# Properties

 Label 920.2.e.b.369.4 Level $920$ Weight $2$ Character 920.369 Analytic conductor $7.346$ Analytic rank $0$ Dimension $14$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$920 = 2^{3} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 920.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.34623698596$$ Analytic rank: $$0$$ Dimension: $$14$$ Coefficient field: $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ Defining polynomial: $$x^{14} - 2 x^{11} + 39 x^{10} - 10 x^{9} + 2 x^{8} - 26 x^{7} + 297 x^{6} - 116 x^{5} + 24 x^{4} - 20 x^{3} + 64 x^{2} - 32 x + 8$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 369.4 Root $$-1.71470 - 1.71470i$$ of defining polynomial Character $$\chi$$ $$=$$ 920.369 Dual form 920.2.e.b.369.11

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.58319i q^{3} +(-2.09277 - 0.787606i) q^{5} +2.84620i q^{7} +0.493499 q^{9} +O(q^{10})$$ $$q-1.58319i q^{3} +(-2.09277 - 0.787606i) q^{5} +2.84620i q^{7} +0.493499 q^{9} +1.98637 q^{11} +4.69204i q^{13} +(-1.24693 + 3.31326i) q^{15} -3.16675i q^{17} +6.16110 q^{19} +4.50609 q^{21} +1.00000i q^{23} +(3.75935 + 3.29655i) q^{25} -5.53088i q^{27} +6.61816 q^{29} -8.29732 q^{31} -3.14481i q^{33} +(2.24169 - 5.95644i) q^{35} +1.71181i q^{37} +7.42840 q^{39} +6.72440 q^{41} -0.177968i q^{43} +(-1.03278 - 0.388683i) q^{45} -11.4749i q^{47} -1.10086 q^{49} -5.01358 q^{51} +6.18762i q^{53} +(-4.15701 - 1.56448i) q^{55} -9.75422i q^{57} +7.61559 q^{59} +11.8577 q^{61} +1.40460i q^{63} +(3.69548 - 9.81934i) q^{65} -3.07554i q^{67} +1.58319 q^{69} -1.96195 q^{71} +4.94732i q^{73} +(5.21908 - 5.95178i) q^{75} +5.65361i q^{77} -8.53182 q^{79} -7.27596 q^{81} +3.49429i q^{83} +(-2.49415 + 6.62728i) q^{85} -10.4778i q^{87} -7.07506 q^{89} -13.3545 q^{91} +13.1363i q^{93} +(-12.8938 - 4.85252i) q^{95} +7.00705i q^{97} +0.980272 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$14q + 2q^{5} - 4q^{9} + O(q^{10})$$ $$14q + 2q^{5} - 4q^{9} - 14q^{11} - 6q^{15} + 14q^{19} - 12q^{21} - 14q^{25} + 22q^{29} - 20q^{31} - 2q^{35} + 48q^{39} - 32q^{41} - 26q^{45} + 34q^{49} - 14q^{51} - 38q^{55} + 22q^{59} + 10q^{61} - 38q^{65} + 6q^{69} - 28q^{71} - 24q^{75} + 64q^{79} - 10q^{81} - 50q^{85} + 48q^{89} - 14q^{91} - 30q^{95} + 122q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$$.

 $$n$$ $$231$$ $$281$$ $$461$$ $$737$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 1.58319i 0.914057i −0.889452 0.457029i $$-0.848914\pi$$
0.889452 0.457029i $$-0.151086\pi$$
$$4$$ 0 0
$$5$$ −2.09277 0.787606i −0.935914 0.352228i
$$6$$ 0 0
$$7$$ 2.84620i 1.07576i 0.843020 + 0.537881i $$0.180775\pi$$
−0.843020 + 0.537881i $$0.819225\pi$$
$$8$$ 0 0
$$9$$ 0.493499 0.164500
$$10$$ 0 0
$$11$$ 1.98637 0.598913 0.299457 0.954110i $$-0.403195\pi$$
0.299457 + 0.954110i $$0.403195\pi$$
$$12$$ 0 0
$$13$$ 4.69204i 1.30134i 0.759362 + 0.650668i $$0.225511\pi$$
−0.759362 + 0.650668i $$0.774489\pi$$
$$14$$ 0 0
$$15$$ −1.24693 + 3.31326i −0.321957 + 0.855479i
$$16$$ 0 0
$$17$$ 3.16675i 0.768050i −0.923323 0.384025i $$-0.874538\pi$$
0.923323 0.384025i $$-0.125462\pi$$
$$18$$ 0 0
$$19$$ 6.16110 1.41345 0.706727 0.707486i $$-0.250171\pi$$
0.706727 + 0.707486i $$0.250171\pi$$
$$20$$ 0 0
$$21$$ 4.50609 0.983309
$$22$$ 0 0
$$23$$ 1.00000i 0.208514i
$$24$$ 0 0
$$25$$ 3.75935 + 3.29655i 0.751871 + 0.659311i
$$26$$ 0 0
$$27$$ 5.53088i 1.06442i
$$28$$ 0 0
$$29$$ 6.61816 1.22896 0.614481 0.788932i $$-0.289365\pi$$
0.614481 + 0.788932i $$0.289365\pi$$
$$30$$ 0 0
$$31$$ −8.29732 −1.49024 −0.745121 0.666929i $$-0.767608\pi$$
−0.745121 + 0.666929i $$0.767608\pi$$
$$32$$ 0 0
$$33$$ 3.14481i 0.547441i
$$34$$ 0 0
$$35$$ 2.24169 5.95644i 0.378914 1.00682i
$$36$$ 0 0
$$37$$ 1.71181i 0.281420i 0.990051 + 0.140710i $$0.0449386\pi$$
−0.990051 + 0.140710i $$0.955061\pi$$
$$38$$ 0 0
$$39$$ 7.42840 1.18950
$$40$$ 0 0
$$41$$ 6.72440 1.05018 0.525088 0.851048i $$-0.324033\pi$$
0.525088 + 0.851048i $$0.324033\pi$$
$$42$$ 0 0
$$43$$ 0.177968i 0.0271399i −0.999908 0.0135700i $$-0.995680\pi$$
0.999908 0.0135700i $$-0.00431958\pi$$
$$44$$ 0 0
$$45$$ −1.03278 0.388683i −0.153958 0.0579414i
$$46$$ 0 0
$$47$$ 11.4749i 1.67378i −0.547369 0.836891i $$-0.684371\pi$$
0.547369 0.836891i $$-0.315629\pi$$
$$48$$ 0 0
$$49$$ −1.10086 −0.157266
$$50$$ 0 0
$$51$$ −5.01358 −0.702042
$$52$$ 0 0
$$53$$ 6.18762i 0.849934i 0.905209 + 0.424967i $$0.139714\pi$$
−0.905209 + 0.424967i $$0.860286\pi$$
$$54$$ 0 0
$$55$$ −4.15701 1.56448i −0.560531 0.210954i
$$56$$ 0 0
$$57$$ 9.75422i 1.29198i
$$58$$ 0 0
$$59$$ 7.61559 0.991465 0.495733 0.868475i $$-0.334900\pi$$
0.495733 + 0.868475i $$0.334900\pi$$
$$60$$ 0 0
$$61$$ 11.8577 1.51822 0.759109 0.650964i $$-0.225635\pi$$
0.759109 + 0.650964i $$0.225635\pi$$
$$62$$ 0 0
$$63$$ 1.40460i 0.176963i
$$64$$ 0 0
$$65$$ 3.69548 9.81934i 0.458367 1.21794i
$$66$$ 0 0
$$67$$ 3.07554i 0.375737i −0.982194 0.187868i $$-0.939842\pi$$
0.982194 0.187868i $$-0.0601579\pi$$
$$68$$ 0 0
$$69$$ 1.58319 0.190594
$$70$$ 0 0
$$71$$ −1.96195 −0.232840 −0.116420 0.993200i $$-0.537142\pi$$
−0.116420 + 0.993200i $$0.537142\pi$$
$$72$$ 0 0
$$73$$ 4.94732i 0.579041i 0.957172 + 0.289520i $$0.0934958\pi$$
−0.957172 + 0.289520i $$0.906504\pi$$
$$74$$ 0 0
$$75$$ 5.21908 5.95178i 0.602647 0.687253i
$$76$$ 0 0
$$77$$ 5.65361i 0.644289i
$$78$$ 0 0
$$79$$ −8.53182 −0.959905 −0.479952 0.877295i $$-0.659346\pi$$
−0.479952 + 0.877295i $$0.659346\pi$$
$$80$$ 0 0
$$81$$ −7.27596 −0.808440
$$82$$ 0 0
$$83$$ 3.49429i 0.383548i 0.981439 + 0.191774i $$0.0614241\pi$$
−0.981439 + 0.191774i $$0.938576\pi$$
$$84$$ 0 0
$$85$$ −2.49415 + 6.62728i −0.270529 + 0.718829i
$$86$$ 0 0
$$87$$ 10.4778i 1.12334i
$$88$$ 0 0
$$89$$ −7.07506 −0.749954 −0.374977 0.927034i $$-0.622349\pi$$
−0.374977 + 0.927034i $$0.622349\pi$$
$$90$$ 0 0
$$91$$ −13.3545 −1.39993
$$92$$ 0 0
$$93$$ 13.1363i 1.36217i
$$94$$ 0 0
$$95$$ −12.8938 4.85252i −1.32287 0.497858i
$$96$$ 0 0
$$97$$ 7.00705i 0.711458i 0.934589 + 0.355729i $$0.115767\pi$$
−0.934589 + 0.355729i $$0.884233\pi$$
$$98$$ 0 0
$$99$$ 0.980272 0.0985210
$$100$$ 0 0
$$101$$ 7.22362 0.718777 0.359389 0.933188i $$-0.382985\pi$$
0.359389 + 0.933188i $$0.382985\pi$$
$$102$$ 0 0
$$103$$ 12.8178i 1.26297i −0.775386 0.631487i $$-0.782445\pi$$
0.775386 0.631487i $$-0.217555\pi$$
$$104$$ 0 0
$$105$$ −9.43019 3.54902i −0.920293 0.346349i
$$106$$ 0 0
$$107$$ 11.6841i 1.12954i 0.825247 + 0.564772i $$0.191036\pi$$
−0.825247 + 0.564772i $$0.808964\pi$$
$$108$$ 0 0
$$109$$ 13.6019 1.30283 0.651413 0.758723i $$-0.274176\pi$$
0.651413 + 0.758723i $$0.274176\pi$$
$$110$$ 0 0
$$111$$ 2.71013 0.257234
$$112$$ 0 0
$$113$$ 1.44526i 0.135959i 0.997687 + 0.0679795i $$0.0216553\pi$$
−0.997687 + 0.0679795i $$0.978345\pi$$
$$114$$ 0 0
$$115$$ 0.787606 2.09277i 0.0734446 0.195152i
$$116$$ 0 0
$$117$$ 2.31552i 0.214069i
$$118$$ 0 0
$$119$$ 9.01322 0.826240
$$120$$ 0 0
$$121$$ −7.05433 −0.641303
$$122$$ 0 0
$$123$$ 10.6460i 0.959920i
$$124$$ 0 0
$$125$$ −5.27107 9.85981i −0.471459 0.881888i
$$126$$ 0 0
$$127$$ 9.12328i 0.809561i 0.914414 + 0.404780i $$0.132652\pi$$
−0.914414 + 0.404780i $$0.867348\pi$$
$$128$$ 0 0
$$129$$ −0.281758 −0.0248074
$$130$$ 0 0
$$131$$ 9.33180 0.815323 0.407661 0.913133i $$-0.366344\pi$$
0.407661 + 0.913133i $$0.366344\pi$$
$$132$$ 0 0
$$133$$ 17.5357i 1.52054i
$$134$$ 0 0
$$135$$ −4.35616 + 11.5749i −0.374918 + 0.996205i
$$136$$ 0 0
$$137$$ 21.0013i 1.79426i 0.441768 + 0.897129i $$0.354351\pi$$
−0.441768 + 0.897129i $$0.645649\pi$$
$$138$$ 0 0
$$139$$ 16.1299 1.36812 0.684061 0.729425i $$-0.260212\pi$$
0.684061 + 0.729425i $$0.260212\pi$$
$$140$$ 0 0
$$141$$ −18.1669 −1.52993
$$142$$ 0 0
$$143$$ 9.32012i 0.779388i
$$144$$ 0 0
$$145$$ −13.8503 5.21251i −1.15020 0.432875i
$$146$$ 0 0
$$147$$ 1.74288i 0.143750i
$$148$$ 0 0
$$149$$ 9.57227 0.784191 0.392096 0.919925i $$-0.371750\pi$$
0.392096 + 0.919925i $$0.371750\pi$$
$$150$$ 0 0
$$151$$ 3.04120 0.247489 0.123745 0.992314i $$-0.460510\pi$$
0.123745 + 0.992314i $$0.460510\pi$$
$$152$$ 0 0
$$153$$ 1.56279i 0.126344i
$$154$$ 0 0
$$155$$ 17.3644 + 6.53502i 1.39474 + 0.524905i
$$156$$ 0 0
$$157$$ 12.4786i 0.995900i 0.867206 + 0.497950i $$0.165914\pi$$
−0.867206 + 0.497950i $$0.834086\pi$$
$$158$$ 0 0
$$159$$ 9.79619 0.776889
$$160$$ 0 0
$$161$$ −2.84620 −0.224312
$$162$$ 0 0
$$163$$ 16.3939i 1.28407i −0.766676 0.642034i $$-0.778091\pi$$
0.766676 0.642034i $$-0.221909\pi$$
$$164$$ 0 0
$$165$$ −2.47687 + 6.58135i −0.192824 + 0.512358i
$$166$$ 0 0
$$167$$ 8.13265i 0.629323i 0.949204 + 0.314662i $$0.101891\pi$$
−0.949204 + 0.314662i $$0.898109\pi$$
$$168$$ 0 0
$$169$$ −9.01521 −0.693477
$$170$$ 0 0
$$171$$ 3.04050 0.232513
$$172$$ 0 0
$$173$$ 10.5256i 0.800250i −0.916461 0.400125i $$-0.868967\pi$$
0.916461 0.400125i $$-0.131033\pi$$
$$174$$ 0 0
$$175$$ −9.38265 + 10.6999i −0.709262 + 0.808835i
$$176$$ 0 0
$$177$$ 12.0570i 0.906256i
$$178$$ 0 0
$$179$$ −20.5421 −1.53539 −0.767695 0.640816i $$-0.778596\pi$$
−0.767695 + 0.640816i $$0.778596\pi$$
$$180$$ 0 0
$$181$$ −22.0754 −1.64085 −0.820424 0.571756i $$-0.806263\pi$$
−0.820424 + 0.571756i $$0.806263\pi$$
$$182$$ 0 0
$$183$$ 18.7730i 1.38774i
$$184$$ 0 0
$$185$$ 1.34823 3.58243i 0.0991242 0.263385i
$$186$$ 0 0
$$187$$ 6.29034i 0.459995i
$$188$$ 0 0
$$189$$ 15.7420 1.14506
$$190$$ 0 0
$$191$$ −4.50910 −0.326267 −0.163133 0.986604i $$-0.552160\pi$$
−0.163133 + 0.986604i $$0.552160\pi$$
$$192$$ 0 0
$$193$$ 21.1534i 1.52266i 0.648366 + 0.761329i $$0.275453\pi$$
−0.648366 + 0.761329i $$0.724547\pi$$
$$194$$ 0 0
$$195$$ −15.5459 5.85065i −1.11327 0.418974i
$$196$$ 0 0
$$197$$ 10.1475i 0.722980i −0.932376 0.361490i $$-0.882268\pi$$
0.932376 0.361490i $$-0.117732\pi$$
$$198$$ 0 0
$$199$$ −6.57598 −0.466159 −0.233079 0.972458i $$-0.574880\pi$$
−0.233079 + 0.972458i $$0.574880\pi$$
$$200$$ 0 0
$$201$$ −4.86917 −0.343445
$$202$$ 0 0
$$203$$ 18.8366i 1.32207i
$$204$$ 0 0
$$205$$ −14.0726 5.29618i −0.982874 0.369901i
$$206$$ 0 0
$$207$$ 0.493499i 0.0343005i
$$208$$ 0 0
$$209$$ 12.2382 0.846536
$$210$$ 0 0
$$211$$ −26.5357 −1.82680 −0.913398 0.407069i $$-0.866551\pi$$
−0.913398 + 0.407069i $$0.866551\pi$$
$$212$$ 0 0
$$213$$ 3.10614i 0.212829i
$$214$$ 0 0
$$215$$ −0.140169 + 0.372446i −0.00955944 + 0.0254006i
$$216$$ 0 0
$$217$$ 23.6158i 1.60315i
$$218$$ 0 0
$$219$$ 7.83257 0.529276
$$220$$ 0 0
$$221$$ 14.8585 0.999492
$$222$$ 0 0
$$223$$ 20.9231i 1.40111i −0.713597 0.700557i $$-0.752935\pi$$
0.713597 0.700557i $$-0.247065\pi$$
$$224$$ 0 0
$$225$$ 1.85524 + 1.62685i 0.123682 + 0.108456i
$$226$$ 0 0
$$227$$ 9.32581i 0.618975i 0.950903 + 0.309488i $$0.100158\pi$$
−0.950903 + 0.309488i $$0.899842\pi$$
$$228$$ 0 0
$$229$$ −29.5189 −1.95066 −0.975332 0.220742i $$-0.929152\pi$$
−0.975332 + 0.220742i $$0.929152\pi$$
$$230$$ 0 0
$$231$$ 8.95076 0.588917
$$232$$ 0 0
$$233$$ 28.9849i 1.89886i −0.313974 0.949431i $$-0.601661\pi$$
0.313974 0.949431i $$-0.398339\pi$$
$$234$$ 0 0
$$235$$ −9.03768 + 24.0142i −0.589553 + 1.56652i
$$236$$ 0 0
$$237$$ 13.5075i 0.877408i
$$238$$ 0 0
$$239$$ 9.62209 0.622401 0.311201 0.950344i $$-0.399269\pi$$
0.311201 + 0.950344i $$0.399269\pi$$
$$240$$ 0 0
$$241$$ 15.5745 1.00324 0.501621 0.865088i $$-0.332737\pi$$
0.501621 + 0.865088i $$0.332737\pi$$
$$242$$ 0 0
$$243$$ 5.07340i 0.325459i
$$244$$ 0 0
$$245$$ 2.30385 + 0.867045i 0.147187 + 0.0553935i
$$246$$ 0 0
$$247$$ 28.9081i 1.83938i
$$248$$ 0 0
$$249$$ 5.53214 0.350585
$$250$$ 0 0
$$251$$ −22.8066 −1.43954 −0.719770 0.694213i $$-0.755753\pi$$
−0.719770 + 0.694213i $$0.755753\pi$$
$$252$$ 0 0
$$253$$ 1.98637i 0.124882i
$$254$$ 0 0
$$255$$ 10.4923 + 3.94873i 0.657051 + 0.247279i
$$256$$ 0 0
$$257$$ 11.5591i 0.721038i −0.932752 0.360519i $$-0.882600\pi$$
0.932752 0.360519i $$-0.117400\pi$$
$$258$$ 0 0
$$259$$ −4.87216 −0.302742
$$260$$ 0 0
$$261$$ 3.26606 0.202164
$$262$$ 0 0
$$263$$ 6.57534i 0.405453i 0.979235 + 0.202726i $$0.0649802\pi$$
−0.979235 + 0.202726i $$0.935020\pi$$
$$264$$ 0 0
$$265$$ 4.87340 12.9492i 0.299371 0.795466i
$$266$$ 0 0
$$267$$ 11.2012i 0.685501i
$$268$$ 0 0
$$269$$ 16.6536 1.01539 0.507694 0.861537i $$-0.330498\pi$$
0.507694 + 0.861537i $$0.330498\pi$$
$$270$$ 0 0
$$271$$ −23.8675 −1.44985 −0.724925 0.688828i $$-0.758126\pi$$
−0.724925 + 0.688828i $$0.758126\pi$$
$$272$$ 0 0
$$273$$ 21.1427i 1.27962i
$$274$$ 0 0
$$275$$ 7.46747 + 6.54817i 0.450305 + 0.394870i
$$276$$ 0 0
$$277$$ 5.65369i 0.339697i −0.985470 0.169849i $$-0.945672\pi$$
0.985470 0.169849i $$-0.0543279\pi$$
$$278$$ 0 0
$$279$$ −4.09472 −0.245144
$$280$$ 0 0
$$281$$ −31.7408 −1.89350 −0.946750 0.321971i $$-0.895655\pi$$
−0.946750 + 0.321971i $$0.895655\pi$$
$$282$$ 0 0
$$283$$ 0.998092i 0.0593304i −0.999560 0.0296652i $$-0.990556\pi$$
0.999560 0.0296652i $$-0.00944412\pi$$
$$284$$ 0 0
$$285$$ −7.68248 + 20.4133i −0.455071 + 1.20918i
$$286$$ 0 0
$$287$$ 19.1390i 1.12974i
$$288$$ 0 0
$$289$$ 6.97168 0.410099
$$290$$ 0 0
$$291$$ 11.0935 0.650314
$$292$$ 0 0
$$293$$ 13.8947i 0.811739i 0.913931 + 0.405869i $$0.133031\pi$$
−0.913931 + 0.405869i $$0.866969\pi$$
$$294$$ 0 0
$$295$$ −15.9377 5.99808i −0.927927 0.349222i
$$296$$ 0 0
$$297$$ 10.9864i 0.637495i
$$298$$ 0 0
$$299$$ −4.69204 −0.271347
$$300$$ 0 0
$$301$$ 0.506534 0.0291961
$$302$$ 0 0
$$303$$ 11.4364i 0.657003i
$$304$$ 0 0
$$305$$ −24.8153 9.33916i −1.42092 0.534759i
$$306$$ 0 0
$$307$$ 3.66633i 0.209249i −0.994512 0.104624i $$-0.966636\pi$$
0.994512 0.104624i $$-0.0333640\pi$$
$$308$$ 0 0
$$309$$ −20.2930 −1.15443
$$310$$ 0 0
$$311$$ −14.4210 −0.817741 −0.408870 0.912593i $$-0.634077\pi$$
−0.408870 + 0.912593i $$0.634077\pi$$
$$312$$ 0 0
$$313$$ 10.5046i 0.593754i −0.954916 0.296877i $$-0.904055\pi$$
0.954916 0.296877i $$-0.0959451\pi$$
$$314$$ 0 0
$$315$$ 1.10627 2.93950i 0.0623312 0.165622i
$$316$$ 0 0
$$317$$ 32.0818i 1.80189i −0.433931 0.900946i $$-0.642874\pi$$
0.433931 0.900946i $$-0.357126\pi$$
$$318$$ 0 0
$$319$$ 13.1461 0.736042
$$320$$ 0 0
$$321$$ 18.4982 1.03247
$$322$$ 0 0
$$323$$ 19.5107i 1.08560i
$$324$$ 0 0
$$325$$ −15.4675 + 17.6390i −0.857985 + 0.978437i
$$326$$ 0 0
$$327$$ 21.5344i 1.19086i
$$328$$ 0 0
$$329$$ 32.6598 1.80059
$$330$$ 0 0
$$331$$ 9.71307 0.533879 0.266939 0.963713i $$-0.413988\pi$$
0.266939 + 0.963713i $$0.413988\pi$$
$$332$$ 0 0
$$333$$ 0.844778i 0.0462935i
$$334$$ 0 0
$$335$$ −2.42231 + 6.43639i −0.132345 + 0.351657i
$$336$$ 0 0
$$337$$ 0.131832i 0.00718136i −0.999994 0.00359068i $$-0.998857\pi$$
0.999994 0.00359068i $$-0.00114295\pi$$
$$338$$ 0 0
$$339$$ 2.28813 0.124274
$$340$$ 0 0
$$341$$ −16.4815 −0.892526
$$342$$ 0 0
$$343$$ 16.7901i 0.906582i
$$344$$ 0 0
$$345$$ −3.31326 1.24693i −0.178380 0.0671326i
$$346$$ 0 0
$$347$$ 13.1981i 0.708512i −0.935148 0.354256i $$-0.884734\pi$$
0.935148 0.354256i $$-0.115266\pi$$
$$348$$ 0 0
$$349$$ 34.0451 1.82239 0.911197 0.411971i $$-0.135159\pi$$
0.911197 + 0.411971i $$0.135159\pi$$
$$350$$ 0 0
$$351$$ 25.9511 1.38517
$$352$$ 0 0
$$353$$ 10.8593i 0.577984i −0.957331 0.288992i $$-0.906680\pi$$
0.957331 0.288992i $$-0.0933201\pi$$
$$354$$ 0 0
$$355$$ 4.10590 + 1.54524i 0.217919 + 0.0820129i
$$356$$ 0 0
$$357$$ 14.2697i 0.755231i
$$358$$ 0 0
$$359$$ 20.3091 1.07188 0.535938 0.844257i $$-0.319958\pi$$
0.535938 + 0.844257i $$0.319958\pi$$
$$360$$ 0 0
$$361$$ 18.9592 0.997853
$$362$$ 0 0
$$363$$ 11.1684i 0.586188i
$$364$$ 0 0
$$365$$ 3.89654 10.3536i 0.203954 0.541932i
$$366$$ 0 0
$$367$$ 18.6731i 0.974727i −0.873199 0.487364i $$-0.837959\pi$$
0.873199 0.487364i $$-0.162041\pi$$
$$368$$ 0 0
$$369$$ 3.31848 0.172753
$$370$$ 0 0
$$371$$ −17.6112 −0.914328
$$372$$ 0 0
$$373$$ 9.51979i 0.492916i −0.969153 0.246458i $$-0.920733\pi$$
0.969153 0.246458i $$-0.0792667\pi$$
$$374$$ 0 0
$$375$$ −15.6100 + 8.34512i −0.806096 + 0.430940i
$$376$$ 0 0
$$377$$ 31.0527i 1.59929i
$$378$$ 0 0
$$379$$ −18.8304 −0.967251 −0.483625 0.875275i $$-0.660680\pi$$
−0.483625 + 0.875275i $$0.660680\pi$$
$$380$$ 0 0
$$381$$ 14.4439 0.739985
$$382$$ 0 0
$$383$$ 10.9401i 0.559015i 0.960144 + 0.279507i $$0.0901712\pi$$
−0.960144 + 0.279507i $$0.909829\pi$$
$$384$$ 0 0
$$385$$ 4.45282 11.8317i 0.226937 0.602999i
$$386$$ 0 0
$$387$$ 0.0878272i 0.00446451i
$$388$$ 0 0
$$389$$ −22.2830 −1.12979 −0.564896 0.825162i $$-0.691084\pi$$
−0.564896 + 0.825162i $$0.691084\pi$$
$$390$$ 0 0
$$391$$ 3.16675 0.160150
$$392$$ 0 0
$$393$$ 14.7740i 0.745252i
$$394$$ 0 0
$$395$$ 17.8551 + 6.71971i 0.898389 + 0.338105i
$$396$$ 0 0
$$397$$ 10.8388i 0.543983i −0.962300 0.271991i $$-0.912318\pi$$
0.962300 0.271991i $$-0.0876822\pi$$
$$398$$ 0 0
$$399$$ 27.7625 1.38986
$$400$$ 0 0
$$401$$ −2.71329 −0.135495 −0.0677476 0.997702i $$-0.521581\pi$$
−0.0677476 + 0.997702i $$0.521581\pi$$
$$402$$ 0 0
$$403$$ 38.9313i 1.93931i
$$404$$ 0 0
$$405$$ 15.2269 + 5.73059i 0.756631 + 0.284755i
$$406$$ 0 0
$$407$$ 3.40029i 0.168546i
$$408$$ 0 0
$$409$$ −21.6271 −1.06939 −0.534696 0.845044i $$-0.679574\pi$$
−0.534696 + 0.845044i $$0.679574\pi$$
$$410$$ 0 0
$$411$$ 33.2490 1.64005
$$412$$ 0 0
$$413$$ 21.6755i 1.06658i
$$414$$ 0 0
$$415$$ 2.75212 7.31274i 0.135097 0.358968i
$$416$$ 0 0
$$417$$ 25.5368i 1.25054i
$$418$$ 0 0
$$419$$ −4.00587 −0.195700 −0.0978498 0.995201i $$-0.531196\pi$$
−0.0978498 + 0.995201i $$0.531196\pi$$
$$420$$ 0 0
$$421$$ 25.4251 1.23914 0.619572 0.784940i $$-0.287306\pi$$
0.619572 + 0.784940i $$0.287306\pi$$
$$422$$ 0 0
$$423$$ 5.66284i 0.275337i
$$424$$ 0 0
$$425$$ 10.4394 11.9049i 0.506384 0.577475i
$$426$$ 0 0
$$427$$ 33.7493i 1.63324i
$$428$$ 0 0
$$429$$ 14.7556 0.712405
$$430$$ 0 0
$$431$$ 1.07679 0.0518673 0.0259336 0.999664i $$-0.491744\pi$$
0.0259336 + 0.999664i $$0.491744\pi$$
$$432$$ 0 0
$$433$$ 3.93871i 0.189283i 0.995511 + 0.0946413i $$0.0301704\pi$$
−0.995511 + 0.0946413i $$0.969830\pi$$
$$434$$ 0 0
$$435$$ −8.25240 + 21.9277i −0.395672 + 1.05135i
$$436$$ 0 0
$$437$$ 6.16110i 0.294726i
$$438$$ 0 0
$$439$$ −13.1539 −0.627802 −0.313901 0.949456i $$-0.601636\pi$$
−0.313901 + 0.949456i $$0.601636\pi$$
$$440$$ 0 0
$$441$$ −0.543274 −0.0258702
$$442$$ 0 0
$$443$$ 8.95394i 0.425415i 0.977116 + 0.212707i $$0.0682281\pi$$
−0.977116 + 0.212707i $$0.931772\pi$$
$$444$$ 0 0
$$445$$ 14.8064 + 5.57236i 0.701893 + 0.264155i
$$446$$ 0 0
$$447$$ 15.1548i 0.716795i
$$448$$ 0 0
$$449$$ −8.23267 −0.388524 −0.194262 0.980950i $$-0.562231\pi$$
−0.194262 + 0.980950i $$0.562231\pi$$
$$450$$ 0 0
$$451$$ 13.3571 0.628964
$$452$$ 0 0
$$453$$ 4.81480i 0.226219i
$$454$$ 0 0
$$455$$ 27.9478 + 10.5181i 1.31021 + 0.493095i
$$456$$ 0 0
$$457$$ 36.3473i 1.70026i 0.526576 + 0.850128i $$0.323476\pi$$
−0.526576 + 0.850128i $$0.676524\pi$$
$$458$$ 0 0
$$459$$ −17.5149 −0.817527
$$460$$ 0 0
$$461$$ −15.2421 −0.709894 −0.354947 0.934886i $$-0.615501\pi$$
−0.354947 + 0.934886i $$0.615501\pi$$
$$462$$ 0 0
$$463$$ 5.57424i 0.259057i 0.991576 + 0.129528i $$0.0413463\pi$$
−0.991576 + 0.129528i $$0.958654\pi$$
$$464$$ 0 0
$$465$$ 10.3462 27.4911i 0.479793 1.27487i
$$466$$ 0 0
$$467$$ 6.21488i 0.287590i −0.989607 0.143795i $$-0.954069\pi$$
0.989607 0.143795i $$-0.0459306\pi$$
$$468$$ 0 0
$$469$$ 8.75360 0.404204
$$470$$ 0 0
$$471$$ 19.7560 0.910309
$$472$$ 0 0
$$473$$ 0.353511i 0.0162545i
$$474$$ 0 0
$$475$$ 23.1618 + 20.3104i 1.06273 + 0.931905i
$$476$$ 0 0
$$477$$ 3.05358i 0.139814i
$$478$$ 0 0
$$479$$ 34.4168 1.57254 0.786272 0.617880i $$-0.212008\pi$$
0.786272 + 0.617880i $$0.212008\pi$$
$$480$$ 0 0
$$481$$ −8.03189 −0.366223
$$482$$ 0 0
$$483$$ 4.50609i 0.205034i
$$484$$ 0 0
$$485$$ 5.51880 14.6641i 0.250596 0.665864i
$$486$$ 0 0
$$487$$ 22.7752i 1.03204i 0.856576 + 0.516021i $$0.172587\pi$$
−0.856576 + 0.516021i $$0.827413\pi$$
$$488$$ 0 0
$$489$$ −25.9547 −1.17371
$$490$$ 0 0
$$491$$ 3.16911 0.143020 0.0715099 0.997440i $$-0.477218\pi$$
0.0715099 + 0.997440i $$0.477218\pi$$
$$492$$ 0 0
$$493$$ 20.9581i 0.943905i
$$494$$ 0 0
$$495$$ −2.05148 0.772068i −0.0922072 0.0347019i
$$496$$ 0 0
$$497$$ 5.58410i 0.250481i
$$498$$ 0 0
$$499$$ 14.0809 0.630346 0.315173 0.949034i $$-0.397937\pi$$
0.315173 + 0.949034i $$0.397937\pi$$
$$500$$ 0 0
$$501$$ 12.8756 0.575237
$$502$$ 0 0
$$503$$ 21.4946i 0.958399i −0.877706 0.479199i $$-0.840927\pi$$
0.877706 0.479199i $$-0.159073\pi$$
$$504$$ 0 0
$$505$$ −15.1174 5.68937i −0.672714 0.253173i
$$506$$ 0 0
$$507$$ 14.2728i 0.633878i
$$508$$ 0 0
$$509$$ 34.0952 1.51124 0.755622 0.655008i $$-0.227335\pi$$
0.755622 + 0.655008i $$0.227335\pi$$
$$510$$ 0 0
$$511$$ −14.0811 −0.622910
$$512$$ 0 0
$$513$$ 34.0764i 1.50451i
$$514$$ 0 0
$$515$$ −10.0954 + 26.8247i −0.444855 + 1.18204i
$$516$$ 0 0
$$517$$ 22.7933i 1.00245i
$$518$$ 0 0
$$519$$ −16.6641 −0.731474
$$520$$ 0 0
$$521$$ −14.1367 −0.619339 −0.309669 0.950844i $$-0.600218\pi$$
−0.309669 + 0.950844i $$0.600218\pi$$
$$522$$ 0 0
$$523$$ 11.2020i 0.489828i 0.969545 + 0.244914i $$0.0787598\pi$$
−0.969545 + 0.244914i $$0.921240\pi$$
$$524$$ 0 0
$$525$$ 16.9400 + 14.8546i 0.739321 + 0.648306i
$$526$$ 0 0
$$527$$ 26.2756i 1.14458i
$$528$$ 0 0
$$529$$ −1.00000 −0.0434783
$$530$$ 0 0
$$531$$ 3.75829 0.163096
$$532$$ 0 0
$$533$$ 31.5511i 1.36663i
$$534$$ 0 0
$$535$$ 9.20247 24.4521i 0.397857 1.05716i
$$536$$ 0 0
$$537$$ 32.5221i 1.40343i
$$538$$ 0 0
$$539$$ −2.18672 −0.0941887
$$540$$ 0 0
$$541$$ −33.6704 −1.44760 −0.723802 0.690008i $$-0.757607\pi$$
−0.723802 + 0.690008i $$0.757607\pi$$
$$542$$ 0 0
$$543$$ 34.9496i 1.49983i
$$544$$ 0 0
$$545$$ −28.4656 10.7129i −1.21933 0.458892i
$$546$$ 0 0
$$547$$ 23.1062i 0.987949i 0.869476 + 0.493975i $$0.164456\pi$$
−0.869476 + 0.493975i $$0.835544\pi$$
$$548$$ 0 0
$$549$$ 5.85174 0.249746
$$550$$ 0 0
$$551$$ 40.7752 1.73708
$$552$$ 0 0
$$553$$ 24.2833i 1.03263i
$$554$$ 0 0
$$555$$ −5.67167 2.13452i −0.240749 0.0906051i
$$556$$ 0 0
$$557$$ 3.48937i 0.147849i −0.997264 0.0739246i $$-0.976448\pi$$
0.997264 0.0739246i $$-0.0235524\pi$$
$$558$$ 0 0
$$559$$ 0.835034 0.0353182
$$560$$ 0 0
$$561$$ −9.95883 −0.420462
$$562$$ 0 0
$$563$$ 38.8593i 1.63772i −0.573991 0.818862i $$-0.694606\pi$$
0.573991 0.818862i $$-0.305394\pi$$
$$564$$ 0 0
$$565$$ 1.13830 3.02460i 0.0478886 0.127246i
$$566$$ 0 0
$$567$$ 20.7089i 0.869690i
$$568$$ 0 0
$$569$$ 23.2055 0.972823 0.486412 0.873730i $$-0.338306\pi$$
0.486412 + 0.873730i $$0.338306\pi$$
$$570$$ 0 0
$$571$$ −5.39836 −0.225914 −0.112957 0.993600i $$-0.536032\pi$$
−0.112957 + 0.993600i $$0.536032\pi$$
$$572$$ 0 0
$$573$$ 7.13877i 0.298226i
$$574$$ 0 0
$$575$$ −3.29655 + 3.75935i −0.137476 + 0.156776i
$$576$$ 0 0
$$577$$ 13.1082i 0.545701i 0.962056 + 0.272850i $$0.0879664\pi$$
−0.962056 + 0.272850i $$0.912034\pi$$
$$578$$ 0 0
$$579$$ 33.4900 1.39180
$$580$$ 0 0
$$581$$ −9.94546 −0.412607
$$582$$ 0 0
$$583$$ 12.2909i 0.509037i
$$584$$ 0 0
$$585$$ 1.82371 4.84584i 0.0754013 0.200351i
$$586$$ 0 0
$$587$$ 12.9646i 0.535108i −0.963543 0.267554i $$-0.913785\pi$$
0.963543 0.267554i $$-0.0862154\pi$$
$$588$$ 0 0
$$589$$ −51.1206 −2.10639
$$590$$ 0 0
$$591$$ −16.0655 −0.660845
$$592$$ 0 0
$$593$$ 17.0225i 0.699030i −0.936931 0.349515i $$-0.886346\pi$$
0.936931 0.349515i $$-0.113654\pi$$
$$594$$ 0 0
$$595$$ −18.8626 7.09886i −0.773290 0.291025i
$$596$$ 0 0
$$597$$ 10.4110i 0.426096i
$$598$$ 0 0
$$599$$ 5.98111 0.244381 0.122191 0.992507i $$-0.461008\pi$$
0.122191 + 0.992507i $$0.461008\pi$$
$$600$$ 0 0
$$601$$ −21.3680 −0.871617 −0.435809 0.900039i $$-0.643538\pi$$
−0.435809 + 0.900039i $$0.643538\pi$$
$$602$$ 0 0
$$603$$ 1.51778i 0.0618086i
$$604$$ 0 0
$$605$$ 14.7631 + 5.55604i 0.600205 + 0.225885i
$$606$$ 0 0
$$607$$ 17.5464i 0.712186i −0.934450 0.356093i $$-0.884109\pi$$
0.934450 0.356093i $$-0.115891\pi$$
$$608$$ 0 0
$$609$$ 29.8220 1.20845
$$610$$ 0 0
$$611$$ 53.8405 2.17815
$$612$$ 0 0
$$613$$ 45.4601i 1.83612i 0.396444 + 0.918059i $$0.370244\pi$$
−0.396444 + 0.918059i $$0.629756\pi$$
$$614$$ 0 0
$$615$$ −8.38487 + 22.2797i −0.338111 + 0.898403i
$$616$$ 0 0
$$617$$ 25.8720i 1.04157i −0.853688 0.520785i $$-0.825640\pi$$
0.853688 0.520785i $$-0.174360\pi$$
$$618$$ 0 0
$$619$$ 3.20381 0.128772 0.0643859 0.997925i $$-0.479491\pi$$
0.0643859 + 0.997925i $$0.479491\pi$$
$$620$$ 0 0
$$621$$ 5.53088 0.221947
$$622$$ 0 0
$$623$$ 20.1370i 0.806773i
$$624$$ 0 0
$$625$$ 3.26548 + 24.7858i 0.130619 + 0.991433i
$$626$$ 0 0
$$627$$ 19.3755i 0.773783i
$$628$$ 0 0
$$629$$ 5.42089 0.216145
$$630$$ 0 0
$$631$$ 0.0248650 0.000989858 0.000494929 1.00000i $$-0.499842\pi$$
0.000494929 1.00000i $$0.499842\pi$$
$$632$$ 0 0
$$633$$ 42.0112i 1.66980i
$$634$$ 0 0
$$635$$ 7.18555 19.0929i 0.285150 0.757679i
$$636$$ 0 0
$$637$$ 5.16528i 0.204656i
$$638$$ 0 0
$$639$$ −0.968219 −0.0383022
$$640$$ 0 0
$$641$$ −9.77145 −0.385949 −0.192975 0.981204i $$-0.561813\pi$$
−0.192975 + 0.981204i $$0.561813\pi$$
$$642$$ 0 0
$$643$$ 36.8211i 1.45208i −0.687651 0.726041i $$-0.741358\pi$$
0.687651 0.726041i $$-0.258642\pi$$
$$644$$ 0 0
$$645$$ 0.589655 + 0.221914i 0.0232176 + 0.00873787i
$$646$$ 0 0
$$647$$ 46.5570i 1.83034i −0.403064 0.915172i $$-0.632055\pi$$
0.403064 0.915172i $$-0.367945\pi$$
$$648$$ 0 0
$$649$$ 15.1274 0.593802
$$650$$ 0 0
$$651$$ −37.3884 −1.46537
$$652$$ 0 0
$$653$$ 2.76029i 0.108018i 0.998540 + 0.0540092i $$0.0172000\pi$$
−0.998540 + 0.0540092i $$0.982800\pi$$
$$654$$ 0 0
$$655$$ −19.5293 7.34978i −0.763072 0.287180i
$$656$$ 0 0
$$657$$ 2.44150i 0.0952520i
$$658$$ 0 0
$$659$$ −39.3922 −1.53450 −0.767252 0.641346i $$-0.778376\pi$$
−0.767252 + 0.641346i $$0.778376\pi$$
$$660$$ 0 0
$$661$$ −17.7641 −0.690943 −0.345472 0.938429i $$-0.612281\pi$$
−0.345472 + 0.938429i $$0.612281\pi$$
$$662$$ 0 0
$$663$$ 23.5239i 0.913593i
$$664$$ 0 0
$$665$$ 13.8113 36.6982i 0.535578 1.42310i
$$666$$ 0 0
$$667$$ 6.61816i 0.256256i
$$668$$ 0 0
$$669$$ −33.1253 −1.28070
$$670$$ 0 0
$$671$$ 23.5537 0.909280
$$672$$ 0 0
$$673$$ 23.7072i 0.913847i −0.889506 0.456923i $$-0.848951\pi$$
0.889506 0.456923i $$-0.151049\pi$$
$$674$$ 0 0
$$675$$ 18.2329 20.7925i 0.701783 0.800306i
$$676$$ 0 0
$$677$$ 49.3507i 1.89670i −0.317221 0.948352i $$-0.602750\pi$$
0.317221 0.948352i $$-0.397250\pi$$
$$678$$ 0 0
$$679$$ −19.9435 −0.765361
$$680$$ 0 0
$$681$$ 14.7646 0.565779
$$682$$ 0 0
$$683$$ 15.6461i 0.598682i 0.954146 + 0.299341i $$0.0967669\pi$$
−0.954146 + 0.299341i $$0.903233\pi$$
$$684$$ 0 0
$$685$$ 16.5407 43.9507i 0.631988 1.67927i
$$686$$ 0 0
$$687$$ 46.7341i 1.78302i
$$688$$ 0 0
$$689$$ −29.0325 −1.10605
$$690$$ 0 0
$$691$$ 3.79498 0.144368 0.0721839 0.997391i $$-0.477003\pi$$
0.0721839 + 0.997391i $$0.477003\pi$$
$$692$$ 0 0
$$693$$ 2.79005i 0.105985i
$$694$$ 0 0
$$695$$ −33.7562 12.7040i −1.28044 0.481891i
$$696$$ 0 0
$$697$$ 21.2945i 0.806587i
$$698$$ 0 0
$$699$$ −45.8887 −1.73567
$$700$$ 0 0
$$701$$ 0.751725 0.0283923 0.0141961 0.999899i $$-0.495481\pi$$
0.0141961 + 0.999899i $$0.495481\pi$$
$$702$$ 0 0
$$703$$ 10.5467i 0.397775i
$$704$$ 0 0
$$705$$ 38.0192 + 14.3084i 1.43189 + 0.538885i
$$706$$ 0 0
$$707$$ 20.5599i 0.773234i
$$708$$ 0 0
$$709$$ −4.52035 −0.169765 −0.0848827 0.996391i $$-0.527052\pi$$
−0.0848827 + 0.996391i $$0.527052\pi$$
$$710$$ 0 0
$$711$$ −4.21044 −0.157904
$$712$$ 0 0
$$713$$ 8.29732i 0.310737i
$$714$$ 0 0
$$715$$ 7.34058 19.5048i 0.274522 0.729440i
$$716$$ 0 0
$$717$$ 15.2336i 0.568910i
$$718$$ 0 0
$$719$$ 36.6742 1.36772 0.683859 0.729614i $$-0.260300\pi$$
0.683859 + 0.729614i $$0.260300\pi$$
$$720$$ 0 0
$$721$$ 36.4820 1.35866
$$722$$ 0 0
$$723$$ 24.6574i 0.917020i
$$724$$ 0 0
$$725$$ 24.8800 + 21.8171i 0.924021 + 0.810268i
$$726$$ 0 0
$$727$$ 33.6449i 1.24782i 0.781496 + 0.623910i $$0.214457\pi$$
−0.781496 + 0.623910i $$0.785543\pi$$
$$728$$ 0 0
$$729$$ −29.8601 −1.10593
$$730$$ 0 0
$$731$$ −0.563582 −0.0208448
$$732$$ 0 0
$$733$$ 47.5745i 1.75720i 0.477555 + 0.878602i $$0.341523\pi$$
−0.477555 + 0.878602i $$0.658477\pi$$
$$734$$ 0 0
$$735$$ 1.37270 3.64744i 0.0506328 0.134538i
$$736$$ 0 0
$$737$$ 6.10916i 0.225034i
$$738$$ 0 0
$$739$$ −28.8914 −1.06279 −0.531395 0.847124i $$-0.678332\pi$$
−0.531395 + 0.847124i $$0.678332\pi$$
$$740$$ 0 0
$$741$$ 45.7672 1.68130
$$742$$ 0 0
$$743$$ 3.61970i 0.132794i 0.997793 + 0.0663969i $$0.0211504\pi$$
−0.997793 + 0.0663969i $$0.978850\pi$$
$$744$$ 0 0
$$745$$ −20.0325 7.53918i −0.733936 0.276214i
$$746$$ 0 0
$$747$$ 1.72443i 0.0630936i
$$748$$ 0 0
$$749$$ −33.2553 −1.21512
$$750$$ 0 0
$$751$$ 19.2050 0.700801 0.350401 0.936600i $$-0.386045\pi$$
0.350401 + 0.936600i $$0.386045\pi$$
$$752$$ 0 0
$$753$$ 36.1073i 1.31582i
$$754$$ 0 0
$$755$$ −6.36452 2.39527i −0.231629 0.0871726i
$$756$$ 0 0
$$757$$ 12.6638i 0.460275i 0.973158 + 0.230137i $$0.0739176\pi$$
−0.973158 + 0.230137i $$0.926082\pi$$
$$758$$ 0 0
$$759$$ 3.14481 0.114149
$$760$$ 0 0
$$761$$ −38.9053 −1.41032 −0.705159 0.709050i $$-0.749124\pi$$
−0.705159 + 0.709050i $$0.749124\pi$$
$$762$$ 0 0
$$763$$ 38.7138i 1.40153i
$$764$$ 0 0
$$765$$ −1.23086 + 3.27055i −0.0445019 + 0.118247i
$$766$$ 0 0
$$767$$ 35.7326i 1.29023i
$$768$$ 0 0
$$769$$ −4.16816 −0.150308 −0.0751539 0.997172i $$-0.523945\pi$$
−0.0751539 + 0.997172i $$0.523945\pi$$
$$770$$ 0 0
$$771$$ −18.3003 −0.659070
$$772$$ 0 0
$$773$$ 26.6030i 0.956842i 0.878131 + 0.478421i $$0.158791\pi$$
−0.878131 + 0.478421i $$0.841209\pi$$
$$774$$ 0 0
$$775$$ −31.1926 27.3525i −1.12047 0.982533i
$$776$$ 0 0
$$777$$ 7.71358i 0.276723i
$$778$$ 0 0
$$779$$ 41.4297 1.48437
$$780$$ 0 0
$$781$$ −3.89716 −0.139451
$$782$$ 0 0
$$783$$ 36.6043i 1.30813i
$$784$$ 0 0
$$785$$ 9.82821 26.1148i 0.350784 0.932077i
$$786$$ 0 0
$$787$$ 21.7538i 0.775440i −0.921777 0.387720i $$-0.873263\pi$$
0.921777 0.387720i $$-0.126737\pi$$
$$788$$ 0 0
$$789$$ 10.4100 0.370607
$$790$$ 0 0
$$791$$ −4.11351 −0.146260
$$792$$ 0 0
$$793$$ 55.6366i 1.97571i
$$794$$ 0 0
$$795$$ −20.5012 7.71554i −0.727101 0.273642i
$$796$$ 0 0
$$797$$ 10.2490i 0.363039i −0.983387 0.181519i $$-0.941898\pi$$
0.983387 0.181519i $$-0.0581015\pi$$
$$798$$ 0 0
$$799$$ −36.3381 −1.28555
$$800$$ 0 0
$$801$$ −3.49153 −0.123367
$$802$$ 0 0
$$803$$ 9.82722i 0.346795i