LMFDB - Embedded newform 850.2.l.e.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(151,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("850.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.l (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 286x^{12} + 1412x^{10} + 3709x^{8} + 5264x^{6} + 3780x^{4} + 1072x^{2} + 4 $ x^16 + 28x^14 + 286x^12 + 1412x^10 + 3709x^8 + 5264x^6 + 3780x^4 + 1072*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			451.1
Root			$-1.09612i$ of defining polynomial
Character	$\chi$	$=$	850.451
Dual form			850.2.l.e.801.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.93656 - 0.802151i) q^{3} -1.00000i q^{4} +(1.93656 - 0.802151i) q^{6} +(0.434936 + 1.05003i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.985516 + 0.985516i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.93656 - 0.802151i) q^{3} -1.00000i q^{4} +(1.93656 - 0.802151i) q^{6} +(0.434936 + 1.05003i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.985516 + 0.985516i) q^{9} +(-0.233094 + 0.0965508i) q^{11} +(-0.802151 + 1.93656i) q^{12} -3.10869i q^{13} +(-1.05003 - 0.434936i) q^{14} -1.00000 q^{16} +(3.02187 + 2.80505i) q^{17} -1.39373 q^{18} +(-0.972524 + 0.972524i) q^{19} -2.38233i q^{21} +(0.0965508 - 0.233094i) q^{22} +(0.694615 - 0.287719i) q^{23} +(-0.802151 - 1.93656i) q^{24} +(2.19817 + 2.19817i) q^{26} +(1.28847 + 3.11065i) q^{27} +(1.05003 - 0.434936i) q^{28} +(-0.432553 + 1.04428i) q^{29} +(-0.863307 - 0.357593i) q^{31} +(0.707107 - 0.707107i) q^{32} +0.528851 q^{33} +(-4.12025 + 0.153319i) q^{34} +(0.985516 - 0.985516i) q^{36} +(-4.54149 - 1.88115i) q^{37} -1.37536i q^{38} +(-2.49364 + 6.02017i) q^{39} +(-3.67824 - 8.88006i) q^{41} +(1.68456 + 1.68456i) q^{42} +(-5.13048 - 5.13048i) q^{43} +(0.0965508 + 0.233094i) q^{44} +(-0.287719 + 0.694615i) q^{46} -9.71535i q^{47} +(1.93656 + 0.802151i) q^{48} +(4.03636 - 4.03636i) q^{49} +(-3.60198 - 7.85615i) q^{51} -3.10869 q^{52} +(9.25847 - 9.25847i) q^{53} +(-3.11065 - 1.28847i) q^{54} +(-0.434936 + 1.05003i) q^{56} +(2.66347 - 1.10324i) q^{57} +(-0.432553 - 1.04428i) q^{58} +(1.67839 + 1.67839i) q^{59} +(-2.81251 - 6.79001i) q^{61} +(0.863307 - 0.357593i) q^{62} +(-0.606184 + 1.46346i) q^{63} +1.00000i q^{64} +(-0.373954 + 0.373954i) q^{66} -15.8174 q^{67} +(2.80505 - 3.02187i) q^{68} -1.57596 q^{69} +(2.35153 + 0.974036i) q^{71} +1.39373i q^{72} +(3.80933 - 9.19654i) q^{73} +(4.54149 - 1.88115i) q^{74} +(0.972524 + 0.972524i) q^{76} +(-0.202762 - 0.202762i) q^{77} +(-2.49364 - 6.02017i) q^{78} +(12.9573 - 5.36708i) q^{79} -11.2387i q^{81} +(8.88006 + 3.67824i) q^{82} +(-11.0125 + 11.0125i) q^{83} -2.38233 q^{84} +7.25559 q^{86} +(1.67534 - 1.67534i) q^{87} +(-0.233094 - 0.0965508i) q^{88} -11.9252i q^{89} +(3.26421 - 1.35208i) q^{91} +(-0.287719 - 0.694615i) q^{92} +(1.38501 + 1.38501i) q^{93} +(6.86979 + 6.86979i) q^{94} +(-1.93656 + 0.802151i) q^{96} +(-6.02292 + 14.5406i) q^{97} +5.70827i q^{98} +(-0.324871 - 0.134566i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} - 8 q^{14} - 16 q^{16} - 8 q^{18} + 8 q^{22} - 8 q^{23} + 24 q^{27} + 8 q^{28} + 8 q^{29} + 32 q^{31} - 16 q^{33} + 16 q^{34} + 8 q^{37} - 32 q^{39} - 32 q^{41} - 32 q^{42} + 16 q^{43} + 8 q^{44} - 24 q^{46} - 8 q^{49} - 8 q^{51} + 8 q^{52} + 40 q^{53} + 16 q^{57} + 8 q^{58} + 16 q^{59} - 24 q^{61} - 32 q^{62} - 56 q^{63} - 8 q^{66} - 16 q^{67} - 16 q^{69} + 8 q^{71} - 16 q^{73} - 8 q^{74} - 24 q^{77} - 32 q^{78} + 40 q^{79} - 16 q^{82} - 32 q^{83} + 16 q^{84} + 32 q^{87} - 8 q^{88} + 24 q^{91} - 24 q^{92} + 32 q^{93} + 40 q^{94} - 24 q^{97} - 56 q^{99}+O(q^{100}) $ 16 * q - 8 * q^11 - 8 * q^14 - 16 * q^16 - 8 * q^18 + 8 * q^22 - 8 * q^23 + 24 * q^27 + 8 * q^28 + 8 * q^29 + 32 * q^31 - 16 * q^33 + 16 * q^34 + 8 * q^37 - 32 * q^39 - 32 * q^41 - 32 * q^42 + 16 * q^43 + 8 * q^44 - 24 * q^46 - 8 * q^49 - 8 * q^51 + 8 * q^52 + 40 * q^53 + 16 * q^57 + 8 * q^58 + 16 * q^59 - 24 * q^61 - 32 * q^62 - 56 * q^63 - 8 * q^66 - 16 * q^67 - 16 * q^69 + 8 * q^71 - 16 * q^73 - 8 * q^74 - 24 * q^77 - 32 * q^78 + 40 * q^79 - 16 * q^82 - 32 * q^83 + 16 * q^84 + 32 * q^87 - 8 * q^88 + 24 * q^91 - 24 * q^92 + 32 * q^93 + 40 * q^94 - 24 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.93656	−	0.802151i	−1.11808	−	0.463122i	−0.254364	−	0.967108i	$-0.581866\pi$
$3$	−1.93656	−	0.802151i	−1.11808	−	0.463122i	−0.863712	+	0.503986i	$0.831866\pi$
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	1.93656	−	0.802151i	0.790599	−	0.327477i
$7$	0.434936	+	1.05003i	0.164390	+	0.396874i	0.984512	−	0.175315i	$-0.0560944\pi$
$7$	0.434936	+	1.05003i	0.164390	+	0.396874i	−0.820122	+	0.572189i	$0.806094\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.985516	+	0.985516i	0.328505	+	0.328505i
$10$		0			0
$11$	−0.233094	+	0.0965508i	−0.0702806	+	0.0291112i	−0.417547	−	0.908655i	$-0.637110\pi$
$11$	−0.233094	+	0.0965508i	−0.0702806	+	0.0291112i	0.347266	+	0.937767i	$0.387110\pi$
$12$	−0.802151	+	1.93656i	−0.231561	+	0.559038i
$13$		−	3.10869i		−	0.862194i	−0.902305	−	0.431097i	$-0.858127\pi$
$13$		−	3.10869i		−	0.862194i	0.902305	−	0.431097i	$-0.141873\pi$
$14$	−1.05003	−	0.434936i	−0.280632	−	0.116242i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	3.02187	+	2.80505i	0.732912	+	0.680324i
$17$	3.02187	+	2.80505i	0.732912	+	0.680324i
$18$	−1.39373			−0.328505
$19$	−0.972524	+	0.972524i	−0.223112	+	0.223112i	−0.809808	−	0.586695i	$-0.800429\pi$
$19$	−0.972524	+	0.972524i	−0.223112	+	0.223112i	0.586695	+	0.809808i	$0.300429\pi$
$20$		0			0
$21$		−	2.38233i		−	0.519868i
$22$	0.0965508	−	0.233094i	0.0205847	−	0.0496959i
$23$	0.694615	−	0.287719i	0.144837	−	0.0599935i	−0.309087	−	0.951034i	$-0.600024\pi$
$23$	0.694615	−	0.287719i	0.144837	−	0.0599935i	0.453925	+	0.891040i	$0.350024\pi$
$24$	−0.802151	−	1.93656i	−0.163738	−	0.395300i
$25$		0			0
$26$	2.19817	+	2.19817i	0.431097	+	0.431097i
$27$	1.28847	+	3.11065i	0.247966	+	0.598644i
$28$	1.05003	−	0.434936i	0.198437	−	0.0821952i
$29$	−0.432553	+	1.04428i	−0.0803231	+	0.193917i	−0.958939	−	0.283612i	$-0.908467\pi$
$29$	−0.432553	+	1.04428i	−0.0803231	+	0.193917i	0.878616	+	0.477529i	$0.158467\pi$
$30$		0			0
$31$	−0.863307	−	0.357593i	−0.155054	−	0.0642257i	0.303806	−	0.952734i	$-0.401742\pi$
$31$	−0.863307	−	0.357593i	−0.155054	−	0.0642257i	−0.458861	+	0.888508i	$0.651742\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.528851			0.0920611
$34$	−4.12025	+	0.153319i	−0.706618	+	0.0262940i
$35$		0			0
$36$	0.985516	−	0.985516i	0.164253	−	0.164253i
$37$	−4.54149	−	1.88115i	−0.746617	−	0.309259i	−0.0232565	−	0.999730i	$-0.507403\pi$
$37$	−4.54149	−	1.88115i	−0.746617	−	0.309259i	−0.723360	+	0.690471i	$0.757403\pi$
$38$		−	1.37536i		−	0.223112i
$39$	−2.49364	+	6.02017i	−0.399302	+	0.963999i
$40$		0			0
$41$	−3.67824	−	8.88006i	−0.574445	−	1.38683i	−0.897737	−	0.440533i	$-0.854790\pi$
$41$	−3.67824	−	8.88006i	−0.574445	−	1.38683i	0.323292	−	0.946299i	$-0.395210\pi$
$42$	1.68456	+	1.68456i	0.259934	+	0.259934i
$43$	−5.13048	−	5.13048i	−0.782391	−	0.782391i	0.197843	−	0.980234i	$-0.436606\pi$
$43$	−5.13048	−	5.13048i	−0.782391	−	0.782391i	−0.980234	+	0.197843i	$0.936606\pi$
$44$	0.0965508	+	0.233094i	0.0145556	+	0.0351403i
$45$		0			0
$46$	−0.287719	+	0.694615i	−0.0424218	+	0.102415i
$47$		−	9.71535i		−	1.41713i	−0.705646	−	0.708565i	$-0.749343\pi$
$47$		−	9.71535i		−	1.41713i	0.705646	−	0.708565i	$-0.250657\pi$
$48$	1.93656	+	0.802151i	0.279519	+	0.115781i
$49$	4.03636	−	4.03636i	0.576622	−	0.576622i
$50$		0			0
$51$	−3.60198	−	7.85615i	−0.504378	−	1.10008i
$52$	−3.10869			−0.431097
$53$	9.25847	−	9.25847i	1.27175	−	1.27175i	0.326579	−	0.945170i	$-0.394104\pi$
$53$	9.25847	−	9.25847i	1.27175	−	1.27175i	0.945170	−	0.326579i	$-0.105896\pi$
$54$	−3.11065	−	1.28847i	−0.423305	−	0.175339i
$55$		0			0
$56$	−0.434936	+	1.05003i	−0.0581208	+	0.140316i
$57$	2.66347	−	1.10324i	0.352785	−	0.146128i
$58$	−0.432553	−	1.04428i	−0.0567970	−	0.137120i
$59$	1.67839	+	1.67839i	0.218508	+	0.218508i	0.807870	−	0.589361i	$-0.200621\pi$
$59$	1.67839	+	1.67839i	0.218508	+	0.218508i	−0.589361	+	0.807870i	$0.700621\pi$
$60$		0			0
$61$	−2.81251	−	6.79001i	−0.360105	−	0.869371i	−0.995284	−	0.0970059i	$-0.969073\pi$
$61$	−2.81251	−	6.79001i	−0.360105	−	0.869371i	0.635178	−	0.772365i	$-0.280927\pi$
$62$	0.863307	−	0.357593i	0.109640	−	0.0454144i
$63$	−0.606184	+	1.46346i	−0.0763720	+	0.184378i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−0.373954	+	0.373954i	−0.0460305	+	0.0460305i
$67$	−15.8174			−1.93240			−0.966201	−	0.257788i	$-0.917006\pi$
$67$	−15.8174			−1.93240			−0.966201	+	0.257788i	$0.917006\pi$
$68$	2.80505	−	3.02187i	0.340162	−	0.366456i
$69$	−1.57596			−0.189723
$70$		0			0
$71$	2.35153	+	0.974036i	0.279075	+	0.115597i	0.517831	−	0.855483i	$-0.326740\pi$
$71$	2.35153	+	0.974036i	0.279075	+	0.115597i	−0.238756	+	0.971080i	$0.576740\pi$
$72$			1.39373i			0.164253i
$73$	3.80933	−	9.19654i	0.445849	−	1.07637i	−0.528014	−	0.849236i	$-0.677063\pi$
$73$	3.80933	−	9.19654i	0.445849	−	1.07637i	0.973863	−	0.227138i	$-0.0729369\pi$
$74$	4.54149	−	1.88115i	0.527938	−	0.218679i
$75$		0			0
$76$	0.972524	+	0.972524i	0.111556	+	0.111556i
$77$	−0.202762	−	0.202762i	−0.0231069	−	0.0231069i
$78$	−2.49364	−	6.02017i	−0.282349	−	0.681650i
$79$	12.9573	−	5.36708i	1.45781	−	0.603844i	0.493766	−	0.869595i	$-0.335620\pi$
$79$	12.9573	−	5.36708i	1.45781	−	0.603844i	0.964042	+	0.265751i	$0.0856200\pi$
$80$		0			0
$81$		−	11.2387i		−	1.24875i
$82$	8.88006	+	3.67824i	0.980638	+	0.406194i
$83$	−11.0125	+	11.0125i	−1.20877	+	1.20877i	−0.237349	+	0.971424i	$0.576279\pi$
$83$	−11.0125	+	11.0125i	−1.20877	+	1.20877i	−0.971424	+	0.237349i	$0.923721\pi$
$84$	−2.38233			−0.259934
$85$		0			0
$86$	7.25559			0.782391
$87$	1.67534	−	1.67534i	0.179615	−	0.179615i
$88$	−0.233094	−	0.0965508i	−0.0248479	−	0.0102924i
$89$		−	11.9252i		−	1.26407i	−0.774941	−	0.632034i	$-0.782220\pi$
$89$		−	11.9252i		−	1.26407i	0.774941	−	0.632034i	$-0.217780\pi$
$90$		0			0
$91$	3.26421	−	1.35208i	0.342182	−	0.141737i
$92$	−0.287719	−	0.694615i	−0.0299968	−	0.0724186i
$93$	1.38501	+	1.38501i	0.143618	+	0.143618i
$94$	6.86979	+	6.86979i	0.708565	+	0.708565i
$95$		0			0
$96$	−1.93656	+	0.802151i	−0.197650	+	0.0818692i
$97$	−6.02292	+	14.5406i	−0.611535	+	1.47638i	0.249780	+	0.968303i	$0.419642\pi$
$97$	−6.02292	+	14.5406i	−0.611535	+	1.47638i	−0.861314	+	0.508073i	$0.830358\pi$
$98$			5.70827i			0.576622i
$99$	−0.324871	−	0.134566i	−0.0326507	−	0.0135244i
$100$		0			0
$101$	−1.90803			−0.189857			−0.0949283	−	0.995484i	$-0.530262\pi$
$101$	−1.90803			−0.189857			−0.0949283	+	0.995484i	$0.530262\pi$
$102$	8.10212	+	3.00816i	0.802230	+	0.297852i
$103$	−1.64495			−0.162082			−0.0810408	−	0.996711i	$-0.525824\pi$
$103$	−1.64495			−0.162082			−0.0810408	+	0.996711i	$0.525824\pi$
$104$	2.19817	−	2.19817i	0.215549	−	0.215549i
$105$		0			0
$106$			13.0935i			1.27175i
$107$	4.48481	−	10.8273i	0.433563	−	1.04671i	−0.544566	−	0.838718i	$-0.683306\pi$
$107$	4.48481	−	10.8273i	0.433563	−	1.04671i	0.978130	−	0.207996i	$-0.0666942\pi$
$108$	3.11065	−	1.28847i	0.299322	−	0.123983i
$109$	0.796977	+	1.92407i	0.0763366	+	0.184293i	0.957441	−	0.288629i	$-0.0931994\pi$
$109$	0.796977	+	1.92407i	0.0763366	+	0.184293i	−0.881104	+	0.472922i	$0.843199\pi$
$110$		0			0
$111$	7.28593	+	7.28593i	0.691550	+	0.691550i
$112$	−0.434936	−	1.05003i	−0.0410976	−	0.0992184i
$113$	8.16143	−	3.38057i	0.767763	−	0.318018i	0.0357968	−	0.999359i	$-0.488603\pi$
$113$	8.16143	−	3.38057i	0.767763	−	0.318018i	0.731966	+	0.681341i	$0.238603\pi$
$114$	−1.10324	+	2.66347i	−0.103328	+	0.249457i
$115$		0			0
$116$	1.04428	+	0.432553i	0.0969586	+	0.0401616i
$117$	3.06366	−	3.06366i	0.283235	−	0.283235i
$118$	−2.37361			−0.218508
$119$	−1.63106	+	4.39307i	−0.149519	+	0.402712i
$120$		0			0
$121$	−7.73316	+	7.73316i	−0.703015	+	0.703015i
$122$	6.79001	+	2.81251i	0.614738	+	0.254633i
$123$			20.1473i			1.81662i
$124$	−0.357593	+	0.863307i	−0.0321128	+	0.0775272i
$125$		0			0
$126$	−0.606184	−	1.46346i	−0.0540032	−	0.130375i
$127$	−7.38362	−	7.38362i	−0.655191	−	0.655191i	0.299048	−	0.954238i	$-0.403331\pi$
$127$	−7.38362	−	7.38362i	−0.655191	−	0.655191i	−0.954238	+	0.299048i	$0.903331\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	5.82008	+	14.0509i	0.512430	+	1.23712i
$130$		0			0
$131$	−3.71255	+	8.96288i	−0.324367	+	0.783090i	0.674624	+	0.738162i	$0.264306\pi$
$131$	−3.71255	+	8.96288i	−0.324367	+	0.783090i	−0.998990	+	0.0449283i	$0.985694\pi$
$132$		−	0.528851i		−	0.0460305i
$133$	−1.44417	−	0.598193i	−0.125225	−	0.0518699i
$134$	11.1846	−	11.1846i	0.966201	−	0.966201i
$135$		0			0
$136$	0.153319	+	4.12025i	0.0131470	+	0.353309i
$137$	4.55218			0.388919			0.194460	−	0.980911i	$-0.437705\pi$
$137$	4.55218			0.388919			0.194460	+	0.980911i	$0.437705\pi$
$138$	1.11437	−	1.11437i	0.0948617	−	0.0948617i
$139$	−11.5541	−	4.78586i	−0.980004	−	0.405931i	−0.165577	−	0.986197i	$-0.552949\pi$
$139$	−11.5541	−	4.78586i	−0.980004	−	0.405931i	−0.814427	+	0.580266i	$0.802949\pi$
$140$		0			0
$141$	−7.79318	+	18.8144i	−0.656304	+	1.58446i
$142$	−2.35153	+	0.974036i	−0.197336	+	0.0817393i
$143$	0.300146	+	0.724617i	0.0250995	+	0.0605955i
$144$	−0.985516	−	0.985516i	−0.0821263	−	0.0821263i
$145$		0			0
$146$	3.80933	+	9.19654i	0.315263	+	0.761111i
$147$	−11.0544	+	4.57890i	−0.911754	+	0.377661i
$148$	−1.88115	+	4.54149i	−0.154629	+	0.373308i
$149$		−	22.2607i		−	1.82367i	−0.410556	−	0.911835i	$-0.634666\pi$
$149$		−	22.2607i		−	1.82367i	0.410556	−	0.911835i	$-0.365334\pi$
$150$		0			0
$151$	−7.13341	+	7.13341i	−0.580509	+	0.580509i	−0.935043	−	0.354534i	$-0.884639\pi$
$151$	−7.13341	+	7.13341i	−0.580509	+	0.580509i	0.354534	+	0.935043i	$0.384639\pi$
$152$	−1.37536			−0.111556
$153$	0.213685	+	5.74252i	0.0172754	+	0.464255i
$154$	0.286749			0.0231069
$155$		0			0
$156$	6.02017	+	2.49364i	0.482000	+	0.199651i
$157$		−	16.5315i		−	1.31936i	−0.751549	−	0.659678i	$-0.770693\pi$
$157$		−	16.5315i		−	1.31936i	0.751549	−	0.659678i	$-0.229307\pi$
$158$	−5.36708	+	12.9573i	−0.426982	+	1.03083i
$159$	−25.3563	+	10.5029i	−2.01089	+	0.832937i
$160$		0			0
$161$	0.604226	+	0.604226i	0.0476197	+	0.0476197i
$162$	7.94697	+	7.94697i	0.624373	+	0.624373i
$163$	−0.715103	−	1.72641i	−0.0560112	−	0.135223i	0.893397	−	0.449269i	$-0.148315\pi$
$163$	−0.715103	−	1.72641i	−0.0560112	−	0.135223i	−0.949408	+	0.314046i	$0.898315\pi$
$164$	−8.88006	+	3.67824i	−0.693416	+	0.287222i
$165$		0			0
$166$		−	15.5740i		−	1.20877i
$167$	21.9273	+	9.08260i	1.69679	+	0.702833i	0.999897	−	0.0143440i	$-0.00456599\pi$
$167$	21.9273	+	9.08260i	1.69679	+	0.702833i	0.696891	+	0.717177i	$0.254566\pi$
$168$	1.68456	−	1.68456i	0.129967	−	0.129967i
$169$	3.33607			0.256621
$170$		0			0
$171$	−1.91688			−0.146587
$172$	−5.13048	+	5.13048i	−0.391195	+	0.391195i
$173$	3.84503	+	1.59266i	0.292332	+	0.121088i	0.524030	−	0.851700i	$-0.324428\pi$
$173$	3.84503	+	1.59266i	0.292332	+	0.121088i	−0.231698	+	0.972788i	$0.574428\pi$
$174$			2.36928i			0.179615i
$175$		0			0
$176$	0.233094	−	0.0965508i	0.0175701	−	0.00727779i
$177$	−1.90399	−	4.59664i	−0.143113	−	0.345505i
$178$	8.43238	+	8.43238i	0.632034	+	0.632034i
$179$	9.42514	+	9.42514i	0.704468	+	0.704468i	0.965366	−	0.260898i	$-0.0840186\pi$
$179$	9.42514	+	9.42514i	0.704468	+	0.704468i	−0.260898	+	0.965366i	$0.584019\pi$
$180$		0			0
$181$	−7.74313	+	3.20731i	−0.575543	+	0.238398i	−0.651417	−	0.758720i	$-0.725825\pi$
$181$	−7.74313	+	3.20731i	−0.575543	+	0.238398i	0.0758745	+	0.997117i	$0.475825\pi$
$182$	−1.35208	+	3.26421i	−0.100223	+	0.241959i
$183$			15.4054i			1.13880i
$184$	0.694615	+	0.287719i	0.0512077	+	0.0212109i
$185$		0			0
$186$	−1.95869			−0.143618
$187$	−0.975211	−	0.362076i	−0.0713145	−	0.0264776i
$188$	−9.71535			−0.708565
$189$	−2.70587	+	2.70587i	−0.196823	+	0.196823i
$190$		0			0
$191$			8.37154i			0.605743i	0.953031	+	0.302872i	$0.0979453\pi$
$191$			8.37154i			0.605743i	−0.953031	+	0.302872i	$0.902055\pi$
$192$	0.802151	−	1.93656i	0.0578903	−	0.139760i
$193$	7.26832	−	3.01064i	0.523185	−	0.216710i	−0.105430	−	0.994427i	$-0.533622\pi$
$193$	7.26832	−	3.01064i	0.523185	−	0.216710i	0.628615	+	0.777716i	$0.283622\pi$
$194$	−6.02292	−	14.5406i	−0.432420	−	1.04395i
$195$		0			0
$196$	−4.03636	−	4.03636i	−0.288311	−	0.288311i
$197$	0.174372	+	0.420971i	0.0124235	+	0.0299929i	0.929970	−	0.367637i	$-0.119833\pi$
$197$	0.174372	+	0.420971i	0.0124235	+	0.0299929i	−0.917546	+	0.397629i	$0.869833\pi$
$198$	0.324871	−	0.134566i	0.0230875	−	0.00956318i
$199$	−3.51474	+	8.48532i	−0.249153	+	0.601509i	−0.998133	−	0.0610845i	$-0.980544\pi$
$199$	−3.51474	+	8.48532i	−0.249153	+	0.601509i	0.748980	+	0.662593i	$0.230544\pi$
$200$		0			0
$201$	30.6314	+	12.6879i	2.16057	+	0.894939i
$202$	1.34918	−	1.34918i	0.0949283	−	0.0949283i
$203$	−1.28465			−0.0901650
$204$	−7.85615	+	3.60198i	−0.550041	+	0.252189i
$205$		0			0
$206$	1.16315	−	1.16315i	0.0810408	−	0.0810408i
$207$	0.968106	+	0.401002i	0.0672880	+	0.0278716i
$208$			3.10869i			0.215549i
$209$	0.132792	−	0.320588i	0.00918541	−	0.0221755i
$210$		0			0
$211$	−2.91050	−	7.02656i	−0.200367	−	0.483728i	0.791475	−	0.611201i	$-0.209313\pi$
$211$	−2.91050	−	7.02656i	−0.200367	−	0.483728i	−0.991842	+	0.127473i	$0.959313\pi$
$212$	−9.25847	−	9.25847i	−0.635875	−	0.635875i
$213$	−3.77257	−	3.77257i	−0.258492	−	0.258492i
$214$	4.48481	+	10.8273i	0.306575	+	0.740139i
$215$		0			0
$216$	−1.28847	+	3.11065i	−0.0876694	+	0.211653i
$217$		−	1.06203i		−	0.0720951i
$218$	−1.92407	−	0.796977i	−0.130315	−	0.0539781i
$219$	−14.7540	+	14.7540i	−0.996986	+	0.996986i
$220$		0			0
$221$	8.72001	−	9.39405i	0.586571	−	0.631912i
$222$	−10.3039			−0.691550
$223$	−1.91171	+	1.91171i	−0.128017	+	0.128017i	−0.768212	−	0.640195i	$-0.778854\pi$
$223$	−1.91171	+	1.91171i	−0.128017	+	0.128017i	0.640195	+	0.768212i	$0.278854\pi$
$224$	1.05003	+	0.434936i	0.0701580	+	0.0290604i
$225$		0			0
$226$	−3.38057	+	8.16143i	−0.224872	+	0.542890i
$227$	8.71853	−	3.61134i	0.578669	−	0.239693i	−0.0740982	−	0.997251i	$-0.523608\pi$
$227$	8.71853	−	3.61134i	0.578669	−	0.239693i	0.652768	+	0.757558i	$0.273608\pi$
$228$	−1.10324	−	2.66347i	−0.0730642	−	0.176392i
$229$	−6.37289	−	6.37289i	−0.421133	−	0.421133i	0.464461	−	0.885594i	$-0.346248\pi$
$229$	−6.37289	−	6.37289i	−0.421133	−	0.421133i	−0.885594	+	0.464461i	$0.846248\pi$
$230$		0			0
$231$	0.230016	+	0.555309i	0.0151340	+	0.0365366i
$232$	−1.04428	+	0.432553i	−0.0685601	+	0.0283985i
$233$	−5.08986	+	12.2880i	−0.333448	+	0.805015i	0.664866	+	0.746963i	$0.268489\pi$
$233$	−5.08986	+	12.2880i	−0.333448	+	0.805015i	−0.998314	+	0.0580517i	$0.981511\pi$
$234$			4.33267i			0.283235i
$235$		0			0
$236$	1.67839	−	1.67839i	0.109254	−	0.109254i
$237$	−29.3978			−1.90959
$238$	−1.95304	−	4.25970i	−0.126597	−	0.276116i
$239$	−2.66720			−0.172527			−0.0862633	−	0.996272i	$-0.527493\pi$
$239$	−2.66720			−0.172527			−0.0862633	+	0.996272i	$0.527493\pi$
$240$		0			0
$241$	−0.493333	−	0.204345i	−0.0317784	−	0.0131630i	0.366738	−	0.930324i	$-0.380475\pi$
$241$	−0.493333	−	0.204345i	−0.0317784	−	0.0131630i	−0.398516	+	0.917161i	$0.630475\pi$
$242$		−	10.9363i		−	0.703015i
$243$	−5.14973	+	12.4325i	−0.330355	+	0.797548i
$244$	−6.79001	+	2.81251i	−0.434686	+	0.180053i
$245$		0			0
$246$	−14.2463	−	14.2463i	−0.908311	−	0.908311i
$247$	3.02327	+	3.02327i	0.192366	+	0.192366i
$248$	−0.357593	−	0.863307i	−0.0227072	−	0.0548200i
$249$	30.1600	−	12.4927i	1.91131	−	0.791691i
$250$		0			0
$251$		−	13.3789i		−	0.844468i	−0.906487	−	0.422234i	$-0.861246\pi$
$251$		−	13.3789i		−	0.844468i	0.906487	−	0.422234i	$-0.138754\pi$
$252$	1.46346	+	0.606184i	0.0921892	+	0.0381860i
$253$	−0.134131	+	0.134131i	−0.00843276	+	0.00843276i
$254$	10.4420			0.655191
$255$		0			0
$256$	1.00000			0.0625000
$257$	13.6909	−	13.6909i	0.854013	−	0.854013i	−0.136612	−	0.990625i	$-0.543621\pi$
$257$	13.6909	−	13.6909i	0.854013	−	0.854013i	0.990625	+	0.136612i	$0.0436213\pi$
$258$	−14.0509	−	5.82008i	−0.874773	−	0.362343i
$259$		−	5.58688i		−	0.347152i
$260$		0			0
$261$	−1.45544	+	0.602863i	−0.0900894	+	0.0373163i
$262$	−3.71255	−	8.96288i	−0.229362	−	0.553728i
$263$	−8.55368	−	8.55368i	−0.527442	−	0.527442i	0.392367	−	0.919809i	$-0.371656\pi$
$263$	−8.55368	−	8.55368i	−0.527442	−	0.527442i	−0.919809	+	0.392367i	$0.871656\pi$
$264$	0.373954	+	0.373954i	0.0230153	+	0.0230153i
$265$		0			0
$266$	1.44417	−	0.598193i	0.0885474	−	0.0366776i
$267$	−9.56581	+	23.0939i	−0.585418	+	1.41332i
$268$			15.8174i			0.966201i
$269$	18.4733	+	7.65189i	1.12634	+	0.466544i	0.866534	−	0.499118i	$-0.166343\pi$
$269$	18.4733	+	7.65189i	1.12634	+	0.466544i	0.259802	+	0.965662i	$0.416343\pi$
$270$		0			0
$271$	−3.67946			−0.223511			−0.111756	−	0.993736i	$-0.535647\pi$
$271$	−3.67946			−0.223511			−0.111756	+	0.993736i	$0.535647\pi$
$272$	−3.02187	−	2.80505i	−0.183228	−	0.170081i
$273$	−7.40593			−0.448227
$274$	−3.21888	+	3.21888i	−0.194460	+	0.194460i
$275$		0			0
$276$			1.57596i			0.0948617i
$277$	−5.03180	+	12.1478i	−0.302331	+	0.729892i	0.697579	+	0.716508i	$0.254261\pi$
$277$	−5.03180	+	12.1478i	−0.302331	+	0.729892i	−0.999910	+	0.0133845i	$0.995739\pi$
$278$	11.5541	−	4.78586i	0.692967	−	0.287037i
$279$	−0.498389	−	1.20322i	−0.0298377	−	0.0720347i
$280$		0			0
$281$	6.24669	+	6.24669i	0.372646	+	0.372646i	0.868440	−	0.495794i	$-0.165123\pi$
$281$	6.24669	+	6.24669i	0.372646	+	0.372646i	−0.495794	+	0.868440i	$0.665123\pi$
$282$	−7.79318	−	18.8144i	−0.464077	−	1.12038i
$283$	−5.15384	+	2.13479i	−0.306364	+	0.126900i	−0.530569	−	0.847642i	$-0.678022\pi$
$283$	−5.15384	+	2.13479i	−0.306364	+	0.126900i	0.224205	+	0.974542i	$0.428022\pi$
$284$	0.974036	−	2.35153i	0.0577984	−	0.139538i
$285$		0			0
$286$	−0.724617	−	0.300146i	−0.0428475	−	0.0177480i
$287$	7.72452	−	7.72452i	0.455964	−	0.455964i
$288$	1.39373			0.0821263
$289$	1.26343	+	16.9530i	0.0743192	+	0.997235i
$290$		0			0
$291$	23.3275	−	23.3275i	1.36748	−	1.36748i
$292$	−9.19654	−	3.80933i	−0.538187	−	0.222924i
$293$			23.5631i			1.37657i	0.725439	+	0.688286i	$0.241637\pi$
$293$			23.5631i			1.37657i	−0.725439	+	0.688286i	$0.758363\pi$
$294$	4.57890	−	11.0544i	0.267047	−	0.644708i
$295$		0			0
$296$	−1.88115	−	4.54149i	−0.109339	−	0.263969i
$297$	−0.600671	−	0.600671i	−0.0348545	−	0.0348545i
$298$	15.7407	+	15.7407i	0.911835	+	0.911835i
$299$	−0.894428	−	2.15934i	−0.0517261	−	0.124878i
$300$		0			0
$301$	3.15572	−	7.61859i	0.181893	−	0.439128i
$302$		−	10.0882i		−	0.580509i
$303$	3.69503	+	1.53053i	0.212274	+	0.0879268i
$304$	0.972524	−	0.972524i	0.0557781	−	0.0557781i
$305$		0			0
$306$	−4.21167	−	3.90948i	−0.240765	−	0.223490i
$307$	13.7608			0.785371			0.392686	−	0.919673i	$-0.371546\pi$
$307$	13.7608			0.785371			0.392686	+	0.919673i	$0.371546\pi$
$308$	−0.202762	+	0.202762i	−0.0115535	+	0.0115535i
$309$	3.18555	+	1.31950i	0.181220	+	0.0750636i
$310$		0			0
$311$	−7.91601	+	19.1109i	−0.448876	+	1.08368i	0.523868	+	0.851799i	$0.324488\pi$
$311$	−7.91601	+	19.1109i	−0.448876	+	1.08368i	−0.972744	+	0.231882i	$0.925512\pi$
$312$	−6.02017	+	2.49364i	−0.340825	+	0.141174i
$313$	−9.54896	−	23.0532i	−0.539739	−	1.30305i	−0.924905	−	0.380198i	$-0.875856\pi$
$313$	−9.54896	−	23.0532i	−0.539739	−	1.30305i	0.385166	−	0.922847i	$-0.374144\pi$
$314$	11.6895	+	11.6895i	0.659678	+	0.659678i
$315$		0			0
$316$	−5.36708	−	12.9573i	−0.301922	−	0.728904i
$317$	8.04517	−	3.33242i	0.451862	−	0.187167i	−0.145133	−	0.989412i	$-0.546361\pi$
$317$	8.04517	−	3.33242i	0.451862	−	0.187167i	0.596995	+	0.802245i	$0.296361\pi$
$318$	10.5029	−	25.3563i	0.588975	−	1.42191i
$319$		−	0.285178i		−	0.0159669i
$320$		0			0
$321$	−17.3703	+	17.3703i	−0.969513	+	0.969513i
$322$	−0.854505			−0.0476197
$323$	−5.66682	+	0.210868i	−0.315310	+	0.0117330i
$324$	−11.2387			−0.624373
$325$		0			0
$326$	1.72641	+	0.715103i	0.0956171	+	0.0396059i
$327$		−	4.36539i		−	0.241407i
$328$	3.67824	−	8.88006i	0.203097	−	0.490319i
$329$	10.2014	−	4.22556i	0.562422	−	0.232963i
$330$		0			0
$331$	−14.5302	−	14.5302i	−0.798649	−	0.798649i	0.184233	−	0.982883i	$-0.441020\pi$
$331$	−14.5302	−	14.5302i	−0.798649	−	0.798649i	−0.982883	+	0.184233i	$0.941020\pi$
$332$	11.0125	+	11.0125i	0.604387	+	0.604387i
$333$	−2.62181	−	6.32962i	−0.143674	−	0.346861i
$334$	−21.9273	+	9.08260i	−1.19981	+	0.496978i
$335$		0			0
$336$			2.38233i			0.129967i
$337$	28.2402	+	11.6975i	1.53834	+	0.637202i	0.981161	−	0.193191i	$-0.0618836\pi$
$337$	28.2402	+	11.6975i	1.53834	+	0.637202i	0.557179	+	0.830392i	$0.311884\pi$
$338$	−2.35896	+	2.35896i	−0.128310	+	0.128310i
$339$	−18.5169			−1.00570
$340$		0			0
$341$	0.235758			0.0127670
$342$	1.35544	−	1.35544i	0.0732936	−	0.0732936i
$343$	13.3441	+	5.52729i	0.720511	+	0.298446i
$344$		−	7.25559i		−	0.391195i
$345$		0			0
$346$	−3.84503	+	1.59266i	−0.206710	+	0.0856221i
$347$	6.49858	+	15.6890i	0.348862	+	0.842228i	0.996755	+	0.0804961i	$0.0256504\pi$
$347$	6.49858	+	15.6890i	0.348862	+	0.842228i	−0.647893	+	0.761731i	$0.724350\pi$
$348$	−1.67534	−	1.67534i	−0.0898074	−	0.0898074i
$349$	−15.8641	−	15.8641i	−0.849188	−	0.849188i	0.140844	−	0.990032i	$-0.455018\pi$
$349$	−15.8641	−	15.8641i	−0.849188	−	0.849188i	−0.990032	+	0.140844i	$0.955018\pi$
$350$		0			0
$351$	9.67002	−	4.00545i	0.516148	−	0.213795i
$352$	−0.0965508	+	0.233094i	−0.00514618	+	0.0124240i
$353$		−	22.5509i		−	1.20026i	−0.799902	−	0.600131i	$-0.795115\pi$
$353$		−	22.5509i		−	1.20026i	0.799902	−	0.600131i	$-0.204885\pi$
$354$	4.59664	+	1.90399i	0.244309	+	0.101196i
$355$		0			0
$356$	−11.9252			−0.632034
$357$	6.68256	−	7.19911i	0.353679	−	0.381017i
$358$	−13.3292			−0.704468
$359$	−7.45653	+	7.45653i	−0.393540	+	0.393540i	−0.875947	−	0.482407i	$-0.839763\pi$
$359$	−7.45653	+	7.45653i	−0.393540	+	0.393540i	0.482407	+	0.875947i	$0.339763\pi$
$360$		0			0
$361$			17.1084i			0.900442i
$362$	3.20731	−	7.74313i	0.168573	−	0.406970i
$363$	21.1789	−	8.77260i	1.11161	−	0.460442i
$364$	−1.35208	−	3.26421i	−0.0708683	−	0.171091i
$365$		0			0
$366$	−10.8932	−	10.8932i	−0.569398	−	0.569398i
$367$	11.9104	+	28.7544i	0.621720	+	1.50097i	0.849682	+	0.527296i	$0.176794\pi$
$367$	11.9104	+	28.7544i	0.621720	+	1.50097i	−0.227962	+	0.973670i	$0.573206\pi$
$368$	−0.694615	+	0.287719i	−0.0362093	+	0.0149984i
$369$	5.12647	−	12.3764i	0.266874	−	0.644290i
$370$		0			0
$371$	13.7485	+	5.69482i	0.713787	+	0.295660i
$372$	1.38501	−	1.38501i	0.0718092	−	0.0718092i
$373$	21.7151			1.12437			0.562183	−	0.827013i	$-0.309962\pi$
$373$	21.7151			1.12437			0.562183	+	0.827013i	$0.309962\pi$
$374$	0.945605	−	0.433552i	0.0488961	−	0.0224184i
$375$		0			0
$376$	6.86979	−	6.86979i	0.354282	−	0.354282i
$377$	3.24633	+	1.34467i	0.167194	+	0.0692542i
$378$		−	3.82667i		−	0.196823i
$379$	9.02028	−	21.7769i	0.463341	−	1.11860i	−0.503677	−	0.863892i	$-0.668020\pi$
$379$	9.02028	−	21.7769i	0.463341	−	1.11860i	0.967017	−	0.254711i	$-0.0819803\pi$
$380$		0			0
$381$	8.37608	+	20.2217i	0.429120	+	1.03599i
$382$	−5.91957	−	5.91957i	−0.302872	−	0.302872i
$383$	−22.8956	−	22.8956i	−1.16991	−	1.16991i	−0.982230	−	0.187683i	$-0.939902\pi$
$383$	−22.8956	−	22.8956i	−1.16991	−	1.16991i	−0.187683	−	0.982230i	$-0.560098\pi$
$384$	0.802151	+	1.93656i	0.0409346	+	0.0988249i
$385$		0			0
$386$	−3.01064	+	7.26832i	−0.153237	+	0.369948i
$387$		−	10.1123i		−	0.514039i
$388$	14.5406	+	6.02292i	0.738188	+	0.305767i
$389$	5.57424	−	5.57424i	0.282625	−	0.282625i	−0.551530	−	0.834155i	$-0.685956\pi$
$389$	5.57424	−	5.57424i	0.282625	−	0.282625i	0.834155	+	0.551530i	$0.185956\pi$
$390$		0			0
$391$	2.90610	+	1.07898i	0.146968	+	0.0545662i
$392$	5.70827			0.288311
$393$	14.3792	−	14.3792i	0.725333	−	0.725333i
$394$	−0.420971	−	0.174372i	−0.0212082	−	0.00878472i
$395$		0			0
$396$	−0.134566	+	0.324871i	−0.00676219	+	0.0163254i
$397$	−33.1614	+	13.7359i	−1.66432	+	0.689386i	−0.998395	−	0.0566296i	$-0.981965\pi$
$397$	−33.1614	+	13.7359i	−1.66432	+	0.689386i	−0.665929	+	0.746015i	$0.731965\pi$
$398$	−3.51474	−	8.48532i	−0.176178	−	0.425331i
$399$	2.31688	+	2.31688i	0.115989	+	0.115989i
$400$		0			0
$401$	−10.1715	−	24.5561i	−0.507940	−	1.22627i	−0.945067	−	0.326875i	$-0.894004\pi$
$401$	−10.1715	−	24.5561i	−0.507940	−	1.22627i	0.437128	−	0.899399i	$-0.355996\pi$
$402$	−30.6314	+	12.6879i	−1.52776	+	0.632817i
$403$	−1.11165	+	2.68375i	−0.0553750	+	0.133687i
$404$			1.90803i			0.0949283i
$405$		0			0
$406$	0.908387	−	0.908387i	0.0450825	−	0.0450825i
$407$	1.24022			0.0614756
$408$	3.00816	−	8.10212i	0.148926	−	0.401115i
$409$	10.6807			0.528128			0.264064	−	0.964505i	$-0.414937\pi$
$409$	10.6807			0.528128			0.264064	+	0.964505i	$0.414937\pi$
$410$		0			0
$411$	−8.81560	−	3.65154i	−0.434841	−	0.180117i
$412$			1.64495i			0.0810408i
$413$	−1.03237	+	2.49236i	−0.0507995	+	0.122641i
$414$	−0.968106	+	0.401002i	−0.0475798	+	0.0197082i
$415$		0			0
$416$	−2.19817	−	2.19817i	−0.107774	−	0.107774i
$417$	18.5362	+	18.5362i	0.907723	+	0.907723i
$418$	0.132792	+	0.320588i	0.00649506	+	0.0156805i
$419$	26.3201	−	10.9021i	1.28582	−	0.532604i	0.368083	−	0.929793i	$-0.380014\pi$
$419$	26.3201	−	10.9021i	1.28582	−	0.532604i	0.917737	+	0.397189i	$0.130014\pi$
$420$		0			0
$421$			9.11011i			0.444000i	0.975047	+	0.222000i	$0.0712584\pi$
$421$			9.11011i			0.444000i	−0.975047	+	0.222000i	$0.928742\pi$
$422$	7.02656	+	2.91050i	0.342048	+	0.141681i
$423$	9.57464	−	9.57464i	0.465535	−	0.465535i
$424$	13.0935			0.635875
$425$		0			0
$426$	5.33522			0.258492
$427$	5.90644	−	5.90644i	0.285833	−	0.285833i
$428$	−10.8273	−	4.48481i	−0.523357	−	0.216782i
$429$		−	1.64403i		−	0.0793746i
$430$		0			0
$431$	35.6926	−	14.7843i	1.71925	−	0.712137i	0.719405	−	0.694591i	$-0.244415\pi$
$431$	35.6926	−	14.7843i	1.71925	−	0.712137i	0.999846	−	0.0175458i	$-0.00558529\pi$
$432$	−1.28847	−	3.11065i	−0.0619916	−	0.149661i
$433$	−4.09685	−	4.09685i	−0.196882	−	0.196882i	0.601780	−	0.798662i	$-0.294458\pi$
$433$	−4.09685	−	4.09685i	−0.196882	−	0.196882i	−0.798662	+	0.601780i	$0.794458\pi$
$434$	0.750967	+	0.750967i	0.0360476	+	0.0360476i
$435$		0			0
$436$	1.92407	−	0.796977i	0.0921464	−	0.0381683i
$437$	−0.395716	+	0.955343i	−0.0189297	+	0.0457003i
$438$		−	20.8654i		−	0.996986i
$439$	−29.9651	−	12.4119i	−1.43015	−	0.592390i	−0.472765	−	0.881188i	$-0.656744\pi$
$439$	−29.9651	−	12.4119i	−1.43015	−	0.592390i	−0.957390	+	0.288799i	$0.906744\pi$
$440$		0			0
$441$	7.95579			0.378847
$442$	0.476621	+	12.8086i	0.0226705	+	0.609242i
$443$	10.1719			0.483280			0.241640	−	0.970366i	$-0.422315\pi$
$443$	10.1719			0.483280			0.241640	+	0.970366i	$0.422315\pi$
$444$	7.28593	−	7.28593i	0.345775	−	0.345775i
$445$		0			0
$446$		−	2.70356i		−	0.128017i
$447$	−17.8565	+	43.1094i	−0.844582	+	2.03900i
$448$	−1.05003	+	0.434936i	−0.0496092	+	0.0205488i
$449$	1.99926	+	4.82665i	0.0943510	+	0.227783i	0.964008	−	0.265873i	$-0.0856601\pi$
$449$	1.99926	+	4.82665i	0.0943510	+	0.227783i	−0.869657	+	0.493656i	$0.835660\pi$
$450$		0			0
$451$	1.71475	+	1.71475i	0.0807446	+	0.0807446i
$452$	−3.38057	−	8.16143i	−0.159009	−	0.383881i
$453$	19.5364	−	8.09224i	0.917899	−	0.380206i
$454$	−3.61134	+	8.71853i	−0.169488	+	0.409181i
$455$		0			0
$456$	2.66347	+	1.10324i	0.124728	+	0.0516642i
$457$	0.312397	−	0.312397i	0.0146133	−	0.0146133i	−0.699762	−	0.714376i	$-0.746711\pi$
$457$	0.312397	−	0.312397i	0.0146133	−	0.0146133i	0.714376	+	0.699762i	$0.246711\pi$
$458$	9.01263			0.421133
$459$	−4.83191	+	13.0142i	−0.225534	+	0.607451i
$460$		0			0
$461$	2.56589	−	2.56589i	0.119505	−	0.119505i	−0.644825	−	0.764330i	$-0.723070\pi$
$461$	2.56589	−	2.56589i	0.119505	−	0.119505i	0.764330	+	0.644825i	$0.223070\pi$
$462$	−0.555309	−	0.230016i	−0.0258353	−	0.0107013i
$463$		−	12.2323i		−	0.568483i	−0.958753	−	0.284241i	$-0.908258\pi$
$463$		−	12.2323i		−	0.568483i	0.958753	−	0.284241i	$-0.0917417\pi$
$464$	0.432553	−	1.04428i	0.0200808	−	0.0484793i
$465$		0			0
$466$	−5.08986	−	12.2880i	−0.235783	−	0.569231i
$467$	−22.0816	−	22.0816i	−1.02182	−	1.02182i	−0.999757	−	0.0220584i	$-0.992978\pi$
$467$	−22.0816	−	22.0816i	−1.02182	−	1.02182i	−0.0220584	−	0.999757i	$-0.507022\pi$
$468$	−3.06366	−	3.06366i	−0.141618	−	0.141618i
$469$	−6.87956	−	16.6087i	−0.317669	−	0.766920i
$470$		0			0
$471$	−13.2607	+	32.0143i	−0.611023	+	1.47514i
$472$			2.37361i			0.109254i
$473$	1.69124	+	0.700534i	0.0777632	+	0.0322106i
$474$	20.7874	−	20.7874i	0.954797	−	0.954797i
$475$		0			0
$476$	4.39307	+	1.63106i	0.201356	+	0.0747595i
$477$	18.2487			0.835553
$478$	1.88599	−	1.88599i	0.0862633	−	0.0862633i
$479$	−3.32393	−	1.37682i	−0.151874	−	0.0629084i	0.305451	−	0.952208i	$-0.401193\pi$
$479$	−3.32393	−	1.37682i	−0.151874	−	0.0629084i	−0.457326	+	0.889299i	$0.651193\pi$
$480$		0			0
$481$	−5.84790	+	14.1181i	−0.266641	+	0.643729i
$482$	0.493333	−	0.204345i	0.0224707	−	0.00930766i
$483$	−0.685443	−	1.65480i	−0.0311887	−	0.0752962i
$484$	7.73316	+	7.73316i	0.351507	+	0.351507i
$485$		0			0
$486$	−5.14973	−	12.4325i	−0.233596	−	0.563952i
$487$	−19.9459	+	8.26188i	−0.903837	+	0.374381i	−0.785694	−	0.618615i	$-0.787694\pi$
$487$	−19.9459	+	8.26188i	−0.903837	+	0.374381i	−0.118143	+	0.992997i	$0.537694\pi$
$488$	2.81251	−	6.79001i	0.127316	−	0.307369i
$489$			3.91693i			0.177130i
$490$		0			0
$491$	26.3349	−	26.3349i	1.18848	−	1.18848i	0.210992	−	0.977488i	$-0.432331\pi$
$491$	26.3349	−	26.3349i	1.18848	−	1.18848i	0.977488	−	0.210992i	$-0.0676693\pi$
$492$	20.1473			0.908311
$493$	−4.23636	+	1.94234i	−0.190796	+	0.0874785i
$494$	−4.27555			−0.192366
$495$		0			0
$496$	0.863307	+	0.357593i	0.0387636	+	0.0160564i
$497$			2.89282i			0.129761i
$498$	−12.4927	+	30.1600i	−0.559810	+	1.35150i
$499$	14.3055	−	5.92555i	0.640404	−	0.265264i	−0.0387621	−	0.999248i	$-0.512341\pi$
$499$	14.3055	−	5.92555i	0.640404	−	0.265264i	0.679166	+	0.733984i	$0.262341\pi$
$500$		0			0
$501$	−35.1781	−	35.1781i	−1.57164	−	1.57164i
$502$	9.46030	+	9.46030i	0.422234	+	0.422234i
$503$	−0.469717	−	1.13400i	−0.0209436	−	0.0505624i	0.913062	−	0.407821i	$-0.133711\pi$
$503$	−0.469717	−	1.13400i	−0.0209436	−	0.0505624i	−0.934005	+	0.357259i	$0.883711\pi$
$504$	−1.46346	+	0.606184i	−0.0651876	+	0.0270016i
$505$		0			0
$506$		−	0.189690i		−	0.00843276i
$507$	−6.46052	−	2.67603i	−0.286922	−	0.118847i
$508$	−7.38362	+	7.38362i	−0.327595	+	0.327595i
$509$	−25.8063			−1.14384			−0.571922	−	0.820308i	$-0.693802\pi$
$509$	−25.8063			−1.14384			−0.571922	+	0.820308i	$0.693802\pi$
$510$		0			0
$511$	11.3135			0.500478
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−4.27825	−	1.77211i	−0.188889	−	0.0782405i
$514$			19.3618i			0.854013i
$515$		0			0
$516$	14.0509	−	5.82008i	0.618558	−	0.256215i
$517$	0.938025	+	2.26459i	0.0412543	+	0.0995967i
$518$	3.95052	+	3.95052i	0.173576	+	0.173576i
$519$	−6.16859	−	6.16859i	−0.270771	−	0.270771i
$520$		0			0
$521$	−26.9444	+	11.1607i	−1.18046	+	0.488961i	−0.884636	−	0.466283i	$-0.845593\pi$
$521$	−26.9444	+	11.1607i	−1.18046	+	0.488961i	−0.295820	+	0.955244i	$0.595593\pi$
$522$	0.602863	−	1.45544i	0.0263866	−	0.0637028i
$523$		−	33.4958i		−	1.46467i	−0.680946	−	0.732334i	$-0.738431\pi$
$523$		−	33.4958i		−	1.46467i	0.680946	−	0.732334i	$-0.261569\pi$
$524$	8.96288	+	3.71255i	0.391545	+	0.162183i
$525$		0			0
$526$	12.0967			0.527442
$527$	−1.60574	−	3.50222i	−0.0699470	−	0.152559i
$528$	−0.528851			−0.0230153
$529$	−15.8637	+	15.8637i	−0.689728	+	0.689728i
$530$		0			0
$531$			3.30817i			0.143562i
$532$	−0.598193	+	1.44417i	−0.0259349	+	0.0626125i
$533$	−27.6053	+	11.4345i	−1.19572	+	0.495283i
$534$	−9.56581	−	23.0939i	−0.413953	−	0.999371i
$535$		0			0
$536$	−11.1846	−	11.1846i	−0.483101	−	0.483101i
$537$	−10.6920	−	25.8128i	−0.461394	−	1.11390i
$538$	−18.4733	+	7.65189i	−0.796440	+	0.329896i
$539$	−0.551138	+	1.33057i	−0.0237392	+	0.0573115i
$540$		0			0
$541$	38.3693	+	15.8931i	1.64962	+	0.683297i	0.997216	−	0.0745705i	$-0.0237586\pi$
$541$	38.3693	+	15.8931i	1.64962	+	0.683297i	0.652409	+	0.757867i	$0.273759\pi$
$542$	2.60177	−	2.60177i	0.111756	−	0.111756i
$543$	17.5678			0.753908
$544$	4.12025	−	0.153319i	0.176654	−	0.00657350i
$545$		0			0
$546$	5.23678	−	5.23678i	0.224114	−	0.224114i
$547$	−11.2756	−	4.67049i	−0.482109	−	0.199696i	0.128374	−	0.991726i	$-0.459024\pi$
$547$	−11.2756	−	4.67049i	−0.482109	−	0.199696i	−0.610482	+	0.792030i	$0.709024\pi$
$548$		−	4.55218i		−	0.194460i
$549$	3.91988	−	9.46344i	0.167297	−	0.403890i
$550$		0			0
$551$	−0.594915	−	1.43625i	−0.0253442	−	0.0611864i
$552$	−1.11437	−	1.11437i	−0.0474308	−	0.0474308i
$553$	11.2712	+	11.2712i	0.479299	+	0.479299i
$554$	−5.03180	−	12.1478i	−0.213780	−	0.516112i
$555$		0			0
$556$	−4.78586	+	11.5541i	−0.202965	+	0.490002i
$557$		−	11.7983i		−	0.499909i	−0.968258	−	0.249954i	$-0.919584\pi$
$557$		−	11.7983i		−	0.499909i	0.968258	−	0.249954i	$-0.0804156\pi$
$558$	1.20322	+	0.498389i	0.0509362	+	0.0210985i
$559$	−15.9491	+	15.9491i	−0.674573	+	0.674573i
$560$		0			0
$561$	1.59812	+	1.48345i	0.0674726	+	0.0626313i
$562$	−8.83415			−0.372646
$563$	−24.1004	+	24.1004i	−1.01571	+	1.01571i	−0.0158341	+	0.999875i	$0.505040\pi$
$563$	−24.1004	+	24.1004i	−1.01571	+	1.01571i	−0.999875	+	0.0158341i	$0.994960\pi$
$564$	18.8144	+	7.79318i	0.792230	+	0.328152i
$565$		0			0
$566$	2.13479	−	5.15384i	0.0897319	−	0.216632i
$567$	11.8010	−	4.88812i	0.495594	−	0.205282i
$568$	0.974036	+	2.35153i	0.0408697	+	0.0986681i
$569$	20.1508	+	20.1508i	0.844766	+	0.844766i	0.989474	−	0.144708i	$-0.0462244\pi$
$569$	20.1508	+	20.1508i	0.844766	+	0.844766i	−0.144708	+	0.989474i	$0.546224\pi$
$570$		0			0
$571$	−11.0538	−	26.6863i	−0.462589	−	1.11679i	−0.967331	−	0.253518i	$-0.918412\pi$
$571$	−11.0538	−	26.6863i	−0.462589	−	1.11679i	0.504742	−	0.863270i	$-0.331588\pi$
$572$	0.724617	−	0.300146i	0.0302978	−	0.0125497i
$573$	6.71524	−	16.2120i	0.280533	−	0.677267i
$574$			10.9241i			0.455964i
$575$		0			0
$576$	−0.985516	+	0.985516i	−0.0410632	+	0.0410632i
$577$	3.90595			0.162607			0.0813033	−	0.996689i	$-0.474092\pi$
$577$	3.90595			0.162607			0.0813033	+	0.996689i	$0.474092\pi$
$578$	−12.8809	−	11.0942i	−0.535777	−	0.461458i
$579$	−16.4906			−0.685324
$580$		0			0
$581$	−16.3531	−	6.77368i	−0.678441	−	0.281020i
$582$			32.9901i			1.36748i
$583$	−1.26418	+	3.05201i	−0.0523572	+	0.126401i
$584$	9.19654	−	3.80933i	0.380556	−	0.157631i
$585$		0			0
$586$	−16.6616	−	16.6616i	−0.688286	−	0.688286i
$587$	−28.0684	−	28.0684i	−1.15851	−	1.15851i	−0.984797	−	0.173712i	$-0.944424\pi$
$587$	−28.0684	−	28.0684i	−1.15851	−	1.15851i	−0.173712	−	0.984797i	$-0.555576\pi$
$588$	4.57890	+	11.0544i	0.188830	+	0.455877i
$589$	1.18736	−	0.491819i	0.0489241	−	0.0202650i
$590$		0			0
$591$		−	0.955110i		−	0.0392880i
$592$	4.54149	+	1.88115i	0.186654	+	0.0773147i
$593$	−24.5468	+	24.5468i	−1.00802	+	1.00802i	−0.00804758	+	0.999968i	$0.502562\pi$
$593$	−24.5468	+	24.5468i	−1.00802	+	1.00802i	−0.999968	+	0.00804758i	$0.997438\pi$
$594$	0.849477			0.0348545
$595$		0			0
$596$	−22.2607			−0.911835
$597$	13.6130	−	13.6130i	0.557144	−	0.557144i
$598$	2.15934	+	0.894428i	0.0883020	+	0.0365759i
$599$			2.16423i			0.0884281i	0.999022	+	0.0442140i	$0.0140784\pi$
$599$			2.16423i			0.0884281i	−0.999022	+	0.0442140i	$0.985922\pi$
$600$		0			0
$601$	19.5522	−	8.09879i	0.797551	−	0.330356i	0.0535758	−	0.998564i	$-0.482938\pi$
$601$	19.5522	−	8.09879i	0.797551	−	0.330356i	0.743975	+	0.668207i	$0.232938\pi$
$602$	3.15572	+	7.61859i	0.128618	+	0.310510i
$603$	−15.5883	−	15.5883i	−0.634805	−	0.634805i
$604$	7.13341	+	7.13341i	0.290254	+	0.290254i
$605$		0			0
$606$	−3.69503	+	1.53053i	−0.150100	+	0.0621736i
$607$	6.25210	−	15.0939i	0.253765	−	0.612642i	−0.744737	−	0.667358i	$-0.767425\pi$
$607$	6.25210	−	15.0939i	0.253765	−	0.612642i	0.998502	+	0.0547155i	$0.0174252\pi$
$608$			1.37536i			0.0557781i
$609$	2.48782	+	1.03049i	0.100811	+	0.0417574i
$610$		0			0
$611$	−30.2020			−1.22184
$612$	5.74252	−	0.213685i	0.232128	−	0.00863771i
$613$	19.6808			0.794900			0.397450	−	0.917624i	$-0.369895\pi$
$613$	19.6808			0.794900			0.397450	+	0.917624i	$0.369895\pi$
$614$	−9.73037	+	9.73037i	−0.392686	+	0.392686i
$615$		0			0
$616$		−	0.286749i		−	0.0115535i
$617$	−15.1106	+	36.4803i	−0.608331	+	1.46864i	0.256483	+	0.966549i	$0.417436\pi$
$617$	−15.1106	+	36.4803i	−0.608331	+	1.46864i	−0.864814	+	0.502092i	$0.832564\pi$
$618$	−3.18555	+	1.31950i	−0.128142	+	0.0530780i
$619$	15.9641	+	38.5407i	0.641650	+	1.54908i	0.824453	+	0.565930i	$0.191483\pi$
$619$	15.9641	+	38.5407i	0.641650	+	1.54908i	−0.182803	+	0.983150i	$0.558517\pi$
$620$		0			0
$621$	1.78998	+	1.78998i	0.0718295	+	0.0718295i
$622$	−7.91601	−	19.1109i	−0.317403	−	0.766278i
$623$	12.5218	−	5.18670i	0.501675	−	0.207801i
$624$	2.49364	−	6.02017i	0.0998254	−	0.241000i
$625$		0			0
$626$	23.0532	+	9.54896i	0.921392	+	0.381653i
$627$	−0.514320	+	0.514320i	−0.0205400	+	0.0205400i
$628$	−16.5315			−0.659678
$629$	−8.44710	−	18.4237i	−0.336808	−	0.734601i
$630$		0			0
$631$	27.0298	−	27.0298i	1.07604	−	1.07604i	0.0791769	−	0.996861i	$-0.474771\pi$
$631$	27.0298	−	27.0298i	1.07604	−	1.07604i	0.996861	−	0.0791769i	$-0.0252292\pi$
$632$	12.9573	+	5.36708i	0.515413	+	0.213491i
$633$			15.9421i			0.633640i
$634$	−3.33242	+	8.04517i	−0.132347	+	0.319515i
$635$		0			0
$636$	10.5029	+	25.3563i	0.416469	+	1.00544i
$637$	−12.5478	−	12.5478i	−0.497160	−	0.497160i
$638$	0.201651	+	0.201651i	0.00798346	+	0.00798346i
$639$	1.35754	+	3.27740i	0.0537036	+	0.129652i
$640$		0			0
$641$	3.93638	−	9.50327i	0.155478	−	0.375356i	−0.826877	−	0.562382i	$-0.809885\pi$
$641$	3.93638	−	9.50327i	0.155478	−	0.375356i	0.982355	+	0.187026i	$0.0598849\pi$
$642$		−	24.5653i		−	0.969513i
$643$	1.11434	+	0.461573i	0.0439451	+	0.0182027i	0.404548	−	0.914517i	$-0.367429\pi$
$643$	1.11434	+	0.461573i	0.0439451	+	0.0182027i	−0.360603	+	0.932720i	$0.617429\pi$
$644$	0.604226	−	0.604226i	0.0238099	−	0.0238099i
$645$		0			0
$646$	3.85794	−	4.15615i	0.151789	−	0.163522i
$647$	40.9502			1.60992			0.804958	−	0.593331i	$-0.202188\pi$
$647$	40.9502			1.60992			0.804958	+	0.593331i	$0.202188\pi$
$648$	7.94697	−	7.94697i	0.312186	−	0.312186i
$649$	−0.553274	−	0.229174i	−0.0217179	−	0.00899585i
$650$		0			0
$651$	−0.851907	+	2.05669i	−0.0333889	+	0.0806079i
$652$	−1.72641	+	0.715103i	−0.0676115	+	0.0280056i
$653$	5.10972	+	12.3360i	0.199959	+	0.482743i	0.991771	−	0.128021i	$-0.0408624\pi$
$653$	5.10972	+	12.3360i	0.199959	+	0.482743i	−0.791813	+	0.610764i	$0.790862\pi$
$654$	3.08680	+	3.08680i	0.120703	+	0.120703i
$655$		0			0
$656$	3.67824	+	8.88006i	0.143611	+	0.346708i
$657$	12.8175	−	5.30918i	0.500058	−	0.207131i
$658$	−4.22556	+	10.2014i	−0.164729	+	0.397692i
$659$			25.9742i			1.01181i	0.862589	+	0.505905i	$0.168841\pi$
$659$			25.9742i			1.01181i	−0.862589	+	0.505905i	$0.831159\pi$
$660$		0			0
$661$	−18.2918	+	18.2918i	−0.711470	+	0.711470i	−0.966843	−	0.255372i	$-0.917802\pi$
$661$	−18.2918	+	18.2918i	−0.711470	+	0.711470i	0.255372	+	0.966843i	$0.417802\pi$
$662$	20.5487			0.798649
$663$	−24.4223	+	11.1974i	−0.948484	+	0.434872i
$664$	−15.5740			−0.604387
$665$		0			0
$666$	6.32962	+	2.62181i	0.245268	+	0.101593i
$667$			0.849823i			0.0329053i
$668$	9.08260	−	21.9273i	0.351416	−	0.848394i
$669$	5.23562	−	2.16866i	0.202421	−	0.0838454i
$670$		0			0
$671$	1.31116	+	1.31116i	0.0506168	+	0.0506168i
$672$	−1.68456	−	1.68456i	−0.0649835	−	0.0649835i
$673$	−1.77044	−	4.27421i	−0.0682453	−	0.164759i	0.886077	−	0.463538i	$-0.153420\pi$
$673$	−1.77044	−	4.27421i	−0.0682453	−	0.164759i	−0.954322	+	0.298780i	$0.903420\pi$
$674$	−28.2402	+	11.6975i	−1.08777	+	0.450570i
$675$		0			0
$676$		−	3.33607i		−	0.128310i
$677$	−23.6515	−	9.79677i	−0.909001	−	0.376521i	−0.121327	−	0.992613i	$-0.538715\pi$
$677$	−23.6515	−	9.79677i	−0.909001	−	0.376521i	−0.787674	+	0.616092i	$0.788715\pi$
$678$	13.0934	−	13.0934i	0.502849	−	0.502849i
$679$	−17.8877			−0.686465
$680$		0			0
$681$	−19.7808			−0.758004
$682$	−0.166706	+	0.166706i	−0.00638350	+	0.00638350i
$683$	19.9779	+	8.27510i	0.764431	+	0.316638i	0.730614	−	0.682790i	$-0.239234\pi$
$683$	19.9779	+	8.27510i	0.764431	+	0.316638i	0.0338169	+	0.999428i	$0.489234\pi$
$684$			1.91688i			0.0732936i
$685$		0			0
$686$	−13.3441	+	5.52729i	−0.509478	+	0.211033i
$687$	7.22949	+	17.4535i	0.275822	+	0.665894i
$688$	5.13048	+	5.13048i	0.195598	+	0.195598i
$689$	−28.7817	−	28.7817i	−1.09650	−	1.09650i
$690$		0			0
$691$	−25.4956	+	10.5606i	−0.969899	+	0.401745i	−0.810674	−	0.585497i	$-0.800899\pi$
$691$	−25.4956	+	10.5606i	−0.969899	+	0.401745i	−0.159224	+	0.987242i	$0.550899\pi$
$692$	1.59266	−	3.84503i	0.0605439	−	0.146166i
$693$		−	0.399651i		−	0.0151815i
$694$	−15.6890	−	6.49858i	−0.595545	−	0.246683i
$695$		0			0
$696$	2.36928			0.0898074
$697$	13.7938	−	37.1520i	0.522478	−	1.40723i
$698$	22.4353			0.849188
$699$	19.7137	−	19.7137i	0.745641	−	0.745641i
$700$		0			0
$701$		−	11.3549i		−	0.428868i	−0.976739	−	0.214434i	$-0.931209\pi$
$701$		−	11.3549i		−	0.428868i	0.976739	−	0.214434i	$-0.0687906\pi$
$702$	−4.00545	+	9.67002i	−0.151176	+	0.364971i
$703$	6.24617	−	2.58725i	0.235579	−	0.0975800i
$704$	−0.0965508	−	0.233094i	−0.00363890	−	0.00878507i
$705$		0			0
$706$	15.9459	+	15.9459i	0.600131	+	0.600131i
$707$	−0.829874	−	2.00349i	−0.0312106	−	0.0753491i
$708$	−4.59664	+	1.90399i	−0.172752	+	0.0715564i
$709$	−3.45727	+	8.34658i	−0.129840	+	0.313462i	−0.975408	−	0.220405i	$-0.929262\pi$
$709$	−3.45727	+	8.34658i	−0.129840	+	0.313462i	0.845568	+	0.533868i	$0.179262\pi$
$710$		0			0
$711$	18.0589	+	7.48026i	0.677263	+	0.280532i
$712$	8.43238	−	8.43238i	0.316017	−	0.316017i
$713$	−0.702552			−0.0263108
$714$	0.365257	+	9.81582i	0.0136694	+	0.367348i
$715$		0			0
$716$	9.42514	−	9.42514i	0.352234	−	0.352234i
$717$	5.16520	+	2.13950i	0.192898	+	0.0799010i
$718$		−	10.5451i		−	0.393540i
$719$	−1.58656	+	3.83030i	−0.0591688	+	0.142846i	−0.950699	−	0.310115i	$-0.899632\pi$
$719$	−1.58656	+	3.83030i	−0.0591688	+	0.142846i	0.891530	+	0.452961i	$0.149632\pi$
$720$		0			0
$721$	−0.715448	−	1.72724i	−0.0266447	−	0.0643259i
$722$	−12.0975	−	12.0975i	−0.450221	−	0.450221i
$723$	0.791455	+	0.791455i	0.0294345	+	0.0294345i
$724$	3.20731	+	7.74313i	0.119199	+	0.287771i
$725$		0			0
$726$	−8.77260	+	21.1789i	−0.325582	+	0.786024i
$727$			5.28370i			0.195961i	0.995188	+	0.0979807i	$0.0312383\pi$
$727$			5.28370i			0.195961i	−0.995188	+	0.0979807i	$0.968762\pi$
$728$	3.26421	+	1.35208i	0.120980	+	0.0501114i
$729$	−3.89533	+	3.89533i	−0.144271	+	0.144271i
$730$		0			0
$731$	−1.11242	−	29.8949i	−0.0411443	−	1.10570i
$732$	15.4054			0.569398
$733$	−15.0917	+	15.0917i	−0.557424	+	0.557424i	−0.928573	−	0.371149i	$-0.878964\pi$
$733$	−15.0917	+	15.0917i	−0.557424	+	0.557424i	0.371149	+	0.928573i	$0.378964\pi$
$734$	−28.7544	−	11.9104i	−1.06134	−	0.439623i
$735$		0			0
$736$	0.287719	−	0.694615i	0.0106055	−	0.0256038i
$737$	3.68695	−	1.52718i	0.135810	−	0.0562545i
$738$	5.12647	+	12.3764i	0.188708	+	0.455582i
$739$	10.3591	+	10.3591i	0.381065	+	0.381065i	0.871486	−	0.490420i	$-0.163157\pi$
$739$	10.3591	+	10.3591i	0.381065	+	0.381065i	−0.490420	+	0.871486i	$0.663157\pi$
$740$		0			0
$741$	−3.42964	−	8.27989i	−0.125991	−	0.304169i
$742$	−13.7485	+	5.69482i	−0.504724	+	0.209063i
$743$	−13.9748	+	33.7382i	−0.512687	+	1.23774i	0.429627	+	0.903006i	$0.358645\pi$
$743$	−13.9748	+	33.7382i	−0.512687	+	1.23774i	−0.942314	+	0.334730i	$0.891355\pi$
$744$			1.95869i			0.0718092i
$745$		0			0
$746$	−15.3549	+	15.3549i	−0.562183	+	0.562183i
$747$	−21.7059			−0.794177
$748$	−0.362076	+	0.975211i	−0.0132388	+	0.0356572i
$749$	13.3196			0.486687
$750$		0			0
$751$	17.6508	+	7.31120i	0.644087	+	0.266790i	0.680725	−	0.732539i	$-0.261665\pi$
$751$	17.6508	+	7.31120i	0.644087	+	0.266790i	−0.0366379	+	0.999329i	$0.511665\pi$
$752$			9.71535i			0.354282i
$753$	−10.7319	+	25.9091i	−0.391092	+	0.944180i
$754$	−3.24633	+	1.34467i	−0.118224	+	0.0489701i
$755$		0			0
$756$	2.70587	+	2.70587i	0.0984114	+	0.0984114i
$757$	14.2078	+	14.2078i	0.516390	+	0.516390i	0.916477	−	0.400087i	$-0.131020\pi$
$757$	14.2078	+	14.2078i	0.516390	+	0.516390i	−0.400087	+	0.916477i	$0.631020\pi$
$758$	9.02028	+	21.7769i	0.327631	+	0.790972i
$759$	0.367347	−	0.152160i	0.0133339	−	0.00552307i
$760$		0			0
$761$			12.0122i			0.435441i	0.976011	+	0.217721i	$0.0698622\pi$
$761$			12.0122i			0.435441i	−0.976011	+	0.217721i	$0.930138\pi$
$762$	−20.2217	−	8.37608i	−0.732553	−	0.303433i
$763$	−1.67370	+	1.67370i	−0.0605920	+	0.0605920i
$764$	8.37154			0.302872
$765$		0			0
$766$	32.3793			1.16991
$767$	5.21760	−	5.21760i	0.188396	−	0.188396i
$768$	−1.93656	−	0.802151i	−0.0698798	−	0.0289451i
$769$		−	28.5106i		−	1.02812i	−0.857755	−	0.514059i	$-0.828141\pi$
$769$		−	28.5106i		−	1.02812i	0.857755	−	0.514059i	$-0.171859\pi$
$770$		0			0
$771$	−37.4954	+	15.5311i	−1.35036	+	0.559339i
$772$	−3.01064	−	7.26832i	−0.108355	−	0.261593i
$773$	16.8373	+	16.8373i	0.605596	+	0.605596i	0.941792	−	0.336196i	$-0.109141\pi$
$773$	16.8373	+	16.8373i	0.605596	+	0.605596i	−0.336196	+	0.941792i	$0.609141\pi$
$774$	7.15050	+	7.15050i	0.257020	+	0.257020i
$775$		0			0
$776$	−14.5406	+	6.02292i	−0.521977	+	0.216210i
$777$	−4.48152	+	10.8194i	−0.160774	+	0.388142i
$778$			7.88317i			0.282625i
$779$	12.2132	+	5.05889i	0.437585	+	0.181254i
$780$		0			0
$781$	−0.642173			−0.0229787
$782$	−2.81788	+	1.29197i	−0.100767	+	0.0462008i
$783$	−3.80571			−0.136005
$784$	−4.03636	+	4.03636i	−0.144156	+	0.144156i
$785$		0			0
$786$			20.3352i			0.725333i
$787$	−9.12132	+	22.0208i	−0.325140	+	0.784958i	0.673799	+	0.738914i	$0.264661\pi$
$787$	−9.12132	+	22.0208i	−0.325140	+	0.784958i	−0.998939	+	0.0460433i	$0.985339\pi$
$788$	0.420971	−	0.174372i	0.0149965	−	0.00621174i
$789$	9.70341	+	23.4261i	0.345450	+	0.833991i
$790$		0			0
$791$	7.09940	+	7.09940i	0.252426	+	0.252426i
$792$	−0.134566	−	0.324871i	−0.00478159	−	0.0115438i
$793$	−21.1080	+	8.74322i	−0.749567	+	0.310481i
$794$	13.7359	−	33.1614i	0.487469	−	1.17685i
$795$		0			0
$796$	8.48532	+	3.51474i	0.300754	+	0.124577i
$797$	−28.2603	+	28.2603i	−1.00103	+	1.00103i	−0.00103330	+	0.999999i	$0.500329\pi$
$797$	−28.2603	+	28.2603i	−1.00103	+	1.00103i	−0.999999	+	0.00103330i	$0.999671\pi$
$798$	−3.27656			−0.115989
$799$	27.2520	−	29.3586i	0.964107	−	1.03863i
$800$		0			0
$801$	11.7525	−	11.7525i	0.415253	−	0.415253i
$802$	24.5561	+	10.1715i	0.867107	+	0.359168i
$803$			2.51146i			0.0886274i
$804$	12.6879	−	30.6314i	0.447469	−	1.08029i
$805$		0			0
$806$	−1.11165	−	2.68375i	−0.0391560	−	0.0945311i
$807$	−29.6368	−	29.6368i	−1.04326	−	1.04326i
$808$	−1.34918	−	1.34918i	−0.0474641	−	0.0474641i
$809$	17.1684	+	41.4483i	0.603610	+	1.45724i	0.869840	+	0.493334i	$0.164222\pi$
$809$	17.1684	+	41.4483i	0.603610	+	1.45724i	−0.266230	+	0.963910i	$0.585778\pi$
$810$		0			0
$811$	−11.6694	+	28.1724i	−0.409768	+	0.989266i	0.575431	+	0.817850i	$0.304834\pi$
$811$	−11.6694	+	28.1724i	−0.409768	+	0.989266i	−0.985199	+	0.171416i	$0.945166\pi$
$812$			1.28465i			0.0450825i
$813$	7.12551	+	2.95148i	0.249902	+	0.103513i
$814$	−0.876970	+	0.876970i	−0.0307378	+	0.0307378i
$815$		0			0
$816$	3.60198	+	7.85615i	0.126095	+	0.275020i
$817$	9.97903			0.349122
$818$	−7.55242	+	7.55242i	−0.264064	+	0.264064i
$819$	4.54943	+	1.88444i	0.158970	+	0.0658475i
$820$		0			0
$821$	−18.7827	+	45.3455i	−0.655522	+	1.58257i	0.149126	+	0.988818i	$0.452354\pi$
$821$	−18.7827	+	45.3455i	−0.655522	+	1.58257i	−0.804648	+	0.593752i	$0.797646\pi$
$822$	8.81560	−	3.65154i	0.307479	−	0.127362i
$823$	1.69527	+	4.09274i	0.0590933	+	0.142664i	0.950668	−	0.310209i	$-0.100399\pi$
$823$	1.69527	+	4.09274i	0.0590933	+	0.142664i	−0.891575	+	0.452873i	$0.850399\pi$
$824$	−1.16315	−	1.16315i	−0.0405204	−	0.0405204i
$825$		0			0
$826$	−1.03237	−	2.49236i	−0.0359207	−	0.0867201i
$827$	−5.92635	+	2.45477i	−0.206079	+	0.0853609i	−0.483336	−	0.875435i	$-0.660575\pi$
$827$	−5.92635	+	2.45477i	−0.206079	+	0.0853609i	0.277256	+	0.960796i	$0.410575\pi$
$828$	0.401002	−	0.968106i	0.0139358	−	0.0336440i
$829$			24.9754i			0.867432i	0.901050	+	0.433716i	$0.142798\pi$
$829$			24.9754i			0.867432i	−0.901050	+	0.433716i	$0.857202\pi$
$830$		0			0
$831$	19.4888	−	19.4888i	0.676059	−	0.676059i
$832$	3.10869			0.107774
$833$	23.5195	−	0.875186i	0.814903	−	0.0303234i
$834$	−26.2142			−0.907723
$835$		0			0
$836$	−0.320588	−	0.132792i	−0.0110878	−	0.00459270i
$837$		−	3.14619i		−	0.108748i
$838$	−10.9021	+	26.3201i	−0.376608	+	0.909212i
$839$	5.83303	−	2.41612i	0.201379	−	0.0834138i	−0.279715	−	0.960083i	$-0.590240\pi$
$839$	5.83303	−	2.41612i	0.201379	−	0.0834138i	0.481093	+	0.876669i	$0.340240\pi$
$840$		0			0
$841$	19.6027	+	19.6027i	0.675955	+	0.675955i
$842$	−6.44182	−	6.44182i	−0.222000	−	0.222000i
$843$	−7.08633	−	17.1079i	−0.244066	−	0.589227i
$844$	−7.02656	+	2.91050i	−0.241864	+	0.100183i
$845$		0			0
$846$			13.5406i			0.465535i
$847$	−11.4835	−	4.75661i	−0.394577	−	0.163439i
$848$	−9.25847	+	9.25847i	−0.317937	+	0.317937i
$849$	11.6932			0.401309
$850$		0			0
$851$	−3.69583			−0.126691
$852$	−3.77257	+	3.77257i	−0.129246	+	0.129246i
$853$	−5.80811	−	2.40580i	−0.198866	−	0.0823730i	0.281028	−	0.959700i	$-0.409325\pi$
$853$	−5.80811	−	2.40580i	−0.198866	−	0.0823730i	−0.479894	+	0.877327i	$0.659325\pi$
$854$			8.35297i			0.285833i
$855$		0			0
$856$	10.8273	−	4.48481i	0.370069	−	0.153288i
$857$	17.4626	+	42.1583i	0.596510	+	1.44010i	0.877116	+	0.480278i	$0.159464\pi$
$857$	17.4626	+	42.1583i	0.596510	+	1.44010i	−0.280607	+	0.959823i	$0.590536\pi$
$858$	1.16251	+	1.16251i	0.0396873	+	0.0396873i
$859$	−20.4579	−	20.4579i	−0.698015	−	0.698015i	0.265967	−	0.963982i	$-0.414309\pi$
$859$	−20.4579	−	20.4579i	−0.698015	−	0.698015i	−0.963982	+	0.265967i	$0.914309\pi$
$860$		0			0
$861$	−21.1553	+	8.76280i	−0.720970	+	0.298635i
$862$	−14.7843	+	35.6926i	−0.503557	+	1.21569i
$863$			7.31084i			0.248864i	0.992228	+	0.124432i	$0.0397109\pi$
$863$			7.31084i			0.248864i	−0.992228	+	0.124432i	$0.960289\pi$
$864$	3.11065	+	1.28847i	0.105826	+	0.0438347i
$865$		0			0
$866$	5.79382			0.196882
$867$	11.1522	−	33.8440i	0.378747	−	1.14940i
$868$	−1.06203			−0.0360476
$869$	−2.50207	+	2.50207i	−0.0848770	+	0.0848770i
$870$		0			0
$871$			49.1713i			1.66611i
$872$	−0.796977	+	1.92407i	−0.0269890	+	0.0651573i
$873$	−20.2657	+	8.39432i	−0.685890	+	0.284105i
$874$	−0.395716	−	0.955343i	−0.0133853	−	0.0323150i
$875$		0			0
$876$	14.7540	+	14.7540i	0.498493	+	0.498493i
$877$	−13.4790	−	32.5412i	−0.455153	−	1.09884i	−0.970337	−	0.241757i	$-0.922276\pi$
$877$	−13.4790	−	32.5412i	−0.455153	−	1.09884i	0.515184	−	0.857080i	$-0.327724\pi$
$878$	29.9651	−	12.4119i	1.01127	−	0.418883i
$879$	18.9012	−	45.6315i	0.637521	−	1.53911i
$880$		0			0
$881$	−11.8515	−	4.90905i	−0.399287	−	0.165390i	0.173998	−	0.984746i	$-0.444331\pi$
$881$	−11.8515	−	4.90905i	−0.399287	−	0.165390i	−0.573285	+	0.819356i	$0.694331\pi$
$882$	−5.62559	+	5.62559i	−0.189423	+	0.189423i
$883$	−25.2939			−0.851208			−0.425604	−	0.904910i	$-0.639938\pi$
$883$	−25.2939			−0.851208			−0.425604	+	0.904910i	$0.639938\pi$
$884$	−9.39405	−	8.72001i	−0.315956	−	0.293286i
$885$		0			0
$886$	−7.19260	+	7.19260i	−0.241640	+	0.241640i
$887$	21.6520	+	8.96853i	0.727001	+	0.301134i	0.715319	−	0.698798i	$-0.246281\pi$
$887$	21.6520	+	8.96853i	0.727001	+	0.301134i	0.0116823	+	0.999932i	$0.496281\pi$
$888$			10.3039i			0.345775i
$889$	4.54161	−	10.9644i	0.152321	−	0.367735i
$890$		0			0
$891$	1.08511	+	2.61968i	0.0363524	+	0.0877625i
$892$	1.91171	+	1.91171i	0.0640086	+	0.0640086i
$893$	9.44842	+	9.44842i	0.316179	+	0.316179i
$894$	−17.8565	−	43.1094i	−0.597210	−	1.44179i
$895$		0			0
$896$	0.434936	−	1.05003i	0.0145302	−	0.0350790i
$897$			4.89917i			0.163578i
$898$	−4.82665	−	1.99926i	−0.161067	−	0.0667162i
$899$	0.746852	−	0.746852i	0.0249089	−	0.0249089i
$900$		0			0
$901$	53.9484	−	2.00748i	1.79728	−	0.0668787i
$902$	−2.42503			−0.0807446
$903$	−12.2225	+	12.2225i	−0.406740	+	0.406740i
$904$	8.16143	+	3.38057i	0.271445	+	0.112436i
$905$		0			0
$906$	−8.09224	+	19.5364i	−0.268847	+	0.649053i
$907$	46.1626	−	19.1212i	1.53280	−	0.634908i	0.552697	−	0.833382i	$-0.313599\pi$
$907$	46.1626	−	19.1212i	1.53280	−	0.634908i	0.980106	+	0.198474i	$0.0635986\pi$
$908$	−3.61134	−	8.71853i	−0.119846	−	0.289335i
$909$	−1.88040	−	1.88040i	−0.0623689	−	0.0623689i
$910$		0			0
$911$	14.9768	+	36.1572i	0.496204	+	1.19794i	0.951513	+	0.307609i	$0.0995289\pi$
$911$	14.9768	+	36.1572i	0.496204	+	1.19794i	−0.455309	+	0.890334i	$0.650471\pi$
$912$	−2.66347	+	1.10324i	−0.0881962	+	0.0365321i
$913$	1.50368	−	3.63020i	0.0497645	−	0.120142i
$914$			0.441796i			0.0146133i
$915$		0			0
$916$	−6.37289	+	6.37289i	−0.210566	+	0.210566i
$917$	−11.0260			−0.364111
$918$	−5.78575	−	12.6191i	−0.190958	−	0.416492i
$919$	34.5751			1.14053			0.570263	−	0.821462i	$-0.306841\pi$
$919$	34.5751			1.14053			0.570263	+	0.821462i	$0.306841\pi$
$920$		0			0
$921$	−26.6487	−	11.0383i	−0.878105	−	0.363723i
$922$			3.62872i			0.119505i
$923$	3.02797	−	7.31017i	0.0996670	−	0.240617i
$924$	0.555309	−	0.230016i	0.0182683	−	0.00756698i
$925$		0			0
$926$	8.64954	+	8.64954i	0.284241	+	0.284241i
$927$	−1.62112	−	1.62112i	−0.0532447	−	0.0532447i
$928$	0.432553	+	1.04428i	0.0141993	+	0.0342800i
$929$	−17.4963	+	7.24720i	−0.574035	+	0.237773i	−0.650765	−	0.759279i	$-0.725552\pi$
$929$	−17.4963	+	7.24720i	−0.574035	+	0.237773i	0.0767308	+	0.997052i	$0.475552\pi$
$930$		0			0
$931$			7.85091i			0.257303i
$932$	12.2880	+	5.08986i	0.402507	+	0.166724i
$933$	30.6597	−	30.6597i	1.00375	−	1.00375i
$934$	31.2281			1.02182
$935$		0			0
$936$	4.33267			0.141618
$937$	10.1161	−	10.1161i	0.330478	−	0.330478i	−0.522290	−	0.852768i	$-0.674922\pi$
$937$	10.1161	−	10.1161i	0.330478	−	0.330478i	0.852768	+	0.522290i	$0.174922\pi$
$938$	16.6087	+	6.87956i	0.542294	+	0.224626i
$939$			52.3038i			1.70687i
$940$		0			0
$941$	13.0487	−	5.40494i	0.425375	−	0.176196i	−0.159717	−	0.987163i	$-0.551058\pi$
$941$	13.0487	−	5.40494i	0.425375	−	0.176196i	0.585092	+	0.810967i	$0.301058\pi$
$942$	−13.2607	−	32.0143i	−0.432058	−	1.04308i
$943$	−5.10992	−	5.10992i	−0.166402	−	0.166402i
$944$	−1.67839	−	1.67839i	−0.0546270	−	0.0546270i
$945$		0			0
$946$	−1.69124	+	0.700534i	−0.0549869	+	0.0227763i
$947$	11.2228	−	27.0944i	0.364694	−	0.880448i	−0.629907	−	0.776671i	$-0.716907\pi$
$947$	11.2228	−	27.0944i	0.364694	−	0.880448i	0.994601	−	0.103778i	$-0.0330930\pi$
$948$			29.3978i			0.954797i
$949$	−28.5892	−	11.8420i	−0.928044	−	0.384408i
$950$		0			0
$951$	−18.2531			−0.591897
$952$	−4.25970	+	1.95304i	−0.138058	+	0.0632983i
$953$	11.5308			0.373521			0.186760	−	0.982406i	$-0.440201\pi$
$953$	11.5308			0.373521			0.186760	+	0.982406i	$0.440201\pi$
$954$	−12.9038	+	12.9038i	−0.417776	+	0.417776i
$955$		0			0
$956$			2.66720i			0.0862633i
$957$	−0.228756	+	0.552266i	−0.00739464	+	0.0178522i
$958$	3.32393	−	1.37682i	0.107391	−	0.0444829i
$959$	1.97991	+	4.77993i	0.0639346	+	0.154352i
$960$		0			0
$961$	−21.3029	−	21.3029i	−0.687190	−	0.687190i
$962$	−5.84790	−	14.1181i	−0.188544	−	0.455185i
$963$	15.0903	−	6.25062i	0.486279	−	0.201423i
$964$	−0.204345	+	0.493333i	−0.00658151	+	0.0158892i
$965$		0			0
$966$	1.65480	+	0.685443i	0.0532425	+	0.0220538i
$967$	−30.1392	+	30.1392i	−0.969211	+	0.969211i	−0.999540	−	0.0303294i	$-0.990344\pi$
$967$	−30.1392	+	30.1392i	−0.969211	+	0.969211i	0.0303294	+	0.999540i	$0.490344\pi$
$968$	−10.9363			−0.351507
$969$	11.1433	+	4.13729i	0.357975	+	0.132909i
$970$		0			0
$971$	11.6594	−	11.6594i	0.374167	−	0.374167i	−0.494825	−	0.868993i	$-0.664768\pi$
$971$	11.6594	−	11.6594i	0.374167	−	0.374167i	0.868993	+	0.494825i	$0.164768\pi$
$972$	12.4325	+	5.14973i	0.398774	+	0.165178i
$973$		−	14.2137i		−	0.455669i
$974$	8.26188	−	19.9459i	0.264728	−	0.639109i
$975$		0			0
$976$	2.81251	+	6.79001i	0.0900264	+	0.217343i
$977$	−13.4637	−	13.4637i	−0.430741	−	0.430741i	0.458139	−	0.888880i	$-0.348516\pi$
$977$	−13.4637	−	13.4637i	−0.430741	−	0.430741i	−0.888880	+	0.458139i	$0.848516\pi$
$978$	−2.76969	−	2.76969i	−0.0885648	−	0.0885648i
$979$	1.15139	+	2.77969i	0.0367985	+	0.0888394i
$980$		0			0
$981$	−1.11077	+	2.68164i	−0.0354642	+	0.0856181i
$982$			37.2432i			1.18848i
$983$	−2.07283	−	0.858595i	−0.0661131	−	0.0273849i	0.349382	−	0.936980i	$-0.386392\pi$
$983$	−2.07283	−	0.858595i	−0.0661131	−	0.0273849i	−0.415495	+	0.909595i	$0.636392\pi$
$984$	−14.2463	+	14.2463i	−0.454155	+	0.454155i
$985$		0			0
$986$	1.62212	−	4.36900i	0.0516589	−	0.139137i
$987$	−23.1452			−0.736721
$988$	3.02327	−	3.02327i	0.0961831	−	0.0961831i
$989$	−5.03984	−	2.08757i	−0.160258	−	0.0663809i
$990$		0			0
$991$	6.12684	−	14.7915i	0.194625	−	0.469867i	−0.796197	−	0.605038i	$-0.793158\pi$
$991$	6.12684	−	14.7915i	0.194625	−	0.469867i	0.990822	+	0.135170i	$0.0431581\pi$
$992$	−0.863307	+	0.357593i	−0.0274100	+	0.0113536i
$993$	16.4832	+	39.7940i	0.523079	+	1.26282i
$994$	−2.04553	−	2.04553i	−0.0648804	−	0.0648804i
$995$		0			0
$996$	−12.4927	−	30.1600i	−0.395846	−	0.955656i
$997$	22.0338	−	9.12670i	0.697818	−	0.289046i	−0.00543534	−	0.999985i	$-0.501730\pi$
$997$	22.0338	−	9.12670i	0.697818	−	0.289046i	0.703253	+	0.710940i	$0.251730\pi$
$998$	−5.92555	+	14.3055i	−0.187570	+	0.452834i
$999$		−	16.5508i		−	0.523643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.l.e.451.1		16
5.2	odd	4		850.2.o.g.349.1		16
5.3	odd	4		850.2.o.j.349.4		16
5.4	even	2		170.2.k.b.111.4	✓	16
17.2	even	8	inner	850.2.l.e.801.1		16
85.2	odd	8		850.2.o.j.699.4		16
85.19	even	8		170.2.k.b.121.4	yes	16
85.24	odd	16		2890.2.b.r.2311.4		16
85.44	odd	16		2890.2.b.r.2311.13		16
85.53	odd	8		850.2.o.g.699.1		16
85.74	odd	16		2890.2.a.bj.1.6		8
85.79	odd	16		2890.2.a.bi.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.k.b.111.4	✓	16	5.4	even	2
170.2.k.b.121.4	yes	16	85.19	even	8
850.2.l.e.451.1		16	1.1	even	1	trivial
850.2.l.e.801.1		16	17.2	even	8	inner
850.2.o.g.349.1		16	5.2	odd	4
850.2.o.g.699.1		16	85.53	odd	8
850.2.o.j.349.4		16	5.3	odd	4
850.2.o.j.699.4		16	85.2	odd	8
2890.2.a.bi.1.3		8	85.79	odd	16
2890.2.a.bj.1.6		8	85.74	odd	16
2890.2.b.r.2311.4		16	85.24	odd	16
2890.2.b.r.2311.13		16	85.44	odd	16

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.93656 - 0.802151i) q^{3} -1.00000i q^{4} +(1.93656 - 0.802151i) q^{6} +(0.434936 + 1.05003i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.985516 + 0.985516i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.93656 - 0.802151i) q^{3} -1.00000i q^{4} +(1.93656 - 0.802151i) q^{6} +(0.434936 + 1.05003i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.985516 + 0.985516i) q^{9} +(-0.233094 + 0.0965508i) q^{11} +(-0.802151 + 1.93656i) q^{12} -3.10869i q^{13} +(-1.05003 - 0.434936i) q^{14} -1.00000 q^{16} +(3.02187 + 2.80505i) q^{17} -1.39373 q^{18} +(-0.972524 + 0.972524i) q^{19} -2.38233i q^{21} +(0.0965508 - 0.233094i) q^{22} +(0.694615 - 0.287719i) q^{23} +(-0.802151 - 1.93656i) q^{24} +(2.19817 + 2.19817i) q^{26} +(1.28847 + 3.11065i) q^{27} +(1.05003 - 0.434936i) q^{28} +(-0.432553 + 1.04428i) q^{29} +(-0.863307 - 0.357593i) q^{31} +(0.707107 - 0.707107i) q^{32} +0.528851 q^{33} +(-4.12025 + 0.153319i) q^{34} +(0.985516 - 0.985516i) q^{36} +(-4.54149 - 1.88115i) q^{37} -1.37536i q^{38} +(-2.49364 + 6.02017i) q^{39} +(-3.67824 - 8.88006i) q^{41} +(1.68456 + 1.68456i) q^{42} +(-5.13048 - 5.13048i) q^{43} +(0.0965508 + 0.233094i) q^{44} +(-0.287719 + 0.694615i) q^{46} -9.71535i q^{47} +(1.93656 + 0.802151i) q^{48} +(4.03636 - 4.03636i) q^{49} +(-3.60198 - 7.85615i) q^{51} -3.10869 q^{52} +(9.25847 - 9.25847i) q^{53} +(-3.11065 - 1.28847i) q^{54} +(-0.434936 + 1.05003i) q^{56} +(2.66347 - 1.10324i) q^{57} +(-0.432553 - 1.04428i) q^{58} +(1.67839 + 1.67839i) q^{59} +(-2.81251 - 6.79001i) q^{61} +(0.863307 - 0.357593i) q^{62} +(-0.606184 + 1.46346i) q^{63} +1.00000i q^{64} +(-0.373954 + 0.373954i) q^{66} -15.8174 q^{67} +(2.80505 - 3.02187i) q^{68} -1.57596 q^{69} +(2.35153 + 0.974036i) q^{71} +1.39373i q^{72} +(3.80933 - 9.19654i) q^{73} +(4.54149 - 1.88115i) q^{74} +(0.972524 + 0.972524i) q^{76} +(-0.202762 - 0.202762i) q^{77} +(-2.49364 - 6.02017i) q^{78} +(12.9573 - 5.36708i) q^{79} -11.2387i q^{81} +(8.88006 + 3.67824i) q^{82} +(-11.0125 + 11.0125i) q^{83} -2.38233 q^{84} +7.25559 q^{86} +(1.67534 - 1.67534i) q^{87} +(-0.233094 - 0.0965508i) q^{88} -11.9252i q^{89} +(3.26421 - 1.35208i) q^{91} +(-0.287719 - 0.694615i) q^{92} +(1.38501 + 1.38501i) q^{93} +(6.86979 + 6.86979i) q^{94} +(-1.93656 + 0.802151i) q^{96} +(-6.02292 + 14.5406i) q^{97} +5.70827i q^{98} +(-0.324871 - 0.134566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} - 8 q^{14} - 16 q^{16} - 8 q^{18} + 8 q^{22} - 8 q^{23} + 24 q^{27} + 8 q^{28} + 8 q^{29} + 32 q^{31} - 16 q^{33} + 16 q^{34} + 8 q^{37} - 32 q^{39} - 32 q^{41} - 32 q^{42} + 16 q^{43} + 8 q^{44} - 24 q^{46} - 8 q^{49} - 8 q^{51} + 8 q^{52} + 40 q^{53} + 16 q^{57} + 8 q^{58} + 16 q^{59} - 24 q^{61} - 32 q^{62} - 56 q^{63} - 8 q^{66} - 16 q^{67} - 16 q^{69} + 8 q^{71} - 16 q^{73} - 8 q^{74} - 24 q^{77} - 32 q^{78} + 40 q^{79} - 16 q^{82} - 32 q^{83} + 16 q^{84} + 32 q^{87} - 8 q^{88} + 24 q^{91} - 24 q^{92} + 32 q^{93} + 40 q^{94} - 24 q^{97} - 56 q^{99}+O(q^{100}) \) 16 * q - 8 * q^11 - 8 * q^14 - 16 * q^16 - 8 * q^18 + 8 * q^22 - 8 * q^23 + 24 * q^27 + 8 * q^28 + 8 * q^29 + 32 * q^31 - 16 * q^33 + 16 * q^34 + 8 * q^37 - 32 * q^39 - 32 * q^41 - 32 * q^42 + 16 * q^43 + 8 * q^44 - 24 * q^46 - 8 * q^49 - 8 * q^51 + 8 * q^52 + 40 * q^53 + 16 * q^57 + 8 * q^58 + 16 * q^59 - 24 * q^61 - 32 * q^62 - 56 * q^63 - 8 * q^66 - 16 * q^67 - 16 * q^69 + 8 * q^71 - 16 * q^73 - 8 * q^74 - 24 * q^77 - 32 * q^78 + 40 * q^79 - 16 * q^82 - 32 * q^83 + 16 * q^84 + 32 * q^87 - 8 * q^88 + 24 * q^91 - 24 * q^92 + 32 * q^93 + 40 * q^94 - 24 * q^97 - 56 * q^99

Introduction

L-functions

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