207902i	−0.994582	+	0.103951i	$0.966852\pi$
$908$	−80.6385	−	110.989i	−2.67608	−	3.68331i
$909$	4.19195	+	12.9015i	0.139038	+	0.427915i
$910$		0			0
$911$	0.279838	−	0.861253i	0.00927145	−	0.0285346i	−0.946314	−	0.323250i	$-0.895225\pi$
$911$	0.279838	−	0.861253i	0.00927145	−	0.0285346i	0.955585	+	0.294715i	$0.0952247\pi$
$912$	−14.3461	+	4.66135i	−0.475048	+	0.154353i
$913$	9.10571	−	2.95862i	0.301355	−	0.0979162i
$914$	−6.82669	+	21.0104i	−0.225807	+	0.694962i
$915$		0			0
$916$	3.21988	+	9.90978i	0.106388	+	0.327428i
$917$	3.02455	+	4.16293i	0.0998794	+	0.137472i
$918$			10.5646i			0.348682i
$919$	35.5913	−	25.8586i	1.17405	−	0.852997i	0.182561	−	0.983194i	$-0.441561\pi$
$919$	35.5913	−	25.8586i	1.17405	−	0.852997i	0.991488	+	0.130198i	$0.0415612\pi$
$920$		0			0
$921$	9.15903	+	6.65443i	0.301800	+	0.219271i
$922$	−2.00926	+	2.76551i	−0.0661714	+	0.0910771i
$923$	15.2385	+	4.95129i	0.501582	+	0.162974i
$924$	9.50081			0.312554
$925$		0			0
$926$	−87.8029			−2.88538
$927$	1.30203	+	0.423056i	0.0427643	+	0.0138950i
$928$	59.9184	−	82.4707i	1.96692	−	2.70723i
$929$	−29.7271	−	21.5980i	−0.975313	−	0.708606i	−0.0186568	−	0.999826i	$-0.505939\pi$
$929$	−29.7271	−	21.5980i	−0.975313	−	0.708606i	−0.956656	+	0.291220i	$0.905939\pi$
$930$		0			0
$931$	−3.95722	+	2.87509i	−0.129693	+	0.0942273i
$932$		−	2.74347i		−	0.0898652i
$933$	−10.9113	−	15.0181i	−0.357221	−	0.491672i
$934$	11.9857	+	36.8883i	0.392185	+	1.20702i
$935$		0			0
$936$	−7.15855	+	22.0318i	−0.233985	+	0.720131i
$937$	−23.4426	+	7.61696i	−0.765836	+	0.248835i	−0.665782	−	0.746147i	$-0.731902\pi$
$937$	−23.4426	+	7.61696i	−0.765836	+	0.248835i	−0.100055	+	0.994982i	$0.531902\pi$
$938$	−53.6542	+	17.4333i	−1.75187	+	0.569217i
$939$	−2.99731	+	9.22478i	−0.0978137	+	0.301039i
$940$		0			0
$941$	−18.2777	−	56.2530i	−0.595836	−	1.83379i	−0.550520	−	0.834822i	$-0.685571\pi$
$941$	−18.2777	−	56.2530i	−0.595836	−	1.83379i	−0.0453159	−	0.998973i	$-0.514429\pi$
$942$	8.10045	+	11.1493i	0.263927	+	0.363264i
$943$		−	45.7546i		−	1.48998i
$944$	13.8456	−	10.0594i	0.450635	−	0.327406i
$945$		0			0
$946$	6.06439	+	4.40604i	0.197170	+	0.143253i
$947$	−17.6900	+	24.3482i	−0.574848	+	0.791210i	−0.993119	−	0.117112i	$-0.962636\pi$
$947$	−17.6900	+	24.3482i	−0.574848	+	0.791210i	0.418271	+	0.908322i	$0.362636\pi$
$948$	−19.8789	−	6.45903i	−0.645635	−	0.209780i
$949$	8.83661			0.286849
$950$		0			0
$951$	−7.47647			−0.242441
$952$	54.5841	+	17.7354i	1.76908	+	0.574809i
$953$	12.1315	−	16.6975i	0.392977	−	0.540886i	−0.565987	−	0.824414i	$-0.691505\pi$
$953$	12.1315	−	16.6975i	0.392977	−	0.540886i	0.958964	+	0.283528i	$0.0915049\pi$
$954$	5.54032	+	4.02528i	0.179375	+	0.130323i
$955$		0			0
$956$	29.6036	−	21.5083i	0.957449	−	0.695628i
$957$		−	6.42538i		−	0.207703i
$958$	26.6316	+	36.6553i	0.860429	+	1.18428i
$959$	10.6924	+	32.9078i	0.345275	+	1.06265i
$960$		0			0
$961$	6.01162	−	18.5019i	0.193923	−	0.596834i
$962$	−31.3480	+	10.1856i	−1.01070	+	0.328396i
$963$	10.4726	−	3.40275i	0.337474	−	0.109652i
$964$	−3.73527	+	11.4960i	−0.120305	+	0.370260i
$965$		0			0
$966$	−5.69146	−	17.5165i	−0.183120	−	0.563585i
$967$	13.2849	+	18.2850i	0.427212	+	0.588007i	0.967311	−	0.253595i	$-0.0816130\pi$
$967$	13.2849	+	18.2850i	0.427212	+	0.588007i	−0.540098	+	0.841602i	$0.681613\pi$
$968$		−	85.1103i		−	2.73555i
$969$	−3.74552	+	2.72128i	−0.120324	+	0.0874202i
$970$		0			0
$971$	−19.5281	−	14.1880i	−0.626687	−	0.455315i	0.228564	−	0.973529i	$-0.426597\pi$
$971$	−19.5281	−	14.1880i	−0.626687	−	0.455315i	−0.855251	+	0.518214i	$0.826597\pi$
$972$	−3.06835	+	4.22323i	−0.0984175	+	0.135460i
$973$	−29.3913	−	9.54981i	−0.942242	−	0.306153i
$974$	107.007			3.42874
$975$		0			0
$976$	−93.2708			−2.98553
$977$	21.9224	+	7.12302i	0.701360	+	0.227886i	0.637923	−	0.770100i	$-0.279794\pi$
$977$	21.9224	+	7.12302i	0.701360	+	0.227886i	0.0634371	+	0.997986i	$0.479794\pi$
$978$	38.3184	−	52.7407i	1.22529	−	1.68646i
$979$	13.4789	+	9.79299i	0.430787	+	0.312985i
$980$		0			0
$981$	−2.79022	+	2.02721i	−0.0890847	+	0.0647239i
$982$		−	37.6870i		−	1.20264i
$983$	17.5579	+	24.1664i	0.560010	+	0.770787i	0.991328	−	0.131413i	$-0.0419513\pi$
$983$	17.5579	+	24.1664i	0.560010	+	0.770787i	−0.431318	+	0.902200i	$0.641951\pi$
$984$	30.1116	+	92.6738i	0.959921	+	2.95433i
$985$		0			0
$986$	19.4440	−	59.8424i	0.619222	−	1.90577i
$987$	−3.07709	+	0.999807i	−0.0979449	+	0.0318242i
$988$	−15.6515	+	5.08550i	−0.497942	+	0.161791i
$989$	3.24661	−	9.99204i	0.103236	−	0.317728i
$990$		0			0
$991$	5.14700	+	15.8408i	0.163500	+	0.503201i	0.998923	−	0.0464072i	$-0.0147772\pi$
$991$	5.14700	+	15.8408i	0.163500	+	0.503201i	−0.835423	+	0.549608i	$0.814777\pi$
$992$	−71.4591	−	98.3550i	−2.26883	−	3.12277i
$993$		−	25.2570i		−	0.801507i
$994$	21.9487	−	15.9466i	0.696169	−	0.505797i
$995$		0			0
$996$	37.4804	+	27.2311i	1.18761	+	0.862850i
$997$	7.34343	−	10.1074i	0.232569	−	0.320103i	−0.676743	−	0.736220i	$-0.736609\pi$
$997$	7.34343	−	10.1074i	0.232569	−	0.320103i	0.909311	+	0.416116i	$0.136609\pi$
$998$	38.9246	+	12.6474i	1.23214	+	0.400346i
$999$	−4.58187			−0.144964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.d.274.1		24
5.2	odd	4		375.2.g.c.226.3		12
5.3	odd	4		75.2.g.c.46.1	yes	12
5.4	even	2	inner	375.2.i.d.274.6		24
15.8	even	4		225.2.h.d.46.3		12
25.6	even	5	inner	375.2.i.d.349.6		24
25.8	odd	20		75.2.g.c.31.1	✓	12
25.9	even	10		1875.2.b.f.1249.12		12
25.12	odd	20		1875.2.a.k.1.6		6
25.13	odd	20		1875.2.a.j.1.1		6
25.16	even	5		1875.2.b.f.1249.1		12
25.17	odd	20		375.2.g.c.151.3		12
25.19	even	10	inner	375.2.i.d.349.1		24
75.8	even	20		225.2.h.d.181.3		12
75.38	even	20		5625.2.a.p.1.6		6
75.62	even	20		5625.2.a.q.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.1	✓	12	25.8	odd	20
75.2.g.c.46.1	yes	12	5.3	odd	4
225.2.h.d.46.3		12	15.8	even	4
225.2.h.d.181.3		12	75.8	even	20
375.2.g.c.151.3		12	25.17	odd	20
375.2.g.c.226.3		12	5.2	odd	4
375.2.i.d.274.1		24	1.1	even	1	trivial
375.2.i.d.274.6		24	5.4	even	2	inner
375.2.i.d.349.1		24	25.19	even	10	inner
375.2.i.d.349.6		24	25.6	even	5	inner
1875.2.a.j.1.1		6	25.13	odd	20
1875.2.a.k.1.6		6	25.12	odd	20
1875.2.b.f.1249.1		12	25.16	even	5
1875.2.b.f.1249.12		12	25.9	even	10
5625.2.a.p.1.6		6	75.38	even	20
5625.2.a.q.1.1		6	75.62	even	20

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.55553 - 0.830342i) q^{2} +(0.587785 - 0.809017i) q^{3} +(4.22323 + 3.06835i) q^{4} +(-2.17386 + 1.57940i) q^{6} +1.68704i q^{7} +(-5.08599 - 7.00026i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-2.55553 - 0.830342i) q^{2} +(0.587785 - 0.809017i) q^{3} +(4.22323 + 3.06835i) q^{4} +(-2.17386 + 1.57940i) q^{6} +1.68704i q^{7} +(-5.08599 - 7.00026i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(0.333373 - 1.02602i) q^{11} +(4.96470 - 1.61313i) q^{12} +(2.54620 - 0.827310i) q^{13} +(1.40082 - 4.31129i) q^{14} +(3.95852 + 12.1831i) q^{16} +(2.31098 + 3.18079i) q^{17} +2.68704i q^{18} +(-0.952655 + 0.692144i) q^{19} +(1.36485 + 0.991619i) q^{21} +(-1.70389 + 2.34520i) q^{22} +(3.86409 + 1.25552i) q^{23} -8.65280 q^{24} -7.19384 q^{26} +(-0.951057 - 0.309017i) q^{27} +(-5.17644 + 7.12476i) q^{28} +(4.81846 + 3.50082i) q^{29} +(5.74653 - 4.17510i) q^{31} -17.1155i q^{32} +(-0.634113 - 0.872782i) q^{33} +(-3.26463 - 10.0475i) q^{34} +(1.61313 - 4.96470i) q^{36} +(4.35761 - 1.41587i) q^{37} +(3.00925 - 0.977766i) q^{38} +(0.827310 - 2.54620i) q^{39} +(-3.47998 - 10.7103i) q^{41} +(-2.66452 - 3.66740i) q^{42} -2.58587i q^{43} +(4.55609 - 3.31019i) q^{44} +(-8.83229 - 6.41703i) q^{46} +(-1.12727 + 1.55155i) q^{47} +(12.1831 + 3.95852i) q^{48} +4.15389 q^{49} +3.93167 q^{51} +(13.2917 + 4.31872i) q^{52} +(1.49803 - 2.06187i) q^{53} +(2.17386 + 1.57940i) q^{54} +(11.8097 - 8.58028i) q^{56} +1.17755i q^{57} +(-9.40685 - 12.9474i) q^{58} +(-0.412843 - 1.27060i) q^{59} +(-2.24997 + 6.92470i) q^{61} +(-18.1522 + 5.89800i) q^{62} +(1.60447 - 0.521325i) q^{63} +(-6.29470 + 19.3731i) q^{64} +(0.895787 + 2.75695i) q^{66} +(-7.31502 - 10.0683i) q^{67} +20.5241i q^{68} +(3.28699 - 2.38814i) q^{69} +(4.84181 + 3.51778i) q^{71} +(-5.08599 + 7.00026i) q^{72} +(3.13911 + 1.01996i) q^{73} -12.3117 q^{74} -6.14702 q^{76} +(1.73093 + 0.562414i) q^{77} +(-4.22843 + 5.81994i) q^{78} +(-3.23934 - 2.35351i) q^{79} +(-0.809017 + 0.587785i) q^{81} +30.2600i q^{82} +(5.21649 + 7.17988i) q^{83} +(2.72142 + 8.37566i) q^{84} +(-2.14716 + 6.60827i) q^{86} +(5.66445 - 1.84049i) q^{87} +(-8.87792 + 2.88461i) q^{88} +(-4.77234 + 14.6877i) q^{89} +(1.39571 + 4.29555i) q^{91} +(12.4666 + 17.1587i) q^{92} -7.10310i q^{93} +(4.16908 - 3.02901i) q^{94} +(-13.8468 - 10.0603i) q^{96} +(6.32939 - 8.71166i) q^{97} +(-10.6154 - 3.44915i) q^{98} -1.07882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{4} + 6 q^{9}+O(q^{10}) \) 24 * q + 20 * q^4 + 6 * q^9	\( 24 q + 20 q^{4} + 6 q^{9} - 8 q^{11} - 12 q^{14} + 32 q^{16} - 14 q^{19} - 6 q^{21} - 12 q^{24} - 112 q^{26} + 2 q^{29} + 26 q^{31} + 50 q^{34} - 4 q^{39} + 16 q^{41} - 66 q^{44} - 44 q^{46} + 56 q^{49} + 52 q^{51} + 90 q^{56} + 44 q^{59} - 16 q^{61} - 98 q^{64} - 6 q^{66} - 12 q^{69} - 42 q^{71} + 88 q^{74} - 104 q^{76} - 20 q^{79} - 6 q^{81} + 12 q^{84} + 112 q^{86} - 114 q^{89} - 14 q^{91} + 46 q^{94} - 46 q^{96} - 12 q^{99}+O(q^{100}) \) 24 * q + 20 * q^4 + 6 * q^9 - 8 * q^11 - 12 * q^14 + 32 * q^16 - 14 * q^19 - 6 * q^21 - 12 * q^24 - 112 * q^26 + 2 * q^29 + 26 * q^31 + 50 * q^34 - 4 * q^39 + 16 * q^41 - 66 * q^44 - 44 * q^46 + 56 * q^49 + 52 * q^51 + 90 * q^56 + 44 * q^59 - 16 * q^61 - 98 * q^64 - 6 * q^66 - 12 * q^69 - 42 * q^71 + 88 * q^74 - 104 * q^76 - 20 * q^79 - 6 * q^81 + 12 * q^84 + 112 * q^86 - 114 * q^89 - 14 * q^91 + 46 * q^94 - 46 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

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